# Properties

 Label 1950.2.z.i.1699.1 Level $1950$ Weight $2$ Character 1950.1699 Analytic conductor $15.571$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.z (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1699.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.1699 Dual form 1950.2.z.i.1849.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} -1.00000i q^{18} +(-2.50000 - 4.33013i) q^{19} +3.00000 q^{21} +(0.866025 - 0.500000i) q^{22} +(-3.46410 - 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 - 1.50000i) q^{28} +10.0000 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +(-0.500000 + 0.866025i) q^{36} +(0.866025 + 0.500000i) q^{37} +5.00000i q^{38} +(1.00000 + 3.46410i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-2.59808 - 1.50000i) q^{42} +(1.73205 - 1.00000i) q^{43} -1.00000 q^{44} +(2.00000 + 3.46410i) q^{46} -9.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(1.00000 - 1.73205i) q^{49} +(0.866025 - 3.50000i) q^{52} +13.0000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{56} +5.00000i q^{57} +(2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-8.66025 - 5.00000i) q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(10.3923 + 6.00000i) q^{67} +(2.00000 + 3.46410i) q^{69} +(1.00000 + 1.73205i) q^{71} +(0.866025 - 0.500000i) q^{72} +16.0000i q^{73} +(-0.500000 - 0.866025i) q^{74} +(2.50000 - 4.33013i) q^{76} -3.00000i q^{77} +(0.866025 - 3.50000i) q^{78} +10.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.19615 - 3.00000i) q^{82} -12.0000i q^{83} +(1.50000 + 2.59808i) q^{84} -2.00000 q^{86} +(0.866025 + 0.500000i) q^{88} +(0.500000 - 0.866025i) q^{89} +(10.5000 + 2.59808i) q^{91} -4.00000i q^{92} +(-8.66025 - 5.00000i) q^{93} +(-4.50000 + 7.79423i) q^{94} -1.00000 q^{96} +(10.3923 - 6.00000i) q^{97} +(-1.73205 + 1.00000i) q^{98} -1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + 2q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} + 2q^{6} + 2q^{9} - 2q^{11} + 12q^{14} - 2q^{16} - 10q^{19} + 12q^{21} - 2q^{24} + 4q^{26} + 40q^{31} - 2q^{36} + 4q^{39} - 12q^{41} - 4q^{44} + 8q^{46} + 4q^{49} - 2q^{54} + 6q^{56} + 8q^{59} + 4q^{61} - 4q^{64} - 4q^{66} + 8q^{69} + 4q^{71} - 2q^{74} + 10q^{76} + 40q^{79} - 2q^{81} + 6q^{84} - 8q^{86} + 2q^{89} + 42q^{91} - 18q^{94} - 4q^{96} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 0.500000i −0.612372 0.353553i
$$3$$ −0.866025 0.500000i −0.500000 0.288675i
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0.500000 + 0.866025i 0.204124 + 0.353553i
$$7$$ −2.59808 + 1.50000i −0.981981 + 0.566947i −0.902867 0.429919i $$-0.858542\pi$$
−0.0791130 + 0.996866i $$0.525209\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i $$-0.881504\pi$$
0.780750 + 0.624844i $$0.214837\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −2.59808 2.50000i −0.720577 0.693375i
$$14$$ 3.00000 0.801784
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i $$-0.972237\pi$$
0.422659 0.906289i $$-0.361097\pi$$
$$20$$ 0 0
$$21$$ 3.00000 0.654654
$$22$$ 0.866025 0.500000i 0.184637 0.106600i
$$23$$ −3.46410 2.00000i −0.722315 0.417029i 0.0932891 0.995639i $$-0.470262\pi$$
−0.815604 + 0.578610i $$0.803595\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ 1.00000 + 3.46410i 0.196116 + 0.679366i
$$27$$ 1.00000i 0.192450i
$$28$$ −2.59808 1.50000i −0.490990 0.283473i
$$29$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$30$$ 0 0
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ 0.866025 0.500000i 0.153093 0.0883883i
$$33$$ 0.866025 0.500000i 0.150756 0.0870388i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ 0.866025 + 0.500000i 0.142374 + 0.0821995i 0.569495 0.821995i $$-0.307139\pi$$
−0.427121 + 0.904194i $$0.640472\pi$$
$$38$$ 5.00000i 0.811107i
$$39$$ 1.00000 + 3.46410i 0.160128 + 0.554700i
$$40$$ 0 0
$$41$$ −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i $$-0.988546\pi$$
0.530831 + 0.847477i $$0.321880\pi$$
$$42$$ −2.59808 1.50000i −0.400892 0.231455i
$$43$$ 1.73205 1.00000i 0.264135 0.152499i −0.362084 0.932145i $$-0.617935\pi$$
0.626219 + 0.779647i $$0.284601\pi$$
$$44$$ −1.00000 −0.150756
$$45$$ 0 0
$$46$$ 2.00000 + 3.46410i 0.294884 + 0.510754i
$$47$$ 9.00000i 1.31278i −0.754420 0.656392i $$-0.772082\pi$$
0.754420 0.656392i $$-0.227918\pi$$
$$48$$ 0.866025 0.500000i 0.125000 0.0721688i
$$49$$ 1.00000 1.73205i 0.142857 0.247436i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.866025 3.50000i 0.120096 0.485363i
$$53$$ 13.0000i 1.78569i 0.450367 + 0.892844i $$0.351293\pi$$
−0.450367 + 0.892844i $$0.648707\pi$$
$$54$$ −0.500000 + 0.866025i −0.0680414 + 0.117851i
$$55$$ 0 0
$$56$$ 1.50000 + 2.59808i 0.200446 + 0.347183i
$$57$$ 5.00000i 0.662266i
$$58$$ 0 0
$$59$$ 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i $$-0.0828195\pi$$
−0.705965 + 0.708247i $$0.749486\pi$$
$$60$$ 0 0
$$61$$ 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i $$-0.125799\pi$$
−0.794879 + 0.606768i $$0.792466\pi$$
$$62$$ −8.66025 5.00000i −1.09985 0.635001i
$$63$$ −2.59808 1.50000i −0.327327 0.188982i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ −1.00000 −0.123091
$$67$$ 10.3923 + 6.00000i 1.26962 + 0.733017i 0.974916 0.222571i $$-0.0714450\pi$$
0.294706 + 0.955588i $$0.404778\pi$$
$$68$$ 0 0
$$69$$ 2.00000 + 3.46410i 0.240772 + 0.417029i
$$70$$ 0 0
$$71$$ 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i $$-0.128801\pi$$
−0.800566 + 0.599245i $$0.795468\pi$$
$$72$$ 0.866025 0.500000i 0.102062 0.0589256i
$$73$$ 16.0000i 1.87266i 0.351123 + 0.936329i $$0.385800\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ −0.500000 0.866025i −0.0581238 0.100673i
$$75$$ 0 0
$$76$$ 2.50000 4.33013i 0.286770 0.496700i
$$77$$ 3.00000i 0.341882i
$$78$$ 0.866025 3.50000i 0.0980581 0.396297i
$$79$$ 10.0000 1.12509 0.562544 0.826767i $$-0.309823\pi$$
0.562544 + 0.826767i $$0.309823\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 5.19615 3.00000i 0.573819 0.331295i
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 1.50000 + 2.59808i 0.163663 + 0.283473i
$$85$$ 0 0
$$86$$ −2.00000 −0.215666
$$87$$ 0 0
$$88$$ 0.866025 + 0.500000i 0.0923186 + 0.0533002i
$$89$$ 0.500000 0.866025i 0.0529999 0.0917985i −0.838308 0.545197i $$-0.816455\pi$$
0.891308 + 0.453398i $$0.149788\pi$$
$$90$$ 0 0
$$91$$ 10.5000 + 2.59808i 1.10070 + 0.272352i
$$92$$ 4.00000i 0.417029i
$$93$$ −8.66025 5.00000i −0.898027 0.518476i
$$94$$ −4.50000 + 7.79423i −0.464140 + 0.803913i
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 10.3923 6.00000i 1.05518 0.609208i 0.131084 0.991371i $$-0.458154\pi$$
0.924095 + 0.382164i $$0.124821\pi$$
$$98$$ −1.73205 + 1.00000i −0.174964 + 0.101015i
$$99$$ −1.00000 −0.100504
$$100$$ 0 0
$$101$$ −2.00000 + 3.46410i −0.199007 + 0.344691i −0.948207 0.317653i $$-0.897105\pi$$
0.749199 + 0.662344i $$0.230438\pi$$
$$102$$ 0 0
$$103$$ 9.00000i 0.886796i 0.896325 + 0.443398i $$0.146227\pi$$
−0.896325 + 0.443398i $$0.853773\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ 0 0
$$106$$ 6.50000 11.2583i 0.631336 1.09351i
$$107$$ 5.19615 + 3.00000i 0.502331 + 0.290021i 0.729676 0.683793i $$-0.239671\pi$$
−0.227345 + 0.973814i $$0.573004\pi$$
$$108$$ 0.866025 0.500000i 0.0833333 0.0481125i
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ −0.500000 0.866025i −0.0474579 0.0821995i
$$112$$ 3.00000i 0.283473i
$$113$$ −13.8564 + 8.00000i −1.30350 + 0.752577i −0.981003 0.193993i $$-0.937856\pi$$
−0.322498 + 0.946570i $$0.604523\pi$$
$$114$$ 2.50000 4.33013i 0.234146 0.405554i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.866025 3.50000i 0.0800641 0.323575i
$$118$$ 4.00000i 0.368230i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 + 8.66025i 0.454545 + 0.787296i
$$122$$ 2.00000i 0.181071i
$$123$$ 5.19615 3.00000i 0.468521 0.270501i
$$124$$ 5.00000 + 8.66025i 0.449013 + 0.777714i
$$125$$ 0 0
$$126$$ 1.50000 + 2.59808i 0.133631 + 0.231455i
$$127$$ −4.33013 2.50000i −0.384237 0.221839i 0.295423 0.955366i $$-0.404539\pi$$
−0.679660 + 0.733527i $$0.737873\pi$$
$$128$$ 0.866025 + 0.500000i 0.0765466 + 0.0441942i
$$129$$ −2.00000 −0.176090
$$130$$ 0 0
$$131$$ −15.0000 −1.31056 −0.655278 0.755388i $$-0.727449\pi$$
−0.655278 + 0.755388i $$0.727449\pi$$
$$132$$ 0.866025 + 0.500000i 0.0753778 + 0.0435194i
$$133$$ 12.9904 + 7.50000i 1.12641 + 0.650332i
$$134$$ −6.00000 10.3923i −0.518321 0.897758i
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 13.8564 8.00000i 1.18383 0.683486i 0.226935 0.973910i $$-0.427130\pi$$
0.956898 + 0.290424i $$0.0937963\pi$$
$$138$$ 4.00000i 0.340503i
$$139$$ −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i $$-0.291323\pi$$
−0.991303 + 0.131597i $$0.957989\pi$$
$$140$$ 0 0
$$141$$ −4.50000 + 7.79423i −0.378968 + 0.656392i
$$142$$ 2.00000i 0.167836i
$$143$$ 3.46410 1.00000i 0.289683 0.0836242i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 8.00000 13.8564i 0.662085 1.14676i
$$147$$ −1.73205 + 1.00000i −0.142857 + 0.0824786i
$$148$$ 1.00000i 0.0821995i
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 0 0
$$151$$ −6.00000 −0.488273 −0.244137 0.969741i $$-0.578505\pi$$
−0.244137 + 0.969741i $$0.578505\pi$$
$$152$$ −4.33013 + 2.50000i −0.351220 + 0.202777i
$$153$$ 0 0
$$154$$ −1.50000 + 2.59808i −0.120873 + 0.209359i
$$155$$ 0 0
$$156$$ −2.50000 + 2.59808i −0.200160 + 0.208013i
$$157$$ 1.00000i 0.0798087i 0.999204 + 0.0399043i $$0.0127053\pi$$
−0.999204 + 0.0399043i $$0.987295\pi$$
$$158$$ −8.66025 5.00000i −0.688973 0.397779i
$$159$$ 6.50000 11.2583i 0.515484 0.892844i
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 0.866025 0.500000i 0.0680414 0.0392837i
$$163$$ 17.3205 10.0000i 1.35665 0.783260i 0.367477 0.930033i $$-0.380222\pi$$
0.989170 + 0.146772i $$0.0468885\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −6.00000 + 10.3923i −0.465690 + 0.806599i
$$167$$ 11.2583 + 6.50000i 0.871196 + 0.502985i 0.867745 0.497009i $$-0.165568\pi$$
0.00345033 + 0.999994i $$0.498902\pi$$
$$168$$ 3.00000i 0.231455i
$$169$$ 0.500000 + 12.9904i 0.0384615 + 0.999260i
$$170$$ 0 0
$$171$$ 2.50000 4.33013i 0.191180 0.331133i
$$172$$ 1.73205 + 1.00000i 0.132068 + 0.0762493i
$$173$$ 7.79423 4.50000i 0.592584 0.342129i −0.173534 0.984828i $$-0.555519\pi$$
0.766119 + 0.642699i $$0.222185\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.500000 0.866025i −0.0376889 0.0652791i
$$177$$ 4.00000i 0.300658i
$$178$$ −0.866025 + 0.500000i −0.0649113 + 0.0374766i
$$179$$ 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i $$-0.685306\pi$$
0.998286 + 0.0585225i $$0.0186389\pi$$
$$180$$ 0 0
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ −7.79423 7.50000i −0.577747 0.555937i
$$183$$ 2.00000i 0.147844i
$$184$$ −2.00000 + 3.46410i −0.147442 + 0.255377i
$$185$$ 0 0
$$186$$ 5.00000 + 8.66025i 0.366618 + 0.635001i
$$187$$ 0 0
$$188$$ 7.79423 4.50000i 0.568453 0.328196i
$$189$$ 1.50000 + 2.59808i 0.109109 + 0.188982i
$$190$$ 0 0
$$191$$ 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i $$0.0590746\pi$$
−0.331611 + 0.943416i $$0.607592\pi$$
$$192$$ 0.866025 + 0.500000i 0.0625000 + 0.0360844i
$$193$$ 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i $$-0.138004\pi$$
0.0899262 + 0.995948i $$0.471337\pi$$
$$194$$ −12.0000 −0.861550
$$195$$ 0 0
$$196$$ 2.00000 0.142857
$$197$$ 12.9904 + 7.50000i 0.925526 + 0.534353i 0.885394 0.464841i $$-0.153889\pi$$
0.0401324 + 0.999194i $$0.487222\pi$$
$$198$$ 0.866025 + 0.500000i 0.0615457 + 0.0355335i
$$199$$ −1.00000 1.73205i −0.0708881 0.122782i 0.828403 0.560133i $$-0.189250\pi$$
−0.899291 + 0.437351i $$0.855917\pi$$
$$200$$ 0 0
$$201$$ −6.00000 10.3923i −0.423207 0.733017i
$$202$$ 3.46410 2.00000i 0.243733 0.140720i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 4.50000 7.79423i 0.313530 0.543050i
$$207$$ 4.00000i 0.278019i
$$208$$ 3.46410 1.00000i 0.240192 0.0693375i
$$209$$ 5.00000 0.345857
$$210$$ 0 0
$$211$$ 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i $$-0.660634\pi$$
0.999820 0.0189499i $$-0.00603229\pi$$
$$212$$ −11.2583 + 6.50000i −0.773225 + 0.446422i
$$213$$ 2.00000i 0.137038i
$$214$$ −3.00000 5.19615i −0.205076 0.355202i
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ −25.9808 + 15.0000i −1.76369 + 1.01827i
$$218$$ −8.66025 5.00000i −0.586546 0.338643i
$$219$$ 8.00000 13.8564i 0.540590 0.936329i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 1.00000i 0.0671156i
$$223$$ 9.52628 + 5.50000i 0.637927 + 0.368307i 0.783815 0.620994i $$-0.213271\pi$$
−0.145889 + 0.989301i $$0.546604\pi$$
$$224$$ −1.50000 + 2.59808i −0.100223 + 0.173591i
$$225$$ 0 0
$$226$$ 16.0000 1.06430
$$227$$ −17.3205 + 10.0000i −1.14960 + 0.663723i −0.948790 0.315906i $$-0.897691\pi$$
−0.200812 + 0.979630i $$0.564358\pi$$
$$228$$ −4.33013 + 2.50000i −0.286770 + 0.165567i
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ −1.50000 + 2.59808i −0.0986928 + 0.170941i
$$232$$ 0 0
$$233$$ 10.0000i 0.655122i −0.944830 0.327561i $$-0.893773\pi$$
0.944830 0.327561i $$-0.106227\pi$$
$$234$$ −2.50000 + 2.59808i −0.163430 + 0.169842i
$$235$$ 0 0
$$236$$ −2.00000 + 3.46410i −0.130189 + 0.225494i
$$237$$ −8.66025 5.00000i −0.562544 0.324785i
$$238$$ 0 0
$$239$$ 2.00000 0.129369 0.0646846 0.997906i $$-0.479396\pi$$
0.0646846 + 0.997906i $$0.479396\pi$$
$$240$$ 0 0
$$241$$ −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i $$-0.327162\pi$$
−0.999812 + 0.0193858i $$0.993829\pi$$
$$242$$ 10.0000i 0.642824i
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ −1.00000 + 1.73205i −0.0640184 + 0.110883i
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ −4.33013 + 17.5000i −0.275519 + 1.11350i
$$248$$ 10.0000i 0.635001i
$$249$$ −6.00000 + 10.3923i −0.380235 + 0.658586i
$$250$$ 0 0
$$251$$ −5.50000 9.52628i −0.347157 0.601293i 0.638586 0.769550i $$-0.279520\pi$$
−0.985743 + 0.168257i $$0.946186\pi$$
$$252$$ 3.00000i 0.188982i
$$253$$ 3.46410 2.00000i 0.217786 0.125739i
$$254$$ 2.50000 + 4.33013i 0.156864 + 0.271696i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 20.7846 + 12.0000i 1.29651 + 0.748539i 0.979799 0.199983i $$-0.0640888\pi$$
0.316709 + 0.948523i $$0.397422\pi$$
$$258$$ 1.73205 + 1.00000i 0.107833 + 0.0622573i
$$259$$ −3.00000 −0.186411
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 12.9904 + 7.50000i 0.802548 + 0.463352i
$$263$$ 2.59808 + 1.50000i 0.160204 + 0.0924940i 0.577959 0.816066i $$-0.303849\pi$$
−0.417755 + 0.908560i $$0.637183\pi$$
$$264$$ −0.500000 0.866025i −0.0307729 0.0533002i
$$265$$ 0 0
$$266$$ −7.50000 12.9904i −0.459855 0.796491i
$$267$$ −0.866025 + 0.500000i −0.0529999 + 0.0305995i
$$268$$ 12.0000i 0.733017i
$$269$$ −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i $$-0.957952\pi$$
0.381577 0.924337i $$-0.375381\pi$$
$$270$$ 0 0
$$271$$ 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i $$-0.573343\pi$$
0.957328 0.289003i $$-0.0933238\pi$$
$$272$$ 0 0
$$273$$ −7.79423 7.50000i −0.471728 0.453921i
$$274$$ −16.0000 −0.966595
$$275$$ 0 0
$$276$$ −2.00000 + 3.46410i −0.120386 + 0.208514i
$$277$$ 19.9186 11.5000i 1.19679 0.690968i 0.236953 0.971521i $$-0.423851\pi$$
0.959839 + 0.280553i $$0.0905179\pi$$
$$278$$ 9.00000i 0.539784i
$$279$$ 5.00000 + 8.66025i 0.299342 + 0.518476i
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 7.79423 4.50000i 0.464140 0.267971i
$$283$$ 1.73205 + 1.00000i 0.102960 + 0.0594438i 0.550596 0.834772i $$-0.314401\pi$$
−0.447636 + 0.894216i $$0.647734\pi$$
$$284$$ −1.00000 + 1.73205i −0.0593391 + 0.102778i
$$285$$ 0 0
$$286$$ −3.50000 0.866025i −0.206959 0.0512092i
$$287$$ 18.0000i 1.06251i
$$288$$ 0.866025 + 0.500000i 0.0510310 + 0.0294628i
$$289$$ −8.50000 + 14.7224i −0.500000 + 0.866025i
$$290$$ 0 0
$$291$$ −12.0000 −0.703452
$$292$$ −13.8564 + 8.00000i −0.810885 + 0.468165i
$$293$$ −11.2583 + 6.50000i −0.657719 + 0.379734i −0.791407 0.611289i $$-0.790651\pi$$
0.133689 + 0.991023i $$0.457318\pi$$
$$294$$ 2.00000 0.116642
$$295$$ 0 0
$$296$$ 0.500000 0.866025i 0.0290619 0.0503367i
$$297$$ 0.866025 + 0.500000i 0.0502519 + 0.0290129i
$$298$$ 6.00000i 0.347571i
$$299$$ 4.00000 + 13.8564i 0.231326 + 0.801337i
$$300$$ 0 0
$$301$$ −3.00000 + 5.19615i −0.172917 + 0.299501i
$$302$$ 5.19615 + 3.00000i 0.299005 + 0.172631i
$$303$$ 3.46410 2.00000i 0.199007 0.114897i
$$304$$ 5.00000 0.286770
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 18.0000i 1.02731i 0.857996 + 0.513657i $$0.171710\pi$$
−0.857996 + 0.513657i $$0.828290\pi$$
$$308$$ 2.59808 1.50000i 0.148039 0.0854704i
$$309$$ 4.50000 7.79423i 0.255996 0.443398i
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 3.46410 1.00000i 0.196116 0.0566139i
$$313$$ 34.0000i 1.92179i 0.276907 + 0.960897i $$0.410691\pi$$
−0.276907 + 0.960897i $$0.589309\pi$$
$$314$$ 0.500000 0.866025i 0.0282166 0.0488726i
$$315$$ 0 0
$$316$$ 5.00000 + 8.66025i 0.281272 + 0.487177i
$$317$$ 19.0000i 1.06715i 0.845754 + 0.533573i $$0.179151\pi$$
−0.845754 + 0.533573i $$0.820849\pi$$
$$318$$ −11.2583 + 6.50000i −0.631336 + 0.364502i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −3.00000 5.19615i −0.167444 0.290021i
$$322$$ −10.3923 6.00000i −0.579141 0.334367i
$$323$$ 0 0
$$324$$ −1.00000 −0.0555556
$$325$$ 0 0
$$326$$ −20.0000 −1.10770
$$327$$ −8.66025 5.00000i −0.478913 0.276501i
$$328$$ 5.19615 + 3.00000i 0.286910 + 0.165647i
$$329$$ 13.5000 + 23.3827i 0.744279 + 1.28913i
$$330$$ 0 0
$$331$$ −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i $$-0.887167\pi$$
0.168320 0.985732i $$-0.446166\pi$$
$$332$$ 10.3923 6.00000i 0.570352 0.329293i
$$333$$ 1.00000i 0.0547997i
$$334$$ −6.50000 11.2583i −0.355664 0.616028i
$$335$$ 0 0
$$336$$ −1.50000 + 2.59808i −0.0818317 + 0.141737i
$$337$$ 2.00000i 0.108947i 0.998515 + 0.0544735i $$0.0173480\pi$$
−0.998515 + 0.0544735i $$0.982652\pi$$
$$338$$ 6.06218 11.5000i 0.329739 0.625518i
$$339$$ 16.0000 0.869001
$$340$$ 0 0
$$341$$ −5.00000 + 8.66025i −0.270765 + 0.468979i
$$342$$ −4.33013 + 2.50000i −0.234146 + 0.135185i
$$343$$ 15.0000i 0.809924i
$$344$$ −1.00000 1.73205i −0.0539164 0.0933859i
$$345$$ 0 0
$$346$$ −9.00000 −0.483843
$$347$$ −24.2487 + 14.0000i −1.30174 + 0.751559i −0.980702 0.195507i $$-0.937365\pi$$
−0.321037 + 0.947067i $$0.604031\pi$$
$$348$$ 0 0
$$349$$ 18.0000 31.1769i 0.963518 1.66886i 0.249973 0.968253i $$-0.419578\pi$$
0.713545 0.700609i $$-0.247088\pi$$
$$350$$ 0 0
$$351$$ −2.50000 + 2.59808i −0.133440 + 0.138675i
$$352$$ 1.00000i 0.0533002i
$$353$$ −31.1769 18.0000i −1.65938 0.958043i −0.973002 0.230799i $$-0.925866\pi$$
−0.686378 0.727245i $$-0.740800\pi$$
$$354$$ −2.00000 + 3.46410i −0.106299 + 0.184115i
$$355$$ 0 0
$$356$$ 1.00000 0.0529999
$$357$$ 0 0
$$358$$ −10.3923 + 6.00000i −0.549250 + 0.317110i
$$359$$ −34.0000 −1.79445 −0.897226 0.441572i $$-0.854421\pi$$
−0.897226 + 0.441572i $$0.854421\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ −5.19615 3.00000i −0.273104 0.157676i
$$363$$ 10.0000i 0.524864i
$$364$$ 3.00000 + 10.3923i 0.157243 + 0.544705i
$$365$$ 0 0
$$366$$ −1.00000 + 1.73205i −0.0522708 + 0.0905357i
$$367$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$368$$ 3.46410 2.00000i 0.180579 0.104257i
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ −19.5000 33.7750i −1.01239 1.75351i
$$372$$ 10.0000i 0.518476i
$$373$$ −8.66025 + 5.00000i −0.448411 + 0.258890i −0.707159 0.707055i $$-0.750023\pi$$
0.258748 + 0.965945i $$0.416690\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −9.00000 −0.464140
$$377$$ 0 0
$$378$$ 3.00000i 0.154303i
$$379$$ −0.500000 + 0.866025i −0.0256833 + 0.0444847i −0.878581 0.477593i $$-0.841509\pi$$
0.852898 + 0.522077i $$0.174843\pi$$
$$380$$ 0 0
$$381$$ 2.50000 + 4.33013i 0.128079 + 0.221839i
$$382$$ 18.0000i 0.920960i
$$383$$ 24.2487 14.0000i 1.23905 0.715367i 0.270151 0.962818i $$-0.412926\pi$$
0.968900 + 0.247451i $$0.0795931\pi$$
$$384$$ −0.500000 0.866025i −0.0255155 0.0441942i
$$385$$ 0 0
$$386$$ −8.00000 13.8564i −0.407189 0.705273i
$$387$$ 1.73205 + 1.00000i 0.0880451 + 0.0508329i
$$388$$ 10.3923 + 6.00000i 0.527589 + 0.304604i
$$389$$ 16.0000 0.811232 0.405616 0.914044i $$-0.367057\pi$$
0.405616 + 0.914044i $$0.367057\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.73205 1.00000i −0.0874818 0.0505076i
$$393$$ 12.9904 + 7.50000i 0.655278 + 0.378325i
$$394$$ −7.50000 12.9904i −0.377845 0.654446i
$$395$$ 0 0
$$396$$ −0.500000 0.866025i −0.0251259 0.0435194i
$$397$$ −28.5788 + 16.5000i −1.43433 + 0.828111i −0.997447 0.0714068i $$-0.977251\pi$$
−0.436884 + 0.899518i $$0.643918\pi$$
$$398$$ 2.00000i 0.100251i
$$399$$ −7.50000 12.9904i −0.375470 0.650332i
$$400$$ 0 0
$$401$$ −12.5000 + 21.6506i −0.624220 + 1.08118i 0.364471 + 0.931215i $$0.381250\pi$$
−0.988691 + 0.149966i $$0.952083\pi$$
$$402$$ 12.0000i 0.598506i
$$403$$ −25.9808 25.0000i −1.29419 1.24534i
$$404$$ −4.00000 −0.199007
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −0.866025 + 0.500000i −0.0429273 + 0.0247841i
$$408$$ 0 0
$$409$$ 8.50000 + 14.7224i 0.420298 + 0.727977i 0.995968 0.0897044i $$-0.0285922\pi$$
−0.575670 + 0.817682i $$0.695259\pi$$
$$410$$ 0 0
$$411$$ −16.0000 −0.789222
$$412$$ −7.79423 + 4.50000i −0.383994 + 0.221699i
$$413$$ −10.3923 6.00000i −0.511372 0.295241i
$$414$$ −2.00000 + 3.46410i −0.0982946 + 0.170251i
$$415$$ 0 0
$$416$$ −3.50000 0.866025i −0.171602 0.0424604i
$$417$$ 9.00000i 0.440732i
$$418$$ −4.33013 2.50000i −0.211793 0.122279i
$$419$$ −14.0000 + 24.2487i −0.683945 + 1.18463i 0.289822 + 0.957080i $$0.406404\pi$$
−0.973767 + 0.227547i $$0.926930\pi$$
$$420$$ 0 0
$$421$$ 20.0000 0.974740 0.487370 0.873195i $$-0.337956\pi$$
0.487370 + 0.873195i $$0.337956\pi$$
$$422$$ −12.9904 + 7.50000i −0.632362 + 0.365094i
$$423$$ 7.79423 4.50000i 0.378968 0.218797i
$$424$$ 13.0000 0.631336
$$425$$ 0 0
$$426$$ −1.00000 + 1.73205i −0.0484502 + 0.0839181i
$$427$$ −5.19615 3.00000i −0.251459 0.145180i
$$428$$ 6.00000i 0.290021i
$$429$$ −3.50000 0.866025i −0.168982 0.0418121i
$$430$$ 0 0
$$431$$ −18.0000 + 31.1769i −0.867029 + 1.50174i −0.00201168 + 0.999998i $$0.500640\pi$$
−0.865018 + 0.501741i $$0.832693\pi$$
$$432$$ 0.866025 + 0.500000i 0.0416667 + 0.0240563i
$$433$$ −13.8564 + 8.00000i −0.665896 + 0.384455i −0.794520 0.607238i $$-0.792277\pi$$
0.128624 + 0.991693i $$0.458944\pi$$
$$434$$ 30.0000 1.44005
$$435$$ 0 0
$$436$$ 5.00000 + 8.66025i 0.239457 + 0.414751i
$$437$$ 20.0000i 0.956730i
$$438$$ −13.8564 + 8.00000i −0.662085 + 0.382255i
$$439$$ −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i $$-0.910034\pi$$
0.721686 + 0.692220i $$0.243367\pi$$
$$440$$ 0 0
$$441$$ 2.00000 0.0952381
$$442$$ 0 0
$$443$$ 18.0000i 0.855206i 0.903967 + 0.427603i $$0.140642\pi$$
−0.903967 + 0.427603i $$0.859358\pi$$
$$444$$ 0.500000 0.866025i 0.0237289 0.0410997i
$$445$$ 0 0
$$446$$ −5.50000 9.52628i −0.260433 0.451082i
$$447$$ 6.00000i 0.283790i
$$448$$ 2.59808 1.50000i 0.122748 0.0708683i
$$449$$ −7.50000 12.9904i −0.353947 0.613054i 0.632990 0.774160i $$-0.281827\pi$$
−0.986937 + 0.161106i $$0.948494\pi$$
$$450$$ 0 0
$$451$$ −3.00000 5.19615i −0.141264 0.244677i
$$452$$ −13.8564 8.00000i −0.651751 0.376288i
$$453$$ 5.19615 + 3.00000i 0.244137 + 0.140952i
$$454$$ 20.0000 0.938647
$$455$$ 0 0
$$456$$ 5.00000 0.234146
$$457$$ −19.0526 11.0000i −0.891241 0.514558i −0.0168929 0.999857i $$-0.505377\pi$$
−0.874348 + 0.485299i $$0.838711\pi$$
$$458$$ −8.66025 5.00000i −0.404667 0.233635i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 6.00000 + 10.3923i 0.279448 + 0.484018i 0.971248 0.238071i $$-0.0765153\pi$$
−0.691800 + 0.722089i $$0.743182\pi$$
$$462$$ 2.59808 1.50000i 0.120873 0.0697863i
$$463$$ 16.0000i 0.743583i 0.928316 + 0.371792i $$0.121256\pi$$
−0.928316 + 0.371792i $$0.878744\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −5.00000 + 8.66025i −0.231621 + 0.401179i
$$467$$ 36.0000i 1.66588i −0.553362 0.832941i $$-0.686655\pi$$
0.553362 0.832941i $$-0.313345\pi$$
$$468$$ 3.46410 1.00000i 0.160128 0.0462250i
$$469$$ −36.0000 −1.66233
$$470$$ 0 0
$$471$$ 0.500000 0.866025i 0.0230388 0.0399043i
$$472$$ 3.46410 2.00000i 0.159448 0.0920575i
$$473$$ 2.00000i 0.0919601i
$$474$$ 5.00000 + 8.66025i 0.229658 + 0.397779i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −11.2583 + 6.50000i −0.515484 + 0.297615i
$$478$$ −1.73205 1.00000i −0.0792222 0.0457389i
$$479$$ −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
$$481$$ −1.00000 3.46410i −0.0455961 0.157949i
$$482$$ 15.0000i 0.683231i
$$483$$ −10.3923 6.00000i −0.472866 0.273009i
$$484$$ −5.00000 + 8.66025i −0.227273 + 0.393648i
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 30.3109 17.5000i 1.37352 0.793001i 0.382148 0.924101i $$-0.375184\pi$$
0.991369 + 0.131100i $$0.0418510\pi$$
$$488$$ 1.73205 1.00000i 0.0784063 0.0452679i
$$489$$ −20.0000 −0.904431
$$490$$ 0 0
$$491$$ −12.5000 + 21.6506i −0.564117 + 0.977079i 0.433014 + 0.901387i $$0.357450\pi$$
−0.997131 + 0.0756923i $$0.975883\pi$$
$$492$$ 5.19615 + 3.00000i 0.234261 + 0.135250i
$$493$$ 0 0
$$494$$ 12.5000 12.9904i 0.562402 0.584465i
$$495$$ 0 0
$$496$$ −5.00000 + 8.66025i −0.224507 + 0.388857i
$$497$$ −5.19615 3.00000i −0.233079 0.134568i
$$498$$ 10.3923 6.00000i 0.465690 0.268866i
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ 0 0
$$501$$ −6.50000 11.2583i −0.290399 0.502985i
$$502$$ 11.0000i 0.490954i
$$503$$ 0.866025 0.500000i 0.0386142 0.0222939i −0.480569 0.876957i $$-0.659570\pi$$
0.519183 + 0.854663i $$0.326236\pi$$
$$504$$ −1.50000 + 2.59808i −0.0668153 + 0.115728i
$$505$$ 0 0
$$506$$ −4.00000 −0.177822
$$507$$ 6.06218 11.5000i 0.269231 0.510733i
$$508$$ 5.00000i 0.221839i
$$509$$ 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i $$-0.702719\pi$$
0.993593 + 0.113020i $$0.0360525\pi$$
$$510$$ 0 0
$$511$$ −24.0000 41.5692i −1.06170 1.83891i
$$512$$ 1.00000i 0.0441942i
$$513$$ −4.33013 + 2.50000i −0.191180 + 0.110378i
$$514$$ −12.0000 20.7846i −0.529297 0.916770i
$$515$$ 0 0
$$516$$ −1.00000 1.73205i −0.0440225 0.0762493i
$$517$$ 7.79423 + 4.50000i 0.342790 + 0.197910i
$$518$$ 2.59808 + 1.50000i 0.114153 + 0.0659062i
$$519$$ −9.00000 −0.395056
$$520$$ 0 0
$$521$$ 33.0000 1.44576 0.722878 0.690976i $$-0.242819\pi$$
0.722878 + 0.690976i $$0.242819\pi$$
$$522$$ 0 0
$$523$$ 5.19615 + 3.00000i 0.227212 + 0.131181i 0.609285 0.792951i $$-0.291456\pi$$
−0.382073 + 0.924132i $$0.624790\pi$$
$$524$$ −7.50000 12.9904i −0.327639 0.567487i
$$525$$ 0 0
$$526$$ −1.50000 2.59808i −0.0654031 0.113282i
$$527$$ 0 0
$$528$$ 1.00000i 0.0435194i
$$529$$ −3.50000 6.06218i −0.152174 0.263573i
$$530$$ 0 0
$$531$$ −2.00000 + 3.46410i −0.0867926 + 0.150329i
$$532$$ 15.0000i 0.650332i
$$533$$ 20.7846 6.00000i 0.900281 0.259889i
$$534$$ 1.00000 0.0432742
$$535$$ 0 0
$$536$$ 6.00000 10.3923i 0.259161 0.448879i
$$537$$ −10.3923 + 6.00000i −0.448461 + 0.258919i
$$538$$ 20.0000i 0.862261i
$$539$$ 1.00000 + 1.73205i 0.0430730 + 0.0746047i
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ −20.7846 + 12.0000i −0.892775 + 0.515444i
$$543$$ −5.19615 3.00000i −0.222988 0.128742i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 3.00000 + 10.3923i 0.128388 + 0.444750i
$$547$$ 34.0000i 1.45374i 0.686778 + 0.726868i $$0.259025\pi$$
−0.686778 + 0.726868i $$0.740975\pi$$
$$548$$ 13.8564 + 8.00000i 0.591916 + 0.341743i
$$549$$ −1.00000 + 1.73205i −0.0426790 + 0.0739221i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 3.46410 2.00000i 0.147442 0.0851257i
$$553$$ −25.9808 + 15.0000i −1.10481 + 0.637865i
$$554$$ −23.0000 −0.977176
$$555$$ 0 0
$$556$$ 4.50000 7.79423i 0.190843 0.330549i
$$557$$ 2.59808 + 1.50000i 0.110084 + 0.0635570i 0.554031 0.832496i $$-0.313089\pi$$
−0.443947 + 0.896053i $$0.646422\pi$$
$$558$$ 10.0000i 0.423334i
$$559$$ −7.00000 1.73205i −0.296068 0.0732579i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −8.66025 5.00000i −0.365311 0.210912i
$$563$$ −20.7846 + 12.0000i −0.875967 + 0.505740i −0.869326 0.494238i $$-0.835447\pi$$
−0.00664037 + 0.999978i $$0.502114\pi$$
$$564$$ −9.00000 −0.378968
$$565$$ 0 0
$$566$$ −1.00000 1.73205i −0.0420331 0.0728035i
$$567$$ 3.00000i 0.125988i
$$568$$ 1.73205 1.00000i 0.0726752 0.0419591i
$$569$$ −5.50000 + 9.52628i −0.230572 + 0.399362i −0.957977 0.286846i $$-0.907393\pi$$
0.727405 + 0.686209i $$0.240726\pi$$
$$570$$ 0 0
$$571$$ 7.00000 0.292941 0.146470 0.989215i $$-0.453209\pi$$
0.146470 + 0.989215i $$0.453209\pi$$
$$572$$ 2.59808 + 2.50000i 0.108631 + 0.104530i
$$573$$ 18.0000i 0.751961i
$$574$$ −9.00000 + 15.5885i −0.375653 + 0.650650i
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ 18.0000i 0.749350i 0.927156 + 0.374675i $$0.122246\pi$$
−0.927156 + 0.374675i $$0.877754\pi$$
$$578$$ 14.7224 8.50000i 0.612372 0.353553i
$$579$$ −8.00000 13.8564i −0.332469 0.575853i
$$580$$ 0 0
$$581$$ 18.0000 + 31.1769i 0.746766 + 1.29344i
$$582$$ 10.3923 + 6.00000i 0.430775 + 0.248708i
$$583$$ −11.2583 6.50000i −0.466272 0.269202i
$$584$$ 16.0000 0.662085
$$585$$ 0 0
$$586$$ 13.0000 0.537025
$$587$$ 15.5885 + 9.00000i 0.643404 + 0.371470i 0.785925 0.618322i $$-0.212187\pi$$
−0.142520 + 0.989792i $$0.545521\pi$$
$$588$$ −1.73205 1.00000i −0.0714286 0.0412393i
$$589$$ −25.0000 43.3013i −1.03011 1.78420i
$$590$$ 0 0
$$591$$ −7.50000 12.9904i −0.308509 0.534353i
$$592$$ −0.866025 + 0.500000i −0.0355934 + 0.0205499i
$$593$$ 28.0000i 1.14982i −0.818216 0.574911i $$-0.805037\pi$$
0.818216 0.574911i $$-0.194963\pi$$
$$594$$ −0.500000 0.866025i −0.0205152 0.0355335i
$$595$$ 0 0
$$596$$ 3.00000 5.19615i 0.122885 0.212843i
$$597$$ 2.00000i 0.0818546i
$$598$$ 3.46410 14.0000i 0.141658 0.572503i
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ 13.5000 23.3827i 0.550676 0.953800i −0.447549 0.894259i $$-0.647703\pi$$
0.998226 0.0595404i $$-0.0189635\pi$$
$$602$$ 5.19615 3.00000i 0.211779 0.122271i
$$603$$ 12.0000i 0.488678i
$$604$$ −3.00000 5.19615i −0.122068 0.211428i
$$605$$ 0 0
$$606$$ −4.00000 −0.162489
$$607$$ 32.0429 18.5000i 1.30058 0.750892i 0.320079 0.947391i $$-0.396291\pi$$
0.980504 + 0.196499i $$0.0629573\pi$$
$$608$$ −4.33013 2.50000i −0.175610 0.101388i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −22.5000 + 23.3827i −0.910253 + 0.945962i
$$612$$ 0 0
$$613$$ 19.9186 + 11.5000i 0.804504 + 0.464481i 0.845044 0.534697i $$-0.179574\pi$$
−0.0405396 + 0.999178i $$0.512908\pi$$
$$614$$ 9.00000 15.5885i 0.363210 0.629099i
$$615$$ 0 0
$$616$$ −3.00000 −0.120873
$$617$$ −5.19615 + 3.00000i −0.209189 + 0.120775i −0.600935 0.799298i $$-0.705205\pi$$
0.391745 + 0.920074i $$0.371871\pi$$
$$618$$ −7.79423 + 4.50000i −0.313530 + 0.181017i
$$619$$ 31.0000 1.24600 0.622998 0.782224i $$-0.285915\pi$$
0.622998 + 0.782224i $$0.285915\pi$$
$$620$$ 0 0
$$621$$ −2.00000 + 3.46410i −0.0802572 + 0.139010i
$$622$$ 10.3923 + 6.00000i 0.416693 + 0.240578i
$$623$$ 3.00000i 0.120192i
$$624$$ −3.50000 0.866025i −0.140112 0.0346688i
$$625$$ 0 0
$$626$$ 17.0000 29.4449i 0.679457 1.17685i
$$627$$ −4.33013 2.50000i −0.172929 0.0998404i
$$628$$ −0.866025 + 0.500000i −0.0345582 + 0.0199522i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 2.00000 + 3.46410i 0.0796187 + 0.137904i 0.903085 0.429461i $$-0.141296\pi$$
−0.823467 + 0.567365i $$0.807963\pi$$
$$632$$ 10.0000i 0.397779i
$$633$$ −12.9904 + 7.50000i −0.516321 + 0.298098i
$$634$$ 9.50000 16.4545i 0.377293 0.653491i
$$635$$ 0 0
$$636$$ 13.0000 0.515484
$$637$$ −6.92820 + 2.00000i −0.274505 + 0.0792429i
$$638$$ 0 0
$$639$$ −1.00000 + 1.73205i −0.0395594 + 0.0685189i
$$640$$ 0 0
$$641$$ 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i $$-0.109788\pi$$
−0.763367 + 0.645966i $$0.776455\pi$$
$$642$$ 6.00000i 0.236801i
$$643$$ 38.1051 22.0000i 1.50272 0.867595i 0.502724 0.864447i $$-0.332331\pi$$
0.999995 0.00314839i $$-0.00100217\pi$$
$$644$$ 6.00000 + 10.3923i 0.236433 + 0.409514i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −7.79423 4.50000i −0.306423 0.176913i 0.338902 0.940822i $$-0.389945\pi$$
−0.645325 + 0.763908i $$0.723278\pi$$
$$648$$ 0.866025 + 0.500000i 0.0340207 + 0.0196419i
$$649$$ −4.00000 −0.157014
$$650$$ 0 0
$$651$$ 30.0000 1.17579
$$652$$ 17.3205 + 10.0000i 0.678323 + 0.391630i
$$653$$ 35.5070 + 20.5000i 1.38950 + 0.802227i 0.993259 0.115920i $$-0.0369817\pi$$
0.396239 + 0.918147i $$0.370315\pi$$
$$654$$ 5.00000 + 8.66025i 0.195515 + 0.338643i
$$655$$ 0 0
$$656$$ −3.00000 5.19615i −0.117130 0.202876i
$$657$$ −13.8564 + 8.00000i −0.540590 + 0.312110i
$$658$$ 27.0000i 1.05257i
$$659$$ 2.00000 + 3.46410i 0.0779089 + 0.134942i 0.902348 0.431009i $$-0.141842\pi$$
−0.824439 + 0.565951i $$0.808509\pi$$
$$660$$ 0 0
$$661$$ −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i $$-0.921107\pi$$
0.697174 + 0.716902i $$0.254441\pi$$
$$662$$ 28.0000i 1.08825i
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 0.500000 0.866025i 0.0193746 0.0335578i
$$667$$ 0 0
$$668$$ 13.0000i 0.502985i
$$669$$ −5.50000 9.52628i −0.212642 0.368307i
$$670$$ 0 0
$$671$$ −2.00000 −0.0772091
$$672$$ 2.59808 1.50000i 0.100223 0.0578638i
$$673$$ −27.7128 16.0000i −1.06825 0.616755i −0.140548 0.990074i $$-0.544886\pi$$
−0.927703 + 0.373319i $$0.878220\pi$$
$$674$$ 1.00000 1.73205i 0.0385186 0.0667161i
$$675$$ 0 0
$$676$$ −11.0000 + 6.92820i −0.423077 + 0.266469i
$$677$$ 26.0000i 0.999261i −0.866239 0.499631i $$-0.833469\pi$$
0.866239 0.499631i $$-0.166531\pi$$
$$678$$ −13.8564 8.00000i −0.532152 0.307238i
$$679$$ −18.0000 + 31.1769i −0.690777 + 1.19646i
$$680$$ 0 0
$$681$$ 20.0000 0.766402
$$682$$ 8.66025 5.00000i 0.331618 0.191460i
$$683$$ 22.5167 13.0000i 0.861576 0.497431i −0.00296369 0.999996i $$-0.500943\pi$$
0.864540 + 0.502564i $$0.167610\pi$$
$$684$$ 5.00000 0.191180
$$685$$ 0 0
$$686$$ −7.50000 + 12.9904i −0.286351 + 0.495975i
$$687$$ −8.66025 5.00000i −0.330409 0.190762i
$$688$$ 2.00000i 0.0762493i
$$689$$ 32.5000 33.7750i 1.23815 1.28672i
$$690$$ 0 0
$$691$$ −16.5000 + 28.5788i −0.627690 + 1.08719i 0.360325 + 0.932827i $$0.382666\pi$$
−0.988014 + 0.154363i $$0.950667\pi$$
$$692$$ 7.79423 + 4.50000i 0.296292 + 0.171064i
$$693$$ 2.59808 1.50000i 0.0986928 0.0569803i
$$694$$ 28.0000 1.06287
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −31.1769 + 18.0000i −1.18006 + 0.681310i
$$699$$ −5.00000 + 8.66025i −0.189117 + 0.327561i
$$700$$ 0 0
$$701$$ 4.00000 0.151078 0.0755390 0.997143i $$-0.475932\pi$$
0.0755390 + 0.997143i $$0.475932\pi$$
$$702$$ 3.46410 1.00000i 0.130744 0.0377426i
$$703$$ 5.00000i 0.188579i
$$704$$ 0.500000 0.866025i 0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ 18.0000 + 31.1769i 0.677439 + 1.17336i
$$707$$ 12.0000i 0.451306i
$$708$$ 3.46410 2.00000i 0.130189 0.0751646i
$$709$$ 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i $$-0.142735\pi$$
−0.826023 + 0.563636i $$0.809402\pi$$
$$710$$ 0 0
$$711$$ 5.00000 + 8.66025i 0.187515 + 0.324785i
$$712$$ −0.866025 0.500000i −0.0324557 0.0187383i
$$713$$ −34.6410 20.0000i −1.29732 0.749006i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ −1.73205 1.00000i −0.0646846 0.0373457i
$$718$$ 29.4449 + 17.0000i 1.09887 + 0.634434i
$$719$$ 18.0000 + 31.1769i 0.671287 + 1.16270i 0.977539 + 0.210752i $$0.0675914\pi$$
−0.306253 + 0.951950i $$0.599075\pi$$
$$720$$ 0 0
$$721$$ −13.5000 23.3827i −0.502766 0.870817i
$$722$$ 5.19615 3.00000i 0.193381 0.111648i
$$723$$ 15.0000i 0.557856i
$$724$$ 3.00000 + 5.19615i 0.111494 + 0.193113i
$$725$$ 0 0
$$726$$ −5.00000 + 8.66025i −0.185567 + 0.321412i
$$727$$ 37.0000i 1.37225i −0.727482 0.686127i $$-0.759309\pi$$
0.727482 0.686127i $$-0.240691\pi$$
$$728$$ 2.59808 10.5000i 0.0962911 0.389156i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 1.73205 1.00000i 0.0640184 0.0369611i
$$733$$ 5.00000i 0.184679i 0.995728 + 0.0923396i $$0.0294345\pi$$
−0.995728 + 0.0923396i $$0.970565\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ −10.3923 + 6.00000i −0.382805 + 0.221013i
$$738$$ 5.19615 + 3.00000i 0.191273 + 0.110432i
$$739$$ 17.5000 30.3109i 0.643748 1.11500i −0.340841 0.940121i $$-0.610712\pi$$
0.984589 0.174883i $$-0.0559548\pi$$
$$740$$ 0 0
$$741$$ 12.5000 12.9904i 0.459199 0.477214i
$$742$$ 39.0000i 1.43174i
$$743$$ 20.7846 + 12.0000i 0.762513 + 0.440237i 0.830197 0.557470i $$-0.188228\pi$$
−0.0676840 + 0.997707i $$0.521561\pi$$
$$744$$ −5.00000 + 8.66025i −0.183309 + 0.317500i
$$745$$ 0 0
$$746$$ 10.0000 0.366126
$$747$$ 10.3923 6.00000i 0.380235 0.219529i
$$748$$ 0 0
$$749$$ −18.0000 −0.657706
$$750$$ 0 0
$$751$$ −22.0000 + 38.1051i −0.802791 + 1.39048i 0.114981 + 0.993368i $$0.463319\pi$$
−0.917772 + 0.397108i $$0.870014\pi$$
$$752$$ 7.79423 + 4.50000i 0.284226 + 0.164098i
$$753$$ 11.0000i 0.400862i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −1.50000 + 2.59808i −0.0545545 + 0.0944911i
$$757$$ −33.7750 19.5000i −1.22757 0.708740i −0.261051 0.965325i $$-0.584069\pi$$
−0.966522 + 0.256585i $$0.917403\pi$$
$$758$$ 0.866025 0.500000i 0.0314555 0.0181608i
$$759$$ −4.00000 −0.145191
$$760$$ 0 0
$$761$$ −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i $$-0.863060\pi$$
0.0932544 0.995642i $$-0.470273\pi$$
$$762$$ 5.00000i 0.181131i
$$763$$ −25.9808 + 15.0000i −0.940567 + 0.543036i
$$764$$ −9.00000 + 15.5885i −0.325609 + 0.563971i
$$765$$ 0 0
$$766$$ −28.0000 −1.01168
$$767$$ 3.46410 14.0000i 0.125081 0.505511i
$$768$$ 1.00000i 0.0360844i
$$769$$ −13.0000 + 22.5167i −0.468792 + 0.811972i −0.999364 0.0356685i $$-0.988644\pi$$
0.530572 + 0.847640i $$0.321977\pi$$
$$770$$ 0 0
$$771$$ −12.0000 20.7846i −0.432169 0.748539i
$$772$$ 16.0000i 0.575853i
$$773$$ 32.0429 18.5000i 1.15250 0.665399i 0.203008 0.979177i $$-0.434928\pi$$
0.949496 + 0.313778i $$0.101595\pi$$
$$774$$ −1.00000 1.73205i −0.0359443 0.0622573i
$$775$$ 0 0
$$776$$ −6.00000 10.3923i −0.215387 0.373062i
$$777$$ 2.59808 + 1.50000i 0.0932055 + 0.0538122i
$$778$$ −13.8564 8.00000i −0.496776 0.286814i
$$779$$ 30.0000 1.07486
$$780$$ 0 0
$$781$$ −2.00000 −0.0715656
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 + 1.73205i 0.0357143 + 0.0618590i
$$785$$ 0 0
$$786$$ −7.50000 12.9904i −0.267516 0.463352i