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lfunc_lfunctions • Show schema
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{'Lhash': '1826634148548497133346959669686', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.068615452926602, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-2.068615452926602, 0.0], 'a7': [0.7016747393242684, 0.0], 'a8': [1.0, 0.0], 'a9': [1.27916989208673, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.17971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 13, 31], 'central_character': '4030.1', 'coefficient_field': 'CDF', 'conductor': 4030, 'conductor_radical': 4030, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.068615452926602, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7016747393242684, 0], [7.0, 0]], [[1.0, 0], [4.568849609531507, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-7.121888095460056, 0], [17.0, 0]], [[1.0, 0], 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[-4.365221340837446, 0], [109.0, 0]], [[1.0, 0], [-5.216111574530106, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 93, 'label': '2-4030-1.1-c1-0-93', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4030/2/a/g/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.26161911297263e-60, 0.18576117434765912, 0.3708372143761014, 0.5545042441228354, 0.7359632104377788, 0.9143079008665583, 1.0884992658978163, 1.257347500038844, 1.4195028855607341, 1.573455943419667, 1.7175470053694188, 1.8499849449173, 1.968874494571362, 2.0722513333537673, 2.1581239443610585, 2.224521105618824, 2.2695437762040496, 2.2914200628241277, 2.288561891961185, 2.259621964946026, 2.2035495367502156, 2.1196435353130307, 2.0076015301334658, 1.8675630710167155, 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'5.02131268623076049431122666088108', '5.81383049798487493026225372432395', '6.24763426462944770271954027704883', '7.19297401196295751549720939465445', '7.88327007713128977658157475422214'], 'prelabel': '2-4030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.672716458150893, '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': '1.44096026793157959599940722278', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56666051846758708496482413492', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41395779453875954296860723131', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.17971201457601, 'bad_primes': [2, 5, 13, 31], 'central_character': '1.1', 'conductor': 4030, 'conductor_radical': 4030, 'degree': 2, 'index': 93, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4030/2/a/g/1/2'], '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': '2-4030-1.1-c1-0-93', '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': '2-4030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.672716458150893, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44096026793157959599940722278', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1826634148548497133346959669686', 'Lhash_array': ['1826634148548497133346959669686'], 'label': '2-4030-1.1-c1-0-93', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4030/2/a/g/1/2'}