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lfunc_lfunctions • Show schema
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{'Lhash': '1815961786435117613370912127581', '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': '1078.67', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1190752132491711044739038755720', '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': 22, 'label': '2-1078-7.4-c1-0-22', 'leading_term': '2.143871110183669408555601347760614584483073080910661130', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.14354881026837107, 'root_number': '0.90002393947020927090529184082550088268367033197304540820 + 0.4358404620735953176193279339569067765431043146877962003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07177440513418554', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43254125869397259724395104169', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90454780051418567248627330187', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78314046931653629738575030484', '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': '7.4', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/s/67/2'], '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': '2-1078-7.4-c1-0-22', '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': '2-1078-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.07177440513418554, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43254125869397259724395104169', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1815961786435117613370912127581', 'Lhash_array': ['1815961786435117613370912127581'], 'label': '2-1078-7.4-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/s/67/2'}