# Properties

 Label 1216.2.i.d.961.1 Level $1216$ Weight $2$ Character 1216.961 Analytic conductor $9.710$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1216.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.70980888579$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 38) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 961.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1216.961 Dual form 1216.2.i.d.577.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(3.00000 - 5.19615i) q^{17} +(-3.50000 - 2.59808i) q^{19} +(-2.00000 + 3.46410i) q^{21} +(-3.00000 - 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} -5.00000 q^{27} -2.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +10.0000 q^{37} -2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(2.00000 - 3.46410i) q^{43} +9.00000 q^{49} +(3.00000 + 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} +(4.00000 - 1.73205i) q^{57} +(4.50000 - 7.79423i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(4.00000 + 6.92820i) q^{63} +(3.50000 + 6.06218i) q^{67} +6.00000 q^{69} +(-3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{73} -5.00000 q^{75} +12.0000 q^{77} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000 q^{83} +(-3.00000 - 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{91} +(1.00000 - 1.73205i) q^{93} +(-8.50000 + 14.7224i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} + 8q^{7} + 2q^{9} + O(q^{10})$$ $$2q - q^{3} + 8q^{7} + 2q^{9} + 6q^{11} + 2q^{13} + 6q^{17} - 7q^{19} - 4q^{21} - 6q^{23} + 5q^{25} - 10q^{27} - 4q^{31} - 3q^{33} + 20q^{37} - 4q^{39} - 9q^{41} + 4q^{43} + 18q^{49} + 6q^{51} + 6q^{53} + 8q^{57} + 9q^{59} - 4q^{61} + 8q^{63} + 7q^{67} + 12q^{69} - 6q^{71} + q^{73} - 10q^{75} + 24q^{77} - 4q^{79} - q^{81} + 6q^{83} - 6q^{89} + 8q^{91} + 2q^{93} - 17q^{97} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$705$$ $$837$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i $$-0.926548\pi$$
0.684819 + 0.728714i $$0.259881\pi$$
$$4$$ 0 0
$$5$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 0 0
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ 0 0
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i $$-0.0772105\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i $$-0.573966\pi$$
0.957892 0.287129i $$-0.0927008\pi$$
$$18$$ 0 0
$$19$$ −3.50000 2.59808i −0.802955 0.596040i
$$20$$ 0 0
$$21$$ −2.00000 + 3.46410i −0.436436 + 0.755929i
$$22$$ 0 0
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0 0
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0 0
$$33$$ −1.50000 + 2.59808i −0.261116 + 0.452267i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i $$0.414726\pi$$
−0.967486 + 0.252924i $$0.918608\pi$$
$$42$$ 0 0
$$43$$ 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i $$-0.734678\pi$$
0.977261 + 0.212041i $$0.0680112\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0 0
$$49$$ 9.00000 1.28571
$$50$$ 0 0
$$51$$ 3.00000 + 5.19615i 0.420084 + 0.727607i
$$52$$ 0 0
$$53$$ 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i $$-0.0314685\pi$$
−0.583036 + 0.812447i $$0.698135\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000 1.73205i 0.529813 0.229416i
$$58$$ 0 0
$$59$$ 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i $$-0.634094\pi$$
0.994769 0.102151i $$-0.0325726\pi$$
$$60$$ 0 0
$$61$$ −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i $$-0.249096\pi$$
−0.965187 + 0.261562i $$0.915762\pi$$
$$62$$ 0 0
$$63$$ 4.00000 + 6.92820i 0.503953 + 0.872872i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i $$-0.0260283\pi$$
−0.569066 + 0.822292i $$0.692695\pi$$
$$68$$ 0 0
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i $$-0.949205\pi$$
0.631260 + 0.775571i $$0.282538\pi$$
$$72$$ 0 0
$$73$$ 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i $$-0.814695\pi$$
0.893801 + 0.448463i $$0.148028\pi$$
$$74$$ 0 0
$$75$$ −5.00000 −0.577350
$$76$$ 0 0
$$77$$ 12.0000 1.36753
$$78$$ 0 0
$$79$$ −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i $$-0.905577\pi$$
0.731307 + 0.682048i $$0.238911\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 3.00000 0.329293 0.164646 0.986353i $$-0.447352\pi$$
0.164646 + 0.986353i $$0.447352\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 0 0
$$91$$ 4.00000 + 6.92820i 0.419314 + 0.726273i
$$92$$ 0 0
$$93$$ 1.00000 1.73205i 0.103695 0.179605i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −8.50000 + 14.7224i −0.863044 + 1.49484i 0.00593185 + 0.999982i $$0.498112\pi$$
−0.868976 + 0.494854i $$0.835222\pi$$
$$98$$ 0 0
$$99$$ 3.00000 + 5.19615i 0.301511 + 0.522233i
$$100$$ 0 0
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ 0 0
$$103$$ −2.00000 −0.197066 −0.0985329 0.995134i $$-0.531415\pi$$
−0.0985329 + 0.995134i $$0.531415\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −8.00000 + 13.8564i −0.766261 + 1.32720i 0.173316 + 0.984866i $$0.444552\pi$$
−0.939577 + 0.342337i $$0.888782\pi$$
$$110$$ 0 0
$$111$$ −5.00000 + 8.66025i −0.474579 + 0.821995i
$$112$$ 0 0
$$113$$ 15.0000 1.41108 0.705541 0.708669i $$-0.250704\pi$$
0.705541 + 0.708669i $$0.250704\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −2.00000 + 3.46410i −0.184900 + 0.320256i
$$118$$ 0 0
$$119$$ 12.0000 20.7846i 1.10004 1.90532i
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ −4.50000 7.79423i −0.405751 0.702782i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i $$-0.138384\pi$$
−0.818241 + 0.574875i $$0.805051\pi$$
$$128$$ 0 0
$$129$$ 2.00000 + 3.46410i 0.176090 + 0.304997i
$$130$$ 0 0
$$131$$ −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i $$-0.961954\pi$$
0.599699 + 0.800226i $$0.295287\pi$$
$$132$$ 0 0
$$133$$ −14.0000 10.3923i −1.21395 0.901127i
$$134$$ 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
$$139$$ −5.50000 9.52628i −0.466504 0.808008i 0.532764 0.846264i $$-0.321153\pi$$
−0.999268 + 0.0382553i $$0.987820\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 3.00000 + 5.19615i 0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −4.50000 + 7.79423i −0.371154 + 0.642857i
$$148$$ 0 0
$$149$$ 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i $$-0.569430\pi$$
0.953703 0.300750i $$-0.0972370\pi$$
$$150$$ 0 0
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ 0 0
$$153$$ 12.0000 0.970143
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −8.00000 + 13.8564i −0.638470 + 1.10586i 0.347299 + 0.937754i $$0.387099\pi$$
−0.985769 + 0.168107i $$0.946235\pi$$
$$158$$ 0 0
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ −12.0000 20.7846i −0.945732 1.63806i
$$162$$ 0 0
$$163$$ −19.0000 −1.48819 −0.744097 0.668071i $$-0.767120\pi$$
−0.744097 + 0.668071i $$0.767120\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −12.0000 20.7846i −0.928588 1.60836i −0.785687 0.618624i $$-0.787690\pi$$
−0.142901 0.989737i $$-0.545643\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 0 0
$$171$$ 1.00000 8.66025i 0.0764719 0.662266i
$$172$$ 0 0
$$173$$ 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i $$-0.760087\pi$$
0.957241 + 0.289292i $$0.0934200\pi$$
$$174$$ 0 0
$$175$$ 10.0000 + 17.3205i 0.755929 + 1.30931i
$$176$$ 0 0
$$177$$ 4.50000 + 7.79423i 0.338241 + 0.585850i
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 0 0
$$181$$ 1.00000 + 1.73205i 0.0743294 + 0.128742i 0.900794 0.434246i $$-0.142985\pi$$
−0.826465 + 0.562988i $$0.809652\pi$$
$$182$$ 0 0
$$183$$ 4.00000 0.295689
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 9.00000 15.5885i 0.658145 1.13994i
$$188$$ 0 0
$$189$$ −20.0000 −1.45479
$$190$$ 0 0
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ 0 0
$$193$$ −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i $$-0.856266\pi$$
0.827788 + 0.561041i $$0.189599\pi$$
$$194$$ 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
$$199$$ −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i $$-0.281995\pi$$
−0.987022 + 0.160585i $$0.948662\pi$$
$$200$$ 0 0
$$201$$ −7.00000 −0.493742
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 6.00000 10.3923i 0.417029 0.722315i
$$208$$ 0 0
$$209$$ −10.5000 7.79423i −0.726300 0.539138i
$$210$$ 0 0
$$211$$ −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i $$0.408366\pi$$
−0.972346 + 0.233544i $$0.924968\pi$$
$$212$$ 0 0
$$213$$ −3.00000 5.19615i −0.205557 0.356034i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −8.00000 −0.543075
$$218$$ 0 0
$$219$$ 0.500000 + 0.866025i 0.0337869 + 0.0585206i
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 7.00000 12.1244i 0.468755 0.811907i −0.530607 0.847618i $$-0.678036\pi$$
0.999362 + 0.0357107i $$0.0113695\pi$$
$$224$$ 0 0
$$225$$ −5.00000 + 8.66025i −0.333333 + 0.577350i
$$226$$ 0 0
$$227$$ 3.00000 0.199117 0.0995585 0.995032i $$-0.468257\pi$$
0.0995585 + 0.995032i $$0.468257\pi$$
$$228$$ 0 0
$$229$$ 16.0000 1.05731 0.528655 0.848837i $$-0.322697\pi$$
0.528655 + 0.848837i $$0.322697\pi$$
$$230$$ 0 0
$$231$$ −6.00000 + 10.3923i −0.394771 + 0.683763i
$$232$$ 0 0
$$233$$ −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i $$-0.864664\pi$$
0.812700 + 0.582683i $$0.197997\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −2.00000 3.46410i −0.129914 0.225018i
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i $$-0.218151\pi$$
−0.935242 + 0.354010i $$0.884818\pi$$
$$242$$ 0 0
$$243$$ −8.00000 13.8564i −0.513200 0.888889i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.00000 8.66025i 0.0636285 0.551039i
$$248$$ 0 0
$$249$$ −1.50000 + 2.59808i −0.0950586 + 0.164646i
$$250$$ 0 0
$$251$$ 1.50000 + 2.59808i 0.0946792 + 0.163989i 0.909475 0.415759i $$-0.136484\pi$$
−0.814795 + 0.579748i $$0.803151\pi$$
$$252$$ 0 0
$$253$$ −9.00000 15.5885i −0.565825 0.980038i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i $$-0.196494\pi$$
−0.909010 + 0.416775i $$0.863160\pi$$
$$258$$ 0 0
$$259$$ 40.0000 2.48548
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i $$-0.953967\pi$$
0.619586 + 0.784929i $$0.287301\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 0 0
$$269$$ 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i $$-0.714120\pi$$
0.988908 + 0.148527i $$0.0474530\pi$$
$$270$$ 0 0
$$271$$ −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i $$-0.994865\pi$$
0.513905 + 0.857847i $$0.328199\pi$$
$$272$$ 0 0
$$273$$ −8.00000 −0.484182
$$274$$ 0 0
$$275$$ 7.50000 + 12.9904i 0.452267 + 0.783349i
$$276$$ 0 0
$$277$$ −8.00000 −0.480673 −0.240337 0.970690i $$-0.577258\pi$$
−0.240337 + 0.970690i $$0.577258\pi$$
$$278$$ 0 0
$$279$$ −2.00000 3.46410i −0.119737 0.207390i
$$280$$ 0 0
$$281$$ −13.5000 23.3827i −0.805342 1.39489i −0.916060 0.401042i $$-0.868648\pi$$
0.110717 0.993852i $$-0.464685\pi$$
$$282$$ 0 0
$$283$$ −2.50000 + 4.33013i −0.148610 + 0.257399i −0.930714 0.365748i $$-0.880813\pi$$
0.782104 + 0.623148i $$0.214146\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −18.0000 + 31.1769i −1.06251 + 1.84032i
$$288$$ 0 0
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 0 0
$$291$$ −8.50000 14.7224i −0.498279 0.863044i
$$292$$ 0 0
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −15.0000 −0.870388
$$298$$ 0 0
$$299$$ 6.00000 10.3923i 0.346989 0.601003i
$$300$$ 0 0
$$301$$ 8.00000 13.8564i 0.461112 0.798670i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 3.50000 6.06218i 0.199756 0.345987i −0.748694 0.662916i $$-0.769319\pi$$
0.948449 + 0.316929i $$0.102652\pi$$
$$308$$ 0 0
$$309$$ 1.00000 1.73205i 0.0568880 0.0985329i
$$310$$ 0 0
$$311$$ 30.0000 1.70114 0.850572 0.525859i $$-0.176256\pi$$
0.850572 + 0.525859i $$0.176256\pi$$
$$312$$ 0 0
$$313$$ 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i $$0.0137652\pi$$
−0.462093 + 0.886831i $$0.652902\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i $$-0.997978\pi$$
0.494489 0.869184i $$-0.335355\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −24.0000 + 10.3923i −1.33540 + 0.578243i
$$324$$ 0 0
$$325$$ −5.00000 + 8.66025i −0.277350 + 0.480384i
$$326$$ 0 0
$$327$$ −8.00000 13.8564i −0.442401 0.766261i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 5.00000 0.274825 0.137412 0.990514i $$-0.456121\pi$$
0.137412 + 0.990514i $$0.456121\pi$$
$$332$$ 0 0
$$333$$ 10.0000 + 17.3205i 0.547997 + 0.949158i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −5.50000 + 9.52628i −0.299604 + 0.518930i −0.976045 0.217567i $$-0.930188\pi$$
0.676441 + 0.736497i $$0.263521\pi$$
$$338$$ 0 0
$$339$$ −7.50000 + 12.9904i −0.407344 + 0.705541i
$$340$$ 0 0
$$341$$ −6.00000 −0.324918
$$342$$ 0 0
$$343$$ 8.00000 0.431959
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i $$-0.755670\pi$$
0.961162 + 0.275983i $$0.0890035\pi$$
$$348$$ 0 0
$$349$$ 4.00000 0.214115 0.107058 0.994253i $$-0.465857\pi$$
0.107058 + 0.994253i $$0.465857\pi$$
$$350$$ 0 0
$$351$$ −5.00000 8.66025i −0.266880 0.462250i
$$352$$ 0 0
$$353$$ 3.00000 0.159674 0.0798369 0.996808i $$-0.474560\pi$$
0.0798369 + 0.996808i $$0.474560\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 12.0000 + 20.7846i 0.635107 + 1.10004i
$$358$$ 0 0
$$359$$ −3.00000 + 5.19615i −0.158334 + 0.274242i −0.934268 0.356572i $$-0.883946\pi$$
0.775934 + 0.630814i $$0.217279\pi$$
$$360$$ 0 0
$$361$$ 5.50000 + 18.1865i 0.289474 + 0.957186i
$$362$$ 0 0
$$363$$ 1.00000 1.73205i 0.0524864 0.0909091i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −11.0000 19.0526i −0.574195 0.994535i −0.996129 0.0879086i $$-0.971982\pi$$
0.421933 0.906627i $$-0.361352\pi$$
$$368$$ 0 0
$$369$$ −18.0000 −0.937043
$$370$$ 0 0
$$371$$ 12.0000 + 20.7846i 0.623009 + 1.07908i
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ −2.00000 −0.102463
$$382$$ 0 0
$$383$$ −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i $$0.538281\pi$$
−0.799783 + 0.600289i $$0.795052\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 8.00000 0.406663
$$388$$ 0 0
$$389$$ −18.0000 31.1769i −0.912636 1.58073i −0.810326 0.585980i $$-0.800710\pi$$
−0.102311 0.994753i $$-0.532624\pi$$
$$390$$ 0 0
$$391$$ −36.0000 −1.82060
$$392$$ 0 0
$$393$$ −4.50000 7.79423i −0.226995 0.393167i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −5.00000 + 8.66025i −0.250943 + 0.434646i −0.963786 0.266678i $$-0.914074\pi$$
0.712843 + 0.701324i $$0.247407\pi$$
$$398$$ 0 0
$$399$$ 16.0000 6.92820i 0.801002 0.346844i
$$400$$ 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
$$403$$ −2.00000 3.46410i −0.0996271 0.172559i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 30.0000 1.48704
$$408$$ 0 0
$$409$$ −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i $$-0.206116\pi$$
−0.921192 + 0.389109i $$0.872783\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ 18.0000 31.1769i 0.885722 1.53412i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 11.0000 0.538672
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i $$-0.911690\pi$$
0.718076 + 0.695965i $$0.245023\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 30.0000 1.45521
$$426$$ 0 0
$$427$$ −8.00000 13.8564i −0.387147 0.670559i
$$428$$ 0 0
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i $$-0.909648\pi$$
0.237460 0.971397i $$-0.423685\pi$$
$$432$$ 0 0
$$433$$ −13.0000 22.5167i −0.624740 1.08208i −0.988591 0.150624i $$-0.951872\pi$$
0.363851 0.931457i $$-0.381462\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.00000 + 25.9808i −0.143509 + 1.24283i
$$438$$ 0 0
$$439$$ 7.00000 12.1244i 0.334092 0.578664i −0.649218 0.760602i $$-0.724904\pi$$
0.983310 + 0.181938i $$0.0582371\pi$$
$$440$$ 0 0
$$441$$ 9.00000 + 15.5885i 0.428571 + 0.742307i
$$442$$ 0 0
$$443$$ −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i $$-0.235251\pi$$
−0.952901 + 0.303281i $$0.901918\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 9.00000 + 15.5885i 0.425685 + 0.737309i
$$448$$ 0 0
$$449$$ 9.00000 0.424736 0.212368 0.977190i $$-0.431882\pi$$
0.212368 + 0.977190i $$0.431882\pi$$
$$450$$ 0 0
$$451$$ −13.5000 + 23.3827i −0.635690 + 1.10105i
$$452$$ 0 0
$$453$$ −5.00000 + 8.66025i −0.234920 + 0.406894i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5.00000 0.233890 0.116945 0.993138i $$-0.462690\pi$$
0.116945 + 0.993138i $$0.462690\pi$$
$$458$$ 0 0
$$459$$ −15.0000 + 25.9808i −0.700140 + 1.21268i
$$460$$ 0 0
$$461$$ 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i $$-0.788712\pi$$
0.927392 + 0.374091i $$0.122045\pi$$
$$462$$ 0 0
$$463$$ 34.0000 1.58011 0.790057 0.613033i $$-0.210051\pi$$
0.790057 + 0.613033i $$0.210051\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −27.0000 −1.24941 −0.624705 0.780860i $$-0.714781\pi$$
−0.624705 + 0.780860i $$0.714781\pi$$
$$468$$ 0 0
$$469$$ 14.0000 + 24.2487i 0.646460 + 1.11970i
$$470$$ 0 0
$$471$$ −8.00000 13.8564i −0.368621 0.638470i
$$472$$ 0 0
$$473$$ 6.00000 10.3923i 0.275880 0.477839i
$$474$$ 0 0
$$475$$ 2.50000 21.6506i 0.114708 0.993399i
$$476$$ 0 0
$$477$$ −6.00000 + 10.3923i −0.274721 + 0.475831i
$$478$$ 0 0
$$479$$ 18.0000 + 31.1769i 0.822441 + 1.42451i 0.903859 + 0.427830i $$0.140722\pi$$
−0.0814184 + 0.996680i $$0.525945\pi$$
$$480$$ 0 0
$$481$$ 10.0000 + 17.3205i 0.455961 + 0.789747i
$$482$$ 0 0
$$483$$ 24.0000 1.09204
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −2.00000 −0.0906287 −0.0453143 0.998973i $$-0.514429\pi$$
−0.0453143 + 0.998973i $$0.514429\pi$$
$$488$$ 0 0
$$489$$ 9.50000 16.4545i 0.429605 0.744097i
$$490$$ 0 0
$$491$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −12.0000 + 20.7846i −0.538274 + 0.932317i
$$498$$ 0 0
$$499$$ 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i $$-0.644297\pi$$
0.997532 0.0702185i $$-0.0223697\pi$$
$$500$$ 0 0
$$501$$ 24.0000 1.07224
$$502$$ 0 0
$$503$$ 3.00000 + 5.19615i 0.133763 + 0.231685i 0.925124 0.379664i $$-0.123960\pi$$
−0.791361 + 0.611349i $$0.790627\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 4.50000 + 7.79423i 0.199852 + 0.346154i
$$508$$ 0 0
$$509$$ −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i $$-0.988148\pi$$
0.467416 0.884037i $$-0.345185\pi$$
$$510$$ 0 0
$$511$$ 2.00000 3.46410i 0.0884748 0.153243i
$$512$$ 0 0
$$513$$ 17.5000 + 12.9904i 0.772644 + 0.573539i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 3.00000 + 5.19615i 0.131685 + 0.228086i
$$520$$ 0 0
$$521$$ 9.00000 0.394297 0.197149 0.980374i $$-0.436832\pi$$
0.197149 + 0.980374i $$0.436832\pi$$
$$522$$ 0 0
$$523$$ 14.0000 + 24.2487i 0.612177 + 1.06032i 0.990873 + 0.134801i $$0.0430394\pi$$
−0.378695 + 0.925521i $$0.623627\pi$$
$$524$$ 0 0
$$525$$ −20.0000 −0.872872
$$526$$ 0 0
$$527$$ −6.00000 + 10.3923i −0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ 18.0000 0.781133
$$532$$ 0 0
$$533$$ −18.0000 −0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −4.50000 + 7.79423i −0.194189 + 0.336346i
$$538$$ 0 0
$$539$$ 27.0000 1.16297
$$540$$ 0 0
$$541$$ 22.0000 + 38.1051i 0.945854 + 1.63827i 0.754032 + 0.656837i $$0.228106\pi$$
0.191821 + 0.981430i $$0.438561\pi$$
$$542$$ 0 0
$$543$$ −2.00000 −0.0858282
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 2.00000 + 3.46410i 0.0855138 + 0.148114i 0.905610 0.424111i $$-0.139413\pi$$
−0.820096 + 0.572226i $$0.806080\pi$$
$$548$$ 0 0
$$549$$ 4.00000 6.92820i 0.170716 0.295689i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −8.00000 + 13.8564i −0.340195 + 0.589234i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 12.0000 + 20.7846i 0.508456 + 0.880672i 0.999952 + 0.00979220i $$0.00311700\pi$$
−0.491496 + 0.870880i $$0.663550\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 9.00000 + 15.5885i 0.379980 + 0.658145i
$$562$$ 0 0
$$563$$ −21.0000 −0.885044 −0.442522 0.896758i $$-0.645916\pi$$
−0.442522 + 0.896758i $$0.645916\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −2.00000 + 3.46410i −0.0839921 + 0.145479i
$$568$$ 0 0
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ −7.00000 −0.292941 −0.146470 0.989215i $$-0.546791\pi$$
−0.146470 + 0.989215i $$0.546791\pi$$
$$572$$ 0 0
$$573$$ 6.00000 10.3923i 0.250654 0.434145i
$$574$$ 0 0
$$575$$ 15.0000 25.9808i 0.625543 1.08347i
$$576$$ 0 0
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ 0 0
$$579$$ −1.00000 1.73205i −0.0415586 0.0719816i
$$580$$ 0 0
$$581$$ 12.0000 0.497844
$$582$$ 0 0
$$583$$ 9.00000 + 15.5885i 0.372742 + 0.645608i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i $$-0.753676\pi$$
0.962872 + 0.269957i $$0.0870095\pi$$
$$588$$ 0 0
$$589$$ 7.00000 + 5.19615i 0.288430 + 0.214104i
$$590$$ 0 0
$$591$$ 9.00000 15.5885i 0.370211 0.641223i
$$592$$ 0 0
$$593$$ 10.5000 + 18.1865i 0.431183 + 0.746831i 0.996976 0.0777165i $$-0.0247629\pi$$
−0.565792 + 0.824548i $$0.691430\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 10.0000 0.409273
$$598$$ 0 0
$$599$$ −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i $$-0.205782\pi$$
−0.920783 + 0.390075i $$0.872449\pi$$
$$600$$ 0 0
$$601$$ −13.0000 −0.530281 −0.265141 0.964210i $$-0.585418\pi$$
−0.265141 + 0.964210i $$0.585418\pi$$
$$602$$ 0 0
$$603$$ −7.00000 + 12.1244i −0.285062 + 0.493742i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −20.0000 −0.811775 −0.405887 0.913923i $$-0.633038\pi$$
−0.405887 + 0.913923i $$0.633038\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 1.00000 1.73205i 0.0403896 0.0699569i −0.845124 0.534570i $$-0.820473\pi$$
0.885514 + 0.464614i $$0.153807\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i $$-0.185900\pi$$
−0.894639 + 0.446790i $$0.852567\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 15.0000 + 25.9808i 0.601929 + 1.04257i
$$622$$ 0 0
$$623$$ −12.0000 20.7846i −0.480770 0.832718i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ 0 0
$$627$$ 12.0000 5.19615i 0.479234 0.207514i
$$628$$ 0 0
$$629$$ 30.0000 51.9615i 1.19618 2.07184i
$$630$$ 0 0
$$631$$ −14.0000 24.2487i −0.557331 0.965326i −0.997718 0.0675178i $$-0.978492\pi$$
0.440387 0.897808i $$-0.354841\pi$$
$$632$$ 0 0
$$633$$ −10.0000 17.3205i −0.397464 0.688428i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 9.00000 + 15.5885i 0.356593 + 0.617637i
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ 0 0
$$641$$ 19.5000 33.7750i 0.770204 1.33403i −0.167247 0.985915i $$-0.553488\pi$$
0.937451 0.348117i $$-0.113179\pi$$
$$642$$ 0 0
$$643$$ 21.5000 37.2391i 0.847877 1.46857i −0.0352216 0.999380i $$-0.511214\pi$$
0.883099 0.469187i $$-0.155453\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 0 0
$$649$$ 13.5000 23.3827i 0.529921 0.917851i
$$650$$ 0 0
$$651$$ 4.00000 6.92820i 0.156772 0.271538i
$$652$$ 0 0
$$653$$ 12.0000 0.469596 0.234798 0.972044i $$-0.424557\pi$$
0.234798 + 0.972044i $$0.424557\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 2.00000 0.0780274
$$658$$ 0 0
$$659$$ −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i $$-0.919323\pi$$
0.266872 0.963732i $$-0.414010\pi$$
$$660$$ 0 0
$$661$$ −20.0000 34.6410i −0.777910 1.34738i −0.933144 0.359502i $$-0.882947\pi$$
0.155235 0.987878i $$-0.450387\pi$$
$$662$$ 0 0
$$663$$ −6.00000 + 10.3923i −0.233021 + 0.403604i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 7.00000 + 12.1244i 0.270636 + 0.468755i
$$670$$ 0 0
$$671$$ −6.00000 10.3923i −0.231627 0.401190i
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ 0 0
$$675$$ −12.5000 21.6506i −0.481125 0.833333i
$$676$$ 0 0
$$677$$ 42.0000 1.61419 0.807096 0.590421i $$-0.201038\pi$$
0.807096 + 0.590421i $$0.201038\pi$$
$$678$$ 0 0
$$679$$ −34.0000 + 58.8897i −1.30480 + 2.25998i
$$680$$ 0 0
$$681$$ −1.50000 + 2.59808i −0.0574801 + 0.0995585i
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −8.00000 + 13.8564i −0.305219 + 0.528655i
$$688$$ 0 0
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ 44.0000 1.67384 0.836919 0.547326i $$-0.184354\pi$$
0.836919 + 0.547326i $$0.184354\pi$$
$$692$$ 0 0
$$693$$ 12.0000 + 20.7846i 0.455842 + 0.789542i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 27.0000 + 46.7654i 1.02270 + 1.77136i
$$698$$ 0 0
$$699$$ −1.50000 2.59808i −0.0567352 0.0982683i
$$700$$ 0 0
$$701$$ −12.0000 + 20.7846i −0.453234 + 0.785024i −0.998585 0.0531839i $$-0.983063\pi$$
0.545351 + 0.838208i $$0.316396\pi$$
$$702$$ 0 0
$$703$$ −35.0000 25.9808i −1.32005 0.979883i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i $$-0.0819909\pi$$
−0.704118 + 0.710083i $$0.748658\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 6.00000 + 10.3923i 0.224702 + 0.389195i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ 0 0
$$719$$ 15.0000 25.9808i 0.559406 0.968919i −0.438141 0.898906i $$-0.644363\pi$$
0.997546 0.0700124i $$-0.0223039\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 0 0
$$723$$ 5.00000 0.185952
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 16.0000 27.7128i 0.593407 1.02781i −0.400362 0.916357i $$-0.631116\pi$$
0.993770 0.111454i $$-0.0355509\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −12.0000 20.7846i −0.443836 0.768747i
$$732$$ 0 0
$$733$$ 22.0000 0.812589 0.406294 0.913742i $$-0.366821\pi$$
0.406294 + 0.913742i $$0.366821\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 10.5000 + 18.1865i 0.386772 + 0.669910i
$$738$$ 0 0
$$739$$ −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i $$0.389288\pi$$
−0.984589 + 0.174883i $$0.944045\pi$$
$$740$$ 0 0
$$741$$ 7.00000 + 5.19615i 0.257151 + 0.190885i
$$742$$ 0 0
$$743$$ −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i $$-0.940442\pi$$
0.652369 + 0.757902i $$0.273775\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 3.00000 + 5.19615i 0.109764 + 0.190117i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 19.0000 + 32.9090i 0.693320 + 1.20087i 0.970744 + 0.240118i $$0.0771860\pi$$
−0.277424 + 0.960748i $$0.589481\pi$$
$$752$$ 0 0
$$753$$ −3.00000 −0.109326
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −5.00000 + 8.66025i −0.181728 + 0.314762i −0.942469 0.334293i $$-0.891502\pi$$
0.760741 + 0.649056i $$0.224836\pi$$
$$758$$ 0 0
$$759$$ 18.0000 0.653359
$$760$$ 0 0
$$761$$ −39.0000 −1.41375 −0.706874 0.707339i $$-0.749895\pi$$
−0.706874 + 0.707339i $$0.749895\pi$$
$$762$$ 0 0
$$763$$ −32.0000 + 55.4256i −1.15848 + 2.00654i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 18.0000 0.649942
$$768$$ 0 0
$$769$$ −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i $$-0.178148\pi$$
−0.883493 + 0.468445i $$0.844814\pi$$
$$770$$ 0 0
$$771$$ 3.00000 0.108042
$$772$$ 0 0
$$773$$ −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i $$-0.835111\pi$$
0.00558380 0.999984i $$-0.498223\pi$$
$$774$$ 0 0
$$775$$ −5.00000 8.66025i −0.179605 0.311086i
$$776$$ 0 0
$$777$$ −20.0000 + 34.6410i −0.717496 + 1.24274i
$$778$$ 0 0
$$779$$ 36.0000 15.5885i 1.28983 0.558514i
$$780$$ 0 0
$$781$$ −9.00000 + 15.5885i −0.322045 + 0.557799i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −7.00000 −0.249523 −0.124762 0.992187i $$-0.539817\pi$$
−0.124762 + 0.992187i $$0.539817\pi$$
$$788$$ 0 0
$$789$$ −6.00000 10.3923i −0.213606 0.369976i
$$790$$ 0 0
$$791$$ 60.0000 2.13335
$$792$$ 0 0
$$793$$ 4.00000 6.92820i 0.142044 0.246028i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −6.00000 −0.212531 −0.106265 0.994338i $$-0.533889\pi$$
−0.106265 + 0.994338i $$0.533889\pi$$
$$798$$ 0 0
$$799$$ 0 0