# Properties

 Label 668.2.e.a.21.3 Level $668$ Weight $2$ Character 668.21 Analytic conductor $5.334$ Analytic rank $0$ Dimension $1148$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$668 = 2^{2} \cdot 167$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 668.e (of order $$83$$, degree $$82$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.33400685502$$ Analytic rank: $$0$$ Dimension: $$1148$$ Relative dimension: $$14$$ over $$\Q(\zeta_{83})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

## Embedding invariants

 Embedding label 21.3 Character $$\chi$$ $$=$$ 668.21 Dual form 668.2.e.a.509.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.90829 - 0.291147i) q^{3} +(1.01478 + 1.20422i) q^{5} +(2.44900 - 3.39773i) q^{7} +(0.693279 + 0.216588i) q^{9} +O(q^{10})$$ $$q+(-1.90829 - 0.291147i) q^{3} +(1.01478 + 1.20422i) q^{5} +(2.44900 - 3.39773i) q^{7} +(0.693279 + 0.216588i) q^{9} +(0.410057 - 0.387413i) q^{11} +(-0.251414 + 1.88668i) q^{13} +(-1.58589 - 2.59345i) q^{15} +(-2.11599 + 3.18308i) q^{17} +(0.744309 + 0.172002i) q^{19} +(-5.66262 + 5.77082i) q^{21} +(-1.46291 - 6.92542i) q^{23} +(0.427164 - 2.48360i) q^{25} +(3.94403 + 1.92568i) q^{27} +(2.16132 - 10.2317i) q^{29} +(4.67062 - 0.894634i) q^{31} +(-0.895301 + 0.619908i) q^{33} +(6.57681 - 0.498825i) q^{35} +(6.06457 - 1.89464i) q^{37} +(1.02907 - 3.52713i) q^{39} +(-3.75057 + 1.49153i) q^{41} +(7.49058 + 2.65521i) q^{43} +(0.442708 + 1.05465i) q^{45} +(0.564216 - 2.24684i) q^{47} +(-3.33350 - 10.0012i) q^{49} +(4.96466 - 5.45816i) q^{51} +(-6.20880 - 4.65619i) q^{53} +(0.882650 + 0.100659i) q^{55} +(-1.37028 - 0.544933i) q^{57} +(-1.69167 - 2.54477i) q^{59} +(5.65813 + 7.25464i) q^{61} +(2.43375 - 1.82515i) q^{63} +(-2.52711 + 1.61181i) q^{65} +(6.95757 - 8.25639i) q^{67} +(0.775347 + 13.6416i) q^{69} +(-0.707032 - 7.44952i) q^{71} +(2.02670 - 3.61492i) q^{73} +(-1.53824 + 4.61505i) q^{75} +(-0.312093 - 2.34204i) q^{77} +(-10.3455 - 0.391771i) q^{79} +(-8.75713 - 6.06345i) q^{81} +(3.43858 - 0.933000i) q^{83} +(-5.98040 + 0.682018i) q^{85} +(-7.10334 + 18.8957i) q^{87} +(-4.06478 + 6.64722i) q^{89} +(5.79471 + 5.47471i) q^{91} +(-9.17336 + 0.347382i) q^{93} +(0.548184 + 1.07086i) q^{95} +(7.06846 + 1.35393i) q^{97} +(0.368193 - 0.179772i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$1148q - 2q^{5} - 14q^{9} + O(q^{10})$$ $$1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$335$$ $$\chi(n)$$ $$e\left(\frac{23}{83}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.90829 0.291147i −1.10175 0.168094i −0.425639 0.904893i $$-0.639951\pi$$
−0.676111 + 0.736800i $$0.736336\pi$$
$$4$$ 0 0
$$5$$ 1.01478 + 1.20422i 0.453825 + 0.538544i 0.942626 0.333852i $$-0.108349\pi$$
−0.488800 + 0.872396i $$0.662565\pi$$
$$6$$ 0 0
$$7$$ 2.44900 3.39773i 0.925634 1.28422i −0.0329643 0.999457i $$-0.510495\pi$$
0.958598 0.284763i $$-0.0919149\pi$$
$$8$$ 0 0
$$9$$ 0.693279 + 0.216588i 0.231093 + 0.0721961i
$$10$$ 0 0
$$11$$ 0.410057 0.387413i 0.123637 0.116809i −0.622445 0.782664i $$-0.713860\pi$$
0.746082 + 0.665854i $$0.231933\pi$$
$$12$$ 0 0
$$13$$ −0.251414 + 1.88668i −0.0697297 + 0.523271i 0.921221 + 0.389041i $$0.127193\pi$$
−0.990950 + 0.134230i $$0.957144\pi$$
$$14$$ 0 0
$$15$$ −1.58589 2.59345i −0.409476 0.669625i
$$16$$ 0 0
$$17$$ −2.11599 + 3.18308i −0.513203 + 0.772010i −0.994521 0.104536i $$-0.966664\pi$$
0.481318 + 0.876546i $$0.340158\pi$$
$$18$$ 0 0
$$19$$ 0.744309 + 0.172002i 0.170756 + 0.0394600i 0.309668 0.950845i $$-0.399782\pi$$
−0.138912 + 0.990305i $$0.544360\pi$$
$$20$$ 0 0
$$21$$ −5.66262 + 5.77082i −1.23569 + 1.25930i
$$22$$ 0 0
$$23$$ −1.46291 6.92542i −0.305039 1.44405i −0.812795 0.582550i $$-0.802055\pi$$
0.507756 0.861501i $$-0.330475\pi$$
$$24$$ 0 0
$$25$$ 0.427164 2.48360i 0.0854328 0.496720i
$$26$$ 0 0
$$27$$ 3.94403 + 1.92568i 0.759029 + 0.370598i
$$28$$ 0 0
$$29$$ 2.16132 10.2317i 0.401348 1.89998i −0.0334349 0.999441i $$-0.510645\pi$$
0.434783 0.900535i $$-0.356825\pi$$
$$30$$ 0 0
$$31$$ 4.67062 0.894634i 0.838869 0.160681i 0.249327 0.968419i $$-0.419790\pi$$
0.589541 + 0.807738i $$0.299309\pi$$
$$32$$ 0 0
$$33$$ −0.895301 + 0.619908i −0.155852 + 0.107912i
$$34$$ 0 0
$$35$$ 6.57681 0.498825i 1.11168 0.0843168i
$$36$$ 0 0
$$37$$ 6.06457 1.89464i 0.997009 0.311477i 0.244206 0.969723i $$-0.421473\pi$$
0.752803 + 0.658246i $$0.228701\pi$$
$$38$$ 0 0
$$39$$ 1.02907 3.52713i 0.164783 0.564792i
$$40$$ 0 0
$$41$$ −3.75057 + 1.49153i −0.585741 + 0.232938i −0.643568 0.765389i $$-0.722547\pi$$
0.0578271 + 0.998327i $$0.481583\pi$$
$$42$$ 0 0
$$43$$ 7.49058 + 2.65521i 1.14230 + 0.404916i 0.836926 0.547316i $$-0.184350\pi$$
0.305376 + 0.952232i $$0.401218\pi$$
$$44$$ 0 0
$$45$$ 0.442708 + 1.05465i 0.0659950 + 0.157218i
$$46$$ 0 0
$$47$$ 0.564216 2.24684i 0.0822994 0.327735i −0.914794 0.403920i $$-0.867647\pi$$
0.997094 + 0.0761848i $$0.0242739\pi$$
$$48$$ 0 0
$$49$$ −3.33350 10.0012i −0.476214 1.42874i
$$50$$ 0 0
$$51$$ 4.96466 5.45816i 0.695191 0.764296i
$$52$$ 0 0
$$53$$ −6.20880 4.65619i −0.852844 0.639577i 0.0812141 0.996697i $$-0.474120\pi$$
−0.934059 + 0.357120i $$0.883759\pi$$
$$54$$ 0 0
$$55$$ 0.882650 + 0.100659i 0.119017 + 0.0135729i
$$56$$ 0 0
$$57$$ −1.37028 0.544933i −0.181498 0.0721781i
$$58$$ 0 0
$$59$$ −1.69167 2.54477i −0.220237 0.331301i 0.706022 0.708190i $$-0.250488\pi$$
−0.926259 + 0.376889i $$0.876994\pi$$
$$60$$ 0 0
$$61$$ 5.65813 + 7.25464i 0.724449 + 0.928861i 0.999469 0.0325769i $$-0.0103714\pi$$
−0.275020 + 0.961438i $$0.588685\pi$$
$$62$$ 0 0
$$63$$ 2.43375 1.82515i 0.306623 0.229947i
$$64$$ 0 0
$$65$$ −2.52711 + 1.61181i −0.313449 + 0.199921i
$$66$$ 0 0
$$67$$ 6.95757 8.25639i 0.850003 1.00868i −0.149798 0.988717i $$-0.547862\pi$$
0.999801 0.0199620i $$-0.00635453\pi$$
$$68$$ 0 0
$$69$$ 0.775347 + 13.6416i 0.0933408 + 1.64226i
$$70$$ 0 0
$$71$$ −0.707032 7.44952i −0.0839092 0.884095i −0.933956 0.357388i $$-0.883667\pi$$
0.850047 0.526707i $$-0.176574\pi$$
$$72$$ 0 0
$$73$$ 2.02670 3.61492i 0.237207 0.423095i −0.727619 0.685981i $$-0.759373\pi$$
0.964827 + 0.262886i $$0.0846745\pi$$
$$74$$ 0 0
$$75$$ −1.53824 + 4.61505i −0.177621 + 0.532900i
$$76$$ 0 0
$$77$$ −0.312093 2.34204i −0.0355663 0.266900i
$$78$$ 0 0
$$79$$ −10.3455 0.391771i −1.16396 0.0440777i −0.551221 0.834359i $$-0.685838\pi$$
−0.612744 + 0.790282i $$0.709934\pi$$
$$80$$ 0 0
$$81$$ −8.75713 6.06345i −0.973015 0.673717i
$$82$$ 0 0
$$83$$ 3.43858 0.933000i 0.377434 0.102410i −0.0680926 0.997679i $$-0.521691\pi$$
0.445526 + 0.895269i $$0.353017\pi$$
$$84$$ 0 0
$$85$$ −5.98040 + 0.682018i −0.648666 + 0.0739752i
$$86$$ 0 0
$$87$$ −7.10334 + 18.8957i −0.761558 + 2.02583i
$$88$$ 0 0
$$89$$ −4.06478 + 6.64722i −0.430865 + 0.704604i −0.992428 0.122830i $$-0.960803\pi$$
0.561562 + 0.827434i $$0.310200\pi$$
$$90$$ 0 0
$$91$$ 5.79471 + 5.47471i 0.607451 + 0.573905i
$$92$$ 0 0
$$93$$ −9.17336 + 0.347382i −0.951233 + 0.0360218i
$$94$$ 0 0
$$95$$ 0.548184 + 1.07086i 0.0562425 + 0.109868i
$$96$$ 0 0
$$97$$ 7.06846 + 1.35393i 0.717693 + 0.137470i 0.533965 0.845507i $$-0.320701\pi$$
0.183728 + 0.982977i $$0.441183\pi$$
$$98$$ 0 0
$$99$$ 0.368193 0.179772i 0.0370048 0.0180677i
$$100$$ 0 0
$$101$$ −5.90222 + 2.09218i −0.587293 + 0.208180i −0.611122 0.791536i $$-0.709282\pi$$
0.0238296 + 0.999716i $$0.492414\pi$$
$$102$$ 0 0
$$103$$ 0.238422 12.5966i 0.0234924 1.24118i −0.772162 0.635425i $$-0.780825\pi$$
0.795655 0.605750i $$-0.207127\pi$$
$$104$$ 0 0
$$105$$ −12.6957 0.962916i −1.23897 0.0939709i
$$106$$ 0 0
$$107$$ 0.220685 + 11.6595i 0.0213345 + 1.12717i 0.836510 + 0.547952i $$0.184592\pi$$
−0.815175 + 0.579215i $$0.803359\pi$$
$$108$$ 0 0
$$109$$ −7.17969 + 14.0253i −0.687690 + 1.34338i 0.240274 + 0.970705i $$0.422763\pi$$
−0.927964 + 0.372671i $$0.878442\pi$$
$$110$$ 0 0
$$111$$ −12.1246 + 1.84984i −1.15081 + 0.175579i
$$112$$ 0 0
$$113$$ 5.58984 + 4.89436i 0.525848 + 0.460423i 0.880142 0.474711i $$-0.157447\pi$$
−0.354294 + 0.935134i $$0.615279\pi$$
$$114$$ 0 0
$$115$$ 6.85520 8.78948i 0.639250 0.819623i
$$116$$ 0 0
$$117$$ −0.582933 + 1.25354i −0.0538921 + 0.115890i
$$118$$ 0 0
$$119$$ 5.63318 + 14.9849i 0.516392 + 1.37366i
$$120$$ 0 0
$$121$$ −0.606140 + 10.6646i −0.0551036 + 0.969505i
$$122$$ 0 0
$$123$$ 7.59142 1.75430i 0.684495 0.158180i
$$124$$ 0 0
$$125$$ 10.2183 5.98581i 0.913953 0.535387i
$$126$$ 0 0
$$127$$ −1.17928 + 12.4253i −0.104645 + 1.10257i 0.776628 + 0.629960i $$0.216929\pi$$
−0.881272 + 0.472609i $$0.843312\pi$$
$$128$$ 0 0
$$129$$ −13.5211 7.24776i −1.19047 0.638130i
$$130$$ 0 0
$$131$$ 3.46403 + 3.80837i 0.302654 + 0.332739i 0.872135 0.489266i $$-0.162735\pi$$
−0.569481 + 0.822005i $$0.692856\pi$$
$$132$$ 0 0
$$133$$ 2.40723 2.10773i 0.208733 0.182763i
$$134$$ 0 0
$$135$$ 1.68339 + 6.70363i 0.144883 + 0.576957i
$$136$$ 0 0
$$137$$ 6.44608 + 22.0939i 0.550725 + 1.88761i 0.450834 + 0.892608i $$0.351127\pi$$
0.0998916 + 0.994998i $$0.468150\pi$$
$$138$$ 0 0
$$139$$ −5.24107 + 2.31764i −0.444541 + 0.196580i −0.614575 0.788858i $$-0.710673\pi$$
0.170034 + 0.985438i $$0.445612\pi$$
$$140$$ 0 0
$$141$$ −1.73085 + 4.12334i −0.145764 + 0.347248i
$$142$$ 0 0
$$143$$ 0.627830 + 0.871048i 0.0525018 + 0.0728407i
$$144$$ 0 0
$$145$$ 14.5145 7.78024i 1.20536 0.646114i
$$146$$ 0 0
$$147$$ 3.44946 + 20.0557i 0.284506 + 1.65417i
$$148$$ 0 0
$$149$$ −6.97952 4.45161i −0.571785 0.364690i 0.219991 0.975502i $$-0.429397\pi$$
−0.791776 + 0.610812i $$0.790843\pi$$
$$150$$ 0 0
$$151$$ −3.88296 6.92584i −0.315991 0.563617i 0.667492 0.744617i $$-0.267368\pi$$
−0.983483 + 0.181000i $$0.942067\pi$$
$$152$$ 0 0
$$153$$ −2.15639 + 1.74846i −0.174334 + 0.141355i
$$154$$ 0 0
$$155$$ 5.81701 + 4.71660i 0.467233 + 0.378846i
$$156$$ 0 0
$$157$$ −4.94755 10.6392i −0.394857 0.849104i −0.998649 0.0519621i $$-0.983453\pi$$
0.603792 0.797142i $$-0.293656\pi$$
$$158$$ 0 0
$$159$$ 10.4925 + 10.6930i 0.832112 + 0.848011i
$$160$$ 0 0
$$161$$ −27.1134 11.9898i −2.13683 0.944925i
$$162$$ 0 0
$$163$$ −7.89579 4.62529i −0.618446 0.362281i 0.162657 0.986683i $$-0.447993\pi$$
−0.781103 + 0.624402i $$0.785343\pi$$
$$164$$ 0 0
$$165$$ −1.65504 0.449067i −0.128845 0.0349598i
$$166$$ 0 0
$$167$$ −12.5320 + 3.15409i −0.969757 + 0.244071i
$$168$$ 0 0
$$169$$ 9.05001 + 2.45556i 0.696154 + 0.188889i
$$170$$ 0 0
$$171$$ 0.478760 + 0.280454i 0.0366117 + 0.0214469i
$$172$$ 0 0
$$173$$ 13.0565 + 5.77367i 0.992664 + 0.438964i 0.836025 0.548692i $$-0.184874\pi$$
0.156639 + 0.987656i $$0.449934\pi$$
$$174$$ 0 0
$$175$$ −7.39247 7.53371i −0.558818 0.569495i
$$176$$ 0 0
$$177$$ 2.48729 + 5.34868i 0.186956 + 0.402031i
$$178$$ 0 0
$$179$$ −8.03152 6.51219i −0.600304 0.486744i 0.280736 0.959785i $$-0.409421\pi$$
−0.881041 + 0.473041i $$0.843156\pi$$
$$180$$ 0 0
$$181$$ 6.85299 5.55660i 0.509379 0.413019i −0.340302 0.940316i $$-0.610529\pi$$
0.849681 + 0.527297i $$0.176794\pi$$
$$182$$ 0 0
$$183$$ −8.68516 15.4913i −0.642026 1.14515i
$$184$$ 0 0
$$185$$ 8.43579 + 5.38043i 0.620212 + 0.395577i
$$186$$ 0 0
$$187$$ 0.365488 + 2.12501i 0.0267271 + 0.155396i
$$188$$ 0 0
$$189$$ 16.2019 8.68473i 1.17851 0.631721i
$$190$$ 0 0
$$191$$ −2.72683 3.78319i −0.197306 0.273742i 0.700953 0.713207i $$-0.252758\pi$$
−0.898260 + 0.439465i $$0.855168\pi$$
$$192$$ 0 0
$$193$$ −1.90046 + 4.52741i −0.136798 + 0.325890i −0.975946 0.218014i $$-0.930042\pi$$
0.839148 + 0.543904i $$0.183054\pi$$
$$194$$ 0 0
$$195$$ 5.29172 2.34004i 0.378948 0.167574i
$$196$$ 0 0
$$197$$ 3.42029 + 11.7230i 0.243686 + 0.835230i 0.986222 + 0.165425i $$0.0528995\pi$$
−0.742537 + 0.669805i $$0.766378\pi$$
$$198$$ 0 0
$$199$$ −3.16532 12.6050i −0.224384 0.893547i −0.973049 0.230599i $$-0.925931\pi$$
0.748665 0.662948i $$-0.230695\pi$$
$$200$$ 0 0
$$201$$ −15.6809 + 13.7299i −1.10604 + 0.968431i
$$202$$ 0 0
$$203$$ −29.4714 32.4009i −2.06849 2.27410i
$$204$$ 0 0
$$205$$ −5.60215 3.00294i −0.391271 0.209734i
$$206$$ 0 0
$$207$$ 0.485758 5.11810i 0.0337625 0.355733i
$$208$$ 0 0
$$209$$ 0.371846 0.217824i 0.0257211 0.0150672i
$$210$$ 0 0
$$211$$ 12.6037 2.91260i 0.867678 0.200511i 0.232235 0.972660i $$-0.425396\pi$$
0.635442 + 0.772148i $$0.280818\pi$$
$$212$$ 0 0
$$213$$ −0.819682 + 14.4217i −0.0561637 + 0.988156i
$$214$$ 0 0
$$215$$ 4.40386 + 11.7148i 0.300340 + 0.798941i
$$216$$ 0 0
$$217$$ 8.39862 18.0604i 0.570135 1.22602i
$$218$$ 0 0
$$219$$ −4.92000 + 6.30824i −0.332463 + 0.426271i
$$220$$ 0 0
$$221$$ −5.47346 4.79247i −0.368185 0.322376i
$$222$$ 0 0
$$223$$ −12.6757 + 1.93392i −0.848827 + 0.129505i −0.560630 0.828066i $$-0.689441\pi$$
−0.288196 + 0.957571i $$0.593056\pi$$
$$224$$ 0 0
$$225$$ 0.834062 1.62931i 0.0556042 0.108621i
$$226$$ 0 0
$$227$$ 0.337455 + 17.8288i 0.0223977 + 1.18334i 0.817157 + 0.576415i $$0.195549\pi$$
−0.794760 + 0.606924i $$0.792403\pi$$
$$228$$ 0 0
$$229$$ 8.51009 + 0.645456i 0.562363 + 0.0426529i 0.353741 0.935343i $$-0.384909\pi$$
0.208622 + 0.977996i $$0.433102\pi$$
$$230$$ 0 0
$$231$$ −0.0863121 + 4.56014i −0.00567892 + 0.300035i
$$232$$ 0 0
$$233$$ 16.8200 5.96225i 1.10191 0.390600i 0.279879 0.960035i $$-0.409706\pi$$
0.822036 + 0.569436i $$0.192838\pi$$
$$234$$ 0 0
$$235$$ 3.27825 1.60062i 0.213849 0.104413i
$$236$$ 0 0
$$237$$ 19.6282 + 3.75968i 1.27499 + 0.244218i
$$238$$ 0 0
$$239$$ −6.92720 13.5320i −0.448084 0.875314i −0.999165 0.0408627i $$-0.986989\pi$$
0.551081 0.834452i $$-0.314215\pi$$
$$240$$ 0 0
$$241$$ −30.2885 + 1.14698i −1.95105 + 0.0738836i −0.983728 0.179662i $$-0.942500\pi$$
−0.967323 + 0.253546i $$0.918403\pi$$
$$242$$ 0 0
$$243$$ 5.37470 + 5.07789i 0.344787 + 0.325747i
$$244$$ 0 0
$$245$$ 8.66087 14.1633i 0.553323 0.904862i
$$246$$ 0 0
$$247$$ −0.511643 + 1.36103i −0.0325551 + 0.0866003i
$$248$$ 0 0
$$249$$ −6.83344 + 0.779300i −0.433052 + 0.0493861i
$$250$$ 0 0
$$251$$ 6.84278 1.85667i 0.431912 0.117192i −0.0392682 0.999229i $$-0.512503\pi$$
0.471181 + 0.882037i $$0.343828\pi$$
$$252$$ 0 0
$$253$$ −3.28288 2.27307i −0.206393 0.142907i
$$254$$ 0 0
$$255$$ 11.6109 + 0.439688i 0.727102 + 0.0275343i
$$256$$ 0 0
$$257$$ −1.30378 9.78393i −0.0813276 0.610305i −0.983762 0.179478i $$-0.942559\pi$$
0.902434 0.430827i $$-0.141778\pi$$
$$258$$ 0 0
$$259$$ 8.41464 25.2457i 0.522860 1.56869i
$$260$$ 0 0
$$261$$ 3.71446 6.62530i 0.229919 0.410095i
$$262$$ 0 0
$$263$$ 1.89454 + 19.9615i 0.116822 + 1.23088i 0.840912 + 0.541172i $$0.182019\pi$$
−0.724090 + 0.689706i $$0.757740\pi$$
$$264$$ 0 0
$$265$$ −0.693511 12.2018i −0.0426021 0.749550i
$$266$$ 0 0
$$267$$ 9.69207 11.5014i 0.593145 0.703872i
$$268$$ 0 0
$$269$$ −18.8524 + 12.0243i −1.14945 + 0.733132i −0.968169 0.250298i $$-0.919471\pi$$
−0.181284 + 0.983431i $$0.558025\pi$$
$$270$$ 0 0
$$271$$ 10.4286 7.82080i 0.633495 0.475080i −0.234192 0.972190i $$-0.575244\pi$$
0.867687 + 0.497111i $$0.165606\pi$$
$$272$$ 0 0
$$273$$ −9.46402 12.1344i −0.572789 0.734409i
$$274$$ 0 0
$$275$$ −0.787017 1.18391i −0.0474589 0.0713923i
$$276$$ 0 0
$$277$$ 25.1156 + 9.98800i 1.50905 + 0.600121i 0.970206 0.242283i $$-0.0778963\pi$$
0.538847 + 0.842404i $$0.318860\pi$$
$$278$$ 0 0
$$279$$ 3.43181 + 0.391371i 0.205457 + 0.0234308i
$$280$$ 0 0
$$281$$ 9.17793 + 6.88284i 0.547509 + 0.410596i 0.837503 0.546433i $$-0.184015\pi$$
−0.289994 + 0.957029i $$0.593653\pi$$
$$282$$ 0 0
$$283$$ −11.7235 + 12.8888i −0.696888 + 0.766161i −0.981288 0.192545i $$-0.938326\pi$$
0.284400 + 0.958706i $$0.408205\pi$$
$$284$$ 0 0
$$285$$ −0.734317 2.20311i −0.0434972 0.130501i
$$286$$ 0 0
$$287$$ −4.11733 + 16.3962i −0.243038 + 0.967835i
$$288$$ 0 0
$$289$$ 0.925277 + 2.20426i 0.0544281 + 0.129662i
$$290$$ 0 0
$$291$$ −13.0945 4.64164i −0.767610 0.272098i
$$292$$ 0 0
$$293$$ 7.05648 2.80622i 0.412244 0.163941i −0.154204 0.988039i $$-0.549281\pi$$
0.566448 + 0.824098i $$0.308317\pi$$
$$294$$ 0 0
$$295$$ 1.34779 4.61954i 0.0784713 0.268960i
$$296$$ 0 0
$$297$$ 2.36331 0.738326i 0.137133 0.0428420i
$$298$$ 0 0
$$299$$ 13.4339 1.01890i 0.776900 0.0589247i
$$300$$ 0 0
$$301$$ 27.3661 18.9483i 1.57735 1.09216i
$$302$$ 0 0
$$303$$ 11.8723 2.27407i 0.682043 0.130642i
$$304$$ 0 0
$$305$$ −2.99441 + 14.1755i −0.171460 + 0.811688i
$$306$$ 0 0
$$307$$ 25.7144 + 12.5551i 1.46760 + 0.716560i 0.987051 0.160408i $$-0.0512810\pi$$
0.480548 + 0.876968i $$0.340438\pi$$
$$308$$ 0 0
$$309$$ −4.12242 + 23.9684i −0.234516 + 1.36352i
$$310$$ 0 0
$$311$$ 4.62163 + 21.8788i 0.262069 + 1.24063i 0.887667 + 0.460486i $$0.152325\pi$$
−0.625598 + 0.780146i $$0.715145\pi$$
$$312$$ 0 0
$$313$$ −11.4909 + 11.7104i −0.649502 + 0.661912i −0.957151 0.289588i $$-0.906482\pi$$
0.307649 + 0.951500i $$0.400458\pi$$
$$314$$ 0 0
$$315$$ 4.66760 + 1.07864i 0.262990 + 0.0607742i
$$316$$ 0 0
$$317$$ −10.7372 + 16.1520i −0.603062 + 0.907184i −0.999943 0.0106857i $$-0.996599\pi$$
0.396881 + 0.917870i $$0.370093\pi$$
$$318$$ 0 0
$$319$$ −3.07762 5.03290i −0.172314 0.281789i
$$320$$ 0 0
$$321$$ 2.97349 22.3139i 0.165964 1.24544i
$$322$$ 0 0
$$323$$ −2.12245 + 2.00524i −0.118096 + 0.111575i
$$324$$ 0 0
$$325$$ 4.57836 + 1.43033i 0.253962 + 0.0793406i
$$326$$ 0 0
$$327$$ 17.7843 24.6739i 0.983475 1.36447i
$$328$$ 0 0
$$329$$ −6.25238 7.41956i −0.344705 0.409053i
$$330$$ 0 0
$$331$$ −25.2865 3.85795i −1.38987 0.212052i −0.587667 0.809103i $$-0.699953\pi$$
−0.802203 + 0.597051i $$0.796339\pi$$
$$332$$ 0 0
$$333$$ 4.61479 0.252889
$$334$$ 0 0
$$335$$ 17.0029 0.928970
$$336$$ 0 0
$$337$$ −18.3825 2.80460i −1.00136 0.152777i −0.370629 0.928781i $$-0.620858\pi$$
−0.630727 + 0.776005i $$0.717243\pi$$
$$338$$ 0 0
$$339$$ −9.24203 10.9673i −0.501958 0.595662i
$$340$$ 0 0
$$341$$ 1.56863 2.17631i 0.0849461 0.117854i
$$342$$ 0 0
$$343$$ −14.1606 4.42394i −0.764602 0.238870i
$$344$$ 0 0
$$345$$ −15.6407 + 14.7770i −0.842067 + 0.795566i
$$346$$ 0 0
$$347$$ −0.0857410 + 0.643425i −0.00460282 + 0.0345408i −0.993389 0.114799i $$-0.963378\pi$$
0.988786 + 0.149340i $$0.0477149\pi$$
$$348$$ 0 0
$$349$$ 8.50292 + 13.9050i 0.455151 + 0.744319i 0.995257 0.0972777i $$-0.0310135\pi$$
−0.540106 + 0.841597i $$0.681616\pi$$
$$350$$ 0 0
$$351$$ −4.62473 + 6.95697i −0.246850 + 0.371336i
$$352$$ 0 0
$$353$$ −4.15508 0.960196i −0.221153 0.0511061i 0.113125 0.993581i $$-0.463914\pi$$
−0.334278 + 0.942475i $$0.608492\pi$$
$$354$$ 0 0
$$355$$ 8.25338 8.41107i 0.438044 0.446413i
$$356$$ 0 0
$$357$$ −6.38691 30.2356i −0.338031 1.60024i
$$358$$ 0 0
$$359$$ 2.90482 16.8891i 0.153310 0.891371i −0.802340 0.596867i $$-0.796412\pi$$
0.955650 0.294504i $$-0.0951544\pi$$
$$360$$ 0 0
$$361$$ −16.5492 8.08019i −0.871009 0.425273i
$$362$$ 0 0
$$363$$ 4.26164 20.1745i 0.223678 1.05889i
$$364$$ 0 0
$$365$$ 6.40983 1.22777i 0.335506 0.0642644i
$$366$$ 0 0
$$367$$ 7.24387 5.01566i 0.378127 0.261816i −0.364943 0.931030i $$-0.618911\pi$$
0.743069 + 0.669214i $$0.233369\pi$$
$$368$$ 0 0
$$369$$ −2.92324 + 0.221716i −0.152178 + 0.0115421i
$$370$$ 0 0
$$371$$ −31.0258 + 9.69281i −1.61078 + 0.503226i
$$372$$ 0 0
$$373$$ −5.18296 + 17.7645i −0.268363 + 0.919813i 0.708457 + 0.705754i $$0.249391\pi$$
−0.976821 + 0.214059i $$0.931331\pi$$
$$374$$ 0 0
$$375$$ −21.2422 + 8.44761i −1.09694 + 0.436233i
$$376$$ 0 0
$$377$$ 18.7605 + 6.65011i 0.966216 + 0.342498i
$$378$$ 0 0
$$379$$ 2.09480 + 4.99038i 0.107603 + 0.256339i 0.966909 0.255123i $$-0.0821161\pi$$
−0.859306 + 0.511462i $$0.829104\pi$$
$$380$$ 0 0
$$381$$ 5.86800 23.3677i 0.300627 1.19716i
$$382$$ 0 0
$$383$$ 4.99573 + 14.9883i 0.255270 + 0.765864i 0.995607 + 0.0936286i $$0.0298466\pi$$
−0.740337 + 0.672236i $$0.765334\pi$$
$$384$$ 0 0
$$385$$ 2.50362 2.75249i 0.127596 0.140280i
$$386$$ 0 0
$$387$$ 4.61797 + 3.46317i 0.234745 + 0.176043i
$$388$$ 0 0
$$389$$ −12.4991 1.42542i −0.633727 0.0722716i −0.209473 0.977815i $$-0.567175\pi$$
−0.424255 + 0.905543i $$0.639464\pi$$
$$390$$ 0 0
$$391$$ 25.1397 + 9.99756i 1.27137 + 0.505599i
$$392$$ 0 0
$$393$$ −5.50157 8.27599i −0.277517 0.417469i
$$394$$ 0 0
$$395$$ −10.0267 12.8559i −0.504499 0.646850i
$$396$$ 0 0
$$397$$ 30.1017 22.5743i 1.51076 1.13297i 0.557758 0.830004i $$-0.311662\pi$$
0.953002 0.302965i $$-0.0979767\pi$$
$$398$$ 0 0
$$399$$ −5.20734 + 3.32129i −0.260693 + 0.166272i
$$400$$ 0 0
$$401$$ −2.79696 + 3.31908i −0.139673 + 0.165747i −0.830024 0.557728i $$-0.811673\pi$$
0.690350 + 0.723475i $$0.257456\pi$$
$$402$$ 0 0
$$403$$ 0.513629 + 9.03689i 0.0255857 + 0.450160i
$$404$$ 0 0
$$405$$ −1.58486 16.6986i −0.0787524 0.829761i
$$406$$ 0 0
$$407$$ 1.75281 3.12640i 0.0868838 0.154970i
$$408$$ 0 0
$$409$$ −2.39010 + 7.17081i −0.118183 + 0.354574i −0.991069 0.133350i $$-0.957426\pi$$
0.872886 + 0.487924i $$0.162246\pi$$
$$410$$ 0 0
$$411$$ −5.86841 44.0382i −0.289467 2.17224i
$$412$$ 0 0
$$413$$ −12.7893 0.484314i −0.629322 0.0238315i
$$414$$ 0 0
$$415$$ 4.61296 + 3.19402i 0.226441 + 0.156788i
$$416$$ 0 0
$$417$$ 10.6762 2.89681i 0.522817 0.141857i
$$418$$ 0 0
$$419$$ −7.34723 + 0.837894i −0.358936 + 0.0409338i −0.290912 0.956750i $$-0.593959\pi$$
−0.0680240 + 0.997684i $$0.521669\pi$$
$$420$$ 0 0
$$421$$ −0.842178 + 2.24029i −0.0410452 + 0.109185i −0.954974 0.296689i $$-0.904117\pi$$
0.913929 + 0.405875i $$0.133033\pi$$
$$422$$ 0 0
$$423$$ 0.877798 1.43548i 0.0426800 0.0697956i
$$424$$ 0 0
$$425$$ 7.00162 + 6.61497i 0.339629 + 0.320873i
$$426$$ 0 0
$$427$$ 38.5060 1.45817i 1.86344 0.0705657i
$$428$$ 0 0
$$429$$ −0.944477 1.84500i −0.0455998 0.0890774i
$$430$$ 0 0
$$431$$ −30.3581 5.81495i −1.46230 0.280096i −0.605542 0.795814i $$-0.707043\pi$$
−0.856759 + 0.515718i $$0.827525\pi$$
$$432$$ 0 0
$$433$$ 11.9300 5.82488i 0.573321 0.279926i −0.129165 0.991623i $$-0.541230\pi$$
0.702486 + 0.711697i $$0.252073\pi$$
$$434$$ 0 0
$$435$$ −29.9630 + 10.6211i −1.43661 + 0.509242i
$$436$$ 0 0
$$437$$ 0.102328 5.40628i 0.00489499 0.258618i
$$438$$ 0 0
$$439$$ 22.2484 + 1.68745i 1.06186 + 0.0805375i 0.594945 0.803767i $$-0.297174\pi$$
0.466911 + 0.884304i $$0.345367\pi$$
$$440$$ 0 0
$$441$$ −0.144902 7.65562i −0.00690009 0.364553i
$$442$$ 0 0
$$443$$ 5.00270 9.77258i 0.237685 0.464309i −0.740496 0.672060i $$-0.765410\pi$$
0.978182 + 0.207751i $$0.0666144\pi$$
$$444$$ 0 0
$$445$$ −12.1296 + 1.85061i −0.574998 + 0.0877272i
$$446$$ 0 0
$$447$$ 12.0229 + 10.5270i 0.568662 + 0.497910i
$$448$$ 0 0
$$449$$ −0.600226 + 0.769588i −0.0283264 + 0.0363191i −0.802482 0.596676i $$-0.796488\pi$$
0.774156 + 0.632995i $$0.218175\pi$$
$$450$$ 0 0
$$451$$ −0.960113 + 2.06463i −0.0452099 + 0.0972198i
$$452$$ 0 0
$$453$$ 5.39337 + 14.3470i 0.253403 + 0.674081i
$$454$$ 0 0
$$455$$ −0.712379 + 12.5338i −0.0333968 + 0.587591i
$$456$$ 0 0
$$457$$ 19.8696 4.59167i 0.929463 0.214789i 0.266839 0.963741i $$-0.414021\pi$$
0.662624 + 0.748952i $$0.269443\pi$$
$$458$$ 0 0
$$459$$ −14.4751 + 8.47942i −0.675641 + 0.395786i
$$460$$ 0 0
$$461$$ 2.60878 27.4870i 0.121503 1.28020i −0.701709 0.712463i $$-0.747580\pi$$
0.823213 0.567733i $$-0.192180\pi$$
$$462$$ 0 0
$$463$$ 6.72587 + 3.60529i 0.312578 + 0.167552i 0.621241 0.783619i $$-0.286629\pi$$
−0.308663 + 0.951171i $$0.599882\pi$$
$$464$$ 0 0
$$465$$ −9.72730 10.6942i −0.451093 0.495933i
$$466$$ 0 0
$$467$$ −15.7101 + 13.7554i −0.726975 + 0.636526i −0.940257 0.340464i $$-0.889416\pi$$
0.213283 + 0.976991i $$0.431584\pi$$
$$468$$ 0 0
$$469$$ −11.0139 43.8598i −0.508574 2.02526i
$$470$$ 0 0
$$471$$ 6.34376 + 21.7432i 0.292305 + 1.00187i
$$472$$ 0 0
$$473$$ 4.10023 1.81316i 0.188529 0.0833690i
$$474$$ 0 0
$$475$$ 0.745127 1.77509i 0.0341888 0.0814469i
$$476$$ 0 0
$$477$$ −3.29596 4.57279i −0.150911 0.209374i
$$478$$ 0 0
$$479$$ 23.5133 12.6039i 1.07435 0.575888i 0.162626 0.986688i $$-0.448004\pi$$
0.911725 + 0.410800i $$0.134751\pi$$
$$480$$ 0 0
$$481$$ 2.04986 + 11.9182i 0.0934657 + 0.543425i
$$482$$ 0 0
$$483$$ 48.2493 + 30.7739i 2.19542 + 1.40026i
$$484$$ 0 0
$$485$$ 5.54253 + 9.88592i 0.251673 + 0.448897i
$$486$$ 0 0
$$487$$ 29.1360 23.6243i 1.32028 1.07052i 0.328238 0.944595i $$-0.393545\pi$$
0.992040 0.125925i $$-0.0401899\pi$$
$$488$$ 0 0
$$489$$ 13.7208 + 11.1252i 0.620476 + 0.503100i
$$490$$ 0 0
$$491$$ −7.26115 15.6144i −0.327691 0.704670i 0.671653 0.740866i $$-0.265584\pi$$
−0.999345 + 0.0361958i $$0.988476\pi$$
$$492$$ 0 0
$$493$$ 27.9949 + 28.5298i 1.26083 + 1.28492i
$$494$$ 0 0
$$495$$ 0.590121 + 0.260957i 0.0265240 + 0.0117291i
$$496$$ 0 0
$$497$$ −27.0429 15.8415i −1.21304 0.710590i
$$498$$ 0 0
$$499$$ 29.7943 + 8.08417i 1.33378 + 0.361897i 0.856178 0.516681i $$-0.172833\pi$$
0.477598 + 0.878578i $$0.341508\pi$$
$$500$$ 0 0
$$501$$ 24.8330 2.37026i 1.10946 0.105895i
$$502$$ 0 0
$$503$$ −19.6169 5.32270i −0.874672 0.237327i −0.203901 0.978991i $$-0.565362\pi$$
−0.670771 + 0.741664i $$0.734037\pi$$
$$504$$ 0 0
$$505$$ −8.50892 4.98446i −0.378642 0.221806i
$$506$$ 0 0
$$507$$ −16.5551 7.32080i −0.735237 0.325128i
$$508$$ 0 0
$$509$$ 16.6988 + 17.0179i 0.740163 + 0.754305i 0.976067 0.217472i $$-0.0697810\pi$$
−0.235904 + 0.971776i $$0.575805\pi$$
$$510$$ 0 0
$$511$$ −7.31913 15.7391i −0.323779 0.696257i
$$512$$ 0 0
$$513$$ 2.60436 + 2.11169i 0.114985 + 0.0932333i
$$514$$ 0 0
$$515$$ 15.4110 12.4957i 0.679089 0.550625i
$$516$$ 0 0
$$517$$ −0.639094 1.13992i −0.0281073 0.0501335i
$$518$$ 0 0
$$519$$ −23.2345 14.8192i −1.01988 0.650489i
$$520$$ 0 0
$$521$$ 1.44572 + 8.40568i 0.0633383 + 0.368259i 0.999845 + 0.0176094i $$0.00560554\pi$$
−0.936507 + 0.350650i $$0.885961\pi$$
$$522$$ 0 0
$$523$$ −11.0384 + 5.91695i −0.482676 + 0.258730i −0.695721 0.718312i $$-0.744915\pi$$
0.213045 + 0.977042i $$0.431662\pi$$
$$524$$ 0 0
$$525$$ 11.9135 + 16.5288i 0.519949 + 0.721375i
$$526$$ 0 0
$$527$$ −7.03530 + 16.7600i −0.306463 + 0.730077i
$$528$$ 0 0
$$529$$ −24.7863 + 10.9607i −1.07767 + 0.476553i
$$530$$ 0 0
$$531$$ −0.621631 2.13063i −0.0269765 0.0924616i
$$532$$ 0 0
$$533$$ −1.87109 7.45112i −0.0810460 0.322744i
$$534$$ 0 0
$$535$$ −13.8167 + 12.0976i −0.597347 + 0.523026i
$$536$$ 0 0
$$537$$ 13.4304 + 14.7655i 0.579567 + 0.637178i
$$538$$ 0 0
$$539$$ −5.24152 2.80963i −0.225768 0.121019i
$$540$$ 0 0
$$541$$ 2.92832 30.8537i 0.125898 1.32650i −0.679458 0.733714i $$-0.737785\pi$$
0.805357 0.592791i $$-0.201974\pi$$
$$542$$ 0 0
$$543$$ −14.6953 + 8.60837i −0.630634 + 0.369420i
$$544$$ 0 0
$$545$$ −24.1753 + 5.58667i −1.03556 + 0.239307i
$$546$$ 0 0
$$547$$ −1.61929 + 28.4901i −0.0692358 + 1.21815i 0.756462 + 0.654037i $$0.226926\pi$$
−0.825698 + 0.564112i $$0.809218\pi$$
$$548$$ 0 0
$$549$$ 2.35139 + 6.25497i 0.100355 + 0.266956i
$$550$$ 0 0
$$551$$ 3.36857 7.24379i 0.143506 0.308596i
$$552$$ 0 0
$$553$$ −26.6673 + 34.1919i −1.13401 + 1.45399i
$$554$$ 0 0
$$555$$ −14.5314 12.7234i −0.616824 0.540080i
$$556$$ 0 0
$$557$$ 10.6225 1.62067i 0.450089 0.0686699i 0.0781805 0.996939i $$-0.475089\pi$$
0.371909 + 0.928269i $$0.378703\pi$$
$$558$$ 0 0
$$559$$ −6.89277 + 13.4648i −0.291533 + 0.569499i
$$560$$ 0 0
$$561$$ −0.0787675 4.16153i −0.00332557 0.175700i
$$562$$ 0 0
$$563$$ −34.5114 2.61755i −1.45448 0.110317i −0.675500 0.737360i $$-0.736072\pi$$
−0.778984 + 0.627044i $$0.784265\pi$$
$$564$$ 0 0
$$565$$ −0.221416 + 11.6981i −0.00931505 + 0.492143i
$$566$$ 0 0
$$567$$ −42.0481 + 14.9050i −1.76586 + 0.625949i
$$568$$ 0 0
$$569$$ 6.11784 2.98706i 0.256473 0.125224i −0.306022 0.952024i $$-0.598998\pi$$
0.562495 + 0.826801i $$0.309841\pi$$
$$570$$ 0 0
$$571$$ −43.1947 8.27371i −1.80764 0.346244i −0.830201 0.557464i $$-0.811775\pi$$
−0.977439 + 0.211219i $$0.932257\pi$$
$$572$$ 0 0
$$573$$ 4.10211 + 8.01332i 0.171368 + 0.334761i
$$574$$ 0 0
$$575$$ −17.8249 + 0.675004i −0.743349 + 0.0281496i
$$576$$ 0 0
$$577$$ −22.1067 20.8859i −0.920312 0.869490i 0.0714681 0.997443i $$-0.477232\pi$$
−0.991780 + 0.127953i $$0.959159\pi$$
$$578$$ 0 0
$$579$$ 4.94476 8.08628i 0.205497 0.336054i
$$580$$ 0 0
$$581$$ 5.25100 13.9683i 0.217848 0.579502i
$$582$$ 0 0
$$583$$ −4.34983 + 0.496064i −0.180152 + 0.0205449i
$$584$$ 0 0
$$585$$ −2.10109 + 0.570095i −0.0868694 + 0.0235705i
$$586$$ 0 0
$$587$$ 2.41319 + 1.67089i 0.0996029 + 0.0689652i 0.618018 0.786164i $$-0.287936\pi$$
−0.518415 + 0.855129i $$0.673478\pi$$
$$588$$ 0 0
$$589$$ 3.63027 + 0.137473i 0.149583 + 0.00566448i
$$590$$ 0 0
$$591$$ −3.11378 23.3667i −0.128084 0.961176i
$$592$$ 0 0
$$593$$ 0.175527 0.526619i 0.00720804 0.0216257i −0.945024 0.327000i $$-0.893962\pi$$
0.952232 + 0.305374i $$0.0987816\pi$$
$$594$$ 0 0
$$595$$ −12.3287 + 21.9900i −0.505426 + 0.901503i
$$596$$ 0 0
$$597$$ 2.37043 + 24.9756i 0.0970151 + 1.02218i
$$598$$ 0 0
$$599$$ −2.23606 39.3417i −0.0913628 1.60746i −0.637965 0.770065i $$-0.720224\pi$$
0.546602 0.837392i $$-0.315921\pi$$
$$600$$ 0 0
$$601$$ −14.5037 + 17.2112i −0.591619 + 0.702061i −0.975170 0.221459i $$-0.928918\pi$$
0.383550 + 0.923520i $$0.374701\pi$$
$$602$$ 0 0
$$603$$ 6.61178 4.21705i 0.269252 0.171732i
$$604$$ 0 0
$$605$$ −13.4576 + 10.0923i −0.547128 + 0.410310i
$$606$$ 0 0
$$607$$ 24.4204 + 31.3110i 0.991194 + 1.27087i 0.962499 + 0.271285i $$0.0874484\pi$$
0.0286951 + 0.999588i $$0.490865\pi$$
$$608$$ 0 0
$$609$$ 46.8064 + 70.4108i 1.89669 + 2.85319i
$$610$$ 0 0
$$611$$ 4.09722 + 1.62938i 0.165756 + 0.0659178i
$$612$$ 0 0
$$613$$ 28.4595 + 3.24558i 1.14947 + 0.131088i 0.667160 0.744915i $$-0.267510\pi$$
0.482307 + 0.876002i $$0.339799\pi$$
$$614$$ 0 0
$$615$$ 9.81621 + 7.36151i 0.395828 + 0.296845i
$$616$$ 0 0
$$617$$ 4.64585 5.10766i 0.187035 0.205627i −0.639062 0.769156i $$-0.720677\pi$$
0.826096 + 0.563529i $$0.190557\pi$$
$$618$$ 0 0
$$619$$ 1.97269 + 5.91848i 0.0792890 + 0.237884i 0.980849 0.194771i $$-0.0623963\pi$$
−0.901560 + 0.432655i $$0.857577\pi$$
$$620$$ 0 0
$$621$$ 7.56641 30.1312i 0.303630 1.20912i
$$622$$ 0 0
$$623$$ 12.6308 + 30.0900i 0.506043 + 1.20553i
$$624$$ 0 0
$$625$$ 5.70133 + 2.02097i 0.228053 + 0.0808388i
$$626$$ 0 0
$$627$$ −0.773007 + 0.307410i −0.0308709 + 0.0122768i
$$628$$ 0 0
$$629$$ −6.80178 + 23.3130i −0.271205 + 0.929552i
$$630$$ 0 0
$$631$$ −0.222181 + 0.0694119i −0.00884489 + 0.00276324i −0.302617 0.953112i $$-0.597860\pi$$
0.293772 + 0.955875i $$0.405089\pi$$
$$632$$ 0 0
$$633$$ −24.8996 + 1.88853i −0.989668 + 0.0750624i
$$634$$ 0 0
$$635$$ −16.1595 + 11.1889i −0.641272 + 0.444018i
$$636$$ 0 0
$$637$$ 19.7072 3.77481i 0.780826 0.149563i
$$638$$ 0 0
$$639$$ 1.12331 5.31773i 0.0444374 0.210366i
$$640$$ 0 0
$$641$$ −2.02441 0.988425i −0.0799594 0.0390405i 0.398335 0.917240i $$-0.369588\pi$$
−0.478294 + 0.878200i $$0.658745\pi$$
$$642$$ 0 0
$$643$$ 0.551951 3.20914i 0.0217668 0.126556i −0.972612 0.232433i $$-0.925331\pi$$
0.994379 + 0.105877i $$0.0337650\pi$$
$$644$$ 0 0
$$645$$ −4.99310 23.6373i −0.196603 0.930718i
$$646$$ 0 0
$$647$$ −30.7614 + 31.3492i −1.20936 + 1.23246i −0.244511 + 0.969647i $$0.578627\pi$$
−0.964846 + 0.262817i $$0.915348\pi$$
$$648$$ 0 0
$$649$$ −1.67956 0.388129i −0.0659285 0.0152354i
$$650$$ 0 0
$$651$$ −21.2852 + 32.0193i −0.834233 + 1.25493i
$$652$$ 0 0
$$653$$ 12.3835 + 20.2510i 0.484602 + 0.792481i 0.997835 0.0657681i $$-0.0209498\pi$$
−0.513233 + 0.858250i $$0.671552\pi$$
$$654$$ 0 0
$$655$$ −1.07087 + 8.03612i −0.0418424 + 0.313997i
$$656$$ 0 0
$$657$$ 2.18802 2.06719i 0.0853627 0.0806488i
$$658$$ 0 0
$$659$$ 13.3448 + 4.16907i 0.519840 + 0.162404i 0.546849 0.837231i $$-0.315827\pi$$
−0.0270089 + 0.999635i $$0.508598\pi$$
$$660$$ 0 0
$$661$$ −7.00629 + 9.72049i −0.272513 + 0.378083i −0.925159 0.379580i $$-0.876069\pi$$
0.652646 + 0.757663i $$0.273659\pi$$
$$662$$ 0 0
$$663$$ 9.04963 + 10.7390i 0.351458 + 0.417068i
$$664$$ 0 0
$$665$$ 4.98098 + 0.759947i 0.193154 + 0.0294695i
$$666$$ 0 0
$$667$$ −74.0206 −2.86609
$$668$$ 0 0
$$669$$ 24.7519 0.956963
$$670$$ 0 0
$$671$$ 5.13070 + 0.782789i 0.198068 + 0.0302192i
$$672$$ 0 0
$$673$$ −25.5979 30.3764i −0.986725 1.17092i −0.985284 0.170925i $$-0.945324\pi$$
−0.00144148 0.999999i $$-0.500459\pi$$
$$674$$ 0 0
$$675$$ 6.46738 8.97281i 0.248929 0.345363i
$$676$$ 0 0
$$677$$ 26.0426 + 8.13600i 1.00090 + 0.312692i 0.754374 0.656445i $$-0.227941\pi$$
0.246524 + 0.969137i $$0.420712\pi$$
$$678$$ 0 0
$$679$$ 21.9109 20.7009i 0.840863 0.794428i
$$680$$ 0 0
$$681$$ 4.54683 34.1207i 0.174235 1.30751i
$$682$$ 0 0
$$683$$ 8.59312 + 14.0525i 0.328806 + 0.537705i 0.974068 0.226257i $$-0.0726490\pi$$
−0.645261 + 0.763962i $$0.723251\pi$$
$$684$$ 0 0
$$685$$ −20.0645 + 30.1830i −0.766626 + 1.15323i
$$686$$ 0 0
$$687$$ −16.0518 3.70940i −0.612413 0.141522i
$$688$$ 0 0
$$689$$ 10.3457 10.5434i 0.394141 0.401671i
$$690$$ 0 0
$$691$$ 2.78739 + 13.1955i 0.106037 + 0.501980i 0.998687 + 0.0512289i $$0.0163138\pi$$
−0.892649 + 0.450751i $$0.851156\pi$$
$$692$$ 0 0
$$693$$ 0.290890 1.69128i 0.0110500 0.0642464i
$$694$$ 0 0
$$695$$ −8.10950 3.95949i −0.307611 0.150192i
$$696$$ 0 0
$$697$$ 3.18852 15.0944i 0.120774 0.571742i
$$698$$ 0 0
$$699$$ −33.8333 + 6.48059i −1.27969 + 0.245118i
$$700$$ 0 0
$$701$$ 19.3153 13.3739i 0.729528 0.505126i −0.145404 0.989372i $$-0.546448\pi$$
0.874932 + 0.484246i $$0.160906\pi$$
$$702$$ 0 0
$$703$$ 4.83980 0.367079i 0.182536 0.0138447i
$$704$$ 0 0
$$705$$ −6.72185 + 2.09998i −0.253160 + 0.0790899i
$$706$$ 0 0
$$707$$ −7.34586 + 25.1779i −0.276269 + 0.946911i
$$708$$ 0 0
$$709$$ −33.3436 + 13.2601i −1.25224 + 0.497993i −0.899169 0.437602i $$-0.855828\pi$$
−0.353075 + 0.935595i $$0.614864\pi$$
$$710$$ 0 0
$$711$$ −7.08750 2.51233i −0.265802 0.0942197i
$$712$$ 0 0
$$713$$ −13.0284 31.0373i −0.487919 1.16236i
$$714$$ 0 0
$$715$$ −0.411822 + 1.63997i −0.0154013 + 0.0613315i
$$716$$ 0 0
$$717$$ 9.27929 + 27.8398i 0.346541 + 1.03970i
$$718$$ 0 0
$$719$$ −12.9380 + 14.2241i −0.482506 + 0.530469i −0.931828 0.362901i $$-0.881786\pi$$
0.449322 + 0.893370i $$0.351666\pi$$
$$720$$ 0 0
$$721$$ −42.2157 31.6590i −1.57220 1.17904i
$$722$$ 0 0
$$723$$ 58.1330 + 6.62961i 2.16199 + 0.246558i
$$724$$ 0 0
$$725$$ −24.4882 9.73847i −0.909468 0.361678i
$$726$$ 0 0
$$727$$ −10.0099 15.0579i −0.371247 0.558466i 0.598949 0.800787i $$-0.295585\pi$$
−0.970196 + 0.242321i $$0.922091\pi$$
$$728$$ 0 0
$$729$$ 10.8738 + 13.9420i 0.402732 + 0.516369i
$$730$$ 0 0
$$731$$ −24.3017 + 18.2247i −0.898833 + 0.674065i
$$732$$ 0 0
$$733$$ 37.3406 23.8162i 1.37921 0.879671i 0.380230 0.924892i $$-0.375845\pi$$
0.998977 + 0.0452206i $$0.0143991\pi$$
$$734$$ 0 0
$$735$$ −20.6510 + 24.5061i −0.761725 + 0.903921i
$$736$$ 0 0
$$737$$ −0.345628 6.08105i −0.0127314 0.223998i
$$738$$ 0 0
$$739$$ 1.49529 + 15.7548i 0.0550050 + 0.579550i 0.979922 + 0.199381i $$0.0638932\pi$$
−0.924917 + 0.380169i $$0.875866\pi$$
$$740$$ 0 0
$$741$$ 1.37262 2.44827i 0.0504245 0.0899395i
$$742$$ 0 0
$$743$$ 14.6665 44.0027i 0.538063 1.61430i −0.229486 0.973312i $$-0.573704\pi$$
0.767549 0.640991i $$-0.221476\pi$$
$$744$$ 0 0
$$745$$ −1.72199 12.9223i −0.0630889 0.473437i
$$746$$ 0 0
$$747$$ 2.58597 + 0.0979272i 0.0946159 + 0.00358297i
$$748$$ 0 0
$$749$$ 40.1563 + 27.8043i 1.46728 + 1.01595i
$$750$$ 0 0
$$751$$ 20.1781 5.47499i 0.736310 0.199785i 0.126092 0.992019i $$-0.459757\pi$$
0.610218 + 0.792233i $$0.291082\pi$$
$$752$$ 0 0
$$753$$ −13.5985 + 1.55081i −0.495559 + 0.0565146i
$$754$$ 0 0
$$755$$ 4.39987 11.7042i 0.160128 0.425958i
$$756$$ 0 0
$$757$$ −15.4440 + 25.2560i −0.561323 + 0.917944i 0.438493 + 0.898735i $$0.355512\pi$$
−0.999815 + 0.0192092i $$0.993885\pi$$
$$758$$ 0 0
$$759$$ 5.60288 + 5.29347i 0.203371 + 0.192141i
$$760$$ 0 0
$$761$$ 47.7811 1.80940i 1.73206 0.0655909i 0.847153 0.531350i $$-0.178315\pi$$
0.884912 + 0.465759i $$0.154219\pi$$
$$762$$ 0 0
$$763$$ 30.0709 + 58.7424i 1.08864 + 2.12662i
$$764$$ 0 0
$$765$$ −4.29380 0.822456i −0.155243 0.0297360i
$$766$$ 0 0
$$767$$ 5.22648 2.55185i 0.188717 0.0921418i
$$768$$ 0 0
$$769$$ −7.37397 + 2.61388i −0.265912 + 0.0942588i −0.463719 0.885982i $$-0.653485\pi$$
0.197807 + 0.980241i $$0.436618\pi$$
$$770$$ 0 0
$$771$$ −0.360572 + 19.0501i −0.0129857 + 0.686074i
$$772$$ 0 0
$$773$$ −7.23974 0.549105i −0.260395 0.0197499i −0.0552163 0.998474i $$-0.517585\pi$$
−0.205179 + 0.978724i $$0.565778\pi$$
$$774$$ 0 0
$$775$$ −0.226792 11.9821i −0.00814660 0.430410i
$$776$$ 0 0
$$777$$ −23.4077 + 45.7261i −0.839748 + 1.64042i
$$778$$ 0 0
$$779$$ −3.04813 + 0.465052i −0.109211 + 0.0166622i
$$780$$ 0 0
$$781$$ −3.17596 2.78082i −0.113645 0.0995055i
$$782$$ 0 0
$$783$$ 28.2273 36.1920i 1.00876 1.29340i
$$784$$ 0 0
$$785$$ 7.79130 16.7545i 0.278084 0.597993i
$$786$$ 0 0
$$787$$ −4.92098 13.0904i −0.175414 0.466622i 0.818795 0.574086i $$-0.194643\pi$$
−0.994209 + 0.107464i $$0.965727\pi$$
$$788$$ 0 0
$$789$$ 2.19639 38.6438i 0.0781936 1.37576i
$$790$$ 0 0
$$791$$ 30.3192 7.00645i 1.07803 0.249121i
$$792$$ 0 0
$$793$$ −15.1097 + 8.85116i −0.536562 + 0.314314i
$$794$$ 0 0
$$795$$ −2.22909 + 23.4864i −0.0790577 + 0.832978i
$$796$$ 0 0