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lfunc_lfunctions • Show schema
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{'Lhash': '540167448462828505766427939026,1374568298586530764407828602828', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 437, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31124.79328594121, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1, -242, 14641]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.1', 'coefficient_field': '1.1.1.1', 'conductor': 1210000, 'conductor_radical': 110, 'degree': 4, 'euler_factors': [[1], [1, 0, -437, 0, 59049], [1], [1, 0, -31114, 0, 282475249], [1, -242, 14641], [1, 0, -598186, 0, 137858491849], [1, 0, -1507998, 0, 2015993900449], [1, -3648, 8279174, -9032809152, 6131066257801], [1, 0, 22595, 0, 41426511213649], [1, 16064, 105535322, 329491097536, 420707233300201], [1, 5890, 65931327, 168625699390, 819628286980801], [1, 0, -89981473, 0, 4808584372417849], [1, 1040, 231982802, 120490449040, 13422659310152401], [1, 0, -287836690, 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'data': '1.08434319231107670095343860710', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.35808723449671520236525505996', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31124.79328594121, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 1210000, 'conductor_radical': 110, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 437, 0, 242, 0, 0, 0, 0, 0, 0, 0, 3648, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16064, 0, -5890, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1040, 0, 0, 0, 0, 0, 0, 0, 31114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63558, 0, 68312, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29942, 0, 0, 0, 0, 0, 0, 0, 57076, 0, 131920, 0, 0, 0, 0, 0, 0, 0, -72542, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105754, 0], 'euler11': [1, -242, 14641, 0, 0], 'euler13': [1, 0, -598186, 0, 137858491849], 'euler17': [1, 0, -1507998, 0, 2015993900449], 'euler19': [1, -3648, 8279174, -9032809152, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 22595, 0, 41426511213649], 'euler29': [1, 16064, 105535322, 329491097536, 420707233300201], 'euler3': [1, 0, -437, 0, 59049], 'euler31': [1, 5890, 65931327, 168625699390, 819628286980801], 'euler37': [1, 0, -89981473, 0, 4808584372417849], 'euler41': [1, 1040, 231982802, 120490449040, 13422659310152401], 'euler43': [1, 0, -287836690, 0, 21611482313284249], 'euler47': [1, 0, -410803614, 0, 52599132235830049], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -648207462, 0, 174887470365513049], 'euler59': [1, -63558, 2439753439, -45439158595842, 511116753300641401], 'euler61': [1, -68312, 2855824938, -57696062513912, 713342911662882601], 'euler67': [1, 0, 1082368795, 0, 1822837804551761449], 'euler7': [1, 0, -31114, 0, 282475249], 'euler71': [1, 29942, 3832589543, 54022235227642, 3255243551009881201], 'euler73': [1, 0, -2817978050, 0, 4297625829703557649], 'euler79': [1, -57076, 6968530242, -175626071029324, 9468276082626847201], 'euler83': [1, 0, -1874620962, 0, 15516041187205853449], 'euler89': [1, 72542, 12483704339, 405078840549358, 31181719929966183601], 'euler97': [1, 0, -14694740113, 0, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -437, 0, 59049], [1, 0, 0, 0, 0], [1, 0, -31114, 0, 282475249], [1, -242, 14641, 0, 0], [1, 0, -598186, 0, 137858491849], [1, 0, -1507998, 0, 2015993900449], [1, -3648, 8279174, -9032809152, 6131066257801], [1, 0, 22595, 0, 41426511213649], [1, 16064, 105535322, 329491097536, 420707233300201], [1, 5890, 65931327, 168625699390, 819628286980801], [1, 0, -89981473, 0, 4808584372417849], [1, 1040, 231982802, 120490449040, 13422659310152401], [1, 0, -287836690, 0, 21611482313284249], [1, 0, -410803614, 0, 52599132235830049], [1, 0, -648207462, 0, 174887470365513049], [1, -63558, 2439753439, -45439158595842, 511116753300641401], [1, -68312, 2855824938, -57696062513912, 713342911662882601], [1, 0, 1082368795, 0, 1822837804551761449], [1, 29942, 3832589543, 54022235227642, 3255243551009881201], [1, 0, -2817978050, 0, 4297625829703557649], [1, -57076, 6968530242, -175626071029324, 9468276082626847201], [1, 0, -1874620962, 0, 15516041187205853449], [1, 72542, 12483704339, 405078840549358, 31181719929966183601], [1, 0, -14694740113, 0, 73742412689492826049]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1100/6/b/a'], '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': '4-1100e2-1.1-c5e2-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-1100e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 13.282401958767801, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 569054612121234277, 'z1': {'__RealLiteral__': 0, 'data': '0.42611698236531113692811863463', 'prec': 103}}
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{'Lhash': '540167448462828505766427939026,1374568298586530764407828602828', 'Lhash_array': ['540167448462828505766427939026', '1374568298586530764407828602828'], 'label': '4-1100e2-1.1-c5e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1100/6/b/a'}