# Properties

 Label 120.2.f.a.49.1 Level $120$ Weight $2$ Character 120.49 Analytic conductor $0.958$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.958204824255$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 49.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 120.49 Dual form 120.2.f.a.49.2

## $q$-expansion

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

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$41$$ $$61$$ $$97$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 2.00000 + 1.00000i 0.894427 + 0.447214i
$$6$$ 0 0
$$7$$ 2.00000i 0.755929i −0.925820 0.377964i $$-0.876624\pi$$
0.925820 0.377964i $$-0.123376\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 2.00000i 0.554700i −0.960769 0.277350i $$-0.910544\pi$$
0.960769 0.277350i $$-0.0894562\pi$$
$$14$$ 0 0
$$15$$ 1.00000 2.00000i 0.258199 0.516398i
$$16$$ 0 0
$$17$$ 6.00000i 1.45521i 0.685994 + 0.727607i $$0.259367\pi$$
−0.685994 + 0.727607i $$0.740633\pi$$
$$18$$ 0 0
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ −2.00000 −0.436436
$$22$$ 0 0
$$23$$ 4.00000i 0.834058i 0.908893 + 0.417029i $$0.136929\pi$$
−0.908893 + 0.417029i $$0.863071\pi$$
$$24$$ 0 0
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 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
$$35$$ 2.00000 4.00000i 0.338062 0.676123i
$$36$$ 0 0
$$37$$ 10.0000i 1.64399i −0.569495 0.821995i $$-0.692861\pi$$
0.569495 0.821995i $$-0.307139\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 12.0000i 1.82998i 0.403473 + 0.914991i $$0.367803\pi$$
−0.403473 + 0.914991i $$0.632197\pi$$
$$44$$ 0 0
$$45$$ −2.00000 1.00000i −0.298142 0.149071i
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 3.00000 0.428571
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ 0 0
$$53$$ 10.0000i 1.37361i −0.726844 0.686803i $$-0.759014\pi$$
0.726844 0.686803i $$-0.240986\pi$$
$$54$$ 0 0
$$55$$ 4.00000 + 2.00000i 0.539360 + 0.269680i
$$56$$ 0 0
$$57$$ 8.00000i 1.05963i
$$58$$ 0 0
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ 2.00000i 0.251976i
$$64$$ 0 0
$$65$$ 2.00000 4.00000i 0.248069 0.496139i
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 0 0
$$69$$ 4.00000 0.481543
$$70$$ 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
$$75$$ 4.00000 3.00000i 0.461880 0.346410i
$$76$$ 0 0
$$77$$ 4.00000i 0.455842i
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 4.00000i 0.439057i −0.975606 0.219529i $$-0.929548\pi$$
0.975606 0.219529i $$-0.0704519\pi$$
$$84$$ 0 0
$$85$$ −6.00000 + 12.0000i −0.650791 + 1.30158i
$$86$$ 0 0
$$87$$ 8.00000i 0.857690i
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 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 $$0.133125\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 2.00000i 0.197066i 0.995134 + 0.0985329i $$0.0314150\pi$$
−0.995134 + 0.0985329i $$0.968585\pi$$
$$104$$ 0 0
$$105$$ −4.00000 2.00000i −0.390360 0.195180i
$$106$$ 0 0
$$107$$ 4.00000i 0.386695i 0.981130 + 0.193347i $$0.0619344\pi$$
−0.981130 + 0.193347i $$0.938066\pi$$
$$108$$ 0 0
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ 0 0
$$113$$ 2.00000i 0.188144i −0.995565 0.0940721i $$-0.970012\pi$$
0.995565 0.0940721i $$-0.0299884\pi$$
$$114$$ 0 0
$$115$$ −4.00000 + 8.00000i −0.373002 + 0.746004i
$$116$$ 0 0
$$117$$ 2.00000i 0.184900i
$$118$$ 0 0
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 2.00000i 0.180334i
$$124$$ 0 0
$$125$$ 2.00000 + 11.0000i 0.178885 + 0.983870i
$$126$$ 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
$$131$$ −18.0000 −1.57267 −0.786334 0.617802i $$-0.788023\pi$$
−0.786334 + 0.617802i $$0.788023\pi$$
$$132$$ 0 0
$$133$$ 16.0000i 1.38738i
$$134$$ 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
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 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
$$147$$ 3.00000i 0.247436i
$$148$$ 0 0
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 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
$$157$$ 14.0000i 1.11732i −0.829396 0.558661i $$-0.811315\pi$$
0.829396 0.558661i $$-0.188685\pi$$
$$158$$ 0 0
$$159$$ −10.0000 −0.793052
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 16.0000i 1.25322i −0.779334 0.626608i $$-0.784443\pi$$
0.779334 0.626608i $$-0.215557\pi$$
$$164$$ 0 0
$$165$$ 2.00000 4.00000i 0.155700 0.311400i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ 0 0
$$171$$ 8.00000 0.611775
$$172$$ 0 0
$$173$$ 18.0000i 1.36851i 0.729241 + 0.684257i $$0.239873\pi$$
−0.729241 + 0.684257i $$0.760127\pi$$
$$174$$ 0 0
$$175$$ 8.00000 6.00000i 0.604743 0.453557i
$$176$$ 0 0
$$177$$ 6.00000i 0.450988i
$$178$$ 0 0
$$179$$ 22.0000 1.64436 0.822179 0.569230i $$-0.192758\pi$$
0.822179 + 0.569230i $$0.192758\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ 0 0
$$185$$ 10.0000 20.0000i 0.735215 1.47043i
$$186$$ 0 0
$$187$$ 12.0000i 0.877527i
$$188$$ 0 0
$$189$$ 2.00000 0.145479
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ 4.00000i 0.287926i −0.989583 0.143963i $$-0.954015\pi$$
0.989583 0.143963i $$-0.0459847\pi$$
$$194$$ 0 0
$$195$$ −4.00000 2.00000i −0.286446 0.143223i
$$196$$ 0 0
$$197$$ 6.00000i 0.427482i −0.976890 0.213741i $$-0.931435\pi$$
0.976890 0.213741i $$-0.0685649\pi$$
$$198$$ 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
$$203$$ 16.0000i 1.12298i
$$204$$ 0 0
$$205$$ 4.00000 + 2.00000i 0.279372 + 0.139686i
$$206$$ 0 0
$$207$$ 4.00000i 0.278019i
$$208$$ 0 0
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 4.00000i 0.274075i
$$214$$ 0 0
$$215$$ −12.0000 + 24.0000i −0.818393 + 1.63679i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 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
$$227$$ 4.00000i 0.265489i −0.991150 0.132745i $$-0.957621\pi$$
0.991150 0.132745i $$-0.0423790\pi$$
$$228$$ 0 0
$$229$$ −6.00000 −0.396491 −0.198246 0.980152i $$-0.563524\pi$$
−0.198246 + 0.980152i $$0.563524\pi$$
$$230$$ 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
$$237$$ 8.00000i 0.519656i
$$238$$ 0 0
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ 6.00000 + 3.00000i 0.383326 + 0.191663i
$$246$$ 0 0
$$247$$ 16.0000i 1.01806i
$$248$$ 0 0
$$249$$ −4.00000 −0.253490
$$250$$ 0 0
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ 8.00000i 0.502956i
$$254$$ 0 0
$$255$$ 12.0000 + 6.00000i 0.751469 + 0.375735i
$$256$$ 0 0
$$257$$ 6.00000i 0.374270i −0.982334 0.187135i $$-0.940080\pi$$
0.982334 0.187135i $$-0.0599201\pi$$
$$258$$ 0 0
$$259$$ −20.0000 −1.24274
$$260$$ 0 0
$$261$$ 8.00000 0.495188
$$262$$ 0 0
$$263$$ 12.0000i 0.739952i −0.929041 0.369976i $$-0.879366\pi$$
0.929041 0.369976i $$-0.120634\pi$$
$$264$$ 0 0
$$265$$ 10.0000 20.0000i 0.614295 1.22859i
$$266$$ 0 0
$$267$$ 6.00000i 0.367194i
$$268$$ 0 0
$$269$$ −24.0000 −1.46331 −0.731653 0.681677i $$-0.761251\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 0 0
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 0 0
$$273$$ 4.00000i 0.242091i
$$274$$ 0 0
$$275$$ 6.00000 + 8.00000i 0.361814 + 0.482418i
$$276$$ 0 0
$$277$$ 6.00000i 0.360505i 0.983620 + 0.180253i $$0.0576915\pi$$
−0.983620 + 0.180253i $$0.942309\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ −8.00000 + 16.0000i −0.473879 + 0.947758i
$$286$$ 0 0
$$287$$ 4.00000i 0.236113i
$$288$$ 0 0
$$289$$ −19.0000 −1.11765
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ 0 0
$$293$$ 22.0000i 1.28525i 0.766179 + 0.642627i $$0.222155\pi$$
−0.766179 + 0.642627i $$0.777845\pi$$
$$294$$ 0 0
$$295$$ 12.0000 + 6.00000i 0.698667 + 0.349334i
$$296$$ 0 0
$$297$$ 2.00000i 0.116052i
$$298$$ 0 0
$$299$$ 8.00000 0.462652
$$300$$ 0 0
$$301$$ 24.0000 1.38334
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.00000 + 2.00000i 0.229039 + 0.114520i
$$306$$ 0 0
$$307$$ 20.0000i 1.14146i 0.821138 + 0.570730i $$0.193340\pi$$
−0.821138 + 0.570730i $$0.806660\pi$$
$$308$$ 0 0
$$309$$ 2.00000 0.113776
$$310$$ 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
$$315$$ −2.00000 + 4.00000i −0.112687 + 0.225374i
$$316$$ 0 0
$$317$$ 18.0000i 1.01098i −0.862832 0.505490i $$-0.831312\pi$$
0.862832 0.505490i $$-0.168688\pi$$
$$318$$ 0 0
$$319$$ −16.0000 −0.895828
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 48.0000i 2.67079i
$$324$$ 0 0
$$325$$ 8.00000 6.00000i 0.443760 0.332820i
$$326$$ 0 0
$$327$$ 6.00000i 0.331801i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 16.0000 0.879440 0.439720 0.898135i $$-0.355078\pi$$
0.439720 + 0.898135i $$0.355078\pi$$
$$332$$ 0 0
$$333$$ 10.0000i 0.547997i
$$334$$ 0 0
$$335$$ 8.00000 16.0000i 0.437087 0.874173i
$$336$$ 0 0
$$337$$ 28.0000i 1.52526i 0.646837 + 0.762629i $$0.276092\pi$$
−0.646837 + 0.762629i $$0.723908\pi$$
$$338$$ 0 0
$$339$$ −2.00000 −0.108625
$$340$$ 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
$$347$$ 28.0000i 1.50312i −0.659665 0.751559i $$-0.729302\pi$$
0.659665 0.751559i $$-0.270698\pi$$
$$348$$ 0 0
$$349$$ 22.0000 1.17763 0.588817 0.808267i $$-0.299594\pi$$
0.588817 + 0.808267i $$0.299594\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 0 0
$$353$$ 6.00000i 0.319348i −0.987170 0.159674i $$-0.948956\pi$$
0.987170 0.159674i $$-0.0510443\pi$$
$$354$$ 0 0
$$355$$ −8.00000 4.00000i −0.424596 0.212298i
$$356$$ 0 0
$$357$$ 12.0000i 0.635107i
$$358$$ 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
$$363$$ 7.00000i 0.367405i
$$364$$ 0 0
$$365$$ 4.00000 8.00000i 0.209370 0.418739i
$$366$$ 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
$$371$$ −20.0000 −1.03835
$$372$$ 0 0
$$373$$ 2.00000i 0.103556i −0.998659 0.0517780i $$-0.983511\pi$$
0.998659 0.0517780i $$-0.0164888\pi$$
$$374$$ 0 0
$$375$$ 11.0000 2.00000i 0.568038 0.103280i
$$376$$ 0 0
$$377$$ 16.0000i 0.824042i
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 0 0
$$381$$ −18.0000 −0.922168
$$382$$ 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
$$387$$ 12.0000i 0.609994i
$$388$$ 0 0
$$389$$ −12.0000 −0.608424 −0.304212 0.952604i $$-0.598393\pi$$
−0.304212 + 0.952604i $$0.598393\pi$$
$$390$$ 0 0
$$391$$ −24.0000 −1.21373
$$392$$ 0 0
$$393$$ 18.0000i 0.907980i
$$394$$ 0 0
$$395$$ 16.0000 + 8.00000i 0.805047 + 0.402524i
$$396$$ 0 0
$$397$$ 6.00000i 0.301131i 0.988600 + 0.150566i $$0.0481095\pi$$
−0.988600 + 0.150566i $$0.951890\pi$$
$$398$$ 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
$$405$$ 2.00000 + 1.00000i 0.0993808 + 0.0496904i
$$406$$ 0 0
$$407$$ 20.0000i 0.991363i
$$408$$ 0 0
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ 0 0
$$413$$ 12.0000i 0.590481i
$$414$$ 0 0
$$415$$ 4.00000 8.00000i 0.196352 0.392705i
$$416$$ 0 0
$$417$$ 4.00000i 0.195881i
$$418$$ 0 0
$$419$$ −6.00000 −0.293119 −0.146560 0.989202i $$-0.546820\pi$$
−0.146560 + 0.989202i $$0.546820\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −24.0000 + 18.0000i −1.16417 + 0.873128i
$$426$$ 0 0
$$427$$ 4.00000i 0.193574i
$$428$$ 0 0
$$429$$ −4.00000 −0.193122
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ 12.0000i 0.576683i 0.957528 + 0.288342i $$0.0931039\pi$$
−0.957528 + 0.288342i $$0.906896\pi$$
$$434$$ 0 0
$$435$$ −8.00000 + 16.0000i −0.383571 + 0.767141i
$$436$$ 0 0
$$437$$ 32.0000i 1.53077i
$$438$$ 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
$$443$$ 36.0000i 1.71041i 0.518289 + 0.855206i $$0.326569\pi$$
−0.518289 + 0.855206i $$0.673431\pi$$
$$444$$ 0 0
$$445$$ −12.0000 6.00000i −0.568855 0.284427i
$$446$$ 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
$$451$$ 4.00000 0.188353
$$452$$ 0 0
$$453$$ 16.0000i 0.751746i
$$454$$ 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
$$459$$ −6.00000 −0.280056
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 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
$$467$$ 36.0000i 1.66588i 0.553362 + 0.832941i $$0.313345\pi$$
−0.553362 + 0.832941i $$0.686655\pi$$
$$468$$ 0 0
$$469$$ −16.0000 −0.738811
$$470$$ 0 0
$$471$$ −14.0000 −0.645086
$$472$$ 0 0
$$473$$ 24.0000i 1.10352i
$$474$$ 0 0
$$475$$ −24.0000 32.0000i −1.10120 1.46826i
$$476$$ 0 0
$$477$$ 10.0000i 0.457869i
$$478$$ 0 0
$$479$$ 28.0000 1.27935 0.639676 0.768644i $$-0.279068\pi$$
0.639676 + 0.768644i $$0.279068\pi$$
$$480$$ 0 0
$$481$$ −20.0000 −0.911922
$$482$$ 0 0
$$483$$ 8.00000i 0.364013i
$$484$$ 0 0
$$485$$ −8.00000 + 16.0000i −0.363261 + 0.726523i
$$486$$ 0 0
$$487$$ 34.0000i 1.54069i 0.637629 + 0.770344i $$0.279915\pi$$
−0.637629 + 0.770344i $$0.720085\pi$$
$$488$$ 0 0
$$489$$ −16.0000 −0.723545
$$490$$ 0 0
$$491$$ −34.0000 −1.53440 −0.767199 0.641409i $$-0.778350\pi$$
−0.767199 + 0.641409i $$0.778350\pi$$
$$492$$ 0 0
$$493$$ 48.0000i 2.16181i
$$494$$ 0 0
$$495$$ −4.00000 2.00000i −0.179787 0.0898933i
$$496$$ 0 0
$$497$$ 8.00000i 0.358849i
$$498$$ 0 0
$$499$$ 40.0000 1.79065 0.895323 0.445418i $$-0.146945\pi$$
0.895323 + 0.445418i $$0.146945\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ 0 0
$$503$$ 16.0000i 0.713405i −0.934218 0.356702i $$-0.883901\pi$$
0.934218 0.356702i $$-0.116099\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.00000i 0.399704i
$$508$$ 0 0
$$509$$ 8.00000 0.354594 0.177297 0.984157i $$-0.443265\pi$$
0.177297 + 0.984157i $$0.443265\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 0 0
$$513$$ 8.00000i 0.353209i
$$514$$ 0 0
$$515$$ −2.00000 + 4.00000i −0.0881305 + 0.176261i
$$516$$ 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 $$-0.692879\pi$$
−0.569540 + 0.821963i $$0.692879\pi$$
$$522$$ 0 0
$$523$$ 16.0000i 0.699631i 0.936819 + 0.349816i $$0.113756\pi$$
−0.936819 + 0.349816i $$0.886244\pi$$
$$524$$ 0 0
$$525$$ −6.00000 8.00000i −0.261861 0.349149i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ 4.00000i 0.173259i
$$534$$ 0 0
$$535$$ −4.00000 + 8.00000i −0.172935 + 0.345870i
$$536$$ 0 0
$$537$$ 22.0000i 0.949370i
$$538$$ 0 0
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ 0 0
$$543$$ 14.0000i 0.600798i
$$544$$ 0 0
$$545$$ 12.0000 + 6.00000i 0.514024 + 0.257012i
$$546$$ 0 0
$$547$$ 20.0000i 0.855138i −0.903983 0.427569i $$-0.859370\pi$$
0.903983 0.427569i $$-0.140630\pi$$
$$548$$ 0 0
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 64.0000 2.72649
$$552$$ 0 0
$$553$$ 16.0000i 0.680389i
$$554$$ 0 0
$$555$$ −20.0000 10.0000i −0.848953 0.424476i
$$556$$ 0 0
$$557$$ 18.0000i 0.762684i 0.924434 + 0.381342i $$0.124538\pi$$
−0.924434 + 0.381342i $$0.875462\pi$$
$$558$$ 0 0
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 0 0
$$563$$ 36.0000i 1.51722i 0.651546 + 0.758610i $$0.274121\pi$$
−0.651546 + 0.758610i $$0.725879\pi$$
$$564$$ 0 0
$$565$$ 2.00000 4.00000i 0.0841406 0.168281i
$$566$$ 0 0
$$567$$ 2.00000i 0.0839921i
$$568$$ 0 0
$$569$$ 42.0000 1.76073 0.880366 0.474295i $$-0.157297\pi$$
0.880366 + 0.474295i $$0.157297\pi$$
$$570$$ 0 0
$$571$$ 16.0000 0.669579 0.334790 0.942293i $$-0.391335\pi$$
0.334790 + 0.942293i $$0.391335\pi$$
$$572$$ 0 0
$$573$$ 12.0000i 0.501307i
$$574$$ 0 0
$$575$$ −16.0000 + 12.0000i −0.667246 + 0.500435i
$$576$$ 0 0
$$577$$ 16.0000i 0.666089i 0.942911 + 0.333044i $$0.108076\pi$$
−0.942911 + 0.333044i $$0.891924\pi$$
$$578$$ 0 0
$$579$$ −4.00000 −0.166234
$$580$$ 0 0
$$581$$ −8.00000 −0.331896
$$582$$ 0 0
$$583$$ 20.0000i 0.828315i
$$584$$ 0 0
$$585$$ −2.00000 + 4.00000i −0.0826898 + 0.165380i
$$586$$ 0 0
$$587$$ 4.00000i 0.165098i 0.996587 + 0.0825488i $$0.0263060\pi$$
−0.996587 + 0.0825488i $$0.973694\pi$$
$$588$$ 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 $$-0.754026\pi$$
0.715994 0.698106i $$-0.245974\pi$$
$$594$$ 0 0
$$595$$ 24.0000 + 12.0000i 0.983904 + 0.491952i
$$596$$ 0 0
$$597$$ 8.00000i 0.327418i
$$598$$ 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 $$-0.709580\pi$$
−0.611863 + 0.790964i $$0.709580\pi$$
$$602$$ 0 0
$$603$$ 8.00000i 0.325785i
$$604$$ 0 0
$$605$$ −14.0000 7.00000i −0.569181 0.284590i
$$606$$ 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
$$613$$ 14.0000i 0.565455i −0.959200 0.282727i $$-0.908761\pi$$
0.959200 0.282727i $$-0.0912392\pi$$
$$614$$ 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
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ −4.00000 −0.160514
$$622$$ 0 0
$$623$$ 12.0000i 0.480770i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 0 0
$$627$$ 16.0000i 0.638978i
$$628$$ 0 0
$$629$$ 60.0000 2.39236
$$630$$ 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
$$635$$ 18.0000 36.0000i 0.714308 1.42862i
$$636$$ 0 0
$$637$$ 6.00000i 0.237729i
$$638$$ 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
$$643$$ 24.0000i 0.946468i −0.880937 0.473234i $$-0.843087\pi$$
0.880937 0.473234i $$-0.156913\pi$$
$$644$$ 0 0
$$645$$ 24.0000 + 12.0000i 0.944999 + 0.472500i
$$646$$ 0 0
$$647$$ 8.00000i 0.314512i −0.987558 0.157256i $$-0.949735\pi$$
0.987558 0.157256i $$-0.0502649\pi$$
$$648$$ 0 0
$$649$$ 12.0000 0.471041
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 6.00000i 0.234798i −0.993085 0.117399i $$-0.962544\pi$$
0.993085 0.117399i $$-0.0374557\pi$$
$$654$$ 0 0
$$655$$ −36.0000 18.0000i −1.40664 0.703318i
$$656$$ 0 0
$$657$$ 4.00000i 0.156055i
$$658$$ 0 0
$$659$$ −30.0000 −1.16863 −0.584317 0.811525i $$-0.698638\pi$$
−0.584317 + 0.811525i $$0.698638\pi$$
$$660$$ 0 0
$$661$$ 2.00000 0.0777910 0.0388955 0.999243i $$-0.487616\pi$$
0.0388955 + 0.999243i $$0.487616\pi$$
$$662$$ 0 0
$$663$$ 12.0000i 0.466041i
$$664$$ 0 0
$$665$$ −16.0000 + 32.0000i −0.620453 + 1.24091i
$$666$$ 0 0
$$667$$ 32.0000i 1.23904i
$$668$$ 0 0
$$669$$ −6.00000 −0.231973
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ 20.0000i 0.770943i 0.922720 + 0.385472i $$0.125961\pi$$
−0.922720 + 0.385472i $$0.874039\pi$$
$$674$$ 0 0
$$675$$ −4.00000 + 3.00000i −0.153960 + 0.115470i
$$676$$ 0 0
$$677$$ 30.0000i 1.15299i 0.817099 + 0.576497i $$0.195581\pi$$
−0.817099 + 0.576497i $$0.804419\pi$$
$$678$$ 0 0
$$679$$ 16.0000 0.614024
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ 20.0000i 0.765279i −0.923898 0.382639i $$-0.875015\pi$$
0.923898 0.382639i $$-0.124985\pi$$
$$684$$ 0 0
$$685$$ −10.0000 + 20.0000i −0.382080 + 0.764161i
$$686$$ 0 0
$$687$$ 6.00000i 0.228914i
$$688$$ 0 0
$$689$$ −20.0000 −0.761939
$$690$$ 0 0
$$691$$ 48.0000 1.82601 0.913003 0.407953i $$-0.133757\pi$$
0.913003 + 0.407953i $$0.133757\pi$$
$$692$$ 0 0
$$693$$ 4.00000i 0.151947i
$$694$$ 0 0
$$695$$ −8.00000 4.00000i −0.303457 0.151729i
$$696$$ 0 0
$$697$$ 12.0000i 0.454532i
$$698$$ 0 0
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 0 0
$$703$$ 80.0000i 3.01726i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 4.00000 8.00000i 0.149592 0.299183i
$$716$$ 0 0
$$717$$ 20.0000i 0.746914i
$$718$$ 0 0
$$719$$ −40.0000 −1.49175 −0.745874 0.666087i $$-0.767968\pi$$
−0.745874 + 0.666087i $$0.767968\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ 0 0
$$723$$ 10.0000i 0.371904i
$$724$$ 0 0
$$725$$ −24.0000 32.0000i −0.891338 1.18845i
$$726$$ 0 0
$$727$$ 30.0000i 1.11264i −0.830969 0.556319i $$-0.812213\pi$$
0.830969 0.556319i $$-0.187787\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −72.0000 −2.66302
$$732$$ 0 0
$$733$$ 42.0000i 1.55131i 0.631160 + 0.775653i $$0.282579\pi$$
−0.631160 + 0.775653i $$0.717421\pi$$
$$734$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ 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
$$747$$ 4.00000i 0.146352i
$$748$$ 0 0
$$749$$ 8.00000 0.292314
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ 2.00000i 0.0728841i
$$754$$ 0 0
$$755$$ 32.0000 + 16.0000i 1.16460 + 0.582300i
$$756$$ 0 0
$$757$$ 38.0000i 1.38113i 0.723269 + 0.690567i $$0.242639\pi$$
−0.723269 + 0.690567i $$0.757361\pi$$
$$758$$ 0 0
$$759$$ 8.00000 0.290382
$$760$$ 0 0
$$761$$ −2.00000 −0.0724999 −0.0362500 0.999343i $$-0.511541\pi$$
−0.0362500 + 0.999343i $$0.511541\pi$$
$$762$$ 0 0
$$763$$ 12.0000i 0.434429i
$$764$$ 0 0
$$765$$ 6.00000 12.0000i 0.216930 0.433861i
$$766$$ 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
$$771$$ −6.00000 −0.216085
$$772$$ 0 0
$$773$$ 38.0000i 1.36677i −0.730061 0.683383i $$-0.760508\pi$$
0.730061 0.683383i $$-0.239492\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 20.0000i 0.717496i
$$778$$ 0 0
$$779$$ −16.0000 −0.573259
$$780$$ 0 0
$$781$$ −8.00000 −0.286263
$$782$$ 0 0
$$783$$ 8.00000i 0.285897i
$$784$$ 0 0
$$785$$ 14.0000 28.0000i 0.499681 0.999363i
$$786$$ 0 0
$$787$$ 32.0000i 1.14068i 0.821410 + 0.570338i $$0.193188\pi$$
−0.821410 + 0.570338i $$0.806812\pi$$
$$788$$ 0 0
$$789$$ −12.0000 −0.427211
$$790$$ 0 0
$$791$$ −4.00000 −0.142224
$$792$$ 0 0
$$793$$ 4.00000i 0.142044i
$$794$$ 0 0
$$795$$ −20.0000 10.0000i −0.709327 0.354663i
$$796$$ 0 0
$$797$$ 30.0000i 1.06265i 0.847167 + 0.531327i $$0.178307\pi$$
−0.847167 + 0.531327i $$0.821693\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 0 0
$$803$$