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lfunc_lfunctions • Show schema
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{'Lhash': '2889520674908028696589113630044', 'a10': [1.5811388300841898, -4.743416490252569], 'a2': [0.3497980978537706, -2.208538270154693], 'a3': [-1.260073510670101, -0.6420395219202062], 'a4': [-2.853169548885461, -0.9270509831248422], 'a5': [2.205819241042368, 0.3665535102099988], 'a6': [-1.8587401723009225, 2.5583363680084634], 'a7': [0.0, 0.0], 'a8': [-1.0151536185567271, 1.9923511564810013], 'a9': [-0.5877852522924731, -0.8090169943749475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.205819241042368, -0.3665535102099988]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.602', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'conjugate': '629451267681169307629442867542', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3497980978537706, 2.208538270154693], [-1.902113032590307, 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'positive_zeros': ['2.27942989526277649049319842440413', '4.40277114423705436529110060647206', '5.03946958230128504326206239585272', '5.86239692107538045936573345868910', '6.46484028899394460149247961094010', '7.45750028527755110145875512077175', '8.440847743584976785907157273340201', '9.315378670777033210041275948699900', '10.23183869956558133436592133479246', '11.03123577351796664976946708149656'], 'prelabel': '2-605-55.52-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': -0.7162243346208732, 'root_number': '-0.6282398406757123 - 0.7780197314899897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.35811216731', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27942989526277649049319842440', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.40277114423705436529110060647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03946958230128504326206239585', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'bad_primes': [5, 11], 'central_character': '55.52', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/2/m/b/602/2'], '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': '2-605-55.52-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-605-55.52-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': -0.3581121673104366, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27942989526277649049319842440', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2889520674908028696589113630044', 'Lhash_array': ['2889520674908028696589113630044'], 'label': '2-605-55.52-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/2/m/b/602/2'}