# Properties

 Label 450.2.p.c.293.2 Level 450 Weight 2 Character 450.293 Analytic conductor 3.593 Analytic rank 0 Dimension 8 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$450 = 2 \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 450.p (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.59326809096$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{12})$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 293.2 Root $$-0.965926 - 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 450.293 Dual form 450.2.p.c.407.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.258819 - 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.22474 - 0.328169i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})$$ $$q+(0.258819 - 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.866025 + 1.50000i) q^{6} +(-1.22474 - 0.328169i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 - 1.73205i) q^{11} +(1.67303 - 0.448288i) q^{12} +(1.22474 - 0.328169i) q^{13} +(-0.633975 + 1.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.89778 - 0.776457i) q^{18} -7.19615i q^{19} +(1.90192 - 1.09808i) q^{21} +(-0.896575 - 3.34607i) q^{22} +(-2.12132 - 7.91688i) q^{23} -1.73205i q^{24} -1.26795i q^{26} +(3.67423 + 3.67423i) q^{27} +(0.896575 + 0.896575i) q^{28} +(3.63397 + 6.29423i) q^{29} +(5.09808 - 8.83013i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.55291 + 5.79555i) q^{33} +(-1.50000 + 2.59808i) q^{36} +(-1.55291 + 1.55291i) q^{37} +(-6.95095 - 1.86250i) q^{38} +(-1.09808 + 1.90192i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(-0.568406 - 2.12132i) q^{42} +(1.67303 - 6.24384i) q^{43} -3.46410 q^{44} -8.19615 q^{46} +(-1.55291 + 5.79555i) q^{47} +(-1.67303 - 0.448288i) q^{48} +(-4.66987 - 2.69615i) q^{49} +(-1.22474 - 0.328169i) q^{52} +(1.55291 - 1.55291i) q^{53} +(4.50000 - 2.59808i) q^{54} +(1.09808 - 0.633975i) q^{56} +(8.81345 + 8.81345i) q^{57} +(7.02030 - 1.88108i) q^{58} +(-6.23205 + 10.7942i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-7.20977 - 7.20977i) q^{62} +(-0.984508 + 3.67423i) q^{63} -1.00000i q^{64} +(5.19615 + 3.00000i) q^{66} +(-3.22595 - 12.0394i) q^{67} +(12.2942 + 7.09808i) q^{69} +10.7321i q^{71} +(2.12132 + 2.12132i) q^{72} +(3.67423 + 3.67423i) q^{73} +(1.09808 + 1.90192i) q^{74} +(-3.59808 + 6.23205i) q^{76} +(-4.24264 + 1.13681i) q^{77} +(1.55291 + 1.55291i) q^{78} +(-8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(-1.22474 + 1.22474i) q^{82} +(6.57201 + 1.76097i) q^{83} -2.19615 q^{84} +(-5.59808 - 3.23205i) q^{86} +(-12.1595 - 3.25813i) q^{87} +(-0.896575 + 3.34607i) q^{88} +8.66025 q^{89} -1.60770 q^{91} +(-2.12132 + 7.91688i) q^{92} +(4.57081 + 17.0585i) q^{93} +(5.19615 + 3.00000i) q^{94} +(-0.866025 + 1.50000i) q^{96} +(14.1607 + 3.79435i) q^{97} +(-3.81294 + 3.81294i) q^{98} +(-5.19615 - 9.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + O(q^{10})$$ $$8q + 24q^{11} - 12q^{14} + 4q^{16} + 36q^{21} + 36q^{29} + 20q^{31} - 12q^{36} + 12q^{39} - 12q^{41} - 24q^{46} - 72q^{49} + 36q^{54} - 12q^{56} - 36q^{59} + 16q^{61} + 36q^{69} - 12q^{74} - 8q^{76} - 72q^{81} + 24q^{84} - 24q^{86} - 96q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.258819 0.965926i 0.183013 0.683013i
$$3$$ −1.22474 + 1.22474i −0.707107 + 0.707107i
$$4$$ −0.866025 0.500000i −0.433013 0.250000i
$$5$$ 0 0
$$6$$ 0.866025 + 1.50000i 0.353553 + 0.612372i
$$7$$ −1.22474 0.328169i −0.462910 0.124036i 0.0198238 0.999803i $$-0.493689\pi$$
−0.482734 + 0.875767i $$0.660356\pi$$
$$8$$ −0.707107 + 0.707107i −0.250000 + 0.250000i
$$9$$ 3.00000i 1.00000i
$$10$$ 0 0
$$11$$ 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i $$-0.491766\pi$$
0.878668 + 0.477432i $$0.158432\pi$$
$$12$$ 1.67303 0.448288i 0.482963 0.129410i
$$13$$ 1.22474 0.328169i 0.339683 0.0910178i −0.0849451 0.996386i $$-0.527071\pi$$
0.424628 + 0.905368i $$0.360405\pi$$
$$14$$ −0.633975 + 1.09808i −0.169437 + 0.293473i
$$15$$ 0 0
$$16$$ 0.500000 + 0.866025i 0.125000 + 0.216506i
$$17$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$18$$ −2.89778 0.776457i −0.683013 0.183013i
$$19$$ 7.19615i 1.65091i −0.564467 0.825455i $$-0.690918\pi$$
0.564467 0.825455i $$-0.309082\pi$$
$$20$$ 0 0
$$21$$ 1.90192 1.09808i 0.415034 0.239620i
$$22$$ −0.896575 3.34607i −0.191151 0.713384i
$$23$$ −2.12132 7.91688i −0.442326 1.65078i −0.722902 0.690951i $$-0.757192\pi$$
0.280576 0.959832i $$-0.409475\pi$$
$$24$$ 1.73205i 0.353553i
$$25$$ 0 0
$$26$$ 1.26795i 0.248665i
$$27$$ 3.67423 + 3.67423i 0.707107 + 0.707107i
$$28$$ 0.896575 + 0.896575i 0.169437 + 0.169437i
$$29$$ 3.63397 + 6.29423i 0.674812 + 1.16881i 0.976524 + 0.215410i $$0.0691087\pi$$
−0.301712 + 0.953399i $$0.597558\pi$$
$$30$$ 0 0
$$31$$ 5.09808 8.83013i 0.915642 1.58594i 0.109682 0.993967i $$-0.465017\pi$$
0.805959 0.591971i $$-0.201650\pi$$
$$32$$ 0.965926 0.258819i 0.170753 0.0457532i
$$33$$ −1.55291 + 5.79555i −0.270328 + 1.00888i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −1.50000 + 2.59808i −0.250000 + 0.433013i
$$37$$ −1.55291 + 1.55291i −0.255298 + 0.255298i −0.823138 0.567841i $$-0.807779\pi$$
0.567841 + 0.823138i $$0.307779\pi$$
$$38$$ −6.95095 1.86250i −1.12759 0.302138i
$$39$$ −1.09808 + 1.90192i −0.175833 + 0.304552i
$$40$$ 0 0
$$41$$ −1.50000 0.866025i −0.234261 0.135250i 0.378275 0.925693i $$-0.376517\pi$$
−0.612536 + 0.790443i $$0.709851\pi$$
$$42$$ −0.568406 2.12132i −0.0877070 0.327327i
$$43$$ 1.67303 6.24384i 0.255135 0.952177i −0.712880 0.701286i $$-0.752610\pi$$
0.968015 0.250891i $$-0.0807237\pi$$
$$44$$ −3.46410 −0.522233
$$45$$ 0 0
$$46$$ −8.19615 −1.20846
$$47$$ −1.55291 + 5.79555i −0.226516 + 0.845369i 0.755276 + 0.655407i $$0.227503\pi$$
−0.981792 + 0.189961i $$0.939164\pi$$
$$48$$ −1.67303 0.448288i −0.241481 0.0647048i
$$49$$ −4.66987 2.69615i −0.667125 0.385165i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −1.22474 0.328169i −0.169842 0.0455089i
$$53$$ 1.55291 1.55291i 0.213309 0.213309i −0.592362 0.805672i $$-0.701805\pi$$
0.805672 + 0.592362i $$0.201805\pi$$
$$54$$ 4.50000 2.59808i 0.612372 0.353553i
$$55$$ 0 0
$$56$$ 1.09808 0.633975i 0.146737 0.0847184i
$$57$$ 8.81345 + 8.81345i 1.16737 + 1.16737i
$$58$$ 7.02030 1.88108i 0.921811 0.246998i
$$59$$ −6.23205 + 10.7942i −0.811344 + 1.40529i 0.100580 + 0.994929i $$0.467930\pi$$
−0.911924 + 0.410360i $$0.865403\pi$$
$$60$$ 0 0
$$61$$ 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i $$-0.0842377\pi$$
−0.709113 + 0.705095i $$0.750904\pi$$
$$62$$ −7.20977 7.20977i −0.915642 0.915642i
$$63$$ −0.984508 + 3.67423i −0.124036 + 0.462910i
$$64$$ 1.00000i 0.125000i
$$65$$ 0 0
$$66$$ 5.19615 + 3.00000i 0.639602 + 0.369274i
$$67$$ −3.22595 12.0394i −0.394112 1.47085i −0.823287 0.567625i $$-0.807862\pi$$
0.429175 0.903221i $$-0.358804\pi$$
$$68$$ 0 0
$$69$$ 12.2942 + 7.09808i 1.48005 + 0.854508i
$$70$$ 0 0
$$71$$ 10.7321i 1.27366i 0.771004 + 0.636830i $$0.219755\pi$$
−0.771004 + 0.636830i $$0.780245\pi$$
$$72$$ 2.12132 + 2.12132i 0.250000 + 0.250000i
$$73$$ 3.67423 + 3.67423i 0.430037 + 0.430037i 0.888641 0.458604i $$-0.151650\pi$$
−0.458604 + 0.888641i $$0.651650\pi$$
$$74$$ 1.09808 + 1.90192i 0.127649 + 0.221094i
$$75$$ 0 0
$$76$$ −3.59808 + 6.23205i −0.412728 + 0.714865i
$$77$$ −4.24264 + 1.13681i −0.483494 + 0.129552i
$$78$$ 1.55291 + 1.55291i 0.175833 + 0.175833i
$$79$$ −8.66025 + 5.00000i −0.974355 + 0.562544i −0.900561 0.434730i $$-0.856844\pi$$
−0.0737937 + 0.997274i $$0.523511\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ −1.22474 + 1.22474i −0.135250 + 0.135250i
$$83$$ 6.57201 + 1.76097i 0.721372 + 0.193291i 0.600784 0.799412i $$-0.294855\pi$$
0.120588 + 0.992703i $$0.461522\pi$$
$$84$$ −2.19615 −0.239620
$$85$$ 0 0
$$86$$ −5.59808 3.23205i −0.603656 0.348521i
$$87$$ −12.1595 3.25813i −1.30364 0.349308i
$$88$$ −0.896575 + 3.34607i −0.0955753 + 0.356692i
$$89$$ 8.66025 0.917985 0.458993 0.888440i $$-0.348210\pi$$
0.458993 + 0.888440i $$0.348210\pi$$
$$90$$ 0 0
$$91$$ −1.60770 −0.168532
$$92$$ −2.12132 + 7.91688i −0.221163 + 0.825391i
$$93$$ 4.57081 + 17.0585i 0.473971 + 1.76888i
$$94$$ 5.19615 + 3.00000i 0.535942 + 0.309426i
$$95$$ 0 0
$$96$$ −0.866025 + 1.50000i −0.0883883 + 0.153093i
$$97$$ 14.1607 + 3.79435i 1.43780 + 0.385258i 0.891764 0.452501i $$-0.149468\pi$$
0.546039 + 0.837760i $$0.316135\pi$$
$$98$$ −3.81294 + 3.81294i −0.385165 + 0.385165i
$$99$$ −5.19615 9.00000i −0.522233 0.904534i
$$100$$ 0 0
$$101$$ −9.29423 + 5.36603i −0.924810 + 0.533939i −0.885167 0.465274i $$-0.845956\pi$$
−0.0396438 + 0.999214i $$0.512622\pi$$
$$102$$ 0 0
$$103$$ 10.0382 2.68973i 0.989093 0.265027i 0.272223 0.962234i $$-0.412241\pi$$
0.716869 + 0.697207i $$0.245574\pi$$
$$104$$ −0.633975 + 1.09808i −0.0621663 + 0.107675i
$$105$$ 0 0
$$106$$ −1.09808 1.90192i −0.106655 0.184731i
$$107$$ −0.568406 0.568406i −0.0549499 0.0549499i 0.679098 0.734048i $$-0.262371\pi$$
−0.734048 + 0.679098i $$0.762371\pi$$
$$108$$ −1.34486 5.01910i −0.129410 0.482963i
$$109$$ 12.1962i 1.16818i −0.811689 0.584090i $$-0.801452\pi$$
0.811689 0.584090i $$-0.198548\pi$$
$$110$$ 0 0
$$111$$ 3.80385i 0.361045i
$$112$$ −0.328169 1.22474i −0.0310091 0.115728i
$$113$$ −1.91327 7.14042i −0.179985 0.671714i −0.995649 0.0931872i $$-0.970294\pi$$
0.815663 0.578527i $$-0.196372\pi$$
$$114$$ 10.7942 6.23205i 1.01097 0.583685i
$$115$$ 0 0
$$116$$ 7.26795i 0.674812i
$$117$$ −0.984508 3.67423i −0.0910178 0.339683i
$$118$$ 8.81345 + 8.81345i 0.811344 + 0.811344i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.500000 0.866025i 0.0454545 0.0787296i
$$122$$ 3.86370 1.03528i 0.349803 0.0937295i
$$123$$ 2.89778 0.776457i 0.261284 0.0700108i
$$124$$ −8.83013 + 5.09808i −0.792969 + 0.457821i
$$125$$ 0 0
$$126$$ 3.29423 + 1.90192i 0.293473 + 0.169437i
$$127$$ −1.55291 + 1.55291i −0.137799 + 0.137799i −0.772641 0.634843i $$-0.781065\pi$$
0.634843 + 0.772641i $$0.281065\pi$$
$$128$$ −0.965926 0.258819i −0.0853766 0.0228766i
$$129$$ 5.59808 + 9.69615i 0.492883 + 0.853699i
$$130$$ 0 0
$$131$$ −6.00000 3.46410i −0.524222 0.302660i 0.214438 0.976738i $$-0.431208\pi$$
−0.738661 + 0.674078i $$0.764541\pi$$
$$132$$ 4.24264 4.24264i 0.369274 0.369274i
$$133$$ −2.36156 + 8.81345i −0.204773 + 0.764223i
$$134$$ −12.4641 −1.07673
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1.91327 + 7.14042i −0.163462 + 0.610047i 0.834770 + 0.550599i $$0.185601\pi$$
−0.998231 + 0.0594480i $$0.981066\pi$$
$$138$$ 10.0382 10.0382i 0.854508 0.854508i
$$139$$ 6.92820 + 4.00000i 0.587643 + 0.339276i 0.764165 0.645021i $$-0.223151\pi$$
−0.176522 + 0.984297i $$0.556485\pi$$
$$140$$ 0 0
$$141$$ −5.19615 9.00000i −0.437595 0.757937i
$$142$$ 10.3664 + 2.77766i 0.869926 + 0.233096i
$$143$$ 3.10583 3.10583i 0.259722 0.259722i
$$144$$ 2.59808 1.50000i 0.216506 0.125000i
$$145$$ 0 0
$$146$$ 4.50000 2.59808i 0.372423 0.215018i
$$147$$ 9.02150 2.41730i 0.744081 0.199376i
$$148$$ 2.12132 0.568406i 0.174371 0.0467227i
$$149$$ 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i $$-0.569430\pi$$
0.953703 0.300750i $$-0.0972370\pi$$
$$150$$ 0 0
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ 5.08845 + 5.08845i 0.412728 + 0.412728i
$$153$$ 0 0
$$154$$ 4.39230i 0.353942i
$$155$$ 0 0
$$156$$ 1.90192 1.09808i 0.152276 0.0879165i
$$157$$ −2.03339 7.58871i −0.162282 0.605645i −0.998371 0.0570512i $$-0.981830\pi$$
0.836089 0.548593i $$-0.184837\pi$$
$$158$$ 2.58819 + 9.65926i 0.205905 + 0.768449i
$$159$$ 3.80385i 0.301665i
$$160$$ 0 0
$$161$$ 10.3923i 0.819028i
$$162$$ −2.32937 + 8.69333i −0.183013 + 0.683013i
$$163$$ −14.3688 14.3688i −1.12545 1.12545i −0.990908 0.134541i $$-0.957044\pi$$
−0.134541 0.990908i $$-0.542956\pi$$
$$164$$ 0.866025 + 1.50000i 0.0676252 + 0.117130i
$$165$$ 0 0
$$166$$ 3.40192 5.89230i 0.264040 0.457332i
$$167$$ 4.24264 1.13681i 0.328305 0.0879692i −0.0909015 0.995860i $$-0.528975\pi$$
0.419207 + 0.907891i $$0.362308\pi$$
$$168$$ −0.568406 + 2.12132i −0.0438535 + 0.163663i
$$169$$ −9.86603 + 5.69615i −0.758925 + 0.438166i
$$170$$ 0 0
$$171$$ −21.5885 −1.65091
$$172$$ −4.57081 + 4.57081i −0.348521 + 0.348521i
$$173$$ 4.24264 + 1.13681i 0.322562 + 0.0864302i 0.416467 0.909151i $$-0.363268\pi$$
−0.0939047 + 0.995581i $$0.529935\pi$$
$$174$$ −6.29423 + 10.9019i −0.477164 + 0.826473i
$$175$$ 0 0
$$176$$ 3.00000 + 1.73205i 0.226134 + 0.130558i
$$177$$ −5.58750 20.8528i −0.419983 1.56740i
$$178$$ 2.24144 8.36516i 0.168003 0.626995i
$$179$$ −4.85641 −0.362985 −0.181492 0.983392i $$-0.558093\pi$$
−0.181492 + 0.983392i $$0.558093\pi$$
$$180$$ 0 0
$$181$$ 8.39230 0.623795 0.311898 0.950116i $$-0.399035\pi$$
0.311898 + 0.950116i $$0.399035\pi$$
$$182$$ −0.416102 + 1.55291i −0.0308435 + 0.115110i
$$183$$ −6.69213 1.79315i −0.494697 0.132554i
$$184$$ 7.09808 + 4.09808i 0.523277 + 0.302114i
$$185$$ 0 0
$$186$$ 17.6603 1.29491
$$187$$ 0 0
$$188$$ 4.24264 4.24264i 0.309426 0.309426i
$$189$$ −3.29423 5.70577i −0.239620 0.415034i
$$190$$ 0 0
$$191$$ 3.00000 1.73205i 0.217072 0.125327i −0.387522 0.921861i $$-0.626669\pi$$
0.604594 + 0.796534i $$0.293335\pi$$
$$192$$ 1.22474 + 1.22474i 0.0883883 + 0.0883883i
$$193$$ −24.0788 + 6.45189i −1.73323 + 0.464417i −0.980923 0.194396i $$-0.937725\pi$$
−0.752306 + 0.658813i $$0.771059\pi$$
$$194$$ 7.33013 12.6962i 0.526272 0.911531i
$$195$$ 0 0
$$196$$ 2.69615 + 4.66987i 0.192582 + 0.333562i
$$197$$ 2.68973 + 2.68973i 0.191635 + 0.191635i 0.796402 0.604767i $$-0.206734\pi$$
−0.604767 + 0.796402i $$0.706734\pi$$
$$198$$ −10.0382 + 2.68973i −0.713384 + 0.191151i
$$199$$ 0.392305i 0.0278098i 0.999903 + 0.0139049i $$0.00442620\pi$$
−0.999903 + 0.0139049i $$0.995574\pi$$
$$200$$ 0 0
$$201$$ 18.6962 + 10.7942i 1.31872 + 0.761366i
$$202$$ 2.77766 + 10.3664i 0.195435 + 0.729375i
$$203$$ −2.38512 8.90138i −0.167403 0.624755i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 10.3923i 0.724066i
$$207$$ −23.7506 + 6.36396i −1.65078 + 0.442326i
$$208$$ 0.896575 + 0.896575i 0.0621663 + 0.0621663i
$$209$$ −12.4641 21.5885i −0.862160 1.49330i
$$210$$ 0 0
$$211$$ 4.59808 7.96410i 0.316545 0.548271i −0.663220 0.748424i $$-0.730811\pi$$
0.979765 + 0.200153i $$0.0641440\pi$$
$$212$$ −2.12132 + 0.568406i −0.145693 + 0.0390383i
$$213$$ −13.1440 13.1440i −0.900614 0.900614i
$$214$$ −0.696152 + 0.401924i −0.0475880 + 0.0274749i
$$215$$ 0 0
$$216$$ −5.19615 −0.353553
$$217$$ −9.14162 + 9.14162i −0.620574 + 0.620574i
$$218$$ −11.7806 3.15660i −0.797881 0.213792i
$$219$$ −9.00000 −0.608164
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −3.67423 0.984508i −0.246598 0.0660759i
$$223$$ −2.44949 + 9.14162i −0.164030 + 0.612168i 0.834132 + 0.551565i $$0.185969\pi$$
−0.998162 + 0.0606032i $$0.980698\pi$$
$$224$$ −1.26795 −0.0847184
$$225$$ 0 0
$$226$$ −7.39230 −0.491729
$$227$$ 6.00361 22.4058i 0.398473 1.48712i −0.417310 0.908764i $$-0.637027\pi$$
0.815783 0.578358i $$-0.196306\pi$$
$$228$$ −3.22595 12.0394i −0.213644 0.797329i
$$229$$ 14.0263 + 8.09808i 0.926883 + 0.535136i 0.885824 0.464021i $$-0.153594\pi$$
0.0410583 + 0.999157i $$0.486927\pi$$
$$230$$ 0 0
$$231$$ 3.80385 6.58846i 0.250275 0.433489i
$$232$$ −7.02030 1.88108i −0.460905 0.123499i
$$233$$ −17.9551 + 17.9551i −1.17628 + 1.17628i −0.195590 + 0.980686i $$0.562662\pi$$
−0.980686 + 0.195590i $$0.937338\pi$$
$$234$$ −3.80385 −0.248665
$$235$$ 0 0
$$236$$ 10.7942 6.23205i 0.702644 0.405672i
$$237$$ 4.48288 16.7303i 0.291194 1.08675i
$$238$$ 0 0
$$239$$ −7.09808 + 12.2942i −0.459136 + 0.795248i −0.998916 0.0465591i $$-0.985174\pi$$
0.539779 + 0.841807i $$0.318508\pi$$
$$240$$ 0 0
$$241$$ 5.69615 + 9.86603i 0.366921 + 0.635527i 0.989083 0.147363i $$-0.0470785\pi$$
−0.622161 + 0.782889i $$0.713745\pi$$
$$242$$ −0.707107 0.707107i −0.0454545 0.0454545i
$$243$$ 11.0227 11.0227i 0.707107 0.707107i
$$244$$ 4.00000i 0.256074i
$$245$$ 0 0
$$246$$ 3.00000i 0.191273i
$$247$$ −2.36156 8.81345i −0.150262 0.560786i
$$248$$ 2.63896 + 9.84873i 0.167574 + 0.625395i
$$249$$ −10.2058 + 5.89230i −0.646764 + 0.373410i
$$250$$ 0 0
$$251$$ 9.00000i 0.568075i 0.958813 + 0.284037i $$0.0916740\pi$$
−0.958813 + 0.284037i $$0.908326\pi$$
$$252$$ 2.68973 2.68973i 0.169437 0.169437i
$$253$$ −20.0764 20.0764i −1.26219 1.26219i
$$254$$ 1.09808 + 1.90192i 0.0688994 + 0.119337i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −4.45069 + 1.19256i −0.277627 + 0.0743898i −0.394946 0.918704i $$-0.629237\pi$$
0.117319 + 0.993094i $$0.462570\pi$$
$$258$$ 10.8147 2.89778i 0.673291 0.180408i
$$259$$ 2.41154 1.39230i 0.149846 0.0865136i
$$260$$ 0 0
$$261$$ 18.8827 10.9019i 1.16881 0.674812i
$$262$$ −4.89898 + 4.89898i −0.302660 + 0.302660i
$$263$$ 17.9551 + 4.81105i 1.10716 + 0.296662i 0.765676 0.643227i $$-0.222405\pi$$
0.341481 + 0.939889i $$0.389071\pi$$
$$264$$ −3.00000 5.19615i −0.184637 0.319801i
$$265$$ 0 0
$$266$$ 7.90192 + 4.56218i 0.484498 + 0.279725i
$$267$$ −10.6066 + 10.6066i −0.649113 + 0.649113i
$$268$$ −3.22595 + 12.0394i −0.197056 + 0.735423i
$$269$$ 28.0526 1.71039 0.855197 0.518303i $$-0.173436\pi$$
0.855197 + 0.518303i $$0.173436\pi$$
$$270$$ 0 0
$$271$$ −4.58846 −0.278729 −0.139364 0.990241i $$-0.544506\pi$$
−0.139364 + 0.990241i $$0.544506\pi$$
$$272$$ 0 0
$$273$$ 1.96902 1.96902i 0.119170 0.119170i
$$274$$ 6.40192 + 3.69615i 0.386754 + 0.223293i
$$275$$ 0 0
$$276$$ −7.09808 12.2942i −0.427254 0.740026i
$$277$$ 24.6472 + 6.60420i 1.48091 + 0.396808i 0.906656 0.421871i $$-0.138627\pi$$
0.574251 + 0.818679i $$0.305293\pi$$
$$278$$ 5.65685 5.65685i 0.339276 0.339276i
$$279$$ −26.4904 15.2942i −1.58594 0.915642i
$$280$$ 0 0
$$281$$ 9.00000 5.19615i 0.536895 0.309976i −0.206925 0.978357i $$-0.566345\pi$$
0.743820 + 0.668380i $$0.233012\pi$$
$$282$$ −10.0382 + 2.68973i −0.597766 + 0.160171i
$$283$$ −9.58991 + 2.56961i −0.570061 + 0.152747i −0.532325 0.846540i $$-0.678681\pi$$
−0.0377364 + 0.999288i $$0.512015\pi$$
$$284$$ 5.36603 9.29423i 0.318415 0.551511i
$$285$$ 0 0
$$286$$ −2.19615 3.80385i −0.129861 0.224926i
$$287$$ 1.55291 + 1.55291i 0.0916656 + 0.0916656i
$$288$$ −0.776457 2.89778i −0.0457532 0.170753i
$$289$$ 17.0000i 1.00000i
$$290$$ 0 0
$$291$$ −21.9904 + 12.6962i −1.28910 + 0.744262i
$$292$$ −1.34486 5.01910i −0.0787022 0.293720i
$$293$$ 3.67423 + 13.7124i 0.214651 + 0.801089i 0.986289 + 0.165027i $$0.0527711\pi$$
−0.771638 + 0.636062i $$0.780562\pi$$
$$294$$ 9.33975i 0.544705i
$$295$$ 0 0
$$296$$ 2.19615i 0.127649i
$$297$$ 17.3867 + 4.65874i 1.00888 + 0.270328i
$$298$$ −12.7279 12.7279i −0.737309 0.737309i
$$299$$ −5.19615 9.00000i −0.300501 0.520483i
$$300$$ 0 0
$$301$$ −4.09808 + 7.09808i −0.236209 + 0.409126i
$$302$$ 7.72741 2.07055i 0.444662 0.119147i
$$303$$ 4.81105 17.9551i 0.276387 1.03149i
$$304$$ 6.23205 3.59808i 0.357433 0.206364i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −2.44949 + 2.44949i −0.139800 + 0.139800i −0.773543 0.633743i $$-0.781517\pi$$
0.633743 + 0.773543i $$0.281517\pi$$
$$308$$ 4.24264 + 1.13681i 0.241747 + 0.0647759i
$$309$$ −9.00000 + 15.5885i −0.511992 + 0.886796i
$$310$$ 0 0
$$311$$ 21.5885 + 12.4641i 1.22417 + 0.706774i 0.965804 0.259273i $$-0.0834829\pi$$
0.258365 + 0.966047i $$0.416816\pi$$
$$312$$ −0.568406 2.12132i −0.0321797 0.120096i
$$313$$ −0.864390 + 3.22595i −0.0488582 + 0.182341i −0.986043 0.166493i $$-0.946756\pi$$
0.937184 + 0.348834i $$0.113422\pi$$
$$314$$ −7.85641 −0.443363
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ 6.36396 23.7506i 0.357436 1.33397i −0.519956 0.854193i $$-0.674052\pi$$
0.877392 0.479775i $$-0.159282\pi$$
$$318$$ 3.67423 + 0.984508i 0.206041 + 0.0552085i
$$319$$ 21.8038 + 12.5885i 1.22078 + 0.704818i
$$320$$ 0 0
$$321$$ 1.39230 0.0777109
$$322$$ 10.0382 + 2.68973i 0.559407 + 0.149893i
$$323$$ 0 0
$$324$$ 7.79423 + 4.50000i 0.433013 + 0.250000i
$$325$$ 0 0
$$326$$ −17.5981 + 10.1603i −0.974667 + 0.562724i
$$327$$ 14.9372 + 14.9372i 0.826028 + 0.826028i
$$328$$ 1.67303 0.448288i 0.0923778 0.0247525i
$$329$$ 3.80385 6.58846i 0.209713 0.363233i
$$330$$ 0 0
$$331$$ −8.79423 15.2321i −0.483375 0.837229i 0.516443 0.856321i $$-0.327256\pi$$
−0.999818 + 0.0190922i $$0.993922\pi$$
$$332$$ −4.81105 4.81105i −0.264040 0.264040i
$$333$$ 4.65874 + 4.65874i 0.255298 + 0.255298i
$$334$$ 4.39230i 0.240336i
$$335$$ 0 0
$$336$$ 1.90192 + 1.09808i 0.103758 + 0.0599050i
$$337$$ 7.10823 + 26.5283i 0.387210 + 1.44509i 0.834653 + 0.550775i $$0.185668\pi$$
−0.447443 + 0.894312i $$0.647665\pi$$
$$338$$ 2.94855 + 11.0041i 0.160380 + 0.598545i
$$339$$ 11.0885 + 6.40192i 0.602242 + 0.347705i
$$340$$ 0 0
$$341$$ 35.3205i 1.91271i
$$342$$ −5.58750 + 20.8528i −0.302138 + 1.12759i
$$343$$ 11.1106 + 11.1106i 0.599918 + 0.599918i
$$344$$ 3.23205 + 5.59808i 0.174261 + 0.301828i
$$345$$ 0 0
$$346$$ 2.19615 3.80385i 0.118066 0.204496i
$$347$$ 31.6675 8.48528i 1.70000 0.455514i 0.727061 0.686573i $$-0.240886\pi$$
0.972940 + 0.231059i $$0.0742191\pi$$
$$348$$ 8.90138 + 8.90138i 0.477164 + 0.477164i
$$349$$ −1.73205 + 1.00000i −0.0927146 + 0.0535288i −0.545640 0.838019i $$-0.683714\pi$$
0.452926 + 0.891548i $$0.350380\pi$$
$$350$$ 0 0
$$351$$ 5.70577 + 3.29423i 0.304552 + 0.175833i
$$352$$ 2.44949 2.44949i 0.130558 0.130558i
$$353$$ 14.4889 + 3.88229i 0.771166 + 0.206633i 0.622886 0.782312i $$-0.285960\pi$$
0.148279 + 0.988946i $$0.452627\pi$$
$$354$$ −21.5885 −1.14741
$$355$$ 0 0
$$356$$ −7.50000 4.33013i −0.397499 0.229496i
$$357$$ 0 0
$$358$$ −1.25693 + 4.69093i −0.0664308 + 0.247923i
$$359$$ −0.679492 −0.0358622 −0.0179311 0.999839i $$-0.505708\pi$$
−0.0179311 + 0.999839i $$0.505708\pi$$
$$360$$ 0 0
$$361$$ −32.7846 −1.72551
$$362$$ 2.17209 8.10634i 0.114162 0.426060i
$$363$$ 0.448288 + 1.67303i 0.0235290 + 0.0878114i
$$364$$ 1.39230 + 0.803848i 0.0729766 + 0.0421331i
$$365$$ 0 0
$$366$$ −3.46410 + 6.00000i −0.181071 + 0.313625i
$$367$$ −30.7709 8.24504i −1.60623 0.430388i −0.659313 0.751868i $$-0.729153\pi$$
−0.946916 + 0.321481i $$0.895819\pi$$
$$368$$ 5.79555 5.79555i 0.302114 0.302114i
$$369$$ −2.59808 + 4.50000i −0.135250 + 0.234261i
$$370$$ 0 0
$$371$$ −2.41154 + 1.39230i −0.125201 + 0.0722849i
$$372$$ 4.57081 17.0585i 0.236985 0.884442i
$$373$$ 10.9348 2.92996i 0.566181 0.151708i 0.0356365 0.999365i $$-0.488654\pi$$
0.530545 + 0.847657i $$0.321987\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −3.00000 5.19615i −0.154713 0.267971i
$$377$$ 6.51626 + 6.51626i 0.335605 + 0.335605i
$$378$$ −6.36396 + 1.70522i −0.327327 + 0.0877070i
$$379$$ 20.3923i 1.04748i 0.851877 + 0.523741i $$0.175464\pi$$
−0.851877 + 0.523741i $$0.824536\pi$$
$$380$$ 0 0
$$381$$ 3.80385i 0.194877i
$$382$$ −0.896575 3.34607i −0.0458728 0.171200i
$$383$$ 9.46979 + 35.3417i 0.483884 + 1.80588i 0.585036 + 0.811007i $$0.301080\pi$$
−0.101152 + 0.994871i $$0.532253\pi$$
$$384$$ 1.50000 0.866025i 0.0765466 0.0441942i
$$385$$ 0 0
$$386$$ 24.9282i 1.26881i
$$387$$ −18.7315 5.01910i −0.952177 0.255135i
$$388$$ −10.3664 10.3664i −0.526272 0.526272i
$$389$$ −5.19615 9.00000i −0.263455 0.456318i 0.703702 0.710495i $$-0.251529\pi$$
−0.967158 + 0.254177i $$0.918196\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 5.20857 1.39563i 0.263072 0.0704900i
$$393$$ 11.5911 3.10583i 0.584694 0.156668i
$$394$$ 3.29423 1.90192i 0.165961 0.0958175i
$$395$$ 0 0
$$396$$ 10.3923i 0.522233i
$$397$$ −6.03579 + 6.03579i −0.302928 + 0.302928i −0.842158 0.539231i $$-0.818715\pi$$
0.539231 + 0.842158i $$0.318715\pi$$
$$398$$ 0.378937 + 0.101536i 0.0189944 + 0.00508954i
$$399$$ −7.90192 13.6865i −0.395591 0.685184i
$$400$$ 0 0
$$401$$ 9.00000 + 5.19615i 0.449439 + 0.259483i 0.707593 0.706620i $$-0.249781\pi$$
−0.258154 + 0.966104i $$0.583114\pi$$
$$402$$ 15.2653 15.2653i 0.761366 0.761366i
$$403$$ 3.34607 12.4877i 0.166679 0.622056i
$$404$$ 10.7321 0.533939
$$405$$ 0 0
$$406$$ −9.21539 −0.457352
$$407$$ −1.96902 + 7.34847i −0.0976005 + 0.364250i
$$408$$ 0 0
$$409$$ 0.526279 + 0.303848i 0.0260228 + 0.0150243i 0.512955 0.858416i $$-0.328551\pi$$
−0.486932 + 0.873440i $$0.661884\pi$$
$$410$$ 0 0
$$411$$ −6.40192 11.0885i −0.315784 0.546953i
$$412$$ −10.0382 2.68973i −0.494546 0.132513i
$$413$$ 11.1750 11.1750i 0.549886 0.549886i
$$414$$ 24.5885i 1.20846i
$$415$$ 0 0
$$416$$ 1.09808 0.633975i 0.0538376 0.0310832i
$$417$$ −13.3843 + 3.58630i −0.655430 + 0.175622i
$$418$$ −24.0788 + 6.45189i −1.17773 + 0.315572i
$$419$$ −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i $$-0.903887\pi$$
0.734919 + 0.678155i $$0.237220\pi$$
$$420$$ 0 0
$$421$$ 4.29423 + 7.43782i 0.209288 + 0.362497i 0.951490 0.307678i $$-0.0995521\pi$$
−0.742203 + 0.670176i $$0.766219\pi$$
$$422$$ −6.50266 6.50266i −0.316545 0.316545i
$$423$$ 17.3867 + 4.65874i 0.845369 + 0.226516i
$$424$$ 2.19615i 0.106655i
$$425$$ 0 0
$$426$$ −16.0981 + 9.29423i −0.779954 + 0.450307i
$$427$$ −1.31268 4.89898i −0.0635249 0.237078i
$$428$$ 0.208051 + 0.776457i 0.0100565 + 0.0375315i
$$429$$ 7.60770i 0.367303i
$$430$$ 0 0
$$431$$ 3.12436i 0.150495i 0.997165 + 0.0752475i $$0.0239747\pi$$
−0.997165 + 0.0752475i $$0.976025\pi$$
$$432$$ −1.34486 + 5.01910i −0.0647048 + 0.241481i
$$433$$ 21.8695 + 21.8695i 1.05098 + 1.05098i 0.998629 + 0.0523546i $$0.0166726\pi$$
0.0523546 + 0.998629i $$0.483327\pi$$
$$434$$ 6.46410 + 11.1962i 0.310287 + 0.537433i
$$435$$ 0 0
$$436$$ −6.09808 + 10.5622i −0.292045 + 0.505837i
$$437$$ −56.9710 + 15.2653i −2.72529 + 0.730240i
$$438$$ −2.32937 + 8.69333i −0.111302 + 0.415383i
$$439$$ 28.2224 16.2942i 1.34698 0.777681i 0.359162 0.933275i $$-0.383063\pi$$
0.987821 + 0.155594i $$0.0497292\pi$$
$$440$$ 0 0
$$441$$ −8.08846 + 14.0096i −0.385165 + 0.667125i
$$442$$ 0 0
$$443$$ −10.0382 2.68973i −0.476929 0.127793i 0.0123433 0.999924i $$-0.496071\pi$$
−0.489272 + 0.872131i $$0.662738\pi$$
$$444$$ −1.90192 + 3.29423i −0.0902613 + 0.156337i
$$445$$ 0 0
$$446$$ 8.19615 + 4.73205i 0.388099 + 0.224069i
$$447$$ 8.06918 + 30.1146i 0.381659 + 1.42437i
$$448$$ −0.328169 + 1.22474i −0.0155045 + 0.0578638i
$$449$$ 5.87564 0.277289 0.138644 0.990342i $$-0.455725\pi$$
0.138644 + 0.990342i $$0.455725\pi$$
$$450$$ 0 0
$$451$$ −6.00000 −0.282529
$$452$$ −1.91327 + 7.14042i −0.0899926 + 0.335857i
$$453$$ −13.3843 3.58630i −0.628847 0.168499i
$$454$$ −20.0885 11.5981i −0.942798 0.544325i
$$455$$ 0 0
$$456$$ −12.4641 −0.583685
$$457$$ −3.46618 0.928761i −0.162141 0.0434456i 0.176835 0.984240i $$-0.443414\pi$$
−0.338976 + 0.940795i $$0.610081\pi$$
$$458$$ 11.4524 11.4524i 0.535136 0.535136i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −24.2942 + 14.0263i −1.13150 + 0.653269i −0.944310 0.329056i $$-0.893270\pi$$
−0.187185 + 0.982325i $$0.559936\pi$$
$$462$$ −5.37945 5.37945i −0.250275 0.250275i
$$463$$ 7.91688 2.12132i 0.367928 0.0985861i −0.0701175 0.997539i $$-0.522337\pi$$
0.438046 + 0.898953i $$0.355671\pi$$
$$464$$ −3.63397 + 6.29423i −0.168703 + 0.292202i
$$465$$ 0 0
$$466$$ 12.6962 + 21.9904i 0.588138 + 1.01868i
$$467$$ 15.2653 + 15.2653i 0.706396 + 0.706396i 0.965775 0.259380i $$-0.0835181\pi$$
−0.259380 + 0.965775i $$0.583518\pi$$
$$468$$ −0.984508 + 3.67423i −0.0455089 + 0.169842i
$$469$$ 15.8038i 0.729754i
$$470$$ 0 0
$$471$$ 11.7846 + 6.80385i 0.543006 + 0.313505i
$$472$$ −3.22595 12.0394i −0.148486 0.554158i
$$473$$ −5.79555 21.6293i −0.266480 0.994517i
$$474$$ −15.0000 8.66025i −0.688973 0.397779i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −4.65874 4.65874i −0.213309 0.213309i
$$478$$ 10.0382 + 10.0382i 0.459136 + 0.459136i
$$479$$ 10.5622 + 18.2942i 0.482598 + 0.835885i 0.999800 0.0199786i $$-0.00635981\pi$$
−0.517202 + 0.855863i $$0.673026\pi$$
$$480$$ 0 0
$$481$$ −1.39230 + 2.41154i −0.0634836 + 0.109957i
$$482$$ 11.0041 2.94855i 0.501224 0.134303i
$$483$$ −12.7279 12.7279i −0.579141 0.579141i
$$484$$ −0.866025 + 0.500000i −0.0393648 + 0.0227273i
$$485$$ 0 0
$$486$$ −7.79423 13.5000i −0.353553 0.612372i
$$487$$ −15.5935 + 15.5935i −0.706610 + 0.706610i −0.965821 0.259211i $$-0.916537\pi$$
0.259211 + 0.965821i $$0.416537\pi$$
$$488$$ −3.86370 1.03528i −0.174902 0.0468648i
$$489$$ 35.1962 1.59163
$$490$$ 0 0
$$491$$ −31.7942 18.3564i −1.43485 0.828413i −0.437368 0.899283i $$-0.644089\pi$$
−0.997486 + 0.0708697i $$0.977423\pi$$
$$492$$ −2.89778 0.776457i −0.130642 0.0350054i
$$493$$ 0 0
$$494$$ −9.12436 −0.410524
$$495$$ 0 0
$$496$$ 10.1962 0.457821
$$497$$ 3.52193 13.1440i 0.157980 0.589590i
$$498$$ 3.05008 + 11.3831i 0.136677 + 0.510087i
$$499$$ 16.9641 + 9.79423i 0.759417 + 0.438450i 0.829087 0.559120i $$-0.188861\pi$$
−0.0696691 + 0.997570i $$0.522194\pi$$
$$500$$ 0 0
$$501$$ −3.80385 + 6.58846i −0.169943 + 0.294351i
$$502$$ 8.69333 + 2.32937i 0.388002 + 0.103965i
$$503$$ −25.8719 + 25.8719i −1.15357 + 1.15357i −0.167742 + 0.985831i $$0.553648\pi$$
−0.985831 + 0.167742i $$0.946352\pi$$
$$504$$ −1.90192 3.29423i −0.0847184 0.146737i
$$505$$ 0 0
$$506$$ −24.5885 + 14.1962i −1.09309 + 0.631096i
$$507$$ 5.10703 19.0597i 0.226811 0.846471i
$$508$$ 2.12132 0.568406i 0.0941184 0.0252189i
$$509$$ −10.3923 + 18.0000i −0.460631 + 0.797836i −0.998992 0.0448779i $$-0.985710\pi$$
0.538362 + 0.842714i $$0.319043\pi$$
$$510$$ 0 0
$$511$$ −3.29423 5.70577i −0.145728 0.252408i
$$512$$ 0.707107 + 0.707107i 0.0312500 + 0.0312500i
$$513$$ 26.4404 26.4404i 1.16737 1.16737i
$$514$$ 4.60770i 0.203237i
$$515$$ 0 0
$$516$$ 11.1962i 0.492883i
$$517$$ 5.37945 + 20.0764i 0.236588 + 0.882959i
$$518$$ −0.720710 2.68973i −0.0316662 0.118180i
$$519$$ −6.58846 + 3.80385i −0.289201 + 0.166970i
$$520$$ 0 0
$$521$$ 38.7846i 1.69918i −0.527440 0.849592i $$-0.676848\pi$$
0.527440 0.849592i $$-0.323152\pi$$
$$522$$ −5.64325 21.0609i −0.246998 0.921811i
$$523$$ 14.1929 + 14.1929i 0.620612 + 0.620612i 0.945688 0.325076i $$-0.105390\pi$$
−0.325076 + 0.945688i $$0.605390\pi$$
$$524$$ 3.46410 + 6.00000i 0.151330 + 0.262111i
$$525$$ 0 0
$$526$$ 9.29423 16.0981i 0.405248 0.701909i
$$527$$ 0 0
$$528$$ −5.79555 + 1.55291i −0.252219 + 0.0675819i
$$529$$ −38.2583 + 22.0885i −1.66341 + 0.960368i
$$530$$ 0 0
$$531$$ 32.3827 + 18.6962i 1.40529 + 0.811344i
$$532$$ 6.45189 6.45189i 0.279725 0.279725i
$$533$$ −2.12132 0.568406i −0.0918846 0.0246204i
$$534$$ 7.50000 + 12.9904i 0.324557 + 0.562149i
$$535$$ 0 0
$$536$$ 10.7942 + 6.23205i 0.466240 + 0.269184i
$$537$$ 5.94786 5.94786i 0.256669 0.256669i
$$538$$ 7.26054 27.0967i 0.313024 1.16822i
$$539$$ −18.6795 −0.804583
$$540$$ 0 0
$$541$$ 12.3923 0.532787 0.266393 0.963864i $$-0.414168\pi$$
0.266393 + 0.963864i $$0.414168\pi$$
$$542$$ −1.18758 + 4.43211i −0.0510109 + 0.190375i
$$543$$ −10.2784 + 10.2784i −0.441090 + 0.441090i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ −1.39230 2.41154i −0.0595851 0.103205i
$$547$$ 21.4213 + 5.73981i 0.915907 + 0.245416i 0.685835 0.727757i $$-0.259437\pi$$
0.230072 + 0.973174i $$0.426104\pi$$
$$548$$ 5.22715 5.22715i 0.223293 0.223293i
$$549$$ 10.3923 6.00000i 0.443533 0.256074i
$$550$$ 0 0
$$551$$ 45.2942 26.1506i 1.92960 1.11405i
$$552$$ −13.7124 + 3.67423i −0.583640 + 0.156386i
$$553$$ 12.2474 3.28169i 0.520814 0.139552i
$$554$$ 12.7583 22.0981i 0.542050 0.938857i
$$555$$ 0 0
$$556$$ −4.00000 6.92820i −0.169638 0.293821i
$$557$$ 11.5911 + 11.5911i 0.491131 + 0.491131i 0.908662 0.417531i $$-0.137105\pi$$
−0.417531 + 0.908662i $$0.637105\pi$$
$$558$$ −21.6293 + 21.6293i −0.915642 + 0.915642i
$$559$$ 8.19615i 0.346660i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −2.68973 10.0382i −0.113459 0.423436i
$$563$$ −8.69333 32.4440i −0.366380 1.36735i −0.865540 0.500840i $$-0.833025\pi$$
0.499160 0.866510i $$-0.333642\pi$$
$$564$$ 10.3923i 0.437595i
$$565$$ 0 0
$$566$$ 9.92820i 0.417314i
$$567$$ 11.0227 + 2.95352i 0.462910 + 0.124036i
$$568$$ −7.58871 7.58871i −0.318415 0.318415i
$$569$$ −5.53590 9.58846i −0.232077 0.401969i 0.726342 0.687333i $$-0.241219\pi$$
−0.958419 + 0.285364i $$0.907885\pi$$
$$570$$ 0 0
$$571$$ −4.40192 + 7.62436i −0.184215 + 0.319069i −0.943312 0.331908i $$-0.892308\pi$$
0.759097 + 0.650978i $$0.225641\pi$$
$$572$$ −4.24264 + 1.13681i −0.177394 + 0.0475325i
$$573$$ −1.55291 + 5.79555i −0.0648739 + 0.242113i
$$574$$ 1.90192 1.09808i 0.0793848 0.0458328i
$$575$$ 0 0
$$576$$ −3.00000 −0.125000
$$577$$ 15.9217 15.9217i 0.662828 0.662828i −0.293217 0.956046i $$-0.594726\pi$$
0.956046 + 0.293217i $$0.0947260\pi$$
$$578$$ −16.4207 4.39992i −0.683013 0.183013i
$$579$$ 21.5885 37.3923i 0.897186 1.55397i
$$580$$ 0 0
$$581$$ −7.47114 4.31347i −0.309955 0.178953i
$$582$$ 6.57201 + 24.5271i 0.272419 + 1.01668i
$$583$$ 1.96902 7.34847i 0.0815483 0.304342i
$$584$$ −5.19615 −0.215018
$$585$$ 0 0
$$586$$ 14.1962 0.586438
$$587$$ −4.24264 + 15.8338i −0.175113 + 0.653529i 0.821420 + 0.570324i $$0.193182\pi$$
−0.996532 + 0.0832050i $$0.973484\pi$$
$$588$$ −9.02150 2.41730i −0.372040 0.0996879i
$$589$$ −63.5429 36.6865i −2.61824 1.51164i
$$590$$ 0 0
$$591$$ −6.58846 −0.271013
$$592$$ −2.12132 0.568406i −0.0871857 0.0233613i
$$593$$ 14.8492 14.8492i 0.609785 0.609785i −0.333105 0.942890i $$-0.608096\pi$$
0.942890 + 0.333105i $$0.108096\pi$$
$$594$$ 9.00000 15.5885i 0.369274 0.639602i
$$595$$ 0 0
$$596$$ −15.5885 + 9.00000i −0.638528 + 0.368654i
$$597$$ −0.480473 0.480473i −0.0196645 0.0196645i
$$598$$ −10.0382 + 2.68973i −0.410492 + 0.109991i
$$599$$ −5.36603 + 9.29423i −0.219250 + 0.379752i −0.954579 0.297958i $$-0.903694\pi$$
0.735329 + 0.677710i $$0.237028\pi$$
$$600$$ 0 0
$$601$$ −6.39230 11.0718i −0.260748 0.451628i 0.705693 0.708518i $$-0.250636\pi$$
−0.966441 + 0.256890i $$0.917302\pi$$
$$602$$ 5.79555 + 5.79555i 0.236209 + 0.236209i
$$603$$ −36.1182 + 9.67784i −1.47085 + 0.394112i
$$604$$ 8.00000i 0.325515i
$$605$$ 0 0
$$606$$ −16.0981 9.29423i −0.653940 0.377552i
$$607$$ −4.50644 16.8183i −0.182911 0.682632i −0.995068 0.0991937i $$-0.968374\pi$$
0.812157 0.583438i $$-0.198293\pi$$
$$608$$ −1.86250 6.95095i −0.0755344 0.281898i
$$609$$ 13.8231 + 7.98076i 0.560140 + 0.323397i
$$610$$ 0 0
$$611$$ 7.60770i 0.307774i
$$612$$ 0 0
$$613$$ 2.68973 + 2.68973i 0.108637 + 0.108637i 0.759336 0.650699i $$-0.225524\pi$$
−0.650699 + 0.759336i $$0.725524\pi$$
$$614$$ 1.73205 + 3.00000i 0.0698999 + 0.121070i
$$615$$ 0 0
$$616$$ 2.19615 3.80385i 0.0884855 0.153261i
$$617$$ −28.7697 + 7.70882i −1.15823 + 0.310346i −0.786257 0.617900i $$-0.787984\pi$$
−0.371969 + 0.928245i $$0.621317\pi$$
$$618$$ 12.7279 + 12.7279i 0.511992 + 0.511992i
$$619$$ 14.2128 8.20577i 0.571261 0.329818i −0.186392 0.982476i $$-0.559679\pi$$
0.757653 + 0.652658i $$0.226346\pi$$
$$620$$ 0 0
$$621$$ 21.2942 36.8827i 0.854508 1.48005i
$$622$$ 17.6269 17.6269i 0.706774 0.706774i
$$623$$ −10.6066 2.84203i −0.424945 0.113864i
$$624$$ −2.19615 −0.0879165
$$625$$ 0 0
$$626$$ 2.89230 + 1.66987i 0.115600 + 0.0667415i
$$627$$ 41.7057 + 11.1750i 1.66557 + 0.446287i
$$628$$ −2.03339 + 7.58871i −0.0811410 + 0.302822i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 40.7846 1.62361 0.811805 0.583929i $$-0.198485\pi$$
0.811805 + 0.583929i $$0.198485\pi$$
$$632$$ 2.58819 9.65926i 0.102953 0.384225i
$$633$$ 4.12252 + 15.3855i 0.163856 + 0.611517i
$$634$$ −21.2942 12.2942i −0.845702 0.488266i
$$635$$ 0 0
$$636$$ 1.90192 3.29423i 0.0754162 0.130625i
$$637$$ −6.60420 1.76959i −0.261668 0.0701137i
$$638$$ 17.8028 17.8028i 0.704818 0.704818i
$$639$$ 32.1962 1.27366
$$640$$ 0 0
$$641$$ −0.911543 + 0.526279i −0.0360038 + 0.0207868i −0.517894 0.855445i $$-0.673284\pi$$
0.481890 + 0.876232i $$0.339950\pi$$
$$642$$ 0.360355 1.34486i 0.0142221 0.0530775i
$$643$$ 16.0418 4.29839i 0.632627 0.169512i 0.0717654 0.997422i $$-0.477137\pi$$
0.560861 + 0.827910i $$0.310470\pi$$
$$644$$ 5.19615 9.00000i 0.204757 0.354650i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.68973 2.68973i −0.105744 0.105744i 0.652255 0.757999i $$-0.273823\pi$$
−0.757999 + 0.652255i $$0.773823\pi$$
$$648$$ 6.36396 6.36396i 0.250000 0.250000i
$$649$$ 43.1769i 1.69484i
$$650$$ 0 0
$$651$$ 22.3923i 0.877624i
$$652$$ 5.25933 + 19.6281i 0.205971 + 0.768696i
$$653$$ 0.568406 + 2.12132i 0.0222434 + 0.0830137i 0.976155 0.217073i $$-0.0696510\pi$$
−0.953912 + 0.300087i $$0.902984\pi$$
$$654$$ 18.2942 10.5622i 0.715361 0.413014i
$$655$$ 0 0
$$656$$ 1.73205i 0.0676252i
$$657$$ 11.0227 11.0227i 0.430037 0.430037i
$$658$$ −5.37945 5.37945i −0.209713 0.209713i
$$659$$ −11.0885 19.2058i −0.431945 0.748151i 0.565096 0.825025i $$-0.308839\pi$$
−0.997041 + 0.0768747i $$0.975506\pi$$
$$660$$ 0 0
$$661$$ −11.5885 + 20.0718i −0.450739 + 0.780702i −0.998432 0.0559768i $$-0.982173\pi$$
0.547693 + 0.836679i $$0.315506\pi$$
$$662$$ −16.9891 + 4.55223i −0.660302 + 0.176927i
$$663$$ 0 0
$$664$$ −5.89230 + 3.40192i −0.228666 + 0.132020i
$$665$$ 0 0
$$666$$ 5.70577 3.29423i 0.221094 0.127649i
$$667$$ 42.1218 42.1218i 1.63096 1.63096i
$$668$$ −4.24264 1.13681i −0.164153 0.0439846i
$$669$$ −8.19615 14.1962i −0.316882 0.548855i
$$670$$ 0 0
$$671$$ 12.0000 + 6.92820i 0.463255 + 0.267460i
$$672$$ 1.55291 1.55291i 0.0599050 0.0599050i
$$673$$ −0.416102 + 1.55291i −0.0160396 + 0.0598604i −0.973482 0.228765i $$-0.926531\pi$$
0.957442 + 0.288625i $$0.0931981\pi$$
$$674$$ 27.4641 1.05788
$$675$$ 0 0
$$676$$ 11.3923 0.438166
$$677$$ −1.70522 + 6.36396i −0.0655369 + 0.244587i −0.990921 0.134443i $$-0.957076\pi$$
0.925384 + 0.379030i $$0.123742\pi$$
$$678$$ 9.05369 9.05369i 0.347705 0.347705i
$$679$$ −16.0981 9.29423i −0.617787 0.356680i
$$680$$ 0 0
$$681$$ 20.0885 + 34.7942i 0.769791 + 1.33332i
$$682$$ −34.1170 9.14162i −1.30641 0.350051i
$$683$$ −27.9933 + 27.9933i −1.07113 + 1.07113i −0.0738643 + 0.997268i $$0.523533\pi$$
−0.997268 + 0.0738643i $$0.976467\pi$$
$$684$$ 18.6962 + 10.7942i 0.714865 + 0.412728i
$$685$$ 0 0
$$686$$ 13.6077 7.85641i 0.519544 0.299959i
$$687$$ −27.0967 + 7.26054i −1.03380 + 0.277007i
$$688$$ 6.24384 1.67303i 0.238044 0.0637838i
$$689$$ 1.39230 2.41154i 0.0530426 0.0918725i
$$690$$ 0 0
$$691$$ −6.20577 10.7487i −0.236079 0.408900i 0.723507 0.690317i $$-0.242529\pi$$
−0.959586 + 0.281417i $$0.909196\pi$$
$$692$$ −3.10583 3.10583i −0.118066 0.118066i
$$693$$ 3.41044 + 12.7279i 0.129552 + 0.483494i
$$694$$ 32.7846i 1.24449i
$$695$$ 0 0
$$696$$ 10.9019 6.29423i 0.413236 0.238582i
$$697$$ 0 0
$$698$$ 0.517638 + 1.93185i 0.0195929 + 0.0731217i
$$699$$ 43.9808i 1.66351i
$$700$$ 0 0
$$701$$ 21.4641i 0.810688i 0.914164 + 0.405344i $$0.132848\pi$$
−0.914164 + 0.405344i $$0.867152\pi$$
$$702$$ 4.65874 4.65874i 0.175833 0.175833i
$$703$$ 11.1750 + 11.1750i 0.421473 + 0.421473i
$$704$$ −1.73205 3.00000i −0.0652791 0.113067i
$$705$$ 0 0
$$706$$ 7.50000 12.9904i 0.282266 0.488899i
$$707$$ 13.1440 3.52193i 0.494332 0.132456i
$$708$$ −5.58750 + 20.8528i −0.209991 + 0.783698i
$$709$$ 22.3468 12.9019i 0.839251 0.484542i −0.0177584 0.999842i $$-0.505653\pi$$
0.857010 + 0.515300i $$0.172320\pi$$
$$710$$ 0 0
$$711$$ 15.0000 + 25.9808i 0.562544 + 0.974355i
$$712$$ −6.12372 + 6.12372i −0.229496 + 0.229496i
$$713$$ −80.7217 21.6293i −3.02305 0.810024i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 4.20577 + 2.42820i 0.157177 + 0.0907462i
$$717$$ −6.36396 23.7506i −0.237666 0.886983i
$$718$$ −0.175865 + 0.656339i −0.00656324 + 0.0244943i
$$719$$ −39.1244 −1.45909 −0.729546 0.683932i $$-0.760269\pi$$
−0.729546 + 0.683932i $$0.760269\pi$$
$$720$$ 0 0
$$721$$ −13.1769 −0.490734
$$722$$ −8.48528 + 31.6675i −0.315789 + 1.17854i
$$723$$ −19.0597 5.10703i −0.708838 0.189933i
$$724$$ −7.26795 4.19615i −0.270111 0.155949i
$$725$$ 0 0
$$726$$ 1.73205 0.0642824
$$727$$ −6.69213 1.79315i −0.248197 0.0665043i 0.132575 0.991173i $$-0.457675\pi$$
−0.380773 + 0.924669i $$0.624342\pi$$
$$728$$ 1.13681 1.13681i 0.0421331 0.0421331i
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 4.89898 + 4.89898i 0.181071 + 0.181071i
$$733$$ 33.2204 8.90138i 1.22702 0.328780i 0.413604 0.910457i $$-0.364270\pi$$
0.813420 + 0.581677i $$0.197603\pi$$
$$734$$ −15.9282 + 27.5885i −0.587921 + 1.01831i
$$735$$ 0 0
$$736$$ −4.09808 7.09808i −0.151057 0.261639i
$$737$$ −30.5307 30.5307i −1.12461 1.12461i
$$738$$ 3.67423 + 3.67423i 0.135250 + 0.135250i
$$739$$ 11.5885i 0.426288i −0.977021 0.213144i $$-0.931630\pi$$
0.977021 0.213144i $$-0.0683704\pi$$
$$740$$ 0 0
$$741$$ 13.6865 + 7.90192i 0.502787 + 0.290284i
$$742$$ 0.720710 + 2.68973i 0.0264581 + 0.0987430i
$$743$$ −10.1905 38.0315i −0.373853 1.39524i −0.855013 0.518606i $$-0.826451\pi$$
0.481160 0.876633i $$-0.340216\pi$$
$$744$$ −15.2942 8.83013i −0.560714 0.323728i
$$745$$ 0 0
$$746$$ 11.3205i 0.414473i
$$747$$ 5.28290 19.7160i 0.193291 0.721372i
$$748$$ 0 0
$$749$$ 0.509619 + 0.882686i 0.0186211 + 0.0322526i
$$750$$ 0 0
$$751$$ 10.2942 17.8301i 0.375642 0.650631i −0.614781 0.788698i $$-0.710756\pi$$
0.990423 + 0.138067i $$0.0440890\pi$$
$$752$$ −5.79555 + 1.55291i −0.211342 + 0.0566290i
$$753$$ −11.0227 11.0227i −0.401690 0.401690i
$$754$$ 7.98076 4.60770i 0.290642 0.167802i
$$755$$ 0 0
$$756$$ 6.58846i 0.239620i
$$757$$ 10.5187 10.5187i 0.382308 0.382308i −0.489625 0.871933i $$-0.662866\pi$$
0.871933 + 0.489625i $$0.162866\pi$$
$$758$$ 19.6975 + 5.27792i 0.715444 + 0.191703i
$$759$$ 49.1769 1.78501
$$760$$ 0 0
$$761$$ −9.91154 5.72243i −0.359293 0.207438i 0.309478 0.950907i $$-0.399846\pi$$
−0.668771 + 0.743469i $$0.733179\pi$$
$$762$$ −3.67423 0.984508i −0.133103 0.0356650i
$$763$$ −4.00240 + 14.9372i −0.144897 + 0.540762i
$$764$$ −3.46410 −0.125327
$$765$$ 0 0
$$766$$ 36.5885 1.32199
$$767$$ −4.09034 + 15.2653i −0.147693 + 0.551200i
$$768$$ −0.448288 1.67303i −0.0161762 0.0603704i
$$769$$ −28.9186 16.6962i −1.04283 0.602079i −0.122197 0.992506i $$-0.538994\pi$$
−0.920634 + 0.390427i $$0.872327\pi$$
$$770$$ 0 0
$$771$$ 3.99038 6.91154i 0.143710 0.248913i
$$772$$ 24.0788 + 6.45189i 0.866615 + 0.232209i
$$773$$ −6.51626 + 6.51626i −0.234374 + 0.234374i −0.814516 0.580142i $$-0.802997\pi$$
0.580142 + 0.814516i $$0.302997\pi$$
$$774$$ −9.69615 + 16.7942i −0.348521 + 0.603656i
$$775$$ 0 0
$$776$$ −12.6962 + 7.33013i −0.455765 + 0.263136i
$$777$$ −1.24831 + 4.65874i −0.0447827 + 0.167131i
$$778$$ −10.0382 + 2.68973i −0.359887 + 0.0964314i
$$779$$ −6.23205 + 10.7942i −0.223286 + 0.386743i
$$780$$ 0 0
$$781$$ 18.5885 + 32.1962i 0.665147 + 1.15207i
$$782$$ 0 0
$$783$$ −9.77440 + 36.4785i −0.349308 + 1.30364i
$$784$$ 5.39230i 0.192582i
$$785$$ 0 0
$$786$$ 12.0000i