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lfunc_lfunctions • Show schema
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{'Lhash': '6051224718785092741722186608909', 'a10': [-11.622098116193632, -6.710021475932637], 'a2': [1.9901389534984086, -1.1490072605270663], 'a3': [-3.70079200773015, 2.1366532618778176], 'a4': [0.6404353694878275, -1.109266598917064], 'a5': [-2.919921268754495, -5.057451991583764], 'a6': [-4.910060222252904, 8.504473773164962], 'a7': [9.381861922457118, 0.0], 'a8': [0.0, 6.248598526457138], 'a9': [4.630574322986236, -8.020389995636018], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5177125022845641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [3.4001991757513124, -18.693278085055603]]]], 'bad_primes': [19], 'central_character': '19.12', 'coefficient_field': 'CDF', 'conductor': 19, 'conductor_radical': 19, 'conjugate': '5802667080402279618395315947492', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9901389534984086, 1.1490072605270663], [2.0, -3.4641016151377544]], [[1.0, 0], [3.70079200773015, 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'11.74121906508611467267455215420330', '13.18270717677479768273629001599074', '14.61564884122049346344017253086647', '15.47023759318547032022257150719670', '17.23770555245501602632259664816308', '18.17645069165681164424062427326693'], 'prelabel': '2-19-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7195224126353287, 'root_angle': 0.08843266546196636, 'root_number': '0.9616557707112054 + 0.2742593273853006*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.044216332731', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.77357460935657086079466821249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.33304559245663433956941880392', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.52892446315695115894033998545', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5177125022845641, 'bad_primes': [19], 'central_character': '19.12', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/19/3/d/a/12/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-19-19.12-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-19-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7195224126353287, 'root_angle': 0.04421633273098318, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.77357460935657086079466821249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '6051224718785092741722186608909', 'Lhash_array': ['6051224718785092741722186608909'], 'label': '2-19-19.12-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/3/d/a/12/3'}