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lfunc_lfunctions • Show schema
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{'Lhash': '1309427409146359013619512931383', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.4012585384440734, -1.0180739209102543], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.269', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1426766965625612355882727783837', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-1.4012585384440734, 1.0180739209102543], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5352331346596348, 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[0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.5352331346596348, -1.647278207092664], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.30901699437494745, 0.9510565162951535], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.8090169943749475, 0.5877852522924731], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-3267-33.5-c0-0-4', 'leading_term': '1.2552856791565932281730447381209', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 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-0.047921599210562445, 'root_number': '0.95501075355614574795924737502328 - 0.29657117289467405621211582611058*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.047921599210562445', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03295609130040096468983528000', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09238739695922480170274799493', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22801539631462225947397688744', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '33.5', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/m/c/269/2'], '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': '2-3267-33.5-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-33.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.047921599210562445, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03295609130040096468983528000', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1309427409146359013619512931383', 'Lhash_array': ['1309427409146359013619512931383'], 'factors': ['2-3267-33.5-c0-0-4'], 'label': '2-3267-33.5-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/m/c/269/2'}