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lfunc_lfunctions • Show schema
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{'Lhash': '396742274092106355545883610285', 'a10': [0.0, 0.0], 'a2': [-0.7922869913932613, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.3722813232690143, 0.0], 'a5': [0.0, 0.0], 'a6': [0.7922869913932613, 0.0], 'a7': [-2.5243377989621387, 0.0], 'a8': [2.6718146237444933, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.46423983431198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '9075.1', 'coefficient_field': 'CDF', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7922869913932613, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5243377989621387, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.780726405493154, 0], [13.0, 0]], [[1.0, 0], [6.6332495807108, 0], [17.0, 0]], [[1.0, 0], [-7.72049022166877, 0], [19.0, 0]], [[1.0, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-9075-1.1-c1-0-12', 'leading_term': '0.30240223567809090275272093116749', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9075/2/a/cw/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.3024022356780909, 0.295419591721892, 0.2745208131128427, 0.2398578004901987, 0.19169815764739423, 0.130445594407139, 0.05666610039970719, -0.028882256458244392, -0.12521835857378713, -0.23110848190339883, -0.3450407191653901, -0.46520579190926276, -0.5894863981345715, -0.7154569025634625, -0.8403947838820742, -0.96130482584364, -1.074956590122165, -1.1779352469876694, -1.2667053714362815, -1.3376868426706645, -1.3873415196173962, -1.4122689117587428, -1.4093086321261497, -1.3756470189962673, 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'4.94886801440622726841952345872547', '5.48369505572690581021023959685281', '6.69645395729456967319265324049266', '6.97313359155605649135322374470169', '7.64463086674054385348181414627838'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31297446947974179927242880302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.43197190776712929730520281370', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66578267326586907416951650500', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.46423983431198, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9075/2/a/cw/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': '2-9075-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31297446947974179927242880302', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '396742274092106355545883610285', 'Lhash_array': ['396742274092106355545883610285'], 'label': '2-9075-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/cw/1/2'}