# Properties

 Label 4608.2.k.n.3457.1 Level $4608$ Weight $2$ Character 4608.3457 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 3457.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 4608.3457 Dual form 4608.2.k.n.1153.1

## $q$-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 $$\left(\mathbb{Z}/4608\mathbb{Z}\right)^\times$$.

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

## 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 $$-0.147584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i 0.654654 + 0.755929i $$0.272814\pi$$
−0.654654 + 0.755929i $$0.727186\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −4.00000 4.00000i −1.20605 1.20605i −0.972297 0.233748i $$-0.924901\pi$$
−0.233748 0.972297i $$-0.575099\pi$$
$$12$$ 0 0
$$13$$ 3.00000 3.00000i 0.832050 0.832050i −0.155747 0.987797i $$-0.549778\pi$$
0.987797 + 0.155747i $$0.0497784\pi$$
$$14$$ 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 $$-0.974765\pi$$
0.0791961 + 0.996859i $$0.474765\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 8.00000i 1.66812i −0.551677 0.834058i $$-0.686012\pi$$
0.551677 0.834058i $$-0.313988\pi$$
$$24$$ 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 $$-0.621119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 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 $$-0.212913\pi$$
−0.620113 + 0.784512i $$0.712913\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.00000i 0.312348i 0.987730 + 0.156174i $$0.0499160\pi$$
−0.987730 + 0.156174i $$0.950084\pi$$
$$42$$ 0 0
$$43$$ −4.00000 4.00000i −0.609994 0.609994i 0.332950 0.942944i $$-0.391956\pi$$
−0.942944 + 0.332950i $$0.891956\pi$$
$$44$$ 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 $$-0.487977\pi$$
−0.999287 + 0.0377628i $$0.987977\pi$$
$$54$$ 0 0
$$55$$ 8.00000i 1.07872i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$60$$ 0 0
$$61$$ −3.00000 + 3.00000i −0.384111 + 0.384111i −0.872581 0.488470i $$-0.837555\pi$$
0.488470 + 0.872581i $$0.337555\pi$$
$$62$$ 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 $$-0.507129\pi$$
0.999749 + 0.0223937i $$0.00712872\pi$$
$$68$$ 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 $$-0.801014\pi$$
0.810885 0.585206i $$-0.198986\pi$$
$$74$$ 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 $$-0.649517\pi$$
0.891695 + 0.452638i $$0.149517\pi$$
$$84$$ 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 $$0.322192\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 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 $$-0.413924\pi$$
−0.963660 + 0.267133i $$0.913924\pi$$
$$102$$ 0 0
$$103$$ 4.00000i 0.394132i −0.980390 0.197066i $$-0.936859\pi$$
0.980390 0.197066i $$-0.0631413\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 8.00000 + 8.00000i 0.773389 + 0.773389i 0.978697 0.205308i $$-0.0658197\pi$$
−0.205308 + 0.978697i $$0.565820\pi$$
$$108$$ 0 0
$$109$$ 5.00000 5.00000i 0.478913 0.478913i −0.425871 0.904784i $$-0.640032\pi$$
0.904784 + 0.425871i $$0.140032\pi$$
$$110$$ 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 $$-0.585446\pi$$
0.964187 + 0.265224i $$0.0854458\pi$$
$$132$$ 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 $$-0.972772\pi$$
0.996344 0.0854358i $$-0.0272282\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$140$$ 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 $$-0.231550\pi$$
−0.664958 + 0.746881i $$0.731550\pi$$
$$150$$ 0 0
$$151$$ 4.00000i 0.325515i 0.986666 + 0.162758i $$0.0520389\pi$$
−0.986666 + 0.162758i $$0.947961\pi$$
$$152$$ 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 $$-0.804151\pi$$
0.577186 + 0.816612i $$0.304151\pi$$
$$158$$ 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 $$-0.981406\pi$$
0.0583818 + 0.998294i $$0.481406\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.00000i 0.619059i 0.950890 + 0.309529i $$0.100171\pi$$
−0.950890 + 0.309529i $$0.899829\pi$$
$$168$$ 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 $$-0.548590\pi$$
0.988372 + 0.152057i $$0.0485898\pi$$
$$174$$ 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 $$-0.888957\pi$$
0.341818 + 0.939766i $$0.388957\pi$$
$$180$$ 0 0
$$181$$ 9.00000 + 9.00000i 0.668965 + 0.668965i 0.957476 0.288512i $$-0.0931604\pi$$
−0.288512 + 0.957476i $$0.593160\pi$$
$$182$$ 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 $$-0.266043\pi$$
−0.741832 + 0.670585i $$0.766043\pi$$
$$198$$ 0 0
$$199$$ 4.00000i 0.283552i 0.989899 + 0.141776i $$0.0452813\pi$$
−0.989899 + 0.141776i $$0.954719\pi$$
$$200$$ 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 −0.107254 + 0.994232i $$0.534206\pi$$
−0.994232 + 0.107254i $$0.965794\pi$$
$$212$$ 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 $$-0.559575\pi$$
0.982537 + 0.186069i $$0.0595747\pi$$
$$228$$ 0 0
$$229$$ −7.00000 7.00000i −0.462573 0.462573i 0.436925 0.899498i $$-0.356068\pi$$
−0.899498 + 0.436925i $$0.856068\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 16.0000i 1.04819i 0.851658 + 0.524097i $$0.175597\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 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 $$-0.307134\pi$$
−0.821986 + 0.569508i $$0.807134\pi$$
$$252$$ 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 $$-0.835790\pi$$
0.869859 0.493301i $$-0.164210\pi$$
$$264$$ 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 $$-0.708714\pi$$
0.792624 + 0.609711i $$0.208714\pi$$
$$270$$ 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 $$-0.0300558\pi$$
−0.0942828 + 0.995545i $$0.530056\pi$$
$$278$$ 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 $$-0.140836\pi$$
−0.428155 + 0.903705i $$0.640836\pi$$
$$284$$ 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 $$-0.263153\pi$$
−0.735714 + 0.677293i $$0.763153\pi$$
$$294$$ 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 0.508965 0.860787i $$-0.330028\pi$$
0.860787 0.508965i $$-0.169972\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 16.0000i 0.907277i −0.891186 0.453638i $$-0.850126\pi$$
0.891186 0.453638i $$-0.149874\pi$$
$$312$$ 0 0
$$313$$ 8.00000i 0.452187i 0.974106 + 0.226093i $$0.0725954\pi$$
−0.974106 + 0.226093i $$0.927405\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 19.0000 19.0000i 1.06715 1.06715i 0.0695692 0.997577i $$-0.477838\pi$$
0.997577 0.0695692i $$-0.0221625\pi$$
$$318$$ 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 $$-0.0363782\pi$$
−0.114037 + 0.993477i $$0.536378\pi$$
$$332$$ 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 −0.997062 0.0765939i $$-0.975596\pi$$
−0.0765939 0.997062i $$-0.524404\pi$$
$$348$$ 0 0
$$349$$ 11.0000 11.0000i 0.588817 0.588817i −0.348494 0.937311i $$-0.613307\pi$$
0.937311 + 0.348494i $$0.113307\pi$$
$$350$$ 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 $$-0.861250\pi$$
0.906492 0.422224i $$-0.138750\pi$$
$$360$$ 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 $$-0.435063\pi$$
−0.979263 + 0.202593i $$0.935063\pi$$
$$374$$ 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 $$-0.393556\pi$$
−0.944606 + 0.328207i $$0.893556\pi$$
$$380$$ 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 −0.947350 0.320201i $$-0.896250\pi$$
−0.320201 0.947350i $$-0.603750\pi$$
$$390$$ 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 0.475229 0.879862i $$-0.342365\pi$$
0.879862 0.475229i $$-0.157635\pi$$
$$398$$ 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 $$0.0633755\pi$$
−0.980245 + 0.197787i $$0.936624\pi$$
$$410$$ 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 $$-0.886055\pi$$
0.350372 + 0.936611i $$0.386055\pi$$
$$420$$ 0 0
$$421$$ 9.00000 + 9.00000i 0.438633 + 0.438633i 0.891552 0.452919i $$-0.149617\pi$$
−0.452919 + 0.891552i $$0.649617\pi$$
$$422$$ 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 $$-0.841625\pi$$
0.878755 0.477274i $$-0.158375\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 12.0000 + 12.0000i 0.570137 + 0.570137i 0.932167 0.362029i $$-0.117916\pi$$
−0.362029 + 0.932167i $$0.617916\pi$$
$$444$$ 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 $$-0.940087\pi$$
0.982339 0.187112i $$-0.0599128\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −19.0000 + 19.0000i −0.884918 + 0.884918i −0.994030 0.109111i $$-0.965200\pi$$
0.109111 + 0.994030i $$0.465200\pi$$
$$462$$ 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 $$-0.708218\pi$$
0.793573 + 0.608475i $$0.208218\pi$$
$$468$$ 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 $$0.0876473\pi$$
−0.962329 + 0.271886i $$0.912353\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 8.00000 + 8.00000i 0.361035 + 0.361035i 0.864194 0.503159i $$-0.167829\pi$$
−0.503159 + 0.864194i $$0.667829\pi$$
$$492$$ 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 $$-0.831495\pi$$
0.504994 + 0.863123i $$0.331495\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 16.0000i 0.713405i −0.934218 0.356702i $$-0.883901\pi$$
0.934218 0.356702i $$-0.116099\pi$$
$$504$$ 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 $$-0.862040\pi$$
0.419971 + 0.907537i $$0.362040\pi$$
$$510$$ 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 $$-0.771757\pi$$
0.753749 0.657162i $$-0.228243\pi$$
$$522$$ 0 0
$$523$$ −12.0000 12.0000i −0.524723 0.524723i 0.394271 0.918994i $$-0.370997\pi$$
−0.918994 + 0.394271i $$0.870997\pi$$
$$524$$ 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 $$-0.720929\pi$$
0.768650 + 0.639670i $$0.220929\pi$$
$$542$$ 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 $$-0.868181\pi$$
0.402387 + 0.915470i $$0.368181\pi$$
$$548$$ 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 $$-0.643096\pi$$
0.900644 + 0.434559i $$0.143096\pi$$
$$558$$ 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 $$-0.953252\pi$$
0.146336 + 0.989235i $$0.453252\pi$$
$$564$$ 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 $$-0.876853\pi$$
0.926091 0.377300i $$-0.123147\pi$$
$$570$$ 0 0
$$571$$ 24.0000 + 24.0000i 1.00437 + 1.00437i 0.999990 + 0.00437833i $$0.00139367\pi$$
0.00437833 + 0.999990i $$0.498606\pi$$
$$572$$ 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 $$-0.0953468\pi$$
−0.295081 + 0.955472i $$0.595347\pi$$
$$588$$ 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 $$0.304463\pi$$
−0.576386 + 0.817178i $$0.695537\pi$$
$$600$$ 0 0
$$601$$ 38.0000i 1.55005i 0.631929 + 0.775026i $$0.282263\pi$$
−0.631929 + 0.775026i $$0.717737\pi$$
$$602$$ 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 $$-0.185932\pi$$
−0.551468 + 0.834196i $$0.685932\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 32.0000i 1.28827i 0.764911 + 0.644136i $$0.222783\pi$$
−0.764911 + 0.644136i $$0.777217\pi$$
$$618$$ 0 0
$$619$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$620$$ 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 $$0.130328\pi$$
−0.917345 + 0.398094i $$0.869672\pi$$
$$632$$ 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 $$-0.641390\pi$$
0.902959 + 0.429726i $$0.141390\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.0000i 0.943537i 0.881722 + 0.471769i $$0.156384\pi$$
−0.881722 + 0.471769i $$0.843616\pi$$
$$648$$ 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 $$-0.926216\pi$$
0.229728 + 0.973255i $$0.426216\pi$$
$$654$$ 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 $$-0.679277\pi$$
0.845543 + 0.533907i $$0.179277\pi$$
$$660$$ 0 0
$$661$$ 7.00000 + 7.00000i 0.272268 + 0.272268i 0.830013 0.557744i $$-0.188333\pi$$
−0.557744 + 0.830013i $$0.688333\pi$$
$$662$$ 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 $$-0.328652\pi$$
−0.858579 + 0.512681i $$0.828652\pi$$
$$678$$ 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 $$-0.144743\pi$$
−0.439215 + 0.898382i $$0.644743\pi$$
$$684$$ 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 −0.508360 + 0.861145i $$0.669748\pi$$
−0.861145 + 0.508360i $$0.830252\pi$$
$$692$$ 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 $$-0.844913\pi$$
0.468173 + 0.883637i $$0.344913\pi$$
$$702$$ 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 −0.960271 0.279070i $$-0.909974\pi$$
−0.279070 0.960271i $$-0.590026\pi$$
$$710$$ 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 $$-0.585326\pi$$
0.264861 0.964287i $$-0.414674\pi$$
$$728$$ 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 0.501425 0.865201i $$-0.332809\pi$$
0.865201 0.501425i $$-0.167191\pi$$
$$734$$ 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 $$-0.535396\pi$$
0.993824 + 0.110970i $$0.0353956\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000i 0.880475i −0.897881 0.440237i $$-0.854894\pi$$
0.897881 0.440237i $$-0.145106\pi$$
$$744$$ 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 $$-0.307578\pi$$
−0.822780 + 0.568360i $$0.807578\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 18.0000i 0.652499i 0.945284 + 0.326250i $$0.105785\pi$$
−0.945284 + 0.326250i $$0.894215\pi$$
$$762$$ 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 $$-0.176489\pi$$
−0.526480 + 0.850188i $$0.676489\pi$$
$$774$$ 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 $$-0.652190\pi$$
0.887863 + 0.460109i $$0.152190\pi$$
$$788$$ 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 $$-0.789968\pi$$
0.612985 + 0.790094i $$0.289968\pi$$
$$798$$ 0 0
$$799$$ 48.0000 1.69812
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −40.0000 + 40.0000i −1.41157 + 1.41157i