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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '128219831641354774', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 747.3997629191848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '93600.1', 'coefficient_field': '1.1.1.1', 'conductor': 93600, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -2, 7], [1, -2, 11], [1, -1], [1, 4, 17], [1, -1, 19], [1, -6, 23], [1, -9, 29], [1, 4, 31], [1, -3, 37], [1, -7, 41], [1, 4, 43], [1, 9, 47], [1, 1, 53], [1, -6, 59], [1, 6, 61], [1, -13, 67], [1, -11, 71], [1, -8, 73], [1, -1, 79], [1, 0, 83], [1, 6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 48, 'label': '2-93600-1.1-c1-0-48', 'leading_term': '3.33280296724', '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/93600/ds', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.332802967237162, 2.650860868023843, 0.9496468966238657, -0.7365403669875543, -1.151620505832915, 0.02383864175358489, 1.487183047837239, 1.397459004635, -0.4540018817515877, -1.985517846490636, -1.107525980460151, 1.418234375923048, 2.485834075335569, 0.5742083785517859, -1.925697631642592, -1.681050768652795, 0.9458747715392762, 2.340117888448207, 0.9436202149359945, -0.461745369486161, 0.6519134489696669, 2.149802995675585, 0.5075443560032759, -3.035508559187628, -3.803370539669593, -1.041841187297479, 0.8078704013897212, -0.4726409291177012, -1.206041071482041, 1.480310772378015, 4.125998116810421, 2.697794148012703, -0.2765064262044864, -0.1673512122200705, 1.565993341946039, 0.5237788448723606, -1.989779912465875, -1.408560035553513, 0.8565878059201546, -0.5206862734703223, -4.406794282360579, -4.415120217735764, -0.3528000475578949, 1.492080364180458, -0.2275305009502209, -0.6769076633966805, 0.6050623338412229, -0.8788098961427159, -4.111354107509583, -3.319459934036256, 0.409332114365853, 0.5239938390070684, -2.239342561291765, -1.398202051101723, 2.108081973152385, 1.843428148311419, -1.101989747793669, -0.8406933420946393, 1.006684710811947, -0.4753290561630107, -2.281240972098696, 0.00808749504514963, 1.975351956862188, -0.5385481983760987, -2.002261318896621, 1.387348753982736, 3.250457584868958, 0.1658468021664635, -1.328477374428244, 1.280504014837758, 1.843498390112706, -0.4949479330277396, -0.2597189198369066, 0.9047545511519933, -2.11265123361534, -4.817583718713101, -1.467506175187263, 2.186071965612841, 0.5321413482868992, -0.8396789156022109, 1.349053987225199, 0.9003450601188567, -2.784433875073666, -2.499483240346795, 0.729430239640607, 0.2512390498734921, -1.188356969904659, 1.027114472854496, 1.454604541803316, -2.733214495125416, -3.834557087745326, -0.2405119631094842, 0.2562455949271284, -1.595135265491004, 1.078148263419948, 4.341824061340436, 1.921756300588248, -0.7596080277423278, 0.4320216625458787, -0.232202647848725, -2.889504138210612, -1.368466942941848, 0.6238442001300758, -2.743139587738894, -4.50498226367502, 0.2184260800280374, 2.810223444565122, -0.002136748606256708, -0.6170362601268652, 0.8400889353639196, -0.8697695924247018, -1.290404576059985, 2.329230585350189, 2.225087242259751, -1.90663170112838, -1.431772109564286, 1.289784293355741, -0.3712582067393301, -0.5323919674987662, 4.380302694734134, 5.382419884082745], 'positive_zeros': ['0.6278294571943276', '1.246383015908560', '1.947603643833811', '2.613141202704541', '3.299441236911225', '3.915449766949720', '4.624659974849718', '4.910740611472727', '5.536724045100780', '6.342193015847842', '6.687891532722252', '7.142472359461486', '7.966798698957404', '8.272921216716673', '8.797759112495490', '9.386179312816773', '9.711037261926236', '10.52312627230445', '10.97091834667033', '11.36952301484874', '11.67252162912634', '12.46625317674230', '12.79915711825385', '13.34494271619564', '13.89613575530880', '14.34181316899577', '14.70625567824114', '15.24941109809404', '15.71099450540848', '16.16746643025177', '16.76157302923977', '17.14303595483222', '17.69047006861239', '18.03430917666829', '18.36675568865793', '19.07245940059198', '19.54704289392063', '19.86467297865606'], 'prelabel': '2-93600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.338613039420725, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 128219831641354774, 'z1': {'__RealLiteral__': 0, 'data': '0.6278294571943276', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.246383015908560', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.947603643833811', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 747.3997629191848, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 93600, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, -4, 0, 1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 9, 0, -4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 7, 0, -4, 0, 0, 0, -9, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 0, 0, 13, 0, 0, 0, 11, 0, 8, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 0], 'euler17': [1, 4, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -3, 37], 'euler41': [1, -7, 41], 'euler43': [1, 4, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, -6, 59], 'euler61': [1, 6, 61], 'euler67': [1, -13, 67], 'euler7': [1, -2, 7], 'euler71': [1, -11, 71], 'euler73': [1, -8, 73], 'euler79': [1, -1, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -2, 7], [1, -2, 11], [1, -1, 0], [1, 4, 17], [1, -1, 19], [1, -6, 23], [1, -9, 29], [1, 4, 31], [1, -3, 37], [1, -7, 41], [1, 4, 43], [1, 9, 47], [1, 1, 53], [1, -6, 59], [1, 6, 61], [1, -13, 67], [1, -11, 71], [1, -8, 73], [1, -1, 79], [1, 0, 83], [1, 6, 89], [1, -10, 97]], 'index': 48, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/93600/ds'], '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': '2-93600-1.1-c1-0-48', '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': '2-93600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.338613039420725, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 128219831641354774, 'z1': {'__RealLiteral__': 0, 'data': '0.6278294571943276', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '128219831641354774', 'Lhash_array': ['128219831641354774'], 'label': '2-93600-1.1-c1-0-48', 'type': 'ECQ', 'url': 'EllipticCurve/Q/93600/ds'}