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lfunc_lfunctions • Show schema
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{'Lhash': '1380461900612176240648216534575', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.7196548075482363, 0.206851016135377], 'a4': [0, 0], 'a5': [-4.186710899296014, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [2.914425314247524, 0.7114246886868778], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.085610916553867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7196548075482363, -0.206851016135377]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.1697', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '859131239457295710370588076308', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7196548075482363, -0.206851016135377]], [[1.0, 0], [4.186710899296014, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4228493773737556], [-11.0, 0]], [[1.0, 0], [-0.8507385749106384, -0.4911741452346557], [6.5, 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'7.14446803324142779729810627593165', '7.979888184197476059444615663904676', '8.402580394259178176919751986135032', '9.098462600921621190151863269821594'], 'prelabel': '2-42e2-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7530801905306883, 'root_angle': 0.20749458790789033, 'root_number': '0.7949546684431588796597992968229467122820206698802356977 + 0.6066688348023387097691649314884577788598117517000148425*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10374729395394516', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08899242454003978017365315579', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66670454196793040020472467650', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47947607103633684848048257854', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.085610916553867, 'bad_primes': [2, 3, 7], 'central_character': '63.59', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/2/bm/b/1697/8'], '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': '2-42e2-63.59-c1-0-19', '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': '2-42e2-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7530801905306883, 'root_angle': 0.10374729395394516, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08899242454003978017365315579', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1380461900612176240648216534575', 'Lhash_array': ['1380461900612176240648216534575'], 'label': '2-42e2-63.59-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/2/bm/b/1697/8'}