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lfunc_lfunctions • Show schema
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{'Lhash': '930622405402999709916025405642', 'a10': [0.0, 0.0], 'a2': [0.037714938262194735, 0.0], 'a3': [-2.7168314143912413, 0.0], 'a4': [-1.9985775834318789, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.10246512906255685, 0.0], 'a7': [-0.3660486133879866, 0.0], 'a8': [-0.1508061066957291, 0.0], 'a9': [4.381172934223112, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.69191546037511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 17], 'central_character': '7225.1', 'coefficient_field': 'CDF', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.037714938262194735, 0], [2.0, 0]], [[1.0, 0], [2.7168314143912413, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3660486133879866, 0], [7.0, 0]], [[1.0, 0], [-1.4399575187079714, 0], [11.0, 0]], [[1.0, 0], [-4.614815144755508, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[[1.0, 0], [11.835845253279006, 0], [109.0, 0]], [[1.0, 0], [6.675478525812521, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 135, 'label': '2-85e2-1.1-c1-0-135', 'leading_term': '1.087407323640804753246102124079', '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/7225/2/a/bw/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0874073236408048, 1.0807578345140174, 1.0608563012015955, 1.027850748179462, 0.9820113184921458, 0.9237632581643825, 0.8537289825153938, 0.7727755972838837, 0.6820638067007403, 0.5830940069437988, 0.47774549772874214, 0.3683050896849945, 0.2574818801322444, 0.14840556252317355, 0.04460628643612817, -0.05002522893846001, -0.13129791757898462, -0.19480079319520596, -0.23600271369385098, -0.2503698780617501, 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'3.88076114589475993880832346530851', '4.53809728863019964140760652922136', '5.05179561975298486598099819647807', '5.82227610327888668626337695813777', '6.49798380518576908138647843721664', '6.78669914045574447021627532301453', '8.100035470018131878937588460489640'], 'prelabel': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73413163314516577885381582160', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15312957064579406197223828476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84893419611356005748497592989', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.69191546037511, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'index': 135, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7225/2/a/bw/1/8'], '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': '2-85e2-1.1-c1-0-135', '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': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73413163314516577885381582160', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '930622405402999709916025405642', 'Lhash_array': ['930622405402999709916025405642'], 'label': '2-85e2-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7225/2/a/bw/1/8'}