# Properties

 Label 3840.2.d.v.2689.1 Level $3840$ Weight $2$ Character 3840.2689 Analytic conductor $30.663$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3840 = 2^{8} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3840.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$30.6625543762$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 120) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 2689.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3840.2689 Dual form 3840.2.d.v.2689.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} +(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} +(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +1.00000 q^{9} +2.00000i q^{11} -2.00000 q^{13} +(-1.00000 - 2.00000i) q^{15} -6.00000i q^{17} +8.00000i q^{19} +2.00000i q^{21} -4.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +1.00000 q^{27} -8.00000i q^{29} +2.00000i q^{33} +(4.00000 - 2.00000i) q^{35} +10.0000 q^{37} -2.00000 q^{39} -2.00000 q^{41} +12.0000 q^{43} +(-1.00000 - 2.00000i) q^{45} +3.00000 q^{49} -6.00000i q^{51} +10.0000 q^{53} +(4.00000 - 2.00000i) q^{55} +8.00000i q^{57} +6.00000i q^{59} +2.00000i q^{61} +2.00000i q^{63} +(2.00000 + 4.00000i) q^{65} +8.00000 q^{67} -4.00000i q^{69} -4.00000 q^{71} -4.00000i q^{73} +(-3.00000 + 4.00000i) q^{75} -4.00000 q^{77} -8.00000 q^{79} +1.00000 q^{81} +4.00000 q^{83} +(-12.0000 + 6.00000i) q^{85} -8.00000i q^{87} +6.00000 q^{89} -4.00000i q^{91} +(16.0000 - 8.00000i) q^{95} -8.00000i q^{97} +2.00000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{3} - 2q^{5} + 2q^{9} + O(q^{10})$$ $$2q + 2q^{3} - 2q^{5} + 2q^{9} - 4q^{13} - 2q^{15} - 6q^{25} + 2q^{27} + 8q^{35} + 20q^{37} - 4q^{39} - 4q^{41} + 24q^{43} - 2q^{45} + 6q^{49} + 20q^{53} + 8q^{55} + 4q^{65} + 16q^{67} - 8q^{71} - 6q^{75} - 8q^{77} - 16q^{79} + 2q^{81} + 8q^{83} - 24q^{85} + 12q^{89} + 32q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times$$.

 $$n$$ $$511$$ $$1537$$ $$2561$$ $$2821$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$-1$$

## 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 0
$$3$$ 1.00000 0.577350
$$4$$ 0 0
$$5$$ −1.00000 2.00000i −0.447214 0.894427i
$$6$$ 0 0
$$7$$ 2.00000i 0.755929i 0.925820 + 0.377964i $$0.123376\pi$$
−0.925820 + 0.377964i $$0.876624\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 2.00000i 0.603023i 0.953463 + 0.301511i $$0.0974911\pi$$
−0.953463 + 0.301511i $$0.902509\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ −1.00000 2.00000i −0.258199 0.516398i
$$16$$ 0 0
$$17$$ 6.00000i 1.45521i −0.685994 0.727607i $$-0.740633\pi$$
0.685994 0.727607i $$-0.259367\pi$$
$$18$$ 0 0
$$19$$ 8.00000i 1.83533i 0.397360 + 0.917663i $$0.369927\pi$$
−0.397360 + 0.917663i $$0.630073\pi$$
$$20$$ 0 0
$$21$$ 2.00000i 0.436436i
$$22$$ 0 0
$$23$$ 4.00000i 0.834058i −0.908893 0.417029i $$-0.863071\pi$$
0.908893 0.417029i $$-0.136929\pi$$
$$24$$ 0 0
$$25$$ −3.00000 + 4.00000i −0.600000 + 0.800000i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 8.00000i 1.48556i −0.669534 0.742781i $$-0.733506\pi$$
0.669534 0.742781i $$-0.266494\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 2.00000i 0.348155i
$$34$$ 0 0
$$35$$ 4.00000 2.00000i 0.676123 0.338062i
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 12.0000 1.82998 0.914991 0.403473i $$-0.132197\pi$$
0.914991 + 0.403473i $$0.132197\pi$$
$$44$$ 0 0
$$45$$ −1.00000 2.00000i −0.149071 0.298142i
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 3.00000 0.428571
$$50$$ 0 0
$$51$$ 6.00000i 0.840168i
$$52$$ 0 0
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ 0 0
$$55$$ 4.00000 2.00000i 0.539360 0.269680i
$$56$$ 0 0
$$57$$ 8.00000i 1.05963i
$$58$$ 0 0
$$59$$ 6.00000i 0.781133i 0.920575 + 0.390567i $$0.127721\pi$$
−0.920575 + 0.390567i $$0.872279\pi$$
$$60$$ 0 0
$$61$$ 2.00000i 0.256074i 0.991769 + 0.128037i $$0.0408676\pi$$
−0.991769 + 0.128037i $$0.959132\pi$$
$$62$$ 0 0
$$63$$ 2.00000i 0.251976i
$$64$$ 0 0
$$65$$ 2.00000 + 4.00000i 0.248069 + 0.496139i
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 0 0
$$69$$ 4.00000i 0.481543i
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0 0
$$73$$ 4.00000i 0.468165i −0.972217 0.234082i $$-0.924791\pi$$
0.972217 0.234082i $$-0.0752085\pi$$
$$74$$ 0 0
$$75$$ −3.00000 + 4.00000i −0.346410 + 0.461880i
$$76$$ 0 0
$$77$$ −4.00000 −0.455842
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ −12.0000 + 6.00000i −1.30158 + 0.650791i
$$86$$ 0 0
$$87$$ 8.00000i 0.857690i
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 4.00000i 0.419314i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 16.0000 8.00000i 1.64157 0.820783i
$$96$$ 0 0
$$97$$ 8.00000i 0.812277i −0.913812 0.406138i $$-0.866875\pi$$
0.913812 0.406138i $$-0.133125\pi$$
$$98$$ 0 0
$$99$$ 2.00000i 0.201008i
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 2.00000i 0.197066i −0.995134 0.0985329i $$-0.968585\pi$$
0.995134 0.0985329i $$-0.0314150\pi$$
$$104$$ 0 0
$$105$$ 4.00000 2.00000i 0.390360 0.195180i
$$106$$ 0 0
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 0 0
$$109$$ 6.00000i 0.574696i 0.957826 + 0.287348i $$0.0927736\pi$$
−0.957826 + 0.287348i $$0.907226\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ 2.00000i 0.188144i 0.995565 + 0.0940721i $$0.0299884\pi$$
−0.995565 + 0.0940721i $$0.970012\pi$$
$$114$$ 0 0
$$115$$ −8.00000 + 4.00000i −0.746004 + 0.373002i
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ 0 0
$$123$$ −2.00000 −0.180334
$$124$$ 0 0
$$125$$ 11.0000 + 2.00000i 0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 18.0000i 1.59724i −0.601834 0.798621i $$-0.705563\pi$$
0.601834 0.798621i $$-0.294437\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ 18.0000i 1.57267i 0.617802 + 0.786334i $$0.288023\pi$$
−0.617802 + 0.786334i $$0.711977\pi$$
$$132$$ 0 0
$$133$$ −16.0000 −1.38738
$$134$$ 0 0
$$135$$ −1.00000 2.00000i −0.0860663 0.172133i
$$136$$ 0 0
$$137$$ 10.0000i 0.854358i 0.904167 + 0.427179i $$0.140493\pi$$
−0.904167 + 0.427179i $$0.859507\pi$$
$$138$$ 0 0
$$139$$ 4.00000i 0.339276i −0.985506 0.169638i $$-0.945740\pi$$
0.985506 0.169638i $$-0.0542598\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.00000i 0.334497i
$$144$$ 0 0
$$145$$ −16.0000 + 8.00000i −1.32873 + 0.664364i
$$146$$ 0 0
$$147$$ 3.00000 0.247436
$$148$$ 0 0
$$149$$ 12.0000i 0.983078i −0.870855 0.491539i $$-0.836434\pi$$
0.870855 0.491539i $$-0.163566\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −14.0000 −1.11732 −0.558661 0.829396i $$-0.688685\pi$$
−0.558661 + 0.829396i $$0.688685\pi$$
$$158$$ 0 0
$$159$$ 10.0000 0.793052
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 16.0000 1.25322 0.626608 0.779334i $$-0.284443\pi$$
0.626608 + 0.779334i $$0.284443\pi$$
$$164$$ 0 0
$$165$$ 4.00000 2.00000i 0.311400 0.155700i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 8.00000i 0.611775i
$$172$$ 0 0
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ −8.00000 6.00000i −0.604743 0.453557i
$$176$$ 0 0
$$177$$ 6.00000i 0.450988i
$$178$$ 0 0
$$179$$ 22.0000i 1.64436i −0.569230 0.822179i $$-0.692758\pi$$
0.569230 0.822179i $$-0.307242\pi$$
$$180$$ 0 0
$$181$$ 14.0000i 1.04061i 0.853980 + 0.520306i $$0.174182\pi$$
−0.853980 + 0.520306i $$0.825818\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ 0 0
$$185$$ −10.0000 20.0000i −0.735215 1.47043i
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ 2.00000i 0.145479i
$$190$$ 0 0
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ 0 0
$$193$$ 4.00000i 0.287926i 0.989583 + 0.143963i $$0.0459847\pi$$
−0.989583 + 0.143963i $$0.954015\pi$$
$$194$$ 0 0
$$195$$ 2.00000 + 4.00000i 0.143223 + 0.286446i
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ 0 0
$$201$$ 8.00000 0.564276
$$202$$ 0 0
$$203$$ 16.0000 1.12298
$$204$$ 0 0
$$205$$ 2.00000 + 4.00000i 0.139686 + 0.279372i
$$206$$ 0 0
$$207$$ 4.00000i 0.278019i
$$208$$ 0 0
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ 4.00000i 0.275371i −0.990476 0.137686i $$-0.956034\pi$$
0.990476 0.137686i $$-0.0439664\pi$$
$$212$$ 0 0
$$213$$ −4.00000 −0.274075
$$214$$ 0 0
$$215$$ −12.0000 24.0000i −0.818393 1.63679i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 4.00000i 0.270295i
$$220$$ 0 0
$$221$$ 12.0000i 0.807207i
$$222$$ 0 0
$$223$$ 6.00000i 0.401790i −0.979613 0.200895i $$-0.935615\pi$$
0.979613 0.200895i $$-0.0643850\pi$$
$$224$$ 0 0
$$225$$ −3.00000 + 4.00000i −0.200000 + 0.266667i
$$226$$ 0 0
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ 0 0
$$229$$ 6.00000i 0.396491i 0.980152 + 0.198246i $$0.0635244\pi$$
−0.980152 + 0.198246i $$0.936476\pi$$
$$230$$ 0 0
$$231$$ −4.00000 −0.263181
$$232$$ 0 0
$$233$$ 6.00000i 0.393073i −0.980497 0.196537i $$-0.937031\pi$$
0.980497 0.196537i $$-0.0629694\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −8.00000 −0.519656
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ 1.00000 0.0641500
$$244$$ 0 0
$$245$$ −3.00000 6.00000i −0.191663 0.383326i
$$246$$ 0 0
$$247$$ 16.0000i 1.01806i
$$248$$ 0 0
$$249$$ 4.00000 0.253490
$$250$$ 0 0
$$251$$ 2.00000i 0.126239i −0.998006 0.0631194i $$-0.979895\pi$$
0.998006 0.0631194i $$-0.0201049\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ 0 0
$$255$$ −12.0000 + 6.00000i −0.751469 + 0.375735i
$$256$$ 0 0
$$257$$ 6.00000i 0.374270i 0.982334 + 0.187135i $$0.0599201\pi$$
−0.982334 + 0.187135i $$0.940080\pi$$
$$258$$ 0 0
$$259$$ 20.0000i 1.24274i
$$260$$ 0 0
$$261$$ 8.00000i 0.495188i
$$262$$ 0 0
$$263$$ 12.0000i 0.739952i 0.929041 + 0.369976i $$0.120634\pi$$
−0.929041 + 0.369976i $$0.879366\pi$$
$$264$$ 0 0
$$265$$ −10.0000 20.0000i −0.614295 1.22859i
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 0 0
$$269$$ 24.0000i 1.46331i −0.681677 0.731653i $$-0.738749\pi$$
0.681677 0.731653i $$-0.261251\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 0 0
$$273$$ 4.00000i 0.242091i
$$274$$ 0 0
$$275$$ −8.00000 6.00000i −0.482418 0.361814i
$$276$$ 0 0
$$277$$ −6.00000 −0.360505 −0.180253 0.983620i $$-0.557691\pi$$
−0.180253 + 0.983620i $$0.557691\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 16.0000 8.00000i 0.947758 0.473879i
$$286$$ 0 0
$$287$$ 4.00000i 0.236113i
$$288$$ 0 0
$$289$$ −19.0000 −1.11765
$$290$$ 0 0
$$291$$ 8.00000i 0.468968i
$$292$$ 0 0
$$293$$ −22.0000 −1.28525 −0.642627 0.766179i $$-0.722155\pi$$
−0.642627 + 0.766179i $$0.722155\pi$$
$$294$$ 0 0
$$295$$ 12.0000 6.00000i 0.698667 0.349334i
$$296$$ 0 0
$$297$$ 2.00000i 0.116052i
$$298$$ 0 0
$$299$$ 8.00000i 0.462652i
$$300$$ 0 0
$$301$$ 24.0000i 1.38334i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.00000 2.00000i 0.229039 0.114520i
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 2.00000i 0.113776i
$$310$$ 0 0
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0 0
$$313$$ 4.00000i 0.226093i −0.993590 0.113047i $$-0.963939\pi$$
0.993590 0.113047i $$-0.0360610\pi$$
$$314$$ 0 0
$$315$$ 4.00000 2.00000i 0.225374 0.112687i
$$316$$ 0 0
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ 16.0000 0.895828
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 48.0000 2.67079
$$324$$ 0 0
$$325$$ 6.00000 8.00000i 0.332820 0.443760i
$$326$$ 0 0
$$327$$ 6.00000i 0.331801i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 16.0000i 0.879440i 0.898135 + 0.439720i $$0.144922\pi$$
−0.898135 + 0.439720i $$0.855078\pi$$
$$332$$ 0 0
$$333$$ 10.0000 0.547997
$$334$$ 0 0
$$335$$ −8.00000 16.0000i −0.437087 0.874173i
$$336$$ 0 0
$$337$$ 28.0000i 1.52526i −0.646837 0.762629i $$-0.723908\pi$$
0.646837 0.762629i $$-0.276092\pi$$
$$338$$ 0 0
$$339$$ 2.00000i 0.108625i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 20.0000i 1.07990i
$$344$$ 0 0
$$345$$ −8.00000 + 4.00000i −0.430706 + 0.215353i
$$346$$ 0 0
$$347$$ −28.0000 −1.50312 −0.751559 0.659665i $$-0.770698\pi$$
−0.751559 + 0.659665i $$0.770698\pi$$
$$348$$ 0 0
$$349$$ 22.0000i 1.17763i 0.808267 + 0.588817i $$0.200406\pi$$
−0.808267 + 0.588817i $$0.799594\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 0 0
$$353$$ 6.00000i 0.319348i 0.987170 + 0.159674i $$0.0510443\pi$$
−0.987170 + 0.159674i $$0.948956\pi$$
$$354$$ 0 0
$$355$$ 4.00000 + 8.00000i 0.212298 + 0.424596i
$$356$$ 0 0
$$357$$ 12.0000 0.635107
$$358$$ 0 0
$$359$$ −16.0000 −0.844448 −0.422224 0.906492i $$-0.638750\pi$$
−0.422224 + 0.906492i $$0.638750\pi$$
$$360$$ 0 0
$$361$$ −45.0000 −2.36842
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ −8.00000 + 4.00000i −0.418739 + 0.209370i
$$366$$ 0 0
$$367$$ 14.0000i 0.730794i 0.930852 + 0.365397i $$0.119067\pi$$
−0.930852 + 0.365397i $$0.880933\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ 20.0000i 1.03835i
$$372$$ 0 0
$$373$$ 2.00000 0.103556 0.0517780 0.998659i $$-0.483511\pi$$
0.0517780 + 0.998659i $$0.483511\pi$$
$$374$$ 0 0
$$375$$ 11.0000 + 2.00000i 0.568038 + 0.103280i
$$376$$ 0 0
$$377$$ 16.0000i 0.824042i
$$378$$ 0 0
$$379$$ 4.00000i 0.205466i 0.994709 + 0.102733i $$0.0327588\pi$$
−0.994709 + 0.102733i $$0.967241\pi$$
$$380$$ 0 0
$$381$$ 18.0000i 0.922168i
$$382$$ 0 0
$$383$$ 24.0000i 1.22634i 0.789950 + 0.613171i $$0.210106\pi$$
−0.789950 + 0.613171i $$0.789894\pi$$
$$384$$ 0 0
$$385$$ 4.00000 + 8.00000i 0.203859 + 0.407718i
$$386$$ 0 0
$$387$$ 12.0000 0.609994
$$388$$ 0 0
$$389$$ 12.0000i 0.608424i 0.952604 + 0.304212i $$0.0983931\pi$$
−0.952604 + 0.304212i $$0.901607\pi$$
$$390$$ 0 0
$$391$$ −24.0000 −1.21373
$$392$$ 0 0
$$393$$ 18.0000i 0.907980i
$$394$$ 0 0
$$395$$ 8.00000 + 16.0000i 0.402524 + 0.805047i
$$396$$ 0 0
$$397$$ 6.00000 0.301131 0.150566 0.988600i $$-0.451890\pi$$
0.150566 + 0.988600i $$0.451890\pi$$
$$398$$ 0 0
$$399$$ −16.0000 −0.801002
$$400$$ 0 0
$$401$$ 22.0000 1.09863 0.549314 0.835616i $$-0.314889\pi$$
0.549314 + 0.835616i $$0.314889\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −1.00000 2.00000i −0.0496904 0.0993808i
$$406$$ 0 0
$$407$$ 20.0000i 0.991363i
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 10.0000i 0.493264i
$$412$$ 0 0
$$413$$ −12.0000 −0.590481
$$414$$ 0 0
$$415$$ −4.00000 8.00000i −0.196352 0.392705i
$$416$$ 0 0
$$417$$ 4.00000i 0.195881i
$$418$$ 0 0
$$419$$ 6.00000i 0.293119i 0.989202 + 0.146560i $$0.0468200\pi$$
−0.989202 + 0.146560i $$0.953180\pi$$
$$420$$ 0 0
$$421$$ 26.0000i 1.26716i 0.773676 + 0.633581i $$0.218416\pi$$
−0.773676 + 0.633581i $$0.781584\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 24.0000 + 18.0000i 1.16417 + 0.873128i
$$426$$ 0 0
$$427$$ −4.00000 −0.193574
$$428$$ 0 0
$$429$$ 4.00000i 0.193122i
$$430$$ 0 0
$$431$$ −16.0000 −0.770693 −0.385346 0.922772i $$-0.625918\pi$$
−0.385346 + 0.922772i $$0.625918\pi$$
$$432$$ 0 0
$$433$$ 12.0000i 0.576683i −0.957528 0.288342i $$-0.906896\pi$$
0.957528 0.288342i $$-0.0931039\pi$$
$$434$$ 0 0
$$435$$ −16.0000 + 8.00000i −0.767141 + 0.383571i
$$436$$ 0 0
$$437$$ 32.0000 1.53077
$$438$$ 0 0
$$439$$ −24.0000 −1.14546 −0.572729 0.819745i $$-0.694115\pi$$
−0.572729 + 0.819745i $$0.694115\pi$$
$$440$$ 0 0
$$441$$ 3.00000 0.142857
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 0 0
$$445$$ −6.00000 12.0000i −0.284427 0.568855i
$$446$$ 0 0
$$447$$ 12.0000i 0.567581i
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ 4.00000i 0.188353i
$$452$$ 0 0
$$453$$ 16.0000 0.751746
$$454$$ 0 0
$$455$$ −8.00000 + 4.00000i −0.375046 + 0.187523i
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 6.00000i 0.280056i
$$460$$ 0 0
$$461$$ 12.0000i 0.558896i −0.960161 0.279448i $$-0.909849\pi$$
0.960161 0.279448i $$-0.0901514\pi$$
$$462$$ 0 0
$$463$$ 22.0000i 1.02243i 0.859454 + 0.511213i $$0.170804\pi$$
−0.859454 + 0.511213i $$0.829196\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ 0 0
$$469$$ 16.0000i 0.738811i
$$470$$ 0 0
$$471$$ −14.0000 −0.645086
$$472$$ 0 0
$$473$$ 24.0000i 1.10352i
$$474$$ 0 0
$$475$$ −32.0000 24.0000i −1.46826 1.10120i
$$476$$ 0 0
$$477$$ 10.0000 0.457869
$$478$$ 0 0
$$479$$ −28.0000 −1.27935 −0.639676 0.768644i $$-0.720932\pi$$
−0.639676 + 0.768644i $$0.720932\pi$$
$$480$$ 0 0
$$481$$ −20.0000 −0.911922
$$482$$ 0 0
$$483$$ 8.00000 0.364013
$$484$$ 0 0
$$485$$ −16.0000 + 8.00000i −0.726523 + 0.363261i
$$486$$ 0 0
$$487$$ 34.0000i 1.54069i −0.637629 0.770344i $$-0.720085\pi$$
0.637629 0.770344i $$-0.279915\pi$$
$$488$$ 0 0
$$489$$ 16.0000 0.723545
$$490$$ 0 0
$$491$$ 34.0000i 1.53440i −0.641409 0.767199i $$-0.721650\pi$$
0.641409 0.767199i $$-0.278350\pi$$
$$492$$ 0 0
$$493$$ −48.0000 −2.16181
$$494$$ 0 0
$$495$$ 4.00000 2.00000i 0.179787 0.0898933i
$$496$$ 0 0
$$497$$ 8.00000i 0.358849i
$$498$$ 0 0
$$499$$ 40.0000i 1.79065i −0.445418 0.895323i $$-0.646945\pi$$
0.445418 0.895323i $$-0.353055\pi$$
$$500$$ 0 0
$$501$$ 12.0000i 0.536120i
$$502$$ 0 0
$$503$$ 16.0000i 0.713405i 0.934218 + 0.356702i $$0.116099\pi$$
−0.934218 + 0.356702i $$0.883901\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −9.00000 −0.399704
$$508$$ 0 0
$$509$$ 8.00000i 0.354594i 0.984157 + 0.177297i $$0.0567353\pi$$
−0.984157 + 0.177297i $$0.943265\pi$$
$$510$$ 0 0
$$511$$ 8.00000 0.353899
$$512$$ 0 0
$$513$$ 8.00000i 0.353209i
$$514$$ 0 0
$$515$$ −4.00000 + 2.00000i −0.176261 + 0.0881305i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 18.0000 0.790112
$$520$$ 0 0
$$521$$ 26.0000 1.13908 0.569540 0.821963i $$-0.307121\pi$$
0.569540 + 0.821963i $$0.307121\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 0 0
$$525$$ −8.00000 6.00000i −0.349149 0.261861i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 0 0
$$531$$ 6.00000i 0.260378i
$$532$$ 0 0
$$533$$ 4.00000 0.173259
$$534$$ 0 0
$$535$$ −4.00000 8.00000i −0.172935 0.345870i
$$536$$ 0 0
$$537$$ 22.0000i 0.949370i
$$538$$ 0 0
$$539$$ 6.00000i 0.258438i
$$540$$ 0 0
$$541$$ 10.0000i 0.429934i 0.976621 + 0.214967i $$0.0689643\pi$$
−0.976621 + 0.214967i $$0.931036\pi$$
$$542$$ 0 0
$$543$$ 14.0000i 0.600798i
$$544$$ 0 0
$$545$$ 12.0000 6.00000i 0.514024 0.257012i
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 0 0
$$549$$ 2.00000i 0.0853579i
$$550$$ 0 0
$$551$$ 64.0000 2.72649
$$552$$ 0 0
$$553$$ 16.0000i 0.680389i
$$554$$ 0 0
$$555$$ −10.0000 20.0000i −0.424476 0.848953i
$$556$$ 0 0
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 0 0
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ 0 0
$$565$$ 4.00000 2.00000i 0.168281 0.0841406i
$$566$$ 0 0
$$567$$ 2.00000i 0.0839921i
$$568$$ 0 0
$$569$$ −42.0000 −1.76073 −0.880366 0.474295i $$-0.842703\pi$$
−0.880366 + 0.474295i $$0.842703\pi$$
$$570$$ 0 0
$$571$$ 16.0000i 0.669579i 0.942293 + 0.334790i $$0.108665\pi$$
−0.942293 + 0.334790i $$0.891335\pi$$
$$572$$ 0 0
$$573$$ −12.0000 −0.501307
$$574$$ 0 0
$$575$$ 16.0000 + 12.0000i 0.667246 + 0.500435i
$$576$$ 0 0
$$577$$ 16.0000i 0.666089i −0.942911 0.333044i $$-0.891924\pi$$
0.942911 0.333044i $$-0.108076\pi$$
$$578$$ 0 0
$$579$$ 4.00000i 0.166234i
$$580$$ 0 0
$$581$$ 8.00000i 0.331896i
$$582$$ 0 0
$$583$$ 20.0000i 0.828315i
$$584$$ 0 0
$$585$$ 2.00000 + 4.00000i 0.0826898 + 0.165380i
$$586$$ 0 0
$$587$$ 4.00000 0.165098 0.0825488 0.996587i $$-0.473694\pi$$
0.0825488 + 0.996587i $$0.473694\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ 0 0
$$593$$ 34.0000i 1.39621i 0.715994 + 0.698106i $$0.245974\pi$$
−0.715994 + 0.698106i $$0.754026\pi$$
$$594$$ 0 0
$$595$$ −12.0000 24.0000i −0.491952 0.983904i
$$596$$ 0 0
$$597$$ 8.00000 0.327418
$$598$$ 0 0
$$599$$ −16.0000 −0.653742 −0.326871 0.945069i $$-0.605994\pi$$
−0.326871 + 0.945069i $$0.605994\pi$$
$$600$$ 0 0
$$601$$ 30.0000 1.22373 0.611863 0.790964i $$-0.290420\pi$$
0.611863 + 0.790964i $$0.290420\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ 0 0
$$605$$ −7.00000 14.0000i −0.284590 0.569181i
$$606$$ 0 0
$$607$$ 22.0000i 0.892952i −0.894795 0.446476i $$-0.852679\pi$$
0.894795 0.446476i $$-0.147321\pi$$
$$608$$ 0 0
$$609$$ 16.0000 0.648353
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 14.0000 0.565455 0.282727 0.959200i $$-0.408761\pi$$
0.282727 + 0.959200i $$0.408761\pi$$
$$614$$ 0 0
$$615$$ 2.00000 + 4.00000i 0.0806478 + 0.161296i
$$616$$ 0 0
$$617$$ 10.0000i 0.402585i −0.979531 0.201292i $$-0.935486\pi$$
0.979531 0.201292i $$-0.0645141\pi$$
$$618$$ 0 0
$$619$$ 20.0000i 0.803868i 0.915669 + 0.401934i $$0.131662\pi$$
−0.915669 + 0.401934i $$0.868338\pi$$
$$620$$ 0 0
$$621$$ 4.00000i 0.160514i
$$622$$ 0 0
$$623$$ 12.0000i 0.480770i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 0 0
$$627$$ −16.0000 −0.638978
$$628$$ 0 0
$$629$$ 60.0000i 2.39236i
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 0 0
$$633$$ 4.00000i 0.158986i
$$634$$ 0 0
$$635$$ −36.0000 + 18.0000i −1.42862 + 0.714308i
$$636$$ 0 0
$$637$$ −6.00000 −0.237729
$$638$$ 0 0
$$639$$ −4.00000 −0.158238
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 0 0
$$643$$ 24.0000 0.946468 0.473234 0.880937i $$-0.343087\pi$$
0.473234 + 0.880937i $$0.343087\pi$$
$$644$$ 0 0
$$645$$ −12.0000 24.0000i −0.472500 0.944999i
$$646$$ 0 0
$$647$$ 8.00000i 0.314512i 0.987558 + 0.157256i $$0.0502649\pi$$
−0.987558 + 0.157256i $$0.949735\pi$$
$$648$$ 0 0
$$649$$ −12.0000 −0.471041
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.00000 −0.234798 −0.117399 0.993085i $$-0.537456\pi$$
−0.117399 + 0.993085i $$0.537456\pi$$
$$654$$ 0 0
$$655$$ 36.0000 18.0000i 1.40664 0.703318i
$$656$$ 0 0
$$657$$ 4.00000i 0.156055i
$$658$$ 0 0
$$659$$ 30.0000i 1.16863i 0.811525 + 0.584317i $$0.198638\pi$$
−0.811525 + 0.584317i $$0.801362\pi$$
$$660$$ 0 0
$$661$$ 2.00000i 0.0777910i −0.999243 0.0388955i $$-0.987616\pi$$
0.999243 0.0388955i $$-0.0123839\pi$$
$$662$$ 0 0
$$663$$ 12.0000i 0.466041i
$$664$$ 0 0
$$665$$ 16.0000 + 32.0000i 0.620453 + 1.24091i
$$666$$ 0 0
$$667$$ −32.0000 −1.23904
$$668$$ 0 0
$$669$$ 6.00000i 0.231973i
$$670$$ 0 0
$$671$$ −4.00000 −0.154418
$$672$$ 0 0
$$673$$ 20.0000i 0.770943i −0.922720 0.385472i $$-0.874039\pi$$
0.922720 0.385472i $$-0.125961\pi$$
$$674$$ 0 0
$$675$$ −3.00000 + 4.00000i −0.115470 + 0.153960i
$$676$$ 0 0
$$677$$ −30.0000 −1.15299 −0.576497 0.817099i $$-0.695581\pi$$
−0.576497 + 0.817099i $$0.695581\pi$$
$$678$$ 0 0
$$679$$ 16.0000 0.614024
$$680$$ 0 0
$$681$$ 4.00000 0.153280
$$682$$ 0 0
$$683$$ −20.0000 −0.765279 −0.382639 0.923898i $$-0.624985\pi$$
−0.382639 + 0.923898i $$0.624985\pi$$
$$684$$ 0 0
$$685$$ 20.0000 10.0000i 0.764161 0.382080i
$$686$$ 0 0
$$687$$ 6.00000i 0.228914i
$$688$$ 0 0
$$689$$ −20.0000 −0.761939
$$690$$ 0 0
$$691$$ 48.0000i 1.82601i −0.407953 0.913003i $$-0.633757\pi$$
0.407953 0.913003i $$-0.366243\pi$$
$$692$$ 0 0
$$693$$ −4.00000 −0.151947
$$694$$ 0 0
$$695$$ −8.00000 + 4.00000i −0.303457 + 0.151729i
$$696$$ 0 0
$$697$$ 12.0000i 0.454532i
$$698$$ 0 0
$$699$$ 6.00000i 0.226941i
$$700$$ 0 0
$$701$$ 8.00000i 0.302156i −0.988522 0.151078i $$-0.951726\pi$$
0.988522 0.151078i $$-0.0482744\pi$$
$$702$$ 0 0
$$703$$ 80.0000i 3.01726i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 46.0000i 1.72757i 0.503864 + 0.863783i $$0.331911\pi$$
−0.503864 + 0.863783i $$0.668089\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −8.00000 + 4.00000i −0.299183 + 0.149592i
$$716$$ 0 0
$$717$$ 20.0000 0.746914
$$718$$ 0 0
$$719$$ 40.0000 1.49175 0.745874 0.666087i $$-0.232032\pi$$
0.745874 + 0.666087i $$0.232032\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ 0 0
$$723$$ −10.0000 −0.371904
$$724$$ 0 0
$$725$$ 32.0000 + 24.0000i 1.18845 + 0.891338i
$$726$$ 0 0
$$727$$ 30.0000i 1.11264i 0.830969 + 0.556319i $$0.187787\pi$$
−0.830969 + 0.556319i $$0.812213\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 72.0000i 2.66302i
$$732$$ 0 0
$$733$$ 42.0000 1.55131 0.775653 0.631160i $$-0.217421\pi$$
0.775653 + 0.631160i $$0.217421\pi$$
$$734$$ 0 0
$$735$$ −3.00000 6.00000i −0.110657 0.221313i
$$736$$ 0 0
$$737$$ 16.0000i 0.589368i
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 16.0000i 0.587775i
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ −24.0000 + 12.0000i −0.879292 + 0.439646i
$$746$$ 0 0
$$747$$ 4.00000 0.146352
$$748$$ 0 0
$$749$$ 8.00000i 0.292314i
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ 0 0
$$753$$ 2.00000i 0.0728841i
$$754$$ 0 0
$$755$$ −16.0000 32.0000i −0.582300 1.16460i
$$756$$ 0 0
$$757$$ −38.0000 −1.38113 −0.690567 0.723269i $$-0.742639\pi$$
−0.690567 + 0.723269i $$0.742639\pi$$
$$758$$ 0 0
$$759$$ 8.00000 0.290382
$$760$$ 0 0
$$761$$ 2.00000 0.0724999 0.0362500 0.999343i $$-0.488459\pi$$
0.0362500 + 0.999343i $$0.488459\pi$$
$$762$$ 0 0
$$763$$ −12.0000 −0.434429
$$764$$ 0 0
$$765$$ −12.0000 + 6.00000i −0.433861 + 0.216930i
$$766$$ 0 0
$$767$$ 12.0000i 0.433295i
$$768$$ 0 0
$$769$$ −34.0000 −1.22607 −0.613036 0.790055i $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 0 0
$$771$$ 6.00000i 0.216085i
$$772$$ 0 0
$$773$$ 38.0000 1.36677 0.683383 0.730061i $$-0.260508\pi$$
0.683383 + 0.730061i $$0.260508\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 20.0000i 0.717496i
$$778$$ 0 0
$$779$$ 16.0000i 0.573259i
$$780$$ 0 0
$$781$$ 8.00000i 0.286263i
$$782$$ 0 0
$$783$$ 8.00000i 0.285897i
$$784$$ 0 0
$$785$$ 14.0000 + 28.0000i 0.499681 + 0.999363i
$$786$$ 0 0
$$787$$ −32.0000 −1.14068 −0.570338 0.821410i $$-0.693188\pi$$
−0.570338 + 0.821410i $$0.693188\pi$$
$$788$$ 0 0
$$789$$ 12.0000i 0.427211i
$$790$$ 0 0
$$791$$ −4.00000 −0.142224
$$792$$ 0 0
$$793$$ 4.00000i 0.142044i
$$794$$ 0 0
$$795$$ −10.0000 20.0000i −0.354663 0.709327i
$$796$$ 0 0
$$797$$ 30.0000 1.06265 0.531327 0.847167i $$-0.321693\pi$$
0.531327 + 0.847167i $$0.321693\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 0 0
$$803$$ 8.00000 0.282314
$$804$$ 0 0