-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_153.70', 'a10': [-0.7071067811865476, -0.7071067811865476], 'a2': [0.8660254037844386, -0.5], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.25881904510252074, -0.9659258262890683], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.25881904510252074, 0.9659258262890683], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '153.70', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 153, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_153.94', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 0, 'a^20', 'a^17', 0, 'a^7', 'a^18', 0, 'a^15', 'a^19', 0, 'a^20', 'a^5', 0, 'a^16', 0, 0, 'a^6', 'a^13', 0, 'a^17', 'a^11', 0, 'a^10', 'a^18', 0, 'a^3', 'a^1', 0, 'a^5', 'a^14', 0, 0, 'a^0', 0, 'a^21', 'a^4', 0, 'a^11', 'a^23', 0, 'a^10', 'a^15', 0, 'a^9', 'a^4', 0, 'a^14', 'a^8', 0, 'a^16', 'a^6', 0, 'a^12', 'a^1', 0, 'a^23', 'a^2', 0, 'a^7', 'a^3', 0, 'a^12', 'a^13', 0, 'a^8', 0, 0, 'a^22', 'a^21', 0, 'a^9', 'a^19', 0, 'a^2', 'a^2', 0, 'a^19', 'a^9', 0, 'a^21', 'a^22', 0, 0, 'a^8', 0, 'a^13', 'a^12', 0, 'a^3', 'a^7', 0, 'a^2', 'a^23', 0, 'a^1', 'a^12', 0, 'a^6'], 'euler_factors': [[1, 'a^22'], [0], [1, 'a^17'], [1, 'a^7'], [1, 'a^19'], [1, 'a^20'], [0], [1, 'a^6'], [1, 'a^11'], [1, 'a^1'], [1, 'a^5'], [1, 'a^21'], [1, 'a^23'], [1, 'a^10'], [1, 'a^4'], [1, 'a^6'], [1, 'a^2'], [1, 'a^7'], [1, 'a^8'], [1, 'a^21'], [1, 'a^9'], [1, 'a^19'], [1, 'a^22'], [1, 'a^12'], [1, 'a^1'], [1, 'a^16']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-153-153.70-r0-0-0', 'leading_term': '1.20636743584803609080293303189-1.15819907896994669816442577585*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/153/70', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6723478994519643, 1.5462705244067663, 1.3872232773195439, 0.8629098017122582, 0.004668916142921703, -0.9289325192127329, -1.5926423556317482, -1.7086648445314851, -1.208191582654226, -0.29640820724037514, 0.6099771807605168, 1.0674352053154164, 0.835356743935807, 0.0284830341012184, -0.911979205933015, -1.4450665111262477, -1.2525667477822942, -0.47442921619049466, 0.30755673455400434, 0.37417047831790806, -0.6808081589649903, -2.617688871651514, -4.571337740896196, -5.473091408172781, -4.669551095229368, -2.3736421249305555, 0.36120624527962875, 2.185107006644612, 2.2243461542447416, 0.6138816540416857, -1.5655893838103998, -2.939175618656448, -2.68270191229717, -1.0166137369265549, 0.9815170585826383, 2.1222461699925645, 1.8956480668511944, 0.7578135012331118, -0.28170603522548593, -0.4556396751041316, 0.18674819733186895, 0.8689718762811119, 0.7714868697118742, -0.2350193036628765, -1.4150423022722343, -1.7314917500790397, -0.7217253776760438, 1.0346455817107838, 2.2949839341590206, 2.1432621683537176, 0.8135118049653665, -0.36951326186922334, 0.017674623787792727, 2.296623907959882, 5.247345446335404, 6.86577018224008, 5.817012998810529, 2.4842552978582937, -1.2313436608531438, -3.251266031041082, -2.7860704387224775, -0.7975354983786673, 0.8777735860951748, 1.004871738011314, -0.17764745444414828, -1.3594288794036806, -1.4167961357347558, -0.3995218199928205, 0.6048915019796709, 0.5593947256864804, -0.5100499201872359, -1.5273245375977518, -1.399930504010078, -0.10317455823196847, 1.232430634932709, 1.3610593414775076, 0.13466009953363967, -1.2917100750146298, -1.543743046322486, -0.44455972009269906, 0.6045239190086394, -0.22383398753895792, -3.4261099367217316, -7.403781674149269, -9.513338795766895, -8.152373328861142, -4.112213480043403, 0.008587978768340452, 1.8624813736210992, 1.1203678464571654, -0.5455534791763541, -1.1521213120974125, -0.177907009852306, 1.171105429359077, 1.332425797100652, -0.005574359199592041, -1.6161449256189746, -1.9853805954562744, -0.8097305341029267, 0.7587764133548606, 1.3301456997971266, 0.681361251966491, -0.10880536361203899, 0.06807350968146778, 1.0230305811506701, 1.3511554392908836, -0.05505801988230401, -2.593613732968427, -4.213973077842935, -3.295293573308402, -0.37084523617002746, 2.0982122579106703, 1.8773252114379193, -0.9195299983917741, -3.805541594250058, -4.121279975265258, -1.4392831104477644, 2.087737053846548, 3.7455137550940827, 2.6957687918632662, 0.5311138965221565, -0.4682097821512292, 0.4438410973500566, 1.9626571044938026, 2.2895114988711005, 1.0295845339816976, -0.5378899466146578, -0.9814752483016665, -0.29255300234817083, 0.21212880141974944, -0.49540499766450274, -1.8727675747305401, -2.352795155959023, -1.1673786912551016, 0.5996298405414041, 1.031228164968763, -0.5050296859030304, -2.453004099343975, -2.534575891738052, -0.20197348194210707, 2.5273944943593025, 2.9210617809886723, 0.32748463191783456, -2.9530057066753397, -3.7482974082302762, -1.0646600261574268, 2.927237027118676, 4.956498532521374, 3.6863020322776037, 0.7214617622158033, -1.2540236425354019, -1.1247823998992372, -0.05464088357287525, 0.23694679702354096, -0.47663621369390063, -0.8426025928662148, 0.24565896390156577, 2.1361951522799845, 3.026122684198689, 2.0031730350469874, 0.13790404807791343, -0.691554832213192, 0.07327253745772079, 1.0742017805616282, 0.7347375787408817, -0.6863694117027691, -1.1848649972712946, 0.6329328692850837, 3.52040397611759, 4.38347970972316, 1.3801498479481156, -3.8781541296195763, -7.52156590035064, -6.993036385326676, -3.395963028188593, -0.22945207051374253, 0.11245766914395389, -1.5747015876928647, -2.646028903573561, -1.6712026798046447, 0.1821799328532191, 0.7767736468820665, -0.42965280862645194, -1.855977390181266, -1.7771630624594927, -0.366150345165783, 0.6099451054255605, -0.008829821690449095, -1.3786376108474945, -1.747429747645112, -0.6792641245356195, 0.3654133251265612, -0.11277947868644335, -1.6038374919729002, -1.9940770827351677, -0.1858444994654228, 2.136951538602165, 1.958990024135113, -1.7027731788847693, -6.2679578347425196, -7.865535238985043, -5.185292530408935, -0.7863581253096864, 1.5860081605382876, 0.7788348870167198, -0.9449006498008846, -0.7545589843362425, 1.5498120944247877, 3.518253665924964, 3.0020826418834132, 0.5537648431025812, -1.3886182494945027, -1.346263776196251, -0.23982105122674913, 0.11121159738049582, -0.6382490879956243, -1.1039836334313065, -0.24230325991481516, 1.02186739372924, 0.8193312726917014, -1.1865389974662022, -3.062830194040246, -2.7716672669127824, -0.7275488056984704, 0.49494292119382755, -0.7871477610748525, -3.1334253955263827, -3.4425274994652106, -0.6607376363225499, 2.58396059795375, 2.5790098508234807, -1.3657449710565723, -5.929993357824651, -7.124957202172483, -4.303514004372867, -0.47717707931106085, 1.172575881424632, 0.4870860499050721, -0.21949345870592615, 0.6386065824798288, 2.093607306917562, 2.185478953068112, 0.6541189418333045, -0.7242341633161896, -0.4801282394049178, 0.6467504353276894, 0.7394159820065818, -0.6760909389996196, -1.875517611303884, -1.1292094884793475, 0.9387836306715596, 1.9708006109232865, 0.85799840848318, -0.7128984941385987, -0.3540862369152017, 1.6957739268823733, 2.2926011632470464, -1.0503966762895693, -6.7822473571608235, -10.320160981214473, -8.665817645852448, -3.5327273168931677, 0.5430360340688424, 0.9223026930934553, -0.8952437610075834, -1.719543015166816, -0.5371812778686638, 0.7910581778484381, 0.40831333674554804, -1.0170865678467087, -1.2804154130328702, 0.3490616121296381, 2.09816706500032, 1.9439626156769914, 0.16570847841745856, -1.112433267005628, -0.7043962756213744, 0.25565173638984595, 0.14980543798489307, -0.6151598291543033, 0.00610871599634725, 2.683092529949363, 5.082764211091171, 4.215904035488837, 0.23248983471678034, -3.1427280202198986, -2.546133283937266, 1.151789312768349, 3.7266428451260896, 2.3727733310359103, -1.1932958644888907, -2.905863469113148, -1.1089053432967289, 1.766847683915933, 2.3791094364895335, 0.41309547350643455, -1.4391506410079558, -1.0624819362106592, 0.6254433474387339, 1.246613425486539, 0.18515428649613544, -0.8186219117420431, -0.26234568140629827, 1.0190996989069834, 1.1035379163028958, -0.22072274953717771, -1.063042592399045, -0.10435250883073124, 1.3215020870526184, 0.8068764462830389, -1.7518631714413058, -3.561331646549804, -2.313314788145548, 0.6065019235954816, 1.4353711307462407, -1.3740465349065327, -4.939792882912455, -5.1286160364600955, -1.4760678787841472, 2.139555869760628, 1.969821614327923, -1.3546767531242445, -3.821661560909693, -2.836322180496798, 0.08776099035751317, 1.6972668152044403, 1.023288960154407, -0.004460970141579446, 0.3719608473742387, 1.4177035420046806, 1.3385165875656346, 0.16773185476895588, -0.10018650537329044, 1.62443731252748, 3.7011720747307515, 3.6826477684475973, 1.5124551179767804, -0.3812772548969439, -0.3348489197982996, 0.3805862675352687, -0.41016941442198984, -2.2034020481791936, -1.801025955466969, 2.5367464668405058, 7.98513984322679, 9.556978633820515, 5.6398540168853195, 0.021184546178024063, -2.232533565267124, -0.20573118080875213, 2.494755413372487, 2.4784915809374564, 0.35134986441216454, -0.8429015842451761, 0.08123575515310466, 1.1698055406662822, 0.3832972179955151, -1.4834349807600646, -1.97346152729974, -0.41879957857859146, 1.1748369782696975, 0.9472036927830927, -0.31687899582355006, -0.49130551150142154, 0.7128261635553048, 1.2976744145162495, -0.01174899381881831, -1.6166637642276696, -1.089790546389398, 1.1717951071812442, 1.947813381534189, -0.5697541995936511, -3.7463093177789784, -3.1284153246225777, 2.0654228371917065, 7.475322333590457, 8.302902885120805, 4.5852254172567, 0.6715498279190473, -0.18338870446077374, 0.7647049377248369, 0.2739952372893977, -2.2111315237831355, -3.9397662039859718, -2.747675841226032, 0.018639188262257612, 1.3653060808490154, 0.49996277408019363, -0.5829951106507706, -0.24095902522444773, 0.6108396665821485, 0.25384739457737515, -0.9271665551146868, -0.8416853108641719, 1.0473193573460706, 2.4472248401910996, 1.1970095863477814, -1.4453549385785658, -2.0385892362431193, 0.5032281571394053, 3.172984980192023, 2.662014666164791, -0.09268011511625736, -0.8134222912458455, 2.5629078631526636, 6.819477470529121, 7.078574353367733, 2.6894182227239924, -2.0215234487344156, -2.9563385718635344, -0.7287383495169795, 0.9380815016019463, 0.21262212626169413, -1.116552212504635, -0.8783240802535826, 0.29621197240947444, 0.22029801319363704, -1.3655363019929754, -2.3118781630196557, -1.2405426682478284, 0.3530032430195026, 0.2354871515725029, -1.2626943191396731, -1.671687039584076, -0.06245372184560921, 1.372022987017626, 0.37732886850568087, -1.8863639681141864, -2.1732189587457262, 0.1460023582040807, 1.5982919697960916, -1.0186175194434548, -5.8928904757560305, -7.681227697195746, -3.8558960993336617, 2.0494416163998093, 4.512517690205152, 2.2947737721388908, -0.835574355867844, -1.287685759068011, 0.3125852698450021, 1.058754050869676, 0.2272558385307218, -0.0859847908569454, 1.4329647361437443, 3.06747180864577, 2.474980025441383, 0.13517403425725158, -1.2405939629931015, -0.47924077752164973, 0.583354264152114, -0.003046472634840893, -1.4023695827530793, -1.4350752367921142, -0.18667292343045921, -0.14655088959781448, -2.227888236254195, -3.4604027323639874, -0.4083631221921067, 5.73890298761535, 9.561663400799313, 7.549040187816457, 2.33225260658822, -0.5644430379111589, 0.6494876552521145, 2.493930248223097, 1.3933579163692076, -1.5933357696894657, -2.60687066397636, -0.42045544521142225, 2.0623032365048513, 1.9301735804907085, -0.020619849601587064, -0.9423440214380578, -0.12351496364201893, 0.3885386910878239, -0.7458570680850911, -2.032748692120729, -1.506070719131272, 0.1471265150683322, 0.5739296222046788, -0.5524630925543826, -0.8393786931530344, 1.1457029010531055, 3.209052066096275, 2.25442438634867, -1.069806742753151, -2.632848098454983, -0.2712748957539863, 2.9044323735127953, 2.2919447105838535, -2.0396674168048983, -5.126522358266529, -3.3597490767174634, 0.9951278154152485, 2.902941300261865, 0.968402978832994, -1.327667807612136, -0.7208801126427423, 1.6797028343434475, 2.5185276576927276, 0.9952029050428024, -0.49555455645871826, -0.21133665666500548, 0.635451931901384, 0.31678435535033683, -0.35740760312250486, 0.7295699016250102, 3.3408501710163017, 4.5971374224216275, 2.8920764387406623, 0.32494665610583356, -0.1549556287265776, 1.1244529837992525, 1.324079640133079, -0.20599953073409755, -0.39482439613990333, 3.052997791417333, 7.294297478850982, 6.9139811381121845, 0.8037520973274099, -5.764976608451811, -7.059147626011429, -3.362896536479637, 0.1548157520728545, 0.20229112855126588, -1.3132717881317644, -1.1002576608013657, 0.6839188637887437, 1.286282568187325, -0.08504922898708542, -1.056080498532097, 0.1851510869116671, 2.0694678431996625, 1.9842904502228016, 0.14217541690305838, -0.8661149044764078, -0.04364557641581017, 0.6504848195891689, -0.38333916982523825, -1.614978409422063, -0.6826561332287198, 1.5963182466147787, 1.9417702610677439, -0.40070344196283986, -1.7682842293646273, 1.1627669217715244, 6.165141410164137, 7.475643639014641, 3.0237443741244854, -2.690223480264662, -4.095299794926721, -1.1942279186252267, 1.2690066784671497, 0.4283695032944839, -1.5168509451105667, -1.3184747183935637, 0.4906497761075673, 0.8101999700741661, -1.110544949894821, -2.534306970692744, -1.3386406122574463, 0.9518863762184536, 1.5787115169523491, 0.4888311950669737, -0.1362516001085902, 0.33176583254702885, 0.048377701148237744, -1.8567626930029193, -3.1161713994196125, -1.4083590387768083, 1.6505996710358197, 2.0662059827548136, -0.9638252524559391, -3.5033550934215016, -2.163807563687942, 0.9637915982045843, 0.9858056824960857, -2.8875948125502213, -5.888943405916708, -3.985140253991032, 0.6667389913093645, 2.591452967675531, 0.13719714921882825, -2.849455178584522, -2.603883583415354, -0.14431136356285298, 1.0334583894617988, 0.11573856392268536, -0.5937641531419966, 0.16031722487267228, 0.6767317199238149, -0.574702157077866, -2.06880157273022, -1.3722147002274463, 0.9603371705912339, 1.9678752696992943, 0.6686381564385956, -0.5155396837186561, 0.3280682696662915, 1.3654670643161455, -0.21870617334725267, -3.3656836299669486, -3.9046615233392155, -0.565657858924019, 2.4633886400479694, 0.8626009494752898, -3.6074343706208443, -4.940901065397681, -0.7105838751524363, 4.6889460834113095, 5.723502855371744, 2.4605412481206783, -0.4895231281885145, -0.521680723961748, 0.3395903368962428, -0.4111801521932335, -1.820003650065917, -1.4939699387109049, 0.19102369392770605, 0.5299512933853903, -1.2014682489867647, -2.4688367354885887, -1.3257530028162938, 0.6010455504555863, 0.6616459869388776, -0.728708342584218, -0.9060960977370761, 0.6268027456839943, 1.3671040481063388, 0.22871502417117695, 0.2070891667298535, 4.271017636456564, 9.931973083345115, 11.060018702926854, 5.573717724659585, -1.3637976858028178, -3.4473047611504146, -0.6403808729108562, 1.8820523650184122, 1.189535218794255], 'positive_zeros': ['1.25153371554648601017404551353', '2.9069581731389716363773043261', '4.071696806763438139579651654666', '5.48312281389038818116960420292', '6.09047768609382550300610567463', '8.08078524133850262112135156568', '9.14998836954815073166275213005', '10.46521144752427094434275056524', '11.768534326933818649530748124235', '12.42794149178951671133138745373', '13.378475687343655540471041803933', '14.50780853194626530052824223416', '15.80753365319148961223711186409', '16.24605625094344565680219222026', '18.01285959934843169190471162892', '19.186225634890112216092864506445', '19.961134050563004166506867881398', '21.041253239237509200462937087809', '21.74635438078852741162623418813', '22.833142515013807886716592648029', '23.77635566986236462732275825069', '24.78930569699577781765934144129', '25.27688158590529824961856767079', '27.186673973838139136198863746610', '28.01582116967432153991072574623', '28.78768075352674644499539839609', '29.68651070980610834864337338526', '30.776173456251176785654582373578', '31.809615846450738270625220882765', '32.156483116721013710117852678389', '33.11725401974387538128496606357', '34.41187604014278603322073178831', '35.22567339941277816334821763044', '36.37163102619648536302217372579', '37.600683000762986668503702436785', '38.02679501709593458994561295076', '39.252846644738062040106240285744', '40.11746696574554789258877041832', '40.475650829188483878533446760534', '41.758348453936649414564575318553', '42.42342353676723010403571650784', '43.45827019549669781965369115810', '44.40397145147035287548147838207', '45.39477412910000473475648505624', '46.646778843433059944031673319340', '47.519886873354809392284131503639', '47.944887380595185397552160846645', '48.70430423128346289474694994472', '50.02766374857078594791046747991', '50.605950818014138964215539021416', '51.41735742623020566330848629176', '52.11197515302702696388699584653', '53.211535512869260790160720095', '54.730054086716072412183516334080', '55.030292713012784748342425927314', '56.21424503945972033183520592196', '56.79235424362757180279990465544', '57.89232810600882487232897819275', '58.435349801155752609492436246012', '59.539708328799577186789746685439', '59.97092012587272597026016332375', '60.95999384337437211762235569092', '61.75649225588723704438408131236', '63.192855765706358760865226333914', '63.876686739952436066671657987950', '64.497878629086175601270634315599', '65.6933971588547635090128924126', '66.65446593823520266562086503473', '66.94883651802529548416361025857', '67.86624831903915627983976038787', '68.58779021076291593357891510929', '69.81004763582029026283754450752', '70.18862629229498014907391944347', '71.30555505340070833802083196612', '72.09977961709015525092877650171', '73.489730994918797196611362340027', '74.21189868988049632140107252316', '74.525001201258583015746985833311', '75.7428649860955340870684637403', '76.38155355644291461088135959322', '77.06142169130359438366775489362', '77.986213270504412905088891297495', '78.89753574901408771348175889671', '79.43854292481653338085522490519', '80.24480889739688498474587433798', '81.81257221829784473299035356756', '82.35582600218300151699410717327', '83.22585946265485641123373902500', '83.842345321361166969485107126247', '84.63537750392939043071465925835', '85.65266091873142584170055836168', '86.458745700798974149535211666494', '86.934609241404302526853344251432', '87.4989361105307553389203601722', '88.76641548061242985952933035406', '89.59777576318276389211911963045', '90.519483575350099462694477492679', '91.361838011221843887277382513711', '92.24092735712390932083346202045', '93.00801381716987926474960555382', '93.79127671485983655614780968221', '94.43735450266773038948010684992', '95.26636826696761707686487568780', '95.95743564952608181700996373310', '96.67698375924298696684981776455', '97.742284254792329115345554415020', '98.320807284208176418838884388018', '99.480874826403752393827352487530', '100.197874678042963832427243253588', '101.24001410613991175114502196700', '102.184310872476439734989709624743', '102.34794719241408909272653630633', '103.49019714850126974308504519876', '103.784783415335149952554744367505', '105.21991055338520590677506604911', '105.7440863334861124117290383762', '106.16366806276748779325779670760', '107.03513684504529425643578399007', '108.438953695560983948822883051626', '109.08285742193293879181344245535', '110.05412911976507793766168745838', '110.607799236384344965129367755627', '111.31574370614479141015236280614', '112.252765154614072799451042690809', '113.039550799486441084392525625452', '113.58522880944739931105979122711', '114.373094287314131368496471464748', '115.15657853454103223088938279535', '115.88707803735254637938600648008', '116.76969364118636457601881454001', '118.23281609900519869177445536', '118.50995748764936919095968230279', '119.10726375708611478534593359343', '120.31015239627469080757904324951', '121.05087798195200350786290792567', '121.63912728979344581057030647594', '122.25600372427259041466783929742', '122.973071995249894475295305328655', '123.88800145180919502062688562642', '124.63979174806928127948562398157', '125.61345150705488763524083806002', '126.05071144454723071945570869470', '127.346064026217221077582328248', '128.22031186839719355895282938276', '128.79295548719056753614148751565', '129.597619605066924784446214863116', '130.05702133719821242887220958915', '131.16021934879747069014589898120', '131.620204755453235971294909637867', '132.50953048218847685361111916183', '133.1774779052326453716355822060', '134.045457552630917882620088019', '134.61080895010847655886031655616', '135.8212491442837658460481895536', '136.77257559739824151130428189308', '137.44186130479613720983583453254', '138.204368294868817591104010948832', '138.47276266777217993965907461165', '139.70607803183309821051950523831', '140.42230790519398163581987931515', '140.936804476329465057384102992223', '141.9377792997552095234092293685', '142.142792582231749155496768157589', '143.14852586571794047160811079020', '144.57019703848742875374740621585', '144.906798509057933784924030090896', '145.770883663662833161622821304211', '146.60610383576193342332004752739', '147.49652518246586986374853791191', '148.161479421419024155058126386764', '148.59162807852376078355185431907', '149.65566959529486592469368625429', '150.17815487825047216510117774603', '150.79208727924895158978457976012', '151.77679306902963045988325145375', '152.52307015929464001238322977669', '153.3040999017039036229432195490', '154.29982324104492951756501544238', '155.105924995151702692543932734796', '155.72287420770061055801755435060', '156.733122212545324537128853128509', '157.25373628824639397235525024962', '157.92264642485509725583860250523', '158.30873404918978729363041490383', '159.75254541351886457396421752277', '160.05097283004581978312995155016', '160.89728115120982337971607442817', '161.31089585599765194426358121361', '162.53324472927633894599309432075', '163.726137117853845092995748247234', '164.1051789185719998655690316945', '164.88256040007628031180453579407', '165.609308351644965967485348060215', '166.22145914463483992334216128279', '167.2119718416780870021633571549', '167.823810369303552814622062565803', '168.36006291358838119304935843697', '169.1562683390736435743510516212', '169.95412476968717994783652622658', '170.54367172217502479983780962075', '171.71359980238280765704092930426', '172.61254299998936400080819079206', '173.1871258029447142399038407620', '173.97417555852693388017120014714', '174.53234027149586452093982544875', '175.48549434229765843896903860156', '176.40831091076523812136767561386', '176.691971487852360458590186455559', '177.199462424267506729636353386', '178.26122555544012456822069374963', '178.979932271023838906962581665994', '179.8911636909547337033474800676', '180.41397825966903088305384807467', '181.51414678160969277462776918302', '182.19937887072147623829138795804', '183.14498106363505631032421420629', '183.77907066024948074543681187354', '184.32814008410487735974375115436', '184.897021935609155199459874928175', '185.81063264616387213830150900853', '186.68862829837861227830895804434', '187.11683826504955033563828456268', '187.78881342070273519182425918809', '188.792808561124987468993469088192', '189.43907620066628524547225613643', '190.34953747956009382245612956250', '191.482825834731791563666696548157', '192.027208519507697420715347023434', '192.40526905144050325499850013343', '193.39848622369819598358730399647', '193.8734277232257125110289331748', '194.88415502394010267092777857318', '195.46524160992229927785899448039', '196.13587493532112252819372033094', '196.93591815318540636737736190921', '197.14651977759053968919446319759', '198.67637137971037553834207551739', '199.431961554986371887121349930295'], 'prelabel': '1-153-153.70-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': -0.4870332733117953, 'root_number': '0.0407249077287082241364963121025-0.999170396824529725394779971435*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.243516636656', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.36241468696623421525276976329-0.736876396793220472099409323295*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25153371555', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90695817314', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.07169680676', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'bad_primes': [3, 17], 'central_character': '153.70', 'conductor': 153, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/153/70'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-153-153.70-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-153-153.70-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': -0.24351663665589765, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25153371555', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_153.70', 'Lhash_array': ['dirichlet_L_153.70'], 'label': '1-153-153.70-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/153/70'}
Lfunction data - 1-153-153.70-r0-0-0