# Properties

 Label 1344.2.bl.f.703.1 Level $1344$ Weight $2$ Character 1344.703 Analytic conductor $10.732$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1344.bl (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.7318940317$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 336) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 703.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1344.703 Dual form 1344.2.bl.f.1279.1

## $q$-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 $$\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$449$$ $$577$$ $$1093$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0 0
$$5$$ −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i $$-0.793258\pi$$
0.125567 + 0.992085i $$0.459925\pi$$
$$6$$ 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 0.256520 0.966539i $$-0.417424\pi$$
−0.708787 + 0.705422i $$0.750757\pi$$
$$12$$ 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 0.728219 0.685344i $$-0.240348\pi$$
−0.957635 + 0.287984i $$0.907015\pi$$
$$20$$ 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 $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ 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 $$0.140472\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 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 $$0.0850865\pi$$
−0.964486 + 0.264135i $$0.914913\pi$$
$$44$$ 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 $$0.378773\pi$$
−0.989828 + 0.142269i $$0.954560\pi$$
$$54$$ 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 $$0.365906\pi$$
−0.994769 + 0.102151i $$0.967427\pi$$
$$60$$ 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 0.999279 0.0379722i $$-0.0120898\pi$$
0.466755 + 0.884387i $$0.345423\pi$$
$$68$$ 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 $$-0.552648\pi$$
−0.164646 + 0.986353i $$0.552648\pi$$
$$84$$ 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 0.959221 0.282656i $$-0.0912155\pi$$
0.234823 + 0.972038i $$0.424549\pi$$
$$102$$ 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 0.102400 0.994743i $$-0.467348\pi$$
0.912673 + 0.408690i $$0.134014\pi$$
$$108$$ 0 0
$$109$$ −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i $$-0.894690\pi$$
0.754204 + 0.656640i $$0.228023\pi$$
$$110$$ 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 0.599699 0.800226i $$-0.295287\pi$$
−0.992865 + 0.119241i $$0.961954\pi$$
$$132$$ 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 $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 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 0.962348 0.271821i $$-0.0876260\pi$$
−0.716578 + 0.697507i $$0.754293\pi$$
$$150$$ 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 0.241086 0.970504i $$-0.422496\pi$$
−0.719938 + 0.694038i $$0.755830\pi$$
$$158$$ 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 0.0499796 0.998750i $$-0.484084\pi$$
0.889933 + 0.456091i $$0.150751\pi$$
$$164$$ 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 $$-0.972291\pi$$
−0.573400 0.819275i $$-0.694376\pi$$
$$180$$ 0 0
$$181$$ 10.3923i 0.772454i 0.922404 + 0.386227i $$0.126222\pi$$
−0.922404 + 0.386227i $$0.873778\pi$$
$$182$$ 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 $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 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 $$-0.923351\pi$$
0.971148 0.238479i $$-0.0766487\pi$$
$$212$$ 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 $$0.412109\pi$$
−0.969533 + 0.244962i $$0.921225\pi$$
$$228$$ 0 0
$$229$$ 3.00000 1.73205i 0.198246 0.114457i −0.397591 0.917563i $$-0.630154\pi$$
0.595837 + 0.803105i $$0.296820\pi$$
$$230$$ 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 $$-0.343028\pi$$
0.473396 + 0.880850i $$0.343028\pi$$
$$252$$ 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 0.851488 0.524375i $$-0.175701\pi$$
−0.0283781 + 0.999597i $$0.509034\pi$$
$$270$$ 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 $$-0.515196\pi$$
0.888899 0.458103i $$-0.151471\pi$$
$$278$$ 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 −0.995544 0.0942988i $$-0.969939\pi$$
0.579437 + 0.815017i $$0.303272\pi$$
$$284$$ 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 $$0.0485009\pi$$
−0.988414 + 0.151781i $$0.951499\pi$$
$$294$$ 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 $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 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 $$-0.965897\pi$$
0.404528 0.914526i $$-0.367436\pi$$
$$318$$ 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 −0.792117 0.610370i $$-0.791021\pi$$
0.132537 + 0.991178i $$0.457688\pi$$
$$332$$ 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 0.845301 0.534291i $$-0.179421\pi$$
−0.0400587 + 0.999197i $$0.512754\pi$$
$$348$$ 0 0
$$349$$ 6.92820i 0.370858i −0.982658 0.185429i $$-0.940632\pi$$
0.982658 0.185429i $$-0.0593675\pi$$
$$350$$ 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 0.890753 0.454488i $$-0.150178\pi$$
−0.838975 + 0.544170i $$0.816844\pi$$
$$374$$ 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 $$-0.786001\pi$$
0.782392 0.622786i $$-0.213999\pi$$
$$380$$ 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 −0.932002 0.362454i $$-0.881939\pi$$
0.779895 + 0.625910i $$0.215272\pi$$
$$390$$ 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 0.0250943 0.999685i $$-0.492011\pi$$
0.878300 + 0.478110i $$0.158678\pi$$
$$398$$ 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 $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 20.0000 0.974740 0.487370 0.873195i $$-0.337956\pi$$
0.487370 + 0.873195i $$0.337956\pi$$
$$422$$ 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 −0.728247 0.685315i $$-0.759665\pi$$
0.229377 + 0.973338i $$0.426331\pi$$
$$444$$ 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 $$-0.948419\pi$$
0.986899 0.161339i $$-0.0515813\pi$$
$$462$$ 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 0.970799 0.239892i $$-0.0771121\pi$$
−0.693153 + 0.720791i $$0.743779\pi$$
$$468$$ 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 $$-0.800605\pi$$
0.810132 0.586248i $$-0.199395\pi$$
$$492$$ 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 −0.565644 0.824650i $$-0.691372\pi$$
0.431346 + 0.902187i $$0.358039\pi$$
$$500$$ 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 −0.973700 0.227834i $$-0.926836\pi$$
−0.289540 + 0.957166i $$0.593502\pi$$
$$510$$ 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 $$-0.956961\pi$$
0.378695 0.925521i $$-0.376373\pi$$
$$524$$ 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 0.999520 0.0309841i $$-0.00986412\pi$$
−0.526593 + 0.850118i $$0.676531\pi$$
$$542$$ 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 $$-0.928686\pi$$
0.975008 0.222171i $$-0.0713145\pi$$
$$548$$ 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 $$0.360504\pi$$
−0.996359 + 0.0852559i $$0.972829\pi$$
$$558$$ 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 $$0.563827\pi$$
−0.749085 + 0.662474i $$0.769506\pi$$
$$564$$ 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 0.826877 0.562383i $$-0.190115\pi$$
−0.0736000 + 0.997288i $$0.523449\pi$$
$$572$$ 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 $$-0.261533\pi$$
0.681028 + 0.732257i $$0.261533\pi$$
$$588$$ 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 −0.903585 0.428409i $$-0.859074\pi$$
0.822806 + 0.568323i $$0.192408\pi$$
$$614$$ 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 $$0.356907\pi$$
−0.997259 + 0.0739910i $$0.976426\pi$$
$$620$$ 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 $$-0.602169\pi$$
−0.315489 + 0.948929i $$0.602169\pi$$
$$644$$ 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 $$-0.989498\pi$$
0.471160 0.882048i $$-0.343835\pi$$
$$654$$ 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 $$0.0648785\pi$$
−0.979300 + 0.202413i $$0.935122\pi$$
$$660$$ 0 0
$$661$$ −3.00000 1.73205i −0.116686 0.0673690i 0.440521 0.897742i $$-0.354794\pi$$
−0.557207 + 0.830373i $$0.688127\pi$$
$$662$$ 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 −0.902284 0.431143i $$-0.858110\pi$$
−0.0777610 + 0.996972i $$0.524777\pi$$
$$678$$ 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 0.864326 0.502931i $$-0.167745\pi$$
−0.00338791 + 0.999994i $$0.501078\pi$$
$$684$$ 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 0.577325 0.816514i $$-0.304097\pi$$
−0.995785 + 0.0917209i $$0.970763\pi$$
$$692$$ 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 $$-0.176715\pi$$
0.849813 + 0.527084i $$0.176715\pi$$
$$702$$ 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 0.756730 0.653727i $$-0.226796\pi$$
−0.944509 + 0.328484i $$0.893462\pi$$
$$710$$ 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 −0.324494 0.945888i $$-0.605194\pi$$
0.656916 + 0.753964i $$0.271861\pi$$
$$734$$ 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 0.325246 0.945629i $$-0.394553\pi$$
−0.656316 + 0.754486i $$0.727886\pi$$
$$740$$ 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 $$-0.476841\pi$$
0.0726912 + 0.997354i $$0.476841\pi$$
$$758$$ 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 −0.999999 0.00110111i $$-0.999650\pi$$
0.500953 + 0.865474i $$0.332983\pi$$
$$788$$ 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 $$0.0293351\pi$$
−0.995756 + 0.0920286i $$0.970665\pi$$