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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': 1, 'A8': 0, 'A9': 1, 'Lhash': '2229293180082647048', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, '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, 8, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, 6, 41], [1, 12, 43], [1, 0, 47], [1, -2, 53], [1, -4, 59], [1, -2, 61], [1, -8, 67], [1, -8, 71], [1, 2, 73], [1, 12, 79], [1, -8, 83], [1, -18, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 133, 'label': '2-369600-1.1-c1-0-133', 'leading_term': '3.25331411232', '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/369600/tc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.253314112319503, 2.095167289896976, -0.5119151903051219, -2.380092472918802, -1.736476976582975, 0.6230561796555483, 1.860188119470334, 0.7029971988387793, -0.5965459834116226, 0.4530544253038218, 2.420043779617117, 1.873821915235334, -0.9074743200495503, -2.026479925839735, -0.5129598815314934, -0.0529526893282546, -2.060801600005258, -2.487440712993887, 0.7027718561628012, 2.823032961922138, 0.6358549478109804, -1.102983148739945, 1.769563264376411, 4.517470445134786, 2.254018768533637, -0.4098328325204592, 1.714647107238129, 3.912666436663996, 0.8055029881329762, 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-1.994330164992365, 0.1703428991773682, -1.628486001319095, -1.607956975530494, 0.8574831153798979, -0.9308547570849389, -2.654273716831145, -0.3621307644204141, -0.3847543382846931, 0.4576613259350741, 8.01788185412803, 10.36376427619339, 2.143911709928312, -1.903330141996489, 0.5576794898426157, -0.6374864750610298, -1.483490919570742, 1.12493457654959, -1.063101991666824, -3.950915150767103, 0.3640620135728079, 3.158239053805205, 0.5447019970708197, 0.2923389128370488, 0.2686205293044326, -1.751799495074034, 0.6752158728341451, 3.00867115671435, -0.4812825597373745, -0.6760803411126648, 2.779387413941775, 0.9204346489119901, -0.5898781415833217, 1.267938026910827, -1.976850105810348, -4.217008601556042, 0.8955705703341472, 0.3459088047871283, -5.798831699414096, -3.288711476079408, 1.705412087445667, 0.3454787145211938], 'positive_zeros': ['0.4527356348880673', '1.185314864905352', '1.850895255815996', '2.191512062056003', '2.919737249079896', '3.595287061255275', '3.736945135768605', '4.453842681225111', '5.051582791893604', '5.385404484087363', '6.169878333720094', '6.360724213657699', '7.041775301081632', '7.599808848632676', '8.090569254714627', '8.285157500875865', '8.726896663222409', '9.303390387093813', '9.959087420704282', '10.23696094358825', '10.44316445355699', '11.20287252105763', '11.72310158117119', '11.97848839402374', '12.52478261927379', '13.01472120910868', '13.36260155817297', '13.92715256964429', '14.26744943623616', '14.59231887835357', '15.06938769305065', '15.48635849256632', '16.05162213100192', '16.26932113508696', '16.80392812730066', '17.23510740012527', '17.71635119803588', '18.29005409381074', '18.49410650529320', '18.82185338147305', '19.37353314427038', '19.94191210664103'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2229293180082647048, 'z1': {'__RealLiteral__': 0, 'data': '0.4527356348880673', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.185314864905352', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.850895255815996', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 2, 0, 0, 0, 6, 0, -4, 0, 1, 0, -8, 0, 0, 0, 1, 0, 6, 0, -4, 0, -1, 0, 0, 0, 2, 0, 2, 0, -6, 0, -12, 0, 0, 0, 0, 0, 1, 0, 6, 0, 2, 0, 0, 0, -4, 0, 4, 0, 2, 0, 1, 0, 0, 0, 8, 0, -8, 0, 8, 0, -2, 0, 0, 0, -1, 0, -12, 0, 1, 0, 8, 0, 0, 0, 6, 0, 18, 0, 2, 0, -4, 0, 0, 0, 10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 12, 79], 'euler83': [1, -8, 83], 'euler89': [1, -18, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, 8, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, 6, 41], [1, 12, 43], [1, 0, 47], [1, -2, 53], [1, -4, 59], [1, -2, 61], [1, -8, 67], [1, -8, 71], [1, 2, 73], [1, 12, 79], [1, -8, 83], [1, -18, 89], [1, -10, 97]], 'index': 133, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/tc'], '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': '2-369600-1.1-c1-0-133', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2229293180082647048, 'z1': {'__RealLiteral__': 0, 'data': '0.4527356348880673', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2229293180082647048', 'Lhash_array': ['2229293180082647048'], 'label': '2-369600-1.1-c1-0-133', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/tc'}