# Properties

 Label 273.2.bw.a.11.1 Level $273$ Weight $2$ Character 273.11 Analytic conductor $2.180$ Analytic rank $0$ Dimension $4$ CM discriminant -3 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.bw (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.17991597518$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{12}]$

## Embedding invariants

 Embedding label 11.1 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 273.11 Dual form 273.2.bw.a.149.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.73205 q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.866025 + 2.50000i) q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q+1.73205 q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.866025 + 2.50000i) q^{7} +3.00000 q^{9} +(3.00000 - 1.73205i) q^{12} +(-3.46410 + 1.00000i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-3.83013 - 3.83013i) q^{19} +(-1.50000 + 4.33013i) q^{21} +(-4.33013 - 2.50000i) q^{25} +5.19615 q^{27} +(1.00000 + 5.19615i) q^{28} +(-1.13397 + 0.303848i) q^{31} +(5.19615 - 3.00000i) q^{36} +(1.06218 + 3.96410i) q^{37} +(-6.00000 + 1.73205i) q^{39} +(9.00000 + 5.19615i) q^{43} +(3.46410 - 6.00000i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(-5.00000 + 5.19615i) q^{52} +(-6.63397 - 6.63397i) q^{57} -15.5885 q^{61} +(-2.59808 + 7.50000i) q^{63} -8.00000i q^{64} +(-11.5622 - 11.5622i) q^{67} +(4.36603 + 16.2942i) q^{73} +(-7.50000 - 4.33013i) q^{75} +(-10.4641 - 2.80385i) q^{76} +(6.06218 + 10.5000i) q^{79} +9.00000 q^{81} +(1.73205 + 9.00000i) q^{84} +(0.500000 - 9.52628i) q^{91} +(-1.96410 + 0.526279i) q^{93} +(9.42820 - 2.52628i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 12q^{9} + O(q^{10})$$ $$4q + 12q^{9} + 12q^{12} + 8q^{16} + 2q^{19} - 6q^{21} + 4q^{28} - 8q^{31} - 20q^{37} - 24q^{39} + 36q^{43} - 22q^{49} - 20q^{52} - 30q^{57} - 22q^{67} + 14q^{73} - 30q^{75} - 28q^{76} + 36q^{81} + 2q^{91} + 6q^{93} + 10q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$$.

 $$n$$ $$92$$ $$106$$ $$157$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$3$$ 1.73205 1.00000
$$4$$ 1.73205 1.00000i 0.866025 0.500000i
$$5$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$6$$ 0 0
$$7$$ −0.866025 + 2.50000i −0.327327 + 0.944911i
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$12$$ 3.00000 1.73205i 0.866025 0.500000i
$$13$$ −3.46410 + 1.00000i −0.960769 + 0.277350i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 0 0
$$19$$ −3.83013 3.83013i −0.878691 0.878691i 0.114708 0.993399i $$-0.463407\pi$$
−0.993399 + 0.114708i $$0.963407\pi$$
$$20$$ 0 0
$$21$$ −1.50000 + 4.33013i −0.327327 + 0.944911i
$$22$$ 0 0
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ −4.33013 2.50000i −0.866025 0.500000i
$$26$$ 0 0
$$27$$ 5.19615 1.00000
$$28$$ 1.00000 + 5.19615i 0.188982 + 0.981981i
$$29$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ −1.13397 + 0.303848i −0.203668 + 0.0545726i −0.359211 0.933257i $$-0.616954\pi$$
0.155543 + 0.987829i $$0.450287\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 5.19615 3.00000i 0.866025 0.500000i
$$37$$ 1.06218 + 3.96410i 0.174621 + 0.651694i 0.996616 + 0.0821995i $$0.0261945\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ −6.00000 + 1.73205i −0.960769 + 0.277350i
$$40$$ 0 0
$$41$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$42$$ 0 0
$$43$$ 9.00000 + 5.19615i 1.37249 + 0.792406i 0.991241 0.132068i $$-0.0421616\pi$$
0.381246 + 0.924473i $$0.375495\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$48$$ 3.46410 6.00000i 0.500000 0.866025i
$$49$$ −5.50000 4.33013i −0.785714 0.618590i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −5.00000 + 5.19615i −0.693375 + 0.720577i
$$53$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −6.63397 6.63397i −0.878691 0.878691i
$$58$$ 0 0
$$59$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$60$$ 0 0
$$61$$ −15.5885 −1.99590 −0.997949 0.0640184i $$-0.979608\pi$$
−0.997949 + 0.0640184i $$0.979608\pi$$
$$62$$ 0 0
$$63$$ −2.59808 + 7.50000i −0.327327 + 0.944911i
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −11.5622 11.5622i −1.41254 1.41254i −0.740613 0.671932i $$-0.765465\pi$$
−0.671932 0.740613i $$-0.734535\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$72$$ 0 0
$$73$$ 4.36603 + 16.2942i 0.511005 + 1.90710i 0.409644 + 0.912245i $$0.365653\pi$$
0.101361 + 0.994850i $$0.467680\pi$$
$$74$$ 0 0
$$75$$ −7.50000 4.33013i −0.866025 0.500000i
$$76$$ −10.4641 2.80385i −1.20031 0.321623i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 6.06218 + 10.5000i 0.682048 + 1.18134i 0.974355 + 0.225018i $$0.0722440\pi$$
−0.292306 + 0.956325i $$0.594423\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$84$$ 1.73205 + 9.00000i 0.188982 + 0.981981i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$90$$ 0 0
$$91$$ 0.500000 9.52628i 0.0524142 0.998625i
$$92$$ 0 0
$$93$$ −1.96410 + 0.526279i −0.203668 + 0.0545726i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 9.42820 2.52628i 0.957289 0.256505i 0.253837 0.967247i $$-0.418307\pi$$
0.703452 + 0.710742i $$0.251641\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −10.0000 −1.00000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −3.00000 + 1.73205i −0.295599 + 0.170664i −0.640464 0.767988i $$-0.721258\pi$$
0.344865 + 0.938652i $$0.387925\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ 9.00000 5.19615i 0.866025 0.500000i
$$109$$ 15.5622 4.16987i 1.49059 0.399401i 0.580651 0.814152i $$-0.302798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 0 0
$$111$$ 1.83975 + 6.86603i 0.174621 + 0.651694i
$$112$$ 6.92820 + 8.00000i 0.654654 + 0.755929i
$$113$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −10.3923 + 3.00000i −0.960769 + 0.277350i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 11.0000i 1.00000i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −1.66025 + 1.66025i −0.149095 + 0.149095i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 17.3205 10.0000i 1.53695 0.887357i 0.537931 0.842989i $$-0.319206\pi$$
0.999015 0.0443678i $$-0.0141274\pi$$
$$128$$ 0 0
$$129$$ 15.5885 + 9.00000i 1.37249 + 0.792406i
$$130$$ 0 0
$$131$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ 0 0
$$133$$ 12.8923 6.25833i 1.11790 0.542666i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$138$$ 0 0
$$139$$ 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i $$-0.737392\pi$$
0.975417 + 0.220366i $$0.0707252\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 6.00000 10.3923i 0.500000 0.866025i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −9.52628 7.50000i −0.785714 0.618590i
$$148$$ 5.80385 + 5.80385i 0.477073 + 0.477073i
$$149$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$150$$ 0 0
$$151$$ 3.70577 + 13.8301i 0.301571 + 1.12548i 0.935857 + 0.352381i $$0.114628\pi$$
−0.634285 + 0.773099i $$0.718706\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −8.66025 + 9.00000i −0.693375 + 0.720577i
$$157$$ −12.5000 + 21.6506i −0.997609 + 1.72791i −0.438948 + 0.898513i $$0.644649\pi$$
−0.558661 + 0.829396i $$0.688685\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 18.0263 18.0263i 1.41193 1.41193i 0.665771 0.746156i $$-0.268103\pi$$
0.746156 0.665771i $$-0.231897\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$168$$ 0 0
$$169$$ 11.0000 6.92820i 0.846154 0.532939i
$$170$$ 0 0
$$171$$ −11.4904 11.4904i −0.878691 0.878691i
$$172$$ 20.7846 1.58481
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 10.0000 8.66025i 0.755929 0.654654i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 19.0526i 1.41617i 0.706129 + 0.708083i $$0.250440\pi$$
−0.706129 + 0.708083i $$0.749560\pi$$
$$182$$ 0 0
$$183$$ −27.0000 −1.99590
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −4.50000 + 12.9904i −0.327327 + 0.944911i
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 13.8564i 1.00000i
$$193$$ −14.8564 + 14.8564i −1.06939 + 1.06939i −0.0719816 + 0.997406i $$0.522932\pi$$
−0.997406 + 0.0719816i $$0.977068\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −13.8564 2.00000i −0.989743 0.142857i
$$197$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$198$$ 0 0
$$199$$ 9.52628 5.50000i 0.675300 0.389885i −0.122782 0.992434i $$-0.539182\pi$$
0.798082 + 0.602549i $$0.205848\pi$$
$$200$$ 0 0
$$201$$ −20.0263 20.0263i −1.41254 1.41254i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −3.46410 + 14.0000i −0.240192 + 0.970725i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0.866025 + 1.50000i 0.0596196 + 0.103264i 0.894295 0.447478i $$-0.147678\pi$$
−0.834675 + 0.550743i $$0.814345\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0.222432 3.09808i 0.0150997 0.210311i
$$218$$ 0 0
$$219$$ 7.56218 + 28.2224i 0.511005 + 1.90710i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 7.02628 26.2224i 0.470514 1.75598i −0.167412 0.985887i $$-0.553541\pi$$
0.637927 0.770097i $$-0.279792\pi$$
$$224$$ 0 0
$$225$$ −12.9904 7.50000i −0.866025 0.500000i
$$226$$ 0 0
$$227$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$228$$ −18.1244 4.85641i −1.20031 0.321623i
$$229$$ 25.7224 + 6.89230i 1.69979 + 0.455456i 0.972886 0.231287i $$-0.0742935\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 10.5000 + 18.1865i 0.682048 + 1.18134i
$$238$$ 0 0
$$239$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$240$$ 0 0
$$241$$ −28.4904 7.63397i −1.83523 0.491748i −0.836784 0.547533i $$-0.815567\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ 0 0
$$243$$ 15.5885 1.00000
$$244$$ −27.0000 + 15.5885i −1.72850 + 0.997949i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 17.0981 + 9.43782i 1.08792 + 0.600514i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$252$$ 3.00000 + 15.5885i 0.188982 + 0.981981i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$258$$ 0 0
$$259$$ −10.8301 0.777568i −0.672951 0.0483157i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −31.5885 8.46410i −1.92957 0.517027i
$$269$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 0 0
$$271$$ −6.20577 23.1603i −0.376974 1.40689i −0.850439 0.526073i $$-0.823664\pi$$
0.473466 0.880812i $$-0.343003\pi$$
$$272$$ 0 0
$$273$$ 0.866025 16.5000i 0.0524142 0.998625i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −28.5000 + 16.4545i −1.71240 + 0.988654i −0.781094 + 0.624413i $$0.785338\pi$$
−0.931305 + 0.364241i $$0.881328\pi$$
$$278$$ 0 0
$$279$$ −3.40192 + 0.911543i −0.203668 + 0.0545726i
$$280$$ 0 0
$$281$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$282$$ 0 0
$$283$$ 32.0000i 1.90220i −0.308879 0.951101i $$-0.599954\pi$$
0.308879 0.951101i $$-0.400046\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 16.3301 4.37564i 0.957289 0.256505i
$$292$$ 23.8564 + 23.8564i 1.39609 + 1.39609i
$$293$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −17.3205 −1.00000
$$301$$ −20.7846 + 18.0000i −1.19800 + 1.03750i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −20.9282 + 5.60770i −1.20031 + 0.321623i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 18.3660 18.3660i 1.04820 1.04820i 0.0494267 0.998778i $$-0.484261\pi$$
0.998778 0.0494267i $$-0.0157394\pi$$
$$308$$ 0 0
$$309$$ −5.19615 + 3.00000i −0.295599 + 0.170664i
$$310$$ 0 0
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ 0 0
$$313$$ 13.8564 + 24.0000i 0.783210 + 1.35656i 0.930062 + 0.367402i $$0.119753\pi$$
−0.146852 + 0.989158i $$0.546914\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 21.0000 + 12.1244i 1.18134 + 0.682048i
$$317$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 15.5885 9.00000i 0.866025 0.500000i
$$325$$ 17.5000 + 4.33013i 0.970725 + 0.240192i
$$326$$ 0 0
$$327$$ 26.9545 7.22243i 1.49059 0.399401i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −24.6603 24.6603i −1.35545 1.35545i −0.879440 0.476011i $$-0.842082\pi$$
−0.476011 0.879440i $$-0.657918\pi$$
$$332$$ 0 0
$$333$$ 3.18653 + 11.8923i 0.174621 + 0.651694i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 12.0000 + 13.8564i 0.654654 + 0.755929i
$$337$$ 34.0000i 1.85210i 0.377403 + 0.926049i $$0.376817\pi$$
−0.377403 + 0.926049i $$0.623183\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 15.5885 10.0000i 0.841698 0.539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$348$$ 0 0
$$349$$ −21.7224 5.82051i −1.16278 0.311565i −0.374701 0.927146i $$-0.622255\pi$$
−0.788074 + 0.615581i $$0.788921\pi$$
$$350$$ 0 0
$$351$$ −18.0000 + 5.19615i −0.960769 + 0.277350i
$$352$$ 0 0
$$353$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$360$$ 0 0
$$361$$ 10.3397i 0.544197i
$$362$$ 0 0
$$363$$ 19.0526i 1.00000i
$$364$$ −8.66025 17.0000i −0.453921 0.891042i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.00000 0.208798 0.104399 0.994535i $$-0.466708\pi$$
0.104399 + 0.994535i $$0.466708\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.87564 + 2.87564i −0.149095 + 0.149095i
$$373$$ −36.3731 −1.88333 −0.941663 0.336557i $$-0.890737\pi$$
−0.941663 + 0.336557i $$0.890737\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −8.99038 + 33.5526i −0.461805 + 1.72348i 0.205466 + 0.978664i $$0.434129\pi$$
−0.667271 + 0.744815i $$0.732538\pi$$
$$380$$ 0 0
$$381$$ 30.0000 17.3205i 1.53695 0.887357i
$$382$$ 0 0
$$383$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 27.0000 + 15.5885i 1.37249 + 0.792406i
$$388$$ 13.8038 13.8038i 0.700784 0.700784i
$$389$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 27.3923 27.3923i 1.37478 1.37478i 0.521575 0.853206i $$-0.325345\pi$$
0.853206 0.521575i $$-0.174655\pi$$
$$398$$ 0 0
$$399$$ 22.3301 10.8397i 1.11790 0.542666i
$$400$$ −17.3205 + 10.0000i −0.866025 + 0.500000i
$$401$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$402$$ 0 0
$$403$$ 3.62436 2.18653i 0.180542 0.108919i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −4.41858 + 16.4904i −0.218485 + 0.815397i 0.766426 + 0.642333i $$0.222033\pi$$
−0.984911 + 0.173064i $$0.944633\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −3.46410 + 6.00000i −0.170664 + 0.295599i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 6.06218 10.5000i 0.296866 0.514187i
$$418$$ 0 0
$$419$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$420$$ 0 0
$$421$$ −8.68653 8.68653i −0.423356 0.423356i 0.463002 0.886357i $$-0.346772\pi$$
−0.886357 + 0.463002i $$0.846772\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 13.5000 38.9711i 0.653311 1.88595i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$432$$ 10.3923 18.0000i 0.500000 0.866025i
$$433$$ 30.3109 + 17.5000i 1.45665 + 0.840996i 0.998845 0.0480569i $$-0.0153029\pi$$
0.457804 + 0.889053i $$0.348636\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 22.7846 22.7846i 1.09118 1.09118i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 7.50000 + 4.33013i 0.357955 + 0.206666i 0.668184 0.743996i $$-0.267072\pi$$
−0.310228 + 0.950662i $$0.600405\pi$$
$$440$$ 0 0
$$441$$ −16.5000 12.9904i −0.785714 0.618590i
$$442$$ 0 0
$$443$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$444$$ 10.0526 + 10.0526i 0.477073 + 0.477073i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 20.0000 + 6.92820i 0.944911 + 0.327327i
$$449$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 6.41858 + 23.9545i 0.301571 + 1.12548i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −19.7224 + 5.28461i −0.922576 + 0.247204i −0.688686 0.725059i $$-0.741812\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$462$$ 0 0
$$463$$ −9.05256 + 9.05256i −0.420708 + 0.420708i −0.885448 0.464739i $$-0.846148\pi$$
0.464739 + 0.885448i $$0.346148\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$468$$ −15.0000 + 15.5885i −0.693375 + 0.720577i
$$469$$ 38.9186 18.8923i 1.79709 0.872366i
$$470$$ 0 0
$$471$$ −21.6506 + 37.5000i −0.997609 + 1.72791i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 7.00962 + 26.1603i 0.321623 + 1.20031i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$480$$ 0 0
$$481$$ −7.64359 12.6699i −0.348518 0.577696i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −11.0000 19.0526i −0.500000 0.866025i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −10.7679 + 40.1865i −0.487942 + 1.82103i 0.0784867 + 0.996915i $$0.474991\pi$$
−0.566429 + 0.824110i $$0.691675\pi$$
$$488$$ 0 0
$$489$$ 31.2224 31.2224i 1.41193 1.41193i
$$490$$ 0 0
$$491$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −1.21539 + 4.53590i −0.0545726 + 0.203668i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −5.91154 + 22.0622i −0.264637 + 0.987639i 0.697835 + 0.716258i $$0.254147\pi$$
−0.962472 + 0.271380i $$0.912520\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 19.0526 12.0000i 0.846154 0.532939i
$$508$$ 20.0000 34.6410i 0.887357 1.53695i
$$509$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$510$$ 0 0
$$511$$ −44.5167 3.19615i −1.96930 0.141389i
$$512$$ 0 0
$$513$$ −19.9019 19.9019i −0.878691 0.878691i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 36.0000 1.58481
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ −21.5000 + 37.2391i −0.940129 + 1.62835i −0.174908 + 0.984585i $$0.555963\pi$$
−0.765222 + 0.643767i $$0.777371\pi$$
$$524$$ 0 0
$$525$$ 17.3205 15.0000i 0.755929 0.654654i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 16.0718 23.7321i 0.696801 1.02891i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −36.1506 9.68653i −1.55424 0.416457i −0.623404 0.781900i $$-0.714251\pi$$
−0.930834 + 0.365444i $$0.880917\pi$$
$$542$$ 0 0
$$543$$ 33.0000i 1.41617i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.00000 −0.0427569 −0.0213785 0.999771i $$-0.506805\pi$$
−0.0213785 + 0.999771i $$0.506805\pi$$
$$548$$ 0 0
$$549$$ −46.7654 −1.99590
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −31.5000 + 6.06218i −1.33952 + 0.257790i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 14.0000i 0.593732i
$$557$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$558$$ 0 0
$$559$$ −36.3731 9.00000i −1.53842 0.380659i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −7.79423 + 22.5000i −0.327327 + 0.944911i
$$568$$ 0 0
$$569$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$570$$ 0 0
$$571$$ −40.7032 23.5000i −1.70338 0.983444i −0.942293 0.334790i $$-0.891335\pi$$
−0.761083 0.648655i $$-0.775332\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 24.0000i 1.00000i
$$577$$ −39.4545 + 10.5718i −1.64251 + 0.440110i −0.957503 0.288425i $$-0.906868\pi$$
−0.685009 + 0.728535i $$0.740202\pi$$
$$578$$ 0 0
$$579$$ −25.7321 + 25.7321i −1.06939 + 1.06939i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$588$$ −24.0000 3.46410i −0.989743 0.142857i
$$589$$ 5.50704 + 3.17949i 0.226914 + 0.131009i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 15.8564 + 4.24871i 0.651694 + 0.174621i
$$593$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 16.5000 9.52628i 0.675300 0.389885i
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ −21.6506 37.5000i −0.883148 1.52966i −0.847822 0.530281i $$-0.822086\pi$$
−0.0353259 0.999376i $$-0.511247\pi$$
$$602$$ 0 0
$$603$$ −34.6865 34.6865i −1.41254 1.41254i
$$604$$ 20.2487 + 20.2487i 0.823908 + 0.823908i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −29.0000 −1.17707 −0.588537 0.808470i $$-0.700296\pi$$
−0.588537 + 0.808470i $$0.700296\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 31.2942 + 31.2942i 1.26396 + 1.26396i 0.949156 + 0.314806i $$0.101939\pi$$
0.314806 + 0.949156i $$0.398061\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$618$$ 0 0
$$619$$ −12.8301 47.8827i −0.515686 1.92457i −0.341644 0.939829i $$-0.610984\pi$$
−0.174042 0.984738i $$-0.555683\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −6.00000 + 24.2487i −0.240192 + 0.970725i
$$625$$ 12.5000 + 21.6506i 0.500000 + 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 50.0000i 1.99522i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 3.11474 + 11.6244i 0.123996 + 0.462758i 0.999802 0.0199047i $$-0.00633628\pi$$
−0.875806 + 0.482663i $$0.839670\pi$$
$$632$$ 0 0
$$633$$ 1.50000 + 2.59808i 0.0596196 + 0.103264i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 23.3827 + 9.50000i 0.926456 + 0.376404i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$642$$ 0 0
$$643$$ −6.02628 + 1.61474i −0.237653 + 0.0636790i −0.375680 0.926750i $$-0.622591\pi$$
0.138027 + 0.990429i $$0.455924\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0.385263 5.36603i 0.0150997 0.210311i
$$652$$ 13.1962 49.2487i 0.516801 1.92873i
$$653$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 13.0981 + 48.8827i 0.511005 + 1.90710i
$$658$$ 0 0
$$659$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$660$$ 0 0
$$661$$ −16.7058 + 16.7058i −0.649779 + 0.649779i −0.952940 0.303160i $$-0.901958\pi$$
0.303160 + 0.952940i $$0.401958\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 12.1699 45.4186i 0.470514 1.75598i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 12.0000 6.92820i 0.462566 0.267063i −0.250557 0.968102i $$-0.580614\pi$$
0.713123 + 0.701039i $$0.247280\pi$$
$$674$$ 0 0
$$675$$ −22.5000 12.9904i −0.866025 0.500000i
$$676$$ 12.1244 23.0000i 0.466321 0.884615i
$$677$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$678$$ 0 0
$$679$$ −1.84936 + 25.7583i −0.0709721 + 0.988514i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$684$$ −31.3923 8.41154i −1.20031 0.321623i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 44.5526 + 11.9378i 1.69979 + 0.455456i
$$688$$ 36.0000 20.7846i 1.37249 0.792406i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 30.0263 8.04552i 1.14225 0.306066i 0.362397 0.932024i $$-0.381959\pi$$
0.779857 + 0.625958i $$0.215292\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 8.66025 25.0000i 0.327327 0.944911i
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 11.1147 19.2513i 0.419200 0.726076i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 6.15064 6.15064i 0.230992 0.230992i −0.582115 0.813107i $$-0.697775\pi$$
0.813107 + 0.582115i $$0.197775\pi$$
$$710$$ 0 0
$$711$$ 18.1865 + 31.5000i 0.682048 + 1.18134i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ −1.73205 9.00000i −0.0645049 0.335178i
$$722$$ 0 0
$$723$$ −49.3468 13.2224i −1.83523 0.491748i
$$724$$ 19.0526 + 33.0000i 0.708083 + 1.22644i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 49.0000i 1.81731i 0.417548 + 0.908655i $$0.362889\pi$$
−0.417548 + 0.908655i $$0.637111\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −46.7654 + 27.0000i −1.72850 + 0.997949i
$$733$$ 8.54552 31.8923i 0.315636 1.17797i −0.607760 0.794121i $$-0.707932\pi$$
0.923396 0.383849i $$-0.125402\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 38.4186 38.4186i 1.41325 1.41325i 0.680534 0.732717i $$-0.261748\pi$$
0.732717 0.680534i $$-0.238252\pi$$
$$740$$ 0 0
$$741$$ 29.6147 + 16.3468i 1.08792 + 0.600514i
$$742$$ 0 0
$$743$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 46.5000 + 26.8468i 1.69681 + 0.979653i 0.948753 + 0.316017i $$0.102346\pi$$
0.748056 + 0.663636i $$0.230988\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 5.19615 + 27.0000i 0.188982 + 0.981981i
$$757$$ −24.2487 42.0000i −0.881334 1.52652i −0.849858 0.527011i $$-0.823312\pi$$
−0.0314762 0.999505i $$-0.510021\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$762$$ 0 0
$$763$$ −3.05256 + 42.5167i −0.110510 + 1.53921i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −13.8564 24.0000i −0.500000 0.866025i
$$769$$ 3.21281 11.9904i 0.115857 0.432384i −0.883493 0.468445i $$-0.844814\pi$$
0.999350 + 0.0360609i $$0.0114810\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −10.8756 + 40.5885i −0.391423 + 1.46081i
$$773$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$774$$ 0 0
$$775$$ 5.66987 + 1.51924i 0.203668 + 0.0545726i
$$776$$ 0 0
$$777$$ −18.7583 1.34679i −0.672951 0.0483157i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −26.0000 + 10.3923i −0.928571 + 0.371154i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 53.1147 + 14.2321i 1.89334 + 0.507318i 0.998092 + 0.0617409i $$0.0196653\pi$$
0.895244 + 0.445577i $$0.147001\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 54.0000 15.5885i 1.91760 0.553562i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 11.0000 19.0526i 0.389885 0.675300i
$$797$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$