data:
- - Lhash: dirichlet_L_177.98
    a10:
    - -0.9766205557100867
    - 0.21497044021102407
    a2:
    - 0.6473862847818277
    - 0.7621620551276365
    a3:
    - 1.0
    - -2.8163065144692913e-30
    a4:
    - -0.16178199655276473
    - 0.9868265225415261
    a5:
    - -0.46840844069979015
    - 0.8835120444460229
    a6:
    - 1.0
    - -2.8163065144692913e-30
    a7:
    - -0.9941379571543596
    - 0.10811901842394177
    a8:
    - -0.8568571761675893
    - 0.5155538571770217
    a9:
    - 1.0
    - -2.8163065144692913e-30
    algebraic: true
    analytic_conductor: 0.8219845443046324
    analytic_normalization: 0
    bad_lfactors:
    - - 3
      - - 1
    - - 59
      - - 1
    bad_primes:
    - 3
    - 59
    central_character: '177.98'
    coeff_info:
    - x^58 - 1
    - 0.994137957154360 + 0.108119018423942*I
    - \\zeta_{58}
    conductor: 177
    conductor_radical: 177
    conjugate: dirichlet_L_177.56
    degree: 1
    dirichlet_coefficients:
    - a^0
    - a^8
    - 0
    - a^16
    - a^19
    - 0
    - a^28
    - a^24
    - 0
    - a^27
    - a^26
    - 0
    - a^41
    - a^36
    - 0
    - a^32
    - a^1
    - 0
    - a^14
    - a^35
    - 0
    - a^34
    - a^4
    - 0
    - a^38
    - a^49
    - 0
    - a^44
    - a^21
    - 0
    - a^15
    - a^40
    - 0
    - a^9
    - a^47
    - 0
    - a^5
    - a^22
    - 0
    - a^43
    - a^25
    - 0
    - a^3
    - a^42
    - 0
    - a^12
    - a^10
    - 0
    - a^56
    - a^46
    - 0
    - a^57
    - a^31
    - 0
    - a^45
    - a^52
    - 0
    - a^29
    - 0
    - 0
    - a^37
    - a^23
    - 0
    - a^48
    - a^2
    - 0
    - a^53
    - a^17
    - 0
    - a^55
    - a^39
    - 0
    - a^7
    - a^13
    - 0
    - a^30
    - a^54
    - 0
    - a^6
    - a^51
    - 0
    - a^33
    - a^18
    - 0
    - a^20
    - a^11
    - 0
    - a^50
    - a^50
    - 0
    - a^11
    - a^20
    - 0
    - a^18
    - a^33
    - 0
    - a^51
    - a^6
    - 0
    - a^54
    euler_factors:
    - - 1
      - a^8
    - - 0
    - - 1
      - a^19
    - - 1
      - a^28
    - - 1
      - a^26
    - - 1
      - a^41
    - - 1
      - a^1
    - - 1
      - a^14
    - - 1
      - a^4
    - - 1
      - a^21
    - - 1
      - a^15
    - - 1
      - a^5
    - - 1
      - a^25
    - - 1
      - a^3
    - - 1
      - a^10
    - - 1
      - a^31
    - - 0
    - - 1
      - a^37
    - - 1
      - a^53
    - - 1
      - a^39
    - - 1
      - a^7
    - - 1
      - a^6
    - - 1
      - a^18
    - - 1
      - a^50
    - - 1
      - a^51
    - - 1
      - a^30
    gamma_factors:
    - - 0
    - []
    id: 5813
    index: 0
    label: 1-177-177.98-r0-0-0
    leading_term: 0.0664732746907484043511347647163+0.960467254773234094782831820876*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/177/98
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
    plot_values:
    - 0.9627647914936153
    - 1.692817652639028
    - 2.8685657934818884
    - 4.180085909681065
    - 5.180127155859415
    - 5.471295515237143
    - 4.860527662765697
    - 3.471502945615841
    - 1.7443076186597464
    - 0.28595987997806616
    - -0.3886367878961534
    - -0.1106076299231864
    - 0.8340966559890302
    - 1.8263728228979583
    - 2.231287485831526
    - 1.7521857258260969
    - 0.6145945497258304
    - -0.5515043074308681
    - -1.0884928103824494
    - -0.7302418152270984
    - 0.20922638352444764
    - 1.028639701565755
    - 1.1203751309307357
    - 0.43060108725824026
    - -0.4370041583287468
    - -0.5982003368243584
    - 0.46394036673350825
    - 2.4207705799533255
    - 4.170933269485749
    - 4.496114600410125
    - 2.907242118029492
    - 0.09492475714225794
    - -2.3892916248632643
    - -3.0804154136984403
    - -1.5670324318547506
    - 1.2005190256216085
    - 3.5162743726742924
    - 4.0507033434927875
    - 2.720986985430388
    - 0.6757036969661292
    - -0.5921653171586445
    - -0.3410564021217997
    - 0.9370828303033513
    - 1.9978060752089994
    - 1.8838662942793811
    - 0.6791803212740468
    - -0.628020316971655
    - -1.0374578963219545
    - -0.4113328375005086
    - 0.43312642696044223
    - 0.5051205263172949
    - -0.3907791364282644
    - -1.387949011489835
    - -1.2952294362131946
    - 0.2636186638707482
    - 2.3375634051283356
    - 3.314889930190592
    - 2.2940672494878727
    - -0.009328607813068351
    - -1.6902536557221497
    - -1.1776544435037508
    - 1.3802710621008654
    - 4.0853220953537015
    - 4.737812290217348
    - 2.6172733141706805
    - -0.8925739118563136
    - -3.3859439770686106
    - -3.332890725502276
    - -1.204494194114063
    - 1.08674765854161
    - 1.8760172527898793
    - 1.0524035169791395
    - -0.12274466587108122
    - -0.40104483790697787
    - 0.2345702293891116
    - 0.6675585028399715
    - -0.09501583218187414
    - -1.7970638511370798
    - -3.093884662586576
    - -2.865630737153798
    - -1.371360754533488
    - -0.044781833962998306
    - -0.0739853494724468
    - -1.1711858955340206
    - -1.8316152038644753
    - -0.9275645443115845
    - 0.9210241948934
    - 1.674258072006654
    - -0.22949018244918848
    - -4.149209269309611
    - -7.438029901751422
    - -7.573795406223729
    - -4.362526630584287
    - -0.17233278417848913
    - 2.074255286063439
    - 1.3391295552467832
    - -0.8684527478766746
    - -2.1207797900474628
    - -1.3544398553411097
    - 0.3646406971347311
    - 1.189798429596554
    - 0.46168025555663356
    - -0.7193276803791799
    - -0.8066333050200679
    - 0.46871836371554226
    - 1.8140555962982465
    - 1.8029993055813138
    - 0.4425524575836587
    - -0.8373804303616572
    - -0.7682372541527185
    - 0.345096571862921
    - 0.9859017436810872
    - 0.2263856768198092
    - -1.02751969704747
    - -0.8630771406499
    - 1.4504991987366957
    - 4.24706687809261
    - 4.737940272771797
    - 1.7274111660953015
    - -2.9390802400709153
    - -5.810062050850117
    - -4.899674549387462
    - -1.429276237563091
    - 1.4672772399205574
    - 1.7617259373135545
    - 0.2652637570535573
    - -0.5537839541242601
    - 0.7037209932105629
    - 2.970452709487833
    - 3.993258193088827
    - 2.777029176716546
    - 0.5402378615700087
    - -0.7308967322788914
    - -0.40354120234145124
    - 0.3677362610731238
    - 0.2527559215568374
    - -0.5757966700376751
    - -0.6962280884346282
    - 0.6825358602101577
    - 2.4915959905162404
    - 2.8151028642864158
    - 1.111160943059489
    - -0.9490970350851784
    - -1.1917914382746153
    - 0.557282346994558
    - 2.0397084262732195
    - 0.9230302672805858
    - -2.4781341264207732
    - -5.1709260283293474
    - -4.4150861984632765
    - -0.6275298431988287
    - 2.8595126062446456
    - 3.037251859005316
    - 0.11802350943667764
    - -2.88193194031939
    - -3.3131071953012645
    - -1.3978280752442018
    - 0.45485746932454546
    - 0.49244529174475776
    - -0.643142885451621
    - -1.0590297864047258
    - -0.04695895989875762
    - 1.1309654981305046
    - 0.9309908100548796
    - -0.4775093412669426
    - -1.3929735361940434
    - -0.7224664156274606
    - 0.5733639549391615
    - 0.5928208342247208
    - -1.1028710731511997
    - -2.750569107351823
    - -2.371939382059674
    - -0.21419377459689795
    - 1.3759653102205038
    - 0.739467106897423
    - -0.8343913119505972
    - -0.23244479770343046
    - 3.9241440495924786
    - 9.229241838473747
    - 11.473311757614592
    - 8.759479612820678
    - 3.387914245232838
    - -0.5002755757910105
    - -0.9338816342628732
    - 0.4862730815866264
    - 0.9955523746236348
    - -0.13766352506439875
    - -1.2328250381661252
    - -0.7123839352839197
    - 0.7733373916652357
    - 1.1812586037801798
    - -0.3028560209371317
    - -2.1852688802235445
    - -2.4609484604465575
    - -1.0183795870181813
    - 0.3460164329940467
    - 0.2744745831540904
    - -0.4645678197279771
    - -0.1401560120249927
    - 1.4050490731916896
    - 2.2222896454602825
    - 0.6919395780162471
    - -1.9817916254966148
    - -2.5688029300825224
    - 0.5830695146518421
    - 5.246413606911457
    - 7.276894077164194
    - 4.939077183429153
    - 0.7811049134422039
    - -1.1275324099360164
    - 0.47432253126638113
    - 2.975566498288237
    - 3.122731384840484
    - 0.6735087419069612
    - -1.6675965160510247
    - -1.648245487696352
    - 0.010628158478025042
    - 0.8371368201400939
    - -0.2198771676053359
    - -1.6703745266458183
    - -1.6192139807018742
    - -0.24531467164831017
    - 0.5553600517013082
    - -0.23551534230402715
    - -1.4188631629763042
    - -1.277390963025663
    - -0.030182544630236344
    - 0.3342338133462738
    - -1.1932491039432467
    - -2.9130569692045425
    - -2.261593657592051
    - 0.7973174713902261
    - 3.1757855986144756
    - 2.021692077699597
    - -1.7875594004330186
    - -4.3644766912015704
    - -3.1831072953842243
    - -0.03257018140375423
    - 1.0177905587968128
    - -1.6701097046456768
    - -5.428072423323717
    - -6.377228245708835
    - -3.7542793573870425
    - -0.44258926475589927
    - 0.605190247985011
    - -0.4557818494691492
    - -1.2193239735140269
    - -0.37565527981535335
    - 0.860998991276773
    - 0.8082807946374131
    - -0.1980482869905297
    - -0.31075802069107994
    - 1.0912541872028911
    - 2.277482973447374
    - 1.3465896121255825
    - -1.1163689862245232
    - -2.5488918803942284
    - -1.5954488293844973
    - 0.20075965645774657
    - 0.5734369314607646
    - -0.1885706152708033
    - 0.6412411214584574
    - 4.46797150747251
    - 8.69798461288781
    - 8.975282615859427
    - 4.129493983480959
    - -2.0626151635297703
    - -4.6766581989549065
    - -2.7375948101199823
    - 0.23626646654842756
    - 0.624907513021981
    - -1.3691387277924476
    - -2.724206067378373
    - -1.7499413630304903
    - 0.010773026408528416
    - 0.21123184059812228
    - -1.1029187687885185
    - -1.7725399281745513
    - -0.6580284239331333
    - 0.7656640307876841
    - 0.4914993546807699
    - -1.1914914230479456
    - -2.045646620959461
    - -0.9364878663794012
    - 0.6387092625628309
    - 0.7111729184336955
    - -0.28528028164346364
    - -0.05225710915322835
    - 2.1305962836304375
    - 3.818353937329783
    - 2.301597300850955
    - -1.43505425760451
    - -3.077139590404446
    - 0.14920928881471823
    - 5.864959671295097
    - 8.830466985782069
    - 6.649967658349302
    - 2.1440352089966064
    - -0.27765022490072533
    - 0.3927182733591439
    - 1.4023848664286283
    - 0.4184872568681991
    - -1.4306195257654162
    - -1.3995683484650936
    - 0.9600318355817681
    - 3.122174041385586
    - 2.8686302385648363
    - 0.9863195315651897
    - -0.11627196315503553
    - 0.2912335060497814
    - 0.6521002254327584
    - -0.17199643776080392
    - -0.9766400988676024
    - 0.0078314344211192
    - 2.1434961118657143
    - 2.707519970845856
    - 0.507444354762777
    - -2.1010646553262697
    - -1.9538058779023908
    - 0.6952339777532288
    - 2.1736216345841246
    - 0.04733345098411729
    - -3.4475060048777046
    - -3.885613566244995
    - -0.19074695571600067
    - 3.7734255631335594
    - 3.7173193959725026
    - -0.030744970354598975
    - -3.1621618610135487
    - -2.6748534229081677
    - -0.07478742830436283
    - 1.1829583872177714
    - 0.19706518860128341
    - -0.8046744279079345
    - -0.021015431655604704
    - 1.4590802813066506
    - 1.5198303353814826
    - 0.21890000906252471
    - -0.35881194061177657
    - 0.711476931823991
    - 1.7001697715518573
    - 0.7054459876532715
    - -1.425899311718849
    - -2.088247333498401
    - -0.6245562939427904
    - 0.5423960271620134
    - -0.7435956890772971
    - -3.0690576970854204
    - -3.069522564807401
    - -0.1730247887032444
    - 2.025921768687032
    - 0.1513060347309026
    - -4.237475895130584
    - -5.975669932166872
    - -2.414109884858314
    - 3.270298179095063
    - 5.757314966814302
    - 3.6102034230479894
    - 0.25457846048890664
    - -0.7540134940894494
    - 0.2878808789474017
    - 0.7711937628844532
    - -0.06357097126911496
    - -0.3260299107709552
    - 1.2405974324959967
    - 3.000596355226395
    - 2.571191895061906
    - 0.2435694369883934
    - -1.3147126378548324
    - -0.6917457495565166
    - 0.5009136969849124
    - 0.21010133396370478
    - -0.983299605691411
    - -0.9000524060006405
    - 0.5677520222937784
    - 0.7790210732827603
    - -1.8135503899286878
    - -4.600520565638129
    - -3.452480520155966
    - 1.7591238748401585
    - 6.139905097695407
    - 5.221760548580278
    - 0.2679541930173784
    - -3.3355487173541176
    - -2.5535230066450065
    - 0.1912838320524608
    - 0.8799247120809972
    - -0.7881824138779296
    - -1.584542747581959
    - 0.37244736327380085
    - 3.011020286264576
    - 3.3044752460252256
    - 1.3400096346072559
    - -0.18868465218137126
    - 0.04596270979758562
    - 0.43229979529482665
    - -0.7182720129311833
    - -2.378476396662298
    - -2.2955215453919506
    - -0.46104947922462214
    - 0.7702933588425606
    - 0.23284806018729004
    - -0.18361633303936775
    - 1.5415249861185172
    - 3.947119470247216
    - 3.4487151368618276
    - -0.6038173118595337
    - -4.225207143323094
    - -3.4549909302192363
    - 0.4469858143933451
    - 2.374613254909976
    - -0.16068095019707607
    - -3.912989147188692
    - -4.238102159395824
    - -1.079477892473934
    - 1.2605611129922687
    - -0.050060672595262236
    - -2.902435711850898
    - -3.471144449806017
    - -1.2903018768906562
    - 0.6849174563627155
    - 0.49706604225154966
    - -0.4604705842378718
    - -0.11826916032844312
    - 1.0321900653434015
    - 1.0146910762625392
    - -0.1662462307698278
    - -0.24360556302740521
    - 1.7736272665261308
    - 3.641242725708822
    - 2.8024804358585893
    - 0.14933250964106523
    - -1.0349031335013763
    - 0.3066477329193299
    - 1.56094342414004
    - 0.5686003602103613
    - -0.5840900700990155
    - 1.9244569945915713
    - 7.767906911997374
    - 11.553810009168476
    - 8.938593297544664
    - 2.1103301272182033
    - -2.644842531682391
    - -2.2433433536230583
    - 0.35924474894679687
    - 0.8980809147709524
    - -0.7748889512354407
    - -1.5868870682333425
    - -0.27082413998166244
    - 0.9832777044729282
    - 0.17550228226814837
    - -1.41384673353182
    - -1.2795865061347278
    - 0.4314315859144573
    - 1.1593071920444884
    - -0.14544849810682126
    - -1.4400173580276532
    - -0.7691860355334793
    - 0.679051776532171
    - 0.40913864787869114
    - -1.38675509294901
    - -1.930171743449652
    - -0.21573835684188927
    - 0.9992574901574474
    - -0.8437703093533178
    - -3.6017989731261615
    - -2.424651532086641
    - 3.6456250341921765
    - 9.452187875020172
    - 9.516323353960068
    - 4.58172972527895
    - 0.3705424209351488
    - 0.3796904367598896
    - 2.2939022387963073
    - 2.18697763575454
    - 0.029196964651117548
    - -1.0300629297226265
    - 0.21587472290235424
    - 1.3092629215988885
    - 0.03908904656224084
    - -2.158109791416316
    - -2.348429475480999
    - -0.3892935693703185
    - 1.0604504009855962
    - 0.562117488115067
    - -0.3007074815462575
    - 0.09967922513842084
    - 0.6405544358201367
    - -0.5301460965349962
    - -2.291805337579674
    - -1.42009513309037
    - 2.546653023698466
    - 5.69957946874178
    - 4.5790801212562755
    - 1.0429554595152428
    - -0.023132349948752347
    - 2.5602743415994196
    - 4.477478792053283
    - 1.8649461020895248
    - -3.129790904945216
    - -4.9665516804969725
    - -1.9587235387913429
    - 1.7653887221136297
    - 1.9880106669290953
    - -0.3413140339312244
    - -1.251699070106831
    - 0.4452172905415095
    - 2.0516811076321693
    - 1.4574241801498848
    - 0.07700694956133715
    - 0.16195236520821749
    - 1.1556936340014778
    - 0.8395702567935994
    - -0.7771670402869679
    - -1.2067002893189887
    - 0.5678540397147936
    - 2.195806811098818
    - 1.376748853360335
    - -0.5267650182591526
    - -0.48074066205173455
    - 1.3725331253205866
    - 1.5740008017456617
    - -1.328597265384203
    - -3.865126345944911
    - -2.1132141934496853
    - 2.373042176634718
    - 3.970430243565937
    - 0.4176658755395256
    - -3.912374613509343
    - -3.6485364199374253
    - 0.6374235455541375
    - 3.533865778613835
    - 2.0313450233328996
    - -1.1545873346021303
    - -2.0678265258708093
    - -0.7111583660344117
    - 0.16870594890767449
    - -0.14909945331467594
    - 0.3590234460754491
    - 2.500017277608364
    - 3.9577199815465387
    - 2.664246945644038
    - 0.14362010014325727
    - -0.5655881250971151
    - 0.6711146309260696
    - 1.1435806724623776
    - -0.2979682794931062
    - -1.4758289890818397
    - -0.6211954231138511
    - 0.4022858260912015
    - -1.0105550849458824
    - -3.2717665795974753
    - -1.7517668068535597
    - 4.519195909832508
    - 10.118357276968037
    - 9.2934450629768
    - 3.180453763504234
    - -1.6643778869901629
    - -1.4757346669957296
    - 0.8594691560268006
    - 0.9259022266094539
    - -1.0190461483543696
    - -1.35832461852703
    - 0.8883059434995388
    - 2.615146261228499
    - 1.4771304148823854
    - -0.6726284628915937
    - -0.8074955281070624
    - 0.7632740242327092
    - 1.2763092131663
    - 0.006081274744042888
    - -0.847909368845488
    - -0.04342379836364436
    - 0.5599708163589465
    - -0.8149667765303543
    - -2.5580643462645156
    - -1.934238133711238
    - 0.3599594431882515
    - 0.8403991376220189
    - -1.2557523355404763
    - -2.0686236000581086
    - 1.447903054840676
    - 6.314070636300794
    - 6.711144640829178
    - 1.7796513718462088
    - -2.9438618031567856
    - -2.7493653669385663
    - 0.37085278020675333
    - 1.2053313215416845
    - -1.2126290889397244
    - -2.8172789799117592
    - -0.9104816610590774
    - 1.988712642123362
    - 2.13493041907403
    - -0.07809475616795314
    - -1.2474801390338515
    - -0.21135272802064559
    - 0.7738639528646877
    - 0.14236418572463289
    - -0.5910436358067495
    - 0.15354854452188432
    - 0.938045834843569
    - -0.43997836321275924
    - -2.896340203060044
    - -3.1203259574426636
    - -0.6176454485039814
    - 1.1967123559450585
    - 0.056510350313401146
    - -1.5683149289126965
    - -0.24346399061187624
    - 2.7804203311344957
    - 3.0308372452988914
    - -0.17189569331268706
    - -1.712826565446692
    - 2.5010365086266813
    - 9.257555975804834
    - 11.538602666809293
    - 7.289637864883061
    - 1.497456133157676
    - -0.7401222126814291
    - -0.03574919314563792
    - 0.0431739313090264
    - -1.0750242790838973
    - -0.8906888720576245
    - 1.257397931891066
    - 2.6942379628539466
    - 1.608825890335576
    - -0.059722591290770066
    - 0.24449673489873225
    - 1.6521581071615565
    - 1.4510108750797135
    - -0.3406629928900343
    - -0.9347601110398044
    - 0.5795163019379463
    - 1.5404608433998805
    - 0.008364643016848519
    - -1.8310167463446376
    - -1.107346080934915
    - 0.5184622128828439
    - -1.3796737717670136
    - -6.937662027214239
    positive_zeros:
    - '2.90095280743092263935957442628'
    - '3.48391634056884322401427145349'
    - '5.153444295481801117600313697592'
    - '6.18554758344366703701453082091'
    - '7.33112482630818331423548621735'
    - '8.026927905284433854773445874218'
    - '9.69761988194653919121364475962'
    - '10.80731687269709927335542243270'
    - '12.314095982053233688306614883699'
    - '12.91006617840314338960282505618'
    - '14.210368649395517281369552064846'
    - '15.13741280915531115919357221127'
    - '15.82711174964999509767226533832'
    - '16.83439859315335814976439095226'
    - '18.12375547809218371048219544791'
    - '18.913914106051239167961426595144'
    - '20.23289916503402475873682290100'
    - '21.39945234826487790857040393564'
    - '22.458333131009433295776109175122'
    - '23.02996409919370874110265686303'
    - '23.72815905580367404244279116021'
    - '25.33258355172385618379831214112'
    - '25.5912340126731173993432284484'
    - '26.72026611461165497397381765686'
    - '27.47723653904618597681162708590'
    - '29.077627051299267788827999554826'
    - '29.87862879809869130881340726773'
    - '30.867731721928888910337724366418'
    - '31.674324101030853763988218629687'
    - '32.40624342760991182373520420770'
    - '33.52541204269631128613705868229'
    - '34.2851058901442657162500452822'
    - '35.05252655768371034367356025928'
    - '35.77127025783463443248810876181'
    - '36.99158039388855914979698326500'
    - '38.25316579733538027868516183090'
    - '39.118330103456791036158065369147'
    - '39.56905150774771019407424120321'
    - '41.02908830986369799974814975658'
    - '41.70708218594903724076382529891'
    - '42.2903938014139702388929298444'
    - '43.00422594317856313850213592691'
    - '44.21419914925741258987934075753'
    - '44.91731328411969929236617503971'
    - '45.72262001123846788971442881214'
    - '46.92105405138924494664641672640'
    - '47.82287666660900775222934051601'
    - '48.95892629078636675518369286059'
    - '49.519066724697242632782105776175'
    - '50.32286450021949082967641086067'
    - '51.1524390093758182383410901307'
    - '52.037282228712726028970187116060'
    - '52.63619988396803513175075322440'
    - '53.77926235319768834702454028717'
    - '54.50964607128003253994679554606'
    - '55.02759028324895356295110817833'
    - '56.8134311294249958856298141909'
    - '57.39675024235238806230417252607'
    - '58.096140324969534474011474179961'
    - '58.89937251696351382381082243276'
    - '59.64083916864652837267689202340'
    - '60.82777109182610769362718813537'
    - '61.35827686299984231326251303282'
    - '61.91133273447302204154928907904'
    - '62.89241794809872055182166385607'
    - '63.70907227699715158321952850885'
    - '65.07485982191561695885614767393'
    - '65.56761529263428519319900822807'
    - '66.63528283323281520566371831708'
    - '67.49797053782678300592452418567'
    - '68.08221604132015219204787064609'
    - '69.119266632672386946831947341728'
    - '69.62974572728997336554210943903'
    - '70.633214035964089968830840278791'
    - '71.04287299192079835570779099551'
    - '72.11446730981068806749097992490'
    - '72.98686125012799724208769003142'
    - '74.06625723305751787242658058048'
    - '74.537763354841160918432216946583'
    - '76.00066335524190774572843403347'
    - '76.4568526166475745447704585852'
    - '77.27009715426776573818809617225'
    - '78.05982479537260978604094633320'
    - '78.53323043999554661295277348590'
    - '79.55048477751864677889186867078'
    - '80.58138847967457239303812981921'
    - '81.16077979301901449982918041455'
    - '81.45163398751165684333228754863'
    - '83.01087657939998828135365730688'
    - '84.02868535630503150931101337293'
    - '84.49458006513771927704308798785'
    - '85.62229945880049621588976618877'
    - '86.00394620378069144198252928039'
    - '86.99746410874856438607943288025'
    - '87.602605868428343926251678217268'
    - '88.60358375098306235193082326860'
    - '89.27891005912093177980624407676'
    - '89.69901613684472976512214752464'
    - '90.818697977077451665720030825144'
    - '91.55360920860027391383584728193'
    - '93.04552356512586652488068343737'
    - '93.34546454993403980989134376046'
    - '94.129113272392666641488017279215'
    - '94.89160907518721264874319392679'
    - '96.17021244325149601493262533070'
    - '96.42714733944843492445756649583'
    - '97.14140274379825405883943650171'
    - '97.81123027618439583501132498879'
    - '98.80201691854618294891473182243'
    - '99.61186073092313675264390389233'
    - '100.316656206687501919529857685969'
    - '101.26259686930371959965079796208'
    - '102.18523679515869349974981511781'
    - '103.13481635144873132442360639636'
    - '103.79213165416574700591049271832'
    - '104.379294226176829008982809166795'
    - '105.368718655666050797624475213921'
    - '105.77324336898363705310419107995'
    - '106.66594738659762233647677289498'
    - '107.61328187323774411611200942473'
    - '108.01191195112428015679693524145'
    - '109.07878982070349622266298705179'
    - '109.69957783507368793311028468389'
    - '110.75374166953239472108768826979'
    - '111.9088550244248591625042789629'
    - '112.42654255513437527213523118316'
    - '113.10446042634826953582452538754'
    - '113.53784261485715103738808456723'
    - '114.71972805694810782906119446197'
    - '115.46865479961442399869535184771'
    - '115.99354480309606087191531267825'
    - '116.758980930253850201007946682467'
    - '117.315842280700855980729761067'
    - '118.34360447057755132310362887293'
    - '119.39124109648884277138854245677'
    - '120.28640824177350596092609622324'
    - '120.80991919794204586531502548221'
    - '121.52140161369510331392550312540'
    - '122.74114634497466445798920090361'
    - '123.10504099641761570652851858226'
    - '123.60740225313304383636116595805'
    - '124.76566631178692304767670081854'
    - '125.39190664202570530260845270898'
    - '125.69434853172892189508368984211'
    - '126.8352011646986025323947598044'
    - '127.77657393137514593628582720378'
    - '128.42499285604168249671224551007'
    - '129.47680472055921280757518572023'
    - '129.994331745411099130776830782577'
    - '131.10565082922576823152405633659'
    - '131.703841213338662802228429664143'
    - '132.22062264134390272551026554250'
    - '133.07864773881414852571579096144'
    - '133.49544647171437913257653734725'
    - '134.707149563974688457493975616406'
    - '135.26162013752713227208531259280'
    - '136.03975232230398540112429782199'
    - '136.39555602687154421820152859270'
    - '137.917397072926849723374449440197'
    - '138.69954711915886206763337753278'
    - '139.24624476361333674657922578980'
    - '140.047467185584522925472822148293'
    - '140.657172883666803710863479380089'
    - '141.48623278928019668367878583240'
    - '142.1620565810893442319117054422'
    - '142.961539517431484607295586526162'
    - '143.51778188867549455601370972084'
    - '144.40740364275555590031622799347'
    - '144.906888060581469524760334244857'
    - '145.770533798302450366360559083865'
    - '147.25865186908614334599081887804'
    - '147.41349267567959440980148529723'
    - '148.44178508146093774739729614615'
    - '149.02378354285843248865832624248'
    - '149.69288619939198089402576554738'
    - '150.68254395791108834321488933201'
    - '151.414256010459865697861570007505'
    - '151.83816740059564406449319358651'
    - '152.40793939404422826876537020783'
    - '153.254386727864317891646290024317'
    - '154.52456845613340480924799671485'
    - '154.69374103225660666022460213344'
    - '155.74047519832388108710051046561'
    - '156.70571905650480923570491600616'
    - '157.45411915855275054177956863548'
    - '158.062517418302769565101132265452'
    - '159.09423842545879747112129475488'
    - '159.30929783538756378992682184488'
    - '160.16672356710014936789417904063'
    - '160.858456619660882971163918331342'
    - '161.77346884865370066664928230342'
    - '162.27879639092976393372558757319'
    - '163.0068123225635459217999475946'
    - '163.898126147127448914757008295956'
    - '164.71319565231994369650697920341'
    - '165.58202420513070722043300859862'
    - '166.43883122312317481736159992777'
    - '167.3726911309643956496015473586'
    - '167.698352561925694817842552526321'
    - '168.02942958050285502976176509835'
    - '169.39853536749591244510248450363'
    - '169.853356811022490584111639797722'
    - '170.5740805483816758306770042565'
    - '171.38419107004615677063802096286'
    - '171.72466783854850244175507874409'
    - '172.60560738558473127939839165816'
    - '173.91930435528228532321292138062'
    - '174.560908007021461312593980895988'
    - '175.15425082050942878375211123491'
    - '175.83345690689123985877094979158'
    - '176.7605519771138894817777864018'
    - '177.35589139541230982959080931453'
    - '178.12626276231542413860861194322'
    - '178.76158136705842631427851453301'
    - '179.23980581415614827605457694711'
    - '180.25877166567948279122694096240'
    - '180.77370586667946919324169162152'
    - '181.46915211767781462492018712155'
    - '182.59531869487930753282919832646'
    - '183.39687211723248030523975387696'
    - '183.93035995519904061895738228180'
    - '184.775066597643665938205855344361'
    - '185.61415869478388791558630594838'
    - '186.29473023879849398475795209425'
    - '186.91536571400571342513897105836'
    - '187.46050883187038058776373127804'
    - '188.06488218846872205883007950931'
    - '189.1334328363467937656577673250'
    - '189.69584090413993533069688546781'
    - '190.33841083926743194509970135974'
    - '191.23463671043788667658457075895'
    - '191.7398776403507288816963120873'
    - '193.25861950816814671931704836343'
    - '193.763015424248039034819331965725'
    - '194.07833178997033967696317046695'
    - '194.8355402777239294659787171476'
    - '195.918013097891397074975898931044'
    - '196.18382177575987832141877849873'
    - '197.12773294977232574825445170954'
    - '197.71490817267735510833562670174'
    - '198.43862295498247300440829775974'
    - '199.23859539314916530159182199883'
    - '199.559366477262067401811534961294'
    prelabel: 1-177-177.98-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.8219845443046324
    root_angle: 0.9560101322933612
    root_number: -0.990465811271786863099053900317+0.137758762703942312117672532643*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '0.478005066147'
      prec: 47
    spectral_label: r0-0
    st_group: mu(58)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.723509836046866305986002863344+0.736146085655739637779545870670*I
    z1:
      __RealLiteral__: 0
      data: '2.90095280743'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '3.48391634057'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '5.15344429548'
      prec: 44
- - algebraic: true
    analytic_conductor: 0.8219845443046324
    bad_primes:
    - 3
    - 59
    central_character: '177.98'
    conductor: 177
    conductor_radical: 177
    degree: 1
    id: 5813
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/177/98
    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: 1-177-177.98-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: 1-177-177.98-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.8219845443046324
    root_angle: 0.4780050661466806
    self_dual: false
    spectral_label: r0-0
    z1:
      __RealLiteral__: 0
      data: '2.90095280743'
      prec: 44
- - Lhash: dirichlet_L_177.98
    Lhash_array:
    - dirichlet_L_177.98
    id: 1787203
    label: 1-177-177.98-r0-0-0
    type: DIR
    url: Character/Dirichlet/177/98
label_cols:
- label
- label
- label
labels:
- 1-177-177.98-r0-0-0
- 1-177-177.98-r0-0-0
- 1-177-177.98-r0-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-05-12T01:19:24.404676'