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lfunc_lfunctions • Show schema
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{'Lhash': '1074871212808504545646092484965', 'a10': [0.0, 0.0], 'a2': [3.16483232779592, 0.0], 'a3': [-9.0, 0.0], 'a4': [-21.98383633693786, 0.0], 'a5': [0.0, 0.0], 'a6': [-28.48349095016328, 0.0], 'a7': [223.5850413916739, 0.0], 'a8': [-170.849790417585, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.16483232779592, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-223.5850413916739, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-999.1925610291544, 0], [371293.0, 0]], [[1.0, 0], [-2010.5921481493424, 0], [1419857.0, 0]], [[1.0, 0], [856.9655529580227, 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['0.847923877932123714902892218700551', '1.57980249301412511509472623355344', '3.39113453725364784004951592564892', '4.18437952267859031940193030898526', '5.17847799397588923346627100366989', '5.57030606653562485152625107150805', '6.69012448648957592629044496286979', '7.966204895532718862783957639021613', '8.505171956261822806929087825179212', '9.384897433245037825354952705871075'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.847923877932123714902892218701', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.57980249301412511509472623355', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39113453725364784004951592565', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 70, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/u/1/7'], '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': '2-825-1.1-c5-0-70', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.847923877932123714902892218701', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1074871212808504545646092484965', 'Lhash_array': ['1074871212808504545646092484965'], 'label': '2-825-1.1-c5-0-70', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/u/1/7'}