# Properties

 Label 2268.2.i.g.865.1 Level $2268$ Weight $2$ Character 2268.865 Analytic conductor $18.110$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2268.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.1100711784$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2268.865 Dual form 2268.2.i.g.2053.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})$$ $$q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{13} +(-4.00000 + 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{29} +3.00000 q^{31} +(5.00000 - 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-3.00000 - 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +4.00000 q^{59} -6.00000 q^{61} +6.00000 q^{65} +13.0000 q^{67} -10.0000 q^{71} +(5.50000 - 9.52628i) q^{73} +(1.00000 - 5.19615i) q^{77} -3.00000 q^{79} +(-1.00000 + 1.73205i) q^{83} +(8.00000 + 13.8564i) q^{85} +(-1.50000 + 7.79423i) q^{91} +2.00000 q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{5} + 4q^{7} + O(q^{10})$$ $$2q + 2q^{5} + 4q^{7} - 2q^{11} + 3q^{13} - 8q^{17} + q^{19} - 8q^{23} + q^{25} - 4q^{29} + 6q^{31} + 10q^{35} + q^{37} - 6q^{41} - 11q^{43} + 12q^{47} + 2q^{49} + 12q^{53} - 8q^{55} + 8q^{59} - 12q^{61} + 12q^{65} + 26q^{67} - 20q^{71} + 11q^{73} + 2q^{77} - 6q^{79} - 2q^{83} + 16q^{85} - 3q^{91} + 4q^{95} - 10q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1541$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i $$-0.685750\pi$$
0.998203 + 0.0599153i $$0.0190830\pi$$
$$6$$ 0 0
$$7$$ 2.00000 + 1.73205i 0.755929 + 0.654654i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i $$-0.264158\pi$$
−0.976478 + 0.215615i $$0.930824\pi$$
$$12$$ 0 0
$$13$$ 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i $$-0.0300895\pi$$
−0.579510 + 0.814965i $$0.696756\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −4.00000 + 6.92820i −0.970143 + 1.68034i −0.275029 + 0.961436i $$0.588688\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 0 0
$$19$$ 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i $$-0.130073\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.00000 + 6.92820i −0.834058 + 1.44463i 0.0607377 + 0.998154i $$0.480655\pi$$
−0.894795 + 0.446476i $$0.852679\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i $$-0.954452\pi$$
0.618389 + 0.785872i $$0.287786\pi$$
$$30$$ 0 0
$$31$$ 3.00000 0.538816 0.269408 0.963026i $$-0.413172\pi$$
0.269408 + 0.963026i $$0.413172\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 5.00000 1.73205i 0.845154 0.292770i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i $$-0.321880\pi$$
−0.999353 + 0.0359748i $$0.988546\pi$$
$$42$$ 0 0
$$43$$ −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i $$0.483375\pi$$
−0.890947 + 0.454108i $$0.849958\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i $$-0.524979\pi$$
0.902557 0.430570i $$-0.141688\pi$$
$$54$$ 0 0
$$55$$ −4.00000 −0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 6.00000 0.744208
$$66$$ 0 0
$$67$$ 13.0000 1.58820 0.794101 0.607785i $$-0.207942\pi$$
0.794101 + 0.607785i $$0.207942\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.00000 5.19615i 0.113961 0.592157i
$$78$$ 0 0
$$79$$ −3.00000 −0.337526 −0.168763 0.985657i $$-0.553977\pi$$
−0.168763 + 0.985657i $$0.553977\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1.00000 + 1.73205i −0.109764 + 0.190117i −0.915675 0.401920i $$-0.868343\pi$$
0.805910 + 0.592037i $$0.201676\pi$$
$$84$$ 0 0
$$85$$ 8.00000 + 13.8564i 0.867722 + 1.50294i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ −1.50000 + 7.79423i −0.157243 + 0.817057i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2.00000 0.205196
$$96$$ 0 0
$$97$$ −5.00000 + 8.66025i −0.507673 + 0.879316i 0.492287 + 0.870433i $$0.336161\pi$$
−0.999961 + 0.00888289i $$0.997172\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i $$-0.332422\pi$$
−0.999996 + 0.00286291i $$0.999089\pi$$
$$102$$ 0 0
$$103$$ −5.50000 + 9.52628i −0.541931 + 0.938652i 0.456862 + 0.889538i $$0.348973\pi$$
−0.998793 + 0.0491146i $$0.984360\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$108$$ 0 0
$$109$$ 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i $$-0.656723\pi$$
0.999512 0.0312328i $$-0.00994332\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 7.00000 + 12.1244i 0.658505 + 1.14056i 0.981003 + 0.193993i $$0.0621440\pi$$
−0.322498 + 0.946570i $$0.604523\pi$$
$$114$$ 0 0
$$115$$ 8.00000 + 13.8564i 0.746004 + 1.29212i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −20.0000 + 6.92820i −1.83340 + 0.635107i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 3.00000 0.266207 0.133103 0.991102i $$-0.457506\pi$$
0.133103 + 0.991102i $$0.457506\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.00000 1.73205i 0.0873704 0.151330i −0.819028 0.573753i $$-0.805487\pi$$
0.906399 + 0.422423i $$0.138820\pi$$
$$132$$ 0 0
$$133$$ −0.500000 + 2.59808i −0.0433555 + 0.225282i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i $$-0.221325\pi$$
−0.938725 + 0.344668i $$0.887992\pi$$
$$138$$ 0 0
$$139$$ 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i $$-0.0986536\pi$$
−0.740308 + 0.672268i $$0.765320\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 3.00000 5.19615i 0.250873 0.434524i
$$144$$ 0 0
$$145$$ 4.00000 + 6.92820i 0.332182 + 0.575356i
$$146$$ 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
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 3.00000 5.19615i 0.240966 0.417365i
$$156$$ 0 0
$$157$$ 2.00000 0.159617 0.0798087 0.996810i $$-0.474569\pi$$
0.0798087 + 0.996810i $$0.474569\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −20.0000 + 6.92820i −1.57622 + 0.546019i
$$162$$ 0 0
$$163$$ 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.00000 + 1.73205i 0.0773823 + 0.134030i 0.902120 0.431486i $$-0.142010\pi$$
−0.824737 + 0.565516i $$0.808677\pi$$
$$168$$ 0 0
$$169$$ 2.00000 3.46410i 0.153846 0.266469i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 16.0000 1.21646 0.608229 0.793762i $$-0.291880\pi$$
0.608229 + 0.793762i $$0.291880\pi$$
$$174$$ 0 0
$$175$$ −0.500000 + 2.59808i −0.0377964 + 0.196396i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i $$-0.905320\pi$$
0.731858 + 0.681457i $$0.238654\pi$$
$$180$$ 0 0
$$181$$ −15.0000 −1.11494 −0.557471 0.830197i $$-0.688228\pi$$
−0.557471 + 0.830197i $$0.688228\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.00000 0.147043
$$186$$ 0 0
$$187$$ 16.0000 1.17004
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 6.00000 0.434145 0.217072 0.976156i $$-0.430349\pi$$
0.217072 + 0.976156i $$0.430349\pi$$
$$192$$ 0 0
$$193$$ 11.0000 0.791797 0.395899 0.918294i $$-0.370433\pi$$
0.395899 + 0.918294i $$0.370433\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 8.00000 0.569976 0.284988 0.958531i $$-0.408010\pi$$
0.284988 + 0.958531i $$0.408010\pi$$
$$198$$ 0 0
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −10.0000 + 3.46410i −0.701862 + 0.243132i
$$204$$ 0 0
$$205$$ −12.0000 −0.838116
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1.00000 1.73205i 0.0691714 0.119808i
$$210$$ 0 0
$$211$$ 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i $$-0.122700\pi$$
−0.788935 + 0.614477i $$0.789367\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 11.0000 + 19.0526i 0.750194 + 1.29937i
$$216$$ 0 0
$$217$$ 6.00000 + 5.19615i 0.407307 + 0.352738i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −24.0000 −1.61441
$$222$$ 0 0
$$223$$ −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i $$-0.919650\pi$$
0.700449 + 0.713702i $$0.252983\pi$$
$$224$$ 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
$$229$$ −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i $$-0.843853\pi$$
0.849032 + 0.528341i $$0.177186\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i $$-0.318310\pi$$
−0.998886 + 0.0471787i $$0.984977\pi$$
$$234$$ 0 0
$$235$$ 6.00000 10.3923i 0.391397 0.677919i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −9.00000 15.5885i −0.582162 1.00833i −0.995223 0.0976302i $$-0.968874\pi$$
0.413061 0.910703i $$-0.364460\pi$$
$$240$$ 0 0
$$241$$ −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i $$-0.315567\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 13.0000 + 5.19615i 0.830540 + 0.331970i
$$246$$ 0 0
$$247$$ −1.50000 + 2.59808i −0.0954427 + 0.165312i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 16.0000 1.00591
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i $$0.356405\pi$$
−0.997374 + 0.0724199i $$0.976928\pi$$
$$258$$ 0 0
$$259$$ −0.500000 + 2.59808i −0.0310685 + 0.161437i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i $$-0.287301\pi$$
−0.989561 + 0.144112i $$0.953967\pi$$
$$264$$ 0 0
$$265$$ −12.0000 20.7846i −0.737154 1.27679i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.00000 1.73205i 0.0609711 0.105605i −0.833929 0.551872i $$-0.813914\pi$$
0.894900 + 0.446267i $$0.147247\pi$$
$$270$$ 0 0
$$271$$ 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i $$0.0933238\pi$$
−0.228380 + 0.973572i $$0.573343\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.00000 1.73205i 0.0603023 0.104447i
$$276$$ 0 0
$$277$$ −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i $$-0.996047\pi$$
0.489207 0.872167i $$-0.337286\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −10.0000 + 17.3205i −0.596550 + 1.03325i 0.396776 + 0.917915i $$0.370129\pi$$
−0.993326 + 0.115339i $$0.963204\pi$$
$$282$$ 0 0
$$283$$ 19.0000 1.12943 0.564716 0.825285i $$-0.308986\pi$$
0.564716 + 0.825285i $$0.308986\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 3.00000 15.5885i 0.177084 0.920158i
$$288$$ 0 0
$$289$$ −23.5000 40.7032i −1.38235 2.39431i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 12.0000 + 20.7846i 0.701047 + 1.21425i 0.968099 + 0.250568i $$0.0806172\pi$$
−0.267052 + 0.963682i $$0.586049\pi$$
$$294$$ 0 0
$$295$$ 4.00000 6.92820i 0.232889 0.403376i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −24.0000 −1.38796
$$300$$ 0 0
$$301$$ −27.5000 + 9.52628i −1.58507 + 0.549086i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −6.00000 + 10.3923i −0.343559 + 0.595062i
$$306$$ 0 0
$$307$$ −23.0000 −1.31268 −0.656340 0.754466i $$-0.727896\pi$$
−0.656340 + 0.754466i $$0.727896\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −2.00000 −0.113410 −0.0567048 0.998391i $$-0.518059\pi$$
−0.0567048 + 0.998391i $$0.518059\pi$$
$$312$$ 0 0
$$313$$ −17.0000 −0.960897 −0.480448 0.877023i $$-0.659526\pi$$
−0.480448 + 0.877023i $$0.659526\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −24.0000 −1.34797 −0.673987 0.738743i $$-0.735420\pi$$
−0.673987 + 0.738743i $$0.735420\pi$$
$$318$$ 0 0
$$319$$ 8.00000 0.447914
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.00000 −0.445132
$$324$$ 0 0
$$325$$ −1.50000 + 2.59808i −0.0832050 + 0.144115i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 12.0000 + 10.3923i 0.661581 + 0.572946i
$$330$$ 0 0
$$331$$ 17.0000 0.934405 0.467202 0.884150i $$-0.345262\pi$$
0.467202 + 0.884150i $$0.345262\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 13.0000 22.5167i 0.710266 1.23022i
$$336$$ 0 0
$$337$$ −10.5000 18.1865i −0.571971 0.990684i −0.996363 0.0852050i $$-0.972845\pi$$
0.424392 0.905479i $$-0.360488\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −3.00000 5.19615i −0.162459 0.281387i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 24.0000 1.28839 0.644194 0.764862i $$-0.277193\pi$$
0.644194 + 0.764862i $$0.277193\pi$$
$$348$$ 0 0
$$349$$ 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i $$-0.711079\pi$$
0.990282 + 0.139072i $$0.0444119\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i $$-0.115622\pi$$
−0.775077 + 0.631867i $$0.782289\pi$$
$$354$$ 0 0
$$355$$ −10.0000 + 17.3205i −0.530745 + 0.919277i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i $$0.0103087\pi$$
−0.471696 + 0.881761i $$0.656358\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −11.0000 19.0526i −0.575766 0.997257i
$$366$$ 0 0
$$367$$ −2.50000 4.33013i −0.130499 0.226031i 0.793370 0.608740i $$-0.208325\pi$$
−0.923869 + 0.382709i $$0.874991\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 30.0000 10.3923i 1.55752 0.539542i
$$372$$ 0 0
$$373$$ 2.50000 4.33013i 0.129445 0.224205i −0.794017 0.607896i $$-0.792014\pi$$
0.923462 + 0.383691i $$0.125347\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 13.0000 0.667765 0.333883 0.942615i $$-0.391641\pi$$
0.333883 + 0.942615i $$0.391641\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i $$-0.579593\pi$$
0.962818 0.270151i $$-0.0870736\pi$$
$$384$$ 0 0
$$385$$ −8.00000 6.92820i −0.407718 0.353094i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i $$-0.248252\pi$$
−0.964490 + 0.264120i $$0.914918\pi$$
$$390$$ 0 0
$$391$$ −32.0000 55.4256i −1.61831 2.80299i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −3.00000 + 5.19615i −0.150946 + 0.261447i
$$396$$ 0 0
$$397$$ −1.50000 2.59808i −0.0752828 0.130394i 0.825926 0.563778i $$-0.190653\pi$$
−0.901209 + 0.433384i $$0.857319\pi$$
$$398$$ 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
$$403$$ 4.50000 + 7.79423i 0.224161 + 0.388258i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1.00000 1.73205i 0.0495682 0.0858546i
$$408$$ 0 0
$$409$$ −19.0000 −0.939490 −0.469745 0.882802i $$-0.655654\pi$$
−0.469745 + 0.882802i $$0.655654\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 8.00000 + 6.92820i 0.393654 + 0.340915i
$$414$$ 0 0
$$415$$ 2.00000 + 3.46410i 0.0981761 + 0.170046i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −9.00000 15.5885i −0.439679 0.761546i 0.557986 0.829851i $$-0.311574\pi$$
−0.997665 + 0.0683046i $$0.978241\pi$$
$$420$$ 0 0
$$421$$ 13.5000 23.3827i 0.657950 1.13960i −0.323196 0.946332i $$-0.604757\pi$$
0.981146 0.193270i $$-0.0619094\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −8.00000 −0.388057
$$426$$ 0 0
$$427$$ −12.0000 10.3923i −0.580721 0.502919i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i $$-0.576315\pi$$
0.959985 0.280052i $$-0.0903517\pi$$
$$432$$ 0 0
$$433$$ −25.0000 −1.20142 −0.600712 0.799466i $$-0.705116\pi$$
−0.600712 + 0.799466i $$0.705116\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −8.00000 −0.382692
$$438$$ 0 0
$$439$$ 24.0000 1.14546 0.572729 0.819745i $$-0.305885\pi$$
0.572729 + 0.819745i $$0.305885\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −4.00000 −0.190046 −0.0950229 0.995475i $$-0.530292\pi$$
−0.0950229 + 0.995475i $$0.530292\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 12.0000 + 10.3923i 0.562569 + 0.487199i
$$456$$ 0 0
$$457$$ 13.0000 0.608114 0.304057 0.952654i $$-0.401659\pi$$
0.304057 + 0.952654i $$0.401659\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 + 3.46410i −0.0931493 + 0.161339i −0.908835 0.417156i $$-0.863027\pi$$
0.815685 + 0.578496i $$0.196360\pi$$
$$462$$ 0 0
$$463$$ 5.50000 + 9.52628i 0.255607 + 0.442724i 0.965060 0.262029i $$-0.0843915\pi$$
−0.709453 + 0.704752i $$0.751058\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −17.0000 29.4449i −0.786666 1.36255i −0.927999 0.372584i $$-0.878472\pi$$
0.141332 0.989962i $$-0.454861\pi$$
$$468$$ 0 0
$$469$$ 26.0000 + 22.5167i 1.20057 + 1.03972i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 22.0000 1.01156
$$474$$ 0 0
$$475$$ −0.500000 + 0.866025i −0.0229416 + 0.0397360i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i $$0.0542649\pi$$
−0.345827 + 0.938298i $$0.612402\pi$$
$$480$$ 0 0
$$481$$ −1.50000 + 2.59808i −0.0683941 + 0.118462i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 10.0000 + 17.3205i 0.454077 + 0.786484i
$$486$$ 0 0
$$487$$ 9.50000 16.4545i 0.430486 0.745624i −0.566429 0.824110i $$-0.691675\pi$$
0.996915 + 0.0784867i $$0.0250088\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 18.0000 + 31.1769i 0.812329 + 1.40699i 0.911230 + 0.411897i $$0.135134\pi$$
−0.0989017 + 0.995097i $$0.531533\pi$$
$$492$$ 0 0
$$493$$ −16.0000 27.7128i −0.720604 1.24812i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −20.0000 17.3205i −0.897123 0.776931i
$$498$$ 0 0
$$499$$ 14.5000 25.1147i 0.649109 1.12429i −0.334227 0.942493i $$-0.608475\pi$$
0.983336 0.181797i $$-0.0581915\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −30.0000 −1.33763 −0.668817 0.743427i $$-0.733199\pi$$
−0.668817 + 0.743427i $$0.733199\pi$$
$$504$$ 0 0
$$505$$ −20.0000 −0.889988
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i $$-0.963948\pi$$
0.594675 + 0.803966i $$0.297281\pi$$
$$510$$ 0 0
$$511$$ 27.5000 9.52628i 1.21653 0.421418i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 11.0000 + 19.0526i 0.484718 + 0.839556i
$$516$$ 0 0
$$517$$ −6.00000 10.3923i −0.263880 0.457053i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 18.0000 31.1769i 0.788594 1.36589i −0.138234 0.990400i $$-0.544143\pi$$
0.926828 0.375486i $$-0.122524\pi$$
$$522$$ 0 0
$$523$$ 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i $$0.0703858\pi$$
−0.297884 + 0.954602i $$0.596281\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −12.0000 + 20.7846i −0.522728 + 0.905392i
$$528$$ 0 0
$$529$$ −20.5000 35.5070i −0.891304 1.54378i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 9.00000 15.5885i 0.389833 0.675211i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 11.0000 8.66025i 0.473804 0.373024i
$$540$$ 0 0
$$541$$ 7.50000 + 12.9904i 0.322450 + 0.558500i 0.980993 0.194043i $$-0.0621602\pi$$
−0.658543 + 0.752543i $$0.728827\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −11.0000 19.0526i −0.471188 0.816122i
$$546$$ 0 0
$$547$$ 6.00000 10.3923i 0.256541 0.444343i −0.708772 0.705438i $$-0.750750\pi$$
0.965313 + 0.261095i $$0.0840836\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −4.00000 −0.170406
$$552$$ 0 0
$$553$$ −6.00000 5.19615i −0.255146 0.220963i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −11.0000 + 19.0526i −0.466085 + 0.807283i −0.999250 0.0387286i $$-0.987669\pi$$
0.533165 + 0.846011i $$0.321003\pi$$
$$558$$ 0 0
$$559$$ −33.0000 −1.39575
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −46.0000 −1.93867 −0.969334 0.245745i $$-0.920967\pi$$
−0.969334 + 0.245745i $$0.920967\pi$$
$$564$$ 0 0
$$565$$ 28.0000 1.17797
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ −21.0000 −0.878823 −0.439411 0.898286i $$-0.644813\pi$$
−0.439411 + 0.898286i $$0.644813\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −8.00000 −0.333623
$$576$$ 0 0
$$577$$ 20.5000 35.5070i 0.853426 1.47818i −0.0246713 0.999696i $$-0.507854\pi$$
0.878097 0.478482i $$-0.158813\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −5.00000 + 1.73205i −0.207435 + 0.0718576i
$$582$$ 0 0
$$583$$ −24.0000 −0.993978
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −16.0000 + 27.7128i −0.660391 + 1.14383i 0.320122 + 0.947376i $$0.396276\pi$$
−0.980513 + 0.196454i $$0.937057\pi$$
$$588$$ 0 0
$$589$$ 1.50000 + 2.59808i 0.0618064 + 0.107052i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i $$-0.127353\pi$$
−0.797831 + 0.602881i $$0.794019\pi$$
$$594$$ 0 0
$$595$$ −8.00000 + 41.5692i −0.327968 + 1.70417i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −12.0000 −0.490307 −0.245153 0.969484i $$-0.578838\pi$$
−0.245153 + 0.969484i $$0.578838\pi$$
$$600$$ 0 0
$$601$$ 0.500000 0.866025i 0.0203954 0.0353259i −0.855648 0.517559i $$-0.826841\pi$$
0.876043 + 0.482233i $$0.160174\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7.00000 12.1244i −0.284590 0.492925i
$$606$$ 0 0
$$607$$ 1.50000 2.59808i 0.0608831 0.105453i −0.833977 0.551799i $$-0.813942\pi$$
0.894860 + 0.446346i $$0.147275\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 9.00000 + 15.5885i 0.364101 + 0.630641i
$$612$$ 0 0
$$613$$ 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i $$-0.626169\pi$$
0.991917 0.126885i $$-0.0404979\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −13.0000 22.5167i −0.523360 0.906487i −0.999630 0.0271876i $$-0.991345\pi$$
0.476270 0.879299i $$-0.341988\pi$$
$$618$$ 0 0
$$619$$ 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i $$-0.0957138\pi$$
−0.734068 + 0.679076i $$0.762380\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3.00000 5.19615i 0.119051 0.206203i
$$636$$ 0 0
$$637$$ −16.5000 + 12.9904i −0.653754 + 0.514698i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 20.0000 + 34.6410i 0.789953 + 1.36824i 0.925995 + 0.377535i $$0.123228\pi$$
−0.136043 + 0.990703i $$0.543438\pi$$
$$642$$ 0 0
$$643$$ −17.5000 30.3109i −0.690133 1.19534i −0.971794 0.235831i $$-0.924219\pi$$
0.281661 0.959514i $$-0.409114\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −3.00000 + 5.19615i −0.117942 + 0.204282i −0.918952 0.394369i $$-0.870963\pi$$
0.801010 + 0.598651i $$0.204296\pi$$
$$648$$ 0 0
$$649$$ −4.00000 6.92820i −0.157014 0.271956i
$$650$$ 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
$$655$$ −2.00000 3.46410i −0.0781465 0.135354i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 14.0000 24.2487i 0.545363 0.944596i −0.453221 0.891398i $$-0.649725\pi$$
0.998584 0.0531977i $$-0.0169414\pi$$
$$660$$ 0 0
$$661$$ −29.0000 −1.12797 −0.563985 0.825785i $$-0.690732\pi$$
−0.563985 + 0.825785i $$0.690732\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 4.00000 + 3.46410i 0.155113 + 0.134332i
$$666$$ 0 0
$$667$$ −16.0000 27.7128i −0.619522 1.07304i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 6.00000 + 10.3923i 0.231627 + 0.401190i
$$672$$ 0 0
$$673$$ 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i $$-0.827198\pi$$
0.875501 + 0.483216i $$0.160531\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 12.0000 0.461197 0.230599 0.973049i $$-0.425932\pi$$
0.230599 + 0.973049i $$0.425932\pi$$
$$678$$ 0 0
$$679$$ −25.0000 + 8.66025i −0.959412 + 0.332350i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i $$0.408507\pi$$
−0.972242 + 0.233977i $$0.924826\pi$$
$$684$$ 0 0
$$685$$ −8.00000 −0.305664
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 36.0000 1.37149
$$690$$ 0 0
$$691$$ −43.0000 −1.63580 −0.817899 0.575362i $$-0.804861\pi$$
−0.817899 + 0.575362i $$0.804861\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 10.0000 0.379322
$$696$$ 0 0
$$697$$ 48.0000 1.81813
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 0 0
$$703$$ −0.500000 + 0.866025i −0.0188579 + 0.0326628i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 5.00000 25.9808i 0.188044 0.977107i
$$708$$ 0 0
$$709$$ 14.0000 0.525781 0.262891 0.964826i $$-0.415324\pi$$
0.262891 + 0.964826i $$0.415324\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −12.0000 + 20.7846i −0.449404 + 0.778390i
$$714$$ 0 0
$$715$$ −6.00000 10.3923i −0.224387 0.388650i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i $$-0.130979\pi$$
−0.804648 + 0.593753i $$0.797646\pi$$
$$720$$ 0 0
$$721$$ −27.5000 + 9.52628i −1.02415 + 0.354777i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −4.00000 −0.148556
$$726$$ 0 0
$$727$$ 11.5000 19.9186i 0.426511 0.738739i −0.570049 0.821611i $$-0.693076\pi$$
0.996560 + 0.0828714i $$0.0264091\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −44.0000 76.2102i −1.62740 2.81874i
$$732$$ 0 0
$$733$$ −22.5000 + 38.9711i −0.831056 + 1.43943i 0.0661448 + 0.997810i $$0.478930\pi$$
−0.897201 + 0.441622i $$0.854403\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −13.0000 22.5167i −0.478861 0.829412i
$$738$$ 0 0
$$739$$ 4.50000 7.79423i 0.165535 0.286715i −0.771310 0.636460i $$-0.780398\pi$$
0.936845 + 0.349744i $$0.113732\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 9.00000 + 15.5885i 0.330178 + 0.571885i 0.982547 0.186017i $$-0.0595579\pi$$
−0.652369 + 0.757902i $$0.726225\pi$$
$$744$$ 0 0
$$745$$ −12.0000 20.7846i −0.439646 0.761489i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.50000 + 12.9904i −0.273679 + 0.474026i −0.969801 0.243898i $$-0.921574\pi$$
0.696122 + 0.717923i $$0.254907\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −4.00000 + 6.92820i −0.145000 + 0.251147i −0.929373 0.369142i $$-0.879652\pi$$
0.784373 + 0.620289i $$0.212985\pi$$
$$762$$ 0 0
$$763$$ 27.5000 9.52628i 0.995567 0.344874i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 6.00000 + 10.3923i 0.216647 + 0.375244i
$$768$$ 0 0
$$769$$ −15.5000 26.8468i −0.558944 0.968120i −0.997585 0.0694574i $$-0.977873\pi$$
0.438641 0.898663i $$-0.355460\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −11.0000 + 19.0526i −0.395643 + 0.685273i −0.993183 0.116566i $$-0.962811\pi$$
0.597540 + 0.801839i $$0.296145\pi$$
$$774$$ 0 0
$$775$$ 1.50000 + 2.59808i 0.0538816 + 0.0933257i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3.00000 5.19615i 0.107486 0.186171i
$$780$$ 0 0
$$781$$ 10.0000 + 17.3205i 0.357828 + 0.619777i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2.00000 3.46410i 0.0713831 0.123639i
$$786$$ 0 0
$$787$$ 24.0000 0.855508 0.427754 0.903895i $$-0.359305\pi$$
0.427754 + 0.903895i $$0.359305\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −7.00000 + 36.3731i −0.248891 + 1.29328i
$$792$$ 0 0
$$793$$ −9.00000 15.5885i −0.319599 0.553562i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 24.0000 + 41.5692i 0.850124 + 1.47246i 0.881096 + 0.472937i $$0.156806\pi$$
−0.0309726 + 0.999520i $$0.509860\pi$$
$$798$$ 0 0
$$799$$ −24.0000 + 41.5692i −0.849059 + 1.47061i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −22.0000 −0.776363