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lfunc_lfunctions • Show schema
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{'Lhash': '681440255528855817053544522679', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.6223630055389735, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.743965517521215, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.36793827825854836, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.17157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.1', 'coefficient_field': 'CDF', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.6223630055389735, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.743965517521215, 0], [7.0, 0]], [[1.0, 0], [-4.480278799330937, 0], [11.0, 0]], [[1.0, 0], [0.843176449159785, 0], [13.0, 0]], [[1.0, 0], [5.523152073900404, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7791865563791885, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1900-1.1-c1-0-1', 'leading_term': '0.63788182161018831902747636456000', '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/1900/2/a/k/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6378818216101884, 0.6307025607975557, 0.6090832853378465, 0.5727893659856472, 0.5214618308012029, 0.4546629472180726, 0.37193534428988134, 0.27287075071745903, 0.15718417579978594, 0.02478946576562424, -0.12412749257559265, -0.28904119889722063, -0.46902741179014235, -0.6627148618497634, -0.8682498441602018, -1.0832754255202193, -1.3049267257253951, -1.5298434526831002, -1.75420055980181, -1.9737575296655079, -2.1839263580155706, -2.379857813096045, -2.55654498241065, -2.708942504113963, 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'6.00569609876773148642158085481291', '6.82319593493255798845869425116969', '7.18169834560311729195130255998429', '8.779309504631923296370568401122313', '9.258511744535299582162002244153548'], 'prelabel': '2-1900-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53756157683053079461003563806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24622620408940308031995104146', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50519090073751939483112350586', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.17157638404328, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/a/k/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': '2-1900-1.1-c1-0-1', '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': '2-1900-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53756157683053079461003563806', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '681440255528855817053544522679', 'Lhash_array': ['681440255528855817053544522679'], 'label': '2-1900-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/a/k/1/2'}