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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2600.253', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.7431448254773942, -0.6691306063588582], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 12.07434923837313, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '2600.253', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 2600, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_2600.2117', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 0, 0, 'a^20', 0, 'a^14', 0, 'a^61', 0, 0, 0, 0, 0, 'a^23', 0, 'a^53', 0, 'a^57', 0, 'a^1', 0, 0, 0, 'a^51', 0, 'a^52', 0, 'a^33', 0, 'a^38', 0, 0, 0, 'a^34', 0, 0, 0, 'a^49', 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'191.56031072318525911042788505840', '192.395687841745102494715955793993', '192.90771195453527689045314084800', '193.26878051134323904574175043138', '193.91598750716722616357437811986', '194.51146992428027794599740287506', '195.17332379716006042080961139297', '195.43621724824805410115125586189', '195.93809658954809749612523774572', '196.80185827448609721149479379510', '197.03668161708722870744324996215', '197.526741055904790060877205429564', '198.690623527083349415084225265841', '198.79825848960928951481070409742', '199.72547077220921004416188189601', '199.96117673340300541331091260131'], 'prelabel': '1-2600-2600.253-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.07434923837313, 'root_angle': -0.01614556948236639, 'root_number': '0.994858805980676690640148545960-0.101271694775501278539121012963*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0161455694824', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.857968052399357272719164774945-0.0657887240701128599531552025769*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.704473676823', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.76741371822', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.50910856162', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.07434923837313, 'bad_primes': [2, 5, 13], 'central_character': '2600.253', 'conductor': 2600, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2600/253'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-2600-2600.253-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2600-2600.253-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.07434923837313, 'root_angle': -0.01614556948236639, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.704473676823', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2600.253', 'Lhash_array': ['dirichlet_L_2600.253'], 'factors': ['1-2600-2600.253-r0-0-0'], 'label': '1-2600-2600.253-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2600/253'}
Lfunction data - 1-2600-2600.253-r0-0-0