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lfunc_lfunctions • Show schema
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{'Lhash': '1791147821155406226840470988225', 'a10': [0.7928932188134524, -1.3733313399617268], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.7928932188134524, 1.3733313399617268], 'a6': [-1.0, 0.0], 'a7': [-2.6213203435596424, -0.3587194676071504], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.372062081298178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [2.6213203435596424, 0.3587194676071504]]], [19, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '798.571', 'coefficient_field': 'CDF', 'conductor': 798, 'conductor_radical': 798, 'conjugate': '962049460942181241706658895706', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 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[0]], 'group': 'GL2', 'index': 14, 'label': '2-798-7.4-c1-0-14', '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/798/2/j/h/571/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2677210625650155, 1.4069847198106076, 1.530008513969301, 1.6312291346754753, 1.7007156325854615, 1.7250310426996953, 1.688730392265837, 1.5762591569000786, 1.3740717831341944, 1.0728249511740977, 0.669490623103051, 0.16919609674555977, -0.4134405515772718, -1.0537285818215005, -1.7173064854731241, -2.3616959227130243, -2.939070379575829, -3.400158521568962, -3.699035934118981, -3.7983891556705824, -3.674687719879607, -3.3226006595845403, -2.7579692870627484, -2.0187175646882864, -1.1632537448377724, -0.2661863131280484, 0.5884790254879311, 1.3161156661427464, 1.8413184153419433, 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'8.764135182241552881162159478740895', '9.631213843771337371779962372231604', '10.12300005515334745799390077874068'], 'prelabel': '2-798-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': 0.5634637625061879, 'root_number': '-0.1980589951144843 + 0.9801901011815212*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.281731881253', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41296649158129671546084947271', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16270185061131601814143916962', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20097969927766368715433452917', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.372062081298178, 'bad_primes': [2, 3, 7, 19], 'central_character': '7.4', 'conductor': 798, 'conductor_radical': 798, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/798/2/j/h/571/1'], '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': '2-798-7.4-c1-0-14', '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': '2-798-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': 0.28173188125309395, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41296649158129671546084947271', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1791147821155406226840470988225', 'Lhash_array': ['1791147821155406226840470988225'], 'label': '2-798-7.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/798/2/j/h/571/1'}