# Properties

 Label 729.2.g.b.28.4 Level $729$ Weight $2$ Character 729.28 Analytic conductor $5.821$ Analytic rank $0$ Dimension $144$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.g (of order $$27$$, degree $$18$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$5.82109430735$$ Analytic rank: $$0$$ Dimension: $$144$$ Relative dimension: $$8$$ over $$\Q(\zeta_{27})$$ Twist minimal: no (minimal twist has level 81) Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

## Embedding invariants

 Embedding label 28.4 Character $$\chi$$ $$=$$ 729.28 Dual form 729.2.g.b.703.4

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.652974 + 0.429468i) q^{2} +(-0.550227 + 1.27557i) q^{4} +(-1.01614 + 1.07704i) q^{5} +(3.77556 + 0.441300i) q^{7} +(-0.459961 - 2.60857i) q^{8} +O(q^{10})$$ $$q+(-0.652974 + 0.429468i) q^{2} +(-0.550227 + 1.27557i) q^{4} +(-1.01614 + 1.07704i) q^{5} +(3.77556 + 0.441300i) q^{7} +(-0.459961 - 2.60857i) q^{8} +(0.200956 - 1.13968i) q^{10} +(1.44963 - 4.84210i) q^{11} +(0.261201 - 4.48466i) q^{13} +(-2.65487 + 1.33332i) q^{14} +(-0.485993 - 0.515122i) q^{16} +(4.30582 - 1.56719i) q^{17} +(4.19524 + 1.52694i) q^{19} +(-0.814736 - 1.88877i) q^{20} +(1.13295 + 3.78433i) q^{22} +(-3.43157 + 0.401093i) q^{23} +(0.163239 + 2.80270i) q^{25} +(1.75546 + 3.04054i) q^{26} +(-2.64032 + 4.57318i) q^{28} +(-0.583488 - 0.293038i) q^{29} +(0.393020 + 0.527918i) q^{31} +(5.69339 + 1.34936i) q^{32} +(-2.13853 + 2.87254i) q^{34} +(-4.31178 + 3.61801i) q^{35} +(0.766165 + 0.642889i) q^{37} +(-3.39516 + 0.804667i) q^{38} +(3.27692 + 2.15526i) q^{40} +(-0.570482 - 0.375212i) q^{41} +(8.16684 - 1.93558i) q^{43} +(5.37881 + 4.51336i) q^{44} +(2.06847 - 1.73565i) q^{46} +(-4.73832 + 6.36466i) q^{47} +(7.24880 + 1.71800i) q^{49} +(-1.31026 - 1.75998i) q^{50} +(5.57677 + 2.80076i) q^{52} +(2.07469 - 3.59347i) q^{53} +(3.74212 + 6.48154i) q^{55} +(-0.585450 - 10.0518i) q^{56} +(0.506853 - 0.0592426i) q^{58} +(1.51145 + 5.04858i) q^{59} +(-2.68977 - 6.23558i) q^{61} +(-0.483356 - 0.175927i) q^{62} +(-2.96617 + 1.07960i) q^{64} +(4.56474 + 4.83835i) q^{65} +(4.73732 - 2.37917i) q^{67} +(-0.370118 + 6.35468i) q^{68} +(1.26166 - 4.21424i) q^{70} +(1.06500 - 6.03991i) q^{71} +(-0.764322 - 4.33469i) q^{73} +(-0.776385 - 0.0907464i) q^{74} +(-4.25606 + 4.51116i) q^{76} +(7.60998 - 17.6419i) q^{77} +(-9.39300 + 6.17788i) q^{79} +1.04864 q^{80} +0.533651 q^{82} +(1.35486 - 0.891108i) q^{83} +(-2.68737 + 6.23002i) q^{85} +(-4.50147 + 4.77127i) q^{86} +(-13.2977 - 1.55428i) q^{88} +(0.181087 + 1.02699i) q^{89} +(2.96526 - 16.8168i) q^{91} +(1.37652 - 4.59790i) q^{92} +(0.360580 - 6.19091i) q^{94} +(-5.90752 + 2.96687i) q^{95} +(-3.42307 - 3.62824i) q^{97} +(-5.47110 + 1.99132i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10})$$ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 $$144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100})$$ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{22}{27}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.652974 + 0.429468i −0.461722 + 0.303679i −0.758975 0.651119i $$-0.774300\pi$$
0.297253 + 0.954799i $$0.403929\pi$$
$$3$$ 0 0
$$4$$ −0.550227 + 1.27557i −0.275114 + 0.637785i
$$5$$ −1.01614 + 1.07704i −0.454430 + 0.481668i −0.913561 0.406701i $$-0.866679\pi$$
0.459132 + 0.888368i $$0.348161\pi$$
$$6$$ 0 0
$$7$$ 3.77556 + 0.441300i 1.42703 + 0.166796i 0.794275 0.607558i $$-0.207851\pi$$
0.632753 + 0.774354i $$0.281925\pi$$
$$8$$ −0.459961 2.60857i −0.162621 0.922268i
$$9$$ 0 0
$$10$$ 0.200956 1.13968i 0.0635478 0.360398i
$$11$$ 1.44963 4.84210i 0.437079 1.45995i −0.401849 0.915706i $$-0.631632\pi$$
0.838929 0.544241i $$-0.183182\pi$$
$$12$$ 0 0
$$13$$ 0.261201 4.48466i 0.0724443 1.24382i −0.744705 0.667394i $$-0.767410\pi$$
0.817149 0.576426i $$-0.195553\pi$$
$$14$$ −2.65487 + 1.33332i −0.709543 + 0.356346i
$$15$$ 0 0
$$16$$ −0.485993 0.515122i −0.121498 0.128781i
$$17$$ 4.30582 1.56719i 1.04431 0.380099i 0.237800 0.971314i $$-0.423574\pi$$
0.806514 + 0.591215i $$0.201352\pi$$
$$18$$ 0 0
$$19$$ 4.19524 + 1.52694i 0.962455 + 0.350305i 0.774995 0.631967i $$-0.217752\pi$$
0.187460 + 0.982272i $$0.439975\pi$$
$$20$$ −0.814736 1.88877i −0.182181 0.422342i
$$21$$ 0 0
$$22$$ 1.13295 + 3.78433i 0.241547 + 0.806822i
$$23$$ −3.43157 + 0.401093i −0.715532 + 0.0836337i −0.466066 0.884750i $$-0.654329\pi$$
−0.249466 + 0.968384i $$0.580255\pi$$
$$24$$ 0 0
$$25$$ 0.163239 + 2.80270i 0.0326477 + 0.560540i
$$26$$ 1.75546 + 3.04054i 0.344273 + 0.596299i
$$27$$ 0 0
$$28$$ −2.64032 + 4.57318i −0.498974 + 0.864249i
$$29$$ −0.583488 0.293038i −0.108351 0.0544159i 0.393798 0.919197i $$-0.371161\pi$$
−0.502149 + 0.864781i $$0.667457\pi$$
$$30$$ 0 0
$$31$$ 0.393020 + 0.527918i 0.0705886 + 0.0948169i 0.836015 0.548706i $$-0.184879\pi$$
−0.765427 + 0.643523i $$0.777472\pi$$
$$32$$ 5.69339 + 1.34936i 1.00646 + 0.238535i
$$33$$ 0 0
$$34$$ −2.13853 + 2.87254i −0.366755 + 0.492637i
$$35$$ −4.31178 + 3.61801i −0.728824 + 0.611556i
$$36$$ 0 0
$$37$$ 0.766165 + 0.642889i 0.125957 + 0.105690i 0.703590 0.710606i $$-0.251579\pi$$
−0.577633 + 0.816296i $$0.696024\pi$$
$$38$$ −3.39516 + 0.804667i −0.550767 + 0.130534i
$$39$$ 0 0
$$40$$ 3.27692 + 2.15526i 0.518126 + 0.340777i
$$41$$ −0.570482 0.375212i −0.0890943 0.0585983i 0.504180 0.863598i $$-0.331795\pi$$
−0.593274 + 0.805000i $$0.702165\pi$$
$$42$$ 0 0
$$43$$ 8.16684 1.93558i 1.24543 0.295173i 0.445510 0.895277i $$-0.353022\pi$$
0.799922 + 0.600104i $$0.204874\pi$$
$$44$$ 5.37881 + 4.51336i 0.810886 + 0.680414i
$$45$$ 0 0
$$46$$ 2.06847 1.73565i 0.304979 0.255908i
$$47$$ −4.73832 + 6.36466i −0.691155 + 0.928382i −0.999740 0.0228150i $$-0.992737\pi$$
0.308585 + 0.951197i $$0.400145\pi$$
$$48$$ 0 0
$$49$$ 7.24880 + 1.71800i 1.03554 + 0.245428i
$$50$$ −1.31026 1.75998i −0.185299 0.248899i
$$51$$ 0 0
$$52$$ 5.57677 + 2.80076i 0.773359 + 0.388396i
$$53$$ 2.07469 3.59347i 0.284981 0.493601i −0.687624 0.726067i $$-0.741346\pi$$
0.972605 + 0.232466i $$0.0746794\pi$$
$$54$$ 0 0
$$55$$ 3.74212 + 6.48154i 0.504587 + 0.873971i
$$56$$ −0.585450 10.0518i −0.0782340 1.34323i
$$57$$ 0 0
$$58$$ 0.506853 0.0592426i 0.0665530 0.00777893i
$$59$$ 1.51145 + 5.04858i 0.196773 + 0.657269i 0.998244 + 0.0592349i $$0.0188661\pi$$
−0.801471 + 0.598034i $$0.795949\pi$$
$$60$$ 0 0
$$61$$ −2.68977 6.23558i −0.344389 0.798384i −0.999096 0.0425013i $$-0.986467\pi$$
0.654707 0.755883i $$-0.272792\pi$$
$$62$$ −0.483356 0.175927i −0.0613862 0.0223428i
$$63$$ 0 0
$$64$$ −2.96617 + 1.07960i −0.370771 + 0.134950i
$$65$$ 4.56474 + 4.83835i 0.566187 + 0.600123i
$$66$$ 0 0
$$67$$ 4.73732 2.37917i 0.578756 0.290662i −0.135239 0.990813i $$-0.543180\pi$$
0.713995 + 0.700151i $$0.246884\pi$$
$$68$$ −0.370118 + 6.35468i −0.0448834 + 0.770618i
$$69$$ 0 0
$$70$$ 1.26166 4.21424i 0.150797 0.503698i
$$71$$ 1.06500 6.03991i 0.126392 0.716805i −0.854079 0.520143i $$-0.825879\pi$$
0.980471 0.196662i $$-0.0630103\pi$$
$$72$$ 0 0
$$73$$ −0.764322 4.33469i −0.0894571 0.507337i −0.996306 0.0858796i $$-0.972630\pi$$
0.906848 0.421457i $$-0.138481\pi$$
$$74$$ −0.776385 0.0907464i −0.0902530 0.0105491i
$$75$$ 0 0
$$76$$ −4.25606 + 4.51116i −0.488204 + 0.517466i
$$77$$ 7.60998 17.6419i 0.867237 2.01048i
$$78$$ 0 0
$$79$$ −9.39300 + 6.17788i −1.05680 + 0.695065i −0.954052 0.299643i $$-0.903133\pi$$
−0.102744 + 0.994708i $$0.532762\pi$$
$$80$$ 1.04864 0.117242
$$81$$ 0 0
$$82$$ 0.533651 0.0589319
$$83$$ 1.35486 0.891108i 0.148716 0.0978119i −0.472971 0.881078i $$-0.656818\pi$$
0.621686 + 0.783266i $$0.286448\pi$$
$$84$$ 0 0
$$85$$ −2.68737 + 6.23002i −0.291486 + 0.675741i
$$86$$ −4.50147 + 4.77127i −0.485406 + 0.514500i
$$87$$ 0 0
$$88$$ −13.2977 1.55428i −1.41754 0.165687i
$$89$$ 0.181087 + 1.02699i 0.0191952 + 0.108861i 0.992900 0.118952i $$-0.0379535\pi$$
−0.973705 + 0.227813i $$0.926842\pi$$
$$90$$ 0 0
$$91$$ 2.96526 16.8168i 0.310844 1.76288i
$$92$$ 1.37652 4.59790i 0.143512 0.479364i
$$93$$ 0 0
$$94$$ 0.360580 6.19091i 0.0371909 0.638544i
$$95$$ −5.90752 + 2.96687i −0.606099 + 0.304394i
$$96$$ 0 0
$$97$$ −3.42307 3.62824i −0.347560 0.368392i 0.529885 0.848070i $$-0.322235\pi$$
−0.877445 + 0.479677i $$0.840754\pi$$
$$98$$ −5.47110 + 1.99132i −0.552664 + 0.201153i
$$99$$ 0 0
$$100$$ −3.66486 1.33390i −0.366486 0.133390i
$$101$$ 3.79067 + 8.78777i 0.377186 + 0.874416i 0.996040 + 0.0889095i $$0.0283382\pi$$
−0.618854 + 0.785506i $$0.712403\pi$$
$$102$$ 0 0
$$103$$ −0.933584 3.11839i −0.0919888 0.307264i 0.899596 0.436723i $$-0.143861\pi$$
−0.991585 + 0.129459i $$0.958676\pi$$
$$104$$ −11.8187 + 1.38140i −1.15892 + 0.135458i
$$105$$ 0 0
$$106$$ 0.188560 + 3.23746i 0.0183146 + 0.314450i
$$107$$ 8.40680 + 14.5610i 0.812716 + 1.40767i 0.910956 + 0.412503i $$0.135345\pi$$
−0.0982402 + 0.995163i $$0.531321\pi$$
$$108$$ 0 0
$$109$$ −3.81772 + 6.61249i −0.365671 + 0.633361i −0.988884 0.148691i $$-0.952494\pi$$
0.623212 + 0.782053i $$0.285827\pi$$
$$110$$ −5.22712 2.62516i −0.498386 0.250299i
$$111$$ 0 0
$$112$$ −1.60757 2.15934i −0.151901 0.204039i
$$113$$ 9.74930 + 2.31063i 0.917137 + 0.217365i 0.661969 0.749531i $$-0.269721\pi$$
0.255168 + 0.966897i $$0.417869\pi$$
$$114$$ 0 0
$$115$$ 3.05495 4.10351i 0.284875 0.382654i
$$116$$ 0.694842 0.583042i 0.0645144 0.0541340i
$$117$$ 0 0
$$118$$ −3.15514 2.64747i −0.290454 0.243720i
$$119$$ 16.9485 4.01686i 1.55366 0.368225i
$$120$$ 0 0
$$121$$ −12.1541 7.99389i −1.10492 0.726717i
$$122$$ 4.43432 + 2.91650i 0.401465 + 0.264048i
$$123$$ 0 0
$$124$$ −0.889647 + 0.210850i −0.0798927 + 0.0189349i
$$125$$ −8.85601 7.43107i −0.792105 0.664655i
$$126$$ 0 0
$$127$$ 2.97665 2.49770i 0.264135 0.221635i −0.501096 0.865392i $$-0.667070\pi$$
0.765230 + 0.643757i $$0.222625\pi$$
$$128$$ −5.51490 + 7.40779i −0.487453 + 0.654763i
$$129$$ 0 0
$$130$$ −5.05857 1.19890i −0.443666 0.105151i
$$131$$ 9.94222 + 13.3547i 0.868656 + 1.16681i 0.984820 + 0.173577i $$0.0555325\pi$$
−0.116165 + 0.993230i $$0.537060\pi$$
$$132$$ 0 0
$$133$$ 15.1656 + 7.61643i 1.31502 + 0.660428i
$$134$$ −2.07157 + 3.58807i −0.178956 + 0.309962i
$$135$$ 0 0
$$136$$ −6.06863 10.5112i −0.520380 0.901325i
$$137$$ 0.539345 + 9.26019i 0.0460793 + 0.791152i 0.939631 + 0.342190i $$0.111169\pi$$
−0.893551 + 0.448961i $$0.851794\pi$$
$$138$$ 0 0
$$139$$ −15.8135 + 1.84833i −1.34128 + 0.156774i −0.756275 0.654253i $$-0.772983\pi$$
−0.585009 + 0.811027i $$0.698909\pi$$
$$140$$ −2.24257 7.49071i −0.189532 0.633080i
$$141$$ 0 0
$$142$$ 1.89853 + 4.40128i 0.159321 + 0.369348i
$$143$$ −21.3365 7.76585i −1.78425 0.649413i
$$144$$ 0 0
$$145$$ 0.908517 0.330673i 0.0754483 0.0274609i
$$146$$ 2.36069 + 2.50218i 0.195372 + 0.207082i
$$147$$ 0 0
$$148$$ −1.24161 + 0.623562i −0.102060 + 0.0512565i
$$149$$ 1.35720 23.3023i 0.111186 1.90900i −0.236899 0.971534i $$-0.576131\pi$$
0.348085 0.937463i $$-0.386832\pi$$
$$150$$ 0 0
$$151$$ 0.668852 2.23412i 0.0544304 0.181810i −0.926452 0.376414i $$-0.877157\pi$$
0.980882 + 0.194604i $$0.0623422\pi$$
$$152$$ 2.05349 11.6459i 0.166560 0.944608i
$$153$$ 0 0
$$154$$ 2.60751 + 14.7879i 0.210119 + 1.19165i
$$155$$ −0.967952 0.113137i −0.0777478 0.00908741i
$$156$$ 0 0
$$157$$ 13.5075 14.3171i 1.07801 1.14263i 0.0888142 0.996048i $$-0.471692\pi$$
0.989199 0.146579i $$-0.0468263\pi$$
$$158$$ 3.48019 8.06798i 0.276869 0.641854i
$$159$$ 0 0
$$160$$ −7.23857 + 4.76088i −0.572259 + 0.376381i
$$161$$ −13.1331 −1.03503
$$162$$ 0 0
$$163$$ −17.6622 −1.38341 −0.691707 0.722179i $$-0.743141\pi$$
−0.691707 + 0.722179i $$0.743141\pi$$
$$164$$ 0.792504 0.521238i 0.0618842 0.0407018i
$$165$$ 0 0
$$166$$ −0.501989 + 1.16374i −0.0389619 + 0.0903238i
$$167$$ 2.32646 2.46590i 0.180027 0.190817i −0.631076 0.775721i $$-0.717386\pi$$
0.811102 + 0.584904i $$0.198868\pi$$
$$168$$ 0 0
$$169$$ −7.13182 0.833590i −0.548601 0.0641223i
$$170$$ −0.920811 5.22218i −0.0706230 0.400523i
$$171$$ 0 0
$$172$$ −2.02465 + 11.4824i −0.154378 + 0.875524i
$$173$$ −5.35719 + 17.8943i −0.407300 + 1.36048i 0.470901 + 0.882186i $$0.343929\pi$$
−0.878201 + 0.478291i $$0.841256\pi$$
$$174$$ 0 0
$$175$$ −0.620513 + 10.6538i −0.0469064 + 0.805351i
$$176$$ −3.19878 + 1.60649i −0.241117 + 0.121094i
$$177$$ 0 0
$$178$$ −0.559306 0.592829i −0.0419217 0.0444344i
$$179$$ 11.1678 4.06476i 0.834723 0.303814i 0.110927 0.993829i $$-0.464618\pi$$
0.723796 + 0.690014i $$0.242396\pi$$
$$180$$ 0 0
$$181$$ 14.8329 + 5.39873i 1.10252 + 0.401284i 0.828244 0.560367i $$-0.189340\pi$$
0.274275 + 0.961651i $$0.411562\pi$$
$$182$$ 5.28604 + 12.2544i 0.391828 + 0.908358i
$$183$$ 0 0
$$184$$ 2.62467 + 8.76699i 0.193493 + 0.646311i
$$185$$ −1.47095 + 0.171929i −0.108146 + 0.0126405i
$$186$$ 0 0
$$187$$ −1.34665 23.1210i −0.0984765 1.69078i
$$188$$ −5.51142 9.54607i −0.401962 0.696219i
$$189$$ 0 0
$$190$$ 2.58328 4.47437i 0.187411 0.324605i
$$191$$ −5.15323 2.58805i −0.372875 0.187265i 0.252486 0.967601i $$-0.418752\pi$$
−0.625361 + 0.780336i $$0.715048\pi$$
$$192$$ 0 0
$$193$$ 0.104955 + 0.140979i 0.00755483 + 0.0101479i 0.805885 0.592073i $$-0.201690\pi$$
−0.798330 + 0.602221i $$0.794283\pi$$
$$194$$ 3.79339 + 0.899050i 0.272349 + 0.0645480i
$$195$$ 0 0
$$196$$ −6.17991 + 8.30106i −0.441422 + 0.592933i
$$197$$ −8.59155 + 7.20917i −0.612123 + 0.513632i −0.895316 0.445431i $$-0.853050\pi$$
0.283194 + 0.959063i $$0.408606\pi$$
$$198$$ 0 0
$$199$$ −15.6873 13.1632i −1.11204 0.933114i −0.113866 0.993496i $$-0.536324\pi$$
−0.998175 + 0.0603824i $$0.980768\pi$$
$$200$$ 7.23595 1.71495i 0.511659 0.121265i
$$201$$ 0 0
$$202$$ −6.24927 4.11021i −0.439697 0.289193i
$$203$$ −2.07367 1.36388i −0.145543 0.0957254i
$$204$$ 0 0
$$205$$ 0.983806 0.233166i 0.0687120 0.0162850i
$$206$$ 1.94885 + 1.63528i 0.135783 + 0.113935i
$$207$$ 0 0
$$208$$ −2.43709 + 2.04496i −0.168982 + 0.141792i
$$209$$ 13.4752 18.1003i 0.932096 1.25202i
$$210$$ 0 0
$$211$$ 1.15927 + 0.274753i 0.0798076 + 0.0189147i 0.270326 0.962769i $$-0.412869\pi$$
−0.190518 + 0.981684i $$0.561017\pi$$
$$212$$ 3.44217 + 4.62364i 0.236409 + 0.317553i
$$213$$ 0 0
$$214$$ −11.7429 5.89751i −0.802728 0.403145i
$$215$$ −6.21393 + 10.7628i −0.423786 + 0.734019i
$$216$$ 0 0
$$217$$ 1.25090 + 2.16663i 0.0849168 + 0.147080i
$$218$$ −0.346977 5.95737i −0.0235003 0.403484i
$$219$$ 0 0
$$220$$ −10.3267 + 1.20702i −0.696224 + 0.0813769i
$$221$$ −5.90362 19.7195i −0.397120 1.32647i
$$222$$ 0 0
$$223$$ −5.90154 13.6813i −0.395197 0.916169i −0.993387 0.114815i $$-0.963373\pi$$
0.598190 0.801354i $$-0.295887\pi$$
$$224$$ 20.9003 + 7.60707i 1.39646 + 0.508269i
$$225$$ 0 0
$$226$$ −7.35838 + 2.67823i −0.489472 + 0.178153i
$$227$$ −16.8807 17.8925i −1.12041 1.18757i −0.980317 0.197430i $$-0.936741\pi$$
−0.140095 0.990138i $$-0.544741\pi$$
$$228$$ 0 0
$$229$$ 1.36456 0.685307i 0.0901726 0.0452864i −0.403141 0.915138i $$-0.632082\pi$$
0.493314 + 0.869851i $$0.335785\pi$$
$$230$$ −0.232477 + 3.99148i −0.0153291 + 0.263191i
$$231$$ 0 0
$$232$$ −0.496029 + 1.65685i −0.0325659 + 0.108778i
$$233$$ −2.44148 + 13.8463i −0.159946 + 0.907101i 0.794177 + 0.607687i $$0.207902\pi$$
−0.954123 + 0.299414i $$0.903209\pi$$
$$234$$ 0 0
$$235$$ −2.04023 11.5707i −0.133090 0.754791i
$$236$$ −7.27145 0.849911i −0.473331 0.0553245i
$$237$$ 0 0
$$238$$ −9.34179 + 9.90172i −0.605539 + 0.641833i
$$239$$ 9.07711 21.0431i 0.587149 1.36116i −0.322809 0.946464i $$-0.604627\pi$$
0.909958 0.414701i $$-0.136114\pi$$
$$240$$ 0 0
$$241$$ 5.90585 3.88434i 0.380429 0.250212i −0.344864 0.938653i $$-0.612075\pi$$
0.725293 + 0.688441i $$0.241704\pi$$
$$242$$ 11.3694 0.730855
$$243$$ 0 0
$$244$$ 9.43390 0.603943
$$245$$ −9.21612 + 6.06153i −0.588796 + 0.387257i
$$246$$ 0 0
$$247$$ 7.94362 18.4154i 0.505441 1.17174i
$$248$$ 1.19634 1.26804i 0.0759674 0.0805207i
$$249$$ 0 0
$$250$$ 8.97414 + 1.04893i 0.567575 + 0.0663400i
$$251$$ −0.0115419 0.0654574i −0.000728518 0.00413163i 0.984441 0.175714i $$-0.0562233\pi$$
−0.985170 + 0.171582i $$0.945112\pi$$
$$252$$ 0 0
$$253$$ −3.03237 + 17.1974i −0.190644 + 1.08119i
$$254$$ −0.870990 + 2.90931i −0.0546508 + 0.182546i
$$255$$ 0 0
$$256$$ 0.786748 13.5079i 0.0491718 0.844246i
$$257$$ −17.2862 + 8.68143i −1.07828 + 0.541533i −0.897060 0.441909i $$-0.854301\pi$$
−0.181221 + 0.983442i $$0.558005\pi$$
$$258$$ 0 0
$$259$$ 2.60900 + 2.76537i 0.162115 + 0.171832i
$$260$$ −8.68330 + 3.16046i −0.538515 + 0.196003i
$$261$$ 0 0
$$262$$ −12.2274 4.45042i −0.755413 0.274948i
$$263$$ −5.96501 13.8284i −0.367818 0.852698i −0.997142 0.0755547i $$-0.975927\pi$$
0.629324 0.777143i $$-0.283332\pi$$
$$264$$ 0 0
$$265$$ 1.76215 + 5.88599i 0.108248 + 0.361573i
$$266$$ −13.1737 + 1.53979i −0.807732 + 0.0944104i
$$267$$ 0 0
$$268$$ 0.428198 + 7.35188i 0.0261564 + 0.449087i
$$269$$ −5.86823 10.1641i −0.357792 0.619715i 0.629799 0.776758i $$-0.283137\pi$$
−0.987592 + 0.157043i $$0.949804\pi$$
$$270$$ 0 0
$$271$$ 1.44013 2.49438i 0.0874817 0.151523i −0.818964 0.573844i $$-0.805451\pi$$
0.906446 + 0.422322i $$0.138785\pi$$
$$272$$ −2.89989 1.45638i −0.175832 0.0883060i
$$273$$ 0 0
$$274$$ −4.32913 5.81503i −0.261532 0.351299i
$$275$$ 13.8076 + 3.27246i 0.832628 + 0.197337i
$$276$$ 0 0
$$277$$ −1.37408 + 1.84571i −0.0825603 + 0.110898i −0.841485 0.540281i $$-0.818318\pi$$
0.758924 + 0.651179i $$0.225725\pi$$
$$278$$ 9.53200 7.99830i 0.571692 0.479706i
$$279$$ 0 0
$$280$$ 11.4211 + 9.58343i 0.682540 + 0.572719i
$$281$$ −6.17447 + 1.46338i −0.368338 + 0.0872977i −0.410616 0.911808i $$-0.634686\pi$$
0.0422786 + 0.999106i $$0.486538\pi$$
$$282$$ 0 0
$$283$$ 12.2665 + 8.06777i 0.729165 + 0.479579i 0.859012 0.511955i $$-0.171078\pi$$
−0.129848 + 0.991534i $$0.541449\pi$$
$$284$$ 7.11834 + 4.68180i 0.422396 + 0.277814i
$$285$$ 0 0
$$286$$ 17.2674 4.09244i 1.02104 0.241991i
$$287$$ −1.98831 1.66839i −0.117366 0.0984819i
$$288$$ 0 0
$$289$$ 3.06122 2.56867i 0.180072 0.151098i
$$290$$ −0.451224 + 0.606100i −0.0264968 + 0.0355914i
$$291$$ 0 0
$$292$$ 5.94975 + 1.41012i 0.348183 + 0.0825208i
$$293$$ 15.1411 + 20.3380i 0.884553 + 1.18816i 0.981229 + 0.192845i $$0.0617714\pi$$
−0.0966764 + 0.995316i $$0.530821\pi$$
$$294$$ 0 0
$$295$$ −6.97336 3.50215i −0.406005 0.203903i
$$296$$ 1.32461 2.29430i 0.0769916 0.133353i
$$297$$ 0 0
$$298$$ 9.12136 + 15.7987i 0.528386 + 0.915191i
$$299$$ 0.902433 + 15.4942i 0.0521891 + 0.896051i
$$300$$ 0 0
$$301$$ 31.6886 3.70386i 1.82650 0.213487i
$$302$$ 0.522740 + 1.74607i 0.0300803 + 0.100475i
$$303$$ 0 0
$$304$$ −1.25230 2.90315i −0.0718241 0.166507i
$$305$$ 9.44914 + 3.43921i 0.541056 + 0.196928i
$$306$$ 0 0
$$307$$ 11.4486 4.16694i 0.653405 0.237820i 0.00601852 0.999982i $$-0.498084\pi$$
0.647386 + 0.762162i $$0.275862\pi$$
$$308$$ 18.3163 + 19.4141i 1.04367 + 1.10622i
$$309$$ 0 0
$$310$$ 0.680636 0.341828i 0.0386575 0.0194145i
$$311$$ −1.46151 + 25.0931i −0.0828745 + 1.42290i 0.658890 + 0.752239i $$0.271026\pi$$
−0.741764 + 0.670661i $$0.766011\pi$$
$$312$$ 0 0
$$313$$ −8.47873 + 28.3209i −0.479246 + 1.60079i 0.286787 + 0.957994i $$0.407413\pi$$
−0.766034 + 0.642800i $$0.777773\pi$$
$$314$$ −2.67130 + 15.1497i −0.150750 + 0.854947i
$$315$$ 0 0
$$316$$ −2.71203 15.3807i −0.152563 0.865230i
$$317$$ 4.25913 + 0.497821i 0.239217 + 0.0279604i 0.234856 0.972030i $$-0.424538\pi$$
0.00436034 + 0.999990i $$0.498612\pi$$
$$318$$ 0 0
$$319$$ −2.26476 + 2.40051i −0.126802 + 0.134403i
$$320$$ 1.85126 4.29170i 0.103489 0.239913i
$$321$$ 0 0
$$322$$ 8.57557 5.64024i 0.477898 0.314318i
$$323$$ 20.4570 1.13826
$$324$$ 0 0
$$325$$ 12.6118 0.699576
$$326$$ 11.5330 7.58536i 0.638752 0.420114i
$$327$$ 0 0
$$328$$ −0.716366 + 1.66072i −0.0395547 + 0.0916981i
$$329$$ −20.6985 + 21.9392i −1.14115 + 1.20954i
$$330$$ 0 0
$$331$$ 27.6432 + 3.23102i 1.51941 + 0.177593i 0.834487 0.551027i $$-0.185764\pi$$
0.684918 + 0.728620i $$0.259838\pi$$
$$332$$ 0.391188 + 2.21854i 0.0214692 + 0.121758i
$$333$$ 0 0
$$334$$ −0.460091 + 2.60930i −0.0251750 + 0.142775i
$$335$$ −2.25130 + 7.51986i −0.123002 + 0.410854i
$$336$$ 0 0
$$337$$ −1.56420 + 26.8562i −0.0852071 + 1.46295i 0.636781 + 0.771045i $$0.280266\pi$$
−0.721988 + 0.691905i $$0.756772\pi$$
$$338$$ 5.01489 2.51857i 0.272774 0.136992i
$$339$$ 0 0
$$340$$ −6.46816 6.85585i −0.350785 0.371811i
$$341$$ 3.12596 1.13776i 0.169280 0.0616130i
$$342$$ 0 0
$$343$$ 1.60598 + 0.584529i 0.0867148 + 0.0315616i
$$344$$ −8.80551 20.4135i −0.474761 1.10062i
$$345$$ 0 0
$$346$$ −4.18690 13.9852i −0.225089 0.751851i
$$347$$ −30.2925 + 3.54069i −1.62619 + 0.190074i −0.879769 0.475402i $$-0.842303\pi$$
−0.746419 + 0.665476i $$0.768229\pi$$
$$348$$ 0 0
$$349$$ 0.463724 + 7.96184i 0.0248226 + 0.426187i 0.987711 + 0.156289i $$0.0499531\pi$$
−0.962889 + 0.269898i $$0.913010\pi$$
$$350$$ −4.17028 7.22314i −0.222911 0.386093i
$$351$$ 0 0
$$352$$ 14.7870 25.6119i 0.788151 1.36512i
$$353$$ 19.5082 + 9.79737i 1.03831 + 0.521461i 0.884452 0.466631i $$-0.154532\pi$$
0.153863 + 0.988092i $$0.450829\pi$$
$$354$$ 0 0
$$355$$ 5.42305 + 7.28442i 0.287826 + 0.386617i
$$356$$ −1.40964 0.334091i −0.0747109 0.0177068i
$$357$$ 0 0
$$358$$ −5.54662 + 7.45040i −0.293148 + 0.393766i
$$359$$ 13.2606 11.1269i 0.699866 0.587258i −0.221869 0.975076i $$-0.571216\pi$$
0.921736 + 0.387819i $$0.126771\pi$$
$$360$$ 0 0
$$361$$ 0.713665 + 0.598836i 0.0375613 + 0.0315177i
$$362$$ −12.0041 + 2.84502i −0.630920 + 0.149531i
$$363$$ 0 0
$$364$$ 19.8195 + 13.0355i 1.03882 + 0.683244i
$$365$$ 5.44529 + 3.58142i 0.285020 + 0.187460i
$$366$$ 0 0
$$367$$ −23.2623 + 5.51327i −1.21428 + 0.287790i −0.787358 0.616496i $$-0.788552\pi$$
−0.426926 + 0.904287i $$0.640403\pi$$
$$368$$ 1.87433 + 1.57275i 0.0977062 + 0.0819853i
$$369$$ 0 0
$$370$$ 0.886651 0.743989i 0.0460948 0.0386781i
$$371$$ 9.41892 12.6518i 0.489006 0.656849i
$$372$$ 0 0
$$373$$ −11.2201 2.65920i −0.580952 0.137688i −0.0703757 0.997521i $$-0.522420\pi$$
−0.510576 + 0.859832i $$0.670568\pi$$
$$374$$ 10.8091 + 14.5191i 0.558923 + 0.750764i
$$375$$ 0 0
$$376$$ 18.7821 + 9.43272i 0.968613 + 0.486456i
$$377$$ −1.46658 + 2.54020i −0.0755329 + 0.130827i
$$378$$ 0 0
$$379$$ −10.3656 17.9537i −0.532443 0.922218i −0.999282 0.0378763i $$-0.987941\pi$$
0.466839 0.884342i $$-0.345393\pi$$
$$380$$ −0.533970 9.16791i −0.0273921 0.470304i
$$381$$ 0 0
$$382$$ 4.47641 0.523217i 0.229033 0.0267701i
$$383$$ −4.54732 15.1891i −0.232357 0.776126i −0.992050 0.125845i $$-0.959836\pi$$
0.759693 0.650282i $$-0.225349\pi$$
$$384$$ 0 0
$$385$$ 11.2683 + 26.1228i 0.574285 + 1.33134i
$$386$$ −0.129079 0.0469808i −0.00656994 0.00239126i
$$387$$ 0 0
$$388$$ 6.51155 2.37001i 0.330574 0.120319i
$$389$$ −19.5641 20.7367i −0.991938 1.05139i −0.998677 0.0514160i $$-0.983627\pi$$
0.00673888 0.999977i $$-0.497855\pi$$
$$390$$ 0 0
$$391$$ −14.1471 + 7.10495i −0.715451 + 0.359313i
$$392$$ 1.14735 19.6992i 0.0579498 0.994959i
$$393$$ 0 0
$$394$$ 2.51395 8.39719i 0.126651 0.423044i
$$395$$ 2.89074 16.3942i 0.145449 0.824882i
$$396$$ 0 0
$$397$$ 5.49087 + 31.1403i 0.275579 + 1.56289i 0.737117 + 0.675765i $$0.236187\pi$$
−0.461538 + 0.887120i $$0.652702\pi$$
$$398$$ 15.8965 + 1.85804i 0.796822 + 0.0931351i
$$399$$ 0 0
$$400$$ 1.36440 1.44618i 0.0682200 0.0723090i
$$401$$ −6.75227 + 15.6535i −0.337192 + 0.781700i 0.662281 + 0.749255i $$0.269588\pi$$
−0.999474 + 0.0324445i $$0.989671\pi$$
$$402$$ 0 0
$$403$$ 2.47019 1.62467i 0.123049 0.0809305i
$$404$$ −13.2952 −0.661458
$$405$$ 0 0
$$406$$ 1.93980 0.0962705
$$407$$ 4.22358 2.77790i 0.209355 0.137695i
$$408$$ 0 0
$$409$$ −9.44133 + 21.8875i −0.466844 + 1.08227i 0.508397 + 0.861123i $$0.330238\pi$$
−0.975241 + 0.221143i $$0.929021\pi$$
$$410$$ −0.542262 + 0.574764i −0.0267804 + 0.0283856i
$$411$$ 0 0
$$412$$ 4.49141 + 0.524970i 0.221276 + 0.0258634i
$$413$$ 3.47862 + 19.7282i 0.171172 + 0.970762i
$$414$$ 0 0
$$415$$ −0.416966 + 2.36473i −0.0204681 + 0.116080i
$$416$$ 7.53853 25.1804i 0.369607 1.23457i
$$417$$ 0 0
$$418$$ −1.02544 + 17.6061i −0.0501560 + 0.861145i
$$419$$ 14.0624 7.06241i 0.686993 0.345021i −0.0708230 0.997489i $$-0.522563\pi$$
0.757816 + 0.652468i $$0.226266\pi$$
$$420$$ 0 0
$$421$$ 16.1664 + 17.1354i 0.787901 + 0.835126i 0.989529 0.144336i $$-0.0461046\pi$$
−0.201628 + 0.979462i $$0.564623\pi$$
$$422$$ −0.874971 + 0.318464i −0.0425929 + 0.0155026i
$$423$$ 0 0
$$424$$ −10.3281 3.75912i −0.501577 0.182559i
$$425$$ 5.09524 + 11.8121i 0.247155 + 0.572970i
$$426$$ 0 0
$$427$$ −7.40361 24.7298i −0.358286 1.19676i
$$428$$ −23.1992 + 2.71160i −1.12138 + 0.131070i
$$429$$ 0 0
$$430$$ −0.564759 9.69653i −0.0272351 0.467608i
$$431$$ −0.705848 1.22256i −0.0339995 0.0588888i 0.848525 0.529155i $$-0.177491\pi$$
−0.882524 + 0.470267i $$0.844158\pi$$
$$432$$ 0 0
$$433$$ −6.50524 + 11.2674i −0.312622 + 0.541477i −0.978929 0.204200i $$-0.934541\pi$$
0.666307 + 0.745677i $$0.267874\pi$$
$$434$$ −1.74730 0.877528i −0.0838732 0.0421227i
$$435$$ 0 0
$$436$$ −6.33408 8.50814i −0.303347 0.407466i
$$437$$ −15.0087 3.55713i −0.717964 0.170161i
$$438$$ 0 0
$$439$$ 12.3841 16.6347i 0.591061 0.793933i −0.401477 0.915869i $$-0.631503\pi$$
0.992538 + 0.121936i $$0.0389103\pi$$
$$440$$ 15.1863 12.7428i 0.723979 0.607490i
$$441$$ 0 0
$$442$$ 12.3238 + 10.3409i 0.586182 + 0.491865i
$$443$$ −33.0519 + 7.83344i −1.57034 + 0.372178i −0.921386 0.388649i $$-0.872942\pi$$
−0.648955 + 0.760826i $$0.724794\pi$$
$$444$$ 0 0
$$445$$ −1.29012 0.848528i −0.0611578 0.0402241i
$$446$$ 9.72924 + 6.39902i 0.460693 + 0.303002i
$$447$$ 0 0
$$448$$ −11.6754 + 2.76711i −0.551609 + 0.130734i
$$449$$ −0.919709 0.771727i −0.0434038 0.0364201i 0.620828 0.783947i $$-0.286797\pi$$
−0.664231 + 0.747527i $$0.731241\pi$$
$$450$$ 0 0
$$451$$ −2.64380 + 2.21841i −0.124492 + 0.104461i
$$452$$ −8.31170 + 11.1645i −0.390949 + 0.525136i
$$453$$ 0 0
$$454$$ 18.7069 + 4.43362i 0.877959 + 0.208080i
$$455$$ 15.0993 + 20.2819i 0.707866 + 0.950830i
$$456$$ 0 0
$$457$$ −28.6438 14.3855i −1.33990 0.672923i −0.372941 0.927855i $$-0.621651\pi$$
−0.966959 + 0.254932i $$0.917947\pi$$
$$458$$ −0.596704 + 1.03352i −0.0278821 + 0.0482933i
$$459$$ 0 0
$$460$$ 3.55340 + 6.15466i 0.165678 + 0.286963i
$$461$$ 0.0195765 + 0.336115i 0.000911768 + 0.0156545i 0.998733 0.0503158i $$-0.0160228\pi$$
−0.997822 + 0.0659703i $$0.978986\pi$$
$$462$$ 0 0
$$463$$ 2.93276 0.342791i 0.136297 0.0159308i −0.0476708 0.998863i $$-0.515180\pi$$
0.183968 + 0.982932i $$0.441106\pi$$
$$464$$ 0.132620 + 0.442982i 0.00615673 + 0.0205649i
$$465$$ 0 0
$$466$$ −4.35232 10.0898i −0.201617 0.467401i
$$467$$ 3.55605 + 1.29430i 0.164554 + 0.0598929i 0.422984 0.906137i $$-0.360983\pi$$
−0.258429 + 0.966030i $$0.583205\pi$$
$$468$$ 0 0
$$469$$ 18.9360 6.89213i 0.874382 0.318249i
$$470$$ 6.30147 + 6.67917i 0.290665 + 0.308087i
$$471$$ 0 0
$$472$$ 12.4744 6.26486i 0.574179 0.288363i
$$473$$ 2.46664 42.3505i 0.113416 1.94728i
$$474$$ 0 0
$$475$$ −3.59474 + 12.0073i −0.164938 + 0.550931i
$$476$$ −4.20172 + 23.8292i −0.192586 + 1.09221i
$$477$$ 0 0
$$478$$ 3.11022 + 17.6389i 0.142258 + 0.806785i
$$479$$ −3.14535 0.367638i −0.143715 0.0167978i 0.0439314 0.999035i $$-0.486012\pi$$
−0.187646 + 0.982237i $$0.560086\pi$$
$$480$$ 0 0
$$481$$ 3.08326 3.26806i 0.140584 0.149011i
$$482$$ −2.18817 + 5.07274i −0.0996683 + 0.231057i
$$483$$ 0 0
$$484$$ 16.8843 11.1050i 0.767468 0.504771i
$$485$$ 7.38607 0.335384
$$486$$ 0 0
$$487$$ 1.22501 0.0555106 0.0277553 0.999615i $$-0.491164\pi$$
0.0277553 + 0.999615i $$0.491164\pi$$
$$488$$ −15.0287 + 9.88456i −0.680319 + 0.447453i
$$489$$ 0 0
$$490$$ 3.41465 7.91605i 0.154258 0.357610i
$$491$$ −27.8255 + 29.4933i −1.25575 + 1.33101i −0.334323 + 0.942459i $$0.608507\pi$$
−0.921425 + 0.388556i $$0.872974\pi$$
$$492$$ 0 0
$$493$$ −2.97164 0.347335i −0.133836 0.0156432i
$$494$$ 2.72183 + 15.4363i 0.122461 + 0.694512i
$$495$$ 0 0
$$496$$ 0.0809373 0.459018i 0.00363419 0.0206105i
$$497$$ 6.68638 22.3341i 0.299925 1.00182i
$$498$$ 0 0
$$499$$ 2.39276 41.0820i 0.107114 1.83908i −0.335109 0.942179i $$-0.608773\pi$$
0.442224 0.896905i $$-0.354190\pi$$
$$500$$ 14.3517 7.20768i 0.641826 0.322337i
$$501$$ 0 0
$$502$$ 0.0356484 + 0.0377851i 0.00159106 + 0.00168643i
$$503$$ −9.54144 + 3.47280i −0.425432 + 0.154845i −0.545858 0.837878i $$-0.683796\pi$$
0.120426 + 0.992722i $$0.461574\pi$$
$$504$$ 0 0
$$505$$ −13.3166 4.84686i −0.592582 0.215682i
$$506$$ −5.40568 12.5318i −0.240312 0.557105i
$$507$$ 0 0
$$508$$ 1.54816 + 5.17123i 0.0686887 + 0.229436i
$$509$$ 24.0833 2.81493i 1.06747 0.124770i 0.435829 0.900029i $$-0.356455\pi$$
0.631642 + 0.775260i $$0.282381\pi$$
$$510$$ 0 0
$$511$$ −0.972849 16.7032i −0.0430363 0.738904i
$$512$$ −3.94773 6.83768i −0.174467 0.302186i
$$513$$ 0 0
$$514$$ 7.55901 13.0926i 0.333414 0.577490i
$$515$$ 4.30728 + 2.16320i 0.189802 + 0.0953219i
$$516$$ 0 0
$$517$$ 23.9495 + 32.1698i 1.05330 + 1.41483i
$$518$$ −2.89124 0.685237i −0.127034 0.0301076i
$$519$$ 0 0
$$520$$ 10.5215 14.1329i 0.461400 0.619768i
$$521$$ 4.86477 4.08202i 0.213129 0.178837i −0.529973 0.848014i $$-0.677798\pi$$
0.743102 + 0.669178i $$0.233354\pi$$
$$522$$ 0 0
$$523$$ 21.5335 + 18.0688i 0.941595 + 0.790092i 0.977862 0.209250i $$-0.0671024\pi$$
−0.0362674 + 0.999342i $$0.511547\pi$$
$$524$$ −22.5054 + 5.33387i −0.983151 + 0.233011i
$$525$$ 0 0
$$526$$ 9.83386 + 6.46783i 0.428777 + 0.282011i
$$527$$ 2.51962 + 1.65718i 0.109756 + 0.0721879i
$$528$$ 0 0
$$529$$ −10.7652 + 2.55141i −0.468054 + 0.110931i
$$530$$ −3.67848 3.08661i −0.159783 0.134074i
$$531$$ 0 0
$$532$$ −18.0598 + 15.1540i −0.782991 + 0.657008i
$$533$$ −1.83171 + 2.46041i −0.0793400 + 0.106572i
$$534$$ 0 0
$$535$$ −24.2253 5.74149i −1.04735 0.248226i
$$536$$ −8.38522 11.2633i −0.362186 0.486501i
$$537$$ 0 0
$$538$$ 8.19694 + 4.11666i 0.353395 + 0.177482i
$$539$$ 18.8268 32.6089i 0.810926 1.40457i
$$540$$ 0 0
$$541$$ −1.34390 2.32771i −0.0577788 0.100076i 0.835689 0.549203i $$-0.185068\pi$$
−0.893468 + 0.449127i $$0.851735\pi$$
$$542$$ 0.130888 + 2.24725i 0.00562211 + 0.0965279i
$$543$$ 0 0
$$544$$ 26.6294 3.11253i 1.14173 0.133449i
$$545$$ −3.24260 10.8310i −0.138898 0.463950i
$$546$$ 0 0
$$547$$ 12.9944 + 30.1244i 0.555600 + 1.28802i 0.932299 + 0.361689i $$0.117800\pi$$
−0.376699 + 0.926336i $$0.622941\pi$$
$$548$$ −12.1088 4.40724i −0.517262 0.188268i
$$549$$ 0 0
$$550$$ −10.4214 + 3.79308i −0.444370 + 0.161737i
$$551$$ −2.00042 2.12032i −0.0852207 0.0903287i
$$552$$ 0 0
$$553$$ −38.1901 + 19.1798i −1.62401 + 0.815608i
$$554$$ 0.104565 1.79532i 0.00444256 0.0762758i
$$555$$ 0 0
$$556$$ 6.34334 21.1882i 0.269018 0.898581i
$$557$$ −1.71906 + 9.74928i −0.0728390 + 0.413090i 0.926485 + 0.376331i $$0.122815\pi$$
−0.999324 + 0.0367591i $$0.988297\pi$$
$$558$$ 0 0
$$559$$ −6.54721 37.1311i −0.276917 1.57048i
$$560$$ 3.95921 + 0.462766i 0.167307 + 0.0195554i
$$561$$ 0 0
$$562$$ 3.40329 3.60728i 0.143559 0.152164i
$$563$$ 2.78662 6.46011i 0.117442 0.272261i −0.849348 0.527833i $$-0.823005\pi$$
0.966790 + 0.255572i $$0.0822638\pi$$
$$564$$ 0 0
$$565$$ −12.3953 + 8.15249i −0.521472 + 0.342978i
$$566$$ −11.4745 −0.482310
$$567$$ 0 0
$$568$$ −16.2454 −0.681640
$$569$$ 3.29025 2.16403i 0.137935 0.0907209i −0.478666 0.877997i $$-0.658880\pi$$
0.616601 + 0.787276i $$0.288509\pi$$
$$570$$ 0 0
$$571$$ 10.1268 23.4765i 0.423791 0.982459i −0.563871 0.825863i $$-0.690689\pi$$
0.987663 0.156596i $$-0.0500521\pi$$
$$572$$ 21.6458 22.9432i 0.905057 0.959304i
$$573$$ 0 0
$$574$$ 2.01483 + 0.235500i 0.0840975 + 0.00982958i
$$575$$ −1.68431 9.55219i −0.0702405 0.398354i
$$576$$ 0 0
$$577$$ 0.816045 4.62802i 0.0339724 0.192667i −0.963099 0.269149i $$-0.913258\pi$$
0.997071 + 0.0764818i $$0.0243687\pi$$
$$578$$ −0.895737 + 2.99197i −0.0372577 + 0.124450i
$$579$$ 0 0
$$580$$ −0.0780940 + 1.34082i −0.00324268 + 0.0556746i
$$581$$ 5.50862 2.76653i 0.228536 0.114775i
$$582$$ 0 0
$$583$$ −14.3924 15.2551i −0.596073 0.631800i
$$584$$ −10.9558 + 3.98757i −0.453353 + 0.165007i
$$585$$ 0 0
$$586$$ −18.6213 6.77759i −0.769238 0.279980i
$$587$$ −11.0004 25.5017i −0.454034 1.05257i −0.979443 0.201719i $$-0.935347\pi$$
0.525410 0.850849i $$-0.323912\pi$$
$$588$$ 0 0
$$589$$ 0.842715 + 2.81486i 0.0347235 + 0.115984i
$$590$$ 6.05748 0.708018i 0.249383 0.0291487i
$$591$$ 0 0
$$592$$ −0.0411844 0.707108i −0.00169267 0.0290620i
$$593$$ −7.16631 12.4124i −0.294285 0.509717i 0.680533 0.732717i $$-0.261748\pi$$
−0.974818 + 0.223000i $$0.928415\pi$$
$$594$$ 0 0
$$595$$ −12.8956 + 22.3359i −0.528669 + 0.915682i
$$596$$ 28.9769 + 14.5528i 1.18694 + 0.596104i
$$597$$ 0 0
$$598$$ −7.24351 9.72973i −0.296209 0.397878i
$$599$$ −26.7617 6.34265i −1.09346 0.259154i −0.355957 0.934502i $$-0.615845\pi$$
−0.737499 + 0.675349i $$0.763993\pi$$
$$600$$ 0 0
$$601$$ 11.1968 15.0400i 0.456729 0.613493i −0.512789 0.858515i $$-0.671388\pi$$
0.969518 + 0.245022i $$0.0787951\pi$$
$$602$$ −19.1011 + 16.0277i −0.778503 + 0.653242i
$$603$$ 0 0
$$604$$ 2.48176 + 2.08244i 0.100981 + 0.0847333i
$$605$$ 20.9600 4.96761i 0.852144 0.201962i
$$606$$ 0 0
$$607$$ −22.0641 14.5118i −0.895556 0.589016i 0.0161458 0.999870i $$-0.494860\pi$$
−0.911701 + 0.410853i $$0.865231\pi$$
$$608$$ 21.8248 + 14.3544i 0.885111 + 0.582146i
$$609$$ 0 0
$$610$$ −7.64707 + 1.81239i −0.309621 + 0.0733815i
$$611$$ 27.3057 + 22.9122i 1.10467 + 0.926928i
$$612$$ 0 0
$$613$$ −26.7821 + 22.4728i −1.08172 + 0.907670i −0.996062 0.0886553i $$-0.971743\pi$$
−0.0856560 + 0.996325i $$0.527299\pi$$
$$614$$ −5.68606 + 7.63770i −0.229471 + 0.308232i
$$615$$ 0 0
$$616$$ −49.5204 11.7365i −1.99523 0.472879i
$$617$$ 4.27053 + 5.73631i 0.171925 + 0.230935i 0.879731 0.475471i $$-0.157722\pi$$
−0.707806 + 0.706407i $$0.750315\pi$$
$$618$$ 0 0
$$619$$ −16.8196 8.44712i −0.676037 0.339518i 0.0774361 0.996997i $$-0.475327\pi$$
−0.753473 + 0.657479i $$0.771623\pi$$
$$620$$ 0.676908 1.17244i 0.0271853 0.0470863i
$$621$$ 0 0
$$622$$ −9.82235 17.0128i −0.393841 0.682152i
$$623$$ 0.230492 + 3.95739i 0.00923446 + 0.158550i
$$624$$ 0 0
$$625$$ 3.06015 0.357680i 0.122406 0.0143072i
$$626$$ −6.62654 22.1342i −0.264850 0.884660i
$$627$$ 0 0
$$628$$ 10.8303 + 25.1074i 0.432174 + 1.00189i
$$629$$ 4.30649 + 1.56744i 0.171711 + 0.0624978i
$$630$$ 0 0
$$631$$ −22.0642 + 8.03070i −0.878361 + 0.319697i −0.741548 0.670900i $$-0.765908\pi$$
−0.136813 + 0.990597i $$0.543686\pi$$
$$632$$ 20.4358 + 21.6607i 0.812893 + 0.861616i
$$633$$ 0 0
$$634$$ −2.99490 + 1.50410i −0.118943 + 0.0597353i
$$635$$ −0.334549 + 5.74398i −0.0132762 + 0.227943i
$$636$$ 0 0
$$637$$ 9.59802 32.0596i 0.380287 1.27025i
$$638$$ 0.447890 2.54011i 0.0177321 0.100564i
$$639$$ 0 0
$$640$$ −2.37461 13.4671i −0.0938648 0.532334i
$$641$$ −4.32954 0.506050i −0.171006 0.0199878i 0.0301588 0.999545i $$-0.490399\pi$$
−0.201165 + 0.979557i $$0.564473\pi$$
$$642$$ 0 0
$$643$$ −13.0468 + 13.8288i −0.514516 + 0.545355i −0.931587 0.363519i $$-0.881575\pi$$
0.417071 + 0.908874i $$0.363057\pi$$
$$644$$ 7.22619 16.7522i 0.284752 0.660129i
$$645$$ 0 0
$$646$$ −13.3579 + 8.78560i −0.525558 + 0.345665i
$$647$$ 20.6268 0.810924 0.405462 0.914112i $$-0.367111\pi$$
0.405462 + 0.914112i $$0.367111\pi$$
$$648$$ 0 0
$$649$$ 26.6367 1.04558
$$650$$ −8.23516 + 5.41635i −0.323010 + 0.212447i
$$651$$ 0 0
$$652$$ 9.71824 22.5294i 0.380596 0.882320i
$$653$$ 4.11111 4.35752i 0.160880 0.170523i −0.641919 0.766772i $$-0.721862\pi$$
0.802799 + 0.596249i $$0.203343\pi$$
$$654$$ 0 0
$$655$$ −24.4862 2.86203i −0.956756 0.111829i
$$656$$ 0.0839701 + 0.476218i 0.00327848 + 0.0185932i
$$657$$ 0 0
$$658$$ 4.09344 23.2150i 0.159579 0.905016i
$$659$$ −11.1391 + 37.2073i −0.433919 + 1.44939i 0.409587 + 0.912271i $$0.365673\pi$$
−0.843506 + 0.537120i $$0.819512\pi$$
$$660$$ 0 0
$$661$$ −1.80224 + 30.9432i −0.0700989 + 1.20355i 0.761496 + 0.648169i $$0.224465\pi$$
−0.831595 + 0.555382i $$0.812572\pi$$
$$662$$ −19.4379 + 9.76207i −0.755474 + 0.379414i
$$663$$ 0 0
$$664$$ −2.94770 3.12438i −0.114393 0.121249i
$$665$$ −23.6135 + 8.59460i −0.915691 + 0.333284i
$$666$$ 0 0
$$667$$ 2.11981 + 0.771549i 0.0820795 + 0.0298745i
$$668$$ 1.86535 + 4.32436i 0.0721725 + 0.167315i
$$669$$ 0 0
$$670$$ −1.75950 5.87713i −0.0679753 0.227053i
$$671$$ −34.0924 + 3.98483i −1.31612 + 0.153833i
$$672$$ 0 0
$$673$$ 2.24379 + 38.5243i 0.0864916 + 1.48500i 0.710562 + 0.703635i $$0.248441\pi$$
−0.624070 + 0.781368i $$0.714522\pi$$
$$674$$ −10.5125 18.2082i −0.404926 0.701352i
$$675$$ 0 0
$$676$$ 4.98742 8.63847i 0.191824 0.332249i
$$677$$ −3.56442 1.79012i −0.136992 0.0688000i 0.378983 0.925404i $$-0.376274\pi$$
−0.515975 + 0.856604i $$0.672570\pi$$
$$678$$ 0 0
$$679$$ −11.3229 15.2093i −0.434532 0.583677i
$$680$$ 17.4875 + 4.14462i 0.670615 + 0.158939i
$$681$$ 0 0
$$682$$ −1.55254 + 2.08543i −0.0594499 + 0.0798551i
$$683$$ −32.2624 + 27.0713i −1.23449 + 1.03586i −0.236551 + 0.971619i $$0.576017\pi$$
−0.997935 + 0.0642370i $$0.979539\pi$$
$$684$$ 0 0
$$685$$ −10.5217 8.82872i −0.402012 0.337328i
$$686$$ −1.29970 + 0.308034i −0.0496227 + 0.0117608i
$$687$$ 0 0
$$688$$ −4.96609 3.26625i −0.189330 0.124524i
$$689$$ −15.5736 10.2429i −0.593306 0.390224i
$$690$$ 0 0
$$691$$ −8.32013 + 1.97191i −0.316513 + 0.0750149i −0.385802 0.922582i $$-0.626075\pi$$
0.0692889 + 0.997597i $$0.477927\pi$$
$$692$$ −19.8777 16.6794i −0.755638 0.634056i
$$693$$ 0 0
$$694$$ 18.2596 15.3216i 0.693125 0.581601i
$$695$$ 14.0779 18.9100i 0.534007 0.717296i
$$696$$ 0 0
$$697$$ −3.04442 0.721541i −0.115316 0.0273303i
$$698$$ −3.72215 4.99972i −0.140885 0.189242i
$$699$$ 0 0
$$700$$ −13.2482 6.65352i −0.500737 0.251479i
$$701$$ 0.440975 0.763791i 0.0166554 0.0288480i −0.857578 0.514355i $$-0.828032\pi$$
0.874233 + 0.485507i $$0.161365\pi$$
$$702$$ 0 0
$$703$$ 2.23259 + 3.86697i 0.0842039 + 0.145845i
$$704$$ 0.927670 + 15.9275i 0.0349629 + 0.600290i
$$705$$ 0 0
$$706$$ −16.9460 + 1.98070i −0.637770 + 0.0745446i
$$707$$ 10.4339 + 34.8516i 0.392406 + 1.31073i
$$708$$ 0 0
$$709$$ −15.9358 36.9432i −0.598480 1.38743i −0.900803 0.434227i $$-0.857022\pi$$
0.302324 0.953205i $$-0.402238\pi$$
$$710$$ −6.66953 2.42751i −0.250303 0.0911028i
$$711$$ 0 0
$$712$$ 2.59569 0.944754i 0.0972777 0.0354062i
$$713$$ −1.56042 1.65395i −0.0584382 0.0619409i
$$714$$ 0 0
$$715$$ 30.0449 15.0891i 1.12362 0.564301i
$$716$$ −0.959961 + 16.4819i −0.0358754 + 0.615957i
$$717$$ 0 0
$$718$$ −3.88015 + 12.9606i −0.144806 + 0.483685i
$$719$$ 2.39151 13.5629i 0.0891883 0.505812i −0.907186 0.420730i $$-0.861774\pi$$
0.996374 0.0850815i $$-0.0271151\pi$$
$$720$$ 0 0
$$721$$ −2.14866 12.1857i −0.0800203 0.453817i
$$722$$ −0.723185 0.0845282i −0.0269142 0.00314581i
$$723$$ 0 0
$$724$$ −15.0479 + 15.9499i −0.559251 + 0.592772i
$$725$$ 0.726051 1.68318i 0.0269649 0.0625116i
$$726$$ 0 0
$$727$$ 10.4310 6.86056i 0.386864 0.254444i −0.341147 0.940010i $$-0.610815\pi$$
0.728011 + 0.685566i $$0.240445\pi$$
$$728$$ −45.2317 −1.67640
$$729$$ 0 0
$$730$$ −5.09374 −0.188528
$$731$$ 32.1315 21.1332i 1.18843 0.781641i
$$732$$ 0 0
$$733$$ −10.6438 + 24.6752i −0.393139 + 0.911398i 0.600587 + 0.799559i $$0.294933\pi$$
−0.993726 + 0.111839i $$0.964326\pi$$
$$734$$ 12.8219 13.5904i 0.473266 0.501632i
$$735$$ 0 0
$$736$$ −20.0785 2.34684i −0.740103 0.0865056i
$$737$$ −4.65283 26.3875i −0.171389 0.971996i
$$738$$ 0 0
$$739$$ −4.23374 + 24.0107i −0.155740 + 0.883248i 0.802365 + 0.596833i $$0.203575\pi$$
−0.958106 + 0.286415i $$0.907536\pi$$
$$740$$ 0.590047 1.97089i 0.0216906 0.0724515i
$$741$$ 0 0
$$742$$ −0.716768 + 12.3064i −0.0263134 + 0.451783i
$$743$$ 32.2333 16.1882i 1.18253 0.593887i 0.254743 0.967009i $$-0.418009\pi$$
0.927782 + 0.373122i $$0.121713\pi$$
$$744$$ 0 0
$$745$$ 23.7184 + 25.1401i 0.868975 + 0.921060i
$$746$$ 8.46844 3.08226i 0.310052 0.112850i
$$747$$ 0 0
$$748$$ 30.2335 + 11.0041i 1.10544 + 0.402349i
$$749$$ 25.3146 + 58.6859i 0.924976 + 2.14434i
$$750$$ 0 0
$$751$$ 0.670091 + 2.23826i 0.0244520 + 0.0816753i 0.969345 0.245705i $$-0.0790194\pi$$
−0.944893 + 0.327380i $$0.893834\pi$$
$$752$$ 5.58137 0.652369i 0.203532 0.0237894i
$$753$$ 0 0
$$754$$ −0.133292 2.28853i −0.00485421 0.0833435i
$$755$$ 1.72660 + 2.99055i 0.0628372 + 0.108837i
$$756$$ 0 0
$$757$$ 8.08646 14.0062i 0.293907 0.509063i −0.680823 0.732448i $$-0.738378\pi$$
0.974730 + 0.223386i $$0.0717109\pi$$
$$758$$ 14.4790 + 7.27161i 0.525899 + 0.264117i
$$759$$ 0 0
$$760$$ 10.4565 + 14.0455i 0.379297 + 0.509485i
$$761$$ 44.1342 + 10.4600i 1.59986 + 0.379175i 0.931234 0.364421i $$-0.118733\pi$$
0.668630 + 0.743595i $$0.266881\pi$$
$$762$$ 0 0
$$763$$ −17.3321 + 23.2811i −0.627465 + 0.842832i
$$764$$ 6.13669 5.14929i 0.222018 0.186295i
$$765$$ 0 0
$$766$$ 9.49250 + 7.96515i 0.342978 + 0.287793i
$$767$$ 23.0359 5.45962i 0.831779 0.197135i
$$768$$ 0 0
$$769$$ −15.3444 10.0922i −0.553334 0.363934i 0.241839 0.970316i $$-0.422250\pi$$
−0.795173 + 0.606383i $$0.792620\pi$$
$$770$$ −18.5768 12.2182i −0.669462 0.440312i
$$771$$ 0 0
$$772$$ −0.237578 + 0.0563069i −0.00855061 + 0.00202653i
$$773$$ −22.5821 18.9486i −0.812222 0.681536i 0.138915 0.990304i $$-0.455639\pi$$
−0.951137 + 0.308769i $$0.900083\pi$$
$$774$$ 0 0
$$775$$ −1.41544 + 1.18769i −0.0508441 + 0.0426633i
$$776$$ −7.89004 + 10.5982i −0.283236 + 0.380452i
$$777$$ 0 0
$$778$$ 21.6806 + 5.13839i 0.777286 + 0.184220i
$$779$$ −1.82038 2.44520i −0.0652220 0.0876083i
$$780$$ 0 0
$$781$$ −27.7020 13.9125i −0.991255 0.497827i
$$782$$ 6.18635 10.7151i 0.221224 0.383170i
$$783$$