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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '1834069139393009358', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2834.753152077072, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [43, [1]]], 'bad_primes': [2, 3, 43], 'central_character': '355008.1', 'coefficient_field': '1.1.1.1', 'conductor': 355008, 'conductor_radical': 258, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -4, 5], [1, -4, 7], [1, -1, 11], [1, -4, 13], [1, 5, 17], [1, 5, 19], [1, -2, 23], [1, -8, 29], [1, 4, 31], [1, -2, 37], [1, -3, 41], [1], [1, 4, 47], [1, 12, 53], [1, -5, 59], [1, 10, 61], [1, -5, 67], [1, 12, 71], [1, -7, 73], [1, 14, 79], [1, -4, 83], [1, 15, 89], [1, 19, 97]], 'gamma_factors': [[], [0]], 'index': 109, 'label': '2-355008-1.1-c1-0-109', 'leading_term': '13.1991885457', '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/355008/ce', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.967163515281541, 4.153523783831374, 2.954010857326654, 0.7490064002061272, -0.2696311284873109, 0.2595804692027844, 0.4214677588511166, -0.808790685069746, -1.395034908911347, 0.4903740910578103, 2.107234726937601, -1.03801399567809, -7.552005349824685, -10.11223850128149, -5.446698122329877, 0.5060128024837057, 1.333903464651684, -0.8930695436615405, -0.8989435415100647, 0.5063250720539135, -0.3822094281311594, -2.093247141026586, -1.253564915326323, 0.2343297844306759, -0.4630755256791938, -0.7542765902444606, 0.9730596347232334, -0.2002250204292844, -5.69446674535383, -7.305552780934845, -1.144539382704876, 3.852233598228523, 1.509695839728584, -1.369789362089506, 0.1601116615341659, 0.5275884044330668, -2.087789595361611, -1.110104404127387, 3.28067804812065, 3.491452673839136, 0.2802059437442307, 0.1973440644734605, 1.556756480123684, 0.4270614276781698, 0.218334407598779, 1.299422130879426, -2.440949762604879, -8.119667812299177, -6.347569962216308, -0.5460158374192183, -0.1433505333170772, -1.658493368181917, 0.8956461426087536, 2.298949988136147, 0.112789205380818, 0.3991570955019851, 1.917565900361848, -0.189774171354076, -0.2465590092094446, 4.338128615339517, 3.900526496648958, -1.345608908317996, 0.6025052786169278, 6.635291620131043, 4.458249380208082, -1.200280594129233, -0.7148586005756081, 1.028413315818648, -0.3536285815806269, -0.5028762738652602, 0.2139381546965729, -0.1863852441292946, 0.8976217448214063, 0.0670286617513996, -5.236677609223601, -4.368874293618779, 3.866038062612433, 2.435613492862299, -8.331594322663316, -9.08669120855935, -1.13488252161534, 0.2636449247270318, -1.953304204143446, -0.5101154305766058, 0.05362819066491526, -0.367111708432088, 1.23242364844888, 0.5236918740796715, -0.3811076083637889, 4.004149634172522, 5.140723726910852, -1.032183146766897, -2.596827518812888, 0.6254691598776843, -1.393763444997121, -3.261789626328724, 0.1440302775486312, 0.4543152547663545, -1.507653462098029, 0.3989055569265602, 0.4696632776838719, -1.145517774844275, 2.286776840555781, 3.129775872876647, -1.7903535990933, 0.1148133326678888, 5.732373688592835, 2.644284860298692, -0.9236948998169797, 1.500814718016709, 0.2221687790126613, -2.852346491783328, -0.5735558564205272, 0.2791534468071271, -1.195570911394463, 0.9694048301876431, 1.513395930796735, -0.3983461615845226, 1.817800567353981, 2.701060609278076], 'positive_zeros': ['1.125029718032157', '1.414166056863015', '1.858456789395725', '2.452398455082927', '2.951560675608125', '3.969864410045307', '4.395256735346636', '4.888251590003112', '5.199525832544352', '5.929214635506668', '6.154073757443525', '6.616784637488908', '6.987254255685014', '7.788514729072183', '8.341791446174814', '8.732093501249808', '9.057769979868493', '9.564722432958790', '10.28524190286529', '10.46825464417707', '11.09143294304026', '11.19596700926899', '11.63798244679363', '12.54208285249506', '12.73297402151704', '13.18477101179585', '13.76648506653420', '13.94591539166967', '14.48249512951469', '14.76788141808310', '15.42242955829048', '15.72518540722666', '16.42707124256698', '16.81523748572305', '17.19631209430556', '17.62139557548965', '17.87357272091466', '18.09034865895486', '18.50426533817152', '19.13049693737974', '19.55986523897462'], 'prelabel': '2-355008-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.24239994663156, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1834069139393009358, 'z1': {'__RealLiteral__': 0, 'data': '1.125029718032157', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.414166056863015', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.858456789395725', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2834.753152077072, 'bad_primes': [2, 3, 43], 'central_character': '1.1', 'conductor': 355008, 'conductor_radical': 258, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 4, 0, 4, 0, 1, 0, 1, 0, 4, 0, -4, 0, -5, 0, -5, 0, -4, 0, 2, 0, 11, 0, -1, 0, 8, 0, -4, 0, -1, 0, 16, 0, 2, 0, -4, 0, 3, 0, 0, 0, 4, 0, -4, 0, 9, 0, 5, 0, -12, 0, 4, 0, 5, 0, 5, 0, -10, 0, 4, 0, 16, 0, 5, 0, -2, 0, -12, 0, 7, 0, -11, 0, 4, 0, -14, 0, 1, 0, 4, 0, -20, 0, -8, 0, -15, 0, 16, 0, 4, 0, -20, 0, -19, 0, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, -4, 13], 'euler17': [1, 5, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -3, 41], 'euler43': [1, 0, 0], 'euler47': [1, 4, 47], 'euler5': [1, -4, 5], 'euler53': [1, 12, 53], 'euler59': [1, -5, 59], 'euler61': [1, 10, 61], 'euler67': [1, -5, 67], 'euler7': [1, -4, 7], 'euler71': [1, 12, 71], 'euler73': [1, -7, 73], 'euler79': [1, 14, 79], 'euler83': [1, -4, 83], 'euler89': [1, 15, 89], 'euler97': [1, 19, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -4, 5], [1, -4, 7], [1, -1, 11], [1, -4, 13], [1, 5, 17], [1, 5, 19], [1, -2, 23], [1, -8, 29], [1, 4, 31], [1, -2, 37], [1, -3, 41], [1, 0, 0], [1, 4, 47], [1, 12, 53], [1, -5, 59], [1, 10, 61], [1, -5, 67], [1, 12, 71], [1, -7, 73], [1, 14, 79], [1, -4, 83], [1, 15, 89], [1, 19, 97]], 'index': 109, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/355008/ce'], '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': '2-355008-1.1-c1-0-109', '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': '2-355008-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.24239994663156, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1834069139393009358, 'z1': {'__RealLiteral__': 0, 'data': '1.125029718032157', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1834069139393009358', 'Lhash_array': ['1834069139393009358'], 'factors': ['2-355008-1.1-c1-0-109'], 'label': '2-355008-1.1-c1-0-109', 'type': 'ECQ', 'url': 'EllipticCurve/Q/355008/ce'}