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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 2, 'A4': 1, 'A5': 0, 'A6': -2, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '702324089827228176', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 546.5760018356644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '68450.1', 'coefficient_field': '1.1.1.1', 'conductor': 68450, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1, 1], [1, -2, 3], [1], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, 8, 17], [1, -5, 19], [1, 1, 23], [1, 10, 29], [1, -4, 31], [1], [1, -7, 41], [1, -9, 43], [1, -6, 47], [1, 3, 53], [1, -11, 59], [1, 2, 61], [1, -2, 67], [1, -14, 71], [1, -3, 73], [1, -11, 79], [1, -8, 83], [1, -2, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-68450-1.1-c1-0-11', 'leading_term': '2.81448764427', '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/68450/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.8144876442729, 2.212837847888618, 0.666321800069114, -1.002880366302395, -1.678306980216343, -0.8363743228041525, 0.7364423430708203, 1.499986651812499, 0.8023363308377341, -0.2037083838265668, 0.1647293779041151, 1.837235728300123, 2.729813963191695, 1.421420912111805, -0.5503330714511668, -0.4793030700367535, 1.325619806076356, 1.046780810397634, -3.44907468865814, -8.3214246309256, -7.45912903008769, -0.6041575247684876, 5.289543244084782, 4.498278057903543, -0.2979545401212478, -2.243461553745843, 0.1697539457304688, 2.090415604066031, 0.4918186222033961, -1.623455778891659, -0.9375975235977757, 0.8090733813035518, 0.4675280520420205, -1.027356011220571, -0.9209925224535239, 0.2462524559272149, 0.2385150441807597, -0.3499173873453638, 0.02568860181528724, -0.445453854258464, -3.78850183291856, -6.704308102276843, -4.707431548574958, -0.2677538142730322, 0.6779680992989258, -0.9530213345736638, 0.517255231478049, 3.844188287120551, 1.999320071780087, -4.223099551935554, -5.614417513571129, -0.078161644756151, 3.497625379295171, 0.5978041467368812, -2.206136130262384, -0.4926691927121179, 0.7847875041441654, -1.390264024491771, -2.152253403535838, 0.4924947558288292, 1.335402183629034, -0.9667481102614733, -1.047149129881577, 1.53773678242188, 1.071081111215247, -1.814879567536716, -0.4880720963515154, 3.953623733256687, 3.998050876951279, 0.2210710828440207, -0.4571479512492221, 1.266584458798144, -0.222288793407888, -2.86067864422434, -1.366081053325512, 1.483985618885229, 0.8383610577031403, -0.6823754160077091, 0.1641608376928118, 0.6455541058653984, -0.4029348959482634, -0.001803309671868905, 0.8840124733448939, -0.3033348152122385, 0.5706550605933735, 5.843870153171065, 7.149033390473383, 0.3605695993828417, -4.041389024250752, -0.60844536764063, 0.4882432092335478, -3.539540165350113, 0.3354464801257773, 13.45482324868211, 18.13167497556748, 8.524116269917544, -0.3637087874426539, -0.6279007722345709, 0.1352899653545488, -0.9429101097401144, 0.482176966023269, 2.384780029181703, 0.9688584340337407, -0.2591061158395353, 0.7715858319734581, 0.4400188328527723, -0.7841597034810665, 0.09309292135586918, 0.07772290811769322, -2.255792983717622, -1.483109545095602, 1.912049462901232, 0.8616952983080892, -2.343857799257114, -0.8961139301214902, 0.433309946264411, -3.519617820975619, -4.716541701528581, 0.6734023744187418, 2.711651415740058, -1.100810060357411], 'positive_zeros': ['0.5929292731353445', '1.381921253229553', '2.178996736043445', '2.463722764475810', '3.415239316507000', '3.822956804428704', '4.330465783325616', '5.269483966065654', '5.983195773810975', '6.486537424659413', '7.045598990129348', '7.617612495218471', '8.073754329439804', '8.686625001297551', '9.081016000717442', '9.488106643557917', '9.670147672233862', '10.77109541921374', '11.09895924468019', '11.46026503067765', '12.08350934549994', '12.75311712656066', '13.28480125572326', '13.79806099275460', '14.11763982331195', '14.70733770934730', '15.15187969878306', '15.60227703582261', '16.08656715277125', '16.52852935207209', '17.26889418103774', '17.56235547580162', '17.98218430389278', '18.60004043550182', '19.10337073904387', '19.47012044288611', '19.90188710769103'], 'prelabel': '2-68450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.378964943633935, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 702324089827228176, 'z1': {'__RealLiteral__': 0, 'data': '0.5929292731353445', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.381921253229553', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.178996736043445', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 546.5760018356644, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 68450, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, -1, 2, 1, 0, -2, 0, -1, 1, 0, 4, 2, 2, 0, 0, 1, -8, -1, 5, 0, 0, -4, -1, -2, 0, -2, -4, 0, -10, 0, 4, -1, 8, 8, 0, 1, 0, -5, 4, 0, 7, 0, 9, 4, 0, 1, 6, 2, -7, 0, -16, 2, -3, 4, 0, 0, 10, 10, 11, 0, -2, -4, 0, 1, 0, -8, 2, -8, -2, 0, 14, -1, 3, 0, 0, 5, 0, -4, 11, 0, -11, -7, 8, 0, 0, -9, -20, -4, 2, 0, 0, -1, 8, -6, 0, -2, 8, 7, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 8, 17], 'euler19': [1, -5, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 23], 'euler29': [1, 10, 29], 'euler3': [1, -2, 3], 'euler31': [1, -4, 31], 'euler37': [1, 0, 0], 'euler41': [1, -7, 41], 'euler43': [1, -9, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 3, 53], 'euler59': [1, -11, 59], 'euler61': [1, 2, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 7], 'euler71': [1, -14, 71], 'euler73': [1, -3, 73], 'euler79': [1, -11, 79], 'euler83': [1, -8, 83], 'euler89': [1, -2, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 1, 0], [1, -2, 3], [1, 0, 0], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, 8, 17], [1, -5, 19], [1, 1, 23], [1, 10, 29], [1, -4, 31], [1, 0, 0], [1, -7, 41], [1, -9, 43], [1, -6, 47], [1, 3, 53], [1, -11, 59], [1, 2, 61], [1, -2, 67], [1, -14, 71], [1, -3, 73], [1, -11, 79], [1, -8, 83], [1, -2, 89], [1, -8, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/68450/r'], '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': '2-68450-1.1-c1-0-11', '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': '2-68450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.378964943633935, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 702324089827228176, 'z1': {'__RealLiteral__': 0, 'data': '0.5929292731353445', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '702324089827228176', 'Lhash_array': ['702324089827228176'], 'factors': ['2-68450-1.1-c1-0-11'], 'label': '2-68450-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/68450/r'}