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lfunc_lfunctions • Show schema
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{'Lhash': '2512932655157495063982882763510', 'a10': [1693.510869339022, -7.521013139240833e-60], 'a2': [12.231802224120067, 7.062034306769983], 'a3': [0.0, 0.0], 'a4': [67.74465709999241, 117.33718803851852], 'a5': [103.83859456946358, -59.95124052695221], 'a6': [0.0, 0.0], 'a7': [-128.89051127519417, 223.24491414216553], 'a8': [0.0, 1009.7199788955025], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.211460257735977, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '27.8', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '3701578596041990670670331259679', 'degree': 2, 'euler_factors': [[[1.0, 0], [-12.231802224120067, -7.062034306769983], [32.0, 55.42562584220407]], [[1.0, 0], [0, 0]], [[1.0, 0], [-103.83859456946358, 59.95124052695221], [7812.5, -13531.646934131853]], [[1.0, 0], [128.89051127519417, 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[1677100110841.0, 0]], [[1.0, 0], [-246874.87234532638, 142533.27400472868], [1040975876304.5, -1803023107212.929]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3e3-9.2-c6-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/27/7/d/a/8/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [3.6542258895082913, 3.4340417583436347, 3.1754626580905962, 2.882985796902438, 2.5615743367831567, 2.216823747929738, 1.855124267249828, 1.4837901653356314, 1.1111259447276336, 0.7464009692872282, 0.399707688425903, 0.08168488974165908, -0.19690347234958622, -0.4257313047968531, -0.5955979934303113, -0.6992065761054339, -0.7319806873269229, -0.6928513334194704, -0.5849300302972785, -0.4159753132547036, -0.1985576141779933, 0.050164665086877454, 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'9.841408692747138538782020713015898', '10.79283520160082938376379525523147', '12.19523753356736156012501509199588', '13.40240872460601434144562715744968', '14.08795653766865631676617574139261', '15.21745865237627371767158767527482'], 'prelabel': '2-3e3-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4922801322756594, 'root_angle': -0.3929942402923763, 'root_number': '0.32987249672865343 - 0.9440254953665206*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.196497120146', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98235432910698225670101650146', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65702259340915853468927871094', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.38092182516226455454686350498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.211460257735977, 'bad_primes': [3], 'central_character': '9.2', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/7/d/a/8/5'], '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': '2-3e3-9.2-c6-0-2', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-3e3-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4922801322756594, 'root_angle': -0.19649712014618814, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98235432910698225670101650146', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2512932655157495063982882763510', 'Lhash_array': ['2512932655157495063982882763510'], 'label': '2-3e3-9.2-c6-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/7/d/a/8/5'}