# Properties

 Label 588.2.i.b.361.1 Level $588$ Weight $2$ Character 588.361 Analytic conductor $4.695$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$588 = 2^{2} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 588.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.69520363885$$ 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 84) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 588.361 Dual form 588.2.i.b.373.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000 q^{13} +2.00000 q^{15} +(4.00000 - 6.92820i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +4.00000 q^{29} +(1.50000 - 2.59808i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(0.500000 + 0.866025i) q^{37} +(-1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +11.0000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{47} +(4.00000 + 6.92820i) q^{51} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +1.00000 q^{57} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-3.00000 - 5.19615i) q^{65} +(-6.50000 + 11.2583i) q^{67} +8.00000 q^{69} -10.0000 q^{71} +(-5.50000 + 9.52628i) q^{73} +(0.500000 + 0.866025i) q^{75} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000 q^{83} -16.0000 q^{85} +(-2.00000 + 3.46410i) q^{87} +(1.50000 + 2.59808i) q^{93} +(-1.00000 + 1.73205i) q^{95} -10.0000 q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} - 2q^{5} - q^{9} + O(q^{10})$$ $$2q - q^{3} - 2q^{5} - q^{9} - 2q^{11} + 6q^{13} + 4q^{15} + 8q^{17} - q^{19} - 8q^{23} + q^{25} + 2q^{27} + 8q^{29} + 3q^{31} - 2q^{33} + q^{37} - 3q^{39} - 12q^{41} + 22q^{43} - 2q^{45} + 6q^{47} + 8q^{51} + 12q^{53} + 8q^{55} + 2q^{57} + 4q^{59} - 6q^{61} - 6q^{65} - 13q^{67} + 16q^{69} - 20q^{71} - 11q^{73} + q^{75} + 3q^{79} - q^{81} - 4q^{83} - 32q^{85} - 4q^{87} + 3q^{93} - 2q^{95} - 20q^{97} + 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$295$$ $$493$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 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 $$-0.930824\pi$$
0.674967 + 0.737848i $$0.264158\pi$$
$$12$$ 0 0
$$13$$ 3.00000 0.832050 0.416025 0.909353i $$-0.363423\pi$$
0.416025 + 0.909353i $$0.363423\pi$$
$$14$$ 0 0
$$15$$ 2.00000 0.516398
$$16$$ 0 0
$$17$$ 4.00000 6.92820i 0.970143 1.68034i 0.275029 0.961436i $$-0.411312\pi$$
0.695113 0.718900i $$-0.255354\pi$$
$$18$$ 0 0
$$19$$ −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i $$-0.203260\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i $$-0.852679\pi$$
0.0607377 0.998154i $$-0.480655\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 1.50000 2.59808i 0.269408 0.466628i −0.699301 0.714827i $$-0.746505\pi$$
0.968709 + 0.248199i $$0.0798387\pi$$
$$32$$ 0 0
$$33$$ −1.00000 1.73205i −0.174078 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ −1.50000 + 2.59808i −0.240192 + 0.416025i
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 11.0000 1.67748 0.838742 0.544529i $$-0.183292\pi$$
0.838742 + 0.544529i $$0.183292\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 1.73205i −0.149071 + 0.258199i
$$46$$ 0 0
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 4.00000 + 6.92820i 0.560112 + 0.970143i
$$52$$ 0 0
$$53$$ 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i $$-0.524979\pi$$
0.902557 0.430570i $$-0.141688\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ 1.00000 0.132453
$$58$$ 0 0
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ 0 0
$$61$$ −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i $$-0.292159\pi$$
−0.991645 + 0.128994i $$0.958825\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −3.00000 5.19615i −0.372104 0.644503i
$$66$$ 0 0
$$67$$ −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i $$0.458725\pi$$
−0.923408 + 0.383819i $$0.874609\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i $$0.389279\pi$$
−0.984594 + 0.174855i $$0.944054\pi$$
$$74$$ 0 0
$$75$$ 0.500000 + 0.866025i 0.0577350 + 0.100000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.50000 + 2.59808i 0.168763 + 0.292306i 0.937985 0.346675i $$-0.112689\pi$$
−0.769222 + 0.638982i $$0.779356\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −2.00000 −0.219529 −0.109764 0.993958i $$-0.535010\pi$$
−0.109764 + 0.993958i $$0.535010\pi$$
$$84$$ 0 0
$$85$$ −16.0000 −1.73544
$$86$$ 0 0
$$87$$ −2.00000 + 3.46410i −0.214423 + 0.371391i
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 1.50000 + 2.59808i 0.155543 + 0.269408i
$$94$$ 0 0
$$95$$ −1.00000 + 1.73205i −0.102598 + 0.177705i
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i $$-0.667578\pi$$
0.999996 + 0.00286291i $$0.000911295\pi$$
$$102$$ 0 0
$$103$$ 5.50000 + 9.52628i 0.541931 + 0.938652i 0.998793 + 0.0491146i $$0.0156400\pi$$
−0.456862 + 0.889538i $$0.651027\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$108$$ 0 0
$$109$$ 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i $$-0.656723\pi$$
0.999512 0.0312328i $$-0.00994332\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ −8.00000 + 13.8564i −0.746004 + 1.29212i
$$116$$ 0 0
$$117$$ −1.50000 2.59808i −0.138675 0.240192i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 0 0
$$123$$ 3.00000 5.19615i 0.270501 0.468521i
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 3.00000 0.266207 0.133103 0.991102i $$-0.457506\pi$$
0.133103 + 0.991102i $$0.457506\pi$$
$$128$$ 0 0
$$129$$ −5.50000 + 9.52628i −0.484248 + 0.838742i
$$130$$ 0 0
$$131$$ −1.00000 1.73205i −0.0873704 0.151330i 0.819028 0.573753i $$-0.194513\pi$$
−0.906399 + 0.422423i $$0.861180\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −1.00000 1.73205i −0.0860663 0.149071i
$$136$$ 0 0
$$137$$ −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i $$-0.887992\pi$$
0.767853 + 0.640626i $$0.221325\pi$$
$$138$$ 0 0
$$139$$ 5.00000 0.424094 0.212047 0.977259i $$-0.431987\pi$$
0.212047 + 0.977259i $$0.431987\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ −3.00000 + 5.19615i −0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ −4.00000 6.92820i −0.332182 0.575356i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i $$-0.00310113\pi$$
−0.508413 + 0.861113i $$0.669768\pi$$
$$150$$ 0 0
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 0 0
$$153$$ −8.00000 −0.646762
$$154$$ 0 0
$$155$$ −6.00000 −0.481932
$$156$$ 0 0
$$157$$ 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i $$-0.807902\pi$$
0.903167 + 0.429289i $$0.141236\pi$$
$$158$$ 0 0
$$159$$ 6.00000 + 10.3923i 0.475831 + 0.824163i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ 0 0
$$165$$ −2.00000 + 3.46410i −0.155700 + 0.269680i
$$166$$ 0 0
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ −0.500000 + 0.866025i −0.0382360 + 0.0662266i
$$172$$ 0 0
$$173$$ 8.00000 + 13.8564i 0.608229 + 1.05348i 0.991532 + 0.129861i $$0.0414530\pi$$
−0.383304 + 0.923622i $$0.625214\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 2.00000 + 3.46410i 0.150329 + 0.260378i
$$178$$ 0 0
$$179$$ −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i $$-0.905320\pi$$
0.731858 + 0.681457i $$0.238654\pi$$
$$180$$ 0 0
$$181$$ 15.0000 1.11494 0.557471 0.830197i $$-0.311772\pi$$
0.557471 + 0.830197i $$0.311772\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 0 0
$$185$$ 1.00000 1.73205i 0.0735215 0.127343i
$$186$$ 0 0
$$187$$ 8.00000 + 13.8564i 0.585018 + 1.01328i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i $$-0.236317\pi$$
−0.953912 + 0.300088i $$0.902984\pi$$
$$192$$ 0 0
$$193$$ −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i $$-0.962900\pi$$
0.597317 + 0.802005i $$0.296234\pi$$
$$194$$ 0 0
$$195$$ 6.00000 0.429669
$$196$$ 0 0
$$197$$ 8.00000 0.569976 0.284988 0.958531i $$-0.408010\pi$$
0.284988 + 0.958531i $$0.408010\pi$$
$$198$$ 0 0
$$199$$ 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i $$-0.741820\pi$$
0.972257 + 0.233915i $$0.0751537\pi$$
$$200$$ 0 0
$$201$$ −6.50000 11.2583i −0.458475 0.794101i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 6.00000 + 10.3923i 0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ −4.00000 + 6.92820i −0.278019 + 0.481543i
$$208$$ 0 0
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 5.00000 8.66025i 0.342594 0.593391i
$$214$$ 0 0
$$215$$ −11.0000 19.0526i −0.750194 1.29937i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −5.50000 9.52628i −0.371656 0.643726i
$$220$$ 0 0
$$221$$ 12.0000 20.7846i 0.807207 1.39812i
$$222$$ 0 0
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i $$0.370447\pi$$
−0.993210 + 0.116331i $$0.962887\pi$$
$$228$$ 0 0
$$229$$ 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i $$-0.156147\pi$$
−0.849032 + 0.528341i $$0.822814\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i $$-0.318310\pi$$
−0.998886 + 0.0471787i $$0.984977\pi$$
$$234$$ 0 0
$$235$$ 6.00000 10.3923i 0.391397 0.677919i
$$236$$ 0 0
$$237$$ −3.00000 −0.194871
$$238$$ 0 0
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ 7.00000 12.1244i 0.450910 0.780998i −0.547533 0.836784i $$-0.684433\pi$$
0.998443 + 0.0557856i $$0.0177663\pi$$
$$242$$ 0 0
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.50000 2.59808i −0.0954427 0.165312i
$$248$$ 0 0
$$249$$ 1.00000 1.73205i 0.0633724 0.109764i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 16.0000 1.00591
$$254$$ 0 0
$$255$$ 8.00000 13.8564i 0.500979 0.867722i
$$256$$ 0 0
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −2.00000 3.46410i −0.123797 0.214423i
$$262$$ 0 0
$$263$$ −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i $$-0.953967\pi$$
0.619586 + 0.784929i $$0.287301\pi$$
$$264$$ 0 0
$$265$$ −24.0000 −1.47431
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.00000 + 1.73205i −0.0609711 + 0.105605i −0.894900 0.446267i $$-0.852753\pi$$
0.833929 + 0.551872i $$0.186086\pi$$
$$270$$ 0 0
$$271$$ −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i $$-0.906676\pi$$
0.228380 0.973572i $$-0.426657\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.00000 + 1.73205i 0.0603023 + 0.104447i
$$276$$ 0 0
$$277$$ −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i $$0.337286\pi$$
−0.999923 + 0.0124177i $$0.996047\pi$$
$$278$$ 0 0
$$279$$ −3.00000 −0.179605
$$280$$ 0 0
$$281$$ 20.0000 1.19310 0.596550 0.802576i $$-0.296538\pi$$
0.596550 + 0.802576i $$0.296538\pi$$
$$282$$ 0 0
$$283$$ 9.50000 16.4545i 0.564716 0.978117i −0.432360 0.901701i $$-0.642319\pi$$
0.997076 0.0764162i $$-0.0243478\pi$$
$$284$$ 0 0
$$285$$ −1.00000 1.73205i −0.0592349 0.102598i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −23.5000 40.7032i −1.38235 2.39431i
$$290$$ 0 0
$$291$$ 5.00000 8.66025i 0.293105 0.507673i
$$292$$ 0 0
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 0 0
$$297$$ −1.00000 + 1.73205i −0.0580259 + 0.100504i
$$298$$ 0 0
$$299$$ −12.0000 20.7846i −0.693978 1.20201i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 5.00000 + 8.66025i 0.287242 + 0.497519i
$$304$$ 0 0
$$305$$ −6.00000 + 10.3923i −0.343559 + 0.595062i
$$306$$ 0 0
$$307$$ 23.0000 1.31268 0.656340 0.754466i $$-0.272104\pi$$
0.656340 + 0.754466i $$0.272104\pi$$
$$308$$ 0 0
$$309$$ −11.0000 −0.625768
$$310$$ 0 0
$$311$$ −1.00000 + 1.73205i −0.0567048 + 0.0982156i −0.892984 0.450088i $$-0.851393\pi$$
0.836280 + 0.548303i $$0.184726\pi$$
$$312$$ 0 0
$$313$$ −8.50000 14.7224i −0.480448 0.832161i 0.519300 0.854592i $$-0.326193\pi$$
−0.999748 + 0.0224310i $$0.992859\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i $$0.0687530\pi$$
−0.302777 + 0.953062i $$0.597914\pi$$
$$318$$ 0 0
$$319$$ −4.00000 + 6.92820i −0.223957 + 0.387905i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.00000 −0.445132
$$324$$ 0 0
$$325$$ 1.50000 2.59808i 0.0832050 0.144115i
$$326$$ 0 0
$$327$$ 5.50000 + 9.52628i 0.304151 + 0.526804i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −8.50000 14.7224i −0.467202 0.809218i 0.532096 0.846684i $$-0.321405\pi$$
−0.999298 + 0.0374662i $$0.988071\pi$$
$$332$$ 0 0
$$333$$ 0.500000 0.866025i 0.0273998 0.0474579i
$$334$$ 0 0
$$335$$ 26.0000 1.42053
$$336$$ 0 0
$$337$$ 21.0000 1.14394 0.571971 0.820274i $$-0.306179\pi$$
0.571971 + 0.820274i $$0.306179\pi$$
$$338$$ 0 0
$$339$$ 7.00000 12.1244i 0.380188 0.658505i
$$340$$ 0 0
$$341$$ 3.00000 + 5.19615i 0.162459 + 0.281387i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −8.00000 13.8564i −0.430706 0.746004i
$$346$$ 0 0
$$347$$ −12.0000 + 20.7846i −0.644194 + 1.11578i 0.340293 + 0.940319i $$0.389474\pi$$
−0.984487 + 0.175457i $$0.943860\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 3.00000 0.160128
$$352$$ 0 0
$$353$$ −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i $$-0.884378\pi$$
0.775077 + 0.631867i $$0.217711\pi$$
$$354$$ 0 0
$$355$$ 10.0000 + 17.3205i 0.530745 + 0.919277i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i $$0.0103087\pi$$
−0.471696 + 0.881761i $$0.656358\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ 0 0
$$363$$ −7.00000 −0.367405
$$364$$ 0 0
$$365$$ 22.0000 1.15153
$$366$$ 0 0
$$367$$ 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i $$-0.791675\pi$$
0.923869 + 0.382709i $$0.125009\pi$$
$$368$$ 0 0
$$369$$ 3.00000 + 5.19615i 0.156174 + 0.270501i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2.50000 + 4.33013i 0.129445 + 0.224205i 0.923462 0.383691i $$-0.125347\pi$$
−0.794017 + 0.607896i $$0.792014\pi$$
$$374$$ 0 0
$$375$$ 6.00000 10.3923i 0.309839 0.536656i
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ 13.0000 0.667765 0.333883 0.942615i $$-0.391641\pi$$
0.333883 + 0.942615i $$0.391641\pi$$
$$380$$ 0 0
$$381$$ −1.50000 + 2.59808i −0.0768473 + 0.133103i
$$382$$ 0 0
$$383$$ −14.0000 24.2487i −0.715367 1.23905i −0.962818 0.270151i $$-0.912926\pi$$
0.247451 0.968900i $$-0.420407\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −5.50000 9.52628i −0.279581 0.484248i
$$388$$ 0 0
$$389$$ −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i $$-0.914918\pi$$
0.710980 + 0.703213i $$0.248252\pi$$
$$390$$ 0 0
$$391$$ −64.0000 −3.23662
$$392$$ 0 0
$$393$$ 2.00000 0.100887
$$394$$ 0 0
$$395$$ 3.00000 5.19615i 0.150946 0.261447i
$$396$$ 0 0
$$397$$ 1.50000 + 2.59808i 0.0752828 + 0.130394i 0.901209 0.433384i $$-0.142681\pi$$
−0.825926 + 0.563778i $$0.809347\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 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
$$403$$ 4.50000 7.79423i 0.224161 0.388258i
$$404$$ 0 0
$$405$$ 2.00000 0.0993808
$$406$$ 0 0
$$407$$ −2.00000 −0.0991363
$$408$$ 0 0
$$409$$ −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i $$-0.988987\pi$$
0.529657 + 0.848212i $$0.322321\pi$$
$$410$$ 0 0
$$411$$ −2.00000 3.46410i −0.0986527 0.170872i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 2.00000 + 3.46410i 0.0981761 + 0.170046i
$$416$$ 0 0
$$417$$ −2.50000 + 4.33013i −0.122426 + 0.212047i
$$418$$ 0 0
$$419$$ −18.0000 −0.879358 −0.439679 0.898155i $$-0.644908\pi$$
−0.439679 + 0.898155i $$0.644908\pi$$
$$420$$ 0 0
$$421$$ −27.0000 −1.31590 −0.657950 0.753062i $$-0.728576\pi$$
−0.657950 + 0.753062i $$0.728576\pi$$
$$422$$ 0 0
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ 0 0
$$425$$ −4.00000 6.92820i −0.194029 0.336067i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −3.00000 5.19615i −0.144841 0.250873i
$$430$$ 0 0
$$431$$ 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i $$-0.576315\pi$$
0.959985 0.280052i $$-0.0903517\pi$$
$$432$$ 0 0
$$433$$ 25.0000 1.20142 0.600712 0.799466i $$-0.294884\pi$$
0.600712 + 0.799466i $$0.294884\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 0 0
$$437$$ −4.00000 + 6.92820i −0.191346 + 0.331421i
$$438$$ 0 0
$$439$$ 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i $$0.0274485\pi$$
−0.423556 + 0.905870i $$0.639218\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i $$-0.136374\pi$$
−0.814595 + 0.580030i $$0.803041\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ 6.00000 10.3923i 0.282529 0.489355i
$$452$$ 0 0
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −6.50000 11.2583i −0.304057 0.526642i 0.672994 0.739648i $$-0.265008\pi$$
−0.977051 + 0.213006i $$0.931675\pi$$
$$458$$ 0 0
$$459$$ 4.00000 6.92820i 0.186704 0.323381i
$$460$$ 0 0
$$461$$ −4.00000 −0.186299 −0.0931493 0.995652i $$-0.529693\pi$$
−0.0931493 + 0.995652i $$0.529693\pi$$
$$462$$ 0 0
$$463$$ −11.0000 −0.511213 −0.255607 0.966781i $$-0.582275\pi$$
−0.255607 + 0.966781i $$0.582275\pi$$
$$464$$ 0 0
$$465$$ 3.00000 5.19615i 0.139122 0.240966i
$$466$$ 0 0
$$467$$ 17.0000 + 29.4449i 0.786666 + 1.36255i 0.927999 + 0.372584i $$0.121528\pi$$
−0.141332 + 0.989962i $$0.545139\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 1.00000 + 1.73205i 0.0460776 + 0.0798087i
$$472$$ 0 0
$$473$$ −11.0000 + 19.0526i −0.505781 + 0.876038i
$$474$$ 0 0
$$475$$ −1.00000 −0.0458831
$$476$$ 0 0
$$477$$ −12.0000 −0.549442
$$478$$ 0 0
$$479$$ −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i $$0.387598\pi$$
−0.985504 + 0.169654i $$0.945735\pi$$
$$480$$ 0 0
$$481$$ 1.50000 + 2.59808i 0.0683941 + 0.118462i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 10.0000 + 17.3205i 0.454077 + 0.786484i
$$486$$ 0 0
$$487$$ 9.50000 16.4545i 0.430486 0.745624i −0.566429 0.824110i $$-0.691675\pi$$
0.996915 + 0.0784867i $$0.0250088\pi$$
$$488$$ 0 0
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 0 0
$$493$$ 16.0000 27.7128i 0.720604 1.24812i
$$494$$ 0 0
$$495$$ −2.00000 3.46410i −0.0898933 0.155700i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 14.5000 + 25.1147i 0.649109 + 1.12429i 0.983336 + 0.181797i $$0.0581915\pi$$
−0.334227 + 0.942493i $$0.608475\pi$$
$$500$$ 0 0
$$501$$ −1.00000 + 1.73205i −0.0446767 + 0.0773823i
$$502$$ 0 0
$$503$$ 30.0000 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$504$$ 0 0
$$505$$ −20.0000 −0.889988
$$506$$ 0 0
$$507$$ 2.00000 3.46410i 0.0888231 0.153846i
$$508$$ 0 0
$$509$$ 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i $$-0.0360525\pi$$
−0.594675 + 0.803966i $$0.702719\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −0.500000 0.866025i −0.0220755 0.0382360i
$$514$$ 0 0
$$515$$ 11.0000 19.0526i 0.484718 0.839556i
$$516$$ 0 0
$$517$$ −12.0000 −0.527759
$$518$$ 0 0
$$519$$ −16.0000 −0.702322
$$520$$ 0 0
$$521$$ −18.0000 + 31.1769i −0.788594 + 1.36589i 0.138234 + 0.990400i $$0.455857\pi$$
−0.926828 + 0.375486i $$0.877476\pi$$
$$522$$ 0 0
$$523$$ −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i $$-0.929614\pi$$
0.297884 0.954602i $$-0.403719\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −12.0000 20.7846i −0.522728 0.905392i
$$528$$ 0 0
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ −18.0000 −0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −3.00000 5.19615i −0.129460 0.224231i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 7.50000 + 12.9904i 0.322450 + 0.558500i 0.980993 0.194043i $$-0.0621602\pi$$
−0.658543 + 0.752543i $$0.728827\pi$$
$$542$$ 0 0
$$543$$ −7.50000 + 12.9904i −0.321856 + 0.557471i
$$544$$ 0 0
$$545$$ −22.0000 −0.942376
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 0 0
$$549$$ −3.00000 + 5.19615i −0.128037 + 0.221766i
$$550$$ 0 0
$$551$$ −2.00000 3.46410i −0.0852029 0.147576i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 1.00000 + 1.73205i 0.0424476 + 0.0735215i
$$556$$ 0 0
$$557$$ −11.0000 + 19.0526i −0.466085 + 0.807283i −0.999250 0.0387286i $$-0.987669\pi$$
0.533165 + 0.846011i $$0.321003\pi$$
$$558$$ 0 0
$$559$$ 33.0000 1.39575
$$560$$ 0 0
$$561$$ −16.0000 −0.675521
$$562$$ 0 0
$$563$$ −23.0000 + 39.8372i −0.969334 + 1.67894i −0.271846 + 0.962341i $$0.587634\pi$$
−0.697489 + 0.716596i $$0.745699\pi$$
$$564$$ 0 0
$$565$$ 14.0000 + 24.2487i 0.588984 + 1.02015i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ 0 0
$$571$$ 10.5000 18.1865i 0.439411 0.761083i −0.558233 0.829684i $$-0.688520\pi$$
0.997644 + 0.0686016i $$0.0218537\pi$$
$$572$$ 0 0
$$573$$ 6.00000 0.250654
$$574$$ 0 0
$$575$$ −8.00000 −0.333623
$$576$$ 0 0
$$577$$ −20.5000 + 35.5070i −0.853426 + 1.47818i 0.0246713 + 0.999696i $$0.492146\pi$$
−0.878097 + 0.478482i $$0.841187\pi$$
$$578$$ 0 0
$$579$$ −5.50000 9.52628i −0.228572 0.395899i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 12.0000 + 20.7846i 0.496989 + 0.860811i
$$584$$ 0 0
$$585$$ −3.00000 + 5.19615i −0.124035 + 0.214834i
$$586$$ 0 0
$$587$$ −32.0000 −1.32078 −0.660391 0.750922i $$-0.729609\pi$$
−0.660391 + 0.750922i $$0.729609\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ −4.00000 + 6.92820i −0.164538 + 0.284988i
$$592$$ 0 0
$$593$$ −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i $$-0.205981\pi$$
−0.921026 + 0.389501i $$0.872647\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 4.00000 + 6.92820i 0.163709 + 0.283552i
$$598$$ 0 0
$$599$$ 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i $$-0.754495\pi$$
0.962175 + 0.272433i $$0.0878284\pi$$
$$600$$ 0 0
$$601$$ 1.00000 0.0407909 0.0203954 0.999792i $$-0.493507\pi$$
0.0203954 + 0.999792i $$0.493507\pi$$
$$602$$ 0 0
$$603$$ 13.0000 0.529401
$$604$$ 0 0
$$605$$ 7.00000 12.1244i 0.284590 0.492925i
$$606$$ 0 0
$$607$$ −1.50000 2.59808i −0.0608831 0.105453i 0.833977 0.551799i $$-0.186058\pi$$
−0.894860 + 0.446346i $$0.852725\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 9.00000 + 15.5885i 0.364101 + 0.630641i
$$612$$ 0 0
$$613$$ 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i $$-0.626169\pi$$
0.991917 0.126885i $$-0.0404979\pi$$
$$614$$ 0 0
$$615$$ −12.0000 −0.483887
$$616$$ 0 0
$$617$$ 26.0000 1.04672 0.523360 0.852111i $$-0.324678\pi$$
0.523360 + 0.852111i $$0.324678\pi$$
$$618$$ 0 0
$$619$$ −5.50000 + 9.52628i −0.221064 + 0.382893i −0.955131 0.296183i $$-0.904286\pi$$
0.734068 + 0.679076i $$0.237620\pi$$
$$620$$ 0 0
$$621$$ −4.00000 6.92820i −0.160514 0.278019i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ −1.00000 + 1.73205i −0.0399362 + 0.0691714i
$$628$$ 0 0
$$629$$ 8.00000 0.318981
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 2.00000 3.46410i 0.0794929 0.137686i
$$634$$ 0 0
$$635$$ −3.00000 5.19615i −0.119051 0.206203i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 5.00000 + 8.66025i 0.197797 + 0.342594i
$$640$$ 0 0
$$641$$ 20.0000 34.6410i 0.789953 1.36824i −0.136043 0.990703i $$-0.543438\pi$$
0.925995 0.377535i $$-0.123228\pi$$
$$642$$ 0 0
$$643$$ −35.0000 −1.38027 −0.690133 0.723683i $$-0.742448\pi$$
−0.690133 + 0.723683i $$0.742448\pi$$
$$644$$ 0 0
$$645$$ 22.0000 0.866249
$$646$$ 0 0
$$647$$ 3.00000 5.19615i 0.117942 0.204282i −0.801010 0.598651i $$-0.795704\pi$$
0.918952 + 0.394369i $$0.129037\pi$$
$$648$$ 0 0
$$649$$ 4.00000 + 6.92820i 0.157014 + 0.271956i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i $$-0.129211\pi$$
−0.801337 + 0.598213i $$0.795878\pi$$
$$654$$ 0 0
$$655$$ −2.00000 + 3.46410i −0.0781465 + 0.135354i
$$656$$ 0 0
$$657$$ 11.0000 0.429151
$$658$$ 0 0
$$659$$ −28.0000 −1.09073 −0.545363 0.838200i $$-0.683608\pi$$
−0.545363 + 0.838200i $$0.683608\pi$$
$$660$$ 0 0
$$661$$ −14.5000 + 25.1147i −0.563985 + 0.976850i 0.433159 + 0.901318i $$0.357399\pi$$
−0.997143 + 0.0755324i $$0.975934\pi$$
$$662$$ 0 0
$$663$$ 12.0000 + 20.7846i 0.466041 + 0.807207i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −16.0000 27.7128i −0.619522 1.07304i
$$668$$ 0 0
$$669$$ 4.00000 6.92820i 0.154649 0.267860i
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ −1.00000 −0.0385472 −0.0192736 0.999814i $$-0.506135\pi$$
−0.0192736 + 0.999814i $$0.506135\pi$$
$$674$$ 0 0
$$675$$ 0.500000 0.866025i 0.0192450 0.0333333i
$$676$$ 0 0
$$677$$ 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i $$-0.0925982\pi$$
−0.727386 + 0.686229i $$0.759265\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −9.00000 15.5885i −0.344881 0.597351i
$$682$$ 0 0
$$683$$ −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i $$0.408507\pi$$
−0.972242 + 0.233977i $$0.924826\pi$$
$$684$$ 0 0
$$685$$ 8.00000 0.305664
$$686$$ 0 0
$$687$$ −1.00000 −0.0381524
$$688$$ 0 0
$$689$$ 18.0000 31.1769i 0.685745 1.18775i
$$690$$ 0 0
$$691$$ −21.5000 37.2391i −0.817899 1.41664i −0.907228 0.420640i $$-0.861806\pi$$
0.0893292 0.996002i $$-0.471528\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −5.00000 8.66025i −0.189661 0.328502i
$$696$$ 0 0
$$697$$ −24.0000 + 41.5692i −0.909065 + 1.57455i
$$698$$ 0 0
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 0 0
$$703$$ 0.500000 0.866025i 0.0188579 0.0326628i
$$704$$ 0 0
$$705$$ 6.00000 + 10.3923i 0.225973 + 0.391397i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −7.00000 12.1244i −0.262891 0.455340i 0.704118 0.710083i $$-0.251342\pi$$
−0.967009 + 0.254743i $$0.918009\pi$$
$$710$$ 0 0
$$711$$ 1.50000 2.59808i 0.0562544 0.0974355i
$$712$$ 0 0
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 12.0000 0.448775
$$716$$ 0 0
$$717$$ −9.00000 + 15.5885i −0.336111 + 0.582162i
$$718$$ 0 0
$$719$$ −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i $$-0.202354\pi$$
−0.916529 + 0.399969i $$0.869021\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 7.00000 + 12.1244i 0.260333 + 0.450910i
$$724$$ 0 0
$$725$$ 2.00000 3.46410i 0.0742781 0.128654i
$$726$$ 0 0
$$727$$ 23.0000 0.853023 0.426511 0.904482i $$-0.359742\pi$$
0.426511 + 0.904482i $$0.359742\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 44.0000 76.2102i 1.62740 2.81874i
$$732$$ 0 0
$$733$$ 22.5000 + 38.9711i 0.831056 + 1.43943i 0.897201 + 0.441622i $$0.145597\pi$$
−0.0661448 + 0.997810i $$0.521070\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −13.0000 22.5167i −0.478861 0.829412i
$$738$$ 0 0
$$739$$ 4.50000 7.79423i 0.165535 0.286715i −0.771310 0.636460i $$-0.780398\pi$$
0.936845 + 0.349744i $$0.113732\pi$$
$$740$$ 0 0
$$741$$ 3.00000 0.110208
$$742$$ 0 0
$$743$$ −18.0000 −0.660356 −0.330178 0.943919i $$-0.607109\pi$$
−0.330178 + 0.943919i $$0.607109\pi$$
$$744$$ 0 0
$$745$$ 12.0000 20.7846i 0.439646 0.761489i
$$746$$ 0 0
$$747$$ 1.00000 + 1.73205i 0.0365881 + 0.0633724i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i $$-0.254907\pi$$
−0.969801 + 0.243898i $$0.921574\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 0 0
$$759$$ −8.00000 + 13.8564i −0.290382 + 0.502956i
$$760$$ 0 0
$$761$$ 4.00000 + 6.92820i 0.145000 + 0.251147i 0.929373 0.369142i $$-0.120348\pi$$
−0.784373 + 0.620289i $$0.787015\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 8.00000 + 13.8564i 0.289241 + 0.500979i
$$766$$ 0 0
$$767$$ 6.00000 10.3923i 0.216647 0.375244i
$$768$$ 0 0
$$769$$ −31.0000 −1.11789 −0.558944 0.829205i $$-0.688793\pi$$
−0.558944 + 0.829205i $$0.688793\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ 11.0000 19.0526i 0.395643 0.685273i −0.597540 0.801839i $$-0.703855\pi$$
0.993183 + 0.116566i $$0.0371886\pi$$
$$774$$ 0 0
$$775$$ −1.50000 2.59808i −0.0538816 0.0933257i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3.00000 + 5.19615i 0.107486 + 0.186171i
$$780$$ 0 0
$$781$$ 10.0000 17.3205i 0.357828 0.619777i
$$782$$ 0 0
$$783$$ 4.00000 0.142948
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 0 0
$$787$$ 12.0000 20.7846i 0.427754 0.740891i −0.568919 0.822393i $$-0.692638\pi$$
0.996673 + 0.0815020i $$0.0259717\pi$$
$$788$$ 0 0
$$789$$ −6.00000 10.3923i −0.213606 0.369976i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −9.00000 15.5885i −0.319599 0.553562i
$$794$$ 0 0
$$795$$ 12.0000 20.7846i 0.425596 0.737154i
$$796$$ 0 0
$$797$$ 48.0000 1.70025 0.850124 0.526583i $$-0.176527\pi$$
0.850124 + 0.526583i $$0.176527\pi$$
$$798$$ 0 0
$$799$$ 48.0000 1.69812