LMFDB - Embedded newform 637.2.x.a.80.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.4
Character	$\chi$	$=$	637.80
Dual form			637.2.x.a.215.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.127046 - 0.474142i) q^{2} +2.44579i q^{3} +(1.52338 - 0.879524i) q^{4} +(0.931242 - 3.47544i) q^{5} +(1.15965 - 0.310728i) q^{6} +(-1.30475 - 1.30475i) q^{8} -2.98191 q^{9} +O(q^{10})$	\(q+(-0.127046 - 0.474142i) q^{2} +2.44579i q^{3} +(1.52338 - 0.879524i) q^{4} +(0.931242 - 3.47544i) q^{5} +(1.15965 - 0.310728i) q^{6} +(-1.30475 - 1.30475i) q^{8} -2.98191 q^{9} -1.76616 q^{10} +(1.49610 + 1.49610i) q^{11} +(2.15114 + 3.72588i) q^{12} +(0.582584 - 3.55817i) q^{13} +(8.50022 + 2.27763i) q^{15} +(1.30618 - 2.26236i) q^{16} +(-0.572121 - 0.990942i) q^{17} +(0.378840 + 1.41385i) q^{18} +(-3.22385 - 3.22385i) q^{19} +(-1.63810 - 6.11348i) q^{20} +(0.519289 - 0.899435i) q^{22} +(-1.28375 - 0.741175i) q^{23} +(3.19115 - 3.19115i) q^{24} +(-6.88137 - 3.97296i) q^{25} +(-1.76109 + 0.175824i) q^{26} +0.0442386i q^{27} +(2.75801 + 4.77701i) q^{29} -4.31968i q^{30} +(5.85632 - 1.56920i) q^{31} +(-4.80327 - 1.28703i) q^{32} +(-3.65915 + 3.65915i) q^{33} +(-0.397162 + 0.397162i) q^{34} +(-4.54259 + 2.62266i) q^{36} +(2.61260 - 0.700045i) q^{37} +(-1.11899 + 1.93814i) q^{38} +(8.70256 + 1.42488i) q^{39} +(-5.74963 + 3.31955i) q^{40} +(-1.21867 + 4.54813i) q^{41} +(-4.55704 - 2.63101i) q^{43} +(3.59498 + 0.963272i) q^{44} +(-2.77688 + 10.3635i) q^{45} +(-0.188327 + 0.702845i) q^{46} +(6.51834 + 1.74658i) q^{47} +(5.53327 + 3.19464i) q^{48} +(-1.00950 + 3.76750i) q^{50} +(2.42364 - 1.39929i) q^{51} +(-2.24200 - 5.93285i) q^{52} +(-1.74389 + 3.02051i) q^{53} +(0.0209754 - 0.00562033i) q^{54} +(6.59283 - 3.80637i) q^{55} +(7.88489 - 7.88489i) q^{57} +(1.91459 - 1.91459i) q^{58} +(11.0394 + 2.95801i) q^{59} +(14.9523 - 4.00646i) q^{60} +9.46949i q^{61} +(-1.48804 - 2.57737i) q^{62} -2.78376i q^{64} +(-11.8237 - 5.33826i) q^{65} +(2.19983 + 1.27007i) q^{66} +(5.44554 - 5.44554i) q^{67} +(-1.74312 - 1.00639i) q^{68} +(1.81276 - 3.13980i) q^{69} +(1.74779 + 6.52285i) q^{71} +(3.89065 + 3.89065i) q^{72} +(-1.46556 - 5.46953i) q^{73} +(-0.663841 - 1.14981i) q^{74} +(9.71705 - 16.8304i) q^{75} +(-7.74662 - 2.07570i) q^{76} +(-0.430029 - 4.30727i) q^{78} +(5.91160 + 10.2392i) q^{79} +(-6.64635 - 6.64635i) q^{80} -9.05394 q^{81} +2.31129 q^{82} +(5.06789 + 5.06789i) q^{83} +(-3.97675 + 1.06557i) q^{85} +(-0.668517 + 2.49494i) q^{86} +(-11.6836 + 6.74552i) q^{87} -3.90407i q^{88} +(2.58048 + 9.63048i) q^{89} +5.26655 q^{90} -2.60753 q^{92} +(3.83793 + 14.3234i) q^{93} -3.31251i q^{94} +(-14.2065 + 8.20214i) q^{95} +(3.14782 - 11.7478i) q^{96} +(-13.1665 + 3.52795i) q^{97} +(-4.46123 - 4.46123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.127046	−	0.474142i	−0.0898350	−	0.335269i	0.906351	−	0.422526i	$-0.138857\pi$
$2$	−0.127046	−	0.474142i	−0.0898350	−	0.335269i	−0.996186	+	0.0872571i	$0.972190\pi$
$3$			2.44579i			1.41208i	0.708172	+	0.706040i	$0.249520\pi$
$3$			2.44579i			1.41208i	−0.708172	+	0.706040i	$0.750480\pi$
$4$	1.52338	−	0.879524i	0.761690	−	0.439762i
$5$	0.931242	−	3.47544i	0.416464	−	1.55427i	−0.365420	−	0.930843i	$-0.619075\pi$
$5$	0.931242	−	3.47544i	0.416464	−	1.55427i	0.781885	−	0.623423i	$-0.214259\pi$
$6$	1.15965	−	0.310728i	0.473427	−	0.126854i
$7$		0			0
$7$		0			0
$8$	−1.30475	−	1.30475i	−0.461299	−	0.461299i
$9$	−2.98191			−0.993971
$10$	−1.76616			−0.558510
$11$	1.49610	+	1.49610i	0.451090	+	0.451090i	0.895716	−	0.444626i	$-0.146663\pi$
$11$	1.49610	+	1.49610i	0.451090	+	0.451090i	−0.444626	+	0.895716i	$0.646663\pi$
$12$	2.15114	+	3.72588i	0.620980	+	1.07557i
$13$	0.582584	−	3.55817i	0.161580	−	0.986860i
$13$	0.582584	−	3.55817i	0.161580	−	0.986860i
$14$		0			0
$15$	8.50022	+	2.27763i	2.19475	+	0.588081i
$16$	1.30618	−	2.26236i	0.326544	−	0.565590i
$17$	−0.572121	−	0.990942i	−0.138760	−	0.240339i	0.788268	−	0.615332i	$-0.210978\pi$
$17$	−0.572121	−	0.990942i	−0.138760	−	0.240339i	−0.927027	+	0.374994i	$0.877645\pi$
$18$	0.378840	+	1.41385i	0.0892934	+	0.333248i
$19$	−3.22385	−	3.22385i	−0.739603	−	0.739603i	0.232898	−	0.972501i	$-0.425179\pi$
$19$	−3.22385	−	3.22385i	−0.739603	−	0.739603i	−0.972501	+	0.232898i	$0.925179\pi$
$20$	−1.63810	−	6.11348i	−0.366291	−	1.36701i
$21$		0			0
$22$	0.519289	−	0.899435i	0.110713	−	0.191760i
$23$	−1.28375	−	0.741175i	−0.267681	−	0.154546i	0.360152	−	0.932894i	$-0.382725\pi$
$23$	−1.28375	−	0.741175i	−0.267681	−	0.154546i	−0.627833	+	0.778348i	$0.716058\pi$
$24$	3.19115	−	3.19115i	0.651391	−	0.651391i
$25$	−6.88137	−	3.97296i	−1.37627	−	0.794593i
$26$	−1.76109	+	0.175824i	−0.345379	+	0.0344819i
$27$			0.0442386i			0.00851372i
$28$		0			0
$29$	2.75801	+	4.77701i	0.512149	+	0.887068i	0.999901	+	0.0140858i	$0.00448381\pi$
$29$	2.75801	+	4.77701i	0.512149	+	0.887068i	−0.487752	+	0.872982i	$0.662183\pi$
$30$		−	4.31968i		−	0.788661i
$31$	5.85632	−	1.56920i	1.05183	−	0.281836i	0.308820	−	0.951121i	$-0.400066\pi$
$31$	5.85632	−	1.56920i	1.05183	−	0.281836i	0.743006	+	0.669285i	$0.233399\pi$
$32$	−4.80327	−	1.28703i	−0.849106	−	0.227517i
$33$	−3.65915	+	3.65915i	−0.636976	+	0.636976i
$34$	−0.397162	+	0.397162i	−0.0681127	+	0.0681127i
$35$		0			0
$36$	−4.54259	+	2.62266i	−0.757098	+	0.437111i
$37$	2.61260	−	0.700045i	0.429509	−	0.115087i	−0.0375866	−	0.999293i	$-0.511967\pi$
$37$	2.61260	−	0.700045i	0.429509	−	0.115087i	0.467096	+	0.884207i	$0.345300\pi$
$38$	−1.11899	+	1.93814i	−0.181524	+	0.314408i
$39$	8.70256	+	1.42488i	1.39353	+	0.228164i
$40$	−5.74963	+	3.31955i	−0.909096	+	0.524867i
$41$	−1.21867	+	4.54813i	−0.190324	+	0.710299i	0.803104	+	0.595839i	$0.203180\pi$
$41$	−1.21867	+	4.54813i	−0.190324	+	0.710299i	−0.993428	+	0.114460i	$0.963486\pi$
$42$		0			0
$43$	−4.55704	−	2.63101i	−0.694942	−	0.401225i	0.110519	−	0.993874i	$-0.464749\pi$
$43$	−4.55704	−	2.63101i	−0.694942	−	0.401225i	−0.805461	+	0.592649i	$0.798082\pi$
$44$	3.59498	+	0.963272i	0.541964	+	0.145219i
$45$	−2.77688	+	10.3635i	−0.413953	+	1.54489i
$46$	−0.188327	+	0.702845i	−0.0277673	+	0.103629i
$47$	6.51834	+	1.74658i	0.950797	+	0.254765i	0.700700	−	0.713456i	$-0.252871\pi$
$47$	6.51834	+	1.74658i	0.950797	+	0.254765i	0.250097	+	0.968221i	$0.419538\pi$
$48$	5.53327	+	3.19464i	0.798659	+	0.461106i
$49$		0			0
$50$	−1.00950	+	3.76750i	−0.142765	+	0.532804i
$51$	2.42364	−	1.39929i	0.339378	−	0.195940i
$52$	−2.24200	−	5.93285i	−0.310910	−	0.822738i
$53$	−1.74389	+	3.02051i	−0.239542	+	0.414899i	−0.960583	−	0.277994i	$-0.910331\pi$
$53$	−1.74389	+	3.02051i	−0.239542	+	0.414899i	0.721041	+	0.692892i	$0.243664\pi$
$54$	0.0209754	−	0.00562033i	0.00285439	−	0.000764830i
$55$	6.59283	−	3.80637i	0.888977	−	0.513251i
$56$		0			0
$57$	7.88489	−	7.88489i	1.04438	−	1.04438i
$58$	1.91459	−	1.91459i	0.251397	−	0.251397i
$59$	11.0394	+	2.95801i	1.43721	+	0.385100i	0.891557	−	0.452909i	$-0.149614\pi$
$59$	11.0394	+	2.95801i	1.43721	+	0.385100i	0.545656	+	0.838009i	$0.316280\pi$
$60$	14.9523	−	4.00646i	1.93033	−	0.517232i
$61$			9.46949i			1.21244i	0.795296	+	0.606222i	$0.207316\pi$
$61$			9.46949i			1.21244i	−0.795296	+	0.606222i	$0.792684\pi$
$62$	−1.48804	−	2.57737i	−0.188982	−	0.327326i
$63$		0			0
$64$		−	2.78376i		−	0.347970i
$65$	−11.8237	−	5.33826i	−1.46655	−	0.662130i
$66$	2.19983	+	1.27007i	0.270781	+	0.156335i
$67$	5.44554	−	5.44554i	0.665279	−	0.665279i	−0.291340	−	0.956619i	$-0.594101\pi$
$67$	5.44554	−	5.44554i	0.665279	−	0.665279i	0.956619	+	0.291340i	$0.0941012\pi$
$68$	−1.74312	−	1.00639i	−0.211384	−	0.122043i
$69$	1.81276	−	3.13980i	0.218231	−	0.377987i
$70$		0			0
$71$	1.74779	+	6.52285i	0.207425	+	0.774120i	0.988697	+	0.149929i	$0.0479045\pi$
$71$	1.74779	+	6.52285i	0.207425	+	0.774120i	−0.781272	+	0.624191i	$0.785429\pi$
$72$	3.89065	+	3.89065i	0.458518	+	0.458518i
$73$	−1.46556	−	5.46953i	−0.171531	−	0.640161i	−0.997117	−	0.0758844i	$-0.975822\pi$
$73$	−1.46556	−	5.46953i	−0.171531	−	0.640161i	0.825586	−	0.564276i	$-0.190845\pi$
$74$	−0.663841	−	1.14981i	−0.0771699	−	0.133662i
$75$	9.71705	−	16.8304i	1.12203	−	1.94341i
$76$	−7.74662	−	2.07570i	−0.888598	−	0.238099i
$77$		0			0
$78$	−0.430029	−	4.30727i	−0.0486912	−	0.487703i
$79$	5.91160	+	10.2392i	0.665107	+	1.15200i	0.979256	+	0.202626i	$0.0649475\pi$
$79$	5.91160	+	10.2392i	0.665107	+	1.15200i	−0.314149	+	0.949374i	$0.601719\pi$
$80$	−6.64635	−	6.64635i	−0.743084	−	0.743084i
$81$	−9.05394			−1.00599
$82$	2.31129			0.255239
$83$	5.06789	+	5.06789i	0.556274	+	0.556274i	0.928244	−	0.371971i	$-0.121318\pi$
$83$	5.06789	+	5.06789i	0.556274	+	0.556274i	−0.371971	+	0.928244i	$0.621318\pi$
$84$		0			0
$85$	−3.97675	+	1.06557i	−0.431339	+	0.115577i
$86$	−0.668517	+	2.49494i	−0.0720881	+	0.269036i
$87$	−11.6836	+	6.74552i	−1.25261	+	0.723196i
$88$		−	3.90407i		−	0.416175i
$89$	2.58048	+	9.63048i	0.273530	+	1.02083i	0.956820	+	0.290681i	$0.0938820\pi$
$89$	2.58048	+	9.63048i	0.273530	+	1.02083i	−0.683290	+	0.730147i	$0.739451\pi$
$90$	5.26655			0.555143
$91$		0			0
$92$	−2.60753			−0.271854
$93$	3.83793	+	14.3234i	0.397975	+	1.48526i
$94$		−	3.31251i		−	0.341660i
$95$	−14.2065	+	8.20214i	−1.45756	+	0.841521i
$96$	3.14782	−	11.7478i	0.321273	−	1.19901i
$97$	−13.1665	+	3.52795i	−1.33685	+	0.358209i	−0.855266	−	0.518190i	$-0.826606\pi$
$97$	−13.1665	+	3.52795i	−1.33685	+	0.358209i	−0.481587	+	0.876398i	$0.659939\pi$
$98$		0			0
$99$	−4.46123	−	4.46123i	−0.448370	−	0.448370i
$100$	−13.9773			−1.39773
$101$	−9.74305			−0.969470			−0.484735	−	0.874661i	$-0.661084\pi$
$101$	−9.74305			−0.969470			−0.484735	+	0.874661i	$0.661084\pi$
$102$	−0.971376	−	0.971376i	−0.0961805	−	0.0961805i
$103$	−6.18363	−	10.7104i	−0.609291	−	1.05532i	−0.991357	−	0.131188i	$-0.958121\pi$
$103$	−6.18363	−	10.7104i	−0.609291	−	1.05532i	0.382067	−	0.924135i	$-0.375213\pi$
$104$	−5.40266	+	3.88240i	−0.529774	+	0.380701i
$105$		0			0
$106$	1.65370	+	0.443108i	0.160622	+	0.0430385i
$107$	4.09359	−	7.09030i	0.395742	−	0.685446i	−0.597453	−	0.801904i	$-0.703821\pi$
$107$	4.09359	−	7.09030i	0.395742	−	0.685446i	0.993196	+	0.116458i	$0.0371541\pi$
$108$	0.0389089	+	0.0673922i	0.00374401	+	0.00648482i
$109$	0.771224	+	2.87825i	0.0738699	+	0.275686i	0.992975	−	0.118327i	$-0.0377531\pi$
$109$	0.771224	+	2.87825i	0.0738699	+	0.275686i	−0.919105	+	0.394013i	$0.871086\pi$
$110$	−2.64235	−	2.64235i	−0.251938	−	0.251938i
$111$	1.71217	+	6.38989i	0.162512	+	0.606501i
$112$		0			0
$113$	−8.19898	+	14.2011i	−0.771295	+	1.33592i	0.165558	+	0.986200i	$0.447057\pi$
$113$	−8.19898	+	14.2011i	−0.771295	+	1.33592i	−0.936853	+	0.349723i	$0.886276\pi$
$114$	−4.74030	−	2.73681i	−0.443970	−	0.256326i
$115$	−3.77140	+	3.77140i	−0.351685	+	0.351685i
$116$	8.40299	+	4.85147i	0.780198	+	0.450448i
$117$	−1.73722	+	10.6102i	−0.160606	+	0.980910i
$118$		−	5.61007i		−	0.516448i
$119$		0			0
$120$	−8.11894	−	14.0624i	−0.741154	−	1.28372i
$121$		−	6.52339i		−	0.593035i
$122$	4.48988	−	1.20306i	0.406495	−	0.108920i
$123$	−11.1238	−	2.98061i	−1.00300	−	0.268753i
$124$	7.54126	−	7.54126i	0.677225	−	0.677225i
$125$	−7.49503	+	7.49503i	−0.670376	+	0.670376i
$126$		0			0
$127$	7.41767	−	4.28259i	0.658212	−	0.380019i	−0.133384	−	0.991064i	$-0.542584\pi$
$127$	7.41767	−	4.28259i	0.658212	−	0.380019i	0.791595	+	0.611046i	$0.209251\pi$
$128$	−10.9264	+	2.92773i	−0.965770	+	0.258777i
$129$	6.43490	−	11.1456i	0.566561	−	0.981313i
$130$	−1.02894	+	6.28432i	−0.0902440	+	0.551171i
$131$	−12.7190	+	7.34330i	−1.11126	+	0.641587i	−0.939156	−	0.343491i	$-0.888390\pi$
$131$	−12.7190	+	7.34330i	−1.11126	+	0.641587i	−0.172106	+	0.985078i	$0.555057\pi$
$132$	−2.35597	+	8.79258i	−0.205060	+	0.765296i
$133$		0			0
$134$	−3.27379	−	1.89013i	−0.282813	−	0.163282i
$135$	0.153749	+	0.0411968i	0.0132326	+	0.00354566i
$136$	−0.546458	+	2.03941i	−0.0468583	+	0.174878i
$137$	0.588910	−	2.19784i	0.0503140	−	0.187774i	−0.936195	−	0.351481i	$-0.885678\pi$
$137$	0.588910	−	2.19784i	0.0503140	−	0.187774i	0.986509	+	0.163706i	$0.0523449\pi$
$138$	−1.71901	−	0.460608i	−0.146332	−	0.0392096i
$139$	−4.23236	−	2.44355i	−0.358984	−	0.207259i	0.309651	−	0.950850i	$-0.399788\pi$
$139$	−4.23236	−	2.44355i	−0.358984	−	0.207259i	−0.668635	+	0.743591i	$0.733121\pi$
$140$		0			0
$141$	−4.27178	+	15.9425i	−0.359749	+	1.34260i
$142$	2.87071	−	1.65740i	0.240904	−	0.139086i
$143$	6.19497	−	4.45177i	0.518050	−	0.372276i
$144$	−3.89490	+	6.74616i	−0.324575	+	0.562180i
$145$	19.1706	−	5.13675i	1.59203	−	0.426584i
$146$	−2.40714	+	1.38976i	−0.199217	+	0.115018i
$147$		0			0
$148$	3.36428	−	3.36428i	0.276542	−	0.276542i
$149$	1.95929	−	1.95929i	0.160511	−	0.160511i	−0.622282	−	0.782793i	$-0.713794\pi$
$149$	1.95929	−	1.95929i	0.160511	−	0.160511i	0.782793	+	0.622282i	$0.213794\pi$
$150$	−9.21452	−	2.46902i	−0.752363	−	0.201595i
$151$	−6.09868	+	1.63414i	−0.496304	+	0.132984i	−0.498284	−	0.867014i	$-0.666036\pi$
$151$	−6.09868	+	1.63414i	−0.496304	+	0.132984i	0.00198027	+	0.999998i	$0.499370\pi$
$152$			8.41265i			0.682356i
$153$	1.70601	+	2.95490i	0.137923	+	0.238890i
$154$		0			0
$155$		−	21.8146i		−	1.75219i
$156$	14.5105	−	5.48348i	1.16177	−	0.439030i
$157$	1.65313	+	0.954436i	0.131934	+	0.0761723i	0.564514	−	0.825423i	$-0.309063\pi$
$157$	1.65313	+	0.954436i	0.131934	+	0.0761723i	−0.432580	+	0.901595i	$0.642397\pi$
$158$	4.10379	−	4.10379i	0.326480	−	0.326480i
$159$	−7.38754	−	4.26520i	−0.585870	−	0.338252i
$160$	−8.94602	+	15.4950i	−0.707245	+	1.22498i
$161$		0			0
$162$	1.15027	+	4.29285i	0.0903734	+	0.337278i
$163$	4.36507	+	4.36507i	0.341899	+	0.341899i	0.857081	−	0.515182i	$-0.172276\pi$
$163$	4.36507	+	4.36507i	0.341899	+	0.341899i	−0.515182	+	0.857081i	$0.672276\pi$
$164$	2.14370	+	8.00038i	0.167395	+	0.624725i
$165$	9.30961	+	16.1247i	0.724752	+	1.25531i
$166$	1.75905	−	3.04676i	0.136528	−	0.236474i
$167$	2.11863	+	0.567684i	0.163944	+	0.0439287i	0.339857	−	0.940477i	$-0.389621\pi$
$167$	2.11863	+	0.567684i	0.163944	+	0.0439287i	−0.175913	+	0.984406i	$0.556288\pi$
$168$		0			0
$169$	−12.3212	−	4.14587i	−0.947784	−	0.318913i
$170$	1.01046	+	1.75017i	0.0774987	+	0.134232i
$171$	9.61325	+	9.61325i	0.735144	+	0.735144i
$172$	−9.25614			−0.705774
$173$	−18.9474			−1.44054			−0.720272	−	0.693692i	$-0.755983\pi$
$173$	−18.9474			−1.44054			−0.720272	+	0.693692i	$0.755983\pi$
$174$	4.68269	+	4.68269i	0.354993	+	0.354993i
$175$		0			0
$176$	5.33888	−	1.43055i	0.402433	−	0.107832i
$177$	−7.23469	+	27.0002i	−0.543792	+	2.02946i
$178$	4.23837	−	2.44703i	0.317680	−	0.183412i
$179$		−	11.8636i		−	0.886725i	−0.896342	−	0.443363i	$-0.853785\pi$
$179$		−	11.8636i		−	0.886725i	0.896342	−	0.443363i	$-0.146215\pi$
$180$	4.88467	+	18.2299i	0.364082	+	1.35877i
$181$	10.2064			0.758635			0.379317	−	0.925267i	$-0.376159\pi$
$181$	10.2064			0.758635			0.379317	+	0.925267i	$0.376159\pi$
$182$		0			0
$183$	−23.1604			−1.71207
$184$	0.707929	+	2.64203i	0.0521892	+	0.194773i
$185$		−	9.73186i		−	0.715501i
$186$	6.30371	−	3.63945i	0.462210	−	0.266857i
$187$	0.626598	−	2.33849i	0.0458213	−	0.171008i
$188$	11.4661	−	3.07232i	0.836249	−	0.224072i
$189$		0			0
$190$	5.69386	+	5.69386i	0.413076	+	0.413076i
$191$	−5.97148			−0.432081			−0.216040	−	0.976384i	$-0.569314\pi$
$191$	−5.97148			−0.432081			−0.216040	+	0.976384i	$0.569314\pi$
$192$	6.80850			0.491361
$193$	−0.709662	−	0.709662i	−0.0510826	−	0.0510826i	0.681104	−	0.732187i	$-0.261500\pi$
$193$	−0.709662	−	0.709662i	−0.0510826	−	0.0510826i	−0.732187	+	0.681104i	$0.761500\pi$
$194$	3.34549	+	5.79456i	0.240192	+	0.416025i
$195$	13.0563	−	28.9184i	0.934981	−	2.07089i
$196$		0			0
$197$	−4.08621	−	1.09490i	−0.291130	−	0.0780081i	0.110298	−	0.993899i	$-0.464819\pi$
$197$	−4.08621	−	1.09490i	−0.291130	−	0.0780081i	−0.401428	+	0.915890i	$0.631486\pi$
$198$	−1.54847	+	2.68204i	−0.110045	+	0.190604i
$199$	7.52706	+	13.0372i	0.533579	+	0.924186i	0.999231	+	0.0392178i	$0.0124866\pi$
$199$	7.52706	+	13.0372i	0.533579	+	0.924186i	−0.465652	+	0.884968i	$0.654180\pi$
$200$	3.79475	+	14.1622i	0.268329	+	1.00142i
$201$	13.3187	+	13.3187i	0.939427	+	0.939427i
$202$	1.23782	+	4.61959i	0.0870924	+	0.325033i
$203$		0			0
$204$	2.46142	−	4.26330i	0.172334	−	0.298491i
$205$	14.6719	+	8.47082i	1.02473	+	0.591628i
$206$	−4.29262	+	4.29262i	−0.299081	+	0.299081i
$207$	3.82804	+	2.21012i	0.266067	+	0.153614i
$208$	−7.28892	−	5.96561i	−0.505395	−	0.413641i
$209$		−	9.64640i		−	0.667255i
$210$		0			0
$211$	12.3556	+	21.4005i	0.850592	+	1.47327i	0.880675	+	0.473721i	$0.157089\pi$
$211$	12.3556	+	21.4005i	0.850592	+	1.47327i	−0.0300832	+	0.999547i	$0.509577\pi$
$212$			6.13518i			0.421366i
$213$	−15.9536	+	4.27474i	−1.09312	+	0.292900i
$214$	−3.88188	−	1.04015i	−0.265360	−	0.0711030i
$215$	−13.3876	+	13.3876i	−0.913028	+	0.913028i
$216$	0.0577203	−	0.0577203i	0.00392737	−	0.00392737i
$217$		0			0
$218$	1.26672	−	0.731339i	0.0857929	−	0.0495325i
$219$	13.3774	−	3.58445i	0.903958	−	0.242215i
$220$	6.69560	−	11.5971i	0.451417	−	0.781877i
$221$	−3.85925	+	1.45840i	−0.259601	+	0.0981024i
$222$	2.81219	−	1.62362i	0.188742	−	0.108970i
$223$	0.193376	−	0.721689i	0.0129494	−	0.0483279i	−0.959149	−	0.282902i	$-0.908703\pi$
$223$	0.193376	−	0.721689i	0.0129494	−	0.0483279i	0.972098	+	0.234574i	$0.0753696\pi$
$224$		0			0
$225$	20.5197	+	11.8470i	1.36798	+	0.789802i
$226$	7.77496	+	2.08329i	0.517183	+	0.138579i
$227$	−2.68443	+	10.0184i	−0.178172	+	0.664946i	0.817818	+	0.575477i	$0.195184\pi$
$227$	−2.68443	+	10.0184i	−0.178172	+	0.664946i	−0.995990	+	0.0894687i	$0.971483\pi$
$228$	5.07674	−	18.9466i	0.336215	−	1.25477i
$229$	−1.65915	−	0.444567i	−0.109639	−	0.0293778i	0.203582	−	0.979058i	$-0.434742\pi$
$229$	−1.65915	−	0.444567i	−0.109639	−	0.0293778i	−0.313222	+	0.949680i	$0.601408\pi$
$230$	2.26732	+	1.30904i	0.149503	+	0.0863154i
$231$		0			0
$232$	2.63429	−	9.83132i	0.172950	−	0.645458i
$233$	−7.19720	+	4.15531i	−0.471504	+	0.272223i	−0.716869	−	0.697208i	$-0.754426\pi$
$233$	−7.19720	+	4.15531i	−0.471504	+	0.272223i	0.245365	+	0.969431i	$0.421092\pi$
$234$	5.25143	−	0.524291i	0.343297	−	0.0342740i
$235$	12.1403	−	21.0276i	0.791946	−	1.37169i
$236$	19.4189	−	5.20328i	1.26406	−	0.338705i
$237$	−25.0430	+	14.4586i	−1.62672	+	0.939185i
$238$		0			0
$239$	5.13978	−	5.13978i	0.332465	−	0.332465i	−0.521057	−	0.853522i	$-0.674462\pi$
$239$	5.13978	−	5.13978i	0.332465	−	0.332465i	0.853522	+	0.521057i	$0.174462\pi$
$240$	16.2556	−	16.2556i	1.04929	−	1.04929i
$241$	−7.48614	−	2.00591i	−0.482225	−	0.129212i	0.00951360	−	0.999955i	$-0.496972\pi$
$241$	−7.48614	−	2.00591i	−0.482225	−	0.129212i	−0.491738	+	0.870743i	$0.663638\pi$
$242$	−3.09301	+	0.828770i	−0.198826	+	0.0532753i
$243$		−	22.0114i		−	1.41203i
$244$	8.32864	+	14.4256i	0.533187	+	0.923507i
$245$		0			0
$246$			5.65293i			0.360418i
$247$	−13.3492	+	9.59286i	−0.849389	+	0.610379i
$248$	−9.68845	−	5.59363i	−0.615217	−	0.355196i
$249$	−12.3950	+	12.3950i	−0.785503	+	0.785503i
$250$	4.50592	+	2.60149i	0.284979	+	0.164533i
$251$	−1.76122	+	3.05052i	−0.111167	+	0.192547i	−0.916241	−	0.400627i	$-0.868792\pi$
$251$	−1.76122	+	3.05052i	−0.111167	+	0.192547i	0.805074	+	0.593174i	$0.202126\pi$
$252$		0			0
$253$	−0.811749	−	3.02949i	−0.0510343	−	0.190462i
$254$	−2.97294	−	2.97294i	−0.186539	−	0.186539i
$255$	−2.60616	−	9.72631i	−0.163204	−	0.609085i
$256$	−0.00743845	−	0.0128838i	−0.000464903	−	0.000805236i
$257$	−5.42573	+	9.39764i	−0.338448	+	0.586209i	−0.984141	−	0.177388i	$-0.943235\pi$
$257$	−5.42573	+	9.39764i	−0.338448	+	0.586209i	0.645693	+	0.763597i	$0.276569\pi$
$258$	−6.10211	−	1.63506i	−0.379901	−	0.101794i
$259$		0			0
$260$	−22.7071	+	2.26703i	−1.40824	+	0.140595i
$261$	−8.22414	−	14.2446i	−0.509061	−	0.881720i
$262$	5.09766	+	5.09766i	0.314935	+	0.314935i
$263$	−4.69913			−0.289761			−0.144881	−	0.989449i	$-0.546280\pi$
$263$	−4.69913			−0.289761			−0.144881	+	0.989449i	$0.546280\pi$
$264$	9.54855			0.587672
$265$	8.87362	+	8.87362i	0.545102	+	0.545102i
$266$		0			0
$267$	−23.5542	+	6.31132i	−1.44149	+	0.386247i
$268$	3.50615	−	13.0851i	0.214172	−	0.799301i
$269$	22.2662	−	12.8554i	1.35760	−	0.783809i	0.368298	−	0.929708i	$-0.379941\pi$
$269$	22.2662	−	12.8554i	1.35760	−	0.783809i	0.989299	+	0.145899i	$0.0466074\pi$
$270$		−	0.0781326i		−	0.00475500i
$271$	0.343245	+	1.28101i	0.0208506	+	0.0778156i	0.975567	−	0.219701i	$-0.0705082\pi$
$271$	0.343245	+	1.28101i	0.0208506	+	0.0778156i	−0.954717	+	0.297517i	$0.903842\pi$
$272$	−2.98916			−0.181244
$273$		0			0
$274$	−1.11691			−0.0674749
$275$	−4.35126	−	16.2391i	−0.262391	−	0.979257i
$276$		−	6.37748i		−	0.383879i
$277$	−0.157067	+	0.0906826i	−0.00943723	+	0.00544859i	−0.504711	−	0.863288i	$-0.668401\pi$
$277$	−0.157067	+	0.0906826i	−0.00943723	+	0.00544859i	0.495274	+	0.868737i	$0.335068\pi$
$278$	−0.620887	+	2.31718i	−0.0372383	+	0.138975i
$279$	−17.4630	+	4.67921i	−1.04548	+	0.280137i
$280$		0			0
$281$	5.50563	+	5.50563i	0.328439	+	0.328439i	0.851993	−	0.523554i	$-0.175394\pi$
$281$	5.50563	+	5.50563i	0.328439	+	0.328439i	−0.523554	+	0.851993i	$0.675394\pi$
$282$	8.10173			0.482451
$283$	7.30850			0.434445			0.217223	−	0.976122i	$-0.430300\pi$
$283$	7.30850			0.434445			0.217223	+	0.976122i	$0.430300\pi$
$284$	8.39956	+	8.39956i	0.498422	+	0.498422i
$285$	−20.0607	−	34.7462i	−1.18830	−	2.05819i
$286$	−2.89782	−	2.37172i	−0.171351	−	0.140243i
$287$		0			0
$288$	14.3229	+	3.83782i	0.843987	+	0.226146i
$289$	7.84536	−	13.5886i	0.461492	−	0.799327i
$290$	−4.87109	−	8.43698i	−0.286040	−	0.495437i
$291$	−8.62863	−	32.2025i	−0.505819	−	1.88774i
$292$	−7.04319	−	7.04319i	−0.412172	−	0.412172i
$293$	−8.30804	−	31.0060i	−0.485361	−	1.81139i	−0.578431	−	0.815731i	$-0.696335\pi$
$293$	−8.30804	−	31.0060i	−0.485361	−	1.81139i	0.0930708	−	0.995659i	$-0.470332\pi$
$294$		0			0
$295$	20.5608	−	35.6123i	1.19710	−	2.07343i
$296$	−4.32218	−	2.49541i	−0.251221	−	0.145043i
$297$	−0.0661852	+	0.0661852i	−0.00384045	+	0.00384045i
$298$	−1.17790	−	0.680061i	−0.0682339	−	0.0393949i
$299$	−3.38513	+	4.13602i	−0.195767	+	0.239192i
$300$		−	34.1855i		−	1.97370i
$301$		0			0
$302$	1.54963	+	2.68403i	0.0891709	+	0.154449i
$303$		−	23.8295i		−	1.36897i
$304$	−11.5044	+	3.08261i	−0.659825	+	0.176800i
$305$	32.9107	+	8.81839i	1.88446	+	0.504939i
$306$	1.18430	−	1.18430i	0.0677020	−	0.0677020i
$307$	9.65602	−	9.65602i	0.551098	−	0.551098i	−0.375659	−	0.926758i	$-0.622584\pi$
$307$	9.65602	−	9.65602i	0.551098	−	0.551098i	0.926758	+	0.375659i	$0.122584\pi$
$308$		0			0
$309$	26.1953	−	15.1239i	1.49020	−	0.860368i
$310$	−10.3432	+	2.77146i	−0.587456	+	0.157408i
$311$	−8.29369	+	14.3651i	−0.470292	+	0.814570i	−0.999423	−	0.0339706i	$-0.989185\pi$
$311$	−8.29369	+	14.3651i	−0.470292	+	0.814570i	0.529131	+	0.848540i	$0.322518\pi$
$312$	−9.49556	−	13.2138i	−0.537580	−	0.748083i
$313$	8.06261	−	4.65495i	0.455725	−	0.263113i	−0.254520	−	0.967068i	$-0.581917\pi$
$313$	8.06261	−	4.65495i	0.455725	−	0.263113i	0.710245	+	0.703954i	$0.248584\pi$
$314$	0.242514	−	0.905076i	0.0136859	−	0.0510764i
$315$		0			0
$316$	18.0112	+	10.3988i	1.01321	+	0.584978i
$317$	−32.0131	−	8.57788i	−1.79803	−	0.481782i	−0.804365	−	0.594135i	$-0.797495\pi$
$317$	−32.0131	−	8.57788i	−1.79803	−	0.481782i	−0.993668	+	0.112353i	$0.964161\pi$
$318$	−1.08375	+	4.04462i	−0.0607738	+	0.226811i
$319$	−3.02062	+	11.2731i	−0.169122	+	0.631173i
$320$	−9.67479	−	2.59235i	−0.540837	−	0.144917i
$321$	17.3414	+	10.0121i	0.967904	+	0.558820i
$322$		0			0
$323$	−1.35022	+	5.03909i	−0.0751282	+	0.280382i
$324$	−13.7926	+	7.96316i	−0.766255	+	0.442398i
$325$	−18.1455	+	22.1705i	−1.00653	+	1.22980i
$326$	1.51510	−	2.62423i	0.0839136	−	0.145343i
$327$	−7.03960	+	1.88626i	−0.389291	+	0.104310i
$328$	7.52423	−	4.34412i	0.415456	−	0.239864i
$329$		0			0
$330$	6.46265	−	6.46265i	0.355757	−	0.355757i
$331$	−16.6506	+	16.6506i	−0.915197	+	0.915197i	−0.996675	−	0.0814779i	$-0.974036\pi$
$331$	−16.6506	+	16.6506i	−0.915197	+	0.915197i	0.0814779	+	0.996675i	$0.474036\pi$
$332$	12.1777	+	3.26300i	0.668336	+	0.179080i
$333$	−7.79055	+	2.08747i	−0.426920	+	0.114393i
$334$		−	1.07665i		−	0.0589117i
$335$	−13.8546	−	23.9968i	−0.756955	−	1.31109i
$336$		0			0
$337$			24.5958i			1.33982i	0.742442	+	0.669911i	$0.233668\pi$
$337$			24.5958i			1.33982i	−0.742442	+	0.669911i	$0.766332\pi$
$338$	−0.400374	+	6.36871i	−0.0217775	+	0.346412i
$339$	−34.7329	−	20.0530i	−1.88643	−	1.08913i
$340$	−5.12091	+	5.12091i	−0.277720	+	0.277720i
$341$	11.1093	+	6.41395i	0.601602	+	0.347335i
$342$	3.33672	−	5.77937i	0.180429	−	0.312512i
$343$		0			0
$344$	2.51299	+	9.37860i	0.135491	+	0.505660i
$345$	−9.22407	−	9.22407i	−0.496607	−	0.496607i
$346$	2.40719	+	8.98376i	0.129411	+	0.482970i
$347$	16.6796	+	28.8899i	0.895406	+	1.55089i	0.833301	+	0.552819i	$0.186448\pi$
$347$	16.6796	+	28.8899i	0.895406	+	1.55089i	0.0621044	+	0.998070i	$0.480219\pi$
$348$	−11.8657	+	20.5520i	−0.636068	+	1.10170i
$349$	5.28189	+	1.41528i	0.282733	+	0.0757580i	0.397399	−	0.917646i	$-0.369913\pi$
$349$	5.28189	+	1.41528i	0.282733	+	0.0757580i	−0.114666	+	0.993404i	$0.536580\pi$
$350$		0			0
$351$	0.157409	+	0.0257727i	0.00840184	+	0.00137564i
$352$	−5.26063	−	9.11168i	−0.280393	−	0.485654i
$353$	−3.12499	−	3.12499i	−0.166326	−	0.166326i	0.619036	−	0.785362i	$-0.287523\pi$
$353$	−3.12499	−	3.12499i	−0.166326	−	0.166326i	−0.785362	+	0.619036i	$0.787523\pi$
$354$	13.7211			0.729267
$355$	24.2974			1.28957
$356$	12.4013	+	12.4013i	0.657267	+	0.657267i
$357$		0			0
$358$	−5.62502	+	1.50722i	−0.297291	+	0.0796590i
$359$	7.18738	−	26.8237i	0.379335	−	1.41570i	−0.467570	−	0.883956i	$-0.654871\pi$
$359$	7.18738	−	26.8237i	0.379335	−	1.41570i	0.846906	−	0.531743i	$-0.178463\pi$
$360$	17.1449	−	9.89860i	0.903615	−	0.521702i
$361$			1.78647i			0.0940247i
$362$	−1.29668	−	4.83927i	−0.0681520	−	0.254347i
$363$	15.9549			0.837413
$364$		0			0
$365$	−20.3739			−1.06642
$366$	2.94244	+	10.9813i	0.153804	+	0.574003i
$367$			16.8497i			0.879548i	0.898108	+	0.439774i	$0.144942\pi$
$367$			16.8497i			0.879548i	−0.898108	+	0.439774i	$0.855058\pi$
$368$	−3.35361	+	1.93621i	−0.174819	+	0.100932i
$369$	3.63396	−	13.5621i	0.189176	−	0.706016i
$370$	−4.61428	+	1.23639i	−0.239885	+	0.0642770i
$371$		0			0
$372$	18.4444	+	18.4444i	0.956296	+	0.956296i
$373$	2.78290			0.144093			0.0720466	−	0.997401i	$-0.477047\pi$
$373$	2.78290			0.144093			0.0720466	+	0.997401i	$0.477047\pi$
$374$	−1.18838			−0.0614499
$375$	−18.3313	−	18.3313i	−0.946624	−	0.946624i
$376$	−6.22595	−	10.7837i	−0.321079	−	0.556125i
$377$	18.6042	−	7.03046i	0.958165	−	0.362087i
$378$		0			0
$379$	0.734071	+	0.196694i	0.0377067	+	0.0101035i	0.277623	−	0.960690i	$-0.410453\pi$
$379$	0.734071	+	0.196694i	0.0377067	+	0.0101035i	−0.239916	+	0.970794i	$0.577120\pi$
$380$	−14.4280	+	24.9900i	−0.740139	+	1.28196i
$381$	10.4743	+	18.1421i	0.536617	+	0.929448i
$382$	0.758652	+	2.83133i	0.0388160	+	0.144863i
$383$	22.2495	+	22.2495i	1.13690	+	1.13690i	0.989003	+	0.147895i	$0.0472497\pi$
$383$	22.2495	+	22.2495i	1.13690	+	1.13690i	0.147895	+	0.989003i	$0.452750\pi$
$384$	−7.16063	−	26.7238i	−0.365414	−	1.36374i
$385$		0			0
$386$	−0.246321	+	0.426640i	−0.0125374	+	0.0217154i
$387$	13.5887	+	7.84543i	0.690752	+	0.398806i
$388$	−16.9546	+	16.9546i	−0.860741	+	0.860741i
$389$	23.4348	+	13.5301i	1.18819	+	0.686003i	0.957895	−	0.287118i	$-0.0926970\pi$
$389$	23.4348	+	13.5301i	1.18819	+	0.686003i	0.230297	+	0.973120i	$0.426030\pi$
$390$	−15.3702	−	2.51658i	−0.778298	−	0.127432i
$391$			1.69617i			0.0857789i
$392$		0			0
$393$	−17.9602	−	31.1080i	−0.905973	−	1.56919i
$394$			2.07654i			0.104615i
$395$	41.0909	−	11.0103i	2.06751	−	0.553987i
$396$	−10.7199	−	2.87239i	−0.538696	−	0.144343i
$397$	−0.161422	+	0.161422i	−0.00810155	+	0.00810155i	−0.711146	−	0.703044i	$-0.751824\pi$
$397$	−0.161422	+	0.161422i	−0.00810155	+	0.00810155i	0.703044	+	0.711146i	$0.251824\pi$
$398$	5.22522	−	5.22522i	0.261917	−	0.261917i
$399$		0			0
$400$	−17.9766	+	10.3788i	−0.898828	+	0.518939i
$401$	24.8210	−	6.65077i	1.23950	−	0.332124i	0.421230	−	0.906954i	$-0.361599\pi$
$401$	24.8210	−	6.65077i	1.23950	−	0.332124i	0.818273	+	0.574830i	$0.194932\pi$
$402$	4.62286	−	8.00703i	0.230567	−	0.399354i
$403$	−2.17167	−	21.7520i	−0.108179	−	1.08354i
$404$	−14.8424	+	8.56925i	−0.738436	+	0.426336i
$405$	−8.43141	+	31.4664i	−0.418960	+	1.56358i
$406$		0			0
$407$	4.95604	+	2.86137i	0.245662	+	0.141833i
$408$	−4.98797	−	1.33652i	−0.246941	−	0.0661678i
$409$	7.72535	−	28.8314i	0.381994	−	1.42562i	−0.460857	−	0.887475i	$-0.652458\pi$
$409$	7.72535	−	28.8314i	0.381994	−	1.42562i	0.842851	−	0.538147i	$-0.180876\pi$
$410$	2.15237	−	8.03274i	0.106298	−	0.396709i
$411$	5.37547	+	1.44035i	0.265153	+	0.0710474i
$412$	−18.8400	−	10.8773i	−0.928182	−	0.535886i
$413$		0			0
$414$	0.561574	−	2.09582i	0.0275998	−	0.103004i
$415$	22.3326	−	12.8937i	1.09627	−	0.632929i
$416$	−7.37779	+	16.3411i	−0.361726	+	0.801186i
$417$	5.97643	−	10.3515i	0.292667	−	0.506914i
$418$	−4.57376	+	1.22554i	−0.223710	+	0.0599429i
$419$	7.72615	−	4.46069i	0.377447	−	0.217919i	−0.299260	−	0.954172i	$-0.596740\pi$
$419$	7.72615	−	4.46069i	0.377447	−	0.217919i	0.676707	+	0.736253i	$0.263406\pi$
$420$		0			0
$421$	18.1408	−	18.1408i	0.884130	−	0.884130i	−0.109821	−	0.993951i	$-0.535028\pi$
$421$	18.1408	−	18.1408i	0.884130	−	0.884130i	0.993951	+	0.109821i	$0.0350278\pi$
$422$	8.57713	−	8.57713i	0.417528	−	0.417528i
$423$	−19.4371	−	5.20816i	−0.945065	−	0.253229i
$424$	6.21635	−	1.66567i	0.301893	−	0.0808919i
$425$			9.09206i			0.441030i
$426$	4.05367	+	7.02116i	0.196401	+	0.340176i
$427$		0			0
$428$		−	14.4016i		−	0.696130i
$429$	10.8881	+	15.1516i	0.525683	+	0.731528i
$430$	8.04848	+	4.64679i	0.388132	+	0.224088i
$431$	−8.32071	+	8.32071i	−0.400795	+	0.400795i	−0.878513	−	0.477718i	$-0.841464\pi$
$431$	−8.32071	+	8.32071i	−0.400795	+	0.400795i	0.477718	+	0.878513i	$0.341464\pi$
$432$	0.100084	+	0.0577833i	0.00481528	+	0.00278010i
$433$	6.26407	−	10.8497i	0.301032	−	0.521403i	−0.675338	−	0.737508i	$-0.736002\pi$
$433$	6.26407	−	10.8497i	0.301032	−	0.521403i	0.976370	+	0.216106i	$0.0693356\pi$
$434$		0			0
$435$	12.5634	+	46.8874i	0.602370	+	2.24808i
$436$	3.70636	+	3.70636i	0.177502	+	0.177502i
$437$	1.74919	+	6.52808i	0.0836752	+	0.312280i
$438$	−3.39908	−	5.88738i	−0.162414	−	0.281310i
$439$	−8.88189	+	15.3839i	−0.423910	+	0.734233i	−0.996318	−	0.0857358i	$-0.972676\pi$
$439$	−8.88189	+	15.3839i	−0.423910	+	0.734233i	0.572408	+	0.819969i	$0.306009\pi$
$440$	−13.5684	−	3.63563i	−0.646847	−	0.173322i
$441$		0			0
$442$	1.18179	+	1.64455i	0.0562120	+	0.0782233i
$443$	3.34945	+	5.80142i	0.159137	+	0.275634i	0.934558	−	0.355811i	$-0.115795\pi$
$443$	3.34945	+	5.80142i	0.159137	+	0.275634i	−0.775421	+	0.631445i	$0.782462\pi$
$444$	8.22834	+	8.22834i	0.390500	+	0.390500i
$445$	35.8732			1.70056
$446$	−0.366750			−0.0173661
$447$	4.79202	+	4.79202i	0.226655	+	0.226655i
$448$		0			0
$449$	22.8700	−	6.12801i	1.07930	−	0.289199i	0.324993	−	0.945716i	$-0.394638\pi$
$449$	22.8700	−	6.12801i	1.07930	−	0.289199i	0.754311	+	0.656518i	$0.227971\pi$
$450$	3.01023	−	11.2343i	0.141904	−	0.529592i
$451$	−8.62769	+	4.98120i	−0.406262	+	0.234555i
$452$			28.8448i			1.35675i
$453$	−3.99676	−	14.9161i	−0.187784	−	0.700821i
$454$	5.09120			0.238942
$455$		0			0
$456$	−20.5756			−0.963542
$457$	−8.26591	−	30.8488i	−0.386663	−	1.44305i	−0.835528	−	0.549447i	$-0.814838\pi$
$457$	−8.26591	−	30.8488i	−0.386663	−	1.44305i	0.448865	−	0.893599i	$-0.351828\pi$
$458$			0.843151i			0.0393978i
$459$	0.0438379	−	0.0253098i	0.00204618	−	0.00118136i
$460$	−2.42824	+	9.06232i	−0.113217	+	0.422533i
$461$	−36.7537	+	9.84812i	−1.71179	+	0.458673i	−0.975862	−	0.218388i	$-0.929920\pi$
$461$	−36.7537	+	9.84812i	−1.71179	+	0.458673i	−0.735927	+	0.677060i	$0.763254\pi$
$462$		0			0
$463$	−9.11397	−	9.11397i	−0.423562	−	0.423562i	0.462866	−	0.886428i	$-0.346821\pi$
$463$	−9.11397	−	9.11397i	−0.423562	−	0.423562i	−0.886428	+	0.462866i	$0.846821\pi$
$464$	14.4098			0.668956
$465$	53.3541			2.47424
$466$	2.88458	+	2.88458i	0.133626	+	0.133626i
$467$	8.92031	+	15.4504i	0.412783	+	0.714960i	0.995193	−	0.0979345i	$-0.0312236\pi$
$467$	8.92031	+	15.4504i	0.412783	+	0.714960i	−0.582410	+	0.812895i	$0.697890\pi$
$468$	6.68545	+	17.6912i	0.309035	+	0.817778i
$469$		0			0
$470$	−11.5125	−	3.08475i	−0.531030	−	0.142289i
$471$	−2.33435	+	4.04322i	−0.107561	+	0.186302i
$472$	−10.5443	−	18.2632i	−0.485339	−	0.840631i
$473$	−2.88153	−	10.7540i	−0.132493	−	0.494470i
$474$	10.0370	+	10.0370i	0.461016	+	0.461016i
$475$	9.37629	+	34.9928i	0.430214	+	1.60558i
$476$		0			0
$477$	5.20013	−	9.00689i	0.238098	−	0.412397i
$478$	−3.08997	−	1.78400i	−0.141332	−	0.0815981i
$479$	6.49925	−	6.49925i	0.296958	−	0.296958i	−0.542863	−	0.839821i	$-0.682660\pi$
$479$	6.49925	−	6.49925i	0.296958	−	0.296958i	0.839821	+	0.542863i	$0.182660\pi$
$480$	−37.8975	−	21.8801i	−1.72978	−	0.998686i
$481$	−0.968819	−	9.70392i	−0.0441743	−	0.442461i
$482$			3.80434i			0.173283i
$483$		0			0
$484$	−5.73748	−	9.93760i	−0.260794	−	0.451709i
$485$			49.0447i			2.22701i
$486$	−10.4365	+	2.79645i	−0.473409	+	0.126850i
$487$	−10.6869	−	2.86354i	−0.484269	−	0.129759i	0.00842076	−	0.999965i	$-0.497320\pi$
$487$	−10.6869	−	2.86354i	−0.484269	−	0.129759i	−0.492690	+	0.870205i	$0.663986\pi$
$488$	12.3553	−	12.3553i	0.559299	−	0.559299i
$489$	−10.6761	+	10.6761i	−0.482789	+	0.482789i
$490$		0			0
$491$	2.45531	−	1.41757i	0.110807	−	0.0639743i	−0.443572	−	0.896239i	$-0.646289\pi$
$491$	2.45531	−	1.41757i	0.110807	−	0.0639743i	0.554379	+	0.832264i	$0.312956\pi$
$492$	−19.5673	+	5.24304i	−0.882162	+	0.236375i
$493$	3.15583	−	5.46605i	0.142131	−	0.246179i
$494$	6.24434	+	5.11068i	0.280946	+	0.229940i
$495$	−19.6592	+	11.3503i	−0.883617	+	0.510157i
$496$	4.09929	−	15.2988i	0.184064	−	0.686935i
$497$		0			0
$498$	7.45174	+	4.30226i	0.333920	+	0.192789i
$499$	37.0495	+	9.92738i	1.65856	+	0.444411i	0.961992	−	0.273077i	$-0.0880413\pi$
$499$	37.0495	+	9.92738i	1.65856	+	0.444411i	0.696571	+	0.717488i	$0.254708\pi$
$500$	−4.82572	+	18.0098i	−0.215813	+	0.805425i
$501$	−1.38844	+	5.18172i	−0.0620309	+	0.231502i
$502$	1.67014	+	0.447511i	0.0745418	+	0.0199734i
$503$	25.0453	+	14.4599i	1.11672	+	0.644736i	0.940561	−	0.339626i	$-0.110301\pi$
$503$	25.0453	+	14.4599i	1.11672	+	0.644736i	0.176155	+	0.984362i	$0.443634\pi$
$504$		0			0
$505$	−9.07314	+	33.8614i	−0.403750	+	1.50681i
$506$	−1.33328	+	0.769769i	−0.0592715	+	0.0342204i
$507$	10.1400	−	30.1351i	0.450331	−	1.33835i
$508$	7.53329	−	13.0480i	0.334236	−	0.578913i
$509$	−12.3628	+	3.31260i	−0.547972	+	0.146829i	−0.522175	−	0.852839i	$-0.674879\pi$
$509$	−12.3628	+	3.31260i	−0.547972	+	0.146829i	−0.0257972	+	0.999667i	$0.508212\pi$
$510$	−4.28055	+	2.47138i	−0.189546	+	0.109434i
$511$		0			0
$512$	−16.0026	+	16.0026i	−0.707221	+	0.707221i
$513$	0.142619	−	0.142619i	0.00629677	−	0.00629677i
$514$	5.14513	+	1.37863i	0.226942	+	0.0608089i
$515$	−42.9817	+	11.5169i	−1.89400	+	0.507496i
$516$		−	22.6386i		−	0.996609i
$517$	7.13901	+	12.3651i	0.313973	+	0.543817i
$518$		0			0
$519$		−	46.3415i		−	2.03416i
$520$	8.46189	+	22.3921i	0.371078	+	0.981958i
$521$	−13.9866	−	8.07515i	−0.612763	−	0.353779i	0.161283	−	0.986908i	$-0.448437\pi$
$521$	−13.9866	−	8.07515i	−0.612763	−	0.353779i	−0.774046	+	0.633129i	$0.781770\pi$
$522$	−5.70913	+	5.70913i	−0.249882	+	0.249882i
$523$	−31.2872	−	18.0636i	−1.36809	−	0.789868i	−0.377407	−	0.926047i	$-0.623184\pi$
$523$	−31.2872	−	18.0636i	−1.36809	−	0.789868i	−0.990684	+	0.136179i	$0.956518\pi$
$524$	−12.9172	+	22.3733i	−0.564292	+	0.977382i
$525$		0			0
$526$	0.597006	+	2.22806i	0.0260307	+	0.0971479i
$527$	−4.90550	−	4.90550i	−0.213687	−	0.213687i
$528$	3.49883	+	13.0578i	0.152267	+	0.568268i
$529$	−10.4013	−	18.0156i	−0.452231	−	0.783287i
$530$	3.08000	−	5.33471i	0.133787	−	0.231725i
$531$	−32.9187	−	8.82053i	−1.42855	−	0.382778i
$532$		0			0
$533$	15.4731	+	6.98590i	0.670212	+	0.302593i
$534$	5.98493	+	10.3662i	0.258993	+	0.448589i
$535$	−20.8298	−	20.8298i	−0.900552	−	0.900552i
$536$	−14.2102			−0.613785
$537$	29.0159			1.25213
$538$	−8.92413	−	8.92413i	−0.384747	−	0.384747i
$539$		0			0
$540$	0.270451	−	0.0724673i	0.0116384	−	0.00311849i
$541$	−6.74062	+	25.1563i	−0.289802	+	1.08155i	0.655457	+	0.755233i	$0.272476\pi$
$541$	−6.74062	+	25.1563i	−0.289802	+	1.08155i	−0.945259	+	0.326322i	$0.894191\pi$
$542$	0.563771	−	0.325493i	0.0242160	−	0.0139811i
$543$			24.9627i			1.07125i
$544$	1.47268	+	5.49610i	0.0631404	+	0.235643i
$545$	10.7214			0.459254
$546$		0			0
$547$	−21.3472			−0.912739			−0.456369	−	0.889790i	$-0.650850\pi$
$547$	−21.3472			−0.912739			−0.456369	+	0.889790i	$0.650850\pi$
$548$	−1.03592	−	3.86611i	−0.0442524	−	0.165152i
$549$		−	28.2372i		−	1.20513i
$550$	−7.14685	+	4.12623i	−0.304743	+	0.175943i
$551$	6.50897	−	24.2918i	0.277291	−	1.03487i
$552$	−6.46186	+	1.73145i	−0.275035	+	0.0736954i
$553$		0			0
$554$	0.0629511	+	0.0629511i	0.00267454	+	0.00267454i
$555$	23.8021			1.01034
$556$	−8.59666			−0.364579
$557$	−4.63838	−	4.63838i	−0.196534	−	0.196534i	0.601978	−	0.798513i	$-0.294379\pi$
$557$	−4.63838	−	4.63838i	−0.196534	−	0.196534i	−0.798513	+	0.601978i	$0.794379\pi$
$558$	4.43721	+	7.68548i	0.187842	+	0.325352i
$559$	−12.0164	+	14.6819i	−0.508241	+	0.620980i
$560$		0			0
$561$	5.71948	+	1.53253i	0.241476	+	0.0647034i
$562$	1.91098	−	3.30992i	0.0806100	−	0.139621i
$563$	5.04580	+	8.73958i	0.212655	+	0.368329i	0.952545	−	0.304399i	$-0.0984556\pi$
$563$	5.04580	+	8.73958i	0.212655	+	0.368329i	−0.739890	+	0.672728i	$0.765122\pi$
$564$	7.51428	+	28.0437i	0.316408	+	1.18085i
$565$	41.7197	+	41.7197i	1.75516	+	1.75516i
$566$	−0.928516	−	3.46527i	−0.0390284	−	0.145656i
$567$		0			0
$568$	6.23026	−	10.7911i	0.261416	−	0.452786i
$569$	−27.1118	−	15.6530i	−1.13658	−	0.656207i	−0.191001	−	0.981590i	$-0.561174\pi$
$569$	−27.1118	−	15.6530i	−1.13658	−	0.656207i	−0.945582	+	0.325383i	$0.894507\pi$
$570$	−13.9260	+	13.9260i	−0.583296	+	0.583296i
$571$	8.05884	+	4.65277i	0.337252	+	0.194713i	0.659056	−	0.752094i	$-0.270956\pi$
$571$	8.05884	+	4.65277i	0.337252	+	0.194713i	−0.321804	+	0.946806i	$0.604289\pi$
$572$	5.52187	−	12.2304i	0.230881	−	0.511378i
$573$		−	14.6050i		−	0.610133i
$574$		0			0
$575$	5.88933	+	10.2006i	0.245602	+	0.425395i
$576$			8.30092i			0.345872i
$577$	16.6022	−	4.44854i	0.691158	−	0.185195i	0.103891	−	0.994589i	$-0.466871\pi$
$577$	16.6022	−	4.44854i	0.691158	−	0.185195i	0.587267	+	0.809393i	$0.300204\pi$
$578$	−7.43962	−	1.99344i	−0.309448	−	0.0829162i
$579$	1.73569	−	1.73569i	0.0721327	−	0.0721327i
$580$	24.6862	−	24.6862i	1.02504	−	1.02504i
$581$		0			0
$582$	−14.1723	+	8.18239i	−0.587461	+	0.339171i
$583$	−7.12800	+	1.90994i	−0.295212	+	0.0791017i
$584$	−5.22419	+	9.04857i	−0.216179	+	0.374432i
$585$	35.2573	+	15.9182i	1.45771	+	0.658138i
$586$	−13.6457	+	7.87838i	−0.563701	+	0.325453i
$587$	5.01190	−	18.7047i	0.206863	−	0.772025i	−0.782010	−	0.623266i	$-0.785805\pi$
$587$	5.01190	−	18.7047i	0.206863	−	0.772025i	0.988873	−	0.148759i	$-0.0475278\pi$
$588$		0			0
$589$	−23.9388	−	13.8211i	−0.986380	−	0.569487i
$590$	−19.4975	−	5.22433i	−0.802698	−	0.215082i
$591$	2.67789	−	9.99403i	0.110154	−	0.411099i
$592$	1.82876	−	6.82503i	0.0751616	−	0.280507i
$593$	9.78085	+	2.62077i	0.401651	+	0.107622i	0.453989	−	0.891007i	$-0.350001\pi$
$593$	9.78085	+	2.62077i	0.401651	+	0.107622i	−0.0523376	+	0.998629i	$0.516667\pi$
$594$	0.0397897	+	0.0229726i	0.00163259	+	0.000942578i
$595$		0			0
$596$	1.26150	−	4.70799i	0.0516731	−	0.192847i
$597$	−31.8864	+	18.4096i	−1.30502	+	0.753456i
$598$	2.39113	+	1.07957i	0.0977804	+	0.0441467i
$599$	−8.96728	+	15.5318i	−0.366393	+	0.634611i	−0.988999	−	0.147924i	$-0.952741\pi$
$599$	−8.96728	+	15.5318i	−0.366393	+	0.634611i	0.622606	+	0.782536i	$0.286074\pi$
$600$	−34.6378	+	9.28118i	−1.41408	+	0.378903i
$601$	29.5092	−	17.0372i	1.20371	−	0.694960i	0.242329	−	0.970194i	$-0.422089\pi$
$601$	29.5092	−	17.0372i	1.20371	−	0.694960i	0.961377	+	0.275234i	$0.0887552\pi$
$602$		0			0
$603$	−16.2381	+	16.2381i	−0.661268	+	0.661268i
$604$	−7.85335	+	7.85335i	−0.319548	+	0.319548i
$605$	−22.6717	−	6.07486i	−0.921734	−	0.246978i
$606$	−11.2986	+	3.02744i	−0.458973	+	0.122981i
$607$		−	32.0123i		−	1.29934i	−0.760217	−	0.649669i	$-0.774907\pi$
$607$		−	32.0123i		−	1.29934i	0.760217	−	0.649669i	$-0.225093\pi$
$608$	11.3358	+	19.6342i	0.459729	+	0.796274i
$609$		0			0
$610$		−	16.7247i		−	0.677162i
$611$	10.0121	−	22.1758i	0.405047	−	0.897138i
$612$	5.19782	+	3.00096i	0.210109	+	0.121307i
$613$	12.2621	−	12.2621i	0.495262	−	0.495262i	−0.414697	−	0.909959i	$-0.636113\pi$
$613$	12.2621	−	12.2621i	0.495262	−	0.495262i	0.909959	+	0.414697i	$0.136113\pi$
$614$	−5.80508	−	3.35157i	−0.234274	−	0.135258i
$615$	−20.7179	+	35.8845i	−0.835426	+	1.44700i
$616$		0			0
$617$	−4.46908	−	16.6788i	−0.179918	−	0.671464i	−0.995661	−	0.0930497i	$-0.970338\pi$
$617$	−4.46908	−	16.6788i	−0.179918	−	0.671464i	0.815743	−	0.578414i	$-0.196328\pi$
$618$	−10.4989	−	10.4989i	−0.422327	−	0.422327i
$619$	0.785345	+	2.93095i	0.0315657	+	0.117805i	0.979911	−	0.199435i	$-0.0639107\pi$
$619$	0.785345	+	2.93095i	0.0315657	+	0.117805i	−0.948345	+	0.317240i	$0.897244\pi$
$620$	−19.1865	−	33.2320i	−0.770548	−	1.33463i
$621$	0.0327885	−	0.0567914i	0.00131576	−	0.00227896i
$622$	7.86477	+	2.10736i	0.315349	+	0.0844974i
$623$		0			0
$624$	14.5907	−	17.8272i	0.584094	−	0.713659i
$625$	−0.795947	−	1.37862i	−0.0318379	−	0.0551448i
$626$	−3.23143	−	3.23143i	−0.129154	−	0.129154i
$627$	23.5931			0.942218
$628$	3.35780			0.133991
$629$	−2.18843	−	2.18843i	−0.0872583	−	0.0872583i
$630$		0			0
$631$	−46.4748	+	12.4529i	−1.85013	+	0.495742i	−0.999547	−	0.0300916i	$-0.990420\pi$
$631$	−46.4748	+	12.4529i	−1.85013	+	0.495742i	−0.850587	+	0.525834i	$0.823753\pi$
$632$	5.64643	−	21.0728i	0.224603	−	0.838229i
$633$	−52.3411	+	30.2192i	−2.08037	+	1.20110i
$634$			16.2685i			0.646106i
$635$	−7.97626	−	29.7678i	−0.316528	−	1.18130i
$636$	−15.0054			−0.595002
$637$		0			0
$638$	5.72881			0.226806
$639$	−5.21176	−	19.4506i	−0.206174	−	0.769452i
$640$			40.7006i			1.60883i
$641$	43.6877	−	25.2231i	1.72556	−	0.996253i	0.819537	−	0.573026i	$-0.194231\pi$
$641$	43.6877	−	25.2231i	1.72556	−	0.996253i	0.906024	−	0.423227i	$-0.139103\pi$
$642$	2.54399	−	9.49429i	0.100403	−	0.374710i
$643$	−23.5329	+	6.30561i	−0.928046	+	0.248669i	−0.691021	−	0.722834i	$-0.742839\pi$
$643$	−23.5329	+	6.30561i	−0.928046	+	0.248669i	−0.237025	+	0.971504i	$0.576172\pi$
$644$		0			0
$645$	−32.7434	−	32.7434i	−1.28927	−	1.28927i
$646$	2.56078			0.100753
$647$	−43.6258			−1.71511			−0.857554	−	0.514394i	$-0.828017\pi$
$647$	−43.6258			−1.71511			−0.857554	+	0.514394i	$0.828017\pi$
$648$	11.8131	+	11.8131i	0.464064	+	0.464064i
$649$	12.0906	+	20.9415i	0.474598	+	0.822028i
$650$	12.8173	+	5.78685i	0.502735	+	0.226979i
$651$		0			0
$652$	10.4889	+	2.81048i	0.410776	+	0.110067i
$653$	−24.0057	+	41.5791i	−0.939416	+	1.62712i	−0.172852	+	0.984948i	$0.555298\pi$
$653$	−24.0057	+	41.5791i	−0.939416	+	1.62712i	−0.766564	+	0.642168i	$0.778035\pi$
$654$	1.78871	+	3.09813i	0.0699439	+	0.121146i
$655$	13.6768	+	51.0425i	0.534396	+	1.99439i
$656$	8.69772	+	8.69772i	0.339589	+	0.339589i
$657$	4.37016	+	16.3097i	0.170496	+	0.636301i
$658$		0			0
$659$	2.00241	−	3.46828i	0.0780030	−	0.135105i	−0.824385	−	0.566029i	$-0.808479\pi$
$659$	2.00241	−	3.46828i	0.0780030	−	0.135105i	0.902388	+	0.430924i	$0.141812\pi$
$660$	28.3642	+	16.3761i	1.10407	+	0.637437i
$661$	14.9051	−	14.9051i	0.579741	−	0.579741i	−0.355091	−	0.934832i	$-0.615550\pi$
$661$	14.9051	−	14.9051i	0.579741	−	0.579741i	0.934832	+	0.355091i	$0.115550\pi$
$662$	10.0101	+	5.77934i	0.389054	+	0.224620i
$663$	−3.56694	−	9.43894i	−0.138528	−	0.366578i
$664$		−	13.2247i		−	0.513217i
$665$		0			0
$666$	1.97952	+	3.42862i	0.0767047	+	0.132856i
$667$		−	8.17667i		−	0.316602i
$668$	3.72677	−	0.998584i	0.144193	−	0.0386364i
$669$	1.76510	+	0.472958i	0.0682428	+	0.0182856i
$670$	−9.61772	+	9.61772i	−0.371565	+	0.371565i
$671$	−14.1673	+	14.1673i	−0.546921	+	0.546921i
$672$		0			0
$673$	−39.2951	+	22.6870i	−1.51471	+	0.874521i	−0.514863	+	0.857273i	$0.672157\pi$
$673$	−39.2951	+	22.6870i	−1.51471	+	0.874521i	−0.999851	+	0.0172480i	$0.994510\pi$
$674$	11.6619	−	3.12480i	0.449200	−	0.120363i
$675$	0.175758	−	0.304422i	0.00676494	−	0.0117172i
$676$	−22.4163	+	4.52105i	−0.862164	+	0.173886i
$677$	12.2354	−	7.06412i	0.470245	−	0.271496i	−0.246097	−	0.969245i	$-0.579148\pi$
$677$	12.2354	−	7.06412i	0.470245	−	0.271496i	0.716342	+	0.697749i	$0.245815\pi$
$678$	−5.09531	+	19.0160i	−0.195684	+	0.730304i
$679$		0			0
$680$	6.57896	+	3.79837i	0.252292	+	0.145661i
$681$	−24.5030	−	6.56556i	−0.938957	−	0.251593i
$682$	1.62973	−	6.08225i	0.0624057	−	0.232901i
$683$	−0.0629256	+	0.234842i	−0.00240778	+	0.00898597i	−0.967119	−	0.254323i	$-0.918147\pi$
$683$	−0.0629256	+	0.234842i	−0.00240778	+	0.00898597i	0.964711	+	0.263309i	$0.0848140\pi$
$684$	23.0997	+	6.18955i	0.883240	+	0.236664i
$685$	−7.09006	−	4.09345i	−0.270897	−	0.156403i
$686$		0			0
$687$	1.08732	−	4.05793i	0.0414838	−	0.154820i
$688$	−11.9046	+	6.87311i	−0.453858	+	0.262035i
$689$	9.73152	+	7.96476i	0.370742	+	0.303433i
$690$	−3.20164	+	5.54540i	−0.121884	+	0.211110i
$691$	−34.8908	+	9.34895i	−1.32731	+	0.355651i	−0.851710	−	0.524013i	$-0.824434\pi$
$691$	−34.8908	+	9.34895i	−1.32731	+	0.355651i	−0.475597	+	0.879664i	$0.657768\pi$
$692$	−28.8641	+	16.6647i	−1.09725	+	0.633497i
$693$		0			0
$694$	11.5788	−	11.5788i	0.439526	−	0.439526i
$695$	−12.4338	+	12.4338i	−0.471640	+	0.471640i
$696$	24.0454	+	6.44294i	0.911438	+	0.244219i
$697$	5.20416	−	1.39445i	0.197122	−	0.0528186i
$698$		−	2.68417i		−	0.101597i
$699$	−10.1630	−	17.6029i	−0.384401	−	0.665802i
$700$		0			0
$701$		−	26.1953i		−	0.989383i	−0.869069	−	0.494691i	$-0.835281\pi$
$701$		−	26.1953i		−	0.989383i	0.869069	−	0.494691i	$-0.164719\pi$
$702$	−0.00777819	−	0.0779083i	−0.000293569	−	0.00294046i
$703$	−10.6795	−	6.16581i	−0.402785	−	0.232548i
$704$	4.16477	−	4.16477i	0.156966	−	0.156966i
$705$	51.4293	+	29.6927i	1.93694	+	1.11829i
$706$	−1.08467	+	1.87871i	−0.0408221	+	0.0707060i
$707$		0			0
$708$	12.7262	+	47.4947i	0.478279	+	1.78496i
$709$	11.0458	+	11.0458i	0.414834	+	0.414834i	0.883419	−	0.468584i	$-0.155236\pi$
$709$	11.0458	+	11.0458i	0.414834	+	0.414834i	−0.468584	+	0.883419i	$0.655236\pi$
$710$	−3.08689	−	11.5204i	−0.115849	−	0.432354i
$711$	−17.6279	−	30.5324i	−0.661097	−	1.14505i
$712$	9.19849	−	15.9323i	0.344728	−	0.597087i
$713$	−8.68112	−	2.32610i	−0.325111	−	0.0871131i
$714$		0			0
$715$	−9.70285	−	25.6760i	−0.362866	−	0.960227i
$716$	−10.4343	−	18.0727i	−0.389948	−	0.675410i
$717$	12.5709	+	12.5709i	0.469467	+	0.469467i
$718$	−13.6314			−0.508718
$719$	1.39754			0.0521194			0.0260597	−	0.999660i	$-0.491704\pi$
$719$	1.39754			0.0521194			0.0260597	+	0.999660i	$0.491704\pi$
$720$	19.8188	+	19.8188i	0.738604	+	0.738604i
$721$		0			0
$722$	0.847040	−	0.226964i	0.0315236	−	0.00844671i
$723$	4.90603	−	18.3096i	0.182457	−	0.680940i
$724$	15.5482	−	8.97676i	0.577845	−	0.333619i
$725$		−	43.8298i		−	1.62780i
$726$	−2.02700	−	7.56487i	−0.0752291	−	0.280759i
$727$	8.63150			0.320124			0.160062	−	0.987107i	$-0.448831\pi$
$727$	8.63150			0.320124			0.160062	+	0.987107i	$0.448831\pi$
$728$		0			0
$729$	26.6734			0.987905
$730$	2.58842	+	9.66010i	0.0958015	+	0.357536i
$731$			6.02101i			0.222695i
$732$	−35.2821	+	20.3702i	−1.30407	+	0.752903i
$733$	−0.210133	+	0.784228i	−0.00776145	+	0.0289661i	−0.969698	−	0.244307i	$-0.921440\pi$
$733$	−0.210133	+	0.784228i	−0.00776145	+	0.0289661i	0.961937	+	0.273273i	$0.0881062\pi$
$734$	7.98916	−	2.14069i	0.294885	−	0.0790143i
$735$		0			0
$736$	5.21230	+	5.21230i	0.192128	+	0.192128i
$737$	16.2941			0.600202
$738$	−6.89205			−0.253700
$739$	−15.8205	−	15.8205i	−0.581966	−	0.581966i	0.353477	−	0.935443i	$-0.384999\pi$
$739$	−15.8205	−	15.8205i	−0.581966	−	0.581966i	−0.935443	+	0.353477i	$0.884999\pi$
$740$	−8.55941	−	14.8253i	−0.314650	−	0.544990i
$741$	−23.4622	−	32.6494i	−0.861905	−	1.19941i
$742$		0			0
$743$	21.2232	+	5.68675i	0.778605	+	0.208627i	0.626170	−	0.779687i	$-0.284622\pi$
$743$	21.2232	+	5.68675i	0.778605	+	0.208627i	0.152436	+	0.988313i	$0.451288\pi$
$744$	13.6809	−	23.6960i	0.501565	−	0.868736i
$745$	−4.98483	−	8.63397i	−0.182630	−	0.316324i
$746$	−0.353557	−	1.31949i	−0.0129446	−	0.0483100i
$747$	−15.1120	−	15.1120i	−0.552920	−	0.552920i
$748$	−1.10222	−	4.11352i	−0.0403010	−	0.150405i
$749$		0			0
$750$	−6.36272	+	11.0206i	−0.232334	+	0.402414i
$751$	−22.0152	−	12.7105i	−0.803347	−	0.463813i	0.0412930	−	0.999147i	$-0.486852\pi$
$751$	−22.0152	−	12.7105i	−0.803347	−	0.463813i	−0.844640	+	0.535334i	$0.820186\pi$
$752$	12.4655	−	12.4655i	0.454570	−	0.454570i
$753$	−7.46095	−	4.30758i	−0.271892	−	0.156977i
$754$	−5.69702	−	7.92784i	−0.207473	−	0.288715i
$755$			22.7174i			0.826771i
$756$		0			0
$757$	19.9731	+	34.5945i	0.725936	+	1.25736i	0.958587	+	0.284799i	$0.0919267\pi$
$757$	19.9731	+	34.5945i	0.725936	+	1.25736i	−0.232651	+	0.972560i	$0.574740\pi$
$758$		−	0.373043i		−	0.0135495i
$759$	7.40951	−	1.98537i	0.268948	−	0.0720645i
$760$	29.2377	+	7.83422i	1.06056	+	0.284177i
$761$	−12.3304	+	12.3304i	−0.446976	+	0.446976i	−0.894348	−	0.447372i	$-0.852360\pi$
$761$	−12.3304	+	12.3304i	−0.446976	+	0.446976i	0.447372	+	0.894348i	$0.352360\pi$
$762$	7.27120	−	7.27120i	0.263408	−	0.263408i
$763$		0			0
$764$	−9.09684	+	5.25206i	−0.329112	+	0.190013i
$765$	11.8583	−	3.17743i	0.428738	−	0.114880i
$766$	7.72272	−	13.3761i	0.279033	−	0.483300i
$767$	16.9565	−	37.5570i	0.612264	−	1.35610i
$768$	0.0315111	−	0.0181929i	0.00113706	−	0.000656480i
$769$	0.710240	−	2.65065i	0.0256119	−	0.0955849i	−0.951937	−	0.306295i	$-0.900911\pi$
$769$	0.710240	−	2.65065i	0.0256119	−	0.0955849i	0.977549	+	0.210710i	$0.0675774\pi$
$770$		0			0
$771$	−22.9847	−	13.2702i	−0.827774	−	0.477915i
$772$	−1.70525	−	0.456920i	−0.0613733	−	0.0164449i
$773$	−3.44100	+	12.8420i	−0.123764	+	0.461894i	−0.999793	−	0.0203654i	$-0.993517\pi$
$773$	−3.44100	+	12.8420i	−0.123764	+	0.461894i	0.876029	+	0.482259i	$0.160184\pi$
$774$	1.99346	−	7.43969i	0.0716534	−	0.267414i
$775$	−46.5339	−	12.4687i	−1.67155	−	0.447890i
$776$	21.7820	+	12.5759i	0.781930	+	0.451448i
$777$		0			0
$778$	3.43789	−	12.8304i	0.123254	−	0.459991i
$779$	18.5913	−	10.7337i	0.666103	−	0.384575i
$780$	−5.54469	−	55.5370i	−0.198532	−	1.98854i
$781$	−7.14395	+	12.3737i	−0.255631	+	0.442765i
$782$	0.804224	−	0.215491i	0.0287590	−	0.00770595i
$783$	−0.211328	+	0.122010i	−0.00755225	+	0.00436029i
$784$		0			0
$785$	4.85655	−	4.85655i	0.173338	−	0.173338i
$786$	−12.4678	+	12.4678i	−0.444713	+	0.444713i
$787$	−21.1891	−	5.67760i	−0.755309	−	0.202385i	−0.139437	−	0.990231i	$-0.544529\pi$
$787$	−21.1891	−	5.67760i	−0.755309	−	0.202385i	−0.615872	+	0.787846i	$0.711196\pi$
$788$	−7.18784	+	1.92598i	−0.256056	+	0.0686101i
$789$		−	11.4931i		−	0.409166i
$790$	−10.4409	−	18.0841i	−0.371469	−	0.643403i
$791$		0			0
$792$			11.6416i			0.413666i
$793$	33.6941	+	5.51677i	1.19651	+	0.195906i
$794$	0.0970451	+	0.0560290i	0.00344400	+	0.00198840i
$795$	−21.7031	+	21.7031i	−0.769728	+	0.769728i
$796$	22.9332	+	13.2405i	0.812844	+	0.469296i
$797$	23.0740	−	39.9654i	0.817324	−	1.41565i	−0.0903225	−	0.995913i	$-0.528790\pi$
$797$	23.0740	−	39.9654i	0.817324	−	1.41565i	0.907647	−	0.419735i	$-0.137877\pi$
$798$		0			0
$799$	−1.99851	−	7.45855i	−0.0707023	−	0.263865i
$800$	27.9398	+	27.9398i	0.987820	+	0.987820i
$801$	−7.69476	−	28.7172i	−0.271881	−	1.01467i
$802$	−6.30682	−	10.9237i	−0.222702	−	0.385730i
$803$	5.99034	−	10.3756i	0.211394	−	0.366146i
$804$	32.0035	+	8.57532i	1.12868	+	0.302428i
$805$		0			0
$806$	−10.0376	+	3.79318i	−0.353560	+	0.133609i
$807$	31.4417	+	54.4587i	1.10680	+	1.91704i
$808$	12.7123	+	12.7123i	0.447215	+	0.447215i
$809$	−37.2030			−1.30799			−0.653994	−	0.756500i	$-0.726908\pi$
$809$	−37.2030			−1.30799			−0.653994	+	0.756500i	$0.726908\pi$
$810$	15.9907			0.561857
$811$	5.71666	+	5.71666i	0.200739	+	0.200739i	0.800317	−	0.599578i	$-0.204665\pi$
$811$	5.71666	+	5.71666i	0.200739	+	0.200739i	−0.599578	+	0.800317i	$0.704665\pi$
$812$		0			0
$813$	−3.13308	+	0.839506i	−0.109882	+	0.0294427i
$814$	0.727051	−	2.71339i	0.0254831	−	0.0951043i
$815$	19.2355	−	11.1056i	0.673791	−	0.389013i
$816$		−	7.31087i		−	0.255932i
$817$	6.20924	+	23.1732i	0.217234	+	0.810728i
$818$	−14.6517			−0.512283
$819$		0			0
$820$	29.8012			1.04070
$821$	1.66286	+	6.20586i	0.0580341	+	0.216586i	0.988853	−	0.148894i	$-0.0475714\pi$
$821$	1.66286	+	6.20586i	0.0580341	+	0.216586i	−0.930819	+	0.365480i	$0.880905\pi$
$822$		−	2.73173i		−	0.0952800i
$823$	7.71255	−	4.45284i	0.268843	−	0.155216i	−0.359519	−	0.933138i	$-0.617059\pi$
$823$	7.71255	−	4.45284i	0.268843	−	0.155216i	0.628362	+	0.777921i	$0.283726\pi$
$824$	−5.90625	+	22.0424i	−0.205754	+	0.767885i
$825$	39.7176	−	10.6423i	1.38279	−	0.370517i
$826$		0			0
$827$	−0.00569088	−	0.00569088i	−0.000197891	−	0.000197891i	0.707008	−	0.707206i	$-0.250045\pi$
$827$	−0.00569088	−	0.00569088i	−0.000197891	−	0.000197891i	−0.707206	+	0.707008i	$0.750045\pi$
$828$	7.77542			0.270214
$829$	16.7230			0.580813			0.290407	−	0.956903i	$-0.406209\pi$
$829$	16.7230			0.580813			0.290407	+	0.956903i	$0.406209\pi$
$830$	−8.95073	−	8.95073i	−0.310684	−	0.310684i
$831$	−0.221791	−	0.384153i	−0.00769384	−	0.0133261i
$832$	−9.90509	−	1.62177i	−0.343397	−	0.0562249i
$833$		0			0
$834$	−5.66735	−	1.51856i	−0.196244	−	0.0525835i
$835$	3.94591	−	6.83451i	0.136554	−	0.236518i
$836$	−8.48424	−	14.6951i	−0.293434	−	0.508242i
$837$	0.0694190	+	0.259075i	0.00239947	+	0.00895495i
$838$	−3.09658	−	3.09658i	−0.106969	−	0.106969i
$839$	−5.65746	−	21.1139i	−0.195317	−	0.728934i	−0.992185	−	0.124779i	$-0.960178\pi$
$839$	−5.65746	−	21.1139i	−0.195317	−	0.728934i	0.796867	−	0.604154i	$-0.206489\pi$
$840$		0			0
$841$	−0.713208	+	1.23531i	−0.0245934	+	0.0425970i
$842$	−10.9060	−	6.29661i	−0.375847	−	0.216996i
$843$	−13.4657	+	13.4657i	−0.463782	+	0.463782i
$844$	37.6444	+	21.7340i	1.29578	+	0.748116i
$845$	−25.8828	+	38.9608i	−0.890394	+	1.34029i
$846$			9.87762i			0.339600i
$847$		0			0
$848$	4.55565	+	7.89062i	0.156442	+	0.270965i
$849$			17.8751i			0.613472i
$850$	4.31093	−	1.15511i	0.147864	−	0.0396199i
$851$	−3.87279	−	1.03771i	−0.132758	−	0.0355723i
$852$	−20.5436	+	20.5436i	−0.703812	+	0.703812i
$853$	−34.9450	+	34.9450i	−1.19649	+	1.19649i	−0.221284	+	0.975209i	$0.571025\pi$
$853$	−34.9450	+	34.9450i	−1.19649	+	1.19649i	−0.975209	+	0.221284i	$0.928975\pi$
$854$		0			0
$855$	42.3626	−	24.4580i	1.44877	−	0.836448i
$856$	−14.5922	+	3.90997i	−0.498751	+	0.133640i
$857$	−12.4193	+	21.5108i	−0.424235	+	0.734796i	−0.996349	−	0.0853781i	$-0.972790\pi$
$857$	−12.4193	+	21.5108i	−0.424235	+	0.734796i	0.572114	+	0.820174i	$0.306124\pi$
$858$	5.80074	−	7.08747i	0.198034	−	0.241962i
$859$	17.8657	−	10.3147i	0.609569	−	0.351935i	−0.163228	−	0.986588i	$-0.552191\pi$
$859$	17.8657	−	10.3147i	0.609569	−	0.351935i	0.772797	+	0.634654i	$0.218857\pi$
$860$	−8.61971	+	32.1692i	−0.293930	+	1.09696i
$861$		0			0
$862$	5.00231	+	2.88809i	0.170379	+	0.0983686i
$863$	21.7857	+	5.83745i	0.741593	+	0.198709i	0.609786	−	0.792566i	$-0.291255\pi$
$863$	21.7857	+	5.83745i	0.741593	+	0.198709i	0.131807	+	0.991275i	$0.457922\pi$
$864$	0.0569365	−	0.212490i	0.00193702	−	0.00722905i
$865$	−17.6446	+	65.8506i	−0.599935	+	2.23899i
$866$	−5.94012	−	1.59165i	−0.201853	−	0.0540864i
$867$	33.2348	+	19.1881i	1.12871	+	0.651663i
$868$		0			0
$869$	−6.47450	+	24.1632i	−0.219632	+	0.819679i
$870$	20.6351	−	11.9137i	0.699596	−	0.403912i
$871$	−16.2037	−	22.5487i	−0.549041	−	0.764033i
$872$	2.74914	−	4.76165i	0.0930976	−	0.161250i
$873$	39.2613	−	10.5200i	1.32879	−	0.356049i
$874$	2.87301	−	1.65873i	0.0971809	−	0.0561074i
$875$		0			0
$876$	17.2262	−	17.2262i	0.582019	−	0.582019i
$877$	9.10624	−	9.10624i	0.307496	−	0.307496i	−0.536442	−	0.843937i	$-0.680232\pi$
$877$	9.10624	−	9.10624i	0.307496	−	0.307496i	0.843937	+	0.536442i	$0.180232\pi$
$878$	8.42255	+	2.25682i	0.284247	+	0.0761639i
$879$	75.8343	−	20.3198i	2.55783	−	0.685368i
$880$		−	19.8872i		−	0.670396i
$881$	−3.52615	−	6.10747i	−0.118799	−	0.205766i	0.800493	−	0.599342i	$-0.204571\pi$
$881$	−3.52615	−	6.10747i	−0.118799	−	0.205766i	−0.919292	+	0.393576i	$0.871238\pi$
$882$		0			0
$883$			55.6508i			1.87280i	0.350938	+	0.936399i	$0.385863\pi$
$883$			55.6508i			1.87280i	−0.350938	+	0.936399i	$0.614137\pi$
$884$	−4.59642	+	5.61600i	−0.154594	+	0.188887i
$885$	87.1005	+	50.2875i	2.92785	+	1.69040i
$886$	2.32516	−	2.32516i	0.0781153	−	0.0781153i
$887$	−12.9108	−	7.45405i	−0.433502	−	0.250282i	0.267335	−	0.963604i	$-0.413857\pi$
$887$	−12.9108	−	7.45405i	−0.433502	−	0.250282i	−0.700837	+	0.713321i	$0.747190\pi$
$888$	6.10326	−	10.5712i	0.204812	−	0.354745i
$889$		0			0
$890$	−4.55755	−	17.0090i	−0.152769	−	0.570143i
$891$	−13.5456	−	13.5456i	−0.453794	−	0.453794i
$892$	−0.340158	−	1.26949i	−0.0113893	−	0.0425055i
$893$	−15.3834	−	26.6449i	−0.514787	−	0.891637i
$894$	1.66329	−	2.88090i	0.0556287	−	0.0963518i
$895$	−41.2312	−	11.0479i	−1.37821	−	0.369289i
$896$		0			0
$897$	−10.1159	−	8.27932i	−0.337759	−	0.276439i
$898$	−5.81109	−	10.0651i	−0.193919	−	0.335877i
$899$	23.6478	+	23.6478i	0.788699	+	0.788699i
$900$	41.6790			1.38930
$901$	3.99086			0.132955
$902$	3.45791	+	3.45791i	0.115136	+	0.115136i
$903$		0			0
$904$	29.2265	−	7.83121i	0.972058	−	0.260462i
$905$	9.50462	−	35.4717i	0.315944	−	1.17912i
$906$	−6.56459	+	3.79007i	−0.218094	+	0.125917i
$907$			2.24261i			0.0744647i	0.999307	+	0.0372324i	$0.0118542\pi$
$907$			2.24261i			0.0744647i	−0.999307	+	0.0372324i	$0.988146\pi$
$908$	4.72204	+	17.6229i	0.156706	+	0.584836i
$909$	29.0529			0.963625
$910$		0			0
$911$	−22.3252			−0.739667			−0.369834	−	0.929098i	$-0.620585\pi$
$911$	−22.3252			−0.739667			−0.369834	+	0.929098i	$0.620585\pi$
$912$	−7.53942	−	28.1375i	−0.249655	−	0.931726i
$913$			15.1641i			0.501859i
$914$	−13.5766	+	7.83843i	−0.449073	+	0.259272i
$915$	−21.5680	+	80.4928i	−0.713015	+	2.66101i
$916$	−2.91852	+	0.782015i	−0.0964305	+	0.0258385i
$917$		0			0
$918$	−0.0175699	−	0.0175699i	−0.000579892	−	0.000579892i
$919$	−41.4889			−1.36859			−0.684297	−	0.729204i	$-0.739891\pi$
$919$	−41.4889			−1.36859			−0.684297	+	0.729204i	$0.739891\pi$
$920$	9.84147			0.324464
$921$	23.6166	+	23.6166i	0.778195	+	0.778195i
$922$	9.33881	+	16.1753i	0.307557	+	0.532705i
$923$	24.2277	−	2.41884i	0.797463	−	0.0796170i
$924$		0			0
$925$	−20.7595	−	5.56250i	−0.682569	−	0.182894i
$926$	−3.16342	+	5.47921i	−0.103956	+	0.180058i
$927$	18.4390	+	31.9373i	0.605617	+	1.04896i
$928$	−7.09929	−	26.4949i	−0.233046	−	0.869738i
$929$	−35.0945	−	35.0945i	−1.15141	−	1.15141i	−0.986270	−	0.165142i	$-0.947192\pi$
$929$	−35.0945	−	35.0945i	−1.15141	−	1.15141i	−0.165142	−	0.986270i	$-0.552808\pi$
$930$	−6.77842	−	25.2974i	−0.222273	−	0.829534i
$931$		0			0
$932$	−7.30938	+	12.6602i	−0.239427	+	0.414699i
$933$	−35.1341	−	20.2847i	−1.15024	−	0.664090i
$934$	6.19241	−	6.19241i	0.202622	−	0.202622i
$935$	−7.54379	−	4.35541i	−0.246708	−	0.142437i
$936$	16.1102	−	11.5770i	0.526580	−	0.378405i
$937$		−	47.8712i		−	1.56388i	−0.623352	−	0.781942i	$-0.714229\pi$
$937$		−	47.8712i		−	1.56388i	0.623352	−	0.781942i	$-0.285771\pi$
$938$		0			0
$939$	11.3850	+	19.7195i	0.371537	+	0.643521i
$940$		−	42.7108i		−	1.39307i
$941$	−7.35402	+	1.97050i	−0.239734	+	0.0642366i	−0.376686	−	0.926341i	$-0.622936\pi$
$941$	−7.35402	+	1.97050i	−0.239734	+	0.0642366i	0.136951	+	0.990578i	$0.456270\pi$
$942$	2.21363	+	0.593140i	0.0721240	+	0.0193256i
$943$	4.93543	−	4.93543i	0.160720	−	0.160720i
$944$	21.1115	−	21.1115i	0.687122	−	0.687122i
$945$		0			0
$946$	−4.73284	+	2.73251i	−0.153878	+	0.0888414i
$947$	6.83743	−	1.83209i	0.222187	−	0.0595348i	−0.146008	−	0.989283i	$-0.546643\pi$
$947$	6.83743	−	1.83209i	0.222187	−	0.0595348i	0.368195	+	0.929749i	$0.379976\pi$
$948$	−25.4333	+	44.0518i	−0.826036	+	1.43074i
$949$	−20.3154	+	2.02824i	−0.659465	+	0.0658395i
$950$	15.4003	−	8.89138i	0.499653	−	0.288475i
$951$	20.9797	−	78.2974i	0.680314	−	2.53897i
$952$		0			0
$953$	41.2624	+	23.8229i	1.33662	+	0.771698i	0.986305	−	0.164933i	$-0.0527408\pi$
$953$	41.2624	+	23.8229i	1.33662	+	0.771698i	0.350316	+	0.936632i	$0.386074\pi$
$954$	−4.93120	−	1.32131i	−0.159653	−	0.0427790i
$955$	−5.56089	+	20.7535i	−0.179946	+	0.671569i
$956$	3.30928	−	12.3504i	0.107030	−	0.399441i
$957$	−27.5717	−	7.38782i	−0.891267	−	0.238814i
$958$	−3.90727	−	2.25586i	−0.126238	−	0.0728836i
$959$		0			0
$960$	6.34036	−	23.6626i	0.204634	−	0.763706i
$961$	4.98732	−	2.87943i	0.160881	−	0.0928848i
$962$	−4.47795	+	1.69220i	−0.144375	+	0.0545588i
$963$	−12.2067	+	21.1427i	−0.393356	+	0.681313i
$964$	−13.1685	+	3.52849i	−0.424128	+	0.113645i
$965$	−3.12726	+	1.80552i	−0.100670	+	0.0581218i
$966$		0			0
$967$	31.2419	−	31.2419i	1.00467	−	1.00467i	0.00468303	−	0.999989i	$-0.498509\pi$
$967$	31.2419	−	31.2419i	1.00467	−	1.00467i	0.999989	−	0.00468303i	$-0.00149066\pi$
$968$	−8.51139	+	8.51139i	−0.273567	+	0.273567i
$969$	−12.3246	−	3.30236i	−0.395922	−	0.106087i
$970$	23.2542	−	6.23093i	0.746646	−	0.200063i
$971$		−	7.43216i		−	0.238509i	−0.992864	−	0.119255i	$-0.961950\pi$
$971$		−	7.43216i		−	0.238509i	0.992864	−	0.119255i	$-0.0380505\pi$
$972$	−19.3595	−	33.5317i	−0.620957	−	1.07553i
$973$		0			0
$974$			5.43090i			0.174017i
$975$	−54.2246	−	44.3801i	−1.73658	−	1.42130i
$976$	21.4234	+	12.3688i	0.685746	+	0.395916i
$977$	27.0613	−	27.0613i	0.865769	−	0.865769i	−0.126232	−	0.992001i	$-0.540288\pi$
$977$	27.0613	−	27.0613i	0.865769	−	0.865769i	0.992001	+	0.126232i	$0.0402884\pi$
$978$	6.41833	+	3.70562i	0.205235	+	0.118493i
$979$	−10.5475	+	18.2688i	−0.337099	+	0.583873i
$980$		0			0
$981$	−2.29972	−	8.58268i	−0.0734245	−	0.274024i
$982$	−0.984069	−	0.984069i	−0.0314029	−	0.0314029i
$983$	−6.66114	−	24.8597i	−0.212458	−	0.792902i	−0.987046	−	0.160437i	$-0.948710\pi$
$983$	−6.66114	−	24.8597i	−0.212458	−	0.792902i	0.774589	−	0.632465i	$-0.217957\pi$
$984$	10.6248	+	18.4027i	0.338707	+	0.586658i
$985$	−7.61050	+	13.1818i	−0.242491	+	0.420006i
$986$	−2.99262	−	0.801870i	−0.0953044	−	0.0255367i
$987$		0			0
$988$	−11.8988	+	26.3545i	−0.378550	+	0.838449i
$989$	3.90007	+	6.75513i	0.124015	+	0.214801i
$990$	7.87927	+	7.87927i	0.250419	+	0.250419i
$991$	−46.8094			−1.48695			−0.743474	−	0.668765i	$-0.766823\pi$
$991$	−46.8094			−1.48695			−0.743474	+	0.668765i	$0.766823\pi$
$992$	−30.1491			−0.957235
$993$	−40.7238	−	40.7238i	−1.29233	−	1.29233i
$994$		0			0
$995$	52.3197	−	14.0190i	1.65865	−	0.444433i
$996$	−7.98062	+	29.7841i	−0.252876	+	0.943745i
$997$	−24.4448	+	14.1132i	−0.774174	+	0.446969i	−0.834361	−	0.551218i	$-0.814163\pi$
$997$	−24.4448	+	14.1132i	−0.774174	+	0.446969i	0.0601878	+	0.998187i	$0.480830\pi$
$998$		−	18.8280i		−	0.595989i
$999$	0.0309690	+	0.115578i	0.000979815	+	0.00365672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.a.80.4		28
7.2	even	3		91.2.ba.a.54.4	yes	28
7.3	odd	6		637.2.bd.a.587.4		28
7.4	even	3		637.2.bd.b.587.4		28
7.5	odd	6		637.2.bb.a.509.4		28
7.6	odd	2		91.2.w.a.80.4	yes	28
13.7	odd	12		637.2.bb.a.423.4		28
21.2	odd	6		819.2.et.b.145.4		28
21.20	even	2		819.2.gh.b.262.4		28
91.20	even	12		91.2.ba.a.59.4	yes	28
91.33	even	12	inner	637.2.x.a.215.4		28
91.46	odd	12		637.2.bd.a.293.4		28
91.59	even	12		637.2.bd.b.293.4		28
91.72	odd	12		91.2.w.a.33.4	✓	28
273.20	odd	12		819.2.et.b.514.4		28
273.254	even	12		819.2.gh.b.397.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.4	✓	28	91.72	odd	12
91.2.w.a.80.4	yes	28	7.6	odd	2
91.2.ba.a.54.4	yes	28	7.2	even	3
91.2.ba.a.59.4	yes	28	91.20	even	12
637.2.x.a.80.4		28	1.1	even	1	trivial
637.2.x.a.215.4		28	91.33	even	12	inner
637.2.bb.a.423.4		28	13.7	odd	12
637.2.bb.a.509.4		28	7.5	odd	6
637.2.bd.a.293.4		28	91.46	odd	12
637.2.bd.a.587.4		28	7.3	odd	6
637.2.bd.b.293.4		28	91.59	even	12
637.2.bd.b.587.4		28	7.4	even	3
819.2.et.b.145.4		28	21.2	odd	6
819.2.et.b.514.4		28	273.20	odd	12
819.2.gh.b.262.4		28	21.20	even	2
819.2.gh.b.397.4		28	273.254	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.127046 - 0.474142i) q^{2} +2.44579i q^{3} +(1.52338 - 0.879524i) q^{4} +(0.931242 - 3.47544i) q^{5} +(1.15965 - 0.310728i) q^{6} +(-1.30475 - 1.30475i) q^{8} -2.98191 q^{9} +O(q^{10})\)	\(q+(-0.127046 - 0.474142i) q^{2} +2.44579i q^{3} +(1.52338 - 0.879524i) q^{4} +(0.931242 - 3.47544i) q^{5} +(1.15965 - 0.310728i) q^{6} +(-1.30475 - 1.30475i) q^{8} -2.98191 q^{9} -1.76616 q^{10} +(1.49610 + 1.49610i) q^{11} +(2.15114 + 3.72588i) q^{12} +(0.582584 - 3.55817i) q^{13} +(8.50022 + 2.27763i) q^{15} +(1.30618 - 2.26236i) q^{16} +(-0.572121 - 0.990942i) q^{17} +(0.378840 + 1.41385i) q^{18} +(-3.22385 - 3.22385i) q^{19} +(-1.63810 - 6.11348i) q^{20} +(0.519289 - 0.899435i) q^{22} +(-1.28375 - 0.741175i) q^{23} +(3.19115 - 3.19115i) q^{24} +(-6.88137 - 3.97296i) q^{25} +(-1.76109 + 0.175824i) q^{26} +0.0442386i q^{27} +(2.75801 + 4.77701i) q^{29} -4.31968i q^{30} +(5.85632 - 1.56920i) q^{31} +(-4.80327 - 1.28703i) q^{32} +(-3.65915 + 3.65915i) q^{33} +(-0.397162 + 0.397162i) q^{34} +(-4.54259 + 2.62266i) q^{36} +(2.61260 - 0.700045i) q^{37} +(-1.11899 + 1.93814i) q^{38} +(8.70256 + 1.42488i) q^{39} +(-5.74963 + 3.31955i) q^{40} +(-1.21867 + 4.54813i) q^{41} +(-4.55704 - 2.63101i) q^{43} +(3.59498 + 0.963272i) q^{44} +(-2.77688 + 10.3635i) q^{45} +(-0.188327 + 0.702845i) q^{46} +(6.51834 + 1.74658i) q^{47} +(5.53327 + 3.19464i) q^{48} +(-1.00950 + 3.76750i) q^{50} +(2.42364 - 1.39929i) q^{51} +(-2.24200 - 5.93285i) q^{52} +(-1.74389 + 3.02051i) q^{53} +(0.0209754 - 0.00562033i) q^{54} +(6.59283 - 3.80637i) q^{55} +(7.88489 - 7.88489i) q^{57} +(1.91459 - 1.91459i) q^{58} +(11.0394 + 2.95801i) q^{59} +(14.9523 - 4.00646i) q^{60} +9.46949i q^{61} +(-1.48804 - 2.57737i) q^{62} -2.78376i q^{64} +(-11.8237 - 5.33826i) q^{65} +(2.19983 + 1.27007i) q^{66} +(5.44554 - 5.44554i) q^{67} +(-1.74312 - 1.00639i) q^{68} +(1.81276 - 3.13980i) q^{69} +(1.74779 + 6.52285i) q^{71} +(3.89065 + 3.89065i) q^{72} +(-1.46556 - 5.46953i) q^{73} +(-0.663841 - 1.14981i) q^{74} +(9.71705 - 16.8304i) q^{75} +(-7.74662 - 2.07570i) q^{76} +(-0.430029 - 4.30727i) q^{78} +(5.91160 + 10.2392i) q^{79} +(-6.64635 - 6.64635i) q^{80} -9.05394 q^{81} +2.31129 q^{82} +(5.06789 + 5.06789i) q^{83} +(-3.97675 + 1.06557i) q^{85} +(-0.668517 + 2.49494i) q^{86} +(-11.6836 + 6.74552i) q^{87} -3.90407i q^{88} +(2.58048 + 9.63048i) q^{89} +5.26655 q^{90} -2.60753 q^{92} +(3.83793 + 14.3234i) q^{93} -3.31251i q^{94} +(-14.2065 + 8.20214i) q^{95} +(3.14782 - 11.7478i) q^{96} +(-13.1665 + 3.52795i) q^{97} +(-4.46123 - 4.46123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

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