# Properties

 Label 2304.2.k.a.577.1 Level $2304$ Weight $2$ Character 2304.577 Analytic conductor $18.398$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2304 = 2^{8} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2304.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.3975326257$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 768) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 577.1 Root $$0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 2304.577 Dual form 2304.2.k.a.1729.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.00000 + 2.00000i) q^{5} -4.24264i q^{7} +O(q^{10})$$ $$q+(-2.00000 + 2.00000i) q^{5} -4.24264i q^{7} +(-2.82843 + 2.82843i) q^{11} +(3.00000 + 3.00000i) q^{13} +6.00000 q^{17} +(-1.41421 - 1.41421i) q^{19} -2.82843i q^{23} -3.00000i q^{25} +(-4.00000 - 4.00000i) q^{29} -4.24264 q^{31} +(8.48528 + 8.48528i) q^{35} +(3.00000 - 3.00000i) q^{37} +10.0000i q^{41} +(-4.24264 + 4.24264i) q^{43} -2.82843 q^{47} -11.0000 q^{49} +(-4.00000 + 4.00000i) q^{53} -11.3137i q^{55} +(3.00000 + 3.00000i) q^{61} -12.0000 q^{65} +(2.82843 + 2.82843i) q^{67} +2.82843i q^{71} +16.0000i q^{73} +(12.0000 + 12.0000i) q^{77} +4.24264 q^{79} +(11.3137 + 11.3137i) q^{83} +(-12.0000 + 12.0000i) q^{85} +14.0000i q^{89} +(12.7279 - 12.7279i) q^{91} +5.65685 q^{95} -4.00000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 8q^{5} + O(q^{10})$$ $$4q - 8q^{5} + 12q^{13} + 24q^{17} - 16q^{29} + 12q^{37} - 44q^{49} - 16q^{53} + 12q^{61} - 48q^{65} + 48q^{77} - 48q^{85} - 16q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times$$.

 $$n$$ $$1279$$ $$1793$$ $$2053$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$5$$ −2.00000 + 2.00000i −0.894427 + 0.894427i −0.994936 0.100509i $$-0.967953\pi$$
0.100509 + 0.994936i $$0.467953\pi$$
$$6$$ 0 0
$$7$$ 4.24264i 1.60357i −0.597614 0.801784i $$-0.703885\pi$$
0.597614 0.801784i $$-0.296115\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.82843 + 2.82843i −0.852803 + 0.852803i −0.990478 0.137675i $$-0.956037\pi$$
0.137675 + 0.990478i $$0.456037\pi$$
$$12$$ 0 0
$$13$$ 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i $$-0.0497784\pi$$
−0.155747 + 0.987797i $$0.549778\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ −1.41421 1.41421i −0.324443 0.324443i 0.526026 0.850469i $$-0.323682\pi$$
−0.850469 + 0.526026i $$0.823682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.82843i 0.589768i −0.955533 0.294884i $$-0.904719\pi$$
0.955533 0.294884i $$-0.0952810\pi$$
$$24$$ 0 0
$$25$$ 3.00000i 0.600000i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.00000 4.00000i −0.742781 0.742781i 0.230331 0.973112i $$-0.426019\pi$$
−0.973112 + 0.230331i $$0.926019\pi$$
$$30$$ 0 0
$$31$$ −4.24264 −0.762001 −0.381000 0.924575i $$-0.624420\pi$$
−0.381000 + 0.924575i $$0.624420\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 8.48528 + 8.48528i 1.43427 + 1.43427i
$$36$$ 0 0
$$37$$ 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i $$-0.636609\pi$$
0.909312 + 0.416115i $$0.136609\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000i 1.56174i 0.624695 + 0.780869i $$0.285223\pi$$
−0.624695 + 0.780869i $$0.714777\pi$$
$$42$$ 0 0
$$43$$ −4.24264 + 4.24264i −0.646997 + 0.646997i −0.952266 0.305269i $$-0.901253\pi$$
0.305269 + 0.952266i $$0.401253\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.82843 −0.412568 −0.206284 0.978492i $$-0.566137\pi$$
−0.206284 + 0.978492i $$0.566137\pi$$
$$48$$ 0 0
$$49$$ −11.0000 −1.57143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4.00000 + 4.00000i −0.549442 + 0.549442i −0.926279 0.376837i $$-0.877012\pi$$
0.376837 + 0.926279i $$0.377012\pi$$
$$54$$ 0 0
$$55$$ 11.3137i 1.52554i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$60$$ 0 0
$$61$$ 3.00000 + 3.00000i 0.384111 + 0.384111i 0.872581 0.488470i $$-0.162445\pi$$
−0.488470 + 0.872581i $$0.662445\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −12.0000 −1.48842
$$66$$ 0 0
$$67$$ 2.82843 + 2.82843i 0.345547 + 0.345547i 0.858448 0.512901i $$-0.171429\pi$$
−0.512901 + 0.858448i $$0.671429\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2.82843i 0.335673i 0.985815 + 0.167836i $$0.0536780\pi$$
−0.985815 + 0.167836i $$0.946322\pi$$
$$72$$ 0 0
$$73$$ 16.0000i 1.87266i 0.351123 + 0.936329i $$0.385800\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 12.0000 + 12.0000i 1.36753 + 1.36753i
$$78$$ 0 0
$$79$$ 4.24264 0.477334 0.238667 0.971101i $$-0.423290\pi$$
0.238667 + 0.971101i $$0.423290\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 11.3137 + 11.3137i 1.24184 + 1.24184i 0.959237 + 0.282604i $$0.0911983\pi$$
0.282604 + 0.959237i $$0.408802\pi$$
$$84$$ 0 0
$$85$$ −12.0000 + 12.0000i −1.30158 + 1.30158i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 14.0000i 1.48400i 0.670402 + 0.741999i $$0.266122\pi$$
−0.670402 + 0.741999i $$0.733878\pi$$
$$90$$ 0 0
$$91$$ 12.7279 12.7279i 1.33425 1.33425i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 5.65685 0.580381
$$96$$ 0 0
$$97$$ −4.00000 −0.406138 −0.203069 0.979164i $$-0.565092\pi$$
−0.203069 + 0.979164i $$0.565092\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −8.00000 + 8.00000i −0.796030 + 0.796030i −0.982467 0.186437i $$-0.940306\pi$$
0.186437 + 0.982467i $$0.440306\pi$$
$$102$$ 0 0
$$103$$ 18.3848i 1.81151i 0.423806 + 0.905753i $$0.360694\pi$$
−0.423806 + 0.905753i $$0.639306\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.82843 + 2.82843i −0.273434 + 0.273434i −0.830481 0.557047i $$-0.811934\pi$$
0.557047 + 0.830481i $$0.311934\pi$$
$$108$$ 0 0
$$109$$ −7.00000 7.00000i −0.670478 0.670478i 0.287348 0.957826i $$-0.407226\pi$$
−0.957826 + 0.287348i $$0.907226\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 5.65685 + 5.65685i 0.527504 + 0.527504i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 25.4558i 2.33353i
$$120$$ 0 0
$$121$$ 5.00000i 0.454545i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −4.00000 4.00000i −0.357771 0.357771i
$$126$$ 0 0
$$127$$ −4.24264 −0.376473 −0.188237 0.982124i $$-0.560277\pi$$
−0.188237 + 0.982124i $$0.560277\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −14.1421 14.1421i −1.23560 1.23560i −0.961780 0.273824i $$-0.911711\pi$$
−0.273824 0.961780i $$-0.588289\pi$$
$$132$$ 0 0
$$133$$ −6.00000 + 6.00000i −0.520266 + 0.520266i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.0000i 0.854358i −0.904167 0.427179i $$-0.859507\pi$$
0.904167 0.427179i $$-0.140493\pi$$
$$138$$ 0 0
$$139$$ −8.48528 + 8.48528i −0.719712 + 0.719712i −0.968546 0.248834i $$-0.919953\pi$$
0.248834 + 0.968546i $$0.419953\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −16.9706 −1.41915
$$144$$ 0 0
$$145$$ 16.0000 1.32873
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −6.00000 + 6.00000i −0.491539 + 0.491539i −0.908791 0.417252i $$-0.862993\pi$$
0.417252 + 0.908791i $$0.362993\pi$$
$$150$$ 0 0
$$151$$ 1.41421i 0.115087i −0.998343 0.0575435i $$-0.981673\pi$$
0.998343 0.0575435i $$-0.0183268\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 8.48528 8.48528i 0.681554 0.681554i
$$156$$ 0 0
$$157$$ 5.00000 + 5.00000i 0.399043 + 0.399043i 0.877896 0.478852i $$-0.158947\pi$$
−0.478852 + 0.877896i $$0.658947\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −12.0000 −0.945732
$$162$$ 0 0
$$163$$ 7.07107 + 7.07107i 0.553849 + 0.553849i 0.927549 0.373701i $$-0.121911\pi$$
−0.373701 + 0.927549i $$0.621911\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 11.3137i 0.875481i −0.899101 0.437741i $$-0.855779\pi$$
0.899101 0.437741i $$-0.144221\pi$$
$$168$$ 0 0
$$169$$ 5.00000i 0.384615i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2.00000 + 2.00000i 0.152057 + 0.152057i 0.779036 0.626979i $$-0.215709\pi$$
−0.626979 + 0.779036i $$0.715709\pi$$
$$174$$ 0 0
$$175$$ −12.7279 −0.962140
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$180$$ 0 0
$$181$$ −1.00000 + 1.00000i −0.0743294 + 0.0743294i −0.743294 0.668965i $$-0.766738\pi$$
0.668965 + 0.743294i $$0.266738\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 12.0000i 0.882258i
$$186$$ 0 0
$$187$$ −16.9706 + 16.9706i −1.24101 + 1.24101i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −22.6274 −1.63726 −0.818631 0.574320i $$-0.805267\pi$$
−0.818631 + 0.574320i $$0.805267\pi$$
$$192$$ 0 0
$$193$$ 18.0000 1.29567 0.647834 0.761781i $$-0.275675\pi$$
0.647834 + 0.761781i $$0.275675\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −4.00000 + 4.00000i −0.284988 + 0.284988i −0.835095 0.550106i $$-0.814587\pi$$
0.550106 + 0.835095i $$0.314587\pi$$
$$198$$ 0 0
$$199$$ 7.07107i 0.501255i −0.968084 0.250627i $$-0.919363\pi$$
0.968084 0.250627i $$-0.0806369\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −16.9706 + 16.9706i −1.19110 + 1.19110i
$$204$$ 0 0
$$205$$ −20.0000 20.0000i −1.39686 1.39686i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 8.00000 0.553372
$$210$$ 0 0
$$211$$ 8.48528 + 8.48528i 0.584151 + 0.584151i 0.936041 0.351890i $$-0.114461\pi$$
−0.351890 + 0.936041i $$0.614461\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 16.9706i 1.15738i
$$216$$ 0 0
$$217$$ 18.0000i 1.22192i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 18.0000 + 18.0000i 1.21081 + 1.21081i
$$222$$ 0 0
$$223$$ 21.2132 1.42054 0.710271 0.703929i $$-0.248573\pi$$
0.710271 + 0.703929i $$0.248573\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$228$$ 0 0
$$229$$ 11.0000 11.0000i 0.726900 0.726900i −0.243101 0.970001i $$-0.578165\pi$$
0.970001 + 0.243101i $$0.0781645\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 18.0000i 1.17922i −0.807688 0.589610i $$-0.799282\pi$$
0.807688 0.589610i $$-0.200718\pi$$
$$234$$ 0 0
$$235$$ 5.65685 5.65685i 0.369012 0.369012i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 11.3137 0.731823 0.365911 0.930650i $$-0.380757\pi$$
0.365911 + 0.930650i $$0.380757\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 22.0000 22.0000i 1.40553 1.40553i
$$246$$ 0 0
$$247$$ 8.48528i 0.539906i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.82843 2.82843i 0.178529 0.178529i −0.612185 0.790714i $$-0.709709\pi$$
0.790714 + 0.612185i $$0.209709\pi$$
$$252$$ 0 0
$$253$$ 8.00000 + 8.00000i 0.502956 + 0.502956i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 14.0000 0.873296 0.436648 0.899632i $$-0.356166\pi$$
0.436648 + 0.899632i $$0.356166\pi$$
$$258$$ 0 0
$$259$$ −12.7279 12.7279i −0.790875 0.790875i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 22.6274i 1.39527i 0.716455 + 0.697633i $$0.245763\pi$$
−0.716455 + 0.697633i $$0.754237\pi$$
$$264$$ 0 0
$$265$$ 16.0000i 0.982872i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$270$$ 0 0
$$271$$ 1.41421 0.0859074 0.0429537 0.999077i $$-0.486323\pi$$
0.0429537 + 0.999077i $$0.486323\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 8.48528 + 8.48528i 0.511682 + 0.511682i
$$276$$ 0 0
$$277$$ 1.00000 1.00000i 0.0600842 0.0600842i −0.676426 0.736510i $$-0.736472\pi$$
0.736510 + 0.676426i $$0.236472\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.00000i 0.357930i 0.983855 + 0.178965i $$0.0572749\pi$$
−0.983855 + 0.178965i $$0.942725\pi$$
$$282$$ 0 0
$$283$$ −2.82843 + 2.82843i −0.168133 + 0.168133i −0.786158 0.618026i $$-0.787933\pi$$
0.618026 + 0.786158i $$0.287933\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 42.4264 2.50435
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −4.00000 + 4.00000i −0.233682 + 0.233682i −0.814228 0.580545i $$-0.802839\pi$$
0.580545 + 0.814228i $$0.302839\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 8.48528 8.48528i 0.490716 0.490716i
$$300$$ 0 0
$$301$$ 18.0000 + 18.0000i 1.03750 + 1.03750i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −12.0000 −0.687118
$$306$$ 0 0
$$307$$ 2.82843 + 2.82843i 0.161427 + 0.161427i 0.783199 0.621772i $$-0.213587\pi$$
−0.621772 + 0.783199i $$0.713587\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 28.2843i 1.60385i 0.597422 + 0.801927i $$0.296192\pi$$
−0.597422 + 0.801927i $$0.703808\pi$$
$$312$$ 0 0
$$313$$ 26.0000i 1.46961i −0.678280 0.734803i $$-0.737274\pi$$
0.678280 0.734803i $$-0.262726\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.0000 12.0000i −0.673987 0.673987i 0.284646 0.958633i $$-0.408124\pi$$
−0.958633 + 0.284646i $$0.908124\pi$$
$$318$$ 0 0
$$319$$ 22.6274 1.26689
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.48528 8.48528i −0.472134 0.472134i
$$324$$ 0 0
$$325$$ 9.00000 9.00000i 0.499230 0.499230i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 12.0000i 0.661581i
$$330$$ 0 0
$$331$$ 2.82843 2.82843i 0.155464 0.155464i −0.625089 0.780553i $$-0.714937\pi$$
0.780553 + 0.625089i $$0.214937\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −11.3137 −0.618134
$$336$$ 0 0
$$337$$ −8.00000 −0.435788 −0.217894 0.975972i $$-0.569919\pi$$
−0.217894 + 0.975972i $$0.569919\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 12.0000 12.0000i 0.649836 0.649836i
$$342$$ 0 0
$$343$$ 16.9706i 0.916324i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 16.9706 16.9706i 0.911028 0.911028i −0.0853256 0.996353i $$-0.527193\pi$$
0.996353 + 0.0853256i $$0.0271930\pi$$
$$348$$ 0 0
$$349$$ −3.00000 3.00000i −0.160586 0.160586i 0.622240 0.782826i $$-0.286223\pi$$
−0.782826 + 0.622240i $$0.786223\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ −5.65685 5.65685i −0.300235 0.300235i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 2.82843i 0.149279i 0.997211 + 0.0746393i $$0.0237806\pi$$
−0.997211 + 0.0746393i $$0.976219\pi$$
$$360$$ 0 0
$$361$$ 15.0000i 0.789474i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −32.0000 32.0000i −1.67496 1.67496i
$$366$$ 0 0
$$367$$ −18.3848 −0.959678 −0.479839 0.877357i $$-0.659305\pi$$
−0.479839 + 0.877357i $$0.659305\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 16.9706 + 16.9706i 0.881068 + 0.881068i
$$372$$ 0 0
$$373$$ 13.0000 13.0000i 0.673114 0.673114i −0.285318 0.958433i $$-0.592099\pi$$
0.958433 + 0.285318i $$0.0920993\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 24.0000i 1.23606i
$$378$$ 0 0
$$379$$ 26.8701 26.8701i 1.38022 1.38022i 0.536011 0.844211i $$-0.319930\pi$$
0.844211 0.536011i $$-0.180070\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 28.2843 1.44526 0.722629 0.691236i $$-0.242933\pi$$
0.722629 + 0.691236i $$0.242933\pi$$
$$384$$ 0 0
$$385$$ −48.0000 −2.44631
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 2.00000 2.00000i 0.101404 0.101404i −0.654585 0.755989i $$-0.727156\pi$$
0.755989 + 0.654585i $$0.227156\pi$$
$$390$$ 0 0
$$391$$ 16.9706i 0.858238i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −8.48528 + 8.48528i −0.426941 + 0.426941i
$$396$$ 0 0
$$397$$ 23.0000 + 23.0000i 1.15434 + 1.15434i 0.985674 + 0.168663i $$0.0539450\pi$$
0.168663 + 0.985674i $$0.446055\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 10.0000 0.499376 0.249688 0.968326i $$-0.419672\pi$$
0.249688 + 0.968326i $$0.419672\pi$$
$$402$$ 0 0
$$403$$ −12.7279 12.7279i −0.634023 0.634023i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 16.9706i 0.841200i
$$408$$ 0 0
$$409$$ 28.0000i 1.38451i 0.721653 + 0.692255i $$0.243383\pi$$
−0.721653 + 0.692255i $$0.756617\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −45.2548 −2.22147
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −11.3137 11.3137i −0.552711 0.552711i 0.374511 0.927222i $$-0.377810\pi$$
−0.927222 + 0.374511i $$0.877810\pi$$
$$420$$ 0 0
$$421$$ −25.0000 + 25.0000i −1.21843 + 1.21843i −0.250242 + 0.968183i $$0.580510\pi$$
−0.968183 + 0.250242i $$0.919490\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 18.0000i 0.873128i
$$426$$ 0 0
$$427$$ 12.7279 12.7279i 0.615947 0.615947i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −36.7696 −1.77113 −0.885564 0.464518i $$-0.846227\pi$$
−0.885564 + 0.464518i $$0.846227\pi$$
$$432$$ 0 0
$$433$$ −8.00000 −0.384455 −0.192228 0.981350i $$-0.561571\pi$$
−0.192228 + 0.981350i $$0.561571\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −4.00000 + 4.00000i −0.191346 + 0.191346i
$$438$$ 0 0
$$439$$ 1.41421i 0.0674967i 0.999430 + 0.0337484i $$0.0107445\pi$$
−0.999430 + 0.0337484i $$0.989256\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −16.9706 + 16.9706i −0.806296 + 0.806296i −0.984071 0.177775i $$-0.943110\pi$$
0.177775 + 0.984071i $$0.443110\pi$$
$$444$$ 0 0
$$445$$ −28.0000 28.0000i −1.32733 1.32733i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 26.0000 1.22702 0.613508 0.789689i $$-0.289758\pi$$
0.613508 + 0.789689i $$0.289758\pi$$
$$450$$ 0 0
$$451$$ −28.2843 28.2843i −1.33185 1.33185i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 50.9117i 2.38678i
$$456$$ 0 0
$$457$$ 12.0000i 0.561336i 0.959805 + 0.280668i $$0.0905560\pi$$
−0.959805 + 0.280668i $$0.909444\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −6.00000 6.00000i −0.279448 0.279448i 0.553441 0.832889i $$-0.313315\pi$$
−0.832889 + 0.553441i $$0.813315\pi$$
$$462$$ 0 0
$$463$$ −12.7279 −0.591517 −0.295758 0.955263i $$-0.595572\pi$$
−0.295758 + 0.955263i $$0.595572\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −16.9706 16.9706i −0.785304 0.785304i 0.195416 0.980720i $$-0.437394\pi$$
−0.980720 + 0.195416i $$0.937394\pi$$
$$468$$ 0 0
$$469$$ 12.0000 12.0000i 0.554109 0.554109i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 24.0000i 1.10352i
$$474$$ 0 0
$$475$$ −4.24264 + 4.24264i −0.194666 + 0.194666i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 25.4558 1.16311 0.581554 0.813508i $$-0.302445\pi$$
0.581554 + 0.813508i $$0.302445\pi$$
$$480$$ 0 0
$$481$$ 18.0000 0.820729
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 8.00000 8.00000i 0.363261 0.363261i
$$486$$ 0 0
$$487$$ 43.8406i 1.98661i 0.115529 + 0.993304i $$0.463144\pi$$
−0.115529 + 0.993304i $$0.536856\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −5.65685 + 5.65685i −0.255290 + 0.255290i −0.823135 0.567845i $$-0.807777\pi$$
0.567845 + 0.823135i $$0.307777\pi$$
$$492$$ 0 0
$$493$$ −24.0000 24.0000i −1.08091 1.08091i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 12.0000 0.538274
$$498$$ 0 0
$$499$$ −14.1421 14.1421i −0.633089 0.633089i 0.315753 0.948842i $$-0.397743\pi$$
−0.948842 + 0.315753i $$0.897743\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 14.1421i 0.630567i 0.948998 + 0.315283i $$0.102100\pi$$
−0.948998 + 0.315283i $$0.897900\pi$$
$$504$$ 0 0
$$505$$ 32.0000i 1.42398i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −16.0000 16.0000i −0.709188 0.709188i 0.257177 0.966364i $$-0.417208\pi$$
−0.966364 + 0.257177i $$0.917208\pi$$
$$510$$ 0 0
$$511$$ 67.8823 3.00293
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −36.7696 36.7696i −1.62026 1.62026i
$$516$$ 0 0
$$517$$ 8.00000 8.00000i 0.351840 0.351840i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 22.0000i 0.963837i 0.876216 + 0.481919i $$0.160060\pi$$
−0.876216 + 0.481919i $$0.839940\pi$$
$$522$$ 0 0
$$523$$ −15.5563 + 15.5563i −0.680232 + 0.680232i −0.960052 0.279821i $$-0.909725\pi$$
0.279821 + 0.960052i $$0.409725\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −25.4558 −1.10887
$$528$$ 0 0
$$529$$ 15.0000 0.652174
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −30.0000 + 30.0000i −1.29944 + 1.29944i
$$534$$ 0 0
$$535$$ 11.3137i 0.489134i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 31.1127 31.1127i 1.34012 1.34012i
$$540$$ 0 0
$$541$$ 29.0000 + 29.0000i 1.24681 + 1.24681i 0.957122 + 0.289685i $$0.0935507\pi$$
0.289685 + 0.957122i $$0.406449\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 28.0000 1.19939
$$546$$ 0 0
$$547$$ −24.0416 24.0416i −1.02795 1.02795i −0.999598 0.0283478i $$-0.990975\pi$$
−0.0283478 0.999598i $$-0.509025\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 11.3137i 0.481980i
$$552$$ 0 0
$$553$$ 18.0000i 0.765438i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 14.0000 + 14.0000i 0.593199 + 0.593199i 0.938494 0.345295i $$-0.112221\pi$$
−0.345295 + 0.938494i $$0.612221\pi$$
$$558$$ 0 0
$$559$$ −25.4558 −1.07667
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −2.82843 2.82843i −0.119204 0.119204i 0.644988 0.764192i $$-0.276862\pi$$
−0.764192 + 0.644988i $$0.776862\pi$$
$$564$$ 0 0
$$565$$ 12.0000 12.0000i 0.504844 0.504844i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000i 0.754599i −0.926091 0.377300i $$-0.876853\pi$$
0.926091 0.377300i $$-0.123147\pi$$
$$570$$ 0 0
$$571$$ 14.1421 14.1421i 0.591830 0.591830i −0.346296 0.938125i $$-0.612561\pi$$
0.938125 + 0.346296i $$0.112561\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −8.48528 −0.353861
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 48.0000 48.0000i 1.99138 1.99138i
$$582$$ 0 0
$$583$$ 22.6274i 0.937132i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 16.9706 16.9706i 0.700450 0.700450i −0.264057 0.964507i $$-0.585061\pi$$
0.964507 + 0.264057i $$0.0850607\pi$$
$$588$$ 0 0
$$589$$ 6.00000 + 6.00000i 0.247226 + 0.247226i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −14.0000 −0.574911 −0.287456 0.957794i $$-0.592809\pi$$
−0.287456 + 0.957794i $$0.592809\pi$$
$$594$$ 0 0
$$595$$ 50.9117 + 50.9117i 2.08718 + 2.08718i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 48.0833i 1.96463i −0.187239 0.982314i $$-0.559954\pi$$
0.187239 0.982314i $$-0.440046\pi$$
$$600$$ 0 0
$$601$$ 28.0000i 1.14214i −0.820900 0.571072i $$-0.806528\pi$$
0.820900 0.571072i $$-0.193472\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 10.0000 + 10.0000i 0.406558 + 0.406558i
$$606$$ 0 0
$$607$$ −4.24264 −0.172203 −0.0861017 0.996286i $$-0.527441\pi$$
−0.0861017 + 0.996286i $$0.527441\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8.48528 8.48528i −0.343278 0.343278i
$$612$$ 0 0
$$613$$ −13.0000 + 13.0000i −0.525065 + 0.525065i −0.919097 0.394032i $$-0.871080\pi$$
0.394032 + 0.919097i $$0.371080\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 22.0000i 0.885687i −0.896599 0.442843i $$-0.853970\pi$$
0.896599 0.442843i $$-0.146030\pi$$
$$618$$ 0 0
$$619$$ −25.4558 + 25.4558i −1.02316 + 1.02316i −0.0234313 + 0.999725i $$0.507459\pi$$
−0.999725 + 0.0234313i $$0.992541\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 59.3970 2.37969
$$624$$ 0 0
$$625$$ 31.0000 1.24000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 18.0000 18.0000i 0.717707 0.717707i
$$630$$ 0 0
$$631$$ 35.3553i 1.40747i 0.710461 + 0.703737i $$0.248487\pi$$
−0.710461 + 0.703737i $$0.751513\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 8.48528 8.48528i 0.336728 0.336728i
$$636$$ 0 0
$$637$$ −33.0000 33.0000i −1.30751 1.30751i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 0 0
$$643$$ 9.89949 + 9.89949i 0.390398 + 0.390398i 0.874829 0.484431i $$-0.160973\pi$$
−0.484431 + 0.874829i $$0.660973\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 14.1421i 0.555985i 0.960583 + 0.277992i $$0.0896690\pi$$
−0.960583 + 0.277992i $$0.910331\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 6.00000 + 6.00000i 0.234798 + 0.234798i 0.814692 0.579894i $$-0.196906\pi$$
−0.579894 + 0.814692i $$0.696906\pi$$
$$654$$ 0 0
$$655$$ 56.5685 2.21032
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$660$$ 0 0
$$661$$ −9.00000 + 9.00000i −0.350059 + 0.350059i −0.860132 0.510072i $$-0.829619\pi$$
0.510072 + 0.860132i $$0.329619\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 24.0000i 0.930680i
$$666$$ 0 0
$$667$$ −11.3137 + 11.3137i −0.438069 + 0.438069i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −16.9706 −0.655141
$$672$$ 0 0
$$673$$ −40.0000 −1.54189 −0.770943 0.636904i $$-0.780215\pi$$
−0.770943 + 0.636904i $$0.780215\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 26.0000 26.0000i 0.999261 0.999261i −0.000738553 1.00000i $$-0.500235\pi$$
1.00000 0.000738553i $$0.000235089\pi$$
$$678$$ 0 0
$$679$$ 16.9706i 0.651270i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −16.9706 + 16.9706i −0.649361 + 0.649361i −0.952838 0.303478i $$-0.901852\pi$$
0.303478 + 0.952838i $$0.401852\pi$$
$$684$$ 0 0
$$685$$ 20.0000 + 20.0000i 0.764161 + 0.764161i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −24.0000 −0.914327
$$690$$ 0 0
$$691$$ 15.5563 + 15.5563i 0.591791 + 0.591791i 0.938115 0.346324i $$-0.112570\pi$$
−0.346324 + 0.938115i $$0.612570\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 33.9411i 1.28746i
$$696$$ 0 0
$$697$$ 60.0000i 2.27266i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 4.00000 + 4.00000i 0.151078 + 0.151078i 0.778599 0.627521i $$-0.215931\pi$$
−0.627521 + 0.778599i $$0.715931\pi$$
$$702$$ 0 0
$$703$$ −8.48528 −0.320028
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 33.9411 + 33.9411i 1.27649 + 1.27649i
$$708$$ 0 0
$$709$$ 13.0000 13.0000i 0.488225 0.488225i −0.419521 0.907746i $$-0.637802\pi$$
0.907746 + 0.419521i $$0.137802\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 12.0000i 0.449404i
$$714$$ 0 0
$$715$$ 33.9411 33.9411i 1.26933 1.26933i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 8.48528 0.316448 0.158224 0.987403i $$-0.449423\pi$$
0.158224 + 0.987403i $$0.449423\pi$$
$$720$$ 0 0
$$721$$ 78.0000 2.90487
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −12.0000 + 12.0000i −0.445669 + 0.445669i
$$726$$ 0 0
$$727$$ 26.8701i 0.996555i −0.867018 0.498278i $$-0.833966\pi$$
0.867018 0.498278i $$-0.166034\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −25.4558 + 25.4558i −0.941518 + 0.941518i
$$732$$ 0 0
$$733$$ −25.0000 25.0000i −0.923396 0.923396i 0.0738717 0.997268i $$-0.476464\pi$$
−0.997268 + 0.0738717i $$0.976464\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −16.0000 −0.589368
$$738$$ 0 0
$$739$$ 25.4558 + 25.4558i 0.936408 + 0.936408i 0.998096 0.0616872i $$-0.0196481\pi$$
−0.0616872 + 0.998096i $$0.519648\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 22.6274i 0.830119i −0.909794 0.415060i $$-0.863761\pi$$
0.909794 0.415060i $$-0.136239\pi$$
$$744$$ 0 0
$$745$$ 24.0000i 0.879292i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 12.0000 + 12.0000i 0.438470 + 0.438470i
$$750$$ 0 0
$$751$$ 12.7279 0.464448 0.232224 0.972662i $$-0.425400\pi$$
0.232224 + 0.972662i $$0.425400\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2.82843 + 2.82843i 0.102937 + 0.102937i
$$756$$ 0 0
$$757$$ 27.0000 27.0000i 0.981332 0.981332i −0.0184972 0.999829i $$-0.505888\pi$$
0.999829 + 0.0184972i $$0.00588818\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 34.0000i 1.23250i −0.787551 0.616250i $$-0.788651\pi$$
0.787551 0.616250i $$-0.211349\pi$$
$$762$$ 0 0
$$763$$ −29.6985 + 29.6985i −1.07516 + 1.07516i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 4.00000 4.00000i 0.143870 0.143870i −0.631503 0.775373i $$-0.717562\pi$$
0.775373 + 0.631503i $$0.217562\pi$$
$$774$$ 0 0
$$775$$ 12.7279i 0.457200i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 14.1421 14.1421i 0.506695 0.506695i
$$780$$ 0 0
$$781$$ −8.00000 8.00000i −0.286263 0.286263i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −20.0000 −0.713831
$$786$$ 0 0
$$787$$ −26.8701 26.8701i −0.957814 0.957814i 0.0413314 0.999145i $$-0.486840\pi$$
−0.999145 + 0.0413314i $$0.986840\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 25.4558i 0.905106i
$$792$$ 0 0
$$793$$ 18.0000i 0.639199i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 22.0000 + 22.0000i 0.779280 + 0.779280i 0.979708 0.200428i $$-0.0642334\pi$$
−0.200428 + 0.979708i $$0.564233\pi$$
$$798$$ 0 0
$$799$$ −16.9706 −0.600375
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −45.2548 45.2548i −1.59701 1.59701i