# Properties

 Label 624.2.bv.e.433.2 Level $624$ Weight $2$ Character 624.433 Analytic conductor $4.983$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$624 = 2^{4} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 624.bv (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.98266508613$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 78) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 433.2 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 624.433 Dual form 624.2.bv.e.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +3.73205i q^{5} +(-2.36603 + 1.36603i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +3.73205i q^{5} +(-2.36603 + 1.36603i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.09808 - 0.633975i) q^{11} +(-2.59808 + 2.50000i) q^{13} +(3.23205 + 1.86603i) q^{15} +(-2.86603 - 4.96410i) q^{17} +(-4.09808 + 2.36603i) q^{19} +2.73205i q^{21} +(-2.09808 + 3.63397i) q^{23} -8.92820 q^{25} -1.00000 q^{27} +(2.23205 - 3.86603i) q^{29} -1.46410i q^{31} +(-1.09808 + 0.633975i) q^{33} +(-5.09808 - 8.83013i) q^{35} +(3.06218 + 1.76795i) q^{37} +(0.866025 + 3.50000i) q^{39} +(8.13397 + 4.69615i) q^{41} +(4.83013 + 8.36603i) q^{43} +(3.23205 - 1.86603i) q^{45} +2.19615i q^{47} +(0.232051 - 0.401924i) q^{49} -5.73205 q^{51} -6.46410 q^{53} +(2.36603 - 4.09808i) q^{55} +4.73205i q^{57} +(6.92820 - 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(2.36603 + 1.36603i) q^{63} +(-9.33013 - 9.69615i) q^{65} +(11.3660 + 6.56218i) q^{67} +(2.09808 + 3.63397i) q^{69} +(-4.09808 + 2.36603i) q^{71} +6.26795i q^{73} +(-4.46410 + 7.73205i) q^{75} +3.46410 q^{77} +2.53590 q^{79} +(-0.500000 + 0.866025i) q^{81} +0.196152i q^{83} +(18.5263 - 10.6962i) q^{85} +(-2.23205 - 3.86603i) q^{87} +(-8.19615 - 4.73205i) q^{89} +(2.73205 - 9.46410i) q^{91} +(-1.26795 - 0.732051i) q^{93} +(-8.83013 - 15.2942i) q^{95} +(-5.19615 + 3.00000i) q^{97} +1.26795i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + O(q^{10})$$ $$4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 6 q^{15} - 8 q^{17} - 6 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{33} - 10 q^{35} - 12 q^{37} + 36 q^{41} + 2 q^{43} + 6 q^{45} - 6 q^{49} - 16 q^{51} - 12 q^{53} + 6 q^{55} + 8 q^{61} + 6 q^{63} - 20 q^{65} + 42 q^{67} - 2 q^{69} - 6 q^{71} - 4 q^{75} + 24 q^{79} - 2 q^{81} + 36 q^{85} - 2 q^{87} - 12 q^{89} + 4 q^{91} - 12 q^{93} - 18 q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$$.

 $$n$$ $$79$$ $$145$$ $$209$$ $$469$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$

## 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 0
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0 0
$$5$$ 3.73205i 1.66902i 0.550990 + 0.834512i $$0.314250\pi$$
−0.550990 + 0.834512i $$0.685750\pi$$
$$6$$ 0 0
$$7$$ −2.36603 + 1.36603i −0.894274 + 0.516309i −0.875338 0.483512i $$-0.839361\pi$$
−0.0189356 + 0.999821i $$0.506028\pi$$
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −1.09808 0.633975i −0.331082 0.191151i 0.325239 0.945632i $$-0.394555\pi$$
−0.656322 + 0.754481i $$0.727889\pi$$
$$12$$ 0 0
$$13$$ −2.59808 + 2.50000i −0.720577 + 0.693375i
$$14$$ 0 0
$$15$$ 3.23205 + 1.86603i 0.834512 + 0.481806i
$$16$$ 0 0
$$17$$ −2.86603 4.96410i −0.695113 1.20397i −0.970143 0.242536i $$-0.922021\pi$$
0.275029 0.961436i $$-0.411312\pi$$
$$18$$ 0 0
$$19$$ −4.09808 + 2.36603i −0.940163 + 0.542803i −0.890011 0.455938i $$-0.849304\pi$$
−0.0501517 + 0.998742i $$0.515970\pi$$
$$20$$ 0 0
$$21$$ 2.73205i 0.596182i
$$22$$ 0 0
$$23$$ −2.09808 + 3.63397i −0.437479 + 0.757736i −0.997494 0.0707462i $$-0.977462\pi$$
0.560015 + 0.828482i $$0.310795\pi$$
$$24$$ 0 0
$$25$$ −8.92820 −1.78564
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 2.23205 3.86603i 0.414481 0.717903i −0.580892 0.813980i $$-0.697296\pi$$
0.995374 + 0.0960774i $$0.0306296\pi$$
$$30$$ 0 0
$$31$$ 1.46410i 0.262960i −0.991319 0.131480i $$-0.958027\pi$$
0.991319 0.131480i $$-0.0419730\pi$$
$$32$$ 0 0
$$33$$ −1.09808 + 0.633975i −0.191151 + 0.110361i
$$34$$ 0 0
$$35$$ −5.09808 8.83013i −0.861732 1.49256i
$$36$$ 0 0
$$37$$ 3.06218 + 1.76795i 0.503419 + 0.290649i 0.730124 0.683314i $$-0.239462\pi$$
−0.226705 + 0.973963i $$0.572795\pi$$
$$38$$ 0 0
$$39$$ 0.866025 + 3.50000i 0.138675 + 0.560449i
$$40$$ 0 0
$$41$$ 8.13397 + 4.69615i 1.27031 + 0.733416i 0.975047 0.221999i $$-0.0712582\pi$$
0.295267 + 0.955415i $$0.404592\pi$$
$$42$$ 0 0
$$43$$ 4.83013 + 8.36603i 0.736587 + 1.27581i 0.954023 + 0.299732i $$0.0968974\pi$$
−0.217436 + 0.976075i $$0.569769\pi$$
$$44$$ 0 0
$$45$$ 3.23205 1.86603i 0.481806 0.278171i
$$46$$ 0 0
$$47$$ 2.19615i 0.320342i 0.987089 + 0.160171i $$0.0512045\pi$$
−0.987089 + 0.160171i $$0.948795\pi$$
$$48$$ 0 0
$$49$$ 0.232051 0.401924i 0.0331501 0.0574177i
$$50$$ 0 0
$$51$$ −5.73205 −0.802648
$$52$$ 0 0
$$53$$ −6.46410 −0.887913 −0.443956 0.896048i $$-0.646425\pi$$
−0.443956 + 0.896048i $$0.646425\pi$$
$$54$$ 0 0
$$55$$ 2.36603 4.09808i 0.319035 0.552584i
$$56$$ 0 0
$$57$$ 4.73205i 0.626775i
$$58$$ 0 0
$$59$$ 6.92820 4.00000i 0.901975 0.520756i 0.0241347 0.999709i $$-0.492317\pi$$
0.877841 + 0.478953i $$0.158984\pi$$
$$60$$ 0 0
$$61$$ 4.59808 + 7.96410i 0.588723 + 1.01970i 0.994400 + 0.105682i $$0.0337026\pi$$
−0.405677 + 0.914017i $$0.632964\pi$$
$$62$$ 0 0
$$63$$ 2.36603 + 1.36603i 0.298091 + 0.172103i
$$64$$ 0 0
$$65$$ −9.33013 9.69615i −1.15726 1.20266i
$$66$$ 0 0
$$67$$ 11.3660 + 6.56218i 1.38858 + 0.801698i 0.993155 0.116800i $$-0.0372638\pi$$
0.395426 + 0.918498i $$0.370597\pi$$
$$68$$ 0 0
$$69$$ 2.09808 + 3.63397i 0.252579 + 0.437479i
$$70$$ 0 0
$$71$$ −4.09808 + 2.36603i −0.486352 + 0.280796i −0.723060 0.690785i $$-0.757265\pi$$
0.236708 + 0.971581i $$0.423932\pi$$
$$72$$ 0 0
$$73$$ 6.26795i 0.733608i 0.930298 + 0.366804i $$0.119548\pi$$
−0.930298 + 0.366804i $$0.880452\pi$$
$$74$$ 0 0
$$75$$ −4.46410 + 7.73205i −0.515470 + 0.892820i
$$76$$ 0 0
$$77$$ 3.46410 0.394771
$$78$$ 0 0
$$79$$ 2.53590 0.285311 0.142655 0.989772i $$-0.454436\pi$$
0.142655 + 0.989772i $$0.454436\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 0.196152i 0.0215305i 0.999942 + 0.0107653i $$0.00342676\pi$$
−0.999942 + 0.0107653i $$0.996573\pi$$
$$84$$ 0 0
$$85$$ 18.5263 10.6962i 2.00946 1.16016i
$$86$$ 0 0
$$87$$ −2.23205 3.86603i −0.239301 0.414481i
$$88$$ 0 0
$$89$$ −8.19615 4.73205i −0.868790 0.501596i −0.00184433 0.999998i $$-0.500587\pi$$
−0.866946 + 0.498402i $$0.833920\pi$$
$$90$$ 0 0
$$91$$ 2.73205 9.46410i 0.286397 0.992107i
$$92$$ 0 0
$$93$$ −1.26795 0.732051i −0.131480 0.0759101i
$$94$$ 0 0
$$95$$ −8.83013 15.2942i −0.905952 1.56915i
$$96$$ 0 0
$$97$$ −5.19615 + 3.00000i −0.527589 + 0.304604i −0.740034 0.672569i $$-0.765191\pi$$
0.212445 + 0.977173i $$0.431857\pi$$
$$98$$ 0 0
$$99$$ 1.26795i 0.127434i
$$100$$ 0 0
$$101$$ 0.964102 1.66987i 0.0959317 0.166159i −0.814065 0.580773i $$-0.802750\pi$$
0.909997 + 0.414615i $$0.136084\pi$$
$$102$$ 0 0
$$103$$ −15.2679 −1.50440 −0.752198 0.658937i $$-0.771006\pi$$
−0.752198 + 0.658937i $$0.771006\pi$$
$$104$$ 0 0
$$105$$ −10.1962 −0.995043
$$106$$ 0 0
$$107$$ 5.09808 8.83013i 0.492850 0.853641i −0.507116 0.861878i $$-0.669289\pi$$
0.999966 + 0.00823695i $$0.00262193\pi$$
$$108$$ 0 0
$$109$$ 1.46410i 0.140236i 0.997539 + 0.0701178i $$0.0223375\pi$$
−0.997539 + 0.0701178i $$0.977662\pi$$
$$110$$ 0 0
$$111$$ 3.06218 1.76795i 0.290649 0.167806i
$$112$$ 0 0
$$113$$ 0.669873 + 1.16025i 0.0630163 + 0.109148i 0.895812 0.444432i $$-0.146595\pi$$
−0.832796 + 0.553580i $$0.813261\pi$$
$$114$$ 0 0
$$115$$ −13.5622 7.83013i −1.26468 0.730163i
$$116$$ 0 0
$$117$$ 3.46410 + 1.00000i 0.320256 + 0.0924500i
$$118$$ 0 0
$$119$$ 13.5622 + 7.83013i 1.24324 + 0.717787i
$$120$$ 0 0
$$121$$ −4.69615 8.13397i −0.426923 0.739452i
$$122$$ 0 0
$$123$$ 8.13397 4.69615i 0.733416 0.423438i
$$124$$ 0 0
$$125$$ 14.6603i 1.31125i
$$126$$ 0 0
$$127$$ 4.92820 8.53590i 0.437307 0.757438i −0.560173 0.828375i $$-0.689266\pi$$
0.997481 + 0.0709368i $$0.0225989\pi$$
$$128$$ 0 0
$$129$$ 9.66025 0.850538
$$130$$ 0 0
$$131$$ −6.53590 −0.571044 −0.285522 0.958372i $$-0.592167\pi$$
−0.285522 + 0.958372i $$0.592167\pi$$
$$132$$ 0 0
$$133$$ 6.46410 11.1962i 0.560509 0.970830i
$$134$$ 0 0
$$135$$ 3.73205i 0.321204i
$$136$$ 0 0
$$137$$ −10.3301 + 5.96410i −0.882562 + 0.509548i −0.871502 0.490391i $$-0.836854\pi$$
−0.0110599 + 0.999939i $$0.503521\pi$$
$$138$$ 0 0
$$139$$ 8.92820 + 15.4641i 0.757280 + 1.31165i 0.944233 + 0.329279i $$0.106806\pi$$
−0.186952 + 0.982369i $$0.559861\pi$$
$$140$$ 0 0
$$141$$ 1.90192 + 1.09808i 0.160171 + 0.0924747i
$$142$$ 0 0
$$143$$ 4.43782 1.09808i 0.371109 0.0918257i
$$144$$ 0 0
$$145$$ 14.4282 + 8.33013i 1.19820 + 0.691779i
$$146$$ 0 0
$$147$$ −0.232051 0.401924i −0.0191392 0.0331501i
$$148$$ 0 0
$$149$$ 11.4282 6.59808i 0.936235 0.540535i 0.0474568 0.998873i $$-0.484888\pi$$
0.888778 + 0.458338i $$0.151555\pi$$
$$150$$ 0 0
$$151$$ 6.73205i 0.547847i 0.961752 + 0.273923i $$0.0883214\pi$$
−0.961752 + 0.273923i $$0.911679\pi$$
$$152$$ 0 0
$$153$$ −2.86603 + 4.96410i −0.231704 + 0.401324i
$$154$$ 0 0
$$155$$ 5.46410 0.438887
$$156$$ 0 0
$$157$$ 7.58846 0.605625 0.302812 0.953050i $$-0.402074\pi$$
0.302812 + 0.953050i $$0.402074\pi$$
$$158$$ 0 0
$$159$$ −3.23205 + 5.59808i −0.256318 + 0.443956i
$$160$$ 0 0
$$161$$ 11.4641i 0.903498i
$$162$$ 0 0
$$163$$ −11.6603 + 6.73205i −0.913302 + 0.527295i −0.881492 0.472199i $$-0.843460\pi$$
−0.0318096 + 0.999494i $$0.510127\pi$$
$$164$$ 0 0
$$165$$ −2.36603 4.09808i −0.184195 0.319035i
$$166$$ 0 0
$$167$$ 8.19615 + 4.73205i 0.634237 + 0.366177i 0.782391 0.622787i $$-0.214000\pi$$
−0.148154 + 0.988964i $$0.547333\pi$$
$$168$$ 0 0
$$169$$ 0.500000 12.9904i 0.0384615 0.999260i
$$170$$ 0 0
$$171$$ 4.09808 + 2.36603i 0.313388 + 0.180934i
$$172$$ 0 0
$$173$$ 2.19615 + 3.80385i 0.166970 + 0.289201i 0.937353 0.348380i $$-0.113268\pi$$
−0.770383 + 0.637582i $$0.779935\pi$$
$$174$$ 0 0
$$175$$ 21.1244 12.1962i 1.59685 0.921942i
$$176$$ 0 0
$$177$$ 8.00000i 0.601317i
$$178$$ 0 0
$$179$$ 8.02628 13.9019i 0.599912 1.03908i −0.392921 0.919572i $$-0.628535\pi$$
0.992833 0.119506i $$-0.0381312\pi$$
$$180$$ 0 0
$$181$$ −19.1962 −1.42684 −0.713419 0.700737i $$-0.752855\pi$$
−0.713419 + 0.700737i $$0.752855\pi$$
$$182$$ 0 0
$$183$$ 9.19615 0.679799
$$184$$ 0 0
$$185$$ −6.59808 + 11.4282i −0.485100 + 0.840218i
$$186$$ 0 0
$$187$$ 7.26795i 0.531485i
$$188$$ 0 0
$$189$$ 2.36603 1.36603i 0.172103 0.0993637i
$$190$$ 0 0
$$191$$ −3.46410 6.00000i −0.250654 0.434145i 0.713052 0.701111i $$-0.247312\pi$$
−0.963706 + 0.266966i $$0.913979\pi$$
$$192$$ 0 0
$$193$$ −10.1603 5.86603i −0.731351 0.422246i 0.0875652 0.996159i $$-0.472091\pi$$
−0.818916 + 0.573913i $$0.805425\pi$$
$$194$$ 0 0
$$195$$ −13.0622 + 3.23205i −0.935402 + 0.231452i
$$196$$ 0 0
$$197$$ 15.4641 + 8.92820i 1.10177 + 0.636108i 0.936686 0.350171i $$-0.113877\pi$$
0.165086 + 0.986279i $$0.447210\pi$$
$$198$$ 0 0
$$199$$ 7.09808 + 12.2942i 0.503169 + 0.871515i 0.999993 + 0.00366345i $$0.00116611\pi$$
−0.496824 + 0.867851i $$0.665501\pi$$
$$200$$ 0 0
$$201$$ 11.3660 6.56218i 0.801698 0.462860i
$$202$$ 0 0
$$203$$ 12.1962i 0.856002i
$$204$$ 0 0
$$205$$ −17.5263 + 30.3564i −1.22409 + 2.12018i
$$206$$ 0 0
$$207$$ 4.19615 0.291653
$$208$$ 0 0
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ 8.19615 14.1962i 0.564246 0.977303i −0.432873 0.901455i $$-0.642500\pi$$
0.997119 0.0758485i $$-0.0241665\pi$$
$$212$$ 0 0
$$213$$ 4.73205i 0.324235i
$$214$$ 0 0
$$215$$ −31.2224 + 18.0263i −2.12935 + 1.22938i
$$216$$ 0 0
$$217$$ 2.00000 + 3.46410i 0.135769 + 0.235159i
$$218$$ 0 0
$$219$$ 5.42820 + 3.13397i 0.366804 + 0.211774i
$$220$$ 0 0
$$221$$ 19.8564 + 5.73205i 1.33569 + 0.385579i
$$222$$ 0 0
$$223$$ −23.3205 13.4641i −1.56166 0.901623i −0.997090 0.0762356i $$-0.975710\pi$$
−0.564567 0.825387i $$-0.690957\pi$$
$$224$$ 0 0
$$225$$ 4.46410 + 7.73205i 0.297607 + 0.515470i
$$226$$ 0 0
$$227$$ 10.5622 6.09808i 0.701036 0.404744i −0.106697 0.994292i $$-0.534027\pi$$
0.807733 + 0.589548i $$0.200694\pi$$
$$228$$ 0 0
$$229$$ 11.8564i 0.783493i 0.920073 + 0.391747i $$0.128129\pi$$
−0.920073 + 0.391747i $$0.871871\pi$$
$$230$$ 0 0
$$231$$ 1.73205 3.00000i 0.113961 0.197386i
$$232$$ 0 0
$$233$$ 7.85641 0.514690 0.257345 0.966320i $$-0.417152\pi$$
0.257345 + 0.966320i $$0.417152\pi$$
$$234$$ 0 0
$$235$$ −8.19615 −0.534658
$$236$$ 0 0
$$237$$ 1.26795 2.19615i 0.0823622 0.142655i
$$238$$ 0 0
$$239$$ 7.66025i 0.495501i −0.968824 0.247750i $$-0.920309\pi$$
0.968824 0.247750i $$-0.0796913\pi$$
$$240$$ 0 0
$$241$$ −11.7679 + 6.79423i −0.758040 + 0.437655i −0.828592 0.559853i $$-0.810857\pi$$
0.0705514 + 0.997508i $$0.477524\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 1.50000 + 0.866025i 0.0958315 + 0.0553283i
$$246$$ 0 0
$$247$$ 4.73205 16.3923i 0.301093 1.04302i
$$248$$ 0 0
$$249$$ 0.169873 + 0.0980762i 0.0107653 + 0.00621533i
$$250$$ 0 0
$$251$$ −6.73205 11.6603i −0.424923 0.735989i 0.571490 0.820609i $$-0.306366\pi$$
−0.996413 + 0.0846203i $$0.973032\pi$$
$$252$$ 0 0
$$253$$ 4.60770 2.66025i 0.289683 0.167249i
$$254$$ 0 0
$$255$$ 21.3923i 1.33964i
$$256$$ 0 0
$$257$$ 4.66987 8.08846i 0.291299 0.504544i −0.682818 0.730588i $$-0.739246\pi$$
0.974117 + 0.226044i $$0.0725793\pi$$
$$258$$ 0 0
$$259$$ −9.66025 −0.600259
$$260$$ 0 0
$$261$$ −4.46410 −0.276321
$$262$$ 0 0
$$263$$ −5.02628 + 8.70577i −0.309934 + 0.536821i −0.978348 0.206969i $$-0.933640\pi$$
0.668414 + 0.743790i $$0.266974\pi$$
$$264$$ 0 0
$$265$$ 24.1244i 1.48195i
$$266$$ 0 0
$$267$$ −8.19615 + 4.73205i −0.501596 + 0.289597i
$$268$$ 0 0
$$269$$ −2.73205 4.73205i −0.166576 0.288518i 0.770638 0.637273i $$-0.219938\pi$$
−0.937214 + 0.348755i $$0.886604\pi$$
$$270$$ 0 0
$$271$$ 18.9282 + 10.9282i 1.14981 + 0.663841i 0.948840 0.315757i $$-0.102258\pi$$
0.200966 + 0.979598i $$0.435592\pi$$
$$272$$ 0 0
$$273$$ −6.83013 7.09808i −0.413378 0.429595i
$$274$$ 0 0
$$275$$ 9.80385 + 5.66025i 0.591194 + 0.341326i
$$276$$ 0 0
$$277$$ −2.86603 4.96410i −0.172203 0.298264i 0.766987 0.641663i $$-0.221755\pi$$
−0.939190 + 0.343399i $$0.888422\pi$$
$$278$$ 0 0
$$279$$ −1.26795 + 0.732051i −0.0759101 + 0.0438267i
$$280$$ 0 0
$$281$$ 12.3205i 0.734980i −0.930027 0.367490i $$-0.880217\pi$$
0.930027 0.367490i $$-0.119783\pi$$
$$282$$ 0 0
$$283$$ −12.8301 + 22.2224i −0.762672 + 1.32099i 0.178797 + 0.983886i $$0.442780\pi$$
−0.941469 + 0.337100i $$0.890554\pi$$
$$284$$ 0 0
$$285$$ −17.6603 −1.04610
$$286$$ 0 0
$$287$$ −25.6603 −1.51468
$$288$$ 0 0
$$289$$ −7.92820 + 13.7321i −0.466365 + 0.807768i
$$290$$ 0 0
$$291$$ 6.00000i 0.351726i
$$292$$ 0 0
$$293$$ −26.4282 + 15.2583i −1.54395 + 0.891401i −0.545368 + 0.838196i $$0.683610\pi$$
−0.998584 + 0.0532048i $$0.983056\pi$$
$$294$$ 0 0
$$295$$ 14.9282 + 25.8564i 0.869154 + 1.50542i
$$296$$ 0 0
$$297$$ 1.09808 + 0.633975i 0.0637168 + 0.0367869i
$$298$$ 0 0
$$299$$ −3.63397 14.6865i −0.210158 0.849344i
$$300$$ 0 0
$$301$$ −22.8564 13.1962i −1.31742 0.760614i
$$302$$ 0 0
$$303$$ −0.964102 1.66987i −0.0553862 0.0959317i
$$304$$ 0 0
$$305$$ −29.7224 + 17.1603i −1.70190 + 0.982593i
$$306$$ 0 0
$$307$$ 22.5885i 1.28919i −0.764524 0.644596i $$-0.777026\pi$$
0.764524 0.644596i $$-0.222974\pi$$
$$308$$ 0 0
$$309$$ −7.63397 + 13.2224i −0.434282 + 0.752198i
$$310$$ 0 0
$$311$$ −1.66025 −0.0941444 −0.0470722 0.998891i $$-0.514989\pi$$
−0.0470722 + 0.998891i $$0.514989\pi$$
$$312$$ 0 0
$$313$$ 6.53590 0.369431 0.184715 0.982792i $$-0.440864\pi$$
0.184715 + 0.982792i $$0.440864\pi$$
$$314$$ 0 0
$$315$$ −5.09808 + 8.83013i −0.287244 + 0.497521i
$$316$$ 0 0
$$317$$ 20.6603i 1.16040i 0.814476 + 0.580198i $$0.197025\pi$$
−0.814476 + 0.580198i $$0.802975\pi$$
$$318$$ 0 0
$$319$$ −4.90192 + 2.83013i −0.274455 + 0.158457i
$$320$$ 0 0
$$321$$ −5.09808 8.83013i −0.284547 0.492850i
$$322$$ 0 0
$$323$$ 23.4904 + 13.5622i 1.30704 + 0.754620i
$$324$$ 0 0
$$325$$ 23.1962 22.3205i 1.28669 1.23812i
$$326$$ 0 0
$$327$$ 1.26795 + 0.732051i 0.0701178 + 0.0404825i
$$328$$ 0 0
$$329$$ −3.00000 5.19615i −0.165395 0.286473i
$$330$$ 0 0
$$331$$ −17.3205 + 10.0000i −0.952021 + 0.549650i −0.893708 0.448649i $$-0.851905\pi$$
−0.0583130 + 0.998298i $$0.518572\pi$$
$$332$$ 0 0
$$333$$ 3.53590i 0.193766i
$$334$$ 0 0
$$335$$ −24.4904 + 42.4186i −1.33805 + 2.31757i
$$336$$ 0 0
$$337$$ 20.8564 1.13612 0.568060 0.822987i $$-0.307694\pi$$
0.568060 + 0.822987i $$0.307694\pi$$
$$338$$ 0 0
$$339$$ 1.33975 0.0727650
$$340$$ 0 0
$$341$$ −0.928203 + 1.60770i −0.0502650 + 0.0870616i
$$342$$ 0 0
$$343$$ 17.8564i 0.964155i
$$344$$ 0 0
$$345$$ −13.5622 + 7.83013i −0.730163 + 0.421560i
$$346$$ 0 0
$$347$$ 16.5622 + 28.6865i 0.889104 + 1.53997i 0.840936 + 0.541135i $$0.182005\pi$$
0.0481683 + 0.998839i $$0.484662\pi$$
$$348$$ 0 0
$$349$$ 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i $$-0.198847\pi$$
−0.100924 + 0.994894i $$0.532180\pi$$
$$350$$ 0 0
$$351$$ 2.59808 2.50000i 0.138675 0.133440i
$$352$$ 0 0
$$353$$ 18.8660 + 10.8923i 1.00414 + 0.579739i 0.909470 0.415770i $$-0.136488\pi$$
0.0946674 + 0.995509i $$0.469821\pi$$
$$354$$ 0 0
$$355$$ −8.83013 15.2942i −0.468654 0.811733i
$$356$$ 0 0
$$357$$ 13.5622 7.83013i 0.717787 0.414414i
$$358$$ 0 0
$$359$$ 1.12436i 0.0593412i −0.999560 0.0296706i $$-0.990554\pi$$
0.999560 0.0296706i $$-0.00944584\pi$$
$$360$$ 0 0
$$361$$ 1.69615 2.93782i 0.0892712 0.154622i
$$362$$ 0 0
$$363$$ −9.39230 −0.492968
$$364$$ 0 0
$$365$$ −23.3923 −1.22441
$$366$$ 0 0
$$367$$ −5.63397 + 9.75833i −0.294091 + 0.509381i −0.974773 0.223198i $$-0.928350\pi$$
0.680682 + 0.732579i $$0.261684\pi$$
$$368$$ 0 0
$$369$$ 9.39230i 0.488944i
$$370$$ 0 0
$$371$$ 15.2942 8.83013i 0.794037 0.458437i
$$372$$ 0 0
$$373$$ 6.86603 + 11.8923i 0.355509 + 0.615760i 0.987205 0.159456i $$-0.0509741\pi$$
−0.631696 + 0.775216i $$0.717641\pi$$
$$374$$ 0 0
$$375$$ −12.6962 7.33013i −0.655626 0.378526i
$$376$$ 0 0
$$377$$ 3.86603 + 15.6244i 0.199110 + 0.804695i
$$378$$ 0 0
$$379$$ −4.73205 2.73205i −0.243069 0.140336i 0.373517 0.927623i $$-0.378152\pi$$
−0.616587 + 0.787287i $$0.711485\pi$$
$$380$$ 0 0
$$381$$ −4.92820 8.53590i −0.252479 0.437307i
$$382$$ 0 0
$$383$$ 1.26795 0.732051i 0.0647892 0.0374060i −0.467255 0.884122i $$-0.654757\pi$$
0.532045 + 0.846716i $$0.321424\pi$$
$$384$$ 0 0
$$385$$ 12.9282i 0.658882i
$$386$$ 0 0
$$387$$ 4.83013 8.36603i 0.245529 0.425269i
$$388$$ 0 0
$$389$$ −11.7846 −0.597503 −0.298752 0.954331i $$-0.596570\pi$$
−0.298752 + 0.954331i $$0.596570\pi$$
$$390$$ 0 0
$$391$$ 24.0526 1.21639
$$392$$ 0 0
$$393$$ −3.26795 + 5.66025i −0.164846 + 0.285522i
$$394$$ 0 0
$$395$$ 9.46410i 0.476191i
$$396$$ 0 0
$$397$$ −17.6603 + 10.1962i −0.886343 + 0.511730i −0.872744 0.488177i $$-0.837662\pi$$
−0.0135983 + 0.999908i $$0.504329\pi$$
$$398$$ 0 0
$$399$$ −6.46410 11.1962i −0.323610 0.560509i
$$400$$ 0 0
$$401$$ 6.99038 + 4.03590i 0.349083 + 0.201543i 0.664281 0.747483i $$-0.268738\pi$$
−0.315198 + 0.949026i $$0.602071\pi$$
$$402$$ 0 0
$$403$$ 3.66025 + 3.80385i 0.182330 + 0.189483i
$$404$$ 0 0
$$405$$ −3.23205 1.86603i −0.160602 0.0927235i
$$406$$ 0 0
$$407$$ −2.24167 3.88269i −0.111115 0.192458i
$$408$$ 0 0
$$409$$ 15.3564 8.86603i 0.759325 0.438397i −0.0697281 0.997566i $$-0.522213\pi$$
0.829053 + 0.559169i $$0.188880\pi$$
$$410$$ 0 0
$$411$$ 11.9282i 0.588375i
$$412$$ 0 0
$$413$$ −10.9282 + 18.9282i −0.537742 + 0.931396i
$$414$$ 0 0
$$415$$ −0.732051 −0.0359350
$$416$$ 0 0
$$417$$ 17.8564 0.874432
$$418$$ 0 0
$$419$$ −8.73205 + 15.1244i −0.426589 + 0.738873i −0.996567 0.0827863i $$-0.973618\pi$$
0.569979 + 0.821659i $$0.306951\pi$$
$$420$$ 0 0
$$421$$ 22.7128i 1.10695i −0.832864 0.553477i $$-0.813301\pi$$
0.832864 0.553477i $$-0.186699\pi$$
$$422$$ 0 0
$$423$$ 1.90192 1.09808i 0.0924747 0.0533903i
$$424$$ 0 0
$$425$$ 25.5885 + 44.3205i 1.24122 + 2.14986i
$$426$$ 0 0
$$427$$ −21.7583 12.5622i −1.05296 0.607926i
$$428$$ 0 0
$$429$$ 1.26795 4.39230i 0.0612172 0.212062i
$$430$$ 0 0
$$431$$ 11.3660 + 6.56218i 0.547482 + 0.316089i 0.748106 0.663579i $$-0.230964\pi$$
−0.200624 + 0.979668i $$0.564297\pi$$
$$432$$ 0 0
$$433$$ 6.42820 + 11.1340i 0.308920 + 0.535065i 0.978126 0.208012i $$-0.0666992\pi$$
−0.669207 + 0.743076i $$0.733366\pi$$
$$434$$ 0 0
$$435$$ 14.4282 8.33013i 0.691779 0.399399i
$$436$$ 0 0
$$437$$ 19.8564i 0.949861i
$$438$$ 0 0
$$439$$ 0.169873 0.294229i 0.00810760 0.0140428i −0.861943 0.507005i $$-0.830753\pi$$
0.870051 + 0.492962i $$0.164086\pi$$
$$440$$ 0 0
$$441$$ −0.464102 −0.0221001
$$442$$ 0 0
$$443$$ −15.6077 −0.741544 −0.370772 0.928724i $$-0.620907\pi$$
−0.370772 + 0.928724i $$0.620907\pi$$
$$444$$ 0 0
$$445$$ 17.6603 30.5885i 0.837176 1.45003i
$$446$$ 0 0
$$447$$ 13.1962i 0.624157i
$$448$$ 0 0
$$449$$ −9.80385 + 5.66025i −0.462672 + 0.267124i −0.713167 0.700994i $$-0.752740\pi$$
0.250495 + 0.968118i $$0.419407\pi$$
$$450$$ 0 0
$$451$$ −5.95448 10.3135i −0.280386 0.485642i
$$452$$ 0 0
$$453$$ 5.83013 + 3.36603i 0.273923 + 0.158150i
$$454$$ 0 0
$$455$$ 35.3205 + 10.1962i 1.65585 + 0.478003i
$$456$$ 0 0
$$457$$ −1.16025 0.669873i −0.0542744 0.0313353i 0.472617 0.881268i $$-0.343309\pi$$
−0.526892 + 0.849932i $$0.676643\pi$$
$$458$$ 0 0
$$459$$ 2.86603 + 4.96410i 0.133775 + 0.231704i
$$460$$ 0 0
$$461$$ 19.2846 11.1340i 0.898174 0.518561i 0.0215666 0.999767i $$-0.493135\pi$$
0.876607 + 0.481207i $$0.159801\pi$$
$$462$$ 0 0
$$463$$ 10.0526i 0.467182i 0.972335 + 0.233591i $$0.0750477\pi$$
−0.972335 + 0.233591i $$0.924952\pi$$
$$464$$ 0 0
$$465$$ 2.73205 4.73205i 0.126696 0.219444i
$$466$$ 0 0
$$467$$ 18.5885 0.860171 0.430086 0.902788i $$-0.358483\pi$$
0.430086 + 0.902788i $$0.358483\pi$$
$$468$$ 0 0
$$469$$ −35.8564 −1.65570
$$470$$ 0 0
$$471$$ 3.79423 6.57180i 0.174829 0.302812i
$$472$$ 0 0
$$473$$ 12.2487i 0.563196i
$$474$$ 0 0
$$475$$ 36.5885 21.1244i 1.67879 0.969252i
$$476$$ 0 0
$$477$$ 3.23205 + 5.59808i 0.147985 + 0.256318i
$$478$$ 0 0
$$479$$ −28.9808 16.7321i −1.32416 0.764507i −0.339775 0.940507i $$-0.610351\pi$$
−0.984390 + 0.176000i $$0.943684\pi$$
$$480$$ 0 0
$$481$$ −12.3756 + 3.06218i −0.564281 + 0.139623i
$$482$$ 0 0
$$483$$ −9.92820 5.73205i −0.451749 0.260817i
$$484$$ 0 0
$$485$$ −11.1962 19.3923i −0.508391 0.880559i
$$486$$ 0 0
$$487$$ 2.70577 1.56218i 0.122610 0.0707890i −0.437441 0.899247i $$-0.644115\pi$$
0.560051 + 0.828458i $$0.310782\pi$$
$$488$$ 0 0
$$489$$ 13.4641i 0.608868i
$$490$$ 0 0
$$491$$ −4.36603 + 7.56218i −0.197036 + 0.341276i −0.947566 0.319560i $$-0.896465\pi$$
0.750530 + 0.660836i $$0.229798\pi$$
$$492$$ 0 0
$$493$$ −25.5885 −1.15245
$$494$$ 0 0
$$495$$ −4.73205 −0.212690
$$496$$ 0 0
$$497$$ 6.46410 11.1962i 0.289955 0.502216i
$$498$$ 0 0
$$499$$ 32.0000i 1.43252i −0.697835 0.716258i $$-0.745853\pi$$
0.697835 0.716258i $$-0.254147\pi$$
$$500$$ 0 0
$$501$$ 8.19615 4.73205i 0.366177 0.211412i
$$502$$ 0 0
$$503$$ 20.4904 + 35.4904i 0.913621 + 1.58244i 0.808908 + 0.587935i $$0.200059\pi$$
0.104713 + 0.994502i $$0.466608\pi$$
$$504$$ 0 0
$$505$$ 6.23205 + 3.59808i 0.277323 + 0.160112i
$$506$$ 0 0
$$507$$ −11.0000 6.92820i −0.488527 0.307692i
$$508$$ 0 0
$$509$$ −11.8923 6.86603i −0.527117 0.304331i 0.212725 0.977112i $$-0.431766\pi$$
−0.739842 + 0.672781i $$0.765100\pi$$
$$510$$ 0 0
$$511$$ −8.56218 14.8301i −0.378768 0.656046i
$$512$$ 0 0
$$513$$ 4.09808 2.36603i 0.180934 0.104463i
$$514$$ 0 0
$$515$$ 56.9808i 2.51087i
$$516$$ 0 0
$$517$$ 1.39230 2.41154i 0.0612335 0.106060i
$$518$$ 0 0
$$519$$ 4.39230 0.192801
$$520$$ 0 0
$$521$$ 41.4449 1.81573 0.907866 0.419260i $$-0.137710\pi$$
0.907866 + 0.419260i $$0.137710\pi$$
$$522$$ 0 0
$$523$$ −11.2224 + 19.4378i −0.490723 + 0.849957i −0.999943 0.0106796i $$-0.996601\pi$$
0.509220 + 0.860636i $$0.329934\pi$$
$$524$$ 0 0
$$525$$ 24.3923i 1.06457i
$$526$$ 0 0
$$527$$ −7.26795 + 4.19615i −0.316597 + 0.182787i
$$528$$ 0 0
$$529$$ 2.69615 + 4.66987i 0.117224 + 0.203038i
$$530$$ 0 0
$$531$$ −6.92820 4.00000i −0.300658 0.173585i
$$532$$ 0 0
$$533$$ −32.8731 + 8.13397i −1.42389 + 0.352322i
$$534$$ 0 0
$$535$$ 32.9545 + 19.0263i 1.42475 + 0.822578i
$$536$$ 0 0
$$537$$ −8.02628 13.9019i −0.346360 0.599912i
$$538$$ 0 0
$$539$$ −0.509619 + 0.294229i −0.0219508 + 0.0126733i
$$540$$ 0 0
$$541$$ 5.67949i 0.244180i −0.992519 0.122090i $$-0.961040\pi$$
0.992519 0.122090i $$-0.0389597\pi$$
$$542$$ 0 0
$$543$$ −9.59808 + 16.6244i −0.411893 + 0.713419i
$$544$$ 0 0
$$545$$ −5.46410 −0.234056
$$546$$ 0 0
$$547$$ 4.19615 0.179415 0.0897073 0.995968i $$-0.471407\pi$$
0.0897073 + 0.995968i $$0.471407\pi$$
$$548$$ 0 0
$$549$$ 4.59808 7.96410i 0.196241 0.339900i
$$550$$ 0 0
$$551$$ 21.1244i 0.899928i
$$552$$ 0 0
$$553$$ −6.00000 + 3.46410i −0.255146 + 0.147309i
$$554$$ 0 0
$$555$$ 6.59808 + 11.4282i 0.280073 + 0.485100i
$$556$$ 0 0
$$557$$ 36.6962 + 21.1865i 1.55487 + 0.897702i 0.997734 + 0.0672780i $$0.0214314\pi$$
0.557132 + 0.830424i $$0.311902\pi$$
$$558$$ 0 0
$$559$$ −33.4641 9.66025i −1.41538 0.408585i
$$560$$ 0 0
$$561$$ 6.29423 + 3.63397i 0.265743 + 0.153427i
$$562$$ 0 0
$$563$$ −17.4641 30.2487i −0.736024 1.27483i −0.954273 0.298938i $$-0.903368\pi$$
0.218248 0.975893i $$-0.429966\pi$$
$$564$$ 0 0
$$565$$ −4.33013 + 2.50000i −0.182170 + 0.105176i
$$566$$ 0 0
$$567$$ 2.73205i 0.114735i
$$568$$ 0 0
$$569$$ 15.3205 26.5359i 0.642269 1.11244i −0.342656 0.939461i $$-0.611326\pi$$
0.984925 0.172982i $$-0.0553402\pi$$
$$570$$ 0 0
$$571$$ 14.0526 0.588081 0.294041 0.955793i $$-0.405000\pi$$
0.294041 + 0.955793i $$0.405000\pi$$
$$572$$ 0 0
$$573$$ −6.92820 −0.289430
$$574$$ 0 0
$$575$$ 18.7321 32.4449i 0.781181 1.35304i
$$576$$ 0 0
$$577$$ 3.73205i 0.155367i 0.996978 + 0.0776837i $$0.0247524\pi$$
−0.996978 + 0.0776837i $$0.975248\pi$$
$$578$$ 0 0
$$579$$ −10.1603 + 5.86603i −0.422246 + 0.243784i
$$580$$ 0 0
$$581$$ −0.267949 0.464102i −0.0111164 0.0192542i
$$582$$ 0 0
$$583$$ 7.09808 + 4.09808i 0.293972 + 0.169725i
$$584$$ 0 0
$$585$$ −3.73205 + 12.9282i −0.154301 + 0.534515i
$$586$$ 0 0
$$587$$ 13.8564 + 8.00000i 0.571915 + 0.330195i 0.757914 0.652355i $$-0.226219\pi$$
−0.185999 + 0.982550i $$0.559552\pi$$
$$588$$ 0 0
$$589$$ 3.46410 + 6.00000i 0.142736 + 0.247226i
$$590$$ 0 0
$$591$$ 15.4641 8.92820i 0.636108 0.367257i
$$592$$ 0 0
$$593$$ 9.14359i 0.375482i 0.982219 + 0.187741i $$0.0601166\pi$$
−0.982219 + 0.187741i $$0.939883\pi$$
$$594$$ 0 0
$$595$$ −29.2224 + 50.6147i −1.19800 + 2.07500i
$$596$$ 0 0
$$597$$ 14.1962 0.581010
$$598$$ 0 0
$$599$$ 2.53590 0.103614 0.0518070 0.998657i $$-0.483502\pi$$
0.0518070 + 0.998657i $$0.483502\pi$$
$$600$$ 0 0
$$601$$ −3.96410 + 6.86603i −0.161699 + 0.280071i −0.935478 0.353385i $$-0.885031\pi$$
0.773779 + 0.633456i $$0.218364\pi$$
$$602$$ 0 0
$$603$$ 13.1244i 0.534465i
$$604$$ 0 0
$$605$$ 30.3564 17.5263i 1.23416 0.712545i
$$606$$ 0 0
$$607$$ −20.3923 35.3205i −0.827698 1.43362i −0.899840 0.436221i $$-0.856317\pi$$
0.0721415 0.997394i $$-0.477017\pi$$
$$608$$ 0 0
$$609$$ 10.5622 + 6.09808i 0.428001 + 0.247107i
$$610$$ 0 0
$$611$$ −5.49038 5.70577i −0.222117 0.230831i
$$612$$ 0 0
$$613$$ 8.13397 + 4.69615i 0.328528 + 0.189676i 0.655187 0.755466i $$-0.272590\pi$$
−0.326659 + 0.945142i $$0.605923\pi$$
$$614$$ 0 0
$$615$$ 17.5263 + 30.3564i 0.706728 + 1.22409i
$$616$$ 0 0
$$617$$ −11.4737 + 6.62436i −0.461915 + 0.266687i −0.712849 0.701318i $$-0.752596\pi$$
0.250934 + 0.968004i $$0.419262\pi$$
$$618$$ 0 0
$$619$$ 17.4641i 0.701942i 0.936386 + 0.350971i $$0.114148\pi$$
−0.936386 + 0.350971i $$0.885852\pi$$
$$620$$ 0 0
$$621$$ 2.09808 3.63397i 0.0841929 0.145826i
$$622$$ 0 0
$$623$$ 25.8564 1.03592
$$624$$ 0 0
$$625$$ 10.0718 0.402872
$$626$$ 0 0
$$627$$ 3.00000 5.19615i 0.119808 0.207514i
$$628$$ 0 0
$$629$$ 20.2679i 0.808136i
$$630$$ 0 0
$$631$$ −6.67949 + 3.85641i −0.265906 + 0.153521i −0.627026 0.778998i $$-0.715728\pi$$
0.361119 + 0.932520i $$0.382395\pi$$
$$632$$ 0 0
$$633$$ −8.19615 14.1962i −0.325768 0.564246i
$$634$$ 0 0
$$635$$ 31.8564 + 18.3923i 1.26418 + 0.729876i
$$636$$ 0 0
$$637$$ 0.401924 + 1.62436i 0.0159248 + 0.0643593i
$$638$$ 0 0
$$639$$ 4.09808 + 2.36603i 0.162117 + 0.0935985i
$$640$$ 0 0
$$641$$ −12.9904 22.5000i −0.513089 0.888697i −0.999885 0.0151806i $$-0.995168\pi$$
0.486796 0.873516i $$-0.338166\pi$$
$$642$$ 0 0
$$643$$ 12.0000 6.92820i 0.473234 0.273222i −0.244359 0.969685i $$-0.578577\pi$$
0.717592 + 0.696463i $$0.245244\pi$$
$$644$$ 0 0
$$645$$ 36.0526i 1.41957i
$$646$$ 0 0
$$647$$ 11.1244 19.2679i 0.437344 0.757501i −0.560140 0.828398i $$-0.689253\pi$$
0.997484 + 0.0708966i $$0.0225860\pi$$
$$648$$ 0 0
$$649$$ −10.1436 −0.398171
$$650$$ 0 0
$$651$$ 4.00000 0.156772
$$652$$ 0 0
$$653$$ 8.73205 15.1244i 0.341712 0.591862i −0.643039 0.765833i $$-0.722327\pi$$
0.984751 + 0.173972i $$0.0556601\pi$$
$$654$$ 0 0
$$655$$ 24.3923i 0.953086i
$$656$$ 0 0
$$657$$ 5.42820 3.13397i 0.211774 0.122268i
$$658$$ 0 0
$$659$$ −5.12436 8.87564i −0.199617 0.345746i 0.748788 0.662810i $$-0.230636\pi$$
−0.948404 + 0.317064i $$0.897303\pi$$
$$660$$ 0 0
$$661$$ 9.86603 + 5.69615i 0.383744 + 0.221555i 0.679446 0.733726i $$-0.262220\pi$$
−0.295702 + 0.955280i $$0.595554\pi$$
$$662$$ 0 0
$$663$$ 14.8923 14.3301i 0.578369 0.556536i
$$664$$ 0 0
$$665$$ 41.7846 + 24.1244i 1.62034 + 0.935502i
$$666$$ 0 0
$$667$$ 9.36603 + 16.2224i 0.362654 + 0.628135i
$$668$$ 0 0
$$669$$ −23.3205 + 13.4641i −0.901623 + 0.520552i
$$670$$ 0 0
$$671$$ 11.6603i 0.450139i
$$672$$ 0 0
$$673$$ 13.9641 24.1865i 0.538277 0.932322i −0.460720 0.887545i $$-0.652409\pi$$
0.998997 0.0447770i $$-0.0142577\pi$$
$$674$$ 0 0
$$675$$ 8.92820 0.343647
$$676$$ 0 0
$$677$$ −45.4641 −1.74733 −0.873664 0.486530i $$-0.838262\pi$$
−0.873664 + 0.486530i $$0.838262\pi$$
$$678$$ 0 0
$$679$$ 8.19615 14.1962i 0.314539 0.544798i
$$680$$ 0 0
$$681$$ 12.1962i 0.467358i
$$682$$ 0 0
$$683$$ −8.78461 + 5.07180i −0.336134 + 0.194067i −0.658561 0.752527i $$-0.728835\pi$$
0.322427 + 0.946594i $$0.395501\pi$$
$$684$$ 0 0
$$685$$ −22.2583 38.5526i −0.850447 1.47302i
$$686$$ 0 0
$$687$$ 10.2679 + 5.92820i 0.391747 + 0.226175i
$$688$$ 0 0
$$689$$ 16.7942 16.1603i 0.639809 0.615657i
$$690$$ 0 0
$$691$$ 37.8109 + 21.8301i 1.43839 + 0.830457i 0.997738 0.0672190i $$-0.0214126\pi$$
0.440656 + 0.897676i $$0.354746\pi$$
$$692$$ 0 0
$$693$$ −1.73205 3.00000i −0.0657952 0.113961i
$$694$$ 0 0
$$695$$ −57.7128 + 33.3205i −2.18917 + 1.26392i
$$696$$ 0 0
$$697$$ 53.8372i 2.03923i
$$698$$ 0 0
$$699$$ 3.92820 6.80385i 0.148578 0.257345i
$$700$$ 0 0
$$701$$ 3.32051 0.125414 0.0627069 0.998032i $$-0.480027\pi$$
0.0627069 + 0.998032i $$0.480027\pi$$
$$702$$ 0 0
$$703$$ −16.7321 −0.631061
$$704$$ 0 0
$$705$$ −4.09808 + 7.09808i −0.154342 + 0.267329i
$$706$$ 0 0
$$707$$ 5.26795i 0.198122i
$$708$$ 0 0
$$709$$ −11.3827 + 6.57180i −0.427486 + 0.246809i −0.698275 0.715830i $$-0.746049\pi$$
0.270789 + 0.962639i $$0.412715\pi$$
$$710$$ 0 0
$$711$$ −1.26795 2.19615i −0.0475518 0.0823622i
$$712$$ 0 0
$$713$$ 5.32051 + 3.07180i 0.199255 + 0.115040i
$$714$$ 0 0
$$715$$ 4.09808 + 16.5622i 0.153259 + 0.619390i
$$716$$ 0 0
$$717$$ −6.63397 3.83013i −0.247750 0.143039i
$$718$$ 0 0
$$719$$ 14.7321 + 25.5167i 0.549413 + 0.951611i 0.998315 + 0.0580299i $$0.0184819\pi$$
−0.448902 + 0.893581i $$0.648185\pi$$
$$720$$ 0 0
$$721$$ 36.1244 20.8564i 1.34534 0.776733i
$$722$$ 0 0
$$723$$ 13.5885i 0.505360i
$$724$$ 0 0
$$725$$ −19.9282 + 34.5167i −0.740115 + 1.28192i
$$726$$ 0 0
$$727$$ −30.9808 −1.14901 −0.574506 0.818500i $$-0.694806\pi$$
−0.574506 + 0.818500i $$0.694806\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 27.6865 47.9545i 1.02402 1.77366i
$$732$$ 0 0
$$733$$ 19.0000i 0.701781i 0.936416 + 0.350891i $$0.114121\pi$$
−0.936416 + 0.350891i $$0.885879\pi$$
$$734$$ 0 0
$$735$$ 1.50000 0.866025i 0.0553283 0.0319438i
$$736$$ 0 0
$$737$$ −8.32051 14.4115i −0.306490 0.530856i
$$738$$ 0 0
$$739$$ −2.53590 1.46410i −0.0932845 0.0538578i 0.452632 0.891697i $$-0.350485\pi$$
−0.545917 + 0.837840i $$0.683818\pi$$
$$740$$ 0 0
$$741$$ −11.8301 12.2942i −0.434591 0.451640i
$$742$$ 0 0
$$743$$ −41.9090 24.1962i −1.53749 0.887671i −0.998985 0.0450491i $$-0.985656\pi$$
−0.538506 0.842622i $$-0.681011\pi$$
$$744$$ 0 0
$$745$$ 24.6244 + 42.6506i 0.902167 + 1.56260i
$$746$$ 0 0
$$747$$ 0.169873 0.0980762i 0.00621533 0.00358842i
$$748$$ 0 0
$$749$$ 27.8564i 1.01785i
$$750$$ 0 0
$$751$$ 24.9545 43.2224i 0.910602 1.57721i 0.0973862 0.995247i $$-0.468952\pi$$
0.813216 0.581962i $$-0.197715\pi$$
$$752$$ 0 0
$$753$$ −13.4641 −0.490659
$$754$$ 0 0
$$755$$ −25.1244 −0.914369
$$756$$ 0 0
$$757$$ −10.4641 + 18.1244i −0.380324 + 0.658741i −0.991109 0.133056i $$-0.957521\pi$$
0.610784 + 0.791797i $$0.290854\pi$$
$$758$$ 0 0
$$759$$ 5.32051i 0.193122i
$$760$$ 0 0
$$761$$ −9.80385 + 5.66025i −0.355389 + 0.205184i −0.667056 0.745007i $$-0.732446\pi$$
0.311667 + 0.950191i $$0.399113\pi$$
$$762$$ 0 0
$$763$$ −2.00000 3.46410i −0.0724049 0.125409i
$$764$$ 0 0
$$765$$ −18.5263 10.6962i −0.669819 0.386720i
$$766$$ 0 0
$$767$$ −8.00000 + 27.7128i −0.288863 + 1.00065i
$$768$$ 0 0
$$769$$ 37.9808 + 21.9282i 1.36962 + 0.790751i 0.990879 0.134751i $$-0.0430235\pi$$
0.378742 + 0.925502i $$0.376357\pi$$
$$770$$ 0 0
$$771$$ −4.66987 8.08846i −0.168181 0.291299i
$$772$$ 0 0
$$773$$ −42.3731 + 24.4641i −1.52405 + 0.879913i −0.524459 + 0.851436i $$0.675732\pi$$
−0.999594 + 0.0284768i $$0.990934\pi$$
$$774$$ 0 0
$$775$$ 13.0718i 0.469553i
$$776$$ 0 0
$$777$$ −4.83013 + 8.36603i −0.173280 + 0.300129i
$$778$$ 0 0
$$779$$ −44.4449 −1.59240
$$780$$ 0 0
$$781$$ 6.00000 0.214697
$$782$$ 0 0
$$783$$ −2.23205 + 3.86603i −0.0797670 + 0.138160i
$$784$$ 0 0
$$785$$ 28.3205i 1.01080i
$$786$$ 0 0
$$787$$ 4.05256 2.33975i 0.144458 0.0834029i −0.426029 0.904710i $$-0.640088\pi$$
0.570487 + 0.821307i $$0.306754\pi$$
$$788$$ 0 0
$$789$$ 5.02628 + 8.70577i 0.178940 + 0.309934i
$$790$$ 0 0
$$791$$ −3.16987 1.83013i −0.112708 0.0650718i
$$792$$ 0 0
$$793$$ −31.8564 9.19615i −1.13125 0.326565i
$$794$$ 0 0
$$795$$ −20.8923 12.0622i −0.740974 0.427801i
$$796$$