-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1778232825228092791992492772005', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [2, 5], 'central_character': '3200.191', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '1374069447637450289387648688661', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-1.118033988749895, -1.5388417685876268], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.5, 1.5388417685876268], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [1.118033988749895, -0.36327126400268045], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.6909830056250525, -0.9510565162951535], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.5, -0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.8090169943749475, -0.5877852522924731], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.118033988749895, 1.5388417685876268], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.5, -0.36327126400268045], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.3090169943749475, 0.9510565162951535], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.5, -1.5388417685876268], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 1.1755705045849463], [-1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.118033988749895, 1.5388417685876268], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-1.3090169943749475, 0.9510565162951535], [0.30901699437494745, -0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3200-200.91-c0-0-1', 'leading_term': '1.49403074608991340365830708774', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3200/1/bd/a/191/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4940307460899134, 1.528298193585452, 1.5717475101006515, 1.6237954434324762, 1.6830831469105811, 1.7476231131490152, 1.8149735339670618, 1.8824069166405994, 1.9470539407474952, 2.006017153857139, 2.056457821195657, 2.095662836983306, 2.1210987630937717, 2.1304585908626024, 2.1217049319339454, 2.093111628990086, 2.043304435955074, 1.9713004547063997, 1.8765453671349375, 1.7589470940418797, 1.618904285213438, 1.4573279544594309, 1.275654590265346, 1.0758491780759354, 0.8603967516540697, 0.6322813395509223, 0.3949514810979209, 0.15227184723363246, -0.09153909309188127, -0.3319849795077383, -0.5643801932394645, -0.7839498927743761, -0.9859396529914485, -1.165732450097495, -1.318970309199258, -1.4416775552850043, -1.5303822982237003, -1.5822325539063737, -1.5951032713778035, -1.567690512352843, -1.4995891249498785, -1.3913504747217729, -1.2445171463409477, -1.0616320076582566, -0.8462196288523498, -0.6027387628391413, -0.33650540405796325, -0.05358683156223561, 0.23933201497897424, 0.5351075090888177, 0.8263183802195817, 1.1054646194116775, 1.365179189927132, 1.5984467410165324, 1.798822920876032, 1.9606474558359268, 2.079243934392802, 2.1510992292367077, 2.174015723970518, 2.1472299923726688, 2.071492307090741, 1.9491023228721682, 1.7838974688140963, 1.581191967273941, 1.3476659376416233, 1.0912056964491936, 0.8206980793833711, 0.5457833280015749, 0.2765727426706604, 0.02333883986027377, -0.20381289679807527, -0.395280476754279, -0.542299074507304, -0.6372604572821312, -0.6740066413824987, -0.6480865895687222, -0.5569655225831925, -0.4001775957769927, -0.17941426621373396, 0.1014573901784382, 0.43644991062431876, 0.8175852452865752, 1.23509750409882, 1.6777043233356026, 2.1329398499026953, 2.587539801936699, 3.0278667640437016, 3.4403619144870614, 3.812007852020643, 4.1307861719344405, 4.386112998321989, 4.569235857212532, 4.673576095306904, 4.695002509413667, 4.632023924395501, 4.4858910886586765, 4.260601366994828, 3.9628031987748518, 3.6016010327809393, 3.1882653098620404, 2.735855891379522, 2.258770969748809, 1.7722367925548521, 1.2917563360963926, 0.8325372437995561, 0.4089207856632468, 0.0338342083739588, -0.28171142578169595, -0.5290569927757449, -0.7022458089988622, -0.7982729533075448, -0.8172211487698656, -0.7622752387875303, -0.6396120564577064, -0.458167535812775, -0.22928804559779908, 0.03372207445915608, 0.31614014609836527, 0.6024312376560991, 0.8768966550699048, 1.1243383872309536, 1.3307117109999937, 1.4837379738286331, 1.5734505872954379, 1.5926494786939414, 1.5372426026880777, 1.4064575008840783, 1.2029111540190602, 0.9325322947863648, 0.604336697428635, 0.23006246381843268, -0.17632130098217558, -0.5992130776419694, -1.0220601880368476, -1.4280938274370176, -1.8010858755471864, -2.126093741939791, -2.3901592373909755, -2.582928738323757, -2.697164715150777, -2.729122944031113, -2.6787752630369095, -2.549864350612354, -2.3497844220458886, -2.089289637788822, -1.7820400424147458, -1.4440026341873122, -1.092732331671657, -0.7465638019577486, -0.42375002590622063, -0.1415868314498151, 0.08443577602273408, 0.2414149418418956, 0.3197106108770215, 0.3134812358098887, 0.22105108810978352, 0.04508801742154045, -0.20742100291985768, -0.525399899823503, -0.8941127530305738, -1.2957763056722904, -1.710330664643825, -2.1163350108364587, -2.491948431090659, -2.8159510402490806, -3.068757667608162, -3.2333757294178405, -3.2962605849841933, -3.2480256532255356, -3.0839707097637334, -2.804399841709736, -2.4147101568234843, -1.925243087681876, -1.3509014947698779, -0.7105472063172609, -0.026204571344475104, 0.677894509261565, 1.3763802865489432, 2.0438795083114085, 2.6561603782098513, 3.191232790476676, 3.630349930014392, 3.958861480082734, 4.16687540013808, 4.249694234224083, 4.208002771988873, 4.047796091455579, 3.7800499660007834, 3.4201486669371413, 2.987097667969137, 2.5025600043054137, 1.9897644529949632, 1.472340760468582, 0.973141438729956, 0.5131109098077392, 0.11026087944682596, -0.22119419017389322, -0.4714955532050003, -0.6357570929049702, -0.7141176453322542, -0.7116195800376338, -0.6378190430389198, -0.5061477447332015, -0.33305979404371633, -0.13700909354766402, 0.0626874565142649, 0.24703881026951155, 0.3985549312125166, 0.502342402867562, 0.54705814573289, 0.5256658555068038, 0.4359498912346921, 0.2807541092743316, 0.06792790898799311, -0.19002224498807316, -0.4765611881336918, -0.7720028251999969, -1.0545923779188813, -1.3017359758062987, -1.49131119298384, -1.6029863897606553, -1.6194748762042046, -1.5276521523746667, -1.3194707493347355, -0.9926172240699705, -0.550869162615404, -0.004125939164291739, 0.6318953734612922, 1.3362890977837378, 2.0838869723938322, 2.846436027853203, 3.5939684665063143, 4.296291998254403, 4.924521182561191, 5.452566731538798, 5.858500717933389, 6.125721229331787, 6.243849979747505, 6.209310243661818, 6.025549498122523, 5.702890435397158, 5.2580144871726295, 4.713102539646443, 4.0946769520797455, 3.432206197628166, 2.7565474110630928, 2.0983120085630067, 1.4862447157685887, 0.9457064379256772, 0.4973463525698142, 0.1560386190361403, -0.069855313288625, -0.17885588397749114, -0.17634390287678678, -0.0741483747463452, 0.11023383764376715, 0.3547426357020183], 'positive_zeros': ['1.40277835620315055846123417586549', '2.39610336335909866678926571751878', '3.50883291287921455210972839355624', '3.99453261065759528227823222209071', '5.38780688575099184344013321588801', '5.88437563566749590847872123990275', '6.63068023174151641243753011139617', '7.64727478356739997118431796567540', '7.932121859423991181769263572763335', '8.888623130732186552172015450641204'], 'prelabel': '2-3200-200.91-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.24000000000000002, 'root_number': '0.72896862742141152314673031905556 + 0.68454710592868867373228335762154*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40277835620315055846123417587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39610336335909866678926571752', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50883291287921455210972839356', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '200.91', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/bd/a/191/1'], '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': '2-3200-200.91-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-200.91-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.12000000000000001, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40277835620315055846123417587', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1778232825228092791992492772005', 'Lhash_array': ['1778232825228092791992492772005'], 'label': '2-3200-200.91-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/bd/a/191/1'}