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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '255534141481960153', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1623.1989722885885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '203280.1', 'coefficient_field': '1.1.1.1', 'conductor': 203280, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 1], [1], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 4, 23], [1, -8, 29], [1, -2, 31], [1, 8, 37], [1, -10, 41], [1, 0, 43], [1, -8, 47], [1, -2, 53], [1, -6, 59], [1, -6, 61], [1, -4, 67], [1, -8, 71], [1, 4, 73], [1, -12, 79], [1, -8, 83], [1, 0, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 31, 'label': '2-203280-1.1-c1-0-31', 'leading_term': '1.16269972283', '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/203280/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.162699722832503, 0.624521520798722, -0.4360531302079343, -0.641783898460503, 1.034066576430104, 3.729113012861144, 4.905822175134925, 3.095965647253314, 0.1896253844645227, -0.4271277816553766, 1.583386740721491, 2.553480447096605, -0.2005427446762141, -4.073680490310857, -4.485331891585571, -1.559828566524362, 0.1811579348009718, -1.007949022945974, -1.723118285857748, 0.07901990684050536, 1.101541378159247, -1.248509602920739, -3.488718417478453, -1.761050603767734, 1.225454433657159, 1.036795950022391, -0.5839811798403235, 0.2328825531427598, 1.427290266032369, -0.659711741496179, -2.794227642744348, -0.2239999995138399, 3.429794814386305, 2.19423077554381, -0.7872365120884376, 0.6155107258662599, 3.145070816146667, 0.6196682621877562, -3.195572483747206, -1.605136373037126, 1.955986511180379, 1.230594314388433, -0.7131164569656655, 0.713205736526857, 1.715343777482232, -0.6848665274579177, -1.51054403811048, 1.158015680636278, 1.896066162822007, 0.09667344634197451, 0.717709629203977, 1.934318462380155, -0.8106465955010208, -2.64485273931653, 1.254901883950509, 3.87820352849935, 0.6811411897788945, 0.06219751047659062, 5.347634296716733, 6.813217977371168, 1.843262151988717, -0.4442401419617544, 1.226638427255922, 0.3424627966859463, -1.229336627313806, 0.5196514130912969, 0.4789849545274882, -3.245386107305727, -3.557555475000057, -0.3715201436625521, -0.3130020037358019, -1.045450472854412, 1.370820240939082, 0.7706519366256439, -4.339335320103975, -4.775430735632518, -0.4297951742173953, 0.1240310283972342, -0.9936338095653905, 1.048493341307236, 0.1538829688139949, -4.39302210802099, -2.872543513916824, 2.262849506962563, 0.3667751501018392, -3.55558177888439, -0.8066170576439244, 1.93250828969082, -0.09127891325952218, -0.2029013065398162, 1.295797117574504, -0.680228200279512, -1.409367021250081, 1.365779396844863, 1.042986806069763, -0.7305309015005184, 1.456646445539937, 1.887664983659489, -1.367879107676891, -0.4226614585622452, 1.241107289261309, -4.028934331187711, -6.843291487263012, -1.013604696793478, 1.52612303320897, -1.820860618647648, -0.8876585305741661, 1.401682423844845, -1.050259981097497, -1.084238714957958, 2.234652362424228, 1.007599230064953, -0.904122485061364, 1.291934293550179, 0.868628264623682, -1.655523576452421, 0.1269208857938026, 0.9533131194033972, -1.625797493423249, -0.273325037086445, 1.31931680937734], 'positive_zeros': ['0.3938279199318298', '0.8809178176888120', '2.022681455801407', '2.322868232456752', '2.987837716198353', '3.922839736074170', '4.085940798353985', '4.741159961946694', '5.149285189052248', '5.879629400008956', '6.386648375206712', '6.717838140949434', '7.197469632143311', '7.762590319292948', '8.407758772644666', '8.700742537519449', '9.282802207054930', '9.845987881061258', '10.37058228082550', '10.67166729451896', '11.19005204682018', '11.65213146348382', '12.27435469096082', '12.38157438683269', '12.94683737835952', '13.43845129902961', '14.05134138280543', '14.24510357770512', '15.11681719746135', '15.33072265284991', '15.78539810379893', '16.19288264414109', '16.53962194432208', '17.30113008107061', '17.44373786296331', '17.87622231807808', '18.29365627358271', '19.03601368827935', '19.26765945582024', '19.64168464204005'], 'prelabel': '2-203280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.288943548926525, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 255534141481960153, 'z1': {'__RealLiteral__': 0, 'data': '0.3938279199318298', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8809178176888120', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '2.022681455801407', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1623.1989722885885, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 203280, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, -2, 0, 1, 0, -6, 0, -4, 0, 1, 0, -4, 0, 1, 0, -1, 0, 8, 0, 2, 0, 0, 0, 1, 0, -8, 0, 2, 0, 10, 0, 0, 0, -1, 0, 8, 0, 1, 0, 6, 0, 2, 0, 0, 0, 4, 0, 6, 0, 6, 0, -1, 0, 2, 0, 4, 0, 4, 0, 8, 0, -4, 0, -1, 0, 0, 0, 12, 0, 1, 0, 8, 0, 6, 0, -8, 0, 0, 0, 2, 0, -2, 0, 4, 0, -14, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 8, 37], 'euler41': [1, -10, 41], 'euler43': [1, 0, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -6, 59], 'euler61': [1, -6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 4, 73], 'euler79': [1, -12, 79], 'euler83': [1, -8, 83], 'euler89': [1, 0, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 4, 23], [1, -8, 29], [1, -2, 31], [1, 8, 37], [1, -10, 41], [1, 0, 43], [1, -8, 47], [1, -2, 53], [1, -6, 59], [1, -6, 61], [1, -4, 67], [1, -8, 71], [1, 4, 73], [1, -12, 79], [1, -8, 83], [1, 0, 89], [1, 14, 97]], 'index': 31, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/203280/h'], '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': '2-203280-1.1-c1-0-31', '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': '2-203280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.288943548926525, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 255534141481960153, 'z1': {'__RealLiteral__': 0, 'data': '0.3938279199318298', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '255534141481960153', 'Lhash_array': ['255534141481960153'], 'label': '2-203280-1.1-c1-0-31', 'type': 'ECQ', 'url': 'EllipticCurve/Q/203280/h'}