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lfunc_lfunctions • Show schema
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{'Lhash': '1897500012469562259632505651937', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [-2.3722813232690143, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '1897500012469562259632505651937', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [-6.372281323269014, 0], [11.0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [-6.744562646538029, 0], [17.0, 0]], [[1.0, 0], [6.372281323269014, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-930-1.1-c1-0-12', '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/930/2/a/r/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.1788693932446477, 3.1722114019162895, 3.148876423016526, 3.0995297043714705, 3.010866047608482, 2.8683038233612224, 2.658797267724039, 2.37338052340831, 2.009238175362167, 1.5711820222292197, 1.0724231693064386, 0.5345191143935636, -0.013609996291673263, -0.5376452893472926, -1.0007645305721964, -1.367292239107002, -1.6067887943520105, -1.6981358470822823, -1.633085605847385, -1.4187127173160172, -1.0782579155679375, -0.6499914262376266, -0.18394738932912427, 0.2633306771179357, 0.635573186711159, 0.8843312487975755, 0.9762846807978253, 0.8991923763773058, 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'7.35335038309971222476904616926550', '8.432811589767721535782102862691929', '9.456302010721688682340875744033794', '9.845877171217146095031777213704209'], 'prelabel': '2-930-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49686357749362007261221879632', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79987541782877139287620011463', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71974408397570493107409839858', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/a/r/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': '2-930-1.1-c1-0-12', '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': '2-930-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49686357749362007261221879632', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1897500012469562259632505651937', 'Lhash_array': ['1897500012469562259632505651937'], 'label': '2-930-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/a/r/1/1'}