# Properties

 Label 1078.2.e.b.67.1 Level $1078$ Weight $2$ Character 1078.67 Analytic conductor $8.608$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.67 Dual form 1078.2.e.b.177.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{20} -1.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -2.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{34} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{40} +10.0000 q^{41} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.00000 - 5.19615i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-4.00000 - 6.92820i) q^{47} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} -2.00000 q^{55} +(1.00000 + 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} +16.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 8.66025i) q^{82} +4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -6.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10})$$ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9 $$2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9} - 2 q^{10} + q^{11} + 4 q^{13} - q^{16} - 2 q^{17} + 3 q^{18} + 4 q^{20} - 2 q^{22} + 8 q^{23} + q^{25} - 2 q^{26} - 4 q^{29} + 8 q^{31} - q^{32} + 4 q^{34} - 6 q^{36} + 2 q^{37} - 2 q^{40} + 20 q^{41} + 8 q^{43} + q^{44} + 6 q^{45} + 8 q^{46} - 8 q^{47} - 2 q^{50} - 2 q^{52} - 6 q^{53} - 4 q^{55} + 2 q^{58} - 10 q^{61} - 16 q^{62} + 2 q^{64} - 4 q^{65} + 12 q^{67} - 2 q^{68} + 32 q^{71} + 3 q^{72} + 14 q^{73} + 2 q^{74} - 2 q^{80} - 9 q^{81} - 10 q^{82} + 8 q^{85} - 4 q^{86} + q^{88} + 6 q^{89} - 12 q^{90} - 16 q^{92} - 8 q^{94} + 20 q^{97} + 6 q^{99}+O(q^{100})$$ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9 - 2 * q^10 + q^11 + 4 * q^13 - q^16 - 2 * q^17 + 3 * q^18 + 4 * q^20 - 2 * q^22 + 8 * q^23 + q^25 - 2 * q^26 - 4 * q^29 + 8 * q^31 - q^32 + 4 * q^34 - 6 * q^36 + 2 * q^37 - 2 * q^40 + 20 * q^41 + 8 * q^43 + q^44 + 6 * q^45 + 8 * q^46 - 8 * q^47 - 2 * q^50 - 2 * q^52 - 6 * q^53 - 4 * q^55 + 2 * q^58 - 10 * q^61 - 16 * q^62 + 2 * q^64 - 4 * q^65 + 12 * q^67 - 2 * q^68 + 32 * q^71 + 3 * q^72 + 14 * q^73 + 2 * q^74 - 2 * q^80 - 9 * q^81 - 10 * q^82 + 8 * q^85 - 4 * q^86 + q^88 + 6 * q^89 - 12 * q^90 - 16 * q^92 - 8 * q^94 + 20 * q^97 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ −1.00000 + 1.73205i −0.316228 + 0.547723i
$$11$$ 0.500000 0.866025i 0.150756 0.261116i
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 1.50000 2.59808i 0.353553 0.612372i
$$19$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$20$$ 2.00000 0.447214
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i $$0.147321\pi$$
−0.0607377 + 0.998154i $$0.519345\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ −1.00000 1.73205i −0.196116 0.339683i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i $$-0.578198\pi$$
0.961625 0.274367i $$-0.0884683\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ 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 $$0.780765\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −1.00000 1.73205i −0.158114 0.273861i
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0.500000 + 0.866025i 0.0753778 + 0.130558i
$$45$$ 3.00000 5.19615i 0.447214 0.774597i
$$46$$ 4.00000 6.92820i 0.589768 1.02151i
$$47$$ −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i $$-0.968365\pi$$
0.411606 0.911362i $$-0.364968\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ −1.00000 + 1.73205i −0.138675 + 0.240192i
$$53$$ −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i $$-0.968532\pi$$
0.583036 + 0.812447i $$0.301865\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.00000 + 1.73205i 0.131306 + 0.227429i
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0 0
$$61$$ −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i $$-0.945525\pi$$
0.345207 0.938527i $$-0.387809\pi$$
$$62$$ −8.00000 −1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 3.46410i −0.248069 0.429669i
$$66$$ 0 0
$$67$$ 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i $$-0.571445\pi$$
0.955588 0.294706i $$-0.0952216\pi$$
$$68$$ −1.00000 1.73205i −0.121268 0.210042i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 16.0000 1.89885 0.949425 0.313993i $$-0.101667\pi$$
0.949425 + 0.313993i $$0.101667\pi$$
$$72$$ 1.50000 + 2.59808i 0.176777 + 0.306186i
$$73$$ 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i $$-0.527702\pi$$
0.906208 0.422833i $$-0.138964\pi$$
$$74$$ 1.00000 1.73205i 0.116248 0.201347i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ −1.00000 + 1.73205i −0.111803 + 0.193649i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −5.00000 8.66025i −0.552158 0.956365i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ −2.00000 3.46410i −0.215666 0.373544i
$$87$$ 0 0
$$88$$ 0.500000 0.866025i 0.0533002 0.0923186i
$$89$$ 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i $$-0.0636557\pi$$
−0.662071 + 0.749441i $$0.730322\pi$$
$$90$$ −6.00000 −0.632456
$$91$$ 0 0
$$92$$ −8.00000 −0.834058
$$93$$ 0 0
$$94$$ −4.00000 + 6.92820i −0.412568 + 0.714590i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ 3.00000 0.301511
$$100$$ 0.500000 + 0.866025i 0.0500000 + 0.0866025i
$$101$$ −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i $$0.519872\pi$$
−0.833143 + 0.553058i $$0.813461\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i $$-0.104732\pi$$
−0.753010 + 0.658009i $$0.771399\pi$$
$$108$$ 0 0
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 1.00000 + 1.73205i 0.0953463 + 0.165145i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 8.00000 13.8564i 0.746004 1.29212i
$$116$$ 1.00000 1.73205i 0.0928477 0.160817i
$$117$$ 3.00000 + 5.19615i 0.277350 + 0.480384i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ −5.00000 + 8.66025i −0.452679 + 0.784063i
$$123$$ 0 0
$$124$$ 4.00000 + 6.92820i 0.359211 + 0.622171i
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −2.00000 + 3.46410i −0.175412 + 0.303822i
$$131$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i $$-0.750827\pi$$
0.965250 + 0.261329i $$0.0841608\pi$$
$$138$$ 0 0
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −8.00000 13.8564i −0.671345 1.16280i
$$143$$ 1.00000 1.73205i 0.0836242 0.144841i
$$144$$ 1.50000 2.59808i 0.125000 0.216506i
$$145$$ 2.00000 + 3.46410i 0.166091 + 0.287678i
$$146$$ −14.0000 −1.15865
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −7.00000 12.1244i −0.573462 0.993266i −0.996207 0.0870170i $$-0.972267\pi$$
0.422744 0.906249i $$-0.361067\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ −16.0000 −1.28515
$$156$$ 0 0
$$157$$ 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i $$-0.644649\pi$$
0.997609 0.0691164i $$-0.0220180\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 2.00000 0.158114
$$161$$ 0 0
$$162$$ 9.00000 0.707107
$$163$$ 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i $$0.119778\pi$$
−0.146772 + 0.989170i $$0.546888\pi$$
$$164$$ −5.00000 + 8.66025i −0.390434 + 0.676252i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ −2.00000 3.46410i −0.153393 0.265684i
$$171$$ 0 0
$$172$$ −2.00000 + 3.46410i −0.152499 + 0.264135i
$$173$$ 7.00000 + 12.1244i 0.532200 + 0.921798i 0.999293 + 0.0375896i $$0.0119679\pi$$
−0.467093 + 0.884208i $$0.654699\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ 0 0
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i $$-0.881096\pi$$
0.781551 + 0.623841i $$0.214429\pi$$
$$180$$ 3.00000 + 5.19615i 0.223607 + 0.387298i
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 4.00000 + 6.92820i 0.294884 + 0.510754i
$$185$$ 2.00000 3.46410i 0.147043 0.254686i
$$186$$ 0 0
$$187$$ 1.00000 + 1.73205i 0.0731272 + 0.126660i
$$188$$ 8.00000 0.583460
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i $$-0.260132\pi$$
−0.973674 + 0.227946i $$0.926799\pi$$
$$192$$ 0 0
$$193$$ −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i $$-0.856266\pi$$
0.827788 + 0.561041i $$0.189599\pi$$
$$194$$ −5.00000 8.66025i −0.358979 0.621770i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ −1.50000 2.59808i −0.106600 0.184637i
$$199$$ −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i $$0.358603\pi$$
−0.996850 + 0.0793045i $$0.974730\pi$$
$$200$$ 0.500000 0.866025i 0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ 18.0000 1.26648
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −10.0000 17.3205i −0.698430 1.20972i
$$206$$ 0 0
$$207$$ −12.0000 + 20.7846i −0.834058 + 1.44463i
$$208$$ −1.00000 1.73205i −0.0693375 0.120096i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ −3.00000 5.19615i −0.206041 0.356873i
$$213$$ 0 0
$$214$$ 2.00000 3.46410i 0.136717 0.236801i
$$215$$ −4.00000 6.92820i −0.272798 0.472500i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ 0 0
$$220$$ 1.00000 1.73205i 0.0674200 0.116775i
$$221$$ −2.00000 + 3.46410i −0.134535 + 0.233021i
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 3.00000 0.200000
$$226$$ −1.00000 1.73205i −0.0665190 0.115214i
$$227$$ −8.00000 + 13.8564i −0.530979 + 0.919682i 0.468368 + 0.883534i $$0.344842\pi$$
−0.999346 + 0.0361484i $$0.988491\pi$$
$$228$$ 0 0
$$229$$ 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i $$0.0923732\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ −16.0000 −1.05501
$$231$$ 0 0
$$232$$ −2.00000 −0.131306
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ 3.00000 5.19615i 0.196116 0.339683i
$$235$$ −8.00000 + 13.8564i −0.521862 + 0.903892i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i $$0.363513\pi$$
−0.995509 + 0.0946700i $$0.969820\pi$$
$$242$$ −0.500000 + 0.866025i −0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ 10.0000 0.640184
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 4.00000 6.92820i 0.254000 0.439941i
$$249$$ 0 0
$$250$$ 6.00000 + 10.3923i 0.379473 + 0.657267i
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ −4.00000 6.92820i −0.250982 0.434714i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i $$0.218541\pi$$
0.162247 + 0.986750i $$0.448126\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 4.00000 0.248069
$$261$$ −3.00000 5.19615i −0.185695 0.321634i
$$262$$ 0 0
$$263$$ 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i $$-0.568182\pi$$
0.952517 0.304487i $$-0.0984850\pi$$
$$264$$ 0 0
$$265$$ 12.0000 0.737154
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 6.00000 + 10.3923i 0.366508 + 0.634811i
$$269$$ −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i $$0.351559\pi$$
−0.998361 + 0.0572259i $$0.981774\pi$$
$$270$$ 0 0
$$271$$ −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i $$-0.328199\pi$$
−0.999870 + 0.0161307i $$0.994865\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ −0.500000 0.866025i −0.0301511 0.0522233i
$$276$$ 0 0
$$277$$ −15.0000 + 25.9808i −0.901263 + 1.56103i −0.0754058 + 0.997153i $$0.524025\pi$$
−0.825857 + 0.563880i $$0.809308\pi$$
$$278$$ 8.00000 + 13.8564i 0.479808 + 0.831052i
$$279$$ 24.0000 1.43684
$$280$$ 0 0
$$281$$ −22.0000 −1.31241 −0.656205 0.754583i $$-0.727839\pi$$
−0.656205 + 0.754583i $$0.727839\pi$$
$$282$$ 0 0
$$283$$ 12.0000 20.7846i 0.713326 1.23552i −0.250276 0.968175i $$-0.580521\pi$$
0.963602 0.267342i $$-0.0861454\pi$$
$$284$$ −8.00000 + 13.8564i −0.474713 + 0.822226i
$$285$$ 0 0
$$286$$ −2.00000 −0.118262
$$287$$ 0 0
$$288$$ −3.00000 −0.176777
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 2.00000 3.46410i 0.117444 0.203419i
$$291$$ 0 0
$$292$$ 7.00000 + 12.1244i 0.409644 + 0.709524i
$$293$$ −30.0000 −1.75262 −0.876309 0.481749i $$-0.840002\pi$$
−0.876309 + 0.481749i $$0.840002\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.00000 + 1.73205i 0.0581238 + 0.100673i
$$297$$ 0 0
$$298$$ −7.00000 + 12.1244i −0.405499 + 0.702345i
$$299$$ 8.00000 + 13.8564i 0.462652 + 0.801337i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −10.0000 + 17.3205i −0.572598 + 0.991769i
$$306$$ 3.00000 + 5.19615i 0.171499 + 0.297044i
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 8.00000 + 13.8564i 0.454369 + 0.786991i
$$311$$ −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i $$-0.906166\pi$$
0.730044 + 0.683400i $$0.239499\pi$$
$$312$$ 0 0
$$313$$ 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i $$-0.0371814\pi$$
−0.597522 + 0.801852i $$0.703848\pi$$
$$314$$ −14.0000 −0.790066
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i $$0.00202172\pi$$
−0.494489 + 0.869184i $$0.664645\pi$$
$$318$$ 0 0
$$319$$ −1.00000 + 1.73205i −0.0559893 + 0.0969762i
$$320$$ −1.00000 1.73205i −0.0559017 0.0968246i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −4.50000 7.79423i −0.250000 0.433013i
$$325$$ 1.00000 1.73205i 0.0554700 0.0960769i
$$326$$ 10.0000 17.3205i 0.553849 0.959294i
$$327$$ 0 0
$$328$$ 10.0000 0.552158
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i $$-0.201729\pi$$
−0.915742 + 0.401768i $$0.868396\pi$$
$$332$$ 0 0
$$333$$ −3.00000 + 5.19615i −0.164399 + 0.284747i
$$334$$ −8.00000 13.8564i −0.437741 0.758189i
$$335$$ −24.0000 −1.31126
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 4.50000 + 7.79423i 0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ −2.00000 + 3.46410i −0.108465 + 0.187867i
$$341$$ −4.00000 6.92820i −0.216612 0.375183i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 7.00000 12.1244i 0.376322 0.651809i
$$347$$ 14.0000 24.2487i 0.751559 1.30174i −0.195507 0.980702i $$-0.562635\pi$$
0.947067 0.321037i $$-0.104031\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.500000 + 0.866025i 0.0266501 + 0.0461593i
$$353$$ −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i $$-0.992342\pi$$
0.520689 + 0.853746i $$0.325675\pi$$
$$354$$ 0 0
$$355$$ −16.0000 27.7128i −0.849192 1.47084i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 4.00000 0.211407
$$359$$ −16.0000 27.7128i −0.844448 1.46263i −0.886100 0.463494i $$-0.846596\pi$$
0.0416523 0.999132i $$-0.486738\pi$$
$$360$$ 3.00000 5.19615i 0.158114 0.273861i
$$361$$ 9.50000 16.4545i 0.500000 0.866025i
$$362$$ 11.0000 + 19.0526i 0.578147 + 1.00138i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −28.0000 −1.46559
$$366$$ 0 0
$$367$$ −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i $$-0.970461\pi$$
0.578101 + 0.815966i $$0.303794\pi$$
$$368$$ 4.00000 6.92820i 0.208514 0.361158i
$$369$$ 15.0000 + 25.9808i 0.780869 + 1.35250i
$$370$$ −4.00000 −0.207950
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i $$-0.284725\pi$$
−0.988363 + 0.152115i $$0.951392\pi$$
$$374$$ 1.00000 1.73205i 0.0517088 0.0895622i
$$375$$ 0 0
$$376$$ −4.00000 6.92820i −0.206284 0.357295i
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −4.00000 + 6.92820i −0.204658 + 0.354478i
$$383$$ −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i $$-0.232188\pi$$
−0.949938 + 0.312437i $$0.898855\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 2.00000 0.101797
$$387$$ 6.00000 + 10.3923i 0.304997 + 0.528271i
$$388$$ −5.00000 + 8.66025i −0.253837 + 0.439658i
$$389$$ 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i $$-0.682501\pi$$
0.998763 + 0.0497253i $$0.0158346\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 9.00000 + 15.5885i 0.453413 + 0.785335i
$$395$$ 0 0
$$396$$ −1.50000 + 2.59808i −0.0753778 + 0.130558i
$$397$$ −9.00000 15.5885i −0.451697 0.782362i 0.546795 0.837267i $$-0.315848\pi$$
−0.998492 + 0.0549046i $$0.982515\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ 0 0
$$403$$ 8.00000 13.8564i 0.398508 0.690237i
$$404$$ −9.00000 15.5885i −0.447767 0.775555i
$$405$$ 18.0000 0.894427
$$406$$ 0 0
$$407$$ 2.00000 0.0991363
$$408$$ 0 0
$$409$$ −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i $$-0.912855\pi$$
0.715523 + 0.698589i $$0.246188\pi$$
$$410$$ −10.0000 + 17.3205i −0.493865 + 0.855399i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 24.0000 1.17954
$$415$$ 0 0
$$416$$ −1.00000 + 1.73205i −0.0490290 + 0.0849208i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 16.0000 0.781651 0.390826 0.920465i $$-0.372190\pi$$
0.390826 + 0.920465i $$0.372190\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ −2.00000 3.46410i −0.0973585 0.168630i
$$423$$ 12.0000 20.7846i 0.583460 1.01058i
$$424$$ −3.00000 + 5.19615i −0.145693 + 0.252347i
$$425$$ 1.00000 + 1.73205i 0.0485071 + 0.0840168i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −4.00000 −0.193347
$$429$$ 0 0
$$430$$ −4.00000 + 6.92820i −0.192897 + 0.334108i
$$431$$ 4.00000 6.92820i 0.192673 0.333720i −0.753462 0.657491i $$-0.771618\pi$$
0.946135 + 0.323772i $$0.104951\pi$$
$$432$$ 0 0
$$433$$ 26.0000 1.24948 0.624740 0.780833i $$-0.285205\pi$$
0.624740 + 0.780833i $$0.285205\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.00000 + 1.73205i 0.0478913 + 0.0829502i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −20.0000 34.6410i −0.954548 1.65333i −0.735399 0.677634i $$-0.763005\pi$$
−0.219149 0.975691i $$-0.570328\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ 4.00000 0.190261
$$443$$ −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i $$-0.258683\pi$$
−0.972626 + 0.232377i $$0.925350\pi$$
$$444$$ 0 0
$$445$$ 6.00000 10.3923i 0.284427 0.492642i
$$446$$ −8.00000 13.8564i −0.378811 0.656120i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ −1.50000 2.59808i −0.0707107 0.122474i
$$451$$ 5.00000 8.66025i 0.235441 0.407795i
$$452$$ −1.00000 + 1.73205i −0.0470360 + 0.0814688i
$$453$$ 0 0
$$454$$ 16.0000 0.750917
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i $$0.00537742\pi$$
−0.485299 + 0.874348i $$0.661289\pi$$
$$458$$ 11.0000 19.0526i 0.513996 0.890268i
$$459$$ 0 0
$$460$$ 8.00000 + 13.8564i 0.373002 + 0.646058i
$$461$$ −30.0000 −1.39724 −0.698620 0.715493i $$-0.746202\pi$$
−0.698620 + 0.715493i $$0.746202\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 1.00000 + 1.73205i 0.0464238 + 0.0804084i
$$465$$ 0 0
$$466$$ 3.00000 5.19615i 0.138972 0.240707i
$$467$$ −12.0000 20.7846i −0.555294 0.961797i −0.997881 0.0650714i $$-0.979272\pi$$
0.442587 0.896726i $$-0.354061\pi$$
$$468$$ −6.00000 −0.277350
$$469$$ 0 0
$$470$$ 16.0000 0.738025
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 2.00000 3.46410i 0.0919601 0.159280i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −18.0000 −0.824163
$$478$$ 4.00000 + 6.92820i 0.182956 + 0.316889i
$$479$$ −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i $$-0.891838\pi$$
0.760056 + 0.649857i $$0.225171\pi$$
$$480$$ 0 0
$$481$$ 2.00000 + 3.46410i 0.0911922 + 0.157949i
$$482$$ 18.0000 0.819878
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −10.0000 17.3205i −0.454077 0.786484i
$$486$$ 0 0
$$487$$ 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i $$-0.472238\pi$$
0.819181 0.573535i $$-0.194428\pi$$
$$488$$ −5.00000 8.66025i −0.226339 0.392031i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 0 0
$$493$$ 2.00000 3.46410i 0.0900755 0.156015i
$$494$$ 0 0
$$495$$ −3.00000 5.19615i −0.134840 0.233550i
$$496$$ −8.00000 −0.359211
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i $$0.0489388\pi$$
−0.361478 + 0.932381i $$0.617728\pi$$
$$500$$ 6.00000 10.3923i 0.268328 0.464758i
$$501$$ 0 0
$$502$$ −12.0000 20.7846i −0.535586 0.927663i
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 36.0000 1.60198
$$506$$ −4.00000 6.92820i −0.177822 0.307996i
$$507$$ 0 0
$$508$$ −4.00000 + 6.92820i −0.177471 + 0.307389i
$$509$$ −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i $$-0.180780\pi$$
−0.887336 + 0.461123i $$0.847447\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 15.0000 25.9808i 0.661622 1.14596i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −8.00000 −0.351840
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −2.00000 3.46410i −0.0877058 0.151911i
$$521$$ −17.0000 + 29.4449i −0.744784 + 1.29000i 0.205512 + 0.978655i $$0.434114\pi$$
−0.950296 + 0.311348i $$0.899219\pi$$
$$522$$ −3.00000 + 5.19615i −0.131306 + 0.227429i
$$523$$ −4.00000 6.92820i −0.174908 0.302949i 0.765222 0.643767i $$-0.222629\pi$$
−0.940129 + 0.340818i $$0.889296\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ 8.00000 + 13.8564i 0.348485 + 0.603595i
$$528$$ 0 0
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ −6.00000 10.3923i −0.260623 0.451413i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 20.0000 0.866296
$$534$$ 0 0
$$535$$ 4.00000 6.92820i 0.172935 0.299532i
$$536$$ 6.00000 10.3923i 0.259161 0.448879i
$$537$$ 0 0
$$538$$ 18.0000 0.776035
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −19.0000 32.9090i −0.816874 1.41487i −0.907975 0.419025i $$-0.862372\pi$$
0.0911008 0.995842i $$-0.470961\pi$$
$$542$$ −8.00000 + 13.8564i −0.343629 + 0.595184i
$$543$$ 0 0
$$544$$ −1.00000 1.73205i −0.0428746 0.0742611i
$$545$$ −4.00000 −0.171341
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ 3.00000 + 5.19615i 0.128154 + 0.221969i
$$549$$ 15.0000 25.9808i 0.640184 1.10883i
$$550$$ −0.500000 + 0.866025i −0.0213201 + 0.0369274i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 30.0000 1.27458
$$555$$ 0 0
$$556$$ 8.00000 13.8564i 0.339276 0.587643i
$$557$$ 5.00000 8.66025i 0.211857 0.366947i −0.740439 0.672124i $$-0.765382\pi$$
0.952296 + 0.305177i $$0.0987156\pi$$
$$558$$ −12.0000 20.7846i −0.508001 0.879883i
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 11.0000 + 19.0526i 0.464007 + 0.803684i
$$563$$ −4.00000 + 6.92820i −0.168580 + 0.291989i −0.937921 0.346850i $$-0.887251\pi$$
0.769341 + 0.638838i $$0.220585\pi$$
$$564$$ 0 0
$$565$$ −2.00000 3.46410i −0.0841406 0.145736i
$$566$$ −24.0000 −1.00880
$$567$$ 0 0
$$568$$ 16.0000 0.671345
$$569$$ 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 0 0
$$571$$ 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i $$-0.460975\pi$$
0.798379 0.602155i $$-0.205691\pi$$
$$572$$ 1.00000 + 1.73205i 0.0418121 + 0.0724207i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.00000 0.333623
$$576$$ 1.50000 + 2.59808i 0.0625000 + 0.108253i
$$577$$ −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i $$-0.846589\pi$$
0.844459 + 0.535620i $$0.179922\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ 0 0
$$580$$ −4.00000 −0.166091
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 3.00000 + 5.19615i 0.124247 + 0.215203i
$$584$$ 7.00000 12.1244i 0.289662 0.501709i
$$585$$ 6.00000 10.3923i 0.248069 0.429669i
$$586$$ 15.0000 + 25.9808i 0.619644 + 1.07326i
$$587$$ 24.0000 0.990586 0.495293 0.868726i $$-0.335061\pi$$
0.495293 + 0.868726i $$0.335061\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.00000 1.73205i 0.0410997 0.0711868i
$$593$$ −21.0000 36.3731i −0.862367 1.49366i −0.869638 0.493689i $$-0.835648\pi$$
0.00727173 0.999974i $$-0.497685\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 14.0000 0.573462
$$597$$ 0 0
$$598$$ 8.00000 13.8564i 0.327144 0.566631i
$$599$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 0 0
$$601$$ −46.0000 −1.87638 −0.938190 0.346122i $$-0.887498\pi$$
−0.938190 + 0.346122i $$0.887498\pi$$
$$602$$ 0 0
$$603$$ 36.0000 1.46603
$$604$$ 0 0
$$605$$ −1.00000 + 1.73205i −0.0406558 + 0.0704179i
$$606$$ 0 0
$$607$$ 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i $$-0.0614000\pi$$
−0.656744 + 0.754114i $$0.728067\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 20.0000 0.809776
$$611$$ −8.00000 13.8564i −0.323645 0.560570i
$$612$$ 3.00000 5.19615i 0.121268 0.210042i
$$613$$ −11.0000 + 19.0526i −0.444286 + 0.769526i −0.998002 0.0631797i $$-0.979876\pi$$
0.553716 + 0.832705i $$0.313209\pi$$
$$614$$ 8.00000 + 13.8564i 0.322854 + 0.559199i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ 8.00000 13.8564i 0.321547 0.556936i −0.659260 0.751915i $$-0.729130\pi$$
0.980807 + 0.194979i $$0.0624638\pi$$
$$620$$ 8.00000 13.8564i 0.321288 0.556487i
$$621$$ 0 0
$$622$$ 8.00000 0.320771
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 7.00000 12.1244i 0.279776 0.484587i
$$627$$ 0 0
$$628$$ 7.00000 + 12.1244i 0.279330 + 0.483814i
$$629$$ −4.00000 −0.159490
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 9.00000 15.5885i 0.357436 0.619097i
$$635$$ −8.00000 13.8564i −0.317470 0.549875i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 2.00000 0.0791808
$$639$$ 24.0000 + 41.5692i 0.949425 + 1.64445i
$$640$$ −1.00000 + 1.73205i −0.0395285 + 0.0684653i
$$641$$ 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i $$-0.631488\pi$$
0.993899 0.110291i $$-0.0351782\pi$$
$$642$$ 0 0
$$643$$ −32.0000 −1.26196 −0.630978 0.775800i $$-0.717346\pi$$
−0.630978 + 0.775800i $$0.717346\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ −4.50000 + 7.79423i −0.176777 + 0.306186i
$$649$$ 0 0
$$650$$ −2.00000 −0.0784465
$$651$$ 0 0
$$652$$ −20.0000 −0.783260
$$653$$ 13.0000 + 22.5167i 0.508729 + 0.881145i 0.999949 + 0.0101092i $$0.00321793\pi$$
−0.491220 + 0.871036i $$0.663449\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −5.00000 8.66025i −0.195217 0.338126i
$$657$$ 42.0000 1.63858
$$658$$ 0 0
$$659$$ 28.0000 1.09073 0.545363 0.838200i $$-0.316392\pi$$
0.545363 + 0.838200i $$0.316392\pi$$
$$660$$ 0 0
$$661$$ −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i $$-0.845717\pi$$
0.845922 + 0.533306i $$0.179051\pi$$
$$662$$ −2.00000 + 3.46410i −0.0777322 + 0.134636i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ −8.00000 13.8564i −0.309761 0.536522i
$$668$$ −8.00000 + 13.8564i −0.309529 + 0.536120i
$$669$$ 0 0
$$670$$ 12.0000 + 20.7846i 0.463600 + 0.802980i
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ −14.0000 −0.539660 −0.269830 0.962908i $$-0.586968\pi$$
−0.269830 + 0.962908i $$0.586968\pi$$
$$674$$ −9.00000 15.5885i −0.346667 0.600445i
$$675$$ 0 0
$$676$$ 4.50000 7.79423i 0.173077 0.299778i
$$677$$ −13.0000 22.5167i −0.499631 0.865386i 0.500369 0.865812i $$-0.333198\pi$$
−1.00000 0.000426509i $$0.999864\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 4.00000 0.153393
$$681$$ 0 0
$$682$$ −4.00000 + 6.92820i −0.153168 + 0.265295i
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −2.00000 3.46410i −0.0762493 0.132068i
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −12.0000 20.7846i −0.456502 0.790684i 0.542272 0.840203i $$-0.317564\pi$$
−0.998773 + 0.0495194i $$0.984231\pi$$
$$692$$ −14.0000 −0.532200
$$693$$ 0 0
$$694$$ −28.0000 −1.06287
$$695$$ 16.0000 + 27.7128i 0.606915 + 1.05121i
$$696$$ 0 0
$$697$$ −10.0000 + 17.3205i −0.378777 + 0.656061i
$$698$$ −1.00000 1.73205i −0.0378506 0.0655591i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.500000 0.866025i 0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −15.0000 25.9808i −0.563337 0.975728i −0.997202 0.0747503i $$-0.976184\pi$$
0.433865 0.900978i $$-0.357149\pi$$
$$710$$ −16.0000 + 27.7128i −0.600469 + 1.04004i
$$711$$ 0 0
$$712$$ 3.00000 + 5.19615i 0.112430 + 0.194734i
$$713$$ 64.0000 2.39682
$$714$$ 0 0
$$715$$ −4.00000 −0.149592
$$716$$ −2.00000 3.46410i −0.0747435 0.129460i
$$717$$ 0 0
$$718$$ −16.0000 + 27.7128i −0.597115 + 1.03423i
$$719$$ 4.00000 + 6.92820i 0.149175 + 0.258378i 0.930923 0.365216i $$-0.119005\pi$$
−0.781748 + 0.623595i $$0.785672\pi$$
$$720$$ −6.00000 −0.223607
$$721$$ 0 0
$$722$$ −19.0000 −0.707107
$$723$$ 0 0
$$724$$ 11.0000 19.0526i 0.408812 0.708083i
$$725$$ −1.00000 + 1.73205i −0.0371391 + 0.0643268i
$$726$$ 0 0
$$727$$ 32.0000 1.18681 0.593407 0.804902i $$-0.297782\pi$$
0.593407 + 0.804902i $$0.297782\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 14.0000 + 24.2487i 0.518163 + 0.897485i
$$731$$ −4.00000 + 6.92820i −0.147945 + 0.256249i
$$732$$ 0 0
$$733$$ 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i $$-0.0334875\pi$$
−0.588177 + 0.808732i $$0.700154\pi$$
$$734$$ 16.0000 0.590571
$$735$$ 0 0
$$736$$ −8.00000 −0.294884
$$737$$ −6.00000 10.3923i −0.221013 0.382805i
$$738$$ 15.0000 25.9808i 0.552158 0.956365i
$$739$$ −6.00000 + 10.3923i −0.220714 + 0.382287i −0.955025 0.296526i $$-0.904172\pi$$
0.734311 + 0.678813i $$0.237505\pi$$
$$740$$ 2.00000 + 3.46410i 0.0735215 + 0.127343i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ −14.0000 + 24.2487i −0.512920 + 0.888404i
$$746$$ −7.00000 + 12.1244i −0.256288 + 0.443904i
$$747$$ 0 0
$$748$$ −2.00000 −0.0731272
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i $$0.0317870\pi$$
−0.411170 + 0.911559i $$0.634880\pi$$
$$752$$ −4.00000 + 6.92820i −0.145865 + 0.252646i
$$753$$ 0 0
$$754$$ 2.00000 + 3.46410i 0.0728357 + 0.126155i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 14.0000 0.508839 0.254419 0.967094i $$-0.418116\pi$$
0.254419 + 0.967094i $$0.418116\pi$$
$$758$$ −2.00000 3.46410i −0.0726433 0.125822i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i $$-0.131982\pi$$
−0.806514 + 0.591215i $$0.798649\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 8.00000 0.289430
$$765$$ 6.00000 + 10.3923i 0.216930 + 0.375735i
$$766$$ −4.00000 + 6.92820i −0.144526 + 0.250326i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −1.00000 1.73205i −0.0359908 0.0623379i
$$773$$ −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i $$-0.938263\pi$$
0.657542 + 0.753418i $$0.271596\pi$$
$$774$$ 6.00000 10.3923i 0.215666 0.373544i
$$775$$ −4.00000 6.92820i −0.143684 0.248868i
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −18.0000 −0.645331
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 8.00000 13.8564i 0.286263 0.495821i
$$782$$ 8.00000 + 13.8564i 0.286079 + 0.495504i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −28.0000 −0.999363
$$786$$ 0 0
$$787$$ −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i $$0.359855\pi$$
−0.996531 + 0.0832226i $$0.973479\pi$$
$$788$$ 9.00000 15.5885i 0.320612 0.555316i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 3.00000 0.106600
$$793$$ −10.0000 17.3205i