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lfunc_lfunctions • Show schema
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{'Lhash': '1257666950755863092531747919071', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [9.465485281243435, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.722062806199894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.1', 'coefficient_field': 'CDF', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-9.465485281243435, 0], [343.0, 0]], [[1.0, 0], [-49.04737504948102, 0], [1331.0, 0]], [[1.0, 0], [-55.44383089321132, 0], [2197.0, 0]], [[1.0, 0], [27.97834561196789, 0], [4913.0, 0]], [[1.0, 0], [-26.396455843730305, 0], [6859.0, 0]], [[1.0, 0], [-9.534514718756565, 0], [12167.0, 0]], 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'3.27860737584968292133941066062907', '4.21839909669030073962912585537789', '5.19677863524265578883424733607797', '6.27689104271426081196683858938414', '6.74915740501309006672081450449287', '7.995159477919477882055771280876411', '8.734278928703078546158023486227616', '9.400941184565015510979159469289743'], 'prelabel': '2-1080-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.982610024684902, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.992124289239819836623910230322', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.85855150732230445912457256292', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27860737584968292133941066063', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.722062806199894, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/4/a/n/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': '2-1080-1.1-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1080-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.982610024684902, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.992124289239819836623910230322', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1257666950755863092531747919071', 'Lhash_array': ['1257666950755863092531747919071'], 'label': '2-1080-1.1-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/4/a/n/1/2'}