-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2447464941465988540471926465252', 'a10': [32.08860457304397, 0.0], 'a2': [3.4581286128855617, 0.0], 'a3': [0.0, 0.0], 'a4': [3.9586535032578207, 0.0], 'a5': [9.279181940624332, 0.0], 'a6': [0.0, 0.0], 'a7': [27.22991330895667, 0.0], 'a8': [-13.975495954968958, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.4581286128855617, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-9.279181940624332, 0], [125.0, 0]], [[1.0, 0], [-27.22991330895667, 0], [343.0, 0]], [[1.0, 0], [38.35567406593326, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [85.08436116057332, 0], [4913.0, 0]], [[1.0, 0], [114.35966353905998, 0], [6859.0, 0]], [[1.0, 0], [49.42323155930668, 0], [12167.0, 0]], [[1.0, 0], [-11.564438315378366, 0], [24389.0, 0]], [[1.0, 0], [220.90424219492544, 0], [29791.0, 0]], [[1.0, 0], [24.740598419675514, 0], [50653.0, 0]], [[1.0, 0], [-30.83652624620759, 0], [68921.0, 0]], [[1.0, 0], [409.3460557569788, 0], [79507.0, 0]], [[1.0, 0], [-434.5192793586982, 0], [103823.0, 0]], [[1.0, 0], [716.1359288060239, 0], [148877.0, 0]], [[1.0, 0], [-618.0550435734798, 0], [205379.0, 0]], [[1.0, 0], [-213.0582020717188, 0], [226981.0, 0]], [[1.0, 0], [578.5039496633544, 0], [300763.0, 0]], [[1.0, 0], [-238.26287328965347, 0], [357911.0, 0]], [[1.0, 0], [-748.8373844362865, 0], [389017.0, 0]], [[1.0, 0], [-883.0904472493546, 0], [493039.0, 0]], [[1.0, 0], [-1401.6703917054938, 0], [571787.0, 0]], [[1.0, 0], [1301.0982587198023, 0], [704969.0, 0]], [[1.0, 0], [-258.03035524891646, 0], [912673.0, 0]], [[1.0, 0], [261.46897657528405, 0], [1030301.0, 0]], [[1.0, 0], [1088.2314184349368, 0], [1092727.0, 0]], [[1.0, 0], [-618.4659631882662, 0], [1225043.0, 0]], [[1.0, 0], [-474.86736741395146, 0], [1295029.0, 0]], [[1.0, 0], [-1590.0469234255381, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 184, 'label': '2-39e2-1.1-c3-0-184', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bm/1/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-2.1440596954307402e-58, 0.4378776181411139, 0.8721578146012801, 1.2992654172340223, 1.715670149107867, 2.117910040859851, 2.5026159300013138, 2.8665372945156977, 3.2065695752528423, 3.519783032428757, 3.803453060112135, 4.055091753477497, 4.272480391651181, 4.453702369089958, 4.597175985477036, 4.701686392766651, 4.7664159026124935, 4.79097178191661, 4.775410612073629, 4.720258261529052, 4.62652452376098, 4.495711505297149, 4.329814911742308, 4.131317474113294, 3.903173882381386, 3.648786746526653, 3.371973285331345, 3.0769226464860426, 2.768143984468168, 2.450405660434395, 2.128666175698002, 1.8079977012620922, 1.4935033138436353, 1.1902292869408557, 0.9030740066012164, 0.6366952783881268, 0.39541795747688985, 0.18314396100304875, 0.0032668044393943324, -0.14140716365356992, -0.24872867624333544, -0.31726453966305784, -0.3463437706676251, -0.3360891473046561, -0.28743270199441623, -0.20211400114913458, -0.08266042283101924, 0.06765094440502122, 0.24484971075706188, 0.44434635848220033, 0.6610231479161145, 0.8893402364713362, 1.1234550153145357, 1.357352220161437, 1.5849819663348046, 1.8004025083165132, 1.997924244178116, 2.172251287984682, 2.3186168293465825, 2.432908497421014, 2.5117800529586636, 2.55274594964021, 2.554255634908107, 2.5157448972737253, 2.4376621045955513, 2.321467805419011, 2.169606868996695, 1.9854531016662422, 1.7732270775434384, 1.5378887372491254, 1.2850071150435605, 1.020610326547742, 0.7510196600631246, 0.48267223869281733, 0.22193723369186474, -0.02506901036223029, -0.25266334986894945, -0.4557660662371742, -0.6300554063405284, -0.7721012050123747, -0.8794728358622498, -0.9508173922100362, -0.9859048171547007, -0.9856376614058703, -0.9520242243262024, -0.8881149971392635, -0.7979035423416082, -0.6861941712784276, -0.558439981373627, -0.4205559432394848, -0.27871274366226384, -0.13911795284575476, -0.007791756144094643, 0.10965506054857421, 0.20823298274555055, 0.283767675619408, 0.3330684534721599, 0.3540644600324066, 0.3459026034786084, 0.3090024346862163, 0.24506452283120914, 0.15703043042445888, 0.04899407281924182, -0.0739339893320261, -0.205805992521318, -0.3400550756382976, -0.46974534530080714, -0.5878457419963535, -0.6875183269585278, -0.7624106805786408, -0.8069415136454313, -0.8165683805048074, -0.7880265738470604, -0.7195288860052185, -0.6109169382153466, -0.46375618851986083, -0.28136849651643414, -0.06879819945790117, 0.1672900242442704, 0.41878073712629, 0.6763414289900215, 0.9297144013344736, 1.1680584860854497, 1.3803299819087227, 1.5556902379883155, 1.6839257489745243, 1.7558655229295421, 1.7637799094522864, 1.7017450734257094, 1.5659578968313943, 1.3549872908569704, 1.0699496841378286, 0.7145987781486335, 0.29532246243043087, -0.17895702587116286, -0.6969801370852483, -1.2454410372497644, -1.8093657565487071, -2.372567022135011, -2.918162026865783, -3.429136461009471, -3.888935726495385, -4.2820624768913165, -4.594658575340135, -4.815049307104223, -4.934228264904514, -4.94626275459442, -4.848601823783076, -4.642272041431847, -4.331949864331125, -3.9259036985392113, -3.435803455296721, -2.8764003444295043, -2.265084660266142, -1.6213342023951665, -0.9660705406305031, -0.3209443902387202, 0.29242526700943633, 0.8532311539823256, 1.3422480441581013, 1.7425642744645256, 2.04024584577142, 2.2249062915668065, 2.290158352892219, 2.233927374612233, 2.058611112669828, 1.771076152167023, 1.3824871850851594, 0.9079717593971713, 0.3661295436634146, -0.2215986019837903, -0.8316806514369157, -1.4393363172362919, -2.019442405981225, -2.54746708911791, -3.0003977041714034, -3.3576262166422794, -3.6017574066643494, -3.719307194373061, -3.7012622226845937, -3.5434767572894827, -3.2468889684452096, -2.8175455065264137, -2.2664307117237086, -1.6091045156954893, -0.8651607882556617, -0.05752523781566886, 0.7883813203296641, 1.645582749055277, 2.48655428218102, 3.2842568228934907, 4.013157957011617, 4.650198863620553, 5.175668066726893, 5.573946375010357, 5.834092286065732, 5.950243402923874, 5.9218167793728815, 5.753499280344571, 5.455027678298897, 5.040766944131226, 4.52910365905269, 3.941679305100359, 3.302495041158531, 2.6369251307758232, 1.9706802015343028, 1.3287637911800856, 0.7344660547791434, 0.2084370317117451, -0.23212145338415757, -0.5741112275788169, -0.8090130772792005, -0.9331622584336354, -0.9478132430529927, -0.858991960039834, -0.6771431267073604, -0.41658930176610504, -0.0948266119492965, 0.2683106681577226, 0.6515787051840066, 1.0333037907921174, 1.3923688494768196, 1.7091623143895291, 1.9664467613191685, 2.150108493995557, 2.2497548677122836, 2.259133271560388, 2.176354036620872, 2.00390871272083, 1.7484847319760186, 1.4205870030785361, 1.0339860047375307, 0.6050200388931332, 0.15178607474768574, -0.3067412656115634, -0.7516198118661509, -1.164835118670843, -1.5301379581246635, -1.8337841397435328, -2.0651417654896678, -2.217137728900629, -2.286523345835791, -2.2739480642936516, -2.183839795188345, -2.0241000582503337, -1.8056313645070947, -1.541722594269622, -1.247325153949861, -0.9382580465193364, -0.6303833914693447, -0.3387952005496153, -0.07706328272327025, 0.14342894446087726, 0.31401906796430906, 0.4291459109481927, 0.4865568457820779, 0.4873328992164706], 'positive_zeros': ['1.93070940922155039215162174084087', '2.36505758918027776979352908940581', '3.80327197265172626601806223711322', '4.67504449708069838786499323997677', '5.20053831358247058051117327283062', '5.95666206454033150732789311448070', '6.78613815565366344271421877694310', '7.948006865582326159827767644876816', '8.614002433457741250454395437163583'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93070940922155039215162174084', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36505758918027776979352908941', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80327197265172626601806223711', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 184, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bm/1/14'], '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': '2-39e2-1.1-c3-0-184', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93070940922155039215162174084', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2447464941465988540471926465252', 'Lhash_array': ['2447464941465988540471926465252'], 'label': '2-39e2-1.1-c3-0-184', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bm/1/14'}