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lfunc_lfunctions • Show schema
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{'Lhash': '278674393439319346276698975476', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4415.91880161717, -7648.595726499609], 'a6': [0, 0], 'a7': [-36564.98527324724, 25304.714876228347], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 193.62248150101644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [36564.98527324724, -25304.714876228347]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.109', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '913144083767870952420550630759', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4415.91880161717, 7648.595726499609], [-24414062.5, 42286396.66916204]], [[1.0, 0], [36564.98527324724, -25304.714876228347]], [[1.0, 0], [-163744.21702391328, 283613.3033310025], [-142655835305.5, -247087154745.30405]], 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[-1593417036.5104797, -2759879264.8819838], [-6921169353622228000000, 11987816968262345000000]], [[1.0, 0], [-127835543224.32564, -221417655877.69934], [-10524259761499174000000, 18228552618969286000000]], [[1.0, 0], [-83357784310.96292, 144379917632.95563], [-12902132026527038000000, -22347148195906435000000]], [[1.0, 0], [-144147631057.6337, -2.5054265465570614e-66], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-252-7.4-c11-0-3', 'leading_term': '0.861536838669449685312380832811566670668329608796185106', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/252/12/k/e/109/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8615368386694496, 0.6587115841336809, 0.4191839771026209, 0.14924582635250097, 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'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21983533427045785290388746909', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55131376920736651563699244436', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12581142663277741843363931462', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 193.62248150101644, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/12/k/e/109/3'], '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': '2-252-7.4-c11-0-3', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-252-7.4-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.91482955343027, 'root_angle': -0.16959431033297712, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21983533427045785290388746909', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '278674393439319346276698975476', 'Lhash_array': ['278674393439319346276698975476'], 'label': '2-252-7.4-c11-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/12/k/e/109/3'}