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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '1096265838520568882', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '235200.1', 'coefficient_field': '1.1.1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1], [1, -2, 11], [1, -2, 13], [1, -4, 17], [1, 0, 19], [1, -8, 23], [1, 0, 29], [1, -2, 31], [1, -8, 37], [1, 2, 41], [1, -2, 43], [1, -10, 47], [1, 2, 53], [1, -4, 59], [1, -10, 61], [1, 2, 67], [1, -12, 71], [1, 10, 73], [1, 16, 79], [1, 16, 83], [1, -14, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 398, 'label': '2-235200-1.1-c1-0-398', 'leading_term': '5.37906991141', '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/235200/zm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.379069911406002, 4.349782435847388, 1.896557935471029, -0.2720607261356606, -0.5341165823853214, 0.8184201577335422, 1.470068778894862, -0.2162328515890679, -2.735899704163823, -3.082122797577386, -0.9584383971658174, 0.5575331587092656, -0.4415431592264861, -1.678389850666792, -0.4722906306749438, 1.49703982544132, 0.9158800966607026, -0.9523920260227795, 0.1407481760077318, 3.641994993295046, 4.136121927228248, 0.5961330462722958, -1.170151353931496, 1.540682250163414, 3.316693415209961, 0.3333825365716819, -2.591844775514433, -0.9337245313741612, 1.312951013807571, -0.2268110159266343, -1.85553275542996, 0.3325617554382486, 2.362699201622043, 0.5564929517226311, -1.037256702614785, 0.6258407039185218, 1.38700584833895, -0.5434835698710782, -0.3865290869322451, 2.225333994254193, 1.520388427343193, -1.559041413861992, -0.1967672830224036, 3.602550729398205, 2.318143412727117, -1.295446700622051, -0.03744318125584841, 2.092645505641845, -1.342726103160881, -4.757653245081415, -2.237594670184757, 0.1765559612788086, -1.747123244067159, -1.933971927622642, 1.058167762971239, 0.7849832402736732, -1.827725326787799, -0.7930976509161346, 1.138855476618312, 0.02037860527692489, 0.5233236743747302, 3.60871459976783, 2.686650629062988, -0.4410567365004831, 1.375062125631875, 3.590106913784243, -0.03062288669628141, -2.571499561442677, -0.004416516251386273, -0.3721440470847546, -3.554070739190721, -0.4123078072895524, 5.035875490291211, 3.16485486329655, -0.6950081846681782, 0.311719187415398, 0.7503149319239147, -0.7474985835732514, 1.540508613488456, 3.92247723869565, 1.20328520557424, -0.3868411424989309, 1.501619982107796, 0.4044043394201944, -1.494656748954675, 0.8305375867276517, 1.331715043911731, -1.337537647103746, 1.200905273250386, 5.206608033525686, 1.653591615571106, -1.931127577913984, 1.050099501912956, 1.705424255688914, -0.8628745946502823, 1.840228726493201, 4.268214405834143, -0.4325711150050803, -3.114188870090333, -0.2720998098430664, -0.2674514013210072, -1.768006045775943, -0.2629582174174775, -0.6919323355015073, -1.663774946798588, 2.766308537868067, 5.481796814787767, 1.759204571396171, 0.03421578311052686, 0.260554072081192, -2.833189136889749, -2.077807712194968, 3.42664945210847, 2.541027786918638, -1.012993629177922, 1.447783319284155, 0.9129390625072659, -5.210266061440962, -4.413984171673488, 0.8448888025867552, 0.5835806211592446], 'positive_zeros': ['0.7062712995359448', '1.114890885942714', '1.728953277383248', '2.611930172920119', '2.933789617012846', '3.551198476333617', '4.107820978653783', '4.488090999166247', '5.291765990555502', '5.638398343993129', '6.269796886286753', '6.825026403366721', '7.228882145207619', '7.724199385712190', '8.302027047815861', '8.680033051464979', '9.182702340767381', '9.540147150296317', '10.11104389903063', '10.51218959978729', '11.13808807262601', '11.50282340835252', '11.93307222460168', '12.68149613583307', '12.80783673796627', '13.40791969213998', '13.81788741129754', '14.32320225483319', '14.75371244432166', '14.94025626215019', '15.69098834804284', '15.89602672661872', '16.49843497226369', '17.00043706385915', '17.21902831164655', '17.76590058649203', '18.42534919726803', '18.71244434608554', '19.10270822991872', '19.38885265911998'], 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1096265838520568882, 'z1': {'__RealLiteral__': 0, 'data': '0.7062712995359448', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.114890885942714', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.728953277383248', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 8, 0, 2, 0, -2, 0, 2, 0, 0, 0, 10, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 4, 0, 10, 0, 0, 0, 0, 0, -2, 0, 8, 0, 12, 0, -10, 0, 0, 0, 0, 0, -16, 0, 1, 0, -16, 0, 0, 0, 0, 0, 14, 0, 0, 0, 2, 0, 0, 0, -6, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -2, 13], 'euler17': [1, -4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -8, 37], 'euler41': [1, 2, 41], 'euler43': [1, -2, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 2, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 10, 73], 'euler79': [1, 16, 79], 'euler83': [1, 16, 83], 'euler89': [1, -14, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, -2, 11], [1, -2, 13], [1, -4, 17], [1, 0, 19], [1, -8, 23], [1, 0, 29], [1, -2, 31], [1, -8, 37], [1, 2, 41], [1, -2, 43], [1, -10, 47], [1, 2, 53], [1, -4, 59], [1, -10, 61], [1, 2, 67], [1, -12, 71], [1, 10, 73], [1, 16, 79], [1, 16, 83], [1, -14, 89], [1, 6, 97]], 'index': 398, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/235200/zm'], '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': '2-235200-1.1-c1-0-398', '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': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1096265838520568882, 'z1': {'__RealLiteral__': 0, 'data': '0.7062712995359448', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1096265838520568882', 'Lhash_array': ['1096265838520568882'], 'factors': ['2-235200-1.1-c1-0-398'], 'label': '2-235200-1.1-c1-0-398', 'type': 'ECQ', 'url': 'EllipticCurve/Q/235200/zm'}