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lfunc_lfunctions • Show schema
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{'Lhash': '1501717248475204789325871631605', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 2.449489742783178], 'a6': [0, 0], 'a7': [0, -3.4641016151377544], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.397532625703008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.2303', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '923988993692230750561294936323', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.449489742783178], [-5.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-7.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [11.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-17.0, 0]], [[1.0, 0], [0, 4.0], [-19.0, 0]], [[1.0, 0], [4.898979485566356, 0], [23.0, 0]], 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'6.43144061485152315080174373108863', '7.88101944046959768622250718484150', '8.413897218055468798755219089464831', '9.015620882638554307700994015131662'], 'prelabel': '2-48e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.19591327601530362, 'root_number': '0.81649658092772603273242802490196379732198249355222337614 + 0.5773502691896257645091487805019574556476017512701268761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09795663800765182', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18464602801815716047137983163', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07153323832881752355832951138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42436671939666613294547594605', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.397532625703008, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/2/c/i/2303/6'], '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': '2-48e2-12.11-c1-0-22', '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': '2-48e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.09795663800765181, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18464602801815716047137983163', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1501717248475204789325871631605', 'Lhash_array': ['1501717248475204789325871631605'], 'label': '2-48e2-12.11-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/c/i/2303/6'}