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lfunc_lfunctions • Show schema
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{'Lhash': '174405728997096412658479318243', 'a10': [0, 0], 'a2': [-1.1417741966146464, -0.6592036397692348], 'a3': [0, 0], 'a4': [-0.13090112262998585, -0.22672739516293963], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-1.5743692431630218, 2.12634933305473], 'a8': [0, 2.9819765450272016], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.576438318351666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.5743692431630218, -2.12634933305473]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.26', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'conjugate': '1679521805112658346404429794937', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1417741966146464, 0.6592036397692348], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5743692431630218, -2.12634933305473]], [[1.0, 0], [-2.0868765243234666, 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'7.59176831415267985319752637785157', '8.418699864000399403135432293005777', '9.183984605591919677579487258361709'], 'prelabel': '2-1575-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.546327440938254, 'root_angle': -0.619364043553303, 'root_number': '-0.366266203793679622521754694060868817314072073941364595 - 0.930510111690661181549496905849406567389178860790760184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3096820217766515', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13758186125237994350181838941', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58890020707008276256449650951', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29851539059329412306490935648', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.576438318351666, 'bad_primes': [3, 5, 7], 'central_character': '21.5', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/2/bk/i/26/5'], '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': '2-1575-21.5-c1-0-0', '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': '2-1575-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.546327440938254, 'root_angle': -0.3096820217766515, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13758186125237994350181838941', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '174405728997096412658479318243', 'Lhash_array': ['174405728997096412658479318243'], 'label': '2-1575-21.5-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/2/bk/i/26/5'}