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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '2078822069020923664', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3181.2400165278123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [83, [1, 1]]], 'bad_primes': [2, 3, 5, 83], 'central_character': '398400.1', 'coefficient_field': '1.1.1.1', 'conductor': 398400, 'conductor_radical': 2490, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 4, 7], [1, -3, 11], [1, 6, 13], [1, -4, 17], [1, 3, 19], [1, 1, 23], [1, 4, 29], [1, -2, 31], [1, -3, 37], [1, -6, 41], [1, -12, 43], [1, 0, 47], [1, 9, 53], [1, 7, 59], [1, -1, 61], [1, 7, 67], [1, 0, 71], [1, 4, 73], [1, -4, 79], [1, 1], [1, -5, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-398400-1.1-c1-0-4', 'leading_term': '0.400016962281', '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/398400/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.4000169622813668, -0.2536480122174497, -1.465034949607724, -1.554339377313939, 0.2594410985319159, 2.208851052451475, 1.421750571749426, -2.120482744515494, -4.579248783816885, -3.045616035773979, 0.02105328518303354, 0.1506056206742432, -2.149517557803485, -2.13178317704786, 1.109005704297085, 2.838692100422047, 0.9830974154214727, -0.05482061992180779, 2.365496770346866, 3.749740370583999, 0.7100499035659443, -2.281116836773937, -0.9341692255254597, 1.185130632790582, 0.1721294568909114, -0.9100558981056914, 0.4513858522170553, 0.5275270658986837, -1.886376685642685, -1.922182519065123, 0.3211250511029337, -1.316300241556339, -4.812080897595758, -1.199830676364322, 7.201055640789332, 8.731648066324418, 3.061790488598769, -0.08736932387848027, 0.2951190899014548, -0.9531274549583798, -1.49364752957343, 1.318100429680663, 1.868065162271404, -0.9650776282304915, 0.2281371020345656, 4.624217397931102, 3.668185761570813, -0.76913485177344, -1.109025069597735, 0.2918388882940953, -0.2522338302818398, 1.026903067722251, 2.876702927279328, -0.1403629345181011, -2.194197943243898, 2.995679715580636, 6.233257049547819, 1.625660199461475, -1.022664510338736, 0.8228067330312716, -1.746160161754613, -5.64593099322852, -2.293048807052504, 1.814020576976892, 0.05527786337170036, -0.816770229071423, 1.092318747354646, 0.1911266813267891, -0.8937363848262742, 0.2410681231163782, -1.467948738272881, -2.570723024910342, 3.194277251526587, 6.626250609914535, 1.254156643613951, -2.225328798506448, -0.1055969043863202, 0.07103762426928142, 0.2448824219925335, 2.431540635995816, -0.3504524349815373, -3.506687951437687, 1.87639107920394, 5.063293296431377, -1.549243377434106, -4.310611752861771, 0.610738945699611, 1.662647894714969, -0.04772318201668391, 1.213340755244535, 0.913290942261755, -0.3281958831294922, 0.7537885736463856, -1.398738665385764, -4.432156292283009, -0.4600200192899577, 2.693334993387213, -0.3051264241804606, 0.5177082054505769, 3.436155521347883, -0.0918108376006778, -1.922924982239285, 1.253137908480331, -0.005657643404694436, -1.062824883606294, 3.765875812112386, 3.653295380862667, -0.9189286179649993, 0.4970693357829023, 1.183726014512453, -3.035812017545257, -2.416562640771743, 0.1089010181465337, -1.592256850619483, 0.1941011626485547, 4.084156525209934, 1.965652749372419, -0.2237381490643698, 0.3919619679928298, -0.3056154797384418, 2.126053572600977], 'positive_zeros': ['0.1915748125626917', '0.9725663972447573', '1.612286927751797', '2.497514761579964', '2.770263009853869', '3.422314586355747', '4.130535075181663', '4.263345183539766', '5.042711207913748', '5.583340894179643', '6.022322244198530', '6.433057205533278', '6.813894955847327', '7.448388471438079', '7.648523191858636', '8.286531252518389', '9.219696327360085', '9.353054614704198', '9.613427496485473', '10.14638067741305', '10.65913341759554', '10.98595680155878', '11.69599197690091', '12.15870002578754', '12.40697309371696', '12.63102703508000', '13.24215259211899', '13.63478954307432', '14.33312509032363', '14.63383008897435', '14.90228764123346', '15.60253403852322', '16.00497144755328', '16.35344343845181', '16.77255500886529', '17.17955207706718', '17.35610809611536', '17.88719104070632', '18.55023679590541', '19.01376550548331', '19.26722176330063', '19.46523859433052', '19.98310193291166'], 'prelabel': '2-398400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.402482361398, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2078822069020923664, 'z1': {'__RealLiteral__': 0, 'data': '0.1915748125626917', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9725663972447573', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.612286927751797', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3181.2400165278123, 'bad_primes': [2, 3, 5, 83], 'central_character': '1.1', 'conductor': 398400, 'conductor_radical': 2490, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -4, 0, 1, 0, 3, 0, -6, 0, 0, 0, 4, 0, -3, 0, 4, 0, -1, 0, 0, 0, -1, 0, -4, 0, 2, 0, -3, 0, 0, 0, 3, 0, 6, 0, 6, 0, 12, 0, 0, 0, 0, 0, 9, 0, -4, 0, -9, 0, 0, 0, 3, 0, -7, 0, 1, 0, -4, 0, 0, 0, -7, 0, 1, 0, 0, 0, -4, 0, 0, 0, -12, 0, 4, 0, 1, 0, -1, 0, 0, 0, 4, 0, 5, 0, 24, 0, -2, 0, 0, 0, -10, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, 6, 13], 'euler17': [1, -4, 17], 'euler19': [1, 3, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -3, 37], 'euler41': [1, -6, 41], 'euler43': [1, -12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, 7, 59], 'euler61': [1, -1, 61], 'euler67': [1, 7, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 4, 73], 'euler79': [1, -4, 79], 'euler83': [1, 1, 0], 'euler89': [1, -5, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, -3, 11], [1, 6, 13], [1, -4, 17], [1, 3, 19], [1, 1, 23], [1, 4, 29], [1, -2, 31], [1, -3, 37], [1, -6, 41], [1, -12, 43], [1, 0, 47], [1, 9, 53], [1, 7, 59], [1, -1, 61], [1, 7, 67], [1, 0, 71], [1, 4, 73], [1, -4, 79], [1, 1, 0], [1, -5, 89], [1, 10, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/398400/k'], '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': '2-398400-1.1-c1-0-4', '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': '2-398400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.402482361398, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2078822069020923664, 'z1': {'__RealLiteral__': 0, 'data': '0.1915748125626917', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2078822069020923664', 'Lhash_array': ['2078822069020923664'], 'factors': ['2-398400-1.1-c1-0-4'], 'label': '2-398400-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/398400/k'}