# Properties

 Label 450.2.e.f.301.1 Level $450$ Weight $2$ Character 450.301 Analytic conductor $3.593$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$450 = 2 \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 450.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.59326809096$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 301.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 450.301 Dual form 450.2.e.f.151.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(-1.50000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -7.00000 q^{19} +(-3.00000 + 1.73205i) q^{21} -1.73205i q^{24} -4.00000 q^{26} -5.19615i q^{27} -2.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(5.00000 - 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(-3.50000 - 6.06218i) q^{38} +(-6.00000 - 3.46410i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(-3.00000 - 1.73205i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +10.3923i q^{51} +(-2.00000 - 3.46410i) q^{52} +12.0000 q^{53} +(4.50000 - 2.59808i) q^{54} +(-1.00000 - 1.73205i) q^{56} -12.1244i q^{57} +(-3.00000 + 5.19615i) q^{58} +(4.50000 - 7.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +10.0000 q^{62} +(-3.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-6.50000 + 11.2583i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{71} +3.00000 q^{72} +1.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(3.50000 - 6.06218i) q^{76} -6.92820i q^{78} +(-1.00000 - 1.73205i) q^{79} +9.00000 q^{81} -9.00000 q^{82} +(4.50000 + 7.79423i) q^{83} -3.46410i q^{84} +(0.500000 - 0.866025i) q^{86} +(-9.00000 + 5.19615i) q^{87} +15.0000 q^{89} -8.00000 q^{91} +(15.0000 + 8.66025i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(1.50000 + 0.866025i) q^{96} +(8.50000 + 14.7224i) q^{97} +3.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} - 3q^{6} + 2q^{7} - 2q^{8} - 6q^{9} + O(q^{10})$$ $$2q + q^{2} - q^{4} - 3q^{6} + 2q^{7} - 2q^{8} - 6q^{9} - 3q^{12} - 4q^{13} - 2q^{14} - q^{16} + 12q^{17} - 3q^{18} - 14q^{19} - 6q^{21} - 8q^{26} - 4q^{28} + 6q^{29} + 10q^{31} + q^{32} + 6q^{34} + 3q^{36} - 4q^{37} - 7q^{38} - 12q^{39} - 9q^{41} - 6q^{42} - q^{43} + 6q^{47} + 3q^{48} + 3q^{49} - 4q^{52} + 24q^{53} + 9q^{54} - 2q^{56} - 6q^{58} + 9q^{59} + 4q^{61} + 20q^{62} - 6q^{63} + 2q^{64} - 13q^{67} - 6q^{68} + 12q^{71} + 6q^{72} + 2q^{73} - 2q^{74} + 7q^{76} - 2q^{79} + 18q^{81} - 18q^{82} + 9q^{83} + q^{86} - 18q^{87} + 30q^{89} - 16q^{91} + 30q^{93} - 6q^{94} + 3q^{96} + 17q^{97} + 6q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 1.73205i 1.00000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ −1.50000 + 0.866025i −0.612372 + 0.353553i
$$7$$ 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i $$-0.0432908\pi$$
−0.612801 + 0.790237i $$0.709957\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −3.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$12$$ −1.50000 0.866025i −0.433013 0.250000i
$$13$$ −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i $$0.353834\pi$$
−0.997927 + 0.0643593i $$0.979500\pi$$
$$14$$ −1.00000 + 1.73205i −0.267261 + 0.462910i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ −1.50000 2.59808i −0.353553 0.612372i
$$19$$ −7.00000 −1.60591 −0.802955 0.596040i $$-0.796740\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ −3.00000 + 1.73205i −0.654654 + 0.377964i
$$22$$ 0 0
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 1.73205i 0.353553i
$$25$$ 0 0
$$26$$ −4.00000 −0.784465
$$27$$ 5.19615i 1.00000i
$$28$$ −2.00000 −0.377964
$$29$$ 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i $$0.0214140\pi$$
−0.440652 + 0.897678i $$0.645253\pi$$
$$30$$ 0 0
$$31$$ 5.00000 8.66025i 0.898027 1.55543i 0.0680129 0.997684i $$-0.478334\pi$$
0.830014 0.557743i $$-0.188333\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 3.00000 + 5.19615i 0.514496 + 0.891133i
$$35$$ 0 0
$$36$$ 1.50000 2.59808i 0.250000 0.433013i
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −3.50000 6.06218i −0.567775 0.983415i
$$39$$ −6.00000 3.46410i −0.960769 0.554700i
$$40$$ 0 0
$$41$$ −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i $$0.414726\pi$$
−0.967486 + 0.252924i $$0.918608\pi$$
$$42$$ −3.00000 1.73205i −0.462910 0.267261i
$$43$$ −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i $$-0.190961\pi$$
−0.901629 + 0.432511i $$0.857628\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 1.50000 0.866025i 0.216506 0.125000i
$$49$$ 1.50000 2.59808i 0.214286 0.371154i
$$50$$ 0 0
$$51$$ 10.3923i 1.45521i
$$52$$ −2.00000 3.46410i −0.277350 0.480384i
$$53$$ 12.0000 1.64833 0.824163 0.566352i $$-0.191646\pi$$
0.824163 + 0.566352i $$0.191646\pi$$
$$54$$ 4.50000 2.59808i 0.612372 0.353553i
$$55$$ 0 0
$$56$$ −1.00000 1.73205i −0.133631 0.231455i
$$57$$ 12.1244i 1.60591i
$$58$$ −3.00000 + 5.19615i −0.393919 + 0.682288i
$$59$$ 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i $$-0.634094\pi$$
0.994769 0.102151i $$-0.0325726\pi$$
$$60$$ 0 0
$$61$$ 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i $$-0.0842377\pi$$
−0.709113 + 0.705095i $$0.750904\pi$$
$$62$$ 10.0000 1.27000
$$63$$ −3.00000 5.19615i −0.377964 0.654654i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i $$0.458725\pi$$
−0.923408 + 0.383819i $$0.874609\pi$$
$$68$$ −3.00000 + 5.19615i −0.363803 + 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 3.00000 0.353553
$$73$$ 1.00000 0.117041 0.0585206 0.998286i $$-0.481362\pi$$
0.0585206 + 0.998286i $$0.481362\pi$$
$$74$$ −1.00000 1.73205i −0.116248 0.201347i
$$75$$ 0 0
$$76$$ 3.50000 6.06218i 0.401478 0.695379i
$$77$$ 0 0
$$78$$ 6.92820i 0.784465i
$$79$$ −1.00000 1.73205i −0.112509 0.194871i 0.804272 0.594261i $$-0.202555\pi$$
−0.916781 + 0.399390i $$0.869222\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ −9.00000 −0.993884
$$83$$ 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i $$-0.00222321\pi$$
−0.506036 + 0.862512i $$0.668890\pi$$
$$84$$ 3.46410i 0.377964i
$$85$$ 0 0
$$86$$ 0.500000 0.866025i 0.0539164 0.0933859i
$$87$$ −9.00000 + 5.19615i −0.964901 + 0.557086i
$$88$$ 0 0
$$89$$ 15.0000 1.59000 0.794998 0.606612i $$-0.207472\pi$$
0.794998 + 0.606612i $$0.207472\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ 15.0000 + 8.66025i 1.55543 + 0.898027i
$$94$$ −3.00000 + 5.19615i −0.309426 + 0.535942i
$$95$$ 0 0
$$96$$ 1.50000 + 0.866025i 0.153093 + 0.0883883i
$$97$$ 8.50000 + 14.7224i 0.863044 + 1.49484i 0.868976 + 0.494854i $$0.164778\pi$$
−0.00593185 + 0.999982i $$0.501888\pi$$
$$98$$ 3.00000 0.303046
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i $$-0.963017\pi$$
0.396236 0.918149i $$-0.370316\pi$$
$$102$$ −9.00000 + 5.19615i −0.891133 + 0.514496i
$$103$$ 1.00000 1.73205i 0.0985329 0.170664i −0.812545 0.582899i $$-0.801918\pi$$
0.911078 + 0.412235i $$0.135252\pi$$
$$104$$ 2.00000 3.46410i 0.196116 0.339683i
$$105$$ 0 0
$$106$$ 6.00000 + 10.3923i 0.582772 + 1.00939i
$$107$$ −9.00000 −0.870063 −0.435031 0.900415i $$-0.643263\pi$$
−0.435031 + 0.900415i $$0.643263\pi$$
$$108$$ 4.50000 + 2.59808i 0.433013 + 0.250000i
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ 3.46410i 0.328798i
$$112$$ 1.00000 1.73205i 0.0944911 0.163663i
$$113$$ 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i $$-0.788267\pi$$
0.927914 + 0.372794i $$0.121600\pi$$
$$114$$ 10.5000 6.06218i 0.983415 0.567775i
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ 6.00000 10.3923i 0.554700 0.960769i
$$118$$ 9.00000 0.828517
$$119$$ 6.00000 + 10.3923i 0.550019 + 0.952661i
$$120$$ 0 0
$$121$$ 5.50000 9.52628i 0.500000 0.866025i
$$122$$ −2.00000 + 3.46410i −0.181071 + 0.313625i
$$123$$ −13.5000 7.79423i −1.21725 0.702782i
$$124$$ 5.00000 + 8.66025i 0.449013 + 0.777714i
$$125$$ 0 0
$$126$$ 3.00000 5.19615i 0.267261 0.462910i
$$127$$ −20.0000 −1.77471 −0.887357 0.461084i $$-0.847461\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 1.50000 0.866025i 0.132068 0.0762493i
$$130$$ 0 0
$$131$$ 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i $$-0.657689\pi$$
0.999602 0.0281993i $$-0.00897729\pi$$
$$132$$ 0 0
$$133$$ −7.00000 12.1244i −0.606977 1.05131i
$$134$$ −13.0000 −1.12303
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i $$-0.207572\pi$$
−0.922961 + 0.384893i $$0.874238\pi$$
$$138$$ 0 0
$$139$$ 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i $$-0.779074\pi$$
0.938293 + 0.345843i $$0.112407\pi$$
$$140$$ 0 0
$$141$$ −9.00000 + 5.19615i −0.757937 + 0.437595i
$$142$$ 3.00000 + 5.19615i 0.251754 + 0.436051i
$$143$$ 0 0
$$144$$ 1.50000 + 2.59808i 0.125000 + 0.216506i
$$145$$ 0 0
$$146$$ 0.500000 + 0.866025i 0.0413803 + 0.0716728i
$$147$$ 4.50000 + 2.59808i 0.371154 + 0.214286i
$$148$$ 1.00000 1.73205i 0.0821995 0.142374i
$$149$$ 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i $$-0.754293\pi$$
0.962348 + 0.271821i $$0.0876260\pi$$
$$150$$ 0 0
$$151$$ 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i $$-0.114628\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ 7.00000 0.567775
$$153$$ −18.0000 −1.45521
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 6.00000 3.46410i 0.480384 0.277350i
$$157$$ 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i $$-0.644649\pi$$
0.997609 0.0691164i $$-0.0220180\pi$$
$$158$$ 1.00000 1.73205i 0.0795557 0.137795i
$$159$$ 20.7846i 1.64833i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 4.50000 + 7.79423i 0.353553 + 0.612372i
$$163$$ 7.00000 0.548282 0.274141 0.961689i $$-0.411606\pi$$
0.274141 + 0.961689i $$0.411606\pi$$
$$164$$ −4.50000 7.79423i −0.351391 0.608627i
$$165$$ 0 0
$$166$$ −4.50000 + 7.79423i −0.349268 + 0.604949i
$$167$$ 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i $$-0.679641\pi$$
0.999169 + 0.0407502i $$0.0129748\pi$$
$$168$$ 3.00000 1.73205i 0.231455 0.133631i
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ 0 0
$$171$$ 21.0000 1.60591
$$172$$ 1.00000 0.0762493
$$173$$ −6.00000 10.3923i −0.456172 0.790112i 0.542583 0.840002i $$-0.317446\pi$$
−0.998755 + 0.0498898i $$0.984113\pi$$
$$174$$ −9.00000 5.19615i −0.682288 0.393919i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 13.5000 + 7.79423i 1.01472 + 0.585850i
$$178$$ 7.50000 + 12.9904i 0.562149 + 0.973670i
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ −4.00000 6.92820i −0.296500 0.513553i
$$183$$ −6.00000 + 3.46410i −0.443533 + 0.256074i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 17.3205i 1.27000i
$$187$$ 0 0
$$188$$ −6.00000 −0.437595
$$189$$ 9.00000 5.19615i 0.654654 0.377964i
$$190$$ 0 0
$$191$$ −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i $$-0.236317\pi$$
−0.953912 + 0.300088i $$0.902984\pi$$
$$192$$ 1.73205i 0.125000i
$$193$$ 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i $$-0.810401\pi$$
0.899770 + 0.436365i $$0.143734\pi$$
$$194$$ −8.50000 + 14.7224i −0.610264 + 1.05701i
$$195$$ 0 0
$$196$$ 1.50000 + 2.59808i 0.107143 + 0.185577i
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ −19.5000 11.2583i −1.37542 0.794101i
$$202$$ 6.00000 10.3923i 0.422159 0.731200i
$$203$$ −6.00000 + 10.3923i −0.421117 + 0.729397i
$$204$$ −9.00000 5.19615i −0.630126 0.363803i
$$205$$ 0 0
$$206$$ 2.00000 0.139347
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −2.50000 + 4.33013i −0.172107 + 0.298098i −0.939156 0.343490i $$-0.888391\pi$$
0.767049 + 0.641588i $$0.221724\pi$$
$$212$$ −6.00000 + 10.3923i −0.412082 + 0.713746i
$$213$$ 10.3923i 0.712069i
$$214$$ −4.50000 7.79423i −0.307614 0.532803i
$$215$$ 0 0
$$216$$ 5.19615i 0.353553i
$$217$$ 20.0000 1.35769
$$218$$ 1.00000 + 1.73205i 0.0677285 + 0.117309i
$$219$$ 1.73205i 0.117041i
$$220$$ 0 0
$$221$$ −12.0000 + 20.7846i −0.807207 + 1.39812i
$$222$$ 3.00000 1.73205i 0.201347 0.116248i
$$223$$ −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i $$-0.986707\pi$$
0.463409 0.886145i $$-0.346626\pi$$
$$224$$ 2.00000 0.133631
$$225$$ 0 0
$$226$$ 3.00000 0.199557
$$227$$ −7.50000 12.9904i −0.497792 0.862202i 0.502204 0.864749i $$-0.332523\pi$$
−0.999997 + 0.00254715i $$0.999189\pi$$
$$228$$ 10.5000 + 6.06218i 0.695379 + 0.401478i
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −3.00000 5.19615i −0.196960 0.341144i
$$233$$ −3.00000 −0.196537 −0.0982683 0.995160i $$-0.531330\pi$$
−0.0982683 + 0.995160i $$0.531330\pi$$
$$234$$ 12.0000 0.784465
$$235$$ 0 0
$$236$$ 4.50000 + 7.79423i 0.292925 + 0.507361i
$$237$$ 3.00000 1.73205i 0.194871 0.112509i
$$238$$ −6.00000 + 10.3923i −0.388922 + 0.673633i
$$239$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$240$$ 0 0
$$241$$ 9.50000 + 16.4545i 0.611949 + 1.05993i 0.990912 + 0.134515i $$0.0429475\pi$$
−0.378963 + 0.925412i $$0.623719\pi$$
$$242$$ 11.0000 0.707107
$$243$$ 15.5885i 1.00000i
$$244$$ −4.00000 −0.256074
$$245$$ 0 0
$$246$$ 15.5885i 0.993884i
$$247$$ 14.0000 24.2487i 0.890799 1.54291i
$$248$$ −5.00000 + 8.66025i −0.317500 + 0.549927i
$$249$$ −13.5000 + 7.79423i −0.855528 + 0.493939i
$$250$$ 0 0
$$251$$ 15.0000 0.946792 0.473396 0.880850i $$-0.343028\pi$$
0.473396 + 0.880850i $$0.343028\pi$$
$$252$$ 6.00000 0.377964
$$253$$ 0 0
$$254$$ −10.0000 17.3205i −0.627456 1.08679i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i $$-0.803506\pi$$
0.909010 + 0.416775i $$0.136840\pi$$
$$258$$ 1.50000 + 0.866025i 0.0933859 + 0.0539164i
$$259$$ −2.00000 3.46410i −0.124274 0.215249i
$$260$$ 0 0
$$261$$ −9.00000 15.5885i −0.557086 0.964901i
$$262$$ 12.0000 0.741362
$$263$$ −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i $$-0.225891\pi$$
−0.943572 + 0.331166i $$0.892558\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 7.00000 12.1244i 0.429198 0.743392i
$$267$$ 25.9808i 1.59000i
$$268$$ −6.50000 11.2583i −0.397051 0.687712i
$$269$$ −30.0000 −1.82913 −0.914566 0.404436i $$-0.867468\pi$$
−0.914566 + 0.404436i $$0.867468\pi$$
$$270$$ 0 0
$$271$$ −28.0000 −1.70088 −0.850439 0.526073i $$-0.823664\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ −3.00000 5.19615i −0.181902 0.315063i
$$273$$ 13.8564i 0.838628i
$$274$$ 1.50000 2.59808i 0.0906183 0.156956i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i $$-0.147530\pi$$
−0.834419 + 0.551131i $$0.814196\pi$$
$$278$$ 4.00000 0.239904
$$279$$ −15.0000 + 25.9808i −0.898027 + 1.55543i
$$280$$ 0 0
$$281$$ 9.00000 + 15.5885i 0.536895 + 0.929929i 0.999069 + 0.0431402i $$0.0137362\pi$$
−0.462174 + 0.886789i $$0.652930\pi$$
$$282$$ −9.00000 5.19615i −0.535942 0.309426i
$$283$$ −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i $$0.357681\pi$$
−0.997076 + 0.0764162i $$0.975652\pi$$
$$284$$ −3.00000 + 5.19615i −0.178017 + 0.308335i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −18.0000 −1.06251
$$288$$ −1.50000 + 2.59808i −0.0883883 + 0.153093i
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −25.5000 + 14.7224i −1.49484 + 0.863044i
$$292$$ −0.500000 + 0.866025i −0.0292603 + 0.0506803i
$$293$$ 6.00000 10.3923i 0.350524 0.607125i −0.635818 0.771839i $$-0.719337\pi$$
0.986341 + 0.164714i $$0.0526703\pi$$
$$294$$ 5.19615i 0.303046i
$$295$$ 0 0
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 1.00000 1.73205i 0.0576390 0.0998337i
$$302$$ −2.00000 + 3.46410i −0.115087 + 0.199337i
$$303$$ 18.0000 10.3923i 1.03407 0.597022i
$$304$$ 3.50000 + 6.06218i 0.200739 + 0.347690i
$$305$$ 0 0
$$306$$ −9.00000 15.5885i −0.514496 0.891133i
$$307$$ −8.00000 −0.456584 −0.228292 0.973593i $$-0.573314\pi$$
−0.228292 + 0.973593i $$0.573314\pi$$
$$308$$ 0 0
$$309$$ 3.00000 + 1.73205i 0.170664 + 0.0985329i
$$310$$ 0 0
$$311$$ 15.0000 25.9808i 0.850572 1.47323i −0.0301210 0.999546i $$-0.509589\pi$$
0.880693 0.473688i $$-0.157077\pi$$
$$312$$ 6.00000 + 3.46410i 0.339683 + 0.196116i
$$313$$ −9.50000 16.4545i −0.536972 0.930062i −0.999065 0.0432311i $$-0.986235\pi$$
0.462093 0.886831i $$-0.347098\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ 2.00000 0.112509
$$317$$ 15.0000 + 25.9808i 0.842484 + 1.45922i 0.887788 + 0.460252i $$0.152241\pi$$
−0.0453045 + 0.998973i $$0.514426\pi$$
$$318$$ −18.0000 + 10.3923i −1.00939 + 0.582772i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 15.5885i 0.870063i
$$322$$ 0 0
$$323$$ −42.0000 −2.33694
$$324$$ −4.50000 + 7.79423i −0.250000 + 0.433013i
$$325$$ 0 0
$$326$$ 3.50000 + 6.06218i 0.193847 + 0.335753i
$$327$$ 3.46410i 0.191565i
$$328$$ 4.50000 7.79423i 0.248471 0.430364i
$$329$$ −6.00000 + 10.3923i −0.330791 + 0.572946i
$$330$$ 0 0
$$331$$ −5.50000 9.52628i −0.302307 0.523612i 0.674351 0.738411i $$-0.264424\pi$$
−0.976658 + 0.214799i $$0.931090\pi$$
$$332$$ −9.00000 −0.493939
$$333$$ 6.00000 0.328798
$$334$$ 12.0000 0.656611
$$335$$ 0 0
$$336$$ 3.00000 + 1.73205i 0.163663 + 0.0944911i
$$337$$ 7.00000 12.1244i 0.381314 0.660456i −0.609936 0.792451i $$-0.708805\pi$$
0.991250 + 0.131995i $$0.0421382\pi$$
$$338$$ 1.50000 2.59808i 0.0815892 0.141317i
$$339$$ 4.50000 + 2.59808i 0.244406 + 0.141108i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 10.5000 + 18.1865i 0.567775 + 0.983415i
$$343$$ 20.0000 1.07990
$$344$$ 0.500000 + 0.866025i 0.0269582 + 0.0466930i
$$345$$ 0 0
$$346$$ 6.00000 10.3923i 0.322562 0.558694i
$$347$$ −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i $$-0.937721\pi$$
0.658824 + 0.752297i $$0.271054\pi$$
$$348$$ 10.3923i 0.557086i
$$349$$ 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i $$-0.0804216\pi$$
−0.700609 + 0.713545i $$0.747088\pi$$
$$350$$ 0 0
$$351$$ 18.0000 + 10.3923i 0.960769 + 0.554700i
$$352$$ 0 0
$$353$$ 7.50000 + 12.9904i 0.399185 + 0.691408i 0.993626 0.112731i $$-0.0359599\pi$$
−0.594441 + 0.804139i $$0.702627\pi$$
$$354$$ 15.5885i 0.828517i
$$355$$ 0 0
$$356$$ −7.50000 + 12.9904i −0.397499 + 0.688489i
$$357$$ −18.0000 + 10.3923i −0.952661 + 0.550019i
$$358$$ −4.50000 7.79423i −0.237832 0.411938i
$$359$$ 12.0000 0.633336 0.316668 0.948536i $$-0.397436\pi$$
0.316668 + 0.948536i $$0.397436\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ −8.00000 13.8564i −0.420471 0.728277i
$$363$$ 16.5000 + 9.52628i 0.866025 + 0.500000i
$$364$$ 4.00000 6.92820i 0.209657 0.363137i
$$365$$ 0 0
$$366$$ −6.00000 3.46410i −0.313625 0.181071i
$$367$$ −5.00000 8.66025i −0.260998 0.452062i 0.705509 0.708700i $$-0.250718\pi$$
−0.966507 + 0.256639i $$0.917385\pi$$
$$368$$ 0 0
$$369$$ 13.5000 23.3827i 0.702782 1.21725i
$$370$$ 0 0
$$371$$ 12.0000 + 20.7846i 0.623009 + 1.07908i
$$372$$ −15.0000 + 8.66025i −0.777714 + 0.449013i
$$373$$ −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i $$-0.866355\pi$$
0.809591 + 0.586994i $$0.199689\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −3.00000 5.19615i −0.154713 0.267971i
$$377$$ −24.0000 −1.23606
$$378$$ 9.00000 + 5.19615i 0.462910 + 0.267261i
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ 34.6410i 1.77471i
$$382$$ 3.00000 5.19615i 0.153493 0.265858i
$$383$$ 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i $$-0.623227\pi$$
0.990702 0.136047i $$-0.0434398\pi$$
$$384$$ −1.50000 + 0.866025i −0.0765466 + 0.0441942i
$$385$$ 0 0
$$386$$ 2.00000 0.101797
$$387$$ 1.50000 + 2.59808i 0.0762493 + 0.132068i
$$388$$ −17.0000 −0.863044
$$389$$ −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i $$-0.215272\pi$$
−0.932002 + 0.362454i $$0.881939\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.50000 + 2.59808i −0.0757614 + 0.131223i
$$393$$ 18.0000 + 10.3923i 0.907980 + 0.524222i
$$394$$ −9.00000 15.5885i −0.453413 0.785335i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 22.0000 1.10415 0.552074 0.833795i $$-0.313837\pi$$
0.552074 + 0.833795i $$0.313837\pi$$
$$398$$ −8.00000 13.8564i −0.401004 0.694559i
$$399$$ 21.0000 12.1244i 1.05131 0.606977i
$$400$$ 0 0
$$401$$ −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i $$-0.981709\pi$$
0.548911 + 0.835881i $$0.315043\pi$$
$$402$$ 22.5167i 1.12303i
$$403$$ 20.0000 + 34.6410i 0.996271 + 1.72559i
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ −12.0000 −0.595550
$$407$$ 0 0
$$408$$ 10.3923i 0.514496i
$$409$$ 15.5000 26.8468i 0.766426 1.32749i −0.173064 0.984911i $$-0.555367\pi$$
0.939490 0.342578i $$-0.111300\pi$$
$$410$$ 0 0
$$411$$ 4.50000 2.59808i 0.221969 0.128154i
$$412$$ 1.00000 + 1.73205i 0.0492665 + 0.0853320i
$$413$$ 18.0000 0.885722
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 2.00000 + 3.46410i 0.0980581 + 0.169842i
$$417$$ 6.00000 + 3.46410i 0.293821 + 0.169638i
$$418$$ 0 0
$$419$$ −1.50000 + 2.59808i −0.0732798 + 0.126924i −0.900337 0.435194i $$-0.856680\pi$$
0.827057 + 0.562118i $$0.190013\pi$$
$$420$$ 0 0
$$421$$ 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i $$-0.0883103\pi$$
−0.718076 + 0.695965i $$0.754977\pi$$
$$422$$ −5.00000 −0.243396
$$423$$ −9.00000 15.5885i −0.437595 0.757937i
$$424$$ −12.0000 −0.582772
$$425$$ 0 0
$$426$$ −9.00000 + 5.19615i −0.436051 + 0.251754i
$$427$$ −4.00000 + 6.92820i −0.193574 + 0.335279i
$$428$$ 4.50000 7.79423i 0.217516 0.376748i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6.00000 0.289010 0.144505 0.989504i $$-0.453841\pi$$
0.144505 + 0.989504i $$0.453841\pi$$
$$432$$ −4.50000 + 2.59808i −0.216506 + 0.125000i
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 10.0000 + 17.3205i 0.480015 + 0.831411i
$$435$$ 0 0
$$436$$ −1.00000 + 1.73205i −0.0478913 + 0.0829502i
$$437$$ 0 0
$$438$$ −1.50000 + 0.866025i −0.0716728 + 0.0413803i
$$439$$ 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i $$-0.136236\pi$$
−0.814344 + 0.580383i $$0.802903\pi$$
$$440$$ 0 0
$$441$$ −4.50000 + 7.79423i −0.214286 + 0.371154i
$$442$$ −24.0000 −1.14156
$$443$$ 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i $$0.159903\pi$$
−0.0212481 + 0.999774i $$0.506764\pi$$
$$444$$ 3.00000 + 1.73205i 0.142374 + 0.0821995i
$$445$$ 0 0
$$446$$ 8.00000 13.8564i 0.378811 0.656120i
$$447$$ 9.00000 + 5.19615i 0.425685 + 0.245770i
$$448$$ 1.00000 + 1.73205i 0.0472456 + 0.0818317i
$$449$$ −15.0000 −0.707894 −0.353947 0.935266i $$-0.615161\pi$$
−0.353947 + 0.935266i $$0.615161\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 1.50000 + 2.59808i 0.0705541 + 0.122203i
$$453$$ −6.00000 + 3.46410i −0.281905 + 0.162758i
$$454$$ 7.50000 12.9904i 0.351992 0.609669i
$$455$$ 0 0
$$456$$ 12.1244i 0.567775i
$$457$$ −9.50000 16.4545i −0.444391 0.769708i 0.553618 0.832771i $$-0.313247\pi$$
−0.998010 + 0.0630623i $$0.979913\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 31.1769i 1.45521i
$$460$$ 0 0
$$461$$ −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i $$-0.211288\pi$$
−0.927392 + 0.374091i $$0.877955\pi$$
$$462$$ 0 0
$$463$$ 13.0000 22.5167i 0.604161 1.04644i −0.388022 0.921650i $$-0.626842\pi$$
0.992183 0.124788i $$-0.0398251\pi$$
$$464$$ 3.00000 5.19615i 0.139272 0.241225i
$$465$$ 0 0
$$466$$ −1.50000 2.59808i −0.0694862 0.120354i
$$467$$ 15.0000 0.694117 0.347059 0.937843i $$-0.387180\pi$$
0.347059 + 0.937843i $$0.387180\pi$$
$$468$$ 6.00000 + 10.3923i 0.277350 + 0.480384i
$$469$$ −26.0000 −1.20057
$$470$$ 0 0
$$471$$ 21.0000 + 12.1244i 0.967629 + 0.558661i
$$472$$ −4.50000 + 7.79423i −0.207129 + 0.358758i
$$473$$ 0 0
$$474$$ 3.00000 + 1.73205i 0.137795 + 0.0795557i
$$475$$ 0 0
$$476$$ −12.0000 −0.550019
$$477$$ −36.0000 −1.64833
$$478$$ 0 0
$$479$$ −18.0000 31.1769i −0.822441 1.42451i −0.903859 0.427830i $$-0.859278\pi$$
0.0814184 0.996680i $$-0.474055\pi$$
$$480$$ 0 0
$$481$$ 4.00000 6.92820i 0.182384 0.315899i
$$482$$ −9.50000 + 16.4545i −0.432713 + 0.749481i
$$483$$ 0 0
$$484$$ 5.50000 + 9.52628i 0.250000 + 0.433013i
$$485$$ 0 0
$$486$$ −13.5000 + 7.79423i −0.612372 + 0.353553i
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ −2.00000 3.46410i −0.0905357 0.156813i
$$489$$ 12.1244i 0.548282i
$$490$$ 0 0
$$491$$ 1.50000 2.59808i 0.0676941 0.117250i −0.830192 0.557478i $$-0.811769\pi$$
0.897886 + 0.440228i $$0.145102\pi$$
$$492$$ 13.5000 7.79423i 0.608627 0.351391i
$$493$$ 18.0000 + 31.1769i 0.810679 + 1.40414i
$$494$$ 28.0000 1.25978
$$495$$ 0 0
$$496$$ −10.0000 −0.449013
$$497$$ 6.00000 + 10.3923i 0.269137 + 0.466159i
$$498$$ −13.5000 7.79423i −0.604949 0.349268i
$$499$$ −5.50000 + 9.52628i −0.246214 + 0.426455i −0.962472 0.271380i $$-0.912520\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ 0 0
$$501$$ 18.0000 + 10.3923i 0.804181 + 0.464294i
$$502$$ 7.50000 + 12.9904i 0.334741 + 0.579789i
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 3.00000 + 5.19615i 0.133631 + 0.231455i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 4.50000 2.59808i 0.199852 0.115385i
$$508$$ 10.0000 17.3205i 0.443678 0.768473i
$$509$$ 18.0000 31.1769i 0.797836 1.38189i −0.123187 0.992384i $$-0.539311\pi$$
0.921023 0.389509i $$-0.127355\pi$$
$$510$$ 0 0
$$511$$ 1.00000 + 1.73205i 0.0442374 + 0.0766214i
$$512$$ −1.00000 −0.0441942
$$513$$ 36.3731i 1.60591i
$$514$$ 3.00000 0.132324
$$515$$ 0 0
$$516$$ 1.73205i 0.0762493i
$$517$$ 0 0
$$518$$ 2.00000 3.46410i 0.0878750 0.152204i
$$519$$ 18.0000 10.3923i 0.790112 0.456172i
$$520$$ 0 0
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ 9.00000 15.5885i 0.393919 0.682288i
$$523$$ 1.00000 0.0437269 0.0218635 0.999761i $$-0.493040\pi$$
0.0218635 + 0.999761i $$0.493040\pi$$
$$524$$ 6.00000 + 10.3923i 0.262111 + 0.453990i
$$525$$ 0 0
$$526$$ 3.00000 5.19615i 0.130806 0.226563i
$$527$$ 30.0000 51.9615i 1.30682 2.26348i
$$528$$ 0 0
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ −13.5000 + 23.3827i −0.585850 + 1.01472i
$$532$$ 14.0000 0.606977
$$533$$ −18.0000 31.1769i −0.779667 1.35042i
$$534$$ −22.5000 + 12.9904i −0.973670 + 0.562149i
$$535$$ 0 0
$$536$$ 6.50000 11.2583i 0.280757 0.486286i
$$537$$ 15.5885i 0.672692i
$$538$$ −15.0000 25.9808i −0.646696 1.12011i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 32.0000 1.37579 0.687894 0.725811i $$-0.258536\pi$$
0.687894 + 0.725811i $$0.258536\pi$$
$$542$$ −14.0000 24.2487i −0.601351 1.04157i
$$543$$ 27.7128i 1.18927i
$$544$$ 3.00000 5.19615i 0.128624 0.222783i
$$545$$ 0 0
$$546$$ 12.0000 6.92820i 0.513553 0.296500i
$$547$$ 2.50000 + 4.33013i 0.106892 + 0.185143i 0.914510 0.404564i $$-0.132577\pi$$
−0.807617 + 0.589707i $$0.799243\pi$$
$$548$$ 3.00000 0.128154
$$549$$ −6.00000 10.3923i −0.256074 0.443533i
$$550$$ 0 0
$$551$$ −21.0000 36.3731i −0.894630 1.54954i
$$552$$ 0 0
$$553$$ 2.00000 3.46410i 0.0850487 0.147309i
$$554$$ −1.00000 + 1.73205i −0.0424859 + 0.0735878i
$$555$$ 0 0
$$556$$ 2.00000 + 3.46410i 0.0848189 + 0.146911i
$$557$$ 12.0000 0.508456 0.254228 0.967144i $$-0.418179\pi$$
0.254228 + 0.967144i $$0.418179\pi$$
$$558$$ −30.0000 −1.27000
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −9.00000 + 15.5885i −0.379642 + 0.657559i
$$563$$ 4.50000 7.79423i 0.189652 0.328488i −0.755482 0.655169i $$-0.772597\pi$$
0.945134 + 0.326682i $$0.105931\pi$$
$$564$$ 10.3923i 0.437595i
$$565$$ 0 0
$$566$$ −19.0000 −0.798630
$$567$$ 9.00000 + 15.5885i 0.377964 + 0.654654i
$$568$$ −6.00000 −0.251754
$$569$$ 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i $$0.176036\pi$$
0.0294311 + 0.999567i $$0.490630\pi$$
$$570$$ 0 0
$$571$$ −17.5000 + 30.3109i −0.732352 + 1.26847i 0.223523 + 0.974699i $$0.428244\pi$$
−0.955875 + 0.293773i $$0.905089\pi$$
$$572$$ 0 0
$$573$$ 9.00000 5.19615i 0.375980 0.217072i
$$574$$ −9.00000 15.5885i −0.375653 0.650650i
$$575$$ 0 0
$$576$$ −3.00000 −0.125000
$$577$$ −35.0000 −1.45707 −0.728535 0.685009i $$-0.759798\pi$$
−0.728535 + 0.685009i $$0.759798\pi$$
$$578$$ 9.50000 + 16.4545i 0.395148 + 0.684416i
$$579$$ 3.00000 + 1.73205i 0.124676 + 0.0719816i
$$580$$ 0 0
$$581$$ −9.00000 + 15.5885i −0.373383 + 0.646718i
$$582$$ −25.5000 14.7224i −1.05701 0.610264i
$$583$$ 0 0
$$584$$ −1.00000 −0.0413803
$$585$$ 0 0
$$586$$ 12.0000 0.495715
$$587$$ 18.0000 + 31.1769i 0.742940 + 1.28681i 0.951151 + 0.308725i $$0.0999023\pi$$
−0.208212 + 0.978084i $$0.566764\pi$$
$$588$$ −4.50000 + 2.59808i −0.185577 + 0.107143i
$$589$$ −35.0000 + 60.6218i −1.44215 + 2.49788i
$$590$$ 0 0
$$591$$ 31.1769i 1.28245i
$$592$$ 1.00000 + 1.73205i 0.0410997 + 0.0711868i
$$593$$ 9.00000 0.369586 0.184793 0.982777i $$-0.440839\pi$$
0.184793 + 0.982777i $$0.440839\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 3.00000 + 5.19615i 0.122885 + 0.212843i
$$597$$ 27.7128i 1.13421i
$$598$$ 0 0
$$599$$ −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i $$0.376657\pi$$
−0.990752 + 0.135686i $$0.956676\pi$$
$$600$$ 0 0
$$601$$ 5.00000 + 8.66025i 0.203954 + 0.353259i 0.949799 0.312861i $$-0.101287\pi$$
−0.745845 + 0.666120i $$0.767954\pi$$
$$602$$ 2.00000 0.0815139
$$603$$ 19.5000 33.7750i 0.794101 1.37542i
$$604$$ −4.00000 −0.162758
$$605$$ 0 0
$$606$$ 18.0000 + 10.3923i 0.731200 + 0.422159i
$$607$$ −20.0000 + 34.6410i −0.811775 + 1.40604i 0.0998457 + 0.995003i $$0.468165\pi$$
−0.911621 + 0.411033i $$0.865168\pi$$
$$608$$ −3.50000 + 6.06218i −0.141944 + 0.245854i
$$609$$ −18.0000 10.3923i −0.729397 0.421117i
$$610$$ 0 0
$$611$$ −24.0000 −0.970936
$$612$$ 9.00000 15.5885i 0.363803 0.630126i
$$613$$ −44.0000 −1.77714 −0.888572 0.458738i $$-0.848302\pi$$
−0.888572 + 0.458738i $$0.848302\pi$$
$$614$$ −4.00000 6.92820i −0.161427 0.279600i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −4.50000 + 7.79423i −0.181163 + 0.313784i −0.942277 0.334835i $$-0.891320\pi$$
0.761114 + 0.648618i $$0.224653\pi$$
$$618$$ 3.46410i 0.139347i
$$619$$ −11.5000 19.9186i −0.462224 0.800595i 0.536847 0.843679i $$-0.319615\pi$$
−0.999071 + 0.0430838i $$0.986282\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 30.0000 1.20289
$$623$$ 15.0000 + 25.9808i 0.600962 + 1.04090i
$$624$$ 6.92820i 0.277350i
$$625$$ 0 0
$$626$$ 9.50000 16.4545i 0.379696 0.657653i
$$627$$ 0 0
$$628$$ 7.00000 + 12.1244i 0.279330 + 0.483814i
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 1.00000 + 1.73205i 0.0397779 + 0.0688973i
$$633$$ −7.50000 4.33013i −0.298098 0.172107i
$$634$$ −15.0000 + 25.9808i −0.595726 + 1.03183i
$$635$$ 0 0
$$636$$ −18.0000 10.3923i −0.713746 0.412082i
$$637$$ 6.00000 + 10.3923i 0.237729 + 0.411758i
$$638$$ 0 0
$$639$$ −18.0000 −0.712069
$$640$$ 0 0
$$641$$ −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i $$-0.940718\pi$$
0.330997 0.943632i $$-0.392615\pi$$
$$642$$ 13.5000 7.79423i 0.532803 0.307614i
$$643$$ −6.50000 + 11.2583i −0.256335 + 0.443985i −0.965257 0.261301i $$-0.915848\pi$$
0.708922 + 0.705287i $$0.249182\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −21.0000 36.3731i −0.826234 1.43108i
$$647$$ 48.0000 1.88707 0.943537 0.331266i $$-0.107476\pi$$
0.943537 + 0.331266i $$0.107476\pi$$
$$648$$ −9.00000 −0.353553
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 34.6410i 1.35769i
$$652$$ −3.50000 + 6.06218i −0.137071 + 0.237413i
$$653$$ −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i $$0.415448\pi$$
−0.966910 + 0.255119i $$0.917885\pi$$
$$654$$ −3.00000 + 1.73205i −0.117309 + 0.0677285i
$$655$$ 0 0
$$656$$ 9.00000 0.351391
$$657$$ −3.00000 −0.117041
$$658$$ −12.0000 −0.467809
$$659$$ −16.5000 28.5788i −0.642749 1.11327i −0.984817 0.173598i $$-0.944461\pi$$
0.342068 0.939675i $$-0.388873\pi$$
$$660$$ 0 0
$$661$$ −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i $$-0.845717\pi$$
0.845922 + 0.533306i $$0.179051\pi$$
$$662$$ 5.50000 9.52628i 0.213764 0.370249i
$$663$$ −36.0000 20.7846i −1.39812 0.807207i
$$664$$ −4.50000 7.79423i −0.174634 0.302475i
$$665$$ 0 0
$$666$$ 3.00000 + 5.19615i 0.116248 + 0.201347i
$$667$$ 0 0
$$668$$ 6.00000 + 10.3923i 0.232147 + 0.402090i
$$669$$ 24.0000 13.8564i 0.927894 0.535720i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 3.46410i 0.133631i
$$673$$ 1.00000 + 1.73205i 0.0385472 + 0.0667657i 0.884655 0.466246i $$-0.154394\pi$$
−0.846108 + 0.533011i $$0.821060\pi$$
$$674$$ 14.0000 0.539260
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ −6.00000 10.3923i −0.230599 0.399409i 0.727386 0.686229i $$-0.240735\pi$$
−0.957984 + 0.286820i $$0.907402\pi$$
$$678$$ 5.19615i 0.199557i
$$679$$ −17.0000 + 29.4449i −0.652400 + 1.12999i
$$680$$ 0 0
$$681$$ 22.5000 12.9904i 0.862202 0.497792i
$$682$$ 0 0
$$683$$ 3.00000 0.114792 0.0573959 0.998351i $$-0.481720\pi$$
0.0573959 + 0.998351i $$0.481720\pi$$
$$684$$ −10.5000 + 18.1865i −0.401478 + 0.695379i
$$685$$ 0 0
$$686$$ 10.0000 + 17.3205i 0.381802 + 0.661300i
$$687$$ 15.0000 + 8.66025i 0.572286 + 0.330409i
$$688$$ −0.500000 + 0.866025i −0.0190623 + 0.0330169i
$$689$$ −24.0000 + 41.5692i −0.914327 + 1.58366i
$$690$$ 0 0
$$691$$ −17.5000 30.3109i −0.665731 1.15308i −0.979086 0.203445i $$-0.934786\pi$$
0.313355 0.949636i $$-0.398547\pi$$
$$692$$ 12.0000 0.456172
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 0 0
$$696$$ 9.00000 5.19615i 0.341144 0.196960i
$$697$$ −27.0000 + 46.7654i −1.02270 + 1.77136i
$$698$$ −5.00000 + 8.66025i −0.189253 + 0.327795i
$$699$$ 5.19615i 0.196537i
$$700$$ 0 0
$$701$$ −48.0000 −1.81293 −0.906467 0.422276i $$-0.861231\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ 20.7846i 0.784465i
$$703$$ 14.0000 0.528020
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −7.50000 + 12.9904i −0.282266 + 0.488899i
$$707$$ 12.0000 20.7846i 0.451306 0.781686i
$$708$$ −13.5000 + 7.79423i −0.507361 + 0.292925i
$$709$$ 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i $$0.00956021\pi$$
−0.473768 + 0.880650i $$0.657106\pi$$
$$710$$ 0 0
$$711$$ 3.00000 + 5.19615i 0.112509 + 0.194871i
$$712$$ −15.0000 −0.562149
$$713$$ 0 0
$$714$$ −18.0000 10.3923i −0.673633 0.388922i
$$715$$ 0 0
$$716$$ 4.50000 7.79423i 0.168173 0.291284i
$$717$$ 0 0
$$718$$ 6.00000 + 10.3923i 0.223918 + 0.387837i
$$719$$ 18.0000 0.671287 0.335643 0.941989i $$-0.391046\pi$$
0.335643 + 0.941989i $$0.391046\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ 15.0000 + 25.9808i 0.558242 + 0.966904i
$$723$$ −28.5000 + 16.4545i −1.05993 + 0.611949i
$$724$$ 8.00000 13.8564i 0.297318 0.514969i
$$725$$ 0 0
$$726$$ 19.0526i 0.707107i
$$727$$ −20.0000 34.6410i −0.741759 1.28476i −0.951694 0.307049i $$-0.900659\pi$$
0.209935 0.977715i $$-0.432675\pi$$
$$728$$ 8.00000 0.296500
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −3.00000 5.19615i −0.110959 0.192187i
$$732$$ 6.92820i 0.256074i
$$733$$ −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i $$-0.966513\pi$$
0.588177 + 0.808732i $$0.299846\pi$$
$$734$$ 5.00000 8.66025i 0.184553 0.319656i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 27.0000 0.993884
$$739$$ −25.0000 −0.919640 −0.459820 0.888012i $$-0.652086\pi$$
−0.459820 + 0.888012i $$0.652086\pi$$
$$740$$ 0 0
$$741$$ 42.0000 + 24.2487i 1.54291 + 0.890799i
$$742$$ −12.0000 + 20.7846i −0.440534 + 0.763027i
$$743$$ 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i $$-0.798229\pi$$
0.915794 + 0.401648i $$0.131563\pi$$
$$744$$ −15.0000 8.66025i −0.549927 0.317500i
$$745$$ 0 0
$$746$$ −4.00000 −0.146450
$$747$$ −13.5000 23.3827i −0.493939 0.855528i
$$748$$ 0 0
$$749$$ −9.00000 15.5885i −0.328853 0.569590i
$$750$$ 0 0
$$751$$ 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i $$-0.810082\pi$$
0.900207 + 0.435463i $$0.143415\pi$$
$$752$$ 3.00000 5.19615i 0.109399 0.189484i
$$753$$ 25.9808i 0.946792i
$$754$$ −12.0000 20.7846i −0.437014 0.756931i
$$755$$ 0 0
$$756$$ 10.3923i 0.377964i
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 10.0000 + 17.3205i 0.363216 + 0.629109i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −10.5000 + 18.1865i −0.380625 + 0.659261i −0.991152 0.132734i $$-0.957624\pi$$
0.610527 + 0.791995i $$0.290958\pi$$
$$762$$ 30.0000 17.3205i 1.08679 0.627456i
$$763$$ 2.00000 + 3.46410i 0.0724049 + 0.125409i
$$764$$ 6.00000 0.217072
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 18.0000 + 31.1769i 0.649942 + 1.12573i
$$768$$ −1.50000 0.866025i −0.0541266 0.0312500i
$$769$$ −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i $$-0.862069\pi$$
0.817423 + 0.576038i $$0.195402\pi$$
$$770$$ 0 0
$$771$$ 4.50000 + 2.59808i 0.162064 + 0.0935674i
$$772$$ 1.00000 + 1.73205i 0.0359908 + 0.0623379i
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ −1.50000 + 2.59808i −0.0539164 + 0.0933859i
$$775$$ 0 0
$$776$$ −8.50000 14.7224i −0.305132 0.528505i
$$777$$ 6.00000 3.46410i 0.215249 0.124274i
$$778$$ 3.00000 5.19615i 0.107555 0.186291i
$$779$$ 31.5000 54.5596i 1.12860 1.95480i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 27.0000 15.5885i 0.964901 0.557086i
$$784$$ −3.00000 −0.107143
$$785$$ 0 0
$$786$$ 20.7846i 0.741362i
$$787$$ 10.0000 17.3205i 0.356462 0.617409i −0.630905 0.775860i $$-0.717316\pi$$
0.987367 + 0.158450i $$0.0506498\pi$$
$$788$$ 9.00000 15.5885i 0.320612 0.555316i