Properties

Label 459.2.ba.a.25.20
Level 459459
Weight 22
Character 459.25
Analytic conductor 3.6653.665
Analytic rank 00
Dimension 12481248
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [459,2,Mod(25,459)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(459, base_ring=CyclotomicField(72))
 
chi = DirichletCharacter(H, H._module([40, 45]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("459.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 459=3317 459 = 3^{3} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 459.ba (of order 7272, degree 2424, 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: 3.665133452783.66513345278
Analytic rank: 00
Dimension: 12481248
Relative dimension: 5252 over Q(ζ72)\Q(\zeta_{72})
Twist minimal: yes
Sato-Tate group: SU(2)[C72]\mathrm{SU}(2)[C_{72}]

Embedding invariants

Embedding label 25.20
Character χ\chi == 459.25
Dual form 459.2.ba.a.202.20

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+(0.4424020.631815i)q2+(1.705670.301145i)q3+(0.4805691.32035i)q4+(2.01144+0.634203i)q5+(0.9448590.944442i)q6+(1.400321.28316i)q7+(2.53687+0.679752i)q8+(2.818621.02731i)q9+(1.29056+0.990283i)q10+(0.1113840.353264i)q11+(0.4220752.39681i)q12+(3.257360.574361i)q13+(1.430220.317073i)q14+(3.23986+1.68748i)q15+(0.6009300.504240i)q16+(0.8828344.02748i)q17+(1.896031.32637i)q18+(0.4081671.52330i)q19+(0.129262+2.96058i)q20+(2.002072.61034i)q21+(0.272474+0.0859108i)q22+(0.2137264.89512i)q23+(4.12236+1.92340i)q24+(0.452098+0.316562i)q25+(1.803951.80395i)q26+(4.498282.60106i)q27+(1.021272.46556i)q28+(1.71594+2.69349i)q29+(2.49949+1.30045i)q30+(0.3904880.426143i)q31+(0.510539+5.83548i)q32+(0.08360040.636095i)q33+(2.15406+2.33955i)q34+(2.00287+3.46908i)q35+(0.001864674.21527i)q36+(3.61407+0.475801i)q37+(0.781871+0.931797i)q38+(5.383021.96061i)q39+(4.671652.97617i)q40+(4.41666+6.93277i)q41+(2.534970.110118i)q42+(0.357735+4.08893i)q43+(0.4129060.316834i)q44+(5.01796+3.85394i)q45+(2.99826+2.30065i)q46+(2.50086+6.87104i)q47+(1.176840.679101i)q48+(0.295686+3.37970i)q49+(0.400018+0.145595i)q50+(2.718686.60369i)q51+(0.8070294.57689i)q52+(6.826736.82673i)q53+(3.633441.69136i)q54+0.781209iq55+(2.68020+4.20707i)q56+(1.154932.47533i)q57+(2.460920.107446i)q58+(3.354230.293457i)q59+(0.671086+5.08871i)q60+(8.551777.83625i)q61+(0.4419960.0581899i)q62+(2.628785.05530i)q63+(2.554091.47460i)q64+(6.18772+3.22112i)q65+(0.438880+0.228590i)q66+(0.552290+3.13219i)q67+(5.741960.769830i)q68+(1.838698.28511i)q69+(3.077890.269280i)q70+(1.873440.246643i)q71+(6.45216+4.52211i)q72+(2.059571.58036i)q73+(1.89949+2.07293i)q74+(0.675799+0.676098i)q75+(2.207450.193127i)q76+(0.2973210.637606i)q77+(3.620202.53370i)q78+(10.1744+2.25561i)q79+(1.52852+0.633135i)q80+(6.889285.79119i)q81+(2.426295.85758i)q82+(5.80410+8.28911i)q83+(2.484443.89789i)q84+(4.33001+7.54113i)q85+(2.425192.03497i)q86+(2.11570+5.11095i)q87+(0.0424340+0.971898i)q88+(4.34565+2.50897i)q89+(4.65494+1.46543i)q90+(3.824354.98400i)q91+(6.566002.07025i)q92+(0.5377130.844453i)q93+(3.234854.61984i)q94+(1.78709+2.80516i)q95+(0.886515+10.1072i)q96+(7.68940+14.7712i)q97+(2.266161.30837i)q98+(0.04896201.11014i)q99+O(q100)q+(-0.442402 - 0.631815i) q^{2} +(1.70567 - 0.301145i) q^{3} +(0.480569 - 1.32035i) q^{4} +(-2.01144 + 0.634203i) q^{5} +(-0.944859 - 0.944442i) q^{6} +(1.40032 - 1.28316i) q^{7} +(-2.53687 + 0.679752i) q^{8} +(2.81862 - 1.02731i) q^{9} +(1.29056 + 0.990283i) q^{10} +(0.111384 - 0.353264i) q^{11} +(0.422075 - 2.39681i) q^{12} +(3.25736 - 0.574361i) q^{13} +(-1.43022 - 0.317073i) q^{14} +(-3.23986 + 1.68748i) q^{15} +(-0.600930 - 0.504240i) q^{16} +(-0.882834 - 4.02748i) q^{17} +(-1.89603 - 1.32637i) q^{18} +(-0.408167 - 1.52330i) q^{19} +(-0.129262 + 2.96058i) q^{20} +(2.00207 - 2.61034i) q^{21} +(-0.272474 + 0.0859108i) q^{22} +(-0.213726 - 4.89512i) q^{23} +(-4.12236 + 1.92340i) q^{24} +(-0.452098 + 0.316562i) q^{25} +(-1.80395 - 1.80395i) q^{26} +(4.49828 - 2.60106i) q^{27} +(-1.02127 - 2.46556i) q^{28} +(-1.71594 + 2.69349i) q^{29} +(2.49949 + 1.30045i) q^{30} +(0.390488 - 0.426143i) q^{31} +(-0.510539 + 5.83548i) q^{32} +(0.0836004 - 0.636095i) q^{33} +(-2.15406 + 2.33955i) q^{34} +(-2.00287 + 3.46908i) q^{35} +(-0.00186467 - 4.21527i) q^{36} +(-3.61407 + 0.475801i) q^{37} +(-0.781871 + 0.931797i) q^{38} +(5.38302 - 1.96061i) q^{39} +(4.67165 - 2.97617i) q^{40} +(4.41666 + 6.93277i) q^{41} +(-2.53497 - 0.110118i) q^{42} +(0.357735 + 4.08893i) q^{43} +(-0.412906 - 0.316834i) q^{44} +(-5.01796 + 3.85394i) q^{45} +(-2.99826 + 2.30065i) q^{46} +(2.50086 + 6.87104i) q^{47} +(-1.17684 - 0.679101i) q^{48} +(-0.295686 + 3.37970i) q^{49} +(0.400018 + 0.145595i) q^{50} +(-2.71868 - 6.60369i) q^{51} +(0.807029 - 4.57689i) q^{52} +(6.82673 - 6.82673i) q^{53} +(-3.63344 - 1.69136i) q^{54} +0.781209i q^{55} +(-2.68020 + 4.20707i) q^{56} +(-1.15493 - 2.47533i) q^{57} +(2.46092 - 0.107446i) q^{58} +(-3.35423 - 0.293457i) q^{59} +(0.671086 + 5.08871i) q^{60} +(8.55177 - 7.83625i) q^{61} +(-0.441996 - 0.0581899i) q^{62} +(2.62878 - 5.05530i) q^{63} +(2.55409 - 1.47460i) q^{64} +(-6.18772 + 3.22112i) q^{65} +(-0.438880 + 0.228590i) q^{66} +(0.552290 + 3.13219i) q^{67} +(-5.74196 - 0.769830i) q^{68} +(-1.83869 - 8.28511i) q^{69} +(3.07789 - 0.269280i) q^{70} +(1.87344 - 0.246643i) q^{71} +(-6.45216 + 4.52211i) q^{72} +(2.05957 - 1.58036i) q^{73} +(1.89949 + 2.07293i) q^{74} +(-0.675799 + 0.676098i) q^{75} +(-2.20745 - 0.193127i) q^{76} +(-0.297321 - 0.637606i) q^{77} +(-3.62020 - 2.53370i) q^{78} +(-10.1744 + 2.25561i) q^{79} +(1.52852 + 0.633135i) q^{80} +(6.88928 - 5.79119i) q^{81} +(2.42629 - 5.85758i) q^{82} +(5.80410 + 8.28911i) q^{83} +(-2.48444 - 3.89789i) q^{84} +(4.33001 + 7.54113i) q^{85} +(2.42519 - 2.03497i) q^{86} +(-2.11570 + 5.11095i) q^{87} +(-0.0424340 + 0.971898i) q^{88} +(4.34565 + 2.50897i) q^{89} +(4.65494 + 1.46543i) q^{90} +(3.82435 - 4.98400i) q^{91} +(-6.56600 - 2.07025i) q^{92} +(0.537713 - 0.844453i) q^{93} +(3.23485 - 4.61984i) q^{94} +(1.78709 + 2.80516i) q^{95} +(0.886515 + 10.1072i) q^{96} +(7.68940 + 14.7712i) q^{97} +(2.26616 - 1.30837i) q^{98} +(-0.0489620 - 1.11014i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 1248q24q224q324q524q624q712q824q912q1036q11+12q1224q1424q1548q1612q1748q1812q1924q20+168q99+O(q100) 1248 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 36 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{15} - 48 q^{16} - 12 q^{17} - 48 q^{18} - 12 q^{19} - 24 q^{20}+ \cdots - 168 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/459Z)×\left(\mathbb{Z}/459\mathbb{Z}\right)^\times.

nn 137137 190190
χ(n)\chi(n) e(59)e\left(\frac{5}{9}\right) e(58)e\left(\frac{5}{8}\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 −0.442402 0.631815i −0.312825 0.446761i 0.631693 0.775218i 0.282360π-0.282360\pi
−0.944519 + 0.328457i 0.893471π0.893471\pi
33 1.70567 0.301145i 0.984769 0.173866i
44 0.480569 1.32035i 0.240285 0.660176i
55 −2.01144 + 0.634203i −0.899542 + 0.283624i −0.714937 0.699189i 0.753545π-0.753545\pi
−0.184604 + 0.982813i 0.559100π0.559100\pi
66 −0.944859 0.944442i −0.385737 0.385567i
77 1.40032 1.28316i 0.529271 0.484988i −0.365935 0.930641i 0.619251π-0.619251\pi
0.895206 + 0.445653i 0.147028π0.147028\pi
88 −2.53687 + 0.679752i −0.896918 + 0.240329i
99 2.81862 1.02731i 0.939541 0.342436i
1010 1.29056 + 0.990283i 0.408112 + 0.313155i
1111 0.111384 0.353264i 0.0335835 0.106513i −0.935437 0.353493i 0.884994π-0.884994\pi
0.969021 + 0.246980i 0.0794382π0.0794382\pi
1212 0.422075 2.39681i 0.121843 0.691899i
1313 3.25736 0.574361i 0.903430 0.159299i 0.297411 0.954749i 0.403877π-0.403877\pi
0.606019 + 0.795450i 0.292766π0.292766\pi
1414 −1.43022 0.317073i −0.382243 0.0847412i
1515 −3.23986 + 1.68748i −0.836528 + 0.435704i
1616 −0.600930 0.504240i −0.150233 0.126060i
1717 −0.882834 4.02748i −0.214119 0.976808i
1818 −1.89603 1.32637i −0.446899 0.312628i
1919 −0.408167 1.52330i −0.0936400 0.349469i 0.903170 0.429284i 0.141234π-0.141234\pi
−0.996810 + 0.0798144i 0.974567π0.974567\pi
2020 −0.129262 + 2.96058i −0.0289038 + 0.662007i
2121 2.00207 2.61034i 0.436887 0.569623i
2222 −0.272474 + 0.0859108i −0.0580917 + 0.0183162i
2323 −0.213726 4.89512i −0.0445649 1.02070i −0.881141 0.472853i 0.843224π-0.843224\pi
0.836576 0.547851i 0.184554π-0.184554\pi
2424 −4.12236 + 1.92340i −0.841473 + 0.392612i
2525 −0.452098 + 0.316562i −0.0904195 + 0.0633124i
2626 −1.80395 1.80395i −0.353784 0.353784i
2727 4.49828 2.60106i 0.865693 0.500575i
2828 −1.02127 2.46556i −0.193002 0.465947i
2929 −1.71594 + 2.69349i −0.318642 + 0.500168i −0.964782 0.263051i 0.915271π-0.915271\pi
0.646140 + 0.763219i 0.276382π0.276382\pi
3030 2.49949 + 1.30045i 0.456343 + 0.237429i
3131 0.390488 0.426143i 0.0701337 0.0765375i −0.701217 0.712948i 0.747359π-0.747359\pi
0.771350 + 0.636411i 0.219582π0.219582\pi
3232 −0.510539 + 5.83548i −0.0902514 + 1.03158i
3333 0.0836004 0.636095i 0.0145530 0.110730i
3434 −2.15406 + 2.33955i −0.369418 + 0.401230i
3535 −2.00287 + 3.46908i −0.338547 + 0.586381i
3636 −0.00186467 4.21527i −0.000310778 0.702545i
3737 −3.61407 + 0.475801i −0.594149 + 0.0782212i −0.421603 0.906780i 0.638533π-0.638533\pi
−0.172546 + 0.985002i 0.555199π0.555199\pi
3838 −0.781871 + 0.931797i −0.126836 + 0.151157i
3939 5.38302 1.96061i 0.861973 0.313949i
4040 4.67165 2.97617i 0.738653 0.470574i
4141 4.41666 + 6.93277i 0.689766 + 1.08272i 0.991598 + 0.129355i 0.0412907π0.0412907\pi
−0.301832 + 0.953361i 0.597598π0.597598\pi
4242 −2.53497 0.110118i −0.391155 0.0169915i
4343 0.357735 + 4.08893i 0.0545541 + 0.623556i 0.973426 + 0.229001i 0.0735458π0.0735458\pi
−0.918872 + 0.394555i 0.870899π0.870899\pi
4444 −0.412906 0.316834i −0.0622479 0.0477645i
4545 −5.01796 + 3.85394i −0.748033 + 0.574512i
4646 −2.99826 + 2.30065i −0.442069 + 0.339212i
4747 2.50086 + 6.87104i 0.364787 + 1.00224i 0.977314 + 0.211795i 0.0679309π0.0679309\pi
−0.612527 + 0.790450i 0.709847π0.709847\pi
4848 −1.17684 0.679101i −0.169862 0.0980198i
4949 −0.295686 + 3.37970i −0.0422408 + 0.482815i
5050 0.400018 + 0.145595i 0.0565710 + 0.0205902i
5151 −2.71868 6.60369i −0.380691 0.924702i
5252 0.807029 4.57689i 0.111915 0.634700i
5353 6.82673 6.82673i 0.937723 0.937723i −0.0604483 0.998171i 0.519253π-0.519253\pi
0.998171 + 0.0604483i 0.0192530π0.0192530\pi
5454 −3.63344 1.69136i −0.494448 0.230166i
5555 0.781209i 0.105338i
5656 −2.68020 + 4.20707i −0.358157 + 0.562193i
5757 −1.15493 2.47533i −0.152975 0.327866i
5858 2.46092 0.107446i 0.323135 0.0141084i
5959 −3.35423 0.293457i −0.436684 0.0382049i −0.133305 0.991075i 0.542559π-0.542559\pi
−0.303379 + 0.952870i 0.598115π0.598115\pi
6060 0.671086 + 5.08871i 0.0866369 + 0.656949i
6161 8.55177 7.83625i 1.09494 1.00333i 0.0949729 0.995480i 0.469724π-0.469724\pi
0.999969 0.00784973i 0.00249867π-0.00249867\pi
6262 −0.441996 0.0581899i −0.0561336 0.00739012i
6363 2.62878 5.05530i 0.331195 0.636907i
6464 2.55409 1.47460i 0.319261 0.184325i
6565 −6.18772 + 3.22112i −0.767492 + 0.399531i
6666 −0.438880 + 0.228590i −0.0540223 + 0.0281374i
6767 0.552290 + 3.13219i 0.0674730 + 0.382658i 0.999780 + 0.0209898i 0.00668174π0.00668174\pi
−0.932307 + 0.361669i 0.882207π0.882207\pi
6868 −5.74196 0.769830i −0.696315 0.0933557i
6969 −1.83869 8.28511i −0.221352 0.997410i
7070 3.07789 0.269280i 0.367878 0.0321852i
7171 1.87344 0.246643i 0.222336 0.0292711i −0.0185351 0.999828i 0.505900π-0.505900\pi
0.240871 + 0.970557i 0.422567π0.422567\pi
7272 −6.45216 + 4.52211i −0.760395 + 0.532936i
7373 2.05957 1.58036i 0.241054 0.184968i −0.481168 0.876628i 0.659787π-0.659787\pi
0.722222 + 0.691661i 0.243121π0.243121\pi
7474 1.89949 + 2.07293i 0.220811 + 0.240973i
7575 −0.675799 + 0.676098i −0.0780345 + 0.0780690i
7676 −2.20745 0.193127i −0.253212 0.0221531i
7777 −0.297321 0.637606i −0.0338828 0.0726619i
7878 −3.62020 2.53370i −0.409907 0.286885i
7979 −10.1744 + 2.25561i −1.14471 + 0.253776i −0.747699 0.664038i 0.768841π-0.768841\pi
−0.397010 + 0.917814i 0.629952π0.629952\pi
8080 1.52852 + 0.633135i 0.170894 + 0.0707867i
8181 6.88928 5.79119i 0.765475 0.643465i
8282 2.42629 5.85758i 0.267939 0.646862i
8383 5.80410 + 8.28911i 0.637082 + 0.909848i 0.999756 0.0220682i 0.00702509π-0.00702509\pi
−0.362674 + 0.931916i 0.618136π0.618136\pi
8484 −2.48444 3.89789i −0.271075 0.425294i
8585 4.33001 + 7.54113i 0.469655 + 0.817950i
8686 2.42519 2.03497i 0.261514 0.219437i
8787 −2.11570 + 5.11095i −0.226827 + 0.547951i
8888 −0.0424340 + 0.971898i −0.00452348 + 0.103605i
8989 4.34565 + 2.50897i 0.460638 + 0.265950i 0.712313 0.701862i 0.247648π-0.247648\pi
−0.251674 + 0.967812i 0.580981π0.580981\pi
9090 4.65494 + 1.46543i 0.490673 + 0.154470i
9191 3.82435 4.98400i 0.400901 0.522465i
9292 −6.56600 2.07025i −0.684553 0.215839i
9393 0.537713 0.844453i 0.0557583 0.0875657i
9494 3.23485 4.61984i 0.333649 0.476500i
9595 1.78709 + 2.80516i 0.183351 + 0.287804i
9696 0.886515 + 10.1072i 0.0904795 + 1.03156i
9797 7.68940 + 14.7712i 0.780741 + 1.49979i 0.864128 + 0.503272i 0.167871π0.167871\pi
−0.0833875 + 0.996517i 0.526574π0.526574\pi
9898 2.26616 1.30837i 0.228917 0.132165i
9999 −0.0489620 1.11014i −0.00492086 0.111574i
100100 0.200710 + 0.749059i 0.0200710 + 0.0749059i
101101 −2.08572 + 0.759140i −0.207537 + 0.0755372i −0.443697 0.896177i 0.646333π-0.646333\pi
0.236160 + 0.971714i 0.424111π0.424111\pi
102102 −2.96957 + 4.63919i −0.294031 + 0.459348i
103103 −4.25214 + 3.56797i −0.418975 + 0.351562i −0.827773 0.561063i 0.810393π-0.810393\pi
0.408798 + 0.912625i 0.365948π0.365948\pi
104104 −7.87308 + 3.67128i −0.772019 + 0.359998i
105105 −2.37155 + 6.52026i −0.231439 + 0.636312i
106106 −7.33339 1.29307i −0.712281 0.125594i
107107 −1.11365 0.461289i −0.107661 0.0445945i 0.328203 0.944607i 0.393557π-0.393557\pi
−0.435864 + 0.900013i 0.643557π0.643557\pi
108108 −1.27259 7.18930i −0.122455 0.691791i
109109 13.7564 5.69809i 1.31763 0.545778i 0.390526 0.920592i 0.372293π-0.372293\pi
0.927100 + 0.374814i 0.122293π0.122293\pi
110110 0.493580 0.345608i 0.0470610 0.0329524i
111111 −6.02112 + 1.89992i −0.571500 + 0.180332i
112112 −1.48851 + 0.0649899i −0.140651 + 0.00614097i
113113 −0.345817 0.180021i −0.0325318 0.0169350i 0.445405 0.895329i 0.353060π-0.353060\pi
−0.477937 + 0.878394i 0.658615π0.658615\pi
114114 −1.05301 + 1.82480i −0.0986232 + 0.170908i
115115 3.53440 + 9.71068i 0.329585 + 0.905526i
116116 2.73172 + 3.56005i 0.253634 + 0.330543i
117117 8.59123 4.96522i 0.794260 0.459035i
118118 1.29851 + 2.24908i 0.119537 + 0.207045i
119119 −6.40414 4.50695i −0.587067 0.413151i
120120 7.07204 6.48321i 0.645586 0.591833i
121121 8.89828 + 6.23064i 0.808935 + 0.566422i
122122 −8.73438 1.93637i −0.790774 0.175310i
123123 9.62113 + 10.4950i 0.867508 + 0.946299i
124124 −0.375003 0.720373i −0.0336762 0.0646914i
125125 7.12814 9.28957i 0.637560 0.830885i
126126 −4.35699 + 0.575569i −0.388151 + 0.0512758i
127127 −6.47260 + 1.73433i −0.574351 + 0.153897i −0.534291 0.845300i 0.679421π-0.679421\pi
−0.0400595 + 0.999197i 0.512755π0.512755\pi
128128 8.55628 + 3.98986i 0.756276 + 0.352657i
129129 1.84154 + 6.86664i 0.162138 + 0.604574i
130130 4.77261 + 2.48446i 0.418586 + 0.217902i
131131 3.16647 + 2.90153i 0.276656 + 0.253508i 0.801921 0.597430i 0.203812π-0.203812\pi
−0.525265 + 0.850939i 0.676034π0.676034\pi
132132 −0.799694 0.416070i −0.0696044 0.0362142i
133133 −2.52620 1.60937i −0.219049 0.139550i
134134 1.73463 1.73463i 0.149850 0.149850i
135135 −7.39839 + 8.08469i −0.636752 + 0.695819i
136136 4.97732 + 9.61708i 0.426802 + 0.824658i
137137 −1.22606 + 6.95333i −0.104749 + 0.594063i 0.886571 + 0.462593i 0.153081π0.153081\pi
−0.991320 + 0.131470i 0.958030π0.958030\pi
138138 −4.42122 + 4.82706i −0.376359 + 0.410906i
139139 −10.2167 + 11.1496i −0.866573 + 0.945699i −0.998964 0.0454989i 0.985512π-0.985512\pi
0.132391 + 0.991198i 0.457734π0.457734\pi
140140 3.61789 + 4.31163i 0.305767 + 0.364399i
141141 6.33481 + 10.9666i 0.533488 + 0.923556i
142142 −0.984644 1.07455i −0.0826295 0.0901743i
143143 0.159916 1.21468i 0.0133729 0.101577i
144144 −2.21181 0.803924i −0.184317 0.0669937i
145145 1.74329 6.50603i 0.144772 0.540296i
146146 −1.90965 0.602112i −0.158044 0.0498311i
147147 0.513437 + 5.85370i 0.0423476 + 0.482805i
148148 −1.10858 + 5.00050i −0.0911250 + 0.411038i
149149 −22.0235 + 3.88333i −1.80423 + 0.318135i −0.971768 0.235940i 0.924183π-0.924183\pi
−0.832466 + 0.554076i 0.813072π0.813072\pi
150150 0.726143 + 0.127873i 0.0592894 + 0.0104408i
151151 −0.766916 + 0.0670965i −0.0624108 + 0.00546023i −0.118318 0.992976i 0.537750π-0.537750\pi
0.0559076 + 0.998436i 0.482195π0.482195\pi
152152 2.07093 + 3.58696i 0.167975 + 0.290941i
153153 −6.62584 10.4450i −0.535667 0.844429i
154154 −0.271314 + 0.469930i −0.0218631 + 0.0378680i
155155 −0.515181 + 1.10481i −0.0413803 + 0.0887403i
156156 −0.00178043 8.04970i −0.000142549 0.644491i
157157 8.94393 + 10.6590i 0.713804 + 0.850678i 0.994013 0.109261i 0.0348484π-0.0348484\pi
−0.280210 + 0.959939i 0.590404π0.590404\pi
158158 5.92630 + 5.43045i 0.471471 + 0.432024i
159159 9.58831 13.7000i 0.760403 1.08648i
160160 −2.67397 12.0615i −0.211396 0.953545i
161161 −6.58050 6.58050i −0.518616 0.518616i
162162 −6.70679 1.79072i −0.526935 0.140692i
163163 1.37385 0.569066i 0.107608 0.0445727i −0.328230 0.944598i 0.606452π-0.606452\pi
0.435838 + 0.900025i 0.356452π0.356452\pi
164164 11.2762 2.49987i 0.880524 0.195207i
165165 0.235257 + 1.33248i 0.0183147 + 0.103734i
166166 2.66944 7.33423i 0.207189 0.569247i
167167 −2.60176 8.25174i −0.201330 0.638539i −0.999355 0.0359135i 0.988566π-0.988566\pi
0.798024 0.602625i 0.205879π-0.205879\pi
168168 −3.30460 + 7.98300i −0.254955 + 0.615902i
169169 −1.93548 + 0.704459i −0.148883 + 0.0541891i
170170 2.84900 6.07197i 0.218508 0.465699i
171171 −2.71537 3.87430i −0.207649 0.296275i
172172 5.57075 + 1.49268i 0.424765 + 0.113816i
173173 −6.63518 + 3.45406i −0.504463 + 0.262607i −0.694918 0.719089i 0.744559π-0.744559\pi
0.190455 + 0.981696i 0.439004π0.439004\pi
174174 4.16516 0.924361i 0.315760 0.0700756i
175175 −0.226882 + 1.02340i −0.0171507 + 0.0773618i
176176 −0.245064 + 0.156123i −0.0184724 + 0.0117682i
177177 −5.80959 + 0.509568i −0.436676 + 0.0383015i
178178 −0.337323 3.85562i −0.0252834 0.288991i
179179 1.68166 6.27602i 0.125693 0.469092i −0.874171 0.485619i 0.838594π-0.838594\pi
0.999863 + 0.0165269i 0.00526093π0.00526093\pi
180180 2.67709 + 8.47757i 0.199538 + 0.631880i
181181 −26.2428 3.45492i −1.95061 0.256803i −0.951848 0.306570i 0.900819π-0.900819\pi
−0.998761 + 0.0497673i 0.984152π0.984152\pi
182182 −4.84087 0.211357i −0.358829 0.0156668i
183183 12.2267 15.9414i 0.903820 1.17842i
184184 3.86966 + 12.2730i 0.285275 + 0.904778i
185185 6.96771 3.24910i 0.512276 0.238878i
186186 −0.771423 + 0.0338520i −0.0565635 + 0.00248215i
187187 −1.52110 0.136722i −0.111234 0.00999813i
188188 10.2740 0.749311
189189 2.96145 9.41431i 0.215414 0.684790i
190190 0.981734 2.37012i 0.0712225 0.171946i
191191 12.9958 + 2.29152i 0.940346 + 0.165808i 0.622753 0.782419i 0.286014π-0.286014\pi
0.317593 + 0.948227i 0.397125π0.397125\pi
192192 3.91236 3.28434i 0.282351 0.237027i
193193 0.314219 + 7.19680i 0.0226180 + 0.518037i 0.976196 + 0.216891i 0.0695915π0.0695915\pi
−0.953578 + 0.301146i 0.902631π0.902631\pi
194194 5.93087 11.3931i 0.425811 0.817976i
195195 −9.58418 + 7.35757i −0.686337 + 0.526886i
196196 4.32030 + 2.01459i 0.308593 + 0.143899i
197197 2.22981 16.9371i 0.158867 1.20672i −0.707282 0.706931i 0.750079π-0.750079\pi
0.866150 0.499785i 0.166588π-0.166588\pi
198198 −0.679745 + 0.522065i −0.0483074 + 0.0371015i
199199 −3.53208 26.8288i −0.250382 1.90184i −0.405748 0.913985i 0.632989π-0.632989\pi
0.155366 0.987857i 0.450344π-0.450344\pi
200200 0.931729 1.11039i 0.0658832 0.0785165i
201201 1.88527 + 5.17617i 0.132977 + 0.365099i
202202 1.40236 + 0.981944i 0.0986698 + 0.0690894i
203203 1.05330 + 5.97356i 0.0739272 + 0.419262i
204204 −10.0257 + 0.416084i −0.701941 + 0.0291317i
205205 −13.2806 11.1438i −0.927558 0.778314i
206206 4.13545 + 1.10809i 0.288130 + 0.0772043i
207207 −5.63121 13.5780i −0.391396 0.943733i
208208 −2.24706 1.29734i −0.155806 0.0899545i
209209 −0.583591 0.0254801i −0.0403678 0.00176250i
210210 5.16877 1.38619i 0.356679 0.0956565i
211211 8.32016 15.9829i 0.572784 1.10031i −0.409395 0.912357i 0.634260π-0.634260\pi
0.982179 0.187950i 0.0601843π-0.0601843\pi
212212 −5.73297 12.2944i −0.393742 0.844383i
213213 3.12119 0.984866i 0.213860 0.0674819i
214214 0.201232 + 0.907697i 0.0137559 + 0.0620489i
215215 −3.31277 7.99775i −0.225929 0.545442i
216216 −9.64346 + 9.65626i −0.656154 + 0.657025i
217217 1.09779i 0.0745231i
218218 −9.68601 6.17067i −0.656019 0.417930i
219219 3.03703 3.31581i 0.205223 0.224062i
220220 1.03147 + 0.375425i 0.0695418 + 0.0253111i
221221 −5.18894 12.6119i −0.349046 0.848368i
222222 3.86415 + 2.96371i 0.259345 + 0.198911i
223223 −10.9435 + 23.4684i −0.732830 + 1.57156i 0.0851866 + 0.996365i 0.472851π0.472851\pi
−0.818017 + 0.575194i 0.804926π0.804926\pi
224224 6.77292 + 8.82665i 0.452535 + 0.589755i
225225 −0.949087 + 1.35671i −0.0632724 + 0.0904475i
226226 0.0392501 + 0.298134i 0.00261088 + 0.0198316i
227227 7.75900 24.6084i 0.514983 1.63332i −0.235099 0.971972i 0.575541π-0.575541\pi
0.750081 0.661345i 0.230014π-0.230014\pi
228228 −3.82334 + 0.335351i −0.253207 + 0.0222091i
229229 −7.20648 + 10.2919i −0.476218 + 0.680110i −0.983342 0.181763i 0.941820π-0.941820\pi
0.507124 + 0.861873i 0.330708π0.330708\pi
230230 4.57173 6.52911i 0.301451 0.430517i
231231 −0.699143 0.998009i −0.0460002 0.0656642i
232232 2.52221 7.99943i 0.165591 0.525189i
233233 2.37199 + 18.0171i 0.155394 + 1.18034i 0.874355 + 0.485287i 0.161285π0.161285\pi
−0.718961 + 0.695051i 0.755382π0.755382\pi
234234 −6.93788 3.23145i −0.453543 0.211247i
235235 −9.38795 12.2346i −0.612402 0.798098i
236236 −1.99941 + 4.28775i −0.130150 + 0.279108i
237237 −16.6749 + 6.91129i −1.08315 + 0.448937i
238238 −0.0143549 + 6.04011i −0.000930493 + 0.391523i
239239 −3.31573 1.20683i −0.214477 0.0780631i 0.232547 0.972585i 0.425294π-0.425294\pi
−0.447024 + 0.894522i 0.647516π0.647516\pi
240240 2.79782 + 0.619613i 0.180599 + 0.0399959i
241241 −8.65671 5.51493i −0.557628 0.355248i 0.228276 0.973596i 0.426691π-0.426691\pi
−0.785904 + 0.618348i 0.787802π0.787802\pi
242242 8.37852i 0.538592i
243243 10.0069 11.9525i 0.641940 0.766755i
244244 −6.23690 15.0572i −0.399277 0.963940i
245245 −1.54867 6.98558i −0.0989406 0.446292i
246246 2.37447 10.7218i 0.151391 0.683595i
247247 −2.20447 4.72751i −0.140267 0.300804i
248248 −0.700945 + 1.34650i −0.0445101 + 0.0855031i
249249 12.3961 + 12.3906i 0.785571 + 0.785223i
250250 −9.02280 0.393944i −0.570652 0.0249152i
251251 −15.8524 9.15241i −1.00060 0.577695i −0.0921719 0.995743i 0.529381π-0.529381\pi
−0.908425 + 0.418048i 0.862714π0.862714\pi
252252 −5.41146 5.90033i −0.340890 0.371686i
253253 −1.75308 0.469736i −0.110215 0.0295320i
254254 3.95927 + 3.32222i 0.248426 + 0.208455i
255255 9.65654 + 11.5587i 0.604716 + 0.723835i
256256 −2.28871 12.9799i −0.143044 0.811245i
257257 −20.9505 14.6697i −1.30686 0.915070i −0.307521 0.951541i 0.599500π-0.599500\pi
−0.999335 + 0.0364709i 0.988388π0.988388\pi
258258 3.52375 4.20132i 0.219379 0.261563i
259259 −4.45032 + 5.30369i −0.276530 + 0.329555i
260260 1.27939 + 9.71794i 0.0793445 + 0.602681i
261261 −2.06955 + 9.35472i −0.128102 + 0.579043i
262262 0.432382 3.28427i 0.0267127 0.202903i
263263 20.7988 + 9.69865i 1.28251 + 0.598044i 0.939905 0.341435i 0.110913π-0.110913\pi
0.342605 + 0.939480i 0.388691π0.388691\pi
264264 0.220304 + 1.67052i 0.0135588 + 0.102813i
265265 −9.40199 + 18.0611i −0.577560 + 1.10948i
266266 0.100773 + 2.30808i 0.00617878 + 0.141517i
267267 8.16782 + 2.97080i 0.499862 + 0.181810i
268268 4.40102 + 0.776018i 0.268835 + 0.0474028i
269269 −5.37869 + 12.9853i −0.327944 + 0.791728i 0.670800 + 0.741638i 0.265951π0.265951\pi
−0.998745 + 0.0500900i 0.984049π0.984049\pi
270270 8.38109 + 1.09773i 0.510057 + 0.0668060i
271271 −3.99688 −0.242793 −0.121397 0.992604i 0.538737π-0.538737\pi
−0.121397 + 0.992604i 0.538737π0.538737\pi
272272 −1.50030 + 2.86540i −0.0909689 + 0.173740i
273273 5.02218 9.65274i 0.303956 0.584210i
274274 4.93563 2.30152i 0.298172 0.139040i
275275 0.0614738 + 0.194970i 0.00370701 + 0.0117571i
276276 −11.8229 1.55385i −0.711654 0.0935309i
277277 −25.1868 1.09968i −1.51333 0.0660734i −0.728183 0.685383i 0.759635π-0.759635\pi
−0.785147 + 0.619309i 0.787413π0.787413\pi
278278 11.5644 + 1.52248i 0.693587 + 0.0913125i
279279 0.662859 1.60229i 0.0396843 0.0959265i
280280 2.72291 10.1620i 0.162725 0.607298i
281281 1.22446 + 13.9956i 0.0730450 + 0.834908i 0.941031 + 0.338320i 0.109859π0.109859\pi
−0.867986 + 0.496588i 0.834586π0.834586\pi
282282 4.12634 8.85408i 0.245720 0.527253i
283283 16.4151 10.4576i 0.975779 0.621640i 0.0496179 0.998768i 0.484200π-0.484200\pi
0.926161 + 0.377129i 0.123089π0.123089\pi
284284 0.574660 2.59213i 0.0340998 0.153814i
285285 3.89294 + 4.24651i 0.230598 + 0.251542i
286286 −0.838203 + 0.436341i −0.0495640 + 0.0258014i
287287 15.0806 + 4.04082i 0.890177 + 0.238522i
288288 4.55582 + 16.9725i 0.268454 + 1.00012i
289289 −15.4412 + 7.11120i −0.908306 + 0.418306i
290290 −4.88184 + 1.77685i −0.286672 + 0.104340i
291291 17.5639 + 22.8792i 1.02961 + 1.34120i
292292 −1.09687 3.47883i −0.0641896 0.203583i
293293 8.73026 23.9862i 0.510027 1.40129i −0.371181 0.928561i 0.621047π-0.621047\pi
0.881208 0.472728i 0.156731π-0.156731\pi
294294 3.47131 2.91409i 0.202451 0.169953i
295295 6.93294 1.53700i 0.403651 0.0894873i
296296 8.84498 3.66371i 0.514104 0.212949i
297297 −0.417827 1.87880i −0.0242448 0.109019i
298298 12.1968 + 12.1968i 0.706540 + 0.706540i
299299 −3.50775 15.8224i −0.202858 0.915035i
300300 0.567920 + 1.21720i 0.0327889 + 0.0702753i
301301 5.74768 + 5.26678i 0.331291 + 0.303572i
302302 0.381678 + 0.454866i 0.0219631 + 0.0261746i
303303 −3.32894 + 1.92295i −0.191243 + 0.110470i
304304 −0.522830 + 1.12121i −0.0299863 + 0.0643059i
305305 −12.2316 + 21.1857i −0.700377 + 1.21309i
306306 −3.66803 + 8.80720i −0.209688 + 0.503474i
307307 −15.8706 27.4886i −0.905780 1.56886i −0.819866 0.572555i 0.805952π-0.805952\pi
−0.0859137 0.996303i 0.527381π-0.527381\pi
308308 −0.984748 + 0.0861543i −0.0561112 + 0.00490910i
309309 −6.17827 + 7.36628i −0.351469 + 0.419053i
310310 0.925951 0.163270i 0.0525905 0.00927313i
311311 −1.15729 + 5.22021i −0.0656240 + 0.296011i −0.997824 0.0659327i 0.978998π-0.978998\pi
0.932200 + 0.361943i 0.117887π0.117887\pi
312312 −12.3233 + 8.63292i −0.697669 + 0.488743i
313313 0.0592687 + 0.0186873i 0.00335006 + 0.00105627i 0.302380 0.953187i 0.402219π-0.402219\pi
−0.299030 + 0.954244i 0.596663π0.596663\pi
314314 2.77768 10.3665i 0.156754 0.585013i
315315 −2.08154 + 11.8356i −0.117281 + 0.666860i
316316 −1.91130 + 14.5178i −0.107519 + 0.816688i
317317 4.47253 + 4.88091i 0.251202 + 0.274139i 0.850025 0.526742i 0.176587π-0.176587\pi
−0.598823 + 0.800882i 0.704365π0.704365\pi
318318 −12.8977 + 0.00285272i −0.723269 + 0.000159973i
319319 0.760385 + 0.906191i 0.0425734 + 0.0507370i
320320 −4.20219 + 4.58588i −0.234909 + 0.256359i
321321 −2.03844 0.451438i −0.113774 0.0251968i
322322 −1.24643 + 7.06888i −0.0694611 + 0.393933i
323323 −5.77472 + 2.98871i −0.321314 + 0.166296i
324324 −4.33563 11.8793i −0.240869 0.659964i
325325 −1.29083 + 1.29083i −0.0716021 + 0.0716021i
326326 −0.967337 0.616262i −0.0535758 0.0341316i
327327 21.7480 13.8617i 1.20267 0.766556i
328328 −15.9170 14.5853i −0.878872 0.805338i
329329 12.3186 + 6.41267i 0.679148 + 0.353542i
330330 0.737806 0.738132i 0.0406149 0.0406329i
331331 12.9162 + 6.02290i 0.709936 + 0.331049i 0.743823 0.668377i 0.233011π-0.233011\pi
−0.0338866 + 0.999426i 0.510788π0.510788\pi
332332 13.7338 3.67997i 0.753741 0.201964i
333333 −9.69790 + 5.05386i −0.531442 + 0.276950i
334334 −4.06255 + 5.29442i −0.222293 + 0.289698i
335335 −3.09735 5.94995i −0.169226 0.325080i
336336 −2.51934 + 0.559110i −0.137441 + 0.0305019i
337337 11.1964 + 2.48218i 0.609906 + 0.135213i 0.510563 0.859840i 0.329437π-0.329437\pi
0.0993427 + 0.995053i 0.468326π0.468326\pi
338338 1.30135 + 0.911215i 0.0707841 + 0.0495636i
339339 −0.644063 0.202916i −0.0349807 0.0110209i
340340 12.0378 2.09311i 0.652842 0.113515i
341341 −0.107047 0.185411i −0.00579692 0.0100406i
342342 −1.24656 + 3.42961i −0.0674061 + 0.185452i
343343 12.0162 + 15.6599i 0.648815 + 0.845553i
344344 −3.68698 10.1299i −0.198789 0.546168i
345345 8.95284 + 15.4989i 0.482005 + 0.834431i
346346 5.11774 + 2.66413i 0.275131 + 0.143224i
347347 3.02773 0.132194i 0.162537 0.00709653i 0.0377938 0.999286i 0.487967π-0.487967\pi
0.124743 + 0.992189i 0.460189π0.460189\pi
348348 5.73151 + 5.24963i 0.307241 + 0.281410i
349349 −12.3917 + 8.67677i −0.663313 + 0.464457i −0.856118 0.516780i 0.827130π-0.827130\pi
0.192805 + 0.981237i 0.438242π0.438242\pi
350350 0.746973 0.309406i 0.0399274 0.0165385i
351351 13.1586 11.0562i 0.702352 0.590138i
352352 2.00460 + 0.830334i 0.106846 + 0.0442569i
353353 11.5000 + 2.02776i 0.612082 + 0.107927i 0.471091 0.882084i 0.343860π-0.343860\pi
0.140990 + 0.990011i 0.454971π0.454971\pi
354354 2.89213 + 3.44515i 0.153715 + 0.183108i
355355 −3.61188 + 1.68425i −0.191698 + 0.0893905i
356356 5.40111 4.53207i 0.286258 0.240199i
357357 −12.2806 5.75879i −0.649958 0.304788i
358358 −4.70925 + 1.71403i −0.248892 + 0.0905892i
359359 −3.84477 14.3489i −0.202919 0.757305i −0.990074 0.140549i 0.955113π-0.955113\pi
0.787154 0.616756i 0.211553π-0.211553\pi
360360 10.1102 13.1879i 0.532853 0.695064i
361361 14.3006 8.25648i 0.752665 0.434551i
362362 9.42697 + 18.1090i 0.495471 + 0.951790i
363363 17.0539 + 7.94776i 0.895096 + 0.417149i
364364 −4.74277 7.44465i −0.248589 0.390206i
365365 −3.14042 + 4.48499i −0.164377 + 0.234755i
366366 −15.4811 0.672489i −0.809210 0.0351516i
367367 −28.5067 8.98812i −1.48804 0.469176i −0.555889 0.831256i 0.687622π-0.687622\pi
−0.932147 + 0.362081i 0.882067π0.882067\pi
368368 −2.33989 + 3.04940i −0.121975 + 0.158961i
369369 19.5710 + 15.0036i 1.01882 + 0.781056i
370370 −5.13536 2.96490i −0.266974 0.154138i
371371 0.799841 18.3194i 0.0415257 0.951094i
372372 −0.856567 1.11579i −0.0444109 0.0578510i
373373 19.6057 16.4512i 1.01515 0.851809i 0.0261370 0.999658i 0.491679π-0.491679\pi
0.989010 + 0.147849i 0.0472349π0.0472349\pi
374374 0.586553 + 1.02154i 0.0303300 + 0.0528225i
375375 9.36075 17.9916i 0.483387 0.929080i
376376 −11.0149 15.7310i −0.568052 0.811263i
377377 −4.04241 + 9.75923i −0.208194 + 0.502626i
378378 −7.25826 + 2.29382i −0.373324 + 0.117981i
379379 7.64799 + 3.16790i 0.392851 + 0.162724i 0.570360 0.821395i 0.306804π-0.306804\pi
−0.177509 + 0.984119i 0.556804π0.556804\pi
380380 4.56262 1.01151i 0.234058 0.0518893i
381381 −10.5178 + 4.90738i −0.538845 + 0.251413i
382382 −4.30157 9.22474i −0.220087 0.471979i
383383 21.3967 + 1.87197i 1.09332 + 0.0956531i 0.619521 0.784980i 0.287327π-0.287327\pi
0.473799 + 0.880633i 0.342882π0.342882\pi
384384 15.7957 + 4.22871i 0.806072 + 0.215795i
385385 1.00241 + 1.09394i 0.0510877 + 0.0557525i
386386 4.40804 3.38240i 0.224363 0.172160i
387387 5.20891 + 11.1577i 0.264784 + 0.567175i
388388 23.1985 3.05414i 1.17773 0.155050i
389389 −7.57792 + 0.662982i −0.384216 + 0.0336145i −0.277628 0.960689i 0.589548π-0.589548\pi
−0.106588 + 0.994303i 0.533993π0.533993\pi
390390 8.88868 + 2.80043i 0.450096 + 0.141805i
391391 −19.5263 + 5.18236i −0.987489 + 0.262083i
392392 −1.54724 8.77485i −0.0781476 0.443197i
393393 6.27474 + 3.99550i 0.316519 + 0.201546i
394394 −11.6876 + 6.08416i −0.588811 + 0.306516i
395395 19.0346 10.9897i 0.957737 0.552949i
396396 −1.48931 0.468854i −0.0748407 0.0235608i
397397 −1.32465 0.174394i −0.0664824 0.00875258i 0.0972116 0.995264i 0.469008π-0.469008\pi
−0.163694 + 0.986511i 0.552341π0.552341\pi
398398 −15.3882 + 14.1007i −0.771343 + 0.706805i
399399 −4.79352 1.98430i −0.239976 0.0993391i
400400 0.431303 + 0.0377341i 0.0215651 + 0.00188670i
401401 13.8805 0.606037i 0.693160 0.0302640i 0.305669 0.952138i 0.401120π-0.401120\pi
0.387491 + 0.921874i 0.373342π0.373342\pi
402402 2.43634 3.48109i 0.121514 0.173621i
403403 1.02720 1.61238i 0.0511685 0.0803185i
404404 3.11870i 0.155161i
405405 −10.1846 + 16.0178i −0.506075 + 0.795931i
406406 3.30821 3.30821i 0.164183 0.164183i
407407 −0.234465 + 1.32972i −0.0116220 + 0.0659116i
408408 11.3858 + 14.9047i 0.563681 + 0.737892i
409409 −5.39642 1.96414i −0.266836 0.0971204i 0.205137 0.978733i 0.434236π-0.434236\pi
−0.471973 + 0.881613i 0.656458π0.656458\pi
410410 −1.16543 + 13.3209i −0.0575564 + 0.657873i
411411 0.00270488 + 12.2293i 0.000133422 + 0.603227i
412412 2.66753 + 7.32897i 0.131420 + 0.361073i
413413 −5.07355 + 3.89307i −0.249653 + 0.191566i
414414 −6.08750 + 9.56479i −0.299184 + 0.470084i
415415 −16.9316 12.9920i −0.831137 0.637754i
416416 1.68866 + 19.3015i 0.0827936 + 0.946335i
417417 −14.0688 + 22.0943i −0.688950 + 1.08196i
418418 0.242083 + 0.379994i 0.0118407 + 0.0185861i
419419 −31.1266 + 19.8299i −1.52064 + 0.968752i −0.527787 + 0.849377i 0.676978π0.676978\pi
−0.992849 + 0.119375i 0.961911π0.961911\pi
420420 7.46935 + 6.26471i 0.364467 + 0.305687i
421421 −22.1788 + 26.4317i −1.08093 + 1.28820i −0.125786 + 0.992057i 0.540145π0.540145\pi
−0.955143 + 0.296144i 0.904299π0.904299\pi
422422 −13.7791 + 1.81405i −0.670755 + 0.0883066i
423423 14.1076 + 16.7977i 0.685937 + 0.816734i
424424 −12.6780 + 21.9590i −0.615699 + 1.06642i
425425 1.67408 + 1.54134i 0.0812046 + 0.0747661i
426426 −2.00307 1.53631i −0.0970492 0.0744344i
427427 1.92007 21.9465i 0.0929188 1.06207i
428428 −1.14425 + 1.24873i −0.0553095 + 0.0603597i
429429 −0.0930314 2.12001i −0.00449160 0.102355i
430430 −3.58752 + 5.63128i −0.173006 + 0.271564i
431431 2.54495 + 6.14406i 0.122586 + 0.295949i 0.973245 0.229768i 0.0737969π-0.0737969\pi
−0.850659 + 0.525718i 0.823797π0.823797\pi
432432 −4.01471 0.705155i −0.193158 0.0339268i
433433 26.6313 + 26.6313i 1.27982 + 1.27982i 0.940768 + 0.339050i 0.110106π0.110106\pi
0.339050 + 0.940768i 0.389894π0.389894\pi
434434 −0.693603 + 0.485666i −0.0332940 + 0.0233127i
435435 1.01421 11.6221i 0.0486278 0.557238i
436436 −0.912586 20.9017i −0.0437049 1.00101i
437437 −7.36951 + 2.32360i −0.352532 + 0.111153i
438438 −3.43856 0.451922i −0.164301 0.0215937i
439439 1.61836 37.0666i 0.0772401 1.76909i −0.425791 0.904822i 0.640004π-0.640004\pi
0.503031 0.864268i 0.332218π-0.332218\pi
440440 −0.531028 1.98182i −0.0253158 0.0944797i
441441 2.63857 + 9.82987i 0.125646 + 0.468089i
442442 −5.67279 + 8.85798i −0.269827 + 0.421331i
443443 22.0113 + 18.4697i 1.04579 + 0.877522i 0.992645 0.121064i 0.0386308π-0.0386308\pi
0.0531457 + 0.998587i 0.483075π0.483075\pi
444444 −0.385005 + 8.86305i −0.0182715 + 0.420622i
445445 −10.3322 2.29059i −0.489793 0.108585i
446446 19.6691 3.46819i 0.931359 0.164224i
447447 −36.3954 + 13.2559i −1.72144 + 0.626985i
448448 1.68439 5.34221i 0.0795801 0.252396i
449449 −11.0547 8.48253i −0.521701 0.400315i 0.314065 0.949402i 0.398309π-0.398309\pi
−0.835766 + 0.549086i 0.814976π0.814976\pi
450450 1.27707 0.000564924i 0.0602016 2.66308e-5i
451451 2.94104 0.788050i 0.138488 0.0371078i
452452 −0.403881 + 0.370088i −0.0189969 + 0.0174075i
453453 −1.28790 + 0.345397i −0.0605108 + 0.0162282i
454454 −18.9806 + 5.98455i −0.890802 + 0.280869i
455455 −4.53158 + 12.4504i −0.212444 + 0.583684i
456456 4.61252 + 5.49452i 0.216001 + 0.257305i
457457 18.5004 + 26.4213i 0.865412 + 1.23594i 0.970410 + 0.241464i 0.0776275π0.0776275\pi
−0.104998 + 0.994472i 0.533484π0.533484\pi
458458 9.69076 0.452819
459459 −14.4470 15.8204i −0.674326 0.738434i
460460 14.5201 0.677001
461461 −20.7957 29.6993i −0.968552 1.38324i −0.923223 0.384264i 0.874455π-0.874455\pi
−0.0453289 0.998972i 0.514434π-0.514434\pi
462462 −0.321255 + 0.883250i −0.0149462 + 0.0410925i
463463 0.514575 1.41378i 0.0239144 0.0657041i −0.927161 0.374663i 0.877758π-0.877758\pi
0.951075 + 0.308959i 0.0999806π0.0999806\pi
464464 2.38932 0.753351i 0.110922 0.0349735i
465465 −0.546021 + 2.03958i −0.0253211 + 0.0945834i
466466 10.3341 9.46945i 0.478717 0.438664i
467467 −2.72375 + 0.729827i −0.126040 + 0.0337724i −0.321288 0.946982i 0.604116π-0.604116\pi
0.195248 + 0.980754i 0.437449π0.437449\pi
468468 −2.42716 13.7296i −0.112196 0.634651i
469469 4.79248 + 3.67740i 0.221296 + 0.169807i
470470 −3.57677 + 11.3441i −0.164984 + 0.523263i
471471 18.4653 + 15.4873i 0.850836 + 0.713615i
472472 8.70873 1.53558i 0.400852 0.0706810i
473473 1.48432 + 0.329066i 0.0682490 + 0.0151304i
474474 11.7437 + 7.47789i 0.539404 + 0.343471i
475475 0.666751 + 0.559471i 0.0305926 + 0.0256703i
476476 −9.02839 + 6.28983i −0.413816 + 0.288294i
477477 12.2288 26.2551i 0.559920 1.20214i
478478 0.704393 + 2.62883i 0.0322182 + 0.120240i
479479 1.34199 30.7366i 0.0613170 1.40439i −0.679988 0.733223i 0.738015π-0.738015\pi
0.741305 0.671168i 0.234207π-0.234207\pi
480480 −8.19316 19.7677i −0.373965 0.902267i
481481 −11.4990 + 3.62563i −0.524311 + 0.165315i
482482 0.345326 + 7.90926i 0.0157292 + 0.360257i
483483 −13.2058 9.24248i −0.600887 0.420547i
484484 12.5029 8.75462i 0.568313 0.397937i
485485 −24.8347 24.8347i −1.12769 1.12769i
486486 −11.9788 1.03466i −0.543371 0.0469334i
487487 1.87686 + 4.53113i 0.0850484 + 0.205325i 0.960682 0.277651i 0.0895559π-0.0895559\pi
−0.875634 + 0.482976i 0.839556π0.839556\pi
488488 −16.3680 + 25.6926i −0.740945 + 1.16305i
489489 2.17196 1.38437i 0.0982194 0.0626032i
490490 −3.72846 + 4.06890i −0.168435 + 0.183814i
491491 2.03404 23.2492i 0.0917950 1.04922i −0.800972 0.598702i 0.795683π-0.795683\pi
0.892767 0.450519i 0.148761π-0.148761\pi
492492 18.4807 7.65973i 0.833173 0.345327i
493493 12.3629 + 4.53301i 0.556795 + 0.204157i
494494 −2.01165 + 3.48428i −0.0905084 + 0.156765i
495495 0.802541 + 2.20193i 0.0360716 + 0.0989695i
496496 −0.449535 + 0.0591823i −0.0201847 + 0.00265737i
497497 2.30693 2.74929i 0.103480 0.123323i
498498 2.34452 13.3137i 0.105061 0.596600i
499499 −12.9556 + 8.25363i −0.579973 + 0.369483i −0.794527 0.607229i 0.792281π-0.792281\pi
0.214554 + 0.976712i 0.431170π0.431170\pi
500500 −8.83995 13.8759i −0.395335 0.620551i
501501 −6.92272 13.2912i −0.309284 0.593809i
502502 1.23051 + 14.0648i 0.0549206 + 0.627745i
503503 −25.8182 19.8110i −1.15117 0.883328i −0.156632 0.987657i 0.550064π-0.550064\pi
−0.994543 + 0.104329i 0.966730π0.966730\pi
504504 −3.23252 + 14.6115i −0.143988 + 0.650850i
505505 3.71384 2.84973i 0.165264 0.126811i
506506 0.478779 + 1.31543i 0.0212843 + 0.0584781i
507507 −3.08916 + 1.78444i −0.137194 + 0.0792496i
508508 −0.820607 + 9.37959i −0.0364086 + 0.416152i
509509 −16.4744 5.99619i −0.730214 0.265776i −0.0499588 0.998751i 0.515909π-0.515909\pi
−0.680256 + 0.732975i 0.738131π0.738131\pi
510510 3.03090 11.2147i 0.134211 0.496597i
511511 0.856202 4.85577i 0.0378762 0.214806i
512512 6.16295 6.16295i 0.272366 0.272366i
513513 −5.79825 5.79056i −0.255999 0.255659i
514514 19.7267i 0.870109i
515515 6.29009 9.87346i 0.277174 0.435076i
516516 9.95137 + 0.868414i 0.438085 + 0.0382298i
517517 2.70585 0.118140i 0.119003 0.00519579i
518518 5.31978 + 0.465421i 0.233738 + 0.0204494i
519519 −10.2773 + 7.88963i −0.451122 + 0.346316i
520520 13.5079 12.3777i 0.592359 0.542797i
521521 −19.6974 2.59321i −0.862958 0.113611i −0.313962 0.949436i 0.601656π-0.601656\pi
−0.548996 + 0.835825i 0.684990π0.684990\pi
522522 6.82603 2.83097i 0.298767 0.123908i
523523 25.8997 14.9532i 1.13251 0.653857i 0.187948 0.982179i 0.439816π-0.439816\pi
0.944566 + 0.328322i 0.106483π0.106483\pi
524524 5.35276 2.78647i 0.233836 0.121727i
525525 −0.0787950 + 1.81391i −0.00343890 + 0.0791655i
526526 −3.07368 17.4317i −0.134019 0.760059i
527527 −2.06102 1.19647i −0.0897794 0.0521190i
528528 −0.370983 + 0.340094i −0.0161450 + 0.0148007i
529529 −1.00408 + 0.0878457i −0.0436557 + 0.00381938i
530530 15.5707 2.04992i 0.676348 0.0890430i
531531 −9.75579 + 2.61868i −0.423365 + 0.113641i
532532 −3.33894 + 2.56206i −0.144762 + 0.111079i
533533 18.3686 + 20.0458i 0.795631 + 0.868279i
534534 −1.73646 6.47484i −0.0751441 0.280194i
535535 2.53259 + 0.221573i 0.109493 + 0.00957943i
536536 −3.53020 7.57055i −0.152482 0.326998i
537537 0.978359 11.2113i 0.0422193 0.483801i
538538 10.5839 2.34638i 0.456302 0.101160i
539539 1.16099 + 0.480899i 0.0500075 + 0.0207138i
540540 7.11921 + 13.6537i 0.306362 + 0.587563i
541541 2.16987 5.23854i 0.0932901 0.225222i −0.870346 0.492441i 0.836105π-0.836105\pi
0.963636 + 0.267219i 0.0861047π0.0861047\pi
542542 1.76823 + 2.52529i 0.0759518 + 0.108470i
543543 −45.8019 + 2.00991i −1.96555 + 0.0862533i
544544 23.9530 3.09558i 1.02698 0.132722i
545545 −24.0564 + 20.1857i −1.03046 + 0.864661i
546546 −8.32057 + 1.09730i −0.356088 + 0.0469599i
547547 −0.937536 + 21.4731i −0.0400862 + 0.918124i 0.867290 + 0.497804i 0.165860π0.165860\pi
−0.907376 + 0.420320i 0.861918π0.861918\pi
548548 8.59164 + 4.96039i 0.367017 + 0.211897i
549549 16.0540 30.8728i 0.685167 1.31762i
550550 0.0959888 0.125095i 0.00409298 0.00533407i
551551 4.80338 + 1.51450i 0.204631 + 0.0645199i
552552 10.2963 + 19.7684i 0.438241 + 0.841398i
553553 −11.3531 + 16.2139i −0.482783 + 0.689486i
554554 10.4479 + 16.3999i 0.443889 + 0.696766i
555555 10.9062 7.64018i 0.462941 0.324307i
556556 9.81158 + 18.8479i 0.416104 + 0.799328i
557557 3.41268 1.97031i 0.144600 0.0834849i −0.425954 0.904745i 0.640062π-0.640062\pi
0.570555 + 0.821260i 0.306728π0.306728\pi
558558 −1.30560 + 0.290050i −0.0552704 + 0.0122788i
559559 3.51379 + 13.1137i 0.148618 + 0.554649i
560560 2.95284 1.07474i 0.124780 0.0454162i
561561 −2.63567 + 0.224868i −0.111278 + 0.00949392i
562562 8.30094 6.96531i 0.350154 0.293814i
563563 −8.72326 + 4.06772i −0.367642 + 0.171434i −0.597655 0.801753i 0.703901π-0.703901\pi
0.230013 + 0.973187i 0.426123π0.426123\pi
564564 17.5241 3.09397i 0.737899 0.130280i
565565 0.809760 + 0.142782i 0.0340668 + 0.00600690i
566566 −13.8694 5.74488i −0.582972 0.241475i
567567 2.21620 16.9495i 0.0930715 0.711814i
568568 −4.58501 + 1.89917i −0.192383 + 0.0796875i
569569 13.5971 9.52079i 0.570020 0.399132i −0.252729 0.967537i 0.581328π-0.581328\pi
0.822749 + 0.568405i 0.192439π0.192439\pi
570570 0.960767 4.33828i 0.0402421 0.181711i
571571 −18.3387 + 0.800687i −0.767452 + 0.0335077i −0.424000 0.905662i 0.639374π-0.639374\pi
−0.343453 + 0.939170i 0.611597π0.611597\pi
572572 −1.52696 0.794886i −0.0638454 0.0332358i
573573 22.8567 0.00505544i 0.954852 0.000211194i
574574 −4.11861 11.3158i −0.171908 0.472312i
575575 1.64624 + 2.14542i 0.0686528 + 0.0894701i
576576 5.68414 6.78019i 0.236839 0.282508i
577577 11.5868 + 20.0689i 0.482364 + 0.835479i 0.999795 0.0202459i 0.00644491π-0.00644491\pi
−0.517431 + 0.855725i 0.673112π0.673112\pi
578578 11.3242 + 6.60998i 0.471024 + 0.274939i
579579 2.70323 + 12.1807i 0.112342 + 0.506214i
580580 −7.75249 5.42835i −0.321905 0.225400i
581581 18.7638 + 4.15984i 0.778454 + 0.172579i
582582 6.68514 21.2189i 0.277108 0.879552i
583583 −1.65125 3.17203i −0.0683879 0.131372i
584584 −4.15060 + 5.40917i −0.171753 + 0.223833i
585585 −14.1318 + 15.4358i −0.584276 + 0.638192i
586586 −19.0171 + 5.09562i −0.785590 + 0.210498i
587587 −10.2573 4.78307i −0.423366 0.197419i 0.199246 0.979949i 0.436151π-0.436151\pi
−0.622612 + 0.782531i 0.713928π0.713928\pi
588588 7.97570 + 2.13519i 0.328912 + 0.0880538i
589589 −0.808528 0.420893i −0.0333148 0.0173426i
590590 −4.03824 3.70037i −0.166252 0.152342i
591591 −1.29719 29.5606i −0.0533594 1.21596i
592592 2.41172 + 1.53644i 0.0991211 + 0.0631471i
593593 −15.3484 + 15.3484i −0.630283 + 0.630283i −0.948139 0.317856i 0.897037π-0.897037\pi
0.317856 + 0.948139i 0.397037π0.397037\pi
594594 −1.00220 + 1.09517i −0.0411209 + 0.0449355i
595595 15.7398 + 5.00391i 0.645271 + 0.205140i
596596 −5.45643 + 30.9450i −0.223504 + 1.26756i
597597 −14.1039 44.6974i −0.577234 1.82934i
598598 −8.44502 + 9.21612i −0.345343 + 0.376875i
599599 10.8373 + 12.9153i 0.442799 + 0.527707i 0.940569 0.339602i 0.110292π-0.110292\pi
−0.497771 + 0.867309i 0.665848π0.665848\pi
600600 1.25483 2.17455i 0.0512284 0.0887755i
601601 −5.39065 5.88286i −0.219889 0.239967i 0.617504 0.786567i 0.288144π-0.288144\pi
−0.837393 + 0.546601i 0.815922π0.815922\pi
602602 0.784847 5.96151i 0.0319880 0.242973i
603603 4.77443 + 8.26111i 0.194430 + 0.336418i
604604 −0.279965 + 1.04484i −0.0113916 + 0.0425141i
605605 −21.8498 6.88922i −0.888322 0.280087i
606606 2.68767 + 1.25256i 0.109179 + 0.0508818i
607607 0.162180 0.731547i 0.00658269 0.0296926i −0.972892 0.231261i 0.925715π-0.925715\pi
0.979474 + 0.201568i 0.0646038π0.0646038\pi
608608 9.09758 1.60415i 0.368956 0.0650569i
609609 3.59549 + 9.87173i 0.145697 + 0.400023i
610610 18.7967 1.64450i 0.761056 0.0665838i
611611 12.0927 + 20.9451i 0.489216 + 0.847347i
612612 −16.9753 + 3.72889i −0.686185 + 0.150732i
613613 −5.73710 + 9.93695i −0.231719 + 0.401350i −0.958314 0.285716i 0.907768π-0.907768\pi
0.726595 + 0.687066i 0.241102π0.241102\pi
614614 −10.3466 + 22.1883i −0.417553 + 0.895445i
615615 −26.0082 15.0082i −1.04875 0.605189i
616616 1.18768 + 1.41542i 0.0478529 + 0.0570288i
617617 −2.91968 2.67539i −0.117542 0.107707i 0.614669 0.788785i 0.289289π-0.289289\pi
−0.732211 + 0.681078i 0.761512π0.761512\pi
618618 7.38741 + 0.644668i 0.297165 + 0.0259323i
619619 7.36464 + 33.2198i 0.296010 + 1.33521i 0.860363 + 0.509681i 0.170237π0.170237\pi
−0.564353 + 0.825533i 0.690874π0.690874\pi
620620 1.21116 + 1.21116i 0.0486412 + 0.0486412i
621621 −13.6939 21.4637i −0.549518 0.861309i
622622 3.81019 1.57823i 0.152775 0.0632814i
623623 9.30470 2.06280i 0.372785 0.0826445i
624624 −4.22344 1.53615i −0.169073 0.0614951i
625625 −7.50250 + 20.6130i −0.300100 + 0.824518i
626626 −0.0144136 0.0457142i −0.000576084 0.00182710i
627627 −1.00309 + 0.132285i −0.0400594 + 0.00528294i
628628 18.3718 6.68678i 0.733114 0.266832i
629629 5.10690 + 14.1355i 0.203625 + 0.563621i
630630 8.39878 3.92094i 0.334615 0.156214i
631631 −9.62294 2.57846i −0.383083 0.102647i 0.0621378 0.998068i 0.480208π-0.480208\pi
−0.445221 + 0.895421i 0.646875π0.646875\pi
632632 24.2779 12.6382i 0.965721 0.502723i
633633 9.37830 29.7671i 0.372754 1.18314i
634634 1.10518 4.98514i 0.0438923 0.197985i
635635 11.9193 7.59344i 0.473003 0.301336i
636636 −13.4810 19.2437i −0.534555 0.763064i
637637 0.978014 + 11.1787i 0.0387503 + 0.442918i
638638 0.236150 0.881323i 0.00934926 0.0348919i
639639 5.02713 2.61979i 0.198870 0.103637i
640640 −19.7408 2.59893i −0.780324 0.102732i
641641 −26.4921 1.15667i −1.04638 0.0456857i −0.486028 0.873943i 0.661555π-0.661555\pi
−0.560348 + 0.828258i 0.689332π0.689332\pi
642642 0.616583 + 1.48763i 0.0243346 + 0.0587122i
643643 −8.79091 27.8812i −0.346680 1.09953i −0.952657 0.304046i 0.901662π-0.901662\pi
0.605978 0.795481i 0.292782π-0.292782\pi
644644 −11.8510 + 5.52619i −0.466993 + 0.217763i
645645 −8.05898 12.6439i −0.317322 0.497853i
646646 4.44306 + 2.32635i 0.174810 + 0.0915289i
647647 21.4217 0.842173 0.421087 0.907020i 0.361649π-0.361649\pi
0.421087 + 0.907020i 0.361649π0.361649\pi
648648 −13.5406 + 19.3745i −0.531926 + 0.761101i
649649 −0.477275 + 1.15224i −0.0187347 + 0.0452296i
650650 1.38663 + 0.244500i 0.0543880 + 0.00959006i
651651 −0.330595 1.87247i −0.0129570 0.0733881i
652652 −0.0911395 2.08744i −0.00356930 0.0817504i
653653 −15.1275 + 29.0597i −0.591986 + 1.13719i 0.384804 + 0.922998i 0.374269π0.374269\pi
−0.976791 + 0.214197i 0.931287π0.931287\pi
654654 −18.3794 7.60823i −0.718691 0.297505i
655655 −8.20932 3.82807i −0.320765 0.149575i
656656 0.841676 6.39317i 0.0328619 0.249611i
657657 4.18163 6.57026i 0.163141 0.256330i
658658 −1.39816 10.6201i −0.0545059 0.414013i
659659 23.4554 27.9531i 0.913695 1.08890i −0.0820395 0.996629i 0.526143π-0.526143\pi
0.995734 0.0922697i 0.0294122π-0.0294122\pi
660660 1.87241 + 0.329729i 0.0728833 + 0.0128347i
661661 15.7682 + 11.0410i 0.613313 + 0.429446i 0.838525 0.544864i 0.183419π-0.183419\pi
−0.225212 + 0.974310i 0.572307π0.572307\pi
662662 −1.90877 10.8252i −0.0741864 0.420732i
663663 −12.6486 19.9491i −0.491232 0.774760i
664664 −20.3588 17.0830i −0.790073 0.662950i
665665 6.10195 + 1.63501i 0.236624 + 0.0634031i
666666 7.48347 + 3.89144i 0.289979 + 0.150790i
667667 13.5517 + 7.82407i 0.524723 + 0.302949i
668668 −12.1455 0.530285i −0.469925 0.0205174i
669669 −11.5986 + 43.3249i −0.448428 + 1.67504i
670670 −2.38900 + 4.58922i −0.0922949 + 0.177297i
671671 −1.81574 3.89387i −0.0700959 0.150321i
672672 14.2105 + 13.0157i 0.548181 + 0.502092i
673673 −2.65092 11.9575i −0.102186 0.460929i −0.999797 0.0201420i 0.993588π-0.993588\pi
0.897612 0.440787i 0.145301π-0.145301\pi
674674 −3.38502 8.17216i −0.130386 0.314780i
675675 −1.21026 + 2.59992i −0.0465830 + 0.100071i
676676 2.89406i 0.111310i
677677 −1.06609 0.679171i −0.0409730 0.0261027i 0.516655 0.856194i 0.327177π-0.327177\pi
−0.557628 + 0.830091i 0.688288π0.688288\pi
678678 0.156729 + 0.496699i 0.00601916 + 0.0190756i
679679 29.7214 + 10.8177i 1.14060 + 0.415145i
680680 −16.1108 16.1875i −0.617819 0.620763i
681681 5.82361 44.3104i 0.223161 1.69798i
682682 −0.0697876 + 0.149660i −0.00267231 + 0.00573078i
683683 17.0343 + 22.1995i 0.651799 + 0.849441i 0.995991 0.0894588i 0.0285137π-0.0285137\pi
−0.344192 + 0.938899i 0.611847π0.611847\pi
684684 −6.42036 + 1.72338i −0.245489 + 0.0658949i
685685 −1.94369 14.7638i −0.0742644 0.564094i
686686 4.57813 14.5200i 0.174794 0.554376i
687687 −9.19253 + 19.7248i −0.350717 + 0.752549i
688688 1.84683 2.63755i 0.0704097 0.100556i
689689 18.3161 26.1581i 0.697789 0.996545i
690690 5.83166 12.5133i 0.222008 0.476372i
691691 12.4013 39.3318i 0.471767 1.49625i −0.355625 0.934629i 0.615732π-0.615732\pi
0.827392 0.561625i 0.189824π-0.189824\pi
692692 1.37191 + 10.4207i 0.0521522 + 0.396135i
693693 −1.49305 1.49173i −0.0567164 0.0566662i
694694 −1.42300 1.85449i −0.0540162 0.0703953i
695695 13.4792 28.9063i 0.511295 1.09648i
696696 1.89307 14.4039i 0.0717568 0.545980i
697697 24.0224 23.9085i 0.909913 0.905599i
698698 10.9642 + 3.99066i 0.415002 + 0.151049i
699699 9.47159 + 30.0169i 0.358248 + 1.13534i
700700 1.24222 + 0.791380i 0.0469514 + 0.0299113i
701701 40.7151i 1.53779i 0.639377 + 0.768893i 0.279192π0.279192\pi
−0.639377 + 0.768893i 0.720808π0.720808\pi
702702 −12.8069 3.42248i −0.483364 0.129173i
703703 2.19993 + 5.31110i 0.0829720 + 0.200312i
704704 −0.236441 1.06652i −0.00891120 0.0401958i
705705 −19.6971 18.0411i −0.741837 0.679467i
706706 −3.80644 8.16294i −0.143257 0.307216i
707707 −1.94658 + 3.73934i −0.0732086 + 0.140632i
708708 −2.11910 + 7.91559i −0.0796407 + 0.297486i
709709 −29.3508 1.28148i −1.10229 0.0481272i −0.514765 0.857331i 0.672121π-0.672121\pi
−0.587528 + 0.809204i 0.699899π0.699899\pi
710710 2.66203 + 1.53693i 0.0999043 + 0.0576798i
711711 −26.3606 + 16.8099i −0.988599 + 0.630422i
712712 −12.7298 3.41095i −0.477071 0.127831i
713713 −2.16948 1.82041i −0.0812476 0.0681749i
714714 1.79446 + 10.3068i 0.0671561 + 0.385721i
715715 0.448696 + 2.54468i 0.0167803 + 0.0951656i
716716 −7.47841 5.23644i −0.279481 0.195695i
717717 −6.01897 1.05993i −0.224783 0.0395840i
718718 −7.36491 + 8.77716i −0.274856 + 0.327561i
719719 −3.53914 26.8824i −0.131988 1.00255i −0.921382 0.388659i 0.872939π-0.872939\pi
0.789394 0.613887i 0.210395π-0.210395\pi
720720 4.95876 + 0.214306i 0.184802 + 0.00798673i
721721 −1.37609 + 10.4525i −0.0512483 + 0.389270i
722722 −11.5432 5.38268i −0.429593 0.200323i
723723 −16.4263 6.79973i −0.610900 0.252885i
724724 −17.1732 + 32.9894i −0.638236 + 1.22604i
725725 −0.0768835 1.76092i −0.00285538 0.0653990i
726726 −2.52315 14.2910i −0.0936428 0.530388i
727727 27.1404 + 4.78558i 1.00658 + 0.177487i 0.652550 0.757746i 0.273699π-0.273699\pi
0.354032 + 0.935233i 0.384810π0.384810\pi
728728 −6.31400 + 15.2434i −0.234013 + 0.564956i
729729 13.4690 23.4006i 0.498850 0.866688i
730730 4.22301 0.156301
731731 16.1523 5.05062i 0.597413 0.186804i
732732 −15.1725 23.8044i −0.560792 0.879837i
733733 39.3028 18.3272i 1.45168 0.676931i 0.472766 0.881188i 0.343256π-0.343256\pi
0.978917 + 0.204258i 0.0654780π0.0654780\pi
734734 6.93257 + 21.9873i 0.255886 + 0.811566i
735735 −4.74519 11.4487i −0.175029 0.422293i
736736 28.6745 + 1.25196i 1.05696 + 0.0461478i
737737 1.16801 + 0.153771i 0.0430242 + 0.00566424i
738738 0.821261 19.0029i 0.0302310 0.699505i
739739 −11.1550 + 41.6312i −0.410345 + 1.53143i 0.383635 + 0.923485i 0.374672π0.374672\pi
−0.793980 + 0.607944i 0.791995π0.791995\pi
740740 −0.941488 10.7613i −0.0346098 0.395591i
741741 −5.18377 7.39971i −0.190431 0.271835i
742742 −11.9283 + 7.59917i −0.437902 + 0.278974i
743743 −7.69697 + 34.7188i −0.282375 + 1.27371i 0.598792 + 0.800904i 0.295647π0.295647\pi
−0.881167 + 0.472805i 0.843241π0.843241\pi
744744 −0.790089 + 2.50778i −0.0289661 + 0.0919396i
745745 41.8360 21.7784i 1.53275 0.797901i
746746 −19.0677 5.10918i −0.698119 0.187060i
747747 24.8750 + 17.4013i 0.910130 + 0.636680i
748748 −0.911515 + 1.94268i −0.0333283 + 0.0710315i
749749 −2.15137 + 0.783036i −0.0786095 + 0.0286115i
750750 −15.5086 + 2.04523i −0.566292 + 0.0746812i
751751 −13.6682 43.3499i −0.498758 1.58186i −0.782302 0.622900i 0.785954π-0.785954\pi
0.283544 0.958959i 0.408490π-0.408490\pi
752752 1.96182 5.39005i 0.0715401 0.196555i
753753 −29.7952 10.8371i −1.08580 0.394926i
754754 7.95440 1.76345i 0.289682 0.0642210i
755755 1.50005 0.621341i 0.0545924 0.0226129i
756756 −11.0070 8.43439i −0.400322 0.306756i
757757 22.8209 + 22.8209i 0.829441 + 0.829441i 0.987439 0.157998i 0.0505041π-0.0505041\pi
−0.157998 + 0.987439i 0.550504π0.550504\pi
758758 −1.38196 6.23360i −0.0501949 0.226415i
759759 −3.13163 0.273284i −0.113671 0.00991959i
760760 −6.44041 5.90155i −0.233618 0.214072i
761761 7.47222 + 8.90505i 0.270868 + 0.322808i 0.884282 0.466954i 0.154649π-0.154649\pi
−0.613414 + 0.789762i 0.710204π0.710204\pi
762762 7.75367 + 4.47430i 0.280886 + 0.162087i
763763 11.9518 25.6308i 0.432686 0.927897i
764764 9.27101 16.0579i 0.335413 0.580953i
765765 19.9517 + 16.8073i 0.721356 + 0.607671i
766766 −8.28320 14.3469i −0.299284 0.518375i
767767 −11.0945 + 0.970643i −0.400599 + 0.0350479i
768768 −7.81262 21.4502i −0.281914 0.774018i
769769 18.2185 3.21241i 0.656975 0.115842i 0.164784 0.986330i 0.447307π-0.447307\pi
0.492191 + 0.870487i 0.336196π0.336196\pi
770770 0.247700 1.11730i 0.00892648 0.0402648i
771771 −40.1523 18.7125i −1.44605 0.673915i
772772 9.65332 + 3.04368i 0.347430 + 0.109544i
773773 −3.67349 + 13.7097i −0.132126 + 0.493102i −0.999993 0.00369477i 0.998824π-0.998824\pi
0.867867 + 0.496797i 0.165491π0.165491\pi
774774 4.74514 8.22723i 0.170561 0.295722i
775775 −0.0416380 + 0.316272i −0.00149568 + 0.0113608i
776776 −29.5478 32.2457i −1.06070 1.15755i
777777 −5.99361 + 10.3865i −0.215019 + 0.372615i
778778 3.77137 + 4.49454i 0.135210 + 0.161137i
779779 8.75795 9.55763i 0.313786 0.342438i
780780 5.10873 + 16.1903i 0.182922 + 0.579706i
781781 0.121540 0.689290i 0.00434906 0.0246647i
782782 11.9128 + 10.0444i 0.426000 + 0.359185i
783783 −0.712846 + 16.5793i −0.0254751 + 0.592496i
784784 1.88187 1.88187i 0.0672096 0.0672096i
785785 −24.7501 15.7676i −0.883369 0.562768i
786786 −0.251539 5.73209i −0.00897209 0.204457i
787787 13.9206 + 12.7559i 0.496217 + 0.454699i 0.884296 0.466927i 0.154639π-0.154639\pi
−0.388079 + 0.921626i 0.626861π0.626861\pi
788788 −21.2913 11.0836i −0.758472 0.394836i
789789 38.3966 + 10.2792i 1.36696 + 0.365951i
790790 −15.3644 7.16453i −0.546640 0.254903i
791791 −0.715250 + 0.191651i −0.0254314 + 0.00681432i
792792 0.878833 + 2.78301i 0.0312280 + 0.0988899i
793793 23.3554 30.4373i 0.829374 1.08086i
794794 0.475844 + 0.914088i 0.0168871 + 0.0324398i
795795 −10.5977 + 33.6376i −0.375862 + 1.19300i
796796 −37.1209 8.22950i −1.31571 0.291687i
797797 3.01551 + 2.11148i 0.106815 + 0.0747926i 0.625764 0.780013i 0.284788π-0.284788\pi
−0.518949 + 0.854805i 0.673676π0.673676\pi
798798 0.866951 + 3.90647i 0.0306897 + 0.138288i
799799 25.4652 16.1381i 0.900893 0.570926i
800800 −1.61648 2.79983i −0.0571512 0.0989888i
801801 14.8262 + 2.60750i 0.523860 + 0.0921317i
802802 −6.52367 8.50181i −0.230359 0.300209i
803803 −0.328883 0.903599i −0.0116060 0.0318873i
804804 7.74038 0.00171202i 0.272982 6.03781e-5i
805805 17.4096 + 9.06288i 0.613609 + 0.319424i
806806 −1.47316 + 0.0643197i −0.0518900 + 0.00226557i
807807 −5.26382 + 23.7684i −0.185295 + 0.836688i
808808 4.77517 3.34361i 0.167990 0.117628i
809809 −26.6689 + 11.0466i −0.937628 + 0.388378i −0.798567 0.601906i 0.794408π-0.794408\pi
−0.139061 + 0.990284i 0.544408π0.544408\pi
810810 14.6260 0.651548i 0.513904 0.0228931i
811811 −40.4470 16.7537i −1.42029 0.588302i −0.465353 0.885125i 0.654073π-0.654073\pi
−0.954932 + 0.296824i 0.904073π0.904073\pi
812812 8.39339 + 1.47998i 0.294550 + 0.0519372i
813813 −6.81736 + 1.20364i −0.239095 + 0.0422135i
814814 0.943863 0.440131i 0.0330824 0.0154266i
815815 −2.40250 + 2.01594i −0.0841560 + 0.0706153i
816816 −1.69611 + 5.33923i −0.0593758 + 0.186910i
817817 6.08266 2.21391i 0.212805 0.0774547i
818818 1.14642 + 4.27848i 0.0400835 + 0.149594i
819819 5.65932 17.9768i 0.197753 0.628160i
820820 −21.0959 + 12.1797i −0.736702 + 0.425335i
821821 7.20288 + 13.8366i 0.251382 + 0.482901i 0.979207 0.202862i 0.0650243π-0.0650243\pi
−0.727825 + 0.685763i 0.759469π0.759469\pi
822822 7.72547 5.41198i 0.269457 0.188764i
823823 4.40511 + 6.91464i 0.153553 + 0.241029i 0.911513 0.411271i 0.134915π-0.134915\pi
−0.757960 + 0.652301i 0.773804π0.773804\pi
824824 8.36178 11.9419i 0.291296 0.416014i
825825 0.163568 + 0.314042i 0.00569471 + 0.0109335i
826826 4.70425 + 1.48324i 0.163682 + 0.0516087i
827827 −30.5647 + 39.8327i −1.06284 + 1.38512i −0.144418 + 0.989517i 0.546131π0.546131\pi
−0.918422 + 0.395603i 0.870536π0.870536\pi
828828 −20.6339 + 0.910039i −0.717077 + 0.0316261i
829829 −47.2945 27.3055i −1.64261 0.948360i −0.979902 0.199479i 0.936075π-0.936075\pi
−0.662705 0.748880i 0.730592π-0.730592\pi
830830 −0.718018 + 16.4453i −0.0249228 + 0.570825i
831831 −43.2916 + 5.70919i −1.50177 + 0.198050i
832832 7.47264 6.27029i 0.259067 0.217383i
833833 13.8727 1.79285i 0.480662 0.0621185i
834834 20.1836 0.885706i 0.698899 0.0306695i
835835 10.4666 + 14.9478i 0.362210 + 0.517290i
836836 −0.314099 + 0.758301i −0.0108633 + 0.0262264i
837837 0.648099 2.93259i 0.0224016 0.101365i
838838 26.2993 + 10.8935i 0.908494 + 0.376311i
839839 17.5875 3.89905i 0.607187 0.134610i 0.0978848 0.995198i 0.468792π-0.468792\pi
0.509303 + 0.860588i 0.329903π0.329903\pi
840840 1.58414 18.1531i 0.0546582 0.626341i
841841 7.94551 + 17.0392i 0.273983 + 0.587559i
842842 26.5119 + 2.31949i 0.913660 + 0.0799349i
843843 6.30323 + 23.5032i 0.217095 + 0.809492i
844844 −17.1046 18.6664i −0.588766 0.642525i
845845 3.44633 2.64447i 0.118558 0.0909724i
846846 4.37182 16.3448i 0.150306 0.561945i
847847 20.4553 2.69300i 0.702854 0.0925325i
848848 −7.54470 + 0.660076i −0.259086 + 0.0226671i
849849 24.8496 22.7805i 0.852835 0.781826i
850850 0.233230 1.73960i 0.00799972 0.0596678i
851851 3.10152 + 17.5896i 0.106319 + 0.602964i
852852 0.199576 4.59437i 0.00683737 0.157400i
853853 6.57031 3.42029i 0.224963 0.117108i −0.345539 0.938404i 0.612304π-0.612304\pi
0.570503 + 0.821296i 0.306748π0.306748\pi
854854 −14.7156 + 8.49605i −0.503557 + 0.290729i
855855 7.91888 + 6.07081i 0.270820 + 0.207617i
856856 3.13875 + 0.413224i 0.107280 + 0.0141237i
857857 −1.94903 + 1.78596i −0.0665776 + 0.0610071i −0.708190 0.706022i 0.750488π-0.750488\pi
0.641612 + 0.767029i 0.278266π0.278266\pi
858858 −1.29830 + 0.996674i −0.0443231 + 0.0340259i
859859 −35.1708 3.07705i −1.20001 0.104987i −0.530432 0.847727i 0.677970π-0.677970\pi
−0.669580 + 0.742740i 0.733526π0.733526\pi
860860 −12.1519 + 0.530562i −0.414375 + 0.0180920i
861861 26.9393 + 2.35088i 0.918090 + 0.0801179i
862862 2.75602 4.32608i 0.0938704 0.147347i
863863 8.33045i 0.283572i 0.989897 + 0.141786i 0.0452844π0.0452844\pi
−0.989897 + 0.141786i 0.954716π0.954716\pi
864864 12.8819 + 27.5776i 0.438252 + 0.938208i
865865 11.1557 11.1557i 0.379304 0.379304i
866866 5.04433 28.6078i 0.171413 0.972132i
867867 −24.1961 + 16.7794i −0.821743 + 0.569858i
868868 −1.44948 0.527566i −0.0491984 0.0179068i
869869 −0.336437 + 3.84549i −0.0114128 + 0.130449i
870870 −7.79173 + 4.50085i −0.264164 + 0.152593i
871871 3.59802 + 9.88548i 0.121914 + 0.334957i
872872 −31.0249 + 23.8063i −1.05064 + 0.806182i
873873 36.8481 + 33.7351i 1.24712 + 1.14176i
874874 4.72837 + 3.62821i 0.159939 + 0.122726i
875875 −1.93830 22.1549i −0.0655266 0.748972i
876876 −2.91853 5.60342i −0.0986081 0.189322i
877877 2.56280 + 4.02280i 0.0865397 + 0.135840i 0.883922 0.467634i 0.154894π-0.154894\pi
−0.797382 + 0.603475i 0.793782π0.793782\pi
878878 −24.1352 + 15.3758i −0.814523 + 0.518908i
879879 7.66763 43.5416i 0.258623 1.46862i
880880 0.393917 0.469452i 0.0132789 0.0158252i
881881 −45.7738 + 6.02623i −1.54216 + 0.203029i −0.853127 0.521703i 0.825297π-0.825297\pi
−0.689031 + 0.724732i 0.741963π0.741963\pi
882882 5.04335 6.01584i 0.169819 0.202564i
883883 4.08636 7.07778i 0.137517 0.238186i −0.789039 0.614343i 0.789421π-0.789421\pi
0.926556 + 0.376157i 0.122755π0.122755\pi
884884 −19.1458 + 0.790340i −0.643943 + 0.0265820i
885885 11.3625 4.70943i 0.381945 0.158306i
886886 1.93159 22.0781i 0.0648929 0.741729i
887887 4.08343 4.45628i 0.137108 0.149627i −0.664918 0.746917i 0.731533π-0.731533\pi
0.802026 + 0.597289i 0.203756π0.203756\pi
888888 13.9833 8.91271i 0.469250 0.299091i
889889 −6.83830 + 10.7340i −0.229349 + 0.360006i
890890 3.12375 + 7.54141i 0.104708 + 0.252789i
891891 −1.27846 3.07878i −0.0428302 0.103143i
892892 25.7274 + 25.7274i 0.861419 + 0.861419i
893893 9.44590 6.61409i 0.316095 0.221332i
894894 24.4767 + 17.1307i 0.818623 + 0.572936i
895895 0.597733 + 13.6903i 0.0199800 + 0.457617i
896896 17.1012 5.39197i 0.571309 0.180133i
897897 −10.7479 25.9315i −0.358862 0.865828i
898898 −0.468796 + 10.7372i −0.0156439 + 0.358304i
899899 0.477756 + 1.78301i 0.0159341 + 0.0594667i
900900 1.33524 + 1.90512i 0.0445079 + 0.0635041i
901901 −33.5214 21.4676i −1.11676 0.715191i
902902 −1.79902 1.50956i −0.0599010 0.0502629i
903903 11.3897 + 7.25251i 0.379026 + 0.241348i
904904 0.999663 + 0.221620i 0.0332483 + 0.00737097i
905905 54.9768 9.69389i 1.82749 0.322236i
906906 0.787997 + 0.660911i 0.0261794 + 0.0219573i
907907 8.01995 25.4360i 0.266298 0.844590i −0.721979 0.691915i 0.756767π-0.756767\pi
0.988277 0.152674i 0.0487885π-0.0487885\pi
908908 −28.7630 22.0707i −0.954535 0.732440i
909909 −5.09899 + 4.28240i −0.169123 + 0.142038i
910910 9.87114 2.64496i 0.327225 0.0876797i
911911 20.3072 18.6081i 0.672808 0.616515i −0.264761 0.964314i 0.585293π-0.585293\pi
0.937569 + 0.347799i 0.113071π0.113071\pi
912912 −0.554128 + 2.06987i −0.0183490 + 0.0685401i
913913 3.57473 1.12711i 0.118306 0.0373018i
914914 8.50877 23.3777i 0.281445 0.773264i
915915 −14.4831 + 39.8193i −0.478795 + 1.31638i
916916 10.1258 + 14.4611i 0.334565 + 0.477808i
917917 8.15720 0.269374
918918 −3.60422 + 16.1268i −0.118957 + 0.532263i
919919 6.90562 0.227795 0.113898 0.993492i 0.463666π-0.463666\pi
0.113898 + 0.993492i 0.463666π0.463666\pi
920920 −15.5672 22.2322i −0.513234 0.732974i
921921 −35.3480 42.1072i −1.16476 1.38748i
922922 −9.56444 + 26.2781i −0.314988 + 0.865422i
923923 5.96080 1.87943i 0.196202 0.0618623i
924924 −1.65371 + 0.443502i −0.0544031 + 0.0145902i
925925 1.48329 1.35919i 0.0487703 0.0446897i
926926 −1.12090 + 0.300344i −0.0368350 + 0.00986992i
927927 −8.31977 + 14.4250i −0.273257 + 0.473779i
928928 −14.8417 11.3885i −0.487204 0.373845i
929929 −13.3790 + 42.4328i −0.438951 + 1.39217i 0.432475 + 0.901646i 0.357640π0.357640\pi
−0.871426 + 0.490528i 0.836804π0.836804\pi
930930 1.53020 0.557331i 0.0501772 0.0182756i
931931 5.26899 0.929066i 0.172684 0.0304489i
932932 24.9288 + 5.52658i 0.816570 + 0.181029i
933933 −0.401921 + 9.25246i −0.0131583 + 0.302912i
934934 1.66611 + 1.39803i 0.0545167 + 0.0457449i
935935 3.14630 0.689678i 0.102895 0.0225549i
936936 −18.4197 + 18.4360i −0.602067 + 0.602600i
937937 12.6944 + 47.3760i 0.414707 + 1.54771i 0.785422 + 0.618961i 0.212446π0.212446\pi
−0.370715 + 0.928747i 0.620887π0.620887\pi
938938 0.203235 4.65485i 0.00663586 0.151986i
939939 0.106720 + 0.0140260i 0.00348269 + 0.000457721i
940940 −20.6656 + 6.51583i −0.674037 + 0.212523i
941941 −0.433304 9.92429i −0.0141253 0.323523i −0.992928 0.118717i 0.962122π-0.962122\pi
0.978803 0.204805i 0.0656561π-0.0656561\pi
942942 1.61601 18.5182i 0.0526524 0.603357i
943943 32.9928 23.1018i 1.07439 0.752298i
944944 1.86769 + 1.86769i 0.0607881 + 0.0607881i
945945 0.0138112 + 20.8145i 0.000449279 + 0.677094i
946946 −0.448757 1.08339i −0.0145903 0.0352242i
947947 −29.8442 + 46.8460i −0.969805 + 1.52229i −0.121628 + 0.992576i 0.538812π0.538812\pi
−0.848177 + 0.529713i 0.822300π0.822300\pi
948948 1.11190 + 25.3381i 0.0361129 + 0.822944i
949949 5.80107 6.33075i 0.188311 0.205505i
950950 0.0585102 0.668774i 0.00189832 0.0216979i
951951 9.09853 + 6.97835i 0.295040 + 0.226289i
952952 19.3101 + 7.08031i 0.625843 + 0.229474i
953953 −15.5096 + 26.8634i −0.502405 + 0.870191i 0.497591 + 0.867412i 0.334218π0.334218\pi
−0.999996 + 0.00277959i 0.999115π0.999115\pi
954954 −21.9984 + 3.88895i −0.712226 + 0.125909i
955955 −27.5936 + 3.63277i −0.892908 + 0.117554i
956956 −3.18687 + 3.79797i −0.103071 + 0.122835i
957957 1.56986 + 1.31668i 0.0507464 + 0.0425621i
958958 −20.0135 + 12.7500i −0.646608 + 0.411935i
959959 7.20534 + 11.3101i 0.232672 + 0.365223i
960960 −5.78653 + 9.08747i −0.186760 + 0.293297i
961961 2.67271 + 30.5492i 0.0862165 + 0.985459i
962962 7.37793 + 5.66128i 0.237874 + 0.182527i
963963 −3.61285 0.156139i −0.116422 0.00503152i
964964 −11.4418 + 8.77961i −0.368516 + 0.282772i
965965 −5.19627 14.2766i −0.167274 0.459581i
966966 0.00274983 + 12.4325i 8.84742e−5 + 0.400010i
967967 2.26273 25.8631i 0.0727644 0.831701i −0.868865 0.495049i 0.835150π-0.835150\pi
0.941629 0.336652i 0.109294π-0.109294\pi
968968 −26.8091 9.75770i −0.861676 0.313624i
969969 −8.94974 + 6.83678i −0.287507 + 0.219629i
970970 −4.70403 + 26.6779i −0.151037 + 0.856574i
971971 3.54063 3.54063i 0.113624 0.113624i −0.648009 0.761633i 0.724398π-0.724398\pi
0.761633 + 0.648009i 0.224398π0.224398\pi
972972 −10.9726 18.9566i −0.351945 0.608033i
973973 28.7227i 0.920808i
974974 2.03251 3.19040i 0.0651259 0.102227i
975975 −1.81300 + 2.59045i −0.0580624 + 0.0829607i
976976 −9.09038 + 0.396894i −0.290976 + 0.0127043i
977977 −30.6632 2.68268i −0.981003 0.0858266i −0.414643 0.909984i 0.636093π-0.636093\pi
−0.566360 + 0.824158i 0.691649π0.691649\pi
978978 −1.83554 0.759831i −0.0586942 0.0242967i
979979 1.37036 1.25571i 0.0437970 0.0401326i
980980 −9.96767 1.31227i −0.318406 0.0419189i
981981 32.9205 30.1929i 1.05107 0.963984i
982982 −15.5891 + 9.00035i −0.497467 + 0.287213i
983983 −6.28883 + 3.27376i −0.200583 + 0.104417i −0.559079 0.829114i 0.688845π-0.688845\pi
0.358496 + 0.933531i 0.383290π0.383290\pi
984984 −31.5415 20.0844i −1.00551 0.640266i
985985 6.25643 + 35.4820i 0.199346 + 1.13055i
986986 −2.60532 9.81645i −0.0829703 0.312620i
987987 22.9427 + 7.22821i 0.730273 + 0.230077i
988988 −7.30138 + 0.638788i −0.232288 + 0.0203226i
989989 19.9394 2.62507i 0.634035 0.0834723i
990990 1.03617 1.48120i 0.0329316 0.0470755i
991991 28.7828 22.0858i 0.914315 0.701578i −0.0403741 0.999185i 0.512855π-0.512855\pi
0.954689 + 0.297606i 0.0961883π0.0961883\pi
992992 2.28739 + 2.49625i 0.0726247 + 0.0792560i
993993 23.8445 + 6.38345i 0.756681 + 0.202573i
994994 −2.75763 0.241262i −0.0874668 0.00765236i
995995 24.1195 + 51.7243i 0.764638 + 1.63977i
996996 22.3172 10.4127i 0.707146 0.329938i
997997 28.9288 6.41337i 0.916185 0.203113i 0.266958 0.963708i 0.413981π-0.413981\pi
0.649227 + 0.760595i 0.275093π0.275093\pi
998998 10.9464 + 4.53413i 0.346501 + 0.143525i
999999 −15.0195 + 11.5407i −0.475195 + 0.365131i
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 459.2.ba.a.25.20 1248
17.15 even 8 inner 459.2.ba.a.457.33 yes 1248
27.13 even 9 inner 459.2.ba.a.229.33 yes 1248
459.202 even 72 inner 459.2.ba.a.202.20 yes 1248
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
459.2.ba.a.25.20 1248 1.1 even 1 trivial
459.2.ba.a.202.20 yes 1248 459.202 even 72 inner
459.2.ba.a.229.33 yes 1248 27.13 even 9 inner
459.2.ba.a.457.33 yes 1248 17.15 even 8 inner