# Properties

 Label 672.2.q.h.289.1 Level $672$ Weight $2$ Character 672.289 Analytic conductor $5.366$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.36594701583$$ 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 289.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 672.289 Dual form 672.2.q.h.193.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{3} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{3} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(1.00000 + 1.73205i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(4.50000 - 7.79423i) q^{37} +(0.500000 + 0.866025i) q^{39} +2.00000 q^{41} +1.00000 q^{43} +(-4.00000 + 6.92820i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-3.00000 - 5.19615i) q^{53} -5.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(1.00000 - 1.73205i) q^{61} +(0.500000 - 2.59808i) q^{63} +(2.50000 + 4.33013i) q^{67} -6.00000 q^{69} +4.00000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-2.50000 + 4.33013i) q^{75} +(-4.00000 - 3.46410i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(-2.50000 + 0.866025i) q^{91} +(-1.50000 + 2.59808i) q^{93} +18.0000 q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} - 5 q^{7} - q^{9} + O(q^{10})$$ $$2 q + q^{3} - 5 q^{7} - q^{9} + 2 q^{11} + 2 q^{13} + 2 q^{17} - 5 q^{19} - 4 q^{21} - 6 q^{23} + 5 q^{25} - 2 q^{27} - 16 q^{29} + 3 q^{31} - 2 q^{33} + 9 q^{37} + q^{39} + 4 q^{41} + 2 q^{43} - 8 q^{47} + 11 q^{49} - 2 q^{51} - 6 q^{53} - 10 q^{57} - 6 q^{59} + 2 q^{61} + q^{63} + 5 q^{67} - 12 q^{69} + 8 q^{71} + 11 q^{73} - 5 q^{75} - 8 q^{77} + 5 q^{79} - q^{81} - 8 q^{87} - 12 q^{89} - 5 q^{91} - 3 q^{93} + 36 q^{97} - 4 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$421$$ $$449$$ $$577$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$4$$ 0 0
$$5$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i $$-0.0691756\pi$$
−0.674967 + 0.737848i $$0.735842\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ 0 0
$$19$$ −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i $$0.361097\pi$$
−0.996199 + 0.0871106i $$0.972237\pi$$
$$20$$ 0 0
$$21$$ −2.00000 1.73205i −0.436436 0.377964i
$$22$$ 0 0
$$23$$ −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i $$0.381789\pi$$
−0.988436 + 0.151642i $$0.951544\pi$$
$$24$$ 0 0
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 0 0
$$31$$ 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i $$-0.0798387\pi$$
−0.699301 + 0.714827i $$0.746505\pi$$
$$32$$ 0 0
$$33$$ −1.00000 + 1.73205i −0.174078 + 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 4.50000 7.79423i 0.739795 1.28136i −0.212792 0.977098i $$-0.568256\pi$$
0.952587 0.304266i $$-0.0984111\pi$$
$$38$$ 0 0
$$39$$ 0.500000 + 0.866025i 0.0800641 + 0.138675i
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 1.00000 0.152499 0.0762493 0.997089i $$-0.475706\pi$$
0.0762493 + 0.997089i $$0.475706\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i $$0.364968\pi$$
−0.995066 + 0.0992202i $$0.968365\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 0 0
$$51$$ −1.00000 + 1.73205i −0.140028 + 0.242536i
$$52$$ 0 0
$$53$$ −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i $$-0.301865\pi$$
−0.995117 + 0.0987002i $$0.968532\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −5.00000 −0.662266
$$58$$ 0 0
$$59$$ −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i $$-0.294388\pi$$
−0.992524 + 0.122047i $$0.961054\pi$$
$$60$$ 0 0
$$61$$ 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i $$-0.792466\pi$$
0.922916 + 0.385002i $$0.125799\pi$$
$$62$$ 0 0
$$63$$ 0.500000 2.59808i 0.0629941 0.327327i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i $$-0.0678686\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 4.00000 0.474713 0.237356 0.971423i $$-0.423719\pi$$
0.237356 + 0.971423i $$0.423719\pi$$
$$72$$ 0 0
$$73$$ 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i $$0.0559458\pi$$
−0.340868 + 0.940111i $$0.610721\pi$$
$$74$$ 0 0
$$75$$ −2.50000 + 4.33013i −0.288675 + 0.500000i
$$76$$ 0 0
$$77$$ −4.00000 3.46410i −0.455842 0.394771i
$$78$$ 0 0
$$79$$ 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i $$-0.742577\pi$$
0.971698 + 0.236225i $$0.0759104\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −4.00000 6.92820i −0.428845 0.742781i
$$88$$ 0 0
$$89$$ −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i $$0.386078\pi$$
−0.986303 + 0.164946i $$0.947255\pi$$
$$90$$ 0 0
$$91$$ −2.50000 + 0.866025i −0.262071 + 0.0907841i
$$92$$ 0 0
$$93$$ −1.50000 + 2.59808i −0.155543 + 0.269408i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 18.0000 1.82762 0.913812 0.406138i $$-0.133125\pi$$
0.913812 + 0.406138i $$0.133125\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i $$-0.0701767\pi$$
−0.677284 + 0.735721i $$0.736843\pi$$
$$102$$ 0 0
$$103$$ 5.50000 9.52628i 0.541931 0.938652i −0.456862 0.889538i $$-0.651027\pi$$
0.998793 0.0491146i $$-0.0156400\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i $$-0.497411\pi$$
0.861931 0.507026i $$-0.169255\pi$$
$$108$$ 0 0
$$109$$ 1.50000 + 2.59808i 0.143674 + 0.248851i 0.928877 0.370387i $$-0.120775\pi$$
−0.785203 + 0.619238i $$0.787442\pi$$
$$110$$ 0 0
$$111$$ 9.00000 0.854242
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −0.500000 + 0.866025i −0.0462250 + 0.0800641i
$$118$$ 0 0
$$119$$ −4.00000 3.46410i −0.366679 0.317554i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 1.00000 + 1.73205i 0.0901670 + 0.156174i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 9.00000 0.798621 0.399310 0.916816i $$-0.369250\pi$$
0.399310 + 0.916816i $$0.369250\pi$$
$$128$$ 0 0
$$129$$ 0.500000 + 0.866025i 0.0440225 + 0.0762493i
$$130$$ 0 0
$$131$$ 5.00000 8.66025i 0.436852 0.756650i −0.560593 0.828092i $$-0.689427\pi$$
0.997445 + 0.0714417i $$0.0227600\pi$$
$$132$$ 0 0
$$133$$ 2.50000 12.9904i 0.216777 1.12641i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i $$0.00465636\pi$$
−0.487278 + 0.873247i $$0.662010\pi$$
$$138$$ 0 0
$$139$$ −15.0000 −1.27228 −0.636142 0.771572i $$-0.719471\pi$$
−0.636142 + 0.771572i $$0.719471\pi$$
$$140$$ 0 0
$$141$$ −8.00000 −0.673722
$$142$$ 0 0
$$143$$ 1.00000 + 1.73205i 0.0836242 + 0.144841i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 6.50000 + 2.59808i 0.536111 + 0.214286i
$$148$$ 0 0
$$149$$ 10.0000 17.3205i 0.819232 1.41895i −0.0870170 0.996207i $$-0.527733\pi$$
0.906249 0.422744i $$-0.138933\pi$$
$$150$$ 0 0
$$151$$ −8.00000 13.8564i −0.651031 1.12762i −0.982873 0.184284i $$-0.941004\pi$$
0.331842 0.943335i $$-0.392330\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i $$0.174386\pi$$
0.0242497 + 0.999706i $$0.492280\pi$$
$$158$$ 0 0
$$159$$ 3.00000 5.19615i 0.237915 0.412082i
$$160$$ 0 0
$$161$$ 3.00000 15.5885i 0.236433 1.22854i
$$162$$ 0 0
$$163$$ 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i $$-0.546888\pi$$
0.930033 0.367477i $$-0.119778\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −2.50000 4.33013i −0.191180 0.331133i
$$172$$ 0 0
$$173$$ −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i $$0.406540\pi$$
−0.973670 + 0.227964i $$0.926793\pi$$
$$174$$ 0 0
$$175$$ −10.0000 8.66025i −0.755929 0.654654i
$$176$$ 0 0
$$177$$ 3.00000 5.19615i 0.225494 0.390567i
$$178$$ 0 0
$$179$$ −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i $$-0.214429\pi$$
−0.931038 + 0.364922i $$0.881096\pi$$
$$180$$ 0 0
$$181$$ 5.00000 0.371647 0.185824 0.982583i $$-0.440505\pi$$
0.185824 + 0.982583i $$0.440505\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −2.00000 + 3.46410i −0.146254 + 0.253320i
$$188$$ 0 0
$$189$$ 2.50000 0.866025i 0.181848 0.0629941i
$$190$$ 0 0
$$191$$ −10.0000 + 17.3205i −0.723575 + 1.25327i 0.235983 + 0.971757i $$0.424169\pi$$
−0.959558 + 0.281511i $$0.909164\pi$$
$$192$$ 0 0
$$193$$ −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i $$-0.247734\pi$$
−0.964059 + 0.265689i $$0.914400\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ 6.00000 + 10.3923i 0.425329 + 0.736691i 0.996451 0.0841740i $$-0.0268252\pi$$
−0.571122 + 0.820865i $$0.693492\pi$$
$$200$$ 0 0
$$201$$ −2.50000 + 4.33013i −0.176336 + 0.305424i
$$202$$ 0 0
$$203$$ 20.0000 6.92820i 1.40372 0.486265i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −3.00000 5.19615i −0.208514 0.361158i
$$208$$ 0 0
$$209$$ −10.0000 −0.691714
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ 2.00000 + 3.46410i 0.137038 + 0.237356i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −6.00000 5.19615i −0.407307 0.352738i
$$218$$ 0 0
$$219$$ −5.50000 + 9.52628i −0.371656 + 0.643726i
$$220$$ 0 0
$$221$$ 1.00000 + 1.73205i 0.0672673 + 0.116510i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ −5.00000 −0.333333
$$226$$ 0 0
$$227$$ −11.0000 19.0526i −0.730096 1.26456i −0.956842 0.290609i $$-0.906142\pi$$
0.226746 0.973954i $$-0.427191\pi$$
$$228$$ 0 0
$$229$$ −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i $$-0.843853\pi$$
0.849032 + 0.528341i $$0.177186\pi$$
$$230$$ 0 0
$$231$$ 1.00000 5.19615i 0.0657952 0.341882i
$$232$$ 0 0
$$233$$ −2.00000 + 3.46410i −0.131024 + 0.226941i −0.924072 0.382219i $$-0.875160\pi$$
0.793047 + 0.609160i $$0.208493\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 5.00000 0.324785
$$238$$ 0 0
$$239$$ −22.0000 −1.42306 −0.711531 0.702655i $$-0.751998\pi$$
−0.711531 + 0.702655i $$0.751998\pi$$
$$240$$ 0 0
$$241$$ −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i $$-0.271048\pi$$
−0.980917 + 0.194429i $$0.937715\pi$$
$$242$$ 0 0
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2.50000 + 4.33013i −0.159071 + 0.275519i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 16.0000 27.7128i 0.998053 1.72868i 0.445005 0.895528i $$-0.353202\pi$$
0.553047 0.833150i $$-0.313465\pi$$
$$258$$ 0 0
$$259$$ −4.50000 + 23.3827i −0.279616 + 1.45293i
$$260$$ 0 0
$$261$$ 4.00000 6.92820i 0.247594 0.428845i
$$262$$ 0 0
$$263$$ 4.00000 + 6.92820i 0.246651 + 0.427211i 0.962594 0.270947i $$-0.0873367\pi$$
−0.715944 + 0.698158i $$0.754003\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.0000 −0.734388
$$268$$ 0 0
$$269$$ 13.0000 + 22.5167i 0.792624 + 1.37287i 0.924337 + 0.381577i $$0.124619\pi$$
−0.131713 + 0.991288i $$0.542048\pi$$
$$270$$ 0 0
$$271$$ 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i $$-0.755208\pi$$
0.961563 + 0.274586i $$0.0885408\pi$$
$$272$$ 0 0
$$273$$ −2.00000 1.73205i −0.121046 0.104828i
$$274$$ 0 0
$$275$$ −5.00000 + 8.66025i −0.301511 + 0.522233i
$$276$$ 0 0
$$277$$ 5.50000 + 9.52628i 0.330463 + 0.572379i 0.982603 0.185720i $$-0.0594618\pi$$
−0.652140 + 0.758099i $$0.726128\pi$$
$$278$$ 0 0
$$279$$ −3.00000 −0.179605
$$280$$ 0 0
$$281$$ −14.0000 −0.835170 −0.417585 0.908638i $$-0.637123\pi$$
−0.417585 + 0.908638i $$0.637123\pi$$
$$282$$ 0 0
$$283$$ 15.5000 + 26.8468i 0.921379 + 1.59588i 0.797283 + 0.603606i $$0.206270\pi$$
0.124096 + 0.992270i $$0.460397\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −5.00000 + 1.73205i −0.295141 + 0.102240i
$$288$$ 0 0
$$289$$ 6.50000 11.2583i 0.382353 0.662255i
$$290$$ 0 0
$$291$$ 9.00000 + 15.5885i 0.527589 + 0.913812i
$$292$$ 0 0
$$293$$ 28.0000 1.63578 0.817889 0.575376i $$-0.195144\pi$$
0.817889 + 0.575376i $$0.195144\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −1.00000 1.73205i −0.0580259 0.100504i
$$298$$ 0 0
$$299$$ −3.00000 + 5.19615i −0.173494 + 0.300501i
$$300$$ 0 0
$$301$$ −2.50000 + 0.866025i −0.144098 + 0.0499169i
$$302$$ 0 0
$$303$$ −3.00000 + 5.19615i −0.172345 + 0.298511i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ 0 0
$$309$$ 11.0000 0.625768
$$310$$ 0 0
$$311$$ 5.00000 + 8.66025i 0.283524 + 0.491078i 0.972250 0.233944i $$-0.0751631\pi$$
−0.688726 + 0.725022i $$0.741830\pi$$
$$312$$ 0 0
$$313$$ −15.5000 + 26.8468i −0.876112 + 1.51747i −0.0205381 + 0.999789i $$0.506538\pi$$
−0.855574 + 0.517681i $$0.826795\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.00000 + 3.46410i −0.112331 + 0.194563i −0.916710 0.399554i $$-0.869165\pi$$
0.804379 + 0.594117i $$0.202498\pi$$
$$318$$ 0 0
$$319$$ −8.00000 13.8564i −0.447914 0.775810i
$$320$$ 0 0
$$321$$ 18.0000 1.00466
$$322$$ 0 0
$$323$$ −10.0000 −0.556415
$$324$$ 0 0
$$325$$ 2.50000 + 4.33013i 0.138675 + 0.240192i
$$326$$ 0 0
$$327$$ −1.50000 + 2.59808i −0.0829502 + 0.143674i
$$328$$ 0 0
$$329$$ 4.00000 20.7846i 0.220527 1.14589i
$$330$$ 0 0
$$331$$ 8.50000 14.7224i 0.467202 0.809218i −0.532096 0.846684i $$-0.678595\pi$$
0.999298 + 0.0374662i $$0.0119287\pi$$
$$332$$ 0 0
$$333$$ 4.50000 + 7.79423i 0.246598 + 0.427121i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −31.0000 −1.68868 −0.844339 0.535810i $$-0.820006\pi$$
−0.844339 + 0.535810i $$0.820006\pi$$
$$338$$ 0 0
$$339$$ −6.00000 10.3923i −0.325875 0.564433i
$$340$$ 0 0
$$341$$ −3.00000 + 5.19615i −0.162459 + 0.281387i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i $$-0.00616095\pi$$
−0.516667 + 0.856186i $$0.672828\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −0.0533761
$$352$$ 0 0
$$353$$ 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i $$0.0538590\pi$$
−0.347024 + 0.937856i $$0.612808\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 1.00000 5.19615i 0.0529256 0.275010i
$$358$$ 0 0
$$359$$ −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i $$0.486738\pi$$
−0.886100 + 0.463494i $$0.846596\pi$$
$$360$$ 0 0
$$361$$ −3.00000 5.19615i −0.157895 0.273482i
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 18.5000 + 32.0429i 0.965692 + 1.67263i 0.707744 + 0.706469i $$0.249713\pi$$
0.257948 + 0.966159i $$0.416954\pi$$
$$368$$ 0 0
$$369$$ −1.00000 + 1.73205i −0.0520579 + 0.0901670i
$$370$$ 0 0
$$371$$ 12.0000 + 10.3923i 0.623009 + 0.539542i
$$372$$ 0 0
$$373$$ 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i $$-0.825092\pi$$
0.878680 + 0.477412i $$0.158425\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −8.00000 −0.412021
$$378$$ 0 0
$$379$$ −25.0000 −1.28416 −0.642082 0.766636i $$-0.721929\pi$$
−0.642082 + 0.766636i $$0.721929\pi$$
$$380$$ 0 0
$$381$$ 4.50000 + 7.79423i 0.230542 + 0.399310i
$$382$$ 0 0
$$383$$ 1.00000 1.73205i 0.0510976 0.0885037i −0.839345 0.543599i $$-0.817061\pi$$
0.890443 + 0.455095i $$0.150395\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −0.500000 + 0.866025i −0.0254164 + 0.0440225i
$$388$$ 0 0
$$389$$ 4.00000 + 6.92820i 0.202808 + 0.351274i 0.949432 0.313972i $$-0.101660\pi$$
−0.746624 + 0.665246i $$0.768327\pi$$
$$390$$ 0 0
$$391$$ −12.0000 −0.606866
$$392$$ 0 0
$$393$$ 10.0000 0.504433
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i $$-0.956176\pi$$
0.614123 + 0.789210i $$0.289510\pi$$
$$398$$ 0 0
$$399$$ 12.5000 4.33013i 0.625783 0.216777i
$$400$$ 0 0
$$401$$ 11.0000 19.0526i 0.549314 0.951439i −0.449008 0.893528i $$-0.648223\pi$$
0.998322 0.0579116i $$-0.0184442\pi$$
$$402$$ 0 0
$$403$$ 1.50000 + 2.59808i 0.0747203 + 0.129419i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 18.0000 0.892227
$$408$$ 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
$$411$$ −6.00000 + 10.3923i −0.295958 + 0.512615i
$$412$$ 0 0
$$413$$ 12.0000 + 10.3923i 0.590481 + 0.511372i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −7.50000 12.9904i −0.367277 0.636142i
$$418$$ 0 0
$$419$$ −34.0000 −1.66101 −0.830504 0.557012i $$-0.811948\pi$$
−0.830504 + 0.557012i $$0.811948\pi$$
$$420$$ 0 0
$$421$$ −11.0000 −0.536107 −0.268054 0.963404i $$-0.586380\pi$$
−0.268054 + 0.963404i $$0.586380\pi$$
$$422$$ 0 0
$$423$$ −4.00000 6.92820i −0.194487 0.336861i
$$424$$ 0 0
$$425$$ −5.00000 + 8.66025i −0.242536 + 0.420084i
$$426$$ 0 0
$$427$$ −1.00000 + 5.19615i −0.0483934 + 0.251459i
$$428$$ 0 0
$$429$$ −1.00000 + 1.73205i −0.0482805 + 0.0836242i
$$430$$ 0 0
$$431$$ −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i $$-0.259993\pi$$
−0.973574 + 0.228373i $$0.926659\pi$$
$$432$$ 0 0
$$433$$ −25.0000 −1.20142 −0.600712 0.799466i $$-0.705116\pi$$
−0.600712 + 0.799466i $$0.705116\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −15.0000 25.9808i −0.717547 1.24283i
$$438$$ 0 0
$$439$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$440$$ 0 0
$$441$$ 1.00000 + 6.92820i 0.0476190 + 0.329914i
$$442$$ 0 0
$$443$$ 11.0000 19.0526i 0.522626 0.905214i −0.477028 0.878888i $$-0.658286\pi$$
0.999653 0.0263261i $$-0.00838082\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 20.0000 0.945968
$$448$$ 0 0
$$449$$ 24.0000 1.13263 0.566315 0.824189i $$-0.308369\pi$$
0.566315 + 0.824189i $$0.308369\pi$$
$$450$$ 0 0
$$451$$ 2.00000 + 3.46410i 0.0941763 + 0.163118i
$$452$$ 0 0
$$453$$ 8.00000 13.8564i 0.375873 0.651031i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i $$-0.840779\pi$$
0.854094 + 0.520119i $$0.174112\pi$$
$$458$$ 0 0
$$459$$ −1.00000 1.73205i −0.0466760 0.0808452i
$$460$$ 0 0
$$461$$ 12.0000 0.558896 0.279448 0.960161i $$-0.409849\pi$$
0.279448 + 0.960161i $$0.409849\pi$$
$$462$$ 0 0
$$463$$ 11.0000 0.511213 0.255607 0.966781i $$-0.417725\pi$$
0.255607 + 0.966781i $$0.417725\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i $$-0.986469\pi$$
0.536352 + 0.843995i $$0.319802\pi$$
$$468$$ 0 0
$$469$$ −10.0000 8.66025i −0.461757 0.399893i
$$470$$ 0 0
$$471$$ −11.0000 + 19.0526i −0.506853 + 0.877896i
$$472$$ 0 0
$$473$$ 1.00000 + 1.73205i 0.0459800 + 0.0796398i
$$474$$ 0 0
$$475$$ −25.0000 −1.14708
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i $$-0.210436\pi$$
−0.926388 + 0.376571i $$0.877103\pi$$
$$480$$ 0 0
$$481$$ 4.50000 7.79423i 0.205182 0.355386i
$$482$$ 0 0
$$483$$ 15.0000 5.19615i 0.682524 0.236433i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −3.50000 6.06218i −0.158600 0.274703i 0.775764 0.631023i $$-0.217365\pi$$
−0.934364 + 0.356320i $$0.884031\pi$$
$$488$$ 0 0
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ −8.00000 13.8564i −0.360302 0.624061i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −10.0000 + 3.46410i −0.448561 + 0.155386i
$$498$$ 0 0
$$499$$ 11.5000 19.9186i 0.514811 0.891678i −0.485042 0.874491i $$-0.661196\pi$$
0.999852 0.0171872i $$-0.00547113\pi$$
$$500$$ 0 0
$$501$$ 6.00000 + 10.3923i 0.268060 + 0.464294i
$$502$$ 0 0
$$503$$ 42.0000 1.87269 0.936344 0.351085i $$-0.114187\pi$$
0.936344 + 0.351085i $$0.114187\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −6.00000 10.3923i −0.266469 0.461538i
$$508$$ 0 0
$$509$$ 10.0000 17.3205i 0.443242 0.767718i −0.554686 0.832060i $$-0.687161\pi$$
0.997928 + 0.0643419i $$0.0204948\pi$$
$$510$$ 0 0
$$511$$ −22.0000 19.0526i −0.973223 0.842836i
$$512$$ 0 0
$$513$$ 2.50000 4.33013i 0.110378 0.191180i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −16.0000 −0.703679
$$518$$ 0 0
$$519$$ −18.0000 −0.790112
$$520$$ 0 0
$$521$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$522$$ 0 0
$$523$$ 6.50000 11.2583i 0.284225 0.492292i −0.688196 0.725525i $$-0.741597\pi$$
0.972421 + 0.233233i $$0.0749303\pi$$
$$524$$ 0 0
$$525$$ 2.50000 12.9904i 0.109109 0.566947i
$$526$$ 0 0
$$527$$ −3.00000 + 5.19615i −0.130682 + 0.226348i
$$528$$ 0 0
$$529$$ −6.50000 11.2583i −0.282609 0.489493i
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ 0 0
$$533$$ 2.00000 0.0866296
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 2.00000 3.46410i 0.0863064 0.149487i
$$538$$ 0 0
$$539$$ 13.0000 + 5.19615i 0.559950 + 0.223814i
$$540$$ 0 0
$$541$$ −12.5000 + 21.6506i −0.537417 + 0.930834i 0.461625 + 0.887075i $$0.347267\pi$$
−0.999042 + 0.0437584i $$0.986067\pi$$
$$542$$ 0 0
$$543$$ 2.50000 + 4.33013i 0.107285 + 0.185824i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 0 0
$$549$$ 1.00000 + 1.73205i 0.0426790 + 0.0739221i
$$550$$ 0 0
$$551$$ 20.0000 34.6410i 0.852029 1.47576i
$$552$$ 0 0
$$553$$ −2.50000 + 12.9904i −0.106311 + 0.552407i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −13.0000 22.5167i −0.550828 0.954062i −0.998215 0.0597213i $$-0.980979\pi$$
0.447387 0.894340i $$-0.352355\pi$$
$$558$$ 0 0
$$559$$ 1.00000 0.0422955
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 0 0
$$563$$ −10.0000 17.3205i −0.421450 0.729972i 0.574632 0.818412i $$-0.305145\pi$$
−0.996082 + 0.0884397i $$0.971812\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 2.00000 + 1.73205i 0.0839921 + 0.0727393i
$$568$$ 0 0
$$569$$ −13.0000 + 22.5167i −0.544988 + 0.943948i 0.453619 + 0.891196i $$0.350133\pi$$
−0.998608 + 0.0527519i $$0.983201\pi$$
$$570$$ 0 0
$$571$$ 3.50000 + 6.06218i 0.146470 + 0.253694i 0.929921 0.367760i $$-0.119875\pi$$
−0.783450 + 0.621455i $$0.786542\pi$$
$$572$$ 0 0
$$573$$ −20.0000 −0.835512
$$574$$ 0 0
$$575$$ −30.0000 −1.25109
$$576$$ 0 0
$$577$$ 8.50000 + 14.7224i 0.353860 + 0.612903i 0.986922 0.161198i $$-0.0515357\pi$$
−0.633062 + 0.774101i $$0.718202\pi$$
$$578$$ 0 0
$$579$$ 3.50000 6.06218i 0.145455 0.251936i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 6.00000 10.3923i 0.248495 0.430405i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 24.0000 0.990586 0.495293 0.868726i $$-0.335061\pi$$
0.495293 + 0.868726i $$0.335061\pi$$
$$588$$ 0 0
$$589$$ −15.0000 −0.618064
$$590$$ 0 0
$$591$$ −5.00000 8.66025i −0.205673 0.356235i
$$592$$ 0 0
$$593$$ −7.00000 + 12.1244i −0.287456 + 0.497888i −0.973202 0.229953i $$-0.926143\pi$$
0.685746 + 0.727841i $$0.259476\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −6.00000 + 10.3923i −0.245564 + 0.425329i
$$598$$ 0 0
$$599$$ −10.0000 17.3205i −0.408589 0.707697i 0.586143 0.810208i $$-0.300646\pi$$
−0.994732 + 0.102511i $$0.967312\pi$$
$$600$$ 0 0
$$601$$ 3.00000 0.122373 0.0611863 0.998126i $$-0.480512\pi$$
0.0611863 + 0.998126i $$0.480512\pi$$
$$602$$ 0 0
$$603$$ −5.00000 −0.203616
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 6.50000 11.2583i 0.263827 0.456962i −0.703429 0.710766i $$-0.748349\pi$$
0.967256 + 0.253804i $$0.0816819\pi$$
$$608$$ 0 0
$$609$$ 16.0000 + 13.8564i 0.648353 + 0.561490i
$$610$$ 0 0
$$611$$ −4.00000 + 6.92820i −0.161823 + 0.280285i
$$612$$ 0 0
$$613$$ −5.00000 8.66025i −0.201948 0.349784i 0.747208 0.664590i $$-0.231394\pi$$
−0.949156 + 0.314806i $$0.898061\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 34.0000 1.36879 0.684394 0.729112i $$-0.260067\pi$$
0.684394 + 0.729112i $$0.260067\pi$$
$$618$$ 0 0
$$619$$ 2.50000 + 4.33013i 0.100483 + 0.174042i 0.911884 0.410448i $$-0.134628\pi$$
−0.811400 + 0.584491i $$0.801294\pi$$
$$620$$ 0 0
$$621$$ 3.00000 5.19615i 0.120386 0.208514i
$$622$$ 0 0
$$623$$ 6.00000 31.1769i 0.240385 1.24908i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ 0 0
$$627$$ −5.00000 8.66025i −0.199681 0.345857i
$$628$$ 0 0
$$629$$ 18.0000 0.717707
$$630$$ 0 0
$$631$$ 44.0000 1.75161 0.875806 0.482663i $$-0.160330\pi$$
0.875806 + 0.482663i $$0.160330\pi$$
$$632$$ 0 0
$$633$$ 6.00000 + 10.3923i 0.238479 + 0.413057i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 5.50000 4.33013i 0.217918 0.171566i
$$638$$ 0 0
$$639$$ −2.00000 + 3.46410i −0.0791188 + 0.137038i
$$640$$ 0 0
$$641$$ 19.0000 + 32.9090i 0.750455 + 1.29983i 0.947602 + 0.319452i $$0.103499\pi$$
−0.197148 + 0.980374i $$0.563168\pi$$
$$642$$ 0 0
$$643$$ 13.0000 0.512670 0.256335 0.966588i $$-0.417485\pi$$
0.256335 + 0.966588i $$0.417485\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −21.0000 36.3731i −0.825595 1.42997i −0.901464 0.432855i $$-0.857506\pi$$
0.0758684 0.997118i $$-0.475827\pi$$
$$648$$ 0 0
$$649$$ 6.00000 10.3923i 0.235521 0.407934i
$$650$$ 0 0
$$651$$ 1.50000 7.79423i 0.0587896 0.305480i
$$652$$ 0 0
$$653$$ 19.0000 32.9090i 0.743527 1.28783i −0.207352 0.978266i $$-0.566485\pi$$
0.950880 0.309561i $$-0.100182\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −11.0000 −0.429151
$$658$$ 0 0
$$659$$ −6.00000 −0.233727 −0.116863 0.993148i $$-0.537284\pi$$
−0.116863 + 0.993148i $$0.537284\pi$$
$$660$$ 0 0
$$661$$ −7.50000 12.9904i −0.291716 0.505267i 0.682499 0.730886i $$-0.260893\pi$$
−0.974216 + 0.225619i $$0.927560\pi$$
$$662$$ 0 0
$$663$$ −1.00000 + 1.73205i −0.0388368 + 0.0672673i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 24.0000 41.5692i 0.929284 1.60957i
$$668$$ 0 0
$$669$$ 4.00000 + 6.92820i 0.154649 + 0.267860i
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ 35.0000 1.34915 0.674575 0.738206i $$-0.264327\pi$$
0.674575 + 0.738206i $$0.264327\pi$$
$$674$$ 0 0
$$675$$ −2.50000 4.33013i −0.0962250 0.166667i
$$676$$ 0 0
$$677$$ −18.0000 + 31.1769i −0.691796 + 1.19823i 0.279453 + 0.960159i $$0.409847\pi$$
−0.971249 + 0.238067i $$0.923486\pi$$
$$678$$ 0 0
$$679$$ −45.0000 + 15.5885i −1.72694 + 0.598230i
$$680$$ 0 0
$$681$$ 11.0000 19.0526i 0.421521 0.730096i
$$682$$ 0 0
$$683$$ 9.00000 + 15.5885i 0.344375 + 0.596476i 0.985240 0.171178i $$-0.0547574\pi$$
−0.640865 + 0.767654i $$0.721424\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −1.00000 −0.0381524
$$688$$ 0 0
$$689$$ −3.00000 5.19615i −0.114291 0.197958i
$$690$$ 0 0
$$691$$ 14.5000 25.1147i 0.551606 0.955410i −0.446553 0.894757i $$-0.647349\pi$$
0.998159 0.0606524i $$-0.0193181\pi$$
$$692$$ 0 0
$$693$$ 5.00000 1.73205i 0.189934 0.0657952i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 2.00000 + 3.46410i 0.0757554 + 0.131212i
$$698$$ 0 0
$$699$$ −4.00000 −0.151294
$$700$$ 0 0
$$701$$ −14.0000 −0.528773 −0.264386 0.964417i $$-0.585169\pi$$
−0.264386 + 0.964417i $$0.585169\pi$$
$$702$$ 0 0
$$703$$ 22.5000 + 38.9711i 0.848604 + 1.46982i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −12.0000 10.3923i −0.451306 0.390843i
$$708$$ 0 0
$$709$$ −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i $$-0.893462\pi$$
0.756730 + 0.653727i $$0.226796\pi$$
$$710$$ 0 0
$$711$$ 2.50000 + 4.33013i 0.0937573 + 0.162392i
$$712$$ 0 0
$$713$$ −18.0000 −0.674105
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −11.0000 19.0526i −0.410803 0.711531i
$$718$$ 0 0
$$719$$ −15.0000 + 25.9808i −0.559406 + 0.968919i 0.438141 + 0.898906i $$0.355637\pi$$
−0.997546 + 0.0700124i $$0.977696\pi$$
$$720$$ 0 0
$$721$$ −5.50000 + 28.5788i −0.204831 + 1.06433i
$$722$$ 0 0
$$723$$ 5.00000 8.66025i 0.185952 0.322078i
$$724$$ 0 0
$$725$$ −20.0000 34.6410i −0.742781 1.28654i
$$726$$ 0 0
$$727$$ −17.0000 −0.630495 −0.315248 0.949009i $$-0.602088\pi$$
−0.315248 + 0.949009i $$0.602088\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 1.00000 + 1.73205i 0.0369863 + 0.0640622i
$$732$$ 0 0
$$733$$ 19.5000 33.7750i 0.720249 1.24751i −0.240651 0.970612i $$-0.577361\pi$$
0.960900 0.276896i $$-0.0893058\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −5.00000 + 8.66025i −0.184177 + 0.319005i
$$738$$ 0 0
$$739$$ −16.5000 28.5788i −0.606962 1.05129i −0.991738 0.128279i $$-0.959055\pi$$
0.384776 0.923010i $$-0.374279\pi$$
$$740$$ 0 0
$$741$$ −5.00000 −0.183680
$$742$$ 0 0
$$743$$ 54.0000 1.98107 0.990534 0.137268i $$-0.0438322\pi$$
0.990534 + 0.137268i $$0.0438322\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −9.00000 + 46.7654i −0.328853 + 1.70877i
$$750$$ 0 0
$$751$$ 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i $$-0.641977\pi$$
0.996993 0.0774878i $$-0.0246899\pi$$
$$752$$ 0 0
$$753$$ 3.00000 + 5.19615i 0.109326 + 0.189358i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 0 0
$$759$$ −6.00000 10.3923i −0.217786 0.377217i
$$760$$ 0 0
$$761$$ 25.0000 43.3013i 0.906249 1.56967i 0.0870179 0.996207i $$-0.472266\pi$$
0.819231 0.573463i $$-0.194400\pi$$
$$762$$ 0 0
$$763$$ −6.00000 5.19615i −0.217215 0.188113i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −3.00000 5.19615i −0.108324 0.187622i
$$768$$ 0 0
$$769$$ 23.0000 0.829401 0.414701 0.909958i $$-0.363886\pi$$
0.414701 + 0.909958i $$0.363886\pi$$
$$770$$ 0 0
$$771$$ 32.0000 1.15245
$$772$$ 0 0
$$773$$ −21.0000 36.3731i −0.755318 1.30825i −0.945216 0.326445i $$-0.894149\pi$$
0.189899 0.981804i $$-0.439184\pi$$
$$774$$ 0 0
$$775$$ −7.50000 + 12.9904i −0.269408 + 0.466628i
$$776$$ 0 0
$$777$$ −22.5000 + 7.79423i −0.807183 + 0.279616i
$$778$$ 0 0
$$779$$ −5.00000 + 8.66025i −0.179144 + 0.310286i
$$780$$ 0 0
$$781$$ 4.00000 + 6.92820i 0.143131 + 0.247911i
$$782$$ 0 0
$$783$$ 8.00000 0.285897
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 4.00000 + 6.92820i 0.142585 + 0.246964i 0.928469 0.371409i $$-0.121125\pi$$
−0.785885 + 0.618373i $$0.787792\pi$$
$$788$$ 0 0
$$789$$ −4.00000 + 6.92820i −0.142404 + 0.246651i
$$790$$ 0 0
$$791$$ 30.0000 10.3923i 1.06668 0.369508i
$$792$$ 0 0
$$793$$ 1.00000 1.73205i 0.0355110 0.0615069i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6.00000 0.212531 0.106265 0.994338i $$-0.466111\pi$$
0.106265 + 0.994338i $$0.466111\pi$$
$$798$$ 0 0
$$799$$ −16.0000 −0.566039