# Properties

 Label 637.2.q.e.589.1 Level $637$ Weight $2$ Character 637.589 Analytic conductor $5.086$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.q (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-7})$$ Defining polynomial: $$x^{4} - x^{3} - x^{2} - 2x + 4$$ x^4 - x^3 - x^2 - 2*x + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 589.1 Root $$1.39564 - 0.228425i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.589 Dual form 637.2.q.e.491.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.395644 - 0.228425i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.895644 - 1.55130i) q^{4} +0.456850i q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})$$ $$q+(-0.395644 - 0.228425i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.895644 - 1.55130i) q^{4} +0.456850i q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +(0.104356 - 0.180750i) q^{10} +(-3.39564 - 1.96048i) q^{11} +5.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +(-1.10436 - 0.637600i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-1.50000 - 2.59808i) q^{17} +2.18890i q^{18} +(1.18693 - 0.685275i) q^{19} +(0.708712 - 0.409175i) q^{20} +(0.895644 + 1.55130i) q^{22} +(0.791288 - 1.37055i) q^{23} +(-4.18693 - 2.41733i) q^{24} +4.79129 q^{25} +(-1.58258 - 0.456850i) q^{26} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} +8.66025i q^{31} +(4.10436 - 2.36965i) q^{32} +(9.47822 - 5.47225i) q^{33} +1.37055i q^{34} +(-4.29129 + 7.43273i) q^{36} +(6.00000 + 3.46410i) q^{37} -0.626136 q^{38} +(-2.79129 + 9.66930i) q^{39} -0.791288 q^{40} +(6.79129 + 3.92095i) q^{41} +(-4.68693 - 8.11800i) q^{43} +7.02355i q^{44} +(1.89564 - 1.09445i) q^{45} +(-0.626136 + 0.361500i) q^{46} -9.57395i q^{47} +(-3.89564 - 6.74745i) q^{48} +(-1.89564 - 1.09445i) q^{50} +8.37386 q^{51} +(-4.47822 - 4.65390i) q^{52} +6.16515 q^{53} +(-1.97822 - 1.14213i) q^{54} +(0.895644 - 1.55130i) q^{55} +3.82560i q^{57} +(-2.68693 + 1.55130i) q^{58} +(10.6652 - 6.15753i) q^{59} +2.28425i q^{60} +(7.37386 + 12.7719i) q^{61} +(1.97822 - 3.42638i) q^{62} +3.41742 q^{64} +(0.395644 + 1.59898i) q^{65} -5.00000 q^{66} +(-3.87386 - 2.23658i) q^{67} +(-2.68693 + 4.65390i) q^{68} +(2.20871 + 3.82560i) q^{69} +(3.79129 - 2.18890i) q^{71} +(7.18693 - 4.14938i) q^{72} -3.46410i q^{73} +(-1.58258 - 2.74110i) q^{74} +(-6.68693 + 11.5821i) q^{75} +(-2.12614 - 1.22753i) q^{76} +(3.31307 - 3.18800i) q^{78} -6.00000 q^{79} +(-1.10436 - 0.637600i) q^{80} +(0.208712 - 0.361500i) q^{81} +(-1.79129 - 3.10260i) q^{82} -7.02355i q^{83} +(1.18693 - 0.685275i) q^{85} +4.28245i q^{86} +(9.47822 + 16.4168i) q^{87} +(3.39564 - 5.88143i) q^{88} +(-13.9782 - 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(-20.9347 - 12.0866i) q^{93} +(-2.18693 + 3.78788i) q^{94} +(0.313068 + 0.542250i) q^{95} +13.2288i q^{96} +(-6.31307 + 3.64485i) q^{97} +18.7864i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9}+O(q^{10})$$ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9 $$4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9} + 5 q^{10} - 9 q^{11} + 20 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 9 q^{19} + 12 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 10 q^{25} + 12 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} + 15 q^{33} - 8 q^{36} + 24 q^{37} - 30 q^{38} - 2 q^{39} + 6 q^{40} + 18 q^{41} - 5 q^{43} + 3 q^{45} - 30 q^{46} - 11 q^{48} - 3 q^{50} + 6 q^{51} + 5 q^{52} - 12 q^{53} + 15 q^{54} - q^{55} + 3 q^{58} + 6 q^{59} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 3 q^{65} - 20 q^{66} + 12 q^{67} + 3 q^{68} + 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} - 24 q^{79} - 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 15 q^{87} + 9 q^{88} - 33 q^{89} - 4 q^{90} - 48 q^{92} - 15 q^{93} + 5 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100})$$ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9 + 5 * q^10 - 9 * q^11 + 20 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 - 9 * q^19 + 12 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 10 * q^25 + 12 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 + 21 * q^32 + 15 * q^33 - 8 * q^36 + 24 * q^37 - 30 * q^38 - 2 * q^39 + 6 * q^40 + 18 * q^41 - 5 * q^43 + 3 * q^45 - 30 * q^46 - 11 * q^48 - 3 * q^50 + 6 * q^51 + 5 * q^52 - 12 * q^53 + 15 * q^54 - q^55 + 3 * q^58 + 6 * q^59 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 3 * q^65 - 20 * q^66 + 12 * q^67 + 3 * q^68 + 18 * q^69 + 6 * q^71 + 15 * q^72 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 - 24 * q^79 - 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 15 * q^87 + 9 * q^88 - 33 * q^89 - 4 * q^90 - 48 * q^92 - 15 * q^93 + 5 * q^94 + 15 * q^95 - 39 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.395644 0.228425i −0.279763 0.161521i 0.353553 0.935414i $$-0.384973\pi$$
−0.633316 + 0.773893i $$0.718307\pi$$
$$3$$ −1.39564 + 2.41733i −0.805775 + 1.39564i 0.109991 + 0.993933i $$0.464918\pi$$
−0.915766 + 0.401711i $$0.868416\pi$$
$$4$$ −0.895644 1.55130i −0.447822 0.775650i
$$5$$ 0.456850i 0.204310i 0.994769 + 0.102155i $$0.0325737\pi$$
−0.994769 + 0.102155i $$0.967426\pi$$
$$6$$ 1.10436 0.637600i 0.450851 0.260299i
$$7$$ 0 0
$$8$$ 1.73205i 0.612372i
$$9$$ −2.39564 4.14938i −0.798548 1.38313i
$$10$$ 0.104356 0.180750i 0.0330003 0.0571582i
$$11$$ −3.39564 1.96048i −1.02383 0.591106i −0.108616 0.994084i $$-0.534642\pi$$
−0.915210 + 0.402978i $$0.867975\pi$$
$$12$$ 5.00000 1.44338
$$13$$ 3.50000 0.866025i 0.970725 0.240192i
$$14$$ 0 0
$$15$$ −1.10436 0.637600i −0.285144 0.164628i
$$16$$ −1.39564 + 2.41733i −0.348911 + 0.604332i
$$17$$ −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i $$-0.285189\pi$$
−0.988583 + 0.150675i $$0.951855\pi$$
$$18$$ 2.18890i 0.515929i
$$19$$ 1.18693 0.685275i 0.272301 0.157213i −0.357632 0.933863i $$-0.616416\pi$$
0.629933 + 0.776650i $$0.283082\pi$$
$$20$$ 0.708712 0.409175i 0.158473 0.0914943i
$$21$$ 0 0
$$22$$ 0.895644 + 1.55130i 0.190952 + 0.330738i
$$23$$ 0.791288 1.37055i 0.164995 0.285780i −0.771659 0.636037i $$-0.780573\pi$$
0.936653 + 0.350257i $$0.113906\pi$$
$$24$$ −4.18693 2.41733i −0.854654 0.493435i
$$25$$ 4.79129 0.958258
$$26$$ −1.58258 0.456850i −0.310369 0.0895957i
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ 3.39564 5.88143i 0.630555 1.09215i −0.356883 0.934149i $$-0.616161\pi$$
0.987438 0.158005i $$-0.0505061\pi$$
$$30$$ 0.291288 + 0.504525i 0.0531816 + 0.0921133i
$$31$$ 8.66025i 1.55543i 0.628619 + 0.777714i $$0.283621\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 4.10436 2.36965i 0.725555 0.418899i
$$33$$ 9.47822 5.47225i 1.64995 0.952597i
$$34$$ 1.37055i 0.235048i
$$35$$ 0 0
$$36$$ −4.29129 + 7.43273i −0.715215 + 1.23879i
$$37$$ 6.00000 + 3.46410i 0.986394 + 0.569495i 0.904194 0.427121i $$-0.140472\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ −0.626136 −0.101573
$$39$$ −2.79129 + 9.66930i −0.446964 + 1.54833i
$$40$$ −0.791288 −0.125114
$$41$$ 6.79129 + 3.92095i 1.06062 + 0.612350i 0.925604 0.378493i $$-0.123558\pi$$
0.135017 + 0.990843i $$0.456891\pi$$
$$42$$ 0 0
$$43$$ −4.68693 8.11800i −0.714750 1.23798i −0.963056 0.269302i $$-0.913207\pi$$
0.248305 0.968682i $$-0.420126\pi$$
$$44$$ 7.02355i 1.05884i
$$45$$ 1.89564 1.09445i 0.282586 0.163151i
$$46$$ −0.626136 + 0.361500i −0.0923188 + 0.0533003i
$$47$$ 9.57395i 1.39650i −0.715852 0.698252i $$-0.753961\pi$$
0.715852 0.698252i $$-0.246039\pi$$
$$48$$ −3.89564 6.74745i −0.562288 0.973911i
$$49$$ 0 0
$$50$$ −1.89564 1.09445i −0.268085 0.154779i
$$51$$ 8.37386 1.17258
$$52$$ −4.47822 4.65390i −0.621017 0.645380i
$$53$$ 6.16515 0.846849 0.423424 0.905931i $$-0.360828\pi$$
0.423424 + 0.905931i $$0.360828\pi$$
$$54$$ −1.97822 1.14213i −0.269202 0.155424i
$$55$$ 0.895644 1.55130i 0.120769 0.209177i
$$56$$ 0 0
$$57$$ 3.82560i 0.506713i
$$58$$ −2.68693 + 1.55130i −0.352811 + 0.203696i
$$59$$ 10.6652 6.15753i 1.38848 0.801642i 0.395340 0.918535i $$-0.370627\pi$$
0.993145 + 0.116893i $$0.0372935\pi$$
$$60$$ 2.28425i 0.294896i
$$61$$ 7.37386 + 12.7719i 0.944126 + 1.63528i 0.757491 + 0.652846i $$0.226425\pi$$
0.186636 + 0.982429i $$0.440242\pi$$
$$62$$ 1.97822 3.42638i 0.251234 0.435150i
$$63$$ 0 0
$$64$$ 3.41742 0.427178
$$65$$ 0.395644 + 1.59898i 0.0490736 + 0.198329i
$$66$$ −5.00000 −0.615457
$$67$$ −3.87386 2.23658i −0.473268 0.273241i 0.244339 0.969690i $$-0.421429\pi$$
−0.717607 + 0.696449i $$0.754762\pi$$
$$68$$ −2.68693 + 4.65390i −0.325838 + 0.564369i
$$69$$ 2.20871 + 3.82560i 0.265898 + 0.460548i
$$70$$ 0 0
$$71$$ 3.79129 2.18890i 0.449943 0.259775i −0.257863 0.966181i $$-0.583018\pi$$
0.707806 + 0.706407i $$0.249685\pi$$
$$72$$ 7.18693 4.14938i 0.846988 0.489009i
$$73$$ 3.46410i 0.405442i −0.979236 0.202721i $$-0.935021\pi$$
0.979236 0.202721i $$-0.0649785\pi$$
$$74$$ −1.58258 2.74110i −0.183971 0.318647i
$$75$$ −6.68693 + 11.5821i −0.772140 + 1.33739i
$$76$$ −2.12614 1.22753i −0.243885 0.140807i
$$77$$ 0 0
$$78$$ 3.31307 3.18800i 0.375131 0.360970i
$$79$$ −6.00000 −0.675053 −0.337526 0.941316i $$-0.609590\pi$$
−0.337526 + 0.941316i $$0.609590\pi$$
$$80$$ −1.10436 0.637600i −0.123471 0.0712859i
$$81$$ 0.208712 0.361500i 0.0231902 0.0401667i
$$82$$ −1.79129 3.10260i −0.197815 0.342625i
$$83$$ 7.02355i 0.770935i −0.922721 0.385468i $$-0.874040\pi$$
0.922721 0.385468i $$-0.125960\pi$$
$$84$$ 0 0
$$85$$ 1.18693 0.685275i 0.128741 0.0743286i
$$86$$ 4.28245i 0.461789i
$$87$$ 9.47822 + 16.4168i 1.01617 + 1.76006i
$$88$$ 3.39564 5.88143i 0.361977 0.626962i
$$89$$ −13.9782 8.07033i −1.48169 0.855453i −0.481904 0.876224i $$-0.660055\pi$$
−0.999784 + 0.0207708i $$0.993388\pi$$
$$90$$ −1.00000 −0.105409
$$91$$ 0 0
$$92$$ −2.83485 −0.295553
$$93$$ −20.9347 12.0866i −2.17082 1.25333i
$$94$$ −2.18693 + 3.78788i −0.225565 + 0.390690i
$$95$$ 0.313068 + 0.542250i 0.0321201 + 0.0556337i
$$96$$ 13.2288i 1.35015i
$$97$$ −6.31307 + 3.64485i −0.640995 + 0.370079i −0.784998 0.619499i $$-0.787336\pi$$
0.144003 + 0.989577i $$0.454003\pi$$
$$98$$ 0 0
$$99$$ 18.7864i 1.88811i
$$100$$ −4.29129 7.43273i −0.429129 0.743273i
$$101$$ −2.60436 + 4.51088i −0.259143 + 0.448849i −0.966013 0.258495i $$-0.916773\pi$$
0.706869 + 0.707344i $$0.250107\pi$$
$$102$$ −3.31307 1.91280i −0.328043 0.189396i
$$103$$ 4.58258 0.451535 0.225767 0.974181i $$-0.427511\pi$$
0.225767 + 0.974181i $$0.427511\pi$$
$$104$$ 1.50000 + 6.06218i 0.147087 + 0.594445i
$$105$$ 0 0
$$106$$ −2.43920 1.40828i −0.236917 0.136784i
$$107$$ 2.60436 4.51088i 0.251773 0.436083i −0.712241 0.701935i $$-0.752320\pi$$
0.964014 + 0.265852i $$0.0856532\pi$$
$$108$$ −4.47822 7.75650i −0.430917 0.746370i
$$109$$ 7.93725i 0.760251i −0.924935 0.380126i $$-0.875881\pi$$
0.924935 0.380126i $$-0.124119\pi$$
$$110$$ −0.708712 + 0.409175i −0.0675731 + 0.0390133i
$$111$$ −16.7477 + 9.66930i −1.58962 + 0.917770i
$$112$$ 0 0
$$113$$ −5.29129 9.16478i −0.497762 0.862150i 0.502234 0.864732i $$-0.332512\pi$$
−0.999997 + 0.00258173i $$0.999178\pi$$
$$114$$ 0.873864 1.51358i 0.0818448 0.141759i
$$115$$ 0.626136 + 0.361500i 0.0583875 + 0.0337101i
$$116$$ −12.1652 −1.12951
$$117$$ −11.9782 12.4481i −1.10739 1.15083i
$$118$$ −5.62614 −0.517928
$$119$$ 0 0
$$120$$ 1.10436 1.91280i 0.100813 0.174614i
$$121$$ 2.18693 + 3.78788i 0.198812 + 0.344352i
$$122$$ 6.73750i 0.609985i
$$123$$ −18.9564 + 10.9445i −1.70924 + 0.986833i
$$124$$ 13.4347 7.75650i 1.20647 0.696555i
$$125$$ 4.47315i 0.400091i
$$126$$ 0 0
$$127$$ −3.47822 + 6.02445i −0.308642 + 0.534584i −0.978066 0.208297i $$-0.933208\pi$$
0.669423 + 0.742881i $$0.266541\pi$$
$$128$$ −9.56080 5.51993i −0.845063 0.487897i
$$129$$ 26.1652 2.30371
$$130$$ 0.208712 0.723000i 0.0183053 0.0634113i
$$131$$ −17.3739 −1.51796 −0.758981 0.651113i $$-0.774302\pi$$
−0.758981 + 0.651113i $$0.774302\pi$$
$$132$$ −16.9782 9.80238i −1.47776 0.853188i
$$133$$ 0 0
$$134$$ 1.02178 + 1.76978i 0.0882684 + 0.152885i
$$135$$ 2.28425i 0.196597i
$$136$$ 4.50000 2.59808i 0.385872 0.222783i
$$137$$ 10.3521 5.97678i 0.884438 0.510631i 0.0123190 0.999924i $$-0.496079\pi$$
0.872119 + 0.489294i $$0.162745\pi$$
$$138$$ 2.01810i 0.171792i
$$139$$ −1.89564 3.28335i −0.160786 0.278490i 0.774365 0.632740i $$-0.218070\pi$$
−0.935151 + 0.354249i $$0.884736\pi$$
$$140$$ 0 0
$$141$$ 23.1434 + 13.3618i 1.94902 + 1.12527i
$$142$$ −2.00000 −0.167836
$$143$$ −13.5826 3.92095i −1.13583 0.327886i
$$144$$ 13.3739 1.11449
$$145$$ 2.68693 + 1.55130i 0.223138 + 0.128829i
$$146$$ −0.791288 + 1.37055i −0.0654874 + 0.113428i
$$147$$ 0 0
$$148$$ 12.4104i 1.02013i
$$149$$ −0.395644 + 0.228425i −0.0324124 + 0.0187133i −0.516119 0.856517i $$-0.672624\pi$$
0.483706 + 0.875230i $$0.339290\pi$$
$$150$$ 5.29129 3.05493i 0.432032 0.249434i
$$151$$ 12.1244i 0.986666i −0.869841 0.493333i $$-0.835778\pi$$
0.869841 0.493333i $$-0.164222\pi$$
$$152$$ 1.18693 + 2.05583i 0.0962729 + 0.166750i
$$153$$ −7.18693 + 12.4481i −0.581029 + 1.00637i
$$154$$ 0 0
$$155$$ −3.95644 −0.317789
$$156$$ 17.5000 4.33013i 1.40112 0.346688i
$$157$$ −0.956439 −0.0763322 −0.0381661 0.999271i $$-0.512152\pi$$
−0.0381661 + 0.999271i $$0.512152\pi$$
$$158$$ 2.37386 + 1.37055i 0.188854 + 0.109035i
$$159$$ −8.60436 + 14.9032i −0.682370 + 1.18190i
$$160$$ 1.08258 + 1.87508i 0.0855851 + 0.148238i
$$161$$ 0 0
$$162$$ −0.165151 + 0.0953502i −0.0129755 + 0.00749142i
$$163$$ 6.00000 3.46410i 0.469956 0.271329i −0.246265 0.969202i $$-0.579203\pi$$
0.716221 + 0.697873i $$0.245870\pi$$
$$164$$ 14.0471i 1.09689i
$$165$$ 2.50000 + 4.33013i 0.194625 + 0.337100i
$$166$$ −1.60436 + 2.77883i −0.124522 + 0.215679i
$$167$$ 12.7087 + 7.33738i 0.983430 + 0.567783i 0.903304 0.429001i $$-0.141134\pi$$
0.0801258 + 0.996785i $$0.474468\pi$$
$$168$$ 0 0
$$169$$ 11.5000 6.06218i 0.884615 0.466321i
$$170$$ −0.626136 −0.0480225
$$171$$ −5.68693 3.28335i −0.434891 0.251084i
$$172$$ −8.39564 + 14.5417i −0.640162 + 1.10879i
$$173$$ −9.87386 17.1020i −0.750696 1.30024i −0.947486 0.319798i $$-0.896385\pi$$
0.196790 0.980446i $$-0.436948\pi$$
$$174$$ 8.66025i 0.656532i
$$175$$ 0 0
$$176$$ 9.47822 5.47225i 0.714448 0.412487i
$$177$$ 34.3749i 2.58377i
$$178$$ 3.68693 + 6.38595i 0.276347 + 0.478647i
$$179$$ 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i $$-0.724142\pi$$
0.983742 + 0.179585i $$0.0574756\pi$$
$$180$$ −3.39564 1.96048i −0.253096 0.146125i
$$181$$ −9.16515 −0.681240 −0.340620 0.940201i $$-0.610637\pi$$
−0.340620 + 0.940201i $$0.610637\pi$$
$$182$$ 0 0
$$183$$ −41.1652 −3.04302
$$184$$ 2.37386 + 1.37055i 0.175004 + 0.101038i
$$185$$ −1.58258 + 2.74110i −0.116353 + 0.201530i
$$186$$ 5.52178 + 9.56400i 0.404877 + 0.701267i
$$187$$ 11.7629i 0.860185i
$$188$$ −14.8521 + 8.57485i −1.08320 + 0.625386i
$$189$$ 0 0
$$190$$ 0.286051i 0.0207523i
$$191$$ 7.18693 + 12.4481i 0.520028 + 0.900715i 0.999729 + 0.0232830i $$0.00741188\pi$$
−0.479701 + 0.877432i $$0.659255\pi$$
$$192$$ −4.76951 + 8.26103i −0.344210 + 0.596188i
$$193$$ 16.7477 + 9.66930i 1.20553 + 0.696012i 0.961779 0.273827i $$-0.0882895\pi$$
0.243749 + 0.969838i $$0.421623\pi$$
$$194$$ 3.33030 0.239102
$$195$$ −4.41742 1.27520i −0.316338 0.0913190i
$$196$$ 0 0
$$197$$ 1.97822 + 1.14213i 0.140942 + 0.0813731i 0.568813 0.822467i $$-0.307403\pi$$
−0.427871 + 0.903840i $$0.640736\pi$$
$$198$$ 4.29129 7.43273i 0.304969 0.528221i
$$199$$ 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i $$-0.0391815\pi$$
−0.602549 + 0.798082i $$0.705848\pi$$
$$200$$ 8.29875i 0.586811i
$$201$$ 10.8131 6.24293i 0.762695 0.440342i
$$202$$ 2.06080 1.18980i 0.144997 0.0837141i
$$203$$ 0 0
$$204$$ −7.50000 12.9904i −0.525105 0.909509i
$$205$$ −1.79129 + 3.10260i −0.125109 + 0.216695i
$$206$$ −1.81307 1.04678i −0.126322 0.0729323i
$$207$$ −7.58258 −0.527025
$$208$$ −2.79129 + 9.66930i −0.193541 + 0.670446i
$$209$$ −5.37386 −0.371718
$$210$$ 0 0
$$211$$ −5.29129 + 9.16478i −0.364267 + 0.630929i −0.988658 0.150183i $$-0.952014\pi$$
0.624391 + 0.781112i $$0.285347\pi$$
$$212$$ −5.52178 9.56400i −0.379237 0.656859i
$$213$$ 12.2197i 0.837280i
$$214$$ −2.06080 + 1.18980i −0.140873 + 0.0813331i
$$215$$ 3.70871 2.14123i 0.252932 0.146030i
$$216$$ 8.66025i 0.589256i
$$217$$ 0 0
$$218$$ −1.81307 + 3.14033i −0.122796 + 0.212690i
$$219$$ 8.37386 + 4.83465i 0.565853 + 0.326696i
$$220$$ −3.20871 −0.216331
$$221$$ −7.50000 7.79423i −0.504505 0.524297i
$$222$$ 8.83485 0.592956
$$223$$ 16.4347 + 9.48855i 1.10055 + 0.635401i 0.936364 0.351029i $$-0.114168\pi$$
0.164182 + 0.986430i $$0.447502\pi$$
$$224$$ 0 0
$$225$$ −11.4782 19.8809i −0.765215 1.32539i
$$226$$ 4.83465i 0.321596i
$$227$$ −7.66515 + 4.42548i −0.508754 + 0.293729i −0.732321 0.680959i $$-0.761563\pi$$
0.223567 + 0.974688i $$0.428230\pi$$
$$228$$ 5.93466 3.42638i 0.393032 0.226917i
$$229$$ 6.92820i 0.457829i −0.973447 0.228914i $$-0.926482\pi$$
0.973447 0.228914i $$-0.0735176\pi$$
$$230$$ −0.165151 0.286051i −0.0108898 0.0188616i
$$231$$ 0 0
$$232$$ 10.1869 + 5.88143i 0.668805 + 0.386135i
$$233$$ 15.9564 1.04534 0.522671 0.852535i $$-0.324936\pi$$
0.522671 + 0.852535i $$0.324936\pi$$
$$234$$ 1.89564 + 7.66115i 0.123922 + 0.500825i
$$235$$ 4.37386 0.285319
$$236$$ −19.1044 11.0299i −1.24359 0.717986i
$$237$$ 8.37386 14.5040i 0.543941 0.942133i
$$238$$ 0 0
$$239$$ 13.2288i 0.855697i 0.903850 + 0.427849i $$0.140728\pi$$
−0.903850 + 0.427849i $$0.859272\pi$$
$$240$$ 3.08258 1.77973i 0.198979 0.114881i
$$241$$ 17.0608 9.85005i 1.09898 0.634498i 0.163029 0.986621i $$-0.447874\pi$$
0.935954 + 0.352123i $$0.114540\pi$$
$$242$$ 1.99820i 0.128449i
$$243$$ 8.08258 + 13.9994i 0.518497 + 0.898064i
$$244$$ 13.2087 22.8782i 0.845601 1.46462i
$$245$$ 0 0
$$246$$ 10.0000 0.637577
$$247$$ 3.56080 3.42638i 0.226568 0.218015i
$$248$$ −15.0000 −0.952501
$$249$$ 16.9782 + 9.80238i 1.07595 + 0.621201i
$$250$$ 1.02178 1.76978i 0.0646231 0.111930i
$$251$$ −1.41742 2.45505i −0.0894670 0.154961i 0.817819 0.575476i $$-0.195183\pi$$
−0.907286 + 0.420514i $$0.861850\pi$$
$$252$$ 0 0
$$253$$ −5.37386 + 3.10260i −0.337852 + 0.195059i
$$254$$ 2.75227 1.58903i 0.172693 0.0997043i
$$255$$ 3.82560i 0.239568i
$$256$$ −0.895644 1.55130i −0.0559777 0.0969563i
$$257$$ 2.52178 4.36785i 0.157304 0.272459i −0.776591 0.630005i $$-0.783053\pi$$
0.933896 + 0.357546i $$0.116386\pi$$
$$258$$ −10.3521 5.97678i −0.644493 0.372098i
$$259$$ 0 0
$$260$$ 2.12614 2.04588i 0.131857 0.126880i
$$261$$ −32.5390 −2.01411
$$262$$ 6.87386 + 3.96863i 0.424669 + 0.245183i
$$263$$ −4.66515 + 8.08028i −0.287666 + 0.498251i −0.973252 0.229740i $$-0.926212\pi$$
0.685587 + 0.727991i $$0.259546\pi$$
$$264$$ 9.47822 + 16.4168i 0.583344 + 1.01038i
$$265$$ 2.81655i 0.173019i
$$266$$ 0 0
$$267$$ 39.0172 22.5266i 2.38782 1.37861i
$$268$$ 8.01270i 0.489454i
$$269$$ −7.89564 13.6757i −0.481406 0.833819i 0.518366 0.855159i $$-0.326540\pi$$
−0.999772 + 0.0213391i $$0.993207\pi$$
$$270$$ 0.521780 0.903750i 0.0317545 0.0550005i
$$271$$ 11.1261 + 6.42368i 0.675865 + 0.390211i 0.798295 0.602266i $$-0.205736\pi$$
−0.122430 + 0.992477i $$0.539069\pi$$
$$272$$ 8.37386 0.507740
$$273$$ 0 0
$$274$$ −5.46099 −0.329910
$$275$$ −16.2695 9.39320i −0.981088 0.566432i
$$276$$ 3.95644 6.85275i 0.238150 0.412487i
$$277$$ −5.87386 10.1738i −0.352926 0.611286i 0.633835 0.773469i $$-0.281480\pi$$
−0.986761 + 0.162182i $$0.948147\pi$$
$$278$$ 1.73205i 0.103882i
$$279$$ 35.9347 20.7469i 2.15135 1.24208i
$$280$$ 0 0
$$281$$ 30.6446i 1.82810i 0.405597 + 0.914052i $$0.367064\pi$$
−0.405597 + 0.914052i $$0.632936\pi$$
$$282$$ −6.10436 10.5731i −0.363509 0.629616i
$$283$$ 1.37386 2.37960i 0.0816677 0.141453i −0.822299 0.569056i $$-0.807309\pi$$
0.903966 + 0.427603i $$0.140642\pi$$
$$284$$ −6.79129 3.92095i −0.402989 0.232666i
$$285$$ −1.74773 −0.103526
$$286$$ 4.47822 + 4.65390i 0.264803 + 0.275191i
$$287$$ 0 0
$$288$$ −19.6652 11.3537i −1.15878 0.669022i
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ −0.708712 1.22753i −0.0416170 0.0720828i
$$291$$ 20.3477i 1.19280i
$$292$$ −5.37386 + 3.10260i −0.314482 + 0.181566i
$$293$$ −2.20871 + 1.27520i −0.129034 + 0.0744980i −0.563128 0.826370i $$-0.690402\pi$$
0.434093 + 0.900868i $$0.357069\pi$$
$$294$$ 0 0
$$295$$ 2.81307 + 4.87238i 0.163783 + 0.283681i
$$296$$ −6.00000 + 10.3923i −0.348743 + 0.604040i
$$297$$ −16.9782 9.80238i −0.985176 0.568792i
$$298$$ 0.208712 0.0120904
$$299$$ 1.58258 5.48220i 0.0915227 0.317044i
$$300$$ 23.9564 1.38313
$$301$$ 0 0
$$302$$ −2.76951 + 4.79693i −0.159367 + 0.276032i
$$303$$ −7.26951 12.5912i −0.417622 0.723343i
$$304$$ 3.82560i 0.219413i
$$305$$ −5.83485 + 3.36875i −0.334102 + 0.192894i
$$306$$ 5.68693 3.28335i 0.325100 0.187697i
$$307$$ 15.5130i 0.885374i −0.896676 0.442687i $$-0.854025\pi$$
0.896676 0.442687i $$-0.145975\pi$$
$$308$$ 0 0
$$309$$ −6.39564 + 11.0776i −0.363835 + 0.630182i
$$310$$ 1.56534 + 0.903750i 0.0889054 + 0.0513296i
$$311$$ −26.5390 −1.50489 −0.752445 0.658655i $$-0.771126\pi$$
−0.752445 + 0.658655i $$0.771126\pi$$
$$312$$ −16.7477 4.83465i −0.948153 0.273708i
$$313$$ 6.74773 0.381404 0.190702 0.981648i $$-0.438924\pi$$
0.190702 + 0.981648i $$0.438924\pi$$
$$314$$ 0.378409 + 0.218475i 0.0213549 + 0.0123292i
$$315$$ 0 0
$$316$$ 5.37386 + 9.30780i 0.302303 + 0.523605i
$$317$$ 18.5203i 1.04020i −0.854105 0.520101i $$-0.825894\pi$$
0.854105 0.520101i $$-0.174106\pi$$
$$318$$ 6.80852 3.93090i 0.381803 0.220434i
$$319$$ −23.0608 + 13.3142i −1.29116 + 0.745450i
$$320$$ 1.56125i 0.0872766i
$$321$$ 7.26951 + 12.5912i 0.405744 + 0.702770i
$$322$$ 0 0
$$323$$ −3.56080 2.05583i −0.198128 0.114389i
$$324$$ −0.747727 −0.0415404
$$325$$ 16.7695 4.14938i 0.930205 0.230166i
$$326$$ −3.16515 −0.175302
$$327$$ 19.1869 + 11.0776i 1.06104 + 0.612592i
$$328$$ −6.79129 + 11.7629i −0.374986 + 0.649495i
$$329$$ 0 0
$$330$$ 2.28425i 0.125744i
$$331$$ 21.5608 12.4481i 1.18509 0.684211i 0.227902 0.973684i $$-0.426813\pi$$
0.957186 + 0.289473i $$0.0934800\pi$$
$$332$$ −10.8956 + 6.29060i −0.597976 + 0.345242i
$$333$$ 33.1950i 1.81908i
$$334$$ −3.35208 5.80598i −0.183418 0.317689i
$$335$$ 1.02178 1.76978i 0.0558258 0.0966932i
$$336$$ 0 0
$$337$$ 9.95644 0.542362 0.271181 0.962528i $$-0.412586\pi$$
0.271181 + 0.962528i $$0.412586\pi$$
$$338$$ −5.93466 0.228425i −0.322803 0.0124247i
$$339$$ 29.5390 1.60434
$$340$$ −2.12614 1.22753i −0.115306 0.0665719i
$$341$$ 16.9782 29.4071i 0.919422 1.59249i
$$342$$ 1.50000 + 2.59808i 0.0811107 + 0.140488i
$$343$$ 0 0
$$344$$ 14.0608 8.11800i 0.758107 0.437693i
$$345$$ −1.74773 + 1.00905i −0.0940945 + 0.0543255i
$$346$$ 9.02175i 0.485013i
$$347$$ 6.79129 + 11.7629i 0.364575 + 0.631463i 0.988708 0.149855i $$-0.0478808\pi$$
−0.624132 + 0.781319i $$0.714547\pi$$
$$348$$ 16.9782 29.4071i 0.910128 1.57639i
$$349$$ 18.2477 + 10.5353i 0.976778 + 0.563943i 0.901296 0.433204i $$-0.142617\pi$$
0.0754825 + 0.997147i $$0.475950\pi$$
$$350$$ 0 0
$$351$$ 17.5000 4.33013i 0.934081 0.231125i
$$352$$ −18.5826 −0.990455
$$353$$ −15.7259 9.07938i −0.837008 0.483247i 0.0192383 0.999815i $$-0.493876\pi$$
−0.856246 + 0.516568i $$0.827209\pi$$
$$354$$ 7.85208 13.6002i 0.417334 0.722843i
$$355$$ 1.00000 + 1.73205i 0.0530745 + 0.0919277i
$$356$$ 28.9126i 1.53236i
$$357$$ 0 0
$$358$$ −3.56080 + 2.05583i −0.188194 + 0.108654i
$$359$$ 0.552200i 0.0291440i −0.999894 0.0145720i $$-0.995361\pi$$
0.999894 0.0145720i $$-0.00463858\pi$$
$$360$$ 1.89564 + 3.28335i 0.0999092 + 0.173048i
$$361$$ −8.56080 + 14.8277i −0.450568 + 0.780407i
$$362$$ 3.62614 + 2.09355i 0.190586 + 0.110035i
$$363$$ −12.2087 −0.640791
$$364$$ 0 0
$$365$$ 1.58258 0.0828358
$$366$$ 16.2867 + 9.40315i 0.851322 + 0.491511i
$$367$$ −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i $$-0.989006\pi$$
0.529607 + 0.848243i $$0.322339\pi$$
$$368$$ 2.20871 + 3.82560i 0.115137 + 0.199423i
$$369$$ 37.5728i 1.95596i
$$370$$ 1.25227 0.723000i 0.0651026 0.0375870i
$$371$$ 0 0
$$372$$ 43.3013i 2.24507i
$$373$$ −16.1044 27.8936i −0.833852 1.44427i −0.894962 0.446143i $$-0.852797\pi$$
0.0611098 0.998131i $$-0.480536\pi$$
$$374$$ 2.68693 4.65390i 0.138938 0.240648i
$$375$$ −10.8131 6.24293i −0.558384 0.322383i
$$376$$ 16.5826 0.855181
$$377$$ 6.79129 23.5257i 0.349769 1.21164i
$$378$$ 0 0
$$379$$ −24.5608 14.1802i −1.26160 0.728387i −0.288219 0.957565i $$-0.593063\pi$$
−0.973385 + 0.229178i $$0.926396\pi$$
$$380$$ 0.560795 0.971326i 0.0287682 0.0498280i
$$381$$ −9.70871 16.8160i −0.497392 0.861509i
$$382$$ 6.56670i 0.335982i
$$383$$ −1.10436 + 0.637600i −0.0564300 + 0.0325799i −0.527950 0.849276i $$-0.677039\pi$$
0.471520 + 0.881856i $$0.343706\pi$$
$$384$$ 26.6869 15.4077i 1.36186 0.786271i
$$385$$ 0 0
$$386$$ −4.41742 7.65120i −0.224841 0.389436i
$$387$$ −22.4564 + 38.8957i −1.14152 + 1.97718i
$$388$$ 11.3085 + 6.52898i 0.574103 + 0.331459i
$$389$$ −0.330303 −0.0167470 −0.00837351 0.999965i $$-0.502665\pi$$
−0.00837351 + 0.999965i $$0.502665\pi$$
$$390$$ 1.45644 + 1.51358i 0.0737497 + 0.0766429i
$$391$$ −4.74773 −0.240103
$$392$$ 0 0
$$393$$ 24.2477 41.9983i 1.22314 2.11853i
$$394$$ −0.521780 0.903750i −0.0262869 0.0455303i
$$395$$ 2.74110i 0.137920i
$$396$$ 29.1434 16.8259i 1.46451 0.845535i
$$397$$ −28.1216 + 16.2360i −1.41138 + 0.814862i −0.995519 0.0945652i $$-0.969854\pi$$
−0.415864 + 0.909427i $$0.636521\pi$$
$$398$$ 5.02535i 0.251898i
$$399$$ 0 0
$$400$$ −6.68693 + 11.5821i −0.334347 + 0.579105i
$$401$$ 27.0998 + 15.6461i 1.35330 + 0.781328i 0.988710 0.149840i $$-0.0478759\pi$$
0.364590 + 0.931168i $$0.381209\pi$$
$$402$$ −5.70417 −0.284498
$$403$$ 7.50000 + 30.3109i 0.373602 + 1.50989i
$$404$$ 9.33030 0.464200
$$405$$ 0.165151 + 0.0953502i 0.00820644 + 0.00473799i
$$406$$ 0 0
$$407$$ −13.5826 23.5257i −0.673263 1.16613i
$$408$$ 14.5040i 0.718053i
$$409$$ −7.18693 + 4.14938i −0.355371 + 0.205173i −0.667048 0.745015i $$-0.732443\pi$$
0.311677 + 0.950188i $$0.399109\pi$$
$$410$$ 1.41742 0.818350i 0.0700016 0.0404154i
$$411$$ 33.3658i 1.64581i
$$412$$ −4.10436 7.10895i −0.202207 0.350233i
$$413$$ 0 0
$$414$$ 3.00000 + 1.73205i 0.147442 + 0.0851257i
$$415$$ 3.20871 0.157509
$$416$$ 12.3131 11.8483i 0.603698 0.580909i
$$417$$ 10.5826 0.518231
$$418$$ 2.12614 + 1.22753i 0.103993 + 0.0600402i
$$419$$ −0.873864 + 1.51358i −0.0426910 + 0.0739430i −0.886581 0.462573i $$-0.846926\pi$$
0.843890 + 0.536516i $$0.180260\pi$$
$$420$$ 0 0
$$421$$ 4.18710i 0.204067i 0.994781 + 0.102033i $$0.0325349\pi$$
−0.994781 + 0.102033i $$0.967465\pi$$
$$422$$ 4.18693 2.41733i 0.203817 0.117674i
$$423$$ −39.7259 + 22.9358i −1.93154 + 1.11518i
$$424$$ 10.6784i 0.518587i
$$425$$ −7.18693 12.4481i −0.348617 0.603823i
$$426$$ 2.79129 4.83465i 0.135238 0.234240i
$$427$$ 0 0
$$428$$ −9.33030 −0.450997
$$429$$ 28.4347 27.3613i 1.37284 1.32101i
$$430$$ −1.95644 −0.0943479
$$431$$ 30.0172 + 17.3305i 1.44588 + 0.834779i 0.998232 0.0594316i $$-0.0189288\pi$$
0.447647 + 0.894210i $$0.352262\pi$$
$$432$$ −6.97822 + 12.0866i −0.335740 + 0.581518i
$$433$$ −16.2477 28.1419i −0.780816 1.35241i −0.931467 0.363826i $$-0.881470\pi$$
0.150651 0.988587i $$-0.451863\pi$$
$$434$$ 0 0
$$435$$ −7.50000 + 4.33013i −0.359597 + 0.207614i
$$436$$ −12.3131 + 7.10895i −0.589689 + 0.340457i
$$437$$ 2.16900i 0.103757i
$$438$$ −2.20871 3.82560i −0.105536 0.182794i
$$439$$ −10.2695 + 17.7873i −0.490137 + 0.848942i −0.999936 0.0113518i $$-0.996387\pi$$
0.509799 + 0.860294i $$0.329720\pi$$
$$440$$ 2.68693 + 1.55130i 0.128094 + 0.0739554i
$$441$$ 0 0
$$442$$ 1.18693 + 4.79693i 0.0564566 + 0.228167i
$$443$$ −15.1652 −0.720518 −0.360259 0.932852i $$-0.617312\pi$$
−0.360259 + 0.932852i $$0.617312\pi$$
$$444$$ 30.0000 + 17.3205i 1.42374 + 0.821995i
$$445$$ 3.68693 6.38595i 0.174777 0.302723i
$$446$$ −4.33485 7.50818i −0.205261 0.355523i
$$447$$ 1.27520i 0.0603149i
$$448$$ 0 0
$$449$$ −21.7913 + 12.5812i −1.02839 + 0.593744i −0.916524 0.399979i $$-0.869017\pi$$
−0.111870 + 0.993723i $$0.535684\pi$$
$$450$$ 10.4877i 0.494393i
$$451$$ −15.3739 26.6283i −0.723927 1.25388i
$$452$$ −9.47822 + 16.4168i −0.445818 + 0.772179i
$$453$$ 29.3085 + 16.9213i 1.37703 + 0.795031i
$$454$$ 4.04356 0.189774
$$455$$ 0 0
$$456$$ −6.62614 −0.310297
$$457$$ 19.7477 + 11.4014i 0.923760 + 0.533333i 0.884833 0.465909i $$-0.154273\pi$$
0.0389271 + 0.999242i $$0.487606\pi$$
$$458$$ −1.58258 + 2.74110i −0.0739489 + 0.128083i
$$459$$ −7.50000 12.9904i −0.350070 0.606339i
$$460$$ 1.29510i 0.0603844i
$$461$$ −4.02178 + 2.32198i −0.187313 + 0.108145i −0.590724 0.806874i $$-0.701158\pi$$
0.403411 + 0.915019i $$0.367824\pi$$
$$462$$ 0 0
$$463$$ 7.93725i 0.368875i 0.982844 + 0.184438i $$0.0590464\pi$$
−0.982844 + 0.184438i $$0.940954\pi$$
$$464$$ 9.47822 + 16.4168i 0.440015 + 0.762129i
$$465$$ 5.52178 9.56400i 0.256066 0.443520i
$$466$$ −6.31307 3.64485i −0.292447 0.168844i
$$467$$ −30.1652 −1.39588 −0.697938 0.716158i $$-0.745899\pi$$
−0.697938 + 0.716158i $$0.745899\pi$$
$$468$$ −8.58258 + 29.7309i −0.396730 + 1.37431i
$$469$$ 0 0
$$470$$ −1.73049 0.999100i −0.0798217 0.0460851i
$$471$$ 1.33485 2.31203i 0.0615066 0.106533i
$$472$$ 10.6652 + 18.4726i 0.490903 + 0.850270i
$$473$$ 36.7545i 1.68997i
$$474$$ −6.62614 + 3.82560i −0.304349 + 0.175716i
$$475$$ 5.68693 3.28335i 0.260934 0.150651i
$$476$$ 0 0
$$477$$ −14.7695 25.5815i −0.676249 1.17130i
$$478$$ 3.02178 5.23388i 0.138213 0.239392i
$$479$$ 16.3521 + 9.44088i 0.747146 + 0.431365i 0.824662 0.565626i $$-0.191366\pi$$
−0.0775159 + 0.996991i $$0.524699\pi$$
$$480$$ −6.04356 −0.275850
$$481$$ 24.0000 + 6.92820i 1.09431 + 0.315899i
$$482$$ −9.00000 −0.409939
$$483$$ 0 0
$$484$$ 3.91742 6.78518i 0.178065 0.308417i
$$485$$ −1.66515 2.88413i −0.0756106 0.130961i
$$486$$ 7.38505i 0.334993i
$$487$$ 25.4347 14.6847i 1.15255 0.665428i 0.203046 0.979169i $$-0.434916\pi$$
0.949508 + 0.313742i $$0.101583\pi$$
$$488$$ −22.1216 + 12.7719i −1.00140 + 0.578157i
$$489$$ 19.3386i 0.874522i
$$490$$ 0 0
$$491$$ 2.06080 3.56940i 0.0930024 0.161085i −0.815771 0.578375i $$-0.803687\pi$$
0.908773 + 0.417291i $$0.137020\pi$$
$$492$$ 33.9564 + 19.6048i 1.53087 + 0.883851i
$$493$$ −20.3739 −0.917593
$$494$$ −2.19148 + 0.542250i −0.0985992 + 0.0243970i
$$495$$ −8.58258 −0.385758
$$496$$ −20.9347 12.0866i −0.939994 0.542706i
$$497$$ 0 0
$$498$$ −4.47822 7.75650i −0.200674 0.347577i
$$499$$ 18.4050i 0.823921i 0.911202 + 0.411961i $$0.135156\pi$$
−0.911202 + 0.411961i $$0.864844\pi$$
$$500$$ 6.93920 4.00635i 0.310331 0.179169i
$$501$$ −35.4737 + 20.4807i −1.58485 + 0.915012i
$$502$$ 1.29510i 0.0578032i
$$503$$ 9.56080 + 16.5598i 0.426295 + 0.738364i 0.996540 0.0831100i $$-0.0264853\pi$$
−0.570246 + 0.821474i $$0.693152\pi$$
$$504$$ 0 0
$$505$$ −2.06080 1.18980i −0.0917042 0.0529454i
$$506$$ 2.83485 0.126024
$$507$$ −1.39564 + 36.2599i −0.0619827 + 1.61036i
$$508$$ 12.4610 0.552867
$$509$$ 13.0390 + 7.52808i 0.577944 + 0.333676i 0.760316 0.649553i $$-0.225044\pi$$
−0.182372 + 0.983230i $$0.558377\pi$$
$$510$$ 0.873864 1.51358i 0.0386953 0.0670223i
$$511$$ 0 0
$$512$$ 22.8981i 1.01196i
$$513$$ 5.93466 3.42638i 0.262022 0.151278i
$$514$$ −1.99545 + 1.15208i −0.0880157 + 0.0508159i
$$515$$ 2.09355i 0.0922529i
$$516$$ −23.4347 40.5900i −1.03165 1.78688i
$$517$$ −18.7695 + 32.5097i −0.825482 + 1.42978i
$$518$$ 0 0
$$519$$ 55.1216 2.41957
$$520$$ −2.76951 + 0.685275i −0.121451 + 0.0300513i
$$521$$ −16.4174 −0.719260 −0.359630 0.933095i $$-0.617097\pi$$
−0.359630 + 0.933095i $$0.617097\pi$$
$$522$$ 12.8739 + 7.43273i 0.563474 + 0.325322i
$$523$$ 12.1652 21.0707i 0.531945 0.921356i −0.467360 0.884067i $$-0.654795\pi$$
0.999305 0.0372883i $$-0.0118720\pi$$
$$524$$ 15.5608 + 26.9521i 0.679776 + 1.17741i
$$525$$ 0 0
$$526$$ 3.69148 2.13128i 0.160956 0.0929280i
$$527$$ 22.5000 12.9904i 0.980115 0.565870i
$$528$$ 30.5493i 1.32949i
$$529$$ 10.2477 + 17.7496i 0.445553 + 0.771721i
$$530$$ 0.643371 1.11435i 0.0279463 0.0484043i
$$531$$ −51.0998 29.5025i −2.21754 1.28030i
$$532$$ 0 0
$$533$$ 27.1652 + 7.84190i 1.17665 + 0.339671i
$$534$$ −20.5826 −0.890695
$$535$$ 2.06080 + 1.18980i 0.0890960 + 0.0514396i
$$536$$ 3.87386 6.70973i 0.167325 0.289816i
$$537$$ 12.5608 + 21.7559i 0.542038 + 0.938838i
$$538$$ 7.21425i 0.311029i
$$539$$ 0 0
$$540$$ 3.54356 2.04588i 0.152491 0.0880405i
$$541$$ 6.28065i 0.270026i 0.990844 + 0.135013i $$0.0431077\pi$$
−0.990844 + 0.135013i $$0.956892\pi$$
$$542$$ −2.93466 5.08298i −0.126054 0.218333i
$$543$$ 12.7913 22.1552i 0.548927 0.950769i
$$544$$ −12.3131 7.10895i −0.527918 0.304794i
$$545$$ 3.62614 0.155327
$$546$$ 0 0
$$547$$ −11.7477 −0.502297 −0.251148 0.967949i $$-0.580808\pi$$
−0.251148 + 0.967949i $$0.580808\pi$$
$$548$$ −18.5436 10.7061i −0.792142 0.457343i
$$549$$ 35.3303 61.1939i 1.50786 2.61169i
$$550$$ 4.29129 + 7.43273i 0.182981 + 0.316933i
$$551$$ 9.30780i 0.396526i
$$552$$ −6.62614 + 3.82560i −0.282027 + 0.162828i
$$553$$ 0 0
$$554$$ 5.36695i 0.228020i
$$555$$ −4.41742 7.65120i −0.187509 0.324775i
$$556$$ −3.39564 + 5.88143i −0.144007 + 0.249428i
$$557$$ −28.5998 16.5121i −1.21181 0.699640i −0.248659 0.968591i $$-0.579990\pi$$
−0.963154 + 0.268951i $$0.913323\pi$$
$$558$$ −18.9564 −0.802490
$$559$$ −23.4347 24.3540i −0.991180 1.03006i
$$560$$ 0 0
$$561$$ −28.4347 16.4168i −1.20051 0.693116i
$$562$$ 7.00000 12.1244i 0.295277 0.511435i
$$563$$ 18.1652 + 31.4630i 0.765570 + 1.32601i 0.939945 + 0.341327i $$0.110876\pi$$
−0.174375 + 0.984679i $$0.555790\pi$$
$$564$$ 47.8698i 2.01568i
$$565$$ 4.18693 2.41733i 0.176146 0.101698i
$$566$$ −1.08712 + 0.627650i −0.0456951 + 0.0263821i
$$567$$ 0 0
$$568$$ 3.79129 + 6.56670i 0.159079 + 0.275533i
$$569$$ −8.37386 + 14.5040i −0.351051 + 0.608038i −0.986434 0.164159i $$-0.947509\pi$$
0.635383 + 0.772197i $$0.280842\pi$$
$$570$$ 0.691478 + 0.399225i 0.0289628 + 0.0167217i
$$571$$ −2.04356 −0.0855204 −0.0427602 0.999085i $$-0.513615\pi$$
−0.0427602 + 0.999085i $$0.513615\pi$$
$$572$$ 6.08258 + 24.5824i 0.254325 + 1.02784i
$$573$$ −40.1216 −1.67610
$$574$$ 0 0
$$575$$ 3.79129 6.56670i 0.158108 0.273850i
$$576$$ −8.18693 14.1802i −0.341122 0.590841i
$$577$$ 35.6501i 1.48413i −0.670327 0.742066i $$-0.733846\pi$$
0.670327 0.742066i $$-0.266154\pi$$
$$578$$ −3.16515 + 1.82740i −0.131653 + 0.0760099i
$$579$$ −46.7477 + 26.9898i −1.94277 + 1.12166i
$$580$$ 5.55765i 0.230769i
$$581$$ 0 0
$$582$$ −4.64792 + 8.05043i −0.192662 + 0.333701i
$$583$$ −20.9347 12.0866i −0.867025 0.500577i
$$584$$ 6.00000 0.248282
$$585$$ 5.68693 5.47225i 0.235126 0.226250i
$$586$$ 1.16515 0.0481320
$$587$$ 8.22595 + 4.74925i 0.339521 + 0.196023i 0.660060 0.751213i $$-0.270531\pi$$
−0.320539 + 0.947235i $$0.603864\pi$$
$$588$$ 0 0
$$589$$ 5.93466 + 10.2791i 0.244533 + 0.423544i
$$590$$ 2.57030i 0.105818i
$$591$$ −5.52178 + 3.18800i −0.227136 + 0.131137i
$$592$$ −16.7477 + 9.66930i −0.688327 + 0.397406i
$$593$$ 6.37600i 0.261831i −0.991394 0.130916i $$-0.958208\pi$$
0.991394 0.130916i $$-0.0417917\pi$$
$$594$$ 4.47822 + 7.75650i 0.183744 + 0.318253i
$$595$$ 0 0
$$596$$ 0.708712 + 0.409175i 0.0290300 + 0.0167605i
$$597$$ −30.7042 −1.25664
$$598$$ −1.87841 + 1.80750i −0.0768139 + 0.0739142i
$$599$$ −6.62614 −0.270737 −0.135368 0.990795i $$-0.543222\pi$$
−0.135368 + 0.990795i $$0.543222\pi$$
$$600$$ −20.0608 11.5821i −0.818979 0.472837i
$$601$$ −6.18693 + 10.7161i −0.252370 + 0.437118i −0.964178 0.265256i $$-0.914543\pi$$
0.711808 + 0.702374i $$0.247877\pi$$
$$602$$ 0 0
$$603$$ 21.4322i 0.872785i
$$604$$ −18.8085 + 10.8591i −0.765308 + 0.441851i
$$605$$ −1.73049 + 0.999100i −0.0703545 + 0.0406192i
$$606$$ 6.64215i 0.269819i
$$607$$ −9.87386 17.1020i −0.400768 0.694150i 0.593051 0.805165i $$-0.297923\pi$$
−0.993819 + 0.111015i $$0.964590\pi$$
$$608$$ 3.24773 5.62523i 0.131713 0.228133i
$$609$$ 0 0
$$610$$ 3.07803 0.124626
$$611$$ −8.29129 33.5088i −0.335430 1.35562i
$$612$$ 25.7477 1.04079
$$613$$ −15.8085 9.12705i −0.638500 0.368638i 0.145536 0.989353i $$-0.453509\pi$$
−0.784037 + 0.620715i $$0.786843\pi$$
$$614$$ −3.54356 + 6.13763i −0.143006 + 0.247694i
$$615$$ −5.00000 8.66025i −0.201619 0.349215i
$$616$$ 0 0
$$617$$ −14.9174 + 8.61258i −0.600553 + 0.346729i −0.769259 0.638937i $$-0.779374\pi$$
0.168706 + 0.985666i $$0.446041\pi$$
$$618$$ 5.06080 2.92185i 0.203575 0.117534i
$$619$$ 19.3386i 0.777284i −0.921389 0.388642i $$-0.872944\pi$$
0.921389 0.388642i $$-0.127056\pi$$
$$620$$ 3.54356 + 6.13763i 0.142313 + 0.246493i
$$621$$ 3.95644 6.85275i 0.158766 0.274992i
$$622$$ 10.5000 + 6.06218i 0.421012 + 0.243071i
$$623$$ 0 0
$$624$$ −19.4782 20.2424i −0.779753 0.810343i
$$625$$ 21.9129 0.876515
$$626$$ −2.66970 1.54135i −0.106703 0.0616048i
$$627$$ 7.50000 12.9904i 0.299521 0.518786i
$$628$$ 0.856629 + 1.48372i 0.0341832 + 0.0592071i
$$629$$ 20.7846i 0.828737i
$$630$$ 0 0
$$631$$ 23.9347 13.8187i 0.952824 0.550113i 0.0588668 0.998266i $$-0.481251\pi$$
0.893957 + 0.448153i $$0.147918\pi$$
$$632$$ 10.3923i 0.413384i
$$633$$ −14.7695 25.5815i −0.587035 1.01677i
$$634$$ −4.23049 + 7.32743i −0.168014 + 0.291009i
$$635$$ −2.75227 1.58903i −0.109221 0.0630586i
$$636$$ 30.8258 1.22232
$$637$$ 0 0
$$638$$ 12.1652 0.481623
$$639$$ −18.1652 10.4877i −0.718602 0.414885i
$$640$$ 2.52178 4.36785i 0.0996821 0.172654i
$$641$$ −14.6869 25.4385i −0.580099 1.00476i −0.995467 0.0951074i $$-0.969681\pi$$
0.415368 0.909653i $$-0.363653\pi$$
$$642$$ 6.64215i 0.262145i
$$643$$ −39.2477 + 22.6597i −1.54778 + 0.893611i −0.549468 + 0.835515i $$0.685170\pi$$
−0.998311 + 0.0580962i $$0.981497\pi$$
$$644$$ 0 0
$$645$$ 11.9536i 0.470671i
$$646$$ 0.939205 + 1.62675i 0.0369525 + 0.0640036i
$$647$$ 17.5390 30.3785i 0.689530 1.19430i −0.282460 0.959279i $$-0.591151\pi$$
0.971990 0.235022i $$-0.0755161\pi$$
$$648$$ 0.626136 + 0.361500i 0.0245970 + 0.0142011i
$$649$$ −48.2867 −1.89542
$$650$$ −7.58258 2.18890i −0.297413 0.0858558i
$$651$$ 0 0
$$652$$ −10.7477 6.20520i −0.420913 0.243015i
$$653$$ −7.89564 + 13.6757i −0.308980 + 0.535170i −0.978140 0.207949i $$-0.933321\pi$$
0.669159 + 0.743119i $$0.266654\pi$$
$$654$$ −5.06080 8.76555i −0.197893 0.342760i
$$655$$ 7.93725i 0.310134i
$$656$$ −18.9564 + 10.9445i −0.740125 + 0.427311i
$$657$$ −14.3739 + 8.29875i −0.560778 + 0.323765i
$$658$$ 0 0
$$659$$ −3.00000 5.19615i −0.116863 0.202413i 0.801660 0.597781i $$-0.203951\pi$$
−0.918523 + 0.395367i $$0.870617\pi$$
$$660$$ 4.47822 7.75650i 0.174314 0.301922i
$$661$$ 43.7477 + 25.2578i 1.70159 + 0.982413i 0.944155 + 0.329502i $$0.106881\pi$$
0.757434 + 0.652911i $$0.226453\pi$$
$$662$$ −11.3739 −0.442058
$$663$$ 29.3085 7.25198i 1.13825 0.281644i
$$664$$ 12.1652 0.472099
$$665$$ 0 0
$$666$$ −7.58258 + 13.1334i −0.293819 + 0.508909i
$$667$$ −5.37386 9.30780i −0.208077 0.360400i
$$668$$ 26.2867i 1.01706i
$$669$$ −45.8739 + 26.4853i −1.77359 + 1.02398i
$$670$$ −0.808522 + 0.466801i −0.0312359 + 0.0180341i
$$671$$ 57.8251i 2.23231i
$$672$$ 0 0
$$673$$ −13.2477 + 22.9457i −0.510662 + 0.884493i 0.489261 + 0.872137i $$0.337266\pi$$
−0.999924 + 0.0123559i $$0.996067\pi$$
$$674$$ −3.93920 2.27430i −0.151732 0.0876028i
$$675$$ 23.9564 0.922084
$$676$$ −19.7042 12.4104i −0.757853 0.477323i
$$677$$ 29.2087 1.12258 0.561291 0.827619i $$-0.310305\pi$$
0.561291 + 0.827619i $$0.310305\pi$$
$$678$$ −11.6869 6.74745i −0.448834 0.259134i
$$679$$ 0 0
$$680$$ 1.18693 + 2.05583i 0.0455168 + 0.0788373i
$$681$$ 24.7056i 0.946719i
$$682$$ −13.4347 + 7.75650i −0.514440 + 0.297012i
$$683$$ 26.2913 15.1793i 1.00601 0.580819i 0.0959878 0.995383i $$-0.469399\pi$$
0.910020 + 0.414563i $$0.136066\pi$$
$$684$$ 11.7629i 0.449764i
$$685$$ 2.73049 + 4.72935i 0.104327 + 0.180699i
$$686$$ 0 0
$$687$$ 16.7477 + 9.66930i 0.638966 + 0.368907i
$$688$$ 26.1652 0.997537
$$689$$ 21.5780 5.33918i 0.822057 0.203406i
$$690$$ 0.921970 0.0350988
$$691$$ 8.93466 + 5.15843i 0.339890 + 0.196236i 0.660224 0.751069i $$-0.270462\pi$$
−0.320333 + 0.947305i $$0.603795\pi$$
$$692$$ −17.6869 + 30.6347i −0.672356 + 1.16456i
$$693$$ 0 0
$$694$$ 6.20520i 0.235546i
$$695$$ 1.50000 0.866025i 0.0568982 0.0328502i
$$696$$ −28.4347 + 16.4168i −1.07781 + 0.622276i
$$697$$ 23.5257i 0.891100i
$$698$$ −4.81307 8.33648i −0.182177 0.315540i
$$699$$ −22.2695 + 38.5719i −0.842310 + 1.45892i
$$700$$ 0 0
$$701$$ −13.9129 −0.525482 −0.262741 0.964866i $$-0.584627\pi$$
−0.262741 + 0.964866i $$0.584627\pi$$
$$702$$ −7.91288 2.28425i −0.298652 0.0862135i
$$703$$ 9.49545 0.358128
$$704$$ −11.6044 6.69978i −0.437356 0.252507i
$$705$$ −6.10436 + 10.5731i −0.229903 + 0.398204i
$$706$$ 4.14792 + 7.18440i 0.156109 + 0.270389i
$$707$$ 0 0
$$708$$ 53.3258 30.7876i 2.00410 1.15707i
$$709$$ −13.1869 + 7.61348i −0.495246 + 0.285930i −0.726748 0.686904i $$-0.758969\pi$$
0.231502 + 0.972834i $$0.425636\pi$$
$$710$$ 0.913701i 0.0342906i
$$711$$ 14.3739 + 24.8963i 0.539062 + 0.933683i
$$712$$ 13.9782 24.2110i 0.523856 0.907345i
$$713$$ 11.8693 + 6.85275i 0.444509 + 0.256638i
$$714$$ 0 0
$$715$$ 1.79129 6.20520i 0.0669904 0.232061i
$$716$$ −16.1216 −0.602492
$$717$$ −31.9782 18.4626i −1.19425 0.689500i
$$718$$ −0.126136 + 0.218475i −0.00470737 + 0.00815341i
$$719$$ 12.0826 + 20.9276i 0.450604 + 0.780469i 0.998424 0.0561274i $$-0.0178753\pi$$
−0.547820 + 0.836597i $$0.684542\pi$$
$$720$$ 6.10985i 0.227701i
$$721$$ 0 0
$$722$$ 6.77405 3.91100i 0.252104 0.145552i
$$723$$ 54.9887i 2.04505i
$$724$$ 8.20871 + 14.2179i 0.305074 + 0.528404i
$$725$$ 16.2695 28.1796i 0.604234 1.04656i
$$726$$ 4.83030 + 2.78878i 0.179269 + 0.103501i
$$727$$ 0.252273 0.00935628 0.00467814 0.999989i $$-0.498511\pi$$
0.00467814 + 0.999989i $$0.498511\pi$$
$$728$$ 0 0
$$729$$ −43.8693 −1.62479
$$730$$ −0.626136 0.361500i −0.0231744 0.0133797i
$$731$$ −14.0608 + 24.3540i −0.520057 + 0.900766i
$$732$$ 36.8693 + 63.8595i 1.36273 + 2.36032i
$$733$$ 16.9590i 0.626395i −0.949688 0.313198i $$-0.898600\pi$$
0.949688 0.313198i $$-0.101400\pi$$
$$734$$ 7.12159 4.11165i 0.262863 0.151764i
$$735$$ 0 0
$$736$$ 7.50030i 0.276465i
$$737$$ 8.76951 + 15.1892i 0.323029 + 0.559503i
$$738$$ −8.58258 + 14.8655i −0.315929 + 0.547205i
$$739$$ 16.7477 + 9.66930i 0.616075 + 0.355691i 0.775339 0.631545i $$-0.217579\pi$$
−0.159264 + 0.987236i $$0.550912\pi$$
$$740$$ 5.66970 0.208422
$$741$$ 3.31307 + 13.3896i 0.121709 + 0.491879i
$$742$$ 0 0
$$743$$ 29.8521 + 17.2351i 1.09517 + 0.632295i 0.934947 0.354787i $$-0.115446\pi$$
0.160219 + 0.987081i $$0.448780\pi$$
$$744$$ 20.9347 36.2599i 0.767502 1.32935i
$$745$$ −0.104356 0.180750i −0.00382331 0.00662217i
$$746$$ 14.7146i 0.538738i
$$747$$ −29.1434 + 16.8259i −1.06630 + 0.615629i
$$748$$ 18.2477 10.5353i 0.667203 0.385210i
$$749$$ 0 0
$$750$$ 2.85208 + 4.93995i 0.104143 + 0.180382i
$$751$$ −11.8739 + 20.5661i −0.433283 + 0.750469i −0.997154 0.0753944i $$-0.975978\pi$$
0.563870 + 0.825863i $$0.309312\pi$$
$$752$$ 23.1434 + 13.3618i 0.843952 + 0.487256i
$$753$$ 7.91288 0.288361
$$754$$ −8.06080 + 7.75650i −0.293557 + 0.282475i
$$755$$ 5.53901 0.201585
$$756$$ 0 0
$$757$$ −3.00000 + 5.19615i −0.109037 + 0.188857i −0.915380 0.402590i $$-0.868110\pi$$
0.806343 + 0.591448i $$0.201443\pi$$
$$758$$ 6.47822 + 11.2206i 0.235300 + 0.407551i
$$759$$ 17.3205i 0.628695i
$$760$$ −0.939205 + 0.542250i −0.0340685 + 0.0196695i
$$761$$ −11.2259 + 6.48130i −0.406940 + 0.234947i −0.689474 0.724310i $$-0.742158\pi$$
0.282534 + 0.959257i $$0.408825\pi$$
$$762$$ 8.87086i 0.321357i
$$763$$ 0 0
$$764$$ 12.8739 22.2982i 0.465760 0.806720i
$$765$$ −5.68693 3.28335i −0.205611 0.118710i
$$766$$ 0.582576 0.0210493
$$767$$ 31.9955 30.7876i 1.15529 1.11168i
$$768$$ 5.00000 0.180422
$$769$$ 8.12614 + 4.69163i 0.293036 + 0.169184i 0.639310 0.768949i $$-0.279220\pi$$
−0.346274 + 0.938133i $$0.612553\pi$$
$$770$$ 0 0
$$771$$ 7.03901 + 12.1919i 0.253504 + 0.439082i
$$772$$ 34.6410i 1.24676i
$$773$$ −16.8303 + 9.71698i −0.605344 + 0.349495i −0.771141 0.636664i $$-0.780314\pi$$
0.165797 + 0.986160i $$0.446980\pi$$
$$774$$ 17.7695 10.2592i 0.638712 0.368760i
$$775$$ 41.4938i 1.49050i
$$776$$ −6.31307 10.9346i −0.226626 0.392528i
$$777$$ 0 0