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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': '1573910592780179146', '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': 975.7639276598446, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1, 1]], [11, [1, -1]], [23, [1]]], 'bad_primes': [3, 7, 11, 23], 'central_character': '122199.1', 'coefficient_field': '1.1.1.1', 'conductor': 122199, 'conductor_radical': 5313, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 1], [1, -2, 5], [1, 1], [1, -1], [1, -6, 13], [1, 2, 17], [1, 4, 19], [1], [1, 2, 29], [1, -8, 31], [1, 6, 37], [1, -10, 41], [1, -4, 43], [1, 8, 47], [1, 6, 53], [1, -4, 59], [1, -10, 61], [1, -12, 67], [1, 0, 71], [1, -2, 73], [1, 16, 79], [1, 4, 83], [1, 18, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-122199-1.1-c1-0-6', 'leading_term': '4.22239072086', '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/122199/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9207905683467839, 1.121515766833188, 0.3865147559838684, -0.5795172563811452, -0.6050394700319363, 0.5172557099626777, 1.248083717723046, -0.1544018946874927, -2.925471597834274, -3.628708058407213, -0.01091761961731036, 5.345629424262645, 7.124264886450288, 3.695893707872559, -0.509695700300172, -0.7686205337887373, 1.543278248489919, 1.353139836692638, -2.145355560347245, -4.170116687982907, -1.95324945545726, 0.8724922970496536, 0.3291951831573445, -1.5858509453475, -1.075281515319799, 0.3615107358575259, -1.043163302451007, -3.432697680642002, -1.606235111985917, 3.511017992708342, 5.351658202221524, 2.26355311707332, -0.2572425502773297, 0.6548609819055222, 1.340393647766025, -0.2916285228994684, -1.066749987775468, 0.3021969829810356, 0.5825123892477293, -0.8557910969153323, -0.6824744449775818, 0.7973885554235063, -0.1596649048832485, -2.202991253741743, -1.040953198175184, 0.3166573971224741, -4.166079854602485, -10.32635066652891, -8.963008459956994, -2.190902741190808, 0.5475508538552875, -0.6417291675360676, 0.7108244729031074, 2.800415831701007, 0.8450090527783518, -0.6505592848200281, 2.306557580137076, 1.799098682776999, -6.928511405418852, -12.70919680256414, -7.049089078306648, 0.5713094346911317, 0.695908887113475, -0.9065300804840749, 1.629030817098427, 3.14828594700071, 0.6865015897203591, -0.6962458909522946, 0.2964999386888173, 0.1234093323376035, -0.3682673175739772, 0.6040253953999858, 0.2322637908844025, -1.463367013354138, -0.5678616924731393, 0.9075491505599276, -0.6392433915738374, -0.2933525130421167, 4.308469302071998, 3.962838711191657, -3.759505856211106, -6.679074783103553, -1.306936710839682, 1.32035002501995, -0.5150393362574927, 1.621757088084783, 4.988246165711851, 2.201277941356382, -1.24276837881325, 0.148534017015257, 0.3536064046351955, -1.75213137732889, -0.08207145115908641, 1.114466638210724, -3.997176648299391, -5.966713033831652, 1.0561092724952, 4.864066452016685, 0.2036679443446413, -1.554660633932148, 1.988421388446547, 1.953128168896127, -0.469858093016711, 0.1529948106194957, -0.02439519233792556, -1.856454058143597, 0.4016678651411275, 3.636532140388557, 1.587184162583436, -0.9303181168039665, 0.2796711447461348, 0.6405843441122457, -0.1264701401135998, 0.9220596033359284, 0.2593276517538125, -2.14651622471506, -0.6915812903751168, 1.103457925675629, -1.167584761055733, 0.2160227966897792], 'positive_zeros': ['0.8405053847280338', '1.400809249393244', '1.984271032672823', '2.750511490649688', '3.707407460293909', '4.086552548687128', '4.610335249182316', '5.397411396710102', '5.788784041130661', '6.403786281617044', '6.636924482058393', '7.331763703031171', '8.191414551603139', '8.393675128950850', '8.962429789466412', '9.450592278925831', '9.856806123772935', '10.35286424236161', '10.73250753352786', '11.36025295527716', '11.54483926151592', '12.62450928616991', '12.87092658806111', '13.18203879958063', '13.82219625728816', '14.08146723282110', '14.56838445302435', '15.46946335226345', '15.81703726725498', '16.12560610035205', '16.81647505873455', '17.17799168163777', '17.53298956863545', '17.86458208527233', '18.28277541303232', '18.81473613533743', '19.17336915851351', '19.52103223942333'], 'prelabel': '2-122199-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.23722022939693, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1573910592780179146, 'z1': {'__RealLiteral__': 0, 'data': '0.8405053847280338', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.400809249393244', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.984271032672823', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 975.7639276598446, 'bad_primes': [3, 7, 11, 23], 'central_character': '1.1', 'conductor': 122199, 'conductor_radical': 5313, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, -1, 2, 1, -1, 3, 1, -2, 1, 1, 6, 1, -2, -1, -2, -1, -4, -2, 1, -1, 0, -3, -1, -6, -1, 1, -2, 2, 8, -5, -1, 2, -2, -1, -6, 4, -6, 6, 10, -1, 4, -1, 2, 0, -8, 1, 1, 1, 2, -6, -6, 1, 2, -3, 4, 2, 4, 2, 10, -8, -1, 7, 12, 1, 12, 2, 0, 2, 0, 3, 2, 6, 1, 4, -1, 6, -16, -2, 1, -10, -4, -1, -4, -4, 2, 3, -18, -2, -6, 0, -8, 8, -8, 5, -2, -1, 1, 1], 'euler11': [1, -1, 0], 'euler13': [1, -6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 0], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, 16, 79], 'euler83': [1, 4, 83], 'euler89': [1, 18, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 2], [1, 1, 0], [1, -2, 5], [1, 1, 0], [1, -1, 0], [1, -6, 13], [1, 2, 17], [1, 4, 19], [1, 0, 0], [1, 2, 29], [1, -8, 31], [1, 6, 37], [1, -10, 41], [1, -4, 43], [1, 8, 47], [1, 6, 53], [1, -4, 59], [1, -10, 61], [1, -12, 67], [1, 0, 71], [1, -2, 73], [1, 16, 79], [1, 4, 83], [1, 18, 89], [1, 2, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/122199/f'], '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': '2-122199-1.1-c1-0-6', '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': '2-122199-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.23722022939693, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1573910592780179146, 'z1': {'__RealLiteral__': 0, 'data': '0.8405053847280338', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1573910592780179146', 'Lhash_array': ['1573910592780179146'], 'label': '2-122199-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/122199/f'}