# Properties

 Label 273.2.u.b.251.1 Level $273$ Weight $2$ Character 273.251 Analytic conductor $2.180$ Analytic rank $0$ Dimension $2$ 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.u (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.17991597518$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

## Embedding invariants

 Embedding label 251.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 273.251 Dual form 273.2.u.b.62.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +3.46410i q^{12} +(2.50000 - 2.59808i) q^{13} +(-2.00000 + 3.46410i) q^{16} +(-4.00000 - 6.92820i) q^{19} +(-4.50000 - 0.866025i) q^{21} +5.00000 q^{25} +5.19615i q^{27} +(-4.00000 - 3.46410i) q^{28} +7.00000 q^{31} +(-3.00000 + 5.19615i) q^{36} +(6.00000 + 3.46410i) q^{37} +(6.00000 - 1.73205i) q^{39} +(-6.50000 - 11.2583i) q^{43} +(-6.00000 + 3.46410i) q^{48} +(5.50000 - 4.33013i) q^{49} +(7.00000 + 1.73205i) q^{52} -13.8564i q^{57} +(-7.50000 + 4.33013i) q^{61} +(-6.00000 - 5.19615i) q^{63} -8.00000 q^{64} +(-10.5000 - 6.06218i) q^{67} -17.0000 q^{73} +(7.50000 + 4.33013i) q^{75} +(8.00000 - 13.8564i) q^{76} +13.0000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 - 8.66025i) q^{84} +(-4.00000 + 8.66025i) q^{91} +(10.5000 + 6.06218i) q^{93} +(-2.50000 - 4.33013i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 3q^{3} + 2q^{4} - 5q^{7} + 3q^{9} + O(q^{10})$$ $$2q + 3q^{3} + 2q^{4} - 5q^{7} + 3q^{9} + 5q^{13} - 4q^{16} - 8q^{19} - 9q^{21} + 10q^{25} - 8q^{28} + 14q^{31} - 6q^{36} + 12q^{37} + 12q^{39} - 13q^{43} - 12q^{48} + 11q^{49} + 14q^{52} - 15q^{61} - 12q^{63} - 16q^{64} - 21q^{67} - 34q^{73} + 15q^{75} + 16q^{76} + 26q^{79} - 9q^{81} - 6q^{84} - 8q^{91} + 21q^{93} - 5q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$92$$ $$106$$ $$157$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$

## 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 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$3$$ 1.50000 + 0.866025i 0.866025 + 0.500000i
$$4$$ 1.00000 + 1.73205i 0.500000 + 0.866025i
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$12$$ 3.46410i 1.00000i
$$13$$ 2.50000 2.59808i 0.693375 0.720577i
$$14$$ 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
$$19$$ −4.00000 6.92820i −0.917663 1.58944i −0.802955 0.596040i $$-0.796740\pi$$
−0.114708 0.993399i $$-0.536593\pi$$
$$20$$ 0 0
$$21$$ −4.50000 0.866025i −0.981981 0.188982i
$$22$$ 0 0
$$23$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ 0 0
$$25$$ 5.00000 1.00000
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ −4.00000 3.46410i −0.755929 0.654654i
$$29$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ 0 0
$$31$$ 7.00000 1.25724 0.628619 0.777714i $$-0.283621\pi$$
0.628619 + 0.777714i $$0.283621\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −3.00000 + 5.19615i −0.500000 + 0.866025i
$$37$$ 6.00000 + 3.46410i 0.986394 + 0.569495i 0.904194 0.427121i $$-0.140472\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ 0 0
$$39$$ 6.00000 1.73205i 0.960769 0.277350i
$$40$$ 0 0
$$41$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$42$$ 0 0
$$43$$ −6.50000 11.2583i −0.991241 1.71688i −0.609994 0.792406i $$-0.708828\pi$$
−0.381246 0.924473i $$-0.624505\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ −6.00000 + 3.46410i −0.866025 + 0.500000i
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 7.00000 + 1.73205i 0.970725 + 0.240192i
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 13.8564i 1.83533i
$$58$$ 0 0
$$59$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$60$$ 0 0
$$61$$ −7.50000 + 4.33013i −0.960277 + 0.554416i −0.896258 0.443533i $$-0.853725\pi$$
−0.0640184 + 0.997949i $$0.520392\pi$$
$$62$$ 0 0
$$63$$ −6.00000 5.19615i −0.755929 0.654654i
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −10.5000 6.06218i −1.28278 0.740613i −0.305424 0.952217i $$-0.598798\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ 0 0
$$73$$ −17.0000 −1.98970 −0.994850 0.101361i $$-0.967680\pi$$
−0.994850 + 0.101361i $$0.967680\pi$$
$$74$$ 0 0
$$75$$ 7.50000 + 4.33013i 0.866025 + 0.500000i
$$76$$ 8.00000 13.8564i 0.917663 1.58944i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 13.0000 1.46261 0.731307 0.682048i $$-0.238911\pi$$
0.731307 + 0.682048i $$0.238911\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ −3.00000 8.66025i −0.327327 0.944911i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ −4.00000 + 8.66025i −0.419314 + 0.907841i
$$92$$ 0 0
$$93$$ 10.5000 + 6.06218i 1.08880 + 0.628619i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −2.50000 4.33013i −0.253837 0.439658i 0.710742 0.703452i $$-0.248359\pi$$
−0.964579 + 0.263795i $$0.915026\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 5.00000 + 8.66025i 0.500000 + 0.866025i
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 0 0
$$103$$ 15.5885i 1.53598i −0.640464 0.767988i $$-0.721258\pi$$
0.640464 0.767988i $$-0.278742\pi$$
$$104$$ 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
$$109$$ 8.66025i 0.829502i 0.909935 + 0.414751i $$0.136131\pi$$
−0.909935 + 0.414751i $$0.863869\pi$$
$$110$$ 0 0
$$111$$ 6.00000 + 10.3923i 0.569495 + 0.986394i
$$112$$ 2.00000 10.3923i 0.188982 0.981981i
$$113$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 10.5000 + 2.59808i 0.970725 + 0.240192i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.50000 + 9.52628i 0.500000 + 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 7.00000 + 12.1244i 0.628619 + 1.08880i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −0.500000 + 0.866025i −0.0443678 + 0.0768473i −0.887357 0.461084i $$-0.847461\pi$$
0.842989 + 0.537931i $$0.180794\pi$$
$$128$$ 0 0
$$129$$ 22.5167i 1.98248i
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 16.0000 + 13.8564i 1.38738 + 1.20150i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$138$$ 0 0
$$139$$ −19.5000 + 11.2583i −1.65397 + 0.954919i −0.678551 + 0.734553i $$0.737392\pi$$
−0.975417 + 0.220366i $$0.929275\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −12.0000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 12.0000 1.73205i 0.989743 0.142857i
$$148$$ 13.8564i 1.13899i
$$149$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$150$$ 0 0
$$151$$ 24.2487i 1.97333i 0.162758 + 0.986666i $$0.447961\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 9.00000 + 8.66025i 0.720577 + 0.693375i
$$157$$ 22.5167i 1.79703i 0.438948 + 0.898513i $$0.355351\pi$$
−0.438948 + 0.898513i $$0.644649\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −4.50000 + 2.59808i −0.352467 + 0.203497i −0.665771 0.746156i $$-0.731897\pi$$
0.313304 + 0.949653i $$0.398564\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$168$$ 0 0
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 0 0
$$171$$ 12.0000 20.7846i 0.917663 1.58944i
$$172$$ 13.0000 22.5167i 0.991241 1.71688i
$$173$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$174$$ 0 0
$$175$$ −12.5000 + 4.33013i −0.944911 + 0.327327i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ 0 0
$$181$$ 6.92820i 0.514969i −0.966282 0.257485i $$-0.917106\pi$$
0.966282 0.257485i $$-0.0828937\pi$$
$$182$$ 0 0
$$183$$ −15.0000 −1.10883
$$184$$ 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 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ −12.0000 6.92820i −0.866025 0.500000i
$$193$$ 13.5000 + 7.79423i 0.971751 + 0.561041i 0.899770 0.436365i $$-0.143734\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 13.0000 + 5.19615i 0.928571 + 0.371154i
$$197$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$198$$ 0 0
$$199$$ −19.5000 + 11.2583i −1.38232 + 0.798082i −0.992434 0.122782i $$-0.960818\pi$$
−0.389885 + 0.920864i $$0.627485\pi$$
$$200$$ 0 0
$$201$$ −10.5000 18.1865i −0.740613 1.28278i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 4.00000 + 13.8564i 0.277350 + 0.960769i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 6.50000 11.2583i 0.447478 0.775055i −0.550743 0.834675i $$-0.685655\pi$$
0.998221 + 0.0596196i $$0.0189888\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −17.5000 + 6.06218i −1.18798 + 0.411527i
$$218$$ 0 0
$$219$$ −25.5000 14.7224i −1.72313 0.994850i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 14.0000 24.2487i 0.937509 1.62381i 0.167412 0.985887i $$-0.446459\pi$$
0.770097 0.637927i $$-0.220208\pi$$
$$224$$ 0 0
$$225$$ 7.50000 + 12.9904i 0.500000 + 0.866025i
$$226$$ 0 0
$$227$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 24.0000 13.8564i 1.58944 0.917663i
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 19.5000 + 11.2583i 1.26666 + 0.731307i
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i $$-0.0177663\pi$$
−0.547533 + 0.836784i $$0.684433\pi$$
$$242$$ 0 0
$$243$$ −13.5000 + 7.79423i −0.866025 + 0.500000i
$$244$$ −15.0000 8.66025i −0.960277 0.554416i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −28.0000 6.92820i −1.78160 0.440831i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$252$$ 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
$$259$$ −18.0000 3.46410i −1.11847 0.215249i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 24.2487i 1.48123i
$$269$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$270$$ 0 0
$$271$$ −14.5000 + 25.1147i −0.880812 + 1.52561i −0.0303728 + 0.999539i $$0.509669\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 0 0
$$273$$ −13.5000 + 9.52628i −0.817057 + 0.576557i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −13.0000 22.5167i −0.781094 1.35290i −0.931305 0.364241i $$-0.881328\pi$$
0.150210 0.988654i $$-0.452005\pi$$
$$278$$ 0 0
$$279$$ 10.5000 + 18.1865i 0.628619 + 1.08880i
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 19.5000 + 11.2583i 1.15915 + 0.669238i 0.951101 0.308879i $$-0.0999539\pi$$
0.208053 + 0.978117i $$0.433287\pi$$
$$284$$ 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
$$291$$ 8.66025i 0.507673i
$$292$$ −17.0000 29.4449i −0.994850 1.72313i
$$293$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 17.3205i 1.00000i
$$301$$ 26.0000 + 22.5167i 1.49862 + 1.29784i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 32.0000 1.83533
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −35.0000 −1.99756 −0.998778 0.0494267i $$-0.984261\pi$$
−0.998778 + 0.0494267i $$0.984261\pi$$
$$308$$ 0 0
$$309$$ 13.5000 23.3827i 0.767988 1.33019i
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 32.9090i 1.86012i −0.367402 0.930062i $$-0.619753\pi$$
0.367402 0.930062i $$-0.380247\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 13.0000 + 22.5167i 0.731307 + 1.26666i
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −18.0000 −1.00000
$$325$$ 12.5000 12.9904i 0.693375 0.720577i
$$326$$ 0 0
$$327$$ −7.50000 + 12.9904i −0.414751 + 0.718370i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −16.5000 + 9.52628i −0.906922 + 0.523612i −0.879440 0.476011i $$-0.842082\pi$$
−0.0274825 + 0.999622i $$0.508749\pi$$
$$332$$ 0 0
$$333$$ 20.7846i 1.13899i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 12.0000 13.8564i 0.654654 0.755929i
$$337$$ 29.0000 1.57973 0.789865 0.613280i $$-0.210150\pi$$
0.789865 + 0.613280i $$0.210150\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 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
$$349$$ 11.5000 19.9186i 0.615581 1.06622i −0.374701 0.927146i $$-0.622255\pi$$
0.990282 0.139072i $$-0.0444119\pi$$
$$350$$ 0 0
$$351$$ 13.5000 + 12.9904i 0.720577 + 0.693375i
$$352$$ 0 0
$$353$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −22.5000 + 38.9711i −1.18421 + 2.05111i
$$362$$ 0 0
$$363$$ 19.0526i 1.00000i
$$364$$ −19.0000 + 1.73205i −0.995871 + 0.0907841i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −19.5000 11.2583i −1.01789 0.587680i −0.104399 0.994535i $$-0.533292\pi$$
−0.913493 + 0.406855i $$0.866625\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 24.2487i 1.25724i
$$373$$ −6.50000 11.2583i −0.336557 0.582934i 0.647225 0.762299i $$-0.275929\pi$$
−0.983783 + 0.179364i $$0.942596\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −10.5000 6.06218i −0.539349 0.311393i 0.205466 0.978664i $$-0.434129\pi$$
−0.744815 + 0.667271i $$0.767462\pi$$
$$380$$ 0 0
$$381$$ −1.50000 + 0.866025i −0.0768473 + 0.0443678i
$$382$$ 0 0
$$383$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 19.5000 33.7750i 0.991241 1.71688i
$$388$$ 5.00000 8.66025i 0.253837 0.439658i
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i $$-0.158678\pi$$
−0.853206 + 0.521575i $$0.825345\pi$$
$$398$$ 0 0
$$399$$ 12.0000 + 34.6410i 0.600751 + 1.73422i
$$400$$ −10.0000 + 17.3205i −0.500000 + 0.866025i
$$401$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$402$$ 0 0
$$403$$ 17.5000 18.1865i 0.871737 0.905936i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 15.5000 + 26.8468i 0.766426 + 1.32749i 0.939490 + 0.342578i $$0.111300\pi$$
−0.173064 + 0.984911i $$0.555367\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 27.0000 15.5885i 1.33019 0.767988i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −39.0000 −1.90984
$$418$$ 0 0
$$419$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$420$$ 0 0
$$421$$ 36.3731i 1.77271i 0.463002 + 0.886357i $$0.346772\pi$$
−0.463002 + 0.886357i $$0.653228\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 15.0000 17.3205i 0.725901 0.838198i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$432$$ −18.0000 10.3923i −0.866025 0.500000i
$$433$$ 19.5000 11.2583i 0.937110 0.541041i 0.0480569 0.998845i $$-0.484697\pi$$
0.889053 + 0.457804i $$0.151364\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −15.0000 + 8.66025i −0.718370 + 0.414751i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 34.5000 + 19.9186i 1.64660 + 0.950662i 0.978412 + 0.206666i $$0.0662612\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ 19.5000 + 7.79423i 0.928571 + 0.371154i
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ −12.0000 + 20.7846i −0.569495 + 0.986394i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 20.0000 6.92820i 0.944911 0.327327i
$$449$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −21.0000 + 36.3731i −0.986666 + 1.70896i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −10.5000 6.06218i −0.491169 0.283577i 0.233890 0.972263i $$-0.424854\pi$$
−0.725059 + 0.688686i $$0.758188\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$462$$ 0 0
$$463$$ 1.73205i 0.0804952i −0.999190 0.0402476i $$-0.987185\pi$$
0.999190 0.0402476i $$-0.0128147\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 6.00000 + 20.7846i 0.277350 + 0.960769i
$$469$$ 31.5000 + 6.06218i 1.45453 + 0.279925i
$$470$$ 0 0
$$471$$ −19.5000 + 33.7750i −0.898513 + 1.55627i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −20.0000 34.6410i −0.917663 1.58944i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ 24.0000 6.92820i 1.09431 0.315899i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −11.0000 + 19.0526i −0.500000 + 0.866025i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −3.00000 + 1.73205i −0.135943 + 0.0784867i −0.566429 0.824110i $$-0.691675\pi$$
0.430486 + 0.902597i $$0.358342\pi$$
$$488$$ 0 0
$$489$$ −9.00000 −0.406994
$$490$$ 0 0
$$491$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −14.0000 + 24.2487i −0.628619 + 1.08880i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 31.1769i 1.39567i −0.716258 0.697835i $$-0.754147\pi$$
0.716258 0.697835i $$-0.245853\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 10.5000 19.9186i 0.466321 0.884615i
$$508$$ −2.00000 −0.0887357
$$509$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ 42.5000 14.7224i 1.88009 0.651282i
$$512$$ 0 0
$$513$$ 36.0000 20.7846i 1.58944 0.917663i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 39.0000 22.5167i 1.71688 0.991241i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ −39.0000 22.5167i −1.70535 0.984585i −0.940129 0.340818i $$-0.889296\pi$$
−0.765222 0.643767i $$-0.777371\pi$$
$$524$$ 0 0
$$525$$ −22.5000 4.33013i −0.981981 0.188982i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −11.5000 19.9186i −0.500000 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −8.00000 + 41.5692i −0.346844 + 1.80225i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 43.3013i 1.86167i −0.365444 0.930834i $$-0.619083\pi$$
0.365444 0.930834i $$-0.380917\pi$$
$$542$$ 0 0
$$543$$ 6.00000 10.3923i 0.257485 0.445976i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 41.0000 1.75303 0.876517 0.481371i $$-0.159861\pi$$
0.876517 + 0.481371i $$0.159861\pi$$
$$548$$ 0 0
$$549$$ −22.5000 12.9904i −0.960277 0.554416i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −32.5000 + 11.2583i −1.38204 + 0.478753i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −39.0000 22.5167i −1.65397 0.954919i
$$557$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$558$$ 0 0
$$559$$ −45.5000 11.2583i −1.92444 0.476177i
$$560$$ 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
$$567$$ 4.50000 23.3827i 0.188982 0.981981i
$$568$$ 0 0
$$569$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ 0 0
$$571$$ 16.0000 0.669579 0.334790 0.942293i $$-0.391335\pi$$
0.334790 + 0.942293i $$0.391335\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −12.0000 20.7846i −0.500000 0.866025i
$$577$$ −46.0000 −1.91501 −0.957503 0.288425i $$-0.906868\pi$$
−0.957503 + 0.288425i $$0.906868\pi$$
$$578$$ 0 0
$$579$$ 13.5000 + 23.3827i 0.561041 + 0.971751i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 15.0000 + 19.0526i 0.618590 + 0.785714i
$$589$$ −28.0000 48.4974i −1.15372 1.99830i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −24.0000 + 13.8564i −0.986394 + 0.569495i
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −39.0000 −1.59616
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 36.0000 + 20.7846i 1.46847 + 0.847822i 0.999376 0.0353259i $$-0.0112469\pi$$
0.469095 + 0.883148i $$0.344580\pi$$
$$602$$ 0 0
$$603$$ 36.3731i 1.48123i
$$604$$ −42.0000 + 24.2487i −1.70896 + 0.986666i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 39.0000 22.5167i 1.58296 0.913923i 0.588537 0.808470i $$-0.299704\pi$$
0.994424 0.105453i $$-0.0336291\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −28.5000 16.4545i −1.15110 0.664590i −0.201948 0.979396i $$-0.564727\pi$$
−0.949156 + 0.314806i $$0.898061\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$618$$ 0 0
$$619$$ 17.0000 0.683288 0.341644 0.939829i $$-0.389016\pi$$
0.341644 + 0.939829i $$0.389016\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −6.00000 + 24.2487i −0.240192 + 0.970725i
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −39.0000 + 22.5167i −1.55627 + 0.898513i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 43.5000 25.1147i 1.73171 0.999802i 0.855901 0.517139i $$-0.173003\pi$$
0.875806 0.482663i $$-0.160330\pi$$
$$632$$ 0 0
$$633$$ 19.5000 11.2583i 0.775055 0.447478i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 2.50000 25.1147i 0.0990536 0.995082i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ 0 0
$$643$$ 23.5000 + 40.7032i 0.926750 + 1.60518i 0.788723 + 0.614749i $$0.210743\pi$$
0.138027 + 0.990429i $$0.455924\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −31.5000 6.06218i −1.23458 0.237595i
$$652$$ −9.00000 5.19615i −0.352467 0.203497i
$$653$$ 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
$$657$$ −25.5000 44.1673i −0.994850 1.72313i
$$658$$ 0 0
$$659$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0 0
$$661$$ −24.5000 + 42.4352i −0.952940 + 1.65054i −0.213925 + 0.976850i $$0.568625\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 42.0000 24.2487i 1.62381 0.937509i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −6.50000 + 11.2583i −0.250557 + 0.433977i −0.963679 0.267063i $$-0.913947\pi$$
0.713123 + 0.701039i $$0.247280\pi$$
$$674$$ 0 0
$$675$$ 25.9808i 1.00000i
$$676$$ 22.0000 13.8564i 0.846154 0.532939i
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 10.0000 + 8.66025i 0.383765 + 0.332350i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$684$$ 48.0000 1.83533
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 33.0000 + 19.0526i 1.25903 + 0.726900i
$$688$$ 52.0000 1.98248
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −20.5000 + 35.5070i −0.779857 + 1.35075i 0.152167 + 0.988355i $$0.451375\pi$$
−0.932024 + 0.362397i $$0.881959\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −20.0000 17.3205i −0.755929 0.654654i
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 55.4256i 2.09042i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 4.50000 2.59808i 0.169001 0.0975728i −0.413114 0.910679i $$-0.635559\pi$$
0.582115 + 0.813107i $$0.302225\pi$$
$$710$$ 0 0
$$711$$ 19.5000 + 33.7750i 0.731307 + 1.26666i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$720$$ 0 0
$$721$$ 13.5000 + 38.9711i 0.502766 + 1.45136i
$$722$$ 0 0
$$723$$ 24.2487i 0.901819i
$$724$$ 12.0000 6.92820i 0.445976 0.257485i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 22.5167i 0.835097i 0.908655 + 0.417548i $$0.137111\pi$$
−0.908655 + 0.417548i $$0.862889\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −15.0000 25.9808i −0.554416 0.960277i
$$733$$ 7.00000 0.258551 0.129275 0.991609i $$-0.458735\pi$$
0.129275 + 0.991609i $$0.458735\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 45.0000 + 25.9808i 1.65535 + 0.955718i 0.974818 + 0.223001i $$0.0715853\pi$$
0.680534 + 0.732717i $$0.261748\pi$$
$$740$$ 0 0
$$741$$ −36.0000 34.6410i −1.32249 1.27257i
$$742$$ 0 0
$$743$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −26.0000 + 45.0333i −0.948753 + 1.64329i −0.200698 + 0.979653i $$0.564321\pi$$
−0.748056 + 0.663636i $$0.769012\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 18.0000 20.7846i 0.654654 0.755929i
$$757$$ −13.0000 + 22.5167i −0.472493 + 0.818382i −0.999505 0.0314762i $$-0.989979\pi$$
0.527011 + 0.849858i $$0.323312\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$762$$ 0 0
$$763$$ −7.50000 21.6506i −0.271518 0.783806i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 27.7128i 1.00000i
$$769$$ 1.00000 1.73205i 0.0360609 0.0624593i −0.847432 0.530904i $$-0.821852\pi$$
0.883493 + 0.468445i $$0.155186\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 31.1769i 1.12208i
$$773$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$774$$ 0 0
$$775$$ 35.0000 1.25724
$$776$$ 0 0
$$777$$ −24.0000 20.7846i −0.860995 0.745644i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 4.00000 + 27.7128i 0.142857 + 0.989743i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 12.5000 + 21.6506i 0.445577 + 0.771762i 0.998092 0.0617409i $$-0.0196653\pi$$
−0.552515 + 0.833503i $$0.686332\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −7.50000 + 30.3109i −0.266333 + 1.07637i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −39.0000 22.5167i −1.38232 0.798082i
$$797$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 21.0000 36.3731i 0.740613 1.28278i