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lfunc_lfunctions • Show schema
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{'Lhash': '2729111663020420032338261285814', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.7544057079459154, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.30218681787435, -2.5477811099284353], 'a6': [0.0, 0.0], 'a7': [-3.8499679278027856, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.4132491960349605, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.719368459529502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [4.30218681787435, 2.5477811099284353]]]], 'bad_primes': [2, 5], 'central_character': '320.319', 'coefficient_field': 'CDF', 'conductor': 320, 'conductor_radical': 10, 'conjugate': '594132920205880513842353375148', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.7544057079459154, 0], [9.0, 0]], [[1.0, 0], [4.30218681787435, 2.5477811099284353]], [[1.0, 0], [3.8499679278027856, 0], [49.0, 0]], [[1.0, 0], [0, 6.19112443971374], [-121.0, 0]], [[1.0, 0], [0, 16.11318505164053], 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'4.22750422705702766620509826304249', '6.00523295558657510294123113387929', '7.12567616712491269998000023309574', '7.927834244479482774302270786527136', '8.855197806449527835423536015334553', '9.767933290161720482186019582460647', '10.72283289179252834994049702904571', '11.94597275846186719167373695703877'], 'prelabel': '2-320-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.952857676815715, 'root_angle': 0.6701904135155003, 'root_number': '-0.509556221985687 + 0.8604373635748701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.335095206758', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15288949693950947600483807677', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44365412428792927456027975228', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22750422705702766620509826304', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.719368459529502, 'bad_primes': [2, 5], 'central_character': '20.19', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/3/h/f/319/5'], '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': '2-320-20.19-c2-0-20', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-320-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.952857676815715, 'root_angle': 0.3350952067577502, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15288949693950947600483807677', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2729111663020420032338261285814', 'Lhash_array': ['2729111663020420032338261285814'], 'label': '2-320-20.19-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/3/h/f/319/5'}