# Properties

 Label 3024.2.q.f.2881.1 Level 3024 Weight 2 Character 3024.2881 Analytic conductor 24.147 Analytic rank 0 Dimension 2 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3024.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$24.1467615712$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 2881.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 3024.2881 Dual form 3024.2.q.f.2305.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})$$ $$q+(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(4.50000 - 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(1.50000 - 2.59808i) q^{29} -8.00000 q^{31} +(7.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(1.00000 + 6.92820i) q^{49} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +2.00000 q^{61} +3.00000 q^{65} +4.00000 q^{67} +12.0000 q^{71} +(-5.50000 + 9.52628i) q^{73} +(-1.50000 + 7.79423i) q^{77} +16.0000 q^{79} +(4.50000 - 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(1.50000 + 2.59808i) q^{89} +(-0.500000 + 2.59808i) q^{91} -21.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 3q^{5} + 4q^{7} + O(q^{10})$$ $$2q + 3q^{5} + 4q^{7} + 3q^{11} + q^{13} + 3q^{17} - 7q^{19} + 9q^{23} - 4q^{25} + 3q^{29} - 16q^{31} + 15q^{35} + q^{37} + 3q^{41} - q^{43} + 2q^{49} + 3q^{53} + 18q^{55} + 4q^{61} + 6q^{65} + 8q^{67} + 24q^{71} - 11q^{73} - 3q^{77} + 32q^{79} + 9q^{83} - 9q^{85} + 3q^{89} - q^{91} - 42q^{95} + q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$$.

 $$n$$ $$757$$ $$785$$ $$1135$$ $$2593$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$5$$ 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i $$-0.599275\pi$$
0.977672 0.210138i $$-0.0673912\pi$$
$$6$$ 0 0
$$7$$ 2.00000 + 1.73205i 0.755929 + 0.654654i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ 0 0
$$13$$ 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i $$-0.122382\pi$$
−0.788320 + 0.615265i $$0.789049\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i $$-0.714811\pi$$
0.988583 + 0.150675i $$0.0481447\pi$$
$$18$$ 0 0
$$19$$ −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i $$-0.869927\pi$$
0.114708 0.993399i $$-0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i $$-0.445720\pi$$
0.768613 0.639713i $$-0.220947\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i $$-0.743482\pi$$
0.971023 + 0.238987i $$0.0768152\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 7.50000 2.59808i 1.26773 0.439155i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i $$-0.0913998\pi$$
−0.724797 + 0.688963i $$0.758066\pi$$
$$42$$ 0 0
$$43$$ −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i $$-0.857628\pi$$
0.825380 + 0.564578i $$0.190961\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i $$-0.767275\pi$$
0.950464 + 0.310835i $$0.100609\pi$$
$$54$$ 0 0
$$55$$ 9.00000 1.21356
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 3.00000 0.372104
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i $$0.389279\pi$$
−0.984594 + 0.174855i $$0.944054\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1.50000 + 7.79423i −0.170941 + 0.888235i
$$78$$ 0 0
$$79$$ 16.0000 1.80014 0.900070 0.435745i $$-0.143515\pi$$
0.900070 + 0.435745i $$0.143515\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i $$-0.668890\pi$$
0.999976 + 0.00698436i $$0.00222321\pi$$
$$84$$ 0 0
$$85$$ −4.50000 7.79423i −0.488094 0.845403i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1.50000 + 2.59808i 0.159000 + 0.275396i 0.934508 0.355942i $$-0.115840\pi$$
−0.775509 + 0.631337i $$0.782506\pi$$
$$90$$ 0 0
$$91$$ −0.500000 + 2.59808i −0.0524142 + 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −21.0000 −2.15455
$$96$$ 0 0
$$97$$ 0.500000 0.866025i 0.0507673 0.0879316i −0.839525 0.543321i $$-0.817167\pi$$
0.890292 + 0.455389i $$0.150500\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i $$-0.118979\pi$$
−0.781697 + 0.623658i $$0.785646\pi$$
$$102$$ 0 0
$$103$$ −6.50000 + 11.2583i −0.640464 + 1.10932i 0.344865 + 0.938652i $$0.387925\pi$$
−0.985329 + 0.170664i $$0.945409\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −4.50000 7.79423i −0.435031 0.753497i 0.562267 0.826956i $$-0.309929\pi$$
−0.997298 + 0.0734594i $$0.976596\pi$$
$$108$$ 0 0
$$109$$ 6.50000 11.2583i 0.622587 1.07835i −0.366415 0.930451i $$-0.619415\pi$$
0.989002 0.147901i $$-0.0472517\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −4.50000 7.79423i −0.423324 0.733219i 0.572938 0.819599i $$-0.305804\pi$$
−0.996262 + 0.0863794i $$0.972470\pi$$
$$114$$ 0 0
$$115$$ −13.5000 23.3827i −1.25888 2.18045i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 7.50000 2.59808i 0.687524 0.238165i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 3.00000 0.268328
$$126$$ 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
$$131$$ −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i $$0.394115\pi$$
−0.981824 + 0.189794i $$0.939218\pi$$
$$132$$ 0 0
$$133$$ 3.50000 18.1865i 0.303488 1.57697i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i $$-0.292279\pi$$
−0.991694 + 0.128618i $$0.958946\pi$$
$$138$$ 0 0
$$139$$ −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i $$-0.262608\pi$$
−0.975417 + 0.220366i $$0.929275\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1.50000 + 2.59808i −0.125436 + 0.217262i
$$144$$ 0 0
$$145$$ −4.50000 7.79423i −0.373705 0.647275i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i $$-0.953515\pi$$
0.620701 + 0.784047i $$0.286848\pi$$
$$150$$ 0 0
$$151$$ −3.50000 6.06218i −0.284826 0.493333i 0.687741 0.725956i $$-0.258602\pi$$
−0.972567 + 0.232623i $$0.925269\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −12.0000 + 20.7846i −0.963863 + 1.66946i
$$156$$ 0 0
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 22.5000 7.79423i 1.77325 0.614271i
$$162$$ 0 0
$$163$$ −9.50000 16.4545i −0.744097 1.28881i −0.950615 0.310372i $$-0.899546\pi$$
0.206518 0.978443i $$-0.433787\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 7.50000 + 12.9904i 0.580367 + 1.00523i 0.995436 + 0.0954356i $$0.0304244\pi$$
−0.415068 + 0.909790i $$0.636242\pi$$
$$168$$ 0 0
$$169$$ 6.00000 10.3923i 0.461538 0.799408i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 2.00000 10.3923i 0.151186 0.785584i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 10.5000 18.1865i 0.784807 1.35933i −0.144308 0.989533i $$-0.546095\pi$$
0.929114 0.369792i $$-0.120571\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 3.00000 0.220564
$$186$$ 0 0
$$187$$ 9.00000 0.658145
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −12.5000 + 21.6506i −0.886102 + 1.53477i −0.0416556 + 0.999132i $$0.513263\pi$$
−0.844446 + 0.535641i $$0.820070\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 7.50000 2.59808i 0.526397 0.182349i
$$204$$ 0 0
$$205$$ 9.00000 0.628587
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 10.5000 18.1865i 0.726300 1.25799i
$$210$$ 0 0
$$211$$ 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i $$-0.111609\pi$$
−0.767049 + 0.641588i $$0.778276\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.50000 + 2.59808i 0.102299 + 0.177187i
$$216$$ 0 0
$$217$$ −16.0000 13.8564i −1.08615 0.940634i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ −0.500000 + 0.866025i −0.0334825 + 0.0579934i −0.882281 0.470723i $$-0.843993\pi$$
0.848799 + 0.528716i $$0.177326\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i $$-0.134924\pi$$
−0.811943 + 0.583736i $$0.801590\pi$$
$$228$$ 0 0
$$229$$ 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i $$-0.692012\pi$$
0.996832 + 0.0795401i $$0.0253452\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.50000 + 2.59808i 0.0982683 + 0.170206i 0.910968 0.412477i $$-0.135336\pi$$
−0.812700 + 0.582683i $$0.802003\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.50000 + 2.59808i 0.0970269 + 0.168056i 0.910453 0.413613i $$-0.135733\pi$$
−0.813426 + 0.581669i $$0.802400\pi$$
$$240$$ 0 0
$$241$$ 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i $$-0.0291519\pi$$
−0.577107 + 0.816668i $$0.695819\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 19.5000 + 7.79423i 1.24581 + 0.497955i
$$246$$ 0 0
$$247$$ 3.50000 6.06218i 0.222700 0.385727i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 27.0000 1.69748
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −10.5000 + 18.1865i −0.654972 + 1.13444i 0.326929 + 0.945049i $$0.393986\pi$$
−0.981901 + 0.189396i $$0.939347\pi$$
$$258$$ 0 0
$$259$$ −0.500000 + 2.59808i −0.0310685 + 0.161437i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i $$-0.256167\pi$$
−0.970758 + 0.240059i $$0.922833\pi$$
$$264$$ 0 0
$$265$$ −4.50000 7.79423i −0.276433 0.478796i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 7.50000 12.9904i 0.457283 0.792038i −0.541533 0.840679i $$-0.682156\pi$$
0.998816 + 0.0486418i $$0.0154893\pi$$
$$270$$ 0 0
$$271$$ 2.50000 + 4.33013i 0.151864 + 0.263036i 0.931913 0.362682i $$-0.118139\pi$$
−0.780049 + 0.625719i $$0.784806\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 6.00000 10.3923i 0.361814 0.626680i
$$276$$ 0 0
$$277$$ 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i $$-0.157103\pi$$
−0.850613 + 0.525792i $$0.823769\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −10.5000 + 18.1865i −0.626377 + 1.08492i 0.361895 + 0.932219i $$0.382130\pi$$
−0.988273 + 0.152699i $$0.951204\pi$$
$$282$$ 0 0
$$283$$ 4.00000 0.237775 0.118888 0.992908i $$-0.462067\pi$$
0.118888 + 0.992908i $$0.462067\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1.50000 + 7.79423i −0.0885422 + 0.460079i
$$288$$ 0 0
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i $$-0.251343\pi$$
−0.967009 + 0.254741i $$0.918010\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 9.00000 0.520483
$$300$$ 0 0
$$301$$ −2.50000 + 0.866025i −0.144098 + 0.0499169i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 3.00000 5.19615i 0.171780 0.297531i
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ 9.00000 0.503903
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −21.0000 −1.16847
$$324$$ 0 0
$$325$$ 2.00000 3.46410i 0.110940 0.192154i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 6.00000 10.3923i 0.327815 0.567792i
$$336$$ 0 0
$$337$$ 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i $$-0.0514616\pi$$
−0.632882 + 0.774248i $$0.718128\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −12.0000 20.7846i −0.649836 1.12555i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 0 0
$$349$$ −11.5000 + 19.9186i −0.615581 + 1.06622i 0.374701 + 0.927146i $$0.377745\pi$$
−0.990282 + 0.139072i $$0.955588\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i $$-0.141227\pi$$
−0.823343 + 0.567545i $$0.807893\pi$$
$$354$$ 0 0
$$355$$ 18.0000 31.1769i 0.955341 1.65470i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −4.50000 7.79423i −0.237501 0.411364i 0.722496 0.691375i $$-0.242995\pi$$
−0.959997 + 0.280012i $$0.909662\pi$$
$$360$$ 0 0
$$361$$ −15.0000 + 25.9808i −0.789474 + 1.36741i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 16.5000 + 28.5788i 0.863649 + 1.49588i
$$366$$ 0 0
$$367$$ 8.50000 + 14.7224i 0.443696 + 0.768505i 0.997960 0.0638362i $$-0.0203335\pi$$
−0.554264 + 0.832341i $$0.687000\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 7.50000 2.59808i 0.389381 0.134885i
$$372$$ 0 0
$$373$$ 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i $$-0.724071\pi$$
0.983783 + 0.179364i $$0.0574041\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3.00000 0.154508
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i $$-0.958522\pi$$
0.608290 + 0.793715i $$0.291856\pi$$
$$384$$ 0 0
$$385$$ 18.0000 + 15.5885i 0.917365 + 0.794461i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 13.5000 + 23.3827i 0.684477 + 1.18555i 0.973601 + 0.228257i $$0.0733028\pi$$
−0.289124 + 0.957292i $$0.593364\pi$$
$$390$$ 0 0
$$391$$ −13.5000 23.3827i −0.682724 1.18251i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 24.0000 41.5692i 1.20757 2.09157i
$$396$$ 0 0
$$397$$ 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i $$-0.0608897\pi$$
−0.655534 + 0.755166i $$0.727556\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i $$-0.597840\pi$$
0.976714 0.214544i $$-0.0688266\pi$$
$$402$$ 0 0
$$403$$ −4.00000 6.92820i −0.199254 0.345118i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −1.50000 + 2.59808i −0.0743522 + 0.128782i
$$408$$ 0 0
$$409$$ −34.0000 −1.68119 −0.840596 0.541663i $$-0.817795\pi$$
−0.840596 + 0.541663i $$0.817795\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −13.5000 23.3827i −0.662689 1.14781i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i $$-0.237220\pi$$
−0.954759 + 0.297382i $$0.903887\pi$$
$$420$$ 0 0
$$421$$ −17.5000 + 30.3109i −0.852898 + 1.47726i 0.0256838 + 0.999670i $$0.491824\pi$$
−0.878582 + 0.477592i $$0.841510\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −12.0000 −0.582086
$$426$$ 0 0
$$427$$ 4.00000 + 3.46410i 0.193574 + 0.167640i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −13.5000 + 23.3827i −0.650272 + 1.12630i 0.332785 + 0.943003i $$0.392012\pi$$
−0.983057 + 0.183301i $$0.941322\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −63.0000 −3.01370
$$438$$ 0 0
$$439$$ −8.00000 −0.381819 −0.190910 0.981608i $$-0.561144\pi$$
−0.190910 + 0.981608i $$0.561144\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 0 0
$$445$$ 9.00000 0.426641
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ −4.50000 + 7.79423i −0.211897 + 0.367016i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 6.00000 + 5.19615i 0.281284 + 0.243599i
$$456$$ 0 0
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i $$-0.900545\pi$$
0.741998 + 0.670402i $$0.233878\pi$$
$$462$$ 0 0
$$463$$ 20.5000 + 35.5070i 0.952716 + 1.65015i 0.739511 + 0.673145i $$0.235057\pi$$
0.213205 + 0.977007i $$0.431610\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 1.50000 + 2.59808i 0.0694117 + 0.120225i 0.898642 0.438682i $$-0.144554\pi$$
−0.829231 + 0.558906i $$0.811221\pi$$
$$468$$ 0 0
$$469$$ 8.00000 + 6.92820i 0.369406 + 0.319915i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −3.00000 −0.137940
$$474$$ 0 0
$$475$$ −14.0000 + 24.2487i −0.642364 + 1.11261i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 1.50000 + 2.59808i 0.0685367 + 0.118709i 0.898257 0.439470i $$-0.144834\pi$$
−0.829721 + 0.558179i $$0.811500\pi$$
$$480$$ 0 0
$$481$$ −0.500000 + 0.866025i −0.0227980 + 0.0394874i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.50000 2.59808i −0.0681115 0.117973i
$$486$$ 0 0
$$487$$ −12.5000 + 21.6506i −0.566429 + 0.981084i 0.430486 + 0.902597i $$0.358342\pi$$
−0.996915 + 0.0784867i $$0.974991\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i $$-0.323806\pi$$
−0.999552 + 0.0299272i $$0.990472\pi$$
$$492$$ 0 0
$$493$$ −4.50000 7.79423i −0.202670 0.351034i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 24.0000 + 20.7846i 1.07655 + 0.932317i
$$498$$ 0 0
$$499$$ −12.5000 + 21.6506i −0.559577 + 0.969216i 0.437955 + 0.898997i $$0.355703\pi$$
−0.997532 + 0.0702185i $$0.977630\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 9.00000 0.400495
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −4.50000 + 7.79423i −0.199459 + 0.345473i −0.948353 0.317217i $$-0.897252\pi$$
0.748894 + 0.662690i $$0.230585\pi$$
$$510$$ 0 0
$$511$$ −27.5000 + 9.52628i −1.21653 + 0.421418i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 19.5000 + 33.7750i 0.859273 + 1.48830i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.50000 2.59808i 0.0657162 0.113824i −0.831295 0.555831i $$-0.812400\pi$$
0.897011 + 0.442007i $$0.145733\pi$$
$$522$$ 0 0
$$523$$ −3.50000 6.06218i −0.153044 0.265081i 0.779301 0.626650i $$-0.215574\pi$$
−0.932345 + 0.361569i $$0.882241\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −12.0000 + 20.7846i −0.522728 + 0.905392i
$$528$$ 0 0
$$529$$ −29.0000 50.2295i −1.26087 2.18389i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −1.50000 + 2.59808i −0.0649722 + 0.112535i
$$534$$ 0 0
$$535$$ −27.0000 −1.16731
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −16.5000 + 12.9904i −0.710705 + 0.559535i
$$540$$ 0 0
$$541$$ −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i $$-0.242655\pi$$
−0.959697 + 0.281037i $$0.909322\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −19.5000 33.7750i −0.835288 1.44676i
$$546$$ 0 0
$$547$$ 5.50000 9.52628i 0.235163 0.407314i −0.724157 0.689635i $$-0.757771\pi$$
0.959320 + 0.282321i $$0.0911043\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −21.0000 −0.894630
$$552$$ 0 0
$$553$$ 32.0000 + 27.7128i 1.36078 + 1.17847i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −4.50000 + 7.79423i −0.190671 + 0.330252i −0.945473 0.325701i $$-0.894400\pi$$
0.754802 + 0.655953i $$0.227733\pi$$
$$558$$ 0 0
$$559$$ −1.00000 −0.0422955
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ −27.0000 −1.13590
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ −32.0000 −1.33916 −0.669579 0.742741i $$-0.733526\pi$$
−0.669579 + 0.742741i $$0.733526\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −36.0000 −1.50130
$$576$$ 0 0
$$577$$ 12.5000 21.6506i 0.520382 0.901328i −0.479337 0.877631i $$-0.659123\pi$$
0.999719 0.0236970i $$-0.00754370\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 22.5000 7.79423i 0.933457 0.323359i
$$582$$ 0 0
$$583$$ 9.00000 0.372742
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i $$-0.853053\pi$$
0.833408 + 0.552658i $$0.186386\pi$$
$$588$$ 0 0
$$589$$ 28.0000 + 48.4974i 1.15372 + 1.99830i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 19.5000 + 33.7750i 0.800769 + 1.38697i 0.919111 + 0.394000i $$0.128909\pi$$
−0.118342 + 0.992973i $$0.537758\pi$$
$$594$$ 0 0
$$595$$ 4.50000 23.3827i 0.184482 0.958597i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ 12.5000 21.6506i 0.509886 0.883148i −0.490049 0.871695i $$-0.663021\pi$$
0.999934 0.0114528i $$-0.00364562\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −3.00000 5.19615i −0.121967 0.211254i
$$606$$ 0 0
$$607$$ −6.50000 + 11.2583i −0.263827 + 0.456962i −0.967256 0.253804i $$-0.918318\pi$$
0.703429 + 0.710766i $$0.251651\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −11.5000 + 19.9186i −0.464481 + 0.804504i −0.999178 0.0405396i $$-0.987092\pi$$
0.534697 + 0.845044i $$0.320426\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −22.5000 38.9711i −0.905816 1.56892i −0.819818 0.572624i $$-0.805926\pi$$
−0.0859976 0.996295i $$-0.527408\pi$$
$$618$$ 0 0
$$619$$ 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i $$-0.0556830\pi$$
−0.643094 + 0.765787i $$0.722350\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −1.50000 + 7.79423i −0.0600962 + 0.312269i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 6.00000 10.3923i 0.238103 0.412406i
$$636$$ 0 0
$$637$$ −5.50000 + 4.33013i −0.217918 + 0.171566i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i $$-0.940718\pi$$
0.330997 0.943632i $$-0.392615\pi$$
$$642$$ 0 0
$$643$$ 14.5000 + 25.1147i 0.571824 + 0.990429i 0.996379 + 0.0850262i $$0.0270974\pi$$
−0.424555 + 0.905402i $$0.639569\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 10.5000 18.1865i 0.412798 0.714986i −0.582397 0.812905i $$-0.697885\pi$$
0.995194 + 0.0979182i $$0.0312184\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 7.50000 12.9904i 0.293498 0.508353i −0.681137 0.732156i $$-0.738514\pi$$
0.974634 + 0.223803i $$0.0718474\pi$$
$$654$$ 0 0
$$655$$ 22.5000 + 38.9711i 0.879148 + 1.52273i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.50000 + 2.59808i −0.0584317 + 0.101207i −0.893762 0.448542i $$-0.851943\pi$$
0.835330 + 0.549749i $$0.185277\pi$$
$$660$$ 0 0
$$661$$ −22.0000 −0.855701 −0.427850 0.903850i $$-0.640729\pi$$
−0.427850 + 0.903850i $$0.640729\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −42.0000 36.3731i −1.62869 1.41049i
$$666$$ 0 0
$$667$$ −13.5000 23.3827i −0.522722 0.905381i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 3.00000 + 5.19615i 0.115814 + 0.200595i
$$672$$ 0 0
$$673$$ −17.5000 + 30.3109i −0.674575 + 1.16840i 0.302017 + 0.953302i $$0.402340\pi$$
−0.976593 + 0.215096i $$0.930993\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 30.0000 1.15299 0.576497 0.817099i $$-0.304419\pi$$
0.576497 + 0.817099i $$0.304419\pi$$
$$678$$ 0 0
$$679$$ 2.50000 0.866025i 0.0959412 0.0332350i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i $$-0.778250\pi$$
0.939184 + 0.343413i $$0.111583\pi$$
$$684$$ 0 0
$$685$$ −27.0000 −1.03162
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 3.00000 0.114291
$$690$$ 0 0
$$691$$ −44.0000 −1.67384 −0.836919 0.547326i $$-0.815646\pi$$
−0.836919 + 0.547326i $$0.815646\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −21.0000 −0.796575
$$696$$ 0 0
$$697$$ 9.00000 0.340899
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ 3.50000 6.06218i 0.132005 0.228639i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.50000 + 7.79423i −0.0564133 + 0.293132i
$$708$$ 0 0
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −36.0000 + 62.3538i −1.34821 + 2.33517i
$$714$$ 0 0
$$715$$ 4.50000 + 7.79423i 0.168290 + 0.291488i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i $$-0.0764307\pi$$
−0.691608 + 0.722273i $$0.743097\pi$$
$$720$$ 0 0
$$721$$ −32.5000 + 11.2583i −1.21036 + 0.419282i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −12.0000 −0.445669
$$726$$ 0 0
$$727$$ −6.50000 + 11.2583i −0.241072 + 0.417548i −0.961020 0.276479i $$-0.910832\pi$$
0.719948 + 0.694028i $$0.244166\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1.50000 + 2.59808i 0.0554795 + 0.0960933i
$$732$$ 0 0
$$733$$ 0.500000 0.866025i 0.0184679 0.0319874i −0.856644 0.515908i $$-0.827454\pi$$
0.875112 + 0.483921i $$0.160788\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 6.00000 + 10.3923i 0.221013 + 0.382805i
$$738$$ 0 0
$$739$$ 11.5000 19.9186i 0.423034 0.732717i −0.573200 0.819415i $$-0.694298\pi$$
0.996235 + 0.0866983i $$0.0276316\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −10.5000 18.1865i −0.385208 0.667199i 0.606590 0.795015i $$-0.292537\pi$$
−0.991798 + 0.127815i $$0.959204\pi$$
$$744$$ 0 0
$$745$$ 13.5000 + 23.3827i 0.494602 + 0.856675i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 4.50000 23.3827i 0.164426 0.854385i
$$750$$ 0 0
$$751$$ −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i $$-0.909559\pi$$
0.722718 + 0.691143i $$0.242893\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −21.0000 −0.764268
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −22.5000 + 38.9711i −0.815624 + 1.41270i 0.0932544 + 0.995642i $$0.470273\pi$$
−0.908879 + 0.417061i $$0.863060\pi$$
$$762$$ 0 0
$$763$$ 32.5000 11.2583i 1.17658 0.407579i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i $$-0.302780\pi$$
−0.995397 + 0.0958377i $$0.969447\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 13.5000 23.3827i 0.485561 0.841017i −0.514301 0.857610i $$-0.671949\pi$$
0.999862 + 0.0165929i $$0.00528194\pi$$
$$774$$ 0 0
$$775$$ 16.0000 + 27.7128i 0.574737 + 0.995474i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 10.5000 18.1865i 0.376202 0.651600i
$$780$$ 0 0
$$781$$ 18.0000 + 31.1769i 0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −33.0000 + 57.1577i −1.17782 + 2.04004i
$$786$$ 0 0
$$787$$ 28.0000 0.998092 0.499046 0.866575i $$-0.333684\pi$$
0.499046 + 0.866575i $$0.333684\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 4.50000 23.3827i 0.160002 0.831393i
$$792$$ 0 0
$$793$$ 1.00000 + 1.73205i 0.0355110 + 0.0615069i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −10.5000 18.1865i −0.371929 0.644200i 0.617933 0.786231i $$-0.287970\pi$$
−0.989862 + 0.142031i $$0.954637\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −33.0000 −1.16454
$$804$$ 0 0
$$805$$ 13.5000 70.1481i 0.475812 2.47239i
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −16.5000 + 28.5788i −0.580109 + 1.00478i 0.415357 + 0.909659i $$0.363657\pi$$
−0.995466 + 0.0951198i $$0.969677\pi$$
$$810$$ 0 0
$$811$$ −20.0000 −0.702295 −0.351147 0.936320i $$-0.614208\pi$$
−0.351147 + 0.936320i $$0.614208\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −57.0000 −1.99662
$$816$$ 0 0
$$817$$ 7.00000