data:
- - Lhash: dirichlet_L_49.22
    a10:
    - -0.9009688679024191
    - 0.4338837391175581
    a2:
    - 0.6234898018587335
    - -0.7818314824680298
    a3:
    - -0.9009688679024191
    - -0.4338837391175581
    a4:
    - -0.2225209339563144
    - -0.9749279121818236
    a5:
    - -0.9009688679024191
    - -0.4338837391175581
    a6:
    - -0.9009688679024191
    - 0.4338837391175581
    a7:
    - 1.0
    - -2.8163065144692913e-30
    a8:
    - -0.9009688679024191
    - -0.4338837391175581
    a9:
    - 0.6234898018587335
    - 0.7818314824680298
    algebraic: true
    analytic_conductor: 0.22755504333857055
    analytic_normalization: 0
    bad_lfactors:
    - - 7
      - - 1
    bad_primes:
    - 7
    central_character: '49.22'
    coeff_info:
    - x^7 - 1
    - 0.623489801858734 + 0.781831482468030*I
    - \\zeta_{7}
    conductor: 49
    conductor_radical: 7
    conjugate: dirichlet_L_49.29
    degree: 1
    dirichlet_coefficients:
    - a^0
    - a^6
    - a^4
    - a^5
    - a^4
    - a^3
    - 0
    - a^4
    - a^1
    - a^3
    - a^6
    - a^2
    - a^6
    - 0
    - a^1
    - a^3
    - a^2
    - a^0
    - a^0
    - a^2
    - 0
    - a^5
    - a^5
    - a^1
    - a^1
    - a^5
    - a^5
    - 0
    - a^2
    - a^0
    - a^0
    - a^2
    - a^3
    - a^1
    - 0
    - a^6
    - a^2
    - a^6
    - a^3
    - a^1
    - a^4
    - 0
    - a^3
    - a^4
    - a^5
    - a^4
    - a^6
    - a^0
    - 0
    - a^0
    - a^6
    - a^4
    - a^5
    - a^4
    - a^3
    - 0
    - a^4
    - a^1
    - a^3
    - a^6
    - a^2
    - a^6
    - 0
    - a^1
    - a^3
    - a^2
    - a^0
    - a^0
    - a^2
    - 0
    - a^5
    - a^5
    - a^1
    - a^1
    - a^5
    - a^5
    - 0
    - a^2
    - a^0
    - a^0
    - a^2
    - a^3
    - a^1
    - 0
    - a^6
    - a^2
    - a^6
    - a^3
    - a^1
    - a^4
    - 0
    - a^3
    - a^4
    - a^5
    - a^4
    - a^6
    - a^0
    - 0
    - a^0
    - a^6
    euler_factors:
    - - 1
      - a^6
    - - 1
      - a^4
    - - 1
      - a^4
    - - 0
    - - 1
      - a^6
    - - 1
      - a^6
    - - 1
      - a^2
    - - 1
      - a^0
    - - 1
      - a^5
    - - 1
      - a^2
    - - 1
      - a^0
    - - 1
      - a^2
    - - 1
      - a^4
    - - 1
      - a^3
    - - 1
      - a^6
    - - 1
      - a^5
    - - 1
      - a^3
    - - 1
      - a^2
    - - 1
      - a^0
    - - 1
      - a^5
    - - 1
      - a^1
    - - 1
      - a^0
    - - 1
      - a^1
    - - 1
      - a^1
    - - 1
      - a^0
    - - 1
      - a^4
    gamma_factors:
    - - 0
    - []
    id: 444
    index: 0
    label: 1-7e2-49.22-r0-0-0
    leading_term: 0.308401673978063201214703341693-0.696684753550934297339475281382*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/49/22
    plot_delta:
      __RealLiteral__: 0
      data: '0.3125'
      prec: 20
    plot_values:
    - 0.7618931935270175
    - 0.6482224240353442
    - 0.5243721653948804
    - 0.23132398297410672
    - -0.24466487442169255
    - -0.834594341537267
    - -1.4175503830170517
    - -1.8481366943049928
    - -1.9934769742991532
    - -1.7759273535269204
    - -1.209160891892973
    - -0.4126273782972622
    - 0.40705883547155464
    - 1.0097255840013704
    - 1.1989997666598131
    - 0.8998409592401049
    - 0.2066308341561677
    - -0.6232636652168173
    - -1.2395093724121775
    - -1.3178401406676847
    - -0.6905640446786653
    - 0.5612837544080223
    - 2.097865967686495
    - 3.4104752328022387
    - 3.991138645892234
    - 3.5251638515765684
    - 2.031735942357791
    - -0.11102800690868307
    - -2.2795875321698826
    - -3.8238806824023017
    - -4.309756124299668
    - -3.6850941009377327
    - -2.2947326179870715
    - -0.7308044321793823
    - 0.421612446092841
    - 0.8320853760865348
    - 0.551441821495957
    - -0.04471122869896464
    - -0.4713146965218726
    - -0.4032960011984713
    - 0.13878452645415978
    - 0.7892708123226476
    - 1.0346044585038254
    - 0.5126220759848802
    - -0.7439577155953778
    - -2.2613909010267688
    - -3.322625861994638
    - -3.325788930892365
    - -2.1236646546445366
    - -0.15697628277394413
    - 1.7111555757854382
    - 2.5981215414466052
    - 2.046686538733893
    - 0.27838130328798943
    - -1.89103327381887
    - -3.4469855126030104
    - -3.6854955736273176
    - -2.5684838171638202
    - -0.730481209042498
    - 0.8725152576038552
    - 1.4833576629958178
    - 0.9460698926454569
    - -0.23510208051071335
    - -1.212217237678685
    - -1.3015712613454216
    - -0.38540556581568275
    - 1.029844214469023
    - 2.1323330731842747
    - 2.305991214585125
    - 1.5055181140379061
    - 0.27112304483760435
    - -0.627911370463926
    - -0.695051674081704
    - -0.027733064512689296
    - 0.7611639016188159
    - 0.9856016518107384
    - 0.4110788247429338
    - -0.49410826875738106
    - -0.7805718737933449
    - 0.38798386720858646
    - 3.1254353594147917
    - 6.5984687669155395
    - 9.371311033940001
    - 10.1552643217842
    - 8.531439901544507
    - 5.207524770219473
    - 1.639141604763211
    - -0.7673882753830474
    - -1.3943238148381458
    - -0.6538298832054386
    - 0.39347335968424857
    - 0.7738213754018766
    - 0.20394820655486132
    - -0.8191527053908894
    - -1.469837203679868
    - -1.2466720166022842
    - -0.3561933814152554
    - 0.4449722334651042
    - 0.4316461605334328
    - -0.5128962316183355
    - -1.7596588334075227
    - -2.3618619536694823
    - -1.759907452024762
    - -0.2536080546144016
    - 1.1275221794902646
    - 1.306364881678221
    - -0.06422279208523957
    - -2.2849374040312598
    - -4.014094092076842
    - -4.150538842488172
    - -2.598633330469118
    - -0.3717534610285375
    - 1.0665423241336667
    - 0.7916108338959502
    - -0.9415864360122069
    - -2.8594333986429756
    - -3.533918652392233
    - -2.358167696718774
    - 0.041991807038376454
    - 2.242444115116216
    - 2.988927909918955
    - 2.0155435105349526
    - 0.14941940006576454
    - -1.3405330401338789
    - -1.6498054299478326
    - -0.9326425347865058
    - -0.04808249961613663
    - 0.204177318364612
    - -0.2624323430060821
    - -0.796445683014339
    - -0.622256632192038
    - 0.4180459614594234
    - 1.626445001174487
    - 1.9577341152242618
    - 0.9117485882850346
    - -0.903764026027705
    - -2.049413612770744
    - -1.2509526398672666
    - 1.5857943014454834
    - 5.1219024556221715
    - 7.354173717431689
    - 6.915195962118332
    - 3.995282120802786
    - 0.2212158949942845
    - -2.4293231611164714
    - -2.903033822717234
    - -1.6359688606563365
    - -0.04892166583095639
    - 0.5897018542728167
    - 0.05019207566454415
    - -0.8680660778856435
    - -1.1616976981468885
    - -0.5459978756585561
    - 0.29151766779780797
    - 0.3034262745096092
    - -0.965373287267181
    - -2.897858916511738
    - -4.22333982836009
    - -4.012938591914761
    - -2.4369677945805135
    - -0.6444462217551667
    - 0.15949388457724686
    - -0.31154486350277977
    - -1.2159804306715278
    - -1.3420966659809026
    - -0.2235461770337986
    - 1.3312505218550448
    - 1.7961820843732226
    - 0.18403945468743746
    - -2.9984082520653845
    - -5.916653248279772
    - -6.651272638800629
    - -4.602419498668286
    - -0.9719414431394628
    - 2.0705500823141296
    - 2.9154025166359454
    - 1.57758874671995
    - -0.48315189772246653
    - -1.5850050298172005
    - -1.088681300077655
    - 0.2755478194114782
    - 1.193995528492675
    - 0.9355848874937966
    - -0.09872602179958168
    - -0.8586082818775896
    - -0.6646820280496281
    - 0.1795967790144916
    - 0.7385601003235351
    - 0.42499380092050143
    - -0.31696208997529096
    - -0.3174331861800852
    - 1.2189613066173621
    - 3.775478755232455
    - 5.6526257938992055
    - 5.195873682897251
    - 2.180581803504764
    - -1.8114549711143386
    - -4.425267502532933
    - -4.226560589887166
    - -1.7300658584604165
    - 1.059085151089502
    - 2.2195937942445902
    - 1.3344873279052216
    - -0.3642333422523235
    - -1.1789504935898585
    - -0.4172626875711274
    - 1.088756757092321
    - 1.8051717605795645
    - 0.8949185712088177
    - -1.04191753131989
    - -2.5120221613299383
    - -2.4440837831597353
    - -1.097238520383289
    - 0.22956884768093352
    - 0.39730377791480787
    - -0.5627966282199095
    - -1.5387560958717335
    - -1.4259326240993848
    - -0.19367138178562748
    - 1.074399000237342
    - 1.2231997879097891
    - 0.18410027295205547
    - -0.8722634010609478
    - -0.6126378370183972
    - 1.0864107122138453
    - 2.762643229013297
    - 2.463191967325583
    - -0.5297098198885557
    - -4.828117313178567
    - -7.767595967975726
    - -7.359634886712386
    - -3.8070001397986637
    - 0.6546181120441354
    - 3.449672749537569
    - 3.497570115776006
    - 1.7346897629260858
    - 0.029501155621867316
    - -0.45242211048237324
    - -0.008274051601162194
    - 0.25227430262123895
    - -0.29826907117516654
    - -1.1562095813535325
    - -1.2755414965960288
    - -0.25690189695493787
    - 1.0909348915378072
    - 1.434607066559312
    - 0.23209670833820073
    - -1.6022145374094101
    - -2.4077188687031987
    - -1.2888419784855278
    - 0.9672908450691278
    - 2.4920323719577064
    - 2.0004826268622757
    - 0.03443392603349068
    - -1.3992993996653837
    - -0.5585131842309319
    - 2.4390054048259993
    - 5.5962554180836666
    - 6.661950024952946
    - 4.99855395254806
    - 2.0603770452410197
    - 0.07934678863935399
    - 0.14617863730151243
    - 1.388358281450842
    - 1.9265632679164948
    - 0.6787442134851133
    - -1.650938991746384
    - -3.263079632209948
    - -2.9348456381331993
    - -1.100637621158386
    - 0.6235756726543856
    - 0.9551082528624761
    - 0.03571043212438905
    - -0.8949080684222126
    - -0.8354809223510244
    - 0.0034880591728010685
    - 0.5573000830963051
    - 0.19381271481749712
    - -0.4474025967409664
    - -0.02971837843802364
    - 1.9593259101110525
    - 4.26401104385489
    - 4.604321488758757
    - 1.6419170230462021
    - -3.565651499227143
    - -8.056550233897312
    - -9.151007110338952
    - -6.524433858262571
    - -2.38722310610194
    - 0.3743041840064593
    - 0.46742147885140833
    - -1.0587111789580987
    - -2.094658581477126
    - -1.47497343307026
    - 0.14290454055865415
    - 1.1963631849017793
    - 0.8812838395413101
    - -0.11215137854413526
    - -0.4471250541708761
    - 0.38099153305734107
    - 1.4896221094108408
    - 1.5560011621461123
    - 0.2869952212564364
    - -1.1316614119560888
    - -1.1382804797586765
    - 0.606789809285902
    - 2.749296489144532
    - 3.4493315907122284
    - 2.146676727679326
    - 0.14289095658041456
    - -0.6345181096601181
    - 0.46912284343374144
    - 2.1417057913100646
    - 2.3658584443567108
    - 0.4756883331339697
    - -1.9972610351685942
    - -2.602459744634455
    - -0.2569691647376456
    - 3.5979918261526627
    - 6.107483267707702
    - 5.413301959177751
    - 2.183818108426529
    - -1.0879329235018405
    - -2.2955451848584967
    - -1.3765172670399193
    - 0.013389050381542377
    - 0.30206176792432526
    - -0.5630041801551228
    - -1.3691919663799041
    - -1.1372167829077067
    - -0.20440452399521541
    - 0.22888999653960998
    - -0.46635712630062737
    - -1.5427114631620154
    - -1.6369765320584235
    - -0.32934540053469413
    - 1.2073090187619084
    - 1.3120246663132087
    - -0.3091678566997028
    - -1.9111113830773192
    - -1.1183459105119975
    - 2.7560740854696597
    - 7.702851365674933
    - 10.439548320933435
    - 9.106963006376585
    - 4.817365668763277
    - 0.6467706532918842
    - -0.980106820285737
    - -0.11546977258191585
    - 1.2378664731000606
    - 1.2967461762813917
    - 0.11927727251579535
    - -0.8113659706835102
    - -0.41883941841562267
    - 0.7159066582560161
    - 0.9784101505495038
    - -0.48726007454171627
    - -2.7407673883496284
    - -3.8826808401870436
    - -2.922285472407456
    - -0.7517724197827799
    - 0.7723392589547982
    - 0.6746336463819409
    - -0.28760100723372417
    - -0.6279866471082256
    - 0.12138912541758874
    - 0.8388114459672553
    - 0.09853304779735897
    - -2.0295405271808424
    - -3.6749013615212505
    - -2.8918390470594586
    - 0.21086145722906707
    - 3.1623519656770354
    - 3.181515714218454
    - -0.23889806323051746
    - -4.699056786989266
    - -6.904631241371018
    - -5.494637336423023
    - -2.0722537925690028
    - 0.4380677109375176
    - 0.4464453299582049
    - -1.1481888814785721
    - -2.218680461811331
    - -1.618894500152691
    - -0.10160045940452725
    - 0.790528217889427
    - 0.47270996640550905
    - -0.2134292032209015
    - -0.2008913066733882
    - 0.4116067648252026
    - 0.4362093068345108
    - -0.8922193145789734
    - -2.6959316023544986
    - -3.0532984229228335
    - -0.9859008540852908
    - 2.2332749516212105
    - 3.9977517692899895
    - 2.799810836153589
    - -0.21212955150849294
    - -2.209964207270563
    - -1.351152391964629
    - 1.463696773969891
    - 3.4983765585934616
    - 2.8696366511924976
    - 0.3500947150299594
    - -1.4831025489157001
    - -0.8486768944150087
    - 1.5245839806976116
    - 3.2465483925576093
    - 2.724141015921775
    - 0.6870146147772334
    - -0.7133397677101403
    - -0.18677919798206533
    - 1.4439798990526582
    - 2.2586966707981775
    - 1.3391626074591196
    - -0.3144305917687745
    - -0.967028287865321
    - -0.06756062114292367
    - 1.2076897067926784
    - 1.3361064068362853
    - 0.16830373917495364
    - -0.9582820545605661
    - -0.8383210560602512
    - 0.1147338709414907
    - 0.3061383114275692
    - -1.0256586483736956
    - -2.4602430939401008
    - -1.4490351705537772
    - 3.015032310264186
    - 8.80733257243376
    - 12.021116542667926
    - 10.23675529294199
    - 4.672534365130077
    - -0.8521979287675661
    - -3.1619943359125626
    - -2.122883099791295
    - -0.09657387221632774
    - 0.6928326827662991
    - 0.11235815741898805
    - -0.3856215951829241
    - 0.18429984646211434
    - 1.1568059738527658
    - 1.132879633196868
    - -0.20802414366915517
    - -1.5789540439494418
    - -1.49785159263212
    - -0.03746723937642456
    - 1.134140588811328
    - 0.5690323472171271
    - -1.2779578660992466
    - -2.43953444530579
    - -1.581084764658515
    - 0.4273096434826015
    - 1.3299307203310888
    - -0.06240704943999008
    - -2.414984743815245
    - -3.09334297916982
    - -0.9105582058599615
    - 2.479684841306069
    - 4.101055261915757
    - 2.59984813272315
    - -0.4152030538492978
    - -2.043040418458715
    - -1.0472031841420555
    - 0.9581143860012393
    - 1.283591793693347
    - -0.9963470435660217
    - -4.09440784790301
    - -5.357740075313561
    - -3.8963190901976943
    - -1.274357595705177
    - 0.284627067588421
    - 0.10986331517753017
    - -0.6180958784851014
    - -0.5629094863394647
    - 0.1780102364248697
    - 0.3983210989628822
    - -0.5043317884910025
    - -1.604990701087748
    - -1.5470010613351062
    - -0.4197100680814462
    - -0.07583536552879391
    - -2.199836431811213
    - -6.095657189673911
    - -8.785609051648029
    - -7.6982833948202884
    - -3.352158822357478
    - 0.8198407504707018
    - 1.546477401806139
    - -1.2753022128853606
    - -4.621377888509829
    - -5.336110330985305
    - -3.032370709652425
    - -0.07479366830295982
    - 1.0749318610491274
    - 0.22908821835233917
    - -0.8074414341279231
    - -0.5477514163825113
    - 0.5628456605507366
    - 0.9504839763886034
    - 0.014487707027967221
    - -1.0266873031504091
    - -0.5597536993716598
    - 1.4034449351331413
    - 3.021109611349641
    - 2.5739401936588013
    - 0.40638110596610083
    - -1.372554442200062
    - -1.1511314102903345
    - 0.48467864591021764
    - 1.5364771755478583
    - 0.9658942711579288
    - -0.0992939858812474
    - 0.202944938334626
    - 1.9785726317554038
    - 2.975919113445661
    - 0.8382864841589436
    - -4.067098217579942
    - -8.405826968779655
    - -8.777354980383135
    - -4.944710458427999
    - -0.09618323205767342
    - 2.1499863807269715
    - 0.9644045088578921
    - -1.4037236731904246
    - -2.2789189653420463
    - -1.1900729066798517
    - 0.16935920148192116
    - 0.22852408278293943
    - -0.6969879473270439
    - -1.0578939895371047
    - -0.12486890832921248
    - 1.1122239529930404
    - 1.2341634574726226
    - 0.21676950897952552
    - -0.512336815857446
    - 0.0777062951332762
    - 1.1309242337976286
    - 0.7574793501878407
    - -1.5489610035378116
    - -3.7644443534982774
    - -3.1066832737035135
    - 0.9107328825367162
    - 5.475012955108095
    - 6.880045812718586
    - 4.05085752394682
    - -0.4355520044848258
    - -2.908569591951359
    - -2.079455826233524
    - 0.11976478958614914
    - 0.9910485308101047
    - -0.015516076712173902
    - -1.0587427528391298
    - -0.3596695063674079
    - 1.5954756921404498
    - 2.6089416915343104
    - 1.3553366757755094
    - -1.0286063699697485
    - -2.1665323161689805
    - -1.048093264857858
    - 0.9518115416789243
    - 1.724853533759393
    - 0.7652376038146302
    - -0.496671600473224
    - -0.6216913340171654
    - 0.05595682357784013
    - -0.03949890803956858
    - -1.5548340419061955
    - -3.1294383277779487
    - -2.8976791658980865
    - -0.9063625970176706
    - 0.5386726768842157
    - -0.657907658086134
    - -3.711260482189201
    - -5.258132133892676
    - -2.6805669438524284
    - 2.940094689360526
    - 7.487092233990711
    - 7.593806672832965
    - 3.7289179426747032
    - -0.5110511586180161
    - -2.0031928361828344
    - -0.788816832064355
    - 0.7062021812783978
    - 0.6376294560759019
    - -0.5186235987453814
    - -1.1013241388653348
    - -0.5215635407210335
    - 0.176628157453405
    - -0.04157379778650825
    - -0.6190961651325796
    - -0.019993297987692785
    - 2.1391440420083945
    - 4.1488927227307855
    - 3.865353581947349
    - 1.2080533089580288
    - -1.4828528520218958
    - -1.871790640863519
    - -0.19479385924389156
    - 1.015363540001788
    - -0.13545488229598038
    - -2.602681857301464
    - -3.4452301284084346
    - -1.160006130515569
    - 2.4270404508761123
    - 3.934613925935226
    - 1.9968583260146864
    - -1.2914614552357455
    - -2.6445398543551106
    - -1.0479224576371025
    - 1.372077737727708
    - 1.8928087988898281
    - 0.18546194929608104
    - -1.5622281946189067
    - -1.332348547707766
    - 0.4322575203189284
    - 1.5022615245970086
    - 0.5426285972199419
    - -1.405978689701739
    - -2.2781587174132527
    - -1.404100399682396
    - -0.08150321829684186
    - 0.24543047277796004
    - -0.19675250390061927
    - -0.008487013880226735
    - 1.2477481075153327
    - 2.13734171606631
    - 1.1134212993093946
    - -1.0347808787815804
    - -1.2610815758351623
    - 2.6376435257497373
    - 9.105136522150879
    - 13.563705624277802
    - 12.484126338813958
    - 6.725584775109028
    - 0.6660290969622784
    - -1.956119027936297
    - -1.1656735160198302
    - 0.1715062934002246
    - -0.12785892389571202
    positive_zeros:
    - '1.10243920634589678238791755155'
    - '3.59021991559673552754788675845'
    - '5.07778570447666233172176451792'
    - '6.43699204361261560893900551562'
    - '8.42221009240629092763690514606'
    - '10.488999912389959454635374465411'
    - '11.53897447740747797473114158446'
    - '12.4345250357034266273340176781'
    - '13.58282255614661952312209072955'
    - '15.336150675731618719359333403939'
    - '16.602729950860218375770954336947'
    - '18.2515969252552190770872343907'
    - '19.3157260086256144632086963924'
    - '20.40135811763955304356491623265'
    - '21.94942948652353453437163745056'
    - '22.822612007233742848441980031426'
    - '23.88846337712835952973659075678'
    - '24.621526593735992455521018558704'
    - '27.061499162392013220642195518484'
    - '27.99680404912355304610707158426'
    - '28.8155034193021144430942922568'
    - '30.11667416769505129577758486392'
    - '30.79743730706022787391175372554'
    - '32.236018278314702227574836393'
    - '33.11484175795562833495853478095'
    - '34.74627775564285254070092504145'
    - '35.47634388963852537777203218257'
    - '36.86987461649000218348693422013'
    - '38.15010061287315528015796006717'
    - '39.3989039600812254937904296086'
    - '39.863512399403731376397087552797'
    - '40.8324834535525632921126903797'
    - '42.03461679213575534046652621976'
    - '42.97227835806535187995499433470'
    - '44.707473543839939525919462838703'
    - '45.949891845920647112945613802884'
    - '46.5794584256713976058416524713'
    - '47.68735576703018385633342227409'
    - '48.23322662347154946391461606460'
    - '50.18619520721980264917104018994'
    - '50.49804695290660155084741692525'
    - '51.606216998356873876326653493067'
    - '52.52148288587948973284993975495'
    - '54.14712851183468244523114357646'
    - '55.234008821619150106006268182524'
    - '56.187949681662532390910791479044'
    - '57.15913490722618588414745795725'
    - '58.0618348210778598719584547307'
    - '58.92223696751160763933658298988'
    - '59.47474741289492333665562835889'
    - '61.105793023567118003630896373691'
    - '62.36896416829222307675029133323'
    - '63.36611636204678256724746844598'
    - '64.15116726742949380520254951119'
    - '65.151271968602851307239431960410'
    - '66.49060872337916926825754449132'
    - '67.03257836733736056030341248893'
    - '68.16585430029670463533521122203'
    - '69.10661521414249844366532255626'
    - '69.8225268617540226573912398728'
    - '70.89544169343755976885970018588'
    - '72.45027846142189167230546801101'
    - '73.75802368852784392269927588254'
    - '74.3798225982962010860644024183'
    - '74.88020525157306235145935651435'
    - '75.993630478459318351185784220508'
    - '76.91486823723133062722773246726'
    - '77.99453346148919652332268375550'
    - '79.06768292939946916630597572353'
    - '79.76058831692945201757124974040'
    - '81.591004285066940591053863317'
    - '81.81920828164476064244655058656'
    - '82.90880216449150899171170775896'
    - '84.23987391773539204109689032395'
    - '85.00961568098861398123437880177'
    - '85.93626792746067979821622553733'
    - '86.644254974061200273758138882870'
    - '87.19476139311599860740340163661'
    - '88.54360935474798964963873036794'
    - '90.24542291453222170387590662892'
    - '90.73662128537576907246046734221'
    - '91.847258836690795156373227478571'
    - '92.773731081543048548352693714228'
    - '93.33130965706910741916862060525'
    - '94.42978141993686482679345780563'
    - '95.2257034238383139941689033305'
    - '96.59043386149275288842480715970'
    - '97.09657747623158218683098459540'
    - '98.18143391292064605471537560754'
    - '99.08488289817524112359174772559'
    - '100.50538911180961318843979150779'
    - '101.55834284764824546350224988191'
    - '102.0148666383046848016093924073'
    - '103.20481283553883996988527079068'
    - '103.5965545710911848501252846320'
    - '104.74678298408260242854342587078'
    - '105.57713950005623853506019398840'
    - '106.36489553768604363299766305929'
    - '108.19748352152951643209642541496'
    - '108.77374448518977683387531332485'
    - '109.71577079949275816427025235301'
    - '110.429411503396562843038813271860'
    - '111.17503967723885395753276101827'
    - '112.62000589274883239638090049514'
    - '113.34309982681926341494903043727'
    - '114.02488114855244218202850335298'
    - '114.70594057927925039040559459392'
    - '115.91900703435769432827612598623'
    - '116.85835078292972548418257454201'
    - '118.35536562824890858745268574680'
    - '118.85238970587181767304627103901'
    - '120.02264194149027474323904996794'
    - '120.822227759644889574025484813070'
    - '121.362125086444881866487173548527'
    - '122.0143987941582074018054390411'
    - '123.22147489742991694686031941430'
    - '124.35308048928928452748136532149'
    - '125.1595938643344977440286244506'
    - '126.292561145811239608088568066307'
    - '126.99832259457635387357361376127'
    - '128.23778877376565336409581326359'
    - '128.79030652570620713108525435887'
    - '129.934595610462351944933349806014'
    - '130.64018962328611598446958115106'
    - '131.599515398195726497975262529514'
    - '132.459829691652150852829967882987'
    - '132.91866576445815913796793162286'
    - '133.87713432474942993891432216180'
    - '135.56641552198232022911571493048'
    - '136.581514192698511486434709007455'
    - '137.231482380238025902725784176953'
    - '137.751856316666359648311640222377'
    - '138.710566758568251047930515862102'
    - '139.69460049478795815108971931659'
    - '140.418863123681802597171341212326'
    - '141.49371505445310556882044673706'
    - '142.17891963100438377055416742160'
    - '143.20847177473100954484486842080'
    - '144.32959673410648946525680674746'
    - '145.15505533852340252447725217621'
    - '145.831933902359204596533569356985'
    - '147.40315437940150144220041866357'
    - '147.85715984056324352888592663152'
    - '148.67561195266473728764441038920'
    - '149.23857080660771087596588601366'
    - '150.475382020045002720401689390589'
    - '150.58462034585072905791284214933'
    - '152.42097274182466639788446490550'
    - '153.01247214290194383046757813566'
    - '154.38523572083757664529720242982'
    - '155.054907746983227448963427590200'
    - '155.781847107532378326188958703904'
    - '156.56597608454889020356344620631'
    - '157.29266613555729130766895871816'
    - '158.492249644790989972971947246296'
    - '159.2881001498440178518998433857'
    - '160.269244229916258077385939285'
    - '160.566503288126324043673028669357'
    - '161.62524538767389384457453819065'
    - '163.13259833204524510074015137220'
    - '163.87278017335757599040742805736'
    - '164.94502369787870123252031284098'
    - '165.40288296455270024227760027613'
    - '166.27847231697019592415241153130'
    - '167.24845010188606442300611344082'
    - '167.7904301709297341977156009717'
    - '168.56312434913825219822869588795'
    - '169.62914233555805279003047944949'
    - '170.90428524926147130382895340144'
    - '171.855506720698929079299995267156'
    - '172.49660945842799887555571472397'
    - '173.18909492421802385447002108733'
    - '174.23803492635224837797759070968'
    - '175.15801685854870855286166616384'
    - '176.10636048422370836213681711430'
    - '176.84534670222158125398097978304'
    - '177.17269680438752321724318556186'
    - '178.58189109793893840771409569679'
    - '178.96876985335636910217583624862'
    - '180.15774709589053281922322851054'
    - '181.51530074566375082351929966526'
    - '182.32691755078722153538985162235'
    - '182.99147075445686931316836713097'
    - '183.948974889384973058045824092057'
    - '184.35397486911332216036044964067'
    - '185.004125326767552217358351384287'
    - '186.37173995789464617534017087984'
    - '187.219605909733876720379801036'
    - '187.793158037393224424951228004664'
    - '188.84913303089839615538199605247'
    - '189.87105321665475330942563676085'
    - '190.749997589537428814320730552668'
    - '191.58901158306886997440348722514'
    - '192.42796042986961176161517533452'
    - '193.21322084002253817781044738139'
    - '194.40321756400210071726260658328'
    - '194.86624939786335900984733591341'
    - '195.31570330992432093565834843027'
    - '196.40842107461092161819377346442'
    - '197.01769840691080178757012957554'
    - '198.79732455826755647152084689883'
    - '199.62438107040909381145186206189'
    - '199.962227792554508889827006425905'
    prelabel: 1-7e2-49.22-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.22755504333857055
    root_angle: -0.7346938775510204
    root_number: -0.672300890261316788086418461638-0.740277997075315538873945518960*I
    self_dual: false
    sign_arg:
      __RealLiteral__: 0
      data: '-0.367346938776'
      prec: 50
    spectral_label: r0-0
    st_group: mu(7)
    symmetry_type: unitary
    types:
    - DIR
    values:
    - - 1
      - 0.667356520073934661676353244387-0.627986489034412688278392425911*I
    z1:
      __RealLiteral__: 0
      data: '1.10243920635'
      prec: 44
    z2:
      __RealLiteral__: 0
      data: '3.5902199156'
      prec: 40
    z3:
      __RealLiteral__: 0
      data: '5.07778570448'
      prec: 44
- - algebraic: true
    analytic_conductor: 0.22755504333857055
    bad_primes:
    - 7
    central_character: '49.22'
    conductor: 49
    conductor_radical: 7
    degree: 1
    id: 444
    index: 0
    instance_types:
    - DIR
    instance_urls:
    - Character/Dirichlet/49/22
    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: 1-7e2-49.22-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: 1-7e2-49.22-r0-0
    primitive: true
    rational: false
    root_analytic_conductor: 0.22755504333857055
    root_angle: -0.3673469387755102
    self_dual: false
    spectral_label: r0-0
    z1:
      __RealLiteral__: 0
      data: '1.10243920635'
      prec: 44
- - Lhash: dirichlet_L_49.22
    Lhash_array:
    - dirichlet_L_49.22
    id: 1781865
    label: 1-7e2-49.22-r0-0-0
    type: DIR
    url: Character/Dirichlet/49/22
label_cols:
- label
- label
- label
labels:
- 1-7e2-49.22-r0-0-0
- 1-7e2-49.22-r0-0-0
- 1-7e2-49.22-r0-0-0
tables:
- lfunc_lfunctions
- lfunc_search
- lfunc_instances
timestamp: '2024-04-24T06:17:08.200668'