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lfunc_lfunctions • Show schema
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{'Lhash': '2639914956720571990228649577625', 'a10': [-0.7071067811865476, -1.224744871391589], 'a2': [0.5, -0.8660254037844386], 'a3': [-0.7071067811865476, -1.224744871391589], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.7071067811865476, -1.224744871391589], 'a6': [-1.4142135623730951, 0], 'a7': [0, 0], 'a8': [-1.0, 0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.177', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '640876523517425607176655289856', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.7071067811865476, 1.224744871391589], [-1.5, 2.598076211353316]], [[1.0, 0], 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[[1.0, 0], [-1.0, -1.7320508075688772], [-33.5, 58.023702053557386]], [[1.0, 0], [10.0, 0], [71.0, 0]], [[1.0, 0], [7.0710678118654755, 12.24744871391589], [-36.5, 63.21985447626402]], [[1.0, 0], [-4.0, 6.928203230275509], [-39.5, -68.41600689897065]], [[1.0, 0], [-2.8284271247461903, 0], [83.0, 0]], [[1.0, 0], [3.5355339059327378, -6.123724356957945], [-44.5, -77.07626093681505]], [[1.0, 0], [-15.556349186104045, 0], [97.0, 0]], [[1.0, 0], [-1.4142135623730951, -2.449489742783178], [-50.5, 87.4685657822283]], [[1.0, 0], [2.1213203435596424, -3.6742346141747673], [-51.5, -89.20061658979718]], [[1.0, 0], [-10.0, 17.320508075688775], [-53.5, -92.66471820493493]], [[1.0, 0], [5.0, 8.660254037844387], [-54.5, 94.39676901250381]], [[1.0, 0], [18.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-1078-7.2-c1-0-28', 'leading_term': '1.2428161167396811067269247117596355055892186429935712294', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': 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'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.8967970958395212, 'root_number': '-0.94789902571847876029577975325132496222626081948551251276 - 0.3185709293735992191067993135106282636721534223528924440*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.44839854791976064', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08252570246507862304766255653', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47508202460065744691953011093', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35159464175674344870093384405', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '7.2', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/s/177/1'], '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': '2-1078-7.2-c1-0-28', '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': '2-1078-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.4483985479197606, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08252570246507862304766255653', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2639914956720571990228649577625', 'Lhash_array': ['2639914956720571990228649577625'], 'label': '2-1078-7.2-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/s/177/1'}