# Properties

 Label 1134.2.f.p.379.1 Level $1134$ Weight $2$ Character 1134.379 Analytic conductor $9.055$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.f (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ 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: no (minimal twist has level 378) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 379.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.379 Dual form 1134.2.f.p.757.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +4.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +2.00000 q^{19} +(2.00000 - 3.46410i) q^{20} +(2.00000 + 3.46410i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-5.50000 + 9.52628i) q^{25} -3.00000 q^{26} -1.00000 q^{28} +(0.500000 - 0.866025i) q^{29} +(4.50000 + 7.79423i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.50000 - 6.06218i) q^{34} +4.00000 q^{35} +2.00000 q^{37} +(1.00000 - 1.73205i) q^{38} +(-2.00000 - 3.46410i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +4.00000 q^{44} -1.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(5.50000 + 9.52628i) q^{50} +(-1.50000 + 2.59808i) q^{52} +9.00000 q^{53} -16.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(3.00000 - 5.19615i) q^{61} +9.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(2.00000 - 3.46410i) q^{70} +7.00000 q^{71} -14.0000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(2.00000 + 3.46410i) q^{77} +(3.00000 - 5.19615i) q^{79} -4.00000 q^{80} +6.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(14.0000 + 24.2487i) q^{85} +(5.50000 + 9.52628i) q^{86} +(2.00000 - 3.46410i) q^{88} +3.00000 q^{89} -3.00000 q^{91} +(-0.500000 + 0.866025i) q^{92} +(3.00000 + 5.19615i) q^{94} +(4.00000 + 6.92820i) q^{95} +(4.00000 - 6.92820i) q^{97} -1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} + 4q^{5} + q^{7} - 2q^{8} + O(q^{10})$$ $$2q + q^{2} - q^{4} + 4q^{5} + q^{7} - 2q^{8} + 8q^{10} - 4q^{11} - 3q^{13} - q^{14} - q^{16} + 14q^{17} + 4q^{19} + 4q^{20} + 4q^{22} - q^{23} - 11q^{25} - 6q^{26} - 2q^{28} + q^{29} + 9q^{31} + q^{32} + 7q^{34} + 8q^{35} + 4q^{37} + 2q^{38} - 4q^{40} + 6q^{41} - 11q^{43} + 8q^{44} - 2q^{46} - 6q^{47} - q^{49} + 11q^{50} - 3q^{52} + 18q^{53} - 32q^{55} - q^{56} - q^{58} - 5q^{59} + 6q^{61} + 18q^{62} + 2q^{64} + 12q^{65} - 7q^{67} - 7q^{68} + 4q^{70} + 14q^{71} - 28q^{73} + 2q^{74} - 2q^{76} + 4q^{77} + 6q^{79} - 8q^{80} + 12q^{82} - 4q^{83} + 28q^{85} + 11q^{86} + 4q^{88} + 6q^{89} - 6q^{91} - q^{92} + 6q^{94} + 8q^{95} + 8q^{97} - 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i $$0.185750\pi$$
0.0599153 + 0.998203i $$0.480917\pi$$
$$6$$ 0 0
$$7$$ 0.500000 0.866025i 0.188982 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 4.00000 1.26491
$$11$$ −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i $$0.372704\pi$$
−0.992361 + 0.123371i $$0.960630\pi$$
$$12$$ 0 0
$$13$$ −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i $$-0.303244\pi$$
−0.995535 + 0.0943882i $$0.969911\pi$$
$$14$$ −0.500000 0.866025i −0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 7.00000 1.69775 0.848875 0.528594i $$-0.177281\pi$$
0.848875 + 0.528594i $$0.177281\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 2.00000 3.46410i 0.447214 0.774597i
$$21$$ 0 0
$$22$$ 2.00000 + 3.46410i 0.426401 + 0.738549i
$$23$$ −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i $$-0.199913\pi$$
−0.913434 + 0.406986i $$0.866580\pi$$
$$24$$ 0 0
$$25$$ −5.50000 + 9.52628i −1.10000 + 1.90526i
$$26$$ −3.00000 −0.588348
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i $$-0.803736\pi$$
0.908708 + 0.417432i $$0.137070\pi$$
$$30$$ 0 0
$$31$$ 4.50000 + 7.79423i 0.808224 + 1.39988i 0.914093 + 0.405505i $$0.132904\pi$$
−0.105869 + 0.994380i $$0.533762\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 3.50000 6.06218i 0.600245 1.03965i
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 1.00000 1.73205i 0.162221 0.280976i
$$39$$ 0 0
$$40$$ −2.00000 3.46410i −0.316228 0.547723i
$$41$$ 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i $$-0.0114536\pi$$
−0.530831 + 0.847477i $$0.678120\pi$$
$$42$$ 0 0
$$43$$ −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i $$0.483375\pi$$
−0.890947 + 0.454108i $$0.849958\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ 5.50000 + 9.52628i 0.777817 + 1.34722i
$$51$$ 0 0
$$52$$ −1.50000 + 2.59808i −0.208013 + 0.360288i
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 0 0
$$55$$ −16.0000 −2.15744
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 0 0
$$58$$ −0.500000 0.866025i −0.0656532 0.113715i
$$59$$ −2.50000 4.33013i −0.325472 0.563735i 0.656136 0.754643i $$-0.272190\pi$$
−0.981608 + 0.190909i $$0.938857\pi$$
$$60$$ 0 0
$$61$$ 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i $$-0.707841\pi$$
0.991645 + 0.128994i $$0.0411748\pi$$
$$62$$ 9.00000 1.14300
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 10.3923i 0.744208 1.28901i
$$66$$ 0 0
$$67$$ −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i $$-0.307305\pi$$
−0.996659 + 0.0816792i $$0.973972\pi$$
$$68$$ −3.50000 6.06218i −0.424437 0.735147i
$$69$$ 0 0
$$70$$ 2.00000 3.46410i 0.239046 0.414039i
$$71$$ 7.00000 0.830747 0.415374 0.909651i $$-0.363651\pi$$
0.415374 + 0.909651i $$0.363651\pi$$
$$72$$ 0 0
$$73$$ −14.0000 −1.63858 −0.819288 0.573382i $$-0.805631\pi$$
−0.819288 + 0.573382i $$0.805631\pi$$
$$74$$ 1.00000 1.73205i 0.116248 0.201347i
$$75$$ 0 0
$$76$$ −1.00000 1.73205i −0.114708 0.198680i
$$77$$ 2.00000 + 3.46410i 0.227921 + 0.394771i
$$78$$ 0 0
$$79$$ 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i $$-0.723743\pi$$
0.983967 + 0.178352i $$0.0570765\pi$$
$$80$$ −4.00000 −0.447214
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ −2.00000 + 3.46410i −0.219529 + 0.380235i −0.954664 0.297686i $$-0.903785\pi$$
0.735135 + 0.677920i $$0.237119\pi$$
$$84$$ 0 0
$$85$$ 14.0000 + 24.2487i 1.51851 + 2.63014i
$$86$$ 5.50000 + 9.52628i 0.593080 + 1.02725i
$$87$$ 0 0
$$88$$ 2.00000 3.46410i 0.213201 0.369274i
$$89$$ 3.00000 0.317999 0.159000 0.987279i $$-0.449173\pi$$
0.159000 + 0.987279i $$0.449173\pi$$
$$90$$ 0 0
$$91$$ −3.00000 −0.314485
$$92$$ −0.500000 + 0.866025i −0.0521286 + 0.0902894i
$$93$$ 0 0
$$94$$ 3.00000 + 5.19615i 0.309426 + 0.535942i
$$95$$ 4.00000 + 6.92820i 0.410391 + 0.710819i
$$96$$ 0 0
$$97$$ 4.00000 6.92820i 0.406138 0.703452i −0.588315 0.808632i $$-0.700208\pi$$
0.994453 + 0.105180i $$0.0335417\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ 11.0000 1.10000
$$101$$ 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i $$-0.667578\pi$$
0.999996 + 0.00286291i $$0.000911295\pi$$
$$102$$ 0 0
$$103$$ −8.50000 14.7224i −0.837530 1.45064i −0.891954 0.452126i $$-0.850666\pi$$
0.0544240 0.998518i $$-0.482668\pi$$
$$104$$ 1.50000 + 2.59808i 0.147087 + 0.254762i
$$105$$ 0 0
$$106$$ 4.50000 7.79423i 0.437079 0.757042i
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 16.0000 1.53252 0.766261 0.642529i $$-0.222115\pi$$
0.766261 + 0.642529i $$0.222115\pi$$
$$110$$ −8.00000 + 13.8564i −0.762770 + 1.32116i
$$111$$ 0 0
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ −4.00000 6.92820i −0.376288 0.651751i 0.614231 0.789127i $$-0.289466\pi$$
−0.990519 + 0.137376i $$0.956133\pi$$
$$114$$ 0 0
$$115$$ 2.00000 3.46410i 0.186501 0.323029i
$$116$$ −1.00000 −0.0928477
$$117$$ 0 0
$$118$$ −5.00000 −0.460287
$$119$$ 3.50000 6.06218i 0.320844 0.555719i
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ −3.00000 5.19615i −0.271607 0.470438i
$$123$$ 0 0
$$124$$ 4.50000 7.79423i 0.404112 0.699942i
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −6.00000 10.3923i −0.526235 0.911465i
$$131$$ 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i $$-0.152757\pi$$
−0.843356 + 0.537355i $$0.819423\pi$$
$$132$$ 0 0
$$133$$ 1.00000 1.73205i 0.0867110 0.150188i
$$134$$ −7.00000 −0.604708
$$135$$ 0 0
$$136$$ −7.00000 −0.600245
$$137$$ 11.0000 19.0526i 0.939793 1.62777i 0.173939 0.984757i $$-0.444351\pi$$
0.765855 0.643013i $$-0.222316\pi$$
$$138$$ 0 0
$$139$$ −5.00000 8.66025i −0.424094 0.734553i 0.572241 0.820086i $$-0.306074\pi$$
−0.996335 + 0.0855324i $$0.972741\pi$$
$$140$$ −2.00000 3.46410i −0.169031 0.292770i
$$141$$ 0 0
$$142$$ 3.50000 6.06218i 0.293713 0.508727i
$$143$$ 12.0000 1.00349
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ −7.00000 + 12.1244i −0.579324 + 1.00342i
$$147$$ 0 0
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i $$-0.205881\pi$$
−0.920904 + 0.389789i $$0.872548\pi$$
$$150$$ 0 0
$$151$$ −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i $$-0.966722\pi$$
0.587646 + 0.809118i $$0.300055\pi$$
$$152$$ −2.00000 −0.162221
$$153$$ 0 0
$$154$$ 4.00000 0.322329
$$155$$ −18.0000 + 31.1769i −1.44579 + 2.50419i
$$156$$ 0 0
$$157$$ −8.50000 14.7224i −0.678374 1.17498i −0.975470 0.220131i $$-0.929352\pi$$
0.297097 0.954847i $$-0.403982\pi$$
$$158$$ −3.00000 5.19615i −0.238667 0.413384i
$$159$$ 0 0
$$160$$ −2.00000 + 3.46410i −0.158114 + 0.273861i
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ −1.00000 −0.0783260 −0.0391630 0.999233i $$-0.512469\pi$$
−0.0391630 + 0.999233i $$0.512469\pi$$
$$164$$ 3.00000 5.19615i 0.234261 0.405751i
$$165$$ 0 0
$$166$$ 2.00000 + 3.46410i 0.155230 + 0.268866i
$$167$$ −4.00000 6.92820i −0.309529 0.536120i 0.668730 0.743505i $$-0.266838\pi$$
−0.978259 + 0.207385i $$0.933505\pi$$
$$168$$ 0 0
$$169$$ 2.00000 3.46410i 0.153846 0.266469i
$$170$$ 28.0000 2.14750
$$171$$ 0 0
$$172$$ 11.0000 0.838742
$$173$$ −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i $$-0.931694\pi$$
0.672949 + 0.739689i $$0.265027\pi$$
$$174$$ 0 0
$$175$$ 5.50000 + 9.52628i 0.415761 + 0.720119i
$$176$$ −2.00000 3.46410i −0.150756 0.261116i
$$177$$ 0 0
$$178$$ 1.50000 2.59808i 0.112430 0.194734i
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −9.00000 −0.668965 −0.334482 0.942402i $$-0.608561\pi$$
−0.334482 + 0.942402i $$0.608561\pi$$
$$182$$ −1.50000 + 2.59808i −0.111187 + 0.192582i
$$183$$ 0 0
$$184$$ 0.500000 + 0.866025i 0.0368605 + 0.0638442i
$$185$$ 4.00000 + 6.92820i 0.294086 + 0.509372i
$$186$$ 0 0
$$187$$ −14.0000 + 24.2487i −1.02378 + 1.77324i
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i $$-0.690384\pi$$
0.997225 + 0.0744412i $$0.0237173\pi$$
$$192$$ 0 0
$$193$$ −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i $$-0.224262\pi$$
−0.941865 + 0.335993i $$0.890928\pi$$
$$194$$ −4.00000 6.92820i −0.287183 0.497416i
$$195$$ 0 0
$$196$$ −0.500000 + 0.866025i −0.0357143 + 0.0618590i
$$197$$ −26.0000 −1.85242 −0.926212 0.377004i $$-0.876954\pi$$
−0.926212 + 0.377004i $$0.876954\pi$$
$$198$$ 0 0
$$199$$ −7.00000 −0.496217 −0.248108 0.968732i $$-0.579809\pi$$
−0.248108 + 0.968732i $$0.579809\pi$$
$$200$$ 5.50000 9.52628i 0.388909 0.673610i
$$201$$ 0 0
$$202$$ −5.00000 8.66025i −0.351799 0.609333i
$$203$$ −0.500000 0.866025i −0.0350931 0.0607831i
$$204$$ 0 0
$$205$$ −12.0000 + 20.7846i −0.838116 + 1.45166i
$$206$$ −17.0000 −1.18445
$$207$$ 0 0
$$208$$ 3.00000 0.208013
$$209$$ −4.00000 + 6.92820i −0.276686 + 0.479234i
$$210$$ 0 0
$$211$$ 0.500000 + 0.866025i 0.0344214 + 0.0596196i 0.882723 0.469894i $$-0.155708\pi$$
−0.848301 + 0.529514i $$0.822374\pi$$
$$212$$ −4.50000 7.79423i −0.309061 0.535310i
$$213$$ 0 0
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ −44.0000 −3.00078
$$216$$ 0 0
$$217$$ 9.00000 0.610960
$$218$$ 8.00000 13.8564i 0.541828 0.938474i
$$219$$ 0 0
$$220$$ 8.00000 + 13.8564i 0.539360 + 0.934199i
$$221$$ −10.5000 18.1865i −0.706306 1.22336i
$$222$$ 0 0
$$223$$ −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i $$-0.919650\pi$$
0.700449 + 0.713702i $$0.252983\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −8.00000 −0.532152
$$227$$ −4.50000 + 7.79423i −0.298675 + 0.517321i −0.975833 0.218517i $$-0.929878\pi$$
0.677158 + 0.735838i $$0.263211\pi$$
$$228$$ 0 0
$$229$$ 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i $$-0.0135930\pi$$
−0.536515 + 0.843891i $$0.680260\pi$$
$$230$$ −2.00000 3.46410i −0.131876 0.228416i
$$231$$ 0 0
$$232$$ −0.500000 + 0.866025i −0.0328266 + 0.0568574i
$$233$$ 4.00000 0.262049 0.131024 0.991379i $$-0.458173\pi$$
0.131024 + 0.991379i $$0.458173\pi$$
$$234$$ 0 0
$$235$$ −24.0000 −1.56559
$$236$$ −2.50000 + 4.33013i −0.162736 + 0.281867i
$$237$$ 0 0
$$238$$ −3.50000 6.06218i −0.226871 0.392953i
$$239$$ 6.00000 + 10.3923i 0.388108 + 0.672222i 0.992195 0.124696i $$-0.0397955\pi$$
−0.604087 + 0.796918i $$0.706462\pi$$
$$240$$ 0 0
$$241$$ 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i $$-0.728952\pi$$
0.980917 + 0.194429i $$0.0622852\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 0 0
$$244$$ −6.00000 −0.384111
$$245$$ 2.00000 3.46410i 0.127775 0.221313i
$$246$$ 0 0
$$247$$ −3.00000 5.19615i −0.190885 0.330623i
$$248$$ −4.50000 7.79423i −0.285750 0.494934i
$$249$$ 0 0
$$250$$ −12.0000 + 20.7846i −0.758947 + 1.31453i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ 0 0
$$255$$ 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
$$259$$ 1.00000 1.73205i 0.0621370 0.107624i
$$260$$ −12.0000 −0.744208
$$261$$ 0 0
$$262$$ 1.00000 0.0617802
$$263$$ 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i $$-0.743833\pi$$
0.970758 + 0.240059i $$0.0771668\pi$$
$$264$$ 0 0
$$265$$ 18.0000 + 31.1769i 1.10573 + 1.91518i
$$266$$ −1.00000 1.73205i −0.0613139 0.106199i
$$267$$ 0 0
$$268$$ −3.50000 + 6.06218i −0.213797 + 0.370306i
$$269$$ −4.00000 −0.243884 −0.121942 0.992537i $$-0.538912\pi$$
−0.121942 + 0.992537i $$0.538912\pi$$
$$270$$ 0 0
$$271$$ 3.00000 0.182237 0.0911185 0.995840i $$-0.470956\pi$$
0.0911185 + 0.995840i $$0.470956\pi$$
$$272$$ −3.50000 + 6.06218i −0.212219 + 0.367574i
$$273$$ 0 0
$$274$$ −11.0000 19.0526i −0.664534 1.15101i
$$275$$ −22.0000 38.1051i −1.32665 2.29783i
$$276$$ 0 0
$$277$$ −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i $$-0.910591\pi$$
0.720473 + 0.693482i $$0.243925\pi$$
$$278$$ −10.0000 −0.599760
$$279$$ 0 0
$$280$$ −4.00000 −0.239046
$$281$$ −5.00000 + 8.66025i −0.298275 + 0.516627i −0.975741 0.218926i $$-0.929745\pi$$
0.677466 + 0.735554i $$0.263078\pi$$
$$282$$ 0 0
$$283$$ −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i $$-0.853740\pi$$
0.0640654 0.997946i $$-0.479593\pi$$
$$284$$ −3.50000 6.06218i −0.207687 0.359724i
$$285$$ 0 0
$$286$$ 6.00000 10.3923i 0.354787 0.614510i
$$287$$ 6.00000 0.354169
$$288$$ 0 0
$$289$$ 32.0000 1.88235
$$290$$ 2.00000 3.46410i 0.117444 0.203419i
$$291$$ 0 0
$$292$$ 7.00000 + 12.1244i 0.409644 + 0.709524i
$$293$$ 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i $$-0.110589\pi$$
−0.764990 + 0.644042i $$0.777256\pi$$
$$294$$ 0 0
$$295$$ 10.0000 17.3205i 0.582223 1.00844i
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ −3.00000 −0.173785
$$299$$ −1.50000 + 2.59808i −0.0867472 + 0.150251i
$$300$$ 0 0
$$301$$ 5.50000 + 9.52628i 0.317015 + 0.549086i
$$302$$ 5.00000 + 8.66025i 0.287718 + 0.498342i
$$303$$ 0 0
$$304$$ −1.00000 + 1.73205i −0.0573539 + 0.0993399i
$$305$$ 24.0000 1.37424
$$306$$ 0 0
$$307$$ −2.00000 −0.114146 −0.0570730 0.998370i $$-0.518177\pi$$
−0.0570730 + 0.998370i $$0.518177\pi$$
$$308$$ 2.00000 3.46410i 0.113961 0.197386i
$$309$$ 0 0
$$310$$ 18.0000 + 31.1769i 1.02233 + 1.77073i
$$311$$ −4.00000 6.92820i −0.226819 0.392862i 0.730044 0.683400i $$-0.239499\pi$$
−0.956864 + 0.290537i $$0.906166\pi$$
$$312$$ 0 0
$$313$$ 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i $$-0.570608\pi$$
0.954810 0.297218i $$-0.0960589\pi$$
$$314$$ −17.0000 −0.959366
$$315$$ 0 0
$$316$$ −6.00000 −0.337526
$$317$$ −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i $$0.335355\pi$$
−0.999980 + 0.00635137i $$0.997978\pi$$
$$318$$ 0 0
$$319$$ 2.00000 + 3.46410i 0.111979 + 0.193952i
$$320$$ 2.00000 + 3.46410i 0.111803 + 0.193649i
$$321$$ 0 0
$$322$$ −0.500000 + 0.866025i −0.0278639 + 0.0482617i
$$323$$ 14.0000 0.778981
$$324$$ 0 0
$$325$$ 33.0000 1.83051
$$326$$ −0.500000 + 0.866025i −0.0276924 + 0.0479647i
$$327$$ 0 0
$$328$$ −3.00000 5.19615i −0.165647 0.286910i
$$329$$ 3.00000 + 5.19615i 0.165395 + 0.286473i
$$330$$ 0 0
$$331$$ 15.5000 26.8468i 0.851957 1.47563i −0.0274825 0.999622i $$-0.508749\pi$$
0.879440 0.476011i $$-0.157918\pi$$
$$332$$ 4.00000 0.219529
$$333$$ 0 0
$$334$$ −8.00000 −0.437741
$$335$$ 14.0000 24.2487i 0.764902 1.32485i
$$336$$ 0 0
$$337$$ −13.5000 23.3827i −0.735392 1.27374i −0.954551 0.298047i $$-0.903665\pi$$
0.219159 0.975689i $$-0.429669\pi$$
$$338$$ −2.00000 3.46410i −0.108786 0.188422i
$$339$$ 0 0
$$340$$ 14.0000 24.2487i 0.759257 1.31507i
$$341$$ −36.0000 −1.94951
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 5.50000 9.52628i 0.296540 0.513623i
$$345$$ 0 0
$$346$$ 4.00000 + 6.92820i 0.215041 + 0.372463i
$$347$$ 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i $$-0.00616095\pi$$
−0.516667 + 0.856186i $$0.672828\pi$$
$$348$$ 0 0
$$349$$ −12.5000 + 21.6506i −0.669110 + 1.15893i 0.309044 + 0.951048i $$0.399991\pi$$
−0.978153 + 0.207884i $$0.933342\pi$$
$$350$$ 11.0000 0.587975
$$351$$ 0 0
$$352$$ −4.00000 −0.213201
$$353$$ 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i $$-0.702627\pi$$
0.993626 + 0.112731i $$0.0359599\pi$$
$$354$$ 0 0
$$355$$ 14.0000 + 24.2487i 0.743043 + 1.28699i
$$356$$ −1.50000 2.59808i −0.0794998 0.137698i
$$357$$ 0 0
$$358$$ 6.00000 10.3923i 0.317110 0.549250i
$$359$$ 11.0000 0.580558 0.290279 0.956942i $$-0.406252\pi$$
0.290279 + 0.956942i $$0.406252\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ −4.50000 + 7.79423i −0.236515 + 0.409656i
$$363$$ 0 0
$$364$$ 1.50000 + 2.59808i 0.0786214 + 0.136176i
$$365$$ −28.0000 48.4974i −1.46559 2.53847i
$$366$$ 0 0
$$367$$ 12.5000 21.6506i 0.652495 1.13015i −0.330021 0.943974i $$-0.607056\pi$$
0.982516 0.186180i $$-0.0596109\pi$$
$$368$$ 1.00000 0.0521286
$$369$$ 0 0
$$370$$ 8.00000 0.415900
$$371$$ 4.50000 7.79423i 0.233628 0.404656i
$$372$$ 0 0
$$373$$ 19.0000 + 32.9090i 0.983783 + 1.70396i 0.647225 + 0.762299i $$0.275929\pi$$
0.336557 + 0.941663i $$0.390737\pi$$
$$374$$ 14.0000 + 24.2487i 0.723923 + 1.25387i
$$375$$ 0 0
$$376$$ 3.00000 5.19615i 0.154713 0.267971i
$$377$$ −3.00000 −0.154508
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 4.00000 6.92820i 0.205196 0.355409i
$$381$$ 0 0
$$382$$ −6.00000 10.3923i −0.306987 0.531717i
$$383$$ −2.00000 3.46410i −0.102195 0.177007i 0.810394 0.585886i $$-0.199253\pi$$
−0.912589 + 0.408879i $$0.865920\pi$$
$$384$$ 0 0
$$385$$ −8.00000 + 13.8564i −0.407718 + 0.706188i
$$386$$ −5.00000 −0.254493
$$387$$ 0 0
$$388$$ −8.00000 −0.406138
$$389$$ −7.00000 + 12.1244i −0.354914 + 0.614729i −0.987103 0.160085i $$-0.948823\pi$$
0.632189 + 0.774814i $$0.282157\pi$$
$$390$$ 0 0
$$391$$ −3.50000 6.06218i −0.177003 0.306578i
$$392$$ 0.500000 + 0.866025i 0.0252538 + 0.0437409i
$$393$$ 0 0
$$394$$ −13.0000 + 22.5167i −0.654931 + 1.13437i
$$395$$ 24.0000 1.20757
$$396$$ 0 0
$$397$$ 6.00000 0.301131 0.150566 0.988600i $$-0.451890\pi$$
0.150566 + 0.988600i $$0.451890\pi$$
$$398$$ −3.50000 + 6.06218i −0.175439 + 0.303870i
$$399$$ 0 0
$$400$$ −5.50000 9.52628i −0.275000 0.476314i
$$401$$ 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i $$0.102830\pi$$
−0.199207 + 0.979957i $$0.563837\pi$$
$$402$$ 0 0
$$403$$ 13.5000 23.3827i 0.672483 1.16477i
$$404$$ −10.0000 −0.497519
$$405$$ 0 0
$$406$$ −1.00000 −0.0496292
$$407$$ −4.00000 + 6.92820i −0.198273 + 0.343418i
$$408$$ 0 0
$$409$$ −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i $$-0.182412\pi$$
−0.889689 + 0.456566i $$0.849079\pi$$
$$410$$ 12.0000 + 20.7846i 0.592638 + 1.02648i
$$411$$ 0 0
$$412$$ −8.50000 + 14.7224i −0.418765 + 0.725322i
$$413$$ −5.00000 −0.246034
$$414$$ 0 0
$$415$$ −16.0000 −0.785409
$$416$$ 1.50000 2.59808i 0.0735436 0.127381i
$$417$$ 0 0
$$418$$ 4.00000 + 6.92820i 0.195646 + 0.338869i
$$419$$ −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i $$-0.868253\pi$$
0.109483 0.993989i $$-0.465080\pi$$
$$420$$ 0 0
$$421$$ 3.00000 5.19615i 0.146211 0.253245i −0.783613 0.621249i $$-0.786625\pi$$
0.929824 + 0.368004i $$0.119959\pi$$
$$422$$ 1.00000 0.0486792
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ −38.5000 + 66.6840i −1.86752 + 3.23465i
$$426$$ 0 0
$$427$$ −3.00000 5.19615i −0.145180 0.251459i
$$428$$ 6.00000 + 10.3923i 0.290021 + 0.502331i
$$429$$ 0 0
$$430$$ −22.0000 + 38.1051i −1.06093 + 1.83759i
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 0 0
$$433$$ 8.00000 0.384455 0.192228 0.981350i $$-0.438429\pi$$
0.192228 + 0.981350i $$0.438429\pi$$
$$434$$ 4.50000 7.79423i 0.216007 0.374135i
$$435$$ 0 0
$$436$$ −8.00000 13.8564i −0.383131 0.663602i
$$437$$ −1.00000 1.73205i −0.0478365 0.0828552i
$$438$$ 0 0
$$439$$ −4.50000 + 7.79423i −0.214773 + 0.371998i −0.953202 0.302333i $$-0.902235\pi$$
0.738429 + 0.674331i $$0.235568\pi$$
$$440$$ 16.0000 0.762770
$$441$$ 0 0
$$442$$ −21.0000 −0.998868
$$443$$ 13.0000 22.5167i 0.617649 1.06980i −0.372265 0.928126i $$-0.621419\pi$$
0.989914 0.141672i $$-0.0452479\pi$$
$$444$$ 0 0
$$445$$ 6.00000 + 10.3923i 0.284427 + 0.492642i
$$446$$ 4.00000 + 6.92820i 0.189405 + 0.328060i
$$447$$ 0 0
$$448$$ 0.500000 0.866025i 0.0236228 0.0409159i
$$449$$ −4.00000 −0.188772 −0.0943858 0.995536i $$-0.530089\pi$$
−0.0943858 + 0.995536i $$0.530089\pi$$
$$450$$ 0 0
$$451$$ −24.0000 −1.13012
$$452$$ −4.00000 + 6.92820i −0.188144 + 0.325875i
$$453$$ 0 0
$$454$$ 4.50000 + 7.79423i 0.211195 + 0.365801i
$$455$$ −6.00000 10.3923i −0.281284 0.487199i
$$456$$ 0 0
$$457$$ 14.5000 25.1147i 0.678281 1.17482i −0.297217 0.954810i $$-0.596058\pi$$
0.975498 0.220008i $$-0.0706083\pi$$
$$458$$ 14.0000 0.654177
$$459$$ 0 0
$$460$$ −4.00000 −0.186501
$$461$$ −7.00000 + 12.1244i −0.326023 + 0.564688i −0.981719 0.190337i $$-0.939042\pi$$
0.655696 + 0.755025i $$0.272375\pi$$
$$462$$ 0 0
$$463$$ −11.0000 19.0526i −0.511213 0.885448i −0.999916 0.0129968i $$-0.995863\pi$$
0.488702 0.872451i $$-0.337470\pi$$
$$464$$ 0.500000 + 0.866025i 0.0232119 + 0.0402042i
$$465$$ 0 0
$$466$$ 2.00000 3.46410i 0.0926482 0.160471i
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ 0 0
$$469$$ −7.00000 −0.323230
$$470$$ −12.0000 + 20.7846i −0.553519 + 0.958723i
$$471$$ 0 0
$$472$$ 2.50000 + 4.33013i 0.115072 + 0.199310i
$$473$$ −22.0000 38.1051i −1.01156 1.75208i
$$474$$ 0 0
$$475$$ −11.0000 + 19.0526i −0.504715 + 0.874191i
$$476$$ −7.00000 −0.320844
$$477$$ 0 0
$$478$$ 12.0000 0.548867
$$479$$ 4.00000 6.92820i 0.182765 0.316558i −0.760056 0.649857i $$-0.774829\pi$$
0.942821 + 0.333300i $$0.108162\pi$$
$$480$$ 0 0
$$481$$ −3.00000 5.19615i −0.136788 0.236924i
$$482$$ −5.00000 8.66025i −0.227744 0.394464i
$$483$$ 0 0
$$484$$ −2.50000 + 4.33013i −0.113636 + 0.196824i
$$485$$ 32.0000 1.45305
$$486$$ 0 0
$$487$$ 26.0000 1.17817 0.589086 0.808070i $$-0.299488\pi$$
0.589086 + 0.808070i $$0.299488\pi$$
$$488$$ −3.00000 + 5.19615i −0.135804 + 0.235219i
$$489$$ 0 0
$$490$$ −2.00000 3.46410i −0.0903508 0.156492i
$$491$$ 12.0000 + 20.7846i 0.541552 + 0.937996i 0.998815 + 0.0486647i $$0.0154966\pi$$
−0.457263 + 0.889332i $$0.651170\pi$$
$$492$$ 0 0
$$493$$ 3.50000 6.06218i 0.157632 0.273027i
$$494$$ −6.00000 −0.269953
$$495$$ 0 0
$$496$$ −9.00000 −0.404112
$$497$$ 3.50000 6.06218i 0.156996 0.271926i
$$498$$ 0 0
$$499$$ −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i $$-0.951061\pi$$
0.361478 0.932381i $$-0.382272\pi$$
$$500$$ 12.0000 + 20.7846i 0.536656 + 0.929516i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ 40.0000 1.77998
$$506$$ 2.00000 3.46410i 0.0889108 0.153998i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i $$-0.209119\pi$$
−0.924821 + 0.380402i $$0.875786\pi$$
$$510$$ 0 0
$$511$$ −7.00000 + 12.1244i −0.309662 + 0.536350i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 30.0000 1.32324
$$515$$ 34.0000 58.8897i 1.49822 2.59499i
$$516$$ 0 0
$$517$$ −12.0000 20.7846i −0.527759 0.914106i
$$518$$ −1.00000 1.73205i −0.0439375 0.0761019i
$$519$$ 0 0
$$520$$ −6.00000 + 10.3923i −0.263117 + 0.455733i
$$521$$ 15.0000 0.657162 0.328581 0.944476i $$-0.393430\pi$$
0.328581 + 0.944476i $$0.393430\pi$$
$$522$$ 0 0
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ 0.500000 0.866025i 0.0218426 0.0378325i
$$525$$ 0 0
$$526$$ −4.50000 7.79423i −0.196209 0.339845i
$$527$$ 31.5000 + 54.5596i 1.37216 + 2.37665i
$$528$$ 0 0
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ 36.0000 1.56374
$$531$$ 0 0
$$532$$ −2.00000 −0.0867110
$$533$$ 9.00000 15.5885i 0.389833 0.675211i
$$534$$ 0 0
$$535$$ −24.0000 41.5692i −1.03761 1.79719i
$$536$$ 3.50000 + 6.06218i 0.151177 + 0.261846i
$$537$$ 0 0
$$538$$ −2.00000 + 3.46410i −0.0862261 + 0.149348i
$$539$$ 4.00000 0.172292
$$540$$ 0 0
$$541$$ −36.0000 −1.54776 −0.773880 0.633332i $$-0.781687\pi$$
−0.773880 + 0.633332i $$0.781687\pi$$
$$542$$ 1.50000 2.59808i 0.0644305 0.111597i
$$543$$ 0 0
$$544$$ 3.50000 + 6.06218i 0.150061 + 0.259914i
$$545$$ 32.0000 + 55.4256i 1.37073 + 2.37417i
$$546$$ 0 0
$$547$$ −18.0000 + 31.1769i −0.769624 + 1.33303i 0.168142 + 0.985763i $$0.446223\pi$$
−0.937767 + 0.347266i $$0.887110\pi$$
$$548$$ −22.0000 −0.939793
$$549$$ 0 0
$$550$$ −44.0000 −1.87617
$$551$$ 1.00000 1.73205i 0.0426014 0.0737878i
$$552$$ 0 0
$$553$$ −3.00000 5.19615i −0.127573 0.220963i
$$554$$ 4.00000 + 6.92820i 0.169944 + 0.294351i
$$555$$ 0 0
$$556$$ −5.00000 + 8.66025i −0.212047 + 0.367277i
$$557$$ −1.00000 −0.0423714 −0.0211857 0.999776i $$-0.506744\pi$$
−0.0211857 + 0.999776i $$0.506744\pi$$
$$558$$ 0 0
$$559$$ 33.0000 1.39575
$$560$$ −2.00000 + 3.46410i −0.0845154 + 0.146385i
$$561$$ 0 0
$$562$$ 5.00000 + 8.66025i 0.210912 + 0.365311i
$$563$$ 5.50000 + 9.52628i 0.231797 + 0.401485i 0.958337 0.285640i $$-0.0922060\pi$$
−0.726540 + 0.687124i $$0.758873\pi$$
$$564$$ 0 0
$$565$$ 16.0000 27.7128i 0.673125 1.16589i
$$566$$ −28.0000 −1.17693
$$567$$ 0 0
$$568$$ −7.00000 −0.293713
$$569$$ 6.00000 10.3923i 0.251533 0.435668i −0.712415 0.701758i $$-0.752399\pi$$
0.963948 + 0.266090i $$0.0857319\pi$$
$$570$$ 0 0
$$571$$ 19.5000 + 33.7750i 0.816050 + 1.41344i 0.908572 + 0.417729i $$0.137174\pi$$
−0.0925222 + 0.995711i $$0.529493\pi$$
$$572$$ −6.00000 10.3923i −0.250873 0.434524i
$$573$$ 0 0
$$574$$ 3.00000 5.19615i 0.125218 0.216883i
$$575$$ 11.0000 0.458732
$$576$$ 0 0
$$577$$ 10.0000 0.416305 0.208153 0.978096i $$-0.433255\pi$$
0.208153 + 0.978096i $$0.433255\pi$$
$$578$$ 16.0000 27.7128i 0.665512 1.15270i
$$579$$ 0 0
$$580$$ −2.00000 3.46410i −0.0830455 0.143839i
$$581$$ 2.00000 + 3.46410i 0.0829740 + 0.143715i
$$582$$ 0 0
$$583$$ −18.0000 + 31.1769i −0.745484 + 1.29122i
$$584$$ 14.0000 0.579324
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ −12.5000 + 21.6506i −0.515930 + 0.893617i 0.483899 + 0.875124i $$0.339220\pi$$
−0.999829 + 0.0184934i $$0.994113\pi$$
$$588$$ 0 0
$$589$$ 9.00000 + 15.5885i 0.370839 + 0.642311i
$$590$$ −10.0000 17.3205i −0.411693 0.713074i
$$591$$ 0 0
$$592$$ −1.00000 + 1.73205i −0.0410997 + 0.0711868i
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 28.0000 1.14789
$$596$$ −1.50000 + 2.59808i −0.0614424 + 0.106421i
$$597$$ 0 0
$$598$$ 1.50000 + 2.59808i 0.0613396 + 0.106243i
$$599$$ 10.5000 + 18.1865i 0.429018 + 0.743082i 0.996786 0.0801071i $$-0.0255262\pi$$
−0.567768 + 0.823189i $$0.692193\pi$$
$$600$$ 0 0
$$601$$ 14.0000 24.2487i 0.571072 0.989126i −0.425384 0.905013i $$-0.639861\pi$$
0.996456 0.0841128i $$-0.0268056\pi$$
$$602$$ 11.0000 0.448327
$$603$$ 0 0
$$604$$ 10.0000 0.406894
$$605$$ 10.0000 17.3205i 0.406558 0.704179i
$$606$$ 0 0
$$607$$ −19.5000 33.7750i −0.791481 1.37088i −0.925050 0.379845i $$-0.875977\pi$$
0.133570 0.991039i $$-0.457356\pi$$
$$608$$ 1.00000 + 1.73205i 0.0405554 + 0.0702439i
$$609$$ 0 0
$$610$$ 12.0000 20.7846i 0.485866 0.841544i
$$611$$ 18.0000 0.728202
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ −1.00000 + 1.73205i −0.0403567 + 0.0698999i
$$615$$ 0 0
$$616$$ −2.00000 3.46410i −0.0805823 0.139573i
$$617$$ 7.00000 + 12.1244i 0.281809 + 0.488108i 0.971830 0.235681i $$-0.0757321\pi$$
−0.690021 + 0.723789i $$0.742399\pi$$
$$618$$ 0 0
$$619$$ 7.00000 12.1244i 0.281354 0.487319i −0.690365 0.723462i $$-0.742550\pi$$
0.971718 + 0.236143i $$0.0758832\pi$$
$$620$$ 36.0000 1.44579
$$621$$ 0 0
$$622$$ −8.00000 −0.320771
$$623$$ 1.50000 2.59808i 0.0600962 0.104090i
$$624$$ 0 0
$$625$$ −20.5000 35.5070i −0.820000 1.42028i
$$626$$ −13.0000 22.5167i −0.519584 0.899947i
$$627$$ 0 0
$$628$$ −8.50000 + 14.7224i −0.339187 + 0.587489i
$$629$$ 14.0000 0.558217
$$630$$ 0 0
$$631$$ −4.00000 −0.159237 −0.0796187 0.996825i $$-0.525370\pi$$
−0.0796187 + 0.996825i $$0.525370\pi$$
$$632$$ −3.00000 + 5.19615i −0.119334 + 0.206692i
$$633$$ 0 0
$$634$$ 9.00000 + 15.5885i 0.357436 + 0.619097i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −1.50000 + 2.59808i −0.0594322 + 0.102940i
$$638$$ 4.00000 0.158362
$$639$$ 0 0
$$640$$ 4.00000 0.158114
$$641$$ −14.0000 + 24.2487i −0.552967 + 0.957767i 0.445092 + 0.895485i $$0.353171\pi$$
−0.998059 + 0.0622816i $$0.980162\pi$$
$$642$$ 0 0
$$643$$ 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i $$-0.141535\pi$$
−0.823891 + 0.566748i $$0.808201\pi$$
$$644$$ 0.500000 + 0.866025i 0.0197028 + 0.0341262i
$$645$$ 0 0
$$646$$ 7.00000 12.1244i 0.275411 0.477026i
$$647$$ −42.0000 −1.65119 −0.825595 0.564263i $$-0.809160\pi$$
−0.825595 + 0.564263i $$0.809160\pi$$
$$648$$ 0 0
$$649$$ 20.0000 0.785069
$$650$$ 16.5000 28.5788i 0.647183 1.12095i
$$651$$ 0 0
$$652$$ 0.500000 + 0.866025i 0.0195815 + 0.0339162i
$$653$$ 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i $$-0.147971\pi$$
−0.835182 + 0.549973i $$0.814638\pi$$
$$654$$ 0 0
$$655$$ −2.00000 + 3.46410i −0.0781465 + 0.135354i
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ 6.00000 0.233904
$$659$$ −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i $$0.350275\pi$$
−0.998584 + 0.0531977i $$0.983059\pi$$
$$660$$ 0 0
$$661$$ 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i $$-0.0788928\pi$$
−0.697174 + 0.716902i $$0.745559\pi$$
$$662$$ −15.5000 26.8468i −0.602425 1.04343i
$$663$$ 0 0
$$664$$ 2.00000 3.46410i 0.0776151 0.134433i
$$665$$ 8.00000 0.310227
$$666$$ 0 0
$$667$$ −1.00000 −0.0387202
$$668$$ −4.00000 + 6.92820i −0.154765 + 0.268060i
$$669$$ 0 0
$$670$$ −14.0000 24.2487i −0.540867 0.936809i
$$671$$ 12.0000 + 20.7846i 0.463255 + 0.802381i
$$672$$ 0 0
$$673$$ −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i $$-0.979523\pi$$
0.554639 + 0.832091i $$0.312856\pi$$
$$674$$ −27.0000 −1.04000
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$678$$ 0 0
$$679$$ −4.00000 6.92820i −0.153506 0.265880i
$$680$$ −14.0000 24.2487i −0.536875 0.929896i
$$681$$ 0 0
$$682$$ −18.0000 + 31.1769i −0.689256 + 1.19383i
$$683$$ 48.0000 1.83667 0.918334 0.395805i $$-0.129534\pi$$
0.918334 + 0.395805i $$0.129534\pi$$
$$684$$ 0 0
$$685$$ 88.0000 3.36231
$$686$$ −0.500000 + 0.866025i −0.0190901 + 0.0330650i
$$687$$ 0 0
$$688$$ −5.50000 9.52628i −0.209686 0.363186i
$$689$$ −13.5000 23.3827i −0.514309 0.890809i
$$690$$ 0 0
$$691$$ 20.0000 34.6410i 0.760836 1.31781i −0.181584 0.983375i $$-0.558123\pi$$
0.942420 0.334431i $$-0.108544\pi$$
$$692$$ 8.00000 0.304114
$$693$$ 0 0
$$694$$ 18.0000 0.683271
$$695$$ 20.0000 34.6410i 0.758643 1.31401i
$$696$$ 0 0
$$697$$ 21.0000 + 36.3731i 0.795432 + 1.37773i
$$698$$ 12.5000 + 21.6506i 0.473132 + 0.819489i
$$699$$ 0 0
$$700$$ 5.50000 9.52628i 0.207880 0.360060i
$$701$$ 2.00000 0.0755390 0.0377695 0.999286i $$-0.487975\pi$$
0.0377695 + 0.999286i $$0.487975\pi$$
$$702$$ 0 0
$$703$$ 4.00000 0.150863
$$704$$ −2.00000 + 3.46410i −0.0753778 + 0.130558i
$$705$$ 0 0
$$706$$ −7.50000 12.9904i −0.282266 0.488899i
$$707$$ −5.00000 8.66025i −0.188044 0.325702i
$$708$$ 0 0
$$709$$ 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i $$-0.562849\pi$$
0.947282 0.320400i $$-0.103817\pi$$
$$710$$ 28.0000 1.05082
$$711$$ 0 0
$$712$$ −3.00000 −0.112430
$$713$$ 4.50000 7.79423i 0.168526 0.291896i
$$714$$ 0 0
$$715$$ 24.0000 + 41.5692i 0.897549 + 1.55460i
$$716$$ −6.00000 10.3923i −0.224231 0.388379i
$$717$$ 0 0
$$718$$ 5.50000 9.52628i 0.205258 0.355518i
$$719$$ −48.0000 −1.79010 −0.895049 0.445968i $$-0.852860\pi$$
−0.895049 + 0.445968i $$0.852860\pi$$
$$720$$ 0 0
$$721$$ −17.0000 −0.633113
$$722$$ −7.50000 + 12.9904i −0.279121 + 0.483452i
$$723$$ 0 0
$$724$$ 4.50000 + 7.79423i 0.167241 + 0.289670i
$$725$$ 5.50000 + 9.52628i 0.204265 + 0.353797i
$$726$$ 0 0
$$727$$ 14.5000 25.1147i 0.537775 0.931454i −0.461248 0.887271i $$-0.652598\pi$$
0.999023 0.0441829i $$-0.0140684\pi$$
$$728$$ 3.00000 0.111187
$$729$$ 0 0
$$730$$ −56.0000 −2.07265
$$731$$ −38.5000 + 66.6840i −1.42397 + 2.46640i
$$732$$ 0 0
$$733$$ 7.50000 + 12.9904i 0.277019 + 0.479811i 0.970642 0.240527i $$-0.0773202\pi$$
−0.693624 + 0.720338i $$0.743987\pi$$
$$734$$ −12.5000 21.6506i −0.461383 0.799140i
$$735$$ 0 0
$$736$$ 0.500000 0.866025i 0.0184302 0.0319221i
$$737$$ 28.0000 1.03139
$$738$$ 0 0
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ 4.00000 6.92820i 0.147043 0.254686i
$$741$$ 0 0
$$742$$ −4.50000 7.79423i −0.165200 0.286135i
$$743$$ 25.5000 + 44.1673i 0.935504 + 1.62034i 0.773732 + 0.633513i $$0.218388\pi$$
0.161772 + 0.986828i $$0.448279\pi$$
$$744$$ 0 0
$$745$$ 6.00000 10.3923i 0.219823 0.380745i
$$746$$ 38.0000 1.39128
$$747$$ 0 0
$$748$$ 28.0000 1.02378
$$749$$ −6.00000 + 10.3923i −0.219235 + 0.379727i
$$750$$ 0 0
$$751$$ −3.00000 5.19615i −0.109472 0.189610i 0.806085 0.591800i $$-0.201583\pi$$
−0.915556 + 0.402190i $$0.868249\pi$$
$$752$$ −3.00000 5.19615i −0.109399 0.189484i
$$753$$ 0 0
$$754$$ −1.50000 + 2.59808i −0.0546268 + 0.0946164i
$$755$$ −40.0000 −1.45575
$$756$$ 0 0
$$757$$ −12.0000 −0.436147 −0.218074 0.975932i $$-0.569977\pi$$
−0.218074 + 0.975932i $$0.569977\pi$$
$$758$$ −4.00000 + 6.92820i −0.145287 + 0.251644i
$$759$$ 0 0
$$760$$ −4.00000 6.92820i −0.145095 0.251312i
$$761$$ −6.50000 11.2583i −0.235625 0.408114i 0.723829 0.689979i $$-0.242380\pi$$
−0.959454 + 0.281865i $$0.909047\pi$$
$$762$$ 0 0
$$763$$ 8.00000 13.8564i 0.289619 0.501636i
$$764$$ −12.0000 −0.434145
$$765$$ 0 0
$$766$$ −4.00000 −0.144526
$$767$$ −7.50000 + 12.9904i −0.270809 + 0.469055i
$$768$$ 0 0
$$769$$ −2.00000 3.46410i −0.0721218 0.124919i 0.827709 0.561157i $$-0.189644\pi$$
−0.899831 + 0.436239i $$0.856310\pi$$
$$770$$ 8.00000 + 13.8564i 0.288300 + 0.499350i
$$771$$ 0 0
$$772$$ −2.50000 + 4.33013i −0.0899770 + 0.155845i
$$773$$ −4.00000 −0.143870 −0.0719350 0.997409i $$-0.522917\pi$$
−0.0719350 + 0.997409i $$0.522917\pi$$
$$774$$ 0 0
$$775$$ −99.0000 −3.55618
$$776$$ −4.00000 + 6.92820i −0.143592 + 0.248708i
$$777$$ 0 0
$$778$$ 7.00000 + 12.1244i 0.250962 + 0.434679i
$$779$$ 6.00000 + 10.3923i 0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ −14.0000 + 24.2487i −0.500959 + 0.867687i
$$782$$ −7.00000 −0.250319
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 34.0000 58.8897i 1.21351 2.10186i
$$786$$ 0 0
$$787$$ −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i $$-0.270624\pi$$
−0.980656 + 0.195737i $$0.937290\pi$$
$$788$$ 13.0000 + 22.5167i 0.463106 + 0.802123i
$$789$$ 0 0
$$790$$