# Properties

 Label 196.2.f.a.19.1 Level $196$ Weight $2$ Character 196.19 Analytic conductor $1.565$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$196 = 2^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 196.f (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.56506787962$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 28) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 19.1 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 196.19 Dual form 196.2.f.a.31.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$$ $$q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 0.633975i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-3.00000 - 1.73205i) q^{12} -3.46410i q^{13} -3.00000i q^{15} +(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} +(4.73205 + 1.26795i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(1.26795 + 4.73205i) q^{26} -5.19615 q^{27} +4.00000 q^{29} +(1.09808 + 4.09808i) q^{30} +(0.866025 + 1.50000i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-1.50000 - 0.866025i) q^{33} +(-1.73205 + 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(-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} -6.92820 q^{48} +(2.00000 + 2.00000i) q^{50} +(-2.59808 - 1.50000i) q^{51} +(-3.46410 - 6.00000i) q^{52} +(0.500000 + 0.866025i) q^{53} +(7.09808 - 1.90192i) q^{54} +1.73205 q^{55} -9.00000 q^{57} +(-5.46410 + 1.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(4.50000 + 2.59808i) q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +(3.00000 - 5.19615i) q^{65} +(2.36603 + 0.633975i) q^{66} +(2.59808 - 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} -1.73205i q^{69} +14.0000i q^{71} +(-7.50000 + 4.33013i) q^{73} +(1.09808 - 4.09808i) q^{74} +(-1.73205 + 3.00000i) q^{75} -10.3923i q^{76} +(6.00000 - 6.00000i) q^{78} +(7.79423 + 4.50000i) q^{79} +(6.00000 - 3.46410i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-1.26795 - 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(0.732051 + 2.73205i) q^{86} +(-3.46410 - 6.00000i) q^{87} +(-0.732051 + 2.73205i) q^{88} +(-13.5000 - 7.79423i) q^{89} +2.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(3.16987 - 11.8301i) q^{94} +(7.79423 - 4.50000i) q^{95} +(9.46410 - 2.53590i) q^{96} +17.3205i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} + 6q^{5} - 8q^{8} + O(q^{10})$$ $$4q - 2q^{2} + 6q^{5} - 8q^{8} - 6q^{10} - 12q^{12} + 8q^{16} + 6q^{17} - 4q^{22} + 12q^{24} - 4q^{25} + 12q^{26} + 16q^{29} - 6q^{30} + 8q^{32} - 6q^{33} - 6q^{37} - 18q^{38} - 12q^{40} + 4q^{44} - 2q^{46} + 8q^{50} + 2q^{53} + 18q^{54} - 36q^{57} - 8q^{58} - 12q^{60} + 18q^{61} + 12q^{65} + 6q^{66} - 30q^{73} - 6q^{74} + 24q^{78} + 24q^{80} + 18q^{81} - 12q^{82} + 12q^{85} - 4q^{86} + 4q^{88} - 54q^{89} + 8q^{92} + 6q^{93} + 30q^{94} + 24q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$$.

 $$n$$ $$99$$ $$101$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.36603 + 0.366025i −0.965926 + 0.258819i
$$3$$ −0.866025 1.50000i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$4$$ 1.73205 1.00000i 0.866025 0.500000i
$$5$$ 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i $$-0.206742\pi$$
−0.125567 + 0.992085i $$0.540075\pi$$
$$6$$ 1.73205 + 1.73205i 0.707107 + 0.707107i
$$7$$ 0 0
$$8$$ −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 $$-0.618496\pi$$
0.624844 + 0.780750i $$0.285163\pi$$
$$12$$ −3.00000 1.73205i −0.866025 0.500000i
$$13$$ 3.46410i 0.960769i −0.877058 0.480384i $$-0.840497\pi$$
0.877058 0.480384i $$-0.159503\pi$$
$$14$$ 0 0
$$15$$ 3.00000i 0.774597i
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 1.50000 0.866025i 0.363803 0.210042i −0.306944 0.951727i $$-0.599307\pi$$
0.670748 + 0.741685i $$0.265973\pi$$
$$18$$ 0 0
$$19$$ 2.59808 4.50000i 0.596040 1.03237i −0.397360 0.917663i $$-0.630073\pi$$
0.993399 0.114708i $$-0.0365932\pi$$
$$20$$ 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 $$-0.300087\pi$$
−0.406986 + 0.913434i $$0.633420\pi$$
$$24$$ 4.73205 + 1.26795i 0.965926 + 0.258819i
$$25$$ −1.00000 1.73205i −0.200000 0.346410i
$$26$$ 1.26795 + 4.73205i 0.248665 + 0.928032i
$$27$$ −5.19615 −1.00000
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 1.09808 + 4.09808i 0.200480 + 0.748203i
$$31$$ 0.866025 + 1.50000i 0.155543 + 0.269408i 0.933257 0.359211i $$-0.116954\pi$$
−0.777714 + 0.628619i $$0.783621\pi$$
$$32$$ −1.46410 + 5.46410i −0.258819 + 0.965926i
$$33$$ −1.50000 0.866025i −0.261116 0.150756i
$$34$$ −1.73205 + 1.73205i −0.297044 + 0.297044i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i $$-0.912646\pi$$
0.715981 + 0.698119i $$0.245980\pi$$
$$38$$ −1.90192 + 7.09808i −0.308533 + 1.15146i
$$39$$ −5.19615 + 3.00000i −0.832050 + 0.480384i
$$40$$ −4.73205 + 1.26795i −0.748203 + 0.200480i
$$41$$ 3.46410i 0.541002i 0.962720 + 0.270501i $$0.0871893\pi$$
−0.962720 + 0.270501i $$0.912811\pi$$
$$42$$ 0 0
$$43$$ 2.00000i 0.304997i −0.988304 0.152499i $$-0.951268\pi$$
0.988304 0.152499i $$-0.0487319\pi$$
$$44$$ 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 0.355608 + 0.934635i $$0.384274\pi$$
−0.987222 + 0.159352i $$0.949059\pi$$
$$48$$ −6.92820 −1.00000
$$49$$ 0 0
$$50$$ 2.00000 + 2.00000i 0.282843 + 0.282843i
$$51$$ −2.59808 1.50000i −0.363803 0.210042i
$$52$$ −3.46410 6.00000i −0.480384 0.832050i
$$53$$ 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i $$-0.144788\pi$$
−0.829640 + 0.558298i $$0.811454\pi$$
$$54$$ 7.09808 1.90192i 0.965926 0.258819i
$$55$$ 1.73205 0.233550
$$56$$ 0 0
$$57$$ −9.00000 −1.19208
$$58$$ −5.46410 + 1.46410i −0.717472 + 0.192246i
$$59$$ 2.59808 + 4.50000i 0.338241 + 0.585850i 0.984102 0.177605i $$-0.0568349\pi$$
−0.645861 + 0.763455i $$0.723502\pi$$
$$60$$ −3.00000 5.19615i −0.387298 0.670820i
$$61$$ 4.50000 + 2.59808i 0.576166 + 0.332650i 0.759608 0.650381i $$-0.225391\pi$$
−0.183442 + 0.983030i $$0.558724\pi$$
$$62$$ −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
$$66$$ 2.36603 + 0.633975i 0.291238 + 0.0780369i
$$67$$ 2.59808 1.50000i 0.317406 0.183254i −0.332830 0.942987i $$-0.608004\pi$$
0.650236 + 0.759733i $$0.274670\pi$$
$$68$$ 1.73205 3.00000i 0.210042 0.363803i
$$69$$ 1.73205i 0.208514i
$$70$$ 0 0
$$71$$ 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 $$-0.835840\pi$$
−0.00787336 + 0.999969i $$0.502506\pi$$
$$74$$ 1.09808 4.09808i 0.127649 0.476392i
$$75$$ −1.73205 + 3.00000i −0.200000 + 0.346410i
$$76$$ 10.3923i 1.19208i
$$77$$ 0 0
$$78$$ 6.00000 6.00000i 0.679366 0.679366i
$$79$$ 7.79423 + 4.50000i 0.876919 + 0.506290i 0.869641 0.493684i $$-0.164350\pi$$
0.00727784 + 0.999974i $$0.497683\pi$$
$$80$$ 6.00000 3.46410i 0.670820 0.387298i
$$81$$ 4.50000 + 7.79423i 0.500000 + 0.866025i
$$82$$ −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
$$87$$ −3.46410 6.00000i −0.371391 0.643268i
$$88$$ −0.732051 + 2.73205i −0.0780369 + 0.291238i
$$89$$ −13.5000 7.79423i −1.43100 0.826187i −0.433800 0.901009i $$-0.642828\pi$$
−0.997197 + 0.0748225i $$0.976161\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 2.00000 0.208514
$$93$$ 1.50000 2.59808i 0.155543 0.269408i
$$94$$ 3.16987 11.8301i 0.326947 1.22018i
$$95$$ 7.79423 4.50000i 0.799671 0.461690i
$$96$$ 9.46410 2.53590i 0.965926 0.258819i
$$97$$ 17.3205i 1.75863i 0.476240 + 0.879316i $$0.342000\pi$$
−0.476240 + 0.879316i $$0.658000\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −3.46410 2.00000i −0.346410 0.200000i
$$101$$ 7.50000 4.33013i 0.746278 0.430864i −0.0780696 0.996948i $$-0.524876\pi$$
0.824347 + 0.566084i $$0.191542\pi$$
$$102$$ 4.09808 + 1.09808i 0.405770 + 0.108726i
$$103$$ 4.33013 7.50000i 0.426660 0.738997i −0.569914 0.821705i $$-0.693023\pi$$
0.996574 + 0.0827075i $$0.0263567\pi$$
$$104$$ 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 $$-0.549614\pi$$
−0.933146 + 0.359498i $$0.882948\pi$$
$$108$$ −9.00000 + 5.19615i −0.866025 + 0.500000i
$$109$$ −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i $$-0.308513\pi$$
−0.996962 + 0.0778949i $$0.975180\pi$$
$$110$$ −2.36603 + 0.633975i −0.225592 + 0.0604471i
$$111$$ 5.19615 0.493197
$$112$$ 0 0
$$113$$ −16.0000 −1.50515 −0.752577 0.658505i $$-0.771189\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ 12.2942 3.29423i 1.15146 0.308533i
$$115$$ 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
$$119$$ 0 0
$$120$$ 6.00000 + 6.00000i 0.547723 + 0.547723i
$$121$$ −5.00000 + 8.66025i −0.454545 + 0.787296i
$$122$$ −7.09808 1.90192i −0.642630 0.172192i
$$123$$ 5.19615 3.00000i 0.468521 0.270501i
$$124$$ 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 $$-0.914230\pi$$
0.963916 0.266207i $$-0.0857705\pi$$
$$128$$ 2.92820 + 10.9282i 0.258819 + 0.965926i
$$129$$ −3.00000 + 1.73205i −0.264135 + 0.152499i
$$130$$ −2.19615 + 8.19615i −0.192615 + 0.718850i
$$131$$ −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i $$-0.906223\pi$$
0.729921 + 0.683531i $$0.239557\pi$$
$$132$$ −3.46410 −0.301511
$$133$$ 0 0
$$134$$ −3.00000 + 3.00000i −0.259161 + 0.259161i
$$135$$ −7.79423 4.50000i −0.670820 0.387298i
$$136$$ −1.26795 + 4.73205i −0.108726 + 0.405770i
$$137$$ −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i $$-0.180268\pi$$
−0.886594 + 0.462549i $$0.846935\pi$$
$$138$$ 0.633975 + 2.36603i 0.0539675 + 0.201409i
$$139$$ −6.92820 −0.587643 −0.293821 0.955860i $$-0.594927\pi$$
−0.293821 + 0.955860i $$0.594927\pi$$
$$140$$ 0 0
$$141$$ 15.0000 1.26323
$$142$$ −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 $$-0.846375\pi$$
0.844818 + 0.535054i $$0.179709\pi$$
$$150$$ 1.26795 4.73205i 0.103528 0.386370i
$$151$$ −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i $$-0.758602\pi$$
0.232623 + 0.972567i $$0.425269\pi$$
$$152$$ 3.80385 + 14.1962i 0.308533 + 1.15146i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 3.00000i 0.240966i
$$156$$ −6.00000 + 10.3923i −0.480384 + 0.832050i
$$157$$ −1.50000 + 0.866025i −0.119713 + 0.0691164i −0.558661 0.829396i $$-0.688685\pi$$
0.438948 + 0.898513i $$0.355351\pi$$
$$158$$ −12.2942 3.29423i −0.978076 0.262075i
$$159$$ 0.866025 1.50000i 0.0686803 0.118958i
$$160$$ −6.92820 + 6.92820i −0.547723 + 0.547723i
$$161$$ 0 0
$$162$$ −9.00000 9.00000i −0.707107 0.707107i
$$163$$ 18.1865 + 10.5000i 1.42448 + 0.822423i 0.996678 0.0814491i $$-0.0259548\pi$$
0.427802 + 0.903873i $$0.359288\pi$$
$$164$$ 3.46410 + 6.00000i 0.270501 + 0.468521i
$$165$$ −1.50000 2.59808i −0.116775 0.202260i
$$166$$ −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 0.842876 0.538107i $$-0.180860\pi$$
−0.0445762 + 0.999006i $$0.514194\pi$$
$$174$$ 6.92820 + 6.92820i 0.525226 + 0.525226i
$$175$$ 0 0
$$176$$ 4.00000i 0.301511i
$$177$$ 4.50000 7.79423i 0.338241 0.585850i
$$178$$ 21.2942 + 5.70577i 1.59607 + 0.427666i
$$179$$ −16.4545 + 9.50000i −1.22987 + 0.710063i −0.967002 0.254770i $$-0.918000\pi$$
−0.262864 + 0.964833i $$0.584667\pi$$
$$180$$ 0 0
$$181$$ 6.92820i 0.514969i −0.966282 0.257485i $$-0.917106\pi$$
0.966282 0.257485i $$-0.0828937\pi$$
$$182$$ 0 0
$$183$$ 9.00000i 0.665299i
$$184$$ −2.73205 + 0.732051i −0.201409 + 0.0539675i
$$185$$ −4.50000 + 2.59808i −0.330847 + 0.191014i
$$186$$ −1.09808 + 4.09808i −0.0805149 + 0.300486i
$$187$$ 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 $$-0.344852\pi$$
−0.531004 + 0.847369i $$0.678185\pi$$
$$192$$ −12.0000 + 6.92820i −0.866025 + 0.500000i
$$193$$ 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i $$0.0148568\pi$$
−0.459049 + 0.888411i $$0.651810\pi$$
$$194$$ −6.33975 23.6603i −0.455167 1.69871i
$$195$$ −10.3923 −0.744208
$$196$$ 0 0
$$197$$ 16.0000 1.13995 0.569976 0.821661i $$-0.306952\pi$$
0.569976 + 0.821661i $$0.306952\pi$$
$$198$$ 0 0
$$199$$ 11.2583 + 19.5000i 0.798082 + 1.38232i 0.920864 + 0.389885i $$0.127485\pi$$
−0.122782 + 0.992434i $$0.539182\pi$$
$$200$$ 5.46410 + 1.46410i 0.386370 + 0.103528i
$$201$$ −4.50000 2.59808i −0.317406 0.183254i
$$202$$ −8.66025 + 8.66025i −0.609333 + 0.609333i
$$203$$ 0 0
$$204$$ −6.00000 −0.420084
$$205$$ −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 $$-0.888145\pi$$
0.938891 0.344214i $$-0.111855\pi$$
$$212$$ 1.73205 + 1.00000i 0.118958 + 0.0686803i
$$213$$ 21.0000 12.1244i 1.43890 0.830747i
$$214$$ 17.7583 + 4.75833i 1.21393 + 0.325273i
$$215$$ 1.73205 3.00000i 0.118125 0.204598i
$$216$$ 10.3923 10.3923i 0.707107 0.707107i
$$217$$ 0 0
$$218$$ 9.00000 + 9.00000i 0.609557 + 0.609557i
$$219$$ 12.9904 + 7.50000i 0.877809 + 0.506803i
$$220$$ 3.00000 1.73205i 0.202260 0.116775i
$$221$$ −3.00000 5.19615i −0.201802 0.349531i
$$222$$ −7.09808 + 1.90192i −0.476392 + 0.127649i
$$223$$ 6.92820 0.463947 0.231973 0.972722i $$-0.425482\pi$$
0.231973 + 0.972722i $$0.425482\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 21.8564 5.85641i 1.45387 0.389562i
$$227$$ −9.52628 16.5000i −0.632281 1.09514i −0.987084 0.160202i $$-0.948785\pi$$
0.354803 0.934941i $$1.61545\pi$$
$$228$$ −15.5885 + 9.00000i −1.03237 + 0.596040i
$$229$$ 13.5000 + 7.79423i 0.892105 + 0.515057i 0.874630 0.484790i $$-0.161104\pi$$
0.0174746 + 0.999847i $$0.494437\pi$$
$$230$$ −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 $$-0.759692\pi$$
0.957599 + 0.288106i $$0.0930254\pi$$
$$234$$ 0 0
$$235$$ −12.9904 + 7.50000i −0.847399 + 0.489246i
$$236$$ 9.00000 + 5.19615i 0.585850 + 0.338241i
$$237$$ 15.5885i 1.01258i
$$238$$ 0 0
$$239$$ 20.0000i 1.29369i −0.762620 0.646846i $$-0.776088\pi$$
0.762620 0.646846i $$-0.223912\pi$$
$$240$$ −10.3923 6.00000i −0.670820 0.387298i
$$241$$ 4.50000 2.59808i 0.289870 0.167357i −0.348013 0.937490i $$-0.613143\pi$$
0.637883 + 0.770133i $$0.279810\pi$$
$$242$$ 3.66025 13.6603i 0.235290 0.878114i
$$243$$ 0 0
$$244$$ 10.3923 0.665299
$$245$$ 0 0
$$246$$ −6.00000 + 6.00000i −0.382546 + 0.382546i
$$247$$ −15.5885 9.00000i −0.991870 0.572656i
$$248$$ −4.73205 1.26795i −0.300486 0.0805149i
$$249$$ −12.0000 20.7846i −0.760469 1.31717i
$$250$$ 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
$$255$$ −2.59808 4.50000i −0.162698 0.281801i
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ −4.50000 2.59808i −0.280702 0.162064i 0.353039 0.935609i $$-0.385148\pi$$
−0.633741 + 0.773545i $$0.718482\pi$$
$$258$$ 3.46410 3.46410i 0.215666 0.215666i
$$259$$ 0 0
$$260$$ 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 $$-0.415759\pi$$
0.966660 + 0.256063i $$0.0824256\pi$$
$$264$$ 4.73205 1.26795i 0.291238 0.0780369i
$$265$$ 1.73205i 0.106399i
$$266$$ 0 0
$$267$$ 27.0000i 1.65237i
$$268$$ 3.00000 5.19615i 0.183254 0.317406i
$$269$$ −19.5000 + 11.2583i −1.18894 + 0.686433i −0.958065 0.286552i $$-0.907491\pi$$
−0.230871 + 0.972984i $$0.574158\pi$$
$$270$$ 12.2942 + 3.29423i 0.748203 + 0.200480i
$$271$$ 7.79423 13.5000i 0.473466 0.820067i −0.526073 0.850439i $$-0.676336\pi$$
0.999539 + 0.0303728i $$0.00966946\pi$$
$$272$$ 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
$$276$$ −1.73205 3.00000i −0.104257 0.180579i
$$277$$ 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i $$-0.0389525\pi$$
−0.601975 + 0.798515i $$0.705619\pi$$
$$278$$ 9.46410 2.53590i 0.567619 0.152093i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −4.00000 −0.238620 −0.119310 0.992857i $$-0.538068\pi$$
−0.119310 + 0.992857i $$0.538068\pi$$
$$282$$ −20.4904 + 5.49038i −1.22018 + 0.326947i
$$283$$ −6.06218 10.5000i −0.360359 0.624160i 0.627661 0.778487i $$-0.284012\pi$$
−0.988020 + 0.154327i $$0.950679\pi$$
$$284$$ 14.0000 + 24.2487i 0.830747 + 1.43890i
$$285$$ −13.5000 7.79423i −0.799671 0.461690i
$$286$$ 3.46410 + 3.46410i 0.204837 + 0.204837i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −7.00000 + 12.1244i −0.411765 + 0.713197i
$$290$$ −9.46410 2.53590i −0.555751 0.148913i
$$291$$ 25.9808 15.0000i 1.52302 0.879316i
$$292$$ −8.66025 + 15.0000i −0.506803 + 0.877809i
$$293$$ 20.7846i 1.21425i 0.794606 + 0.607125i $$0.207677\pi$$
−0.794606 + 0.607125i $$0.792323\pi$$
$$294$$ 0 0
$$295$$ 9.00000i 0.524000i
$$296$$ −2.19615 8.19615i −0.127649 0.476392i
$$297$$ −4.50000 + 2.59808i −0.261116 + 0.150756i
$$298$$ 0.366025 1.36603i 0.0212033 0.0791317i
$$299$$ 1.73205 3.00000i 0.100167 0.173494i
$$300$$ 6.92820i 0.400000i
$$301$$ 0 0
$$302$$ 7.00000 7.00000i 0.402805 0.402805i
$$303$$ −12.9904 7.50000i −0.746278 0.430864i
$$304$$ −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 $$-0.297896\pi$$
0.593120 + 0.805114i $$0.297896\pi$$
$$308$$ 0 0
$$309$$ −15.0000 −0.853320
$$310$$ −1.09808 4.09808i −0.0623665 0.232755i
$$311$$ −4.33013 7.50000i −0.245539 0.425286i 0.716744 0.697336i $$-0.245632\pi$$
−0.962283 + 0.272050i $$0.912298\pi$$
$$312$$ 4.39230 16.3923i 0.248665 0.928032i
$$313$$ −1.50000 0.866025i −0.0847850 0.0489506i 0.457008 0.889463i $$-0.348921\pi$$
−0.541793 + 0.840512i $$0.682254\pi$$
$$314$$ 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 $$-0.933298\pi$$
0.669214 + 0.743070i $$0.266631\pi$$
$$318$$ −0.633975 + 2.36603i −0.0355515 + 0.132680i
$$319$$ 3.46410 2.00000i 0.193952 0.111979i
$$320$$ 6.92820 12.0000i 0.387298 0.670820i
$$321$$ 22.5167i 1.25676i
$$322$$ 0 0
$$323$$ 9.00000i 0.500773i
$$324$$ 15.5885 + 9.00000i 0.866025 + 0.500000i
$$325$$ −6.00000 + 3.46410i −0.332820 + 0.192154i
$$326$$ −28.6865 7.68653i −1.58880 0.425718i
$$327$$ −7.79423 + 13.5000i −0.431022 + 0.746552i
$$328$$ −6.92820 6.92820i −0.382546 0.382546i
$$329$$ 0 0
$$330$$ 3.00000 + 3.00000i 0.165145 + 0.165145i
$$331$$ −6.06218 3.50000i −0.333207 0.192377i 0.324057 0.946038i $$-0.394953\pi$$
−0.657264 + 0.753660i $$0.728286\pi$$
$$332$$ 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
$$339$$ 13.8564 + 24.0000i 0.752577 + 1.30350i
$$340$$ 5.19615 3.00000i 0.281801 0.162698i
$$341$$ 1.50000 + 0.866025i 0.0812296 + 0.0468979i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 4.00000 + 4.00000i 0.215666 + 0.215666i
$$345$$ 1.50000 2.59808i 0.0807573 0.139876i
$$346$$ −16.5622 4.43782i −0.890388 0.238579i
$$347$$ −11.2583 + 6.50000i −0.604379 + 0.348938i −0.770762 0.637123i $$-0.780124\pi$$
0.166383 + 0.986061i $$0.446791\pi$$
$$348$$ −12.0000 6.92820i −0.643268 0.371391i
$$349$$ 10.3923i 0.556287i −0.960539 0.278144i $$-0.910281\pi$$
0.960539 0.278144i $$-0.0897191\pi$$
$$350$$ 0 0
$$351$$ 18.0000i 0.960769i
$$352$$ 1.46410 + 5.46410i 0.0780369 + 0.291238i
$$353$$ 25.5000 14.7224i 1.35723 0.783596i 0.367979 0.929834i $$-0.380050\pi$$
0.989249 + 0.146238i $$0.0467166\pi$$
$$354$$ −3.29423 + 12.2942i −0.175086 + 0.653431i
$$355$$ −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 $$-0.125727\pi$$
0.128260 + 0.991741i $$0.459061\pi$$
$$360$$ 0 0
$$361$$ −4.00000 6.92820i −0.210526 0.364642i
$$362$$ 2.53590 + 9.46410i 0.133284 + 0.497422i
$$363$$ 17.3205 0.909091
$$364$$ 0 0
$$365$$ −15.0000 −0.785136
$$366$$ 3.29423 + 12.2942i 0.172192 + 0.642630i
$$367$$ −0.866025 1.50000i −0.0452062 0.0782994i 0.842537 0.538639i $$-0.181061\pi$$
−0.887743 + 0.460339i $$0.847728\pi$$
$$368$$ 3.46410 2.00000i 0.180579 0.104257i
$$369$$ 0 0
$$370$$ 5.19615 5.19615i 0.270135 0.270135i
$$371$$ 0 0
$$372$$ 6.00000i 0.311086i
$$373$$ 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i $$-0.563010\pi$$
0.947444 0.319921i $$-0.103656\pi$$
$$374$$ −0.633975 + 2.36603i −0.0327820 + 0.122344i
$$375$$ −18.1865 + 10.5000i −0.939149 + 0.542218i
$$376$$ −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 $$0.0658711\pi$$
−0.978664 + 0.205466i $$0.934129\pi$$
$$380$$ 9.00000 15.5885i 0.461690 0.799671i
$$381$$ −9.00000 + 5.19615i −0.461084 + 0.266207i
$$382$$ 1.36603 + 0.366025i 0.0698919 + 0.0187275i
$$383$$ 2.59808 4.50000i 0.132755 0.229939i −0.791982 0.610544i $$-0.790951\pi$$
0.924738 + 0.380605i $$0.124284\pi$$
$$384$$ 13.8564 13.8564i 0.707107 0.707107i
$$385$$ 0 0
$$386$$ −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 $$-0.00669738\pi$$
−0.518110 + 0.855314i $$0.673364\pi$$
$$390$$ 14.1962 3.80385i 0.718850 0.192615i
$$391$$ 1.73205 0.0875936
$$392$$ 0 0
$$393$$ 9.00000 0.453990
$$394$$ −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 $$-0.492011\pi$$
−0.853206 + 0.521575i $$0.825345\pi$$
$$398$$ −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 −0.421837 0.906672i $$-0.638614\pi$$
0.996119 0.0880147i $$-0.0280523\pi$$
$$402$$ 7.09808 + 1.90192i 0.354020 + 0.0948593i
$$403$$ 5.19615 3.00000i 0.258839 0.149441i
$$404$$ 8.66025 15.0000i 0.430864 0.746278i
$$405$$ 15.5885i 0.774597i
$$406$$ 0 0
$$407$$ 3.00000i 0.148704i
$$408$$ 8.19615 2.19615i 0.405770 0.108726i
$$409$$ −22.5000 + 12.9904i −1.11255 + 0.642333i −0.939490 0.342578i $$-0.888700\pi$$
−0.173064 + 0.984911i $$0.555367\pi$$
$$410$$ 2.19615 8.19615i 0.108460 0.404779i
$$411$$ −0.866025 + 1.50000i −0.0427179 + 0.0739895i
$$412$$ 17.3205i 0.853320i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 20.7846 + 12.0000i 1.02028 + 0.589057i
$$416$$ 18.9282 + 5.07180i 0.928032 + 0.248665i
$$417$$ 6.00000 + 10.3923i 0.293821 + 0.508913i
$$418$$ 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
$$426$$ −24.2487 + 24.2487i −1.17485 + 1.17485i
$$427$$ 0 0
$$428$$ −26.0000 −1.25676
$$429$$ −3.00000 + 5.19615i −0.144841 + 0.250873i
$$430$$ −1.26795 + 4.73205i −0.0611459 + 0.228200i
$$431$$ −19.9186 + 11.5000i −0.959444 + 0.553936i −0.896002 0.444050i $$-0.853541\pi$$
−0.0634424 + 0.997985i $$0.520208\pi$$
$$432$$ −10.3923 + 18.0000i −0.500000 + 0.866025i
$$433$$ 10.3923i 0.499422i 0.968320 + 0.249711i $$0.0803357\pi$$
−0.968320 + 0.249711i $$0.919664\pi$$
$$434$$ 0 0
$$435$$ 12.0000i 0.575356i
$$436$$ −15.5885 9.00000i −0.746552 0.431022i
$$437$$ 4.50000 2.59808i 0.215264 0.124283i
$$438$$ −20.4904 5.49038i −0.979068 0.262341i
$$439$$ −11.2583 + 19.5000i −0.537331 + 0.930684i 0.461716 + 0.887028i $$0.347234\pi$$
−0.999047 + 0.0436563i $$0.986099\pi$$
$$440$$ −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 $$-0.465661\pi$$
−0.807155 + 0.590339i $$0.798994\pi$$
$$444$$ 9.00000 5.19615i 0.427121 0.246598i
$$445$$ −13.5000 23.3827i −0.639961 1.10845i
$$446$$ −9.46410 + 2.53590i −0.448138 + 0.120078i
$$447$$ 1.73205 0.0819232
$$448$$ 0 0
$$449$$ 8.00000 0.377543 0.188772 0.982021i $$-0.439549\pi$$
0.188772 + 0.982021i $$0.439549\pi$$
$$450$$ 0 0
$$451$$ 1.73205 + 3.00000i 0.0815591 + 0.141264i
$$452$$ −27.7128 + 16.0000i −1.30350 + 0.752577i
$$453$$ 10.5000 + 6.06218i 0.493333 + 0.284826i
$$454$$ 19.0526 + 19.0526i 0.894181 + 0.894181i
$$455$$ 0 0
$$456$$ 18.0000 18.0000i 0.842927 0.842927i
$$457$$ −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i $$-0.947436\pi$$
0.635561 + 0.772051i $$0.280769\pi$$
$$458$$ −21.2942 5.70577i −0.995014 0.266613i
$$459$$ −7.79423 + 4.50000i −0.363803 + 0.210042i
$$460$$ 3.00000 + 1.73205i 0.139876 + 0.0807573i
$$461$$ 17.3205i 0.806696i 0.915047 + 0.403348i $$0.132154\pi$$
−0.915047 + 0.403348i $$0.867846\pi$$
$$462$$ 0 0
$$463$$ 30.0000i 1.39422i 0.716965 + 0.697109i $$0.245531\pi$$
−0.716965 + 0.697109i $$0.754469\pi$$
$$464$$ 8.00000 13.8564i 0.371391 0.643268i
$$465$$ 4.50000 2.59808i 0.208683 0.120483i
$$466$$ −2.56218 + 9.56218i −0.118691 + 0.442959i
$$467$$ 4.33013 7.50000i 0.200374 0.347059i −0.748275 0.663389i $$-0.769117\pi$$
0.948649 + 0.316330i $$0.102451\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 15.0000 15.0000i 0.691898 0.691898i
$$471$$ 2.59808 + 1.50000i 0.119713 + 0.0691164i
$$472$$ −14.1962 3.80385i −0.653431 0.175086i
$$473$$ −1.00000 1.73205i −0.0459800 0.0796398i
$$474$$ 5.70577 + 21.2942i 0.262075 + 0.978076i
$$475$$ −10.3923 −0.476832
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 7.32051 + 27.3205i 0.334832 + 1.24961i
$$479$$ 6.06218 + 10.5000i 0.276988 + 0.479757i 0.970635 0.240558i $$-0.0773304\pi$$
−0.693647 + 0.720315i $$0.743997\pi$$
$$480$$ 16.3923 + 4.39230i 0.748203 + 0.200480i
$$481$$ 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 0.252367 0.967632i $$-0.418791\pi$$
0.964177 + 0.265260i $$0.0854576\pi$$
$$488$$ −14.1962 + 3.80385i −0.642630 + 0.172192i
$$489$$ 36.3731i 1.64485i
$$490$$ 0 0
$$491$$ 32.0000i 1.44414i −0.691820 0.722070i $$-0.743191\pi$$
0.691820 0.722070i $$-0.256809\pi$$
$$492$$ 6.00000 10.3923i 0.270501 0.468521i
$$493$$ 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
$$497$$ 0 0
$$498$$ 24.0000 + 24.0000i 1.07547 + 1.07547i
$$499$$ −30.3109 17.5000i −1.35690 0.783408i −0.367697 0.929946i $$-0.619854\pi$$
−0.989205 + 0.146538i $$0.953187\pi$$
$$500$$ −12.1244 21.0000i −0.542218 0.939149i
$$501$$ 15.0000 + 25.9808i 0.670151 + 1.16073i
$$502$$ 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
$$507$$ −0.866025 1.50000i −0.0384615 0.0666173i
$$508$$ −6.00000 10.3923i −0.266207 0.461084i
$$509$$ −10.5000 6.06218i −0.465404 0.268701i 0.248910 0.968527i $$-0.419928\pi$$
−0.714314 + 0.699825i $$0.753261\pi$$
$$510$$ 5.19615 + 5.19615i 0.230089 + 0.230089i
$$511$$ 0 0
$$512$$ 16.0000 + 16.0000i 0.707107 + 0.707107i
$$513$$ −13.5000 + 23.3827i −0.596040 + 1.03237i
$$514$$ 7.09808 + 1.90192i 0.313083 + 0.0838903i
$$515$$ 12.9904 7.50000i 0.572425 0.330489i
$$516$$ −3.46410 + 6.00000i −0.152499 + 0.264135i
$$517$$ 8.66025i 0.380878i
$$518$$ 0 0
$$519$$ 21.0000i 0.921798i
$$520$$ 4.39230 + 16.3923i 0.192615 + 0.718850i
$$521$$ −1.50000 + 0.866025i −0.0657162 + 0.0379413i −0.532498 0.846431i $$-0.678747\pi$$
0.466782 + 0.884372i $$0.345413\pi$$
$$522$$ 0 0
$$523$$ 12.9904 22.5000i 0.568030 0.983856i −0.428731 0.903432i $$-0.641039\pi$$
0.996761 0.0804241i $$-0.0256275\pi$$
$$524$$ 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
$$528$$ −6.00000 + 3.46410i −0.261116 + 0.150756i
$$529$$ −11.0000 19.0526i −0.478261 0.828372i
$$530$$ −0.633975 2.36603i −0.0275381 0.102774i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ −9.88269 36.8827i −0.427666 1.59607i
$$535$$ −11.2583 19.5000i −0.486740 0.843059i
$$536$$ −2.19615 + 8.19615i −0.0948593 + 0.354020i
$$537$$ 28.5000 + 16.4545i 1.22987 + 0.710063i
$$538$$ 22.5167 22.5167i 0.970762 0.970762i
$$539$$ 0 0
$$540$$ −18.0000 −0.774597
$$541$$ 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i $$-0.699407\pi$$
0.994715 + 0.102677i $$0.0327407\pi$$
$$542$$ −5.70577 + 21.2942i −0.245084 + 0.914665i
$$543$$ −10.3923 + 6.00000i −0.445976 + 0.257485i
$$544$$ 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
$$552$$ 3.46410 + 3.46410i 0.147442 + 0.147442i
$$553$$ 0 0
$$554$$ −13.0000 13.0000i −0.552317 0.552317i
$$555$$ 7.79423 + 4.50000i 0.330847 + 0.191014i
$$556$$ −12.0000 + 6.92820i −0.508913 + 0.293821i
$$557$$ −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i $$-0.879909\pi$$
0.145802 0.989314i $$-0.453424\pi$$
$$558$$ 0 0
$$559$$ −6.92820 −0.293032
$$560$$ 0 0
$$561$$ −3.00000 −0.126660
$$562$$ 5.46410 1.46410i 0.230489 0.0617594i
$$563$$ −11.2583 19.5000i −0.474482 0.821827i 0.525091 0.851046i $$-0.324031\pi$$
−0.999573 + 0.0292191i $$0.990698\pi$$
$$564$$ 25.9808 15.0000i 1.09399 0.631614i
$$565$$ −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 $$-0.745485\pi$$
0.969500 + 0.245092i $$0.0788181\pi$$
$$570$$ 21.2942 + 5.70577i 0.891917 + 0.238988i
$$571$$ 18.1865 10.5000i 0.761083 0.439411i −0.0686016 0.997644i $$-0.521854\pi$$
0.829684 + 0.558233i $$0.188520\pi$$
$$572$$ −6.00000 3.46410i −0.250873 0.144841i
$$573$$ 1.73205i 0.0723575i
$$574$$ 0 0
$$575$$ 2.00000i 0.0834058i
$$576$$ 0 0
$$577$$ 28.5000 16.4545i 1.18647 0.685009i 0.228968 0.973434i $$-0.426465\pi$$
0.957503 + 0.288425i $$0.0931316\pi$$
$$578$$ 5.12436 19.1244i 0.213145 0.795468i
$$579$$ 12.9904 22.5000i 0.539862 0.935068i
$$580$$ 13.8564 0.575356
$$581$$ 0 0
$$582$$ −30.0000 + 30.0000i −1.24354 + 1.24354i
$$583$$ 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
$$591$$ −13.8564 24.0000i −0.569976 0.987228i
$$592$$ 6.00000 + 10.3923i 0.246598 + 0.427121i
$$593$$ 13.5000 + 7.79423i 0.554379 + 0.320071i 0.750886 0.660432i $$-0.229627\pi$$
−0.196508 + 0.980502i $$0.562960\pi$$
$$594$$ 5.19615 5.19615i 0.213201 0.213201i
$$595$$ 0 0
$$596$$ 2.00000i 0.0819232i
$$597$$ 19.5000 33.7750i 0.798082 1.38232i
$$598$$ −1.26795 + 4.73205i −0.0518503 + 0.193508i
$$599$$ −14.7224 + 8.50000i −0.601542 + 0.347301i −0.769648 0.638468i $$-0.779568\pi$$
0.168106 + 0.985769i $$0.446235\pi$$
$$600$$ −2.53590 9.46410i −0.103528 0.386370i
$$601$$ 38.1051i 1.55434i −0.629291 0.777170i $$-0.716654\pi$$
0.629291 0.777170i $$-0.283346\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −7.00000 + 12.1244i −0.284826 + 0.493333i
$$605$$ −15.0000 + 8.66025i −0.609837 + 0.352089i
$$606$$ 20.4904 + 5.49038i 0.832365 + 0.223031i
$$607$$ −7.79423 + 13.5000i −0.316358 + 0.547948i −0.979725 0.200346i $$-0.935793\pi$$
0.663367 + 0.748294i $$0.269127\pi$$
$$608$$ 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 0.988339 + 0.152270i $$0.0486583\pi$$
−0.362300 + 0.932062i $$0.618008\pi$$
$$614$$ −28.3923 + 7.60770i −1.14582 + 0.307022i
$$615$$ 10.3923 0.419058
$$616$$ 0 0
$$617$$ 20.0000 0.805170 0.402585 0.915383i $$-0.368112\pi$$
0.402585 + 0.915383i $$0.368112\pi$$
$$618$$ 20.4904 5.49038i 0.824244 0.220856i
$$619$$ −7.79423 13.5000i −0.313276 0.542611i 0.665793 0.746136i $$-0.268093\pi$$
−0.979070 + 0.203526i $$0.934760\pi$$
$$620$$ 3.00000 + 5.19615i 0.120483 + 0.208683i
$$621$$ −4.50000 2.59808i −0.180579 0.104257i
$$622$$ 8.66025 + 8.66025i 0.347245 + 0.347245i
$$623$$ 0 0
$$624$$ 24.0000i 0.960769i
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ 2.36603 + 0.633975i 0.0945654 + 0.0253387i
$$627$$ −7.79423 + 4.50000i −0.311272 + 0.179713i
$$628$$ −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 $$-0.796303\pi$$
0.802137 0.597141i $$-0.203697\pi$$
$$632$$ −24.5885 + 6.58846i −0.978076 + 0.262075i
$$633$$ −15.0000 + 8.66025i −0.596196 + 0.344214i
$$634$$ 4.02628 15.0263i 0.159904 0.596770i
$$635$$ 5.19615 9.00000i 0.206203 0.357154i
$$636$$ 3.46410i 0.137361i
$$637$$ 0 0
$$638$$ −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 $$-0.0840201\pi$$
−0.708631 + 0.705580i $$0.750687\pi$$
$$642$$ −8.24167 30.7583i −0.325273 1.21393i
$$643$$ −13.8564 −0.546443 −0.273222 0.961951i $$-0.588089\pi$$
−0.273222 + 0.961951i $$0.588089\pi$$
$$644$$ 0 0
$$645$$ −6.00000 −0.236250
$$646$$ 3.29423 + 12.2942i 0.129610 + 0.483710i
$$647$$ 16.4545 + 28.5000i 0.646892 + 1.12045i 0.983861 + 0.178935i $$0.0572651\pi$$
−0.336968 + 0.941516i $$0.609402\pi$$
$$648$$ −24.5885 6.58846i −0.965926 0.258819i
$$649$$ 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 0.385241 + 0.922816i $$0.374118\pi$$
−0.991803 + 0.127780i $$0.959215\pi$$
$$654$$ 5.70577 21.2942i 0.223113 0.832670i
$$655$$ −7.79423 + 4.50000i −0.304546 + 0.175830i
$$656$$ 12.0000 + 6.92820i 0.468521 + 0.270501i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 38.0000i 1.48027i 0.672458 + 0.740135i $$0.265238\pi$$
−0.672458 + 0.740135i $$0.734762\pi$$
$$660$$ −5.19615 3.00000i −0.202260 0.116775i
$$661$$ 34.5000 19.9186i 1.34189 0.774743i 0.354809 0.934939i $$-0.384546\pi$$
0.987085 + 0.160196i $$0.0512125\pi$$
$$662$$ 9.56218 + 2.56218i 0.371645 + 0.0995819i
$$663$$ −5.19615 + 9.00000i −0.201802 + 0.349531i
$$664$$ −27.7128 + 27.7128i −1.07547 + 1.07547i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3.46410 + 2.00000i 0.134131 + 0.0774403i
$$668$$ −30.0000 + 17.3205i −1.16073 + 0.670151i
$$669$$ −6.00000 10.3923i −0.231973 0.401790i
$$670$$ −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
$$675$$ 5.19615 + 9.00000i 0.200000 + 0.346410i
$$676$$ 1.73205 1.00000i 0.0666173 0.0384615i
$$677$$ 37.5000 + 21.6506i 1.44124 + 0.832102i 0.997933 0.0642672i $$-0.0204710\pi$$
0.443309 + 0.896369i $$0.353804\pi$$
$$678$$ −27.7128 27.7128i −1.06430 1.06430i
$$679$$ 0 0
$$680$$ −6.00000 + 6.00000i −0.230089 + 0.230089i
$$681$$ −16.5000 + 28.5788i −0.632281 + 1.09514i
$$682$$ −2.36603 0.633975i −0.0905998 0.0242761i
$$683$$ 21.6506 12.5000i 0.828439 0.478299i −0.0248792 0.999690i $$-0.507920\pi$$
0.853318 + 0.521391i $$0.174587\pi$$
$$684$$ 0 0
$$685$$ 1.73205i 0.0661783i
$$686$$ 0 0
$$687$$ 27.0000i 1.03011i
$$688$$ −6.92820 4.00000i −0.264135 0.152499i
$$689$$ 3.00000 1.73205i 0.114291 0.0659859i
$$690$$ −1.09808 + 4.09808i −0.0418030 + 0.156011i
$$691$$ −6.06218 + 10.5000i −0.230616 + 0.399439i −0.957990 0.286803i $$-0.907407\pi$$
0.727373 + 0.686242i $$0.240741\pi$$
$$692$$ 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
$$696$$ 18.9282 + 5.07180i 0.717472 + 0.192246i
$$697$$ 3.00000 + 5.19615i 0.113633 + 0.196818i
$$698$$ 3.80385 + 14.1962i 0.143978 + 0.537332i
$$699$$ −12.1244 −0.458585
$$700$$ 0 0
$$701$$ −26.0000 −0.982006 −0.491003 0.871158i $$-0.663370\pi$$
−0.491003 + 0.871158i $$0.663370\pi$$
$$702$$ −6.58846 24.5885i −0.248665 0.928032i
$$703$$ 7.79423 + 13.5000i 0.293965 + 0.509162i
$$704$$ −4.00000 6.92820i −0.150756 0.261116i
$$705$$ 22.5000 + 12.9904i 0.847399 + 0.489246i
$$706$$ −29.4449 + 29.4449i −1.10817 + 1.10817i
$$707$$ 0 0
$$708$$ 18.0000i 0.676481i
$$709$$ 4.50000 7.79423i 0.169001 0.292718i −0.769068 0.639167i $$-0.779279\pi$$
0.938069 + 0.346449i $$0.112613\pi$$
$$710$$ 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
$$717$$ −30.0000 + 17.3205i −1.12037 + 0.646846i
$$718$$ −31.4186 8.41858i −1.17253 0.314179i
$$719$$ −12.9904 + 22.5000i −0.484459 + 0.839108i −0.999841 0.0178527i $$-0.994317\pi$$
0.515381 + 0.856961i $$0.327650\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 8.00000 + 8.00000i 0.297729 + 0.297729i
$$723$$ −7.79423 4.50000i −0.289870 0.167357i
$$724$$ −6.92820 12.0000i −0.257485 0.445976i
$$725$$ −4.00000 6.92820i −0.148556 0.257307i
$$726$$ −23.6603 + 6.33975i −0.878114 + 0.235290i
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 20.4904 5.49038i 0.758383 0.203208i
$$731$$ −1.73205 3.00000i −0.0640622 0.110959i
$$732$$ −9.00000 15.5885i −0.332650 0.576166i
$$733$$ −37.5000 21.6506i −1.38509 0.799684i −0.392337 0.919822i $$-0.628333\pi$$
−0.992757 + 0.120137i $$0.961667\pi$$
$$734$$ 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 −0.639087 + 0.769135i $$0.720687\pi$$
−0.985634 + 0.168898i $$0.945979\pi$$
$$740$$ −5.19615 + 9.00000i −0.191014 + 0.330847i
$$741$$ 31.1769i 1.14531i
$$742$$ 0 0
$$743$$ 34.0000i 1.24734i 0.781688 + 0.623670i $$0.214359\pi$$
−0.781688 + 0.623670i $$0.785641\pi$$
$$744$$ 2.19615 + 8.19615i 0.0805149 + 0.300486i
$$745$$ −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
$$749$$ 0 0
$$750$$ 21.0000 21.0000i 0.766812 0.766812i
$$751$$ −21.6506 12.5000i −0.790043 0.456131i 0.0499348 0.998752i $$-0.484099\pi$$
−0.839978 + 0.542621i $$0.817432\pi$$
$$752$$ 17.3205 + 30.0000i 0.631614 + 1.09399i
$$753$$ 3.00000 + 5.19615i 0.109326 + 0.189358i
$$754$$ 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
$$759$$ −0.866025 1.50000i −0.0314347 0.0544466i
$$760$$ −6.58846 + 24.5885i −0.238988 + 0.891917i
$$761$$ −16.5000 9.52628i −0.598125 0.345327i 0.170179 0.985413i $$-0.445565\pi$$
−0.768303 + 0.640086i $$0.778899\pi$$
$$762$$ 10.3923 10.3923i 0.376473 0.376473i
$$763$$ 0 0
$$764$$ −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
$$768$$ −13.8564 + 24.0000i −0.500000 + 0.866025i
$$769$$ 3.46410i 0.124919i 0.998048 + 0.0624593i $$0.0198944\pi$$
−0.998048 + 0.0624593i $$0.980106\pi$$
$$770$$ 0 0
$$771$$ 9.00000i 0.324127i
$$772$$ 25.9808 + 15.0000i 0.935068 + 0.539862i
$$773$$ −22.5000 + 12.9904i −0.809269 + 0.467232i −0.846702 0.532068i $$-0.821415\pi$$
0.0374331 + 0.999299i $$0.488082\pi$$
$$774$$ 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
$$780$$ −18.0000 + 10.3923i −0.644503 + 0.372104i
$$781$$ 7.00000 + 12.1244i 0.250480 + 0.433844i
$$782$$ −2.36603 + 0.633975i −0.0846089 + 0.0226709i
$$783$$ −20.7846 −0.742781