# Properties

 Label 378.2.f.d.127.2 Level $378$ Weight $2$ Character 378.127 Analytic conductor $3.018$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 378.f (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.01834519640$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} - 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 127.2 Root $$-1.22474 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 378.127 Dual form 378.2.f.d.253.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.72474 + 2.98735i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.72474 + 2.98735i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +3.44949 q^{10} +(1.00000 - 1.73205i) q^{11} +(2.44949 + 4.24264i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +7.44949 q^{19} +(1.72474 - 2.98735i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-3.44949 + 5.97469i) q^{25} +4.89898 q^{26} -1.00000 q^{28} +(1.44949 - 2.51059i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +3.44949 q^{35} -7.79796 q^{37} +(3.72474 - 6.45145i) q^{38} +(-1.72474 - 2.98735i) q^{40} +(-4.89898 - 8.48528i) q^{41} +(1.44949 - 2.51059i) q^{43} -2.00000 q^{44} -1.00000 q^{46} +(-4.89898 + 8.48528i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(3.44949 + 5.97469i) q^{50} +(2.44949 - 4.24264i) q^{52} +1.10102 q^{53} +6.89898 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.44949 - 2.51059i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(-5.72474 + 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-8.44949 + 14.6349i) q^{65} +(1.55051 + 2.68556i) q^{67} +(1.00000 + 1.73205i) q^{68} +(1.72474 - 2.98735i) q^{70} -9.89898 q^{71} +2.89898 q^{73} +(-3.89898 + 6.75323i) q^{74} +(-3.72474 - 6.45145i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(-3.94949 + 6.84072i) q^{79} -3.44949 q^{80} -9.79796 q^{82} +(1.00000 - 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} +(-1.44949 - 2.51059i) q^{86} +(-1.00000 + 1.73205i) q^{88} +7.10102 q^{89} +4.89898 q^{91} +(-0.500000 + 0.866025i) q^{92} +(4.89898 + 8.48528i) q^{94} +(12.8485 + 22.2542i) q^{95} +(3.44949 - 5.97469i) q^{97} -1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 4 q^{8} + O(q^{10})$$ $$4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{11} - 2 q^{14} - 2 q^{16} - 8 q^{17} + 20 q^{19} + 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{28} - 4 q^{29} - 12 q^{31} + 2 q^{32} - 4 q^{34} + 4 q^{35} + 8 q^{37} + 10 q^{38} - 2 q^{40} - 4 q^{43} - 8 q^{44} - 4 q^{46} - 2 q^{49} + 4 q^{50} + 24 q^{53} + 8 q^{55} - 2 q^{56} + 4 q^{58} - 4 q^{59} - 18 q^{61} - 24 q^{62} + 4 q^{64} - 24 q^{65} + 16 q^{67} + 4 q^{68} + 2 q^{70} - 20 q^{71} - 8 q^{73} + 4 q^{74} - 10 q^{76} - 4 q^{77} - 6 q^{79} - 4 q^{80} + 4 q^{83} - 4 q^{85} + 4 q^{86} - 4 q^{88} + 48 q^{89} - 2 q^{92} + 22 q^{95} + 4 q^{97} - 4 q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$29$$ $$325$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 1.72474 + 2.98735i 0.771329 + 1.33598i 0.936835 + 0.349773i $$0.113741\pi$$
−0.165505 + 0.986209i $$0.552925\pi$$
$$6$$ 0 0
$$7$$ 0.500000 0.866025i 0.188982 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 3.44949 1.09082
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ 0 0
$$13$$ 2.44949 + 4.24264i 0.679366 + 1.17670i 0.975172 + 0.221449i $$0.0710785\pi$$
−0.295806 + 0.955248i $$0.595588\pi$$
$$14$$ −0.500000 0.866025i −0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 7.44949 1.70903 0.854515 0.519427i $$-0.173854\pi$$
0.854515 + 0.519427i $$0.173854\pi$$
$$20$$ 1.72474 2.98735i 0.385665 0.667991i
$$21$$ 0 0
$$22$$ −1.00000 1.73205i −0.213201 0.369274i
$$23$$ −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i $$-0.199913\pi$$
−0.913434 + 0.406986i $$0.866580\pi$$
$$24$$ 0 0
$$25$$ −3.44949 + 5.97469i −0.689898 + 1.19494i
$$26$$ 4.89898 0.960769
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ 1.44949 2.51059i 0.269163 0.466205i −0.699483 0.714650i $$-0.746586\pi$$
0.968646 + 0.248445i $$0.0799195\pi$$
$$30$$ 0 0
$$31$$ −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i $$-0.985539\pi$$
0.460152 0.887840i $$-0.347795\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ −1.00000 + 1.73205i −0.171499 + 0.297044i
$$35$$ 3.44949 0.583070
$$36$$ 0 0
$$37$$ −7.79796 −1.28198 −0.640988 0.767551i $$-0.721475\pi$$
−0.640988 + 0.767551i $$0.721475\pi$$
$$38$$ 3.72474 6.45145i 0.604233 1.04656i
$$39$$ 0 0
$$40$$ −1.72474 2.98735i −0.272706 0.472341i
$$41$$ −4.89898 8.48528i −0.765092 1.32518i −0.940198 0.340629i $$-0.889360\pi$$
0.175106 0.984550i $$-0.443973\pi$$
$$42$$ 0 0
$$43$$ 1.44949 2.51059i 0.221045 0.382861i −0.734080 0.679062i $$-0.762387\pi$$
0.955126 + 0.296201i $$0.0957199\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ −4.89898 + 8.48528i −0.714590 + 1.23771i 0.248528 + 0.968625i $$0.420053\pi$$
−0.963118 + 0.269081i $$0.913280\pi$$
$$48$$ 0 0
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ 3.44949 + 5.97469i 0.487832 + 0.844949i
$$51$$ 0 0
$$52$$ 2.44949 4.24264i 0.339683 0.588348i
$$53$$ 1.10102 0.151237 0.0756184 0.997137i $$-0.475907\pi$$
0.0756184 + 0.997137i $$0.475907\pi$$
$$54$$ 0 0
$$55$$ 6.89898 0.930258
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 0 0
$$58$$ −1.44949 2.51059i −0.190327 0.329657i
$$59$$ −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i $$-0.208225\pi$$
−0.923749 + 0.382998i $$0.874892\pi$$
$$60$$ 0 0
$$61$$ −5.72474 + 9.91555i −0.732978 + 1.26956i 0.222626 + 0.974904i $$0.428537\pi$$
−0.955605 + 0.294652i $$0.904796\pi$$
$$62$$ −6.00000 −0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −8.44949 + 14.6349i −1.04803 + 1.81524i
$$66$$ 0 0
$$67$$ 1.55051 + 2.68556i 0.189425 + 0.328094i 0.945059 0.326901i $$-0.106004\pi$$
−0.755634 + 0.654994i $$0.772671\pi$$
$$68$$ 1.00000 + 1.73205i 0.121268 + 0.210042i
$$69$$ 0 0
$$70$$ 1.72474 2.98735i 0.206146 0.357056i
$$71$$ −9.89898 −1.17479 −0.587396 0.809299i $$-0.699847\pi$$
−0.587396 + 0.809299i $$0.699847\pi$$
$$72$$ 0 0
$$73$$ 2.89898 0.339300 0.169650 0.985504i $$-0.445736\pi$$
0.169650 + 0.985504i $$0.445736\pi$$
$$74$$ −3.89898 + 6.75323i −0.453247 + 0.785047i
$$75$$ 0 0
$$76$$ −3.72474 6.45145i −0.427258 0.740032i
$$77$$ −1.00000 1.73205i −0.113961 0.197386i
$$78$$ 0 0
$$79$$ −3.94949 + 6.84072i −0.444352 + 0.769641i −0.998007 0.0631057i $$-0.979899\pi$$
0.553655 + 0.832746i $$0.313233\pi$$
$$80$$ −3.44949 −0.385665
$$81$$ 0 0
$$82$$ −9.79796 −1.08200
$$83$$ 1.00000 1.73205i 0.109764 0.190117i −0.805910 0.592037i $$-0.798324\pi$$
0.915675 + 0.401920i $$0.131657\pi$$
$$84$$ 0 0
$$85$$ −3.44949 5.97469i −0.374150 0.648046i
$$86$$ −1.44949 2.51059i −0.156302 0.270724i
$$87$$ 0 0
$$88$$ −1.00000 + 1.73205i −0.106600 + 0.184637i
$$89$$ 7.10102 0.752707 0.376353 0.926476i $$-0.377178\pi$$
0.376353 + 0.926476i $$0.377178\pi$$
$$90$$ 0 0
$$91$$ 4.89898 0.513553
$$92$$ −0.500000 + 0.866025i −0.0521286 + 0.0902894i
$$93$$ 0 0
$$94$$ 4.89898 + 8.48528i 0.505291 + 0.875190i
$$95$$ 12.8485 + 22.2542i 1.31823 + 2.28323i
$$96$$ 0 0
$$97$$ 3.44949 5.97469i 0.350243 0.606638i −0.636049 0.771649i $$-0.719432\pi$$
0.986292 + 0.165011i $$0.0527658\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ 6.89898 0.689898
$$101$$ 3.62372 6.27647i 0.360574 0.624533i −0.627481 0.778632i $$-0.715914\pi$$
0.988055 + 0.154099i $$0.0492475\pi$$
$$102$$ 0 0
$$103$$ −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i $$-0.924396\pi$$
0.282194 0.959357i $$-0.408938\pi$$
$$104$$ −2.44949 4.24264i −0.240192 0.416025i
$$105$$ 0 0
$$106$$ 0.550510 0.953512i 0.0534703 0.0926132i
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −16.6969 −1.59928 −0.799638 0.600482i $$-0.794975\pi$$
−0.799638 + 0.600482i $$0.794975\pi$$
$$110$$ 3.44949 5.97469i 0.328896 0.569664i
$$111$$ 0 0
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ −7.94949 13.7689i −0.747825 1.29527i −0.948863 0.315688i $$-0.897765\pi$$
0.201038 0.979583i $$-0.435569\pi$$
$$114$$ 0 0
$$115$$ 1.72474 2.98735i 0.160833 0.278571i
$$116$$ −2.89898 −0.269163
$$117$$ 0 0
$$118$$ −2.00000 −0.184115
$$119$$ −1.00000 + 1.73205i −0.0916698 + 0.158777i
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 5.72474 + 9.91555i 0.518294 + 0.897712i
$$123$$ 0 0
$$124$$ −3.00000 + 5.19615i −0.269408 + 0.466628i
$$125$$ −6.55051 −0.585895
$$126$$ 0 0
$$127$$ −3.00000 −0.266207 −0.133103 0.991102i $$-0.542494\pi$$
−0.133103 + 0.991102i $$0.542494\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ 8.44949 + 14.6349i 0.741069 + 1.28357i
$$131$$ −6.72474 11.6476i −0.587544 1.01766i −0.994553 0.104232i $$-0.966762\pi$$
0.407009 0.913424i $$-0.366572\pi$$
$$132$$ 0 0
$$133$$ 3.72474 6.45145i 0.322976 0.559411i
$$134$$ 3.10102 0.267887
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ −5.89898 + 10.2173i −0.503984 + 0.872926i 0.496006 + 0.868319i $$0.334800\pi$$
−0.999989 + 0.00460626i $$0.998534\pi$$
$$138$$ 0 0
$$139$$ −4.72474 8.18350i −0.400748 0.694115i 0.593069 0.805152i $$-0.297916\pi$$
−0.993816 + 0.111037i $$0.964583\pi$$
$$140$$ −1.72474 2.98735i −0.145768 0.252477i
$$141$$ 0 0
$$142$$ −4.94949 + 8.57277i −0.415352 + 0.719411i
$$143$$ 9.79796 0.819346
$$144$$ 0 0
$$145$$ 10.0000 0.830455
$$146$$ 1.44949 2.51059i 0.119961 0.207778i
$$147$$ 0 0
$$148$$ 3.89898 + 6.75323i 0.320494 + 0.555112i
$$149$$ −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
$$151$$ 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i $$-0.768119\pi$$
0.949637 + 0.313353i $$0.101452\pi$$
$$152$$ −7.44949 −0.604233
$$153$$ 0 0
$$154$$ −2.00000 −0.161165
$$155$$ 10.3485 17.9241i 0.831209 1.43970i
$$156$$ 0 0
$$157$$ −3.17423 5.49794i −0.253332 0.438783i 0.711109 0.703081i $$-0.248193\pi$$
−0.964441 + 0.264298i $$0.914860\pi$$
$$158$$ 3.94949 + 6.84072i 0.314205 + 0.544218i
$$159$$ 0 0
$$160$$ −1.72474 + 2.98735i −0.136353 + 0.236170i
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ −0.202041 −0.0158251 −0.00791254 0.999969i $$-0.502519\pi$$
−0.00791254 + 0.999969i $$0.502519\pi$$
$$164$$ −4.89898 + 8.48528i −0.382546 + 0.662589i
$$165$$ 0 0
$$166$$ −1.00000 1.73205i −0.0776151 0.134433i
$$167$$ 9.34847 + 16.1920i 0.723406 + 1.25298i 0.959627 + 0.281277i $$0.0907579\pi$$
−0.236220 + 0.971700i $$0.575909\pi$$
$$168$$ 0 0
$$169$$ −5.50000 + 9.52628i −0.423077 + 0.732791i
$$170$$ −6.89898 −0.529128
$$171$$ 0 0
$$172$$ −2.89898 −0.221045
$$173$$ −6.44949 + 11.1708i −0.490346 + 0.849304i −0.999938 0.0111123i $$-0.996463\pi$$
0.509593 + 0.860416i $$0.329796\pi$$
$$174$$ 0 0
$$175$$ 3.44949 + 5.97469i 0.260757 + 0.451644i
$$176$$ 1.00000 + 1.73205i 0.0753778 + 0.130558i
$$177$$ 0 0
$$178$$ 3.55051 6.14966i 0.266122 0.460937i
$$179$$ 8.69694 0.650040 0.325020 0.945707i $$-0.394629\pi$$
0.325020 + 0.945707i $$0.394629\pi$$
$$180$$ 0 0
$$181$$ 4.34847 0.323219 0.161610 0.986855i $$-0.448331\pi$$
0.161610 + 0.986855i $$0.448331\pi$$
$$182$$ 2.44949 4.24264i 0.181568 0.314485i
$$183$$ 0 0
$$184$$ 0.500000 + 0.866025i 0.0368605 + 0.0638442i
$$185$$ −13.4495 23.2952i −0.988826 1.71270i
$$186$$ 0 0
$$187$$ −2.00000 + 3.46410i −0.146254 + 0.253320i
$$188$$ 9.79796 0.714590
$$189$$ 0 0
$$190$$ 25.6969 1.86425
$$191$$ 6.94949 12.0369i 0.502847 0.870957i −0.497147 0.867666i $$-0.665619\pi$$
0.999995 0.00329106i $$-0.00104758\pi$$
$$192$$ 0 0
$$193$$ 4.05051 + 7.01569i 0.291562 + 0.505000i 0.974179 0.225776i $$-0.0724917\pi$$
−0.682617 + 0.730776i $$0.739158\pi$$
$$194$$ −3.44949 5.97469i −0.247659 0.428958i
$$195$$ 0 0
$$196$$ −0.500000 + 0.866025i −0.0357143 + 0.0618590i
$$197$$ 12.6969 0.904619 0.452310 0.891861i $$-0.350600\pi$$
0.452310 + 0.891861i $$0.350600\pi$$
$$198$$ 0 0
$$199$$ 6.89898 0.489056 0.244528 0.969642i $$-0.421367\pi$$
0.244528 + 0.969642i $$0.421367\pi$$
$$200$$ 3.44949 5.97469i 0.243916 0.422474i
$$201$$ 0 0
$$202$$ −3.62372 6.27647i −0.254964 0.441611i
$$203$$ −1.44949 2.51059i −0.101734 0.176209i
$$204$$ 0 0
$$205$$ 16.8990 29.2699i 1.18028 2.04430i
$$206$$ −14.0000 −0.975426
$$207$$ 0 0
$$208$$ −4.89898 −0.339683
$$209$$ 7.44949 12.9029i 0.515292 0.892512i
$$210$$ 0 0
$$211$$ −1.55051 2.68556i −0.106742 0.184882i 0.807707 0.589584i $$-0.200708\pi$$
−0.914448 + 0.404703i $$0.867375\pi$$
$$212$$ −0.550510 0.953512i −0.0378092 0.0654875i
$$213$$ 0 0
$$214$$ 6.00000 10.3923i 0.410152 0.710403i
$$215$$ 10.0000 0.681994
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ −8.34847 + 14.4600i −0.565430 + 0.979353i
$$219$$ 0 0
$$220$$ −3.44949 5.97469i −0.232565 0.402814i
$$221$$ −4.89898 8.48528i −0.329541 0.570782i
$$222$$ 0 0
$$223$$ 10.4495 18.0990i 0.699750 1.21200i −0.268804 0.963195i $$-0.586628\pi$$
0.968553 0.248807i $$-0.0800384\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −15.8990 −1.05758
$$227$$ −0.275255 + 0.476756i −0.0182693 + 0.0316434i −0.875016 0.484095i $$-0.839149\pi$$
0.856746 + 0.515738i $$0.172482\pi$$
$$228$$ 0 0
$$229$$ 11.6237 + 20.1329i 0.768117 + 1.33042i 0.938583 + 0.345055i $$0.112140\pi$$
−0.170465 + 0.985364i $$0.554527\pi$$
$$230$$ −1.72474 2.98735i −0.113726 0.196980i
$$231$$ 0 0
$$232$$ −1.44949 + 2.51059i −0.0951637 + 0.164828i
$$233$$ 7.00000 0.458585 0.229293 0.973358i $$-0.426359\pi$$
0.229293 + 0.973358i $$0.426359\pi$$
$$234$$ 0 0
$$235$$ −33.7980 −2.20474
$$236$$ −1.00000 + 1.73205i −0.0650945 + 0.112747i
$$237$$ 0 0
$$238$$ 1.00000 + 1.73205i 0.0648204 + 0.112272i
$$239$$ −6.39898 11.0834i −0.413916 0.716923i 0.581398 0.813619i $$-0.302506\pi$$
−0.995314 + 0.0966962i $$0.969172\pi$$
$$240$$ 0 0
$$241$$ 4.44949 7.70674i 0.286617 0.496435i −0.686383 0.727240i $$-0.740803\pi$$
0.973000 + 0.230805i $$0.0741360\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0 0
$$244$$ 11.4495 0.732978
$$245$$ 1.72474 2.98735i 0.110190 0.190855i
$$246$$ 0 0
$$247$$ 18.2474 + 31.6055i 1.16106 + 2.01101i
$$248$$ 3.00000 + 5.19615i 0.190500 + 0.329956i
$$249$$ 0 0
$$250$$ −3.27526 + 5.67291i −0.207145 + 0.358786i
$$251$$ −12.5505 −0.792181 −0.396091 0.918211i $$-0.629633\pi$$
−0.396091 + 0.918211i $$0.629633\pi$$
$$252$$ 0 0
$$253$$ −2.00000 −0.125739
$$254$$ −1.50000 + 2.59808i −0.0941184 + 0.163018i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 13.8990 + 24.0737i 0.866995 + 1.50168i 0.865053 + 0.501680i $$0.167285\pi$$
0.00194150 + 0.999998i $$0.499382\pi$$
$$258$$ 0 0
$$259$$ −3.89898 + 6.75323i −0.242271 + 0.419625i
$$260$$ 16.8990 1.04803
$$261$$ 0 0
$$262$$ −13.4495 −0.830912
$$263$$ 8.05051 13.9439i 0.496416 0.859817i −0.503576 0.863951i $$-0.667983\pi$$
0.999991 + 0.00413383i $$0.00131584\pi$$
$$264$$ 0 0
$$265$$ 1.89898 + 3.28913i 0.116653 + 0.202050i
$$266$$ −3.72474 6.45145i −0.228379 0.395564i
$$267$$ 0 0
$$268$$ 1.55051 2.68556i 0.0947125 0.164047i
$$269$$ 3.65153 0.222638 0.111319 0.993785i $$-0.464493\pi$$
0.111319 + 0.993785i $$0.464493\pi$$
$$270$$ 0 0
$$271$$ 16.8990 1.02654 0.513270 0.858227i $$-0.328434\pi$$
0.513270 + 0.858227i $$0.328434\pi$$
$$272$$ 1.00000 1.73205i 0.0606339 0.105021i
$$273$$ 0 0
$$274$$ 5.89898 + 10.2173i 0.356370 + 0.617252i
$$275$$ 6.89898 + 11.9494i 0.416024 + 0.720575i
$$276$$ 0 0
$$277$$ −5.34847 + 9.26382i −0.321358 + 0.556609i −0.980769 0.195174i $$-0.937473\pi$$
0.659410 + 0.751783i $$0.270806\pi$$
$$278$$ −9.44949 −0.566743
$$279$$ 0 0
$$280$$ −3.44949 −0.206146
$$281$$ −9.50000 + 16.4545i −0.566722 + 0.981592i 0.430165 + 0.902750i $$0.358455\pi$$
−0.996887 + 0.0788417i $$0.974878\pi$$
$$282$$ 0 0
$$283$$ 10.2753 + 17.7973i 0.610801 + 1.05794i 0.991106 + 0.133077i $$0.0424856\pi$$
−0.380305 + 0.924861i $$0.624181\pi$$
$$284$$ 4.94949 + 8.57277i 0.293698 + 0.508700i
$$285$$ 0 0
$$286$$ 4.89898 8.48528i 0.289683 0.501745i
$$287$$ −9.79796 −0.578355
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 5.00000 8.66025i 0.293610 0.508548i
$$291$$ 0 0
$$292$$ −1.44949 2.51059i −0.0848250 0.146921i
$$293$$ 13.6237 + 23.5970i 0.795906 + 1.37855i 0.922262 + 0.386565i $$0.126339\pi$$
−0.126356 + 0.991985i $$0.540328\pi$$
$$294$$ 0 0
$$295$$ 3.44949 5.97469i 0.200837 0.347860i
$$296$$ 7.79796 0.453247
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 2.44949 4.24264i 0.141658 0.245358i
$$300$$ 0 0
$$301$$ −1.44949 2.51059i −0.0835472 0.144708i
$$302$$ −2.50000 4.33013i −0.143859 0.249171i
$$303$$ 0 0
$$304$$ −3.72474 + 6.45145i −0.213629 + 0.370016i
$$305$$ −39.4949 −2.26147
$$306$$ 0 0
$$307$$ 0.752551 0.0429504 0.0214752 0.999769i $$-0.493164\pi$$
0.0214752 + 0.999769i $$0.493164\pi$$
$$308$$ −1.00000 + 1.73205i −0.0569803 + 0.0986928i
$$309$$ 0 0
$$310$$ −10.3485 17.9241i −0.587754 1.01802i
$$311$$ 0.651531 + 1.12848i 0.0369449 + 0.0639905i 0.883907 0.467663i $$-0.154904\pi$$
−0.846962 + 0.531654i $$0.821571\pi$$
$$312$$ 0 0
$$313$$ −12.3485 + 21.3882i −0.697977 + 1.20893i 0.271190 + 0.962526i $$0.412583\pi$$
−0.969167 + 0.246405i $$0.920751\pi$$
$$314$$ −6.34847 −0.358265
$$315$$ 0 0
$$316$$ 7.89898 0.444352
$$317$$ −4.34847 + 7.53177i −0.244234 + 0.423026i −0.961916 0.273345i $$-0.911870\pi$$
0.717682 + 0.696371i $$0.245203\pi$$
$$318$$ 0 0
$$319$$ −2.89898 5.02118i −0.162312 0.281132i
$$320$$ 1.72474 + 2.98735i 0.0964162 + 0.166998i
$$321$$ 0 0
$$322$$ −0.500000 + 0.866025i −0.0278639 + 0.0482617i
$$323$$ −14.8990 −0.829001
$$324$$ 0 0
$$325$$ −33.7980 −1.87477
$$326$$ −0.101021 + 0.174973i −0.00559501 + 0.00969084i
$$327$$ 0 0
$$328$$ 4.89898 + 8.48528i 0.270501 + 0.468521i
$$329$$ 4.89898 + 8.48528i 0.270089 + 0.467809i
$$330$$ 0 0
$$331$$ 12.3485 21.3882i 0.678733 1.17560i −0.296629 0.954993i $$-0.595863\pi$$
0.975363 0.220608i $$-0.0708041\pi$$
$$332$$ −2.00000 −0.109764
$$333$$ 0 0
$$334$$ 18.6969 1.02305
$$335$$ −5.34847 + 9.26382i −0.292218 + 0.506137i
$$336$$ 0 0
$$337$$ −17.6969 30.6520i −0.964014 1.66972i −0.712242 0.701934i $$-0.752320\pi$$
−0.251772 0.967787i $$-0.581013\pi$$
$$338$$ 5.50000 + 9.52628i 0.299161 + 0.518161i
$$339$$ 0 0
$$340$$ −3.44949 + 5.97469i −0.187075 + 0.324023i
$$341$$ −12.0000 −0.649836
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ −1.44949 + 2.51059i −0.0781512 + 0.135362i
$$345$$ 0 0
$$346$$ 6.44949 + 11.1708i 0.346727 + 0.600548i
$$347$$ −9.79796 16.9706i −0.525982 0.911028i −0.999542 0.0302659i $$-0.990365\pi$$
0.473560 0.880762i $$-0.342969\pi$$
$$348$$ 0 0
$$349$$ −10.4495 + 18.0990i −0.559348 + 0.968820i 0.438203 + 0.898876i $$0.355615\pi$$
−0.997551 + 0.0699435i $$0.977718\pi$$
$$350$$ 6.89898 0.368766
$$351$$ 0 0
$$352$$ 2.00000 0.106600
$$353$$ −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
$$355$$ −17.0732 29.5717i −0.906152 1.56950i
$$356$$ −3.55051 6.14966i −0.188177 0.325932i
$$357$$ 0 0
$$358$$ 4.34847 7.53177i 0.229824 0.398066i
$$359$$ −10.7980 −0.569894 −0.284947 0.958543i $$-0.591976\pi$$
−0.284947 + 0.958543i $$0.591976\pi$$
$$360$$ 0 0
$$361$$ 36.4949 1.92078
$$362$$ 2.17423 3.76588i 0.114275 0.197931i
$$363$$ 0 0
$$364$$ −2.44949 4.24264i −0.128388 0.222375i
$$365$$ 5.00000 + 8.66025i 0.261712 + 0.453298i
$$366$$ 0 0
$$367$$ −2.89898 + 5.02118i −0.151325 + 0.262103i −0.931715 0.363190i $$-0.881687\pi$$
0.780389 + 0.625294i $$0.215021\pi$$
$$368$$ 1.00000 0.0521286
$$369$$ 0 0
$$370$$ −26.8990 −1.39841
$$371$$ 0.550510 0.953512i 0.0285811 0.0495039i
$$372$$ 0 0
$$373$$ −1.44949 2.51059i −0.0750517 0.129993i 0.826057 0.563587i $$-0.190579\pi$$
−0.901109 + 0.433593i $$0.857246\pi$$
$$374$$ 2.00000 + 3.46410i 0.103418 + 0.179124i
$$375$$ 0 0
$$376$$ 4.89898 8.48528i 0.252646 0.437595i
$$377$$ 14.2020 0.731442
$$378$$ 0 0
$$379$$ −26.4949 −1.36095 −0.680476 0.732771i $$-0.738227\pi$$
−0.680476 + 0.732771i $$0.738227\pi$$
$$380$$ 12.8485 22.2542i 0.659113 1.14162i
$$381$$ 0 0
$$382$$ −6.94949 12.0369i −0.355567 0.615860i
$$383$$ 3.44949 + 5.97469i 0.176261 + 0.305292i 0.940597 0.339526i $$-0.110266\pi$$
−0.764336 + 0.644818i $$0.776933\pi$$
$$384$$ 0 0
$$385$$ 3.44949 5.97469i 0.175802 0.304498i
$$386$$ 8.10102 0.412331
$$387$$ 0 0
$$388$$ −6.89898 −0.350243
$$389$$ −7.55051 + 13.0779i −0.382826 + 0.663074i −0.991465 0.130373i $$-0.958382\pi$$
0.608639 + 0.793447i $$0.291716\pi$$
$$390$$ 0 0
$$391$$ 1.00000 + 1.73205i 0.0505722 + 0.0875936i
$$392$$ 0.500000 + 0.866025i 0.0252538 + 0.0437409i
$$393$$ 0 0
$$394$$ 6.34847 10.9959i 0.319831 0.553964i
$$395$$ −27.2474 −1.37097
$$396$$ 0 0
$$397$$ 9.30306 0.466907 0.233454 0.972368i $$-0.424997\pi$$
0.233454 + 0.972368i $$0.424997\pi$$
$$398$$ 3.44949 5.97469i 0.172907 0.299484i
$$399$$ 0 0
$$400$$ −3.44949 5.97469i −0.172474 0.298735i
$$401$$ −5.05051 8.74774i −0.252210 0.436841i 0.711924 0.702257i $$-0.247824\pi$$
−0.964134 + 0.265416i $$0.914491\pi$$
$$402$$ 0 0
$$403$$ 14.6969 25.4558i 0.732107 1.26805i
$$404$$ −7.24745 −0.360574
$$405$$ 0 0
$$406$$ −2.89898 −0.143874
$$407$$ −7.79796 + 13.5065i −0.386530 + 0.669490i
$$408$$ 0 0
$$409$$ −2.89898 5.02118i −0.143345 0.248281i 0.785409 0.618977i $$-0.212453\pi$$
−0.928754 + 0.370696i $$0.879119\pi$$
$$410$$ −16.8990 29.2699i −0.834581 1.44554i
$$411$$ 0 0
$$412$$ −7.00000 + 12.1244i −0.344865 + 0.597324i
$$413$$ −2.00000 −0.0984136
$$414$$ 0 0
$$415$$ 6.89898 0.338658
$$416$$ −2.44949 + 4.24264i −0.120096 + 0.208013i
$$417$$ 0 0
$$418$$ −7.44949 12.9029i −0.364366 0.631101i
$$419$$ 12.2753 + 21.2614i 0.599685 + 1.03869i 0.992867 + 0.119225i $$0.0380410\pi$$
−0.393182 + 0.919461i $$0.628626\pi$$
$$420$$ 0 0
$$421$$ −6.55051 + 11.3458i −0.319252 + 0.552961i −0.980332 0.197354i $$-0.936765\pi$$
0.661080 + 0.750316i $$0.270098\pi$$
$$422$$ −3.10102 −0.150955
$$423$$ 0 0
$$424$$ −1.10102 −0.0534703
$$425$$ 6.89898 11.9494i 0.334650 0.579630i
$$426$$ 0 0
$$427$$ 5.72474 + 9.91555i 0.277040 + 0.479847i
$$428$$ −6.00000 10.3923i −0.290021 0.502331i
$$429$$ 0 0
$$430$$ 5.00000 8.66025i 0.241121 0.417635i
$$431$$ 7.59592 0.365882 0.182941 0.983124i $$-0.441438\pi$$
0.182941 + 0.983124i $$0.441438\pi$$
$$432$$ 0 0
$$433$$ 11.7980 0.566974 0.283487 0.958976i $$-0.408509\pi$$
0.283487 + 0.958976i $$0.408509\pi$$
$$434$$ −3.00000 + 5.19615i −0.144005 + 0.249423i
$$435$$ 0 0
$$436$$ 8.34847 + 14.4600i 0.399819 + 0.692507i
$$437$$ −3.72474 6.45145i −0.178179 0.308615i
$$438$$ 0 0
$$439$$ −10.8990 + 18.8776i −0.520180 + 0.900978i 0.479545 + 0.877517i $$0.340802\pi$$
−0.999725 + 0.0234607i $$0.992532\pi$$
$$440$$ −6.89898 −0.328896
$$441$$ 0 0
$$442$$ −9.79796 −0.466041
$$443$$ −2.55051 + 4.41761i −0.121178 + 0.209887i −0.920233 0.391372i $$-0.872001\pi$$
0.799054 + 0.601259i $$0.205334\pi$$
$$444$$ 0 0
$$445$$ 12.2474 + 21.2132i 0.580585 + 1.00560i
$$446$$ −10.4495 18.0990i −0.494798 0.857015i
$$447$$ 0 0
$$448$$ 0.500000 0.866025i 0.0236228 0.0409159i
$$449$$ 18.5959 0.877596 0.438798 0.898586i $$-0.355404\pi$$
0.438798 + 0.898586i $$0.355404\pi$$
$$450$$ 0 0
$$451$$ −19.5959 −0.922736
$$452$$ −7.94949 + 13.7689i −0.373913 + 0.647636i
$$453$$ 0 0
$$454$$ 0.275255 + 0.476756i 0.0129184 + 0.0223753i
$$455$$ 8.44949 + 14.6349i 0.396118 + 0.686097i
$$456$$ 0 0
$$457$$ −15.7474 + 27.2754i −0.736635 + 1.27589i 0.217368 + 0.976090i $$0.430253\pi$$
−0.954002 + 0.299799i $$0.903080\pi$$
$$458$$ 23.2474 1.08628
$$459$$ 0 0
$$460$$ −3.44949 −0.160833
$$461$$ 10.1742 17.6223i 0.473861 0.820752i −0.525691 0.850676i $$-0.676193\pi$$
0.999552 + 0.0299238i $$0.00952645\pi$$
$$462$$ 0 0
$$463$$ 12.8485 + 22.2542i 0.597119 + 1.03424i 0.993244 + 0.116044i $$0.0370213\pi$$
−0.396125 + 0.918197i $$0.629645\pi$$
$$464$$ 1.44949 + 2.51059i 0.0672909 + 0.116551i
$$465$$ 0 0
$$466$$ 3.50000 6.06218i 0.162134 0.280825i
$$467$$ −10.0000 −0.462745 −0.231372 0.972865i $$-0.574322\pi$$
−0.231372 + 0.972865i $$0.574322\pi$$
$$468$$ 0 0
$$469$$ 3.10102 0.143192
$$470$$ −16.8990 + 29.2699i −0.779492 + 1.35012i
$$471$$ 0 0
$$472$$ 1.00000 + 1.73205i 0.0460287 + 0.0797241i
$$473$$ −2.89898 5.02118i −0.133295 0.230874i
$$474$$ 0 0
$$475$$ −25.6969 + 44.5084i −1.17906 + 2.04219i
$$476$$ 2.00000 0.0916698
$$477$$ 0 0
$$478$$ −12.7980 −0.585365
$$479$$ −14.7980 + 25.6308i −0.676136 + 1.17110i 0.299999 + 0.953939i $$0.403013\pi$$
−0.976135 + 0.217163i $$0.930320\pi$$
$$480$$ 0 0
$$481$$ −19.1010 33.0839i −0.870932 1.50850i
$$482$$ −4.44949 7.70674i −0.202669 0.351032i
$$483$$ 0 0
$$484$$ 3.50000 6.06218i 0.159091 0.275554i
$$485$$ 23.7980 1.08061
$$486$$ 0 0
$$487$$ 22.3939 1.01476 0.507382 0.861721i $$-0.330613\pi$$
0.507382 + 0.861721i $$0.330613\pi$$
$$488$$ 5.72474 9.91555i 0.259147 0.448856i
$$489$$ 0 0
$$490$$ −1.72474 2.98735i −0.0779160 0.134955i
$$491$$ −1.89898 3.28913i −0.0856997 0.148436i 0.819989 0.572379i $$-0.193979\pi$$
−0.905689 + 0.423942i $$0.860646\pi$$
$$492$$ 0 0
$$493$$ −2.89898 + 5.02118i −0.130563 + 0.226143i
$$494$$ 36.4949 1.64198
$$495$$ 0 0
$$496$$ 6.00000 0.269408
$$497$$ −4.94949 + 8.57277i −0.222015 + 0.384541i
$$498$$ 0 0
$$499$$ −16.6969 28.9199i −0.747458 1.29463i −0.949038 0.315163i $$-0.897941\pi$$
0.201580 0.979472i $$-0.435392\pi$$
$$500$$ 3.27526 + 5.67291i 0.146474 + 0.253700i
$$501$$ 0 0
$$502$$ −6.27526 + 10.8691i −0.280078 + 0.485110i
$$503$$ −24.4949 −1.09217 −0.546087 0.837729i $$-0.683883\pi$$
−0.546087 + 0.837729i $$0.683883\pi$$
$$504$$ 0 0
$$505$$ 25.0000 1.11249
$$506$$ −1.00000 + 1.73205i −0.0444554 + 0.0769991i
$$507$$ 0 0
$$508$$ 1.50000 + 2.59808i 0.0665517 + 0.115271i
$$509$$ −8.44949 14.6349i −0.374517 0.648683i 0.615738 0.787951i $$-0.288858\pi$$
−0.990255 + 0.139269i $$0.955525\pi$$
$$510$$ 0 0
$$511$$ 1.44949 2.51059i 0.0641217 0.111062i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 27.7980 1.22612
$$515$$ 24.1464 41.8228i 1.06402 1.84293i
$$516$$ 0 0
$$517$$ 9.79796 + 16.9706i 0.430914 + 0.746364i
$$518$$ 3.89898 + 6.75323i 0.171311 + 0.296720i
$$519$$ 0 0
$$520$$ 8.44949 14.6349i 0.370535 0.641785i
$$521$$ 38.6969 1.69534 0.847672 0.530521i $$-0.178004\pi$$
0.847672 + 0.530521i $$0.178004\pi$$
$$522$$ 0 0
$$523$$ 0.348469 0.0152375 0.00761875 0.999971i $$-0.497575\pi$$
0.00761875 + 0.999971i $$0.497575\pi$$
$$524$$ −6.72474 + 11.6476i −0.293772 + 0.508828i
$$525$$ 0 0
$$526$$ −8.05051 13.9439i −0.351019 0.607983i
$$527$$ 6.00000 + 10.3923i 0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ 3.79796 0.164973
$$531$$ 0 0
$$532$$ −7.44949 −0.322976
$$533$$ 24.0000 41.5692i 1.03956 1.80056i
$$534$$ 0 0
$$535$$ 20.6969 + 35.8481i 0.894807 + 1.54985i
$$536$$ −1.55051 2.68556i −0.0669718 0.115999i
$$537$$ 0 0
$$538$$ 1.82577 3.16232i 0.0787143 0.136337i
$$539$$ −2.00000 −0.0861461
$$540$$ 0 0
$$541$$ 30.4949 1.31108 0.655539 0.755161i $$-0.272441\pi$$
0.655539 + 0.755161i $$0.272441\pi$$
$$542$$ 8.44949 14.6349i 0.362937 0.628625i
$$543$$ 0 0
$$544$$ −1.00000 1.73205i −0.0428746 0.0742611i
$$545$$ −28.7980 49.8795i −1.23357 2.13660i
$$546$$ 0 0
$$547$$ −15.7980 + 27.3629i −0.675472 + 1.16995i 0.300859 + 0.953669i $$0.402727\pi$$
−0.976331 + 0.216283i $$0.930607\pi$$
$$548$$ 11.7980 0.503984
$$549$$ 0 0
$$550$$ 13.7980 0.588347
$$551$$ 10.7980 18.7026i 0.460009 0.796758i
$$552$$ 0 0
$$553$$ 3.94949 + 6.84072i 0.167949 + 0.290897i
$$554$$ 5.34847 + 9.26382i 0.227235 + 0.393582i
$$555$$ 0 0
$$556$$ −4.72474 + 8.18350i −0.200374 + 0.347058i
$$557$$ 3.10102 0.131394 0.0656972 0.997840i $$-0.479073\pi$$
0.0656972 + 0.997840i $$0.479073\pi$$
$$558$$ 0 0
$$559$$ 14.2020 0.600682
$$560$$ −1.72474 + 2.98735i −0.0728838 + 0.126238i
$$561$$ 0 0
$$562$$ 9.50000 + 16.4545i 0.400733 + 0.694090i
$$563$$ 6.97219 + 12.0762i 0.293843 + 0.508951i 0.974715 0.223451i $$-0.0717324\pi$$
−0.680872 + 0.732402i $$0.738399\pi$$
$$564$$ 0 0
$$565$$ 27.4217 47.4957i 1.15364 1.99816i
$$566$$ 20.5505 0.863802
$$567$$ 0 0
$$568$$ 9.89898 0.415352
$$569$$ −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i $$0.383134\pi$$
−0.987786 + 0.155815i $$0.950200\pi$$
$$570$$ 0 0
$$571$$ −7.10102 12.2993i −0.297168 0.514711i 0.678319 0.734768i $$-0.262709\pi$$
−0.975487 + 0.220057i $$0.929376\pi$$
$$572$$ −4.89898 8.48528i −0.204837 0.354787i
$$573$$ 0 0
$$574$$ −4.89898 + 8.48528i −0.204479 + 0.354169i
$$575$$ 6.89898 0.287707
$$576$$ 0 0
$$577$$ 23.5959 0.982311 0.491155 0.871072i $$-0.336575\pi$$
0.491155 + 0.871072i $$0.336575\pi$$
$$578$$ −6.50000 + 11.2583i −0.270364 + 0.468285i
$$579$$ 0 0
$$580$$ −5.00000 8.66025i −0.207614 0.359597i
$$581$$ −1.00000 1.73205i −0.0414870 0.0718576i
$$582$$ 0 0
$$583$$ 1.10102 1.90702i 0.0455996 0.0789808i
$$584$$ −2.89898 −0.119961
$$585$$ 0 0
$$586$$ 27.2474 1.12558
$$587$$ −9.07321 + 15.7153i −0.374492 + 0.648639i −0.990251 0.139296i $$-0.955516\pi$$
0.615759 + 0.787934i $$0.288849\pi$$
$$588$$ 0 0
$$589$$ −22.3485 38.7087i −0.920853 1.59496i
$$590$$ −3.44949 5.97469i −0.142013 0.245974i
$$591$$ 0 0
$$592$$ 3.89898 6.75323i 0.160247 0.277556i
$$593$$ 14.6969 0.603531 0.301765 0.953382i $$-0.402424\pi$$
0.301765 + 0.953382i $$0.402424\pi$$
$$594$$ 0 0
$$595$$ −6.89898 −0.282831
$$596$$ −3.00000 + 5.19615i −0.122885 + 0.212843i
$$597$$ 0 0
$$598$$ −2.44949 4.24264i −0.100167 0.173494i
$$599$$ −7.10102 12.2993i −0.290140 0.502537i 0.683703 0.729761i $$-0.260368\pi$$
−0.973843 + 0.227224i $$0.927035\pi$$
$$600$$ 0 0
$$601$$ 6.34847 10.9959i 0.258959 0.448531i −0.707004 0.707210i $$-0.749954\pi$$
0.965963 + 0.258679i $$0.0832871\pi$$
$$602$$ −2.89898 −0.118154
$$603$$ 0 0
$$604$$ −5.00000 −0.203447
$$605$$ −12.0732 + 20.9114i −0.490846 + 0.850170i
$$606$$ 0 0
$$607$$ 4.34847 + 7.53177i 0.176499 + 0.305705i 0.940679 0.339298i $$-0.110189\pi$$
−0.764180 + 0.645003i $$0.776856\pi$$
$$608$$ 3.72474 + 6.45145i 0.151058 + 0.261641i
$$609$$ 0 0
$$610$$ −19.7474 + 34.2036i −0.799551 + 1.38486i
$$611$$ −48.0000 −1.94187
$$612$$ 0 0
$$613$$ 14.6969 0.593604 0.296802 0.954939i $$-0.404080\pi$$
0.296802 + 0.954939i $$0.404080\pi$$
$$614$$ 0.376276 0.651729i 0.0151852 0.0263016i
$$615$$ 0 0
$$616$$ 1.00000 + 1.73205i 0.0402911 + 0.0697863i
$$617$$ 21.6969 + 37.5802i 0.873486 + 1.51292i 0.858367 + 0.513036i $$0.171479\pi$$
0.0151189 + 0.999886i $$0.495187\pi$$
$$618$$ 0 0
$$619$$ 2.07321 3.59091i 0.0833295 0.144331i −0.821349 0.570426i $$-0.806778\pi$$
0.904678 + 0.426096i $$0.140111\pi$$
$$620$$ −20.6969 −0.831209
$$621$$ 0 0
$$622$$ 1.30306 0.0522480
$$623$$ 3.55051 6.14966i 0.142248 0.246381i
$$624$$ 0 0
$$625$$ 5.94949 + 10.3048i 0.237980 + 0.412193i
$$626$$ 12.3485 + 21.3882i 0.493544 + 0.854843i
$$627$$ 0 0
$$628$$ −3.17423 + 5.49794i −0.126666 + 0.219392i
$$629$$ 15.5959 0.621850
$$630$$ 0 0
$$631$$ 18.1010 0.720590 0.360295 0.932838i $$-0.382676\pi$$
0.360295 + 0.932838i $$0.382676\pi$$
$$632$$ 3.94949 6.84072i 0.157102 0.272109i
$$633$$ 0 0
$$634$$ 4.34847 + 7.53177i 0.172700 + 0.299125i
$$635$$ −5.17423 8.96204i −0.205333 0.355648i
$$636$$ 0 0
$$637$$ 2.44949 4.24264i 0.0970523 0.168100i
$$638$$ −5.79796 −0.229543
$$639$$ 0 0
$$640$$ 3.44949 0.136353
$$641$$ 20.7474 35.9356i 0.819475 1.41937i −0.0865947 0.996244i $$-0.527599\pi$$
0.906070 0.423129i $$-0.139068\pi$$
$$642$$ 0 0
$$643$$ −9.69694 16.7956i −0.382410 0.662353i 0.608996 0.793173i $$-0.291572\pi$$
−0.991406 + 0.130820i $$0.958239\pi$$
$$644$$ 0.500000 + 0.866025i 0.0197028 + 0.0341262i
$$645$$ 0 0
$$646$$ −7.44949 + 12.9029i −0.293096 + 0.507658i
$$647$$ 21.3031 0.837510 0.418755 0.908099i $$-0.362467\pi$$
0.418755 + 0.908099i $$0.362467\pi$$
$$648$$ 0 0
$$649$$ −4.00000 −0.157014
$$650$$ −16.8990 + 29.2699i −0.662833 + 1.14806i
$$651$$ 0 0
$$652$$ 0.101021 + 0.174973i 0.00395627 + 0.00685246i
$$653$$ −4.89898 8.48528i −0.191712 0.332055i 0.754106 0.656753i $$-0.228071\pi$$
−0.945818 + 0.324698i $$0.894737\pi$$
$$654$$ 0 0
$$655$$ 23.1969 40.1783i 0.906379 1.56990i
$$656$$ 9.79796 0.382546
$$657$$ 0 0
$$658$$ 9.79796 0.381964
$$659$$ 2.34847 4.06767i 0.0914834 0.158454i −0.816652 0.577130i $$-0.804172\pi$$
0.908136 + 0.418676i $$0.137506\pi$$
$$660$$ 0 0
$$661$$ −4.72474 8.18350i −0.183771 0.318301i 0.759391 0.650635i $$-0.225497\pi$$
−0.943162 + 0.332334i $$0.892164\pi$$
$$662$$ −12.3485 21.3882i −0.479937 0.831275i
$$663$$ 0 0
$$664$$ −1.00000 + 1.73205i −0.0388075 + 0.0672166i
$$665$$ 25.6969 0.996485
$$666$$ 0 0
$$667$$ −2.89898 −0.112249
$$668$$ 9.34847 16.1920i 0.361703 0.626488i
$$669$$ 0 0
$$670$$ 5.34847 + 9.26382i 0.206629 + 0.357893i
$$671$$ 11.4495 + 19.8311i 0.442003 + 0.765571i
$$672$$ 0 0
$$673$$ −15.2980 + 26.4968i −0.589693 + 1.02138i 0.404579 + 0.914503i $$0.367418\pi$$
−0.994272 + 0.106875i $$0.965915\pi$$
$$674$$ −35.3939 −1.36332
$$675$$ 0 0
$$676$$ 11.0000 0.423077
$$677$$ −7.34847 + 12.7279i −0.282425 + 0.489174i −0.971981 0.235058i $$-0.924472\pi$$
0.689557 + 0.724232i $$0.257805\pi$$
$$678$$ 0 0
$$679$$ −3.44949 5.97469i −0.132379 0.229288i
$$680$$ 3.44949 + 5.97469i 0.132282 + 0.229119i
$$681$$ 0 0
$$682$$ −6.00000 + 10.3923i −0.229752 + 0.397942i
$$683$$ −32.2020 −1.23218 −0.616088 0.787677i $$-0.711284\pi$$
−0.616088 + 0.787677i $$0.711284\pi$$
$$684$$ 0 0
$$685$$ −40.6969 −1.55495
$$686$$ −0.500000 + 0.866025i −0.0190901 + 0.0330650i
$$687$$ 0 0
$$688$$ 1.44949 + 2.51059i 0.0552613 + 0.0957153i
$$689$$ 2.69694 + 4.67123i 0.102745 + 0.177960i
$$690$$ 0 0
$$691$$ −3.47730 + 6.02285i −0.132283 + 0.229120i −0.924556 0.381046i $$-0.875564\pi$$
0.792274 + 0.610166i $$0.208897\pi$$
$$692$$ 12.8990 0.490346
$$693$$ 0 0
$$694$$ −19.5959 −0.743851
$$695$$ 16.2980 28.2289i 0.618217 1.07078i
$$696$$ 0 0
$$697$$ 9.79796 + 16.9706i 0.371124 + 0.642806i
$$698$$ 10.4495 + 18.0990i 0.395519 + 0.685059i
$$699$$ 0 0
$$700$$ 3.44949 5.97469i 0.130378 0.225822i
$$701$$ −51.3939 −1.94112 −0.970560 0.240860i $$-0.922571\pi$$
−0.970560 + 0.240860i $$0.922571\pi$$
$$702$$ 0 0
$$703$$ −58.0908 −2.19094
$$704$$ 1.00000 1.73205i 0.0376889 0.0652791i
$$705$$ 0 0
$$706$$ 3.00000 + 5.19615i 0.112906 + 0.195560i
$$707$$ −3.62372 6.27647i −0.136284 0.236051i
$$708$$ 0 0
$$709$$ 5.79796 10.0424i 0.217747 0.377149i −0.736372 0.676577i $$-0.763463\pi$$
0.954119 + 0.299428i $$0.0967959\pi$$
$$710$$ −34.1464 −1.28149
$$711$$ 0 0
$$712$$ −7.10102 −0.266122
$$713$$ −3.00000 + 5.19615i −0.112351 + 0.194597i
$$714$$ 0 0
$$715$$ 16.8990 + 29.2699i 0.631986 + 1.09463i
$$716$$ −4.34847 7.53177i −0.162510 0.281475i
$$717$$ 0 0
$$718$$ −5.39898 + 9.35131i −0.201488 + 0.348988i
$$719$$ 9.79796 0.365402 0.182701 0.983169i $$-0.441516\pi$$
0.182701 + 0.983169i $$0.441516\pi$$
$$720$$ 0 0
$$721$$ −14.0000 −0.521387
$$722$$ 18.2474 31.6055i 0.679100 1.17624i
$$723$$ 0 0
$$724$$ −2.17423 3.76588i −0.0808048 0.139958i
$$725$$ 10.0000 + 17.3205i 0.371391 + 0.643268i
$$726$$ 0 0
$$727$$ −20.2474 + 35.0696i −0.750936 + 1.30066i 0.196433 + 0.980517i $$0.437064\pi$$
−0.947369 + 0.320143i $$0.896269\pi$$
$$728$$ −4.89898 −0.181568
$$729$$ 0 0
$$730$$ 10.0000 0.370117
$$731$$ −2.89898 + 5.02118i −0.107223 + 0.185715i
$$732$$ 0 0
$$733$$ 6.27526 + 10.8691i 0.231782 + 0.401458i 0.958333 0.285655i $$-0.0922111\pi$$
−0.726551 + 0.687113i $$0.758878\pi$$
$$734$$ 2.89898 + 5.02118i 0.107003 + 0.185335i
$$735$$ 0 0
$$736$$ 0.500000 0.866025i 0.0184302 0.0319221i
$$737$$ 6.20204 0.228455
$$738$$ 0 0
$$739$$ −25.5959 −0.941561 −0.470781 0.882250i $$-0.656028\pi$$
−0.470781 + 0.882250i $$0.656028\pi$$
$$740$$ −13.4495 + 23.2952i −0.494413 + 0.856349i
$$741$$ 0 0
$$742$$ −0.550510 0.953512i −0.0202099 0.0350045i
$$743$$ 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i $$0.0629279\pi$$
−0.320166 + 0.947361i $$0.603739\pi$$
$$744$$ 0 0
$$745$$ 10.3485 17.9241i 0.379139 0.656687i
$$746$$ −2.89898 −0.106139
$$747$$ 0 0
$$748$$ 4.00000 0.146254
$$749$$ 6.00000 10.3923i 0.219235 0.379727i
$$750$$ 0 0
$$751$$ −20.2980 35.1571i −0.740683 1.28290i −0.952185 0.305523i $$-0.901169\pi$$
0.211502 0.977378i $$-0.432165\pi$$
$$752$$ −4.89898 8.48528i −0.178647 0.309426i
$$753$$ 0 0
$$754$$ 7.10102 12.2993i 0.258604 0.447915i
$$755$$ 17.2474 0.627699
$$756$$ 0 0
$$757$$ 23.3939 0.850265 0.425132 0.905131i $$-0.360228\pi$$
0.425132 + 0.905131i $$0.360228\pi$$
$$758$$ −13.2474 + 22.9453i −0.481169 + 0.833409i
$$759$$ 0 0
$$760$$ −12.8485 22.2542i −0.466063 0.807245i
$$761$$ 1.00000 + 1.73205i 0.0362500 + 0.0627868i 0.883581 0.468278i $$-0.155125\pi$$
−0.847331 + 0.531065i $$0.821792\pi$$
$$762$$ 0 0
$$763$$ −8.34847 + 14.4600i −0.302235 + 0.523486i
$$764$$ −13.8990 −0.502847
$$765$$ 0 0
$$766$$ 6.89898 0.249270
$$767$$ 4.89898 8.48528i 0.176892 0.306386i
$$768$$ 0 0
$$769$$ −27.0454 46.8440i −0.975282 1.68924i −0.679000 0.734138i $$-0.737586\pi$$
−0.296282 0.955100i $$-0.595747\pi$$
$$770$$ −3.44949 5.97469i −0.124311 0.215313i
$$771$$ 0 0
$$772$$ 4.05051 7.01569i 0.145781 0.252500i
$$773$$ 19.9444 0.717350 0.358675 0.933463i $$-0.383229\pi$$
0.358675 + 0.933463i $$0.383229\pi$$
$$774$$ 0 0
$$775$$ 41.3939 1.48691
$$776$$ −3.44949 + 5.97469i −0.123829 + 0.214479i
$$777$$ 0 0
$$778$$ 7.55051 + 13.0779i 0.270699 + 0.468864i
$$779$$ −36.4949 63.2110i −1.30757 2.26477i
$$780$$ 0 0
$$781$$ −9.89898 + 17.1455i −0.354213 + 0.613515i
$$782$$ 2.00000 0.0715199
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 10.9495 18.9651i 0.390804 0.676892i
$$786$$ 0 0
$$787$$ −23.6969 41.0443i −0.844705 1.46307i −0.885877 0.463919i $$-0.846443\pi$$
0.0411728 0.999152i $$-0.486891\pi$$
$$788$$ −6.34847 10.9959i −0.226155 0.391712i
$$789$$ 0 0
$$790$$ −13.6237 + 23.5970i −0.484710 + 0.839543i
$$791$$