# Properties

 Label 1840.2.m.g.1839.4 Level $1840$ Weight $2$ Character 1840.1839 Analytic conductor $14.692$ Analytic rank $0$ Dimension $40$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.m (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.6924739719$$ Analytic rank: $$0$$ Dimension: $$40$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1839.4 Character $$\chi$$ $$=$$ 1840.1839 Dual form 1840.2.m.g.1839.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.28652 q^{3} +(1.54120 - 1.62009i) q^{5} -2.73174i q^{7} +7.80121 q^{9} +O(q^{10})$$ $$q-3.28652 q^{3} +(1.54120 - 1.62009i) q^{5} -2.73174i q^{7} +7.80121 q^{9} -2.28639 q^{11} +4.92586i q^{13} +(-5.06519 + 5.32446i) q^{15} -5.97341 q^{17} +0.377877 q^{19} +8.97791i q^{21} +(-0.582385 + 4.76034i) q^{23} +(-0.249397 - 4.99378i) q^{25} -15.7793 q^{27} +3.70400 q^{29} -2.89324i q^{31} +7.51426 q^{33} +(-4.42567 - 4.21016i) q^{35} -7.23320 q^{37} -16.1889i q^{39} +0.451624 q^{41} +0.359476i q^{43} +(12.0232 - 12.6387i) q^{45} +12.1733 q^{47} -0.462395 q^{49} +19.6317 q^{51} -9.69298 q^{53} +(-3.52378 + 3.70416i) q^{55} -1.24190 q^{57} +10.7427i q^{59} +6.73249i q^{61} -21.3109i q^{63} +(7.98034 + 7.59174i) q^{65} -7.06480i q^{67} +(1.91402 - 15.6449i) q^{69} +7.34667i q^{71} -1.24543i q^{73} +(0.819647 + 16.4121i) q^{75} +6.24581i q^{77} -13.6417 q^{79} +28.4553 q^{81} +15.1841i q^{83} +(-9.20623 + 9.67748i) q^{85} -12.1733 q^{87} -12.1526i q^{89} +13.4562 q^{91} +9.50868i q^{93} +(0.582385 - 0.612196i) q^{95} +4.34220 q^{97} -17.8366 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$40q + 80q^{9} + O(q^{10})$$ $$40q + 80q^{9} - 24q^{25} + 24q^{41} - 16q^{49} + 80q^{69} + 40q^{81} - 8q^{85} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times$$.

 $$n$$ $$737$$ $$1151$$ $$1201$$ $$1381$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$ $$1$$

## 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
$$3$$ −3.28652 −1.89747 −0.948737 0.316068i $$-0.897637\pi$$
−0.948737 + 0.316068i $$0.897637\pi$$
$$4$$ 0 0
$$5$$ 1.54120 1.62009i 0.689246 0.724527i
$$6$$ 0 0
$$7$$ 2.73174i 1.03250i −0.856438 0.516250i $$-0.827328\pi$$
0.856438 0.516250i $$-0.172672\pi$$
$$8$$ 0 0
$$9$$ 7.80121 2.60040
$$10$$ 0 0
$$11$$ −2.28639 −0.689372 −0.344686 0.938718i $$-0.612015\pi$$
−0.344686 + 0.938718i $$0.612015\pi$$
$$12$$ 0 0
$$13$$ 4.92586i 1.36619i 0.730331 + 0.683094i $$0.239366\pi$$
−0.730331 + 0.683094i $$0.760634\pi$$
$$14$$ 0 0
$$15$$ −5.06519 + 5.32446i −1.30783 + 1.37477i
$$16$$ 0 0
$$17$$ −5.97341 −1.44876 −0.724382 0.689398i $$-0.757875\pi$$
−0.724382 + 0.689398i $$0.757875\pi$$
$$18$$ 0 0
$$19$$ 0.377877 0.0866910 0.0433455 0.999060i $$-0.486198\pi$$
0.0433455 + 0.999060i $$0.486198\pi$$
$$20$$ 0 0
$$21$$ 8.97791i 1.95914i
$$22$$ 0 0
$$23$$ −0.582385 + 4.76034i −0.121436 + 0.992599i
$$24$$ 0 0
$$25$$ −0.249397 4.99378i −0.0498794 0.998755i
$$26$$ 0 0
$$27$$ −15.7793 −3.03672
$$28$$ 0 0
$$29$$ 3.70400 0.687815 0.343907 0.939004i $$-0.388249\pi$$
0.343907 + 0.939004i $$0.388249\pi$$
$$30$$ 0 0
$$31$$ 2.89324i 0.519641i −0.965657 0.259820i $$-0.916337\pi$$
0.965657 0.259820i $$-0.0836634\pi$$
$$32$$ 0 0
$$33$$ 7.51426 1.30806
$$34$$ 0 0
$$35$$ −4.42567 4.21016i −0.748074 0.711647i
$$36$$ 0 0
$$37$$ −7.23320 −1.18913 −0.594566 0.804047i $$-0.702676\pi$$
−0.594566 + 0.804047i $$0.702676\pi$$
$$38$$ 0 0
$$39$$ 16.1889i 2.59230i
$$40$$ 0 0
$$41$$ 0.451624 0.0705318 0.0352659 0.999378i $$-0.488772\pi$$
0.0352659 + 0.999378i $$0.488772\pi$$
$$42$$ 0 0
$$43$$ 0.359476i 0.0548196i 0.999624 + 0.0274098i $$0.00872591\pi$$
−0.999624 + 0.0274098i $$0.991274\pi$$
$$44$$ 0 0
$$45$$ 12.0232 12.6387i 1.79232 1.88406i
$$46$$ 0 0
$$47$$ 12.1733 1.77565 0.887826 0.460179i $$-0.152215\pi$$
0.887826 + 0.460179i $$0.152215\pi$$
$$48$$ 0 0
$$49$$ −0.462395 −0.0660565
$$50$$ 0 0
$$51$$ 19.6317 2.74899
$$52$$ 0 0
$$53$$ −9.69298 −1.33143 −0.665716 0.746205i $$-0.731874\pi$$
−0.665716 + 0.746205i $$0.731874\pi$$
$$54$$ 0 0
$$55$$ −3.52378 + 3.70416i −0.475147 + 0.499468i
$$56$$ 0 0
$$57$$ −1.24190 −0.164494
$$58$$ 0 0
$$59$$ 10.7427i 1.39858i 0.714838 + 0.699290i $$0.246500\pi$$
−0.714838 + 0.699290i $$0.753500\pi$$
$$60$$ 0 0
$$61$$ 6.73249i 0.862007i 0.902350 + 0.431003i $$0.141840\pi$$
−0.902350 + 0.431003i $$0.858160\pi$$
$$62$$ 0 0
$$63$$ 21.3109i 2.68492i
$$64$$ 0 0
$$65$$ 7.98034 + 7.59174i 0.989840 + 0.941639i
$$66$$ 0 0
$$67$$ 7.06480i 0.863103i −0.902088 0.431551i $$-0.857966\pi$$
0.902088 0.431551i $$-0.142034\pi$$
$$68$$ 0 0
$$69$$ 1.91402 15.6449i 0.230421 1.88343i
$$70$$ 0 0
$$71$$ 7.34667i 0.871889i 0.899974 + 0.435945i $$0.143586\pi$$
−0.899974 + 0.435945i $$0.856414\pi$$
$$72$$ 0 0
$$73$$ 1.24543i 0.145767i −0.997340 0.0728834i $$-0.976780\pi$$
0.997340 0.0728834i $$-0.0232201\pi$$
$$74$$ 0 0
$$75$$ 0.819647 + 16.4121i 0.0946447 + 1.89511i
$$76$$ 0 0
$$77$$ 6.24581i 0.711776i
$$78$$ 0 0
$$79$$ −13.6417 −1.53481 −0.767405 0.641163i $$-0.778452\pi$$
−0.767405 + 0.641163i $$0.778452\pi$$
$$80$$ 0 0
$$81$$ 28.4553 3.16170
$$82$$ 0 0
$$83$$ 15.1841i 1.66667i 0.552768 + 0.833335i $$0.313571\pi$$
−0.552768 + 0.833335i $$0.686429\pi$$
$$84$$ 0 0
$$85$$ −9.20623 + 9.67748i −0.998556 + 1.04967i
$$86$$ 0 0
$$87$$ −12.1733 −1.30511
$$88$$ 0 0
$$89$$ 12.1526i 1.28818i −0.764951 0.644089i $$-0.777237\pi$$
0.764951 0.644089i $$-0.222763\pi$$
$$90$$ 0 0
$$91$$ 13.4562 1.41059
$$92$$ 0 0
$$93$$ 9.50868i 0.986004i
$$94$$ 0 0
$$95$$ 0.582385 0.612196i 0.0597514 0.0628100i
$$96$$ 0 0
$$97$$ 4.34220 0.440883 0.220442 0.975400i $$-0.429250\pi$$
0.220442 + 0.975400i $$0.429250\pi$$
$$98$$ 0 0
$$99$$ −17.8366 −1.79264
$$100$$ 0 0
$$101$$ 3.11922 0.310374 0.155187 0.987885i $$-0.450402\pi$$
0.155187 + 0.987885i $$0.450402\pi$$
$$102$$ 0 0
$$103$$ 3.38893i 0.333921i 0.985964 + 0.166960i $$0.0533952\pi$$
−0.985964 + 0.166960i $$0.946605\pi$$
$$104$$ 0 0
$$105$$ 14.5450 + 13.8368i 1.41945 + 1.35033i
$$106$$ 0 0
$$107$$ 7.94818i 0.768380i 0.923254 + 0.384190i $$0.125519\pi$$
−0.923254 + 0.384190i $$0.874481\pi$$
$$108$$ 0 0
$$109$$ 14.1195i 1.35240i 0.736718 + 0.676200i $$0.236375\pi$$
−0.736718 + 0.676200i $$0.763625\pi$$
$$110$$ 0 0
$$111$$ 23.7721 2.25634
$$112$$ 0 0
$$113$$ 0.322974 0.0303828 0.0151914 0.999885i $$-0.495164\pi$$
0.0151914 + 0.999885i $$0.495164\pi$$
$$114$$ 0 0
$$115$$ 6.81462 + 8.28016i 0.635466 + 0.772129i
$$116$$ 0 0
$$117$$ 38.4277i 3.55264i
$$118$$ 0 0
$$119$$ 16.3178i 1.49585i
$$120$$ 0 0
$$121$$ −5.77244 −0.524767
$$122$$ 0 0
$$123$$ −1.48427 −0.133832
$$124$$ 0 0
$$125$$ −8.47475 7.29237i −0.758005 0.652249i
$$126$$ 0 0
$$127$$ 10.5340 0.934738 0.467369 0.884062i $$-0.345202\pi$$
0.467369 + 0.884062i $$0.345202\pi$$
$$128$$ 0 0
$$129$$ 1.18143i 0.104019i
$$130$$ 0 0
$$131$$ 11.3581i 0.992362i 0.868219 + 0.496181i $$0.165265\pi$$
−0.868219 + 0.496181i $$0.834735\pi$$
$$132$$ 0 0
$$133$$ 1.03226i 0.0895084i
$$134$$ 0 0
$$135$$ −24.3190 + 25.5639i −2.09305 + 2.20019i
$$136$$ 0 0
$$137$$ 19.0252 1.62543 0.812716 0.582660i $$-0.197988\pi$$
0.812716 + 0.582660i $$0.197988\pi$$
$$138$$ 0 0
$$139$$ 9.12171i 0.773693i 0.922144 + 0.386847i $$0.126436\pi$$
−0.922144 + 0.386847i $$0.873564\pi$$
$$140$$ 0 0
$$141$$ −40.0076 −3.36925
$$142$$ 0 0
$$143$$ 11.2624i 0.941810i
$$144$$ 0 0
$$145$$ 5.70860 6.00081i 0.474074 0.498341i
$$146$$ 0 0
$$147$$ 1.51967 0.125340
$$148$$ 0 0
$$149$$ 5.95344i 0.487725i −0.969810 0.243863i $$-0.921585\pi$$
0.969810 0.243863i $$-0.0784146\pi$$
$$150$$ 0 0
$$151$$ 9.94683i 0.809462i 0.914436 + 0.404731i $$0.132635\pi$$
−0.914436 + 0.404731i $$0.867365\pi$$
$$152$$ 0 0
$$153$$ −46.5998 −3.76737
$$154$$ 0 0
$$155$$ −4.68731 4.45906i −0.376494 0.358160i
$$156$$ 0 0
$$157$$ 16.2147 1.29407 0.647036 0.762460i $$-0.276008\pi$$
0.647036 + 0.762460i $$0.276008\pi$$
$$158$$ 0 0
$$159$$ 31.8562 2.52636
$$160$$ 0 0
$$161$$ 13.0040 + 1.59092i 1.02486 + 0.125382i
$$162$$ 0 0
$$163$$ 14.1754 1.11030 0.555151 0.831750i $$-0.312661\pi$$
0.555151 + 0.831750i $$0.312661\pi$$
$$164$$ 0 0
$$165$$ 11.5810 12.1738i 0.901578 0.947728i
$$166$$ 0 0
$$167$$ 8.85134 0.684937 0.342468 0.939529i $$-0.388737\pi$$
0.342468 + 0.939529i $$0.388737\pi$$
$$168$$ 0 0
$$169$$ −11.2641 −0.866467
$$170$$ 0 0
$$171$$ 2.94790 0.225432
$$172$$ 0 0
$$173$$ 24.2863i 1.84645i 0.384260 + 0.923225i $$0.374457\pi$$
−0.384260 + 0.923225i $$0.625543\pi$$
$$174$$ 0 0
$$175$$ −13.6417 + 0.681287i −1.03121 + 0.0515004i
$$176$$ 0 0
$$177$$ 35.3061i 2.65377i
$$178$$ 0 0
$$179$$ 14.8358i 1.10888i −0.832223 0.554441i $$-0.812932\pi$$
0.832223 0.554441i $$-0.187068\pi$$
$$180$$ 0 0
$$181$$ 3.42685i 0.254716i 0.991857 + 0.127358i $$0.0406497\pi$$
−0.991857 + 0.127358i $$0.959350\pi$$
$$182$$ 0 0
$$183$$ 22.1265i 1.63563i
$$184$$ 0 0
$$185$$ −11.1478 + 11.7185i −0.819604 + 0.861558i
$$186$$ 0 0
$$187$$ 13.6575 0.998737
$$188$$ 0 0
$$189$$ 43.1049i 3.13542i
$$190$$ 0 0
$$191$$ 9.37462 0.678324 0.339162 0.940728i $$-0.389857\pi$$
0.339162 + 0.940728i $$0.389857\pi$$
$$192$$ 0 0
$$193$$ 1.72975i 0.124510i 0.998060 + 0.0622550i $$0.0198292\pi$$
−0.998060 + 0.0622550i $$0.980171\pi$$
$$194$$ 0 0
$$195$$ −26.2276 24.9504i −1.87819 1.78673i
$$196$$ 0 0
$$197$$ 15.8158i 1.12683i −0.826174 0.563415i $$-0.809487\pi$$
0.826174 0.563415i $$-0.190513\pi$$
$$198$$ 0 0
$$199$$ −19.9550 −1.41458 −0.707288 0.706926i $$-0.750082\pi$$
−0.707288 + 0.706926i $$0.750082\pi$$
$$200$$ 0 0
$$201$$ 23.2186i 1.63771i
$$202$$ 0 0
$$203$$ 10.1183i 0.710169i
$$204$$ 0 0
$$205$$ 0.696043 0.731672i 0.0486138 0.0511022i
$$206$$ 0 0
$$207$$ −4.54331 + 37.1364i −0.315782 + 2.58116i
$$208$$ 0 0
$$209$$ −0.863973 −0.0597623
$$210$$ 0 0
$$211$$ 19.0013i 1.30810i −0.756449 0.654052i $$-0.773068\pi$$
0.756449 0.654052i $$-0.226932\pi$$
$$212$$ 0 0
$$213$$ 24.1450i 1.65439i
$$214$$ 0 0
$$215$$ 0.582385 + 0.554025i 0.0397183 + 0.0377842i
$$216$$ 0 0
$$217$$ −7.90357 −0.536529
$$218$$ 0 0
$$219$$ 4.09314i 0.276588i
$$220$$ 0 0
$$221$$ 29.4242i 1.97928i
$$222$$ 0 0
$$223$$ −1.87457 −0.125531 −0.0627653 0.998028i $$-0.519992\pi$$
−0.0627653 + 0.998028i $$0.519992\pi$$
$$224$$ 0 0
$$225$$ −1.94560 38.9575i −0.129706 2.59717i
$$226$$ 0 0
$$227$$ 5.18877i 0.344391i −0.985063 0.172195i $$-0.944914\pi$$
0.985063 0.172195i $$-0.0550860\pi$$
$$228$$ 0 0
$$229$$ 15.8023i 1.04425i 0.852870 + 0.522124i $$0.174860\pi$$
−0.852870 + 0.522124i $$0.825140\pi$$
$$230$$ 0 0
$$231$$ 20.5270i 1.35058i
$$232$$ 0 0
$$233$$ 14.6477i 0.959603i 0.877377 + 0.479802i $$0.159291\pi$$
−0.877377 + 0.479802i $$0.840709\pi$$
$$234$$ 0 0
$$235$$ 18.7614 19.7218i 1.22386 1.28651i
$$236$$ 0 0
$$237$$ 44.8337 2.91226
$$238$$ 0 0
$$239$$ 9.60182i 0.621090i 0.950559 + 0.310545i $$0.100512\pi$$
−0.950559 + 0.310545i $$0.899488\pi$$
$$240$$ 0 0
$$241$$ 18.8553i 1.21458i 0.794481 + 0.607289i $$0.207743\pi$$
−0.794481 + 0.607289i $$0.792257\pi$$
$$242$$ 0 0
$$243$$ −46.1810 −2.96251
$$244$$ 0 0
$$245$$ −0.712644 + 0.749123i −0.0455292 + 0.0478597i
$$246$$ 0 0
$$247$$ 1.86137i 0.118436i
$$248$$ 0 0
$$249$$ 49.9028i 3.16246i
$$250$$ 0 0
$$251$$ 24.9057 1.57203 0.786017 0.618205i $$-0.212140\pi$$
0.786017 + 0.618205i $$0.212140\pi$$
$$252$$ 0 0
$$253$$ 1.33156 10.8840i 0.0837143 0.684270i
$$254$$ 0 0
$$255$$ 30.2565 31.8052i 1.89473 1.99172i
$$256$$ 0 0
$$257$$ 16.5764i 1.03401i 0.855983 + 0.517004i $$0.172953\pi$$
−0.855983 + 0.517004i $$0.827047\pi$$
$$258$$ 0 0
$$259$$ 19.7592i 1.22778i
$$260$$ 0 0
$$261$$ 28.8957 1.78860
$$262$$ 0 0
$$263$$ 17.7754i 1.09608i −0.836453 0.548039i $$-0.815374\pi$$
0.836453 0.548039i $$-0.184626\pi$$
$$264$$ 0 0
$$265$$ −14.9388 + 15.7035i −0.917685 + 0.964659i
$$266$$ 0 0
$$267$$ 39.9399i 2.44428i
$$268$$ 0 0
$$269$$ −18.2884 −1.11506 −0.557532 0.830155i $$-0.688252\pi$$
−0.557532 + 0.830155i $$0.688252\pi$$
$$270$$ 0 0
$$271$$ 8.44481i 0.512986i 0.966546 + 0.256493i $$0.0825670\pi$$
−0.966546 + 0.256493i $$0.917433\pi$$
$$272$$ 0 0
$$273$$ −44.2239 −2.67655
$$274$$ 0 0
$$275$$ 0.570218 + 11.4177i 0.0343854 + 0.688513i
$$276$$ 0 0
$$277$$ 27.9612i 1.68003i −0.542565 0.840014i $$-0.682547\pi$$
0.542565 0.840014i $$-0.317453\pi$$
$$278$$ 0 0
$$279$$ 22.5708i 1.35128i
$$280$$ 0 0
$$281$$ 28.3900i 1.69360i 0.531909 + 0.846802i $$0.321475\pi$$
−0.531909 + 0.846802i $$0.678525\pi$$
$$282$$ 0 0
$$283$$ 9.11525i 0.541845i 0.962601 + 0.270923i $$0.0873288\pi$$
−0.962601 + 0.270923i $$0.912671\pi$$
$$284$$ 0 0
$$285$$ −1.91402 + 2.01199i −0.113377 + 0.119180i
$$286$$ 0 0
$$287$$ 1.23372i 0.0728241i
$$288$$ 0 0
$$289$$ 18.6816 1.09892
$$290$$ 0 0
$$291$$ −14.2707 −0.836564
$$292$$ 0 0
$$293$$ −5.14021 −0.300294 −0.150147 0.988664i $$-0.547975\pi$$
−0.150147 + 0.988664i $$0.547975\pi$$
$$294$$ 0 0
$$295$$ 17.4042 + 16.5567i 1.01331 + 0.963966i
$$296$$ 0 0
$$297$$ 36.0775 2.09343
$$298$$ 0 0
$$299$$ −23.4488 2.86874i −1.35608 0.165904i
$$300$$ 0 0
$$301$$ 0.981995 0.0566013
$$302$$ 0 0
$$303$$ −10.2514 −0.588927
$$304$$ 0 0
$$305$$ 10.9072 + 10.3761i 0.624547 + 0.594135i
$$306$$ 0 0
$$307$$ −16.0988 −0.918806 −0.459403 0.888228i $$-0.651937\pi$$
−0.459403 + 0.888228i $$0.651937\pi$$
$$308$$ 0 0
$$309$$ 11.1378i 0.633606i
$$310$$ 0 0
$$311$$ 13.6114i 0.771834i 0.922534 + 0.385917i $$0.126115\pi$$
−0.922534 + 0.385917i $$0.873885\pi$$
$$312$$ 0 0
$$313$$ 16.7024 0.944073 0.472037 0.881579i $$-0.343519\pi$$
0.472037 + 0.881579i $$0.343519\pi$$
$$314$$ 0 0
$$315$$ −34.5256 32.8443i −1.94530 1.85057i
$$316$$ 0 0
$$317$$ 24.1290i 1.35522i 0.735423 + 0.677609i $$0.236984\pi$$
−0.735423 + 0.677609i $$0.763016\pi$$
$$318$$ 0 0
$$319$$ −8.46877 −0.474160
$$320$$ 0 0
$$321$$ 26.1219i 1.45798i
$$322$$ 0 0
$$323$$ −2.25722 −0.125595
$$324$$ 0 0
$$325$$ 24.5986 1.22849i 1.36449 0.0681445i
$$326$$ 0 0
$$327$$ 46.4039i 2.56614i
$$328$$ 0 0
$$329$$ 33.2542i 1.83336i
$$330$$ 0 0
$$331$$ 9.49579i 0.521936i −0.965348 0.260968i $$-0.915958\pi$$
0.965348 0.260968i $$-0.0840416\pi$$
$$332$$ 0 0
$$333$$ −56.4278 −3.09222
$$334$$ 0 0
$$335$$ −11.4456 10.8883i −0.625341 0.594890i
$$336$$ 0 0
$$337$$ −9.95485 −0.542275 −0.271138 0.962541i $$-0.587400\pi$$
−0.271138 + 0.962541i $$0.587400\pi$$
$$338$$ 0 0
$$339$$ −1.06146 −0.0576506
$$340$$ 0 0
$$341$$ 6.61506i 0.358226i
$$342$$ 0 0
$$343$$ 17.8590i 0.964297i
$$344$$ 0 0
$$345$$ −22.3964 27.2129i −1.20578 1.46509i
$$346$$ 0 0
$$347$$ −28.5546 −1.53289 −0.766446 0.642309i $$-0.777977\pi$$
−0.766446 + 0.642309i $$0.777977\pi$$
$$348$$ 0 0
$$349$$ 11.7060 0.626610 0.313305 0.949652i $$-0.398564\pi$$
0.313305 + 0.949652i $$0.398564\pi$$
$$350$$ 0 0
$$351$$ 77.7265i 4.14873i
$$352$$ 0 0
$$353$$ 10.6128i 0.564864i −0.959287 0.282432i $$-0.908859\pi$$
0.959287 0.282432i $$-0.0911411\pi$$
$$354$$ 0 0
$$355$$ 11.9023 + 11.3227i 0.631707 + 0.600946i
$$356$$ 0 0
$$357$$ 53.6288i 2.83833i
$$358$$ 0 0
$$359$$ 16.7030 0.881548 0.440774 0.897618i $$-0.354704\pi$$
0.440774 + 0.897618i $$0.354704\pi$$
$$360$$ 0 0
$$361$$ −18.8572 −0.992485
$$362$$ 0 0
$$363$$ 18.9712 0.995731
$$364$$ 0 0
$$365$$ −2.01771 1.91946i −0.105612 0.100469i
$$366$$ 0 0
$$367$$ 1.96080i 0.102353i −0.998690 0.0511764i $$-0.983703\pi$$
0.998690 0.0511764i $$-0.0162971\pi$$
$$368$$ 0 0
$$369$$ 3.52321 0.183411
$$370$$ 0 0
$$371$$ 26.4787i 1.37470i
$$372$$ 0 0
$$373$$ −31.3228 −1.62183 −0.810916 0.585163i $$-0.801031\pi$$
−0.810916 + 0.585163i $$0.801031\pi$$
$$374$$ 0 0
$$375$$ 27.8524 + 23.9665i 1.43829 + 1.23763i
$$376$$ 0 0
$$377$$ 18.2454i 0.939684i
$$378$$ 0 0
$$379$$ −0.853853 −0.0438595 −0.0219297 0.999760i $$-0.506981\pi$$
−0.0219297 + 0.999760i $$0.506981\pi$$
$$380$$ 0 0
$$381$$ −34.6201 −1.77364
$$382$$ 0 0
$$383$$ 2.33128i 0.119123i −0.998225 0.0595614i $$-0.981030\pi$$
0.998225 0.0595614i $$-0.0189702\pi$$
$$384$$ 0 0
$$385$$ 10.1188 + 9.62605i 0.515701 + 0.490589i
$$386$$ 0 0
$$387$$ 2.80435i 0.142553i
$$388$$ 0 0
$$389$$ 10.4152i 0.528074i 0.964513 + 0.264037i $$0.0850541\pi$$
−0.964513 + 0.264037i $$0.914946\pi$$
$$390$$ 0 0
$$391$$ 3.47882 28.4355i 0.175932 1.43804i
$$392$$ 0 0
$$393$$ 37.3286i 1.88298i
$$394$$ 0 0
$$395$$ −21.0246 + 22.1008i −1.05786 + 1.11201i
$$396$$ 0 0
$$397$$ 9.63854i 0.483745i −0.970308 0.241872i $$-0.922238\pi$$
0.970308 0.241872i $$-0.0777615\pi$$
$$398$$ 0 0
$$399$$ 3.39255i 0.169840i
$$400$$ 0 0
$$401$$ 18.4820i 0.922947i 0.887154 + 0.461473i $$0.152679\pi$$
−0.887154 + 0.461473i $$0.847321\pi$$
$$402$$ 0 0
$$403$$ 14.2517 0.709927
$$404$$ 0 0
$$405$$ 43.8553 46.1002i 2.17919 2.29074i
$$406$$ 0 0
$$407$$ 16.5379 0.819753
$$408$$ 0 0
$$409$$ −26.0001 −1.28562 −0.642811 0.766025i $$-0.722232\pi$$
−0.642811 + 0.766025i $$0.722232\pi$$
$$410$$ 0 0
$$411$$ −62.5267 −3.08421
$$412$$ 0 0
$$413$$ 29.3462 1.44403
$$414$$ 0 0
$$415$$ 24.5996 + 23.4017i 1.20755 + 1.14875i
$$416$$ 0 0
$$417$$ 29.9787i 1.46806i
$$418$$ 0 0
$$419$$ −16.0811 −0.785614 −0.392807 0.919621i $$-0.628496\pi$$
−0.392807 + 0.919621i $$0.628496\pi$$
$$420$$ 0 0
$$421$$ 23.5031i 1.14547i −0.819740 0.572735i $$-0.805882\pi$$
0.819740 0.572735i $$-0.194118\pi$$
$$422$$ 0 0
$$423$$ 94.9662 4.61741
$$424$$ 0 0
$$425$$ 1.48975 + 29.8299i 0.0722635 + 1.44696i
$$426$$ 0 0
$$427$$ 18.3914 0.890022
$$428$$ 0 0
$$429$$ 37.0141i 1.78706i
$$430$$ 0 0
$$431$$ −6.61906 −0.318829 −0.159415 0.987212i $$-0.550961\pi$$
−0.159415 + 0.987212i $$0.550961\pi$$
$$432$$ 0 0
$$433$$ 20.3334 0.977163 0.488581 0.872518i $$-0.337515\pi$$
0.488581 + 0.872518i $$0.337515\pi$$
$$434$$ 0 0
$$435$$ −18.7614 + 19.7218i −0.899542 + 0.945588i
$$436$$ 0 0
$$437$$ −0.220070 + 1.79882i −0.0105274 + 0.0860494i
$$438$$ 0 0
$$439$$ 15.1971i 0.725317i −0.931922 0.362659i $$-0.881869\pi$$
0.931922 0.362659i $$-0.118131\pi$$
$$440$$ 0 0
$$441$$ −3.60724 −0.171774
$$442$$ 0 0
$$443$$ −8.20593 −0.389875 −0.194938 0.980816i $$-0.562450\pi$$
−0.194938 + 0.980816i $$0.562450\pi$$
$$444$$ 0 0
$$445$$ −19.6884 18.7297i −0.933320 0.887872i
$$446$$ 0 0
$$447$$ 19.5661i 0.925445i
$$448$$ 0 0
$$449$$ −23.0265 −1.08669 −0.543343 0.839511i $$-0.682842\pi$$
−0.543343 + 0.839511i $$0.682842\pi$$
$$450$$ 0 0
$$451$$ −1.03259 −0.0486226
$$452$$ 0 0
$$453$$ 32.6905i 1.53593i
$$454$$ 0 0
$$455$$ 20.7386 21.8002i 0.972243 1.02201i
$$456$$ 0 0
$$457$$ −38.0523 −1.78001 −0.890005 0.455951i $$-0.849299\pi$$
−0.890005 + 0.455951i $$0.849299\pi$$
$$458$$ 0 0
$$459$$ 94.2561 4.39950
$$460$$ 0 0
$$461$$ 28.7920 1.34098 0.670489 0.741919i $$-0.266084\pi$$
0.670489 + 0.741919i $$0.266084\pi$$
$$462$$ 0 0
$$463$$ 1.34881 0.0626843 0.0313421 0.999509i $$-0.490022\pi$$
0.0313421 + 0.999509i $$0.490022\pi$$
$$464$$ 0 0
$$465$$ 15.4049 + 14.6548i 0.714387 + 0.679600i
$$466$$ 0 0
$$467$$ 8.23187i 0.380926i −0.981694 0.190463i $$-0.939001\pi$$
0.981694 0.190463i $$-0.0609988\pi$$
$$468$$ 0 0
$$469$$ −19.2992 −0.891154
$$470$$ 0 0
$$471$$ −53.2898 −2.45547
$$472$$ 0 0
$$473$$ 0.821902i 0.0377911i
$$474$$ 0 0
$$475$$ −0.0942413 1.88703i −0.00432409 0.0865831i
$$476$$ 0 0
$$477$$ −75.6170 −3.46226
$$478$$ 0 0
$$479$$ −2.78805 −0.127389 −0.0636946 0.997969i $$-0.520288\pi$$
−0.0636946 + 0.997969i $$0.520288\pi$$
$$480$$ 0 0
$$481$$ 35.6297i 1.62458i
$$482$$ 0 0
$$483$$ −42.7379 5.22860i −1.94464 0.237910i
$$484$$ 0 0
$$485$$ 6.69220 7.03476i 0.303877 0.319432i
$$486$$ 0 0
$$487$$ −1.35672 −0.0614787 −0.0307394 0.999527i $$-0.509786\pi$$
−0.0307394 + 0.999527i $$0.509786\pi$$
$$488$$ 0 0
$$489$$ −46.5877 −2.10677
$$490$$ 0 0
$$491$$ 0.539939i 0.0243671i 0.999926 + 0.0121835i $$0.00387824\pi$$
−0.999926 + 0.0121835i $$0.996122\pi$$
$$492$$ 0 0
$$493$$ −22.1255 −0.996482
$$494$$ 0 0
$$495$$ −27.4898 + 28.8969i −1.23557 + 1.29882i
$$496$$ 0 0
$$497$$ 20.0692 0.900226
$$498$$ 0 0
$$499$$ 23.4902i 1.05157i 0.850619 + 0.525783i $$0.176228\pi$$
−0.850619 + 0.525783i $$0.823772\pi$$
$$500$$ 0 0
$$501$$ −29.0901 −1.29965
$$502$$ 0 0
$$503$$ 17.7835i 0.792929i 0.918050 + 0.396464i $$0.129763\pi$$
−0.918050 + 0.396464i $$0.870237\pi$$
$$504$$ 0 0
$$505$$ 4.80735 5.05343i 0.213924 0.224875i
$$506$$ 0 0
$$507$$ 37.0196 1.64410
$$508$$ 0 0
$$509$$ 29.3504 1.30094 0.650468 0.759534i $$-0.274573\pi$$
0.650468 + 0.759534i $$0.274573\pi$$
$$510$$ 0 0
$$511$$ −3.40219 −0.150504
$$512$$ 0 0
$$513$$ −5.96263 −0.263256
$$514$$ 0 0
$$515$$ 5.49037 + 5.22302i 0.241935 + 0.230154i
$$516$$ 0 0
$$517$$ −27.8328 −1.22408
$$518$$ 0 0
$$519$$ 79.8173i 3.50359i
$$520$$ 0 0
$$521$$ 15.4545i 0.677074i 0.940953 + 0.338537i $$0.109932\pi$$
−0.940953 + 0.338537i $$0.890068\pi$$
$$522$$ 0 0
$$523$$ 31.5873i 1.38122i −0.723229 0.690608i $$-0.757343\pi$$
0.723229 0.690608i $$-0.242657\pi$$
$$524$$ 0 0
$$525$$ 44.8337 2.23906i 1.95670 0.0977207i
$$526$$ 0 0
$$527$$ 17.2825i 0.752837i
$$528$$ 0 0
$$529$$ −22.3217 5.54470i −0.970507 0.241074i
$$530$$ 0 0
$$531$$ 83.8060i 3.63687i
$$532$$ 0 0
$$533$$ 2.22463i 0.0963596i
$$534$$ 0 0
$$535$$ 12.8768 + 12.2497i 0.556712 + 0.529603i
$$536$$ 0 0
$$537$$ 48.7582i 2.10407i
$$538$$ 0 0
$$539$$ 1.05721 0.0455375
$$540$$ 0 0
$$541$$ −20.7309 −0.891292 −0.445646 0.895209i $$-0.647026\pi$$
−0.445646 + 0.895209i $$0.647026\pi$$
$$542$$ 0 0
$$543$$ 11.2624i 0.483316i
$$544$$ 0 0
$$545$$ 22.8749 + 21.7610i 0.979851 + 0.932137i
$$546$$ 0 0
$$547$$ −9.88064 −0.422466 −0.211233 0.977436i $$-0.567748\pi$$
−0.211233 + 0.977436i $$0.567748\pi$$
$$548$$ 0 0
$$549$$ 52.5216i 2.24157i
$$550$$ 0 0
$$551$$ 1.39966 0.0596273
$$552$$ 0 0
$$553$$ 37.2655i 1.58469i
$$554$$ 0 0
$$555$$ 36.6375 38.5129i 1.55518 1.63478i
$$556$$ 0 0
$$557$$ −13.3481 −0.565576 −0.282788 0.959182i $$-0.591259\pi$$
−0.282788 + 0.959182i $$0.591259\pi$$
$$558$$ 0 0
$$559$$ −1.77073 −0.0748939
$$560$$ 0 0
$$561$$ −44.8857 −1.89508
$$562$$ 0 0
$$563$$ 24.9591i 1.05190i −0.850516 0.525950i $$-0.823710\pi$$
0.850516 0.525950i $$-0.176290\pi$$
$$564$$ 0 0
$$565$$ 0.497768 0.523247i 0.0209412 0.0220132i
$$566$$ 0 0
$$567$$ 77.7324i 3.26445i
$$568$$ 0 0
$$569$$ 33.7602i 1.41530i 0.706562 + 0.707651i $$0.250245\pi$$
−0.706562 + 0.707651i $$0.749755\pi$$
$$570$$ 0 0
$$571$$ −38.3767 −1.60602 −0.803008 0.595968i $$-0.796768\pi$$
−0.803008 + 0.595968i $$0.796768\pi$$
$$572$$ 0 0
$$573$$ −30.8099 −1.28710
$$574$$ 0 0
$$575$$ 23.9173 + 1.72109i 0.997421 + 0.0717743i
$$576$$ 0 0
$$577$$ 25.7420i 1.07166i 0.844327 + 0.535828i $$0.180000\pi$$
−0.844327 + 0.535828i $$0.820000\pi$$
$$578$$ 0 0
$$579$$ 5.68485i 0.236254i
$$580$$ 0 0
$$581$$ 41.4790 1.72084
$$582$$ 0 0
$$583$$ 22.1619 0.917852
$$584$$ 0 0
$$585$$ 62.2563 + 59.2248i 2.57398 + 2.44864i
$$586$$ 0 0
$$587$$ 16.8165 0.694091 0.347045 0.937848i $$-0.387185\pi$$
0.347045 + 0.937848i $$0.387185\pi$$
$$588$$ 0 0
$$589$$ 1.09329i 0.0450482i
$$590$$ 0 0
$$591$$ 51.9790i 2.13813i
$$592$$ 0 0
$$593$$ 26.0486i 1.06969i 0.844951 + 0.534843i $$0.179629\pi$$
−0.844951 + 0.534843i $$0.820371\pi$$
$$594$$ 0 0
$$595$$ 26.4363 + 25.1490i 1.08378 + 1.03101i
$$596$$ 0 0
$$597$$ 65.5827 2.68412
$$598$$ 0 0
$$599$$ 20.6703i 0.844567i 0.906464 + 0.422283i $$0.138771\pi$$
−0.906464 + 0.422283i $$0.861229\pi$$
$$600$$ 0 0
$$601$$ 8.32601 0.339625 0.169813 0.985476i $$-0.445684\pi$$
0.169813 + 0.985476i $$0.445684\pi$$
$$602$$ 0 0
$$603$$ 55.1140i 2.24442i
$$604$$ 0 0
$$605$$ −8.89649 + 9.35188i −0.361694 + 0.380208i
$$606$$ 0 0
$$607$$ −15.9501 −0.647396 −0.323698 0.946160i $$-0.604926\pi$$
−0.323698 + 0.946160i $$0.604926\pi$$
$$608$$ 0 0
$$609$$ 33.2542i 1.34753i
$$610$$ 0 0
$$611$$ 59.9637i 2.42587i
$$612$$ 0 0
$$613$$ 23.1501 0.935023 0.467512 0.883987i $$-0.345151\pi$$
0.467512 + 0.883987i $$0.345151\pi$$
$$614$$ 0 0
$$615$$ −2.28756 + 2.40465i −0.0922433 + 0.0969650i
$$616$$ 0 0
$$617$$ −2.88371 −0.116094 −0.0580468 0.998314i $$-0.518487\pi$$
−0.0580468 + 0.998314i $$0.518487\pi$$
$$618$$ 0 0
$$619$$ −6.49465 −0.261042 −0.130521 0.991446i $$-0.541665\pi$$
−0.130521 + 0.991446i $$0.541665\pi$$
$$620$$ 0 0
$$621$$ 9.18961 75.1147i 0.368766 3.01425i
$$622$$ 0 0
$$623$$ −33.1978 −1.33004
$$624$$ 0 0
$$625$$ −24.8756 + 2.49086i −0.995024 + 0.0996345i
$$626$$ 0 0
$$627$$ 2.83947 0.113397
$$628$$ 0 0
$$629$$ 43.2069 1.72277
$$630$$ 0 0
$$631$$ 28.6830 1.14185 0.570927 0.821001i $$-0.306584\pi$$
0.570927 + 0.821001i $$0.306584\pi$$
$$632$$ 0 0
$$633$$ 62.4482i 2.48209i
$$634$$ 0 0
$$635$$ 16.2350 17.0660i 0.644265 0.677243i
$$636$$ 0 0
$$637$$ 2.27769i 0.0902455i
$$638$$ 0 0
$$639$$ 57.3129i 2.26726i
$$640$$ 0 0
$$641$$ 31.5938i 1.24788i −0.781473 0.623939i $$-0.785531\pi$$
0.781473 0.623939i $$-0.214469\pi$$
$$642$$ 0 0
$$643$$ 47.3512i 1.86735i 0.358120 + 0.933675i $$0.383418\pi$$
−0.358120 + 0.933675i $$0.616582\pi$$
$$644$$ 0 0
$$645$$ −1.91402 1.82082i −0.0753644 0.0716945i
$$646$$ 0 0
$$647$$ 21.8763 0.860045 0.430022 0.902818i $$-0.358506\pi$$
0.430022 + 0.902818i $$0.358506\pi$$
$$648$$ 0 0
$$649$$ 24.5619i 0.964141i
$$650$$ 0 0
$$651$$ 25.9752 1.01805
$$652$$ 0 0
$$653$$ 0.359578i 0.0140714i −0.999975 0.00703568i $$-0.997760\pi$$
0.999975 0.00703568i $$-0.00223954\pi$$
$$654$$ 0 0
$$655$$ 18.4012 + 17.5051i 0.718993 + 0.683982i
$$656$$ 0 0
$$657$$ 9.71588i 0.379052i
$$658$$ 0 0
$$659$$ −1.91275 −0.0745104 −0.0372552 0.999306i $$-0.511861\pi$$
−0.0372552 + 0.999306i $$0.511861\pi$$
$$660$$ 0 0
$$661$$ 4.73207i 0.184056i 0.995756 + 0.0920280i $$0.0293349\pi$$
−0.995756 + 0.0920280i $$0.970665\pi$$
$$662$$ 0 0
$$663$$ 96.7031i 3.75564i
$$664$$ 0 0
$$665$$ −1.67236 1.59092i −0.0648513 0.0616933i
$$666$$ 0 0
$$667$$ −2.15715 + 17.6323i −0.0835252 + 0.682725i
$$668$$ 0 0
$$669$$ 6.16082 0.238191
$$670$$ 0 0
$$671$$ 15.3931i 0.594243i
$$672$$ 0 0
$$673$$ 42.7608i 1.64831i −0.566366 0.824154i $$-0.691651\pi$$
0.566366 0.824154i $$-0.308349\pi$$
$$674$$ 0 0
$$675$$ 3.93530 + 78.7982i 0.151470 + 3.03294i
$$676$$ 0 0
$$677$$ −1.30895 −0.0503072 −0.0251536 0.999684i $$-0.508007\pi$$
−0.0251536 + 0.999684i $$0.508007\pi$$
$$678$$ 0 0
$$679$$ 11.8617i 0.455212i
$$680$$ 0 0
$$681$$ 17.0530i 0.653472i
$$682$$ 0 0
$$683$$ 16.4311 0.628718 0.314359 0.949304i $$-0.398210\pi$$
0.314359 + 0.949304i $$0.398210\pi$$
$$684$$ 0 0
$$685$$ 29.3217 30.8226i 1.12032 1.17767i
$$686$$ 0 0
$$687$$ 51.9347i 1.98143i
$$688$$ 0 0
$$689$$ 47.7462i 1.81899i
$$690$$ 0 0
$$691$$ 50.1615i 1.90823i −0.299433 0.954117i $$-0.596797\pi$$
0.299433 0.954117i $$-0.403203\pi$$
$$692$$ 0 0
$$693$$ 48.7249i 1.85091i
$$694$$ 0 0
$$695$$ 14.7780 + 14.0584i 0.560562 + 0.533265i
$$696$$ 0 0
$$697$$ −2.69773 −0.102184
$$698$$ 0 0
$$699$$ 48.1400i 1.82082i
$$700$$ 0 0
$$701$$ 0.199633i 0.00754004i 0.999993 + 0.00377002i $$0.00120004\pi$$
−0.999993 + 0.00377002i $$0.998800\pi$$
$$702$$ 0 0
$$703$$ −2.73326 −0.103087
$$704$$ 0 0
$$705$$ −61.6598 + 64.8161i −2.32224 + 2.44111i
$$706$$ 0 0
$$707$$ 8.52090i 0.320461i
$$708$$ 0 0
$$709$$ 40.1194i 1.50671i −0.657611 0.753357i $$-0.728433\pi$$
0.657611 0.753357i $$-0.271567\pi$$
$$710$$ 0 0
$$711$$ −106.422 −3.99113
$$712$$ 0 0
$$713$$ 13.7728 + 1.68498i 0.515795 + 0.0631029i
$$714$$ 0 0
$$715$$ −18.2461 17.3576i −0.682367 0.649139i
$$716$$ 0 0
$$717$$ 31.5566i 1.17850i
$$718$$ 0 0
$$719$$ 1.40670i 0.0524610i 0.999656 + 0.0262305i $$0.00835039\pi$$
−0.999656 + 0.0262305i $$0.991650\pi$$
$$720$$ 0 0
$$721$$ 9.25766 0.344773
$$722$$ 0 0
$$723$$ 61.9684i 2.30463i
$$724$$ 0 0
$$725$$ −0.923765 18.4969i −0.0343078 0.686959i
$$726$$ 0 0
$$727$$ 36.3686i 1.34884i −0.738349 0.674419i $$-0.764394\pi$$
0.738349 0.674419i $$-0.235606\pi$$
$$728$$ 0 0
$$729$$ 66.4089 2.45959
$$730$$ 0 0
$$731$$ 2.14730i 0.0794208i
$$732$$ 0 0
$$733$$ 35.2005 1.30016 0.650081 0.759865i $$-0.274735\pi$$
0.650081 + 0.759865i $$0.274735\pi$$
$$734$$ 0 0
$$735$$ 2.34212 2.46201i 0.0863904 0.0908125i
$$736$$ 0 0
$$737$$ 16.1529i 0.594998i
$$738$$ 0 0
$$739$$ 6.59702i 0.242675i −0.992611 0.121338i $$-0.961282\pi$$
0.992611 0.121338i $$-0.0387184\pi$$
$$740$$ 0 0
$$741$$ 6.11743i 0.224729i
$$742$$ 0 0
$$743$$ 21.9968i 0.806985i 0.914983 + 0.403493i $$0.132204\pi$$
−0.914983 + 0.403493i $$0.867796\pi$$
$$744$$ 0 0
$$745$$ −9.64513 9.17546i −0.353370 0.336163i
$$746$$ 0 0
$$747$$ 118.454i 4.33402i
$$748$$ 0 0
$$749$$ 21.7124 0.793352
$$750$$ 0 0
$$751$$ −10.8072 −0.394359 −0.197179 0.980367i $$-0.563178\pi$$
−0.197179 + 0.980367i $$0.563178\pi$$
$$752$$ 0 0
$$753$$ −81.8531 −2.98289
$$754$$ 0 0
$$755$$ 16.1148 + 15.3301i 0.586477 + 0.557919i
$$756$$ 0 0
$$757$$ 9.47219 0.344273 0.172136 0.985073i $$-0.444933\pi$$
0.172136 + 0.985073i $$0.444933\pi$$
$$758$$ 0 0
$$759$$ −4.37619 + 35.7704i −0.158846 + 1.29838i
$$760$$ 0 0
$$761$$ −48.3960 −1.75436 −0.877178 0.480166i $$-0.840576\pi$$
−0.877178 + 0.480166i $$0.840576\pi$$
$$762$$ 0 0
$$763$$ 38.5707 1.39635
$$764$$ 0 0
$$765$$ −71.8197 + 75.4960i −2.59665 + 2.72956i
$$766$$ 0 0
$$767$$ −52.9170 −1.91072
$$768$$ 0 0
$$769$$ 5.14793i 0.185639i −0.995683 0.0928195i $$-0.970412\pi$$
0.995683 0.0928195i $$-0.0295880\pi$$
$$770$$ 0 0
$$771$$ 54.4786i 1.96200i
$$772$$ 0 0
$$773$$ −35.7974 −1.28754 −0.643771 0.765218i $$-0.722631\pi$$
−0.643771 + 0.765218i $$0.722631\pi$$
$$774$$ 0 0
$$775$$ −14.4482 + 0.721564i −0.518994 + 0.0259193i
$$776$$ 0 0
$$777$$ 64.9391i 2.32968i
$$778$$ 0 0
$$779$$ 0.170658 0.00611447
$$780$$ 0 0
$$781$$ 16.7973i 0.601056i
$$782$$ 0 0
$$783$$ −58.4464 −2.08870
$$784$$ 0 0
$$785$$ 24.9901 26.2693i 0.891934 0.937590i
$$786$$ 0 0
$$787$$ 29.7273i 1.05966i 0.848103 + 0.529832i $$0.177745\pi$$
−0.848103 + 0.529832i $$0.822255\pi$$
$$788$$ 0 0
$$789$$ 58.4192i 2.07978i
$$790$$ 0 0
$$791$$ 0.882280i 0.0313703i
$$792$$ 0 0
$$793$$ −33.1633 −1.17766
$$794$$ 0 0
$$795$$ 49.0967 51.6099i 1.74128 1.83041i
$$796$$ 0 0
$$797$$ 22.5547 0.798927 0.399464 0.916749i $$-0.369196\pi$$
0.399464 + 0.916749i $$0.369196\pi$$
$$798$$ 0 0
$$799$$ −72.7159 −2.57250
$$800$$ 0 0
$$801$$ 94.8054i 3.34978i
$$802$$ 0 0
$$803$$ 2.84754i 0.100487i