# Properties

 Label 1232.2.e.c.769.2 Level $1232$ Weight $2$ Character 1232.769 Analytic conductor $9.838$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1232 = 2^{4} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1232.e (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.83756952902$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-5})$$ Defining polynomial: $$x^{4} - 4x^{2} + 9$$ x^4 - 4*x^2 + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 77) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 769.2 Root $$1.58114 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1232.769 Dual form 1232.2.e.c.769.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.23607i q^{3} -2.23607i q^{5} +(1.58114 + 2.12132i) q^{7} -2.00000 q^{9} +O(q^{10})$$ $$q-2.23607i q^{3} -2.23607i q^{5} +(1.58114 + 2.12132i) q^{7} -2.00000 q^{9} +(3.00000 + 1.41421i) q^{11} +6.32456 q^{13} -5.00000 q^{15} +3.16228 q^{19} +(4.74342 - 3.53553i) q^{21} +3.00000 q^{23} -2.23607i q^{27} +1.41421i q^{29} +6.70820i q^{31} +(3.16228 - 6.70820i) q^{33} +(4.74342 - 3.53553i) q^{35} -1.00000 q^{37} -14.1421i q^{39} -9.48683 q^{41} +4.24264i q^{43} +4.47214i q^{45} -4.47214i q^{47} +(-2.00000 + 6.70820i) q^{49} +(3.16228 - 6.70820i) q^{55} -7.07107i q^{57} +2.23607i q^{59} -3.16228 q^{61} +(-3.16228 - 4.24264i) q^{63} -14.1421i q^{65} -11.0000 q^{67} -6.70820i q^{69} -9.00000 q^{71} -3.16228 q^{73} +(1.74342 + 8.60003i) q^{77} -8.48528i q^{79} -11.0000 q^{81} -9.48683 q^{83} +3.16228 q^{87} -2.23607i q^{89} +(10.0000 + 13.4164i) q^{91} +15.0000 q^{93} -7.07107i q^{95} +6.70820i q^{97} +(-6.00000 - 2.82843i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{9}+O(q^{10})$$ 4 * q - 8 * q^9 $$4 q - 8 q^{9} + 12 q^{11} - 20 q^{15} + 12 q^{23} - 4 q^{37} - 8 q^{49} - 44 q^{67} - 36 q^{71} - 12 q^{77} - 44 q^{81} + 40 q^{91} + 60 q^{93} - 24 q^{99}+O(q^{100})$$ 4 * q - 8 * q^9 + 12 * q^11 - 20 * q^15 + 12 * q^23 - 4 * q^37 - 8 * q^49 - 44 * q^67 - 36 * q^71 - 12 * q^77 - 44 * q^81 + 40 * q^91 + 60 * q^93 - 24 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$$.

 $$n$$ $$309$$ $$353$$ $$463$$ $$673$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.23607i 1.29099i −0.763763 0.645497i $$-0.776650\pi$$
0.763763 0.645497i $$-0.223350\pi$$
$$4$$ 0 0
$$5$$ 2.23607i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$6$$ 0 0
$$7$$ 1.58114 + 2.12132i 0.597614 + 0.801784i
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 3.00000 + 1.41421i 0.904534 + 0.426401i
$$12$$ 0 0
$$13$$ 6.32456 1.75412 0.877058 0.480384i $$-0.159503\pi$$
0.877058 + 0.480384i $$0.159503\pi$$
$$14$$ 0 0
$$15$$ −5.00000 −1.29099
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 3.16228 0.725476 0.362738 0.931891i $$-0.381842\pi$$
0.362738 + 0.931891i $$0.381842\pi$$
$$20$$ 0 0
$$21$$ 4.74342 3.53553i 1.03510 0.771517i
$$22$$ 0 0
$$23$$ 3.00000 0.625543 0.312772 0.949828i $$-0.398743\pi$$
0.312772 + 0.949828i $$0.398743\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 2.23607i 0.430331i
$$28$$ 0 0
$$29$$ 1.41421i 0.262613i 0.991342 + 0.131306i $$0.0419172\pi$$
−0.991342 + 0.131306i $$0.958083\pi$$
$$30$$ 0 0
$$31$$ 6.70820i 1.20483i 0.798183 + 0.602414i $$0.205795\pi$$
−0.798183 + 0.602414i $$0.794205\pi$$
$$32$$ 0 0
$$33$$ 3.16228 6.70820i 0.550482 1.16775i
$$34$$ 0 0
$$35$$ 4.74342 3.53553i 0.801784 0.597614i
$$36$$ 0 0
$$37$$ −1.00000 −0.164399 −0.0821995 0.996616i $$-0.526194\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 0 0
$$39$$ 14.1421i 2.26455i
$$40$$ 0 0
$$41$$ −9.48683 −1.48159 −0.740797 0.671729i $$-0.765552\pi$$
−0.740797 + 0.671729i $$0.765552\pi$$
$$42$$ 0 0
$$43$$ 4.24264i 0.646997i 0.946229 + 0.323498i $$0.104859\pi$$
−0.946229 + 0.323498i $$0.895141\pi$$
$$44$$ 0 0
$$45$$ 4.47214i 0.666667i
$$46$$ 0 0
$$47$$ 4.47214i 0.652328i −0.945313 0.326164i $$-0.894244\pi$$
0.945313 0.326164i $$-0.105756\pi$$
$$48$$ 0 0
$$49$$ −2.00000 + 6.70820i −0.285714 + 0.958315i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 3.16228 6.70820i 0.426401 0.904534i
$$56$$ 0 0
$$57$$ 7.07107i 0.936586i
$$58$$ 0 0
$$59$$ 2.23607i 0.291111i 0.989350 + 0.145556i $$0.0464970\pi$$
−0.989350 + 0.145556i $$0.953503\pi$$
$$60$$ 0 0
$$61$$ −3.16228 −0.404888 −0.202444 0.979294i $$-0.564888\pi$$
−0.202444 + 0.979294i $$0.564888\pi$$
$$62$$ 0 0
$$63$$ −3.16228 4.24264i −0.398410 0.534522i
$$64$$ 0 0
$$65$$ 14.1421i 1.75412i
$$66$$ 0 0
$$67$$ −11.0000 −1.34386 −0.671932 0.740613i $$-0.734535\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ 0 0
$$69$$ 6.70820i 0.807573i
$$70$$ 0 0
$$71$$ −9.00000 −1.06810 −0.534052 0.845452i $$-0.679331\pi$$
−0.534052 + 0.845452i $$0.679331\pi$$
$$72$$ 0 0
$$73$$ −3.16228 −0.370117 −0.185058 0.982728i $$-0.559247\pi$$
−0.185058 + 0.982728i $$0.559247\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.74342 + 8.60003i 0.198681 + 0.980064i
$$78$$ 0 0
$$79$$ 8.48528i 0.954669i −0.878722 0.477334i $$-0.841603\pi$$
0.878722 0.477334i $$-0.158397\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ −9.48683 −1.04132 −0.520658 0.853766i $$-0.674313\pi$$
−0.520658 + 0.853766i $$0.674313\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 3.16228 0.339032
$$88$$ 0 0
$$89$$ 2.23607i 0.237023i −0.992953 0.118511i $$-0.962188\pi$$
0.992953 0.118511i $$-0.0378122\pi$$
$$90$$ 0 0
$$91$$ 10.0000 + 13.4164i 1.04828 + 1.40642i
$$92$$ 0 0
$$93$$ 15.0000 1.55543
$$94$$ 0 0
$$95$$ 7.07107i 0.725476i
$$96$$ 0 0
$$97$$ 6.70820i 0.681115i 0.940224 + 0.340557i $$0.110616\pi$$
−0.940224 + 0.340557i $$0.889384\pi$$
$$98$$ 0 0
$$99$$ −6.00000 2.82843i −0.603023 0.284268i
$$100$$ 0 0
$$101$$ 9.48683 0.943975 0.471988 0.881605i $$-0.343537\pi$$
0.471988 + 0.881605i $$0.343537\pi$$
$$102$$ 0 0
$$103$$ 13.4164i 1.32196i −0.750404 0.660979i $$-0.770141\pi$$
0.750404 0.660979i $$-0.229859\pi$$
$$104$$ 0 0
$$105$$ −7.90569 10.6066i −0.771517 1.03510i
$$106$$ 0 0
$$107$$ 2.82843i 0.273434i 0.990610 + 0.136717i $$0.0436552\pi$$
−0.990610 + 0.136717i $$0.956345\pi$$
$$108$$ 0 0
$$109$$ 12.7279i 1.21911i 0.792742 + 0.609557i $$0.208653\pi$$
−0.792742 + 0.609557i $$0.791347\pi$$
$$110$$ 0 0
$$111$$ 2.23607i 0.212238i
$$112$$ 0 0
$$113$$ −3.00000 −0.282216 −0.141108 0.989994i $$-0.545067\pi$$
−0.141108 + 0.989994i $$0.545067\pi$$
$$114$$ 0 0
$$115$$ 6.70820i 0.625543i
$$116$$ 0 0
$$117$$ −12.6491 −1.16941
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 7.00000 + 8.48528i 0.636364 + 0.771389i
$$122$$ 0 0
$$123$$ 21.2132i 1.91273i
$$124$$ 0 0
$$125$$ 11.1803i 1.00000i
$$126$$ 0 0
$$127$$ 12.7279i 1.12942i −0.825289 0.564710i $$-0.808988\pi$$
0.825289 0.564710i $$-0.191012\pi$$
$$128$$ 0 0
$$129$$ 9.48683 0.835269
$$130$$ 0 0
$$131$$ −18.9737 −1.65774 −0.828868 0.559444i $$-0.811015\pi$$
−0.828868 + 0.559444i $$0.811015\pi$$
$$132$$ 0 0
$$133$$ 5.00000 + 6.70820i 0.433555 + 0.581675i
$$134$$ 0 0
$$135$$ −5.00000 −0.430331
$$136$$ 0 0
$$137$$ −15.0000 −1.28154 −0.640768 0.767734i $$-0.721384\pi$$
−0.640768 + 0.767734i $$0.721384\pi$$
$$138$$ 0 0
$$139$$ 12.6491 1.07288 0.536442 0.843937i $$-0.319768\pi$$
0.536442 + 0.843937i $$0.319768\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 0 0
$$143$$ 18.9737 + 8.94427i 1.58666 + 0.747958i
$$144$$ 0 0
$$145$$ 3.16228 0.262613
$$146$$ 0 0
$$147$$ 15.0000 + 4.47214i 1.23718 + 0.368856i
$$148$$ 0 0
$$149$$ 19.7990i 1.62200i −0.585049 0.810998i $$-0.698925\pi$$
0.585049 0.810998i $$-0.301075\pi$$
$$150$$ 0 0
$$151$$ 16.9706i 1.38104i 0.723311 + 0.690522i $$0.242619\pi$$
−0.723311 + 0.690522i $$0.757381\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 15.0000 1.20483
$$156$$ 0 0
$$157$$ 6.70820i 0.535373i −0.963506 0.267686i $$-0.913741\pi$$
0.963506 0.267686i $$-0.0862591\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.74342 + 6.36396i 0.373834 + 0.501550i
$$162$$ 0 0
$$163$$ 10.0000 0.783260 0.391630 0.920123i $$-0.371911\pi$$
0.391630 + 0.920123i $$0.371911\pi$$
$$164$$ 0 0
$$165$$ −15.0000 7.07107i −1.16775 0.550482i
$$166$$ 0 0
$$167$$ 9.48683 0.734113 0.367057 0.930199i $$-0.380366\pi$$
0.367057 + 0.930199i $$0.380366\pi$$
$$168$$ 0 0
$$169$$ 27.0000 2.07692
$$170$$ 0 0
$$171$$ −6.32456 −0.483651
$$172$$ 0 0
$$173$$ 9.48683 0.721271 0.360635 0.932707i $$-0.382560\pi$$
0.360635 + 0.932707i $$0.382560\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 5.00000 0.375823
$$178$$ 0 0
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ 0 0
$$181$$ 20.1246i 1.49585i −0.663783 0.747925i $$-0.731050\pi$$
0.663783 0.747925i $$-0.268950\pi$$
$$182$$ 0 0
$$183$$ 7.07107i 0.522708i
$$184$$ 0 0
$$185$$ 2.23607i 0.164399i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 4.74342 3.53553i 0.345033 0.257172i
$$190$$ 0 0
$$191$$ −3.00000 −0.217072 −0.108536 0.994092i $$-0.534616\pi$$
−0.108536 + 0.994092i $$0.534616\pi$$
$$192$$ 0 0
$$193$$ 4.24264i 0.305392i 0.988273 + 0.152696i $$0.0487955\pi$$
−0.988273 + 0.152696i $$0.951204\pi$$
$$194$$ 0 0
$$195$$ −31.6228 −2.26455
$$196$$ 0 0
$$197$$ 5.65685i 0.403034i 0.979485 + 0.201517i $$0.0645872\pi$$
−0.979485 + 0.201517i $$0.935413\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 24.5967i 1.73492i
$$202$$ 0 0
$$203$$ −3.00000 + 2.23607i −0.210559 + 0.156941i
$$204$$ 0 0
$$205$$ 21.2132i 1.48159i
$$206$$ 0 0
$$207$$ −6.00000 −0.417029
$$208$$ 0 0
$$209$$ 9.48683 + 4.47214i 0.656218 + 0.309344i
$$210$$ 0 0
$$211$$ 21.2132i 1.46038i 0.683246 + 0.730189i $$0.260568\pi$$
−0.683246 + 0.730189i $$0.739432\pi$$
$$212$$ 0 0
$$213$$ 20.1246i 1.37892i
$$214$$ 0 0
$$215$$ 9.48683 0.646997
$$216$$ 0 0
$$217$$ −14.2302 + 10.6066i −0.966012 + 0.720023i
$$218$$ 0 0
$$219$$ 7.07107i 0.477818i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 6.70820i 0.449215i −0.974449 0.224607i $$-0.927890\pi$$
0.974449 0.224607i $$-0.0721099\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −9.48683 −0.629663 −0.314832 0.949148i $$-0.601948\pi$$
−0.314832 + 0.949148i $$0.601948\pi$$
$$228$$ 0 0
$$229$$ 6.70820i 0.443291i −0.975127 0.221645i $$-0.928857\pi$$
0.975127 0.221645i $$-0.0711427\pi$$
$$230$$ 0 0
$$231$$ 19.2302 3.89840i 1.26526 0.256496i
$$232$$ 0 0
$$233$$ 18.3848i 1.20443i 0.798335 + 0.602213i $$0.205714\pi$$
−0.798335 + 0.602213i $$0.794286\pi$$
$$234$$ 0 0
$$235$$ −10.0000 −0.652328
$$236$$ 0 0
$$237$$ −18.9737 −1.23247
$$238$$ 0 0
$$239$$ 7.07107i 0.457389i 0.973498 + 0.228695i $$0.0734457\pi$$
−0.973498 + 0.228695i $$0.926554\pi$$
$$240$$ 0 0
$$241$$ −12.6491 −0.814801 −0.407400 0.913250i $$-0.633565\pi$$
−0.407400 + 0.913250i $$0.633565\pi$$
$$242$$ 0 0
$$243$$ 17.8885i 1.14755i
$$244$$ 0 0
$$245$$ 15.0000 + 4.47214i 0.958315 + 0.285714i
$$246$$ 0 0
$$247$$ 20.0000 1.27257
$$248$$ 0 0
$$249$$ 21.2132i 1.34433i
$$250$$ 0 0
$$251$$ 11.1803i 0.705697i −0.935681 0.352848i $$-0.885213\pi$$
0.935681 0.352848i $$-0.114787\pi$$
$$252$$ 0 0
$$253$$ 9.00000 + 4.24264i 0.565825 + 0.266733i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 22.3607i 1.39482i −0.716672 0.697410i $$-0.754335\pi$$
0.716672 0.697410i $$-0.245665\pi$$
$$258$$ 0 0
$$259$$ −1.58114 2.12132i −0.0982472 0.131812i
$$260$$ 0 0
$$261$$ 2.82843i 0.175075i
$$262$$ 0 0
$$263$$ 11.3137i 0.697633i 0.937191 + 0.348817i $$0.113416\pi$$
−0.937191 + 0.348817i $$0.886584\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −5.00000 −0.305995
$$268$$ 0 0
$$269$$ 17.8885i 1.09068i 0.838214 + 0.545342i $$0.183600\pi$$
−0.838214 + 0.545342i $$0.816400\pi$$
$$270$$ 0 0
$$271$$ −25.2982 −1.53676 −0.768379 0.639995i $$-0.778936\pi$$
−0.768379 + 0.639995i $$0.778936\pi$$
$$272$$ 0 0
$$273$$ 30.0000 22.3607i 1.81568 1.35333i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 4.24264i 0.254916i −0.991844 0.127458i $$-0.959318\pi$$
0.991844 0.127458i $$-0.0406817\pi$$
$$278$$ 0 0
$$279$$ 13.4164i 0.803219i
$$280$$ 0 0
$$281$$ 24.0416i 1.43420i −0.696969 0.717102i $$-0.745468\pi$$
0.696969 0.717102i $$-0.254532\pi$$
$$282$$ 0 0
$$283$$ −6.32456 −0.375956 −0.187978 0.982173i $$-0.560193\pi$$
−0.187978 + 0.982173i $$0.560193\pi$$
$$284$$ 0 0
$$285$$ −15.8114 −0.936586
$$286$$ 0 0
$$287$$ −15.0000 20.1246i −0.885422 1.18792i
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ 15.0000 0.879316
$$292$$ 0 0
$$293$$ −9.48683 −0.554227 −0.277113 0.960837i $$-0.589378\pi$$
−0.277113 + 0.960837i $$0.589378\pi$$
$$294$$ 0 0
$$295$$ 5.00000 0.291111
$$296$$ 0 0
$$297$$ 3.16228 6.70820i 0.183494 0.389249i
$$298$$ 0 0
$$299$$ 18.9737 1.09728
$$300$$ 0 0
$$301$$ −9.00000 + 6.70820i −0.518751 + 0.386654i
$$302$$ 0 0
$$303$$ 21.2132i 1.21867i
$$304$$ 0 0
$$305$$ 7.07107i 0.404888i
$$306$$ 0 0
$$307$$ −6.32456 −0.360961 −0.180481 0.983579i $$-0.557765\pi$$
−0.180481 + 0.983579i $$0.557765\pi$$
$$308$$ 0 0
$$309$$ −30.0000 −1.70664
$$310$$ 0 0
$$311$$ 4.47214i 0.253592i −0.991929 0.126796i $$-0.959531\pi$$
0.991929 0.126796i $$-0.0404693\pi$$
$$312$$ 0 0
$$313$$ 6.70820i 0.379170i 0.981864 + 0.189585i $$0.0607143\pi$$
−0.981864 + 0.189585i $$0.939286\pi$$
$$314$$ 0 0
$$315$$ −9.48683 + 7.07107i −0.534522 + 0.398410i
$$316$$ 0 0
$$317$$ 21.0000 1.17948 0.589739 0.807594i $$-0.299231\pi$$
0.589739 + 0.807594i $$0.299231\pi$$
$$318$$ 0 0
$$319$$ −2.00000 + 4.24264i −0.111979 + 0.237542i
$$320$$ 0 0
$$321$$ 6.32456 0.353002
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 28.4605 1.57387
$$328$$ 0 0
$$329$$ 9.48683 7.07107i 0.523026 0.389841i
$$330$$ 0 0
$$331$$ 19.0000 1.04433 0.522167 0.852843i $$-0.325124\pi$$
0.522167 + 0.852843i $$0.325124\pi$$
$$332$$ 0 0
$$333$$ 2.00000 0.109599
$$334$$ 0 0
$$335$$ 24.5967i 1.34386i
$$336$$ 0 0
$$337$$ 16.9706i 0.924445i 0.886764 + 0.462223i $$0.152948\pi$$
−0.886764 + 0.462223i $$0.847052\pi$$
$$338$$ 0 0
$$339$$ 6.70820i 0.364340i
$$340$$ 0 0
$$341$$ −9.48683 + 20.1246i −0.513741 + 1.08981i
$$342$$ 0 0
$$343$$ −17.3925 + 6.36396i −0.939108 + 0.343622i
$$344$$ 0 0
$$345$$ −15.0000 −0.807573
$$346$$ 0 0
$$347$$ 1.41421i 0.0759190i −0.999279 0.0379595i $$-0.987914\pi$$
0.999279 0.0379595i $$-0.0120858\pi$$
$$348$$ 0 0
$$349$$ −12.6491 −0.677091 −0.338546 0.940950i $$-0.609935\pi$$
−0.338546 + 0.940950i $$0.609935\pi$$
$$350$$ 0 0
$$351$$ 14.1421i 0.754851i
$$352$$ 0 0
$$353$$ 15.6525i 0.833097i −0.909113 0.416549i $$-0.863240\pi$$
0.909113 0.416549i $$-0.136760\pi$$
$$354$$ 0 0
$$355$$ 20.1246i 1.06810i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 5.65685i 0.298557i −0.988795 0.149279i $$-0.952305\pi$$
0.988795 0.149279i $$-0.0476951\pi$$
$$360$$ 0 0
$$361$$ −9.00000 −0.473684
$$362$$ 0 0
$$363$$ 18.9737 15.6525i 0.995859 0.821542i
$$364$$ 0 0
$$365$$ 7.07107i 0.370117i
$$366$$ 0 0
$$367$$ 33.5410i 1.75083i 0.483375 + 0.875413i $$0.339411\pi$$
−0.483375 + 0.875413i $$0.660589\pi$$
$$368$$ 0 0
$$369$$ 18.9737 0.987730
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 4.24264i 0.219676i 0.993950 + 0.109838i $$0.0350331\pi$$
−0.993950 + 0.109838i $$0.964967\pi$$
$$374$$ 0 0
$$375$$ −25.0000 −1.29099
$$376$$ 0 0
$$377$$ 8.94427i 0.460653i
$$378$$ 0 0
$$379$$ −17.0000 −0.873231 −0.436616 0.899648i $$-0.643823\pi$$
−0.436616 + 0.899648i $$0.643823\pi$$
$$380$$ 0 0
$$381$$ −28.4605 −1.45808
$$382$$ 0 0
$$383$$ 24.5967i 1.25684i −0.777876 0.628418i $$-0.783703\pi$$
0.777876 0.628418i $$-0.216297\pi$$
$$384$$ 0 0
$$385$$ 19.2302 3.89840i 0.980064 0.198681i
$$386$$ 0 0
$$387$$ 8.48528i 0.431331i
$$388$$ 0 0
$$389$$ 3.00000 0.152106 0.0760530 0.997104i $$-0.475768\pi$$
0.0760530 + 0.997104i $$0.475768\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 42.4264i 2.14013i
$$394$$ 0 0
$$395$$ −18.9737 −0.954669
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 15.0000 11.1803i 0.750939 0.559717i
$$400$$ 0 0
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ 0 0
$$403$$ 42.4264i 2.11341i
$$404$$ 0 0
$$405$$ 24.5967i 1.22222i
$$406$$ 0 0
$$407$$ −3.00000 1.41421i −0.148704 0.0701000i
$$408$$ 0 0
$$409$$ −12.6491 −0.625458 −0.312729 0.949842i $$-0.601243\pi$$
−0.312729 + 0.949842i $$0.601243\pi$$
$$410$$ 0 0
$$411$$ 33.5410i 1.65446i
$$412$$ 0 0
$$413$$ −4.74342 + 3.53553i −0.233408 + 0.173972i
$$414$$ 0 0
$$415$$ 21.2132i 1.04132i
$$416$$ 0 0
$$417$$ 28.2843i 1.38509i
$$418$$ 0 0
$$419$$ 22.3607i 1.09239i 0.837658 + 0.546195i $$0.183924\pi$$
−0.837658 + 0.546195i $$0.816076\pi$$
$$420$$ 0 0
$$421$$ −4.00000 −0.194948 −0.0974740 0.995238i $$-0.531076\pi$$
−0.0974740 + 0.995238i $$0.531076\pi$$
$$422$$ 0 0
$$423$$ 8.94427i 0.434885i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −5.00000 6.70820i −0.241967 0.324633i
$$428$$ 0 0
$$429$$ 20.0000 42.4264i 0.965609 2.04837i
$$430$$ 0 0
$$431$$ 35.3553i 1.70301i −0.524349 0.851503i $$-0.675691\pi$$
0.524349 0.851503i $$-0.324309\pi$$
$$432$$ 0 0
$$433$$ 20.1246i 0.967127i 0.875309 + 0.483564i $$0.160658\pi$$
−0.875309 + 0.483564i $$0.839342\pi$$
$$434$$ 0 0
$$435$$ 7.07107i 0.339032i
$$436$$ 0 0
$$437$$ 9.48683 0.453817
$$438$$ 0 0
$$439$$ −15.8114 −0.754636 −0.377318 0.926084i $$-0.623154\pi$$
−0.377318 + 0.926084i $$0.623154\pi$$
$$440$$ 0 0
$$441$$ 4.00000 13.4164i 0.190476 0.638877i
$$442$$ 0 0
$$443$$ 15.0000 0.712672 0.356336 0.934358i $$-0.384026\pi$$
0.356336 + 0.934358i $$0.384026\pi$$
$$444$$ 0 0
$$445$$ −5.00000 −0.237023
$$446$$ 0 0
$$447$$ −44.2719 −2.09399
$$448$$ 0 0
$$449$$ −27.0000 −1.27421 −0.637104 0.770778i $$-0.719868\pi$$
−0.637104 + 0.770778i $$0.719868\pi$$
$$450$$ 0 0
$$451$$ −28.4605 13.4164i −1.34015 0.631754i
$$452$$ 0 0
$$453$$ 37.9473 1.78292
$$454$$ 0 0
$$455$$ 30.0000 22.3607i 1.40642 1.04828i
$$456$$ 0 0
$$457$$ 8.48528i 0.396925i 0.980109 + 0.198462i $$0.0635948\pi$$
−0.980109 + 0.198462i $$0.936405\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 9.48683 0.441846 0.220923 0.975291i $$-0.429093\pi$$
0.220923 + 0.975291i $$0.429093\pi$$
$$462$$ 0 0
$$463$$ 25.0000 1.16185 0.580924 0.813958i $$-0.302691\pi$$
0.580924 + 0.813958i $$0.302691\pi$$
$$464$$ 0 0
$$465$$ 33.5410i 1.55543i
$$466$$ 0 0
$$467$$ 11.1803i 0.517364i −0.965962 0.258682i $$-0.916712\pi$$
0.965962 0.258682i $$-0.0832882\pi$$
$$468$$ 0 0
$$469$$ −17.3925 23.3345i −0.803112 1.07749i
$$470$$ 0 0
$$471$$ −15.0000 −0.691164
$$472$$ 0 0
$$473$$ −6.00000 + 12.7279i −0.275880 + 0.585230i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 18.9737 0.866929 0.433464 0.901171i $$-0.357291\pi$$
0.433464 + 0.901171i $$0.357291\pi$$
$$480$$ 0 0
$$481$$ −6.32456 −0.288375
$$482$$ 0 0
$$483$$ 14.2302 10.6066i 0.647499 0.482617i
$$484$$ 0 0
$$485$$ 15.0000 0.681115
$$486$$ 0 0
$$487$$ −29.0000 −1.31412 −0.657058 0.753840i $$-0.728199\pi$$
−0.657058 + 0.753840i $$0.728199\pi$$
$$488$$ 0 0
$$489$$ 22.3607i 1.01118i
$$490$$ 0 0
$$491$$ 32.5269i 1.46792i 0.679193 + 0.733959i $$0.262330\pi$$
−0.679193 + 0.733959i $$0.737670\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −6.32456 + 13.4164i −0.284268 + 0.603023i
$$496$$ 0 0
$$497$$ −14.2302 19.0919i −0.638314 0.856388i
$$498$$ 0 0
$$499$$ 16.0000 0.716258 0.358129 0.933672i $$-0.383415\pi$$
0.358129 + 0.933672i $$0.383415\pi$$
$$500$$ 0 0
$$501$$ 21.2132i 0.947736i
$$502$$ 0 0
$$503$$ 28.4605 1.26899 0.634495 0.772927i $$-0.281208\pi$$
0.634495 + 0.772927i $$0.281208\pi$$
$$504$$ 0 0
$$505$$ 21.2132i 0.943975i
$$506$$ 0 0
$$507$$ 60.3738i 2.68130i
$$508$$ 0 0
$$509$$ 15.6525i 0.693784i −0.937905 0.346892i $$-0.887237\pi$$
0.937905 0.346892i $$-0.112763\pi$$
$$510$$ 0 0
$$511$$ −5.00000 6.70820i −0.221187 0.296753i
$$512$$ 0 0
$$513$$ 7.07107i 0.312195i
$$514$$ 0 0
$$515$$ −30.0000 −1.32196
$$516$$ 0 0
$$517$$ 6.32456 13.4164i 0.278154 0.590053i
$$518$$ 0 0
$$519$$ 21.2132i 0.931156i
$$520$$ 0 0
$$521$$ 11.1803i 0.489820i 0.969546 + 0.244910i $$0.0787583\pi$$
−0.969546 + 0.244910i $$0.921242\pi$$
$$522$$ 0 0
$$523$$ 31.6228 1.38277 0.691384 0.722488i $$-0.257001\pi$$
0.691384 + 0.722488i $$0.257001\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ 4.47214i 0.194074i
$$532$$ 0 0
$$533$$ −60.0000 −2.59889
$$534$$ 0 0
$$535$$ 6.32456 0.273434
$$536$$ 0 0
$$537$$ 20.1246i 0.868441i
$$538$$ 0 0
$$539$$ −15.4868 + 17.2962i −0.667065 + 0.744999i
$$540$$ 0 0
$$541$$ 25.4558i 1.09443i −0.836991 0.547216i $$-0.815688\pi$$
0.836991 0.547216i $$-0.184312\pi$$
$$542$$ 0 0
$$543$$ −45.0000 −1.93113
$$544$$ 0 0
$$545$$ 28.4605 1.21911
$$546$$ 0 0
$$547$$ 8.48528i 0.362804i −0.983409 0.181402i $$-0.941936\pi$$
0.983409 0.181402i $$-0.0580636\pi$$
$$548$$ 0 0
$$549$$ 6.32456 0.269925
$$550$$ 0 0
$$551$$ 4.47214i 0.190519i
$$552$$ 0 0
$$553$$ 18.0000 13.4164i 0.765438 0.570524i
$$554$$ 0 0
$$555$$ 5.00000 0.212238
$$556$$ 0 0
$$557$$ 22.6274i 0.958754i 0.877609 + 0.479377i $$0.159137\pi$$
−0.877609 + 0.479377i $$0.840863\pi$$
$$558$$ 0 0
$$559$$ 26.8328i 1.13491i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 37.9473 1.59929 0.799645 0.600473i $$-0.205021\pi$$
0.799645 + 0.600473i $$0.205021\pi$$
$$564$$ 0 0
$$565$$ 6.70820i 0.282216i
$$566$$ 0 0
$$567$$ −17.3925 23.3345i −0.730417 0.979958i
$$568$$ 0 0
$$569$$ 15.5563i 0.652156i −0.945343 0.326078i $$-0.894273\pi$$
0.945343 0.326078i $$-0.105727\pi$$
$$570$$ 0 0
$$571$$ 16.9706i 0.710196i −0.934829 0.355098i $$-0.884448\pi$$
0.934829 0.355098i $$-0.115552\pi$$
$$572$$ 0 0
$$573$$ 6.70820i 0.280239i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 20.1246i 0.837799i 0.908033 + 0.418899i $$0.137584\pi$$
−0.908033 + 0.418899i $$0.862416\pi$$
$$578$$ 0 0
$$579$$ 9.48683 0.394259
$$580$$ 0 0
$$581$$ −15.0000 20.1246i −0.622305 0.834910i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 28.2843i 1.16941i
$$586$$ 0 0
$$587$$ 4.47214i 0.184585i −0.995732 0.0922924i $$-0.970581\pi$$
0.995732 0.0922924i $$-0.0294195\pi$$
$$588$$ 0 0
$$589$$ 21.2132i 0.874075i
$$590$$ 0 0
$$591$$ 12.6491 0.520315
$$592$$ 0 0
$$593$$ −28.4605 −1.16873 −0.584366 0.811490i $$-0.698657\pi$$
−0.584366 + 0.811490i $$0.698657\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 0 0
$$601$$ 15.8114 0.644960 0.322480 0.946576i $$-0.395483\pi$$
0.322480 + 0.946576i $$0.395483\pi$$
$$602$$ 0 0
$$603$$ 22.0000 0.895909
$$604$$ 0 0
$$605$$ 18.9737 15.6525i 0.771389 0.636364i
$$606$$ 0 0
$$607$$ −6.32456 −0.256706 −0.128353 0.991729i $$-0.540969\pi$$
−0.128353 + 0.991729i $$0.540969\pi$$
$$608$$ 0 0
$$609$$ 5.00000 + 6.70820i 0.202610 + 0.271830i
$$610$$ 0 0
$$611$$ 28.2843i 1.14426i
$$612$$ 0 0
$$613$$ 25.4558i 1.02815i 0.857745 + 0.514076i $$0.171865\pi$$
−0.857745 + 0.514076i $$0.828135\pi$$
$$614$$ 0 0
$$615$$ 47.4342 1.91273
$$616$$ 0 0
$$617$$ 24.0000 0.966204 0.483102 0.875564i $$-0.339510\pi$$
0.483102 + 0.875564i $$0.339510\pi$$
$$618$$ 0 0
$$619$$ 46.9574i 1.88738i −0.330833 0.943689i $$-0.607330\pi$$
0.330833 0.943689i $$-0.392670\pi$$
$$620$$ 0 0
$$621$$ 6.70820i 0.269191i
$$622$$ 0 0
$$623$$ 4.74342 3.53553i 0.190041 0.141648i
$$624$$ 0 0
$$625$$ −25.0000 −1.00000
$$626$$ 0 0
$$627$$ 10.0000 21.2132i 0.399362 0.847174i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −11.0000 −0.437903 −0.218952 0.975736i $$-0.570264\pi$$
−0.218952 + 0.975736i $$0.570264\pi$$
$$632$$ 0 0
$$633$$ 47.4342 1.88534
$$634$$ 0 0
$$635$$ −28.4605 −1.12942
$$636$$ 0 0
$$637$$ −12.6491 + 42.4264i −0.501176 + 1.68100i
$$638$$ 0 0
$$639$$ 18.0000 0.712069
$$640$$ 0 0
$$641$$ 21.0000 0.829450 0.414725 0.909947i $$-0.363878\pi$$
0.414725 + 0.909947i $$0.363878\pi$$
$$642$$ 0 0
$$643$$ 6.70820i 0.264546i 0.991213 + 0.132273i $$0.0422275\pi$$
−0.991213 + 0.132273i $$0.957772\pi$$
$$644$$ 0 0
$$645$$ 21.2132i 0.835269i
$$646$$ 0 0
$$647$$ 29.0689i 1.14282i 0.820666 + 0.571408i $$0.193603\pi$$
−0.820666 + 0.571408i $$0.806397\pi$$
$$648$$ 0 0
$$649$$ −3.16228 + 6.70820i −0.124130 + 0.263320i
$$650$$ 0 0
$$651$$ 23.7171 + 31.8198i 0.929546 + 1.24712i
$$652$$ 0 0
$$653$$ 15.0000 0.586995 0.293498 0.955960i $$-0.405181\pi$$
0.293498 + 0.955960i $$0.405181\pi$$
$$654$$ 0 0
$$655$$ 42.4264i 1.65774i
$$656$$ 0 0
$$657$$ 6.32456 0.246744
$$658$$ 0 0
$$659$$ 14.1421i 0.550899i −0.961315 0.275450i $$-0.911173\pi$$
0.961315 0.275450i $$-0.0888267\pi$$
$$660$$ 0 0
$$661$$ 46.9574i 1.82643i −0.407476 0.913216i $$-0.633591\pi$$
0.407476 0.913216i $$-0.366409\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 15.0000 11.1803i 0.581675 0.433555i
$$666$$ 0 0
$$667$$ 4.24264i 0.164276i
$$668$$ 0 0
$$669$$ −15.0000 −0.579934
$$670$$ 0 0
$$671$$ −9.48683 4.47214i −0.366235 0.172645i
$$672$$ 0 0
$$673$$ 29.6985i 1.14479i −0.819977 0.572396i $$-0.806014\pi$$
0.819977 0.572396i $$-0.193986\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 37.9473 1.45843 0.729217 0.684282i $$-0.239884\pi$$
0.729217 + 0.684282i $$0.239884\pi$$
$$678$$ 0 0
$$679$$ −14.2302 + 10.6066i −0.546107 + 0.407044i
$$680$$ 0 0
$$681$$ 21.2132i 0.812892i
$$682$$ 0 0
$$683$$ −18.0000 −0.688751 −0.344375 0.938832i $$-0.611909\pi$$
−0.344375 + 0.938832i $$0.611909\pi$$
$$684$$ 0 0
$$685$$ 33.5410i 1.28154i
$$686$$ 0 0
$$687$$ −15.0000 −0.572286
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 6.70820i 0.255192i −0.991826 0.127596i $$-0.959274\pi$$
0.991826 0.127596i $$-0.0407261\pi$$
$$692$$ 0 0
$$693$$ −3.48683 17.2001i −0.132454 0.653376i
$$694$$ 0 0
$$695$$ 28.2843i 1.07288i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 41.1096 1.55491
$$700$$ 0 0
$$701$$ 7.07107i 0.267071i −0.991044 0.133535i $$-0.957367\pi$$
0.991044 0.133535i $$-0.0426329\pi$$
$$702$$ 0 0
$$703$$ −3.16228 −0.119268
$$704$$ 0 0
$$705$$ 22.3607i 0.842152i
$$706$$ 0 0
$$707$$ 15.0000 + 20.1246i 0.564133 + 0.756864i
$$708$$ 0 0
$$709$$ 41.0000 1.53979 0.769894 0.638172i $$-0.220309\pi$$
0.769894 + 0.638172i $$0.220309\pi$$
$$710$$ 0 0
$$711$$ 16.9706i 0.636446i
$$712$$ 0 0
$$713$$ 20.1246i 0.753673i
$$714$$ 0 0
$$715$$ 20.0000 42.4264i 0.747958 1.58666i
$$716$$ 0 0
$$717$$ 15.8114 0.590487
$$718$$ 0 0
$$719$$ 51.4296i 1.91800i −0.283408 0.959000i $$-0.591465\pi$$
0.283408 0.959000i $$-0.408535\pi$$
$$720$$ 0 0
$$721$$ 28.4605 21.2132i 1.05992 0.790021i
$$722$$ 0 0
$$723$$ 28.2843i 1.05190i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 33.5410i 1.24397i 0.783030 + 0.621984i $$0.213673\pi$$
−0.783030 + 0.621984i $$0.786327\pi$$
$$728$$ 0 0
$$729$$ 7.00000 0.259259
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −12.6491 −0.467206 −0.233603 0.972332i $$-0.575052\pi$$
−0.233603 + 0.972332i $$0.575052\pi$$
$$734$$ 0 0
$$735$$ 10.0000 33.5410i 0.368856 1.23718i
$$736$$ 0 0
$$737$$ −33.0000 15.5563i −1.21557 0.573025i
$$738$$ 0 0
$$739$$ 50.9117i 1.87282i −0.350912 0.936408i $$-0.614128\pi$$
0.350912 0.936408i $$-0.385872\pi$$
$$740$$ 0 0
$$741$$ 44.7214i 1.64288i
$$742$$ 0 0
$$743$$ 19.7990i 0.726354i 0.931720 + 0.363177i $$0.118308\pi$$
−0.931720 + 0.363177i $$0.881692\pi$$
$$744$$ 0 0
$$745$$ −44.2719 −1.62200
$$746$$ 0 0
$$747$$ 18.9737 0.694210
$$748$$ 0 0
$$749$$ −6.00000 + 4.47214i −0.219235 + 0.163408i
$$750$$ 0 0
$$751$$ 7.00000 0.255434 0.127717 0.991811i $$-0.459235\pi$$
0.127717 + 0.991811i $$0.459235\pi$$
$$752$$ 0 0
$$753$$ −25.0000 −0.911051
$$754$$ 0 0
$$755$$ 37.9473 1.38104
$$756$$ 0 0
$$757$$ 44.0000 1.59921 0.799604 0.600528i $$-0.205043\pi$$
0.799604 + 0.600528i $$0.205043\pi$$
$$758$$ 0 0
$$759$$ 9.48683 20.1246i 0.344350 0.730477i
$$760$$ 0 0
$$761$$ −37.9473 −1.37559 −0.687795 0.725905i $$-0.741421\pi$$
−0.687795 + 0.725905i $$0.741421\pi$$
$$762$$ 0 0
$$763$$ −27.0000 + 20.1246i −0.977466 + 0.728560i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 14.1421i 0.510643i
$$768$$ 0 0
$$769$$ 6.32456 0.228069 0.114035 0.993477i $$-0.463623\pi$$
0.114035 + 0.993477i $$0.463623\pi$$
$$770$$ 0 0
$$771$$ −50.0000 −1.80071
$$772$$ 0 0
$$773$$ 8.94427i 0.321703i −0.986979 0.160852i $$-0.948576\pi$$
0.986979 0.160852i $$-0.0514240\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −4.74342 + 3.53553i −0.170169 + 0.126837i
$$778$$ 0 0
$$779$$ −30.0000 −1.07486
$$780$$ 0 0
$$781$$ −27.0000 12.7279i −0.966136 0.455441i
$$782$$ 0 0
$$783$$ 3.16228 0.113011
$$784$$ 0 0
$$785$$ −15.0000 −0.535373
$$786$$ 0 0
$$787$$ 22.1359 0.789061 0.394531 0.918883i $$-0.370907\pi$$
0.394531 + 0.918883i $$0.370907\pi$$
$$788$$ 0 0
$$789$$ 25.2982 0.900641
$$790$$ 0 0
$$791$$ −4.74342 6.36396i −0.168656 0.226276i
$$792$$ 0 0
$$793$$ −20.0000 −0.710221
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 38.0132i 1.34650i 0.739417 + 0.673248i $$0.235101\pi$$
−0.739417 + 0.673248i $$0.764899\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 4.47214i 0.158015i