# Properties

 Label 735.2.s.b.521.1 Level 735 Weight 2 Character 735.521 Analytic conductor 5.869 Analytic rank 0 Dimension 2 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.s (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.86900454856$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 521.1 Root $$0.500000 + 0.866025i$$ of $$x^{2} - x + 1$$ Character $$\chi$$ $$=$$ 735.521 Dual form 735.2.s.b.656.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.00000 q^{6} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(-1.50000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.00000 q^{6} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 - 0.866025i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +1.73205i q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-4.50000 - 2.59808i) q^{18} +(-3.00000 + 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(-3.00000 + 1.73205i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +6.92820i q^{29} +(-1.50000 - 2.59808i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(-3.00000 - 5.19615i) q^{33} -10.3923i q^{34} +3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(1.50000 - 0.866025i) q^{40} +6.00000 q^{41} -8.00000 q^{43} +(-3.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(3.00000 - 5.19615i) q^{46} +(6.00000 + 10.3923i) q^{47} +8.66025i q^{48} -1.73205i q^{50} +(-9.00000 + 5.19615i) q^{51} +(-4.50000 - 7.79423i) q^{54} -3.46410i q^{55} -6.00000 q^{57} +(-6.00000 - 10.3923i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.50000 + 0.866025i) q^{60} +(6.00000 - 3.46410i) q^{61} +6.00000 q^{62} -1.00000 q^{64} +(9.00000 + 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} -6.00000 q^{69} -3.46410i q^{71} +(4.50000 - 2.59808i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-3.00000 - 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +3.46410i q^{76} +(-4.00000 - 6.92820i) q^{79} +(-2.50000 + 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 + 5.19615i) q^{82} -6.00000 q^{85} +(12.0000 - 6.92820i) q^{86} +(-6.00000 + 10.3923i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-3.00000 - 5.19615i) q^{89} -5.19615i q^{90} +3.46410i q^{92} +(-3.00000 - 5.19615i) q^{93} +(-18.0000 - 10.3923i) q^{94} +(-3.00000 - 1.73205i) q^{95} +(-4.50000 - 7.79423i) q^{96} -6.92820i q^{97} -10.3923i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 3q^{2} + 3q^{3} + q^{4} + q^{5} - 6q^{6} + 3q^{9} + O(q^{10})$$ $$2q - 3q^{2} + 3q^{3} + q^{4} + q^{5} - 6q^{6} + 3q^{9} - 3q^{10} - 6q^{11} + 3q^{12} + 5q^{16} - 6q^{17} - 9q^{18} - 6q^{19} + 2q^{20} + 12q^{22} - 6q^{23} + 3q^{24} - q^{25} - 3q^{30} - 6q^{31} - 9q^{32} - 6q^{33} + 6q^{36} + 2q^{37} + 6q^{38} + 3q^{40} + 12q^{41} - 16q^{43} - 6q^{44} - 3q^{45} + 6q^{46} + 12q^{47} - 18q^{51} - 9q^{54} - 12q^{57} - 12q^{58} + 12q^{59} + 3q^{60} + 12q^{61} + 12q^{62} - 2q^{64} + 18q^{66} - 8q^{67} + 6q^{68} - 12q^{69} + 9q^{72} + 12q^{73} - 6q^{74} - 3q^{75} - 8q^{79} - 5q^{80} - 9q^{81} - 18q^{82} - 12q^{85} + 24q^{86} - 12q^{87} - 6q^{88} - 6q^{89} - 6q^{93} - 36q^{94} - 6q^{95} - 9q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$$.

 $$n$$ $$346$$ $$442$$ $$491$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.50000 + 0.866025i −1.06066 + 0.612372i −0.925615 0.378467i $$-0.876451\pi$$
−0.135045 + 0.990839i $$0.543118\pi$$
$$3$$ 1.50000 + 0.866025i 0.866025 + 0.500000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ −3.00000 −1.22474
$$7$$ 0 0
$$8$$ 1.73205i 0.612372i
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ −1.50000 0.866025i −0.474342 0.273861i
$$11$$ −3.00000 1.73205i −0.904534 0.522233i −0.0258656 0.999665i $$-0.508234\pi$$
−0.878668 + 0.477432i $$0.841568\pi$$
$$12$$ 1.50000 0.866025i 0.433013 0.250000i
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 1.73205i 0.447214i
$$16$$ 2.50000 + 4.33013i 0.625000 + 1.08253i
$$17$$ −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i $$0.426034\pi$$
−0.957892 + 0.287129i $$0.907299\pi$$
$$18$$ −4.50000 2.59808i −1.06066 0.612372i
$$19$$ −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i $$-0.796740\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ 6.00000 1.27920
$$23$$ −3.00000 + 1.73205i −0.625543 + 0.361158i −0.779024 0.626994i $$-0.784285\pi$$
0.153481 + 0.988152i $$0.450952\pi$$
$$24$$ 1.50000 2.59808i 0.306186 0.530330i
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ 6.92820i 1.28654i 0.765641 + 0.643268i $$0.222422\pi$$
−0.765641 + 0.643268i $$0.777578\pi$$
$$30$$ −1.50000 2.59808i −0.273861 0.474342i
$$31$$ −3.00000 1.73205i −0.538816 0.311086i 0.205783 0.978598i $$-0.434026\pi$$
−0.744599 + 0.667512i $$0.767359\pi$$
$$32$$ −4.50000 2.59808i −0.795495 0.459279i
$$33$$ −3.00000 5.19615i −0.522233 0.904534i
$$34$$ 10.3923i 1.78227i
$$35$$ 0 0
$$36$$ 3.00000 0.500000
$$37$$ 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i $$-0.114098\pi$$
−0.772043 + 0.635571i $$0.780765\pi$$
$$38$$ 3.00000 5.19615i 0.486664 0.842927i
$$39$$ 0 0
$$40$$ 1.50000 0.866025i 0.237171 0.136931i
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ −3.00000 + 1.73205i −0.452267 + 0.261116i
$$45$$ −1.50000 + 2.59808i −0.223607 + 0.387298i
$$46$$ 3.00000 5.19615i 0.442326 0.766131i
$$47$$ 6.00000 + 10.3923i 0.875190 + 1.51587i 0.856560 + 0.516047i $$0.172597\pi$$
0.0186297 + 0.999826i $$0.494070\pi$$
$$48$$ 8.66025i 1.25000i
$$49$$ 0 0
$$50$$ 1.73205i 0.244949i
$$51$$ −9.00000 + 5.19615i −1.26025 + 0.727607i
$$52$$ 0 0
$$53$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ −4.50000 7.79423i −0.612372 1.06066i
$$55$$ 3.46410i 0.467099i
$$56$$ 0 0
$$57$$ −6.00000 −0.794719
$$58$$ −6.00000 10.3923i −0.787839 1.36458i
$$59$$ 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i $$-0.547975\pi$$
0.931282 0.364299i $$-0.118692\pi$$
$$60$$ 1.50000 + 0.866025i 0.193649 + 0.111803i
$$61$$ 6.00000 3.46410i 0.768221 0.443533i −0.0640184 0.997949i $$-0.520392\pi$$
0.832240 + 0.554416i $$0.187058\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 9.00000 + 5.19615i 1.10782 + 0.639602i
$$67$$ −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i $$-0.995854\pi$$
0.511237 + 0.859440i $$0.329187\pi$$
$$68$$ 3.00000 + 5.19615i 0.363803 + 0.630126i
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 3.46410i 0.411113i −0.978645 0.205557i $$-0.934100\pi$$
0.978645 0.205557i $$-0.0659005\pi$$
$$72$$ 4.50000 2.59808i 0.530330 0.306186i
$$73$$ 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i $$-0.200451\pi$$
−0.105937 + 0.994373i $$0.533784\pi$$
$$74$$ −3.00000 1.73205i −0.348743 0.201347i
$$75$$ −1.50000 + 0.866025i −0.173205 + 0.100000i
$$76$$ 3.46410i 0.397360i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i $$-0.315255\pi$$
−0.998388 + 0.0567635i $$0.981922\pi$$
$$80$$ −2.50000 + 4.33013i −0.279508 + 0.484123i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −9.00000 + 5.19615i −0.993884 + 0.573819i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −6.00000 −0.650791
$$86$$ 12.0000 6.92820i 1.29399 0.747087i
$$87$$ −6.00000 + 10.3923i −0.643268 + 1.11417i
$$88$$ −3.00000 + 5.19615i −0.319801 + 0.553912i
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 5.19615i 0.547723i
$$91$$ 0 0
$$92$$ 3.46410i 0.361158i
$$93$$ −3.00000 5.19615i −0.311086 0.538816i
$$94$$ −18.0000 10.3923i −1.85656 1.07188i
$$95$$ −3.00000 1.73205i −0.307794 0.177705i
$$96$$ −4.50000 7.79423i −0.459279 0.795495i
$$97$$ 6.92820i 0.703452i −0.936103 0.351726i $$-0.885595\pi$$
0.936103 0.351726i $$-0.114405\pi$$
$$98$$ 0 0
$$99$$ 10.3923i 1.04447i
$$100$$ 0.500000 + 0.866025i 0.0500000 + 0.0866025i
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 9.00000 15.5885i 0.891133 1.54349i
$$103$$ 3.00000 1.73205i 0.295599 0.170664i −0.344865 0.938652i $$-0.612075\pi$$
0.640464 + 0.767988i $$0.278742\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −9.00000 + 5.19615i −0.870063 + 0.502331i −0.867369 0.497665i $$-0.834191\pi$$
−0.00269372 + 0.999996i $$0.500857\pi$$
$$108$$ 4.50000 + 2.59808i 0.433013 + 0.250000i
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 3.00000 + 5.19615i 0.286039 + 0.495434i
$$111$$ 3.46410i 0.328798i
$$112$$ 0 0
$$113$$ 6.92820i 0.651751i 0.945413 + 0.325875i $$0.105659\pi$$
−0.945413 + 0.325875i $$0.894341\pi$$
$$114$$ 9.00000 5.19615i 0.842927 0.486664i
$$115$$ −3.00000 1.73205i −0.279751 0.161515i
$$116$$ 6.00000 + 3.46410i 0.557086 + 0.321634i
$$117$$ 0 0
$$118$$ 20.7846i 1.91338i
$$119$$ 0 0
$$120$$ 3.00000 0.273861
$$121$$ 0.500000 + 0.866025i 0.0454545 + 0.0787296i
$$122$$ −6.00000 + 10.3923i −0.543214 + 0.940875i
$$123$$ 9.00000 + 5.19615i 0.811503 + 0.468521i
$$124$$ −3.00000 + 1.73205i −0.269408 + 0.155543i
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −4.00000 −0.354943 −0.177471 0.984126i $$-0.556792\pi$$
−0.177471 + 0.984126i $$0.556792\pi$$
$$128$$ 10.5000 6.06218i 0.928078 0.535826i
$$129$$ −12.0000 6.92820i −1.05654 0.609994i
$$130$$ 0 0
$$131$$ 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i $$0.00897729\pi$$
−0.475380 + 0.879781i $$0.657689\pi$$
$$132$$ −6.00000 −0.522233
$$133$$ 0 0
$$134$$ 13.8564i 1.19701i
$$135$$ −4.50000 + 2.59808i −0.387298 + 0.223607i
$$136$$ 9.00000 + 5.19615i 0.771744 + 0.445566i
$$137$$ 18.0000 + 10.3923i 1.53784 + 0.887875i 0.998965 + 0.0454914i $$0.0144854\pi$$
0.538879 + 0.842383i $$0.318848\pi$$
$$138$$ 9.00000 5.19615i 0.766131 0.442326i
$$139$$ 17.3205i 1.46911i −0.678551 0.734553i $$-0.737392\pi$$
0.678551 0.734553i $$-0.262608\pi$$
$$140$$ 0 0
$$141$$ 20.7846i 1.75038i
$$142$$ 3.00000 + 5.19615i 0.251754 + 0.436051i
$$143$$ 0 0
$$144$$ −7.50000 + 12.9904i −0.625000 + 1.08253i
$$145$$ −6.00000 + 3.46410i −0.498273 + 0.287678i
$$146$$ −12.0000 −0.993127
$$147$$ 0 0
$$148$$ 2.00000 0.164399
$$149$$ −6.00000 + 3.46410i −0.491539 + 0.283790i −0.725213 0.688525i $$-0.758259\pi$$
0.233674 + 0.972315i $$0.424925\pi$$
$$150$$ 1.50000 2.59808i 0.122474 0.212132i
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 3.00000 + 5.19615i 0.243332 + 0.421464i
$$153$$ −18.0000 −1.45521
$$154$$ 0 0
$$155$$ 3.46410i 0.278243i
$$156$$ 0 0
$$157$$ 12.0000 + 6.92820i 0.957704 + 0.552931i 0.895466 0.445130i $$-0.146843\pi$$
0.0622385 + 0.998061i $$0.480176\pi$$
$$158$$ 12.0000 + 6.92820i 0.954669 + 0.551178i
$$159$$ 0 0
$$160$$ 5.19615i 0.410792i
$$161$$ 0 0
$$162$$ 15.5885i 1.22474i
$$163$$ 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i $$0.0488907\pi$$
−0.361619 + 0.932326i $$0.617776\pi$$
$$164$$ 3.00000 5.19615i 0.234261 0.405751i
$$165$$ 3.00000 5.19615i 0.233550 0.404520i
$$166$$ 0 0
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 9.00000 5.19615i 0.690268 0.398527i
$$171$$ −9.00000 5.19615i −0.688247 0.397360i
$$172$$ −4.00000 + 6.92820i −0.304997 + 0.528271i
$$173$$ −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i $$-0.926793\pi$$
0.289412 0.957205i $$-0.406540\pi$$
$$174$$ 20.7846i 1.57568i
$$175$$ 0 0
$$176$$ 17.3205i 1.30558i
$$177$$ 18.0000 10.3923i 1.35296 0.781133i
$$178$$ 9.00000 + 5.19615i 0.674579 + 0.389468i
$$179$$ 9.00000 + 5.19615i 0.672692 + 0.388379i 0.797096 0.603853i $$-0.206369\pi$$
−0.124404 + 0.992232i $$0.539702\pi$$
$$180$$ 1.50000 + 2.59808i 0.111803 + 0.193649i
$$181$$ 20.7846i 1.54491i 0.635071 + 0.772454i $$0.280971\pi$$
−0.635071 + 0.772454i $$0.719029\pi$$
$$182$$ 0 0
$$183$$ 12.0000 0.887066
$$184$$ 3.00000 + 5.19615i 0.221163 + 0.383065i
$$185$$ −1.00000 + 1.73205i −0.0735215 + 0.127343i
$$186$$ 9.00000 + 5.19615i 0.659912 + 0.381000i
$$187$$ 18.0000 10.3923i 1.31629 0.759961i
$$188$$ 12.0000 0.875190
$$189$$ 0 0
$$190$$ 6.00000 0.435286
$$191$$ 9.00000 5.19615i 0.651217 0.375980i −0.137705 0.990473i $$-0.543973\pi$$
0.788922 + 0.614493i $$0.210639\pi$$
$$192$$ −1.50000 0.866025i −0.108253 0.0625000i
$$193$$ 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i $$-0.665242\pi$$
0.999990 0.00447566i $$-0.00142465\pi$$
$$194$$ 6.00000 + 10.3923i 0.430775 + 0.746124i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 13.8564i 0.987228i 0.869681 + 0.493614i $$0.164324\pi$$
−0.869681 + 0.493614i $$0.835676\pi$$
$$198$$ 9.00000 + 15.5885i 0.639602 + 1.10782i
$$199$$ 9.00000 + 5.19615i 0.637993 + 0.368345i 0.783841 0.620962i $$-0.213258\pi$$
−0.145848 + 0.989307i $$0.546591\pi$$
$$200$$ 1.50000 + 0.866025i 0.106066 + 0.0612372i
$$201$$ −12.0000 + 6.92820i −0.846415 + 0.488678i
$$202$$ 10.3923i 0.731200i
$$203$$ 0 0
$$204$$ 10.3923i 0.727607i
$$205$$ 3.00000 + 5.19615i 0.209529 + 0.362915i
$$206$$ −3.00000 + 5.19615i −0.209020 + 0.362033i
$$207$$ −9.00000 5.19615i −0.625543 0.361158i
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 3.00000 5.19615i 0.205557 0.356034i
$$214$$ 9.00000 15.5885i 0.615227 1.06561i
$$215$$ −4.00000 6.92820i −0.272798 0.472500i
$$216$$ 9.00000 0.612372
$$217$$ 0 0
$$218$$ 3.46410i 0.234619i
$$219$$ 6.00000 + 10.3923i 0.405442 + 0.702247i
$$220$$ −3.00000 1.73205i −0.202260 0.116775i
$$221$$ 0 0
$$222$$ −3.00000 5.19615i −0.201347 0.348743i
$$223$$ 17.3205i 1.15987i 0.814664 + 0.579934i $$0.196921\pi$$
−0.814664 + 0.579934i $$0.803079\pi$$
$$224$$ 0 0
$$225$$ −3.00000 −0.200000
$$226$$ −6.00000 10.3923i −0.399114 0.691286i
$$227$$ 12.0000 20.7846i 0.796468 1.37952i −0.125435 0.992102i $$-0.540033\pi$$
0.921903 0.387421i $$-0.126634\pi$$
$$228$$ −3.00000 + 5.19615i −0.198680 + 0.344124i
$$229$$ 6.00000 3.46410i 0.396491 0.228914i −0.288478 0.957487i $$-0.593149\pi$$
0.684969 + 0.728572i $$0.259816\pi$$
$$230$$ 6.00000 0.395628
$$231$$ 0 0
$$232$$ 12.0000 0.787839
$$233$$ −6.00000 + 3.46410i −0.393073 + 0.226941i −0.683491 0.729959i $$-0.739539\pi$$
0.290418 + 0.956900i $$0.406206\pi$$
$$234$$ 0 0
$$235$$ −6.00000 + 10.3923i −0.391397 + 0.677919i
$$236$$ −6.00000 10.3923i −0.390567 0.676481i
$$237$$ 13.8564i 0.900070i
$$238$$ 0 0
$$239$$ 10.3923i 0.672222i 0.941822 + 0.336111i $$0.109112\pi$$
−0.941822 + 0.336111i $$0.890888\pi$$
$$240$$ −7.50000 + 4.33013i −0.484123 + 0.279508i
$$241$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$242$$ −1.50000 0.866025i −0.0964237 0.0556702i
$$243$$ −13.5000 + 7.79423i −0.866025 + 0.500000i
$$244$$ 6.92820i 0.443533i
$$245$$ 0 0
$$246$$ −18.0000 −1.14764
$$247$$ 0 0
$$248$$ −3.00000 + 5.19615i −0.190500 + 0.329956i
$$249$$ 0 0
$$250$$ 1.50000 0.866025i 0.0948683 0.0547723i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 12.0000 0.754434
$$254$$ 6.00000 3.46410i 0.376473 0.217357i
$$255$$ −9.00000 5.19615i −0.563602 0.325396i
$$256$$ −9.50000 + 16.4545i −0.593750 + 1.02841i
$$257$$ −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i $$-0.226587\pi$$
−0.944294 + 0.329104i $$0.893253\pi$$
$$258$$ 24.0000 1.49417
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −18.0000 + 10.3923i −1.11417 + 0.643268i
$$262$$ −18.0000 10.3923i −1.11204 0.642039i
$$263$$ −21.0000 12.1244i −1.29492 0.747620i −0.315394 0.948961i $$-0.602137\pi$$
−0.979521 + 0.201341i $$0.935470\pi$$
$$264$$ −9.00000 + 5.19615i −0.553912 + 0.319801i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 10.3923i 0.635999i
$$268$$ 4.00000 + 6.92820i 0.244339 + 0.423207i
$$269$$ −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i $$0.351559\pi$$
−0.998361 + 0.0572259i $$0.981774\pi$$
$$270$$ 4.50000 7.79423i 0.273861 0.474342i
$$271$$ −21.0000 + 12.1244i −1.27566 + 0.736502i −0.976047 0.217559i $$-0.930191\pi$$
−0.299612 + 0.954061i $$0.596857\pi$$
$$272$$ −30.0000 −1.81902
$$273$$ 0 0
$$274$$ −36.0000 −2.17484
$$275$$ 3.00000 1.73205i 0.180907 0.104447i
$$276$$ −3.00000 + 5.19615i −0.180579 + 0.312772i
$$277$$ −7.00000 + 12.1244i −0.420589 + 0.728482i −0.995997 0.0893846i $$-0.971510\pi$$
0.575408 + 0.817867i $$0.304843\pi$$
$$278$$ 15.0000 + 25.9808i 0.899640 + 1.55822i
$$279$$ 10.3923i 0.622171i
$$280$$ 0 0
$$281$$ 13.8564i 0.826604i −0.910594 0.413302i $$-0.864375\pi$$
0.910594 0.413302i $$-0.135625\pi$$
$$282$$ −18.0000 31.1769i −1.07188 1.85656i
$$283$$ 15.0000 + 8.66025i 0.891657 + 0.514799i 0.874484 0.485054i $$-0.161200\pi$$
0.0171732 + 0.999853i $$0.494533\pi$$
$$284$$ −3.00000 1.73205i −0.178017 0.102778i
$$285$$ −3.00000 5.19615i −0.177705 0.307794i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 15.5885i 0.918559i
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 6.00000 10.3923i 0.352332 0.610257i
$$291$$ 6.00000 10.3923i 0.351726 0.609208i
$$292$$ 6.00000 3.46410i 0.351123 0.202721i
$$293$$ −6.00000 −0.350524 −0.175262 0.984522i $$-0.556077\pi$$
−0.175262 + 0.984522i $$0.556077\pi$$
$$294$$ 0 0
$$295$$ 12.0000 0.698667
$$296$$ 3.00000 1.73205i 0.174371 0.100673i
$$297$$ 9.00000 15.5885i 0.522233 0.904534i
$$298$$ 6.00000 10.3923i 0.347571 0.602010i
$$299$$ 0 0
$$300$$ 1.73205i 0.100000i
$$301$$ 0 0
$$302$$ 13.8564i 0.797347i
$$303$$ 9.00000 5.19615i 0.517036 0.298511i
$$304$$ −15.0000 8.66025i −0.860309 0.496700i
$$305$$ 6.00000 + 3.46410i 0.343559 + 0.198354i
$$306$$ 27.0000 15.5885i 1.54349 0.891133i
$$307$$ 24.2487i 1.38395i 0.721923 + 0.691974i $$0.243259\pi$$
−0.721923 + 0.691974i $$0.756741\pi$$
$$308$$ 0 0
$$309$$ 6.00000 0.341328
$$310$$ 3.00000 + 5.19615i 0.170389 + 0.295122i
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ 0 0
$$313$$ 18.0000 10.3923i 1.01742 0.587408i 0.104065 0.994571i $$-0.466815\pi$$
0.913356 + 0.407163i $$0.133482\pi$$
$$314$$ −24.0000 −1.35440
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −24.0000 + 13.8564i −1.34797 + 0.778253i −0.987962 0.154694i $$-0.950561\pi$$
−0.360012 + 0.932948i $$0.617227\pi$$
$$318$$ 0 0
$$319$$ 12.0000 20.7846i 0.671871 1.16371i
$$320$$ −0.500000 0.866025i −0.0279508 0.0484123i
$$321$$ −18.0000 −1.00466
$$322$$ 0 0
$$323$$ 20.7846i 1.15649i
$$324$$ 4.50000 + 7.79423i 0.250000 + 0.433013i
$$325$$ 0 0
$$326$$ −24.0000 13.8564i −1.32924 0.767435i
$$327$$ 3.00000 1.73205i 0.165900 0.0957826i
$$328$$ 10.3923i 0.573819i
$$329$$ 0 0
$$330$$ 10.3923i 0.572078i
$$331$$ −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i $$-0.887167\pi$$
0.168320 0.985732i $$-0.446166\pi$$
$$332$$ 0 0
$$333$$ −3.00000 + 5.19615i −0.164399 + 0.284747i
$$334$$ −18.0000 + 10.3923i −0.984916 + 0.568642i
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ −19.5000 + 11.2583i −1.06066 + 0.612372i
$$339$$ −6.00000 + 10.3923i −0.325875 + 0.564433i
$$340$$ −3.00000 + 5.19615i −0.162698 + 0.281801i
$$341$$ 6.00000 + 10.3923i 0.324918 + 0.562775i
$$342$$ 18.0000 0.973329
$$343$$ 0 0
$$344$$ 13.8564i 0.747087i
$$345$$ −3.00000 5.19615i −0.161515 0.279751i
$$346$$ 27.0000 + 15.5885i 1.45153 + 0.838041i
$$347$$ −15.0000 8.66025i −0.805242 0.464907i 0.0400587 0.999197i $$-0.487246\pi$$
−0.845301 + 0.534291i $$0.820579\pi$$
$$348$$ 6.00000 + 10.3923i 0.321634 + 0.557086i
$$349$$ 6.92820i 0.370858i −0.982658 0.185429i $$-0.940632\pi$$
0.982658 0.185429i $$-0.0593675\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 9.00000 + 15.5885i 0.479702 + 0.830868i
$$353$$ −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i $$-0.884378\pi$$
0.775077 + 0.631867i $$0.217711\pi$$
$$354$$ −18.0000 + 31.1769i −0.956689 + 1.65703i
$$355$$ 3.00000 1.73205i 0.159223 0.0919277i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −18.0000 −0.951330
$$359$$ −3.00000 + 1.73205i −0.158334 + 0.0914141i −0.577073 0.816692i $$-0.695805\pi$$
0.418740 + 0.908106i $$0.362472\pi$$
$$360$$ 4.50000 + 2.59808i 0.237171 + 0.136931i
$$361$$ −3.50000 + 6.06218i −0.184211 + 0.319062i
$$362$$ −18.0000 31.1769i −0.946059 1.63862i
$$363$$ 1.73205i 0.0909091i
$$364$$ 0 0
$$365$$ 6.92820i 0.362639i
$$366$$ −18.0000 + 10.3923i −0.940875 + 0.543214i
$$367$$ 9.00000 + 5.19615i 0.469796 + 0.271237i 0.716154 0.697942i $$-0.245901\pi$$
−0.246358 + 0.969179i $$0.579234\pi$$
$$368$$ −15.0000 8.66025i −0.781929 0.451447i
$$369$$ 9.00000 + 15.5885i 0.468521 + 0.811503i
$$370$$ 3.46410i 0.180090i
$$371$$ 0 0
$$372$$ −6.00000 −0.311086
$$373$$ −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i $$-0.284725\pi$$
−0.988363 + 0.152115i $$0.951392\pi$$
$$374$$ −18.0000 + 31.1769i −0.930758 + 1.61212i
$$375$$ −1.50000 0.866025i −0.0774597 0.0447214i
$$376$$ 18.0000 10.3923i 0.928279 0.535942i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ −3.00000 + 1.73205i −0.153897 + 0.0888523i
$$381$$ −6.00000 3.46410i −0.307389 0.177471i
$$382$$ −9.00000 + 15.5885i −0.460480 + 0.797575i
$$383$$ −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i $$-0.265853\pi$$
−0.977613 + 0.210411i $$0.932520\pi$$
$$384$$ 21.0000 1.07165
$$385$$ 0 0
$$386$$ 24.2487i 1.23423i
$$387$$ −12.0000 20.7846i −0.609994 1.05654i
$$388$$ −6.00000 3.46410i −0.304604 0.175863i
$$389$$ 6.00000 + 3.46410i 0.304212 + 0.175637i 0.644334 0.764745i $$-0.277135\pi$$
−0.340121 + 0.940382i $$0.610468\pi$$
$$390$$ 0 0
$$391$$ 20.7846i 1.05112i
$$392$$ 0 0
$$393$$ 20.7846i 1.04844i
$$394$$ −12.0000 20.7846i −0.604551 1.04711i
$$395$$ 4.00000 6.92820i 0.201262 0.348596i
$$396$$ −9.00000 5.19615i −0.452267 0.261116i
$$397$$ −12.0000 + 6.92820i −0.602263 + 0.347717i −0.769931 0.638127i $$-0.779710\pi$$
0.167668 + 0.985843i $$0.446376\pi$$
$$398$$ −18.0000 −0.902258
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ 24.0000 13.8564i 1.19850 0.691956i 0.238282 0.971196i $$-0.423416\pi$$
0.960221 + 0.279240i $$0.0900826\pi$$
$$402$$ 12.0000 20.7846i 0.598506 1.03664i
$$403$$ 0 0
$$404$$ −3.00000 5.19615i −0.149256 0.258518i
$$405$$ −9.00000 −0.447214
$$406$$ 0 0
$$407$$ 6.92820i 0.343418i
$$408$$ 9.00000 + 15.5885i 0.445566 + 0.771744i
$$409$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ −9.00000 5.19615i −0.444478 0.256620i
$$411$$ 18.0000 + 31.1769i 0.887875 + 1.53784i
$$412$$ 3.46410i 0.170664i
$$413$$ 0 0
$$414$$ 18.0000 0.884652
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 15.0000 25.9808i 0.734553 1.27228i
$$418$$ −18.0000 + 10.3923i −0.880409 + 0.508304i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ −6.00000 + 3.46410i −0.292075 + 0.168630i
$$423$$ −18.0000 + 31.1769i −0.875190 + 1.51587i
$$424$$ 0 0
$$425$$ −3.00000 5.19615i −0.145521 0.252050i
$$426$$ 10.3923i 0.503509i
$$427$$ 0 0
$$428$$ 10.3923i 0.502331i
$$429$$ 0 0
$$430$$ 12.0000 + 6.92820i 0.578691 + 0.334108i
$$431$$ −9.00000 5.19615i −0.433515 0.250290i 0.267328 0.963606i $$-0.413859\pi$$
−0.700843 + 0.713316i $$0.747193\pi$$
$$432$$ −22.5000 + 12.9904i −1.08253 + 0.625000i
$$433$$ 6.92820i 0.332948i 0.986046 + 0.166474i $$0.0532382\pi$$
−0.986046 + 0.166474i $$0.946762\pi$$
$$434$$ 0 0
$$435$$ −12.0000 −0.575356
$$436$$ −1.00000 1.73205i −0.0478913 0.0829502i
$$437$$ 6.00000 10.3923i 0.287019 0.497131i
$$438$$ −18.0000 10.3923i −0.860073 0.496564i
$$439$$ 15.0000 8.66025i 0.715911 0.413331i −0.0973349 0.995252i $$-0.531032\pi$$
0.813246 + 0.581920i $$0.197698\pi$$
$$440$$ −6.00000 −0.286039
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −9.00000 + 5.19615i −0.427603 + 0.246877i −0.698325 0.715781i $$-0.746071\pi$$
0.270722 + 0.962658i $$0.412738\pi$$
$$444$$ 3.00000 + 1.73205i 0.142374 + 0.0821995i
$$445$$ 3.00000 5.19615i 0.142214 0.246321i
$$446$$ −15.0000 25.9808i −0.710271 1.23022i
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 13.8564i 0.653924i 0.945037 + 0.326962i $$0.106025\pi$$
−0.945037 + 0.326962i $$0.893975\pi$$
$$450$$ 4.50000 2.59808i 0.212132 0.122474i
$$451$$ −18.0000 10.3923i −0.847587 0.489355i
$$452$$ 6.00000 + 3.46410i 0.282216 + 0.162938i
$$453$$ 12.0000 6.92820i 0.563809 0.325515i
$$454$$ 41.5692i 1.95094i
$$455$$ 0 0
$$456$$ 10.3923i 0.486664i
$$457$$ 19.0000 + 32.9090i 0.888783 + 1.53942i 0.841316 + 0.540544i $$0.181781\pi$$
0.0474665 + 0.998873i $$0.484885\pi$$
$$458$$ −6.00000 + 10.3923i −0.280362 + 0.485601i
$$459$$ −27.0000 15.5885i −1.26025 0.727607i
$$460$$ −3.00000 + 1.73205i −0.139876 + 0.0807573i
$$461$$ 18.0000 0.838344 0.419172 0.907907i $$-0.362320\pi$$
0.419172 + 0.907907i $$0.362320\pi$$
$$462$$ 0 0
$$463$$ 20.0000 0.929479 0.464739 0.885448i $$-0.346148\pi$$
0.464739 + 0.885448i $$0.346148\pi$$
$$464$$ −30.0000 + 17.3205i −1.39272 + 0.804084i
$$465$$ 3.00000 5.19615i 0.139122 0.240966i
$$466$$ 6.00000 10.3923i 0.277945 0.481414i
$$467$$ −12.0000 20.7846i −0.555294 0.961797i −0.997881 0.0650714i $$-0.979272\pi$$
0.442587 0.896726i $$-0.354061\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 20.7846i 0.958723i
$$471$$ 12.0000 + 20.7846i 0.552931 + 0.957704i
$$472$$ −18.0000 10.3923i −0.828517 0.478345i
$$473$$ 24.0000 + 13.8564i 1.10352 + 0.637118i
$$474$$ 12.0000 + 20.7846i 0.551178 + 0.954669i
$$475$$ 3.46410i 0.158944i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −9.00000 15.5885i −0.411650 0.712999i
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ 4.50000 7.79423i 0.205396 0.355756i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 6.00000 3.46410i 0.272446 0.157297i
$$486$$ 13.5000 23.3827i 0.612372 1.06066i
$$487$$ −2.00000 + 3.46410i −0.0906287 + 0.156973i −0.907776 0.419456i $$-0.862221\pi$$
0.817147 + 0.576429i $$0.195554\pi$$
$$488$$ −6.00000 10.3923i −0.271607 0.470438i
$$489$$ 27.7128i 1.25322i
$$490$$ 0 0
$$491$$ 24.2487i 1.09433i −0.837025 0.547165i $$-0.815707\pi$$
0.837025 0.547165i $$-0.184293\pi$$
$$492$$ 9.00000 5.19615i 0.405751 0.234261i
$$493$$ −36.0000 20.7846i −1.62136 0.936092i
$$494$$ 0 0
$$495$$ 9.00000 5.19615i 0.404520 0.233550i
$$496$$ 17.3205i 0.777714i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 10.0000 + 17.3205i 0.447661 + 0.775372i 0.998233 0.0594153i $$-0.0189236\pi$$
−0.550572 + 0.834788i $$0.685590\pi$$
$$500$$ −0.500000 + 0.866025i −0.0223607 + 0.0387298i
$$501$$ 18.0000 + 10.3923i 0.804181 + 0.464294i
$$502$$ −18.0000 + 10.3923i −0.803379 + 0.463831i
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ 6.00000 0.266996
$$506$$ −18.0000 + 10.3923i −0.800198 + 0.461994i
$$507$$ 19.5000 + 11.2583i 0.866025 + 0.500000i
$$508$$ −2.00000 + 3.46410i −0.0887357 + 0.153695i
$$509$$ 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i $$0.0648436\pi$$
−0.314459 + 0.949271i $$0.601823\pi$$
$$510$$ 18.0000 0.797053
$$511$$ 0 0
$$512$$ 8.66025i 0.382733i
$$513$$ −9.00000 15.5885i −0.397360 0.688247i
$$514$$ 9.00000 + 5.19615i 0.396973 + 0.229192i
$$515$$ 3.00000 + 1.73205i 0.132196 + 0.0763233i
$$516$$ −12.0000 + 6.92820i −0.528271 + 0.304997i
$$517$$ 41.5692i 1.82821i
$$518$$ 0 0
$$519$$ 31.1769i 1.36851i
$$520$$ 0 0
$$521$$ −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i $$-0.875291\pi$$
0.792797 + 0.609486i $$0.208624\pi$$
$$522$$ 18.0000 31.1769i 0.787839 1.36458i
$$523$$ −15.0000 + 8.66025i −0.655904 + 0.378686i −0.790715 0.612185i $$-0.790291\pi$$
0.134810 + 0.990871i $$0.456957\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 42.0000 1.83129
$$527$$ 18.0000 10.3923i 0.784092 0.452696i
$$528$$ 15.0000 25.9808i 0.652791 1.13067i
$$529$$ −5.50000 + 9.52628i −0.239130 + 0.414186i
$$530$$ 0 0
$$531$$ 36.0000 1.56227
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 9.00000 + 15.5885i 0.389468 + 0.674579i
$$535$$ −9.00000 5.19615i −0.389104 0.224649i
$$536$$ 12.0000 + 6.92820i 0.518321 + 0.299253i
$$537$$ 9.00000 + 15.5885i 0.388379 + 0.672692i
$$538$$ 31.1769i 1.34413i
$$539$$ 0 0
$$540$$ 5.19615i 0.223607i
$$541$$ 17.0000 + 29.4449i 0.730887 + 1.26593i 0.956504 + 0.291718i $$0.0942267\pi$$
−0.225617 + 0.974216i $$0.572440\pi$$
$$542$$ 21.0000 36.3731i 0.902027 1.56236i
$$543$$ −18.0000 + 31.1769i −0.772454 + 1.33793i
$$544$$ 27.0000 15.5885i 1.15762 0.668350i
$$545$$ 2.00000 0.0856706
$$546$$ 0 0
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 18.0000 10.3923i 0.768922 0.443937i
$$549$$ 18.0000 + 10.3923i 0.768221 + 0.443533i
$$550$$ −3.00000 + 5.19615i −0.127920 + 0.221565i
$$551$$ −12.0000 20.7846i −0.511217 0.885454i
$$552$$ 10.3923i 0.442326i
$$553$$ 0 0
$$554$$ 24.2487i 1.03023i
$$555$$ −3.00000 + 1.73205i −0.127343 + 0.0735215i
$$556$$ −15.0000 8.66025i −0.636142 0.367277i
$$557$$ −24.0000 13.8564i −1.01691 0.587115i −0.103704 0.994608i $$-0.533070\pi$$
−0.913208 + 0.407493i $$0.866403\pi$$
$$558$$ 9.00000 + 15.5885i 0.381000 + 0.659912i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 36.0000 1.51992
$$562$$ 12.0000 + 20.7846i 0.506189 + 0.876746i
$$563$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$564$$ 18.0000 + 10.3923i 0.757937 + 0.437595i
$$565$$ −6.00000 + 3.46410i −0.252422 + 0.145736i
$$566$$ −30.0000 −1.26099
$$567$$ 0 0
$$568$$ −6.00000 −0.251754
$$569$$ 24.0000 13.8564i 1.00613 0.580891i 0.0960754 0.995374i $$-0.469371\pi$$
0.910057 + 0.414483i $$0.136038\pi$$
$$570$$ 9.00000 + 5.19615i 0.376969 + 0.217643i
$$571$$ 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i $$-0.806660\pi$$
0.904835 + 0.425762i $$0.139994\pi$$
$$572$$ 0 0
$$573$$ 18.0000 0.751961
$$574$$ 0 0
$$575$$ 3.46410i 0.144463i
$$576$$ −1.50000 2.59808i −0.0625000 0.108253i
$$577$$ 30.0000 + 17.3205i 1.24892 + 0.721062i 0.970893 0.239512i $$-0.0769875\pi$$
0.278023 + 0.960574i $$0.410321\pi$$
$$578$$ 28.5000 + 16.4545i 1.18544 + 0.684416i
$$579$$ 21.0000 12.1244i 0.872730 0.503871i
$$580$$ 6.92820i 0.287678i
$$581$$ 0 0
$$582$$ 20.7846i 0.861550i
$$583$$ 0 0
$$584$$ 6.00000 10.3923i 0.248282 0.430037i
$$585$$ 0 0
$$586$$ 9.00000 5.19615i 0.371787 0.214651i
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 12.0000 0.494451
$$590$$ −18.0000 + 10.3923i −0.741048 + 0.427844i
$$591$$ −12.0000 + 20.7846i −0.493614 + 0.854965i
$$592$$ −5.00000 + 8.66025i −0.205499 + 0.355934i
$$593$$ −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i $$-0.205981\pi$$
−0.921026 + 0.389501i $$0.872647\pi$$
$$594$$ 31.1769i 1.27920i
$$595$$ 0 0
$$596$$ 6.92820i 0.283790i
$$597$$ 9.00000 + 15.5885i 0.368345 + 0.637993i
$$598$$ 0 0
$$599$$ −21.0000 12.1244i −0.858037 0.495388i 0.00531761 0.999986i $$-0.498307\pi$$
−0.863354 + 0.504598i $$0.831641\pi$$
$$600$$ 1.50000 + 2.59808i 0.0612372 + 0.106066i
$$601$$ 13.8564i 0.565215i −0.959236 0.282607i $$-0.908801\pi$$
0.959236 0.282607i $$-0.0911993\pi$$
$$602$$ 0 0
$$603$$ −24.0000 −0.977356
$$604$$ −4.00000 6.92820i −0.162758 0.281905i
$$605$$ −0.500000 + 0.866025i −0.0203279 + 0.0352089i
$$606$$ −9.00000 + 15.5885i −0.365600 + 0.633238i
$$607$$ 15.0000 8.66025i 0.608831 0.351509i −0.163677 0.986514i $$-0.552335\pi$$
0.772508 + 0.635005i $$0.219002\pi$$
$$608$$ 18.0000 0.729996
$$609$$ 0 0
$$610$$ −12.0000 −0.485866
$$611$$ 0 0
$$612$$ −9.00000 + 15.5885i −0.363803 + 0.630126i
$$613$$ 17.0000 29.4449i 0.686624 1.18927i −0.286300 0.958140i $$-0.592425\pi$$
0.972924 0.231127i $$-0.0742412\pi$$
$$614$$ −21.0000 36.3731i −0.847491 1.46790i
$$615$$ 10.3923i 0.419058i
$$616$$ 0 0
$$617$$ 6.92820i 0.278919i 0.990228 + 0.139459i $$0.0445365\pi$$
−0.990228 + 0.139459i $$0.955464\pi$$
$$618$$ −9.00000 + 5.19615i −0.362033 + 0.209020i
$$619$$ 15.0000 + 8.66025i 0.602901 + 0.348085i 0.770182 0.637824i $$-0.220165\pi$$
−0.167281 + 0.985909i $$0.553499\pi$$
$$620$$ −3.00000 1.73205i −0.120483 0.0695608i
$$621$$ −9.00000 15.5885i −0.361158 0.625543i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ −18.0000 + 31.1769i −0.719425 + 1.24608i
$$627$$ 18.0000 + 10.3923i 0.718851 + 0.415029i
$$628$$ 12.0000 6.92820i 0.478852 0.276465i
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ −12.0000 + 6.92820i −0.477334 + 0.275589i
$$633$$ 6.00000 + 3.46410i 0.238479 + 0.137686i
$$634$$ 24.0000 41.5692i 0.953162 1.65092i
$$635$$ −2.00000 3.46410i −0.0793676 0.137469i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 41.5692i 1.64574i
$$639$$ 9.00000 5.19615i 0.356034 0.205557i
$$640$$ 10.5000 + 6.06218i 0.415049 + 0.239629i
$$641$$ 24.0000 + 13.8564i 0.947943 + 0.547295i 0.892441 0.451163i $$-0.148991\pi$$
0.0555017 + 0.998459i $$0.482324\pi$$
$$642$$ 27.0000 15.5885i 1.06561 0.615227i
$$643$$ 31.1769i 1.22950i −0.788723 0.614749i $$-0.789257\pi$$
0.788723 0.614749i $$-0.210743\pi$$
$$644$$ 0 0
$$645$$ 13.8564i 0.545595i
$$646$$ 18.0000 + 31.1769i 0.708201 + 1.22664i
$$647$$ −6.00000 + 10.3923i −0.235884 + 0.408564i −0.959529 0.281609i $$-0.909132\pi$$
0.723645 + 0.690172i $$0.242465\pi$$
$$648$$ 13.5000 + 7.79423i 0.530330 + 0.306186i
$$649$$ −36.0000 + 20.7846i −1.41312 + 0.815867i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 16.0000 0.626608
$$653$$ 36.0000 20.7846i 1.40879 0.813365i 0.413517 0.910496i $$-0.364300\pi$$
0.995272 + 0.0971316i $$0.0309668\pi$$
$$654$$ −3.00000 + 5.19615i −0.117309 + 0.203186i
$$655$$ −6.00000 + 10.3923i −0.234439 + 0.406061i
$$656$$ 15.0000 + 25.9808i 0.585652 + 1.01438i
$$657$$ 20.7846i 0.810885i
$$658$$ 0 0
$$659$$ 10.3923i 0.404827i −0.979300 0.202413i $$-0.935122\pi$$
0.979300 0.202413i $$-0.0648785\pi$$
$$660$$ −3.00000 5.19615i −0.116775 0.202260i
$$661$$ −42.0000 24.2487i −1.63361 0.943166i −0.982967 0.183782i $$-0.941166\pi$$
−0.650644 0.759383i $$-0.725501\pi$$
$$662$$ 42.0000 + 24.2487i 1.63238 + 0.942453i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 10.3923i 0.402694i
$$667$$ −12.0000 20.7846i −0.464642 0.804783i
$$668$$ 6.00000 10.3923i 0.232147 0.402090i
$$669$$ −15.0000 + 25.9808i −0.579934 + 1.00447i
$$670$$ 12.0000 6.92820i 0.463600 0.267660i
$$671$$ −24.0000 −0.926510
$$672$$ 0 0
$$673$$ −14.0000 −0.539660 −0.269830 0.962908i $$-0.586968\pi$$
−0.269830 + 0.962908i $$0.586968\pi$$
$$674$$ 21.0000 12.1244i 0.808890 0.467013i
$$675$$ −4.50000 2.59808i −0.173205 0.100000i
$$676$$ 6.50000 11.2583i 0.250000 0.433013i
$$677$$ 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i $$-0.129884\pi$$
−0.802600 + 0.596518i $$0.796551\pi$$
$$678$$ 20.7846i 0.798228i
$$679$$ 0 0
$$680$$ 10.3923i 0.398527i
$$681$$ 36.0000 20.7846i 1.37952 0.796468i
$$682$$ −18.0000 10.3923i −0.689256 0.397942i
$$683$$ −15.0000 8.66025i −0.573959 0.331375i 0.184770 0.982782i $$-0.440846\pi$$
−0.758729 + 0.651406i $$0.774179\pi$$
$$684$$ −9.00000 + 5.19615i −0.344124 + 0.198680i
$$685$$ 20.7846i 0.794139i
$$686$$ 0 0
$$687$$ 12.0000 0.457829
$$688$$ −20.0000 34.6410i −0.762493 1.32068i
$$689$$ 0 0
$$690$$ 9.00000 + 5.19615i 0.342624 + 0.197814i
$$691$$ −27.0000 + 15.5885i −1.02713 + 0.593013i −0.916161 0.400811i $$-0.868728\pi$$
−0.110968 + 0.993824i $$0.535395\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ 30.0000 1.13878
$$695$$ 15.0000 8.66025i 0.568982 0.328502i
$$696$$ 18.0000 + 10.3923i 0.682288 + 0.393919i
$$697$$ −18.0000 + 31.1769i −0.681799 + 1.18091i
$$698$$ 6.00000 + 10.3923i 0.227103 + 0.393355i
$$699$$ −12.0000 −0.453882
$$700$$ 0 0
$$701$$ 20.7846i 0.785024i 0.919747 + 0.392512i $$0.128394\pi$$
−0.919747 + 0.392512i $$0.871606\pi$$
$$702$$ 0 0
$$703$$ −6.00000 3.46410i −0.226294 0.130651i
$$704$$ 3.00000 + 1.73205i 0.113067 + 0.0652791i
$$705$$ −18.0000 + 10.3923i −0.677919 + 0.391397i
$$706$$ 10.3923i 0.391120i
$$707$$ 0 0
$$708$$ 20.7846i 0.781133i
$$709$$ −11.0000 19.0526i −0.413114 0.715534i 0.582115 0.813107i $$-0.302225\pi$$
−0.995228 + 0.0975728i $$0.968892\pi$$
$$710$$ −3.00000 + 5.19615i −0.112588 + 0.195008i
$$711$$ 12.0000 20.7846i 0.450035 0.779484i
$$712$$ −9.00000 + 5.19615i −0.337289 + 0.194734i
$$713$$ 12.0000 0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 9.00000 5.19615i 0.336346 0.194189i
$$717$$ −9.00000 + 15.5885i −0.336111 + 0.582162i
$$718$$ 3.00000 5.19615i 0.111959 0.193919i
$$719$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$720$$ −15.0000 −0.559017
$$721$$ 0 0
$$722$$ 12.1244i 0.451222i
$$723$$ 0 0
$$724$$ 18.0000 + 10.3923i 0.668965 + 0.386227i
$$725$$ −6.00000 3.46410i −0.222834 0.128654i
$$726$$ −1.50000 2.59808i −0.0556702 0.0964237i
$$727$$ 3.46410i 0.128476i 0.997935 + 0.0642382i $$0.0204617\pi$$
−0.997935 + 0.0642382i $$0.979538\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ −6.00000 10.3923i −0.222070 0.384636i
$$731$$ 24.0000 41.5692i 0.887672 1.53749i
$$732$$ 6.00000 10.3923i 0.221766 0.384111i
$$733$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$734$$ −18.0000 −0.664392
$$735$$ 0 0
$$736$$ 18.0000 0.663489
$$737$$ 24.0000 13.8564i 0.884051 0.510407i
$$738$$ −27.0000 15.5885i −0.993884 0.573819i
$$739$$ 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i $$-0.809894\pi$$
0.900464 + 0.434930i $$0.143227\pi$$
$$740$$ 1.00000 + 1.73205i 0.0367607 + 0.0636715i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 31.1769i 1.14377i −0.820334 0.571885i $$-0.806212\pi$$
0.820334 0.571885i $$-0.193788\pi$$
$$744$$ −9.00000 + 5.19615i −0.329956 + 0.190500i
$$745$$ −6.00000 3.46410i −0.219823 0.126915i
$$746$$ 21.0000 + 12.1244i 0.768865 + 0.443904i
$$747$$ 0 0
$$748$$ 20.7846i 0.759961i
$$749$$ 0 0
$$750$$ 3.00000 0.109545
$$751$$ −8.00000 13.8564i −0.291924 0.505627i 0.682341 0.731034i $$-0.260962\pi$$
−0.974265 + 0.225407i $$0.927629\pi$$
$$752$$ −30.0000 + 51.9615i −1.09399 + 1.89484i
$$753$$ 18.0000 + 10.3923i 0.655956 + 0.378717i
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ −6.00000 + 3.46410i −0.217930 + 0.125822i
$$759$$ 18.0000 + 10.3923i 0.653359 + 0.377217i
$$760$$ −3.00000 + 5.19615i −0.108821 + 0.188484i
$$761$$ 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i $$0.108747\pi$$
−0.180957 + 0.983491i $$0.557920\pi$$
$$762$$ 12.0000 0.434714
$$763$$ 0 0
$$764$$ 10.3923i 0.375980i
$$765$$ −9.00000 15.5885i −0.325396 0.563602i
$$766$$ 18.0000 + 10.3923i 0.650366 + 0.375489i
$$767$$ 0 0
$$768$$ −28.5000 + 16.4545i −1.02841 + 0.593750i
$$769$$ 41.5692i 1.49902i 0.661991 + 0.749512i $$0.269712\pi$$
−0.661991 + 0.749512i $$0.730288\pi$$
$$770$$ 0 0
$$771$$ 10.3923i 0.374270i
$$772$$ −7.00000 12.1244i −0.251936 0.436365i
$$773$$ 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i $$-0.798920\pi$$
0.914920 + 0.403634i $$0.132253\pi$$
$$774$$ 36.0000 + 20.7846i 1.29399 + 0.747087i
$$775$$ 3.00000 1.73205i 0.107763 0.0622171i
$$776$$ −12.0000 −0.430775
$$777$$ 0 0
$$778$$ −12.0000 −0.430221
$$779$$ −18.0000 + 10.3923i −0.644917 + 0.372343i
$$780$$ 0 0
$$781$$ −6.00000 + 10.3923i −0.214697 + 0.371866i
$$782$$ 18.0000 + 31.1769i 0.643679 + 1.11488i
$$783$$ −36.0000 −1.28654
$$784$$ 0 0
$$785$$ 13.8564i 0.494556i
$$786$$ −18.0000 31.1769i −0.642039 1.11204i
$$787$$ −21.0000 12.1244i −0.748569 0.432187i 0.0766075 0.997061i $$-0.475591\pi$$
−0.825177 + 0.564875i $$0.808924\pi$$
$$788$$ 12.0000 + 6.92820i 0.427482 + 0.246807i
$$789$$ −21.0000 36.3731i −0.747620 1.29492i
$$790$$ 13.8564i 0.492989i
$$791$$ 0 0
$$792$$ −18.0000 −0.639602
$$793$$ 0 0
$$794$$ 12.0000 20.7846i 0.425864 0.737618i
$$795$$ 0 0
$$796$$ 9.00000 5.19615i 0.318997 0.184173i