LMFDB - Embedded newform 169.3.f.g.89.10

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			89.10
Character	$\chi$	$=$	169.89
Dual form			169.3.f.g.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.609234 - 2.27369i) q^{2} +(2.51175 + 4.35048i) q^{3} +(-1.33442 - 0.770425i) q^{4} +(-1.10964 - 1.10964i) q^{5} +(11.4219 - 3.06049i) q^{6} +(1.70128 + 6.34925i) q^{7} +(4.09315 - 4.09315i) q^{8} +(-8.11776 + 14.0604i) q^{9} +(-3.19902 + 1.84696i) q^{10} +(-1.12372 - 0.301099i) q^{11} -7.74046i q^{12} +15.4727 q^{14} +(2.04033 - 7.61462i) q^{15} +(-9.89459 - 17.1379i) q^{16} +(21.4473 + 12.3826i) q^{17} +(27.0234 + 27.0234i) q^{18} +(-0.650797 + 0.174381i) q^{19} +(0.625828 + 2.33562i) q^{20} +(-23.3491 + 23.3491i) q^{21} +(-1.36921 + 2.37154i) q^{22} +(1.92917 - 1.11381i) q^{23} +(28.0881 + 7.52619i) q^{24} -22.5374i q^{25} -36.3476 q^{27} +(2.62141 - 9.78324i) q^{28} +(-9.58516 - 16.6020i) q^{29} +(-16.0703 - 9.27818i) q^{30} +(-40.7907 - 40.7907i) q^{31} +(-22.6291 + 6.06346i) q^{32} +(-1.51257 - 5.64498i) q^{33} +(41.2206 - 41.2206i) q^{34} +(5.15759 - 8.93321i) q^{35} +(21.6649 - 12.5082i) q^{36} +(3.84185 + 1.02942i) q^{37} +1.58595i q^{38} -9.08389 q^{40} +(3.12729 - 11.6712i) q^{41} +(38.8636 + 67.3137i) q^{42} +(-43.5991 - 25.1720i) q^{43} +(1.26753 + 1.26753i) q^{44} +(24.6098 - 6.59418i) q^{45} +(-1.35714 - 5.06491i) q^{46} +(-24.3090 + 24.3090i) q^{47} +(49.7054 - 86.0923i) q^{48} +(5.01666 - 2.89637i) q^{49} +(-51.2431 - 13.7305i) q^{50} +124.408i q^{51} +65.5668 q^{53} +(-22.1442 + 82.6433i) q^{54} +(0.912811 + 1.58104i) q^{55} +(32.9520 + 19.0249i) q^{56} +(-2.39328 - 2.39328i) q^{57} +(-43.5874 + 11.6792i) q^{58} +(-19.1991 - 71.6521i) q^{59} +(-8.58915 + 8.58915i) q^{60} +(-45.4338 + 78.6937i) q^{61} +(-117.597 + 67.8945i) q^{62} +(-103.083 - 27.6211i) q^{63} -24.0109i q^{64} -13.7565 q^{66} +(-24.4650 + 91.3047i) q^{67} +(-19.0797 - 33.0470i) q^{68} +(9.69118 + 5.59520i) q^{69} +(-17.1692 - 17.1692i) q^{70} +(-65.5740 + 17.5705i) q^{71} +(24.3240 + 90.7785i) q^{72} +(51.8021 - 51.8021i) q^{73} +(4.68118 - 8.10804i) q^{74} +(98.0483 - 56.6082i) q^{75} +(1.00278 + 0.268695i) q^{76} -7.64700i q^{77} -49.1050 q^{79} +(-8.03753 + 29.9965i) q^{80} +(-18.2361 - 31.5859i) q^{81} +(-24.6315 - 14.2210i) q^{82} +(70.5618 + 70.5618i) q^{83} +(49.1461 - 13.1686i) q^{84} +(-10.0586 - 37.5391i) q^{85} +(-83.7955 + 83.7955i) q^{86} +(48.1510 - 83.4000i) q^{87} +(-5.83198 + 3.36710i) q^{88} +(81.4201 + 21.8165i) q^{89} -59.9726i q^{90} -3.43242 q^{92} +(75.0030 - 279.915i) q^{93} +(40.4613 + 70.0810i) q^{94} +(0.915654 + 0.528653i) q^{95} +(-83.2176 - 83.2176i) q^{96} +(65.3566 - 17.5122i) q^{97} +(-3.52914 - 13.1709i) 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.609234	−	2.27369i	0.304617	−	1.13685i	−0.628657	−	0.777683i	$-0.716395\pi$
$2$	0.609234	−	2.27369i	0.304617	−	1.13685i	0.933274	−	0.359164i	$-0.116938\pi$
$3$	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	0.587381	−	0.809310i	$-0.300159\pi$
$5$	−1.10964	−	1.10964i	−0.221929	−	0.221929i	−0.809310	+	0.587381i	$0.800159\pi$
$6$	11.4219	−	3.06049i	1.90365	−	0.510081i
$7$	1.70128	+	6.34925i	0.243039	+	0.907035i	0.974359	+	0.225000i	$0.0722382\pi$
$7$	1.70128	+	6.34925i	0.243039	+	0.907035i	−0.731319	+	0.682035i	$0.761095\pi$
$8$	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
$11$	−1.12372	−	0.301099i	−0.102156	−	0.0273726i	0.207379	−	0.978261i	$-0.433507\pi$
$11$	−1.12372	−	0.301099i	−0.102156	−	0.0273726i	−0.309535	+	0.950888i	$0.600173\pi$
$12$		−	7.74046i		−	0.645038i
$13$		0			0
$13$		0			0
$14$	15.4727			1.10519
$15$	2.04033	−	7.61462i	0.136022	−	0.507642i
$16$	−9.89459	−	17.1379i	−0.618412	−	1.07112i
$17$	21.4473	+	12.3826i	1.26160	+	0.728387i	0.973385	−	0.229178i	$-0.0736037\pi$
$17$	21.4473	+	12.3826i	1.26160	+	0.728387i	0.288218	+	0.957565i	$0.406937\pi$
$18$	27.0234	+	27.0234i	1.50130	+	1.50130i
$19$	−0.650797	+	0.174381i	−0.0342525	+	0.00917793i	−0.275905	−	0.961185i	$-0.588977\pi$
$19$	−0.650797	+	0.174381i	−0.0342525	+	0.00917793i	0.241652	+	0.970363i	$0.422311\pi$
$20$	0.625828	+	2.33562i	0.0312914	+	0.116781i
$21$	−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	−0.457475	−	0.889223i	$-0.651246\pi$
$23$	1.92917	−	1.11381i	0.0838770	−	0.0484264i	0.541352	+	0.840796i	$0.317913\pi$
$24$	28.0881	+	7.52619i	1.17034	+	0.313591i
$25$		−	22.5374i		−	0.901495i
$26$		0			0
$27$	−36.3476			−1.34621
$28$	2.62141	−	9.78324i	0.0936218	−	0.349401i
$29$	−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	−0.917045	−	0.398785i	$-0.869432\pi$
$31$	−40.7907	−	40.7907i	−1.31583	−	1.31583i	−0.398785	−	0.917045i	$-0.630568\pi$
$32$	−22.6291	+	6.06346i	−0.707160	+	0.189483i
$33$	−1.51257	−	5.64498i	−0.0458354	−	0.171060i
$34$	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
$37$	3.84185	+	1.02942i	0.103834	+	0.0278222i	0.310362	−	0.950618i	$-0.399550\pi$
$37$	3.84185	+	1.02942i	0.103834	+	0.0278222i	−0.206528	+	0.978441i	$0.566216\pi$
$38$			1.58595i			0.0417356i
$39$		0			0
$40$	−9.08389			−0.227097
$41$	3.12729	−	11.6712i	0.0762754	−	0.284664i	−0.917244	−	0.398326i	$-0.869591\pi$
$41$	3.12729	−	11.6712i	0.0762754	−	0.284664i	0.993519	+	0.113662i	$0.0362581\pi$
$42$	38.8636	+	67.3137i	0.925323	+	1.60271i
$43$	−43.5991	−	25.1720i	−1.01393	−	0.585395i	−0.101592	−	0.994826i	$-0.532394\pi$
$43$	−43.5991	−	25.1720i	−1.01393	−	0.585395i	−0.912341	+	0.409431i	$0.865727\pi$
$44$	1.26753	+	1.26753i	0.0288075	+	0.0288075i
$45$	24.6098	−	6.59418i	0.546885	−	0.146537i
$46$	−1.35714	−	5.06491i	−0.0295030	−	0.110107i
$47$	−24.3090	+	24.3090i	−0.517212	+	0.517212i	−0.916727	−	0.399515i	$-0.869179\pi$
$47$	−24.3090	+	24.3090i	−0.517212	+	0.517212i	0.399515	+	0.916727i	$0.369179\pi$
$48$	49.7054	−	86.0923i	1.03553	−	1.79359i
$49$	5.01666	−	2.89637i	0.102381	−	0.0591096i
$50$	−51.2431	−	13.7305i	−1.02486	−	0.274611i
$51$			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	$0.287718\pi$
$54$	−22.1442	+	82.6433i	−0.410078	+	1.53043i
$55$	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
$58$	−43.5874	+	11.6792i	−0.751507	+	0.201366i
$59$	−19.1991	−	71.6521i	−0.325409	−	1.21444i	−0.913900	−	0.405938i	$-0.866945\pi$
$59$	−19.1991	−	71.6521i	−0.325409	−	1.21444i	0.588492	−	0.808503i	$-0.299722\pi$
$60$	−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
$63$	−103.083	−	27.6211i	−1.63624	−	0.438430i
$64$		−	24.0109i		−	0.375171i
$65$		0			0
$66$	−13.7565			−0.208431
$67$	−24.4650	+	91.3047i	−0.365149	+	1.36276i	0.502069	+	0.864828i	$0.332572\pi$
$67$	−24.4650	+	91.3047i	−0.365149	+	1.36276i	−0.867218	+	0.497929i	$0.834094\pi$
$68$	−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
$71$	−65.5740	+	17.5705i	−0.923578	+	0.247472i	−0.689114	−	0.724653i	$-0.742000\pi$
$71$	−65.5740	+	17.5705i	−0.923578	+	0.247472i	−0.234464	+	0.972125i	$0.575333\pi$
$72$	24.3240	+	90.7785i	0.337834	+	1.26081i
$73$	51.8021	−	51.8021i	0.709617	−	0.709617i	−0.256837	−	0.966455i	$-0.582680\pi$
$73$	51.8021	−	51.8021i	0.709617	−	0.709617i	0.966455	+	0.256837i	$0.0826804\pi$
$74$	4.68118	−	8.10804i	0.0632592	−	0.109568i
$75$	98.0483	−	56.6082i	1.30731	−	0.754776i
$76$	1.00278	+	0.268695i	0.0131945	+	0.00353545i
$77$		−	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	$0.600594\pi$
$80$	−8.03753	+	29.9965i	−0.100469	+	0.374956i
$81$	−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	0.990150	−	0.140008i	$-0.0447129\pi$
$83$	70.5618	+	70.5618i	0.850142	+	0.850142i	−0.140008	+	0.990150i	$0.544713\pi$
$84$	49.1461	−	13.1686i	0.585072	−	0.156770i
$85$	−10.0586	−	37.5391i	−0.118336	−	0.441636i
$86$	−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
$89$	81.4201	+	21.8165i	0.914833	+	0.245129i	0.685375	−	0.728190i	$-0.259638\pi$
$89$	81.4201	+	21.8165i	0.914833	+	0.245129i	0.229457	+	0.973319i	$0.426305\pi$
$90$		−	59.9726i		−	0.666362i
$91$		0			0
$92$	−3.43242			−0.0373089
$93$	75.0030	−	279.915i	0.806484	−	3.00984i
$94$	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
$97$	65.3566	−	17.5122i	0.673779	−	0.180539i	0.0943225	−	0.995542i	$-0.469932\pi$
$97$	65.3566	−	17.5122i	0.673779	−	0.180539i	0.579457	+	0.815003i	$0.303265\pi$
$98$	−3.52914	−	13.1709i	−0.0360116	−	0.134397i
$99$	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	−0.139968	−	0.990156i	$-0.544700\pi$
$101$	65.4023	−	37.7600i	0.647547	−	0.373862i	0.787516	+	0.616294i	$0.211367\pi$
$102$	282.865	+	75.7934i	2.77319	+	0.743073i
$103$		−	79.8956i		−	0.775685i	−0.921726	−	0.387843i	$-0.873220\pi$
$103$		−	79.8956i		−	0.775685i	0.921726	−	0.387843i	$-0.126780\pi$
$104$		0			0
$105$	51.8183			0.493507
$106$	39.9456	−	149.079i	0.376845	−	1.40640i
$107$	−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	0.603757	−	0.797169i	$-0.293670\pi$
$109$	−21.0819	−	21.0819i	−0.193412	−	0.193412i	−0.797169	+	0.603757i	$0.793670\pi$
$110$	4.15091	−	1.11223i	0.0377355	−	0.0101112i
$111$	5.17130	+	19.2995i	0.0465882	+	0.173870i
$112$	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
$115$	−3.37662	−	0.904763i	−0.0293619	−	0.00786750i
$116$			29.5386i			0.254643i
$117$		0			0
$118$	−174.612			−1.47976
$119$	−42.1323	+	157.240i	−0.354053	+	1.32134i
$120$	−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
$123$	58.6303	−	15.7099i	0.476669	−	0.127723i
$124$	23.0056	+	85.8579i	0.185529	+	0.692403i
$125$	−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	−0.515752	−	0.856738i	$-0.672487\pi$
$127$	−4.02217	+	2.32220i	−0.0316706	+	0.0182850i	0.484081	+	0.875023i	$0.339154\pi$
$128$	−145.110	−	38.8821i	−1.13367	−	0.303767i
$129$		−	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	$0.428299\pi$
$132$	−2.33064	+	8.69807i	−0.0176564	+	0.0658945i
$133$	−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
$136$	138.471	−	37.1031i	1.01817	−	0.272817i
$137$	42.8498	+	159.918i	0.312772	+	1.16728i	0.926046	+	0.377411i	$0.123186\pi$
$137$	42.8498	+	159.918i	0.312772	+	1.16728i	−0.613274	+	0.789871i	$0.710148\pi$
$138$	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
$141$	−166.814	−	44.6976i	−1.18307	−	0.317004i
$142$			159.800i			1.12535i
$143$		0			0
$144$	321.288			2.23116
$145$	−7.78617	+	29.0584i	−0.0536977	+	0.200403i
$146$	−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
$149$	−115.585	+	30.9709i	−0.775737	+	0.207858i	−0.624904	−	0.780701i	$-0.714862\pi$
$149$	−115.585	+	30.9709i	−0.775737	+	0.207858i	−0.150833	+	0.988559i	$0.548195\pi$
$150$	−68.9754	−	257.420i	−0.459836	−	1.71613i
$151$	−158.935	+	158.935i	−1.05255	+	1.05255i	−0.0540078	+	0.998541i	$0.517200\pi$
$151$	−158.935	+	158.935i	−1.05255	+	1.05255i	−0.998541	+	0.0540078i	$0.982800\pi$
$152$	−1.95005	+	3.37758i	−0.0128293	+	0.0222209i
$153$	−348.207	+	201.037i	−2.27586	+	1.31397i
$154$	−17.3869	−	4.65881i	−0.112902	−	0.0302520i
$155$			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	$0.373434\pi$
$158$	−29.9165	+	111.650i	−0.189345	+	0.706644i
$159$	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
$162$	−82.9268	+	22.2202i	−0.511894	+	0.137162i
$163$	38.3498	+	143.124i	0.235275	+	0.878059i	0.978025	+	0.208489i	$0.0668546\pi$
$163$	38.3498	+	143.124i	0.235275	+	0.878059i	−0.742750	+	0.669569i	$0.766479\pi$
$164$	−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
$167$	−30.6587	−	8.21496i	−0.183585	−	0.0491914i	0.165855	−	0.986150i	$-0.446962\pi$
$167$	−30.6587	−	8.21496i	−0.183585	−	0.0491914i	−0.349440	+	0.936959i	$0.613628\pi$
$168$			191.143i			1.13775i
$169$		0			0
$170$	−91.4803			−0.538120
$171$	2.83116	−	10.5660i	0.0165565	−	0.0617897i
$172$	38.7862	+	67.1797i	0.225501	+	0.390580i
$173$	75.3542	+	43.5058i	0.435574	+	0.251478i	0.701718	−	0.712455i	$-0.252417\pi$
$173$	75.3542	+	43.5058i	0.435574	+	0.251478i	−0.266145	+	0.963933i	$0.585750\pi$
$174$	−160.291	−	160.291i	−0.921211	−	0.921211i
$175$	143.095	−	38.3423i	0.817688	−	0.219099i
$176$	5.95849	+	22.2374i	0.0338551	+	0.126349i
$177$	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	−0.107486	−	0.994207i	$-0.534280\pi$
$179$	125.261	−	72.3192i	0.699780	−	0.404018i	0.807265	+	0.590189i	$0.200947\pi$
$180$	−37.9200	−	10.1606i	−0.210667	−	0.0564480i
$181$			57.4932i			0.317642i	0.987307	+	0.158821i	$0.0507693\pi$
$181$			57.4932i			0.317642i	−0.987307	+	0.158821i	$0.949231\pi$
$182$		0			0
$183$	−456.473			−2.49439
$184$	3.33741	−	12.4554i	0.0181381	−	0.0676923i
$185$	−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
$188$	51.1665	−	13.7100i	0.272162	−	0.0729257i
$189$	−61.8372	−	230.780i	−0.327181	−	1.22106i
$190$	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
$193$	207.634	+	55.6354i	1.07582	+	0.288266i	0.752884	−	0.658153i	$-0.228662\pi$
$193$	207.634	+	55.6354i	1.07582	+	0.288266i	0.322940	+	0.946419i	$0.395329\pi$
$194$		−	159.270i		−	0.820979i
$195$		0			0
$196$	−8.92575			−0.0455395
$197$	−40.9476	+	152.818i	−0.207856	+	0.775728i	0.780704	+	0.624901i	$0.214861\pi$
$197$	−40.9476	+	152.818i	−0.207856	+	0.775728i	−0.988560	+	0.150828i	$0.951806\pi$
$198$	−22.2299	−	38.5032i	−0.112272	−	0.194461i
$199$	36.3122	+	20.9649i	0.182473	+	0.105351i	0.588454	−	0.808530i	$-0.299737\pi$
$199$	36.3122	+	20.9649i	0.182473	+	0.105351i	−0.405981	+	0.913882i	$0.633070\pi$
$200$	−92.2490	−	92.2490i	−0.461245	−	0.461245i
$201$	−458.669	+	122.900i	−2.28193	+	0.611442i
$202$	−46.0094	−	171.710i	−0.227769	−	0.850047i
$203$	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
$206$	−181.658	−	48.6751i	−0.881835	−	0.236287i
$207$			36.1665i			0.174717i
$208$		0			0
$209$	0.783817			0.00375032
$210$	31.5695	−	117.819i	0.150331	−	0.561042i
$211$	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
$214$	−169.959	+	45.5404i	−0.794201	+	0.212806i
$215$	20.4476	+	76.3114i	0.0951050	+	0.354937i
$216$	−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
$219$	355.477	+	95.2499i	1.62318	+	0.434931i
$220$		−	2.81301i		−	0.0127864i
$221$		0			0
$222$	47.0318			0.211855
$223$	39.5031	−	147.428i	0.177144	−	0.661110i	−0.819033	−	0.573747i	$-0.805489\pi$
$223$	39.5031	−	147.428i	0.177144	−	0.661110i	0.996177	−	0.0873632i	$-0.0278441\pi$
$224$	−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
$227$	70.6452	−	18.9293i	0.311212	−	0.0833891i	−0.0998323	−	0.995004i	$-0.531831\pi$
$227$	70.6452	−	18.9293i	0.311212	−	0.0833891i	0.411045	+	0.911615i	$0.365164\pi$
$228$	1.34979	+	5.03747i	0.00592011	+	0.0220942i
$229$	−182.706	+	182.706i	−0.797845	+	0.797845i	−0.982755	−	0.184911i	$-0.940800\pi$
$229$	−182.706	+	182.706i	−0.797845	+	0.797845i	0.184911	+	0.982755i	$0.440800\pi$
$230$	−4.11431	+	7.12619i	−0.0178883	+	0.0309834i
$231$	33.2681	−	19.2073i	0.144018	−	0.0831486i
$232$	−107.188	−	28.7209i	−0.462017	−	0.123797i
$233$			263.622i			1.13142i	0.824603	+	0.565712i	$0.191399\pi$
$233$			263.622i			1.13142i	−0.824603	+	0.565712i	$0.808601\pi$
$234$		0			0
$235$	53.9486			0.229568
$236$	−29.5830	+	110.405i	−0.125352	+	0.467818i
$237$	−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	0.995513	+	0.0946270i	$0.0301659\pi$
$239$	260.543	+	260.543i	1.09014	+	1.09014i	0.0946270	+	0.995513i	$0.469834\pi$
$240$	−150.687	+	40.3765i	−0.627863	+	0.168235i
$241$	−16.0235	−	59.8004i	−0.0664874	−	0.248134i	0.924681	−	0.380742i	$-0.124332\pi$
$241$	−16.0235	−	59.8004i	−0.0664874	−	0.248134i	−0.991169	+	0.132608i	$0.957665\pi$
$242$	−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
$245$	−8.78065	−	2.35277i	−0.0358394	−	0.00960313i
$246$		−	142.878i		−	0.580806i
$247$		0			0
$248$	−333.925			−1.34647
$249$	−129.744	+	484.211i	−0.521060	+	1.94462i
$250$	87.7995	+	152.073i	0.351198	+	0.608293i
$251$	−97.1096	−	56.0663i	−0.386891	−	0.223372i	0.293921	−	0.955830i	$-0.405040\pi$
$251$	−97.1096	−	56.0663i	−0.386891	−	0.223372i	−0.680812	+	0.732458i	$0.738373\pi$
$252$	116.276	+	116.276i	0.461412	+	0.461412i
$253$	−2.50320	+	0.670731i	−0.00989408	+	0.00265111i
$254$	2.82953	+	10.5599i	0.0111399	+	0.0415746i
$255$	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	−0.972748	−	0.231863i	$-0.925518\pi$
$257$	−323.389	+	186.709i	−1.25832	+	0.726493i	−0.285575	+	0.958356i	$0.592185\pi$
$258$	−575.023	−	154.077i	−2.22877	−	0.597198i
$259$			26.1442i			0.100943i
$260$		0			0
$261$	311.240			1.19249
$262$	35.6518	−	133.054i	0.136076	−	0.507841i
$263$	−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
$266$	−10.0696	+	2.69814i	−0.0378557	+	0.0101434i
$267$	109.595	+	409.014i	0.410468	+	1.53189i
$268$	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
$271$	217.372	+	58.2447i	0.802112	+	0.214925i	0.636511	−	0.771268i	$-0.280377\pi$
$271$	217.372	+	58.2447i	0.802112	+	0.214925i	0.165601	+	0.986193i	$0.447044\pi$
$272$		−	490.082i		−	1.80177i
$273$		0			0
$274$	389.709			1.42230
$275$	−6.78597	+	25.3256i	−0.0246763	+	0.0920931i
$276$	−8.62137	−	14.9327i	−0.0312369	−	0.0541038i
$277$	−349.428	−	201.742i	−1.26147	−	0.728312i	−0.288114	−	0.957596i	$-0.593028\pi$
$277$	−349.428	−	201.742i	−1.26147	−	0.728312i	−0.973360	+	0.229284i	$0.926362\pi$
$278$	−127.783	−	127.783i	−0.459651	−	0.459651i
$279$	904.661	−	242.403i	3.24251	−	0.868829i
$280$	−15.4542	−	57.6758i	−0.0551935	−	0.205985i
$281$	356.187	−	356.187i	1.26757	−	1.26757i	0.320228	−	0.947340i	$-0.396240\pi$
$281$	356.187	−	356.187i	1.26757	−	1.26757i	0.947340	−	0.320228i	$-0.103760\pi$
$282$	−203.257	+	352.052i	−0.720770	+	1.24841i
$283$	−302.969	+	174.919i	−1.07056	+	0.618089i	−0.928335	−	0.371746i	$-0.878759\pi$
$283$	−302.969	+	174.919i	−1.07056	+	0.618089i	−0.142226	+	0.989834i	$0.545426\pi$
$284$	101.040	+	27.0735i	0.355774	+	0.0953293i
$285$			5.31137i			0.0186364i
$286$		0			0
$287$	79.4237			0.276738
$288$	98.4433	−	367.396i	0.341817	−	1.27568i
$289$	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
$292$	−109.035	+	29.2159i	−0.373408	+	0.100054i
$293$	−139.304	−	519.890i	−0.475441	−	1.77437i	−0.619710	−	0.784831i	$-0.712750\pi$
$293$	−139.304	−	519.890i	−0.475441	−	1.77437i	0.144269	−	0.989539i	$-0.453917\pi$
$294$	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
$297$	40.8443	+	10.9442i	0.137523	+	0.0368492i
$298$			281.673i			0.945211i
$299$		0			0
$300$	−174.450			−0.581499
$301$	85.6489	−	319.646i	0.284548	−	1.06195i
$302$	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
$305$	137.737	−	36.9066i	0.451598	−	0.121005i
$306$	244.958	+	914.195i	0.800516	+	2.98757i
$307$	−340.580	+	340.580i	−1.10938	+	1.10938i	−0.116150	+	0.993232i	$0.537055\pi$
$307$	−340.580	+	340.580i	−1.10938	+	1.10938i	−0.993232	+	0.116150i	$0.962945\pi$
$308$	−5.89144	+	10.2043i	−0.0191280	+	0.0331307i
$309$	347.584	−	200.678i	1.12487	−	0.649442i
$310$	205.829	+	55.1517i	0.663965	+	0.177909i
$311$			100.353i			0.322679i	0.986899	+	0.161339i	$0.0515814\pi$
$311$			100.353i			0.322679i	−0.986899	+	0.161339i	$0.948419\pi$
$312$		0			0
$313$	89.9264			0.287305			0.143652	−	0.989628i	$-0.454115\pi$
$313$	89.9264			0.287305			0.143652	+	0.989628i	$0.454115\pi$
$314$	74.0761	−	276.456i	0.235911	−	0.880432i
$315$	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	0.0948677	−	0.995490i	$-0.469757\pi$
$317$	−285.497	−	285.497i	−0.900622	−	0.900622i	−0.995490	+	0.0948677i	$0.969757\pi$
$318$	748.897	−	200.666i	2.35502	−	0.631026i
$319$	5.77215	+	21.5420i	0.0180945	+	0.0675297i
$320$	−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
$323$	−16.1171	−	4.31856i	−0.0498981	−	0.0133702i
$324$			56.1983i			0.173452i
$325$		0			0
$326$	348.783			1.06989
$327$	38.7638	−	144.669i	0.118544	−	0.442412i
$328$	−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
$331$	−148.507	+	39.7923i	−0.448661	+	0.120218i	−0.476073	−	0.879406i	$-0.657940\pi$
$331$	−148.507	+	39.7923i	−0.448661	+	0.120218i	0.0274116	+	0.999624i	$0.491274\pi$
$332$	−39.7962	−	148.521i	−0.119868	−	0.447353i
$333$	−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
$336$	631.184	+	169.125i	1.87852	+	0.503349i
$337$		−	366.843i		−	1.08855i	−0.838905	−	0.544277i	$-0.816804\pi$
$337$		−	366.843i		−	1.08855i	0.838905	−	0.544277i	$-0.183196\pi$
$338$		0			0
$339$	−463.183			−1.36632
$340$	−15.4987	+	57.8421i	−0.0455845	+	0.170124i
$341$	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
$344$	−281.491	+	75.4252i	−0.818287	+	0.219259i
$345$	−4.54507	−	16.9624i	−0.0131741	−	0.0491665i
$346$	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
$349$	−435.035	−	116.567i	−1.24652	−	0.334004i	−0.425529	−	0.904945i	$-0.639912\pi$
$349$	−435.035	−	116.567i	−1.24652	−	0.334004i	−0.820991	+	0.570941i	$0.806579\pi$
$350$		−	348.715i		−	0.996327i
$351$		0			0
$352$	27.2544			0.0774273
$353$	116.929	−	436.385i	0.331244	−	1.23622i	−0.576641	−	0.816998i	$-0.695637\pi$
$353$	116.929	−	436.385i	0.331244	−	1.23622i	0.907885	−	0.419220i	$-0.137696\pi$
$354$	−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
$357$	−789.895	+	211.652i	−2.21259	+	0.592862i
$358$	−88.1187	−	328.863i	−0.246142	−	0.918613i
$359$	167.150	−	167.150i	0.465598	−	0.465598i	−0.434887	−	0.900485i	$-0.643212\pi$
$359$	167.150	−	167.150i	0.465598	−	0.465598i	0.900485	+	0.434887i	$0.143212\pi$
$360$	73.7408	−	127.723i	0.204836	−	0.354786i
$361$	−312.242	+	180.273i	−0.864936	+	0.499371i
$362$	130.722	+	35.0269i	0.361111	+	0.0967593i
$363$		−	601.044i		−	1.65577i
$364$		0			0
$365$	−114.964			−0.314969
$366$	−278.099	+	1037.88i	−0.759834	+	2.83574i
$367$	−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
$370$	−14.1915	+	3.80259i	−0.0383553	+	0.0102773i
$371$	111.547	+	416.300i	0.300666	+	1.12210i
$372$	−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
$375$	−361.979	−	96.9920i	−0.965278	−	0.258645i
$376$			199.001i			0.529257i
$377$		0			0
$378$	−562.396			−1.48782
$379$	−89.2768	+	333.186i	−0.235559	+	0.879118i	0.742337	+	0.670027i	$0.233717\pi$
$379$	−89.2768	+	333.186i	−0.235559	+	0.879118i	−0.977896	+	0.209091i	$0.932949\pi$
$380$	−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
$383$	−375.095	+	100.507i	−0.979361	+	0.262419i	−0.712776	−	0.701392i	$-0.752562\pi$
$383$	−375.095	+	100.507i	−0.979361	+	0.262419i	−0.266586	+	0.963811i	$0.585896\pi$
$384$	−195.324	−	728.960i	−0.508657	−	1.89833i
$385$	−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
$388$	−100.705	−	26.9837i	−0.259548	−	0.0695457i
$389$			391.807i			1.00722i	0.863932	+	0.503608i	$0.167994\pi$
$389$			391.807i			1.00722i	−0.863932	+	0.503608i	$0.832006\pi$
$390$		0			0
$391$	55.1672			0.141093
$392$	8.67868	−	32.3893i	0.0221395	−	0.0826257i
$393$	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
$396$	−28.1114	+	7.53243i	−0.0709884	+	0.0190213i
$397$	40.7905	+	152.232i	0.102747	+	0.383456i	0.998080	−	0.0619411i	$-0.0197291\pi$
$397$	40.7905	+	152.232i	0.102747	+	0.383456i	−0.895333	+	0.445397i	$0.853062\pi$
$398$	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
$401$	514.202	+	137.780i	1.28230	+	0.343591i	0.834731	−	0.550658i	$-0.185623\pi$
$401$	514.202	+	137.780i	1.28230	+	0.343591i	0.447569	+	0.894249i	$0.352290\pi$
$402$			1117.75i			2.78047i
$403$		0			0
$404$	−116.365			−0.288032
$405$	−14.8135	+	55.2848i	−0.0365766	+	0.136506i
$406$	−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
$409$	−269.003	+	72.0792i	−0.657710	+	0.176233i	−0.572212	−	0.820106i	$-0.693915\pi$
$409$	−269.003	+	72.0792i	−0.657710	+	0.176233i	−0.0854974	+	0.996338i	$0.527248\pi$
$410$	11.5519	+	43.1124i	0.0281755	+	0.105152i
$411$	−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
$414$	82.2314	+	22.0338i	0.198627	+	0.0532219i
$415$		−	156.597i		−	0.377342i
$416$		0			0
$417$	385.661			0.924847
$418$	0.477528	−	1.78216i	0.00114241	−	0.00426354i
$419$	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	0.102563	−	0.994726i	$-0.467296\pi$
$421$	−375.601	−	375.601i	−0.892163	−	0.892163i	−0.994726	+	0.102563i	$0.967296\pi$
$422$	160.898	−	43.1125i	0.381275	−	0.102162i
$423$	−144.459	−	539.127i	−0.341510	−	1.27453i
$424$	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
$427$	−576.941	−	154.591i	−1.35115	−	0.362039i
$428$			115.179i			0.269110i
$429$		0			0
$430$	185.966			0.432480
$431$	30.7479	−	114.753i	0.0713407	−	0.266247i	−0.921038	−	0.389473i	$-0.872657\pi$
$431$	30.7479	−	114.753i	0.0713407	−	0.266247i	0.992379	+	0.123226i	$0.0393239\pi$
$432$	359.644	+	622.922i	0.832510	+	1.44195i
$433$	−120.208	−	69.4021i	−0.277617	−	0.160282i	0.354727	−	0.934970i	$-0.384574\pi$
$433$	−120.208	−	69.4021i	−0.277617	−	0.160282i	−0.632344	+	0.774688i	$0.717907\pi$
$434$	−631.143	−	631.143i	−1.45425	−	1.45425i
$435$	−145.975	+	39.1138i	−0.335574	+	0.0899168i
$436$	11.8900	+	44.3740i	0.0272706	+	0.101775i
$437$	−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	−0.355182	−	0.934797i	$-0.615581\pi$
$439$	121.509	−	70.1532i	0.276786	−	0.159802i	0.631967	+	0.774995i	$0.282248\pi$
$440$	10.2077	+	2.73515i	0.0231993	+	0.00621624i
$441$			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	$0.354684\pi$
$444$	7.96819	−	29.7377i	0.0179464	−	0.0669768i
$445$	−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
$448$	152.451	−	40.8492i	0.340293	−	0.0911813i
$449$	78.1501	+	291.660i	0.174054	+	0.649577i	0.996711	+	0.0810394i	$0.0258240\pi$
$449$	78.1501	+	291.660i	0.174054	+	0.649577i	−0.822657	+	0.568538i	$0.807509\pi$
$450$	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
$453$	−1090.65	−	292.238i	−2.40761	−	0.645116i
$454$		−	172.158i		−	0.379203i
$455$		0			0
$456$	−19.5921			−0.0429652
$457$	−78.9361	+	294.593i	−0.172727	+	0.644625i	0.824201	+	0.566297i	$0.191625\pi$
$457$	−78.9361	+	294.593i	−0.172727	+	0.644625i	−0.996928	+	0.0783273i	$0.975042\pi$
$458$	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
$461$	780.401	−	209.108i	1.69284	−	0.453596i	0.721722	−	0.692183i	$-0.243351\pi$
$461$	780.401	−	209.108i	1.69284	−	0.453596i	0.971121	+	0.238587i	$0.0766842\pi$
$462$	−23.4035	−	87.3432i	−0.0506570	−	0.189054i
$463$	411.381	−	411.381i	0.888512	−	0.888512i	−0.105868	−	0.994380i	$-0.533762\pi$
$463$	411.381	−	411.381i	0.888512	−	0.888512i	0.994380	+	0.105868i	$0.0337620\pi$
$464$	−189.682	+	328.540i	−0.408798	+	0.708059i
$465$	−393.832	+	227.379i	−0.846951	+	0.488988i
$466$	599.395	+	160.608i	1.28626	+	0.344651i
$467$			279.834i			0.599215i	0.954062	+	0.299608i	$0.0968558\pi$
$467$			279.834i			0.599215i	−0.954062	+	0.299608i	$0.903144\pi$
$468$		0			0
$469$	−621.338			−1.32481
$470$	32.8673	−	122.663i	0.0699305	−	0.260984i
$471$	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
$474$	−560.872	+	150.285i	−1.18327	+	0.317057i
$475$	3.93008	+	14.6673i	0.00827386	+	0.0308785i
$476$	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
$479$	−258.576	−	69.2853i	−0.539825	−	0.144646i	−0.0214037	−	0.999771i	$-0.506814\pi$
$479$	−258.576	−	69.2853i	−0.539825	−	0.144646i	−0.518422	+	0.855125i	$0.673480\pi$
$480$			184.684i			0.384758i
$481$		0			0
$482$	−145.730			−0.302344
$483$	−19.0380	+	71.0507i	−0.0394161	+	0.147103i
$484$	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
$487$	523.877	−	140.372i	1.07572	−	0.288239i	0.322881	−	0.946440i	$-0.395349\pi$
$487$	523.877	−	140.372i	1.07572	−	0.288239i	0.752843	+	0.658201i	$0.228682\pi$
$488$	136.138	+	508.073i	0.278971	+	1.04113i
$489$	−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	−0.520617	−	0.853791i	$-0.674298\pi$
$491$	−20.3866	+	11.7702i	−0.0415205	+	0.0239719i	0.479096	+	0.877762i	$0.340965\pi$
$492$	−90.3405	−	24.2067i	−0.183619	−	0.0492005i
$493$		−	474.756i		−	0.962993i
$494$		0			0
$495$	−29.6399			−0.0598786
$496$	−295.461	+	1102.68i	−0.595688	+	2.22314i
$497$	−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	0.593389	−	0.804916i	$-0.297790\pi$
$499$	−105.552	−	105.552i	−0.211527	−	0.211527i	−0.804916	+	0.593389i	$0.797790\pi$
$500$	111.029	−	29.7502i	0.222059	−	0.0595005i
$501$	−41.2678	−	154.014i	−0.0823709	−	0.307412i
$502$	−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
$505$	−114.473	−	30.6731i	−0.226680	−	0.0607387i
$506$			6.10015i			0.0120556i
$507$		0			0
$508$	7.15632			0.0140873
$509$	202.293	−	754.970i	0.397433	−	1.48324i	−0.420163	−	0.907449i	$-0.638027\pi$
$509$	202.293	−	754.970i	0.397433	−	1.48324i	0.817596	−	0.575792i	$-0.195306\pi$
$510$	−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
$513$	23.6549	−	6.33831i	0.0461109	−	0.0123554i
$514$	227.499	+	849.037i	0.442605	+	1.65182i
$515$	−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
$518$	59.4439	+	15.9279i	0.114757	+	0.0307489i
$519$			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	$0.371652\pi$
$522$	189.618	−	707.664i	0.363253	−	1.35568i
$523$	−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
$526$	−744.867	+	199.586i	−1.41610	+	0.379442i
$527$	−369.754	−	1379.94i	−0.701621	−	2.61849i
$528$	−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
$531$	1163.31	+	311.707i	2.19079	+	0.587020i
$532$			6.82403i			0.0128271i
$533$		0			0
$534$	996.741			1.86656
$535$	−30.3604	+	113.306i	−0.0567484	+	0.211788i
$536$	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
$539$	−6.50939	+	1.74419i	−0.0120768	+	0.00323597i
$540$	−22.7473	−	84.8943i	−0.0421247	−	0.157212i
$541$	−62.1232	+	62.1232i	−0.114830	+	0.114830i	−0.762187	−	0.647357i	$-0.775874\pi$
$541$	−62.1232	+	62.1232i	−0.114830	+	0.114830i	0.647357	+	0.762187i	$0.275874\pi$
$542$	264.861	−	458.753i	0.488674	−	0.846408i
$543$	−250.123	+	144.409i	−0.460632	+	0.265946i
$544$	−560.414	−	150.162i	−1.03017	−	0.276034i
$545$			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	$0.563147\pi$
$548$	66.0251	−	246.409i	0.120484	−	0.449652i
$549$	−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
$552$	62.5695	−	16.7655i	0.113351	−	0.0303722i
$553$	−83.5411	−	311.780i	−0.151069	−	0.563797i
$554$	−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
$557$	879.229	+	235.589i	1.57851	+	0.422960i	0.938464	−	0.345377i	$-0.112249\pi$
$557$	879.229	+	235.589i	1.57851	+	0.422960i	0.640045	+	0.768338i	$0.278916\pi$
$558$		−	2204.60i		−	3.95090i
$559$		0			0
$560$	−204.129			−0.364516
$561$	37.4590	−	139.799i	0.0667718	−	0.249196i
$562$	−592.858	−	1026.86i	−1.05491	−	1.82715i
$563$	−203.525	−	117.505i	−0.361501	−	0.208713i	0.308238	−	0.951309i	$-0.400261\pi$
$563$	−203.525	−	117.505i	−0.361501	−	0.208713i	−0.669739	+	0.742597i	$0.733594\pi$
$564$	188.162	+	188.162i	0.333621	+	0.333621i
$565$	139.762	−	37.4491i	0.247366	−	0.0662816i
$566$	213.133	+	795.425i	0.376561	+	1.40534i
$567$	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	0.139674	−	0.990198i	$-0.455394\pi$
$569$	607.150	−	350.538i	1.06705	−	0.616060i	0.927373	+	0.374137i	$0.122061\pi$
$570$	12.0764	+	3.23587i	0.0211867	+	0.00567697i
$571$			323.381i			0.566341i	0.959070	+	0.283170i	$0.0913862\pi$
$571$			323.381i			0.566341i	−0.959070	+	0.283170i	$0.908614\pi$
$572$		0			0
$573$	341.058			0.595214
$574$	48.3877	−	180.585i	0.0842991	−	0.314608i
$575$	−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	0.984054	−	0.177868i	$-0.0569201\pi$
$577$	465.169	+	465.169i	0.806186	+	0.806186i	−0.177868	+	0.984054i	$0.556920\pi$
$578$	737.388	−	197.583i	1.27576	−	0.341838i
$579$	279.484	+	1043.05i	0.482701	+	1.80147i
$580$	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
$583$	−73.6784	−	19.7421i	−0.126378	−	0.0338629i
$584$		−	424.068i		−	0.726143i
$585$		0			0
$586$	−1266.94			−2.16201
$587$	−59.0221	+	220.274i	−0.100549	+	0.375253i	−0.997802	−	0.0662628i	$-0.978892\pi$
$587$	−59.0221	+	220.274i	−0.100549	+	0.375253i	0.897253	+	0.441516i	$0.145559\pi$
$588$	−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
$591$	−767.683	+	205.700i	−1.29896	+	0.348054i
$592$	−20.3714	−	76.0271i	−0.0344112	−	0.128424i
$593$	332.603	−	332.603i	0.560883	−	0.560883i	−0.368675	−	0.929558i	$-0.620189\pi$
$593$	332.603	−	332.603i	0.560883	−	0.560883i	0.929558	+	0.368675i	$0.120189\pi$
$594$	49.7675	−	86.1999i	0.0837837	−	0.145118i
$595$	221.232	−	127.729i	0.371819	−	0.214670i
$596$	178.099	+	47.7215i	0.298824	+	0.0800696i
$597$			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	$0.828202\pi$
$600$	169.621	−	633.033i	0.282701	−	1.05506i
$601$	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
$604$	334.532	−	89.6377i	0.553862	−	0.148407i
$605$	48.5954	+	181.361i	0.0803230	+	0.299769i
$606$	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
$609$	611.445	+	163.836i	1.00401	+	0.269025i
$610$		−	335.657i		−	0.550258i
$611$		0			0
$612$	619.537			1.01232
$613$	−34.8392	+	130.022i	−0.0568339	+	0.212107i	−0.988503	−	0.151201i	$-0.951686\pi$
$613$	−34.8392	+	130.022i	−0.0568339	+	0.212107i	0.931669	+	0.363308i	$0.118353\pi$
$614$	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
$617$	764.980	−	204.976i	1.23984	−	0.332214i	0.421436	−	0.906858i	$-0.361526\pi$
$617$	764.980	−	204.976i	1.23984	−	0.332214i	0.818403	+	0.574645i	$0.194860\pi$
$618$	−244.519	−	912.559i	−0.395662	−	1.47663i
$619$	170.666	−	170.666i	0.275713	−	0.275713i	−0.555682	−	0.831395i	$-0.687543\pi$
$619$	170.666	−	170.666i	0.275713	−	0.275713i	0.831395	+	0.555682i	$0.187543\pi$
$620$	69.7437	−	120.800i	0.112490	−	0.194838i
$621$	−70.1207	+	40.4842i	−0.112916	+	0.0651919i
$622$	228.172	+	61.1386i	0.366836	+	0.0982935i
$623$			554.072i			0.889361i
$624$		0			0
$625$	−446.368			−0.714189
$626$	54.7863	−	204.465i	0.0875180	−	0.326622i
$627$	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
$630$	380.781	−	102.030i	0.604414	−	0.161952i
$631$	20.6148	+	76.9356i	0.0326701	+	0.121926i	0.980335	−	0.197340i	$-0.0632302\pi$
$631$	20.6148	+	76.9356i	0.0326701	+	0.121926i	−0.947665	+	0.319266i	$0.896564\pi$
$632$	−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
$635$	7.03999	+	1.88636i	0.0110866	+	0.00297064i
$636$		−	507.517i		−	0.797983i
$637$		0			0
$638$	52.4964			0.0822828
$639$	285.266	−	1064.63i	0.446426	−	1.66608i
$640$	117.875	+	204.166i	0.184180	+	0.319009i
$641$	449.661	+	259.612i	0.701500	+	0.405011i	0.807906	−	0.589312i	$-0.200601\pi$
$641$	449.661	+	259.612i	0.701500	+	0.405011i	−0.106406	+	0.994323i	$0.533934\pi$
$642$	−625.017	−	625.017i	−0.973546	−	0.973546i
$643$	−483.537	+	129.563i	−0.752002	+	0.201498i	−0.614406	−	0.788990i	$-0.710604\pi$
$643$	−483.537	+	129.563i	−0.752002	+	0.201498i	−0.137596	+	0.990488i	$0.543938\pi$
$644$	−5.83949	−	21.7933i	−0.00906753	−	0.0338405i
$645$	−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	−0.685419	−	0.728149i	$-0.740381\pi$
$647$	−257.204	+	148.497i	−0.397533	+	0.229516i	0.287886	+	0.957665i	$0.407048\pi$
$648$	−203.929	−	54.6427i	−0.314706	−	0.0843252i
$649$			86.2973i			0.132970i
$650$		0			0
$651$	1904.85			2.92604
$652$	59.0914	−	220.532i	0.0906309	−	0.338239i
$653$	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
$656$	−230.964	+	61.8865i	−0.352079	+	0.0943392i
$657$	307.840	+	1148.87i	0.468553	+	1.74866i
$658$	−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
$661$	196.045	+	52.5302i	0.296589	+	0.0794708i	0.404045	−	0.914739i	$-0.367604\pi$
$661$	196.045	+	52.5302i	0.296589	+	0.0794708i	−0.107456	+	0.994210i	$0.534271\pi$
$662$			361.902i			0.546680i
$663$		0			0
$664$	577.641			0.869941
$665$	−1.79877	+	6.71309i	−0.00270491	+	0.0100949i
$666$	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
$669$	740.602	−	198.444i	1.10703	−	0.296627i
$670$	−90.3717	−	337.272i	−0.134883	−	0.503390i
$671$	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	−0.313998	−	0.949424i	$-0.601669\pi$
$673$	236.376	−	136.472i	0.351228	−	0.202781i	0.665226	+	0.746642i	$0.268335\pi$
$674$	−834.088	−	223.493i	−1.23752	−	0.331592i
$675$			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	$0.598799\pi$
$678$	−282.187	+	1053.14i	−0.416205	+	1.55330i
$679$	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
$682$	152.588	−	40.8859i	0.223736	−	0.0599499i
$683$	−309.658	−	1155.66i	−0.453379	−	1.69203i	−0.692809	−	0.721121i	$-0.743627\pi$
$683$	−309.658	−	1155.66i	−0.453379	−	1.69203i	0.239430	−	0.970914i	$-0.423039\pi$
$684$	−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
$687$	−1253.77	−	335.947i	−1.82500	−	0.489006i
$688$			996.265i			1.44806i
$689$		0			0
$690$	−41.3364			−0.0599078
$691$	−218.661	+	816.053i	−0.316441	+	1.18097i	0.606200	+	0.795313i	$0.292693\pi$
$691$	−218.661	+	816.053i	−0.316441	+	1.18097i	−0.922640	+	0.385661i	$0.873973\pi$
$692$	−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
$695$	−116.370	+	31.1813i	−0.167439	+	0.0448652i
$696$	−144.280	−	538.459i	−0.207298	−	0.773647i
$697$	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
$700$	−220.489	−	59.0797i	−0.314984	−	0.0843996i
$701$		−	765.186i		−	1.09156i	−0.837927	−	0.545782i	$-0.816233\pi$
$701$		−	765.186i		−	1.09156i	0.837927	−	0.545782i	$-0.183767\pi$
$702$		0			0
$703$	−2.67978			−0.00381192
$704$	−7.22966	+	26.9815i	−0.0102694	+	0.0383259i
$705$	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
$708$	−554.620	+	148.610i	−0.783361	+	0.209901i
$709$	125.630	+	468.858i	0.177193	+	0.661295i	0.996168	+	0.0874645i	$0.0278764\pi$
$709$	125.630	+	468.858i	0.177193	+	0.661295i	−0.818974	+	0.573830i	$0.805457\pi$
$710$	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
$713$	−124.125	−	33.2592i	−0.174089	−	0.0466469i
$714$			1924.92i			2.69597i
$715$		0			0
$716$	−222.866			−0.311266
$717$	−479.068	+	1787.91i	−0.668157	+	2.49359i
$718$	−278.214	−	481.881i	−0.387484	−	0.671143i
$719$	732.510	+	422.915i	1.01879	+	0.588199i	0.913753	−	0.406269i	$-0.133170\pi$
$719$	732.510	+	422.915i	1.01879	+	0.588199i	0.105037	+	0.994468i	$0.466504\pi$
$720$	−356.515	−	356.515i	−0.495159	−	0.495159i
$721$	507.277	−	135.924i	0.703574	−	0.188522i
$722$	219.657	+	819.771i	0.304234	+	1.13542i
$723$	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
$726$	−1366.59	−	366.177i	−1.88236	−	0.504376i
$727$		−	1019.65i		−	1.40255i	−0.712892	−	0.701274i	$-0.752615\pi$
$727$		−	1019.65i		−	1.40255i	0.712892	−	0.701274i	$-0.247385\pi$
$728$		0			0
$729$	−1051.18			−1.44195
$730$	−70.0398	+	261.392i	−0.0959450	+	0.358072i
$731$	−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	0.207141	−	0.978311i	$-0.433584\pi$
$733$	−565.267	−	565.267i	−0.771170	−	0.771170i	−0.978311	+	0.207141i	$0.933584\pi$
$734$	−1543.36	+	413.542i	−2.10267	+	0.563409i
$735$	−11.8191	−	44.1096i	−0.0160804	−	0.0600130i
$736$	−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
$739$	−271.089	−	72.6381i	−0.366832	−	0.0982924i	0.0706941	−	0.997498i	$-0.477479\pi$
$739$	−271.089	−	72.6381i	−0.366832	−	0.0982924i	−0.437526	+	0.899206i	$0.644145\pi$
$740$			9.61737i			0.0129964i
$741$		0			0
$742$	1014.50			1.36725
$743$	−252.379	+	941.890i	−0.339675	+	1.26768i	0.559036	+	0.829143i	$0.311171\pi$
$743$	−252.379	+	941.890i	−0.339675	+	1.26768i	−0.898711	+	0.438541i	$0.855495\pi$
$744$	−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
$747$	−1564.93	+	419.321i	−2.09495	+	0.561340i
$748$	11.4897	+	42.8803i	0.0153606	+	0.0573266i
$749$	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	−0.900742	−	0.434355i	$-0.856976\pi$
$751$	−732.187	+	422.729i	−0.974950	+	0.562888i	−0.0742082	+	0.997243i	$0.523643\pi$
$752$	657.133	+	176.078i	0.873847	+	0.234146i
$753$		−	563.297i		−	0.748071i
$754$		0			0
$755$	352.722			0.467181
$756$	−95.2819	+	355.597i	−0.126034	+	0.470366i
$757$	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
$760$	5.91177	−	1.58405i	0.00777865	−	0.00208428i
$761$	−173.566	−	647.756i	−0.228076	−	0.851191i	−0.981149	−	0.193254i	$-0.938096\pi$
$761$	−173.566	−	647.756i	−0.228076	−	0.851191i	0.753073	−	0.657937i	$-0.228571\pi$
$762$	−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
$765$	609.466	+	163.306i	0.796687	+	0.213472i
$766$			914.084i			1.19332i
$767$		0			0
$768$	−1293.95			−1.68484
$769$	282.232	−	1053.30i	0.367011	−	1.36971i	−0.497662	−	0.867371i	$-0.665808\pi$
$769$	282.232	−	1053.30i	0.367011	−	1.36971i	0.864673	−	0.502334i	$-0.167525\pi$
$770$	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
$773$	156.639	−	41.9712i	0.202637	−	0.0542965i	−0.156073	−	0.987746i	$-0.549883\pi$
$773$	156.639	−	41.9712i	0.202637	−	0.0542965i	0.358710	+	0.933449i	$0.383217\pi$
$774$	−497.964	−	1858.43i	−0.643364	−	2.40107i
$775$	−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
$778$	890.849	+	238.702i	1.14505	+	0.306815i
$779$			8.14093i			0.0104505i
$780$		0			0
$781$	78.9770			0.101123
$782$	33.6098	−	125.433i	0.0429792	−	0.160401i
$783$	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
$786$	668.398	−	179.097i	0.850379	−	0.227858i
$787$	2.27714	+	8.49841i	0.00289345	+	0.0107985i	0.967357	−	0.253416i	$-0.0815541\pi$
$787$	2.27714	+	8.49841i	0.00289345	+	0.0107985i	−0.964464	+	0.264214i	$0.914887\pi$
$788$	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
$791$	−585.421	−	156.863i	−0.740103	−	0.198310i
$792$		−	109.333i		−	0.138047i
$793$		0			0
$794$	370.980			0.467230
$795$	133.778	−	499.267i	0.168274	−	0.628008i
$796$	−32.3037	−	55.9517i	−0.0405826	−	0.0702911i
$797$	−618.344	−	357.001i	−0.775840	−	0.447931i	0.0591141	−	0.998251i	$-0.481172\pi$
$797$	−618.344	−	357.001i	−0.775840	−	0.447931i	−0.834954	+	0.550320i	$0.814506\pi$
$798$	−37.0305	−	37.0305i	−0.0464042	−	0.0464042i
$799$	−822.368	+	220.353i	−1.02925	+	0.275786i
$800$	136.654	+	510.001i	0.170818	+	0.637502i
$801$	−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
$804$	706.740	+	189.370i	0.879030	+	0.235535i
$805$		−	22.9782i		−	0.0285444i
$806$		0			0
$807$	−1377.28			−1.70666
$808$	113.144	−	422.259i	0.140030	−	0.522598i
$809$	−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	0.787895	−	0.615809i	$-0.211171\pi$
$811$	139.562	+	139.562i	0.172086	+	0.172086i	−0.615809	+	0.787895i	$0.711171\pi$
$812$	−187.548	+	50.2533i	−0.230970	+	0.0618883i
$813$	292.592	+	1091.97i	0.359892	+	1.34314i
$814$	−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
$817$	32.7637	+	8.77901i	0.0401025	+	0.0107454i
$818$			655.544i			0.801399i
$819$		0			0
$820$	29.2167			0.0356301
$821$	196.368	−	732.854i	0.239181	−	0.892635i	−0.737039	−	0.675851i	$-0.763776\pi$
$821$	196.368	−	732.854i	0.239181	−	0.892635i	0.976219	−	0.216785i	$-0.0695569\pi$
$822$	978.851	+	1695.42i	1.19082	+	2.06256i
$823$	1372.60	+	792.473i	1.66781	+	0.962908i	0.968818	+	0.247773i	$0.0796989\pi$
$823$	1372.60	+	792.473i	1.66781	+	0.962908i	0.698987	+	0.715134i	$0.253634\pi$
$824$	−327.025	−	327.025i	−0.396875	−	0.396875i
$825$	−127.223	+	34.0893i	−0.154210	+	0.0413204i
$826$	−297.062	−	1108.65i	−0.359640	−	1.34219i
$827$	380.972	−	380.972i	0.460668	−	0.460668i	−0.438207	−	0.898874i	$-0.644386\pi$
$827$	380.972	−	380.972i	0.460668	−	0.460668i	0.898874	+	0.438207i	$0.144386\pi$
$828$	27.8635	−	48.2611i	0.0336516	−	0.0582863i
$829$	926.803	−	535.090i	1.11798	−	0.645464i	0.177093	−	0.984194i	$-0.443331\pi$
$829$	926.803	−	535.090i	1.11798	−	0.645464i	0.940884	+	0.338730i	$0.109997\pi$
$830$	−356.053	−	95.4042i	−0.428980	−	0.114945i
$831$		−	2026.91i		−	2.43912i
$832$		0			0
$833$	143.458			0.172219
$834$	234.958	−	876.876i	0.281724	−	1.05141i
$835$	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
$838$	1111.71	−	297.882i	1.32662	−	0.355467i
$839$	217.481	+	811.649i	0.259214	+	0.967400i	0.965697	+	0.259670i	$0.0836139\pi$
$839$	217.481	+	811.649i	0.259214	+	0.967400i	−0.706483	+	0.707730i	$0.749719\pi$
$840$	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
$843$	2444.23	+	654.930i	2.89945	+	0.776904i
$844$		−	109.038i		−	0.129192i
$845$		0			0
$846$	−1313.82			−1.55298
$847$	203.552	−	759.666i	0.240321	−	0.896890i
$848$	−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
$851$	8.55817	−	2.29315i	0.0100566	−	0.00269466i
$852$	136.004	+	507.573i	0.159629	+	0.595743i
$853$	500.522	−	500.522i	0.586778	−	0.586778i	−0.349979	−	0.936757i	$-0.613811\pi$
$853$	500.522	−	500.522i	0.586778	−	0.586778i	0.936757	+	0.349979i	$0.113811\pi$
$854$	−702.984	+	1217.60i	−0.823167	+	1.42577i
$855$	−14.8661	+	8.58295i	−0.0173873	+	0.0100385i
$856$	−417.955	−	111.991i	−0.488265	−	0.130830i
$857$		−	175.305i		−	0.204556i	−0.994756	−	0.102278i	$-0.967387\pi$
$857$		−	175.305i		−	0.204556i	0.994756	−	0.102278i	$-0.0326132\pi$
$858$		0			0
$859$	1523.72			1.77384			0.886918	−	0.461928i	$-0.152842\pi$
$859$	1523.72			1.77384			0.886918	+	0.461928i	$0.152842\pi$
$860$	31.5067	−	117.584i	0.0366357	−	0.136726i
$861$	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	0.333463	−	0.942763i	$-0.391783\pi$
$863$	−525.826	−	525.826i	−0.609300	−	0.609300i	−0.942763	+	0.333463i	$0.891783\pi$
$864$	822.514	−	220.392i	0.951984	−	0.255083i
$865$	−35.3404	−	131.892i	−0.0408560	−	0.152477i
$866$	−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
$869$	55.1800	+	14.7854i	0.0634983	+	0.0170143i
$870$			355.731i			0.408887i
$871$		0			0
$872$	−172.583			−0.197916
$873$	−284.320	+	1061.10i	−0.325682	+	1.21546i
$874$	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
$877$	−618.447	+	165.712i	−0.705185	+	0.188954i	−0.593552	−	0.804796i	$-0.702275\pi$
$877$	−618.447	+	165.712i	−0.705185	+	0.188954i	−0.111633	+	0.993749i	$0.535608\pi$
$878$	−85.4795	−	319.014i	−0.0973571	−	0.363342i
$879$	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	0.159953	−	0.987125i	$-0.448866\pi$
$881$	964.522	−	556.867i	1.09480	−	0.632085i	0.934851	+	0.355039i	$0.115533\pi$
$882$	213.837	+	57.2974i	0.242445	+	0.0649630i
$883$			206.038i			0.233338i	0.993171	+	0.116669i	$0.0372217\pi$
$883$			206.038i			0.233338i	−0.993171	+	0.116669i	$0.962778\pi$
$884$		0			0
$885$	−584.776			−0.660764
$886$	237.953	−	888.052i	0.268570	−	1.00232i
$887$	−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
$890$	−300.759	+	80.5881i	−0.337931	+	0.0905484i
$891$	10.9818	+	40.9845i	0.0123252	+	0.0459983i
$892$	−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
$895$	−219.243	−	58.7460i	−0.244964	−	0.0656380i
$896$		−	987.489i		−	1.10211i
$897$		0			0
$898$	710.758			0.791489
$899$	−286.221	+	1068.19i	−0.318377	+	1.18820i
$900$	−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
$903$	1605.74	−	430.257i	1.77823	−	0.476475i
$904$	138.139	+	515.541i	0.152808	+	0.570289i
$905$	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	−0.703908	−	0.710291i	$-0.748563\pi$
$907$	−399.745	+	230.793i	−0.440733	+	0.254457i	0.263176	+	0.964748i	$0.415230\pi$
$908$	−108.854	−	29.1673i	−0.119883	−	0.0321225i
$909$			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	$0.227014\pi$
$912$	−17.3353	+	64.6964i	−0.0190080	+	0.0709390i
$913$	−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
$916$	384.568	−	103.045i	0.419834	−	0.112494i
$917$	99.5570	+	371.552i	0.108568	+	0.405182i
$918$	−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
$921$	−2337.14	−	626.234i	−2.53761	−	0.679950i
$922$		−	1901.79i		−	2.06268i
$923$		0			0
$924$	−59.1912			−0.0640598
$925$	23.2005	−	86.5853i	0.0250816	−	0.0936058i
$926$	−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
$929$	551.276	−	147.714i	0.593408	−	0.159003i	0.0503975	−	0.998729i	$-0.483951\pi$
$929$	551.276	−	147.714i	0.593408	−	0.159003i	0.543010	+	0.839726i	$0.317285\pi$
$930$	277.055	+	1033.98i	0.297908	+	1.11181i
$931$	−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
$934$	636.256	+	170.484i	0.681216	+	0.182531i
$935$			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	$0.504584\pi$
$938$	−378.540	+	1412.73i	−0.403561	+	1.50611i
$939$	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	0.912119	+	0.409926i	$0.134445\pi$
$941$	1244.04	+	1244.04i	1.32204	+	1.32204i	0.409926	+	0.912119i	$0.365555\pi$
$942$	1388.77	−	372.121i	1.47428	−	0.395033i
$943$	−6.96639	−	25.9989i	−0.00738748	−	0.0275705i
$944$	−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
$947$	71.4365	+	19.1413i	0.0754345	+	0.0202126i	0.296339	−	0.955083i	$-0.404234\pi$
$947$	71.4365	+	19.1413i	0.0754345	+	0.0202126i	−0.220904	+	0.975295i	$0.570901\pi$
$948$			380.095i			0.400944i
$949$		0			0
$950$	35.7432			0.0376245
$951$	524.952	−	1959.15i	0.551999	−	2.06009i
$952$	471.154	+	816.062i	0.494909	+	0.857208i
$953$	−334.954	−	193.386i	−0.351474	−	0.202923i	0.313861	−	0.949469i	$-0.398378\pi$
$953$	−334.954	−	193.386i	−0.351474	−	0.202923i	−0.665334	+	0.746546i	$0.731711\pi$
$954$	1771.84	+	1771.84i	1.85727	+	1.85727i
$955$	−102.912	+	27.5751i	−0.107761	+	0.0288744i
$956$	−146.944	−	548.402i	−0.153707	−	0.573643i
$957$	−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
$960$	−182.834	−	48.9903i	−0.190452	−	0.0510316i
$961$			2366.76i			2.46281i
$962$		0			0
$963$	1213.61			1.26024
$964$	−24.6898	+	92.1435i	−0.0256118	+	0.0955845i
$965$	−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	0.917641	−	0.397409i	$-0.130091\pi$
$967$	503.064	+	503.064i	0.520232	+	0.520232i	−0.397409	+	0.917641i	$0.630091\pi$
$968$	−668.986	+	179.254i	−0.691102	+	0.185180i
$969$	−21.6943	−	80.9642i	−0.0223883	−	0.0835544i
$970$	−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
$973$	487.441	+	130.609i	0.500967	+	0.134234i
$974$		−	1276.66i		−	1.31074i
$975$		0			0
$976$	1798.20			1.84241
$977$	−213.703	+	797.549i	−0.218733	+	0.816324i	0.766085	+	0.642739i	$0.222202\pi$
$977$	−213.703	+	797.549i	−0.218733	+	0.816324i	−0.984819	+	0.173585i	$0.944465\pi$
$978$	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
$981$	467.557	−	125.281i	0.476612	−	0.127708i
$982$	14.3416	+	53.5236i	0.0146045	+	0.0545047i
$983$	99.0983	−	99.0983i	0.100812	−	0.100812i	−0.654902	−	0.755714i	$-0.727290\pi$
$983$	99.0983	−	99.0983i	0.100812	−	0.100812i	0.755714	+	0.654902i	$0.227290\pi$
$984$	175.680	−	304.286i	0.178536	−	0.309234i
$985$	215.011	−	124.137i	0.218286	−	0.126027i
$986$	−1079.45	−	289.238i	−1.09478	−	0.293344i
$987$		−	1135.18i		−	1.15013i
$988$		0			0
$989$	−112.147			−0.113394
$990$	−18.0577	+	67.3921i	−0.0182401	+	0.0680728i
$991$	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
$994$	−1014.61	+	271.864i	−1.02073	+	0.273505i
$995$	−17.0301	−	63.5572i	−0.0171157	−	0.0638766i
$996$	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
$999$	−139.642	−	37.4170i	−0.139782	−	0.0374544i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.e.70.3	✓	24	13.11	odd	12
169.3.d.e.70.10	yes	24	13.2	odd	12
169.3.d.e.99.3	yes	24	13.10	even	6
169.3.d.e.99.10	yes	24	13.3	even	3
169.3.f.g.19.3		48	13.7	odd	12	inner
169.3.f.g.19.10		48	13.6	odd	12	inner
169.3.f.g.80.3		48	13.5	odd	4	inner
169.3.f.g.80.10		48	13.8	odd	4	inner
169.3.f.g.89.3		48	13.12	even	2	inner
169.3.f.g.89.10		48	1.1	even	1	trivial
169.3.f.g.150.3		48	13.9	even	3	inner
169.3.f.g.150.10		48	13.4	even	6	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+(0.609234 - 2.27369i) q^{2} +(2.51175 + 4.35048i) q^{3} +(-1.33442 - 0.770425i) q^{4} +(-1.10964 - 1.10964i) q^{5} +(11.4219 - 3.06049i) q^{6} +(1.70128 + 6.34925i) q^{7} +(4.09315 - 4.09315i) q^{8} +(-8.11776 + 14.0604i) q^{9} +(-3.19902 + 1.84696i) q^{10} +(-1.12372 - 0.301099i) q^{11} -7.74046i q^{12} +15.4727 q^{14} +(2.04033 - 7.61462i) q^{15} +(-9.89459 - 17.1379i) q^{16} +(21.4473 + 12.3826i) q^{17} +(27.0234 + 27.0234i) q^{18} +(-0.650797 + 0.174381i) q^{19} +(0.625828 + 2.33562i) q^{20} +(-23.3491 + 23.3491i) q^{21} +(-1.36921 + 2.37154i) q^{22} +(1.92917 - 1.11381i) q^{23} +(28.0881 + 7.52619i) q^{24} -22.5374i q^{25} -36.3476 q^{27} +(2.62141 - 9.78324i) q^{28} +(-9.58516 - 16.6020i) q^{29} +(-16.0703 - 9.27818i) q^{30} +(-40.7907 - 40.7907i) q^{31} +(-22.6291 + 6.06346i) q^{32} +(-1.51257 - 5.64498i) q^{33} +(41.2206 - 41.2206i) q^{34} +(5.15759 - 8.93321i) q^{35} +(21.6649 - 12.5082i) q^{36} +(3.84185 + 1.02942i) q^{37} +1.58595i q^{38} -9.08389 q^{40} +(3.12729 - 11.6712i) q^{41} +(38.8636 + 67.3137i) q^{42} +(-43.5991 - 25.1720i) q^{43} +(1.26753 + 1.26753i) q^{44} +(24.6098 - 6.59418i) q^{45} +(-1.35714 - 5.06491i) q^{46} +(-24.3090 + 24.3090i) q^{47} +(49.7054 - 86.0923i) q^{48} +(5.01666 - 2.89637i) q^{49} +(-51.2431 - 13.7305i) q^{50} +124.408i q^{51} +65.5668 q^{53} +(-22.1442 + 82.6433i) q^{54} +(0.912811 + 1.58104i) q^{55} +(32.9520 + 19.0249i) q^{56} +(-2.39328 - 2.39328i) q^{57} +(-43.5874 + 11.6792i) q^{58} +(-19.1991 - 71.6521i) q^{59} +(-8.58915 + 8.58915i) q^{60} +(-45.4338 + 78.6937i) q^{61} +(-117.597 + 67.8945i) q^{62} +(-103.083 - 27.6211i) q^{63} -24.0109i q^{64} -13.7565 q^{66} +(-24.4650 + 91.3047i) q^{67} +(-19.0797 - 33.0470i) q^{68} +(9.69118 + 5.59520i) q^{69} +(-17.1692 - 17.1692i) q^{70} +(-65.5740 + 17.5705i) q^{71} +(24.3240 + 90.7785i) q^{72} +(51.8021 - 51.8021i) q^{73} +(4.68118 - 8.10804i) q^{74} +(98.0483 - 56.6082i) q^{75} +(1.00278 + 0.268695i) q^{76} -7.64700i q^{77} -49.1050 q^{79} +(-8.03753 + 29.9965i) q^{80} +(-18.2361 - 31.5859i) q^{81} +(-24.6315 - 14.2210i) q^{82} +(70.5618 + 70.5618i) q^{83} +(49.1461 - 13.1686i) q^{84} +(-10.0586 - 37.5391i) q^{85} +(-83.7955 + 83.7955i) q^{86} +(48.1510 - 83.4000i) q^{87} +(-5.83198 + 3.36710i) q^{88} +(81.4201 + 21.8165i) q^{89} -59.9726i q^{90} -3.43242 q^{92} +(75.0030 - 279.915i) q^{93} +(40.4613 + 70.0810i) q^{94} +(0.915654 + 0.528653i) q^{95} +(-83.2176 - 83.2176i) q^{96} +(65.3566 - 17.5122i) q^{97} +(-3.52914 - 13.1709i) 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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