# Properties

 Label 4608.2.k.k.1153.1 Level $4608$ Weight $2$ Character 4608.1153 Analytic conductor $36.795$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4608 = 2^{9} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4608.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$36.7950652514$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 1153.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 4608.1153 Dual form 4608.2.k.k.3457.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.00000i) q^{5} -4.00000i q^{7} +O(q^{10})$$ $$q+(-1.00000 + 1.00000i) q^{5} -4.00000i q^{7} +(4.00000 - 4.00000i) q^{11} +(-3.00000 - 3.00000i) q^{13} +6.00000 q^{17} +(4.00000 + 4.00000i) q^{19} +8.00000i q^{23} +3.00000i q^{25} +(-3.00000 - 3.00000i) q^{29} +4.00000 q^{31} +(4.00000 + 4.00000i) q^{35} +(-1.00000 + 1.00000i) q^{37} -2.00000i q^{41} +(4.00000 - 4.00000i) q^{43} +8.00000 q^{47} -9.00000 q^{49} +(7.00000 - 7.00000i) q^{53} +8.00000i q^{55} +(3.00000 + 3.00000i) q^{61} +6.00000 q^{65} +(-8.00000 - 8.00000i) q^{67} +10.0000i q^{73} +(-16.0000 - 16.0000i) q^{77} -12.0000 q^{79} +(-4.00000 - 4.00000i) q^{83} +(-6.00000 + 6.00000i) q^{85} -16.0000i q^{89} +(-12.0000 + 12.0000i) q^{91} -8.00000 q^{95} +8.00000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{5}+O(q^{10})$$ 2 * q - 2 * q^5 $$2 q - 2 q^{5} + 8 q^{11} - 6 q^{13} + 12 q^{17} + 8 q^{19} - 6 q^{29} + 8 q^{31} + 8 q^{35} - 2 q^{37} + 8 q^{43} + 16 q^{47} - 18 q^{49} + 14 q^{53} + 6 q^{61} + 12 q^{65} - 16 q^{67} - 32 q^{77} - 24 q^{79} - 8 q^{83} - 12 q^{85} - 24 q^{91} - 16 q^{95} + 16 q^{97}+O(q^{100})$$ 2 * q - 2 * q^5 + 8 * q^11 - 6 * q^13 + 12 * q^17 + 8 * q^19 - 6 * q^29 + 8 * q^31 + 8 * q^35 - 2 * q^37 + 8 * q^43 + 16 * q^47 - 18 * q^49 + 14 * q^53 + 6 * q^61 + 12 * q^65 - 16 * q^67 - 32 * q^77 - 24 * q^79 - 8 * q^83 - 12 * q^85 - 24 * q^91 - 16 * q^95 + 16 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/4608\mathbb{Z}\right)^\times$$.

 $$n$$ $$2053$$ $$3583$$ $$4097$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$1$$ $$1$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.00000 + 1.00000i −0.447214 + 0.447214i −0.894427 0.447214i $$-0.852416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i −0.654654 0.755929i $$-0.727186\pi$$
0.654654 0.755929i $$-0.272814\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 4.00000 4.00000i 1.20605 1.20605i 0.233748 0.972297i $$-0.424901\pi$$
0.972297 0.233748i $$-0.0750991\pi$$
$$12$$ 0 0
$$13$$ −3.00000 3.00000i −0.832050 0.832050i 0.155747 0.987797i $$-0.450222\pi$$
−0.987797 + 0.155747i $$0.950222\pi$$
$$14$$ 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
$$19$$ 4.00000 + 4.00000i 0.917663 + 0.917663i 0.996859 0.0791961i $$-0.0252353\pi$$
−0.0791961 + 0.996859i $$0.525235\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 8.00000i 1.66812i 0.551677 + 0.834058i $$0.313988\pi$$
−0.551677 + 0.834058i $$0.686012\pi$$
$$24$$ 0 0
$$25$$ 3.00000i 0.600000i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3.00000 3.00000i −0.557086 0.557086i 0.371391 0.928477i $$-0.378881\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 4.00000 + 4.00000i 0.676123 + 0.676123i
$$36$$ 0 0
$$37$$ −1.00000 + 1.00000i −0.164399 + 0.164399i −0.784512 0.620113i $$-0.787087\pi$$
0.620113 + 0.784512i $$0.287087\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.00000i 0.312348i −0.987730 0.156174i $$-0.950084\pi$$
0.987730 0.156174i $$-0.0499160\pi$$
$$42$$ 0 0
$$43$$ 4.00000 4.00000i 0.609994 0.609994i −0.332950 0.942944i $$-0.608044\pi$$
0.942944 + 0.332950i $$0.108044\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ −9.00000 −1.28571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 7.00000 7.00000i 0.961524 0.961524i −0.0377628 0.999287i $$-0.512023\pi$$
0.999287 + 0.0377628i $$0.0120231\pi$$
$$54$$ 0 0
$$55$$ 8.00000i 1.07872i
$$56$$ 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
$$65$$ 6.00000 0.744208
$$66$$ 0 0
$$67$$ −8.00000 8.00000i −0.977356 0.977356i 0.0223937 0.999749i $$-0.492871\pi$$
−0.999749 + 0.0223937i $$0.992871\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 10.0000i 1.17041i 0.810885 + 0.585206i $$0.198986\pi$$
−0.810885 + 0.585206i $$0.801014\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −16.0000 16.0000i −1.82337 1.82337i
$$78$$ 0 0
$$79$$ −12.0000 −1.35011 −0.675053 0.737769i $$-0.735879\pi$$
−0.675053 + 0.737769i $$0.735879\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −4.00000 4.00000i −0.439057 0.439057i 0.452638 0.891695i $$-0.350483\pi$$
−0.891695 + 0.452638i $$0.850483\pi$$
$$84$$ 0 0
$$85$$ −6.00000 + 6.00000i −0.650791 + 0.650791i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 16.0000i 1.69600i −0.529999 0.847998i $$-0.677808\pi$$
0.529999 0.847998i $$-0.322192\pi$$
$$90$$ 0 0
$$91$$ −12.0000 + 12.0000i −1.25794 + 1.25794i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −8.00000 −0.820783
$$96$$ 0 0
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 7.00000 7.00000i 0.696526 0.696526i −0.267133 0.963660i $$-0.586076\pi$$
0.963660 + 0.267133i $$0.0860765\pi$$
$$102$$ 0 0
$$103$$ 4.00000i 0.394132i 0.980390 + 0.197066i $$0.0631413\pi$$
−0.980390 + 0.197066i $$0.936859\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −8.00000 + 8.00000i −0.773389 + 0.773389i −0.978697 0.205308i $$-0.934180\pi$$
0.205308 + 0.978697i $$0.434180\pi$$
$$108$$ 0 0
$$109$$ −5.00000 5.00000i −0.478913 0.478913i 0.425871 0.904784i $$-0.359968\pi$$
−0.904784 + 0.425871i $$0.859968\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 0 0
$$115$$ −8.00000 8.00000i −0.746004 0.746004i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 24.0000i 2.20008i
$$120$$ 0 0
$$121$$ 21.0000i 1.90909i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −8.00000 8.00000i −0.715542 0.715542i
$$126$$ 0 0
$$127$$ 4.00000 0.354943 0.177471 0.984126i $$-0.443208\pi$$
0.177471 + 0.984126i $$0.443208\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −8.00000 8.00000i −0.698963 0.698963i 0.265224 0.964187i $$-0.414554\pi$$
−0.964187 + 0.265224i $$0.914554\pi$$
$$132$$ 0 0
$$133$$ 16.0000 16.0000i 1.38738 1.38738i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.00000i 0.170872i 0.996344 + 0.0854358i $$0.0272282\pi$$
−0.996344 + 0.0854358i $$0.972772\pi$$
$$138$$ 0 0
$$139$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −24.0000 −2.00698
$$144$$ 0 0
$$145$$ 6.00000 0.498273
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.00000 + 1.00000i −0.0819232 + 0.0819232i −0.746881 0.664958i $$-0.768450\pi$$
0.664958 + 0.746881i $$0.268450\pi$$
$$150$$ 0 0
$$151$$ 4.00000i 0.325515i −0.986666 0.162758i $$-0.947961\pi$$
0.986666 0.162758i $$-0.0520389\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −4.00000 + 4.00000i −0.321288 + 0.321288i
$$156$$ 0 0
$$157$$ 3.00000 + 3.00000i 0.239426 + 0.239426i 0.816612 0.577186i $$-0.195849\pi$$
−0.577186 + 0.816612i $$0.695849\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 32.0000 2.52195
$$162$$ 0 0
$$163$$ 12.0000 + 12.0000i 0.939913 + 0.939913i 0.998294 0.0583818i $$-0.0185941\pi$$
−0.0583818 + 0.998294i $$0.518594\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.00000i 0.619059i −0.950890 0.309529i $$-0.899829\pi$$
0.950890 0.309529i $$-0.100171\pi$$
$$168$$ 0 0
$$169$$ 5.00000i 0.384615i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −11.0000 11.0000i −0.836315 0.836315i 0.152057 0.988372i $$-0.451410\pi$$
−0.988372 + 0.152057i $$0.951410\pi$$
$$174$$ 0 0
$$175$$ 12.0000 0.907115
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 8.00000 + 8.00000i 0.597948 + 0.597948i 0.939766 0.341818i $$-0.111043\pi$$
−0.341818 + 0.939766i $$0.611043\pi$$
$$180$$ 0 0
$$181$$ −9.00000 + 9.00000i −0.668965 + 0.668965i −0.957476 0.288512i $$-0.906840\pi$$
0.288512 + 0.957476i $$0.406840\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.00000i 0.147043i
$$186$$ 0 0
$$187$$ 24.0000 24.0000i 1.75505 1.75505i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 24.0000 1.73658 0.868290 0.496058i $$-0.165220\pi$$
0.868290 + 0.496058i $$0.165220\pi$$
$$192$$ 0 0
$$193$$ 8.00000 0.575853 0.287926 0.957653i $$-0.407034\pi$$
0.287926 + 0.957653i $$0.407034\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.00000 1.00000i 0.0712470 0.0712470i −0.670585 0.741832i $$-0.733957\pi$$
0.741832 + 0.670585i $$0.233957\pi$$
$$198$$ 0 0
$$199$$ 4.00000i 0.283552i −0.989899 0.141776i $$-0.954719\pi$$
0.989899 0.141776i $$-0.0452813\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −12.0000 + 12.0000i −0.842235 + 0.842235i
$$204$$ 0 0
$$205$$ 2.00000 + 2.00000i 0.139686 + 0.139686i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 32.0000 2.21349
$$210$$ 0 0
$$211$$ 16.0000 + 16.0000i 1.10149 + 1.10149i 0.994232 + 0.107254i $$0.0342057\pi$$
0.107254 + 0.994232i $$0.465794\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.00000i 0.545595i
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −18.0000 18.0000i −1.21081 1.21081i
$$222$$ 0 0
$$223$$ −12.0000 −0.803579 −0.401790 0.915732i $$-0.631612\pi$$
−0.401790 + 0.915732i $$0.631612\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −12.0000 12.0000i −0.796468 0.796468i 0.186069 0.982537i $$-0.440425\pi$$
−0.982537 + 0.186069i $$0.940425\pi$$
$$228$$ 0 0
$$229$$ 7.00000 7.00000i 0.462573 0.462573i −0.436925 0.899498i $$-0.643932\pi$$
0.899498 + 0.436925i $$0.143932\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 16.0000i 1.04819i −0.851658 0.524097i $$-0.824403\pi$$
0.851658 0.524097i $$-0.175597\pi$$
$$234$$ 0 0
$$235$$ −8.00000 + 8.00000i −0.521862 + 0.521862i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ −24.0000 −1.54598 −0.772988 0.634421i $$-0.781239\pi$$
−0.772988 + 0.634421i $$0.781239\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 9.00000 9.00000i 0.574989 0.574989i
$$246$$ 0 0
$$247$$ 24.0000i 1.52708i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 4.00000 4.00000i 0.252478 0.252478i −0.569508 0.821986i $$-0.692866\pi$$
0.821986 + 0.569508i $$0.192866\pi$$
$$252$$ 0 0
$$253$$ 32.0000 + 32.0000i 2.01182 + 2.01182i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 4.00000 + 4.00000i 0.248548 + 0.248548i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 16.0000i 0.986602i 0.869859 + 0.493301i $$0.164210\pi$$
−0.869859 + 0.493301i $$0.835790\pi$$
$$264$$ 0 0
$$265$$ 14.0000i 0.860013i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −3.00000 3.00000i −0.182913 0.182913i 0.609711 0.792624i $$-0.291286\pi$$
−0.792624 + 0.609711i $$0.791286\pi$$
$$270$$ 0 0
$$271$$ 28.0000 1.70088 0.850439 0.526073i $$-0.176336\pi$$
0.850439 + 0.526073i $$0.176336\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 12.0000 + 12.0000i 0.723627 + 0.723627i
$$276$$ 0 0
$$277$$ −15.0000 + 15.0000i −0.901263 + 0.901263i −0.995545 0.0942828i $$-0.969944\pi$$
0.0942828 + 0.995545i $$0.469944\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ −8.00000 + 8.00000i −0.475551 + 0.475551i −0.903705 0.428155i $$-0.859164\pi$$
0.428155 + 0.903705i $$0.359164\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −8.00000 −0.472225
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1.00000 1.00000i 0.0584206 0.0584206i −0.677293 0.735714i $$-0.736847\pi$$
0.735714 + 0.677293i $$0.236847\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 24.0000 24.0000i 1.38796 1.38796i
$$300$$ 0 0
$$301$$ −16.0000 16.0000i −0.922225 0.922225i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −6.00000 −0.343559
$$306$$ 0 0
$$307$$ −24.0000 24.0000i −1.36975 1.36975i −0.860787 0.508965i $$-0.830028\pi$$
−0.508965 0.860787i $$-0.669972\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 16.0000i 0.907277i 0.891186 + 0.453638i $$0.149874\pi$$
−0.891186 + 0.453638i $$0.850126\pi$$
$$312$$ 0 0
$$313$$ 8.00000i 0.452187i −0.974106 0.226093i $$-0.927405\pi$$
0.974106 0.226093i $$-0.0725954\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −19.0000 19.0000i −1.06715 1.06715i −0.997577 0.0695692i $$-0.977838\pi$$
−0.0695692 0.997577i $$-0.522162\pi$$
$$318$$ 0 0
$$319$$ −24.0000 −1.34374
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 24.0000 + 24.0000i 1.33540 + 1.33540i
$$324$$ 0 0
$$325$$ 9.00000 9.00000i 0.499230 0.499230i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 32.0000i 1.76422i
$$330$$ 0 0
$$331$$ −16.0000 + 16.0000i −0.879440 + 0.879440i −0.993477 0.114037i $$-0.963622\pi$$
0.114037 + 0.993477i $$0.463622\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 16.0000 0.874173
$$336$$ 0 0
$$337$$ −30.0000 −1.63420 −0.817102 0.576493i $$-0.804421\pi$$
−0.817102 + 0.576493i $$0.804421\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 16.0000 16.0000i 0.866449 0.866449i
$$342$$ 0 0
$$343$$ 8.00000i 0.431959i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 20.0000 20.0000i 1.07366 1.07366i 0.0765939 0.997062i $$-0.475596\pi$$
0.997062 0.0765939i $$-0.0244045\pi$$
$$348$$ 0 0
$$349$$ −11.0000 11.0000i −0.588817 0.588817i 0.348494 0.937311i $$-0.386693\pi$$
−0.937311 + 0.348494i $$0.886693\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 16.0000 0.851594 0.425797 0.904819i $$-0.359994\pi$$
0.425797 + 0.904819i $$0.359994\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 16.0000i 0.844448i 0.906492 + 0.422224i $$0.138750\pi$$
−0.906492 + 0.422224i $$0.861250\pi$$
$$360$$ 0 0
$$361$$ 13.0000i 0.684211i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −10.0000 10.0000i −0.523424 0.523424i
$$366$$ 0 0
$$367$$ −20.0000 −1.04399 −0.521996 0.852948i $$-0.674812\pi$$
−0.521996 + 0.852948i $$0.674812\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −28.0000 28.0000i −1.45369 1.45369i
$$372$$ 0 0
$$373$$ 15.0000 15.0000i 0.776671 0.776671i −0.202593 0.979263i $$-0.564937\pi$$
0.979263 + 0.202593i $$0.0649367\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 18.0000i 0.927047i
$$378$$ 0 0
$$379$$ 12.0000 12.0000i 0.616399 0.616399i −0.328207 0.944606i $$-0.606444\pi$$
0.944606 + 0.328207i $$0.106444\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −24.0000 −1.22634 −0.613171 0.789950i $$-0.710106\pi$$
−0.613171 + 0.789950i $$0.710106\pi$$
$$384$$ 0 0
$$385$$ 32.0000 1.63087
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 25.0000 25.0000i 1.26755 1.26755i 0.320201 0.947350i $$-0.396250\pi$$
0.947350 0.320201i $$-0.103750\pi$$
$$390$$ 0 0
$$391$$ 48.0000i 2.42746i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 12.0000 12.0000i 0.603786 0.603786i
$$396$$ 0 0
$$397$$ −27.0000 27.0000i −1.35509 1.35509i −0.879862 0.475229i $$-0.842365\pi$$
−0.475229 0.879862i $$-0.657635\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 0 0
$$403$$ −12.0000 12.0000i −0.597763 0.597763i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 8.00000i 0.396545i
$$408$$ 0 0
$$409$$ 8.00000i 0.395575i −0.980245 0.197787i $$-0.936624\pi$$
0.980245 0.197787i $$-0.0633755\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 8.00000 0.392705
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.0000 + 12.0000i 0.586238 + 0.586238i 0.936611 0.350372i $$-0.113945\pi$$
−0.350372 + 0.936611i $$0.613945\pi$$
$$420$$ 0 0
$$421$$ −9.00000 + 9.00000i −0.438633 + 0.438633i −0.891552 0.452919i $$-0.850383\pi$$
0.452919 + 0.891552i $$0.350383\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 18.0000i 0.873128i
$$426$$ 0 0
$$427$$ 12.0000 12.0000i 0.580721 0.580721i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 8.00000 0.385346 0.192673 0.981263i $$-0.438284\pi$$
0.192673 + 0.981263i $$0.438284\pi$$
$$432$$ 0 0
$$433$$ 8.00000 0.384455 0.192228 0.981350i $$-0.438429\pi$$
0.192228 + 0.981350i $$0.438429\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −32.0000 + 32.0000i −1.53077 + 1.53077i
$$438$$ 0 0
$$439$$ 20.0000i 0.954548i 0.878755 + 0.477274i $$0.158375\pi$$
−0.878755 + 0.477274i $$0.841625\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 + 12.0000i −0.570137 + 0.570137i −0.932167 0.362029i $$-0.882084\pi$$
0.362029 + 0.932167i $$0.382084\pi$$
$$444$$ 0 0
$$445$$ 16.0000 + 16.0000i 0.758473 + 0.758473i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 0 0
$$451$$ −8.00000 8.00000i −0.376705 0.376705i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 24.0000i 1.12514i
$$456$$ 0 0
$$457$$ 8.00000i 0.374224i 0.982339 + 0.187112i $$0.0599128\pi$$
−0.982339 + 0.187112i $$0.940087\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 19.0000 + 19.0000i 0.884918 + 0.884918i 0.994030 0.109111i $$-0.0348005\pi$$
−0.109111 + 0.994030i $$0.534800\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −4.00000 4.00000i −0.185098 0.185098i 0.608475 0.793573i $$-0.291782\pi$$
−0.793573 + 0.608475i $$0.791782\pi$$
$$468$$ 0 0
$$469$$ −32.0000 + 32.0000i −1.47762 + 1.47762i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 32.0000i 1.47136i
$$474$$ 0 0
$$475$$ −12.0000 + 12.0000i −0.550598 + 0.550598i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 16.0000 0.731059 0.365529 0.930800i $$-0.380888\pi$$
0.365529 + 0.930800i $$0.380888\pi$$
$$480$$ 0 0
$$481$$ 6.00000 0.273576
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −8.00000 + 8.00000i −0.363261 + 0.363261i
$$486$$ 0 0
$$487$$ 12.0000i 0.543772i −0.962329 0.271886i $$-0.912353\pi$$
0.962329 0.271886i $$-0.0876473\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −8.00000 + 8.00000i −0.361035 + 0.361035i −0.864194 0.503159i $$-0.832171\pi$$
0.503159 + 0.864194i $$0.332171\pi$$
$$492$$ 0 0
$$493$$ −18.0000 18.0000i −0.810679 0.810679i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 8.00000 + 8.00000i 0.358129 + 0.358129i 0.863123 0.504994i $$-0.168505\pi$$
−0.504994 + 0.863123i $$0.668505\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 16.0000i 0.713405i 0.934218 + 0.356702i $$0.116099\pi$$
−0.934218 + 0.356702i $$0.883901\pi$$
$$504$$ 0 0
$$505$$ 14.0000i 0.622992i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 11.0000 + 11.0000i 0.487566 + 0.487566i 0.907537 0.419971i $$-0.137960\pi$$
−0.419971 + 0.907537i $$0.637960\pi$$
$$510$$ 0 0
$$511$$ 40.0000 1.76950
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −4.00000 4.00000i −0.176261 0.176261i
$$516$$ 0 0
$$517$$ 32.0000 32.0000i 1.40736 1.40736i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 30.0000i 1.31432i 0.753749 + 0.657162i $$0.228243\pi$$
−0.753749 + 0.657162i $$0.771757\pi$$
$$522$$ 0 0
$$523$$ 12.0000 12.0000i 0.524723 0.524723i −0.394271 0.918994i $$-0.629003\pi$$
0.918994 + 0.394271i $$0.129003\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 24.0000 1.04546
$$528$$ 0 0
$$529$$ −41.0000 −1.78261
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −6.00000 + 6.00000i −0.259889 + 0.259889i
$$534$$ 0 0
$$535$$ 16.0000i 0.691740i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −36.0000 + 36.0000i −1.55063 + 1.55063i
$$540$$ 0 0
$$541$$ −3.00000 3.00000i −0.128980 0.128980i 0.639670 0.768650i $$-0.279071\pi$$
−0.768650 + 0.639670i $$0.779071\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10.0000 0.428353
$$546$$ 0 0
$$547$$ 12.0000 + 12.0000i 0.513083 + 0.513083i 0.915470 0.402387i $$-0.131819\pi$$
−0.402387 + 0.915470i $$0.631819\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 24.0000i 1.02243i
$$552$$ 0 0
$$553$$ 48.0000i 2.04117i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −11.0000 11.0000i −0.466085 0.466085i 0.434559 0.900644i $$-0.356904\pi$$
−0.900644 + 0.434559i $$0.856904\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 20.0000 + 20.0000i 0.842900 + 0.842900i 0.989235 0.146336i $$-0.0467479\pi$$
−0.146336 + 0.989235i $$0.546748\pi$$
$$564$$ 0 0
$$565$$ −16.0000 + 16.0000i −0.673125 + 0.673125i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000i 0.754599i 0.926091 + 0.377300i $$0.123147\pi$$
−0.926091 + 0.377300i $$0.876853\pi$$
$$570$$ 0 0
$$571$$ −24.0000 + 24.0000i −1.00437 + 1.00437i −0.00437833 + 0.999990i $$0.501394\pi$$
−0.999990 + 0.00437833i $$0.998606\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −24.0000 −1.00087
$$576$$ 0 0
$$577$$ −18.0000 −0.749350 −0.374675 0.927156i $$-0.622246\pi$$
−0.374675 + 0.927156i $$0.622246\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −16.0000 + 16.0000i −0.663792 + 0.663792i
$$582$$ 0 0
$$583$$ 56.0000i 2.31928i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −16.0000 + 16.0000i −0.660391 + 0.660391i −0.955472 0.295081i $$-0.904653\pi$$
0.295081 + 0.955472i $$0.404653\pi$$
$$588$$ 0 0
$$589$$ 16.0000 + 16.0000i 0.659269 + 0.659269i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −16.0000 −0.657041 −0.328521 0.944497i $$-0.606550\pi$$
−0.328521 + 0.944497i $$0.606550\pi$$
$$594$$ 0 0
$$595$$ 24.0000 + 24.0000i 0.983904 + 0.983904i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 40.0000i 1.63436i −0.576386 0.817178i $$-0.695537\pi$$
0.576386 0.817178i $$-0.304463\pi$$
$$600$$ 0 0
$$601$$ 38.0000i 1.55005i −0.631929 0.775026i $$-0.717737\pi$$
0.631929 0.775026i $$-0.282263\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 21.0000 + 21.0000i 0.853771 + 0.853771i
$$606$$ 0 0
$$607$$ −12.0000 −0.487065 −0.243532 0.969893i $$-0.578306\pi$$
−0.243532 + 0.969893i $$0.578306\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −24.0000 24.0000i −0.970936 0.970936i
$$612$$ 0 0
$$613$$ −7.00000 + 7.00000i −0.282727 + 0.282727i −0.834196 0.551468i $$-0.814068\pi$$
0.551468 + 0.834196i $$0.314068\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 32.0000i 1.28827i −0.764911 0.644136i $$-0.777217\pi$$
0.764911 0.644136i $$-0.222783\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −64.0000 −2.56411
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −6.00000 + 6.00000i −0.239236 + 0.239236i
$$630$$ 0 0
$$631$$ 20.0000i 0.796187i −0.917345 0.398094i $$-0.869672\pi$$
0.917345 0.398094i $$-0.130328\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −4.00000 + 4.00000i −0.158735 + 0.158735i
$$636$$ 0 0
$$637$$ 27.0000 + 27.0000i 1.06978 + 1.06978i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −22.0000 −0.868948 −0.434474 0.900684i $$-0.643066\pi$$
−0.434474 + 0.900684i $$0.643066\pi$$
$$642$$ 0 0
$$643$$ −12.0000 12.0000i −0.473234 0.473234i 0.429726 0.902959i $$-0.358610\pi$$
−0.902959 + 0.429726i $$0.858610\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.0000i 0.943537i −0.881722 0.471769i $$-0.843616\pi$$
0.881722 0.471769i $$-0.156384\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 19.0000 + 19.0000i 0.743527 + 0.743527i 0.973255 0.229728i $$-0.0737835\pi$$
−0.229728 + 0.973255i $$0.573784\pi$$
$$654$$ 0 0
$$655$$ 16.0000 0.625172
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −8.00000 8.00000i −0.311636 0.311636i 0.533907 0.845543i $$-0.320723\pi$$
−0.845543 + 0.533907i $$0.820723\pi$$
$$660$$ 0 0
$$661$$ −7.00000 + 7.00000i −0.272268 + 0.272268i −0.830013 0.557744i $$-0.811667\pi$$
0.557744 + 0.830013i $$0.311667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 32.0000i 1.24091i
$$666$$ 0 0
$$667$$ 24.0000 24.0000i 0.929284 0.929284i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 24.0000 0.926510
$$672$$ 0 0
$$673$$ −8.00000 −0.308377 −0.154189 0.988041i $$-0.549276\pi$$
−0.154189 + 0.988041i $$0.549276\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 9.00000 9.00000i 0.345898 0.345898i −0.512681 0.858579i $$-0.671348\pi$$
0.858579 + 0.512681i $$0.171348\pi$$
$$678$$ 0 0
$$679$$ 32.0000i 1.22805i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 + 12.0000i −0.459167 + 0.459167i −0.898382 0.439215i $$-0.855257\pi$$
0.439215 + 0.898382i $$0.355257\pi$$
$$684$$ 0 0
$$685$$ −2.00000 2.00000i −0.0764161 0.0764161i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −42.0000 −1.60007
$$690$$ 0 0
$$691$$ 36.0000 + 36.0000i 1.36950 + 1.36950i 0.861145 + 0.508360i $$0.169748\pi$$
0.508360 + 0.861145i $$0.330252\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 12.0000i 0.454532i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 11.0000 + 11.0000i 0.415464 + 0.415464i 0.883637 0.468173i $$-0.155087\pi$$
−0.468173 + 0.883637i $$0.655087\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −28.0000 28.0000i −1.05305 1.05305i
$$708$$ 0 0
$$709$$ 33.0000 33.0000i 1.23934 1.23934i 0.279070 0.960271i $$-0.409974\pi$$
0.960271 0.279070i $$-0.0900263\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 32.0000i 1.19841i
$$714$$ 0 0
$$715$$ 24.0000 24.0000i 0.897549 0.897549i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 16.0000 0.595871
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 9.00000 9.00000i 0.334252 0.334252i
$$726$$ 0 0
$$727$$ 52.0000i 1.92857i 0.264861 + 0.964287i $$0.414674\pi$$
−0.264861 + 0.964287i $$0.585326\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 24.0000 24.0000i 0.887672 0.887672i
$$732$$ 0 0
$$733$$ −37.0000 37.0000i −1.36663 1.36663i −0.865201 0.501425i $$-0.832809\pi$$
−0.501425 0.865201i $$-0.667191\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −64.0000 −2.35747
$$738$$ 0 0
$$739$$ −24.0000 24.0000i −0.882854 0.882854i 0.110970 0.993824i $$-0.464604\pi$$
−0.993824 + 0.110970i $$0.964604\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000i 0.880475i 0.897881 + 0.440237i $$0.145106\pi$$
−0.897881 + 0.440237i $$0.854894\pi$$
$$744$$ 0 0
$$745$$ 2.00000i 0.0732743i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 32.0000 + 32.0000i 1.16925 + 1.16925i
$$750$$ 0 0
$$751$$ 28.0000 1.02173 0.510867 0.859660i $$-0.329324\pi$$
0.510867 + 0.859660i $$0.329324\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 4.00000 + 4.00000i 0.145575 + 0.145575i
$$756$$ 0 0
$$757$$ 7.00000 7.00000i 0.254419 0.254419i −0.568360 0.822780i $$-0.692422\pi$$
0.822780 + 0.568360i $$0.192422\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 18.0000i 0.652499i −0.945284 0.326250i $$-0.894215\pi$$
0.945284 0.326250i $$-0.105785\pi$$
$$762$$ 0 0
$$763$$ −20.0000 + 20.0000i −0.724049 + 0.724049i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 40.0000 1.44244 0.721218 0.692708i $$-0.243582\pi$$
0.721218 + 0.692708i $$0.243582\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −9.00000 + 9.00000i −0.323708 + 0.323708i −0.850188 0.526480i $$-0.823511\pi$$
0.526480 + 0.850188i $$0.323511\pi$$
$$774$$ 0 0
$$775$$ 12.0000i 0.431053i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 8.00000 8.00000i 0.286630 0.286630i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6.00000 −0.214149
$$786$$ 0 0
$$787$$ −12.0000 12.0000i −0.427754 0.427754i 0.460109 0.887863i $$-0.347810\pi$$
−0.887863 + 0.460109i $$0.847810\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 64.0000i 2.27558i
$$792$$ 0 0
$$793$$ 18.0000i 0.639199i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 5.00000 + 5.00000i 0.177109 + 0.177109i 0.790094 0.612985i $$-0.210032\pi$$
−0.612985 + 0.790094i $$0.710032\pi$$
$$798$$ 0 0
$$799$$ 48.0000 1.69812
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0