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lfunc_lfunctions • Show schema
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{'Lhash': '3872088879757032559319089117170', 'a10': [-2.8352213928686867, -4.910747503154766], 'a2': [1.7213535584326987, -0.9938239403316388], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.9753720487526093, -1.6893939447220674], 'a5': [0.0, -2.8528407073013096], 'a6': [-1.7213535584326987, -0.9938239403316388], 'a7': [-0.8660254037844386, -0.5], 'a8': [0.0, 0.09790339020390915], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-3.5517314428509046, 0.6206478533469948]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.127', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1700616960205952900103928093549', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7213535584326987, 0.9938239403316388], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-273-13.10-c1-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.047999178948057, 2.224316600660507, 2.4270529182272074, 2.657728628838435, 2.9143460176299003, 3.191563739063181, 3.4810776925810623, 3.772080677697522, 4.051757621900654, 4.305835173812632, 4.519225703576646, 4.676796428477338, 4.764269774336247, 4.769231748563743, 4.682196644673617, 4.497651816918578, 4.214987710799536, 3.8392078603202258, 3.3813131656683058, 2.8582661114738768, 2.2924646038729475, 1.710691583184158, 1.1425538411442804, 0.6184782448832102, 0.16739095485248912, -0.1857410025138648, -0.42228333172097315, -0.531975434398695, -0.5143897109576279, 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'11.32334062714117957171093734538339', '12.27805918800910841694198918707166'], 'prelabel': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.3078407372041368, 'root_number': '-0.3554767383229321 + 0.9346851280036982*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.307840737204', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.05453953878134623888870215124', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81430125949280635106310029079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.25963817651951677676932116595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.10', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/7'], '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': '2-273-13.10-c1-0-15', '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': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.3078407372041368, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.05453953878134623888870215124', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3872088879757032559319089117170', 'Lhash_array': ['3872088879757032559319089117170'], 'factors': ['2-273-13.10-c1-0-15'], 'label': '2-273-13.10-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/7'}