Properties

Label 25.3.f.a.23.3
Level 2525
Weight 33
Character 25.23
Analytic conductor 0.6810.681
Analytic rank 00
Dimension 3232
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,3,Mod(2,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 25=52 25 = 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 25.f (of order 2020, degree 88, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.6812006609010.681200660901
Analytic rank: 00
Dimension: 3232
Relative dimension: 44 over Q(ζ20)\Q(\zeta_{20})
Twist minimal: yes
Sato-Tate group: SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Embedding invariants

Embedding label 23.3
Character χ\chi == 25.23
Dual form 25.3.f.a.12.3

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+(0.09334650.589367i)q2+(0.2107300.107372i)q3+(3.46559+1.12604i)q4+(3.314323.74370i)q5+(0.04361080.134220i)q6+(7.64532+7.64532i)q7+(2.070764.06409i)q8+(5.25719+7.23590i)q9+(2.51579+1.60389i)q10+(7.338685.33186i)q11+(0.8512100.134818i)q12+(2.1230613.4044i)q13+(3.79223+5.21956i)q14+(1.100400.433046i)q15+(9.59007+6.96760i)q16+(0.704962+0.359196i)q17+(3.77386+3.77386i)q18+(13.56964.40902i)q19+(7.2705016.7062i)q20+(0.790204+2.43200i)q21+(2.457384.82288i)q22+(13.5597+2.14764i)q231.07877iq24+(3.03063+24.8156i)q258.09832q26+(0.663895+4.19167i)q27+(35.1044+17.8866i)q28+(36.630611.9020i)q29+(0.357941+0.608115i)q30+(2.875308.84925i)q31+(17.902817.9028i)q32+(0.9739871.91156i)q33+(0.2775040.381951i)q34+(53.9608+3.28280i)q35+(26.3671+19.1568i)q36+(9.138201.44735i)q37+(1.331868.40902i)q38+(1.886662.59677i)q39+(22.0779+5.71738i)q40+(33.735124.5100i)q41+(1.35958+0.692738i)q42+(49.4021+49.4021i)q43+(31.436710.2144i)q44+(44.51304.30070i)q45+(2.531507.79114i)q46+(9.65116+18.9415i)q47+(2.76905+0.438574i)q4867.9017iq49+(14.3426+4.10260i)q50+0.187125q51+(7.7362748.8449i)q52+(56.8742+28.9788i)q53+(2.40846+0.782556i)q54+(44.28369.80236i)q55+(15.2397+46.9029i)q56+(2.386112.38611i)q57+(10.4340+20.4778i)q58+(45.6440+62.8235i)q59+(3.325902.73985i)q60+(11.41538.29369i)q61+(5.48385+0.868557i)q62+(15.127995.5136i)q63+(18.9902+26.1378i)q64+(43.1458+52.3747i)q65+(1.035690.752473i)q66+(46.897823.8956i)q67+(2.03864+2.03864i)q68+(3.088031.00336i)q69+(6.9718331.4963i)q70+(0.846117+2.60408i)q71+(18.5210+36.3495i)q72+(60.7976+9.62940i)q735.52086iq74+(2.02587+5.55481i)q75+51.9912q76+(15.3427+96.8703i)q77+(1.70656+0.869536i)q78+(6.189052.01094i)q79+(5.6999258.9952i)q80+(24.564675.6022i)q81+(17.5944+17.5944i)q82+(50.9593100.013i)q83+(5.47704+7.53850i)q84+(0.9917423.82966i)q85+(33.727424.5044i)q86+(8.99712+1.42500i)q87+(6.4725540.8661i)q88+(65.5853+90.2704i)q89+(1.6204526.6360i)q90+(118.713+86.2498i)q91+(44.5739+22.7115i)q92+(1.556081.55608i)q93+(12.06443.91995i)q94+(61.479936.1875i)q95+(1.850405.69493i)q96+(58.6053115.019i)q97+(40.01906.33839i)q98+81.1325iq99+O(q100)q+(0.0933465 - 0.589367i) q^{2} +(0.210730 - 0.107372i) q^{3} +(3.46559 + 1.12604i) q^{4} +(-3.31432 - 3.74370i) q^{5} +(-0.0436108 - 0.134220i) q^{6} +(-7.64532 + 7.64532i) q^{7} +(2.07076 - 4.06409i) q^{8} +(-5.25719 + 7.23590i) q^{9} +(-2.51579 + 1.60389i) q^{10} +(7.33868 - 5.33186i) q^{11} +(0.851210 - 0.134818i) q^{12} +(-2.12306 - 13.4044i) q^{13} +(3.79223 + 5.21956i) q^{14} +(-1.10040 - 0.433046i) q^{15} +(9.59007 + 6.96760i) q^{16} +(0.704962 + 0.359196i) q^{17} +(3.77386 + 3.77386i) q^{18} +(13.5696 - 4.40902i) q^{19} +(-7.27050 - 16.7062i) q^{20} +(-0.790204 + 2.43200i) q^{21} +(-2.45738 - 4.82288i) q^{22} +(13.5597 + 2.14764i) q^{23} -1.07877i q^{24} +(-3.03063 + 24.8156i) q^{25} -8.09832 q^{26} +(-0.663895 + 4.19167i) q^{27} +(-35.1044 + 17.8866i) q^{28} +(-36.6306 - 11.9020i) q^{29} +(-0.357941 + 0.608115i) q^{30} +(-2.87530 - 8.84925i) q^{31} +(17.9028 - 17.9028i) q^{32} +(0.973987 - 1.91156i) q^{33} +(0.277504 - 0.381951i) q^{34} +(53.9608 + 3.28280i) q^{35} +(-26.3671 + 19.1568i) q^{36} +(9.13820 - 1.44735i) q^{37} +(-1.33186 - 8.40902i) q^{38} +(-1.88666 - 2.59677i) q^{39} +(-22.0779 + 5.71738i) q^{40} +(-33.7351 - 24.5100i) q^{41} +(1.35958 + 0.692738i) q^{42} +(49.4021 + 49.4021i) q^{43} +(31.4367 - 10.2144i) q^{44} +(44.5130 - 4.30070i) q^{45} +(2.53150 - 7.79114i) q^{46} +(9.65116 + 18.9415i) q^{47} +(2.76905 + 0.438574i) q^{48} -67.9017i q^{49} +(14.3426 + 4.10260i) q^{50} +0.187125 q^{51} +(7.73627 - 48.8449i) q^{52} +(-56.8742 + 28.9788i) q^{53} +(2.40846 + 0.782556i) q^{54} +(-44.2836 - 9.80236i) q^{55} +(15.2397 + 46.9029i) q^{56} +(2.38611 - 2.38611i) q^{57} +(-10.4340 + 20.4778i) q^{58} +(-45.6440 + 62.8235i) q^{59} +(-3.32590 - 2.73985i) q^{60} +(11.4153 - 8.29369i) q^{61} +(-5.48385 + 0.868557i) q^{62} +(-15.1279 - 95.5136i) q^{63} +(18.9902 + 26.1378i) q^{64} +(-43.1458 + 52.3747i) q^{65} +(-1.03569 - 0.752473i) q^{66} +(-46.8978 - 23.8956i) q^{67} +(2.03864 + 2.03864i) q^{68} +(3.08803 - 1.00336i) q^{69} +(6.97183 - 31.4963i) q^{70} +(-0.846117 + 2.60408i) q^{71} +(18.5210 + 36.3495i) q^{72} +(60.7976 + 9.62940i) q^{73} -5.52086i q^{74} +(2.02587 + 5.55481i) q^{75} +51.9912 q^{76} +(-15.3427 + 96.8703i) q^{77} +(-1.70656 + 0.869536i) q^{78} +(-6.18905 - 2.01094i) q^{79} +(-5.69992 - 58.9952i) q^{80} +(-24.5646 - 75.6022i) q^{81} +(-17.5944 + 17.5944i) q^{82} +(50.9593 - 100.013i) q^{83} +(-5.47704 + 7.53850i) q^{84} +(-0.991742 - 3.82966i) q^{85} +(33.7274 - 24.5044i) q^{86} +(-8.99712 + 1.42500i) q^{87} +(-6.47255 - 40.8661i) q^{88} +(65.5853 + 90.2704i) q^{89} +(1.62045 - 26.6360i) q^{90} +(118.713 + 86.2498i) q^{91} +(44.5739 + 22.7115i) q^{92} +(-1.55608 - 1.55608i) q^{93} +(12.0644 - 3.91995i) q^{94} +(-61.4799 - 36.1875i) q^{95} +(1.85040 - 5.69493i) q^{96} +(-58.6053 - 115.019i) q^{97} +(-40.0190 - 6.33839i) q^{98} +81.1325i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q10q210q310q410q56q610q710q810q910q106q1110q1210q1310q1410q15+2q16+60q17+140q18+90q19++170q98+O(q100) 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19}+ \cdots + 170 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/25Z)×\left(\mathbb{Z}/25\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(1120)e\left(\frac{11}{20}\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 0.0933465 0.589367i 0.0466733 0.294683i −0.953300 0.302026i 0.902337π-0.902337\pi
0.999973 + 0.00734232i 0.00233715π0.00233715\pi
33 0.210730 0.107372i 0.0702435 0.0357908i −0.418516 0.908209i 0.637450π-0.637450\pi
0.488759 + 0.872419i 0.337450π0.337450\pi
44 3.46559 + 1.12604i 0.866397 + 0.281509i
55 −3.31432 3.74370i −0.662863 0.748741i
66 −0.0436108 0.134220i −0.00726847 0.0223701i
77 −7.64532 + 7.64532i −1.09219 + 1.09219i −0.0968934 + 0.995295i 0.530891π0.530891\pi
−0.995295 + 0.0968934i 0.969109π0.969109\pi
88 2.07076 4.06409i 0.258845 0.508011i
99 −5.25719 + 7.23590i −0.584132 + 0.803989i
1010 −2.51579 + 1.60389i −0.251579 + 0.160389i
1111 7.33868 5.33186i 0.667152 0.484715i −0.201918 0.979402i 0.564718π-0.564718\pi
0.869071 + 0.494688i 0.164718π0.164718\pi
1212 0.851210 0.134818i 0.0709342 0.0112349i
1313 −2.12306 13.4044i −0.163312 1.03111i −0.924111 0.382124i 0.875193π-0.875193\pi
0.760799 0.648987i 0.224807π-0.224807\pi
1414 3.79223 + 5.21956i 0.270874 + 0.372826i
1515 −1.10040 0.433046i −0.0733598 0.0288697i
1616 9.59007 + 6.96760i 0.599380 + 0.435475i
1717 0.704962 + 0.359196i 0.0414683 + 0.0211292i 0.474602 0.880201i 0.342592π-0.342592\pi
−0.433133 + 0.901330i 0.642592π0.642592\pi
1818 3.77386 + 3.77386i 0.209659 + 0.209659i
1919 13.5696 4.40902i 0.714187 0.232054i 0.0706862 0.997499i 0.477481π-0.477481\pi
0.643501 + 0.765445i 0.277481π0.277481\pi
2020 −7.27050 16.7062i −0.363525 0.835308i
2121 −0.790204 + 2.43200i −0.0376288 + 0.115809i
2222 −2.45738 4.82288i −0.111699 0.219222i
2323 13.5597 + 2.14764i 0.589551 + 0.0933757i 0.444080 0.895987i 0.353530π-0.353530\pi
0.145470 + 0.989363i 0.453530π0.453530\pi
2424 1.07877i 0.0449488i
2525 −3.03063 + 24.8156i −0.121225 + 0.992625i
2626 −8.09832 −0.311474
2727 −0.663895 + 4.19167i −0.0245887 + 0.155247i
2828 −35.1044 + 17.8866i −1.25373 + 0.638807i
2929 −36.6306 11.9020i −1.26312 0.410413i −0.400517 0.916289i 0.631169π-0.631169\pi
−0.862606 + 0.505876i 0.831169π0.831169\pi
3030 −0.357941 + 0.608115i −0.0119314 + 0.0202705i
3131 −2.87530 8.84925i −0.0927515 0.285460i 0.893910 0.448247i 0.147952π-0.147952\pi
−0.986661 + 0.162787i 0.947952π0.947952\pi
3232 17.9028 17.9028i 0.559462 0.559462i
3333 0.973987 1.91156i 0.0295148 0.0579260i
3434 0.277504 0.381951i 0.00816188 0.0112339i
3535 53.9608 + 3.28280i 1.54174 + 0.0937944i
3636 −26.3671 + 19.1568i −0.732420 + 0.532135i
3737 9.13820 1.44735i 0.246978 0.0391175i −0.0317178 0.999497i 0.510098π-0.510098\pi
0.278696 + 0.960379i 0.410098π0.410098\pi
3838 −1.33186 8.40902i −0.0350489 0.221290i
3939 −1.88666 2.59677i −0.0483759 0.0665838i
4040 −22.0779 + 5.71738i −0.551947 + 0.142934i
4141 −33.7351 24.5100i −0.822807 0.597805i 0.0947079 0.995505i 0.469808π-0.469808\pi
−0.917515 + 0.397701i 0.869808π0.869808\pi
4242 1.35958 + 0.692738i 0.0323708 + 0.0164938i
4343 49.4021 + 49.4021i 1.14889 + 1.14889i 0.986772 + 0.162113i 0.0518308π0.0518308\pi
0.162113 + 0.986772i 0.448169π0.448169\pi
4444 31.4367 10.2144i 0.714470 0.232145i
4545 44.5130 4.30070i 0.989179 0.0955711i
4646 2.53150 7.79114i 0.0550325 0.169373i
4747 9.65116 + 18.9415i 0.205344 + 0.403010i 0.970594 0.240723i 0.0773847π-0.0773847\pi
−0.765250 + 0.643733i 0.777385π0.777385\pi
4848 2.76905 + 0.438574i 0.0576885 + 0.00913696i
4949 67.9017i 1.38575i
5050 14.3426 + 4.10260i 0.286852 + 0.0820521i
5151 0.187125 0.00366911
5252 7.73627 48.8449i 0.148775 0.939325i
5353 −56.8742 + 28.9788i −1.07310 + 0.546771i −0.898996 0.437957i 0.855702π-0.855702\pi
−0.174102 + 0.984728i 0.555702π0.555702\pi
5454 2.40846 + 0.782556i 0.0446011 + 0.0144918i
5555 −44.2836 9.80236i −0.805156 0.178225i
5656 15.2397 + 46.9029i 0.272137 + 0.837551i
5757 2.38611 2.38611i 0.0418616 0.0418616i
5858 −10.4340 + 20.4778i −0.179896 + 0.353066i
5959 −45.6440 + 62.8235i −0.773627 + 1.06481i 0.222330 + 0.974971i 0.428634π0.428634\pi
−0.995957 + 0.0898343i 0.971366π0.971366\pi
6060 −3.32590 2.73985i −0.0554316 0.0456641i
6161 11.4153 8.29369i 0.187136 0.135962i −0.490273 0.871569i 0.663103π-0.663103\pi
0.677409 + 0.735607i 0.263103π0.263103\pi
6262 −5.48385 + 0.868557i −0.0884492 + 0.0140090i
6363 −15.1279 95.5136i −0.240125 1.51609i
6464 18.9902 + 26.1378i 0.296722 + 0.408403i
6565 −43.1458 + 52.3747i −0.663781 + 0.805764i
6666 −1.03569 0.752473i −0.0156923 0.0114011i
6767 −46.8978 23.8956i −0.699968 0.356651i 0.0675175 0.997718i 0.478492π-0.478492\pi
−0.767485 + 0.641067i 0.778492π0.778492\pi
6868 2.03864 + 2.03864i 0.0299800 + 0.0299800i
6969 3.08803 1.00336i 0.0447541 0.0145415i
7070 6.97183 31.4963i 0.0995975 0.449947i
7171 −0.846117 + 2.60408i −0.0119171 + 0.0366772i −0.956838 0.290621i 0.906138π-0.906138\pi
0.944921 + 0.327298i 0.106138π0.106138\pi
7272 18.5210 + 36.3495i 0.257236 + 0.504854i
7373 60.7976 + 9.62940i 0.832844 + 0.131910i 0.558273 0.829657i 0.311464π-0.311464\pi
0.274571 + 0.961567i 0.411464π0.411464\pi
7474 5.52086i 0.0746062i
7575 2.02587 + 5.55481i 0.0270116 + 0.0740642i
7676 51.9912 0.684095
7777 −15.3427 + 96.8703i −0.199256 + 1.25806i
7878 −1.70656 + 0.869536i −0.0218790 + 0.0111479i
7979 −6.18905 2.01094i −0.0783423 0.0254550i 0.269584 0.962977i 0.413114π-0.413114\pi
−0.347926 + 0.937522i 0.613114π0.613114\pi
8080 −5.69992 58.9952i −0.0712490 0.737440i
8181 −24.5646 75.6022i −0.303267 0.933360i
8282 −17.5944 + 17.5944i −0.214566 + 0.214566i
8383 50.9593 100.013i 0.613967 1.20498i −0.349446 0.936957i 0.613630π-0.613630\pi
0.963413 0.268021i 0.0863698π-0.0863698\pi
8484 −5.47704 + 7.53850i −0.0652029 + 0.0897440i
8585 −0.991742 3.82966i −0.0116676 0.0450548i
8686 33.7274 24.5044i 0.392180 0.284935i
8787 −8.99712 + 1.42500i −0.103415 + 0.0163794i
8888 −6.47255 40.8661i −0.0735517 0.464387i
8989 65.5853 + 90.2704i 0.736914 + 1.01427i 0.998790 + 0.0491732i 0.0156586π0.0156586\pi
−0.261877 + 0.965101i 0.584341π0.584341\pi
9090 1.62045 26.6360i 0.0180050 0.295955i
9191 118.713 + 86.2498i 1.30454 + 0.947800i
9292 44.5739 + 22.7115i 0.484499 + 0.246864i
9393 −1.55608 1.55608i −0.0167320 0.0167320i
9494 12.0644 3.91995i 0.128344 0.0417016i
9595 −61.4799 36.1875i −0.647156 0.380921i
9696 1.85040 5.69493i 0.0192749 0.0593222i
9797 −58.6053 115.019i −0.604178 1.18577i −0.967207 0.253989i 0.918257π-0.918257\pi
0.363029 0.931778i 0.381743π-0.381743\pi
9898 −40.0190 6.33839i −0.408357 0.0646775i
9999 81.1325i 0.819521i
100100 −38.4462 + 82.5881i −0.384462 + 0.825881i
101101 −32.5145 −0.321926 −0.160963 0.986960i 0.551460π-0.551460\pi
−0.160963 + 0.986960i 0.551460π0.551460\pi
102102 0.0174674 0.110285i 0.000171249 0.00108123i
103103 −46.2893 + 23.5856i −0.449411 + 0.228986i −0.664022 0.747713i 0.731152π-0.731152\pi
0.214611 + 0.976700i 0.431152π0.431152\pi
104104 −58.8732 19.1291i −0.566089 0.183933i
105105 11.7237 5.10212i 0.111654 0.0485916i
106106 11.7702 + 36.2248i 0.111039 + 0.341744i
107107 −34.7993 + 34.7993i −0.325227 + 0.325227i −0.850768 0.525541i 0.823863π-0.823863\pi
0.525541 + 0.850768i 0.323863π0.323863\pi
108108 −7.02076 + 13.7790i −0.0650071 + 0.127584i
109109 76.0086 104.617i 0.697326 0.959787i −0.302651 0.953101i 0.597872π-0.597872\pi
0.999978 0.00668585i 0.00212819π-0.00212819\pi
110110 −9.91090 + 25.1843i −0.0900991 + 0.228948i
111111 1.77029 1.28619i 0.0159486 0.0115873i
112112 −126.589 + 20.0497i −1.13026 + 0.179015i
113113 11.9724 + 75.5905i 0.105950 + 0.668942i 0.982307 + 0.187279i 0.0599670π0.0599670\pi
−0.876357 + 0.481663i 0.840033π0.840033\pi
114114 −1.18356 1.62903i −0.0103821 0.0142897i
115115 −36.9009 57.8813i −0.320877 0.503316i
116116 −113.544 82.4948i −0.978830 0.711162i
117117 108.155 + 55.1075i 0.924398 + 0.471004i
118118 32.7654 + 32.7654i 0.277673 + 0.277673i
119119 −8.13582 + 2.64349i −0.0683682 + 0.0222142i
120120 −4.03859 + 3.57538i −0.0336550 + 0.0297949i
121121 −11.9636 + 36.8202i −0.0988729 + 0.304299i
122122 −3.82245 7.50197i −0.0313315 0.0614916i
123123 −9.74071 1.54278i −0.0791928 0.0125429i
124124 33.9055i 0.273432i
125125 102.947 70.9011i 0.823574 0.567208i
126126 −57.7047 −0.457974
127127 9.58264 60.5024i 0.0754539 0.476397i −0.920808 0.390016i 0.872470π-0.872470\pi
0.996262 0.0863815i 0.0275304π-0.0275304\pi
128128 107.413 54.7295i 0.839162 0.427575i
129129 15.7149 + 5.10609i 0.121821 + 0.0395821i
130130 26.8404 + 30.3177i 0.206464 + 0.233213i
131131 −1.09573 3.37230i −0.00836432 0.0257427i 0.946787 0.321860i 0.104308π-0.104308\pi
−0.955152 + 0.296117i 0.904308π0.904308\pi
132132 5.52792 5.52792i 0.0418782 0.0418782i
133133 −70.0353 + 137.452i −0.526581 + 1.03347i
134134 −18.4610 + 25.4094i −0.137769 + 0.189623i
135135 17.8927 11.4071i 0.132539 0.0844969i
136136 2.91961 2.12122i 0.0214677 0.0155972i
137137 246.624 39.0615i 1.80018 0.285120i 0.835682 0.549214i 0.185073π-0.185073\pi
0.964497 + 0.264094i 0.0850728π0.0850728\pi
138138 −0.303091 1.91364i −0.00219631 0.0138670i
139139 −81.3839 112.015i −0.585496 0.805866i 0.408789 0.912629i 0.365951π-0.365951\pi
−0.994284 + 0.106763i 0.965951π0.965951\pi
140140 183.309 + 72.1387i 1.30935 + 0.515276i
141141 4.06758 + 2.95527i 0.0288481 + 0.0209594i
142142 1.45578 + 0.741755i 0.0102519 + 0.00522363i
143143 −87.0511 87.0511i −0.608749 0.608749i
144144 −100.834 + 32.7628i −0.700234 + 0.227520i
145145 76.8477 + 176.581i 0.529984 + 1.21780i
146146 11.3505 34.9332i 0.0777431 0.239269i
147147 −7.29078 14.3090i −0.0495971 0.0973399i
148148 33.2990 + 5.27404i 0.224993 + 0.0356354i
149149 103.072i 0.691761i −0.938279 0.345880i 0.887580π-0.887580\pi
0.938279 0.345880i 0.112420π-0.112420\pi
150150 3.46293 0.675459i 0.0230862 0.00450306i
151151 −47.0940 −0.311880 −0.155940 0.987766i 0.549841π-0.549841\pi
−0.155940 + 0.987766i 0.549841π0.549841\pi
152152 10.1806 64.2780i 0.0669778 0.422881i
153153 −6.30522 + 3.21267i −0.0412106 + 0.0209978i
154154 55.6599 + 18.0850i 0.361428 + 0.117435i
155155 −23.5993 + 40.0935i −0.152254 + 0.258667i
156156 −3.61433 11.1238i −0.0231688 0.0713062i
157157 94.7590 94.7590i 0.603561 0.603561i −0.337695 0.941256i 0.609647π-0.609647\pi
0.941256 + 0.337695i 0.109647π0.109647\pi
158158 −1.76291 + 3.45990i −0.0111577 + 0.0218981i
159159 −8.87359 + 12.2134i −0.0558087 + 0.0768141i
160160 −126.358 7.68724i −0.789739 0.0480452i
161161 −120.087 + 87.2486i −0.745884 + 0.541917i
162162 −46.8504 + 7.42038i −0.289200 + 0.0458048i
163163 41.3763 + 261.240i 0.253842 + 1.60270i 0.704302 + 0.709901i 0.251260π0.251260\pi
−0.450459 + 0.892797i 0.648740π0.648740\pi
164164 −89.3128 122.928i −0.544590 0.749564i
165165 −10.3844 + 2.68919i −0.0629358 + 0.0162981i
166166 −54.1876 39.3696i −0.326431 0.237166i
167167 −239.969 122.270i −1.43694 0.732158i −0.449969 0.893044i 0.648565π-0.648565\pi
−0.986973 + 0.160886i 0.948565π0.948565\pi
168168 8.24754 + 8.24754i 0.0490925 + 0.0490925i
169169 −14.4433 + 4.69292i −0.0854634 + 0.0277687i
170170 −2.34965 + 0.227015i −0.0138215 + 0.00133538i
171171 −39.4345 + 121.367i −0.230611 + 0.709749i
172172 115.579 + 226.836i 0.671968 + 1.31881i
173173 −184.026 29.1468i −1.06373 0.168479i −0.400050 0.916493i 0.631007π-0.631007\pi
−0.663682 + 0.748014i 0.731007π0.731007\pi
174174 5.43562i 0.0312392i
175175 −166.553 212.893i −0.951733 1.21653i
176176 107.529 0.610959
177177 −2.87305 + 18.1397i −0.0162319 + 0.102484i
178178 59.3246 30.2274i 0.333284 0.169817i
179179 194.558 + 63.2157i 1.08692 + 0.353161i 0.797054 0.603908i 0.206391π-0.206391\pi
0.289862 + 0.957068i 0.406391π0.406391\pi
180180 159.107 + 35.2189i 0.883925 + 0.195661i
181181 8.53397 + 26.2649i 0.0471490 + 0.145110i 0.971859 0.235562i 0.0756929π-0.0756929\pi
−0.924710 + 0.380671i 0.875693π0.875693\pi
182182 61.9142 61.9142i 0.340188 0.340188i
183183 1.51503 2.97342i 0.00827887 0.0162482i
184184 36.8070 50.6605i 0.200038 0.275329i
185185 −35.7053 29.4137i −0.193002 0.158993i
186186 −1.06236 + 0.771846i −0.00571159 + 0.00414971i
187187 7.08867 1.12273i 0.0379073 0.00600393i
188188 12.1181 + 76.5108i 0.0644581 + 0.406973i
189189 −26.9710 37.1223i −0.142703 0.196414i
190190 −27.0667 + 32.8562i −0.142456 + 0.172927i
191191 75.2465 + 54.6697i 0.393960 + 0.286229i 0.767076 0.641556i 0.221711π-0.221711\pi
−0.373116 + 0.927785i 0.621711π0.621711\pi
192192 6.80830 + 3.46900i 0.0354599 + 0.0180677i
193193 −172.622 172.622i −0.894415 0.894415i 0.100520 0.994935i 0.467949π-0.467949\pi
−0.994935 + 0.100520i 0.967949π0.967949\pi
194194 −73.2592 + 23.8034i −0.377625 + 0.122698i
195195 −3.46853 + 15.6696i −0.0177873 + 0.0803569i
196196 76.4599 235.319i 0.390101 1.20061i
197197 −19.6944 38.6524i −0.0999715 0.196205i 0.835604 0.549333i 0.185118π-0.185118\pi
−0.935575 + 0.353128i 0.885118π0.885118\pi
198198 47.8168 + 7.57344i 0.241499 + 0.0382497i
199199 331.210i 1.66437i 0.554496 + 0.832186i 0.312911π0.312911\pi
−0.554496 + 0.832186i 0.687089π0.687089\pi
200200 94.5773 + 63.7039i 0.472886 + 0.318519i
201201 −12.4485 −0.0619330
202202 −3.03512 + 19.1630i −0.0150253 + 0.0948663i
203203 371.047 189.058i 1.82782 0.931319i
204204 0.648496 + 0.210709i 0.00317890 + 0.00103289i
205205 20.0507 + 207.528i 0.0978081 + 1.01233i
206206 9.57961 + 29.4830i 0.0465030 + 0.143121i
207207 −86.8259 + 86.8259i −0.419449 + 0.419449i
208208 73.0365 143.342i 0.351137 0.689145i
209209 76.0744 104.707i 0.363992 0.500992i
210210 −1.91266 7.38580i −0.00910789 0.0351705i
211211 203.359 147.749i 0.963785 0.700231i 0.00975810 0.999952i 0.496894π-0.496894\pi
0.954027 + 0.299722i 0.0968939π0.0968939\pi
212212 −229.734 + 36.3862i −1.08365 + 0.171633i
213213 0.101304 + 0.639609i 0.000475606 + 0.00300286i
214214 17.2612 + 23.7580i 0.0806597 + 0.111019i
215215 21.2126 348.681i 0.0986634 1.62177i
216216 15.6606 + 11.3781i 0.0725026 + 0.0526762i
217217 89.6379 + 45.6728i 0.413078 + 0.210474i
218218 −54.5625 54.5625i −0.250287 0.250287i
219219 13.8458 4.49879i 0.0632230 0.0205424i
220220 −142.431 83.8359i −0.647413 0.381072i
221221 3.31815 10.2122i 0.0150143 0.0462091i
222222 −0.592788 1.16341i −0.00267022 0.00524060i
223223 −74.7975 11.8468i −0.335415 0.0531245i −0.0135446 0.999908i 0.504312π-0.504312\pi
−0.321870 + 0.946784i 0.604312π0.604312\pi
224224 273.745i 1.22208i
225225 −163.631 152.390i −0.727248 0.677288i
226226 45.6681 0.202071
227227 −53.6868 + 338.965i −0.236506 + 1.49324i 0.528345 + 0.849030i 0.322813π0.322813\pi
−0.764850 + 0.644208i 0.777187π0.777187\pi
228228 10.9561 5.58243i 0.0480532 0.0244843i
229229 22.2341 + 7.22430i 0.0970921 + 0.0315471i 0.357160 0.934043i 0.383745π-0.383745\pi
−0.260068 + 0.965590i 0.583745π0.583745\pi
230230 −37.5579 + 16.3451i −0.163295 + 0.0710658i
231231 7.16802 + 22.0609i 0.0310304 + 0.0955017i
232232 −124.224 + 124.224i −0.535447 + 0.535447i
233233 −86.9078 + 170.566i −0.372995 + 0.732044i −0.998852 0.0478936i 0.984749π-0.984749\pi
0.625858 + 0.779937i 0.284749π0.284749\pi
234234 42.5744 58.5986i 0.181942 0.250421i
235235 38.9242 98.9090i 0.165635 0.420890i
236236 −228.925 + 166.324i −0.970020 + 0.704761i
237237 −1.52014 + 0.240767i −0.00641409 + 0.00101589i
238238 0.798534 + 5.04174i 0.00335518 + 0.0211838i
239239 32.3070 + 44.4668i 0.135176 + 0.186054i 0.871239 0.490860i 0.163317π-0.163317\pi
−0.736063 + 0.676913i 0.763317π0.763317\pi
240240 −7.53561 11.8201i −0.0313984 0.0492503i
241241 −27.3775 19.8909i −0.113600 0.0825349i 0.529535 0.848288i 0.322366π-0.322366\pi
−0.643135 + 0.765753i 0.722366π0.722366\pi
242242 20.5839 + 10.4880i 0.0850573 + 0.0433388i
243243 −40.3022 40.3022i −0.165853 0.165853i
244244 48.8996 15.8885i 0.200408 0.0651166i
245245 −254.204 + 225.048i −1.03757 + 0.918562i
246246 −1.81852 + 5.59684i −0.00739237 + 0.0227514i
247247 −87.9094 172.532i −0.355908 0.698510i
248248 −41.9182 6.63919i −0.169025 0.0267709i
249249 26.5474i 0.106616i
250250 −32.1770 67.2918i −0.128708 0.269167i
251251 221.852 0.883872 0.441936 0.897046i 0.354292π-0.354292\pi
0.441936 + 0.897046i 0.354292π0.354292\pi
252252 55.1250 348.045i 0.218750 1.38113i
253253 110.961 56.5374i 0.438581 0.223468i
254254 −34.7636 11.2954i −0.136865 0.0444700i
255255 −0.620190 0.700539i −0.00243212 0.00274721i
256256 17.7059 + 54.4930i 0.0691635 + 0.212863i
257257 −20.3380 + 20.3380i −0.0791363 + 0.0791363i −0.745567 0.666431i 0.767821π-0.767821\pi
0.666431 + 0.745567i 0.267821π0.267821\pi
258258 4.47630 8.78523i 0.0173500 0.0340513i
259259 −58.7990 + 80.9299i −0.227023 + 0.312471i
260260 −208.501 + 132.925i −0.801928 + 0.511251i
261261 278.695 202.484i 1.06780 0.775801i
262262 −2.08980 + 0.330992i −0.00797634 + 0.00126333i
263263 −0.847808 5.35285i −0.00322361 0.0203530i 0.986024 0.166603i 0.0532797π-0.0532797\pi
−0.989248 + 0.146250i 0.953280π0.953280\pi
264264 −5.75185 7.91675i −0.0217873 0.0299877i
265265 296.987 + 116.875i 1.12071 + 0.441038i
266266 74.4721 + 54.1071i 0.279970 + 0.203410i
267267 23.5134 + 11.9807i 0.0880651 + 0.0448714i
268268 −135.621 135.621i −0.506049 0.506049i
269269 −59.0391 + 19.1830i −0.219476 + 0.0713122i −0.416691 0.909048i 0.636810π-0.636810\pi
0.197215 + 0.980360i 0.436810π0.436810\pi
270270 −5.05274 11.6102i −0.0187138 0.0430007i
271271 −99.9539 + 307.626i −0.368833 + 1.13515i 0.578712 + 0.815532i 0.303556π0.303556\pi
−0.947546 + 0.319621i 0.896444π0.896444\pi
272272 4.25790 + 8.35660i 0.0156540 + 0.0307228i
273273 34.2772 + 5.42898i 0.125558 + 0.0198864i
274274 148.999i 0.543790i
275275 110.073 + 198.273i 0.400264 + 0.720992i
276276 11.8317 0.0428684
277277 11.4134 72.0614i 0.0412036 0.260150i −0.958484 0.285147i 0.907958π-0.907958\pi
0.999688 + 0.0249971i 0.00795767π0.00795767\pi
278278 −73.6150 + 37.5087i −0.264802 + 0.134924i
279279 79.1483 + 25.7168i 0.283686 + 0.0921750i
280280 125.081 212.504i 0.446719 0.758942i
281281 −84.2374 259.256i −0.299777 0.922619i −0.981575 0.191079i 0.938801π-0.938801\pi
0.681798 0.731541i 0.261199π-0.261199\pi
282282 2.12143 2.12143i 0.00752282 0.00752282i
283283 89.6096 175.869i 0.316642 0.621445i −0.676750 0.736212i 0.736612π-0.736612\pi
0.993392 + 0.114768i 0.0366124π0.0366124\pi
284284 −5.86459 + 8.07191i −0.0206499 + 0.0284222i
285285 −16.8412 1.02457i −0.0590920 0.00359497i
286286 −59.4309 + 43.1791i −0.207800 + 0.150976i
287287 445.302 70.5289i 1.55158 0.245745i
288288 35.4245 + 223.661i 0.123002 + 0.776601i
289289 −169.502 233.299i −0.586512 0.807265i
290290 111.244 28.8083i 0.383601 0.0993389i
291291 −24.6998 17.9455i −0.0848792 0.0616683i
292292 199.856 + 101.832i 0.684440 + 0.348739i
293293 237.228 + 237.228i 0.809652 + 0.809652i 0.984581 0.174929i 0.0559695π-0.0559695\pi
−0.174929 + 0.984581i 0.555970π0.555970\pi
294294 −9.11379 + 2.96125i −0.0309993 + 0.0100723i
295295 386.471 37.3396i 1.31007 0.126575i
296296 13.0408 40.1356i 0.0440569 0.135593i
297297 17.4773 + 34.3011i 0.0588461 + 0.115492i
298298 −60.7474 9.62145i −0.203850 0.0322867i
299299 186.319i 0.623142i
300300 0.765905 + 21.5319i 0.00255302 + 0.0717730i
301301 −755.389 −2.50960
302302 −4.39606 + 27.7556i −0.0145565 + 0.0919060i
303303 −6.85180 + 3.49117i −0.0226132 + 0.0115220i
304304 160.853 + 52.2644i 0.529123 + 0.171922i
305305 −68.8829 15.2475i −0.225846 0.0499919i
306306 1.30487 + 4.01598i 0.00426428 + 0.0131241i
307307 −79.0993 + 79.0993i −0.257653 + 0.257653i −0.824099 0.566446i 0.808318π-0.808318\pi
0.566446 + 0.824099i 0.308318π0.308318\pi
308308 −162.251 + 318.436i −0.526789 + 1.03388i
309309 −7.22212 + 9.94040i −0.0233726 + 0.0321696i
310310 21.4268 + 17.6512i 0.0691188 + 0.0569395i
311311 −91.8901 + 66.7620i −0.295466 + 0.214669i −0.725635 0.688080i 0.758454π-0.758454\pi
0.430169 + 0.902748i 0.358454π0.358454\pi
312312 −14.4603 + 2.29029i −0.0463472 + 0.00734067i
313313 −16.0776 101.510i −0.0513662 0.324314i −0.999969 0.00784510i 0.997503π-0.997503\pi
0.948603 0.316469i 0.102497π-0.102497\pi
314314 −47.0024 64.6933i −0.149689 0.206029i
315315 −307.436 + 373.197i −0.975988 + 1.18475i
316316 −19.1843 13.9382i −0.0607097 0.0441082i
317317 −363.850 185.391i −1.14779 0.584829i −0.226618 0.973984i 0.572767π-0.572767\pi
−0.921172 + 0.389155i 0.872767π0.872767\pi
318318 6.36988 + 6.36988i 0.0200311 + 0.0200311i
319319 −332.280 + 107.964i −1.04163 + 0.338446i
320320 34.9126 157.723i 0.109102 0.492884i
321321 −3.59678 + 11.0698i −0.0112049 + 0.0344852i
322322 40.2117 + 78.9199i 0.124881 + 0.245093i
323323 11.1497 + 1.76594i 0.0345193 + 0.00546731i
324324 289.667i 0.894033i
325325 339.074 12.0611i 1.04330 0.0371111i
326326 157.828 0.484136
327327 4.78435 30.2072i 0.0146310 0.0923767i
328328 −169.468 + 86.3483i −0.516671 + 0.263257i
329329 −218.600 71.0273i −0.664437 0.215889i
330330 0.615569 + 6.37125i 0.00186536 + 0.0193068i
331331 −37.2677 114.698i −0.112591 0.346520i 0.878846 0.477106i 0.158314π-0.158314\pi
−0.991437 + 0.130586i 0.958314π0.958314\pi
332332 289.222 289.222i 0.871151 0.871151i
333333 −37.5684 + 73.7321i −0.112818 + 0.221418i
334334 −94.4624 + 130.016i −0.282822 + 0.389271i
335335 65.9760 + 254.769i 0.196943 + 0.760505i
336336 −24.5233 + 17.8172i −0.0729860 + 0.0530274i
337337 −38.2752 + 6.06219i −0.113576 + 0.0179887i −0.212964 0.977060i 0.568312π-0.568312\pi
0.0993876 + 0.995049i 0.468312π0.468312\pi
338338 1.41762 + 8.95048i 0.00419413 + 0.0264807i
339339 10.6393 + 14.6437i 0.0313843 + 0.0431968i
340340 0.875365 14.3887i 0.00257460 0.0423198i
341341 −68.2838 49.6111i −0.200246 0.145487i
342342 67.8486 + 34.5706i 0.198388 + 0.101084i
343343 144.510 + 144.510i 0.421311 + 0.421311i
344344 303.074 98.4748i 0.881030 0.286264i
345345 −13.9910 8.23522i −0.0405536 0.0238702i
346346 −34.3563 + 105.738i −0.0992958 + 0.305601i
347347 −106.794 209.594i −0.307762 0.604018i 0.684381 0.729125i 0.260073π-0.260073\pi
−0.992143 + 0.125107i 0.960073π0.960073\pi
348348 −32.7849 5.19262i −0.0942095 0.0149213i
349349 16.9114i 0.0484568i 0.999706 + 0.0242284i 0.00771289π0.00771289\pi
−0.999706 + 0.0242284i 0.992287π0.992287\pi
350350 −141.019 + 78.2881i −0.402913 + 0.223680i
351351 57.5965 0.164093
352352 35.9276 226.838i 0.102067 0.644426i
353353 −449.055 + 228.805i −1.27211 + 0.648173i −0.953979 0.299873i 0.903056π-0.903056\pi
−0.318132 + 0.948046i 0.603056π0.603056\pi
354354 10.4228 + 3.38656i 0.0294429 + 0.00956656i
355355 12.5532 5.46313i 0.0353611 0.0153891i
356356 125.644 + 386.692i 0.352932 + 1.08621i
357357 −1.43063 + 1.43063i −0.00400736 + 0.00400736i
358358 55.4186 108.765i 0.154800 0.303813i
359359 198.037 272.575i 0.551636 0.759262i −0.438597 0.898684i 0.644525π-0.644525\pi
0.990233 + 0.139422i 0.0445245π0.0445245\pi
360360 74.6973 189.811i 0.207493 0.527252i
361361 −127.362 + 92.5336i −0.352802 + 0.256326i
362362 16.2763 2.57791i 0.0449620 0.00712129i
363363 1.43238 + 9.04370i 0.00394596 + 0.0249138i
364364 314.289 + 432.581i 0.863430 + 1.18841i
365365 −165.453 259.523i −0.453296 0.711022i
366366 −1.61101 1.17047i −0.00440167 0.00319800i
367367 416.928 + 212.435i 1.13604 + 0.578843i 0.917797 0.397050i 0.129966π-0.129966\pi
0.218247 + 0.975894i 0.429966π0.429966\pi
368368 115.074 + 115.074i 0.312702 + 0.312702i
369369 354.704 115.250i 0.961256 0.312331i
370370 −20.6684 + 18.2979i −0.0558607 + 0.0494537i
371371 213.269 656.374i 0.574848 1.76920i
372372 −3.64052 7.14493i −0.00978635 0.0192068i
373373 474.868 + 75.2117i 1.27310 + 0.201640i 0.756164 0.654382i 0.227071π-0.227071\pi
0.516940 + 0.856022i 0.327071π0.327071\pi
374374 4.28263i 0.0114509i
375375 14.0812 25.9947i 0.0375498 0.0693191i
376376 96.9651 0.257886
377377 −81.7709 + 516.281i −0.216899 + 1.36945i
378378 −24.3963 + 12.4305i −0.0645405 + 0.0328850i
379379 −597.265 194.063i −1.57590 0.512040i −0.614901 0.788604i 0.710804π-0.710804\pi
−0.960995 + 0.276564i 0.910804π0.910804\pi
380380 −172.315 194.640i −0.453461 0.512210i
381381 −4.47694 13.7786i −0.0117505 0.0361643i
382382 39.2445 39.2445i 0.102734 0.102734i
383383 175.227 343.902i 0.457511 0.897916i −0.540874 0.841104i 0.681906π-0.681906\pi
0.998385 0.0568121i 0.0180936π-0.0180936\pi
384384 16.7587 23.0664i 0.0436424 0.0600686i
385385 413.504 263.620i 1.07404 0.684727i
386386 −117.851 + 85.6241i −0.305315 + 0.221824i
387387 −617.184 + 97.7524i −1.59479 + 0.252590i
388388 −73.5856 464.601i −0.189654 1.19743i
389389 230.009 + 316.581i 0.591284 + 0.813833i 0.994876 0.101107i 0.0322383π-0.0322383\pi
−0.403592 + 0.914939i 0.632238π0.632238\pi
390390 8.91137 + 3.50694i 0.0228497 + 0.00899216i
391391 8.78762 + 6.38458i 0.0224747 + 0.0163289i
392392 −275.959 140.608i −0.703977 0.358694i
393393 −0.592995 0.592995i −0.00150889 0.00150889i
394394 −24.6188 + 7.99915i −0.0624844 + 0.0203024i
395395 12.9841 + 29.8348i 0.0328711 + 0.0755313i
396396 −91.3583 + 281.172i −0.230703 + 0.710030i
397397 155.364 + 304.919i 0.391345 + 0.768058i 0.999672 0.0256288i 0.00815880π-0.00815880\pi
−0.608326 + 0.793687i 0.708159π0.708159\pi
398398 195.204 + 30.9173i 0.490463 + 0.0776817i
399399 36.4852i 0.0914415i
400400 −201.969 + 216.867i −0.504923 + 0.542169i
401401 665.647 1.65997 0.829983 0.557788i 0.188350π-0.188350\pi
0.829983 + 0.557788i 0.188350π0.188350\pi
402402 −1.16203 + 7.33675i −0.00289062 + 0.0182506i
403403 −112.515 + 57.3292i −0.279193 + 0.142256i
404404 −112.682 36.6126i −0.278916 0.0906252i
405405 −201.617 + 342.532i −0.497820 + 0.845759i
406406 −76.7884 236.331i −0.189134 0.582095i
407407 59.3452 59.3452i 0.145811 0.145811i
408408 0.387490 0.760491i 0.000949730 0.00186395i
409409 −369.812 + 509.003i −0.904187 + 1.24451i 0.0649265 + 0.997890i 0.479319π0.479319\pi
−0.969113 + 0.246616i 0.920681π0.920681\pi
410410 124.182 + 7.55483i 0.302882 + 0.0184264i
411411 47.7771 34.7121i 0.116246 0.0844577i
412412 −186.978 + 29.6144i −0.453830 + 0.0718796i
413413 −131.343 829.269i −0.318022 2.00791i
414414 43.0674 + 59.2772i 0.104028 + 0.143182i
415415 −543.315 + 140.699i −1.30919 + 0.339033i
416416 −277.986 201.968i −0.668235 0.485501i
417417 −29.1774 14.8666i −0.0699699 0.0356514i
418418 −54.6098 54.6098i −0.130645 0.130645i
419419 −111.166 + 36.1200i −0.265312 + 0.0862052i −0.438652 0.898657i 0.644544π-0.644544\pi
0.173340 + 0.984862i 0.444544π0.444544\pi
420420 46.3745 4.48055i 0.110416 0.0106680i
421421 1.06048 3.26382i 0.00251896 0.00775255i −0.949789 0.312891i 0.898703π-0.898703\pi
0.952308 + 0.305138i 0.0987026π0.0987026\pi
422422 −68.0953 133.645i −0.161363 0.316693i
423423 −187.796 29.7440i −0.443963 0.0703169i
424424 291.150i 0.686675i
425425 −11.0501 + 16.4055i −0.0260003 + 0.0386011i
426426 0.386421 0.000907090
427427 −23.8656 + 150.681i −0.0558913 + 0.352884i
428428 −159.785 + 81.4147i −0.373330 + 0.190221i
429429 −27.6912 8.99742i −0.0645482 0.0209730i
430430 −203.521 45.0501i −0.473304 0.104768i
431431 144.037 + 443.300i 0.334193 + 1.02854i 0.967118 + 0.254327i 0.0818538π0.0818538\pi
−0.632926 + 0.774212i 0.718146π0.718146\pi
432432 −35.5727 + 35.5727i −0.0823441 + 0.0823441i
433433 90.0802 176.792i 0.208037 0.408296i −0.763285 0.646062i 0.776415π-0.776415\pi
0.971323 + 0.237765i 0.0764149π0.0764149\pi
434434 35.2854 48.5662i 0.0813028 0.111904i
435435 35.1541 + 28.9596i 0.0808140 + 0.0665739i
436436 381.217 276.970i 0.874350 0.635253i
437437 193.468 30.6423i 0.442718 0.0701196i
438438 −1.35897 8.58022i −0.00310268 0.0195896i
439439 288.145 + 396.598i 0.656367 + 0.903412i 0.999354 0.0359283i 0.0114388π-0.0114388\pi
−0.342987 + 0.939340i 0.611439π0.611439\pi
440440 −131.538 + 159.674i −0.298951 + 0.362896i
441441 491.330 + 356.972i 1.11413 + 0.809461i
442442 −5.70900 2.90888i −0.0129163 0.00658118i
443443 241.629 + 241.629i 0.545437 + 0.545437i 0.925118 0.379681i 0.123966π-0.123966\pi
−0.379681 + 0.925118i 0.623966π0.623966\pi
444444 7.58340 2.46399i 0.0170797 0.00554954i
445445 120.575 544.717i 0.270956 1.22408i
446446 −13.9642 + 42.9773i −0.0313098 + 0.0963617i
447447 −11.0671 21.7205i −0.0247587 0.0485917i
448448 −345.018 54.6455i −0.770130 0.121977i
449449 344.192i 0.766575i −0.923629 0.383288i 0.874792π-0.874792\pi
0.923629 0.383288i 0.125208π-0.125208\pi
450450 −105.088 + 82.2135i −0.233528 + 0.182697i
451451 −378.255 −0.838703
452452 −43.6265 + 275.447i −0.0965187 + 0.609395i
453453 −9.92413 + 5.05660i −0.0219076 + 0.0111625i
454454 194.763 + 63.2824i 0.428994 + 0.139389i
455455 −70.5576 730.284i −0.155072 1.60502i
456456 −4.75632 14.6384i −0.0104305 0.0321018i
457457 −145.902 + 145.902i −0.319260 + 0.319260i −0.848483 0.529223i 0.822484π-0.822484\pi
0.529223 + 0.848483i 0.322484π0.322484\pi
458458 6.33324 12.4297i 0.0138280 0.0271390i
459459 −1.97365 + 2.71650i −0.00429989 + 0.00591829i
460460 −62.7067 242.145i −0.136319 0.526401i
461461 270.507 196.534i 0.586782 0.426322i −0.254381 0.967104i 0.581872π-0.581872\pi
0.841163 + 0.540782i 0.181872π0.181872\pi
462462 13.6711 2.16529i 0.0295911 0.00468676i
463463 −4.34214 27.4152i −0.00937827 0.0592120i 0.982555 0.185970i 0.0595428π-0.0595428\pi
−0.991934 + 0.126758i 0.959543π0.959543\pi
464464 −268.362 369.368i −0.578365 0.796052i
465465 −0.668161 + 10.9828i −0.00143690 + 0.0236190i
466466 92.4135 + 67.1423i 0.198312 + 0.144082i
467467 −365.168 186.062i −0.781943 0.398420i 0.0169777 0.999856i 0.494596π-0.494596\pi
−0.798921 + 0.601436i 0.794596π0.794596\pi
468468 312.766 + 312.766i 0.668303 + 0.668303i
469469 541.238 175.859i 1.15403 0.374966i
470470 −54.6603 32.1735i −0.116298 0.0684542i
471471 9.79409 30.1431i 0.0207943 0.0639981i
472472 160.803 + 315.594i 0.340684 + 0.668631i
473473 625.951 + 99.1408i 1.32336 + 0.209600i
474474 0.918395i 0.00193754i
475475 68.2883 + 350.099i 0.143765 + 0.737051i
476476 −31.1721 −0.0654875
477477 89.3103 563.883i 0.187233 1.18215i
478478 29.2230 14.8899i 0.0611360 0.0311504i
479479 579.516 + 188.296i 1.20985 + 0.393103i 0.843374 0.537326i 0.180566π-0.180566\pi
0.366472 + 0.930429i 0.380566π0.380566\pi
480480 −27.4529 + 11.9475i −0.0571936 + 0.0248906i
481481 −38.8018 119.420i −0.0806691 0.248274i
482482 −14.2786 + 14.2786i −0.0296237 + 0.0296237i
483483 −15.9380 + 31.2800i −0.0329978 + 0.0647619i
484484 −82.9219 + 114.132i −0.171326 + 0.235810i
485485 −236.362 + 600.611i −0.487344 + 1.23837i
486486 −27.5149 + 19.9907i −0.0566150 + 0.0411332i
487487 229.164 36.2960i 0.470563 0.0745298i 0.0833503 0.996520i 0.473438π-0.473438\pi
0.387213 + 0.921990i 0.373438π0.373438\pi
488488 −10.0680 63.5670i −0.0206312 0.130260i
489489 36.7692 + 50.6085i 0.0751927 + 0.103494i
490490 108.907 + 170.827i 0.222258 + 0.348626i
491491 −288.845 209.858i −0.588279 0.427409i 0.253421 0.967356i 0.418444π-0.418444\pi
−0.841699 + 0.539947i 0.818444π0.818444\pi
492492 −32.0200 16.3150i −0.0650814 0.0331606i
493493 −21.5480 21.5480i −0.0437079 0.0437079i
494494 −109.891 + 35.7056i −0.222451 + 0.0722786i
495495 303.736 268.899i 0.613608 0.543230i
496496 34.0837 104.899i 0.0687171 0.211490i
497497 −13.4402 26.3779i −0.0270426 0.0530742i
498498 −15.6462 2.47811i −0.0314180 0.00497613i
499499 752.086i 1.50719i −0.657341 0.753593i 0.728319π-0.728319\pi
0.657341 0.753593i 0.271681π-0.271681\pi
500500 436.608 129.792i 0.873216 0.259584i
501501 −63.6973 −0.127140
502502 20.7091 130.752i 0.0412532 0.260463i
503503 −728.768 + 371.326i −1.44884 + 0.738222i −0.988740 0.149644i 0.952187π-0.952187\pi
−0.460102 + 0.887866i 0.652187π0.652187\pi
504504 −419.502 136.305i −0.832346 0.270446i
505505 107.763 + 121.725i 0.213393 + 0.241039i
506506 −22.9635 70.6743i −0.0453823 0.139672i
507507 −2.53975 + 2.53975i −0.00500938 + 0.00500938i
508508 101.337 198.886i 0.199483 0.391508i
509509 −529.260 + 728.463i −1.03980 + 1.43117i −0.142476 + 0.989798i 0.545506π0.545506\pi
−0.897327 + 0.441367i 0.854494π0.854494\pi
510510 −0.470767 + 0.300126i −0.000923072 + 0.000588483i
511511 −538.437 + 391.197i −1.05369 + 0.765552i
512512 510.041 80.7826i 0.996174 0.157778i
513513 9.47238 + 59.8062i 0.0184647 + 0.116581i
514514 10.0881 + 13.8850i 0.0196266 + 0.0270137i
515515 241.715 + 95.1234i 0.469349 + 0.184706i
516516 48.7118 + 35.3912i 0.0944028 + 0.0685876i
517517 171.820 + 87.5466i 0.332340 + 0.169336i
518518 42.2087 + 42.2087i 0.0814840 + 0.0814840i
519519 −41.9094 + 13.6172i −0.0807503 + 0.0262374i
520520 123.511 + 283.804i 0.237521 + 0.545776i
521521 −145.536 + 447.915i −0.279340 + 0.859721i 0.708698 + 0.705512i 0.249283π0.249283\pi
−0.988038 + 0.154209i 0.950717π0.950717\pi
522522 −93.3221 183.155i −0.178778 0.350872i
523523 −582.366 92.2377i −1.11351 0.176363i −0.427543 0.903995i 0.640621π-0.640621\pi
−0.685967 + 0.727632i 0.740621π0.740621\pi
524524 12.9208i 0.0246580i
525525 −57.9567 26.9799i −0.110394 0.0513902i
526526 −3.23393 −0.00614816
527527 1.15164 7.27118i 0.00218528 0.0137973i
528528 22.6596 11.5456i 0.0429158 0.0218667i
529529 −323.857 105.227i −0.612205 0.198918i
530530 96.6050 164.125i 0.182274 0.309669i
531531 −214.626 660.550i −0.404192 1.24397i
532532 −397.489 + 397.489i −0.747160 + 0.747160i
533533 −256.921 + 504.236i −0.482029 + 0.946035i
534534 9.25590 12.7397i 0.0173331 0.0238570i
535535 245.614 + 14.9424i 0.459092 + 0.0279297i
536536 −194.228 + 141.115i −0.362366 + 0.263274i
537537 47.7869 7.56870i 0.0889887 0.0140944i
538538 5.79471 + 36.5864i 0.0107708 + 0.0680044i
539539 −362.043 498.309i −0.671693 0.924506i
540540 74.8536 19.3844i 0.138618 0.0358970i
541541 4.98311 + 3.62044i 0.00921092 + 0.00669212i 0.592381 0.805658i 0.298188π-0.298188\pi
−0.583170 + 0.812350i 0.698188π0.698188\pi
542542 171.974 + 87.6253i 0.317296 + 0.161670i
543543 4.61849 + 4.61849i 0.00850551 + 0.00850551i
544544 19.0514 6.19017i 0.0350209 0.0113790i
545545 −643.571 + 62.1796i −1.18086 + 0.114091i
546546 6.39932 19.6951i 0.0117204 0.0360716i
547547 −137.666 270.185i −0.251675 0.493940i 0.730257 0.683172i 0.239400π-0.239400\pi
−0.981932 + 0.189232i 0.939400π0.939400\pi
548548 898.683 + 142.337i 1.63993 + 0.259740i
549549 126.201i 0.229875i
550550 127.130 46.3651i 0.231146 0.0843002i
551551 −549.537 −0.997344
552552 2.31681 14.6278i 0.00419712 0.0264996i
553553 62.6915 31.9429i 0.113366 0.0577630i
554554 −41.4052 13.4534i −0.0747387 0.0242841i
555555 −10.6824 2.36460i −0.0192476 0.00426054i
556556 −155.910 479.840i −0.280413 0.863022i
557557 39.2190 39.2190i 0.0704112 0.0704112i −0.671024 0.741435i 0.734145π-0.734145\pi
0.741435 + 0.671024i 0.234145π0.234145\pi
558558 22.5449 44.2468i 0.0404030 0.0792953i
559559 557.324 767.091i 0.997002 1.37226i
560560 494.615 + 407.459i 0.883240 + 0.727606i
561561 1.37325 0.997722i 0.00244786 0.00177847i
562562 −160.660 + 25.4461i −0.285872 + 0.0452777i
563563 93.1829 + 588.334i 0.165511 + 1.04500i 0.920922 + 0.389746i 0.127437π0.127437\pi
−0.755411 + 0.655251i 0.772563π0.772563\pi
564564 10.7688 + 14.8220i 0.0190936 + 0.0262802i
565565 243.308 295.352i 0.430634 0.522746i
566566 −95.2865 69.2297i −0.168351 0.122314i
567567 765.807 + 390.198i 1.35063 + 0.688180i
568568 8.83112 + 8.83112i 0.0155477 + 0.0155477i
569569 258.923 84.1291i 0.455049 0.147854i −0.0725195 0.997367i 0.523104π-0.523104\pi
0.527568 + 0.849513i 0.323104π0.323104\pi
570570 −2.17592 + 9.83002i −0.00381739 + 0.0172456i
571571 −69.9094 + 215.159i −0.122433 + 0.376811i −0.993425 0.114487i 0.963477π-0.963477\pi
0.870991 + 0.491298i 0.163477π0.163477\pi
572572 −203.660 399.706i −0.356049 0.698786i
573573 21.7267 + 3.44118i 0.0379175 + 0.00600555i
574574 269.030i 0.468693i
575575 −94.3893 + 329.983i −0.164155 + 0.573884i
576576 −288.966 −0.501677
577577 140.082 884.446i 0.242777 1.53284i −0.501614 0.865092i 0.667260π-0.667260\pi
0.744391 0.667744i 0.232740π-0.232740\pi
578578 −153.321 + 78.1211i −0.265262 + 0.135158i
579579 −54.9116 17.8419i −0.0948387 0.0308150i
580580 67.4857 + 698.490i 0.116355 + 1.20429i
581581 375.033 + 1154.23i 0.645495 + 1.98663i
582582 −12.8821 + 12.8821i −0.0221342 + 0.0221342i
583583 −262.870 + 515.912i −0.450892 + 0.884926i
584584 165.032 227.147i 0.282589 0.388950i
585585 −152.152 587.542i −0.260089 1.00435i
586586 161.959 117.670i 0.276380 0.200802i
587587 346.752 54.9201i 0.590718 0.0935606i 0.146083 0.989272i 0.453333π-0.453333\pi
0.444635 + 0.895712i 0.353333π0.353333\pi
588588 −9.15440 57.7986i −0.0155687 0.0982970i
589589 −78.0330 107.403i −0.132484 0.182348i
590590 14.0691 231.259i 0.0238459 0.391964i
591591 −8.30041 6.03060i −0.0140447 0.0102041i
592592 97.7205 + 49.7911i 0.165068 + 0.0841066i
593593 −355.629 355.629i −0.599711 0.599711i 0.340525 0.940236i 0.389395π-0.389395\pi
−0.940236 + 0.340525i 0.889395π0.889395\pi
594594 21.8474 7.09864i 0.0367801 0.0119506i
595595 36.8611 + 21.6967i 0.0619514 + 0.0364651i
596596 116.063 357.206i 0.194737 0.599339i
597597 35.5629 + 69.7960i 0.0595693 + 0.116911i
598598 −109.811 17.3923i −0.183630 0.0290841i
599599 1001.80i 1.67245i 0.548390 + 0.836223i 0.315241π0.315241\pi
−0.548390 + 0.836223i 0.684759π0.684759\pi
600600 26.7704 + 3.26935i 0.0446173 + 0.00544891i
601601 796.655 1.32555 0.662775 0.748819i 0.269379π-0.269379\pi
0.662775 + 0.748819i 0.269379π0.269379\pi
602602 −70.5129 + 445.201i −0.117131 + 0.739537i
603603 419.457 213.724i 0.695617 0.354435i
604604 −163.208 53.0295i −0.270212 0.0877973i
605605 177.495 77.2456i 0.293380 0.127679i
606606 1.41799 + 4.36411i 0.00233991 + 0.00720151i
607607 728.906 728.906i 1.20083 1.20083i 0.226920 0.973913i 0.427134π-0.427134\pi
0.973913 0.226920i 0.0728657π-0.0728657\pi
608608 163.999 321.867i 0.269736 0.529386i
609609 57.8912 79.6804i 0.0950595 0.130838i
610610 −15.4164 + 39.1740i −0.0252727 + 0.0642197i
611611 233.410 169.582i 0.382013 0.277549i
612612 −25.4689 + 4.03387i −0.0416158 + 0.00659130i
613613 −19.5383 123.360i −0.0318732 0.201240i 0.966613 0.256240i 0.0824839π-0.0824839\pi
−0.998486 + 0.0550007i 0.982484π0.982484\pi
614614 39.2349 + 54.0022i 0.0639004 + 0.0879514i
615615 26.5081 + 41.5796i 0.0431026 + 0.0676091i
616616 361.919 + 262.949i 0.587530 + 0.426866i
617617 −639.236 325.707i −1.03604 0.527888i −0.148640 0.988891i 0.547490π-0.547490\pi
−0.887399 + 0.461003i 0.847490π0.847490\pi
618618 5.18438 + 5.18438i 0.00838897 + 0.00838897i
619619 −196.553 + 63.8639i −0.317533 + 0.103173i −0.463447 0.886125i 0.653388π-0.653388\pi
0.145914 + 0.989297i 0.453388π0.453388\pi
620620 −126.932 + 112.374i −0.204729 + 0.181248i
621621 −18.0044 + 55.4118i −0.0289926 + 0.0892300i
622622 30.7697 + 60.3889i 0.0494690 + 0.0970883i
623623 −1191.57 188.726i −1.91263 0.302930i
624624 38.0487i 0.0609754i
625625 −606.631 150.414i −0.970609 0.240662i
626626 −61.3275 −0.0979673
627627 4.78849 30.2333i 0.00763714 0.0482190i
628628 435.098 221.693i 0.692831 0.353015i
629629 6.96196 + 2.26208i 0.0110683 + 0.00359631i
630630 191.252 + 216.029i 0.303574 + 0.342904i
631631 68.8404 + 211.869i 0.109097 + 0.335767i 0.990670 0.136281i 0.0435149π-0.0435149\pi
−0.881573 + 0.472048i 0.843515π0.843515\pi
632632 −20.9887 + 20.9887i −0.0332099 + 0.0332099i
633633 26.9897 52.9703i 0.0426377 0.0836813i
634634 −143.227 + 197.135i −0.225910 + 0.310939i
635635 −258.263 + 164.650i −0.406713 + 0.259291i
636636 −44.5050 + 32.3348i −0.0699764 + 0.0508408i
637637 −910.185 + 144.159i −1.42886 + 0.226310i
638638 32.6134 + 205.913i 0.0511181 + 0.322747i
639639 −14.3947 19.8126i −0.0225269 0.0310056i
640640 −560.891 220.731i −0.876392 0.344892i
641641 −709.800 515.700i −1.10733 0.804524i −0.125090 0.992145i 0.539922π-0.539922\pi
−0.982241 + 0.187622i 0.939922π0.939922\pi
642642 6.18840 + 3.15315i 0.00963926 + 0.00491145i
643643 430.122 + 430.122i 0.668929 + 0.668929i 0.957468 0.288539i 0.0931694π-0.0931694\pi
−0.288539 + 0.957468i 0.593169π0.593169\pi
644644 −514.418 + 167.145i −0.798786 + 0.259541i
645645 −32.9686 75.7553i −0.0511141 0.117450i
646646 2.08158 6.40643i 0.00322225 0.00991707i
647647 400.518 + 786.060i 0.619038 + 1.21493i 0.961346 + 0.275343i 0.0887914π0.0887914\pi
−0.342308 + 0.939588i 0.611209π0.611209\pi
648648 −358.122 56.7209i −0.552657 0.0875323i
649649 704.409i 1.08538i
650650 24.5430 200.965i 0.0377584 0.309177i
651651 23.7934 0.0365490
652652 −150.773 + 951.940i −0.231246 + 1.46003i
653653 868.933 442.744i 1.33068 0.678015i 0.363377 0.931642i 0.381624π-0.381624\pi
0.967302 + 0.253627i 0.0816237π0.0816237\pi
654654 −17.3565 5.63947i −0.0265390 0.00862304i
655655 −8.99330 + 15.2789i −0.0137302 + 0.0233266i
656656 −152.746 470.105i −0.232845 0.716624i
657657 −389.302 + 389.302i −0.592545 + 0.592545i
658658 −62.2667 + 122.205i −0.0946302 + 0.185722i
659659 337.348 464.320i 0.511909 0.704582i −0.472331 0.881421i 0.656587π-0.656587\pi
0.984240 + 0.176839i 0.0565872π0.0565872\pi
660660 −39.0162 2.37362i −0.0591154 0.00359639i
661661 83.1335 60.4000i 0.125769 0.0913767i −0.523122 0.852258i 0.675233π-0.675233\pi
0.648892 + 0.760881i 0.275233π0.275233\pi
662662 −71.0781 + 11.2577i −0.107369 + 0.0170055i
663663 −0.397276 2.50830i −0.000599210 0.00378326i
664664 −300.938 414.206i −0.453220 0.623804i
665665 746.698 193.368i 1.12285 0.290779i
666666 39.9484 + 29.0242i 0.0599825 + 0.0435799i
667667 −471.137 240.056i −0.706353 0.359905i
668668 −693.953 693.953i −1.03885 1.03885i
669669 −17.0341 + 5.53472i −0.0254621 + 0.00827313i
670670 156.311 15.1023i 0.233300 0.0225407i
671671 39.5523 121.729i 0.0589453 0.181415i
672672 29.3927 + 57.6864i 0.0437391 + 0.0858429i
673673 742.996 + 117.679i 1.10401 + 0.174857i 0.681726 0.731608i 0.261230π-0.261230\pi
0.422280 + 0.906465i 0.361230π0.361230\pi
674674 23.1240i 0.0343086i
675675 −102.007 29.1784i −0.151121 0.0432272i
676676 −55.3389 −0.0818624
677677 −104.837 + 661.912i −0.154855 + 0.977714i 0.780796 + 0.624786i 0.214814π0.214814\pi
−0.935651 + 0.352928i 0.885186π0.885186\pi
678678 9.62365 4.90350i 0.0141942 0.00723230i
679679 1327.42 + 431.304i 1.95496 + 0.635204i
680680 −17.6177 3.89976i −0.0259084 0.00573494i
681681 25.0821 + 77.1947i 0.0368313 + 0.113355i
682682 −35.6132 + 35.6132i −0.0522188 + 0.0522188i
683683 477.148 936.456i 0.698607 1.37109i −0.219835 0.975537i 0.570552π-0.570552\pi
0.918442 0.395556i 0.129448π-0.129448\pi
684684 −273.328 + 376.203i −0.399602 + 0.550005i
685685 −963.626 793.827i −1.40675 1.15887i
686686 98.6588 71.6798i 0.143817 0.104489i
687687 5.46109 0.864952i 0.00794919 0.00125903i
688688 129.556 + 817.983i 0.188308 + 1.18893i
689689 509.193 + 700.843i 0.739031 + 1.01719i
690690 −6.15957 + 7.47710i −0.00892692 + 0.0108364i
691691 281.760 + 204.711i 0.407757 + 0.296253i 0.772693 0.634780i 0.218909π-0.218909\pi
−0.364936 + 0.931033i 0.618909π0.618909\pi
692692 −604.937 308.231i −0.874186 0.445420i
693693 −620.284 620.284i −0.895071 0.895071i
694694 −133.497 + 43.3757i −0.192358 + 0.0625010i
695695 −149.620 + 675.931i −0.215281 + 0.972563i
696696 −12.8395 + 39.5160i −0.0184476 + 0.0567758i
697697 −14.9781 29.3961i −0.0214893 0.0421752i
698698 9.96703 + 1.57862i 0.0142794 + 0.00226164i
699699 45.2750i 0.0647711i
700700 −337.479 925.346i −0.482112 1.32192i
701701 685.412 0.977764 0.488882 0.872350i 0.337405π-0.337405\pi
0.488882 + 0.872350i 0.337405π0.337405\pi
702702 5.37643 33.9455i 0.00765874 0.0483554i
703703 117.620 59.9304i 0.167312 0.0852495i
704704 278.726 + 90.5637i 0.395918 + 0.128642i
705705 −2.41759 25.0225i −0.00342921 0.0354930i
706706 92.9324 + 286.016i 0.131632 + 0.405122i
707707 248.584 248.584i 0.351604 0.351604i
708708 −30.3828 + 59.6297i −0.0429136 + 0.0842227i
709709 −142.144 + 195.644i −0.200485 + 0.275944i −0.897408 0.441202i 0.854552π-0.854552\pi
0.696922 + 0.717146i 0.254552π0.254552\pi
710710 −2.04799 7.90841i −0.00288450 0.0111386i
711711 47.0880 34.2114i 0.0662278 0.0481173i
712712 502.679 79.6165i 0.706009 0.111821i
713713 −19.9831 126.168i −0.0280267 0.176954i
714714 0.709620 + 0.976708i 0.000993865 + 0.00136794i
715715 −37.3787 + 614.408i −0.0522778 + 0.859312i
716716 603.074 + 438.159i 0.842283 + 0.611954i
717717 11.5826 + 5.90162i 0.0161542 + 0.00823099i
718718 −142.161 142.161i −0.197995 0.197995i
719719 −126.747 + 41.1825i −0.176282 + 0.0572774i −0.395828 0.918325i 0.629542π-0.629542\pi
0.219546 + 0.975602i 0.429542π0.429542\pi
720720 456.849 + 268.905i 0.634512 + 0.373479i
721721 173.577 534.216i 0.240745 0.740937i
722722 42.6475 + 83.7004i 0.0590685 + 0.115928i
723723 −7.90500 1.25203i −0.0109336 0.00173171i
724724 100.633i 0.138996i
725725 406.369 872.940i 0.560509 1.20405i
726726 5.46377 0.00752585
727727 202.138 1276.25i 0.278044 1.75550i −0.313837 0.949477i 0.601615π-0.601615\pi
0.591881 0.806025i 0.298385π-0.298385\pi
728728 596.352 303.857i 0.819165 0.417386i
729729 667.599 + 216.916i 0.915774 + 0.297553i
730730 −168.399 + 73.2869i −0.230683 + 0.100393i
731731 17.0815 + 52.5716i 0.0233674 + 0.0719173i
732732 8.59866 8.59866i 0.0117468 0.0117468i
733733 −379.282 + 744.383i −0.517438 + 1.01553i 0.473448 + 0.880822i 0.343009π0.343009\pi
−0.990885 + 0.134707i 0.956991π0.956991\pi
734734 164.121 225.893i 0.223598 0.307757i
735735 −29.4046 + 74.7189i −0.0400062 + 0.101658i
736736 281.205 204.307i 0.382072 0.277591i
737737 −471.576 + 74.6903i −0.639859 + 0.101344i
738738 −34.8143 219.809i −0.0471738 0.297844i
739739 −651.261 896.383i −0.881273 1.21297i −0.976067 0.217471i 0.930219π-0.930219\pi
0.0947939 0.995497i 0.469781π-0.469781\pi
740740 −90.6189 142.141i −0.122458 0.192083i
741741 −37.0504 26.9187i −0.0500005 0.0363275i
742742 −366.937 186.964i −0.494524 0.251973i
743743 −333.821 333.821i −0.449289 0.449289i 0.445829 0.895118i 0.352909π-0.352909\pi
−0.895118 + 0.445829i 0.852909π0.852909\pi
744744 −9.54631 + 3.10178i −0.0128311 + 0.00416906i
745745 −385.872 + 341.614i −0.517950 + 0.458543i
746746 88.6545 272.851i 0.118840 0.365751i
747747 455.783 + 894.524i 0.610151 + 1.19749i
748748 25.8306 + 4.09117i 0.0345329 + 0.00546948i
749749 532.104i 0.710419i
750750 −14.0060 10.7255i −0.0186746 0.0143007i
751751 698.285 0.929807 0.464904 0.885361i 0.346089π-0.346089\pi
0.464904 + 0.885361i 0.346089π0.346089\pi
752752 −39.4212 + 248.895i −0.0524217 + 0.330978i
753753 46.7510 23.8208i 0.0620863 0.0316345i
754754 296.646 + 96.3861i 0.393430 + 0.127833i
755755 156.084 + 176.306i 0.206734 + 0.233518i
756756 −51.6690 159.021i −0.0683453 0.210345i
757757 −465.289 + 465.289i −0.614648 + 0.614648i −0.944154 0.329505i 0.893118π-0.893118\pi
0.329505 + 0.944154i 0.393118π0.393118\pi
758758 −170.127 + 333.893i −0.224442 + 0.440492i
759759 17.3123 23.8283i 0.0228093 0.0313944i
760760 −274.379 + 174.924i −0.361026 + 0.230163i
761761 −1146.83 + 833.219i −1.50700 + 1.09490i −0.539515 + 0.841976i 0.681392π0.681392\pi
−0.967486 + 0.252924i 0.918608π0.918608\pi
762762 −8.53856 + 1.35238i −0.0112055 + 0.00177477i
763763 218.719 + 1380.94i 0.286657 + 1.80988i
764764 199.213 + 274.193i 0.260750 + 0.358891i
765765 32.9248 + 12.9571i 0.0430389 + 0.0169373i
766766 −186.327 135.375i −0.243247 0.176730i
767767 939.020 + 478.454i 1.22428 + 0.623800i
768768 9.58222 + 9.58222i 0.0124768 + 0.0124768i
769769 −805.374 + 261.682i −1.04730 + 0.340288i −0.781608 0.623770i 0.785600π-0.785600\pi
−0.265692 + 0.964058i 0.585600π0.585600\pi
770770 −116.770 268.314i −0.151649 0.348459i
771771 −2.10210 + 6.46959i −0.00272645 + 0.00839116i
772772 −403.858 792.616i −0.523132 1.02670i
773773 −319.914 50.6693i −0.413860 0.0655489i −0.0539672 0.998543i 0.517187π-0.517187\pi
−0.359893 + 0.932994i 0.617187π0.617187\pi
774774 372.873i 0.481748i
775775 228.314 44.5335i 0.294598 0.0574626i
776776 −588.807 −0.758772
777777 −3.70109 + 23.3678i −0.00476331 + 0.0300744i
778778 208.053 106.008i 0.267420 0.136257i
779779 −565.836 183.851i −0.726361 0.236009i
780780 −29.6651 + 50.3987i −0.0380321 + 0.0646137i
781781 7.67522 + 23.6219i 0.00982742 + 0.0302457i
782782 4.58315 4.58315i 0.00586081 0.00586081i
783783 74.2081 145.642i 0.0947740 0.186005i
784784 473.112 651.183i 0.603459 0.830590i
785785 −668.811 40.6884i −0.851989 0.0518323i
786786 −0.404845 + 0.294137i −0.000515070 + 0.000374221i
787787 −813.494 + 128.845i −1.03366 + 0.163716i −0.650140 0.759815i 0.725290π-0.725290\pi
−0.383524 + 0.923531i 0.625290π0.625290\pi
788788 −24.7285 156.130i −0.0313814 0.198134i
789789 −0.753408 1.03698i −0.000954890 0.00131429i
790790 18.7957 4.86740i 0.0237920 0.00616127i
791791 −669.446 486.381i −0.846328 0.614893i
792792 329.730 + 168.006i 0.416326 + 0.212129i
793793 −135.408 135.408i −0.170754 0.170754i
794794 194.212 63.1033i 0.244599 0.0794751i
795795 75.1334 7.25914i 0.0945074 0.00913099i
796796 −372.955 + 1147.84i −0.468536 + 1.44201i
797797 −393.451 772.191i −0.493665 0.968872i −0.994639 0.103410i 0.967025π-0.967025\pi
0.500974 0.865462i 0.332975π-0.332975\pi
798798 21.5031 + 3.40576i 0.0269463 + 0.00426787i
799799 16.8197i 0.0210509i
800800 390.012 + 498.526i 0.487516 + 0.623157i
801801 −997.982 −1.24592
802802 62.1358 392.310i 0.0774761 0.489165i
803803 497.517 253.497i 0.619573 0.315688i
804804 −43.1415 14.0175i −0.0536585 0.0174347i
805805 724.640 + 160.402i 0.900174 + 0.199257i
806806 23.2851 + 71.6640i 0.0288896 + 0.0889132i
807807 −10.3816 + 10.3816i −0.0128645 + 0.0128645i
808808 −67.3298 + 132.142i −0.0833289 + 0.163542i
809809 72.5617 99.8726i 0.0896931 0.123452i −0.761812 0.647798i 0.775690π-0.775690\pi
0.851505 + 0.524346i 0.175690π0.175690\pi
810810 183.057 + 150.801i 0.225996 + 0.186174i
811811 378.763 275.188i 0.467033 0.339319i −0.329251 0.944242i 0.606796π-0.606796\pi
0.796284 + 0.604923i 0.206796π0.206796\pi
812812 1498.78 237.384i 1.84579 0.292344i
813813 11.9673 + 75.5585i 0.0147199 + 0.0929379i
814814 −29.4364 40.5158i −0.0361627 0.0497737i
815815 840.870 1020.73i 1.03174 1.25243i
816816 1.79454 + 1.30381i 0.00219919 + 0.00159780i
817817 888.179 + 452.550i 1.08712 + 0.553916i
818818 265.469 + 265.469i 0.324534 + 0.324534i
819819 −1248.19 + 405.562i −1.52404 + 0.495191i
820820 −164.197 + 741.784i −0.200240 + 0.904615i
821821 285.639 879.107i 0.347916 1.07078i −0.612088 0.790790i 0.709670π-0.709670\pi
0.960004 0.279986i 0.0903298π-0.0903298\pi
822822 −15.9983 31.3985i −0.0194627 0.0381977i
823823 −757.643 119.999i −0.920587 0.145807i −0.321885 0.946779i 0.604316π-0.604316\pi
−0.598702 + 0.800972i 0.704316π0.704316\pi
824824 236.964i 0.287578i
825825 44.4847 + 29.9633i 0.0539208 + 0.0363192i
826826 −501.004 −0.606542
827827 −36.5445 + 230.733i −0.0441892 + 0.279000i −0.999882 0.0153664i 0.995109π-0.995109\pi
0.955693 + 0.294366i 0.0951085π0.0951085\pi
828828 −398.672 + 203.133i −0.481488 + 0.245330i
829829 −1244.32 404.304i −1.50099 0.487701i −0.560682 0.828031i 0.689461π-0.689461\pi
−0.940306 + 0.340330i 0.889461π0.889461\pi
830830 32.2067 + 333.345i 0.0388033 + 0.401621i
831831 −5.33226 16.4110i −0.00641668 0.0197485i
832832 310.046 310.046i 0.372651 0.372651i
833833 24.3900 47.8681i 0.0292797 0.0574647i
834834 −11.4855 + 15.8085i −0.0137716 + 0.0189550i
835835 337.590 + 1303.62i 0.404299 + 1.56122i
836836 381.547 277.210i 0.456396 0.331591i
837837 39.0020 6.17731i 0.0465974 0.00738030i
838838 10.9110 + 68.8892i 0.0130203 + 0.0822067i
839839 −614.547 845.852i −0.732476 1.00817i −0.999016 0.0443428i 0.985881π-0.985881\pi
0.266541 0.963824i 0.414119π-0.414119\pi
840840 3.54139 58.2113i 0.00421594 0.0692991i
841841 519.757 + 377.626i 0.618023 + 0.449020i
842842 −1.82460 0.929679i −0.00216698 0.00110413i
843843 −45.5884 45.5884i −0.0540787 0.0540787i
844844 871.127 283.046i 1.03214 0.335363i
845845 65.4386 + 38.5177i 0.0774421 + 0.0455830i
846846 −35.0603 + 107.905i −0.0414424 + 0.127547i
847847 −190.037 372.968i −0.224364 0.440340i
848848 −747.341 118.367i −0.881298 0.139584i
849849 46.6825i 0.0549853i
850850 8.63735 + 8.04398i 0.0101616 + 0.00946351i
851851 127.019 0.149259
852852 −0.369145 + 2.33069i −0.000433269 + 0.00273555i
853853 32.3156 16.4656i 0.0378846 0.0193032i −0.434946 0.900457i 0.643232π-0.643232\pi
0.472830 + 0.881154i 0.343232π0.343232\pi
854854 86.5788 + 28.1311i 0.101380 + 0.0329405i
855855 585.061 254.617i 0.684281 0.297798i
856856 69.3667 + 213.489i 0.0810358 + 0.249403i
857857 687.485 687.485i 0.802199 0.802199i −0.181240 0.983439i 0.558011π-0.558011\pi
0.983439 + 0.181240i 0.0580110π0.0580110\pi
858858 −7.88766 + 15.4804i −0.00919307 + 0.0180424i
859859 884.589 1217.53i 1.02979 1.41738i 0.124684 0.992197i 0.460208π-0.460208\pi
0.905106 0.425187i 0.139792π-0.139792\pi
860860 466.142 1184.50i 0.542025 1.37732i
861861 86.2658 62.6758i 0.100193 0.0727942i
862862 274.712 43.5101i 0.318691 0.0504757i
863863 205.361 + 1296.60i 0.237962 + 1.50243i 0.760231 + 0.649653i 0.225086π0.225086\pi
−0.522269 + 0.852781i 0.674914π0.674914\pi
864864 63.1570 + 86.9282i 0.0730984 + 0.100611i
865865 500.802 + 785.540i 0.578962 + 0.908138i
866866 −95.7869 69.5932i −0.110608 0.0803617i
867867 −60.7692 30.9634i −0.0700913 0.0357133i
868868 259.219 + 259.219i 0.298639 + 0.298639i
869869 −56.1415 + 18.2415i −0.0646047 + 0.0209913i
870870 20.3494 18.0154i 0.0233901 0.0207073i
871871 −220.741 + 679.371i −0.253434 + 0.779990i
872872 −267.777 525.542i −0.307084 0.602686i
873873 1140.37 + 180.617i 1.30626 + 0.206892i
874874 116.884i 0.133734i
875875 −245.000 + 1329.12i −0.280000 + 1.51900i
876876 53.0498 0.0605591
877877 −58.9645 + 372.287i −0.0672343 + 0.424501i 0.930996 + 0.365030i 0.118941π0.118941\pi
−0.998230 + 0.0594706i 0.981059π0.981059\pi
878878 260.639 132.802i 0.296855 0.151255i
879879 75.4629 + 24.5194i 0.0858509 + 0.0278947i
880880 −356.384 402.556i −0.404982 0.457449i
881881 −297.148 914.528i −0.337285 1.03806i −0.965585 0.260086i 0.916249π-0.916249\pi
0.628300 0.777971i 0.283751π-0.283751\pi
882882 256.252 256.252i 0.290535 0.290535i
883883 16.1759 31.7470i 0.0183192 0.0359535i −0.881666 0.471875i 0.843577π-0.843577\pi
0.899985 + 0.435921i 0.143577π0.143577\pi
884884 22.9987 31.6549i 0.0260166 0.0358088i
885885 77.4320 49.3650i 0.0874938 0.0557796i
886886 164.963 119.853i 0.186189 0.135274i
887887 −296.686 + 46.9904i −0.334482 + 0.0529768i −0.321417 0.946938i 0.604159π-0.604159\pi
−0.0130655 + 0.999915i 0.504159π0.504159\pi
888888 −1.56136 9.85802i −0.00175828 0.0111014i
889889 389.298 + 535.823i 0.437905 + 0.602725i
890890 −309.783 121.910i −0.348070 0.136978i
891891 −583.372 423.845i −0.654739 0.475696i
892892 −245.877 125.281i −0.275647 0.140449i
893893 214.475 + 214.475i 0.240174 + 0.240174i
894894 −13.8344 + 4.49507i −0.0154747 + 0.00502805i
895895 −408.166 937.884i −0.456051 1.04792i
896896 −402.780 + 1239.63i −0.449531 + 1.38352i
897897 −20.0056 39.2632i −0.0223028 0.0437717i
898898 −202.855 32.1291i −0.225897 0.0357786i
899899 358.375i 0.398637i
900900 −395.480 712.374i −0.439422 0.791527i
901901 −50.5032 −0.0560524
902902 −35.3088 + 222.931i −0.0391450 + 0.247152i
903903 −159.183 + 81.1080i −0.176283 + 0.0898206i
904904 331.998 + 107.873i 0.367255 + 0.119328i
905905 70.0436 118.999i 0.0773962 0.131490i
906906 2.05381 + 6.32097i 0.00226689 + 0.00697678i
907907 −505.478 + 505.478i −0.557307 + 0.557307i −0.928540 0.371233i 0.878935π-0.878935\pi
0.371233 + 0.928540i 0.378935π0.378935\pi
908908 −567.744 + 1114.26i −0.625268 + 1.22716i
909909 170.935 235.272i 0.188047 0.258825i
910910 −436.992 26.5852i −0.480210 0.0292145i
911911 −1112.30 + 808.135i −1.22097 + 0.887086i −0.996180 0.0873220i 0.972169π-0.972169\pi
−0.224788 + 0.974408i 0.572169π0.572169\pi
912912 39.5084 6.25752i 0.0433207 0.00686132i
913913 −159.283 1005.67i −0.174461 1.10150i
914914 72.3704 + 99.6093i 0.0791798 + 0.108982i
915915 −16.1529 + 4.18302i −0.0176534 + 0.00457160i
916916 68.9194 + 50.0728i 0.0752395 + 0.0546647i
917917 34.1594 + 17.4051i 0.0372513 + 0.0189805i
918918 1.41678 + 1.41678i 0.00154333 + 0.00154333i
919919 1241.96 403.536i 1.35142 0.439104i 0.458252 0.888822i 0.348476π-0.348476\pi
0.893170 + 0.449718i 0.148476π0.148476\pi
920920 −311.648 + 30.1104i −0.338748 + 0.0327287i
921921 −8.17554 + 25.1617i −0.00887681 + 0.0273200i
922922 −90.5801 177.773i −0.0982430 0.192813i
923923 36.7026 + 5.81312i 0.0397645 + 0.00629808i
924924 84.5254i 0.0914777i
925925 8.22240 + 231.157i 0.00888909 + 0.249899i
926926 −16.5629 −0.0178865
927927 72.6888 458.939i 0.0784129 0.495080i
928928 −868.868 + 442.711i −0.936281 + 0.477059i
929929 −430.474 139.870i −0.463374 0.150559i 0.0680204 0.997684i 0.478332π-0.478332\pi
−0.531394 + 0.847125i 0.678332π0.678332\pi
930930 6.41054 + 1.41900i 0.00689306 + 0.00152581i
931931 −299.380 921.397i −0.321568 0.989685i
932932 −493.250 + 493.250i −0.529239 + 0.529239i
933933 −12.1956 + 23.9353i −0.0130714 + 0.0256541i
934934 −143.746 + 197.849i −0.153904 + 0.211830i
935935 −27.6973 22.8168i −0.0296227 0.0244030i
936936 447.924 325.436i 0.478551 0.347688i
937937 −517.916 + 82.0298i −0.552738 + 0.0875451i −0.426555 0.904462i 0.640273π-0.640273\pi
−0.126184 + 0.992007i 0.540273π0.540273\pi
938938 −53.1227 335.404i −0.0566341 0.357573i
939939 −14.2874 19.6650i −0.0152156 0.0209425i
940940 246.271 298.948i 0.261990 0.318029i
941941 983.490 + 714.547i 1.04515 + 0.759349i 0.971285 0.237919i 0.0764653π-0.0764653\pi
0.0738692 + 0.997268i 0.476465π0.476465\pi
942942 −16.8511 8.58607i −0.0178887 0.00911472i
943943 −404.798 404.798i −0.429266 0.429266i
944944 −875.458 + 284.454i −0.927392 + 0.301328i
945945 −49.5847 + 224.006i −0.0524706 + 0.237044i
946946 116.861 359.660i 0.123531 0.380190i
947947 561.219 + 1101.45i 0.592628 + 1.16310i 0.971365 + 0.237594i 0.0763588π0.0763588\pi
−0.378736 + 0.925505i 0.623641π0.623641\pi
948948 −5.53929 0.877337i −0.00584313 0.000925461i
949949 835.402i 0.880297i
950950 212.711 7.56630i 0.223907 0.00796452i
951951 −96.5800 −0.101556
952952 −6.10394 + 38.5387i −0.00641170 + 0.0404819i
953953 90.7422 46.2355i 0.0952174 0.0485157i −0.405733 0.913992i 0.632984π-0.632984\pi
0.500951 + 0.865476i 0.332984π0.332984\pi
954954 −323.997 105.273i −0.339620 0.110349i
955955 −44.7232 462.893i −0.0468306 0.484705i
956956 61.8915 + 190.483i 0.0647401 + 0.199250i
957957 −58.4290 + 58.4290i −0.0610544 + 0.0610544i
958958 165.071 323.971i 0.172308 0.338174i
959959 −1586.89 + 2184.16i −1.65473 + 2.27754i
960960 −9.57794 36.9856i −0.00997702 0.0385267i
961961 707.423 513.973i 0.736133 0.534832i
962962 −74.0040 + 11.7211i −0.0769273 + 0.0121841i
963963 −68.8578 434.751i −0.0715034 0.451455i
964964 −72.4811 99.7617i −0.0751879 0.103487i
965965 −74.1218 + 1218.37i −0.0768102 + 1.26256i
966966 16.9476 + 12.3132i 0.0175441 + 0.0127466i
967967 −421.887 214.962i −0.436284 0.222298i 0.222032 0.975039i 0.428731π-0.428731\pi
−0.658316 + 0.752741i 0.728731π0.728731\pi
968968 124.867 + 124.867i 0.128995 + 0.128995i
969969 2.53920 0.825036i 0.00262043 0.000851430i
970970 331.917 + 195.369i 0.342182 + 0.201411i
971971 520.392 1601.60i 0.535934 1.64943i −0.205690 0.978617i 0.565944π-0.565944\pi
0.741623 0.670817i 0.234056π-0.234056\pi
972972 −94.2891 185.053i −0.0970052 0.190383i
973973 1478.60 + 234.187i 1.51963 + 0.240686i
974974 138.450i 0.142146i
975975 70.1582 38.9489i 0.0719571 0.0399475i
976976 167.260 0.171373
977977 17.9443 113.296i 0.0183667 0.115963i −0.976802 0.214146i 0.931303π-0.931303\pi
0.995168 + 0.0981833i 0.0313032π0.0313032\pi
978978 33.2592 16.9464i 0.0340074 0.0173276i
979979 962.619 + 312.774i 0.983267 + 0.319483i
980980 −1134.38 + 493.679i −1.15753 + 0.503755i
981981 357.405 + 1099.98i 0.364328 + 1.12128i
982982 −150.646 + 150.646i −0.153407 + 0.153407i
983983 583.651 1145.48i 0.593744 1.16529i −0.377233 0.926118i 0.623125π-0.623125\pi
0.970978 0.239170i 0.0768755π-0.0768755\pi
984984 −26.4406 + 36.3924i −0.0268706 + 0.0369842i
985985 −79.4297 + 201.836i −0.0806393 + 0.204910i
986986 −14.7111 + 10.6882i −0.0149200 + 0.0108400i
987987 −53.6920 + 8.50397i −0.0543992 + 0.00861598i
988988 −110.380 696.913i −0.111721 0.705378i
989989 563.778 + 775.973i 0.570048 + 0.784604i
990990 −130.127 204.113i −0.131442 0.206174i
991991 −392.287 285.013i −0.395850 0.287602i 0.371999 0.928233i 0.378673π-0.378673\pi
−0.767848 + 0.640631i 0.778673π0.778673\pi
992992 −209.902 106.950i −0.211595 0.107813i
993993 −20.1689 20.1689i −0.0203110 0.0203110i
994994 −16.8008 + 5.45892i −0.0169022 + 0.00549187i
995995 1239.95 1097.73i 1.24618 1.10325i
996996 29.8934 92.0024i 0.0300135 0.0923719i
997997 589.304 + 1156.57i 0.591077 + 1.16005i 0.971897 + 0.235405i 0.0756417π0.0756417\pi
−0.380820 + 0.924649i 0.624358π0.624358\pi
998998 −443.254 70.2046i −0.444143 0.0703453i
999999 39.2652i 0.0393045i
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 25.3.f.a.23.3 yes 32
3.2 odd 2 225.3.r.a.73.2 32
4.3 odd 2 400.3.bg.c.273.2 32
5.2 odd 4 125.3.f.a.32.3 32
5.3 odd 4 125.3.f.b.32.2 32
5.4 even 2 125.3.f.c.93.2 32
25.9 even 10 125.3.f.b.43.2 32
25.12 odd 20 inner 25.3.f.a.12.3 32
25.13 odd 20 125.3.f.c.82.2 32
25.16 even 5 125.3.f.a.43.3 32
75.62 even 20 225.3.r.a.37.2 32
100.87 even 20 400.3.bg.c.337.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.12.3 32 25.12 odd 20 inner
25.3.f.a.23.3 yes 32 1.1 even 1 trivial
125.3.f.a.32.3 32 5.2 odd 4
125.3.f.a.43.3 32 25.16 even 5
125.3.f.b.32.2 32 5.3 odd 4
125.3.f.b.43.2 32 25.9 even 10
125.3.f.c.82.2 32 25.13 odd 20
125.3.f.c.93.2 32 5.4 even 2
225.3.r.a.37.2 32 75.62 even 20
225.3.r.a.73.2 32 3.2 odd 2
400.3.bg.c.273.2 32 4.3 odd 2
400.3.bg.c.337.2 32 100.87 even 20