Formats: - HTML - YAML - JSON - 2026-07-20T04:52:09.886857
  • lfunc_lfunctions • Show schema
    {'Lhash': '2501423001207830740114124551199', 'a10': [-3.8832540853410533, 0.0], 'a2': [2.6690790882822886, 0.0], 'a3': [0.0, 0.0], 'a4': [5.123983179505812, 0.0], 'a5': [-1.4549040912235234, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [8.338158176564576, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '2501423001207830740114124551199', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6690790882822886, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.4549040912235234, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.5450959087764766, 0], [11.0, 0]], [[1.0, 0], [-5.883254085341053, 0], [13.0, 0]], [[1.0, 0], [6.7930622677881, 0], [17.0, 0]], [[1.0, 0], [6.247966359011624, 0], [19.0, 0]], [[1.0, 0], [-2.9098081824470468, 0], [23.0, 0]], [[1.0, 0], [-3.8832540853410533, 0], [29.0, 0]], [[1.0, 0], [-2.0, 0], [31.0, 0]], [[1.0, 0], [-5.0, 0], [37.0, 0]], [[1.0, 0], [2.247966359011624, 0], [41.0, 0]], [[1.0, 0], [7.131220444352677, 0], [43.0, 0]], [[1.0, 0], [5.338158176564577, 0], [47.0, 0]], [[1.0, 0], [9.7930622677881, 0], [53.0, 0]], [[1.0, 0], [4.676316353129153, 0], [59.0, 0]], [[1.0, 0], [2.3647122736705706, 0], [61.0, 0]], [[1.0, 0], [-3.3647122736705706, 0], [67.0, 0]], [[1.0, 0], [-1.3647122736705704, 0], [71.0, 0]], [[1.0, 0], [1.8832540853410533, 0], [73.0, 0]], [[1.0, 0], [-3.3647122736705706, 0], [79.0, 0]], [[1.0, 0], [-2.247966359011624, 0], [83.0, 0]], [[1.0, 0], [-0.7930622677881003, 0], [89.0, 0]], [[1.0, 0], [-10.247966359011624, 0], [97.0, 0]], [[1.0, 0], [-9.090191817552952, 0], [101.0, 0]], [[1.0, 0], [-18.01447452969373, 0], [103.0, 0]], [[1.0, 0], [18.22141226190563, 0], [107.0, 0]], [[1.0, 0], [-16.379186803364302, 0], [109.0, 0]], [[1.0, 0], [-7.495932718023248, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-567-1.1-c1-0-17', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/567/2/a/e/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [4.117880930401806, 4.126719976788721, 4.149710085286298, 4.176882849403351, 4.193452634950004, 4.181964372427158, 4.124502726219693, 4.004702845540801, 3.8094867743130765, 3.5305258455859008, 3.165417960225086, 2.71852350677534, 2.2013652804252866, 1.6324850862222675, 1.036667645415353, 0.44348884671307287, -0.11478538969945823, -0.6058395589944703, -1.0002903579535234, -1.2747322109982608, -1.4145108438911274, -1.4158653392397338, -1.2870996408109632, -1.0485150614479617, -0.7309552707214237, -0.3729761701744459, -0.016838807364323718, 0.29628908329203857, 0.5313759300922275, 0.6641600296022412, 0.684694269469594, 0.5991931832376184, 0.4297469090707817, 0.21173097200298358, -0.010931443086165135, -0.19214962869433536, -0.2908668696179735, -0.2780352992814359, -0.14222856526855313, 0.10715619977258105, 0.4398832798912849, 0.808388070436981, 1.1545963323883153, 1.4192485433261177, 1.5523966210781854, 1.523373828496034, 1.3284210844088913, 0.9943397197458688, 0.5770409581813655, 0.15462991793586947, -0.18440443873553625, -0.35636800130375246, -0.2985791445816554, 0.016192663878294537, 0.5699261648386748, 1.2965711508074251, 2.0877121752554184, 2.8067403525116577, 3.310067530369964, 3.4724599506454563, 3.212464504814019, 2.51339602919818, 1.435613249825764, 0.1168754834197646, -1.2406622144407478, -2.3960384912492017, -3.104569756045542, -3.157348576672136, -2.418808015369789, -0.8557616890049013, 1.4477456570649954, 4.293417005768775, 7.390306590654332, 10.39263994935161, 12.948447872683442, 14.751399000000498, 15.587252072978801, 15.366894869823877, 14.13998018496253, 12.086406635655964, 9.486769406688518, 6.676712216389577, 3.9931116834581344, 1.7216067563264676, 0.054791172446668826, -0.9316004534469513, -1.2806167805451987, -1.1344561350253801, -0.6977901762308871, -0.19184235557950863, 0.19129050465826183, 0.3248585776157105, 0.16720578776231687, -0.2383021161238284, -0.7821569700983737, -1.3212936857791597, -1.7173664174471122, -1.8716232834290458, -1.7483017494475854, -1.3813478794506704, -0.8633473460234612, -0.3198853890531727, 0.12390853312291424, 0.3759933960921277, 0.40084355316502474, 0.22764592659748173, -0.0588497080484184, -0.34244795658435834, -0.508261391951065, -0.4753926245538603, -0.22069509866942386, 0.21303948962178101, 0.727083107296677, 1.1927076569999742, 1.4863623154770345, 1.5246034585236827, 1.288967077327137, 0.8333346635005281, 0.27088435707110037, -0.2566820767742963, -0.6197655627292611, -0.7401715303133312, -0.6175143734338145, -0.33398090867084484, -0.0342139676448899, 0.11606433513039921, -0.017349815243760676, -0.48753437599126476, -1.2346199060815308, -2.083082405536227, -2.772556753867999, -3.0177838527182175, -2.5848584542798574, -1.3651501111798372, 0.5730937496564198, 2.9716472349469134, 5.4154929259250055, 7.408923472844734, 8.47996495709311, 8.290152071461456, 6.72351339709685, 3.9318225721192586, 0.3223245380446738, -3.512720196853836, -6.91132528464398, -9.277169772276968, -10.204578848706447, -9.56408479242579, -7.528221963626689, -4.531074254625194, -1.170807900384179, 1.9219278916771156, 4.218737586407985, 5.399893051840996, 5.40831116636567, 4.44028266314848, 2.8779720205322192, 1.1829769292938388, -0.22074304877066844, -1.044768360749539, -1.1914532074550277, -0.7552542090376186, 0.02628470381443887, 0.8550645180044417, 1.463507284975749, 1.6882809337057691, 1.5071250676772252, 1.0308368547178068, 0.45586956917096677, -0.005743876676730758, -0.19652892015311504, -0.062204320296258137, 0.33524856105849443, 0.8426102185845601, 1.2691034430154835, 1.4505796461071998, 1.3032442807345381, 0.8498232768188895, 0.21032137581274069, -0.43884135292464055, -0.9232519249604059, -1.1268187665166651, -1.0272006652699337, -0.698684844910336, -0.2818769386451624, 0.06911337028389158, 0.2434773246790639, 0.21435451423194135, 0.04843937859705273, -0.11976304768885027, -0.14089301303548557, 0.08736085830553779, 0.5718857379222396, 1.2083127806231642, 1.8063839139803353, 2.1510581376655513, 2.0806477956025122, 1.5555006963451559, 0.6915101534274223, -0.2575626732601194, -0.9689102836268993, -1.153077055840171, -0.6591234472869324, 0.4524611440827027, 1.8971427657081599, 3.2252760614870852, 3.9418695672717132, 3.6559857159397886, 2.216245794869464, -0.21074718606379347, -3.148423356692058, -5.910118252073586, -7.76894079708999, -8.153346303493173, -6.813692564719384, -3.910435086743893, 0.005059418659426139, 4.116309186407698, 7.542667454345315, 9.56154765711201, 9.790808780219203, 8.280644716963197, 5.489683981227592, 2.1529241104547148, -0.9201323363967542, -3.059365188289437, -3.8998650473435577, -3.4549890899921594, -2.0801674703038575, -0.3433850150989215, 1.15505363881444, 1.957878388752223, 1.8700306201781678, 0.9900945560754919, -0.34907225087880206, -1.7054994457661845, -2.6752472242414966, -3.0137720887286186, -2.6952597166161683, -1.896201827683054, -0.9151703547585004, -0.06093204392765319, 0.4507270803263503, 0.5570382372450977, 0.34812532360693793, 0.01202667125080015, -0.2506040192281017, -0.3081366692395172, -0.145296458267397, 0.13999795787835392, 0.3865222421144474, 0.44466970366820274, 0.24547933610072645, -0.16436650304305883, -0.6360443019596423, -0.9757754385599504, -1.0233625030043934], 'positive_zeros': ['1.97327481307346946432861525220133', '3.25618973559653280192275619474253', '4.24350905981333780661521834034644', '4.82726169756478738766241634704092', '6.17642581414690064612506196135160', '6.62036596123719874308845812674193', '7.88560486120336934818194137282970', '8.675807900136106353411101632153736', '10.50520979341109717414166055268480', '11.17963093200107522832920889818999'], 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97327481307346946432861525220', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25618973559653280192275619474', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24350905981333780661521834035', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/a/e/1/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-567-1.1-c1-0-17', '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': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97327481307346946432861525220', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2501423001207830740114124551199', 'Lhash_array': ['2501423001207830740114124551199'], 'factors': ['2-567-1.1-c1-0-17'], 'label': '2-567-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/a/e/1/3'}