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lfunc_lfunctions • Show schema
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{'Lhash': '1752310810530198106517533110879', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.2143197433775352, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.525427560843517, 0.0], 'a8': [0.0, 0.0], 'a9': [1.9032119259115532, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.274522214469247, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3040.1', 'coefficient_field': 'CDF', 'conductor': 3040, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.2143197433775352, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.525427560843517, 0], [7.0, 0]], [[1.0, 0], [-2.9032119259115534, 0], [11.0, 0]], [[1.0, 0], [1.3111078174659818, 0], [13.0, 0]], [[1.0, 0], [7.806423851823107, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'6.00825459924150429446555468115335', '6.78824696016997509612977609770710', '7.25434860183952808228317534126220', '8.479287067223291568801457144413470'], 'prelabel': '2-3040-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.926918125407529, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38232949222341698401447607469', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34203169077999906920532045271', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78459189862710463516581790233', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.274522214469247, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3040, 'conductor_radical': 190, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3040/2/a/l/1/1'], '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': '2-3040-1.1-c1-0-50', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3040-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.926918125407529, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38232949222341698401447607469', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1752310810530198106517533110879', 'Lhash_array': ['1752310810530198106517533110879'], 'label': '2-3040-1.1-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3040/2/a/l/1/1'}