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lfunc_lfunctions • Show schema
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{'Lhash': '816523563347827929130893365373', 'a10': [4.140155553969055, -7.170959770712874], 'a2': [-0.828031110793811, -1.4341919541425747], 'a3': [0.16644381074119466, -0.28828913680912754], 'a4': [2.628728959115135, -4.553092116515064], 'a5': [2.5, 4.330127018922194], 'a6': [-0.551282613971145, 1.1449262627417453e-60], 'a7': [0.0, 0.0], 'a8': [-21.95517521266883, 0.0], 'a9': [13.4445929157319, 23.28671801712824], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.5, -4.330127018922194]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.116', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'conjugate': '2021864719413976646401039170589', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.828031110793811, 1.4341919541425747], [-4.0, 6.928203230275509]], [[1.0, 0], [-0.16644381074119466, 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'7.70128718883956090707370152322479', '8.667038898772841344872883611726039', '9.187352335151299417941215517868487', '10.76161861276569300064908905122297', '11.43342204922436063232660861625731'], 'prelabel': '2-245-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': -0.18978452306496227, 'root_number': '0.8274608818879864 - 0.5615233645585515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0948922615325', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64412351731685371685519377237', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82147425881325501850829444401', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97344469780258031119563783453', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '7.4', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/e/p/116/2'], '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': '2-245-7.4-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-245-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': -0.09489226153248113, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64412351731685371685519377237', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '816523563347827929130893365373', 'Lhash_array': ['816523563347827929130893365373'], 'label': '2-245-7.4-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/e/p/116/2'}