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lfunc_lfunctions • Show schema
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{'Lhash': '735541417606451851219811496385', 'a10': [5.854101966249685, 0.0], 'a2': [-2.618033988749895, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.854101966249685, 0.0], 'a5': [-2.23606797749979, 0.0], 'a6': [2.618033988749895, 0.0], 'a7': [0.0, 0.0], 'a8': [-7.47213595499958, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.911810006841044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.1', 'coefficient_field': 'CDF', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.618033988749895, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.23606797749979, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.4721359549995796, 0], [13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [4.23606797749979, 0], [19.0, 0]], [[1.0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1617-1.1-c1-0-3', 'leading_term': '0.37052663026013854909490082129862', '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/1617/2/a/k/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.37052663026013855, 0.36681731594334394, 0.3556643114501833, 0.3369983665973802, 0.3107233749878833, 0.27674375844299076, 0.23499986406350934, 0.18550888962127693, 0.12840866445644836, 0.06400163943983929, -0.007203387661258382, -0.08445403705477823, -0.16672356035989283, -0.2526882071273649, -0.3407142190125867, -0.42885571375396914, -0.514864510566167, -0.5962127213637402, -0.6701286716291063, -0.7336464084499764, -0.7836686946892069, -0.8170429767562817, -0.8306493539861959, -0.8214990802118581, 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'7.50606998763773376492684119385027', '7.79411292934807206931554205359077', '8.524649432781679522984719247707429', '9.400317977913097710570593126019842'], 'prelabel': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58023986852057187785248996683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74450108306809813732576957408', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16495715504391030713362267660', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.911810006841044, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1617/2/a/k/1/1'], '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': '2-1617-1.1-c1-0-3', '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': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58023986852057187785248996683', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '735541417606451851219811496385', 'Lhash_array': ['735541417606451851219811496385'], 'label': '2-1617-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1617/2/a/k/1/1'}