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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': 1, 'A8': 0, 'A9': 0, 'Lhash': '476876130002302830', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1770.7625152239148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '221760.1', 'coefficient_field': '1.1.1.1', 'conductor': 221760, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -1], [1, 1], [1, -6, 13], [1, -2, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, -8, 47], [1, -6, 53], [1, 0, 59], [1, 2, 61], [1, -12, 67], [1, 0, 71], [1, 6, 73], [1, 0, 79], [1, 12, 83], [1, 14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 123, 'label': '2-221760-1.1-c1-0-123', 'leading_term': '3.80328902139', '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/221760/ml', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.803289021389139, 2.880445826875734, 0.7109964760076646, -1.107827494105589, -1.087350864476589, 0.4585804267012548, 1.360345878348632, 0.160989857448511, -1.621176858168672, -1.20078394751354, 1.352249692254247, 2.633394137096497, 0.7442325086162942, -1.434598767811592, -0.3339317810604224, 2.52361751833917, 2.67875984031309, 0.1064661117687308, -0.5069498690949951, 2.244812463294135, 3.822068009568591, 1.581116793254024, -0.5692021269342386, 0.6406346634173199, 1.941503052257498, 0.1664689907222093, -1.29582764306807, 0.6554871457438264, 1.78586951034396, -1.770437619440554, -5.134979122170274, -2.877460681247769, 1.077826767075481, 1.095098453900366, -0.1383675785375455, 1.060224261580379, 0.810854378850499, -3.481796234802072, -5.720104491917331, -2.312353620955315, 0.5338722993360667, -0.8669285443035443, -1.298627193578489, 0.8974085697236127, 0.313881254014103, -2.440847943791222, -1.091888223259623, 2.057518836319521, 0.2140111051584726, -2.927619012762563, -0.5900885135918964, 2.563443364077208, 0.584772241250833, -1.42268950841712, 0.4719139626996406, 0.9420712349197803, -0.883466949830161, 0.6120099189734619, 2.793467243561847, -0.5078849947123485, -4.034165338209155, -1.639763003711278, 0.5884234577648371, -1.06747782365644, 0.1891168678313766, 4.274119593459533, 3.107157076458844, -0.7348362304048577, 0.1739048686739669, 1.381629024049658, -1.674815741764072, -2.457182996398176, 0.5515308590243228, 0.3625680357689003, -1.400393838860387, 0.1397915212634789, -0.6071557508772689, -5.266789674519347, -4.386876889416862, 1.063288365137434, 0.348054998444431, -3.463718975639585, -1.634099544514079, 1.003209192415509, -0.02264847664856728, 0.6402916129458419, 1.919122946862458, -0.3468041012558618, 0.532443667637317, 6.315554402942727, 6.209170734024419, 0.5036355301864066, -0.4248121189811499, 0.6586741365909013, -1.81847839116991, -1.84654837927095, 0.0948609179246088, -3.672724715190021, -7.03288220026056, -2.727396612093768, 0.6323844021567386, -0.8927218378237687, -0.3417799480798113, -0.01862735164233646, -3.435945763345817, -3.103928193979295, 0.04757092441078815, -2.479151716869971, -4.28458801419731, 0.9438834085141464, 3.145831653296696, -0.0703133983270457, 0.05453294331701749, 0.3486293643780245, -3.068322165478457, -2.449613859158416, 0.4515575252084923, -2.040577035383161, -2.756225494868523, 2.08888307725552, 2.574427711861072], 'positive_zeros': ['0.5800805835855275', '1.182652348435572', '1.770027602596563', '2.376442597392812', '3.066238167418289', '3.529499403889615', '4.261390404890970', '4.564974550917287', '5.391760718440237', '5.672297139902972', '6.266288106138322', '6.689521806048266', '7.154673696021863', '7.913011163865394', '8.427486968429852', '8.572737363146673', '9.062287458373291', '9.905832606804448', '10.14546358452636', '10.64701586220440', '11.02750292152201', '11.57150077440784', '12.01303455077273', '12.53358007760310', '13.04340132120657', '13.45098502263925', '13.86759984694476', '14.19996416177672', '14.72521963941412', '15.37054175746740', '15.61448982052122', '15.98774516033577', '16.68158205505930', '16.98339548853821', '17.38410005678278', '17.94882455327165', '18.28817785782197', '18.73179381761498', '18.95358087190229', '19.68953254689470'], 'prelabel': '2-221760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.080429123571385, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 476876130002302830, 'z1': {'__RealLiteral__': 0, 'data': '0.5800805835855275', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.182652348435572', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.770027602596563', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1770.7625152239148, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 221760, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 6, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 1, 0, -2, 0, 0, 0, -6, 0, -4, 0, 0, 0, 8, 0, 1, 0, 0, 0, 6, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, -6, 0, 0, 0, -1, 0, 0, 0, 0, 0, -12, 0, 2, 0, 0, 0, -14, 0, 6, 0, 0, 0, -4, 0, 2, 0, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 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, -1, 0], [1, 1, 0], [1, -6, 13], [1, -2, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, -8, 47], [1, -6, 53], [1, 0, 59], [1, 2, 61], [1, -12, 67], [1, 0, 71], [1, 6, 73], [1, 0, 79], [1, 12, 83], [1, 14, 89], [1, -2, 97]], 'index': 123, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/221760/ml'], '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': '2-221760-1.1-c1-0-123', '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': '2-221760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.080429123571385, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 476876130002302830, 'z1': {'__RealLiteral__': 0, 'data': '0.5800805835855275', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '476876130002302830', 'Lhash_array': ['476876130002302830'], 'factors': ['2-221760-1.1-c1-0-123'], 'label': '2-221760-1.1-c1-0-123', 'type': 'ECQ', 'url': 'EllipticCurve/Q/221760/ml'}