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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': 1, 'A3': -1, 'A4': -1, 'A5': 2, 'A6': -1, 'A7': -1, 'A8': -3, 'A9': 1, 'Lhash': '1871278667108556579', 'a10': [0.6324555320336759, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [-0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 588.4096274546133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1, 1]], [11, [1]], [29, [1, -1]]], 'bad_primes': [3, 7, 11, 29], 'central_character': '73689.1', 'coefficient_field': '1.1.1.1', 'conductor': 73689, 'conductor_radical': 6699, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 1], [1, -2, 5], [1, 1], [1], [1, 0, 13], [1, -2, 17], [1, -2, 19], [1, -6, 23], [1, -1], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, -2, 43], [1, 4, 47], [1, -6, 53], [1, 10, 59], [1, 6, 61], [1, -8, 67], [1, 6, 71], [1, 10, 73], [1, 14, 79], [1, -4, 83], [1, 4, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-73689-1.1-c1-0-8', 'leading_term': '2.15138703419', '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/73689/w', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.151387034186207, 1.475910285485345, -0.2040648259116538, -1.824262575391888, -2.012215436305105, -0.2650613023709191, 2.121662775423297, 2.813680123153432, 0.7248838333820474, -2.47945487592309, -3.800308363327269, -2.178678812657522, 0.1799880901950374, 0.4303156614274677, -1.347517658157881, -2.349231704999757, -0.9492127544580389, 1.050790772484707, 1.105083492091214, -0.3796249202596549, -0.9172732843687817, 0.07056745009090035, 0.6440365454525827, 0.04992014534183607, 0.1457552451659657, 1.627375650244927, 1.806610815912625, -0.9377136948750759, -3.076913365814135, -0.7553977198139775, 2.848216990869732, 0.8506588826262366, -6.393699225708435, -10.28797054449808, -6.253442220327468, -0.3659737880093911, 0.4712378995286771, -1.410901062282271, -0.4103912465414812, 1.999161209653886, 1.061873017961546, -1.280018155185476, 0.4088020207268613, 4.387565315146818, 4.136321317798393, 0.135015485732971, -0.8238854872653913, 2.296043501139646, 3.559355674260294, 1.163257073918959, -0.3178226168301499, 0.65289011036425, 0.7270516335787918, -0.4122901550734285, 0.1935342544719003, 1.528139034330443, 0.4442920898243175, -1.015918137883049, 0.3903710829659236, 1.372767906174093, -1.59246174107576, -3.685171960841401, -0.3481746753038384, 2.719160108359932, -0.21695841278212, -3.515615320510879, -0.9485768697129139, 2.447480599128643, 1.067404289927283, -0.5798310162978976, 1.322446371505941, 1.855916474611026, -0.9209864394803533, -1.384003416718768, 0.391479848778801, -1.923530759713998, -5.418941060910195, -1.710575895580775, 4.229445498203961, 0.962074843841282, -6.948799508708853, -6.291607846588977, 0.8385079263176839, 2.836216378264194, -0.03997264785500028, -0.366035595638083, 0.9179894620822135, 0.141411511651407, -0.1129068849182372, 1.369355389693592, 1.128183326332978, -0.2518421214343148, 0.2980811813332988, 0.5088733649985246, -1.059874951649894, -0.03827949199693283, 3.120582923920538, 2.137880033787989, -1.003485823748711, 0.2598110611710188, 1.611295145572046, -2.802473583516834, -5.498453870784933, -1.081082527257673, 0.9967826438998755, -3.102896858913896, -2.800254387857767, 3.143430529998803, 3.317847063707235, -1.557976962300409, -1.420338552787352, 0.5709076151627496, -2.606352073924072, -4.136454747332193, 0.9675629699822575, 3.918264647754048, 1.183161932738044, -0.126544329180615, -0.07115086911542391, -2.965210601267396, -3.760231737472318], 'positive_zeros': ['0.4728652801150800', '1.276869405170867', '2.055773425528415', '2.974096867790683', '3.326121355162309', '4.104969243489946', '4.686917039413818', '5.234823367486142', '5.770933054983044', '5.956428415447889', '6.680333644199521', '7.294334850138732', '7.785179719775445', '8.776007572763622', '9.060956410778189', '9.537556787985234', '10.09411928796701', '10.47271779914877', '11.25985177297295', '11.58288394647276', '12.38162262186430', '12.61580945768366', '13.14594464117187', '13.46851344518862', '14.05297833516586', '14.45593117380290', '14.89487229141375', '15.51822264510229', '15.98862309634128', '16.55224666031610', '17.10256641096264', '17.36254532530747', '17.92115699884762', '18.41766560729791', '18.61430330078769', '19.30889623973422', '19.77905294844116'], 'prelabel': '2-73689-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.257156211201124, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1871278667108556579, 'z1': {'__RealLiteral__': 0, 'data': '0.4728652801150800', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.276869405170867', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.055773425528415', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 588.4096274546133, 'bad_primes': [3, 7, 11, 29], 'central_character': '1.1', 'conductor': 73689, 'conductor_radical': 6699, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, -1, 2, -1, -1, -3, 1, 2, 0, 1, 0, -1, -2, -1, 2, 1, 2, -2, 1, 0, 6, 3, -1, 0, -1, 1, 1, -2, -8, 5, 0, 2, -2, -1, -2, 2, 0, -6, 6, 1, 2, 0, 2, 6, -4, 1, 1, -1, -2, 0, 6, -1, 0, 3, -2, 1, -10, 2, -6, -8, -1, 7, 0, 0, 8, -2, -6, -2, -6, -3, -10, -2, 1, -2, 0, 0, -14, -2, 1, 6, 4, -1, 4, 2, -1, 0, -4, 2, 0, -6, 8, -4, 4, -5, 14, 1, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, 0, 13], 'euler17': [1, -2, 17], 'euler19': [1, -2, 19], 'euler2': [1, -1, 2], 'euler23': [1, -6, 23], 'euler29': [1, -1, 0], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 4, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 10, 59], 'euler61': [1, 6, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 6, 71], 'euler73': [1, 10, 73], 'euler79': [1, 14, 79], 'euler83': [1, -4, 83], 'euler89': [1, 4, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, -1, 2], [1, 1, 0], [1, -2, 5], [1, 1, 0], [1, 0, 0], [1, 0, 13], [1, -2, 17], [1, -2, 19], [1, -6, 23], [1, -1, 0], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, -2, 43], [1, 4, 47], [1, -6, 53], [1, 10, 59], [1, 6, 61], [1, -8, 67], [1, 6, 71], [1, 10, 73], [1, 14, 79], [1, -4, 83], [1, 4, 89], [1, -14, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/73689/w'], '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': '2-73689-1.1-c1-0-8', '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': '2-73689-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.257156211201124, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1871278667108556579, 'z1': {'__RealLiteral__': 0, 'data': '0.4728652801150800', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1871278667108556579', 'Lhash_array': ['1871278667108556579'], 'label': '2-73689-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/73689/w'}