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lfunc_lfunctions • Show schema
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{'Lhash': '982503368291844405150874816717', 'a10': [-107948678093.12102, 0], 'a2': [-2300.8785574517974, 0], 'a3': [586390.7647207992, 0], 'a4': [-3094565.863858536, 0], 'a5': [46916286.71296465, 0], 'a6': [-1349213936.833849, 0], 'a7': [0, 0], 'a8': [26421388514.84301, 0], 'a9': [249710950122.8437, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 164.24997829910086, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '11.5', 'prec': 14}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]]], 'bad_primes': [7], 'central_character': '49.1', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'euler_factors': [[[1.0, 0], [2300.8785574517974, 0], [8388608.0, 0]], [[1.0, 0], [-586390.7647207992, 0], [94143178827.0, 0]], [[1.0, 0], [-46916286.71296465, 0], [11920928955078124, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1750530896209.098, 0], [895430243255237400000000, 0]], [[1.0, 0], [1842277292303.6157, 0], [41753905413413120000000000, 0]], [[1.0, 0], 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'1.98806666419809905481974502411584', '2.78130029953167305521141153906735', '3.99341281755490891640004099355795', '5.29387019646410041572394279362727', '7.61997677072175090779548981242661', '7.78093239847906611154262042993449', '8.948170222412823473027160560960368', '9.805772739863419477437508761396825', '10.37373810326239004259615782448913'], 'prelabel': '2-7e2-1.1-c23-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.81600477134356, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c23-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77505849649339752481579077043', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98806666419809905481974502412', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78130029953167305521141153907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 164.24997829910086, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/24/a/g/1/5'], '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': '2-7e2-1.1-c23-0-32', 'motivic_weight': 23, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [23], 'order_of_vanishing': 0, 'prelabel': '2-7e2-1.1-c23-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.81600477134356, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c23-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77505849649339752481579077043', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '982503368291844405150874816717', 'Lhash_array': ['982503368291844405150874816717'], 'factors': ['2-7e2-1.1-c23-0-32'], 'label': '2-7e2-1.1-c23-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/24/a/g/1/5'}