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lfunc_lfunctions • Show schema
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{'Lhash': '4037796826693650383601305461679', 'a10': [-11.070939766702542, -6.391810054487846], 'a2': [1.3660254037844386, -0.36602540378443865], 'a3': [0.8660254037844386, -1.5], 'a4': [1.7320508075688772, -1.0], 'a5': [-6.391810054487846, -6.391810054487846], 'a6': [0.6339745962155614, -2.366025403784439], 'a7': [9.231374910595195, 2.47353945232291], 'a8': [2.0, -2.0], 'a9': [-1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.125346062010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, 0.36602540378443865]]], [3, [[1.0, 0], [-0.8660254037844386, 1.5]]], [13, [[1.0, 0], [3.8131043084302583, -12.428203230275509]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.7', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '2178150599949439852114110334832', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3660254037844386, 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'5.89714304195550361863896705592899', '7.70004399489160677635346583566120', '8.098396779251393265756720560840714', '10.40213509969278274872193023321368', '11.22774547411602237019025045994896', '11.89325531791146016990760858191906', '13.79454768306024270841977814482448', '14.49571305777956417182745109499645'], 'prelabel': '2-78-13.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': 0.3365494737091372, 'root_number': '0.49122447733351177 + 0.8710330147981867*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.168274736855', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.18526005980408196591463513336', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17255629601728924615184353100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.89714304195550361863896705593', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.125346062010316, 'bad_primes': [2, 3, 13], 'central_character': '13.7', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/3/l/c/7/1'], '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': '2-78-13.7-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-78-13.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': 0.1682747368545686, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.18526005980408196591463513336', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4037796826693650383601305461679', 'Lhash_array': ['4037796826693650383601305461679'], 'label': '2-78-13.7-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/3/l/c/7/1'}