# Properties

 Label 896.2.e.a.447.1 Level $896$ Weight $2$ Character 896.447 Analytic conductor $7.155$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$896 = 2^{7} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 896.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.15459602111$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 447.1 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 896.447 Dual form 896.2.e.a.447.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.73205i q^{3} +0.732051 q^{5} +(-2.00000 - 1.73205i) q^{7} -4.46410 q^{9} +O(q^{10})$$ $$q-2.73205i q^{3} +0.732051 q^{5} +(-2.00000 - 1.73205i) q^{7} -4.46410 q^{9} +5.46410 q^{11} -4.73205 q^{13} -2.00000i q^{15} -4.00000i q^{17} -1.26795i q^{19} +(-4.73205 + 5.46410i) q^{21} -5.46410i q^{23} -4.46410 q^{25} +4.00000i q^{27} +6.92820i q^{29} -6.92820 q^{31} -14.9282i q^{33} +(-1.46410 - 1.26795i) q^{35} -4.00000i q^{37} +12.9282i q^{39} +2.92820i q^{41} -2.53590 q^{43} -3.26795 q^{45} +6.92820 q^{47} +(1.00000 + 6.92820i) q^{49} -10.9282 q^{51} +6.92820i q^{53} +4.00000 q^{55} -3.46410 q^{57} +3.80385i q^{59} +11.6603 q^{61} +(8.92820 + 7.73205i) q^{63} -3.46410 q^{65} +2.53590 q^{67} -14.9282 q^{69} -4.53590i q^{71} -6.92820i q^{73} +12.1962i q^{75} +(-10.9282 - 9.46410i) q^{77} +3.46410i q^{79} -2.46410 q^{81} -10.7321i q^{83} -2.92820i q^{85} +18.9282 q^{87} -14.9282i q^{89} +(9.46410 + 8.19615i) q^{91} +18.9282i q^{93} -0.928203i q^{95} +12.0000i q^{97} -24.3923 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{5} - 8q^{7} - 4q^{9} + O(q^{10})$$ $$4q - 4q^{5} - 8q^{7} - 4q^{9} + 8q^{11} - 12q^{13} - 12q^{21} - 4q^{25} + 8q^{35} - 24q^{43} - 20q^{45} + 4q^{49} - 16q^{51} + 16q^{55} + 12q^{61} + 8q^{63} + 24q^{67} - 32q^{69} - 16q^{77} + 4q^{81} + 48q^{87} + 24q^{91} - 56q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$129$$ $$645$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$3$$ 2.73205i 1.57735i −0.614810 0.788675i $$-0.710767\pi$$
0.614810 0.788675i $$-0.289233\pi$$
$$4$$ 0 0
$$5$$ 0.732051 0.327383 0.163692 0.986512i $$-0.447660\pi$$
0.163692 + 0.986512i $$0.447660\pi$$
$$6$$ 0 0
$$7$$ −2.00000 1.73205i −0.755929 0.654654i
$$8$$ 0 0
$$9$$ −4.46410 −1.48803
$$10$$ 0 0
$$11$$ 5.46410 1.64749 0.823744 0.566961i $$-0.191881\pi$$
0.823744 + 0.566961i $$0.191881\pi$$
$$12$$ 0 0
$$13$$ −4.73205 −1.31243 −0.656217 0.754572i $$-0.727845\pi$$
−0.656217 + 0.754572i $$0.727845\pi$$
$$14$$ 0 0
$$15$$ 2.00000i 0.516398i
$$16$$ 0 0
$$17$$ 4.00000i 0.970143i −0.874475 0.485071i $$-0.838794\pi$$
0.874475 0.485071i $$-0.161206\pi$$
$$18$$ 0 0
$$19$$ 1.26795i 0.290887i −0.989367 0.145444i $$-0.953539\pi$$
0.989367 0.145444i $$-0.0464610\pi$$
$$20$$ 0 0
$$21$$ −4.73205 + 5.46410i −1.03262 + 1.19236i
$$22$$ 0 0
$$23$$ 5.46410i 1.13934i −0.821872 0.569672i $$-0.807070\pi$$
0.821872 0.569672i $$-0.192930\pi$$
$$24$$ 0 0
$$25$$ −4.46410 −0.892820
$$26$$ 0 0
$$27$$ 4.00000i 0.769800i
$$28$$ 0 0
$$29$$ 6.92820i 1.28654i 0.765641 + 0.643268i $$0.222422\pi$$
−0.765641 + 0.643268i $$0.777578\pi$$
$$30$$ 0 0
$$31$$ −6.92820 −1.24434 −0.622171 0.782881i $$-0.713749\pi$$
−0.622171 + 0.782881i $$0.713749\pi$$
$$32$$ 0 0
$$33$$ 14.9282i 2.59867i
$$34$$ 0 0
$$35$$ −1.46410 1.26795i −0.247478 0.214323i
$$36$$ 0 0
$$37$$ 4.00000i 0.657596i −0.944400 0.328798i $$-0.893356\pi$$
0.944400 0.328798i $$-0.106644\pi$$
$$38$$ 0 0
$$39$$ 12.9282i 2.07017i
$$40$$ 0 0
$$41$$ 2.92820i 0.457309i 0.973508 + 0.228654i $$0.0734325\pi$$
−0.973508 + 0.228654i $$0.926567\pi$$
$$42$$ 0 0
$$43$$ −2.53590 −0.386721 −0.193360 0.981128i $$-0.561939\pi$$
−0.193360 + 0.981128i $$0.561939\pi$$
$$44$$ 0 0
$$45$$ −3.26795 −0.487157
$$46$$ 0 0
$$47$$ 6.92820 1.01058 0.505291 0.862949i $$-0.331385\pi$$
0.505291 + 0.862949i $$0.331385\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ −10.9282 −1.53025
$$52$$ 0 0
$$53$$ 6.92820i 0.951662i 0.879537 + 0.475831i $$0.157853\pi$$
−0.879537 + 0.475831i $$0.842147\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ −3.46410 −0.458831
$$58$$ 0 0
$$59$$ 3.80385i 0.495219i 0.968860 + 0.247609i $$0.0796450\pi$$
−0.968860 + 0.247609i $$0.920355\pi$$
$$60$$ 0 0
$$61$$ 11.6603 1.49294 0.746471 0.665418i $$-0.231747\pi$$
0.746471 + 0.665418i $$0.231747\pi$$
$$62$$ 0 0
$$63$$ 8.92820 + 7.73205i 1.12485 + 0.974147i
$$64$$ 0 0
$$65$$ −3.46410 −0.429669
$$66$$ 0 0
$$67$$ 2.53590 0.309809 0.154905 0.987929i $$-0.450493\pi$$
0.154905 + 0.987929i $$0.450493\pi$$
$$68$$ 0 0
$$69$$ −14.9282 −1.79714
$$70$$ 0 0
$$71$$ 4.53590i 0.538312i −0.963097 0.269156i $$-0.913255\pi$$
0.963097 0.269156i $$-0.0867447\pi$$
$$72$$ 0 0
$$73$$ 6.92820i 0.810885i −0.914121 0.405442i $$-0.867117\pi$$
0.914121 0.405442i $$-0.132883\pi$$
$$74$$ 0 0
$$75$$ 12.1962i 1.40829i
$$76$$ 0 0
$$77$$ −10.9282 9.46410i −1.24538 1.07853i
$$78$$ 0 0
$$79$$ 3.46410i 0.389742i 0.980829 + 0.194871i $$0.0624288\pi$$
−0.980829 + 0.194871i $$0.937571\pi$$
$$80$$ 0 0
$$81$$ −2.46410 −0.273789
$$82$$ 0 0
$$83$$ 10.7321i 1.17800i −0.808135 0.588998i $$-0.799523\pi$$
0.808135 0.588998i $$-0.200477\pi$$
$$84$$ 0 0
$$85$$ 2.92820i 0.317608i
$$86$$ 0 0
$$87$$ 18.9282 2.02932
$$88$$ 0 0
$$89$$ 14.9282i 1.58239i −0.611566 0.791193i $$-0.709460\pi$$
0.611566 0.791193i $$-0.290540\pi$$
$$90$$ 0 0
$$91$$ 9.46410 + 8.19615i 0.992107 + 0.859190i
$$92$$ 0 0
$$93$$ 18.9282i 1.96276i
$$94$$ 0 0
$$95$$ 0.928203i 0.0952316i
$$96$$ 0 0
$$97$$ 12.0000i 1.21842i 0.793011 + 0.609208i $$0.208512\pi$$
−0.793011 + 0.609208i $$0.791488\pi$$
$$98$$ 0 0
$$99$$ −24.3923 −2.45152
$$100$$ 0 0
$$101$$ 6.19615 0.616540 0.308270 0.951299i $$-0.400250\pi$$
0.308270 + 0.951299i $$0.400250\pi$$
$$102$$ 0 0
$$103$$ −18.9282 −1.86505 −0.932526 0.361104i $$-0.882400\pi$$
−0.932526 + 0.361104i $$0.882400\pi$$
$$104$$ 0 0
$$105$$ −3.46410 + 4.00000i −0.338062 + 0.390360i
$$106$$ 0 0
$$107$$ 8.39230 0.811315 0.405657 0.914025i $$-0.367043\pi$$
0.405657 + 0.914025i $$0.367043\pi$$
$$108$$ 0 0
$$109$$ 6.92820i 0.663602i −0.943349 0.331801i $$-0.892344\pi$$
0.943349 0.331801i $$-0.107656\pi$$
$$110$$ 0 0
$$111$$ −10.9282 −1.03726
$$112$$ 0 0
$$113$$ −9.46410 −0.890308 −0.445154 0.895454i $$-0.646851\pi$$
−0.445154 + 0.895454i $$0.646851\pi$$
$$114$$ 0 0
$$115$$ 4.00000i 0.373002i
$$116$$ 0 0
$$117$$ 21.1244 1.95295
$$118$$ 0 0
$$119$$ −6.92820 + 8.00000i −0.635107 + 0.733359i
$$120$$ 0 0
$$121$$ 18.8564 1.71422
$$122$$ 0 0
$$123$$ 8.00000 0.721336
$$124$$ 0 0
$$125$$ −6.92820 −0.619677
$$126$$ 0 0
$$127$$ 21.4641i 1.90463i −0.305115 0.952316i $$-0.598695\pi$$
0.305115 0.952316i $$-0.401305\pi$$
$$128$$ 0 0
$$129$$ 6.92820i 0.609994i
$$130$$ 0 0
$$131$$ 10.7321i 0.937664i −0.883287 0.468832i $$-0.844675\pi$$
0.883287 0.468832i $$-0.155325\pi$$
$$132$$ 0 0
$$133$$ −2.19615 + 2.53590i −0.190431 + 0.219890i
$$134$$ 0 0
$$135$$ 2.92820i 0.252020i
$$136$$ 0 0
$$137$$ 19.8564 1.69645 0.848224 0.529638i $$-0.177672\pi$$
0.848224 + 0.529638i $$0.177672\pi$$
$$138$$ 0 0
$$139$$ 4.19615i 0.355913i −0.984038 0.177957i $$-0.943051\pi$$
0.984038 0.177957i $$-0.0569486\pi$$
$$140$$ 0 0
$$141$$ 18.9282i 1.59404i
$$142$$ 0 0
$$143$$ −25.8564 −2.16222
$$144$$ 0 0
$$145$$ 5.07180i 0.421190i
$$146$$ 0 0
$$147$$ 18.9282 2.73205i 1.56117 0.225336i
$$148$$ 0 0
$$149$$ 12.0000i 0.983078i −0.870855 0.491539i $$-0.836434\pi$$
0.870855 0.491539i $$-0.163566\pi$$
$$150$$ 0 0
$$151$$ 11.3205i 0.921250i −0.887595 0.460625i $$-0.847625\pi$$
0.887595 0.460625i $$-0.152375\pi$$
$$152$$ 0 0
$$153$$ 17.8564i 1.44360i
$$154$$ 0 0
$$155$$ −5.07180 −0.407377
$$156$$ 0 0
$$157$$ 19.2679 1.53775 0.768875 0.639399i $$-0.220817\pi$$
0.768875 + 0.639399i $$0.220817\pi$$
$$158$$ 0 0
$$159$$ 18.9282 1.50110
$$160$$ 0 0
$$161$$ −9.46410 + 10.9282i −0.745876 + 0.861263i
$$162$$ 0 0
$$163$$ 16.3923 1.28394 0.641972 0.766728i $$-0.278116\pi$$
0.641972 + 0.766728i $$0.278116\pi$$
$$164$$ 0 0
$$165$$ 10.9282i 0.850759i
$$166$$ 0 0
$$167$$ −5.07180 −0.392467 −0.196234 0.980557i $$-0.562871\pi$$
−0.196234 + 0.980557i $$0.562871\pi$$
$$168$$ 0 0
$$169$$ 9.39230 0.722485
$$170$$ 0 0
$$171$$ 5.66025i 0.432850i
$$172$$ 0 0
$$173$$ 3.26795 0.248458 0.124229 0.992254i $$-0.460354\pi$$
0.124229 + 0.992254i $$0.460354\pi$$
$$174$$ 0 0
$$175$$ 8.92820 + 7.73205i 0.674909 + 0.584488i
$$176$$ 0 0
$$177$$ 10.3923 0.781133
$$178$$ 0 0
$$179$$ −0.392305 −0.0293222 −0.0146611 0.999893i $$-0.504667\pi$$
−0.0146611 + 0.999893i $$0.504667\pi$$
$$180$$ 0 0
$$181$$ 16.7321 1.24368 0.621842 0.783143i $$-0.286385\pi$$
0.621842 + 0.783143i $$0.286385\pi$$
$$182$$ 0 0
$$183$$ 31.8564i 2.35489i
$$184$$ 0 0
$$185$$ 2.92820i 0.215286i
$$186$$ 0 0
$$187$$ 21.8564i 1.59830i
$$188$$ 0 0
$$189$$ 6.92820 8.00000i 0.503953 0.581914i
$$190$$ 0 0
$$191$$ 11.4641i 0.829513i −0.909932 0.414757i $$-0.863867\pi$$
0.909932 0.414757i $$-0.136133\pi$$
$$192$$ 0 0
$$193$$ 4.39230 0.316165 0.158083 0.987426i $$-0.449469\pi$$
0.158083 + 0.987426i $$0.449469\pi$$
$$194$$ 0 0
$$195$$ 9.46410i 0.677738i
$$196$$ 0 0
$$197$$ 12.0000i 0.854965i 0.904024 + 0.427482i $$0.140599\pi$$
−0.904024 + 0.427482i $$0.859401\pi$$
$$198$$ 0 0
$$199$$ 16.7846 1.18983 0.594915 0.803789i $$-0.297186\pi$$
0.594915 + 0.803789i $$0.297186\pi$$
$$200$$ 0 0
$$201$$ 6.92820i 0.488678i
$$202$$ 0 0
$$203$$ 12.0000 13.8564i 0.842235 0.972529i
$$204$$ 0 0
$$205$$ 2.14359i 0.149715i
$$206$$ 0 0
$$207$$ 24.3923i 1.69538i
$$208$$ 0 0
$$209$$ 6.92820i 0.479234i
$$210$$ 0 0
$$211$$ −7.60770 −0.523735 −0.261868 0.965104i $$-0.584338\pi$$
−0.261868 + 0.965104i $$0.584338\pi$$
$$212$$ 0 0
$$213$$ −12.3923 −0.849107
$$214$$ 0 0
$$215$$ −1.85641 −0.126606
$$216$$ 0 0
$$217$$ 13.8564 + 12.0000i 0.940634 + 0.814613i
$$218$$ 0 0
$$219$$ −18.9282 −1.27905
$$220$$ 0 0
$$221$$ 18.9282i 1.27325i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ 19.9282 1.32855
$$226$$ 0 0
$$227$$ 1.26795i 0.0841567i −0.999114 0.0420784i $$-0.986602\pi$$
0.999114 0.0420784i $$-0.0133979\pi$$
$$228$$ 0 0
$$229$$ 0.339746 0.0224510 0.0112255 0.999937i $$-0.496427\pi$$
0.0112255 + 0.999937i $$0.496427\pi$$
$$230$$ 0 0
$$231$$ −25.8564 + 29.8564i −1.70123 + 1.96441i
$$232$$ 0 0
$$233$$ −19.8564 −1.30084 −0.650418 0.759576i $$-0.725406\pi$$
−0.650418 + 0.759576i $$0.725406\pi$$
$$234$$ 0 0
$$235$$ 5.07180 0.330848
$$236$$ 0 0
$$237$$ 9.46410 0.614759
$$238$$ 0 0
$$239$$ 0.392305i 0.0253761i 0.999920 + 0.0126880i $$0.00403884\pi$$
−0.999920 + 0.0126880i $$0.995961\pi$$
$$240$$ 0 0
$$241$$ 12.0000i 0.772988i 0.922292 + 0.386494i $$0.126314\pi$$
−0.922292 + 0.386494i $$0.873686\pi$$
$$242$$ 0 0
$$243$$ 18.7321i 1.20166i
$$244$$ 0 0
$$245$$ 0.732051 + 5.07180i 0.0467690 + 0.324025i
$$246$$ 0 0
$$247$$ 6.00000i 0.381771i
$$248$$ 0 0
$$249$$ −29.3205 −1.85811
$$250$$ 0 0
$$251$$ 22.0526i 1.39195i 0.718068 + 0.695973i $$0.245027\pi$$
−0.718068 + 0.695973i $$0.754973\pi$$
$$252$$ 0 0
$$253$$ 29.8564i 1.87706i
$$254$$ 0 0
$$255$$ −8.00000 −0.500979
$$256$$ 0 0
$$257$$ 21.8564i 1.36337i 0.731648 + 0.681683i $$0.238751\pi$$
−0.731648 + 0.681683i $$0.761249\pi$$
$$258$$ 0 0
$$259$$ −6.92820 + 8.00000i −0.430498 + 0.497096i
$$260$$ 0 0
$$261$$ 30.9282i 1.91441i
$$262$$ 0 0
$$263$$ 11.4641i 0.706907i 0.935452 + 0.353453i $$0.114993\pi$$
−0.935452 + 0.353453i $$0.885007\pi$$
$$264$$ 0 0
$$265$$ 5.07180i 0.311558i
$$266$$ 0 0
$$267$$ −40.7846 −2.49598
$$268$$ 0 0
$$269$$ 1.12436 0.0685532 0.0342766 0.999412i $$-0.489087\pi$$
0.0342766 + 0.999412i $$0.489087\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 22.3923 25.8564i 1.35524 1.56490i
$$274$$ 0 0
$$275$$ −24.3923 −1.47091
$$276$$ 0 0
$$277$$ 28.7846i 1.72950i −0.502203 0.864750i $$-0.667477\pi$$
0.502203 0.864750i $$-0.332523\pi$$
$$278$$ 0 0
$$279$$ 30.9282 1.85162
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 15.8038i 0.939441i −0.882815 0.469721i $$-0.844355\pi$$
0.882815 0.469721i $$-0.155645\pi$$
$$284$$ 0 0
$$285$$ −2.53590 −0.150214
$$286$$ 0 0
$$287$$ 5.07180 5.85641i 0.299379 0.345693i
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 32.7846 1.92187
$$292$$ 0 0
$$293$$ −1.80385 −0.105382 −0.0526910 0.998611i $$-0.516780\pi$$
−0.0526910 + 0.998611i $$0.516780\pi$$
$$294$$ 0 0
$$295$$ 2.78461i 0.162126i
$$296$$ 0 0
$$297$$ 21.8564i 1.26824i
$$298$$ 0 0
$$299$$ 25.8564i 1.49531i
$$300$$ 0 0
$$301$$ 5.07180 + 4.39230i 0.292334 + 0.253168i
$$302$$ 0 0
$$303$$ 16.9282i 0.972500i
$$304$$ 0 0
$$305$$ 8.53590 0.488764
$$306$$ 0 0
$$307$$ 13.2679i 0.757242i 0.925552 + 0.378621i $$0.123602\pi$$
−0.925552 + 0.378621i $$0.876398\pi$$
$$308$$ 0 0
$$309$$ 51.7128i 2.94184i
$$310$$ 0 0
$$311$$ 25.8564 1.46618 0.733091 0.680130i $$-0.238077\pi$$
0.733091 + 0.680130i $$0.238077\pi$$
$$312$$ 0 0
$$313$$ 32.7846i 1.85310i 0.376177 + 0.926548i $$0.377238\pi$$
−0.376177 + 0.926548i $$0.622762\pi$$
$$314$$ 0 0
$$315$$ 6.53590 + 5.66025i 0.368256 + 0.318919i
$$316$$ 0 0
$$317$$ 1.85641i 0.104266i −0.998640 0.0521331i $$-0.983398\pi$$
0.998640 0.0521331i $$-0.0166020\pi$$
$$318$$ 0 0
$$319$$ 37.8564i 2.11955i
$$320$$ 0 0
$$321$$ 22.9282i 1.27973i
$$322$$ 0 0
$$323$$ −5.07180 −0.282202
$$324$$ 0 0
$$325$$ 21.1244 1.17177
$$326$$ 0 0
$$327$$ −18.9282 −1.04673
$$328$$ 0 0
$$329$$ −13.8564 12.0000i −0.763928 0.661581i
$$330$$ 0 0
$$331$$ −11.3205 −0.622231 −0.311116 0.950372i $$-0.600703\pi$$
−0.311116 + 0.950372i $$0.600703\pi$$
$$332$$ 0 0
$$333$$ 17.8564i 0.978525i
$$334$$ 0 0
$$335$$ 1.85641 0.101426
$$336$$ 0 0
$$337$$ −3.60770 −0.196524 −0.0982618 0.995161i $$-0.531328\pi$$
−0.0982618 + 0.995161i $$0.531328\pi$$
$$338$$ 0 0
$$339$$ 25.8564i 1.40433i
$$340$$ 0 0
$$341$$ −37.8564 −2.05004
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 0 0
$$345$$ −10.9282 −0.588355
$$346$$ 0 0
$$347$$ 13.4641 0.722791 0.361395 0.932413i $$-0.382300\pi$$
0.361395 + 0.932413i $$0.382300\pi$$
$$348$$ 0 0
$$349$$ 11.6603 0.624159 0.312080 0.950056i $$-0.398974\pi$$
0.312080 + 0.950056i $$0.398974\pi$$
$$350$$ 0 0
$$351$$ 18.9282i 1.01031i
$$352$$ 0 0
$$353$$ 29.8564i 1.58910i −0.607201 0.794548i $$-0.707708\pi$$
0.607201 0.794548i $$-0.292292\pi$$
$$354$$ 0 0
$$355$$ 3.32051i 0.176234i
$$356$$ 0 0
$$357$$ 21.8564 + 18.9282i 1.15676 + 1.00179i
$$358$$ 0 0
$$359$$ 0.392305i 0.0207051i 0.999946 + 0.0103525i $$0.00329537\pi$$
−0.999946 + 0.0103525i $$0.996705\pi$$
$$360$$ 0 0
$$361$$ 17.3923 0.915384
$$362$$ 0 0
$$363$$ 51.5167i 2.70392i
$$364$$ 0 0
$$365$$ 5.07180i 0.265470i
$$366$$ 0 0
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 0 0
$$369$$ 13.0718i 0.680491i
$$370$$ 0 0
$$371$$ 12.0000 13.8564i 0.623009 0.719389i
$$372$$ 0 0
$$373$$ 17.0718i 0.883944i −0.897029 0.441972i $$-0.854279\pi$$
0.897029 0.441972i $$-0.145721\pi$$
$$374$$ 0 0
$$375$$ 18.9282i 0.977448i
$$376$$ 0 0
$$377$$ 32.7846i 1.68849i
$$378$$ 0 0
$$379$$ −21.4641 −1.10254 −0.551268 0.834328i $$-0.685856\pi$$
−0.551268 + 0.834328i $$0.685856\pi$$
$$380$$ 0 0
$$381$$ −58.6410 −3.00427
$$382$$ 0 0
$$383$$ 6.92820 0.354015 0.177007 0.984210i $$-0.443358\pi$$
0.177007 + 0.984210i $$0.443358\pi$$
$$384$$ 0 0
$$385$$ −8.00000 6.92820i −0.407718 0.353094i
$$386$$ 0 0
$$387$$ 11.3205 0.575454
$$388$$ 0 0
$$389$$ 1.85641i 0.0941235i 0.998892 + 0.0470618i $$0.0149858\pi$$
−0.998892 + 0.0470618i $$0.985014\pi$$
$$390$$ 0 0
$$391$$ −21.8564 −1.10533
$$392$$ 0 0
$$393$$ −29.3205 −1.47902
$$394$$ 0 0
$$395$$ 2.53590i 0.127595i
$$396$$ 0 0
$$397$$ −29.9090 −1.50109 −0.750544 0.660821i $$-0.770208\pi$$
−0.750544 + 0.660821i $$0.770208\pi$$
$$398$$ 0 0
$$399$$ 6.92820 + 6.00000i 0.346844 + 0.300376i
$$400$$ 0 0
$$401$$ −23.3205 −1.16457 −0.582285 0.812985i $$-0.697841\pi$$
−0.582285 + 0.812985i $$0.697841\pi$$
$$402$$ 0 0
$$403$$ 32.7846 1.63312
$$404$$ 0 0
$$405$$ −1.80385 −0.0896339
$$406$$ 0 0
$$407$$ 21.8564i 1.08338i
$$408$$ 0 0
$$409$$ 5.07180i 0.250784i −0.992107 0.125392i $$-0.959981\pi$$
0.992107 0.125392i $$-0.0400189\pi$$
$$410$$ 0 0
$$411$$ 54.2487i 2.67589i
$$412$$ 0 0
$$413$$ 6.58846 7.60770i 0.324197 0.374350i
$$414$$ 0 0
$$415$$ 7.85641i 0.385656i
$$416$$ 0 0
$$417$$ −11.4641 −0.561399
$$418$$ 0 0
$$419$$ 3.12436i 0.152635i 0.997084 + 0.0763174i $$0.0243162\pi$$
−0.997084 + 0.0763174i $$0.975684\pi$$
$$420$$ 0 0
$$421$$ 20.0000i 0.974740i 0.873195 + 0.487370i $$0.162044\pi$$
−0.873195 + 0.487370i $$0.837956\pi$$
$$422$$ 0 0
$$423$$ −30.9282 −1.50378
$$424$$ 0 0
$$425$$ 17.8564i 0.866163i
$$426$$ 0 0
$$427$$ −23.3205 20.1962i −1.12856 0.977360i
$$428$$ 0 0
$$429$$ 70.6410i 3.41058i
$$430$$ 0 0
$$431$$ 5.46410i 0.263197i −0.991303 0.131598i $$-0.957989\pi$$
0.991303 0.131598i $$-0.0420109\pi$$
$$432$$ 0 0
$$433$$ 1.85641i 0.0892132i 0.999005 + 0.0446066i $$0.0142034\pi$$
−0.999005 + 0.0446066i $$0.985797\pi$$
$$434$$ 0 0
$$435$$ 13.8564 0.664364
$$436$$ 0 0
$$437$$ −6.92820 −0.331421
$$438$$ 0 0
$$439$$ 4.00000 0.190910 0.0954548 0.995434i $$-0.469569\pi$$
0.0954548 + 0.995434i $$0.469569\pi$$
$$440$$ 0 0
$$441$$ −4.46410 30.9282i −0.212576 1.47277i
$$442$$ 0 0
$$443$$ −5.46410 −0.259607 −0.129804 0.991540i $$-0.541435\pi$$
−0.129804 + 0.991540i $$0.541435\pi$$
$$444$$ 0 0
$$445$$ 10.9282i 0.518047i
$$446$$ 0 0
$$447$$ −32.7846 −1.55066
$$448$$ 0 0
$$449$$ 4.14359 0.195548 0.0977741 0.995209i $$-0.468828\pi$$
0.0977741 + 0.995209i $$0.468828\pi$$
$$450$$ 0 0
$$451$$ 16.0000i 0.753411i
$$452$$ 0 0
$$453$$ −30.9282 −1.45313
$$454$$ 0 0
$$455$$ 6.92820 + 6.00000i 0.324799 + 0.281284i
$$456$$ 0 0
$$457$$ 12.3923 0.579688 0.289844 0.957074i $$-0.406397\pi$$
0.289844 + 0.957074i $$0.406397\pi$$
$$458$$ 0 0
$$459$$ 16.0000 0.746816
$$460$$ 0 0
$$461$$ 17.5167 0.815832 0.407916 0.913019i $$-0.366256\pi$$
0.407916 + 0.913019i $$0.366256\pi$$
$$462$$ 0 0
$$463$$ 27.4641i 1.27637i −0.769885 0.638183i $$-0.779687\pi$$
0.769885 0.638183i $$-0.220313\pi$$
$$464$$ 0 0
$$465$$ 13.8564i 0.642575i
$$466$$ 0 0
$$467$$ 12.5885i 0.582524i 0.956643 + 0.291262i $$0.0940752\pi$$
−0.956643 + 0.291262i $$0.905925\pi$$
$$468$$ 0 0
$$469$$ −5.07180 4.39230i −0.234194 0.202818i
$$470$$ 0 0
$$471$$ 52.6410i 2.42557i
$$472$$ 0 0
$$473$$ −13.8564 −0.637118
$$474$$ 0 0
$$475$$ 5.66025i 0.259710i
$$476$$ 0 0
$$477$$ 30.9282i 1.41611i
$$478$$ 0 0
$$479$$ 17.0718 0.780030 0.390015 0.920808i $$-0.372470\pi$$
0.390015 + 0.920808i $$0.372470\pi$$
$$480$$ 0 0
$$481$$ 18.9282i 0.863052i
$$482$$ 0 0
$$483$$ 29.8564 + 25.8564i 1.35851 + 1.17651i
$$484$$ 0 0
$$485$$ 8.78461i 0.398889i
$$486$$ 0 0
$$487$$ 16.3923i 0.742806i 0.928472 + 0.371403i $$0.121123\pi$$
−0.928472 + 0.371403i $$0.878877\pi$$
$$488$$ 0 0
$$489$$ 44.7846i 2.02523i
$$490$$ 0 0
$$491$$ 19.3205 0.871922 0.435961 0.899965i $$-0.356409\pi$$
0.435961 + 0.899965i $$0.356409\pi$$
$$492$$ 0 0
$$493$$ 27.7128 1.24812
$$494$$ 0 0
$$495$$ −17.8564 −0.802586
$$496$$ 0 0
$$497$$ −7.85641 + 9.07180i −0.352408 + 0.406926i
$$498$$ 0 0
$$499$$ 16.3923 0.733820 0.366910 0.930256i $$-0.380416\pi$$
0.366910 + 0.930256i $$0.380416\pi$$
$$500$$ 0 0
$$501$$ 13.8564i 0.619059i
$$502$$ 0 0
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ 4.53590 0.201845
$$506$$ 0 0
$$507$$ 25.6603i 1.13961i
$$508$$ 0 0
$$509$$ −42.1962 −1.87031 −0.935156 0.354237i $$-0.884741\pi$$
−0.935156 + 0.354237i $$0.884741\pi$$
$$510$$ 0 0
$$511$$ −12.0000 + 13.8564i −0.530849 + 0.612971i
$$512$$ 0 0
$$513$$ 5.07180 0.223925
$$514$$ 0 0
$$515$$ −13.8564 −0.610586
$$516$$ 0 0
$$517$$ 37.8564 1.66492
$$518$$ 0 0
$$519$$ 8.92820i 0.391905i
$$520$$ 0 0
$$521$$ 13.0718i 0.572686i −0.958127 0.286343i $$-0.907560\pi$$
0.958127 0.286343i $$-0.0924397\pi$$
$$522$$ 0 0
$$523$$ 29.3731i 1.28439i 0.766539 + 0.642197i $$0.221977\pi$$
−0.766539 + 0.642197i $$0.778023\pi$$
$$524$$ 0 0
$$525$$ 21.1244 24.3923i 0.921942 1.06457i
$$526$$ 0 0
$$527$$ 27.7128i 1.20719i
$$528$$ 0 0
$$529$$ −6.85641 −0.298105
$$530$$ 0 0
$$531$$ 16.9808i 0.736902i
$$532$$ 0 0
$$533$$ 13.8564i 0.600188i
$$534$$ 0 0
$$535$$ 6.14359 0.265611
$$536$$ 0 0
$$537$$ 1.07180i 0.0462514i
$$538$$ 0 0
$$539$$ 5.46410 + 37.8564i 0.235356 + 1.63059i
$$540$$ 0 0
$$541$$ 28.0000i 1.20381i 0.798566 + 0.601907i $$0.205592\pi$$
−0.798566 + 0.601907i $$0.794408\pi$$
$$542$$ 0 0
$$543$$ 45.7128i 1.96172i
$$544$$ 0 0
$$545$$ 5.07180i 0.217252i
$$546$$ 0 0
$$547$$ −21.4641 −0.917739 −0.458869 0.888504i $$-0.651745\pi$$
−0.458869 + 0.888504i $$0.651745\pi$$
$$548$$ 0 0
$$549$$ −52.0526 −2.22155
$$550$$ 0 0
$$551$$ 8.78461 0.374237
$$552$$ 0 0
$$553$$ 6.00000 6.92820i 0.255146 0.294617i
$$554$$ 0 0
$$555$$ −8.00000 −0.339581
$$556$$ 0 0
$$557$$ 30.9282i 1.31047i 0.755425 + 0.655235i $$0.227430\pi$$
−0.755425 + 0.655235i $$0.772570\pi$$
$$558$$ 0 0
$$559$$ 12.0000 0.507546
$$560$$ 0 0
$$561$$ −59.7128 −2.52108
$$562$$ 0 0
$$563$$ 28.9808i 1.22139i −0.791865 0.610697i $$-0.790889\pi$$
0.791865 0.610697i $$-0.209111\pi$$
$$564$$ 0 0
$$565$$ −6.92820 −0.291472
$$566$$ 0 0
$$567$$ 4.92820 + 4.26795i 0.206965 + 0.179237i
$$568$$ 0 0
$$569$$ 28.3923 1.19027 0.595134 0.803627i $$-0.297099\pi$$
0.595134 + 0.803627i $$0.297099\pi$$
$$570$$ 0 0
$$571$$ −30.2487 −1.26587 −0.632935 0.774205i $$-0.718150\pi$$
−0.632935 + 0.774205i $$0.718150\pi$$
$$572$$ 0 0
$$573$$ −31.3205 −1.30843
$$574$$ 0 0
$$575$$ 24.3923i 1.01723i
$$576$$ 0 0
$$577$$ 10.1436i 0.422283i 0.977455 + 0.211142i $$0.0677181\pi$$
−0.977455 + 0.211142i $$0.932282\pi$$
$$578$$ 0 0
$$579$$ 12.0000i 0.498703i
$$580$$ 0 0
$$581$$ −18.5885 + 21.4641i −0.771179 + 0.890481i
$$582$$ 0 0
$$583$$ 37.8564i 1.56785i
$$584$$ 0 0
$$585$$ 15.4641 0.639362
$$586$$ 0 0
$$587$$ 3.80385i 0.157002i 0.996914 + 0.0785008i $$0.0250133\pi$$
−0.996914 + 0.0785008i $$0.974987\pi$$
$$588$$ 0 0
$$589$$ 8.78461i 0.361964i
$$590$$ 0 0
$$591$$ 32.7846 1.34858
$$592$$ 0 0
$$593$$ 19.7128i 0.809508i 0.914426 + 0.404754i $$0.132643\pi$$
−0.914426 + 0.404754i $$0.867357\pi$$
$$594$$ 0 0
$$595$$ −5.07180 + 5.85641i −0.207923 + 0.240089i
$$596$$ 0 0
$$597$$ 45.8564i 1.87678i
$$598$$ 0 0
$$599$$ 12.5359i 0.512203i 0.966650 + 0.256101i $$0.0824381\pi$$
−0.966650 + 0.256101i $$0.917562\pi$$
$$600$$ 0 0
$$601$$ 34.6410i 1.41304i −0.707695 0.706518i $$-0.750265\pi$$
0.707695 0.706518i $$-0.249735\pi$$
$$602$$ 0 0
$$603$$ −11.3205 −0.461007
$$604$$ 0 0
$$605$$ 13.8038 0.561206
$$606$$ 0 0
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ 0 0
$$609$$ −37.8564 32.7846i −1.53402 1.32850i
$$610$$ 0 0
$$611$$ −32.7846 −1.32632
$$612$$ 0 0
$$613$$ 25.8564i 1.04433i 0.852844 + 0.522165i $$0.174876\pi$$
−0.852844 + 0.522165i $$0.825124\pi$$
$$614$$ 0 0
$$615$$ 5.85641 0.236153
$$616$$ 0 0
$$617$$ 4.39230 0.176828 0.0884138 0.996084i $$-0.471820\pi$$
0.0884138 + 0.996084i $$0.471820\pi$$
$$618$$ 0 0
$$619$$ 24.1962i 0.972525i 0.873813 + 0.486263i $$0.161640\pi$$
−0.873813 + 0.486263i $$0.838360\pi$$
$$620$$ 0 0
$$621$$ 21.8564 0.877067
$$622$$ 0 0
$$623$$ −25.8564 + 29.8564i −1.03592 + 1.19617i
$$624$$ 0 0
$$625$$ 17.2487 0.689948
$$626$$ 0 0
$$627$$ −18.9282 −0.755920
$$628$$ 0 0
$$629$$ −16.0000 −0.637962
$$630$$ 0 0
$$631$$ 24.2487i 0.965326i 0.875806 + 0.482663i $$0.160330\pi$$
−0.875806 + 0.482663i $$0.839670\pi$$
$$632$$ 0 0
$$633$$ 20.7846i 0.826114i
$$634$$ 0 0
$$635$$ 15.7128i 0.623544i
$$636$$ 0 0
$$637$$ −4.73205 32.7846i −0.187491 1.29897i
$$638$$ 0 0
$$639$$ 20.2487i 0.801027i
$$640$$ 0 0
$$641$$ −33.4641 −1.32175 −0.660876 0.750495i $$-0.729815\pi$$
−0.660876 + 0.750495i $$0.729815\pi$$
$$642$$ 0 0
$$643$$ 22.7321i 0.896465i 0.893917 + 0.448232i $$0.147946\pi$$
−0.893917 + 0.448232i $$0.852054\pi$$
$$644$$ 0 0
$$645$$ 5.07180i 0.199702i
$$646$$ 0 0
$$647$$ −22.6410 −0.890110 −0.445055 0.895503i $$-0.646816\pi$$
−0.445055 + 0.895503i $$0.646816\pi$$
$$648$$ 0 0
$$649$$ 20.7846i 0.815867i
$$650$$ 0 0
$$651$$ 32.7846 37.8564i 1.28493 1.48371i
$$652$$ 0 0
$$653$$ 12.0000i 0.469596i 0.972044 + 0.234798i $$0.0754429\pi$$
−0.972044 + 0.234798i $$0.924557\pi$$
$$654$$ 0 0
$$655$$ 7.85641i 0.306975i
$$656$$ 0 0
$$657$$ 30.9282i 1.20662i
$$658$$ 0 0
$$659$$ −36.1051 −1.40646 −0.703228 0.710965i $$-0.748259\pi$$
−0.703228 + 0.710965i $$0.748259\pi$$
$$660$$ 0 0
$$661$$ 14.1962 0.552166 0.276083 0.961134i $$-0.410963\pi$$
0.276083 + 0.961134i $$0.410963\pi$$
$$662$$ 0 0
$$663$$ 51.7128 2.00836
$$664$$ 0 0
$$665$$ −1.60770 + 1.85641i −0.0623437 + 0.0719884i
$$666$$ 0 0
$$667$$ 37.8564 1.46581
$$668$$ 0 0
$$669$$ 21.8564i 0.845017i
$$670$$ 0 0
$$671$$ 63.7128 2.45961
$$672$$ 0 0
$$673$$ 30.0000 1.15642 0.578208 0.815890i $$-0.303752\pi$$
0.578208 + 0.815890i $$0.303752\pi$$
$$674$$ 0 0
$$675$$ 17.8564i 0.687293i
$$676$$ 0 0
$$677$$ 18.8756 0.725450 0.362725 0.931896i $$-0.381846\pi$$
0.362725 + 0.931896i $$0.381846\pi$$
$$678$$ 0 0
$$679$$ 20.7846 24.0000i 0.797640 0.921035i
$$680$$ 0 0
$$681$$ −3.46410 −0.132745
$$682$$ 0 0
$$683$$ −29.4641 −1.12741 −0.563706 0.825975i $$-0.690625\pi$$
−0.563706 + 0.825975i $$0.690625\pi$$
$$684$$ 0 0
$$685$$ 14.5359 0.555388
$$686$$ 0 0
$$687$$ 0.928203i 0.0354132i
$$688$$ 0 0
$$689$$ 32.7846i 1.24899i
$$690$$ 0 0
$$691$$ 32.9808i 1.25465i 0.778759 + 0.627324i $$0.215850\pi$$
−0.778759 + 0.627324i $$0.784150\pi$$
$$692$$ 0 0
$$693$$ 48.7846 + 42.2487i 1.85317 + 1.60490i
$$694$$ 0 0
$$695$$ 3.07180i 0.116520i
$$696$$ 0 0
$$697$$ 11.7128 0.443654
$$698$$ 0 0
$$699$$ 54.2487i 2.05187i
$$700$$ 0 0
$$701$$ 1.85641i 0.0701155i 0.999385 + 0.0350578i $$0.0111615\pi$$
−0.999385 + 0.0350578i $$0.988838\pi$$
$$702$$ 0 0
$$703$$ −5.07180 −0.191286
$$704$$ 0 0
$$705$$ 13.8564i 0.521862i
$$706$$ 0 0
$$707$$ −12.3923 10.7321i −0.466061 0.403620i
$$708$$ 0 0
$$709$$ 30.9282i 1.16153i −0.814070 0.580767i $$-0.802753\pi$$
0.814070 0.580767i $$-0.197247\pi$$
$$710$$ 0 0
$$711$$ 15.4641i 0.579949i
$$712$$ 0 0
$$713$$ 37.8564i 1.41773i
$$714$$ 0 0
$$715$$ −18.9282 −0.707875
$$716$$ 0 0
$$717$$ 1.07180 0.0400270
$$718$$ 0 0
$$719$$ −17.0718 −0.636671 −0.318335 0.947978i $$-0.603124\pi$$
−0.318335 + 0.947978i $$0.603124\pi$$
$$720$$ 0 0
$$721$$ 37.8564 + 32.7846i 1.40985 + 1.22096i
$$722$$ 0 0
$$723$$ 32.7846 1.21927
$$724$$ 0 0
$$725$$ 30.9282i 1.14864i
$$726$$ 0 0
$$727$$ −8.78461 −0.325803 −0.162902 0.986642i $$-0.552085\pi$$
−0.162902 + 0.986642i $$0.552085\pi$$
$$728$$ 0 0
$$729$$ 43.7846 1.62165
$$730$$ 0 0
$$731$$ 10.1436i 0.375174i
$$732$$ 0 0
$$733$$ −2.19615 −0.0811167 −0.0405584 0.999177i $$-0.512914\pi$$
−0.0405584 + 0.999177i $$0.512914\pi$$
$$734$$ 0 0
$$735$$ 13.8564 2.00000i 0.511101 0.0737711i
$$736$$ 0 0
$$737$$ 13.8564 0.510407
$$738$$ 0 0
$$739$$ −11.3205 −0.416432 −0.208216 0.978083i $$-0.566766\pi$$
−0.208216 + 0.978083i $$0.566766\pi$$
$$740$$ 0 0
$$741$$ 16.3923 0.602186
$$742$$ 0 0
$$743$$ 10.5359i 0.386525i 0.981147 + 0.193262i $$0.0619068\pi$$
−0.981147 + 0.193262i $$0.938093\pi$$
$$744$$ 0 0
$$745$$ 8.78461i 0.321843i
$$746$$ 0 0
$$747$$ 47.9090i 1.75290i
$$748$$ 0 0
$$749$$ −16.7846 14.5359i −0.613296 0.531130i
$$750$$ 0 0
$$751$$ 26.5359i 0.968309i 0.874983 + 0.484154i $$0.160873\pi$$
−0.874983 + 0.484154i $$0.839127\pi$$
$$752$$ 0 0
$$753$$ 60.2487 2.19559
$$754$$ 0 0
$$755$$ 8.28719i 0.301602i
$$756$$ 0 0
$$757$$ 29.5692i 1.07471i −0.843356 0.537356i $$-0.819423\pi$$
0.843356 0.537356i $$-0.180577\pi$$
$$758$$ 0 0
$$759$$ −81.5692 −2.96078
$$760$$ 0 0
$$761$$ 16.7846i 0.608442i −0.952602 0.304221i $$-0.901604\pi$$
0.952602 0.304221i $$-0.0983961\pi$$
$$762$$ 0 0
$$763$$ −12.0000 + 13.8564i −0.434429 + 0.501636i
$$764$$ 0 0
$$765$$ 13.0718i 0.472612i
$$766$$ 0 0
$$767$$ 18.0000i 0.649942i
$$768$$ 0 0
$$769$$ 1.85641i 0.0669437i 0.999440 + 0.0334719i $$0.0106564\pi$$
−0.999440 + 0.0334719i $$0.989344\pi$$
$$770$$ 0 0
$$771$$ 59.7128 2.15050
$$772$$ 0 0
$$773$$ 36.4449 1.31083 0.655415 0.755269i $$-0.272494\pi$$
0.655415 + 0.755269i $$0.272494\pi$$
$$774$$ 0 0
$$775$$ 30.9282 1.11097
$$776$$ 0 0
$$777$$ 21.8564 + 18.9282i 0.784094 + 0.679046i
$$778$$ 0 0
$$779$$ 3.71281 0.133025
$$780$$ 0 0
$$781$$ 24.7846i 0.886863i
$$782$$ 0 0
$$783$$ −27.7128 −0.990375
$$784$$ 0 0
$$785$$ 14.1051 0.503433
$$786$$ 0 0
$$787$$ 20.5885i 0.733899i 0.930241 + 0.366950i $$0.119598\pi$$
−0.930241 + 0.366950i $$0.880402\pi$$
$$788$$ 0 0
$$789$$ 31.3205 1.11504
$$790$$ 0 0
$$791$$ 18.9282 + 16.3923i 0.673009 + 0.582843i
$$792$$ 0 0
$$793$$ −55.1769 −1.95939
$$794$$ 0 0
$$795$$ 13.8564 0.491436
$$796$$ 0 0
$$797$$ 41.1244 1.45670 0.728350 0.685206i $$-0.240288\pi$$
0.728350 + 0.685206i $$0.240288\pi$$
$$798$$ 0 0
$$799$$ 27.7128i 0.980409i
$$800$$ 0 0
$$801$$ 66.6410i 2.35464i
$$802$$ 0 0