# Properties

 Label 152.2.i.b.49.1 Level $152$ Weight $2$ Character 152.49 Analytic conductor $1.214$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 152.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.21372611072$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 49.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 152.49 Dual form 152.2.i.b.121.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{15} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} -5.00000 q^{27} +(2.00000 + 3.46410i) q^{29} -10.0000 q^{31} +(-1.50000 + 2.59808i) q^{33} +2.00000 q^{37} +2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(2.00000 - 3.46410i) q^{43} +8.00000 q^{45} +(6.00000 + 10.3923i) q^{47} -7.00000 q^{49} +(-1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{53} +(6.00000 - 10.3923i) q^{55} +(-4.00000 - 1.73205i) q^{57} +(0.500000 - 0.866025i) q^{59} +(4.00000 + 6.92820i) q^{61} -8.00000 q^{65} +(-4.50000 - 7.79423i) q^{67} +6.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(4.50000 - 7.79423i) q^{73} +11.0000 q^{75} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} -5.00000 q^{83} +(4.00000 + 6.92820i) q^{85} -4.00000 q^{87} +(9.00000 + 15.5885i) q^{89} +(5.00000 - 8.66025i) q^{93} +(16.0000 + 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} + 4q^{5} + 2q^{9} + O(q^{10})$$ $$2q - q^{3} + 4q^{5} + 2q^{9} + 6q^{11} - 2q^{13} + 4q^{15} - 2q^{17} + q^{19} - 6q^{23} - 11q^{25} - 10q^{27} + 4q^{29} - 20q^{31} - 3q^{33} + 4q^{37} + 4q^{39} - 9q^{41} + 4q^{43} + 16q^{45} + 12q^{47} - 14q^{49} - 2q^{51} + 2q^{53} + 12q^{55} - 8q^{57} + q^{59} + 8q^{61} - 16q^{65} - 9q^{67} + 12q^{69} + 6q^{71} + 9q^{73} + 22q^{75} + 4q^{79} - q^{81} - 10q^{83} + 8q^{85} - 8q^{87} + 18q^{89} + 10q^{93} + 32q^{95} - q^{97} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$$.

 $$n$$ $$39$$ $$77$$ $$97$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i $$-0.926548\pi$$
0.684819 + 0.728714i $$0.259881\pi$$
$$4$$ 0 0
$$5$$ 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i $$-0.480917\pi$$
0.834512 0.550990i $$-0.185750\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 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 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 2.00000 + 3.46410i 0.516398 + 0.894427i
$$16$$ 0 0
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 0 0
$$19$$ 0.500000 + 4.33013i 0.114708 + 0.993399i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 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
$$25$$ −5.50000 9.52628i −1.10000 1.90526i
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ 2.00000 + 3.46410i 0.371391 + 0.643268i 0.989780 0.142605i $$-0.0455477\pi$$
−0.618389 + 0.785872i $$0.712214\pi$$
$$30$$ 0 0
$$31$$ −10.0000 −1.79605 −0.898027 0.439941i $$-0.854999\pi$$
−0.898027 + 0.439941i $$0.854999\pi$$
$$32$$ 0 0
$$33$$ −1.50000 + 2.59808i −0.261116 + 0.452267i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 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
$$45$$ 8.00000 1.19257
$$46$$ 0 0
$$47$$ 6.00000 + 10.3923i 0.875190 + 1.51587i 0.856560 + 0.516047i $$0.172597\pi$$
0.0186297 + 0.999826i $$0.494070\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ −1.00000 1.73205i −0.140028 0.242536i
$$52$$ 0 0
$$53$$ 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i $$-0.122805\pi$$
−0.789136 + 0.614218i $$0.789471\pi$$
$$54$$ 0 0
$$55$$ 6.00000 10.3923i 0.809040 1.40130i
$$56$$ 0 0
$$57$$ −4.00000 1.73205i −0.529813 0.229416i
$$58$$ 0 0
$$59$$ 0.500000 0.866025i 0.0650945 0.112747i −0.831641 0.555313i $$-0.812598\pi$$
0.896736 + 0.442566i $$0.145932\pi$$
$$60$$ 0 0
$$61$$ 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i $$0.00448323\pi$$
−0.487753 + 0.872982i $$0.662183\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −8.00000 −0.992278
$$66$$ 0 0
$$67$$ −4.50000 7.79423i −0.549762 0.952217i −0.998290 0.0584478i $$-0.981385\pi$$
0.448528 0.893769i $$-0.351948\pi$$
$$68$$ 0 0
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i $$-0.717462\pi$$
0.987294 + 0.158901i $$0.0507952\pi$$
$$72$$ 0 0
$$73$$ 4.50000 7.79423i 0.526685 0.912245i −0.472831 0.881153i $$-0.656768\pi$$
0.999517 0.0310925i $$-0.00989865\pi$$
$$74$$ 0 0
$$75$$ 11.0000 1.27017
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i $$-0.761089\pi$$
0.956325 + 0.292306i $$0.0944227\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −5.00000 −0.548821 −0.274411 0.961613i $$-0.588483\pi$$
−0.274411 + 0.961613i $$0.588483\pi$$
$$84$$ 0 0
$$85$$ 4.00000 + 6.92820i 0.433861 + 0.751469i
$$86$$ 0 0
$$87$$ −4.00000 −0.428845
$$88$$ 0 0
$$89$$ 9.00000 + 15.5885i 0.953998 + 1.65237i 0.736644 + 0.676280i $$0.236409\pi$$
0.217354 + 0.976093i $$0.430258\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 5.00000 8.66025i 0.518476 0.898027i
$$94$$ 0 0
$$95$$ 16.0000 + 6.92820i 1.64157 + 0.710819i
$$96$$ 0 0
$$97$$ −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i $$-0.849500\pi$$
0.839525 + 0.543321i $$0.182833\pi$$
$$98$$ 0 0
$$99$$ 3.00000 + 5.19615i 0.301511 + 0.522233i
$$100$$ 0 0
$$101$$ −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i $$-0.963017\pi$$
0.396236 0.918149i $$-0.370316\pi$$
$$102$$ 0 0
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 16.0000 1.54678 0.773389 0.633932i $$-0.218560\pi$$
0.773389 + 0.633932i $$0.218560\pi$$
$$108$$ 0 0
$$109$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$110$$ 0 0
$$111$$ −1.00000 + 1.73205i −0.0949158 + 0.164399i
$$112$$ 0 0
$$113$$ −1.00000 −0.0940721 −0.0470360 0.998893i $$-0.514978\pi$$
−0.0470360 + 0.998893i $$0.514978\pi$$
$$114$$ 0 0
$$115$$ −24.0000 −2.23801
$$116$$ 0 0
$$117$$ 2.00000 3.46410i 0.184900 0.320256i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ −4.50000 7.79423i −0.405751 0.702782i
$$124$$ 0 0
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ 3.00000 + 5.19615i 0.266207 + 0.461084i 0.967879 0.251416i $$-0.0808962\pi$$
−0.701672 + 0.712500i $$0.747563\pi$$
$$128$$ 0 0
$$129$$ 2.00000 + 3.46410i 0.176090 + 0.304997i
$$130$$ 0 0
$$131$$ 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i $$-0.605885\pi$$
0.981824 0.189794i $$-0.0607819\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −10.0000 + 17.3205i −0.860663 + 1.49071i
$$136$$ 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
$$139$$ 6.50000 + 11.2583i 0.551323 + 0.954919i 0.998179 + 0.0603135i $$0.0192101\pi$$
−0.446857 + 0.894606i $$0.647457\pi$$
$$140$$ 0 0
$$141$$ −12.0000 −1.01058
$$142$$ 0 0
$$143$$ −3.00000 5.19615i −0.250873 0.434524i
$$144$$ 0 0
$$145$$ 16.0000 1.32873
$$146$$ 0 0
$$147$$ 3.50000 6.06218i 0.288675 0.500000i
$$148$$ 0 0
$$149$$ 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i $$-0.698996\pi$$
0.994847 + 0.101391i $$0.0323294\pi$$
$$150$$ 0 0
$$151$$ 2.00000 0.162758 0.0813788 0.996683i $$-0.474068\pi$$
0.0813788 + 0.996683i $$0.474068\pi$$
$$152$$ 0 0
$$153$$ −4.00000 −0.323381
$$154$$ 0 0
$$155$$ −20.0000 + 34.6410i −1.60644 + 2.78243i
$$156$$ 0 0
$$157$$ −4.00000 + 6.92820i −0.319235 + 0.552931i −0.980329 0.197372i $$-0.936759\pi$$
0.661094 + 0.750303i $$0.270093\pi$$
$$158$$ 0 0
$$159$$ −2.00000 −0.158610
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −11.0000 −0.861586 −0.430793 0.902451i $$-0.641766\pi$$
−0.430793 + 0.902451i $$0.641766\pi$$
$$164$$ 0 0
$$165$$ 6.00000 + 10.3923i 0.467099 + 0.809040i
$$166$$ 0 0
$$167$$ −8.00000 13.8564i −0.619059 1.07224i −0.989658 0.143448i $$-0.954181\pi$$
0.370599 0.928793i $$-0.379152\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 0 0
$$171$$ −7.00000 + 5.19615i −0.535303 + 0.397360i
$$172$$ 0 0
$$173$$ 13.0000 22.5167i 0.988372 1.71191i 0.362500 0.931984i $$-0.381923\pi$$
0.625871 0.779926i $$-0.284744\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0.500000 + 0.866025i 0.0375823 + 0.0650945i
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 0 0
$$181$$ −7.00000 12.1244i −0.520306 0.901196i −0.999721 0.0236082i $$-0.992485\pi$$
0.479415 0.877588i $$-0.340849\pi$$
$$182$$ 0 0
$$183$$ −8.00000 −0.591377
$$184$$ 0 0
$$185$$ 4.00000 6.92820i 0.294086 0.509372i
$$186$$ 0 0
$$187$$ −3.00000 + 5.19615i −0.219382 + 0.379980i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i $$-0.764050\pi$$
0.953564 + 0.301189i $$0.0973836\pi$$
$$194$$ 0 0
$$195$$ 4.00000 6.92820i 0.286446 0.496139i
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 9.00000 + 15.5885i 0.637993 + 1.10504i 0.985873 + 0.167497i $$0.0535685\pi$$
−0.347879 + 0.937539i $$0.613098\pi$$
$$200$$ 0 0
$$201$$ 9.00000 0.634811
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 18.0000 + 31.1769i 1.25717 + 2.17749i
$$206$$ 0 0
$$207$$ 6.00000 10.3923i 0.417029 0.722315i
$$208$$ 0 0
$$209$$ 1.50000 + 12.9904i 0.103757 + 0.898563i
$$210$$ 0 0
$$211$$ 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i $$-0.697794\pi$$
0.995222 + 0.0976347i $$0.0311277\pi$$
$$212$$ 0 0
$$213$$ 3.00000 + 5.19615i 0.205557 + 0.356034i
$$214$$ 0 0
$$215$$ −8.00000 13.8564i −0.545595 0.944999i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 4.50000 + 7.79423i 0.304082 + 0.526685i
$$220$$ 0 0
$$221$$ 4.00000 0.269069
$$222$$ 0 0
$$223$$ −5.00000 + 8.66025i −0.334825 + 0.579934i −0.983451 0.181173i $$-0.942010\pi$$
0.648626 + 0.761107i $$0.275344\pi$$
$$224$$ 0 0
$$225$$ 11.0000 19.0526i 0.733333 1.27017i
$$226$$ 0 0
$$227$$ 19.0000 1.26107 0.630537 0.776159i $$-0.282835\pi$$
0.630537 + 0.776159i $$0.282835\pi$$
$$228$$ 0 0
$$229$$ −8.00000 −0.528655 −0.264327 0.964433i $$-0.585150\pi$$
−0.264327 + 0.964433i $$0.585150\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −5.50000 + 9.52628i −0.360317 + 0.624087i −0.988013 0.154371i $$-0.950665\pi$$
0.627696 + 0.778459i $$0.283998\pi$$
$$234$$ 0 0
$$235$$ 48.0000 3.13117
$$236$$ 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
$$241$$ −10.5000 18.1865i −0.676364 1.17150i −0.976068 0.217465i $$-0.930221\pi$$
0.299704 0.954032i $$-0.403112\pi$$
$$242$$ 0 0
$$243$$ −8.00000 13.8564i −0.513200 0.888889i
$$244$$ 0 0
$$245$$ −14.0000 + 24.2487i −0.894427 + 1.54919i
$$246$$ 0 0
$$247$$ 7.00000 5.19615i 0.445399 0.330623i
$$248$$ 0 0
$$249$$ 2.50000 4.33013i 0.158431 0.274411i
$$250$$ 0 0
$$251$$ −2.50000 4.33013i −0.157799 0.273315i 0.776276 0.630393i $$-0.217106\pi$$
−0.934075 + 0.357078i $$0.883773\pi$$
$$252$$ 0 0
$$253$$ −9.00000 15.5885i −0.565825 0.980038i
$$254$$ 0 0
$$255$$ −8.00000 −0.500979
$$256$$ 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
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −4.00000 + 6.92820i −0.247594 + 0.428845i
$$262$$ 0 0
$$263$$ −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i $$-0.997543\pi$$
0.506669 + 0.862141i $$0.330877\pi$$
$$264$$ 0 0
$$265$$ 8.00000 0.491436
$$266$$ 0 0
$$267$$ −18.0000 −1.10158
$$268$$ 0 0
$$269$$ −2.00000 + 3.46410i −0.121942 + 0.211210i −0.920534 0.390664i $$-0.872246\pi$$
0.798591 + 0.601874i $$0.205579\pi$$
$$270$$ 0 0
$$271$$ 10.0000 17.3205i 0.607457 1.05215i −0.384201 0.923249i $$-0.625523\pi$$
0.991658 0.128897i $$-0.0411435\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −16.5000 28.5788i −0.994987 1.72337i
$$276$$ 0 0
$$277$$ 12.0000 0.721010 0.360505 0.932757i $$-0.382604\pi$$
0.360505 + 0.932757i $$0.382604\pi$$
$$278$$ 0 0
$$279$$ −10.0000 17.3205i −0.598684 1.03695i
$$280$$ 0 0
$$281$$ 6.50000 + 11.2583i 0.387757 + 0.671616i 0.992148 0.125073i $$-0.0399165\pi$$
−0.604390 + 0.796689i $$0.706583\pi$$
$$282$$ 0 0
$$283$$ −6.50000 + 11.2583i −0.386385 + 0.669238i −0.991960 0.126550i $$-0.959610\pi$$
0.605575 + 0.795788i $$0.292943\pi$$
$$284$$ 0 0
$$285$$ −14.0000 + 10.3923i −0.829288 + 0.615587i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ −0.500000 0.866025i −0.0293105 0.0507673i
$$292$$ 0 0
$$293$$ −4.00000 −0.233682 −0.116841 0.993151i $$-0.537277\pi$$
−0.116841 + 0.993151i $$0.537277\pi$$
$$294$$ 0 0
$$295$$ −2.00000 3.46410i −0.116445 0.201688i
$$296$$ 0 0
$$297$$ −15.0000 −0.870388
$$298$$ 0 0
$$299$$ −6.00000 + 10.3923i −0.346989 + 0.601003i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 12.0000 0.689382
$$304$$ 0 0
$$305$$ 32.0000 1.83231
$$306$$ 0 0
$$307$$ −12.5000 + 21.6506i −0.713413 + 1.23567i 0.250156 + 0.968206i $$0.419518\pi$$
−0.963569 + 0.267461i $$0.913815\pi$$
$$308$$ 0 0
$$309$$ 7.00000 12.1244i 0.398216 0.689730i
$$310$$ 0 0
$$311$$ −2.00000 −0.113410 −0.0567048 0.998391i $$-0.518059\pi$$
−0.0567048 + 0.998391i $$0.518059\pi$$
$$312$$ 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
$$317$$ −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i $$-0.220558\pi$$
−0.937892 + 0.346929i $$0.887225\pi$$
$$318$$ 0 0
$$319$$ 6.00000 + 10.3923i 0.335936 + 0.581857i
$$320$$ 0 0
$$321$$ −8.00000 + 13.8564i −0.446516 + 0.773389i
$$322$$ 0 0
$$323$$ −8.00000 3.46410i −0.445132 0.192748i
$$324$$ 0 0
$$325$$ −11.0000 + 19.0526i −0.610170 + 1.05685i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 13.0000 0.714545 0.357272 0.934000i $$-0.383707\pi$$
0.357272 + 0.934000i $$0.383707\pi$$
$$332$$ 0 0
$$333$$ 2.00000 + 3.46410i 0.109599 + 0.189832i
$$334$$ 0 0
$$335$$ −36.0000 −1.96689
$$336$$ 0 0
$$337$$ −1.50000 + 2.59808i −0.0817102 + 0.141526i −0.903985 0.427565i $$-0.859372\pi$$
0.822274 + 0.569091i $$0.192705\pi$$
$$338$$ 0 0
$$339$$ 0.500000 0.866025i 0.0271563 0.0470360i
$$340$$ 0 0
$$341$$ −30.0000 −1.62459
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 12.0000 20.7846i 0.646058 1.11901i
$$346$$ 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
$$349$$ −28.0000 −1.49881 −0.749403 0.662114i $$-0.769659\pi$$
−0.749403 + 0.662114i $$0.769659\pi$$
$$350$$ 0 0
$$351$$ 5.00000 + 8.66025i 0.266880 + 0.462250i
$$352$$ 0 0
$$353$$ 11.0000 0.585471 0.292735 0.956193i $$-0.405434\pi$$
0.292735 + 0.956193i $$0.405434\pi$$
$$354$$ 0 0
$$355$$ −12.0000 20.7846i −0.636894 1.10313i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 1.00000 1.73205i 0.0527780 0.0914141i −0.838429 0.545010i $$-0.816526\pi$$
0.891207 + 0.453596i $$0.149859\pi$$
$$360$$ 0 0
$$361$$ −18.5000 + 4.33013i −0.973684 + 0.227901i
$$362$$ 0 0
$$363$$ 1.00000 1.73205i 0.0524864 0.0909091i
$$364$$ 0 0
$$365$$ −18.0000 31.1769i −0.942163 1.63187i
$$366$$ 0 0
$$367$$ 13.0000 + 22.5167i 0.678594 + 1.17536i 0.975404 + 0.220423i $$0.0707439\pi$$
−0.296810 + 0.954937i $$0.595923\pi$$
$$368$$ 0 0
$$369$$ −18.0000 −0.937043
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 12.0000 20.7846i 0.619677 1.07331i
$$376$$ 0 0
$$377$$ 4.00000 6.92820i 0.206010 0.356821i
$$378$$ 0 0
$$379$$ −12.0000 −0.616399 −0.308199 0.951322i $$-0.599726\pi$$
−0.308199 + 0.951322i $$0.599726\pi$$
$$380$$ 0 0
$$381$$ −6.00000 −0.307389
$$382$$ 0 0
$$383$$ 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i $$-0.767812\pi$$
0.949938 + 0.312437i $$0.101145\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 8.00000 0.406663
$$388$$ 0 0
$$389$$ −2.00000 3.46410i −0.101404 0.175637i 0.810859 0.585241i $$-0.199000\pi$$
−0.912263 + 0.409604i $$0.865667\pi$$
$$390$$ 0 0
$$391$$ 12.0000 0.606866
$$392$$ 0 0
$$393$$ 7.50000 + 12.9904i 0.378325 + 0.655278i
$$394$$ 0 0
$$395$$ −8.00000 13.8564i −0.402524 0.697191i
$$396$$ 0 0
$$397$$ 7.00000 12.1244i 0.351320 0.608504i −0.635161 0.772380i $$-0.719066\pi$$
0.986481 + 0.163876i $$0.0523996\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i $$-0.809468\pi$$
0.901046 + 0.433724i $$0.142801\pi$$
$$402$$ 0 0
$$403$$ 10.0000 + 17.3205i 0.498135 + 0.862796i
$$404$$ 0 0
$$405$$ 2.00000 + 3.46410i 0.0993808 + 0.172133i
$$406$$ 0 0
$$407$$ 6.00000 0.297409
$$408$$ 0 0
$$409$$ 17.5000 + 30.3109i 0.865319 + 1.49878i 0.866730 + 0.498778i $$0.166218\pi$$
−0.00141047 + 0.999999i $$0.500449\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −10.0000 + 17.3205i −0.490881 + 0.850230i
$$416$$ 0 0
$$417$$ −13.0000 −0.636613
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 11.0000 19.0526i 0.536107 0.928565i −0.463002 0.886357i $$-0.653228\pi$$
0.999109 0.0422075i $$-0.0134391\pi$$
$$422$$ 0 0
$$423$$ −12.0000 + 20.7846i −0.583460 + 1.01058i
$$424$$ 0 0
$$425$$ 22.0000 1.06716
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 6.00000 0.289683
$$430$$ 0 0
$$431$$ 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i $$0.0903517\pi$$
−0.237460 + 0.971397i $$0.576315\pi$$
$$432$$ 0 0
$$433$$ −5.00000 8.66025i −0.240285 0.416185i 0.720511 0.693444i $$-0.243907\pi$$
−0.960795 + 0.277259i $$0.910574\pi$$
$$434$$ 0 0
$$435$$ −8.00000 + 13.8564i −0.383571 + 0.664364i
$$436$$ 0 0
$$437$$ 21.0000 15.5885i 1.00457 0.745697i
$$438$$ 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
$$441$$ −7.00000 12.1244i −0.333333 0.577350i
$$442$$ 0 0
$$443$$ −0.500000 0.866025i −0.0237557 0.0411461i 0.853903 0.520432i $$-0.174229\pi$$
−0.877659 + 0.479286i $$0.840896\pi$$
$$444$$ 0 0
$$445$$ 72.0000 3.41313
$$446$$ 0 0
$$447$$ 5.00000 + 8.66025i 0.236492 + 0.409616i
$$448$$ 0 0
$$449$$ 33.0000 1.55737 0.778683 0.627417i $$-0.215888\pi$$
0.778683 + 0.627417i $$0.215888\pi$$
$$450$$ 0 0
$$451$$ −13.5000 + 23.3827i −0.635690 + 1.10105i
$$452$$ 0 0
$$453$$ −1.00000 + 1.73205i −0.0469841 + 0.0813788i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −11.0000 −0.514558 −0.257279 0.966337i $$-0.582826\pi$$
−0.257279 + 0.966337i $$0.582826\pi$$
$$458$$ 0 0
$$459$$ 5.00000 8.66025i 0.233380 0.404226i
$$460$$ 0 0
$$461$$ −3.00000 + 5.19615i −0.139724 + 0.242009i −0.927392 0.374091i $$-0.877955\pi$$
0.787668 + 0.616100i $$0.211288\pi$$
$$462$$ 0 0
$$463$$ −34.0000 −1.58011 −0.790057 0.613033i $$-0.789949\pi$$
−0.790057 + 0.613033i $$0.789949\pi$$
$$464$$ 0 0
$$465$$ −20.0000 34.6410i −0.927478 1.60644i
$$466$$ 0 0
$$467$$ 5.00000 0.231372 0.115686 0.993286i $$-0.463093\pi$$
0.115686 + 0.993286i $$0.463093\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −4.00000 6.92820i −0.184310 0.319235i
$$472$$ 0 0
$$473$$ 6.00000 10.3923i 0.275880 0.477839i
$$474$$ 0 0
$$475$$ 38.5000 28.5788i 1.76650 1.31129i
$$476$$ 0 0
$$477$$ −2.00000 + 3.46410i −0.0915737 + 0.158610i
$$478$$ 0 0
$$479$$ −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i $$-0.317711\pi$$
−0.998796 + 0.0490589i $$0.984378\pi$$
$$480$$ 0 0
$$481$$ −2.00000 3.46410i −0.0911922 0.157949i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2.00000 + 3.46410i 0.0908153 + 0.157297i
$$486$$ 0 0
$$487$$ −26.0000 −1.17817 −0.589086 0.808070i $$-0.700512\pi$$
−0.589086 + 0.808070i $$0.700512\pi$$
$$488$$ 0 0
$$489$$ 5.50000 9.52628i 0.248719 0.430793i
$$490$$ 0 0
$$491$$ −8.00000 + 13.8564i −0.361035 + 0.625331i −0.988131 0.153611i $$-0.950910\pi$$
0.627096 + 0.778942i $$0.284243\pi$$
$$492$$ 0 0
$$493$$ −8.00000 −0.360302
$$494$$ 0 0
$$495$$ 24.0000 1.07872
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −3.50000 + 6.06218i −0.156682 + 0.271380i −0.933670 0.358134i $$-0.883413\pi$$
0.776989 + 0.629515i $$0.216746\pi$$
$$500$$ 0 0
$$501$$ 16.0000 0.714827
$$502$$ 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
$$505$$ −48.0000 −2.13597
$$506$$ 0 0
$$507$$ 4.50000 + 7.79423i 0.199852 + 0.346154i
$$508$$ 0 0
$$509$$ −8.00000 13.8564i −0.354594 0.614174i 0.632455 0.774597i $$-0.282047\pi$$
−0.987048 + 0.160423i $$0.948714\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −2.50000 21.6506i −0.110378 0.955899i
$$514$$ 0 0
$$515$$ −28.0000 + 48.4974i −1.23383 + 2.13705i
$$516$$ 0 0
$$517$$ 18.0000 + 31.1769i 0.791639 + 1.37116i
$$518$$ 0 0
$$519$$ 13.0000 + 22.5167i 0.570637 + 0.988372i
$$520$$ 0 0
$$521$$ 1.00000 0.0438108 0.0219054 0.999760i $$-0.493027\pi$$
0.0219054 + 0.999760i $$0.493027\pi$$
$$522$$ 0 0
$$523$$ −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i $$-0.310721\pi$$
−0.997478 + 0.0709788i $$0.977388\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 10.0000 17.3205i 0.435607 0.754493i
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ 2.00000 0.0867926
$$532$$ 0 0
$$533$$ 18.0000 0.779667
$$534$$ 0 0
$$535$$ 32.0000 55.4256i 1.38348 2.39626i
$$536$$ 0 0
$$537$$ −4.50000 + 7.79423i −0.194189 + 0.336346i
$$538$$ 0 0
$$539$$ −21.0000 −0.904534
$$540$$ 0 0
$$541$$ −2.00000 3.46410i −0.0859867 0.148933i 0.819825 0.572615i $$-0.194071\pi$$
−0.905811 + 0.423681i $$0.860738\pi$$
$$542$$ 0 0
$$543$$ 14.0000 0.600798
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −14.0000 24.2487i −0.598597 1.03680i −0.993028 0.117875i $$-0.962392\pi$$
0.394432 0.918925i $$-0.370941\pi$$
$$548$$ 0 0
$$549$$ −8.00000 + 13.8564i −0.341432 + 0.591377i
$$550$$ 0 0
$$551$$ −14.0000 + 10.3923i −0.596420 + 0.442727i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 4.00000 + 6.92820i 0.169791 + 0.294086i
$$556$$ 0 0
$$557$$ 20.0000 + 34.6410i 0.847427 + 1.46779i 0.883497 + 0.468438i $$0.155183\pi$$
−0.0360693 + 0.999349i $$0.511484\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ −3.00000 5.19615i −0.126660 0.219382i
$$562$$ 0 0
$$563$$ 11.0000 0.463595 0.231797 0.972764i $$-0.425539\pi$$
0.231797 + 0.972764i $$0.425539\pi$$
$$564$$ 0 0
$$565$$ −2.00000 + 3.46410i −0.0841406 + 0.145736i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −46.0000 −1.92842 −0.964210 0.265139i $$-0.914582\pi$$
−0.964210 + 0.265139i $$0.914582\pi$$
$$570$$ 0 0
$$571$$ 17.0000 0.711428 0.355714 0.934595i $$-0.384238\pi$$
0.355714 + 0.934595i $$0.384238\pi$$
$$572$$ 0 0
$$573$$ −6.00000 + 10.3923i −0.250654 + 0.434145i
$$574$$ 0 0
$$575$$ −33.0000 + 57.1577i −1.37620 + 2.38364i
$$576$$ 0 0
$$577$$ −37.0000 −1.54033 −0.770165 0.637845i $$-0.779826\pi$$
−0.770165 + 0.637845i $$0.779826\pi$$
$$578$$ 0 0
$$579$$ 3.00000 + 5.19615i 0.124676 + 0.215945i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 3.00000 + 5.19615i 0.124247 + 0.215203i
$$584$$ 0 0
$$585$$ −8.00000 13.8564i −0.330759 0.572892i
$$586$$ 0 0
$$587$$ −2.00000 + 3.46410i −0.0825488 + 0.142979i −0.904344 0.426804i $$-0.859639\pi$$
0.821795 + 0.569783i $$0.192973\pi$$
$$588$$ 0 0
$$589$$ −5.00000 43.3013i −0.206021 1.78420i
$$590$$ 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
$$597$$ −18.0000 −0.736691
$$598$$ 0 0
$$599$$ −19.0000 32.9090i −0.776319 1.34462i −0.934050 0.357142i $$-0.883751\pi$$
0.157731 0.987482i $$-0.449582\pi$$
$$600$$ 0 0
$$601$$ −13.0000 −0.530281 −0.265141 0.964210i $$-0.585418\pi$$
−0.265141 + 0.964210i $$0.585418\pi$$
$$602$$ 0 0
$$603$$ 9.00000 15.5885i 0.366508 0.634811i
$$604$$ 0 0
$$605$$ −4.00000 + 6.92820i −0.162623 + 0.281672i
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 12.0000 20.7846i 0.485468 0.840855i
$$612$$ 0 0
$$613$$ 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i $$-0.686791\pi$$
0.998002 + 0.0631797i $$0.0201241\pi$$
$$614$$ 0 0
$$615$$ −36.0000 −1.45166
$$616$$ 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
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ 15.0000 + 25.9808i 0.601929 + 1.04257i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −20.5000 + 35.5070i −0.820000 + 1.42028i
$$626$$ 0 0
$$627$$ −12.0000 5.19615i −0.479234 0.207514i
$$628$$ 0 0
$$629$$ −2.00000 + 3.46410i −0.0797452 + 0.138123i
$$630$$ 0 0
$$631$$ 4.00000 + 6.92820i 0.159237 + 0.275807i 0.934594 0.355716i $$-0.115763\pi$$
−0.775356 + 0.631524i $$0.782430\pi$$
$$632$$ 0 0
$$633$$ 6.00000 + 10.3923i 0.238479 + 0.413057i
$$634$$ 0 0
$$635$$ 24.0000 0.952411
$$636$$ 0 0
$$637$$ 7.00000 + 12.1244i 0.277350 + 0.480384i
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i $$0.392615\pi$$
−0.982708 + 0.185164i $$0.940718\pi$$
$$642$$ 0 0
$$643$$ −2.50000 + 4.33013i −0.0985904 + 0.170764i −0.911101 0.412182i $$-0.864767\pi$$
0.812511 + 0.582946i $$0.198100\pi$$
$$644$$ 0 0
$$645$$ 16.0000 0.629999
$$646$$ 0 0
$$647$$ −14.0000 −0.550397 −0.275198 0.961387i $$-0.588744\pi$$
−0.275198 + 0.961387i $$0.588744\pi$$
$$648$$ 0 0
$$649$$ 1.50000 2.59808i 0.0588802 0.101983i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 36.0000 1.40879 0.704394 0.709809i $$-0.251219\pi$$
0.704394 + 0.709809i $$0.251219\pi$$
$$654$$ 0 0
$$655$$ −30.0000 51.9615i −1.17220 2.03030i
$$656$$ 0 0
$$657$$ 18.0000 0.702247
$$658$$ 0 0
$$659$$ −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i $$-0.241759\pi$$
−0.958902 + 0.283738i $$0.908425\pi$$
$$660$$ 0 0
$$661$$ −10.0000 17.3205i −0.388955 0.673690i 0.603354 0.797473i $$-0.293830\pi$$
−0.992309 + 0.123784i $$0.960497\pi$$
$$662$$ 0 0
$$663$$ −2.00000 + 3.46410i −0.0776736 + 0.134535i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 12.0000 20.7846i 0.464642 0.804783i
$$668$$ 0 0
$$669$$ −5.00000 8.66025i −0.193311 0.334825i
$$670$$ 0 0
$$671$$ 12.0000 + 20.7846i 0.463255 + 0.802381i
$$672$$ 0 0
$$673$$ 30.0000 1.15642 0.578208 0.815890i $$-0.303752\pi$$
0.578208 + 0.815890i $$0.303752\pi$$
$$674$$ 0 0
$$675$$ 27.5000 + 47.6314i 1.05848 + 1.83333i
$$676$$ 0 0
$$677$$ −2.00000 −0.0768662 −0.0384331 0.999261i $$-0.512237\pi$$
−0.0384331 + 0.999261i $$0.512237\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −9.50000 + 16.4545i −0.364041 + 0.630537i
$$682$$ 0 0
$$683$$ −28.0000 −1.07139 −0.535695 0.844411i $$-0.679950\pi$$
−0.535695 + 0.844411i $$0.679950\pi$$
$$684$$ 0 0
$$685$$ −36.0000 −1.37549
$$686$$ 0 0
$$687$$ 4.00000 6.92820i 0.152610 0.264327i
$$688$$ 0 0
$$689$$ 2.00000 3.46410i 0.0761939 0.131972i
$$690$$ 0 0
$$691$$ 36.0000 1.36950 0.684752 0.728776i $$-0.259910\pi$$
0.684752 + 0.728776i $$0.259910\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 52.0000 1.97247
$$696$$ 0 0
$$697$$ −9.00000 15.5885i −0.340899 0.590455i
$$698$$ 0 0
$$699$$ −5.50000 9.52628i −0.208029 0.360317i
$$700$$ 0 0
$$701$$ 6.00000 10.3923i 0.226617 0.392512i −0.730186 0.683248i $$-0.760567\pi$$
0.956803 + 0.290736i $$0.0939001\pi$$
$$702$$ 0 0
$$703$$ 1.00000 + 8.66025i 0.0377157 + 0.326628i
$$704$$ 0 0
$$705$$ −24.0000 + 41.5692i −0.903892 + 1.56559i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −9.00000 15.5885i −0.338002 0.585437i 0.646055 0.763291i $$-0.276418\pi$$
−0.984057 + 0.177854i $$0.943084\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ 0 0
$$713$$ 30.0000 + 51.9615i 1.12351 + 1.94597i
$$714$$ 0 0
$$715$$ −24.0000 −0.897549
$$716$$ 0 0
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ 0 0
$$719$$ 17.0000 29.4449i 0.633993 1.09811i −0.352735 0.935723i $$-0.614748\pi$$
0.986728 0.162385i $$-0.0519185\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 21.0000 0.780998
$$724$$ 0 0
$$725$$ 22.0000 38.1051i 0.817059 1.41519i
$$726$$ 0 0
$$727$$ 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i $$-0.785937\pi$$
0.930618 + 0.365991i $$0.119270\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 4.00000 + 6.92820i 0.147945 + 0.256249i
$$732$$ 0 0
$$733$$ 22.0000 0.812589 0.406294 0.913742i $$-0.366821\pi$$
0.406294 + 0.913742i $$0.366821\pi$$
$$734$$ 0 0
$$735$$ −14.0000 24.2487i −0.516398 0.894427i
$$736$$ 0 0
$$737$$ −13.5000 23.3827i −0.497279 0.861312i
$$738$$ 0 0
$$739$$ 2.50000 4.33013i 0.0919640 0.159286i −0.816373 0.577524i $$-0.804019\pi$$
0.908337 + 0.418238i $$0.137352\pi$$
$$740$$ 0 0
$$741$$ 1.00000 + 8.66025i 0.0367359 + 0.318142i
$$742$$ 0 0
$$743$$ 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i $$-0.798229\pi$$
0.915794 + 0.401648i $$0.131563\pi$$
$$744$$ 0 0
$$745$$ −20.0000 34.6410i −0.732743 1.26915i
$$746$$ 0 0
$$747$$ −5.00000 8.66025i −0.182940 0.316862i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −19.0000 32.9090i −0.693320 1.20087i −0.970744 0.240118i $$-0.922814\pi$$
0.277424 0.960748i $$-0.410519\pi$$
$$752$$ 0 0
$$753$$ 5.00000 0.182210
$$754$$ 0 0
$$755$$ 4.00000 6.92820i 0.145575 0.252143i
$$756$$ 0 0
$$757$$ −7.00000 + 12.1244i −0.254419 + 0.440667i −0.964738 0.263213i $$-0.915218\pi$$
0.710318 + 0.703881i $$0.248551\pi$$
$$758$$ 0 0
$$759$$ 18.0000 0.653359
$$760$$ 0 0
$$761$$ 17.0000 0.616250 0.308125 0.951346i $$-0.400299\pi$$
0.308125 + 0.951346i $$0.400299\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −8.00000 + 13.8564i −0.289241 + 0.500979i
$$766$$ 0 0
$$767$$ −2.00000 −0.0722158
$$768$$ 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
$$773$$ −26.0000 45.0333i −0.935155 1.61974i −0.774357 0.632749i $$-0.781927\pi$$
−0.160798 0.986987i $$-0.551407\pi$$
$$774$$ 0 0
$$775$$ 55.0000 + 95.2628i 1.97566 + 3.42194i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 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
$$783$$ −10.0000 17.3205i −0.357371 0.618984i
$$784$$ 0 0
$$785$$ 16.0000 + 27.7128i 0.571064 + 0.989113i
$$786$$ 0 0
$$787$$ 41.0000 1.46149 0.730746 0.682649i $$-0.239172\pi$$
0.730746 + 0.682649i $$0.239172\pi$$
$$788$$ 0 0
$$789$$ −8.00000 13.8564i −0.284808 0.493301i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 8.00000 13.8564i 0.284088 0.492055i
$$794$$ 0 0
$$795$$ −4.00000 + 6.92820i −0.141865 + 0.245718i
$$796$$ 0 0
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0 0
$$799$$