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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '2175121014938216555', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1831.1294191520026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '229320.1', 'coefficient_field': '1.1.1.1', 'conductor': 229320, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1], [1, 0, 11], [1, -1], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, -8, 31], [1, -2, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, -10, 53], [1, -4, 59], [1, 14, 61], [1, -4, 67], [1, 12, 71], [1, -10, 73], [1, -8, 79], [1, -12, 83], [1, -14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 111, 'label': '2-229320-1.1-c1-0-111', 'leading_term': '7.75928057451', '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/229320/bv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.694904817902684, 2.096494562720436, 0.8742426935723598, -0.6477467786532888, -0.4346998862258984, 1.791794332786062, 3.561866306455205, 2.365442563324524, -0.7727463463185364, -2.135888213594573, -0.3493383254945912, 1.478295541685803, 0.36386615948648, -1.846696958651998, -1.493281756218836, 0.620343584703295, 0.4365935120359411, -2.11895906733987, -2.606764545126788, -0.02325326045197535, 0.8601903522543063, -2.074936352337824, -4.020285797506026, -1.698906312798564, 0.6166450712997248, -0.7953934194138389, -1.93454235492644, 1.048034072135349, 3.905675034828195, 2.132672202747277, -0.6032363277234537, 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-3.108449818006809, 0.5406320000380926, 0.7951596075704948, -1.180324872695441, 0.3579462838508021, -0.7034642495289489, -6.094473327387479, -5.255287477953543, 0.9490394137873502, 1.795551151611015, -0.2648546589639141, 0.270864456377566, -1.329272082057187, -3.565494372558435, 0.01759862537838681, 2.878029107332883, 0.07620648125855695, 0.3385521476195129, 3.600024919472731, 1.021510802322074, -2.269527412346248, -0.207838690279175, -0.4918589052723364, -3.240200409085257, -0.554325185844351, 1.673705080230845, -2.05006877755509, -2.845538256887683, 0.1850000226797206, -0.4942836747382573, -0.9548207816057637, 0.8057669122907051, -2.471892572754945, -5.734463575255087, -1.356947978264154, 0.8970631924956951, -2.914735774339421, -2.418708890032086, 0.4539450542788954], 'positive_zeros': ['0.8771160115161669', '1.313709980292491', '2.186972436223633', '2.784424767323495', '3.287276052367336', '3.918367710875544', '4.299917814499977', '5.002189037795509', '5.348617370389667', '6.139918067612036', '6.413127352383332', '6.935307287354950', '7.668436180273515', '8.037322682352058', '8.245591651593203', '9.031466631814791', '9.339836397759339', '10.03092850835901', '10.40634576534587', '10.73002777991655', '11.44732713606222', '11.76707524927366', '12.30509332074318', '12.50585607905678', '13.24665317140712', '13.56732963745024', '14.03495802787934', '14.65532155267665', '14.97880186221958', '15.22828155991948', '16.00826435904151', '16.25686477236992', '16.65501330408168', '17.11305593523354', '17.65109808997041', '18.00172928937339', '18.56306567021543', '18.97318165326009', '19.31309874120301', '19.66051387225731'], 'prelabel': '2-229320-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.79169801669481, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2175121014938216555, 'z1': {'__RealLiteral__': 0, 'data': '0.8771160115161669', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.313709980292491', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.186972436223633', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1831.1294191520026, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 229320, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, -14, 0, 0, 0, -1, 0, 4, 0, 0, 0, -12, 0, 10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 12, 0, -6, 0, 0, 0, 14, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 14, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 11], [1, -1, 0], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, -8, 31], [1, -2, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, -10, 53], [1, -4, 59], [1, 14, 61], [1, -4, 67], [1, 12, 71], [1, -10, 73], [1, -8, 79], [1, -12, 83], [1, -14, 89], [1, -2, 97]], 'index': 111, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/229320/bv'], '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': '2-229320-1.1-c1-0-111', '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': '2-229320-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.79169801669481, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2175121014938216555, 'z1': {'__RealLiteral__': 0, 'data': '0.8771160115161669', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2175121014938216555', 'Lhash_array': ['2175121014938216555'], 'label': '2-229320-1.1-c1-0-111', 'type': 'ECQ', 'url': 'EllipticCurve/Q/229320/bv'}