data:
- - Lhash: dirichlet_L_1045.504
    a10:
    - 1.0
    - -2.8163065144692913e-30
    a2:
    - 0.9612616959383189
    - 0.27563735581699916
    a3:
    - -0.882947592858927
    - -0.46947156278589075
    a4:
    - 0.848048096156426
    - 0.5299192642332049
    a5:
    - 1.0
    - -2.8163065144692913e-30
    a6:
    - -0.7193398003386512
    - -0.6946583704589973
    a7:
    - -0.6691306063588582
    - 0.7431448254773942
    a8:
    - 0.6691306063588582
    - 0.7431448254773942
    a9:
    - 0.5591929034707468
    - 0.8290375725550417
    algebraic: true
    analytic_conductor: 112.30084641038314
    analytic_normalization: 0
    bad_lfactors:
    - - 5
      - - 1
    - - 11
      - - 1
    - - 19
      - - 1
    bad_primes:
    - 5
    - 11
    - 19
    central_character: '1045.504'
    coeff_info:
    - x^90 - 1
    - 0.997564050259824 + 0.0697564737441253*I
    - \\zeta_{90}
    conductor: 1045
    conductor_radical: 1045
    conjugate: dirichlet_L_1045.819
    degree: 1
    dirichlet_coefficients:
    - a^0
    - a^4
    - a^52
    - a^8
    - 0
    - a^56
    - a^33
    - a^12
    - a^14
    - 0
    - 0
    - a^60
    - a^74
    - a^37
    - 0
    - a^16
    - a^31
    - a^18
    - 0
    - 0
    - a^85
    - 0
    - a^35
    - a^64
    - 0
    - a^78
    - a^66
    - a^41
    - a^23
    - 0
    - a^69
    - a^20
    - 0
    - a^35
    - 0
    - a^22
    - a^18
    - 0
    - a^36
    - 0
    - a^7
    - a^89
    - a^55
    - 0
    - 0
    - a^39
    - a^77
    - a^68
    - a^66
    - 0
    - a^83
    - a^82
    - a^44
    - a^70
    - 0
    - a^45
    - 0
    - a^27
    - a^13
    - 0
    - a^26
    - a^73
    - a^47
    - a^24
    - 0
    - 0
    - a^50
    - a^39
    - a^87
    - 0
    - a^1
    - a^26
    - a^43
    - a^22
    - 0
    - 0
    - 0
    - a^40
    - a^79
    - 0
    - a^28
    - a^11
    - a^51
    - a^3
    - 0
    - a^59
    - a^75
    - 0
    - a^65
    - 0
    - a^17
    - a^43
    - a^31
    - a^81
    - 0
    - a^72
    - a^4
    - a^70
    - 0
    - 0
    euler_factors:
    - - 1
      - a^4
    - - 1
      - a^52
    - - 0
    - - 1
      - a^33
    - - 0
    - - 1
      - a^74
    - - 1
      - a^31
    - - 0
    - - 1
      - a^35
    - - 1
      - a^23
    - - 1
      - a^69
    - - 1
      - a^18
    - - 1
      - a^7
    - - 1
      - a^55
    - - 1
      - a^77
    - - 1
      - a^44
    - - 1
      - a^13
    - - 1
      - a^26
    - - 1
      - a^50
    - - 1
      - a^1
    - - 1
      - a^43
    - - 1
      - a^79
    - - 1
      - a^51
    - - 1
      - a^65
    - - 1
      - a^4
    - - 1
      - a^74
    gamma_factors:
    - - 1
    - []
    id: 201815
    index: 0
    label: 1-1045-1045.504-r1-0-0
    leading_term: -0.0770456033394596754313917223270+0.736177545154530818208407029253*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/1045/504
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
    plot_values:
    - -0.7401982187115105
    - -2.587113515783261
    - -3.652770913482094
    - -3.3073914429266953
    - -1.5697382555421477
    - 0.6741479983518484
    - 2.0672366985867177
    - 1.714320414564146
    - -0.04192385791556841
    - -1.7571576070726196
    - -1.995840068784744
    - -0.5559392182824242
    - 1.3113589741291674
    - 1.9952678129850365
    - 0.9910532043466374
    - -0.665811448696552
    - -1.4673661894904297
    - -0.9481051644931422
    - -0.056956210336959245
    - 0.03796898840443301
    - -0.6146052300225893
    - -0.7836211995937808
    - 0.3388201432621617
    - 1.8110918632417168
    - 1.7059674593330596
    - -0.5404149514918768
    - -2.8328963025502185
    - -2.0886734762983443
    - 2.4351689332613873
    - 7.7188218367759465
    - 9.427969059077656
    - 6.0710615277181645
    - 0.5509144377897637
    - -2.6686408181430035
    - -1.8596585242048143
    - 0.7403024006481758
    - 1.8560480417409553
    - 0.731783923895424
    - -0.6558922508591338
    - -0.5250005317106579
    - 0.5389258777867867
    - 0.7841430799598612
    - -0.011719991016777578
    - -0.13635629344560704
    - 1.553647555596609
    - 3.6611767924322716
    - 3.714421441946137
    - 1.366129717742453
    - -0.9421784439703453
    - -0.9604368198657919
    - 0.5489518617551908
    - 0.9568281725855515
    - -0.553372845807516
    - -1.7785227503472307
    - -0.5887360646243118
    - 1.8119185337247807
    - 2.16546529324876
    - -0.3659697854040014
    - -2.584828921783935
    - -1.1522654383543598
    - 2.816273655454351
    - 4.713083048085901
    - 2.158381614095419
    - -1.8023594089423445
    - -2.3404867006099757
    - 1.2073362743840395
    - 4.668179146974063
    - 4.324166911740462
    - 1.187199800640997
    - -0.980696779713172
    - -0.6585441314521573
    - 0.22288276176933325
    - -0.1967232810287517
    - -1.0500131445364287
    - -0.6215293644401263
    - 0.612819856023526
    - 0.6992961575021217
    - -0.5016596676606315
    - -0.8479011865975102
    - 0.6688415060526245
    - 1.9641473576546566
    - 0.9579471799834043
    - -0.5940373767014002
    - 1.1072057312439567
    - 6.082335361672492
    - 9.088528379475814
    - 5.6881882270430655
    - -1.6834180561229743
    - -6.127842173913801
    - -4.471053793732517
    - -0.5491727527228789
    - 0.4434555929844517
    - -1.516271027729176
    - -2.5068786457856786
    - -0.931228450634991
    - 0.5732096845031015
    - -0.23382095042883816
    - -1.6357257842798452
    - -0.8850455890072931
    - 1.25300753477154
    - 1.5982671238504107
    - -0.4217368852572408
    - -1.7508272461224956
    - -0.3559549481485893
    - 1.6885995242503835
    - 1.491178358853423
    - -0.18829985308387537
    - -0.30793866333552233
    - 1.5144886189410773
    - 2.4304146971526004
    - 1.0319609849792546
    - -0.43016695866440224
    - -0.048797004259818144
    - 0.18583080015129366
    - -2.2276882510015525
    - -4.901873702765887
    - -2.573051189034006
    - 4.9635046026469425
    - 10.723860346410689
    - 8.70840440718177
    - 1.686591794991429
    - -2.4066152800646954
    - -0.552820364410457
    - 2.6413871365160144
    - 2.4064166896378802
    - -0.043820613782609576
    - -0.8094385869882802
    - 0.4161812506440853
    - 0.7924905352616436
    - -0.45053696489981654
    - -1.0575902058733004
    - -0.03548164841130055
    - 0.6508283780701972
    - -0.20674688872744387
    - -0.7913096419889492
    - 0.22790056932707292
    - 0.5713390644930525
    - -2.161091340924168
    - -5.584517056062614
    - -5.029986927397757
    - -0.6368863292576855
    - 2.2146620888660102
    - 0.6896340805577299
    - -1.2979624551924935
    - 0.6467166890945987
    - 4.226675353141593
    - 3.8009345815323465
    - -0.7455478153748033
    - -3.5082273109019777
    - -1.3062140330001892
    - 1.9158032638132823
    - 1.5400839301540945
    - -0.9749739897410807
    - -1.4123570372183223
    - -0.016407836010813304
    - -0.6558734850325534
    - -3.7754044340352664
    - -5.171774390236719
    - -2.653453538104843
    - 0.46319167169243164
    - 0.6112475757784619
    - -0.8521832749697488
    - -0.6922801184052922
    - 0.7497621855863696
    - 0.8641032943935599
    - -0.23603500716095513
    - -0.23547491105038
    - 0.5870483714520939
    - -0.407542770171328
    - -2.8216630527623012
    - -2.829367182054358
    - 0.04786213615944097
    - 0.5043427950573933
    - -4.628385817976311
    - -9.857089023101711
    - -7.677147361063939
    - 0.2370198578811551
    - 4.502967955159342
    - 0.7731827323405811
    - -4.917773713494739
    - -5.461360802586548
    - -1.9303622813369175
    - 0.15865554530519355
    - -0.3904146930208957
    - -0.5431728937693222
    - 0.4730783564949428
    - 0.3651551937329718
    - -1.0486188757523802
    - -1.09115366376314
    - 0.6270180274760951
    - 1.0608410303042248
    - -0.732065700581616
    - -1.374319887971576
    - 1.0683595982026208
    - 3.2217698497487306
    - 1.7490449330074336
    - -0.9488335594158551
    - -0.7814544370252525
    - 0.9955502493388535
    - 0.18046343524056116
    - -2.453801029161262
    - -1.851977137828263
    - 2.492181730572385
    - 4.800414327476825
    - 2.152561340547577
    - -0.6449045405572665
    - 0.9306230329590862
    - 3.4668361287904945
    - 1.404535572411219
    - -3.2552629175360304
    - -3.6963972632907485
    - 0.8911065660803422
    - 4.149162268881391
    - 2.514765161002099
    - -0.18899369211877667
    - 0.016919523893191197
    - 1.3333462975323862
    - 0.6897171932351482
    - -0.6801379417361925
    - -0.29403488755907836
    - 0.6286361418011917
    - -0.2525672661631284
    - -1.6543206632783969
    - -1.1106278701762808
    - 0.1236265854637181
    - -0.4546634785551499
    - -1.1706929197850453
    - 1.0178520974421883
    - 3.5039531362107854
    - 0.728606558636669
    - -5.633888562500173
    - -6.63950263404238
    - 1.032981877563453
    - 8.995583465080085
    - 8.535900392885427
    - 2.3718995538503105
    - -0.9005919043055118
    - 0.39488836763686724
    - 1.0629105143058883
    - -0.7259302814473887
    - -1.2799384312025208
    - 0.746682594950255
    - 1.8280211572515725
    - 0.372990925708829
    - -0.43437390391775593
    - 1.1186342731649426
    - 2.0314327003144306
    - 0.5264975235087662
    - -0.19664142679953345
    - 2.1360842862160427
    - 4.099336054626516
    - 2.1736932277746317
    - -1.0632979446417463
    - -1.3783040045243458
    - 0.07319702419445594
    - -0.2844034518740286
    - -1.499662099301101
    - -0.44509098710692696
    - 1.212655243806823
    - -0.43289812976856434
    - -3.269037775063341
    - -1.4636916137034826
    - 3.691808780067535
    - 3.775252983867585
    - -3.573551945194453
    - -9.673791401961234
    - -7.326888339236237
    - -1.0685233988387008
    - 0.9033232949587936
    - -1.0389887927829649
    - -0.9723763639504373
    - 1.7079194662919903
    - 2.458408572142453
    - 0.39829842631256723
    - -0.7426579643548971
    - 0.20707499967547743
    - 0.5948073228443237
    - -0.2251876183717913
    - -0.11408340004979897
    - 0.6295231603793504
    - -0.5217264698152708
    - -2.5325175351137634
    - -1.6950833048975087
    - 0.9506407727604372
    - 0.1186277802239269
    - -4.232854998469606
    - -5.489735519720611
    - -1.3534738409259384
    - 1.5748902709143244
    - -1.249630099929956
    - -4.26910185023785
    - -1.1429405336455098
    - 4.308975580923947
    - 4.41472812942723
    - 0.1354265597245649
    - -1.5004126180734199
    - 0.6229569030524629
    - 1.3456348702923757
    - -0.6431759078219649
    - -1.342156040233963
    - -0.06286445790738639
    - -0.8436474975131589
    - -4.053285991692766
    - -4.6839566382394855
    - -1.1550222650340374
    - 1.5922539980133046
    - 0.46700793010386
    - -1.1905838306439307
    - -0.42065318990474726
    - 0.5671977558569224
    - -0.13568132474871872
    - -0.21681587587015766
    - 1.475998929605184
    - 1.7764774216774548
    - -0.47542324155220517
    - -1.2249636144897442
    - 1.1194134054016918
    - 1.5742152686142195
    - -2.09262966432714
    - -2.9740662284696167
    - 4.227131392890575
    - 12.173837173756562
    - 10.23591533858387
    - 0.6934517278028476
    - -4.720536881733794
    - -2.1159505205992843
    - 1.2997738672607986
    - 0.6214352236741341
    - -0.6981235661205932
    - 0.41081272021762893
    - 1.4135372703872027
    - 0.4461902263677515
    - -0.17085624128920784
    - 0.4540019989830427
    - -0.3117914660922789
    - -2.5983347777128643
    - -2.72571457368783
    - -0.2543863531320242
    - 0.5982549549274412
    - -1.0992916576452363
    - -1.0458727358854811
    - 1.6182391673272023
    - 1.7000948452711278
    - -2.3895880545182795
    - -4.628939188199959
    - -1.7010840115795867
    - 0.9016425940435556
    - -1.1754719857309126
    - -3.1777497918304114
    - -0.22927558507781942
    - 3.25587864330484
    - 1.4315390701863657
    - -2.264859756033833
    - -1.4470930728753324
    - 1.5914084525969088
    - 0.4488325366251874
    - -3.3341069663702103
    - -3.0508423910788367
    - 1.0604346608803077
    - 2.5965718153881667
    - 0.35805226127184503
    - -0.7001942311086355
    - 0.8279539635295057
    - 1.262426863284997
    - -0.13765239255448275
    - -0.1256534185893507
    - 1.4254939975594945
    - 1.2581596673032638
    - -0.4684273654126565
    - -0.6225032374416027
    - 0.2618371331187882
    - -0.5243849654323465
    - -1.0619496688646508
    - 1.796976559830319
    - 3.774663605509305
    - -1.6912909404897405
    - -10.221196753062447
    - -10.097317137331974
    - -0.33320953779505036
    - 6.819704051596927
    - 4.279948279263195
    - -0.8001752265504997
    - -0.7540092633277673
    - 1.3140122781302075
    - 0.1507483697027503
    - -1.8530884987672878
    - -0.77373314725276
    - 1.0886403863773062
    - 0.557503495543128
    - -0.20151269627161933
    - 1.0377973228054467
    - 1.6200007611522576
    - -0.10603950939648948
    - -0.6330672743461078
    - 1.6945312357796458
    - 2.4601748705211954
    - -0.7356570997707801
    - -3.146799300685947
    - -1.3049435815502919
    - 0.7889474320907954
    - -0.46491432668304417
    - -1.8046402273209783
    - -0.3800350078371443
    - 0.49982244898967115
    - -0.8217034636207357
    - 0.7058463718455104
    - 6.884101031923893
    - 9.948959111638976
    - 4.564232528649852
    - -2.2167288811875534
    - -2.231354160148299
    - 0.5300206015372492
    - -1.7575826773476346
    - -6.403958797539636
    - -5.58341004341624
    - -0.4627277525877299
    - 1.5801689696333165
    - -0.17573911156239783
    - -0.5272617067350116
    - 1.1877691601033051
    - 1.3133911894838335
    - -0.023491936130772474
    - 0.11227038720842178
    - 0.984859335516088
    - 0.3930753661740794
    - 0.018399709013505343
    - 1.5281148526417547
    - 1.8051307802031158
    - -0.9221829301811142
    - -1.8508478806949165
    - 1.9206962491167172
    - 4.354765834009064
    - 0.5716352081757985
    - -3.276411899054531
    - -0.3668458782808785
    - 3.7537589096169968
    - 0.22984875994040274
    - -7.2227537155831065
    - -8.2365388100105
    - -2.8022348101942605
    - 0.48991436175306957
    - -0.4422108273788047
    - -0.4286558761046687
    - 1.3252921322380942
    - 0.9410210110623827
    - -0.8015348736021011
    - 0.07018357464066438
    - 1.856790973756469
    - 0.05109647303915081
    - -3.2479367609655982
    - -2.6414250854336405
    - 0.5025418544383425
    - 0.8474119337613417
    - -1.0475547483647436
    - -0.9698546512924493
    - 0.23733603537201609
    - -0.6895247091329446
    - -1.911042177465322
    - -0.40893677480477786
    - 1.0640843364169552
    - -0.45137521558791777
    - -1.1915755759196218
    - 1.8430245203421278
    - 3.3081662787749933
    - -0.6818261579067033
    - -2.860273221431667
    - 3.4837753868074324
    - 10.592769866347362
    - 7.2059403284294525
    - -2.8530372988104498
    - -6.838976052535266
    - -2.8227424256390097
    - 0.4812319983203817
    - -0.28876274882809205
    - -0.7228414593455749
    - 0.4397256328896036
    - 0.18068432014704358
    - -0.8915996271119003
    - 0.19567740460873095
    - 1.9004916838048151
    - 1.1757190789194112
    - -0.16029511145979142
    - 0.30394924228031983
    - -0.03456049518066476
    - -2.824543592745952
    - -3.6356182426509793
    - -0.20327873372384767
    - 1.8476676447984821
    - -0.7932784111717568
    - -1.9823885703954365
    - 2.4835363571493363
    - 5.9565638478724265
    - 2.680320148144395
    - -1.4331292241416649
    - 0.2468729292430795
    - 3.1846216682452098
    - 1.232462433892231
    - -1.586675588119654
    - 0.2851704206326864
    - 2.733878024136686
    - 0.29530801027480497
    - -2.9957751451797305
    - -1.6011860229341492
    - 0.9895515659565941
    - -0.33589274830825777
    - -2.510095633484361
    - -1.1991197468167363
    - 0.4777436345631607
    - -1.269777354440917
    - -3.2285267803778863
    - -1.8922037164234677
    - -0.05579430668560151
    - -0.3518707264906583
    - -0.26664506556007916
    - 1.3561248376723538
    - 1.4379038546990053
    - -0.10240760309778066
    - 0.2814877140774485
    - 1.1423994002259266
    - -2.0070192582327877
    - -5.1022475097506925
    - 0.5251122070863645
    - 11.150923039354161
    - 12.8891671960109
    - 3.55782911583555
    - -3.501475253674009
    - -0.9854956300833986
    - 2.9887160922239664
    - 1.5185457357357468
    - -0.721685938851243
    - 0.7157873567961628
    - 1.9852317419037808
    - 0.2873832661597805
    - -0.7897590360674532
    - 0.43559823269255027
    - 0.7604820223069227
    - -0.25589690401343845
    - 0.26339931553581064
    - 1.0895627822178013
    - -0.9936378823841108
    - -3.0331153924213314
    - -0.29645300530965124
    - 3.8795593270664086
    - 3.293525303266191
    - 0.044260084916346254
    - -0.2976857559775824
    - 0.49180942217367096
    - -1.600210806067502
    - -3.1850092648376056
    - -0.39156550614821717
    - 1.7646037638438123
    - -1.4172169501716876
    - -3.8867967843567133
    - 0.4130285765655094
    - 5.279558332704301
    - 3.148228324298601
    - -1.0568334133151036
    - 0.30804372852503814
    - 3.421949345451286
    - 1.4679016453469018
    - -1.8720910620963358
    - -0.07003763935802784
    - 3.603184345735505
    - 2.8307129233758097
    - -0.2985778725030695
    - -0.7908063950854585
    - 0.09851970610946029
    - -0.37408866196954055
    - -0.4807471159644764
    - 0.6869187696387228
    - 0.3054670381475526
    - -1.452706453545247
    - -0.8886445938285108
    - 0.8849125078702291
    - -0.5588078041494243
    - -3.0243228608207358
    - -1.3648744997464215
    - 0.4156310023334716
    - -4.9640905295827755
    - -12.212628910306176
    - -9.751774587338819
    - -0.0645552421416647
    - 3.464820737947436
    - -1.2903308037172452
    - -3.69594848322185
    - -0.0715283552600473
    - 2.32502036320738
    - 0.6138277102357508
    - -0.3734293806230116
    - 0.4207600706422522
    - -0.43755099897571914
    - -1.6721667848258772
    - 0.18268513244524534
    - 2.222419959799559
    - 0.3071735544959051
    - -2.11825204614824
    - -0.5671544726166493
    - 1.587258483111671
    - 0.19380167639210724
    - -1.4726868957631043
    - -0.16693739639236943
    - 0.5549892534663987
    - -1.4819753482572025
    - -2.030757158416001
    - 0.27762011371142475
    - 0.5945793827861757
    - -1.611374045280043
    - -1.056942425790751
    - 1.3764838973970965
    - -0.5920053342550877
    - -4.079512081882155
    - 0.4332333232772825
    - 10.301224757130353
    - 12.107704051443385
    - 3.9386592776248808
    - -1.663293793977914
    - 0.8480478305044459
    - 3.362291505206335
    - 1.0801328467648341
    - -0.7990307944420155
    - 0.44575131043164123
    - 0.9355695547956384
    - -0.17263633946258916
    - 0.2724275576088237
    - 1.3794477250982602
    - 0.16145752635636162
    - -1.3872552529031235
    - -0.5374772629393753
    - 0.14024002447036432
    - -1.066876549331601
    - -0.6691877539149479
    - 1.4247315155128037
    - -0.53615912333975
    - -5.864049271036048
    - -5.557129191114932
    - 1.4702179123799777
    - 4.888511639582391
    - 1.1480004243485418
    - -0.8681447914880591
    - 2.436535123184118
    - 3.1177435689875206
    positive_zeros:
    - '1.46483712241234149484017268549'
    - '2.49352616367310631799276619484'
    - '3.524988767769384642145346602165'
    - '4.55692086749231257072616949222'
    - '5.65612895675440030725672940424'
    - '5.963536651725658530034138884642'
    - '6.80613057784270137421759081019'
    - '7.75154729530678955893385858174'
    - '8.60620273727733157067626708848'
    - '10.035493969732675615750832871327'
    - '10.84463330476379051741292168890'
    - '11.7010766458058723059772290137'
    - '12.34186166281218661008574950584'
    - '13.12048142530296197672987874437'
    - '13.48288547382229386815935181984'
    - '14.845669950446097950248910425943'
    - '15.51310636468239411305019424822'
    - '16.15773592682427220651668871408'
    - '16.95042383590903962393247457257'
    - '17.77588412904283530624034881644'
    - '18.534593378331631981123576436289'
    - '19.53228486040712881252383044714'
    - '20.22535746340677339564411107635'
    - '21.37831069610390973579681313612'
    - '22.07166353424538424721212383057'
    - '22.432085651724237241698665589529'
    - '23.27621745668727032530318921080'
    - '23.94134495069505720371567577006'
    - '24.57704463604529686313849665630'
    - '25.46758082249756160033793092109'
    - '25.82727307485057904575576065621'
    - '27.115731156630275304634792199096'
    - '28.19041906323619034143592180898'
    - '28.532928308434322995143129385404'
    - '29.52181301831800214407798885619'
    - '29.95443608148791437331136666112'
    - '30.75255138300412043108460953060'
    - '31.50626934478860190336873001669'
    - '32.234426290698080054207119606121'
    - '33.08410230549900287922249601012'
    - '33.506379215199593105481017844540'
    - '34.55464458871656180567510809020'
    - '35.01687832310214448654488936698'
    - '35.36011641516656665202331702101'
    - '36.37092585802252949449023364997'
    - '37.58483169930204577775689496186'
    - '38.17156950447569345347177408129'
    - '39.056030828931203237782375079680'
    - '39.59296053688298329151879597218'
    - '40.214115370842123791696977783343'
    - '40.94617193276606161032552313921'
    - '41.5077037539445675787166573071'
    - '42.13378052957603009298108643996'
    - '42.6041551661372105537631978076'
    - '43.79461820801996313767934908784'
    - '44.45243265105549529054828456906'
    - '44.94247167537424991411470874864'
    - '45.8896855921675274001056907107'
    - '46.66956454138550955921399182431'
    - '47.37243490337242398203721730317'
    - '48.13048863819304167306224535846'
    - '48.31708056505751291727300438856'
    - '49.62219132273152933487718201971'
    - '50.1258503832784124702540720147'
    - '50.77229950178519137339166367772'
    - '51.48860671872974153962106813680'
    - '51.95527182283809393532219984011'
    - '52.43651847830875877791068014147'
    - '53.43209766484968786928365684530'
    - '53.80179558763546659015068693394'
    - '54.9904300545546418152557124084'
    - '55.66294961052829249813365432998'
    - '56.80946962222109098779041636519'
    - '57.050293454714742710856789256933'
    - '57.67089098030972501711926374025'
    - '58.21327947052647916272385922390'
    - '58.95426202793748598914029251416'
    - '59.576046613254620801298449136203'
    - '60.20447774916399980630433226344'
    - '61.11896409614634152348607682311'
    - '61.68754657429438346807300521503'
    - '62.20973320089872936188923248610'
    - '62.95888047186703012981323227663'
    - '63.944072537578233189742668678198'
    - '64.27438274242990186895794901601'
    - '65.09148449929109556949642039105'
    - '65.88419739404723851334850088275'
    - '66.83915702240836609673525396654'
    - '67.183836258083836487240667298207'
    - '67.94565662107622007594686366745'
    - '68.51331563235374180351397916258'
    - '69.013211360049978911578176055370'
    - '69.94392798609150091906845214668'
    - '70.18707053559942067961336729841'
    - '70.8357065227724426158374880799'
    - '71.600418173291686298565705913580'
    - '72.467002297072016820294864459504'
    - '73.595459297083979190848948762451'
    - '73.99924721618497978980144319879'
    - '74.57650598375156280849432496640'
    - '75.21355392507177978823953956717'
    - '76.00672790408071855327591522791'
    - '76.374945333092718275424765229854'
    - '77.2873963293586639867637367808'
    - '77.5507130333029220183632135738'
    - '78.62902645993518408330179258465'
    - '79.351701957740871830838103890221'
    - '79.615512817875905577513628333555'
    - '80.37645192897115523635513452469'
    - '80.89398778482970790704910868429'
    - '81.65218904019410526840471010407'
    - '82.36959000530491316887881314090'
    - '83.51552135215442729654024371631'
    - '83.91120035632179897391864015587'
    - '84.49781381720147580728062051251'
    - '85.37176735055256665275533721940'
    - '85.883188770385995733449744739712'
    - '86.47545354051625351560517223061'
    - '86.91504806053455915137598281045'
    - '87.41858872752461044930982484818'
    - '88.310013631894113964863385895334'
    - '88.76074263961611433274411142507'
    - '89.77878524469252768800700318387'
    - '90.2210593463965430118307171102'
    - '90.997486551631799798220668458776'
    - '91.88585638382039541530512408756'
    - '92.42056113316851137735818308019'
    - '93.03369442001251890409681996253'
    - '93.77419411640890509422457296760'
    - '93.90873500827592366940145641199'
    - '95.09203248482730841213812142289'
    - '95.689784674718148979273728473357'
    - '96.33933295140272762683886575782'
    - '96.832042177612801002589494125481'
    - '97.24183925571135858672102239455'
    - '98.06455300335585473066946670417'
    - '98.61984117837355091446936296270'
    - '99.21780866779437028568182592217'
    - '99.85275032866350881625304102535'
    - '100.96133204573928222206613188774'
    - '101.71743213652322937251164359936'
    - '102.28894781020564059016242427320'
    - '102.73695966189685694280277495282'
    - '103.56313438352345460335257050219'
    - '103.85499251538832900518516730822'
    - '104.320764435917914538201246626757'
    - '105.347602240877900642050689087436'
    - '105.755364371686224939183005360270'
    - '106.38220175741174639189694119746'
    - '107.02430640332203849739232907623'
    - '107.95684773278332413551373358108'
    - '108.321631819602641221811833734495'
    - '109.0780543582270680657973678231'
    - '109.79198073073210867284529270203'
    - '110.44412690467746396797894314179'
    - '110.97494657972318277518034909961'
    - '111.79463644625682597616247776922'
    - '112.547714085521662974108102435782'
    - '112.97981895219135145243621854456'
    - '113.71656063933236289642507220679'
    - '114.09194052722237674804515977730'
    - '114.907297232359772484405827968132'
    - '115.49803424768730271161860419511'
    - '115.81259085010689908755466871655'
    - '116.40613008861747643578070957941'
    - '117.12467164292510725801336109506'
    - '118.13470255668758553736193018058'
    - '118.99300314303554014955729823594'
    - '119.46969630820158554892494736394'
    - '120.018445774141772477794651137224'
    - '120.72901221505245574113442834111'
    - '121.3923257827153094630708600205'
    - '121.65554253818737828300826299140'
    - '122.482872913512865001601315003773'
    - '122.92267630750217432206117021519'
    - '123.69181901133580681080729651059'
    - '124.51957463832964051529689078446'
    - '124.93248103981643636810970599860'
    - '125.688959917839939554093161936020'
    - '126.072793228276198377553968784834'
    - '126.50645364702324776566283381139'
    - '127.68437626056930739496794646156'
    - '128.34328054161564900733061516427'
    - '128.61160235967208197231021782597'
    - '129.72068697824285180921232912313'
    - '130.28361063788653182473914573826'
    - '130.730631516472166305295390824513'
    - '131.554654881039222880397196155427'
    - '131.83764746652456537690295017864'
    - '132.640908822335827073639323052476'
    - '132.80387384085619385602178862713'
    - '133.657296633976609385856754528233'
    - '134.24424754626324007528714765181'
    - '135.03227563904789312004313314065'
    - '135.64606374401715666087346503909'
    - '136.25975316727107261893372546912'
    - '137.39576797177544290224503163178'
    - '137.71559062691324893294577569111'
    - '138.20431966184052467131929478047'
    - '138.897221543516545173890256801049'
    - '139.36499036850129945312920524676'
    - '140.00446057305436075542374675655'
    - '140.878434248941280493629514937075'
    - '141.38802615572781472917988417141'
    - '142.09060754953718498478113716306'
    - '142.362855946424725159130106192693'
    - '143.17998261567639338546717522537'
    - '143.6855089812002934088841868813'
    - '144.216344130235249452924331016705'
    - '144.95775895734860850667532556051'
    - '145.49593726701100287529944037318'
    - '146.47001786428668866168589802526'
    - '147.407765607574308138402405821198'
    - '147.7502634397179463391797600644'
    - '148.316871153573108723492640842781'
    - '148.79339128378095940672793350527'
    - '149.34493320384667511081769561778'
    - '150.24076138922287958030326097491'
    - '150.50989367425593854345216916608'
    - '150.93159649803561261471661852334'
    - '151.8910631236646739805394086515'
    - '152.42852859796163762024440083693'
    - '152.98423736070993273021600144214'
    - '153.91352020787183090767977795428'
    - '154.35453346419619421006243533921'
    - '155.10205323341315928210590234989'
    - '155.59944969449601780965495974122'
    - '156.27176735069239123160536445782'
    - '157.03047695805294671005923440106'
    - '157.46201269003520383291938232980'
    - '158.286628854967786224523101463395'
    - '158.59037568714320956050887312647'
    - '159.71735455470052801554467457171'
    - '159.83368528967856371899611464316'
    - '160.374362127362918060216591442181'
    - '161.22137996493099151564900942070'
    - '161.498271493605092431330023672623'
    - '162.039962881857320921724762942032'
    - '162.796164554795146470552338295414'
    - '163.86272271837786293852348203912'
    - '164.43331116048208617829677540650'
    - '165.15836497645237929445298437829'
    - '165.527606881981998687826401324714'
    - '166.29270386413141681312179034955'
    - '166.78248112776096720784800025565'
    - '167.40535832891267669892776136668'
    - '167.7477814776280850178676742101'
    - '168.332550955313088337206131988482'
    - '169.08189500833891744757093281061'
    - '170.00617195590463607376978773171'
    - '170.38555285014811033747175102286'
    - '170.748351315302306263154326074338'
    - '171.59449756178133657322267894456'
    - '172.08734188172722209138748587673'
    - '172.79236426278686743345115386178'
    - '173.6402233690632776492678007077'
    - '174.03632279984809173808676201581'
    - '174.796887008241435802163376098109'
    - '175.31783863048709978637955869832'
    - '176.21139129043952897979201710239'
    - '176.81078585489349460556886720541'
    - '177.03624043749723858472471353254'
    - '177.63470914974507016038714217419'
    - '178.17897956617903603043893607542'
    - '178.87950735477940629590932610401'
    - '179.313631583088647844094996926476'
    - '180.14057270106889291329641295358'
    - '180.37290939015652589496868122759'
    - '181.564869582344474909424671649869'
    - '182.116365085980052632524792213011'
    - '182.81762388882647169009692064927'
    - '183.53760142512113339146108758655'
    - '183.89652418286891315446481158044'
    - '184.29276200954946157961394056754'
    - '184.98065933571974669733659744572'
    - '185.65391276207829501005722067918'
    - '186.3096755691712869422130734677'
    - '186.89898633917140138143936572252'
    - '187.52782229293194496841621401179'
    - '187.925262060003238251318825950981'
    - '188.712180386185989566440262253370'
    - '189.15312545053676308131683668091'
    - '189.804063698575077022455100566047'
    - '190.26782901276926573219084848570'
    - '190.92245908904121161506522108771'
    - '192.03465068755695904305466039886'
    - '192.43711909399787444424259646478'
    - '193.2405598984373241561277934052'
    - '193.66721027579032226732466204978'
    - '194.315048182383435488783277742080'
    - '194.620855515106910777942043682244'
    - '195.33616683368541105783004019838'
    - '196.06818212844269374412363349374'
    - '196.30816875838712415958310347014'
    - '196.96759300214669998481907831517'
    - '197.46319192907028169011554269580'
    - '198.37558208835221261318385087602'
    - '199.14893600736779916210817935948'
    - '199.488021709451126352590686391795'
    prelabel: 1-1045-1045.504-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 112.30084641038314
    root_angle: -0.9336154076891842
    root_number: -0.978331460238012617834897778844-0.207044811353865944045450435227*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.466807703845'
      prec: 50
    spectral_label: r1-0
    st_group: mu(90)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 1.14197090443303184428780527569+0.310702675512448379926568785346*I
    z1:
      __RealLiteral__: 0
      data: '1.46483712241'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '2.49352616367'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '3.52498876777'
      prec: 44
- - algebraic: true
    analytic_conductor: 112.30084641038314
    bad_primes:
    - 5
    - 11
    - 19
    central_character: '1045.504'
    conductor: 1045
    conductor_radical: 1045
    degree: 1
    id: 201815
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/1045/504
    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: 1-1045-1045.504-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: 1-1045-1045.504-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 112.30084641038314
    root_angle: -0.4668077038445921
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '1.46483712241'
      prec: 44
- - Lhash: dirichlet_L_1045.504
    Lhash_array:
    - dirichlet_L_1045.504
    id: 1922694
    label: 1-1045-1045.504-r1-0-0
    type: DIR
    url: Character/Dirichlet/1045/504
label_cols:
- label
- label
- label
labels:
- 1-1045-1045.504-r1-0-0
- 1-1045-1045.504-r1-0-0
- 1-1045-1045.504-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-24T01:24:53.811134'