A. Akbary, Lectures on classical analytic theory of L-functions. Institute for Research in Fundamental Sciences, 2006.

A. Ankeny, The Least Quadratic Non Residue, The Annals of Mathematics, vol.55, issue.1, p.6572, 1952.
DOI : 10.2307/1969420

[. Bach, Explicit bounds for primality testing and related problems, Mathematics of Computation, vol.55, issue.191, p.355380, 1990.
DOI : 10.1090/S0025-5718-1990-1023756-8

D. Bump, J. W. Cogdell, E. De-shalit, D. Gaitsgory, E. Kowalski et al., An introduction to the Langlands program, 1216.
DOI : 10.1007/978-0-8176-8226-2

[. Bosma, J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Computational algebra and number theory, p.235265, 1993.
DOI : 10.1006/jsco.1996.0125

[. Bernard, Statistiques des zéros non-triviaux de fonctions L de formes modulaires, Thèse de doctorat, 2013.

[. Bubboloni and J. Sonn, Intersective S n polynomials with few irreducible factors. ArXiv e-prints, 2015.

[. Bugeaud, Bounds for the solutions of superelliptic equations, Compositio Math, vol.107, issue.2, p.187219, 1997.

J. Brian, C. , and A. Ghosh, On the Selberg class of Dirichlet series : small degrees, Duke Math. J, vol.72, issue.3, p.673693, 1993.

[. Chow and A. Ghitza, Distinguishing newforms. preprint, 2014.

H. Cohen, Number theory. Vol. I. Tools and Diophantine equations, volume 239 de Graduate Texts in Mathematics, 2007.

H. Cohen, Number theory Analytic and modern tools, volume 240 de Graduate Texts in Mathematics, 2007.

J. Michael and . Collins, On Jordan's theorem for complex linear groups, J. Group Theory, vol.10, issue.4, p.411423, 2007.

V. [. Dokchitser and . Dokchitser, Identifying Frobenius elements in Galois groups. ArXiv e-prints, septembre, 2010.

T. Dokchitser, ComputeL -Computing special values of L-functions

J. S. Ellenberg, Points of low height on P 1 over number elds and bounds for torsion in class groups, Computational arithmetic geometry, p.4548, 2008.

C. Euvrard, Majoration explicite sur le nombre de coecients susants pour déterminer une fonction L, J. Théor. Nombres Bordeaux

S. Jordan, A. Ellenberg, and . Venkatesh, The number of extensions of a number eld with xed degree and bounded discriminant, Ann. of Math, vol.163, issue.22, p.723741, 2006.

S. Jordan, A. Ellenberg, and . Venkatesh, Reection principles and bounds for class group torsion, Int. Math. Res. Not. IMRN, vol.18, issue.1, 2007.

[. Fulton and J. Harris, Representation theory, volume 129 de Graduate Texts in Mathematics, 1991.

G. The and . Group, GAP Groups, Algorithms, and Programming, Version 4, 2015.

[. Godement, Analyse mathématique. III, Fonctions analytiques, diérentielles et variétés, surfaces de Riemann. [Analytic functions, dierentials and manifolds, Riemann surfaces], 2002.

[. Iwaniec and E. Kowalski, Analytic number theory, 2004.
DOI : 10.1090/coll/053

URL : https://hal.archives-ouvertes.fr/hal-00180743

P. Kowalski, J. Michel, and . Vanderkam, Rankin-Selberg L -functions in the level aspect, Duke Mathematical Journal, vol.114, issue.1, p.123191, 2002.
DOI : 10.1215/S0012-7094-02-11416-1

[. Kondo, Algebraic number elds with the discriminant equal to that of a quadratic number eld, J. Math. Soc. Japan, vol.47, issue.1, p.3136, 1995.

[. Kaczorowski and A. Perelli, On the structure of the Selberg class, I: 0???d???1, Acta Mathematica, vol.182, issue.2, p.207241, 1999.
DOI : 10.1007/BF02392574

S. Lang, Algebraic number theory, volume 110 de Graduate Texts in Mathematics, 1994.

W. Ch-'ing and W. Li, Newforms and functional equations, Math. Ann, vol.212, p.285315, 1975.

W. Ch-'ing and W. Li, L-series of Rankin type and their functional equations, Math. Ann, vol.244, issue.2, p.135166, 1979.

C. Jerey, H. L. Lagarias, . Montgomery, and M. Andrew, Odlyzko : A bound for the least prime ideal in the Chebotarev density theorem, Invent. Math, vol.54, issue.3, p.271296, 1979.

C. Jerey, . Lagarias, and M. Andrew, Odlyzko : Eective versions of the Chebotarev density theorem, Algebraic number elds : L-functions and Galois properties (Proc. Sympos, p.409464, 1975.

A. Daniel and . Marcus, Number elds, 1977.

[. Martinet, Character theory and Artin L-functions, Algebraic number elds : L-functions and Galois properties (Proc. Sympos, p.187, 1975.

V. [. Murty and . Kumar-murty, Non-vanishing of L-functions and applications, de Progress in Mathematics. Birkhäuser Verlag, 1997.

V. [. Murty and N. Kumar-murty, Saradha : Modular forms and the Chebotarev density theorem, Amer. J. Math, vol.110, issue.2, p.253281, 1988.

]. V. Mur94 and . Kumar-murty, The least prime which does not split completely, Forum Math, vol.6, issue.5, p.555565, 1994.

[. Neukirch, Algebraic number theory, 1992.
DOI : 10.1007/978-3-662-03983-0

[. Nicolas, Répartition des nombres premiers, Séminaire Delange-Pisot-Poitou Théorie des nombres, Fasc. 2, Exp. No. G6, 4p. Secrétariat Mathématique, pp.1967-1968, 1969.

M. Andrew and . Odlyzko, On conductors and discriminants, Algebraic number elds : L-functions and Galois properties (Proc. Sympos, p.377407, 1975.

M. Andrew and . Odlyzko, Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results, Sém. Théor. Nombres Bordeaux, vol.2, issue.21, p.119141, 1990.

[. Oesterlé, Versions eectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisée, Astérisque, issue.61, p.165167, 1979.

P. Andrew and . Ogg, On a convolution of L-series, Invent. Math, vol.7, p.297312, 1969.

[. Odºak and L. Smajlovi¢, On asymptotic behavior of generalized Li coecients in the Selberg class, J. Number Theory, vol.131, issue.3, p.519535, 2011.

[. Perlis, On the equation ? K (s) = ? K (s), J. Number Theory, vol.9, issue.3, p.342360, 1977.

A. Perelli, I. Milan, and J. Math, [Pol13] Paul Pollack : The smallest inert prime in a cyclic number eld of prime degree [Rob83] Guy Robin : Estimation de la fonction de Tchebychef ? sur le k-ième nombre premier et grandes valeurs de la fonction ?(n) nombre de diviseurs premiers de n, ):163179, 2013. [Rém10] Gaël Rémond : Nombre de points rationnels des courbes. Proc. LondRou09] Djamel Rouymi : Formules de trace en niveau primaire et non annulation de valeurs centrales de fonctions L automorphes Thèse de doctorat, pp.759794367389243-256, 1952.

P. Samuel and J. Serre, Représentations linéaires des groupes nis Deuxième édition, Ser68] Jean-Pierre Serre : Corps locaux, 1967.

J. Serre, Linear representations of nite groups [Sny02] Noah Snyder : Artin's L-functions : A Historical Approach [Tho14] Frank Thorne : Shintani's zeta function is not a nite sum of Euler products, Ser81] Jean-Pierre Serre : Quelques applications du théorème de densité de Chebotarev . Inst. Hautes Études Sci Thèse de doctoratTen95] Gérald Tenenbaum : Introduction à la théorie analytique et probabiliste des nombres de Cours Spécialisés [Specialized Courses]. Société Mathématique de France Proc. Amer, p.32340119431952, 1977.

K. Uchida, Unramied extensions of quadratic number elds, Van08] Lotte Van der Zalm : Arithmetically equivalent elds. Master thesis under supervision of Gunther Cornellissen, p.220224, 1970.

C. Lawrence and . Washington, Introduction to cyclotomic elds, volume 83 de Graduate Texts in Mathematics ArXiv e-prints, novembre 2013, On unramied Galois extensions of quadratic number elds, p.5776, 1970.

A. Zaman, Bounding the least prime ideal in the Chebotarev Density Theorem. ArXiv e-prints, 2015.