# Properties

 Label 252.2.bf.e.199.2 Level $252$ Weight $2$ Character 252.199 Analytic conductor $2.012$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.bf (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.01223013094$$ 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: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 28) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 199.2 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.199 Dual form 252.2.bf.e.19.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$$ $$q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.36603 - 0.633975i) q^{10} +(-0.866025 - 0.500000i) q^{11} -3.46410i q^{13} +(-3.09808 + 2.09808i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.50000 + 0.866025i) q^{17} +(-2.59808 - 4.50000i) q^{19} +3.46410 q^{20} +(-1.00000 - 1.00000i) q^{22} +(-0.866025 + 0.500000i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(1.26795 - 4.73205i) q^{26} +(-5.00000 + 1.73205i) q^{28} -4.00000 q^{29} +(-0.866025 + 1.50000i) q^{31} +(1.46410 + 5.46410i) q^{32} +(1.73205 + 1.73205i) q^{34} +(-0.866025 + 4.50000i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(-1.90192 - 7.09808i) q^{38} +(4.73205 + 1.26795i) q^{40} -3.46410i q^{41} +2.00000i q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(-4.33013 - 7.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-2.00000 + 2.00000i) q^{50} +(3.46410 - 6.00000i) q^{52} +(-0.500000 + 0.866025i) q^{53} -1.73205 q^{55} +(-7.46410 + 0.535898i) q^{56} +(-5.46410 - 1.46410i) q^{58} +(2.59808 - 4.50000i) q^{59} +(-4.50000 + 2.59808i) q^{61} +(-1.73205 + 1.73205i) q^{62} +8.00000i q^{64} +(-3.00000 - 5.19615i) q^{65} +(2.59808 + 1.50000i) q^{67} +(1.73205 + 3.00000i) q^{68} +(-2.83013 + 5.83013i) q^{70} +14.0000i q^{71} +(7.50000 + 4.33013i) q^{73} +(-1.09808 - 4.09808i) q^{74} -10.3923i q^{76} +(2.50000 - 0.866025i) q^{77} +(7.79423 - 4.50000i) q^{79} +(6.00000 + 3.46410i) q^{80} +(1.26795 - 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(-0.732051 + 2.73205i) q^{86} +(-0.732051 - 2.73205i) q^{88} +(-13.5000 + 7.79423i) q^{89} +(6.92820 + 6.00000i) q^{91} -2.00000 q^{92} +(-3.16987 - 11.8301i) q^{94} +(-7.79423 - 4.50000i) q^{95} +17.3205i q^{97} +(1.16987 - 9.83013i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} + 6q^{5} + 8q^{8} + O(q^{10})$$ $$4q + 2q^{2} + 6q^{5} + 8q^{8} + 6q^{10} - 2q^{14} + 8q^{16} + 6q^{17} - 4q^{22} - 4q^{25} + 12q^{26} - 20q^{28} - 16q^{29} - 8q^{32} - 6q^{37} - 18q^{38} + 12q^{40} - 4q^{44} - 2q^{46} - 4q^{49} - 8q^{50} - 2q^{53} - 16q^{56} - 8q^{58} - 18q^{61} - 12q^{65} + 6q^{70} + 30q^{73} + 6q^{74} + 10q^{77} + 24q^{80} + 12q^{82} + 12q^{85} + 4q^{86} + 4q^{88} - 54q^{89} - 8q^{92} - 30q^{94} + 22q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.36603 + 0.366025i 0.965926 + 0.258819i
$$3$$ 0 0
$$4$$ 1.73205 + 1.00000i 0.866025 + 0.500000i
$$5$$ 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i $$-0.540075\pi$$
0.796387 + 0.604787i $$0.206742\pi$$
$$6$$ 0 0
$$7$$ −1.73205 + 2.00000i −0.654654 + 0.755929i
$$8$$ 2.00000 + 2.00000i 0.707107 + 0.707107i
$$9$$ 0 0
$$10$$ 2.36603 0.633975i 0.748203 0.200480i
$$11$$ −0.866025 0.500000i −0.261116 0.150756i 0.363727 0.931505i $$-0.381504\pi$$
−0.624844 + 0.780750i $$0.714837\pi$$
$$12$$ 0 0
$$13$$ 3.46410i 0.960769i −0.877058 0.480384i $$-0.840497\pi$$
0.877058 0.480384i $$-0.159503\pi$$
$$14$$ −3.09808 + 2.09808i −0.827996 + 0.560734i
$$15$$ 0 0
$$16$$ 2.00000 + 3.46410i 0.500000 + 0.866025i
$$17$$ 1.50000 + 0.866025i 0.363803 + 0.210042i 0.670748 0.741685i $$-0.265973\pi$$
−0.306944 + 0.951727i $$0.599307\pi$$
$$18$$ 0 0
$$19$$ −2.59808 4.50000i −0.596040 1.03237i −0.993399 0.114708i $$-0.963407\pi$$
0.397360 0.917663i $$1.63007\pi$$
$$20$$ 3.46410 0.774597
$$21$$ 0 0
$$22$$ −1.00000 1.00000i −0.213201 0.213201i
$$23$$ −0.866025 + 0.500000i −0.180579 + 0.104257i −0.587565 0.809177i $$-0.699913\pi$$
0.406986 + 0.913434i $$0.366580\pi$$
$$24$$ 0 0
$$25$$ −1.00000 + 1.73205i −0.200000 + 0.346410i
$$26$$ 1.26795 4.73205i 0.248665 0.928032i
$$27$$ 0 0
$$28$$ −5.00000 + 1.73205i −0.944911 + 0.327327i
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ −0.866025 + 1.50000i −0.155543 + 0.269408i −0.933257 0.359211i $$-0.883046\pi$$
0.777714 + 0.628619i $$0.216379\pi$$
$$32$$ 1.46410 + 5.46410i 0.258819 + 0.965926i
$$33$$ 0 0
$$34$$ 1.73205 + 1.73205i 0.297044 + 0.297044i
$$35$$ −0.866025 + 4.50000i −0.146385 + 0.760639i
$$36$$ 0 0
$$37$$ −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i $$-0.245980\pi$$
−0.962580 + 0.270998i $$0.912646\pi$$
$$38$$ −1.90192 7.09808i −0.308533 1.15146i
$$39$$ 0 0
$$40$$ 4.73205 + 1.26795i 0.748203 + 0.200480i
$$41$$ 3.46410i 0.541002i −0.962720 0.270501i $$-0.912811\pi$$
0.962720 0.270501i $$-0.0871893\pi$$
$$42$$ 0 0
$$43$$ 2.00000i 0.304997i 0.988304 + 0.152499i $$0.0487319\pi$$
−0.988304 + 0.152499i $$0.951268\pi$$
$$44$$ −1.00000 1.73205i −0.150756 0.261116i
$$45$$ 0 0
$$46$$ −1.36603 + 0.366025i −0.201409 + 0.0539675i
$$47$$ −4.33013 7.50000i −0.631614 1.09399i −0.987222 0.159352i $$-0.949059\pi$$
0.355608 0.934635i $$1.61573\pi$$
$$48$$ 0 0
$$49$$ −1.00000 6.92820i −0.142857 0.989743i
$$50$$ −2.00000 + 2.00000i −0.282843 + 0.282843i
$$51$$ 0 0
$$52$$ 3.46410 6.00000i 0.480384 0.832050i
$$53$$ −0.500000 + 0.866025i −0.0686803 + 0.118958i −0.898321 0.439340i $$-0.855212\pi$$
0.829640 + 0.558298i $$0.188546\pi$$
$$54$$ 0 0
$$55$$ −1.73205 −0.233550
$$56$$ −7.46410 + 0.535898i −0.997433 + 0.0716124i
$$57$$ 0 0
$$58$$ −5.46410 1.46410i −0.717472 0.192246i
$$59$$ 2.59808 4.50000i 0.338241 0.585850i −0.645861 0.763455i $$-0.723502\pi$$
0.984102 + 0.177605i $$0.0568349\pi$$
$$60$$ 0 0
$$61$$ −4.50000 + 2.59808i −0.576166 + 0.332650i −0.759608 0.650381i $$-0.774609\pi$$
0.183442 + 0.983030i $$0.441276\pi$$
$$62$$ −1.73205 + 1.73205i −0.219971 + 0.219971i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ −3.00000 5.19615i −0.372104 0.644503i
$$66$$ 0 0
$$67$$ 2.59808 + 1.50000i 0.317406 + 0.183254i 0.650236 0.759733i $$-0.274670\pi$$
−0.332830 + 0.942987i $$0.608004\pi$$
$$68$$ 1.73205 + 3.00000i 0.210042 + 0.363803i
$$69$$ 0 0
$$70$$ −2.83013 + 5.83013i −0.338265 + 0.696833i
$$71$$ 14.0000i 1.66149i 0.556650 + 0.830747i $$0.312086\pi$$
−0.556650 + 0.830747i $$0.687914\pi$$
$$72$$ 0 0
$$73$$ 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i $$-0.164160\pi$$
0.00787336 + 0.999969i $$0.497494\pi$$
$$74$$ −1.09808 4.09808i −0.127649 0.476392i
$$75$$ 0 0
$$76$$ 10.3923i 1.19208i
$$77$$ 2.50000 0.866025i 0.284901 0.0986928i
$$78$$ 0 0
$$79$$ 7.79423 4.50000i 0.876919 0.506290i 0.00727784 0.999974i $$-0.497683\pi$$
0.869641 + 0.493684i $$0.164350\pi$$
$$80$$ 6.00000 + 3.46410i 0.670820 + 0.387298i
$$81$$ 0 0
$$82$$ 1.26795 4.73205i 0.140022 0.522568i
$$83$$ 13.8564 1.52094 0.760469 0.649374i $$-0.224969\pi$$
0.760469 + 0.649374i $$0.224969\pi$$
$$84$$ 0 0
$$85$$ 3.00000 0.325396
$$86$$ −0.732051 + 2.73205i −0.0789391 + 0.294605i
$$87$$ 0 0
$$88$$ −0.732051 2.73205i −0.0780369 0.291238i
$$89$$ −13.5000 + 7.79423i −1.43100 + 0.826187i −0.997197 0.0748225i $$-0.976161\pi$$
−0.433800 + 0.901009i $$0.642828\pi$$
$$90$$ 0 0
$$91$$ 6.92820 + 6.00000i 0.726273 + 0.628971i
$$92$$ −2.00000 −0.208514
$$93$$ 0 0
$$94$$ −3.16987 11.8301i −0.326947 1.22018i
$$95$$ −7.79423 4.50000i −0.799671 0.461690i
$$96$$ 0 0
$$97$$ 17.3205i 1.75863i 0.476240 + 0.879316i $$0.342000\pi$$
−0.476240 + 0.879316i $$0.658000\pi$$
$$98$$ 1.16987 9.83013i 0.118175 0.992993i
$$99$$ 0 0
$$100$$ −3.46410 + 2.00000i −0.346410 + 0.200000i
$$101$$ 7.50000 + 4.33013i 0.746278 + 0.430864i 0.824347 0.566084i $$-0.191542\pi$$
−0.0780696 + 0.996948i $$0.524876\pi$$
$$102$$ 0 0
$$103$$ −4.33013 7.50000i −0.426660 0.738997i 0.569914 0.821705i $$-0.306977\pi$$
−0.996574 + 0.0827075i $$0.973643\pi$$
$$104$$ 6.92820 6.92820i 0.679366 0.679366i
$$105$$ 0 0
$$106$$ −1.00000 + 1.00000i −0.0971286 + 0.0971286i
$$107$$ 11.2583 6.50000i 1.08838 0.628379i 0.155238 0.987877i $$-0.450386\pi$$
0.933146 + 0.359498i $$0.117052\pi$$
$$108$$ 0 0
$$109$$ −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i $$-0.975180\pi$$
0.565940 + 0.824447i $$0.308513\pi$$
$$110$$ −2.36603 0.633975i −0.225592 0.0604471i
$$111$$ 0 0
$$112$$ −10.3923 2.00000i −0.981981 0.188982i
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 0 0
$$115$$ −0.866025 + 1.50000i −0.0807573 + 0.139876i
$$116$$ −6.92820 4.00000i −0.643268 0.371391i
$$117$$ 0 0
$$118$$ 5.19615 5.19615i 0.478345 0.478345i
$$119$$ −4.33013 + 1.50000i −0.396942 + 0.137505i
$$120$$ 0 0
$$121$$ −5.00000 8.66025i −0.454545 0.787296i
$$122$$ −7.09808 + 1.90192i −0.642630 + 0.172192i
$$123$$ 0 0
$$124$$ −3.00000 + 1.73205i −0.269408 + 0.155543i
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 6.00000i 0.532414i 0.963916 + 0.266207i $$0.0857705\pi$$
−0.963916 + 0.266207i $$0.914230\pi$$
$$128$$ −2.92820 + 10.9282i −0.258819 + 0.965926i
$$129$$ 0 0
$$130$$ −2.19615 8.19615i −0.192615 0.718850i
$$131$$ −2.59808 4.50000i −0.226995 0.393167i 0.729921 0.683531i $$-0.239557\pi$$
−0.956916 + 0.290365i $$0.906223\pi$$
$$132$$ 0 0
$$133$$ 13.5000 + 2.59808i 1.17060 + 0.225282i
$$134$$ 3.00000 + 3.00000i 0.259161 + 0.259161i
$$135$$ 0 0
$$136$$ 1.26795 + 4.73205i 0.108726 + 0.405770i
$$137$$ 0.500000 0.866025i 0.0427179 0.0739895i −0.843876 0.536538i $$-0.819732\pi$$
0.886594 + 0.462549i $$0.153065\pi$$
$$138$$ 0 0
$$139$$ 6.92820 0.587643 0.293821 0.955860i $$-0.405073\pi$$
0.293821 + 0.955860i $$0.405073\pi$$
$$140$$ −6.00000 + 6.92820i −0.507093 + 0.585540i
$$141$$ 0 0
$$142$$ −5.12436 + 19.1244i −0.430026 + 1.60488i
$$143$$ −1.73205 + 3.00000i −0.144841 + 0.250873i
$$144$$ 0 0
$$145$$ −6.00000 + 3.46410i −0.498273 + 0.287678i
$$146$$ 8.66025 + 8.66025i 0.716728 + 0.716728i
$$147$$ 0 0
$$148$$ 6.00000i 0.493197i
$$149$$ 0.500000 + 0.866025i 0.0409616 + 0.0709476i 0.885779 0.464107i $$-0.153625\pi$$
−0.844818 + 0.535054i $$0.820291\pi$$
$$150$$ 0 0
$$151$$ −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i $$-0.425269\pi$$
−0.725956 + 0.687741i $$0.758602\pi$$
$$152$$ 3.80385 14.1962i 0.308533 1.15146i
$$153$$ 0 0
$$154$$ 3.73205 0.267949i 0.300737 0.0215920i
$$155$$ 3.00000i 0.240966i
$$156$$ 0 0
$$157$$ 1.50000 + 0.866025i 0.119713 + 0.0691164i 0.558661 0.829396i $$-0.311315\pi$$
−0.438948 + 0.898513i $$0.644649\pi$$
$$158$$ 12.2942 3.29423i 0.978076 0.262075i
$$159$$ 0 0
$$160$$ 6.92820 + 6.92820i 0.547723 + 0.547723i
$$161$$ 0.500000 2.59808i 0.0394055 0.204757i
$$162$$ 0 0
$$163$$ 18.1865 10.5000i 1.42448 0.822423i 0.427802 0.903873i $$-0.359288\pi$$
0.996678 + 0.0814491i $$0.0259548\pi$$
$$164$$ 3.46410 6.00000i 0.270501 0.468521i
$$165$$ 0 0
$$166$$ 18.9282 + 5.07180i 1.46911 + 0.393648i
$$167$$ −17.3205 −1.34030 −0.670151 0.742225i $$-0.733770\pi$$
−0.670151 + 0.742225i $$0.733770\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 4.09808 + 1.09808i 0.314308 + 0.0842186i
$$171$$ 0 0
$$172$$ −2.00000 + 3.46410i −0.152499 + 0.264135i
$$173$$ 10.5000 6.06218i 0.798300 0.460899i −0.0445762 0.999006i $$-0.514194\pi$$
0.842876 + 0.538107i $$0.180860\pi$$
$$174$$ 0 0
$$175$$ −1.73205 5.00000i −0.130931 0.377964i
$$176$$ 4.00000i 0.301511i
$$177$$ 0 0
$$178$$ −21.2942 + 5.70577i −1.59607 + 0.427666i
$$179$$ 16.4545 + 9.50000i 1.22987 + 0.710063i 0.967002 0.254770i $$-0.0819996\pi$$
0.262864 + 0.964833i $$0.415333\pi$$
$$180$$ 0 0
$$181$$ 6.92820i 0.514969i −0.966282 0.257485i $$-0.917106\pi$$
0.966282 0.257485i $$-0.0828937\pi$$
$$182$$ 7.26795 + 10.7321i 0.538736 + 0.795513i
$$183$$ 0 0
$$184$$ −2.73205 0.732051i −0.201409 0.0539675i
$$185$$ −4.50000 2.59808i −0.330847 0.191014i
$$186$$ 0 0
$$187$$ −0.866025 1.50000i −0.0633300 0.109691i
$$188$$ 17.3205i 1.26323i
$$189$$ 0 0
$$190$$ −9.00000 9.00000i −0.652929 0.652929i
$$191$$ 0.866025 0.500000i 0.0626634 0.0361787i −0.468341 0.883548i $$-0.655148\pi$$
0.531004 + 0.847369i $$0.321815\pi$$
$$192$$ 0 0
$$193$$ 7.50000 12.9904i 0.539862 0.935068i −0.459049 0.888411i $$-0.651810\pi$$
0.998911 0.0466572i $$-0.0148568\pi$$
$$194$$ −6.33975 + 23.6603i −0.455167 + 1.69871i
$$195$$ 0 0
$$196$$ 5.19615 13.0000i 0.371154 0.928571i
$$197$$ −16.0000 −1.13995 −0.569976 0.821661i $$-0.693048\pi$$
−0.569976 + 0.821661i $$0.693048\pi$$
$$198$$ 0 0
$$199$$ −11.2583 + 19.5000i −0.798082 + 1.38232i 0.122782 + 0.992434i $$0.460818\pi$$
−0.920864 + 0.389885i $$0.872515\pi$$
$$200$$ −5.46410 + 1.46410i −0.386370 + 0.103528i
$$201$$ 0 0
$$202$$ 8.66025 + 8.66025i 0.609333 + 0.609333i
$$203$$ 6.92820 8.00000i 0.486265 0.561490i
$$204$$ 0 0
$$205$$ −3.00000 5.19615i −0.209529 0.362915i
$$206$$ −3.16987 11.8301i −0.220856 0.824244i
$$207$$ 0 0
$$208$$ 12.0000 6.92820i 0.832050 0.480384i
$$209$$ 5.19615i 0.359425i
$$210$$ 0 0
$$211$$ 10.0000i 0.688428i 0.938891 + 0.344214i $$0.111855\pi$$
−0.938891 + 0.344214i $$0.888145\pi$$
$$212$$ −1.73205 + 1.00000i −0.118958 + 0.0686803i
$$213$$ 0 0
$$214$$ 17.7583 4.75833i 1.21393 0.325273i
$$215$$ 1.73205 + 3.00000i 0.118125 + 0.204598i
$$216$$ 0 0
$$217$$ −1.50000 4.33013i −0.101827 0.293948i
$$218$$ −9.00000 + 9.00000i −0.609557 + 0.609557i
$$219$$ 0 0
$$220$$ −3.00000 1.73205i −0.202260 0.116775i
$$221$$ 3.00000 5.19615i 0.201802 0.349531i
$$222$$ 0 0
$$223$$ −6.92820 −0.463947 −0.231973 0.972722i $$-0.574518\pi$$
−0.231973 + 0.972722i $$0.574518\pi$$
$$224$$ −13.4641 6.53590i −0.899608 0.436698i
$$225$$ 0 0
$$226$$ 21.8564 + 5.85641i 1.45387 + 0.389562i
$$227$$ −9.52628 + 16.5000i −0.632281 + 1.09514i 0.354803 + 0.934941i $$0.384548\pi$$
−0.987084 + 0.160202i $$0.948785\pi$$
$$228$$ 0 0
$$229$$ −13.5000 + 7.79423i −0.892105 + 0.515057i −0.874630 0.484790i $$-0.838896\pi$$
−0.0174746 + 0.999847i $$0.505563\pi$$
$$230$$ −1.73205 + 1.73205i −0.114208 + 0.114208i
$$231$$ 0 0
$$232$$ −8.00000 8.00000i −0.525226 0.525226i
$$233$$ −3.50000 6.06218i −0.229293 0.397146i 0.728306 0.685252i $$-0.240308\pi$$
−0.957599 + 0.288106i $$0.906975\pi$$
$$234$$ 0 0
$$235$$ −12.9904 7.50000i −0.847399 0.489246i
$$236$$ 9.00000 5.19615i 0.585850 0.338241i
$$237$$ 0 0
$$238$$ −6.46410 + 0.464102i −0.419005 + 0.0300832i
$$239$$ 20.0000i 1.29369i −0.762620 0.646846i $$-0.776088\pi$$
0.762620 0.646846i $$-0.223912\pi$$
$$240$$ 0 0
$$241$$ −4.50000 2.59808i −0.289870 0.167357i 0.348013 0.937490i $$-0.386857\pi$$
−0.637883 + 0.770133i $$0.720190\pi$$
$$242$$ −3.66025 13.6603i −0.235290 0.878114i
$$243$$ 0 0
$$244$$ −10.3923 −0.665299
$$245$$ −7.50000 9.52628i −0.479157 0.608612i
$$246$$ 0 0
$$247$$ −15.5885 + 9.00000i −0.991870 + 0.572656i
$$248$$ −4.73205 + 1.26795i −0.300486 + 0.0805149i
$$249$$ 0 0
$$250$$ −4.43782 + 16.5622i −0.280673 + 1.04748i
$$251$$ −3.46410 −0.218652 −0.109326 0.994006i $$-0.534869\pi$$
−0.109326 + 0.994006i $$0.534869\pi$$
$$252$$ 0 0
$$253$$ 1.00000 0.0628695
$$254$$ −2.19615 + 8.19615i −0.137799 + 0.514272i
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.500000 + 0.866025i
$$257$$ −4.50000 + 2.59808i −0.280702 + 0.162064i −0.633741 0.773545i $$-0.718482\pi$$
0.353039 + 0.935609i $$0.385148\pi$$
$$258$$ 0 0
$$259$$ 7.79423 + 1.50000i 0.484310 + 0.0932055i
$$260$$ 12.0000i 0.744208i
$$261$$ 0 0
$$262$$ −1.90192 7.09808i −0.117501 0.438521i
$$263$$ −19.9186 11.5000i −1.22823 0.709120i −0.261573 0.965184i $$-0.584241\pi$$
−0.966660 + 0.256063i $$0.917574\pi$$
$$264$$ 0 0
$$265$$ 1.73205i 0.106399i
$$266$$ 17.4904 + 8.49038i 1.07240 + 0.520579i
$$267$$ 0 0
$$268$$ 3.00000 + 5.19615i 0.183254 + 0.317406i
$$269$$ −19.5000 11.2583i −1.18894 0.686433i −0.230871 0.972984i $$-0.574158\pi$$
−0.958065 + 0.286552i $$0.907491\pi$$
$$270$$ 0 0
$$271$$ −7.79423 13.5000i −0.473466 0.820067i 0.526073 0.850439i $$-0.323664\pi$$
−0.999539 + 0.0303728i $$0.990331\pi$$
$$272$$ 6.92820i 0.420084i
$$273$$ 0 0
$$274$$ 1.00000 1.00000i 0.0604122 0.0604122i
$$275$$ 1.73205 1.00000i 0.104447 0.0603023i
$$276$$ 0 0
$$277$$ 6.50000 11.2583i 0.390547 0.676448i −0.601975 0.798515i $$-0.705619\pi$$
0.992522 + 0.122068i $$0.0389525\pi$$
$$278$$ 9.46410 + 2.53590i 0.567619 + 0.152093i
$$279$$ 0 0
$$280$$ −10.7321 + 7.26795i −0.641363 + 0.434343i
$$281$$ 4.00000 0.238620 0.119310 0.992857i $$-0.461932\pi$$
0.119310 + 0.992857i $$0.461932\pi$$
$$282$$ 0 0
$$283$$ 6.06218 10.5000i 0.360359 0.624160i −0.627661 0.778487i $$-0.715988\pi$$
0.988020 + 0.154327i $$0.0493208\pi$$
$$284$$ −14.0000 + 24.2487i −0.830747 + 1.43890i
$$285$$ 0 0
$$286$$ −3.46410 + 3.46410i −0.204837 + 0.204837i
$$287$$ 6.92820 + 6.00000i 0.408959 + 0.354169i
$$288$$ 0 0
$$289$$ −7.00000 12.1244i −0.411765 0.713197i
$$290$$ −9.46410 + 2.53590i −0.555751 + 0.148913i
$$291$$ 0 0
$$292$$ 8.66025 + 15.0000i 0.506803 + 0.877809i
$$293$$ 20.7846i 1.21425i −0.794606 0.607125i $$-0.792323\pi$$
0.794606 0.607125i $$-0.207677\pi$$
$$294$$ 0 0
$$295$$ 9.00000i 0.524000i
$$296$$ 2.19615 8.19615i 0.127649 0.476392i
$$297$$ 0 0
$$298$$ 0.366025 + 1.36603i 0.0212033 + 0.0791317i
$$299$$ 1.73205 + 3.00000i 0.100167 + 0.173494i
$$300$$ 0 0
$$301$$ −4.00000 3.46410i −0.230556 0.199667i
$$302$$ −7.00000 7.00000i −0.402805 0.402805i
$$303$$ 0 0
$$304$$ 10.3923 18.0000i 0.596040 1.03237i
$$305$$ −4.50000 + 7.79423i −0.257669 + 0.446296i
$$306$$ 0 0
$$307$$ −20.7846 −1.18624 −0.593120 0.805114i $$-0.702104\pi$$
−0.593120 + 0.805114i $$0.702104\pi$$
$$308$$ 5.19615 + 1.00000i 0.296078 + 0.0569803i
$$309$$ 0 0
$$310$$ −1.09808 + 4.09808i −0.0623665 + 0.232755i
$$311$$ −4.33013 + 7.50000i −0.245539 + 0.425286i −0.962283 0.272050i $$-0.912298\pi$$
0.716744 + 0.697336i $$0.245632\pi$$
$$312$$ 0 0
$$313$$ 1.50000 0.866025i 0.0847850 0.0489506i −0.457008 0.889463i $$-0.651079\pi$$
0.541793 + 0.840512i $$0.317746\pi$$
$$314$$ 1.73205 + 1.73205i 0.0977453 + 0.0977453i
$$315$$ 0 0
$$316$$ 18.0000 1.01258
$$317$$ 5.50000 + 9.52628i 0.308911 + 0.535049i 0.978124 0.208021i $$-0.0667022\pi$$
−0.669214 + 0.743070i $$0.733369\pi$$
$$318$$ 0 0
$$319$$ 3.46410 + 2.00000i 0.193952 + 0.111979i
$$320$$ 6.92820 + 12.0000i 0.387298 + 0.670820i
$$321$$ 0 0
$$322$$ 1.63397 3.36603i 0.0910578 0.187581i
$$323$$ 9.00000i 0.500773i
$$324$$ 0 0
$$325$$ 6.00000 + 3.46410i 0.332820 + 0.192154i
$$326$$ 28.6865 7.68653i 1.58880 0.425718i
$$327$$ 0 0
$$328$$ 6.92820 6.92820i 0.382546 0.382546i
$$329$$ 22.5000 + 4.33013i 1.24047 + 0.238728i
$$330$$ 0 0
$$331$$ −6.06218 + 3.50000i −0.333207 + 0.192377i −0.657264 0.753660i $$-0.728286\pi$$
0.324057 + 0.946038i $$0.394953\pi$$
$$332$$ 24.0000 + 13.8564i 1.31717 + 0.760469i
$$333$$ 0 0
$$334$$ −23.6603 6.33975i −1.29463 0.346895i
$$335$$ 5.19615 0.283896
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 1.36603 + 0.366025i 0.0743020 + 0.0199092i
$$339$$ 0 0
$$340$$ 5.19615 + 3.00000i 0.281801 + 0.162698i
$$341$$ 1.50000 0.866025i 0.0812296 0.0468979i
$$342$$ 0 0
$$343$$ 15.5885 + 10.0000i 0.841698 + 0.539949i
$$344$$ −4.00000 + 4.00000i −0.215666 + 0.215666i
$$345$$ 0 0
$$346$$ 16.5622 4.43782i 0.890388 0.238579i
$$347$$ 11.2583 + 6.50000i 0.604379 + 0.348938i 0.770762 0.637123i $$-0.219876\pi$$
−0.166383 + 0.986061i $$0.553209\pi$$
$$348$$ 0 0
$$349$$ 10.3923i 0.556287i −0.960539 0.278144i $$-0.910281\pi$$
0.960539 0.278144i $$-0.0897191\pi$$
$$350$$ −0.535898 7.46410i −0.0286450 0.398973i
$$351$$ 0 0
$$352$$ 1.46410 5.46410i 0.0780369 0.291238i
$$353$$ 25.5000 + 14.7224i 1.35723 + 0.783596i 0.989249 0.146238i $$-0.0467166\pi$$
0.367979 + 0.929834i $$0.380050\pi$$
$$354$$ 0 0
$$355$$ 12.1244 + 21.0000i 0.643494 + 1.11456i
$$356$$ −31.1769 −1.65237
$$357$$ 0 0
$$358$$ 19.0000 + 19.0000i 1.00418 + 1.00418i
$$359$$ −19.9186 + 11.5000i −1.05126 + 0.606947i −0.923003 0.384794i $$-0.874273\pi$$
−0.128260 + 0.991741i $$0.540939\pi$$
$$360$$ 0 0
$$361$$ −4.00000 + 6.92820i −0.210526 + 0.364642i
$$362$$ 2.53590 9.46410i 0.133284 0.497422i
$$363$$ 0 0
$$364$$ 6.00000 + 17.3205i 0.314485 + 0.907841i
$$365$$ 15.0000 0.785136
$$366$$ 0 0
$$367$$ 0.866025 1.50000i 0.0452062 0.0782994i −0.842537 0.538639i $$-0.818939\pi$$
0.887743 + 0.460339i $$0.152272\pi$$
$$368$$ −3.46410 2.00000i −0.180579 0.104257i
$$369$$ 0 0
$$370$$ −5.19615 5.19615i −0.270135 0.270135i
$$371$$ −0.866025 2.50000i −0.0449618 0.129794i
$$372$$ 0 0
$$373$$ 14.5000 + 25.1147i 0.750782 + 1.30039i 0.947444 + 0.319921i $$0.103656\pi$$
−0.196663 + 0.980471i $$0.563010\pi$$
$$374$$ −0.633975 2.36603i −0.0327820 0.122344i
$$375$$ 0 0
$$376$$ 6.33975 23.6603i 0.326947 1.22018i
$$377$$ 13.8564i 0.713641i
$$378$$ 0 0
$$379$$ 8.00000i 0.410932i −0.978664 0.205466i $$-0.934129\pi$$
0.978664 0.205466i $$-0.0658711\pi$$
$$380$$ −9.00000 15.5885i −0.461690 0.799671i
$$381$$ 0 0
$$382$$ 1.36603 0.366025i 0.0698919 0.0187275i
$$383$$ 2.59808 + 4.50000i 0.132755 + 0.229939i 0.924738 0.380605i $$-0.124284\pi$$
−0.791982 + 0.610544i $$0.790951\pi$$
$$384$$ 0 0
$$385$$ 3.00000 3.46410i 0.152894 0.176547i
$$386$$ 15.0000 15.0000i 0.763480 0.763480i
$$387$$ 0 0
$$388$$ −17.3205 + 30.0000i −0.879316 + 1.52302i
$$389$$ −9.50000 + 16.4545i −0.481669 + 0.834275i −0.999779 0.0210389i $$-0.993303\pi$$
0.518110 + 0.855314i $$0.326636\pi$$
$$390$$ 0 0
$$391$$ −1.73205 −0.0875936
$$392$$ 11.8564 15.8564i 0.598839 0.800869i
$$393$$ 0 0
$$394$$ −21.8564 5.85641i −1.10111 0.295041i
$$395$$ 7.79423 13.5000i 0.392170 0.679259i
$$396$$ 0 0
$$397$$ 16.5000 9.52628i 0.828111 0.478110i −0.0250943 0.999685i $$-0.507989\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ −22.5167 + 22.5167i −1.12866 + 1.12866i
$$399$$ 0 0
$$400$$ −8.00000 −0.400000
$$401$$ −11.5000 19.9186i −0.574283 0.994687i −0.996119 0.0880147i $$-0.971948\pi$$
0.421837 0.906672i $$-0.361386\pi$$
$$402$$ 0 0
$$403$$ 5.19615 + 3.00000i 0.258839 + 0.149441i
$$404$$ 8.66025 + 15.0000i 0.430864 + 0.746278i
$$405$$ 0 0
$$406$$ 12.3923 8.39230i 0.615020 0.416503i
$$407$$ 3.00000i 0.148704i
$$408$$ 0 0
$$409$$ 22.5000 + 12.9904i 1.11255 + 0.642333i 0.939490 0.342578i $$-0.111300\pi$$
0.173064 + 0.984911i $$0.444633\pi$$
$$410$$ −2.19615 8.19615i −0.108460 0.404779i
$$411$$ 0 0
$$412$$ 17.3205i 0.853320i
$$413$$ 4.50000 + 12.9904i 0.221431 + 0.639215i
$$414$$ 0 0
$$415$$ 20.7846 12.0000i 1.02028 0.589057i
$$416$$ 18.9282 5.07180i 0.928032 0.248665i
$$417$$ 0 0
$$418$$ −1.90192 + 7.09808i −0.0930261 + 0.347178i
$$419$$ −20.7846 −1.01539 −0.507697 0.861536i $$-0.669503\pi$$
−0.507697 + 0.861536i $$0.669503\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −3.66025 + 13.6603i −0.178178 + 0.664971i
$$423$$ 0 0
$$424$$ −2.73205 + 0.732051i −0.132680 + 0.0355515i
$$425$$ −3.00000 + 1.73205i −0.145521 + 0.0840168i
$$426$$ 0 0
$$427$$ 2.59808 13.5000i 0.125730 0.653311i
$$428$$ 26.0000 1.25676
$$429$$ 0 0
$$430$$ 1.26795 + 4.73205i 0.0611459 + 0.228200i
$$431$$ 19.9186 + 11.5000i 0.959444 + 0.553936i 0.896002 0.444050i $$-0.146459\pi$$
0.0634424 + 0.997985i $$0.479792\pi$$
$$432$$ 0 0
$$433$$ 10.3923i 0.499422i 0.968320 + 0.249711i $$0.0803357\pi$$
−0.968320 + 0.249711i $$0.919664\pi$$
$$434$$ −0.464102 6.46410i −0.0222776 0.310287i
$$435$$ 0 0
$$436$$ −15.5885 + 9.00000i −0.746552 + 0.431022i
$$437$$ 4.50000 + 2.59808i 0.215264 + 0.124283i
$$438$$ 0 0
$$439$$ 11.2583 + 19.5000i 0.537331 + 0.930684i 0.999047 + 0.0436563i $$0.0139007\pi$$
−0.461716 + 0.887028i $$0.652766\pi$$
$$440$$ −3.46410 3.46410i −0.165145 0.165145i
$$441$$ 0 0
$$442$$ 6.00000 6.00000i 0.285391 0.285391i
$$443$$ 14.7224 8.50000i 0.699484 0.403847i −0.107671 0.994187i $$-0.534339\pi$$
0.807155 + 0.590339i $$0.201006\pi$$
$$444$$ 0 0
$$445$$ −13.5000 + 23.3827i −0.639961 + 1.10845i
$$446$$ −9.46410 2.53590i −0.448138 0.120078i
$$447$$ 0 0
$$448$$ −16.0000 13.8564i −0.755929 0.654654i
$$449$$ −8.00000 −0.377543 −0.188772 0.982021i $$-0.560451\pi$$
−0.188772 + 0.982021i $$0.560451\pi$$
$$450$$ 0 0
$$451$$ −1.73205 + 3.00000i −0.0815591 + 0.141264i
$$452$$ 27.7128 + 16.0000i 1.30350 + 0.752577i
$$453$$ 0 0
$$454$$ −19.0526 + 19.0526i −0.894181 + 0.894181i
$$455$$ 15.5885 + 3.00000i 0.730798 + 0.140642i
$$456$$ 0 0
$$457$$ −7.50000 12.9904i −0.350835 0.607664i 0.635561 0.772051i $$-0.280769\pi$$
−0.986396 + 0.164386i $$0.947436\pi$$
$$458$$ −21.2942 + 5.70577i −0.995014 + 0.266613i
$$459$$ 0 0
$$460$$ −3.00000 + 1.73205i −0.139876 + 0.0807573i
$$461$$ 17.3205i 0.806696i −0.915047 0.403348i $$-0.867846\pi$$
0.915047 0.403348i $$-0.132154\pi$$
$$462$$ 0 0
$$463$$ 30.0000i 1.39422i −0.716965 0.697109i $$-0.754469\pi$$
0.716965 0.697109i $$-0.245531\pi$$
$$464$$ −8.00000 13.8564i −0.371391 0.643268i
$$465$$ 0 0
$$466$$ −2.56218 9.56218i −0.118691 0.442959i
$$467$$ 4.33013 + 7.50000i 0.200374 + 0.347059i 0.948649 0.316330i $$-0.102451\pi$$
−0.748275 + 0.663389i $$0.769117\pi$$
$$468$$ 0 0
$$469$$ −7.50000 + 2.59808i −0.346318 + 0.119968i
$$470$$ −15.0000 15.0000i −0.691898 0.691898i
$$471$$ 0 0
$$472$$ 14.1962 3.80385i 0.653431 0.175086i
$$473$$ 1.00000 1.73205i 0.0459800 0.0796398i
$$474$$ 0 0
$$475$$ 10.3923 0.476832
$$476$$ −9.00000 1.73205i −0.412514 0.0793884i
$$477$$ 0 0
$$478$$ 7.32051 27.3205i 0.334832 1.24961i
$$479$$ 6.06218 10.5000i 0.276988 0.479757i −0.693647 0.720315i $$-0.743997\pi$$
0.970635 + 0.240558i $$0.0773304\pi$$
$$480$$ 0 0
$$481$$ −9.00000 + 5.19615i −0.410365 + 0.236924i
$$482$$ −5.19615 5.19615i −0.236678 0.236678i
$$483$$ 0 0
$$484$$ 20.0000i 0.909091i
$$485$$ 15.0000 + 25.9808i 0.681115 + 1.17973i
$$486$$ 0 0
$$487$$ 26.8468 + 15.5000i 1.21654 + 0.702372i 0.964177 0.265260i $$-0.0854576\pi$$
0.252367 + 0.967632i $$0.418791\pi$$
$$488$$ −14.1962 3.80385i −0.642630 0.172192i
$$489$$ 0 0
$$490$$ −6.75833 15.7583i −0.305310 0.711889i
$$491$$ 32.0000i 1.44414i −0.691820 0.722070i $$-0.743191\pi$$
0.691820 0.722070i $$-0.256809\pi$$
$$492$$ 0 0
$$493$$ −6.00000 3.46410i −0.270226 0.156015i
$$494$$ −24.5885 + 6.58846i −1.10629 + 0.296429i
$$495$$ 0 0
$$496$$ −6.92820 −0.311086
$$497$$ −28.0000 24.2487i −1.25597 1.08770i
$$498$$ 0 0
$$499$$ −30.3109 + 17.5000i −1.35690 + 0.783408i −0.989205 0.146538i $$-0.953187\pi$$
−0.367697 + 0.929946i $$0.619854\pi$$
$$500$$ −12.1244 + 21.0000i −0.542218 + 0.939149i
$$501$$ 0 0
$$502$$ −4.73205 1.26795i −0.211202 0.0565913i
$$503$$ −6.92820 −0.308913 −0.154457 0.988000i $$-0.549363\pi$$
−0.154457 + 0.988000i $$0.549363\pi$$
$$504$$ 0 0
$$505$$ 15.0000 0.667491
$$506$$ 1.36603 + 0.366025i 0.0607272 + 0.0162718i
$$507$$ 0 0
$$508$$ −6.00000 + 10.3923i −0.266207 + 0.461084i
$$509$$ −10.5000 + 6.06218i −0.465404 + 0.268701i −0.714314 0.699825i $$-0.753261\pi$$
0.248910 + 0.968527i $$0.419928\pi$$
$$510$$ 0 0
$$511$$ −21.6506 + 7.50000i −0.957768 + 0.331780i
$$512$$ −16.0000 + 16.0000i −0.707107 + 0.707107i
$$513$$ 0 0
$$514$$ −7.09808 + 1.90192i −0.313083 + 0.0838903i
$$515$$ −12.9904 7.50000i −0.572425 0.330489i
$$516$$ 0 0
$$517$$ 8.66025i 0.380878i
$$518$$ 10.0981 + 4.90192i 0.443684 + 0.215378i
$$519$$ 0 0
$$520$$ 4.39230 16.3923i 0.192615 0.718850i
$$521$$ −1.50000 0.866025i −0.0657162 0.0379413i 0.466782 0.884372i $$-0.345413\pi$$
−0.532498 + 0.846431i $$0.678747\pi$$
$$522$$ 0 0
$$523$$ −12.9904 22.5000i −0.568030 0.983856i −0.996761 0.0804241i $$-0.974373\pi$$
0.428731 0.903432i $$1.64104\pi$$
$$524$$ 10.3923i 0.453990i
$$525$$ 0 0
$$526$$ −23.0000 23.0000i −1.00285 1.00285i
$$527$$ −2.59808 + 1.50000i −0.113174 + 0.0653410i
$$528$$ 0 0
$$529$$ −11.0000 + 19.0526i −0.478261 + 0.828372i
$$530$$ −0.633975 + 2.36603i −0.0275381 + 0.102774i
$$531$$ 0 0
$$532$$ 20.7846 + 18.0000i 0.901127 + 0.780399i
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ 11.2583 19.5000i 0.486740 0.843059i
$$536$$ 2.19615 + 8.19615i 0.0948593 + 0.354020i
$$537$$ 0 0
$$538$$ −22.5167 22.5167i −0.970762 0.970762i
$$539$$ −2.59808 + 6.50000i −0.111907 + 0.279975i
$$540$$ 0 0
$$541$$ 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i $$-0.0327407\pi$$
−0.586278 + 0.810110i $$0.699407\pi$$
$$542$$ −5.70577 21.2942i −0.245084 0.914665i
$$543$$ 0 0
$$544$$ −2.53590 + 9.46410i −0.108726 + 0.405770i
$$545$$ 15.5885i 0.667736i
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 1.73205 1.00000i 0.0739895 0.0427179i
$$549$$ 0 0
$$550$$ 2.73205 0.732051i 0.116495 0.0312148i
$$551$$ 10.3923 + 18.0000i 0.442727 + 0.766826i
$$552$$ 0 0
$$553$$ −4.50000 + 23.3827i −0.191359 + 0.994333i
$$554$$ 13.0000 13.0000i 0.552317 0.552317i
$$555$$ 0 0
$$556$$ 12.0000 + 6.92820i 0.508913 + 0.293821i
$$557$$ 18.5000 32.0429i 0.783870 1.35770i −0.145802 0.989314i $$-0.546576\pi$$
0.929672 0.368389i $$-0.120091\pi$$
$$558$$ 0 0
$$559$$ 6.92820 0.293032
$$560$$ −17.3205 + 6.00000i −0.731925 + 0.253546i
$$561$$ 0 0
$$562$$ 5.46410 + 1.46410i 0.230489 + 0.0617594i
$$563$$ −11.2583 + 19.5000i −0.474482 + 0.821827i −0.999573 0.0292191i $$-0.990698\pi$$
0.525091 + 0.851046i $$0.324031\pi$$
$$564$$ 0 0
$$565$$ 24.0000 13.8564i 1.00969 0.582943i
$$566$$ 12.1244 12.1244i 0.509625 0.509625i
$$567$$ 0 0
$$568$$ −28.0000 + 28.0000i −1.17485 + 1.17485i
$$569$$ −6.50000 11.2583i −0.272494 0.471974i 0.697006 0.717066i $$-0.254515\pi$$
−0.969500 + 0.245092i $$0.921182\pi$$
$$570$$ 0 0
$$571$$ 18.1865 + 10.5000i 0.761083 + 0.439411i 0.829684 0.558233i $$-0.188520\pi$$
−0.0686016 + 0.997644i $$0.521854\pi$$
$$572$$ −6.00000 + 3.46410i −0.250873 + 0.144841i
$$573$$ 0 0
$$574$$ 7.26795 + 10.7321i 0.303358 + 0.447947i
$$575$$ 2.00000i 0.0834058i
$$576$$ 0 0
$$577$$ −28.5000 16.4545i −1.18647 0.685009i −0.228968 0.973434i $$-0.573535\pi$$
−0.957503 + 0.288425i $$0.906868\pi$$
$$578$$ −5.12436 19.1244i −0.213145 0.795468i
$$579$$ 0 0
$$580$$ −13.8564 −0.575356
$$581$$ −24.0000 + 27.7128i −0.995688 + 1.14972i
$$582$$ 0 0
$$583$$ 0.866025 0.500000i 0.0358671 0.0207079i
$$584$$ 6.33975 + 23.6603i 0.262341 + 0.979068i
$$585$$ 0 0
$$586$$ 7.60770 28.3923i 0.314271 1.17288i
$$587$$ 6.92820 0.285958 0.142979 0.989726i $$-0.454332\pi$$
0.142979 + 0.989726i $$0.454332\pi$$
$$588$$ 0 0
$$589$$ 9.00000 0.370839
$$590$$ 3.29423 12.2942i 0.135621 0.506145i
$$591$$ 0 0
$$592$$ 6.00000 10.3923i 0.246598 0.427121i
$$593$$ 13.5000 7.79423i 0.554379 0.320071i −0.196508 0.980502i $$-0.562960\pi$$
0.750886 + 0.660432i $$0.229627\pi$$
$$594$$ 0 0
$$595$$ −5.19615 + 6.00000i −0.213021 + 0.245976i
$$596$$ 2.00000i 0.0819232i
$$597$$ 0 0
$$598$$ 1.26795 + 4.73205i 0.0518503 + 0.193508i
$$599$$ 14.7224 + 8.50000i 0.601542 + 0.347301i 0.769648 0.638468i $$-0.220432\pi$$
−0.168106 + 0.985769i $$0.553765\pi$$
$$600$$ 0 0
$$601$$ 38.1051i 1.55434i −0.629291 0.777170i $$-0.716654\pi$$
0.629291 0.777170i $$-0.283346\pi$$
$$602$$ −4.19615 6.19615i −0.171022 0.252536i
$$603$$ 0 0
$$604$$ −7.00000 12.1244i −0.284826 0.493333i
$$605$$ −15.0000 8.66025i −0.609837 0.352089i
$$606$$ 0 0
$$607$$ 7.79423 + 13.5000i 0.316358 + 0.547948i 0.979725 0.200346i $$-0.0642066\pi$$
−0.663367 + 0.748294i $$0.730873\pi$$
$$608$$ 20.7846 20.7846i 0.842927 0.842927i
$$609$$ 0 0
$$610$$ −9.00000 + 9.00000i −0.364399 + 0.364399i
$$611$$ −25.9808 + 15.0000i −1.05107 + 0.606835i
$$612$$ 0 0
$$613$$ 15.5000 26.8468i 0.626039 1.08433i −0.362300 0.932062i $$-0.618008\pi$$
0.988339 0.152270i $$-0.0486583\pi$$
$$614$$ −28.3923 7.60770i −1.14582 0.307022i
$$615$$ 0 0
$$616$$ 6.73205 + 3.26795i 0.271242 + 0.131669i
$$617$$ −20.0000 −0.805170 −0.402585 0.915383i $$-0.631888\pi$$
−0.402585 + 0.915383i $$0.631888\pi$$
$$618$$ 0 0
$$619$$ 7.79423 13.5000i 0.313276 0.542611i −0.665793 0.746136i $$-0.731907\pi$$
0.979070 + 0.203526i $$0.0652400\pi$$
$$620$$ −3.00000 + 5.19615i −0.120483 + 0.208683i
$$621$$ 0 0
$$622$$ −8.66025 + 8.66025i −0.347245 + 0.347245i
$$623$$ 7.79423 40.5000i 0.312269 1.62260i
$$624$$ 0 0
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ 2.36603 0.633975i 0.0945654 0.0253387i
$$627$$ 0 0
$$628$$ 1.73205 + 3.00000i 0.0691164 + 0.119713i
$$629$$ 5.19615i 0.207184i
$$630$$ 0 0
$$631$$ 30.0000i 1.19428i 0.802137 + 0.597141i $$0.203697\pi$$
−0.802137 + 0.597141i $$0.796303\pi$$
$$632$$ 24.5885 + 6.58846i 0.978076 + 0.262075i
$$633$$ 0 0
$$634$$ 4.02628 + 15.0263i 0.159904 + 0.596770i
$$635$$ 5.19615 + 9.00000i 0.206203 + 0.357154i
$$636$$ 0 0
$$637$$ −24.0000 + 3.46410i −0.950915 + 0.137253i
$$638$$ 4.00000 + 4.00000i 0.158362 + 0.158362i
$$639$$ 0 0
$$640$$ 5.07180 + 18.9282i 0.200480 + 0.748203i
$$641$$ −6.50000 + 11.2583i −0.256735 + 0.444677i −0.965365 0.260902i $$-0.915980\pi$$
0.708631 + 0.705580i $$0.249313\pi$$
$$642$$ 0 0
$$643$$ 13.8564 0.546443 0.273222 0.961951i $$-0.411911\pi$$
0.273222 + 0.961951i $$0.411911\pi$$
$$644$$ 3.46410 4.00000i 0.136505 0.157622i
$$645$$ 0 0
$$646$$ 3.29423 12.2942i 0.129610 0.483710i
$$647$$ 16.4545 28.5000i 0.646892 1.12045i −0.336968 0.941516i $$-0.609402\pi$$
0.983861 0.178935i $$-0.0572651\pi$$
$$648$$ 0 0
$$649$$ −4.50000 + 2.59808i −0.176640 + 0.101983i
$$650$$ 6.92820 + 6.92820i 0.271746 + 0.271746i
$$651$$ 0 0
$$652$$ 42.0000 1.64485
$$653$$ 15.5000 + 26.8468i 0.606562 + 1.05060i 0.991803 + 0.127780i $$0.0407851\pi$$
−0.385241 + 0.922816i $$0.625882\pi$$
$$654$$ 0 0
$$655$$ −7.79423 4.50000i −0.304546 0.175830i
$$656$$ 12.0000 6.92820i 0.468521 0.270501i
$$657$$ 0 0
$$658$$ 29.1506 + 14.1506i 1.13641 + 0.551649i
$$659$$ 38.0000i 1.48027i 0.672458 + 0.740135i $$0.265238\pi$$
−0.672458 + 0.740135i $$0.734762\pi$$
$$660$$ 0 0
$$661$$ −34.5000 19.9186i −1.34189 0.774743i −0.354809 0.934939i $$-0.615454\pi$$
−0.987085 + 0.160196i $$0.948788\pi$$
$$662$$ −9.56218 + 2.56218i −0.371645 + 0.0995819i
$$663$$ 0 0
$$664$$ 27.7128 + 27.7128i 1.07547 + 1.07547i
$$665$$ 22.5000 7.79423i 0.872513 0.302247i
$$666$$ 0 0
$$667$$ 3.46410 2.00000i 0.134131 0.0774403i
$$668$$ −30.0000 17.3205i −1.16073 0.670151i
$$669$$ 0 0
$$670$$ 7.09808 + 1.90192i 0.274223 + 0.0734777i
$$671$$ 5.19615 0.200595
$$672$$ 0 0
$$673$$ 24.0000 0.925132 0.462566 0.886585i $$-0.346929\pi$$
0.462566 + 0.886585i $$0.346929\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 1.73205 + 1.00000i 0.0666173 + 0.0384615i
$$677$$ 37.5000 21.6506i 1.44124 0.832102i 0.443309 0.896369i $$-0.353804\pi$$
0.997933 + 0.0642672i $$0.0204710\pi$$
$$678$$ 0 0
$$679$$ −34.6410 30.0000i −1.32940 1.15129i
$$680$$ 6.00000 + 6.00000i 0.230089 + 0.230089i
$$681$$ 0 0
$$682$$ 2.36603 0.633975i 0.0905998 0.0242761i
$$683$$ −21.6506 12.5000i −0.828439 0.478299i 0.0248792 0.999690i $$-0.492080\pi$$
−0.853318 + 0.521391i $$0.825413\pi$$
$$684$$ 0 0
$$685$$ 1.73205i 0.0661783i
$$686$$ 17.6340 + 19.3660i 0.673268 + 0.739398i
$$687$$ 0 0
$$688$$ −6.92820 + 4.00000i −0.264135 + 0.152499i
$$689$$ 3.00000 + 1.73205i 0.114291 + 0.0659859i
$$690$$ 0 0
$$691$$ 6.06218 + 10.5000i 0.230616 + 0.399439i 0.957990 0.286803i $$-0.0925925\pi$$
−0.727373 + 0.686242i $$0.759259\pi$$
$$692$$ 24.2487 0.921798
$$693$$ 0 0
$$694$$ 13.0000 + 13.0000i 0.493473 + 0.493473i
$$695$$ 10.3923 6.00000i 0.394203 0.227593i
$$696$$ 0 0
$$697$$ 3.00000 5.19615i 0.113633 0.196818i
$$698$$ 3.80385 14.1962i 0.143978 0.537332i
$$699$$ 0 0
$$700$$ 2.00000 10.3923i 0.0755929 0.392792i
$$701$$ 26.0000 0.982006 0.491003 0.871158i $$-0.336630\pi$$
0.491003 + 0.871158i $$0.336630\pi$$
$$702$$ 0 0
$$703$$ −7.79423 + 13.5000i −0.293965 + 0.509162i
$$704$$ 4.00000 6.92820i 0.150756 0.261116i
$$705$$ 0 0
$$706$$ 29.4449 + 29.4449i 1.10817 + 1.10817i
$$707$$ −21.6506 + 7.50000i −0.814256 + 0.282067i
$$708$$ 0 0
$$709$$ 4.50000 + 7.79423i 0.169001 + 0.292718i 0.938069 0.346449i $$-0.112613\pi$$
−0.769068 + 0.639167i $$0.779279\pi$$
$$710$$ 8.87564 + 33.1244i 0.333097 + 1.24313i
$$711$$ 0 0
$$712$$ −42.5885 11.4115i −1.59607 0.427666i
$$713$$ 1.73205i 0.0648658i
$$714$$ 0 0
$$715$$ 6.00000i 0.224387i
$$716$$ 19.0000 + 32.9090i 0.710063 + 1.22987i
$$717$$ 0 0
$$718$$ −31.4186 + 8.41858i −1.17253 + 0.314179i
$$719$$ −12.9904 22.5000i −0.484459 0.839108i 0.515381 0.856961i $$-0.327650\pi$$
−0.999841 + 0.0178527i $$0.994317\pi$$
$$720$$ 0 0
$$721$$ 22.5000 + 4.33013i 0.837944 + 0.161262i
$$722$$ −8.00000 + 8.00000i −0.297729 + 0.297729i
$$723$$ 0 0
$$724$$ 6.92820 12.0000i 0.257485 0.445976i
$$725$$ 4.00000 6.92820i 0.148556 0.257307i
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 1.85641 + 25.8564i 0.0688030 + 0.958302i
$$729$$ 0 0
$$730$$ 20.4904 + 5.49038i 0.758383 + 0.203208i
$$731$$ −1.73205 + 3.00000i −0.0640622 + 0.110959i
$$732$$ 0 0
$$733$$ 37.5000 21.6506i 1.38509 0.799684i 0.392337 0.919822i $$-0.371667\pi$$
0.992757 + 0.120137i $$0.0383334\pi$$
$$734$$ 1.73205 1.73205i 0.0639312 0.0639312i
$$735$$ 0 0
$$736$$ −4.00000 4.00000i −0.147442 0.147442i
$$737$$ −1.50000 2.59808i −0.0552532 0.0957014i
$$738$$ 0 0
$$739$$ −44.1673 25.5000i −1.62472 0.938033i −0.985634 0.168898i $$-0.945979\pi$$
−0.639087 0.769135i $$1.27931\pi$$
$$740$$ −5.19615 9.00000i −0.191014 0.330847i
$$741$$ 0 0
$$742$$ −0.267949 3.73205i −0.00983672 0.137008i
$$743$$ 34.0000i 1.24734i 0.781688 + 0.623670i $$0.214359\pi$$
−0.781688 + 0.623670i $$0.785641\pi$$
$$744$$ 0 0
$$745$$ 1.50000 + 0.866025i 0.0549557 + 0.0317287i
$$746$$ 10.6147 + 39.6147i 0.388633 + 1.45040i
$$747$$ 0 0
$$748$$ 3.46410i 0.126660i
$$749$$ −6.50000 + 33.7750i −0.237505 + 1.23411i
$$750$$ 0 0
$$751$$ −21.6506 + 12.5000i −0.790043 + 0.456131i −0.839978 0.542621i $$-0.817432\pi$$
0.0499348 + 0.998752i $$0.484099\pi$$
$$752$$ 17.3205 30.0000i 0.631614 1.09399i
$$753$$ 0 0
$$754$$ −5.07180 + 18.9282i −0.184704 + 0.689325i
$$755$$ −12.1244 −0.441250
$$756$$ 0 0
$$757$$ −48.0000 −1.74459 −0.872295 0.488980i $$-0.837369\pi$$
−0.872295 + 0.488980i $$0.837369\pi$$
$$758$$ 2.92820 10.9282i 0.106357 0.396930i
$$759$$ 0 0
$$760$$ −6.58846 24.5885i −0.238988 0.891917i
$$761$$ −16.5000 + 9.52628i −0.598125 + 0.345327i −0.768303 0.640086i $$-0.778899\pi$$
0.170179 + 0.985413i $$0.445565\pi$$
$$762$$ 0 0
$$763$$ −7.79423 22.5000i −0.282170 0.814555i
$$764$$ 2.00000 0.0723575
$$765$$ 0 0
$$766$$ 1.90192 + 7.09808i 0.0687193 + 0.256464i
$$767$$ −15.5885 9.00000i −0.562867 0.324971i
$$768$$ 0 0
$$769$$ 3.46410i 0.124919i 0.998048 + 0.0624593i $$0.0198944\pi$$
−0.998048 + 0.0624593i $$0.980106\pi$$
$$770$$ 5.36603 3.63397i 0.193378 0.130959i
$$771$$ 0 0
$$772$$ 25.9808 15.0000i 0.935068 0.539862i
$$773$$ −22.5000 12.9904i −0.809269 0.467232i 0.0374331 0.999299i $$-0.488082\pi$$
−0.846702 + 0.532068i $$0.821415\pi$$
$$774$$ 0 0
$$775$$ −1.73205 3.00000i −0.0622171 0.107763i
$$776$$ −34.6410 + 34.6410i −1.24354 + 1.24354i
$$777$$ 0 0
$$778$$ −19.0000 + 19.0000i −0.681183 + 0.681183i
$$779$$ −15.5885 + 9.00000i −0.558514 + 0.322458i
$$780$$ 0 0
$$781$$ 7.00000 12.1244i 0.250480 0.433844i
$$782$$ −2.36603 0.633975i −0.0846089 0.0226709i
$$783$$ 0 0
$$784$$ 22.0000 17.3205i 0.785714 0.618590i
$$785$$ 3.00000 0.107075
$$786$$ 0 0
$$787$$ −2.59808 + 4.50000i −0.0926114 + 0.160408i −0.908609 0.417647i $$-0.862855\pi$$