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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1538210844770057174', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 375.6162911081031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '47040.1', 'coefficient_field': '1.1.1.1', 'conductor': 47040, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1], [1, 4, 11], [1, -7, 13], [1, -6, 17], [1, 3, 19], [1, -2, 23], [1, -2, 29], [1, -7, 31], [1, -7, 37], [1, -8, 41], [1, -5, 43], [1, -10, 47], [1, -8, 53], [1, 10, 59], [1, 6, 61], [1, -3, 67], [1, 0, 71], [1, 15, 73], [1, 1, 79], [1, 8, 83], [1, 2, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 81, 'label': '2-47040-1.1-c1-0-81', 'leading_term': '3.59491034659', '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': 0, 'origin': 'EllipticCurve/Q/47040/ee', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.594910346588757, 3.0447509227738, 1.604397886324466, -0.006935843916617265, -0.6994636928029376, 0.2156892118349748, 2.170398830665597, 3.480939358495333, 2.785616958241625, 0.5323254114052545, -1.259732003484325, -1.105461749972067, 0.20274806224044, 0.5029304621060924, -0.9580874233055582, -2.390331032469103, -1.831645283049853, -0.1485556113964604, -0.2838264477968204, -3.141700394804145, -5.707719764505616, -4.70269892687687, -1.230876146512014, 0.4087669802526088, -1.289981615871389, -2.74804143325138, -0.4921199542975758, 3.510382358416027, 4.487339980629519, 1.73792182249594, 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-1.309589820566465, 1.679035724804731, 0.6501520426259887, -0.9511901444496891, -0.06670687752630139, -0.1154274137339234, -1.119576775435821, 2.687584618436133, 9.368266166674413, 9.00864826471323, 1.379273563051996, -2.921536934875833, -1.004062470893285, 0.2888689357701924, -0.02067323658643977, 2.265477803887703, 3.869373854553802, -0.0678970686065856, -3.917770354701416, -1.498151979098441, 1.757050727967339, 0.2176319928978653, -1.458284581176074, 0.1281146898982202, 0.6518734721779509, -0.273587243968534, 1.898430454246867, 4.389884423621787, 1.633417860682966, -1.810774106995324, -0.07846705922767015, 1.760432551013981, -0.4640552085486693, -0.8263508678845207, 2.054064199830718, 0.5504066960369037, -4.247147400159935, -2.785472177261349, 2.843781626096318, 2.657959076534789, -1.179796066887499], 'positive_zeros': ['0.7487034569804905', '1.215634402896517', '2.307320427535074', '2.958618386364970', '3.363082356488797', '4.283892120359106', '4.448392656506360', '5.618737918000685', '5.852371359215517', '6.530473733117940', '7.397929561028747', '7.799682418349827', '8.178733563300799', '8.811858149415047', '9.145774272969032', '10.07459543061583', '10.43132370002505', '10.87474461444349', '11.45254954464260', '12.07547972827018', '12.69429659726737', '13.05800054349714', '13.55715579290664', '14.10525760843602', '14.49749038518138', '15.26346541533392', '15.63932778781286', '15.85322833965516', '16.56650950980054', '16.90298578280735', '17.73894341157758', '18.21270058708414', '18.65152720949096', '18.95548668969316', '19.41271011746374'], 'prelabel': '2-47040-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.38082276654175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1538210844770057174, 'z1': {'__RealLiteral__': 0, 'data': '0.7487034569804905', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.215634402896517', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.307320427535074', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 375.6162911081031, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 47040, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, 1, 0, -4, 0, 7, 0, -1, 0, 6, 0, -3, 0, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 7, 0, -4, 0, 0, 0, 7, 0, 7, 0, 8, 0, 5, 0, -1, 0, 10, 0, 0, 0, 6, 0, 8, 0, 4, 0, -3, 0, -10, 0, -6, 0, 0, 0, -7, 0, 3, 0, 2, 0, 0, 0, -15, 0, 1, 0, 0, 0, -1, 0, 1, 0, -8, 0, -6, 0, 2, 0, -2, 0, 0, 0, 7, 0, 3, 0, 10, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -7, 13], 'euler17': [1, -6, 17], 'euler19': [1, 3, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -7, 31], 'euler37': [1, -7, 37], 'euler41': [1, -8, 41], 'euler43': [1, -5, 43], 'euler47': [1, -10, 47], 'euler5': [1, 1, 0], 'euler53': [1, -8, 53], 'euler59': [1, 10, 59], 'euler61': [1, 6, 61], 'euler67': [1, -3, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 15, 73], 'euler79': [1, 1, 79], 'euler83': [1, 8, 83], 'euler89': [1, 2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, 4, 11], [1, -7, 13], [1, -6, 17], [1, 3, 19], [1, -2, 23], [1, -2, 29], [1, -7, 31], [1, -7, 37], [1, -8, 41], [1, -5, 43], [1, -10, 47], [1, -8, 53], [1, 10, 59], [1, 6, 61], [1, -3, 67], [1, 0, 71], [1, 15, 73], [1, 1, 79], [1, 8, 83], [1, 2, 89], [1, -10, 97]], 'index': 81, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/47040/ee'], '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': '2-47040-1.1-c1-0-81', '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': '2-47040-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.38082276654175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1538210844770057174, 'z1': {'__RealLiteral__': 0, 'data': '0.7487034569804905', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1538210844770057174', 'Lhash_array': ['1538210844770057174'], 'factors': ['2-47040-1.1-c1-0-81'], 'label': '2-47040-1.1-c1-0-81', 'type': 'ECQ', 'url': 'EllipticCurve/Q/47040/ee'}