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lfunc_lfunctions • Show schema
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{'Lhash': '2056512131423519219622560863540', 'a10': [2.2078863133335114, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.406969735103595, 0.0], 'a4': [1.0, 0.0], 'a5': [2.2078863133335114, 0.0], 'a6': [-2.406969735103595, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [2.7935033057046708, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.693484254447895, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 29], 'central_character': '2842.1', 'coefficient_field': 'CDF', 'conductor': 2842, 'conductor_radical': 406, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.406969735103595, 0], [3.0, 0]], [[1.0, 0], [-2.2078863133335114, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1874501488309919, 0], [11.0, 0]], [[1.0, 0], [1.2433005217433506, 0], [13.0, 0]], [[1.0, 0], [5.964585791590161, 0], [17.0, 0]], [[1.0, 0], 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0], [109.0, 0]], [[1.0, 0], [1.0100059144214237, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 77, 'label': '2-2842-1.1-c1-0-77', '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/2842/2/a/x/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.422663941940716e-60, 0.1872503503694028, 0.37408761577164756, 0.5600473199059928, 0.7445653181047702, 0.9269355003282248, 1.106275882643847, 1.2815048988986644, 1.4513290494454336, 1.6142424263675506, 1.7685380708687675, 1.9123306591113642, 2.043589664218901, 2.1601818925590734, 2.2599221197245654, 2.3406304310615287, 2.400194781171174, 2.4366372104177247, 2.448182084866763, 2.4333246564052065, 2.390898174360554, 2.320137724665978, 2.2207389355734235, 2.0929096790372044, 1.937412922980843, 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'5.94432127309126770530840730405495', '6.82651662222004008508547463026777', '7.01449603554066323796229114942939', '8.476975119599703023820426059951222'], 'prelabel': '2-2842-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.763767863199035, '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': '1.62230202159274976889338111277', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51790914657472791020462889923', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78533211784464000497506071189', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.693484254447895, 'bad_primes': [2, 7, 29], 'central_character': '1.1', 'conductor': 2842, 'conductor_radical': 406, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2842/2/a/x/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': '2-2842-1.1-c1-0-77', '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': '2-2842-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.763767863199035, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62230202159274976889338111277', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2056512131423519219622560863540', 'Lhash_array': ['2056512131423519219622560863540'], 'label': '2-2842-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2842/2/a/x/1/2'}