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lfunc_lfunctions • Show schema
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{'Lhash': '1185348781911563212225637671028', 'a10': 0, 'a2': 0, 'a3': -12, 'a4': 0, 'a5': -25, 'a6': 0, 'a7': -54, 'a8': 0, 'a9': -99, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 141.137761435423, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 25]], [11, [1, -121]]], 'bad_primes': [2, 5, 11], 'central_character': '880.1', 'coefficient_field': '1.1.1.1', 'conductor': 880, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1], [1, 12, 243], [1, 25], [1, 54, 16807], [1, -121], [1, 540, 371293], [1, -340, 1419857], [1, -952, 2476099], [1, 1092, 6436343], [1, 62, 20511149], [1, -7560, 28629151], [1, 9186, 69343957], [1, 6818, 115856201], [1, -13310, 147008443], [1, -22420, 229345007], [1, -19654, 418195493], [1, 48292, 714924299], [1, -17530, 844596301], [1, -35344, 1350125107], [1, -22912, 1804229351], [1, -47852, 2073071593], [1, 52396, 3077056399], [1, 7890, 3939040643], [1, -41958, 5584059449], [1, 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60194, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-880-1.1-c5-0-50', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/880/6/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-5.900925619924969e-61, 0.17911335941774925, 0.35268927880888984, 0.5153039808291805, 0.6617593103814107, 0.7871912909387747, 0.8871735846443218, 0.9578141767343561, 0.9958436279634474, 0.9986932754361483, 0.9645618171356405, 0.892468793337717, 0.7822935838646863, 0.6347986783093276, 0.45163615085324266, 0.23533648508312946, -0.010720850994792624, -0.2823553834872037, -0.5746521325907148, -0.8820462296028861, -1.1984248430798563, -1.5172451788867547, -1.8316668768428241, -2.134696680952958, -2.4193428234376797, -2.6787761488096593, 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'7.17004559320051432429081183930527', '8.072198113466222306502601504104759', '9.019577677285468485662836995592701'], 'prelabel': '2-880-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.880141473712465, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1585633949232188859, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.935075313101379459893891486611', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.49995112888818036194355710561', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51800654043730597279596304988', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 141.137761435423, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 880, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 0, -12, 0, -25, 0, -54, 0, -99, 0, 121, 0, -540, 0, 300, 0, 340, 0, 952, 0, 648, 0, -1092, 0, 625, 0, 4104, 0, -62, 0, 7560, 0, -1452, 0, 1350, 0, -9186, 0, 6480, 0, -6818, 0, 13310, 0, 2475, 0, 22420, 0, -13891, 0, -4080, 0, 19654, 0, -3025, 0, -11424, 0, -48292, 0, 17530, 0, 5346, 0, 13500, 0, 35344, 0, 13104, 0, 22912, 0, 47852, 0, -7500, 0, -6534, 0, -52396, 0, -25191, 0, -7890, 0, -8500, 0, 744, 0, 41958, 0, 29160, 0, -90720, 0, -23800, 0, -37602, 0, -11979, 0], 'euler11': [1, -121, 0], 'euler13': [1, 540, 371293], 'euler17': [1, -340, 1419857], 'euler19': [1, -952, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, 1092, 6436343], 'euler29': [1, 62, 20511149], 'euler3': [1, 12, 243], 'euler31': [1, -7560, 28629151], 'euler37': [1, 9186, 69343957], 'euler41': [1, 6818, 115856201], 'euler43': [1, -13310, 147008443], 'euler47': [1, -22420, 229345007], 'euler5': [1, 25, 0], 'euler53': [1, -19654, 418195493], 'euler59': [1, 48292, 714924299], 'euler61': [1, -17530, 844596301], 'euler67': [1, -35344, 1350125107], 'euler7': [1, 54, 16807], 'euler71': [1, -22912, 1804229351], 'euler73': [1, -47852, 2073071593], 'euler79': [1, 52396, 3077056399], 'euler83': [1, 7890, 3939040643], 'euler89': [1, -41958, 5584059449], 'euler97': [1, 37602, 8587340257], 'euler_factors': [[1, 0, 0], [1, 12, 243], [1, 25, 0], [1, 54, 16807], [1, -121, 0], [1, 540, 371293], [1, -340, 1419857], [1, -952, 2476099], [1, 1092, 6436343], [1, 62, 20511149], [1, -7560, 28629151], [1, 9186, 69343957], [1, 6818, 115856201], [1, -13310, 147008443], [1, -22420, 229345007], [1, -19654, 418195493], [1, 48292, 714924299], [1, -17530, 844596301], [1, -35344, 1350125107], [1, -22912, 1804229351], [1, -47852, 2073071593], [1, 52396, 3077056399], [1, 7890, 3939040643], [1, -41958, 5584059449], [1, 37602, 8587340257]], 'index': 50, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/880/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/880/6/a/b'], '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': '2-880-1.1-c5-0-50', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-880-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.880141473712465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1585633949232188859, 'z1': {'__RealLiteral__': 0, 'data': '0.935075313101379459893891486611', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20820477
{'Lhash': '1185348781911563212225637671028', 'Lhash_array': ['1185348781911563212225637671028'], 'label': '2-880-1.1-c5-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/880/6/a/b'}
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id: 24593485
{'Lhash': '1185348781911563212225637671028', 'Lhash_array': ['1185348781911563212225637671028'], 'label': '2-880-1.1-c5-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/880/6/a/b/1/1'}