# Properties

 Label 637.2.k.d.569.1 Level $637$ Weight $2$ Character 637.569 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.k (of order $$6$$, degree $$2$$, not 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 569.1 Root $$1.39564 - 0.228425i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.569 Dual form 637.2.k.d.459.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})$$ $$q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) 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} +(-2.50000 + 4.33013i) q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +2.79129 q^{16} +3.00000 q^{17} +(-1.89564 + 1.09445i) q^{18} +(-1.18693 + 0.685275i) q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} -1.58258 q^{23} +(4.18693 + 2.41733i) q^{24} +(-2.39564 - 4.14938i) q^{25} +(0.395644 - 1.59898i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} +(-7.50000 + 4.33013i) q^{31} -4.73930i q^{32} +(-9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +6.92820i q^{37} +(0.313068 + 0.542250i) q^{38} +(-6.97822 + 7.25198i) q^{39} +(0.395644 - 0.685275i) q^{40} +(6.79129 - 3.92095i) q^{41} +(-4.68693 + 8.11800i) q^{43} +(6.08258 + 3.51178i) q^{44} -2.18890i q^{45} +0.723000i q^{46} +(-8.29129 - 4.78698i) q^{47} +(-3.89564 + 6.74745i) q^{48} +(-1.89564 + 1.09445i) q^{50} +(-4.18693 + 7.25198i) q^{51} +(6.26951 + 1.55130i) q^{52} +(-3.08258 - 5.33918i) q^{53} -2.28425i q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +(2.68693 - 1.55130i) q^{58} -12.3151i q^{59} +(-1.97822 + 1.14213i) q^{60} +(7.37386 + 12.7719i) q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(1.18693 + 1.14213i) q^{65} +(2.50000 + 4.33013i) q^{66} +(3.87386 + 2.23658i) q^{67} +5.37386 q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} +(-7.18693 + 4.14938i) q^{72} +(3.00000 - 1.73205i) q^{73} +3.16515 q^{74} +13.3739 q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} +(3.00000 - 5.19615i) 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} +(3.70871 + 2.14123i) q^{86} -18.9564 q^{87} +(3.39564 - 5.88143i) q^{88} -16.1407i q^{89} -1.00000 q^{90} -2.83485 q^{92} -24.1733i q^{93} +(-2.18693 + 3.78788i) q^{94} -0.626136 q^{95} +(11.4564 + 6.61438i) q^{96} +(-6.31307 - 3.64485i) q^{97} -18.7864i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10})$$ 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9 $$4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100})$$ 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9 + 5 * q^10 + 9 * q^11 - 10 * q^12 + 14 * q^13 - 9 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^18 + 9 * q^19 + 12 * q^20 - q^22 + 12 * q^23 + 3 * q^24 - 5 * q^25 - 3 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 - 30 * q^31 - 15 * q^33 - 8 * q^36 + 15 * q^38 - 5 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 + 6 * q^44 - 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 - 7 * q^52 + 6 * q^53 - q^55 - 3 * q^58 + 15 * q^60 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 9 * q^65 + 10 * q^66 - 12 * q^67 - 6 * q^68 + 18 * q^69 + 6 * q^71 - 15 * q^72 + 12 * q^73 - 24 * q^74 + 26 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 + 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 24 * q^86 - 30 * q^87 + 9 * q^88 - 4 * q^90 - 48 * q^92 + 5 * q^94 - 30 * q^95 - 39 * q^97

## Character values

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

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.456850i 0.323042i −0.986869 0.161521i $$-0.948360\pi$$
0.986869 0.161521i $$-0.0516399\pi$$
$$3$$ −1.39564 + 2.41733i −0.805775 + 1.39564i 0.109991 + 0.993933i $$0.464918\pi$$
−0.915766 + 0.401711i $$0.868416\pi$$
$$4$$ 1.79129 0.895644
$$5$$ 0.395644 + 0.228425i 0.176937 + 0.102155i 0.585853 0.810417i $$-0.300760\pi$$
−0.408916 + 0.912572i $$0.634093\pi$$
$$6$$ 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 0.915210 0.402978i $$-0.132025\pi$$
0.108616 + 0.994084i $$0.465358\pi$$
$$12$$ −2.50000 + 4.33013i −0.721688 + 1.25000i
$$13$$ 3.50000 + 0.866025i 0.970725 + 0.240192i
$$14$$ 0 0
$$15$$ −1.10436 + 0.637600i −0.285144 + 0.164628i
$$16$$ 2.79129 0.697822
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ −1.89564 + 1.09445i −0.446808 + 0.257964i
$$19$$ −1.18693 + 0.685275i −0.272301 + 0.157213i −0.629933 0.776650i $$-0.716918\pi$$
0.357632 + 0.933863i $$0.383584\pi$$
$$20$$ 0.708712 + 0.409175i 0.158473 + 0.0914943i
$$21$$ 0 0
$$22$$ 0.895644 1.55130i 0.190952 0.330738i
$$23$$ −1.58258 −0.329990 −0.164995 0.986294i $$-0.552761\pi$$
−0.164995 + 0.986294i $$0.552761\pi$$
$$24$$ 4.18693 + 2.41733i 0.854654 + 0.493435i
$$25$$ −2.39564 4.14938i −0.479129 0.829875i
$$26$$ 0.395644 1.59898i 0.0775922 0.313585i
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ 3.39564 + 5.88143i 0.630555 + 1.09215i 0.987438 + 0.158005i $$0.0505061\pi$$
−0.356883 + 0.934149i $$0.616161\pi$$
$$30$$ 0.291288 + 0.504525i 0.0531816 + 0.0921133i
$$31$$ −7.50000 + 4.33013i −1.34704 + 0.777714i −0.987829 0.155543i $$-0.950287\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 4.73930i 0.837798i
$$33$$ −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
$$37$$ 6.92820i 1.13899i 0.821995 + 0.569495i $$0.192861\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0.313068 + 0.542250i 0.0507864 + 0.0879646i
$$39$$ −6.97822 + 7.25198i −1.11741 + 1.16125i
$$40$$ 0.395644 0.685275i 0.0625568 0.108352i
$$41$$ 6.79129 3.92095i 1.06062 0.612350i 0.135017 0.990843i $$-0.456891\pi$$
0.925604 + 0.378493i $$0.123558\pi$$
$$42$$ 0 0
$$43$$ −4.68693 + 8.11800i −0.714750 + 1.23798i 0.248305 + 0.968682i $$0.420126\pi$$
−0.963056 + 0.269302i $$0.913207\pi$$
$$44$$ 6.08258 + 3.51178i 0.916983 + 0.529420i
$$45$$ 2.18890i 0.326302i
$$46$$ 0.723000i 0.106601i
$$47$$ −8.29129 4.78698i −1.20941 0.698252i −0.246778 0.969072i $$-0.579372\pi$$
−0.962630 + 0.270820i $$0.912705\pi$$
$$48$$ −3.89564 + 6.74745i −0.562288 + 0.973911i
$$49$$ 0 0
$$50$$ −1.89564 + 1.09445i −0.268085 + 0.154779i
$$51$$ −4.18693 + 7.25198i −0.586288 + 1.01548i
$$52$$ 6.26951 + 1.55130i 0.869424 + 0.215127i
$$53$$ −3.08258 5.33918i −0.423424 0.733392i 0.572848 0.819662i $$-0.305839\pi$$
−0.996272 + 0.0862695i $$0.972505\pi$$
$$54$$ 2.28425i 0.310847i
$$55$$ 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
$$59$$ 12.3151i 1.60328i −0.597805 0.801642i $$-0.703960\pi$$
0.597805 0.801642i $$-0.296040\pi$$
$$60$$ −1.97822 + 1.14213i −0.255387 + 0.147448i
$$61$$ 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
$$65$$ 1.18693 + 1.14213i 0.147221 + 0.141663i
$$66$$ 2.50000 + 4.33013i 0.307729 + 0.533002i
$$67$$ 3.87386 + 2.23658i 0.473268 + 0.273241i 0.717607 0.696449i $$-0.245238\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ 5.37386 0.651677
$$69$$ 2.20871 3.82560i 0.265898 0.460548i
$$70$$ 0 0
$$71$$ 3.79129 + 2.18890i 0.449943 + 0.259775i 0.707806 0.706407i $$-0.249685\pi$$
−0.257863 + 0.966181i $$0.583018\pi$$
$$72$$ −7.18693 + 4.14938i −0.846988 + 0.489009i
$$73$$ 3.00000 1.73205i 0.351123 0.202721i −0.314057 0.949404i $$-0.601688\pi$$
0.665180 + 0.746683i $$0.268355\pi$$
$$74$$ 3.16515 0.367941
$$75$$ 13.3739 1.54428
$$76$$ −2.12614 + 1.22753i −0.243885 + 0.140807i
$$77$$ 0 0
$$78$$ 3.31307 + 3.18800i 0.375131 + 0.360970i
$$79$$ 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i $$-0.723743\pi$$
0.983967 + 0.178352i $$0.0570765\pi$$
$$80$$ 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 $$0.125960\pi$$
−0.922721 + 0.385468i $$0.874040\pi$$
$$84$$ 0 0
$$85$$ 1.18693 + 0.685275i 0.128741 + 0.0743286i
$$86$$ 3.70871 + 2.14123i 0.399921 + 0.230894i
$$87$$ −18.9564 −2.03234
$$88$$ 3.39564 5.88143i 0.361977 0.626962i
$$89$$ 16.1407i 1.71091i −0.517880 0.855453i $$-0.673279\pi$$
0.517880 0.855453i $$-0.326721\pi$$
$$90$$ −1.00000 −0.105409
$$91$$ 0 0
$$92$$ −2.83485 −0.295553
$$93$$ 24.1733i 2.50665i
$$94$$ −2.18693 + 3.78788i −0.225565 + 0.390690i
$$95$$ −0.626136 −0.0642402
$$96$$ 11.4564 + 6.61438i 1.16927 + 0.675077i
$$97$$ −6.31307 3.64485i −0.640995 0.370079i 0.144003 0.989577i $$-0.454003\pi$$
−0.784998 + 0.619499i $$0.787336\pi$$
$$98$$ 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
$$103$$ −2.29129 + 3.96863i −0.225767 + 0.391040i −0.956549 0.291570i $$-0.905822\pi$$
0.730782 + 0.682611i $$0.239156\pi$$
$$104$$ 1.50000 6.06218i 0.147087 0.594445i
$$105$$ 0 0
$$106$$ −2.43920 + 1.40828i −0.236917 + 0.136784i
$$107$$ −5.20871 −0.503545 −0.251773 0.967786i $$-0.581014\pi$$
−0.251773 + 0.967786i $$0.581014\pi$$
$$108$$ 8.95644 0.861834
$$109$$ 6.87386 3.96863i 0.658397 0.380126i −0.133269 0.991080i $$-0.542547\pi$$
0.791666 + 0.610954i $$0.209214\pi$$
$$110$$ 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 −0.999997 0.00258173i $$-0.999178\pi$$
0.502234 + 0.864732i $$0.332512\pi$$
$$114$$ −1.74773 −0.163690
$$115$$ −0.626136 0.361500i −0.0583875 0.0337101i
$$116$$ 6.08258 + 10.5353i 0.564753 + 0.978181i
$$117$$ −4.79129 16.5975i −0.442955 1.53444i
$$118$$ −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
$$122$$ 5.83485 3.36875i 0.528262 0.304992i
$$123$$ 21.8890i 1.97367i
$$124$$ −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 0.669423 0.742881i $$-0.266541\pi$$
−0.978066 + 0.208297i $$0.933208\pi$$
$$128$$ 11.0399i 0.975795i
$$129$$ −13.0826 22.6597i −1.15186 1.99507i
$$130$$ 0.521780 0.542250i 0.0457632 0.0475585i
$$131$$ 8.68693 15.0462i 0.758981 1.31459i −0.184390 0.982853i $$-0.559031\pi$$
0.943371 0.331740i $$-0.107636\pi$$
$$132$$ −16.9782 + 9.80238i −1.47776 + 0.853188i
$$133$$ 0 0
$$134$$ 1.02178 1.76978i 0.0882684 0.152885i
$$135$$ 1.97822 + 1.14213i 0.170258 + 0.0982985i
$$136$$ 5.19615i 0.445566i
$$137$$ 11.9536i 1.02126i −0.859800 0.510631i $$-0.829412\pi$$
0.859800 0.510631i $$-0.170588\pi$$
$$138$$ −1.74773 1.00905i −0.148776 0.0858961i
$$139$$ −1.89564 + 3.28335i −0.160786 + 0.278490i −0.935151 0.354249i $$-0.884736\pi$$
0.774365 + 0.632740i $$0.218070\pi$$
$$140$$ 0 0
$$141$$ 23.1434 13.3618i 1.94902 1.12527i
$$142$$ 1.00000 1.73205i 0.0839181 0.145350i
$$143$$ 10.1869 + 9.80238i 0.851874 + 0.819716i
$$144$$ −6.68693 11.5821i −0.557244 0.965175i
$$145$$ 3.10260i 0.257657i
$$146$$ −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 −0.483706 0.875230i $$-0.660710\pi$$
0.516119 + 0.856517i $$0.327376\pi$$
$$150$$ 6.10985i 0.498867i
$$151$$ 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i $$-0.502445\pi$$
0.862159 + 0.506637i $$0.169112\pi$$
$$152$$ 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
$$156$$ −12.5000 + 12.9904i −1.00080 + 1.04006i
$$157$$ 0.478220 + 0.828301i 0.0381661 + 0.0661056i 0.884477 0.466583i $$-0.154515\pi$$
−0.846311 + 0.532689i $$0.821182\pi$$
$$158$$ −2.37386 1.37055i −0.188854 0.109035i
$$159$$ 17.2087 1.36474
$$160$$ 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 −0.716221 0.697873i $$-0.754130\pi$$
0.246265 + 0.969202i $$0.420797\pi$$
$$164$$ 12.1652 7.02355i 0.949939 0.548447i
$$165$$ −5.00000 −0.389249
$$166$$ 3.20871 0.249044
$$167$$ 12.7087 7.33738i 0.983430 0.567783i 0.0801258 0.996785i $$-0.474468\pi$$
0.903304 + 0.429001i $$0.141134\pi$$
$$168$$ 0 0
$$169$$ 11.5000 + 6.06218i 0.884615 + 0.466321i
$$170$$ 0.313068 0.542250i 0.0240112 0.0415887i
$$171$$ 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
$$177$$ 29.7695 + 17.1874i 2.23761 + 1.29189i
$$178$$ −7.37386 −0.552694
$$179$$ 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i $$-0.724142\pi$$
0.983742 + 0.179585i $$0.0574756\pi$$
$$180$$ 3.92095i 0.292250i
$$181$$ −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
$$184$$ 2.74110i 0.202077i
$$185$$ −1.58258 + 2.74110i −0.116353 + 0.201530i
$$186$$ −11.0436 −0.809753
$$187$$ 10.1869 + 5.88143i 0.744942 + 0.430093i
$$188$$ −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 −0.243749 0.969838i $$-0.578377\pi$$
−0.961779 + 0.273827i $$0.911711\pi$$
$$194$$ −1.66515 + 2.88413i −0.119551 + 0.207068i
$$195$$ −4.41742 + 1.27520i −0.316338 + 0.0913190i
$$196$$ 0 0
$$197$$ 1.97822 1.14213i 0.140942 0.0813731i −0.427871 0.903840i $$-0.640736\pi$$
0.568813 + 0.822467i $$0.307403\pi$$
$$198$$ −8.58258 −0.609937
$$199$$ −11.0000 −0.779769 −0.389885 0.920864i $$-0.627485\pi$$
−0.389885 + 0.920864i $$0.627485\pi$$
$$200$$ −7.18693 + 4.14938i −0.508193 + 0.293405i
$$201$$ −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
$$205$$ 3.58258 0.250218
$$206$$ 1.81307 + 1.04678i 0.126322 + 0.0729323i
$$207$$ 3.79129 + 6.56670i 0.263513 + 0.456417i
$$208$$ 9.76951 + 2.41733i 0.677393 + 0.167611i
$$209$$ −5.37386 −0.371718
$$210$$ 0 0
$$211$$ −5.29129 9.16478i −0.364267 0.630929i 0.624391 0.781112i $$-0.285347\pi$$
−0.988658 + 0.150183i $$0.952014\pi$$
$$212$$ −5.52178 9.56400i −0.379237 0.656859i
$$213$$ −10.5826 + 6.10985i −0.725106 + 0.418640i
$$214$$ 2.37960i 0.162666i
$$215$$ −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
$$219$$ 9.66930i 0.653391i
$$220$$ 1.60436 + 2.77883i 0.108166 + 0.187348i
$$221$$ 10.5000 + 2.59808i 0.706306 + 0.174766i
$$222$$ −4.41742 + 7.65120i −0.296478 + 0.513515i
$$223$$ 16.4347 9.48855i 1.10055 0.635401i 0.164182 0.986430i $$-0.447502\pi$$
0.936364 + 0.351029i $$0.114168\pi$$
$$224$$ 0 0
$$225$$ −11.4782 + 19.8809i −0.765215 + 1.32539i
$$226$$ 4.18693 + 2.41733i 0.278511 + 0.160798i
$$227$$ 8.85095i 0.587458i 0.955889 + 0.293729i $$0.0948964\pi$$
−0.955889 + 0.293729i $$0.905104\pi$$
$$228$$ 6.85275i 0.453835i
$$229$$ −6.00000 3.46410i −0.396491 0.228914i 0.288478 0.957487i $$-0.406851\pi$$
−0.684969 + 0.728572i $$0.740184\pi$$
$$230$$ −0.165151 + 0.286051i −0.0108898 + 0.0188616i
$$231$$ 0 0
$$232$$ 10.1869 5.88143i 0.668805 0.386135i
$$233$$ −7.97822 + 13.8187i −0.522671 + 0.905292i 0.476981 + 0.878913i $$0.341731\pi$$
−0.999652 + 0.0263786i $$0.991602\pi$$
$$234$$ −7.58258 + 2.18890i −0.495688 + 0.143093i
$$235$$ −2.18693 3.78788i −0.142660 0.247094i
$$236$$ 22.0598i 1.43597i
$$237$$ 8.37386 + 14.5040i 0.543941 + 0.942133i
$$238$$ 0 0
$$239$$ 13.2288i 0.855697i −0.903850 0.427849i $$-0.859272\pi$$
0.903850 0.427849i $$-0.140728\pi$$
$$240$$ −3.08258 + 1.77973i −0.198979 + 0.114881i
$$241$$ 19.7001i 1.26900i −0.772925 0.634498i $$-0.781207\pi$$
0.772925 0.634498i $$-0.218793\pi$$
$$242$$ 1.73049 0.999100i 0.111240 0.0642246i
$$243$$ 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
$$247$$ −4.74773 + 1.37055i −0.302091 + 0.0872061i
$$248$$ 7.50000 + 12.9904i 0.476250 + 0.824890i
$$249$$ −16.9782 9.80238i −1.07595 0.621201i
$$250$$ −2.04356 −0.129246
$$251$$ −1.41742 + 2.45505i −0.0894670 + 0.154961i −0.907286 0.420514i $$-0.861850\pi$$
0.817819 + 0.575476i $$0.195183\pi$$
$$252$$ 0 0
$$253$$ −5.37386 3.10260i −0.337852 0.195059i
$$254$$ −2.75227 + 1.58903i −0.172693 + 0.0997043i
$$255$$ −3.31307 + 1.91280i −0.207472 + 0.119784i
$$256$$ 1.79129 0.111955
$$257$$ −5.04356 −0.314609 −0.157304 0.987550i $$-0.550280\pi$$
−0.157304 + 0.987550i $$0.550280\pi$$
$$258$$ −10.3521 + 5.97678i −0.644493 + 0.372098i
$$259$$ 0 0
$$260$$ 2.12614 + 2.04588i 0.131857 + 0.126880i
$$261$$ 16.2695 28.1796i 1.00706 1.74427i
$$262$$ −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
$$268$$ 6.93920 + 4.00635i 0.423879 + 0.244727i
$$269$$ 15.7913 0.962812 0.481406 0.876498i $$-0.340126\pi$$
0.481406 + 0.876498i $$0.340126\pi$$
$$270$$ 0.521780 0.903750i 0.0317545 0.0550005i
$$271$$ 12.8474i 0.780421i 0.920726 + 0.390211i $$0.127598\pi$$
−0.920726 + 0.390211i $$0.872402\pi$$
$$272$$ 8.37386 0.507740
$$273$$ 0 0
$$274$$ −5.46099 −0.329910
$$275$$ 18.7864i 1.13286i
$$276$$ 3.95644 6.85275i 0.238150 0.412487i
$$277$$ 11.7477 0.705853 0.352926 0.935651i $$-0.385187\pi$$
0.352926 + 0.935651i $$0.385187\pi$$
$$278$$ 1.50000 + 0.866025i 0.0899640 + 0.0519408i
$$279$$ 35.9347 + 20.7469i 2.15135 + 1.24208i
$$280$$ 0 0
$$281$$ 30.6446i 1.82810i −0.405597 0.914052i $$-0.632936\pi$$
0.405597 0.914052i $$-0.367064\pi$$
$$282$$ −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
$$285$$ 0.873864 1.51358i 0.0517632 0.0896565i
$$286$$ 4.47822 4.65390i 0.264803 0.275191i
$$287$$ 0 0
$$288$$ −19.6652 + 11.3537i −1.15878 + 0.669022i
$$289$$ −8.00000 −0.470588
$$290$$ 1.41742 0.0832340
$$291$$ 17.6216 10.1738i 1.03300 0.596400i
$$292$$ 5.37386 3.10260i 0.314482 0.181566i
$$293$$ −2.20871 1.27520i −0.129034 0.0744980i 0.434093 0.900868i $$-0.357069\pi$$
−0.563128 + 0.826370i $$0.690402\pi$$
$$294$$ 0 0
$$295$$ 2.81307 4.87238i 0.163783 0.283681i
$$296$$ 12.0000 0.697486
$$297$$ 16.9782 + 9.80238i 0.985176 + 0.568792i
$$298$$ −0.104356 0.180750i −0.00604519 0.0104706i
$$299$$ −5.53901 1.37055i −0.320330 0.0792610i
$$300$$ 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
$$304$$ −3.31307 + 1.91280i −0.190017 + 0.109707i
$$305$$ 6.73750i 0.385788i
$$306$$ −5.68693 + 3.28335i −0.325100 + 0.187697i
$$307$$ 15.5130i 0.885374i 0.896676 + 0.442687i $$0.145975\pi$$
−0.896676 + 0.442687i $$0.854025\pi$$
$$308$$ 0 0
$$309$$ −6.39564 11.0776i −0.363835 0.630182i
$$310$$ 1.80750i 0.102659i
$$311$$ 13.2695 + 22.9835i 0.752445 + 1.30327i 0.946635 + 0.322309i $$0.104459\pi$$
−0.194190 + 0.980964i $$0.562208\pi$$
$$312$$ 12.5608 + 12.0866i 0.711115 + 0.684271i
$$313$$ −3.37386 + 5.84370i −0.190702 + 0.330306i −0.945483 0.325671i $$-0.894410\pi$$
0.754781 + 0.655977i $$0.227743\pi$$
$$314$$ 0.378409 0.218475i 0.0213549 0.0123292i
$$315$$ 0 0
$$316$$ 5.37386 9.30780i 0.302303 0.523605i
$$317$$ −16.0390 9.26013i −0.900841 0.520101i −0.0233679 0.999727i $$-0.507439\pi$$
−0.877473 + 0.479626i $$0.840772\pi$$
$$318$$ 7.86180i 0.440868i
$$319$$ 26.6283i 1.49090i
$$320$$ 1.35208 + 0.780626i 0.0755837 + 0.0436383i
$$321$$ 7.26951 12.5912i 0.405744 0.702770i
$$322$$ 0 0
$$323$$ −3.56080 + 2.05583i −0.198128 + 0.114389i
$$324$$ 0.373864 0.647551i 0.0207702 0.0359750i
$$325$$ −4.79129 16.5975i −0.265773 0.920664i
$$326$$ 1.58258 + 2.74110i 0.0876508 + 0.151816i
$$327$$ 22.1552i 1.22518i
$$328$$ −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 −0.957186 0.289473i $$-0.906520\pi$$
−0.227902 + 0.973684i $$0.573187\pi$$
$$332$$ 12.5812i 0.690483i
$$333$$ 28.7477 16.5975i 1.57537 0.909538i
$$334$$ −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 $$0.412586\pi$$
$$338$$ 2.76951 5.25378i 0.150641 0.285768i
$$339$$ −14.7695 25.5815i −0.802170 1.38940i
$$340$$ 2.12614 + 1.22753i 0.115306 + 0.0665719i
$$341$$ −33.9564 −1.83884
$$342$$ 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
$$346$$ −7.81307 + 4.51088i −0.420033 + 0.242506i
$$347$$ −13.5826 −0.729151 −0.364575 0.931174i $$-0.618786\pi$$
−0.364575 + 0.931174i $$0.618786\pi$$
$$348$$ −33.9564 −1.82026
$$349$$ 18.2477 10.5353i 0.976778 0.563943i 0.0754825 0.997147i $$-0.475950\pi$$
0.901296 + 0.433204i $$0.142617\pi$$
$$350$$ 0 0
$$351$$ 17.5000 + 4.33013i 0.934081 + 0.231125i
$$352$$ 9.29129 16.0930i 0.495227 0.857759i
$$353$$ 15.7259 + 9.07938i 0.837008 + 0.483247i 0.856246 0.516568i $$-0.172791\pi$$
−0.0192383 + 0.999815i $$0.506124\pi$$
$$354$$ 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
$$359$$ −0.478220 0.276100i −0.0252395 0.0145720i 0.487327 0.873219i $$-0.337972\pi$$
−0.512567 + 0.858647i $$0.671305\pi$$
$$360$$ −3.79129 −0.199818
$$361$$ −8.56080 + 14.8277i −0.450568 + 0.780407i
$$362$$ 4.18710i 0.220069i
$$363$$ −12.2087 −0.640791
$$364$$ 0 0
$$365$$ 1.58258 0.0828358
$$366$$ 18.8063i 0.983022i
$$367$$ −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i $$-0.989006\pi$$
0.529607 + 0.848243i $$0.322339\pi$$
$$368$$ −4.41742 −0.230274
$$369$$ −32.5390 18.7864i −1.69391 0.977981i
$$370$$ 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
$$376$$ −8.29129 + 14.3609i −0.427591 + 0.740609i
$$377$$ 6.79129 + 23.5257i 0.349769 + 1.21164i
$$378$$ 0 0
$$379$$ −24.5608 + 14.1802i −1.26160 + 0.728387i −0.973385 0.229178i $$-0.926396\pi$$
−0.288219 + 0.957565i $$0.593063\pi$$
$$380$$ −1.12159 −0.0575364
$$381$$ 19.4174 0.994785
$$382$$ 5.68693 3.28335i 0.290969 0.167991i
$$383$$ 1.10436 0.637600i 0.0564300 0.0325799i −0.471520 0.881856i $$-0.656294\pi$$
0.527950 + 0.849276i $$0.322961\pi$$
$$384$$ 26.6869 + 15.4077i 1.36186 + 0.786271i
$$385$$ 0 0
$$386$$ −4.41742 + 7.65120i −0.224841 + 0.389436i
$$387$$ 44.9129 2.28305
$$388$$ −11.3085 6.52898i −0.574103 0.331459i
$$389$$ 0.165151 + 0.286051i 0.00837351 + 0.0145033i 0.870182 0.492731i $$-0.164001\pi$$
−0.861808 + 0.507234i $$0.830668\pi$$
$$390$$ 0.582576 + 2.01810i 0.0294999 + 0.102191i
$$391$$ −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
$$395$$ 2.37386 1.37055i 0.119442 0.0689599i
$$396$$ 33.6519i 1.69107i
$$397$$ 28.1216 16.2360i 1.41138 0.814862i 0.415864 0.909427i $$-0.363479\pi$$
0.995519 + 0.0945652i $$0.0301461\pi$$
$$398$$ 5.02535i 0.251898i
$$399$$ 0 0
$$400$$ −6.68693 11.5821i −0.334347 0.579105i
$$401$$ 31.2922i 1.56266i 0.624121 + 0.781328i $$0.285457\pi$$
−0.624121 + 0.781328i $$0.714543\pi$$
$$402$$ 2.85208 + 4.93995i 0.142249 + 0.246382i
$$403$$ −30.0000 + 8.66025i −1.49441 + 0.431398i
$$404$$ −4.66515 + 8.08028i −0.232100 + 0.402009i
$$405$$ 0.165151 0.0953502i 0.00820644 0.00473799i
$$406$$ 0 0
$$407$$ −13.5826 + 23.5257i −0.673263 + 1.16613i
$$408$$ 12.5608 + 7.25198i 0.621852 + 0.359026i
$$409$$ 8.29875i 0.410347i 0.978726 + 0.205173i $$0.0657759\pi$$
−0.978726 + 0.205173i $$0.934224\pi$$
$$410$$ 1.63670i 0.0808309i
$$411$$ 28.8956 + 16.6829i 1.42532 + 0.822907i
$$412$$ −4.10436 + 7.10895i −0.202207 + 0.350233i
$$413$$ 0 0
$$414$$ 3.00000 1.73205i 0.147442 0.0851257i
$$415$$ −1.60436 + 2.77883i −0.0787547 + 0.136407i
$$416$$ 4.10436 16.5876i 0.201233 0.813272i
$$417$$ −5.29129 9.16478i −0.259115 0.448801i
$$418$$ 2.45505i 0.120080i
$$419$$ −0.873864 1.51358i −0.0426910 0.0739430i 0.843890 0.536516i $$-0.180260\pi$$
−0.886581 + 0.462573i $$0.846926\pi$$
$$420$$ 0 0
$$421$$ 4.18710i 0.204067i −0.994781 0.102033i $$-0.967465\pi$$
0.994781 0.102033i $$-0.0325349\pi$$
$$422$$ −4.18693 + 2.41733i −0.203817 + 0.117674i
$$423$$ 45.8716i 2.23035i
$$424$$ −9.24773 + 5.33918i −0.449109 + 0.259293i
$$425$$ −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
$$429$$ −37.9129 + 10.9445i −1.83045 + 0.528406i
$$430$$ 0.978220 + 1.69433i 0.0471739 + 0.0817077i
$$431$$ −30.0172 17.3305i −1.44588 0.834779i −0.447647 0.894210i $$-0.647738\pi$$
−0.998232 + 0.0594316i $$0.981071\pi$$
$$432$$ 13.9564 0.671479
$$433$$ −16.2477 + 28.1419i −0.780816 + 1.35241i 0.150651 + 0.988587i $$0.451863\pi$$
−0.931467 + 0.363826i $$0.881470\pi$$
$$434$$ 0 0
$$435$$ −7.50000 4.33013i −0.359597 0.207614i
$$436$$ 12.3131 7.10895i 0.589689 0.340457i
$$437$$ 1.87841 1.08450i 0.0898565 0.0518787i
$$438$$ 4.41742 0.211073
$$439$$ 20.5390 0.980274 0.490137 0.871645i $$-0.336947\pi$$
0.490137 + 0.871645i $$0.336947\pi$$
$$440$$ 2.68693 1.55130i 0.128094 0.0739554i
$$441$$ 0 0
$$442$$ 1.18693 4.79693i 0.0564566 0.228167i
$$443$$ 7.58258 13.1334i 0.360259 0.623987i −0.627744 0.778420i $$-0.716022\pi$$
0.988003 + 0.154433i $$0.0493550\pi$$
$$444$$ −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 −0.111870 0.993723i $$-0.535684\pi$$
−0.916524 + 0.399979i $$0.869017\pi$$
$$450$$ 9.08258 + 5.24383i 0.428157 + 0.247196i
$$451$$ 30.7477 1.44785
$$452$$ −9.47822 + 16.4168i −0.445818 + 0.772179i
$$453$$ 33.8426i 1.59006i
$$454$$ 4.04356 0.189774
$$455$$ 0 0
$$456$$ −6.62614 −0.310297
$$457$$ 22.8027i 1.06667i 0.845905 + 0.533333i $$0.179061\pi$$
−0.845905 + 0.533333i $$0.820939\pi$$
$$458$$ −1.58258 + 2.74110i −0.0739489 + 0.128083i
$$459$$ 15.0000 0.700140
$$460$$ −1.12159 0.647551i −0.0522944 0.0301922i
$$461$$ −4.02178 2.32198i −0.187313 0.108145i 0.403411 0.915019i $$-0.367824\pi$$
−0.590724 + 0.806874i $$0.701158\pi$$
$$462$$ 0 0
$$463$$ 7.93725i 0.368875i −0.982844 0.184438i $$-0.940954\pi$$
0.982844 0.184438i $$-0.0590464\pi$$
$$464$$ 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
$$467$$ 15.0826 26.1238i 0.697938 1.20886i −0.271242 0.962511i $$-0.587434\pi$$
0.969180 0.246353i $$-0.0792324\pi$$
$$468$$ −8.58258 29.7309i −0.396730 1.37431i
$$469$$ 0 0
$$470$$ −1.73049 + 0.999100i −0.0798217 + 0.0460851i
$$471$$ −2.66970 −0.123013
$$472$$ −21.3303 −0.981807
$$473$$ −31.8303 + 18.3772i −1.46356 + 0.844986i
$$474$$ 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
$$478$$ −6.04356 −0.276426
$$479$$ −16.3521 9.44088i −0.747146 0.431365i 0.0775159 0.996991i $$-0.475301\pi$$
−0.824662 + 0.565626i $$0.808634\pi$$
$$480$$ 3.02178 + 5.23388i 0.137925 + 0.238893i
$$481$$ −6.00000 + 24.2487i −0.273576 + 1.10565i
$$482$$ −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
$$486$$ 6.39564 3.69253i 0.290112 0.167496i
$$487$$ 29.3694i 1.33086i −0.746462 0.665428i $$-0.768249\pi$$
0.746462 0.665428i $$-0.231751\pi$$
$$488$$ 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 0.908773 0.417291i $$-0.137020\pi$$
−0.815771 + 0.578375i $$0.803687\pi$$
$$492$$ 39.2095i 1.76770i
$$493$$ 10.1869 + 17.6443i 0.458796 + 0.794659i
$$494$$ 0.626136 + 2.16900i 0.0281712 + 0.0975879i
$$495$$ 4.29129 7.43273i 0.192879 0.334076i
$$496$$ −20.9347 + 12.0866i −0.939994 + 0.542706i
$$497$$ 0 0
$$498$$ −4.47822 + 7.75650i −0.200674 + 0.347577i
$$499$$ 15.9392 + 9.20250i 0.713537 + 0.411961i 0.812369 0.583143i $$-0.198177\pi$$
−0.0988324 + 0.995104i $$0.531511\pi$$
$$500$$ 8.01270i 0.358339i
$$501$$ 40.9615i 1.83002i
$$502$$ 1.12159 + 0.647551i 0.0500590 + 0.0289016i
$$503$$ 9.56080 16.5598i 0.426295 0.738364i −0.570246 0.821474i $$-0.693152\pi$$
0.996540 + 0.0831100i $$0.0264853\pi$$
$$504$$ 0 0
$$505$$ −2.06080 + 1.18980i −0.0917042 + 0.0529454i
$$506$$ −1.41742 + 2.45505i −0.0630122 + 0.109140i
$$507$$ −30.7042 + 19.3386i −1.36362 + 0.858858i
$$508$$ −6.23049 10.7915i −0.276433 0.478797i
$$509$$ 15.0562i 0.667352i 0.942688 + 0.333676i $$0.108289\pi$$
−0.942688 + 0.333676i $$0.891711\pi$$
$$510$$ 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
$$514$$ 2.30415i 0.101632i
$$515$$ −1.81307 + 1.04678i −0.0798933 + 0.0461264i
$$516$$ −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
$$520$$ 1.97822 2.05583i 0.0867507 0.0901539i
$$521$$ 8.20871 + 14.2179i 0.359630 + 0.622898i 0.987899 0.155099i $$-0.0495695\pi$$
−0.628269 + 0.777996i $$0.716236\pi$$
$$522$$ −12.8739 7.43273i −0.563474 0.325322i
$$523$$ −24.3303 −1.06389 −0.531945 0.846779i $$-0.678539\pi$$
−0.531945 + 0.846779i $$0.678539\pi$$
$$524$$ 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
$$528$$ −26.4564 + 15.2746i −1.15137 + 0.664743i
$$529$$ −20.4955 −0.891107
$$530$$ −1.28674 −0.0558925
$$531$$ −51.0998 + 29.5025i −2.21754 + 1.28030i
$$532$$ 0 0
$$533$$ 27.1652 7.84190i 1.17665 0.339671i
$$534$$ 10.2913 17.8250i 0.445348 0.771365i
$$535$$ −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
$$541$$ 5.43920 + 3.14033i 0.233850 + 0.135013i 0.612347 0.790589i $$-0.290226\pi$$
−0.378497 + 0.925602i $$0.623559\pi$$
$$542$$ 5.86932 0.252109
$$543$$ 12.7913 22.1552i 0.548927 0.950769i
$$544$$ 14.2179i 0.609588i
$$545$$ 3.62614 0.155327
$$546$$ 0 0
$$547$$ −11.7477 −0.502297 −0.251148 0.967949i $$-0.580808\pi$$
−0.251148 + 0.967949i $$0.580808\pi$$
$$548$$ 21.4123i 0.914686i
$$549$$ 35.3303 61.1939i 1.50786 2.61169i
$$550$$ −8.58258 −0.365962
$$551$$ −8.06080 4.65390i −0.343401 0.198263i
$$552$$ −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 0.963154 0.268951i $$-0.0866769\pi$$
0.248659 + 0.968591i $$0.420010\pi$$
$$558$$ 9.47822 16.4168i 0.401245 0.694977i
$$559$$ −23.4347 + 24.3540i −0.991180 + 1.03006i
$$560$$ 0 0
$$561$$ −28.4347 + 16.4168i −1.20051 + 0.693116i
$$562$$ −14.0000 −0.590554
$$563$$ −36.3303 −1.53114 −0.765570 0.643353i $$-0.777543\pi$$
−0.765570 + 0.643353i $$0.777543\pi$$
$$564$$ 41.4564 23.9349i 1.74563 1.00784i
$$565$$ −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
$$569$$ 16.7477 0.702101 0.351051 0.936356i $$-0.385825\pi$$
0.351051 + 0.936356i $$0.385825\pi$$
$$570$$ −0.691478 0.399225i −0.0289628 0.0167217i
$$571$$ 1.02178 + 1.76978i 0.0427602 + 0.0740628i 0.886613 0.462511i $$-0.153052\pi$$
−0.843853 + 0.536574i $$0.819718\pi$$
$$572$$ 18.2477 + 17.5589i 0.762976 + 0.734174i
$$573$$ −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
$$577$$ 30.8739 17.8250i 1.28530 0.742066i 0.307484 0.951553i $$-0.400513\pi$$
0.977811 + 0.209487i $$0.0671795\pi$$
$$578$$ 3.65480i 0.152020i
$$579$$ 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
$$583$$ 24.1733i 1.00115i
$$584$$ −3.00000 5.19615i −0.124141 0.215018i
$$585$$ 1.89564 7.66115i 0.0783752 0.316750i
$$586$$ −0.582576 + 1.00905i −0.0240660 + 0.0416835i
$$587$$ 8.22595 4.74925i 0.339521 0.196023i −0.320539 0.947235i $$-0.603864\pi$$
0.660060 + 0.751213i $$0.270531\pi$$
$$588$$ 0 0
$$589$$ 5.93466 10.2791i 0.244533 0.423544i
$$590$$ −2.22595 1.28515i −0.0916408 0.0529088i
$$591$$ 6.37600i 0.262274i
$$592$$ 19.3386i 0.794812i
$$593$$ −5.52178 3.18800i −0.226752 0.130916i 0.382321 0.924030i $$-0.375125\pi$$
−0.609073 + 0.793114i $$0.708458\pi$$
$$594$$ 4.47822 7.75650i 0.183744 0.318253i
$$595$$ 0 0
$$596$$ 0.708712 0.409175i 0.0290300 0.0167605i
$$597$$ 15.3521 26.5906i 0.628319 1.08828i
$$598$$ −0.626136 + 2.53050i −0.0256046 + 0.103480i
$$599$$ 3.31307 + 5.73840i 0.135368 + 0.234465i 0.925738 0.378165i $$-0.123445\pi$$
−0.790370 + 0.612630i $$0.790112\pi$$
$$600$$ 23.1642i 0.945675i
$$601$$ −6.18693 10.7161i −0.252370 0.437118i 0.711808 0.702374i $$-0.247877\pi$$
−0.964178 + 0.265256i $$0.914543\pi$$
$$602$$ 0 0
$$603$$ 21.4322i 0.872785i
$$604$$ 18.8085 10.8591i 0.765308 0.441851i
$$605$$ 1.99820i 0.0812384i
$$606$$ −5.75227 + 3.32108i −0.233670 + 0.134910i
$$607$$ −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
$$611$$ −24.8739 23.9349i −1.00629 0.968302i
$$612$$ −12.8739 22.2982i −0.520395 0.901351i
$$613$$ 15.8085 + 9.12705i 0.638500 + 0.368638i 0.784037 0.620715i $$-0.213157\pi$$
−0.145536 + 0.989353i $$0.546491\pi$$
$$614$$ 7.08712 0.286013
$$615$$ −5.00000 + 8.66025i −0.201619 + 0.349215i
$$616$$ 0 0
$$617$$ −14.9174 8.61258i −0.600553 0.346729i 0.168706 0.985666i $$-0.446041\pi$$
−0.769259 + 0.638937i $$0.779374\pi$$
$$618$$ −5.06080 + 2.92185i −0.203575 + 0.117534i
$$619$$ 16.7477 9.66930i 0.673148 0.388642i −0.124120 0.992267i $$-0.539611\pi$$
0.797268 + 0.603625i $$0.206278\pi$$
$$620$$ −7.08712 −0.284626
$$621$$ −7.91288 −0.317533
$$622$$ 10.5000 6.06218i 0.421012 0.243071i
$$623$$ 0 0
$$624$$ −19.4782 + 20.2424i −0.779753 + 0.810343i
$$625$$ −10.9564 + 18.9771i −0.438258 + 0.759084i
$$626$$ 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 0.893957 0.448153i $$-0.147918\pi$$
0.0588668 + 0.998266i $$0.481251\pi$$
$$632$$ −9.00000 5.19615i −0.358001 0.206692i
$$633$$ 29.5390 1.17407
$$634$$ −4.23049 + 7.32743i −0.168014 + 0.291009i
$$635$$ 3.17805i 0.126117i
$$636$$ 30.8258 1.22232
$$637$$ 0 0
$$638$$ 12.1652 0.481623
$$639$$ 20.9753i 0.829770i
$$640$$ 2.52178 4.36785i 0.0996821 0.172654i
$$641$$ 29.3739 1.16020 0.580099 0.814546i $$-0.303014\pi$$
0.580099 + 0.814546i $$0.303014\pi$$
$$642$$ −5.75227 3.32108i −0.227024 0.131072i
$$643$$ −39.2477 22.6597i −1.54778 0.893611i −0.998311 0.0580962i $$-0.981497\pi$$
−0.549468 0.835515i $$-0.685170\pi$$
$$644$$ 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
$$649$$ 24.1434 41.8175i 0.947710 1.64148i
$$650$$ −7.58258 + 2.18890i −0.297413 + 0.0858558i
$$651$$ 0 0
$$652$$ −10.7477 + 6.20520i −0.420913 + 0.243015i
$$653$$ 15.7913 0.617961 0.308980 0.951068i $$-0.400012\pi$$
0.308980 + 0.951068i $$0.400012\pi$$
$$654$$ 10.1216 0.395786
$$655$$ 6.87386 3.96863i 0.268584 0.155067i
$$656$$ 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 −0.918523 0.395367i $$-0.870617\pi$$
0.801660 + 0.597781i $$0.203951\pi$$
$$660$$ −8.95644 −0.348629
$$661$$ −43.7477 25.2578i −1.70159 0.982413i −0.944155 0.329502i $$-0.893119\pi$$
−0.757434 0.652911i $$-0.773547\pi$$
$$662$$ 5.68693 + 9.85005i 0.221029 + 0.382833i
$$663$$ −20.9347 + 21.7559i −0.813035 + 0.844931i
$$664$$ 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
$$668$$ 22.7650 13.1434i 0.880803 0.508532i
$$669$$ 52.9706i 2.04796i
$$670$$ 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 −0.999924 0.0123559i $$-0.996067\pi$$
0.489261 0.872137i $$-0.337266\pi$$
$$674$$ 4.54860i 0.175206i
$$675$$ −11.9782 20.7469i −0.461042 0.798548i
$$676$$ 20.5998 + 10.8591i 0.792300 + 0.417658i
$$677$$ −14.6044 + 25.2955i −0.561291 + 0.972185i 0.436093 + 0.899902i $$0.356362\pi$$
−0.997384 + 0.0722830i $$0.976972\pi$$
$$678$$ −11.6869 + 6.74745i −0.448834 + 0.259134i
$$679$$ 0 0
$$680$$ 1.18693 2.05583i 0.0455168 0.0788373i
$$681$$ −21.3956 12.3528i −0.819883 0.473360i
$$682$$ 15.5130i 0.594024i
$$683$$ 30.3586i 1.16164i −0.814033 0.580819i $$-0.802732\pi$$
0.814033 0.580819i $$-0.197268\pi$$
$$684$$ 10.1869 + 5.88143i 0.389507 + 0.224882i
$$685$$ 2.73049 4.72935i 0.104327 0.180699i
$$686$$ 0 0
$$687$$ 16.7477 9.66930i 0.638966 0.368907i
$$688$$ −13.0826 + 22.6597i −0.498769 + 0.863892i
$$689$$ −6.16515 21.3567i −0.234874 0.813626i
$$690$$ −0.460985 0.798450i −0.0175494 0.0303965i
$$691$$ 10.3169i 0.392472i 0.980557 + 0.196236i $$0.0628718\pi$$
−0.980557 + 0.196236i $$0.937128\pi$$
$$692$$ −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
$$696$$ 32.8335i 1.24455i
$$697$$ 20.3739 11.7629i 0.771715 0.445550i
$$698$$ −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 $$0.584627\pi$$
$$702$$ 1.97822 7.99488i 0.0746631 0.301747i
$$703$$ −4.74773 8.22330i −0.179064 0.310148i
$$704$$ 11.6044 + 6.69978i 0.437356 + 0.252507i
$$705$$ 12.2087 0.459807
$$706$$ 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 −0.231502 0.972834i $$-0.574364\pi$$
0.726748 + 0.686904i $$0.241031\pi$$
$$710$$ 0.791288 0.456850i 0.0296965 0.0171453i
$$711$$ −28.7477 −1.07812
$$712$$ −27.9564 −1.04771
$$713$$ 11.8693 6.85275i 0.444509 0.256638i
$$714$$ 0 0
$$715$$ 1.79129 + 6.20520i 0.0669904 + 0.232061i
$$716$$ 8.06080 13.9617i 0.301246 0.521773i
$$717$$ 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
$$723$$ 47.6216 + 27.4943i 1.77107 + 1.02253i
$$724$$ −16.4174 −0.610149
$$725$$ 16.2695 28.1796i 0.604234 1.04656i
$$726$$ 5.57755i 0.207002i
$$727$$ 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
$$730$$ 0.723000i 0.0267594i
$$731$$ −14.0608 + 24.3540i −0.520057 + 0.900766i
$$732$$ −73.7386 −2.72546
$$733$$ −14.6869 8.47950i −0.542474 0.313198i 0.203607 0.979053i $$-0.434734\pi$$
−0.746081 + 0.665855i $$0.768067\pi$$
$$734$$ 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 0.159264 0.987236i $$-0.449088\pi$$
−0.775339 + 0.631545i $$0.782421\pi$$
$$740$$ −2.83485 + 4.91010i −0.104211 + 0.180499i
$$741$$ 3.31307 13.3896i 0.121709 0.491879i
$$742$$ 0 0
$$743$$ 29.8521 17.2351i 1.09517 0.632295i 0.160219 0.987081i $$-0.448780\pi$$
0.934947 + 0.354787i $$0.115446\pi$$
$$744$$ −41.8693 −1.53500
$$745$$ 0.208712 0.00764662
$$746$$ −12.7432 + 7.35728i −0.466561 + 0.269369i
$$747$$ 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
$$751$$ 23.7477 0.866567 0.433283 0.901258i $$-0.357355\pi$$
0.433283 + 0.901258i $$0.357355\pi$$
$$752$$ −23.1434 13.3618i −0.843952 0.487256i
$$753$$ −3.95644 6.85275i −0.144181 0.249728i
$$754$$ 10.7477 3.10260i 0.391409 0.112990i
$$755$$ 5.53901 0.201585
$$756$$ 0 0
$$757$$ −3.00000 5.19615i −0.109037 0.188857i 0.806343 0.591448i $$-0.201443\pi$$
−0.915380 + 0.402590i $$0.868110\pi$$
$$758$$ 6.47822 + 11.2206i 0.235300 + 0.407551i
$$759$$ 15.0000 8.66025i 0.544466 0.314347i
$$760$$ 1.08450i 0.0393390i
$$761$$ 11.2259 6.48130i 0.406940 0.234947i −0.282534 0.959257i $$-0.591175\pi$$
0.689474 + 0.724310i $$0.257842\pi$$
$$762$$ 8.87086i 0.321357i
$$763$$ 0 0
$$764$$ 12.8739 + 22.2982i 0.465760 + 0.806720i
$$765$$ 6.56670i 0.237420i
$$766$$ −0.291288 0.504525i −0.0105247 0.0182292i
$$767$$ 10.6652 43.1027i 0.385096 1.55635i
$$768$$ −2.50000 + 4.33013i −0.0902110 + 0.156250i
$$769$$ 8.12614 4.69163i 0.293036 0.169184i −0.346274 0.938133i $$-0.612553\pi$$
0.639310 + 0.768949i $$0.279220\pi$$
$$770$$ 0 0
$$771$$ 7.03901 12.1919i 0.253504 0.439082i
$$772$$ −30.0000 17.3205i −1.07972 0.623379i
$$773$$ 19.4340i 0.698991i 0.936938 + 0.349495i $$0.113647\pi$$
−0.936938 + 0.349495i $$0.886353\pi$$
$$774$$ 20.5185i 0.737521i
$$775$$ 35.9347 + 20.7469i 1.29081 + 0.745250i
$$776$$ −6.31307 + 10.9346i −0.226626 + 0.392528i
$$777$$ 0 0
$$778$$ 0.130682 0.0754495i