# Properties

 Label 567.2.w.a.37.14 Level $567$ Weight $2$ Character 567.37 Analytic conductor $4.528$ Analytic rank $0$ Dimension $132$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 6]))

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

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

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.w (of order $$9$$, degree $$6$$, 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: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$132$$ Relative dimension: $$22$$ over $$\Q(\zeta_{9})$$ Twist minimal: no (minimal twist has level 189) Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 37.14 Character $$\chi$$ $$=$$ 567.37 Dual form 567.2.w.a.46.14

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.162149 + 0.919594i) q^{2} +(1.06003 - 0.385818i) q^{4} +(-0.575026 + 3.26114i) q^{5} +(1.06445 + 2.42218i) q^{7} +(1.46046 + 2.52959i) q^{8} +O(q^{10})$$ $$q+(0.162149 + 0.919594i) q^{2} +(1.06003 - 0.385818i) q^{4} +(-0.575026 + 3.26114i) q^{5} +(1.06445 + 2.42218i) q^{7} +(1.46046 + 2.52959i) q^{8} -3.09216 q^{10} +(-0.163478 - 0.927130i) q^{11} +(-1.92659 - 1.61660i) q^{13} +(-2.05482 + 1.37161i) q^{14} +(-0.361099 + 0.302998i) q^{16} -2.09645 q^{17} +1.93419 q^{19} +(0.648661 + 3.67874i) q^{20} +(0.826075 - 0.300667i) q^{22} +(-3.45552 - 2.89952i) q^{23} +(-5.60589 - 2.04038i) q^{25} +(1.17422 - 2.03381i) q^{26} +(2.06286 + 2.15689i) q^{28} +(5.49145 - 4.60787i) q^{29} +(-8.64990 + 3.14831i) q^{31} +(4.13791 + 3.47212i) q^{32} +(-0.339938 - 1.92788i) q^{34} +(-8.51114 + 2.07848i) q^{35} +(1.95591 + 3.38773i) q^{37} +(0.313628 + 1.77867i) q^{38} +(-9.08913 + 3.30817i) q^{40} +(6.70881 + 5.62936i) q^{41} +(9.55542 + 3.47789i) q^{43} +(-0.530994 - 0.919708i) q^{44} +(2.10607 - 3.64783i) q^{46} +(10.2711 + 3.73837i) q^{47} +(-4.73391 + 5.15656i) q^{49} +(0.967327 - 5.48599i) q^{50} +(-2.66595 - 0.970325i) q^{52} +(-2.04238 - 3.53751i) q^{53} +3.11750 q^{55} +(-4.57254 + 6.23010i) q^{56} +(5.12781 + 4.30274i) q^{58} +(-6.09905 - 5.11771i) q^{59} +(-5.03423 - 1.83231i) q^{61} +(-4.29774 - 7.44390i) q^{62} +(-2.99336 + 5.18466i) q^{64} +(6.37979 - 5.35328i) q^{65} +(-0.175689 + 0.996384i) q^{67} +(-2.22229 + 0.808848i) q^{68} +(-3.29144 - 7.48977i) q^{70} +(1.14666 - 1.98608i) q^{71} +(8.29219 - 14.3625i) q^{73} +(-2.79818 + 2.34796i) q^{74} +(2.05029 - 0.746246i) q^{76} +(2.07166 - 1.38285i) q^{77} +(-2.47430 - 14.0324i) q^{79} +(-0.780475 - 1.35182i) q^{80} +(-4.08889 + 7.08217i) q^{82} +(-3.77228 + 3.16532i) q^{83} +(1.20552 - 6.83682i) q^{85} +(-1.64884 + 9.35104i) q^{86} +(2.10650 - 1.76757i) q^{88} +1.69093 q^{89} +(1.86495 - 6.38733i) q^{91} +(-4.78163 - 1.74037i) q^{92} +(-1.77233 + 10.0514i) q^{94} +(-1.11221 + 6.30766i) q^{95} +(11.8249 + 4.30390i) q^{97} +(-5.50954 - 3.51714i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10})$$ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 $$132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100})$$ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.162149 + 0.919594i 0.114657 + 0.650251i 0.986920 + 0.161213i $$0.0515407\pi$$
−0.872263 + 0.489037i $$0.837348\pi$$
$$3$$ 0 0
$$4$$ 1.06003 0.385818i 0.530013 0.192909i
$$5$$ −0.575026 + 3.26114i −0.257160 + 1.45842i 0.533308 + 0.845921i $$0.320949\pi$$
−0.790468 + 0.612503i $$0.790163\pi$$
$$6$$ 0 0
$$7$$ 1.06445 + 2.42218i 0.402323 + 0.915498i
$$8$$ 1.46046 + 2.52959i 0.516350 + 0.894344i
$$9$$ 0 0
$$10$$ −3.09216 −0.977827
$$11$$ −0.163478 0.927130i −0.0492905 0.279540i 0.950194 0.311660i $$-0.100885\pi$$
−0.999484 + 0.0321203i $$0.989774\pi$$
$$12$$ 0 0
$$13$$ −1.92659 1.61660i −0.534340 0.448364i 0.335257 0.942127i $$-0.391177\pi$$
−0.869597 + 0.493762i $$0.835621\pi$$
$$14$$ −2.05482 + 1.37161i −0.549174 + 0.366579i
$$15$$ 0 0
$$16$$ −0.361099 + 0.302998i −0.0902746 + 0.0757494i
$$17$$ −2.09645 −0.508464 −0.254232 0.967143i $$-0.581823\pi$$
−0.254232 + 0.967143i $$0.581823\pi$$
$$18$$ 0 0
$$19$$ 1.93419 0.443734 0.221867 0.975077i $$-0.428785\pi$$
0.221867 + 0.975077i $$0.428785\pi$$
$$20$$ 0.648661 + 3.67874i 0.145045 + 0.822592i
$$21$$ 0 0
$$22$$ 0.826075 0.300667i 0.176120 0.0641023i
$$23$$ −3.45552 2.89952i −0.720526 0.604593i 0.207005 0.978340i $$-0.433628\pi$$
−0.927531 + 0.373747i $$0.878073\pi$$
$$24$$ 0 0
$$25$$ −5.60589 2.04038i −1.12118 0.408075i
$$26$$ 1.17422 2.03381i 0.230284 0.398863i
$$27$$ 0 0
$$28$$ 2.06286 + 2.15689i 0.389844 + 0.407614i
$$29$$ 5.49145 4.60787i 1.01974 0.855661i 0.0301424 0.999546i $$-0.490404\pi$$
0.989594 + 0.143885i $$0.0459595\pi$$
$$30$$ 0 0
$$31$$ −8.64990 + 3.14831i −1.55357 + 0.565452i −0.969251 0.246073i $$-0.920860\pi$$
−0.584317 + 0.811526i $$0.698637\pi$$
$$32$$ 4.13791 + 3.47212i 0.731487 + 0.613790i
$$33$$ 0 0
$$34$$ −0.339938 1.92788i −0.0582989 0.330629i
$$35$$ −8.51114 + 2.07848i −1.43865 + 0.351328i
$$36$$ 0 0
$$37$$ 1.95591 + 3.38773i 0.321549 + 0.556939i 0.980808 0.194977i $$-0.0624632\pi$$
−0.659259 + 0.751916i $$0.729130\pi$$
$$38$$ 0.313628 + 1.77867i 0.0508771 + 0.288539i
$$39$$ 0 0
$$40$$ −9.08913 + 3.30817i −1.43712 + 0.523068i
$$41$$ 6.70881 + 5.62936i 1.04774 + 0.879158i 0.992854 0.119335i $$-0.0380761\pi$$
0.0548856 + 0.998493i $$0.482521\pi$$
$$42$$ 0 0
$$43$$ 9.55542 + 3.47789i 1.45719 + 0.530373i 0.944589 0.328255i $$-0.106460\pi$$
0.512599 + 0.858628i $$0.328683\pi$$
$$44$$ −0.530994 0.919708i −0.0800503 0.138651i
$$45$$ 0 0
$$46$$ 2.10607 3.64783i 0.310524 0.537843i
$$47$$ 10.2711 + 3.73837i 1.49819 + 0.545298i 0.955592 0.294693i $$-0.0952175\pi$$
0.542601 + 0.839991i $$0.317440\pi$$
$$48$$ 0 0
$$49$$ −4.73391 + 5.15656i −0.676273 + 0.736651i
$$50$$ 0.967327 5.48599i 0.136801 0.775836i
$$51$$ 0 0
$$52$$ −2.66595 0.970325i −0.369700 0.134560i
$$53$$ −2.04238 3.53751i −0.280543 0.485914i 0.690976 0.722878i $$-0.257181\pi$$
−0.971519 + 0.236964i $$0.923848\pi$$
$$54$$ 0 0
$$55$$ 3.11750 0.420364
$$56$$ −4.57254 + 6.23010i −0.611031 + 0.832532i
$$57$$ 0 0
$$58$$ 5.12781 + 4.30274i 0.673314 + 0.564977i
$$59$$ −6.09905 5.11771i −0.794029 0.666269i 0.152710 0.988271i $$-0.451200\pi$$
−0.946739 + 0.322002i $$0.895644\pi$$
$$60$$ 0 0
$$61$$ −5.03423 1.83231i −0.644567 0.234603i −0.00100763 0.999999i $$-0.500321\pi$$
−0.643559 + 0.765396i $$0.722543\pi$$
$$62$$ −4.29774 7.44390i −0.545813 0.945376i
$$63$$ 0 0
$$64$$ −2.99336 + 5.18466i −0.374170 + 0.648082i
$$65$$ 6.37979 5.35328i 0.791316 0.663993i
$$66$$ 0 0
$$67$$ −0.175689 + 0.996384i −0.0214639 + 0.121728i −0.993657 0.112452i $$-0.964129\pi$$
0.972193 + 0.234180i $$0.0752405\pi$$
$$68$$ −2.22229 + 0.808848i −0.269493 + 0.0980873i
$$69$$ 0 0
$$70$$ −3.29144 7.48977i −0.393402 0.895198i
$$71$$ 1.14666 1.98608i 0.136084 0.235704i −0.789927 0.613201i $$-0.789882\pi$$
0.926011 + 0.377497i $$0.123215\pi$$
$$72$$ 0 0
$$73$$ 8.29219 14.3625i 0.970527 1.68100i 0.276558 0.960997i $$-0.410806\pi$$
0.693969 0.720005i $$-0.255860\pi$$
$$74$$ −2.79818 + 2.34796i −0.325282 + 0.272944i
$$75$$ 0 0
$$76$$ 2.05029 0.746246i 0.235185 0.0856002i
$$77$$ 2.07166 1.38285i 0.236088 0.157591i
$$78$$ 0 0
$$79$$ −2.47430 14.0324i −0.278380 1.57877i −0.728016 0.685560i $$-0.759557\pi$$
0.449636 0.893212i $$-0.351554\pi$$
$$80$$ −0.780475 1.35182i −0.0872598 0.151138i
$$81$$ 0 0
$$82$$ −4.08889 + 7.08217i −0.451543 + 0.782095i
$$83$$ −3.77228 + 3.16532i −0.414061 + 0.347439i −0.825898 0.563819i $$-0.809332\pi$$
0.411837 + 0.911257i $$0.364887\pi$$
$$84$$ 0 0
$$85$$ 1.20552 6.83682i 0.130757 0.741557i
$$86$$ −1.64884 + 9.35104i −0.177799 + 1.00835i
$$87$$ 0 0
$$88$$ 2.10650 1.76757i 0.224554 0.188423i
$$89$$ 1.69093 0.179238 0.0896191 0.995976i $$-0.471435\pi$$
0.0896191 + 0.995976i $$0.471435\pi$$
$$90$$ 0 0
$$91$$ 1.86495 6.38733i 0.195500 0.669574i
$$92$$ −4.78163 1.74037i −0.498519 0.181446i
$$93$$ 0 0
$$94$$ −1.77233 + 10.0514i −0.182802 + 1.03672i
$$95$$ −1.11221 + 6.30766i −0.114110 + 0.647153i
$$96$$ 0 0
$$97$$ 11.8249 + 4.30390i 1.20063 + 0.436995i 0.863446 0.504442i $$-0.168302\pi$$
0.337189 + 0.941437i $$0.390524\pi$$
$$98$$ −5.50954 3.51714i −0.556547 0.355285i
$$99$$ 0 0
$$100$$ −6.72960 −0.672960
$$101$$ 2.96186 2.48529i 0.294716 0.247296i −0.483425 0.875386i $$-0.660607\pi$$
0.778141 + 0.628090i $$0.216163\pi$$
$$102$$ 0 0
$$103$$ −0.923416 + 5.23695i −0.0909868 + 0.516012i 0.904917 + 0.425589i $$0.139933\pi$$
−0.995903 + 0.0904231i $$0.971178\pi$$
$$104$$ 1.27563 7.23445i 0.125086 0.709396i
$$105$$ 0 0
$$106$$ 2.92190 2.45177i 0.283800 0.238137i
$$107$$ 4.21924 7.30793i 0.407889 0.706484i −0.586764 0.809758i $$-0.699598\pi$$
0.994653 + 0.103274i $$0.0329317\pi$$
$$108$$ 0 0
$$109$$ 2.89902 + 5.02125i 0.277676 + 0.480949i 0.970807 0.239863i $$-0.0771025\pi$$
−0.693131 + 0.720812i $$0.743769\pi$$
$$110$$ 0.505500 + 2.86683i 0.0481975 + 0.273342i
$$111$$ 0 0
$$112$$ −1.11828 0.552121i −0.105668 0.0521705i
$$113$$ −7.46610 + 2.71744i −0.702352 + 0.255635i −0.668415 0.743789i $$-0.733027\pi$$
−0.0339371 + 0.999424i $$0.510805\pi$$
$$114$$ 0 0
$$115$$ 11.4428 9.60161i 1.06704 0.895355i
$$116$$ 4.04328 7.00316i 0.375409 0.650227i
$$117$$ 0 0
$$118$$ 3.71726 6.43848i 0.342201 0.592710i
$$119$$ −2.23156 5.07799i −0.204567 0.465498i
$$120$$ 0 0
$$121$$ 9.50377 3.45909i 0.863979 0.314463i
$$122$$ 0.868684 4.92655i 0.0786469 0.446029i
$$123$$ 0 0
$$124$$ −7.95444 + 6.67457i −0.714330 + 0.599394i
$$125$$ 1.59887 2.76933i 0.143007 0.247696i
$$126$$ 0 0
$$127$$ 4.07469 + 7.05757i 0.361570 + 0.626258i 0.988219 0.153043i $$-0.0489074\pi$$
−0.626649 + 0.779302i $$0.715574\pi$$
$$128$$ 4.89866 + 1.78297i 0.432984 + 0.157593i
$$129$$ 0 0
$$130$$ 5.95732 + 4.99879i 0.522492 + 0.438423i
$$131$$ −1.11560 0.936099i −0.0974703 0.0817873i 0.592750 0.805386i $$-0.298042\pi$$
−0.690221 + 0.723599i $$0.742487\pi$$
$$132$$ 0 0
$$133$$ 2.05884 + 4.68496i 0.178524 + 0.406238i
$$134$$ −0.944756 −0.0816145
$$135$$ 0 0
$$136$$ −3.06178 5.30316i −0.262545 0.454742i
$$137$$ 1.26758 + 0.461363i 0.108297 + 0.0394169i 0.395600 0.918423i $$-0.370537\pi$$
−0.287303 + 0.957840i $$0.592759\pi$$
$$138$$ 0 0
$$139$$ 2.03091 11.5179i 0.172260 0.976933i −0.769000 0.639249i $$-0.779245\pi$$
0.941259 0.337684i $$-0.109644\pi$$
$$140$$ −8.22011 + 5.48699i −0.694726 + 0.463736i
$$141$$ 0 0
$$142$$ 2.01231 + 0.732423i 0.168870 + 0.0614635i
$$143$$ −1.18384 + 2.05048i −0.0989980 + 0.171469i
$$144$$ 0 0
$$145$$ 11.8692 + 20.5580i 0.985682 + 1.70725i
$$146$$ 14.5522 + 5.29658i 1.20435 + 0.438348i
$$147$$ 0 0
$$148$$ 3.38035 + 2.83645i 0.277863 + 0.233155i
$$149$$ −2.77336 + 1.00942i −0.227203 + 0.0826951i −0.453113 0.891453i $$-0.649687\pi$$
0.225910 + 0.974148i $$0.427464\pi$$
$$150$$ 0 0
$$151$$ −2.81725 15.9774i −0.229264 1.30022i −0.854363 0.519677i $$-0.826052\pi$$
0.625098 0.780546i $$-0.285059\pi$$
$$152$$ 2.82481 + 4.89271i 0.229122 + 0.396851i
$$153$$ 0 0
$$154$$ 1.60758 + 1.68086i 0.129543 + 0.135447i
$$155$$ −5.29313 30.0189i −0.425155 2.41117i
$$156$$ 0 0
$$157$$ 1.55569 + 1.30538i 0.124158 + 0.104181i 0.702752 0.711434i $$-0.251954\pi$$
−0.578595 + 0.815615i $$0.696399\pi$$
$$158$$ 12.5029 4.55069i 0.994680 0.362034i
$$159$$ 0 0
$$160$$ −13.7025 + 11.4977i −1.08328 + 0.908976i
$$161$$ 3.34496 11.4563i 0.263620 0.902881i
$$162$$ 0 0
$$163$$ 6.60942 11.4478i 0.517690 0.896665i −0.482099 0.876117i $$-0.660126\pi$$
0.999789 0.0205480i $$-0.00654108\pi$$
$$164$$ 9.28341 + 3.37889i 0.724913 + 0.263847i
$$165$$ 0 0
$$166$$ −3.52248 2.95571i −0.273397 0.229407i
$$167$$ −12.3823 + 4.50678i −0.958168 + 0.348745i −0.773316 0.634021i $$-0.781403\pi$$
−0.184853 + 0.982766i $$0.559181\pi$$
$$168$$ 0 0
$$169$$ −1.15908 6.57345i −0.0891598 0.505650i
$$170$$ 6.48257 0.497190
$$171$$ 0 0
$$172$$ 11.4708 0.874642
$$173$$ −7.61204 + 6.38726i −0.578733 + 0.485615i −0.884531 0.466482i $$-0.845521\pi$$
0.305798 + 0.952096i $$0.401077\pi$$
$$174$$ 0 0
$$175$$ −1.02500 15.7503i −0.0774830 1.19061i
$$176$$ 0.339950 + 0.285252i 0.0256247 + 0.0215017i
$$177$$ 0 0
$$178$$ 0.274183 + 1.55497i 0.0205509 + 0.116550i
$$179$$ 3.18668 0.238184 0.119092 0.992883i $$-0.462002\pi$$
0.119092 + 0.992883i $$0.462002\pi$$
$$180$$ 0 0
$$181$$ 8.86337 + 15.3518i 0.658809 + 1.14109i 0.980924 + 0.194390i $$0.0622729\pi$$
−0.322115 + 0.946701i $$0.604394\pi$$
$$182$$ 6.17615 + 0.679294i 0.457806 + 0.0503526i
$$183$$ 0 0
$$184$$ 2.28796 12.9757i 0.168671 0.956579i
$$185$$ −12.1725 + 4.43044i −0.894943 + 0.325733i
$$186$$ 0 0
$$187$$ 0.342724 + 1.94368i 0.0250625 + 0.142136i
$$188$$ 12.3299 0.899254
$$189$$ 0 0
$$190$$ −5.98083 −0.433895
$$191$$ −1.78703 10.1348i −0.129305 0.733326i −0.978657 0.205500i $$-0.934118\pi$$
0.849352 0.527827i $$-0.176993\pi$$
$$192$$ 0 0
$$193$$ 2.19199 0.797818i 0.157783 0.0574282i −0.261921 0.965089i $$-0.584356\pi$$
0.419704 + 0.907661i $$0.362134\pi$$
$$194$$ −2.04045 + 11.5720i −0.146496 + 0.830818i
$$195$$ 0 0
$$196$$ −3.02858 + 7.29251i −0.216327 + 0.520893i
$$197$$ 12.3597 + 21.4077i 0.880596 + 1.52524i 0.850680 + 0.525684i $$0.176191\pi$$
0.0299156 + 0.999552i $$0.490476\pi$$
$$198$$ 0 0
$$199$$ −1.13809 −0.0806771 −0.0403386 0.999186i $$-0.512844\pi$$
−0.0403386 + 0.999186i $$0.512844\pi$$
$$200$$ −3.02585 17.1605i −0.213960 1.21343i
$$201$$ 0 0
$$202$$ 2.76572 + 2.32072i 0.194596 + 0.163285i
$$203$$ 17.0065 + 8.39645i 1.19362 + 0.589315i
$$204$$ 0 0
$$205$$ −22.2158 + 18.6413i −1.55162 + 1.30197i
$$206$$ −4.96560 −0.345970
$$207$$ 0 0
$$208$$ 1.18551 0.0822006
$$209$$ −0.316198 1.79325i −0.0218719 0.124042i
$$210$$ 0 0
$$211$$ −14.8216 + 5.39463i −1.02036 + 0.371382i −0.797404 0.603446i $$-0.793794\pi$$
−0.222959 + 0.974828i $$0.571572\pi$$
$$212$$ −3.52981 2.96186i −0.242428 0.203422i
$$213$$ 0 0
$$214$$ 7.40447 + 2.69501i 0.506159 + 0.184227i
$$215$$ −16.8365 + 29.1617i −1.14824 + 1.98881i
$$216$$ 0 0
$$217$$ −16.8331 17.6004i −1.14271 1.19479i
$$218$$ −4.14744 + 3.48011i −0.280900 + 0.235703i
$$219$$ 0 0
$$220$$ 3.30463 1.20279i 0.222798 0.0810919i
$$221$$ 4.03900 + 3.38913i 0.271693 + 0.227977i
$$222$$ 0 0
$$223$$ −2.74368 15.5602i −0.183730 1.04199i −0.927576 0.373635i $$-0.878111\pi$$
0.743846 0.668352i $$-0.233000\pi$$
$$224$$ −4.00552 + 13.7187i −0.267630 + 0.916616i
$$225$$ 0 0
$$226$$ −3.70956 6.42515i −0.246756 0.427395i
$$227$$ 2.55088 + 14.4667i 0.169308 + 0.960191i 0.944511 + 0.328479i $$0.106536\pi$$
−0.775204 + 0.631711i $$0.782353\pi$$
$$228$$ 0 0
$$229$$ −8.17259 + 2.97458i −0.540060 + 0.196566i −0.597625 0.801776i $$-0.703889\pi$$
0.0575646 + 0.998342i $$0.481666\pi$$
$$230$$ 10.6850 + 8.96579i 0.704549 + 0.591187i
$$231$$ 0 0
$$232$$ 19.6760 + 7.16150i 1.29180 + 0.470175i
$$233$$ −6.13981 10.6345i −0.402233 0.696687i 0.591762 0.806112i $$-0.298432\pi$$
−0.993995 + 0.109425i $$0.965099\pi$$
$$234$$ 0 0
$$235$$ −18.0975 + 31.3458i −1.18055 + 2.04477i
$$236$$ −8.43965 3.07178i −0.549374 0.199956i
$$237$$ 0 0
$$238$$ 4.30784 2.87552i 0.279236 0.186392i
$$239$$ 4.39857 24.9455i 0.284520 1.61359i −0.422475 0.906375i $$-0.638839\pi$$
0.706995 0.707218i $$-0.250050\pi$$
$$240$$ 0 0
$$241$$ −14.1976 5.16752i −0.914550 0.332869i −0.158482 0.987362i $$-0.550660\pi$$
−0.756068 + 0.654493i $$0.772882\pi$$
$$242$$ 4.72199 + 8.17872i 0.303541 + 0.525748i
$$243$$ 0 0
$$244$$ −6.04335 −0.386886
$$245$$ −14.0941 18.4031i −0.900440 1.17573i
$$246$$ 0 0
$$247$$ −3.72639 3.12682i −0.237105 0.198955i
$$248$$ −20.5967 17.2827i −1.30789 1.09745i
$$249$$ 0 0
$$250$$ 2.80591 + 1.02127i 0.177461 + 0.0645906i
$$251$$ −9.55450 16.5489i −0.603075 1.04456i −0.992353 0.123435i $$-0.960609\pi$$
0.389278 0.921120i $$-0.372725\pi$$
$$252$$ 0 0
$$253$$ −2.12333 + 3.67772i −0.133493 + 0.231216i
$$254$$ −5.82939 + 4.89144i −0.365768 + 0.306916i
$$255$$ 0 0
$$256$$ −2.92446 + 16.5854i −0.182779 + 1.03659i
$$257$$ 27.3779 9.96475i 1.70779 0.621584i 0.711114 0.703076i $$-0.248191\pi$$
0.996674 + 0.0814921i $$0.0259685\pi$$
$$258$$ 0 0
$$259$$ −6.12373 + 8.34361i −0.380510 + 0.518446i
$$260$$ 4.69735 8.13605i 0.291317 0.504576i
$$261$$ 0 0
$$262$$ 0.679937 1.17769i 0.0420066 0.0727576i
$$263$$ −13.5286 + 11.3518i −0.834208 + 0.699984i −0.956253 0.292541i $$-0.905499\pi$$
0.122045 + 0.992525i $$0.461055\pi$$
$$264$$ 0 0
$$265$$ 12.7107 4.62633i 0.780814 0.284193i
$$266$$ −3.97442 + 2.65296i −0.243687 + 0.162663i
$$267$$ 0 0
$$268$$ 0.198187 + 1.12398i 0.0121062 + 0.0686578i
$$269$$ −0.462202 0.800557i −0.0281809 0.0488108i 0.851591 0.524207i $$-0.175638\pi$$
−0.879772 + 0.475396i $$0.842305\pi$$
$$270$$ 0 0
$$271$$ −1.95927 + 3.39355i −0.119017 + 0.206143i −0.919378 0.393374i $$-0.871308\pi$$
0.800361 + 0.599518i $$0.204641\pi$$
$$272$$ 0.757026 0.635220i 0.0459014 0.0385159i
$$273$$ 0 0
$$274$$ −0.218729 + 1.24047i −0.0132139 + 0.0749397i
$$275$$ −0.975255 + 5.53095i −0.0588101 + 0.333529i
$$276$$ 0 0
$$277$$ −18.9191 + 15.8750i −1.13674 + 0.953836i −0.999327 0.0366777i $$-0.988323\pi$$
−0.137411 + 0.990514i $$0.543878\pi$$
$$278$$ 10.9211 0.655002
$$279$$ 0 0
$$280$$ −17.6879 18.4941i −1.05705 1.10524i
$$281$$ −2.20028 0.800835i −0.131257 0.0477738i 0.275556 0.961285i $$-0.411138\pi$$
−0.406814 + 0.913511i $$0.633360\pi$$
$$282$$ 0 0
$$283$$ 1.89733 10.7603i 0.112785 0.639633i −0.875039 0.484053i $$-0.839164\pi$$
0.987823 0.155580i $$-0.0497247\pi$$
$$284$$ 0.449227 2.54769i 0.0266567 0.151178i
$$285$$ 0 0
$$286$$ −2.07756 0.756172i −0.122849 0.0447134i
$$287$$ −6.49416 + 22.2421i −0.383338 + 1.31291i
$$288$$ 0 0
$$289$$ −12.6049 −0.741464
$$290$$ −16.9804 + 14.2483i −0.997126 + 0.836688i
$$291$$ 0 0
$$292$$ 3.24863 18.4239i 0.190111 1.07818i
$$293$$ 0.0827719 0.469423i 0.00483559 0.0274240i −0.982294 0.187343i $$-0.940012\pi$$
0.987130 + 0.159919i $$0.0511234\pi$$
$$294$$ 0 0
$$295$$ 20.1967 16.9470i 1.17590 0.986693i
$$296$$ −5.71303 + 9.89526i −0.332063 + 0.575151i
$$297$$ 0 0
$$298$$ −1.37796 2.38669i −0.0798229 0.138257i
$$299$$ 1.96999 + 11.1724i 0.113928 + 0.646116i
$$300$$ 0 0
$$301$$ 1.74715 + 26.8470i 0.100704 + 1.54743i
$$302$$ 14.2359 5.18145i 0.819185 0.298159i
$$303$$ 0 0
$$304$$ −0.698434 + 0.586056i −0.0400579 + 0.0336126i
$$305$$ 8.87022 15.3637i 0.507907 0.879722i
$$306$$ 0 0
$$307$$ −0.00102554 + 0.00177629i −5.85309e−5 + 0.000101378i −0.866055 0.499949i $$-0.833352\pi$$
0.865996 + 0.500051i $$0.166685\pi$$
$$308$$ 1.66249 2.26514i 0.0947289 0.129068i
$$309$$ 0 0
$$310$$ 26.7469 9.73507i 1.51912 0.552915i
$$311$$ −0.483384 + 2.74140i −0.0274102 + 0.155451i −0.995441 0.0953811i $$-0.969593\pi$$
0.968031 + 0.250832i $$0.0807041\pi$$
$$312$$ 0 0
$$313$$ 13.7935 11.5741i 0.779655 0.654208i −0.163507 0.986542i $$-0.552281\pi$$
0.943162 + 0.332334i $$0.107836\pi$$
$$314$$ −0.948167 + 1.64227i −0.0535082 + 0.0926788i
$$315$$ 0 0
$$316$$ −8.03678 13.9201i −0.452104 0.783067i
$$317$$ −8.40466 3.05905i −0.472053 0.171813i 0.0950294 0.995474i $$-0.469705\pi$$
−0.567082 + 0.823661i $$0.691928\pi$$
$$318$$ 0 0
$$319$$ −5.16983 4.33800i −0.289455 0.242881i
$$320$$ −15.1866 12.7431i −0.848957 0.712360i
$$321$$ 0 0
$$322$$ 11.0775 + 1.21838i 0.617325 + 0.0678975i
$$323$$ −4.05494 −0.225623
$$324$$ 0 0
$$325$$ 7.50177 + 12.9935i 0.416123 + 0.720747i
$$326$$ 11.5991 + 4.22172i 0.642413 + 0.233819i
$$327$$ 0 0
$$328$$ −4.44202 + 25.1919i −0.245270 + 1.39099i
$$329$$ 1.87801 + 28.8577i 0.103538 + 1.59098i
$$330$$ 0 0
$$331$$ 23.6794 + 8.61858i 1.30153 + 0.473720i 0.897496 0.441022i $$-0.145384\pi$$
0.404039 + 0.914742i $$0.367606\pi$$
$$332$$ −2.77747 + 4.81072i −0.152434 + 0.264023i
$$333$$ 0 0
$$334$$ −6.15218 10.6559i −0.336632 0.583064i
$$335$$ −3.14832 1.14589i −0.172011 0.0626069i
$$336$$ 0 0
$$337$$ −7.25619 6.08867i −0.395270 0.331671i 0.423392 0.905947i $$-0.360839\pi$$
−0.818662 + 0.574276i $$0.805284\pi$$
$$338$$ 5.85696 2.13176i 0.318577 0.115952i
$$339$$ 0 0
$$340$$ −1.35989 7.71231i −0.0737503 0.418259i
$$341$$ 4.33296 + 7.50490i 0.234643 + 0.406413i
$$342$$ 0 0
$$343$$ −17.5291 5.97751i −0.946482 0.322755i
$$344$$ 5.15767 + 29.2506i 0.278083 + 1.57709i
$$345$$ 0 0
$$346$$ −7.10797 5.96430i −0.382127 0.320643i
$$347$$ 4.55625 1.65834i 0.244592 0.0890242i −0.216815 0.976213i $$-0.569567\pi$$
0.461407 + 0.887188i $$0.347345\pi$$
$$348$$ 0 0
$$349$$ −14.0136 + 11.7588i −0.750130 + 0.629434i −0.935537 0.353228i $$-0.885084\pi$$
0.185407 + 0.982662i $$0.440640\pi$$
$$350$$ 14.3177 3.49649i 0.765314 0.186895i
$$351$$ 0 0
$$352$$ 2.54265 4.40400i 0.135524 0.234734i
$$353$$ −5.51180 2.00613i −0.293364 0.106776i 0.191146 0.981562i $$-0.438780\pi$$
−0.484509 + 0.874786i $$0.661002\pi$$
$$354$$ 0 0
$$355$$ 5.81751 + 4.88147i 0.308761 + 0.259081i
$$356$$ 1.79243 0.652390i 0.0949985 0.0345766i
$$357$$ 0 0
$$358$$ 0.516717 + 2.93045i 0.0273094 + 0.154879i
$$359$$ −17.1710 −0.906253 −0.453126 0.891446i $$-0.649691\pi$$
−0.453126 + 0.891446i $$0.649691\pi$$
$$360$$ 0 0
$$361$$ −15.2589 −0.803100
$$362$$ −12.6802 + 10.6400i −0.666458 + 0.559225i
$$363$$ 0 0
$$364$$ −0.487452 7.49026i −0.0255494 0.392596i
$$365$$ 42.0698 + 35.3008i 2.20203 + 1.84773i
$$366$$ 0 0
$$367$$ −1.04397 5.92066i −0.0544949 0.309056i 0.945361 0.326025i $$-0.105709\pi$$
−0.999856 + 0.0169692i $$0.994598\pi$$
$$368$$ 2.12633 0.110843
$$369$$ 0 0
$$370$$ −6.04797 10.4754i −0.314419 0.544590i
$$371$$ 6.39448 8.71250i 0.331985 0.452331i
$$372$$ 0 0
$$373$$ −3.65399 + 20.7228i −0.189196 + 1.07299i 0.731248 + 0.682112i $$0.238938\pi$$
−0.920444 + 0.390874i $$0.872173\pi$$
$$374$$ −1.73183 + 0.630333i −0.0895506 + 0.0325938i
$$375$$ 0 0
$$376$$ 5.54396 + 31.4413i 0.285908 + 1.62146i
$$377$$ −18.0289 −0.928534
$$378$$ 0 0
$$379$$ 9.96553 0.511895 0.255947 0.966691i $$-0.417613\pi$$
0.255947 + 0.966691i $$0.417613\pi$$
$$380$$ 1.25464 + 7.11539i 0.0643615 + 0.365012i
$$381$$ 0 0
$$382$$ 9.03011 3.28669i 0.462020 0.168162i
$$383$$ 6.58758 37.3600i 0.336610 1.90901i −0.0741152 0.997250i $$-0.523613\pi$$
0.410725 0.911759i $$-0.365276\pi$$
$$384$$ 0 0
$$385$$ 3.31841 + 7.55115i 0.169122 + 0.384842i
$$386$$ 1.08910 + 1.88637i 0.0554336 + 0.0960137i
$$387$$ 0 0
$$388$$ 14.1952 0.720651
$$389$$ 6.53697 + 37.0730i 0.331437 + 1.87967i 0.459916 + 0.887962i $$0.347880\pi$$
−0.128479 + 0.991712i $$0.541009\pi$$
$$390$$ 0 0
$$391$$ 7.24433 + 6.07872i 0.366362 + 0.307414i
$$392$$ −19.9576 4.44391i −1.00801 0.224451i
$$393$$ 0 0
$$394$$ −17.6823 + 14.8372i −0.890820 + 0.747487i
$$395$$ 47.1845 2.37411
$$396$$ 0 0
$$397$$ −1.75414 −0.0880376 −0.0440188 0.999031i $$-0.514016\pi$$
−0.0440188 + 0.999031i $$0.514016\pi$$
$$398$$ −0.184540 1.04658i −0.00925018 0.0524604i
$$399$$ 0 0
$$400$$ 2.64251 0.961794i 0.132125 0.0480897i
$$401$$ −2.12519 1.78324i −0.106127 0.0890510i 0.588180 0.808730i $$-0.299845\pi$$
−0.694307 + 0.719679i $$0.744289\pi$$
$$402$$ 0 0
$$403$$ 21.7544 + 7.91794i 1.08366 + 0.394421i
$$404$$ 2.18077 3.77721i 0.108498 0.187923i
$$405$$ 0 0
$$406$$ −4.96374 + 17.0005i −0.246346 + 0.843721i
$$407$$ 2.82112 2.36720i 0.139838 0.117338i
$$408$$ 0 0
$$409$$ −16.5654 + 6.02932i −0.819107 + 0.298131i −0.717380 0.696682i $$-0.754659\pi$$
−0.101727 + 0.994812i $$0.532437\pi$$
$$410$$ −20.7447 17.4069i −1.02451 0.859664i
$$411$$ 0 0
$$412$$ 1.04166 + 5.90757i 0.0513191 + 0.291045i
$$413$$ 5.90391 20.2205i 0.290512 0.994987i
$$414$$ 0 0
$$415$$ −8.15337 14.1220i −0.400233 0.693224i
$$416$$ −2.35903 13.3787i −0.115661 0.655945i
$$417$$ 0 0
$$418$$ 1.59779 0.581547i 0.0781504 0.0284444i
$$419$$ −27.7705 23.3022i −1.35668 1.13839i −0.976993 0.213270i $$-0.931589\pi$$
−0.379683 0.925117i $$-0.623967\pi$$
$$420$$ 0 0
$$421$$ 6.59183 + 2.39923i 0.321266 + 0.116931i 0.497619 0.867396i $$-0.334208\pi$$
−0.176353 + 0.984327i $$0.556430\pi$$
$$422$$ −7.36418 12.7551i −0.358483 0.620910i
$$423$$ 0 0
$$424$$ 5.96562 10.3328i 0.289716 0.501803i
$$425$$ 11.7525 + 4.27755i 0.570079 + 0.207492i
$$426$$ 0 0
$$427$$ −0.920479 14.1442i −0.0445451 0.684486i
$$428$$ 1.65297 9.37445i 0.0798992 0.453131i
$$429$$ 0 0
$$430$$ −29.5469 10.7542i −1.42488 0.518613i
$$431$$ 5.59564 + 9.69194i 0.269533 + 0.466844i 0.968741 0.248074i $$-0.0797975\pi$$
−0.699209 + 0.714918i $$0.746464\pi$$
$$432$$ 0 0
$$433$$ 2.32810 0.111881 0.0559406 0.998434i $$-0.482184\pi$$
0.0559406 + 0.998434i $$0.482184\pi$$
$$434$$ 13.4558 18.3335i 0.645897 0.880037i
$$435$$ 0 0
$$436$$ 5.01033 + 4.20416i 0.239951 + 0.201343i
$$437$$ −6.68364 5.60824i −0.319722 0.268278i
$$438$$ 0 0
$$439$$ −19.7599 7.19202i −0.943089 0.343256i −0.175704 0.984443i $$-0.556220\pi$$
−0.767385 + 0.641186i $$0.778443\pi$$
$$440$$ 4.55298 + 7.88599i 0.217055 + 0.375950i
$$441$$ 0 0
$$442$$ −2.46170 + 4.26378i −0.117091 + 0.202808i
$$443$$ 13.2231 11.0955i 0.628250 0.527165i −0.272134 0.962259i $$-0.587729\pi$$
0.900385 + 0.435095i $$0.143285\pi$$
$$444$$ 0 0
$$445$$ −0.972329 + 5.51435i −0.0460928 + 0.261405i
$$446$$ 13.8642 5.04614i 0.656487 0.238942i
$$447$$ 0 0
$$448$$ −15.7444 1.73168i −0.743855 0.0818142i
$$449$$ −15.5314 + 26.9012i −0.732972 + 1.26955i 0.222635 + 0.974902i $$0.428534\pi$$
−0.955607 + 0.294643i $$0.904799\pi$$
$$450$$ 0 0
$$451$$ 4.12240 7.14021i 0.194116 0.336219i
$$452$$ −6.86582 + 5.76111i −0.322941 + 0.270980i
$$453$$ 0 0
$$454$$ −12.8899 + 4.69154i −0.604953 + 0.220185i
$$455$$ 19.7576 + 9.75473i 0.926248 + 0.457309i
$$456$$ 0 0
$$457$$ 5.37599 + 30.4888i 0.251478 + 1.42620i 0.804953 + 0.593339i $$0.202191\pi$$
−0.553474 + 0.832866i $$0.686698\pi$$
$$458$$ −4.06058 7.03314i −0.189739 0.328637i
$$459$$ 0 0
$$460$$ 8.42514 14.5928i 0.392824 0.680392i
$$461$$ 2.51229 2.10806i 0.117009 0.0981823i −0.582406 0.812898i $$-0.697888\pi$$
0.699415 + 0.714716i $$0.253444\pi$$
$$462$$ 0 0
$$463$$ 5.00213 28.3685i 0.232469 1.31840i −0.615410 0.788207i $$-0.711010\pi$$
0.847879 0.530190i $$-0.177879\pi$$
$$464$$ −0.586780 + 3.32779i −0.0272406 + 0.154489i
$$465$$ 0 0
$$466$$ 8.78382 7.37050i 0.406903 0.341432i
$$467$$ −2.07669 −0.0960976 −0.0480488 0.998845i $$-0.515300\pi$$
−0.0480488 + 0.998845i $$0.515300\pi$$
$$468$$ 0 0
$$469$$ −2.60043 + 0.635045i −0.120077 + 0.0293237i
$$470$$ −31.7599 11.5596i −1.46497 0.533207i
$$471$$ 0 0
$$472$$ 4.03829 22.9023i 0.185877 1.05416i
$$473$$ 1.66235 9.42768i 0.0764351 0.433485i
$$474$$ 0 0
$$475$$ −10.8429 3.94648i −0.497505 0.181077i
$$476$$ −4.32469 4.52182i −0.198222 0.207257i
$$477$$ 0 0
$$478$$ 23.6530 1.08186
$$479$$ −7.21876 + 6.05726i −0.329834 + 0.276763i −0.792632 0.609700i $$-0.791290\pi$$
0.462798 + 0.886464i $$0.346845\pi$$
$$480$$ 0 0
$$481$$ 1.70838 9.68868i 0.0778952 0.441766i
$$482$$ 2.44988 13.8940i 0.111589 0.632853i
$$483$$ 0 0
$$484$$ 8.73966 7.33345i 0.397257 0.333339i
$$485$$ −20.8352 + 36.0877i −0.946079 + 1.63866i
$$486$$ 0 0
$$487$$ 4.36325 + 7.55738i 0.197718 + 0.342457i 0.947788 0.318901i $$-0.103314\pi$$
−0.750070 + 0.661358i $$0.769980\pi$$
$$488$$ −2.71729 15.4105i −0.123006 0.697602i
$$489$$ 0 0
$$490$$ 14.6380 15.9449i 0.661278 0.720317i
$$491$$ 15.4437 5.62105i 0.696965 0.253674i 0.0308503 0.999524i $$-0.490178\pi$$
0.666114 + 0.745850i $$0.267956\pi$$
$$492$$ 0 0
$$493$$ −11.5126 + 9.66019i −0.518500 + 0.435073i
$$494$$ 2.27117 3.93378i 0.102185 0.176989i
$$495$$ 0 0
$$496$$ 2.16954 3.75775i 0.0974151 0.168728i
$$497$$ 6.03120 + 0.663351i 0.270536 + 0.0297554i
$$498$$ 0 0
$$499$$ −20.9435 + 7.62282i −0.937561 + 0.341244i −0.765202 0.643790i $$-0.777361\pi$$
−0.172359 + 0.985034i $$0.555139\pi$$
$$500$$ 0.626389 3.55243i 0.0280130 0.158869i
$$501$$ 0 0
$$502$$ 13.6690 11.4696i 0.610077 0.511915i
$$503$$ −8.81372 + 15.2658i −0.392984 + 0.680669i −0.992842 0.119438i $$-0.961891\pi$$
0.599857 + 0.800107i $$0.295224\pi$$
$$504$$ 0 0
$$505$$ 6.40174 + 11.0881i 0.284874 + 0.493415i
$$506$$ −3.72631 1.35627i −0.165655 0.0602933i
$$507$$ 0 0
$$508$$ 7.04221 + 5.90912i 0.312448 + 0.262175i
$$509$$ 4.41293 + 3.70288i 0.195599 + 0.164127i 0.735327 0.677712i $$-0.237028\pi$$
−0.539728 + 0.841840i $$0.681473\pi$$
$$510$$ 0 0
$$511$$ 43.6151 + 4.79708i 1.92942 + 0.212210i
$$512$$ −5.29997 −0.234228
$$513$$ 0 0
$$514$$ 13.6028 + 23.5608i 0.599995 + 1.03922i
$$515$$ −16.5474 6.02277i −0.729166 0.265395i
$$516$$ 0 0
$$517$$ 1.78686 10.1338i 0.0785859 0.445683i
$$518$$ −8.66569 4.27844i −0.380748 0.187984i
$$519$$ 0 0
$$520$$ 22.8590 + 8.32000i 1.00243 + 0.364856i
$$521$$ 7.19384 12.4601i 0.315168 0.545887i −0.664305 0.747461i $$-0.731272\pi$$
0.979473 + 0.201575i $$0.0646058\pi$$
$$522$$ 0 0
$$523$$ 0.204128 + 0.353560i 0.00892588 + 0.0154601i 0.870454 0.492250i $$-0.163825\pi$$
−0.861528 + 0.507710i $$0.830492\pi$$
$$524$$ −1.54373 0.561870i −0.0674380 0.0245454i
$$525$$ 0 0
$$526$$ −12.6327 10.6001i −0.550813 0.462187i
$$527$$ 18.1341 6.60027i 0.789934 0.287512i
$$528$$ 0 0
$$529$$ −0.460540 2.61185i −0.0200235 0.113559i
$$530$$ 6.31537 + 10.9385i 0.274322 + 0.475140i
$$531$$ 0 0
$$532$$ 3.98997 + 4.17184i 0.172987 + 0.180872i
$$533$$ −3.82469 21.6909i −0.165666 0.939538i
$$534$$ 0 0
$$535$$ 21.4060 + 17.9618i 0.925461 + 0.776554i
$$536$$ −2.77703 + 1.01076i −0.119949 + 0.0436580i
$$537$$ 0 0
$$538$$ 0.661242 0.554848i 0.0285082 0.0239212i
$$539$$ 5.55469 + 3.54597i 0.239257 + 0.152736i
$$540$$ 0 0
$$541$$ 7.96991 13.8043i 0.342653 0.593493i −0.642271 0.766477i $$-0.722008\pi$$
0.984925 + 0.172985i $$0.0553411\pi$$
$$542$$ −3.43838 1.25147i −0.147691 0.0537551i
$$543$$ 0 0
$$544$$ −8.67494 7.27914i −0.371935 0.312091i
$$545$$ −18.0420 + 6.56675i −0.772835 + 0.281289i
$$546$$ 0 0
$$547$$ 6.47172 + 36.7030i 0.276711 + 1.56931i 0.733474 + 0.679717i $$0.237898\pi$$
−0.456763 + 0.889588i $$0.650991\pi$$
$$548$$ 1.52167 0.0650027
$$549$$ 0 0
$$550$$ −5.24436 −0.223620
$$551$$ 10.6215 8.91252i 0.452492 0.379686i
$$552$$ 0 0
$$553$$ 31.3553 20.9300i 1.33336 0.890032i
$$554$$ −17.6663 14.8238i −0.750568 0.629801i
$$555$$ 0 0
$$556$$ −2.29098 12.9928i −0.0971592 0.551017i
$$557$$ −7.75920 −0.328768 −0.164384 0.986396i $$-0.552564\pi$$
−0.164384 + 0.986396i $$0.552564\pi$$
$$558$$ 0 0
$$559$$ −12.7870 22.1478i −0.540833 0.936751i
$$560$$ 2.44359 3.32939i 0.103260 0.140693i
$$561$$ 0 0
$$562$$ 0.379670 2.15321i 0.0160154 0.0908278i
$$563$$ 4.40208 1.60223i 0.185526 0.0675258i −0.247587 0.968866i $$-0.579638\pi$$
0.433112 + 0.901340i $$0.357415\pi$$
$$564$$ 0 0
$$565$$ −4.56873 25.9106i −0.192208 1.09007i
$$566$$ 10.2028 0.428854
$$567$$ 0 0
$$568$$ 6.69861 0.281067
$$569$$ 3.60604 + 20.4509i 0.151173 + 0.857345i 0.962202 + 0.272338i $$0.0877970\pi$$
−0.811029 + 0.585007i $$0.801092\pi$$
$$570$$ 0 0
$$571$$ 24.6949 8.98821i 1.03345 0.376145i 0.231056 0.972940i $$-0.425782\pi$$
0.802393 + 0.596796i $$0.203560\pi$$
$$572$$ −0.463794 + 2.63030i −0.0193922 + 0.109979i
$$573$$ 0 0
$$574$$ −21.5067 2.36545i −0.897672 0.0987320i
$$575$$ 13.4551 + 23.3050i 0.561118 + 0.971885i
$$576$$ 0 0
$$577$$ 21.8729 0.910580 0.455290 0.890343i $$-0.349536\pi$$
0.455290 + 0.890343i $$0.349536\pi$$
$$578$$ −2.04387 11.5914i −0.0850139 0.482138i
$$579$$ 0 0
$$580$$ 20.5133 + 17.2127i 0.851767 + 0.714718i
$$581$$ −11.6823 5.76783i −0.484665 0.239290i
$$582$$ 0 0
$$583$$ −2.94585 + 2.47186i −0.122004 + 0.102374i
$$584$$ 48.4415 2.00453
$$585$$ 0 0
$$586$$ 0.445100 0.0183869
$$587$$ −6.79402 38.5308i −0.280419 1.59034i −0.721204 0.692723i $$-0.756411\pi$$
0.440785 0.897613i $$-0.354700\pi$$
$$588$$ 0 0
$$589$$ −16.7306 + 6.08943i −0.689371 + 0.250911i
$$590$$ 18.8592 + 15.8248i 0.776422 + 0.651496i
$$591$$ 0 0
$$592$$ −1.73275 0.630669i −0.0712155 0.0259203i
$$593$$ 15.6172 27.0498i 0.641322 1.11080i −0.343816 0.939037i $$-0.611720\pi$$
0.985138 0.171765i $$-0.0549471\pi$$
$$594$$ 0 0
$$595$$ 17.8432 4.35744i 0.731500 0.178638i
$$596$$ −2.55038 + 2.14003i −0.104468 + 0.0876589i
$$597$$ 0 0
$$598$$ −9.95462 + 3.62319i −0.407075 + 0.148163i
$$599$$ 4.00860 + 3.36361i 0.163787 + 0.137433i 0.720997 0.692938i $$-0.243684\pi$$
−0.557211 + 0.830371i $$0.688128\pi$$
$$600$$ 0 0
$$601$$ −7.71508 43.7544i −0.314705 1.78478i −0.573871 0.818946i $$-0.694559\pi$$
0.259166 0.965833i $$-0.416552\pi$$
$$602$$ −24.4050 + 5.95989i −0.994674 + 0.242907i
$$603$$ 0 0
$$604$$ −9.15072 15.8495i −0.372338 0.644908i
$$605$$ 5.81565 + 32.9822i 0.236440 + 1.34092i
$$606$$ 0 0
$$607$$ −21.0134 + 7.64824i −0.852907 + 0.310433i −0.731225 0.682137i $$-0.761051\pi$$
−0.121682 + 0.992569i $$0.538829\pi$$
$$608$$ 8.00352 + 6.71575i 0.324586 + 0.272360i
$$609$$ 0 0
$$610$$ 15.5666 + 5.66579i 0.630275 + 0.229401i
$$611$$ −13.7447 23.8066i −0.556052 0.963110i
$$612$$ 0 0
$$613$$ 19.5149 33.8008i 0.788200 1.36520i −0.138869 0.990311i $$-0.544347\pi$$
0.927069 0.374891i $$-0.122320\pi$$
$$614$$ −0.00179976 0.000655059i −7.26324e−5 2.64360e-5i
$$615$$ 0 0
$$616$$ 6.52362 + 3.22085i 0.262844 + 0.129772i
$$617$$ −2.82811 + 16.0390i −0.113855 + 0.645705i 0.873455 + 0.486904i $$0.161874\pi$$
−0.987311 + 0.158801i $$0.949237\pi$$
$$618$$ 0 0
$$619$$ 13.2292 + 4.81503i 0.531726 + 0.193533i 0.593909 0.804532i $$-0.297584\pi$$
−0.0621826 + 0.998065i $$0.519806\pi$$
$$620$$ −17.1927 29.7786i −0.690474 1.19594i
$$621$$ 0 0
$$622$$ −2.59936 −0.104225
$$623$$ 1.79990 + 4.09573i 0.0721115 + 0.164092i
$$624$$ 0 0
$$625$$ −14.7381 12.3667i −0.589522 0.494668i
$$626$$ 12.8801 + 10.8077i 0.514792 + 0.431962i
$$627$$ 0 0
$$628$$ 2.15271 + 0.783524i 0.0859027 + 0.0312660i
$$629$$ −4.10046 7.10221i −0.163496 0.283184i
$$630$$ 0 0
$$631$$ −15.0249 + 26.0240i −0.598134 + 1.03600i 0.394963 + 0.918697i $$0.370757\pi$$
−0.993096 + 0.117301i $$0.962576\pi$$
$$632$$ 31.8826 26.7527i 1.26822 1.06417i
$$633$$ 0 0
$$634$$ 1.45027 8.22489i 0.0575976 0.326652i
$$635$$ −25.3588 + 9.22983i −1.00633 + 0.366275i
$$636$$ 0 0
$$637$$ 17.4564 2.28172i 0.691648 0.0904052i
$$638$$ 3.15092 5.45755i 0.124746 0.216066i
$$639$$ 0 0
$$640$$ −8.63135 + 14.9499i −0.341184 + 0.590948i
$$641$$ 6.71816 5.63721i 0.265351 0.222656i −0.500398 0.865796i $$-0.666813\pi$$
0.765749 + 0.643139i $$0.222368\pi$$
$$642$$ 0 0
$$643$$ −25.0319 + 9.11085i −0.987160 + 0.359297i −0.784620 0.619977i $$-0.787142\pi$$
−0.202540 + 0.979274i $$0.564920\pi$$
$$644$$ −0.874292 13.4345i −0.0344519 0.529393i
$$645$$ 0 0
$$646$$ −0.657506 3.72890i −0.0258692 0.146712i
$$647$$ −21.1893 36.7009i −0.833036 1.44286i −0.895620 0.444820i $$-0.853268\pi$$
0.0625843 0.998040i $$-0.480066\pi$$
$$648$$ 0 0
$$649$$ −3.74772 + 6.49124i −0.147111 + 0.254804i
$$650$$ −10.7323 + 9.00546i −0.420955 + 0.353223i
$$651$$ 0 0
$$652$$ 2.58937 14.6850i 0.101407 0.575110i
$$653$$ −0.630967 + 3.57839i −0.0246917 + 0.140033i −0.994661 0.103192i $$-0.967094\pi$$
0.969970 + 0.243225i $$0.0782055\pi$$
$$654$$ 0 0
$$655$$ 3.69424 3.09984i 0.144346 0.121121i
$$656$$ −4.12822 −0.161180
$$657$$ 0 0
$$658$$ −26.2329 + 6.40626i −1.02266 + 0.249742i
$$659$$ −34.3400 12.4987i −1.33770 0.486882i −0.428611 0.903489i $$-0.640997\pi$$
−0.909087 + 0.416607i $$0.863219\pi$$
$$660$$ 0 0
$$661$$ −7.34938 + 41.6804i −0.285858 + 1.62118i 0.416347 + 0.909206i $$0.363310\pi$$
−0.702205 + 0.711975i $$0.747801\pi$$
$$662$$ −4.08600 + 23.1729i −0.158807 + 0.900639i
$$663$$ 0 0
$$664$$ −13.5162 4.91949i −0.524530 0.190913i
$$665$$ −16.4622 + 4.02019i −0.638376 + 0.155896i
$$666$$ 0 0
$$667$$ −32.3365 −1.25207
$$668$$ −11.3867 + 9.55459i −0.440565 + 0.369678i
$$669$$ 0 0
$$670$$ 0.543260 3.08098i 0.0209880 0.119029i
$$671$$ −0.875803 + 4.96693i −0.0338100 + 0.191746i
$$672$$ 0 0
$$673$$ −17.6276 + 14.7913i −0.679493 + 0.570163i −0.915858 0.401502i $$-0.868488\pi$$
0.236365 + 0.971664i $$0.424044\pi$$
$$674$$ 4.42251 7.66002i 0.170349 0.295053i
$$675$$ 0 0
$$676$$ −3.76480 6.52083i −0.144800 0.250801i
$$677$$ 1.80122 + 10.2152i 0.0692264 + 0.392603i 0.999658 + 0.0261378i $$0.00832087\pi$$
−0.930432 + 0.366465i $$0.880568\pi$$
$$678$$ 0 0
$$679$$ 2.16211 + 33.2232i 0.0829741 + 1.27499i
$$680$$ 19.0549 6.93543i 0.730723 0.265961i
$$681$$ 0 0
$$682$$ −6.19887 + 5.20147i −0.237367 + 0.199175i
$$683$$ −7.07481 + 12.2539i −0.270710 + 0.468884i −0.969044 0.246888i $$-0.920592\pi$$
0.698334 + 0.715772i $$0.253925\pi$$
$$684$$ 0 0
$$685$$ −2.23346 + 3.86847i −0.0853362 + 0.147807i
$$686$$ 2.65455 17.0889i 0.101351 0.652457i
$$687$$ 0 0
$$688$$ −4.50424 + 1.63941i −0.171723 + 0.0625019i
$$689$$ −1.78391 + 10.1170i −0.0679615 + 0.385429i
$$690$$ 0 0
$$691$$ −9.84214 + 8.25853i −0.374413 + 0.314169i −0.810504 0.585733i $$-0.800807\pi$$
0.436092 + 0.899902i $$0.356362\pi$$
$$692$$ −5.60464 + 9.70752i −0.213056 + 0.369025i
$$693$$ 0 0
$$694$$ 2.26379 + 3.92100i 0.0859322 + 0.148839i
$$695$$ 36.3935 + 13.2462i 1.38049 + 0.502456i
$$696$$ 0 0
$$697$$ −14.0647 11.8017i −0.532738 0.447021i
$$698$$ −13.0856 10.9801i −0.495298 0.415604i
$$699$$ 0 0
$$700$$ −7.16329 16.3003i −0.270747 0.616093i
$$701$$ −10.6569 −0.402504 −0.201252 0.979539i $$-0.564501\pi$$
−0.201252 + 0.979539i $$0.564501\pi$$
$$702$$ 0 0
$$703$$ 3.78310 + 6.55252i 0.142682 + 0.247133i
$$704$$ 5.29620 + 1.92766i 0.199608 + 0.0726514i
$$705$$ 0 0
$$706$$ 0.951092 5.39391i 0.0357948 0.203003i
$$707$$ 9.17257 + 4.52869i 0.344970 + 0.170319i
$$708$$ 0 0
$$709$$ −13.9753 5.08659i −0.524853 0.191031i 0.0659855 0.997821i $$-0.478981\pi$$
−0.590839 + 0.806790i $$0.701203\pi$$
$$710$$ −3.54566 + 6.14127i −0.133066 + 0.230478i
$$711$$ 0 0
$$712$$ 2.46953 + 4.27735i 0.0925496 + 0.160301i
$$713$$ 39.0185 + 14.2016i 1.46125 + 0.531853i
$$714$$ 0 0
$$715$$ −6.00614 5.03975i −0.224617 0.188476i
$$716$$ 3.37796 1.22948i 0.126240 0.0459477i
$$717$$ 0 0
$$718$$ −2.78427 15.7904i −0.103908 0.589292i
$$719$$ −21.0035 36.3791i −0.783298 1.35671i −0.930010 0.367533i $$-0.880202\pi$$
0.146712 0.989179i $$-0.453131\pi$$
$$720$$ 0 0
$$721$$ −13.6678 + 3.33777i −0.509014 + 0.124305i
$$722$$ −2.47422 14.0320i −0.0920808 0.522216i
$$723$$ 0 0
$$724$$ 15.3184 + 12.8537i 0.569304 + 0.477702i
$$725$$ −40.1863 + 14.6266i −1.49248 + 0.543219i
$$726$$ 0 0
$$727$$ 18.2193 15.2878i 0.675718 0.566994i −0.239034 0.971011i $$-0.576831\pi$$
0.914752 + 0.404017i $$0.132386\pi$$
$$728$$ 18.8810 4.61087i 0.699776 0.170890i
$$729$$ 0 0
$$730$$ −25.6408 + 44.4111i −0.949007 + 1.64373i
$$731$$ −20.0325 7.29123i −0.740929 0.269676i
$$732$$ 0 0
$$733$$ 26.7274 + 22.4270i 0.987200 + 0.828359i 0.985160 0.171639i $$-0.0549063\pi$$
0.00203972 + 0.999998i $$0.499351\pi$$
$$734$$ 5.27532 1.92006i 0.194716 0.0708707i
$$735$$ 0 0
$$736$$ −4.23114 23.9960i −0.155962 0.884503i
$$737$$ 0.952499 0.0350857
$$738$$ 0 0
$$739$$ −8.22260 −0.302473 −0.151237 0.988498i $$-0.548326\pi$$
−0.151237 + 0.988498i $$0.548326\pi$$
$$740$$ −11.1939 + 9.39276i −0.411494 + 0.345285i
$$741$$ 0 0
$$742$$ 9.04882 + 4.46760i 0.332193 + 0.164011i
$$743$$ −19.4758 16.3421i −0.714497 0.599534i 0.211360 0.977408i $$-0.432211\pi$$
−0.925857 + 0.377874i $$0.876655\pi$$
$$744$$ 0 0
$$745$$ −1.69711 9.62476i −0.0621771 0.352624i
$$746$$ −19.6490 −0.719402
$$747$$ 0 0
$$748$$ 1.11320 + 1.92813i 0.0407028 + 0.0704992i
$$749$$ 22.1923 + 2.44085i 0.810888 + 0.0891869i
$$750$$ 0 0
$$751$$ 4.50351 25.5407i 0.164336 0.931993i −0.785411 0.618974i $$-0.787548\pi$$
0.949747 0.313019i $$-0.101340\pi$$
$$752$$ −4.84159 + 1.76220i −0.176555 + 0.0642607i
$$753$$ 0 0
$$754$$ −2.92336 16.5792i −0.106463 0.603780i
$$755$$ 53.7245 1.95524
$$756$$ 0 0
$$757$$ −51.8493 −1.88449 −0.942247 0.334918i $$-0.891291\pi$$
−0.942247 + 0.334918i $$0.891291\pi$$
$$758$$ 1.61590 + 9.16423i 0.0586922 + 0.332860i
$$759$$ 0 0
$$760$$ −17.5801 + 6.39864i −0.637698 + 0.232103i
$$761$$ 2.33892 13.2647i 0.0847858 0.480844i −0.912617 0.408816i $$-0.865942\pi$$
0.997403 0.0720282i $$-0.0229472\pi$$
$$762$$ 0 0
$$763$$ −9.07653 + 12.3668i −0.328592 + 0.447708i
$$764$$ −5.80448 10.0536i −0.209999 0.363728i
$$765$$ 0 0
$$766$$ 35.4242 1.27993
$$767$$ 3.47707 + 19.7194i 0.125550 + 0.712028i
$$768$$ 0 0
$$769$$ 9.94513 + 8.34496i 0.358631 + 0.300927i 0.804245 0.594298i $$-0.202570\pi$$
−0.445614 + 0.895225i $$0.647015\pi$$
$$770$$ −6.40591 + 4.27600i −0.230853 + 0.154096i
$$771$$ 0 0
$$772$$ 2.01575 1.69141i 0.0725484 0.0608753i
$$773$$ 33.8415 1.21719 0.608596 0.793480i $$-0.291733\pi$$
0.608596 + 0.793480i $$0.291733\pi$$
$$774$$ 0 0
$$775$$ 54.9141 1.97257
$$776$$ 6.38263 + 36.1977i 0.229123 + 1.29942i
$$777$$ 0 0
$$778$$ −33.0321 + 12.0227i −1.18426 + 0.431035i
$$779$$ 12.9761 + 10.8883i 0.464918 + 0.390112i
$$780$$ 0 0
$$781$$ −2.02881 0.738425i −0.0725964 0.0264229i
$$782$$ −4.41529 + 7.64750i −0.157890 + 0.273474i
$$783$$ 0 0