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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 0, 'Lhash': '2131171966422637582', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2167.459312465636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [13, [1, 1]], [29, [1, -1]]], 'bad_primes': [2, 3, 5, 13, 29], 'central_character': '271440.1', 'coefficient_field': '1.1.1.1', 'conductor': 271440, 'conductor_radical': 11310, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 2, 7], [1, 6, 11], [1, 1], [1, 2, 17], [1, 6, 19], [1, -2, 23], [1, -1], [1, 10, 31], [1, 2, 37], [1, 2, 41], [1, 12, 43], [1, 12, 47], [1, 2, 53], [1, 4, 59], [1, -2, 61], [1, -10, 67], [1, 16, 71], [1, 10, 73], [1, -14, 79], [1, -14, 83], [1, -14, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 24, 'label': '2-271440-1.1-c1-0-24', 'leading_term': '3.79920780366', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/271440/cv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6672854991607863, -0.1309958806408249, -2.663527595189589, -5.253975580472768, -5.471634293534605, -2.929321917688429, -0.256800627850179, -0.07902802421677241, -1.473457152397022, -1.292065008281776, 0.9204915165664218, 2.024699551571485, 0.5943668881667893, -0.0163022972714943, 3.02605723239508, 6.433049542534661, 5.201961955883925, 0.7827553560402989, -1.098941743652966, 0.1206746757382603, -0.3096436169871354, -3.054451069477596, -3.381075381695092, -0.5761714427192604, 0.33278980141061, -1.563592639291388, -1.217575000706985, 1.837731433142327, 1.904127770327919, -1.269137912289906, -1.243818004695564, 2.279377143964566, 2.535078968993, -0.6527887170264557, -0.6404849109159586, 2.064140372817368, 0.953406583549715, -2.543292772848926, -2.044824189857303, 0.543847639850689, 0.1467422215275991, -0.2720184145512898, 2.19314784395851, 2.370165499819729, -0.7189147397322003, 0.8322060696749265, 6.96865712616818, 7.421321049446125, 1.544166378386106, -1.020434175048106, 0.6315113529147264, 0.5125687697227019, -0.00371844746482986, 0.9932286403797915, -1.694680625426779, -6.932659751199885, -5.702316781485468, 0.1313962657249847, 1.083760149400345, -0.2737697965678157, 2.58274657324271, 4.26668170109254, 0.9968904812870855, -0.01299600775841373, 2.140526101871383, 0.7610631181948271, -0.9233382352306428, 2.34354231706517, 3.530562924200849, -0.7252665081570087, -1.842892193758616, 0.6577548962456853, -0.6795240831406569, -2.470219808833924, -0.07759249475821912, -0.1339063407578656, -3.292462193992546, -1.572391612401495, 1.213834615186644, -1.995259233422513, -3.703947698564701, 0.3079737118743229, 1.204249378443458, -0.9721173676050977, 1.075375973437862, 2.764109313683448, 0.3737211903143758, 0.8526018819780955, 2.391333016454611, -1.947321213732396, -4.876190270412052, -1.113286844067301, 0.362818071865966, -1.458935065593145, -0.2758956483303799, -1.549572965918789, -7.019454855174365, -5.82889490971643, 0.0002750567134754591, -0.3960554377660613, -1.926716603090445, 1.12924427806993, 1.591034924165138, -0.2862254107279056, 0.6713151268573678, -0.4831542794252229, -2.468801076879888, 2.406404125000606, 5.745267636485156, 0.3489135987144474, -1.849885407060884, 1.64718003581862, -0.1488124827960536, -3.291083078472881, -0.7224387510091852, 0.6615884403356164, -0.2804083101211458, 0.2174793774753417, -3.018849184209188, -6.551603005336577], 'positive_zeros': ['0.4807943978105975', '1.797482870969406', '1.980691423197631', '2.654337800779480', '3.347458870220213', '3.503309422449107', '4.554990637485292', '4.975821804583155', '5.209310772119883', '6.060920946203507', '6.307324218278954', '6.852495490132033', '7.399121161209503', '7.843279131386983', '8.443716402634333', '8.808385354055530', '9.313380802474606', '9.928663845356283', '10.27530025178208', '10.54148160394933', '11.18315501492451', '11.45535906613732', '12.33127117547875', '12.66019877427817', '13.12303918797905', '13.25134338568357', '13.65514703522338', '14.49260762682842', '14.88648204206910', '15.05562688724439', '15.84050800893475', '16.00193758895997', '16.56296784432978', '16.85352999171065', '17.45926045542699', '17.91816425028951', '18.19193771764036', '18.75772217232089', '18.98788280195832', '19.59604534005228', '19.88678274169417'], 'prelabel': '2-271440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.5559804156849, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2131171966422637582, 'z1': {'__RealLiteral__': 0, 'data': '0.4807943978105975', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.797482870969406', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.980691423197631', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2167.459312465636, 'bad_primes': [2, 3, 5, 13, 29], 'central_character': '1.1', 'conductor': 271440, 'conductor_radical': 11310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -6, 0, -1, 0, 0, 0, -2, 0, -6, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, -10, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -12, 0, 0, 0, -12, 0, -3, 0, 0, 0, -2, 0, -6, 0, 0, 0, -4, 0, 2, 0, 0, 0, -1, 0, 10, 0, 0, 0, -16, 0, -10, 0, 0, 0, 12, 0, 14, 0, 0, 0, 14, 0, -2, 0, 0, 0, 14, 0, 2, 0, 0, 0, -6, 0, 6, 0, 0, 0], 'euler11': [1, 6, 11], 'euler13': [1, 1, 0], 'euler17': [1, 2, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -1, 0], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -10, 67], 'euler7': [1, 2, 7], 'euler71': [1, 16, 71], 'euler73': [1, 10, 73], 'euler79': [1, -14, 79], 'euler83': [1, -14, 83], 'euler89': [1, -14, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 2, 7], [1, 6, 11], [1, 1, 0], [1, 2, 17], [1, 6, 19], [1, -2, 23], [1, -1, 0], [1, 10, 31], [1, 2, 37], [1, 2, 41], [1, 12, 43], [1, 12, 47], [1, 2, 53], [1, 4, 59], [1, -2, 61], [1, -10, 67], [1, 16, 71], [1, 10, 73], [1, -14, 79], [1, -14, 83], [1, -14, 89], [1, -6, 97]], 'index': 24, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/271440/cv'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-271440-1.1-c1-0-24', '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': '2-271440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.5559804156849, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2131171966422637582, 'z1': {'__RealLiteral__': 0, 'data': '0.4807943978105975', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2131171966422637582', 'Lhash_array': ['2131171966422637582'], 'label': '2-271440-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/271440/cv'}