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lfunc_lfunctions • Show schema
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{'Lhash': '1479392964216195499454313199854', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.8284271247461903, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [7.0, 0]], [[1.0, 0], [-0.8284271247461901, 0], [11.0, 0]], [[1.0, 0], [-3.414213562373095, 0], [13.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.0, 0], [23.0, 0]], [[1.0, 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'group': 'GL2', 'index': 12, 'label': '2-1520-1.1-c1-0-12', 'leading_term': '2.43117575166760315250941550810', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1520/2/a/m/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4311757516676034, 2.4268937820600742, 2.413901349832617, 2.3917693216648868, 2.3598164343190318, 2.3171574640294526, 2.262765582902493, 2.1955447566646153, 2.1144079036623173, 2.0183568074458913, 1.9065602971670792, 1.778427822072728, 1.633676125537327, 1.4723871995455913, 1.2950560509188607, 1.102627050463712, 0.8965178001031502, 0.6786295816979081, 0.4513435825060849, 0.21750225602390386, -0.01962460636387445, -0.2563892370409475, -0.48883048451679545, -0.7127530253917095, -0.9238201247861342, -1.1176583772025377, -1.2899723443320683, 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'7.41891593420163043447895604176771', '8.002401702181419939965463193504075', '8.497137364131764817345041504282050', '9.279899583000994898532622480356846'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16703527292918390729128663720', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39117902522840006617867281474', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49860584015460536087637147757', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/m/1/2'], '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': '2-1520-1.1-c1-0-12', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16703527292918390729128663720', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1479392964216195499454313199854', 'Lhash_array': ['1479392964216195499454313199854'], 'label': '2-1520-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/m/1/2'}