# Properties

 Label 378.2.k.d.215.4 Level $378$ Weight $2$ Character 378.215 Analytic conductor $3.018$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 378.k (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.01834519640$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ x^8 - x^4 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}\cdot 3^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 215.4 Root $$-0.965926 - 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 378.215 Dual form 378.2.k.d.269.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.00000 - 2.44949i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.00000 - 2.44949i) q^{7} +1.00000i q^{8} +(2.12132 - 1.22474i) q^{10} +(3.67423 - 2.12132i) q^{11} +0.717439i q^{13} +(0.358719 - 2.62132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.22474 + 2.12132i) q^{17} +(-4.24264 - 2.44949i) q^{19} +2.44949 q^{20} +4.24264 q^{22} +(5.19615 + 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.358719 + 0.621320i) q^{26} +(1.62132 - 2.09077i) q^{28} +1.75736i q^{29} +(-7.86396 + 4.54026i) q^{31} +(-0.866025 + 0.500000i) q^{32} +2.44949i q^{34} +(-6.42090 - 0.878680i) q^{35} +(-2.62132 + 4.54026i) q^{37} +(-2.44949 - 4.24264i) q^{38} +(2.12132 + 1.22474i) q^{40} +2.44949 q^{41} +7.00000 q^{43} +(3.67423 + 2.12132i) q^{44} +(3.00000 + 5.19615i) q^{46} +(6.42090 - 11.1213i) q^{47} +(-5.00000 + 4.89898i) q^{49} -1.00000i q^{50} +(-0.621320 + 0.358719i) q^{52} +(-12.5446 + 7.24264i) q^{53} -10.3923i q^{55} +(2.44949 - 1.00000i) q^{56} +(-0.878680 + 1.52192i) q^{58} +(-1.22474 - 2.12132i) q^{59} +(3.62132 + 2.09077i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(1.52192 + 0.878680i) q^{65} +(-6.74264 - 11.6786i) q^{67} +(-1.22474 + 2.12132i) q^{68} +(-5.12132 - 3.97141i) q^{70} +12.7279i q^{71} +(-4.75736 + 2.74666i) q^{73} +(-4.54026 + 2.62132i) q^{74} -4.89898i q^{76} +(-8.87039 - 6.87868i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(1.22474 + 2.12132i) q^{80} +(2.12132 + 1.22474i) q^{82} -15.2913 q^{83} +6.00000 q^{85} +(6.06218 + 3.50000i) q^{86} +(2.12132 + 3.67423i) q^{88} +(1.52192 - 2.63604i) q^{89} +(1.75736 - 0.717439i) q^{91} +6.00000i q^{92} +(11.1213 - 6.42090i) q^{94} +(-10.3923 + 6.00000i) q^{95} -3.16693i q^{97} +(-6.77962 + 1.74264i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{4} - 8 q^{7}+O(q^{10})$$ 8 * q + 4 * q^4 - 8 * q^7 $$8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 4 q^{25} - 4 q^{28} - 12 q^{31} - 4 q^{37} + 56 q^{43} + 24 q^{46} - 40 q^{49} + 12 q^{52} - 24 q^{58} + 12 q^{61} - 8 q^{64} - 20 q^{67} - 24 q^{70} - 72 q^{73} - 20 q^{79} + 48 q^{85} + 48 q^{91} + 72 q^{94}+O(q^{100})$$ 8 * q + 4 * q^4 - 8 * q^7 - 4 * q^16 - 4 * q^25 - 4 * q^28 - 12 * q^31 - 4 * q^37 + 56 * q^43 + 24 * q^46 - 40 * q^49 + 12 * q^52 - 24 * q^58 + 12 * q^61 - 8 * q^64 - 20 * q^67 - 24 * q^70 - 72 * q^73 - 20 * q^79 + 48 * q^85 + 48 * q^91 + 72 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$325$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 + 0.500000i 0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 1.22474 2.12132i 0.547723 0.948683i −0.450708 0.892672i $$-0.648828\pi$$
0.998430 0.0560116i $$-0.0178384\pi$$
$$6$$ 0 0
$$7$$ −1.00000 2.44949i −0.377964 0.925820i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 2.12132 1.22474i 0.670820 0.387298i
$$11$$ 3.67423 2.12132i 1.10782 0.639602i 0.169559 0.985520i $$-0.445766\pi$$
0.938265 + 0.345918i $$0.112432\pi$$
$$12$$ 0 0
$$13$$ 0.717439i 0.198982i 0.995038 + 0.0994909i $$0.0317214\pi$$
−0.995038 + 0.0994909i $$0.968279\pi$$
$$14$$ 0.358719 2.62132i 0.0958718 0.700577i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.22474 + 2.12132i 0.297044 + 0.514496i 0.975458 0.220184i $$-0.0706658\pi$$
−0.678414 + 0.734680i $$0.737332\pi$$
$$18$$ 0 0
$$19$$ −4.24264 2.44949i −0.973329 0.561951i −0.0730792 0.997326i $$-0.523283\pi$$
−0.900249 + 0.435375i $$0.856616\pi$$
$$20$$ 2.44949 0.547723
$$21$$ 0 0
$$22$$ 4.24264 0.904534
$$23$$ 5.19615 + 3.00000i 1.08347 + 0.625543i 0.931831 0.362892i $$-0.118211\pi$$
0.151642 + 0.988436i $$0.451544\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −0.358719 + 0.621320i −0.0703507 + 0.121851i
$$27$$ 0 0
$$28$$ 1.62132 2.09077i 0.306401 0.395118i
$$29$$ 1.75736i 0.326333i 0.986599 + 0.163167i $$0.0521708\pi$$
−0.986599 + 0.163167i $$0.947829\pi$$
$$30$$ 0 0
$$31$$ −7.86396 + 4.54026i −1.41241 + 0.815455i −0.995615 0.0935461i $$-0.970180\pi$$
−0.416794 + 0.909001i $$0.636846\pi$$
$$32$$ −0.866025 + 0.500000i −0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 2.44949i 0.420084i
$$35$$ −6.42090 0.878680i −1.08533 0.148524i
$$36$$ 0 0
$$37$$ −2.62132 + 4.54026i −0.430942 + 0.746414i −0.996955 0.0779826i $$-0.975152\pi$$
0.566012 + 0.824397i $$0.308485\pi$$
$$38$$ −2.44949 4.24264i −0.397360 0.688247i
$$39$$ 0 0
$$40$$ 2.12132 + 1.22474i 0.335410 + 0.193649i
$$41$$ 2.44949 0.382546 0.191273 0.981537i $$-0.438738\pi$$
0.191273 + 0.981537i $$0.438738\pi$$
$$42$$ 0 0
$$43$$ 7.00000 1.06749 0.533745 0.845645i $$-0.320784\pi$$
0.533745 + 0.845645i $$0.320784\pi$$
$$44$$ 3.67423 + 2.12132i 0.553912 + 0.319801i
$$45$$ 0 0
$$46$$ 3.00000 + 5.19615i 0.442326 + 0.766131i
$$47$$ 6.42090 11.1213i 0.936584 1.62221i 0.164800 0.986327i $$-0.447302\pi$$
0.771784 0.635884i $$-0.219364\pi$$
$$48$$ 0 0
$$49$$ −5.00000 + 4.89898i −0.714286 + 0.699854i
$$50$$ 1.00000i 0.141421i
$$51$$ 0 0
$$52$$ −0.621320 + 0.358719i −0.0861616 + 0.0497454i
$$53$$ −12.5446 + 7.24264i −1.72314 + 0.994853i −0.810905 + 0.585178i $$0.801025\pi$$
−0.912231 + 0.409675i $$0.865642\pi$$
$$54$$ 0 0
$$55$$ 10.3923i 1.40130i
$$56$$ 2.44949 1.00000i 0.327327 0.133631i
$$57$$ 0 0
$$58$$ −0.878680 + 1.52192i −0.115376 + 0.199838i
$$59$$ −1.22474 2.12132i −0.159448 0.276172i 0.775222 0.631689i $$-0.217638\pi$$
−0.934670 + 0.355517i $$0.884305\pi$$
$$60$$ 0 0
$$61$$ 3.62132 + 2.09077i 0.463663 + 0.267696i 0.713583 0.700571i $$-0.247071\pi$$
−0.249920 + 0.968266i $$0.580404\pi$$
$$62$$ −9.08052 −1.15323
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 1.52192 + 0.878680i 0.188771 + 0.108987i
$$66$$ 0 0
$$67$$ −6.74264 11.6786i −0.823745 1.42677i −0.902875 0.429903i $$-0.858548\pi$$
0.0791303 0.996864i $$-0.474786\pi$$
$$68$$ −1.22474 + 2.12132i −0.148522 + 0.257248i
$$69$$ 0 0
$$70$$ −5.12132 3.97141i −0.612115 0.474674i
$$71$$ 12.7279i 1.51053i 0.655422 + 0.755263i $$0.272491\pi$$
−0.655422 + 0.755263i $$0.727509\pi$$
$$72$$ 0 0
$$73$$ −4.75736 + 2.74666i −0.556807 + 0.321473i −0.751863 0.659320i $$-0.770844\pi$$
0.195056 + 0.980792i $$0.437511\pi$$
$$74$$ −4.54026 + 2.62132i −0.527795 + 0.304722i
$$75$$ 0 0
$$76$$ 4.89898i 0.561951i
$$77$$ −8.87039 6.87868i −1.01087 0.783898i
$$78$$ 0 0
$$79$$ −0.378680 + 0.655892i −0.0426048 + 0.0737937i −0.886541 0.462649i $$-0.846899\pi$$
0.843937 + 0.536443i $$0.180232\pi$$
$$80$$ 1.22474 + 2.12132i 0.136931 + 0.237171i
$$81$$ 0 0
$$82$$ 2.12132 + 1.22474i 0.234261 + 0.135250i
$$83$$ −15.2913 −1.67844 −0.839218 0.543795i $$-0.816987\pi$$
−0.839218 + 0.543795i $$0.816987\pi$$
$$84$$ 0 0
$$85$$ 6.00000 0.650791
$$86$$ 6.06218 + 3.50000i 0.653701 + 0.377415i
$$87$$ 0 0
$$88$$ 2.12132 + 3.67423i 0.226134 + 0.391675i
$$89$$ 1.52192 2.63604i 0.161323 0.279420i −0.774020 0.633161i $$-0.781757\pi$$
0.935343 + 0.353741i $$0.115091\pi$$
$$90$$ 0 0
$$91$$ 1.75736 0.717439i 0.184221 0.0752080i
$$92$$ 6.00000i 0.625543i
$$93$$ 0 0
$$94$$ 11.1213 6.42090i 1.14708 0.662265i
$$95$$ −10.3923 + 6.00000i −1.06623 + 0.615587i
$$96$$ 0 0
$$97$$ 3.16693i 0.321553i −0.986991 0.160776i $$-0.948600\pi$$
0.986991 0.160776i $$-0.0513998\pi$$
$$98$$ −6.77962 + 1.74264i −0.684845 + 0.176033i
$$99$$ 0 0
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ 3.67423 + 6.36396i 0.365600 + 0.633238i 0.988872 0.148767i $$-0.0475305\pi$$
−0.623272 + 0.782005i $$0.714197\pi$$
$$102$$ 0 0
$$103$$ 9.62132 + 5.55487i 0.948017 + 0.547338i 0.892464 0.451118i $$-0.148975\pi$$
0.0555525 + 0.998456i $$0.482308\pi$$
$$104$$ −0.717439 −0.0703507
$$105$$ 0 0
$$106$$ −14.4853 −1.40693
$$107$$ −2.15232 1.24264i −0.208072 0.120131i 0.392343 0.919819i $$-0.371665\pi$$
−0.600415 + 0.799688i $$0.704998\pi$$
$$108$$ 0 0
$$109$$ 8.86396 + 15.3528i 0.849013 + 1.47053i 0.882090 + 0.471082i $$0.156136\pi$$
−0.0330761 + 0.999453i $$0.510530\pi$$
$$110$$ 5.19615 9.00000i 0.495434 0.858116i
$$111$$ 0 0
$$112$$ 2.62132 + 0.358719i 0.247691 + 0.0338958i
$$113$$ 10.2426i 0.963547i −0.876296 0.481773i $$-0.839993\pi$$
0.876296 0.481773i $$-0.160007\pi$$
$$114$$ 0 0
$$115$$ 12.7279 7.34847i 1.18688 0.685248i
$$116$$ −1.52192 + 0.878680i −0.141307 + 0.0815834i
$$117$$ 0 0
$$118$$ 2.44949i 0.225494i
$$119$$ 3.97141 5.12132i 0.364058 0.469471i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 2.09077 + 3.62132i 0.189289 + 0.327859i
$$123$$ 0 0
$$124$$ −7.86396 4.54026i −0.706205 0.407727i
$$125$$ 9.79796 0.876356
$$126$$ 0 0
$$127$$ −7.72792 −0.685742 −0.342871 0.939382i $$-0.611399\pi$$
−0.342871 + 0.939382i $$0.611399\pi$$
$$128$$ −0.866025 0.500000i −0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 0.878680 + 1.52192i 0.0770653 + 0.133481i
$$131$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$132$$ 0 0
$$133$$ −1.75736 + 12.8418i −0.152382 + 1.11352i
$$134$$ 13.4853i 1.16495i
$$135$$ 0 0
$$136$$ −2.12132 + 1.22474i −0.181902 + 0.105021i
$$137$$ −5.19615 + 3.00000i −0.443937 + 0.256307i −0.705266 0.708942i $$-0.749173\pi$$
0.261329 + 0.965250i $$0.415839\pi$$
$$138$$ 0 0
$$139$$ 8.06591i 0.684141i −0.939674 0.342071i $$-0.888872\pi$$
0.939674 0.342071i $$-0.111128\pi$$
$$140$$ −2.44949 6.00000i −0.207020 0.507093i
$$141$$ 0 0
$$142$$ −6.36396 + 11.0227i −0.534052 + 0.925005i
$$143$$ 1.52192 + 2.63604i 0.127269 + 0.220437i
$$144$$ 0 0
$$145$$ 3.72792 + 2.15232i 0.309587 + 0.178740i
$$146$$ −5.49333 −0.454631
$$147$$ 0 0
$$148$$ −5.24264 −0.430942
$$149$$ 14.0665 + 8.12132i 1.15238 + 0.665324i 0.949465 0.313873i $$-0.101627\pi$$
0.202911 + 0.979197i $$0.434960\pi$$
$$150$$ 0 0
$$151$$ −4.37868 7.58410i −0.356332 0.617185i 0.631013 0.775772i $$-0.282639\pi$$
−0.987345 + 0.158587i $$0.949306\pi$$
$$152$$ 2.44949 4.24264i 0.198680 0.344124i
$$153$$ 0 0
$$154$$ −4.24264 10.3923i −0.341882 0.837436i
$$155$$ 22.2426i 1.78657i
$$156$$ 0 0
$$157$$ −9.00000 + 5.19615i −0.718278 + 0.414698i −0.814119 0.580699i $$-0.802779\pi$$
0.0958404 + 0.995397i $$0.469446\pi$$
$$158$$ −0.655892 + 0.378680i −0.0521800 + 0.0301261i
$$159$$ 0 0
$$160$$ 2.44949i 0.193649i
$$161$$ 2.15232 15.7279i 0.169626 1.23953i
$$162$$ 0 0
$$163$$ 4.74264 8.21449i 0.371472 0.643409i −0.618320 0.785926i $$-0.712186\pi$$
0.989792 + 0.142518i $$0.0455197\pi$$
$$164$$ 1.22474 + 2.12132i 0.0956365 + 0.165647i
$$165$$ 0 0
$$166$$ −13.2426 7.64564i −1.02783 0.593417i
$$167$$ 0.594346 0.0459919 0.0229959 0.999736i $$-0.492680\pi$$
0.0229959 + 0.999736i $$0.492680\pi$$
$$168$$ 0 0
$$169$$ 12.4853 0.960406
$$170$$ 5.19615 + 3.00000i 0.398527 + 0.230089i
$$171$$ 0 0
$$172$$ 3.50000 + 6.06218i 0.266872 + 0.462237i
$$173$$ 10.3923 18.0000i 0.790112 1.36851i −0.135785 0.990738i $$-0.543356\pi$$
0.925897 0.377776i $$-0.123311\pi$$
$$174$$ 0 0
$$175$$ −1.62132 + 2.09077i −0.122560 + 0.158047i
$$176$$ 4.24264i 0.319801i
$$177$$ 0 0
$$178$$ 2.63604 1.52192i 0.197579 0.114073i
$$179$$ 5.82655 3.36396i 0.435497 0.251434i −0.266189 0.963921i $$-0.585764\pi$$
0.701686 + 0.712487i $$0.252431\pi$$
$$180$$ 0 0
$$181$$ 9.79796i 0.728277i 0.931345 + 0.364138i $$0.118636\pi$$
−0.931345 + 0.364138i $$0.881364\pi$$
$$182$$ 1.88064 + 0.257359i 0.139402 + 0.0190767i
$$183$$ 0 0
$$184$$ −3.00000 + 5.19615i −0.221163 + 0.383065i
$$185$$ 6.42090 + 11.1213i 0.472074 + 0.817656i
$$186$$ 0 0
$$187$$ 9.00000 + 5.19615i 0.658145 + 0.379980i
$$188$$ 12.8418 0.936584
$$189$$ 0 0
$$190$$ −12.0000 −0.870572
$$191$$ 18.3712 + 10.6066i 1.32929 + 0.767467i 0.985190 0.171466i $$-0.0548503\pi$$
0.344101 + 0.938933i $$0.388184\pi$$
$$192$$ 0 0
$$193$$ 0.742641 + 1.28629i 0.0534564 + 0.0925893i 0.891515 0.452990i $$-0.149643\pi$$
−0.838059 + 0.545580i $$0.816310\pi$$
$$194$$ 1.58346 2.74264i 0.113686 0.196910i
$$195$$ 0 0
$$196$$ −6.74264 1.88064i −0.481617 0.134331i
$$197$$ 16.9706i 1.20910i −0.796566 0.604551i $$-0.793352\pi$$
0.796566 0.604551i $$-0.206648\pi$$
$$198$$ 0 0
$$199$$ −18.1066 + 10.4539i −1.28354 + 0.741054i −0.977494 0.210962i $$-0.932340\pi$$
−0.306049 + 0.952016i $$0.599007\pi$$
$$200$$ 0.866025 0.500000i 0.0612372 0.0353553i
$$201$$ 0 0
$$202$$ 7.34847i 0.517036i
$$203$$ 4.30463 1.75736i 0.302126 0.123342i
$$204$$ 0 0
$$205$$ 3.00000 5.19615i 0.209529 0.362915i
$$206$$ 5.55487 + 9.62132i 0.387026 + 0.670349i
$$207$$ 0 0
$$208$$ −0.621320 0.358719i −0.0430808 0.0248727i
$$209$$ −20.7846 −1.43770
$$210$$ 0 0
$$211$$ 3.48528 0.239937 0.119968 0.992778i $$-0.461721\pi$$
0.119968 + 0.992778i $$0.461721\pi$$
$$212$$ −12.5446 7.24264i −0.861568 0.497427i
$$213$$ 0 0
$$214$$ −1.24264 2.15232i −0.0849452 0.147129i
$$215$$ 8.57321 14.8492i 0.584688 1.01271i
$$216$$ 0 0
$$217$$ 18.9853 + 14.7224i 1.28880 + 0.999424i
$$218$$ 17.7279i 1.20069i
$$219$$ 0 0
$$220$$ 9.00000 5.19615i 0.606780 0.350325i
$$221$$ −1.52192 + 0.878680i −0.102375 + 0.0591064i
$$222$$ 0 0
$$223$$ 10.3923i 0.695920i 0.937509 + 0.347960i $$0.113126\pi$$
−0.937509 + 0.347960i $$0.886874\pi$$
$$224$$ 2.09077 + 1.62132i 0.139695 + 0.108329i
$$225$$ 0 0
$$226$$ 5.12132 8.87039i 0.340665 0.590049i
$$227$$ −12.5446 21.7279i −0.832616 1.44213i −0.895957 0.444141i $$-0.853509\pi$$
0.0633412 0.997992i $$-0.479824\pi$$
$$228$$ 0 0
$$229$$ −4.86396 2.80821i −0.321420 0.185572i 0.330606 0.943769i $$-0.392747\pi$$
−0.652025 + 0.758197i $$0.726080\pi$$
$$230$$ 14.6969 0.969087
$$231$$ 0 0
$$232$$ −1.75736 −0.115376
$$233$$ 17.7408 + 10.2426i 1.16224 + 0.671018i 0.951839 0.306598i $$-0.0991908\pi$$
0.210398 + 0.977616i $$0.432524\pi$$
$$234$$ 0 0
$$235$$ −15.7279 27.2416i −1.02598 1.77704i
$$236$$ 1.22474 2.12132i 0.0797241 0.138086i
$$237$$ 0 0
$$238$$ 6.00000 2.44949i 0.388922 0.158777i
$$239$$ 16.2426i 1.05065i −0.850902 0.525325i $$-0.823944\pi$$
0.850902 0.525325i $$-0.176056\pi$$
$$240$$ 0 0
$$241$$ −0.985281 + 0.568852i −0.0634676 + 0.0366430i −0.531398 0.847122i $$-0.678333\pi$$
0.467930 + 0.883765i $$0.345000\pi$$
$$242$$ 6.06218 3.50000i 0.389692 0.224989i
$$243$$ 0 0
$$244$$ 4.18154i 0.267696i
$$245$$ 4.26858 + 16.6066i 0.272710 + 1.06096i
$$246$$ 0 0
$$247$$ 1.75736 3.04384i 0.111818 0.193675i
$$248$$ −4.54026 7.86396i −0.288307 0.499362i
$$249$$ 0 0
$$250$$ 8.48528 + 4.89898i 0.536656 + 0.309839i
$$251$$ 15.2913 0.965177 0.482589 0.875847i $$-0.339697\pi$$
0.482589 + 0.875847i $$0.339697\pi$$
$$252$$ 0 0
$$253$$ 25.4558 1.60040
$$254$$ −6.69258 3.86396i −0.419930 0.242446i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −12.5446 + 21.7279i −0.782512 + 1.35535i 0.147962 + 0.988993i $$0.452729\pi$$
−0.930474 + 0.366358i $$0.880605\pi$$
$$258$$ 0 0
$$259$$ 13.7426 + 1.88064i 0.853926 + 0.116857i
$$260$$ 1.75736i 0.108987i
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −5.82655 + 3.36396i −0.359281 + 0.207431i −0.668765 0.743474i $$-0.733177\pi$$
0.309485 + 0.950904i $$0.399843\pi$$
$$264$$ 0 0
$$265$$ 35.4815i 2.17961i
$$266$$ −7.94282 + 10.2426i −0.487005 + 0.628017i
$$267$$ 0 0
$$268$$ 6.74264 11.6786i 0.411872 0.713384i
$$269$$ −4.89898 8.48528i −0.298696 0.517357i 0.677142 0.735853i $$-0.263218\pi$$
−0.975838 + 0.218496i $$0.929885\pi$$
$$270$$ 0 0
$$271$$ −16.3492 9.43924i −0.993146 0.573393i −0.0869326 0.996214i $$-0.527706\pi$$
−0.906213 + 0.422821i $$0.861040\pi$$
$$272$$ −2.44949 −0.148522
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ −3.67423 2.12132i −0.221565 0.127920i
$$276$$ 0 0
$$277$$ −11.8640 20.5490i −0.712836 1.23467i −0.963788 0.266669i $$-0.914077\pi$$
0.250952 0.968000i $$-0.419256\pi$$
$$278$$ 4.03295 6.98528i 0.241881 0.418949i
$$279$$ 0 0
$$280$$ 0.878680 6.42090i 0.0525112 0.383722i
$$281$$ 13.7574i 0.820695i 0.911929 + 0.410348i $$0.134593\pi$$
−0.911929 + 0.410348i $$0.865407\pi$$
$$282$$ 0 0
$$283$$ 5.22792 3.01834i 0.310768 0.179422i −0.336502 0.941683i $$-0.609244\pi$$
0.647270 + 0.762261i $$0.275911\pi$$
$$284$$ −11.0227 + 6.36396i −0.654077 + 0.377632i
$$285$$ 0 0
$$286$$ 3.04384i 0.179986i
$$287$$ −2.44949 6.00000i −0.144589 0.354169i
$$288$$ 0 0
$$289$$ 5.50000 9.52628i 0.323529 0.560369i
$$290$$ 2.15232 + 3.72792i 0.126388 + 0.218911i
$$291$$ 0 0
$$292$$ −4.75736 2.74666i −0.278403 0.160736i
$$293$$ 12.8418 0.750226 0.375113 0.926979i $$-0.377604\pi$$
0.375113 + 0.926979i $$0.377604\pi$$
$$294$$ 0 0
$$295$$ −6.00000 −0.349334
$$296$$ −4.54026 2.62132i −0.263897 0.152361i
$$297$$ 0 0
$$298$$ 8.12132 + 14.0665i 0.470455 + 0.814853i
$$299$$ −2.15232 + 3.72792i −0.124472 + 0.215591i
$$300$$ 0 0
$$301$$ −7.00000 17.1464i −0.403473 0.988304i
$$302$$ 8.75736i 0.503929i
$$303$$ 0 0
$$304$$ 4.24264 2.44949i 0.243332 0.140488i
$$305$$ 8.87039 5.12132i 0.507917 0.293246i
$$306$$ 0 0
$$307$$ 26.8213i 1.53077i −0.643571 0.765386i $$-0.722548\pi$$
0.643571 0.765386i $$-0.277452\pi$$
$$308$$ 1.52192 11.1213i 0.0867193 0.633696i
$$309$$ 0 0
$$310$$ −11.1213 + 19.2627i −0.631649 + 1.09405i
$$311$$ 8.57321 + 14.8492i 0.486142 + 0.842023i 0.999873 0.0159282i $$-0.00507031\pi$$
−0.513731 + 0.857951i $$0.671737\pi$$
$$312$$ 0 0
$$313$$ −17.4853 10.0951i −0.988327 0.570611i −0.0835529 0.996503i $$-0.526627\pi$$
−0.904774 + 0.425893i $$0.859960\pi$$
$$314$$ −10.3923 −0.586472
$$315$$ 0 0
$$316$$ −0.757359 −0.0426048
$$317$$ −19.2627 11.1213i −1.08190 0.624636i −0.150492 0.988611i $$-0.548086\pi$$
−0.931408 + 0.363976i $$0.881419\pi$$
$$318$$ 0 0
$$319$$ 3.72792 + 6.45695i 0.208724 + 0.361520i
$$320$$ −1.22474 + 2.12132i −0.0684653 + 0.118585i
$$321$$ 0 0
$$322$$ 9.72792 12.5446i 0.542116 0.699084i
$$323$$ 12.0000i 0.667698i
$$324$$ 0 0
$$325$$ 0.621320 0.358719i 0.0344647 0.0198982i
$$326$$ 8.21449 4.74264i 0.454959 0.262671i
$$327$$ 0 0
$$328$$ 2.44949i 0.135250i
$$329$$ −33.6625 4.60660i −1.85587 0.253970i
$$330$$ 0 0
$$331$$ −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i $$-0.921953\pi$$
0.695266 + 0.718752i $$0.255287\pi$$
$$332$$ −7.64564 13.2426i −0.419609 0.726784i
$$333$$ 0 0
$$334$$ 0.514719 + 0.297173i 0.0281642 + 0.0162606i
$$335$$ −33.0321 −1.80473
$$336$$ 0 0
$$337$$ −21.4558 −1.16877 −0.584387 0.811475i $$-0.698665\pi$$
−0.584387 + 0.811475i $$0.698665\pi$$
$$338$$ 10.8126 + 6.24264i 0.588126 + 0.339555i
$$339$$ 0 0
$$340$$ 3.00000 + 5.19615i 0.162698 + 0.281801i
$$341$$ −19.2627 + 33.3640i −1.04313 + 1.80676i
$$342$$ 0 0
$$343$$ 17.0000 + 7.34847i 0.917914 + 0.396780i
$$344$$ 7.00000i 0.377415i
$$345$$ 0 0
$$346$$ 18.0000 10.3923i 0.967686 0.558694i
$$347$$ −4.30463 + 2.48528i −0.231085 + 0.133417i −0.611072 0.791575i $$-0.709262\pi$$
0.379988 + 0.924992i $$0.375928\pi$$
$$348$$ 0 0
$$349$$ 0.123093i 0.00658902i 0.999995 + 0.00329451i $$0.00104868\pi$$
−0.999995 + 0.00329451i $$0.998951\pi$$
$$350$$ −2.44949 + 1.00000i −0.130931 + 0.0534522i
$$351$$ 0 0
$$352$$ −2.12132 + 3.67423i −0.113067 + 0.195837i
$$353$$ −5.49333 9.51472i −0.292380 0.506417i 0.681992 0.731360i $$-0.261114\pi$$
−0.974372 + 0.224942i $$0.927781\pi$$
$$354$$ 0 0
$$355$$ 27.0000 + 15.5885i 1.43301 + 0.827349i
$$356$$ 3.04384 0.161323
$$357$$ 0 0
$$358$$ 6.72792 0.355582
$$359$$ −12.5446 7.24264i −0.662080 0.382252i 0.130989 0.991384i $$-0.458185\pi$$
−0.793069 + 0.609132i $$0.791518\pi$$
$$360$$ 0 0
$$361$$ 2.50000 + 4.33013i 0.131579 + 0.227901i
$$362$$ −4.89898 + 8.48528i −0.257485 + 0.445976i
$$363$$ 0 0
$$364$$ 1.50000 + 1.16320i 0.0786214 + 0.0609682i
$$365$$ 13.4558i 0.704311i
$$366$$ 0 0
$$367$$ −25.9706 + 14.9941i −1.35565 + 0.782686i −0.989034 0.147685i $$-0.952818\pi$$
−0.366618 + 0.930372i $$0.619484\pi$$
$$368$$ −5.19615 + 3.00000i −0.270868 + 0.156386i
$$369$$ 0 0
$$370$$ 12.8418i 0.667613i
$$371$$ 30.2854 + 23.4853i 1.57234 + 1.21930i
$$372$$ 0 0
$$373$$ 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i $$-0.640448\pi$$
0.996610 0.0822766i $$-0.0262191\pi$$
$$374$$ 5.19615 + 9.00000i 0.268687 + 0.465379i
$$375$$ 0 0
$$376$$ 11.1213 + 6.42090i 0.573538 + 0.331132i
$$377$$ −1.26080 −0.0649344
$$378$$ 0 0
$$379$$ −7.48528 −0.384493 −0.192247 0.981347i $$-0.561577\pi$$
−0.192247 + 0.981347i $$0.561577\pi$$
$$380$$ −10.3923 6.00000i −0.533114 0.307794i
$$381$$ 0 0
$$382$$ 10.6066 + 18.3712i 0.542681 + 0.939951i
$$383$$ −2.74666 + 4.75736i −0.140348 + 0.243090i −0.927628 0.373506i $$-0.878155\pi$$
0.787280 + 0.616596i $$0.211489\pi$$
$$384$$ 0 0
$$385$$ −25.4558 + 10.3923i −1.29735 + 0.529641i
$$386$$ 1.48528i 0.0755988i
$$387$$ 0 0
$$388$$ 2.74264 1.58346i 0.139236 0.0803882i
$$389$$ 13.4361 7.75736i 0.681239 0.393314i −0.119082 0.992884i $$-0.537995\pi$$
0.800322 + 0.599571i $$0.204662\pi$$
$$390$$ 0 0
$$391$$ 14.6969i 0.743256i
$$392$$ −4.89898 5.00000i −0.247436 0.252538i
$$393$$ 0 0
$$394$$ 8.48528 14.6969i 0.427482 0.740421i
$$395$$ 0.927572 + 1.60660i 0.0466712 + 0.0808369i
$$396$$ 0 0
$$397$$ −13.1360 7.58410i −0.659279 0.380635i 0.132723 0.991153i $$-0.457628\pi$$
−0.792002 + 0.610518i $$0.790961\pi$$
$$398$$ −20.9077 −1.04801
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ −17.1104 9.87868i −0.854451 0.493318i 0.00769892 0.999970i $$-0.497549\pi$$
−0.862150 + 0.506653i $$0.830883\pi$$
$$402$$ 0 0
$$403$$ −3.25736 5.64191i −0.162261 0.281044i
$$404$$ −3.67423 + 6.36396i −0.182800 + 0.316619i
$$405$$ 0 0
$$406$$ 4.60660 + 0.630399i 0.228622 + 0.0312862i
$$407$$ 22.2426i 1.10253i
$$408$$ 0 0
$$409$$ −3.25736 + 1.88064i −0.161066 + 0.0929915i −0.578366 0.815777i $$-0.696310\pi$$
0.417300 + 0.908769i $$0.362976\pi$$
$$410$$ 5.19615 3.00000i 0.256620 0.148159i
$$411$$ 0 0
$$412$$ 11.1097i 0.547338i
$$413$$ −3.97141 + 5.12132i −0.195420 + 0.252004i
$$414$$ 0 0
$$415$$ −18.7279 + 32.4377i −0.919318 + 1.59230i
$$416$$ −0.358719 0.621320i −0.0175877 0.0304627i
$$417$$ 0 0
$$418$$ −18.0000 10.3923i −0.880409 0.508304i
$$419$$ 7.94282 0.388032 0.194016 0.980998i $$-0.437849\pi$$
0.194016 + 0.980998i $$0.437849\pi$$
$$420$$ 0 0
$$421$$ −23.4558 −1.14317 −0.571584 0.820544i $$-0.693671\pi$$
−0.571584 + 0.820544i $$0.693671\pi$$
$$422$$ 3.01834 + 1.74264i 0.146931 + 0.0848304i
$$423$$ 0 0
$$424$$ −7.24264 12.5446i −0.351734 0.609221i
$$425$$ 1.22474 2.12132i 0.0594089 0.102899i
$$426$$ 0 0
$$427$$ 1.50000 10.9612i 0.0725901 0.530448i
$$428$$ 2.48528i 0.120131i
$$429$$ 0 0
$$430$$ 14.8492 8.57321i 0.716094 0.413437i
$$431$$ 1.52192 0.878680i 0.0733082 0.0423245i −0.462898 0.886412i $$-0.653190\pi$$
0.536206 + 0.844087i $$0.319857\pi$$
$$432$$ 0 0
$$433$$ 2.57258i 0.123630i −0.998088 0.0618152i $$-0.980311\pi$$
0.998088 0.0618152i $$-0.0196889\pi$$
$$434$$ 9.08052 + 22.2426i 0.435879 + 1.06768i
$$435$$ 0 0
$$436$$ −8.86396 + 15.3528i −0.424507 + 0.735267i
$$437$$ −14.6969 25.4558i −0.703050 1.21772i
$$438$$ 0 0
$$439$$ 3.72792 + 2.15232i 0.177924 + 0.102724i 0.586317 0.810082i $$-0.300577\pi$$
−0.408393 + 0.912806i $$0.633911\pi$$
$$440$$ 10.3923 0.495434
$$441$$ 0 0
$$442$$ −1.75736 −0.0835891
$$443$$ −22.0454 12.7279i −1.04741 0.604722i −0.125486 0.992095i $$-0.540049\pi$$
−0.921923 + 0.387374i $$0.873382\pi$$
$$444$$ 0 0
$$445$$ −3.72792 6.45695i −0.176720 0.306089i
$$446$$ −5.19615 + 9.00000i −0.246045 + 0.426162i
$$447$$ 0 0
$$448$$ 1.00000 + 2.44949i 0.0472456 + 0.115728i
$$449$$ 5.27208i 0.248805i −0.992232 0.124402i $$-0.960299\pi$$
0.992232 0.124402i $$-0.0397014\pi$$
$$450$$ 0 0
$$451$$ 9.00000 5.19615i 0.423793 0.244677i
$$452$$ 8.87039 5.12132i 0.417228 0.240887i
$$453$$ 0 0
$$454$$ 25.0892i 1.17750i
$$455$$ 0.630399 4.60660i 0.0295536 0.215961i
$$456$$ 0 0
$$457$$ 11.5000 19.9186i 0.537947 0.931752i −0.461067 0.887365i $$-0.652533\pi$$
0.999014 0.0443868i $$-0.0141334\pi$$
$$458$$ −2.80821 4.86396i −0.131219 0.227278i
$$459$$ 0 0
$$460$$ 12.7279 + 7.34847i 0.593442 + 0.342624i
$$461$$ 21.4511 0.999076 0.499538 0.866292i $$-0.333503\pi$$
0.499538 + 0.866292i $$0.333503\pi$$
$$462$$ 0 0
$$463$$ −22.0000 −1.02243 −0.511213 0.859454i $$-0.670804\pi$$
−0.511213 + 0.859454i $$0.670804\pi$$
$$464$$ −1.52192 0.878680i −0.0706533 0.0407917i
$$465$$ 0 0
$$466$$ 10.2426 + 17.7408i 0.474481 + 0.821825i
$$467$$ −8.87039 + 15.3640i −0.410473 + 0.710959i −0.994941 0.100457i $$-0.967970\pi$$
0.584469 + 0.811416i $$0.301303\pi$$
$$468$$ 0 0
$$469$$ −21.8640 + 28.1946i −1.00958 + 1.30191i
$$470$$ 31.4558i 1.45095i
$$471$$ 0 0
$$472$$ 2.12132 1.22474i 0.0976417 0.0563735i
$$473$$ 25.7196 14.8492i 1.18259 0.682769i
$$474$$ 0 0
$$475$$ 4.89898i 0.224781i
$$476$$ 6.42090 + 0.878680i 0.294301 + 0.0402742i
$$477$$ 0 0
$$478$$ 8.12132 14.0665i 0.371461 0.643389i
$$479$$ −1.22474 2.12132i −0.0559600 0.0969256i 0.836688 0.547679i $$-0.184489\pi$$
−0.892648 + 0.450754i $$0.851155\pi$$
$$480$$ 0 0
$$481$$ −3.25736 1.88064i −0.148523 0.0857497i
$$482$$ −1.13770 −0.0518210
$$483$$ 0 0
$$484$$ 7.00000 0.318182
$$485$$ −6.71807 3.87868i −0.305052 0.176122i
$$486$$ 0 0
$$487$$ −11.0000 19.0526i −0.498458 0.863354i 0.501541 0.865134i $$-0.332767\pi$$
−0.999998 + 0.00178012i $$0.999433\pi$$
$$488$$ −2.09077 + 3.62132i −0.0946447 + 0.163929i
$$489$$ 0 0
$$490$$ −4.60660 + 16.5160i −0.208105 + 0.746118i
$$491$$ 34.9706i 1.57820i −0.614265 0.789100i $$-0.710547\pi$$
0.614265 0.789100i $$-0.289453\pi$$
$$492$$ 0 0
$$493$$ −3.72792 + 2.15232i −0.167897 + 0.0969355i
$$494$$ 3.04384 1.75736i 0.136949 0.0790673i
$$495$$ 0 0
$$496$$ 9.08052i 0.407727i
$$497$$ 31.1769 12.7279i 1.39848 0.570925i
$$498$$ 0 0
$$499$$ 12.2279 21.1794i 0.547397 0.948119i −0.451055 0.892496i $$-0.648952\pi$$
0.998452 0.0556231i $$-0.0177145\pi$$
$$500$$ 4.89898 + 8.48528i 0.219089 + 0.379473i
$$501$$ 0 0
$$502$$ 13.2426 + 7.64564i 0.591048 + 0.341242i
$$503$$ −0.594346 −0.0265006 −0.0132503 0.999912i $$-0.504218\pi$$
−0.0132503 + 0.999912i $$0.504218\pi$$
$$504$$ 0 0
$$505$$ 18.0000 0.800989
$$506$$ 22.0454 + 12.7279i 0.980038 + 0.565825i
$$507$$ 0 0
$$508$$ −3.86396 6.69258i −0.171436 0.296935i
$$509$$ 4.60181 7.97056i 0.203971 0.353289i −0.745833 0.666133i $$-0.767948\pi$$
0.949805 + 0.312844i $$0.101282\pi$$
$$510$$ 0 0
$$511$$ 11.4853 + 8.90644i 0.508079 + 0.393998i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ −21.7279 + 12.5446i −0.958378 + 0.553320i
$$515$$ 23.5673 13.6066i 1.03850 0.599579i
$$516$$ 0 0
$$517$$ 54.4831i 2.39616i
$$518$$ 10.9612 + 8.50000i 0.481606 + 0.373469i
$$519$$ 0 0
$$520$$ −0.878680 + 1.52192i −0.0385327 + 0.0667405i
$$521$$ 14.9941 + 25.9706i 0.656904 + 1.13779i 0.981413 + 0.191908i $$0.0614676\pi$$
−0.324509 + 0.945883i $$0.605199\pi$$
$$522$$ 0 0
$$523$$ 23.7426 + 13.7078i 1.03819 + 0.599401i 0.919321 0.393508i $$-0.128739\pi$$
0.118872 + 0.992910i $$0.462072\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −6.72792 −0.293351
$$527$$ −19.2627 11.1213i −0.839096 0.484452i
$$528$$ 0 0
$$529$$ 6.50000 + 11.2583i 0.282609 + 0.489493i
$$530$$ −17.7408 + 30.7279i −0.770610 + 1.33474i
$$531$$ 0 0
$$532$$ −12.0000 + 4.89898i −0.520266 + 0.212398i
$$533$$ 1.75736i 0.0761197i
$$534$$ 0 0
$$535$$ −5.27208 + 3.04384i −0.227932 + 0.131596i
$$536$$ 11.6786 6.74264i 0.504439 0.291238i
$$537$$ 0 0
$$538$$ 9.79796i 0.422420i
$$539$$ −7.97887 + 28.6066i −0.343674 + 1.23217i
$$540$$ 0 0
$$541$$ 2.72792 4.72490i 0.117283 0.203139i −0.801407 0.598119i $$-0.795915\pi$$
0.918690 + 0.394980i $$0.129248\pi$$
$$542$$ −9.43924 16.3492i −0.405450 0.702260i
$$543$$ 0 0
$$544$$ −2.12132 1.22474i −0.0909509 0.0525105i
$$545$$ 43.4244 1.86010
$$546$$ 0 0
$$547$$ 39.9706 1.70902 0.854509 0.519437i $$-0.173858\pi$$
0.854509 + 0.519437i $$0.173858\pi$$
$$548$$ −5.19615 3.00000i −0.221969 0.128154i
$$549$$ 0 0
$$550$$ −2.12132 3.67423i −0.0904534 0.156670i
$$551$$ 4.30463 7.45584i 0.183384 0.317630i
$$552$$ 0 0
$$553$$ 1.98528 + 0.271680i 0.0844228 + 0.0115530i
$$554$$ 23.7279i 1.00810i
$$555$$ 0 0
$$556$$ 6.98528 4.03295i 0.296242 0.171035i
$$557$$ −18.3712 + 10.6066i −0.778412 + 0.449416i −0.835867 0.548932i $$-0.815035\pi$$
0.0574555 + 0.998348i $$0.481701\pi$$
$$558$$ 0 0
$$559$$ 5.02207i 0.212411i
$$560$$ 3.97141 5.12132i 0.167823 0.216415i
$$561$$ 0 0
$$562$$ −6.87868 + 11.9142i −0.290160 + 0.502571i
$$563$$ 22.9369 + 39.7279i 0.966676 + 1.67433i 0.705043 + 0.709165i $$0.250928\pi$$
0.261634 + 0.965167i $$0.415739\pi$$
$$564$$ 0 0
$$565$$ −21.7279 12.5446i −0.914101 0.527756i
$$566$$ 6.03668 0.253741
$$567$$ 0 0
$$568$$ −12.7279 −0.534052
$$569$$ −8.87039 5.12132i −0.371866 0.214697i 0.302407 0.953179i $$-0.402210\pi$$
−0.674273 + 0.738482i $$0.735543\pi$$
$$570$$ 0 0
$$571$$ 11.0000 + 19.0526i 0.460336 + 0.797325i 0.998978 0.0452101i $$-0.0143957\pi$$
−0.538642 + 0.842535i $$0.681062\pi$$
$$572$$ −1.52192 + 2.63604i −0.0636346 + 0.110218i
$$573$$ 0 0
$$574$$ 0.878680 6.42090i 0.0366754 0.268003i
$$575$$ 6.00000i 0.250217i
$$576$$ 0 0
$$577$$ 23.7426 13.7078i 0.988419 0.570664i 0.0836177 0.996498i $$-0.473353\pi$$
0.904801 + 0.425834i $$0.140019\pi$$
$$578$$ 9.52628 5.50000i 0.396241 0.228770i
$$579$$ 0 0
$$580$$ 4.30463i 0.178740i
$$581$$ 15.2913 + 37.4558i 0.634389 + 1.55393i
$$582$$ 0 0
$$583$$ −30.7279 + 53.2223i −1.27262 + 2.20424i
$$584$$ −2.74666 4.75736i −0.113658 0.196861i
$$585$$ 0 0
$$586$$ 11.1213 + 6.42090i 0.459418 + 0.265245i
$$587$$ 32.4377 1.33885 0.669424 0.742881i $$-0.266541\pi$$
0.669424 + 0.742881i $$0.266541\pi$$
$$588$$ 0 0
$$589$$ 44.4853 1.83298
$$590$$ −5.19615 3.00000i −0.213922 0.123508i
$$591$$ 0 0
$$592$$ −2.62132 4.54026i −0.107736 0.186604i
$$593$$ 0.927572 1.60660i 0.0380908 0.0659752i −0.846352 0.532625i $$-0.821206\pi$$
0.884442 + 0.466650i $$0.154539\pi$$
$$594$$ 0 0
$$595$$ −6.00000 14.6969i −0.245976 0.602516i
$$596$$ 16.2426i 0.665324i
$$597$$ 0 0
$$598$$ −3.72792 + 2.15232i −0.152446 + 0.0880148i
$$599$$ 3.04384 1.75736i 0.124368 0.0718038i −0.436526 0.899692i $$-0.643791\pi$$
0.560893 + 0.827888i $$0.310458\pi$$
$$600$$ 0 0
$$601$$ 41.5182i 1.69356i −0.531940 0.846782i $$-0.678537\pi$$
0.531940 0.846782i $$-0.321463\pi$$
$$602$$ 2.51104 18.3492i 0.102342 0.747859i
$$603$$ 0 0
$$604$$ 4.37868 7.58410i 0.178166 0.308592i
$$605$$ −8.57321 14.8492i −0.348551 0.603708i
$$606$$ 0 0
$$607$$ 31.2426 + 18.0379i 1.26810 + 0.732138i 0.974628 0.223830i $$-0.0718561\pi$$
0.293471 + 0.955968i $$0.405189\pi$$
$$608$$ 4.89898 0.198680
$$609$$ 0 0
$$610$$ 10.2426 0.414712
$$611$$ 7.97887 + 4.60660i 0.322790 + 0.186363i
$$612$$ 0 0
$$613$$ 14.1066 + 24.4334i 0.569760 + 0.986854i 0.996589 + 0.0825214i $$0.0262973\pi$$
−0.426829 + 0.904332i $$0.640369\pi$$
$$614$$ 13.4106 23.2279i 0.541210 0.937403i
$$615$$ 0 0
$$616$$ 6.87868 8.87039i 0.277150 0.357398i
$$617$$ 4.24264i 0.170802i −0.996347 0.0854011i $$-0.972783\pi$$
0.996347 0.0854011i $$-0.0272172\pi$$
$$618$$ 0 0
$$619$$ −11.0147 + 6.35935i −0.442719 + 0.255604i −0.704750 0.709455i $$-0.748941\pi$$
0.262031 + 0.965059i $$0.415608\pi$$
$$620$$ −19.2627 + 11.1213i −0.773608 + 0.446643i
$$621$$ 0 0
$$622$$ 17.1464i 0.687509i
$$623$$ −7.97887 1.09188i −0.319667 0.0437454i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ −10.0951 17.4853i −0.403483 0.698852i
$$627$$ 0 0
$$628$$ −9.00000 5.19615i −0.359139 0.207349i
$$629$$ −12.8418 −0.512036
$$630$$ 0 0
$$631$$ −14.7574 −0.587481 −0.293741 0.955885i $$-0.594900\pi$$
−0.293741 + 0.955885i $$0.594900\pi$$
$$632$$ −0.655892 0.378680i −0.0260900 0.0150631i
$$633$$ 0 0
$$634$$ −11.1213 19.2627i −0.441684 0.765019i
$$635$$ −9.46473 + 16.3934i −0.375596 + 0.650552i
$$636$$ 0 0
$$637$$ −3.51472 3.58719i −0.139258 0.142130i
$$638$$ 7.45584i 0.295180i
$$639$$ 0 0
$$640$$ −2.12132 + 1.22474i −0.0838525 + 0.0484123i
$$641$$ 28.7635 16.6066i 1.13609 0.655921i 0.190630 0.981662i $$-0.438947\pi$$
0.945459 + 0.325741i $$0.105614\pi$$
$$642$$ 0 0
$$643$$ 1.73205i 0.0683054i 0.999417 + 0.0341527i $$0.0108733\pi$$
−0.999417 + 0.0341527i $$0.989127\pi$$
$$644$$ 14.6969 6.00000i 0.579141 0.236433i
$$645$$ 0 0
$$646$$ 6.00000 10.3923i 0.236067 0.408880i
$$647$$ −10.3923 18.0000i −0.408564 0.707653i 0.586165 0.810191i $$-0.300637\pi$$
−0.994729 + 0.102538i $$0.967304\pi$$
$$648$$ 0 0
$$649$$ −9.00000 5.19615i −0.353281 0.203967i
$$650$$ 0.717439 0.0281403
$$651$$ 0 0
$$652$$ 9.48528 0.371472
$$653$$ −2.15232 1.24264i −0.0842267 0.0486283i 0.457295 0.889315i $$-0.348818\pi$$
−0.541522 + 0.840687i $$0.682152\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.22474 + 2.12132i −0.0478183 + 0.0828236i
$$657$$ 0 0
$$658$$ −26.8492 20.8207i −1.04669 0.811674i
$$659$$ 22.2426i 0.866450i −0.901286 0.433225i $$-0.857376\pi$$
0.901286 0.433225i $$-0.142624\pi$$
$$660$$ 0 0
$$661$$ −4.24264 + 2.44949i −0.165020 + 0.0952741i −0.580235 0.814449i $$-0.697039\pi$$
0.415216 + 0.909723i $$0.363706\pi$$
$$662$$ −8.66025 + 5.00000i −0.336590 + 0.194331i
$$663$$ 0 0
$$664$$ 15.2913i 0.593417i
$$665$$ 25.0892 + 19.4558i 0.972919 + 0.754465i
$$666$$ 0 0
$$667$$ −5.27208 + 9.13151i −0.204136 + 0.353573i
$$668$$ 0.297173 + 0.514719i 0.0114980 + 0.0199151i
$$669$$ 0 0
$$670$$ −28.6066 16.5160i −1.10517 0.638070i
$$671$$ 17.7408 0.684875
$$672$$ 0 0
$$673$$ −45.4558 −1.75219 −0.876097 0.482135i $$-0.839862\pi$$
−0.876097 + 0.482135i $$0.839862\pi$$
$$674$$ −18.5813 10.7279i −0.715725 0.413224i
$$675$$ 0 0
$$676$$ 6.24264 + 10.8126i 0.240102 + 0.415868i
$$677$$ 7.34847 12.7279i 0.282425 0.489174i −0.689557 0.724232i $$-0.742195\pi$$
0.971981 + 0.235058i $$0.0755280\pi$$
$$678$$ 0 0
$$679$$ −7.75736 + 3.16693i −0.297700 + 0.121536i
$$680$$ 6.00000i 0.230089i
$$681$$ 0 0
$$682$$ −33.3640 + 19.2627i −1.27757 + 0.737607i
$$683$$ 8.87039 5.12132i 0.339416 0.195962i −0.320598 0.947215i $$-0.603884\pi$$
0.660014 + 0.751254i $$0.270550\pi$$
$$684$$ 0 0
$$685$$ 14.6969i 0.561541i
$$686$$ 11.0482 + 14.8640i 0.421822 + 0.567509i
$$687$$ 0 0
$$688$$ −3.50000 + 6.06218i −0.133436 + 0.231118i
$$689$$ −5.19615 9.00000i −0.197958 0.342873i
$$690$$ 0 0
$$691$$ 2.22792 + 1.28629i 0.0847541 + 0.0489328i 0.541778 0.840522i $$-0.317751\pi$$
−0.457024 + 0.889454i $$0.651085\pi$$
$$692$$ 20.7846 0.790112
$$693$$ 0 0
$$694$$ −4.97056 −0.188680
$$695$$ −17.1104 9.87868i −0.649034 0.374720i
$$696$$ 0 0
$$697$$ 3.00000 + 5.19615i 0.113633 + 0.196818i
$$698$$ −0.0615465 + 0.106602i −0.00232957 + 0.00403493i
$$699$$ 0 0
$$700$$ −2.62132 0.358719i −0.0990766 0.0135583i
$$701$$ 20.4853i 0.773718i −0.922139 0.386859i $$-0.873560\pi$$
0.922139 0.386859i $$-0.126440\pi$$
$$702$$ 0 0
$$703$$ 22.2426 12.8418i 0.838897 0.484337i
$$704$$ −3.67423 + 2.12132i −0.138478 + 0.0799503i
$$705$$ 0 0
$$706$$ 10.9867i 0.413488i
$$707$$ 11.9142 15.3640i 0.448080 0.577821i
$$708$$ 0 0
$$709$$ −8.10660 + 14.0410i −0.304450 + 0.527323i −0.977139 0.212603i $$-0.931806\pi$$
0.672689 + 0.739925i $$0.265139\pi$$
$$710$$ 15.5885 + 27.0000i 0.585024 + 1.01329i
$$711$$ 0 0
$$712$$ 2.63604 + 1.52192i 0.0987897 + 0.0570363i
$$713$$ −54.4831 −2.04041
$$714$$ 0 0
$$715$$ 7.45584 0.278833
$$716$$ 5.82655 + 3.36396i 0.217748 + 0.125717i
$$717$$ 0 0
$$718$$ −7.24264 12.5446i −0.270293 0.468161i
$$719$$ −26.3140 + 45.5772i −0.981346 + 1.69974i −0.324181 + 0.945995i $$0.605089\pi$$
−0.657166 + 0.753746i $$0.728245\pi$$
$$720$$ 0 0
$$721$$ 3.98528 29.1222i 0.148420 1.08457i
$$722$$ 5.00000i 0.186081i
$$723$$ 0 0
$$724$$ −8.48528 + 4.89898i −0.315353 + 0.182069i
$$725$$ 1.52192 0.878680i 0.0565226 0.0326333i
$$726$$ 0 0
$$727$$ 28.0821i 1.04151i 0.853707 + 0.520754i $$0.174349\pi$$
−0.853707 + 0.520754i $$0.825651\pi$$
$$728$$ 0.717439 + 1.75736i 0.0265901 + 0.0651321i
$$729$$ 0 0
$$730$$ −6.72792 + 11.6531i −0.249012 + 0.431301i
$$731$$ 8.57321 + 14.8492i 0.317092 + 0.549219i
$$732$$ 0 0
$$733$$ 1.13604 + 0.655892i 0.0419606 + 0.0242259i 0.520834 0.853658i $$-0.325621\pi$$
−0.478873 + 0.877884i $$0.658955\pi$$
$$734$$ −29.9882 −1.10689
$$735$$ 0 0
$$736$$ −6.00000 −0.221163
$$737$$ −49.5481 28.6066i −1.82513 1.05374i
$$738$$ 0 0
$$739$$ 4.22792 + 7.32298i 0.155527 + 0.269380i 0.933251 0.359226i $$-0.116959\pi$$
−0.777724 + 0.628606i $$0.783626\pi$$
$$740$$ −6.42090 + 11.1213i −0.236037 + 0.408828i
$$741$$ 0 0
$$742$$ 14.4853 + 35.4815i 0.531771 + 1.30257i
$$743$$ 18.7279i 0.687061i −0.939142 0.343530i $$-0.888377\pi$$
0.939142 0.343530i $$-0.111623\pi$$
$$744$$ 0 0
$$745$$ 34.4558 19.8931i 1.26236 0.728826i
$$746$$ 19.0526 11.0000i 0.697564 0.402739i
$$747$$ 0 0
$$748$$ 10.3923i 0.379980i
$$749$$ −0.891519 + 6.51472i −0.0325754 + 0.238043i
$$750$$ 0 0
$$751$$ −26.7279 + 46.2941i −0.975316 + 1.68930i −0.296427 + 0.955056i $$0.595795\pi$$
−0.678889 + 0.734241i $$0.737538\pi$$
$$752$$ 6.42090 + 11.1213i 0.234146 + 0.405553i
$$753$$ 0 0
$$754$$ −1.09188 0.630399i −0.0397640 0.0229578i
$$755$$ −21.4511 −0.780684
$$756$$ 0 0
$$757$$ 32.7574 1.19059 0.595293 0.803509i $$-0.297036\pi$$
0.595293 + 0.803509i $$0.297036\pi$$
$$758$$ −6.48244 3.74264i −0.235453 0.135939i
$$759$$ 0 0
$$760$$ −6.00000 10.3923i −0.217643 0.376969i
$$761$$ −12.2474 + 21.2132i −0.443970 + 0.768978i −0.997980 0.0635319i $$-0.979764\pi$$
0.554010 + 0.832510i $$0.313097\pi$$
$$762$$ 0 0
$$763$$ 28.7426 37.0650i 1.04055 1.34184i
$$764$$ 21.2132i 0.767467i
$$765$$ 0 0
$$766$$ −4.75736 + 2.74666i −0.171890 + 0.0992410i
$$767$$ 1.52192 0.878680i 0.0549533 0.0317273i
$$768$$ 0 0
$$769$$ 40.3805i 1.45616i 0.685493 + 0.728080i $$0.259587\pi$$
−0.685493 + 0.728080i $$0.740413\pi$$
$$770$$ −27.2416 3.72792i −0.981718 0.134345i
$$771$$ 0 0
$$772$$ −0.742641 + 1.28629i −0.0267282 + 0.0462946i
$$773$$ 4.89898 + 8.48528i 0.176204 + 0.305194i 0.940577 0.339580i $$-0.110285\pi$$
−0.764373 + 0.644774i $$0.776951\pi$$
$$774$$ 0 0
$$775$$ 7.86396 + 4.54026i 0.282482 + 0.163091i
$$776$$ 3.16693 0.113686
$$777$$ 0 0
$$778$$ 15.5147 0.556230
$$779$$ −10.3923 6.00000i −0.372343 0.214972i
$$780$$ 0 0
$$781$$ 27.0000 + 46.7654i 0.966136 + 1.67340i
$$782$$ −7.34847 + 12.7279i −0.262781 + 0.455150i
$$783$$ 0 0
$$784$$ −1.74264 6.77962i −0.0622372 0.242129i
$$785$$ 25.4558i 0.908558i
$$786$$ 0 0
$$787$$ −24.4706 + 14.1281i −0.872281 + 0.503612i −0.868106 0.496379i $$-0.834662\pi$$
−0.00417567 + 0.999991i $$0.501329\pi$$
$$788$$ 14.6969 8.48528i 0.523557