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lfunc_lfunctions • Show schema
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{'Lhash': '524576549329580559320633063206', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 27.0], 'a4': [0, 0], 'a5': [0, 446.1480942334113], 'a6': [0, 0], 'a7': [-1632.9507988393848, 0], 'a8': [0, 0], 'a9': [-729.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.97792489295141, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -27.0]]]], 'bad_primes': [2, 3], 'central_character': '192.97', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '2781179556782081234067208558983', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -27.0]], [[1.0, 0], [0, -446.1480942334113], [-78125.0, 0]], [[1.0, 0], [1632.9507988393848, 0], [823543.0, 0]], [[1.0, 0], [0, -7538.20983352459], [-19487171.0, 0]], [[1.0, 0], [0, -5165.380660137483], [-62748517.0, 0]], [[1.0, 0], [-2933.39415228521, 0], [410338673.0, 0]], [[1.0, 0], [0, -46958.28451591152], 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-0.7288011796740423, -0.7750387665181602, -0.7330003183114685, -0.6173235184285896], 'positive_zeros': ['0.41381793156184767354006607275843', '0.68578258863824911962671792052885', '2.67604775232997153224642225489643', '3.86315833071470789884345135573556', '5.51486644615718817831920925695622', '6.14569694672377699235101011914320', '7.52234844992556282154179885777472', '8.816214279499726625981470673753731', '9.141943847776307190492756134965700', '10.52293562967638533031634960419072'], 'prelabel': '2-192-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.744541619292352, 'root_angle': 0.5833333333333334, 'root_number': '-0.2588190451025207623488988376240483283490689013199305138 + 0.9659258262890682867497431997288973676339048390084045504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2916666666666667', 'prec': 60}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41381793156184767354006607276', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.68578258863824911962671792053', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67604775232997153224642225490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.97792489295141, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/8/d/d/97/12'], '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': '2-192-8.5-c7-0-6', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-192-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.744541619292352, 'root_angle': 0.2916666666666667, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41381793156184767354006607276', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '524576549329580559320633063206', 'Lhash_array': ['524576549329580559320633063206'], 'label': '2-192-8.5-c7-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/8/d/d/97/12'}