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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': -4, 'A6': 0, 'A7': 2, 'A8': 1, 'A9': 0, 'Lhash': '1244402155760414563', 'a10': [-1.2649110640673518, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 295.6540985239929, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [11, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '37026.1', 'coefficient_field': '1.1.1.1', 'conductor': 37026, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 4, 5], [1, -2, 7], [1], [1, 0, 13], [1, 1], [1, 0, 19], [1, -6, 23], [1, 2, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, -4, 43], [1, -6, 47], [1, 8, 53], [1, 8, 59], [1, -8, 61], [1, 4, 67], [1, -6, 71], [1, 10, 73], [1, -6, 79], [1, 4, 83], [1, -14, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-37026-1.1-c1-0-8', 'leading_term': '2.66543057918', '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/37026/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.665430579177201, 2.075031895810647, 0.5045370067926864, -1.326935797582428, -2.240397407404239, -1.309031099183382, 1.173892621861137, 3.517487672467535, 3.824674685084941, 1.737420678796951, -1.021591536895476, -2.183715622182804, -1.189795893047115, 0.3106215062319737, 0.4448531432670869, -0.6820905544015317, -1.330750920827362, -0.616931366079367, 0.2518236821067786, -0.1124226395259662, -0.8618207659210174, 0.1646204056325725, 2.972399493042487, 4.504456438727328, 2.433022743216884, -1.246574101553673, -2.381023336456149, -0.1571913942589112, 1.915997388977324, 1.232679513905725, -0.2495592501586091, 0.3806243242959485, 1.891472306545022, 0.9814437636410227, -1.430882389975862, -0.6478503457823432, 3.841060606569581, 5.540616384632605, -0.3449410654334926, -8.833640605790457, -10.84858946344345, -5.275095148816995, 0.323008536729357, 0.816779180807693, -0.8104497100570631, -0.434472544297276, 0.7455677798837314, 0.265767935075785, -0.2790948112112833, 1.22479623835529, 2.554845230386298, 1.142919727573589, -0.3752610732281365, 1.591563405136709, 4.549224417439498, 3.555116687285364, -0.2029072075997089, -1.379882320329264, 0.4670926148852838, 1.094137479264607, -0.1844834398014439, -0.1647218721009152, 1.012433467513188, 0.3867105021194041, -0.6389014980785613, 1.651856395501378, 4.724530924160417, 3.069330347029307, -0.5774807803476171, 1.383121380860919, 6.826442822452038, 5.632374667961906, -2.707173354211281, -7.090369581895621, -3.092754281157661, 0.9339277124201398, -0.2967044057805388, -1.368878864319304, 1.152227391206481, 2.338935127802117, 0.004926612850466452, -0.9090967522179779, 0.918316584173204, 0.7177710686268598, -1.443041585344346, -0.1121249536766664, 3.762211598680727, 3.565141380578077, -0.2496676171418684, -1.120229732312337, 1.118468901918668, 1.296602883745581, -0.2682181507539427, 0.1283653646441972, 1.084945324335933, 0.1475711975220022, -0.1997204614457516, 0.9449084244409407, -0.3097246012456947, -3.099152860170816, -1.552382061334722, 1.824643648954526, -1.667547905025758, -9.108516962204888, -8.84333436908759, -1.657481894638435, 1.019501687310037, -1.736740982745221, -1.751226080747087, 0.255000425664465, -1.413900043604753, -3.016386640661118, 0.1545721293235997, 1.903350979406482, -1.739992549259931, -2.494845715821065, 3.132143007397959, 5.110725122316625, -0.6756843235824294, -4.466586408235577, -1.691510791045684], 'positive_zeros': ['0.5664085747496719', '1.392467857726960', '2.400048565261870', '3.185082721491055', '3.613143329599662', '4.397701907202875', '4.717671939953681', '5.230844817607960', '6.158816566220627', '6.763687508631081', '7.435226316041863', '7.685623577919244', '8.345034709714413', '8.794582729203753', '9.490119654054022', '10.47654614850827', '10.86342420682284', '11.32557447465787', '11.81335303970030', '12.08093768581224', '12.88746128574261', '13.10389050562664', '13.98455567158238', '14.44269917098991', '14.96187105040578', '15.28462321288521', '15.81054163423350', '16.11932430171446', '16.94044339888983', '17.17116439144908', '17.92335623486978', '18.65433891735876', '18.96978003959488', '19.40583633784227'], 'prelabel': '2-37026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.194595038092434, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1244402155760414563, 'z1': {'__RealLiteral__': 0, 'data': '0.5664085747496719', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.392467857726960', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.400048565261870', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 295.6540985239929, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 37026, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -4, 0, 2, 1, 0, -4, 0, 0, 0, 2, 0, 1, -1, 0, 0, -4, 0, 0, 6, 0, 11, 0, 0, 2, -2, 0, 4, 1, 0, -1, -8, 0, 2, 0, 0, -4, -6, 0, 4, 0, 0, 6, 6, 0, -3, 11, 0, 0, -8, 0, 0, 2, 0, -2, -8, 0, 8, 4, 0, 1, 0, 0, -4, -1, 0, -8, 6, 0, -10, 2, 0, 0, 0, 0, 6, -4, 0, -6, -4, 0, 4, 4, 0, 0, 14, 0, 0, 6, 0, 6, 0, 0, 14, -3, 0, 11], 'euler11': [1, 0, 0], 'euler13': [1, 0, 13], 'euler17': [1, 1, 0], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 4, 5], 'euler53': [1, 8, 53], 'euler59': [1, 8, 59], 'euler61': [1, -8, 61], 'euler67': [1, 4, 67], 'euler7': [1, -2, 7], 'euler71': [1, -6, 71], 'euler73': [1, 10, 73], 'euler79': [1, -6, 79], 'euler83': [1, 4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 4, 5], [1, -2, 7], [1, 0, 0], [1, 0, 13], [1, 1, 0], [1, 0, 19], [1, -6, 23], [1, 2, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, -4, 43], [1, -6, 47], [1, 8, 53], [1, 8, 59], [1, -8, 61], [1, 4, 67], [1, -6, 71], [1, 10, 73], [1, -6, 79], [1, 4, 83], [1, -14, 89], [1, -14, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/37026/v'], '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': '2-37026-1.1-c1-0-8', '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': '2-37026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.194595038092434, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1244402155760414563, 'z1': {'__RealLiteral__': 0, 'data': '0.5664085747496719', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1244402155760414563', 'Lhash_array': ['1244402155760414563'], 'label': '2-37026-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/37026/v'}