LMFDB - Embedded newform 637.2.bc.c.460.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			460.10
Character	$\chi$	$=$	637.460
Dual form			637.2.bc.c.619.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.383841 - 1.43251i) q^{2} +(0.765995 - 0.442247i) q^{3} +(-0.172712 + 0.0997153i) q^{4} +(3.78973 - 1.01546i) q^{5} +(-0.927546 - 0.927546i) q^{6} +(-1.88821 - 1.88821i) q^{8} +(-1.10883 + 1.92056i) q^{9} +(-2.90931 - 5.03907i) q^{10} +(0.673262 - 2.51265i) q^{11} +(-0.0881976 + 0.152763i) q^{12} +(-3.36514 - 1.29454i) q^{13} +(2.45383 - 2.45383i) q^{15} +(-2.17954 + 3.77508i) q^{16} +(-0.680066 - 1.17791i) q^{17} +(3.17684 + 0.851232i) q^{18} +(-3.09237 + 0.828597i) q^{19} +(-0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +(1.39284 + 0.804158i) q^{23} +(-2.28141 - 0.611303i) q^{24} +(9.00081 - 5.19662i) q^{25} +(-0.562767 + 5.31751i) q^{26} +4.61500i q^{27} +9.34669 q^{29} +(-4.45703 - 2.57327i) q^{30} +(2.20361 - 8.22399i) q^{31} +(1.08577 + 0.290932i) q^{32} +(-0.595497 - 2.22242i) q^{33} +(-1.42633 + 1.42633i) q^{34} -0.442271i q^{36} +(4.65133 - 1.24632i) q^{37} +(2.37395 + 4.11181i) q^{38} +(-3.15019 + 0.496614i) q^{39} +(-9.07320 - 5.23842i) q^{40} +(-2.14628 - 2.14628i) q^{41} +11.5495i q^{43} +(0.134269 + 0.501099i) q^{44} +(-2.25195 + 8.40438i) q^{45} +(0.617338 - 2.30394i) q^{46} +(2.56800 + 9.58391i) q^{47} +3.85559i q^{48} +(-10.8991 - 10.8991i) q^{50} +(-1.04185 - 0.601515i) q^{51} +(0.710285 - 0.111973i) q^{52} +(1.51173 + 2.61840i) q^{53} +(6.61105 - 1.77143i) q^{54} -10.2059i q^{55} +(-2.00229 + 2.00229i) q^{57} +(-3.58764 - 13.3893i) q^{58} +(-0.250278 - 0.0670618i) q^{59} +(-0.179122 + 0.668491i) q^{60} +(0.288679 + 0.166669i) q^{61} -12.6268 q^{62} +7.05112i q^{64} +(-14.0675 - 1.48881i) q^{65} +(-2.95508 + 1.70611i) q^{66} +(-1.01621 - 0.272292i) q^{67} +(0.234911 + 0.135626i) q^{68} +1.42255 q^{69} +(-0.333748 + 0.333748i) q^{71} +(5.72013 - 1.53270i) q^{72} +(-8.11275 - 2.17380i) q^{73} +(-3.57074 - 6.18470i) q^{74} +(4.59638 - 7.96117i) q^{75} +(0.451465 - 0.451465i) q^{76} +(1.92058 + 4.32207i) q^{78} +(-1.45162 + 2.51428i) q^{79} +(-4.42646 + 16.5198i) q^{80} +(-1.28553 - 2.22661i) q^{81} +(-2.25074 + 3.89840i) q^{82} +(3.84570 + 3.84570i) q^{83} +(-3.77338 - 3.77338i) q^{85} +(16.5448 - 4.43317i) q^{86} +(7.15951 - 4.13355i) q^{87} +(-6.01566 + 3.47314i) q^{88} +(-1.91363 - 7.14176i) q^{89} +12.9038 q^{90} -0.320747 q^{92} +(-1.94908 - 7.27408i) q^{93} +(12.7434 - 7.35740i) q^{94} +(-10.8778 + 6.28033i) q^{95} +(0.960361 - 0.257328i) q^{96} +(7.45885 + 7.45885i) q^{97} +(4.07915 + 4.07915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 56 q^{9} + 16 q^{11} + 96 q^{15} + 56 q^{16} + 32 q^{18} - 96 q^{29} + 32 q^{39} + 64 q^{44} - 32 q^{46} - 80 q^{50} + 16 q^{53} - 192 q^{57} - 72 q^{58} + 64 q^{60} - 32 q^{65} + 64 q^{71} - 208 q^{72}+ \cdots - 64 q^{93}+O(q^{100}) $ 112 * q + 56 * q^9 + 16 * q^11 + 96 * q^15 + 56 * q^16 + 32 * q^18 - 96 * q^29 + 32 * q^39 + 64 * q^44 - 32 * q^46 - 80 * q^50 + 16 * q^53 - 192 * q^57 - 72 * q^58 + 64 * q^60 - 32 * q^65 + 64 * q^71 - 208 * q^72 - 208 * q^74 + 320 * q^78 + 80 * q^79 - 152 * q^81 + 48 * q^85 - 64 * q^86 - 256 * q^92 - 64 * q^93

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.383841	−	1.43251i	−0.271417	−	1.01294i	−0.958205	−	0.286083i	$-0.907647\pi$
$2$	−0.383841	−	1.43251i	−0.271417	−	1.01294i	0.686788	−	0.726858i	$-0.259020\pi$
$3$	0.765995	−	0.442247i	0.442247	−	0.255332i	−0.262303	−	0.964986i	$-0.584482\pi$
$3$	0.765995	−	0.442247i	0.442247	−	0.255332i	0.704550	+	0.709654i	$0.251149\pi$
$4$	−0.172712	+	0.0997153i	−0.0863560	+	0.0498576i
$5$	3.78973	−	1.01546i	1.69482	−	0.454126i	0.723194	−	0.690645i	$-0.242673\pi$
$5$	3.78973	−	1.01546i	1.69482	−	0.454126i	0.971627	+	0.236519i	$0.0760066\pi$
$6$	−0.927546	−	0.927546i	−0.378669	−	0.378669i
$7$		0			0
$7$		0			0
$8$	−1.88821	−	1.88821i	−0.667583	−	0.667583i
$9$	−1.10883	+	1.92056i	−0.369612	+	0.640186i
$10$	−2.90931	−	5.03907i	−0.920005	−	1.59350i
$11$	0.673262	−	2.51265i	0.202996	−	0.757592i	−0.787055	−	0.616883i	$-0.788395\pi$
$11$	0.673262	−	2.51265i	0.202996	−	0.757592i	0.990051	−	0.140709i	$-0.0449381\pi$
$12$	−0.0881976	+	0.152763i	−0.0254605	+	0.0440988i
$13$	−3.36514	−	1.29454i	−0.933322	−	0.359041i
$13$	−3.36514	−	1.29454i	−0.933322	−	0.359041i
$14$		0			0
$15$	2.45383	−	2.45383i	0.633577	−	0.633577i
$16$	−2.17954	+	3.77508i	−0.544886	+	0.943770i
$17$	−0.680066	−	1.17791i	−0.164940	−	0.285685i	0.771694	−	0.635994i	$-0.219410\pi$
$17$	−0.680066	−	1.17791i	−0.164940	−	0.285685i	−0.936634	+	0.350309i	$0.886076\pi$
$18$	3.17684	+	0.851232i	0.748789	+	0.200637i
$19$	−3.09237	+	0.828597i	−0.709437	+	0.190093i	−0.595454	−	0.803389i	$-0.703028\pi$
$19$	−3.09237	+	0.828597i	−0.709437	+	0.190093i	−0.113984	+	0.993483i	$0.536361\pi$
$20$	−0.553276	+	0.553276i	−0.123716	+	0.123716i
$21$		0			0
$22$	−3.85783			−0.822492
$23$	1.39284	+	0.804158i	0.290428	+	0.167679i	0.638135	−	0.769925i	$-0.279706\pi$
$23$	1.39284	+	0.804158i	0.290428	+	0.167679i	−0.347707	+	0.937603i	$0.613040\pi$
$24$	−2.28141	−	0.611303i	−0.465692	−	0.124782i
$25$	9.00081	−	5.19662i	1.80016	−	1.03932i
$26$	−0.562767	+	5.31751i	−0.110368	+	1.04285i
$27$			4.61500i			0.888157i
$28$		0			0
$29$	9.34669			1.73564			0.867818	−	0.496882i	$-0.165522\pi$
$29$	9.34669			1.73564			0.867818	+	0.496882i	$0.165522\pi$
$30$	−4.45703	−	2.57327i	−0.813739	−	0.469813i
$31$	2.20361	−	8.22399i	0.395781	−	1.47707i	−0.424666	−	0.905350i	$-0.639609\pi$
$31$	2.20361	−	8.22399i	0.395781	−	1.47707i	0.820447	−	0.571723i	$-0.193725\pi$
$32$	1.08577	+	0.290932i	0.191939	+	0.0514300i
$33$	−0.595497	−	2.22242i	−0.103663	−	0.386874i
$34$	−1.42633	+	1.42633i	−0.244614	+	0.244614i
$35$		0			0
$36$		−	0.442271i		−	0.0737118i
$37$	4.65133	−	1.24632i	0.764673	−	0.204894i	0.144656	−	0.989482i	$-0.453792\pi$
$37$	4.65133	−	1.24632i	0.764673	−	0.204894i	0.620017	+	0.784588i	$0.287126\pi$
$38$	2.37395	+	4.11181i	0.385106	+	0.667023i
$39$	−3.15019	+	0.496614i	−0.504434	+	0.0795218i
$40$	−9.07320	−	5.23842i	−1.43460	−	0.828266i
$41$	−2.14628	−	2.14628i	−0.335192	−	0.335192i	0.519362	−	0.854554i	$-0.326170\pi$
$41$	−2.14628	−	2.14628i	−0.335192	−	0.335192i	−0.854554	+	0.519362i	$0.826170\pi$
$42$		0			0
$43$			11.5495i			1.76128i	0.473786	+	0.880640i	$0.342887\pi$
$43$			11.5495i			1.76128i	−0.473786	+	0.880640i	$0.657113\pi$
$44$	0.134269	+	0.501099i	0.0202418	+	0.0755435i
$45$	−2.25195	+	8.40438i	−0.335700	+	1.25285i
$46$	0.617338	−	2.30394i	0.0910215	−	0.339697i
$47$	2.56800	+	9.58391i	0.374582	+	1.39796i	0.853955	+	0.520347i	$0.174197\pi$
$47$	2.56800	+	9.58391i	0.374582	+	1.39796i	−0.479374	+	0.877611i	$0.659136\pi$
$48$			3.85559i			0.556507i
$49$		0			0
$50$	−10.8991	−	10.8991i	−1.54137	−	1.54137i
$51$	−1.04185	−	0.601515i	−0.145889	−	0.0842289i
$52$	0.710285	−	0.111973i	0.0984988	−	0.0155279i
$53$	1.51173	+	2.61840i	0.207652	+	0.359665i	0.950975	−	0.309269i	$-0.100084\pi$
$53$	1.51173	+	2.61840i	0.207652	+	0.359665i	−0.743322	+	0.668934i	$0.766751\pi$
$54$	6.61105	−	1.77143i	0.899650	−	0.241061i
$55$		−	10.2059i		−	1.37617i
$56$		0			0
$57$	−2.00229	+	2.00229i	−0.265210	+	0.265210i
$58$	−3.58764	−	13.3893i	−0.471080	−	1.75810i
$59$	−0.250278	−	0.0670618i	−0.0325834	−	0.00873071i	0.242491	−	0.970154i	$-0.422036\pi$
$59$	−0.250278	−	0.0670618i	−0.0325834	−	0.00873071i	−0.275074	+	0.961423i	$0.588702\pi$
$60$	−0.179122	+	0.668491i	−0.0231245	+	0.0863018i
$61$	0.288679	+	0.166669i	0.0369616	+	0.0213398i	0.518367	−	0.855158i	$-0.326540\pi$
$61$	0.288679	+	0.166669i	0.0369616	+	0.0213398i	−0.481405	+	0.876498i	$0.659873\pi$
$62$	−12.6268			−1.60361
$63$		0			0
$64$			7.05112i			0.881390i
$65$	−14.0675	−	1.48881i	−1.74486	−	0.184664i
$66$	−2.95508	+	1.70611i	−0.363745	+	0.210008i
$67$	−1.01621	−	0.272292i	−0.124150	−	0.0332658i	0.196209	−	0.980562i	$-0.437137\pi$
$67$	−1.01621	−	0.272292i	−0.124150	−	0.0332658i	−0.320359	+	0.947296i	$0.603804\pi$
$68$	0.234911	+	0.135626i	0.0284871	+	0.0164471i
$69$	1.42255			0.171255
$70$		0			0
$71$	−0.333748	+	0.333748i	−0.0396086	+	0.0396086i	−0.726634	−	0.687025i	$-0.758916\pi$
$71$	−0.333748	+	0.333748i	−0.0396086	+	0.0396086i	0.687025	+	0.726634i	$0.258916\pi$
$72$	5.72013	−	1.53270i	0.674123	−	0.180631i
$73$	−8.11275	−	2.17380i	−0.949525	−	0.254425i	−0.249365	−	0.968410i	$-0.580222\pi$
$73$	−8.11275	−	2.17380i	−0.949525	−	0.254425i	−0.700161	+	0.713985i	$0.746888\pi$
$74$	−3.57074	−	6.18470i	−0.415090	−	0.718957i
$75$	4.59638	−	7.96117i	0.530744	−	0.919276i
$76$	0.451465	−	0.451465i	0.0517866	−	0.0517866i
$77$		0			0
$78$	1.92058	+	4.32207i	0.217462	+	0.489378i
$79$	−1.45162	+	2.51428i	−0.163320	+	0.282878i	−0.936057	−	0.351847i	$-0.885554\pi$
$79$	−1.45162	+	2.51428i	−0.163320	+	0.282878i	0.772738	+	0.634726i	$0.218887\pi$
$80$	−4.42646	+	16.5198i	−0.494894	+	1.84697i
$81$	−1.28553	−	2.22661i	−0.142837	−	0.247401i
$82$	−2.25074	+	3.89840i	−0.248553	+	0.430506i
$83$	3.84570	+	3.84570i	0.422120	+	0.422120i	0.885933	−	0.463813i	$-0.153519\pi$
$83$	3.84570	+	3.84570i	0.422120	+	0.422120i	−0.463813	+	0.885933i	$0.653519\pi$
$84$		0			0
$85$	−3.77338	−	3.77338i	−0.409281	−	0.409281i
$86$	16.5448	−	4.43317i	1.78407	−	0.478041i
$87$	7.15951	−	4.13355i	0.767580	−	0.443163i
$88$	−6.01566	+	3.47314i	−0.641272	+	0.370238i
$89$	−1.91363	−	7.14176i	−0.202844	−	0.757025i	−0.990096	−	0.140393i	$-0.955163\pi$
$89$	−1.91363	−	7.14176i	−0.202844	−	0.757025i	0.787251	−	0.616632i	$-0.211503\pi$
$90$	12.9038			1.36018
$91$		0			0
$92$	−0.320747			−0.0334402
$93$	−1.94908	−	7.27408i	−0.202111	−	0.754287i
$94$	12.7434	−	7.35740i	1.31438	−	0.758858i
$95$	−10.8778	+	6.28033i	−1.11604	+	0.644348i
$96$	0.960361	−	0.257328i	0.0980164	−	0.0262634i
$97$	7.45885	+	7.45885i	0.757332	+	0.757332i	0.975836	−	0.218504i	$-0.0701178\pi$
$97$	7.45885	+	7.45885i	0.757332	+	0.757332i	−0.218504	+	0.975836i	$0.570118\pi$
$98$		0			0
$99$	4.07915	+	4.07915i	0.409970	+	0.409970i
$100$	−1.03636	+	1.79504i	−0.103636	+	0.179504i
$101$	0.104651	+	0.181261i	0.0104132	+	0.0180362i	0.871185	−	0.490955i	$-0.163352\pi$
$101$	0.104651	+	0.181261i	0.0104132	+	0.0180362i	−0.860772	+	0.508991i	$0.830019\pi$
$102$	−0.461772	+	1.72336i	−0.0457222	+	0.170638i
$103$	−8.17798	+	14.1647i	−0.805800	+	1.39569i	0.109949	+	0.993937i	$0.464931\pi$
$103$	−8.17798	+	14.1647i	−0.805800	+	1.39569i	−0.915749	+	0.401750i	$0.868402\pi$
$104$	3.90973	+	8.79845i	0.383380	+	0.862759i
$105$		0			0
$106$	3.17063	−	3.17063i	0.307958	−	0.307958i
$107$	−8.52958	+	14.7737i	−0.824585	+	1.42822i	0.0776502	+	0.996981i	$0.475258\pi$
$107$	−8.52958	+	14.7737i	−0.824585	+	1.42822i	−0.902236	+	0.431243i	$0.858075\pi$
$108$	−0.460186	−	0.797066i	−0.0442814	−	0.0766977i
$109$	6.77341	+	1.81493i	0.648775	+	0.173839i	0.568175	−	0.822908i	$-0.307650\pi$
$109$	6.77341	+	1.81493i	0.648775	+	0.173839i	0.0806001	+	0.996747i	$0.474316\pi$
$110$	−14.6201	+	3.91746i	−1.39398	+	0.373515i
$111$	3.01171	−	3.01171i	0.285859	−	0.285859i
$112$		0			0
$113$	4.56982			0.429892			0.214946	−	0.976626i	$-0.431042\pi$
$113$	4.56982			0.429892			0.214946	+	0.976626i	$0.431042\pi$
$114$	3.63687	+	2.09975i	0.340624	+	0.196660i
$115$	6.09509	+	1.63318i	0.568370	+	0.152294i
$116$	−1.61428	+	0.932007i	−0.149883	+	0.0865347i
$117$	6.21762	−	5.02752i	0.574819	−	0.464794i
$118$			0.384268i			0.0353747i
$119$		0			0
$120$	−9.26670			−0.845930
$121$	3.66616	+	2.11666i	0.333287	+	0.192424i
$122$	0.127949	−	0.477511i	0.0115839	−	0.0432318i
$123$	−2.59322	−	0.694851i	−0.233823	−	0.0626526i
$124$	0.439468	+	1.64012i	0.0394654	+	0.147287i
$125$	14.9623	−	14.9623i	1.33827	−	1.33827i
$126$		0			0
$127$		−	10.4126i		−	0.923968i	−0.886888	−	0.461984i	$-0.847138\pi$
$127$		−	10.4126i		−	0.923968i	0.886888	−	0.461984i	$-0.152862\pi$
$128$	12.2724	−	3.28837i	1.08473	−	0.290654i
$129$	5.10773	+	8.84684i	0.449710	+	0.778921i
$130$	3.26696	+	20.7234i	0.286531	+	1.81756i
$131$	−15.1481	−	8.74577i	−1.32350	−	0.764121i	−0.339212	−	0.940710i	$-0.610160\pi$
$131$	−15.1481	−	8.74577i	−1.32350	−	0.764121i	−0.984285	+	0.176589i	$0.943494\pi$
$132$	0.324459	+	0.324459i	0.0282405	+	0.0282405i
$133$		0			0
$134$			1.56025i			0.134785i
$135$	4.68633	+	17.4896i	0.403335	+	1.50527i
$136$	−0.940031	+	3.50824i	−0.0806070	+	0.300829i
$137$	−5.21021	+	19.4448i	−0.445138	+	1.66128i	0.270433	+	0.962739i	$0.412833\pi$
$137$	−5.21021	+	19.4448i	−0.445138	+	1.66128i	−0.715571	+	0.698540i	$0.753833\pi$
$138$	−0.546032	−	2.03782i	−0.0464813	−	0.173471i
$139$		−	14.6578i		−	1.24326i	−0.783310	−	0.621631i	$-0.786470\pi$
$139$		−	14.6578i		−	1.24326i	0.783310	−	0.621631i	$-0.213530\pi$
$140$		0			0
$141$	6.20554	+	6.20554i	0.522600	+	0.522600i
$142$	0.606204	+	0.349992i	0.0508715	+	0.0293707i
$143$	−5.51834	+	7.58385i	−0.461467	+	0.634193i
$144$	−4.83351	−	8.37188i	−0.402792	−	0.697657i
$145$	35.4215	−	9.49115i	2.94159	−	0.788197i
$146$			12.4560i			1.03087i
$147$		0			0
$148$	−0.679062	+	0.679062i	−0.0558186	+	0.0558186i
$149$	5.66017	+	21.1240i	0.463699	+	1.73055i	0.661166	+	0.750239i	$0.270062\pi$
$149$	5.66017	+	21.1240i	0.463699	+	1.73055i	−0.197467	+	0.980310i	$0.563272\pi$
$150$	−13.1688	−	3.52856i	−1.07523	−	0.288106i
$151$	3.50181	−	13.0689i	0.284973	−	1.06353i	−0.663886	−	0.747834i	$-0.731094\pi$
$151$	3.50181	−	13.0689i	0.284973	−	1.06353i	0.948859	−	0.315700i	$-0.102239\pi$
$152$	7.40360	+	4.27447i	0.600511	+	0.346705i
$153$	3.01632			0.243855
$154$		0			0
$155$		−	33.4044i		−	2.68311i
$156$	0.494555	−	0.399893i	0.0395961	−	0.0320170i
$157$	11.1379	−	6.43044i	0.888897	−	0.513205i	0.0153156	−	0.999883i	$-0.495125\pi$
$157$	11.1379	−	6.43044i	0.888897	−	0.513205i	0.873582	+	0.486678i	$0.161791\pi$
$158$	4.15893	+	1.11438i	0.330867	+	0.0886554i
$159$	2.31596	+	1.33712i	0.183667	+	0.106040i
$160$	4.41022			0.348659
$161$		0			0
$162$	−2.69621	+	2.69621i	−0.211834	+	0.211834i
$163$	10.3474	−	2.77257i	0.810468	−	0.217164i	0.170293	−	0.985393i	$-0.445529\pi$
$163$	10.3474	−	2.77257i	0.810468	−	0.217164i	0.640175	+	0.768229i	$0.278862\pi$
$164$	0.584704	+	0.156671i	0.0456577	+	0.0122339i
$165$	−4.51355	−	7.81769i	−0.351379	−	0.608607i
$166$	4.03288	−	6.98516i	0.313012	−	0.542153i
$167$	−6.07140	+	6.07140i	−0.469819	+	0.469819i	−0.901856	−	0.432037i	$-0.857795\pi$
$167$	−6.07140	+	6.07140i	−0.469819	+	0.469819i	0.432037	+	0.901856i	$0.357795\pi$
$168$		0			0
$169$	9.64834	+	8.71261i	0.742180	+	0.670201i
$170$	−3.95705	+	6.85380i	−0.303492	+	0.525663i
$171$	1.83755	−	6.85785i	0.140521	−	0.524433i
$172$	−1.15166	−	1.99473i	−0.0878132	−	0.152097i
$173$	1.77614	−	3.07637i	0.135037	−	0.233892i	−0.790574	−	0.612366i	$-0.790218\pi$
$173$	1.77614	−	3.07637i	0.135037	−	0.233892i	0.925612	+	0.378474i	$0.123551\pi$
$174$	−8.66948	−	8.66948i	−0.657232	−	0.657232i
$175$		0			0
$176$	8.01805	+	8.01805i	0.604383	+	0.604383i
$177$	−0.221370	+	0.0593158i	−0.0166392	+	0.00445845i
$178$	−9.49615	+	5.48260i	−0.711766	+	0.410938i
$179$	−14.9201	+	8.61412i	−1.11518	+	0.643850i	−0.940166	−	0.340716i	$-0.889330\pi$
$179$	−14.9201	+	8.61412i	−1.11518	+	0.643850i	−0.175014	+	0.984566i	$0.555997\pi$
$180$	−0.449107	−	1.67609i	−0.0334744	−	0.124928i
$181$	−6.21868			−0.462231			−0.231115	−	0.972926i	$-0.574238\pi$
$181$	−6.21868			−0.462231			−0.231115	+	0.972926i	$0.574238\pi$
$182$		0			0
$183$	0.294836			0.0217949
$184$	−1.11156	−	4.14840i	−0.0819453	−	0.305824i
$185$	16.3617	−	9.44644i	1.20294	−	0.694516i
$186$	−9.67208	+	5.58418i	−0.709192	+	0.409452i
$187$	−3.41753	+	0.915725i	−0.249915	+	0.0669644i
$188$	−1.39919	−	1.39919i	−0.102046	−	0.102046i
$189$		0			0
$190$	13.1720	+	13.1720i	0.955599	+	0.955599i
$191$	6.15368	−	10.6585i	0.445264	−	0.771221i	−0.552806	−	0.833310i	$-0.686443\pi$
$191$	6.15368	−	10.6585i	0.445264	−	0.771221i	0.998071	+	0.0620893i	$0.0197763\pi$
$192$	3.11834	+	5.40112i	0.225047	+	0.389792i
$193$	5.55301	−	20.7241i	0.399715	−	1.49176i	−0.413885	−	0.910329i	$-0.635828\pi$
$193$	5.55301	−	20.7241i	0.399715	−	1.49176i	0.813599	−	0.581426i	$-0.197505\pi$
$194$	7.82190	−	13.5479i	0.561579	−	0.972684i
$195$	−11.4341	+	5.08091i	−0.818812	+	0.363852i
$196$		0			0
$197$	−1.42501	+	1.42501i	−0.101528	+	0.101528i	−0.756046	−	0.654518i	$-0.772872\pi$
$197$	−1.42501	+	1.42501i	−0.101528	+	0.101528i	0.654518	+	0.756046i	$0.272872\pi$
$198$	4.27769	−	7.40918i	0.304002	−	0.526548i
$199$	−3.33814	−	5.78184i	−0.236635	−	0.409863i	0.723112	−	0.690731i	$-0.242711\pi$
$199$	−3.33814	−	5.78184i	−0.236635	−	0.409863i	−0.959747	+	0.280868i	$0.909378\pi$
$200$	−26.8077	−	7.18310i	−1.89559	−	0.507922i
$201$	−0.898832	+	0.240841i	−0.0633987	+	0.0169876i
$202$	0.219490	−	0.219490i	0.0154432	−	0.0154432i
$203$		0			0
$204$	0.239921			0.0167978
$205$	−10.3133	−	5.95437i	−0.720310	−	0.415871i
$206$	23.4301	+	6.27809i	1.63246	+	0.437415i
$207$	−3.08886	+	1.78336i	−0.214691	+	0.123952i
$208$	12.2215	−	9.88217i	0.847406	−	0.685205i
$209$			8.32789i			0.576052i
$210$		0			0
$211$	−18.9896			−1.30730			−0.653648	−	0.756798i	$-0.726762\pi$
$211$	−18.9896			−1.30730			−0.653648	+	0.756798i	$0.726762\pi$
$212$	−0.522188	−	0.301486i	−0.0358640	−	0.0207061i
$213$	−0.108050	+	0.403248i	−0.00740346	+	0.0276301i
$214$	24.4375	+	6.54800i	1.67051	+	0.447612i
$215$	11.7280	+	43.7695i	0.799843	+	2.98505i
$216$	8.71408	−	8.71408i	0.592918	−	0.592918i
$217$		0			0
$218$		−	10.3996i		−	0.704353i
$219$	−7.17568	+	1.92272i	−0.484888	+	0.129925i
$220$	1.01769	+	1.76269i	0.0686125	+	0.118840i
$221$	0.763668	+	4.84420i	0.0513698	+	0.325856i
$222$	−5.47034	−	3.15830i	−0.367145	−	0.211971i
$223$	−2.04467	−	2.04467i	−0.136921	−	0.136921i	0.635324	−	0.772245i	$-0.280866\pi$
$223$	−2.04467	−	2.04467i	−0.136921	−	0.136921i	−0.772245	+	0.635324i	$0.780866\pi$
$224$		0			0
$225$			23.0488i			1.53658i
$226$	−1.75408	−	6.54633i	−0.116680	−	0.435455i
$227$	1.69881	−	6.34006i	0.112754	−	0.420805i	−0.886355	−	0.463007i	$-0.846771\pi$
$227$	1.69881	−	6.34006i	0.112754	−	0.420805i	0.999109	+	0.0422019i	$0.0134373\pi$
$228$	0.146161	−	0.545479i	0.00967972	−	0.0361252i
$229$	−0.369136	−	1.37763i	−0.0243932	−	0.0910366i	0.952656	−	0.304050i	$-0.0983389\pi$
$229$	−0.369136	−	1.37763i	−0.0243932	−	0.0910366i	−0.977049	+	0.213013i	$0.931672\pi$
$230$		−	9.35819i		−	0.617060i
$231$		0			0
$232$	−17.6485	−	17.6485i	−1.15868	−	1.15868i
$233$	7.35621	+	4.24711i	0.481921	+	0.278237i	0.721217	−	0.692709i	$-0.243583\pi$
$233$	7.35621	+	4.24711i	0.481921	+	0.278237i	−0.239295	+	0.970947i	$0.576916\pi$
$234$	−9.58857	−	6.97706i	−0.626824	−	0.456105i
$235$	19.4641	+	33.7128i	1.26970	+	2.19918i
$236$	0.0499131	−	0.0133742i	0.00324907	−	0.000870585i
$237$			2.56790i			0.166803i
$238$		0			0
$239$	−4.64810	+	4.64810i	−0.300661	+	0.300661i	−0.841272	−	0.540612i	$-0.818193\pi$
$239$	−4.64810	+	4.64810i	−0.300661	+	0.300661i	0.540612	+	0.841272i	$0.318193\pi$
$240$	3.91518	+	14.6117i	0.252724	+	0.943179i
$241$	−10.4173	−	2.79130i	−0.671034	−	0.179803i	−0.0928137	−	0.995683i	$-0.529586\pi$
$241$	−10.4173	−	2.79130i	−0.671034	−	0.179803i	−0.578221	+	0.815880i	$0.696253\pi$
$242$	1.62492	−	6.06429i	0.104454	−	0.389827i
$243$	−13.9595	−	8.05955i	−0.895505	−	0.517020i
$244$	−0.0664778			−0.00425580
$245$		0			0
$246$			3.98154i			0.253854i
$247$	11.4789	+	1.21485i	0.730385	+	0.0772987i
$248$	−19.6895	+	11.3677i	−1.25028	+	0.721852i
$249$	4.64654	+	1.24504i	0.294462	+	0.0789009i
$250$	−27.1769	−	15.6906i	−1.71882	−	0.992361i
$251$	−28.0524			−1.77065			−0.885327	−	0.464968i	$-0.846066\pi$
$251$	−28.0524			−1.77065			−0.885327	+	0.464968i	$0.846066\pi$
$252$		0			0
$253$	2.95831	−	2.95831i	0.185988	−	0.185988i
$254$	−14.9162	+	3.99678i	−0.935925	+	0.250780i
$255$	−4.55916	−	1.22162i	−0.285506	−	0.0765010i
$256$	−2.37016	−	4.10524i	−0.148135	−	0.256578i
$257$	−7.06032	+	12.2288i	−0.440411	+	0.762813i	−0.997720	−	0.0674915i	$-0.978500\pi$
$257$	−7.06032	+	12.2288i	−0.440411	+	0.762813i	0.557309	+	0.830305i	$0.311834\pi$
$258$	10.7127	−	10.7127i	0.666942	−	0.666942i
$259$		0			0
$260$	2.57809	−	1.14561i	0.159886	−	0.0710479i
$261$	−10.3639	+	17.9509i	−0.641511	+	1.11113i
$262$	−6.71397	+	25.0569i	−0.414790	+	1.54802i
$263$	−11.1615	−	19.3323i	−0.688248	−	1.19208i	−0.972404	−	0.233302i	$-0.925047\pi$
$263$	−11.1615	−	19.3323i	−0.688248	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$264$	−3.07198	+	5.32082i	−0.189067	+	0.327474i
$265$	8.38793	+	8.38793i	0.515267	+	0.515267i
$266$		0			0
$267$	−4.62426	−	4.62426i	−0.283000	−	0.283000i
$268$	0.202663	−	0.0543034i	0.0123796	−	0.00331711i
$269$	10.2451	−	5.91503i	0.624656	−	0.360645i	−0.154023	−	0.988067i	$-0.549223\pi$
$269$	10.2451	−	5.91503i	0.624656	−	0.360645i	0.778680	+	0.627422i	$0.215890\pi$
$270$	23.2553	−	13.4265i	1.41527	−	0.817109i
$271$	1.27932	+	4.77450i	0.0777134	+	0.290030i	0.993835	−	0.110870i	$-0.0353639\pi$
$271$	1.27932	+	4.77450i	0.0777134	+	0.290030i	−0.916121	+	0.400901i	$0.868697\pi$
$272$	5.92893			0.359494
$273$		0			0
$274$	29.8548			1.80359
$275$	−6.99737	−	26.1145i	−0.421957	−	1.57477i
$276$	−0.245691	+	0.141850i	−0.0147889	+	0.00853835i
$277$	−0.730512	+	0.421761i	−0.0438922	+	0.0253412i	−0.521786	−	0.853077i	$-0.674734\pi$
$277$	−0.730512	+	0.421761i	−0.0438922	+	0.0253412i	0.477893	+	0.878418i	$0.341401\pi$
$278$	−20.9976	+	5.62628i	−1.25935	+	0.337442i
$279$	13.3512	+	13.3512i	0.799316	+	0.799316i
$280$		0			0
$281$	−6.80029	−	6.80029i	−0.405671	−	0.405671i	0.474555	−	0.880226i	$-0.342609\pi$
$281$	−6.80029	−	6.80029i	−0.405671	−	0.405671i	−0.880226	+	0.474555i	$0.842609\pi$
$282$	6.50758	−	11.2715i	0.387521	−	0.671206i
$283$	9.91175	+	17.1677i	0.589192	+	1.02051i	0.994338	+	0.106259i	$0.0338873\pi$
$283$	9.91175	+	17.1677i	0.589192	+	1.02051i	−0.405146	+	0.914252i	$0.632779\pi$
$284$	0.0243625	−	0.0909219i	0.00144565	−	0.00539522i
$285$	−5.55491	+	9.62139i	−0.329045	+	0.569922i
$286$	12.9821	+	4.99411i	0.767650	+	0.295308i
$287$		0			0
$288$	−1.76270	+	1.76270i	−0.103868	+	0.103868i
$289$	7.57502	−	13.1203i	0.445589	−	0.771784i
$290$	−27.1924	−	47.0987i	−1.59679	−	2.76573i
$291$	9.01210	+	2.41478i	0.528299	+	0.141557i
$292$	1.61793	−	0.433523i	0.0946822	−	0.0253700i
$293$	−6.47711	+	6.47711i	−0.378397	+	0.378397i	−0.870524	−	0.492127i	$-0.836220\pi$
$293$	−6.47711	+	6.47711i	−0.378397	+	0.378397i	0.492127	+	0.870524i	$0.336220\pi$
$294$		0			0
$295$	−1.01659			−0.0591879
$296$	−11.1360	−	6.42936i	−0.647266	−	0.373699i
$297$	11.5959	+	3.10710i	0.672861	+	0.180292i
$298$	28.0879	−	16.2165i	1.62709	−	0.939399i
$299$	−3.64610	−	4.50920i	−0.210859	−	0.260773i
$300$			1.83332i			0.105847i
$301$		0			0
$302$	−20.0656			−1.15464
$303$	0.160325	+	0.0925634i	0.00921040	+	0.00531763i
$304$	3.61193	−	13.4799i	0.207158	−	0.773125i
$305$	1.26326	+	0.338490i	0.0723342	+	0.0193819i
$306$	−1.15779	−	4.32092i	−0.0661863	−	0.247011i
$307$	−17.9487	+	17.9487i	−1.02438	+	1.02438i	−0.0246898	+	0.999695i	$0.507860\pi$
$307$	−17.9487	+	17.9487i	−1.02438	+	1.02438i	−0.999695	+	0.0246898i	$0.992140\pi$
$308$		0			0
$309$			14.4668i			0.822985i
$310$	−47.8523	+	12.8220i	−2.71783	+	0.728240i
$311$	6.73937	+	11.6729i	0.382155	+	0.661912i	0.991370	−	0.131093i	$-0.0418488\pi$
$311$	6.73937	+	11.6729i	0.382155	+	0.661912i	−0.609215	+	0.793005i	$0.708515\pi$
$312$	6.88592	+	5.01050i	0.389838	+	0.283664i
$313$	−5.61548	−	3.24210i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391997\pi$
$313$	−5.61548	−	3.24210i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$314$	−13.4869	−	13.4869i	−0.761108	−	0.761108i
$315$		0			0
$316$		−	0.578994i		−	0.0325710i
$317$	−8.10220	−	30.2378i	−0.455065	−	1.69833i	−0.687897	−	0.725808i	$-0.741466\pi$
$317$	−8.10220	−	30.2378i	−0.455065	−	1.69833i	0.232832	−	0.972517i	$-0.425201\pi$
$318$	1.02648	−	3.83088i	0.0575623	−	0.214825i
$319$	6.29277	−	23.4849i	0.352327	−	1.31490i
$320$	7.16010	+	26.7219i	0.400262	+	1.49380i
$321$			15.0887i			0.842171i
$322$		0			0
$323$	3.07902	+	3.07902i	0.171322	+	0.171322i
$324$	0.444054	+	0.256374i	0.0246696	+	0.0142430i
$325$	−37.0162	+	5.83545i	−2.05329	+	0.323693i
$326$	−7.94348	−	13.7585i	−0.439949	−	0.762013i
$327$	5.99104	−	1.60530i	0.331306	−	0.0887730i
$328$			8.10523i			0.447537i
$329$		0			0
$330$	−9.46647	+	9.46647i	−0.521112	+	0.521112i
$331$	−3.23943	−	12.0897i	−0.178055	−	0.664512i	−0.996011	−	0.0892305i	$-0.971559\pi$
$331$	−3.23943	−	12.0897i	−0.178055	−	0.664512i	0.817956	−	0.575281i	$-0.195107\pi$
$332$	−1.04767	−	0.280723i	−0.0574985	−	0.0154067i
$333$	−2.76392	+	10.3151i	−0.151462	+	0.565264i
$334$	11.0278	+	6.36691i	0.603415	+	0.348382i
$335$	−4.12767			−0.225518
$336$		0			0
$337$		−	4.54349i		−	0.247500i	−0.992313	−	0.123750i	$-0.960508\pi$
$337$		−	4.54349i		−	0.247500i	0.992313	−	0.123750i	$-0.0394920\pi$
$338$	8.77751	−	17.1656i	0.477434	−	0.933687i
$339$	3.50046	−	2.02099i	0.190119	−	0.109765i
$340$	1.02797	+	0.275444i	0.0557496	+	0.0149381i
$341$	−19.1804	−	11.0738i	−1.03868	−	0.599680i
$342$	−10.5293			−0.569359
$343$		0			0
$344$	21.8078	−	21.8078i	1.17580	−	1.17580i
$345$	5.39108	−	1.44453i	0.290246	−	0.0777711i
$346$	−5.08869	−	1.36351i	−0.273570	−	0.0733028i
$347$	5.56642	+	9.64133i	0.298821	+	0.517574i	0.975867	−	0.218368i	$-0.0700732\pi$
$347$	5.56642	+	9.64133i	0.298821	+	0.517574i	−0.677045	+	0.735941i	$0.736740\pi$
$348$	−0.824356	+	1.42783i	−0.0441901	+	0.0765395i
$349$	16.7058	−	16.7058i	0.894240	−	0.894240i	−0.100679	−	0.994919i	$-0.532101\pi$
$349$	16.7058	−	16.7058i	0.894240	−	0.894240i	0.994919	+	0.100679i	$0.0321014\pi$
$350$		0			0
$351$	5.97430	−	15.5301i	0.318885	−	0.828937i
$352$	1.46202	−	2.53229i	0.0779259	−	0.134972i
$353$	−1.58513	+	5.91578i	−0.0843678	+	0.314865i	−0.995194	−	0.0979257i	$-0.968779\pi$
$353$	−1.58513	+	5.91578i	−0.0843678	+	0.314865i	0.910826	+	0.412791i	$0.135446\pi$
$354$	0.169942	+	0.294347i	0.00903229	+	0.0156444i
$355$	−0.925909	+	1.60372i	−0.0491421	+	0.0851167i
$356$	1.04265	+	1.04265i	0.0552603	+	0.0552603i
$357$		0			0
$358$	18.0668	+	18.0668i	0.954860	+	0.954860i
$359$	−21.0100	+	5.62963i	−1.10887	+	0.297120i	−0.766371	−	0.642399i	$-0.777939\pi$
$359$	−21.0100	+	5.62963i	−1.10887	+	0.297120i	−0.342497	+	0.939519i	$0.611273\pi$
$360$	20.1214	−	11.6171i	1.06049	−	0.612274i
$361$	−7.57833	+	4.37535i	−0.398859	+	0.230282i
$362$	2.38698	+	8.90835i	0.125457	+	0.468212i
$363$	3.74435			0.196527
$364$		0			0
$365$	−32.9526			−1.72482
$366$	−0.113170	−	0.422356i	−0.00591549	−	0.0220769i
$367$	−14.0740	+	8.12564i	−0.734658	+	0.424155i	−0.820124	−	0.572186i	$-0.806095\pi$
$367$	−14.0740	+	8.12564i	−0.734658	+	0.424155i	0.0854660	+	0.996341i	$0.472762\pi$
$368$	−6.07153	+	3.50540i	−0.316500	+	0.182731i
$369$	6.50191	−	1.74218i	0.338476	−	0.0906944i
$370$	−19.8124	−	19.8124i	−1.03000	−	1.03000i
$371$		0			0
$372$	1.06197	+	1.06197i	0.0550604	+	0.0550604i
$373$	−2.10783	+	3.65087i	−0.109139	+	0.189035i	−0.915422	−	0.402496i	$-0.868143\pi$
$373$	−2.10783	+	3.65087i	−0.109139	+	0.189035i	0.806283	+	0.591531i	$0.201476\pi$
$374$	2.62358	+	4.54417i	0.135662	+	0.234973i
$375$	4.84402	−	18.0781i	0.250144	−	0.933551i
$376$	13.2475	−	22.9454i	0.683188	−	1.18332i
$377$	−31.4529	−	12.0997i	−1.61991	−	0.623164i
$378$		0			0
$379$	18.1305	−	18.1305i	0.931303	−	0.931303i	−0.0664849	−	0.997787i	$-0.521178\pi$
$379$	18.1305	−	18.1305i	0.931303	−	0.931303i	0.997787	+	0.0664849i	$0.0211784\pi$
$380$	1.25249	−	2.16937i	0.0642513	−	0.111287i
$381$	−4.60494	−	7.97599i	−0.235918	−	0.408623i
$382$	−17.6305	−	4.72407i	−0.902053	−	0.241704i
$383$	22.6703	−	6.07450i	1.15840	−	0.310392i	0.372073	−	0.928203i	$-0.378647\pi$
$383$	22.6703	−	6.07450i	1.15840	−	0.310392i	0.786327	+	0.617811i	$0.211980\pi$
$384$	7.94630	−	7.94630i	0.405508	−	0.405508i
$385$		0			0
$386$	−31.8191			−1.61955
$387$	−22.1815	−	12.8065i	−1.12755	−	0.650989i
$388$	−2.03199	−	0.544471i	−0.103159	−	0.0276413i
$389$	16.8646	−	9.73676i	0.855067	−	0.493673i	−0.00729024	−	0.999973i	$-0.502321\pi$
$389$	16.8646	−	9.73676i	0.855067	−	0.493673i	0.862357	+	0.506300i	$0.168987\pi$
$390$	11.6673	+	14.4292i	0.590799	+	0.730652i
$391$		−	2.18752i		−	0.110628i
$392$		0			0
$393$	−15.4712			−0.780417
$394$	2.58833	+	1.49437i	0.130398	+	0.0752855i
$395$	−2.94811	+	11.0025i	−0.148336	+	0.553596i
$396$	−1.11127	−	0.297764i	−0.0558435	−	0.0149632i
$397$	−3.09522	−	11.5515i	−0.155345	−	0.579755i	−0.999076	−	0.0429883i	$-0.986312\pi$
$397$	−3.09522	−	11.5515i	−0.155345	−	0.579755i	0.843731	−	0.536767i	$-0.180354\pi$
$398$	−7.00124	+	7.00124i	−0.350941	+	0.350941i
$399$		0			0
$400$			45.3051i			2.26525i
$401$	9.07687	−	2.43214i	0.453277	−	0.121455i	−0.0249551	−	0.999689i	$-0.507944\pi$
$401$	9.07687	−	2.43214i	0.453277	−	0.121455i	0.478233	+	0.878233i	$0.341278\pi$
$402$	0.690017	+	1.19514i	0.0344149	+	0.0596084i
$403$	−18.0618	+	24.8222i	−0.899720	+	1.23648i
$404$	−0.0361490	−	0.0208706i	−0.00179848	−	0.00103835i
$405$	−7.13285	−	7.13285i	−0.354434	−	0.354434i
$406$		0			0
$407$		−	12.5262i		−	0.620903i
$408$	0.831452	+	3.10302i	0.0411630	+	0.153623i
$409$	4.99635	−	18.6466i	0.247054	−	0.922017i	−0.725286	−	0.688447i	$-0.758293\pi$
$409$	4.99635	−	18.6466i	0.247054	−	0.922017i	0.972340	−	0.233570i	$-0.0750407\pi$
$410$	−4.57106	+	17.0594i	−0.225749	+	0.842505i
$411$	4.60840	+	17.1988i	0.227316	+	0.848354i
$412$		−	3.26188i		−	0.160701i
$413$		0			0
$414$	3.74032	+	3.74032i	0.183827	+	0.183827i
$415$	18.4793	+	10.6690i	0.907114	+	0.523723i
$416$	−3.27716	−	2.38460i	−0.160676	−	0.116915i
$417$	−6.48239	−	11.2278i	−0.317444	−	0.549829i
$418$	11.9298	−	3.19659i	0.583507	−	0.156350i
$419$		−	24.1967i		−	1.18208i	−0.806641	−	0.591042i	$-0.798717\pi$
$419$		−	24.1967i		−	1.18208i	0.806641	−	0.591042i	$-0.201283\pi$
$420$		0			0
$421$	−16.9872	+	16.9872i	−0.827906	+	0.827906i	−0.987227	−	0.159321i	$-0.949070\pi$
$421$	−16.9872	+	16.9872i	−0.827906	+	0.827906i	0.159321	+	0.987227i	$0.449070\pi$
$422$	7.28898	+	27.2028i	0.354822	+	1.32421i
$423$	−21.2540	−	5.69498i	−1.03340	−	0.276899i
$424$	2.08961	−	7.79855i	0.101481	−	0.378731i
$425$	−12.2423	−	7.06809i	−0.593838	−	0.342853i
$426$	0.619132			0.0299971
$427$		0			0
$428$		−	3.40212i		−	0.164448i
$429$	−0.873086	+	8.24966i	−0.0421530	+	0.398297i
$430$	58.1987	−	33.6010i	2.80659	−	1.62039i
$431$	26.5171	+	7.10522i	1.27728	+	0.342247i	0.832816	−	0.553549i	$-0.186727\pi$
$431$	26.5171	+	7.10522i	1.27728	+	0.342247i	0.444465	+	0.895796i	$0.353394\pi$
$432$	−17.4220	−	10.0586i	−0.838216	−	0.483945i
$433$	26.0271			1.25078			0.625391	−	0.780312i	$-0.284940\pi$
$433$	26.0271			1.25078			0.625391	+	0.780312i	$0.284940\pi$
$434$		0			0
$435$	22.9352	−	22.9352i	1.09966	−	1.09966i
$436$	−1.35082	+	0.361952i	−0.0646928	+	0.0173344i
$437$	−4.97350	−	1.33265i	−0.237915	−	0.0637491i
$438$	5.50864	+	9.54125i	0.263213	+	0.455899i
$439$	1.85272	−	3.20901i	0.0884257	−	0.153158i	−0.818420	−	0.574620i	$-0.805150\pi$
$439$	1.85272	−	3.20901i	0.0884257	−	0.153158i	0.906846	+	0.421463i	$0.138483\pi$
$440$	−19.2709	+	19.2709i	−0.918706	+	0.918706i
$441$		0			0
$442$	6.64626	−	2.95337i	0.316130	−	0.140477i
$443$	−1.34404	+	2.32795i	−0.0638573	+	0.110604i	−0.896187	−	0.443678i	$-0.853674\pi$
$443$	−1.34404	+	2.32795i	−0.0638573	+	0.110604i	0.832329	+	0.554282i	$0.187007\pi$
$444$	−0.219845	+	0.820472i	−0.0104334	+	0.0389379i
$445$	−14.5043	−	25.1222i	−0.687570	−	1.19091i
$446$	−2.14419	+	3.71384i	−0.101530	+	0.175855i
$447$	13.6777	+	13.6777i	0.646934	+	0.646934i
$448$		0			0
$449$	24.6366	+	24.6366i	1.16267	+	1.16267i	0.983888	+	0.178784i	$0.0572164\pi$
$449$	24.6366	+	24.6366i	1.16267	+	1.16267i	0.178784	+	0.983888i	$0.442784\pi$
$450$	33.0177	−	8.84706i	1.55647	−	0.417054i
$451$	−6.83784	+	3.94783i	−0.321981	+	0.185896i
$452$	−0.789262	+	0.455681i	−0.0371238	+	0.0214334i
$453$	−3.09733	−	11.5594i	−0.145525	−	0.543108i
$454$	−9.73430			−0.456854
$455$		0			0
$456$	7.56149			0.354099
$457$	1.76442	+	6.58491i	0.0825361	+	0.308029i	0.994836	−	0.101493i	$-0.0323621\pi$
$457$	1.76442	+	6.58491i	0.0825361	+	0.308029i	−0.912300	+	0.409522i	$0.865695\pi$
$458$	−1.83179	+	1.05758i	−0.0855939	+	0.0494177i
$459$	5.43605	−	3.13850i	0.253733	−	0.146493i
$460$	−1.21555	+	0.325705i	−0.0566752	+	0.0151861i
$461$	−5.06375	−	5.06375i	−0.235842	−	0.235842i	0.579284	−	0.815126i	$-0.303332\pi$
$461$	−5.06375	−	5.06375i	−0.235842	−	0.235842i	−0.815126	+	0.579284i	$0.803332\pi$
$462$		0			0
$463$	−14.8196	−	14.8196i	−0.688725	−	0.688725i	0.273226	−	0.961950i	$-0.411909\pi$
$463$	−14.8196	−	14.8196i	−0.688725	−	0.688725i	−0.961950	+	0.273226i	$0.911909\pi$
$464$	−20.3715	+	35.2845i	−0.945724	+	1.63804i
$465$	−14.7730	−	25.5876i	−0.685082	−	1.18660i
$466$	3.26043	−	12.1681i	0.151036	−	0.563676i
$467$	0.228257	−	0.395352i	0.0105625	−	0.0182947i	−0.860696	−	0.509119i	$-0.829971\pi$
$467$	0.228257	−	0.395352i	0.0105625	−	0.0182947i	0.871258	+	0.490825i	$0.163304\pi$
$468$	−0.572537	+	1.48830i	−0.0264655	+	0.0687969i
$469$		0			0
$470$	40.8229	−	40.8229i	1.88302	−	1.88302i
$471$	5.68769	−	9.85137i	0.262075	−	0.453927i
$472$	0.345951	+	0.599204i	0.0159237	+	0.0275806i
$473$	29.0198	+	7.77583i	1.33433	+	0.357533i
$474$	3.67855	−	0.985664i	0.168961	−	0.0452731i
$475$	−23.5279	+	23.5279i	−1.07953	+	1.07953i
$476$		0			0
$477$	−6.70504			−0.307003
$478$	8.44260	+	4.87434i	0.386155	+	0.222947i
$479$	31.7426	+	8.50540i	1.45036	+	0.388622i	0.896148	−	0.443756i	$-0.146354\pi$
$479$	31.7426	+	8.50540i	1.45036	+	0.388622i	0.554209	+	0.832378i	$0.313021\pi$
$480$	3.37821	−	1.95041i	0.154193	−	0.0890236i
$481$	−17.2658	−	1.82729i	−0.787251	−	0.0833171i
$482$			15.9943i			0.728519i
$483$		0			0
$484$	−0.844253			−0.0383751
$485$	35.8412	+	20.6929i	1.62747	+	0.939617i
$486$	−6.18717	+	23.0908i	−0.280656	+	1.04742i
$487$	−11.1655	−	2.99178i	−0.505956	−	0.135571i	−0.00319321	−	0.999995i	$-0.501016\pi$
$487$	−11.1655	−	2.99178i	−0.505956	−	0.135571i	−0.502763	+	0.864424i	$0.667683\pi$
$488$	−0.230381	−	0.859792i	−0.0104288	−	0.0389210i
$489$	6.69986	−	6.69986i	0.302978	−	0.302978i
$490$		0			0
$491$		−	0.946627i		−	0.0427207i	−0.999772	−	0.0213603i	$-0.993200\pi$
$491$		−	0.946627i		−	0.0427207i	0.999772	−	0.0213603i	$-0.00679973\pi$
$492$	0.517167	−	0.138575i	0.0233157	−	0.00624743i
$493$	−6.35636	−	11.0095i	−0.286276	−	0.495845i
$494$	−2.66579	−	16.9100i	−0.119940	−	0.760816i
$495$	19.6011	+	11.3167i	0.881004	+	0.508648i
$496$	26.2434	+	26.2434i	1.17836	+	1.17836i
$497$		0			0
$498$		−	7.13412i		−	0.319688i
$499$	5.69198	+	21.2427i	0.254808	+	0.950956i	0.968197	+	0.250188i	$0.0804924\pi$
$499$	5.69198	+	21.2427i	0.254808	+	0.950956i	−0.713389	+	0.700768i	$0.752841\pi$
$500$	−1.09220	+	4.07615i	−0.0488447	+	0.182291i
$501$	−1.96560	+	7.33572i	−0.0878165	+	0.327736i
$502$	10.7677	+	40.1855i	0.480585	+	1.79357i
$503$			1.12263i			0.0500556i	0.999687	+	0.0250278i	$0.00796742\pi$
$503$			1.12263i			0.0500556i	−0.999687	+	0.0250278i	$0.992033\pi$
$504$		0			0
$505$	0.580663	+	0.580663i	0.0258392	+	0.0258392i
$506$	−5.37335	−	3.10230i	−0.238875	−	0.137914i
$507$	11.2437	+	2.40687i	0.499350	+	0.106893i
$508$	1.03829	+	1.79838i	0.0460669	+	0.0797902i
$509$	18.5635	−	4.97409i	0.822815	−	0.220473i	0.177238	−	0.984168i	$-0.443284\pi$
$509$	18.5635	−	4.97409i	0.822815	−	0.220473i	0.645577	+	0.763695i	$0.276617\pi$
$510$			6.99997i			0.309964i
$511$		0			0
$512$	12.9970	−	12.9970i	0.574390	−	0.574390i
$513$	−3.82398	−	14.2713i	−0.168833	−	0.630092i
$514$	20.2280	+	5.42008i	0.892219	+	0.239069i
$515$	−16.6088	+	61.9848i	−0.731870	+	2.73137i
$516$	−1.76433	−	1.01864i	−0.0776703	−	0.0448430i
$517$	25.8099			1.13512
$518$		0			0
$519$		−	3.14197i		−	0.137917i
$520$	23.7513	+	29.3736i	1.04156	+	1.28812i
$521$	−19.3198	+	11.1543i	−0.846416	+	0.488678i	−0.859440	−	0.511237i	$-0.829187\pi$
$521$	−19.3198	+	11.1543i	−0.846416	+	0.488678i	0.0130243	+	0.999915i	$0.495854\pi$
$522$	29.6930	+	7.95620i	1.29963	+	0.348234i
$523$	−15.3793	−	8.87924i	−0.672489	−	0.388262i	0.124530	−	0.992216i	$-0.460258\pi$
$523$	−15.3793	−	8.87924i	−0.672489	−	0.388262i	−0.797019	+	0.603954i	$0.793591\pi$
$524$	3.48835			0.152389
$525$		0			0
$526$	−23.4095	+	23.4095i	−1.02070	+	1.02070i
$527$	−11.1857	+	2.99720i	−0.487257	+	0.130560i
$528$	9.68774	+	2.59582i	0.421605	+	0.112969i
$529$	−10.2067	−	17.6785i	−0.443768	−	0.768628i
$530$	8.79620	−	15.2355i	0.382082	−	0.661786i
$531$	0.406313	−	0.406313i	0.0176325	−	0.0176325i
$532$		0			0
$533$	4.44408	+	10.0010i	0.192494	+	0.433190i
$534$	−4.84933	+	8.39929i	−0.209851	+	0.363473i
$535$	−17.3228	+	64.6497i	−0.748931	+	2.79505i
$536$	1.40467	+	2.43296i	0.0606725	+	0.105088i
$537$	−7.61914	+	13.1967i	−0.328790	+	0.569482i
$538$	−12.4059	−	12.4059i	−0.534854	−	0.534854i
$539$		0			0
$540$	−2.55337	−	2.55337i	−0.109879	−	0.109879i
$541$	−12.8109	+	3.43267i	−0.550783	+	0.147582i	−0.523468	−	0.852045i	$-0.675362\pi$
$541$	−12.8109	+	3.43267i	−0.550783	+	0.147582i	−0.0273145	+	0.999627i	$0.508696\pi$
$542$	6.34848	−	3.66530i	0.272691	−	0.157438i
$543$	−4.76348	+	2.75019i	−0.204420	+	0.118022i
$544$	−0.395706	−	1.47680i	−0.0169658	−	0.0633171i
$545$	27.5124			1.17850
$546$		0			0
$547$	−14.0683			−0.601515			−0.300757	−	0.953701i	$-0.597239\pi$
$547$	−14.0683			−0.601515			−0.300757	+	0.953701i	$0.597239\pi$
$548$	−1.03908	−	3.87788i	−0.0443871	−	0.165655i
$549$	−0.640195	+	0.369617i	−0.0273229	+	0.0157749i
$550$	−34.7236	+	20.0477i	−1.48062	+	0.854835i
$551$	−28.9034	+	7.74464i	−1.23133	+	0.329933i
$552$	−2.68607	−	2.68607i	−0.114327	−	0.114327i
$553$		0			0
$554$	0.884579	+	0.884579i	0.0375822	+	0.0375822i
$555$	8.35532	−	14.4718i	0.354664	−	0.614295i
$556$	1.46161	+	2.53158i	0.0619861	+	0.107363i
$557$	−4.39869	+	16.4161i	−0.186379	+	0.695574i	0.807953	+	0.589247i	$0.200576\pi$
$557$	−4.39869	+	16.4161i	−0.186379	+	0.695574i	−0.994331	+	0.106327i	$0.966091\pi$
$558$	14.0011	−	24.2505i	0.592712	−	1.02661i
$559$	14.9513	−	38.8656i	0.632371	−	1.64384i
$560$		0			0
$561$	−2.21283	+	2.21283i	−0.0934260	+	0.0934260i
$562$	−7.13128	+	12.3517i	−0.300815	+	0.521026i
$563$	−8.62337	−	14.9361i	−0.363432	−	0.629482i	0.625091	−	0.780552i	$-0.285062\pi$
$563$	−8.62337	−	14.9361i	−0.363432	−	0.629482i	−0.988523	+	0.151069i	$0.951728\pi$
$564$	−1.69056	−	0.452983i	−0.0711853	−	0.0190740i
$565$	17.3184	−	4.64045i	0.728590	−	0.195225i
$566$	20.7884	−	20.7884i	0.873800	−	0.873800i
$567$		0			0
$568$	1.26037			0.0528840
$569$	13.5496	+	7.82285i	0.568028	+	0.327951i	0.756361	−	0.654154i	$-0.226975\pi$
$569$	13.5496	+	7.82285i	0.568028	+	0.327951i	−0.188333	+	0.982105i	$0.560309\pi$
$570$	15.9150	+	4.26441i	0.666605	+	0.178616i
$571$	−10.5267	+	6.07757i	−0.440527	+	0.254338i	−0.703821	−	0.710377i	$-0.748524\pi$
$571$	−10.5267	+	6.07757i	−0.440527	+	0.254338i	0.263294	+	0.964716i	$0.415191\pi$
$572$	0.196858	−	1.86008i	0.00823105	−	0.0777740i
$573$		−	10.8858i		−	0.454760i
$574$		0			0
$575$	16.7156			0.697089
$576$	−13.5421	−	7.81853i	−0.564253	−	0.325772i
$577$	10.1232	−	37.7804i	0.421435	−	1.57282i	−0.350151	−	0.936693i	$-0.613870\pi$
$577$	10.1232	−	37.7804i	0.421435	−	1.57282i	0.771586	−	0.636125i	$-0.219464\pi$
$578$	−21.7026	−	5.81521i	−0.902711	−	0.241881i
$579$	−4.91161	−	18.3304i	−0.204120	−	0.761785i
$580$	−5.17130	+	5.17130i	−0.214726	+	0.214726i
$581$		0			0
$582$		−	13.8369i		−	0.573556i
$583$	7.59690	−	2.03558i	0.314632	−	0.0843053i
$584$	11.2140	+	19.4232i	0.464037	+	0.803736i
$585$	18.4579	−	25.3667i	0.763141	−	1.04878i
$586$	11.7647	+	6.79237i	0.485996	+	0.280590i
$587$	6.17868	+	6.17868i	0.255021	+	0.255021i	0.823026	−	0.568004i	$-0.192284\pi$
$587$	6.17868	+	6.17868i	0.255021	+	0.255021i	−0.568004	+	0.823026i	$0.692284\pi$
$588$		0			0
$589$			27.2575i			1.12313i
$590$	0.390207	+	1.45627i	0.0160646	+	0.0599538i
$591$	−0.461345	+	1.72176i	−0.0189772	+	0.0708239i
$592$	−5.43281	+	20.2755i	−0.223287	+	0.833320i
$593$	−8.75200	−	32.6629i	−0.359402	−	1.34130i	−0.874854	−	0.484387i	$-0.839043\pi$
$593$	−8.75200	−	32.6629i	−0.359402	−	1.34130i	0.515453	−	0.856918i	$-0.327624\pi$
$594$		−	17.8039i		−	0.730502i
$595$		0			0
$596$	−3.08397	−	3.08397i	−0.126324	−	0.126324i
$597$	−5.11400	−	2.95257i	−0.209302	−	0.120841i
$598$	−5.05996	+	6.95390i	−0.206917	+	0.284366i
$599$	−5.13357	−	8.89161i	−0.209752	−	0.363301i	0.741884	−	0.670528i	$-0.233932\pi$
$599$	−5.13357	−	8.89161i	−0.209752	−	0.363301i	−0.951636	+	0.307227i	$0.900599\pi$
$600$	−23.7113	+	6.35342i	−0.968009	+	0.259377i
$601$		−	4.09959i		−	0.167226i	−0.996498	−	0.0836128i	$-0.973354\pi$
$601$		−	4.09959i		−	0.167226i	0.996498	−	0.0836128i	$-0.0266459\pi$
$602$		0			0
$603$	1.64976	−	1.64976i	0.0671835	−	0.0671835i
$604$	0.698368	+	2.60634i	0.0284162	+	0.106051i
$605$	16.0432	+	4.29875i	0.652247	+	0.174769i
$606$	0.0710593	−	0.265197i	0.00288658	−	0.0107729i
$607$	6.28556	+	3.62897i	0.255123	+	0.147295i	0.622108	−	0.782932i	$-0.286277\pi$
$607$	6.28556	+	3.62897i	0.255123	+	0.147295i	−0.366985	+	0.930227i	$0.619610\pi$
$608$	−3.59867			−0.145946
$609$		0			0
$610$		−	1.93957i		−	0.0785308i
$611$	3.76507	−	35.5756i	0.152318	−	1.43923i
$612$	−0.520955	+	0.300773i	−0.0210583	+	0.0121580i
$613$	−20.8038	−	5.57436i	−0.840257	−	0.225146i	−0.187073	−	0.982346i	$-0.559900\pi$
$613$	−20.8038	−	5.57436i	−0.840257	−	0.225146i	−0.653183	+	0.757200i	$0.726567\pi$
$614$	32.6012	+	18.8223i	1.31568	+	0.759606i
$615$	−10.5332			−0.424740
$616$		0			0
$617$	−28.5301	+	28.5301i	−1.14858	+	1.14858i	−0.161748	+	0.986832i	$0.551713\pi$
$617$	−28.5301	+	28.5301i	−1.14858	+	1.14858i	−0.986832	+	0.161748i	$0.948287\pi$
$618$	20.7238	−	5.55294i	0.833635	−	0.223372i
$619$	−33.2819	−	8.91786i	−1.33771	−	0.358439i	−0.482128	−	0.876101i	$-0.660136\pi$
$619$	−33.2819	−	8.91786i	−1.33771	−	0.358439i	−0.855585	+	0.517662i	$0.826803\pi$
$620$	3.33093	+	5.76934i	0.133773	+	0.231702i
$621$	−3.71119	+	6.42797i	−0.148925	+	0.257946i
$622$	14.1348	−	14.1348i	0.566754	−	0.566754i
$623$		0			0
$624$	4.99121	−	12.9746i	0.199808	−	0.519400i
$625$	15.5266	−	26.8929i	0.621065	−	1.07572i
$626$	−2.48890	+	9.28871i	−0.0994766	+	0.371252i
$627$	3.68299	+	6.37912i	0.147084	+	0.254758i
$628$	−1.28243	+	2.22123i	−0.0511744	+	0.0886366i
$629$	−4.63126	−	4.63126i	−0.184660	−	0.184660i
$630$		0			0
$631$	−26.1762	−	26.1762i	−1.04206	−	1.04206i	−0.999076	−	0.0429839i	$-0.986314\pi$
$631$	−26.1762	−	26.1762i	−1.04206	−	1.04206i	−0.0429839	−	0.999076i	$-0.513686\pi$
$632$	7.48844	−	2.00652i	0.297874	−	0.0798151i
$633$	−14.5459	+	8.39809i	−0.578148	+	0.333794i
$634$	−40.2062	+	23.2130i	−1.59679	+	0.921907i
$635$	−10.5735	−	39.4610i	−0.419598	−	1.56596i
$636$	−0.533325			−0.0211477
$637$		0			0
$638$	−36.0579			−1.42755
$639$	−0.270911	−	1.01105i	−0.0107171	−	0.0399966i
$640$	43.1698	−	24.9241i	1.70644	−	0.985212i
$641$	−10.1134	+	5.83896i	−0.399454	+	0.230625i	−0.686248	−	0.727367i	$-0.740744\pi$
$641$	−10.1134	+	5.83896i	−0.399454	+	0.230625i	0.286794	+	0.957992i	$0.407410\pi$
$642$	21.6148	−	5.79167i	0.853069	−	0.228579i
$643$	12.8214	+	12.8214i	0.505627	+	0.505627i	0.913181	−	0.407554i	$-0.133618\pi$
$643$	12.8214	+	12.8214i	0.505627	+	0.505627i	−0.407554	+	0.913181i	$0.633618\pi$
$644$		0			0
$645$	28.3405	+	28.3405i	1.11591	+	1.11591i
$646$	3.22889	−	5.59260i	0.127039	−	0.220038i
$647$	5.73484	+	9.93304i	0.225460	+	0.390508i	0.956457	−	0.291872i	$-0.0942782\pi$
$647$	5.73484	+	9.93304i	0.225460	+	0.390508i	−0.730997	+	0.682380i	$0.760945\pi$
$648$	−1.77695	+	6.63165i	−0.0698050	+	0.260516i
$649$	−0.337005	+	0.583711i	−0.0132286	+	0.0229126i
$650$	22.5677	+	50.7864i	0.885178	+	1.99200i
$651$		0			0
$652$	−1.51064	+	1.51064i	−0.0591614	+	0.0591614i
$653$	4.47691	−	7.75423i	0.175195	−	0.303446i	−0.765034	−	0.643990i	$-0.777278\pi$
$653$	4.47691	−	7.75423i	0.175195	−	0.303446i	0.940229	+	0.340544i	$0.110611\pi$
$654$	−4.59922	−	7.96608i	−0.179844	−	0.311498i
$655$	−66.2883	−	17.7619i	−2.59010	−	0.694014i
$656$	12.7803	−	3.42446i	0.498986	−	0.133703i
$657$	13.1706	−	13.1706i	0.513835	−	0.513835i
$658$		0			0
$659$	22.2313			0.866009			0.433005	−	0.901392i	$-0.357453\pi$
$659$	22.2313			0.866009			0.433005	+	0.901392i	$0.357453\pi$
$660$	1.55909	+	0.900139i	0.0606874	+	0.0350379i
$661$	−2.37521	−	0.636436i	−0.0923850	−	0.0247545i	0.212330	−	0.977198i	$-0.431895\pi$
$661$	−2.37521	−	0.636436i	−0.0923850	−	0.0247545i	−0.304715	+	0.952443i	$0.598561\pi$
$662$	−16.0753	+	9.28107i	−0.624784	+	0.360719i
$663$	2.72730	+	3.37290i	0.105920	+	0.130993i
$664$		−	14.5230i		−	0.563600i
$665$		0			0
$666$	15.8374			0.613688
$667$	13.0185	+	7.51622i	0.504077	+	0.291029i
$668$	0.443192	−	1.65401i	0.0171476	−	0.0639957i
$669$	−2.47045	−	0.661955i	−0.0955132	−	0.0255927i
$670$	1.58437	+	5.91294i	0.0612094	+	0.228437i
$671$	0.613137	−	0.613137i	0.0236699	−	0.0236699i
$672$		0			0
$673$		−	6.44000i		−	0.248244i	−0.992267	−	0.124122i	$-0.960389\pi$
$673$		−	6.44000i		−	0.248244i	0.992267	−	0.124122i	$-0.0396114\pi$
$674$	−6.50861	+	1.74398i	−0.250702	+	0.0671755i
$675$	23.9824	+	41.5387i	0.923083	+	1.59883i
$676$	−2.53516	−	0.542686i	−0.0975063	−	0.0208725i
$677$	−4.00871	−	2.31443i	−0.154067	−	0.0889507i	0.420984	−	0.907068i	$-0.361685\pi$
$677$	−4.00871	−	2.31443i	−0.154067	−	0.0889507i	−0.575052	+	0.818117i	$0.695018\pi$
$678$	−4.23871	−	4.23871i	−0.162787	−	0.162787i
$679$		0			0
$680$			14.2499i			0.546458i
$681$	−1.50259	−	5.60775i	−0.0575795	−	0.214889i
$682$	−8.50116	+	31.7268i	−0.325526	+	1.21488i
$683$	4.69368	−	17.5171i	0.179599	−	0.670272i	−0.816124	−	0.577877i	$-0.803881\pi$
$683$	4.69368	−	17.5171i	0.179599	−	0.670272i	0.995722	−	0.0923945i	$-0.0294521\pi$
$684$	0.366464	+	1.36766i	0.0140121	+	0.0522939i
$685$			78.9813i			3.01772i
$686$		0			0
$687$	−0.892011	−	0.892011i	−0.0340323	−	0.0340323i
$688$	−43.6002	−	25.1726i	−1.66224	−	0.959697i
$689$	−1.69757	−	10.7683i	−0.0646724	−	0.410238i
$690$	−4.13863	−	7.16832i	−0.157555	−	0.272893i
$691$	−0.596708	+	0.159887i	−0.0226998	+	0.00608240i	−0.270151	−	0.962818i	$-0.587074\pi$
$691$	−0.596708	+	0.159887i	−0.0226998	+	0.00608240i	0.247451	+	0.968900i	$0.420407\pi$
$692$			0.708433i			0.0269306i
$693$		0			0
$694$	11.6747	−	11.6747i	0.443166	−	0.443166i
$695$	−14.8844	−	55.5493i	−0.564597	−	2.10711i
$696$	−21.3237	−	5.71366i	−0.808271	−	0.216576i
$697$	−1.06851	+	3.98773i	−0.0404726	+	0.151046i
$698$	−30.3436	−	17.5189i	−1.14852	−	0.663101i
$699$	7.51309			0.284171
$700$		0			0
$701$		−	14.4452i		−	0.545586i	−0.962073	−	0.272793i	$-0.912053\pi$
$701$		−	14.4452i		−	0.545586i	0.962073	−	0.272793i	$-0.0879474\pi$
$702$	−24.5403	−	2.59717i	−0.926214	−	0.0980239i
$703$	−13.3509	+	7.70815i	−0.503539	+	0.290718i
$704$	17.7170	+	4.74725i	0.667734	+	0.178919i
$705$	29.8188	+	17.2159i	1.12304	+	0.648388i
$706$	9.08287			0.341838
$707$		0			0
$708$	0.0323185	−	0.0323185i	0.00121460	−	0.00121460i
$709$	−3.17903	+	0.851819i	−0.119391	+	0.0319907i	−0.318020	−	0.948084i	$-0.603018\pi$
$709$	−3.17903	+	0.851819i	−0.119391	+	0.0319907i	0.198629	+	0.980075i	$0.436351\pi$
$710$	2.65275	+	0.710803i	0.0995561	+	0.0266760i
$711$	−3.21921	−	5.57583i	−0.120730	−	0.209110i
$712$	−9.87181	+	17.0985i	−0.369962	+	0.640792i
$713$	9.68268	−	9.68268i	0.362619	−	0.362619i
$714$		0			0
$715$	−13.2120	+	34.3444i	−0.494100	+	1.28441i
$716$	1.71792	−	2.97552i	0.0642016	−	0.111201i
$717$	−1.50481	+	5.61603i	−0.0561982	+	0.209734i
$718$	16.1290	+	27.9363i	0.601930	+	1.04257i
$719$	−24.6176	+	42.6390i	−0.918083	+	1.59017i	−0.115760	+	0.993277i	$0.536930\pi$
$719$	−24.6176	+	42.6390i	−0.918083	+	1.59017i	−0.802323	+	0.596890i	$0.796403\pi$
$720$	−26.8190	−	26.8190i	−0.999485	−	0.999485i
$721$		0			0
$722$	9.17662	+	9.17662i	0.341518	+	0.341518i
$723$	−9.21401	+	2.46889i	−0.342673	+	0.0918188i
$724$	1.07404	−	0.620097i	0.0399164	−	0.0230457i
$725$	84.1277	−	48.5712i	3.12443	−	1.80389i
$726$	−1.43723	−	5.36383i	−0.0533408	−	0.199070i
$727$	−34.0096			−1.26135			−0.630674	−	0.776048i	$-0.717221\pi$
$727$	−34.0096			−1.26135			−0.630674	+	0.776048i	$0.717221\pi$
$728$		0			0
$729$	−6.54406			−0.242372
$730$	12.6485	+	47.2050i	0.468144	+	1.74714i
$731$	13.6042	−	7.85441i	0.503171	−	0.290506i
$732$	−0.0509216	+	0.0293996i	−0.00188212	+	0.00108664i
$733$	−36.2160	+	9.70406i	−1.33767	+	0.358428i	−0.855569	−	0.517688i	$-0.826793\pi$
$733$	−36.2160	+	9.70406i	−1.33767	+	0.358428i	−0.482101	+	0.876116i	$0.660126\pi$
$734$	17.0423	+	17.0423i	0.629042	+	0.629042i
$735$		0			0
$736$	1.27836	+	1.27836i	0.0471208	+	0.0471208i
$737$	−1.36835	+	2.37005i	−0.0504038	+	0.0873020i
$738$	−4.99140	−	8.64536i	−0.183736	−	0.318240i
$739$	1.10850	−	4.13697i	0.0407767	−	0.152181i	−0.942536	−	0.334105i	$-0.891566\pi$
$739$	1.10850	−	4.13697i	0.0407767	−	0.152181i	0.983313	+	0.181924i	$0.0582326\pi$
$740$	−1.88391	+	3.26302i	−0.0692538	+	0.119951i
$741$	9.33004	−	4.14595i	0.342748	−	0.152305i
$742$		0			0
$743$	−25.3436	+	25.3436i	−0.929767	+	0.929767i	−0.997691	−	0.0679234i	$-0.978363\pi$
$743$	−25.3436	+	25.3436i	−0.929767	+	0.929767i	0.0679234	+	0.997691i	$0.478363\pi$
$744$	−10.0547	+	17.4153i	−0.368623	+	0.638474i
$745$	42.9011	+	74.3069i	1.57177	+	2.72239i
$746$	6.03899	+	1.61814i	0.221103	+	0.0592444i
$747$	−11.6501	+	3.12164i	−0.426256	+	0.114215i
$748$	0.498937	−	0.498937i	0.0182429	−	0.0182429i
$749$		0			0
$750$	−27.7565			−1.01352
$751$	39.9450	+	23.0623i	1.45761	+	0.841554i	0.998894	−	0.0470273i	$-0.0149748\pi$
$751$	39.9450	+	23.0623i	1.45761	+	0.841554i	0.458720	+	0.888581i	$0.348308\pi$
$752$	−41.7771	−	11.1941i	−1.52346	−	0.408209i
$753$	−21.4880	+	12.4061i	−0.783067	+	0.452104i
$754$	−5.26001	+	49.7011i	−0.191558	+	1.81001i
$755$		−	53.0837i		−	1.93191i
$756$		0			0
$757$	−38.5756			−1.40205			−0.701027	−	0.713135i	$-0.747275\pi$
$757$	−38.5756			−1.40205			−0.701027	+	0.713135i	$0.747275\pi$
$758$	−32.9315	−	19.0130i	−1.19612	−	0.690583i
$759$	0.957747	−	3.57436i	0.0347640	−	0.129741i
$760$	32.3982	+	8.68107i	1.17521	+	0.314896i
$761$	2.57337	+	9.60394i	0.0932845	+	0.348142i	0.996754	−	0.0805104i	$-0.0256550\pi$
$761$	2.57337	+	9.60394i	0.0932845	+	0.348142i	−0.903469	+	0.428653i	$0.858988\pi$
$762$	−9.65816	+	9.65816i	−0.349878	+	0.349878i
$763$		0			0
$764$			2.45446i			0.0887993i
$765$	11.4311	−	3.06294i	0.413291	−	0.110741i
$766$	−17.4036	−	30.1439i	−0.628818	−	1.08914i
$767$	0.755407	+	0.549667i	0.0272762	+	0.0198473i
$768$	−3.63106	−	2.09640i	−0.131025	−	0.0756472i
$769$	28.4649	+	28.4649i	1.02647	+	1.02647i	0.999640	+	0.0268295i	$0.00854111\pi$
$769$	28.4649	+	28.4649i	1.02647	+	1.02647i	0.0268295	+	0.999640i	$0.491459\pi$
$770$		0			0
$771$			12.4896i			0.449803i
$772$	1.10744	+	4.13302i	0.0398577	+	0.148751i
$773$	−6.61690	+	24.6946i	−0.237993	+	0.888203i	0.738783	+	0.673943i	$0.235401\pi$
$773$	−6.61690	+	24.6946i	−0.237993	+	0.888203i	−0.976777	+	0.214260i	$0.931266\pi$
$774$	−9.83129	+	36.6909i	−0.353379	+	1.31883i
$775$	−22.9027	−	85.4739i	−0.822688	−	3.07031i
$776$		−	28.1677i		−	1.01116i
$777$		0			0
$778$	−20.4214	−	20.4214i	−0.732141	−	0.732141i
$779$	8.41547	+	4.85867i	0.301515	+	0.174080i
$780$	1.46816	−	2.01769i	0.0525685	−	0.0722448i
$781$	0.613891	+	1.06329i	0.0219667	+	0.0380475i
$782$	−3.13366	+	0.839661i	−0.112059	+	0.0300262i
$783$			43.1350i			1.54152i
$784$		0			0
$785$	35.6797	−	35.6797i	1.27346	−	1.27346i
$786$	5.93847	+	22.1627i	0.211818	+	0.790516i
$787$	−17.5248	−	4.69577i	−0.624693	−	0.167386i	−0.0674326	−	0.997724i	$-0.521481\pi$
$787$	−17.5248	−	4.69577i	−0.624693	−	0.167386i	−0.557260	+	0.830338i	$0.688147\pi$
$788$	0.104021	−	0.388213i	0.00370561	−	0.0138295i
$789$	−17.0993	−	9.87229i	−0.608751	−	0.351463i
$790$	16.8928			0.601020
$791$		0			0
$792$		−	15.4046i		−	0.547378i
$793$	−0.755686	−	0.934571i	−0.0268352	−	0.0331876i
$794$	−15.3597	+	8.86791i	−0.545094	+	0.314710i
$795$	10.1347	+	2.71557i	0.359439	+	0.0963114i
$796$	1.15307	+	0.665728i	0.0408696	+	0.0235961i
$797$	6.98547			0.247438			0.123719	−	0.992317i	$-0.460518\pi$
$797$	6.98547			0.247438			0.123719	+	0.992317i	$0.460518\pi$
$798$		0			0
$799$	9.54256	−	9.54256i	0.337592	−	0.337592i
$800$	11.2847	−	3.02373i	0.398975	−	0.106905i
$801$	15.8381	+	4.24380i	0.559611	+	0.149947i
$802$	−6.96815	−	12.0692i	−0.246054	−	0.426178i
$803$	−10.9240	+	18.9209i	−0.385500	+	0.667706i
$804$	0.131223	−	0.131223i	0.00462789	−	0.00462789i
$805$		0			0
$806$	42.4910	+	16.3459i	1.49668	+	0.575761i
$807$	5.23181	−	9.06176i	0.184168	−	0.318989i
$808$	0.144656	−	0.539862i	0.00508897	−	0.0189923i
$809$	−1.00660	−	1.74348i	−0.0353902	−	0.0612976i	0.847788	−	0.530336i	$-0.177934\pi$
$809$	−1.00660	−	1.74348i	−0.0353902	−	0.0612976i	−0.883178	+	0.469038i	$0.844601\pi$
$810$	−7.48003	+	12.9558i	−0.262821	+	0.455220i
$811$	−19.2255	−	19.2255i	−0.675097	−	0.675097i	0.283790	−	0.958887i	$-0.408408\pi$
$811$	−19.2255	−	19.2255i	−0.675097	−	0.675097i	−0.958887	+	0.283790i	$0.908408\pi$
$812$		0			0
$813$	3.09147	+	3.09147i	0.108422	+	0.108422i
$814$	−17.9440	+	4.80809i	−0.628938	+	0.168523i
$815$	36.3983	−	21.0146i	1.27498	−	0.736109i
$816$	4.54153	−	2.62206i	0.158985	−	0.0917903i
$817$	−9.56987	−	35.7152i	−0.334807	−	1.24952i
$818$	−28.6294			−1.00100
$819$		0			0
$820$	2.37497			0.0829374
$821$	2.49536	+	9.31280i	0.0870885	+	0.325019i	0.995702	−	0.0926203i	$-0.0295243\pi$
$821$	2.49536	+	9.31280i	0.0870885	+	0.325019i	−0.908613	+	0.417639i	$0.862858\pi$
$822$	22.8686	−	13.2032i	0.797635	−	0.460515i
$823$	15.6607	−	9.04171i	0.545898	−	0.315174i	−0.201568	−	0.979475i	$-0.564604\pi$
$823$	15.6607	−	9.04171i	0.545898	−	0.315174i	0.747466	+	0.664300i	$0.231270\pi$
$824$	42.1876	−	11.3041i	1.46967	−	0.393798i
$825$	−16.9090	−	16.9090i	−0.588697	−	0.588697i
$826$		0			0
$827$	12.8291	+	12.8291i	0.446111	+	0.446111i	0.894059	−	0.447949i	$-0.147845\pi$
$827$	12.8291	+	12.8291i	0.446111	+	0.446111i	−0.447949	+	0.894059i	$0.647845\pi$
$828$	0.355656	−	0.616014i	0.0123599	−	0.0214080i
$829$	−14.1033	−	24.4277i	−0.489829	−	0.848409i	0.510102	−	0.860114i	$-0.329608\pi$
$829$	−14.1033	−	24.4277i	−0.489829	−	0.848409i	−0.999931	+	0.0117047i	$0.996274\pi$
$830$	8.19043	−	30.5671i	0.284294	−	1.06100i
$831$	−0.373046	+	0.646134i	−0.0129408	+	0.0224141i
$832$	9.12795	−	23.7280i	0.316455	−	0.822621i
$833$		0			0
$834$	−13.5958	+	13.5958i	−0.470785	+	0.470785i
$835$	−16.8438	+	29.1742i	−0.582902	+	1.00962i
$836$	−0.830418	−	1.43833i	−0.0287206	−	0.0497455i
$837$	37.9537	+	10.1697i	1.31187	+	0.351515i
$838$	−34.6620	+	9.28767i	−1.19738	+	0.320837i
$839$	−7.67294	+	7.67294i	−0.264899	+	0.264899i	−0.827041	−	0.562142i	$-0.809978\pi$
$839$	−7.67294	+	7.67294i	−0.264899	+	0.264899i	0.562142	+	0.827041i	$0.309978\pi$
$840$		0			0
$841$	58.3606			2.01243
$842$	30.8548	+	17.8140i	1.06333	+	0.613912i
$843$	−8.21639	−	2.20158i	−0.282988	−	0.0758263i
$844$	3.27973	−	1.89355i	0.112893	−	0.0651787i
$845$	45.4119	+	23.2210i	1.56222	+	0.798828i
$846$			32.6326i			1.12193i
$847$		0			0
$848$	−13.1796			−0.452588
$849$	15.1847	+	8.76689i	0.521137	+	0.300879i
$850$	−5.42604	+	20.2503i	−0.186112	+	0.694579i
$851$	7.48080	+	2.00448i	0.256439	+	0.0687125i
$852$	−0.0215485	−	0.0804200i	−0.000738238	−	0.00275514i
$853$	−10.4908	+	10.4908i	−0.359198	+	0.359198i	−0.863517	−	0.504319i	$-0.831744\pi$
$853$	−10.4908	+	10.4908i	−0.359198	+	0.359198i	0.504319	+	0.863517i	$0.331744\pi$
$854$		0			0
$855$		−	27.8554i		−	0.952634i
$856$	44.0014	−	11.7901i	1.50394	−	0.402979i
$857$	−8.61727	−	14.9255i	−0.294360	−	0.509847i	0.680476	−	0.732771i	$-0.261773\pi$
$857$	−8.61727	−	14.9255i	−0.294360	−	0.509847i	−0.974836	+	0.222924i	$0.928440\pi$
$858$	12.1529	−	1.91585i	0.414892	−	0.0654061i
$859$	32.5438	+	18.7892i	1.11038	+	0.641079i	0.938928	−	0.344113i	$-0.111820\pi$
$859$	32.5438	+	18.7892i	1.11038	+	0.641079i	0.171453	+	0.985192i	$0.445154\pi$
$860$	−6.39005	−	6.39005i	−0.217899	−	0.217899i
$861$		0			0
$862$		−	40.7133i		−	1.38670i
$863$	0.319657	+	1.19297i	0.0108812	+	0.0406093i	0.971153	−	0.238457i	$-0.0766417\pi$
$863$	0.319657	+	1.19297i	0.0108812	+	0.0406093i	−0.960272	+	0.279067i	$0.909975\pi$
$864$	−1.34265	+	5.01085i	−0.0456779	+	0.170472i
$865$	3.60719	−	13.4622i	0.122648	−	0.457729i
$866$	−9.99026	−	37.2842i	−0.339483	−	1.26697i
$867$		−	13.4001i		−	0.455092i
$868$		0			0
$869$	5.34017	+	5.34017i	0.181153	+	0.181153i
$870$	−41.6585	−	24.0515i	−1.41236	−	0.815424i
$871$	3.06719	+	2.23183i	0.103928	+	0.0756225i
$872$	−9.36265	−	16.2166i	−0.317059	−	0.549163i
$873$	−22.5958	+	6.05452i	−0.764752	+	0.204915i
$874$			7.63614i			0.258296i
$875$		0			0
$876$	1.04760	−	1.04760i	0.0353952	−	0.0353952i
$877$	−12.2540	−	45.7327i	−0.413789	−	1.54428i	−0.787249	−	0.616636i	$-0.788495\pi$
$877$	−12.2540	−	45.7327i	−0.413789	−	1.54428i	0.373460	−	0.927646i	$-0.378171\pi$
$878$	−5.30810	−	1.42230i	−0.179140	−	0.0480004i
$879$	−2.09695	+	7.82591i	−0.0707283	+	0.263962i
$880$	38.5282	+	22.2443i	1.29879	+	0.749855i
$881$	−25.5041			−0.859255			−0.429627	−	0.903006i	$-0.641355\pi$
$881$	−25.5041			−0.859255			−0.429627	+	0.903006i	$0.641355\pi$
$882$		0			0
$883$			34.7968i			1.17101i	0.810670	+	0.585503i	$0.199103\pi$
$883$			34.7968i			1.17101i	−0.810670	+	0.585503i	$0.800897\pi$
$884$	−0.614935	−	0.760502i	−0.0206825	−	0.0255784i
$885$	−0.778700	+	0.449582i	−0.0261757	+	0.0151125i
$886$	3.85071	+	1.03180i	0.129367	+	0.0346638i
$887$	39.3189	+	22.7008i	1.32020	+	0.762217i	0.983760	−	0.179488i	$-0.0574441\pi$
$887$	39.3189	+	22.7008i	1.32020	+	0.762217i	0.336439	+	0.941705i	$0.390777\pi$
$888$	−11.3735			−0.381669
$889$		0			0
$890$	−30.4205	+	30.4205i	−1.01970	+	1.01970i
$891$	−6.46018	+	1.73100i	−0.216424	+	0.0579907i
$892$	0.557023	+	0.149254i	0.0186505	+	0.00499739i
$893$	−15.8824	−	27.5091i	−0.531484	−	0.920558i
$894$	14.3434	−	24.8436i	0.479717	−	0.830894i
$895$	−47.7959	+	47.7959i	−1.59764	+	1.59764i
$896$		0			0
$897$	−4.78707	−	1.84154i	−0.159836	−	0.0614873i
$898$	25.8357	−	44.7488i	0.862149	−	1.49329i
$899$	20.5965	−	76.8671i	0.686931	−	2.56366i
$900$	−2.29831	−	3.98080i	−0.0766105	−	0.132693i
$901$	2.05616	−	3.56137i	0.0685005	−	0.118646i
$902$	8.27996	+	8.27996i	0.275693	+	0.275693i
$903$		0			0
$904$	−8.62877	−	8.62877i	−0.286989	−	0.286989i
$905$	−23.5671	+	6.31480i	−0.783398	+	0.209911i
$906$	−15.3701	+	8.87394i	−0.510638	+	0.294817i
$907$	0.0976763	−	0.0563935i	0.00324329	−	0.00187251i	−0.498377	−	0.866960i	$-0.666071\pi$
$907$	0.0976763	−	0.0563935i	0.00324329	−	0.00187251i	0.501621	+	0.865088i	$0.332737\pi$
$908$	0.338796	+	1.26440i	0.0112433	+	0.0419607i
$909$	−0.464163			−0.0153953
$910$		0			0
$911$	−0.606928			−0.0201084			−0.0100542	−	0.999949i	$-0.503200\pi$
$911$	−0.606928			−0.0201084			−0.0100542	+	0.999949i	$0.503200\pi$
$912$	−3.19473	−	11.9229i	−0.105788	−	0.394807i
$913$	12.2521	−	7.07372i	0.405484	−	0.234106i
$914$	8.75571	−	5.05511i	0.289613	−	0.167208i
$915$	1.11735	−	0.299393i	0.0369384	−	0.00989762i
$916$	0.201125	+	0.201125i	0.00664536	+	0.00664536i
$917$		0			0
$918$	−6.58253	−	6.58253i	−0.217256	−	0.217256i
$919$	−24.4824	+	42.4048i	−0.807600	+	1.39880i	0.106922	+	0.994267i	$0.465900\pi$
$919$	−24.4824	+	42.4048i	−0.807600	+	1.39880i	−0.914522	+	0.404536i	$0.867433\pi$
$920$	−8.42503	−	14.5926i	−0.277765	−	0.481103i
$921$	−5.81084	+	21.6863i	−0.191474	+	0.714589i
$922$	−5.31022	+	9.19757i	−0.174883	+	0.302906i
$923$	1.55516	−	0.691058i	0.0511886	−	0.0227465i
$924$		0			0
$925$	35.3890	−	35.3890i	1.16358	−	1.16358i
$926$	−15.5409	+	26.9176i	−0.510706	+	0.884568i
$927$	−18.1361	−	31.4126i	−0.595666	−	1.03172i
$928$	10.1484	+	2.71925i	0.333137	+	0.0892638i
$929$	15.1918	−	4.07062i	0.498426	−	0.133553i	−0.000843401	−	1.00000i	$-0.500268\pi$
$929$	15.1918	−	4.07062i	0.498426	−	0.133553i	0.499269	+	0.866447i	$0.333602\pi$
$930$	−30.9841	+	30.9841i	−1.01601	+	1.01601i
$931$		0			0
$932$	−1.69401			−0.0554890
$933$	10.3247	+	5.96094i	0.338014	+	0.195152i
$934$	−0.653962	−	0.175229i	−0.0213983	−	0.00573366i
$935$	−12.0217	+	6.94071i	−0.393150	+	0.226985i
$936$	−21.2332	−	2.24717i	−0.694028	−	0.0734510i
$937$			2.27169i			0.0742129i	0.999311	+	0.0371065i	$0.0118141\pi$
$937$			2.27169i			0.0742129i	−0.999311	+	0.0371065i	$0.988186\pi$
$938$		0			0
$939$	−5.73524			−0.187163
$940$	−6.72336	−	3.88173i	−0.219292	−	0.126608i
$941$	7.39357	−	27.5932i	0.241023	−	0.899512i	−0.734317	−	0.678807i	$-0.762498\pi$
$941$	7.39357	−	27.5932i	0.241023	−	0.899512i	0.975341	−	0.220705i	$-0.0708358\pi$
$942$	−16.2954	−	4.36634i	−0.530933	−	0.142263i
$943$	−1.26348	−	4.71537i	−0.0411446	−	0.153554i
$944$	0.798656	−	0.798656i	0.0259940	−	0.0259940i
$945$		0			0
$946$		−	44.5559i		−	1.44864i
$947$	0.735176	−	0.196990i	0.0238900	−	0.00640131i	−0.246854	−	0.969053i	$-0.579397\pi$
$947$	0.735176	−	0.196990i	0.0238900	−	0.00640131i	0.270744	+	0.962651i	$0.412730\pi$
$948$	−0.256059	−	0.443506i	−0.00831640	−	0.0144044i
$949$	24.4865	+	17.8174i	0.794864	+	0.578378i
$950$	42.7350	+	24.6731i	1.38651	+	0.800500i
$951$	−19.5788	−	19.5788i	−0.634887	−	0.634887i
$952$		0			0
$953$			7.93535i			0.257051i	0.991706	+	0.128526i	$0.0410244\pi$
$953$			7.93535i			0.257051i	−0.991706	+	0.128526i	$0.958976\pi$
$954$	2.57367	+	9.60507i	0.0833257	+	0.310976i
$955$	12.4976	−	46.6416i	0.404412	−	1.50929i
$956$	0.339296	−	1.26627i	0.0109736	−	0.0409540i
$957$	−5.56592	−	20.7723i	−0.179921	−	0.671473i
$958$		−	48.7364i		−	1.57460i
$959$		0			0
$960$	17.3023	+	17.3023i	0.558429	+	0.558429i
$961$	−35.9314	−	20.7450i	−1.15908	−	0.669194i
$962$	4.00970	+	25.4348i	0.129278	+	0.820052i
$963$	−18.9158	−	32.7631i	−0.609553	−	1.05578i
$964$	2.07752	−	0.556670i	0.0669124	−	0.0179291i
$965$		−	84.1778i		−	2.70978i
$966$		0			0
$967$	−1.26298	+	1.26298i	−0.0406147	+	0.0406147i	−0.727122	−	0.686508i	$-0.759143\pi$
$967$	−1.26298	+	1.26298i	−0.0406147	+	0.0406147i	0.686508	+	0.727122i	$0.259143\pi$
$968$	−2.92578	−	10.9192i	−0.0940383	−	0.350956i
$969$	3.72021	+	0.996826i	0.119510	+	0.0320227i
$970$	15.8856	−	59.2858i	0.510055	−	1.90355i
$971$	−0.300693	−	0.173605i	−0.00964970	−	0.00557126i	0.495167	−	0.868798i	$-0.335107\pi$
$971$	−0.300693	−	0.173605i	−0.00964970	−	0.00557126i	−0.504817	+	0.863226i	$0.668440\pi$
$972$	3.21464			0.103110
$973$		0			0
$974$			17.1431i			0.549299i
$975$	−25.7735	+	20.8402i	−0.825413	+	0.667422i
$976$	−1.25838	+	0.726525i	−0.0402797	+	0.0232555i
$977$	10.7627	+	2.88386i	0.344329	+	0.0922627i	0.426839	−	0.904328i	$-0.359627\pi$
$977$	10.7627	+	2.88386i	0.344329	+	0.0922627i	−0.0825101	+	0.996590i	$0.526294\pi$
$978$	−12.1693	−	7.02596i	−0.389132	−	0.224666i
$979$	−19.2331			−0.614693
$980$		0			0
$981$	−10.9963	+	10.9963i	−0.351084	+	0.351084i
$982$	−1.35606	+	0.363354i	−0.0432735	+	0.0115951i
$983$	−32.3796	−	8.67608i	−1.03275	−	0.276724i	−0.297643	−	0.954677i	$-0.596201\pi$
$983$	−32.3796	−	8.67608i	−1.03275	−	0.276724i	−0.735105	+	0.677953i	$0.762867\pi$
$984$	3.58452	+	6.20857i	0.114270	+	0.197922i
$985$	−3.95339	+	6.84747i	−0.125965	+	0.218178i
$986$	−13.3315	+	13.3315i	−0.424561	+	0.424561i
$987$		0			0
$988$	−2.10368	+	0.934803i	−0.0669270	+	0.0297400i
$989$	−9.28761	+	16.0866i	−0.295329	+	0.511525i
$990$	8.68762	−	32.4227i	0.276111	−	1.03046i
$991$	−17.8999	−	31.0035i	−0.568608	−	0.984858i	−0.996704	−	0.0811244i	$-0.974149\pi$
$991$	−17.8999	−	31.0035i	−0.568608	−	0.984858i	0.428096	−	0.903733i	$-0.359184\pi$
$992$	4.78525	−	8.28829i	0.151932	−	0.263154i
$993$	−7.82804	−	7.82804i	−0.248415	−	0.248415i
$994$		0			0
$995$	−18.5219	−	18.5219i	−0.587183	−	0.587183i
$996$	−0.926661	+	0.248298i	−0.0293624	+	0.00786763i
$997$	−53.9761	+	31.1631i	−1.70944	+	0.986946i	−0.774193	+	0.632949i	$0.781844\pi$
$997$	−53.9761	+	31.1631i	−1.70944	+	0.986946i	−0.935247	+	0.353996i	$0.884823\pi$
$998$	28.2457	−	16.3077i	0.894102	−	0.516210i
$999$	5.75176	+	21.4659i	0.181978	+	0.679150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.c.460.10		112
7.2	even	3		637.2.i.b.538.10	yes	56
7.3	odd	6	inner	637.2.bc.c.31.20		112
7.4	even	3	inner	637.2.bc.c.31.19		112
7.5	odd	6		637.2.i.b.538.9	yes	56
7.6	odd	2	inner	637.2.bc.c.460.9		112
13.8	odd	4	inner	637.2.bc.c.411.20		112
91.34	even	4	inner	637.2.bc.c.411.19		112
91.47	even	12		637.2.i.b.489.9	✓	56
91.60	odd	12	inner	637.2.bc.c.619.9		112
91.73	even	12	inner	637.2.bc.c.619.10		112
91.86	odd	12		637.2.i.b.489.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.i.b.489.9	✓	56	91.47	even	12
637.2.i.b.489.10	yes	56	91.86	odd	12
637.2.i.b.538.9	yes	56	7.5	odd	6
637.2.i.b.538.10	yes	56	7.2	even	3
637.2.bc.c.31.19		112	7.4	even	3	inner
637.2.bc.c.31.20		112	7.3	odd	6	inner
637.2.bc.c.411.19		112	91.34	even	4	inner
637.2.bc.c.411.20		112	13.8	odd	4	inner
637.2.bc.c.460.9		112	7.6	odd	2	inner
637.2.bc.c.460.10		112	1.1	even	1	trivial
637.2.bc.c.619.9		112	91.60	odd	12	inner
637.2.bc.c.619.10		112	91.73	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.383841 - 1.43251i) q^{2} +(0.765995 - 0.442247i) q^{3} +(-0.172712 + 0.0997153i) q^{4} +(3.78973 - 1.01546i) q^{5} +(-0.927546 - 0.927546i) q^{6} +(-1.88821 - 1.88821i) q^{8} +(-1.10883 + 1.92056i) q^{9} +(-2.90931 - 5.03907i) q^{10} +(0.673262 - 2.51265i) q^{11} +(-0.0881976 + 0.152763i) q^{12} +(-3.36514 - 1.29454i) q^{13} +(2.45383 - 2.45383i) q^{15} +(-2.17954 + 3.77508i) q^{16} +(-0.680066 - 1.17791i) q^{17} +(3.17684 + 0.851232i) q^{18} +(-3.09237 + 0.828597i) q^{19} +(-0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +(1.39284 + 0.804158i) q^{23} +(-2.28141 - 0.611303i) q^{24} +(9.00081 - 5.19662i) q^{25} +(-0.562767 + 5.31751i) q^{26} +4.61500i q^{27} +9.34669 q^{29} +(-4.45703 - 2.57327i) q^{30} +(2.20361 - 8.22399i) q^{31} +(1.08577 + 0.290932i) q^{32} +(-0.595497 - 2.22242i) q^{33} +(-1.42633 + 1.42633i) q^{34} -0.442271i q^{36} +(4.65133 - 1.24632i) q^{37} +(2.37395 + 4.11181i) q^{38} +(-3.15019 + 0.496614i) q^{39} +(-9.07320 - 5.23842i) q^{40} +(-2.14628 - 2.14628i) q^{41} +11.5495i q^{43} +(0.134269 + 0.501099i) q^{44} +(-2.25195 + 8.40438i) q^{45} +(0.617338 - 2.30394i) q^{46} +(2.56800 + 9.58391i) q^{47} +3.85559i q^{48} +(-10.8991 - 10.8991i) q^{50} +(-1.04185 - 0.601515i) q^{51} +(0.710285 - 0.111973i) q^{52} +(1.51173 + 2.61840i) q^{53} +(6.61105 - 1.77143i) q^{54} -10.2059i q^{55} +(-2.00229 + 2.00229i) q^{57} +(-3.58764 - 13.3893i) q^{58} +(-0.250278 - 0.0670618i) q^{59} +(-0.179122 + 0.668491i) q^{60} +(0.288679 + 0.166669i) q^{61} -12.6268 q^{62} +7.05112i q^{64} +(-14.0675 - 1.48881i) q^{65} +(-2.95508 + 1.70611i) q^{66} +(-1.01621 - 0.272292i) q^{67} +(0.234911 + 0.135626i) q^{68} +1.42255 q^{69} +(-0.333748 + 0.333748i) q^{71} +(5.72013 - 1.53270i) q^{72} +(-8.11275 - 2.17380i) q^{73} +(-3.57074 - 6.18470i) q^{74} +(4.59638 - 7.96117i) q^{75} +(0.451465 - 0.451465i) q^{76} +(1.92058 + 4.32207i) q^{78} +(-1.45162 + 2.51428i) q^{79} +(-4.42646 + 16.5198i) q^{80} +(-1.28553 - 2.22661i) q^{81} +(-2.25074 + 3.89840i) q^{82} +(3.84570 + 3.84570i) q^{83} +(-3.77338 - 3.77338i) q^{85} +(16.5448 - 4.43317i) q^{86} +(7.15951 - 4.13355i) q^{87} +(-6.01566 + 3.47314i) q^{88} +(-1.91363 - 7.14176i) q^{89} +12.9038 q^{90} -0.320747 q^{92} +(-1.94908 - 7.27408i) q^{93} +(12.7434 - 7.35740i) q^{94} +(-10.8778 + 6.28033i) q^{95} +(0.960361 - 0.257328i) q^{96} +(7.45885 + 7.45885i) q^{97} +(4.07915 + 4.07915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 56 q^{9} + 16 q^{11} + 96 q^{15} + 56 q^{16} + 32 q^{18} - 96 q^{29} + 32 q^{39} + 64 q^{44} - 32 q^{46} - 80 q^{50} + 16 q^{53} - 192 q^{57} - 72 q^{58} + 64 q^{60} - 32 q^{65} + 64 q^{71} - 208 q^{72}+ \cdots - 64 q^{93}+O(q^{100}) \) 112 * q + 56 * q^9 + 16 * q^11 + 96 * q^15 + 56 * q^16 + 32 * q^18 - 96 * q^29 + 32 * q^39 + 64 * q^44 - 32 * q^46 - 80 * q^50 + 16 * q^53 - 192 * q^57 - 72 * q^58 + 64 * q^60 - 32 * q^65 + 64 * q^71 - 208 * q^72 - 208 * q^74 + 320 * q^78 + 80 * q^79 - 152 * q^81 + 48 * q^85 - 64 * q^86 - 256 * q^92 - 64 * q^93

Introduction

L-functions

Modular forms

Varieties

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Database

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