# Properties

 Label 196.2.f.a.19.2 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 19.2 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 196.19 Dual form 196.2.f.a.31.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.366025 + 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$$ $$q+(0.366025 + 1.36603i) 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} +(-0.633975 + 2.36603i) 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} +(1.26795 - 4.73205i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(4.73205 - 1.26795i) q^{26} +5.19615 q^{27} +4.00000 q^{29} +(-4.09808 + 1.09808i) q^{30} +(-0.866025 - 1.50000i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-1.50000 - 0.866025i) q^{33} +(1.73205 + 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{37} +(-7.09808 - 1.90192i) q^{38} +(5.19615 - 3.00000i) q^{39} +(-1.26795 - 4.73205i) q^{40} +3.46410i q^{41} +2.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(0.366025 - 1.36603i) 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} +(1.90192 + 7.09808i) q^{54} -1.73205 q^{55} -9.00000 q^{57} +(1.46410 + 5.46410i) 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} +(0.633975 - 2.36603i) 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} +(-4.09808 - 1.09808i) 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} +(-4.73205 + 1.26795i) q^{82} -13.8564 q^{83} +3.00000 q^{85} +(-2.73205 + 0.732051i) q^{86} +(3.46410 + 6.00000i) q^{87} +(2.73205 + 0.732051i) q^{88} +(-13.5000 - 7.79423i) q^{89} +2.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(11.8301 + 3.16987i) q^{94} +(-7.79423 + 4.50000i) q^{95} +(2.53590 + 9.46410i) 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 1.36603i 0.258819 + 0.965926i
$$3$$ 0.866025 + 1.50000i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$4$$ −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
$$10$$ −0.633975 + 2.36603i −0.200480 + 0.748203i
$$11$$ −0.866025 + 0.500000i −0.261116 + 0.150756i −0.624844 0.780750i $$-0.714837\pi$$
0.363727 + 0.931505i $$0.381504\pi$$
$$12$$ −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 $$0.369927\pi$$
−0.993399 + 0.114708i $$0.963407\pi$$
$$20$$ −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 0.406986 0.913434i $$-0.366580\pi$$
−0.587565 + 0.809177i $$0.699913\pi$$
$$24$$ 1.26795 4.73205i 0.258819 0.965926i
$$25$$ −1.00000 1.73205i −0.200000 0.346410i
$$26$$ 4.73205 1.26795i 0.928032 0.248665i
$$27$$ 5.19615 1.00000
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ −4.09808 + 1.09808i −0.748203 + 0.200480i
$$31$$ −0.866025 1.50000i −0.155543 0.269408i 0.777714 0.628619i $$-0.216379\pi$$
−0.933257 + 0.359211i $$0.883046\pi$$
$$32$$ 5.46410 + 1.46410i 0.965926 + 0.258819i
$$33$$ −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 $$0.245980\pi$$
$$38$$ −7.09808 1.90192i −1.15146 0.308533i
$$39$$ 5.19615 3.00000i 0.832050 0.480384i
$$40$$ −1.26795 4.73205i −0.200480 0.748203i
$$41$$ 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 $$0.0487319\pi$$
−0.988304 + 0.152499i $$0.951268\pi$$
$$44$$ 1.00000 1.73205i 0.150756 0.261116i
$$45$$ 0 0
$$46$$ 0.366025 1.36603i 0.0539675 0.201409i
$$47$$ 4.33013 7.50000i 0.631614 1.09399i −0.355608 0.934635i $$-0.615726\pi$$
0.987222 0.159352i $$-0.0509405\pi$$
$$48$$ 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 $$0.811454\pi$$
$$54$$ 1.90192 + 7.09808i 0.258819 + 0.965926i
$$55$$ −1.73205 −0.233550
$$56$$ 0 0
$$57$$ −9.00000 −1.19208
$$58$$ 1.46410 + 5.46410i 0.192246 + 0.717472i
$$59$$ −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i $$-0.276498\pi$$
−0.984102 + 0.177605i $$0.943165\pi$$
$$60$$ −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
$$66$$ 0.633975 2.36603i 0.0780369 0.291238i
$$67$$ −2.59808 + 1.50000i −0.317406 + 0.183254i −0.650236 0.759733i $$-0.725330\pi$$
0.332830 + 0.942987i $$0.391996\pi$$
$$68$$ −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 $$-0.687914\pi$$
0.556650 0.830747i $$-0.312086\pi$$
$$72$$ 0 0
$$73$$ −7.50000 + 4.33013i −0.877809 + 0.506803i −0.869935 0.493166i $$-0.835840\pi$$
−0.00787336 + 0.999969i $$0.502506\pi$$
$$74$$ −4.09808 1.09808i −0.476392 0.127649i
$$75$$ 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 −0.00727784 0.999974i $$-0.502317\pi$$
−0.869641 + 0.493684i $$0.835650\pi$$
$$80$$ 6.00000 3.46410i 0.670820 0.387298i
$$81$$ 4.50000 + 7.79423i 0.500000 + 0.866025i
$$82$$ −4.73205 + 1.26795i −0.522568 + 0.140022i
$$83$$ −13.8564 −1.52094 −0.760469 0.649374i $$-0.775031\pi$$
−0.760469 + 0.649374i $$0.775031\pi$$
$$84$$ 0 0
$$85$$ 3.00000 0.325396
$$86$$ −2.73205 + 0.732051i −0.294605 + 0.0789391i
$$87$$ 3.46410 + 6.00000i 0.371391 + 0.643268i
$$88$$ 2.73205 + 0.732051i 0.291238 + 0.0780369i
$$89$$ −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
$$94$$ 11.8301 + 3.16987i 1.22018 + 0.326947i
$$95$$ −7.79423 + 4.50000i −0.799671 + 0.461690i
$$96$$ 2.53590 + 9.46410i 0.258819 + 0.965926i
$$97$$ 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 $$0.191542\pi$$
$$102$$ −1.09808 + 4.09808i −0.108726 + 0.405770i
$$103$$ −4.33013 + 7.50000i −0.426660 + 0.738997i −0.996574 0.0827075i $$-0.973643\pi$$
0.569914 + 0.821705i $$0.306977\pi$$
$$104$$ −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 0.933146 0.359498i $$-0.117052\pi$$
0.155238 + 0.987877i $$0.450386\pi$$
$$108$$ −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 $$0.975180\pi$$
$$110$$ −0.633975 2.36603i −0.0604471 0.225592i
$$111$$ −5.19615 −0.493197
$$112$$ 0 0
$$113$$ −16.0000 −1.50515 −0.752577 0.658505i $$-0.771189\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ −3.29423 12.2942i −0.308533 1.15146i
$$115$$ −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
$$122$$ −1.90192 + 7.09808i −0.172192 + 0.642630i
$$123$$ −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 $$0.0857705\pi$$
−0.963916 + 0.266207i $$0.914230\pi$$
$$128$$ −10.9282 + 2.92820i −0.965926 + 0.258819i
$$129$$ −3.00000 + 1.73205i −0.264135 + 0.152499i
$$130$$ 8.19615 + 2.19615i 0.718850 + 0.192615i
$$131$$ 2.59808 4.50000i 0.226995 0.393167i −0.729921 0.683531i $$-0.760443\pi$$
0.956916 + 0.290365i $$0.0937766\pi$$
$$132$$ 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
$$136$$ −4.73205 1.26795i −0.405770 0.108726i
$$137$$ −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i $$-0.180268\pi$$
−0.886594 + 0.462549i $$0.846935\pi$$
$$138$$ 2.36603 0.633975i 0.201409 0.0539675i
$$139$$ 6.92820 0.587643 0.293821 0.955860i $$-0.405073\pi$$
0.293821 + 0.955860i $$0.405073\pi$$
$$140$$ 0 0
$$141$$ 15.0000 1.26323
$$142$$ 19.1244 5.12436i 1.60488 0.430026i
$$143$$ 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 $$0.179709\pi$$
$$150$$ 4.73205 + 1.26795i 0.386370 + 0.103528i
$$151$$ 6.06218 3.50000i 0.493333 0.284826i −0.232623 0.972567i $$-0.574731\pi$$
0.725956 + 0.687741i $$0.241398\pi$$
$$152$$ 14.1962 3.80385i 1.15146 0.308533i
$$153$$ 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 $$0.355351\pi$$
$$158$$ 3.29423 12.2942i 0.262075 0.978076i
$$159$$ −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 −0.427802 0.903873i $$-0.640712\pi$$
−0.996678 + 0.0814491i $$0.974045\pi$$
$$164$$ −3.46410 6.00000i −0.270501 0.468521i
$$165$$ −1.50000 2.59808i −0.116775 0.202260i
$$166$$ −5.07180 18.9282i −0.393648 1.46911i
$$167$$ 17.3205 1.34030 0.670151 0.742225i $$-0.266230\pi$$
0.670151 + 0.742225i $$0.266230\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 1.09808 + 4.09808i 0.0842186 + 0.314308i
$$171$$ 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
$$178$$ 5.70577 21.2942i 0.427666 1.59607i
$$179$$ 16.4545 9.50000i 1.22987 0.710063i 0.262864 0.964833i $$-0.415333\pi$$
0.967002 + 0.254770i $$0.0819996\pi$$
$$180$$ 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
$$184$$ 0.732051 + 2.73205i 0.0539675 + 0.201409i
$$185$$ −4.50000 + 2.59808i −0.330847 + 0.191014i
$$186$$ 4.09808 + 1.09808i 0.300486 + 0.0805149i
$$187$$ −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 0.531004 0.847369i $$-0.321815\pi$$
−0.468341 + 0.883548i $$0.655148\pi$$
$$192$$ −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 $$0.651810\pi$$
$$194$$ −23.6603 + 6.33975i −1.69871 + 0.455167i
$$195$$ 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 $$-0.872515\pi$$
0.122782 0.992434i $$1.53918\pi$$
$$200$$ −1.46410 + 5.46410i −0.103528 + 0.386370i
$$201$$ −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
$$206$$ −11.8301 3.16987i −0.824244 0.220856i
$$207$$ 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
$$213$$ 21.0000 12.1244i 1.43890 0.830747i
$$214$$ −4.75833 + 17.7583i −0.325273 + 1.21393i
$$215$$ −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
$$222$$ −1.90192 7.09808i −0.127649 0.476392i
$$223$$ −6.92820 −0.463947 −0.231973 0.972722i $$-0.574518\pi$$
−0.231973 + 0.972722i $$0.574518\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −5.85641 21.8564i −0.389562 1.45387i
$$227$$ 9.52628 + 16.5000i 0.632281 + 1.09514i 0.987084 + 0.160202i $$0.0512147\pi$$
−0.354803 + 0.934941i $$0.615452\pi$$
$$228$$ 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 $$0.223912\pi$$
−0.762620 + 0.646846i $$0.776088\pi$$
$$240$$ 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 $$0.279810\pi$$
$$242$$ −13.6603 3.66025i −0.878114 0.235290i
$$243$$ 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
$$248$$ −1.26795 + 4.73205i −0.0805149 + 0.300486i
$$249$$ −12.0000 20.7846i −0.760469 1.31717i
$$250$$ 16.5622 4.43782i 1.04748 0.280673i
$$251$$ 3.46410 0.218652 0.109326 0.994006i $$-0.465131\pi$$
0.109326 + 0.994006i $$0.465131\pi$$
$$252$$ 0 0
$$253$$ 1.00000 0.0628695
$$254$$ −8.19615 + 2.19615i −0.514272 + 0.137799i
$$255$$ 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
$$262$$ 7.09808 + 1.90192i 0.438521 + 0.117501i
$$263$$ −19.9186 + 11.5000i −1.22823 + 0.709120i −0.966660 0.256063i $$-0.917574\pi$$
−0.261573 + 0.965184i $$0.584241\pi$$
$$264$$ 1.26795 + 4.73205i 0.0780369 + 0.291238i
$$265$$ 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 $$0.574158\pi$$
$$270$$ −3.29423 + 12.2942i −0.200480 + 0.748203i
$$271$$ −7.79423 + 13.5000i −0.473466 + 0.820067i −0.999539 0.0303728i $$-0.990331\pi$$
0.526073 + 0.850439i $$0.323664\pi$$
$$272$$ 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 $$0.705619\pi$$
$$278$$ 2.53590 + 9.46410i 0.152093 + 0.567619i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −4.00000 −0.238620 −0.119310 0.992857i $$-0.538068\pi$$
−0.119310 + 0.992857i $$0.538068\pi$$
$$282$$ 5.49038 + 20.4904i 0.326947 + 1.22018i
$$283$$ 6.06218 + 10.5000i 0.360359 + 0.624160i 0.988020 0.154327i $$-0.0493208\pi$$
−0.627661 + 0.778487i $$0.715988\pi$$
$$284$$ 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
$$290$$ −2.53590 + 9.46410i −0.148913 + 0.555751i
$$291$$ −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
$$296$$ 8.19615 2.19615i 0.476392 0.127649i
$$297$$ −4.50000 + 2.59808i −0.261116 + 0.150756i
$$298$$ −1.36603 0.366025i −0.0791317 0.0212033i
$$299$$ −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 $$-0.702104\pi$$
−0.593120 + 0.805114i $$0.702104\pi$$
$$308$$ 0 0
$$309$$ −15.0000 −0.853320
$$310$$ 4.09808 1.09808i 0.232755 0.0623665i
$$311$$ 4.33013 + 7.50000i 0.245539 + 0.425286i 0.962283 0.272050i $$-0.0877017\pi$$
−0.716744 + 0.697336i $$0.754368\pi$$
$$312$$ −16.3923 4.39230i −0.928032 0.248665i
$$313$$ −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 $$0.266631\pi$$
$$318$$ −2.36603 0.633975i −0.132680 0.0355515i
$$319$$ −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
$$326$$ 7.68653 28.6865i 0.425718 1.58880i
$$327$$ 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 0.657264 0.753660i $$-0.271714\pi$$
−0.324057 + 0.946038i $$0.605047\pi$$
$$332$$ 24.0000 13.8564i 1.31717 0.760469i
$$333$$ 0 0
$$334$$ 6.33975 + 23.6603i 0.346895 + 1.29463i
$$335$$ −5.19615 −0.283896
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 0.366025 + 1.36603i 0.0199092 + 0.0743020i
$$339$$ −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
$$346$$ −4.43782 + 16.5622i −0.238579 + 0.890388i
$$347$$ 11.2583 6.50000i 0.604379 0.348938i −0.166383 0.986061i $$-0.553209\pi$$
0.770762 + 0.637123i $$0.219876\pi$$
$$348$$ −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
$$352$$ −5.46410 + 1.46410i −0.291238 + 0.0780369i
$$353$$ 25.5000 14.7224i 1.35723 0.783596i 0.367979 0.929834i $$-0.380050\pi$$
0.989249 + 0.146238i $$0.0467166\pi$$
$$354$$ 12.2942 + 3.29423i 0.653431 + 0.175086i
$$355$$ 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 −0.128260 0.991741i $$-0.540939\pi$$
−0.923003 + 0.384794i $$0.874273\pi$$
$$360$$ 0 0
$$361$$ −4.00000 6.92820i −0.210526 0.364642i
$$362$$ 9.46410 2.53590i 0.497422 0.133284i
$$363$$ −17.3205 −0.909091
$$364$$ 0 0
$$365$$ −15.0000 −0.785136
$$366$$ −12.2942 + 3.29423i −0.642630 + 0.172192i
$$367$$ 0.866025 + 1.50000i 0.0452062 + 0.0782994i 0.887743 0.460339i $$-0.152272\pi$$
−0.842537 + 0.538639i $$0.818939\pi$$
$$368$$ −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 $$-0.103656\pi$$
$$374$$ −2.36603 0.633975i −0.122344 0.0327820i
$$375$$ 18.1865 10.5000i 0.939149 0.542218i
$$376$$ −23.6603 + 6.33975i −1.22018 + 0.326947i
$$377$$ 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
$$381$$ −9.00000 + 5.19615i −0.461084 + 0.266207i
$$382$$ −0.366025 + 1.36603i −0.0187275 + 0.0698919i
$$383$$ −2.59808 + 4.50000i −0.132755 + 0.229939i −0.924738 0.380605i $$-0.875716\pi$$
0.791982 + 0.610544i $$0.209049\pi$$
$$384$$ −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 $$0.673364\pi$$
$$390$$ 3.80385 + 14.1962i 0.192615 + 0.718850i
$$391$$ −1.73205 −0.0875936
$$392$$ 0 0
$$393$$ 9.00000 0.453990
$$394$$ 5.85641 + 21.8564i 0.295041 + 1.10111i
$$395$$ −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 $$-0.0280523\pi$$
$$402$$ 1.90192 7.09808i 0.0948593 0.354020i
$$403$$ −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
$$408$$ −2.19615 8.19615i −0.108726 0.405770i
$$409$$ −22.5000 + 12.9904i −1.11255 + 0.642333i −0.939490 0.342578i $$-0.888700\pi$$
−0.173064 + 0.984911i $$0.555367\pi$$
$$410$$ −8.19615 2.19615i −0.404779 0.108460i
$$411$$ 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
$$416$$ 5.07180 18.9282i 0.248665 0.928032i
$$417$$ 6.00000 + 10.3923i 0.293821 + 0.508913i
$$418$$ 7.09808 1.90192i 0.347178 0.0930261i
$$419$$ 20.7846 1.01539 0.507697 0.861536i $$-0.330497\pi$$
0.507697 + 0.861536i $$0.330497\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −13.6603 + 3.66025i −0.664971 + 0.178178i
$$423$$ 0 0
$$424$$ 0.732051 2.73205i 0.0355515 0.132680i
$$425$$ −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
$$430$$ −4.73205 1.26795i −0.228200 0.0611459i
$$431$$ 19.9186 11.5000i 0.959444 0.553936i 0.0634424 0.997985i $$-0.479792\pi$$
0.896002 + 0.444050i $$0.146459\pi$$
$$432$$ 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
$$438$$ 5.49038 20.4904i 0.262341 0.979068i
$$439$$ 11.2583 19.5000i 0.537331 0.930684i −0.461716 0.887028i $$-0.652766\pi$$
0.999047 0.0436563i $$-0.0139007\pi$$
$$440$$ 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 0.807155 0.590339i $$-0.201006\pi$$
−0.107671 + 0.994187i $$0.534339\pi$$
$$444$$ 9.00000 5.19615i 0.427121 0.246598i
$$445$$ −13.5000 23.3827i −0.639961 1.10845i
$$446$$ −2.53590 9.46410i −0.120078 0.448138i
$$447$$ −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 $$0.280769\pi$$
$$458$$ −5.70577 + 21.2942i −0.266613 + 0.995014i
$$459$$ 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 $$-0.754469\pi$$
0.716965 0.697109i $$-0.245531\pi$$
$$464$$ 8.00000 13.8564i 0.371391 0.643268i
$$465$$ 4.50000 2.59808i 0.208683 0.120483i
$$466$$ 9.56218 + 2.56218i 0.442959 + 0.118691i
$$467$$ −4.33013 + 7.50000i −0.200374 + 0.347059i −0.948649 0.316330i $$-0.897549\pi$$
0.748275 + 0.663389i $$0.230883\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 15.0000 + 15.0000i 0.691898 + 0.691898i
$$471$$ −2.59808 1.50000i −0.119713 0.0691164i
$$472$$ −3.80385 + 14.1962i −0.175086 + 0.653431i
$$473$$ −1.00000 1.73205i −0.0459800 0.0796398i
$$474$$ 21.2942 5.70577i 0.978076 0.262075i
$$475$$ 10.3923 0.476832
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −27.3205 + 7.32051i −1.24961 + 0.334832i
$$479$$ −6.06218 10.5000i −0.276988 0.479757i 0.693647 0.720315i $$-0.256003\pi$$
−0.970635 + 0.240558i $$0.922670\pi$$
$$480$$ −4.39230 + 16.3923i −0.200480 + 0.748203i
$$481$$ 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 $$-0.914542\pi$$
−0.252367 + 0.967632i $$0.581209\pi$$
$$488$$ −3.80385 14.1962i −0.172192 0.642630i
$$489$$ 36.3731i 1.64485i
$$490$$ 0 0
$$491$$ 32.0000i 1.44414i 0.691820 + 0.722070i $$0.256809\pi$$
−0.691820 + 0.722070i $$0.743191\pi$$
$$492$$ 6.00000 10.3923i 0.270501 0.468521i
$$493$$ 6.00000 3.46410i 0.270226 0.156015i
$$494$$ −6.58846 + 24.5885i −0.296429 + 1.10629i
$$495$$ 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 0.989205 0.146538i $$-0.0468131\pi$$
0.367697 + 0.929946i $$0.380146\pi$$
$$500$$ 12.1244 + 21.0000i 0.542218 + 0.939149i
$$501$$ 15.0000 + 25.9808i 0.670151 + 1.16073i
$$502$$ 1.26795 + 4.73205i 0.0565913 + 0.211202i
$$503$$ 6.92820 0.308913 0.154457 0.988000i $$-0.450637\pi$$
0.154457 + 0.988000i $$0.450637\pi$$
$$504$$ 0 0
$$505$$ 15.0000 0.667491
$$506$$ 0.366025 + 1.36603i 0.0162718 + 0.0607272i
$$507$$ 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
$$514$$ 1.90192 7.09808i 0.0838903 0.313083i
$$515$$ −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
$$520$$ −16.3923 + 4.39230i −0.718850 + 0.192615i
$$521$$ −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 $$0.358961\pi$$
−0.996761 + 0.0804241i $$0.974373\pi$$
$$524$$ 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
$$530$$ −2.36603 + 0.633975i −0.102774 + 0.0275381i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 36.8827 9.88269i 1.59607 0.427666i
$$535$$ 11.2583 + 19.5000i 0.486740 + 0.843059i
$$536$$ 8.19615 + 2.19615i 0.354020 + 0.0948593i
$$537$$ 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 $$0.0327407\pi$$
$$542$$ −21.2942 5.70577i −0.914665 0.245084i
$$543$$ 10.3923 6.00000i 0.445976 0.257485i
$$544$$ 9.46410 2.53590i 0.405770 0.108726i
$$545$$ 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
$$550$$ −0.732051 + 2.73205i −0.0312148 + 0.116495i
$$551$$ −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
$$562$$ −1.46410 5.46410i −0.0617594 0.230489i
$$563$$ 11.2583 + 19.5000i 0.474482 + 0.821827i 0.999573 0.0292191i $$-0.00930205\pi$$
−0.525091 + 0.851046i $$0.675969\pi$$
$$564$$ −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 $$0.0788181\pi$$
$$570$$ 5.70577 21.2942i 0.238988 0.891917i
$$571$$ −18.1865 + 10.5000i −0.761083 + 0.439411i −0.829684 0.558233i $$-0.811480\pi$$
0.0686016 + 0.997644i $$0.478146\pi$$
$$572$$ −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 $$0.0931316\pi$$
$$578$$ −19.1244 5.12436i −0.795468 0.213145i
$$579$$ −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
$$584$$ 23.6603 + 6.33975i 0.979068 + 0.262341i
$$585$$ 0 0
$$586$$ −28.3923 + 7.60770i −1.17288 + 0.314271i
$$587$$ −6.92820 −0.285958 −0.142979 0.989726i $$-0.545668\pi$$
−0.142979 + 0.989726i $$0.545668\pi$$
$$588$$ 0 0
$$589$$ 9.00000 0.370839
$$590$$ 12.2942 3.29423i 0.506145 0.135621i
$$591$$ 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
$$598$$ −4.73205 1.26795i −0.193508 0.0518503i
$$599$$ 14.7224 8.50000i 0.601542 0.347301i −0.168106 0.985769i $$-0.553765\pi$$
0.769648 + 0.638468i $$0.220432\pi$$
$$600$$ −9.46410 + 2.53590i −0.386370 + 0.103528i
$$601$$ 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
$$606$$ −5.49038 + 20.4904i −0.223031 + 0.832365i
$$607$$ 7.79423 13.5000i 0.316358 0.547948i −0.663367 0.748294i $$-0.730873\pi$$
0.979725 + 0.200346i $$0.0642066\pi$$
$$608$$ −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 $$0.618008\pi$$
$$614$$ −7.60770 28.3923i −0.307022 1.14582i
$$615$$ −10.3923 −0.419058
$$616$$ 0 0
$$617$$ 20.0000 0.805170 0.402585 0.915383i $$-0.368112\pi$$
0.402585 + 0.915383i $$0.368112\pi$$
$$618$$ −5.49038 20.4904i −0.220856 0.824244i
$$619$$ 7.79423 + 13.5000i 0.313276 + 0.542611i 0.979070 0.203526i $$-0.0652400\pi$$
−0.665793 + 0.746136i $$0.731907\pi$$
$$620$$ 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
$$626$$ 0.633975 2.36603i 0.0253387 0.0945654i
$$627$$ 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 $$0.203697\pi$$
−0.802137 + 0.597141i $$0.796303\pi$$
$$632$$ 6.58846 + 24.5885i 0.262075 + 0.978076i
$$633$$ −15.0000 + 8.66025i −0.596196 + 0.344214i
$$634$$ −15.0263 4.02628i −0.596770 0.159904i
$$635$$ −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
$$640$$ −18.9282 5.07180i −0.748203 0.200480i
$$641$$ 6.50000 + 11.2583i 0.256735 + 0.444677i 0.965365 0.260902i $$-0.0840201\pi$$
−0.708631 + 0.705580i $$0.750687\pi$$
$$642$$ −30.7583 + 8.24167i −1.21393 + 0.325273i
$$643$$ 13.8564 0.546443 0.273222 0.961951i $$-0.411911\pi$$
0.273222 + 0.961951i $$0.411911\pi$$
$$644$$ 0 0
$$645$$ −6.00000 −0.236250
$$646$$ −12.2942 + 3.29423i −0.483710 + 0.129610i
$$647$$ −16.4545 28.5000i −0.646892 1.12045i −0.983861 0.178935i $$-0.942735\pi$$
0.336968 0.941516i $$1.60940\pi$$
$$648$$ 6.58846 24.5885i 0.258819 0.965926i
$$649$$ 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 $$0.959215\pi$$
$$654$$ 21.2942 + 5.70577i 0.832670 + 0.223113i
$$655$$ 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 $$-0.734762\pi$$
0.672458 0.740135i $$-0.265238\pi$$
$$660$$ 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 $$0.0512125\pi$$
$$662$$ −2.56218 + 9.56218i −0.0995819 + 0.371645i
$$663$$ 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
$$670$$ −1.90192 7.09808i −0.0734777 0.274223i
$$671$$ −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
$$682$$ −0.633975 + 2.36603i −0.0242761 + 0.0905998i
$$683$$ −21.6506 + 12.5000i −0.828439 + 0.478299i −0.853318 0.521391i $$-0.825413\pi$$
0.0248792 + 0.999690i $$0.492080\pi$$
$$684$$ 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
$$690$$ 4.09808 + 1.09808i 0.156011 + 0.0418030i
$$691$$ 6.06218 10.5000i 0.230616 0.399439i −0.727373 0.686242i $$-0.759259\pi$$
0.957990 + 0.286803i $$0.0925925\pi$$
$$692$$ −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
$$696$$ 5.07180 18.9282i 0.192246 0.717472i
$$697$$ 3.00000 + 5.19615i 0.113633 + 0.196818i
$$698$$ 14.1962 3.80385i 0.537332 0.143978i
$$699$$ 12.1244 0.458585
$$700$$ 0 0
$$701$$ −26.0000 −0.982006 −0.491003 0.871158i $$-0.663370\pi$$
−0.491003 + 0.871158i $$0.663370\pi$$
$$702$$ 24.5885 6.58846i 0.928032 0.248665i
$$703$$ −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 $$0.112613\pi$$
$$710$$ 33.1244 + 8.87564i 1.24313 + 0.333097i
$$711$$ 0 0
$$712$$ 11.4115 + 42.5885i 0.427666 + 1.59607i
$$713$$ 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
$$718$$ 8.41858 31.4186i 0.314179 1.17253i
$$719$$ 12.9904 22.5000i 0.484459 0.839108i −0.515381 0.856961i $$-0.672350\pi$$
0.999841 + 0.0178527i $$0.00568298\pi$$
$$720$$ 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
$$726$$ −6.33975 23.6603i −0.235290 0.878114i
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ −5.49038 20.4904i −0.203208 0.758383i
$$731$$ 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 $$-0.279313\pi$$
0.985634 0.168898i $$-0.0540208\pi$$
$$740$$ 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 $$-0.785641\pi$$
0.781688 0.623670i $$-0.214359\pi$$
$$744$$ −8.19615 + 2.19615i −0.300486 + 0.0805149i
$$745$$ −1.50000 + 0.866025i −0.0549557 + 0.0317287i
$$746$$ 39.6147 + 10.6147i 1.45040 + 0.388633i
$$747$$ 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 0.839978 0.542621i $$-0.182568\pi$$
−0.0499348 + 0.998752i $$0.515901\pi$$
$$752$$ −17.3205 30.0000i −0.631614 1.09399i
$$753$$ 3.00000 + 5.19615i 0.109326 + 0.189358i
$$754$$ 18.9282 5.07180i 0.689325 0.184704i
$$755$$ 12.1244 0.441250
$$756$$ 0 0
$$757$$ −48.0000 −1.74459 −0.872295 0.488980i $$-0.837369\pi$$
−0.872295 + 0.488980i $$0.837369\pi$$
$$758$$ 10.9282 2.92820i 0.396930 0.106357i
$$759$$ 0.866025 + 1.50000i 0.0314347 + 0.0544466i
$$760$$ 24.5885 + 6.58846i 0.891917 + 0.238988i
$$761$$ −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
$$766$$ −7.09808 1.90192i −0.256464 0.0687193i
$$767$$ −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
$$782$$ −0.633975 2.36603i −0.0226709 0.0846089i
$$783$$ 20.7846 0.742781