# Properties

 Label 637.2.u.e.30.2 Level $637$ Weight $2$ Character 637.30 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.u (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 30.2 Root $$1.39564 + 0.228425i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.30 Dual form 637.2.u.e.361.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.395644 - 0.228425i) q^{2} +2.79129 q^{3} +(-0.895644 + 1.55130i) q^{4} +(-0.395644 - 0.228425i) q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +4.79129 q^{9} +O(q^{10})$$ $$q+(0.395644 - 0.228425i) q^{2} +2.79129 q^{3} +(-0.895644 + 1.55130i) q^{4} +(-0.395644 - 0.228425i) q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +4.79129 q^{9} -0.208712 q^{10} +3.92095i q^{11} +(-2.50000 + 4.33013i) 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} +(1.89564 - 1.09445i) q^{18} +1.37055i q^{19} +(0.708712 - 0.409175i) q^{20} +(0.895644 + 1.55130i) q^{22} +(0.791288 + 1.37055i) q^{23} +4.83465i q^{24} +(-2.39564 - 4.14938i) q^{25} +(1.18693 - 1.14213i) q^{26} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} -0.582576 q^{30} +(7.50000 - 4.33013i) q^{31} +(-4.10436 - 2.36965i) q^{32} +10.9445i q^{33} +1.37055i q^{34} +(-4.29129 + 7.43273i) q^{36} +(-6.00000 + 3.46410i) q^{37} +(0.313068 + 0.542250i) q^{38} +(9.76951 - 2.41733i) 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} +(-1.89564 - 1.09445i) q^{45} +(0.626136 + 0.361500i) 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} +(-1.79129 + 6.20520i) q^{52} +(-3.08258 - 5.33918i) q^{53} +(1.97822 - 1.14213i) q^{54} +(0.895644 - 1.55130i) q^{55} +3.82560i q^{57} -3.10260i q^{58} +(-10.6652 - 6.15753i) q^{59} +(1.97822 - 1.14213i) q^{60} -14.7477 q^{61} +(1.97822 - 3.42638i) q^{62} +3.41742 q^{64} +(-1.58258 - 0.456850i) q^{65} +(2.50000 + 4.33013i) q^{66} +4.47315i q^{67} +(-2.68693 - 4.65390i) q^{68} +(2.20871 + 3.82560i) q^{69} +(3.79129 - 2.18890i) q^{71} +8.29875i q^{72} +(-3.00000 + 1.73205i) 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} +(3.00000 - 5.19615i) q^{79} +1.27520i q^{80} -0.417424 q^{81} +3.58258 q^{82} -7.02355i q^{83} +(1.18693 - 0.685275i) q^{85} +(-3.70871 - 2.14123i) q^{86} +(9.47822 - 16.4168i) q^{87} -6.79129 q^{88} +(13.9782 - 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(20.9347 - 12.0866i) q^{93} +4.37386 q^{94} +(0.313068 - 0.542250i) q^{95} +(-11.4564 - 6.61438i) q^{96} +(-6.31307 + 3.64485i) q^{97} +18.7864i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9}+O(q^{10})$$ 4 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 + 9 * q^6 + 10 * q^9 $$4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9} - 10 q^{10} - 10 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} - 9 q^{26} + 20 q^{27} + 9 q^{29} + 16 q^{30} + 30 q^{31} - 21 q^{32} - 8 q^{36} - 24 q^{37} + 15 q^{38} + 7 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} - 6 q^{44} - 3 q^{45} + 30 q^{46} + 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} + 2 q^{52} + 6 q^{53} - 15 q^{54} - q^{55} - 6 q^{59} - 15 q^{60} - 4 q^{61} - 15 q^{62} + 32 q^{64} + 12 q^{65} + 10 q^{66} + 3 q^{68} + 18 q^{69} + 6 q^{71} - 12 q^{73} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} - 20 q^{81} - 4 q^{82} - 9 q^{85} - 24 q^{86} + 15 q^{87} - 18 q^{88} + 33 q^{89} - 4 q^{90} - 48 q^{92} + 15 q^{93} - 10 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100})$$ 4 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 + 9 * q^6 + 10 * q^9 - 10 * q^10 - 10 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 + 3 * q^18 + 12 * q^20 - q^22 - 6 * q^23 - 5 * q^25 - 9 * q^26 + 20 * q^27 + 9 * q^29 + 16 * q^30 + 30 * q^31 - 21 * q^32 - 8 * q^36 - 24 * q^37 + 15 * q^38 + 7 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 - 6 * q^44 - 3 * q^45 + 30 * q^46 + 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 + 2 * q^52 + 6 * q^53 - 15 * q^54 - q^55 - 6 * q^59 - 15 * q^60 - 4 * q^61 - 15 * q^62 + 32 * q^64 + 12 * q^65 + 10 * q^66 + 3 * q^68 + 18 * q^69 + 6 * q^71 - 12 * q^73 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 - 20 * q^81 - 4 * q^82 - 9 * q^85 - 24 * q^86 + 15 * q^87 - 18 * q^88 + 33 * q^89 - 4 * q^90 - 48 * q^92 + 15 * q^93 - 10 * q^94 + 15 * q^95 - 39 * q^97

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.395644 0.228425i 0.279763 0.161521i −0.353553 0.935414i $$-0.615027\pi$$
0.633316 + 0.773893i $$0.281693\pi$$
$$3$$ 2.79129 1.61155 0.805775 0.592221i $$-0.201749\pi$$
0.805775 + 0.592221i $$0.201749\pi$$
$$4$$ −0.895644 + 1.55130i −0.447822 + 0.775650i
$$5$$ −0.395644 0.228425i −0.176937 0.102155i 0.408916 0.912572i $$-0.365907\pi$$
−0.585853 + 0.810417i $$0.699240\pi$$
$$6$$ 1.10436 0.637600i 0.450851 0.260299i
$$7$$ 0 0
$$8$$ 1.73205i 0.612372i
$$9$$ 4.79129 1.59710
$$10$$ −0.208712 −0.0660006
$$11$$ 3.92095i 1.18221i 0.806594 + 0.591106i $$0.201308\pi$$
−0.806594 + 0.591106i $$0.798692\pi$$
$$12$$ −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
$$16$$ −1.39564 2.41733i −0.348911 0.604332i
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ 1.89564 1.09445i 0.446808 0.257964i
$$19$$ 1.37055i 0.314426i 0.987565 + 0.157213i $$0.0502509\pi$$
−0.987565 + 0.157213i $$0.949749\pi$$
$$20$$ 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 0.936653 0.350257i $$-0.113906\pi$$
−0.771659 + 0.636037i $$0.780573\pi$$
$$24$$ 4.83465i 0.986869i
$$25$$ −2.39564 4.14938i −0.479129 0.829875i
$$26$$ 1.18693 1.14213i 0.232776 0.223989i
$$27$$ 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 $$-0.0505061\pi$$
$$30$$ −0.582576 −0.106363
$$31$$ 7.50000 4.33013i 1.34704 0.777714i 0.359211 0.933257i $$-0.383046\pi$$
0.987829 + 0.155543i $$0.0497126\pi$$
$$32$$ −4.10436 2.36965i −0.725555 0.418899i
$$33$$ 10.9445i 1.90519i
$$34$$ 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 $$-0.859528\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 0.313068 + 0.542250i 0.0507864 + 0.0879646i
$$39$$ 9.76951 2.41733i 1.56437 0.387082i
$$40$$ 0.395644 0.685275i 0.0625568 0.108352i
$$41$$ 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 $$-0.420126\pi$$
$$44$$ −6.08258 3.51178i −0.916983 0.529420i
$$45$$ −1.89564 1.09445i −0.282586 0.163151i
$$46$$ 0.626136 + 0.361500i 0.0923188 + 0.0533003i
$$47$$ 8.29129 + 4.78698i 1.20941 + 0.698252i 0.962630 0.270820i $$-0.0872947\pi$$
0.246778 + 0.969072i $$0.420628\pi$$
$$48$$ −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
$$52$$ −1.79129 + 6.20520i −0.248407 + 0.860507i
$$53$$ −3.08258 5.33918i −0.423424 0.733392i 0.572848 0.819662i $$-0.305839\pi$$
−0.996272 + 0.0862695i $$0.972505\pi$$
$$54$$ 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
$$58$$ 3.10260i 0.407392i
$$59$$ −10.6652 6.15753i −1.38848 0.801642i −0.395340 0.918535i $$-0.629373\pi$$
−0.993145 + 0.116893i $$0.962707\pi$$
$$60$$ 1.97822 1.14213i 0.255387 0.147448i
$$61$$ −14.7477 −1.88825 −0.944126 0.329583i $$-0.893092\pi$$
−0.944126 + 0.329583i $$0.893092\pi$$
$$62$$ 1.97822 3.42638i 0.251234 0.435150i
$$63$$ 0 0
$$64$$ 3.41742 0.427178
$$65$$ −1.58258 0.456850i −0.196294 0.0566653i
$$66$$ 2.50000 + 4.33013i 0.307729 + 0.533002i
$$67$$ 4.47315i 0.546483i 0.961946 + 0.273241i $$0.0880957\pi$$
−0.961946 + 0.273241i $$0.911904\pi$$
$$68$$ −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 $$0.249685\pi$$
$$72$$ 8.29875i 0.978018i
$$73$$ −3.00000 + 1.73205i −0.351123 + 0.202721i −0.665180 0.746683i $$-0.731645\pi$$
0.314057 + 0.949404i $$0.398312\pi$$
$$74$$ −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
$$79$$ 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i $$-0.723743\pi$$
0.983967 + 0.178352i $$0.0570765\pi$$
$$80$$ 1.27520i 0.142572i
$$81$$ −0.417424 −0.0463805
$$82$$ 3.58258 0.395629
$$83$$ 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
$$86$$ −3.70871 2.14123i −0.399921 0.230894i
$$87$$ 9.47822 16.4168i 1.01617 1.76006i
$$88$$ −6.79129 −0.723954
$$89$$ 13.9782 8.07033i 1.48169 0.855453i 0.481904 0.876224i $$-0.339945\pi$$
0.999784 + 0.0207708i $$0.00661204\pi$$
$$90$$ −1.00000 −0.105409
$$91$$ 0 0
$$92$$ −2.83485 −0.295553
$$93$$ 20.9347 12.0866i 2.17082 1.25333i
$$94$$ 4.37386 0.451130
$$95$$ 0.313068 0.542250i 0.0321201 0.0556337i
$$96$$ −11.4564 6.61438i −1.16927 0.675077i
$$97$$ −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
$$100$$ 8.58258 0.858258
$$101$$ 5.20871 0.518286 0.259143 0.965839i $$-0.416560\pi$$
0.259143 + 0.965839i $$0.416560\pi$$
$$102$$ 3.82560i 0.378791i
$$103$$ −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
$$107$$ 2.60436 + 4.51088i 0.251773 + 0.436083i 0.964014 0.265852i $$-0.0856532\pi$$
−0.712241 + 0.701935i $$0.752320\pi$$
$$108$$ −4.47822 + 7.75650i −0.430917 + 0.746370i
$$109$$ −6.87386 + 3.96863i −0.658397 + 0.380126i −0.791666 0.610954i $$-0.790786\pi$$
0.133269 + 0.991080i $$0.457453\pi$$
$$110$$ 0.818350i 0.0780266i
$$111$$ −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
$$115$$ 0.723000i 0.0674201i
$$116$$ 6.08258 + 10.5353i 0.564753 + 0.978181i
$$117$$ 16.7695 4.14938i 1.55034 0.383610i
$$118$$ −5.62614 −0.517928
$$119$$ 0 0
$$120$$ 1.10436 1.91280i 0.100813 0.174614i
$$121$$ −4.37386 −0.397624
$$122$$ −5.83485 + 3.36875i −0.528262 + 0.304992i
$$123$$ 18.9564 + 10.9445i 1.70924 + 0.986833i
$$124$$ 15.5130i 1.39311i
$$125$$ 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
$$129$$ −13.0826 22.6597i −1.15186 1.99507i
$$130$$ −0.730493 + 0.180750i −0.0640684 + 0.0158528i
$$131$$ 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
$$136$$ −4.50000 2.59808i −0.385872 0.222783i
$$137$$ −10.3521 5.97678i −0.884438 0.510631i −0.0123190 0.999924i $$-0.503921\pi$$
−0.872119 + 0.489294i $$0.837255\pi$$
$$138$$ 1.74773 + 1.00905i 0.148776 + 0.0858961i
$$139$$ −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
$$142$$ 1.00000 1.73205i 0.0839181 0.145350i
$$143$$ 3.39564 + 13.7233i 0.283958 + 1.14760i
$$144$$ −6.68693 11.5821i −0.557244 0.965175i
$$145$$ −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
$$149$$ 0.456850i 0.0374266i −0.999825 0.0187133i $$-0.994043\pi$$
0.999825 0.0187133i $$-0.00595698\pi$$
$$150$$ −5.29129 3.05493i −0.432032 0.249434i
$$151$$ −10.5000 + 6.06218i −0.854478 + 0.493333i −0.862159 0.506637i $$-0.830888\pi$$
0.00768132 + 0.999970i $$0.497555\pi$$
$$152$$ −2.37386 −0.192546
$$153$$ −7.18693 + 12.4481i −0.581029 + 1.00637i
$$154$$ 0 0
$$155$$ −3.95644 −0.317789
$$156$$ −5.00000 + 17.3205i −0.400320 + 1.38675i
$$157$$ 0.478220 + 0.828301i 0.0381661 + 0.0661056i 0.884477 0.466583i $$-0.154515\pi$$
−0.846311 + 0.532689i $$0.821182\pi$$
$$158$$ 2.74110i 0.218070i
$$159$$ −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
$$163$$ 6.92820i 0.542659i 0.962487 + 0.271329i $$0.0874633\pi$$
−0.962487 + 0.271329i $$0.912537\pi$$
$$164$$ −12.1652 + 7.02355i −0.949939 + 0.548447i
$$165$$ 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
$$170$$ 0.313068 0.542250i 0.0240112 0.0415887i
$$171$$ 6.56670i 0.502168i
$$172$$ 16.7913 1.28032
$$173$$ 19.7477 1.50139 0.750696 0.660648i $$-0.229718\pi$$
0.750696 + 0.660648i $$0.229718\pi$$
$$174$$ 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
$$178$$ 3.68693 6.38595i 0.276347 0.478647i
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ 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
$$185$$ 3.16515 0.232707
$$186$$ 5.52178 9.56400i 0.404877 0.701267i
$$187$$ −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
$$191$$ −14.3739 −1.04006 −0.520028 0.854149i $$-0.674079\pi$$
−0.520028 + 0.854149i $$0.674079\pi$$
$$192$$ 9.53901 0.688419
$$193$$ 19.3386i 1.39202i −0.718030 0.696012i $$-0.754956\pi$$
0.718030 0.696012i $$-0.245044\pi$$
$$194$$ −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 0.568813 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 −0.602549 0.798082i $$-0.705848\pi$$
0.992434 + 0.122782i $$0.0391815\pi$$
$$200$$ 7.18693 4.14938i 0.508193 0.293405i
$$201$$ 12.4859i 0.880684i
$$202$$ 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
$$206$$ 2.09355i 0.145865i
$$207$$ 3.79129 + 6.56670i 0.263513 + 0.456417i
$$208$$ −6.97822 7.25198i −0.483852 0.502834i
$$209$$ −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 $$0.285347\pi$$
$$212$$ 11.0436 0.758475
$$213$$ 10.5826 6.10985i 0.725106 0.418640i
$$214$$ 2.06080 + 1.18980i 0.140873 + 0.0813331i
$$215$$ 4.28245i 0.292061i
$$216$$ 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
$$220$$ 1.60436 + 2.77883i 0.108166 + 0.187348i
$$221$$ −3.00000 + 10.3923i −0.201802 + 0.699062i
$$222$$ −4.41742 + 7.65120i −0.296478 + 0.513515i
$$223$$ 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
$$226$$ −4.18693 2.41733i −0.278511 0.160798i
$$227$$ 7.66515 + 4.42548i 0.508754 + 0.293729i 0.732321 0.680959i $$-0.238437\pi$$
−0.223567 + 0.974688i $$0.571770\pi$$
$$228$$ −5.93466 3.42638i −0.393032 0.226917i
$$229$$ 6.00000 + 3.46410i 0.396491 + 0.228914i 0.684969 0.728572i $$-0.259816\pi$$
−0.288478 + 0.957487i $$0.593149\pi$$
$$230$$ −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 $$0.991602\pi$$
$$234$$ 5.68693 5.47225i 0.371766 0.357732i
$$235$$ −2.18693 3.78788i −0.142660 0.247094i
$$236$$ 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 $$0.859272\pi$$
$$240$$ 3.55945i 0.229762i
$$241$$ −17.0608 9.85005i −1.09898 0.634498i −0.163029 0.986621i $$-0.552126\pi$$
−0.935954 + 0.352123i $$0.885460\pi$$
$$242$$ −1.73049 + 0.999100i −0.111240 + 0.0642246i
$$243$$ −16.1652 −1.03699
$$244$$ 13.2087 22.8782i 0.845601 1.46462i
$$245$$ 0 0
$$246$$ 10.0000 0.637577
$$247$$ 1.18693 + 4.79693i 0.0755227 + 0.305221i
$$248$$ 7.50000 + 12.9904i 0.476250 + 0.824890i
$$249$$ 19.6048i 1.24240i
$$250$$ 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
$$254$$ 3.17805i 0.199409i
$$255$$ 3.31307 1.91280i 0.207472 0.119784i
$$256$$ −0.895644 + 1.55130i −0.0559777 + 0.0969563i
$$257$$ 2.52178 + 4.36785i 0.157304 + 0.272459i 0.933896 0.357546i $$-0.116386\pi$$
−0.776591 + 0.630005i $$0.783053\pi$$
$$258$$ −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
$$262$$ 7.93725i 0.490365i
$$263$$ 9.33030 0.575331 0.287666 0.957731i $$-0.407121\pi$$
0.287666 + 0.957731i $$0.407121\pi$$
$$264$$ −18.9564 −1.16669
$$265$$ 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
$$269$$ −7.89564 + 13.6757i −0.481406 + 0.833819i −0.999772 0.0213391i $$-0.993207\pi$$
0.518366 + 0.855159i $$0.326540\pi$$
$$270$$ −1.04356 −0.0635091
$$271$$ −11.1261 + 6.42368i −0.675865 + 0.390211i −0.798295 0.602266i $$-0.794264\pi$$
0.122430 + 0.992477i $$0.460931\pi$$
$$272$$ 8.37386 0.507740
$$273$$ 0 0
$$274$$ −5.46099 −0.329910
$$275$$ 16.2695 9.39320i 0.981088 0.566432i
$$276$$ −7.91288 −0.476299
$$277$$ −5.87386 + 10.1738i −0.352926 + 0.611286i −0.986761 0.162182i $$-0.948147\pi$$
0.633835 + 0.773469i $$0.281480\pi$$
$$278$$ −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 $$0.367064\pi$$
−0.405597 + 0.914052i $$0.632936\pi$$
$$282$$ 12.2087 0.727018
$$283$$ −2.74773 −0.163335 −0.0816677 0.996660i $$-0.526025\pi$$
−0.0816677 + 0.996660i $$0.526025\pi$$
$$284$$ 7.84190i 0.465331i
$$285$$ 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
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ −0.708712 + 1.22753i −0.0416170 + 0.0720828i
$$291$$ −17.6216 + 10.1738i −1.03300 + 0.596400i
$$292$$ 6.20520i 0.363132i
$$293$$ −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
$$297$$ 19.6048i 1.13758i
$$298$$ −0.104356 0.180750i −0.00604519 0.0104706i
$$299$$ 3.95644 + 4.11165i 0.228807 + 0.237783i
$$300$$ 23.9564 1.38313
$$301$$ 0 0
$$302$$ −2.76951 + 4.79693i −0.159367 + 0.276032i
$$303$$ 14.5390 0.835245
$$304$$ 3.31307 1.91280i 0.190017 0.109707i
$$305$$ 5.83485 + 3.36875i 0.334102 + 0.192894i
$$306$$ 6.56670i 0.375393i
$$307$$ 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
$$311$$ 13.2695 + 22.9835i 0.752445 + 1.30327i 0.946635 + 0.322309i $$0.104459\pi$$
−0.194190 + 0.980964i $$0.562208\pi$$
$$312$$ 4.18693 + 16.9213i 0.237038 + 0.957979i
$$313$$ −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 0.877473 0.479626i $$-0.159228\pi$$
0.0233679 + 0.999727i $$0.492561\pi$$
$$318$$ −6.80852 3.93090i −0.381803 0.220434i
$$319$$ 23.0608 + 13.3142i 1.29116 + 0.745450i
$$320$$ −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
$$325$$ −11.9782 12.4481i −0.664432 0.690498i
$$326$$ 1.58258 + 2.74110i 0.0876508 + 0.151816i
$$327$$ −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
$$331$$ 24.8963i 1.36842i 0.729284 + 0.684211i $$0.239853\pi$$
−0.729284 + 0.684211i $$0.760147\pi$$
$$332$$ 10.8956 + 6.29060i 0.597976 + 0.345242i
$$333$$ −28.7477 + 16.5975i −1.57537 + 0.909538i
$$334$$ 6.70417 0.366836
$$335$$ 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 $$0.412586\pi$$
$$338$$ 3.16515 5.02535i 0.172162 0.273343i
$$339$$ −14.7695 25.5815i −0.802170 1.38940i
$$340$$ 2.45505i 0.133144i
$$341$$ 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
$$345$$ 2.01810i 0.108651i
$$346$$ 7.81307 4.51088i 0.420033 0.242506i
$$347$$ 6.79129 11.7629i 0.364575 0.631463i −0.624132 0.781319i $$-0.714547\pi$$
0.988708 + 0.149855i $$0.0478808\pi$$
$$348$$ 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
$$352$$ 9.29129 16.0930i 0.495227 0.857759i
$$353$$ 18.1588i 0.966493i 0.875484 + 0.483247i $$0.160543\pi$$
−0.875484 + 0.483247i $$0.839457\pi$$
$$354$$ −15.7042 −0.834667
$$355$$ −2.00000 −0.106149
$$356$$ 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 0.512567 0.858647i $$-0.328695\pi$$
−0.487327 + 0.873219i $$0.662028\pi$$
$$360$$ 1.89564 3.28335i 0.0999092 0.173048i
$$361$$ 17.1216 0.901136
$$362$$ −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
$$367$$ 18.0000 0.939592 0.469796 0.882775i $$-0.344327\pi$$
0.469796 + 0.882775i $$0.344327\pi$$
$$368$$ 2.20871 3.82560i 0.115137 0.199423i
$$369$$ 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
$$373$$ 32.2087 1.66770 0.833852 0.551988i $$-0.186131\pi$$
0.833852 + 0.551988i $$0.186131\pi$$
$$374$$ −5.37386 −0.277876
$$375$$ 12.4859i 0.644767i
$$376$$ −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 −0.288219 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
$$382$$ −5.68693 + 3.28335i −0.290969 + 0.167991i
$$383$$ 1.27520i 0.0651597i −0.999469 0.0325799i $$-0.989628\pi$$
0.999469 0.0325799i $$-0.0103723\pi$$
$$384$$ 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
$$388$$ 13.0580i 0.662917i
$$389$$ 0.165151 + 0.286051i 0.00837351 + 0.0145033i 0.870182 0.492731i $$-0.164001\pi$$
−0.861808 + 0.507234i $$0.830668\pi$$
$$390$$ −2.03901 + 0.504525i −0.103250 + 0.0255476i
$$391$$ −4.74773 −0.240103
$$392$$ 0 0
$$393$$ 24.2477 41.9983i 1.22314 2.11853i
$$394$$ 1.04356 0.0525738
$$395$$ −2.37386 + 1.37055i −0.119442 + 0.0689599i
$$396$$ −29.1434 16.8259i −1.46451 0.845535i
$$397$$ 32.4720i 1.62972i −0.579655 0.814862i $$-0.696813\pi$$
0.579655 0.814862i $$-0.303187\pi$$
$$398$$ 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 $$-0.952124\pi$$
−0.364590 + 0.931168i $$0.618791\pi$$
$$402$$ 2.85208 + 4.93995i 0.142249 + 0.246382i
$$403$$ 22.5000 21.6506i 1.12080 1.07849i
$$404$$ −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
$$409$$ 7.18693 + 4.14938i 0.355371 + 0.205173i 0.667048 0.745015i $$-0.267557\pi$$
−0.311677 + 0.950188i $$0.600891\pi$$
$$410$$ −1.41742 0.818350i −0.0700016 0.0404154i
$$411$$ −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
$$416$$ −16.4174 4.73930i −0.804930 0.232363i
$$417$$ −5.29129 9.16478i −0.259115 0.448801i
$$418$$ −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 $$0.967465\pi$$
$$422$$ 4.83465i 0.235347i
$$423$$ 39.7259 + 22.9358i 1.93154 + 1.11518i
$$424$$ 9.24773 5.33918i 0.449109 0.259293i
$$425$$ 14.3739 0.697235
$$426$$ 2.79129 4.83465i 0.135238 0.234240i
$$427$$ 0 0
$$428$$ −9.33030 −0.450997
$$429$$ 9.47822 + 38.3058i 0.457613 + 1.84942i
$$430$$ 0.978220 + 1.69433i 0.0471739 + 0.0817077i
$$431$$ 34.6609i 1.66956i −0.550585 0.834779i $$-0.685595\pi$$
0.550585 0.834779i $$-0.314405\pi$$
$$432$$ −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
$$436$$ 14.2179i 0.680914i
$$437$$ −1.87841 + 1.08450i −0.0898565 + 0.0518787i
$$438$$ −2.20871 + 3.82560i −0.105536 + 0.182794i
$$439$$ −10.2695 17.7873i −0.490137 0.848942i 0.509799 0.860294i $$-0.329720\pi$$
−0.999936 + 0.0113518i $$0.996387\pi$$
$$440$$ 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 $$0.0493550\pi$$
$$444$$ 34.6410i 1.64399i
$$445$$ −7.37386 −0.349555
$$446$$ 8.66970 0.410522
$$447$$ 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 $$0.535684\pi$$
$$450$$ −9.08258 5.24383i −0.428157 0.247196i
$$451$$ −15.3739 + 26.6283i −0.723927 + 1.25388i
$$452$$ 18.9564 0.891636
$$453$$ −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 $$-0.845727\pi$$
−0.0389271 + 0.999242i $$0.512394\pi$$
$$458$$ 3.16515 0.147898
$$459$$ −7.50000 + 12.9904i −0.350070 + 0.606339i
$$460$$ 1.12159 + 0.647551i 0.0522944 + 0.0301922i
$$461$$ −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 $$0.940954\pi$$
$$464$$ −18.9564 −0.880031
$$465$$ −11.0436 −0.512133
$$466$$ 7.28970i 0.337689i
$$467$$ 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
$$471$$ 1.33485 + 2.31203i 0.0615066 + 0.106533i
$$472$$ 10.6652 18.4726i 0.490903 0.850270i
$$473$$ 31.8303 18.3772i 1.46356 0.844986i
$$474$$ 7.65120i 0.351431i
$$475$$ 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
$$479$$ 18.8818i 0.862730i −0.902178 0.431365i $$-0.858032\pi$$
0.902178 0.431365i $$-0.141968\pi$$
$$480$$ 3.02178 + 5.23388i 0.137925 + 0.238893i
$$481$$ −18.0000 + 17.3205i −0.820729 + 0.789747i
$$482$$ −9.00000 −0.409939
$$483$$ 0 0
$$484$$ 3.91742 6.78518i 0.178065 0.308417i
$$485$$ 3.33030 0.151221
$$486$$ −6.39564 + 3.69253i −0.290112 + 0.167496i
$$487$$ −25.4347 14.6847i −1.15255 0.665428i −0.203046 0.979169i $$-0.565084\pi$$
−0.949508 + 0.313742i $$0.898417\pi$$
$$488$$ 25.5438i 1.15631i
$$489$$ 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
$$493$$ 10.1869 + 17.6443i 0.458796 + 0.794659i
$$494$$ 1.56534 + 1.62675i 0.0704280 + 0.0731910i
$$495$$ 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 0.0988324 0.995104i $$-0.468489\pi$$
−0.812369 + 0.583143i $$0.801823\pi$$
$$500$$ −6.93920 4.00635i −0.310331 0.179169i
$$501$$ 35.4737 + 20.4807i 1.58485 + 0.915012i
$$502$$ −1.12159 0.647551i −0.0500590 0.0289016i
$$503$$ 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
$$506$$ −1.41742 + 2.45505i −0.0630122 + 0.109140i
$$507$$ 32.0998 16.9213i 1.42560 0.751501i
$$508$$ −6.23049 10.7915i −0.276433 0.478797i
$$509$$ −13.0390 + 7.52808i −0.577944 + 0.333676i −0.760316 0.649553i $$-0.774956\pi$$
0.182372 + 0.983230i $$0.441623\pi$$
$$510$$ 0.873864 1.51358i 0.0386953 0.0670223i
$$511$$ 0 0
$$512$$ 22.8981i 1.01196i
$$513$$ 6.85275i 0.302556i
$$514$$ 1.99545 + 1.15208i 0.0880157 + 0.0508159i
$$515$$ 1.81307 1.04678i 0.0798933 0.0461264i
$$516$$ 46.8693 2.06331
$$517$$ −18.7695 + 32.5097i −0.825482 + 1.42978i
$$518$$ 0 0
$$519$$ 55.1216 2.41957
$$520$$ 0.791288 2.74110i 0.0347003 0.120205i
$$521$$ 8.20871 + 14.2179i 0.359630 + 0.622898i 0.987899 0.155099i $$-0.0495695\pi$$
−0.628269 + 0.777996i $$0.716236\pi$$
$$522$$ 14.8655i 0.650643i
$$523$$ 12.1652 + 21.0707i 0.531945 + 0.921356i 0.999305 + 0.0372883i $$0.0118720\pi$$
−0.467360 + 0.884067i $$0.654795\pi$$
$$524$$ 15.5608 + 26.9521i 0.679776 + 1.17741i
$$525$$ 0 0
$$526$$ 3.69148 2.13128i 0.160956 0.0929280i
$$527$$ 25.9808i 1.13174i
$$528$$ 26.4564 15.2746i 1.15137 0.664743i
$$529$$ 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
$$534$$ 10.2913 17.8250i 0.445348 0.771365i
$$535$$ 2.37960i 0.102879i
$$536$$ −7.74773 −0.334651
$$537$$ −25.1216 −1.08408
$$538$$ 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 0.378497 0.925602i $$-0.376441\pi$$
−0.612347 + 0.790589i $$0.709774\pi$$
$$542$$ −2.93466 + 5.08298i −0.126054 + 0.218333i
$$543$$ −25.5826 −1.09785
$$544$$ 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
$$549$$ −70.6606 −3.01572
$$550$$ 4.29129 7.43273i 0.182981 0.316933i
$$551$$ 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
$$555$$ 8.83485 0.375018
$$556$$ 6.79129 0.288015
$$557$$ 33.0242i 1.39928i 0.714495 + 0.699640i $$0.246656\pi$$
−0.714495 + 0.699640i $$0.753344\pi$$
$$558$$ 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
$$562$$ 7.00000 + 12.1244i 0.295277 + 0.511435i
$$563$$ 18.1652 31.4630i 0.765570 1.32601i −0.174375 0.984679i $$-0.555790\pi$$
0.939945 0.341327i $$-0.110876\pi$$
$$564$$ −41.4564 + 23.9349i −1.74563 + 1.00784i
$$565$$ 4.83465i 0.203395i
$$566$$ −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 0.635383 0.772197i $$-0.280842\pi$$
−0.986434 + 0.164159i $$0.947509\pi$$
$$570$$ 0.798450i 0.0334434i
$$571$$ 1.02178 + 1.76978i 0.0427602 + 0.0740628i 0.886613 0.462511i $$-0.153052\pi$$
−0.843853 + 0.536574i $$0.819718\pi$$
$$572$$ −24.3303 7.02355i −1.01730 0.293670i
$$573$$ −40.1216 −1.67610
$$574$$ 0 0
$$575$$ 3.79129 6.56670i 0.158108 0.273850i
$$576$$ 16.3739 0.682244
$$577$$ −30.8739 + 17.8250i −1.28530 + 0.742066i −0.977811 0.209487i $$-0.932821\pi$$
−0.307484 + 0.951553i $$0.599487\pi$$
$$578$$ 3.16515 + 1.82740i 0.131653 + 0.0760099i
$$579$$ 53.9796i 2.24332i
$$580$$ 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
$$584$$ −3.00000 5.19615i −0.124141 0.215018i
$$585$$ −7.58258 2.18890i −0.313501 0.0904999i
$$586$$ −0.582576 + 1.00905i −0.0240660 + 0.0416835i
$$587$$ 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
$$590$$ 2.22595 + 1.28515i 0.0916408 + 0.0529088i
$$591$$ 5.52178 + 3.18800i 0.227136 + 0.131137i
$$592$$ 16.7477 + 9.66930i 0.688327 + 0.397406i
$$593$$ 5.52178 + 3.18800i 0.226752 + 0.130916i 0.609073 0.793114i $$-0.291542\pi$$
−0.382321 + 0.924030i $$0.624875\pi$$
$$594$$ 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
$$598$$ 2.50455 + 0.723000i 0.102418 + 0.0295657i
$$599$$ 3.31307 + 5.73840i 0.135368 + 0.234465i 0.925738 0.378165i $$-0.123445\pi$$
−0.790370 + 0.612630i $$0.790112\pi$$
$$600$$ 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
$$604$$ 21.7182i 0.883701i
$$605$$ 1.73049 + 0.999100i 0.0703545 + 0.0406192i
$$606$$ 5.75227 3.32108i 0.233670 0.134910i
$$607$$ 19.7477 0.801536 0.400768 0.916180i $$-0.368743\pi$$
0.400768 + 0.916180i $$0.368743\pi$$
$$608$$ 3.24773 5.62523i 0.131713 0.228133i
$$609$$ 0 0
$$610$$ 3.07803 0.124626
$$611$$ 33.1652 + 9.57395i 1.34172 + 0.387321i
$$612$$ −12.8739 22.2982i −0.520395 0.901351i
$$613$$ 18.2541i 0.737277i 0.929573 + 0.368638i $$0.120176\pi$$
−0.929573 + 0.368638i $$0.879824\pi$$
$$614$$ −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 $$0.446041\pi$$
$$618$$ 5.84370i 0.235068i
$$619$$ −16.7477 + 9.66930i −0.673148 + 0.388642i −0.797268 0.603625i $$-0.793722\pi$$
0.124120 + 0.992267i $$0.460389\pi$$
$$620$$ 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
$$625$$ −10.9564 + 18.9771i −0.438258 + 0.759084i
$$626$$ 3.08270i 0.123210i
$$627$$ −15.0000 −0.599042
$$628$$ −1.71326 −0.0683664
$$629$$ 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 $$0.147918\pi$$
$$632$$ 9.00000 + 5.19615i 0.358001 + 0.206692i
$$633$$ −14.7695 + 25.5815i −0.587035 + 1.01677i
$$634$$ 8.46099 0.336029
$$635$$ 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
$$640$$ −5.04356 −0.199364
$$641$$ −14.6869 + 25.4385i −0.580099 + 1.00476i 0.415368 + 0.909653i $$0.363653\pi$$
−0.995467 + 0.0951074i $$0.969681\pi$$
$$642$$ 5.75227 + 3.32108i 0.227024 + 0.131072i
$$643$$ −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
$$646$$ −1.87841 −0.0739050
$$647$$ −35.0780 −1.37906 −0.689530 0.724257i $$-0.742183\pi$$
−0.689530 + 0.724257i $$0.742183\pi$$
$$648$$ 0.723000i 0.0284021i
$$649$$ 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
$$653$$ −7.89564 13.6757i −0.308980 0.535170i 0.669159 0.743119i $$-0.266654\pi$$
−0.978140 + 0.207949i $$0.933321\pi$$
$$654$$ −5.06080 + 8.76555i −0.197893 + 0.342760i
$$655$$ −6.87386 + 3.96863i −0.268584 + 0.155067i
$$656$$ 21.8890i 0.854622i
$$657$$ −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
$$661$$ 50.5155i 1.96483i −0.186720 0.982413i $$-0.559786\pi$$
0.186720 0.982413i $$-0.440214\pi$$
$$662$$ 5.68693 + 9.85005i 0.221029 + 0.382833i
$$663$$ −8.37386 + 29.0079i −0.325214 + 1.12657i
$$664$$ 12.1652 0.472099
$$665$$ 0 0
$$666$$ −7.58258 + 13.1334i −0.293819 + 0.508909i
$$667$$ 10.7477 0.416154
$$668$$ −22.7650 + 13.1434i −0.880803 + 0.508532i
$$669$$ 45.8739 + 26.4853i 1.77359 + 1.02398i
$$670$$ 0.933601i 0.0360682i
$$671$$ 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
$$675$$ −11.9782 20.7469i −0.461042 0.798548i
$$676$$ −0.895644 + 23.2695i −0.0344478 + 0.894981i
$$677$$ −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
$$682$$ 13.4347 + 7.75650i 0.514440 + 0.297012i
$$683$$ −26.2913 15.1793i −1.00601 0.580819i −0.0959878 0.995383i $$-0.530601\pi$$
−0.910020 + 0.414563i $$0.863934\pi$$
$$684$$ −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
$$689$$ −15.4129 16.0175i −0.587184 0.610219i
$$690$$ −0.460985 0.798450i −0.0175494 0.0303965i
$$691$$ −8.93466 + 5.15843i −0.339890 + 0.196236i −0.660224 0.751069i $$-0.729538\pi$$
0.320333 + 0.947305i $$0.396205\pi$$
$$692$$ −17.6869 + 30.6347i −0.672356 + 1.16456i
$$693$$ 0 0
$$694$$ 6.20520i 0.235546i
$$695$$ 1.73205i 0.0657004i
$$696$$ 28.4347 + 16.4168i 1.07781 + 0.622276i
$$697$$ −20.3739 + 11.7629i −0.771715 + 0.445550i
$$698$$ 9.62614 0.364355
$$699$$ −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 $$0.584627\pi$$
$$702$$ 5.93466 5.71063i 0.223989 0.215534i
$$703$$ −4.74773 8.22330i −0.179064 0.310148i
$$704$$ 13.3996i 0.505015i
$$705$$ −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
$$709$$ 15.2270i 0.571860i −0.958250 0.285930i $$-0.907697\pi$$
0.958250 0.285930i $$-0.0923025\pi$$
$$710$$ −0.791288 + 0.456850i −0.0296965 + 0.0171453i
$$711$$ 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
$$716$$ 8.06080 13.9617i 0.301246 0.521773i
$$717$$ 36.9253i 1.37900i
$$718$$ 0.252273 0.00941474
$$719$$ −24.1652 −0.901208 −0.450604 0.892724i $$-0.648791\pi$$
−0.450604 + 0.892724i $$0.648791\pi$$
$$720$$ 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
$$724$$ 8.20871 14.2179i 0.305074 0.528404i
$$725$$ −32.5390 −1.20847
$$726$$ −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
$$731$$ 28.1216 1.04011
$$732$$ 36.8693 63.8595i 1.36273 2.36032i
$$733$$ 14.6869 + 8.47950i 0.542474 + 0.313198i 0.746081 0.665855i $$-0.231933\pi$$
−0.203607 + 0.979053i $$0.565266\pi$$
$$734$$ 7.12159 4.11165i 0.262863 0.151764i
$$735$$ 0 0
$$736$$ 7.50030i 0.276465i
$$737$$ −17.5390 −0.646058
$$738$$ 17.1652 0.631858
$$739$$ 19.3386i 0.711382i −0.934604 0.355691i $$-0.884246\pi$$
0.934604 0.355691i $$-0.115754\pi$$
$$740$$ −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 0.934947 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
$$746$$ 12.7432 7.35728i 0.466561 0.269369i
$$747$$ 33.6519i 1.23126i
$$748$$ 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 0.563870 0.825863i $$-0.309312\pi$$
−0.997154 + 0.0753944i $$0.975978\pi$$
$$752$$ 26.7237i 0.974512i
$$753$$ −3.95644 6.85275i −0.144181 0.249728i
$$754$$ −2.68693 10.8591i −0.0978523 0.395465i
$$755$$ 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 $$0.201443\pi$$
$$758$$ −12.9564 −0.470599
$$759$$ −15.0000 + 8.66025i −0.544466 + 0.314347i
$$760$$ 0.939205 + 0.542250i 0.0340685 + 0.0196695i
$$761$$ 12.9626i 0.469894i −0.972008 0.234947i $$-0.924508\pi$$
0.972008 0.234947i $$-0.0754917\pi$$
$$762$$ 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
$$766$$ −0.291288 0.504525i −0.0105247 0.0182292i
$$767$$ −42.6606 12.3151i −1.54039 0.444671i
$$768$$ −2.50000 + 4.33013i −0.0902110 + 0.156250i
$$769$$ 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
$$772$$ 30.0000 + 17.3205i 1.07972 + 0.623379i
$$773$$ 16.8303 + 9.71698i 0.605344 + 0.349495i 0.771141 0.636664i $$-0.219686\pi$$
−0.165797 + 0.986160i $$0.553020\pi$$
$$774$$ −17.7695 10.2592i −0.638712 0.368760i
$$775$$ −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 0.00468519 + 0.00270499i