# Properties

 Label 800.2.y.a.501.1 Level $800$ Weight $2$ Character 800.501 Analytic conductor $6.388$ Analytic rank $1$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$800 = 2^{5} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 800.y (of order $$8$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.38803216170$$ Analytic rank: $$1$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 32) Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

## Embedding invariants

 Embedding label 501.1 Root $$-0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 800.501 Dual form 800.2.y.a.701.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.41421i q^{2} +(0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(-0.414214 - 1.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 + 1.70711i) q^{9} +O(q^{10})$$ $$q-1.41421i q^{2} +(0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(-0.414214 - 1.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 + 1.70711i) q^{9} +(-4.12132 - 1.70711i) q^{11} +(-1.41421 + 0.585786i) q^{12} +(-0.292893 - 0.707107i) q^{13} +(-1.41421 + 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(2.41421 + 2.41421i) q^{18} +(1.53553 + 3.70711i) q^{19} +(-1.00000 - 0.414214i) q^{21} +(-2.41421 + 5.82843i) q^{22} +(-5.82843 + 5.82843i) q^{23} +(0.828427 + 2.00000i) q^{24} +(-1.00000 + 0.414214i) q^{26} +(-1.58579 + 3.82843i) q^{27} +(2.00000 + 2.00000i) q^{28} +(-3.12132 + 1.29289i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -3.41421 q^{33} -4.00000 q^{34} +(3.41421 - 3.41421i) q^{36} +(-0.292893 + 0.707107i) q^{37} +(5.24264 - 2.17157i) q^{38} +(-0.414214 - 0.414214i) q^{39} +(-0.171573 + 0.171573i) q^{41} +(-0.585786 + 1.41421i) q^{42} +(-4.70711 - 1.94975i) q^{43} +(8.24264 + 3.41421i) q^{44} +(8.24264 + 8.24264i) q^{46} -0.343146i q^{47} +(2.82843 - 1.17157i) q^{48} -5.00000i q^{49} +(-0.828427 - 2.00000i) q^{51} +(0.585786 + 1.41421i) q^{52} +(1.12132 + 0.464466i) q^{53} +(5.41421 + 2.24264i) q^{54} +(2.82843 - 2.82843i) q^{56} +(2.17157 + 2.17157i) q^{57} +(1.82843 + 4.41421i) q^{58} +(-1.87868 + 4.53553i) q^{59} +(1.70711 - 0.707107i) q^{61} +5.65685i q^{62} +3.41421 q^{63} -8.00000 q^{64} +4.82843i q^{66} +(5.53553 - 2.29289i) q^{67} +5.65685i q^{68} +(-2.41421 + 5.82843i) q^{69} +(-5.82843 - 5.82843i) q^{71} +(-4.82843 - 4.82843i) q^{72} +(-7.00000 + 7.00000i) q^{73} +(1.00000 + 0.414214i) q^{74} +(-3.07107 - 7.41421i) q^{76} +(2.41421 + 5.82843i) q^{77} +(-0.585786 + 0.585786i) q^{78} -6.00000i q^{79} -4.07107i q^{81} +(0.242641 + 0.242641i) q^{82} +(-1.87868 - 4.53553i) q^{83} +(2.00000 + 0.828427i) q^{84} +(-2.75736 + 6.65685i) q^{86} +(-1.82843 + 1.82843i) q^{87} +(4.82843 - 11.6569i) q^{88} +(8.65685 + 8.65685i) q^{89} +(-0.414214 + 1.00000i) q^{91} +(11.6569 - 11.6569i) q^{92} +(-2.82843 + 1.17157i) q^{93} -0.485281 q^{94} +(-1.65685 - 4.00000i) q^{96} +18.4853 q^{97} -7.07107 q^{98} +(9.94975 - 4.12132i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{9} + O(q^{10})$$ $$4 q - 8 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{9} - 8 q^{11} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 8 q^{19} - 4 q^{21} - 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{26} - 12 q^{27} + 8 q^{28} - 4 q^{29} - 16 q^{31} - 8 q^{33} - 16 q^{34} + 8 q^{36} - 4 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} - 8 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{46} + 8 q^{51} + 8 q^{52} - 4 q^{53} + 16 q^{54} + 20 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{61} + 8 q^{63} - 32 q^{64} + 8 q^{67} - 4 q^{69} - 12 q^{71} - 8 q^{72} - 28 q^{73} + 4 q^{74} + 16 q^{76} + 4 q^{77} - 8 q^{78} - 16 q^{82} - 16 q^{83} + 8 q^{84} - 28 q^{86} + 4 q^{87} + 8 q^{88} + 12 q^{89} + 4 q^{91} + 24 q^{92} + 32 q^{94} + 16 q^{96} + 40 q^{97} + 20 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$351$$ $$577$$ $$\chi(n)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421i 1.00000i
$$3$$ 0.707107 0.292893i 0.408248 0.169102i −0.169102 0.985599i $$-0.554087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ −2.00000 −1.00000
$$5$$ 0 0
$$6$$ −0.414214 1.00000i −0.169102 0.408248i
$$7$$ −1.00000 1.00000i −0.377964 0.377964i 0.492403 0.870367i $$-0.336119\pi$$
−0.870367 + 0.492403i $$0.836119\pi$$
$$8$$ 2.82843i 1.00000i
$$9$$ −1.70711 + 1.70711i −0.569036 + 0.569036i
$$10$$ 0 0
$$11$$ −4.12132 1.70711i −1.24262 0.514712i −0.338091 0.941113i $$-0.609781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ −1.41421 + 0.585786i −0.408248 + 0.169102i
$$13$$ −0.292893 0.707107i −0.0812340 0.196116i 0.878044 0.478580i $$-0.158848\pi$$
−0.959278 + 0.282464i $$0.908848\pi$$
$$14$$ −1.41421 + 1.41421i −0.377964 + 0.377964i
$$15$$ 0 0
$$16$$ 4.00000 1.00000
$$17$$ 2.82843i 0.685994i −0.939336 0.342997i $$-0.888558\pi$$
0.939336 0.342997i $$-0.111442\pi$$
$$18$$ 2.41421 + 2.41421i 0.569036 + 0.569036i
$$19$$ 1.53553 + 3.70711i 0.352276 + 0.850469i 0.996339 + 0.0854961i $$0.0272475\pi$$
−0.644063 + 0.764973i $$0.722752\pi$$
$$20$$ 0 0
$$21$$ −1.00000 0.414214i −0.218218 0.0903888i
$$22$$ −2.41421 + 5.82843i −0.514712 + 1.24262i
$$23$$ −5.82843 + 5.82843i −1.21531 + 1.21531i −0.246055 + 0.969256i $$0.579134\pi$$
−0.969256 + 0.246055i $$0.920866\pi$$
$$24$$ 0.828427 + 2.00000i 0.169102 + 0.408248i
$$25$$ 0 0
$$26$$ −1.00000 + 0.414214i −0.196116 + 0.0812340i
$$27$$ −1.58579 + 3.82843i −0.305185 + 0.736781i
$$28$$ 2.00000 + 2.00000i 0.377964 + 0.377964i
$$29$$ −3.12132 + 1.29289i −0.579615 + 0.240084i −0.653176 0.757206i $$-0.726564\pi$$
0.0735609 + 0.997291i $$0.476564\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 5.65685i 1.00000i
$$33$$ −3.41421 −0.594338
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 3.41421 3.41421i 0.569036 0.569036i
$$37$$ −0.292893 + 0.707107i −0.0481513 + 0.116248i −0.946125 0.323802i $$-0.895039\pi$$
0.897974 + 0.440049i $$0.145039\pi$$
$$38$$ 5.24264 2.17157i 0.850469 0.352276i
$$39$$ −0.414214 0.414214i −0.0663273 0.0663273i
$$40$$ 0 0
$$41$$ −0.171573 + 0.171573i −0.0267952 + 0.0267952i −0.720377 0.693582i $$-0.756031\pi$$
0.693582 + 0.720377i $$0.256031\pi$$
$$42$$ −0.585786 + 1.41421i −0.0903888 + 0.218218i
$$43$$ −4.70711 1.94975i −0.717827 0.297334i −0.00628798 0.999980i $$-0.502002\pi$$
−0.711539 + 0.702647i $$0.752002\pi$$
$$44$$ 8.24264 + 3.41421i 1.24262 + 0.514712i
$$45$$ 0 0
$$46$$ 8.24264 + 8.24264i 1.21531 + 1.21531i
$$47$$ 0.343146i 0.0500530i −0.999687 0.0250265i $$-0.992033\pi$$
0.999687 0.0250265i $$-0.00796701\pi$$
$$48$$ 2.82843 1.17157i 0.408248 0.169102i
$$49$$ 5.00000i 0.714286i
$$50$$ 0 0
$$51$$ −0.828427 2.00000i −0.116003 0.280056i
$$52$$ 0.585786 + 1.41421i 0.0812340 + 0.196116i
$$53$$ 1.12132 + 0.464466i 0.154025 + 0.0637993i 0.458364 0.888764i $$-0.348436\pi$$
−0.304339 + 0.952564i $$0.598436\pi$$
$$54$$ 5.41421 + 2.24264i 0.736781 + 0.305185i
$$55$$ 0 0
$$56$$ 2.82843 2.82843i 0.377964 0.377964i
$$57$$ 2.17157 + 2.17157i 0.287632 + 0.287632i
$$58$$ 1.82843 + 4.41421i 0.240084 + 0.579615i
$$59$$ −1.87868 + 4.53553i −0.244583 + 0.590476i −0.997727 0.0673793i $$-0.978536\pi$$
0.753144 + 0.657855i $$0.228536\pi$$
$$60$$ 0 0
$$61$$ 1.70711 0.707107i 0.218573 0.0905357i −0.270710 0.962661i $$-0.587259\pi$$
0.489283 + 0.872125i $$0.337259\pi$$
$$62$$ 5.65685i 0.718421i
$$63$$ 3.41421 0.430150
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 4.82843i 0.594338i
$$67$$ 5.53553 2.29289i 0.676273 0.280121i −0.0179949 0.999838i $$-0.505728\pi$$
0.694268 + 0.719717i $$0.255728\pi$$
$$68$$ 5.65685i 0.685994i
$$69$$ −2.41421 + 5.82843i −0.290637 + 0.701660i
$$70$$ 0 0
$$71$$ −5.82843 5.82843i −0.691707 0.691707i 0.270900 0.962607i $$-0.412679\pi$$
−0.962607 + 0.270900i $$0.912679\pi$$
$$72$$ −4.82843 4.82843i −0.569036 0.569036i
$$73$$ −7.00000 + 7.00000i −0.819288 + 0.819288i −0.986005 0.166717i $$-0.946683\pi$$
0.166717 + 0.986005i $$0.446683\pi$$
$$74$$ 1.00000 + 0.414214i 0.116248 + 0.0481513i
$$75$$ 0 0
$$76$$ −3.07107 7.41421i −0.352276 0.850469i
$$77$$ 2.41421 + 5.82843i 0.275125 + 0.664211i
$$78$$ −0.585786 + 0.585786i −0.0663273 + 0.0663273i
$$79$$ 6.00000i 0.675053i −0.941316 0.337526i $$-0.890410\pi$$
0.941316 0.337526i $$-0.109590\pi$$
$$80$$ 0 0
$$81$$ 4.07107i 0.452341i
$$82$$ 0.242641 + 0.242641i 0.0267952 + 0.0267952i
$$83$$ −1.87868 4.53553i −0.206212 0.497840i 0.786609 0.617452i $$-0.211835\pi$$
−0.992821 + 0.119612i $$0.961835\pi$$
$$84$$ 2.00000 + 0.828427i 0.218218 + 0.0903888i
$$85$$ 0 0
$$86$$ −2.75736 + 6.65685i −0.297334 + 0.717827i
$$87$$ −1.82843 + 1.82843i −0.196028 + 0.196028i
$$88$$ 4.82843 11.6569i 0.514712 1.24262i
$$89$$ 8.65685 + 8.65685i 0.917625 + 0.917625i 0.996856 0.0792315i $$-0.0252466\pi$$
−0.0792315 + 0.996856i $$0.525247\pi$$
$$90$$ 0 0
$$91$$ −0.414214 + 1.00000i −0.0434214 + 0.104828i
$$92$$ 11.6569 11.6569i 1.21531 1.21531i
$$93$$ −2.82843 + 1.17157i −0.293294 + 0.121486i
$$94$$ −0.485281 −0.0500530
$$95$$ 0 0
$$96$$ −1.65685 4.00000i −0.169102 0.408248i
$$97$$ 18.4853 1.87690 0.938448 0.345421i $$-0.112264\pi$$
0.938448 + 0.345421i $$0.112264\pi$$
$$98$$ −7.07107 −0.714286
$$99$$ 9.94975 4.12132i 0.999987 0.414208i
$$100$$ 0 0
$$101$$ −1.36396 + 3.29289i −0.135719 + 0.327655i −0.977098 0.212791i $$-0.931745\pi$$
0.841379 + 0.540446i $$0.181745\pi$$
$$102$$ −2.82843 + 1.17157i −0.280056 + 0.116003i
$$103$$ −9.48528 9.48528i −0.934613 0.934613i 0.0633771 0.997990i $$-0.479813\pi$$
−0.997990 + 0.0633771i $$0.979813\pi$$
$$104$$ 2.00000 0.828427i 0.196116 0.0812340i
$$105$$ 0 0
$$106$$ 0.656854 1.58579i 0.0637993 0.154025i
$$107$$ 4.12132 + 1.70711i 0.398423 + 0.165032i 0.572893 0.819630i $$-0.305821\pi$$
−0.174470 + 0.984663i $$0.555821\pi$$
$$108$$ 3.17157 7.65685i 0.305185 0.736781i
$$109$$ −5.70711 13.7782i −0.546642 1.31971i −0.919962 0.392007i $$-0.871781\pi$$
0.373320 0.927702i $$-0.378219\pi$$
$$110$$ 0 0
$$111$$ 0.585786i 0.0556004i
$$112$$ −4.00000 4.00000i −0.377964 0.377964i
$$113$$ 6.34315i 0.596713i −0.954455 0.298356i $$-0.903562\pi$$
0.954455 0.298356i $$-0.0964384\pi$$
$$114$$ 3.07107 3.07107i 0.287632 0.287632i
$$115$$ 0 0
$$116$$ 6.24264 2.58579i 0.579615 0.240084i
$$117$$ 1.70711 + 0.707107i 0.157822 + 0.0653720i
$$118$$ 6.41421 + 2.65685i 0.590476 + 0.244583i
$$119$$ −2.82843 + 2.82843i −0.259281 + 0.259281i
$$120$$ 0 0
$$121$$ 6.29289 + 6.29289i 0.572081 + 0.572081i
$$122$$ −1.00000 2.41421i −0.0905357 0.218573i
$$123$$ −0.0710678 + 0.171573i −0.00640797 + 0.0154702i
$$124$$ 8.00000 0.718421
$$125$$ 0 0
$$126$$ 4.82843i 0.430150i
$$127$$ −12.9706 −1.15095 −0.575476 0.817819i $$-0.695183\pi$$
−0.575476 + 0.817819i $$0.695183\pi$$
$$128$$ 11.3137i 1.00000i
$$129$$ −3.89949 −0.343331
$$130$$ 0 0
$$131$$ −16.3640 + 6.77817i −1.42973 + 0.592212i −0.957284 0.289150i $$-0.906627\pi$$
−0.472442 + 0.881362i $$0.656627\pi$$
$$132$$ 6.82843 0.594338
$$133$$ 2.17157 5.24264i 0.188299 0.454595i
$$134$$ −3.24264 7.82843i −0.280121 0.676273i
$$135$$ 0 0
$$136$$ 8.00000 0.685994
$$137$$ 8.65685 8.65685i 0.739605 0.739605i −0.232897 0.972502i $$-0.574820\pi$$
0.972502 + 0.232897i $$0.0748204\pi$$
$$138$$ 8.24264 + 3.41421i 0.701660 + 0.290637i
$$139$$ 13.1924 + 5.46447i 1.11896 + 0.463490i 0.864016 0.503465i $$-0.167942\pi$$
0.254948 + 0.966955i $$0.417942\pi$$
$$140$$ 0 0
$$141$$ −0.100505 0.242641i −0.00846405 0.0204340i
$$142$$ −8.24264 + 8.24264i −0.691707 + 0.691707i
$$143$$ 3.41421i 0.285511i
$$144$$ −6.82843 + 6.82843i −0.569036 + 0.569036i
$$145$$ 0 0
$$146$$ 9.89949 + 9.89949i 0.819288 + 0.819288i
$$147$$ −1.46447 3.53553i −0.120787 0.291606i
$$148$$ 0.585786 1.41421i 0.0481513 0.116248i
$$149$$ −15.6066 6.46447i −1.27854 0.529590i −0.362992 0.931792i $$-0.618245\pi$$
−0.915551 + 0.402203i $$0.868245\pi$$
$$150$$ 0 0
$$151$$ −1.48528 + 1.48528i −0.120870 + 0.120870i −0.764955 0.644084i $$-0.777239\pi$$
0.644084 + 0.764955i $$0.277239\pi$$
$$152$$ −10.4853 + 4.34315i −0.850469 + 0.352276i
$$153$$ 4.82843 + 4.82843i 0.390355 + 0.390355i
$$154$$ 8.24264 3.41421i 0.664211 0.275125i
$$155$$ 0 0
$$156$$ 0.828427 + 0.828427i 0.0663273 + 0.0663273i
$$157$$ −1.70711 + 0.707107i −0.136242 + 0.0564333i −0.449763 0.893148i $$-0.648491\pi$$
0.313521 + 0.949581i $$0.398491\pi$$
$$158$$ −8.48528 −0.675053
$$159$$ 0.928932 0.0736691
$$160$$ 0 0
$$161$$ 11.6569 0.918689
$$162$$ −5.75736 −0.452341
$$163$$ −0.464466 + 0.192388i −0.0363798 + 0.0150690i −0.400799 0.916166i $$-0.631267\pi$$
0.364419 + 0.931235i $$0.381267\pi$$
$$164$$ 0.343146 0.343146i 0.0267952 0.0267952i
$$165$$ 0 0
$$166$$ −6.41421 + 2.65685i −0.497840 + 0.206212i
$$167$$ −14.6569 14.6569i −1.13418 1.13418i −0.989475 0.144707i $$-0.953776\pi$$
−0.144707 0.989475i $$-0.546224\pi$$
$$168$$ 1.17157 2.82843i 0.0903888 0.218218i
$$169$$ 8.77817 8.77817i 0.675244 0.675244i
$$170$$ 0 0
$$171$$ −8.94975 3.70711i −0.684404 0.283490i
$$172$$ 9.41421 + 3.89949i 0.717827 + 0.297334i
$$173$$ −3.12132 7.53553i −0.237310 0.572916i 0.759693 0.650282i $$-0.225349\pi$$
−0.997003 + 0.0773656i $$0.975349\pi$$
$$174$$ 2.58579 + 2.58579i 0.196028 + 0.196028i
$$175$$ 0 0
$$176$$ −16.4853 6.82843i −1.24262 0.514712i
$$177$$ 3.75736i 0.282420i
$$178$$ 12.2426 12.2426i 0.917625 0.917625i
$$179$$ −1.63604 3.94975i −0.122283 0.295218i 0.850870 0.525377i $$-0.176076\pi$$
−0.973153 + 0.230159i $$0.926076\pi$$
$$180$$ 0 0
$$181$$ 16.1924 + 6.70711i 1.20357 + 0.498535i 0.892151 0.451737i $$-0.149196\pi$$
0.311420 + 0.950272i $$0.399196\pi$$
$$182$$ 1.41421 + 0.585786i 0.104828 + 0.0434214i
$$183$$ 1.00000 1.00000i 0.0739221 0.0739221i
$$184$$ −16.4853 16.4853i −1.21531 1.21531i
$$185$$ 0 0
$$186$$ 1.65685 + 4.00000i 0.121486 + 0.293294i
$$187$$ −4.82843 + 11.6569i −0.353090 + 0.852434i
$$188$$ 0.686292i 0.0500530i
$$189$$ 5.41421 2.24264i 0.393826 0.163128i
$$190$$ 0 0
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ −5.65685 + 2.34315i −0.408248 + 0.169102i
$$193$$ 1.51472 0.109032 0.0545159 0.998513i $$-0.482638\pi$$
0.0545159 + 0.998513i $$0.482638\pi$$
$$194$$ 26.1421i 1.87690i
$$195$$ 0 0
$$196$$ 10.0000i 0.714286i
$$197$$ −4.63604 + 11.1924i −0.330304 + 0.797425i 0.668264 + 0.743924i $$0.267038\pi$$
−0.998568 + 0.0535002i $$0.982962\pi$$
$$198$$ −5.82843 14.0711i −0.414208 0.999987i
$$199$$ −15.9706 15.9706i −1.13212 1.13212i −0.989824 0.142300i $$-0.954550\pi$$
−0.142300 0.989824i $$-0.545450\pi$$
$$200$$ 0 0
$$201$$ 3.24264 3.24264i 0.228718 0.228718i
$$202$$ 4.65685 + 1.92893i 0.327655 + 0.135719i
$$203$$ 4.41421 + 1.82843i 0.309817 + 0.128330i
$$204$$ 1.65685 + 4.00000i 0.116003 + 0.280056i
$$205$$ 0 0
$$206$$ −13.4142 + 13.4142i −0.934613 + 0.934613i
$$207$$ 19.8995i 1.38311i
$$208$$ −1.17157 2.82843i −0.0812340 0.196116i
$$209$$ 17.8995i 1.23813i
$$210$$ 0 0
$$211$$ 7.53553 + 18.1924i 0.518768 + 1.25242i 0.938661 + 0.344842i $$0.112068\pi$$
−0.419893 + 0.907574i $$0.637932\pi$$
$$212$$ −2.24264 0.928932i −0.154025 0.0637993i
$$213$$ −5.82843 2.41421i −0.399357 0.165419i
$$214$$ 2.41421 5.82843i 0.165032 0.398423i
$$215$$ 0 0
$$216$$ −10.8284 4.48528i −0.736781 0.305185i
$$217$$ 4.00000 + 4.00000i 0.271538 + 0.271538i
$$218$$ −19.4853 + 8.07107i −1.31971 + 0.546642i
$$219$$ −2.89949 + 7.00000i −0.195930 + 0.473016i
$$220$$ 0 0
$$221$$ −2.00000 + 0.828427i −0.134535 + 0.0557260i
$$222$$ 0.828427 0.0556004
$$223$$ 20.9706 1.40429 0.702146 0.712033i $$-0.252225\pi$$
0.702146 + 0.712033i $$0.252225\pi$$
$$224$$ −5.65685 + 5.65685i −0.377964 + 0.377964i
$$225$$ 0 0
$$226$$ −8.97056 −0.596713
$$227$$ −18.6066 + 7.70711i −1.23496 + 0.511539i −0.902137 0.431449i $$-0.858002\pi$$
−0.332826 + 0.942988i $$0.608002\pi$$
$$228$$ −4.34315 4.34315i −0.287632 0.287632i
$$229$$ −9.22183 + 22.2635i −0.609395 + 1.47121i 0.254264 + 0.967135i $$0.418167\pi$$
−0.863659 + 0.504076i $$0.831833\pi$$
$$230$$ 0 0
$$231$$ 3.41421 + 3.41421i 0.224639 + 0.224639i
$$232$$ −3.65685 8.82843i −0.240084 0.579615i
$$233$$ 2.65685 2.65685i 0.174056 0.174056i −0.614703 0.788759i $$-0.710724\pi$$
0.788759 + 0.614703i $$0.210724\pi$$
$$234$$ 1.00000 2.41421i 0.0653720 0.157822i
$$235$$ 0 0
$$236$$ 3.75736 9.07107i 0.244583 0.590476i
$$237$$ −1.75736 4.24264i −0.114153 0.275589i
$$238$$ 4.00000 + 4.00000i 0.259281 + 0.259281i
$$239$$ 5.31371i 0.343715i 0.985122 + 0.171858i $$0.0549769\pi$$
−0.985122 + 0.171858i $$0.945023\pi$$
$$240$$ 0 0
$$241$$ 8.48528i 0.546585i 0.961931 + 0.273293i $$0.0881127\pi$$
−0.961931 + 0.273293i $$0.911887\pi$$
$$242$$ 8.89949 8.89949i 0.572081 0.572081i
$$243$$ −5.94975 14.3640i −0.381676 0.921449i
$$244$$ −3.41421 + 1.41421i −0.218573 + 0.0905357i
$$245$$ 0 0
$$246$$ 0.242641 + 0.100505i 0.0154702 + 0.00640797i
$$247$$ 2.17157 2.17157i 0.138174 0.138174i
$$248$$ 11.3137i 0.718421i
$$249$$ −2.65685 2.65685i −0.168371 0.168371i
$$250$$ 0 0
$$251$$ 6.60660 15.9497i 0.417005 1.00674i −0.566205 0.824264i $$-0.691589\pi$$
0.983210 0.182475i $$-0.0584109\pi$$
$$252$$ −6.82843 −0.430150
$$253$$ 33.9706 14.0711i 2.13571 0.884640i
$$254$$ 18.3431i 1.15095i
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 5.51472i 0.343331i
$$259$$ 1.00000 0.414214i 0.0621370 0.0257380i
$$260$$ 0 0
$$261$$ 3.12132 7.53553i 0.193205 0.466438i
$$262$$ 9.58579 + 23.1421i 0.592212 + 1.42973i
$$263$$ 5.82843 + 5.82843i 0.359396 + 0.359396i 0.863590 0.504194i $$-0.168210\pi$$
−0.504194 + 0.863590i $$0.668210\pi$$
$$264$$ 9.65685i 0.594338i
$$265$$ 0 0
$$266$$ −7.41421 3.07107i −0.454595 0.188299i
$$267$$ 8.65685 + 3.58579i 0.529791 + 0.219447i
$$268$$ −11.0711 + 4.58579i −0.676273 + 0.280121i
$$269$$ 9.12132 + 22.0208i 0.556137 + 1.34263i 0.912803 + 0.408401i $$0.133913\pi$$
−0.356666 + 0.934232i $$0.616087\pi$$
$$270$$ 0 0
$$271$$ 18.0000i 1.09342i −0.837321 0.546711i $$-0.815880\pi$$
0.837321 0.546711i $$-0.184120\pi$$
$$272$$ 11.3137i 0.685994i
$$273$$ 0.828427i 0.0501387i
$$274$$ −12.2426 12.2426i −0.739605 0.739605i
$$275$$ 0 0
$$276$$ 4.82843 11.6569i 0.290637 0.701660i
$$277$$ −1.70711 0.707107i −0.102570 0.0424859i 0.330808 0.943698i $$-0.392679\pi$$
−0.433378 + 0.901212i $$0.642679\pi$$
$$278$$ 7.72792 18.6569i 0.463490 1.11896i
$$279$$ 6.82843 6.82843i 0.408807 0.408807i
$$280$$ 0 0
$$281$$ −11.8284 11.8284i −0.705625 0.705625i 0.259987 0.965612i $$-0.416282\pi$$
−0.965612 + 0.259987i $$0.916282\pi$$
$$282$$ −0.343146 + 0.142136i −0.0204340 + 0.00846405i
$$283$$ −5.77817 + 13.9497i −0.343477 + 0.829226i 0.653882 + 0.756596i $$0.273139\pi$$
−0.997359 + 0.0726300i $$0.976861\pi$$
$$284$$ 11.6569 + 11.6569i 0.691707 + 0.691707i
$$285$$ 0 0
$$286$$ 4.82843 0.285511
$$287$$ 0.343146 0.0202553
$$288$$ 9.65685 + 9.65685i 0.569036 + 0.569036i
$$289$$ 9.00000 0.529412
$$290$$ 0 0
$$291$$ 13.0711 5.41421i 0.766240 0.317387i
$$292$$ 14.0000 14.0000i 0.819288 0.819288i
$$293$$ −9.60660 + 23.1924i −0.561224 + 1.35491i 0.347565 + 0.937656i $$0.387009\pi$$
−0.908788 + 0.417258i $$0.862991\pi$$
$$294$$ −5.00000 + 2.07107i −0.291606 + 0.120787i
$$295$$ 0 0
$$296$$ −2.00000 0.828427i −0.116248 0.0481513i
$$297$$ 13.0711 13.0711i 0.758460 0.758460i
$$298$$ −9.14214 + 22.0711i −0.529590 + 1.27854i
$$299$$ 5.82843 + 2.41421i 0.337067 + 0.139618i
$$300$$ 0 0
$$301$$ 2.75736 + 6.65685i 0.158932 + 0.383695i
$$302$$ 2.10051 + 2.10051i 0.120870 + 0.120870i
$$303$$ 2.72792i 0.156715i
$$304$$ 6.14214 + 14.8284i 0.352276 + 0.850469i
$$305$$ 0 0
$$306$$ 6.82843 6.82843i 0.390355 0.390355i
$$307$$ 6.94975 + 16.7782i 0.396643 + 0.957581i 0.988456 + 0.151506i $$0.0484123\pi$$
−0.591813 + 0.806075i $$0.701588\pi$$
$$308$$ −4.82843 11.6569i −0.275125 0.664211i
$$309$$ −9.48528 3.92893i −0.539599 0.223509i
$$310$$ 0 0
$$311$$ −2.65685 + 2.65685i −0.150656 + 0.150656i −0.778411 0.627755i $$-0.783974\pi$$
0.627755 + 0.778411i $$0.283974\pi$$
$$312$$ 1.17157 1.17157i 0.0663273 0.0663273i
$$313$$ 7.48528 + 7.48528i 0.423093 + 0.423093i 0.886267 0.463174i $$-0.153290\pi$$
−0.463174 + 0.886267i $$0.653290\pi$$
$$314$$ 1.00000 + 2.41421i 0.0564333 + 0.136242i
$$315$$ 0 0
$$316$$ 12.0000i 0.675053i
$$317$$ −17.3640 + 7.19239i −0.975257 + 0.403965i −0.812667 0.582729i $$-0.801985\pi$$
−0.162591 + 0.986694i $$0.551985\pi$$
$$318$$ 1.31371i 0.0736691i
$$319$$ 15.0711 0.843818
$$320$$ 0 0
$$321$$ 3.41421 0.190563
$$322$$ 16.4853i 0.918689i
$$323$$ 10.4853 4.34315i 0.583417 0.241659i
$$324$$ 8.14214i 0.452341i
$$325$$ 0 0
$$326$$ 0.272078 + 0.656854i 0.0150690 + 0.0363798i
$$327$$ −8.07107 8.07107i −0.446331 0.446331i
$$328$$ −0.485281 0.485281i −0.0267952 0.0267952i
$$329$$ −0.343146 + 0.343146i −0.0189182 + 0.0189182i
$$330$$ 0 0
$$331$$ −1.29289 0.535534i −0.0710638 0.0294356i 0.346868 0.937914i $$-0.387245\pi$$
−0.417932 + 0.908478i $$0.637245\pi$$
$$332$$ 3.75736 + 9.07107i 0.206212 + 0.497840i
$$333$$ −0.707107 1.70711i −0.0387492 0.0935489i
$$334$$ −20.7279 + 20.7279i −1.13418 + 1.13418i
$$335$$ 0 0
$$336$$ −4.00000 1.65685i −0.218218 0.0903888i
$$337$$ 16.9706i 0.924445i −0.886764 0.462223i $$-0.847052\pi$$
0.886764 0.462223i $$-0.152948\pi$$
$$338$$ −12.4142 12.4142i −0.675244 0.675244i
$$339$$ −1.85786 4.48528i −0.100905 0.243607i
$$340$$ 0 0
$$341$$ 16.4853 + 6.82843i 0.892728 + 0.369780i
$$342$$ −5.24264 + 12.6569i −0.283490 + 0.684404i
$$343$$ −12.0000 + 12.0000i −0.647939 + 0.647939i
$$344$$ 5.51472 13.3137i 0.297334 0.717827i
$$345$$ 0 0
$$346$$ −10.6569 + 4.41421i −0.572916 + 0.237310i
$$347$$ −1.63604 + 3.94975i −0.0878272 + 0.212034i −0.961690 0.274139i $$-0.911607\pi$$
0.873863 + 0.486172i $$0.161607\pi$$
$$348$$ 3.65685 3.65685i 0.196028 0.196028i
$$349$$ 24.6777 10.2218i 1.32097 0.547162i 0.392901 0.919581i $$-0.371472\pi$$
0.928065 + 0.372419i $$0.121472\pi$$
$$350$$ 0 0
$$351$$ 3.17157 0.169286
$$352$$ −9.65685 + 23.3137i −0.514712 + 1.24262i
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 5.31371 0.282420
$$355$$ 0 0
$$356$$ −17.3137 17.3137i −0.917625 0.917625i
$$357$$ −1.17157 + 2.82843i −0.0620062 + 0.149696i
$$358$$ −5.58579 + 2.31371i −0.295218 + 0.122283i
$$359$$ −17.8284 17.8284i −0.940948 0.940948i 0.0574027 0.998351i $$-0.481718\pi$$
−0.998351 + 0.0574027i $$0.981718\pi$$
$$360$$ 0 0
$$361$$ 2.05025 2.05025i 0.107908 0.107908i
$$362$$ 9.48528 22.8995i 0.498535 1.20357i
$$363$$ 6.29289 + 2.60660i 0.330291 + 0.136811i
$$364$$ 0.828427 2.00000i 0.0434214 0.104828i
$$365$$ 0 0
$$366$$ −1.41421 1.41421i −0.0739221 0.0739221i
$$367$$ 6.00000i 0.313197i −0.987662 0.156599i $$-0.949947\pi$$
0.987662 0.156599i $$-0.0500529\pi$$
$$368$$ −23.3137 + 23.3137i −1.21531 + 1.21531i
$$369$$ 0.585786i 0.0304948i
$$370$$ 0 0
$$371$$ −0.656854 1.58579i −0.0341022 0.0823299i
$$372$$ 5.65685 2.34315i 0.293294 0.121486i
$$373$$ 10.2929 + 4.26346i 0.532946 + 0.220753i 0.632893 0.774239i $$-0.281867\pi$$
−0.0999471 + 0.994993i $$0.531867\pi$$
$$374$$ 16.4853 + 6.82843i 0.852434 + 0.353090i
$$375$$ 0 0
$$376$$ 0.970563 0.0500530
$$377$$ 1.82843 + 1.82843i 0.0941688 + 0.0941688i
$$378$$ −3.17157 7.65685i −0.163128 0.393826i
$$379$$ −13.6777 + 33.0208i −0.702575 + 1.69617i 0.0151948 + 0.999885i $$0.495163\pi$$
−0.717769 + 0.696281i $$0.754837\pi$$
$$380$$ 0 0
$$381$$ −9.17157 + 3.79899i −0.469874 + 0.194628i
$$382$$ 16.9706i 0.868290i
$$383$$ 16.9706 0.867155 0.433578 0.901116i $$-0.357251\pi$$
0.433578 + 0.901116i $$0.357251\pi$$
$$384$$ 3.31371 + 8.00000i 0.169102 + 0.408248i
$$385$$ 0 0
$$386$$ 2.14214i 0.109032i
$$387$$ 11.3640 4.70711i 0.577663 0.239276i
$$388$$ −36.9706 −1.87690
$$389$$ −8.39340 + 20.2635i −0.425562 + 1.02740i 0.555117 + 0.831773i $$0.312674\pi$$
−0.980679 + 0.195625i $$0.937326\pi$$
$$390$$ 0 0
$$391$$ 16.4853 + 16.4853i 0.833697 + 0.833697i
$$392$$ 14.1421 0.714286
$$393$$ −9.58579 + 9.58579i −0.483539 + 0.483539i
$$394$$ 15.8284 + 6.55635i 0.797425 + 0.330304i
$$395$$ 0 0
$$396$$ −19.8995 + 8.24264i −0.999987 + 0.414208i
$$397$$ 9.22183 + 22.2635i 0.462830 + 1.11737i 0.967230 + 0.253901i $$0.0817137\pi$$
−0.504400 + 0.863470i $$0.668286\pi$$
$$398$$ −22.5858 + 22.5858i −1.13212 + 1.13212i
$$399$$ 4.34315i 0.217429i
$$400$$ 0 0
$$401$$ 2.82843i 0.141245i 0.997503 + 0.0706225i $$0.0224986\pi$$
−0.997503 + 0.0706225i $$0.977501\pi$$
$$402$$ −4.58579 4.58579i −0.228718 0.228718i
$$403$$ 1.17157 + 2.82843i 0.0583602 + 0.140894i
$$404$$ 2.72792 6.58579i 0.135719 0.327655i
$$405$$ 0 0
$$406$$ 2.58579 6.24264i 0.128330 0.309817i
$$407$$ 2.41421 2.41421i 0.119668 0.119668i
$$408$$ 5.65685 2.34315i 0.280056 0.116003i
$$409$$ 21.4853 + 21.4853i 1.06238 + 1.06238i 0.997920 + 0.0644584i $$0.0205320\pi$$
0.0644584 + 0.997920i $$0.479468\pi$$
$$410$$ 0 0
$$411$$ 3.58579 8.65685i 0.176874 0.427011i
$$412$$ 18.9706 + 18.9706i 0.934613 + 0.934613i
$$413$$ 6.41421 2.65685i 0.315623 0.130735i
$$414$$ −28.1421 −1.38311
$$415$$ 0 0
$$416$$ −4.00000 + 1.65685i −0.196116 + 0.0812340i
$$417$$ 10.9289 0.535192
$$418$$ −25.3137 −1.23813
$$419$$ 12.6066 5.22183i 0.615873 0.255103i −0.0528644 0.998602i $$-0.516835\pi$$
0.668737 + 0.743499i $$0.266835\pi$$
$$420$$ 0 0
$$421$$ 6.29289 15.1924i 0.306697 0.740432i −0.693111 0.720831i $$-0.743760\pi$$
0.999808 0.0196009i $$-0.00623955\pi$$
$$422$$ 25.7279 10.6569i 1.25242 0.518768i
$$423$$ 0.585786 + 0.585786i 0.0284819 + 0.0284819i
$$424$$ −1.31371 + 3.17157i −0.0637993 + 0.154025i
$$425$$ 0 0
$$426$$ −3.41421 + 8.24264i −0.165419 + 0.399357i
$$427$$ −2.41421 1.00000i −0.116832 0.0483934i
$$428$$ −8.24264 3.41421i −0.398423 0.165032i
$$429$$ 1.00000 + 2.41421i 0.0482805 + 0.116559i
$$430$$ 0 0
$$431$$ 12.3431i 0.594548i 0.954792 + 0.297274i $$0.0960775\pi$$
−0.954792 + 0.297274i $$0.903922\pi$$
$$432$$ −6.34315 + 15.3137i −0.305185 + 0.736781i
$$433$$ 15.5147i 0.745590i −0.927914 0.372795i $$-0.878400\pi$$
0.927914 0.372795i $$-0.121600\pi$$
$$434$$ 5.65685 5.65685i 0.271538 0.271538i
$$435$$ 0 0
$$436$$ 11.4142 + 27.5563i 0.546642 + 1.31971i
$$437$$ −30.5563 12.6569i −1.46171 0.605459i
$$438$$ 9.89949 + 4.10051i 0.473016 + 0.195930i
$$439$$ −17.0000 + 17.0000i −0.811366 + 0.811366i −0.984839 0.173473i $$-0.944501\pi$$
0.173473 + 0.984839i $$0.444501\pi$$
$$440$$ 0 0
$$441$$ 8.53553 + 8.53553i 0.406454 + 0.406454i
$$442$$ 1.17157 + 2.82843i 0.0557260 + 0.134535i
$$443$$ −0.606602 + 1.46447i −0.0288205 + 0.0695789i −0.937635 0.347623i $$-0.886989\pi$$
0.908814 + 0.417201i $$0.136989\pi$$
$$444$$ 1.17157i 0.0556004i
$$445$$ 0 0
$$446$$ 29.6569i 1.40429i
$$447$$ −12.9289 −0.611518
$$448$$ 8.00000 + 8.00000i 0.377964 + 0.377964i
$$449$$ −19.4558 −0.918178 −0.459089 0.888390i $$-0.651824\pi$$
−0.459089 + 0.888390i $$0.651824\pi$$
$$450$$ 0 0
$$451$$ 1.00000 0.414214i 0.0470882 0.0195046i
$$452$$ 12.6863i 0.596713i
$$453$$ −0.615224 + 1.48528i −0.0289057 + 0.0697846i
$$454$$ 10.8995 + 26.3137i 0.511539 + 1.23496i
$$455$$ 0 0
$$456$$ −6.14214 + 6.14214i −0.287632 + 0.287632i
$$457$$ 7.48528 7.48528i 0.350147 0.350147i −0.510017 0.860164i $$-0.670361\pi$$
0.860164 + 0.510017i $$0.170361\pi$$
$$458$$ 31.4853 + 13.0416i 1.47121 + 0.609395i
$$459$$ 10.8284 + 4.48528i 0.505428 + 0.209355i
$$460$$ 0 0
$$461$$ 0.636039 + 1.53553i 0.0296233 + 0.0715169i 0.937999 0.346638i $$-0.112677\pi$$
−0.908376 + 0.418155i $$0.862677\pi$$
$$462$$ 4.82843 4.82843i 0.224639 0.224639i
$$463$$ 22.9706i 1.06753i 0.845632 + 0.533766i $$0.179224\pi$$
−0.845632 + 0.533766i $$0.820776\pi$$
$$464$$ −12.4853 + 5.17157i −0.579615 + 0.240084i
$$465$$ 0 0
$$466$$ −3.75736 3.75736i −0.174056 0.174056i
$$467$$ 9.09188 + 21.9497i 0.420722 + 1.01571i 0.982135 + 0.188177i $$0.0602580\pi$$
−0.561413 + 0.827536i $$0.689742\pi$$
$$468$$ −3.41421 1.41421i −0.157822 0.0653720i
$$469$$ −7.82843 3.24264i −0.361483 0.149731i
$$470$$ 0 0
$$471$$ −1.00000 + 1.00000i −0.0460776 + 0.0460776i
$$472$$ −12.8284 5.31371i −0.590476 0.244583i
$$473$$ 16.0711 + 16.0711i 0.738948 + 0.738948i
$$474$$ −6.00000 + 2.48528i −0.275589 + 0.114153i
$$475$$ 0 0
$$476$$ 5.65685 5.65685i 0.259281 0.259281i
$$477$$ −2.70711 + 1.12132i −0.123950 + 0.0513417i
$$478$$ 7.51472 0.343715
$$479$$ 28.9706 1.32370 0.661849 0.749637i $$-0.269772\pi$$
0.661849 + 0.749637i $$0.269772\pi$$
$$480$$ 0 0
$$481$$ 0.585786 0.0267096
$$482$$ 12.0000 0.546585
$$483$$ 8.24264 3.41421i 0.375053 0.155352i
$$484$$ −12.5858 12.5858i −0.572081 0.572081i
$$485$$ 0 0
$$486$$ −20.3137 + 8.41421i −0.921449 + 0.381676i
$$487$$ 11.0000 + 11.0000i 0.498458 + 0.498458i 0.910958 0.412500i $$-0.135344\pi$$
−0.412500 + 0.910958i $$0.635344\pi$$
$$488$$ 2.00000 + 4.82843i 0.0905357 + 0.218573i
$$489$$ −0.272078 + 0.272078i −0.0123038 + 0.0123038i
$$490$$ 0 0
$$491$$ 39.3345 + 16.2929i 1.77514 + 0.735288i 0.993800 + 0.111186i $$0.0354648\pi$$
0.781343 + 0.624102i $$0.214535\pi$$
$$492$$ 0.142136 0.343146i 0.00640797 0.0154702i
$$493$$ 3.65685 + 8.82843i 0.164696 + 0.397612i
$$494$$ −3.07107 3.07107i −0.138174 0.138174i
$$495$$ 0 0
$$496$$ −16.0000 −0.718421
$$497$$ 11.6569i 0.522881i
$$498$$ −3.75736 + 3.75736i −0.168371 + 0.168371i
$$499$$ −0.949747 2.29289i −0.0425165 0.102644i 0.901195 0.433415i $$-0.142691\pi$$
−0.943711 + 0.330771i $$0.892691\pi$$
$$500$$ 0 0
$$501$$ −14.6569 6.07107i −0.654820 0.271235i
$$502$$ −22.5563 9.34315i −1.00674 0.417005i
$$503$$ 11.1421 11.1421i 0.496803 0.496803i −0.413638 0.910441i $$-0.635742\pi$$
0.910441 + 0.413638i $$0.135742\pi$$
$$504$$ 9.65685i 0.430150i
$$505$$ 0 0
$$506$$ −19.8995 48.0416i −0.884640 2.13571i
$$507$$ 3.63604 8.77817i 0.161482 0.389852i
$$508$$ 25.9411 1.15095
$$509$$ −26.0919 + 10.8076i −1.15650 + 0.479039i −0.876709 0.481021i $$-0.840266\pi$$
−0.279793 + 0.960060i $$0.590266\pi$$
$$510$$ 0 0
$$511$$ 14.0000 0.619324
$$512$$ 22.6274i 1.00000i
$$513$$ −16.6274 −0.734118
$$514$$ 8.48528i 0.374270i
$$515$$ 0 0
$$516$$ 7.79899 0.343331
$$517$$ −0.585786 + 1.41421i −0.0257629 + 0.0621970i
$$518$$ −0.585786 1.41421i −0.0257380 0.0621370i
$$519$$ −4.41421 4.41421i −0.193762 0.193762i
$$520$$ 0 0
$$521$$ 3.34315 3.34315i 0.146466 0.146466i −0.630071 0.776537i $$-0.716974\pi$$
0.776537 + 0.630071i $$0.216974\pi$$
$$522$$ −10.6569 4.41421i −0.466438 0.193205i
$$523$$ −19.1924 7.94975i −0.839225 0.347618i −0.0786768 0.996900i $$-0.525070\pi$$
−0.760548 + 0.649282i $$0.775070\pi$$
$$524$$ 32.7279 13.5563i 1.42973 0.592212i
$$525$$ 0 0
$$526$$ 8.24264 8.24264i 0.359396 0.359396i
$$527$$ 11.3137i 0.492833i
$$528$$ −13.6569 −0.594338
$$529$$ 44.9411i 1.95396i
$$530$$ 0 0
$$531$$ −4.53553 10.9497i −0.196825 0.475179i
$$532$$ −4.34315 + 10.4853i −0.188299 + 0.454595i
$$533$$ 0.171573 + 0.0710678i 0.00743165 + 0.00307829i
$$534$$ 5.07107 12.2426i 0.219447 0.529791i
$$535$$ 0 0
$$536$$ 6.48528 + 15.6569i 0.280121 + 0.676273i
$$537$$ −2.31371 2.31371i −0.0998439 0.0998439i
$$538$$ 31.1421 12.8995i 1.34263 0.556137i
$$539$$ −8.53553 + 20.6066i −0.367651 + 0.887589i
$$540$$ 0 0
$$541$$ −27.2635 + 11.2929i −1.17215 + 0.485519i −0.881902 0.471433i $$-0.843737\pi$$
−0.290246 + 0.956952i $$0.593737\pi$$
$$542$$ −25.4558 −1.09342
$$543$$ 13.4142 0.575659
$$544$$ −16.0000 −0.685994
$$545$$ 0 0
$$546$$ 1.17157 0.0501387
$$547$$ 17.5355 7.26346i 0.749765 0.310563i 0.0251195 0.999684i $$-0.492003\pi$$
0.724646 + 0.689122i $$0.242003\pi$$
$$548$$ −17.3137 + 17.3137i −0.739605 + 0.739605i
$$549$$ −1.70711 + 4.12132i −0.0728575 + 0.175894i
$$550$$ 0 0
$$551$$ −9.58579 9.58579i −0.408368 0.408368i
$$552$$ −16.4853 6.82843i −0.701660 0.290637i
$$553$$ −6.00000 + 6.00000i −0.255146 + 0.255146i
$$554$$ −1.00000 + 2.41421i −0.0424859 + 0.102570i
$$555$$ 0 0
$$556$$ −26.3848 10.9289i −1.11896 0.463490i
$$557$$ −15.1213 36.5061i −0.640711 1.54681i −0.825722 0.564077i $$-0.809232\pi$$
0.185012 0.982736i $$-0.440768\pi$$
$$558$$ −9.65685 9.65685i −0.408807 0.408807i
$$559$$ 3.89949i 0.164931i
$$560$$ 0 0
$$561$$ 9.65685i 0.407713i
$$562$$ −16.7279 + 16.7279i −0.705625 + 0.705625i
$$563$$ −7.87868 19.0208i −0.332047 0.801632i −0.998430 0.0560220i $$-0.982158\pi$$
0.666383 0.745610i $$-0.267842\pi$$
$$564$$ 0.201010 + 0.485281i 0.00846405 + 0.0204340i
$$565$$ 0 0
$$566$$ 19.7279 + 8.17157i 0.829226 + 0.343477i
$$567$$ −4.07107 + 4.07107i −0.170969 + 0.170969i
$$568$$ 16.4853 16.4853i 0.691707 0.691707i
$$569$$ 14.6569 + 14.6569i 0.614447 + 0.614447i 0.944102 0.329654i $$-0.106932\pi$$
−0.329654 + 0.944102i $$0.606932\pi$$
$$570$$ 0 0
$$571$$ −2.70711 + 6.53553i −0.113289 + 0.273504i −0.970347 0.241716i $$-0.922290\pi$$
0.857058 + 0.515220i $$0.172290\pi$$
$$572$$ 6.82843i 0.285511i
$$573$$ −8.48528 + 3.51472i −0.354478 + 0.146829i
$$574$$ 0.485281i 0.0202553i
$$575$$ 0 0
$$576$$ 13.6569 13.6569i 0.569036 0.569036i
$$577$$ −18.9706 −0.789755 −0.394877 0.918734i $$-0.629213\pi$$
−0.394877 + 0.918734i $$0.629213\pi$$
$$578$$ 12.7279i 0.529412i
$$579$$ 1.07107 0.443651i 0.0445121 0.0184375i
$$580$$ 0 0
$$581$$ −2.65685 + 6.41421i −0.110225 + 0.266106i
$$582$$ −7.65685 18.4853i −0.317387 0.766240i
$$583$$ −3.82843 3.82843i −0.158557 0.158557i
$$584$$ −19.7990 19.7990i −0.819288 0.819288i
$$585$$ 0 0
$$586$$ 32.7990 + 13.5858i 1.35491 + 0.561224i
$$587$$ 12.6066 + 5.22183i 0.520330 + 0.215528i 0.627362 0.778728i $$-0.284135\pi$$
−0.107032 + 0.994256i $$0.534135\pi$$
$$588$$ 2.92893 + 7.07107i 0.120787 + 0.291606i
$$589$$ −6.14214 14.8284i −0.253082 0.610995i
$$590$$ 0 0
$$591$$ 9.27208i 0.381402i
$$592$$ −1.17157 + 2.82843i −0.0481513 + 0.116248i
$$593$$ 28.2843i 1.16150i −0.814083 0.580748i $$-0.802760\pi$$
0.814083 0.580748i $$-0.197240\pi$$
$$594$$ −18.4853 18.4853i −0.758460 0.758460i
$$595$$ 0 0
$$596$$ 31.2132 + 12.9289i 1.27854 + 0.529590i
$$597$$ −15.9706 6.61522i −0.653632 0.270743i
$$598$$ 3.41421 8.24264i 0.139618 0.337067i
$$599$$ −26.6569 + 26.6569i −1.08917 + 1.08917i −0.0935555 + 0.995614i $$0.529823\pi$$
−0.995614 + 0.0935555i $$0.970177\pi$$
$$600$$ 0 0
$$601$$ −21.9706 21.9706i −0.896198 0.896198i 0.0988995 0.995097i $$-0.468468\pi$$
−0.995097 + 0.0988995i $$0.968468\pi$$
$$602$$ 9.41421 3.89949i 0.383695 0.158932i
$$603$$ −5.53553 + 13.3640i −0.225424 + 0.544223i
$$604$$ 2.97056 2.97056i 0.120870 0.120870i
$$605$$ 0 0
$$606$$ 3.85786 0.156715
$$607$$ 32.9706 1.33823 0.669117 0.743157i $$-0.266673\pi$$
0.669117 + 0.743157i $$0.266673\pi$$
$$608$$ 20.9706 8.68629i 0.850469 0.352276i
$$609$$ 3.65685 0.148183
$$610$$ 0 0
$$611$$ −0.242641 + 0.100505i −0.00981619 + 0.00406600i
$$612$$ −9.65685 9.65685i −0.390355 0.390355i
$$613$$ −1.32233 + 3.19239i −0.0534084 + 0.128939i −0.948332 0.317281i $$-0.897230\pi$$
0.894923 + 0.446220i $$0.147230\pi$$
$$614$$ 23.7279 9.82843i 0.957581 0.396643i
$$615$$ 0 0
$$616$$ −16.4853 + 6.82843i −0.664211 + 0.275125i
$$617$$ −22.7990 + 22.7990i −0.917853 + 0.917853i −0.996873 0.0790202i $$-0.974821\pi$$
0.0790202 + 0.996873i $$0.474821\pi$$
$$618$$ −5.55635 + 13.4142i −0.223509 + 0.539599i
$$619$$ −21.7782 9.02082i −0.875339 0.362577i −0.100651 0.994922i $$-0.532093\pi$$
−0.774687 + 0.632345i $$0.782093\pi$$
$$620$$ 0 0
$$621$$ −13.0711 31.5563i −0.524524 1.26631i
$$622$$ 3.75736 + 3.75736i 0.150656 + 0.150656i
$$623$$ 17.3137i 0.693659i
$$624$$ −1.65685 1.65685i −0.0663273 0.0663273i
$$625$$ 0 0
$$626$$ 10.5858 10.5858i 0.423093 0.423093i
$$627$$ −5.24264 12.6569i −0.209371 0.505466i
$$628$$ 3.41421 1.41421i 0.136242 0.0564333i
$$629$$ 2.00000 + 0.828427i 0.0797452 + 0.0330316i
$$630$$ 0 0
$$631$$ 32.4558 32.4558i 1.29205 1.29205i 0.358528 0.933519i $$-0.383279\pi$$
0.933519 0.358528i $$-0.116721\pi$$
$$632$$ 16.9706 0.675053
$$633$$ 10.6569 + 10.6569i 0.423572 + 0.423572i
$$634$$ 10.1716 + 24.5563i 0.403965 + 0.975257i
$$635$$ 0 0
$$636$$ −1.85786 −0.0736691
$$637$$ −3.53553 + 1.46447i −0.140083 + 0.0580243i
$$638$$ 21.3137i 0.843818i
$$639$$ 19.8995 0.787212
$$640$$ 0 0
$$641$$ 7.45584 0.294488 0.147244 0.989100i $$-0.452960\pi$$
0.147244 + 0.989100i $$0.452960\pi$$
$$642$$ 4.82843i 0.190563i
$$643$$ −11.4350 + 4.73654i −0.450954 + 0.186791i −0.596588 0.802547i $$-0.703478\pi$$
0.145635 + 0.989338i $$0.453478\pi$$
$$644$$ −23.3137 −0.918689
$$645$$ 0 0
$$646$$ −6.14214 14.8284i −0.241659 0.583417i
$$647$$ −6.17157 6.17157i −0.242630 0.242630i 0.575308 0.817937i $$-0.304882\pi$$
−0.817937 + 0.575308i $$0.804882\pi$$
$$648$$ 11.5147 0.452341
$$649$$ 15.4853 15.4853i 0.607850 0.607850i
$$650$$ 0 0
$$651$$ 4.00000 + 1.65685i 0.156772 + 0.0649372i
$$652$$ 0.928932 0.384776i 0.0363798 0.0150690i
$$653$$ −2.09188 5.05025i −0.0818617 0.197632i 0.877649 0.479304i $$-0.159111\pi$$
−0.959511 + 0.281672i $$0.909111\pi$$
$$654$$ −11.4142 + 11.4142i −0.446331 + 0.446331i
$$655$$ 0 0
$$656$$ −0.686292 + 0.686292i −0.0267952 + 0.0267952i
$$657$$ 23.8995i 0.932408i
$$658$$ 0.485281 + 0.485281i 0.0189182 + 0.0189182i
$$659$$ −10.1213 24.4350i −0.394271 0.951854i −0.988998 0.147926i $$-0.952740\pi$$
0.594728 0.803927i $$-0.297260\pi$$
$$660$$ 0 0
$$661$$ −41.7487 17.2929i −1.62384 0.672616i −0.629316 0.777149i $$-0.716665\pi$$
−0.994521 + 0.104534i $$0.966665\pi$$
$$662$$ −0.757359 + 1.82843i −0.0294356 + 0.0710638i
$$663$$ −1.17157 + 1.17157i −0.0455001 + 0.0455001i
$$664$$ 12.8284 5.31371i 0.497840 0.206212i
$$665$$ 0 0
$$666$$ −2.41421 + 1.00000i −0.0935489 + 0.0387492i
$$667$$ 10.6569 25.7279i 0.412635 0.996189i
$$668$$ 29.3137 + 29.3137i 1.13418 + 1.13418i
$$669$$ 14.8284 6.14214i 0.573300 0.237469i
$$670$$ 0 0
$$671$$ −8.24264 −0.318204
$$672$$ −2.34315 + 5.65685i −0.0903888 + 0.218218i
$$673$$ −22.4853 −0.866744 −0.433372 0.901215i $$-0.642676\pi$$
−0.433372 + 0.901215i $$0.642676\pi$$
$$674$$ −24.0000 −0.924445
$$675$$ 0 0
$$676$$ −17.5563 + 17.5563i −0.675244 + 0.675244i
$$677$$ −15.6066 + 37.6777i −0.599810 + 1.44807i 0.273964 + 0.961740i $$0.411665\pi$$
−0.873775 + 0.486331i $$0.838335\pi$$
$$678$$ −6.34315 + 2.62742i −0.243607 + 0.100905i
$$679$$ −18.4853 18.4853i −0.709400 0.709400i
$$680$$ 0 0
$$681$$ −10.8995 + 10.8995i −0.417670 + 0.417670i
$$682$$ 9.65685 23.3137i 0.369780 0.892728i
$$683$$ 10.1213 + 4.19239i 0.387282 + 0.160417i 0.567824 0.823150i $$-0.307785\pi$$
−0.180543 + 0.983567i $$0.557785\pi$$
$$684$$ 17.8995 + 7.41421i 0.684404 + 0.283490i
$$685$$ 0 0
$$686$$ 16.9706 + 16.9706i 0.647939 + 0.647939i
$$687$$ 18.4437i 0.703669i
$$688$$ −18.8284 7.79899i −0.717827 0.297334i
$$689$$ 0.928932i 0.0353895i
$$690$$ 0 0
$$691$$ 12.5061 + 30.1924i 0.475754 + 1.14857i 0.961582 + 0.274518i $$0.0885183\pi$$
−0.485828 + 0.874055i $$0.661482\pi$$
$$692$$ 6.24264 + 15.0711i 0.237310 + 0.572916i
$$693$$ −14.0711 5.82843i −0.534516 0.221404i
$$694$$ 5.58579 + 2.31371i 0.212034 + 0.0878272i
$$695$$ 0 0
$$696$$ −5.17157 5.17157i −0.196028 0.196028i
$$697$$ 0.485281 + 0.485281i 0.0183813 + 0.0183813i
$$698$$ −14.4558 34.8995i −0.547162 1.32097i
$$699$$ 1.10051 2.65685i 0.0416249 0.100491i
$$700$$ 0 0
$$701$$ 2.87868 1.19239i 0.108726 0.0450359i −0.327657 0.944797i $$-0.606259\pi$$
0.436383 + 0.899761i $$0.356259\pi$$
$$702$$ 4.48528i 0.169286i
$$703$$ −3.07107 −0.115828
$$704$$ 32.9706 + 13.6569i 1.24262 + 0.514712i
$$705$$ 0 0
$$706$$ 8.48528i 0.319348i
$$707$$ 4.65685 1.92893i 0.175139 0.0725450i
$$708$$ 7.51472i 0.282420i
$$709$$ 8.77817 21.1924i 0.329671 0.795897i −0.668945 0.743312i $$-0.733254\pi$$
0.998616 0.0525851i $$-0.0167461\pi$$
$$710$$ 0 0
$$711$$ 10.2426 + 10.2426i 0.384129 + 0.384129i
$$712$$ −24.4853 + 24.4853i −0.917625 + 0.917625i
$$713$$ 23.3137 23.3137i 0.873105 0.873105i
$$714$$ 4.00000 + 1.65685i 0.149696 + 0.0620062i
$$715$$ 0 0
$$716$$ 3.27208 + 7.89949i 0.122283 + 0.295218i
$$717$$ 1.55635 + 3.75736i 0.0581229 + 0.140321i
$$718$$ −25.2132 + 25.2132i −0.940948 + 0.940948i
$$719$$ 35.6569i 1.32978i −0.746943 0.664888i $$-0.768479\pi$$
0.746943 0.664888i $$-0.231521\pi$$
$$720$$ 0 0
$$721$$ 18.9706i 0.706501i
$$722$$ −2.89949 2.89949i −0.107908 0.107908i
$$723$$ 2.48528 + 6.00000i 0.0924286 + 0.223142i
$$724$$ −32.3848 13.4142i −1.20357 0.498535i
$$725$$ 0 0
$$726$$ 3.68629 8.89949i 0.136811 0.330291i
$$727$$ 9.97056 9.97056i 0.369788 0.369788i −0.497612 0.867400i $$-0.665790\pi$$
0.867400 + 0.497612i $$0.165790\pi$$
$$728$$ −2.82843 1.17157i −0.104828 0.0434214i
$$729$$ 0.221825 + 0.221825i 0.00821576 + 0.00821576i
$$730$$ 0 0
$$731$$ −5.51472 + 13.3137i −0.203969 + 0.492425i
$$732$$ −2.00000 + 2.00000i −0.0739221 + 0.0739221i
$$733$$ 33.2635 13.7782i 1.22861 0.508908i 0.328475 0.944513i $$-0.393465\pi$$
0.900138 + 0.435604i $$0.143465\pi$$
$$734$$ −8.48528 −0.313197
$$735$$ 0 0
$$736$$ 32.9706 + 32.9706i 1.21531 + 1.21531i
$$737$$ −26.7279 −0.984536
$$738$$ −0.828427 −0.0304948
$$739$$ 0.464466 0.192388i 0.0170857 0.00707711i −0.374124 0.927379i $$-0.622057\pi$$
0.391210 + 0.920301i $$0.372057\pi$$
$$740$$ 0 0
$$741$$ 0.899495 2.17157i 0.0330438 0.0797747i
$$742$$ −2.24264 + 0.928932i −0.0823299 + 0.0341022i
$$743$$ −31.6274 31.6274i −1.16030 1.16030i −0.984410 0.175887i $$-0.943721\pi$$
−0.175887 0.984410i $$-0.556279\pi$$
$$744$$ −3.31371 8.00000i −0.121486 0.293294i
$$745$$ 0 0
$$746$$ 6.02944 14.5563i 0.220753 0.532946i
$$747$$ 10.9497 + 4.53553i 0.400630 + 0.165947i
$$748$$ 9.65685 23.3137i 0.353090 0.852434i
$$749$$ −2.41421 5.82843i −0.0882134 0.212966i
$$750$$ 0 0
$$751$$ 10.9706i 0.400322i 0.979763 + 0.200161i $$0.0641464\pi$$
−0.979763 + 0.200161i $$0.935854\pi$$
$$752$$ 1.37258i 0.0500530i
$$753$$ 13.2132i 0.481516i
$$754$$ 2.58579 2.58579i 0.0941688 0.0941688i
$$755$$ 0 0
$$756$$ −10.8284 + 4.48528i −0.393826 + 0.163128i
$$757$$ 33.2635 + 13.7782i 1.20898 + 0.500776i 0.893890 0.448285i $$-0.147965\pi$$
0.315090 + 0.949062i $$0.397965\pi$$
$$758$$ 46.6985 + 19.3431i 1.69617 + 0.702575i
$$759$$ 19.8995 19.8995i 0.722306 0.722306i
$$760$$ 0 0
$$761$$ −29.8284 29.8284i −1.08128 1.08128i −0.996390 0.0848892i $$-0.972946\pi$$
−0.0848892 0.996390i $$-0.527054\pi$$
$$762$$ 5.37258 + 12.9706i 0.194628 + 0.469874i
$$763$$ −8.07107 + 19.4853i −0.292192 + 0.705415i
$$764$$ 24.0000 0.868290
$$765$$ 0 0
$$766$$ 24.0000i 0.867155i
$$767$$ 3.75736 0.135670
$$768$$ 11.3137 4.68629i 0.408248 0.169102i
$$769$$ 5.51472 0.198866 0.0994329 0.995044i $$-0.468297\pi$$
0.0994329 + 0.995044i $$0.468297\pi$$
$$770$$ 0 0
$$771$$ −4.24264 + 1.75736i −0.152795 + 0.0632897i
$$772$$ −3.02944 −0.109032
$$773$$ −12.0919 + 29.1924i −0.434915 + 1.04998i 0.542766 + 0.839884i $$0.317377\pi$$
−0.977681 + 0.210094i $$0.932623\pi$$
$$774$$ −6.65685 16.0711i −0.239276 0.577663i
$$775$$ 0 0
$$776$$ 52.2843i 1.87690i
$$777$$ 0.585786 0.585786i 0.0210150 0.0210150i
$$778$$ 28.6569 + 11.8701i 1.02740 + 0.425562i
$$779$$ −0.899495 0.372583i −0.0322278 0.0133492i
$$780$$ 0 0
$$781$$ 14.0711 + 33.9706i 0.503502 + 1.21556i