Properties

Label 81.2.g.a.31.5
Level 8181
Weight 22
Character 81.31
Analytic conductor 0.6470.647
Analytic rank 00
Dimension 144144
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 81=34 81 = 3^{4}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 81.g (of order 2727, degree 1818, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.6467882563720.646788256372
Analytic rank: 00
Dimension: 144144
Relative dimension: 88 over Q(ζ27)\Q(\zeta_{27})
Twist minimal: yes
Sato-Tate group: SU(2)[C27]\mathrm{SU}(2)[C_{27}]

Embedding invariants

Embedding label 31.5
Character χ\chi == 81.31
Dual form 81.2.g.a.34.5

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.130814+0.303261i)q2+(0.919544+1.46780i)q3+(1.297631.37541i)q4+(0.175343+3.01052i)q5+(0.5654150.0868526i)q6+(0.008954930.00212236i)q7+(1.20756+0.439517i)q8+(1.308882.69941i)q9+(0.935909+0.340643i)q10+(2.973121.95545i)q11+(0.825596+3.16941i)q12+(3.51646+0.411015i)q13+(0.00181506+0.00243804i)q14+(4.257613.02567i)q15+(0.1952173.35174i)q16+(3.093192.59549i)q17+(0.6474060.750053i)q18+(5.540964.64941i)q19+(3.91316+4.14770i)q20+(0.00511925+0.0150957i)q21+(0.981937+0.645830i)q22+(5.003171.18577i)q23+(1.75553+1.36831i)q24+(4.066290.475281i)q25+(0.5846471.01264i)q26+(5.16577+0.561054i)q27+(0.008701070.0150707i)q28+(2.83907+3.81353i)q29+(0.3606131.68696i)q30+(2.59221+8.65858i)q31+(3.287661.65112i)q32+(0.136301+6.16207i)q33+(0.3824791.27757i)q34+(0.00481921+0.0273311i)q35+(5.411231.70260i)q36+(0.02419860.137237i)q37+(2.13482+1.07215i)q38+(2.630255.53941i)q39+(1.53491+3.55832i)q40+(1.42815+3.31082i)q41+(0.00524759+0.000422254i)q42+(1.09801+0.551444i)q43+(1.168476.62670i)q44+(8.356143.46708i)q45+(0.2948861.67238i)q46+(0.2989730.998641i)q47+(5.09920+2.79553i)q48+(6.25535+3.14156i)q49+(0.3877931.29532i)q50+(6.653992.15352i)q51+(3.99775+5.36991i)q52+(1.887783.26973i)q53+(0.505609+1.63997i)q54+(5.36561+9.29351i)q55+(0.0117464+0.00137296i)q56+(1.72926+12.4084i)q57+(1.527880.362115i)q58+(4.336152.85193i)q59+(9.68632+1.92974i)q60+(4.702814.98469i)q61+(2.28671+1.91878i)q62+(0.01745000.0213951i)q63+(4.213083.53519i)q64+(0.62078410.6584i)q65+(1.85088+0.847419i)q66+(4.97104+6.67727i)q67+(7.58367+0.886403i)q68+(6.341116.25329i)q69+(0.00765804+0.00503677i)q70+(2.49894+0.909541i)q71+(0.3941163.83498i)q72+(2.10657+0.766729i)q73+(0.04478410.0106140i)q74+(4.436755.53146i)q75+(0.79527113.6543i)q76+(0.02247390.0238210i)q77+(2.02396+0.0730195i)q78+(1.637893.79706i)q79+10.1247q80+(5.57367+7.06641i)q811.19086q82+(5.1095911.8454i)q83+(0.0141198+0.0266296i)q84+(8.356158.85700i)q85+(0.0235956+0.405121i)q86+(2.986867.67390i)q87+(4.449681.05459i)q88+(9.213133.35330i)q89+(2.14453+2.08055i)q90+(0.0306173+0.0111438i)q91+(8.12317+5.34270i)q92+(15.09274.15709i)q93+(0.3419580.0399692i)q94+(13.0256+17.4964i)q95+(0.599623+6.34391i)q96+(0.917855+15.7590i)q97+(1.771001.48604i)q98+(9.170035.46623i)q99+O(q100)q+(0.130814 + 0.303261i) q^{2} +(-0.919544 + 1.46780i) q^{3} +(1.29763 - 1.37541i) q^{4} +(-0.175343 + 3.01052i) q^{5} +(-0.565415 - 0.0868526i) q^{6} +(0.00895493 - 0.00212236i) q^{7} +(1.20756 + 0.439517i) q^{8} +(-1.30888 - 2.69941i) q^{9} +(-0.935909 + 0.340643i) q^{10} +(2.97312 - 1.95545i) q^{11} +(0.825596 + 3.16941i) q^{12} +(-3.51646 + 0.411015i) q^{13} +(0.00181506 + 0.00243804i) q^{14} +(-4.25761 - 3.02567i) q^{15} +(-0.195217 - 3.35174i) q^{16} +(-3.09319 - 2.59549i) q^{17} +(0.647406 - 0.750053i) q^{18} +(5.54096 - 4.64941i) q^{19} +(3.91316 + 4.14770i) q^{20} +(-0.00511925 + 0.0150957i) q^{21} +(0.981937 + 0.645830i) q^{22} +(-5.00317 - 1.18577i) q^{23} +(-1.75553 + 1.36831i) q^{24} +(-4.06629 - 0.475281i) q^{25} +(-0.584647 - 1.01264i) q^{26} +(5.16577 + 0.561054i) q^{27} +(0.00870107 - 0.0150707i) q^{28} +(-2.83907 + 3.81353i) q^{29} +(0.360613 - 1.68696i) q^{30} +(2.59221 + 8.65858i) q^{31} +(3.28766 - 1.65112i) q^{32} +(0.136301 + 6.16207i) q^{33} +(0.382479 - 1.27757i) q^{34} +(0.00481921 + 0.0273311i) q^{35} +(-5.41123 - 1.70260i) q^{36} +(0.0241986 - 0.137237i) q^{37} +(2.13482 + 1.07215i) q^{38} +(2.63025 - 5.53941i) q^{39} +(-1.53491 + 3.55832i) q^{40} +(-1.42815 + 3.31082i) q^{41} +(-0.00524759 + 0.000422254i) q^{42} +(1.09801 + 0.551444i) q^{43} +(1.16847 - 6.62670i) q^{44} +(8.35614 - 3.46708i) q^{45} +(-0.294886 - 1.67238i) q^{46} +(0.298973 - 0.998641i) q^{47} +(5.09920 + 2.79553i) q^{48} +(-6.25535 + 3.14156i) q^{49} +(-0.387793 - 1.29532i) q^{50} +(6.65399 - 2.15352i) q^{51} +(-3.99775 + 5.36991i) q^{52} +(1.88778 - 3.26973i) q^{53} +(0.505609 + 1.63997i) q^{54} +(5.36561 + 9.29351i) q^{55} +(0.0117464 + 0.00137296i) q^{56} +(1.72926 + 12.4084i) q^{57} +(-1.52788 - 0.362115i) q^{58} +(-4.33615 - 2.85193i) q^{59} +(-9.68632 + 1.92974i) q^{60} +(-4.70281 - 4.98469i) q^{61} +(-2.28671 + 1.91878i) q^{62} +(-0.0174500 - 0.0213951i) q^{63} +(-4.21308 - 3.53519i) q^{64} +(-0.620784 - 10.6584i) q^{65} +(-1.85088 + 0.847419i) q^{66} +(4.97104 + 6.67727i) q^{67} +(-7.58367 + 0.886403i) q^{68} +(6.34111 - 6.25329i) q^{69} +(-0.00765804 + 0.00503677i) q^{70} +(-2.49894 + 0.909541i) q^{71} +(-0.394116 - 3.83498i) q^{72} +(2.10657 + 0.766729i) q^{73} +(0.0447841 - 0.0106140i) q^{74} +(4.43675 - 5.53146i) q^{75} +(0.795271 - 13.6543i) q^{76} +(0.0224739 - 0.0238210i) q^{77} +(2.02396 + 0.0730195i) q^{78} +(-1.63789 - 3.79706i) q^{79} +10.1247 q^{80} +(-5.57367 + 7.06641i) q^{81} -1.19086 q^{82} +(-5.10959 - 11.8454i) q^{83} +(0.0141198 + 0.0266296i) q^{84} +(8.35615 - 8.85700i) q^{85} +(-0.0235956 + 0.405121i) q^{86} +(-2.98686 - 7.67390i) q^{87} +(4.44968 - 1.05459i) q^{88} +(-9.21313 - 3.35330i) q^{89} +(2.14453 + 2.08055i) q^{90} +(-0.0306173 + 0.0111438i) q^{91} +(-8.12317 + 5.34270i) q^{92} +(-15.0927 - 4.15709i) q^{93} +(0.341958 - 0.0399692i) q^{94} +(13.0256 + 17.4964i) q^{95} +(-0.599623 + 6.34391i) q^{96} +(0.917855 + 15.7590i) q^{97} +(-1.77100 - 1.48604i) q^{98} +(-9.17003 - 5.46623i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q18q218q318q418q518q618q718q818q918q1018q1118q1218q1318q1418q1518q1618q179q1818q19++54q99+O(q100) 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/81Z)×\left(\mathbb{Z}/81\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(1027)e\left(\frac{10}{27}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.130814 + 0.303261i 0.0924994 + 0.214438i 0.958184 0.286151i 0.0923760π-0.0923760\pi
−0.865685 + 0.500589i 0.833117π0.833117\pi
33 −0.919544 + 1.46780i −0.530899 + 0.847435i
44 1.29763 1.37541i 0.648814 0.687703i
55 −0.175343 + 3.01052i −0.0784157 + 1.34635i 0.697988 + 0.716109i 0.254079π0.254079\pi
−0.776404 + 0.630236i 0.782958π0.782958\pi
66 −0.565415 0.0868526i −0.230830 0.0354574i
77 0.00895493 0.00212236i 0.00338465 0.000802176i −0.228923 0.973444i 0.573520π-0.573520\pi
0.232308 + 0.972642i 0.425372π0.425372\pi
88 1.20756 + 0.439517i 0.426938 + 0.155393i
99 −1.30888 2.69941i −0.436293 0.899805i
1010 −0.935909 + 0.340643i −0.295961 + 0.107721i
1111 2.97312 1.95545i 0.896429 0.589591i −0.0155264 0.999879i 0.504942π-0.504942\pi
0.911956 + 0.410289i 0.134572π0.134572\pi
1212 0.825596 + 3.16941i 0.238329 + 0.914929i
1313 −3.51646 + 0.411015i −0.975291 + 0.113995i −0.588783 0.808291i 0.700393π-0.700393\pi
−0.386508 + 0.922286i 0.626319π0.626319\pi
1414 0.00181506 + 0.00243804i 0.000485094 + 0.000651595i
1515 −4.25761 3.02567i −1.09931 0.781225i
1616 −0.195217 3.35174i −0.0488042 0.837936i
1717 −3.09319 2.59549i −0.750208 0.629500i 0.185350 0.982673i 0.440658π-0.440658\pi
−0.935558 + 0.353173i 0.885103π0.885103\pi
1818 0.647406 0.750053i 0.152595 0.176789i
1919 5.54096 4.64941i 1.27118 1.06665i 0.276786 0.960931i 0.410731π-0.410731\pi
0.994396 0.105717i 0.0337139π-0.0337139\pi
2020 3.91316 + 4.14770i 0.875008 + 0.927455i
2121 −0.00511925 + 0.0150957i −0.00111711 + 0.00329414i
2222 0.981937 + 0.645830i 0.209350 + 0.137691i
2323 −5.00317 1.18577i −1.04323 0.247251i −0.326936 0.945046i 0.606016π-0.606016\pi
−0.716297 + 0.697796i 0.754164π0.754164\pi
2424 −1.75553 + 1.36831i −0.358346 + 0.279304i
2525 −4.06629 0.475281i −0.813258 0.0950562i
2626 −0.584647 1.01264i −0.114659 0.198595i
2727 5.16577 + 0.561054i 0.994154 + 0.107975i
2828 0.00870107 0.0150707i 0.00164435 0.00284809i
2929 −2.83907 + 3.81353i −0.527202 + 0.708155i −0.983345 0.181751i 0.941823π-0.941823\pi
0.456142 + 0.889907i 0.349231π0.349231\pi
3030 0.360613 1.68696i 0.0658386 0.307996i
3131 2.59221 + 8.65858i 0.465574 + 1.55513i 0.792376 + 0.610033i 0.208844π0.208844\pi
−0.326801 + 0.945093i 0.605971π0.605971\pi
3232 3.28766 1.65112i 0.581181 0.291880i
3333 0.136301 + 6.16207i 0.0237269 + 1.07268i
3434 0.382479 1.27757i 0.0655946 0.219101i
3535 0.00481921 + 0.0273311i 0.000814596 + 0.00461980i
3636 −5.41123 1.70260i −0.901871 0.283766i
3737 0.0241986 0.137237i 0.00397822 0.0225616i −0.982754 0.184918i 0.940798π-0.940798\pi
0.986732 + 0.162356i 0.0519093π0.0519093\pi
3838 2.13482 + 1.07215i 0.346313 + 0.173925i
3939 2.63025 5.53941i 0.421177 0.887016i
4040 −1.53491 + 3.55832i −0.242691 + 0.562620i
4141 −1.42815 + 3.31082i −0.223039 + 0.517063i −0.992588 0.121525i 0.961222π-0.961222\pi
0.769549 + 0.638587i 0.220481π0.220481\pi
4242 −0.00524759 0.000422254i −0.000809720 6.51553e-5i
4343 1.09801 + 0.551444i 0.167446 + 0.0840943i 0.530548 0.847655i 0.321986π-0.321986\pi
−0.363102 + 0.931749i 0.618282π0.618282\pi
4444 1.16847 6.62670i 0.176153 0.999012i
4545 8.35614 3.46708i 1.24566 0.516842i
4646 −0.294886 1.67238i −0.0434785 0.246579i
4747 0.298973 0.998641i 0.0436098 0.145667i −0.933412 0.358807i 0.883184π-0.883184\pi
0.977022 + 0.213140i 0.0683690π0.0683690\pi
4848 5.09920 + 2.79553i 0.736006 + 0.403500i
4949 −6.25535 + 3.14156i −0.893622 + 0.448794i
5050 −0.387793 1.29532i −0.0548422 0.183186i
5151 6.65399 2.15352i 0.931745 0.301553i
5252 −3.99775 + 5.36991i −0.554388 + 0.744672i
5353 1.88778 3.26973i 0.259307 0.449133i −0.706750 0.707464i 0.749839π-0.749839\pi
0.966056 + 0.258331i 0.0831726π0.0831726\pi
5454 0.505609 + 1.63997i 0.0688047 + 0.223172i
5555 5.36561 + 9.29351i 0.723499 + 1.25314i
5656 0.0117464 + 0.00137296i 0.00156968 + 0.000183470i
5757 1.72926 + 12.4084i 0.229047 + 1.64353i
5858 −1.52788 0.362115i −0.200621 0.0475481i
5959 −4.33615 2.85193i −0.564519 0.371290i 0.234941 0.972010i 0.424510π-0.424510\pi
−0.799460 + 0.600720i 0.794881π0.794881\pi
6060 −9.68632 + 1.92974i −1.25050 + 0.249128i
6161 −4.70281 4.98469i −0.602133 0.638224i 0.352569 0.935786i 0.385308π-0.385308\pi
−0.954703 + 0.297562i 0.903827π0.903827\pi
6262 −2.28671 + 1.91878i −0.290412 + 0.243685i
6363 −0.0174500 0.0213951i −0.00219850 0.00269554i
6464 −4.21308 3.53519i −0.526635 0.441899i
6565 −0.620784 10.6584i −0.0769987 1.32202i
6666 −1.85088 + 0.847419i −0.227828 + 0.104310i
6767 4.97104 + 6.67727i 0.607310 + 0.815758i 0.994333 0.106312i 0.0339041π-0.0339041\pi
−0.387023 + 0.922070i 0.626497π0.626497\pi
6868 −7.58367 + 0.886403i −0.919655 + 0.107492i
6969 6.34111 6.25329i 0.763380 0.752807i
7070 −0.00765804 + 0.00503677i −0.000915310 + 0.000602009i
7171 −2.49894 + 0.909541i −0.296570 + 0.107943i −0.486020 0.873948i 0.661552π-0.661552\pi
0.189450 + 0.981890i 0.439330π0.439330\pi
7272 −0.394116 3.83498i −0.0464470 0.451957i
7373 2.10657 + 0.766729i 0.246555 + 0.0897388i 0.462342 0.886702i 0.347009π-0.347009\pi
−0.215786 + 0.976441i 0.569232π0.569232\pi
7474 0.0447841 0.0106140i 0.00520604 0.00123385i
7575 4.43675 5.53146i 0.512311 0.638718i
7676 0.795271 13.6543i 0.0912238 1.56625i
7777 0.0224739 0.0238210i 0.00256114 0.00271465i
7878 2.02396 + 0.0730195i 0.229168 + 0.00826783i
7979 −1.63789 3.79706i −0.184277 0.427203i 0.800887 0.598815i 0.204362π-0.204362\pi
−0.985165 + 0.171612i 0.945102π0.945102\pi
8080 10.1247 1.13198
8181 −5.57367 + 7.06641i −0.619297 + 0.785157i
8282 −1.19086 −0.131509
8383 −5.10959 11.8454i −0.560850 1.30020i −0.928879 0.370382i 0.879227π-0.879227\pi
0.368030 0.929814i 0.380033π-0.380033\pi
8484 0.0141198 + 0.0266296i 0.00154059 + 0.00290553i
8585 8.35615 8.85700i 0.906352 0.960677i
8686 −0.0235956 + 0.405121i −0.00254438 + 0.0436853i
8787 −2.98686 7.67390i −0.320225 0.822728i
8888 4.44968 1.05459i 0.474337 0.112420i
8989 −9.21313 3.35330i −0.976590 0.355450i −0.196076 0.980589i 0.562820π-0.562820\pi
−0.780513 + 0.625139i 0.785042π0.785042\pi
9090 2.14453 + 2.08055i 0.226053 + 0.219309i
9191 −0.0306173 + 0.0111438i −0.00320957 + 0.00116819i
9292 −8.12317 + 5.34270i −0.846899 + 0.557014i
9393 −15.0927 4.15709i −1.56504 0.431070i
9494 0.341958 0.0399692i 0.0352703 0.00412251i
9595 13.0256 + 17.4964i 1.33640 + 1.79509i
9696 −0.599623 + 6.34391i −0.0611988 + 0.647473i
9797 0.917855 + 15.7590i 0.0931941 + 1.60008i 0.643719 + 0.765262i 0.277390π0.277390\pi
−0.550525 + 0.834819i 0.685573π0.685573\pi
9898 −1.77100 1.48604i −0.178898 0.150113i
9999 −9.17003 5.46623i −0.921623 0.549377i
100100 −5.93024 + 4.97606i −0.593024 + 0.497606i
101101 13.2093 + 14.0010i 1.31437 + 1.39315i 0.866600 + 0.499003i 0.166300π0.166300\pi
0.447771 + 0.894149i 0.352218π0.352218\pi
102102 1.52351 + 1.73618i 0.150850 + 0.171908i
103103 −7.29517 4.79811i −0.718815 0.472772i 0.136659 0.990618i 0.456364π-0.456364\pi
−0.855474 + 0.517846i 0.826734π0.826734\pi
104104 −4.42699 1.04922i −0.434102 0.102884i
105105 −0.0445481 0.0180585i −0.00434745 0.00176233i
106106 1.23853 + 0.144763i 0.120297 + 0.0140607i
107107 7.06211 + 12.2319i 0.682720 + 1.18251i 0.974147 + 0.225913i 0.0725365π0.0725365\pi
−0.291427 + 0.956593i 0.594130π0.594130\pi
108108 7.47493 6.37700i 0.719276 0.613627i
109109 −3.80056 + 6.58277i −0.364028 + 0.630515i −0.988620 0.150437i 0.951932π-0.951932\pi
0.624592 + 0.780951i 0.285265π0.285265\pi
110110 −2.11646 + 2.84290i −0.201797 + 0.271060i
111111 0.179185 + 0.161714i 0.0170075 + 0.0153492i
112112 −0.00886175 0.0296003i −0.000837356 0.00279696i
113113 17.2409 8.65873i 1.62189 0.814544i 0.622399 0.782701i 0.286158π-0.286158\pi
0.999493 0.0318440i 0.0101380π-0.0101380\pi
114114 −3.53676 + 2.14760i −0.331248 + 0.201142i
115115 4.44706 14.8542i 0.414691 1.38516i
116116 1.56110 + 8.85342i 0.144944 + 0.822020i
117117 5.71212 + 8.95441i 0.528086 + 0.827836i
118118 0.297650 1.68806i 0.0274009 0.155398i
119119 −0.0332078 0.0166776i −0.00304416 0.00152883i
120120 −3.81149 5.52498i −0.347940 0.504359i
121121 0.658773 1.52721i 0.0598885 0.138837i
122122 0.896467 2.07824i 0.0811623 0.188155i
123123 −3.54638 5.14067i −0.319766 0.463519i
124124 15.2728 + 7.67028i 1.37154 + 0.688811i
125125 −0.474449 + 2.69073i −0.0424360 + 0.240667i
126126 0.00420560 0.00809070i 0.000374665 0.000720776i
127127 −1.36077 7.71730i −0.120749 0.684800i −0.983742 0.179585i 0.942524π-0.942524\pi
0.862994 0.505214i 0.168587π-0.168587\pi
128128 2.63124 8.78897i 0.232571 0.776842i
129129 −1.81908 + 1.10459i −0.160161 + 0.0972537i
130130 3.15108 1.58253i 0.276368 0.138797i
131131 −1.23950 4.14021i −0.108295 0.361732i 0.886613 0.462511i 0.153052π-0.153052\pi
−0.994909 + 0.100780i 0.967866π0.967866\pi
132132 8.65222 + 7.80861i 0.753079 + 0.679652i
133133 0.0397512 0.0533951i 0.00344686 0.00462994i
134134 −1.37467 + 2.38100i −0.118754 + 0.205687i
135135 −2.59484 + 15.4533i −0.223329 + 1.33001i
136136 −2.59445 4.49373i −0.222473 0.385334i
137137 −0.116944 0.0136688i −0.00999123 0.00116781i 0.111096 0.993810i 0.464564π-0.464564\pi
−0.121087 + 0.992642i 0.538638π0.538638\pi
138138 2.72588 + 1.10499i 0.232042 + 0.0940632i
139139 1.26696 + 0.300276i 0.107462 + 0.0254691i 0.283995 0.958826i 0.408340π-0.408340\pi
−0.176533 + 0.984295i 0.556488π0.556488\pi
140140 0.0438449 + 0.0288373i 0.00370557 + 0.00243719i
141141 1.19089 + 1.35713i 0.100291 + 0.114291i
142142 −0.602724 0.638851i −0.0505795 0.0536111i
143143 −9.65114 + 8.09827i −0.807069 + 0.677211i
144144 −8.79222 + 4.91400i −0.732685 + 0.409500i
145145 −10.9829 9.21575i −0.912081 0.765326i
146146 0.0430499 + 0.739139i 0.00356284 + 0.0611716i
147147 1.14089 12.0704i 0.0940990 0.995551i
148148 −0.157356 0.211365i −0.0129346 0.0173741i
149149 6.89069 0.805406i 0.564507 0.0659815i 0.170947 0.985280i 0.445317π-0.445317\pi
0.393560 + 0.919299i 0.371243π0.371243\pi
150150 2.25786 + 0.621899i 0.184354 + 0.0507778i
151151 7.88747 5.18767i 0.641874 0.422167i −0.186413 0.982471i 0.559686π-0.559686\pi
0.828287 + 0.560305i 0.189316π0.189316\pi
152152 8.73454 3.17911i 0.708465 0.257860i
153153 −2.95770 + 11.7470i −0.239116 + 0.949687i
154154 0.0101639 + 0.00369934i 0.000819027 + 0.000298102i
155155 −26.5213 + 6.28567i −2.13025 + 0.504877i
156156 −4.20585 10.8058i −0.336738 0.865153i
157157 −0.356933 + 6.12831i −0.0284864 + 0.489092i 0.953650 + 0.300920i 0.0972936π0.0972936\pi
−0.982136 + 0.188173i 0.939743π0.939743\pi
158158 0.937241 0.993417i 0.0745629 0.0790320i
159159 3.06342 + 5.77755i 0.242945 + 0.458190i
160160 4.39427 + 10.1871i 0.347398 + 0.805359i
161161 −0.0473197 −0.00372931
162162 −2.87208 0.765890i −0.225652 0.0601740i
163163 1.40640 0.110158 0.0550788 0.998482i 0.482459π-0.482459\pi
0.0550788 + 0.998482i 0.482459π0.482459\pi
164164 2.70051 + 6.26049i 0.210875 + 0.488862i
165165 −18.5749 0.670138i −1.44606 0.0521702i
166166 2.92382 3.09907i 0.226933 0.240535i
167167 0.855100 14.6815i 0.0661696 1.13609i −0.787857 0.615859i 0.788809π-0.788809\pi
0.854026 0.520230i 0.174154π-0.174154\pi
168168 −0.0128166 + 0.0159789i −0.000988822 + 0.00123280i
169169 −0.453017 + 0.107367i −0.0348475 + 0.00825900i
170170 3.77908 + 1.37547i 0.289842 + 0.105494i
171171 −19.8031 8.87181i −1.51438 0.678444i
172172 2.18327 0.794647i 0.166473 0.0605912i
173173 6.40528 4.21282i 0.486984 0.320295i −0.282163 0.959367i 0.591052π-0.591052\pi
0.769147 + 0.639072i 0.220681π0.220681\pi
174174 1.93647 1.90965i 0.146803 0.144770i
175175 −0.0374220 + 0.00437401i −0.00282884 + 0.000330644i
176176 −7.13457 9.58339i −0.537789 0.722376i
177177 8.17334 3.74213i 0.614346 0.281276i
178178 −0.188280 3.23264i −0.0141122 0.242296i
179179 4.59366 + 3.85454i 0.343347 + 0.288102i 0.798112 0.602509i 0.205832π-0.205832\pi
−0.454765 + 0.890611i 0.650277π0.650277\pi
180180 6.07452 15.9921i 0.452768 1.19198i
181181 7.92436 6.64933i 0.589013 0.494241i −0.298880 0.954291i 0.596613π-0.596613\pi
0.887893 + 0.460050i 0.152169π0.152169\pi
182182 −0.00738465 0.00782727i −0.000547387 0.000580196i
183183 11.6410 2.31915i 0.860525 0.171437i
184184 −5.52047 3.63087i −0.406974 0.267671i
185185 0.408911 + 0.0969138i 0.0300638 + 0.00712524i
186186 −0.713654 5.12083i −0.0523277 0.375478i
187187 −14.2718 1.66813i −1.04366 0.121986i
188188 −0.985580 1.70707i −0.0718808 0.124501i
189189 0.0474499 0.00593942i 0.00345147 0.000432029i
190190 −3.60204 + 6.23892i −0.261320 + 0.452619i
191191 −9.48044 + 12.7344i −0.685981 + 0.921432i −0.999605 0.0281152i 0.991049π-0.991049\pi
0.313624 + 0.949547i 0.398457π0.398457\pi
192192 9.06306 2.93320i 0.654070 0.211685i
193193 −5.63752 18.8306i −0.405798 1.35546i −0.879971 0.475027i 0.842438π-0.842438\pi
0.474174 0.880431i 0.342747π-0.342747\pi
194194 −4.65901 + 2.33984i −0.334497 + 0.167991i
195195 16.2153 + 8.88971i 1.16120 + 0.636606i
196196 −3.79621 + 12.6802i −0.271158 + 0.905730i
197197 −0.0147762 0.0837998i −0.00105276 0.00597049i 0.984277 0.176633i 0.0565204π-0.0565204\pi
−0.985330 + 0.170662i 0.945409π0.945409\pi
198198 0.458126 3.49597i 0.0325576 0.248448i
199199 −3.10186 + 17.5915i −0.219885 + 1.24703i 0.652340 + 0.757927i 0.273788π0.273788\pi
−0.872225 + 0.489105i 0.837324π0.837324\pi
200200 −4.70140 2.36113i −0.332439 0.166957i
201201 −14.3720 + 1.15646i −1.01372 + 0.0815705i
202202 −2.51800 + 5.83738i −0.177166 + 0.410716i
203203 −0.0173300 + 0.0401754i −0.00121633 + 0.00281976i
204204 5.67245 11.9464i 0.397151 0.836415i
205205 −9.71686 4.87999i −0.678655 0.340833i
206206 0.500769 2.84000i 0.0348902 0.197872i
207207 3.34765 + 15.0577i 0.232678 + 1.04658i
208208 2.06409 + 11.7060i 0.143119 + 0.811667i
209209 7.38222 24.6583i 0.510639 1.70565i
210210 −0.000351078 0.0158720i −2.42267e−5 0.00109527i
211211 6.97370 3.50232i 0.480089 0.241110i −0.192260 0.981344i 0.561582π-0.561582\pi
0.672349 + 0.740234i 0.265285π0.265285\pi
212212 −2.04757 6.83937i −0.140628 0.469730i
213213 0.962862 4.50431i 0.0659742 0.308630i
214214 −2.78564 + 3.74177i −0.190423 + 0.255782i
215215 −1.85266 + 3.20890i −0.126350 + 0.218845i
216216 5.99140 + 2.94795i 0.407663 + 0.200583i
217217 0.0415896 + 0.0720354i 0.00282329 + 0.00489008i
218218 −2.49346 0.291444i −0.168879 0.0197391i
219219 −3.06249 + 2.38698i −0.206944 + 0.161297i
220220 19.7449 + 4.67963i 1.33120 + 0.315501i
221221 11.9439 + 7.85560i 0.803431 + 0.528425i
222222 −0.0256016 + 0.0754942i −0.00171827 + 0.00506684i
223223 15.4174 + 16.3415i 1.03243 + 1.09431i 0.995478 + 0.0949935i 0.0302830π0.0302830\pi
0.0369509 + 0.999317i 0.488235π0.488235\pi
224224 0.0259365 0.0217633i 0.00173295 0.00145412i
225225 4.03930 + 11.5987i 0.269287 + 0.773245i
226226 4.88121 + 4.09582i 0.324693 + 0.272450i
227227 −0.942461 16.1814i −0.0625533 1.07400i −0.872853 0.487983i 0.837733π-0.837733\pi
0.810300 0.586016i 0.199304π-0.199304\pi
228228 19.3105 + 13.7230i 1.27887 + 0.908828i
229229 −8.71685 11.7088i −0.576026 0.773737i 0.414650 0.909981i 0.363904π-0.363904\pi
−0.990675 + 0.136245i 0.956497π0.956497\pi
230230 5.08644 0.594519i 0.335390 0.0392014i
231231 0.0142987 + 0.0548916i 0.000940784 + 0.00361160i
232232 −5.10446 + 3.35726i −0.335125 + 0.220415i
233233 −9.97733 + 3.63145i −0.653637 + 0.237904i −0.647487 0.762077i 0.724180π-0.724180\pi
−0.00615012 + 0.999981i 0.501958π0.501958\pi
234234 −1.96830 + 2.90362i −0.128672 + 0.189816i
235235 2.95400 + 1.07517i 0.192698 + 0.0701363i
236236 −9.54927 + 2.26322i −0.621605 + 0.147323i
237237 7.07945 + 1.08746i 0.459860 + 0.0706384i
238238 0.000713615 0.0122523i 4.62568e−5 0.000794199i
239239 −3.47849 + 3.68698i −0.225005 + 0.238491i −0.830035 0.557712i 0.811680π-0.811680\pi
0.605030 + 0.796202i 0.293161π0.293161\pi
240240 −9.31011 + 14.8611i −0.600965 + 0.959278i
241241 −0.140741 0.326274i −0.00906593 0.0210172i 0.913623 0.406562i 0.133273π-0.133273\pi
−0.922689 + 0.385545i 0.874013π0.874013\pi
242242 0.549319 0.0353116
243243 −5.24686 14.6789i −0.336586 0.941653i
244244 −12.9585 −0.829581
245245 −8.36088 19.3827i −0.534157 1.23832i
246246 1.09505 1.74795i 0.0698178 0.111445i
247247 −17.5736 + 18.6269i −1.11818 + 1.18520i
248248 −0.675337 + 11.5951i −0.0428839 + 0.736289i
249249 22.0851 + 3.39246i 1.39959 + 0.214988i
250250 −0.878059 + 0.208104i −0.0555333 + 0.0131616i
251251 20.8143 + 7.57577i 1.31378 + 0.478179i 0.901462 0.432859i 0.142495π-0.142495\pi
0.412323 + 0.911038i 0.364717π0.364717\pi
252252 −0.0520707 0.00376206i −0.00328015 0.000236988i
253253 −17.1937 + 6.25801i −1.08096 + 0.393438i
254254 2.16235 1.42220i 0.135678 0.0892366i
255255 5.31647 + 20.4096i 0.332930 + 1.27810i
256256 −7.91564 + 0.925205i −0.494727 + 0.0578253i
257257 −12.2561 16.4628i −0.764513 1.02692i −0.998504 0.0546803i 0.982586π-0.982586\pi
0.233991 0.972239i 0.424821π-0.424821\pi
258258 −0.572940 0.407160i −0.0356697 0.0253487i
259259 −7.45693e−5 0.00128030i −4.63351e−6 7.95543e-5i
260260 −15.4652 12.9769i −0.959113 0.804791i
261261 14.0103 + 2.67237i 0.867216 + 0.165416i
262262 1.09342 0.917488i 0.0675517 0.0566826i
263263 15.2357 + 16.1489i 0.939472 + 0.995782i 0.999997 0.00238468i 0.000759067π-0.000759067\pi
−0.0605253 + 0.998167i 0.519278π0.519278\pi
264264 −2.54374 + 7.50099i −0.156556 + 0.461654i
265265 9.51259 + 6.25653i 0.584354 + 0.384336i
266266 0.0213926 + 0.00507015i 0.00131167 + 0.000310871i
267267 13.3939 10.4395i 0.819691 0.638889i
268268 15.6345 + 1.82741i 0.955031 + 0.111627i
269269 −8.77459 15.1980i −0.534996 0.926641i −0.999164 0.0408933i 0.986980π-0.986980\pi
0.464167 0.885748i 0.346354π-0.346354\pi
270270 −5.02582 + 1.23459i −0.305861 + 0.0751348i
271271 11.7223 20.3037i 0.712082 1.23336i −0.251992 0.967729i 0.581086π-0.581086\pi
0.964074 0.265633i 0.0855809π-0.0855809\pi
272272 −8.09558 + 10.8743i −0.490867 + 0.659348i
273273 0.0117971 0.0551874i 0.000713993 0.00334009i
274274 −0.0111527 0.0372527i −0.000673761 0.00225052i
275275 −13.0190 + 6.53836i −0.785072 + 0.394278i
276276 −0.372402 16.8360i −0.0224160 1.01341i
277277 −0.0988045 + 0.330030i −0.00593659 + 0.0198296i −0.960906 0.276873i 0.910702π-0.910702\pi
0.954970 + 0.296703i 0.0958870π0.0958870\pi
278278 0.0746746 + 0.423500i 0.00447868 + 0.0253999i
279279 19.9802 18.3305i 1.19618 1.09742i
280280 −0.00619298 + 0.0351222i −0.000370102 + 0.00209895i
281281 27.0285 + 13.5742i 1.61238 + 0.809770i 0.999813 + 0.0193542i 0.00616100π0.00616100\pi
0.612571 + 0.790415i 0.290135π0.290135\pi
282282 −0.255779 + 0.538680i −0.0152314 + 0.0320780i
283283 −2.19004 + 5.07708i −0.130184 + 0.301801i −0.970824 0.239794i 0.922920π-0.922920\pi
0.840640 + 0.541595i 0.182179π0.182179\pi
284284 −1.99171 + 4.61731i −0.118186 + 0.273987i
285285 −37.6588 + 3.03027i −2.23072 + 0.179498i
286286 −3.71839 1.86745i −0.219873 0.110424i
287287 −0.00576222 + 0.0326792i −0.000340133 + 0.00192899i
288288 −8.76022 6.71363i −0.516201 0.395604i
289289 −0.120790 0.685032i −0.00710527 0.0402960i
290290 1.35806 4.53623i 0.0797479 0.266377i
291291 −23.9750 13.1438i −1.40544 0.770505i
292292 3.78811 1.90246i 0.221682 0.111333i
293293 5.73668 + 19.1618i 0.335140 + 1.11945i 0.945036 + 0.326965i 0.106026π0.106026\pi
−0.609896 + 0.792481i 0.708789π0.708789\pi
294294 3.80973 1.23299i 0.222188 0.0719095i
295295 9.34610 12.5540i 0.544151 0.730922i
296296 0.0895392 0.155086i 0.00520436 0.00901421i
297297 16.4556 8.43334i 0.954850 0.489352i
298298 1.14565 + 1.98432i 0.0663655 + 0.114948i
299299 18.0808 + 2.11334i 1.04564 + 0.122218i
300300 −1.85075 13.2801i −0.106853 0.766727i
301301 0.0110030 + 0.00260776i 0.000634202 + 0.000150309i
302302 2.60501 + 1.71334i 0.149901 + 0.0985917i
303303 −32.6972 + 6.51404i −1.87840 + 0.374222i
304304 −16.6653 17.6642i −0.955822 1.01311i
305305 15.8311 13.2839i 0.906487 0.760632i
306306 −3.94931 + 0.639715i −0.225767 + 0.0365701i
307307 0.858198 + 0.720114i 0.0489799 + 0.0410991i 0.666949 0.745103i 0.267600π-0.267600\pi
−0.617969 + 0.786202i 0.712044π0.712044\pi
308308 −0.00360069 0.0618215i −0.000205168 0.00352261i
309309 13.7509 6.29579i 0.782262 0.358155i
310310 −5.37556 7.22063i −0.305311 0.410104i
311311 0.819543 0.0957909i 0.0464720 0.00543180i −0.0928251 0.995682i 0.529590π-0.529590\pi
0.139297 + 0.990251i 0.455516π0.455516\pi
312312 5.61085 5.53314i 0.317652 0.313253i
313313 −0.974256 + 0.640778i −0.0550682 + 0.0362189i −0.576745 0.816925i 0.695677π-0.695677\pi
0.521676 + 0.853143i 0.325307π0.325307\pi
314314 −1.90517 + 0.693424i −0.107515 + 0.0391322i
315315 0.0674702 0.0487822i 0.00380152 0.00274857i
316316 −7.34788 2.67441i −0.413351 0.150447i
317317 −4.51524 + 1.07013i −0.253601 + 0.0601045i −0.355450 0.934695i 0.615672π-0.615672\pi
0.101849 + 0.994800i 0.467524π0.467524\pi
318318 −1.35137 + 1.68480i −0.0757809 + 0.0944789i
319319 −0.983716 + 16.8898i −0.0550775 + 0.945645i
320320 11.3815 12.0637i 0.636245 0.674380i
321321 −24.4480 0.882023i −1.36455 0.0492297i
322322 −0.00619007 0.0143502i −0.000344959 0.000799705i
323323 −29.2067 −1.62511
324324 2.48664 + 16.8356i 0.138146 + 0.935313i
325325 14.4943 0.803999
326326 0.183976 + 0.426505i 0.0101895 + 0.0236219i
327327 −6.16741 11.6316i −0.341059 0.643230i
328328 −3.17973 + 3.37032i −0.175571 + 0.186095i
329329 0.000557814 0.00957729i 3.07533e−5 0.000528013i
330330 −2.22663 5.72071i −0.122572 0.314915i
331331 −6.47768 + 1.53524i −0.356046 + 0.0843844i −0.404746 0.914429i 0.632640π-0.632640\pi
0.0487006 + 0.998813i 0.484492π0.484492\pi
332332 −22.9225 8.34311i −1.25804 0.457888i
333333 −0.402132 + 0.114305i −0.0220367 + 0.00626386i
334334 4.56418 1.66123i 0.249741 0.0908982i
335335 −20.9737 + 13.7946i −1.14591 + 0.753680i
336336 0.0515961 + 0.0142115i 0.00281480 + 0.000775300i
337337 16.4774 1.92593i 0.897581 0.104912i 0.345225 0.938520i 0.387803π-0.387803\pi
0.552357 + 0.833608i 0.313729π0.313729\pi
338338 −0.0918211 0.123337i −0.00499441 0.00670866i
339339 −3.14451 + 33.2683i −0.170786 + 1.80689i
340340 −1.33879 22.9862i −0.0726063 1.24660i
341341 24.6384 + 20.6741i 1.33424 + 1.11956i
342342 0.0999459 7.16607i 0.00540446 0.387497i
343343 −0.0986981 + 0.0828175i −0.00532920 + 0.00447173i
344344 1.08355 + 1.14850i 0.0584212 + 0.0619228i
345345 17.7138 + 20.1865i 0.953677 + 1.08680i
346346 2.11548 + 1.39137i 0.113729 + 0.0748007i
347347 13.3534 + 3.16483i 0.716851 + 0.169897i 0.572826 0.819677i 0.305847π-0.305847\pi
0.144025 + 0.989574i 0.453995π0.453995\pi
348348 −14.4306 5.84973i −0.773559 0.313578i
349349 14.0327 + 1.64018i 0.751152 + 0.0877971i 0.483049 0.875593i 0.339529π-0.339529\pi
0.268103 + 0.963390i 0.413603π0.413603\pi
350350 −0.00622179 0.0107765i −0.000332569 0.000576026i
351351 −18.3958 + 0.150289i −0.981898 + 0.00802181i
352352 6.54591 11.3378i 0.348898 0.604309i
353353 5.52814 7.42558i 0.294233 0.395224i −0.630284 0.776365i 0.717061π-0.717061\pi
0.924517 + 0.381141i 0.124469π0.124469\pi
354354 2.20403 + 1.98913i 0.117143 + 0.105721i
355355 −2.30002 7.68260i −0.122072 0.407750i
356356 −16.5674 + 8.32045i −0.878069 + 0.440983i
357357 0.0550155 0.0334067i 0.00291173 0.00176807i
358358 −0.568016 + 1.89731i −0.0300206 + 0.100276i
359359 −3.82037 21.6664i −0.201631 1.14351i −0.902653 0.430368i 0.858384π-0.858384\pi
0.701022 0.713140i 0.252727π-0.252727\pi
360360 11.6144 0.514057i 0.612132 0.0270932i
361361 5.78583 32.8131i 0.304517 1.72700i
362362 3.05310 + 1.53332i 0.160467 + 0.0805897i
363363 1.63587 + 2.37128i 0.0858607 + 0.124460i
364364 −0.0244027 + 0.0565718i −0.00127905 + 0.00296517i
365365 −2.67762 + 6.20743i −0.140153 + 0.324912i
366366 2.22611 + 3.22687i 0.116361 + 0.168671i
367367 −17.6586 8.86848i −0.921772 0.462931i −0.0763804 0.997079i 0.524336π-0.524336\pi
−0.845391 + 0.534148i 0.820633π0.820633\pi
368368 −2.99770 + 17.0008i −0.156266 + 0.886229i
369369 10.8065 0.478301i 0.562566 0.0248993i
370370 0.0241011 + 0.136684i 0.00125296 + 0.00710588i
371371 0.00996541 0.0332868i 0.000517378 0.00172816i
372372 −25.3024 + 15.3642i −1.31187 + 0.796599i
373373 6.63183 3.33063i 0.343383 0.172454i −0.268746 0.963211i 0.586609π-0.586609\pi
0.612130 + 0.790757i 0.290313π0.290313\pi
374374 −1.36107 4.54629i −0.0703792 0.235083i
375375 −3.51319 3.17064i −0.181420 0.163731i
376376 0.799948 1.07452i 0.0412542 0.0554140i
377377 8.41606 14.5770i 0.433449 0.750756i
378378 0.00800830 + 0.0136127i 0.000411902 + 0.000700163i
379379 4.80243 + 8.31805i 0.246684 + 0.427269i 0.962604 0.270913i 0.0873257π-0.0873257\pi
−0.715920 + 0.698183i 0.753992π0.753992\pi
380380 40.9670 + 4.78836i 2.10156 + 0.245638i
381381 12.5787 + 5.09906i 0.644429 + 0.261233i
382382 −5.10203 1.20920i −0.261043 0.0618682i
383383 −7.63456 5.02133i −0.390108 0.256578i 0.339270 0.940689i 0.389820π-0.389820\pi
−0.729378 + 0.684111i 0.760190π0.760190\pi
384384 10.4809 + 11.9440i 0.534852 + 0.609514i
385385 0.0677728 + 0.0718350i 0.00345402 + 0.00366105i
386386 4.97312 4.17295i 0.253125 0.212397i
387387 0.0514058 3.68577i 0.00261310 0.187358i
388388 22.8660 + 19.1869i 1.16085 + 0.974065i
389389 0.926398 + 15.9056i 0.0469702 + 0.806448i 0.936737 + 0.350033i 0.113830π0.113830\pi
−0.889767 + 0.456415i 0.849133π0.849133\pi
390390 −0.574713 + 6.08036i −0.0291017 + 0.307891i
391391 12.3981 + 16.6535i 0.626998 + 0.842204i
392392 −8.93449 + 1.04429i −0.451260 + 0.0527447i
393393 7.21677 + 1.98777i 0.364038 + 0.100270i
394394 0.0234803 0.0154432i 0.00118292 0.000778017i
395395 11.7183 4.26512i 0.589613 0.214602i
396396 −19.4176 + 5.51938i −0.975770 + 0.277359i
397397 −5.92327 2.15589i −0.297280 0.108201i 0.189074 0.981963i 0.439451π-0.439451\pi
−0.486354 + 0.873762i 0.661674π0.661674\pi
398398 −5.74059 + 1.36054i −0.287750 + 0.0681980i
399399 0.0418204 + 0.107446i 0.00209364 + 0.00537902i
400400 −0.799211 + 13.7219i −0.0399606 + 0.686097i
401401 −21.9497 + 23.2654i −1.09612 + 1.16182i −0.110317 + 0.993896i 0.535187π0.535187\pi
−0.985801 + 0.167920i 0.946295π0.946295\pi
402402 −2.23077 4.20718i −0.111260 0.209835i
403403 −12.6742 29.3821i −0.631347 1.46363i
404404 36.3978 1.81086
405405 −20.2963 18.0187i −1.00853 0.895355i
406406 −0.0144506 −0.000717173
407407 −0.196415 0.455341i −0.00973593 0.0225704i
408408 8.98161 + 0.324035i 0.444656 + 0.0160421i
409409 −24.6088 + 26.0838i −1.21683 + 1.28976i −0.271958 + 0.962309i 0.587671π0.587671\pi
−0.944868 + 0.327451i 0.893810π0.893810\pi
410410 0.208809 3.58511i 0.0103123 0.177056i
411411 0.127599 0.159082i 0.00629397 0.00784693i
412412 −16.0658 + 3.80766i −0.791504 + 0.187590i
413413 −0.0448827 0.0163360i −0.00220853 0.000803841i
414414 −4.12848 + 2.98496i −0.202904 + 0.146703i
415415 36.5566 13.3055i 1.79449 0.653142i
416416 −10.8823 + 7.15739i −0.533548 + 0.350920i
417417 −1.60577 + 1.58353i −0.0786350 + 0.0775460i
418418 8.44360 0.986916i 0.412990 0.0482716i
419419 −4.32862 5.81434i −0.211467 0.284049i 0.683716 0.729748i 0.260363π-0.260363\pi
−0.895183 + 0.445699i 0.852955π0.852955\pi
420420 −0.0826447 + 0.0378385i −0.00403265 + 0.00184633i
421421 0.169004 + 2.90168i 0.00823673 + 0.141419i 0.999919 + 0.0127108i 0.00404607π0.00404607\pi
−0.991682 + 0.128708i 0.958917π0.958917\pi
422422 1.97437 + 1.65670i 0.0961111 + 0.0806467i
423423 −3.08707 + 0.500048i −0.150098 + 0.0243131i
424424 3.71672 3.11870i 0.180500 0.151457i
425425 11.3442 + 12.0242i 0.550275 + 0.583257i
426426 1.49194 0.297229i 0.0722846 0.0144008i
427427 −0.0526926 0.0346565i −0.00254998 0.00167715i
428428 25.9879 + 6.15924i 1.25617 + 0.297718i
429429 −3.01200 21.6127i −0.145421 1.04347i
430430 −1.21549 0.142070i −0.0586160 0.00685123i
431431 −0.349866 0.605986i −0.0168525 0.0291893i 0.857476 0.514524i 0.172031π-0.172031\pi
−0.874329 + 0.485334i 0.838698π0.838698\pi
432432 0.872062 17.4239i 0.0419571 0.838306i
433433 −8.81031 + 15.2599i −0.423397 + 0.733344i −0.996269 0.0863000i 0.972496π-0.972496\pi
0.572873 + 0.819644i 0.305829π0.305829\pi
434434 −0.0164050 + 0.0220357i −0.000787465 + 0.00105775i
435435 23.6261 7.64643i 1.13279 0.366618i
436436 4.12226 + 13.7693i 0.197420 + 0.659430i
437437 −33.2355 + 16.6915i −1.58987 + 0.798462i
438438 −1.12449 0.616481i −0.0537304 0.0294566i
439439 −6.92464 + 23.1299i −0.330495 + 1.10393i 0.617745 + 0.786378i 0.288046π0.288046\pi
−0.948241 + 0.317553i 0.897139π0.897139\pi
440440 2.39465 + 13.5808i 0.114161 + 0.647437i
441441 16.6679 + 12.7739i 0.793708 + 0.608279i
442442 −0.819872 + 4.64973i −0.0389974 + 0.221165i
443443 −6.10266 3.06487i −0.289946 0.145616i 0.297881 0.954603i 0.403720π-0.403720\pi
−0.587827 + 0.808987i 0.700016π0.700016\pi
444444 0.454938 0.0366072i 0.0215904 0.00173730i
445445 11.7106 27.1483i 0.555138 1.28695i
446446 −2.93893 + 6.81321i −0.139162 + 0.322615i
447447 −5.15411 + 10.8548i −0.243781 + 0.513413i
448448 −0.0452307 0.0227157i −0.00213695 0.00107322i
449449 0.451728 2.56188i 0.0213184 0.120902i −0.972291 0.233772i 0.924893π-0.924893\pi
0.993610 + 0.112870i 0.0360042π0.0360042\pi
450450 −2.98903 + 2.74223i −0.140904 + 0.129270i
451451 2.22809 + 12.6361i 0.104917 + 0.595012i
452452 10.4631 34.9491i 0.492142 1.64387i
453453 0.361596 + 16.3475i 0.0169893 + 0.768074i
454454 4.78390 2.40257i 0.224520 0.112758i
455455 −0.0281801 0.0941281i −0.00132110 0.00441279i
456456 −3.36549 + 15.7439i −0.157603 + 0.737276i
457457 4.63782 6.22968i 0.216948 0.291412i −0.680304 0.732930i 0.738152π-0.738152\pi
0.897253 + 0.441518i 0.145560π0.145560\pi
458458 2.41052 4.17515i 0.112636 0.195092i
459459 −14.5225 15.1432i −0.677852 0.706823i
460460 −14.6599 25.3918i −0.683523 1.18390i
461461 −0.674287 0.0788128i −0.0314047 0.00367068i 0.100376 0.994950i 0.467995π-0.467995\pi
−0.131781 + 0.991279i 0.542069π0.542069\pi
462462 −0.0147760 + 0.0115168i −0.000687442 + 0.000535811i
463463 −19.6840 4.66519i −0.914793 0.216810i −0.253848 0.967244i 0.581696π-0.581696\pi
−0.660945 + 0.750434i 0.729844π0.729844\pi
464464 13.3362 + 8.77137i 0.619118 + 0.407200i
465465 15.1614 44.7080i 0.703093 2.07328i
466466 −2.40645 2.55069i −0.111477 0.118158i
467467 6.20374 5.20555i 0.287075 0.240884i −0.487866 0.872919i 0.662224π-0.662224\pi
0.774940 + 0.632035i 0.217780π0.217780\pi
468468 19.7282 + 3.76301i 0.911935 + 0.173945i
469469 0.0586869 + 0.0492442i 0.00270991 + 0.00227388i
470470 0.0603681 + 1.03648i 0.00278457 + 0.0478093i
471471 −8.66692 6.15915i −0.399351 0.283799i
472472 −3.98270 5.34969i −0.183319 0.246240i
473473 4.34285 0.507606i 0.199684 0.0233398i
474474 0.596305 + 2.28917i 0.0273892 + 0.105145i
475475 −24.7409 + 16.2723i −1.13519 + 0.746627i
476476 −0.0660299 + 0.0240329i −0.00302648 + 0.00110155i
477477 −11.2972 0.816217i −0.517265 0.0373720i
478478 −1.57315 0.572580i −0.0719542 0.0261892i
479479 −28.3209 + 6.71218i −1.29401 + 0.306687i −0.819256 0.573429i 0.805613π-0.805613\pi
−0.474759 + 0.880116i 0.657465π0.657465\pi
480480 −18.9933 2.91754i −0.866923 0.133167i
481481 −0.0286869 + 0.492534i −0.00130801 + 0.0224576i
482482 0.0805353 0.0853625i 0.00366828 0.00388815i
483483 0.0435125 0.0694558i 0.00197989 0.00316035i
484484 −1.24569 2.88783i −0.0566222 0.131265i
485485 −47.6036 −2.16157
486486 3.76518 3.51137i 0.170792 0.159279i
487487 3.59484 0.162898 0.0814489 0.996678i 0.474045π-0.474045\pi
0.0814489 + 0.996678i 0.474045π0.474045\pi
488488 −3.48808 8.08629i −0.157898 0.366049i
489489 −1.29324 + 2.06431i −0.0584825 + 0.0933514i
490490 4.78429 5.07106i 0.216132 0.229087i
491491 1.95535 33.5720i 0.0882436 1.51508i −0.606070 0.795411i 0.707255π-0.707255\pi
0.694314 0.719672i 0.255708π-0.255708\pi
492492 −11.6724 1.79298i −0.526232 0.0808337i
493493 18.6798 4.42719i 0.841295 0.199391i
494494 −7.94768 2.89272i −0.357583 0.130150i
495495 18.0641 26.6481i 0.811920 1.19774i
496496 28.5153 10.3787i 1.28037 0.466018i
497497 −0.0204475 + 0.0134485i −0.000917195 + 0.000603249i
498498 1.86024 + 7.14133i 0.0833593 + 0.320010i
499499 13.6291 1.59301i 0.610121 0.0713129i 0.194579 0.980887i 0.437666π-0.437666\pi
0.415542 + 0.909574i 0.363592π0.363592\pi
500500 3.08519 + 4.14413i 0.137974 + 0.185331i
501501 20.7632 + 14.7554i 0.927632 + 0.659222i
502502 0.425361 + 7.30316i 0.0189848 + 0.325956i
503503 −2.12583 1.78378i −0.0947859 0.0795348i 0.594163 0.804344i 0.297483π-0.297483\pi
−0.688949 + 0.724810i 0.741928π0.741928\pi
504504 −0.0116685 0.0335056i −0.000519756 0.00149246i
505505 −44.4664 + 37.3118i −1.97873 + 1.66035i
506506 −4.14699 4.39555i −0.184356 0.195406i
507507 0.258975 0.763667i 0.0115015 0.0339157i
508508 −12.3802 8.14258i −0.549282 0.361268i
509509 −7.12682 1.68909i −0.315891 0.0748675i 0.0696121 0.997574i 0.477824π-0.477824\pi
−0.385503 + 0.922707i 0.625972π0.625972\pi
510510 −5.49395 + 4.28213i −0.243276 + 0.189616i
511511 0.0204915 + 0.00239511i 0.000906489 + 0.000105953i
512512 −10.4904 18.1700i −0.463616 0.803007i
513513 31.2319 20.9090i 1.37892 0.923157i
514514 3.38924 5.87034i 0.149493 0.258930i
515515 15.7240 21.1209i 0.692881 0.930700i
516516 −0.841232 + 3.93532i −0.0370332 + 0.173243i
517517 −1.06391 3.55371i −0.0467907 0.156292i
518518 0.000378511 0 0.000190096i 1.66308e−5 0 8.35232e-6i
519519 0.293646 + 13.2755i 0.0128896 + 0.582732i
520520 3.93493 13.1436i 0.172558 0.576384i
521521 −6.17963 35.0464i −0.270734 1.53541i −0.752193 0.658942i 0.771004π-0.771004\pi
0.481459 0.876469i 0.340107π-0.340107\pi
522522 1.02232 + 4.59836i 0.0447456 + 0.201265i
523523 −5.30847 + 30.1059i −0.232123 + 1.31644i 0.616465 + 0.787383i 0.288564π0.288564\pi
−0.848588 + 0.529054i 0.822547π0.822547\pi
524524 −7.30287 3.66764i −0.319028 0.160222i
525525 0.0279910 0.0589502i 0.00122163 0.00257280i
526526 −2.90428 + 6.73288i −0.126633 + 0.293567i
527527 14.4551 33.5107i 0.629674 1.45975i
528528 20.6271 1.65978i 0.897678 0.0722329i
529529 3.07209 + 1.54286i 0.133569 + 0.0670810i
530530 −0.652980 + 3.70324i −0.0283637 + 0.160858i
531531 −2.02304 + 15.4379i −0.0877926 + 0.669948i
532532 −0.0218577 0.123961i −0.000947650 0.00537439i
533533 3.66123 12.2293i 0.158585 0.529712i
534534 4.91800 + 2.69619i 0.212823 + 0.116676i
535535 −38.0628 + 19.1158i −1.64560 + 0.826450i
536536 3.06807 + 10.2481i 0.132521 + 0.442649i
537537 −9.88177 + 3.19817i −0.426430 + 0.138011i
538538 3.46113 4.64910i 0.149220 0.200437i
539539 −12.4548 + 21.5723i −0.536464 + 0.929183i
540540 17.8874 + 23.6216i 0.769751 + 1.01651i
541541 −14.2816 24.7364i −0.614012 1.06350i −0.990557 0.137102i 0.956221π-0.956221\pi
0.376545 0.926398i 0.377112π-0.377112\pi
542542 7.69076 + 0.898921i 0.330347 + 0.0386120i
543543 2.47310 + 17.7457i 0.106131 + 0.761542i
544544 −14.4548 3.42586i −0.619746 0.146882i
545545 −19.1511 12.5959i −0.820345 0.539549i
546546 0.0182794 0.00364168i 0.000782286 0.000155850i
547547 20.5203 + 21.7502i 0.877384 + 0.929973i 0.998031 0.0627227i 0.0199784π-0.0199784\pi
−0.120647 + 0.992695i 0.538497π0.538497\pi
548548 −0.170550 + 0.143109i −0.00728555 + 0.00611331i
549549 −7.30032 + 19.2192i −0.311570 + 0.820255i
550550 −3.68589 3.09283i −0.157167 0.131879i
551551 1.99953 + 34.3306i 0.0851829 + 1.46253i
552552 10.4057 4.76421i 0.442896 0.202778i
553553 −0.0227259 0.0305262i −0.000966406 0.00129811i
554554 −0.113010 + 0.0132090i −0.00480134 + 0.000561196i
555555 −0.518262 + 0.511084i −0.0219990 + 0.0216943i
556556 2.05705 1.35294i 0.0872383 0.0573775i
557557 −11.4069 + 4.15178i −0.483327 + 0.175917i −0.572180 0.820128i 0.693902π-0.693902\pi
0.0888529 + 0.996045i 0.471680π0.471680\pi
558558 8.17260 + 3.66133i 0.345974 + 0.154996i
559559 −4.08778 1.48783i −0.172895 0.0629285i
560560 0.0906661 0.0214883i 0.00383134 0.000908045i
561561 15.5720 19.4142i 0.657451 0.819669i
562562 −0.580824 + 9.97237i −0.0245006 + 0.420659i
563563 12.6158 13.3720i 0.531694 0.563563i −0.404729 0.914437i 0.632634π-0.632634\pi
0.936423 + 0.350874i 0.114115π0.114115\pi
564564 3.41193 + 0.123094i 0.143668 + 0.00518320i
565565 23.0442 + 53.4224i 0.969476 + 2.24750i
566566 −1.82617 −0.0767595
567567 −0.0349144 + 0.0751086i −0.00146627 + 0.00315426i
568568 −3.41739 −0.143390
569569 3.37933 + 7.83416i 0.141669 + 0.328425i 0.974247 0.225482i 0.0723956π-0.0723956\pi
−0.832579 + 0.553907i 0.813136π0.813136\pi
570570 −5.84526 11.0240i −0.244831 0.461746i
571571 28.4066 30.1092i 1.18878 1.26003i 0.230862 0.972986i 0.425845π-0.425845\pi
0.957917 0.287046i 0.0926732π-0.0926732\pi
572572 −1.38519 + 23.7828i −0.0579177 + 0.994408i
573573 −9.97395 25.6253i −0.416668 1.07051i
574574 −0.0106641 + 0.00252743i −0.000445110 + 0.000105493i
575575 19.7808 + 7.19960i 0.824914 + 0.300244i
576576 −4.02853 + 16.0000i −0.167856 + 0.666666i
577577 −41.2655 + 15.0194i −1.71791 + 0.625266i −0.997655 0.0684479i 0.978195π-0.978195\pi
−0.720250 + 0.693714i 0.755973π0.755973\pi
578578 0.191942 0.126242i 0.00798375 0.00525099i
579579 32.8236 + 9.04082i 1.36410 + 0.375724i
580580 −26.9271 + 3.14733i −1.11809 + 0.130686i
581581 −0.0708961 0.0952299i −0.00294126 0.00395080i
582582 0.849738 8.99008i 0.0352228 0.372651i
583583 −0.781206 13.4128i −0.0323542 0.555501i
584584 2.20682 + 1.85174i 0.0913190 + 0.0766258i
585585 −27.9590 + 15.6264i −1.15596 + 0.646071i
586586 −5.06059 + 4.24634i −0.209051 + 0.175415i
587587 −9.02510 9.56605i −0.372506 0.394833i 0.513818 0.857899i 0.328231π-0.328231\pi
−0.886324 + 0.463066i 0.846749π0.846749\pi
588588 −15.1213 17.2321i −0.623590 0.710640i
589589 54.6206 + 35.9246i 2.25060 + 1.48025i
590590 5.02973 + 1.19207i 0.207071 + 0.0490767i
591591 0.136589 + 0.0553691i 0.00561851 + 0.00227758i
592592 −0.464707 0.0543164i −0.0190993 0.00223239i
593593 10.7252 + 18.5766i 0.440432 + 0.762850i 0.997721 0.0674679i 0.0214920π-0.0214920\pi
−0.557290 + 0.830318i 0.688159π0.688159\pi
594594 4.71012 + 3.88713i 0.193259 + 0.159491i
595595 0.0560310 0.0970486i 0.00229705 0.00397860i
596596 7.83380 10.5226i 0.320885 0.431023i
597597 −22.9686 20.7291i −0.940042 0.848386i
598598 1.72433 + 5.75966i 0.0705130 + 0.235530i
599599 20.0409 10.0649i 0.818850 0.411242i 0.0105004 0.999945i 0.496658π-0.496658\pi
0.808349 + 0.588703i 0.200361π0.200361\pi
600600 7.78881 4.72956i 0.317977 0.193083i
601601 −2.72865 + 9.11434i −0.111304 + 0.371782i −0.995433 0.0954612i 0.969567π-0.969567\pi
0.884129 + 0.467243i 0.154753π0.154753\pi
602602 0.000648515 0.00367791i 2.64315e−5 0.000149900i
603603 11.5182 22.1586i 0.469058 0.902370i
604604 3.09986 17.5802i 0.126131 0.715326i
605605 4.48218 + 2.25103i 0.182226 + 0.0915176i
606606 −6.25270 9.06364i −0.253998 0.368185i
607607 9.70931 22.5087i 0.394089 0.913601i −0.599482 0.800388i 0.704627π-0.704627\pi
0.993571 0.113212i 0.0361141π-0.0361141\pi
608608 10.5400 24.4345i 0.427454 0.990950i
609609 −0.0430339 0.0623801i −0.00174382 0.00252777i
610610 6.09941 + 3.06324i 0.246958 + 0.124027i
611611 −0.640872 + 3.63457i −0.0259269 + 0.147039i
612612 12.3189 + 19.3113i 0.497961 + 0.780611i
613613 −1.29645 7.35253i −0.0523631 0.296966i 0.947368 0.320146i 0.103732π-0.103732\pi
−0.999731 + 0.0231801i 0.992621π0.992621\pi
614614 −0.106118 + 0.354459i −0.00428257 + 0.0143048i
615615 16.0979 9.77505i 0.649131 0.394168i
616616 0.0376083 0.0188876i 0.00151528 0.000761004i
617617 −4.10354 13.7068i −0.165202 0.551814i −0.999999 0.00125610i 0.999600π-0.999600\pi
0.834797 0.550558i 0.185585π-0.185585\pi
618618 3.70808 + 3.34653i 0.149161 + 0.134617i
619619 −2.49473 + 3.35100i −0.100272 + 0.134688i −0.849427 0.527706i 0.823052π-0.823052\pi
0.749155 + 0.662394i 0.230460π0.230460\pi
620620 −25.7695 + 44.6341i −1.03493 + 1.79255i
621621 −25.1800 8.93248i −1.01044 0.358448i
622622 0.136257 + 0.236004i 0.00546342 + 0.00946292i
623623 −0.0896198 0.0104751i −0.00359054 0.000419674i
624624 −19.0801 7.73453i −0.763817 0.309629i
625625 −27.9354 6.62081i −1.11742 0.264832i
626626 −0.321769 0.211631i −0.0128605 0.00845847i
627627 29.4053 + 33.5101i 1.17433 + 1.33826i
628628 7.96575 + 8.44320i 0.317868 + 0.336920i
629629 −0.431048 + 0.361692i −0.0171870 + 0.0144216i
630630 0.0236198 + 0.0140797i 0.000941034 + 0.000560948i
631631 14.2403 + 11.9490i 0.566896 + 0.475683i 0.880614 0.473834i 0.157130π-0.157130\pi
−0.313718 + 0.949516i 0.601575π0.601575\pi
632632 −0.308985 5.30507i −0.0122908 0.211024i
633633 −1.27191 + 13.4565i −0.0505537 + 0.534850i
634634 −0.915184 1.22931i −0.0363466 0.0488220i
635635 23.4717 2.74345i 0.931445 0.108870i
636636 11.9217 + 3.28367i 0.472725 + 0.130206i
637637 20.7055 13.6182i 0.820381 0.539573i
638638 −5.25068 + 1.91109i −0.207877 + 0.0756609i
639639 5.72604 + 5.55520i 0.226519 + 0.219760i
640640 25.9980 + 9.46249i 1.02766 + 0.374038i
641641 −15.6267 + 3.70359i −0.617216 + 0.146283i −0.527318 0.849668i 0.676802π-0.676802\pi
−0.0898984 + 0.995951i 0.528654π0.528654\pi
642642 −2.93065 7.52949i −0.115664 0.297165i
643643 1.55848 26.7581i 0.0614606 1.05524i −0.816758 0.576980i 0.804231π-0.804231\pi
0.878219 0.478259i 0.158732π-0.158732\pi
644644 −0.0614033 + 0.0650837i −0.00241963 + 0.00256466i
645645 −3.00643 5.67006i −0.118378 0.223258i
646646 −3.82065 8.85726i −0.150321 0.348484i
647647 16.2621 0.639328 0.319664 0.947531i 0.396430π-0.396430\pi
0.319664 + 0.947531i 0.396430π0.396430\pi
648648 −9.83636 + 6.08341i −0.386409 + 0.238979i
649649 −18.4687 −0.724960
650650 1.89605 + 4.39555i 0.0743694 + 0.172408i
651651 −0.143977 0.00519434i −0.00564291 0.000203582i
652652 1.82498 1.93437i 0.0714718 0.0757556i
653653 −2.54255 + 43.6539i −0.0994976 + 1.70831i 0.467010 + 0.884252i 0.345331π0.345331\pi
−0.566508 + 0.824057i 0.691706π0.691706\pi
654654 2.72063 3.39191i 0.106385 0.132634i
655655 12.6815 3.00557i 0.495508 0.117437i
656656 11.3758 + 4.14045i 0.444150 + 0.161657i
657657 −0.687528 6.69006i −0.0268230 0.261004i
658658 0.00297738 0.00108368i 0.000116071 4.22462e-5i
659659 −22.2684 + 14.6462i −0.867455 + 0.570534i −0.903390 0.428820i 0.858929π-0.858929\pi
0.0359352 + 0.999354i 0.488559π0.488559\pi
660660 −25.0251 + 24.6785i −0.974100 + 0.960609i
661661 17.3882 2.03239i 0.676323 0.0790508i 0.229004 0.973425i 0.426453π-0.426453\pi
0.447319 + 0.894375i 0.352379π0.352379\pi
662662 −1.31295 1.76360i −0.0510292 0.0685441i
663663 −22.5134 + 10.3076i −0.874347 + 0.400316i
664664 −0.963913 16.5497i −0.0374071 0.642255i
665665 0.153777 + 0.129034i 0.00596321 + 0.00500373i
666666 −0.0872686 0.106998i −0.00338159 0.00414610i
667667 18.7263 15.7133i 0.725086 0.608420i
668668 −19.0834 20.2272i −0.738360 0.782616i
669669 −38.1631 + 7.60299i −1.47547 + 0.293949i
670670 −6.92701 4.55597i −0.267614 0.176012i
671671 −23.7293 5.62396i −0.916061 0.217110i
672672 0.00809446 + 0.0580819i 0.000312250 + 0.00224056i
673673 −7.95363 0.929646i −0.306590 0.0358352i −0.0385930 0.999255i 0.512288π-0.512288\pi
−0.267997 + 0.963420i 0.586362π0.586362\pi
674674 2.73953 + 4.74501i 0.105523 + 0.182771i
675675 −20.7389 4.73660i −0.798239 0.182312i
676676 −0.440175 + 0.762405i −0.0169298 + 0.0293233i
677677 −25.3648 + 34.0708i −0.974847 + 1.30945i −0.0240237 + 0.999711i 0.507648π0.507648\pi
−0.950823 + 0.309735i 0.899760π0.899760\pi
678678 −10.5003 + 3.39836i −0.403263 + 0.130513i
679679 0.0416655 + 0.139172i 0.00159897 + 0.00534095i
680680 13.9834 7.02271i 0.536238 0.269309i
681681 24.6177 + 13.4962i 0.943354 + 0.517175i
682682 −3.04659 + 10.1763i −0.116660 + 0.389671i
683683 3.92505 + 22.2600i 0.150188 + 0.851757i 0.963054 + 0.269307i 0.0867947π0.0867947\pi
−0.812867 + 0.582450i 0.802094π0.802094\pi
684684 −37.8995 + 15.7250i −1.44912 + 0.601262i
685685 0.0616556 0.349666i 0.00235574 0.0133601i
686686 −0.0380264 0.0190976i −0.00145185 0.000729148i
687687 25.2016 2.02788i 0.961503 0.0773686i
688688 1.63395 3.78791i 0.0622936 0.144413i
689689 −5.29440 + 12.2738i −0.201701 + 0.467595i
690690 −3.80457 + 8.01257i −0.144837 + 0.305033i
691691 −7.58174 3.80769i −0.288423 0.144851i 0.298705 0.954345i 0.403445π-0.403445\pi
−0.587128 + 0.809494i 0.699742π0.699742\pi
692692 2.51734 14.2765i 0.0956948 0.542712i
693693 −0.0937183 0.0294876i −0.00356006 0.00112014i
694694 0.787049 + 4.46358i 0.0298760 + 0.169435i
695695 −1.12614 + 3.76157i −0.0427169 + 0.142684i
696696 −0.234011 10.5795i −0.00887017 0.401014i
697697 13.0107 6.53423i 0.492816 0.247502i
698698 1.33827 + 4.47012i 0.0506541 + 0.169196i
699699 3.84434 17.9840i 0.145406 0.680218i
700700 −0.0425439 + 0.0571463i −0.00160801 + 0.00215993i
701701 18.1146 31.3755i 0.684181 1.18504i −0.289513 0.957174i 0.593493π-0.593493\pi
0.973694 0.227861i 0.0731733π-0.0731733\pi
702702 −2.45201 5.55908i −0.0925451 0.209814i
703703 −0.503988 0.872933i −0.0190083 0.0329233i
704704 −19.4389 2.27208i −0.732630 0.0856322i
705705 −4.29447 + 3.34723i −0.161739 + 0.126064i
706706 2.97504 + 0.705099i 0.111967 + 0.0265367i
707707 0.148003 + 0.0973432i 0.00556623 + 0.00366097i
708708 5.45902 16.0976i 0.205162 0.604983i
709709 7.03434 + 7.45597i 0.264180 + 0.280015i 0.845862 0.533402i 0.179087π-0.179087\pi
−0.581682 + 0.813416i 0.697605π0.697605\pi
710710 2.02896 1.70250i 0.0761453 0.0638935i
711711 −8.10604 + 9.39125i −0.304000 + 0.352199i
712712 −9.65159 8.09865i −0.361709 0.303510i
713713 −2.70215 46.3941i −0.101196 1.73747i
714714 0.0173277 + 0.0123140i 0.000648474 + 0.000460839i
715715 −22.6877 30.4749i −0.848473 1.13970i
716716 11.2624 1.31639i 0.420897 0.0491958i
717717 −2.21313 8.49606i −0.0826510 0.317291i
718718 6.07080 3.99283i 0.226560 0.149011i
719719 34.8714 12.6922i 1.30048 0.473338i 0.403330 0.915055i 0.367853π-0.367853\pi
0.897154 + 0.441717i 0.145630π0.145630\pi
720720 −13.2520 27.3308i −0.493874 1.01856i
721721 −0.0755111 0.0274838i −0.00281218 0.00102355i
722722 10.7078 2.53779i 0.398502 0.0944468i
723723 0.608323 + 0.0934437i 0.0226238 + 0.00347521i
724724 1.13735 19.5276i 0.0422693 0.725737i
725725 13.3570 14.1576i 0.496066 0.525799i
726726 −0.505123 + 0.806291i −0.0187469 + 0.0299243i
727727 −13.1970 30.5941i −0.489450 1.13467i −0.966702 0.255906i 0.917626π-0.917626\pi
0.477252 0.878767i 0.341633π-0.341633\pi
728728 −0.0418702 −0.00155181
729729 26.3704 + 5.79655i 0.976683 + 0.214687i
730730 −2.23274 −0.0826374
731731 −1.96510 4.55561i −0.0726817 0.168495i
732732 11.9159 19.0205i 0.440424 0.703016i
733733 25.7806 27.3259i 0.952230 1.00930i −0.0477158 0.998861i 0.515194π-0.515194\pi
0.999945 0.0104436i 0.00332435π-0.00332435\pi
734734 0.379472 6.51528i 0.0140066 0.240483i
735735 36.1382 + 5.55113i 1.33298 + 0.204756i
736736 −18.4066 + 4.36244i −0.678475 + 0.160802i
737737 27.8366 + 10.1317i 1.02537 + 0.373206i
738738 1.55869 + 3.21463i 0.0573763 + 0.118332i
739739 −12.4039 + 4.51464i −0.456283 + 0.166074i −0.559929 0.828541i 0.689172π-0.689172\pi
0.103645 + 0.994614i 0.466949π0.466949\pi
740740 0.663911 0.436661i 0.0244058 0.0160520i
741741 −11.1809 42.9228i −0.410741 1.57681i
742742 0.0113982 0.00133226i 0.000418441 4.89087e-5i
743743 −4.10039 5.50778i −0.150429 0.202061i 0.720521 0.693433i 0.243903π-0.243903\pi
−0.870950 + 0.491372i 0.836495π0.836495\pi
744744 −16.3983 11.6534i −0.601190 0.427236i
745745 1.21646 + 20.8858i 0.0445676 + 0.765196i
746746 1.87759 + 1.57548i 0.0687433 + 0.0576825i
747747 −25.2877 + 29.2970i −0.925228 + 1.07192i
748748 −20.8138 + 17.4649i −0.761029 + 0.638579i
749749 0.0892013 + 0.0945478i 0.00325934 + 0.00345470i
750750 0.501958 1.48018i 0.0183289 0.0540484i
751751 −15.1165 9.94229i −0.551610 0.362799i 0.242900 0.970051i 0.421901π-0.421901\pi
−0.794509 + 0.607252i 0.792272π0.792272\pi
752752 −3.40555 0.807131i −0.124188 0.0294330i
753753 −30.2593 + 23.5849i −1.10271 + 0.859483i
754754 5.52158 + 0.645380i 0.201084 + 0.0235034i
755755 14.2346 + 24.6550i 0.518049 + 0.897288i
756756 0.0534032 0.0729700i 0.00194226 0.00265389i
757757 −2.10262 + 3.64185i −0.0764211 + 0.132365i −0.901703 0.432355i 0.857683π-0.857683\pi
0.825282 + 0.564720i 0.191016π0.191016\pi
758758 −1.89431 + 2.54450i −0.0688045 + 0.0924205i
759759 6.62488 30.9915i 0.240468 1.12492i
760760 8.03924 + 26.8529i 0.291614 + 0.974059i
761761 17.4823 8.77996i 0.633735 0.318273i −0.102771 0.994705i 0.532771π-0.532771\pi
0.736505 + 0.676432i 0.236475π0.236475\pi
762762 0.0991314 + 4.48167i 0.00359115 + 0.162354i
763763 −0.0200628 + 0.0670144i −0.000726322 + 0.00242608i
764764 5.21294 + 29.5640i 0.188597 + 1.06959i
765765 −34.8459 10.9640i −1.25986 0.396403i
766766 0.524065 2.97212i 0.0189353 0.107387i
767767 16.4201 + 8.24648i 0.592895 + 0.297763i
768768 5.92075 12.4693i 0.213647 0.449949i
769769 9.37175 21.7261i 0.337954 0.783465i −0.661485 0.749959i 0.730073π-0.730073\pi
0.999439 0.0335063i 0.0106674π-0.0106674\pi
770770 −0.0129191 + 0.0299498i −0.000465572 + 0.00107932i
771771 35.4341 2.85125i 1.27613 0.102685i
772772 −33.2152 16.6813i −1.19544 0.600372i
773773 −7.96472 + 45.1702i −0.286471 + 1.62466i 0.413511 + 0.910499i 0.364302π0.364302\pi
−0.699983 + 0.714160i 0.746809π0.746809\pi
774774 1.12447 0.466560i 0.0404184 0.0167702i
775775 −6.42541 36.4403i −0.230807 1.30897i
776776 −5.81796 + 19.4333i −0.208853 + 0.697616i
777777 0.00194780 + 0.00106784i 6.98770e−5 + 3.83087e-5i
778778 −4.70237 + 2.36162i −0.168588 + 0.0846681i
779779 7.48006 + 24.9851i 0.268001 + 0.895185i
780780 33.2684 10.7671i 1.19120 0.385523i
781781 −5.65109 + 7.59074i −0.202212 + 0.271618i
782782 −3.42851 + 5.93836i −0.122603 + 0.212355i
783783 −16.8056 + 18.1070i −0.600583 + 0.647091i
784784 11.7508 + 20.3530i 0.419673 + 0.726894i
785785 −18.3868 2.14911i −0.656253 0.0767050i
786786 0.341243 + 2.44859i 0.0121717 + 0.0873384i
787787 13.0689 + 3.09738i 0.465855 + 0.110410i 0.456838 0.889550i 0.348982π-0.348982\pi
0.00901649 + 0.999959i 0.497130π0.497130\pi
788788 −0.134433 0.0884178i −0.00478897 0.00314975i
789789 −37.7132 + 7.51335i −1.34263 + 0.267482i
790790 2.82636 + 2.99577i 0.100558 + 0.106585i
791791 0.136015 0.114130i 0.00483612 0.00405799i
792792 −8.67088 10.6312i −0.308106 0.377763i
793793 18.5860 + 15.5955i 0.660010 + 0.553814i
794794 −0.121048 2.07832i −0.00429584 0.0737567i
795795 −17.9306 + 8.20944i −0.635932 + 0.291159i
796796 20.1704 + 27.0936i 0.714922 + 0.960307i
797797 −32.0603 + 3.74731i −1.13563 + 0.132737i −0.663069 0.748559i 0.730746π-0.730746\pi
−0.472566 + 0.881295i 0.656672π0.656672\pi
798798 −0.0271134 + 0.0267379i −0.000959805 + 0.000946512i
799799 −3.51675 + 2.31300i −0.124414 + 0.0818281i
800800 −14.1533 + 5.15139i −0.500395 + 0.182129i
801801 3.00692 + 29.2591i 0.106244 + 1.03382i
802802 −9.92680 3.61306i −0.350527 0.127582i
803803 7.76239 1.83972i 0.273929 0.0649223i
804804 −17.0589 + 21.2680i −0.601621 + 0.750064i
805805 0.00829716 0.142457i 0.000292436 0.00502094i
806806 7.25248 7.68718i 0.255458 0.270769i
807807 30.3763 + 1.09590i 1.06930 + 0.0385776i
808808 9.79733 + 22.7128i 0.344669 + 0.799032i
809809 −17.1245 −0.602066 −0.301033 0.953614i 0.597332π-0.597332\pi
−0.301033 + 0.953614i 0.597332π0.597332\pi
810810 2.80932 8.51216i 0.0987096 0.299087i
811811 −12.0048 −0.421545 −0.210772 0.977535i 0.567598π-0.567598\pi
−0.210772 + 0.977535i 0.567598π0.567598\pi
812812 0.0327696 + 0.0759686i 0.00114999 + 0.00266597i
813813 19.0226 + 35.8762i 0.667151 + 1.25823i
814814 0.112393 0.119130i 0.00393938 0.00417550i
815815 −0.246602 + 4.23398i −0.00863807 + 0.148310i
816816 −8.51700 21.8821i −0.298155 0.766025i
817817 8.64794 2.04960i 0.302553 0.0717064i
818818 −11.1294 4.05076i −0.389129 0.141631i
819819 0.0701561 + 0.0680630i 0.00245145 + 0.00237831i
820820 −19.3208 + 7.03221i −0.674713 + 0.245575i
821821 30.2085 19.8684i 1.05428 0.693413i 0.100814 0.994905i 0.467855π-0.467855\pi
0.953468 + 0.301493i 0.0974849π0.0974849\pi
822822 0.0649349 + 0.0178855i 0.00226487 + 0.000623828i
823823 −52.8276 + 6.17466i −1.84145 + 0.215235i −0.964271 0.264919i 0.914655π-0.914655\pi
−0.877184 + 0.480154i 0.840581π0.840581\pi
824824 −6.70053 9.00037i −0.233424 0.313543i
825825 2.37448 25.1215i 0.0826686 0.874620i
826826 −0.000917225 0.0157481i −3.19143e−5 0.000547948i
827827 14.2860 + 11.9874i 0.496773 + 0.416842i 0.856446 0.516236i 0.172667π-0.172667\pi
−0.359673 + 0.933078i 0.617112π0.617112\pi
828828 25.0544 + 14.9349i 0.870701 + 0.519022i
829829 34.9024 29.2866i 1.21221 1.01716i 0.213014 0.977049i 0.431672π-0.431672\pi
0.999195 0.0401151i 0.0127725π-0.0127725\pi
830830 8.81715 + 9.34563i 0.306048 + 0.324392i
831831 −0.393563 0.448502i −0.0136526 0.0155584i
832832 16.2681 + 10.6997i 0.563996 + 0.370946i
833833 27.5029 + 6.51830i 0.952918 + 0.225846i
834834 −0.690281 0.279820i −0.0239025 0.00968936i
835835 44.0490 + 5.14859i 1.52438 + 0.178174i
836836 −24.3358 42.1509i −0.841673 1.45782i
837837 8.53283 + 46.1826i 0.294938 + 1.59630i
838838 1.19702 2.07330i 0.0413503 0.0716208i
839839 3.98907 5.35824i 0.137718 0.184987i −0.727914 0.685669i 0.759510π-0.759510\pi
0.865632 + 0.500682i 0.166917π0.166917\pi
840840 −0.0458576 0.0413864i −0.00158224 0.00142797i
841841 1.83458 + 6.12792i 0.0632613 + 0.211307i
842842 −0.857857 + 0.430832i −0.0295637 + 0.0148474i
843843 −44.7781 + 27.1903i −1.54224 + 0.936485i
844844 4.23216 14.1364i 0.145677 0.486595i
845845 −0.243797 1.38264i −0.00838688 0.0475643i
846846 −0.555476 0.870772i −0.0190977 0.0299378i
847847 0.00265799 0.0150742i 9.13295e−5 0.000517955i
848848 −11.3278 5.68905i −0.388999 0.195363i
849849 −5.43831 7.88314i −0.186642 0.270549i
850850 −2.16247 + 5.01318i −0.0741723 + 0.171951i
851851 −0.283801 + 0.657925i −0.00972858 + 0.0225534i
852852 −4.94582 7.16925i −0.169441 0.245614i
853853 41.7453 + 20.9653i 1.42933 + 0.717838i 0.984106 0.177580i 0.0568269π-0.0568269\pi
0.445226 + 0.895418i 0.353123π0.353123\pi
854854 0.00361702 0.0205132i 0.000123772 0.000701946i
855855 30.1811 58.0621i 1.03217 1.98568i
856856 3.15180 + 17.8747i 0.107726 + 0.610946i
857857 −14.7882 + 49.3962i −0.505157 + 1.68734i 0.201255 + 0.979539i 0.435498π0.435498\pi
−0.706411 + 0.707802i 0.749687π0.749687\pi
858858 6.16026 3.74066i 0.210308 0.127704i
859859 18.4183 9.25001i 0.628423 0.315606i −0.105930 0.994374i 0.533782π-0.533782\pi
0.734353 + 0.678767i 0.237486π0.237486\pi
860860 2.00948 + 6.71212i 0.0685226 + 0.228881i
861861 −0.0426679 0.0385077i −0.00145412 0.00131234i
862862 0.138004 0.185372i 0.00470045 0.00631380i
863863 26.9774 46.7263i 0.918322 1.59058i 0.116359 0.993207i 0.462878π-0.462878\pi
0.801963 0.597373i 0.203789π-0.203789\pi
864864 17.9097 6.68478i 0.609299 0.227421i
865865 11.5596 + 20.0219i 0.393040 + 0.680765i
866866 −5.78024 0.675613i −0.196421 0.0229583i
867867 1.11656 + 0.452621i 0.0379204 + 0.0153718i
868868 0.153046 + 0.0362725i 0.00519471 + 0.00123117i
869869 −12.2946 8.08630i −0.417067 0.274309i
870870 5.40949 + 6.16462i 0.183399 + 0.209000i
871871 −20.2249 21.4372i −0.685296 0.726371i
872872 −7.48265 + 6.27869i −0.253395 + 0.212623i
873873 41.3386 23.1043i 1.39910 0.781960i
874874 −9.40954 7.89554i −0.318282 0.267071i
875875 0.00146204 + 0.0251023i 4.94260e−5 + 0.000848612i
876876 −0.690898 + 7.30958i −0.0233433 + 0.246968i
877877 9.68370 + 13.0075i 0.326995 + 0.439231i 0.934971 0.354725i 0.115425π-0.115425\pi
−0.607975 + 0.793956i 0.708018π0.708018\pi
878878 −7.92024 + 0.925743i −0.267295 + 0.0312423i
879879 −33.4009 9.19984i −1.12658 0.310303i
880880 30.1020 19.7984i 1.01474 0.667404i
881881 −36.0488 + 13.1207i −1.21451 + 0.442047i −0.868267 0.496097i 0.834766π-0.834766\pi
−0.346246 + 0.938144i 0.612544π0.612544\pi
882882 −1.69342 + 6.72571i −0.0570205 + 0.226466i
883883 −51.0003 18.5626i −1.71630 0.624681i −0.718788 0.695229i 0.755303π-0.755303\pi
−0.997508 + 0.0705487i 0.977525π0.977525\pi
884884 26.3033 6.23401i 0.884677 0.209672i
885885 9.83262 + 25.2622i 0.330520 + 0.849178i
886886 0.131142 2.25163i 0.00440581 0.0756449i
887887 2.56518 2.71893i 0.0861303 0.0912928i −0.682875 0.730535i 0.739271π-0.739271\pi
0.769005 + 0.639243i 0.220752π0.220752\pi
888888 0.145301 + 0.274034i 0.00487598 + 0.00919599i
889889 −0.0285644 0.0662198i −0.000958021 0.00222094i
890890 9.76493 0.327321
891891 −2.75315 + 31.9083i −0.0922341 + 1.06897i
892892 42.4824 1.42242
893893 −2.98650 6.92348i −0.0999393 0.231685i
894894 −3.96605 0.143086i −0.132645 0.00478550i
895895 −12.4096 + 13.1534i −0.414808 + 0.439671i
896896 0.00490928 0.0842890i 0.000164007 0.00281590i
897897 −19.7281 + 24.5957i −0.658701 + 0.821228i
898898 0.836009 0.198138i 0.0278980 0.00661194i
899899 −40.3792 14.6968i −1.34672 0.490167i
900900 21.1944 + 9.49510i 0.706480 + 0.316503i
901901 −14.3258 + 5.21418i −0.477263 + 0.173710i
902902 −3.54057 + 2.32867i −0.117888 + 0.0775363i
903903 −0.0139454 + 0.0137523i −0.000464074 + 0.000457647i
904904 24.6252 2.87827i 0.819021 0.0957298i
905905 18.6285 + 25.0224i 0.619231 + 0.831771i
906906 −4.91026 + 2.24814i −0.163133 + 0.0746895i
907907 1.10404 + 18.9556i 0.0366590 + 0.629411i 0.965736 + 0.259525i 0.0835661π0.0835661\pi
−0.929077 + 0.369886i 0.879397π0.879397\pi
908908 −23.4790 19.7012i −0.779178 0.653808i
909909 20.5052 53.9829i 0.680113 1.79050i
910910 0.0248590 0.0208592i 0.000824068 0.000691475i
911911 −10.0667 10.6701i −0.333524 0.353515i 0.538808 0.842429i 0.318875π-0.318875\pi
−0.872332 + 0.488914i 0.837393π0.837393\pi
912912 41.2520 8.21837i 1.36599 0.272137i
913913 −38.3544 25.2261i −1.26935 0.834862i
914914 2.49591 + 0.591541i 0.0825573 + 0.0195664i
915915 4.94069 + 35.4520i 0.163334 + 1.17201i
916916 −27.4155 3.20442i −0.905834 0.105877i
917917 −0.0198866 0.0344446i −0.000656714 0.00113746i
918918 2.69259 6.38504i 0.0888686 0.210738i
919919 −14.0757 + 24.3798i −0.464315 + 0.804216i −0.999170 0.0407270i 0.987033π-0.987033\pi
0.534856 + 0.844943i 0.320366π0.320366\pi
920920 11.8988 15.9828i 0.392291 0.526938i
921921 −1.84613 + 0.597488i −0.0608322 + 0.0196879i
922922 −0.0643052 0.214794i −0.00211778 0.00707388i
923923 8.41360 4.22547i 0.276937 0.139083i
924924 0.0940527 + 0.0515625i 0.00309411 + 0.00169628i
925925 −0.163624 + 0.546544i −0.00537994 + 0.0179702i
926926 −1.16017 6.57965i −0.0381256 0.216221i
927927 −3.40358 + 25.9728i −0.111788 + 0.853060i
928928 −3.03728 + 17.2253i −0.0997035 + 0.565447i
929929 −33.7421 16.9459i −1.10704 0.555977i −0.201181 0.979554i 0.564478π-0.564478\pi
−0.905860 + 0.423577i 0.860774π0.860774\pi
930930 15.5415 1.25057i 0.509626 0.0410077i
931931 −20.0542 + 46.4910i −0.657251 + 1.52368i
932932 −7.95215 + 18.4352i −0.260481 + 0.603864i
933933 −0.613004 + 1.29101i −0.0200688 + 0.0422658i
934934 2.39017 + 1.20039i 0.0782089 + 0.0392780i
935935 7.52440 42.6730i 0.246074 1.39556i
936936 2.96213 + 13.3236i 0.0968203 + 0.435495i
937937 4.74619 + 26.9170i 0.155051 + 0.879339i 0.958739 + 0.284288i 0.0917572π0.0917572\pi
−0.803688 + 0.595051i 0.797132π0.797132\pi
938938 −0.00725675 + 0.0242392i −0.000236941 + 0.000791440i
939939 −0.0446642 2.01924i −0.00145756 0.0658953i
940940 5.31200 2.66778i 0.173258 0.0870135i
941941 −14.2198 47.4974i −0.463551 1.54837i −0.796029 0.605259i 0.793070π-0.793070\pi
0.332477 0.943111i 0.392115π-0.392115\pi
942942 0.734076 3.43404i 0.0239175 0.111887i
943943 11.0711 14.8711i 0.360526 0.484270i
944944 −8.71245 + 15.0904i −0.283566 + 0.491151i
945945 0.00956074 + 0.143890i 0.000311011 + 0.00468075i
946946 0.722042 + 1.25061i 0.0234756 + 0.0406610i
947947 −6.59374 0.770698i −0.214268 0.0250443i 0.00828174 0.999966i 0.497364π-0.497364\pi
−0.222549 + 0.974921i 0.571438π0.571438\pi
948948 10.6822 8.32599i 0.346942 0.270416i
949949 −7.72281 1.83034i −0.250693 0.0594153i
950950 −8.17122 5.37429i −0.265109 0.174365i
951951 2.58122 7.61150i 0.0837017 0.246820i
952952 −0.0327704 0.0347346i −0.00106210 0.00112576i
953953 −3.58202 + 3.00567i −0.116033 + 0.0973632i −0.698958 0.715163i 0.746353π-0.746353\pi
0.582925 + 0.812526i 0.301908π0.301908\pi
954954 −1.23031 3.53278i −0.0398328 0.114378i
955955 −36.6750 30.7739i −1.18677 0.995822i
956956 0.557311 + 9.56866i 0.0180247 + 0.309473i
957957 −23.8862 16.9748i −0.772132 0.548716i
958958 −5.74031 7.71057i −0.185461 0.249117i
959959 −0.00107624 0.000125794i −3.47535e−5 4.06211e-6i
960960 7.24130 + 27.7988i 0.233712 + 0.897204i
961961 −42.3513 + 27.8549i −1.36617 + 0.898545i
962962 −0.153119 + 0.0557307i −0.00493675 + 0.00179683i
963963 23.7756 35.0737i 0.766158 1.13023i
964964 −0.631389 0.229807i −0.0203357 0.00740158i
965965 57.6785 13.6700i 1.85674 0.440054i
966966 0.0267553 + 0.00410984i 0.000860837 + 0.000132232i
967967 0.543701 9.33499i 0.0174843 0.300193i −0.978218 0.207580i 0.933441π-0.933441\pi
0.995702 0.0926127i 0.0295218π-0.0295218\pi
968968 1.46674 1.55466i 0.0471429 0.0499686i
969969 26.8569 42.8697i 0.862767 1.37717i
970970 −6.22721 14.4363i −0.199944 0.463522i
971971 33.5606 1.07701 0.538505 0.842622i 0.318989π-0.318989\pi
0.538505 + 0.842622i 0.318989π0.318989\pi
972972 −26.9979 11.8312i −0.865959 0.379486i
973973 0.0119829 0.000384153
974974 0.470255 + 1.09017i 0.0150679 + 0.0349314i
975975 −13.3281 + 21.2747i −0.426842 + 0.681337i
976976 −15.7893 + 16.7357i −0.505404 + 0.535697i
977977 −0.410464 + 7.04739i −0.0131319 + 0.225466i 0.985357 + 0.170506i 0.0545402π0.0545402\pi
−0.998489 + 0.0549601i 0.982497π0.982497\pi
978978 −0.795199 0.122149i −0.0254276 0.00390590i
979979 −33.9490 + 8.04605i −1.08501 + 0.257153i
980980 −37.5084 13.6519i −1.19816 0.436095i
981981 22.7441 + 1.64324i 0.726163 + 0.0524647i
982982 10.4369 3.79871i 0.333054 0.121222i
983983 35.0570 23.0574i 1.11815 0.735416i 0.150722 0.988576i 0.451840π-0.451840\pi
0.967424 + 0.253160i 0.0814699π0.0814699\pi
984984 −2.02306 7.76637i −0.0644927 0.247583i
985985 0.254872 0.0297902i 0.00812089 0.000949196i
986986 3.78617 + 5.08571i 0.120576 + 0.161962i
987987 0.0135446 + 0.00962549i 0.000431130 + 0.000306383i
988988 2.81558 + 48.3416i 0.0895755 + 1.53795i
989989 −4.83966 4.06096i −0.153892 0.129131i
990990 10.4444 + 1.99219i 0.331943 + 0.0633159i
991991 10.7027 8.98062i 0.339982 0.285279i −0.456770 0.889585i 0.650994π-0.650994\pi
0.796753 + 0.604306i 0.206549π0.206549\pi
992992 22.8187 + 24.1864i 0.724494 + 0.767919i
993993 3.70309 10.9197i 0.117514 0.346525i
994994 −0.00675322 0.00444167i −0.000214199 0.000140881i
995995 −52.4158 12.4228i −1.66169 0.393828i
996996 33.3243 25.9738i 1.05592 0.823012i
997997 −17.4776 2.04284i −0.553521 0.0646973i −0.165265 0.986249i 0.552848π-0.552848\pi
−0.388255 + 0.921552i 0.626922π0.626922\pi
998998 2.26597 + 3.92477i 0.0717280 + 0.124237i
999999 0.202002 0.695358i 0.00639105 0.0220002i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 81.2.g.a.31.5 144
3.2 odd 2 243.2.g.a.145.4 144
9.2 odd 6 729.2.g.a.190.4 144
9.4 even 3 729.2.g.c.433.4 144
9.5 odd 6 729.2.g.b.433.5 144
9.7 even 3 729.2.g.d.190.5 144
81.7 even 27 729.2.g.c.298.4 144
81.14 odd 54 6561.2.a.d.1.30 72
81.20 odd 54 729.2.g.a.541.4 144
81.34 even 27 inner 81.2.g.a.34.5 yes 144
81.47 odd 54 243.2.g.a.181.4 144
81.61 even 27 729.2.g.d.541.5 144
81.67 even 27 6561.2.a.c.1.43 72
81.74 odd 54 729.2.g.b.298.5 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.31.5 144 1.1 even 1 trivial
81.2.g.a.34.5 yes 144 81.34 even 27 inner
243.2.g.a.145.4 144 3.2 odd 2
243.2.g.a.181.4 144 81.47 odd 54
729.2.g.a.190.4 144 9.2 odd 6
729.2.g.a.541.4 144 81.20 odd 54
729.2.g.b.298.5 144 81.74 odd 54
729.2.g.b.433.5 144 9.5 odd 6
729.2.g.c.298.4 144 81.7 even 27
729.2.g.c.433.4 144 9.4 even 3
729.2.g.d.190.5 144 9.7 even 3
729.2.g.d.541.5 144 81.61 even 27
6561.2.a.c.1.43 72 81.67 even 27
6561.2.a.d.1.30 72 81.14 odd 54