Properties

Label 81.2.g.a.58.3
Level 8181
Weight 22
Character 81.58
Analytic conductor 0.6470.647
Analytic rank 00
Dimension 144144
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [81,2,Mod(4,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage: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")
 
Copy content magma://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

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content 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 58.3
Character χ\chi == 81.58
Dual form 81.2.g.a.7.3

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.886934+1.19136i)q2+(0.340526+1.69825i)q3+(0.05907880.197337i)q4+(1.339260.880846i)q5+(1.721201.91192i)q6+(1.30515+1.38337i)q7+(2.503870.911335i)q8+(2.768081.15659i)q9+(2.237240.814290i)q10+(3.62327+1.81967i)q11+(0.3552450.0331322i)q12+(0.669348+1.55172i)q13+(2.80567+0.327936i)q14+(1.951951.97445i)q15+(3.650712.40111i)q16+(4.14727+3.47997i)q17+(3.833032.27196i)q18+(3.701673.10607i)q19+(0.0947016+0.316325i)q20+(2.79374+1.74539i)q21+(5.38148+2.70268i)q22+(0.459550+0.487095i)q23+(2.400303.94186i)q24+(0.9626672.23171i)q25+(1.254992.17371i)q26+(2.906784.30704i)q27+(0.1958840.339282i)q28+(4.75422+0.555689i)q29+(0.621027+4.07668i)q30+(4.735431.12232i)q31+(0.0674931+1.15881i)q32+(4.32407+5.53356i)q33+(7.82425+1.85438i)q34+(0.5293923.00233i)q35+(0.0647034+0.614576i)q36+(2.07926+11.7921i)q37+(0.417308+7.16489i)q38+(2.407281.66512i)q39+(2.55060+3.42604i)q40+(6.040058.11319i)q41+(0.3984874.87640i)q42+(0.4972278.53705i)q43+(0.1450310.822509i)q44+(2.68841+3.98724i)q45+(0.1727140.979511i)q46+(0.196235+0.0465086i)q47+(2.83451+7.01744i)q48+(0.1966973.37715i)q49+(3.51259+0.832500i)q50+(7.32210+5.85806i)q51+(0.345757+0.0404132i)q52+(2.481384.29788i)q53+(2.55311+7.28309i)q54+(3.249655.62856i)q55+(2.007204.65322i)q56+(4.01436+7.34404i)q57+(4.87871+5.17113i)q58+(1.69552+0.851522i)q59+(0.5049500.268544i)q60+(0.05183550.173143i)q61+(5.537104.64618i)q62+(2.012755.33882i)q63+(5.37384+4.50919i)q64+(2.263261.48857i)q65+(2.7572910.0594i)q66+(13.23681.54716i)q67+(0.4417111.02400i)q68+(0.6707190.946298i)q69+(4.04639+2.03218i)q70+(9.412163.42575i)q71+(5.87689+5.41861i)q72+(10.93273.97917i)q73+(12.204512.9360i)q74+(4.117810.874891i)q75+(0.8316320.546973i)q76+(2.21160+7.38727i)q77+(4.118861.39108i)q78+(2.19201+2.94438i)q797.00426q80+(6.32459+6.40309i)q81+15.0229q82+(3.27719+4.40202i)q83+(0.509481+0.448194i)q84+(2.488968.31370i)q85+(10.6117+6.97943i)q86+(2.56263+7.88461i)q87+(7.413877.85824i)q88+(6.652182.42120i)q89+(7.134680.333556i)q90+(3.02021+1.09927i)q91+(0.123272+0.0619093i)q92+(3.518517.65975i)q93+(0.1186390.275037i)q94+(7.69347+0.899238i)q95+(1.944970.509225i)q96+(1.117990.735313i)q97+(3.84894+3.22965i)q98+(7.924899.22765i)q99+O(q100)q+(-0.886934 + 1.19136i) q^{2} +(-0.340526 + 1.69825i) q^{3} +(-0.0590788 - 0.197337i) q^{4} +(-1.33926 - 0.880846i) q^{5} +(-1.72120 - 1.91192i) q^{6} +(1.30515 + 1.38337i) q^{7} +(-2.50387 - 0.911335i) q^{8} +(-2.76808 - 1.15659i) q^{9} +(2.23724 - 0.814290i) q^{10} +(3.62327 + 1.81967i) q^{11} +(0.355245 - 0.0331322i) q^{12} +(-0.669348 + 1.55172i) q^{13} +(-2.80567 + 0.327936i) q^{14} +(1.95195 - 1.97445i) q^{15} +(3.65071 - 2.40111i) q^{16} +(4.14727 + 3.47997i) q^{17} +(3.83303 - 2.27196i) q^{18} +(3.70167 - 3.10607i) q^{19} +(-0.0947016 + 0.316325i) q^{20} +(-2.79374 + 1.74539i) q^{21} +(-5.38148 + 2.70268i) q^{22} +(-0.459550 + 0.487095i) q^{23} +(2.40030 - 3.94186i) q^{24} +(-0.962667 - 2.23171i) q^{25} +(-1.25499 - 2.17371i) q^{26} +(2.90678 - 4.30704i) q^{27} +(0.195884 - 0.339282i) q^{28} +(4.75422 + 0.555689i) q^{29} +(0.621027 + 4.07668i) q^{30} +(-4.73543 - 1.12232i) q^{31} +(-0.0674931 + 1.15881i) q^{32} +(-4.32407 + 5.53356i) q^{33} +(-7.82425 + 1.85438i) q^{34} +(-0.529392 - 3.00233i) q^{35} +(-0.0647034 + 0.614576i) q^{36} +(-2.07926 + 11.7921i) q^{37} +(0.417308 + 7.16489i) q^{38} +(-2.40728 - 1.66512i) q^{39} +(2.55060 + 3.42604i) q^{40} +(-6.04005 - 8.11319i) q^{41} +(0.398487 - 4.87640i) q^{42} +(-0.497227 - 8.53705i) q^{43} +(0.145031 - 0.822509i) q^{44} +(2.68841 + 3.98724i) q^{45} +(-0.172714 - 0.979511i) q^{46} +(-0.196235 + 0.0465086i) q^{47} +(2.83451 + 7.01744i) q^{48} +(0.196697 - 3.37715i) q^{49} +(3.51259 + 0.832500i) q^{50} +(-7.32210 + 5.85806i) q^{51} +(0.345757 + 0.0404132i) q^{52} +(2.48138 - 4.29788i) q^{53} +(2.55311 + 7.28309i) q^{54} +(-3.24965 - 5.62856i) q^{55} +(-2.00720 - 4.65322i) q^{56} +(4.01436 + 7.34404i) q^{57} +(-4.87871 + 5.17113i) q^{58} +(-1.69552 + 0.851522i) q^{59} +(-0.504950 - 0.268544i) q^{60} +(0.0518355 - 0.173143i) q^{61} +(5.53710 - 4.64618i) q^{62} +(-2.01275 - 5.33882i) q^{63} +(5.37384 + 4.50919i) q^{64} +(2.26326 - 1.48857i) q^{65} +(-2.75729 - 10.0594i) q^{66} +(13.2368 - 1.54716i) q^{67} +(0.441711 - 1.02400i) q^{68} +(-0.670719 - 0.946298i) q^{69} +(4.04639 + 2.03218i) q^{70} +(9.41216 - 3.42575i) q^{71} +(5.87689 + 5.41861i) q^{72} +(-10.9327 - 3.97917i) q^{73} +(-12.2045 - 12.9360i) q^{74} +(4.11781 - 0.874891i) q^{75} +(-0.831632 - 0.546973i) q^{76} +(2.21160 + 7.38727i) q^{77} +(4.11886 - 1.39108i) q^{78} +(-2.19201 + 2.94438i) q^{79} -7.00426 q^{80} +(6.32459 + 6.40309i) q^{81} +15.0229 q^{82} +(-3.27719 + 4.40202i) q^{83} +(0.509481 + 0.448194i) q^{84} +(-2.48896 - 8.31370i) q^{85} +(10.6117 + 6.97943i) q^{86} +(-2.56263 + 7.88461i) q^{87} +(-7.41387 - 7.85824i) q^{88} +(-6.65218 - 2.42120i) q^{89} +(-7.13468 - 0.333556i) q^{90} +(-3.02021 + 1.09927i) q^{91} +(0.123272 + 0.0619093i) q^{92} +(3.51851 - 7.65975i) q^{93} +(0.118639 - 0.275037i) q^{94} +(-7.69347 + 0.899238i) q^{95} +(-1.94497 - 0.509225i) q^{96} +(1.11799 - 0.735313i) q^{97} +(3.84894 + 3.22965i) q^{98} +(-7.92489 - 9.22765i) 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(1927)e\left(\frac{19}{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 −0.886934 + 1.19136i −0.627157 + 0.842419i −0.996209 0.0869903i 0.972275π-0.972275\pi
0.369052 + 0.929409i 0.379683π0.379683\pi
33 −0.340526 + 1.69825i −0.196602 + 0.980483i
44 −0.0590788 0.197337i −0.0295394 0.0986686i
55 −1.33926 0.880846i −0.598936 0.393927i 0.213529 0.976937i 0.431504π-0.431504\pi
−0.812465 + 0.583010i 0.801875π0.801875\pi
66 −1.72120 1.91192i −0.702677 0.780539i
77 1.30515 + 1.38337i 0.493299 + 0.522866i 0.925417 0.378951i 0.123715π-0.123715\pi
−0.432118 + 0.901817i 0.642234π0.642234\pi
88 −2.50387 0.911335i −0.885253 0.322206i
99 −2.76808 1.15659i −0.922695 0.385531i
1010 2.23724 0.814290i 0.707478 0.257501i
1111 3.62327 + 1.81967i 1.09246 + 0.548652i 0.901426 0.432932i 0.142521π-0.142521\pi
0.191029 + 0.981584i 0.438817π0.438817\pi
1212 0.355245 0.0331322i 0.102550 0.00956443i
1313 −0.669348 + 1.55172i −0.185644 + 0.430371i −0.985467 0.169864i 0.945667π-0.945667\pi
0.799824 + 0.600235i 0.204926π0.204926\pi
1414 −2.80567 + 0.327936i −0.749848 + 0.0876447i
1515 1.95195 1.97445i 0.503991 0.509800i
1616 3.65071 2.40111i 0.912676 0.600277i
1717 4.14727 + 3.47997i 1.00586 + 0.844017i 0.987785 0.155820i 0.0498020π-0.0498020\pi
0.0180743 + 0.999837i 0.494246π0.494246\pi
1818 3.83303 2.27196i 0.903453 0.535507i
1919 3.70167 3.10607i 0.849220 0.712581i −0.110397 0.993888i 0.535212π-0.535212\pi
0.959618 + 0.281307i 0.0907679π0.0907679\pi
2020 −0.0947016 + 0.316325i −0.0211759 + 0.0707325i
2121 −2.79374 + 1.74539i −0.609645 + 0.380874i
2222 −5.38148 + 2.70268i −1.14734 + 0.576214i
2323 −0.459550 + 0.487095i −0.0958228 + 0.101566i −0.773510 0.633784i 0.781501π-0.781501\pi
0.677687 + 0.735350i 0.262982π0.262982\pi
2424 2.40030 3.94186i 0.489960 0.804629i
2525 −0.962667 2.23171i −0.192533 0.446342i
2626 −1.25499 2.17371i −0.246124 0.426300i
2727 2.90678 4.30704i 0.559411 0.828891i
2828 0.195884 0.339282i 0.0370187 0.0641182i
2929 4.75422 + 0.555689i 0.882837 + 0.103189i 0.545416 0.838165i 0.316372π-0.316372\pi
0.337420 + 0.941354i 0.390446π0.390446\pi
3030 0.621027 + 4.07668i 0.113383 + 0.744296i
3131 −4.73543 1.12232i −0.850508 0.201574i −0.217828 0.975987i 0.569897π-0.569897\pi
−0.632680 + 0.774413i 0.718045π0.718045\pi
3232 −0.0674931 + 1.15881i −0.0119312 + 0.204851i
3333 −4.32407 + 5.53356i −0.752724 + 0.963268i
3434 −7.82425 + 1.85438i −1.34185 + 0.318024i
3535 −0.529392 3.00233i −0.0894836 0.507487i
3636 −0.0647034 + 0.614576i −0.0107839 + 0.102429i
3737 −2.07926 + 11.7921i −0.341829 + 1.93861i 0.00314382 + 0.999995i 0.498999π0.498999\pi
−0.344973 + 0.938613i 0.612112π0.612112\pi
3838 0.417308 + 7.16489i 0.0676962 + 1.16230i
3939 −2.40728 1.66512i −0.385473 0.266633i
4040 2.55060 + 3.42604i 0.403285 + 0.541705i
4141 −6.04005 8.11319i −0.943297 1.26707i −0.963621 0.267274i 0.913877π-0.913877\pi
0.0203240 0.999793i 0.493530π-0.493530\pi
4242 0.398487 4.87640i 0.0614879 0.752445i
4343 −0.497227 8.53705i −0.0758264 1.30189i −0.794809 0.606860i 0.792429π-0.792429\pi
0.718982 0.695028i 0.244608π-0.244608\pi
4444 0.145031 0.822509i 0.0218642 0.123998i
4545 2.68841 + 3.98724i 0.400765 + 0.594382i
4646 −0.172714 0.979511i −0.0254653 0.144421i
4747 −0.196235 + 0.0465086i −0.0286238 + 0.00678397i −0.244903 0.969548i 0.578756π-0.578756\pi
0.216279 + 0.976332i 0.430608π0.430608\pi
4848 2.83451 + 7.01744i 0.409127 + 1.01288i
4949 0.196697 3.37715i 0.0280995 0.482450i
5050 3.51259 + 0.832500i 0.496756 + 0.117733i
5151 −7.32210 + 5.85806i −1.02530 + 0.820293i
5252 0.345757 + 0.0404132i 0.0479479 + 0.00560430i
5353 2.48138 4.29788i 0.340844 0.590359i −0.643746 0.765240i 0.722621π-0.722621\pi
0.984590 + 0.174880i 0.0559538π0.0559538\pi
5454 2.55311 + 7.28309i 0.347434 + 0.991103i
5555 −3.24965 5.62856i −0.438183 0.758955i
5656 −2.00720 4.65322i −0.268224 0.621812i
5757 4.01436 + 7.34404i 0.531715 + 0.972742i
5858 −4.87871 + 5.17113i −0.640606 + 0.679002i
5959 −1.69552 + 0.851522i −0.220738 + 0.110859i −0.555732 0.831362i 0.687562π-0.687562\pi
0.334994 + 0.942220i 0.391266π0.391266\pi
6060 −0.504950 0.268544i −0.0651888 0.0346688i
6161 0.0518355 0.173143i 0.00663685 0.0221686i −0.954607 0.297868i 0.903724π-0.903724\pi
0.961244 + 0.275700i 0.0889095π0.0889095\pi
6262 5.53710 4.64618i 0.703212 0.590065i
6363 −2.01275 5.33882i −0.253583 0.672628i
6464 5.37384 + 4.50919i 0.671730 + 0.563648i
6565 2.26326 1.48857i 0.280723 0.184635i
6666 −2.75729 10.0594i −0.339399 1.23823i
6767 13.2368 1.54716i 1.61713 0.189015i 0.741141 0.671350i 0.234285π-0.234285\pi
0.875987 + 0.482335i 0.160211π0.160211\pi
6868 0.441711 1.02400i 0.0535654 0.124178i
6969 −0.670719 0.946298i −0.0807450 0.113921i
7070 4.04639 + 2.03218i 0.483637 + 0.242891i
7171 9.41216 3.42575i 1.11702 0.406561i 0.283455 0.958985i 0.408519π-0.408519\pi
0.833563 + 0.552424i 0.186297π0.186297\pi
7272 5.87689 + 5.41861i 0.692598 + 0.638590i
7373 −10.9327 3.97917i −1.27957 0.465726i −0.389282 0.921119i 0.627277π-0.627277\pi
−0.890291 + 0.455392i 0.849499π0.849499\pi
7474 −12.2045 12.9360i −1.41874 1.50378i
7575 4.11781 0.874891i 0.475484 0.101024i
7676 −0.831632 0.546973i −0.0953948 0.0627421i
7777 2.21160 + 7.38727i 0.252036 + 0.841857i
7878 4.11886 1.39108i 0.466369 0.157509i
7979 −2.19201 + 2.94438i −0.246620 + 0.331269i −0.908146 0.418654i 0.862502π-0.862502\pi
0.661525 + 0.749923i 0.269909π0.269909\pi
8080 −7.00426 −0.783100
8181 6.32459 + 6.40309i 0.702732 + 0.711455i
8282 15.0229 1.65900
8383 −3.27719 + 4.40202i −0.359718 + 0.483185i −0.944735 0.327836i 0.893681π-0.893681\pi
0.585017 + 0.811021i 0.301088π0.301088\pi
8484 0.509481 + 0.448194i 0.0555889 + 0.0489020i
8585 −2.48896 8.31370i −0.269965 0.901747i
8686 10.6117 + 6.97943i 1.14429 + 0.752611i
8787 −2.56263 + 7.88461i −0.274743 + 0.845319i
8888 −7.41387 7.85824i −0.790321 0.837691i
8989 −6.65218 2.42120i −0.705130 0.256646i −0.0355305 0.999369i 0.511312π-0.511312\pi
−0.669600 + 0.742722i 0.733534π0.733534\pi
9090 −7.13468 0.333556i −0.752061 0.0351598i
9191 −3.02021 + 1.09927i −0.316604 + 0.115234i
9292 0.123272 + 0.0619093i 0.0128519 + 0.00645449i
9393 3.51851 7.65975i 0.364852 0.794279i
9494 0.118639 0.275037i 0.0122367 0.0283679i
9595 −7.69347 + 0.899238i −0.789333 + 0.0922598i
9696 −1.94497 0.509225i −0.198507 0.0519725i
9797 1.11799 0.735313i 0.113515 0.0746597i −0.491482 0.870888i 0.663545π-0.663545\pi
0.604997 + 0.796228i 0.293174π0.293174\pi
9898 3.84894 + 3.22965i 0.388802 + 0.326244i
9999 −7.92489 9.22765i −0.796481 0.927414i
100100 −0.383526 + 0.321817i −0.0383526 + 0.0321817i
101101 −1.42152 + 4.74821i −0.141447 + 0.472465i −0.999130 0.0417141i 0.986718π-0.986718\pi
0.857683 + 0.514179i 0.171903π0.171903\pi
102102 −0.484841 13.9190i −0.0480064 1.37818i
103103 −2.03699 + 1.02302i −0.200711 + 0.100801i −0.546316 0.837579i 0.683970π-0.683970\pi
0.345605 + 0.938380i 0.387674π0.387674\pi
104104 3.09010 3.27532i 0.303010 0.321171i
105105 5.27897 + 0.123332i 0.515175 + 0.0120360i
106106 2.91950 + 6.76816i 0.283567 + 0.657382i
107107 2.21467 + 3.83593i 0.214101 + 0.370833i 0.952994 0.302989i 0.0979846π-0.0979846\pi
−0.738893 + 0.673822i 0.764651π0.764651\pi
108108 −1.02167 0.319161i −0.0983101 0.0307113i
109109 −9.21824 + 15.9665i −0.882947 + 1.52931i −0.0348978 + 0.999391i 0.511111π0.511111\pi
−0.848049 + 0.529918i 0.822223π0.822223\pi
110110 9.58787 + 1.12066i 0.914167 + 0.106851i
111111 −19.3178 7.54661i −1.83357 0.716293i
112112 8.08633 + 1.91650i 0.764086 + 0.181092i
113113 −0.524386 + 9.00337i −0.0493301 + 0.846965i 0.879371 + 0.476137i 0.157963π0.157963\pi
−0.928701 + 0.370829i 0.879074π0.879074\pi
114114 −12.3099 1.73114i −1.15292 0.162136i
115115 1.04451 0.247554i 0.0974014 0.0230846i
116116 −0.171216 0.971014i −0.0158970 0.0901563i
117117 3.64753 3.52114i 0.337214 0.325530i
118118 0.489346 2.77522i 0.0450479 0.255479i
119119 0.598688 + 10.2791i 0.0548817 + 0.942282i
120120 −6.68681 + 3.16489i −0.610420 + 0.288913i
121121 3.24810 + 4.36296i 0.295282 + 0.396633i
122122 0.160300 + 0.215321i 0.0145129 + 0.0194942i
123123 15.8350 7.49474i 1.42779 0.675778i
124124 0.0582888 + 1.00078i 0.00523449 + 0.0898728i
125125 −2.06830 + 11.7299i −0.184994 + 1.04915i
126126 8.14563 + 2.33727i 0.725671 + 0.208220i
127127 −0.304561 1.72725i −0.0270254 0.153269i 0.968309 0.249756i 0.0803504π-0.0803504\pi
−0.995334 + 0.0964872i 0.969239π0.969239\pi
128128 −12.3973 + 2.93821i −1.09577 + 0.259703i
129129 14.6673 + 2.06267i 1.29139 + 0.181608i
130130 −0.233942 + 4.01663i −0.0205181 + 0.352281i
131131 6.97041 + 1.65202i 0.609008 + 0.144338i 0.523537 0.852003i 0.324612π-0.324612\pi
0.0854711 + 0.996341i 0.472760π0.472760\pi
132132 1.34744 + 0.526383i 0.117279 + 0.0458158i
133133 9.12806 + 1.06692i 0.791504 + 0.0925135i
134134 −9.89692 + 17.1420i −0.854964 + 1.48084i
135135 −7.68679 + 3.20783i −0.661573 + 0.276086i
136136 −7.21281 12.4930i −0.618493 1.07126i
137137 −6.92074 16.0441i −0.591279 1.37074i −0.906696 0.421785i 0.861404π-0.861404\pi
0.315417 0.948953i 0.397856π-0.397856\pi
138138 1.72226 + 0.0402371i 0.146609 + 0.00342521i
139139 13.0385 13.8200i 1.10591 1.17220i 0.122188 0.992507i 0.461009π-0.461009\pi
0.983723 0.179691i 0.0575097π-0.0575097\pi
140140 −0.561196 + 0.281843i −0.0474297 + 0.0238201i
141141 −0.0121600 0.349093i −0.00102406 0.0293989i
142142 −4.26668 + 14.2517i −0.358051 + 1.19598i
143143 −5.24886 + 4.40431i −0.438931 + 0.368307i
144144 −12.8826 + 2.42409i −1.07355 + 0.202007i
145145 −5.87767 4.93195i −0.488114 0.409576i
146146 14.4372 9.49549i 1.19483 0.785852i
147147 5.66825 + 1.48404i 0.467510 + 0.122402i
148148 2.44986 0.286347i 0.201377 0.0235376i
149149 2.92032 6.77006i 0.239242 0.554625i −0.755718 0.654897i 0.772712π-0.772712\pi
0.994960 + 0.100272i 0.0319714π0.0319714\pi
150150 −2.60992 + 5.68176i −0.213099 + 0.463914i
151151 −2.38668 1.19863i −0.194225 0.0975434i 0.349029 0.937112i 0.386512π-0.386512\pi
−0.543254 + 0.839569i 0.682808π0.682808\pi
152152 −12.0992 + 4.40374i −0.981372 + 0.357190i
153153 −7.45508 14.4295i −0.602707 1.16656i
154154 −10.7624 3.91721i −0.867262 0.315658i
155155 5.35339 + 5.67426i 0.429995 + 0.455768i
156156 −0.186371 + 0.573419i −0.0149216 + 0.0459103i
157157 4.77413 + 3.14000i 0.381017 + 0.250599i 0.725542 0.688178i 0.241589π-0.241589\pi
−0.344524 + 0.938777i 0.611960π0.611960\pi
158158 −1.56365 5.22294i −0.124397 0.415515i
159159 6.45389 + 5.67754i 0.511827 + 0.450258i
160160 1.11113 1.49250i 0.0878422 0.117993i
161161 −1.27361 −0.100375
162162 −13.2379 + 1.85573i −1.04007 + 0.145800i
163163 16.0381 1.25620 0.628100 0.778132i 0.283833π-0.283833\pi
0.628100 + 0.778132i 0.283833π0.283833\pi
164164 −1.24419 + 1.67124i −0.0971553 + 0.130502i
165165 10.6653 3.60204i 0.830290 0.280418i
166166 −2.33775 7.80862i −0.181444 0.606066i
167167 −15.9980 10.5220i −1.23796 0.814220i −0.249898 0.968272i 0.580397π-0.580397\pi
−0.988063 + 0.154052i 0.950768π0.950768\pi
168168 8.58581 1.82419i 0.662410 0.140739i
169169 6.96132 + 7.37857i 0.535486 + 0.567582i
170170 12.1121 + 4.40846i 0.928959 + 0.338113i
171171 −13.8390 + 4.31654i −1.05829 + 0.330094i
172172 −1.65530 + 0.602480i −0.126216 + 0.0459387i
173173 −21.1226 10.6082i −1.60592 0.806526i −0.999939 0.0110500i 0.996483π-0.996483\pi
−0.605986 0.795476i 0.707221π-0.707221\pi
174174 −7.12053 10.0462i −0.539806 0.761597i
175175 1.83087 4.24444i 0.138401 0.320849i
176176 17.5967 2.05676i 1.32640 0.155034i
177177 −0.868726 3.16937i −0.0652975 0.238225i
178178 8.78457 5.77770i 0.658431 0.433057i
179179 −3.43489 2.88222i −0.256736 0.215427i 0.505331 0.862926i 0.331371π-0.331371\pi
−0.762066 + 0.647499i 0.775815π0.775815\pi
180180 0.628002 0.766085i 0.0468085 0.0571006i
181181 2.92076 2.45081i 0.217098 0.182167i −0.527752 0.849398i 0.676965π-0.676965\pi
0.744851 + 0.667231i 0.232521π0.232521\pi
182182 1.36911 4.57314i 0.101485 0.338983i
183183 0.276388 + 0.146989i 0.0204312 + 0.0108657i
184184 1.59456 0.800819i 0.117553 0.0590372i
185185 13.1717 13.9612i 0.968403 1.02645i
186186 6.00483 + 10.9855i 0.440296 + 0.805496i
187187 8.69424 + 20.1555i 0.635786 + 1.47392i
188188 0.0207712 + 0.0359768i 0.00151490 + 0.00262388i
189189 9.75202 1.60015i 0.709355 0.116394i
190190 5.75229 9.96325i 0.417315 0.722810i
191191 18.2731 + 2.13582i 1.32220 + 0.154543i 0.747739 0.663993i 0.231139π-0.231139\pi
0.574457 + 0.818535i 0.305213π0.305213\pi
192192 −9.48764 + 7.59061i −0.684711 + 0.547805i
193193 −15.9799 3.78730i −1.15026 0.272616i −0.389107 0.921193i 0.627216π-0.627216\pi
−0.761149 + 0.648577i 0.775365π0.775365\pi
194194 −0.115561 + 1.98410i −0.00829677 + 0.142450i
195195 1.75726 + 4.35048i 0.125840 + 0.311544i
196196 −0.678058 + 0.160703i −0.0484327 + 0.0114788i
197197 −3.25113 18.4381i −0.231633 1.31366i −0.849589 0.527445i 0.823150π-0.823150\pi
0.617956 0.786213i 0.287961π-0.287961\pi
198198 18.0223 1.25707i 1.28079 0.0893361i
199199 0.155470 0.881713i 0.0110210 0.0625029i −0.978801 0.204812i 0.934342π-0.934342\pi
0.989822 + 0.142309i 0.0454527π0.0454527\pi
200200 0.376557 + 6.46524i 0.0266266 + 0.457161i
201201 −1.88000 + 23.0061i −0.132605 + 1.62273i
202202 −4.39603 5.90490i −0.309304 0.415467i
203203 5.43622 + 7.30212i 0.381548 + 0.512508i
204204 1.58859 + 1.09883i 0.111224 + 0.0769338i
205205 0.942729 + 16.1860i 0.0658431 + 1.13048i
206206 0.587899 3.33414i 0.0409609 0.232301i
207207 1.83544 0.816807i 0.127572 0.0567720i
208208 1.28226 + 7.27206i 0.0889088 + 0.504227i
209209 19.0641 4.51829i 1.31869 0.312536i
210210 −4.82904 + 6.17977i −0.333235 + 0.426445i
211211 −0.869893 + 14.9355i −0.0598859 + 1.02820i 0.825814 + 0.563943i 0.190716π0.190716\pi
−0.885700 + 0.464258i 0.846321π0.846321\pi
212212 −0.994728 0.235755i −0.0683182 0.0161917i
213213 2.61268 + 17.1507i 0.179018 + 1.17515i
214214 −6.53424 0.763743i −0.446672 0.0522084i
215215 −6.85392 + 11.8713i −0.467433 + 0.809618i
216216 −11.2034 + 8.13523i −0.762293 + 0.553532i
217217 −4.62784 8.01565i −0.314158 0.544138i
218218 −10.8458 25.1434i −0.734571 1.70293i
219219 10.4805 17.2114i 0.708204 1.16304i
220220 −0.918738 + 0.973805i −0.0619413 + 0.0656539i
221221 −8.17592 + 4.10610i −0.549972 + 0.276206i
222222 26.1244 16.3211i 1.75335 1.09540i
223223 1.77843 5.94037i 0.119093 0.397797i −0.877568 0.479452i 0.840835π-0.840835\pi
0.996661 + 0.0816552i 0.0260206π0.0260206\pi
224224 −1.69116 + 1.41905i −0.112995 + 0.0948142i
225225 0.0835609 + 7.29098i 0.00557072 + 0.486065i
226226 −10.2612 8.61013i −0.682562 0.572737i
227227 −11.9336 + 7.84886i −0.792061 + 0.520947i −0.879884 0.475189i 0.842380π-0.842380\pi
0.0878224 + 0.996136i 0.472009π0.472009\pi
228228 1.21209 1.22606i 0.0802725 0.0811977i
229229 −19.4011 + 2.26766i −1.28206 + 0.149851i −0.729707 0.683760i 0.760343π-0.760343\pi
−0.552351 + 0.833611i 0.686269π0.686269\pi
230230 −0.631489 + 1.46396i −0.0416392 + 0.0965304i
231231 −13.2985 + 1.24029i −0.874978 + 0.0816054i
232232 −11.3975 5.72406i −0.748286 0.375803i
233233 8.91628 3.24526i 0.584125 0.212604i −0.0330187 0.999455i 0.510512π-0.510512\pi
0.617143 + 0.786851i 0.288290π0.288290\pi
234234 0.959828 + 7.46854i 0.0627459 + 0.488234i
235235 0.303777 + 0.110566i 0.0198162 + 0.00721252i
236236 0.268206 + 0.284282i 0.0174587 + 0.0185052i
237237 −4.25385 4.72521i −0.276317 0.306935i
238238 −12.7771 8.40362i −0.828215 0.544726i
239239 −3.15591 10.5415i −0.204139 0.681871i −0.997339 0.0729094i 0.976772π-0.976772\pi
0.793200 0.608961i 0.208414π-0.208414\pi
240240 2.38513 11.8950i 0.153959 0.767816i
241241 −1.30807 + 1.75705i −0.0842605 + 0.113181i −0.842255 0.539080i 0.818772π-0.818772\pi
0.757994 + 0.652261i 0.226180π0.226180\pi
242242 −8.07871 −0.519319
243243 −13.0277 + 8.56029i −0.835728 + 0.549143i
244244 −0.0372298 −0.00238340
245245 −3.23818 + 4.34963i −0.206880 + 0.277888i
246246 −5.11566 + 25.5125i −0.326163 + 1.62662i
247247 2.34205 + 7.82301i 0.149021 + 0.497766i
248248 10.8341 + 7.12570i 0.687966 + 0.452483i
249249 −6.35976 7.06447i −0.403033 0.447693i
250250 −12.1401 12.8677i −0.767806 0.813827i
251251 6.59388 + 2.39998i 0.416202 + 0.151485i 0.541629 0.840618i 0.317808π-0.317808\pi
−0.125427 + 0.992103i 0.540030π0.540030\pi
252252 −0.934635 + 0.712602i −0.0588765 + 0.0448897i
253253 −2.55143 + 0.928643i −0.160407 + 0.0583833i
254254 2.32790 + 1.16912i 0.146066 + 0.0733570i
255255 14.9663 1.39584i 0.937224 0.0874108i
256256 1.93807 4.49296i 0.121130 0.280810i
257257 0.464504 0.0542928i 0.0289750 0.00338669i −0.101593 0.994826i 0.532394π-0.532394\pi
0.130568 + 0.991439i 0.458320π0.458320\pi
258258 −15.4664 + 15.6446i −0.962893 + 0.973992i
259259 −19.0266 + 12.5140i −1.18226 + 0.777582i
260260 −0.427461 0.358683i −0.0265100 0.0222446i
261261 −12.5174 7.03689i −0.774806 0.435573i
262262 −8.15045 + 6.83904i −0.503536 + 0.422517i
263263 −5.47384 + 18.2839i −0.337532 + 1.12743i 0.605810 + 0.795610i 0.292849π0.292849\pi
−0.943341 + 0.331824i 0.892336π0.892336\pi
264264 15.8698 9.91464i 0.976721 0.610204i
265265 −7.10899 + 3.57027i −0.436702 + 0.219320i
266266 −9.36708 + 9.92852i −0.574332 + 0.608757i
267267 6.37703 10.4726i 0.390268 0.640911i
268268 −1.08732 2.52070i −0.0664189 0.153976i
269269 −2.12061 3.67300i −0.129296 0.223947i 0.794108 0.607776i 0.207938π-0.207938\pi
−0.923404 + 0.383830i 0.874605π0.874605\pi
270270 2.99600 12.0029i 0.182331 0.730471i
271271 −3.83162 + 6.63656i −0.232754 + 0.403142i −0.958618 0.284697i 0.908107π-0.908107\pi
0.725863 + 0.687839i 0.241440π0.241440\pi
272272 23.4962 + 2.74631i 1.42467 + 0.166520i
273273 −0.838368 5.50339i −0.0507403 0.333080i
274274 25.2525 + 5.98496i 1.52556 + 0.361564i
275275 0.572988 9.83782i 0.0345525 0.593243i
276276 −0.147114 + 0.188264i −0.00885525 + 0.0113322i
277277 14.4352 3.42121i 0.867329 0.205561i 0.227219 0.973844i 0.427037π-0.427037\pi
0.640110 + 0.768283i 0.278889π0.278889\pi
278278 4.90030 + 27.7910i 0.293901 + 1.66679i
279279 11.8100 + 8.58363i 0.707046 + 0.513888i
280280 −1.41060 + 7.99991i −0.0842995 + 0.478086i
281281 −0.0647163 1.11114i −0.00386065 0.0662848i 0.995828 0.0912552i 0.0290879π-0.0290879\pi
−0.999688 + 0.0249704i 0.992051π0.992051\pi
282282 0.426681 + 0.295136i 0.0254085 + 0.0175751i
283283 −3.94683 5.30152i −0.234615 0.315142i 0.669187 0.743094i 0.266643π-0.266643\pi
−0.903802 + 0.427952i 0.859235π0.859235\pi
284284 −1.23209 1.65498i −0.0731109 0.0982050i
285285 1.09270 13.3716i 0.0647257 0.792067i
286286 −0.591730 10.1596i −0.0349897 0.600751i
287287 3.34043 18.9445i 0.197179 1.11826i
288288 1.52710 3.12963i 0.0899852 0.184415i
289289 2.13761 + 12.1230i 0.125742 + 0.713117i
290290 11.0888 2.62810i 0.651159 0.154328i
291291 0.868039 + 2.14901i 0.0508853 + 0.125977i
292292 −0.139348 + 2.39251i −0.00815470 + 0.140011i
293293 3.02889 + 0.717859i 0.176949 + 0.0419378i 0.318135 0.948045i 0.396943π-0.396943\pi
−0.141186 + 0.989983i 0.545092π0.545092\pi
294294 −6.79540 + 5.43668i −0.396316 + 0.317074i
295295 3.02080 + 0.353081i 0.175878 + 0.0205572i
296296 15.9528 27.6310i 0.927235 1.60602i
297297 18.3695 10.3162i 1.06590 0.598605i
298298 5.47544 + 9.48374i 0.317184 + 0.549379i
299299 −0.448237 1.03913i −0.0259222 0.0600945i
300300 −0.415924 0.760909i −0.0240134 0.0439311i
301301 11.1610 11.8299i 0.643308 0.681867i
302302 3.54483 1.78028i 0.203982 0.102444i
303303 −7.57957 4.03098i −0.435435 0.231574i
304304 6.05570 20.2274i 0.347318 1.16012i
305305 −0.221933 + 0.186224i −0.0127079 + 0.0106632i
306306 23.8029 + 3.91639i 1.36072 + 0.223885i
307307 −5.76257 4.83537i −0.328887 0.275969i 0.463359 0.886171i 0.346644π-0.346644\pi
−0.792246 + 0.610202i 0.791088π0.791088\pi
308308 1.32712 0.872863i 0.0756199 0.0497360i
309309 −1.04369 3.80768i −0.0593732 0.216611i
310310 −11.5082 + 1.34511i −0.653621 + 0.0763974i
311311 −6.09456 + 14.1288i −0.345591 + 0.801169i 0.653433 + 0.756984i 0.273328π0.273328\pi
−0.999023 + 0.0441844i 0.985931π0.985931\pi
312312 4.51004 + 6.36309i 0.255331 + 0.360239i
313313 −3.54777 1.78176i −0.200532 0.100711i 0.345699 0.938345i 0.387642π-0.387642\pi
−0.546231 + 0.837635i 0.683938π0.683938\pi
314314 −7.97521 + 2.90274i −0.450067 + 0.163811i
315315 −2.00707 + 8.92300i −0.113086 + 0.502754i
316316 0.710537 + 0.258614i 0.0399708 + 0.0145482i
317317 −5.88460 6.23731i −0.330512 0.350323i 0.540712 0.841208i 0.318155π-0.318155\pi
−0.871224 + 0.490885i 0.836673π0.836673\pi
318318 −12.4882 + 2.65330i −0.700302 + 0.148790i
319319 16.2146 + 10.6645i 0.907845 + 0.597099i
320320 −3.22508 10.7725i −0.180287 0.602202i
321321 −7.26851 + 2.45483i −0.405689 + 0.137015i
322322 1.12961 1.51733i 0.0629508 0.0845576i
323323 26.1608 1.45563
324324 0.889919 1.62636i 0.0494399 0.0903535i
325325 4.10736 0.227835
326326 −14.2247 + 19.1071i −0.787836 + 1.05825i
327327 −23.9759 21.0918i −1.32587 1.16638i
328328 7.72967 + 25.8189i 0.426800 + 1.42561i
329329 −0.320454 0.210766i −0.0176672 0.0116199i
330330 −5.16807 + 15.9010i −0.284493 + 0.875318i
331331 6.40317 + 6.78697i 0.351950 + 0.373045i 0.879027 0.476772i 0.158193π-0.158193\pi
−0.527077 + 0.849818i 0.676712π0.676712\pi
332332 1.06230 + 0.386644i 0.0583010 + 0.0212198i
333333 19.3942 30.2366i 1.06280 1.65696i
334334 26.7247 9.72699i 1.46231 0.532237i
335335 −19.0903 9.58751i −1.04301 0.523822i
336336 −6.00828 + 13.0800i −0.327779 + 0.713571i
337337 1.74575 4.04710i 0.0950970 0.220460i −0.864027 0.503445i 0.832066π-0.832066\pi
0.959124 + 0.282986i 0.0913249π0.0913249\pi
338338 −14.9648 + 1.74913i −0.813976 + 0.0951401i
339339 −15.1114 3.95641i −0.820737 0.214883i
340340 −1.49356 + 0.982327i −0.0809994 + 0.0532742i
341341 −15.1155 12.6834i −0.818548 0.686844i
342342 7.13172 20.3157i 0.385639 1.09855i
343343 15.1270 12.6931i 0.816782 0.685362i
344344 −6.53512 + 21.8288i −0.352350 + 1.17693i
345345 0.0647248 + 1.85814i 0.00348466 + 0.100039i
346346 31.3726 15.7559i 1.68660 0.847042i
347347 −13.7512 + 14.5754i −0.738201 + 0.782448i −0.982302 0.187302i 0.940026π-0.940026\pi
0.244101 + 0.969750i 0.421507π0.421507\pi
348348 1.70732 + 0.0398880i 0.0915222 + 0.00213822i
349349 −13.3272 30.8958i −0.713387 1.65382i −0.755872 0.654719i 0.772787π-0.772787\pi
0.0424857 0.999097i 0.486472π-0.486472\pi
350350 3.43279 + 5.94576i 0.183490 + 0.317814i
351351 4.73769 + 7.39344i 0.252879 + 0.394633i
352352 −2.35320 + 4.07587i −0.125426 + 0.217244i
353353 −8.01065 0.936311i −0.426364 0.0498348i −0.0997947 0.995008i 0.531819π-0.531819\pi
−0.326569 + 0.945173i 0.605893π0.605893\pi
354354 4.54637 + 1.77606i 0.241637 + 0.0943966i
355355 −15.6229 3.70270i −0.829178 0.196519i
356356 −0.0847886 + 1.45576i −0.00449379 + 0.0771554i
357357 −17.6603 2.48357i −0.934682 0.131444i
358358 6.48028 1.53585i 0.342493 0.0811724i
359359 −2.83469 16.0764i −0.149609 0.848477i −0.963550 0.267529i 0.913793π-0.913793\pi
0.813940 0.580948i 0.197318π-0.197318\pi
360360 −3.09773 12.4336i −0.163265 0.655307i
361361 0.755367 4.28390i 0.0397562 0.225468i
362362 0.329272 + 5.65339i 0.0173062 + 0.297135i
363363 −8.51545 + 4.03038i −0.446945 + 0.211540i
364364 0.395357 + 0.531056i 0.0207223 + 0.0278349i
365365 11.1367 + 14.9592i 0.582920 + 0.782998i
366366 −0.420254 + 0.198907i −0.0219670 + 0.0103971i
367367 −0.765272 13.1392i −0.0399469 0.685861i −0.957533 0.288324i 0.906902π-0.906902\pi
0.917586 0.397537i 0.130135π-0.130135\pi
368368 −0.508116 + 2.88167i −0.0264874 + 0.150217i
369369 7.33570 + 29.4439i 0.381881 + 1.53279i
370370 4.95036 + 28.0749i 0.257357 + 1.45954i
371371 9.18414 2.17668i 0.476817 0.113008i
372372 −1.71942 0.241803i −0.0891479 0.0125369i
373373 −0.0126555 + 0.217287i −0.000655279 + 0.0112507i −0.998620 0.0525186i 0.983275π-0.983275\pi
0.997965 + 0.0637693i 0.0203122π0.0203122\pi
374374 −31.7237 7.51866i −1.64039 0.388780i
375375 −19.2160 7.50681i −0.992307 0.387650i
376376 0.533733 + 0.0623844i 0.0275252 + 0.00321723i
377377 −4.04451 + 7.00529i −0.208303 + 0.360791i
378378 −6.74305 + 13.0374i −0.346825 + 0.670571i
379379 12.0931 + 20.9458i 0.621180 + 1.07592i 0.989266 + 0.146124i 0.0466797π0.0466797\pi
−0.368086 + 0.929792i 0.619987π0.619987\pi
380380 0.631974 + 1.46508i 0.0324196 + 0.0751571i
381381 3.03701 + 0.0709534i 0.155591 + 0.00363505i
382382 −18.7516 + 19.8755i −0.959414 + 1.01692i
383383 −7.55923 + 3.79639i −0.386258 + 0.193986i −0.631322 0.775521i 0.717487π-0.717487\pi
0.245064 + 0.969507i 0.421191π0.421191\pi
384384 −0.768215 22.0542i −0.0392028 1.12545i
385385 3.54513 11.8416i 0.180677 0.603502i
386386 18.6851 15.6787i 0.951048 0.798024i
387387 −8.49753 + 24.2064i −0.431954 + 1.23048i
388388 −0.211154 0.177179i −0.0107197 0.00899491i
389389 20.9831 13.8008i 1.06389 0.699729i 0.108204 0.994129i 0.465490π-0.465490\pi
0.955682 + 0.294399i 0.0951196π0.0951196\pi
390390 −6.74156 1.76506i −0.341372 0.0893770i
391391 −3.60095 + 0.420891i −0.182108 + 0.0212854i
392392 −3.57022 + 8.27670i −0.180323 + 0.418036i
393393 −5.17914 + 11.2749i −0.261253 + 0.568745i
394394 24.8499 + 12.4801i 1.25192 + 0.628738i
395395 5.52922 2.01247i 0.278205 0.101258i
396396 −1.35276 + 2.10903i −0.0679790 + 0.105983i
397397 23.8173 + 8.66880i 1.19536 + 0.435074i 0.861602 0.507585i 0.169462π-0.169462\pi
0.333756 + 0.942660i 0.391684π0.391684\pi
398398 0.912545 + 0.967242i 0.0457418 + 0.0484834i
399399 −4.92023 + 15.1384i −0.246319 + 0.757868i
400400 −8.87299 5.83586i −0.443650 0.291793i
401401 6.80813 + 22.7407i 0.339982 + 1.13562i 0.941572 + 0.336813i 0.109349π0.109349\pi
−0.601590 + 0.798805i 0.705466π0.705466\pi
402402 −25.7411 22.6447i −1.28385 1.12941i
403403 4.91118 6.59686i 0.244643 0.328613i
404404 1.02098 0.0507957
405405 −2.83014 14.1464i −0.140631 0.702941i
406406 −13.5210 −0.671037
407407 −28.9915 + 38.9423i −1.43705 + 1.93030i
408408 23.6723 7.99496i 1.17195 0.395810i
409409 −2.69238 8.99318i −0.133130 0.444684i 0.865266 0.501314i 0.167150π-0.167150\pi
−0.998395 + 0.0566295i 0.981965π0.981965\pi
410410 −20.1195 13.2328i −0.993633 0.653523i
411411 29.6035 6.28971i 1.46023 0.310248i
412412 0.322222 + 0.341536i 0.0158748 + 0.0168263i
413413 −3.39087 1.23418i −0.166854 0.0607298i
414414 −0.654808 + 2.91113i −0.0321820 + 0.143074i
415415 8.26652 3.00877i 0.405787 0.147695i
416416 −1.75298 0.880379i −0.0859469 0.0431642i
417417 19.0298 + 26.8487i 0.931895 + 1.31478i
418418 −11.5257 + 26.7197i −0.563743 + 1.30690i
419419 11.6606 1.36293i 0.569659 0.0665836i 0.173613 0.984814i 0.444456π-0.444456\pi
0.396047 + 0.918230i 0.370382π0.370382\pi
420420 −0.287538 1.04902i −0.0140304 0.0511871i
421421 −5.65294 + 3.71800i −0.275507 + 0.181204i −0.679742 0.733451i 0.737908π-0.737908\pi
0.404235 + 0.914655i 0.367538π0.367538\pi
422422 −17.0220 14.2831i −0.828618 0.695293i
423423 0.596987 + 0.0982244i 0.0290265 + 0.00477584i
424424 −10.1299 + 8.49998i −0.491950 + 0.412795i
425425 3.77386 12.6056i 0.183059 0.611459i
426426 −22.7500 12.0989i −1.10224 0.586195i
427427 0.307174 0.154268i 0.0148652 0.00746557i
428428 0.626131 0.663660i 0.0302652 0.0320792i
429429 −5.69224 10.4136i −0.274824 0.502775i
430430 −8.06405 18.6946i −0.388883 0.901532i
431431 3.90563 + 6.76475i 0.188128 + 0.325846i 0.944626 0.328149i 0.106425π-0.106425\pi
−0.756498 + 0.653996i 0.773092π0.773092\pi
432432 0.270143 22.7032i 0.0129972 1.09231i
433433 −2.20878 + 3.82573i −0.106147 + 0.183853i −0.914206 0.405249i 0.867185π-0.867185\pi
0.808059 + 0.589102i 0.200518π0.200518\pi
434434 13.6541 + 1.59594i 0.655419 + 0.0766074i
435435 10.3772 8.30228i 0.497547 0.398064i
436436 3.69538 + 0.875820i 0.176976 + 0.0419442i
437437 −0.188153 + 3.23046i −0.00900056 + 0.154534i
438438 11.2094 + 27.7514i 0.535608 + 1.32601i
439439 −14.6281 + 3.46693i −0.698162 + 0.165468i −0.564346 0.825539i 0.690871π-0.690871\pi
−0.133817 + 0.991006i 0.542723π0.542723\pi
440440 3.00721 + 17.0547i 0.143363 + 0.813052i
441441 −4.45046 + 9.12074i −0.211927 + 0.434321i
442442 2.35966 13.3823i 0.112238 0.636531i
443443 −0.660317 11.3372i −0.0313726 0.538647i −0.976979 0.213334i 0.931568π-0.931568\pi
0.945607 0.325312i 0.105469π-0.105469\pi
444444 −0.347951 + 4.25797i −0.0165130 + 0.202074i
445445 6.77632 + 9.10217i 0.321228 + 0.431484i
446446 5.49977 + 7.38748i 0.260422 + 0.349807i
447447 10.5028 + 7.26480i 0.496765 + 0.343613i
448448 0.775753 + 13.3192i 0.0366509 + 0.629272i
449449 −1.16004 + 6.57891i −0.0547457 + 0.310478i −0.999868 0.0162381i 0.994831π-0.994831\pi
0.945122 + 0.326716i 0.105942π0.105942\pi
450450 −8.76029 6.36707i −0.412964 0.300147i
451451 −7.12134 40.3871i −0.335331 1.90176i
452452 1.80768 0.428428i 0.0850260 0.0201515i
453453 2.84830 3.64500i 0.133825 0.171257i
454454 1.23352 21.1786i 0.0578917 0.993963i
455455 5.01314 + 1.18814i 0.235020 + 0.0557007i
456456 −3.35856 22.0470i −0.157279 1.03244i
457457 −11.9315 1.39459i −0.558133 0.0652364i −0.167650 0.985847i 0.553618π-0.553618\pi
−0.390483 + 0.920610i 0.627692π0.627692\pi
458458 14.5059 25.1249i 0.677815 1.17401i
459459 27.0436 7.74693i 1.26229 0.361596i
460460 −0.110560 0.191496i −0.00515490 0.00892855i
461461 2.77206 + 6.42636i 0.129108 + 0.299305i 0.970493 0.241131i 0.0775184π-0.0775184\pi
−0.841385 + 0.540436i 0.818259π0.818259\pi
462462 10.3173 16.9434i 0.480003 0.788277i
463463 −19.2377 + 20.3908i −0.894052 + 0.947639i −0.998902 0.0468486i 0.985082π-0.985082\pi
0.104850 + 0.994488i 0.466564π0.466564\pi
464464 18.6905 9.38674i 0.867686 0.435768i
465465 −11.4593 + 7.15915i −0.531411 + 0.331997i
466466 −4.04188 + 13.5008i −0.187237 + 0.625414i
467467 −10.9662 + 9.20178i −0.507458 + 0.425807i −0.860233 0.509900i 0.829682π-0.829682\pi
0.352776 + 0.935708i 0.385238π0.385238\pi
468468 −0.910343 0.511767i −0.0420806 0.0236565i
469469 19.4162 + 16.2921i 0.896557 + 0.752300i
470470 −0.401154 + 0.263843i −0.0185039 + 0.0121702i
471471 −6.95820 + 7.03841i −0.320617 + 0.324313i
472472 5.02139 0.586916i 0.231128 0.0270150i
473473 13.7331 31.8368i 0.631447 1.46386i
474474 9.40231 0.876913i 0.431862 0.0402779i
475475 −10.4953 5.27095i −0.481558 0.241848i
476476 1.99307 0.725420i 0.0913524 0.0332496i
477477 −11.8396 + 9.02695i −0.542097 + 0.413316i
478478 15.3578 + 5.58977i 0.702448 + 0.255670i
479479 15.4383 + 16.3636i 0.705392 + 0.747672i 0.976650 0.214835i 0.0689212π-0.0689212\pi
−0.271258 + 0.962507i 0.587440π0.587440\pi
480480 2.15627 + 2.39520i 0.0984198 + 0.109325i
481481 −16.9063 11.1195i −0.770862 0.507004i
482482 −0.933101 3.11677i −0.0425016 0.141965i
483483 0.433698 2.16291i 0.0197339 0.0984158i
484484 0.669080 0.898730i 0.0304127 0.0408514i
485485 −2.14498 −0.0973984
486486 1.35634 23.1131i 0.0615249 1.04843i
487487 −41.7203 −1.89053 −0.945264 0.326307i 0.894196π-0.894196\pi
−0.945264 + 0.326307i 0.894196π0.894196\pi
488488 −0.287580 + 0.386288i −0.0130182 + 0.0174864i
489489 −5.46138 + 27.2367i −0.246972 + 1.23168i
490490 −2.30992 7.71567i −0.104352 0.348559i
491491 9.24805 + 6.08254i 0.417359 + 0.274501i 0.740772 0.671757i 0.234460π-0.234460\pi
−0.323413 + 0.946258i 0.604830π0.604830\pi
492492 −2.41450 2.68205i −0.108854 0.120916i
493493 17.7832 + 18.8491i 0.800917 + 0.848922i
494494 −11.3973 4.14826i −0.512787 0.186639i
495495 2.48536 + 19.3389i 0.111708 + 0.869217i
496496 −19.9825 + 7.27302i −0.897239 + 0.326568i
497497 17.0233 + 8.54944i 0.763601 + 0.383495i
498498 14.0570 1.31104i 0.629910 0.0587490i
499499 3.09519 7.17545i 0.138560 0.321217i −0.834781 0.550582i 0.814406π-0.814406\pi
0.973340 + 0.229365i 0.0736650π0.0736650\pi
500500 2.43694 0.284837i 0.108983 0.0127383i
501501 23.3167 23.5855i 1.04171 1.05372i
502502 −8.70757 + 5.72706i −0.388638 + 0.255611i
503503 18.1547 + 15.2336i 0.809478 + 0.679233i 0.950483 0.310776i 0.100589π-0.100589\pi
−0.141005 + 0.990009i 0.545033π0.545033\pi
504504 0.174228 + 15.2020i 0.00776073 + 0.677152i
505505 6.08624 5.10696i 0.270834 0.227257i
506506 1.15660 3.86331i 0.0514171 0.171745i
507507 −14.9011 + 9.30945i −0.661783 + 0.413447i
508508 −0.322858 + 0.162145i −0.0143245 + 0.00719403i
509509 −8.55338 + 9.06605i −0.379122 + 0.401846i −0.888634 0.458618i 0.848345π-0.848345\pi
0.509512 + 0.860464i 0.329826π0.329826\pi
510510 −11.6111 + 19.0682i −0.514150 + 0.844355i
511511 −8.76405 20.3174i −0.387699 0.898787i
512512 −9.10692 15.7736i −0.402473 0.697103i
513513 −2.61802 24.9719i −0.115588 1.10254i
514514 −0.347303 + 0.601546i −0.0153189 + 0.0265331i
515515 3.62919 + 0.424191i 0.159921 + 0.0186921i
516516 −0.459488 3.01627i −0.0202278 0.132784i
517517 −0.795643 0.188571i −0.0349923 0.00829333i
518518 1.96668 33.7666i 0.0864111 1.48362i
519519 25.2081 32.2591i 1.10651 1.41602i
520520 −7.02351 + 1.66460i −0.308001 + 0.0729977i
521521 3.66734 + 20.7985i 0.160669 + 0.911200i 0.953418 + 0.301652i 0.0975380π0.0975380\pi
−0.792749 + 0.609548i 0.791351π0.791351\pi
522522 19.4856 8.67144i 0.852860 0.379539i
523523 7.23247 41.0174i 0.316254 1.79356i −0.248848 0.968543i 0.580052π-0.580052\pi
0.565102 0.825021i 0.308837π-0.308837\pi
524524 −0.0857995 1.47312i −0.00374817 0.0643536i
525525 6.58464 + 4.55461i 0.287377 + 0.198779i
526526 −16.9278 22.7379i −0.738086 0.991421i
527527 −15.7335 21.1337i −0.685360 0.920598i
528528 −2.49924 + 30.5839i −0.108765 + 1.33099i
529529 1.31126 + 22.5134i 0.0570111 + 0.978843i
530530 2.05173 11.6360i 0.0891217 0.505434i
531531 5.67820 0.396059i 0.246413 0.0171875i
532532 −0.328733 1.86434i −0.0142524 0.0808293i
533533 16.6323 3.94193i 0.720426 0.170744i
534534 6.82059 + 16.8858i 0.295156 + 0.730721i
535535 0.412835 7.08810i 0.0178484 0.306445i
536536 −34.5531 8.18925i −1.49247 0.353722i
537537 6.06438 4.85183i 0.261697 0.209372i
538538 6.25670 + 0.731303i 0.269746 + 0.0315287i
539539 6.85799 11.8784i 0.295395 0.511638i
540540 1.08715 + 1.32737i 0.0467835 + 0.0571211i
541541 −4.87647 8.44629i −0.209656 0.363134i 0.741950 0.670455i 0.233901π-0.233901\pi
−0.951606 + 0.307320i 0.900568π0.900568\pi
542542 −4.50813 10.4510i −0.193641 0.448910i
543543 3.16749 + 5.79474i 0.135930 + 0.248676i
544544 −4.31254 + 4.57103i −0.184899 + 0.195981i
545545 26.4096 13.2634i 1.13126 0.568142i
546546 7.30010 + 3.88235i 0.312415 + 0.166149i
547547 −0.198805 + 0.664056i −0.00850030 + 0.0283930i −0.962134 0.272575i 0.912125π-0.912125\pi
0.953634 + 0.300968i 0.0973098π0.0973098\pi
548548 −2.75722 + 2.31358i −0.117783 + 0.0988314i
549549 −0.343740 + 0.419321i −0.0146705 + 0.0178962i
550550 11.2122 + 9.40814i 0.478089 + 0.401164i
551551 19.3245 12.7100i 0.823253 0.541462i
552552 0.817000 + 2.98066i 0.0347738 + 0.126865i
553553 −6.93407 + 0.810476i −0.294867 + 0.0344650i
554554 −8.72721 + 20.2319i −0.370783 + 0.859573i
555555 19.2242 + 27.1229i 0.816024 + 1.15130i
556556 −3.49750 1.75651i −0.148327 0.0744926i
557557 −28.7125 + 10.4505i −1.21659 + 0.442801i −0.868984 0.494841i 0.835226π-0.835226\pi
−0.347602 + 0.937642i 0.613004π0.613004\pi
558558 −20.7009 + 6.45684i −0.876339 + 0.273340i
559559 13.5800 + 4.94270i 0.574371 + 0.209054i
560560 −9.14158 9.68950i −0.386302 0.409456i
561561 −37.1897 + 7.90150i −1.57015 + 0.333602i
562562 1.38116 + 0.908405i 0.0582608 + 0.0383187i
563563 2.79565 + 9.33813i 0.117823 + 0.393555i 0.996473 0.0839099i 0.0267408π-0.0267408\pi
−0.878651 + 0.477465i 0.841556π0.841556\pi
564564 −0.0681706 + 0.0230236i −0.00287050 + 0.000969470i
565565 8.63287 11.5960i 0.363188 0.487846i
566566 9.81660 0.412622
567567 −0.603363 + 17.1062i −0.0253389 + 0.718394i
568568 −26.6889 −1.11984
569569 −11.7532 + 15.7873i −0.492720 + 0.661838i −0.977041 0.213053i 0.931659π-0.931659\pi
0.484321 + 0.874891i 0.339067π0.339067\pi
570570 14.9613 + 13.1615i 0.626658 + 0.551277i
571571 9.46443 + 31.6134i 0.396074 + 1.32298i 0.890984 + 0.454035i 0.150016π0.150016\pi
−0.494910 + 0.868944i 0.664799π0.664799\pi
572572 1.17923 + 0.775592i 0.0493061 + 0.0324292i
573573 −9.84961 + 30.3049i −0.411473 + 1.26601i
574574 19.6070 + 20.7822i 0.818381 + 0.867433i
575575 1.52945 + 0.556674i 0.0637824 + 0.0232149i
576576 −9.65995 18.6972i −0.402498 0.779048i
577577 −19.1279 + 6.96197i −0.796303 + 0.289831i −0.707954 0.706259i 0.750381π-0.750381\pi
−0.0883494 + 0.996090i 0.528159π0.528159\pi
578578 −16.3388 8.20563i −0.679603 0.341309i
579579 11.8733 25.8481i 0.493438 1.07421i
580580 −0.626011 + 1.45126i −0.0259937 + 0.0602601i
581581 −10.3668 + 1.21171i −0.430089 + 0.0502702i
582582 −3.33014 0.871887i −0.138039 0.0361409i
583583 16.8114 11.0571i 0.696259 0.457937i
584584 23.7477 + 19.9267i 0.982686 + 0.824571i
585585 −7.98658 + 1.50282i −0.330204 + 0.0621339i
586586 −3.54165 + 2.97180i −0.146304 + 0.122764i
587587 10.0799 33.6693i 0.416043 1.38968i −0.451479 0.892281i 0.649104π-0.649104\pi
0.867522 0.497398i 0.165711π-0.165711\pi
588588 −0.0420168 1.20623i −0.00173274 0.0497442i
589589 −21.0150 + 10.5541i −0.865907 + 0.434875i
590590 −3.09990 + 3.28570i −0.127621 + 0.135270i
591591 32.4195 + 0.757413i 1.33356 + 0.0311558i
592592 20.7233 + 48.0420i 0.851722 + 1.97451i
593593 −4.46816 7.73909i −0.183485 0.317806i 0.759580 0.650414i 0.225405π-0.225405\pi
−0.943065 + 0.332608i 0.892071π0.892071\pi
594594 −4.00224 + 31.0344i −0.164214 + 1.27336i
595595 8.25249 14.2937i 0.338319 0.585986i
596596 −1.50851 0.176320i −0.0617911 0.00722234i
597597 1.44442 + 0.564272i 0.0591163 + 0.0230941i
598598 1.63554 + 0.387629i 0.0668821 + 0.0158513i
599599 2.30662 39.6032i 0.0942460 1.61814i −0.537705 0.843133i 0.680709π-0.680709\pi
0.631951 0.775008i 0.282254π-0.282254\pi
600600 −11.1078 1.56209i −0.453474 0.0637721i
601601 23.0255 5.45715i 0.939231 0.222602i 0.267636 0.963520i 0.413758π-0.413758\pi
0.671595 + 0.740918i 0.265609π0.265609\pi
602602 4.19466 + 23.7891i 0.170962 + 0.969572i
603603 −38.4299 11.0269i −1.56499 0.449049i
604604 −0.0955328 + 0.541794i −0.00388718 + 0.0220453i
605605 −0.506964 8.70423i −0.0206110 0.353877i
606606 11.5249 5.45478i 0.468169 0.221585i
607607 10.6054 + 14.2455i 0.430460 + 0.578208i 0.963441 0.267919i 0.0863359π-0.0863359\pi
−0.532982 + 0.846127i 0.678928π0.678928\pi
608608 3.34951 + 4.49917i 0.135841 + 0.182466i
609609 −14.2520 + 6.74549i −0.577519 + 0.273341i
610610 −0.0250197 0.429571i −0.00101302 0.0173928i
611611 0.0591812 0.335633i 0.00239422 0.0135783i
612612 −2.40705 + 2.32364i −0.0972991 + 0.0939278i
613613 −0.410662 2.32898i −0.0165865 0.0940666i 0.975391 0.220483i 0.0707635π-0.0707635\pi
−0.991977 + 0.126417i 0.959652π0.959652\pi
614614 10.8717 2.57664i 0.438745 0.103985i
615615 −27.8089 3.91077i −1.12136 0.157698i
616616 1.19470 20.5123i 0.0481360 0.826464i
617617 32.8897 + 7.79500i 1.32409 + 0.313815i 0.831053 0.556194i 0.187739π-0.187739\pi
0.493036 + 0.870009i 0.335887π0.335887\pi
618618 5.46200 + 2.13376i 0.219714 + 0.0858323i
619619 −47.1703 5.51342i −1.89594 0.221603i −0.913319 0.407246i 0.866489π-0.866489\pi
−0.982617 + 0.185643i 0.940563π0.940563\pi
620620 0.803470 1.39165i 0.0322681 0.0558901i
621621 0.762125 + 3.39518i 0.0305830 + 0.136244i
622622 −11.4270 19.7921i −0.458180 0.793591i
623623 −5.33265 12.3625i −0.213648 0.495292i
624624 −12.7864 0.298727i −0.511866 0.0119587i
625625 4.76272 5.04819i 0.190509 0.201928i
626626 5.26935 2.64637i 0.210606 0.105770i
627627 1.18134 + 33.9142i 0.0471780 + 1.35440i
628628 0.337588 1.12762i 0.0134712 0.0449970i
629629 −49.6594 + 41.6692i −1.98005 + 1.66146i
630630 −8.85036 10.3053i −0.352607 0.410572i
631631 −14.6874 12.3242i −0.584695 0.490617i 0.301790 0.953374i 0.402416π-0.402416\pi
−0.886485 + 0.462757i 0.846860π0.846860\pi
632632 8.17183 5.37470i 0.325058 0.213794i
633633 −25.0679 6.56320i −0.996360 0.260864i
634634 12.6501 1.47859i 0.502401 0.0587223i
635635 −1.11356 + 2.58151i −0.0441901 + 0.102444i
636636 0.739101 1.60901i 0.0293072 0.0638016i
637637 5.10875 + 2.56571i 0.202416 + 0.101657i
638638 −27.0866 + 9.85872i −1.07237 + 0.390311i
639639 −30.0159 1.40328i −1.18741 0.0555129i
640640 19.1913 + 6.98507i 0.758603 + 0.276109i
641641 −1.44451 1.53109i −0.0570547 0.0604744i 0.698218 0.715886i 0.253977π-0.253977\pi
−0.755272 + 0.655411i 0.772495π0.772495\pi
642642 3.52210 10.8367i 0.139006 0.427690i
643643 36.6084 + 24.0777i 1.44369 + 0.949533i 0.998537 + 0.0540808i 0.0172228π0.0172228\pi
0.445158 + 0.895452i 0.353148π0.353148\pi
644644 0.0752436 + 0.251331i 0.00296501 + 0.00990384i
645645 −17.8265 15.6821i −0.701918 0.617483i
646646 −23.2029 + 31.1669i −0.912907 + 1.22625i
647647 2.17952 0.0856859 0.0428430 0.999082i 0.486358π-0.486358\pi
0.0428430 + 0.999082i 0.486358π0.486358\pi
648648 −10.0006 21.7964i −0.392861 0.856242i
649649 −7.69281 −0.301969
650650 −3.64296 + 4.89334i −0.142889 + 0.191933i
651651 15.1885 5.12968i 0.595282 0.201048i
652652 −0.947512 3.16491i −0.0371075 0.123948i
653653 15.6357 + 10.2838i 0.611873 + 0.402435i 0.817279 0.576242i 0.195481π-0.195481\pi
−0.205407 + 0.978677i 0.565852π0.565852\pi
654654 46.3930 9.85690i 1.81411 0.385435i
655655 −7.88003 8.35235i −0.307898 0.326353i
656656 −41.5311 15.1161i −1.62152 0.590183i
657657 25.6603 + 23.6593i 1.00110 + 0.923038i
658658 0.535320 0.194841i 0.0208689 0.00759568i
659659 −12.7829 6.41983i −0.497953 0.250081i 0.182052 0.983289i 0.441726π-0.441726\pi
−0.680005 + 0.733208i 0.738022π0.738022\pi
660660 −1.34091 1.89185i −0.0521948 0.0736401i
661661 9.89935 22.9493i 0.385040 0.892623i −0.609930 0.792455i 0.708803π-0.708803\pi
0.994971 0.100168i 0.0319381π-0.0319381\pi
662662 −13.7649 + 1.60889i −0.534989 + 0.0625312i
663663 −4.18906 15.2830i −0.162690 0.593541i
664664 12.2174 8.03550i 0.474126 0.311838i
665665 −11.2851 9.46931i −0.437617 0.367204i
666666 18.8213 + 49.9234i 0.729311 + 1.93449i
667667 −2.45548 + 2.06039i −0.0950764 + 0.0797786i
668668 −1.13125 + 3.77862i −0.0437692 + 0.146199i
669669 9.48262 + 5.04306i 0.366619 + 0.194976i
670670 28.3540 14.2399i 1.09541 0.550136i
671671 0.502877 0.533018i 0.0194133 0.0205769i
672672 −1.83401 3.35523i −0.0707486 0.129431i
673673 −11.7597 27.2621i −0.453304 1.05088i −0.979669 0.200619i 0.935705π-0.935705\pi
0.526365 0.850259i 0.323554π-0.323554\pi
674674 3.27319 + 5.66933i 0.126078 + 0.218374i
675675 −12.4103 2.34086i −0.477674 0.0900997i
676676 1.04480 1.80964i 0.0401846 0.0696017i
677677 −38.5222 4.50260i −1.48053 0.173049i −0.662862 0.748741i 0.730659π-0.730659\pi
−0.817666 + 0.575692i 0.804733π0.804733\pi
678678 18.1163 14.4940i 0.695753 0.556639i
679679 2.47635 + 0.586906i 0.0950336 + 0.0225234i
680680 −1.34453 + 23.0847i −0.0515604 + 0.885258i
681681 −9.26560 22.9389i −0.355058 0.879022i
682682 28.5169 6.75863i 1.09197 0.258801i
683683 −2.81006 15.9367i −0.107524 0.609799i −0.990182 0.139784i 0.955359π-0.955359\pi
0.882658 0.470016i 0.155752π-0.155752\pi
684684 1.66940 + 2.47593i 0.0638312 + 0.0946695i
685685 −4.86369 + 27.5833i −0.185832 + 1.05391i
686686 1.70535 + 29.2797i 0.0651104 + 1.11790i
687687 2.75551 33.7200i 0.105129 1.28650i
688688 −22.3136 29.9724i −0.850698 1.14269i
689689 5.00822 + 6.72720i 0.190798 + 0.256286i
690690 −2.27112 1.57094i −0.0864601 0.0598046i
691691 1.02377 + 17.5774i 0.0389460 + 0.668677i 0.960131 + 0.279551i 0.0901857π0.0901857\pi
−0.921185 + 0.389125i 0.872777π0.872777\pi
692692 −0.845488 + 4.79500i −0.0321406 + 0.182279i
693693 2.42216 23.0065i 0.0920101 0.873945i
694694 −5.16814 29.3100i −0.196180 1.11259i
695695 −29.6353 + 7.02369i −1.12413 + 0.266424i
696696 13.6020 17.4067i 0.515584 0.659798i
697697 3.18397 54.6667i 0.120602 2.07065i
698698 48.6284 + 11.5251i 1.84061 + 0.436233i
699699 2.47503 + 16.2471i 0.0936143 + 0.614523i
700700 −0.945751 0.110542i −0.0357460 0.00417811i
701701 −9.33660 + 16.1715i −0.352639 + 0.610788i −0.986711 0.162486i 0.948049π-0.948049\pi
0.634072 + 0.773274i 0.281382π0.281382\pi
702702 −13.0103 0.913202i −0.491041 0.0344666i
703703 28.9303 + 50.1087i 1.09113 + 1.88989i
704704 11.2656 + 26.1166i 0.424588 + 0.984307i
705705 −0.291212 + 0.478238i −0.0109677 + 0.0180115i
706706 8.22041 8.71312i 0.309379 0.327923i
707707 −8.42384 + 4.23061i −0.316811 + 0.159109i
708708 −0.574112 + 0.358675i −0.0215764 + 0.0134798i
709709 −9.44848 + 31.5601i −0.354845 + 1.18527i 0.575260 + 0.817971i 0.304901π0.304901\pi
−0.930105 + 0.367294i 0.880284π0.880284\pi
710710 18.2677 15.3285i 0.685576 0.575267i
711711 9.47312 5.61503i 0.355270 0.210580i
712712 14.4497 + 12.1247i 0.541526 + 0.454394i
713713 2.72284 1.79084i 0.101971 0.0670675i
714714 18.6223 18.8370i 0.696924 0.704957i
715715 10.9091 1.27509i 0.407978 0.0476858i
716716 −0.365839 + 0.848110i −0.0136720 + 0.0316953i
717717 18.9767 1.76987i 0.708697 0.0660971i
718718 21.6669 + 10.8815i 0.808602 + 0.406095i
719719 43.1137 15.6921i 1.60787 0.585216i 0.626852 0.779139i 0.284343π-0.284343\pi
0.981017 + 0.193922i 0.0621209π0.0621209\pi
720720 19.3884 + 8.10107i 0.722562 + 0.301909i
721721 −4.07379 1.48274i −0.151716 0.0552200i
722722 4.43370 + 4.69945i 0.165005 + 0.174895i
723723 −2.53847 2.81975i −0.0944067 0.104868i
724724 −0.656191 0.431584i −0.0243871 0.0160397i
725725 −3.33659 11.1450i −0.123918 0.413915i
726726 2.75101 13.7196i 0.102099 0.509184i
727727 9.64105 12.9502i 0.357567 0.480295i −0.586547 0.809915i 0.699513π-0.699513\pi
0.944114 + 0.329620i 0.106921π0.106921\pi
728728 8.56403 0.317404
729729 −10.1012 25.0393i −0.374119 0.927381i
730730 −27.6992 −1.02519
731731 27.6465 37.1358i 1.02254 1.37352i
732732 0.0126777 0.0632254i 0.000468582 0.00233688i
733733 7.38479 + 24.6669i 0.272763 + 0.911093i 0.979128 + 0.203245i 0.0651488π0.0651488\pi
−0.706364 + 0.707848i 0.749666π0.749666\pi
734734 16.3323 + 10.7419i 0.602835 + 0.396491i
735735 −6.28406 6.98039i −0.231791 0.257475i
736736 −0.533435 0.565408i −0.0196627 0.0208412i
737737 50.7756 + 18.4808i 1.87034 + 0.680750i
738738 −41.5845 17.3753i −1.53075 0.639594i
739739 −16.9934 + 6.18508i −0.625111 + 0.227522i −0.635102 0.772428i 0.719042π-0.719042\pi
0.00999089 + 0.999950i 0.496820π0.496820\pi
740740 −3.53323 1.77445i −0.129884 0.0652302i
741741 −14.0829 + 1.31345i −0.517349 + 0.0482509i
742742 −5.55252 + 12.8722i −0.203839 + 0.472553i
743743 44.0370 5.14719i 1.61556 0.188832i 0.740229 0.672355i 0.234717π-0.234717\pi
0.875332 + 0.483523i 0.160643π0.160643\pi
744744 −15.7905 + 15.9725i −0.578907 + 0.585580i
745745 −9.87445 + 6.49453i −0.361772 + 0.237941i
746746 −0.247642 0.207797i −0.00906683 0.00760798i
747747 14.1629 8.39481i 0.518193 0.307150i
748748 3.46379 2.90646i 0.126649 0.106271i
749749 −2.41605 + 8.07017i −0.0882805 + 0.294878i
750750 25.9866 16.2351i 0.948896 0.592821i
751751 2.23887 1.12440i 0.0816977 0.0410301i −0.407481 0.913214i 0.633593π-0.633593\pi
0.489179 + 0.872183i 0.337297π0.337297\pi
752752 −0.604725 + 0.640971i −0.0220520 + 0.0233738i
753753 −6.32113 + 10.3808i −0.230355 + 0.378297i
754754 −4.75861 11.0317i −0.173298 0.401751i
755755 2.14057 + 3.70758i 0.0779034 + 0.134933i
756756 −0.891907 1.82990i −0.0324384 0.0665529i
757757 21.8769 37.8919i 0.795129 1.37720i −0.127629 0.991822i 0.540737π-0.540737\pi
0.922757 0.385381i 0.125930π-0.125930\pi
758758 −35.6798 4.17037i −1.29595 0.151475i
759759 −0.708240 4.64918i −0.0257075 0.168754i
760760 20.0830 + 4.75975i 0.728486 + 0.172654i
761761 −2.68708 + 46.1354i −0.0974065 + 1.67241i 0.496626 + 0.867964i 0.334572π0.334572\pi
−0.594033 + 0.804441i 0.702465π0.702465\pi
762762 −2.77816 + 3.55524i −0.100642 + 0.128793i
763763 −34.1187 + 8.08628i −1.23518 + 0.292743i
764764 −0.658078 3.73214i −0.0238084 0.135024i
765765 −2.72592 + 25.8917i −0.0985557 + 0.936117i
766766 2.18168 12.3729i 0.0788272 0.447051i
767767 −0.186434 3.20094i −0.00673173 0.115579i
768768 6.97019 + 4.82129i 0.251515 + 0.173973i
769769 17.4122 + 23.3886i 0.627899 + 0.843414i 0.996272 0.0862635i 0.0274927π-0.0274927\pi
−0.368374 + 0.929678i 0.620085π0.620085\pi
770770 10.9633 + 14.7262i 0.395089 + 0.530696i
771771 −0.0659731 + 0.807331i −0.00237596 + 0.0290753i
772772 0.196698 + 3.37717i 0.00707931 + 0.121547i
773773 −6.90323 + 39.1502i −0.248292 + 1.40813i 0.564429 + 0.825481i 0.309096π0.309096\pi
−0.812721 + 0.582653i 0.802015π0.802015\pi
774774 −21.3017 31.5931i −0.765676 1.13559i
775775 2.05395 + 11.6485i 0.0737801 + 0.418427i
776776 −3.46942 + 0.822267i −0.124545 + 0.0295177i
777777 −14.7728 36.5732i −0.529972 1.31206i
778778 −2.16892 + 37.2389i −0.0777595 + 1.33508i
779779 −47.5583 11.2715i −1.70395 0.403845i
780780 0.754693 0.603794i 0.0270224 0.0216193i
781781 40.3365 + 4.71466i 1.44335 + 0.168704i
782782 2.69238 4.66333i 0.0962792 0.166760i
783783 16.2129 18.8614i 0.579400 0.674050i
784784 −7.39082 12.8013i −0.263958 0.457188i
785785 −3.62796 8.41056i −0.129487 0.300186i
786786 −8.83894 16.1703i −0.315275 0.576777i
787787 10.5965 11.2316i 0.377725 0.400365i −0.510423 0.859924i 0.670511π-0.670511\pi
0.888147 + 0.459559i 0.151993π0.151993\pi
788788 −3.44644 + 1.73087i −0.122774 + 0.0616596i
789789 −29.1866 15.5221i −1.03907 0.552600i
790790 −2.50648 + 8.37222i −0.0891765 + 0.297870i
791791 −13.1394 + 11.0253i −0.467184 + 0.392014i
792792 11.4334 + 30.3271i 0.406269 + 1.07763i
793793 0.233973 + 0.196327i 0.00830864 + 0.00697178i
794794 −31.4521 + 20.6863i −1.11619 + 0.734131i
795795 −3.64241 13.2886i −0.129183 0.471298i
796796 −0.183180 + 0.0214106i −0.00649263 + 0.000758879i
797797 −10.9980 + 25.4961i −0.389568 + 0.903120i 0.604725 + 0.796434i 0.293283π0.293283\pi
−0.994293 + 0.106685i 0.965976π0.965976\pi
798798 −13.6714 19.2885i −0.483961 0.682806i
799799 −0.975688 0.490009i −0.0345174 0.0173353i
800800 2.65111 0.964924i 0.0937308 0.0341152i
801801 15.6135 + 14.3959i 0.551675 + 0.508656i
802802 −33.1308 12.0586i −1.16989 0.425804i
803803 −32.3712 34.3115i −1.14235 1.21083i
804804 4.65103 0.988182i 0.164029 0.0348505i
805805 1.70570 + 1.12186i 0.0601181 + 0.0395403i
806806 3.50334 + 11.7020i 0.123400 + 0.412184i
807807 6.95978 2.35056i 0.244996 0.0827438i
808808 7.88652 10.5934i 0.277447 0.372676i
809809 −1.83050 −0.0643571 −0.0321785 0.999482i 0.510245π-0.510245\pi
−0.0321785 + 0.999482i 0.510245π0.510245\pi
810810 19.3636 + 9.17523i 0.680368 + 0.322385i
811811 −14.4506 −0.507429 −0.253715 0.967279i 0.581652π-0.581652\pi
−0.253715 + 0.967279i 0.581652π0.581652\pi
812812 1.11981 1.50417i 0.0392977 0.0527860i
813813 −9.96575 8.76695i −0.349514 0.307470i
814814 −20.6808 69.0785i −0.724860 2.42120i
815815 −21.4792 14.1271i −0.752384 0.494851i
816816 −12.6650 + 38.9672i −0.443363 + 1.36412i
817817 −28.3572 30.0569i −0.992094 1.05156i
818818 13.1021 + 4.76877i 0.458104 + 0.166736i
819819 9.63160 + 0.450290i 0.336556 + 0.0157344i
820820 3.13841 1.14229i 0.109598 0.0398904i
821821 −19.2932 9.68942i −0.673338 0.338163i 0.0790618 0.996870i 0.474808π-0.474808\pi
−0.752400 + 0.658707i 0.771104π0.771104\pi
822822 −18.7631 + 40.8470i −0.654437 + 1.42470i
823823 −4.35435 + 10.0945i −0.151783 + 0.351873i −0.977095 0.212805i 0.931740π-0.931740\pi
0.825312 + 0.564678i 0.190999π0.190999\pi
824824 6.03268 0.705120i 0.210158 0.0245640i
825825 16.5119 + 4.32311i 0.574872 + 0.150511i
826826 4.47783 2.94511i 0.155804 0.102474i
827827 −21.6075 18.1309i −0.751367 0.630472i 0.184497 0.982833i 0.440934π-0.440934\pi
−0.935864 + 0.352361i 0.885379π0.885379\pi
828828 −0.269622 0.313945i −0.00937002 0.0109104i
829829 −36.5129 + 30.6380i −1.26815 + 1.06410i −0.273382 + 0.961906i 0.588142π0.588142\pi
−0.994764 + 0.102196i 0.967413π0.967413\pi
830830 −3.74734 + 12.5170i −0.130072 + 0.434471i
831831 0.894499 + 25.6796i 0.0310298 + 0.890815i
832832 −10.5940 + 5.32050i −0.367280 + 0.184455i
833833 12.5681 13.3214i 0.435460 0.461561i
834834 −48.8646 1.14162i −1.69204 0.0395310i
835835 12.1572 + 28.1835i 0.420717 + 0.975331i
836836 −2.01791 3.49513i −0.0697910 0.120882i
837837 −18.5987 + 17.1334i −0.642866 + 0.592215i
838838 −8.71848 + 15.1008i −0.301175 + 0.521650i
839839 51.2931 + 5.99530i 1.77083 + 0.206981i 0.938022 0.346575i 0.112655π-0.112655\pi
0.832812 + 0.553555i 0.186729π0.186729\pi
840840 −13.1055 5.11972i −0.452182 0.176647i
841841 −5.92448 1.40413i −0.204292 0.0484182i
842842 0.584315 10.0323i 0.0201368 0.345736i
843843 1.90902 + 0.268466i 0.0657502 + 0.00924646i
844844 2.99872 0.710709i 0.103220 0.0244636i
845845 −2.82365 16.0137i −0.0971364 0.550888i
846846 −0.646509 + 0.624108i −0.0222274 + 0.0214573i
847847 −1.79636 + 10.1876i −0.0617235 + 0.350051i
848848 −1.26087 21.6484i −0.0432986 0.743408i
849849 10.3473 4.89739i 0.355118 0.168078i
850850 11.6706 + 15.6763i 0.400298 + 0.537693i
851851 −4.78834 6.43186i −0.164142 0.220481i
852852 3.23012 1.52882i 0.110662 0.0523767i
853853 −2.28555 39.2414i −0.0782558 1.34360i −0.777575 0.628791i 0.783550π-0.783550\pi
0.699319 0.714810i 0.253487π-0.253487\pi
854854 −0.0886537 + 0.502780i −0.00303367 + 0.0172048i
855855 22.3362 + 6.40904i 0.763883 + 0.219185i
856856 −2.04945 11.6230i −0.0700487 0.397266i
857857 19.0168 4.50706i 0.649601 0.153958i 0.107412 0.994215i 0.465744π-0.465744\pi
0.542189 + 0.840256i 0.317595π0.317595\pi
858858 17.4550 + 2.45470i 0.595905 + 0.0838022i
859859 −1.38709 + 23.8154i −0.0473270 + 0.812572i 0.888231 + 0.459398i 0.151935π0.151935\pi
−0.935557 + 0.353174i 0.885102π0.885102\pi
860860 2.74758 + 0.651187i 0.0936915 + 0.0222053i
861861 31.0350 + 12.1240i 1.05767 + 0.413184i
862862 −11.5233 1.34688i −0.392485 0.0458749i
863863 −12.6584 + 21.9249i −0.430896 + 0.746334i −0.996951 0.0780339i 0.975136π-0.975136\pi
0.566055 + 0.824368i 0.308469π0.308469\pi
864864 4.79486 + 3.65911i 0.163125 + 0.124485i
865865 18.9446 + 32.8129i 0.644134 + 1.11567i
866866 −2.59877 6.02462i −0.0883098 0.204725i
867867 −21.3157 0.497997i −0.723920 0.0169129i
868868 −1.30838 + 1.38680i −0.0444092 + 0.0470711i
869869 −13.3000 + 6.67953i −0.451173 + 0.226588i
870870 0.687135 + 19.7265i 0.0232961 + 0.668792i
871871 −6.45925 + 21.5754i −0.218863 + 0.731054i
872872 37.6321 31.5771i 1.27438 1.06933i
873873 −3.94514 + 0.742350i −0.133523 + 0.0251247i
874874 −3.68176 3.08936i −0.124537 0.104499i
875875 −18.9263 + 12.4480i −0.639824 + 0.420819i
876876 −4.01562 1.05136i −0.135675 0.0355220i
877877 41.0895 4.80267i 1.38749 0.162175i 0.610666 0.791888i 0.290902π-0.290902\pi
0.776827 + 0.629714i 0.216828π0.216828\pi
878878 8.84383 20.5023i 0.298465 0.691919i
879879 −2.25051 + 4.89935i −0.0759080 + 0.165251i
880880 −25.3783 12.7455i −0.855502 0.429649i
881881 −5.70063 + 2.07486i −0.192059 + 0.0699038i −0.436259 0.899821i 0.643697π-0.643697\pi
0.244200 + 0.969725i 0.421475π0.421475\pi
882882 −6.91882 13.3916i −0.232969 0.450918i
883883 13.5249 + 4.92265i 0.455148 + 0.165660i 0.559413 0.828889i 0.311027π-0.311027\pi
−0.104265 + 0.994550i 0.533249π0.533249\pi
884884 1.29331 + 1.37083i 0.0434987 + 0.0461059i
885885 −1.62828 + 5.00984i −0.0547340 + 0.168404i
886886 14.0923 + 9.26868i 0.473442 + 0.311387i
887887 1.86023 + 6.21360i 0.0624604 + 0.208632i 0.983523 0.180782i 0.0578628π-0.0578628\pi
−0.921063 + 0.389414i 0.872678π0.872678\pi
888888 41.4919 + 36.5008i 1.39238 + 1.22489i
889889 1.99194 2.67564i 0.0668075 0.0897380i
890890 −16.8541 −0.564951
891891 11.2641 + 34.7088i 0.377362 + 1.16279i
892892 −1.27732 −0.0427680
893893 −0.581938 + 0.781679i −0.0194738 + 0.0261579i
894894 −17.9703 + 6.06920i −0.601016 + 0.202984i
895895 2.06143 + 6.88566i 0.0689060 + 0.230162i
896896 −20.2449 13.3153i −0.676334 0.444832i
897897 1.91734 0.407367i 0.0640180 0.0136016i
898898 −6.80897 7.21709i −0.227218 0.240837i
899899 −21.8896 7.96717i −0.730059 0.265720i
900900 1.43384 0.447232i 0.0477948 0.0149077i
901901 25.2474 9.18932i 0.841114 0.306141i
902902 54.4318 + 27.3367i 1.81238 + 0.910212i
903903 16.2896 + 22.9825i 0.542083 + 0.764810i
904904 9.51808 22.0654i 0.316567 0.733884i
905905 −6.07045 + 0.709534i −0.201789 + 0.0235857i
906906 1.81625 + 6.62623i 0.0603409 + 0.220142i
907907 −21.7933 + 14.3337i −0.723635 + 0.475942i −0.857125 0.515108i 0.827752π-0.827752\pi
0.133491 + 0.991050i 0.457381π0.457381\pi
908908 2.25389 + 1.89124i 0.0747981 + 0.0627631i
909909 9.42664 11.4993i 0.312662 0.381409i
910910 −5.86182 + 4.91865i −0.194318 + 0.163052i
911911 3.60153 12.0299i 0.119324 0.398570i −0.877370 0.479814i 0.840704π-0.840704\pi
0.996694 + 0.0812442i 0.0258894π0.0258894\pi
912912 32.2891 + 17.1720i 1.06920 + 0.568622i
913913 −19.8844 + 9.98630i −0.658076 + 0.330498i
914914 12.2439 12.9778i 0.404993 0.429268i
915915 −0.240681 0.440312i −0.00795666 0.0145563i
916916 1.59369 + 3.69458i 0.0526569 + 0.122072i
917917 6.81205 + 11.7988i 0.224954 + 0.389631i
918918 −14.7565 + 39.0897i −0.487037 + 1.29015i
919919 19.5883 33.9279i 0.646158 1.11918i −0.337875 0.941191i 0.609708π-0.609708\pi
0.984033 0.177987i 0.0569586π-0.0569586\pi
920920 −2.84094 0.332058i −0.0936629 0.0109476i
921921 10.1740 8.13970i 0.335243 0.268212i
922922 −10.1147 2.39724i −0.333111 0.0789488i
923923 −0.984202 + 16.8981i −0.0323954 + 0.556208i
924924 1.03042 + 2.55101i 0.0338982 + 0.0839222i
925925 28.3182 6.71153i 0.931096 0.220674i
926926 −7.23016 41.0043i −0.237598 1.34748i
927927 6.82178 0.475825i 0.224057 0.0156281i
928928 −0.964816 + 5.47174i −0.0316716 + 0.179619i
929929 −2.80667 48.1887i −0.0920839 1.58102i −0.655725 0.755000i 0.727637π-0.727637\pi
0.563641 0.826020i 0.309400π-0.309400\pi
930930 1.63450 20.0018i 0.0535972 0.655885i
931931 −9.76155 13.1120i −0.319922 0.429730i
932932 −1.16717 1.56779i −0.0382320 0.0513545i
933933 −21.9188 15.1613i −0.717589 0.496358i
934934 −1.23628 21.2261i −0.0404523 0.694540i
935935 6.11005 34.6518i 0.199820 1.13324i
936936 −12.3419 + 5.49237i −0.403407 + 0.179524i
937937 2.06159 + 11.6919i 0.0673494 + 0.381957i 0.999787 + 0.0206269i 0.00656621π0.00656621\pi
−0.932438 + 0.361330i 0.882323π0.882323\pi
938938 −36.6307 + 8.68163i −1.19603 + 0.283465i
939939 4.23397 5.41825i 0.138170 0.176818i
940940 0.00387194 0.0664786i 0.000126289 0.00216829i
941941 8.47250 + 2.00802i 0.276196 + 0.0654596i 0.366379 0.930466i 0.380597π-0.380597\pi
−0.0901836 + 0.995925i 0.528745π0.528745\pi
942942 −2.21381 14.5323i −0.0721297 0.473489i
943943 6.72760 + 0.786343i 0.219081 + 0.0256069i
944944 −4.14525 + 7.17978i −0.134916 + 0.233682i
945945 −14.4700 6.44702i −0.470709 0.209721i
946946 25.7488 + 44.5982i 0.837164 + 1.45001i
947947 13.9682 + 32.3820i 0.453907 + 1.05227i 0.979483 + 0.201527i 0.0645905π0.0645905\pi
−0.525576 + 0.850746i 0.676150π0.676150\pi
948948 −0.681147 + 1.11860i −0.0221226 + 0.0363305i
949949 13.4923 14.3010i 0.437980 0.464231i
950950 15.5883 7.82871i 0.505750 0.253997i
951951 12.5964 7.86954i 0.408465 0.255187i
952952 7.86865 26.2831i 0.255024 0.851841i
953953 22.5161 18.8933i 0.729369 0.612013i −0.200591 0.979675i 0.564286π-0.564286\pi
0.929959 + 0.367662i 0.119842π0.119842\pi
954954 −0.253417 22.1115i −0.00820467 0.715886i
955955 −22.5912 18.9562i −0.731032 0.613409i
956956 −1.89378 + 1.24556i −0.0612491 + 0.0402841i
957957 −23.6325 + 23.9049i −0.763930 + 0.772736i
958958 −33.1877 + 3.87908i −1.07224 + 0.125327i
959959 13.1624 30.5138i 0.425035 0.985343i
960960 19.3926 1.80866i 0.625893 0.0583744i
961961 −6.53793 3.28347i −0.210901 0.105918i
962962 28.2421 10.2793i 0.910561 0.331417i
963963 −1.69380 13.1797i −0.0545819 0.424708i
964964 0.424010 + 0.154327i 0.0136565 + 0.00497054i
965965 18.0652 + 19.1480i 0.581540 + 0.616396i
966966 2.19214 + 2.43505i 0.0705311 + 0.0783465i
967967 −23.3194 15.3374i −0.749901 0.493218i 0.116114 0.993236i 0.462956π-0.462956\pi
−0.866015 + 0.500018i 0.833327π0.833327\pi
968968 −4.15672 13.8844i −0.133602 0.446262i
969969 −8.90842 + 44.4275i −0.286180 + 1.42722i
970970 1.90245 2.55544i 0.0610841 0.0820502i
971971 −32.8139 −1.05305 −0.526524 0.850160i 0.676505π-0.676505\pi
−0.526524 + 0.850160i 0.676505π0.676505\pi
972972 2.45893 + 2.06512i 0.0788701 + 0.0662387i
973973 36.1354 1.15845
974974 37.0032 49.7039i 1.18566 1.59262i
975975 −1.39866 + 6.97531i −0.0447930 + 0.223389i
976976 −0.226498 0.756555i −0.00725001 0.0242167i
977977 8.44583 + 5.55491i 0.270206 + 0.177717i 0.677380 0.735633i 0.263115π-0.263115\pi
−0.407174 + 0.913351i 0.633486π0.633486\pi
978978 −27.6048 30.6636i −0.882703 0.980514i
979979 −19.6968 20.8774i −0.629514 0.667246i
980980 1.04965 + 0.382042i 0.0335299 + 0.0122039i
981981 43.9835 33.5347i 1.40429 1.07068i
982982 −15.4489 + 5.62294i −0.492994 + 0.179435i
983983 44.4143 + 22.3057i 1.41660 + 0.711441i 0.981947 0.189159i 0.0605760π-0.0605760\pi
0.434649 + 0.900600i 0.356872π0.356872\pi
984984 −46.4790 + 4.33490i −1.48170 + 0.138191i
985985 −11.8870 + 27.5571i −0.378751 + 0.878044i
986986 −38.2287 + 4.46829i −1.21745 + 0.142299i
987987 0.467056 0.472439i 0.0148665 0.0150379i
988988 1.40540 0.924348i 0.0447118 0.0294074i
989989 4.38685 + 3.68101i 0.139494 + 0.117049i
990990 −25.2439 14.1913i −0.802303 0.451030i
991991 −20.4874 + 17.1909i −0.650802 + 0.546088i −0.907314 0.420453i 0.861871π-0.861871\pi
0.256512 + 0.966541i 0.417427π0.417427\pi
992992 1.62016 5.41172i 0.0514402 0.171822i
993993 −13.7064 + 8.56303i −0.434959 + 0.271740i
994994 −25.2840 + 12.6981i −0.801961 + 0.402760i
995995 −0.984868 + 1.04390i −0.0312224 + 0.0330938i
996996 −1.01836 + 1.67238i −0.0322678 + 0.0529913i
997997 16.7707 + 38.8789i 0.531134 + 1.23131i 0.946810 + 0.321794i 0.104286π0.104286\pi
−0.415675 + 0.909513i 0.636455π0.636455\pi
998998 5.80331 + 10.0516i 0.183701 + 0.318179i
999999 44.7451 + 43.2325i 1.41567 + 1.36782i
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.58.3 yes 144
3.2 odd 2 243.2.g.a.226.6 144
9.2 odd 6 729.2.g.a.433.3 144
9.4 even 3 729.2.g.c.676.3 144
9.5 odd 6 729.2.g.b.676.6 144
9.7 even 3 729.2.g.d.433.6 144
81.7 even 27 inner 81.2.g.a.7.3 144
81.13 even 27 6561.2.a.c.1.21 72
81.20 odd 54 729.2.g.b.55.6 144
81.34 even 27 729.2.g.d.298.6 144
81.47 odd 54 729.2.g.a.298.3 144
81.61 even 27 729.2.g.c.55.3 144
81.68 odd 54 6561.2.a.d.1.52 72
81.74 odd 54 243.2.g.a.100.6 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.7.3 144 81.7 even 27 inner
81.2.g.a.58.3 yes 144 1.1 even 1 trivial
243.2.g.a.100.6 144 81.74 odd 54
243.2.g.a.226.6 144 3.2 odd 2
729.2.g.a.298.3 144 81.47 odd 54
729.2.g.a.433.3 144 9.2 odd 6
729.2.g.b.55.6 144 81.20 odd 54
729.2.g.b.676.6 144 9.5 odd 6
729.2.g.c.55.3 144 81.61 even 27
729.2.g.c.676.3 144 9.4 even 3
729.2.g.d.298.6 144 81.34 even 27
729.2.g.d.433.6 144 9.7 even 3
6561.2.a.c.1.21 72 81.13 even 27
6561.2.a.d.1.52 72 81.68 odd 54