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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -6, 'Lhash': '171845760336522473,823669738576213693', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.197428424270418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]]], 'bad_primes': [2, 7], 'central_character': '175616.1', 'coefficient_field': '1.1.1.1', 'conductor': 175616, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 6, 0, 9], [1, 4, 14, 20, 25], [1, -1], [1, 8, 38, 88, 121], [1, 4, 30, 52, 169], [1, 0, -2, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 16, 126, 496, 961], [1, 0, 70, 0, 1369], [1, 0, 78, 0, 1681], [1, 8, 102, 344, 1849], [1, -16, 158, -752, 2209], [1, 0, 70, 0, 2809], [1, 0, 118, 0, 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['2.40145156924384381758797773878204', '2.50561452898491372410349134800922', '3.60173413237973468362473708204551', '3.68340574560716411313233602486573', '4.92225264716551837532790929786000', '4.98409920426632935260415692638049', '5.69394971603405508863657314834040', '5.92791093661634117809390012383476', '7.26382021666693896035142333426890', '7.30264187759595822059178656689263', '7.79292083571821938290976650763015', '8.078246359041317001571436271674870', '8.749304120934004278681759852830629'], 'prelabel': '4-56e3-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8292774205870685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 995515498912736166, 'z1': {'__RealLiteral__': 0, 'data': '2.40145156924384381758797773878204', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.50561452898491372410349134800922', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.60173413237973468362473708204551', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.197428424270418, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 175616, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 1, 0, -6, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -16, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 24, 0, 16, 0, 1, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 12, 0, -6, 0, 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 48, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, 0, 102, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 0, 158, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 6, 0, 9], [1, 4, 14, 20, 25], [1, -1, 0, 0, 0], [1, 8, 38, 88, 121], [1, 4, 30, 52, 169], [1, 0, -2, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 16, 126, 496, 961], [1, 0, 70, 0, 1369], [1, 0, 78, 0, 1681], [1, 8, 102, 344, 1849], [1, -16, 158, -752, 2209], [1, 0, 70, 0, 2809], [1, 0, 118, 0, 3481], [1, -12, 158, -732, 3721], [1, 8, 150, 536, 4489], [1, 0, 78, 0, 5041], [1, 0, 46, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, 102, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, 158, 0, 9409]], 'index': 31, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.56.1/56.1/d', 'ModularForm/GL2/TotallyReal/2.2.56.1/holomorphic/2.2.56.1-56.1-d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-56e3-1.1-c1e2-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-56e3-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8292774205870685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 995515498912736166, 'z1': {'__RealLiteral__': 0, 'data': '2.40145156924384381758797773878204', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9476759
{'Lhash': '171845760336522473,823669738576213693', 'Lhash_array': ['171845760336522473', '823669738576213693'], 'label': '4-56e3-1.1-c1e2-0-31', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.56.1/holomorphic/2.2.56.1-56.1-d'}
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id: 9476726
{'Lhash': '171845760336522473,823669738576213693', 'Lhash_array': ['171845760336522473', '823669738576213693'], 'label': '4-56e3-1.1-c1e2-0-31', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.56.1/56.1/d'}