# Properties

 Label 690.2.i.f.47.14 Level $690$ Weight $2$ Character 690.47 Analytic conductor $5.510$ Analytic rank $0$ Dimension $32$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$690 = 2 \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 690.i (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.50967773947$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 47.14 Character $$\chi$$ $$=$$ 690.47 Dual form 690.2.i.f.323.14

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 - 0.707107i) q^{2} +(1.31559 - 1.12660i) q^{3} -1.00000i q^{4} +(0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.461565 - 2.96428i) q^{9} +O(q^{10})$$ $$q+(0.707107 - 0.707107i) q^{2} +(1.31559 - 1.12660i) q^{3} -1.00000i q^{4} +(0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.461565 - 2.96428i) q^{9} +(-1.43919 - 1.71135i) q^{10} -2.97195i q^{11} +(-1.12660 - 1.31559i) q^{12} +(-1.33263 + 1.33263i) q^{13} +2.77200 q^{14} +(-2.25662 - 3.14764i) q^{15} -1.00000 q^{16} +(-0.217329 + 0.217329i) q^{17} +(-1.76969 - 2.42244i) q^{18} +6.42606i q^{19} +(-2.22777 - 0.192443i) q^{20} +(4.78694 + 0.370453i) q^{21} +(-2.10149 - 2.10149i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.72689 - 0.133641i) q^{24} +(-4.92593 - 0.857436i) q^{25} +1.88462i q^{26} +(-2.73231 - 4.41978i) q^{27} +(1.96010 - 1.96010i) q^{28} +1.22002 q^{29} +(-3.82139 - 0.630048i) q^{30} +6.33502 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.34819 - 3.90988i) q^{33} +0.307349i q^{34} +(4.74387 - 3.98945i) q^{35} +(-2.96428 - 0.461565i) q^{36} +(1.43305 + 1.43305i) q^{37} +(4.54391 + 4.54391i) q^{38} +(-0.251863 + 3.25453i) q^{39} +(-1.71135 + 1.43919i) q^{40} +3.04579i q^{41} +(3.64682 - 3.12292i) q^{42} +(-1.80190 + 1.80190i) q^{43} -2.97195 q^{44} +(-6.51491 - 1.59872i) q^{45} +1.00000 q^{46} +(-0.199419 + 0.199419i) q^{47} +(-1.31559 + 1.12660i) q^{48} +0.683996i q^{49} +(-4.08946 + 2.87686i) q^{50} +(-0.0410744 + 0.530758i) q^{51} +(1.33263 + 1.33263i) q^{52} +(-9.17886 - 9.17886i) q^{53} +(-5.05729 - 1.19322i) q^{54} +(-6.62083 - 0.571930i) q^{55} -2.77200i q^{56} +(7.23957 + 8.45408i) q^{57} +(0.862686 - 0.862686i) q^{58} -9.43000 q^{59} +(-3.14764 + 2.25662i) q^{60} +5.57225 q^{61} +(4.47954 - 4.47954i) q^{62} +(6.71501 - 4.90558i) q^{63} +1.00000i q^{64} +(2.71234 + 3.22525i) q^{65} +(-5.13223 - 0.397175i) q^{66} +(9.41060 + 9.41060i) q^{67} +(0.217329 + 0.217329i) q^{68} +(1.72689 + 0.133641i) q^{69} +(0.533451 - 6.17539i) q^{70} +7.64983i q^{71} +(-2.42244 + 1.76969i) q^{72} +(-4.05708 + 4.05708i) q^{73} +2.02664 q^{74} +(-7.44650 + 4.42150i) q^{75} +6.42606 q^{76} +(5.82533 - 5.82533i) q^{77} +(2.12321 + 2.47940i) q^{78} -14.4298i q^{79} +(-0.192443 + 2.22777i) q^{80} +(-8.57391 - 2.73642i) q^{81} +(2.15370 + 2.15370i) q^{82} +(12.1736 + 12.1736i) q^{83} +(0.370453 - 4.78694i) q^{84} +(0.442336 + 0.525982i) q^{85} +2.54827i q^{86} +(1.60505 - 1.37447i) q^{87} +(-2.10149 + 2.10149i) q^{88} +2.45643 q^{89} +(-5.73720 + 3.47628i) q^{90} -5.22418 q^{91} +(0.707107 - 0.707107i) q^{92} +(8.33431 - 7.13701i) q^{93} +0.282021i q^{94} +(14.3158 + 1.23665i) q^{95} +(-0.133641 + 1.72689i) q^{96} +(8.98748 + 8.98748i) q^{97} +(0.483658 + 0.483658i) q^{98} +(-8.80970 - 1.37175i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10})$$ $$32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$$.

 $$n$$ $$277$$ $$461$$ $$511$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 0.707107i 0.500000 0.500000i
$$3$$ 1.31559 1.12660i 0.759557 0.650440i
$$4$$ 1.00000i 0.500000i
$$5$$ 0.192443 2.22777i 0.0860629 0.996290i
$$6$$ 0.133641 1.72689i 0.0545587 0.704999i
$$7$$ 1.96010 + 1.96010i 0.740849 + 0.740849i 0.972741 0.231893i $$-0.0744918\pi$$
−0.231893 + 0.972741i $$0.574492\pi$$
$$8$$ −0.707107 0.707107i −0.250000 0.250000i
$$9$$ 0.461565 2.96428i 0.153855 0.988093i
$$10$$ −1.43919 1.71135i −0.455113 0.541176i
$$11$$ 2.97195i 0.896078i −0.894014 0.448039i $$-0.852123\pi$$
0.894014 0.448039i $$-0.147877\pi$$
$$12$$ −1.12660 1.31559i −0.325220 0.379779i
$$13$$ −1.33263 + 1.33263i −0.369605 + 0.369605i −0.867333 0.497728i $$-0.834168\pi$$
0.497728 + 0.867333i $$0.334168\pi$$
$$14$$ 2.77200 0.740849
$$15$$ −2.25662 3.14764i −0.582657 0.812718i
$$16$$ −1.00000 −0.250000
$$17$$ −0.217329 + 0.217329i −0.0527100 + 0.0527100i −0.732970 0.680260i $$-0.761867\pi$$
0.680260 + 0.732970i $$0.261867\pi$$
$$18$$ −1.76969 2.42244i −0.417119 0.570974i
$$19$$ 6.42606i 1.47424i 0.675762 + 0.737120i $$0.263815\pi$$
−0.675762 + 0.737120i $$0.736185\pi$$
$$20$$ −2.22777 0.192443i −0.498145 0.0430315i
$$21$$ 4.78694 + 0.370453i 1.04459 + 0.0808394i
$$22$$ −2.10149 2.10149i −0.448039 0.448039i
$$23$$ 0.707107 + 0.707107i 0.147442 + 0.147442i
$$24$$ −1.72689 0.133641i −0.352499 0.0272793i
$$25$$ −4.92593 0.857436i −0.985186 0.171487i
$$26$$ 1.88462i 0.369605i
$$27$$ −2.73231 4.41978i −0.525834 0.850587i
$$28$$ 1.96010 1.96010i 0.370424 0.370424i
$$29$$ 1.22002 0.226552 0.113276 0.993564i $$-0.463866\pi$$
0.113276 + 0.993564i $$0.463866\pi$$
$$30$$ −3.82139 0.630048i −0.697688 0.115030i
$$31$$ 6.33502 1.13780 0.568902 0.822405i $$-0.307368\pi$$
0.568902 + 0.822405i $$0.307368\pi$$
$$32$$ −0.707107 + 0.707107i −0.125000 + 0.125000i
$$33$$ −3.34819 3.90988i −0.582845 0.680623i
$$34$$ 0.307349i 0.0527100i
$$35$$ 4.74387 3.98945i 0.801860 0.674340i
$$36$$ −2.96428 0.461565i −0.494047 0.0769276i
$$37$$ 1.43305 + 1.43305i 0.235592 + 0.235592i 0.815022 0.579430i $$-0.196725\pi$$
−0.579430 + 0.815022i $$0.696725\pi$$
$$38$$ 4.54391 + 4.54391i 0.737120 + 0.737120i
$$39$$ −0.251863 + 3.25453i −0.0403303 + 0.521142i
$$40$$ −1.71135 + 1.43919i −0.270588 + 0.227557i
$$41$$ 3.04579i 0.475672i 0.971305 + 0.237836i $$0.0764380\pi$$
−0.971305 + 0.237836i $$0.923562\pi$$
$$42$$ 3.64682 3.12292i 0.562717 0.481878i
$$43$$ −1.80190 + 1.80190i −0.274786 + 0.274786i −0.831024 0.556237i $$-0.812245\pi$$
0.556237 + 0.831024i $$0.312245\pi$$
$$44$$ −2.97195 −0.448039
$$45$$ −6.51491 1.59872i −0.971186 0.238323i
$$46$$ 1.00000 0.147442
$$47$$ −0.199419 + 0.199419i −0.0290883 + 0.0290883i −0.721501 0.692413i $$-0.756548\pi$$
0.692413 + 0.721501i $$0.256548\pi$$
$$48$$ −1.31559 + 1.12660i −0.189889 + 0.162610i
$$49$$ 0.683996i 0.0977137i
$$50$$ −4.08946 + 2.87686i −0.578337 + 0.406850i
$$51$$ −0.0410744 + 0.530758i −0.00575157 + 0.0743210i
$$52$$ 1.33263 + 1.33263i 0.184803 + 0.184803i
$$53$$ −9.17886 9.17886i −1.26081 1.26081i −0.950699 0.310114i $$-0.899633\pi$$
−0.310114 0.950699i $$-0.600367\pi$$
$$54$$ −5.05729 1.19322i −0.688211 0.162377i
$$55$$ −6.62083 0.571930i −0.892753 0.0771191i
$$56$$ 2.77200i 0.370424i
$$57$$ 7.23957 + 8.45408i 0.958905 + 1.11977i
$$58$$ 0.862686 0.862686i 0.113276 0.113276i
$$59$$ −9.43000 −1.22768 −0.613841 0.789430i $$-0.710376\pi$$
−0.613841 + 0.789430i $$0.710376\pi$$
$$60$$ −3.14764 + 2.25662i −0.406359 + 0.291329i
$$61$$ 5.57225 0.713454 0.356727 0.934209i $$-0.383893\pi$$
0.356727 + 0.934209i $$0.383893\pi$$
$$62$$ 4.47954 4.47954i 0.568902 0.568902i
$$63$$ 6.71501 4.90558i 0.846011 0.618044i
$$64$$ 1.00000i 0.125000i
$$65$$ 2.71234 + 3.22525i 0.336425 + 0.400043i
$$66$$ −5.13223 0.397175i −0.631734 0.0488888i
$$67$$ 9.41060 + 9.41060i 1.14969 + 1.14969i 0.986614 + 0.163074i $$0.0521410\pi$$
0.163074 + 0.986614i $$0.447859\pi$$
$$68$$ 0.217329 + 0.217329i 0.0263550 + 0.0263550i
$$69$$ 1.72689 + 0.133641i 0.207893 + 0.0160885i
$$70$$ 0.533451 6.17539i 0.0637596 0.738100i
$$71$$ 7.64983i 0.907868i 0.891035 + 0.453934i $$0.149980\pi$$
−0.891035 + 0.453934i $$0.850020\pi$$
$$72$$ −2.42244 + 1.76969i −0.285487 + 0.208560i
$$73$$ −4.05708 + 4.05708i −0.474845 + 0.474845i −0.903479 0.428633i $$-0.858995\pi$$
0.428633 + 0.903479i $$0.358995\pi$$
$$74$$ 2.02664 0.235592
$$75$$ −7.44650 + 4.42150i −0.859848 + 0.510550i
$$76$$ 6.42606 0.737120
$$77$$ 5.82533 5.82533i 0.663858 0.663858i
$$78$$ 2.12321 + 2.47940i 0.240406 + 0.280736i
$$79$$ 14.4298i 1.62348i −0.584018 0.811741i $$-0.698520\pi$$
0.584018 0.811741i $$-0.301480\pi$$
$$80$$ −0.192443 + 2.22777i −0.0215157 + 0.249072i
$$81$$ −8.57391 2.73642i −0.952657 0.304047i
$$82$$ 2.15370 + 2.15370i 0.237836 + 0.237836i
$$83$$ 12.1736 + 12.1736i 1.33622 + 1.33622i 0.899688 + 0.436533i $$0.143794\pi$$
0.436533 + 0.899688i $$0.356206\pi$$
$$84$$ 0.370453 4.78694i 0.0404197 0.522297i
$$85$$ 0.442336 + 0.525982i 0.0479780 + 0.0570508i
$$86$$ 2.54827i 0.274786i
$$87$$ 1.60505 1.37447i 0.172080 0.147359i
$$88$$ −2.10149 + 2.10149i −0.224019 + 0.224019i
$$89$$ 2.45643 0.260381 0.130191 0.991489i $$-0.458441\pi$$
0.130191 + 0.991489i $$0.458441\pi$$
$$90$$ −5.73720 + 3.47628i −0.604754 + 0.366432i
$$91$$ −5.22418 −0.547643
$$92$$ 0.707107 0.707107i 0.0737210 0.0737210i
$$93$$ 8.33431 7.13701i 0.864227 0.740073i
$$94$$ 0.282021i 0.0290883i
$$95$$ 14.3158 + 1.23665i 1.46877 + 0.126877i
$$96$$ −0.133641 + 1.72689i −0.0136397 + 0.176250i
$$97$$ 8.98748 + 8.98748i 0.912541 + 0.912541i 0.996472 0.0839309i $$-0.0267475\pi$$
−0.0839309 + 0.996472i $$0.526748\pi$$
$$98$$ 0.483658 + 0.483658i 0.0488568 + 0.0488568i
$$99$$ −8.80970 1.37175i −0.885409 0.137866i
$$100$$ −0.857436 + 4.92593i −0.0857436 + 0.492593i
$$101$$ 3.00976i 0.299482i 0.988725 + 0.149741i $$0.0478440\pi$$
−0.988725 + 0.149741i $$0.952156\pi$$
$$102$$ 0.346258 + 0.404346i 0.0342847 + 0.0400363i
$$103$$ −1.81831 + 1.81831i −0.179163 + 0.179163i −0.790991 0.611828i $$-0.790435\pi$$
0.611828 + 0.790991i $$0.290435\pi$$
$$104$$ 1.88462 0.184803
$$105$$ 1.74649 10.5929i 0.170440 1.03376i
$$106$$ −12.9809 −1.26081
$$107$$ 10.1552 10.1552i 0.981744 0.981744i −0.0180921 0.999836i $$-0.505759\pi$$
0.999836 + 0.0180921i $$0.00575922\pi$$
$$108$$ −4.41978 + 2.73231i −0.425294 + 0.262917i
$$109$$ 3.22282i 0.308690i −0.988017 0.154345i $$-0.950673\pi$$
0.988017 0.154345i $$-0.0493268\pi$$
$$110$$ −5.08605 + 4.27722i −0.484936 + 0.407817i
$$111$$ 3.49978 + 0.270842i 0.332184 + 0.0257072i
$$112$$ −1.96010 1.96010i −0.185212 0.185212i
$$113$$ 3.72990 + 3.72990i 0.350880 + 0.350880i 0.860437 0.509557i $$-0.170191\pi$$
−0.509557 + 0.860437i $$0.670191\pi$$
$$114$$ 11.0971 + 0.858785i 1.03934 + 0.0804326i
$$115$$ 1.71135 1.43919i 0.159584 0.134206i
$$116$$ 1.22002i 0.113276i
$$117$$ 3.33519 + 4.56539i 0.308339 + 0.422070i
$$118$$ −6.66802 + 6.66802i −0.613841 + 0.613841i
$$119$$ −0.851973 −0.0781003
$$120$$ −0.630048 + 3.82139i −0.0575152 + 0.348844i
$$121$$ 2.16749 0.197044
$$122$$ 3.94018 3.94018i 0.356727 0.356727i
$$123$$ 3.43137 + 4.00701i 0.309396 + 0.361300i
$$124$$ 6.33502i 0.568902i
$$125$$ −2.85813 + 10.8088i −0.255639 + 0.966772i
$$126$$ 1.27946 8.21699i 0.113983 0.732028i
$$127$$ −9.95020 9.95020i −0.882938 0.882938i 0.110895 0.993832i $$-0.464628\pi$$
−0.993832 + 0.110895i $$0.964628\pi$$
$$128$$ 0.707107 + 0.707107i 0.0625000 + 0.0625000i
$$129$$ −0.340552 + 4.40057i −0.0299840 + 0.387448i
$$130$$ 4.19851 + 0.362682i 0.368234 + 0.0318093i
$$131$$ 4.14724i 0.362346i 0.983451 + 0.181173i $$0.0579894\pi$$
−0.983451 + 0.181173i $$0.942011\pi$$
$$132$$ −3.90988 + 3.34819i −0.340311 + 0.291423i
$$133$$ −12.5957 + 12.5957i −1.09219 + 1.09219i
$$134$$ 13.3086 1.14969
$$135$$ −10.3721 + 5.23641i −0.892686 + 0.450679i
$$136$$ 0.307349 0.0263550
$$137$$ −6.71805 + 6.71805i −0.573962 + 0.573962i −0.933233 0.359271i $$-0.883025\pi$$
0.359271 + 0.933233i $$0.383025\pi$$
$$138$$ 1.31559 1.12660i 0.111991 0.0959022i
$$139$$ 21.3303i 1.80921i −0.426247 0.904607i $$-0.640165\pi$$
0.426247 0.904607i $$-0.359835\pi$$
$$140$$ −3.98945 4.74387i −0.337170 0.400930i
$$141$$ −0.0376896 + 0.487019i −0.00317404 + 0.0410144i
$$142$$ 5.40925 + 5.40925i 0.453934 + 0.453934i
$$143$$ 3.96052 + 3.96052i 0.331195 + 0.331195i
$$144$$ −0.461565 + 2.96428i −0.0384638 + 0.247023i
$$145$$ 0.234784 2.71793i 0.0194978 0.225712i
$$146$$ 5.73758i 0.474845i
$$147$$ 0.770587 + 0.899860i 0.0635569 + 0.0742192i
$$148$$ 1.43305 1.43305i 0.117796 0.117796i
$$149$$ −2.04707 −0.167703 −0.0838514 0.996478i $$-0.526722\pi$$
−0.0838514 + 0.996478i $$0.526722\pi$$
$$150$$ −2.13900 + 8.39194i −0.174649 + 0.685199i
$$151$$ −2.64015 −0.214852 −0.107426 0.994213i $$-0.534261\pi$$
−0.107426 + 0.994213i $$0.534261\pi$$
$$152$$ 4.54391 4.54391i 0.368560 0.368560i
$$153$$ 0.543912 + 0.744535i 0.0439727 + 0.0601921i
$$154$$ 8.23826i 0.663858i
$$155$$ 1.21913 14.1130i 0.0979227 1.13358i
$$156$$ 3.25453 + 0.251863i 0.260571 + 0.0201652i
$$157$$ 0.750993 + 0.750993i 0.0599358 + 0.0599358i 0.736439 0.676504i $$-0.236506\pi$$
−0.676504 + 0.736439i $$0.736506\pi$$
$$158$$ −10.2034 10.2034i −0.811741 0.811741i
$$159$$ −22.4165 1.73477i −1.77774 0.137577i
$$160$$ 1.43919 + 1.71135i 0.113778 + 0.135294i
$$161$$ 2.77200i 0.218464i
$$162$$ −7.99761 + 4.12773i −0.628352 + 0.324305i
$$163$$ 6.60415 6.60415i 0.517277 0.517277i −0.399469 0.916747i $$-0.630806\pi$$
0.916747 + 0.399469i $$0.130806\pi$$
$$164$$ 3.04579 0.237836
$$165$$ −9.35465 + 6.70657i −0.728259 + 0.522106i
$$166$$ 17.2160 1.33622
$$167$$ −5.25056 + 5.25056i −0.406300 + 0.406300i −0.880446 0.474146i $$-0.842757\pi$$
0.474146 + 0.880446i $$0.342757\pi$$
$$168$$ −3.12292 3.64682i −0.240939 0.281359i
$$169$$ 9.44819i 0.726784i
$$170$$ 0.684704 + 0.0591471i 0.0525144 + 0.00453638i
$$171$$ 19.0487 + 2.96605i 1.45669 + 0.226819i
$$172$$ 1.80190 + 1.80190i 0.137393 + 0.137393i
$$173$$ 16.1787 + 16.1787i 1.23004 + 1.23004i 0.963947 + 0.266093i $$0.0857329\pi$$
0.266093 + 0.963947i $$0.414267\pi$$
$$174$$ 0.163045 2.10684i 0.0123604 0.159719i
$$175$$ −7.97466 11.3360i −0.602828 0.856920i
$$176$$ 2.97195i 0.224019i
$$177$$ −12.4060 + 10.6238i −0.932495 + 0.798533i
$$178$$ 1.73696 1.73696i 0.130191 0.130191i
$$179$$ −12.6087 −0.942418 −0.471209 0.882022i $$-0.656182\pi$$
−0.471209 + 0.882022i $$0.656182\pi$$
$$180$$ −1.59872 + 6.51491i −0.119161 + 0.485593i
$$181$$ −1.75381 −0.130360 −0.0651799 0.997874i $$-0.520762\pi$$
−0.0651799 + 0.997874i $$0.520762\pi$$
$$182$$ −3.69405 + 3.69405i −0.273822 + 0.273822i
$$183$$ 7.33081 6.27767i 0.541909 0.464059i
$$184$$ 1.00000i 0.0737210i
$$185$$ 3.46829 2.91673i 0.254994 0.214442i
$$186$$ 0.846618 10.9399i 0.0620771 0.802150i
$$187$$ 0.645891 + 0.645891i 0.0472322 + 0.0472322i
$$188$$ 0.199419 + 0.199419i 0.0145441 + 0.0145441i
$$189$$ 3.30761 14.0188i 0.240593 1.01972i
$$190$$ 10.9972 9.24836i 0.797824 0.670946i
$$191$$ 26.9285i 1.94848i 0.225520 + 0.974238i $$0.427592\pi$$
−0.225520 + 0.974238i $$0.572408\pi$$
$$192$$ 1.12660 + 1.31559i 0.0813050 + 0.0949447i
$$193$$ −10.9317 + 10.9317i −0.786878 + 0.786878i −0.980981 0.194103i $$-0.937820\pi$$
0.194103 + 0.980981i $$0.437820\pi$$
$$194$$ 12.7102 0.912541
$$195$$ 7.20189 + 1.18740i 0.515738 + 0.0850317i
$$196$$ 0.683996 0.0488568
$$197$$ 1.97929 1.97929i 0.141019 0.141019i −0.633073 0.774092i $$-0.718207\pi$$
0.774092 + 0.633073i $$0.218207\pi$$
$$198$$ −7.19938 + 5.25943i −0.511637 + 0.373771i
$$199$$ 15.8892i 1.12636i −0.826336 0.563178i $$-0.809579\pi$$
0.826336 0.563178i $$-0.190421\pi$$
$$200$$ 2.87686 + 4.08946i 0.203425 + 0.289168i
$$201$$ 22.9825 + 1.77857i 1.62106 + 0.125451i
$$202$$ 2.12822 + 2.12822i 0.149741 + 0.149741i
$$203$$ 2.39137 + 2.39137i 0.167841 + 0.167841i
$$204$$ 0.530758 + 0.0410744i 0.0371605 + 0.00287579i
$$205$$ 6.78531 + 0.586139i 0.473907 + 0.0409377i
$$206$$ 2.57147i 0.179163i
$$207$$ 2.42244 1.76969i 0.168371 0.123002i
$$208$$ 1.33263 1.33263i 0.0924013 0.0924013i
$$209$$ 19.0980 1.32103
$$210$$ −6.25536 8.72527i −0.431661 0.602101i
$$211$$ 11.3907 0.784169 0.392085 0.919929i $$-0.371754\pi$$
0.392085 + 0.919929i $$0.371754\pi$$
$$212$$ −9.17886 + 9.17886i −0.630407 + 0.630407i
$$213$$ 8.61826 + 10.0641i 0.590514 + 0.689578i
$$214$$ 14.3617i 0.981744i
$$215$$ 3.66745 + 4.36097i 0.250118 + 0.297416i
$$216$$ −1.19322 + 5.05729i −0.0811884 + 0.344105i
$$217$$ 12.4173 + 12.4173i 0.842941 + 0.842941i
$$218$$ −2.27888 2.27888i −0.154345 0.154345i
$$219$$ −0.766775 + 9.90815i −0.0518138 + 0.669531i
$$220$$ −0.571930 + 6.62083i −0.0385595 + 0.446377i
$$221$$ 0.579238i 0.0389638i
$$222$$ 2.66623 2.28320i 0.178946 0.153239i
$$223$$ −10.4680 + 10.4680i −0.700989 + 0.700989i −0.964623 0.263634i $$-0.915079\pi$$
0.263634 + 0.964623i $$0.415079\pi$$
$$224$$ −2.77200 −0.185212
$$225$$ −4.81532 + 14.2061i −0.321021 + 0.947072i
$$226$$ 5.27488 0.350880
$$227$$ 16.1663 16.1663i 1.07299 1.07299i 0.0758747 0.997117i $$-0.475825\pi$$
0.997117 0.0758747i $$-0.0241749\pi$$
$$228$$ 8.45408 7.23957i 0.559885 0.479453i
$$229$$ 16.0298i 1.05928i −0.848224 0.529638i $$-0.822328\pi$$
0.848224 0.529638i $$-0.177672\pi$$
$$230$$ 0.192443 2.22777i 0.0126893 0.146895i
$$231$$ 1.10097 14.2266i 0.0724384 0.936038i
$$232$$ −0.862686 0.862686i −0.0566381 0.0566381i
$$233$$ 4.14654 + 4.14654i 0.271649 + 0.271649i 0.829764 0.558115i $$-0.188475\pi$$
−0.558115 + 0.829764i $$0.688475\pi$$
$$234$$ 5.58655 + 0.869877i 0.365204 + 0.0568657i
$$235$$ 0.405884 + 0.482637i 0.0264769 + 0.0314838i
$$236$$ 9.43000i 0.613841i
$$237$$ −16.2566 18.9838i −1.05598 1.23313i
$$238$$ −0.602436 + 0.602436i −0.0390501 + 0.0390501i
$$239$$ −29.7656 −1.92538 −0.962690 0.270608i $$-0.912775\pi$$
−0.962690 + 0.270608i $$0.912775\pi$$
$$240$$ 2.25662 + 3.14764i 0.145664 + 0.203180i
$$241$$ −18.1553 −1.16949 −0.584743 0.811219i $$-0.698805\pi$$
−0.584743 + 0.811219i $$0.698805\pi$$
$$242$$ 1.53265 1.53265i 0.0985222 0.0985222i
$$243$$ −14.3626 + 6.05932i −0.921362 + 0.388706i
$$244$$ 5.57225i 0.356727i
$$245$$ 1.52379 + 0.131630i 0.0973512 + 0.00840953i
$$246$$ 5.25973 + 0.407041i 0.335348 + 0.0259520i
$$247$$ −8.56357 8.56357i −0.544887 0.544887i
$$248$$ −4.47954 4.47954i −0.284451 0.284451i
$$249$$ 29.7301 + 2.30076i 1.88407 + 0.145805i
$$250$$ 5.62200 + 9.66401i 0.355567 + 0.611206i
$$251$$ 19.1213i 1.20693i −0.797390 0.603464i $$-0.793787\pi$$
0.797390 0.603464i $$-0.206213\pi$$
$$252$$ −4.90558 6.71501i −0.309022 0.423006i
$$253$$ 2.10149 2.10149i 0.132119 0.132119i
$$254$$ −14.0717 −0.882938
$$255$$ 1.17450 + 0.193645i 0.0735502 + 0.0121265i
$$256$$ 1.00000 0.0625000
$$257$$ −17.0084 + 17.0084i −1.06096 + 1.06096i −0.0629387 + 0.998017i $$0.520047\pi$$
−0.998017 + 0.0629387i $$0.979953\pi$$
$$258$$ 2.87086 + 3.35248i 0.178732 + 0.208716i
$$259$$ 5.61785i 0.349076i
$$260$$ 3.22525 2.71234i 0.200022 0.168212i
$$261$$ 0.563120 3.61649i 0.0348563 0.223855i
$$262$$ 2.93254 + 2.93254i 0.181173 + 0.181173i
$$263$$ −12.3574 12.3574i −0.761992 0.761992i 0.214690 0.976682i $$-0.431126\pi$$
−0.976682 + 0.214690i $$0.931126\pi$$
$$264$$ −0.397175 + 5.13223i −0.0244444 + 0.315867i
$$265$$ −22.2148 + 18.6820i −1.36464 + 1.14763i
$$266$$ 17.8131i 1.09219i
$$267$$ 3.23166 2.76740i 0.197774 0.169362i
$$268$$ 9.41060 9.41060i 0.574844 0.574844i
$$269$$ −20.0999 −1.22552 −0.612758 0.790271i $$-0.709940\pi$$
−0.612758 + 0.790271i $$0.709940\pi$$
$$270$$ −3.63146 + 11.0369i −0.221004 + 0.671682i
$$271$$ −27.8676 −1.69284 −0.846419 0.532518i $$-0.821246\pi$$
−0.846419 + 0.532518i $$0.821246\pi$$
$$272$$ 0.217329 0.217329i 0.0131775 0.0131775i
$$273$$ −6.87289 + 5.88554i −0.415966 + 0.356209i
$$274$$ 9.50076i 0.573962i
$$275$$ −2.54826 + 14.6396i −0.153666 + 0.882804i
$$276$$ 0.133641 1.72689i 0.00804423 0.103946i
$$277$$ 7.04930 + 7.04930i 0.423551 + 0.423551i 0.886424 0.462873i $$-0.153182\pi$$
−0.462873 + 0.886424i $$0.653182\pi$$
$$278$$ −15.0828 15.0828i −0.904607 0.904607i
$$279$$ 2.92403 18.7788i 0.175057 1.12426i
$$280$$ −6.17539 0.533451i −0.369050 0.0318798i
$$281$$ 15.7886i 0.941867i −0.882169 0.470934i $$-0.843917\pi$$
0.882169 0.470934i $$-0.156083\pi$$
$$282$$ 0.317724 + 0.371025i 0.0189202 + 0.0220942i
$$283$$ 13.2043 13.2043i 0.784912 0.784912i −0.195743 0.980655i $$-0.562712\pi$$
0.980655 + 0.195743i $$0.0627118\pi$$
$$284$$ 7.64983 0.453934
$$285$$ 20.2270 14.5012i 1.19814 0.858977i
$$286$$ 5.60102 0.331195
$$287$$ −5.97005 + 5.97005i −0.352401 + 0.352401i
$$288$$ 1.76969 + 2.42244i 0.104280 + 0.142744i
$$289$$ 16.9055i 0.994443i
$$290$$ −1.75585 2.08788i −0.103107 0.122605i
$$291$$ 21.9491 + 1.69860i 1.28668 + 0.0995740i
$$292$$ 4.05708 + 4.05708i 0.237423 + 0.237423i
$$293$$ −6.93824 6.93824i −0.405336 0.405336i 0.474772 0.880109i $$-0.342530\pi$$
−0.880109 + 0.474772i $$0.842530\pi$$
$$294$$ 1.18118 + 0.0914098i 0.0688880 + 0.00533113i
$$295$$ −1.81473 + 21.0079i −0.105658 + 1.22313i
$$296$$ 2.02664i 0.117796i
$$297$$ −13.1354 + 8.12031i −0.762192 + 0.471188i
$$298$$ −1.44750 + 1.44750i −0.0838514 + 0.0838514i
$$299$$ −1.88462 −0.108991
$$300$$ 4.42150 + 7.44650i 0.255275 + 0.429924i
$$301$$ −7.06380 −0.407150
$$302$$ −1.86687 + 1.86687i −0.107426 + 0.107426i
$$303$$ 3.39078 + 3.95962i 0.194795 + 0.227474i
$$304$$ 6.42606i 0.368560i
$$305$$ 1.07234 12.4137i 0.0614019 0.710807i
$$306$$ 0.911070 + 0.141862i 0.0520824 + 0.00810970i
$$307$$ −8.38939 8.38939i −0.478808 0.478808i 0.425943 0.904750i $$-0.359943\pi$$
−0.904750 + 0.425943i $$0.859943\pi$$
$$308$$ −5.82533 5.82533i −0.331929 0.331929i
$$309$$ −0.343654 + 4.44065i −0.0195498 + 0.252620i
$$310$$ −9.11733 10.8414i −0.517830 0.615753i
$$311$$ 22.7094i 1.28773i −0.765139 0.643865i $$-0.777330\pi$$
0.765139 0.643865i $$-0.222670\pi$$
$$312$$ 2.47940 2.12321i 0.140368 0.120203i
$$313$$ −19.0911 + 19.0911i −1.07909 + 1.07909i −0.0825035 + 0.996591i $$0.526292\pi$$
−0.996591 + 0.0825035i $$0.973708\pi$$
$$314$$ 1.06206 0.0599358
$$315$$ −9.63625 15.9035i −0.542941 0.896063i
$$316$$ −14.4298 −0.811741
$$317$$ 0.0275450 0.0275450i 0.00154708 0.00154708i −0.706333 0.707880i $$-0.749652\pi$$
0.707880 + 0.706333i $$0.249652\pi$$
$$318$$ −17.0775 + 14.6242i −0.957660 + 0.820084i
$$319$$ 3.62585i 0.203009i
$$320$$ 2.22777 + 0.192443i 0.124536 + 0.0107579i
$$321$$ 1.91931 24.8010i 0.107125 1.38426i
$$322$$ 1.96010 + 1.96010i 0.109232 + 0.109232i
$$323$$ −1.39657 1.39657i −0.0777072 0.0777072i
$$324$$ −2.73642 + 8.57391i −0.152023 + 0.476329i
$$325$$ 7.70709 5.42180i 0.427513 0.300747i
$$326$$ 9.33968i 0.517277i
$$327$$ −3.63082 4.23992i −0.200785 0.234468i
$$328$$ 2.15370 2.15370i 0.118918 0.118918i
$$329$$ −0.781764 −0.0431000
$$330$$ −1.87247 + 11.3570i −0.103076 + 0.625182i
$$331$$ 1.05162 0.0578024 0.0289012 0.999582i $$-0.490799\pi$$
0.0289012 + 0.999582i $$0.490799\pi$$
$$332$$ 12.1736 12.1736i 0.668111 0.668111i
$$333$$ 4.90941 3.58652i 0.269034 0.196540i
$$334$$ 7.42541i 0.406300i
$$335$$ 22.7757 19.1537i 1.24437 1.04648i
$$336$$ −4.78694 0.370453i −0.261149 0.0202099i
$$337$$ −10.0242 10.0242i −0.546054 0.546054i 0.379243 0.925297i $$-0.376184\pi$$
−0.925297 + 0.379243i $$0.876184\pi$$
$$338$$ 6.68088 + 6.68088i 0.363392 + 0.363392i
$$339$$ 9.10912 + 0.704939i 0.494740 + 0.0382871i
$$340$$ 0.525982 0.442336i 0.0285254 0.0239890i
$$341$$ 18.8274i 1.01956i
$$342$$ 15.5667 11.3721i 0.841753 0.614934i
$$343$$ 12.3800 12.3800i 0.668458 0.668458i
$$344$$ 2.54827 0.137393
$$345$$ 0.630048 3.82139i 0.0339206 0.205737i
$$346$$ 22.8801 1.23004
$$347$$ −18.2887 + 18.2887i −0.981790 + 0.981790i −0.999837 0.0180467i $$-0.994255\pi$$
0.0180467 + 0.999837i $$0.494255\pi$$
$$348$$ −1.37447 1.60505i −0.0736794 0.0860398i
$$349$$ 28.7041i 1.53649i −0.640154 0.768247i $$-0.721129\pi$$
0.640154 0.768247i $$-0.278871\pi$$
$$350$$ −13.6547 2.37681i −0.729874 0.127046i
$$351$$ 9.53110 + 2.24877i 0.508732 + 0.120031i
$$352$$ 2.10149 + 2.10149i 0.112010 + 0.112010i
$$353$$ −10.4582 10.4582i −0.556631 0.556631i 0.371715 0.928347i $$-0.378770\pi$$
−0.928347 + 0.371715i $$0.878770\pi$$
$$354$$ −1.26023 + 16.2846i −0.0669807 + 0.865514i
$$355$$ 17.0421 + 1.47215i 0.904499 + 0.0781337i
$$356$$ 2.45643i 0.130191i
$$357$$ −1.12085 + 0.959829i −0.0593216 + 0.0507995i
$$358$$ −8.91569 + 8.91569i −0.471209 + 0.471209i
$$359$$ 10.4419 0.551105 0.275552 0.961286i $$-0.411139\pi$$
0.275552 + 0.961286i $$0.411139\pi$$
$$360$$ 3.47628 + 5.73720i 0.183216 + 0.302377i
$$361$$ −22.2943 −1.17338
$$362$$ −1.24013 + 1.24013i −0.0651799 + 0.0651799i
$$363$$ 2.85153 2.44188i 0.149667 0.128166i
$$364$$ 5.22418i 0.273822i
$$365$$ 8.25749 + 9.81900i 0.432217 + 0.513950i
$$366$$ 0.744681 9.62265i 0.0389251 0.502984i
$$367$$ 11.3139 + 11.3139i 0.590580 + 0.590580i 0.937788 0.347208i $$-0.112870\pi$$
−0.347208 + 0.937788i $$0.612870\pi$$
$$368$$ −0.707107 0.707107i −0.0368605 0.0368605i
$$369$$ 9.02856 + 1.40583i 0.470008 + 0.0731846i
$$370$$ 0.390012 4.51489i 0.0202758 0.234718i
$$371$$ 35.9830i 1.86814i
$$372$$ −7.13701 8.33431i −0.370037 0.432114i
$$373$$ −20.2494 + 20.2494i −1.04847 + 1.04847i −0.0497082 + 0.998764i $$0.515829\pi$$
−0.998764 + 0.0497082i $$0.984171\pi$$
$$374$$ 0.913428 0.0472322
$$375$$ 8.41706 + 17.4400i 0.434655 + 0.900597i
$$376$$ 0.282021 0.0145441
$$377$$ −1.62584 + 1.62584i −0.0837349 + 0.0837349i
$$378$$ −7.57398 12.2516i −0.389563 0.630157i
$$379$$ 31.4641i 1.61620i −0.589042 0.808102i $$-0.700495\pi$$
0.589042 0.808102i $$-0.299505\pi$$
$$380$$ 1.23665 14.3158i 0.0634387 0.734385i
$$381$$ −24.3003 1.88056i −1.24494 0.0963438i
$$382$$ 19.0413 + 19.0413i 0.974238 + 0.974238i
$$383$$ 5.10098 + 5.10098i 0.260648 + 0.260648i 0.825317 0.564669i $$-0.190996\pi$$
−0.564669 + 0.825317i $$0.690996\pi$$
$$384$$ 1.72689 + 0.133641i 0.0881249 + 0.00681983i
$$385$$ −11.8565 14.0985i −0.604261 0.718529i
$$386$$ 15.4597i 0.786878i
$$387$$ 4.50963 + 6.17302i 0.229237 + 0.313792i
$$388$$ 8.98748 8.98748i 0.456270 0.456270i
$$389$$ −18.3647 −0.931129 −0.465565 0.885014i $$-0.654149\pi$$
−0.465565 + 0.885014i $$0.654149\pi$$
$$390$$ 5.93212 4.25288i 0.300385 0.215353i
$$391$$ −0.307349 −0.0155433
$$392$$ 0.483658 0.483658i 0.0244284 0.0244284i
$$393$$ 4.67226 + 5.45608i 0.235685 + 0.275223i
$$394$$ 2.79914i 0.141019i
$$395$$ −32.1463 2.77691i −1.61746 0.139722i
$$396$$ −1.37175 + 8.80970i −0.0689331 + 0.442704i
$$397$$ −6.90089 6.90089i −0.346346 0.346346i 0.512401 0.858746i $$-0.328756\pi$$
−0.858746 + 0.512401i $$0.828756\pi$$
$$398$$ −11.2354 11.2354i −0.563178 0.563178i
$$399$$ −2.38055 + 30.7612i −0.119177 + 1.53998i
$$400$$ 4.92593 + 0.857436i 0.246297 + 0.0428718i
$$401$$ 18.3481i 0.916261i 0.888885 + 0.458131i $$0.151481\pi$$
−0.888885 + 0.458131i $$0.848519\pi$$
$$402$$ 17.5087 14.9934i 0.873254 0.747803i
$$403$$ −8.44225 + 8.44225i −0.420538 + 0.420538i
$$404$$ 3.00976 0.149741
$$405$$ −7.74610 + 18.5741i −0.384907 + 0.922955i
$$406$$ 3.38190 0.167841
$$407$$ 4.25896 4.25896i 0.211109 0.211109i
$$408$$ 0.404346 0.346258i 0.0200181 0.0171423i
$$409$$ 15.8713i 0.784783i 0.919798 + 0.392392i $$0.128352\pi$$
−0.919798 + 0.392392i $$0.871648\pi$$
$$410$$ 5.21240 4.38348i 0.257422 0.216485i
$$411$$ −1.26969 + 16.4067i −0.0626292 + 0.809285i
$$412$$ 1.81831 + 1.81831i 0.0895816 + 0.0895816i
$$413$$ −18.4838 18.4838i −0.909526 0.909526i
$$414$$ 0.461565 2.96428i 0.0226847 0.145686i
$$415$$ 29.4626 24.7772i 1.44626 1.21626i
$$416$$ 1.88462i 0.0924013i
$$417$$ −24.0306 28.0620i −1.17679 1.37420i
$$418$$ 13.5043 13.5043i 0.660517 0.660517i
$$419$$ 19.9035 0.972349 0.486175 0.873862i $$-0.338392\pi$$
0.486175 + 0.873862i $$0.338392\pi$$
$$420$$ −10.5929 1.74649i −0.516881 0.0852202i
$$421$$ −9.07200 −0.442142 −0.221071 0.975258i $$-0.570955\pi$$
−0.221071 + 0.975258i $$0.570955\pi$$
$$422$$ 8.05445 8.05445i 0.392085 0.392085i
$$423$$ 0.499089 + 0.683180i 0.0242666 + 0.0332173i
$$424$$ 12.9809i 0.630407i
$$425$$ 1.25689 0.884201i 0.0609682 0.0428901i
$$426$$ 13.2104 + 1.02233i 0.640046 + 0.0495320i
$$427$$ 10.9222 + 10.9222i 0.528561 + 0.528561i
$$428$$ −10.1552 10.1552i −0.490872 0.490872i
$$429$$ 9.67232 + 0.748525i 0.466984 + 0.0361391i
$$430$$ 5.67695 + 0.490395i 0.273767 + 0.0236489i
$$431$$ 6.60333i 0.318071i −0.987273 0.159036i $$-0.949162\pi$$
0.987273 0.159036i $$-0.0508384\pi$$
$$432$$ 2.73231 + 4.41978i 0.131458 + 0.212647i
$$433$$ −2.95935 + 2.95935i −0.142217 + 0.142217i −0.774631 0.632414i $$-0.782064\pi$$
0.632414 + 0.774631i $$0.282064\pi$$
$$434$$ 17.5607 0.842941
$$435$$ −2.75313 3.84019i −0.132002 0.184123i
$$436$$ −3.22282 −0.154345
$$437$$ −4.54391 + 4.54391i −0.217365 + 0.217365i
$$438$$ 6.46393 + 7.54831i 0.308858 + 0.360672i
$$439$$ 11.2528i 0.537068i −0.963270 0.268534i $$-0.913461\pi$$
0.963270 0.268534i $$-0.0865392\pi$$
$$440$$ 4.27722 + 5.08605i 0.203909 + 0.242468i
$$441$$ 2.02756 + 0.315709i 0.0965503 + 0.0150338i
$$442$$ −0.409583 0.409583i −0.0194819 0.0194819i
$$443$$ −16.2317 16.2317i −0.771194 0.771194i 0.207122 0.978315i $$-0.433590\pi$$
−0.978315 + 0.207122i $$0.933590\pi$$
$$444$$ 0.270842 3.49978i 0.0128536 0.166092i
$$445$$ 0.472722 5.47236i 0.0224092 0.259415i
$$446$$ 14.8040i 0.700989i
$$447$$ −2.69311 + 2.30622i −0.127380 + 0.109081i
$$448$$ −1.96010 + 1.96010i −0.0926061 + 0.0926061i
$$449$$ −3.47861 −0.164166 −0.0820828 0.996626i $$-0.526157\pi$$
−0.0820828 + 0.996626i $$0.526157\pi$$
$$450$$ 6.64027 + 13.4502i 0.313025 + 0.634047i
$$451$$ 9.05193 0.426239
$$452$$ 3.72990 3.72990i 0.175440 0.175440i
$$453$$ −3.47336 + 2.97438i −0.163193 + 0.139749i
$$454$$ 22.8625i 1.07299i
$$455$$ −1.00535 + 11.6383i −0.0471318 + 0.545611i
$$456$$ 0.858785 11.0971i 0.0402163 0.519669i
$$457$$ 24.5212 + 24.5212i 1.14705 + 1.14705i 0.987129 + 0.159925i $$0.0511251\pi$$
0.159925 + 0.987129i $$0.448875\pi$$
$$458$$ −11.3347 11.3347i −0.529638 0.529638i
$$459$$ 1.55436 + 0.366736i 0.0725511 + 0.0171178i
$$460$$ −1.43919 1.71135i −0.0671028 0.0797921i
$$461$$ 7.06441i 0.329022i −0.986375 0.164511i $$-0.947395\pi$$
0.986375 0.164511i $$-0.0526047\pi$$
$$462$$ −9.28119 10.8382i −0.431800 0.504238i
$$463$$ 4.91698 4.91698i 0.228512 0.228512i −0.583559 0.812071i $$-0.698340\pi$$
0.812071 + 0.583559i $$0.198340\pi$$
$$464$$ −1.22002 −0.0566381
$$465$$ −14.2957 19.9404i −0.662950 0.924714i
$$466$$ 5.86409 0.271649
$$467$$ 0.279235 0.279235i 0.0129214 0.0129214i −0.700617 0.713538i $$-0.747092\pi$$
0.713538 + 0.700617i $$0.247092\pi$$
$$468$$ 4.56539 3.33519i 0.211035 0.154169i
$$469$$ 36.8915i 1.70349i
$$470$$ 0.628279 + 0.0542729i 0.0289804 + 0.00250342i
$$471$$ 1.83407 + 0.141935i 0.0845093 + 0.00654003i
$$472$$ 6.66802 + 6.66802i 0.306920 + 0.306920i
$$473$$ 5.35515 + 5.35515i 0.246230 + 0.246230i
$$474$$ −24.9187 1.92841i −1.14455 0.0885750i
$$475$$ 5.50994 31.6544i 0.252813 1.45240i
$$476$$ 0.851973i 0.0390501i
$$477$$ −31.4454 + 22.9721i −1.43978 + 1.05182i
$$478$$ −21.0475 + 21.0475i −0.962690 + 0.962690i
$$479$$ −19.9714 −0.912518 −0.456259 0.889847i $$-0.650811\pi$$
−0.456259 + 0.889847i $$0.650811\pi$$
$$480$$ 3.82139 + 0.630048i 0.174422 + 0.0287576i
$$481$$ −3.81946 −0.174152
$$482$$ −12.8377 + 12.8377i −0.584743 + 0.584743i
$$483$$ 3.12292 + 3.64682i 0.142098 + 0.165936i
$$484$$ 2.16749i 0.0985222i
$$485$$ 21.7516 18.2925i 0.987691 0.830619i
$$486$$ −5.87131 + 14.4405i −0.266328 + 0.655034i
$$487$$ −1.40410 1.40410i −0.0636258 0.0636258i 0.674578 0.738204i $$-0.264326\pi$$
−0.738204 + 0.674578i $$0.764326\pi$$
$$488$$ −3.94018 3.94018i −0.178363 0.178363i
$$489$$ 1.24816 16.1286i 0.0564439 0.729360i
$$490$$ 1.17056 0.984403i 0.0528803 0.0444708i
$$491$$ 6.45884i 0.291483i 0.989323 + 0.145742i $$0.0465568\pi$$
−0.989323 + 0.145742i $$0.953443\pi$$
$$492$$ 4.00701 3.43137i 0.180650 0.154698i
$$493$$ −0.265146 + 0.265146i −0.0119416 + 0.0119416i
$$494$$ −12.1107 −0.544887
$$495$$ −4.75131 + 19.3620i −0.213556 + 0.870258i
$$496$$ −6.33502 −0.284451
$$497$$ −14.9944 + 14.9944i −0.672593 + 0.672593i
$$498$$ 22.6492 19.3955i 1.01494 0.869132i
$$499$$ 9.53761i 0.426962i 0.976947 + 0.213481i $$0.0684802\pi$$
−0.976947 + 0.213481i $$0.931520\pi$$
$$500$$ 10.8088 + 2.85813i 0.483386 + 0.127819i
$$501$$ −0.992338 + 12.8228i −0.0443344 + 0.572883i
$$502$$ −13.5208 13.5208i −0.603464 0.603464i
$$503$$ 15.2096 + 15.2096i 0.678161 + 0.678161i 0.959584 0.281423i $$-0.0908064\pi$$
−0.281423 + 0.959584i $$0.590806\pi$$
$$504$$ −8.21699 1.27946i −0.366014 0.0569917i
$$505$$ 6.70506 + 0.579206i 0.298371 + 0.0257743i
$$506$$ 2.97195i 0.132119i
$$507$$ 10.6443 + 12.4300i 0.472730 + 0.552034i
$$508$$ −9.95020 + 9.95020i −0.441469 + 0.441469i
$$509$$ −27.1370 −1.20282 −0.601412 0.798939i $$-0.705395\pi$$
−0.601412 + 0.798939i $$0.705395\pi$$
$$510$$ 0.967426 0.693571i 0.0428384 0.0307118i
$$511$$ −15.9046 −0.703577
$$512$$ 0.707107 0.707107i 0.0312500 0.0312500i
$$513$$ 28.4018 17.5580i 1.25397 0.775205i
$$514$$ 24.0535i 1.06096i
$$515$$ 3.70085 + 4.40069i 0.163079 + 0.193918i
$$516$$ 4.40057 + 0.340552i 0.193724 + 0.0149920i
$$517$$ 0.592665 + 0.592665i 0.0260654 + 0.0260654i
$$518$$ 3.97242 + 3.97242i 0.174538 + 0.174538i
$$519$$ 39.5113 + 3.05771i 1.73435 + 0.134219i
$$520$$ 0.362682 4.19851i 0.0159047 0.184117i
$$521$$ 41.9658i 1.83855i −0.393611 0.919277i $$-0.628774\pi$$
0.393611 0.919277i $$-0.371226\pi$$
$$522$$ −2.15906 2.95543i −0.0944994 0.129356i
$$523$$ 22.7710 22.7710i 0.995704 0.995704i −0.00428643 0.999991i $$-0.501364\pi$$
0.999991 + 0.00428643i $$0.00136442\pi$$
$$524$$ 4.14724 0.181173
$$525$$ −23.2625 5.92932i −1.01526 0.258777i
$$526$$ −17.4761 −0.761992
$$527$$ −1.37678 + 1.37678i −0.0599736 + 0.0599736i
$$528$$ 3.34819 + 3.90988i 0.145711 + 0.170156i
$$529$$ 1.00000i 0.0434783i
$$530$$ −2.49807 + 28.9184i −0.108509 + 1.25614i
$$531$$ −4.35256 + 27.9532i −0.188885 + 1.21306i
$$532$$ 12.5957 + 12.5957i 0.546094 + 0.546094i
$$533$$ −4.05891 4.05891i −0.175811 0.175811i
$$534$$ 0.328279 4.24198i 0.0142060 0.183568i
$$535$$ −20.6693 24.5779i −0.893610 1.06259i
$$536$$ 13.3086i 0.574844i
$$537$$ −16.5879 + 14.2049i −0.715820 + 0.612986i
$$538$$ −14.2128 + 14.2128i −0.612758 + 0.612758i
$$539$$ 2.03280 0.0875591
$$540$$ 5.23641 + 10.3721i 0.225339 + 0.446343i
$$541$$ 8.43337 0.362579 0.181290 0.983430i $$-0.441973\pi$$
0.181290 + 0.983430i $$0.441973\pi$$
$$542$$ −19.7054 + 19.7054i −0.846419 + 0.846419i
$$543$$ −2.30730 + 1.97584i −0.0990157 + 0.0847912i
$$544$$ 0.307349i 0.0131775i
$$545$$ −7.17971 0.620208i −0.307545 0.0265668i
$$546$$ −0.698164 + 9.02157i −0.0298787 + 0.386088i
$$547$$ −13.9532 13.9532i −0.596597 0.596597i 0.342808 0.939405i $$-0.388622\pi$$
−0.939405 + 0.342808i $$0.888622\pi$$
$$548$$ 6.71805 + 6.71805i 0.286981 + 0.286981i
$$549$$ 2.57196 16.5177i 0.109769 0.704959i
$$550$$ 8.54990 + 12.1537i 0.364569 + 0.518235i
$$551$$ 7.83994i 0.333993i
$$552$$ −1.12660 1.31559i −0.0479511 0.0559953i
$$553$$ 28.2839 28.2839i 1.20275 1.20275i
$$554$$ 9.96921 0.423551
$$555$$ 1.27688 7.74459i 0.0542006 0.328739i
$$556$$ −21.3303 −0.904607
$$557$$ 19.9924 19.9924i 0.847106 0.847106i −0.142665 0.989771i $$-0.545567\pi$$
0.989771 + 0.142665i $$0.0455671\pi$$
$$558$$ −11.2110 15.3462i −0.474600 0.649657i
$$559$$ 4.80252i 0.203125i
$$560$$ −4.74387 + 3.98945i −0.200465 + 0.168585i
$$561$$ 1.57739 + 0.122071i 0.0665974 + 0.00515386i
$$562$$ −11.1642 11.1642i −0.470934 0.470934i
$$563$$ 31.0332 + 31.0332i 1.30789 + 1.30789i 0.922935 + 0.384957i $$0.125784\pi$$
0.384957 + 0.922935i $$0.374216\pi$$
$$564$$ 0.487019 + 0.0376896i 0.0205072 + 0.00158702i
$$565$$ 9.02716 7.59158i 0.379776 0.319380i
$$566$$ 18.6737i 0.784912i
$$567$$ −11.4421 22.1694i −0.480522 0.931027i
$$568$$ 5.40925 5.40925i 0.226967 0.226967i
$$569$$ 30.3632 1.27289 0.636447 0.771321i $$-0.280404\pi$$
0.636447 + 0.771321i $$0.280404\pi$$
$$570$$ 4.04873 24.5565i 0.169583 1.02856i
$$571$$ −13.6437 −0.570973 −0.285486 0.958383i $$-0.592155\pi$$
−0.285486 + 0.958383i $$0.592155\pi$$
$$572$$ 3.96052 3.96052i 0.165598 0.165598i
$$573$$ 30.3375 + 35.4269i 1.26737 + 1.47998i
$$574$$ 8.44292i 0.352401i
$$575$$ −2.87686 4.08946i −0.119973 0.170542i
$$576$$ 2.96428 + 0.461565i 0.123512 + 0.0192319i
$$577$$ 29.2454 + 29.2454i 1.21750 + 1.21750i 0.968503 + 0.249001i $$0.0801021\pi$$
0.249001 + 0.968503i $$0.419898\pi$$
$$578$$ 11.9540 + 11.9540i 0.497222 + 0.497222i
$$579$$ −2.06605 + 26.6972i −0.0858620 + 1.10950i
$$580$$ −2.71793 0.234784i −0.112856 0.00974888i
$$581$$ 47.7228i 1.97988i
$$582$$ 16.7215 14.3193i 0.693127 0.593553i
$$583$$ −27.2791 + 27.2791i −1.12979 + 1.12979i
$$584$$ 5.73758 0.237423
$$585$$ 10.8125 6.55147i 0.447041 0.270870i
$$586$$ −9.81215 −0.405336
$$587$$ 30.7364 30.7364i 1.26863 1.26863i 0.321830 0.946798i $$-0.395702\pi$$
0.946798 0.321830i $$-0.104298\pi$$
$$588$$ 0.899860 0.770587i 0.0371096 0.0317785i
$$589$$ 40.7093i 1.67740i
$$590$$ 13.5716 + 16.1380i 0.558734 + 0.664392i
$$591$$ 0.374079 4.83380i 0.0153876 0.198836i
$$592$$ −1.43305 1.43305i −0.0588980 0.0588980i
$$593$$ −24.9741 24.9741i −1.02557 1.02557i −0.999665 0.0259005i $$-0.991755\pi$$
−0.0259005 0.999665i $$-0.508245\pi$$
$$594$$ −3.54620 + 15.0300i −0.145502 + 0.616690i
$$595$$ −0.163956 + 1.89800i −0.00672154 + 0.0778105i
$$596$$ 2.04707i 0.0838514i
$$597$$ −17.9007 20.9037i −0.732627 0.855531i
$$598$$ −1.33263 + 1.33263i −0.0544953 + 0.0544953i
$$599$$ −35.3695 −1.44516 −0.722579 0.691288i $$-0.757044\pi$$
−0.722579 + 0.691288i $$0.757044\pi$$
$$600$$ 8.39194 + 2.13900i 0.342600 + 0.0873244i
$$601$$ 36.5041 1.48903 0.744517 0.667604i $$-0.232680\pi$$
0.744517 + 0.667604i $$0.232680\pi$$
$$602$$ −4.99486 + 4.99486i −0.203575 + 0.203575i
$$603$$ 32.2393 23.5521i 1.31288 0.959114i
$$604$$ 2.64015i 0.107426i
$$605$$ 0.417117 4.82867i 0.0169582 0.196313i
$$606$$ 5.19752 + 0.402227i 0.211135 + 0.0163394i
$$607$$ 22.0917 + 22.0917i 0.896673 + 0.896673i 0.995140 0.0984669i $$-0.0313939\pi$$
−0.0984669 + 0.995140i $$0.531394\pi$$
$$608$$ −4.54391 4.54391i −0.184280 0.184280i
$$609$$ 5.84017 + 0.451961i 0.236656 + 0.0183144i
$$610$$ −8.01956 9.53607i −0.324702 0.386104i
$$611$$ 0.531504i 0.0215024i
$$612$$ 0.744535 0.543912i 0.0300960 0.0219863i
$$613$$ 16.7926 16.7926i 0.678246 0.678246i −0.281357 0.959603i $$-0.590784\pi$$
0.959603 + 0.281357i $$0.0907845\pi$$
$$614$$ −11.8644 −0.478808
$$615$$ 9.58705 6.87318i 0.386587 0.277154i
$$616$$ −8.23826 −0.331929
$$617$$ −26.9980 + 26.9980i −1.08690 + 1.08690i −0.0910505 + 0.995846i $$0.529022\pi$$
−0.995846 + 0.0910505i $$0.970978\pi$$
$$618$$ 2.89701 + 3.38301i 0.116535 + 0.136085i
$$619$$ 31.5835i 1.26945i 0.772739 + 0.634724i $$0.218886\pi$$
−0.772739 + 0.634724i $$0.781114\pi$$
$$620$$ −14.1130 1.21913i −0.566791 0.0489614i
$$621$$ 1.19322 5.05729i 0.0478823 0.202942i
$$622$$ −16.0579 16.0579i −0.643865 0.643865i
$$623$$ 4.81485 + 4.81485i 0.192903 + 0.192903i
$$624$$ 0.251863 3.25453i 0.0100826 0.130286i
$$625$$ 23.5296 + 8.44734i 0.941184 + 0.337894i
$$626$$ 26.9989i 1.07909i
$$627$$ 25.1251 21.5157i 1.00340 0.859254i
$$628$$ 0.750993 0.750993i 0.0299679 0.0299679i
$$629$$ −0.622887 −0.0248361
$$630$$ −18.0594 4.43164i −0.719502 0.176561i
$$631$$ −27.4404 −1.09239 −0.546193 0.837659i $$-0.683924\pi$$
−0.546193 + 0.837659i $$0.683924\pi$$
$$632$$ −10.2034 + 10.2034i −0.405870 + 0.405870i
$$633$$ 14.9855 12.8327i 0.595622 0.510055i
$$634$$ 0.0389545i 0.00154708i
$$635$$ −24.0816 + 20.2519i −0.955650 + 0.803673i
$$636$$ −1.73477 + 22.4165i −0.0687883 + 0.888872i
$$637$$ −0.911514 0.911514i −0.0361155 0.0361155i
$$638$$ −2.56386 2.56386i −0.101504 0.101504i
$$639$$ 22.6762 + 3.53090i 0.897058 + 0.139680i
$$640$$ 1.71135 1.43919i 0.0676470 0.0568892i
$$641$$ 1.78898i 0.0706606i 0.999376 + 0.0353303i $$0.0112483\pi$$
−0.999376 + 0.0353303i $$0.988752\pi$$
$$642$$ −16.1798 18.8941i −0.638566 0.745691i
$$643$$ 24.6839 24.6839i 0.973437 0.973437i −0.0262188 0.999656i $$-0.508347\pi$$
0.999656 + 0.0262188i $$0.00834667\pi$$
$$644$$ 2.77200 0.109232
$$645$$ 9.73792 + 1.60553i 0.383430 + 0.0632177i
$$646$$ −1.97505 −0.0777072
$$647$$ −2.36727 + 2.36727i −0.0930671 + 0.0930671i −0.752108 0.659040i $$-0.770963\pi$$
0.659040 + 0.752108i $$0.270963\pi$$
$$648$$ 4.12773 + 7.99761i 0.162153 + 0.314176i
$$649$$ 28.0255i 1.10010i
$$650$$ 1.61594 9.28353i 0.0633826 0.364130i
$$651$$ 30.3254 + 2.34683i 1.18854 + 0.0919794i
$$652$$ −6.60415 6.60415i −0.258639 0.258639i
$$653$$ −2.10868 2.10868i −0.0825189 0.0825189i 0.664643 0.747161i $$-0.268584\pi$$
−0.747161 + 0.664643i $$0.768584\pi$$
$$654$$ −5.56545 0.430701i −0.217626 0.0168417i
$$655$$ 9.23911 + 0.798106i 0.361002 + 0.0311846i
$$656$$ 3.04579i 0.118918i
$$657$$ 10.1537 + 13.8989i 0.396134 + 0.542249i
$$658$$ −0.552791 + 0.552791i −0.0215500 + 0.0215500i
$$659$$ −40.8784 −1.59240 −0.796199 0.605035i $$-0.793159\pi$$
−0.796199 + 0.605035i $$0.793159\pi$$
$$660$$ 6.70657 + 9.35465i 0.261053 + 0.364129i
$$661$$ 17.8125 0.692828 0.346414 0.938082i $$-0.387399\pi$$
0.346414 + 0.938082i $$0.387399\pi$$
$$662$$ 0.743610 0.743610i 0.0289012 0.0289012i
$$663$$ −0.652567 0.762041i −0.0253436 0.0295952i
$$664$$ 17.2160i 0.668111i
$$665$$ 25.6365 + 30.4844i 0.994140 + 1.18213i
$$666$$ 0.935427 6.00753i 0.0362471 0.232787i
$$667$$ 0.862686 + 0.862686i 0.0334033 + 0.0334033i
$$668$$ 5.25056 + 5.25056i 0.203150 + 0.203150i
$$669$$ −1.97842 + 25.5648i −0.0764900 + 0.988392i
$$670$$ 2.56114 29.6485i 0.0989455 1.14542i
$$671$$ 16.5605i 0.639310i
$$672$$ −3.64682 + 3.12292i −0.140679 + 0.120469i
$$673$$ 13.7420 13.7420i 0.529714 0.529714i −0.390773 0.920487i $$-0.627792\pi$$
0.920487 + 0.390773i $$0.127792\pi$$
$$674$$ −14.1764 −0.546054
$$675$$ 9.66951 + 24.1143i 0.372179 + 0.928161i
$$676$$ 9.44819 0.363392
$$677$$ −1.91031 + 1.91031i −0.0734192 + 0.0734192i −0.742863 0.669444i $$-0.766533\pi$$
0.669444 + 0.742863i $$0.266533\pi$$
$$678$$ 6.93959 5.94265i 0.266513 0.228226i
$$679$$ 35.2328i 1.35211i
$$680$$ 0.0591471 0.684704i 0.00226819 0.0262572i
$$681$$ 3.05537 39.4810i 0.117082 1.51292i
$$682$$ −13.3130 13.3130i −0.509780 0.509780i
$$683$$ 33.5563 + 33.5563i 1.28400 + 1.28400i 0.938374 + 0.345623i $$0.112332\pi$$
0.345623 + 0.938374i $$0.387668\pi$$
$$684$$ 2.96605 19.0487i 0.113410 0.728344i
$$685$$ 13.6735 + 16.2591i 0.522436 + 0.621229i
$$686$$ 17.5080i 0.668458i
$$687$$ −18.0590 21.0886i −0.688996 0.804581i
$$688$$ 1.80190 1.80190i 0.0686966 0.0686966i
$$689$$ 24.4641 0.932006
$$690$$ −2.25662 3.14764i −0.0859081 0.119829i
$$691$$ −27.4000 −1.04234 −0.521172 0.853451i $$-0.674505\pi$$
−0.521172 + 0.853451i $$0.674505\pi$$
$$692$$ 16.1787 16.1787i 0.615020 0.615020i
$$693$$ −14.5791 19.9567i −0.553816 0.758092i
$$694$$ 25.8642i 0.981790i
$$695$$ −47.5191 4.10486i −1.80250 0.155706i
$$696$$ −2.10684 0.163045i −0.0798596 0.00618020i
$$697$$ −0.661937 0.661937i −0.0250727 0.0250727i
$$698$$ −20.2968 20.2968i −0.768247 0.768247i
$$699$$ 10.1266 + 0.783682i 0.383024 + 0.0296416i
$$700$$ −11.3360 + 7.97466i −0.428460 + 0.301414i
$$701$$ 17.7628i 0.670893i 0.942059 + 0.335446i $$0.108887\pi$$
−0.942059 + 0.335446i $$0.891113\pi$$
$$702$$ 8.32963 5.14938i 0.314381 0.194351i
$$703$$ −9.20888 + 9.20888i −0.347319 + 0.347319i
$$704$$ 2.97195 0.112010
$$705$$ 1.07771 + 0.177687i 0.0405891 + 0.00669208i
$$706$$ −14.7901 −0.556631
$$707$$ −5.89944 + 5.89944i −0.221871 + 0.221871i
$$708$$ 10.6238 + 12.4060i 0.399267 + 0.466247i
$$709$$ 25.1030i 0.942763i 0.881929 + 0.471382i $$0.156245\pi$$
−0.881929 + 0.471382i $$0.843755\pi$$
$$710$$ 13.0915 11.0096i 0.491316 0.413183i
$$711$$ −42.7740 6.66031i −1.60415 0.249781i
$$712$$ −1.73696 1.73696i −0.0650953 0.0650953i
$$713$$ 4.47954 + 4.47954i 0.167760 + 0.167760i
$$714$$ −0.113858 + 1.47126i −0.00426104 + 0.0550606i
$$715$$ 9.58530 8.06095i 0.358470 0.301463i
$$716$$ 12.6087i 0.471209i
$$717$$ −39.1594 + 33.5338i −1.46244 + 1.25234i
$$718$$ 7.38357 7.38357i 0.275552 0.275552i
$$719$$ −7.11858 −0.265478 −0.132739 0.991151i $$-0.542377\pi$$
−0.132739 + 0.991151i $$0.542377\pi$$
$$720$$ 6.51491 + 1.59872i 0.242797 + 0.0595806i
$$721$$ −7.12813 −0.265466
$$722$$ −15.7644 + 15.7644i −0.586692 + 0.586692i
$$723$$ −23.8850 + 20.4537i −0.888292 + 0.760681i
$$724$$ 1.75381i 0.0651799i
$$725$$ −6.00975 1.04609i −0.223196 0.0388508i
$$726$$ 0.289665 3.74301i 0.0107505 0.138916i
$$727$$ −21.0233 21.0233i −0.779711 0.779711i 0.200070 0.979782i $$-0.435883\pi$$
−0.979782 + 0.200070i $$0.935883\pi$$
$$728$$ 3.69405 + 3.69405i 0.136911 + 0.136911i
$$729$$ −12.0689 + 24.1524i −0.446998 + 0.894535i
$$730$$ 12.7820 + 1.10415i 0.473083 + 0.0408666i
$$731$$ 0.783208i 0.0289680i
$$732$$ −6.27767 7.33081i −0.232030 0.270955i
$$733$$ −8.70985 + 8.70985i −0.321706 + 0.321706i −0.849421 0.527715i $$-0.823049\pi$$
0.527715 + 0.849421i $$0.323049\pi$$
$$734$$ 16.0003 0.590580
$$735$$ 2.15298 1.54352i 0.0794137 0.0569336i
$$736$$ −1.00000 −0.0368605
$$737$$ 27.9679 27.9679i 1.03021 1.03021i
$$738$$ 7.37823 5.39009i 0.271596 0.198412i
$$739$$ 13.3134i 0.489743i −0.969556 0.244871i $$-0.921254\pi$$
0.969556 0.244871i $$-0.0787458\pi$$
$$740$$ −2.91673 3.46829i −0.107221 0.127497i
$$741$$ −20.9138 1.61849i −0.768289 0.0594566i
$$742$$ −25.4438 25.4438i −0.934072 0.934072i
$$743$$ 31.8345 + 31.8345i 1.16789 + 1.16789i 0.982702 + 0.185193i $$0.0592909\pi$$
0.185193 + 0.982702i $$0.440709\pi$$
$$744$$ −10.9399 0.846618i −0.401075 0.0310385i
$$745$$ −0.393944 + 4.56041i −0.0144330 + 0.167081i
$$746$$ 28.6369i 1.04847i
$$747$$ 41.7047 30.4669i 1.52590 1.11473i
$$748$$ 0.645891 0.645891i 0.0236161 0.0236161i
$$749$$ 39.8106 1.45465
$$750$$ 18.2837 + 6.38017i 0.667626 + 0.232971i
$$751$$ 1.87068 0.0682622 0.0341311 0.999417i $$-0.489134\pi$$
0.0341311 + 0.999417i $$0.489134\pi$$
$$752$$ 0.199419 0.199419i 0.00727207 0.00727207i
$$753$$ −21.5420 25.1559i −0.785035 0.916732i
$$754$$ 2.29928i 0.0837349i
$$755$$ −0.508077 + 5.88165i −0.0184908 + 0.214055i
$$756$$ −14.0188 3.30761i −0.509860 0.120297i
$$757$$ −4.50446 4.50446i −0.163717 0.163717i 0.620494 0.784211i $$-0.286932\pi$$
−0.784211 + 0.620494i $$0.786932\pi$$
$$758$$ −22.2485 22.2485i −0.808102 0.808102i
$$759$$ 0.397175 5.13223i 0.0144165 0.186288i
$$760$$ −9.24836 10.9972i −0.335473 0.398912i
$$761$$ 29.5482i 1.07112i 0.844497 + 0.535561i $$0.179900\pi$$
−0.844497 + 0.535561i $$0.820100\pi$$
$$762$$ −18.5126 + 15.8531i −0.670642 + 0.574298i
$$763$$ 6.31706 6.31706i 0.228693 0.228693i
$$764$$ 26.9285 0.974238
$$765$$ 1.76333 1.06843i 0.0637532 0.0386292i
$$766$$ 7.21387 0.260648
$$767$$ 12.5667 12.5667i 0.453757 0.453757i
$$768$$ 1.31559 1.12660i 0.0474723 0.0406525i
$$769$$ 14.7558i 0.532107i 0.963958 + 0.266054i $$0.0857199\pi$$
−0.963958 + 0.266054i $$0.914280\pi$$
$$770$$ −18.3530 1.58539i −0.661395 0.0571336i
$$771$$ −3.21454 + 41.5378i −0.115769 + 1.49595i
$$772$$ 10.9317 + 10.9317i 0.393439 + 0.393439i
$$773$$ −9.22983 9.22983i −0.331974 0.331974i 0.521362 0.853336i $$-0.325424\pi$$
−0.853336 + 0.521362i $$0.825424\pi$$
$$774$$ 7.55377 + 1.17619i 0.271515 + 0.0422773i
$$775$$ −31.2059 5.43188i −1.12095 0.195119i
$$776$$ 12.7102i 0.456270i
$$777$$ 6.32905 + 7.39080i 0.227053 + 0.265144i
$$778$$ −12.9858