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lfunc_lfunctions • Show schema
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{'Lhash': '751583425724767875668824546083', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.5529142706151247], 'a6': [0, 0], 'a7': [-12.392304845413264, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.31344226109448, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.161', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '781292455427667388320213149550', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.5529142706151247], [-25.0, 0]], [[1.0, 0], [12.392304845413264, 0], [49.0, 0]], [[1.0, 0], [0, -14.696938456699069], [-121.0, 0]], [[1.0, 0], [10.803847577293368, 0], [169.0, 0]], [[1.0, 0], [0, 28.977774788672047], [-289.0, 0]], [[1.0, 0], [3.6076951545867364, 0], [361.0, 0]], [[1.0, 0], [0, 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'3.99676020802141707732509991083224', '5.55308525064078227101288899381568', '6.18507873942567468096268557500887', '6.82329841934416079082101531541341', '7.84352384581794493081423288282467', '8.761927816063163961664142065427884', '9.489460901027580149829772817263082'], 'prelabel': '2-6e4-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.942511443917839, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59289478156634947715199915868', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40488931889244623305361437806', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34493001838919030456233567788', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.31344226109448, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/3/e/d/161/2'], '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': '2-6e4-3.2-c2-0-14', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-6e4-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.942511443917839, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59289478156634947715199915868', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '751583425724767875668824546083', 'Lhash_array': ['751583425724767875668824546083'], 'label': '2-6e4-3.2-c2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/3/e/d/161/2'}