data:
- - Lhash: dirichlet_L_104.75
    a10:
    - 1.0
    - -2.8163065144692913e-30
    a2:
    - 1.0
    - -2.8163065144692913e-30
    a3:
    - -0.5
    - 0.8660254037844386
    a4:
    - 1.0
    - -2.8163065144692913e-30
    a5:
    - 1.0
    - 0.0
    a6:
    - 1.0
    - -2.8163065144692913e-30
    a7:
    - -0.5
    - -0.8660254037844386
    a8:
    - 1.0
    - -2.8163065144692913e-30
    a9:
    - -0.5
    - -0.8660254037844386
    algebraic: true
    analytic_conductor: 11.176352178641002
    analytic_normalization: 0
    bad_lfactors:
    - - 2
      - - 1
    - - 13
      - - 1
    bad_primes:
    - 2
    - 13
    central_character: '104.75'
    coeff_info:
    - x^6 - 1
    - 0.500000000000000 + 0.866025403784439*I
    - \\zeta_{6}
    conductor: 104
    conductor_radical: 26
    conjugate: dirichlet_L_104.43
    degree: 1
    dirichlet_coefficients:
    - a^0
    - 0
    - a^2
    - 0
    - a^0
    - 0
    - a^4
    - 0
    - a^4
    - 0
    - a^5
    - 0
    - 0
    - 0
    - a^8
    - 0
    - a^4
    - 0
    - a^1
    - 0
    - a^0
    - 0
    - a^5
    - 0
    - a^0
    - 0
    - a^0
    - 0
    - a^5
    - 0
    - a^0
    - 0
    - a^1
    - 0
    - a^4
    - 0
    - a^8
    - 0
    - 0
    - 0
    - a^5
    - 0
    - a^4
    - 0
    - a^4
    - 0
    - a^0
    - 0
    - a^2
    - 0
    - a^0
    - 0
    - a^3
    - 0
    - a^5
    - 0
    - a^3
    - 0
    - a^1
    - 0
    - a^7
    - 0
    - a^8
    - 0
    - 0
    - 0
    - a^5
    - 0
    - a^7
    - 0
    - a^4
    - 0
    - a^3
    - 0
    - a^2
    - 0
    - a^3
    - 0
    - a^3
    - 0
    - a^2
    - 0
    - a^3
    - 0
    - a^4
    - 0
    - a^7
    - 0
    - a^5
    - 0
    - 0
    - 0
    - a^8
    - 0
    - a^7
    - 0
    - a^1
    - 0
    - a^3
    - 0
    euler_factors:
    - - 0
    - - 1
      - a^2
    - - 1
      - a^0
    - - 1
      - a^4
    - - 1
      - a^5
    - - 0
    - - 1
      - a^4
    - - 1
      - a^1
    - - 1
      - a^5
    - - 1
      - a^5
    - - 1
      - a^0
    - - 1
      - a^8
    - - 1
      - a^5
    - - 1
      - a^4
    - - 1
      - a^0
    - - 1
      - a^3
    - - 1
      - a^1
    - - 1
      - a^7
    - - 1
      - a^5
    - - 1
      - a^4
    - - 1
      - a^3
    - - 1
      - a^3
    - - 1
      - a^3
    - - 1
      - a^5
    - - 1
      - a^1
    - - 1
      - a^5
    gamma_factors:
    - - 1
    - []
    id: 2032
    index: 0
    label: 1-104-104.75-r1-0-0
    leading_term: 1.46975933467818937544065801178-0.403938809833613594651725698911*I
    load_key: dirichlet
    motivic_weight: 0
    mu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    mu_real:
    - 1
    nu_imag: []
    nu_real_doubled: []
    order_of_vanishing: 0
    origin: Character/Dirichlet/104/75
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
    plot_values:
    - 1.5242568890982482
    - 1.0900161344594834
    - 0.3961864241822306
    - -0.5159143901803857
    - -1.5236342731919454
    - -2.413138405326015
    - -2.928116849216168
    - -2.8628553397816865
    - -2.1627941101866717
    - -0.9855186852144646
    - 0.3174390643628259
    - 1.3095577743462867
    - 1.6388493069604153
    - 1.199911509643681
    - 0.20806179994503998
    - -0.8680276378338287
    - -1.5069752543289456
    - -1.3890432478884087
    - -0.5810910424428993
    - 0.45606702477738886
    - 1.068622986951307
    - 0.7409642355517981
    - -0.605037263844266
    - -2.511083167247781
    - -4.163643264722767
    - -4.7874405096533446
    - -4.054341985297719
    - -2.27959795373465
    - -0.2764973484384351
    - 1.0724061909760556
    - 1.2969170097603842
    - 0.5928847325355106
    - -0.31574480597744237
    - -0.6408632486250659
    - -0.04608905144225177
    - 1.1115591539978302
    - 1.9871824143643995
    - 1.7950947331214766
    - 0.35909089866254407
    - -1.700914506864069
    - -3.2989758207287054
    - -3.549041029872636
    - -2.3467470168135303
    - -0.4735116942540102
    - 0.8750288528897624
    - 0.8510626999967779
    - -0.4909783914234421
    - -2.2287454756414387
    - -3.1887666765264377
    - -2.736377470096332
    - -1.1946425141566968
    - 0.4071233934080396
    - 1.0850749347857196
    - 0.6160491032618186
    - -0.31102009754176163
    - -0.6361069171485919
    - 0.22315021668838408
    - 1.8503735563805974
    - 3.0572137560004267
    - 2.732364411631587
    - 0.7055314170653413
    - -2.0283986729264654
    - -3.9318857895406154
    - -3.9722556690087507
    - -2.33443443830499
    - -0.26468833387180607
    - 0.8478901853544837
    - 0.4665370915044034
    - -0.7729891990656722
    - -1.6531523702807127
    - -1.4013766480509031
    - -0.3280739564696633
    - 0.4468650467920289
    - -0.030546492416206338
    - -1.6658594402301603
    - -3.275998679632589
    - -3.475916309860322
    - -1.811076790571657
    - 0.7851101076887544
    - 2.6218017487676217
    - 2.5112359531488355
    - 0.6700896963276026
    - -1.4672757734514061
    - -2.3868438153621634
    - -1.6718487279088234
    - -0.2660959762106273
    - 0.3813708135159418
    - -0.432776074301911
    - -2.0750800584420146
    - -3.1431480373803082
    - -2.701693564486323
    - -1.1124378943326552
    - 0.2801146714619328
    - 0.3557903863060456
    - -0.7307384922440021
    - -1.6065721295983968
    - -0.8528710884155779
    - 1.6872199665630618
    - 4.612065406674441
    - 5.990233656986727
    - 4.889174285316198
    - 2.121822776223296
    - -0.4257237841995747
    - -1.3129666616219149
    - -0.6131565221508314
    - 0.3618940473511856
    - 0.38429172014909213
    - -0.5398116007305135
    - -1.2403841577040715
    - -0.5975686572203307
    - 1.2437669045127906
    - 2.831662362746343
    - 2.647448029792249
    - 0.5356246029311729
    - -2.004696477237892
    - -3.0072094245572427
    - -1.7027095331778739
    - 0.8143730541700954
    - 2.5322952643420855
    - 2.2555100667838497
    - 0.5841388637972682
    - -0.7231586330894286
    - -0.39616864610409763
    - 1.211878735725406
    - 2.5333014160812746
    - 2.3227932736224117
    - 0.848799693930847
    - -0.40057598270191075
    - -0.214722332488472
    - 1.0911629602891506
    - 1.9179719980189218
    - 0.9363553910328289
    - -1.5173465661224217
    - -3.5828304570601492
    - -3.5063040079688603
    - -1.2758285589724494
    - 1.2841125523967591
    - 2.0938639910532313
    - 0.6389848502047041
    - -1.6441753444988576
    - -2.7491710668580653
    - -1.921384717862585
    - -0.20766537660440781
    - 0.7264011745673298
    - 0.2892093063499773
    - -0.5294681838613078
    - -0.3282006689674202
    - 1.0669891626346129
    - 2.2083643761381406
    - 1.372248146182791
    - -1.6252542785581727
    - -4.9660809814821345
    - -6.288660707510887
    - -4.759248280700349
    - -1.7984347022554998
    - 0.2428722587818776
    - 0.20110724216886522
    - -1.0010276389678328
    - -1.482117388257038
    - -0.3778731066525437
    - 1.3173219156640075
    - 1.8517949097892878
    - 0.5961991543294591
    - -1.247412101354009
    - -1.8517428207954365
    - -0.6529911073436164
    - 1.0414709197620662
    - 1.400848506199185
    - 0.02708097774614238
    - -1.5101902262909725
    - -1.1904208919992612
    - 1.3574234270032934
    - 4.298739655658286
    - 5.213257385454912
    - 3.345420970785547
    - 0.28255998610736843
    - -1.589632313982358
    - -1.2977893705295627
    - 0.025656581842027484
    - 0.5647502959623029
    - -0.20677345178136175
    - -1.0792717613307619
    - -0.6081705726122578
    - 1.1057728650895076
    - 2.3409943532954514
    - 1.555590766944862
    - -0.8143102732242729
    - -2.5370243763035027
    - -1.7088514953305851
    - 1.285672626178134
    - 4.010033790334343
    - 4.244762751817027
    - 2.0454356822580912
    - -0.4522324023010615
    - -1.224158610564617
    - -0.2711084473618007
    - 0.6676637762529898
    - 0.1801631831422419
    - -1.2472034695840268
    - -1.8387981812478709
    - -0.616259716494479
    - 1.3621224484418621
    - 2.0302856061431456
    - 0.5556285746427203
    - -1.6430355942049792
    - -2.2879351984725678
    - -0.6447963695146338
    - 1.6178125532002974
    - 2.0939816801262814
    - 0.1399495073722769
    - -2.4107553220529434
    - -3.0905966914368626
    - -1.2874589138636143
    - 1.2057148134916726
    - 2.10471607267238
    - 0.9400566840590621
    - -0.6685633917307433
    - -0.9475712613907072
    - 0.0967442285918438
    - 0.8888950588931748
    - 0.34476918294957093
    - -0.6204065032596647
    - 0.03882556864129308
    - 3.0957549362233845
    - 6.778938123122497
    - 8.194278616456883
    - 6.107923491956041
    - 2.2014071409884397
    - -0.5532107818895332
    - -0.7265983336354221
    - 0.45444141887625955
    - 0.7669150410253354
    - -0.49060412185684055
    - -1.874439522448357
    - -1.6415548611546384
    - 0.11649996894027823
    - 1.5085139417021738
    - 1.010773818858451
    - -0.7236851701090818
    - -1.538228379025369
    - -0.24508618814434296
    - 1.886464659872858
    - 2.3940681193045403
    - 0.34189494899051587
    - -2.5024933203835573
    - -3.4146164042161002
    - -1.5573522177799615
    - 1.1496785534702756
    - 2.0786426535008484
    - 0.6250817096050514
    - -1.325158869693193
    - -1.607626740455216
    - -0.13809403385782734
    - 1.1877480243320586
    - 0.8194012965774002
    - -0.6490447281162202
    - -1.29129654872858
    - -0.28939155664361976
    - 0.918758205129345
    - 0.24670134153756035
    - -2.441899466682412
    - -4.786828258557371
    - -4.2612205504861755
    - -0.9265542146547013
    - 2.4445591092926473
    - 3.1047458825955943
    - 1.013609611792048
    - -1.3769298362547515
    - -1.8654977782075295
    - -0.6674010439791693
    - 0.3053078187377958
    - -0.0013337441116047176
    - -0.49487786780983223
    - 0.5762829024837162
    - 3.194610358749767
    - 5.208081414766392
    - 4.627041583235755
    - 1.986939575511926
    - -0.04045176078036435
    - 0.499703243621286
    - 2.700949834978624
    - 3.8237983759765513
    - 2.38631238135358
    - -0.1604728152679184
    - -1.0666960802029488
    - 0.6321348293177678
    - 3.071426377580201
    - 3.6868572694099058
    - 2.0292826341771413
    - 0.06652651617644999
    - -0.2470559421021204
    - 0.8110336485368141
    - 1.3230876126994002
    - 0.3202758412125521
    - -0.8572074086282591
    - -0.18235733590114783
    - 2.339761400990216
    - 4.205423834749789
    - 3.0016368795385926
    - -0.7851426627066306
    - -4.011252285930621
    - -4.046569703567013
    - -1.405627696715596
    - 1.0385969774277009
    - 1.2652183023283354
    - 0.06712823548346042
    - -0.3259644180225945
    - 0.8786548206529522
    - 2.1535913933265114
    - 1.7233083190943816
    - -0.060571467616410656
    - -1.0466174061633282
    - 0.013667202965870099
    - 1.7054412550054765
    - 1.4317597247826874
    - -1.4568059105542828
    - -4.592287984588439
    - -5.000433898580662
    - -2.3361773033648685
    - 0.7600092783540069
    - 1.6000525046608343
    - 0.29765899865077355
    - -0.6977375649734388
    - 0.30536197126303655
    - 2.2428454940695364
    - 2.7039948450124642
    - 0.9397053340763186
    - -1.2085307653225366
    - -1.5465946889168034
    - -0.14410737760093473
    - 0.9008462180719413
    - 0.2450645792446358
    - -0.8627246356123823
    - -0.08820545099474723
    - 2.8648331847023236
    - 5.375488698782643
    - 4.582090633436014
    - 0.6498403611646781
    - -3.1916023995053466
    - -3.980446624903329
    - -1.9651946926573276
    - 0.09682848919293487
    - 0.25147436058648953
    - -0.7059666433793679
    - -0.7685726760269204
    - 0.4428537640214856
    - 1.1996107441554584
    - 0.11319014192930493
    - -1.695313905576025
    - -1.6446329737080125
    - 1.1323946435487147
    - 4.39493352398293
    - 5.096500947869984
    - 2.8187206892417405
    - 0.2663732171372019
    - 0.1655560860147372
    - 2.189876301578488
    - 3.514196792234321
    - 2.2607374576345536
    - -0.3169978223864831
    - -1.4571615548042705
    - -0.22879065355204373
    - 1.5025977843370437
    - 1.5493048052805367
    - 0.12493478820271645
    - -0.5967078028122988
    - 0.5418059660668605
    - 2.027587246688615
    - 1.5497972555467516
    - -0.8987403164063672
    - -2.6807512532615063
    - -1.5855152466679405
    - 1.3455836957763674
    - 2.786209025313895
    - 0.9007763564406459
    - -2.5125599630566207
    - -4.0635184057894325
    - -2.5615145702372253
    - -0.09693835469674522
    - 0.6855951487688858
    - -0.35804566698440327
    - -1.1575290248593295
    - -0.4151429865418503
    - 0.6905769078842379
    - 0.2789464059893543
    - -1.3753998192302745
    - -1.7982867345567874
    - 0.5891458007870921
    - 4.071019514387966
    - 5.16468517656402
    - 2.5176792349258603
    - -1.4464734514479838
    - -3.17997240261069
    - -1.8572975458738805
    - 0.09388669141585886
    - 0.21819236293164745
    - -1.0631945424283413
    - -1.3621053677858292
    - 0.3212479365861465
    - 2.1727020233438625
    - 1.8724667496222085
    - -0.37476378926660825
    - -2.0193499274950684
    - -1.351751487674569
    - 0.4043405630391633
    - 0.8239225348122157
    - -0.3633357988519542
    - -0.6902784803622036
    - 1.9095593802716138
    - 6.106279085744059
    - 8.219845146241738
    - 6.274612905442891
    - 2.238806501597369
    - -0.24247817194590116
    - 0.14026049082148836
    - 1.3771044397780552
    - 1.0911035888618272
    - -0.4922957289546246
    - -1.231796245107319
    - -0.23560091039995532
    - 0.8319104760849856
    - 0.07642703639998105
    - -1.7931078990369795
    - -2.0582067858603112
    - 0.4898180707038695
    - 3.588530443210286
    - 3.8553202109923523
    - 0.7857926329781156
    - -2.509673392001532
    - -2.835997365045506
    - -0.47065732349598527
    - 1.4962639550090229
    - 1.0425674078949791
    - -0.5704916545807937
    - -0.8327828056664315
    - 0.5930702140579688
    - 1.545233007284271
    - 0.4319504479427748
    - -1.4781827859227186
    - -1.6613209560184388
    - 0.23422919553636154
    - 1.7194929795001912
    - 0.6056511390467102
    - -2.035475029222
    - -3.0244692500775017
    - -1.0442589061967689
    - 1.5895882100203755
    - 1.7090223673685863
    - -0.781636697762695
    - -2.7512351702771483
    - -1.6594290475474427
    - 1.4162683712199269
    - 3.229106711090743
    - 2.295045030405619
    - 0.324385086728496
    - -0.4037368192108049
    - -0.013722899245970224
    - -0.40119796998575996
    - -2.0334735365319547
    - -2.762052650972376
    - -0.5603738287360962
    - 3.303553880675331
    - 5.079003316589999
    - 2.7507975401712663
    - -1.4601682464806771
    - -3.533233276884985
    - -2.142356475385706
    - 0.21963771617350603
    - 0.6495479615347813
    - -0.6872805584521391
    - -1.3006734974590979
    - -0.039650348749908054
    - 1.312260316910164
    - 0.560898424942119
    - -1.7655030051023188
    - -2.9794209440837194
    - -1.8028519490616532
    - -0.1406852772206265
    - -0.5660292079678574
    - -2.7667808456992335
    - -3.742428564339124
    - -1.6943042876708525
    - 1.3975174315926013
    - 1.9967914600741954
    - -0.6406794830596432
    - -3.4911059083417464
    - -3.414037079346215
    - -0.8198747352822814
    - 1.1804783658562694
    - 0.8245971615810894
    - -0.35567789707695413
    - -0.00842535673434069
    - 1.6999669041761973
    - 2.4133102557773283
    - 1.010322257115107
    - -0.6969315779496765
    - -0.46153191269619087
    - 1.0460808425815307
    - 0.7679808465909875
    - -2.6799452951473457
    - -6.662797861974486
    - -7.220827908188918
    - -3.678587626031671
    - 0.5498409744860795
    - 1.9462775958737297
    - 0.6647899555960893
    - -0.42934370496442564
    - 0.2057111487215265
    - 1.103061054456706
    - 0.4083672926741538
    - -1.109763999497006
    - -0.9647722779639297
    - 1.440446093357013
    - 3.57905044947548
    - 2.8983863100996743
    - 0.25614353658858985
    - -0.9967692691326301
    - 0.7097474852867476
    - 3.090692605795726
    - 2.937804122877205
    - 0.3020465607782216
    - -1.5360776082207666
    - -0.2932777665306156
    - 2.3902408328108455
    - 3.0903401751215673
    - 0.9374600950164086
    - -1.481537891780018
    - -1.632256009194504
    - -0.14443600350838603
    - 0.5036445824082177
    - -0.36483275759415934
    - -0.8292333483106896
    - 0.4845950254844447
    - 1.8598639815877491
    - 0.4287582531130908
    - -3.712821110768507
    - -6.841593101845713
    - -5.7300959356505
    - -1.5187595041249309
    - 1.6247780079718053
    - 1.410448141754386
    - -0.2700911776475512
    - -0.3129078865853799
    - 1.5112199695578155
    - 2.6695152325278895
    - 1.6529585003309801
    - 0.05174197613427052
    - 0.13858180241324541
    - 1.504998672469144
    - 1.6026238150950034
    - -0.4626016725004832
    - -2.2341226617107783
    - -0.9542294573388435
    - 2.5529576365323177
    - 4.507768980022638
    - 2.780684320419847
    - -0.44591949004424314
    - -1.46834122045398
    - 0.31700168316349264
    - 1.946943631378786
    - 1.0171855491387043
    - -1.186525803004097
    - -1.6233765521385493
    - 0.31210141938024516
    - 2.067947923083432
    - 1.5203085704194135
    - -0.18466281953194402
    - -0.4239387962339591
    - 1.0996638086210766
    - 1.9799712872560815
    - 0.7617555733200927
    - -0.5577484517376763
    - 1.0142488615216232
    - 5.103182820135204
    - 7.702514038163608
    - 5.785552262279306
    - 1.0267462479219782
    - -2.1587328383046747
    - -1.7329944363910201
    - 0.16444621267620935
    - 0.6321445542057773
    - -0.28475627029974193
    - -0.4489231997915846
    - 0.6570686082835965
    - 0.9355359088450204
    - -1.114916751250103
    - -3.6758302959169256
    - -3.579935858925546
    - -0.5813723800970446
    - 1.9796273789452687
    - 1.3389214427204905
    - -1.114763792529451
    - -1.6877423267738452
    - 0.7167010934267217
    - 3.1472781742673273
    - 2.5084443804901158
    - -0.42946728960659947
    - -2.2064591407591863
    - -1.2805898710990749
    - 0.2015016278551343
    - -0.32813891467286055
    - -2.266605127898427
    - -2.8776843028080403
    - -1.309524529137241
    - 0.20949952936425387
    - -0.28775085892713703
    - -1.4548594423700596
    - -0.4195930417135202
    - 2.883017549448551
    - 4.980815875015944
    - 3.154023569983176
    - -0.8280540327061199
    - -2.6537641107612435
    - -0.7304264631000509
    - 2.057347580301002
    - 2.2483033996758612
    - 0.06548980149743452
    - -1.4549679930981887
    - -0.8408197156210073
    - 0.116340905825786
    - -0.5864320391071391
    - -2.060780925719831
    - -1.9660783996871807
    - -0.35758025655240494
    - -0.1297663644296039
    - -2.988425750264839
    - -6.467103288666461
    - -6.496460869325741
    - -2.5055133743171454
    - 1.6791251817715274
    - 2.446243818678206
    - 0.5202132054777374
    - -0.663157417368129
    - 0.1934182927900976
    - 0.8424102766162657
    - -0.8229620140101381
    - -3.421020720913658
    - -3.832522358290014
    - -1.5126585474313259
    - 0.7677664649066426
    - 0.7703432109776058
    positive_zeros:
    - '0.76826862225171870991262097020'
    - '3.04594545321128796953490673115'
    - '4.43254381036835566955231921860'
    - '5.79630429585982221964808173847'
    - '6.75799398717826870672030393544'
    - '8.79952005128423266839034177917'
    - '9.88069692202636063957018295517'
    - '10.63933945616126462579863663786'
    - '11.932121411986731881396440339210'
    - '13.5237836784220866875259898522'
    - '14.28269651330522567465458281918'
    - '15.84608787519206771703447491607'
    - '16.76479999640116125118336249946'
    - '17.44727974473013530611299999523'
    - '18.831493384114091035277031247721'
    - '20.361380452743022436234511944017'
    - '21.06441087542475272451805819903'
    - '22.28369218002022411082905718136'
    - '22.80429082056762554636361240684'
    - '24.28042525776768898978638648477'
    - '25.40354549531544962266508782535'
    - '26.63580938991335027383718744034'
    - '27.07977883387228510840204991317'
    - '28.6644305548210518559220803081'
    - '29.188130169917287374168489058598'
    - '30.12524002911720166660835574434'
    - '31.80945731442646236167670132760'
    - '32.67581770760648171702101577343'
    - '33.2761278942701772889268160817'
    - '34.177884139470552510311715555397'
    - '35.374357914845771162600900767036'
    - '36.46251352438568641902979621995'
    - '37.607960355972736694244591071214'
    - '38.21647363577754920399326852661'
    - '39.55442889326160673612959959206'
    - '40.06331665967074450204010921903'
    - '41.06865116177714576159507521729'
    - '42.330667706670505360215885413879'
    - '43.211223008075534265157360979831'
    - '44.418481251731394734173850460285'
    - '45.09760798107217307969393334461'
    - '45.71739383805037915459048452726'
    - '46.72558796656505387017502490971'
    - '48.37615288873967883435460058030'
    - '48.810929331589954585507938902'
    - '49.75499487436353997480152906061'
    - '50.72125272509866408358919781076'
    - '51.67396074145563845895043400212'
    - '52.504616935530827384692960188269'
    - '53.29551002497119943142548807622'
    - '54.71976937084091147630433444518'
    - '55.618251922700076914014780005116'
    - '56.190832933622450426347484588551'
    - '56.99968232748022619427478193469'
    - '58.02479533552478797403574009133'
    - '58.941481264650100510832934506560'
    - '60.24319922650477704438349559991'
    - '61.00441641027397140241955117215'
    - '61.60665499236836919416348485561'
    - '62.594956522483719167763751163477'
    - '63.51300686668628313079373955346'
    - '64.4575435340697371979367821795'
    - '65.3285804465876216694085372895'
    - '66.401873154676154042330110976611'
    - '67.35384040004552872651482819091'
    - '68.10040705266421838208264897142'
    - '68.84608031058679304983248406719'
    - '69.368666069717745525851516500335'
    - '71.15812456273120428304271438261'
    - '71.75670488641834232375324107273'
    - '72.405182298964612595537865184996'
    - '73.41891127996434735989807206992'
    - '74.24793779882256917437335559540'
    - '75.03547689529679834000255654336'
    - '75.97351433601244952067406176788'
    - '77.04514617963243473589024309357'
    - '77.90225041531021269729471712466'
    - '78.774416924027281315300050899416'
    - '79.55241306921016592694787364991'
    - '80.37268219242502799846963542059'
    - '80.97535881461527506252025851302'
    - '82.261739547103512101431980142685'
    - '83.2416724740853434272064401004'
    - '84.230718773081778763118913596168'
    - '84.686925598404097902024955220439'
    - '85.21001331827769310012790264879'
    - '86.86124045194662885409696390815'
    - '87.07451155998772985683285244252'
    - '88.4146142878567458712983189548'
    - '88.980448435142092151280829123707'
    - '90.32894972230911946179380038924'
    - '90.71802226797599882774393337768'
    - '91.630313962324728694107347248404'
    - '92.21675150923464820112439491112'
    - '93.37836851326101735076714707889'
    - '94.528114665823130307150180843223'
    - '95.331547092025495234270076621946'
    - '95.74743383637565347307896726258'
    - '96.86439473307336778989004190894'
    - '97.49764028271920672244401898151'
    - '98.30396455529604127063438730515'
    - '99.595444785230368185642002188435'
    - '100.372375510246839723828957184840'
    - '100.88313238490693358174576366294'
    - '101.996763329214835385209067564959'
    - '102.84075957145545656714953499353'
    - '103.49543043612163370561622135859'
    - '104.07534727713154069234217610606'
    - '105.35744253134413915530185092123'
    - '106.53908425476750486209648653075'
    - '106.96414498179804199108104577585'
    - '107.71281686233227640159630056141'
    - '108.45635860526099369823742447551'
    - '109.271847700809206182716910059889'
    - '110.68967235936019735578554582518'
    - '110.89188349816891154963185420855'
    - '112.14560578197297567948271882745'
    - '112.84895096247597657684605707487'
    - '113.77750640506367507086771165142'
    - '114.27068008966740454335929339090'
    - '115.20872329774588191947210490757'
    - '116.10938119529899873227692715705'
    - '116.95796819317544227823973910847'
    - '118.14123739676824499089412209292'
    - '118.66549497707798779386428884561'
    - '119.47354050155090080168685227236'
    - '120.05977641457835956340788305241'
    - '120.88269123063385627401721459691'
    - '122.06585525461103302323632316072'
    - '123.10285190101467036426494868255'
    - '123.50175049973891944275977014318'
    - '124.32955658357340998850532553952'
    - '125.26495928556815291357766617257'
    - '126.17001332140877594509052645162'
    - '126.79122968916788601321544055609'
    - '127.31443881794495014548072772177'
    - '129.00210790878242389636548958122'
    - '129.34009983876702198701336387293'
    - '130.21810453297068822172717612680'
    - '130.9884147334030842627183450890'
    - '131.576386258965545878580081768732'
    - '132.45464671826560028828909227659'
    - '133.50109068184162405725274536071'
    - '134.430141790614123515510273496393'
    - '135.193979149290793198241301502151'
    - '135.82596907905834079017980553289'
    - '136.62924575440787666208112461868'
    - '137.46729939955852969958670666108'
    - '138.19989879892138348771314696806'
    - '139.1725517571199776256436406881'
    - '139.91541993049086611336254444249'
    - '140.79772807954934334830959371390'
    - '141.947537072788394698505576182382'
    - '142.51524243792671907051639515102'
    - '142.64385700907743243405352364898'
    - '143.79739338715873539300447068951'
    - '144.8876798641131653052196859287'
    - '145.899693890025947798233985104140'
    - '146.419067028585509036653337222895'
    - '147.19448695580345189655292101699'
    - '147.89546891307830800497680840207'
    - '149.13733815696137117096161897541'
    - '149.20046242861500738478035185161'
    - '150.47251530021713034727465769856'
    - '151.19073505579409031380601700308'
    - '152.28322419850195190166494538086'
    - '153.00888036181241190854165691809'
    - '153.43947459707132090849043973112'
    - '154.53384034215446335858658170982'
    - '155.09763556646434652402131358355'
    - '155.72086145149835246450088963822'
    - '157.13699878578903583657280220582'
    - '157.94917577234132100296599451344'
    - '158.38098730056571969356306739434'
    - '159.14296070949020782290172085693'
    - '159.83631262188907772520146030410'
    - '160.970627521248957255194573237036'
    - '161.473970861770269673502831430472'
    - '162.53358342972466971844041919012'
    - '163.159990309069201990184807221728'
    - '164.165546736184004423658286235362'
    - '165.032726812060777860130318954639'
    - '165.521838193306500431803292913310'
    - '166.16601644874170644816564228633'
    - '166.914767373363577149245619391810'
    - '168.24236556200113843053251287411'
    - '169.002241805837914868378625507641'
    - '169.44478779701175863116849468532'
    - '170.6424645373214834706326904849'
    - '170.89238837039633827981678210586'
    - '171.81758114354968661341957274747'
    - '172.592587972257223326850993812026'
    - '173.70003056274883776765419150869'
    - '174.33243795387416498159295511073'
    - '175.139324992767531928753213203042'
    - '175.89675102174839657955316252422'
    - '176.834395357111278270360073188606'
    - '177.296652911887968046953772250386'
    - '178.259315756294254916929961444306'
    - '178.632144349163541621392692149696'
    - '180.072628825569332281950138078842'
    - '180.90479229570650189068779127853'
    - '181.47157921272945088656627983162'
    - '182.02107702918904574741877839105'
    - '182.67986595340534914709844874568'
    - '183.80333285092041974605595578093'
    - '184.54348508110186872660103338793'
    - '185.23936085712234413731123567999'
    - '186.20539046292866445857758269733'
    - '187.12038762524230167494165046149'
    - '187.42812147952400743488448624154'
    - '188.67491133972098653311269264275'
    - '188.98753367148054358443066587086'
    - '189.73560411888327019413465151535'
    - '190.86921620892708392329887123208'
    - '191.63518689912792165481189795713'
    - '192.508674471542474903054693602837'
    - '193.36266697381831751961598974104'
    - '193.59080658639464017953641986066'
    - '194.78098197038188394443418223482'
    - '194.96527619235743563016914657536'
    - '196.41612127835015654917516243189'
    - '197.27195800615793625525098440326'
    - '197.76563669378623485521521850006'
    - '198.33036281090057524025627586874'
    - '199.55262897473632487196266681862'
    prelabel: 1-104-104.75-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 11.176352178641002
    root_angle: -0.17074856945180006
    root_number: 0.859542535098774820163672132762-0.511064213534827202887027112333*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.0853742847259'
      prec: 54
    spectral_label: r1-0
    st_group: mu(6)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 1.06705822059625176506116327156+0.0136843588071865101276037853867*I
    z1:
      __RealLiteral__: 0
      data: '0.768268622252'
      prec: 47
    z2:
      __RealLiteral__: 0
      data: '3.04594545321'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '4.43254381037'
      prec: 44
- - algebraic: true
    analytic_conductor: 11.176352178641002
    bad_primes:
    - 2
    - 13
    central_character: '104.75'
    conductor: 104
    conductor_radical: 26
    degree: 1
    id: 2032
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/104/75
    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: 1-104-104.75-r1-0-0
    motivic_weight: 0
    mu_imag:
    - __RealLiteral__: 0
      data: '0.0'
      prec: 10
    mu_real:
    - 1
    nu_imag: []
    nu_real_doubled: []
    order_of_vanishing: 0
    prelabel: 1-104-104.75-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 11.176352178641002
    root_angle: -0.08537428472590003
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '0.768268622252'
      prec: 47
- - Lhash: dirichlet_L_104.75
    Lhash_array:
    - dirichlet_L_104.75
    id: 1783446
    label: 1-104-104.75-r1-0-0
    type: DIR
    url: Character/Dirichlet/104/75
label_cols:
- label
- label
- label
labels:
- 1-104-104.75-r1-0-0
- 1-104-104.75-r1-0-0
- 1-104-104.75-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-26T16:57:26.369958'