# Properties

 Label 400.2.q.b.149.1 Level $400$ Weight $2$ Character 400.149 Analytic conductor $3.194$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 400.q (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.19401608085$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 16) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 149.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 400.149 Dual form 400.2.q.b.349.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.00000i) q^{2} +(1.00000 + 1.00000i) q^{3} -2.00000i q^{4} +2.00000 q^{6} +2.00000 q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.00000i) q^{2} +(1.00000 + 1.00000i) q^{3} -2.00000i q^{4} +2.00000 q^{6} +2.00000 q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(2.00000 - 2.00000i) q^{12} +(1.00000 + 1.00000i) q^{13} +(2.00000 - 2.00000i) q^{14} -4.00000 q^{16} -2.00000i q^{17} +(-1.00000 - 1.00000i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +2.00000 q^{22} +6.00000 q^{23} -4.00000i q^{24} +2.00000 q^{26} +(4.00000 - 4.00000i) q^{27} -4.00000i q^{28} +(-3.00000 + 3.00000i) q^{29} -8.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +2.00000i q^{33} +(-2.00000 - 2.00000i) q^{34} -2.00000 q^{36} +(-3.00000 + 3.00000i) q^{37} +6.00000i q^{38} +2.00000i q^{39} +4.00000 q^{42} +(5.00000 - 5.00000i) q^{43} +(2.00000 - 2.00000i) q^{44} +(6.00000 - 6.00000i) q^{46} +8.00000i q^{47} +(-4.00000 - 4.00000i) q^{48} -3.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(2.00000 - 2.00000i) q^{52} +(-5.00000 + 5.00000i) q^{53} -8.00000i q^{54} +(-4.00000 - 4.00000i) q^{56} -6.00000 q^{57} +6.00000i q^{58} +(3.00000 + 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} +(-8.00000 + 8.00000i) q^{62} -2.00000i q^{63} +8.00000i q^{64} +(2.00000 + 2.00000i) q^{66} +(-5.00000 - 5.00000i) q^{67} -4.00000 q^{68} +(6.00000 + 6.00000i) q^{69} -10.0000i q^{71} +(-2.00000 + 2.00000i) q^{72} -4.00000 q^{73} +6.00000i q^{74} +(6.00000 + 6.00000i) q^{76} +(2.00000 + 2.00000i) q^{77} +(2.00000 + 2.00000i) q^{78} +5.00000 q^{81} +(1.00000 + 1.00000i) q^{83} +(4.00000 - 4.00000i) q^{84} -10.0000i q^{86} -6.00000 q^{87} -4.00000i q^{88} -4.00000i q^{89} +(2.00000 + 2.00000i) q^{91} -12.0000i q^{92} +(-8.00000 - 8.00000i) q^{93} +(8.00000 + 8.00000i) q^{94} -8.00000 q^{96} -2.00000i q^{97} +(-3.00000 + 3.00000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 $$2 q + 2 q^{2} + 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{11} + 4 q^{12} + 2 q^{13} + 4 q^{14} - 8 q^{16} - 2 q^{18} - 6 q^{19} + 4 q^{21} + 4 q^{22} + 12 q^{23} + 4 q^{26} + 8 q^{27} - 6 q^{29} - 16 q^{31} - 8 q^{32} - 4 q^{34} - 4 q^{36} - 6 q^{37} + 8 q^{42} + 10 q^{43} + 4 q^{44} + 12 q^{46} - 8 q^{48} - 6 q^{49} + 4 q^{51} + 4 q^{52} - 10 q^{53} - 8 q^{56} - 12 q^{57} + 6 q^{59} - 18 q^{61} - 16 q^{62} + 4 q^{66} - 10 q^{67} - 8 q^{68} + 12 q^{69} - 4 q^{72} - 8 q^{73} + 12 q^{76} + 4 q^{77} + 4 q^{78} + 10 q^{81} + 2 q^{83} + 8 q^{84} - 12 q^{87} + 4 q^{91} - 16 q^{93} + 16 q^{94} - 16 q^{96} - 6 q^{98} + 2 q^{99}+O(q^{100})$$ 2 * q + 2 * q^2 + 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^11 + 4 * q^12 + 2 * q^13 + 4 * q^14 - 8 * q^16 - 2 * q^18 - 6 * q^19 + 4 * q^21 + 4 * q^22 + 12 * q^23 + 4 * q^26 + 8 * q^27 - 6 * q^29 - 16 * q^31 - 8 * q^32 - 4 * q^34 - 4 * q^36 - 6 * q^37 + 8 * q^42 + 10 * q^43 + 4 * q^44 + 12 * q^46 - 8 * q^48 - 6 * q^49 + 4 * q^51 + 4 * q^52 - 10 * q^53 - 8 * q^56 - 12 * q^57 + 6 * q^59 - 18 * q^61 - 16 * q^62 + 4 * q^66 - 10 * q^67 - 8 * q^68 + 12 * q^69 - 4 * q^72 - 8 * q^73 + 12 * q^76 + 4 * q^77 + 4 * q^78 + 10 * q^81 + 2 * q^83 + 8 * q^84 - 12 * q^87 + 4 * q^91 - 16 * q^93 + 16 * q^94 - 16 * q^96 - 6 * q^98 + 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$177$$ $$351$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000i 0.707107 0.707107i
$$3$$ 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i $$-0.116140\pi$$
−0.356822 + 0.934172i $$0.616140\pi$$
$$4$$ 2.00000i 1.00000i
$$5$$ 0 0
$$6$$ 2.00000 0.816497
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ 1.00000 + 1.00000i 0.301511 + 0.301511i 0.841605 0.540094i $$-0.181611\pi$$
−0.540094 + 0.841605i $$0.681611\pi$$
$$12$$ 2.00000 2.00000i 0.577350 0.577350i
$$13$$ 1.00000 + 1.00000i 0.277350 + 0.277350i 0.832050 0.554700i $$-0.187167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 2.00000 2.00000i 0.534522 0.534522i
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ −1.00000 1.00000i −0.235702 0.235702i
$$19$$ −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i $$-0.911786\pi$$
0.273597 + 0.961844i $$0.411786\pi$$
$$20$$ 0 0
$$21$$ 2.00000 + 2.00000i 0.436436 + 0.436436i
$$22$$ 2.00000 0.426401
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 4.00000i 0.816497i
$$25$$ 0 0
$$26$$ 2.00000 0.392232
$$27$$ 4.00000 4.00000i 0.769800 0.769800i
$$28$$ 4.00000i 0.755929i
$$29$$ −3.00000 + 3.00000i −0.557086 + 0.557086i −0.928477 0.371391i $$-0.878881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ −4.00000 + 4.00000i −0.707107 + 0.707107i
$$33$$ 2.00000i 0.348155i
$$34$$ −2.00000 2.00000i −0.342997 0.342997i
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ −3.00000 + 3.00000i −0.493197 + 0.493197i −0.909312 0.416115i $$-0.863391\pi$$
0.416115 + 0.909312i $$0.363391\pi$$
$$38$$ 6.00000i 0.973329i
$$39$$ 2.00000i 0.320256i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 4.00000 0.617213
$$43$$ 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i $$-0.568740\pi$$
0.976772 + 0.214280i $$0.0687403\pi$$
$$44$$ 2.00000 2.00000i 0.301511 0.301511i
$$45$$ 0 0
$$46$$ 6.00000 6.00000i 0.884652 0.884652i
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ −4.00000 4.00000i −0.577350 0.577350i
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 2.00000 2.00000i 0.280056 0.280056i
$$52$$ 2.00000 2.00000i 0.277350 0.277350i
$$53$$ −5.00000 + 5.00000i −0.686803 + 0.686803i −0.961524 0.274721i $$-0.911414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 8.00000i 1.08866i
$$55$$ 0 0
$$56$$ −4.00000 4.00000i −0.534522 0.534522i
$$57$$ −6.00000 −0.794719
$$58$$ 6.00000i 0.787839i
$$59$$ 3.00000 + 3.00000i 0.390567 + 0.390567i 0.874889 0.484323i $$-0.160934\pi$$
−0.484323 + 0.874889i $$0.660934\pi$$
$$60$$ 0 0
$$61$$ −9.00000 + 9.00000i −1.15233 + 1.15233i −0.166248 + 0.986084i $$0.553165\pi$$
−0.986084 + 0.166248i $$0.946835\pi$$
$$62$$ −8.00000 + 8.00000i −1.01600 + 1.01600i
$$63$$ 2.00000i 0.251976i
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 2.00000 + 2.00000i 0.246183 + 0.246183i
$$67$$ −5.00000 5.00000i −0.610847 0.610847i 0.332320 0.943167i $$-0.392169\pi$$
−0.943167 + 0.332320i $$0.892169\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 6.00000 + 6.00000i 0.722315 + 0.722315i
$$70$$ 0 0
$$71$$ 10.0000i 1.18678i −0.804914 0.593391i $$-0.797789\pi$$
0.804914 0.593391i $$-0.202211\pi$$
$$72$$ −2.00000 + 2.00000i −0.235702 + 0.235702i
$$73$$ −4.00000 −0.468165 −0.234082 0.972217i $$-0.575209\pi$$
−0.234082 + 0.972217i $$0.575209\pi$$
$$74$$ 6.00000i 0.697486i
$$75$$ 0 0
$$76$$ 6.00000 + 6.00000i 0.688247 + 0.688247i
$$77$$ 2.00000 + 2.00000i 0.227921 + 0.227921i
$$78$$ 2.00000 + 2.00000i 0.226455 + 0.226455i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 5.00000 0.555556
$$82$$ 0 0
$$83$$ 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i $$-0.225269\pi$$
−0.650092 + 0.759856i $$0.725269\pi$$
$$84$$ 4.00000 4.00000i 0.436436 0.436436i
$$85$$ 0 0
$$86$$ 10.0000i 1.07833i
$$87$$ −6.00000 −0.643268
$$88$$ 4.00000i 0.426401i
$$89$$ 4.00000i 0.423999i −0.977270 0.212000i $$-0.932002\pi$$
0.977270 0.212000i $$-0.0679975\pi$$
$$90$$ 0 0
$$91$$ 2.00000 + 2.00000i 0.209657 + 0.209657i
$$92$$ 12.0000i 1.25109i
$$93$$ −8.00000 8.00000i −0.829561 0.829561i
$$94$$ 8.00000 + 8.00000i 0.825137 + 0.825137i
$$95$$ 0 0
$$96$$ −8.00000 −0.816497
$$97$$ 2.00000i 0.203069i −0.994832 0.101535i $$-0.967625\pi$$
0.994832 0.101535i $$-0.0323753\pi$$
$$98$$ −3.00000 + 3.00000i −0.303046 + 0.303046i
$$99$$ 1.00000 1.00000i 0.100504 0.100504i
$$100$$ 0 0
$$101$$ 11.0000 + 11.0000i 1.09454 + 1.09454i 0.995037 + 0.0995037i $$0.0317255\pi$$
0.0995037 + 0.995037i $$0.468274\pi$$
$$102$$ 4.00000i 0.396059i
$$103$$ 6.00000 0.591198 0.295599 0.955312i $$-0.404481\pi$$
0.295599 + 0.955312i $$0.404481\pi$$
$$104$$ 4.00000i 0.392232i
$$105$$ 0 0
$$106$$ 10.0000i 0.971286i
$$107$$ 7.00000 7.00000i 0.676716 0.676716i −0.282540 0.959256i $$-0.591177\pi$$
0.959256 + 0.282540i $$0.0911770\pi$$
$$108$$ −8.00000 8.00000i −0.769800 0.769800i
$$109$$ −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i $$-0.815129\pi$$
0.548683 + 0.836031i $$0.315129\pi$$
$$110$$ 0 0
$$111$$ −6.00000 −0.569495
$$112$$ −8.00000 −0.755929
$$113$$ 6.00000i 0.564433i 0.959351 + 0.282216i $$0.0910696\pi$$
−0.959351 + 0.282216i $$0.908930\pi$$
$$114$$ −6.00000 + 6.00000i −0.561951 + 0.561951i
$$115$$ 0 0
$$116$$ 6.00000 + 6.00000i 0.557086 + 0.557086i
$$117$$ 1.00000 1.00000i 0.0924500 0.0924500i
$$118$$ 6.00000 0.552345
$$119$$ 4.00000i 0.366679i
$$120$$ 0 0
$$121$$ 9.00000i 0.818182i
$$122$$ 18.0000i 1.62964i
$$123$$ 0 0
$$124$$ 16.0000i 1.43684i
$$125$$ 0 0
$$126$$ −2.00000 2.00000i −0.178174 0.178174i
$$127$$ 8.00000i 0.709885i 0.934888 + 0.354943i $$0.115500\pi$$
−0.934888 + 0.354943i $$0.884500\pi$$
$$128$$ 8.00000 + 8.00000i 0.707107 + 0.707107i
$$129$$ 10.0000 0.880451
$$130$$ 0 0
$$131$$ 11.0000 11.0000i 0.961074 0.961074i −0.0381958 0.999270i $$-0.512161\pi$$
0.999270 + 0.0381958i $$0.0121611\pi$$
$$132$$ 4.00000 0.348155
$$133$$ −6.00000 + 6.00000i −0.520266 + 0.520266i
$$134$$ −10.0000 −0.863868
$$135$$ 0 0
$$136$$ −4.00000 + 4.00000i −0.342997 + 0.342997i
$$137$$ −8.00000 −0.683486 −0.341743 0.939793i $$-0.611017\pi$$
−0.341743 + 0.939793i $$0.611017\pi$$
$$138$$ 12.0000 1.02151
$$139$$ 3.00000 + 3.00000i 0.254457 + 0.254457i 0.822795 0.568338i $$-0.192414\pi$$
−0.568338 + 0.822795i $$0.692414\pi$$
$$140$$ 0 0
$$141$$ −8.00000 + 8.00000i −0.673722 + 0.673722i
$$142$$ −10.0000 10.0000i −0.839181 0.839181i
$$143$$ 2.00000i 0.167248i
$$144$$ 4.00000i 0.333333i
$$145$$ 0 0
$$146$$ −4.00000 + 4.00000i −0.331042 + 0.331042i
$$147$$ −3.00000 3.00000i −0.247436 0.247436i
$$148$$ 6.00000 + 6.00000i 0.493197 + 0.493197i
$$149$$ −7.00000 7.00000i −0.573462 0.573462i 0.359632 0.933094i $$-0.382902\pi$$
−0.933094 + 0.359632i $$0.882902\pi$$
$$150$$ 0 0
$$151$$ 10.0000i 0.813788i −0.913475 0.406894i $$-0.866612\pi$$
0.913475 0.406894i $$-0.133388\pi$$
$$152$$ 12.0000 0.973329
$$153$$ −2.00000 −0.161690
$$154$$ 4.00000 0.322329
$$155$$ 0 0
$$156$$ 4.00000 0.320256
$$157$$ 15.0000 + 15.0000i 1.19713 + 1.19713i 0.975022 + 0.222108i $$0.0712939\pi$$
0.222108 + 0.975022i $$0.428706\pi$$
$$158$$ 0 0
$$159$$ −10.0000 −0.793052
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 5.00000 5.00000i 0.392837 0.392837i
$$163$$ 1.00000 + 1.00000i 0.0783260 + 0.0783260i 0.745184 0.666858i $$-0.232361\pi$$
−0.666858 + 0.745184i $$0.732361\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 2.00000 0.155230
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ 8.00000i 0.617213i
$$169$$ 11.0000i 0.846154i
$$170$$ 0 0
$$171$$ 3.00000 + 3.00000i 0.229416 + 0.229416i
$$172$$ −10.0000 10.0000i −0.762493 0.762493i
$$173$$ 1.00000 + 1.00000i 0.0760286 + 0.0760286i 0.744099 0.668070i $$-0.232879\pi$$
−0.668070 + 0.744099i $$0.732879\pi$$
$$174$$ −6.00000 + 6.00000i −0.454859 + 0.454859i
$$175$$ 0 0
$$176$$ −4.00000 4.00000i −0.301511 0.301511i
$$177$$ 6.00000i 0.450988i
$$178$$ −4.00000 4.00000i −0.299813 0.299813i
$$179$$ 17.0000 17.0000i 1.27064 1.27064i 0.324887 0.945753i $$-0.394674\pi$$
0.945753 0.324887i $$-0.105326\pi$$
$$180$$ 0 0
$$181$$ −9.00000 9.00000i −0.668965 0.668965i 0.288512 0.957476i $$-0.406840\pi$$
−0.957476 + 0.288512i $$0.906840\pi$$
$$182$$ 4.00000 0.296500
$$183$$ −18.0000 −1.33060
$$184$$ −12.0000 12.0000i −0.884652 0.884652i
$$185$$ 0 0
$$186$$ −16.0000 −1.17318
$$187$$ 2.00000 2.00000i 0.146254 0.146254i
$$188$$ 16.0000 1.16692
$$189$$ 8.00000 8.00000i 0.581914 0.581914i
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ −8.00000 + 8.00000i −0.577350 + 0.577350i
$$193$$ 14.0000i 1.00774i −0.863779 0.503871i $$-0.831909\pi$$
0.863779 0.503871i $$-0.168091\pi$$
$$194$$ −2.00000 2.00000i −0.143592 0.143592i
$$195$$ 0 0
$$196$$ 6.00000i 0.428571i
$$197$$ 17.0000 17.0000i 1.21120 1.21120i 0.240567 0.970632i $$-0.422666\pi$$
0.970632 0.240567i $$-0.0773335\pi$$
$$198$$ 2.00000i 0.142134i
$$199$$ 14.0000i 0.992434i −0.868199 0.496217i $$-0.834722\pi$$
0.868199 0.496217i $$-0.165278\pi$$
$$200$$ 0 0
$$201$$ 10.0000i 0.705346i
$$202$$ 22.0000 1.54791
$$203$$ −6.00000 + 6.00000i −0.421117 + 0.421117i
$$204$$ −4.00000 4.00000i −0.280056 0.280056i
$$205$$ 0 0
$$206$$ 6.00000 6.00000i 0.418040 0.418040i
$$207$$ 6.00000i 0.417029i
$$208$$ −4.00000 4.00000i −0.277350 0.277350i
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −9.00000 + 9.00000i −0.619586 + 0.619586i −0.945425 0.325840i $$-0.894353\pi$$
0.325840 + 0.945425i $$0.394353\pi$$
$$212$$ 10.0000 + 10.0000i 0.686803 + 0.686803i
$$213$$ 10.0000 10.0000i 0.685189 0.685189i
$$214$$ 14.0000i 0.957020i
$$215$$ 0 0
$$216$$ −16.0000 −1.08866
$$217$$ −16.0000 −1.08615
$$218$$ 6.00000i 0.406371i
$$219$$ −4.00000 4.00000i −0.270295 0.270295i
$$220$$ 0 0
$$221$$ 2.00000 2.00000i 0.134535 0.134535i
$$222$$ −6.00000 + 6.00000i −0.402694 + 0.402694i
$$223$$ 24.0000i 1.60716i −0.595198 0.803579i $$-0.702926\pi$$
0.595198 0.803579i $$-0.297074\pi$$
$$224$$ −8.00000 + 8.00000i −0.534522 + 0.534522i
$$225$$ 0 0
$$226$$ 6.00000 + 6.00000i 0.399114 + 0.399114i
$$227$$ 15.0000 + 15.0000i 0.995585 + 0.995585i 0.999990 0.00440533i $$-0.00140226\pi$$
−0.00440533 + 0.999990i $$0.501402\pi$$
$$228$$ 12.0000i 0.794719i
$$229$$ −7.00000 7.00000i −0.462573 0.462573i 0.436925 0.899498i $$-0.356068\pi$$
−0.899498 + 0.436925i $$0.856068\pi$$
$$230$$ 0 0
$$231$$ 4.00000i 0.263181i
$$232$$ 12.0000 0.787839
$$233$$ −4.00000 −0.262049 −0.131024 0.991379i $$-0.541827\pi$$
−0.131024 + 0.991379i $$0.541827\pi$$
$$234$$ 2.00000i 0.130744i
$$235$$ 0 0
$$236$$ 6.00000 6.00000i 0.390567 0.390567i
$$237$$ 0 0
$$238$$ −4.00000 4.00000i −0.259281 0.259281i
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ −9.00000 9.00000i −0.578542 0.578542i
$$243$$ −7.00000 7.00000i −0.449050 0.449050i
$$244$$ 18.0000 + 18.0000i 1.15233 + 1.15233i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 16.0000 + 16.0000i 1.01600 + 1.01600i
$$249$$ 2.00000i 0.126745i
$$250$$ 0 0
$$251$$ 21.0000 + 21.0000i 1.32551 + 1.32551i 0.909243 + 0.416265i $$0.136661\pi$$
0.416265 + 0.909243i $$0.363339\pi$$
$$252$$ −4.00000 −0.251976
$$253$$ 6.00000 + 6.00000i 0.377217 + 0.377217i
$$254$$ 8.00000 + 8.00000i 0.501965 + 0.501965i
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 22.0000i 1.37232i −0.727450 0.686161i $$-0.759294\pi$$
0.727450 0.686161i $$-0.240706\pi$$
$$258$$ 10.0000 10.0000i 0.622573 0.622573i
$$259$$ −6.00000 + 6.00000i −0.372822 + 0.372822i
$$260$$ 0 0
$$261$$ 3.00000 + 3.00000i 0.185695 + 0.185695i
$$262$$ 22.0000i 1.35916i
$$263$$ 6.00000 0.369976 0.184988 0.982741i $$-0.440775\pi$$
0.184988 + 0.982741i $$0.440775\pi$$
$$264$$ 4.00000 4.00000i 0.246183 0.246183i
$$265$$ 0 0
$$266$$ 12.0000i 0.735767i
$$267$$ 4.00000 4.00000i 0.244796 0.244796i
$$268$$ −10.0000 + 10.0000i −0.610847 + 0.610847i
$$269$$ −3.00000 + 3.00000i −0.182913 + 0.182913i −0.792624 0.609711i $$-0.791286\pi$$
0.609711 + 0.792624i $$0.291286\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 8.00000i 0.485071i
$$273$$ 4.00000i 0.242091i
$$274$$ −8.00000 + 8.00000i −0.483298 + 0.483298i
$$275$$ 0 0
$$276$$ 12.0000 12.0000i 0.722315 0.722315i
$$277$$ −3.00000 + 3.00000i −0.180253 + 0.180253i −0.791466 0.611213i $$-0.790682\pi$$
0.611213 + 0.791466i $$0.290682\pi$$
$$278$$ 6.00000 0.359856
$$279$$ 8.00000i 0.478947i
$$280$$ 0 0
$$281$$ 20.0000i 1.19310i −0.802576 0.596550i $$-0.796538\pi$$
0.802576 0.596550i $$-0.203462\pi$$
$$282$$ 16.0000i 0.952786i
$$283$$ −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i $$-0.967149\pi$$
0.103022 + 0.994679i $$0.467149\pi$$
$$284$$ −20.0000 −1.18678
$$285$$ 0 0
$$286$$ 2.00000 + 2.00000i 0.118262 + 0.118262i
$$287$$ 0 0
$$288$$ 4.00000 + 4.00000i 0.235702 + 0.235702i
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ 2.00000 2.00000i 0.117242 0.117242i
$$292$$ 8.00000i 0.468165i
$$293$$ 15.0000 15.0000i 0.876309 0.876309i −0.116841 0.993151i $$-0.537277\pi$$
0.993151 + 0.116841i $$0.0372769\pi$$
$$294$$ −6.00000 −0.349927
$$295$$ 0 0
$$296$$ 12.0000 0.697486
$$297$$ 8.00000 0.464207
$$298$$ −14.0000 −0.810998
$$299$$ 6.00000 + 6.00000i 0.346989 + 0.346989i
$$300$$ 0 0
$$301$$ 10.0000 10.0000i 0.576390 0.576390i
$$302$$ −10.0000 10.0000i −0.575435 0.575435i
$$303$$ 22.0000i 1.26387i
$$304$$ 12.0000 12.0000i 0.688247 0.688247i
$$305$$ 0 0
$$306$$ −2.00000 + 2.00000i −0.114332 + 0.114332i
$$307$$ −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i $$-0.314674\pi$$
−0.835244 + 0.549879i $$0.814674\pi$$
$$308$$ 4.00000 4.00000i 0.227921 0.227921i
$$309$$ 6.00000 + 6.00000i 0.341328 + 0.341328i
$$310$$ 0 0
$$311$$ 30.0000i 1.70114i 0.525859 + 0.850572i $$0.323744\pi$$
−0.525859 + 0.850572i $$0.676256\pi$$
$$312$$ 4.00000 4.00000i 0.226455 0.226455i
$$313$$ 16.0000 0.904373 0.452187 0.891923i $$-0.350644\pi$$
0.452187 + 0.891923i $$0.350644\pi$$
$$314$$ 30.0000 1.69300
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −5.00000 5.00000i −0.280828 0.280828i 0.552611 0.833439i $$-0.313631\pi$$
−0.833439 + 0.552611i $$0.813631\pi$$
$$318$$ −10.0000 + 10.0000i −0.560772 + 0.560772i
$$319$$ −6.00000 −0.335936
$$320$$ 0 0
$$321$$ 14.0000 0.781404
$$322$$ 12.0000 12.0000i 0.668734 0.668734i
$$323$$ 6.00000 + 6.00000i 0.333849 + 0.333849i
$$324$$ 10.0000i 0.555556i
$$325$$ 0 0
$$326$$ 2.00000 0.110770
$$327$$ −6.00000 −0.331801
$$328$$ 0 0
$$329$$ 16.0000i 0.882109i
$$330$$ 0 0
$$331$$ 1.00000 + 1.00000i 0.0549650 + 0.0549650i 0.734055 0.679090i $$-0.237625\pi$$
−0.679090 + 0.734055i $$0.737625\pi$$
$$332$$ 2.00000 2.00000i 0.109764 0.109764i
$$333$$ 3.00000 + 3.00000i 0.164399 + 0.164399i
$$334$$ 2.00000 2.00000i 0.109435 0.109435i
$$335$$ 0 0
$$336$$ −8.00000 8.00000i −0.436436 0.436436i
$$337$$ 18.0000i 0.980522i 0.871576 + 0.490261i $$0.163099\pi$$
−0.871576 + 0.490261i $$0.836901\pi$$
$$338$$ −11.0000 11.0000i −0.598321 0.598321i
$$339$$ −6.00000 + 6.00000i −0.325875 + 0.325875i
$$340$$ 0 0
$$341$$ −8.00000 8.00000i −0.433224 0.433224i
$$342$$ 6.00000 0.324443
$$343$$ −20.0000 −1.07990
$$344$$ −20.0000 −1.07833
$$345$$ 0 0
$$346$$ 2.00000 0.107521
$$347$$ −13.0000 + 13.0000i −0.697877 + 0.697877i −0.963952 0.266076i $$-0.914273\pi$$
0.266076 + 0.963952i $$0.414273\pi$$
$$348$$ 12.0000i 0.643268i
$$349$$ −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i $$-0.786223\pi$$
0.622240 + 0.782826i $$0.286223\pi$$
$$350$$ 0 0
$$351$$ 8.00000 0.427008
$$352$$ −8.00000 −0.426401
$$353$$ 6.00000i 0.319348i 0.987170 + 0.159674i $$0.0510443\pi$$
−0.987170 + 0.159674i $$0.948956\pi$$
$$354$$ 6.00000 + 6.00000i 0.318896 + 0.318896i
$$355$$ 0 0
$$356$$ −8.00000 −0.423999
$$357$$ 4.00000 4.00000i 0.211702 0.211702i
$$358$$ 34.0000i 1.79696i
$$359$$ 26.0000i 1.37223i 0.727494 + 0.686114i $$0.240685\pi$$
−0.727494 + 0.686114i $$0.759315\pi$$
$$360$$ 0 0
$$361$$ 1.00000i 0.0526316i
$$362$$ −18.0000 −0.946059
$$363$$ 9.00000 9.00000i 0.472377 0.472377i
$$364$$ 4.00000 4.00000i 0.209657 0.209657i
$$365$$ 0 0
$$366$$ −18.0000 + 18.0000i −0.940875 + 0.940875i
$$367$$ 8.00000i 0.417597i 0.977959 + 0.208798i $$0.0669552\pi$$
−0.977959 + 0.208798i $$0.933045\pi$$
$$368$$ −24.0000 −1.25109
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −10.0000 + 10.0000i −0.519174 + 0.519174i
$$372$$ −16.0000 + 16.0000i −0.829561 + 0.829561i
$$373$$ −5.00000 + 5.00000i −0.258890 + 0.258890i −0.824603 0.565712i $$-0.808601\pi$$
0.565712 + 0.824603i $$0.308601\pi$$
$$374$$ 4.00000i 0.206835i
$$375$$ 0 0
$$376$$ 16.0000 16.0000i 0.825137 0.825137i
$$377$$ −6.00000 −0.309016
$$378$$ 16.0000i 0.822951i
$$379$$ 3.00000 + 3.00000i 0.154100 + 0.154100i 0.779946 0.625847i $$-0.215246\pi$$
−0.625847 + 0.779946i $$0.715246\pi$$
$$380$$ 0 0
$$381$$ −8.00000 + 8.00000i −0.409852 + 0.409852i
$$382$$ −8.00000 + 8.00000i −0.409316 + 0.409316i
$$383$$ 16.0000i 0.817562i 0.912633 + 0.408781i $$0.134046\pi$$
−0.912633 + 0.408781i $$0.865954\pi$$
$$384$$ 16.0000i 0.816497i
$$385$$ 0 0
$$386$$ −14.0000 14.0000i −0.712581 0.712581i
$$387$$ −5.00000 5.00000i −0.254164 0.254164i
$$388$$ −4.00000 −0.203069
$$389$$ 13.0000 + 13.0000i 0.659126 + 0.659126i 0.955173 0.296047i $$-0.0956686\pi$$
−0.296047 + 0.955173i $$0.595669\pi$$
$$390$$ 0 0
$$391$$ 12.0000i 0.606866i
$$392$$ 6.00000 + 6.00000i 0.303046 + 0.303046i
$$393$$ 22.0000 1.10975
$$394$$ 34.0000i 1.71290i
$$395$$ 0 0
$$396$$ −2.00000 2.00000i −0.100504 0.100504i
$$397$$ −5.00000 5.00000i −0.250943 0.250943i 0.570414 0.821357i $$-0.306783\pi$$
−0.821357 + 0.570414i $$0.806783\pi$$
$$398$$ −14.0000 14.0000i −0.701757 0.701757i
$$399$$ −12.0000 −0.600751
$$400$$ 0 0
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ −10.0000 10.0000i −0.498755 0.498755i
$$403$$ −8.00000 8.00000i −0.398508 0.398508i
$$404$$ 22.0000 22.0000i 1.09454 1.09454i
$$405$$ 0 0
$$406$$ 12.0000i 0.595550i
$$407$$ −6.00000 −0.297409
$$408$$ −8.00000 −0.396059
$$409$$ 16.0000i 0.791149i 0.918434 + 0.395575i $$0.129455\pi$$
−0.918434 + 0.395575i $$0.870545\pi$$
$$410$$ 0 0
$$411$$ −8.00000 8.00000i −0.394611 0.394611i
$$412$$ 12.0000i 0.591198i
$$413$$ 6.00000 + 6.00000i 0.295241 + 0.295241i
$$414$$ −6.00000 6.00000i −0.294884 0.294884i
$$415$$ 0 0
$$416$$ −8.00000 −0.392232
$$417$$ 6.00000i 0.293821i
$$418$$ −6.00000 + 6.00000i −0.293470 + 0.293470i
$$419$$ −3.00000 + 3.00000i −0.146560 + 0.146560i −0.776579 0.630020i $$-0.783047\pi$$
0.630020 + 0.776579i $$0.283047\pi$$
$$420$$ 0 0
$$421$$ −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i $$-0.350383\pi$$
−0.891552 + 0.452919i $$0.850383\pi$$
$$422$$ 18.0000i 0.876226i
$$423$$ 8.00000 0.388973
$$424$$ 20.0000 0.971286
$$425$$ 0 0
$$426$$ 20.0000i 0.969003i
$$427$$ −18.0000 + 18.0000i −0.871081 + 0.871081i
$$428$$ −14.0000 14.0000i −0.676716 0.676716i
$$429$$ −2.00000 + 2.00000i −0.0965609 + 0.0965609i
$$430$$ 0 0
$$431$$ 32.0000 1.54139 0.770693 0.637207i $$-0.219910\pi$$
0.770693 + 0.637207i $$0.219910\pi$$
$$432$$ −16.0000 + 16.0000i −0.769800 + 0.769800i
$$433$$ 14.0000i 0.672797i −0.941720 0.336399i $$-0.890791\pi$$
0.941720 0.336399i $$-0.109209\pi$$
$$434$$ −16.0000 + 16.0000i −0.768025 + 0.768025i
$$435$$ 0 0
$$436$$ 6.00000 + 6.00000i 0.287348 + 0.287348i
$$437$$ −18.0000 + 18.0000i −0.861057 + 0.861057i
$$438$$ −8.00000 −0.382255
$$439$$ 14.0000i 0.668184i −0.942541 0.334092i $$-0.891570\pi$$
0.942541 0.334092i $$-0.108430\pi$$
$$440$$ 0 0
$$441$$ 3.00000i 0.142857i
$$442$$ 4.00000i 0.190261i
$$443$$ −15.0000 + 15.0000i −0.712672 + 0.712672i −0.967093 0.254422i $$-0.918115\pi$$
0.254422 + 0.967093i $$0.418115\pi$$
$$444$$ 12.0000i 0.569495i
$$445$$ 0 0
$$446$$ −24.0000 24.0000i −1.13643 1.13643i
$$447$$ 14.0000i 0.662177i
$$448$$ 16.0000i 0.755929i
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 12.0000 0.564433
$$453$$ 10.0000 10.0000i 0.469841 0.469841i
$$454$$ 30.0000 1.40797
$$455$$ 0 0
$$456$$ 12.0000 + 12.0000i 0.561951 + 0.561951i
$$457$$ 32.0000 1.49690 0.748448 0.663193i $$-0.230799\pi$$
0.748448 + 0.663193i $$0.230799\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ −8.00000 8.00000i −0.373408 0.373408i
$$460$$ 0 0
$$461$$ 11.0000 11.0000i 0.512321 0.512321i −0.402916 0.915237i $$-0.632003\pi$$
0.915237 + 0.402916i $$0.132003\pi$$
$$462$$ 4.00000 + 4.00000i 0.186097 + 0.186097i
$$463$$ 16.0000i 0.743583i 0.928316 + 0.371792i $$0.121256\pi$$
−0.928316 + 0.371792i $$0.878744\pi$$
$$464$$ 12.0000 12.0000i 0.557086 0.557086i
$$465$$ 0 0
$$466$$ −4.00000 + 4.00000i −0.185296 + 0.185296i
$$467$$ −5.00000 5.00000i −0.231372 0.231372i 0.581893 0.813265i $$-0.302312\pi$$
−0.813265 + 0.581893i $$0.802312\pi$$
$$468$$ −2.00000 2.00000i −0.0924500 0.0924500i
$$469$$ −10.0000 10.0000i −0.461757 0.461757i
$$470$$ 0 0
$$471$$ 30.0000i 1.38233i
$$472$$ 12.0000i 0.552345i
$$473$$ 10.0000 0.459800
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −8.00000 −0.366679
$$477$$ 5.00000 + 5.00000i 0.228934 + 0.228934i
$$478$$ 0 0
$$479$$ 40.0000 1.82765 0.913823 0.406112i $$-0.133116\pi$$
0.913823 + 0.406112i $$0.133116\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ −18.0000 + 18.0000i −0.819878 + 0.819878i
$$483$$ 12.0000 + 12.0000i 0.546019 + 0.546019i
$$484$$ −18.0000 −0.818182
$$485$$ 0 0
$$486$$ −14.0000 −0.635053
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ 36.0000 1.62964
$$489$$ 2.00000i 0.0904431i
$$490$$ 0 0
$$491$$ −19.0000 19.0000i −0.857458 0.857458i 0.133580 0.991038i $$-0.457353\pi$$
−0.991038 + 0.133580i $$0.957353\pi$$
$$492$$ 0 0
$$493$$ 6.00000 + 6.00000i 0.270226 + 0.270226i
$$494$$ −6.00000 + 6.00000i −0.269953 + 0.269953i
$$495$$ 0 0
$$496$$ 32.0000 1.43684
$$497$$ 20.0000i 0.897123i
$$498$$ 2.00000 + 2.00000i 0.0896221 + 0.0896221i
$$499$$ −23.0000 + 23.0000i −1.02962 + 1.02962i −0.0300737 + 0.999548i $$0.509574\pi$$
−0.999548 + 0.0300737i $$0.990426\pi$$
$$500$$ 0 0
$$501$$ 2.00000 + 2.00000i 0.0893534 + 0.0893534i
$$502$$ 42.0000 1.87455
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ −4.00000 + 4.00000i −0.178174 + 0.178174i
$$505$$ 0 0
$$506$$ 12.0000 0.533465
$$507$$ 11.0000 11.0000i 0.488527 0.488527i
$$508$$ 16.0000 0.709885
$$509$$ −23.0000 + 23.0000i −1.01946 + 1.01946i −0.0196502 + 0.999807i $$0.506255\pi$$
−0.999807 + 0.0196502i $$0.993745\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 24.0000i 1.05963i
$$514$$ −22.0000 22.0000i −0.970378 0.970378i
$$515$$ 0 0
$$516$$ 20.0000i 0.880451i
$$517$$ −8.00000 + 8.00000i −0.351840 + 0.351840i
$$518$$ 12.0000i 0.527250i
$$519$$ 2.00000i 0.0877903i
$$520$$ 0 0
$$521$$ 40.0000i 1.75243i 0.481919 + 0.876216i $$0.339940\pi$$
−0.481919 + 0.876216i $$0.660060\pi$$
$$522$$ 6.00000 0.262613
$$523$$ 25.0000 25.0000i 1.09317 1.09317i 0.0979859 0.995188i $$-0.468760\pi$$
0.995188 0.0979859i $$-0.0312400\pi$$
$$524$$ −22.0000 22.0000i −0.961074 0.961074i
$$525$$ 0 0
$$526$$ 6.00000 6.00000i 0.261612 0.261612i
$$527$$ 16.0000i 0.696971i
$$528$$ 8.00000i 0.348155i
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 3.00000 3.00000i 0.130189 0.130189i
$$532$$ 12.0000 + 12.0000i 0.520266 + 0.520266i
$$533$$ 0 0
$$534$$ 8.00000i 0.346194i
$$535$$ 0 0
$$536$$ 20.0000i 0.863868i
$$537$$ 34.0000 1.46721
$$538$$ 6.00000i 0.258678i
$$539$$ −3.00000 3.00000i −0.129219 0.129219i
$$540$$ 0 0
$$541$$ −9.00000 + 9.00000i −0.386940 + 0.386940i −0.873595 0.486654i $$-0.838217\pi$$
0.486654 + 0.873595i $$0.338217\pi$$
$$542$$ −8.00000 + 8.00000i −0.343629 + 0.343629i
$$543$$ 18.0000i 0.772454i
$$544$$ 8.00000 + 8.00000i 0.342997 + 0.342997i
$$545$$ 0 0
$$546$$ 4.00000 + 4.00000i 0.171184 + 0.171184i
$$547$$ −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i $$-0.298304\pi$$
−0.805873 + 0.592088i $$0.798304\pi$$
$$548$$ 16.0000i 0.683486i
$$549$$ 9.00000 + 9.00000i 0.384111 + 0.384111i
$$550$$ 0 0
$$551$$ 18.0000i 0.766826i
$$552$$ 24.0000i 1.02151i
$$553$$ 0 0
$$554$$ 6.00000i 0.254916i
$$555$$ 0 0
$$556$$ 6.00000 6.00000i 0.254457 0.254457i
$$557$$ −25.0000 25.0000i −1.05928 1.05928i −0.998128 0.0611558i $$-0.980521\pi$$
−0.0611558 0.998128i $$-0.519479\pi$$
$$558$$ 8.00000 + 8.00000i 0.338667 + 0.338667i
$$559$$ 10.0000 0.422955
$$560$$ 0 0
$$561$$ 4.00000 0.168880
$$562$$ −20.0000 20.0000i −0.843649 0.843649i
$$563$$ −19.0000 19.0000i −0.800755 0.800755i 0.182459 0.983213i $$-0.441594\pi$$
−0.983213 + 0.182459i $$0.941594\pi$$
$$564$$ 16.0000 + 16.0000i 0.673722 + 0.673722i
$$565$$ 0 0
$$566$$ 30.0000i 1.26099i
$$567$$ 10.0000 0.419961
$$568$$ −20.0000 + 20.0000i −0.839181 + 0.839181i
$$569$$ 24.0000i 1.00613i −0.864248 0.503066i $$-0.832205\pi$$
0.864248 0.503066i $$-0.167795\pi$$
$$570$$ 0 0
$$571$$ 1.00000 + 1.00000i 0.0418487 + 0.0418487i 0.727721 0.685873i $$-0.240579\pi$$
−0.685873 + 0.727721i $$0.740579\pi$$
$$572$$ 4.00000 0.167248
$$573$$ −8.00000 8.00000i −0.334205 0.334205i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 8.00000 0.333333
$$577$$ 18.0000i 0.749350i 0.927156 + 0.374675i $$0.122246\pi$$
−0.927156 + 0.374675i $$0.877754\pi$$
$$578$$ 13.0000 13.0000i 0.540729 0.540729i
$$579$$ 14.0000 14.0000i 0.581820 0.581820i
$$580$$ 0 0
$$581$$ 2.00000 + 2.00000i 0.0829740 + 0.0829740i
$$582$$ 4.00000i 0.165805i
$$583$$ −10.0000 −0.414158
$$584$$ 8.00000 + 8.00000i 0.331042 + 0.331042i
$$585$$ 0 0
$$586$$ 30.0000i 1.23929i
$$587$$ 7.00000 7.00000i 0.288921 0.288921i −0.547733 0.836653i $$-0.684509\pi$$
0.836653 + 0.547733i $$0.184509\pi$$
$$588$$ −6.00000 + 6.00000i −0.247436 + 0.247436i
$$589$$ 24.0000 24.0000i 0.988903 0.988903i
$$590$$ 0 0
$$591$$ 34.0000 1.39857
$$592$$ 12.0000 12.0000i 0.493197 0.493197i
$$593$$ 34.0000i 1.39621i −0.715994 0.698106i $$-0.754026\pi$$
0.715994 0.698106i $$-0.245974\pi$$
$$594$$ 8.00000 8.00000i 0.328244 0.328244i
$$595$$ 0 0
$$596$$ −14.0000 + 14.0000i −0.573462 + 0.573462i
$$597$$ 14.0000 14.0000i 0.572982 0.572982i
$$598$$ 12.0000 0.490716
$$599$$ 14.0000i 0.572024i −0.958226 0.286012i $$-0.907670\pi$$
0.958226 0.286012i $$-0.0923298\pi$$
$$600$$ 0 0
$$601$$ 20.0000i 0.815817i 0.913023 + 0.407909i $$0.133742\pi$$
−0.913023 + 0.407909i $$0.866258\pi$$
$$602$$ 20.0000i 0.815139i
$$603$$ −5.00000 + 5.00000i −0.203616 + 0.203616i
$$604$$ −20.0000 −0.813788
$$605$$ 0 0
$$606$$ 22.0000 + 22.0000i 0.893689 + 0.893689i
$$607$$ 32.0000i 1.29884i −0.760430 0.649420i $$-0.775012\pi$$
0.760430 0.649420i $$-0.224988\pi$$
$$608$$ 24.0000i 0.973329i
$$609$$ −12.0000 −0.486265
$$610$$ 0 0
$$611$$ −8.00000 + 8.00000i −0.323645 + 0.323645i
$$612$$ 4.00000i 0.161690i
$$613$$ −25.0000 + 25.0000i −1.00974 + 1.00974i −0.00978840 + 0.999952i $$0.503116\pi$$
−0.999952 + 0.00978840i $$0.996884\pi$$
$$614$$ −10.0000 −0.403567
$$615$$ 0 0
$$616$$ 8.00000i 0.322329i
$$617$$ 12.0000 0.483102 0.241551 0.970388i $$-0.422344\pi$$
0.241551 + 0.970388i $$0.422344\pi$$
$$618$$ 12.0000 0.482711
$$619$$ −17.0000 17.0000i −0.683288 0.683288i 0.277452 0.960740i $$-0.410510\pi$$
−0.960740 + 0.277452i $$0.910510\pi$$
$$620$$ 0 0
$$621$$ 24.0000 24.0000i 0.963087 0.963087i
$$622$$ 30.0000 + 30.0000i 1.20289 + 1.20289i
$$623$$ 8.00000i 0.320513i
$$624$$ 8.00000i 0.320256i
$$625$$ 0 0
$$626$$ 16.0000 16.0000i 0.639489 0.639489i
$$627$$ −6.00000 6.00000i −0.239617 0.239617i
$$628$$ 30.0000 30.0000i 1.19713 1.19713i
$$629$$ 6.00000 + 6.00000i 0.239236 + 0.239236i
$$630$$ 0 0
$$631$$ 10.0000i 0.398094i −0.979990 0.199047i $$-0.936215\pi$$
0.979990 0.199047i $$-0.0637846\pi$$
$$632$$ 0 0
$$633$$ −18.0000 −0.715436
$$634$$ −10.0000 −0.397151
$$635$$ 0 0
$$636$$ 20.0000i 0.793052i
$$637$$ −3.00000 3.00000i −0.118864 0.118864i
$$638$$ −6.00000 + 6.00000i −0.237542 + 0.237542i
$$639$$ −10.0000 −0.395594
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 14.0000 14.0000i 0.552536 0.552536i
$$643$$ 21.0000 + 21.0000i 0.828159 + 0.828159i 0.987262 0.159103i $$-0.0508601\pi$$
−0.159103 + 0.987262i $$0.550860\pi$$
$$644$$ 24.0000i 0.945732i
$$645$$ 0 0
$$646$$ 12.0000 0.472134
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ −10.0000 10.0000i −0.392837 0.392837i
$$649$$ 6.00000i 0.235521i
$$650$$ 0 0
$$651$$ −16.0000 16.0000i −0.627089 0.627089i
$$652$$ 2.00000 2.00000i 0.0783260 0.0783260i
$$653$$ −19.0000 19.0000i −0.743527 0.743527i 0.229728 0.973255i $$-0.426216\pi$$
−0.973255 + 0.229728i $$0.926216\pi$$
$$654$$ −6.00000 + 6.00000i −0.234619 + 0.234619i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 4.00000i 0.156055i
$$658$$ 16.0000 + 16.0000i 0.623745 + 0.623745i
$$659$$ 17.0000 17.0000i 0.662226 0.662226i −0.293678 0.955904i $$-0.594879\pi$$
0.955904 + 0.293678i $$0.0948794\pi$$
$$660$$ 0 0
$$661$$ −9.00000 9.00000i −0.350059 0.350059i 0.510072 0.860132i $$-0.329619\pi$$
−0.860132 + 0.510072i $$0.829619\pi$$
$$662$$ 2.00000 0.0777322
$$663$$ 4.00000 0.155347
$$664$$ 4.00000i 0.155230i
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ −18.0000 + 18.0000i −0.696963 + 0.696963i
$$668$$ 4.00000i 0.154765i
$$669$$ 24.0000 24.0000i 0.927894 0.927894i
$$670$$ 0 0
$$671$$ −18.0000 −0.694882
$$672$$ −16.0000 −0.617213
$$673$$ 14.0000i 0.539660i −0.962908 0.269830i $$-0.913032\pi$$
0.962908 0.269830i $$-0.0869676\pi$$
$$674$$ 18.0000 + 18.0000i 0.693334 + 0.693334i
$$675$$ 0 0
$$676$$ −22.0000 −0.846154
$$677$$ −3.00000 + 3.00000i −0.115299 + 0.115299i −0.762402 0.647103i $$-0.775980\pi$$
0.647103 + 0.762402i $$0.275980\pi$$
$$678$$ 12.0000i 0.460857i
$$679$$ 4.00000i 0.153506i
$$680$$ 0 0
$$681$$ 30.0000i 1.14960i
$$682$$ −16.0000 −0.612672
$$683$$ 5.00000 5.00000i 0.191320 0.191320i −0.604946 0.796266i $$-0.706805\pi$$
0.796266 + 0.604946i $$0.206805\pi$$
$$684$$ 6.00000 6.00000i 0.229416 0.229416i
$$685$$ 0 0
$$686$$ −20.0000 + 20.0000i −0.763604 + 0.763604i
$$687$$ 14.0000i 0.534133i
$$688$$ −20.0000 + 20.0000i −0.762493 + 0.762493i
$$689$$ −10.0000 −0.380970
$$690$$ 0 0
$$691$$ −9.00000 + 9.00000i −0.342376 + 0.342376i −0.857260 0.514884i $$-0.827835\pi$$
0.514884 + 0.857260i $$0.327835\pi$$
$$692$$ 2.00000 2.00000i 0.0760286 0.0760286i
$$693$$ 2.00000 2.00000i 0.0759737 0.0759737i
$$694$$ 26.0000i 0.986947i
$$695$$ 0 0
$$696$$ 12.0000 + 12.0000i 0.454859 + 0.454859i
$$697$$ 0 0
$$698$$ 6.00000i 0.227103i
$$699$$ −4.00000 4.00000i −0.151294 0.151294i
$$700$$ 0 0
$$701$$ 31.0000 31.0000i 1.17085 1.17085i 0.188847 0.982006i $$-0.439525\pi$$
0.982006 0.188847i $$-0.0604752\pi$$
$$702$$ 8.00000 8.00000i 0.301941 0.301941i
$$703$$ 18.0000i 0.678883i
$$704$$ −8.00000 + 8.00000i −0.301511 + 0.301511i
$$705$$ 0 0
$$706$$ 6.00000 + 6.00000i 0.225813 + 0.225813i
$$707$$ 22.0000 + 22.0000i 0.827395 + 0.827395i
$$708$$ 12.0000 0.450988
$$709$$ −27.0000 27.0000i −1.01401 1.01401i −0.999901 0.0141058i $$-0.995510\pi$$
−0.0141058 0.999901i $$-0.504490\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −8.00000 + 8.00000i −0.299813 + 0.299813i
$$713$$ −48.0000 −1.79761
$$714$$ 8.00000i 0.299392i
$$715$$ 0 0
$$716$$ −34.0000 34.0000i −1.27064 1.27064i
$$717$$ 0 0
$$718$$ 26.0000 + 26.0000i 0.970311 + 0.970311i
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 12.0000 0.446903
$$722$$ 1.00000 + 1.00000i 0.0372161 + 0.0372161i
$$723$$ −18.0000 18.0000i −0.669427 0.669427i
$$724$$ −18.0000 + 18.0000i −0.668965 + 0.668965i
$$725$$ 0 0
$$726$$ 18.0000i 0.668043i
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 8.00000i 0.296500i
$$729$$ 29.0000i 1.07407i
$$730$$ 0 0
$$731$$ −10.0000 10.0000i −0.369863 0.369863i
$$732$$ 36.0000i 1.33060i
$$733$$ 21.0000 + 21.0000i 0.775653 + 0.775653i 0.979088 0.203436i $$-0.0652108\pi$$
−0.203436 + 0.979088i $$0.565211\pi$$
$$734$$ 8.00000 + 8.00000i 0.295285 + 0.295285i
$$735$$ 0 0
$$736$$ −24.0000 + 24.0000i −0.884652 + 0.884652i
$$737$$ 10.0000i 0.368355i
$$738$$ 0 0
$$739$$ −23.0000 + 23.0000i −0.846069 + 0.846069i −0.989640 0.143571i $$-0.954141\pi$$
0.143571 + 0.989640i $$0.454141\pi$$
$$740$$ 0 0
$$741$$ −6.00000 6.00000i −0.220416 0.220416i
$$742$$ 20.0000i 0.734223i
$$743$$ 46.0000 1.68758 0.843788 0.536676i $$-0.180320\pi$$
0.843788 + 0.536676i $$0.180320\pi$$
$$744$$ 32.0000i 1.17318i
$$745$$ 0 0
$$746$$ 10.0000i 0.366126i
$$747$$ 1.00000 1.00000i 0.0365881 0.0365881i
$$748$$ −4.00000 4.00000i −0.146254 0.146254i
$$749$$ 14.0000 14.0000i 0.511549 0.511549i
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 32.0000i 1.16692i
$$753$$ 42.0000i 1.53057i
$$754$$ −6.00000 + 6.00000i −0.218507 + 0.218507i
$$755$$ 0 0
$$756$$ −16.0000 16.0000i −0.581914 0.581914i
$$757$$ −23.0000 + 23.0000i −0.835949 + 0.835949i −0.988323 0.152374i $$-0.951308\pi$$
0.152374 + 0.988323i $$0.451308\pi$$
$$758$$ 6.00000 0.217930
$$759$$ 12.0000i 0.435572i
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 16.0000i 0.579619i
$$763$$ −6.00000 + 6.00000i −0.217215 + 0.217215i
$$764$$ 16.0000i 0.578860i
$$765$$ 0 0
$$766$$ 16.0000 + 16.0000i 0.578103 + 0.578103i
$$767$$ 6.00000i 0.216647i
$$768$$ 16.0000 + 16.0000i 0.577350 + 0.577350i
$$769$$ 50.0000 1.80305 0.901523 0.432731i $$-0.142450\pi$$
0.901523 + 0.432731i $$0.142450\pi$$
$$770$$ 0 0
$$771$$ 22.0000 22.0000i 0.792311 0.792311i
$$772$$ −28.0000 −1.00774
$$773$$ −5.00000 + 5.00000i −0.179838 + 0.179838i −0.791285 0.611448i $$-0.790588\pi$$
0.611448 + 0.791285i $$0.290588\pi$$
$$774$$ −10.0000 −0.359443
$$775$$ 0 0
$$776$$ −4.00000 + 4.00000i −0.143592 + 0.143592i
$$777$$ −12.0000 −0.430498
$$778$$ 26.0000 0.932145
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 10.0000 10.0000i 0.357828 0.357828i
$$782$$ −12.0000 12.0000i −0.429119 0.429119i
$$783$$ 24.0000i 0.857690i
$$784$$ 12.0000 0.428571
$$785$$ 0 0
$$786$$ 22.0000 22.0000i 0.784714 0.784714i
$$787$$ 15.0000 + 15.0000i