# Properties

 Label 720.2.u.a.179.14 Level $720$ Weight $2$ Character 720.179 Analytic conductor $5.749$ Analytic rank $0$ Dimension $96$ CM no Inner twists $8$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 720.u (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.74922894553$$ Analytic rank: $$0$$ Dimension: $$96$$ Relative dimension: $$48$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 179.14 Character $$\chi$$ $$=$$ 720.179 Dual form 720.2.u.a.539.14

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.93984 - 1.11222i) q^{5} +1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +O(q^{10})$$ $$q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.93984 - 1.11222i) q^{5} +1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +(-0.697143 + 3.08448i) q^{10} +(3.34421 - 3.34421i) q^{11} +(-2.90349 + 2.90349i) q^{13} +(-1.86224 - 1.71025i) q^{14} +(-3.94229 + 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 - 0.0693845i) q^{19} +(-2.54591 - 3.67673i) q^{20} +(0.284286 + 6.68237i) q^{22} -1.07695 q^{23} +(2.52593 - 4.31505i) q^{25} +(-0.246821 - 5.80172i) q^{26} +(3.56280 - 0.303692i) q^{28} +(-1.23988 + 1.23988i) q^{29} -8.56612i q^{31} +(3.06600 - 4.75391i) q^{32} +(-4.36907 + 4.75733i) q^{34} +(1.98849 + 3.46816i) q^{35} +(7.62458 + 7.62458i) q^{37} +(0.00589828 + 0.138644i) q^{38} +(6.26508 + 0.865308i) q^{40} +7.91601 q^{41} +(-2.35179 + 2.35179i) q^{43} +(-7.23230 - 6.09619i) q^{44} +(1.03020 - 1.12175i) q^{46} -6.32188i q^{47} +3.80356 q^{49} +(2.07827 + 6.75876i) q^{50} +(6.27919 + 5.29279i) q^{52} +(3.61429 - 3.61429i) q^{53} +(2.76772 - 10.2067i) q^{55} +(-3.09182 + 4.00152i) q^{56} +(-0.105400 - 2.47751i) q^{58} +(2.25080 - 2.25080i) q^{59} +(4.29893 + 4.29893i) q^{61} +(8.92248 + 8.19429i) q^{62} +(2.01876 + 7.74110i) q^{64} +(-2.40297 + 8.86160i) q^{65} +(-5.85271 - 5.85271i) q^{67} +(-0.775822 - 9.10164i) q^{68} +(-5.51461 - 1.24639i) q^{70} +15.1431i q^{71} -6.88118 q^{73} +(-15.2354 + 0.648155i) q^{74} +(-0.150054 - 0.126482i) q^{76} +(5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-6.89443 + 5.69797i) q^{80} +(-7.57239 + 8.24532i) q^{82} +(-6.88840 + 6.88840i) q^{83} +(8.85986 - 5.07987i) q^{85} +(-0.199923 - 4.69933i) q^{86} +(13.2682 - 1.70161i) q^{88} +6.31609 q^{89} +(-5.19103 - 5.19103i) q^{91} +(0.182935 + 2.14612i) q^{92} +(6.58487 + 6.04746i) q^{94} +(0.0574238 - 0.211766i) q^{95} +4.56728i q^{97} +(-3.63845 + 3.96179i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$96q + O(q^{10})$$ $$96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$$.

 $$n$$ $$181$$ $$271$$ $$577$$ $$641$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.956592 + 1.04160i −0.676413 + 0.736523i
$$3$$ 0 0
$$4$$ −0.169864 1.99277i −0.0849318 0.996387i
$$5$$ 1.93984 1.11222i 0.867521 0.497400i
$$6$$ 0 0
$$7$$ 1.78786i 0.675747i 0.941191 + 0.337874i $$0.109708\pi$$
−0.941191 + 0.337874i $$0.890292\pi$$
$$8$$ 2.23816 + 1.72934i 0.791311 + 0.611414i
$$9$$ 0 0
$$10$$ −0.697143 + 3.08448i −0.220456 + 0.975397i
$$11$$ 3.34421 3.34421i 1.00832 1.00832i 0.00835103 0.999965i $$-0.497342\pi$$
0.999965 0.00835103i $$-0.00265824\pi$$
$$12$$ 0 0
$$13$$ −2.90349 + 2.90349i −0.805282 + 0.805282i −0.983916 0.178634i $$-0.942832\pi$$
0.178634 + 0.983916i $$0.442832\pi$$
$$14$$ −1.86224 1.71025i −0.497703 0.457084i
$$15$$ 0 0
$$16$$ −3.94229 + 0.676999i −0.985573 + 0.169250i
$$17$$ 4.56733 1.10774 0.553870 0.832603i $$-0.313151\pi$$
0.553870 + 0.832603i $$0.313151\pi$$
$$18$$ 0 0
$$19$$ 0.0693845 0.0693845i 0.0159179 0.0159179i −0.699103 0.715021i $$-0.746417\pi$$
0.715021 + 0.699103i $$0.246417\pi$$
$$20$$ −2.54591 3.67673i −0.569283 0.822142i
$$21$$ 0 0
$$22$$ 0.284286 + 6.68237i 0.0606100 + 1.42469i
$$23$$ −1.07695 −0.224560 −0.112280 0.993677i $$-0.535815\pi$$
−0.112280 + 0.993677i $$0.535815\pi$$
$$24$$ 0 0
$$25$$ 2.52593 4.31505i 0.505186 0.863010i
$$26$$ −0.246821 5.80172i −0.0484056 1.13781i
$$27$$ 0 0
$$28$$ 3.56280 0.303692i 0.673306 0.0573924i
$$29$$ −1.23988 + 1.23988i −0.230239 + 0.230239i −0.812792 0.582553i $$-0.802054\pi$$
0.582553 + 0.812792i $$0.302054\pi$$
$$30$$ 0 0
$$31$$ 8.56612i 1.53852i −0.638935 0.769261i $$-0.720625\pi$$
0.638935 0.769261i $$-0.279375\pi$$
$$32$$ 3.06600 4.75391i 0.541998 0.840380i
$$33$$ 0 0
$$34$$ −4.36907 + 4.75733i −0.749289 + 0.815875i
$$35$$ 1.98849 + 3.46816i 0.336117 + 0.586225i
$$36$$ 0 0
$$37$$ 7.62458 + 7.62458i 1.25347 + 1.25347i 0.954153 + 0.299321i $$0.0967600\pi$$
0.299321 + 0.954153i $$0.403240\pi$$
$$38$$ 0.00589828 + 0.138644i 0.000956828 + 0.0224910i
$$39$$ 0 0
$$40$$ 6.26508 + 0.865308i 0.990596 + 0.136817i
$$41$$ 7.91601 1.23627 0.618137 0.786071i $$-0.287888\pi$$
0.618137 + 0.786071i $$0.287888\pi$$
$$42$$ 0 0
$$43$$ −2.35179 + 2.35179i −0.358645 + 0.358645i −0.863313 0.504668i $$-0.831615\pi$$
0.504668 + 0.863313i $$0.331615\pi$$
$$44$$ −7.23230 6.09619i −1.09031 0.919035i
$$45$$ 0 0
$$46$$ 1.03020 1.12175i 0.151895 0.165394i
$$47$$ 6.32188i 0.922141i −0.887364 0.461070i $$-0.847466\pi$$
0.887364 0.461070i $$-0.152534\pi$$
$$48$$ 0 0
$$49$$ 3.80356 0.543365
$$50$$ 2.07827 + 6.75876i 0.293912 + 0.955832i
$$51$$ 0 0
$$52$$ 6.27919 + 5.29279i 0.870766 + 0.733978i
$$53$$ 3.61429 3.61429i 0.496461 0.496461i −0.413874 0.910334i $$-0.635824\pi$$
0.910334 + 0.413874i $$0.135824\pi$$
$$54$$ 0 0
$$55$$ 2.76772 10.2067i 0.373199 1.37627i
$$56$$ −3.09182 + 4.00152i −0.413162 + 0.534726i
$$57$$ 0 0
$$58$$ −0.105400 2.47751i −0.0138397 0.325313i
$$59$$ 2.25080 2.25080i 0.293030 0.293030i −0.545246 0.838276i $$-0.683564\pi$$
0.838276 + 0.545246i $$0.183564\pi$$
$$60$$ 0 0
$$61$$ 4.29893 + 4.29893i 0.550421 + 0.550421i 0.926562 0.376141i $$-0.122749\pi$$
−0.376141 + 0.926562i $$0.622749\pi$$
$$62$$ 8.92248 + 8.19429i 1.13316 + 1.04068i
$$63$$ 0 0
$$64$$ 2.01876 + 7.74110i 0.252345 + 0.967637i
$$65$$ −2.40297 + 8.86160i −0.298052 + 1.09915i
$$66$$ 0 0
$$67$$ −5.85271 5.85271i −0.715022 0.715022i 0.252559 0.967581i $$-0.418728\pi$$
−0.967581 + 0.252559i $$0.918728\pi$$
$$68$$ −0.775822 9.10164i −0.0940822 1.10374i
$$69$$ 0 0
$$70$$ −5.51461 1.24639i −0.659122 0.148973i
$$71$$ 15.1431i 1.79716i 0.438812 + 0.898579i $$0.355399\pi$$
−0.438812 + 0.898579i $$0.644601\pi$$
$$72$$ 0 0
$$73$$ −6.88118 −0.805381 −0.402691 0.915336i $$-0.631925\pi$$
−0.402691 + 0.915336i $$0.631925\pi$$
$$74$$ −15.2354 + 0.648155i −1.77108 + 0.0753465i
$$75$$ 0 0
$$76$$ −0.150054 0.126482i −0.0172123 0.0145085i
$$77$$ 5.97897 + 5.97897i 0.681367 + 0.681367i
$$78$$ 0 0
$$79$$ 12.9721i 1.45947i 0.683730 + 0.729735i $$0.260357\pi$$
−0.683730 + 0.729735i $$0.739643\pi$$
$$80$$ −6.89443 + 5.69797i −0.770821 + 0.637052i
$$81$$ 0 0
$$82$$ −7.57239 + 8.24532i −0.836231 + 0.910544i
$$83$$ −6.88840 + 6.88840i −0.756100 + 0.756100i −0.975610 0.219510i $$-0.929554\pi$$
0.219510 + 0.975610i $$0.429554\pi$$
$$84$$ 0 0
$$85$$ 8.85986 5.07987i 0.960987 0.550989i
$$86$$ −0.199923 4.69933i −0.0215582 0.506742i
$$87$$ 0 0
$$88$$ 13.2682 1.70161i 1.41439 0.181392i
$$89$$ 6.31609 0.669504 0.334752 0.942306i $$-0.391347\pi$$
0.334752 + 0.942306i $$0.391347\pi$$
$$90$$ 0 0
$$91$$ −5.19103 5.19103i −0.544167 0.544167i
$$92$$ 0.182935 + 2.14612i 0.0190723 + 0.223749i
$$93$$ 0 0
$$94$$ 6.58487 + 6.04746i 0.679178 + 0.623748i
$$95$$ 0.0574238 0.211766i 0.00589155 0.0217267i
$$96$$ 0 0
$$97$$ 4.56728i 0.463737i 0.972747 + 0.231869i $$0.0744839\pi$$
−0.972747 + 0.231869i $$0.925516\pi$$
$$98$$ −3.63845 + 3.96179i −0.367539 + 0.400201i
$$99$$ 0 0
$$100$$ −9.02798 4.30064i −0.902798 0.430064i
$$101$$ −6.24690 6.24690i −0.621589 0.621589i 0.324348 0.945938i $$-0.394855\pi$$
−0.945938 + 0.324348i $$0.894855\pi$$
$$102$$ 0 0
$$103$$ 13.8548i 1.36515i −0.730815 0.682576i $$-0.760860\pi$$
0.730815 0.682576i $$-0.239140\pi$$
$$104$$ −11.5196 + 1.47736i −1.12959 + 0.144867i
$$105$$ 0 0
$$106$$ 0.307245 + 7.22204i 0.0298423 + 0.701467i
$$107$$ 0.922209 + 0.922209i 0.0891533 + 0.0891533i 0.750277 0.661124i $$-0.229920\pi$$
−0.661124 + 0.750277i $$0.729920\pi$$
$$108$$ 0 0
$$109$$ −2.28662 2.28662i −0.219019 0.219019i 0.589066 0.808085i $$-0.299496\pi$$
−0.808085 + 0.589066i $$0.799496\pi$$
$$110$$ 7.98373 + 12.6465i 0.761219 + 1.20580i
$$111$$ 0 0
$$112$$ −1.21038 7.04827i −0.114370 0.665999i
$$113$$ 7.53772 0.709089 0.354544 0.935039i $$-0.384636\pi$$
0.354544 + 0.935039i $$0.384636\pi$$
$$114$$ 0 0
$$115$$ −2.08911 + 1.19781i −0.194811 + 0.111696i
$$116$$ 2.68140 + 2.26018i 0.248962 + 0.209853i
$$117$$ 0 0
$$118$$ 0.191338 + 4.49754i 0.0176141 + 0.414032i
$$119$$ 8.16574i 0.748552i
$$120$$ 0 0
$$121$$ 11.3674i 1.03340i
$$122$$ −8.59008 + 0.365446i −0.777710 + 0.0330859i
$$123$$ 0 0
$$124$$ −17.0703 + 1.45507i −1.53296 + 0.130669i
$$125$$ 0.100608 11.1799i 0.00899866 0.999960i
$$126$$ 0 0
$$127$$ 0.00277854 0.000246555 0.000123278 1.00000i $$-0.499961\pi$$
0.000123278 1.00000i $$0.499961\pi$$
$$128$$ −9.99426 5.30233i −0.883376 0.468665i
$$129$$ 0 0
$$130$$ −6.93159 10.9799i −0.607940 0.962999i
$$131$$ 8.71989 + 8.71989i 0.761860 + 0.761860i 0.976658 0.214798i $$-0.0689095\pi$$
−0.214798 + 0.976658i $$0.568909\pi$$
$$132$$ 0 0
$$133$$ 0.124050 + 0.124050i 0.0107565 + 0.0107565i
$$134$$ 11.6948 0.497531i 1.01028 0.0429801i
$$135$$ 0 0
$$136$$ 10.2224 + 7.89846i 0.876566 + 0.677288i
$$137$$ 23.1771i 1.98016i −0.140516 0.990078i $$-0.544876\pi$$
0.140516 0.990078i $$-0.455124\pi$$
$$138$$ 0 0
$$139$$ −7.85331 7.85331i −0.666109 0.666109i 0.290704 0.956813i $$-0.406111\pi$$
−0.956813 + 0.290704i $$0.906111\pi$$
$$140$$ 6.57348 4.55173i 0.555560 0.384691i
$$141$$ 0 0
$$142$$ −15.7731 14.4858i −1.32365 1.21562i
$$143$$ 19.4197i 1.62396i
$$144$$ 0 0
$$145$$ −1.02614 + 3.78417i −0.0852164 + 0.314258i
$$146$$ 6.58248 7.16744i 0.544770 0.593182i
$$147$$ 0 0
$$148$$ 13.8989 16.4892i 1.14248 1.35540i
$$149$$ −13.6076 13.6076i −1.11478 1.11478i −0.992495 0.122285i $$-0.960978\pi$$
−0.122285 0.992495i $$-0.539022\pi$$
$$150$$ 0 0
$$151$$ 15.2447 1.24059 0.620297 0.784367i $$-0.287012\pi$$
0.620297 + 0.784367i $$0.287012\pi$$
$$152$$ 0.275284 0.0353044i 0.0223284 0.00286357i
$$153$$ 0 0
$$154$$ −11.9471 + 0.508264i −0.962728 + 0.0409571i
$$155$$ −9.52742 16.6169i −0.765261 1.33470i
$$156$$ 0 0
$$157$$ −5.76894 + 5.76894i −0.460411 + 0.460411i −0.898790 0.438379i $$-0.855553\pi$$
0.438379 + 0.898790i $$0.355553\pi$$
$$158$$ −13.5117 12.4090i −1.07493 0.987204i
$$159$$ 0 0
$$160$$ 0.660154 12.6319i 0.0521898 0.998637i
$$161$$ 1.92544i 0.151746i
$$162$$ 0 0
$$163$$ −10.4511 10.4511i −0.818594 0.818594i 0.167311 0.985904i $$-0.446492\pi$$
−0.985904 + 0.167311i $$0.946492\pi$$
$$164$$ −1.34464 15.7748i −0.104999 1.23181i
$$165$$ 0 0
$$166$$ −0.585573 13.7644i −0.0454493 1.06832i
$$167$$ −9.41872 −0.728842 −0.364421 0.931234i $$-0.618733\pi$$
−0.364421 + 0.931234i $$0.618733\pi$$
$$168$$ 0 0
$$169$$ 3.86046i 0.296958i
$$170$$ −3.18408 + 14.0878i −0.244208 + 1.08049i
$$171$$ 0 0
$$172$$ 5.08607 + 4.28711i 0.387810 + 0.326889i
$$173$$ 6.21995 + 6.21995i 0.472894 + 0.472894i 0.902850 0.429956i $$-0.141471\pi$$
−0.429956 + 0.902850i $$0.641471\pi$$
$$174$$ 0 0
$$175$$ 7.71471 + 4.51601i 0.583177 + 0.341378i
$$176$$ −10.9198 + 15.4479i −0.823112 + 1.16443i
$$177$$ 0 0
$$178$$ −6.04192 + 6.57884i −0.452861 + 0.493105i
$$179$$ −18.4020 18.4020i −1.37543 1.37543i −0.852179 0.523251i $$-0.824719\pi$$
−0.523251 0.852179i $$-0.675281\pi$$
$$180$$ 0 0
$$181$$ −18.5731 + 18.5731i −1.38053 + 1.38053i −0.536851 + 0.843677i $$0.680386\pi$$
−0.843677 + 0.536851i $$0.819614\pi$$
$$182$$ 10.3727 0.441282i 0.768873 0.0327100i
$$183$$ 0 0
$$184$$ −2.41040 1.86242i −0.177697 0.137299i
$$185$$ 23.2707 + 6.31023i 1.71089 + 0.463937i
$$186$$ 0 0
$$187$$ 15.2741 15.2741i 1.11695 1.11695i
$$188$$ −12.5981 + 1.07386i −0.918809 + 0.0783190i
$$189$$ 0 0
$$190$$ 0.165644 + 0.262386i 0.0120171 + 0.0190355i
$$191$$ 4.73383 0.342528 0.171264 0.985225i $$-0.445215\pi$$
0.171264 + 0.985225i $$0.445215\pi$$
$$192$$ 0 0
$$193$$ 16.7218i 1.20366i 0.798625 + 0.601829i $$0.205561\pi$$
−0.798625 + 0.601829i $$0.794439\pi$$
$$194$$ −4.75728 4.36902i −0.341553 0.313678i
$$195$$ 0 0
$$196$$ −0.646086 7.57963i −0.0461490 0.541402i
$$197$$ −7.93066 + 7.93066i −0.565036 + 0.565036i −0.930734 0.365698i $$-0.880830\pi$$
0.365698 + 0.930734i $$0.380830\pi$$
$$198$$ 0 0
$$199$$ −2.34717 −0.166386 −0.0831932 0.996533i $$-0.526512\pi$$
−0.0831932 + 0.996533i $$0.526512\pi$$
$$200$$ 13.1156 5.28959i 0.927416 0.374031i
$$201$$ 0 0
$$202$$ 12.4825 0.531040i 0.878266 0.0373638i
$$203$$ −2.21672 2.21672i −0.155583 0.155583i
$$204$$ 0 0
$$205$$ 15.3558 8.80435i 1.07249 0.614922i
$$206$$ 14.4311 + 13.2534i 1.00547 + 0.923406i
$$207$$ 0 0
$$208$$ 9.48073 13.4120i 0.657371 0.929958i
$$209$$ 0.464072i 0.0321006i
$$210$$ 0 0
$$211$$ −3.00077 + 3.00077i −0.206581 + 0.206581i −0.802813 0.596231i $$-0.796664\pi$$
0.596231 + 0.802813i $$0.296664\pi$$
$$212$$ −7.81639 6.58852i −0.536832 0.452502i
$$213$$ 0 0
$$214$$ −1.84275 + 0.0783956i −0.125968 + 0.00535902i
$$215$$ −1.94638 + 7.17781i −0.132742 + 0.489522i
$$216$$ 0 0
$$217$$ 15.3150 1.03965
$$218$$ 4.56911 0.194382i 0.309459 0.0131652i
$$219$$ 0 0
$$220$$ −20.8098 3.78169i −1.40300 0.254962i
$$221$$ −13.2612 + 13.2612i −0.892042 + 0.892042i
$$222$$ 0 0
$$223$$ −24.6842 −1.65298 −0.826489 0.562952i $$-0.809665\pi$$
−0.826489 + 0.562952i $$0.809665\pi$$
$$224$$ 8.49932 + 5.48158i 0.567885 + 0.366254i
$$225$$ 0 0
$$226$$ −7.21052 + 7.85129i −0.479637 + 0.522260i
$$227$$ −5.05360 + 5.05360i −0.335419 + 0.335419i −0.854640 0.519221i $$-0.826222\pi$$
0.519221 + 0.854640i $$0.326222\pi$$
$$228$$ 0 0
$$229$$ −13.4816 + 13.4816i −0.890886 + 0.890886i −0.994606 0.103720i $$-0.966925\pi$$
0.103720 + 0.994606i $$0.466925\pi$$
$$230$$ 0.750789 3.32183i 0.0495056 0.219035i
$$231$$ 0 0
$$232$$ −4.91921 + 0.630877i −0.322962 + 0.0414191i
$$233$$ 11.8466i 0.776096i 0.921639 + 0.388048i $$0.126851\pi$$
−0.921639 + 0.388048i $$0.873149\pi$$
$$234$$ 0 0
$$235$$ −7.03132 12.2634i −0.458673 0.799977i
$$236$$ −4.86767 4.10301i −0.316858 0.267083i
$$237$$ 0 0
$$238$$ −8.50544 7.81128i −0.551326 0.506330i
$$239$$ −24.8620 −1.60819 −0.804093 0.594503i $$-0.797349\pi$$
−0.804093 + 0.594503i $$0.797349\pi$$
$$240$$ 0 0
$$241$$ 18.8396 1.21356 0.606782 0.794868i $$-0.292460\pi$$
0.606782 + 0.794868i $$0.292460\pi$$
$$242$$ 11.8403 + 10.8740i 0.761125 + 0.699007i
$$243$$ 0 0
$$244$$ 7.83656 9.29702i 0.501684 0.595181i
$$245$$ 7.37828 4.23039i 0.471381 0.270270i
$$246$$ 0 0
$$247$$ 0.402914i 0.0256368i
$$248$$ 14.8138 19.1724i 0.940674 1.21745i
$$249$$ 0 0
$$250$$ 11.5487 + 10.7994i 0.730406 + 0.683013i
$$251$$ 21.6723 21.6723i 1.36795 1.36795i 0.504582 0.863364i $$-0.331647\pi$$
0.863364 0.504582i $$-0.168353\pi$$
$$252$$ 0 0
$$253$$ −3.60155 + 3.60155i −0.226428 + 0.226428i
$$254$$ −0.00265793 + 0.00289413i −0.000166773 + 0.000181594i
$$255$$ 0 0
$$256$$ 15.0833 5.33786i 0.942709 0.333616i
$$257$$ 0.914423 0.0570402 0.0285201 0.999593i $$-0.490921\pi$$
0.0285201 + 0.999593i $$0.490921\pi$$
$$258$$ 0 0
$$259$$ −13.6317 + 13.6317i −0.847031 + 0.847031i
$$260$$ 18.0673 + 3.28332i 1.12049 + 0.203623i
$$261$$ 0 0
$$262$$ −17.4240 + 0.741265i −1.07646 + 0.0457955i
$$263$$ 1.19643 0.0737752 0.0368876 0.999319i $$-0.488256\pi$$
0.0368876 + 0.999319i $$0.488256\pi$$
$$264$$ 0 0
$$265$$ 2.99124 11.0310i 0.183751 0.677630i
$$266$$ −0.247875 + 0.0105453i −0.0151982 + 0.000646574i
$$267$$ 0 0
$$268$$ −10.6690 + 12.6573i −0.651711 + 0.773167i
$$269$$ −7.54542 + 7.54542i −0.460053 + 0.460053i −0.898673 0.438620i $$-0.855467\pi$$
0.438620 + 0.898673i $$0.355467\pi$$
$$270$$ 0 0
$$271$$ 4.45852i 0.270836i 0.990789 + 0.135418i $$0.0432377\pi$$
−0.990789 + 0.135418i $$0.956762\pi$$
$$272$$ −18.0057 + 3.09207i −1.09176 + 0.187485i
$$273$$ 0 0
$$274$$ 24.1413 + 22.1711i 1.45843 + 1.33940i
$$275$$ −5.98318 22.8777i −0.360800 1.37957i
$$276$$ 0 0
$$277$$ −5.28152 5.28152i −0.317336 0.317336i 0.530407 0.847743i $$-0.322039\pi$$
−0.847743 + 0.530407i $$0.822039\pi$$
$$278$$ 15.6924 0.667599i 0.941169 0.0400399i
$$279$$ 0 0
$$280$$ −1.54705 + 11.2011i −0.0924539 + 0.669393i
$$281$$ −26.3280 −1.57060 −0.785298 0.619118i $$-0.787490\pi$$
−0.785298 + 0.619118i $$0.787490\pi$$
$$282$$ 0 0
$$283$$ −13.6186 + 13.6186i −0.809540 + 0.809540i −0.984564 0.175024i $$-0.944000\pi$$
0.175024 + 0.984564i $$0.444000\pi$$
$$284$$ 30.1768 2.57226i 1.79066 0.152636i
$$285$$ 0 0
$$286$$ −20.2276 18.5767i −1.19608 1.09847i
$$287$$ 14.1527i 0.835409i
$$288$$ 0 0
$$289$$ 3.86046 0.227086
$$290$$ −2.96000 4.68874i −0.173817 0.275332i
$$291$$ 0 0
$$292$$ 1.16886 + 13.7126i 0.0684024 + 0.802471i
$$293$$ −9.23746 + 9.23746i −0.539658 + 0.539658i −0.923429 0.383770i $$-0.874625\pi$$
0.383770 + 0.923429i $$0.374625\pi$$
$$294$$ 0 0
$$295$$ 1.86280 6.86958i 0.108457 0.399962i
$$296$$ 3.87956 + 30.2506i 0.225495 + 1.75828i
$$297$$ 0 0
$$298$$ 27.1907 1.15676i 1.57511 0.0670096i
$$299$$ 3.12692 3.12692i 0.180834 0.180834i
$$300$$ 0 0
$$301$$ −4.20468 4.20468i −0.242353 0.242353i
$$302$$ −14.5829 + 15.8789i −0.839153 + 0.913725i
$$303$$ 0 0
$$304$$ −0.226561 + 0.320507i −0.0129942 + 0.0183824i
$$305$$ 13.1206 + 3.55786i 0.751282 + 0.203723i
$$306$$ 0 0
$$307$$ −2.37148 2.37148i −0.135348 0.135348i 0.636187 0.771535i $$-0.280511\pi$$
−0.771535 + 0.636187i $$0.780511\pi$$
$$308$$ 10.8991 12.9303i 0.621035 0.736775i
$$309$$ 0 0
$$310$$ 26.4220 + 5.97181i 1.50067 + 0.339176i
$$311$$ 14.5352i 0.824214i 0.911135 + 0.412107i $$0.135207\pi$$
−0.911135 + 0.412107i $$0.864793\pi$$
$$312$$ 0 0
$$313$$ −21.2104 −1.19888 −0.599442 0.800418i $$-0.704611\pi$$
−0.599442 + 0.800418i $$0.704611\pi$$
$$314$$ −0.490409 11.5274i −0.0276754 0.650531i
$$315$$ 0 0
$$316$$ 25.8504 2.20348i 1.45420 0.123955i
$$317$$ 0.575423 + 0.575423i 0.0323190 + 0.0323190i 0.723082 0.690763i $$-0.242725\pi$$
−0.690763 + 0.723082i $$0.742725\pi$$
$$318$$ 0 0
$$319$$ 8.29280i 0.464308i
$$320$$ 12.5259 + 12.7712i 0.700217 + 0.713930i
$$321$$ 0 0
$$322$$ 2.00554 + 1.84186i 0.111764 + 0.102643i
$$323$$ 0.316902 0.316902i 0.0176329 0.0176329i
$$324$$ 0 0
$$325$$ 5.19468 + 19.8627i 0.288149 + 1.10178i
$$326$$ 20.8833 0.888433i 1.15662 0.0492058i
$$327$$ 0 0
$$328$$ 17.7173 + 13.6895i 0.978276 + 0.755875i
$$329$$ 11.3026 0.623134
$$330$$ 0 0
$$331$$ 5.54595 + 5.54595i 0.304833 + 0.304833i 0.842901 0.538068i $$-0.180846\pi$$
−0.538068 + 0.842901i $$0.680846\pi$$
$$332$$ 14.8971 + 12.5569i 0.817585 + 0.689151i
$$333$$ 0 0
$$334$$ 9.00987 9.81054i 0.492998 0.536809i
$$335$$ −17.8628 4.84380i −0.975949 0.264645i
$$336$$ 0 0
$$337$$ 16.3650i 0.891460i −0.895167 0.445730i $$-0.852944\pi$$
0.895167 0.445730i $$-0.147056\pi$$
$$338$$ 4.02106 + 3.69289i 0.218717 + 0.200866i
$$339$$ 0 0
$$340$$ −11.6280 16.7928i −0.630617 0.910718i
$$341$$ −28.6469 28.6469i −1.55132 1.55132i
$$342$$ 0 0
$$343$$ 19.3152i 1.04293i
$$344$$ −9.33075 + 1.19665i −0.503080 + 0.0645188i
$$345$$ 0 0
$$346$$ −12.4287 + 0.528749i −0.668168 + 0.0284257i
$$347$$ −18.6768 18.6768i −1.00262 1.00262i −0.999997 0.00262421i $$-0.999165\pi$$
−0.00262421 0.999997i $$-0.500835\pi$$
$$348$$ 0 0
$$349$$ 15.2350 + 15.2350i 0.815511 + 0.815511i 0.985454 0.169943i $$-0.0543583\pi$$
−0.169943 + 0.985454i $$0.554358\pi$$
$$350$$ −12.0837 + 3.71566i −0.645901 + 0.198610i
$$351$$ 0 0
$$352$$ −5.64470 26.1514i −0.300863 1.39387i
$$353$$ 8.23255 0.438175 0.219087 0.975705i $$-0.429692\pi$$
0.219087 + 0.975705i $$0.429692\pi$$
$$354$$ 0 0
$$355$$ 16.8425 + 29.3752i 0.893906 + 1.55907i
$$356$$ −1.07287 12.5865i −0.0568621 0.667085i
$$357$$ 0 0
$$358$$ 36.7707 1.56433i 1.94339 0.0826773i
$$359$$ 4.96843i 0.262224i −0.991368 0.131112i $$-0.958145\pi$$
0.991368 0.131112i $$-0.0418547\pi$$
$$360$$ 0 0
$$361$$ 18.9904i 0.999493i
$$362$$ −1.57887 37.1126i −0.0829837 1.95060i
$$363$$ 0 0
$$364$$ −9.46277 + 11.2263i −0.495984 + 0.588418i
$$365$$ −13.3484 + 7.65339i −0.698685 + 0.400597i
$$366$$ 0 0
$$367$$ 25.3790 1.32477 0.662385 0.749163i $$-0.269544\pi$$
0.662385 + 0.749163i $$0.269544\pi$$
$$368$$ 4.24566 0.729096i 0.221320 0.0380067i
$$369$$ 0 0
$$370$$ −28.8333 + 18.2024i −1.49897 + 0.946298i
$$371$$ 6.46184 + 6.46184i 0.335482 + 0.335482i
$$372$$ 0 0
$$373$$ 2.85715 + 2.85715i 0.147938 + 0.147938i 0.777196 0.629259i $$-0.216641\pi$$
−0.629259 + 0.777196i $$0.716641\pi$$
$$374$$ 1.29843 + 30.5205i 0.0671401 + 1.57818i
$$375$$ 0 0
$$376$$ 10.9327 14.1494i 0.563810 0.729700i
$$377$$ 7.19992i 0.370815i
$$378$$ 0 0
$$379$$ −8.96148 8.96148i −0.460320 0.460320i 0.438440 0.898760i $$-0.355531\pi$$
−0.898760 + 0.438440i $$0.855531\pi$$
$$380$$ −0.431755 0.0784613i −0.0221486 0.00402498i
$$381$$ 0 0
$$382$$ −4.52834 + 4.93076i −0.231690 + 0.252280i
$$383$$ 9.83688i 0.502641i −0.967904 0.251321i $$-0.919135\pi$$
0.967904 0.251321i $$-0.0808648\pi$$
$$384$$ 0 0
$$385$$ 18.2482 + 4.94829i 0.930012 + 0.252188i
$$386$$ −17.4174 15.9959i −0.886522 0.814170i
$$387$$ 0 0
$$388$$ 9.10156 0.775814i 0.462062 0.0393860i
$$389$$ −8.69886 8.69886i −0.441050 0.441050i 0.451315 0.892365i $$-0.350955\pi$$
−0.892365 + 0.451315i $$0.850955\pi$$
$$390$$ 0 0
$$391$$ −4.91879 −0.248754
$$392$$ 8.51299 + 6.57765i 0.429971 + 0.332221i
$$393$$ 0 0
$$394$$ −0.674174 15.8470i −0.0339644 0.798359i
$$395$$ 14.4278 + 25.1637i 0.725941 + 1.26612i
$$396$$ 0 0
$$397$$ −2.52696 + 2.52696i −0.126824 + 0.126824i −0.767670 0.640845i $$-0.778584\pi$$
0.640845 + 0.767670i $$0.278584\pi$$
$$398$$ 2.24528 2.44481i 0.112546 0.122547i
$$399$$ 0 0
$$400$$ −7.03668 + 18.7212i −0.351834 + 0.936062i
$$401$$ 11.5176i 0.575161i −0.957757 0.287580i $$-0.907149\pi$$
0.957757 0.287580i $$-0.0928508\pi$$
$$402$$ 0 0
$$403$$ 24.8716 + 24.8716i 1.23894 + 1.23894i
$$404$$ −11.3875 + 13.5098i −0.566551 + 0.672136i
$$405$$ 0 0
$$406$$ 4.42944 0.188441i 0.219829 0.00935215i
$$407$$ 50.9963 2.52779
$$408$$ 0 0
$$409$$ 17.5055i 0.865591i −0.901492 0.432795i $$-0.857527\pi$$
0.901492 0.432795i $$-0.142473\pi$$
$$410$$ −5.51859 + 24.4167i −0.272544 + 1.20586i
$$411$$ 0 0
$$412$$ −27.6094 + 2.35342i −1.36022 + 0.115945i
$$413$$ 4.02412 + 4.02412i 0.198014 + 0.198014i
$$414$$ 0 0
$$415$$ −5.70095 + 21.0238i −0.279849 + 1.03202i
$$416$$ 4.90080 + 22.7050i 0.240282 + 1.11320i
$$417$$ 0 0
$$418$$ 0.483378 + 0.443928i 0.0236428 + 0.0217132i
$$419$$ −3.30068 3.30068i −0.161249 0.161249i 0.621871 0.783120i $$-0.286373\pi$$
−0.783120 + 0.621871i $$0.786373\pi$$
$$420$$ 0 0
$$421$$ −6.14311 + 6.14311i −0.299397 + 0.299397i −0.840778 0.541381i $$-0.817902\pi$$
0.541381 + 0.840778i $$0.317902\pi$$
$$422$$ −0.255091 5.99611i −0.0124176 0.291886i
$$423$$ 0 0
$$424$$ 14.3397 1.83903i 0.696398 0.0893113i
$$425$$ 11.5368 19.7082i 0.559615 0.955990i
$$426$$ 0 0
$$427$$ −7.68588 + 7.68588i −0.371946 + 0.371946i
$$428$$ 1.68110 1.99440i 0.0812592 0.0964031i
$$429$$ 0 0
$$430$$ −5.61451 8.89358i −0.270756 0.428887i
$$431$$ 8.73359 0.420682 0.210341 0.977628i $$-0.432543\pi$$
0.210341 + 0.977628i $$0.432543\pi$$
$$432$$ 0 0
$$433$$ 2.28479i 0.109800i −0.998492 0.0548999i $$-0.982516\pi$$
0.998492 0.0548999i $$-0.0174840\pi$$
$$434$$ −14.6502 + 15.9521i −0.703234 + 0.765727i
$$435$$ 0 0
$$436$$ −4.16831 + 4.94513i −0.199626 + 0.236829i
$$437$$ −0.0747238 + 0.0747238i −0.00357452 + 0.00357452i
$$438$$ 0 0
$$439$$ 27.7235 1.32317 0.661585 0.749870i $$-0.269884\pi$$
0.661585 + 0.749870i $$0.269884\pi$$
$$440$$ 23.8455 18.0580i 1.13679 0.860879i
$$441$$ 0 0
$$442$$ −1.12731 26.4984i −0.0536208 1.26040i
$$443$$ 15.8575 + 15.8575i 0.753410 + 0.753410i 0.975114 0.221704i $$-0.0711618\pi$$
−0.221704 + 0.975114i $$0.571162\pi$$
$$444$$ 0 0
$$445$$ 12.2522 7.02488i 0.580809 0.333011i
$$446$$ 23.6127 25.7111i 1.11810 1.21746i
$$447$$ 0 0
$$448$$ −13.8400 + 3.60926i −0.653878 + 0.170521i
$$449$$ 22.7098i 1.07174i 0.844301 + 0.535870i $$0.180016\pi$$
−0.844301 + 0.535870i $$0.819984\pi$$
$$450$$ 0 0
$$451$$ 26.4728 26.4728i 1.24655 1.24655i
$$452$$ −1.28038 15.0210i −0.0602242 0.706527i
$$453$$ 0 0
$$454$$ −0.429599 10.0981i −0.0201621 0.473925i
$$455$$ −15.8433 4.29618i −0.742746 0.201408i
$$456$$ 0 0
$$457$$ 23.3185 1.09079 0.545397 0.838178i $$-0.316379\pi$$
0.545397 + 0.838178i $$0.316379\pi$$
$$458$$ −1.14605 26.9387i −0.0535513 1.25876i
$$459$$ 0 0
$$460$$ 2.74182 + 3.95966i 0.127838 + 0.184620i
$$461$$ 6.98422 6.98422i 0.325288 0.325288i −0.525504 0.850791i $$-0.676123\pi$$
0.850791 + 0.525504i $$0.176123\pi$$
$$462$$ 0 0
$$463$$ 0.177929 0.00826905 0.00413453 0.999991i $$-0.498684\pi$$
0.00413453 + 0.999991i $$0.498684\pi$$
$$464$$ 4.04856 5.72735i 0.187950 0.265885i
$$465$$ 0 0
$$466$$ −12.3394 11.3324i −0.571613 0.524961i
$$467$$ −25.8586 + 25.8586i −1.19659 + 1.19659i −0.221414 + 0.975180i $$0.571067\pi$$
−0.975180 + 0.221414i $$0.928933\pi$$
$$468$$ 0 0
$$469$$ 10.4638 10.4638i 0.483175 0.483175i
$$470$$ 19.4997 + 4.40725i 0.899453 + 0.203291i
$$471$$ 0 0
$$472$$ 8.93008 1.14526i 0.411040 0.0527149i
$$473$$ 15.7298i 0.723255i
$$474$$ 0 0
$$475$$ −0.124137 0.474658i −0.00569581 0.0217788i
$$476$$ 16.2725 1.38706i 0.745847 0.0635758i
$$477$$ 0 0
$$478$$ 23.7828 25.8962i 1.08780 1.18447i
$$479$$ −6.74528 −0.308200 −0.154100 0.988055i $$-0.549248\pi$$
−0.154100 + 0.988055i $$0.549248\pi$$
$$480$$ 0 0
$$481$$ −44.2757 −2.01880
$$482$$ −18.0218 + 19.6233i −0.820870 + 0.893818i
$$483$$ 0 0
$$484$$ −22.6527 + 1.93091i −1.02967 + 0.0877687i
$$485$$ 5.07982 + 8.85978i 0.230663 + 0.402302i
$$486$$ 0 0
$$487$$ 27.5084i 1.24652i 0.782014 + 0.623261i $$0.214193\pi$$
−0.782014 + 0.623261i $$0.785807\pi$$
$$488$$ 2.18739 + 17.0560i 0.0990186 + 0.772090i
$$489$$ 0 0
$$490$$ −2.65162 + 11.7320i −0.119788 + 0.529997i
$$491$$ −1.96277 + 1.96277i −0.0885786 + 0.0885786i −0.750008 0.661429i $$-0.769950\pi$$
0.661429 + 0.750008i $$0.269950\pi$$
$$492$$ 0 0
$$493$$ −5.66291 + 5.66291i −0.255045 + 0.255045i
$$494$$ −0.419675 0.385424i −0.0188821 0.0173411i
$$495$$ 0 0
$$496$$ 5.79926 + 33.7702i 0.260394 + 1.51633i
$$497$$ −27.0738 −1.21442
$$498$$ 0 0
$$499$$ −10.0400 + 10.0400i −0.449452 + 0.449452i −0.895172 0.445720i $$-0.852948\pi$$
0.445720 + 0.895172i $$0.352948\pi$$
$$500$$ −22.2961 + 1.69857i −0.997111 + 0.0759622i
$$501$$ 0 0
$$502$$ 1.84233 + 43.3055i 0.0822274 + 1.93282i
$$503$$ 15.8104 0.704952 0.352476 0.935821i $$-0.385340\pi$$
0.352476 + 0.935821i $$0.385340\pi$$
$$504$$ 0 0
$$505$$ −19.0659 5.17003i −0.848421 0.230063i
$$506$$ −0.306163 7.19659i −0.0136106 0.319927i
$$507$$ 0 0
$$508$$ −0.000471972 0.00553700i −2.09404e−5 0.000245664i
$$509$$ 16.6015 16.6015i 0.735849 0.735849i −0.235922 0.971772i $$-0.575811\pi$$
0.971772 + 0.235922i $$0.0758111\pi$$
$$510$$ 0 0
$$511$$ 12.3026i 0.544234i
$$512$$ −8.86869 + 20.8170i −0.391945 + 0.919989i
$$513$$ 0 0
$$514$$ −0.874730 + 0.952464i −0.0385827 + 0.0420114i
$$515$$ −15.4096 26.8760i −0.679027 1.18430i
$$516$$ 0 0
$$517$$ −21.1417 21.1417i −0.929809 0.929809i
$$518$$ −1.15881 27.2387i −0.0509152 1.19680i
$$519$$ 0 0
$$520$$ −20.7030 + 15.6782i −0.907886 + 0.687533i
$$521$$ 7.96468 0.348939 0.174469 0.984663i $$-0.444179\pi$$
0.174469 + 0.984663i $$0.444179\pi$$
$$522$$ 0 0
$$523$$ −15.2514 + 15.2514i −0.666897 + 0.666897i −0.956997 0.290099i $$-0.906312\pi$$
0.290099 + 0.956997i $$0.406312\pi$$
$$524$$ 15.8956 18.8579i 0.694401 0.823813i
$$525$$ 0 0
$$526$$ −1.14450 + 1.24621i −0.0499025 + 0.0543372i
$$527$$ 39.1243i 1.70428i
$$528$$ 0 0
$$529$$ −21.8402 −0.949573
$$530$$ 8.62851 + 13.6679i 0.374798 + 0.593694i
$$531$$ 0 0
$$532$$ 0.226132 0.268275i 0.00980405 0.0116312i
$$533$$ −22.9840 + 22.9840i −0.995549 + 0.995549i
$$534$$ 0 0
$$535$$ 2.81463 + 0.763235i 0.121687 + 0.0329975i
$$536$$ −2.97799 23.2207i −0.128630 1.00298i
$$537$$ 0 0
$$538$$ −0.641426 15.0772i −0.0276538 0.650025i
$$539$$ 12.7199 12.7199i 0.547884 0.547884i
$$540$$ 0 0
$$541$$ −6.80924 6.80924i −0.292752 0.292752i 0.545414 0.838167i $$-0.316372\pi$$
−0.838167 + 0.545414i $$0.816372\pi$$
$$542$$ −4.64399 4.26498i −0.199477 0.183197i
$$543$$ 0 0
$$544$$ 14.0034 21.7126i 0.600392 0.930922i
$$545$$ −6.97890 1.89245i −0.298943 0.0810635i
$$546$$ 0 0
$$547$$ −24.8809 24.8809i −1.06383 1.06383i −0.997819 0.0660132i $$-0.978972\pi$$
−0.0660132 0.997819i $$-0.521028\pi$$
$$548$$ −46.1868 + 3.93695i −1.97300 + 0.168178i
$$549$$ 0 0
$$550$$ 29.5528 + 15.6525i 1.26014 + 0.667425i
$$551$$ 0.172056i 0.00732985i
$$552$$ 0 0
$$553$$ −23.1922 −0.986233
$$554$$ 10.5535 0.448974i 0.448375 0.0190751i
$$555$$ 0 0
$$556$$ −14.3159 + 16.9839i −0.607129 + 0.720276i
$$557$$ −3.05959 3.05959i −0.129639 0.129639i 0.639310 0.768949i $$-0.279220\pi$$
−0.768949 + 0.639310i $$0.779220\pi$$
$$558$$ 0 0
$$559$$ 13.6568i 0.577621i
$$560$$ −10.1872 12.3263i −0.430486 0.520880i
$$561$$ 0 0
$$562$$ 25.1851 27.4232i 1.06237 1.15678i
$$563$$ 32.0945 32.0945i 1.35262 1.35262i 0.469906 0.882716i $$-0.344288\pi$$
0.882716 0.469906i $$-0.155712\pi$$
$$564$$ 0 0
$$565$$ 14.6219 8.38360i 0.615150 0.352701i
$$566$$ −1.15769 27.2125i −0.0486615 1.14383i
$$567$$ 0 0
$$568$$ −26.1876 + 33.8928i −1.09881 + 1.42211i
$$569$$ 28.4585 1.19304 0.596521 0.802597i $$-0.296549\pi$$
0.596521 + 0.802597i $$0.296549\pi$$
$$570$$ 0 0
$$571$$ −26.7837 26.7837i −1.12086 1.12086i −0.991612 0.129250i $$-0.958743\pi$$
−0.129250 0.991612i $$-0.541257\pi$$
$$572$$ 38.6991 3.29870i 1.61809 0.137926i
$$573$$ 0 0
$$574$$ −14.7415 13.5384i −0.615297 0.565081i
$$575$$ −2.72031 + 4.64710i −0.113445 + 0.193798i
$$576$$ 0 0
$$577$$ 33.4904i 1.39423i −0.716962 0.697113i $$-0.754468\pi$$
0.716962 0.697113i $$-0.245532\pi$$
$$578$$ −3.69289 + 4.02106i −0.153604 + 0.167254i
$$579$$ 0 0
$$580$$ 7.71530 + 1.40207i 0.320360 + 0.0582180i
$$581$$ −12.3155 12.3155i −0.510933 0.510933i
$$582$$ 0 0
$$583$$ 24.1738i 1.00118i
$$584$$ −15.4012 11.8999i −0.637306 0.492422i
$$585$$ 0 0
$$586$$ −0.785264 18.4582i −0.0324389 0.762502i
$$587$$ −12.3666 12.3666i −0.510425 0.510425i 0.404232 0.914657i $$-0.367539\pi$$
−0.914657 + 0.404232i $$0.867539\pi$$
$$588$$ 0 0
$$589$$ −0.594357 0.594357i −0.0244900 0.0244900i
$$590$$ 5.37342 + 8.51168i 0.221220 + 0.350420i
$$591$$ 0 0
$$592$$ −35.2202 24.8965i −1.44754 1.02324i
$$593$$ −24.1105 −0.990099 −0.495050 0.868865i $$-0.664850\pi$$
−0.495050 + 0.868865i $$0.664850\pi$$
$$594$$ 0 0
$$595$$ 9.08210 + 15.8402i 0.372330 + 0.649385i
$$596$$ −24.8055 + 29.4284i −1.01607 + 1.20543i
$$597$$ 0 0
$$598$$ 0.265815 + 6.24818i 0.0108700 + 0.255507i
$$599$$ 18.0184i 0.736213i 0.929784 + 0.368107i $$0.119994\pi$$
−0.929784 + 0.368107i $$0.880006\pi$$
$$600$$ 0 0
$$601$$ 18.8361i 0.768342i 0.923262 + 0.384171i $$0.125513\pi$$
−0.923262 + 0.384171i $$0.874487\pi$$
$$602$$ 8.40175 0.357433i 0.342430 0.0145679i
$$603$$ 0 0
$$604$$ −2.58951 30.3792i −0.105366 1.23611i
$$605$$ −12.6431 22.0510i −0.514015 0.896499i
$$606$$ 0 0
$$607$$ 10.4336 0.423486 0.211743 0.977325i $$-0.432086\pi$$
0.211743 + 0.977325i $$0.432086\pi$$
$$608$$ −0.117114 0.542581i −0.00474962 0.0220046i
$$609$$ 0 0
$$610$$ −16.2569 + 10.2630i −0.658223 + 0.415536i
$$611$$ 18.3555 + 18.3555i 0.742583 + 0.742583i
$$612$$ 0 0
$$613$$ −9.35631 9.35631i −0.377898 0.377898i 0.492445 0.870343i $$-0.336103\pi$$
−0.870343 + 0.492445i $$0.836103\pi$$
$$614$$ 4.73868 0.201596i 0.191237 0.00813577i
$$615$$ 0 0
$$616$$ 3.04224 + 23.7216i 0.122575 + 0.955771i
$$617$$ 22.8927i 0.921626i 0.887497 + 0.460813i $$0.152442\pi$$
−0.887497 + 0.460813i $$0.847558\pi$$
$$618$$ 0 0
$$619$$ 32.9542 + 32.9542i 1.32454 + 1.32454i 0.910057 + 0.414484i $$0.136038\pi$$
0.414484 + 0.910057i $$0.363962\pi$$
$$620$$ −31.4953 + 21.8086i −1.26488 + 0.875854i
$$621$$ 0 0
$$622$$ −15.1398 13.9042i −0.607052 0.557509i
$$623$$ 11.2923i 0.452415i
$$624$$ 0 0
$$625$$ −12.2393 21.7991i −0.489573 0.871962i
$$626$$ 20.2897 22.0928i 0.810941 0.883006i
$$627$$ 0 0
$$628$$ 12.4761 + 10.5163i 0.497851 + 0.419644i
$$629$$ 34.8239 + 34.8239i 1.38852 + 1.38852i
$$630$$ 0 0
$$631$$ 14.9668 0.595817 0.297908 0.954594i $$-0.403711\pi$$
0.297908 + 0.954594i $$0.403711\pi$$
$$632$$ −22.4331 + 29.0336i −0.892341 + 1.15489i
$$633$$ 0 0
$$634$$ −1.14981 + 0.0489159i −0.0456646 + 0.00194270i
$$635$$ 0.00538991 0.00309035i 0.000213892 0.000122637i
$$636$$ 0 0
$$637$$ −11.0436 + 11.0436i −0.437562 + 0.437562i
$$638$$ −8.63778 7.93283i −0.341973 0.314064i
$$639$$ 0 0
$$640$$ −25.2846 + 0.830157i −0.999461 + 0.0328148i
$$641$$ 3.08889i 0.122004i 0.998138 + 0.0610019i $$0.0194296\pi$$
−0.998138 + 0.0610019i $$0.980570\pi$$
$$642$$ 0 0
$$643$$ −18.1306 18.1306i −0.715001 0.715001i 0.252576 0.967577i $$-0.418722\pi$$
−0.967577 + 0.252576i $$0.918722\pi$$
$$644$$ −3.83696 + 0.327062i −0.151198 + 0.0128880i
$$645$$ 0 0
$$646$$ 0.0269394 + 0.633231i 0.00105992 + 0.0249141i
$$647$$ 6.79255 0.267043 0.133521 0.991046i $$-0.457372\pi$$
0.133521 + 0.991046i $$0.457372\pi$$
$$648$$ 0 0
$$649$$ 15.0543i 0.590933i
$$650$$ −25.6582 13.5897i −1.00640 0.533032i
$$651$$ 0 0
$$652$$ −19.0514 + 22.6019i −0.746111 + 0.885160i
$$653$$ −12.2088 12.2088i −0.477769 0.477769i 0.426649 0.904417i $$-0.359694\pi$$
−0.904417 + 0.426649i $$0.859694\pi$$
$$654$$ 0 0
$$655$$ 26.6136 + 7.21672i 1.03988 + 0.281981i
$$656$$ −31.2072 + 5.35913i −1.21844 + 0.209239i
$$657$$ 0 0
$$658$$ −10.8120 + 11.7728i −0.421496 + 0.458953i
$$659$$ 24.8761 + 24.8761i 0.969034 + 0.969034i 0.999535 0.0305007i $$-0.00971017\pi$$
−0.0305007 + 0.999535i $$0.509710\pi$$
$$660$$ 0 0
$$661$$ −21.1349 + 21.1349i −0.822052 + 0.822052i −0.986402 0.164350i $$-0.947447\pi$$
0.164350 + 0.986402i $$0.447447\pi$$
$$662$$ −11.0819 + 0.471454i −0.430710 + 0.0183236i
$$663$$ 0 0
$$664$$ −27.3298 + 3.50498i −1.06060 + 0.136019i
$$665$$ 0.378607 + 0.102666i 0.0146818 + 0.00398120i
$$666$$ 0 0
$$667$$ 1.33529 1.33529i 0.0517025 0.0517025i
$$668$$ 1.59990 + 18.7694i 0.0619019 + 0.726209i
$$669$$ 0 0
$$670$$ 22.1327 13.9724i 0.855062 0.539800i
$$671$$ 28.7530 1.11000
$$672$$ 0 0
$$673$$ 48.6471i 1.87521i −0.347705 0.937604i $$-0.613039\pi$$
0.347705 0.937604i $$-0.386961\pi$$
$$674$$ 17.0458 + 15.6547i 0.656581 + 0.602995i
$$675$$ 0 0
$$676$$ −7.69302 + 0.655751i −0.295886 + 0.0252212i
$$677$$ 8.69556 8.69556i 0.334197 0.334197i −0.519981 0.854178i $$-0.674061\pi$$
0.854178 + 0.519981i $$0.174061\pi$$
$$678$$ 0 0
$$679$$ −8.16566 −0.313369
$$680$$ 28.6147 + 3.95214i 1.09732 + 0.151558i
$$681$$ 0 0
$$682$$ 57.2420 2.43523i 2.19191 0.0932498i
$$683$$ 26.4514 + 26.4514i 1.01213 + 1.01213i 0.999925 + 0.0122093i $$0.00388645\pi$$
0.0122093 + 0.999925i $$0.496114\pi$$
$$684$$ 0 0
$$685$$ −25.7781 44.9599i −0.984930 1.71783i
$$686$$ −20.1188 18.4768i −0.768138 0.705448i
$$687$$ 0 0
$$688$$ 7.67929 10.8636i 0.292770 0.414172i
$$689$$ 20.9881i 0.799582i
$$690$$ 0 0
$$691$$ 8.89820 8.89820i 0.338503 0.338503i −0.517301 0.855804i $$-0.673063\pi$$
0.855804 + 0.517301i $$0.173063\pi$$
$$692$$ 11.3384 13.4515i 0.431021 0.511349i
$$693$$ 0 0
$$694$$ 37.3198 1.58768i 1.41664 0.0602677i
$$695$$ −23.9688 6.49953i −0.909187 0.246541i
$$696$$ 0 0
$$697$$ 36.1550 1.36947
$$698$$ −30.4425 + 1.29511i −1.15226 + 0.0490205i
$$699$$ 0 0
$$700$$ 7.68894 16.1408i 0.290615 0.610064i
$$701$$ −15.7989 + 15.7989i −0.596716 + 0.596716i −0.939437 0.342721i $$-0.888651\pi$$
0.342721 + 0.939437i $$0.388651\pi$$
$$702$$ 0 0
$$703$$ 1.05806 0.0399053
$$704$$ 32.6390 + 19.1367i 1.23013 + 0.721241i
$$705$$ 0 0
$$706$$ −7.87519 + 8.57503i −0.296387 + 0.322726i
$$707$$ 11.1686 11.1686i 0.420037 0.420037i
$$708$$ 0 0
$$709$$ 18.9259 18.9259i 0.710776 0.710776i −0.255922 0.966697i $$-0.582379\pi$$
0.966697 + 0.255922i $$0.0823790\pi$$
$$710$$ −46.7086 10.5569i −1.75294 0.396194i
$$711$$ 0 0
$$712$$ 14.1364 + 10.9227i 0.529785 + 0.409344i
$$713$$ 9.22531i 0.345490i
$$714$$ 0 0
$$715$$ 21.5990 + 37.6711i 0.807757 + 1.40882i
$$716$$ −33.5452 + 39.7968i −1.25364 + 1.48728i
$$717$$ 0 0
$$718$$ 5.17512 + 4.75276i 0.193134 + 0.177372i
$$719$$ 10.6789 0.398256 0.199128 0.979973i $$-0.436189\pi$$
0.199128 + 0.979973i $$0.436189\pi$$
$$720$$ 0 0
$$721$$ 24.7704 0.922498
$$722$$ −19.7804 18.1660i −0.736150 0.676070i
$$723$$ 0 0
$$724$$ 40.1669 + 33.8571i 1.49279 + 1.25829i
$$725$$ 2.21828 + 8.48197i 0.0823850 + 0.315012i
$$726$$ 0 0
$$727$$ 32.2573i 1.19636i 0.801363 + 0.598179i $$0.204109\pi$$
−0.801363 + 0.598179i $$0.795891\pi$$
$$728$$ −2.64131 20.5954i −0.0978935 0.763317i
$$729$$ 0 0
$$730$$ 4.79716 21.2248i 0.177551 0.785566i
$$731$$ −10.7414 + 10.7414i −0.397285 + 0.397285i
$$732$$ 0 0
$$733$$ 29.6986 29.6986i 1.09694 1.09694i 0.102175 0.994766i $$-0.467420\pi$$
0.994766 0.102175i $$-0.0325801\pi$$
$$734$$ −24.2773 + 26.4347i −0.896092 + 0.975724i
$$735$$ 0 0
$$736$$ −3.30194 + 5.11973i −0.121711 + 0.188716i
$$737$$ −39.1453 −1.44194
$$738$$ 0 0
$$739$$ 19.7806 19.7806i 0.727640 0.727640i −0.242509 0.970149i $$-0.577970\pi$$
0.970149 + 0.242509i $$0.0779704\pi$$
$$740$$ 8.62202 47.4450i 0.316952 1.74411i
$$741$$ 0 0
$$742$$ −12.9120 + 0.549312i −0.474014 + 0.0201659i
$$743$$ −34.3449 −1.25999 −0.629996 0.776598i $$-0.716944\pi$$
−0.629996 + 0.776598i $$0.716944\pi$$
$$744$$ 0 0
$$745$$ −41.5312 11.2619i −1.52159 0.412604i
$$746$$ −5.70913 + 0.242882i −0.209026 + 0.00889255i
$$747$$ 0 0
$$748$$ −33.0323 27.8433i −1.20778 1.01805i
$$749$$ −1.64878 + 1.64878i −0.0602451 + 0.0602451i
$$750$$ 0 0
$$751$$ 48.4556i 1.76817i −0.467326 0.884085i $$-0.654783\pi$$
0.467326 0.884085i $$-0.345217\pi$$
$$752$$ 4.27991 + 24.9227i 0.156072 + 0.908837i
$$753$$ 0 0
$$754$$ 7.49944 + 6.88739i 0.273114 + 0.250824i
$$755$$ 29.5722 16.9554i 1.07624 0.617071i
$$756$$ 0 0
$$757$$ −24.8358 24.8358i −0.902672 0.902672i 0.0929947 0.995667i $$-0.470356\pi$$
−0.995667 + 0.0929947i $$0.970356\pi$$
$$758$$ 17.9068 0.761803i 0.650403 0.0276699i
$$759$$ 0 0
$$760$$ 0.494739 0.374661i 0.0179461 0.0135904i
$$761$$ −26.2421 −0.951274 −0.475637 0.879642i $$-0.657782\pi$$
−0.475637 + 0.879642i $$0.657782\pi$$
$$762$$ 0 0
$$763$$ 4.08816 4.08816i 0.148001 0.148001i
$$764$$ −0.804105 9.43345i −0.0290915 0.341290i
$$765$$ 0 0
$$766$$ 10.2461 + 9.40988i 0.370207 + 0.339993i
$$767$$ 13.0704i 0.471943i
$$768$$ 0 0
$$769$$ 25.4168 0.916552 0.458276 0.888810i $$-0.348467\pi$$
0.458276 + 0.888810i $$0.348467\pi$$
$$770$$ −22.6102 + 14.2738i −0.814815 + 0.514392i
$$771$$ 0 0
$$772$$ 33.3227 2.84042i 1.19931 0.102229i
$$773$$ 30.1984 30.1984i 1.08616 1.08616i 0.0902412 0.995920i $$-0.471236\pi$$
0.995920 0.0902412i $$-0.0287638\pi$$
$$774$$ 0 0
$$775$$ −36.9633 21.6374i −1.32776 0.777240i
$$776$$ −7.89839 + 10.2223i −0.283536 + 0.366960i
$$777$$ 0 0
$$778$$ 17.3820 0.739478i 0.623175 0.0265116i
$$779$$ 0.549249 0.549249i 0.0196789 0.0196789i
$$780$$ 0 0
$$781$$ 50.6417 + 50.6417i 1.81210 + 1.81210i
$$782$$ 4.70528 5.12341i 0.168260 0.183213i
$$783$$ 0 0
$$784$$ −14.9947 + 2.57501i −0.535526 + 0.0919645i
$$785$$ −4.77447 + 17.6071i −0.170408 + 0.628425i
$$786$$ 0 0
$$787$$ 19.3428 + 19.3428i 0.689496 + 0.689496i 0.962120 0.272625i $$-0.0878917\pi$$
−0.272625 + 0.962120i $$0.587892\pi$$
$$788$$ 17.1511 + 14.4569i 0.610984 + 0.515005i
$$789$$ 0 0
$$790$$ −40.0120 9.04338i −1.42356 0.321749i
$$791$$ 13.4764i 0.479165i</