LMFDB - Embedded newform 637.2.bb.a.423.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (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			423.6
Character	$\chi$	$=$	637.423
Dual form			637.2.bb.a.509.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28453 + 1.28453i) q^{2} +(2.65867 - 1.53499i) q^{3} +1.30006i q^{4} +(-1.07541 - 0.288156i) q^{5} +(5.38690 + 1.44342i) q^{6} +(0.899098 - 0.899098i) q^{8} +(3.21237 - 5.56398i) q^{9} +O(q^{10})$	\(q+(1.28453 + 1.28453i) q^{2} +(2.65867 - 1.53499i) q^{3} +1.30006i q^{4} +(-1.07541 - 0.288156i) q^{5} +(5.38690 + 1.44342i) q^{6} +(0.899098 - 0.899098i) q^{8} +(3.21237 - 5.56398i) q^{9} +(-1.01126 - 1.75155i) q^{10} +(0.124181 + 0.0332742i) q^{11} +(1.99557 + 3.45643i) q^{12} +(-3.59376 + 0.291296i) q^{13} +(-3.30149 + 0.884632i) q^{15} +4.90996 q^{16} +0.273570 q^{17} +(11.2735 - 3.02073i) q^{18} +(1.02731 + 3.83397i) q^{19} +(0.374620 - 1.39810i) q^{20} +(0.116773 + 0.202257i) q^{22} -0.491955i q^{23} +(1.01031 - 3.77051i) q^{24} +(-3.25665 - 1.88023i) q^{25} +(-4.99050 - 4.24214i) q^{26} -10.5138i q^{27} +(-4.62230 + 8.00606i) q^{29} +(-5.37722 - 3.10454i) q^{30} +(1.85433 + 6.92046i) q^{31} +(4.50882 + 4.50882i) q^{32} +(0.381233 - 0.102151i) q^{33} +(0.351410 + 0.351410i) q^{34} +(7.23351 + 4.17627i) q^{36} +(-2.82056 + 2.82056i) q^{37} +(-3.60526 + 6.24449i) q^{38} +(-9.10751 + 6.29084i) q^{39} +(-1.22598 + 0.707822i) q^{40} +(2.31500 + 8.63969i) q^{41} +(8.44566 - 4.87610i) q^{43} +(-0.0432585 + 0.161443i) q^{44} +(-5.05792 + 5.05792i) q^{45} +(0.631934 - 0.631934i) q^{46} +(1.51665 - 5.66021i) q^{47} +(13.0540 - 7.53673i) q^{48} +(-1.76806 - 6.59849i) q^{50} +(0.727333 - 0.419926i) q^{51} +(-0.378703 - 4.67211i) q^{52} +(0.467445 - 0.809639i) q^{53} +(13.5054 - 13.5054i) q^{54} +(-0.123958 - 0.0715671i) q^{55} +(8.61638 + 8.61638i) q^{57} +(-16.2216 + 4.34656i) q^{58} +(-4.86699 - 4.86699i) q^{59} +(-1.15007 - 4.29214i) q^{60} +(-6.74429 - 3.89382i) q^{61} +(-6.50761 + 11.2715i) q^{62} +1.76356i q^{64} +(3.94872 + 0.722302i) q^{65} +(0.620923 + 0.358490i) q^{66} +(-0.316671 + 1.18183i) q^{67} +0.355657i q^{68} +(-0.755145 - 1.30795i) q^{69} +(-0.793943 + 2.96304i) q^{71} +(-2.11433 - 7.89080i) q^{72} +(-0.118802 + 0.0318328i) q^{73} -7.24621 q^{74} -11.5445 q^{75} +(-4.98439 + 1.33556i) q^{76} +(-19.7797 - 3.61811i) q^{78} +(-5.72736 - 9.92007i) q^{79} +(-5.28024 - 1.41484i) q^{80} +(-6.50149 - 11.2609i) q^{81} +(-8.12429 + 14.0717i) q^{82} +(8.07011 - 8.07011i) q^{83} +(-0.294201 - 0.0788309i) q^{85} +(17.1123 + 4.58522i) q^{86} +28.3807i q^{87} +(0.141568 - 0.0817342i) q^{88} +(-2.99430 - 2.99430i) q^{89} -12.9941 q^{90} +0.639571 q^{92} +(15.5529 + 15.5529i) q^{93} +(9.21893 - 5.32255i) q^{94} -4.41913i q^{95} +(18.9085 + 5.06651i) q^{96} +(-2.39359 - 0.641359i) q^{97} +(0.584052 - 0.584052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.28453	+	1.28453i	0.908303	+	0.908303i	0.996135	−	0.0878320i	$-0.0279939\pi$
$2$	1.28453	+	1.28453i	0.908303	+	0.908303i	−0.0878320	+	0.996135i	$0.527994\pi$
$3$	2.65867	−	1.53499i	1.53499	−	0.886225i	0.535865	−	0.844303i	$-0.319985\pi$
$3$	2.65867	−	1.53499i	1.53499	−	0.886225i	0.999121	−	0.0419214i	$-0.0133479\pi$
$4$			1.30006i			0.650030i
$5$	−1.07541	−	0.288156i	−0.480940	−	0.128867i	0.0102004	−	0.999948i	$-0.496753\pi$
$5$	−1.07541	−	0.288156i	−0.480940	−	0.128867i	−0.491140	+	0.871081i	$0.663420\pi$
$6$	5.38690	+	1.44342i	2.19919	+	0.589272i
$7$		0			0
$7$		0			0
$8$	0.899098	−	0.899098i	0.317879	−	0.317879i
$9$	3.21237	−	5.56398i	1.07079	−	1.85466i
$10$	−1.01126	−	1.75155i	−0.319788	−	0.553890i
$11$	0.124181	+	0.0332742i	0.0374420	+	0.0100326i	0.277491	−	0.960728i	$-0.410497\pi$
$11$	0.124181	+	0.0332742i	0.0374420	+	0.0100326i	−0.240049	+	0.970761i	$0.577164\pi$
$12$	1.99557	+	3.45643i	0.576072	+	0.997787i
$13$	−3.59376	+	0.291296i	−0.996731	+	0.0807911i
$13$	−3.59376	+	0.291296i	−0.996731	+	0.0807911i
$14$		0			0
$15$	−3.30149	+	0.884632i	−0.852441	+	0.228411i
$16$	4.90996			1.22749
$17$	0.273570			0.0663504			0.0331752	−	0.999450i	$-0.489438\pi$
$17$	0.273570			0.0663504			0.0331752	+	0.999450i	$0.489438\pi$
$18$	11.2735	−	3.02073i	2.65720	−	0.711993i
$19$	1.02731	+	3.83397i	0.235681	+	0.879574i	0.977841	+	0.209351i	$0.0671350\pi$
$19$	1.02731	+	3.83397i	0.235681	+	0.879574i	−0.742159	+	0.670223i	$0.766198\pi$
$20$	0.374620	−	1.39810i	0.0837676	−	0.312625i
$21$		0			0
$22$	0.116773	+	0.202257i	0.0248961	+	0.0431213i
$23$		−	0.491955i		−	0.102580i	−0.998684	−	0.0512899i	$-0.983667\pi$
$23$		−	0.491955i		−	0.102580i	0.998684	−	0.0512899i	$-0.0163332\pi$
$24$	1.01031	−	3.77051i	0.206228	−	0.769652i
$25$	−3.25665	−	1.88023i	−0.651329	−	0.376045i
$26$	−4.99050	−	4.24214i	−0.978717	−	0.831951i
$27$		−	10.5138i		−	2.02339i
$28$		0			0
$29$	−4.62230	+	8.00606i	−0.858340	+	1.48669i	0.0151718	+	0.999885i	$0.495170\pi$
$29$	−4.62230	+	8.00606i	−0.858340	+	1.48669i	−0.873512	+	0.486803i	$0.838163\pi$
$30$	−5.37722	−	3.10454i	−0.981742	−	0.566809i
$31$	1.85433	+	6.92046i	0.333048	+	1.24295i	0.905970	+	0.423341i	$0.139143\pi$
$31$	1.85433	+	6.92046i	0.333048	+	1.24295i	−0.572923	+	0.819609i	$0.694190\pi$
$32$	4.50882	+	4.50882i	0.797055	+	0.797055i
$33$	0.381233	−	0.102151i	0.0663641	−	0.0177822i
$34$	0.351410	+	0.351410i	0.0602663	+	0.0602663i
$35$		0			0
$36$	7.23351	+	4.17627i	1.20558	+	0.696045i
$37$	−2.82056	+	2.82056i	−0.463697	+	0.463697i	−0.899865	−	0.436168i	$-0.856335\pi$
$37$	−2.82056	+	2.82056i	−0.463697	+	0.463697i	0.436168	+	0.899865i	$0.356335\pi$
$38$	−3.60526	+	6.24449i	−0.584850	+	1.01299i
$39$	−9.10751	+	6.29084i	−1.45837	+	1.00734i
$40$	−1.22598	+	0.707822i	−0.193845	+	0.111916i
$41$	2.31500	+	8.63969i	0.361542	+	1.34929i	0.872049	+	0.489419i	$0.162791\pi$
$41$	2.31500	+	8.63969i	0.361542	+	1.34929i	−0.510507	+	0.859874i	$0.670542\pi$
$42$		0			0
$43$	8.44566	−	4.87610i	1.28795	−	0.743599i	0.309662	−	0.950847i	$-0.399784\pi$
$43$	8.44566	−	4.87610i	1.28795	−	0.743599i	0.978288	+	0.207248i	$0.0664506\pi$
$44$	−0.0432585	+	0.161443i	−0.00652146	+	0.0243384i
$45$	−5.05792	+	5.05792i	−0.753990	+	0.753990i
$46$	0.631934	−	0.631934i	0.0931735	−	0.0931735i
$47$	1.51665	−	5.66021i	0.221226	−	0.825627i	−0.762655	−	0.646805i	$-0.776105\pi$
$47$	1.51665	−	5.66021i	0.221226	−	0.825627i	0.983881	−	0.178822i	$-0.0572286\pi$
$48$	13.0540	−	7.53673i	1.88418	−	1.08783i
$49$		0			0
$50$	−1.76806	−	6.59849i	−0.250041	−	0.933167i
$51$	0.727333	−	0.419926i	0.101847	−	0.0588014i
$52$	−0.378703	−	4.67211i	−0.0525166	−	0.647905i
$53$	0.467445	−	0.809639i	0.0642086	−	0.111212i	−0.832134	−	0.554574i	$-0.812881\pi$
$53$	0.467445	−	0.809639i	0.0642086	−	0.111212i	0.896343	+	0.443362i	$0.146214\pi$
$54$	13.5054	−	13.5054i	1.83785	−	1.83785i
$55$	−0.123958	−	0.0715671i	−0.0167145	−	0.00965011i
$56$		0			0
$57$	8.61638	+	8.61638i	1.14127	+	1.14127i
$58$	−16.2216	+	4.34656i	−2.13000	+	0.570731i
$59$	−4.86699	−	4.86699i	−0.633628	−	0.633628i	0.315348	−	0.948976i	$-0.397879\pi$
$59$	−4.86699	−	4.86699i	−0.633628	−	0.633628i	−0.948976	+	0.315348i	$0.897879\pi$
$60$	−1.15007	−	4.29214i	−0.148474	−	0.554112i
$61$	−6.74429	−	3.89382i	−0.863518	−	0.498552i	0.00167083	−	0.999999i	$-0.499468\pi$
$61$	−6.74429	−	3.89382i	−0.863518	−	0.498552i	−0.865189	+	0.501446i	$0.832801\pi$
$62$	−6.50761	+	11.2715i	−0.826468	+	1.43148i
$63$		0			0
$64$			1.76356i			0.220444i
$65$	3.94872	+	0.722302i	0.489779	+	0.0895905i
$66$	0.620923	+	0.358490i	0.0764303	+	0.0441271i
$67$	−0.316671	+	1.18183i	−0.0386875	+	0.144384i	−0.982568	−	0.185903i	$-0.940479\pi$
$67$	−0.316671	+	1.18183i	−0.0386875	+	0.144384i	0.943881	+	0.330287i	$0.107146\pi$
$68$			0.355657i			0.0431298i
$69$	−0.755145	−	1.30795i	−0.0909087	−	0.157459i
$70$		0			0
$71$	−0.793943	+	2.96304i	−0.0942237	+	0.351648i	−0.996901	−	0.0786713i	$-0.974932\pi$
$71$	−0.793943	+	2.96304i	−0.0942237	+	0.351648i	0.902677	+	0.430319i	$0.141599\pi$
$72$	−2.11433	−	7.89080i	−0.249176	−	0.929939i
$73$	−0.118802	+	0.0318328i	−0.0139047	+	0.00372575i	−0.265765	−	0.964038i	$-0.585624\pi$
$73$	−0.118802	+	0.0318328i	−0.0139047	+	0.00372575i	0.251860	+	0.967764i	$0.418958\pi$
$74$	−7.24621			−0.842355
$75$	−11.5445			−1.33304
$76$	−4.98439	+	1.33556i	−0.571749	+	0.153200i
$77$		0			0
$78$	−19.7797	−	3.61811i	−2.23961	−	0.409671i
$79$	−5.72736	−	9.92007i	−0.644378	−	1.11610i	−0.984445	−	0.175694i	$-0.943783\pi$
$79$	−5.72736	−	9.92007i	−0.644378	−	1.11610i	0.340067	−	0.940401i	$-0.389550\pi$
$80$	−5.28024	−	1.41484i	−0.590349	−	0.158184i
$81$	−6.50149	−	11.2609i	−0.722388	−	1.25121i
$82$	−8.12429	+	14.0717i	−0.897178	+	1.55396i
$83$	8.07011	−	8.07011i	0.885810	−	0.885810i	−0.108308	−	0.994117i	$-0.534543\pi$
$83$	8.07011	−	8.07011i	0.885810	−	0.885810i	0.994117	+	0.108308i	$0.0345432\pi$
$84$		0			0
$85$	−0.294201	−	0.0788309i	−0.0319106	−	0.00855041i
$86$	17.1123	+	4.58522i	1.84526	+	0.494437i
$87$			28.3807i			3.04273i
$88$	0.141568	−	0.0817342i	0.0150912	−	0.00871289i
$89$	−2.99430	−	2.99430i	−0.317395	−	0.317395i	0.530371	−	0.847766i	$-0.322053\pi$
$89$	−2.99430	−	2.99430i	−0.317395	−	0.317395i	−0.847766	+	0.530371i	$0.822053\pi$
$90$	−12.9941			−1.36970
$91$		0			0
$92$	0.639571			0.0666799
$93$	15.5529	+	15.5529i	1.61276	+	1.61276i
$94$	9.21893	−	5.32255i	0.950860	−	0.548979i
$95$		−	4.41913i		−	0.453394i
$96$	18.9085	+	5.06651i	1.92984	+	0.517099i
$97$	−2.39359	−	0.641359i	−0.243032	−	0.0651202i	0.135247	−	0.990812i	$-0.456817\pi$
$97$	−2.39359	−	0.641359i	−0.243032	−	0.0651202i	−0.378279	+	0.925692i	$0.623484\pi$
$98$		0			0
$99$	0.584052	−	0.584052i	0.0586995	−	0.0586995i
$100$	2.44440	−	4.23383i	0.244440	−	0.423383i
$101$	−0.844219	−	1.46223i	−0.0840029	−	0.145497i	0.820963	−	0.570981i	$-0.193437\pi$
$101$	−0.844219	−	1.46223i	−0.0840029	−	0.145497i	−0.904966	+	0.425484i	$0.860104\pi$
$102$	1.47369	+	0.394875i	0.145917	+	0.0390985i
$103$	4.38460	+	7.59435i	0.432027	+	0.748293i	0.997048	−	0.0767837i	$-0.0244651\pi$
$103$	4.38460	+	7.59435i	0.432027	+	0.748293i	−0.565021	+	0.825077i	$0.691132\pi$
$104$	−2.96924	+	3.49305i	−0.291158	+	0.342522i
$105$		0			0
$106$	1.64046	−	0.439560i	0.159336	−	0.0426938i
$107$	−2.69786			−0.260812			−0.130406	−	0.991461i	$-0.541628\pi$
$107$	−2.69786			−0.260812			−0.130406	+	0.991461i	$0.541628\pi$
$108$	13.6686			1.31526
$109$	−8.97655	+	2.40526i	−0.859798	+	0.230382i	−0.661671	−	0.749794i	$-0.730152\pi$
$109$	−8.97655	+	2.40526i	−0.859798	+	0.230382i	−0.198127	+	0.980176i	$0.563486\pi$
$110$	−0.0672978	−	0.251159i	−0.00641659	−	0.0239470i
$111$	−3.16943	+	11.8285i	−0.300829	+	1.12271i
$112$		0			0
$113$	−1.73470	−	3.00459i	−0.163187	−	0.282648i	0.772823	−	0.634622i	$-0.218844\pi$
$113$	−1.73470	−	3.00459i	−0.163187	−	0.282648i	−0.936010	+	0.351973i	$0.885511\pi$
$114$			22.1361i			2.07323i
$115$	−0.141760	+	0.529055i	−0.0132192	+	0.0493347i
$116$	−10.4084	−	6.00927i	−0.966392	−	0.557946i
$117$	−9.92372	+	20.9314i	−0.917448	+	1.93511i
$118$		−	12.5036i		−	1.15105i
$119$		0			0
$120$	−2.17299	+	3.76373i	−0.198366	+	0.343580i
$121$	−9.51197	−	5.49174i	−0.864724	−	0.499249i
$122$	−3.66153	−	13.6650i	−0.331499	−	1.23717i
$123$	19.4166	+	19.4166i	1.75074	+	1.75074i
$124$	−8.99700	+	2.41074i	−0.807955	+	0.216491i
$125$	6.89673	+	6.89673i	0.616862	+	0.616862i
$126$		0			0
$127$	−1.51307	−	0.873573i	−0.134264	−	0.0775171i	0.431364	−	0.902178i	$-0.358033\pi$
$127$	−1.51307	−	0.873573i	−0.134264	−	0.0775171i	−0.565627	+	0.824661i	$0.691366\pi$
$128$	6.75230	−	6.75230i	0.596825	−	0.596825i
$129$	14.9695	−	25.9279i	1.31799	−	2.28283i
$130$	4.14445	+	6.00009i	0.363492	+	0.526243i
$131$	5.14945	−	2.97304i	0.449909	−	0.259755i	−0.257882	−	0.966176i	$-0.583025\pi$
$131$	5.14945	−	2.97304i	0.449909	−	0.259755i	0.707792	+	0.706421i	$0.249691\pi$
$132$	0.132802	+	0.495625i	0.0115590	+	0.0431386i
$133$		0			0
$134$	−1.92488	+	1.11133i	−0.166284	+	0.0960043i
$135$	−3.02963	+	11.3067i	−0.260749	+	0.973128i
$136$	0.245966	−	0.245966i	0.0210914	−	0.0210914i
$137$	−13.8892	+	13.8892i	−1.18663	+	1.18663i	−0.208639	+	0.977993i	$0.566904\pi$
$137$	−13.8892	+	13.8892i	−1.18663	+	1.18663i	−0.977993	+	0.208639i	$0.933096\pi$
$138$	0.710096	−	2.65012i	0.0604474	−	0.225593i
$139$	−4.80542	+	2.77441i	−0.407590	+	0.235322i	−0.689754	−	0.724044i	$-0.742281\pi$
$139$	−4.80542	+	2.77441i	−0.407590	+	0.235322i	0.282164	+	0.959366i	$0.408948\pi$
$140$		0			0
$141$	−4.65607	−	17.3767i	−0.392112	−	1.46338i
$142$	−4.82597	+	2.78627i	−0.404986	+	0.233819i
$143$	−0.455970	−	0.0834062i	−0.0381302	−	0.00697478i
$144$	15.7726	−	27.3189i	1.31438	−	2.27658i
$145$	7.27788	−	7.27788i	0.604395	−	0.604395i
$146$	−0.193495	−	0.111715i	−0.0160138	−	0.00924556i
$147$		0			0
$148$	−3.66689	−	3.66689i	−0.301417	−	0.301417i
$149$	0.416259	−	0.111536i	0.0341012	−	0.00913740i	−0.241728	−	0.970344i	$-0.577714\pi$
$149$	0.416259	−	0.111536i	0.0341012	−	0.00913740i	0.275829	+	0.961207i	$0.411048\pi$
$150$	−14.8293	−	14.8293i	−1.21081	−	1.21081i
$151$	0.918204	+	3.42678i	0.0747224	+	0.278868i	0.993170	−	0.116674i	$-0.0372234\pi$
$151$	0.918204	+	3.42678i	0.0747224	+	0.278868i	−0.918448	+	0.395542i	$0.870557\pi$
$152$	4.37077	+	2.52347i	0.354516	+	0.204680i
$153$	0.878806	−	1.52214i	0.0710473	−	0.123058i
$154$		0			0
$155$		−	7.97669i		−	0.640703i
$156$	−8.17847	−	11.8403i	−0.654802	−	0.947984i
$157$	−3.24916	−	1.87590i	−0.259311	−	0.149713i	0.364709	−	0.931122i	$-0.381168\pi$
$157$	−3.24916	−	1.87590i	−0.259311	−	0.149713i	−0.624020	+	0.781408i	$0.714502\pi$
$158$	5.38569	−	20.0997i	0.428462	−	1.59904i
$159$		−	2.87009i		−	0.227613i
$160$	−3.54961	−	6.14810i	−0.280621	−	0.486050i
$161$		0			0
$162$	6.11365	−	22.8164i	0.480333	−	1.79263i
$163$	1.74265	+	6.50367i	0.136495	+	0.509407i	0.999987	+	0.00504443i	$0.00160570\pi$
$163$	1.74265	+	6.50367i	0.136495	+	0.509407i	−0.863492	+	0.504362i	$0.831728\pi$
$164$	−11.2321	+	3.00964i	−0.877081	+	0.235013i
$165$	−0.439418			−0.0342087
$166$	20.7327			1.60917
$167$	11.3562	−	3.04289i	0.878770	−	0.235466i	0.208894	−	0.977938i	$-0.433014\pi$
$167$	11.3562	−	3.04289i	0.878770	−	0.235466i	0.669876	+	0.742473i	$0.266347\pi$
$168$		0			0
$169$	12.8303	−	2.09370i	0.986946	−	0.161054i
$170$	−0.276650	−	0.479172i	−0.0212181	−	0.0367508i
$171$	24.6323	+	6.60019i	1.88368	+	0.504729i
$172$	6.33922	+	10.9799i	0.483361	+	0.837206i
$173$	8.07033	−	13.9782i	0.613576	−	1.06274i	−0.377057	−	0.926190i	$-0.623064\pi$
$173$	8.07033	−	13.9782i	0.613576	−	1.06274i	0.990633	−	0.136555i	$-0.0436029\pi$
$174$	−36.4560	+	36.4560i	−2.76372	+	2.76372i
$175$		0			0
$176$	0.609725	+	0.163375i	0.0459597	+	0.0123149i
$177$	−20.4105	−	5.46898i	−1.53415	−	0.411074i
$178$		−	7.69257i		−	0.576583i
$179$	7.96378	−	4.59789i	0.595241	−	0.343663i	−0.171926	−	0.985110i	$-0.554999\pi$
$179$	7.96378	−	4.59789i	0.595241	−	0.343663i	0.767167	+	0.641447i	$0.221666\pi$
$180$	−6.57560	−	6.57560i	−0.490116	−	0.490116i
$181$	−14.6492			−1.08887			−0.544433	−	0.838804i	$-0.683255\pi$
$181$	−14.6492			−1.08887			−0.544433	+	0.838804i	$0.683255\pi$
$182$		0			0
$183$	−23.9078			−1.76732
$184$	−0.442316	−	0.442316i	−0.0326080	−	0.0326080i
$185$	3.84603	−	2.22051i	0.282766	−	0.163255i
$186$			39.9564i			2.92975i
$187$	0.0339722	+	0.00910282i	0.00248429	+	0.000665664i
$188$	7.35861	+	1.97173i	0.536682	+	0.143804i
$189$		0			0
$190$	5.67653	−	5.67653i	0.411819	−	0.411819i
$191$	−3.01632	+	5.22442i	−0.218253	+	0.378026i	−0.954274	−	0.298933i	$-0.903369\pi$
$191$	−3.01632	+	5.22442i	−0.218253	+	0.378026i	0.736021	+	0.676959i	$0.236703\pi$
$192$	2.70703	+	4.68872i	0.195363	+	0.338379i
$193$	−0.397063	−	0.106393i	−0.0285812	−	0.00765832i	0.244500	−	0.969649i	$-0.421376\pi$
$193$	−0.397063	−	0.106393i	−0.0285812	−	0.00765832i	−0.273081	+	0.961991i	$0.588043\pi$
$194$	−2.25080	−	3.89849i	−0.161598	−	0.279895i
$195$	11.6071	−	4.14087i	0.831201	−	0.296534i
$196$		0			0
$197$	18.9784	−	5.08526i	1.35216	−	0.362309i	0.491227	−	0.871032i	$-0.336549\pi$
$197$	18.9784	−	5.08526i	1.35216	−	0.362309i	0.860931	+	0.508722i	$0.169882\pi$
$198$	1.50047			0.106634
$199$	−17.4220			−1.23502			−0.617508	−	0.786565i	$-0.711858\pi$
$199$	−17.4220			−1.23502			−0.617508	+	0.786565i	$0.711858\pi$
$200$	−4.61855	+	1.23754i	−0.326581	+	0.0875071i
$201$	0.972172	+	3.62820i	0.0685717	+	0.255913i
$202$	0.793857	−	2.96271i	0.0558556	−	0.208456i
$203$		0			0
$204$	0.545929	+	0.945576i	0.0382227	+	0.0662036i
$205$		−	9.95832i		−	0.695520i
$206$	−4.12303	+	15.3874i	−0.287265	+	1.07209i
$207$	−2.73723	−	1.58034i	−0.190251	−	0.109841i
$208$	−17.6453	+	1.43025i	−1.22348	+	0.0991703i
$209$			0.510290i			0.0352975i
$210$		0			0
$211$	7.69760	−	13.3326i	0.529925	−	0.917856i	−0.469466	−	0.882951i	$-0.655554\pi$
$211$	7.69760	−	13.3326i	0.529925	−	0.917856i	0.999391	−	0.0349058i	$-0.0111131\pi$
$212$	1.05258	+	0.607707i	0.0722914	+	0.0417375i
$213$	2.43738	+	9.09644i	0.167007	+	0.623278i
$214$	−3.46550	−	3.46550i	−0.236897	−	0.236897i
$215$	−10.4877	+	2.81016i	−0.715252	+	0.191651i
$216$	−9.45297	−	9.45297i	−0.643193	−	0.643193i
$217$		0			0
$218$	−14.6203	−	8.44105i	−0.990214	−	0.571700i
$219$	−0.266992	+	0.266992i	−0.0180417	+	0.0180417i
$220$	0.0930415	−	0.161153i	0.00627286	−	0.0108649i
$221$	−0.983146	+	0.0796899i	−0.0661335	+	0.00536052i
$222$	−19.2653	+	11.1228i	−1.29300	+	0.746516i
$223$	−3.59157	−	13.4039i	−0.240509	−	0.897592i	−0.975588	−	0.219610i	$-0.929521\pi$
$223$	−3.59157	−	13.4039i	−0.240509	−	0.897592i	0.735079	−	0.677982i	$-0.237145\pi$
$224$		0			0
$225$	−20.9231	+	12.0799i	−1.39487	+	0.805330i
$226$	1.63122	−	6.08779i	0.108507	−	0.404954i
$227$	8.44643	−	8.44643i	0.560610	−	0.560610i	−0.368871	−	0.929481i	$-0.620256\pi$
$227$	8.44643	−	8.44643i	0.560610	−	0.560610i	0.929481	+	0.368871i	$0.120256\pi$
$228$	−11.2018	+	11.2018i	−0.741858	+	0.741858i
$229$	6.35901	−	23.7322i	0.420215	−	1.56826i	−0.353939	−	0.935268i	$-0.615158\pi$
$229$	6.35901	−	23.7322i	0.420215	−	1.56826i	0.774155	−	0.632997i	$-0.218175\pi$
$230$	−0.861686	+	0.497495i	−0.0568179	+	0.0328038i
$231$		0			0
$232$	3.04233	+	11.3541i	0.199739	+	0.745435i
$233$	15.3919	−	8.88654i	1.00836	−	0.582177i	0.0976486	−	0.995221i	$-0.468868\pi$
$233$	15.3919	−	8.88654i	1.00836	−	0.582177i	0.910711	+	0.413044i	$0.135535\pi$
$234$	−39.6345	+	14.1397i	−2.59099	+	0.924343i
$235$	−3.26205	+	5.65004i	−0.212793	+	0.368568i
$236$	6.32738	−	6.32738i	0.411877	−	0.411877i
$237$	−30.4544	−	17.5828i	−1.97822	−	1.14213i
$238$		0			0
$239$	17.0580	+	17.0580i	1.10339	+	1.10339i	0.993999	+	0.109392i	$0.0348902\pi$
$239$	17.0580	+	17.0580i	1.10339	+	1.10339i	0.109392	+	0.993999i	$0.465110\pi$
$240$	−16.2102	+	4.34351i	−1.04636	+	0.280372i
$241$	−7.33684	−	7.33684i	−0.472607	−	0.472607i	0.430150	−	0.902757i	$-0.358461\pi$
$241$	−7.33684	−	7.33684i	−0.472607	−	0.472607i	−0.902757	+	0.430150i	$0.858461\pi$
$242$	−5.16413	−	19.2728i	−0.331963	−	1.23890i
$243$	−7.25497	−	4.18866i	−0.465406	−	0.268702i
$244$	5.06220	−	8.76798i	0.324074	−	0.561312i
$245$		0			0
$246$			49.8827i			3.18040i
$247$	−4.80873	−	13.4792i	−0.305972	−	0.857658i
$248$	7.88939	+	4.55494i	0.500977	+	0.289239i
$249$	9.06829	−	33.8433i	0.574679	−	2.14473i
$250$			17.7182i			1.12060i
$251$	4.56198	+	7.90158i	0.287950	+	0.498743i	0.973320	−	0.229451i	$-0.0736931\pi$
$251$	4.56198	+	7.90158i	0.287950	+	0.498743i	−0.685371	+	0.728194i	$0.740360\pi$
$252$		0			0
$253$	0.0163694	−	0.0610915i	0.00102914	−	0.00384079i
$254$	−0.821460	−	3.06573i	−0.0515430	−	0.192361i
$255$	−0.903188	+	0.242009i	−0.0565599	+	0.0151552i
$256$	20.8742			1.30464
$257$	30.7159			1.91601			0.958003	−	0.286758i	$-0.0925777\pi$
$257$	30.7159			1.91601			0.958003	+	0.286758i	$0.0925777\pi$
$258$	52.5342	−	14.0765i	3.27064	−	0.876364i
$259$		0			0
$260$	−0.939035	+	5.13358i	−0.0582365	+	0.318371i
$261$	29.6970	+	51.4368i	1.83820	+	3.18386i
$262$	10.4336	+	2.79568i	0.644591	+	0.172718i
$263$	−2.77339	−	4.80365i	−0.171015	−	0.296206i	0.767760	−	0.640737i	$-0.221371\pi$
$263$	−2.77339	−	4.80365i	−0.171015	−	0.296206i	−0.938775	+	0.344531i	$0.888038\pi$
$264$	0.250922	−	0.434609i	0.0154432	−	0.0267483i
$265$	−0.736000	+	0.736000i	−0.0452121	+	0.0452121i
$266$		0			0
$267$	−12.5571	−	3.36466i	−0.768481	−	0.205914i
$268$	−1.53645	−	0.411691i	−0.0938538	−	0.0251481i
$269$		−	5.45085i		−	0.332344i	−0.986097	−	0.166172i	$-0.946859\pi$
$269$		−	5.45085i		−	0.332344i	0.986097	−	0.166172i	$-0.0531407\pi$
$270$	−18.4155	+	10.6322i	−1.12073	+	0.647056i
$271$	7.56230	+	7.56230i	0.459377	+	0.459377i	0.898451	−	0.439074i	$-0.144693\pi$
$271$	7.56230	+	7.56230i	0.459377	+	0.459377i	−0.439074	+	0.898451i	$0.644693\pi$
$272$	1.34322			0.0814446
$273$		0			0
$274$	−35.6823			−2.15564
$275$	−0.341851	−	0.341851i	−0.0206144	−	0.0206144i
$276$	1.70041	−	0.981733i	0.102353	−	0.0590934i
$277$		−	24.5511i		−	1.47513i	−0.675275	−	0.737566i	$-0.735975\pi$
$277$		−	24.5511i		−	1.47513i	0.675275	−	0.737566i	$-0.264025\pi$
$278$	−9.73655	−	2.60890i	−0.583960	−	0.156472i
$279$	44.4621	+	11.9136i	2.66187	+	0.713247i
$280$		0			0
$281$	8.66937	−	8.66937i	0.517172	−	0.517172i	−0.399543	−	0.916714i	$-0.630831\pi$
$281$	8.66937	−	8.66937i	0.517172	−	0.517172i	0.916714	+	0.399543i	$0.130831\pi$
$282$	16.3401	−	28.3019i	0.973038	−	1.68535i
$283$	−1.41770	−	2.45554i	−0.0842738	−	0.145967i	0.820808	−	0.571205i	$-0.193524\pi$
$283$	−1.41770	−	2.45554i	−0.0842738	−	0.145967i	−0.905082	+	0.425238i	$0.860190\pi$
$284$	−3.85212	−	1.03217i	−0.228581	−	0.0612482i
$285$	−6.78331	−	11.7490i	−0.401809	−	0.695953i
$286$	−0.478571	−	0.692848i	−0.0282985	−	0.0409690i
$287$		0			0
$288$	39.5710	−	10.6030i	2.33174	−	0.624789i
$289$	−16.9252			−0.995598
$290$	18.6974			1.09795
$291$	−7.34824	+	1.96896i	−0.430762	+	0.115422i
$292$	−0.0413846	−	0.154449i	−0.00242185	−	0.00903846i
$293$	−5.11331	+	19.0831i	−0.298723	+	1.11485i	0.639493	+	0.768797i	$0.279144\pi$
$293$	−5.11331	+	19.0831i	−0.298723	+	1.11485i	−0.938215	+	0.346052i	$0.887522\pi$
$294$		0			0
$295$	3.83157	+	6.63648i	0.223083	+	0.386391i
$296$			5.07192i			0.294799i
$297$	0.349840	−	1.30562i	0.0202998	−	0.0757597i
$298$	0.677971	+	0.391427i	0.0392738	+	0.0226747i
$299$	0.143305	+	1.76797i	0.00828753	+	0.102244i
$300$		−	15.0085i		−	0.866517i
$301$		0			0
$302$	−3.22236	+	5.58129i	−0.185426	+	0.321167i
$303$	−4.48901	−	2.59173i	−0.257887	−	0.148891i
$304$	5.04406	+	18.8247i	0.289296	+	1.07967i
$305$	6.13088	+	6.13088i	0.351053	+	0.351053i
$306$	3.08410	−	0.826381i	0.176306	−	0.0472411i
$307$	6.98294	+	6.98294i	0.398537	+	0.398537i	0.877717	−	0.479180i	$-0.159066\pi$
$307$	6.98294	+	6.98294i	0.398537	+	0.398537i	−0.479180	+	0.877717i	$0.659066\pi$
$308$		0			0
$309$	23.3144	+	13.4606i	1.32631	+	0.765746i
$310$	10.2463	−	10.2463i	0.581953	−	0.581953i
$311$	−13.2286	+	22.9126i	−0.750126	+	1.29926i	0.197636	+	0.980276i	$0.436674\pi$
$311$	−13.2286	+	22.9126i	−0.750126	+	1.29926i	−0.947761	+	0.318980i	$0.896660\pi$
$312$	−2.53246	+	13.8446i	−0.143373	+	0.783798i
$313$	−10.2371	+	5.91040i	−0.578636	+	0.334076i	−0.760591	−	0.649231i	$-0.775091\pi$
$313$	−10.2371	+	5.91040i	−0.578636	+	0.334076i	0.181955	+	0.983307i	$0.441757\pi$
$314$	−1.76400	−	6.58332i	−0.0995480	−	0.371518i
$315$		0			0
$316$	12.8967	−	7.44590i	0.725495	−	0.418865i
$317$	0.945407	−	3.52831i	0.0530994	−	0.198170i	−0.934281	−	0.356538i	$-0.883957\pi$
$317$	0.945407	−	3.52831i	0.0530994	−	0.198170i	0.987380	+	0.158369i	$0.0506235\pi$
$318$	3.68673	−	3.68673i	0.206742	−	0.206742i
$319$	−0.840398	+	0.840398i	−0.0470532	+	0.0470532i
$320$	0.508180	−	1.89655i	0.0284081	−	0.106020i
$321$	−7.17274	+	4.14118i	−0.400343	+	0.231138i
$322$		0			0
$323$	0.281041	+	1.04886i	0.0156375	+	0.0583601i
$324$	14.6399	−	8.45233i	0.813326	−	0.469574i
$325$	12.2513	+	5.80844i	0.679581	+	0.322194i
$326$	−6.11569	+	10.5927i	−0.338717	+	0.586675i
$327$	−20.1737	+	20.1737i	−1.11561	+	1.11561i
$328$	9.84934	+	5.68652i	0.543839	+	0.313985i
$329$		0			0
$330$	−0.564448	−	0.564448i	−0.0310718	−	0.0310718i
$331$	−8.31943	+	2.22918i	−0.457277	+	0.122527i	−0.480102	−	0.877212i	$-0.659401\pi$
$331$	−8.31943	+	2.22918i	−0.457277	+	0.122527i	0.0228253	+	0.999739i	$0.492734\pi$
$332$	10.4916	+	10.4916i	0.575803	+	0.575803i
$333$	6.63287	+	24.7542i	0.363479	+	1.35652i
$334$	18.4961	+	10.6788i	1.01206	+	0.584315i
$335$	0.681105	−	1.17971i	0.0372128	−	0.0644544i
$336$		0			0
$337$			26.3426i			1.43497i	0.696572	+	0.717487i	$0.254708\pi$
$337$			26.3426i			1.43497i	−0.696572	+	0.717487i	$0.745292\pi$
$338$	19.1704	+	13.7915i	1.04273	+	0.750160i
$339$	−9.22402	−	5.32549i	−0.500980	−	0.289241i
$340$	0.102485	−	0.382479i	0.00555802	−	0.0207428i
$341$			0.921091i			0.0498799i
$342$	23.1628	+	40.1192i	1.25250	+	2.16940i
$343$		0			0
$344$	3.20938	−	11.9776i	0.173038	−	0.645787i
$345$	0.435199	+	1.62419i	0.0234303	+	0.0874432i
$346$	28.3221	−	7.58889i	1.52261	−	0.407981i
$347$	5.22676			0.280587			0.140294	−	0.990110i	$-0.455195\pi$
$347$	5.22676			0.280587			0.140294	+	0.990110i	$0.455195\pi$
$348$	−36.8966			−1.97786
$349$	11.2071	−	3.00292i	0.599900	−	0.160743i	0.0539262	−	0.998545i	$-0.482826\pi$
$349$	11.2071	−	3.00292i	0.599900	−	0.160743i	0.545974	+	0.837802i	$0.316160\pi$
$350$		0			0
$351$	3.06264	+	37.7842i	0.163472	+	2.01677i
$352$	0.409883	+	0.709938i	0.0218468	+	0.0378398i
$353$	−8.33853	−	2.23430i	−0.443815	−	0.118920i	0.0299889	−	0.999550i	$-0.490453\pi$
$353$	−8.33853	−	2.23430i	−0.443815	−	0.118920i	−0.473804	+	0.880630i	$0.657119\pi$
$354$	−19.1929	−	33.2431i	−1.02009	−	1.76685i
$355$	1.70763	−	2.95771i	0.0906318	−	0.156979i
$356$	3.89277	−	3.89277i	0.206316	−	0.206316i
$357$		0			0
$358$	16.1359	+	4.32360i	0.852809	+	0.228510i
$359$	29.9910	+	8.03606i	1.58286	+	0.424127i	0.939811	−	0.341695i	$-0.111001\pi$
$359$	29.9910	+	8.03606i	1.58286	+	0.424127i	0.643053	+	0.765822i	$0.277668\pi$
$360$			9.09513i			0.479355i
$361$	2.81049	−	1.62264i	0.147921	−	0.0854020i
$362$	−18.8174	−	18.8174i	−0.989021	−	0.989021i
$363$	−33.7190			−1.76979
$364$		0			0
$365$	0.136934			0.00716744
$366$	−30.7104	−	30.7104i	−1.60526	−	1.60526i
$367$	2.26835	−	1.30963i	0.118407	−	0.0683622i	−0.439627	−	0.898180i	$-0.644889\pi$
$367$	2.26835	−	1.30963i	0.118407	−	0.0683622i	0.558034	+	0.829818i	$0.311556\pi$
$368$		−	2.41548i		−	0.125916i
$369$	55.5077	+	14.8732i	2.88962	+	0.774270i
$370$	7.79268	+	2.08804i	0.405122	+	0.108552i
$371$		0			0
$372$	−20.2197	+	20.2197i	−1.04834	+	1.04834i
$373$	−17.9182	+	31.0351i	−0.927767	+	1.60694i	−0.140717	+	0.990050i	$0.544941\pi$
$373$	−17.9182	+	31.0351i	−0.927767	+	1.60694i	−0.787050	+	0.616889i	$0.788393\pi$
$374$	0.0319456	+	0.0553314i	0.00165187	+	0.00286112i
$375$	28.9226	+	7.74977i	1.49355	+	0.400197i
$376$	−3.72547	−	6.45270i	−0.192126	−	0.332773i
$377$	14.2793	−	30.1184i	0.735423	−	1.55117i
$378$		0			0
$379$	−22.2660	+	5.96617i	−1.14373	+	0.306461i	−0.780450	−	0.625219i	$-0.785010\pi$
$379$	−22.2660	+	5.96617i	−1.14373	+	0.306461i	−0.363280	+	0.931680i	$0.618343\pi$
$380$	5.74514			0.294719
$381$	−5.36369			−0.274790
$382$	−10.5855	+	2.83638i	−0.541602	+	0.145122i
$383$	−3.37720	−	12.6039i	−0.172567	−	0.644029i	−0.996953	−	0.0780010i	$-0.975146\pi$
$383$	−3.37720	−	12.6039i	−0.172567	−	0.644029i	0.824386	−	0.566028i	$-0.191520\pi$
$384$	7.58748	−	28.3169i	0.387197	−	1.44504i
$385$		0			0
$386$	−0.373376	−	0.646707i	−0.0190044	−	0.0329165i
$387$		−	62.6553i		−	3.18495i
$388$	0.833805	−	3.11180i	0.0423301	−	0.157978i
$389$	21.4938	+	12.4094i	1.08978	+	0.629183i	0.933517	−	0.358533i	$-0.116723\pi$
$389$	21.4938	+	12.4094i	1.08978	+	0.629183i	0.156260	+	0.987716i	$0.450056\pi$
$390$	20.2288	+	9.59062i	1.02433	+	0.485640i
$391$		−	0.134584i		−	0.00680621i
$392$		0			0
$393$	9.12714	−	15.8087i	0.460403	−	0.797442i
$394$	30.9106	+	17.8463i	1.55726	+	0.899082i
$395$	3.30075	+	12.3186i	0.166079	+	0.619814i
$396$	0.759303	+	0.759303i	0.0381564	+	0.0381564i
$397$	−9.34451	+	2.50385i	−0.468987	+	0.125665i	−0.485570	−	0.874198i	$-0.661388\pi$
$397$	−9.34451	+	2.50385i	−0.468987	+	0.125665i	0.0165827	+	0.999862i	$0.494721\pi$
$398$	−22.3792	−	22.3792i	−1.12177	−	1.12177i
$399$		0			0
$400$	−15.9900	−	9.23184i	−0.799501	−	0.461592i
$401$	−4.95225	+	4.95225i	−0.247304	+	0.247304i	−0.819863	−	0.572559i	$-0.805951\pi$
$401$	−4.95225	+	4.95225i	−0.247304	+	0.247304i	0.572559	+	0.819863i	$0.305951\pi$
$402$	−3.41175	+	5.90933i	−0.170163	+	0.294731i
$403$	−8.67993	−	24.3303i	−0.432378	−	1.21198i
$404$	1.90099	−	1.09754i	0.0945776	−	0.0546044i
$405$	3.74689	+	13.9836i	0.186185	+	0.694850i
$406$		0			0
$407$	−0.444112	+	0.256408i	−0.0220138	+	0.0127097i
$408$	0.276389	−	1.03150i	0.0136833	−	0.0510668i
$409$	−10.7508	+	10.7508i	−0.531591	+	0.531591i	−0.921045	−	0.389455i	$-0.872663\pi$
$409$	−10.7508	+	10.7508i	−0.531591	+	0.531591i	0.389455	+	0.921045i	$0.372663\pi$
$410$	12.7918	−	12.7918i	0.631743	−	0.631743i
$411$	−15.6071	+	58.2465i	−0.769841	+	2.87309i
$412$	−9.87310	+	5.70024i	−0.486413	+	0.280831i
$413$		0			0
$414$	−1.48606	−	5.54607i	−0.0730361	−	0.272574i
$415$	−11.0042	+	6.35326i	−0.540173	+	0.311869i
$416$	−17.5171	−	14.8903i	−0.858844	−	0.730055i
$417$	−8.51736	+	14.7525i	−0.417097	+	0.722433i
$418$	−0.655485	+	0.655485i	−0.0320608	+	0.0320608i
$419$	−21.4435	−	12.3804i	−1.04758	−	0.604823i	−0.125612	−	0.992079i	$-0.540089\pi$
$419$	−21.4435	−	12.3804i	−1.04758	−	0.604823i	−0.921972	+	0.387257i	$0.873423\pi$
$420$		0			0
$421$	−4.11077	−	4.11077i	−0.200347	−	0.200347i	0.599802	−	0.800149i	$-0.295246\pi$
$421$	−4.11077	−	4.11077i	−0.200347	−	0.200347i	−0.800149	+	0.599802i	$0.795246\pi$
$422$	27.0141	−	7.23840i	1.31502	−	0.352360i
$423$	−26.6213	−	26.6213i	−1.29437	−	1.29437i
$424$	−0.307666	−	1.14822i	−0.0149416	−	0.0557627i
$425$	−0.890920	−	0.514373i	−0.0432160	−	0.0249508i
$426$	−8.55379	+	14.8156i	−0.414432	+	0.717818i
$427$		0			0
$428$		−	3.50738i		−	0.169536i
$429$	−1.34030	+	0.478158i	−0.0647105	+	0.0230857i
$430$	−17.0815	−	9.86201i	−0.823744	−	0.475589i
$431$	−5.00354	+	18.6735i	−0.241012	+	0.899470i	0.734334	+	0.678789i	$0.237495\pi$
$431$	−5.00354	+	18.6735i	−0.241012	+	0.899470i	−0.975346	+	0.220681i	$0.929172\pi$
$432$		−	51.6226i		−	2.48369i
$433$	−1.10640	−	1.91634i	−0.0531702	−	0.0920934i	0.838215	−	0.545339i	$-0.183599\pi$
$433$	−1.10640	−	1.91634i	−0.0531702	−	0.0920934i	−0.891385	+	0.453246i	$0.850266\pi$
$434$		0			0
$435$	8.17807	−	30.5210i	0.392108	−	1.46337i
$436$	−3.12698	−	11.6700i	−0.149755	−	0.558894i
$437$	1.88614	−	0.505391i	0.0902265	−	0.0241761i
$438$	−0.685921			−0.0327746
$439$	−7.34269			−0.350447			−0.175224	−	0.984529i	$-0.556065\pi$
$439$	−7.34269			−0.350447			−0.175224	+	0.984529i	$0.556065\pi$
$440$	−0.175796	+	0.0471044i	−0.00838075	+	0.00224562i
$441$		0			0
$442$	−1.36525	−	1.16052i	−0.0649383	−	0.0552003i
$443$	−13.2926	−	23.0235i	−0.631552	−	1.09388i	−0.987235	−	0.159273i	$-0.949085\pi$
$443$	−13.2926	−	23.0235i	−0.631552	−	1.09388i	0.355683	−	0.934607i	$-0.384248\pi$
$444$	−15.3777	−	4.12044i	−0.729794	−	0.195548i
$445$	2.35729	+	4.08294i	0.111746	+	0.193550i
$446$	12.6043	−	21.8313i	0.596831	−	1.03374i
$447$	0.935490	−	0.935490i	0.0442472	−	0.0442472i
$448$		0			0
$449$	−21.6019	−	5.78821i	−1.01946	−	0.273163i	−0.289881	−	0.957063i	$-0.593616\pi$
$449$	−21.6019	−	5.78821i	−1.01946	−	0.273163i	−0.729576	+	0.683900i	$0.760282\pi$
$450$	−42.3935	−	11.3593i	−1.99845	−	0.535483i
$451$			1.14992i			0.0541474i
$452$	3.90615	−	2.25522i	0.183730	−	0.106076i
$453$	7.70127	+	7.70127i	0.361837	+	0.361837i
$454$	21.6995			1.01841
$455$		0			0
$456$	15.4939			0.725570
$457$	1.59916	+	1.59916i	0.0748054	+	0.0748054i	0.743520	−	0.668714i	$-0.233155\pi$
$457$	1.59916	+	1.59916i	0.0748054	+	0.0748054i	−0.668714	+	0.743520i	$0.733155\pi$
$458$	38.6532	−	22.3164i	1.80614	−	1.04278i
$459$		−	2.87627i		−	0.134253i
$460$	−0.687804	−	0.184296i	−0.0320690	−	0.00859287i
$461$	3.60574	+	0.966154i	0.167936	+	0.0449983i	0.341807	−	0.939770i	$-0.388961\pi$
$461$	3.60574	+	0.966154i	0.167936	+	0.0449983i	−0.173871	+	0.984768i	$0.555628\pi$
$462$		0			0
$463$	−15.5412	+	15.5412i	−0.722262	+	0.722262i	−0.969066	−	0.246804i	$-0.920620\pi$
$463$	−15.5412	+	15.5412i	−0.722262	+	0.722262i	0.246804	+	0.969066i	$0.420620\pi$
$464$	−22.6953	+	39.3095i	−1.05360	+	1.82490i
$465$	−12.2441	−	21.2074i	−0.567807	−	0.983471i
$466$	31.1866	+	8.35641i	1.44469	+	0.387103i
$467$	2.73553	+	4.73808i	0.126585	+	0.219252i	0.922351	−	0.386352i	$-0.126265\pi$
$467$	2.73553	+	4.73808i	0.126585	+	0.219252i	−0.795766	+	0.605604i	$0.792932\pi$
$468$	−27.2121	−	12.9014i	−1.25788	−	0.596369i
$469$		0			0
$470$	−11.4479	+	3.06745i	−0.528052	+	0.141491i
$471$	−11.5179			−0.530719
$472$	−8.75180			−0.402834
$473$	1.21104	−	0.324497i	0.0556837	−	0.0149204i
$474$	−16.5339	−	61.7054i	−0.759428	−	2.83422i
$475$	3.86315	−	14.4175i	0.177253	−	0.661519i
$476$		0			0
$477$	−3.00321	−	5.20171i	−0.137508	−	0.238170i
$478$			43.8232i			2.00443i
$479$	−0.410401	+	1.53164i	−0.0187517	+	0.0699822i	−0.974668	−	0.223658i	$-0.928200\pi$
$479$	−0.410401	+	1.53164i	−0.0187517	+	0.0699822i	0.955916	+	0.293640i	$0.0948668\pi$
$480$	−18.8745	−	10.8972i	−0.861499	−	0.497387i
$481$	9.31480	−	10.9580i	0.424719	−	0.499644i
$482$		−	18.8489i		−	0.858542i
$483$		0			0
$484$	7.13958	−	12.3661i	0.324527	−	0.562096i
$485$	2.38928	+	1.37945i	0.108492	+	0.0626378i
$486$	−3.93878	−	14.6997i	−0.178667	−	0.666793i
$487$	5.57627	+	5.57627i	0.252685	+	0.252685i	0.822071	−	0.569386i	$-0.192819\pi$
$487$	5.57627	+	5.57627i	0.252685	+	0.252685i	−0.569386	+	0.822071i	$0.692819\pi$
$488$	−9.56470	+	2.56285i	−0.432974	+	0.116015i
$489$	14.6162	+	14.6162i	0.660967	+	0.660967i
$490$		0			0
$491$	7.46842	+	4.31189i	0.337045	+	0.194593i	0.658965	−	0.752174i	$-0.270995\pi$
$491$	7.46842	+	4.31189i	0.337045	+	0.194593i	−0.321919	+	0.946767i	$0.604328\pi$
$492$	−25.2428	+	25.2428i	−1.13803	+	1.13803i
$493$	−1.26452	+	2.19022i	−0.0569512	+	0.0986424i
$494$	11.1375	−	23.4914i	0.501098	−	1.05693i
$495$	−0.796396	+	0.459800i	−0.0357953	+	0.0206665i
$496$	9.10470	+	33.9792i	0.408813	+	1.52571i
$497$		0			0
$498$	55.1214	−	31.8244i	2.47005	−	1.42608i
$499$	4.10435	−	15.3177i	0.183736	−	0.685712i	−0.811161	−	0.584822i	$-0.801164\pi$
$499$	4.10435	−	15.3177i	0.183736	−	0.685712i	0.994898	−	0.100890i	$-0.0321691\pi$
$500$	−8.96616	+	8.96616i	−0.400979	+	0.400979i
$501$	25.5217	−	25.5217i	1.14022	−	1.14022i
$502$	−4.28983	+	16.0099i	−0.191465	+	0.714556i
$503$	−21.6152	+	12.4795i	−0.963773	+	0.556435i	−0.897332	−	0.441356i	$-0.854498\pi$
$503$	−21.6152	+	12.4795i	−0.963773	+	0.556435i	−0.0664408	+	0.997790i	$0.521164\pi$
$504$		0			0
$505$	0.486534	+	1.81577i	0.0216505	+	0.0808007i
$506$	0.0995013	−	0.0574471i	0.00442337	−	0.00255384i
$507$	30.8978	−	25.2608i	1.37222	−	1.12187i
$508$	1.13570	−	1.96709i	0.0503884	−	0.0872753i
$509$	3.66666	−	3.66666i	0.162522	−	0.162522i	−0.621161	−	0.783683i	$-0.713339\pi$
$509$	3.66666	−	3.66666i	0.162522	−	0.162522i	0.783683	+	0.621161i	$0.213339\pi$
$510$	−1.47105	−	0.849308i	−0.0651390	−	0.0376080i
$511$		0			0
$512$	13.3091	+	13.3091i	0.588184	+	0.588184i
$513$	40.3098	−	10.8010i	1.77972	−	0.476874i
$514$	39.4557	+	39.4557i	1.74031	+	1.74031i
$515$	−2.52690	−	9.43051i	−0.111348	−	0.415558i
$516$	33.7079	+	19.4612i	1.48391	+	0.856734i
$517$	0.376678	−	0.652426i	0.0165663	−	0.0286937i
$518$		0			0
$519$		−	49.5514i		−	2.17506i
$520$	4.19971	−	2.90087i	0.184169	−	0.127212i
$521$	12.8926	+	7.44352i	0.564833	+	0.326107i	0.755083	−	0.655629i	$-0.227596\pi$
$521$	12.8926	+	7.44352i	0.564833	+	0.326107i	−0.190250	+	0.981736i	$0.560930\pi$
$522$	−27.9255	+	104.219i	−1.22226	+	4.56155i
$523$		−	18.3892i		−	0.804101i	−0.915617	−	0.402051i	$-0.868298\pi$
$523$		−	18.3892i		−	0.804101i	0.915617	−	0.402051i	$-0.131702\pi$
$524$	3.86512	+	6.69459i	0.168849	+	0.292455i
$525$		0			0
$526$	2.60794	−	9.73298i	0.113712	−	0.424378i
$527$	0.507289	+	1.89323i	0.0220979	+	0.0824703i
$528$	1.87184	−	0.501558i	0.0814613	−	0.0218275i
$529$	22.7580			0.989477
$530$	−1.89083			−0.0821326
$531$	−42.7144	+	11.4453i	−1.85365	+	0.496683i
$532$		0			0
$533$	−10.8363	−	30.3747i	−0.469371	−	1.31567i
$534$	−11.8080	−	20.4520i	−0.510982	−	0.885046i
$535$	2.90132	+	0.777406i	0.125435	+	0.0336102i
$536$	0.777865	+	1.34730i	0.0335987	+	0.0581946i
$537$	14.1154	−	24.4486i	0.609124	−	1.05503i
$538$	7.00181	−	7.00181i	0.301869	−	0.301869i
$539$		0			0
$540$	−14.6994	−	3.93870i	−0.632562	−	0.169494i
$541$	25.0540	+	6.71321i	1.07716	+	0.288623i	0.753431	−	0.657527i	$-0.228398\pi$
$541$	25.0540	+	6.71321i	1.07716	+	0.288623i	0.323726	+	0.946151i	$0.395064\pi$
$542$			19.4281i			0.834507i
$543$	−38.9475	+	22.4863i	−1.67140	+	0.964981i
$544$	1.23348	+	1.23348i	0.0528849	+	0.0528849i
$545$	10.3466			0.443200
$546$		0			0
$547$	−32.7020			−1.39824			−0.699119	−	0.715006i	$-0.746424\pi$
$547$	−32.7020			−1.39824			−0.699119	+	0.715006i	$0.746424\pi$
$548$	−18.0568	−	18.0568i	−0.771346	−	0.771346i
$549$	−43.3303	+	25.0167i	−1.84929	+	1.06769i
$550$		−	0.878239i		−	0.0374482i
$551$	−35.4436	−	9.49708i	−1.50995	−	0.404589i
$552$	−1.85492	−	0.497025i	−0.0789508	−	0.0211548i
$553$		0			0
$554$	31.5367	−	31.5367i	1.33987	−	1.33987i
$555$	6.81689	−	11.8072i	0.289361	−	0.501188i
$556$	−3.60690	−	6.24733i	−0.152967	−	0.264946i
$557$	−8.96735	−	2.40279i	−0.379959	−	0.101810i	0.0637843	−	0.997964i	$-0.479683\pi$
$557$	−8.96735	−	2.40279i	−0.379959	−	0.101810i	−0.443743	+	0.896154i	$0.646350\pi$
$558$	41.8097	+	72.4165i	1.76994	+	3.06563i
$559$	−28.9313	+	19.9838i	−1.22366	+	0.845223i
$560$		0			0
$561$	0.104294	−	0.0279454i	0.00440328	−	0.00117986i
$562$	22.2722			0.939497
$563$	34.6988			1.46238			0.731189	−	0.682175i	$-0.238966\pi$
$563$	34.6988			1.46238			0.731189	+	0.682175i	$0.238966\pi$
$564$	22.5907	−	6.05317i	0.951242	−	0.254884i
$565$	0.999731	+	3.73105i	0.0420590	+	0.156966i
$566$	1.33313	−	4.97531i	0.0560357	−	0.209128i
$567$		0			0
$568$	1.95023	+	3.37789i	0.0818297	+	0.141733i
$569$		−	28.8468i		−	1.20932i	−0.796484	−	0.604659i	$-0.793309\pi$
$569$		−	28.8468i		−	1.20932i	0.796484	−	0.604659i	$-0.206691\pi$
$570$	6.37865	−	23.8055i	0.267172	−	0.997101i
$571$	−21.3819	−	12.3448i	−0.894804	−	0.516615i	−0.0192930	−	0.999814i	$-0.506142\pi$
$571$	−21.3819	−	12.3448i	−0.894804	−	0.516615i	−0.875511	+	0.483199i	$0.839475\pi$
$572$	0.108433	−	0.592789i	0.00453381	−	0.0247857i
$573$			18.5200i			0.773686i
$574$		0			0
$575$	−0.924987	+	1.60212i	−0.0385746	+	0.0668132i
$576$	9.81239	+	5.66519i	0.408850	+	0.236049i
$577$	0.963094	+	3.59432i	0.0400941	+	0.149633i	0.983071	−	0.183225i	$-0.0586536\pi$
$577$	0.963094	+	3.59432i	0.0400941	+	0.149633i	−0.942977	+	0.332858i	$0.891987\pi$
$578$	−21.7410	−	21.7410i	−0.904305	−	0.904305i
$579$	−1.21897	+	0.326623i	−0.0506588	+	0.0135740i
$580$	9.46168	+	9.46168i	0.392875	+	0.392875i
$581$		0			0
$582$	−11.9683	−	6.90988i	−0.496101	−	0.286424i
$583$	0.0849880	−	0.0849880i	0.00351984	−	0.00351984i
$584$	−0.0781935	+	0.135435i	−0.00323567	+	0.00560435i
$585$	16.7036	−	19.6503i	0.690610	−	0.812441i
$586$	−31.0812	+	17.9447i	−1.28395	+	0.741290i
$587$	−4.43305	−	16.5444i	−0.182972	−	0.682859i	−0.995056	−	0.0993189i	$-0.968334\pi$
$587$	−4.43305	−	16.5444i	−0.182972	−	0.682859i	0.812084	−	0.583540i	$-0.198333\pi$
$588$		0			0
$589$	−24.6279	+	14.2189i	−1.01477	+	0.585880i
$590$	−3.60300	+	13.4466i	−0.148333	+	0.553587i
$591$	42.6517	−	42.6517i	1.75446	−	1.75446i
$592$	−13.8488	+	13.8488i	−0.569184	+	0.569184i
$593$	5.30494	−	19.7983i	0.217848	−	0.813019i	−0.767297	−	0.641292i	$-0.778399\pi$
$593$	5.30494	−	19.7983i	0.217848	−	0.813019i	0.985145	−	0.171727i	$-0.0549347\pi$
$594$	2.12649	−	1.22773i	0.0872511	−	0.0503745i
$595$		0			0
$596$	0.145004	+	0.541161i	0.00593958	+	0.0221668i
$597$	−46.3195	+	26.7426i	−1.89573	+	1.09450i
$598$	−2.08694	+	2.45510i	−0.0853414	+	0.100397i
$599$	19.5672	−	33.8914i	0.799494	−	1.38476i	−0.120452	−	0.992719i	$-0.538434\pi$
$599$	19.5672	−	33.8914i	0.799494	−	1.38476i	0.919946	−	0.392045i	$-0.128232\pi$
$600$	−10.3796	+	10.3796i	−0.423746	+	0.423746i
$601$	29.2750	+	16.9020i	1.19415	+	0.689445i	0.959246	−	0.282573i	$-0.0911878\pi$
$601$	29.2750	+	16.9020i	1.19415	+	0.689445i	0.234908	+	0.972018i	$0.424521\pi$
$602$		0			0
$603$	5.55843	+	5.55843i	0.226357	+	0.226357i
$604$	−4.45502	+	1.19372i	−0.181272	+	0.0485718i
$605$	8.64682	+	8.64682i	0.351543	+	0.351543i
$606$	−2.43712	−	9.09545i	−0.0990012	−	0.369478i
$607$	25.0478	+	14.4613i	1.01666	+	0.586968i	0.913134	−	0.407659i	$-0.133655\pi$
$607$	25.0478	+	14.4613i	1.01666	+	0.586968i	0.103524	+	0.994627i	$0.466988\pi$
$608$	−12.6548	+	21.9187i	−0.513218	+	0.888920i
$609$		0			0
$610$			15.7506i			0.637725i
$611$	−3.80168	+	20.7833i	−0.153800	+	0.840801i
$612$	1.97887	+	1.14250i	0.0799910	+	0.0461829i
$613$	−4.75410	+	17.7425i	−0.192016	+	0.716614i	0.801003	+	0.598660i	$0.204300\pi$
$613$	−4.75410	+	17.7425i	−0.192016	+	0.716614i	−0.993019	+	0.117954i	$0.962367\pi$
$614$			17.9397i			0.723986i
$615$	−15.2859	−	26.4759i	−0.616387	−	1.06761i
$616$		0			0
$617$	−3.13670	+	11.7063i	−0.126279	+	0.471279i	−0.999882	−	0.0153601i	$-0.995111\pi$
$617$	−3.13670	+	11.7063i	−0.126279	+	0.471279i	0.873603	+	0.486639i	$0.161777\pi$
$618$	12.6576	+	47.2388i	0.509163	+	1.90022i
$619$	−23.3947	+	6.26859i	−0.940312	+	0.251956i	−0.696246	−	0.717803i	$-0.745148\pi$
$619$	−23.3947	+	6.26859i	−0.940312	+	0.251956i	−0.244065	+	0.969759i	$0.578481\pi$
$620$	10.3702			0.416476
$621$	−5.17234			−0.207559
$622$	−46.4247	+	12.4395i	−1.86146	+	0.498777i
$623$		0			0
$624$	−44.7176	+	30.8878i	−1.79014	+	1.23650i
$625$	3.97162	+	6.87905i	0.158865	+	0.275162i
$626$	−20.7420	−	5.55781i	−0.829019	−	0.222135i
$627$	0.783288	+	1.35669i	0.0312815	+	0.0541812i
$628$	2.43879	−	4.22410i	0.0973182	−	0.168560i
$629$	−0.771620	+	0.771620i	−0.0307665	+	0.0307665i
$630$		0			0
$631$	−7.36652	−	1.97385i	−0.293256	−	0.0785778i	0.109191	−	0.994021i	$-0.465174\pi$
$631$	−7.36652	−	1.97385i	−0.293256	−	0.0785778i	−0.402448	+	0.915443i	$0.631841\pi$
$632$	−14.0686	−	3.76966i	−0.559618	−	0.149949i
$633$		−	47.2628i		−	1.87853i
$634$	5.74664	−	3.31783i	0.228228	−	0.131768i
$635$	1.37545	+	1.37545i	0.0545833	+	0.0545833i
$636$	3.73129			0.147955
$637$		0			0
$638$	−2.15904			−0.0854772
$639$	13.9358	+	13.9358i	0.551293	+	0.551293i
$640$	−9.20724	+	5.31580i	−0.363948	+	0.210125i
$641$		−	26.5132i		−	1.04721i	−0.851962	−	0.523603i	$-0.824587\pi$
$641$		−	26.5132i		−	1.04721i	0.851962	−	0.523603i	$-0.175413\pi$
$642$	−14.5331	−	3.89414i	−0.573577	−	0.153689i
$643$	−11.1885	−	2.99795i	−0.441231	−	0.118228i	0.0313623	−	0.999508i	$-0.490015\pi$
$643$	−11.1885	−	2.99795i	−0.441231	−	0.118228i	−0.472593	+	0.881281i	$0.656682\pi$
$644$		0			0
$645$	−23.5697	+	23.5697i	−0.928057	+	0.928057i
$646$	−0.986290	+	1.70830i	−0.0388050	+	0.0672123i
$647$	−19.2967	−	33.4228i	−0.758631	−	1.31399i	−0.943549	−	0.331233i	$-0.892535\pi$
$647$	−19.2967	−	33.4228i	−0.758631	−	1.31399i	0.184918	−	0.982754i	$-0.440798\pi$
$648$	−15.9701	−	4.27919i	−0.627367	−	0.168102i
$649$	−0.442443	−	0.766333i	−0.0173674	−	0.0300812i
$650$	8.27611	+	23.1984i	0.324616	+	0.909916i
$651$		0			0
$652$	−8.45516	+	2.26555i	−0.331129	+	0.0887259i
$653$	26.0323			1.01872			0.509361	−	0.860553i	$-0.329882\pi$
$653$	26.0323			1.01872			0.509361	+	0.860553i	$0.329882\pi$
$654$	−51.8276			−2.02662
$655$	−6.39449	+	1.71340i	−0.249853	+	0.0669480i
$656$	11.3666	+	42.4206i	0.443790	+	1.65625i
$657$	−0.204517	+	0.763269i	−0.00797898	+	0.0297780i
$658$		0			0
$659$	24.8221	+	42.9932i	0.966933	+	1.67478i	0.704328	+	0.709874i	$0.251248\pi$
$659$	24.8221	+	42.9932i	0.966933	+	1.67478i	0.262605	+	0.964903i	$0.415418\pi$
$660$		−	0.571270i		−	0.0222366i
$661$	−3.13750	+	11.7093i	−0.122034	+	0.455439i	−0.999717	−	0.0238044i	$-0.992422\pi$
$661$	−3.13750	+	11.7093i	−0.122034	+	0.455439i	0.877682	+	0.479243i	$0.159089\pi$
$662$	−13.5501	−	7.82313i	−0.526638	−	0.304055i
$663$	−2.49154	+	1.72098i	−0.0967634	+	0.0668375i
$664$		−	14.5116i		−	0.563161i
$665$		0			0
$666$	−23.2775	+	40.3178i	−0.901984	+	1.56228i
$667$	3.93862	+	2.27397i	0.152504	+	0.0880483i
$668$	3.95594	+	14.7638i	0.153060	+	0.571227i
$669$	−30.1236	−	30.1236i	−1.16465	−	1.16465i
$670$	2.39028	−	0.640474i	0.0923446	−	0.0247437i
$671$	−0.707950	−	0.707950i	−0.0273301	−	0.0273301i
$672$		0			0
$673$	34.6870	+	20.0265i	1.33708	+	0.771966i	0.986374	−	0.164519i	$-0.0526070\pi$
$673$	34.6870	+	20.0265i	1.33708	+	0.771966i	0.350710	+	0.936484i	$0.385940\pi$
$674$	−33.8380	+	33.8380i	−1.30339	+	1.30339i
$675$	−19.7684	+	34.2398i	−0.760885	+	1.31789i
$676$	2.72194	+	16.6801i	0.104690	+	0.641544i
$677$	−33.3532	+	19.2565i	−1.28187	+	0.740086i	−0.977190	−	0.212369i	$-0.931882\pi$
$677$	−33.3532	+	19.2565i	−1.28187	+	0.740086i	−0.304678	+	0.952455i	$0.598549\pi$
$678$	−5.00780	−	18.6894i	−0.192323	−	0.717760i
$679$		0			0
$680$	−0.335392	+	0.193639i	−0.0128617	+	0.00742570i
$681$	9.49116	−	35.4215i	0.363702	−	1.35735i
$682$	−1.18317	+	1.18317i	−0.0453061	+	0.0453061i
$683$	−26.9693	+	26.9693i	−1.03195	+	1.03195i	−0.0324804	+	0.999472i	$0.510341\pi$
$683$	−26.9693	+	26.9693i	−1.03195	+	1.03195i	−0.999472	+	0.0324804i	$0.989659\pi$
$684$	−8.58064	+	32.0234i	−0.328089	+	1.22445i
$685$	18.9389	−	10.9344i	0.723617	−	0.417780i
$686$		0			0
$687$	−19.5220	−	72.8571i	−0.744810	−	2.77967i
$688$	41.4679	−	23.9415i	1.58095	−	0.912761i
$689$	−1.44404	+	3.04582i	−0.0550137	+	0.116036i
$690$	−1.52729	+	2.64535i	−0.0581431	+	0.100707i
$691$	−4.16816	+	4.16816i	−0.158564	+	0.158564i	−0.781930	−	0.623366i	$-0.785765\pi$
$691$	−4.16816	+	4.16816i	−0.158564	+	0.158564i	0.623366	+	0.781930i	$0.285765\pi$
$692$	18.1725	+	10.4919i	0.690816	+	0.398843i
$693$		0			0
$694$	6.71396	+	6.71396i	0.254858	+	0.254858i
$695$	5.96728	−	1.59893i	0.226352	−	0.0606508i
$696$	25.5170	+	25.5170i	0.967220	+	0.967220i
$697$	0.633314	+	2.36356i	0.0239885	+	0.0895262i
$698$	18.2532	+	10.5385i	0.690894	+	0.398888i
$699$	27.2814	−	47.2528i	1.03188	−	1.78727i
$700$		0			0
$701$		−	39.7256i		−	1.50041i	−0.661203	−	0.750207i	$-0.729954\pi$
$701$		−	39.7256i		−	1.50041i	0.661203	−	0.750207i	$-0.270046\pi$
$702$	−44.6011	+	52.4693i	−1.68336	+	1.98032i
$703$	−13.7115	−	7.91636i	−0.517140	−	0.298571i
$704$	−0.0586809	+	0.219000i	−0.00221162	+	0.00825388i
$705$			20.0288i			0.754329i
$706$	−7.84109	−	13.5812i	−0.295103	−	0.511134i
$707$		0			0
$708$	7.11000	−	26.5349i	0.267210	−	0.997241i
$709$	0.109951	+	0.410342i	0.00412929	+	0.0154107i	0.967960	−	0.251105i	$-0.0807941\pi$
$709$	0.109951	+	0.410342i	0.00412929	+	0.0154107i	−0.963830	+	0.266516i	$0.914127\pi$
$710$	5.99280	−	1.60577i	0.224906	−	0.0602633i
$711$	−73.5935			−2.75997
$712$	−5.38434			−0.201787
$713$	3.40455	−	0.912248i	0.127502	−	0.0341639i
$714$		0			0
$715$	0.466323	+	0.221087i	0.0174395	+	0.00826818i
$716$	5.97753	+	10.3534i	0.223391	+	0.386924i
$717$	71.5355	+	19.1679i	2.67154	+	0.715837i
$718$	28.2019	+	48.8471i	1.05248	+	1.82296i
$719$	2.75054	−	4.76407i	0.102578	−	0.177670i	−0.810168	−	0.586197i	$-0.800624\pi$
$719$	2.75054	−	4.76407i	0.102578	−	0.177670i	0.912746	+	0.408528i	$0.133958\pi$
$720$	−24.8342	+	24.8342i	−0.925516	+	0.925516i
$721$		0			0
$722$	5.69451	+	1.52584i	0.211928	+	0.0567859i
$723$	−30.7682	−	8.24432i	−1.14428	−	0.306610i
$724$		−	19.0448i		−	0.707796i
$725$	30.1064	−	17.3819i	1.11812	−	0.645549i
$726$	−43.3132	−	43.3132i	−1.60750	−	1.60750i
$727$	−10.8373			−0.401935			−0.200967	−	0.979598i	$-0.564409\pi$
$727$	−10.8373			−0.401935			−0.200967	+	0.979598i	$0.564409\pi$
$728$		0			0
$729$	13.2908			0.492253
$730$	0.175896	+	0.175896i	0.00651021	+	0.00651021i
$731$	2.31048	−	1.33395i	0.0854561	−	0.0493381i
$732$		−	31.0816i		−	1.14881i
$733$	−29.0463	−	7.78294i	−1.07285	−	0.287469i	−0.321187	−	0.947016i	$-0.604082\pi$
$733$	−29.0463	−	7.78294i	−1.07285	−	0.287469i	−0.751664	+	0.659547i	$0.770748\pi$
$734$	4.59604	+	1.23150i	0.169643	+	0.0454557i
$735$		0			0
$736$	2.21814	−	2.21814i	0.0817617	−	0.0817617i
$737$	−0.0786492	+	0.136224i	−0.00289708	+	0.00501789i
$738$	52.1964	+	90.4068i	1.92138	+	3.32792i
$739$	−43.9327	−	11.7717i	−1.61609	−	0.433030i	−0.666241	−	0.745737i	$-0.732098\pi$
$739$	−43.9327	−	11.7717i	−1.61609	−	0.433030i	−0.949850	+	0.312707i	$0.898764\pi$
$740$	2.88679	+	5.00007i	0.106121	+	0.183806i
$741$	−33.4752	−	28.4553i	−1.22974	−	1.04533i
$742$		0			0
$743$	−43.4013	+	11.6293i	−1.59224	+	0.426639i	−0.942687	−	0.333678i	$-0.891710\pi$
$743$	−43.4013	+	11.6293i	−1.59224	+	0.426639i	−0.649552	+	0.760317i	$0.725044\pi$
$744$	27.9671			1.02532
$745$	−0.479790			−0.0175782
$746$	−62.8822	+	16.8492i	−2.30228	+	0.616894i
$747$	−18.9778	−	70.8261i	−0.694361	−	2.59139i
$748$	−0.0118342	+	0.0441659i	−0.000432702	+	0.00161486i
$749$		0			0
$750$	27.1972	+	47.1069i	0.993100	+	1.72010i
$751$		−	16.7889i		−	0.612636i	−0.951929	−	0.306318i	$-0.900903\pi$
$751$		−	16.7889i		−	0.612636i	0.951929	−	0.306318i	$-0.0990971\pi$
$752$	7.44669	−	27.7914i	0.271553	−	1.01345i
$753$	24.2576	+	14.0052i	0.883997	+	0.510376i
$754$	57.0304	−	20.3458i	2.07692	−	0.740950i
$755$		−	3.94980i		−	0.143748i
$756$		0			0
$757$	7.76400	−	13.4476i	0.282187	−	0.488763i	−0.689736	−	0.724061i	$-0.742273\pi$
$757$	7.76400	−	13.4476i	0.282187	−	0.488763i	0.971923	+	0.235298i	$0.0756067\pi$
$758$	−36.2652	−	20.9377i	−1.31721	−	0.760493i
$759$	−0.0502537	−	0.187549i	−0.00182409	−	0.00680761i
$760$	−3.97324	−	3.97324i	−0.144124	−	0.144124i
$761$	38.7077	−	10.3717i	1.40315	−	0.375974i	0.523678	−	0.851916i	$-0.324559\pi$
$761$	38.7077	−	10.3717i	1.40315	−	0.375974i	0.879477	+	0.475942i	$0.157893\pi$
$762$	−6.88985	−	6.88985i	−0.249593	−	0.249593i
$763$		0			0
$764$	−6.79206	−	3.92140i	−0.245728	−	0.141871i
$765$	−1.38369	+	1.38369i	−0.0500276	+	0.0500276i
$766$	11.8520	−	20.5283i	0.428230	−	0.741716i
$767$	18.9086	+	16.0731i	0.682748	+	0.580365i
$768$	55.4978	−	32.0417i	2.00260	−	1.15620i
$769$	12.5630	+	46.8857i	0.453033	+	1.69074i	0.693807	+	0.720161i	$0.255932\pi$
$769$	12.5630	+	46.8857i	0.453033	+	1.69074i	−0.240774	+	0.970581i	$0.577401\pi$
$770$		0			0
$771$	81.6636	−	47.1485i	2.94104	−	1.69801i
$772$	0.138317	−	0.516206i	0.00497813	−	0.0185786i
$773$	−33.2811	+	33.2811i	−1.19704	+	1.19704i	−0.221987	+	0.975050i	$0.571254\pi$
$773$	−33.2811	+	33.2811i	−1.19704	+	1.19704i	−0.975050	+	0.221987i	$0.928746\pi$
$774$	80.4829	−	80.4829i	2.89290	−	2.89290i
$775$	6.97312	−	26.0240i	0.250482	−	0.934811i
$776$	−2.72871	+	1.57542i	−0.0979551	+	0.0565544i
$777$		0			0
$778$	11.6691	+	43.5498i	0.418359	+	1.56134i
$779$	−30.7461	+	17.7513i	−1.10159	+	0.636006i
$780$	5.38338	+	15.0899i	0.192756	+	0.540306i
$781$	−0.197185	+	0.341535i	−0.00705585	+	0.0122211i
$782$	0.172878	−	0.172878i	0.00618210	−	0.00618210i
$783$	84.1744	+	48.5981i	3.00815	+	1.73675i
$784$		0			0
$785$	2.95364	+	2.95364i	0.105420	+	0.105420i
$786$	32.0309	−	8.58266i	1.14250	−	0.306133i
$787$	−19.6291	−	19.6291i	−0.699701	−	0.699701i	0.264645	−	0.964346i	$-0.414745\pi$
$787$	−19.6291	−	19.6291i	−0.699701	−	0.699701i	−0.964346	+	0.264645i	$0.914745\pi$
$788$	6.61113	+	24.6731i	0.235512	+	0.878942i
$789$	−14.7471	−	8.51423i	−0.525010	−	0.303115i
$790$	−11.5837	+	20.0635i	−0.412129	+	0.713829i
$791$		0			0
$792$		−	1.05024i		−	0.0373187i
$793$	25.3717	+	12.0289i	0.900974	+	0.427158i
$794$	−15.2196	−	8.78706i	−0.540125	−	0.311841i
$795$	−0.827034	+	3.08653i	−0.0293319	+	0.109468i
$796$		−	22.6497i		−	0.802797i
$797$	12.9913	+	22.5016i	0.460177	+	0.797049i	0.998969	−	0.0453891i	$-0.0144528\pi$
$797$	12.9913	+	22.5016i	0.460177	+	0.797049i	−0.538793	+	0.842438i	$0.681119\pi$
$798$		0			0
$799$	0.414909	−	1.54846i	0.0146784	−	0.0547807i
$800$	−6.20604	−	23.1613i	−0.219417	−	0.818874i
$801$	−26.2790	+	7.04145i	−0.928524	+	0.248797i
$802$	−12.7227			−0.449253
$803$	−0.0158121			−0.000557998
$804$	−4.71687	+	1.26388i	−0.166351	+	0.0445737i
$805$		0			0
$806$	20.1035	−	42.4028i	0.708115	−	1.49358i
$807$	−8.36698	−	14.4920i	−0.294532	−	0.510144i
$808$	−2.07372	−	0.555653i	−0.0729534	−	0.0195478i
$809$	15.0480	+	26.0639i	0.529060	+	0.916359i	0.999426	+	0.0338872i	$0.0107887\pi$
$809$	15.0480	+	26.0639i	0.529060	+	0.916359i	−0.470366	+	0.882472i	$0.655878\pi$
$810$	−13.1494	+	22.7754i	−0.462023	+	0.800247i
$811$	25.5228	−	25.5228i	0.896227	−	0.896227i	−0.0988731	−	0.995100i	$-0.531524\pi$
$811$	25.5228	−	25.5228i	0.896227	−	0.896227i	0.995100	+	0.0988731i	$0.0315238\pi$
$812$		0			0
$813$	31.7137	+	8.49766i	1.11225	+	0.298026i
$814$	−0.899842	−	0.241112i	−0.0315395	−	0.00845097i
$815$		−	7.49629i		−	0.262584i
$816$	3.57118	−	2.06182i	0.125016	−	0.0721782i
$817$	27.3712	+	27.3712i	0.957596	+	0.957596i
$818$	−27.6194			−0.965691
$819$		0			0
$820$	12.9464			0.452108
$821$	−34.1562	−	34.1562i	−1.19206	−	1.19206i	−0.976488	−	0.215573i	$-0.930838\pi$
$821$	−34.1562	−	34.1562i	−1.19206	−	1.19206i	−0.215573	−	0.976488i	$-0.569162\pi$
$822$	−94.8675	+	54.7718i	−3.30888	+	1.91038i
$823$			21.5128i			0.749890i	0.927047	+	0.374945i	$0.122338\pi$
$823$			21.5128i			0.749890i	−0.927047	+	0.374945i	$0.877662\pi$
$824$	10.7702	+	2.88588i	0.375199	+	0.100534i
$825$	−1.43361	−	0.384134i	−0.0499118	−	0.0133738i
$826$		0			0
$827$	−19.3309	+	19.3309i	−0.672200	+	0.672200i	−0.958223	−	0.286023i	$-0.907667\pi$
$827$	−19.3309	+	19.3309i	−0.672200	+	0.672200i	0.286023	+	0.958223i	$0.407667\pi$
$828$	2.05454	−	3.55856i	0.0714001	−	0.123669i
$829$	0.800615	+	1.38671i	0.0278065	+	0.0481623i	0.879594	−	0.475726i	$-0.157814\pi$
$829$	0.800615	+	1.38671i	0.0278065	+	0.0481623i	−0.851787	+	0.523888i	$0.824481\pi$
$830$	−22.2962	−	5.97425i	−0.773913	−	0.207369i
$831$	−37.6856	−	65.2733i	−1.30730	−	2.26431i
$832$	−0.513717	−	6.33780i	−0.0178099	−	0.219724i
$833$		0			0
$834$	−29.8910	+	8.00926i	−1.03504	+	0.277338i
$835$	−13.0895			−0.452979
$836$	−0.663407			−0.0229444
$837$	72.7605	−	19.4961i	2.51497	−	0.673885i
$838$	−11.6419	−	43.4480i	−0.402161	−	1.50089i
$839$	0.167923	−	0.626698i	0.00579736	−	0.0216360i	−0.962967	−	0.269621i	$-0.913102\pi$
$839$	0.167923	−	0.626698i	0.00579736	−	0.0216360i	0.968764	+	0.247985i	$0.0797683\pi$
$840$		0			0
$841$	−28.2313	−	48.8981i	−0.973495	−	1.68614i
$842$		−	10.5608i		−	0.363951i
$843$	9.74167	−	36.3564i	0.335521	−	1.25218i
$844$	17.3332	+	10.0073i	0.596634	+	0.344467i
$845$	−14.4012	−	1.44553i	−0.495416	−	0.0497279i
$846$		−	68.3919i		−	2.35136i
$847$		0			0
$848$	2.29514	−	3.97530i	0.0788154	−	0.136512i
$849$	−7.53843	−	4.35232i	−0.258718	−	0.149371i
$850$	−0.483688	−	1.80515i	−0.0165904	−	0.0619161i
$851$	1.38759	+	1.38759i	0.0475659	+	0.0475659i
$852$	−11.8259	+	3.16874i	−0.405149	+	0.108559i
$853$	19.5375	+	19.5375i	0.668953	+	0.668953i	0.957474	−	0.288521i	$-0.0931635\pi$
$853$	19.5375	+	19.5375i	0.668953	+	0.668953i	−0.288521	+	0.957474i	$0.593163\pi$
$854$		0			0
$855$	−24.5880	−	14.1959i	−0.840891	−	0.485489i
$856$	−2.42564	+	2.42564i	−0.0829068	+	0.0829068i
$857$	−16.1513	+	27.9748i	−0.551717	+	0.955602i	0.446434	+	0.894817i	$0.352694\pi$
$857$	−16.1513	+	27.9748i	−0.551717	+	0.955602i	−0.998151	+	0.0607851i	$0.980640\pi$
$858$	−2.33588	−	1.10746i	−0.0797456	−	0.0378079i
$859$	−25.7564	+	14.8704i	−0.878796	+	0.507373i	−0.870261	−	0.492591i	$-0.836050\pi$
$859$	−25.7564	+	14.8704i	−0.878796	+	0.507373i	−0.00853452	+	0.999964i	$0.502717\pi$
$860$	−3.65337	−	13.6346i	−0.124579	−	0.464935i
$861$		0			0
$862$	−30.4140	+	17.5595i	−1.03590	+	0.598079i
$863$	8.22555	−	30.6982i	0.280001	−	1.04498i	−0.672414	−	0.740175i	$-0.734743\pi$
$863$	8.22555	−	30.6982i	0.280001	−	1.04498i	0.952415	−	0.304803i	$-0.0985907\pi$
$864$	47.4050	−	47.4050i	1.61275	−	1.61275i
$865$	−12.7069	+	12.7069i	−0.432046	+	0.432046i
$866$	1.04040	−	3.88281i	0.0353541	−	0.131943i
$867$	−44.9985	+	25.9799i	−1.52823	+	0.882323i
$868$		0			0
$869$	−0.381147	−	1.42246i	−0.0129295	−	0.0482536i
$870$	49.7103	−	28.7002i	1.68534	−	0.973029i
$871$	0.793778	−	4.33948i	0.0268962	−	0.147038i
$872$	−5.90823	+	10.2334i	−0.200078	+	0.346545i
$873$	−11.2576	+	11.2576i	−0.381012	+	0.381012i
$874$	3.07201	+	1.77363i	0.103912	+	0.0599938i
$875$		0			0
$876$	−0.347106	−	0.347106i	−0.0117276	−	0.0117276i
$877$	−15.7460	+	4.21914i	−0.531706	+	0.142470i	−0.514676	−	0.857385i	$-0.672088\pi$
$877$	−15.7460	+	4.21914i	−0.531706	+	0.142470i	−0.0170302	+	0.999855i	$0.505421\pi$
$878$	−9.43194	−	9.43194i	−0.318313	−	0.318313i
$879$	15.6977	+	58.5847i	0.529471	+	1.97601i
$880$	−0.608629	−	0.351392i	−0.0205169	−	0.0118454i
$881$	24.6284	−	42.6577i	0.829752	−	1.43717i	−0.0684801	−	0.997652i	$-0.521815\pi$
$881$	24.6284	−	42.6577i	0.829752	−	1.43717i	0.898232	−	0.439521i	$-0.144852\pi$
$882$		0			0
$883$			40.1403i			1.35083i	0.737439	+	0.675414i	$0.236035\pi$
$883$			40.1403i			1.35083i	−0.737439	+	0.675414i	$0.763965\pi$
$884$	−0.103602	−	1.27815i	−0.00348450	−	0.0429888i
$885$	20.3738	+	11.7628i	0.684858	+	0.395403i
$886$	12.4997	−	46.6493i	0.419934	−	1.56721i
$887$			44.3159i			1.48798i	0.668189	+	0.743992i	$0.267070\pi$
$887$			44.3159i			1.48798i	−0.668189	+	0.743992i	$0.732930\pi$
$888$	7.78532	+	13.4846i	0.261258	+	0.452513i
$889$		0			0
$890$	−2.21666	+	8.27270i	−0.0743027	+	0.277301i
$891$	−0.432664	−	1.61473i	−0.0144948	−	0.0540953i
$892$	17.4259	−	4.66925i	0.583462	−	0.156338i
$893$	23.2592			0.778339
$894$	2.40334			0.0803797
$895$	−9.88927	+	2.64982i	−0.330562	+	0.0885738i
$896$		0			0
$897$	3.09481	+	4.48049i	0.103333	+	0.149599i
$898$	−20.3132	−	35.1836i	−0.677862	−	1.17409i
$899$	−63.9769	−	17.1426i	−2.13375	−	0.571736i
$900$	−15.7046	−	27.2012i	−0.523488	−	0.906708i
$901$	0.127879	−	0.221493i	0.00426027	−	0.00737900i
$902$	−1.47711	+	1.47711i	−0.0491823	+	0.0491823i
$903$		0			0
$904$	−4.26109	−	1.14176i	−0.141722	−	0.0379742i
$905$	15.7540	+	4.22126i	0.523679	+	0.140319i
$906$			19.7851i			0.657316i
$907$	46.9022	−	27.0790i	1.55736	−	0.899143i	0.559854	−	0.828591i	$-0.310857\pi$
$907$	46.9022	−	27.0790i	1.55736	−	0.899143i	0.997508	−	0.0705521i	$-0.0224761\pi$
$908$	10.9809	+	10.9809i	0.364413	+	0.364413i
$909$	−10.8478			−0.359798
$910$		0			0
$911$	5.80658			0.192381			0.0961903	−	0.995363i	$-0.469334\pi$
$911$	5.80658			0.192381			0.0961903	+	0.995363i	$0.469334\pi$
$912$	42.3061	+	42.3061i	1.40090	+	1.40090i
$913$	1.27068	−	0.733628i	0.0420534	−	0.0242796i
$914$			4.10835i			0.135892i
$915$	25.7108	+	6.88919i	0.849973	+	0.227750i
$916$	30.8532	+	8.26709i	1.01942	+	0.273152i
$917$		0			0
$918$	3.69467	−	3.69467i	0.121942	−	0.121942i
$919$	9.41959	−	16.3152i	0.310724	−	0.538189i	−0.667796	−	0.744345i	$-0.732762\pi$
$919$	9.41959	−	16.3152i	0.310724	−	0.538189i	0.978519	+	0.206156i	$0.0660953\pi$
$920$	0.348217	+	0.603129i	0.0114804	+	0.0198846i
$921$	29.2841	+	7.84664i	0.964943	+	0.258556i
$922$	3.39063	+	5.87275i	0.111665	+	0.193409i
$923$	1.99012	−	10.8797i	0.0655057	−	0.358111i
$924$		0			0
$925$	14.4888	−	3.88227i	0.476390	−	0.127648i
$926$	−39.9265			−1.31207
$927$	56.3397			1.85044
$928$	−56.9391	+	15.2568i	−1.86912	+	0.500828i
$929$	7.82322	+	29.1966i	0.256671	+	0.957911i	0.967153	+	0.254195i	$0.0818105\pi$
$929$	7.82322	+	29.1966i	0.256671	+	0.957911i	−0.710482	+	0.703716i	$0.751523\pi$
$930$	11.5137	−	42.9697i	0.377549	−	1.40903i
$931$		0			0
$932$	11.5530	+	20.0104i	0.378432	+	0.655464i
$933$			81.2229i			2.65912i
$934$	−2.57234	+	9.60011i	−0.0841696	+	0.314125i
$935$	−0.0339111	−	0.0195786i	−0.00110901	−	0.000640289i
$936$	9.89697	+	27.7418i	0.323493	+	0.906768i
$937$		−	29.0475i		−	0.948939i	−0.880272	−	0.474470i	$-0.842640\pi$
$937$		−	29.0475i		−	0.948939i	0.880272	−	0.474470i	$-0.157360\pi$
$938$		0			0
$939$	−18.1448	+	31.4277i	−0.592132	+	1.02560i
$940$	−7.34539	−	4.24086i	−0.239580	−	0.138322i
$941$	−13.7211	−	51.2078i	−0.447295	−	1.66933i	−0.709805	−	0.704398i	$-0.751217\pi$
$941$	−13.7211	−	51.2078i	−0.447295	−	1.66933i	0.262510	−	0.964929i	$-0.415450\pi$
$942$	−14.7952	−	14.7952i	−0.482054	−	0.482054i
$943$	4.25034	−	1.13888i	0.138410	−	0.0370869i
$944$	−23.8967	−	23.8967i	−0.777773	−	0.777773i
$945$		0			0
$946$	1.97245	+	1.13879i	0.0641299	+	0.0370254i
$947$	27.5374	−	27.5374i	0.894846	−	0.894846i	−0.100128	−	0.994975i	$-0.531925\pi$
$947$	27.5374	−	27.5374i	0.894846	−	0.894846i	0.994975	+	0.100128i	$0.0319253\pi$
$948$	22.8587	−	39.5925i	0.742417	−	1.28590i
$949$	0.417673	−	0.149006i	0.0135582	−	0.00483695i
$950$	23.4821	−	13.5574i	0.761860	−	0.439860i
$951$	−2.90237	−	10.8318i	−0.0941160	−	0.351246i
$952$		0			0
$953$	−2.01127	+	1.16121i	−0.0651515	+	0.0376153i	−0.532222	−	0.846605i	$-0.678643\pi$
$953$	−2.01127	+	1.16121i	−0.0651515	+	0.0376153i	0.467070	+	0.884220i	$0.345309\pi$
$954$	2.82405	−	10.5395i	0.0914321	−	0.341229i
$955$	4.74924	−	4.74924i	0.153682	−	0.153682i
$956$	−22.1764	+	22.1764i	−0.717236	+	0.717236i
$957$	−0.944345	+	3.52434i	−0.0305263	+	0.113926i
$958$	−2.49461	+	1.44027i	−0.0805973	+	0.0465329i
$959$		0			0
$960$	−1.56010	−	5.82236i	−0.0503519	−	0.187916i
$961$	−17.6074	+	10.1656i	−0.567980	+	0.327923i
$962$	26.0412	−	2.11079i	0.839601	−	0.0680547i
$963$	−8.66653	+	15.0109i	−0.279275	+	0.483718i
$964$	9.53833	−	9.53833i	0.307209	−	0.307209i
$965$	0.396349	+	0.228832i	0.0127589	+	0.00736638i
$966$		0			0
$967$	−20.9764	−	20.9764i	−0.674557	−	0.674557i	0.284206	−	0.958763i	$-0.408270\pi$
$967$	−20.9764	−	20.9764i	−0.674557	−	0.674557i	−0.958763	+	0.284206i	$0.908270\pi$
$968$	−13.4898	+	3.61458i	−0.433579	+	0.116177i
$969$	2.35718	+	2.35718i	0.0757236	+	0.0757236i
$970$	1.29716	+	4.84107i	0.0416494	+	0.155438i
$971$	−36.1562	−	20.8748i	−1.16031	−	0.669904i	−0.208930	−	0.977931i	$-0.566998\pi$
$971$	−36.1562	−	20.8748i	−1.16031	−	0.669904i	−0.951378	+	0.308027i	$0.900331\pi$
$972$	5.44550	−	9.43189i	0.174665	−	0.302528i
$973$		0			0
$974$			14.3258i			0.459029i
$975$	41.4882	−	3.36286i	1.32868	−	0.107698i
$976$	−33.1142	−	19.1185i	−1.05996	−	0.611969i
$977$	1.25510	−	4.68409i	0.0401542	−	0.149857i	−0.942938	−	0.332968i	$-0.891950\pi$
$977$	1.25510	−	4.68409i	0.0401542	−	0.149857i	0.983092	+	0.183110i	$0.0586166\pi$
$978$			37.5500i			1.20072i
$979$	−0.272203	−	0.471469i	−0.00869963	−	0.0150682i
$980$		0			0
$981$	−15.4531	+	57.6719i	−0.493381	+	1.84132i
$982$	4.05467	+	15.1322i	0.129390	+	0.482889i
$983$	4.11013	−	1.10131i	0.131093	−	0.0351262i	−0.192676	−	0.981262i	$-0.561717\pi$
$983$	4.11013	−	1.10131i	0.131093	−	0.0351262i	0.323769	+	0.946136i	$0.395050\pi$
$984$	34.9149			1.11305
$985$	−21.8750			−0.696996
$986$	−4.43773	+	1.18909i	−0.141326	+	0.0378682i
$987$		0			0
$988$	17.5237	−	6.25164i	0.557503	−	0.198891i
$989$	−2.39882	−	4.15489i	−0.0762782	−	0.132118i
$990$	−1.61363	−	0.432370i	−0.0512844	−	0.0137416i
$991$	23.4457	+	40.6091i	0.744776	+	1.28999i	0.950299	+	0.311337i	$0.100777\pi$
$991$	23.4457	+	40.6091i	0.744776	+	1.28999i	−0.205524	+	0.978652i	$0.565890\pi$
$992$	−22.8423	+	39.5640i	−0.725243	+	1.25616i
$993$	−18.6969	+	18.6969i	−0.593328	+	0.593328i
$994$		0			0
$995$	18.7359	+	5.02027i	0.593968	+	0.159153i
$996$	43.9983	+	11.7893i	1.39414	+	0.373559i
$997$		−	9.66903i		−	0.306221i	−0.988209	−	0.153111i	$-0.951071\pi$
$997$		−	9.66903i		−	0.306221i	0.988209	−	0.153111i	$-0.0489291\pi$
$998$	24.9482	−	14.4039i	0.789723	−	0.455947i
$999$	29.6549	+	29.6549i	0.938239	+	0.938239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.423.6		28
7.2	even	3		91.2.w.a.33.6	✓	28
7.3	odd	6		637.2.bd.b.293.2		28
7.4	even	3		637.2.bd.a.293.2		28
7.5	odd	6		637.2.x.a.215.6		28
7.6	odd	2		91.2.ba.a.59.6	yes	28
13.2	odd	12		637.2.x.a.80.6		28
21.2	odd	6		819.2.gh.b.397.2		28
21.20	even	2		819.2.et.b.514.2		28
91.2	odd	12		91.2.ba.a.54.6	yes	28
91.41	even	12		91.2.w.a.80.6	yes	28
91.54	even	12	inner	637.2.bb.a.509.6		28
91.67	odd	12		637.2.bd.b.587.2		28
91.80	even	12		637.2.bd.a.587.2		28
273.2	even	12		819.2.et.b.145.2		28
273.41	odd	12		819.2.gh.b.262.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.6	✓	28	7.2	even	3
91.2.w.a.80.6	yes	28	91.41	even	12
91.2.ba.a.54.6	yes	28	91.2	odd	12
91.2.ba.a.59.6	yes	28	7.6	odd	2
637.2.x.a.80.6		28	13.2	odd	12
637.2.x.a.215.6		28	7.5	odd	6
637.2.bb.a.423.6		28	1.1	even	1	trivial
637.2.bb.a.509.6		28	91.54	even	12	inner
637.2.bd.a.293.2		28	7.4	even	3
637.2.bd.a.587.2		28	91.80	even	12
637.2.bd.b.293.2		28	7.3	odd	6
637.2.bd.b.587.2		28	91.67	odd	12
819.2.et.b.145.2		28	273.2	even	12
819.2.et.b.514.2		28	21.20	even	2
819.2.gh.b.262.2		28	273.41	odd	12
819.2.gh.b.397.2		28	21.2	odd	6

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28453 + 1.28453i) q^{2} +(2.65867 - 1.53499i) q^{3} +1.30006i q^{4} +(-1.07541 - 0.288156i) q^{5} +(5.38690 + 1.44342i) q^{6} +(0.899098 - 0.899098i) q^{8} +(3.21237 - 5.56398i) q^{9} +O(q^{10})\)	\(q+(1.28453 + 1.28453i) q^{2} +(2.65867 - 1.53499i) q^{3} +1.30006i q^{4} +(-1.07541 - 0.288156i) q^{5} +(5.38690 + 1.44342i) q^{6} +(0.899098 - 0.899098i) q^{8} +(3.21237 - 5.56398i) q^{9} +(-1.01126 - 1.75155i) q^{10} +(0.124181 + 0.0332742i) q^{11} +(1.99557 + 3.45643i) q^{12} +(-3.59376 + 0.291296i) q^{13} +(-3.30149 + 0.884632i) q^{15} +4.90996 q^{16} +0.273570 q^{17} +(11.2735 - 3.02073i) q^{18} +(1.02731 + 3.83397i) q^{19} +(0.374620 - 1.39810i) q^{20} +(0.116773 + 0.202257i) q^{22} -0.491955i q^{23} +(1.01031 - 3.77051i) q^{24} +(-3.25665 - 1.88023i) q^{25} +(-4.99050 - 4.24214i) q^{26} -10.5138i q^{27} +(-4.62230 + 8.00606i) q^{29} +(-5.37722 - 3.10454i) q^{30} +(1.85433 + 6.92046i) q^{31} +(4.50882 + 4.50882i) q^{32} +(0.381233 - 0.102151i) q^{33} +(0.351410 + 0.351410i) q^{34} +(7.23351 + 4.17627i) q^{36} +(-2.82056 + 2.82056i) q^{37} +(-3.60526 + 6.24449i) q^{38} +(-9.10751 + 6.29084i) q^{39} +(-1.22598 + 0.707822i) q^{40} +(2.31500 + 8.63969i) q^{41} +(8.44566 - 4.87610i) q^{43} +(-0.0432585 + 0.161443i) q^{44} +(-5.05792 + 5.05792i) q^{45} +(0.631934 - 0.631934i) q^{46} +(1.51665 - 5.66021i) q^{47} +(13.0540 - 7.53673i) q^{48} +(-1.76806 - 6.59849i) q^{50} +(0.727333 - 0.419926i) q^{51} +(-0.378703 - 4.67211i) q^{52} +(0.467445 - 0.809639i) q^{53} +(13.5054 - 13.5054i) q^{54} +(-0.123958 - 0.0715671i) q^{55} +(8.61638 + 8.61638i) q^{57} +(-16.2216 + 4.34656i) q^{58} +(-4.86699 - 4.86699i) q^{59} +(-1.15007 - 4.29214i) q^{60} +(-6.74429 - 3.89382i) q^{61} +(-6.50761 + 11.2715i) q^{62} +1.76356i q^{64} +(3.94872 + 0.722302i) q^{65} +(0.620923 + 0.358490i) q^{66} +(-0.316671 + 1.18183i) q^{67} +0.355657i q^{68} +(-0.755145 - 1.30795i) q^{69} +(-0.793943 + 2.96304i) q^{71} +(-2.11433 - 7.89080i) q^{72} +(-0.118802 + 0.0318328i) q^{73} -7.24621 q^{74} -11.5445 q^{75} +(-4.98439 + 1.33556i) q^{76} +(-19.7797 - 3.61811i) q^{78} +(-5.72736 - 9.92007i) q^{79} +(-5.28024 - 1.41484i) q^{80} +(-6.50149 - 11.2609i) q^{81} +(-8.12429 + 14.0717i) q^{82} +(8.07011 - 8.07011i) q^{83} +(-0.294201 - 0.0788309i) q^{85} +(17.1123 + 4.58522i) q^{86} +28.3807i q^{87} +(0.141568 - 0.0817342i) q^{88} +(-2.99430 - 2.99430i) q^{89} -12.9941 q^{90} +0.639571 q^{92} +(15.5529 + 15.5529i) q^{93} +(9.21893 - 5.32255i) q^{94} -4.41913i q^{95} +(18.9085 + 5.06651i) q^{96} +(-2.39359 - 0.641359i) q^{97} +(0.584052 - 0.584052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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