LMFDB - Embedded newform 169.3.f.g.80.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(19,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("169.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.f (of order $12$, degree $4$, 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:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.3
Character	$\chi$	$=$	169.80
Dual form			169.3.f.g.150.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.27369 - 0.609234i) q^{2} +(2.51175 + 4.35048i) q^{3} +(1.33442 + 0.770425i) q^{4} +(-1.10964 + 1.10964i) q^{5} +(-3.06049 - 11.4219i) q^{6} +(-6.34925 + 1.70128i) q^{7} +(4.09315 + 4.09315i) q^{8} +(-8.11776 + 14.0604i) q^{9} +(3.19902 - 1.84696i) q^{10} +(0.301099 - 1.12372i) q^{11} +7.74046i q^{12} +15.4727 q^{14} +(-7.61462 - 2.04033i) q^{15} +(-9.89459 - 17.1379i) q^{16} +(-21.4473 - 12.3826i) q^{17} +(27.0234 - 27.0234i) q^{18} +(0.174381 + 0.650797i) q^{19} +(-2.33562 + 0.625828i) q^{20} +(-23.3491 - 23.3491i) q^{21} +(-1.36921 + 2.37154i) q^{22} +(-1.92917 + 1.11381i) q^{23} +(-7.52619 + 28.0881i) q^{24} +22.5374i q^{25} -36.3476 q^{27} +(-9.78324 - 2.62141i) q^{28} +(-9.58516 - 16.6020i) q^{29} +(16.0703 + 9.27818i) q^{30} +(-40.7907 + 40.7907i) q^{31} +(6.06346 + 22.6291i) q^{32} +(5.64498 - 1.51257i) q^{33} +(41.2206 + 41.2206i) q^{34} +(5.15759 - 8.93321i) q^{35} +(-21.6649 + 12.5082i) q^{36} +(-1.02942 + 3.84185i) q^{37} -1.58595i q^{38} -9.08389 q^{40} +(-11.6712 - 3.12729i) q^{41} +(38.8636 + 67.3137i) q^{42} +(43.5991 + 25.1720i) q^{43} +(1.26753 - 1.26753i) q^{44} +(-6.59418 - 24.6098i) q^{45} +(5.06491 - 1.35714i) q^{46} +(-24.3090 - 24.3090i) q^{47} +(49.7054 - 86.0923i) q^{48} +(-5.01666 + 2.89637i) q^{49} +(13.7305 - 51.2431i) q^{50} -124.408i q^{51} +65.5668 q^{53} +(82.6433 + 22.1442i) q^{54} +(0.912811 + 1.58104i) q^{55} +(-32.9520 - 19.0249i) q^{56} +(-2.39328 + 2.39328i) q^{57} +(11.6792 + 43.5874i) q^{58} +(71.6521 - 19.1991i) q^{59} +(-8.58915 - 8.58915i) q^{60} +(-45.4338 + 78.6937i) q^{61} +(117.597 - 67.8945i) q^{62} +(27.6211 - 103.083i) q^{63} +24.0109i q^{64} -13.7565 q^{66} +(91.3047 + 24.4650i) q^{67} +(-19.0797 - 33.0470i) q^{68} +(-9.69118 - 5.59520i) q^{69} +(-17.1692 + 17.1692i) q^{70} +(17.5705 + 65.5740i) q^{71} +(-90.7785 + 24.3240i) q^{72} +(51.8021 + 51.8021i) q^{73} +(4.68118 - 8.10804i) q^{74} +(-98.0483 + 56.6082i) q^{75} +(-0.268695 + 1.00278i) q^{76} +7.64700i q^{77} -49.1050 q^{79} +(29.9965 + 8.03753i) q^{80} +(-18.2361 - 31.5859i) q^{81} +(24.6315 + 14.2210i) q^{82} +(70.5618 - 70.5618i) q^{83} +(-13.1686 - 49.1461i) q^{84} +(37.5391 - 10.0586i) q^{85} +(-83.7955 - 83.7955i) q^{86} +(48.1510 - 83.4000i) q^{87} +(5.83198 - 3.36710i) q^{88} +(-21.8165 + 81.4201i) q^{89} +59.9726i q^{90} -3.43242 q^{92} +(-279.915 - 75.0030i) q^{93} +(40.4613 + 70.0810i) q^{94} +(-0.915654 - 0.528653i) q^{95} +(-83.2176 + 83.2176i) q^{96} +(-17.5122 - 65.3566i) q^{97} +(13.1709 - 3.52914i) q^{98} +(13.3556 + 13.3556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) $ 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.27369	−	0.609234i	−1.13685	−	0.304617i	−0.359164	−	0.933274i	$-0.616938\pi$
$2$	−2.27369	−	0.609234i	−1.13685	−	0.304617i	−0.777683	+	0.628657i	$0.783605\pi$
$3$	2.51175	+	4.35048i	0.837249	+	1.45016i	0.892186	+	0.451669i	$0.149171\pi$
$3$	2.51175	+	4.35048i	0.837249	+	1.45016i	−0.0549364	+	0.998490i	$0.517496\pi$
$4$	1.33442	+	0.770425i	0.333604	+	0.192606i
$5$	−1.10964	+	1.10964i	−0.221929	+	0.221929i	−0.809310	−	0.587381i	$-0.800159\pi$
$5$	−1.10964	+	1.10964i	−0.221929	+	0.221929i	0.587381	+	0.809310i	$0.300159\pi$
$6$	−3.06049	−	11.4219i	−0.510081	−	1.90365i
$7$	−6.34925	+	1.70128i	−0.907035	+	0.243039i	−0.682035	−	0.731319i	$-0.738905\pi$
$7$	−6.34925	+	1.70128i	−0.907035	+	0.243039i	−0.225000	+	0.974359i	$0.572238\pi$
$8$	4.09315	+	4.09315i	0.511644	+	0.511644i
$9$	−8.11776	+	14.0604i	−0.901973	+	1.56226i
$10$	3.19902	−	1.84696i	0.319902	−	0.184696i
$11$	0.301099	−	1.12372i	0.0273726	−	0.102156i	−0.950888	−	0.309535i	$-0.899827\pi$
$11$	0.301099	−	1.12372i	0.0273726	−	0.102156i	0.978261	+	0.207379i	$0.0664933\pi$
$12$			7.74046i			0.645038i
$13$		0			0
$13$		0			0
$14$	15.4727			1.10519
$15$	−7.61462	−	2.04033i	−0.507642	−	0.136022i
$16$	−9.89459	−	17.1379i	−0.618412	−	1.07112i
$17$	−21.4473	−	12.3826i	−1.26160	−	0.728387i	−0.288218	−	0.957565i	$-0.593063\pi$
$17$	−21.4473	−	12.3826i	−1.26160	−	0.728387i	−0.973385	+	0.229178i	$0.926396\pi$
$18$	27.0234	−	27.0234i	1.50130	−	1.50130i
$19$	0.174381	+	0.650797i	0.00917793	+	0.0342525i	0.970363	−	0.241652i	$-0.0776893\pi$
$19$	0.174381	+	0.650797i	0.00917793	+	0.0342525i	−0.961185	+	0.275905i	$0.911023\pi$
$20$	−2.33562	+	0.625828i	−0.116781	+	0.0312914i
$21$	−23.3491	−	23.3491i	−1.11186	−	1.11186i
$22$	−1.36921	+	2.37154i	−0.0622369	+	0.107797i
$23$	−1.92917	+	1.11381i	−0.0838770	+	0.0484264i	−0.541352	−	0.840796i	$-0.682087\pi$
$23$	−1.92917	+	1.11381i	−0.0838770	+	0.0484264i	0.457475	+	0.889223i	$0.348754\pi$
$24$	−7.52619	+	28.0881i	−0.313591	+	1.17034i
$25$			22.5374i			0.901495i
$26$		0			0
$27$	−36.3476			−1.34621
$28$	−9.78324	−	2.62141i	−0.349401	−	0.0936218i
$29$	−9.58516	−	16.6020i	−0.330523	−	0.572482i	0.652092	−	0.758140i	$-0.273892\pi$
$29$	−9.58516	−	16.6020i	−0.330523	−	0.572482i	−0.982614	+	0.185658i	$0.940558\pi$
$30$	16.0703	+	9.27818i	0.535676	+	0.309273i
$31$	−40.7907	+	40.7907i	−1.31583	+	1.31583i	−0.398785	+	0.917045i	$0.630568\pi$
$31$	−40.7907	+	40.7907i	−1.31583	+	1.31583i	−0.917045	+	0.398785i	$0.869432\pi$
$32$	6.06346	+	22.6291i	0.189483	+	0.707160i
$33$	5.64498	−	1.51257i	0.171060	−	0.0458354i
$34$	41.2206	+	41.2206i	1.21237	+	1.21237i
$35$	5.15759	−	8.93321i	0.147360	−	0.255235i
$36$	−21.6649	+	12.5082i	−0.601803	+	0.347451i
$37$	−1.02942	+	3.84185i	−0.0278222	+	0.103834i	−0.978441	−	0.206528i	$-0.933784\pi$
$37$	−1.02942	+	3.84185i	−0.0278222	+	0.103834i	0.950618	+	0.310362i	$0.100450\pi$
$38$		−	1.58595i		−	0.0417356i
$39$		0			0
$40$	−9.08389			−0.227097
$41$	−11.6712	−	3.12729i	−0.284664	−	0.0762754i	0.113662	−	0.993519i	$-0.463742\pi$
$41$	−11.6712	−	3.12729i	−0.284664	−	0.0762754i	−0.398326	+	0.917244i	$0.630409\pi$
$42$	38.8636	+	67.3137i	0.925323	+	1.60271i
$43$	43.5991	+	25.1720i	1.01393	+	0.585395i	0.912341	−	0.409431i	$-0.134273\pi$
$43$	43.5991	+	25.1720i	1.01393	+	0.585395i	0.101592	+	0.994826i	$0.467606\pi$
$44$	1.26753	−	1.26753i	0.0288075	−	0.0288075i
$45$	−6.59418	−	24.6098i	−0.146537	−	0.546885i
$46$	5.06491	−	1.35714i	0.110107	−	0.0295030i
$47$	−24.3090	−	24.3090i	−0.517212	−	0.517212i	0.399515	−	0.916727i	$-0.369179\pi$
$47$	−24.3090	−	24.3090i	−0.517212	−	0.517212i	−0.916727	+	0.399515i	$0.869179\pi$
$48$	49.7054	−	86.0923i	1.03553	−	1.79359i
$49$	−5.01666	+	2.89637i	−0.102381	+	0.0591096i
$50$	13.7305	−	51.2431i	0.274611	−	1.02486i
$51$		−	124.408i		−	2.43937i
$52$		0			0
$53$	65.5668			1.23711			0.618555	−	0.785742i	$-0.287718\pi$
$53$	65.5668			1.23711			0.618555	+	0.785742i	$0.287718\pi$
$54$	82.6433	+	22.1442i	1.53043	+	0.410078i
$55$	0.912811	+	1.58104i	0.0165966	+	0.0287461i
$56$	−32.9520	−	19.0249i	−0.588429	−	0.339730i
$57$	−2.39328	+	2.39328i	−0.0419873	+	0.0419873i
$58$	11.6792	+	43.5874i	0.201366	+	0.751507i
$59$	71.6521	−	19.1991i	1.21444	−	0.325409i	0.405938	−	0.913900i	$-0.366945\pi$
$59$	71.6521	−	19.1991i	1.21444	−	0.325409i	0.808503	+	0.588492i	$0.200278\pi$
$60$	−8.58915	−	8.58915i	−0.143152	−	0.143152i
$61$	−45.4338	+	78.6937i	−0.744816	+	1.29006i	0.205464	+	0.978665i	$0.434130\pi$
$61$	−45.4338	+	78.6937i	−0.744816	+	1.29006i	−0.950280	+	0.311395i	$0.899204\pi$
$62$	117.597	−	67.8945i	1.89672	−	1.09507i
$63$	27.6211	−	103.083i	0.438430	−	1.63624i
$64$			24.0109i			0.375171i
$65$		0			0
$66$	−13.7565			−0.208431
$67$	91.3047	+	24.4650i	1.36276	+	0.365149i	0.864828	−	0.502069i	$-0.167428\pi$
$67$	91.3047	+	24.4650i	1.36276	+	0.365149i	0.497929	+	0.867218i	$0.334094\pi$
$68$	−19.0797	−	33.0470i	−0.280584	−	0.485985i
$69$	−9.69118	−	5.59520i	−0.140452	−	0.0810899i
$70$	−17.1692	+	17.1692i	−0.245274	+	0.245274i
$71$	17.5705	+	65.5740i	0.247472	+	0.923578i	0.972125	+	0.234464i	$0.0753335\pi$
$71$	17.5705	+	65.5740i	0.247472	+	0.923578i	−0.724653	+	0.689114i	$0.758000\pi$
$72$	−90.7785	+	24.3240i	−1.26081	+	0.337834i
$73$	51.8021	+	51.8021i	0.709617	+	0.709617i	0.966455	−	0.256837i	$-0.0826804\pi$
$73$	51.8021	+	51.8021i	0.709617	+	0.709617i	−0.256837	+	0.966455i	$0.582680\pi$
$74$	4.68118	−	8.10804i	0.0632592	−	0.109568i
$75$	−98.0483	+	56.6082i	−1.30731	+	0.754776i
$76$	−0.268695	+	1.00278i	−0.00353545	+	0.0131945i
$77$			7.64700i			0.0993116i
$78$		0			0
$79$	−49.1050			−0.621582			−0.310791	−	0.950478i	$-0.600594\pi$
$79$	−49.1050			−0.621582			−0.310791	+	0.950478i	$0.600594\pi$
$80$	29.9965	+	8.03753i	0.374956	+	0.100469i
$81$	−18.2361	−	31.5859i	−0.225138	−	0.389950i
$82$	24.6315	+	14.2210i	0.300384	+	0.173427i
$83$	70.5618	−	70.5618i	0.850142	−	0.850142i	−0.140008	−	0.990150i	$-0.544713\pi$
$83$	70.5618	−	70.5618i	0.850142	−	0.850142i	0.990150	+	0.140008i	$0.0447129\pi$
$84$	−13.1686	−	49.1461i	−0.156770	−	0.585072i
$85$	37.5391	−	10.0586i	0.441636	−	0.118336i
$86$	−83.7955	−	83.7955i	−0.974366	−	0.974366i
$87$	48.1510	−	83.4000i	0.553460	−	0.958621i
$88$	5.83198	−	3.36710i	0.0662725	−	0.0382625i
$89$	−21.8165	+	81.4201i	−0.245129	+	0.914833i	0.728190	+	0.685375i	$0.240362\pi$
$89$	−21.8165	+	81.4201i	−0.245129	+	0.914833i	−0.973319	+	0.229457i	$0.926305\pi$
$90$			59.9726i			0.666362i
$91$		0			0
$92$	−3.43242			−0.0373089
$93$	−279.915	−	75.0030i	−3.00984	−	0.806484i
$94$	40.4613	+	70.0810i	0.430439	+	0.745543i
$95$	−0.915654	−	0.528653i	−0.00963846	−	0.00556477i
$96$	−83.2176	+	83.2176i	−0.866850	+	0.866850i
$97$	−17.5122	−	65.3566i	−0.180539	−	0.673779i	−0.995542	−	0.0943225i	$-0.969932\pi$
$97$	−17.5122	−	65.3566i	−0.180539	−	0.673779i	0.815003	−	0.579457i	$-0.196735\pi$
$98$	13.1709	−	3.52914i	0.134397	−	0.0360116i
$99$	13.3556	+	13.3556i	0.134905	+	0.134905i
$100$	−17.3634	+	30.0742i	−0.173634	+	0.300742i
$101$	−65.4023	+	37.7600i	−0.647547	+	0.373862i	−0.787516	−	0.616294i	$-0.788633\pi$
$101$	−65.4023	+	37.7600i	−0.647547	+	0.373862i	0.139968	+	0.990156i	$0.455300\pi$
$102$	−75.7934	+	282.865i	−0.743073	+	2.77319i
$103$			79.8956i			0.775685i	0.921726	+	0.387843i	$0.126780\pi$
$103$			79.8956i			0.775685i	−0.921726	+	0.387843i	$0.873220\pi$
$104$		0			0
$105$	51.8183			0.493507
$106$	−149.079	−	39.9456i	−1.40640	−	0.376845i
$107$	−37.3751	−	64.7356i	−0.349300	−	0.605005i	0.636825	−	0.771008i	$-0.280247\pi$
$107$	−37.3751	−	64.7356i	−0.349300	−	0.605005i	−0.986125	+	0.166003i	$0.946914\pi$
$108$	−48.5028	−	28.0031i	−0.449100	−	0.259288i
$109$	−21.0819	+	21.0819i	−0.193412	+	0.193412i	−0.797169	−	0.603757i	$-0.793670\pi$
$109$	−21.0819	+	21.0819i	−0.193412	+	0.193412i	0.603757	+	0.797169i	$0.293670\pi$
$110$	−1.11223	−	4.15091i	−0.0101112	−	0.0377355i
$111$	−19.2995	+	5.17130i	−0.173870	+	0.0465882i
$112$	91.9795	+	91.9795i	0.821246	+	0.821246i
$113$	−46.1016	+	79.8504i	−0.407979	+	0.706641i	−0.994663	−	0.103175i	$-0.967100\pi$
$113$	−46.1016	+	79.8504i	−0.407979	+	0.706641i	0.586684	+	0.809816i	$0.300433\pi$
$114$	6.89965	−	3.98351i	0.0605232	−	0.0349431i
$115$	0.904763	−	3.37662i	0.00786750	−	0.0293619i
$116$		−	29.5386i		−	0.254643i
$117$		0			0
$118$	−174.612			−1.47976
$119$	157.240	+	42.1323i	1.32134	+	0.354053i
$120$	−22.8164	−	39.5192i	−0.190137	−	0.329327i
$121$	103.617	+	59.8233i	0.856339	+	0.494407i
$122$	151.245	−	151.245i	1.23972	−	1.23972i
$123$	−15.7099	−	58.6303i	−0.127723	−	0.476669i
$124$	−85.8579	+	23.0056i	−0.692403	+	0.185529i
$125$	−52.7496	−	52.7496i	−0.421996	−	0.421996i
$126$	−125.604	+	217.552i	−0.996855	+	1.72660i
$127$	4.02217	−	2.32220i	0.0316706	−	0.0182850i	−0.484081	−	0.875023i	$-0.660846\pi$
$127$	4.02217	−	2.32220i	0.0316706	−	0.0182850i	0.515752	+	0.856738i	$0.327513\pi$
$128$	38.8821	−	145.110i	0.303767	−	1.13367i
$129$			252.903i			1.96049i
$130$		0			0
$131$	58.5190			0.446710			0.223355	−	0.974737i	$-0.428299\pi$
$131$	58.5190			0.446710			0.223355	+	0.974737i	$0.428299\pi$
$132$	8.69807	+	2.33064i	0.0658945	+	0.0176564i
$133$	−2.21437	−	3.83540i	−0.0166494	−	0.0288376i
$134$	−192.694	−	111.252i	−1.43801	−	0.830238i
$135$	40.3329	−	40.3329i	0.298762	−	0.298762i
$136$	−37.1031	−	138.471i	−0.272817	−	1.01817i
$137$	−159.918	+	42.8498i	−1.16728	+	0.312772i	−0.789871	−	0.613274i	$-0.789852\pi$
$137$	−159.918	+	42.8498i	−1.16728	+	0.312772i	−0.377411	+	0.926046i	$0.623186\pi$
$138$	18.6260	+	18.6260i	0.134971	+	0.134971i
$139$	38.3858	−	66.4861i	0.276156	−	0.478317i	−0.694270	−	0.719715i	$-0.744273\pi$
$139$	38.3858	−	66.4861i	0.276156	−	0.478317i	0.970426	+	0.241398i	$0.0776059\pi$
$140$	13.7647	−	7.94708i	0.0983196	−	0.0567648i
$141$	44.6976	−	166.814i	0.317004	−	1.18307i
$142$		−	159.800i		−	1.12535i
$143$		0			0
$144$	321.288			2.23116
$145$	29.0584	+	7.78617i	0.200403	+	0.0536977i
$146$	−86.2225	−	149.342i	−0.590565	−	1.02289i
$147$	−25.2012	−	14.5499i	−0.171437	−	0.0989790i
$148$	−4.33354	+	4.33354i	−0.0292807	+	0.0292807i
$149$	30.9709	+	115.585i	0.207858	+	0.775737i	0.988559	+	0.150833i	$0.0481954\pi$
$149$	30.9709	+	115.585i	0.207858	+	0.775737i	−0.780701	+	0.624904i	$0.785138\pi$
$150$	257.420	−	68.9754i	1.71613	−	0.459836i
$151$	−158.935	−	158.935i	−1.05255	−	1.05255i	−0.998541	−	0.0540078i	$-0.982800\pi$
$151$	−158.935	−	158.935i	−1.05255	−	1.05255i	−0.0540078	−	0.998541i	$-0.517200\pi$
$152$	−1.95005	+	3.37758i	−0.0128293	+	0.0222209i
$153$	348.207	−	201.037i	2.27586	−	1.31397i
$154$	4.65881	−	17.3869i	0.0302520	−	0.112902i
$155$		−	90.5263i		−	0.584041i
$156$		0			0
$157$	121.589			0.774451			0.387225	−	0.921985i	$-0.373434\pi$
$157$	121.589			0.774451			0.387225	+	0.921985i	$0.373434\pi$
$158$	111.650	+	29.9165i	0.706644	+	0.189345i
$159$	164.687	+	285.247i	1.03577	+	1.79401i
$160$	−31.8385	−	18.3820i	−0.198991	−	0.114887i
$161$	10.3539	−	10.3539i	0.0643098	−	0.0643098i
$162$	22.2202	+	82.9268i	0.137162	+	0.511894i
$163$	−143.124	+	38.3498i	−0.878059	+	0.235275i	−0.669569	−	0.742750i	$-0.733521\pi$
$163$	−143.124	+	38.3498i	−0.878059	+	0.235275i	−0.208489	+	0.978025i	$0.566855\pi$
$164$	−13.1649	−	13.1649i	−0.0802738	−	0.0802738i
$165$	−4.58550	+	7.94233i	−0.0277909	+	0.0481353i
$166$	−203.425	+	117.447i	−1.22545	+	0.707513i
$167$	8.21496	−	30.6587i	0.0491914	−	0.183585i	−0.936959	−	0.349440i	$-0.886372\pi$
$167$	8.21496	−	30.6587i	0.0491914	−	0.183585i	0.986150	+	0.165855i	$0.0530385\pi$
$168$		−	191.143i		−	1.13775i
$169$		0			0
$170$	−91.4803			−0.538120
$171$	−10.5660	−	2.83116i	−0.0617897	−	0.0165565i
$172$	38.7862	+	67.1797i	0.225501	+	0.390580i
$173$	−75.3542	−	43.5058i	−0.435574	−	0.251478i	0.266145	−	0.963933i	$-0.414250\pi$
$173$	−75.3542	−	43.5058i	−0.435574	−	0.251478i	−0.701718	+	0.712455i	$0.747583\pi$
$174$	−160.291	+	160.291i	−0.921211	+	0.921211i
$175$	−38.3423	−	143.095i	−0.219099	−	0.817688i
$176$	−22.2374	+	5.95849i	−0.126349	+	0.0338551i
$177$	263.497	+	263.497i	1.48868	+	1.48868i
$178$	99.2079	−	171.833i	0.557348	−	0.965354i
$179$	−125.261	+	72.3192i	−0.699780	+	0.404018i	−0.807265	−	0.590189i	$-0.799053\pi$
$179$	−125.261	+	72.3192i	−0.699780	+	0.404018i	0.107486	+	0.994207i	$0.465720\pi$
$180$	10.1606	−	37.9200i	0.0564480	−	0.210667i
$181$		−	57.4932i		−	0.317642i	−0.987307	−	0.158821i	$-0.949231\pi$
$181$		−	57.4932i		−	0.317642i	0.987307	−	0.158821i	$-0.0507693\pi$
$182$		0			0
$183$	−456.473			−2.49439
$184$	−12.4554	−	3.33741i	−0.0676923	−	0.0181381i
$185$	−3.12080	−	5.40538i	−0.0168692	−	0.0292183i
$186$	590.746	+	341.068i	3.17606	+	1.83370i
$187$	−20.3722	+	20.3722i	−0.108942	+	0.108942i
$188$	−13.7100	−	51.1665i	−0.0729257	−	0.272162i
$189$	230.780	−	61.8372i	1.22106	−	0.327181i
$190$	1.75984	+	1.75984i	0.00926233	+	0.00926233i
$191$	33.9463	−	58.7966i	0.177729	−	0.307836i	−0.763373	−	0.645958i	$-0.776458\pi$
$191$	33.9463	−	58.7966i	0.177729	−	0.307836i	0.941102	+	0.338122i	$0.109792\pi$
$192$	−104.459	+	60.3095i	−0.544058	+	0.314112i
$193$	−55.6354	+	207.634i	−0.288266	+	1.07582i	0.658153	+	0.752884i	$0.271338\pi$
$193$	−55.6354	+	207.634i	−0.288266	+	1.07582i	−0.946419	+	0.322940i	$0.895329\pi$
$194$			159.270i			0.820979i
$195$		0			0
$196$	−8.92575			−0.0455395
$197$	152.818	+	40.9476i	0.775728	+	0.207856i	0.624901	−	0.780704i	$-0.285139\pi$
$197$	152.818	+	40.9476i	0.775728	+	0.207856i	0.150828	+	0.988560i	$0.451806\pi$
$198$	−22.2299	−	38.5032i	−0.112272	−	0.194461i
$199$	−36.3122	−	20.9649i	−0.182473	−	0.105351i	0.405981	−	0.913882i	$-0.366930\pi$
$199$	−36.3122	−	20.9649i	−0.182473	−	0.105351i	−0.588454	+	0.808530i	$0.700263\pi$
$200$	−92.2490	+	92.2490i	−0.461245	+	0.461245i
$201$	122.900	+	458.669i	0.611442	+	2.28193i
$202$	171.710	−	46.0094i	0.850047	−	0.227769i
$203$	89.1031	+	89.1031i	0.438931	+	0.438931i
$204$	95.8468	−	166.012i	0.469837	−	0.813782i
$205$	16.4211	−	9.48070i	0.0801027	−	0.0462473i
$206$	48.6751	−	181.658i	0.236287	−	0.881835i
$207$		−	36.1665i		−	0.174717i
$208$		0			0
$209$	0.783817			0.00375032
$210$	−117.819	−	31.5695i	−0.561042	−	0.150331i
$211$	35.3826	+	61.2844i	0.167690	+	0.290447i	0.937607	−	0.347696i	$-0.113036\pi$
$211$	35.3826	+	61.2844i	0.167690	+	0.290447i	−0.769917	+	0.638144i	$0.779703\pi$
$212$	87.4934	+	50.5143i	0.412705	+	0.238275i
$213$	−241.146	+	241.146i	−1.13214	+	1.13214i
$214$	45.5404	+	169.959i	0.212806	+	0.794201i
$215$	−76.3114	+	20.4476i	−0.354937	+	0.0951050i
$216$	−148.776	−	148.776i	−0.688779	−	0.688779i
$217$	189.594	−	328.386i	0.873705	−	1.51330i
$218$	60.7776	−	35.0899i	0.278796	−	0.160963i
$219$	−95.2499	+	355.477i	−0.434931	+	1.62318i
$220$			2.81301i			0.0127864i
$221$		0			0
$222$	47.0318			0.211855
$223$	−147.428	−	39.5031i	−0.661110	−	0.177144i	−0.0873632	−	0.996177i	$-0.527844\pi$
$223$	−147.428	−	39.5031i	−0.661110	−	0.177144i	−0.573747	+	0.819033i	$0.694511\pi$
$224$	−76.9968	−	133.362i	−0.343735	−	0.595367i
$225$	−316.884	−	182.953i	−1.40837	−	0.813124i
$226$	153.469	−	153.469i	0.679065	−	0.679065i
$227$	−18.9293	−	70.6452i	−0.0833891	−	0.311212i	0.911615	−	0.411045i	$-0.134836\pi$
$227$	−18.9293	−	70.6452i	−0.0833891	−	0.311212i	−0.995004	+	0.0998323i	$0.968169\pi$
$228$	−5.03747	+	1.34979i	−0.0220942	+	0.00592011i
$229$	−182.706	−	182.706i	−0.797845	−	0.797845i	0.184911	−	0.982755i	$-0.440800\pi$
$229$	−182.706	−	182.706i	−0.797845	−	0.797845i	−0.982755	+	0.184911i	$0.940800\pi$
$230$	−4.11431	+	7.12619i	−0.0178883	+	0.0309834i
$231$	−33.2681	+	19.2073i	−0.144018	+	0.0831486i
$232$	28.7209	−	107.188i	0.123797	−	0.462017i
$233$		−	263.622i		−	1.13142i	−0.824603	−	0.565712i	$-0.808601\pi$
$233$		−	263.622i		−	1.13142i	0.824603	−	0.565712i	$-0.191399\pi$
$234$		0			0
$235$	53.9486			0.229568
$236$	110.405	+	29.5830i	0.467818	+	0.125352i
$237$	−123.339	−	213.630i	−0.520419	−	0.901393i
$238$	−331.847	−	191.592i	−1.39432	−	0.805009i
$239$	260.543	−	260.543i	1.09014	−	1.09014i	0.0946270	−	0.995513i	$-0.469834\pi$
$239$	260.543	−	260.543i	1.09014	−	1.09014i	0.995513	−	0.0946270i	$-0.0301659\pi$
$240$	40.3765	+	150.687i	0.168235	+	0.627863i
$241$	59.8004	−	16.0235i	0.248134	−	0.0664874i	−0.132608	−	0.991169i	$-0.542335\pi$
$241$	59.8004	−	16.0235i	0.248134	−	0.0664874i	0.380742	+	0.924681i	$0.375668\pi$
$242$	−199.147	−	199.147i	−0.822921	−	0.822921i
$243$	−71.9549	+	124.630i	−0.296111	+	0.512879i
$244$	−121.255	+	70.0067i	−0.496947	+	0.286913i
$245$	2.35277	−	8.78065i	0.00960313	−	0.0358394i
$246$			142.878i			0.580806i
$247$		0			0
$248$	−333.925			−1.34647
$249$	484.211	+	129.744i	1.94462	+	0.521060i
$250$	87.7995	+	152.073i	0.351198	+	0.608293i
$251$	97.1096	+	56.0663i	0.386891	+	0.223372i	0.680812	−	0.732458i	$-0.261627\pi$
$251$	97.1096	+	56.0663i	0.386891	+	0.223372i	−0.293921	+	0.955830i	$0.594960\pi$
$252$	116.276	−	116.276i	0.461412	−	0.461412i
$253$	0.670731	+	2.50320i	0.00265111	+	0.00989408i
$254$	−10.5599	+	2.82953i	−0.0415746	+	0.0111399i
$255$	138.048	+	138.048i	0.541365	+	0.541365i
$256$	−128.790	+	223.071i	−0.503087	+	0.871372i
$257$	323.389	−	186.709i	1.25832	−	0.726493i	0.285575	−	0.958356i	$-0.407815\pi$
$257$	323.389	−	186.709i	1.25832	−	0.726493i	0.972748	+	0.231863i	$0.0744822\pi$
$258$	154.077	−	575.023i	0.597198	−	2.22877i
$259$		−	26.1442i		−	0.100943i
$260$		0			0
$261$	311.240			1.19249
$262$	−133.054	−	35.6518i	−0.507841	−	0.136076i
$263$	−163.801	−	283.712i	−0.622818	−	1.07875i	−0.988959	−	0.148192i	$-0.952655\pi$
$263$	−163.801	−	283.712i	−0.622818	−	1.07875i	0.366141	−	0.930559i	$-0.380679\pi$
$264$	29.2969	+	16.9146i	0.110973	+	0.0640704i
$265$	−72.7558	+	72.7558i	−0.274550	+	0.274550i
$266$	2.69814	+	10.0696i	0.0101434	+	0.0378557i
$267$	−409.014	+	109.595i	−1.53189	+	0.410468i
$268$	102.990	+	102.990i	0.384291	+	0.384291i
$269$	−137.084	+	237.436i	−0.509605	+	0.882661i	0.490333	+	0.871535i	$0.336875\pi$
$269$	−137.084	+	237.436i	−0.509605	+	0.882661i	−0.999938	+	0.0111263i	$0.996458\pi$
$270$	−116.277	+	67.1324i	−0.430655	+	0.248639i
$271$	−58.2447	+	217.372i	−0.214925	+	0.802112i	0.771268	+	0.636511i	$0.219623\pi$
$271$	−58.2447	+	217.372i	−0.214925	+	0.802112i	−0.986193	+	0.165601i	$0.947044\pi$
$272$			490.082i			1.80177i
$273$		0			0
$274$	389.709			1.42230
$275$	25.3256	+	6.78597i	0.0920931	+	0.0246763i
$276$	−8.62137	−	14.9327i	−0.0312369	−	0.0541038i
$277$	349.428	+	201.742i	1.26147	+	0.728312i	0.973360	−	0.229284i	$-0.0736384\pi$
$277$	349.428	+	201.742i	1.26147	+	0.728312i	0.288114	+	0.957596i	$0.406972\pi$
$278$	−127.783	+	127.783i	−0.459651	+	0.459651i
$279$	−242.403	−	904.661i	−0.868829	−	3.24251i
$280$	57.6758	−	15.4542i	0.205985	−	0.0551935i
$281$	356.187	+	356.187i	1.26757	+	1.26757i	0.947340	+	0.320228i	$0.103760\pi$
$281$	356.187	+	356.187i	1.26757	+	1.26757i	0.320228	+	0.947340i	$0.396240\pi$
$282$	−203.257	+	352.052i	−0.720770	+	1.24841i
$283$	302.969	−	174.919i	1.07056	−	0.618089i	0.142226	−	0.989834i	$-0.454574\pi$
$283$	302.969	−	174.919i	1.07056	−	0.618089i	0.928335	+	0.371746i	$0.121241\pi$
$284$	−27.0735	+	101.040i	−0.0953293	+	0.355774i
$285$		−	5.31137i		−	0.0186364i
$286$		0			0
$287$	79.4237			0.276738
$288$	−367.396	−	98.4433i	−1.27568	−	0.341817i
$289$	162.156	+	280.863i	0.561095	+	0.971845i
$290$	−61.3263	−	35.4067i	−0.211470	−	0.122092i
$291$	240.346	−	240.346i	0.825931	−	0.825931i
$292$	29.2159	+	109.035i	0.100054	+	0.373408i
$293$	519.890	−	139.304i	1.77437	−	0.475441i	0.784831	−	0.619710i	$-0.212750\pi$
$293$	519.890	−	139.304i	1.77437	−	0.475441i	0.989539	+	0.144269i	$0.0460829\pi$
$294$	48.4355	+	48.4355i	0.164747	+	0.164747i
$295$	−58.2041	+	100.812i	−0.197302	+	0.341737i
$296$	−19.9389	+	11.5117i	−0.0673611	+	0.0388909i
$297$	−10.9442	+	40.8443i	−0.0368492	+	0.137523i
$298$		−	281.673i		−	0.945211i
$299$		0			0
$300$	−174.450			−0.581499
$301$	−319.646	−	85.6489i	−1.06195	−	0.284548i
$302$	264.541	+	458.198i	0.875962	+	1.51721i
$303$	−328.548	−	189.687i	−1.08432	−	0.626031i
$304$	9.42790	−	9.42790i	0.0310128	−	0.0310128i
$305$	−36.9066	−	137.737i	−0.121005	−	0.451598i
$306$	−914.195	+	244.958i	−2.98757	+	0.800516i
$307$	−340.580	−	340.580i	−1.10938	−	1.10938i	−0.993232	−	0.116150i	$-0.962945\pi$
$307$	−340.580	−	340.580i	−1.10938	−	1.10938i	−0.116150	−	0.993232i	$-0.537055\pi$
$308$	−5.89144	+	10.2043i	−0.0191280	+	0.0331307i
$309$	−347.584	+	200.678i	−1.12487	+	0.649442i
$310$	−55.1517	+	205.829i	−0.177909	+	0.663965i
$311$		−	100.353i		−	0.322679i	−0.986899	−	0.161339i	$-0.948419\pi$
$311$		−	100.353i		−	0.322679i	0.986899	−	0.161339i	$-0.0515814\pi$
$312$		0			0
$313$	89.9264			0.287305			0.143652	−	0.989628i	$-0.454115\pi$
$313$	89.9264			0.287305			0.143652	+	0.989628i	$0.454115\pi$
$314$	−276.456	−	74.0761i	−0.880432	−	0.235911i
$315$	83.7361	+	145.035i	0.265829	+	0.460429i
$316$	−65.5265	−	37.8317i	−0.207362	−	0.119721i
$317$	−285.497	+	285.497i	−0.900622	+	0.900622i	−0.995490	−	0.0948677i	$-0.969757\pi$
$317$	−285.497	+	285.497i	−0.900622	+	0.900622i	0.0948677	+	0.995490i	$0.469757\pi$
$318$	−200.666	−	748.897i	−0.631026	−	2.35502i
$319$	−21.5420	+	5.77215i	−0.0675297	+	0.0180945i
$320$	−26.6436	−	26.6436i	−0.0832612	−	0.0832612i
$321$	187.754	−	325.199i	0.584902	−	1.01308i
$322$	−29.8495	+	17.2336i	−0.0927003	+	0.0535205i
$323$	4.31856	−	16.1171i	0.0133702	−	0.0498981i
$324$		−	56.1983i		−	0.173452i
$325$		0			0
$326$	348.783			1.06989
$327$	−144.669	−	38.7638i	−0.442412	−	0.118544i
$328$	−34.9716	−	60.5725i	−0.106621	−	0.184672i
$329$	195.700	+	112.987i	0.594832	+	0.343427i
$330$	15.2648	−	15.2648i	0.0462569	−	0.0462569i
$331$	39.7923	+	148.507i	0.120218	+	0.448661i	0.999624	−	0.0274116i	$-0.00872647\pi$
$331$	39.7923	+	148.507i	0.120218	+	0.448661i	−0.879406	+	0.476073i	$0.842060\pi$
$332$	148.521	−	39.7962i	0.447353	−	0.119868i
$333$	−45.6613	−	45.6613i	−0.137121	−	0.137121i
$334$	−37.3566	+	64.7036i	−0.111846	+	0.193723i
$335$	−128.463	+	74.1682i	−0.383472	+	0.221398i
$336$	−169.125	+	631.184i	−0.503349	+	1.87852i
$337$			366.843i			1.08855i	0.838905	+	0.544277i	$0.183196\pi$
$337$			366.843i			1.08855i	−0.838905	+	0.544277i	$0.816804\pi$
$338$		0			0
$339$	−463.183			−1.36632
$340$	57.8421	+	15.4987i	0.170124	+	0.0455845i
$341$	33.5551	+	58.1192i	0.0984021	+	0.170437i
$342$	22.2991	+	12.8744i	0.0652020	+	0.0376444i
$343$	254.675	−	254.675i	0.742493	−	0.742493i
$344$	75.4252	+	281.491i	0.219259	+	0.818287i
$345$	16.9624	−	4.54507i	0.0491665	−	0.0131741i
$346$	144.827	+	144.827i	0.418576	+	0.418576i
$347$	−200.347	+	347.011i	−0.577369	+	1.00003i	0.418411	+	0.908258i	$0.362587\pi$
$347$	−200.347	+	347.011i	−0.577369	+	1.00003i	−0.995780	+	0.0917743i	$0.970746\pi$
$348$	128.507	−	74.1935i	0.369273	−	0.213200i
$349$	116.567	−	435.035i	0.334004	−	1.24652i	−0.570941	−	0.820991i	$-0.693421\pi$
$349$	116.567	−	435.035i	0.334004	−	1.24652i	0.904945	−	0.425529i	$-0.139912\pi$
$350$			348.715i			0.996327i
$351$		0			0
$352$	27.2544			0.0774273
$353$	−436.385	−	116.929i	−1.23622	−	0.331244i	−0.419220	−	0.907885i	$-0.637696\pi$
$353$	−436.385	−	116.929i	−1.23622	−	0.331244i	−0.816998	+	0.576641i	$0.804363\pi$
$354$	−438.580	−	759.643i	−1.23893	−	2.14589i
$355$	−92.2608	−	53.2668i	−0.259890	−	0.150047i
$356$	−91.8403	+	91.8403i	−0.257978	+	0.257978i
$357$	211.652	+	789.895i	0.592862	+	2.21259i
$358$	328.863	−	88.1187i	0.918613	−	0.246142i
$359$	167.150	+	167.150i	0.465598	+	0.465598i	0.900485	−	0.434887i	$-0.143212\pi$
$359$	167.150	+	167.150i	0.465598	+	0.465598i	−0.434887	+	0.900485i	$0.643212\pi$
$360$	73.7408	−	127.723i	0.204836	−	0.354786i
$361$	312.242	−	180.273i	0.864936	−	0.499371i
$362$	−35.0269	+	130.722i	−0.0967593	+	0.361111i
$363$			601.044i			1.65577i
$364$		0			0
$365$	−114.964			−0.314969
$366$	1037.88	+	278.099i	2.83574	+	0.759834i
$367$	−339.395	−	587.849i	−0.924782	−	1.60177i	−0.791912	−	0.610635i	$-0.790914\pi$
$367$	−339.395	−	587.849i	−0.924782	−	1.60177i	−0.132870	−	0.991133i	$-0.542419\pi$
$368$	38.1767	+	22.0413i	0.103741	+	0.0598949i
$369$	138.715	−	138.715i	0.375921	−	0.375921i
$370$	3.80259	+	14.1915i	0.0102773	+	0.0383553i
$371$	−416.300	+	111.547i	−1.12210	+	0.300666i
$372$	−315.739	−	315.739i	−0.848760	−	0.848760i
$373$	55.5691	−	96.2484i	0.148979	−	0.258039i	−0.781872	−	0.623440i	$-0.785735\pi$
$373$	55.5691	−	96.2484i	0.148979	−	0.258039i	0.930850	+	0.365401i	$0.119068\pi$
$374$	58.7317	−	33.9087i	0.157037	−	0.0906651i
$375$	96.9920	−	361.979i	0.258645	−	0.965278i
$376$		−	199.001i		−	0.529257i
$377$		0			0
$378$	−562.396			−1.48782
$379$	333.186	+	89.2768i	0.879118	+	0.235559i	0.670027	−	0.742337i	$-0.266283\pi$
$379$	333.186	+	89.2768i	0.879118	+	0.235559i	0.209091	+	0.977896i	$0.432949\pi$
$380$	−0.814575	−	1.41089i	−0.00214362	−	0.00371286i
$381$	20.2053	+	11.6656i	0.0530324	+	0.0306183i
$382$	−113.004	+	113.004i	−0.295823	+	0.295823i
$383$	100.507	+	375.095i	0.262419	+	0.979361i	0.963811	+	0.266586i	$0.0858956\pi$
$383$	100.507	+	375.095i	0.262419	+	0.979361i	−0.701392	+	0.712776i	$0.747438\pi$
$384$	728.960	−	195.324i	1.89833	−	0.508657i
$385$	−8.48544	−	8.48544i	−0.0220401	−	0.0220401i
$386$	252.996	−	438.201i	0.655429	−	1.13524i
$387$	−707.854	+	408.680i	−1.82908	+	1.05602i
$388$	26.9837	−	100.705i	0.0695457	−	0.259548i
$389$		−	391.807i		−	1.00722i	−0.863932	−	0.503608i	$-0.832006\pi$
$389$		−	391.807i		−	1.00722i	0.863932	−	0.503608i	$-0.167994\pi$
$390$		0			0
$391$	55.1672			0.141093
$392$	−32.3893	−	8.67868i	−0.0826257	−	0.0221395i
$393$	146.985	+	254.586i	0.374008	+	0.647801i
$394$	−322.516	−	186.205i	−0.818568	−	0.472600i
$395$	54.4890	−	54.4890i	0.137947	−	0.137947i
$396$	7.53243	+	28.1114i	0.0190213	+	0.0709884i
$397$	−152.232	+	40.7905i	−0.383456	+	0.102747i	−0.445397	−	0.895333i	$-0.646938\pi$
$397$	−152.232	+	40.7905i	−0.383456	+	0.102747i	0.0619411	+	0.998080i	$0.480271\pi$
$398$	69.7904	+	69.7904i	0.175353	+	0.175353i
$399$	11.1239	−	19.2671i	0.0278794	−	0.0482886i
$400$	386.244	−	222.998i	0.965610	−	0.557495i
$401$	−137.780	+	514.202i	−0.343591	+	1.28230i	0.550658	+	0.834731i	$0.314377\pi$
$401$	−137.780	+	514.202i	−0.343591	+	1.28230i	−0.894249	+	0.447569i	$0.852290\pi$
$402$		−	1117.75i		−	2.78047i
$403$		0			0
$404$	−116.365			−0.288032
$405$	55.2848	+	14.8135i	0.136506	+	0.0365766i
$406$	−148.308	−	256.878i	−0.365292	−	0.632704i
$407$	4.00719	+	2.31355i	0.00984568	+	0.00568441i
$408$	509.220	−	509.220i	1.24809	−	1.24809i
$409$	72.0792	+	269.003i	0.176233	+	0.657710i	0.996338	+	0.0854974i	$0.0272479\pi$
$409$	72.0792	+	269.003i	0.176233	+	0.657710i	−0.820106	+	0.572212i	$0.806085\pi$
$410$	−43.1124	+	11.5519i	−0.105152	+	0.0281755i
$411$	−588.090	−	588.090i	−1.43088	−	1.43088i
$412$	−61.5536	+	106.614i	−0.149402	+	0.258772i
$413$	−422.274	+	243.800i	−1.02245	+	0.590314i
$414$	−22.0338	+	82.2314i	−0.0532219	+	0.198627i
$415$			156.597i			0.377342i
$416$		0			0
$417$	385.661			0.924847
$418$	−1.78216	−	0.477528i	−0.00426354	−	0.00114241i
$419$	244.472	+	423.438i	0.583465	+	1.01059i	0.995065	+	0.0992269i	$0.0316370\pi$
$419$	244.472	+	423.438i	0.583465	+	1.01059i	−0.411599	+	0.911365i	$0.635030\pi$
$420$	69.1471	+	39.9221i	0.164636	+	0.0950526i
$421$	−375.601	+	375.601i	−0.892163	+	0.892163i	−0.994726	−	0.102563i	$-0.967296\pi$
$421$	−375.601	+	375.601i	−0.892163	+	0.892163i	0.102563	+	0.994726i	$0.467296\pi$
$422$	−43.1125	−	160.898i	−0.102162	−	0.381275i
$423$	539.127	−	144.459i	1.27453	−	0.341510i
$424$	268.375	+	268.375i	0.632960	+	0.632960i
$425$	279.071	−	483.365i	0.656637	−	1.13733i
$426$	695.205	−	401.377i	1.63194	−	0.942200i
$427$	154.591	−	576.941i	0.362039	−	1.35115i
$428$		−	115.179i		−	0.269110i
$429$		0			0
$430$	185.966			0.432480
$431$	−114.753	−	30.7479i	−0.266247	−	0.0713407i	0.123226	−	0.992379i	$-0.460676\pi$
$431$	−114.753	−	30.7479i	−0.266247	−	0.0713407i	−0.389473	+	0.921038i	$0.627343\pi$
$432$	359.644	+	622.922i	0.832510	+	1.44195i
$433$	120.208	+	69.4021i	0.277617	+	0.160282i	0.632344	−	0.774688i	$-0.282093\pi$
$433$	120.208	+	69.4021i	0.277617	+	0.160282i	−0.354727	+	0.934970i	$0.615426\pi$
$434$	−631.143	+	631.143i	−1.45425	+	1.45425i
$435$	39.1138	+	145.975i	0.0899168	+	0.335574i
$436$	−44.3740	+	11.8900i	−0.101775	+	0.0272706i
$437$	−1.06127	−	1.06127i	−0.00242854	−	0.00242854i
$438$	433.138	−	750.217i	0.988900	−	1.71282i
$439$	−121.509	+	70.1532i	−0.276786	+	0.159802i	−0.631967	−	0.774995i	$-0.717752\pi$
$439$	−121.509	+	70.1532i	−0.276786	+	0.159802i	0.355182	+	0.934797i	$0.384419\pi$
$440$	−2.73515	+	10.2077i	−0.00621624	+	0.0231993i
$441$		−	94.0482i		−	0.213261i
$442$		0			0
$443$	390.577			0.881664			0.440832	−	0.897590i	$-0.354684\pi$
$443$	390.577			0.881664			0.440832	+	0.897590i	$0.354684\pi$
$444$	−29.7377	−	7.96819i	−0.0669768	−	0.0179464i
$445$	−66.1388	−	114.556i	−0.148627	−	0.257429i
$446$	311.139	+	179.636i	0.697620	+	0.402771i
$447$	−425.058	+	425.058i	−0.950913	+	0.950913i
$448$	−40.8492	−	152.451i	−0.0911813	−	0.340293i
$449$	−291.660	+	78.1501i	−0.649577	+	0.174054i	−0.568538	−	0.822657i	$-0.692491\pi$
$449$	−291.660	+	78.1501i	−0.649577	+	0.174054i	−0.0810394	+	0.996711i	$0.525824\pi$
$450$	609.036	+	609.036i	1.35341	+	1.35341i
$451$	−7.02837	+	12.1735i	−0.0155840	+	0.0269922i
$452$	−123.038	+	71.0357i	−0.272207	+	0.157159i
$453$	292.238	−	1090.65i	0.645116	−	2.40761i
$454$			172.158i			0.379203i
$455$		0			0
$456$	−19.5921			−0.0429652
$457$	294.593	+	78.9361i	0.644625	+	0.172727i	0.566297	−	0.824201i	$-0.308375\pi$
$457$	294.593	+	78.9361i	0.644625	+	0.172727i	0.0783273	+	0.996928i	$0.475042\pi$
$458$	304.107	+	526.729i	0.663990	+	1.15006i
$459$	779.556	+	450.077i	1.69838	+	0.980559i
$460$	3.80876	−	3.80876i	0.00827992	−	0.00827992i
$461$	−209.108	−	780.401i	−0.453596	−	1.69284i	−0.692183	−	0.721722i	$-0.743351\pi$
$461$	−209.108	−	780.401i	−0.453596	−	1.69284i	0.238587	−	0.971121i	$-0.423316\pi$
$462$	87.3432	−	23.4035i	0.189054	−	0.0506570i
$463$	411.381	+	411.381i	0.888512	+	0.888512i	0.994380	−	0.105868i	$-0.0337620\pi$
$463$	411.381	+	411.381i	0.888512	+	0.888512i	−0.105868	+	0.994380i	$0.533762\pi$
$464$	−189.682	+	328.540i	−0.408798	+	0.708059i
$465$	393.832	−	227.379i	0.846951	−	0.488988i
$466$	−160.608	+	599.395i	−0.344651	+	1.28626i
$467$		−	279.834i		−	0.599215i	−0.954062	−	0.299608i	$-0.903144\pi$
$467$		−	279.834i		−	0.599215i	0.954062	−	0.299608i	$-0.0968558\pi$
$468$		0			0
$469$	−621.338			−1.32481
$470$	−122.663	−	32.8673i	−0.260984	−	0.0699305i
$471$	305.400	+	528.969i	0.648408	+	1.12308i
$472$	371.868	+	214.698i	0.787856	+	0.454869i
$473$	41.4138	−	41.4138i	0.0875555	−	0.0875555i
$474$	150.285	+	560.872i	0.317057	+	1.18327i
$475$	−14.6673	+	3.93008i	−0.0308785	+	0.00827386i
$476$	177.364	+	177.364i	0.372613	+	0.372613i
$477$	−532.255	+	921.894i	−1.11584	+	1.93269i
$478$	−751.128	+	433.664i	−1.57140	+	0.907247i
$479$	69.2853	−	258.576i	0.144646	−	0.539825i	−0.855125	−	0.518422i	$-0.826520\pi$
$479$	69.2853	−	258.576i	0.144646	−	0.539825i	0.999771	−	0.0214037i	$-0.00681354\pi$
$480$		−	184.684i		−	0.384758i
$481$		0			0
$482$	−145.730			−0.302344
$483$	71.0507	+	19.0380i	0.147103	+	0.0394161i
$484$	92.1788	+	159.658i	0.190452	+	0.329873i
$485$	91.9548	+	53.0902i	0.189598	+	0.109464i
$486$	239.532	−	239.532i	0.492864	−	0.492864i
$487$	−140.372	−	523.877i	−0.288239	−	1.07572i	−0.946440	−	0.322881i	$-0.895349\pi$
$487$	−140.372	−	523.877i	−0.288239	−	1.07572i	0.658201	−	0.752843i	$-0.271318\pi$
$488$	−508.073	+	136.138i	−1.04113	+	0.278971i
$489$	−526.330	−	526.330i	−1.07634	−	1.07634i
$490$	−10.6989	+	18.5311i	−0.0218346	+	0.0378186i
$491$	20.3866	−	11.7702i	0.0415205	−	0.0239719i	−0.479096	−	0.877762i	$-0.659035\pi$
$491$	20.3866	−	11.7702i	0.0415205	−	0.0239719i	0.520617	+	0.853791i	$0.325702\pi$
$492$	24.2067	−	90.3405i	0.0492005	−	0.183619i
$493$			474.756i			0.962993i
$494$		0			0
$495$	−29.6399			−0.0598786
$496$	1102.68	+	295.461i	2.22314	+	0.595688i
$497$	−223.119	−	386.453i	−0.448932	−	0.777572i
$498$	−1021.90	−	589.996i	−2.05201	−	1.18473i
$499$	−105.552	+	105.552i	−0.211527	+	0.211527i	−0.804916	−	0.593389i	$-0.797790\pi$
$499$	−105.552	+	105.552i	−0.211527	+	0.211527i	0.593389	+	0.804916i	$0.297790\pi$
$500$	−29.7502	−	111.029i	−0.0595005	−	0.222059i
$501$	154.014	−	41.2678i	0.307412	−	0.0823709i
$502$	−186.640	−	186.640i	−0.371793	−	0.371793i
$503$	328.495	−	568.970i	0.653071	−	1.13115i	−0.329302	−	0.944225i	$-0.606813\pi$
$503$	328.495	−	568.970i	0.653071	−	1.13115i	0.982374	−	0.186928i	$-0.0598532\pi$
$504$	534.993	−	308.878i	1.06149	−	0.612854i
$505$	30.6731	−	114.473i	0.0607387	−	0.226680i
$506$		−	6.10015i		−	0.0120556i
$507$		0			0
$508$	7.15632			0.0140873
$509$	−754.970	−	202.293i	−1.48324	−	0.397433i	−0.575792	−	0.817596i	$-0.695306\pi$
$509$	−754.970	−	202.293i	−1.48324	−	0.397433i	−0.907449	+	0.420163i	$0.861973\pi$
$510$	−229.776	−	397.983i	−0.450540	−	0.780359i
$511$	−417.034	−	240.775i	−0.816113	−	0.471183i
$512$	3.82036	−	3.82036i	0.00746164	−	0.00746164i
$513$	−6.33831	−	23.6549i	−0.0123554	−	0.0461109i
$514$	−849.037	+	227.499i	−1.65182	+	0.442605i
$515$	−88.6556	−	88.6556i	−0.172147	−	0.172147i
$516$	−194.843	+	337.477i	−0.377602	+	0.654026i
$517$	−34.6357	+	19.9970i	−0.0669937	+	0.0386788i
$518$	−15.9279	+	59.4439i	−0.0307489	+	0.114757i
$519$		−	437.102i		−	0.842201i
$520$		0			0
$521$	408.859			0.784758			0.392379	−	0.919804i	$-0.371652\pi$
$521$	408.859			0.784758			0.392379	+	0.919804i	$0.371652\pi$
$522$	−707.664	−	189.618i	−1.35568	−	0.363253i
$523$	−179.678	−	311.211i	−0.343553	−	0.595050i	0.641537	−	0.767092i	$-0.278297\pi$
$523$	−179.678	−	311.211i	−0.343553	−	0.595050i	−0.985090	+	0.172042i	$0.944964\pi$
$524$	78.0887	+	45.0845i	0.149024	+	0.0860392i
$525$	526.227	−	526.227i	1.00234	−	1.00234i
$526$	199.586	+	744.867i	0.379442	+	1.41610i
$527$	1379.94	−	369.754i	2.61849	−	0.701621i
$528$	−81.7770	−	81.7770i	−0.154881	−	0.154881i
$529$	−262.019	+	453.830i	−0.495310	+	0.857902i
$530$	209.750	−	121.099i	0.395754	−	0.228489i
$531$	−311.707	+	1163.31i	−0.587020	+	2.19079i
$532$		−	6.82403i		−	0.0128271i
$533$		0			0
$534$	996.741			1.86656
$535$	113.306	+	30.3604i	0.211788	+	0.0567484i
$536$	273.585	+	473.863i	0.510420	+	0.884073i
$537$	−629.246	−	363.295i	−1.17178	−	0.676528i
$538$	456.340	−	456.340i	0.848216	−	0.848216i
$539$	1.74419	+	6.50939i	0.00323597	+	0.0120768i
$540$	84.8943	−	22.7473i	0.157212	−	0.0421247i
$541$	−62.1232	−	62.1232i	−0.114830	−	0.114830i	0.647357	−	0.762187i	$-0.275874\pi$
$541$	−62.1232	−	62.1232i	−0.114830	−	0.114830i	−0.762187	+	0.647357i	$0.775874\pi$
$542$	264.861	−	458.753i	0.488674	−	0.846408i
$543$	250.123	−	144.409i	0.460632	−	0.265946i
$544$	150.162	−	560.414i	0.276034	−	1.03017i
$545$		−	46.7868i		−	0.0858473i
$546$		0			0
$547$	−215.610			−0.394167			−0.197084	−	0.980387i	$-0.563147\pi$
$547$	−215.610			−0.394167			−0.197084	+	0.980387i	$0.563147\pi$
$548$	−246.409	−	66.0251i	−0.449652	−	0.120484i
$549$	−737.641	−	1277.63i	−1.34361	−	2.32720i
$550$	−53.4484	−	30.8585i	−0.0971789	−	0.0561063i
$551$	9.13306	−	9.13306i	0.0165754	−	0.0165754i
$552$	−16.7655	−	62.5695i	−0.0303722	−	0.113351i
$553$	311.780	−	83.5411i	0.563797	−	0.151069i
$554$	−671.584	−	671.584i	−1.21225	−	1.21225i
$555$	15.6773	−	27.1539i	0.0282474	−	0.0489260i
$556$	102.445	−	59.1467i	0.184254	−	0.106379i
$557$	−235.589	+	879.229i	−0.422960	+	1.57851i	0.345377	+	0.938464i	$0.387751\pi$
$557$	−235.589	+	879.229i	−0.422960	+	1.57851i	−0.768338	+	0.640045i	$0.778916\pi$
$558$			2204.60i			3.95090i
$559$		0			0
$560$	−204.129			−0.364516
$561$	−139.799	−	37.4590i	−0.249196	−	0.0667718i
$562$	−592.858	−	1026.86i	−1.05491	−	1.82715i
$563$	203.525	+	117.505i	0.361501	+	0.208713i	0.669739	−	0.742597i	$-0.266406\pi$
$563$	203.525	+	117.505i	0.361501	+	0.208713i	−0.308238	+	0.951309i	$0.599739\pi$
$564$	188.162	−	188.162i	0.333621	−	0.333621i
$565$	−37.4491	−	139.762i	−0.0662816	−	0.247366i
$566$	−795.425	+	213.133i	−1.40534	+	0.376561i
$567$	169.522	+	169.522i	0.298981	+	0.298981i
$568$	−196.486	+	340.324i	−0.345926	+	0.599161i
$569$	−607.150	+	350.538i	−1.06705	+	0.616060i	−0.927373	−	0.374137i	$-0.877939\pi$
$569$	−607.150	+	350.538i	−1.06705	+	0.616060i	−0.139674	+	0.990198i	$0.544606\pi$
$570$	−3.23587	+	12.0764i	−0.00567697	+	0.0211867i
$571$		−	323.381i		−	0.566341i	−0.959070	−	0.283170i	$-0.908614\pi$
$571$		−	323.381i		−	0.566341i	0.959070	−	0.283170i	$-0.0913862\pi$
$572$		0			0
$573$	341.058			0.595214
$574$	−180.585	−	48.3877i	−0.314608	−	0.0842991i
$575$	−25.1023	−	43.4784i	−0.0436562	−	0.0756147i
$576$	−337.603	−	194.915i	−0.586116	−	0.338394i
$577$	465.169	−	465.169i	0.806186	−	0.806186i	−0.177868	−	0.984054i	$-0.556920\pi$
$577$	465.169	−	465.169i	0.806186	−	0.806186i	0.984054	+	0.177868i	$0.0569201\pi$
$578$	−197.583	−	737.388i	−0.341838	−	1.27576i
$579$	−1043.05	+	279.484i	−1.80147	+	0.482701i
$580$	32.7773	+	32.7773i	0.0565126	+	0.0565126i
$581$	−327.969	+	568.059i	−0.564491	+	0.977727i
$582$	−692.900	+	400.046i	−1.19055	+	0.687364i
$583$	19.7421	−	73.6784i	0.0338629	−	0.126378i
$584$			424.068i			0.726143i
$585$		0			0
$586$	−1266.94			−2.16201
$587$	220.274	+	59.0221i	0.375253	+	0.100549i	0.441516	−	0.897253i	$-0.354441\pi$
$587$	220.274	+	59.0221i	0.375253	+	0.100549i	−0.0662628	+	0.997802i	$0.521108\pi$
$588$	−22.4192	−	38.8313i	−0.0381280	−	0.0660396i
$589$	−33.6596	−	19.4334i	−0.0571470	−	0.0329939i
$590$	193.757	−	193.757i	0.328401	−	0.328401i
$591$	205.700	+	767.683i	0.348054	+	1.29896i
$592$	76.0271	−	20.3714i	0.128424	−	0.0344112i
$593$	332.603	+	332.603i	0.560883	+	0.560883i	0.929558	−	0.368675i	$-0.120189\pi$
$593$	332.603	+	332.603i	0.560883	+	0.560883i	−0.368675	+	0.929558i	$0.620189\pi$
$594$	49.7675	−	86.1999i	0.0837837	−	0.145118i
$595$	−221.232	+	127.729i	−0.371819	+	0.214670i
$596$	−47.7215	+	178.099i	−0.0800696	+	0.298824i
$597$		−	210.634i		−	0.352821i
$598$		0			0
$599$	−1027.71			−1.71571			−0.857853	−	0.513895i	$-0.828202\pi$
$599$	−1027.71			−1.71571			−0.857853	+	0.513895i	$0.828202\pi$
$600$	−633.033	−	169.621i	−1.05506	−	0.282701i
$601$	230.493	+	399.225i	0.383515	+	0.664268i	0.991562	−	0.129633i	$-0.0413799\pi$
$601$	230.493	+	399.225i	0.383515	+	0.664268i	−0.608047	+	0.793901i	$0.708047\pi$
$602$	674.597	+	389.479i	1.12059	+	0.646975i
$603$	−1085.18	+	1085.18i	−1.79963	+	1.79963i
$604$	−89.6377	−	334.532i	−0.148407	−	0.553862i
$605$	−181.361	+	48.5954i	−0.299769	+	0.0803230i
$606$	631.454	+	631.454i	1.04200	+	1.04200i
$607$	−183.169	+	317.257i	−0.301761	+	0.522665i	−0.976535	−	0.215360i	$-0.930908\pi$
$607$	−183.169	+	317.257i	−0.301761	+	0.522665i	0.674774	+	0.738024i	$0.264241\pi$
$608$	−13.6696	+	7.89216i	−0.0224829	+	0.0129805i
$609$	−163.836	+	611.445i	−0.269025	+	1.00401i
$610$			335.657i			0.550258i
$611$		0			0
$612$	619.537			1.01232
$613$	130.022	+	34.8392i	0.212107	+	0.0568339i	0.363308	−	0.931669i	$-0.381647\pi$
$613$	130.022	+	34.8392i	0.212107	+	0.0568339i	−0.151201	+	0.988503i	$0.548314\pi$
$614$	566.882	+	981.868i	0.923260	+	1.59913i
$615$	82.4911	+	47.6263i	0.134132	+	0.0774411i
$616$	−31.3003	+	31.3003i	−0.0508122	+	0.0508122i
$617$	−204.976	−	764.980i	−0.332214	−	1.23984i	−0.906858	−	0.421436i	$-0.861526\pi$
$617$	−204.976	−	764.980i	−0.332214	−	1.23984i	0.574645	−	0.818403i	$-0.305140\pi$
$618$	912.559	−	244.519i	1.47663	−	0.395662i
$619$	170.666	+	170.666i	0.275713	+	0.275713i	0.831395	−	0.555682i	$-0.187543\pi$
$619$	170.666	+	170.666i	0.275713	+	0.275713i	−0.555682	+	0.831395i	$0.687543\pi$
$620$	69.7437	−	120.800i	0.112490	−	0.194838i
$621$	70.1207	−	40.4842i	0.112916	−	0.0651919i
$622$	−61.1386	+	228.172i	−0.0982935	+	0.366836i
$623$		−	554.072i		−	0.889361i
$624$		0			0
$625$	−446.368			−0.714189
$626$	−204.465	−	54.7863i	−0.326622	−	0.0875180i
$627$	1.96875	+	3.40998i	0.00313995	+	0.00543856i
$628$	162.250	+	93.6750i	0.258360	+	0.149164i
$629$	69.6503	−	69.6503i	0.110732	−	0.110732i
$630$	−102.030	−	380.781i	−0.161952	−	0.604414i
$631$	−76.9356	+	20.6148i	−0.121926	+	0.0326701i	−0.319266	−	0.947665i	$-0.603436\pi$
$631$	−76.9356	+	20.6148i	−0.121926	+	0.0326701i	0.197340	+	0.980335i	$0.436770\pi$
$632$	−200.994	−	200.994i	−0.318029	−	0.318029i
$633$	−177.744	+	307.862i	−0.280796	+	0.486354i
$634$	823.068	−	475.199i	1.29821	−	0.749525i
$635$	−1.88636	+	7.03999i	−0.00297064	+	0.0110866i
$636$			507.517i			0.797983i
$637$		0			0
$638$	52.4964			0.0822828
$639$	−1064.63	−	285.266i	−1.66608	−	0.446426i
$640$	117.875	+	204.166i	0.184180	+	0.319009i
$641$	−449.661	−	259.612i	−0.701500	−	0.405011i	0.106406	−	0.994323i	$-0.466066\pi$
$641$	−449.661	−	259.612i	−0.701500	−	0.405011i	−0.807906	+	0.589312i	$0.799399\pi$
$642$	−625.017	+	625.017i	−0.973546	+	0.973546i
$643$	129.563	+	483.537i	0.201498	+	0.752002i	0.990488	+	0.137596i	$0.0439376\pi$
$643$	129.563	+	483.537i	0.201498	+	0.752002i	−0.788990	+	0.614406i	$0.789396\pi$
$644$	21.7933	−	5.83949i	0.0338405	−	0.00906753i
$645$	−280.632	−	280.632i	−0.435088	−	0.435088i
$646$	−19.6382	+	34.0143i	−0.0303997	+	0.0526538i
$647$	257.204	−	148.497i	0.397533	−	0.229516i	−0.287886	−	0.957665i	$-0.592952\pi$
$647$	257.204	−	148.497i	0.397533	−	0.229516i	0.685419	+	0.728149i	$0.259619\pi$
$648$	54.6427	−	203.929i	0.0843252	−	0.314706i
$649$		−	86.2973i		−	0.132970i
$650$		0			0
$651$	1904.85			2.92604
$652$	−220.532	−	59.0914i	−0.338239	−	0.0906309i
$653$	445.183	+	771.079i	0.681750	+	1.18083i	0.974446	+	0.224620i	$0.0721142\pi$
$653$	445.183	+	771.079i	0.681750	+	1.18083i	−0.292696	+	0.956205i	$0.594552\pi$
$654$	305.316	+	176.274i	0.466844	+	0.269532i
$655$	−64.9353	+	64.9353i	−0.0991378	+	0.0991378i
$656$	61.8865	+	230.964i	0.0943392	+	0.352079i
$657$	−1148.87	+	307.840i	−1.74866	+	0.468553i
$658$	−376.126	−	376.126i	−0.571620	−	0.571620i
$659$	321.640	−	557.097i	0.488073	−	0.845367i	−0.511833	−	0.859085i	$-0.671033\pi$
$659$	321.640	−	557.097i	0.488073	−	0.845367i	0.999906	+	0.0137177i	$0.00436660\pi$
$660$	−12.2379	+	7.06558i	−0.0185423	+	0.0107054i
$661$	−52.5302	+	196.045i	−0.0794708	+	0.296589i	−0.994210	−	0.107456i	$-0.965729\pi$
$661$	−52.5302	+	196.045i	−0.0794708	+	0.296589i	0.914739	+	0.404045i	$0.132396\pi$
$662$		−	361.902i		−	0.546680i
$663$		0			0
$664$	577.641			0.869941
$665$	6.71309	+	1.79877i	0.0100949	+	0.00270491i
$666$	76.0014	+	131.638i	0.114116	+	0.197655i
$667$	36.9828	+	21.3520i	0.0554465	+	0.0320120i
$668$	34.5824	−	34.5824i	0.0517700	−	0.0517700i
$669$	−198.444	−	740.602i	−0.296627	−	1.10703i
$670$	337.272	−	90.3717i	0.503390	−	0.134883i
$671$	74.7492	+	74.7492i	0.111400	+	0.111400i
$672$	386.793	−	669.945i	0.575585	−	0.996942i
$673$	−236.376	+	136.472i	−0.351228	+	0.202781i	−0.665226	−	0.746642i	$-0.731665\pi$
$673$	−236.376	+	136.472i	−0.351228	+	0.202781i	0.313998	+	0.949424i	$0.398331\pi$
$674$	223.493	−	834.088i	0.331592	−	1.23752i
$675$		−	819.179i		−	1.21360i
$676$		0			0
$677$	−413.547			−0.610852			−0.305426	−	0.952216i	$-0.598799\pi$
$677$	−413.547			−0.610852			−0.305426	+	0.952216i	$0.598799\pi$
$678$	1053.14	+	282.187i	1.55330	+	0.416205i
$679$	222.379	+	385.172i	0.327510	+	0.567263i
$680$	194.824	+	112.482i	0.286506	+	0.165415i
$681$	259.795	−	259.795i	0.381490	−	0.381490i
$682$	−40.8859	−	152.588i	−0.0599499	−	0.223736i
$683$	1155.66	−	309.658i	1.69203	−	0.453379i	0.721121	−	0.692809i	$-0.243627\pi$
$683$	1155.66	−	309.658i	1.69203	−	0.453379i	0.970914	+	0.239430i	$0.0769606\pi$
$684$	−11.9183	−	11.9183i	−0.0174244	−	0.0174244i
$685$	129.904	−	225.000i	0.189640	−	0.328466i
$686$	−734.210	+	423.896i	−1.07028	+	0.617925i
$687$	335.947	−	1253.77i	0.489006	−	1.82500i
$688$		−	996.265i		−	1.44806i
$689$		0			0
$690$	−41.3364			−0.0599078
$691$	816.053	+	218.661i	1.18097	+	0.316441i	0.795313	−	0.606200i	$-0.207307\pi$
$691$	816.053	+	218.661i	1.18097	+	0.316441i	0.385661	+	0.922640i	$0.373973\pi$
$692$	−67.0359	−	116.110i	−0.0968727	−	0.167788i
$693$	−107.520	−	62.0764i	−0.155151	−	0.0895764i
$694$	666.939	−	666.939i	0.961007	−	0.961007i
$695$	31.1813	+	116.370i	0.0448652	+	0.167439i
$696$	538.459	−	144.280i	0.773647	−	0.207298i
$697$	211.591	+	211.591i	0.303574	+	0.303574i
$698$	−530.077	+	918.121i	−0.759423	+	1.31536i
$699$	1146.88	−	662.152i	1.64074	−	0.947284i
$700$	59.0797	−	220.489i	0.0843996	−	0.314984i
$701$			765.186i			1.09156i	0.837927	+	0.545782i	$0.183767\pi$
$701$			765.186i			1.09156i	−0.837927	+	0.545782i	$0.816233\pi$
$702$		0			0
$703$	−2.67978			−0.00381192
$704$	26.9815	+	7.22966i	0.0383259	+	0.0102694i
$705$	135.505	+	234.702i	0.192206	+	0.332911i
$706$	920.969	+	531.721i	1.30449	+	0.753147i
$707$	351.015	−	351.015i	0.496485	−	0.496485i
$708$	148.610	+	554.620i	0.209901	+	0.783361i
$709$	−468.858	+	125.630i	−0.661295	+	0.177193i	−0.573830	−	0.818974i	$-0.694543\pi$
$709$	−468.858	+	125.630i	−0.661295	+	0.177193i	−0.0874645	+	0.996168i	$0.527876\pi$
$710$	177.321	+	177.321i	0.249748	+	0.249748i
$711$	398.622	−	690.434i	0.560650	−	0.971075i
$712$	−422.563	+	243.967i	−0.593488	+	0.342650i
$713$	33.2592	−	124.125i	0.0466469	−	0.174089i
$714$		−	1924.92i		−	2.69597i
$715$		0			0
$716$	−222.866			−0.311266
$717$	1787.91	+	479.068i	2.49359	+	0.668157i
$718$	−278.214	−	481.881i	−0.387484	−	0.671143i
$719$	−732.510	−	422.915i	−1.01879	−	0.588199i	−0.105037	−	0.994468i	$-0.533496\pi$
$719$	−732.510	−	422.915i	−1.01879	−	0.588199i	−0.913753	+	0.406269i	$0.866830\pi$
$720$	−356.515	+	356.515i	−0.495159	+	0.495159i
$721$	−135.924	−	507.277i	−0.188522	−	0.703574i
$722$	−819.771	+	219.657i	−1.13542	+	0.304234i
$723$	219.913	+	219.913i	0.304168	+	0.304168i
$724$	44.2942	−	76.7199i	0.0611799	−	0.105967i
$725$	374.165	−	216.024i	0.516090	−	0.297965i
$726$	366.177	−	1366.59i	0.504376	−	1.88236i
$727$			1019.65i			1.40255i	0.712892	+	0.701274i	$0.247385\pi$
$727$			1019.65i			1.40255i	−0.712892	+	0.701274i	$0.752615\pi$
$728$		0			0
$729$	−1051.18			−1.44195
$730$	261.392	+	70.0398i	0.358072	+	0.0959450i
$731$	−623.388	−	1079.74i	−0.852788	−	1.47707i
$732$	−609.125	−	351.678i	−0.832138	−	0.480435i
$733$	−565.267	+	565.267i	−0.771170	+	0.771170i	−0.978311	−	0.207141i	$-0.933584\pi$
$733$	−565.267	+	565.267i	−0.771170	+	0.771170i	0.207141	+	0.978311i	$0.433584\pi$
$734$	413.542	+	1543.36i	0.563409	+	2.10267i
$735$	44.1096	−	11.8191i	0.0600130	−	0.0160804i
$736$	−36.9019	−	36.9019i	−0.0501385	−	0.0501385i
$737$	54.9834	−	95.2341i	0.0746044	−	0.129219i
$738$	−399.905	+	230.885i	−0.541877	+	0.312853i
$739$	72.6381	−	271.089i	0.0982924	−	0.366832i	−0.899206	−	0.437526i	$-0.855855\pi$
$739$	72.6381	−	271.089i	0.0982924	−	0.366832i	0.997498	+	0.0706941i	$0.0225214\pi$
$740$		−	9.61737i		−	0.0129964i
$741$		0			0
$742$	1014.50			1.36725
$743$	941.890	+	252.379i	1.26768	+	0.339675i	0.829143	−	0.559036i	$-0.188829\pi$
$743$	941.890	+	252.379i	1.26768	+	0.339675i	0.438541	+	0.898711i	$0.355495\pi$
$744$	−838.736	−	1452.73i	−1.12733	−	1.95260i
$745$	−162.625	−	93.8913i	−0.218288	−	0.126029i
$746$	−184.985	+	184.985i	−0.247969	+	0.247969i
$747$	419.321	+	1564.93i	0.561340	+	2.09495i
$748$	−42.8803	+	11.4897i	−0.0573266	+	0.0153606i
$749$	347.437	+	347.437i	0.463867	+	0.463867i
$750$	−441.060	+	763.939i	−0.588081	+	1.01859i
$751$	732.187	−	422.729i	0.974950	−	0.562888i	0.0742082	−	0.997243i	$-0.476357\pi$
$751$	732.187	−	422.729i	0.974950	−	0.562888i	0.900742	+	0.434355i	$0.143024\pi$
$752$	−176.078	+	657.133i	−0.234146	+	0.873847i
$753$			563.297i			0.748071i
$754$		0			0
$755$	352.722			0.467181
$756$	355.597	+	95.2819i	0.470366	+	0.126034i
$757$	607.165	+	1051.64i	0.802067	+	1.38922i	0.918253	+	0.395994i	$0.129600\pi$
$757$	607.165	+	1051.64i	0.802067	+	1.38922i	−0.116186	+	0.993227i	$0.537067\pi$
$758$	−703.172	−	405.976i	−0.927667	−	0.535589i
$759$	−9.20542	+	9.20542i	−0.0121283	+	0.0121283i
$760$	−1.58405	−	5.91177i	−0.00208428	−	0.00777865i
$761$	647.756	−	173.566i	0.851191	−	0.228076i	0.193254	−	0.981149i	$-0.438096\pi$
$761$	647.756	−	173.566i	0.851191	−	0.228076i	0.657937	+	0.753073i	$0.271429\pi$
$762$	−38.8337	−	38.8337i	−0.0509629	−	0.0509629i
$763$	97.9880	−	169.720i	0.128425	−	0.222438i
$764$	90.5968	−	52.3061i	0.118582	−	0.0684635i
$765$	−163.306	+	609.466i	−0.213472	+	0.796687i
$766$		−	914.084i		−	1.19332i
$767$		0			0
$768$	−1293.95			−1.68484
$769$	−1053.30	−	282.232i	−1.36971	−	0.367011i	−0.502334	−	0.864673i	$-0.667525\pi$
$769$	−1053.30	−	282.232i	−1.36971	−	0.367011i	−0.867371	+	0.497662i	$0.834192\pi$
$770$	14.1237	+	24.4629i	0.0183424	+	0.0317700i
$771$	1624.54	+	937.931i	2.10706	+	1.21651i
$772$	−234.207	+	234.207i	−0.303377	+	0.303377i
$773$	−41.9712	−	156.639i	−0.0542965	−	0.202637i	0.933449	−	0.358710i	$-0.116783\pi$
$773$	−41.9712	−	156.639i	−0.0542965	−	0.202637i	−0.987746	+	0.156073i	$0.950117\pi$
$774$	1858.43	−	497.964i	2.40107	−	0.643364i
$775$	−919.316	−	919.316i	−1.18621	−	1.18621i
$776$	195.834	−	339.195i	0.252364	−	0.437107i
$777$	113.740	−	65.6677i	0.146383	−	0.0845144i
$778$	−238.702	+	890.849i	−0.306815	+	1.14505i
$779$		−	8.14093i		−	0.0104505i
$780$		0			0
$781$	78.9770			0.101123
$782$	−125.433	−	33.6098i	−0.160401	−	0.0429792i
$783$	348.397	+	603.442i	0.444952	+	0.770679i
$784$	99.2756	+	57.3168i	0.126627	+	0.0731082i
$785$	−134.920	+	134.920i	−0.171873	+	0.171873i
$786$	−179.097	−	668.398i	−0.227858	−	0.850379i
$787$	−8.49841	+	2.27714i	−0.0107985	+	0.00289345i	−0.264214	−	0.964464i	$-0.585113\pi$
$787$	−8.49841	+	2.27714i	−0.0107985	+	0.00289345i	0.253416	+	0.967357i	$0.418446\pi$
$788$	172.376	+	172.376i	0.218752	+	0.218752i
$789$	822.854	−	1425.22i	1.04291	−	1.80637i
$790$	−157.088	+	90.6948i	−0.198846	+	0.114804i
$791$	156.863	−	585.421i	0.198310	−	0.740103i
$792$			109.333i			0.138047i
$793$		0			0
$794$	370.980			0.467230
$795$	−499.267	−	133.778i	−0.628008	−	0.168274i
$796$	−32.3037	−	55.9517i	−0.0405826	−	0.0702911i
$797$	618.344	+	357.001i	0.775840	+	0.447931i	0.834954	−	0.550320i	$-0.185494\pi$
$797$	618.344	+	357.001i	0.775840	+	0.447931i	−0.0591141	+	0.998251i	$0.518828\pi$
$798$	−37.0305	+	37.0305i	−0.0464042	+	0.0464042i
$799$	220.353	+	822.368i	0.275786	+	1.02925i
$800$	−510.001	+	136.654i	−0.637502	+	0.170818i
$801$	−967.696	−	967.696i	−1.20811	−	1.20811i
$802$	626.540	−	1085.20i	0.781221	−	1.35312i
$803$	73.8083	−	42.6132i	0.0919157	−	0.0530676i
$804$	−189.370	+	706.740i	−0.235535	+	0.879030i
$805$			22.9782i			0.0285444i
$806$		0			0
$807$	−1377.28			−1.70666
$808$	−422.259	−	113.144i	−0.522598	−	0.140030i
$809$	−190.814	−	330.499i	−0.235864	−	0.408528i	0.723659	−	0.690157i	$-0.242459\pi$
$809$	−190.814	−	330.499i	−0.235864	−	0.408528i	−0.959523	+	0.281629i	$0.909125\pi$
$810$	−116.676	−	67.3627i	−0.144044	−	0.0831639i
$811$	139.562	−	139.562i	0.172086	−	0.172086i	−0.615809	−	0.787895i	$-0.711171\pi$
$811$	139.562	−	139.562i	0.172086	−	0.172086i	0.787895	+	0.615809i	$0.211171\pi$
$812$	50.2533	+	187.548i	0.0618883	+	0.230970i
$813$	−1091.97	+	292.592i	−1.34314	+	0.359892i
$814$	−7.70163	−	7.70163i	−0.00946146	−	0.00946146i
$815$	116.261	−	201.371i	0.142652	−	0.247081i
$816$	−2132.09	+	1230.96i	−2.61286	+	1.50853i
$817$	−8.77901	+	32.7637i	−0.0107454	+	0.0401025i
$818$		−	655.544i		−	0.801399i
$819$		0			0
$820$	29.2167			0.0356301
$821$	−732.854	−	196.368i	−0.892635	−	0.239181i	−0.216785	−	0.976219i	$-0.569557\pi$
$821$	−732.854	−	196.368i	−0.892635	−	0.239181i	−0.675851	+	0.737039i	$0.736224\pi$
$822$	978.851	+	1695.42i	1.19082	+	2.06256i
$823$	−1372.60	−	792.473i	−1.66781	−	0.962908i	−0.968818	−	0.247773i	$-0.920301\pi$
$823$	−1372.60	−	792.473i	−1.66781	−	0.962908i	−0.698987	−	0.715134i	$-0.746366\pi$
$824$	−327.025	+	327.025i	−0.396875	+	0.396875i
$825$	34.0893	+	127.223i	0.0413204	+	0.154210i
$826$	1108.65	−	297.062i	1.34219	−	0.359640i
$827$	380.972	+	380.972i	0.460668	+	0.460668i	0.898874	−	0.438207i	$-0.144386\pi$
$827$	380.972	+	380.972i	0.460668	+	0.460668i	−0.438207	+	0.898874i	$0.644386\pi$
$828$	27.8635	−	48.2611i	0.0336516	−	0.0582863i
$829$	−926.803	+	535.090i	−1.11798	+	0.645464i	−0.940884	−	0.338730i	$-0.890003\pi$
$829$	−926.803	+	535.090i	−1.11798	+	0.645464i	−0.177093	+	0.984194i	$0.556669\pi$
$830$	95.4042	−	356.053i	0.114945	−	0.428980i
$831$			2026.91i			2.43912i
$832$		0			0
$833$	143.458			0.172219
$834$	−876.876	−	234.958i	−1.05141	−	0.281724i
$835$	24.9045	+	43.1359i	0.0298258	+	0.0516597i
$836$	1.04594	+	0.603872i	0.00125112	+	0.000722335i
$837$	1482.64	−	1482.64i	1.77138	−	1.77138i
$838$	−297.882	−	1111.71i	−0.355467	−	1.32662i
$839$	−811.649	+	217.481i	−0.967400	+	0.259214i	−0.707730	−	0.706483i	$-0.750281\pi$
$839$	−811.649	+	217.481i	−0.967400	+	0.259214i	−0.259670	+	0.965697i	$0.583614\pi$
$840$	212.100	+	212.100i	0.252500	+	0.252500i
$841$	236.750	−	410.062i	0.281510	−	0.487589i
$842$	1082.83	−	625.172i	1.28602	−	0.742485i
$843$	−654.930	+	2444.23i	−0.776904	+	2.89945i
$844$			109.038i			0.129192i
$845$		0			0
$846$	−1313.82			−1.55298
$847$	−759.666	−	203.552i	−0.896890	−	0.240321i
$848$	−648.757	−	1123.68i	−0.765043	−	1.32509i
$849$	1521.96	+	878.705i	1.79265	+	1.03499i
$850$	−929.004	+	929.004i	−1.09295	+	1.09295i
$851$	−2.29315	−	8.55817i	−0.00269466	−	0.0100566i
$852$	−507.573	+	136.004i	−0.595743	+	0.159629i
$853$	500.522	+	500.522i	0.586778	+	0.586778i	0.936757	−	0.349979i	$-0.113811\pi$
$853$	500.522	+	500.522i	0.586778	+	0.586778i	−0.349979	+	0.936757i	$0.613811\pi$
$854$	−702.984	+	1217.60i	−0.823167	+	1.42577i
$855$	14.8661	−	8.58295i	0.0173873	−	0.0100385i
$856$	111.991	−	417.955i	0.130830	−	0.488265i
$857$			175.305i			0.204556i	0.994756	+	0.102278i	$0.0326132\pi$
$857$			175.305i			0.204556i	−0.994756	+	0.102278i	$0.967387\pi$
$858$		0			0
$859$	1523.72			1.77384			0.886918	−	0.461928i	$-0.152842\pi$
$859$	1523.72			1.77384			0.886918	+	0.461928i	$0.152842\pi$
$860$	−117.584	−	31.5067i	−0.136726	−	0.0366357i
$861$	199.492	+	345.531i	0.231698	+	0.401314i
$862$	242.180	+	139.822i	0.280951	+	0.162207i
$863$	−525.826	+	525.826i	−0.609300	+	0.609300i	−0.942763	−	0.333463i	$-0.891783\pi$
$863$	−525.826	+	525.826i	−0.609300	+	0.609300i	0.333463	+	0.942763i	$0.391783\pi$
$864$	−220.392	−	822.514i	−0.255083	−	0.951984i
$865$	131.892	−	35.3404i	0.152477	−	0.0408560i
$866$	−231.034	−	231.034i	−0.266783	−	0.266783i
$867$	−814.592	+	1410.91i	−0.939552	+	1.62735i
$868$	505.994	−	292.136i	0.582943	−	0.336562i
$869$	−14.7854	+	55.1800i	−0.0170143	+	0.0634983i
$870$		−	355.731i		−	0.408887i
$871$		0			0
$872$	−172.583			−0.197916
$873$	1061.10	+	284.320i	1.21546	+	0.325682i
$874$	1.76645	+	3.05957i	0.00202110	+	0.00350066i
$875$	424.661	+	245.178i	0.485327	+	0.280204i
$876$	−400.972	+	400.972i	−0.457730	+	0.457730i
$877$	165.712	+	618.447i	0.188954	+	0.705185i	0.993749	+	0.111633i	$0.0356082\pi$
$877$	165.712	+	618.447i	0.188954	+	0.705185i	−0.804796	+	0.593552i	$0.797725\pi$
$878$	319.014	−	85.4795i	0.363342	−	0.0973571i
$879$	1911.87	+	1911.87i	2.17505	+	2.17505i
$880$	18.0638	−	31.2874i	0.0205270	−	0.0355539i
$881$	−964.522	+	556.867i	−1.09480	+	0.632085i	−0.934851	−	0.355039i	$-0.884467\pi$
$881$	−964.522	+	556.867i	−1.09480	+	0.632085i	−0.159953	+	0.987125i	$0.551134\pi$
$882$	−57.2974	+	213.837i	−0.0649630	+	0.242445i
$883$		−	206.038i		−	0.233338i	−0.993171	−	0.116669i	$-0.962778\pi$
$883$		−	206.038i		−	0.233338i	0.993171	−	0.116669i	$-0.0372217\pi$
$884$		0			0
$885$	−584.776			−0.660764
$886$	−888.052	−	237.953i	−1.00232	−	0.268570i
$887$	−299.698	−	519.092i	−0.337878	−	0.585222i	0.646155	−	0.763206i	$-0.276376\pi$
$887$	−299.698	−	519.092i	−0.337878	−	0.585222i	−0.984033	+	0.177984i	$0.943042\pi$
$888$	−100.163	−	57.8291i	−0.112796	−	0.0651228i
$889$	−21.5870	+	21.5870i	−0.0242824	+	0.0242824i
$890$	80.5881	+	300.759i	0.0905484	+	0.337931i
$891$	−40.9845	+	10.9818i	−0.0459983	+	0.0123252i
$892$	−166.295	−	166.295i	−0.186430	−	0.186430i
$893$	11.5812	−	20.0592i	0.0129689	−	0.0224627i
$894$	1225.41	−	707.492i	1.37071	−	0.791378i
$895$	58.7460	−	219.243i	0.0656380	−	0.244964i
$896$			987.489i			1.10211i
$897$		0			0
$898$	710.758			0.791489
$899$	1068.19	+	286.221i	1.18820	+	0.318377i
$900$	−281.903	−	488.271i	−0.313226	−	0.542523i
$901$	−1406.23	−	811.886i	−1.56074	−	0.901094i
$902$	23.3969	−	23.3969i	0.0259389	−	0.0259389i
$903$	−430.257	−	1605.74i	−0.476475	−	1.77823i
$904$	−515.541	+	138.139i	−0.570289	+	0.152808i
$905$	63.7970	+	63.7970i	0.0704939	+	0.0704939i
$906$	−1328.92	+	2301.75i	−1.46680	+	2.54057i
$907$	399.745	−	230.793i	0.440733	−	0.254457i	−0.263176	−	0.964748i	$-0.584770\pi$
$907$	399.745	−	230.793i	0.440733	−	0.254457i	0.703908	+	0.710291i	$0.251437\pi$
$908$	29.1673	−	108.854i	0.0321225	−	0.119883i
$909$		−	1226.11i		−	1.34885i
$910$		0			0
$911$	1377.94			1.51256			0.756281	−	0.654247i	$-0.227014\pi$
$911$	1377.94			1.51256			0.756281	+	0.654247i	$0.227014\pi$
$912$	64.6964	+	17.3353i	0.0709390	+	0.0190080i
$913$	−58.0453	−	100.537i	−0.0635765	−	0.110118i
$914$	−621.725	−	358.953i	−0.680224	−	0.392728i
$915$	506.523	−	506.523i	0.553577	−	0.553577i
$916$	−103.045	−	384.568i	−0.112494	−	0.419834i
$917$	−371.552	+	99.5570i	−0.405182	+	0.108568i
$918$	−1498.27	−	1498.27i	−1.63210	−	1.63210i
$919$	58.7147	−	101.697i	0.0638898	−	0.110660i	−0.832311	−	0.554309i	$-0.812983\pi$
$919$	58.7147	−	101.697i	0.0638898	−	0.110660i	0.896201	+	0.443648i	$0.146316\pi$
$920$	17.5244	−	10.1177i	0.0190482	−	0.0109975i
$921$	626.234	−	2337.14i	0.679950	−	2.53761i
$922$			1901.79i			2.06268i
$923$		0			0
$924$	−59.1912			−0.0640598
$925$	−86.5853	−	23.2005i	−0.0936058	−	0.0250816i
$926$	−684.727	−	1185.98i	−0.739446	−	1.28076i
$927$	−1123.36	−	648.573i	−1.21182	−	0.699647i
$928$	317.569	−	317.569i	0.342208	−	0.342208i
$929$	−147.714	−	551.276i	−0.159003	−	0.593408i	−0.998729	−	0.0503975i	$-0.983951\pi$
$929$	−147.714	−	551.276i	−0.159003	−	0.593408i	0.839726	−	0.543010i	$-0.182715\pi$
$930$	−1033.98	+	277.055i	−1.11181	+	0.297908i
$931$	−2.75976	−	2.75976i	−0.00296430	−	0.00296430i
$932$	203.101	−	351.781i	0.217919	−	0.377448i
$933$	436.584	−	252.062i	0.467935	−	0.270163i
$934$	−170.484	+	636.256i	−0.182531	+	0.681216i
$935$		−	45.2118i		−	0.0483549i
$936$		0			0
$937$	−26.9894			−0.0288040			−0.0144020	−	0.999896i	$-0.504584\pi$
$937$	−26.9894			−0.0288040			−0.0144020	+	0.999896i	$0.504584\pi$
$938$	1412.73	+	378.540i	1.50611	+	0.403561i
$939$	225.873	+	391.223i	0.240546	+	0.416638i
$940$	71.9898	+	41.5633i	0.0765849	+	0.0442163i
$941$	1244.04	−	1244.04i	1.32204	−	1.32204i	0.409926	−	0.912119i	$-0.365555\pi$
$941$	1244.04	−	1244.04i	1.32204	−	1.32204i	0.912119	−	0.409926i	$-0.134445\pi$
$942$	−372.121	−	1388.77i	−0.395033	−	1.47428i
$943$	25.9989	−	6.96639i	0.0275705	−	0.00738748i
$944$	−1038.00	−	1038.00i	−1.09958	−	1.09958i
$945$	−187.466	+	324.701i	−0.198377	+	0.343598i
$946$	−119.393	+	68.9315i	−0.126208	+	0.0728663i
$947$	−19.1413	+	71.4365i	−0.0202126	+	0.0754345i	−0.975295	−	0.220904i	$-0.929099\pi$
$947$	−19.1413	+	71.4365i	−0.0202126	+	0.0754345i	0.955083	+	0.296339i	$0.0957658\pi$
$948$		−	380.095i		−	0.400944i
$949$		0			0
$950$	35.7432			0.0376245
$951$	−1959.15	−	524.952i	−2.06009	−	0.551999i
$952$	471.154	+	816.062i	0.494909	+	0.857208i
$953$	334.954	+	193.386i	0.351474	+	0.202923i	0.665334	−	0.746546i	$-0.268289\pi$
$953$	334.954	+	193.386i	0.351474	+	0.202923i	−0.313861	+	0.949469i	$0.601622\pi$
$954$	1771.84	−	1771.84i	1.85727	−	1.85727i
$955$	27.5751	+	102.912i	0.0288744	+	0.107761i
$956$	548.402	−	146.944i	0.573643	−	0.153707i
$957$	−79.2196	−	79.2196i	−0.0827791	−	0.0827791i
$958$	−315.067	+	545.712i	−0.328880	+	0.569637i
$959$	942.457	−	544.128i	0.982749	−	0.567391i
$960$	48.9903	−	182.834i	0.0510316	−	0.190452i
$961$		−	2366.76i		−	2.46281i
$962$		0			0
$963$	1213.61			1.26024
$964$	92.1435	+	24.6898i	0.0955845	+	0.0256118i
$965$	−168.664	−	292.135i	−0.174782	−	0.302731i
$966$	−149.949	−	86.5730i	−0.155227	−	0.0896201i
$967$	503.064	−	503.064i	0.520232	−	0.520232i	−0.397409	−	0.917641i	$-0.630091\pi$
$967$	503.064	−	503.064i	0.520232	−	0.520232i	0.917641	+	0.397409i	$0.130091\pi$
$968$	179.254	+	668.986i	0.185180	+	0.691102i
$969$	80.9642	−	21.6943i	0.0835544	−	0.0223883i
$970$	−176.733	−	176.733i	−0.182199	−	0.182199i
$971$	−452.612	+	783.946i	−0.466129	+	0.807360i	−0.999252	−	0.0386784i	$-0.987685\pi$
$971$	−452.612	+	783.946i	−0.466129	+	0.807360i	0.533122	+	0.846038i	$0.321019\pi$
$972$	−192.035	+	110.872i	−0.197567	+	0.114066i
$973$	−130.609	+	487.441i	−0.134234	+	0.500967i
$974$			1276.66i			1.31074i
$975$		0			0
$976$	1798.20			1.84241
$977$	797.549	+	213.703i	0.816324	+	0.218733i	0.642739	−	0.766085i	$-0.277798\pi$
$977$	797.549	+	213.703i	0.816324	+	0.218733i	0.173585	+	0.984819i	$0.444465\pi$
$978$	876.055	+	1517.37i	0.895762	+	1.55151i
$979$	84.9241	+	49.0310i	0.0867458	+	0.0500827i
$980$	9.90440	−	9.90440i	0.0101065	−	0.0101065i
$981$	−125.281	−	467.557i	−0.127708	−	0.476612i
$982$	−53.5236	+	14.3416i	−0.0545047	+	0.0146045i
$983$	99.0983	+	99.0983i	0.100812	+	0.100812i	0.755714	−	0.654902i	$-0.227290\pi$
$983$	99.0983	+	99.0983i	0.100812	+	0.100812i	−0.654902	+	0.755714i	$0.727290\pi$
$984$	175.680	−	304.286i	0.178536	−	0.309234i
$985$	−215.011	+	124.137i	−0.218286	+	0.126027i
$986$	289.238	−	1079.45i	0.293344	−	1.09478i
$987$			1135.18i			1.15013i
$988$		0			0
$989$	−112.147			−0.113394
$990$	67.3921	+	18.0577i	0.0680728	+	0.0182401i
$991$	58.8966	+	102.012i	0.0594315	+	0.102938i	0.894210	−	0.447647i	$-0.147738\pi$
$991$	58.8966	+	102.012i	0.0594315	+	0.102938i	−0.834779	+	0.550585i	$0.814405\pi$
$992$	−1170.39	−	675.725i	−1.17983	−	0.681175i
$993$	−546.127	+	546.127i	−0.549977	+	0.549977i
$994$	271.864	+	1014.61i	0.273505	+	1.02073i
$995$	63.5572	−	17.0301i	0.0638766	−	0.0171157i
$996$	546.180	+	546.180i	0.548374	+	0.548374i
$997$	531.702	−	920.934i	0.533302	−	0.923705i	−0.465942	−	0.884815i	$-0.654284\pi$
$997$	531.702	−	920.934i	0.533302	−	0.923705i	0.999243	−	0.0388901i	$-0.0123822\pi$
$998$	304.298	−	175.687i	0.304908	−	0.176039i
$999$	37.4170	−	139.642i	0.0374544	−	0.139782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.g.80.3		48
13.2	odd	12		169.3.d.e.99.3	yes	24
13.3	even	3		169.3.d.e.70.10	yes	24
13.4	even	6	inner	169.3.f.g.19.3		48
13.5	odd	4	inner	169.3.f.g.89.3		48
13.6	odd	12	inner	169.3.f.g.150.10		48
13.7	odd	12	inner	169.3.f.g.150.3		48
13.8	odd	4	inner	169.3.f.g.89.10		48
13.9	even	3	inner	169.3.f.g.19.10		48
13.10	even	6		169.3.d.e.70.3	✓	24
13.11	odd	12		169.3.d.e.99.10	yes	24
13.12	even	2	inner	169.3.f.g.80.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.e.70.3	✓	24	13.10	even	6
169.3.d.e.70.10	yes	24	13.3	even	3
169.3.d.e.99.3	yes	24	13.2	odd	12
169.3.d.e.99.10	yes	24	13.11	odd	12
169.3.f.g.19.3		48	13.4	even	6	inner
169.3.f.g.19.10		48	13.9	even	3	inner
169.3.f.g.80.3		48	1.1	even	1	trivial
169.3.f.g.80.10		48	13.12	even	2	inner
169.3.f.g.89.3		48	13.5	odd	4	inner
169.3.f.g.89.10		48	13.8	odd	4	inner
169.3.f.g.150.3		48	13.7	odd	12	inner
169.3.f.g.150.10		48	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.27369 - 0.609234i) q^{2} +(2.51175 + 4.35048i) q^{3} +(1.33442 + 0.770425i) q^{4} +(-1.10964 + 1.10964i) q^{5} +(-3.06049 - 11.4219i) q^{6} +(-6.34925 + 1.70128i) q^{7} +(4.09315 + 4.09315i) q^{8} +(-8.11776 + 14.0604i) q^{9} +(3.19902 - 1.84696i) q^{10} +(0.301099 - 1.12372i) q^{11} +7.74046i q^{12} +15.4727 q^{14} +(-7.61462 - 2.04033i) q^{15} +(-9.89459 - 17.1379i) q^{16} +(-21.4473 - 12.3826i) q^{17} +(27.0234 - 27.0234i) q^{18} +(0.174381 + 0.650797i) q^{19} +(-2.33562 + 0.625828i) q^{20} +(-23.3491 - 23.3491i) q^{21} +(-1.36921 + 2.37154i) q^{22} +(-1.92917 + 1.11381i) q^{23} +(-7.52619 + 28.0881i) q^{24} +22.5374i q^{25} -36.3476 q^{27} +(-9.78324 - 2.62141i) q^{28} +(-9.58516 - 16.6020i) q^{29} +(16.0703 + 9.27818i) q^{30} +(-40.7907 + 40.7907i) q^{31} +(6.06346 + 22.6291i) q^{32} +(5.64498 - 1.51257i) q^{33} +(41.2206 + 41.2206i) q^{34} +(5.15759 - 8.93321i) q^{35} +(-21.6649 + 12.5082i) q^{36} +(-1.02942 + 3.84185i) q^{37} -1.58595i q^{38} -9.08389 q^{40} +(-11.6712 - 3.12729i) q^{41} +(38.8636 + 67.3137i) q^{42} +(43.5991 + 25.1720i) q^{43} +(1.26753 - 1.26753i) q^{44} +(-6.59418 - 24.6098i) q^{45} +(5.06491 - 1.35714i) q^{46} +(-24.3090 - 24.3090i) q^{47} +(49.7054 - 86.0923i) q^{48} +(-5.01666 + 2.89637i) q^{49} +(13.7305 - 51.2431i) q^{50} -124.408i q^{51} +65.5668 q^{53} +(82.6433 + 22.1442i) q^{54} +(0.912811 + 1.58104i) q^{55} +(-32.9520 - 19.0249i) q^{56} +(-2.39328 + 2.39328i) q^{57} +(11.6792 + 43.5874i) q^{58} +(71.6521 - 19.1991i) q^{59} +(-8.58915 - 8.58915i) q^{60} +(-45.4338 + 78.6937i) q^{61} +(117.597 - 67.8945i) q^{62} +(27.6211 - 103.083i) q^{63} +24.0109i q^{64} -13.7565 q^{66} +(91.3047 + 24.4650i) q^{67} +(-19.0797 - 33.0470i) q^{68} +(-9.69118 - 5.59520i) q^{69} +(-17.1692 + 17.1692i) q^{70} +(17.5705 + 65.5740i) q^{71} +(-90.7785 + 24.3240i) q^{72} +(51.8021 + 51.8021i) q^{73} +(4.68118 - 8.10804i) q^{74} +(-98.0483 + 56.6082i) q^{75} +(-0.268695 + 1.00278i) q^{76} +7.64700i q^{77} -49.1050 q^{79} +(29.9965 + 8.03753i) q^{80} +(-18.2361 - 31.5859i) q^{81} +(24.6315 + 14.2210i) q^{82} +(70.5618 - 70.5618i) q^{83} +(-13.1686 - 49.1461i) q^{84} +(37.5391 - 10.0586i) q^{85} +(-83.7955 - 83.7955i) q^{86} +(48.1510 - 83.4000i) q^{87} +(5.83198 - 3.36710i) q^{88} +(-21.8165 + 81.4201i) q^{89} +59.9726i q^{90} -3.43242 q^{92} +(-279.915 - 75.0030i) q^{93} +(40.4613 + 70.0810i) q^{94} +(-0.915654 - 0.528653i) q^{95} +(-83.2176 + 83.2176i) q^{96} +(-17.5122 - 65.3566i) q^{97} +(13.1709 - 3.52914i) q^{98} +(13.3556 + 13.3556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) \) 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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