# Properties

 Label 252.2.b.d.55.2 Level $252$ Weight $2$ Character 252.55 Analytic conductor $2.012$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.01223013094$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: 4.0.2312.1 Defining polynomial: $$x^{4} - x^{3} - 2 x + 4$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 55.2 Root $$-0.780776 + 1.17915i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.55 Dual form 252.2.b.d.55.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.780776 + 1.17915i) q^{2} +(-0.780776 - 1.84130i) q^{4} -1.69614i q^{5} +(-2.56155 + 0.662153i) q^{7} +(2.78078 + 0.516994i) q^{8} +O(q^{10})$$ $$q+(-0.780776 + 1.17915i) q^{2} +(-0.780776 - 1.84130i) q^{4} -1.69614i q^{5} +(-2.56155 + 0.662153i) q^{7} +(2.78078 + 0.516994i) q^{8} +(2.00000 + 1.32431i) q^{10} -3.02045i q^{11} -6.04090i q^{13} +(1.21922 - 3.53744i) q^{14} +(-2.78078 + 2.87529i) q^{16} -4.34475i q^{17} +1.12311 q^{19} +(-3.12311 + 1.32431i) q^{20} +(3.56155 + 2.35829i) q^{22} +3.02045i q^{23} +2.12311 q^{25} +(7.12311 + 4.71659i) q^{26} +(3.21922 + 4.19960i) q^{28} +2.00000 q^{29} +(-1.21922 - 5.52390i) q^{32} +(5.12311 + 3.39228i) q^{34} +(1.12311 + 4.34475i) q^{35} -7.12311 q^{37} +(-0.876894 + 1.32431i) q^{38} +(0.876894 - 4.71659i) q^{40} +7.73704i q^{41} -8.10887i q^{43} +(-5.56155 + 2.35829i) q^{44} +(-3.56155 - 2.35829i) q^{46} -10.2462 q^{47} +(6.12311 - 3.39228i) q^{49} +(-1.65767 + 2.50345i) q^{50} +(-11.1231 + 4.71659i) q^{52} +4.24621 q^{53} -5.12311 q^{55} +(-7.46543 + 0.516994i) q^{56} +(-1.56155 + 2.35829i) q^{58} +4.00000 q^{59} +9.43318i q^{61} +(7.46543 + 2.87529i) q^{64} -10.2462 q^{65} +2.06798i q^{67} +(-8.00000 + 3.39228i) q^{68} +(-6.00000 - 2.06798i) q^{70} -12.4536i q^{71} +3.39228i q^{73} +(5.56155 - 8.39919i) q^{74} +(-0.876894 - 2.06798i) q^{76} +(2.00000 + 7.73704i) q^{77} +4.71659i q^{79} +(4.87689 + 4.71659i) q^{80} +(-9.12311 - 6.04090i) q^{82} +6.24621 q^{83} -7.36932 q^{85} +(9.56155 + 6.33122i) q^{86} +(1.56155 - 8.39919i) q^{88} -7.73704i q^{89} +(4.00000 + 15.4741i) q^{91} +(5.56155 - 2.35829i) q^{92} +(8.00000 - 12.0818i) q^{94} -1.90495i q^{95} +8.68951i q^{97} +(-0.780776 + 9.86866i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + q^{2} + q^{4} - 2 q^{7} + 7 q^{8} + O(q^{10})$$ $$4 q + q^{2} + q^{4} - 2 q^{7} + 7 q^{8} + 8 q^{10} + 9 q^{14} - 7 q^{16} - 12 q^{19} + 4 q^{20} + 6 q^{22} - 8 q^{25} + 12 q^{26} + 17 q^{28} + 8 q^{29} - 9 q^{32} + 4 q^{34} - 12 q^{35} - 12 q^{37} - 20 q^{38} + 20 q^{40} - 14 q^{44} - 6 q^{46} - 8 q^{47} + 8 q^{49} - 19 q^{50} - 28 q^{52} - 16 q^{53} - 4 q^{55} - q^{56} + 2 q^{58} + 16 q^{59} + q^{64} - 8 q^{65} - 32 q^{68} - 24 q^{70} + 14 q^{74} - 20 q^{76} + 8 q^{77} + 36 q^{80} - 20 q^{82} - 8 q^{83} + 20 q^{85} + 30 q^{86} - 2 q^{88} + 16 q^{91} + 14 q^{92} + 32 q^{94} + q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.780776 + 1.17915i −0.552092 + 0.833783i
$$3$$ 0 0
$$4$$ −0.780776 1.84130i −0.390388 0.920650i
$$5$$ 1.69614i 0.758537i −0.925287 0.379269i $$-0.876176\pi$$
0.925287 0.379269i $$-0.123824\pi$$
$$6$$ 0 0
$$7$$ −2.56155 + 0.662153i −0.968176 + 0.250270i
$$8$$ 2.78078 + 0.516994i 0.983153 + 0.182785i
$$9$$ 0 0
$$10$$ 2.00000 + 1.32431i 0.632456 + 0.418783i
$$11$$ 3.02045i 0.910699i −0.890313 0.455350i $$-0.849514\pi$$
0.890313 0.455350i $$-0.150486\pi$$
$$12$$ 0 0
$$13$$ 6.04090i 1.67544i −0.546098 0.837722i $$-0.683887\pi$$
0.546098 0.837722i $$-0.316113\pi$$
$$14$$ 1.21922 3.53744i 0.325851 0.945421i
$$15$$ 0 0
$$16$$ −2.78078 + 2.87529i −0.695194 + 0.718822i
$$17$$ 4.34475i 1.05376i −0.849940 0.526879i $$-0.823362\pi$$
0.849940 0.526879i $$-0.176638\pi$$
$$18$$ 0 0
$$19$$ 1.12311 0.257658 0.128829 0.991667i $$-0.458878\pi$$
0.128829 + 0.991667i $$0.458878\pi$$
$$20$$ −3.12311 + 1.32431i −0.698348 + 0.296124i
$$21$$ 0 0
$$22$$ 3.56155 + 2.35829i 0.759326 + 0.502790i
$$23$$ 3.02045i 0.629807i 0.949124 + 0.314903i $$0.101972\pi$$
−0.949124 + 0.314903i $$0.898028\pi$$
$$24$$ 0 0
$$25$$ 2.12311 0.424621
$$26$$ 7.12311 + 4.71659i 1.39696 + 0.924999i
$$27$$ 0 0
$$28$$ 3.21922 + 4.19960i 0.608376 + 0.793649i
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.21922 5.52390i −0.215530 0.976497i
$$33$$ 0 0
$$34$$ 5.12311 + 3.39228i 0.878605 + 0.581772i
$$35$$ 1.12311 + 4.34475i 0.189839 + 0.734398i
$$36$$ 0 0
$$37$$ −7.12311 −1.17103 −0.585516 0.810661i $$-0.699108\pi$$
−0.585516 + 0.810661i $$0.699108\pi$$
$$38$$ −0.876894 + 1.32431i −0.142251 + 0.214831i
$$39$$ 0 0
$$40$$ 0.876894 4.71659i 0.138649 0.745758i
$$41$$ 7.73704i 1.20832i 0.796862 + 0.604161i $$0.206492\pi$$
−0.796862 + 0.604161i $$0.793508\pi$$
$$42$$ 0 0
$$43$$ 8.10887i 1.23659i −0.785946 0.618296i $$-0.787823\pi$$
0.785946 0.618296i $$-0.212177\pi$$
$$44$$ −5.56155 + 2.35829i −0.838436 + 0.355526i
$$45$$ 0 0
$$46$$ −3.56155 2.35829i −0.525122 0.347712i
$$47$$ −10.2462 −1.49456 −0.747282 0.664507i $$-0.768641\pi$$
−0.747282 + 0.664507i $$0.768641\pi$$
$$48$$ 0 0
$$49$$ 6.12311 3.39228i 0.874729 0.484612i
$$50$$ −1.65767 + 2.50345i −0.234430 + 0.354042i
$$51$$ 0 0
$$52$$ −11.1231 + 4.71659i −1.54250 + 0.654073i
$$53$$ 4.24621 0.583262 0.291631 0.956531i $$-0.405802\pi$$
0.291631 + 0.956531i $$0.405802\pi$$
$$54$$ 0 0
$$55$$ −5.12311 −0.690799
$$56$$ −7.46543 + 0.516994i −0.997611 + 0.0690862i
$$57$$ 0 0
$$58$$ −1.56155 + 2.35829i −0.205042 + 0.309659i
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ 9.43318i 1.20779i 0.797062 + 0.603897i $$0.206386\pi$$
−0.797062 + 0.603897i $$0.793614\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 7.46543 + 2.87529i 0.933179 + 0.359411i
$$65$$ −10.2462 −1.27089
$$66$$ 0 0
$$67$$ 2.06798i 0.252643i 0.991989 + 0.126322i $$0.0403172\pi$$
−0.991989 + 0.126322i $$0.959683\pi$$
$$68$$ −8.00000 + 3.39228i −0.970143 + 0.411375i
$$69$$ 0 0
$$70$$ −6.00000 2.06798i −0.717137 0.247170i
$$71$$ 12.4536i 1.47797i −0.673720 0.738987i $$-0.735305\pi$$
0.673720 0.738987i $$-0.264695\pi$$
$$72$$ 0 0
$$73$$ 3.39228i 0.397037i 0.980097 + 0.198518i $$0.0636129\pi$$
−0.980097 + 0.198518i $$0.936387\pi$$
$$74$$ 5.56155 8.39919i 0.646517 0.976386i
$$75$$ 0 0
$$76$$ −0.876894 2.06798i −0.100587 0.237213i
$$77$$ 2.00000 + 7.73704i 0.227921 + 0.881717i
$$78$$ 0 0
$$79$$ 4.71659i 0.530658i 0.964158 + 0.265329i $$0.0854805\pi$$
−0.964158 + 0.265329i $$0.914519\pi$$
$$80$$ 4.87689 + 4.71659i 0.545253 + 0.527331i
$$81$$ 0 0
$$82$$ −9.12311 6.04090i −1.00748 0.667105i
$$83$$ 6.24621 0.685611 0.342805 0.939406i $$-0.388623\pi$$
0.342805 + 0.939406i $$0.388623\pi$$
$$84$$ 0 0
$$85$$ −7.36932 −0.799315
$$86$$ 9.56155 + 6.33122i 1.03105 + 0.682712i
$$87$$ 0 0
$$88$$ 1.56155 8.39919i 0.166462 0.895357i
$$89$$ 7.73704i 0.820124i −0.912058 0.410062i $$-0.865507\pi$$
0.912058 0.410062i $$-0.134493\pi$$
$$90$$ 0 0
$$91$$ 4.00000 + 15.4741i 0.419314 + 1.62212i
$$92$$ 5.56155 2.35829i 0.579832 0.245869i
$$93$$ 0 0
$$94$$ 8.00000 12.0818i 0.825137 1.24614i
$$95$$ 1.90495i 0.195443i
$$96$$ 0 0
$$97$$ 8.68951i 0.882286i 0.897437 + 0.441143i $$0.145427\pi$$
−0.897437 + 0.441143i $$0.854573\pi$$
$$98$$ −0.780776 + 9.86866i −0.0788703 + 0.996885i
$$99$$ 0 0
$$100$$ −1.65767 3.90928i −0.165767 0.390928i
$$101$$ 6.99337i 0.695866i 0.937519 + 0.347933i $$0.113116\pi$$
−0.937519 + 0.347933i $$0.886884\pi$$
$$102$$ 0 0
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ 3.12311 16.7984i 0.306246 1.64722i
$$105$$ 0 0
$$106$$ −3.31534 + 5.00691i −0.322014 + 0.486314i
$$107$$ 5.66906i 0.548049i 0.961723 + 0.274024i $$0.0883549\pi$$
−0.961723 + 0.274024i $$0.911645\pi$$
$$108$$ 0 0
$$109$$ 8.24621 0.789844 0.394922 0.918715i $$-0.370772\pi$$
0.394922 + 0.918715i $$0.370772\pi$$
$$110$$ 4.00000 6.04090i 0.381385 0.575977i
$$111$$ 0 0
$$112$$ 5.21922 9.20650i 0.493170 0.869933i
$$113$$ −12.2462 −1.15203 −0.576013 0.817440i $$-0.695392\pi$$
−0.576013 + 0.817440i $$0.695392\pi$$
$$114$$ 0 0
$$115$$ 5.12311 0.477732
$$116$$ −1.56155 3.68260i −0.144987 0.341921i
$$117$$ 0 0
$$118$$ −3.12311 + 4.71659i −0.287505 + 0.434197i
$$119$$ 2.87689 + 11.1293i 0.263724 + 1.02022i
$$120$$ 0 0
$$121$$ 1.87689 0.170627
$$122$$ −11.1231 7.36520i −1.00704 0.666814i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0818i 1.08063i
$$126$$ 0 0
$$127$$ 19.4470i 1.72564i −0.505510 0.862821i $$-0.668696\pi$$
0.505510 0.862821i $$-0.331304\pi$$
$$128$$ −9.21922 + 6.55789i −0.814872 + 0.579641i
$$129$$ 0 0
$$130$$ 8.00000 12.0818i 0.701646 1.05964i
$$131$$ 22.2462 1.94366 0.971830 0.235682i $$-0.0757323\pi$$
0.971830 + 0.235682i $$0.0757323\pi$$
$$132$$ 0 0
$$133$$ −2.87689 + 0.743668i −0.249458 + 0.0644842i
$$134$$ −2.43845 1.61463i −0.210650 0.139482i
$$135$$ 0 0
$$136$$ 2.24621 12.0818i 0.192611 1.03601i
$$137$$ 16.2462 1.38801 0.694004 0.719971i $$-0.255845\pi$$
0.694004 + 0.719971i $$0.255845\pi$$
$$138$$ 0 0
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 7.12311 5.46026i 0.602012 0.461476i
$$141$$ 0 0
$$142$$ 14.6847 + 9.72350i 1.23231 + 0.815978i
$$143$$ −18.2462 −1.52582
$$144$$ 0 0
$$145$$ 3.39228i 0.281714i
$$146$$ −4.00000 2.64861i −0.331042 0.219201i
$$147$$ 0 0
$$148$$ 5.56155 + 13.1158i 0.457157 + 1.07811i
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ 8.10887i 0.659891i 0.944000 + 0.329945i $$0.107030\pi$$
−0.944000 + 0.329945i $$0.892970\pi$$
$$152$$ 3.12311 + 0.580639i 0.253317 + 0.0470960i
$$153$$ 0 0
$$154$$ −10.6847 3.68260i −0.860994 0.296752i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 4.13595i 0.330085i −0.986286 0.165042i $$-0.947224\pi$$
0.986286 0.165042i $$-0.0527761\pi$$
$$158$$ −5.56155 3.68260i −0.442453 0.292972i
$$159$$ 0 0
$$160$$ −9.36932 + 2.06798i −0.740710 + 0.163488i
$$161$$ −2.00000 7.73704i −0.157622 0.609764i
$$162$$ 0 0
$$163$$ 11.5012i 0.900840i −0.892817 0.450420i $$-0.851274\pi$$
0.892817 0.450420i $$-0.148726\pi$$
$$164$$ 14.2462 6.04090i 1.11244 0.471715i
$$165$$ 0 0
$$166$$ −4.87689 + 7.36520i −0.378520 + 0.571651i
$$167$$ −2.24621 −0.173817 −0.0869085 0.996216i $$-0.527699\pi$$
−0.0869085 + 0.996216i $$0.527699\pi$$
$$168$$ 0 0
$$169$$ −23.4924 −1.80711
$$170$$ 5.75379 8.68951i 0.441295 0.666455i
$$171$$ 0 0
$$172$$ −14.9309 + 6.33122i −1.13847 + 0.482751i
$$173$$ 8.48071i 0.644776i 0.946608 + 0.322388i $$0.104486\pi$$
−0.946608 + 0.322388i $$0.895514\pi$$
$$174$$ 0 0
$$175$$ −5.43845 + 1.40582i −0.411108 + 0.106270i
$$176$$ 8.68466 + 8.39919i 0.654631 + 0.633113i
$$177$$ 0 0
$$178$$ 9.12311 + 6.04090i 0.683806 + 0.452784i
$$179$$ 2.27678i 0.170175i 0.996374 + 0.0850873i $$0.0271169\pi$$
−0.996374 + 0.0850873i $$0.972883\pi$$
$$180$$ 0 0
$$181$$ 6.04090i 0.449016i 0.974472 + 0.224508i $$0.0720775\pi$$
−0.974472 + 0.224508i $$0.927922\pi$$
$$182$$ −21.3693 7.36520i −1.58400 0.545945i
$$183$$ 0 0
$$184$$ −1.56155 + 8.39919i −0.115119 + 0.619197i
$$185$$ 12.0818i 0.888271i
$$186$$ 0 0
$$187$$ −13.1231 −0.959657
$$188$$ 8.00000 + 18.8664i 0.583460 + 1.37597i
$$189$$ 0 0
$$190$$ 2.24621 + 1.48734i 0.162957 + 0.107903i
$$191$$ 9.06134i 0.655656i −0.944737 0.327828i $$-0.893683\pi$$
0.944737 0.327828i $$-0.106317\pi$$
$$192$$ 0 0
$$193$$ 9.36932 0.674418 0.337209 0.941430i $$-0.390517\pi$$
0.337209 + 0.941430i $$0.390517\pi$$
$$194$$ −10.2462 6.78456i −0.735635 0.487103i
$$195$$ 0 0
$$196$$ −11.0270 8.62586i −0.787642 0.616133i
$$197$$ −0.246211 −0.0175418 −0.00877091 0.999962i $$-0.502792\pi$$
−0.00877091 + 0.999962i $$0.502792\pi$$
$$198$$ 0 0
$$199$$ −5.12311 −0.363167 −0.181584 0.983375i $$-0.558122\pi$$
−0.181584 + 0.983375i $$0.558122\pi$$
$$200$$ 5.90388 + 1.09763i 0.417468 + 0.0776143i
$$201$$ 0 0
$$202$$ −8.24621 5.46026i −0.580201 0.384182i
$$203$$ −5.12311 + 1.32431i −0.359572 + 0.0929481i
$$204$$ 0 0
$$205$$ 13.1231 0.916557
$$206$$ −6.24621 + 9.43318i −0.435194 + 0.657241i
$$207$$ 0 0
$$208$$ 17.3693 + 16.7984i 1.20435 + 1.16476i
$$209$$ 3.39228i 0.234649i
$$210$$ 0 0
$$211$$ 3.97292i 0.273507i 0.990605 + 0.136754i $$0.0436668\pi$$
−0.990605 + 0.136754i $$0.956333\pi$$
$$212$$ −3.31534 7.81855i −0.227699 0.536980i
$$213$$ 0 0
$$214$$ −6.68466 4.42627i −0.456954 0.302574i
$$215$$ −13.7538 −0.938001
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −6.43845 + 9.72350i −0.436067 + 0.658558i
$$219$$ 0 0
$$220$$ 4.00000 + 9.43318i 0.269680 + 0.635985i
$$221$$ −26.2462 −1.76551
$$222$$ 0 0
$$223$$ −18.8769 −1.26409 −0.632045 0.774932i $$-0.717784\pi$$
−0.632045 + 0.774932i $$0.717784\pi$$
$$224$$ 6.78078 + 13.3425i 0.453060 + 0.891480i
$$225$$ 0 0
$$226$$ 9.56155 14.4401i 0.636025 0.960540i
$$227$$ 16.4924 1.09464 0.547320 0.836923i $$-0.315648\pi$$
0.547320 + 0.836923i $$0.315648\pi$$
$$228$$ 0 0
$$229$$ 18.1227i 1.19758i −0.800906 0.598790i $$-0.795648\pi$$
0.800906 0.598790i $$-0.204352\pi$$
$$230$$ −4.00000 + 6.04090i −0.263752 + 0.398325i
$$231$$ 0 0
$$232$$ 5.56155 + 1.03399i 0.365134 + 0.0678846i
$$233$$ 10.4924 0.687381 0.343691 0.939083i $$-0.388323\pi$$
0.343691 + 0.939083i $$0.388323\pi$$
$$234$$ 0 0
$$235$$ 17.3790i 1.13368i
$$236$$ −3.12311 7.36520i −0.203297 0.479434i
$$237$$ 0 0
$$238$$ −15.3693 5.29723i −0.996245 0.343368i
$$239$$ 2.27678i 0.147273i −0.997285 0.0736363i $$-0.976540\pi$$
0.997285 0.0736363i $$-0.0234604\pi$$
$$240$$ 0 0
$$241$$ 1.90495i 0.122708i −0.998116 0.0613542i $$-0.980458\pi$$
0.998116 0.0613542i $$-0.0195419\pi$$
$$242$$ −1.46543 + 2.21313i −0.0942017 + 0.142266i
$$243$$ 0 0
$$244$$ 17.3693 7.36520i 1.11196 0.471509i
$$245$$ −5.75379 10.3857i −0.367596 0.663515i
$$246$$ 0 0
$$247$$ 6.78456i 0.431691i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 14.2462 + 9.43318i 0.901010 + 0.596607i
$$251$$ −22.2462 −1.40417 −0.702084 0.712094i $$-0.747747\pi$$
−0.702084 + 0.712094i $$0.747747\pi$$
$$252$$ 0 0
$$253$$ 9.12311 0.573565
$$254$$ 22.9309 + 15.1838i 1.43881 + 0.952713i
$$255$$ 0 0
$$256$$ −0.534565 15.9911i −0.0334103 0.999442i
$$257$$ 19.8188i 1.23626i 0.786074 + 0.618132i $$0.212110\pi$$
−0.786074 + 0.618132i $$0.787890\pi$$
$$258$$ 0 0
$$259$$ 18.2462 4.71659i 1.13376 0.293075i
$$260$$ 8.00000 + 18.8664i 0.496139 + 1.17004i
$$261$$ 0 0
$$262$$ −17.3693 + 26.2316i −1.07308 + 1.62059i
$$263$$ 4.92539i 0.303713i 0.988403 + 0.151856i $$0.0485251\pi$$
−0.988403 + 0.151856i $$0.951475\pi$$
$$264$$ 0 0
$$265$$ 7.20217i 0.442426i
$$266$$ 1.36932 3.97292i 0.0839582 0.243595i
$$267$$ 0 0
$$268$$ 3.80776 1.61463i 0.232596 0.0986290i
$$269$$ 22.4674i 1.36986i −0.728607 0.684932i $$-0.759832\pi$$
0.728607 0.684932i $$-0.240168\pi$$
$$270$$ 0 0
$$271$$ −4.49242 −0.272895 −0.136448 0.990647i $$-0.543569\pi$$
−0.136448 + 0.990647i $$0.543569\pi$$
$$272$$ 12.4924 + 12.0818i 0.757464 + 0.732566i
$$273$$ 0 0
$$274$$ −12.6847 + 19.1567i −0.766308 + 1.15730i
$$275$$ 6.41273i 0.386702i
$$276$$ 0 0
$$277$$ 3.12311 0.187649 0.0938246 0.995589i $$-0.470091\pi$$
0.0938246 + 0.995589i $$0.470091\pi$$
$$278$$ −9.36932 + 14.1498i −0.561934 + 0.848647i
$$279$$ 0 0
$$280$$ 0.876894 + 12.6624i 0.0524045 + 0.756725i
$$281$$ 0.246211 0.0146877 0.00734387 0.999973i $$-0.497662\pi$$
0.00734387 + 0.999973i $$0.497662\pi$$
$$282$$ 0 0
$$283$$ −17.1231 −1.01786 −0.508931 0.860807i $$-0.669959\pi$$
−0.508931 + 0.860807i $$0.669959\pi$$
$$284$$ −22.9309 + 9.72350i −1.36070 + 0.576983i
$$285$$ 0 0
$$286$$ 14.2462 21.5150i 0.842396 1.27221i
$$287$$ −5.12311 19.8188i −0.302407 1.16987i
$$288$$ 0 0
$$289$$ −1.87689 −0.110406
$$290$$ 4.00000 + 2.64861i 0.234888 + 0.155532i
$$291$$ 0 0
$$292$$ 6.24621 2.64861i 0.365532 0.154998i
$$293$$ 6.99337i 0.408557i 0.978913 + 0.204278i $$0.0654848\pi$$
−0.978913 + 0.204278i $$0.934515\pi$$
$$294$$ 0 0
$$295$$ 6.78456i 0.395013i
$$296$$ −19.8078 3.68260i −1.15130 0.214047i
$$297$$ 0 0
$$298$$ −7.80776 + 11.7915i −0.452292 + 0.683062i
$$299$$ 18.2462 1.05521
$$300$$ 0 0
$$301$$ 5.36932 + 20.7713i 0.309482 + 1.19724i
$$302$$ −9.56155 6.33122i −0.550206 0.364320i
$$303$$ 0 0
$$304$$ −3.12311 + 3.22925i −0.179122 + 0.185210i
$$305$$ 16.0000 0.916157
$$306$$ 0 0
$$307$$ 21.6155 1.23366 0.616832 0.787095i $$-0.288416\pi$$
0.616832 + 0.787095i $$0.288416\pi$$
$$308$$ 12.6847 9.72350i 0.722775 0.554048i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 8.00000 0.453638 0.226819 0.973937i $$-0.427167\pi$$
0.226819 + 0.973937i $$0.427167\pi$$
$$312$$ 0 0
$$313$$ 25.6509i 1.44988i −0.688814 0.724938i $$-0.741868\pi$$
0.688814 0.724938i $$-0.258132\pi$$
$$314$$ 4.87689 + 3.22925i 0.275219 + 0.182237i
$$315$$ 0 0
$$316$$ 8.68466 3.68260i 0.488550 0.207163i
$$317$$ −18.4924 −1.03864 −0.519319 0.854580i $$-0.673814\pi$$
−0.519319 + 0.854580i $$0.673814\pi$$
$$318$$ 0 0
$$319$$ 6.04090i 0.338225i
$$320$$ 4.87689 12.6624i 0.272627 0.707851i
$$321$$ 0 0
$$322$$ 10.6847 + 3.68260i 0.595433 + 0.205223i
$$323$$ 4.87962i 0.271509i
$$324$$ 0 0
$$325$$ 12.8255i 0.711429i
$$326$$ 13.5616 + 8.97983i 0.751105 + 0.497347i
$$327$$ 0 0
$$328$$ −4.00000 + 21.5150i −0.220863 + 1.18797i
$$329$$ 26.2462 6.78456i 1.44700 0.374045i
$$330$$ 0 0
$$331$$ 5.46026i 0.300123i 0.988677 + 0.150061i $$0.0479472\pi$$
−0.988677 + 0.150061i $$0.952053\pi$$
$$332$$ −4.87689 11.5012i −0.267654 0.631208i
$$333$$ 0 0
$$334$$ 1.75379 2.64861i 0.0959631 0.144926i
$$335$$ 3.50758 0.191639
$$336$$ 0 0
$$337$$ −8.24621 −0.449200 −0.224600 0.974451i $$-0.572108\pi$$
−0.224600 + 0.974451i $$0.572108\pi$$
$$338$$ 18.3423 27.7010i 0.997691 1.50674i
$$339$$ 0 0
$$340$$ 5.75379 + 13.5691i 0.312043 + 0.735889i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −13.4384 + 12.7439i −0.725608 + 0.688108i
$$344$$ 4.19224 22.5490i 0.226030 1.21576i
$$345$$ 0 0
$$346$$ −10.0000 6.62153i −0.537603 0.355976i
$$347$$ 34.7123i 1.86345i 0.363162 + 0.931726i $$0.381697\pi$$
−0.363162 + 0.931726i $$0.618303\pi$$
$$348$$ 0 0
$$349$$ 4.13595i 0.221392i −0.993854 0.110696i $$-0.964692\pi$$
0.993854 0.110696i $$-0.0353080\pi$$
$$350$$ 2.58854 7.51036i 0.138363 0.401446i
$$351$$ 0 0
$$352$$ −16.6847 + 3.68260i −0.889295 + 0.196283i
$$353$$ 6.24970i 0.332638i −0.986072 0.166319i $$-0.946812\pi$$
0.986072 0.166319i $$-0.0531881\pi$$
$$354$$ 0 0
$$355$$ −21.1231 −1.12110
$$356$$ −14.2462 + 6.04090i −0.755048 + 0.320167i
$$357$$ 0 0
$$358$$ −2.68466 1.77766i −0.141889 0.0939520i
$$359$$ 1.11550i 0.0588740i 0.999567 + 0.0294370i $$0.00937144\pi$$
−0.999567 + 0.0294370i $$0.990629\pi$$
$$360$$ 0 0
$$361$$ −17.7386 −0.933612
$$362$$ −7.12311 4.71659i −0.374382 0.247898i
$$363$$ 0 0
$$364$$ 25.3693 19.4470i 1.32971 1.01930i
$$365$$ 5.75379 0.301167
$$366$$ 0 0
$$367$$ 8.63068 0.450518 0.225259 0.974299i $$-0.427677\pi$$
0.225259 + 0.974299i $$0.427677\pi$$
$$368$$ −8.68466 8.39919i −0.452719 0.437838i
$$369$$ 0 0
$$370$$ −14.2462 9.43318i −0.740625 0.490408i
$$371$$ −10.8769 + 2.81164i −0.564700 + 0.145973i
$$372$$ 0 0
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ 10.2462 15.4741i 0.529819 0.800145i
$$375$$ 0 0
$$376$$ −28.4924 5.29723i −1.46938 0.273184i
$$377$$ 12.0818i 0.622244i
$$378$$ 0 0
$$379$$ 18.7033i 0.960725i −0.877070 0.480363i $$-0.840505\pi$$
0.877070 0.480363i $$-0.159495\pi$$
$$380$$ −3.50758 + 1.48734i −0.179935 + 0.0762988i
$$381$$ 0 0
$$382$$ 10.6847 + 7.07488i 0.546675 + 0.361983i
$$383$$ −26.2462 −1.34112 −0.670559 0.741856i $$-0.733946\pi$$
−0.670559 + 0.741856i $$0.733946\pi$$
$$384$$ 0 0
$$385$$ 13.1231 3.39228i 0.668815 0.172887i
$$386$$ −7.31534 + 11.0478i −0.372341 + 0.562318i
$$387$$ 0 0
$$388$$ 16.0000 6.78456i 0.812277 0.344434i
$$389$$ −0.246211 −0.0124834 −0.00624170 0.999981i $$-0.501987\pi$$
−0.00624170 + 0.999981i $$0.501987\pi$$
$$390$$ 0 0
$$391$$ 13.1231 0.663664
$$392$$ 18.7808 6.26757i 0.948572 0.316560i
$$393$$ 0 0
$$394$$ 0.192236 0.290319i 0.00968471 0.0146261i
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ 16.2177i 0.813945i 0.913440 + 0.406973i $$0.133416\pi$$
−0.913440 + 0.406973i $$0.866584\pi$$
$$398$$ 4.00000 6.04090i 0.200502 0.302803i
$$399$$ 0 0
$$400$$ −5.90388 + 6.10454i −0.295194 + 0.305227i
$$401$$ 8.24621 0.411796 0.205898 0.978573i $$-0.433988\pi$$
0.205898 + 0.978573i $$0.433988\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 12.8769 5.46026i 0.640649 0.271658i
$$405$$ 0 0
$$406$$ 2.43845 7.07488i 0.121018 0.351121i
$$407$$ 21.5150i 1.06646i
$$408$$ 0 0
$$409$$ 27.5559i 1.36255i 0.732028 + 0.681275i $$0.238574\pi$$
−0.732028 + 0.681275i $$0.761426\pi$$
$$410$$ −10.2462 + 15.4741i −0.506024 + 0.764210i
$$411$$ 0 0
$$412$$ −6.24621 14.7304i −0.307729 0.725715i
$$413$$ −10.2462 + 2.64861i −0.504183 + 0.130330i
$$414$$ 0 0
$$415$$ 10.5945i 0.520061i
$$416$$ −33.3693 + 7.36520i −1.63607 + 0.361109i
$$417$$ 0 0
$$418$$ 4.00000 + 2.64861i 0.195646 + 0.129548i
$$419$$ 16.4924 0.805708 0.402854 0.915264i $$-0.368018\pi$$
0.402854 + 0.915264i $$0.368018\pi$$
$$420$$ 0 0
$$421$$ 19.1231 0.932003 0.466002 0.884784i $$-0.345694\pi$$
0.466002 + 0.884784i $$0.345694\pi$$
$$422$$ −4.68466 3.10196i −0.228046 0.151001i
$$423$$ 0 0
$$424$$ 11.8078 + 2.19526i 0.573436 + 0.106611i
$$425$$ 9.22437i 0.447448i
$$426$$ 0 0
$$427$$ −6.24621 24.1636i −0.302275 1.16936i
$$428$$ 10.4384 4.42627i 0.504561 0.213952i
$$429$$ 0 0
$$430$$ 10.7386 16.2177i 0.517863 0.782089i
$$431$$ 15.1022i 0.727449i 0.931507 + 0.363725i $$0.118495\pi$$
−0.931507 + 0.363725i $$0.881505\pi$$
$$432$$ 0 0
$$433$$ 6.78456i 0.326045i −0.986622 0.163023i $$-0.947876\pi$$
0.986622 0.163023i $$-0.0521244\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −6.43845 15.1838i −0.308346 0.727170i
$$437$$ 3.39228i 0.162275i
$$438$$ 0 0
$$439$$ 31.3693 1.49718 0.748588 0.663036i $$-0.230732\pi$$
0.748588 + 0.663036i $$0.230732\pi$$
$$440$$ −14.2462 2.64861i −0.679161 0.126268i
$$441$$ 0 0
$$442$$ 20.4924 30.9481i 0.974725 1.47205i
$$443$$ 35.8735i 1.70440i −0.523213 0.852202i $$-0.675267\pi$$
0.523213 0.852202i $$-0.324733\pi$$
$$444$$ 0 0
$$445$$ −13.1231 −0.622095
$$446$$ 14.7386 22.2586i 0.697895 1.05398i
$$447$$ 0 0
$$448$$ −21.0270 2.42194i −0.993432 0.114426i
$$449$$ −28.2462 −1.33302 −0.666511 0.745496i $$-0.732213\pi$$
−0.666511 + 0.745496i $$0.732213\pi$$
$$450$$ 0 0
$$451$$ 23.3693 1.10042
$$452$$ 9.56155 + 22.5490i 0.449738 + 1.06061i
$$453$$ 0 0
$$454$$ −12.8769 + 19.4470i −0.604343 + 0.912693i
$$455$$ 26.2462 6.78456i 1.23044 0.318065i
$$456$$ 0 0
$$457$$ −16.2462 −0.759966 −0.379983 0.924994i $$-0.624070\pi$$
−0.379983 + 0.924994i $$0.624070\pi$$
$$458$$ 21.3693 + 14.1498i 0.998523 + 0.661175i
$$459$$ 0 0
$$460$$ −4.00000 9.43318i −0.186501 0.439824i
$$461$$ 17.1702i 0.799697i 0.916581 + 0.399848i $$0.130937\pi$$
−0.916581 + 0.399848i $$0.869063\pi$$
$$462$$ 0 0
$$463$$ 39.4746i 1.83454i 0.398264 + 0.917271i $$0.369613\pi$$
−0.398264 + 0.917271i $$0.630387\pi$$
$$464$$ −5.56155 + 5.75058i −0.258189 + 0.266964i
$$465$$ 0 0
$$466$$ −8.19224 + 12.3721i −0.379498 + 0.573127i
$$467$$ 17.7538 0.821547 0.410774 0.911737i $$-0.365259\pi$$
0.410774 + 0.911737i $$0.365259\pi$$
$$468$$ 0 0
$$469$$ −1.36932 5.29723i −0.0632292 0.244603i
$$470$$ −20.4924 13.5691i −0.945245 0.625897i
$$471$$ 0 0
$$472$$ 11.1231 + 2.06798i 0.511982 + 0.0951863i
$$473$$ −24.4924 −1.12616
$$474$$ 0 0
$$475$$ 2.38447 0.109407
$$476$$ 18.2462 13.9867i 0.836314 0.641081i
$$477$$ 0 0
$$478$$ 2.68466 + 1.77766i 0.122793 + 0.0813081i
$$479$$ −20.4924 −0.936323 −0.468161 0.883643i $$-0.655083\pi$$
−0.468161 + 0.883643i $$0.655083\pi$$
$$480$$ 0 0
$$481$$ 43.0299i 1.96200i
$$482$$ 2.24621 + 1.48734i 0.102312 + 0.0677463i
$$483$$ 0 0
$$484$$ −1.46543 3.45593i −0.0666107 0.157088i
$$485$$ 14.7386 0.669247
$$486$$ 0 0
$$487$$ 32.2725i 1.46240i 0.682161 + 0.731202i $$0.261040\pi$$
−0.682161 + 0.731202i $$0.738960\pi$$
$$488$$ −4.87689 + 26.2316i −0.220767 + 1.18745i
$$489$$ 0 0
$$490$$ 16.7386 + 1.32431i 0.756174 + 0.0598261i
$$491$$ 11.7100i 0.528463i −0.964459 0.264231i $$-0.914882\pi$$
0.964459 0.264231i $$-0.0851183\pi$$
$$492$$ 0 0
$$493$$ 8.68951i 0.391356i
$$494$$ 8.00000 + 5.29723i 0.359937 + 0.238334i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 8.24621 + 31.9006i 0.369893 + 1.43094i
$$498$$ 0 0
$$499$$ 17.5420i 0.785290i 0.919690 + 0.392645i $$0.128440\pi$$
−0.919690 + 0.392645i $$0.871560\pi$$
$$500$$ −22.2462 + 9.43318i −0.994881 + 0.421865i
$$501$$ 0 0
$$502$$ 17.3693 26.2316i 0.775231 1.17077i
$$503$$ 22.7386 1.01387 0.506933 0.861986i $$-0.330779\pi$$
0.506933 + 0.861986i $$0.330779\pi$$
$$504$$ 0 0
$$505$$ 11.8617 0.527840
$$506$$ −7.12311 + 10.7575i −0.316661 + 0.478229i
$$507$$ 0 0
$$508$$ −35.8078 + 15.1838i −1.58871 + 0.673670i
$$509$$ 1.69614i 0.0751801i 0.999293 + 0.0375901i $$0.0119681\pi$$
−0.999293 + 0.0375901i $$0.988032\pi$$
$$510$$ 0 0
$$511$$ −2.24621 8.68951i −0.0993665 0.384401i
$$512$$ 19.2732 + 11.8551i 0.851763 + 0.523927i
$$513$$ 0 0
$$514$$ −23.3693 15.4741i −1.03078 0.682532i
$$515$$ 13.5691i 0.597927i
$$516$$ 0 0
$$517$$ 30.9481i 1.36110i
$$518$$ −8.68466 + 25.1976i −0.381582 + 1.10712i
$$519$$ 0 0
$$520$$ −28.4924 5.29723i −1.24948 0.232299i
$$521$$ 33.8056i 1.48105i 0.672030 + 0.740524i $$0.265423\pi$$
−0.672030 + 0.740524i $$0.734577\pi$$
$$522$$ 0 0
$$523$$ 0.492423 0.0215321 0.0107661 0.999942i $$-0.496573\pi$$
0.0107661 + 0.999942i $$0.496573\pi$$
$$524$$ −17.3693 40.9620i −0.758782 1.78943i
$$525$$ 0 0
$$526$$ −5.80776 3.84563i −0.253231 0.167677i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.8769 0.603343
$$530$$ 8.49242 + 5.62329i 0.368887 + 0.244260i
$$531$$ 0 0
$$532$$ 3.61553 + 4.71659i 0.156753 + 0.204490i
$$533$$ 46.7386 2.02447
$$534$$ 0 0
$$535$$ 9.61553 0.415716
$$536$$ −1.06913 + 5.75058i −0.0461794 + 0.248387i
$$537$$ 0 0
$$538$$ 26.4924 + 17.5420i 1.14217 + 0.756291i
$$539$$ −10.2462 18.4945i −0.441336 0.796615i
$$540$$ 0 0
$$541$$ 11.1231 0.478220 0.239110 0.970993i $$-0.423144\pi$$
0.239110 + 0.970993i $$0.423144\pi$$
$$542$$ 3.50758 5.29723i 0.150663 0.227535i
$$543$$ 0 0
$$544$$ −24.0000 + 5.29723i −1.02899 + 0.227117i
$$545$$ 13.9867i 0.599126i
$$546$$ 0 0
$$547$$ 33.0161i 1.41167i 0.708378 + 0.705834i $$0.249427\pi$$
−0.708378 + 0.705834i $$0.750573\pi$$
$$548$$ −12.6847 29.9142i −0.541862 1.27787i
$$549$$ 0 0
$$550$$ 7.56155 + 5.00691i 0.322426 + 0.213495i
$$551$$ 2.24621 0.0956918
$$552$$ 0 0
$$553$$ −3.12311 12.0818i −0.132808 0.513770i
$$554$$ −2.43845 + 3.68260i −0.103600 + 0.156459i
$$555$$ 0 0
$$556$$ −9.36932 22.0956i −0.397348 0.937063i
$$557$$ −14.0000 −0.593199 −0.296600 0.955002i $$-0.595853\pi$$
−0.296600 + 0.955002i $$0.595853\pi$$
$$558$$ 0 0
$$559$$ −48.9848 −2.07184
$$560$$ −15.6155 8.85254i −0.659877 0.374088i
$$561$$ 0 0
$$562$$ −0.192236 + 0.290319i −0.00810898 + 0.0122464i
$$563$$ −14.2462 −0.600406 −0.300203 0.953875i $$-0.597054\pi$$
−0.300203 + 0.953875i $$0.597054\pi$$
$$564$$ 0 0
$$565$$ 20.7713i 0.873855i
$$566$$ 13.3693 20.1907i 0.561954 0.848677i
$$567$$ 0 0
$$568$$ 6.43845 34.6307i 0.270151 1.45307i
$$569$$ −34.9848 −1.46664 −0.733320 0.679883i $$-0.762031\pi$$
−0.733320 + 0.679883i $$0.762031\pi$$
$$570$$ 0 0
$$571$$ 40.9620i 1.71420i −0.515146 0.857102i $$-0.672262\pi$$
0.515146 0.857102i $$-0.327738\pi$$
$$572$$ 14.2462 + 33.5968i 0.595664 + 1.40475i
$$573$$ 0 0
$$574$$ 27.3693 + 9.43318i 1.14237 + 0.393733i
$$575$$ 6.41273i 0.267429i
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 1.46543 2.21313i 0.0609541 0.0920543i
$$579$$ 0 0
$$580$$ −6.24621 + 2.64861i −0.259360 + 0.109978i
$$581$$ −16.0000 + 4.13595i −0.663792 + 0.171588i
$$582$$ 0 0
$$583$$ 12.8255i 0.531176i
$$584$$ −1.75379 + 9.43318i −0.0725723 + 0.390348i
$$585$$ 0 0
$$586$$ −8.24621 5.46026i −0.340648 0.225561i
$$587$$ −38.2462 −1.57859 −0.789295 0.614014i $$-0.789554\pi$$
−0.789295 + 0.614014i $$0.789554\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 8.00000 + 5.29723i 0.329355 + 0.218083i
$$591$$ 0 0
$$592$$ 19.8078 20.4810i 0.814094 0.841763i
$$593$$ 21.7238i 0.892088i −0.895011 0.446044i $$-0.852832\pi$$
0.895011 0.446044i $$-0.147168\pi$$
$$594$$ 0 0
$$595$$ 18.8769 4.87962i 0.773877 0.200045i
$$596$$ −7.80776 18.4130i −0.319818 0.754226i
$$597$$ 0 0
$$598$$ −14.2462 + 21.5150i −0.582571 + 0.879813i
$$599$$ 19.2382i 0.786051i −0.919528 0.393026i $$-0.871428\pi$$
0.919528 0.393026i $$-0.128572\pi$$
$$600$$ 0 0
$$601$$ 5.29723i 0.216078i 0.994147 + 0.108039i $$0.0344572\pi$$
−0.994147 + 0.108039i $$0.965543\pi$$
$$602$$ −28.6847 9.88653i −1.16910 0.402945i
$$603$$ 0 0
$$604$$ 14.9309 6.33122i 0.607528 0.257613i
$$605$$ 3.18348i 0.129427i
$$606$$ 0 0
$$607$$ 33.6155 1.36441 0.682206 0.731160i $$-0.261021\pi$$
0.682206 + 0.731160i $$0.261021\pi$$
$$608$$ −1.36932 6.20393i −0.0555331 0.251602i
$$609$$ 0 0
$$610$$ −12.4924 + 18.8664i −0.505803 + 0.763876i
$$611$$ 61.8963i 2.50406i
$$612$$ 0 0
$$613$$ −40.7386 −1.64542 −0.822709 0.568463i $$-0.807538\pi$$
−0.822709 + 0.568463i $$0.807538\pi$$
$$614$$ −16.8769 + 25.4879i −0.681096 + 1.02861i
$$615$$ 0 0
$$616$$ 1.56155 + 22.5490i 0.0629168 + 0.908523i
$$617$$ −15.7538 −0.634224 −0.317112 0.948388i $$-0.602713\pi$$
−0.317112 + 0.948388i $$0.602713\pi$$
$$618$$ 0 0
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −6.24621 + 9.43318i −0.250450 + 0.378236i
$$623$$ 5.12311 + 19.8188i 0.205253 + 0.794025i
$$624$$ 0 0
$$625$$ −9.87689 −0.395076
$$626$$ 30.2462 + 20.0276i 1.20888 + 0.800465i
$$627$$ 0 0
$$628$$ −7.61553 + 3.22925i −0.303893 + 0.128861i
$$629$$ 30.9481i 1.23398i
$$630$$ 0 0
$$631$$ 17.9597i 0.714963i −0.933920 0.357481i $$-0.883636\pi$$
0.933920 0.357481i $$-0.116364\pi$$
$$632$$ −2.43845 + 13.1158i −0.0969962 + 0.521718i
$$633$$ 0 0
$$634$$ 14.4384 21.8053i 0.573424 0.865999i
$$635$$ −32.9848 −1.30896
$$636$$ 0 0
$$637$$ −20.4924 36.9890i −0.811939 1.46556i
$$638$$ 7.12311 + 4.71659i 0.282006 + 0.186732i
$$639$$ 0 0
$$640$$ 11.1231 + 15.6371i 0.439679 + 0.618111i
$$641$$ 9.50758 0.375527 0.187763 0.982214i $$-0.439876\pi$$
0.187763 + 0.982214i $$0.439876\pi$$
$$642$$ 0 0
$$643$$ −29.6155 −1.16792 −0.583961 0.811782i $$-0.698498\pi$$
−0.583961 + 0.811782i $$0.698498\pi$$
$$644$$ −12.6847 + 9.72350i −0.499846 + 0.383159i
$$645$$ 0 0
$$646$$ 5.75379 + 3.80989i 0.226380 + 0.149898i
$$647$$ 32.9848 1.29677 0.648384 0.761313i $$-0.275445\pi$$
0.648384 + 0.761313i $$0.275445\pi$$
$$648$$ 0 0
$$649$$ 12.0818i 0.474252i
$$650$$ 15.1231 + 10.0138i 0.593177 + 0.392774i
$$651$$ 0 0
$$652$$ −21.1771 + 8.97983i −0.829358 + 0.351677i
$$653$$ 32.7386 1.28116 0.640581 0.767891i $$-0.278694\pi$$
0.640581 + 0.767891i $$0.278694\pi$$
$$654$$ 0 0
$$655$$ 37.7327i 1.47434i
$$656$$ −22.2462 21.5150i −0.868569 0.840018i
$$657$$ 0 0
$$658$$ −12.4924 + 36.2454i −0.487005 + 1.41299i
$$659$$ 38.1045i 1.48434i 0.670210 + 0.742171i $$0.266204\pi$$
−0.670210 + 0.742171i $$0.733796\pi$$
$$660$$ 0 0
$$661$$ 2.64861i 0.103019i −0.998673 0.0515096i $$-0.983597\pi$$
0.998673 0.0515096i $$-0.0164033\pi$$
$$662$$ −6.43845 4.26324i −0.250237 0.165696i
$$663$$ 0 0
$$664$$ 17.3693 + 3.22925i 0.674060 + 0.125319i
$$665$$ 1.26137 + 4.87962i 0.0489137 + 0.189223i
$$666$$ 0 0
$$667$$ 6.04090i 0.233904i
$$668$$ 1.75379 + 4.13595i 0.0678561 + 0.160025i
$$669$$ 0 0
$$670$$ −2.73863 + 4.13595i −0.105803 + 0.159786i
$$671$$ 28.4924 1.09994
$$672$$ 0 0
$$673$$ 29.8617 1.15109 0.575543 0.817772i $$-0.304791\pi$$
0.575543 + 0.817772i $$0.304791\pi$$
$$674$$ 6.43845 9.72350i 0.248000 0.374535i
$$675$$ 0 0
$$676$$ 18.3423 + 43.2566i 0.705474 + 1.66372i
$$677$$ 32.6443i 1.25462i −0.778769 0.627311i $$-0.784156\pi$$
0.778769 0.627311i $$-0.215844\pi$$
$$678$$ 0 0
$$679$$ −5.75379 22.2586i −0.220810 0.854208i
$$680$$ −20.4924 3.80989i −0.785849 0.146103i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 29.0890i 1.11306i −0.830828 0.556529i $$-0.812133\pi$$
0.830828 0.556529i $$-0.187867\pi$$
$$684$$ 0 0
$$685$$ 27.5559i 1.05286i
$$686$$ −4.53457 25.7961i −0.173131 0.984899i
$$687$$ 0 0
$$688$$ 23.3153 + 22.5490i 0.888889 + 0.859671i
$$689$$ 25.6509i 0.977222i
$$690$$ 0 0
$$691$$ −12.0000 −0.456502 −0.228251 0.973602i $$-0.573301\pi$$
−0.228251 + 0.973602i $$0.573301\pi$$
$$692$$ 15.6155 6.62153i 0.593613 0.251713i
$$693$$ 0 0
$$694$$ −40.9309 27.1025i −1.55371 1.02880i
$$695$$ 20.3537i 0.772060i
$$696$$ 0 0
$$697$$ 33.6155 1.27328
$$698$$ 4.87689 + 3.22925i 0.184593 + 0.122229i
$$699$$ 0 0
$$700$$ 6.83475 + 8.91618i 0.258329 + 0.337000i
$$701$$ 34.0000 1.28416 0.642081 0.766637i $$-0.278071\pi$$
0.642081 + 0.766637i $$0.278071\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ 8.68466 22.5490i 0.327315 0.849846i
$$705$$ 0 0
$$706$$ 7.36932 + 4.87962i 0.277348 + 0.183647i
$$707$$ −4.63068 17.9139i −0.174155 0.673721i
$$708$$ 0 0
$$709$$ 6.00000 0.225335 0.112667 0.993633i $$-0.464061\pi$$
0.112667 + 0.993633i $$0.464061\pi$$
$$710$$ 16.4924 24.9073i 0.618950 0.934752i
$$711$$ 0 0
$$712$$ 4.00000 21.5150i 0.149906 0.806308i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 30.9481i 1.15740i
$$716$$ 4.19224 1.77766i 0.156671 0.0664341i
$$717$$ 0 0
$$718$$ −1.31534 0.870958i −0.0490881 0.0325039i
$$719$$ −4.49242 −0.167539 −0.0837695 0.996485i $$-0.526696\pi$$
−0.0837695 + 0.996485i $$0.526696\pi$$
$$720$$ 0 0
$$721$$ −20.4924 + 5.29723i −0.763178 + 0.197279i
$$722$$ 13.8499 20.9165i 0.515440 0.778430i
$$723$$ 0 0
$$724$$ 11.1231 4.71659i 0.413387 0.175291i
$$725$$ 4.24621 0.157700
$$726$$ 0 0
$$727$$ 32.9848 1.22334 0.611670 0.791113i $$-0.290498\pi$$
0.611670 + 0.791113i $$0.290498\pi$$
$$728$$ 3.12311 + 45.0979i 0.115750 + 1.67144i
$$729$$ 0 0
$$730$$ −4.49242 + 6.78456i −0.166272 + 0.251108i
$$731$$ −35.2311 −1.30307
$$732$$ 0 0
$$733$$ 16.6354i 0.614441i −0.951638 0.307220i $$-0.900601\pi$$
0.951638 0.307220i $$-0.0993989\pi$$
$$734$$ −6.73863 + 10.1768i −0.248728 + 0.375634i
$$735$$ 0 0
$$736$$ 16.6847 3.68260i 0.615005 0.135742i
$$737$$ 6.24621 0.230082
$$738$$ 0 0
$$739$$ 5.87787i 0.216221i 0.994139 + 0.108110i $$0.0344800\pi$$
−0.994139 + 0.108110i $$0.965520\pi$$
$$740$$ 22.2462 9.43318i 0.817787 0.346771i
$$741$$ 0 0
$$742$$ 5.17708 15.0207i 0.190057 0.551428i
$$743$$ 13.6149i 0.499482i 0.968313 + 0.249741i $$0.0803455\pi$$
−0.968313 + 0.249741i $$0.919654\pi$$
$$744$$ 0 0
$$745$$ 16.9614i 0.621418i
$$746$$ 7.80776 11.7915i 0.285863 0.431716i
$$747$$ 0 0
$$748$$ 10.2462 + 24.1636i 0.374639 + 0.883508i
$$749$$ −3.75379 14.5216i −0.137160 0.530608i
$$750$$ 0 0
$$751$$ 30.7851i 1.12336i 0.827353 + 0.561682i $$0.189846\pi$$
−0.827353 + 0.561682i $$0.810154\pi$$
$$752$$ 28.4924 29.4608i 1.03901 1.07433i
$$753$$ 0 0
$$754$$ 14.2462 + 9.43318i 0.518816 + 0.343536i
$$755$$ 13.7538 0.500552
$$756$$ 0 0
$$757$$ 30.9848 1.12616 0.563082 0.826401i $$-0.309616\pi$$
0.563082 + 0.826401i $$0.309616\pi$$
$$758$$ 22.0540 + 14.6031i 0.801036 + 0.530409i
$$759$$ 0 0
$$760$$ 0.984845 5.29723i 0.0357241 0.192151i
$$761$$ 33.8056i 1.22545i −0.790296 0.612725i $$-0.790073\pi$$
0.790296 0.612725i $$-0.209927\pi$$
$$762$$ 0 0
$$763$$ −21.1231 + 5.46026i −0.764708 + 0.197675i
$$764$$ −16.6847 + 7.07488i −0.603630 + 0.255960i
$$765$$ 0 0
$$766$$ 20.4924 30.9481i 0.740421 1.11820i
$$767$$ 24.1636i 0.872496i
$$768$$ 0 0
$$769$$ 44.5173i 1.60533i −0.596427 0.802667i $$-0.703414\pi$$
0.596427 0.802667i $$-0.296586\pi$$
$$770$$ −6.24621 + 18.1227i −0.225098 + 0.653096i
$$771$$ 0 0
$$772$$ −7.31534 17.2517i −0.263285 0.620903i
$$773$$ 1.69614i 0.0610060i −0.999535 0.0305030i $$-0.990289\pi$$
0.999535 0.0305030i $$-0.00971091\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −4.49242 + 24.1636i −0.161269 + 0.867422i
$$777$$ 0 0
$$778$$ 0.192236 0.290319i 0.00689199 0.0104085i
$$779$$ 8.68951i 0.311334i
$$780$$ 0 0
$$781$$ −37.6155 −1.34599
$$782$$ −10.2462 + 15.4741i −0.366404 + 0.553352i
$$783$$ 0 0
$$784$$ −7.27320 + 27.0389i −0.259757 + 0.965674i
$$785$$ −7.01515 −0.250382
$$786$$ 0 0
$$787$$ −20.9848 −0.748029 −0.374014 0.927423i $$-0.622019\pi$$
−0.374014 + 0.927423i $$0.622019\pi$$
$$788$$ 0.192236 + 0.453349i 0.00684812 + 0.0161499i
$$789$$ 0 0
$$790$$ −6.24621 + 9.43318i −0.222230 + 0.335617i
$$791$$ 31.3693 8.10887i 1.11536 0.288318i