# Properties

 Label 1008.2.cs.b.271.1 Level 1008 Weight 2 Character 1008.271 Analytic conductor 8.049 Analytic rank 0 Dimension 2 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.cs (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.04892052375$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 336) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 271.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.271 Dual form 1008.2.cs.b.703.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-3.00000 - 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$$ $$q+(-3.00000 - 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +(3.00000 - 1.73205i) q^{11} +1.73205i q^{13} +(2.50000 - 4.33013i) q^{19} +(-6.00000 - 3.46410i) q^{23} +(3.50000 + 6.06218i) q^{25} +(-2.50000 - 4.33013i) q^{31} +(3.00000 - 8.66025i) q^{35} +(5.50000 - 9.52628i) q^{37} -3.46410i q^{41} -8.66025i q^{43} +(3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(6.00000 + 10.3923i) q^{53} -12.0000 q^{55} +(-6.00000 - 10.3923i) q^{59} +(-12.0000 - 6.92820i) q^{61} +(3.00000 - 5.19615i) q^{65} +(7.50000 - 4.33013i) q^{67} +3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +(6.00000 + 6.92820i) q^{77} +(10.5000 + 6.06218i) q^{79} +18.0000 q^{83} +(-6.00000 - 3.46410i) q^{89} +(-4.50000 + 0.866025i) q^{91} +(-15.0000 + 8.66025i) q^{95} -6.92820i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 6q^{5} + q^{7} + O(q^{10})$$ $$2q - 6q^{5} + q^{7} + 6q^{11} + 5q^{19} - 12q^{23} + 7q^{25} - 5q^{31} + 6q^{35} + 11q^{37} + 6q^{47} - 13q^{49} + 12q^{53} - 24q^{55} - 12q^{59} - 24q^{61} + 6q^{65} + 15q^{67} - 9q^{73} + 12q^{77} + 21q^{79} + 36q^{83} - 12q^{89} - 9q^{91} - 30q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$

## 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 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −3.00000 1.73205i −1.34164 0.774597i −0.354593 0.935021i $$-0.615380\pi$$
−0.987048 + 0.160424i $$0.948714\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i $$-0.491766\pi$$
0.878668 + 0.477432i $$0.158432\pi$$
$$12$$ 0 0
$$13$$ 1.73205i 0.480384i 0.970725 + 0.240192i $$0.0772105\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$18$$ 0 0
$$19$$ 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i $$-0.638903\pi$$
0.996199 0.0871106i $$-0.0277634\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −6.00000 3.46410i −1.25109 0.722315i −0.279761 0.960070i $$-0.590255\pi$$
−0.971325 + 0.237754i $$0.923589\pi$$
$$24$$ 0 0
$$25$$ 3.50000 + 6.06218i 0.700000 + 1.21244i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i $$-0.314891\pi$$
−0.998322 + 0.0579057i $$0.981558\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 3.00000 8.66025i 0.507093 1.46385i
$$36$$ 0 0
$$37$$ 5.50000 9.52628i 0.904194 1.56611i 0.0821995 0.996616i $$-0.473806\pi$$
0.821995 0.569495i $$-0.192861\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.46410i 0.541002i −0.962720 0.270501i $$-0.912811\pi$$
0.962720 0.270501i $$-0.0871893\pi$$
$$42$$ 0 0
$$43$$ 8.66025i 1.32068i −0.750968 0.660338i $$-0.770413\pi$$
0.750968 0.660338i $$-0.229587\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i $$0.141688\pi$$
−0.0783936 + 0.996922i $$0.524979\pi$$
$$54$$ 0 0
$$55$$ −12.0000 −1.61808
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i $$-0.881308\pi$$
0.150148 0.988663i $$1.54798\pi$$
$$60$$ 0 0
$$61$$ −12.0000 6.92820i −1.53644 0.887066i −0.999043 0.0437377i $$-0.986073\pi$$
−0.537400 0.843328i $$-0.680593\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 3.00000 5.19615i 0.372104 0.644503i
$$66$$ 0 0
$$67$$ 7.50000 4.33013i 0.916271 0.529009i 0.0338274 0.999428i $$-0.489230\pi$$
0.882443 + 0.470418i $$0.155897\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 3.46410i 0.411113i 0.978645 + 0.205557i $$0.0659005\pi$$
−0.978645 + 0.205557i $$0.934100\pi$$
$$72$$ 0 0
$$73$$ −4.50000 + 2.59808i −0.526685 + 0.304082i −0.739666 0.672975i $$-0.765016\pi$$
0.212980 + 0.977056i $$0.431683\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 6.00000 + 6.92820i 0.683763 + 0.789542i
$$78$$ 0 0
$$79$$ 10.5000 + 6.06218i 1.18134 + 0.682048i 0.956325 0.292306i $$-0.0944227\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 18.0000 1.97576 0.987878 0.155230i $$-0.0496119\pi$$
0.987878 + 0.155230i $$0.0496119\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −6.00000 3.46410i −0.635999 0.367194i 0.147073 0.989126i $$-0.453015\pi$$
−0.783072 + 0.621932i $$0.786348\pi$$
$$90$$ 0 0
$$91$$ −4.50000 + 0.866025i −0.471728 + 0.0907841i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −15.0000 + 8.66025i −1.53897 + 0.888523i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i −0.936103 0.351726i $$-0.885595\pi$$
0.936103 0.351726i $$-0.114405\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −9.00000 + 5.19615i −0.895533 + 0.517036i −0.875748 0.482768i $$-0.839632\pi$$
−0.0197851 + 0.999804i $$0.506298\pi$$
$$102$$ 0 0
$$103$$ −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i $$-0.912559\pi$$
0.716173 + 0.697923i $$0.245892\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ 0 0
$$109$$ 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i $$-0.0578495\pi$$
−0.648292 + 0.761392i $$0.724516\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 12.0000 + 20.7846i 1.11901 + 1.93817i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.500000 0.866025i 0.0454545 0.0787296i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 12.1244i 1.07586i −0.842989 0.537931i $$-0.819206\pi$$
0.842989 0.537931i $$-0.180794\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i $$-0.917752\pi$$
0.704692 + 0.709514i $$0.251085\pi$$
$$132$$ 0 0
$$133$$ 12.5000 + 4.33013i 1.08389 + 0.375470i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i $$0.00465636\pi$$
−0.487278 + 0.873247i $$0.662010\pi$$
$$138$$ 0 0
$$139$$ −7.00000 −0.593732 −0.296866 0.954919i $$-0.595942\pi$$
−0.296866 + 0.954919i $$0.595942\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 3.00000 + 5.19615i 0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i $$-0.669768\pi$$
0.999953 + 0.00974235i $$0.00310113\pi$$
$$150$$ 0 0
$$151$$ 3.00000 1.73205i 0.244137 0.140952i −0.372940 0.927855i $$-0.621650\pi$$
0.617076 + 0.786903i $$0.288317\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 17.3205i 1.39122i
$$156$$ 0 0
$$157$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 6.00000 17.3205i 0.472866 1.36505i
$$162$$ 0 0
$$163$$ −3.00000 1.73205i −0.234978 0.135665i 0.377888 0.925851i $$-0.376650\pi$$
−0.612866 + 0.790186i $$0.709984\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.00000 0.464294 0.232147 0.972681i $$-0.425425\pi$$
0.232147 + 0.972681i $$0.425425\pi$$
$$168$$ 0 0
$$169$$ 10.0000 0.769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −6.00000 3.46410i −0.456172 0.263371i 0.254262 0.967135i $$-0.418168\pi$$
−0.710433 + 0.703765i $$0.751501\pi$$
$$174$$ 0 0
$$175$$ −14.0000 + 12.1244i −1.05830 + 0.916515i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 9.00000 5.19615i 0.672692 0.388379i −0.124404 0.992232i $$-0.539702\pi$$
0.797096 + 0.603853i $$0.206369\pi$$
$$180$$ 0 0
$$181$$ 5.19615i 0.386227i 0.981176 + 0.193113i $$0.0618586\pi$$
−0.981176 + 0.193113i $$0.938141\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −33.0000 + 19.0526i −2.42621 + 1.40077i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −15.0000 8.66025i −1.08536 0.626634i −0.153024 0.988222i $$-0.548901\pi$$
−0.932338 + 0.361588i $$0.882235\pi$$
$$192$$ 0 0
$$193$$ 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i $$-0.0370998\pi$$
−0.597317 + 0.802005i $$0.703766\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −24.0000 −1.70993 −0.854965 0.518686i $$-0.826421\pi$$
−0.854965 + 0.518686i $$0.826421\pi$$
$$198$$ 0 0
$$199$$ −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i $$-0.974730\pi$$
0.429745 0.902950i $$1.64140\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −6.00000 + 10.3923i −0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 17.3205i 1.19808i
$$210$$ 0 0
$$211$$ 3.46410i 0.238479i −0.992866 0.119239i $$-0.961954\pi$$
0.992866 0.119239i $$-0.0380456\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −15.0000 + 25.9808i −1.02299 + 1.77187i
$$216$$ 0 0
$$217$$ 10.0000 8.66025i 0.678844 0.587896i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i $$0.0371134\pi$$
−0.395860 + 0.918311i $$0.629553\pi$$
$$228$$ 0 0
$$229$$ 7.50000 + 4.33013i 0.495614 + 0.286143i 0.726900 0.686743i $$-0.240960\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i $$-0.896303\pi$$
0.750867 + 0.660454i $$0.229636\pi$$
$$234$$ 0 0
$$235$$ −18.0000 + 10.3923i −1.17419 + 0.677919i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 10.3923i 0.672222i 0.941822 + 0.336111i $$0.109112\pi$$
−0.941822 + 0.336111i $$0.890888\pi$$
$$240$$ 0 0
$$241$$ −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i $$-0.813920\pi$$
0.0609515 + 0.998141i $$0.480586\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 24.0000 + 3.46410i 1.53330 + 0.221313i
$$246$$ 0 0
$$247$$ 7.50000 + 4.33013i 0.477214 + 0.275519i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −24.0000 −1.50887
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 15.0000 + 8.66025i 0.935674 + 0.540212i 0.888602 0.458680i $$-0.151677\pi$$
0.0470726 + 0.998891i $$0.485011\pi$$
$$258$$ 0 0
$$259$$ 27.5000 + 9.52628i 1.70877 + 0.591934i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −12.0000 + 6.92820i −0.739952 + 0.427211i −0.822052 0.569413i $$-0.807171\pi$$
0.0821001 + 0.996624i $$0.473837\pi$$
$$264$$ 0 0
$$265$$ 41.5692i 2.55358i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 15.0000 8.66025i 0.914566 0.528025i 0.0326687 0.999466i $$-0.489599\pi$$
0.881897 + 0.471441i $$0.156266\pi$$
$$270$$ 0 0
$$271$$ −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i $$-0.911459\pi$$
0.718580 + 0.695444i $$0.244792\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 21.0000 + 12.1244i 1.26635 + 0.731126i
$$276$$ 0 0
$$277$$ −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i $$-0.973300\pi$$
0.425684 0.904872i $$-0.360033\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ −3.50000 6.06218i −0.208053 0.360359i 0.743048 0.669238i $$-0.233379\pi$$
−0.951101 + 0.308879i $$0.900046\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 9.00000 1.73205i 0.531253 0.102240i
$$288$$ 0 0
$$289$$ −8.50000 + 14.7224i −0.500000 + 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 20.7846i 1.21425i −0.794606 0.607125i $$-0.792323\pi$$
0.794606 0.607125i $$-0.207677\pi$$
$$294$$ 0 0
$$295$$ 41.5692i 2.42025i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 6.00000 10.3923i 0.346989 0.601003i
$$300$$ 0 0
$$301$$ 22.5000 4.33013i 1.29688 0.249584i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 24.0000 + 41.5692i 1.37424 + 2.38025i
$$306$$ 0 0
$$307$$ −11.0000 −0.627803 −0.313902 0.949456i $$-0.601636\pi$$
−0.313902 + 0.949456i $$0.601636\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i $$0.00381495\pi$$
−0.489585 + 0.871956i $$0.662852\pi$$
$$312$$ 0 0
$$313$$ 13.5000 + 7.79423i 0.763065 + 0.440556i 0.830395 0.557175i $$-0.188115\pi$$
−0.0673300 + 0.997731i $$0.521448\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i $$-0.942743\pi$$
0.646872 + 0.762598i $$0.276077\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −10.5000 + 6.06218i −0.582435 + 0.336269i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 15.0000 + 5.19615i 0.826977 + 0.286473i
$$330$$ 0 0
$$331$$ 13.5000 + 7.79423i 0.742027 + 0.428410i 0.822806 0.568323i $$-0.192407\pi$$
−0.0807788 + 0.996732i $$0.525741\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −30.0000 −1.63908
$$336$$ 0 0
$$337$$ −19.0000 −1.03500 −0.517498 0.855684i $$-0.673136\pi$$
−0.517498 + 0.855684i $$0.673136\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −15.0000 8.66025i −0.812296 0.468979i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 24.0000 13.8564i 1.28839 0.743851i 0.310021 0.950730i $$-0.399664\pi$$
0.978367 + 0.206879i $$0.0663306\pi$$
$$348$$ 0 0
$$349$$ 13.8564i 0.741716i 0.928689 + 0.370858i $$0.120936\pi$$
−0.928689 + 0.370858i $$0.879064\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −21.0000 + 12.1244i −1.11772 + 0.645314i −0.940817 0.338914i $$-0.889940\pi$$
−0.176900 + 0.984229i $$0.556607\pi$$
$$354$$ 0 0
$$355$$ 6.00000 10.3923i 0.318447 0.551566i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 18.0000 + 10.3923i 0.950004 + 0.548485i 0.893082 0.449894i $$-0.148538\pi$$
0.0569216 + 0.998379i $$0.481871\pi$$
$$360$$ 0 0
$$361$$ −3.00000 5.19615i −0.157895 0.273482i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 18.0000 0.942163
$$366$$ 0 0
$$367$$ 5.50000 + 9.52628i 0.287098 + 0.497268i 0.973116 0.230317i $$-0.0739762\pi$$
−0.686018 + 0.727585i $$0.740643\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −24.0000 + 20.7846i −1.24602 + 1.07908i
$$372$$ 0 0
$$373$$ 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i $$-0.825092\pi$$
0.878680 + 0.477412i $$0.158425\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 8.66025i 0.444847i −0.974950 0.222424i $$-0.928603\pi$$
0.974950 0.222424i $$-0.0713968\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i $$-0.623227\pi$$
0.990702 0.136047i $$-0.0434398\pi$$
$$384$$ 0 0
$$385$$ −6.00000 31.1769i −0.305788 1.58892i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i $$-0.215272\pi$$
−0.932002 + 0.362454i $$0.881939\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −21.0000 36.3731i −1.05662 1.83013i
$$396$$ 0 0
$$397$$ −1.50000 0.866025i −0.0752828 0.0434646i 0.461886 0.886939i $$-0.347173\pi$$
−0.537169 + 0.843475i $$0.680506\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i $$-0.736472\pi$$
0.976050 + 0.217545i $$0.0698049\pi$$
$$402$$ 0 0
$$403$$ 7.50000 4.33013i 0.373602 0.215699i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 38.1051i 1.88880i
$$408$$ 0 0
$$409$$ −19.5000 + 11.2583i −0.964213 + 0.556689i −0.897467 0.441081i $$-0.854595\pi$$
−0.0667458 + 0.997770i $$0.521262\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 24.0000 20.7846i 1.18096 1.02274i
$$414$$ 0 0
$$415$$ −54.0000 31.1769i −2.65076 1.53041i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6.00000 0.293119 0.146560 0.989202i $$-0.453180\pi$$
0.146560 + 0.989202i $$0.453180\pi$$
$$420$$ 0 0
$$421$$ 7.00000 0.341159 0.170580 0.985344i $$-0.445436\pi$$
0.170580 + 0.985344i $$0.445436\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 12.0000 34.6410i 0.580721 1.67640i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −21.0000 + 12.1244i −1.01153 + 0.584010i −0.911641 0.410988i $$-0.865184\pi$$
−0.0998939 + 0.994998i $$0.531850\pi$$
$$432$$ 0 0
$$433$$ 1.73205i 0.0832370i 0.999134 + 0.0416185i $$0.0132514\pi$$
−0.999134 + 0.0416185i $$0.986749\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −30.0000 + 17.3205i −1.43509 + 0.828552i
$$438$$ 0 0
$$439$$ 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i $$-0.772190\pi$$
0.945552 + 0.325471i $$0.105523\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 6.92820i −0.570137 0.329169i 0.187067 0.982347i $$-0.440102\pi$$
−0.757204 + 0.653178i $$0.773435\pi$$
$$444$$ 0 0
$$445$$ 12.0000 + 20.7846i 0.568855 + 0.985285i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ −6.00000 10.3923i −0.282529 0.489355i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 15.0000 + 5.19615i 0.703211 + 0.243599i
$$456$$ 0 0
$$457$$ 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i $$-0.686753\pi$$
0.998010 + 0.0630623i $$0.0200867\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 13.8564i 0.645357i −0.946509 0.322679i $$-0.895417\pi$$
0.946509 0.322679i $$-0.104583\pi$$
$$462$$ 0 0
$$463$$ 15.5885i 0.724457i 0.932089 + 0.362229i $$0.117984\pi$$
−0.932089 + 0.362229i $$0.882016\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 15.0000 25.9808i 0.694117 1.20225i −0.276360 0.961054i $$-0.589128\pi$$
0.970477 0.241192i $$-0.0775384\pi$$
$$468$$ 0 0
$$469$$ 15.0000 + 17.3205i 0.692636 + 0.799787i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −15.0000 25.9808i −0.689701 1.19460i
$$474$$ 0 0
$$475$$ 35.0000 1.60591
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i $$-0.255062\pi$$
−0.969920 + 0.243426i $$0.921729\pi$$
$$480$$ 0 0
$$481$$ 16.5000 + 9.52628i 0.752335 + 0.434361i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −12.0000 + 20.7846i −0.544892 + 0.943781i
$$486$$ 0 0
$$487$$ 22.5000 12.9904i 1.01957 0.588650i 0.105592 0.994410i $$-0.466326\pi$$
0.913980 + 0.405759i $$0.132993\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 34.6410i 1.56333i −0.623700 0.781664i $$-0.714371\pi$$
0.623700 0.781664i $$-0.285629\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −9.00000 + 1.73205i −0.403705 + 0.0776931i
$$498$$ 0 0
$$499$$ −28.5000 16.4545i −1.27584 0.736604i −0.299755 0.954016i $$-0.596905\pi$$
−0.976080 + 0.217412i $$0.930238\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 0 0
$$505$$ 36.0000 1.60198
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −27.0000 15.5885i −1.19675 0.690946i −0.236924 0.971528i $$-0.576139\pi$$
−0.959830 + 0.280582i $$0.909473\pi$$
$$510$$ 0 0
$$511$$ −9.00000 10.3923i −0.398137 0.459728i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 15.0000 8.66025i 0.660979 0.381616i
$$516$$ 0 0
$$517$$ 20.7846i 0.914106i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 12.0000 6.92820i 0.525730 0.303530i −0.213546 0.976933i $$-0.568501\pi$$
0.739276 + 0.673403i $$0.235168\pi$$
$$522$$ 0 0
$$523$$ −5.50000 + 9.52628i −0.240498 + 0.416555i −0.960856 0.277047i $$-0.910644\pi$$
0.720358 + 0.693602i $$0.243977\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 12.5000 + 21.6506i 0.543478 + 0.941332i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 6.00000 0.259889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −15.0000 + 19.0526i −0.646096 + 0.820652i
$$540$$ 0 0
$$541$$ 2.50000 4.33013i 0.107483 0.186167i −0.807267 0.590187i $$-0.799054\pi$$
0.914750 + 0.404020i $$0.132387\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 24.2487i 1.03870i
$$546$$ 0 0
$$547$$ 3.46410i 0.148114i 0.997254 + 0.0740571i $$0.0235947\pi$$
−0.997254 + 0.0740571i $$0.976405\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −10.5000 + 30.3109i −0.446505 + 1.28895i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 21.0000 + 36.3731i 0.889799 + 1.54118i 0.840113 + 0.542411i $$0.182489\pi$$
0.0496855 + 0.998765i $$0.484178\pi$$
$$558$$ 0 0
$$559$$ 15.0000 0.634432
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 3.00000 + 5.19615i 0.126435 + 0.218992i 0.922293 0.386492i $$-0.126313\pi$$
−0.795858 + 0.605483i $$0.792980\pi$$
$$564$$ 0 0
$$565$$ −18.0000 10.3923i −0.757266 0.437208i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 21.0000 36.3731i 0.880366 1.52484i 0.0294311 0.999567i $$-0.490630\pi$$
0.850935 0.525271i $$-0.176036\pi$$
$$570$$ 0 0
$$571$$ −40.5000 + 23.3827i −1.69487 + 0.978535i −0.744396 + 0.667739i $$0.767262\pi$$
−0.950477 + 0.310796i $$0.899404\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 48.4974i 2.02248i
$$576$$ 0 0
$$577$$ 10.5000 6.06218i 0.437121 0.252372i −0.265255 0.964178i $$-0.585456\pi$$
0.702376 + 0.711807i $$0.252123\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 9.00000 + 46.7654i 0.373383 + 1.94015i
$$582$$ 0 0
$$583$$ 36.0000 + 20.7846i 1.49097 + 0.860811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −25.0000 −1.03011
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −3.00000 1.73205i −0.123195 0.0711268i 0.437136 0.899395i $$-0.355993\pi$$
−0.560331 + 0.828269i $$0.689326\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 42.0000 24.2487i 1.71607 0.990775i 0.790280 0.612746i $$-0.209935\pi$$
0.925794 0.378030i $$-0.123398\pi$$
$$600$$ 0 0
$$601$$ 39.8372i 1.62499i 0.582967 + 0.812496i $$0.301892\pi$$
−0.582967 + 0.812496i $$0.698108\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −3.00000 + 1.73205i −0.121967 + 0.0704179i
$$606$$ 0 0
$$607$$ −6.50000 + 11.2583i −0.263827 + 0.456962i −0.967256 0.253804i $$-0.918318\pi$$
0.703429 + 0.710766i $$0.251651\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 9.00000 + 5.19615i 0.364101 + 0.210214i
$$612$$ 0 0
$$613$$ −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i $$-0.179527\pi$$
−0.885514 + 0.464614i $$0.846193\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 0.724653 0.362326 0.932051i $$-0.381983\pi$$
0.362326 + 0.932051i $$0.381983\pi$$
$$618$$ 0 0
$$619$$ 0.500000 + 0.866025i 0.0200967 + 0.0348085i 0.875899 0.482495i $$-0.160269\pi$$
−0.855802 + 0.517303i $$0.826936\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 6.00000 17.3205i 0.240385 0.693932i
$$624$$ 0 0
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 3.46410i 0.137904i −0.997620 0.0689519i $$-0.978035\pi$$
0.997620 0.0689519i $$-0.0219655\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −21.0000 + 36.3731i −0.833360 + 1.44342i
$$636$$ 0 0
$$637$$ −4.50000 11.2583i −0.178296 0.446071i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 12.0000 + 20.7846i 0.473972 + 0.820943i 0.999556 0.0297987i $$-0.00948663\pi$$
−0.525584 + 0.850741i $$0.676153\pi$$
$$642$$ 0 0
$$643$$ 31.0000 1.22252 0.611260 0.791430i $$-0.290663\pi$$
0.611260 + 0.791430i $$0.290663\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 15.0000 + 25.9808i 0.589711 + 1.02141i 0.994270 + 0.106897i $$0.0340916\pi$$
−0.404559 + 0.914512i $$0.632575\pi$$
$$648$$ 0 0
$$649$$ −36.0000 20.7846i −1.41312 0.815867i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i $$-0.795878\pi$$
0.918736 + 0.394872i $$0.129211\pi$$
$$654$$ 0 0
$$655$$ 18.0000 10.3923i 0.703318 0.406061i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 13.8564i 0.539769i 0.962893 + 0.269884i $$0.0869855\pi$$
−0.962893 + 0.269884i $$0.913014\pi$$
$$660$$ 0 0
$$661$$ 22.5000 12.9904i 0.875149 0.505267i 0.00609283 0.999981i $$-0.498061\pi$$
0.869056 + 0.494714i $$0.164727\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −30.0000 34.6410i −1.16335 1.34332i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −48.0000 −1.85302
$$672$$ 0 0
$$673$$ 1.00000 0.0385472 0.0192736 0.999814i $$-0.493865\pi$$
0.0192736 + 0.999814i $$0.493865\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 6.00000 + 3.46410i 0.230599 + 0.133136i 0.610848 0.791748i $$-0.290829\pi$$
−0.380250 + 0.924884i $$0.624162\pi$$
$$678$$ 0 0
$$679$$ 18.0000 3.46410i 0.690777 0.132940i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −6.00000 + 3.46410i −0.229584 + 0.132550i −0.610380 0.792109i $$-0.708983\pi$$
0.380796 + 0.924659i $$0.375650\pi$$
$$684$$ 0 0
$$685$$ 41.5692i 1.58828i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −18.0000 + 10.3923i −0.685745 + 0.395915i
$$690$$ 0 0
$$691$$ −11.5000 + 19.9186i −0.437481 + 0.757739i −0.997494 0.0707446i $$-0.977462\pi$$
0.560014 + 0.828483i $$0.310796\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 21.0000 + 12.1244i 0.796575 + 0.459903i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −12.0000 −0.453234 −0.226617 0.973984i $$-0.572767\pi$$
−0.226617 + 0.973984i $$0.572767\pi$$
$$702$$ 0 0
$$703$$ −27.5000 47.6314i −1.03718 1.79645i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −18.0000 20.7846i −0.676960 0.781686i
$$708$$ 0 0
$$709$$ 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i $$-0.773204\pi$$
0.944509 + 0.328484i $$0.106538\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 34.6410i 1.29732i
$$714$$ 0 0
$$715$$ 20.7846i 0.777300i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 15.0000 25.9808i 0.559406 0.968919i −0.438141 0.898906i $$-0.644363\pi$$
0.997546 0.0700124i $$-0.0223039\pi$$
$$720$$ 0 0
$$721$$ −12.5000 4.33013i −0.465524 0.161262i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 23.0000 0.853023 0.426511 0.904482i $$-0.359742\pi$$
0.426511 + 0.904482i $$0.359742\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −25.5000 14.7224i −0.941864 0.543785i −0.0513199 0.998682i $$-0.516343\pi$$
−0.890544 + 0.454897i $$0.849676\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 15.0000 25.9808i 0.552532 0.957014i
$$738$$ 0 0
$$739$$ −46.5000 + 26.8468i −1.71053 + 0.987575i −0.776691 + 0.629882i $$0.783103\pi$$
−0.933839 + 0.357693i $$0.883563\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 3.46410i 0.127086i 0.997979 + 0.0635428i $$0.0202399\pi$$
−0.997979 + 0.0635428i $$0.979760\pi$$
$$744$$ 0 0
$$745$$ −36.0000 + 20.7846i −1.31894 + 0.761489i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −4.50000 2.59808i −0.164207 0.0948051i 0.415644 0.909527i $$-0.363556\pi$$
−0.579852 + 0.814722i $$0.696889\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −12.0000 −0.436725
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 36.0000 + 20.7846i 1.30500 + 0.753442i 0.981257 0.192704i $$-0.0617257\pi$$
0.323742 + 0.946145i $$0.395059\pi$$
$$762$$ 0 0
$$763$$ −14.0000 + 12.1244i −0.506834 + 0.438931i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 18.0000 10.3923i 0.649942 0.375244i
$$768$$ 0 0
$$769$$ 15.5885i 0.562134i 0.959688 + 0.281067i $$0.0906883\pi$$
−0.959688 + 0.281067i $$0.909312\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 39.0000 22.5167i 1.40273 0.809868i 0.408060 0.912955i $$-0.366205\pi$$
0.994672 + 0.103087i $$0.0328720\pi$$
$$774$$ 0 0
$$775$$ 17.5000 30.3109i 0.628619 1.08880i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −15.0000 8.66025i −0.537431 0.310286i
$$780$$ 0 0
$$781$$ 6.00000 + 10.3923i 0.214697 + 0.371866i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 8.00000 + 13.8564i 0.285169 + 0.493928i 0.972650 0.232275i $$-0.0746169\pi$$
−0.687481 + 0.726202i $$0.741284\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 3.00000 + 15.5885i 0.106668 + 0.554262i
$$792$$ 0 0
$$793$$ 12.0000 20.7846i 0.426132 0.738083i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 34.6410i 1.22705i 0.789676 + 0.613524i $$0.210249\pi$$
−0.789676 + 0.613524i $$0.789751\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −9.00000 + 15.5885i −0.317603 + 0.550105i
$$804$$ 0 0
$$805$$ −48.0000 + 41.5692i −1.69178 + 1.46512i
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 9.00000 + 15.5885i 0.316423 + 0.548061i 0.979739 0.200279i $$-0.0641847\pi$$
−0.663316 + 0.748340i $$0.730851\pi$$
$$810$$ 0 0
$$811$$ −40.0000 −1.40459 −0.702295 0.711886i $$-0.747841\pi$$
−0.702295 + 0.711886i $$0.747841\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 6.00000 + 10.3923i 0.210171 + 0.364027i
$$816$$ 0 <