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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '56054968661490407', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2064.691845064248, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [13, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '258570.1', 'coefficient_field': '1.1.1.1', 'conductor': 258570, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1, 0, 7], [1, 0, 11], [1], [1, -1], [1, -2, 19], [1, 0, 23], [1, -8, 29], [1, 8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -12, 53], [1, 2, 59], [1, 8, 61], [1, -12, 67], [1, 0, 71], [1, 4, 73], [1, -6, 79], [1, 4, 83], [1, 4, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 32, 'label': '2-258570-1.1-c1-0-32', 'leading_term': '1.52541003796', '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/258570/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.525410037958882, 0.9414373894873271, -0.2788345466917837, -0.8527135598820597, 0.07509126355175699, 1.601940862861713, 1.66692396393271, -0.2341466733637025, -1.707635415404498, -0.3357729540058951, 2.488323821964827, 2.926006597710821, 0.4293397455740648, -0.9072475069648613, 1.243677606476311, 2.962450762950623, 0.03379068075635844, -4.329460614530737, -3.752326539919966, 0.6460424019831604, 1.502270487426992, -2.423704535870127, -3.929691073660794, 0.0933393679262001, 3.224126266345999, 1.038603492995512, -1.433022794184526, 0.357174121401223, 2.471912690322339, 1.06578158686431, -0.3650261920549228, 0.9903687149509259, 1.504274866409478, -0.5923506917013581, -1.264890939068512, 0.2845905100195021, -0.2999972409282615, -2.586986032510418, -1.671028940002098, 1.113723636604028, 0.815066010929065, -0.3623632334729327, 1.68683173412416, 3.067705881616703, 0.2454362711846572, -1.668795963888526, -0.171717124848892, -0.7642293398355684, -3.299193990056438, -1.257173374563076, 2.379452697926432, 0.2930614527600113, -1.555789179752847, 4.495836708006194, 9.306997804296255, 4.353944573543344, -0.2190594726575031, 3.201328242638565, 4.778749968169247, -0.04980013875592067, -1.704095632807146, 1.181348027188217, 0.4342800930035444, -1.954299083157605, -0.02198538271632828, 1.57671892257415, -0.3830060489754532, -0.4250970578985067, 0.7363417718703634, -2.251748699773208, -4.812057453993098, -2.058845335579786, 0.1718717936073455, -0.4876746575283368, 0.939598182096754, 2.292391600659912, -0.3292387355618367, -1.435240970065499, 0.8991701765748654, 0.6888447860398031, -0.5713280862319472, 0.8160655147411038, -0.862756027469321, -5.305588014462444, -3.407997388197606, 0.5958633614597062, -2.087321801878517, -3.217728018789761, 1.704126797033922, 0.3024997143105414, -6.459102213571399, -4.284490630789226, 1.501442188548794, -0.7444599035295815, -2.864548857891195, 0.01702500298956678, -1.683572456101005, -5.360570839798781, -2.288939417205762, 0.1819471566942365, -2.527262551831018, -1.98566119956193, 0.3863969270412095, -1.790932641880212, -2.374718256881875, 0.7874796669009488, 0.3577312627846667, -1.232761785035121, 0.6869477140392759, 0.9274876628411711, -0.4828132579361722, 0.5200948005577231, -0.7901126869035598, -4.071569239120974, -2.066117069048808, 0.6343670485361463, -0.8655512143258505, -0.3468375634724616, -0.4719034880429366, -6.748209982914269, -8.45654381462051], 'positive_zeros': ['0.4416785695900186', '0.9876841014042345', '1.724132061702402', '2.280049103986347', '3.041237207039903', '3.390379445602651', '4.001747872057167', '4.710118050567181', '5.111558167734402', '5.745350931276425', '6.323179948498582', '6.720617505241656', '7.377748303014305', '7.609675156062309', '8.186170828371194', '8.698388529553451', '8.963295548507972', '9.635346356168681', '10.11545644366319', '10.33534156050523', '11.01742192047767', '11.53595193311367', '11.64826754809345', '12.31845279511595', '12.76806396094665', '13.09732105647750', '13.95088554678182', '14.05582442201089', '14.74748604544124', '15.14535111499523', '15.53482797881381', '16.00174886217143', '16.45493532291014', '16.80867733419639', '17.10358229867794', '17.93577749599858', '18.09396103790651', '18.39777988119855', '18.97458891019255', '19.40499468543210', '19.83887663738049'], 'prelabel': '2-258570-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 45.438880323619856, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 56054968661490407, 'z1': {'__RealLiteral__': 0, 'data': '0.4416785695900186', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9876841014042345', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.724132061702402', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2064.691845064248, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 258570, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 8, 0, -8, -1, 0, -1, 0, 0, 6, -2, 0, 1, -6, 0, -4, 0, 0, 0, 0, 0, -7, -1, 0, 0, 12, 0, 0, 0, 0, -8, -2, 0, -8, 8, 0, 1, 0, 0, 12, 1, 0, 0, 0, 0, -4, -6, 0, 2, 0, 0, 6, -1, 0, 6, -4, 0, -1, 4, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 8, 7, 0, 1], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, -1, 0], 'euler19': [1, -2, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, 2, 59], 'euler61': [1, 8, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 4, 73], 'euler79': [1, -6, 79], 'euler83': [1, 4, 83], 'euler89': [1, 4, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 0, 7], [1, 0, 11], [1, 0, 0], [1, -1, 0], [1, -2, 19], [1, 0, 23], [1, -8, 29], [1, 8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -12, 53], [1, 2, 59], [1, 8, 61], [1, -12, 67], [1, 0, 71], [1, 4, 73], [1, -6, 79], [1, 4, 83], [1, 4, 89], [1, -8, 97]], 'index': 32, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/258570/z'], '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': '2-258570-1.1-c1-0-32', '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': '2-258570-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 45.438880323619856, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 56054968661490407, 'z1': {'__RealLiteral__': 0, 'data': '0.4416785695900186', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '56054968661490407', 'Lhash_array': ['56054968661490407'], 'label': '2-258570-1.1-c1-0-32', 'type': 'ECQ', 'url': 'EllipticCurve/Q/258570/z'}