# Properties

 Label 2352.2.q.n.1537.1 Level $2352$ Weight $2$ Character 2352.1537 Analytic conductor $18.781$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2352.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.7808145554$$ 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 42) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1537.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2352.1537 Dual form 2352.2.q.n.961.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} -6.00000 q^{13} -2.00000 q^{15} +(1.00000 - 1.73205i) q^{17} +(2.00000 + 3.46410i) q^{19} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(2.00000 + 3.46410i) q^{33} +(5.00000 + 8.66025i) q^{37} +(-3.00000 + 5.19615i) q^{39} +6.00000 q^{41} +4.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{51} +(-3.00000 + 5.19615i) q^{53} +8.00000 q^{55} +4.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(6.00000 + 10.3923i) q^{65} +(2.00000 - 3.46410i) q^{67} +8.00000 q^{69} -8.00000 q^{71} +(5.00000 - 8.66025i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{81} -4.00000 q^{83} -4.00000 q^{85} +(-1.00000 + 1.73205i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{95} +14.0000 q^{97} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{3} - 2q^{5} - q^{9} + O(q^{10})$$ $$2q + q^{3} - 2q^{5} - q^{9} - 4q^{11} - 12q^{13} - 4q^{15} + 2q^{17} + 4q^{19} + 8q^{23} + q^{25} - 2q^{27} - 4q^{29} + 4q^{33} + 10q^{37} - 6q^{39} + 12q^{41} + 8q^{43} - 2q^{45} - 2q^{51} - 6q^{53} + 16q^{55} + 8q^{57} - 4q^{59} + 6q^{61} + 12q^{65} + 4q^{67} + 16q^{69} - 16q^{71} + 10q^{73} - q^{75} - q^{81} - 8q^{83} - 8q^{85} - 2q^{87} - 6q^{89} + 8q^{95} + 28q^{97} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1471$$ $$1765$$ $$2257$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$11$$ −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i $$0.372704\pi$$
−0.992361 + 0.123371i $$0.960630\pi$$
$$12$$ 0 0
$$13$$ −6.00000 −1.66410 −0.832050 0.554700i $$-0.812833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 0 0
$$17$$ 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i $$-0.755354\pi$$
0.961436 + 0.275029i $$0.0886875\pi$$
$$18$$ 0 0
$$19$$ 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i $$-0.0149348\pi$$
−0.540068 + 0.841621i $$0.681602\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i $$0.147321\pi$$
−0.0607377 + 0.998154i $$0.519345\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 0 0
$$33$$ 2.00000 + 3.46410i 0.348155 + 0.603023i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 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
$$39$$ −3.00000 + 5.19615i −0.480384 + 0.832050i
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 1.73205i −0.149071 + 0.258199i
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −1.00000 1.73205i −0.140028 0.242536i
$$52$$ 0 0
$$53$$ −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i $$-0.968532\pi$$
0.583036 + 0.812447i $$0.301865\pi$$
$$54$$ 0 0
$$55$$ 8.00000 1.07872
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ 0 0
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ 0 0
$$61$$ 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i $$-0.0411748\pi$$
−0.607535 + 0.794293i $$0.707841\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 6.00000 + 10.3923i 0.744208 + 1.28901i
$$66$$ 0 0
$$67$$ 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i $$-0.754762\pi$$
0.961946 + 0.273241i $$0.0880957\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i $$-0.634347\pi$$
0.994850 0.101361i $$-0.0323196\pi$$
$$74$$ 0 0
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ −1.00000 + 1.73205i −0.107211 + 0.185695i
$$88$$ 0 0
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 4.00000 6.92820i 0.410391 0.710819i
$$96$$ 0 0
$$97$$ 14.0000 1.42148 0.710742 0.703452i $$-0.248359\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i $$-0.865059\pi$$
0.811976 + 0.583691i $$0.198392\pi$$
$$102$$ 0 0
$$103$$ −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i $$-0.295621\pi$$
−0.992990 + 0.118199i $$0.962288\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i $$0.0302972\pi$$
−0.415432 + 0.909624i $$0.636370\pi$$
$$108$$ 0 0
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 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
$$117$$ 3.00000 + 5.19615i 0.277350 + 0.480384i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 0 0
$$123$$ 3.00000 5.19615i 0.270501 0.468521i
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0 0
$$129$$ 2.00000 3.46410i 0.176090 0.304997i
$$130$$ 0 0
$$131$$ 10.0000 + 17.3205i 0.873704 + 1.51330i 0.858137 + 0.513421i $$0.171622\pi$$
0.0155672 + 0.999879i $$0.495045\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 1.00000 + 1.73205i 0.0860663 + 0.149071i
$$136$$ 0 0
$$137$$ −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i $$-0.973826\pi$$
0.569442 + 0.822031i $$0.307159\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 12.0000 20.7846i 1.00349 1.73810i
$$144$$ 0 0
$$145$$ 2.00000 + 3.46410i 0.166091 + 0.287678i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 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
$$151$$ −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i $$-0.938871\pi$$
0.656101 + 0.754673i $$0.272204\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −5.00000 + 8.66025i −0.399043 + 0.691164i −0.993608 0.112884i $$-0.963991\pi$$
0.594565 + 0.804048i $$0.297324\pi$$
$$158$$ 0 0
$$159$$ 3.00000 + 5.19615i 0.237915 + 0.412082i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i $$0.119778\pi$$
−0.146772 + 0.989170i $$0.546888\pi$$
$$164$$ 0 0
$$165$$ 4.00000 6.92820i 0.311400 0.539360i
$$166$$ 0 0
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 2.00000 3.46410i 0.152944 0.264906i
$$172$$ 0 0
$$173$$ 11.0000 + 19.0526i 0.836315 + 1.44854i 0.892956 + 0.450145i $$0.148628\pi$$
−0.0566411 + 0.998395i $$0.518039\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 2.00000 + 3.46410i 0.150329 + 0.260378i
$$178$$ 0 0
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ 0 0
$$181$$ 18.0000 1.33793 0.668965 0.743294i $$-0.266738\pi$$
0.668965 + 0.743294i $$0.266738\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 0 0
$$185$$ 10.0000 17.3205i 0.735215 1.27343i
$$186$$ 0 0
$$187$$ 4.00000 + 6.92820i 0.292509 + 0.506640i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$192$$ 0 0
$$193$$ −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i $$-0.856266\pi$$
0.827788 + 0.561041i $$0.189599\pi$$
$$194$$ 0 0
$$195$$ 12.0000 0.859338
$$196$$ 0 0
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ −2.00000 3.46410i −0.141069 0.244339i
$$202$$ 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
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ 0 0
$$213$$ −4.00000 + 6.92820i −0.274075 + 0.474713i
$$214$$ 0 0
$$215$$ −4.00000 6.92820i −0.272798 0.472500i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −5.00000 8.66025i −0.337869 0.585206i
$$220$$ 0 0
$$221$$ −6.00000 + 10.3923i −0.403604 + 0.699062i
$$222$$ 0 0
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i $$-0.963710\pi$$
0.595274 + 0.803523i $$0.297043\pi$$
$$228$$ 0 0
$$229$$ −1.00000 1.73205i −0.0660819 0.114457i 0.831092 0.556136i $$-0.187717\pi$$
−0.897173 + 0.441679i $$0.854383\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 11.0000 + 19.0526i 0.720634 + 1.24817i 0.960746 + 0.277429i $$0.0894825\pi$$
−0.240112 + 0.970745i $$0.577184\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i $$-0.812815\pi$$
0.896435 + 0.443176i $$0.146148\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −12.0000 20.7846i −0.763542 1.32249i
$$248$$ 0 0
$$249$$ −2.00000 + 3.46410i −0.126745 + 0.219529i
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −32.0000 −2.01182
$$254$$ 0 0
$$255$$ −2.00000 + 3.46410i −0.125245 + 0.216930i
$$256$$ 0 0
$$257$$ −15.0000 25.9808i −0.935674 1.62064i −0.773427 0.633885i $$-0.781459\pi$$
−0.162247 0.986750i $$-0.551874\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 1.00000 + 1.73205i 0.0618984 + 0.107211i
$$262$$ 0 0
$$263$$ −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i $$0.431818\pi$$
−0.952517 + 0.304487i $$0.901515\pi$$
$$264$$ 0 0
$$265$$ 12.0000 0.737154
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 0 0
$$269$$ 11.0000 19.0526i 0.670682 1.16166i −0.307029 0.951700i $$-0.599335\pi$$
0.977711 0.209955i $$-0.0673317\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.00000 + 3.46410i 0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 26.0000 1.55103 0.775515 0.631329i $$-0.217490\pi$$
0.775515 + 0.631329i $$0.217490\pi$$
$$282$$ 0 0
$$283$$ −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i $$-0.871266\pi$$
0.800439 + 0.599414i $$0.204600\pi$$
$$284$$ 0 0
$$285$$ −4.00000 6.92820i −0.236940 0.410391i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ 7.00000 12.1244i 0.410347 0.710742i
$$292$$ 0 0
$$293$$ −30.0000 −1.75262 −0.876309 0.481749i $$-0.840002\pi$$
−0.876309 + 0.481749i $$0.840002\pi$$
$$294$$ 0 0
$$295$$ 8.00000 0.465778
$$296$$ 0 0
$$297$$ 2.00000 3.46410i 0.116052 0.201008i
$$298$$ 0 0
$$299$$ −24.0000 41.5692i −1.38796 2.40401i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.00000 + 1.73205i 0.0574485 + 0.0995037i
$$304$$ 0 0
$$305$$ 6.00000 10.3923i 0.343559 0.595062i
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i $$-0.760501\pi$$
0.956864 + 0.290537i $$0.0938340\pi$$
$$312$$ 0 0
$$313$$ 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i $$-0.0754642\pi$$
−0.689412 + 0.724370i $$0.742131\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i $$0.00202172\pi$$
−0.494489 + 0.869184i $$0.664645\pi$$
$$318$$ 0 0
$$319$$ 4.00000 6.92820i 0.223957 0.387905i
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ −3.00000 + 5.19615i −0.166410 + 0.288231i
$$326$$ 0 0
$$327$$ −1.00000 1.73205i −0.0553001 0.0957826i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i $$-0.201729\pi$$
−0.915742 + 0.401768i $$0.868396\pi$$
$$332$$ 0 0
$$333$$ 5.00000 8.66025i 0.273998 0.474579i
$$334$$ 0 0
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 0 0
$$339$$ −7.00000 + 12.1244i −0.380188 + 0.658505i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −8.00000 13.8564i −0.430706 0.746004i
$$346$$ 0 0
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ 0 0
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ 0 0
$$351$$ 6.00000 0.320256
$$352$$ 0 0
$$353$$ −15.0000 + 25.9808i −0.798369 + 1.38282i 0.122308 + 0.992492i $$0.460970\pi$$
−0.920677 + 0.390324i $$0.872363\pi$$
$$354$$ 0 0
$$355$$ 8.00000 + 13.8564i 0.424596 + 0.735422i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −4.00000 6.92820i −0.211112 0.365657i 0.740951 0.671559i $$-0.234375\pi$$
−0.952063 + 0.305903i $$0.901042\pi$$
$$360$$ 0 0
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ 0 0
$$363$$ −5.00000 −0.262432
$$364$$ 0 0
$$365$$ −20.0000 −1.04685
$$366$$ 0 0
$$367$$ −16.0000 + 27.7128i −0.835193 + 1.44660i 0.0586798 + 0.998277i $$0.481311\pi$$
−0.893873 + 0.448320i $$0.852022\pi$$
$$368$$ 0 0
$$369$$ −3.00000 5.19615i −0.156174 0.270501i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i $$-0.973781\pi$$
0.427051 0.904227i $$-0.359552\pi$$
$$374$$ 0 0
$$375$$ −6.00000 + 10.3923i −0.309839 + 0.536656i
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 8.00000 + 13.8564i 0.408781 + 0.708029i 0.994753 0.102302i $$-0.0326207\pi$$
−0.585973 + 0.810331i $$0.699287\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −2.00000 3.46410i −0.101666 0.176090i
$$388$$ 0 0
$$389$$ 13.0000 22.5167i 0.659126 1.14164i −0.321716 0.946836i $$-0.604260\pi$$
0.980842 0.194804i $$-0.0624070\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ 20.0000 1.00887
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 3.00000 + 5.19615i 0.150566 + 0.260787i 0.931436 0.363906i $$-0.118557\pi$$
−0.780870 + 0.624694i $$0.785224\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 2.00000 0.0993808
$$406$$ 0 0
$$407$$ −40.0000 −1.98273
$$408$$ 0 0
$$409$$ −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i $$0.349725\pi$$
−0.998674 + 0.0514740i $$0.983608\pi$$
$$410$$ 0 0
$$411$$ 5.00000 + 8.66025i 0.246632 + 0.427179i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4.00000 + 6.92820i 0.196352 + 0.340092i
$$416$$ 0 0
$$417$$ 2.00000 3.46410i 0.0979404 0.169638i
$$418$$ 0 0
$$419$$ −36.0000 −1.75872 −0.879358 0.476162i $$-0.842028\pi$$
−0.879358 + 0.476162i $$0.842028\pi$$
$$420$$ 0 0
$$421$$ 6.00000 0.292422 0.146211 0.989253i $$-0.453292\pi$$
0.146211 + 0.989253i $$0.453292\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −1.00000 1.73205i −0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −12.0000 20.7846i −0.579365 1.00349i
$$430$$ 0 0
$$431$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 4.00000 0.191785
$$436$$ 0 0
$$437$$ −16.0000 + 27.7128i −0.765384 + 1.32568i
$$438$$ 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 0.814595 0.580030i $$-0.196959\pi$$
−0.909618 + 0.415445i $$0.863626\pi$$
$$444$$ 0 0
$$445$$ −6.00000 + 10.3923i −0.284427 + 0.492642i
$$446$$ 0 0
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ 34.0000 1.60456 0.802280 0.596948i $$-0.203620\pi$$
0.802280 + 0.596948i $$0.203620\pi$$
$$450$$ 0 0
$$451$$ −12.0000 + 20.7846i −0.565058 + 0.978709i
$$452$$ 0 0
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i $$-0.241812\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ 0 0
$$459$$ −1.00000 + 1.73205i −0.0466760 + 0.0808452i
$$460$$ 0 0
$$461$$ −22.0000 −1.02464 −0.512321 0.858794i $$-0.671214\pi$$
−0.512321 + 0.858794i $$0.671214\pi$$
$$462$$ 0 0
$$463$$ 32.0000 1.48717 0.743583 0.668644i $$-0.233125\pi$$
0.743583 + 0.668644i $$0.233125\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −14.0000 24.2487i −0.647843 1.12210i −0.983637 0.180161i $$-0.942338\pi$$
0.335794 0.941935i $$-0.390995\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 5.00000 + 8.66025i 0.230388 + 0.399043i
$$472$$ 0 0
$$473$$ −8.00000 + 13.8564i −0.367840 + 0.637118i
$$474$$ 0 0
$$475$$ 4.00000 0.183533
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 8.00000 13.8564i 0.365529 0.633115i −0.623332 0.781958i $$-0.714221\pi$$
0.988861 + 0.148842i $$0.0475547\pi$$
$$480$$ 0 0
$$481$$ −30.0000 51.9615i −1.36788 2.36924i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −14.0000 24.2487i −0.635707 1.10108i
$$486$$ 0 0
$$487$$ 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i $$-0.775317\pi$$
0.942309 + 0.334744i $$0.108650\pi$$
$$488$$ 0 0
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 0 0
$$493$$ −2.00000 + 3.46410i −0.0900755 + 0.156015i
$$494$$ 0 0
$$495$$ −4.00000 6.92820i −0.179787 0.311400i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −22.0000 38.1051i −0.984855 1.70582i −0.642578 0.766220i $$-0.722135\pi$$
−0.342277 0.939599i $$-0.611198\pi$$
$$500$$ 0 0
$$501$$ −4.00000 + 6.92820i −0.178707 + 0.309529i
$$502$$ 0 0
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ 4.00000 0.177998
$$506$$ 0 0
$$507$$ 11.5000 19.9186i 0.510733 0.884615i
$$508$$ 0 0
$$509$$ 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i $$-0.124214\pi$$
−0.791849 + 0.610718i $$0.790881\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −2.00000 3.46410i −0.0883022 0.152944i
$$514$$ 0 0
$$515$$ −8.00000 + 13.8564i −0.352522 + 0.610586i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 22.0000 0.965693
$$520$$ 0 0
$$521$$ −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i $$-0.875291\pi$$
0.792797 + 0.609486i $$0.208624\pi$$
$$522$$ 0 0
$$523$$ −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i $$-0.310721\pi$$
−0.997478 + 0.0709788i $$0.977388\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ −36.0000 −1.55933
$$534$$ 0 0
$$535$$ 12.0000 20.7846i 0.518805 0.898597i
$$536$$ 0 0
$$537$$ 6.00000 + 10.3923i 0.258919 + 0.448461i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −15.0000 25.9808i −0.644900 1.11700i −0.984325 0.176367i $$-0.943566\pi$$
0.339424 0.940633i $$-0.389768\pi$$
$$542$$ 0 0
$$543$$ 9.00000 15.5885i 0.386227 0.668965i
$$544$$ 0 0
$$545$$ −4.00000 −0.171341
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 0 0
$$549$$ 3.00000 5.19615i 0.128037 0.221766i
$$550$$ 0 0
$$551$$ −4.00000 6.92820i −0.170406 0.295151i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −10.0000 17.3205i −0.424476 0.735215i
$$556$$ 0 0
$$557$$ 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i $$-0.819842\pi$$
0.886433 + 0.462856i $$0.153175\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ 0 0
$$563$$ −22.0000 + 38.1051i −0.927189 + 1.60594i −0.139188 + 0.990266i $$0.544449\pi$$
−0.788002 + 0.615673i $$0.788884\pi$$
$$564$$ 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 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 0 0
$$571$$ 6.00000 10.3923i 0.251092 0.434904i −0.712735 0.701434i $$-0.752544\pi$$
0.963827 + 0.266529i $$0.0858769\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.00000 0.333623
$$576$$ 0 0
$$577$$ 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i $$-0.583058\pi$$
0.965701 0.259656i $$-0.0836092\pi$$
$$578$$ 0 0
$$579$$ 1.00000 + 1.73205i 0.0415586 + 0.0719816i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −12.0000 20.7846i −0.496989 0.860811i
$$584$$ 0 0
$$585$$ 6.00000 10.3923i 0.248069 0.429669i
$$586$$ 0 0
$$587$$ −28.0000 −1.15568 −0.577842 0.816149i $$-0.696105\pi$$
−0.577842 + 0.816149i $$0.696105\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −5.00000 + 8.66025i −0.205673 + 0.356235i
$$592$$ 0 0
$$593$$ 9.00000 + 15.5885i 0.369586 + 0.640141i 0.989501 0.144528i $$-0.0461663\pi$$
−0.619915 + 0.784669i $$0.712833\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 4.00000 + 6.92820i 0.163709 + 0.283552i
$$598$$ 0 0
$$599$$ 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i $$-0.670218\pi$$
0.999938 + 0.0111569i $$0.00355143\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ 0 0
$$605$$ −5.00000 + 8.66025i −0.203279 + 0.352089i
$$606$$ 0 0
$$607$$ −24.0000 41.5692i −0.974130 1.68724i −0.682777 0.730627i $$-0.739228\pi$$
−0.291353 0.956616i $$-0.594105\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 21.0000 36.3731i 0.848182 1.46909i −0.0346469 0.999400i $$-0.511031\pi$$
0.882829 0.469695i $$-0.155636\pi$$
$$614$$ 0 0
$$615$$ −12.0000 −0.483887
$$616$$ 0 0
$$617$$ −22.0000 −0.885687 −0.442843 0.896599i $$-0.646030\pi$$
−0.442843 + 0.896599i $$0.646030\pi$$
$$618$$ 0 0
$$619$$ 22.0000 38.1051i 0.884255 1.53157i 0.0376891 0.999290i $$-0.488000\pi$$
0.846566 0.532284i $$-0.178666\pi$$
$$620$$ 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
$$627$$ −8.00000 + 13.8564i −0.319489 + 0.553372i
$$628$$ 0 0
$$629$$ 20.0000 0.797452
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ −10.0000 + 17.3205i −0.397464 + 0.688428i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 4.00000 + 6.92820i 0.158238 + 0.274075i
$$640$$ 0 0
$$641$$ −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i $$-0.845909\pi$$
0.845601 + 0.533816i $$0.179242\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ −8.00000 −0.315000
$$646$$ 0 0
$$647$$ −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i $$-0.989718\pi$$
0.527710 + 0.849425i $$0.323051\pi$$
$$648$$ 0 0
$$649$$ −8.00000 13.8564i −0.314027 0.543912i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i $$-0.0521013\pi$$
−0.634437 + 0.772975i $$0.718768\pi$$
$$654$$ 0 0
$$655$$ 20.0000 34.6410i 0.781465 1.35354i
$$656$$ 0 0
$$657$$ −10.0000 −0.390137
$$658$$ 0 0
$$659$$ 28.0000 1.09073 0.545363 0.838200i $$-0.316392\pi$$
0.545363 + 0.838200i $$0.316392\pi$$
$$660$$ 0 0
$$661$$ −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i $$-0.845717\pi$$
0.845922 + 0.533306i $$0.179051\pi$$
$$662$$ 0 0
$$663$$ 6.00000 + 10.3923i 0.233021 + 0.403604i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −8.00000 13.8564i −0.309761 0.536522i
$$668$$ 0 0
$$669$$ −8.00000 + 13.8564i −0.309298 + 0.535720i
$$670$$ 0 0
$$671$$ −24.0000 −0.926510
$$672$$ 0 0
$$673$$ 2.00000 0.0770943 0.0385472 0.999257i $$-0.487727\pi$$
0.0385472 + 0.999257i $$0.487727\pi$$
$$674$$ 0 0
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ 0 0
$$677$$ −9.00000 15.5885i −0.345898 0.599113i 0.639618 0.768693i $$-0.279092\pi$$
−0.985517 + 0.169580i $$0.945759\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 6.00000 + 10.3923i 0.229920 + 0.398234i
$$682$$ 0 0
$$683$$ 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i $$-0.759597\pi$$
0.957685 + 0.287819i $$0.0929302\pi$$
$$684$$ 0 0
$$685$$ 20.0000 0.764161
$$686$$ 0 0
$$687$$ −2.00000 −0.0763048
$$688$$ 0 0
$$689$$ 18.0000 31.1769i 0.685745 1.18775i
$$690$$ 0 0
$$691$$ 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i $$-0.142425\pi$$
−0.825473 + 0.564441i $$0.809092\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −4.00000 6.92820i −0.151729 0.262802i
$$696$$ 0 0
$$697$$ 6.00000 10.3923i 0.227266 0.393637i
$$698$$ 0 0
$$699$$ 22.0000 0.832116
$$700$$ 0 0
$$701$$ −2.00000 −0.0755390 −0.0377695 0.999286i $$-0.512025\pi$$
−0.0377695 + 0.999286i $$0.512025\pi$$
$$702$$ 0 0
$$703$$ −20.0000 + 34.6410i −0.754314 + 1.30651i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 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
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −48.0000 −1.79510
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −1.00000 1.73205i −0.0371904 0.0644157i
$$724$$ 0 0
$$725$$ −1.00000 + 1.73205i −0.0371391 + 0.0643268i
$$726$$ 0 0
$$727$$ −8.00000 −0.296704 −0.148352 0.988935i $$-0.547397\pi$$
−0.148352 + 0.988935i $$0.547397\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 4.00000 6.92820i 0.147945 0.256249i
$$732$$ 0 0
$$733$$ 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i $$-0.131323\pi$$
−0.805289 + 0.592883i $$0.797990\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 8.00000 + 13.8564i 0.294684 + 0.510407i
$$738$$ 0 0
$$739$$ −6.00000 + 10.3923i −0.220714 + 0.382287i −0.955025 0.296526i $$-0.904172\pi$$
0.734311 + 0.678813i $$0.237505\pi$$
$$740$$ 0 0
$$741$$ −24.0000 −0.881662
$$742$$ 0 0
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ −6.00000 + 10.3923i −0.219823 + 0.380745i
$$746$$ 0 0
$$747$$ 2.00000 + 3.46410i 0.0731762 + 0.126745i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 24.0000 + 41.5692i 0.875772 + 1.51688i 0.855938 + 0.517079i $$0.172981\pi$$
0.0198348 + 0.999803i $$0.493686\pi$$
$$752$$ 0 0
$$753$$ −6.00000 + 10.3923i −0.218652 + 0.378717i
$$754$$ 0 0
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ 0 0
$$759$$ −16.0000 + 27.7128i −0.580763 + 1.00591i
$$760$$ 0 0
$$761$$ −11.0000 19.0526i −0.398750 0.690655i 0.594822 0.803857i $$-0.297222\pi$$
−0.993572 + 0.113203i $$0.963889\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 2.00000 + 3.46410i 0.0723102 + 0.125245i
$$766$$ 0 0
$$767$$ 12.0000 20.7846i 0.433295 0.750489i
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ −30.0000 −1.08042
$$772$$ 0 0
$$773$$ −1.00000 + 1.73205i −0.0359675 + 0.0622975i −0.883449 0.468528i $$-0.844785\pi$$
0.847481 + 0.530825i $$0.178118\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 12.0000 + 20.7846i 0.429945 + 0.744686i
$$780$$ 0 0
$$781$$ 16.0000 27.7128i 0.572525 0.991642i
$$782$$ 0 0
$$783$$ 2.00000 0.0714742
$$784$$ 0 0
$$785$$ 20.0000 0.713831
$$786$$ 0 0
$$787$$ 18.0000 31.1769i 0.641631 1.11134i −0.343438 0.939175i $$-0.611592\pi$$
0.985069 0.172162i $$-0.0550751\pi$$
$$788$$ 0 0
$$789$$ 12.0000 + 20.7846i 0.427211 + 0.739952i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −18.0000 31.1769i −0.639199 1.10712i
$$794$$ 0 0
$$795$$ 6.00000 10.3923i 0.212798 0.368577i
$$796$$ 0 0
$$797$$ −6.00000 −0.212531 −0.106265 0.994338i $$-0.533889\pi$$
−0.106265 + 0.994338i $$0.533889\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −3.00000 + 5.19615i −0.106000 + 0.183597i