# Properties

 Label 76.2.i.a.5.2 Level $76$ Weight $2$ Character 76.5 Analytic conductor $0.607$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 76.i (of order $$9$$, degree $$6$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.606863055362$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{9})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 5.2 Root $$-1.75227 - 0.342020i$$ of defining polynomial Character $$\chi$$ $$=$$ 76.5 Dual form 76.2.i.a.61.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +O(q^{10})$$ $$q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +(-0.622469 + 1.07815i) q^{11} +(0.977096 + 5.54139i) q^{13} +(0.391845 - 0.328797i) q^{15} +(-6.25251 + 2.27573i) q^{17} +(3.09208 - 3.07231i) q^{19} +(-1.97557 + 0.719049i) q^{21} +(-4.65029 + 3.90205i) q^{23} +(-0.854412 - 4.84561i) q^{25} +(2.46018 - 4.26116i) q^{27} +(3.64892 + 1.32810i) q^{29} +(-0.0400606 - 0.0693870i) q^{31} +(1.72862 + 1.45048i) q^{33} +(0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +10.1991 q^{39} +(1.11697 - 6.33464i) q^{41} +(0.189407 + 0.158931i) q^{43} +(-0.0402752 - 0.0697587i) q^{45} +(-10.8939 - 3.96505i) q^{47} +(2.82735 - 4.89711i) q^{49} +(2.09428 + 11.8773i) q^{51} +(3.50255 - 2.93899i) q^{53} +(-0.330140 + 0.120161i) q^{55} +(-4.51095 - 6.48649i) q^{57} +(-9.32947 + 3.39565i) q^{59} +(-4.27534 + 3.58744i) q^{61} +(0.0574889 + 0.326036i) q^{63} +(-0.793965 + 1.37519i) q^{65} +(-3.47734 - 1.26565i) q^{67} +(5.50164 + 9.52912i) q^{69} +(7.14016 + 5.99131i) q^{71} +(0.191208 - 1.08439i) q^{73} -8.91853 q^{75} +1.44397 q^{77} +(-1.50923 + 8.55928i) q^{79} +(-7.48795 - 6.28314i) q^{81} +(5.77114 + 9.99591i) q^{83} +(-1.76449 - 0.642221i) q^{85} +(3.51920 - 6.09544i) q^{87} +(-0.418534 - 2.37362i) q^{89} +(4.99955 - 4.19512i) q^{91} +(-0.136468 + 0.0496702i) q^{93} +(1.22576 - 0.103280i) q^{95} +(-13.4638 + 4.90042i) q^{97} +(0.272211 - 0.228412i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10})$$ $$12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$

## 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
$$3$$ 0.314751 1.78504i 0.181721 1.03059i −0.748375 0.663276i $$-0.769165\pi$$
0.930096 0.367317i $$-0.119723\pi$$
$$4$$ 0 0
$$5$$ 0.216181 + 0.181398i 0.0966793 + 0.0811235i 0.689846 0.723956i $$-0.257678\pi$$
−0.593167 + 0.805079i $$0.702123\pi$$
$$6$$ 0 0
$$7$$ −0.579936 1.00448i −0.219195 0.379657i 0.735367 0.677669i $$-0.237010\pi$$
−0.954562 + 0.298012i $$0.903677\pi$$
$$8$$ 0 0
$$9$$ −0.268219 0.0976237i −0.0894063 0.0325412i
$$10$$ 0 0
$$11$$ −0.622469 + 1.07815i −0.187682 + 0.325074i −0.944477 0.328578i $$-0.893431\pi$$
0.756795 + 0.653652i $$0.226764\pi$$
$$12$$ 0 0
$$13$$ 0.977096 + 5.54139i 0.270998 + 1.53690i 0.751395 + 0.659853i $$0.229381\pi$$
−0.480397 + 0.877051i $$0.659508\pi$$
$$14$$ 0 0
$$15$$ 0.391845 0.328797i 0.101174 0.0848951i
$$16$$ 0 0
$$17$$ −6.25251 + 2.27573i −1.51646 + 0.551945i −0.960260 0.279106i $$-0.909962\pi$$
−0.556196 + 0.831051i $$0.687740\pi$$
$$18$$ 0 0
$$19$$ 3.09208 3.07231i 0.709371 0.704835i
$$20$$ 0 0
$$21$$ −1.97557 + 0.719049i −0.431105 + 0.156909i
$$22$$ 0 0
$$23$$ −4.65029 + 3.90205i −0.969652 + 0.813635i −0.982496 0.186283i $$-0.940356\pi$$
0.0128443 + 0.999918i $$0.495911\pi$$
$$24$$ 0 0
$$25$$ −0.854412 4.84561i −0.170882 0.969122i
$$26$$ 0 0
$$27$$ 2.46018 4.26116i 0.473462 0.820060i
$$28$$ 0 0
$$29$$ 3.64892 + 1.32810i 0.677587 + 0.246621i 0.657811 0.753183i $$-0.271483\pi$$
0.0197756 + 0.999804i $$0.493705\pi$$
$$30$$ 0 0
$$31$$ −0.0400606 0.0693870i −0.00719510 0.0124623i 0.862405 0.506218i $$-0.168957\pi$$
−0.869601 + 0.493756i $$0.835624\pi$$
$$32$$ 0 0
$$33$$ 1.72862 + 1.45048i 0.300913 + 0.252496i
$$34$$ 0 0
$$35$$ 0.0568388 0.322349i 0.00960751 0.0544869i
$$36$$ 0 0
$$37$$ 3.71365 0.610521 0.305260 0.952269i $$-0.401256\pi$$
0.305260 + 0.952269i $$0.401256\pi$$
$$38$$ 0 0
$$39$$ 10.1991 1.63317
$$40$$ 0 0
$$41$$ 1.11697 6.33464i 0.174441 0.989305i −0.764346 0.644806i $$-0.776938\pi$$
0.938787 0.344498i $$-0.111951\pi$$
$$42$$ 0 0
$$43$$ 0.189407 + 0.158931i 0.0288842 + 0.0242368i 0.657115 0.753790i $$-0.271776\pi$$
−0.628231 + 0.778027i $$0.716221\pi$$
$$44$$ 0 0
$$45$$ −0.0402752 0.0697587i −0.00600387 0.0103990i
$$46$$ 0 0
$$47$$ −10.8939 3.96505i −1.58904 0.578362i −0.611893 0.790940i $$-0.709592\pi$$
−0.977144 + 0.212578i $$0.931814\pi$$
$$48$$ 0 0
$$49$$ 2.82735 4.89711i 0.403907 0.699587i
$$50$$ 0 0
$$51$$ 2.09428 + 11.8773i 0.293258 + 1.66315i
$$52$$ 0 0
$$53$$ 3.50255 2.93899i 0.481113 0.403702i −0.369716 0.929145i $$-0.620545\pi$$
0.850829 + 0.525443i $$0.176100\pi$$
$$54$$ 0 0
$$55$$ −0.330140 + 0.120161i −0.0445161 + 0.0162025i
$$56$$ 0 0
$$57$$ −4.51095 6.48649i −0.597490 0.859156i
$$58$$ 0 0
$$59$$ −9.32947 + 3.39565i −1.21459 + 0.442076i −0.868295 0.496049i $$-0.834784\pi$$
−0.346298 + 0.938124i $$0.612562\pi$$
$$60$$ 0 0
$$61$$ −4.27534 + 3.58744i −0.547401 + 0.459324i −0.874060 0.485818i $$-0.838522\pi$$
0.326659 + 0.945142i $$0.394077\pi$$
$$62$$ 0 0
$$63$$ 0.0574889 + 0.326036i 0.00724292 + 0.0410766i
$$64$$ 0 0
$$65$$ −0.793965 + 1.37519i −0.0984792 + 0.170571i
$$66$$ 0 0
$$67$$ −3.47734 1.26565i −0.424824 0.154623i 0.120756 0.992682i $$-0.461468\pi$$
−0.545580 + 0.838059i $$0.683691\pi$$
$$68$$ 0 0
$$69$$ 5.50164 + 9.52912i 0.662319 + 1.14717i
$$70$$ 0 0
$$71$$ 7.14016 + 5.99131i 0.847382 + 0.711038i 0.959211 0.282690i $$-0.0912267\pi$$
−0.111830 + 0.993727i $$0.535671\pi$$
$$72$$ 0 0
$$73$$ 0.191208 1.08439i 0.0223792 0.126919i −0.971571 0.236747i $$-0.923919\pi$$
0.993951 + 0.109828i $$0.0350300\pi$$
$$74$$ 0 0
$$75$$ −8.91853 −1.02982
$$76$$ 0 0
$$77$$ 1.44397 0.164556
$$78$$ 0 0
$$79$$ −1.50923 + 8.55928i −0.169802 + 0.962994i 0.774172 + 0.632975i $$0.218166\pi$$
−0.943974 + 0.330019i $$0.892945\pi$$
$$80$$ 0 0
$$81$$ −7.48795 6.28314i −0.831995 0.698126i
$$82$$ 0 0
$$83$$ 5.77114 + 9.99591i 0.633465 + 1.09719i 0.986838 + 0.161711i $$0.0517014\pi$$
−0.353373 + 0.935483i $$0.614965\pi$$
$$84$$ 0 0
$$85$$ −1.76449 0.642221i −0.191386 0.0696587i
$$86$$ 0 0
$$87$$ 3.51920 6.09544i 0.377298 0.653500i
$$88$$ 0 0
$$89$$ −0.418534 2.37362i −0.0443645 0.251603i 0.954557 0.298027i $$-0.0963286\pi$$
−0.998922 + 0.0464239i $$0.985218\pi$$
$$90$$ 0 0
$$91$$ 4.99955 4.19512i 0.524095 0.439768i
$$92$$ 0 0
$$93$$ −0.136468 + 0.0496702i −0.0141510 + 0.00515056i
$$94$$ 0 0
$$95$$ 1.22576 0.103280i 0.125760 0.0105963i
$$96$$ 0 0
$$97$$ −13.4638 + 4.90042i −1.36704 + 0.497562i −0.918224 0.396062i $$-0.870376\pi$$
−0.448816 + 0.893624i $$0.648154\pi$$
$$98$$ 0 0
$$99$$ 0.272211 0.228412i 0.0273582 0.0229563i
$$100$$ 0 0
$$101$$ −2.97288 16.8600i −0.295813 1.67764i −0.663881 0.747838i $$-0.731092\pi$$
0.368068 0.929799i $$-0.380019\pi$$
$$102$$ 0 0
$$103$$ 6.64081 11.5022i 0.654339 1.13335i −0.327720 0.944775i $$-0.606280\pi$$
0.982059 0.188573i $$-0.0603863\pi$$
$$104$$ 0 0
$$105$$ −0.557515 0.202919i −0.0544079 0.0198029i
$$106$$ 0 0
$$107$$ −0.494870 0.857140i −0.0478409 0.0828628i 0.841113 0.540859i $$-0.181901\pi$$
−0.888954 + 0.457996i $$0.848567\pi$$
$$108$$ 0 0
$$109$$ 10.3519 + 8.68625i 0.991529 + 0.831991i 0.985788 0.167992i $$-0.0537283\pi$$
0.00574045 + 0.999984i $$0.498173\pi$$
$$110$$ 0 0
$$111$$ 1.16887 6.62902i 0.110945 0.629198i
$$112$$ 0 0
$$113$$ 16.5369 1.55566 0.777829 0.628476i $$-0.216321\pi$$
0.777829 + 0.628476i $$0.216321\pi$$
$$114$$ 0 0
$$115$$ −1.71313 −0.159750
$$116$$ 0 0
$$117$$ 0.278895 1.58169i 0.0257838 0.146227i
$$118$$ 0 0
$$119$$ 5.91198 + 4.96074i 0.541950 + 0.454750i
$$120$$ 0 0
$$121$$ 4.72506 + 8.18405i 0.429551 + 0.744005i
$$122$$ 0 0
$$123$$ −10.9560 3.98766i −0.987871 0.359555i
$$124$$ 0 0
$$125$$ 1.39979 2.42450i 0.125201 0.216854i
$$126$$ 0 0
$$127$$ −0.388935 2.20576i −0.0345124 0.195729i 0.962677 0.270653i $$-0.0872397\pi$$
−0.997189 + 0.0749239i $$0.976129\pi$$
$$128$$ 0 0
$$129$$ 0.343314 0.288075i 0.0302271 0.0253636i
$$130$$ 0 0
$$131$$ 16.5173 6.01181i 1.44313 0.525255i 0.502463 0.864599i $$-0.332427\pi$$
0.940662 + 0.339344i $$0.110205\pi$$
$$132$$ 0 0
$$133$$ −4.87927 1.32418i −0.423087 0.114821i
$$134$$ 0 0
$$135$$ 1.30481 0.474912i 0.112300 0.0408739i
$$136$$ 0 0
$$137$$ 4.36728 3.66458i 0.373122 0.313086i −0.436873 0.899523i $$-0.643914\pi$$
0.809995 + 0.586437i $$0.199470\pi$$
$$138$$ 0 0
$$139$$ 0.891090 + 5.05362i 0.0755813 + 0.428643i 0.998994 + 0.0448352i $$0.0142763\pi$$
−0.923413 + 0.383808i $$0.874613\pi$$
$$140$$ 0 0
$$141$$ −10.5066 + 18.1980i −0.884818 + 1.53255i
$$142$$ 0 0
$$143$$ −6.58265 2.39589i −0.550469 0.200354i
$$144$$ 0 0
$$145$$ 0.547914 + 0.949015i 0.0455018 + 0.0788114i
$$146$$ 0 0
$$147$$ −7.85162 6.58829i −0.647591 0.543393i
$$148$$ 0 0
$$149$$ −2.06723 + 11.7238i −0.169354 + 0.960454i 0.775107 + 0.631830i $$0.217696\pi$$
−0.944461 + 0.328624i $$0.893415\pi$$
$$150$$ 0 0
$$151$$ −14.8628 −1.20952 −0.604759 0.796409i $$-0.706731\pi$$
−0.604759 + 0.796409i $$0.706731\pi$$
$$152$$ 0 0
$$153$$ 1.89921 0.153542
$$154$$ 0 0
$$155$$ 0.00392629 0.0222671i 0.000315367 0.00178854i
$$156$$ 0 0
$$157$$ −8.45258 7.09255i −0.674589 0.566047i 0.239831 0.970815i $$-0.422908\pi$$
−0.914420 + 0.404767i $$0.867353\pi$$
$$158$$ 0 0
$$159$$ −4.14379 7.17725i −0.328624 0.569193i
$$160$$ 0 0
$$161$$ 6.61640 + 2.40817i 0.521446 + 0.189791i
$$162$$ 0 0
$$163$$ −1.99237 + 3.45089i −0.156055 + 0.270295i −0.933443 0.358727i $$-0.883211\pi$$
0.777388 + 0.629021i $$0.216544\pi$$
$$164$$ 0 0
$$165$$ 0.110581 + 0.627134i 0.00860869 + 0.0488223i
$$166$$ 0 0
$$167$$ −6.19785 + 5.20061i −0.479604 + 0.402436i −0.850283 0.526325i $$-0.823569\pi$$
0.370679 + 0.928761i $$0.379125\pi$$
$$168$$ 0 0
$$169$$ −17.5362 + 6.38267i −1.34894 + 0.490974i
$$170$$ 0 0
$$171$$ −1.12928 + 0.522190i −0.0863584 + 0.0399329i
$$172$$ 0 0
$$173$$ 6.13327 2.23233i 0.466304 0.169721i −0.0981735 0.995169i $$-0.531300\pi$$
0.564477 + 0.825449i $$0.309078\pi$$
$$174$$ 0 0
$$175$$ −4.37181 + 3.66838i −0.330478 + 0.277304i
$$176$$ 0 0
$$177$$ 3.12491 + 17.7222i 0.234883 + 1.33209i
$$178$$ 0 0
$$179$$ 4.91617 8.51506i 0.367452 0.636445i −0.621715 0.783244i $$-0.713564\pi$$
0.989166 + 0.146799i $$0.0468969\pi$$
$$180$$ 0 0
$$181$$ 12.9463 + 4.71208i 0.962293 + 0.350246i 0.774932 0.632045i $$-0.217784\pi$$
0.187361 + 0.982291i $$0.440007\pi$$
$$182$$ 0 0
$$183$$ 5.05805 + 8.76080i 0.373902 + 0.647617i
$$184$$ 0 0
$$185$$ 0.802823 + 0.673648i 0.0590247 + 0.0495276i
$$186$$ 0 0
$$187$$ 1.43842 8.15771i 0.105188 0.596551i
$$188$$ 0 0
$$189$$ −5.70699 −0.415123
$$190$$ 0 0
$$191$$ 1.03137 0.0746275 0.0373137 0.999304i $$-0.488120\pi$$
0.0373137 + 0.999304i $$0.488120\pi$$
$$192$$ 0 0
$$193$$ −0.407183 + 2.30925i −0.0293097 + 0.166224i −0.995949 0.0899169i $$-0.971340\pi$$
0.966640 + 0.256140i $$0.0824510\pi$$
$$194$$ 0 0
$$195$$ 2.20486 + 1.85010i 0.157893 + 0.132488i
$$196$$ 0 0
$$197$$ −7.78406 13.4824i −0.554592 0.960581i −0.997935 0.0642291i $$-0.979541\pi$$
0.443344 0.896352i $$-0.353792\pi$$
$$198$$ 0 0
$$199$$ 12.8701 + 4.68434i 0.912339 + 0.332064i 0.755186 0.655510i $$-0.227546\pi$$
0.157153 + 0.987574i $$0.449769\pi$$
$$200$$ 0 0
$$201$$ −3.35372 + 5.80882i −0.236553 + 0.409722i
$$202$$ 0 0
$$203$$ −0.782093 4.43547i −0.0548922 0.311309i
$$204$$ 0 0
$$205$$ 1.39056 1.16682i 0.0971207 0.0814940i
$$206$$ 0 0
$$207$$ 1.62823 0.592626i 0.113170 0.0411904i
$$208$$ 0 0
$$209$$ 1.38768 + 5.24614i 0.0959878 + 0.362883i
$$210$$ 0 0
$$211$$ 20.2595 7.37386i 1.39472 0.507638i 0.468116 0.883667i $$-0.344933\pi$$
0.926608 + 0.376030i $$0.122711\pi$$
$$212$$ 0 0
$$213$$ 12.9421 10.8597i 0.886778 0.744095i
$$214$$ 0 0
$$215$$ 0.0121165 + 0.0687159i 0.000826336 + 0.00468638i
$$216$$ 0 0
$$217$$ −0.0464652 + 0.0804801i −0.00315426 + 0.00546335i
$$218$$ 0 0
$$219$$ −1.87550 0.682627i −0.126735 0.0461276i
$$220$$ 0 0
$$221$$ −18.7200 32.4240i −1.25924 2.18107i
$$222$$ 0 0
$$223$$ −19.9848 16.7693i −1.33828 1.12295i −0.982063 0.188551i $$-0.939621\pi$$
−0.356220 0.934402i $$-0.615935\pi$$
$$224$$ 0 0
$$225$$ −0.243877 + 1.38309i −0.0162585 + 0.0922063i
$$226$$ 0 0
$$227$$ 21.7357 1.44265 0.721325 0.692596i $$-0.243533\pi$$
0.721325 + 0.692596i $$0.243533\pi$$
$$228$$ 0 0
$$229$$ −20.1255 −1.32993 −0.664964 0.746875i $$-0.731553\pi$$
−0.664964 + 0.746875i $$0.731553\pi$$
$$230$$ 0 0
$$231$$ 0.454491 2.57754i 0.0299033 0.169590i
$$232$$ 0 0
$$233$$ 16.8667 + 14.1529i 1.10498 + 0.927184i 0.997750 0.0670504i $$-0.0213588\pi$$
0.107226 + 0.994235i $$0.465803\pi$$
$$234$$ 0 0
$$235$$ −1.63581 2.83330i −0.106708 0.184824i
$$236$$ 0 0
$$237$$ 14.8036 + 5.38808i 0.961598 + 0.349993i
$$238$$ 0 0
$$239$$ −2.18637 + 3.78691i −0.141425 + 0.244955i −0.928033 0.372497i $$-0.878502\pi$$
0.786609 + 0.617452i $$0.211835\pi$$
$$240$$ 0 0
$$241$$ −2.60506 14.7740i −0.167807 0.951679i −0.946123 0.323807i $$-0.895037\pi$$
0.778317 0.627872i $$-0.216074\pi$$
$$242$$ 0 0
$$243$$ −2.26484 + 1.90042i −0.145289 + 0.121912i
$$244$$ 0 0
$$245$$ 1.49954 0.545790i 0.0958024 0.0348692i
$$246$$ 0 0
$$247$$ 20.0461 + 14.1325i 1.27550 + 0.899226i
$$248$$ 0 0
$$249$$ 19.6596 7.15550i 1.24587 0.453461i
$$250$$ 0 0
$$251$$ −17.9754 + 15.0832i −1.13460 + 0.952042i −0.999249 0.0387556i $$-0.987661\pi$$
−0.135351 + 0.990798i $$0.543216\pi$$
$$252$$ 0 0
$$253$$ −1.31233 7.44261i −0.0825057 0.467913i
$$254$$ 0 0
$$255$$ −1.70176 + 2.94754i −0.106569 + 0.184582i
$$256$$ 0 0
$$257$$ −0.0996901 0.0362842i −0.00621850 0.00226335i 0.338909 0.940819i $$-0.389942\pi$$
−0.345128 + 0.938556i $$0.612164\pi$$
$$258$$ 0 0
$$259$$ −2.15368 3.73029i −0.133823 0.231789i
$$260$$ 0 0
$$261$$ −0.849054 0.712441i −0.0525551 0.0440990i
$$262$$ 0 0
$$263$$ −2.70397 + 15.3350i −0.166734 + 0.945594i 0.780525 + 0.625124i $$0.214952\pi$$
−0.947259 + 0.320469i $$0.896159\pi$$
$$264$$ 0 0
$$265$$ 1.29031 0.0792633
$$266$$ 0 0
$$267$$ −4.36874 −0.267363
$$268$$ 0 0
$$269$$ 2.43886 13.8315i 0.148700 0.843321i −0.815621 0.578586i $$-0.803605\pi$$
0.964321 0.264734i $$-0.0852843\pi$$
$$270$$ 0 0
$$271$$ 8.77391 + 7.36218i 0.532977 + 0.447221i 0.869128 0.494587i $$-0.164681\pi$$
−0.336151 + 0.941808i $$0.609125\pi$$
$$272$$ 0 0
$$273$$ −5.91485 10.2448i −0.357983 0.620044i
$$274$$ 0 0
$$275$$ 5.75613 + 2.09506i 0.347108 + 0.126337i
$$276$$ 0 0
$$277$$ −12.8642 + 22.2814i −0.772932 + 1.33876i 0.163017 + 0.986623i $$0.447878\pi$$
−0.935949 + 0.352135i $$0.885456\pi$$
$$278$$ 0 0
$$279$$ 0.00397120 + 0.0225218i 0.000237749 + 0.00134834i
$$280$$ 0 0
$$281$$ −20.6252 + 17.3066i −1.23039 + 1.03242i −0.232181 + 0.972673i $$0.574586\pi$$
−0.998213 + 0.0597510i $$0.980969\pi$$
$$282$$ 0 0
$$283$$ −2.78007 + 1.01186i −0.165258 + 0.0601491i −0.423324 0.905978i $$-0.639137\pi$$
0.258066 + 0.966127i $$0.416915\pi$$
$$284$$ 0 0
$$285$$ 0.201450 2.22053i 0.0119329 0.131533i
$$286$$ 0 0
$$287$$ −7.01078 + 2.55172i −0.413834 + 0.150623i
$$288$$ 0 0
$$289$$ 20.8922 17.5306i 1.22895 1.03121i
$$290$$ 0 0
$$291$$ 4.50970 + 25.5758i 0.264363 + 1.49928i
$$292$$ 0 0
$$293$$ −5.01204 + 8.68111i −0.292807 + 0.507156i −0.974472 0.224508i $$-0.927923\pi$$
0.681666 + 0.731664i $$0.261256\pi$$
$$294$$ 0 0
$$295$$ −2.63282 0.958268i −0.153289 0.0557925i
$$296$$ 0 0
$$297$$ 3.06277 + 5.30488i 0.177720 + 0.307820i
$$298$$ 0 0
$$299$$ −26.1666 21.9564i −1.51325 1.26977i
$$300$$ 0 0
$$301$$ 0.0497991 0.282425i 0.00287037 0.0162787i
$$302$$ 0 0
$$303$$ −31.0316 −1.78272
$$304$$ 0 0
$$305$$ −1.57500 −0.0901844
$$306$$ 0 0
$$307$$ −2.87822 + 16.3232i −0.164269 + 0.931614i 0.785547 + 0.618802i $$0.212382\pi$$
−0.949815 + 0.312811i $$0.898729\pi$$
$$308$$ 0 0
$$309$$ −18.4417 15.4744i −1.04911 0.880310i
$$310$$ 0 0
$$311$$ −0.215620 0.373465i −0.0122267 0.0211772i 0.859847 0.510551i $$-0.170559\pi$$
−0.872074 + 0.489374i $$0.837225\pi$$
$$312$$ 0 0
$$313$$ 13.0841 + 4.76223i 0.739557 + 0.269177i 0.684205 0.729290i $$-0.260149\pi$$
0.0553527 + 0.998467i $$0.482372\pi$$
$$314$$ 0 0
$$315$$ −0.0467141 + 0.0809112i −0.00263204 + 0.00455883i
$$316$$ 0 0
$$317$$ −2.87712 16.3170i −0.161595 0.916452i −0.952506 0.304521i $$-0.901504\pi$$
0.790911 0.611932i $$-0.209607\pi$$
$$318$$ 0 0
$$319$$ −3.70322 + 3.10737i −0.207341 + 0.173980i
$$320$$ 0 0
$$321$$ −1.68579 + 0.613577i −0.0940915 + 0.0342465i
$$322$$ 0 0
$$323$$ −12.3415 + 26.2463i −0.686700 + 1.46039i
$$324$$ 0 0
$$325$$ 26.0165 9.46925i 1.44314 0.525259i
$$326$$ 0 0
$$327$$ 18.7635 15.7445i 1.03763 0.870672i
$$328$$ 0 0
$$329$$ 2.33495 + 13.2422i 0.128730 + 0.730064i
$$330$$ 0 0
$$331$$ −4.74773 + 8.22332i −0.260959 + 0.451994i −0.966497 0.256678i $$-0.917372\pi$$
0.705538 + 0.708672i $$0.250705\pi$$
$$332$$ 0 0
$$333$$ −0.996072 0.362540i −0.0545844 0.0198671i
$$334$$ 0 0
$$335$$ −0.522150 0.904390i −0.0285281 0.0494121i
$$336$$ 0 0
$$337$$ 9.65934 + 8.10515i 0.526178 + 0.441515i 0.866779 0.498692i $$-0.166186\pi$$
−0.340601 + 0.940208i $$0.610631\pi$$
$$338$$ 0 0
$$339$$ 5.20499 29.5190i 0.282696 1.60325i
$$340$$ 0 0
$$341$$ 0.0997461 0.00540155
$$342$$ 0 0
$$343$$ −14.6778 −0.792529
$$344$$ 0 0
$$345$$ −0.539208 + 3.05800i −0.0290300 + 0.164637i
$$346$$ 0 0
$$347$$ 8.36688 + 7.02065i 0.449158 + 0.376888i 0.839123 0.543941i $$-0.183069\pi$$
−0.389965 + 0.920830i $$0.627513\pi$$
$$348$$ 0 0
$$349$$ −4.20032 7.27517i −0.224838 0.389431i 0.731433 0.681913i $$-0.238852\pi$$
−0.956271 + 0.292483i $$0.905519\pi$$
$$350$$ 0 0
$$351$$ 26.0165 + 9.46925i 1.38866 + 0.505431i
$$352$$ 0 0
$$353$$ −6.69379 + 11.5940i −0.356274 + 0.617086i −0.987335 0.158648i $$-0.949287\pi$$
0.631061 + 0.775733i $$0.282620\pi$$
$$354$$ 0 0
$$355$$ 0.456761 + 2.59042i 0.0242423 + 0.137485i
$$356$$ 0 0
$$357$$ 10.7159 8.99172i 0.567146 0.475892i
$$358$$ 0 0
$$359$$ 26.6099 9.68521i 1.40442 0.511166i 0.474931 0.880023i $$-0.342473\pi$$
0.929486 + 0.368857i $$0.120251\pi$$
$$360$$ 0 0
$$361$$ 0.121876 18.9996i 0.00641452 0.999979i
$$362$$ 0 0
$$363$$ 16.0961 5.85849i 0.844824 0.307491i
$$364$$ 0 0
$$365$$ 0.238042 0.199741i 0.0124597 0.0104549i
$$366$$ 0 0
$$367$$ 0.0720091 + 0.408384i 0.00375884 + 0.0213175i 0.986629 0.162979i $$-0.0521104\pi$$
−0.982871 + 0.184297i $$0.940999\pi$$
$$368$$ 0 0
$$369$$ −0.918003 + 1.59003i −0.0477893 + 0.0827735i
$$370$$ 0 0
$$371$$ −4.98342 1.81381i −0.258726 0.0941686i
$$372$$ 0 0
$$373$$ 2.01032 + 3.48198i 0.104090 + 0.180290i 0.913366 0.407139i $$-0.133474\pi$$
−0.809276 + 0.587429i $$0.800140\pi$$
$$374$$ 0 0
$$375$$ −3.88725 3.26179i −0.200737 0.168438i
$$376$$ 0 0
$$377$$ −3.79416 + 21.5177i −0.195409 + 1.10822i
$$378$$ 0 0
$$379$$ 14.1791 0.728332 0.364166 0.931334i $$-0.381354\pi$$
0.364166 + 0.931334i $$0.381354\pi$$
$$380$$ 0 0
$$381$$ −4.05978 −0.207989
$$382$$ 0 0
$$383$$ 1.88738 10.7039i 0.0964407 0.546943i −0.897856 0.440290i $$-0.854876\pi$$
0.994296 0.106653i $$-0.0340133\pi$$
$$384$$ 0 0
$$385$$ 0.312160 + 0.261933i 0.0159091 + 0.0133493i
$$386$$ 0 0
$$387$$ −0.0352870 0.0611189i −0.00179374 0.00310685i
$$388$$ 0 0
$$389$$ −24.0167 8.74136i −1.21769 0.443205i −0.348328 0.937373i $$-0.613251\pi$$
−0.869367 + 0.494168i $$0.835473\pi$$
$$390$$ 0 0
$$391$$ 20.1960 34.9804i 1.02135 1.76904i
$$392$$ 0 0
$$393$$ −5.53249 31.3763i −0.279077 1.58272i
$$394$$ 0 0
$$395$$ −1.87890 + 1.57659i −0.0945378 + 0.0793267i
$$396$$ 0 0
$$397$$ 16.1594 5.88155i 0.811018 0.295186i 0.0969735 0.995287i $$-0.469084\pi$$
0.714044 + 0.700101i $$0.246862\pi$$
$$398$$ 0 0
$$399$$ −3.89948 + 8.29291i −0.195218 + 0.415165i
$$400$$ 0 0
$$401$$ −14.4376 + 5.25485i −0.720979 + 0.262415i −0.676341 0.736588i $$-0.736436\pi$$
−0.0446377 + 0.999003i $$0.514213\pi$$
$$402$$ 0 0
$$403$$ 0.345357 0.289789i 0.0172035 0.0144354i
$$404$$ 0 0
$$405$$ −0.479009 2.71659i −0.0238021 0.134989i
$$406$$ 0 0
$$407$$ −2.31164 + 4.00387i −0.114584 + 0.198465i
$$408$$ 0 0
$$409$$ −13.4638 4.90042i −0.665741 0.242310i −0.0130280 0.999915i $$-0.504147\pi$$
−0.652713 + 0.757605i $$0.726369\pi$$
$$410$$ 0 0
$$411$$ −5.16682 8.94920i −0.254860 0.441431i
$$412$$ 0 0
$$413$$ 8.82135 + 7.40200i 0.434070 + 0.364228i
$$414$$ 0 0
$$415$$ −0.565622 + 3.20780i −0.0277653 + 0.157465i
$$416$$ 0 0
$$417$$ 9.30139 0.455491
$$418$$ 0 0
$$419$$ −17.2723 −0.843805 −0.421902 0.906641i $$-0.638637\pi$$
−0.421902 + 0.906641i $$0.638637\pi$$
$$420$$ 0 0
$$421$$ −4.83458 + 27.4183i −0.235623 + 1.33629i 0.605674 + 0.795713i $$0.292903\pi$$
−0.841297 + 0.540573i $$0.818208\pi$$
$$422$$ 0 0
$$423$$ 2.53486 + 2.12700i 0.123249 + 0.103418i
$$424$$ 0 0
$$425$$ 16.3695 + 28.3528i 0.794038 + 1.37531i
$$426$$ 0 0
$$427$$ 6.08293 + 2.21401i 0.294374 + 0.107143i
$$428$$ 0 0
$$429$$ −6.34865 + 10.9962i −0.306516 + 0.530901i
$$430$$ 0 0
$$431$$ −6.57872 37.3098i −0.316886 1.79715i −0.561444 0.827515i $$-0.689754\pi$$
0.244558 0.969635i $$-0.421357\pi$$
$$432$$ 0 0
$$433$$ 5.76405 4.83661i 0.277003 0.232433i −0.493693 0.869636i $$-0.664353\pi$$
0.770696 + 0.637204i $$0.219909\pi$$
$$434$$ 0 0
$$435$$ 1.86648 0.679345i 0.0894911 0.0325721i
$$436$$ 0 0
$$437$$ −2.39074 + 26.3526i −0.114365 + 1.26061i
$$438$$ 0 0
$$439$$ −19.9813 + 7.27259i −0.953655 + 0.347102i −0.771544 0.636176i $$-0.780515\pi$$
−0.182111 + 0.983278i $$0.558293\pi$$
$$440$$ 0 0
$$441$$ −1.23642 + 1.03748i −0.0588772 + 0.0494039i
$$442$$ 0 0
$$443$$ −2.59412 14.7120i −0.123250 0.698988i −0.982332 0.187149i $$-0.940075\pi$$
0.859081 0.511839i $$-0.171036\pi$$
$$444$$ 0 0
$$445$$ 0.340090 0.589054i 0.0161218 0.0279238i
$$446$$ 0 0
$$447$$ 20.2768 + 7.38017i 0.959062 + 0.349070i
$$448$$ 0 0
$$449$$ −8.47286 14.6754i −0.399859 0.692576i 0.593849 0.804576i $$-0.297608\pi$$
−0.993708 + 0.112000i $$0.964274\pi$$
$$450$$ 0 0
$$451$$ 6.13441 + 5.14738i 0.288858 + 0.242381i
$$452$$ 0 0
$$453$$ −4.67808 + 26.5307i −0.219795 + 1.24652i
$$454$$ 0 0
$$455$$ 1.84180 0.0863447
$$456$$ 0 0
$$457$$ −10.2922 −0.481448 −0.240724 0.970594i $$-0.577385\pi$$
−0.240724 + 0.970594i $$0.577385\pi$$
$$458$$ 0 0
$$459$$ −5.68507 + 32.2416i −0.265356 + 1.50491i
$$460$$ 0 0
$$461$$ 4.59397 + 3.85480i 0.213962 + 0.179536i 0.743470 0.668770i $$-0.233179\pi$$
−0.529507 + 0.848305i $$0.677623\pi$$
$$462$$ 0 0
$$463$$ −1.69033 2.92774i −0.0785563 0.136063i 0.824071 0.566487i $$-0.191698\pi$$
−0.902627 + 0.430423i $$0.858364\pi$$
$$464$$ 0 0
$$465$$ −0.0385118 0.0140172i −0.00178594 0.000650030i
$$466$$ 0 0
$$467$$ −1.03045 + 1.78480i −0.0476837 + 0.0825906i −0.888882 0.458136i $$-0.848517\pi$$
0.841198 + 0.540727i $$0.181851\pi$$
$$468$$ 0 0
$$469$$ 0.745318 + 4.22691i 0.0344156 + 0.195180i
$$470$$ 0 0
$$471$$ −15.3209 + 12.8558i −0.705952 + 0.592364i
$$472$$ 0 0
$$473$$ −0.289251 + 0.105279i −0.0132998 + 0.00484073i
$$474$$ 0 0
$$475$$ −17.5291 12.3580i −0.804290 0.567023i
$$476$$ 0 0
$$477$$ −1.22637 + 0.446361i −0.0561515 + 0.0204375i
$$478$$ 0 0
$$479$$ −4.53663 + 3.80668i −0.207284 + 0.173932i −0.740519 0.672035i $$-0.765420\pi$$
0.533235 + 0.845967i $$0.320976\pi$$
$$480$$ 0 0
$$481$$ 3.62860 + 20.5788i 0.165450 + 0.938312i
$$482$$ 0 0
$$483$$ 6.38120 11.0526i 0.290355 0.502909i
$$484$$ 0 0
$$485$$ −3.79954 1.38292i −0.172528 0.0627952i
$$486$$ 0 0
$$487$$ 13.3232 + 23.0764i 0.603731 + 1.04569i 0.992251 + 0.124252i $$0.0396532\pi$$
−0.388520 + 0.921440i $$0.627013\pi$$
$$488$$ 0 0
$$489$$ 5.53287 + 4.64263i 0.250205 + 0.209947i
$$490$$ 0 0
$$491$$ 6.15100 34.8841i 0.277591 1.57430i −0.453019 0.891501i $$-0.649653\pi$$
0.730610 0.682795i $$-0.239236\pi$$
$$492$$ 0 0
$$493$$ −25.8373 −1.16365
$$494$$ 0 0
$$495$$ 0.100280 0.00450727
$$496$$ 0 0
$$497$$ 1.87730 10.6467i 0.0842086 0.477571i
$$498$$ 0 0
$$499$$ −26.5322 22.2631i −1.18774 0.996634i −0.999896 0.0144356i $$-0.995405\pi$$
−0.187846 0.982198i $$-0.560151\pi$$
$$500$$ 0 0
$$501$$ 7.33252 + 12.7003i 0.327593 + 0.567408i
$$502$$ 0 0
$$503$$ −29.0173 10.5614i −1.29382 0.470912i −0.398840 0.917020i $$-0.630587\pi$$
−0.894979 + 0.446109i $$0.852810\pi$$
$$504$$ 0 0
$$505$$ 2.41569 4.18410i 0.107497 0.186190i
$$506$$ 0 0
$$507$$ 5.87377 + 33.3118i 0.260863 + 1.47943i
$$508$$ 0 0
$$509$$ 11.9255 10.0067i 0.528590 0.443540i −0.339024 0.940778i $$-0.610097\pi$$
0.867614 + 0.497238i $$0.165652\pi$$
$$510$$ 0 0
$$511$$ −1.20014 + 0.436815i −0.0530910 + 0.0193235i
$$512$$ 0 0
$$513$$ −5.48451 20.7343i −0.242147 0.915440i
$$514$$ 0 0
$$515$$ 3.52210 1.28194i 0.155202 0.0564890i
$$516$$ 0 0
$$517$$ 11.0560 9.27711i 0.486244 0.408007i
$$518$$ 0 0
$$519$$ −2.05434 11.6507i −0.0901756 0.511411i
$$520$$ 0 0
$$521$$ −11.1132 + 19.2486i −0.486877 + 0.843295i −0.999886 0.0150876i $$-0.995197\pi$$
0.513009 + 0.858383i $$0.328531\pi$$
$$522$$ 0 0
$$523$$ −10.1135 3.68103i −0.442234 0.160960i 0.111299 0.993787i $$-0.464499\pi$$
−0.553534 + 0.832827i $$0.686721\pi$$
$$524$$ 0 0
$$525$$ 5.17218 + 8.95848i 0.225732 + 0.390980i
$$526$$ 0 0
$$527$$ 0.408385 + 0.342676i 0.0177895 + 0.0149272i
$$528$$ 0 0
$$529$$ 2.40523 13.6408i 0.104575 0.593077i
$$530$$ 0 0
$$531$$ 2.83383 0.122978
$$532$$ 0 0
$$533$$ 36.1941 1.56774
$$534$$ 0 0
$$535$$ 0.0485015 0.275066i 0.00209690 0.0118921i
$$536$$ 0 0
$$537$$ −13.6523 11.4557i −0.589142 0.494349i
$$538$$ 0 0
$$539$$ 3.51988 + 6.09660i 0.151612 + 0.262599i
$$540$$ 0 0
$$541$$ 11.5235 + 4.19422i 0.495435 + 0.180323i 0.577639 0.816292i $$-0.303974\pi$$
−0.0822049 + 0.996615i $$0.526196\pi$$
$$542$$ 0 0
$$543$$ 12.4861 21.6266i 0.535830 0.928085i
$$544$$ 0 0
$$545$$ 0.662215 + 3.75561i 0.0283662 + 0.160873i
$$546$$ 0 0
$$547$$ 14.2562 11.9624i 0.609552 0.511475i −0.284948 0.958543i $$-0.591976\pi$$
0.894500 + 0.447068i $$0.147532\pi$$
$$548$$ 0 0
$$549$$ 1.49695 0.544844i 0.0638881 0.0232534i
$$550$$ 0 0
$$551$$ 15.3630 7.10401i 0.654488 0.302641i
$$552$$ 0 0
$$553$$ 9.47288 3.44785i 0.402828 0.146617i
$$554$$ 0 0
$$555$$ 1.45518 1.22104i 0.0617688 0.0518302i
$$556$$ 0 0
$$557$$ −0.706865 4.00883i −0.0299508 0.169860i 0.966163 0.257931i $$-0.0830407\pi$$
−0.996114 + 0.0880715i $$0.971930\pi$$
$$558$$ 0 0
$$559$$ −0.695630 + 1.20487i −0.0294220 + 0.0509604i
$$560$$ 0 0
$$561$$ −14.1091 5.13529i −0.595686 0.216812i
$$562$$ 0 0
$$563$$ 12.4377 + 21.5428i 0.524188 + 0.907920i 0.999603 + 0.0281586i $$0.00896435\pi$$
−0.475416 + 0.879761i $$0.657702\pi$$
$$564$$ 0 0
$$565$$ 3.57496 + 2.99975i 0.150400 + 0.126201i
$$566$$ 0 0
$$567$$ −1.96875 + 11.1653i −0.0826795 + 0.468899i
$$568$$ 0 0
$$569$$ 19.2420 0.806667 0.403334 0.915053i $$-0.367851\pi$$
0.403334 + 0.915053i $$0.367851\pi$$
$$570$$ 0 0
$$571$$ 13.5395 0.566612 0.283306 0.959030i $$-0.408569\pi$$
0.283306 + 0.959030i $$0.408569\pi$$
$$572$$ 0 0
$$573$$ 0.324625 1.84104i 0.0135614 0.0769106i
$$574$$ 0 0
$$575$$ 22.8811 + 19.1995i 0.954207 + 0.800675i
$$576$$ 0 0
$$577$$ −12.8402 22.2398i −0.534543 0.925855i −0.999185 0.0403567i $$-0.987151\pi$$
0.464643 0.885498i $$-0.346183\pi$$
$$578$$ 0 0
$$579$$ 3.99394 + 1.45368i 0.165983 + 0.0604127i
$$580$$ 0 0
$$581$$ 6.69379 11.5940i 0.277705 0.481000i
$$582$$ 0 0
$$583$$ 0.988438 + 5.60571i 0.0409369 + 0.232165i
$$584$$ 0 0
$$585$$ 0.347207 0.291341i 0.0143552 0.0120455i
$$586$$ 0 0
$$587$$ 17.4378 6.34683i 0.719734 0.261962i 0.0439211 0.999035i $$-0.486015\pi$$
0.675813 + 0.737073i $$0.263793\pi$$
$$588$$ 0 0
$$589$$ −0.337049 0.0914715i −0.0138878 0.00376902i
$$590$$ 0 0
$$591$$ −26.5166 + 9.65127i −1.09075 + 0.397000i
$$592$$ 0 0
$$593$$ 2.75772 2.31400i 0.113246 0.0950248i −0.584406 0.811461i $$-0.698673\pi$$
0.697652 + 0.716437i $$0.254228\pi$$
$$594$$ 0 0
$$595$$ 0.378193 + 2.14484i 0.0155044 + 0.0879298i
$$596$$ 0 0
$$597$$ 12.4126 21.4993i 0.508014 0.879907i
$$598$$ 0 0
$$599$$ 12.3328 + 4.48878i 0.503905 + 0.183407i 0.581450 0.813582i $$-0.302486\pi$$
−0.0775443 + 0.996989i $$0.524708\pi$$
$$600$$ 0 0
$$601$$ −6.78825 11.7576i −0.276898 0.479602i 0.693714 0.720251i $$-0.255973\pi$$
−0.970612 + 0.240649i $$0.922640\pi$$
$$602$$ 0 0
$$603$$ 0.809130 + 0.678941i 0.0329503 + 0.0276486i
$$604$$ 0 0
$$605$$ −0.463097 + 2.62635i −0.0188276 + 0.106777i
$$606$$ 0 0
$$607$$ −18.3633 −0.745343 −0.372672 0.927963i $$-0.621558\pi$$
−0.372672 + 0.927963i $$0.621558\pi$$
$$608$$ 0 0
$$609$$ −8.16365 −0.330808
$$610$$ 0 0
$$611$$ 11.3275 64.2415i 0.458262 2.59893i
$$612$$ 0 0
$$613$$ 4.42518 + 3.71316i 0.178731 + 0.149973i 0.727764 0.685827i $$-0.240559\pi$$
−0.549033 + 0.835801i $$0.685004\pi$$
$$614$$ 0 0
$$615$$ −1.64513 2.84945i −0.0663382 0.114901i
$$616$$ 0 0
$$617$$ −39.3443 14.3201i −1.58394 0.576507i −0.607885 0.794025i $$-0.707982\pi$$
−0.976056 + 0.217518i $$0.930204\pi$$
$$618$$ 0 0
$$619$$ −18.0480 + 31.2601i −0.725412 + 1.25645i 0.233392 + 0.972383i $$0.425017\pi$$
−0.958804 + 0.284068i $$0.908316\pi$$
$$620$$ 0 0
$$621$$ 5.18672 + 29.4154i 0.208136 + 1.18040i
$$622$$ 0 0
$$623$$ −2.14153 + 1.79696i −0.0857986 + 0.0719936i
$$624$$ 0 0
$$625$$ −22.3757 + 8.14410i −0.895029 + 0.325764i
$$626$$ 0 0
$$627$$ 9.80133 0.825838i 0.391427 0.0329808i
$$628$$ 0 0
$$629$$ −23.2197 + 8.45126i −0.925828 + 0.336974i
$$630$$ 0 0
$$631$$ −29.6886 + 24.9117i −1.18188 + 0.991717i −0.181918 + 0.983314i $$0.558231\pi$$
−0.999965 + 0.00840360i $$0.997325\pi$$
$$632$$ 0 0
$$633$$ −6.78594 38.4850i −0.269717 1.52964i
$$634$$ 0 0
$$635$$ 0.316039 0.547396i 0.0125416 0.0217227i
$$636$$ 0 0
$$637$$ 29.8994 + 10.8825i 1.18466 + 0.431179i
$$638$$ 0 0
$$639$$ −1.33023 2.30403i −0.0526232 0.0911461i
$$640$$ 0 0
$$641$$ 5.24003 + 4.39691i 0.206969 + 0.173667i 0.740380 0.672189i $$-0.234646\pi$$
−0.533411 + 0.845856i $$0.679090\pi$$
$$642$$ 0 0
$$643$$ −2.89363 + 16.4106i −0.114114 + 0.647171i 0.873072 + 0.487592i $$0.162125\pi$$
−0.987185 + 0.159579i $$0.948986\pi$$
$$644$$ 0 0
$$645$$ 0.126474 0.00497992
$$646$$ 0 0
$$647$$ 36.1664 1.42185 0.710924 0.703269i $$-0.248277\pi$$
0.710924 + 0.703269i $$0.248277\pi$$
$$648$$ 0 0
$$649$$ 2.14629 12.1722i 0.0842494 0.477802i
$$650$$ 0 0
$$651$$ 0.129035 + 0.108273i 0.00505729 + 0.00424357i
$$652$$ 0 0
$$653$$ 4.83426 + 8.37319i 0.189179 + 0.327668i 0.944977 0.327137i $$-0.106084\pi$$
−0.755798 + 0.654805i $$0.772751\pi$$
$$654$$ 0 0
$$655$$ 4.66127 + 1.69656i 0.182131 + 0.0662902i
$$656$$ 0 0
$$657$$ −0.157148 + 0.272188i −0.00613093 + 0.0106191i
$$658$$ 0 0
$$659$$ 4.94409 + 28.0393i 0.192594 + 1.09226i 0.915803 + 0.401627i $$0.131555\pi$$
−0.723209 + 0.690629i $$0.757334\pi$$
$$660$$ 0 0
$$661$$ −19.5360 + 16.3927i −0.759863 + 0.637601i −0.938091 0.346388i $$-0.887408\pi$$
0.178228 + 0.983989i $$0.442964\pi$$
$$662$$ 0 0
$$663$$ −63.7702 + 23.2104i −2.47663 + 0.901419i
$$664$$ 0 0
$$665$$ −0.814604 1.17135i −0.0315890 0.0454231i
$$666$$ 0 0
$$667$$ −22.1508 + 8.06223i −0.857683 + 0.312171i
$$668$$ 0 0
$$669$$ −36.2240 + 30.3956i −1.40050 + 1.17516i
$$670$$ 0 0
$$671$$ −1.20652 6.84252i −0.0465772 0.264153i
$$672$$ 0 0
$$673$$ 20.3192 35.1938i 0.783246 1.35662i −0.146795 0.989167i $$-0.546896\pi$$
0.930041 0.367456i $$-0.119771\pi$$
$$674$$ 0 0
$$675$$ −22.7499 8.28029i −0.875644 0.318708i
$$676$$ 0 0
$$677$$ −10.2220 17.7050i −0.392862 0.680457i 0.599964 0.800027i $$-0.295182\pi$$
−0.992826 + 0.119570i $$0.961848\pi$$
$$678$$ 0 0
$$679$$ 12.7305 + 10.6822i 0.488552 + 0.409944i
$$680$$ 0 0
$$681$$ 6.84133 38.7991i 0.262160 1.48679i
$$682$$ 0 0
$$683$$ 39.8318 1.52412 0.762061 0.647505i $$-0.224187\pi$$
0.762061 + 0.647505i $$0.224187\pi$$
$$684$$ 0 0
$$685$$ 1.60887 0.0614718
$$686$$ 0 0
$$687$$ −6.33450 + 35.9247i −0.241676 + 1.37061i
$$688$$ 0 0
$$689$$ 19.7084 + 16.5373i 0.750831 + 0.630022i
$$690$$ 0 0
$$691$$ 14.0389 + 24.3160i 0.534064 + 0.925025i 0.999208 + 0.0397906i $$0.0126691\pi$$
−0.465144 + 0.885235i $$0.653998\pi$$
$$692$$ 0 0
$$693$$ −0.387300 0.140966i −0.0147123 0.00535484i
$$694$$ 0 0
$$695$$ −0.724079 + 1.25414i −0.0274659 + 0.0475723i
$$696$$ 0 0
$$697$$ 7.43206 + 42.1493i 0.281509 + 1.59652i
$$698$$ 0 0
$$699$$ 30.5722 25.6531i 1.15635 0.970290i
$$700$$ 0 0
$$701$$ −4.02822 + 1.46615i −0.152144 + 0.0553757i −0.416969 0.908921i $$-0.636908\pi$$
0.264826 + 0.964296i $$0.414686\pi$$
$$702$$ 0 0
$$703$$ 11.4829 11.4095i 0.433086 0.430317i
$$704$$ 0 0
$$705$$ −5.57242 + 2.02819i −0.209869 + 0.0763862i
$$706$$ 0 0
$$707$$ −15.2115 + 12.7639i −0.572087 + 0.480038i
$$708$$ 0 0
$$709$$ −0.715927 4.06022i −0.0268872 0.152485i 0.968408 0.249369i $$-0.0802234\pi$$
−0.995296 + 0.0968845i $$0.969112\pi$$
$$710$$ 0 0
$$711$$ 1.24039 2.14842i 0.0465184 0.0805722i
$$712$$ 0 0
$$713$$ 0.457045 + 0.166351i 0.0171165 + 0.00622989i
$$714$$ 0 0
$$715$$ −0.988438 1.71202i −0.0369655 0.0640261i
$$716$$ 0 0
$$717$$ 6.07162 + 5.09469i 0.226749 + 0.190265i
$$718$$ 0 0
$$719$$ −7.79796 + 44.2244i −0.290815 + 1.64929i 0.392927 + 0.919570i $$0.371462\pi$$
−0.683742 + 0.729724i $$0.739649\pi$$
$$720$$ 0 0
$$721$$ −15.4050 −0.573712
$$722$$ 0 0
$$723$$ −27.1922 −1.01129
$$724$$ 0 0
$$725$$ 3.31776 18.8160i 0.123219 0.698807i
$$726$$ 0 0
$$727$$ −26.7341 22.4326i −0.991514 0.831979i −0.00572754 0.999984i $$-0.501823\pi$$
−0.985786 + 0.168005i $$0.946268\pi$$
$$728$$ 0 0
$$729$$ −11.9828 20.7548i −0.443806 0.768695i
$$730$$ 0 0
$$731$$ −1.54595 0.562680i −0.0571791 0.0208115i
$$732$$ 0 0
$$733$$ 0.524006 0.907605i 0.0193546 0.0335232i −0.856186 0.516668i $$-0.827172\pi$$
0.875540 + 0.483145i $$0.160506\pi$$
$$734$$ 0 0
$$735$$ −0.502273 2.84853i −0.0185266 0.105070i
$$736$$ 0 0
$$737$$ 3.52909 2.96126i 0.129996 0.109079i
$$738$$ 0 0
$$739$$ −20.8426 + 7.58607i −0.766706 + 0.279058i −0.695618 0.718412i $$-0.744869\pi$$
−0.0710882 + 0.997470i $$0.522647\pi$$
$$740$$ 0 0
$$741$$ 31.5365 31.3348i 1.15852 1.15111i
$$742$$ 0 0
$$743$$ 35.7965 13.0288i 1.31325 0.477982i 0.411957 0.911203i $$-0.364845\pi$$
0.901288 + 0.433221i $$0.142623\pi$$
$$744$$ 0 0
$$745$$ −2.57357 + 2.15948i −0.0942884 + 0.0791174i
$$746$$ 0 0
$$747$$ −0.572091 3.24449i −0.0209317 0.118710i
$$748$$ 0 0
$$749$$ −0.573986 + 0.994173i −0.0209730 + 0.0363263i
$$750$$ 0 0
$$751$$ 11.9657 + 4.35515i 0.436634 + 0.158922i 0.550979 0.834519i $$-0.314255\pi$$
−0.114345 + 0.993441i $$0.536477\pi$$
$$752$$ 0 0
$$753$$ 21.2663 + 36.8343i 0.774987 + 1.34232i
$$754$$ 0 0
$$755$$ −3.21306 2.69608i −0.116935 0.0981203i
$$756$$ 0 0
$$757$$ 7.21125 40.8970i 0.262097 1.48643i −0.515078 0.857143i $$-0.672237\pi$$
0.777175 0.629284i $$-0.216652\pi$$
$$758$$ 0 0
$$759$$ −13.6984 −0.497221
$$760$$ 0 0
$$761$$ 36.4398 1.32094 0.660471 0.750851i $$-0.270357\pi$$
0.660471 + 0.750851i $$0.270357\pi$$
$$762$$ 0 0
$$763$$ 2.72173 15.4357i 0.0985333 0.558810i
$$764$$ 0 0
$$765$$ 0.410573 + 0.344512i 0.0148443 + 0.0124558i
$$766$$ 0 0
$$767$$ −27.9324 48.3803i −1.00858 1.74691i
$$768$$ 0 0
$$769$$ −11.0091 4.00697i −0.396997 0.144495i 0.135804 0.990736i $$-0.456638\pi$$
−0.532801 + 0.846241i $$0.678860\pi$$
$$770$$ 0 0
$$771$$ −0.0961463 + 0.166530i −0.00346263 + 0.00599744i
$$772$$ 0 0
$$773$$ 6.22310 + 35.2929i 0.223829 + 1.26940i 0.864911 + 0.501926i $$0.167375\pi$$
−0.641081 + 0.767473i $$0.721514\pi$$
$$774$$ 0 0
$$775$$ −0.301994 + 0.253403i −0.0108480 + 0.00910251i
$$776$$ 0 0
$$777$$ −7.33658 + 2.67030i −0.263198 + 0.0957964i
$$778$$ 0 0
$$779$$ −16.0082 23.0189i −0.573553 0.824736i
$$780$$ 0 0
$$781$$ −10.9041 + 3.96875i −0.390178 + 0.142013i
$$782$$ 0 0
$$783$$ 14.6362 12.2812i 0.523056 0.438896i
$$784$$ 0 0
$$785$$ −0.540717 3.06656i −0.0192990 0.109450i
$$786$$ 0 0
$$787$$ −1.05573 + 1.82858i −0.0376328 + 0.0651819i −0.884228 0.467055i $$-0.845315\pi$$
0.846596 + 0.532237i $$0.178648\pi$$
$$788$$ 0 0
$$789$$ 26.5224 + 9.65337i 0.944223 + 0.343669i
$$790$$ 0 0
$$791$$ −9.59033 16.6109i −0.340993 0.590617i
$$792$$ 0 0
$$793$$ −24.0568 20.1860i −0.854282 0.716827i
$$794$$ 0