data:
- - Lhash: dirichlet_L_1375.498
    a10:
    - 1.0
    - -2.8163065144692913e-30
    a2:
    - -0.368124552684678
    - 0.9297764858882515
    a3:
    - 0.9822872507286887
    - -0.18738131458572463
    a4:
    - -0.7289686274214116
    - -0.6845471059286887
    a5:
    - 1.0
    - -2.8163065144692913e-30
    a6:
    - -0.18738131458572463
    - 0.9822872507286887
    a7:
    - 0.9510565162951535
    - -0.30901699437494745
    a8:
    - 0.9048270524660196
    - -0.42577929156507266
    a9:
    - 0.9297764858882515
    - -0.368124552684678
    algebraic: true
    analytic_conductor: 147.76427159260942
    analytic_normalization: 0
    bad_lfactors:
    - - 5
      - - 1
    - - 11
      - - 1
    bad_primes:
    - 5
    - 11
    central_character: '1375.498'
    coeff_info:
    - x^100 - 1
    - 0.998026728428272 + 0.0627905195293134*I
    - \\zeta_{100}
    conductor: 1375
    conductor_radical: 55
    conjugate: dirichlet_L_1375.312
    degree: 1
    dirichlet_coefficients:
    - a^0
    - a^31
    - a^97
    - a^62
    - 0
    - a^28
    - a^95
    - a^93
    - a^94
    - 0
    - 0
    - a^59
    - a^69
    - a^26
    - 0
    - a^24
    - a^43
    - a^25
    - a^58
    - 0
    - a^92
    - 0
    - a^81
    - a^90
    - 0
    - a^0
    - a^91
    - a^57
    - a^22
    - 0
    - a^28
    - a^55
    - 0
    - a^74
    - 0
    - a^56
    - a^39
    - a^89
    - a^66
    - 0
    - a^84
    - a^23
    - a^45
    - 0
    - 0
    - a^12
    - a^87
    - a^21
    - a^90
    - 0
    - a^40
    - a^31
    - a^97
    - a^22
    - 0
    - a^88
    - a^55
    - a^53
    - a^94
    - 0
    - a^76
    - a^59
    - a^89
    - a^86
    - 0
    - 0
    - a^63
    - a^5
    - a^78
    - 0
    - a^92
    - a^87
    - a^1
    - a^70
    - 0
    - a^20
    - 0
    - a^97
    - a^62
    - 0
    - a^88
    - a^15
    - a^13
    - a^54
    - 0
    - a^76
    - a^19
    - 0
    - a^66
    - 0
    - a^64
    - a^43
    - a^25
    - a^18
    - 0
    - a^52
    - a^67
    - a^21
    - 0
    - 0
    euler_factors:
    - - 1
      - a^31
    - - 1
      - a^97
    - - 0
    - - 1
      - a^95
    - - 0
    - - 1
      - a^69
    - - 1
      - a^43
    - - 1
      - a^58
    - - 1
      - a^81
    - - 1
      - a^22
    - - 1
      - a^28
    - - 1
      - a^39
    - - 1
      - a^84
    - - 1
      - a^45
    - - 1
      - a^87
    - - 1
      - a^97
    - - 1
      - a^94
    - - 1
      - a^76
    - - 1
      - a^63
    - - 1
      - a^92
    - - 1
      - a^1
    - - 1
      - a^62
    - - 1
      - a^13
    - - 1
      - a^66
    - - 1
      - a^67
    - - 1
      - a^40
    gamma_factors:
    - - 1
    - []
    id: 349582
    index: 0
    label: 1-1375-1375.498-r1-0-0
    leading_term: 1.56200001467678752105039745900-1.13323881125732808836361863767*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/1375/498
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
    plot_values:
    - 1.929786063062486
    - 0.25300354076446974
    - -1.365047470847493
    - -1.9943443643590866
    - -1.150813549292573
    - 0.6415480994610995
    - 1.935349027325276
    - 1.3666120201127792
    - -1.0780754410011222
    - -3.73408781875658
    - -4.459001174797512
    - -2.517946294989271
    - 0.5905973314254933
    - 2.3622157633296172
    - 1.6007299515643914
    - -0.41445261010238665
    - -1.199186784381039
    - 0.3928811751561639
    - 2.9734527351281796
    - 4.087997204526258
    - 2.8109802552176677
    - 0.6359247032788942
    - -0.29836223679162005
    - 0.43446014199884414
    - 1.3441274963252041
    - 1.0937898475170653
    - 0.16685908815181522
    - -0.009569160055356567
    - 0.7175676142859456
    - 0.7750818671363067
    - -0.9472319965427152
    - -3.1146292025292235
    - -3.2207132838233727
    - -1.0248519559701952
    - 0.3041965603645349
    - -2.456856373835313
    - -8.260536658853747
    - -11.994838632343898
    - -9.719569805612267
    - -3.125844744582521
    - 2.1499778570696666
    - 2.541370564007738
    - -0.12508340334143353
    - -1.6218831967384386
    - -0.4815769913400729
    - 1.074619314384476
    - 0.9034344986355761
    - -0.18247900870265174
    - -0.1787415409687956
    - 0.7521304848446635
    - 0.48329090366385297
    - -1.6057758321670221
    - -3.1928760528980504
    - -2.0608768924061205
    - 0.6241037536062983
    - 1.718546246692936
    - 0.408414719356624
    - -0.7752662540765861
    - 0.19483646573417732
    - 1.750629599127104
    - 1.087642526335103
    - -1.4187489603616446
    - -2.491152210630391
    - -0.8557479943057877
    - 0.5269120681331486
    - -1.2753551908676095
    - -4.34553101103195
    - -4.028348796514131
    - 0.3454708708986216
    - 3.7190020332255265
    - 1.6941415228509438
    - -3.43535996881511
    - -5.472458047528995
    - -2.25731328232349
    - 2.012597128239766
    - 2.7921848983989577
    - 0.7524009576530624
    - -0.39783578786019613
    - 0.40393294688816916
    - 0.9119634546625324
    - -0.059758765787404355
    - -0.7541896184713269
    - 0.20836068222229662
    - 1.2775255419769476
    - 0.6019191756095902
    - -0.6901207103269769
    - -0.3841535107317852
    - 0.7474473998300459
    - -0.04357508138743842
    - -2.318816193681266
    - -1.8458455564019256
    - 3.0645735069755657
    - 7.550880616558268
    - 5.809959219645795
    - -0.7291170661644271
    - -4.712469670508851
    - -2.4492963775462377
    - 1.7019177683320679
    - 2.132656630189725
    - -0.3612704178490719
    - -0.9804041963079384
    - 1.2825223523798637
    - 2.6483719023396217
    - 1.0678095172787716
    - -0.7083731740351857
    - -0.10044681287296107
    - 0.9655461541668996
    - -0.44953841758412516
    - -3.044318480886103
    - -3.206783473553923
    - -0.959114794237107
    - 0.030862587994177144
    - -1.5641991225637548
    - -2.684101303912454
    - -1.0759594810261928
    - 1.0646282558196587
    - 0.9843834913436037
    - -0.10208739685908604
    - 0.35552805739969306
    - 1.361672409697008
    - 0.3538450634278485
    - -1.1089005698837253
    - 1.222314433869554
    - 6.487906662184476
    - 7.645815379196646
    - 1.0698071502149549
    - -7.008495265156084
    - -8.05913228519077
    - -2.5883394754525013
    - 1.2967874299350526
    - -0.45459180820762135
    - -3.4019913161521287
    - -2.7103952972045846
    - -0.07079669656022873
    - 0.45091503496017393
    - -0.8420131254641543
    - -0.9252984872166136
    - 0.25133875163552394
    - 0.3328659887934162
    - -0.5588264245368761
    - -0.12665658468714522
    - 1.3562915775330318
    - 1.249723641116404
    - -0.10010201632190642
    - 0.97684194587709
    - 4.930689519651004
    - 6.867698271267346
    - 3.8003897733427023
    - -0.2658204256249677
    - -0.5324304251987484
    - 0.9312386006299995
    - -0.87491754659424
    - -4.6608229311695535
    - -4.196160344597348
    - 1.361071011454717
    - 5.300022559252706
    - 3.368113451936434
    - -0.23397169538551893
    - -0.28510582327520906
    - 1.4298907057131123
    - 0.48703385744859606
    - -1.8991024973489408
    - -1.1967267510142148
    - 2.035163219476449
    - 2.6579288162107058
    - -0.47477130723740923
    - -2.705865355549002
    - -1.3213984872463633
    - 0.6274710577490366
    - 0.23726173599599742
    - -0.7399871955625509
    - -0.16948490487130696
    - 0.32599962025322116
    - -0.9189818441178426
    - -1.8002458034132724
    - -0.4670857101519718
    - 0.4860823505515424
    - -1.3636463538632133
    - -2.829999082343138
    - -0.253502571938828
    - 2.5538203467549208
    - -1.0475075777761302
    - -8.742495107295728
    - -10.404428424975656
    - -2.6732788606931717
    - 5.4677395781226314
    - 5.3519069546134235
    - -0.030085089535411204
    - -2.539265340674319
    - -0.9628025163806103
    - 0.08844469220127879
    - -0.6337926078202384
    - -0.384193574894817
    - 0.907193272960124
    - 0.4545136534888283
    - -1.367620126875114
    - -1.2499646707616026
    - 0.6828396030274595
    - 0.8558811732650292
    - -0.8783452055267069
    - -0.6031657575340973
    - 2.221621468361106
    - 3.1010910523321216
    - 0.4047301844365025
    - -1.4708537442695864
    - 0.097944155439828
    - 1.3236891442068772
    - -0.6726308845425165
    - -2.0273659224426486
    - 0.8882247681138012
    - 4.144578750044981
    - 2.662990184387037
    - -0.5822873900509992
    - 0.34011545777257646
    - 3.324786136580227
    - 1.3151213594364715
    - -5.077927716791399
    - -7.4983404432646905
    - -3.0167629660067408
    - 1.6658268669198504
    - 1.4244707292756518
    - -0.27373855424318577
    - 0.8507750049366138
    - 2.628481317540467
    - 1.7337968468016371
    - 0.034499016317918844
    - 0.42342144097135714
    - 1.3191852283712073
    - 0.40720976890609584
    - -0.5576552156377399
    - 0.42133357941486244
    - 1.26090465737494
    - 0.17231317315025904
    - -0.24018294313035263
    - 1.4108958700310141
    - 0.6683896744562476
    - -5.111690514966579
    - -9.388635792537622
    - -5.120634187799778
    - 2.906376496113311
    - 4.037608277692183
    - -2.094626777965161
    - -5.657436062108546
    - -2.416459874598971
    - 1.2163103055119597
    - 0.47755623636258615
    - -0.7843049072071641
    - 1.038105094972337
    - 2.708394008642207
    - 1.1533835828559347
    - -0.660649476132444
    - 0.10293098348069969
    - 0.856698019385967
    - -0.5573988917013284
    - -1.0876829030494135
    - 1.2837572798528842
    - 2.6012259848883885
    - -0.23855008539745595
    - -3.3997920196873297
    - -2.5747779585893396
    - -0.1401714093979272
    - 0.02400995326623129
    - -0.5048455812385422
    - 0.849960152992556
    - 1.6251242972503797
    - -0.4977273136794782
    - -1.8494572816536348
    - 0.4357568213272929
    - 1.2713950005912888
    - -4.056299194080749
    - -9.517931248192902
    - -6.49007276844392
    - 1.5737288607187243
    - 3.8071755524152575
    - -1.008146054603593
    - -3.7221466076240652
    - -0.5531588068980858
    - 2.223294971831126
    - 0.5992339732858705
    - -1.190190575488489
    - 0.19984317659800632
    - 1.7160632774581073
    - 0.8524632362572528
    - -0.10152787504662861
    - 0.24842791850886253
    - -0.1259040273959693
    - -1.189012613805068
    - -0.11814485499094075
    - 2.2080577957416225
    - 1.6455661347542088
    - -0.9569430097581846
    - -0.33918873672714817
    - 3.022013615170964
    - 2.7839570413719747
    - -1.3688309165418202
    - -2.114533201262363
    - 2.2209536570656114
    - 3.769340159064074
    - -0.9996901525312143
    - -4.491880629502984
    - -1.0694903569309935
    - 3.450966466530332
    - 2.478992348563206
    - -0.6606169196300851
    - -0.500975686575426
    - 0.7180681682821298
    - -0.8034862696639073
    - -2.148498640092426
    - 0.05906406181602841
    - 1.9855405443450507
    - -0.5723097696767935
    - -3.9008473664646575
    - -2.850099722116878
    - 0.23682729972738503
    - 0.6149117705886642
    - -0.5525635720920973
    - -0.19725137933606546
    - 0.0503814141953178
    - -1.796568584255871
    - -2.8796506403383373
    - -1.104081697589175
    - 0.18793017321485672
    - -0.9055796839762802
    - -0.5079746937160272
    - 2.504390055769358
    - 2.3172415656472207
    - -2.345276474294967
    - -2.2670064457261456
    - 7.572680400815732
    - 16.760861014723883
    - 13.809830053589229
    - 3.5953998264152736
    - -1.2280034926692747
    - 0.8265575870978269
    - 1.9416107708924353
    - 0.03427917014064007
    - -0.5285256507168328
    - 0.6620696627974781
    - 0.2835157820305341
    - -0.9213722421903303
    - -0.10391004756051236
    - 1.048179205162088
    - -0.1709851346084694
    - -1.3412430708747272
    - 0.1900979851339416
    - 1.3095550992227933
    - -0.6886689532560585
    - -1.9900191069860136
    - 0.27389369246464673
    - 1.420406119841044
    - -2.0736233617866953
    - -4.8661014203845285
    - -2.1313694756250596
    - 1.3624284239649465
    - 0.3569855273801995
    - -1.1921153330668113
    - 1.0682533060295436
    - 2.196809076515265
    - -2.5762686367985874
    - -7.271572694768834
    - -4.993051366358117
    - -0.2426382606595239
    - -0.2960476199808
    - -2.1192891861256915
    - 0.6670965220708388
    - 5.047747864118566
    - 4.385112044629902
    - 0.5682062320797394
    - -0.48616949981366375
    - 0.36791745410932597
    - -0.84795053528071
    - -2.5105480803247904
    - -1.356007830231141
    - 0.45426200294139035
    - -0.003382158725607409
    - -0.6450225596275151
    - 0.39699246752201567
    - 0.7014542381338381
    - -0.1951875954324243
    - 1.132571086181271
    - 3.4515012701543264
    - 0.7528071962727177
    - -5.1071822316058695
    - -3.9937191432380175
    - 5.109038911276432
    - 9.83842067431163
    - 4.040309872574714
    - -2.34255581272124
    - -0.5687670103545782
    - 3.571773840699667
    - 2.419936962914059
    - -0.5664751407576737
    - 0.20049515024722478
    - 1.9246409941834162
    - 0.7028764117454462
    - -0.7141040906774592
    - 0.24198169887504078
    - 0.7254507417446854
    - -0.40018096386035795
    - 0.31288645144366484
    - 2.6991016958702323
    - 1.9004226336153545
    - -1.751792021351112
    - -2.284503611986166
    - 0.7295508969915154
    - 1.4766728006375869
    - -0.8117250005665692
    - -1.2080674967739995
    - 0.43194924787993577
    - -0.056927107793330184
    - -1.4849347780812883
    - -0.09165077916042591
    - 0.624181944399576
    - -4.337546517906585
    - -9.519289089660985
    - -6.603352561128734
    - 0.2206955963880205
    - 1.0973885589999965
    - -1.9039233357514656
    - 0.3859250969550078
    - 6.230095913952955
    - 6.0458946381198
    - 0.07589070864861831
    - -2.6494050602355643
    - -0.30764287813515334
    - 1.0240322212335076
    - -0.07733659764286965
    - 0.061871168468229404
    - 1.1280700169462905
    - 0.3005152892518689
    - -0.9262316801948703
    - -0.3273361676833008
    - -0.12471866087641749
    - -1.4433327165666934
    - -0.8070678597954958
    - 1.9304783925175757
    - 1.4000294412706646
    - -2.533827557567484
    - -3.076903816900235
    - 0.09439283414721364
    - -0.8890273465103724
    - -6.098040716632211
    - -5.349443301035633
    - 3.206678810285918
    - 8.108023023036056
    - 3.872100864809388
    - -0.7320740663402918
    - 0.6050109329195762
    - 2.4822228165661575
    - 0.7199347011475583
    - -0.5198184557945653
    - 0.5998486077612033
    - -0.17724439399659608
    - -2.8151333252093176
    - -2.035699959977317
    - 1.4897083636822384
    - 1.722309438738495
    - -0.9352264169127331
    - -0.8134545633011879
    - 1.5734271375898696
    - 1.2991324081838909
    - -0.6466169208508613
    - -0.19258287371550803
    - 0.9209651608088251
    - -0.4998639237815303
    - -1.7090146337696004
    - -0.2541709904253571
    - 0.10099891892401602
    - -2.2640975079954653
    - -2.458653106048798
    - -0.034477911775482165
    - -1.7005264662552002
    - -6.439033019876307
    - -3.184797590333106
    - 9.096063101896071
    - 15.634768080183429
    - 8.649383720104925
    - -0.7109044580514817
    - -1.718181280226797
    - 1.0574608939830965
    - 0.5719551065809467
    - -0.6763171506606424
    - 0.5290198895161113
    - 1.0801645754796863
    - -0.3900083743573236
    - -0.33988901315807324
    - 1.4125621737654526
    - 1.20319391895548
    - -0.3564486688253859
    - -0.20464778848172538
    - -0.20275543017067726
    - -2.5356215825473023
    - -3.0718990893206723
    - 0.6372084386378986
    - 2.4885890159620137
    - -1.1649538235341959
    - -3.607357479588236
    - -0.5056720746489931
    - 1.4213034007384642
    - -2.0398772218889007
    - -3.9524040080532328
    - -0.37201547878598634
    - 1.5359480324878316
    - -1.808052105886011
    - -3.0170592711340047
    - 1.1032781749457883
    - 2.9100331065987683
    - -0.7575976015416236
    - -2.61723860274825
    - 0.23385431773867826
    - 1.406312197340363
    - -0.9775472562647634
    - -1.1318764154474916
    - 1.4806526856423
    - 1.0418930729143172
    - -2.2416199914874944
    - -2.5924862350981024
    - -0.21059312267490501
    - 0.22555223284385645
    - -0.7454236887641725
    - -0.21507041210984287
    - 0.03358187685853441
    - -1.4682259284592845
    - -1.5013751837288154
    - 0.1976090389750812
    - -0.7759415790901164
    - -2.8467193230410754
    - 0.365166889666468
    - 5.117391897690011
    - 0.6672015070040256
    - -10.028056476292393
    - -11.915511120052118
    - -2.8133732155237143
    - 3.43169798125058
    - 1.1121258539152965
    - -0.6150829526765753
    - 2.633933651859539
    - 4.092170928741187
    - 1.167118490516276
    - -0.6354111454380192
    - 0.13468354224883414
    - -0.19459283478169123
    - -1.0763815381731765
    - 0.040612478675150346
    - 0.7016278192926563
    - -0.8779433081608614
    - -0.49526434959952076
    - 3.122337241933038
    - 4.035248431544107
    - 0.5772071327833015
    - -0.8226682694283804
    - 1.7028723499632685
    - 2.389876099683538
    - 0.26937502425430615
    - 0.16132957806034703
    - 0.8328860079869618
    - -2.4773528244842336
    - -5.805375128842603
    - -2.6773626186413426
    - 2.0675623550481133
    - 0.8845172464450819
    - -1.3297872508237198
    - 2.7619673159452534
    - 7.275707836301486
    - 4.192185805074993
    - -0.7440518784828436
    - 0.5994433185228571
    - 3.2741871002014187
    - 0.17036478500094202
    - -3.9447422121973057
    - -2.587080026166795
    - 0.5503619582333538
    - 0.4926082536341404
    - -0.37056499774158924
    - 0.1184671863442403
    - -0.3531249011776293
    - -1.3721722334766158
    - -0.016403478611832372
    - 1.6456220425533004
    - 0.3725528317424023
    - -0.7672578560227695
    - 0.8688276892313977
    - 1.1315406042861638
    - -0.9156393741885585
    - 1.4371438862268855
    - 7.776285769138257
    - 6.938434448424499
    - -2.7035583912620362
    - -7.4246380740145135
    - -1.4661194223646876
    - 3.4283580001624743
    - -0.0845908652381541
    - -3.7750658316592043
    - -1.7203888662538223
    - 0.3771418301678028
    - -0.7524448082044055
    - -0.7626648521618214
    - 0.6820938012643261
    - -0.5009781152028927
    - -2.241931127058507
    - -0.06909600698468085
    - 2.6698109897216655
    - 1.4030526825787275
    - -0.1198616660342109
    - 1.8218416821975174
    - 2.934208440844371
    - 0.5596489778183834
    - -0.5252387312407204
    - 1.2569355740377577
    - 1.028045584993538
    - -1.3901530947357128
    - -1.0552034225883204
    - 0.9946685201119395
    - 0.4685790089435269
    - 0.0609045084170217
    - 2.6638851911429633
    - 2.290274886485819
    - -3.5796673530191163
    - -4.543439826825818
    - 4.574591808085494
    - 10.97480194396069
    - 4.75270630442458
    - -4.022717137943957
    - -3.8589655934376585
    - 0.018275718526592162
    - -0.504222820191273
    - -1.9496954571083132
    - -0.04079508475144243
    - 1.305962667465693
    - -0.11465295785670525
    - -0.5360166147907865
    - 0.4387931217966303
    - -0.44149955970871607
    - -1.7264000175270486
    - -0.5366896383783744
    - 0.5535624600654006
    - -0.24462062367185794
    - 0.45529215363922626
    - 1.937423609430072
    - -1.6156182780272632
    - -7.676126824003299
    positive_zeros:
    - '0.3564136125094280554456807136'
    - '1.45557770622886321239291630291'
    - '2.38072556750218016527521840575'
    - '3.687489034686578686970726508743'
    - '4.61973263336653126740916026997'
    - '5.26121064116939809827565928670'
    - '6.697225719818430720967758705781'
    - '7.05835156595588017568103315591'
    - '8.20986168013201384893643488218'
    - '8.444245439315432728454201371158'
    - '9.23821016919920079196992116092'
    - '10.46676061663937839024554814365'
    - '10.71254588296638254115065604549'
    - '12.34274481324830289760764202996'
    - '13.110649113190315982581760434226'
    - '13.82985139304305950111130245950'
    - '14.62386480410815354175073141563'
    - '15.06541840424556925988840687753'
    - '15.71660459024805701108258901701'
    - '16.79830761137854125346734401298'
    - '17.573172993447947275448615809548'
    - '18.09014599599697156899404701933'
    - '18.89200891135285285316999664534'
    - '19.81889657718173870758722255526'
    - '20.16191111968158420771511797176'
    - '21.22835715414239573752627161302'
    - '21.980751041427904707885930173024'
    - '22.96061484869241386906079921538'
    - '23.880220275153395775023697029142'
    - '24.26133571188275916137914983067'
    - '24.98516057320441088195248948824'
    - '25.57968766773711020157404772312'
    - '26.376432051421909657682949174828'
    - '26.96892345810655071090063148044'
    - '27.49329474133498910396236251814'
    - '28.26739718388239214130384820833'
    - '29.34080472462271448478031041765'
    - '30.167894505963634303905729964414'
    - '30.89066775095700491821717762198'
    - '31.40914344723987368885240003672'
    - '32.33642310267020603605748830734'
    - '32.83356231476537536901705670985'
    - '33.38059268380773525793335922661'
    - '34.567329576365642258937075369780'
    - '34.703356771000566061721487136673'
    - '35.75900386923617782175649054496'
    - '36.51501035445029642657453205988'
    - '36.76929713258190464547395402113'
    - '37.55551706844217131456104111783'
    - '38.03014059766003717219850221228'
    - '39.09925719211048866149491827604'
    - '40.1541809145570251508558166531'
    - '40.58322994112803015716291984938'
    - '41.57376074610452439642371969522'
    - '41.99371371602430612671524901728'
    - '42.74007195290878004945000573514'
    - '43.23825563265578953196341348928'
    - '43.778112571588564763649373136403'
    - '44.65161585209971565258469388379'
    - '44.85676219772118544413871455590'
    - '46.2194209911782366971756546705'
    - '46.65775960449968749367545418867'
    - '47.10529105353888235611280850255'
    - '48.05651630524336185812582761777'
    - '49.03208675545493423269552797622'
    - '49.42366174061251947808508386968'
    - '50.059041699723511222892572869666'
    - '50.74420577222344633308118285681'
    - '51.52194048783937816059157791774'
    - '52.36465129605918306420336052477'
    - '52.870154720112895608182350436155'
    - '53.48992443125705511902200009998'
    - '53.87376283896752021314410897482'
    - '54.77137853417685890476397584398'
    - '55.13030548767099997614654793675'
    - '55.957344716663056504414797149150'
    - '56.51319523993135782546866735956'
    - '57.584418104230039658924656575389'
    - '58.43561544673666042847845065345'
    - '59.26747910081332302395208052812'
    - '59.44593906650314526554091388678'
    - '60.08997494451170080963612407013'
    - '60.70340045078669349618069399222'
    - '61.44928807714509580516710623473'
    - '62.03155074669534370341942949568'
    - '62.5785753856254906581405377107'
    - '63.4778260805929939264377247988'
    - '64.0493710032847675350430555309'
    - '64.609948546720053499455740737115'
    - '65.24569036768090591772320915860'
    - '66.170906412398221211703141857552'
    - '66.52668676588803963939054238688'
    - '67.258124100509961365848486524772'
    - '68.292995551361216811305102289380'
    - '68.97416280379974001379423683377'
    - '69.23564944123452661644802965075'
    - '70.32698694081340185917463732343'
    - '70.490477845433263850588696922000'
    - '71.33695981094023517108134089903'
    - '71.785010012541365049893951368088'
    - '72.54043207670536191435057485680'
    - '72.875892952932907883066220410117'
    - '73.48891919642876288171066949724'
    - '74.56226011420054463627675090154'
    - '75.21715910595718502352494651130'
    - '76.10538457509543630861643458309'
    - '76.635333898827037962715095328993'
    - '77.05859514054161003258823080252'
    - '77.96594254737715960773683162958'
    - '78.4156719491937145050738528541'
    - '78.965603334006527319891976460340'
    - '79.546243924386315806301417904010'
    - '80.29408211048891912680560569263'
    - '81.28116373273197613396394880891'
    - '81.571199911169738105250861051491'
    - '82.03572135262680380739734750365'
    - '82.75554699116606177121147209365'
    - '83.39162627523355177045035193688'
    - '83.862015718198257301207782656365'
    - '84.932497709219897559582247081461'
    - '85.56839682616447062192837488788'
    - '86.29061112287266729319183215131'
    - '86.94440085108778466769968845905'
    - '87.47210112191189401558915597657'
    - '88.35438648310162744712100633621'
    - '88.58984706746046973120102045046'
    - '89.0254065120400872898057549049'
    - '89.702894610993408465496458936210'
    - '90.49710889715877974416794984998'
    - '90.97223279763107320784271486657'
    - '91.77288476462981885994388030172'
    - '92.35663240745162046967136783301'
    - '93.0722804075113348837288428361'
    - '93.80921002858658381865940849270'
    - '94.6009019435369929070099695630'
    - '95.09121002409991145811882426954'
    - '95.51428543007162274047643204465'
    - '96.244193458723363699370505357829'
    - '96.83062666295251915812830187140'
    - '97.78038732512413138777134274666'
    - '98.27172323149480386769272498159'
    - '98.82107622947069936204020389233'
    - '99.07909080184891118132907258071'
    - '100.18762984712727706392329307521'
    - '100.40914044142844497663471139007'
    - '100.99907696594270148801440826080'
    - '101.72614334693318251383530713172'
    - '102.286147004179108623821473088671'
    - '103.59637506836338414729550471208'
    - '103.9742937141987964050909091769'
    - '104.69314950430554621531250362046'
    - '105.13933944710306797919058269188'
    - '105.685921598361532985744754681250'
    - '106.26944166082023699006045961803'
    - '106.84760312137235223673925172852'
    - '107.4729876353271991057618258125'
    - '108.044030572902648235778240344599'
    - '108.72067102683060893812649604484'
    - '109.22629694916423566493964565180'
    - '110.15386446584354006678261842692'
    - '110.66900465330130760688660587863'
    - '111.14231040874906022768427966563'
    - '111.74305925986410764630827144333'
    - '112.841903643811342523538354979322'
    - '113.081341815536358653661519056156'
    - '113.706070187940578716180963871161'
    - '114.75503259853579665042015483396'
    - '115.15068955789255480209121427774'
    - '115.48529313163916387896455828955'
    - '116.44890243147463806763748468840'
    - '116.87410882671947501161650105367'
    - '117.40381088063087856241393165307'
    - '118.02925903737721787694705256952'
    - '118.26613796706626448167343046274'
    - '119.10210396632372103463197772264'
    - '119.837789965042409112989882455609'
    - '120.784187708194924395490441174015'
    - '121.28610373786609924006371981543'
    - '122.10000471386683177125010529220'
    - '122.4717175903972124793373773742'
    - '123.23126233304281265122834453852'
    - '123.69673855089974045654475685371'
    - '124.2614483894229425822773355968'
    - '124.63938804100386483444337744483'
    - '125.47394358433186510778154041477'
    - '126.17554249082194206865786925628'
    - '126.768662123782159791234183675052'
    - '127.40489051275180649324057974830'
    - '127.80232251650644282110687400956'
    - '128.450092636892513202944967204742'
    - '128.82062578066771996930832523600'
    - '129.98627299725658033155120557598'
    - '130.418703591248809920296569849673'
    - '130.91535437967376593689782441691'
    - '131.87918139763272547513512057736'
    - '132.53546472146557170787192762990'
    - '133.101820006095674801935037677412'
    - '133.4202809346661851274178627456'
    - '134.11906107321925956385229645611'
    - '134.821644852309475920750259821819'
    - '134.94133195686562878201186196964'
    - '135.71858863315971915213931578040'
    - '136.36691815137922062941679149852'
    - '137.17529213574940457739421547599'
    - '137.4234903781163969069509130482'
    - '138.33040495030448372576864280616'
    - '139.286178025787766590971168135617'
    - '139.62221182221822812870753541569'
    - '140.41427641424451712308709070417'
    - '140.7882375500606976586194034284'
    - '141.22662416466133734569528443140'
    - '142.049015473640219478865178853447'
    - '142.69602283982997374120033654663'
    - '143.22917855334385818141558385783'
    - '143.93754106176415506810360205688'
    - '144.41217316027622612236783819577'
    - '144.92650984992805134622733776984'
    - '145.67308014844950322772113097430'
    - '145.95761246766617203532057221306'
    - '146.88297780152158515899992970216'
    - '147.01874501280229364895527615683'
    - '147.90492624443258396494405030783'
    - '149.02690229048114728683235393086'
    - '149.54874055906433347005619275940'
    - '150.09598436374055347212061681467'
    - '150.52643835079138052953054724818'
    - '151.1693366345510302366232848398'
    - '151.62701699901772781501010399485'
    - '152.40897484384942272986224479535'
    - '152.90241953959894842762042423089'
    - '153.06257770649281306693011702248'
    - '154.01607951823203472478115757601'
    - '154.60977991470701523082084669727'
    - '155.35226804286890984674502513402'
    - '155.78949326318140746210426453082'
    - '156.59015384572656134731075627371'
    - '157.047673254451960572451769083298'
    - '157.73970898257458479639425090227'
    - '158.38316276969904006206677986176'
    - '159.04027637099642164978715133644'
    - '159.56992217797653937538582149477'
    - '160.13623137076177930539679403219'
    - '160.72686686003274066120818052178'
    - '161.59933434485242834140432627906'
    - '161.94225989398022489712797478133'
    - '162.57266653910742369729039185053'
    - '162.82401805350283153264538679180'
    - '163.698978939528073840697908892518'
    - '163.95151377336092783832999756944'
    - '164.667630757191739520832254337644'
    - '165.33329193050902600844347374863'
    - '166.34409783721106673097305198015'
    - '166.974517773086591483109908350865'
    - '167.27778632751776934123630481268'
    - '168.253846406365496879256602940977'
    - '168.69885780897353544908703346354'
    - '169.00783686643606586013416347716'
    - '169.679724480918830023394521314399'
    - '170.159208272829718979658097661824'
    - '170.67811397880711995261048662645'
    - '171.61648676626801735168822595407'
    - '172.00212171486727083889058778494'
    - '172.87031376116791550517093977832'
    - '173.08096996506883345559016371927'
    - '173.563926145252478627282589805488'
    - '174.52178527923081140020068504057'
    - '175.07833062634189749477493001657'
    - '175.47063236408982909293878489682'
    - '176.48710910194425695970610845728'
    - '176.82272203749160690413597743352'
    - '177.51016728624546360133409666122'
    - '178.35988934181420251978572883692'
    - '178.87400275867753383540649777327'
    - '179.30708730122321737629365310631'
    - '179.58640681360645348940059045864'
    - '180.314699967023409659460317923929'
    - '180.99356567501829477285864837511'
    - '181.4289821918473578150225025434'
    - '182.0358135523868278691324034151'
    - '182.407044262587398742661776523710'
    - '183.35549279686041885754536042721'
    - '184.1219904973645475737966859591'
    - '184.68275910689266680153112982305'
    - '185.5034234272435076884824007592'
    - '185.78231611661937632064329718987'
    - '186.39315687413508153888818029668'
    - '186.80752881639357631647365052698'
    - '187.50593409568563566055705812299'
    - '188.33897278976869575697929507339'
    - '188.4914899843244670575641085647'
    - '189.44593888015661703237275856282'
    - '189.80072416382985478247046920092'
    - '190.441453343295798449842523625886'
    - '191.07880322617822174294312764398'
    - '191.67372586929878342244691847150'
    - '191.86023913664688339853093887181'
    - '192.636246897671713206221170244855'
    - '193.30480352624486023426201416485'
    - '194.206839247600735106788425585605'
    - '194.99729487257621742017300555466'
    - '195.23609117093102951232840697646'
    - '195.94240691839346018775197317772'
    - '196.540605893919163318722884853470'
    - '197.02840054621347491026046304754'
    - '197.41737927574288737255145157578'
    - '198.2190862305223281226756301069'
    - '198.66257891548682428974177305749'
    - '198.98035104301312354831215712474'
    - '199.59960664310705987326102231241'
    prelabel: 1-1375-1375.498-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 147.76427159260942
    root_angle: -0.39956747420434346
    root_number: 0.310309023178484850136149046691-0.950635739983519950573166916132*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.199783737102'
      prec: 50
    spectral_label: r1-0
    st_group: mu(100)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 1.18477001682485939566617655079+0.116289961918898093143640254704*I
    z1:
      __RealLiteral__: 0
      data: '0.356413612509'
      prec: 47
    z2:
      __RealLiteral__: 0
      data: '1.45557770623'
      prec: 44
    z3:
      __RealLiteral__: 0
      data: '2.3807255675'
      prec: 40
- - algebraic: true
    analytic_conductor: 147.76427159260942
    bad_primes:
    - 5
    - 11
    central_character: '1375.498'
    conductor: 1375
    conductor_radical: 55
    degree: 1
    id: 349582
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/1375/498
    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: 1-1375-1375.498-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: 1-1375-1375.498-r1-0
    primitive: true
    rational: false
    root_analytic_conductor: 147.76427159260942
    root_angle: -0.19978373710217173
    self_dual: false
    spectral_label: r1-0
    z1:
      __RealLiteral__: 0
      data: '0.356413612509'
      prec: 47
- - Lhash: dirichlet_L_1375.498
    Lhash_array:
    - dirichlet_L_1375.498
    id: 2070285
    label: 1-1375-1375.498-r1-0-0
    type: DIR
    url: Character/Dirichlet/1375/498
label_cols:
- label
- label
- label
labels:
- 1-1375-1375.498-r1-0-0
- 1-1375-1375.498-r1-0-0
- 1-1375-1375.498-r1-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-25T07:30:24.203083'