-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '977725486010698287154045692193', 'a10': [0, 0], 'a2': [-2.8284271247461903, 2.8284271247461903], 'a3': [0, 0], 'a4': [0, -16.0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-117.17031385648728, -117.17031385648728], 'a8': [45.254833995939045, 45.254833995939045], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.1727189158413, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.8284271247461903, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.107', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '452600619396038356578271939788', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.8284271247461903, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [117.17031385648728, 117.17031385648728], [0, 16807.0]], [[1.0, 0], [0, -28.277077393178555], [-161051.0, 0]], [[1.0, 0], [283.2373451427327, -283.2373451427327], [0, -371293.0]], [[1.0, 0], [-137.84240419714612, 137.84240419714612], [0, -1419857.0]], [[1.0, 0], [0, -2809.9889864330494], [-2476099.0, 0]], [[1.0, 0], [-902.8090086217316, -902.8090086217316], [0, 6436343.0]], [[1.0, 0], [827.5732707789247, 0], [20511149.0, 0]], [[1.0, 0], [-2049.644812568686, 0], [28629151.0, 0]], [[1.0, 0], [-1320.8316215348436, -1320.8316215348436], [0, 69343957.0]], [[1.0, 0], [0, -10791.579361594035], [-115856201.0, 0]], [[1.0, 0], [-7831.778909860296, 7831.778909860296], [0, -147008443.0]], [[1.0, 0], [-11749.396868760105, 11749.396868760105], [0, -229345007.0]], [[1.0, 0], [22576.276747912154, 22576.276747912154], [0, 418195493.0]], [[1.0, 0], [33192.39188924058, 0], [714924299.0, 0]], [[1.0, 0], [-32011.68725924491, 0], [844596301.0, 0]], [[1.0, 0], [27419.270955367072, 27419.270955367072], [0, 1350125107.0]], [[1.0, 0], [0, 54641.45021589574], [-1804229351.0, 0]], [[1.0, 0], [14250.400849288893, -14250.400849288893], [0, -2073071593.0]], [[1.0, 0], [0, -79274.88632870167], [-3077056399.0, 0]], [[1.0, 0], [36508.781507912085, 36508.781507912085], [0, 3939040643.0]], [[1.0, 0], [-69924.73185460627, 0], [5584059449.0, 0]], [[1.0, 0], [69381.8375318627, 69381.8375318627], [0, 8587340257.0]], [[1.0, 0], [0, 163404.11879327774], [-10510100501.0, 0]], [[1.0, 0], [-78791.90054335007, 78791.90054335007], [0, -11592740743.0]], [[1.0, 0], [59824.6376024745, -59824.6376024745], [0, -14025517307.0]], [[1.0, 0], [0, -3640.346939331997], [-15386239549.0, 0]], [[1.0, 0], [141328.32837175028, 141328.32837175028], [0, 18424351793.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-450-15.2-c5-0-15', 'leading_term': '0.898486711146294089857363846579009712938802381568737857', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/450/6/f/g/107/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8984867111462941, 0.9820033966339684, 1.037645929755237, 1.064222201601279, 1.0610893547482223, 1.0281629478790988, 0.9659183684642054, 0.8753843225648128, 0.7581282536840809, 0.6162335784894198, 0.45226867961388567, 0.26924766735071193, 0.07058301476437646, -0.1399697145595797, -0.3583746904226543, -0.5803856789801013, -0.8016222574124718, -1.017651504069828, -1.2240740897160942, -1.4166134939958734, -1.5912068731769424, -1.7440959181221802, -1.8719158733740953, -1.9717807475379003, -2.041362640185398, -2.078963049354737, -2.083574013885946, -2.0549269928978524, -1.993527496041081, -1.9006736565802016, -1.7784571868658783, -1.629745472271747, -1.4581439428108018, -1.2679383065782142, -1.0640167285135318, -0.8517725818000933, -0.6369889751058058, -0.4257068520846057, -0.22407905331955974, -0.03821330672816699, 0.12599234932619585, 0.2630177257351268, 0.3678878388393325, 0.4363347731230764, 0.46494917327472407, 0.451316434077707, 0.3941327482122208, 0.2932964192913917, 0.1499702555895394, -0.03338857072815763, -0.25303408857197734, -0.5039745359490629, -0.7800538303726631, -1.07407141523438, -1.377939211705573, -1.6828731764715381, -1.9796157283675608, -2.2586841023859305, -2.5106385603218007, -2.7263633770949327, -2.897352673403166, -3.0159925194145214, -3.0758303273166017, -3.071822413737105, -3.000550770163619, -2.860400545729287, -2.6516905274291047, -2.3767499924888402, -2.0399366892526647, -1.6475923478933168, -1.2079339902428503, -0.7308813479451817, -0.22782284898765143, 0.2886751747220503, 0.8052092471441636, 1.3079206177143532, 1.7829075306276059, 2.2166556029488524, 2.5964727854279275, 2.9109145554599065, 3.150184632226321, 3.3064966498233925, 3.3743828987370508, 3.3509374544224184, 3.2359827390952245, 3.0321507735899593, 2.7448730141399214, 2.3822756583574027, 1.9549805517809513, 1.4758152220281127, 0.9594389908311005, 0.4218954361918509, -0.11989543442521008, -0.6486892135764772, -1.1474950003844777, -1.6001592152765525, -1.991934399019618, -2.3100118748612037, -2.5439977557932543, -2.686313195443612, -2.7325019915095385, -2.6814316025344853, -2.5353772470725855, -2.2999829028999956, -1.9840975692989682, -1.599489930895506, -1.1604493831989193, -0.6832860536765445, -0.18574678109844028, 0.3136321911600486, 0.7962119722580768, 1.2439511837523363, 1.6400922548237797, 1.9698064461638278, 2.2207711821861724, 2.3836553824019595, 2.4524916694457195, 2.4249184956087695, 2.302280227770974, 2.0895788762873777, 1.7952772250880584, 1.4309593691600613, 1.010860825598987, 0.5512861833843787, 0.06993742873872105, -0.41481962058924615, -0.8847201352233789, -1.322363777001911, -1.711943773493157, -2.0399093733401594, -2.2955318742406816, -2.4713481950417826, -2.563461008356975, -2.571680565551224, -2.4995002808684283, -2.353905598283512, -2.145023311436517, -1.885625991999178, -1.590513149456176, -1.275796852999923, -0.9581244814263721, -0.6538747630577215, -0.37836511893183683, -0.1451083957392326, 0.0348446808751251, 0.153444550791561, 0.20603579662678287, 0.19158316297697664, 0.11271757016762128, -0.024402268381705377, -0.2104079526021211, -0.4332055224971041, -0.6786033543171385, -0.9310539524080951, -1.1744734719024053, -1.3930982009537405, -1.5723345873170114, -1.6995588993146795, -1.7648243481057164, -1.761437437350646, -1.6863713044087019, -1.5404916201354257, -1.3285798670985451, -1.05914907749136, -0.744057875176132, -0.3979393825145399, -0.03747165910945235, 0.31947471160258534, 0.6547689843522553, 0.9509844637256943, 1.1923436968420027, 1.3655936486054998, 1.460762451812245, 1.4717545728766763, 1.3967489332461458, 1.2383743316743137, 1.003647954378834, 0.7036752668466634, 0.3531225055413578, -0.03051435974912194, -0.42780863797827245, -0.8184242974631616, -1.1822062879652795, -1.5002812783447943, -1.7561082662595884, -1.936419780302284, -2.031998966306578, -2.0382455723765185, -1.9554943863929772, -1.7890625337034376, -1.5490165656179633, -1.249665702450297, -0.908803104991022, -0.5467317719919571, -0.18512475198034434, 0.15421996600509305, 0.4506619268900981, 0.6859661053406598, 0.8454442258820527, 0.9189215129008405, 0.9014688297430973, 0.7938517403249287, 0.6026626758892161, 0.34011937741500337, 0.02353121919958972, -0.3255460996458741, -0.6824287384722176, -1.020640410201054, -1.3133962761640554, -1.5351553059599696, -1.6631551666860704, -1.6788422015794047, -1.5691124711193052, -1.327288106085341, -0.953766028150641, -0.4562928264407544, 0.15016060718299148, 0.8439292316787809, 1.5975706542299817, 2.379128165244178, 3.1536790591628936, 3.885089680161004, 4.5378850432875595, 5.079132194709212, 5.48023331044781, 5.7185272090388075, 5.778606457551235, 5.653271231981454, 5.344059875214798, 4.861318706190652, 4.223798854248909, 3.4577943237784603, 2.5958616340923544, 1.6751857086061213, 0.7356777585340237, -0.18209256881689379, -1.0390175777402408, -1.799506657186395, -2.4333605003763434, -2.9173576033543, -3.236461404836962, -3.3845771362812846, -3.364812569002351, -3.189224966298031, -2.878066060455066, -2.4585660532259226, -1.9633247498453836, -1.428401341202045, -0.8912126019139268, -0.38836121565655735, 0.046479223045522954, 0.3844986285228182, 0.6033904271647692, 0.6886002677652108, 0.6341094754971689, 0.4427068274185517, 0.12573277357649706], 'positive_zeros': ['0.77128941195205316534657454850465', '2.45126095477426295105983209980551', '3.05202215415637436044275561789136', '4.52767444987573213071152726126897', '5.73610955911808004170164908864912', '6.77314919800301221701219766590151', '7.75898824338598750471449775613644', '8.986139824560553415941494326596000', '9.302942338229337174104133009242901', '10.38147805276089491487567695643188'], 'prelabel': '2-450-15.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.495452837597375, 'root_angle': 0.2376579764160328, 'root_number': '0.7339855318679454573528462757454493330118999662995461048 + 0.679165104380760439742321268069008844683323964243860971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1188289882080164', 'prec': 60}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77128941195205316534657454850', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45126095477426295105983209981', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05202215415637436044275561789', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 72.1727189158413, 'bad_primes': [2, 3, 5], 'central_character': '15.2', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/6/f/g/107/1'], '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': '2-450-15.2-c5-0-15', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-450-15.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.495452837597375, 'root_angle': 0.1188289882080164, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77128941195205316534657454850', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '977725486010698287154045692193', 'Lhash_array': ['977725486010698287154045692193'], 'label': '2-450-15.2-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/6/f/g/107/1'}