# Properties

 Label 336.2.bl.c.31.1 Level $336$ Weight $2$ Character 336.31 Analytic conductor $2.683$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 336.bl (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.68297350792$$ 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: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 31.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 336.31 Dual form 336.2.bl.c.271.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 0.866025i) q^{11} +1.73205i q^{15} +(3.00000 + 1.73205i) q^{17} +(1.00000 + 1.73205i) q^{19} +(-2.50000 - 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{25} +1.00000 q^{27} +9.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-1.50000 + 0.866025i) q^{33} +(3.00000 + 3.46410i) q^{35} +(-5.00000 - 8.66025i) q^{37} +10.3923i q^{41} -3.46410i q^{43} +(-1.50000 - 0.866025i) q^{45} +(-6.00000 - 10.3923i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-3.00000 + 1.73205i) q^{51} +(4.50000 - 7.79423i) q^{53} +3.00000 q^{55} -2.00000 q^{57} +(4.50000 - 7.79423i) q^{59} +(2.00000 - 1.73205i) q^{63} +(-12.0000 - 6.92820i) q^{67} -13.8564i q^{71} +(-6.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 + 4.33013i) q^{77} +(4.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000 q^{83} +6.00000 q^{85} +(-4.50000 + 7.79423i) q^{87} +(-3.00000 + 1.73205i) q^{89} +(-2.50000 - 4.33013i) q^{93} +(3.00000 + 1.73205i) q^{95} +19.0526i q^{97} -1.73205i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} + 3q^{5} + q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{3} + 3q^{5} + q^{7} - q^{9} + 3q^{11} + 6q^{17} + 2q^{19} - 5q^{21} - 2q^{25} + 2q^{27} + 18q^{29} - 5q^{31} - 3q^{33} + 6q^{35} - 10q^{37} - 3q^{45} - 12q^{47} - 13q^{49} - 6q^{51} + 9q^{53} + 6q^{55} - 4q^{57} + 9q^{59} + 4q^{63} - 24q^{67} - 12q^{73} - 2q^{75} - 3q^{77} + 9q^{79} - q^{81} + 6q^{83} + 12q^{85} - 9q^{87} - 6q^{89} - 5q^{93} + 6q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$$.

 $$n$$ $$85$$ $$113$$ $$127$$ $$241$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$5$$ 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i $$-0.540075\pi$$
0.796387 + 0.604787i $$0.206742\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 1.50000 + 0.866025i 0.452267 + 0.261116i 0.708787 0.705422i $$-0.249243\pi$$
−0.256520 + 0.966539i $$0.582576\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 1.73205i 0.447214i
$$16$$ 0 0
$$17$$ 3.00000 + 1.73205i 0.727607 + 0.420084i 0.817546 0.575863i $$-0.195334\pi$$
−0.0899392 + 0.995947i $$0.528667\pi$$
$$18$$ 0 0
$$19$$ 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i $$-0.0929851\pi$$
−0.728219 + 0.685344i $$0.759652\pi$$
$$20$$ 0 0
$$21$$ −2.50000 0.866025i −0.545545 0.188982i
$$22$$ 0 0
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ −1.00000 + 1.73205i −0.200000 + 0.346410i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 9.00000 1.67126 0.835629 0.549294i $$-0.185103\pi$$
0.835629 + 0.549294i $$0.185103\pi$$
$$30$$ 0 0
$$31$$ −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i $$-0.981558\pi$$
0.549309 + 0.835619i $$0.314891\pi$$
$$32$$ 0 0
$$33$$ −1.50000 + 0.866025i −0.261116 + 0.150756i
$$34$$ 0 0
$$35$$ 3.00000 + 3.46410i 0.507093 + 0.585540i
$$36$$ 0 0
$$37$$ −5.00000 8.66025i −0.821995 1.42374i −0.904194 0.427121i $$-0.859528\pi$$
0.0821995 0.996616i $$-0.473806\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.3923i 1.62301i 0.584349 + 0.811503i $$0.301350\pi$$
−0.584349 + 0.811503i $$0.698650\pi$$
$$42$$ 0 0
$$43$$ 3.46410i 0.528271i −0.964486 0.264135i $$-0.914913\pi$$
0.964486 0.264135i $$-0.0850865\pi$$
$$44$$ 0 0
$$45$$ −1.50000 0.866025i −0.223607 0.129099i
$$46$$ 0 0
$$47$$ −6.00000 10.3923i −0.875190 1.51587i −0.856560 0.516047i $$-0.827403\pi$$
−0.0186297 0.999826i $$-0.505930\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ −3.00000 + 1.73205i −0.420084 + 0.242536i
$$52$$ 0 0
$$53$$ 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i $$-0.621227\pi$$
0.989828 0.142269i $$-0.0454398\pi$$
$$54$$ 0 0
$$55$$ 3.00000 0.404520
$$56$$ 0 0
$$57$$ −2.00000 −0.264906
$$58$$ 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
$$61$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$62$$ 0 0
$$63$$ 2.00000 1.73205i 0.251976 0.218218i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −12.0000 6.92820i −1.46603 0.846415i −0.466755 0.884387i $$-0.654577\pi$$
−0.999279 + 0.0379722i $$0.987910\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 13.8564i 1.64445i −0.569160 0.822226i $$-0.692732\pi$$
0.569160 0.822226i $$-0.307268\pi$$
$$72$$ 0 0
$$73$$ −6.00000 3.46410i −0.702247 0.405442i 0.105937 0.994373i $$-0.466216\pi$$
−0.808184 + 0.588930i $$0.799549\pi$$
$$74$$ 0 0
$$75$$ −1.00000 1.73205i −0.115470 0.200000i
$$76$$ 0 0
$$77$$ −1.50000 + 4.33013i −0.170941 + 0.493464i
$$78$$ 0 0
$$79$$ 4.50000 2.59808i 0.506290 0.292306i −0.225018 0.974355i $$-0.572244\pi$$
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
$$85$$ 6.00000 0.650791
$$86$$ 0 0
$$87$$ −4.50000 + 7.79423i −0.482451 + 0.835629i
$$88$$ 0 0
$$89$$ −3.00000 + 1.73205i −0.317999 + 0.183597i −0.650500 0.759506i $$-0.725441\pi$$
0.332501 + 0.943103i $$0.392107\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −2.50000 4.33013i −0.259238 0.449013i
$$94$$ 0 0
$$95$$ 3.00000 + 1.73205i 0.307794 + 0.177705i
$$96$$ 0 0
$$97$$ 19.0526i 1.93449i 0.253837 + 0.967247i $$0.418307\pi$$
−0.253837 + 0.967247i $$0.581693\pi$$
$$98$$ 0 0
$$99$$ 1.73205i 0.174078i
$$100$$ 0 0
$$101$$ −12.0000 6.92820i −1.19404 0.689382i −0.234823 0.972038i $$-0.575451\pi$$
−0.959221 + 0.282656i $$0.908784\pi$$
$$102$$ 0 0
$$103$$ 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i $$-0.103525\pi$$
−0.750510 + 0.660859i $$0.770192\pi$$
$$104$$ 0 0
$$105$$ −4.50000 + 0.866025i −0.439155 + 0.0845154i
$$106$$ 0 0
$$107$$ −10.5000 + 6.06218i −1.01507 + 0.586053i −0.912673 0.408690i $$-0.865986\pi$$
−0.102400 + 0.994743i $$0.532652\pi$$
$$108$$ 0 0
$$109$$ 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i $$-0.771977\pi$$
0.945769 + 0.324840i $$0.105310\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −3.00000 + 8.66025i −0.275010 + 0.793884i
$$120$$ 0 0
$$121$$ −4.00000 6.92820i −0.363636 0.629837i
$$122$$ 0 0
$$123$$ −9.00000 5.19615i −0.811503 0.468521i
$$124$$ 0 0
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 5.19615i 0.461084i −0.973062 0.230542i $$-0.925950\pi$$
0.973062 0.230542i $$-0.0740499\pi$$
$$128$$ 0 0
$$129$$ 3.00000 + 1.73205i 0.264135 + 0.152499i
$$130$$ 0 0
$$131$$ 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i $$-0.0380462\pi$$
−0.599699 + 0.800226i $$0.704713\pi$$
$$132$$ 0 0
$$133$$ −4.00000 + 3.46410i −0.346844 + 0.300376i
$$134$$ 0 0
$$135$$ 1.50000 0.866025i 0.129099 0.0745356i
$$136$$ 0 0
$$137$$ 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i $$-0.662010\pi$$
0.999893 0.0146279i $$-0.00465636\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 0 0
$$141$$ 12.0000 1.01058
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 13.5000 7.79423i 1.12111 0.647275i
$$146$$ 0 0
$$147$$ 1.00000 6.92820i 0.0824786 0.571429i
$$148$$ 0 0
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 0 0
$$151$$ 4.50000 + 2.59808i 0.366205 + 0.211428i 0.671799 0.740733i $$-0.265522\pi$$
−0.305594 + 0.952162i $$0.598855\pi$$
$$152$$ 0 0
$$153$$ 3.46410i 0.280056i
$$154$$ 0 0
$$155$$ 8.66025i 0.695608i
$$156$$ 0 0
$$157$$ 6.00000 + 3.46410i 0.478852 + 0.276465i 0.719938 0.694038i $$-0.244170\pi$$
−0.241086 + 0.970504i $$0.577504\pi$$
$$158$$ 0 0
$$159$$ 4.50000 + 7.79423i 0.356873 + 0.618123i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −12.0000 + 6.92820i −0.939913 + 0.542659i −0.889933 0.456091i $$-0.849249\pi$$
−0.0499796 + 0.998750i $$0.515916\pi$$
$$164$$ 0 0
$$165$$ −1.50000 + 2.59808i −0.116775 + 0.202260i
$$166$$ 0 0
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 1.00000 1.73205i 0.0764719 0.132453i
$$172$$ 0 0
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 0 0
$$175$$ −5.00000 1.73205i −0.377964 0.130931i
$$176$$ 0 0
$$177$$ 4.50000 + 7.79423i 0.338241 + 0.585850i
$$178$$ 0 0
$$179$$ 21.0000 + 12.1244i 1.56961 + 0.906217i 0.996213 + 0.0869415i $$0.0277093\pi$$
0.573400 + 0.819275i $$0.305624\pi$$
$$180$$ 0 0
$$181$$ 10.3923i 0.772454i −0.922404 0.386227i $$-0.873778\pi$$
0.922404 0.386227i $$-0.126222\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −15.0000 8.66025i −1.10282 0.636715i
$$186$$ 0 0
$$187$$ 3.00000 + 5.19615i 0.219382 + 0.379980i
$$188$$ 0 0
$$189$$ 0.500000 + 2.59808i 0.0363696 + 0.188982i
$$190$$ 0 0
$$191$$ −12.0000 + 6.92820i −0.868290 + 0.501307i −0.866779 0.498692i $$-0.833814\pi$$
−0.00151007 + 0.999999i $$0.500481\pi$$
$$192$$ 0 0
$$193$$ 2.50000 4.33013i 0.179954 0.311689i −0.761911 0.647682i $$-0.775738\pi$$
0.941865 + 0.335993i $$0.109072\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i $$0.358603\pi$$
−0.996850 + 0.0793045i $$0.974730\pi$$
$$200$$ 0 0
$$201$$ 12.0000 6.92820i 0.846415 0.488678i
$$202$$ 0 0
$$203$$ 4.50000 + 23.3827i 0.315838 + 1.64114i
$$204$$ 0 0
$$205$$ 9.00000 + 15.5885i 0.628587 + 1.08875i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 3.46410i 0.239617i
$$210$$ 0 0
$$211$$ 6.92820i 0.476957i 0.971148 + 0.238479i $$0.0766487\pi$$
−0.971148 + 0.238479i $$0.923351\pi$$
$$212$$ 0 0
$$213$$ 12.0000 + 6.92820i 0.822226 + 0.474713i
$$214$$ 0 0
$$215$$ −3.00000 5.19615i −0.204598 0.354375i
$$216$$ 0 0
$$217$$ −12.5000 4.33013i −0.848555 0.293948i
$$218$$ 0 0
$$219$$ 6.00000 3.46410i 0.405442 0.234082i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 19.0000 1.27233 0.636167 0.771551i $$-0.280519\pi$$
0.636167 + 0.771551i $$0.280519\pi$$
$$224$$ 0 0
$$225$$ 2.00000 0.133333
$$226$$ 0 0
$$227$$ 10.5000 18.1865i 0.696909 1.20708i −0.272623 0.962121i $$-0.587891\pi$$
0.969533 0.244962i $$-0.0787754\pi$$
$$228$$ 0 0
$$229$$ −3.00000 + 1.73205i −0.198246 + 0.114457i −0.595837 0.803105i $$-0.703180\pi$$
0.397591 + 0.917563i $$0.369846\pi$$
$$230$$ 0 0
$$231$$ −3.00000 3.46410i −0.197386 0.227921i
$$232$$ 0 0
$$233$$ −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i $$-0.965948\pi$$
0.404674 0.914461i $$-0.367385\pi$$
$$234$$ 0 0
$$235$$ −18.0000 10.3923i −1.17419 0.677919i
$$236$$ 0 0
$$237$$ 5.19615i 0.337526i
$$238$$ 0 0
$$239$$ 6.92820i 0.448148i −0.974572 0.224074i $$-0.928064\pi$$
0.974572 0.224074i $$-0.0719358\pi$$
$$240$$ 0 0
$$241$$ 19.5000 + 11.2583i 1.25611 + 0.725213i 0.972315 0.233674i $$-0.0750747\pi$$
0.283790 + 0.958886i $$0.408408\pi$$
$$242$$ 0 0
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ −7.50000 + 9.52628i −0.479157 + 0.608612i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.50000 + 2.59808i −0.0950586 + 0.164646i
$$250$$ 0 0
$$251$$ −15.0000 −0.946792 −0.473396 0.880850i $$-0.656972\pi$$
−0.473396 + 0.880850i $$0.656972\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ −3.00000 + 5.19615i −0.187867 + 0.325396i
$$256$$ 0 0
$$257$$ −9.00000 + 5.19615i −0.561405 + 0.324127i −0.753709 0.657208i $$-0.771737\pi$$
0.192304 + 0.981335i $$0.438404\pi$$
$$258$$ 0 0
$$259$$ 20.0000 17.3205i 1.24274 1.07624i
$$260$$ 0 0
$$261$$ −4.50000 7.79423i −0.278543 0.482451i
$$262$$ 0 0
$$263$$ 15.0000 + 8.66025i 0.924940 + 0.534014i 0.885208 0.465196i $$-0.154016\pi$$
0.0397320 + 0.999210i $$0.487350\pi$$
$$264$$ 0 0
$$265$$ 15.5885i 0.957591i
$$266$$ 0 0
$$267$$ 3.46410i 0.212000i
$$268$$ 0 0
$$269$$ −13.5000 7.79423i −0.823110 0.475223i 0.0283781 0.999597i $$-0.490966\pi$$
−0.851488 + 0.524375i $$0.824299\pi$$
$$270$$ 0 0
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −3.00000 + 1.73205i −0.180907 + 0.104447i
$$276$$ 0 0
$$277$$ −14.0000 + 24.2487i −0.841178 + 1.45696i 0.0477206 + 0.998861i $$0.484804\pi$$
−0.888899 + 0.458103i $$0.848529\pi$$
$$278$$ 0 0
$$279$$ 5.00000 0.299342
$$280$$ 0 0
$$281$$ −24.0000 −1.43172 −0.715860 0.698244i $$-0.753965\pi$$
−0.715860 + 0.698244i $$0.753965\pi$$
$$282$$ 0 0
$$283$$ 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i $$-0.696728\pi$$
0.995544 + 0.0942988i $$0.0300609\pi$$
$$284$$ 0 0
$$285$$ −3.00000 + 1.73205i −0.177705 + 0.102598i
$$286$$ 0 0
$$287$$ −27.0000 + 5.19615i −1.59376 + 0.306719i
$$288$$ 0 0
$$289$$ −2.50000 4.33013i −0.147059 0.254713i
$$290$$ 0 0
$$291$$ −16.5000 9.52628i −0.967247 0.558440i
$$292$$ 0 0
$$293$$ 5.19615i 0.303562i −0.988414 0.151781i $$-0.951499\pi$$
0.988414 0.151781i $$-0.0485009\pi$$
$$294$$ 0 0
$$295$$ 15.5885i 0.907595i
$$296$$ 0 0
$$297$$ 1.50000 + 0.866025i 0.0870388 + 0.0502519i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 9.00000 1.73205i 0.518751 0.0998337i
$$302$$ 0 0
$$303$$ 12.0000 6.92820i 0.689382 0.398015i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ −4.00000 −0.227552
$$310$$ 0 0
$$311$$ 9.00000 15.5885i 0.510343 0.883940i −0.489585 0.871956i $$-0.662852\pi$$
0.999928 0.0119847i $$-0.00381495\pi$$
$$312$$ 0 0
$$313$$ −4.50000 + 2.59808i −0.254355 + 0.146852i −0.621757 0.783210i $$-0.713581\pi$$
0.367402 + 0.930062i $$0.380247\pi$$
$$314$$ 0 0
$$315$$ 1.50000 4.33013i 0.0845154 0.243975i
$$316$$ 0 0
$$317$$ 10.5000 + 18.1865i 0.589739 + 1.02146i 0.994266 + 0.106932i $$0.0341026\pi$$
−0.404528 + 0.914526i $$0.632564\pi$$
$$318$$ 0 0
$$319$$ 13.5000 + 7.79423i 0.755855 + 0.436393i
$$320$$ 0 0
$$321$$ 12.1244i 0.676716i
$$322$$ 0 0
$$323$$ 6.92820i 0.385496i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 2.00000 + 3.46410i 0.110600 + 0.191565i
$$328$$ 0 0
$$329$$ 24.0000 20.7846i 1.32316 1.14589i
$$330$$ 0 0
$$331$$ 12.0000 6.92820i 0.659580 0.380808i −0.132537 0.991178i $$-0.542312\pi$$
0.792117 + 0.610370i $$0.208979\pi$$
$$332$$ 0 0
$$333$$ −5.00000 + 8.66025i −0.273998 + 0.474579i
$$334$$ 0 0
$$335$$ −24.0000 −1.31126
$$336$$ 0 0
$$337$$ −1.00000 −0.0544735 −0.0272367 0.999629i $$-0.508671\pi$$
−0.0272367 + 0.999629i $$0.508671\pi$$
$$338$$ 0 0
$$339$$ −3.00000 + 5.19615i −0.162938 + 0.282216i
$$340$$ 0 0
$$341$$ −7.50000 + 4.33013i −0.406148 + 0.234490i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −15.0000 8.66025i −0.805242 0.464907i 0.0400587 0.999197i $$-0.487246\pi$$
−0.845301 + 0.534291i $$0.820579\pi$$
$$348$$ 0 0
$$349$$ 6.92820i 0.370858i 0.982658 + 0.185429i $$0.0593675\pi$$
−0.982658 + 0.185429i $$0.940632\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 + 3.46410i 0.319348 + 0.184376i 0.651102 0.758990i $$-0.274307\pi$$
−0.331754 + 0.943366i $$0.607640\pi$$
$$354$$ 0 0
$$355$$ −12.0000 20.7846i −0.636894 1.10313i
$$356$$ 0 0
$$357$$ −6.00000 6.92820i −0.317554 0.366679i
$$358$$ 0 0
$$359$$ 24.0000 13.8564i 1.26667 0.731313i 0.292315 0.956322i $$-0.405574\pi$$
0.974357 + 0.225009i $$0.0722411\pi$$
$$360$$ 0 0
$$361$$ 7.50000 12.9904i 0.394737 0.683704i
$$362$$ 0 0
$$363$$ 8.00000 0.419891
$$364$$ 0 0
$$365$$ −12.0000 −0.628109
$$366$$ 0 0
$$367$$ −9.50000 + 16.4545i −0.495896 + 0.858917i −0.999989 0.00473247i $$-0.998494\pi$$
0.504093 + 0.863649i $$0.331827\pi$$
$$368$$ 0 0
$$369$$ 9.00000 5.19615i 0.468521 0.270501i
$$370$$ 0 0
$$371$$ 22.5000 + 7.79423i 1.16814 + 0.404656i
$$372$$ 0 0
$$373$$ −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i $$-0.183156\pi$$
−0.890753 + 0.454488i $$0.849822\pi$$
$$374$$ 0 0
$$375$$ −10.5000 6.06218i −0.542218 0.313050i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 24.2487i 1.24557i 0.782392 + 0.622786i $$0.213999\pi$$
−0.782392 + 0.622786i $$0.786001\pi$$
$$380$$ 0 0
$$381$$ 4.50000 + 2.59808i 0.230542 + 0.133103i
$$382$$ 0 0
$$383$$ −9.00000 15.5885i −0.459879 0.796533i 0.539076 0.842257i $$-0.318774\pi$$
−0.998954 + 0.0457244i $$0.985440\pi$$
$$384$$ 0 0
$$385$$ 1.50000 + 7.79423i 0.0764471 + 0.397231i
$$386$$ 0 0
$$387$$ −3.00000 + 1.73205i −0.152499 + 0.0880451i
$$388$$ 0 0
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −9.00000 −0.453990
$$394$$ 0 0
$$395$$ 4.50000 7.79423i 0.226420 0.392170i
$$396$$ 0 0
$$397$$ −18.0000 + 10.3923i −0.903394 + 0.521575i −0.878300 0.478110i $$-0.841322\pi$$
−0.0250943 + 0.999685i $$0.507989\pi$$
$$398$$ 0 0
$$399$$ −1.00000 5.19615i −0.0500626 0.260133i
$$400$$ 0 0
$$401$$ 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i $$-0.0698049\pi$$
−0.676425 + 0.736512i $$0.736472\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 1.73205i 0.0860663i
$$406$$ 0 0
$$407$$ 17.3205i 0.858546i
$$408$$ 0 0
$$409$$ −19.5000 11.2583i −0.964213 0.556689i −0.0667458 0.997770i $$-0.521262\pi$$
−0.897467 + 0.441081i $$0.854595\pi$$
$$410$$ 0 0
$$411$$ 6.00000 + 10.3923i 0.295958 + 0.512615i
$$412$$ 0 0
$$413$$ 22.5000 + 7.79423i 1.10715 + 0.383529i
$$414$$ 0 0
$$415$$ 4.50000 2.59808i 0.220896 0.127535i
$$416$$ 0 0
$$417$$ −7.00000 + 12.1244i −0.342791 + 0.593732i
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ 0 0
$$423$$ −6.00000 + 10.3923i −0.291730 + 0.505291i
$$424$$ 0 0
$$425$$ −6.00000 + 3.46410i −0.291043 + 0.168034i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 33.0000 + 19.0526i 1.58955 + 0.917729i 0.993380 + 0.114874i $$0.0366465\pi$$
0.596174 + 0.802855i $$0.296687\pi$$
$$432$$ 0 0
$$433$$ 34.6410i 1.66474i −0.554220 0.832370i $$-0.686983\pi$$
0.554220 0.832370i $$-0.313017\pi$$
$$434$$ 0 0
$$435$$ 15.5885i 0.747409i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 14.5000 + 25.1147i 0.692047 + 1.19866i 0.971166 + 0.238404i $$0.0766244\pi$$
−0.279119 + 0.960257i $$0.590042\pi$$
$$440$$ 0 0
$$441$$ 5.50000 + 4.33013i 0.261905 + 0.206197i
$$442$$ 0 0
$$443$$ 10.5000 6.06218i 0.498870 0.288023i −0.229377 0.973338i $$-0.573669\pi$$
0.728247 + 0.685315i $$0.240335\pi$$
$$444$$ 0 0
$$445$$ −3.00000 + 5.19615i −0.142214 + 0.246321i
$$446$$ 0 0
$$447$$ 6.00000 0.283790
$$448$$ 0 0
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 0 0
$$451$$ −9.00000 + 15.5885i −0.423793 + 0.734032i
$$452$$ 0 0
$$453$$ −4.50000 + 2.59808i −0.211428 + 0.122068i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 15.5000 + 26.8468i 0.725059 + 1.25584i 0.958950 + 0.283577i $$0.0915211\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 0 0
$$459$$ 3.00000 + 1.73205i 0.140028 + 0.0808452i
$$460$$ 0 0
$$461$$ 6.92820i 0.322679i 0.986899 + 0.161339i $$0.0515813\pi$$
−0.986899 + 0.161339i $$0.948419\pi$$
$$462$$ 0 0
$$463$$ 38.1051i 1.77090i 0.464739 + 0.885448i $$0.346148\pi$$
−0.464739 + 0.885448i $$0.653852\pi$$
$$464$$ 0 0
$$465$$ −7.50000 4.33013i −0.347804 0.200805i
$$466$$ 0 0
$$467$$ −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i $$-0.256221\pi$$
−0.970799 + 0.239892i $$0.922888\pi$$
$$468$$ 0 0
$$469$$ 12.0000 34.6410i 0.554109 1.59957i
$$470$$ 0 0
$$471$$ −6.00000 + 3.46410i −0.276465 + 0.159617i
$$472$$ 0 0
$$473$$ 3.00000 5.19615i 0.137940 0.238919i
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ −9.00000 −0.412082
$$478$$ 0 0
$$479$$ −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i $$-0.877103\pi$$
0.789314 + 0.613990i $$0.210436\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 16.5000 + 28.5788i 0.749226 + 1.29770i
$$486$$ 0 0
$$487$$ −7.50000 4.33013i −0.339857 0.196217i 0.320352 0.947299i $$-0.396199\pi$$
−0.660209 + 0.751082i $$0.729532\pi$$
$$488$$ 0 0
$$489$$ 13.8564i 0.626608i
$$490$$ 0 0
$$491$$ 25.9808i 1.17250i 0.810132 + 0.586248i $$0.199395\pi$$
−0.810132 + 0.586248i $$0.800605\pi$$
$$492$$ 0 0
$$493$$ 27.0000 + 15.5885i 1.21602 + 0.702069i
$$494$$ 0 0
$$495$$ −1.50000 2.59808i −0.0674200 0.116775i
$$496$$ 0 0
$$497$$ 36.0000 6.92820i 1.61482 0.310772i
$$498$$ 0 0
$$499$$ 3.00000 1.73205i 0.134298 0.0775372i −0.431346 0.902187i $$-0.641961\pi$$
0.565644 + 0.824650i $$0.308628\pi$$
$$500$$ 0 0
$$501$$ 6.00000 10.3923i 0.268060 0.464294i
$$502$$ 0 0
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 0 0
$$505$$ −24.0000 −1.06799
$$506$$ 0 0
$$507$$ −6.50000 + 11.2583i −0.288675 + 0.500000i
$$508$$ 0 0
$$509$$ 28.5000 16.4545i 1.26324 0.729332i 0.289540 0.957166i $$-0.406498\pi$$
0.973700 + 0.227834i $$0.0731643\pi$$
$$510$$ 0 0
$$511$$ 6.00000 17.3205i 0.265424 0.766214i
$$512$$ 0 0
$$513$$ 1.00000 + 1.73205i 0.0441511 + 0.0764719i
$$514$$ 0 0
$$515$$ 6.00000 + 3.46410i 0.264392 + 0.152647i
$$516$$ 0 0
$$517$$ 20.7846i 0.914106i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 33.0000 + 19.0526i 1.44576 + 0.834708i 0.998225 0.0595604i $$-0.0189699\pi$$
0.447532 + 0.894268i $$0.352303\pi$$
$$522$$ 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
$$525$$ 4.00000 3.46410i 0.174574 0.151186i
$$526$$ 0 0
$$527$$ −15.0000 + 8.66025i −0.653410 + 0.377247i
$$528$$ 0 0
$$529$$ −11.5000 + 19.9186i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ −9.00000 −0.390567
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −10.5000 + 18.1865i −0.453955 + 0.786272i
$$536$$ 0 0
$$537$$ −21.0000 + 12.1244i −0.906217 + 0.523205i
$$538$$ 0 0
$$539$$ −12.0000 1.73205i −0.516877 0.0746047i
$$540$$ 0 0
$$541$$ −11.0000 19.0526i −0.472927 0.819133i 0.526593 0.850118i $$-0.323469\pi$$
−0.999520 + 0.0309841i $$0.990136\pi$$
$$542$$ 0 0
$$543$$ 9.00000 + 5.19615i 0.386227 + 0.222988i
$$544$$ 0 0
$$545$$ 6.92820i 0.296772i
$$546$$ 0 0
$$547$$ 10.3923i 0.444343i 0.975008 + 0.222171i $$0.0713145\pi$$
−0.975008 + 0.222171i $$0.928686\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 9.00000 + 15.5885i 0.383413 + 0.664091i
$$552$$ 0 0
$$553$$ 9.00000 + 10.3923i 0.382719 + 0.441926i
$$554$$ 0 0
$$555$$ 15.0000 8.66025i 0.636715 0.367607i
$$556$$ 0 0
$$557$$ 13.5000 23.3827i 0.572013 0.990756i −0.424346 0.905500i $$-0.639496\pi$$
0.996359 0.0852559i $$-0.0271708\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −6.00000 −0.253320
$$562$$ 0 0
$$563$$ 22.5000 38.9711i 0.948262 1.64244i 0.199177 0.979963i $$-0.436173\pi$$
0.749085 0.662474i $$-0.230494\pi$$
$$564$$ 0 0
$$565$$ 9.00000 5.19615i 0.378633 0.218604i
$$566$$ 0 0
$$567$$ −2.50000 0.866025i −0.104990 0.0363696i
$$568$$ 0 0
$$569$$ 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 0 0
$$571$$ −18.0000 10.3923i −0.753277 0.434904i 0.0736000 0.997288i $$-0.476551\pi$$
−0.826877 + 0.562383i $$0.809885\pi$$
$$572$$ 0 0
$$573$$ 13.8564i 0.578860i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1.50000 0.866025i −0.0624458 0.0360531i 0.468452 0.883489i $$-0.344812\pi$$
−0.530898 + 0.847436i $$0.678145\pi$$
$$578$$ 0 0
$$579$$ 2.50000 + 4.33013i 0.103896 + 0.179954i
$$580$$ 0 0
$$581$$ 1.50000 + 7.79423i 0.0622305 + 0.323359i
$$582$$ 0 0
$$583$$ 13.5000 7.79423i 0.559113 0.322804i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −33.0000 −1.36206 −0.681028 0.732257i $$-0.738467\pi$$
−0.681028 + 0.732257i $$0.738467\pi$$
$$588$$ 0 0
$$589$$ −10.0000 −0.412043
$$590$$ 0 0
$$591$$ 3.00000 5.19615i 0.123404 0.213741i
$$592$$ 0 0
$$593$$ −24.0000 + 13.8564i −0.985562 + 0.569014i −0.903945 0.427649i $$-0.859342\pi$$
−0.0816172 + 0.996664i $$0.526008\pi$$
$$594$$ 0 0
$$595$$ 3.00000 + 15.5885i 0.122988 + 0.639064i
$$596$$ 0 0
$$597$$ −8.00000 13.8564i −0.327418 0.567105i
$$598$$ 0 0
$$599$$ 24.0000 + 13.8564i 0.980613 + 0.566157i 0.902455 0.430784i $$-0.141763\pi$$
0.0781581 + 0.996941i $$0.475096\pi$$
$$600$$ 0 0
$$601$$ 15.5885i 0.635866i 0.948113 + 0.317933i $$0.102989\pi$$
−0.948113 + 0.317933i $$0.897011\pi$$
$$602$$ 0 0
$$603$$ 13.8564i 0.564276i
$$604$$ 0 0
$$605$$ −12.0000 6.92820i −0.487869 0.281672i
$$606$$ 0 0
$$607$$ −9.50000 16.4545i −0.385593 0.667867i 0.606258 0.795268i $$-0.292670\pi$$
−0.991851 + 0.127401i $$0.959336\pi$$
$$608$$ 0 0
$$609$$ −22.5000 7.79423i −0.911746 0.315838i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 2.00000 3.46410i 0.0807792 0.139914i −0.822806 0.568323i $$-0.807592\pi$$
0.903585 + 0.428409i $$0.140926\pi$$
$$614$$ 0 0
$$615$$ −18.0000 −0.725830
$$616$$ 0 0
$$617$$ 12.0000 0.483102 0.241551 0.970388i $$-0.422344\pi$$
0.241551 + 0.970388i $$0.422344\pi$$
$$618$$ 0 0
$$619$$ 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i $$-0.643093\pi$$
0.997259 0.0739910i $$-0.0235736\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −6.00000 6.92820i −0.240385 0.277573i
$$624$$ 0 0
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ 0 0
$$627$$ −3.00000 1.73205i −0.119808 0.0691714i
$$628$$ 0 0
$$629$$ 34.6410i 1.38123i
$$630$$ 0 0
$$631$$ 32.9090i 1.31009i −0.755592 0.655043i $$-0.772651\pi$$
0.755592 0.655043i $$-0.227349\pi$$
$$632$$ 0 0
$$633$$ −6.00000 3.46410i −0.238479 0.137686i
$$634$$ 0 0
$$635$$ −4.50000 7.79423i −0.178577 0.309305i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −12.0000 + 6.92820i −0.474713 + 0.274075i
$$640$$ 0 0
$$641$$ −18.0000 + 31.1769i −0.710957 + 1.23141i 0.253541 + 0.967325i $$0.418405\pi$$
−0.964498 + 0.264089i $$0.914929\pi$$
$$642$$ 0 0
$$643$$ 16.0000 0.630978 0.315489 0.948929i $$-0.397831\pi$$
0.315489 + 0.948929i $$0.397831\pi$$
$$644$$ 0 0
$$645$$ 6.00000 0.236250
$$646$$ 0 0
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ 0 0
$$649$$ 13.5000 7.79423i 0.529921 0.305950i
$$650$$ 0 0
$$651$$ 10.0000 8.66025i 0.391931 0.339422i
$$652$$ 0 0
$$653$$ 13.5000 + 23.3827i 0.528296 + 0.915035i 0.999456 + 0.0329874i $$0.0105021\pi$$
−0.471160 + 0.882048i $$0.656165\pi$$
$$654$$ 0 0
$$655$$ 13.5000 + 7.79423i 0.527489 + 0.304546i
$$656$$ 0 0
$$657$$ 6.92820i 0.270295i
$$658$$ 0 0
$$659$$ 10.3923i 0.404827i −0.979300 0.202413i $$-0.935122\pi$$
0.979300 0.202413i $$-0.0648785\pi$$
$$660$$ 0 0
$$661$$ 3.00000 + 1.73205i 0.116686 + 0.0673690i 0.557207 0.830373i $$-0.311873\pi$$
−0.440521 + 0.897742i $$0.645206\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −3.00000 + 8.66025i −0.116335 + 0.335830i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −9.50000 + 16.4545i −0.367291 + 0.636167i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −35.0000 −1.34915 −0.674575 0.738206i $$-0.735673\pi$$
−0.674575 + 0.738206i $$0.735673\pi$$
$$674$$ 0 0
$$675$$ −1.00000 + 1.73205i −0.0384900 + 0.0666667i
$$676$$ 0 0
$$677$$ 25.5000 14.7224i 0.980045 0.565829i 0.0777610 0.996972i $$-0.475223\pi$$
0.902284 + 0.431143i $$0.141890\pi$$
$$678$$ 0 0
$$679$$ −49.5000 + 9.52628i −1.89964 + 0.365585i
$$680$$ 0 0
$$681$$ 10.5000 + 18.1865i 0.402361 + 0.696909i
$$682$$ 0 0
$$683$$ −22.5000 12.9904i −0.860939 0.497063i 0.00338791 0.999994i $$-0.498922\pi$$
−0.864326 + 0.502931i $$0.832255\pi$$
$$684$$ 0 0
$$685$$ 20.7846i 0.794139i
$$686$$ 0 0
$$687$$ 3.46410i 0.132164i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 11.0000 + 19.0526i 0.418460 + 0.724793i 0.995785 0.0917209i $$-0.0292368\pi$$
−0.577325 + 0.816514i $$0.695903\pi$$
$$692$$ 0 0
$$693$$ 4.50000 0.866025i 0.170941 0.0328976i
$$694$$ 0 0
$$695$$ 21.0000 12.1244i 0.796575 0.459903i
$$696$$ 0 0
$$697$$ −18.0000 + 31.1769i −0.681799 + 1.18091i
$$698$$ 0 0
$$699$$ 18.0000 0.680823
$$700$$ 0 0
$$701$$ −45.0000 −1.69963 −0.849813 0.527084i $$-0.823285\pi$$
−0.849813 + 0.527084i $$0.823285\pi$$
$$702$$ 0 0
$$703$$ 10.0000 17.3205i 0.377157 0.653255i
$$704$$ 0 0
$$705$$ 18.0000 10.3923i 0.677919 0.391397i
$$706$$ 0 0
$$707$$ 12.0000 34.6410i 0.451306 1.30281i
$$708$$ 0 0
$$709$$ 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i $$-0.106538\pi$$
−0.756730 + 0.653727i $$0.773204\pi$$
$$710$$ 0 0
$$711$$ −4.50000 2.59808i −0.168763 0.0974355i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 6.00000 + 3.46410i 0.224074 + 0.129369i
$$718$$ 0 0
$$719$$ −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i $$-0.275620\pi$$
−0.983608 + 0.180319i $$0.942287\pi$$
$$720$$ 0 0
$$721$$ −8.00000 + 6.92820i −0.297936 + 0.258020i
$$722$$ 0 0
$$723$$ −19.5000 + 11.2583i −0.725213 + 0.418702i
$$724$$ 0 0
$$725$$ −9.00000 + 15.5885i −0.334252 + 0.578941i
$$726$$ 0 0
$$727$$ −37.0000 −1.37225 −0.686127 0.727482i $$-0.740691\pi$$
−0.686127 + 0.727482i $$0.740691\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 6.00000 10.3923i 0.221918 0.384373i
$$732$$ 0 0
$$733$$ −9.00000 + 5.19615i −0.332423 + 0.191924i −0.656916 0.753964i $$-0.728139\pi$$
0.324494 + 0.945888i $$0.394806\pi$$
$$734$$ 0 0
$$735$$ −4.50000 11.2583i −0.165985 0.415270i
$$736$$ 0 0
$$737$$ −12.0000 20.7846i −0.442026 0.765611i
$$738$$ 0 0
$$739$$ 9.00000 + 5.19615i 0.331070 + 0.191144i 0.656316 0.754486i $$-0.272114\pi$$
−0.325246 + 0.945629i $$0.605447\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 13.8564i 0.508342i 0.967159 + 0.254171i $$0.0818026\pi$$
−0.967159 + 0.254171i $$0.918197\pi$$
$$744$$ 0 0
$$745$$ −9.00000 5.19615i −0.329734 0.190372i
$$746$$ 0 0
$$747$$ −1.50000 2.59808i −0.0548821 0.0950586i
$$748$$ 0 0
$$749$$ −21.0000 24.2487i −0.767323 0.886029i
$$750$$ 0 0
$$751$$ 4.50000 2.59808i 0.164207 0.0948051i −0.415644 0.909527i $$-0.636444\pi$$
0.579852 + 0.814722i $$0.303111\pi$$
$$752$$ 0 0
$$753$$ 7.50000 12.9904i 0.273315 0.473396i
$$754$$ 0 0
$$755$$ 9.00000 0.327544
$$756$$ 0 0
$$757$$ −4.00000 −0.145382 −0.0726912 0.997354i $$-0.523159\pi$$
−0.0726912 + 0.997354i $$0.523159\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −42.0000 + 24.2487i −1.52250 + 0.879015i −0.522852 + 0.852423i $$0.675132\pi$$
−0.999646 + 0.0265919i $$0.991535\pi$$
$$762$$ 0 0
$$763$$ 10.0000 + 3.46410i 0.362024 + 0.125409i
$$764$$ 0 0
$$765$$ −3.00000 5.19615i −0.108465 0.187867i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 19.0526i 0.687053i −0.939143 0.343526i $$-0.888379\pi$$
0.939143 0.343526i $$-0.111621\pi$$
$$770$$ 0 0
$$771$$ 10.3923i 0.374270i
$$772$$ 0 0
$$773$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$774$$ 0 0
$$775$$ −5.00000 8.66025i −0.179605 0.311086i
$$776$$ 0 0
$$777$$ 5.00000 + 25.9808i 0.179374 + 0.932055i
$$778$$ 0 0
$$779$$ −18.0000 + 10.3923i −0.644917 + 0.372343i
$$780$$ 0 0
$$781$$ 12.0000 20.7846i 0.429394 0.743732i
$$782$$ 0 0
$$783$$ 9.00000 0.321634
$$784$$ 0 0
$$785$$ 12.0000 0.428298
$$786$$ 0 0
$$787$$ 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i $$-0.667017\pi$$
0.999999 + 0.00110111i $$0.000350496\pi$$
$$788$$ 0 0
$$789$$ −15.0000 + 8.66025i −0.534014 + 0.308313i
$$790$$ 0 0
$$791$$ 3.00000 + 15.5885i 0.106668 + 0.554262i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 13.5000 + 7.79423i 0.478796 + 0.276433i
$$796$$ 0 0
$$797$$ 5.19615i 0.184057i −0.995756 0.0920286i $$-0.970665\pi$$
0.995756 0.0920286i $$-0.0293351\pi$$
$$798$$ 0