-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1998163771631438108428456449383', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.549044428938494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [19, [1, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '6080.1', 'coefficient_field': '1.1.1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 1], [1, 0, 7], [1, -4, 11], [1, 4, 13], [1, 2, 17], [1, 1], [1, 4, 23], [1, -6, 29], [1, 8, 31], [1, -4, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, 0, 53], [1, -8, 59], [1, 2, 61], [1, -14, 67], [1, 8, 71], [1, -6, 73], [1, 4, 79], [1, 16, 83], [1, 18, 89], [1, 4, 97], [1, 10, 101], [1, -6, 103], [1, 6, 107], [1, -2, 109], [1, -12, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 4, 13], 1]], [[[1, 2, 17], 1]], [[[1, 1], 1]], [[[1, 4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 8, 31], 1]], [[[1, -4, 37], 1]], [[[1, 2, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, 0, 53], 1]], [[[1, -8, 59], 1]], [[[1, 2, 61], 1]], [[[1, -14, 67], 1]], [[[1, 8, 71], 1]], [[[1, -6, 73], 1]], [[[1, 4, 79], 1]], [[[1, 16, 83], 1]], [[[1, 18, 89], 1]], [[[1, 4, 97], 1]], [[[1, 10, 101], 1]], [[[1, -6, 103], 1]], [[[1, 6, 107], 1]], [[[1, -2, 109], 1]], [[[1, -12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 129, 'label': '2-6080-1.1-c1-0-129', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/6080/2/a/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.4986284839067945e-60, 0.24503813418295708, 0.4891723319504737, 0.7314516982364502, 0.9708345470830646, 1.2061505978410918, 1.4360716823566535, 1.6590928831425615, 1.8735253808177883, 2.07750163181184, 2.268992877623145, 2.445838441436071, 2.6057858153312443, 2.746540184757534, 2.8658217684407763, 2.961429157714499, 3.0313067043023367, 3.0736139167257823, 3.0867947733391854, 3.069644839347557, 3.021374084786537, 2.941663342114811, 2.830712419510065, 2.689278003747715, 2.51869964913443, 2.3209123599017345, 2.098444534736973, 1.8544003537619183, 1.5924260480285506, 1.316659894854013, 1.031666222011292, 0.7423541705490402, 0.45388244831300395, 0.1715517907018275, -0.09931268306721838, -0.35348658681915035, -0.5859758281029224, -0.7921472470737654, -0.9678567091441538, -1.1095708603001773, -1.214478692222448, -1.2805891177982203, -1.3068109334988216, -1.293011847088158, -1.240053676890685, -1.149801377731793, -1.0251042095165497, -0.8697481235352772, -0.6883792808527478, -0.4863995142941452, -0.2698354746590708, -0.045184133916071595, 0.18076177793847711, 0.4011039824157822, 0.6090393386496173, 0.7980652115671748, 0.9621832576859727, 1.0960950752746161, 1.1953830795648557, 1.256670096463529, 1.277751529147015, 1.2576945429061481, 1.1968995284453674, 1.0971201279081249, 0.9614393181181142, 0.7942004106107322, 0.6008933090936316, 0.3879979164472814, 0.1627881542379753, -0.06689840696750086, -0.292918865490692, -0.507103520756289, -0.7015457981261627, -0.8688939129245983, -1.0026340893113763, -1.0973549558092963, -1.1489829084342595, -1.1549787784819714, -1.1144870658506851, -1.028430287026314, -0.8995426118296266, -0.7323388828248125, -0.5330172705646111, -0.30929614912567027, -0.0701882019509298, 0.17428279770448962, 0.4134147350037868, 0.6361994555131616, 0.831722732723899, 0.9895784499048, 1.1002824088884902, 1.1556705331357877, 1.1492661266797277, 1.0766013146312041, 0.9354788346928541, 0.7261619605233642, 0.45148248217692916, 0.1168592891691192, -0.269776880351552, -0.6981536429452218, -1.1559197404941302, -1.628994429720841, -2.101994054806521, -2.5587230937916448, -2.9827140460068367, -3.3577980829434786, -3.6686865340959374, -3.901542119343164, -4.0445184441692055, -4.088246690018706, -4.026249675581172, -3.8552655196817294, -3.5754659534797897, -3.1905578270155113, -2.7077604203208385, -2.137655662487218, -1.4939131206253544, -0.7928964648705006, -0.053162855416833917, 0.7051288600072939, 1.4608812928864163, 2.192769863325869, 2.879976729542385, 3.502920135632082, 4.043951510676605, 4.487993234076126, 4.823091660534584, 5.0408627379975455, 5.136811272423275, 5.110509470445103, 4.965625660899732, 4.709799860820204, 4.35436888588176, 3.9139497662873355, 3.4058960651232173, 2.84964705786143, 2.2659943824254616, 1.676294496128873, 1.101657899439858, 0.5621474698996547, 0.07601830527122798, -0.34096982924771657, -0.6761389934454687, -0.9203539363096228, -1.0683377615601042, -1.1188287372213124, -1.0745711829007334, -0.9421403634169672, -0.7316084182608809, -0.4560652531622889, -0.13101470470291626, 0.22632813081946387, 0.5978080000724387, 0.9651353977174787, 1.3106918750606067, 1.6182991447089008, 1.8739177618107927, 2.066244112047563, 2.1871788395202074, 2.2321455268980746, 2.200245155887438, 2.094239335443772, 1.9203631547482134, 1.6879764383368498, 1.4090697826984633, 1.0976486753502008, 0.7690249017819085, 0.4390490369493286, 0.12332085678095514, -0.16358417882835155, -0.40883471816134515, -0.6019742499116265, -0.7354314976154157, -0.8048848273121033, -0.8094619734768768, -0.7517643511966318, -0.6377138224775553, -0.476228610655153, -0.2787436786071082, -0.05859887431660305, 0.16967490606025087, 0.39113574664295914, 0.591237308404945, 0.7566204707372925, 0.8758486605065046, 0.9400477746329642, 0.9434158916763953, 0.8835741080585346, 0.7617375530438876, 0.5826945753149008, 0.3545918249266159, 0.08853299960900149, -0.20199112128457902, -0.5018145756803267, -0.7949152967384315, -1.0653002587806093, -1.2979112029244808, -1.4795033277595375, -1.5994496169498589, -1.6504262177162285, -1.6289393994755774, -1.5356619044315956, -1.3755556291376378, -1.157768122672073, -0.89530184413919, -0.6044669212196646, -0.3041396921009938, -0.014859993284204896, 0.24219059721980582, 0.4462800509760282, 0.5782322749084079, 0.6214919079189419, 0.5630914676022122, 0.3944683154771081, 0.11208523360224658, -0.282182733000852, -0.7809215108838241, -1.3713250247835806, -2.035616092026411, -2.751727289536952, -3.4942143094888816, -4.235361823623358, -4.946431143539997, -5.598990589302832, -6.1662639470772005, -6.624430056983013, -6.953807615445779, -7.139863720741537, -7.173992378131402, -7.054019781511059, -6.784406212482209, -6.376129219083539, -5.8462486221996715, -5.217170044460715, -4.515639231081101, -3.7715136149451345, -3.016369606777779, -2.2820133013920376, -1.5989681543096974, -0.995015337272881, -0.49386075272726, -0.11399710418628818, 0.13217978677633418, 0.2389536282737777, 0.20753747685545423, 0.045975770868508285, -0.23129855819613301, -0.6042311565081155, -1.0481997706706652, -1.5353012980078824, -2.0358068691166795, -2.519710219279869, -2.9582892110134402, -3.3255991614475673, -3.599819717054471, -3.764384286404186, -3.808832144417845], 'positive_zeros': ['1.57627328166900737534293331639677', '2.39997476846146324193645404637681', '3.22071942562529138236974484894691', '3.95097490604572529266494142424772', '4.56167028297120356741738344518121', '5.53455893855568254608021175525729', '6.57045410636979315315418809555957', '7.04880601046469492217157591640679', '7.894449068725322050081731416646124'], 'prelabel': '2-6080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 569514082648624189, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57627328166900737534293331640', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39997476846146324193645404638', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22071942562529138236974484895', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.549044428938494, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -1, 0, 0, 0, 1, 0, 4, 0, -4, 0, -2, 0, -2, 0, -1, 0, 0, 0, -4, 0, 1, 0, -4, 0, 6, 0, -8, 0, 8, 0, 0, 0, 4, 0, -8, 0, -2, 0, -4, 0, -1, 0, -8, 0, -7, 0, -4, 0, 0, 0, -4, 0, -2, 0, 8, 0, -2, 0, 0, 0, 4, 0, 14, 0, -8, 0, -8, 0, 6, 0, 2, 0, 0, 0, -4, 0, -11, 0, -16, 0, 2, 0, 12, 0, -18, 0, 0, 0, -16, 0, 1, 0, -4, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -2, 3], 'euler31': [1, 8, 31], 'euler37': [1, -4, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 0, 53], 'euler59': [1, -8, 59], 'euler61': [1, 2, 61], 'euler67': [1, -14, 67], 'euler7': [1, 0, 7], 'euler71': [1, 8, 71], 'euler73': [1, -6, 73], 'euler79': [1, 4, 79], 'euler83': [1, 16, 83], 'euler89': [1, 18, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 1, 0], [1, 0, 7], [1, -4, 11], [1, 4, 13], [1, 2, 17], [1, 1, 0], [1, 4, 23], [1, -6, 29], [1, 8, 31], [1, -4, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, 0, 53], [1, -8, 59], [1, 2, 61], [1, -14, 67], [1, 8, 71], [1, -6, 73], [1, 4, 79], [1, 16, 83], [1, 18, 89], [1, 4, 97]], 'index': 129, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6080/t', 'ModularForm/GL2/Q/holomorphic/6080/2/a/t/1/1', 'ModularForm/GL2/Q/holomorphic/6080/2/a/t'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-6080-1.1-c1-0-129', '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': '2-6080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 569514082648624189, 'z1': {'__RealLiteral__': 0, 'data': '1.57627328166900737534293331640', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21669833
{'Lhash': '1998163771631438108428456449383', 'Lhash_array': ['1998163771631438108428456449383'], 'label': '2-6080-1.1-c1-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/t'}
-
id: 24573385
{'Lhash': '1998163771631438108428456449383', 'Lhash_array': ['1998163771631438108428456449383'], 'label': '2-6080-1.1-c1-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/t/1/1'}
-
id: 29494
{'Lhash': '569514082648624189', 'Lhash_array': ['569514082648624189'], 'label': '2-6080-1.1-c1-0-129', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6080/t'}