LMFDB - Embedded newform 820.2.y.a.137.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			137.8
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.764781 - 0.316783i) q^{3} +(-0.0345804 + 2.23580i) q^{5} +(0.341602 - 0.824700i) q^{7} +(-1.63678 - 1.63678i) q^{9} +(-0.433349 + 0.179499i) q^{11} +(3.16640 + 1.31157i) q^{13} +(0.734709 - 1.69894i) q^{15} +(-1.33369 + 0.552431i) q^{17} +(5.73531 + 2.37564i) q^{19} +(-0.522501 + 0.522501i) q^{21} +(4.43764 + 4.43764i) q^{23} +(-4.99761 - 0.154630i) q^{25} +(1.68362 + 4.06463i) q^{27} +(-4.61805 + 1.91286i) q^{29} +8.60190i q^{31} +0.388279 q^{33} +(1.83205 + 0.792272i) q^{35} +(-6.94637 - 6.94637i) q^{37} +(-2.00612 - 2.00612i) q^{39} +(3.40548 + 5.42242i) q^{41} +6.44371 q^{43} +(3.71612 - 3.60292i) q^{45} +(-9.27541 + 3.84200i) q^{47} +(4.38631 + 4.38631i) q^{49} +1.19498 q^{51} +(0.0511732 - 0.123543i) q^{53} +(-0.386339 - 0.975089i) q^{55} +(-3.63369 - 3.63369i) q^{57} +11.4143i q^{59} +(6.16451 + 6.16451i) q^{61} +(-1.90898 + 0.790726i) q^{63} +(-3.04190 + 7.03409i) q^{65} +(7.02036 - 2.90793i) q^{67} +(-1.98805 - 4.79958i) q^{69} +(-3.37473 - 8.14731i) q^{71} +7.31507 q^{73} +(3.77309 + 1.70141i) q^{75} +0.418700i q^{77} +(1.58861 + 3.83524i) q^{79} +3.30239i q^{81} +(2.28375 - 2.28375i) q^{83} +(-1.18901 - 3.00096i) q^{85} +4.13776 q^{87} +(6.68004 - 2.76696i) q^{89} +(2.16330 - 2.16330i) q^{91} +(2.72493 - 6.57857i) q^{93} +(-5.50979 + 12.7408i) q^{95} +(-3.39000 - 8.18418i) q^{97} +(1.00310 + 0.415497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	−0.764781	−	0.316783i	−0.441546	−	0.182894i	0.150823	−	0.988561i	$-0.451808\pi$
$3$	−0.764781	−	0.316783i	−0.441546	−	0.182894i	−0.592370	+	0.805666i	$0.701808\pi$
$4$		0			0
$5$	−0.0345804	+	2.23580i	−0.0154648	+	0.999880i
$5$	−0.0345804	+	2.23580i	−0.0154648	+	0.999880i
$6$		0			0
$7$	0.341602	−	0.824700i	0.129113	−	0.311707i	−0.846082	−	0.533053i	$-0.821045\pi$
$7$	0.341602	−	0.824700i	0.129113	−	0.311707i	0.975195	+	0.221345i	$0.0710448\pi$
$8$		0			0
$9$	−1.63678	−	1.63678i	−0.545594	−	0.545594i
$10$		0			0
$11$	−0.433349	+	0.179499i	−0.130660	+	0.0541210i	−0.447055	−	0.894506i	$-0.647527\pi$
$11$	−0.433349	+	0.179499i	−0.130660	+	0.0541210i	0.316396	+	0.948627i	$0.397527\pi$
$12$		0			0
$13$	3.16640	+	1.31157i	0.878202	+	0.363763i	0.775799	−	0.630980i	$-0.217347\pi$
$13$	3.16640	+	1.31157i	0.878202	+	0.363763i	0.102403	+	0.994743i	$0.467347\pi$
$14$		0			0
$15$	0.734709	−	1.69894i	0.189701	−	0.438665i
$16$		0			0
$17$	−1.33369	+	0.552431i	−0.323467	+	0.133984i	−0.538507	−	0.842621i	$-0.681012\pi$
$17$	−1.33369	+	0.552431i	−0.323467	+	0.133984i	0.215041	+	0.976605i	$0.431012\pi$
$18$		0			0
$19$	5.73531	+	2.37564i	1.31577	+	0.545009i	0.926562	−	0.376141i	$-0.122749\pi$
$19$	5.73531	+	2.37564i	1.31577	+	0.545009i	0.389207	+	0.921150i	$0.372749\pi$
$20$		0			0
$21$	−0.522501	+	0.522501i	−0.114019	+	0.114019i
$22$		0			0
$23$	4.43764	+	4.43764i	0.925311	+	0.925311i	0.997398	−	0.0720873i	$-0.0229660\pi$
$23$	4.43764	+	4.43764i	0.925311	+	0.925311i	−0.0720873	+	0.997398i	$0.522966\pi$
$24$		0			0
$25$	−4.99761	−	0.154630i	−0.999522	−	0.0309260i
$26$		0			0
$27$	1.68362	+	4.06463i	0.324013	+	0.782238i
$28$		0			0
$29$	−4.61805	+	1.91286i	−0.857551	+	0.355209i	−0.767749	−	0.640750i	$-0.778623\pi$
$29$	−4.61805	+	1.91286i	−0.857551	+	0.355209i	−0.0898019	+	0.995960i	$0.528623\pi$
$30$		0			0
$31$			8.60190i			1.54495i	0.635047	+	0.772473i	$0.280981\pi$
$31$			8.60190i			1.54495i	−0.635047	+	0.772473i	$0.719019\pi$
$32$		0			0
$33$	0.388279			0.0675907
$34$		0			0
$35$	1.83205	+	0.792272i	0.309673	+	0.133918i
$36$		0			0
$37$	−6.94637	−	6.94637i	−1.14198	−	1.14198i	−0.988088	−	0.153889i	$-0.950820\pi$
$37$	−6.94637	−	6.94637i	−1.14198	−	1.14198i	−0.153889	−	0.988088i	$-0.549180\pi$
$38$		0			0
$39$	−2.00612	−	2.00612i	−0.321237	−	0.321237i
$40$		0			0
$41$	3.40548	+	5.42242i	0.531847	+	0.846840i
$41$	3.40548	+	5.42242i	0.531847	+	0.846840i
$42$		0			0
$43$	6.44371			0.982656			0.491328	−	0.870975i	$-0.336512\pi$
$43$	6.44371			0.982656			0.491328	+	0.870975i	$0.336512\pi$
$44$		0			0
$45$	3.71612	−	3.60292i	0.553966	−	0.537091i
$46$		0			0
$47$	−9.27541	+	3.84200i	−1.35296	+	0.560413i	−0.937114	−	0.349023i	$-0.886513\pi$
$47$	−9.27541	+	3.84200i	−1.35296	+	0.560413i	−0.415843	+	0.909436i	$0.636513\pi$
$48$		0			0
$49$	4.38631	+	4.38631i	0.626616	+	0.626616i
$50$		0			0
$51$	1.19498			0.167331
$52$		0			0
$53$	0.0511732	−	0.123543i	0.00702919	−	0.0169700i	−0.920326	−	0.391152i	$-0.872077\pi$
$53$	0.0511732	−	0.123543i	0.00702919	−	0.0169700i	0.927355	+	0.374182i	$0.122077\pi$
$54$		0			0
$55$	−0.386339	−	0.975089i	−0.0520939	−	0.131481i
$56$		0			0
$57$	−3.63369	−	3.63369i	−0.481294	−	0.481294i
$58$		0			0
$59$			11.4143i			1.48602i	0.669280	+	0.743010i	$0.266603\pi$
$59$			11.4143i			1.48602i	−0.669280	+	0.743010i	$0.733397\pi$
$60$		0			0
$61$	6.16451	+	6.16451i	0.789285	+	0.789285i	0.981377	−	0.192092i	$-0.0615273\pi$
$61$	6.16451	+	6.16451i	0.789285	+	0.789285i	−0.192092	+	0.981377i	$0.561527\pi$
$62$		0			0
$63$	−1.90898	+	0.790726i	−0.240509	+	0.0996221i
$64$		0			0
$65$	−3.04190	+	7.03409i	−0.377301	+	0.872472i
$66$		0			0
$67$	7.02036	−	2.90793i	0.857674	−	0.355260i	0.0898763	−	0.995953i	$-0.471353\pi$
$67$	7.02036	−	2.90793i	0.857674	−	0.355260i	0.767797	+	0.640693i	$0.221353\pi$
$68$		0			0
$69$	−1.98805	−	4.79958i	−0.239333	−	0.577802i
$70$		0			0
$71$	−3.37473	−	8.14731i	−0.400506	−	0.966907i	−0.987543	−	0.157347i	$-0.949706\pi$
$71$	−3.37473	−	8.14731i	−0.400506	−	0.966907i	0.587037	−	0.809560i	$-0.300294\pi$
$72$		0			0
$73$	7.31507			0.856164			0.428082	−	0.903740i	$-0.359189\pi$
$73$	7.31507			0.856164			0.428082	+	0.903740i	$0.359189\pi$
$74$		0			0
$75$	3.77309	+	1.70141i	0.435679	+	0.196462i
$76$		0			0
$77$			0.418700i			0.0477153i
$78$		0			0
$79$	1.58861	+	3.83524i	0.178732	+	0.431498i	0.987701	−	0.156354i	$-0.0499739\pi$
$79$	1.58861	+	3.83524i	0.178732	+	0.431498i	−0.808969	+	0.587852i	$0.799974\pi$
$80$		0			0
$81$			3.30239i			0.366932i
$82$		0			0
$83$	2.28375	−	2.28375i	0.250674	−	0.250674i	−0.570573	−	0.821247i	$-0.693279\pi$
$83$	2.28375	−	2.28375i	0.250674	−	0.250674i	0.821247	+	0.570573i	$0.193279\pi$
$84$		0			0
$85$	−1.18901	−	3.00096i	−0.128966	−	0.325500i
$86$		0			0
$87$	4.13776			0.443614
$88$		0			0
$89$	6.68004	−	2.76696i	0.708083	−	0.293298i	0.000571890	−	1.00000i	$-0.499818\pi$
$89$	6.68004	−	2.76696i	0.708083	−	0.293298i	0.707511	+	0.706702i	$0.249818\pi$
$90$		0			0
$91$	2.16330	−	2.16330i	0.226775	−	0.226775i
$92$		0			0
$93$	2.72493	−	6.57857i	0.282562	−	0.682166i
$94$		0			0
$95$	−5.50979	+	12.7408i	−0.565292	+	1.30718i
$96$		0			0
$97$	−3.39000	−	8.18418i	−0.344202	−	0.830978i	−0.997281	−	0.0736881i	$-0.976523\pi$
$97$	−3.39000	−	8.18418i	−0.344202	−	0.830978i	0.653079	−	0.757290i	$-0.273477\pi$
$98$		0			0
$99$	1.00310	+	0.415497i	0.100815	+	0.0417590i
$100$		0			0
$101$	2.05242	−	4.95497i	0.204223	−	0.493038i	−0.788271	−	0.615328i	$-0.789024\pi$
$101$	2.05242	−	4.95497i	0.204223	−	0.493038i	0.992494	+	0.122290i	$0.0390237\pi$
$102$		0			0
$103$			4.63637i			0.456835i	0.973563	+	0.228418i	$0.0733552\pi$
$103$			4.63637i			0.456835i	−0.973563	+	0.228418i	$0.926645\pi$
$104$		0			0
$105$	−1.15014	−	1.18628i	−0.112242	−	0.115769i
$106$		0			0
$107$	11.2573	−	11.2573i	1.08828	−	1.08828i	0.0925796	−	0.995705i	$-0.470489\pi$
$107$	11.2573	−	11.2573i	1.08828	−	1.08828i	0.995705	−	0.0925796i	$-0.0295113\pi$
$108$		0			0
$109$	−1.54948	+	3.74077i	−0.148413	+	0.358301i	−0.980550	−	0.196269i	$-0.937117\pi$
$109$	−1.54948	+	3.74077i	−0.148413	+	0.358301i	0.832137	+	0.554570i	$0.187117\pi$
$110$		0			0
$111$	3.11196	+	7.51294i	0.295374	+	0.713097i
$112$		0			0
$113$	−14.5082	−	14.5082i	−1.36482	−	1.36482i	−0.867659	−	0.497160i	$-0.834376\pi$
$113$	−14.5082	−	14.5082i	−1.36482	−	1.36482i	−0.497160	−	0.867659i	$-0.665624\pi$
$114$		0			0
$115$	−10.0751	+	9.76821i	−0.939510	+	0.910891i
$116$		0			0
$117$	−3.03596	−	7.32946i	−0.280675	−	0.677609i
$118$		0			0
$119$			1.28860i			0.118126i
$120$		0			0
$121$	−7.62260	+	7.62260i	−0.692964	+	0.692964i
$122$		0			0
$123$	−0.886719	−	5.22576i	−0.0799528	−	0.471191i
$124$		0			0
$125$	0.518541	−	11.1683i	0.0463797	−	0.998924i
$126$		0			0
$127$	10.9116	−	10.9116i	0.968245	−	0.968245i	−0.0312656	−	0.999511i	$-0.509954\pi$
$127$	10.9116	−	10.9116i	0.968245	−	0.968245i	0.999511	+	0.0312656i	$0.00995378\pi$
$128$		0			0
$129$	−4.92802	−	2.04125i	−0.433888	−	0.179722i
$130$		0			0
$131$	−4.16707	+	4.16707i	−0.364079	+	0.364079i	−0.865312	−	0.501233i	$-0.832880\pi$
$131$	−4.16707	+	4.16707i	−0.364079	+	0.364079i	0.501233	+	0.865312i	$0.332880\pi$
$132$		0			0
$133$	3.91838	−	3.91838i	0.339767	−	0.339767i
$134$		0			0
$135$	−9.14591	+	3.62369i	−0.787155	+	0.311877i
$136$		0			0
$137$	2.12144	−	0.878728i	0.181247	−	0.0750748i	−0.290215	−	0.956962i	$-0.593727\pi$
$137$	2.12144	−	0.878728i	0.181247	−	0.0750748i	0.471461	+	0.881887i	$0.343727\pi$
$138$		0			0
$139$		−	4.21477i		−	0.357492i	−0.983895	−	0.178746i	$-0.942796\pi$
$139$		−	4.21477i		−	0.357492i	0.983895	−	0.178746i	$-0.0572041\pi$
$140$		0			0
$141$	8.31073			0.699890
$142$		0			0
$143$	−1.60758			−0.134433
$144$		0			0
$145$	−4.11708	−	10.3912i	−0.341905	−	0.862942i
$146$		0			0
$147$	−1.96506	−	4.74407i	−0.162075	−	0.391284i
$148$		0			0
$149$	−15.9072	−	6.58899i	−1.30317	−	0.539791i	−0.380287	−	0.924868i	$-0.624175\pi$
$149$	−15.9072	−	6.58899i	−1.30317	−	0.539791i	−0.922884	+	0.385077i	$0.874175\pi$
$150$		0			0
$151$	−5.82490	+	2.41275i	−0.474024	+	0.196347i	−0.606888	−	0.794787i	$-0.707582\pi$
$151$	−5.82490	+	2.41275i	−0.474024	+	0.196347i	0.132865	+	0.991134i	$0.457582\pi$
$152$		0			0
$153$	3.08717	+	1.27875i	0.249583	+	0.103380i
$154$		0			0
$155$	−19.2321	−	0.297457i	−1.54476	−	0.0238924i
$156$		0			0
$157$	−19.1756	−	7.94281i	−1.53038	−	0.633905i	−0.550744	−	0.834674i	$-0.685656\pi$
$157$	−19.1756	−	7.94281i	−1.53038	−	0.633905i	−0.979639	+	0.200769i	$0.935656\pi$
$158$		0			0
$159$	−0.0782726	+	0.0782726i	−0.00620742	+	0.00620742i
$160$		0			0
$161$	5.17562	−	2.14381i	0.407896	−	0.168956i
$162$		0			0
$163$	−7.19041	−	7.19041i	−0.563196	−	0.563196i	0.367018	−	0.930214i	$-0.380379\pi$
$163$	−7.19041	−	7.19041i	−0.563196	−	0.563196i	−0.930214	+	0.367018i	$0.880379\pi$
$164$		0			0
$165$	−0.0134269	+	0.868114i	−0.00104528	+	0.0675826i
$166$		0			0
$167$	−5.51128	+	13.3054i	−0.426476	+	1.02960i	0.553921	+	0.832569i	$0.313131\pi$
$167$	−5.51128	+	13.3054i	−0.426476	+	1.02960i	−0.980397	+	0.197034i	$0.936869\pi$
$168$		0			0
$169$	−0.886483	−	0.886483i	−0.0681910	−	0.0681910i
$170$		0			0
$171$	−5.49904	−	13.2759i	−0.420522	−	1.01523i
$172$		0			0
$173$			16.6299i			1.26435i	0.774827	+	0.632173i	$0.217837\pi$
$173$			16.6299i			1.26435i	−0.774827	+	0.632173i	$0.782163\pi$
$174$		0			0
$175$	−1.83471	+	4.06870i	−0.138691	+	0.307565i
$176$		0			0
$177$	3.61586	−	8.72947i	0.271785	−	0.656147i
$178$		0			0
$179$	−7.01029	+	16.9243i	−0.523974	+	1.26499i	0.411442	+	0.911436i	$0.365025\pi$
$179$	−7.01029	+	16.9243i	−0.523974	+	1.26499i	−0.935416	+	0.353549i	$0.884975\pi$
$180$		0			0
$181$	6.33147	−	15.2855i	0.470614	−	1.13616i	−0.493278	−	0.869872i	$-0.664201\pi$
$181$	6.33147	−	15.2855i	0.470614	−	1.13616i	0.963892	−	0.266292i	$-0.0857986\pi$
$182$		0			0
$183$	−2.76169	−	6.66731i	−0.204150	−	0.492861i
$184$		0			0
$185$	15.7709	−	15.2905i	1.15950	−	1.12418i
$186$		0			0
$187$	0.478791	−	0.478791i	0.0350127	−	0.0350127i
$188$		0			0
$189$	3.92722			0.285663
$190$		0			0
$191$	22.9531	+	9.50748i	1.66083	+	0.687937i	0.998140	−	0.0609600i	$-0.0194162\pi$
$191$	22.9531	+	9.50748i	1.66083	+	0.687937i	0.662686	+	0.748897i	$0.269416\pi$
$192$		0			0
$193$	16.8542	+	6.98126i	1.21320	+	0.502522i	0.895240	−	0.445584i	$-0.147004\pi$
$193$	16.8542	+	6.98126i	1.21320	+	0.502522i	0.317955	+	0.948106i	$0.397004\pi$
$194$		0			0
$195$	4.55466	−	4.41592i	0.326166	−	0.316230i
$196$		0			0
$197$			1.39832i			0.0996262i	0.998759	+	0.0498131i	$0.0158626\pi$
$197$			1.39832i			0.0996262i	−0.998759	+	0.0498131i	$0.984137\pi$
$198$		0			0
$199$	−4.28295	+	10.3400i	−0.303610	+	0.732980i	0.696274	+	0.717776i	$0.254840\pi$
$199$	−4.28295	+	10.3400i	−0.303610	+	0.732980i	−0.999884	+	0.0152040i	$0.995160\pi$
$200$		0			0
$201$	−6.29022			−0.443678
$202$		0			0
$203$			4.46194i			0.313167i
$204$		0			0
$205$	−12.2412	+	7.42647i	−0.854964	+	0.518687i
$206$		0			0
$207$		−	14.5269i		−	1.00969i
$208$		0			0
$209$	−2.91181			−0.201414
$210$		0			0
$211$	11.0586	−	26.6978i	0.761305	−	1.83795i	0.285598	−	0.958349i	$-0.407808\pi$
$211$	11.0586	−	26.6978i	0.761305	−	1.83795i	0.475707	−	0.879604i	$-0.342192\pi$
$212$		0			0
$213$			7.29996i			0.500185i
$214$		0			0
$215$	−0.222826	+	14.4068i	−0.0151966	+	0.982538i
$216$		0			0
$217$	7.09398	+	2.93842i	0.481571	+	0.199473i
$218$		0			0
$219$	−5.59442	−	2.31729i	−0.378036	−	0.156588i
$220$		0			0
$221$	−4.94754			−0.332808
$222$		0			0
$223$	1.42061	−	1.42061i	0.0951311	−	0.0951311i	−0.657940	−	0.753071i	$-0.728572\pi$
$223$	1.42061	−	1.42061i	0.0951311	−	0.0951311i	0.753071	+	0.657940i	$0.228572\pi$
$224$		0			0
$225$	7.92690	+	8.43309i	0.528460	+	0.562206i
$226$		0			0
$227$	−6.44654	−	15.5633i	−0.427872	−	1.03297i	−0.979961	−	0.199189i	$-0.936169\pi$
$227$	−6.44654	−	15.5633i	−0.427872	−	1.03297i	0.552090	−	0.833785i	$-0.313831\pi$
$228$		0			0
$229$	9.73706	−	23.5073i	0.643443	−	1.55341i	−0.178562	−	0.983929i	$-0.557145\pi$
$229$	9.73706	−	23.5073i	0.643443	−	1.55341i	0.822005	−	0.569480i	$-0.192855\pi$
$230$		0			0
$231$	0.132637	−	0.320214i	0.00872686	−	0.0210685i
$232$		0			0
$233$	1.87329	−	4.52252i	0.122723	−	0.296280i	−0.850564	−	0.525872i	$-0.823739\pi$
$233$	1.87329	−	4.52252i	0.122723	−	0.296280i	0.973287	+	0.229592i	$0.0737391\pi$
$234$		0			0
$235$	−8.26920	−	20.8708i	−0.539423	−	1.36146i
$236$		0			0
$237$		−	3.43636i		−	0.223216i
$238$		0			0
$239$	1.14603	+	2.76675i	0.0741303	+	0.178966i	0.956601	−	0.291401i	$-0.0941214\pi$
$239$	1.14603	+	2.76675i	0.0741303	+	0.178966i	−0.882471	+	0.470367i	$0.844121\pi$
$240$		0			0
$241$	−5.75408	−	5.75408i	−0.370653	−	0.370653i	0.497062	−	0.867715i	$-0.334412\pi$
$241$	−5.75408	−	5.75408i	−0.370653	−	0.370653i	−0.867715	+	0.497062i	$0.834412\pi$
$242$		0			0
$243$	6.09701	−	14.7195i	0.391123	−	0.944255i
$244$		0			0
$245$	−9.95859	+	9.65523i	−0.636231	+	0.616850i
$246$		0			0
$247$	15.0445	+	15.0445i	0.957257	+	0.957257i
$248$		0			0
$249$	−2.47002	+	1.02311i	−0.156531	+	0.0648373i
$250$		0			0
$251$	−5.39957	+	5.39957i	−0.340818	+	0.340818i	−0.856675	−	0.515857i	$-0.827474\pi$
$251$	−5.39957	+	5.39957i	−0.340818	+	0.340818i	0.515857	+	0.856675i	$0.327474\pi$
$252$		0			0
$253$	−2.71960	−	1.12649i	−0.170980	−	0.0708220i
$254$		0			0
$255$	−0.0413229	+	2.67173i	−0.00258774	+	0.167311i
$256$		0			0
$257$	10.2260	+	4.23574i	0.637879	+	0.264218i	0.678096	−	0.734973i	$-0.262805\pi$
$257$	10.2260	+	4.23574i	0.637879	+	0.264218i	−0.0402177	+	0.999191i	$0.512805\pi$
$258$		0			0
$259$	−8.10157	+	3.35578i	−0.503407	+	0.208518i
$260$		0			0
$261$	10.6897	+	4.42781i	0.661675	+	0.274075i
$262$		0			0
$263$	2.20866	+	5.33218i	0.136192	+	0.328796i	0.977231	−	0.212178i	$-0.0680556\pi$
$263$	2.20866	+	5.33218i	0.136192	+	0.328796i	−0.841039	+	0.540974i	$0.818056\pi$
$264$		0			0
$265$	0.274448	+	0.118685i	0.0168592	+	0.00729078i
$266$		0			0
$267$	−5.98529			−0.366294
$268$		0			0
$269$	−25.4521			−1.55184			−0.775920	−	0.630831i	$-0.782714\pi$
$269$	−25.4521			−1.55184			−0.775920	+	0.630831i	$0.782714\pi$
$270$		0			0
$271$		−	3.61010i		−	0.219298i	−0.993970	−	0.109649i	$-0.965027\pi$
$271$		−	3.61010i		−	0.219298i	0.993970	−	0.109649i	$-0.0349727\pi$
$272$		0			0
$273$	−2.33974	+	0.969154i	−0.141608	+	0.0586558i
$274$		0			0
$275$	2.19346	−	0.830057i	0.132271	−	0.0500543i
$276$		0			0
$277$	4.16054	−	4.16054i	0.249983	−	0.249983i	−0.570981	−	0.820963i	$-0.693437\pi$
$277$	4.16054	−	4.16054i	0.249983	−	0.249983i	0.820963	+	0.570981i	$0.193437\pi$
$278$		0			0
$279$	14.0794	−	14.0794i	0.842914	−	0.842914i
$280$		0			0
$281$	18.3928	+	7.61856i	1.09722	+	0.454485i	0.856520	−	0.516113i	$-0.172622\pi$
$281$	18.3928	+	7.61856i	1.09722	+	0.454485i	0.240704	+	0.970599i	$0.422622\pi$
$282$		0			0
$283$	16.3296	−	16.3296i	0.970695	−	0.970695i	−0.0288872	−	0.999583i	$-0.509196\pi$
$283$	16.3296	−	16.3296i	0.970695	−	0.970695i	0.999583	+	0.0288872i	$0.00919637\pi$
$284$		0			0
$285$	8.24986	−	7.99855i	0.488679	−	0.473793i
$286$		0			0
$287$	5.63519	−	0.956192i	0.332635	−	0.0564422i
$288$		0			0
$289$	−10.5473	+	10.5473i	−0.620428	+	0.620428i
$290$		0			0
$291$			7.33300i			0.429868i
$292$		0			0
$293$	10.8198	+	26.1214i	0.632102	+	1.52603i	0.836976	+	0.547240i	$0.184321\pi$
$293$	10.8198	+	26.1214i	0.632102	+	1.52603i	−0.204874	+	0.978788i	$0.565679\pi$
$294$		0			0
$295$	−25.5202	−	0.394713i	−1.48584	−	0.0229811i
$296$		0			0
$297$	−1.45919	−	1.45919i	−0.0846709	−	0.0846709i
$298$		0			0
$299$	8.23109	+	19.8716i	0.476016	+	1.14920i
$300$		0			0
$301$	2.20118	−	5.31412i	0.126874	−	0.306301i
$302$		0			0
$303$	−3.13930	+	3.13930i	−0.180348	+	0.180348i
$304$		0			0
$305$	−13.9958	+	13.5694i	−0.801396	+	0.776984i
$306$		0			0
$307$			5.82119i			0.332233i	0.986106	+	0.166116i	$0.0531227\pi$
$307$			5.82119i			0.332233i	−0.986106	+	0.166116i	$0.946877\pi$
$308$		0			0
$309$	1.46872	−	3.54581i	0.0835527	−	0.201714i
$310$		0			0
$311$	9.34834	+	3.87221i	0.530096	+	0.219573i	0.631645	−	0.775258i	$-0.282380\pi$
$311$	9.34834	+	3.87221i	0.530096	+	0.219573i	−0.101550	+	0.994830i	$0.532380\pi$
$312$		0			0
$313$	−2.98401	−	7.20403i	−0.168666	−	0.407196i	0.816834	−	0.576873i	$-0.195727\pi$
$313$	−2.98401	−	7.20403i	−0.168666	−	0.407196i	−0.985500	+	0.169678i	$0.945727\pi$
$314$		0			0
$315$	−1.70189	−	4.29544i	−0.0958907	−	0.242021i
$316$		0			0
$317$	7.05665	−	17.0363i	0.396341	−	0.956852i	−0.592185	−	0.805802i	$-0.701735\pi$
$317$	7.05665	−	17.0363i	0.396341	−	0.956852i	0.988526	−	0.151050i	$-0.0482654\pi$
$318$		0			0
$319$	1.65787	−	1.65787i	0.0928230	−	0.0928230i
$320$		0			0
$321$	−12.1755	+	5.04325i	−0.679569	+	0.281487i
$322$		0			0
$323$	−8.96148			−0.498630
$324$		0			0
$325$	−15.6216	−	7.04432i	−0.866533	−	0.390749i
$326$		0			0
$327$	2.37002	−	2.37002i	0.131062	−	0.131062i
$328$		0			0
$329$			8.96186i			0.494083i
$330$		0			0
$331$	10.4803	+	25.3017i	0.576049	+	1.39071i	0.896332	+	0.443383i	$0.146222\pi$
$331$	10.4803	+	25.3017i	0.576049	+	1.39071i	−0.320283	+	0.947322i	$0.603778\pi$
$332$		0			0
$333$			22.7394i			1.24611i
$334$		0			0
$335$	6.25878	+	15.7967i	0.341954	+	0.863065i
$336$		0			0
$337$	−31.9584			−1.74089			−0.870443	−	0.492269i	$-0.836168\pi$
$337$	−31.9584			−1.74089			−0.870443	+	0.492269i	$0.836168\pi$
$338$		0			0
$339$	6.49966	+	15.6916i	0.353013	+	0.852249i
$340$		0			0
$341$	−1.54403	−	3.72762i	−0.0836140	−	0.201862i
$342$		0			0
$343$	10.8887	−	4.51023i	0.587932	−	0.243529i
$344$		0			0
$345$	10.7997	−	4.27892i	0.581434	−	0.230369i
$346$		0			0
$347$	2.73966	−	1.13480i	0.147073	−	0.0609195i	−0.307933	−	0.951408i	$-0.599637\pi$
$347$	2.73966	−	1.13480i	0.147073	−	0.0609195i	0.455006	+	0.890489i	$0.349637\pi$
$348$		0			0
$349$	11.5391	+	11.5391i	0.617674	+	0.617674i	0.944934	−	0.327261i	$-0.106125\pi$
$349$	11.5391	+	11.5391i	0.617674	+	0.617674i	−0.327261	+	0.944934i	$0.606125\pi$
$350$		0			0
$351$			15.0784i			0.804827i
$352$		0			0
$353$	−8.56102	−	8.56102i	−0.455657	−	0.455657i	0.441570	−	0.897227i	$-0.354422\pi$
$353$	−8.56102	−	8.56102i	−0.455657	−	0.455657i	−0.897227	+	0.441570i	$0.854422\pi$
$354$		0			0
$355$	18.3325	−	7.26347i	0.972986	−	0.385505i
$356$		0			0
$357$	0.408207	−	0.985499i	0.0216046	−	0.0521581i
$358$		0			0
$359$	14.5415			0.767469			0.383734	−	0.923444i	$-0.374638\pi$
$359$	14.5415			0.767469			0.383734	+	0.923444i	$0.374638\pi$
$360$		0			0
$361$	13.8150	+	13.8150i	0.727107	+	0.727107i
$362$		0			0
$363$	8.24433	−	3.41491i	0.432715	−	0.179236i
$364$		0			0
$365$	−0.252958	+	16.3550i	−0.0132404	+	0.856062i
$366$		0			0
$367$	−10.9128			−0.569644			−0.284822	−	0.958580i	$-0.591935\pi$
$367$	−10.9128			−0.569644			−0.284822	+	0.958580i	$0.591935\pi$
$368$		0			0
$369$	3.30129	−	14.4494i	0.171858	−	0.752204i
$370$		0			0
$371$	−0.0844051	−	0.0844051i	−0.00438209	−	0.00438209i
$372$		0			0
$373$	−18.4183	−	18.4183i	−0.953663	−	0.953663i	0.0453099	−	0.998973i	$-0.485572\pi$
$373$	−18.4183	−	18.4183i	−0.953663	−	0.953663i	−0.998973	+	0.0453099i	$0.985572\pi$
$374$		0			0
$375$	−3.93450	+	8.37704i	−0.203176	+	0.432589i
$376$		0			0
$377$	−17.1315			−0.882316
$378$		0			0
$379$		−	17.7328i		−	0.910873i	−0.890268	−	0.455436i	$-0.849483\pi$
$379$		−	17.7328i		−	0.910873i	0.890268	−	0.455436i	$-0.150517\pi$
$380$		0			0
$381$	−11.8016	+	4.88836i	−0.604612	+	0.250438i
$382$		0			0
$383$	−2.37377	−	5.73080i	−0.121294	−	0.292830i	0.851557	−	0.524262i	$-0.175659\pi$
$383$	−2.37377	−	5.73080i	−0.121294	−	0.292830i	−0.972851	+	0.231432i	$0.925659\pi$
$384$		0			0
$385$	−0.936129	−	0.0144788i	−0.0477096	−	0.000737909i
$386$		0			0
$387$	−10.5469	−	10.5469i	−0.536131	−	0.536131i
$388$		0			0
$389$	−1.09009	+	1.09009i	−0.0552695	+	0.0552695i	−0.734201	−	0.678932i	$-0.762443\pi$
$389$	−1.09009	+	1.09009i	−0.0552695	+	0.0552695i	0.678932	+	0.734201i	$0.262443\pi$
$390$		0			0
$391$	−8.36991	−	3.46693i	−0.423284	−	0.175330i
$392$		0			0
$393$	4.50695	−	1.86684i	0.227346	−	0.0941697i
$394$		0			0
$395$	−8.62976	+	3.41919i	−0.434211	+	0.172038i
$396$		0			0
$397$	1.85870	+	0.769899i	0.0932855	+	0.0386401i	0.428838	−	0.903381i	$-0.358923\pi$
$397$	1.85870	+	0.769899i	0.0932855	+	0.0386401i	−0.335553	+	0.942021i	$0.608923\pi$
$398$		0			0
$399$	−4.23798	+	1.75543i	−0.212164	+	0.0878813i
$400$		0			0
$401$	5.65205	+	5.65205i	0.282250	+	0.282250i	0.834006	−	0.551756i	$-0.186042\pi$
$401$	5.65205	+	5.65205i	0.282250	+	0.282250i	−0.551756	+	0.834006i	$0.686042\pi$
$402$		0			0
$403$	−11.2820	+	27.2371i	−0.561995	+	1.35678i
$404$		0			0
$405$	−7.38348	−	0.114198i	−0.366888	−	0.00567455i
$406$		0			0
$407$	4.25707	+	1.76334i	0.211015	+	0.0874053i
$408$		0			0
$409$	0.0148021			0.000731915			0.000365957	−	1.00000i	$-0.499884\pi$
$409$	0.0148021			0.000731915			0.000365957		1.00000i	$0.499884\pi$
$410$		0			0
$411$	−1.90080			−0.0937596
$412$		0			0
$413$	9.41340	+	3.89916i	0.463203	+	0.191865i
$414$		0			0
$415$	5.02703	+	5.18498i	0.246767	+	0.254521i
$416$		0			0
$417$	−1.33517	+	3.22338i	−0.0653834	+	0.157849i
$418$		0			0
$419$	−18.0750	−	18.0750i	−0.883019	−	0.883019i	0.110821	−	0.993840i	$-0.464652\pi$
$419$	−18.0750	−	18.0750i	−0.883019	−	0.883019i	−0.993840	+	0.110821i	$0.964652\pi$
$420$		0			0
$421$	−26.8822	+	11.1350i	−1.31016	+	0.542686i	−0.924931	−	0.380135i	$-0.875878\pi$
$421$	−26.8822	+	11.1350i	−1.31016	+	0.542686i	−0.385229	+	0.922821i	$0.625878\pi$
$422$		0			0
$423$	21.4703	+	8.89330i	1.04392	+	0.432407i
$424$		0			0
$425$	6.75067	−	2.55461i	0.327456	−	0.123917i
$426$		0			0
$427$	7.18967	−	2.97806i	0.347933	−	0.144118i
$428$		0			0
$429$	1.22945	+	0.509254i	0.0593583	+	0.0245870i
$430$		0			0
$431$	−13.6102	+	13.6102i	−0.655580	+	0.655580i	−0.954331	−	0.298751i	$-0.903430\pi$
$431$	−13.6102	+	13.6102i	−0.655580	+	0.655580i	0.298751	+	0.954331i	$0.403430\pi$
$432$		0			0
$433$	23.7840	+	23.7840i	1.14299	+	1.14299i	0.987901	+	0.155084i	$0.0495647\pi$
$433$	23.7840	+	23.7840i	1.14299	+	1.14299i	0.155084	+	0.987901i	$0.450435\pi$
$434$		0			0
$435$	−0.143086	+	9.25121i	−0.00686043	+	0.443561i
$436$		0			0
$437$	14.9090	+	35.9934i	0.713193	+	1.72180i
$438$		0			0
$439$	33.9593	−	14.0664i	1.62079	−	0.671352i	0.626633	−	0.779315i	$-0.284433\pi$
$439$	33.9593	−	14.0664i	1.62079	−	0.671352i	0.994155	+	0.107963i	$0.0344327\pi$
$440$		0			0
$441$		−	14.3589i		−	0.683756i
$442$		0			0
$443$	−11.4590			−0.544436			−0.272218	−	0.962236i	$-0.587757\pi$
$443$	−11.4590			−0.544436			−0.272218	+	0.962236i	$0.587757\pi$
$444$		0			0
$445$	5.95538	+	15.0309i	0.282312	+	0.712534i
$446$		0			0
$447$	10.0783	+	10.0783i	0.476686	+	0.476686i
$448$		0			0
$449$	−17.0096	−	17.0096i	−0.802730	−	0.802730i	0.180791	−	0.983522i	$-0.442134\pi$
$449$	−17.0096	−	17.0096i	−0.802730	−	0.802730i	−0.983522	+	0.180791i	$0.942134\pi$
$450$		0			0
$451$	−2.44908	−	1.73852i	−0.115323	−	0.0818637i
$452$		0			0
$453$	5.21909			0.245214
$454$		0			0
$455$	4.76190	+	4.91151i	0.223241	+	0.230255i
$456$		0			0
$457$	7.44816	−	3.08513i	0.348410	−	0.144316i	−0.201614	−	0.979465i	$-0.564619\pi$
$457$	7.44816	−	3.08513i	0.348410	−	0.144316i	0.550024	+	0.835149i	$0.314619\pi$
$458$		0			0
$459$	−4.49085	−	4.49085i	−0.209615	−	0.209615i
$460$		0			0
$461$	41.3965			1.92803			0.964014	−	0.265850i	$-0.0856527\pi$
$461$	41.3965			1.92803			0.964014	+	0.265850i	$0.0856527\pi$
$462$		0			0
$463$	8.70088	−	21.0058i	0.404364	−	0.976221i	−0.582230	−	0.813024i	$-0.697820\pi$
$463$	8.70088	−	21.0058i	0.404364	−	0.976221i	0.986594	−	0.163197i	$-0.0521805\pi$
$464$		0			0
$465$	14.6141	+	6.31989i	0.677714	+	0.293078i
$466$		0			0
$467$	−7.90749	−	7.90749i	−0.365915	−	0.365915i	0.500070	−	0.865985i	$-0.333308\pi$
$467$	−7.90749	−	7.90749i	−0.365915	−	0.365915i	−0.865985	+	0.500070i	$0.833308\pi$
$468$		0			0
$469$		−	6.78304i		−	0.313212i
$470$		0			0
$471$	12.1490	+	12.1490i	0.559797	+	0.559797i
$472$		0			0
$473$	−2.79237	+	1.15664i	−0.128393	+	0.0531823i
$474$		0			0
$475$	−28.2955	−	12.7594i	−1.29828	−	0.585440i
$476$		0			0
$477$	−0.285973	+	0.118454i	−0.0130938	+	0.00542362i
$478$		0			0
$479$	2.52395	+	6.09336i	0.115322	+	0.278413i	0.970993	−	0.239108i	$-0.0768550\pi$
$479$	2.52395	+	6.09336i	0.115322	+	0.278413i	−0.855671	+	0.517521i	$0.826855\pi$
$480$		0			0
$481$	−12.8844	−	31.1057i	−0.587478	−	1.41830i
$482$		0			0
$483$	−4.63734			−0.211006
$484$		0			0
$485$	18.4154	−	7.29635i	0.836202	−	0.331310i
$486$		0			0
$487$			22.7355i			1.03025i	0.857116	+	0.515123i	$0.172254\pi$
$487$			22.7355i			1.03025i	−0.857116	+	0.515123i	$0.827746\pi$
$488$		0			0
$489$	3.22129	+	7.77688i	0.145672	+	0.351683i
$490$		0			0
$491$			8.56472i			0.386521i	0.981148	+	0.193260i	$0.0619062\pi$
$491$			8.56472i			0.386521i	−0.981148	+	0.193260i	$0.938094\pi$
$492$		0			0
$493$	5.10232	−	5.10232i	0.229797	−	0.229797i
$494$		0			0
$495$	−0.963656	+	2.22836i	−0.0433131	+	0.100157i
$496$		0			0
$497$	−7.87189			−0.353103
$498$		0			0
$499$	−14.7117	+	6.09380i	−0.658587	+	0.272796i	−0.686844	−	0.726805i	$-0.741004\pi$
$499$	−14.7117	+	6.09380i	−0.658587	+	0.272796i	0.0282566	+	0.999601i	$0.491004\pi$
$500$		0			0
$501$	8.42985	−	8.42985i	0.376618	−	0.376618i
$502$		0			0
$503$	3.96798	−	9.57954i	0.176923	−	0.427131i	−0.810395	−	0.585884i	$-0.800747\pi$
$503$	3.96798	−	9.57954i	0.176923	−	0.427131i	0.987318	+	0.158753i	$0.0507474\pi$
$504$		0			0
$505$	11.0074	+	4.76014i	0.489821	+	0.211823i
$506$		0			0
$507$	0.397143	+	0.958788i	0.0176377	+	0.0425813i
$508$		0			0
$509$	2.59641	+	1.07547i	0.115084	+	0.0476693i	0.439482	−	0.898251i	$-0.355162\pi$
$509$	2.59641	+	1.07547i	0.115084	+	0.0476693i	−0.324399	+	0.945920i	$0.605162\pi$
$510$		0			0
$511$	2.49884	−	6.03273i	0.110542	−	0.266872i
$512$		0			0
$513$			27.3116i			1.20583i
$514$		0			0
$515$	−10.3660	−	0.160328i	−0.456781	−	0.00706489i
$516$		0			0
$517$	3.32985	−	3.32985i	0.146447	−	0.146447i
$518$		0			0
$519$	5.26805	−	12.7182i	0.231242	−	0.558267i
$520$		0			0
$521$	6.05087	+	14.6081i	0.265093	+	0.639992i	0.999239	−	0.0389997i	$-0.0124171\pi$
$521$	6.05087	+	14.6081i	0.265093	+	0.639992i	−0.734146	+	0.678992i	$0.762417\pi$
$522$		0			0
$523$	−0.206851	−	0.206851i	−0.00904498	−	0.00904498i	0.702570	−	0.711615i	$-0.252036\pi$
$523$	−0.206851	−	0.206851i	−0.00904498	−	0.00904498i	−0.711615	+	0.702570i	$0.752036\pi$
$524$		0			0
$525$	2.69205	−	2.53046i	0.117491	−	0.110438i
$526$		0			0
$527$	−4.75196	−	11.4722i	−0.206999	−	0.499739i
$528$		0			0
$529$			16.3852i			0.712401i
$530$		0			0
$531$	18.6828	−	18.6828i	0.810764	−	0.810764i
$532$		0			0
$533$	3.67126	+	21.6361i	0.159020	+	0.937164i
$534$		0			0
$535$	24.7798	+	25.5584i	1.07132	+	1.10498i
$536$		0			0
$537$	10.7227	−	10.7227i	0.462718	−	0.462718i
$538$		0			0
$539$	−2.68814	−	1.11346i	−0.115786	−	0.0479603i
$540$		0			0
$541$	−15.3594	+	15.3594i	−0.660354	+	0.660354i	−0.955463	−	0.295110i	$-0.904644\pi$
$541$	−15.3594	+	15.3594i	−0.660354	+	0.660354i	0.295110	+	0.955463i	$0.404644\pi$
$542$		0			0
$543$	−9.68437	+	9.68437i	−0.415596	+	0.415596i
$544$		0			0
$545$	−8.31003	−	3.59368i	−0.355963	−	0.153936i
$546$		0			0
$547$	22.2919	−	9.23362i	0.953135	−	0.394801i	0.148726	−	0.988878i	$-0.452483\pi$
$547$	22.2919	−	9.23362i	0.953135	−	0.394801i	0.804408	+	0.594077i	$0.202483\pi$
$548$		0			0
$549$		−	20.1799i		−	0.861258i
$550$		0			0
$551$	−31.0302			−1.32193
$552$		0			0
$553$	3.70559			0.157578
$554$		0			0
$555$	−16.9051	+	6.69793i	−0.717580	+	0.284311i
$556$		0			0
$557$	8.57718	+	20.7071i	0.363427	+	0.877389i	0.994794	+	0.101906i	$0.0324940\pi$
$557$	8.57718	+	20.7071i	0.363427	+	0.877389i	−0.631368	+	0.775484i	$0.717506\pi$
$558$		0			0
$559$	20.4034	+	8.45136i	0.862971	+	0.357454i
$560$		0			0
$561$	−0.517843	+	0.214498i	−0.0218633	+	0.00905609i
$562$		0			0
$563$	−26.1805	−	10.8443i	−1.10338	−	0.457034i	−0.244725	−	0.969593i	$-0.578698\pi$
$563$	−26.1805	−	10.8443i	−1.10338	−	0.457034i	−0.858652	+	0.512559i	$0.828698\pi$
$564$		0			0
$565$	32.9392	−	31.9358i	1.38576	−	1.34355i
$566$		0			0
$567$	2.72348	+	1.12810i	0.114375	+	0.0473758i
$568$		0			0
$569$	−2.16560	+	2.16560i	−0.0907865	+	0.0907865i	−0.751042	−	0.660255i	$-0.770448\pi$
$569$	−2.16560	+	2.16560i	−0.0907865	+	0.0907865i	0.660255	+	0.751042i	$0.270448\pi$
$570$		0			0
$571$	9.70092	−	4.01825i	0.405971	−	0.168159i	−0.170347	−	0.985384i	$-0.554489\pi$
$571$	9.70092	−	4.01825i	0.405971	−	0.168159i	0.576318	+	0.817225i	$0.304489\pi$
$572$		0			0
$573$	−14.5423	−	14.5423i	−0.607512	−	0.607512i
$574$		0			0
$575$	−21.4914	−	22.8638i	−0.896252	−	0.953485i
$576$		0			0
$577$	−10.5705	+	25.5194i	−0.440056	+	1.06239i	0.535873	+	0.844299i	$0.319983\pi$
$577$	−10.5705	+	25.5194i	−0.440056	+	1.06239i	−0.975929	+	0.218090i	$0.930017\pi$
$578$		0			0
$579$	−10.6783	−	10.6783i	−0.443773	−	0.443773i
$580$		0			0
$581$	−1.10327	−	2.66354i	−0.0457715	−	0.110502i
$582$		0			0
$583$			0.0627228i			0.00259771i
$584$		0			0
$585$	16.4922	−	6.53435i	0.681869	−	0.270162i
$586$		0			0
$587$	−5.76278	+	13.9126i	−0.237855	+	0.574233i	−0.997061	−	0.0766179i	$-0.975588\pi$
$587$	−5.76278	+	13.9126i	−0.237855	+	0.574233i	0.759205	+	0.650851i	$0.225588\pi$
$588$		0			0
$589$	−20.4350	+	49.3345i	−0.842011	+	2.03279i
$590$		0			0
$591$	0.442964	−	1.06941i	0.0182211	−	0.0439896i
$592$		0			0
$593$	−0.116221	−	0.280582i	−0.00477262	−	0.0115221i	0.921475	−	0.388437i	$-0.126985\pi$
$593$	−0.116221	−	0.280582i	−0.00477262	−	0.0115221i	−0.926248	+	0.376915i	$0.876985\pi$
$594$		0			0
$595$	−2.88106	−	0.0445605i	−0.118112	−	0.00182680i
$596$		0			0
$597$	6.55103	−	6.55103i	0.268116	−	0.268116i
$598$		0			0
$599$	−1.70225			−0.0695522			−0.0347761	−	0.999395i	$-0.511072\pi$
$599$	−1.70225			−0.0695522			−0.0347761	+	0.999395i	$0.511072\pi$
$600$		0			0
$601$	10.5361	+	4.36420i	0.429777	+	0.178019i	0.587076	−	0.809532i	$-0.300279\pi$
$601$	10.5361	+	4.36420i	0.429777	+	0.178019i	−0.157300	+	0.987551i	$0.550279\pi$
$602$		0			0
$603$	−16.2504	−	6.73115i	−0.661769	−	0.274114i
$604$		0			0
$605$	−16.7790	−	17.3062i	−0.682164	−	0.703598i
$606$		0			0
$607$		−	10.5284i		−	0.427334i	−0.976907	−	0.213667i	$-0.931459\pi$
$607$		−	10.5284i		−	0.427334i	0.976907	−	0.213667i	$-0.0685407\pi$
$608$		0			0
$609$	1.41347	−	3.41241i	0.0572765	−	0.138278i
$610$		0			0
$611$	−34.4087			−1.39203
$612$		0			0
$613$			0.432786i			0.0174801i	0.999962	+	0.00874003i	$0.00278207\pi$
$613$			0.432786i			0.0174801i	−0.999962	+	0.00874003i	$0.997218\pi$
$614$		0			0
$615$	11.7144	−	1.80182i	0.472371	−	0.0726563i
$616$		0			0
$617$			27.5809i			1.11036i	0.831729	+	0.555182i	$0.187351\pi$
$617$			27.5809i			1.11036i	−0.831729	+	0.555182i	$0.812649\pi$
$618$		0			0
$619$	23.1816			0.931746			0.465873	−	0.884852i	$-0.345740\pi$
$619$	23.1816			0.931746			0.465873	+	0.884852i	$0.345740\pi$
$620$		0			0
$621$	−10.5660	+	25.5086i	−0.424000	+	1.02363i
$622$		0			0
$623$		−	6.45423i		−	0.258583i
$624$		0			0
$625$	24.9522	+	1.54556i	0.998087	+	0.0618224i
$626$		0			0
$627$	2.22690	+	0.922412i	0.0889338	+	0.0368376i
$628$		0			0
$629$	13.1017	+	5.42690i	0.522399	+	0.216385i
$630$		0			0
$631$	−32.6449			−1.29957			−0.649786	−	0.760117i	$-0.725142\pi$
$631$	−32.6449			−1.29957			−0.649786	+	0.760117i	$0.725142\pi$
$632$		0			0
$633$	−16.9148	+	16.9148i	−0.672303	+	0.672303i
$634$		0			0
$635$	24.0188	+	24.7734i	0.953156	+	0.983103i
$636$		0			0
$637$	8.13589	+	19.6418i	0.322356	+	0.778235i
$638$		0			0
$639$	−7.81168	+	18.8591i	−0.309025	+	0.746053i
$640$		0			0
$641$	16.3081	−	39.3711i	0.644129	−	1.55507i	−0.176930	−	0.984223i	$-0.556617\pi$
$641$	16.3081	−	39.3711i	0.644129	−	1.55507i	0.821060	−	0.570842i	$-0.193383\pi$
$642$		0			0
$643$	16.2231	−	39.1661i	0.639777	−	1.54456i	−0.187199	−	0.982322i	$-0.559941\pi$
$643$	16.2231	−	39.1661i	0.639777	−	1.54456i	0.826976	−	0.562237i	$-0.190059\pi$
$644$		0			0
$645$	4.73425	−	10.9475i	0.186411	−	0.431057i
$646$		0			0
$647$			18.5073i			0.727595i	0.931478	+	0.363798i	$0.118520\pi$
$647$			18.5073i			0.727595i	−0.931478	+	0.363798i	$0.881480\pi$
$648$		0			0
$649$	−2.04886	−	4.94639i	−0.0804249	−	0.194163i
$650$		0			0
$651$	−4.49450	−	4.49450i	−0.176153	−	0.176153i
$652$		0			0
$653$	3.48999	−	8.42559i	0.136574	−	0.329719i	−0.840765	−	0.541401i	$-0.817894\pi$
$653$	3.48999	−	8.42559i	0.136574	−	0.329719i	0.977339	+	0.211682i	$0.0678941\pi$
$654$		0			0
$655$	−9.17264	−	9.46084i	−0.358405	−	0.369666i
$656$		0			0
$657$	−11.9732	−	11.9732i	−0.467118	−	0.467118i
$658$		0			0
$659$	40.6740	−	16.8477i	1.58444	−	0.656295i	0.595327	−	0.803484i	$-0.297023\pi$
$659$	40.6740	−	16.8477i	1.58444	−	0.656295i	0.989108	+	0.147189i	$0.0470226\pi$
$660$		0			0
$661$	−17.7114	+	17.7114i	−0.688894	+	0.688894i	−0.961988	−	0.273093i	$-0.911953\pi$
$661$	−17.7114	+	17.7114i	−0.688894	+	0.688894i	0.273093	+	0.961988i	$0.411953\pi$
$662$		0			0
$663$	3.78379	+	1.56730i	0.146950	+	0.0608687i
$664$		0			0
$665$	8.62522	+	8.89622i	0.334472	+	0.344980i
$666$		0			0
$667$	−28.9818	−	12.0047i	−1.12218	−	0.464823i
$668$		0			0
$669$	−1.53648	+	0.636431i	−0.0594037	+	0.0246058i
$670$		0			0
$671$	−3.77791	−	1.56486i	−0.145844	−	0.0604108i
$672$		0			0
$673$	−12.4579	−	30.0762i	−0.480219	−	1.15935i	−0.959505	−	0.281692i	$-0.909104\pi$
$673$	−12.4579	−	30.0762i	−0.480219	−	1.15935i	0.479286	−	0.877659i	$-0.340896\pi$
$674$		0			0
$675$	−7.78558	−	20.5737i	−0.299667	−	0.791884i
$676$		0			0
$677$	−35.8032			−1.37603			−0.688014	−	0.725697i	$-0.741517\pi$
$677$	−35.8032			−1.37603			−0.688014	+	0.725697i	$0.741517\pi$
$678$		0			0
$679$	−7.90752			−0.303463
$680$		0			0
$681$			13.9447i			0.534361i
$682$		0			0
$683$	25.6580	−	10.6279i	0.981778	−	0.406666i	0.166694	−	0.986009i	$-0.446691\pi$
$683$	25.6580	−	10.6279i	0.981778	−	0.406666i	0.815084	+	0.579343i	$0.196691\pi$
$684$		0			0
$685$	1.89130	+	4.77350i	0.0722629	+	0.182386i
$686$		0			0
$687$	−14.8934	+	14.8934i	−0.568220	+	0.568220i
$688$		0			0
$689$	0.324070	−	0.324070i	0.0123461	−	0.0123461i
$690$		0			0
$691$	−16.9108	−	7.00470i	−0.643318	−	0.266471i	0.0370815	−	0.999312i	$-0.488194\pi$
$691$	−16.9108	−	7.00470i	−0.643318	−	0.266471i	−0.680400	+	0.732841i	$0.738194\pi$
$692$		0			0
$693$	0.685320	−	0.685320i	0.0260332	−	0.0260332i
$694$		0			0
$695$	9.42339	+	0.145749i	0.357450	+	0.00552856i
$696$		0			0
$697$	−7.53737	−	5.35052i	−0.285498	−	0.202665i
$698$		0			0
$699$	−2.86531	+	2.86531i	−0.108376	+	0.108376i
$700$		0			0
$701$		−	51.1404i		−	1.93155i	−0.259388	−	0.965773i	$-0.583521\pi$
$701$		−	51.1404i		−	1.93155i	0.259388	−	0.965773i	$-0.416479\pi$
$702$		0			0
$703$	−23.3375	−	56.3417i	−0.880190	−	2.12497i
$704$		0			0
$705$	−0.287389	+	18.5811i	−0.0108237	+	0.699806i
$706$		0			0
$707$	−3.38525	−	3.38525i	−0.127316	−	0.127316i
$708$		0			0
$709$	−8.63115	−	20.8374i	−0.324150	−	0.782567i	−0.999004	−	0.0446158i	$-0.985794\pi$
$709$	−8.63115	−	20.8374i	−0.324150	−	0.782567i	0.674855	−	0.737951i	$-0.264206\pi$
$710$		0			0
$711$	3.67724	−	8.87765i	0.137907	−	0.332938i
$712$		0			0
$713$	−38.1721	+	38.1721i	−1.42956	+	1.42956i
$714$		0			0
$715$	0.0555909	−	3.59423i	0.00207898	−	0.134417i
$716$		0			0
$717$		−	2.47900i		−	0.0925800i
$718$		0			0
$719$	1.27454	−	3.07701i	0.0475324	−	0.114753i	−0.898330	−	0.439321i	$-0.855219\pi$
$719$	1.27454	−	3.07701i	0.0475324	−	0.114753i	0.945862	+	0.324568i	$0.105219\pi$
$720$		0			0
$721$	3.82362	+	1.58379i	0.142399	+	0.0589835i
$722$		0			0
$723$	2.57782	+	6.22340i	0.0958700	+	0.231451i
$724$		0			0
$725$	23.3750	−	8.84564i	0.868126	−	0.328519i
$726$		0			0
$727$	5.68563	−	13.7263i	0.210868	−	0.509082i	−0.782689	−	0.622413i	$-0.786152\pi$
$727$	5.68563	−	13.7263i	0.210868	−	0.509082i	0.993557	+	0.113332i	$0.0361523\pi$
$728$		0			0
$729$	−2.32032	+	2.32032i	−0.0859379	+	0.0859379i
$730$		0			0
$731$	−8.59389	+	3.55971i	−0.317856	+	0.131660i
$732$		0			0
$733$	−23.9700			−0.885354			−0.442677	−	0.896681i	$-0.645971\pi$
$733$	−23.9700			−0.885354			−0.442677	+	0.896681i	$0.645971\pi$
$734$		0			0
$735$	10.6748	−	4.22943i	0.393744	−	0.156005i
$736$		0			0
$737$	−2.52030	+	2.52030i	−0.0928363	+	0.0928363i
$738$		0			0
$739$		−	2.48118i		−	0.0912718i	−0.998958	−	0.0456359i	$-0.985469\pi$
$739$		−	2.48118i		−	0.0912718i	0.998958	−	0.0456359i	$-0.0145314\pi$
$740$		0			0
$741$	−6.73990	−	16.2716i	−0.247596	−	0.597751i
$742$		0			0
$743$			33.1371i			1.21568i	0.794059	+	0.607840i	$0.207964\pi$
$743$			33.1371i			1.21568i	−0.794059	+	0.607840i	$0.792036\pi$
$744$		0			0
$745$	15.2818	−	35.3376i	0.559880	−	1.29467i
$746$		0			0
$747$	−7.47600			−0.273532
$748$		0			0
$749$	−5.43838	−	13.1294i	−0.198714	−	0.479738i
$750$		0			0
$751$	−0.924929	−	2.23298i	−0.0337512	−	0.0814825i	0.906105	−	0.423052i	$-0.139041\pi$
$751$	−0.924929	−	2.23298i	−0.0337512	−	0.0814825i	−0.939856	+	0.341570i	$0.889041\pi$
$752$		0			0
$753$	5.83998	−	2.41900i	0.212821	−	0.0881532i
$754$		0			0
$755$	−5.19301	−	13.1067i	−0.188993	−	0.477003i
$756$		0			0
$757$	33.8206	−	14.0089i	1.22923	−	0.509163i	0.328897	−	0.944366i	$-0.393323\pi$
$757$	33.8206	−	14.0089i	1.22923	−	0.509163i	0.900333	+	0.435203i	$0.143323\pi$
$758$		0			0
$759$	1.72304	+	1.72304i	0.0625424	+	0.0625424i
$760$		0			0
$761$		−	34.2999i		−	1.24337i	−0.783268	−	0.621684i	$-0.786449\pi$
$761$		−	34.2999i		−	1.24337i	0.783268	−	0.621684i	$-0.213551\pi$
$762$		0			0
$763$	2.55571	+	2.55571i	0.0925228	+	0.0925228i
$764$		0			0
$765$	−2.96578	+	6.85807i	−0.107228	+	0.247954i
$766$		0			0
$767$	−14.9707	+	36.1424i	−0.540560	+	1.30503i
$768$		0			0
$769$	6.31659			0.227782			0.113891	−	0.993493i	$-0.463669\pi$
$769$	6.31659			0.227782			0.113891	+	0.993493i	$0.463669\pi$
$770$		0			0
$771$	−6.47882	−	6.47882i	−0.233329	−	0.233329i
$772$		0			0
$773$	−12.0339	+	4.98461i	−0.432830	+	0.179284i	−0.588451	−	0.808533i	$-0.700262\pi$
$773$	−12.0339	+	4.98461i	−0.432830	+	0.179284i	0.155621	+	0.987817i	$0.450262\pi$
$774$		0			0
$775$	1.33011	−	42.9889i	0.0477790	−	1.54421i
$776$		0			0
$777$	7.25897			0.260414
$778$		0			0
$779$	6.64976	+	39.1895i	0.238252	+	1.40411i
$780$		0			0
$781$	2.92487	+	2.92487i	0.104660	+	0.104660i
$782$		0			0
$783$	−15.5501	−	15.5501i	−0.555716	−	0.555716i
$784$		0			0
$785$	18.4216	−	42.5982i	0.657496	−	1.52040i
$786$		0			0
$787$	48.7397			1.73738			0.868691	−	0.495355i	$-0.164962\pi$
$787$	48.7397			1.73738			0.868691	+	0.495355i	$0.164962\pi$
$788$		0			0
$789$		−	4.77761i		−	0.170088i
$790$		0			0
$791$	−16.9210	+	7.00889i	−0.601640	+	0.249207i
$792$		0			0
$793$	11.4342	+	27.6045i	0.406039	+	0.980264i
$794$		0			0
$795$	−0.172295	−	0.177709i	−0.00611068	−	0.00630268i
$796$		0			0
$797$	−9.44830	−	9.44830i	−0.334676	−	0.334676i	0.519683	−	0.854359i	$-0.326050\pi$
$797$	−9.44830	−	9.44830i	−0.334676	−	0.334676i	−0.854359	+	0.519683i	$0.826050\pi$
$798$		0			0
$799$	10.2481	−	10.2481i	0.362550	−	0.362550i
$800$		0			0
$801$	−15.4627	−	6.40485i	−0.546347	−	0.226304i
$802$		0			0
$803$	−3.16998	+	1.31305i	−0.111866	+	0.0463364i
$804$		0			0
$805$	4.61416	+	11.6458i	0.162628	+	0.410460i
$806$		0			0
$807$	19.4653	+	8.06277i	0.685209	+	0.283823i
$808$		0			0
$809$	−14.6552	+	6.07038i	−0.515249	+	0.213423i	−0.625129	−	0.780522i	$-0.714953\pi$
$809$	−14.6552	+	6.07038i	−0.515249	+	0.213423i	0.109880	+	0.993945i	$0.464953\pi$
$810$		0			0
$811$	−22.2617	−	22.2617i	−0.781713	−	0.781713i	0.198407	−	0.980120i	$-0.436423\pi$
$811$	−22.2617	−	22.2617i	−0.781713	−	0.781713i	−0.980120	+	0.198407i	$0.936423\pi$
$812$		0			0
$813$	−1.14362	+	2.76093i	−0.0401084	+	0.0968302i
$814$		0			0
$815$	16.3250	−	15.8277i	0.571838	−	0.554419i
$816$		0			0
$817$	36.9566	+	15.3079i	1.29295	+	0.535557i
$818$		0			0
$819$	−7.08169			−0.247454
$820$		0			0
$821$	24.2580			0.846611			0.423306	−	0.905987i	$-0.360870\pi$
$821$	24.2580			0.846611			0.423306	+	0.905987i	$0.360870\pi$
$822$		0			0
$823$	4.88030	+	2.02148i	0.170116	+	0.0704645i	0.466116	−	0.884723i	$-0.345653\pi$
$823$	4.88030	+	2.02148i	0.170116	+	0.0704645i	−0.296000	+	0.955188i	$0.595653\pi$
$824$		0			0
$825$	−1.94047	−	0.0600395i	−0.0675584	−	0.00209031i
$826$		0			0
$827$	9.23717	−	22.3005i	0.321208	−	0.775464i	−0.677977	−	0.735083i	$-0.737143\pi$
$827$	9.23717	−	22.3005i	0.321208	−	0.775464i	0.999184	−	0.0403806i	$-0.0128570\pi$
$828$		0			0
$829$	11.6114	+	11.6114i	0.403279	+	0.403279i	0.879387	−	0.476108i	$-0.157953\pi$
$829$	11.6114	+	11.6114i	0.403279	+	0.403279i	−0.476108	+	0.879387i	$0.657953\pi$
$830$		0			0
$831$	−4.49989	+	1.86391i	−0.156099	+	0.0646585i
$832$		0			0
$833$	−8.27310	−	3.42683i	−0.286646	−	0.118733i
$834$		0			0
$835$	−29.5577	−	12.7822i	−1.02289	−	0.442348i
$836$		0			0
$837$	−34.9635	+	14.4824i	−1.20852	+	0.500583i
$838$		0			0
$839$	5.31638	+	2.20212i	0.183542	+	0.0760256i	0.472562	−	0.881298i	$-0.343329\pi$
$839$	5.31638	+	2.20212i	0.183542	+	0.0760256i	−0.289020	+	0.957323i	$0.593329\pi$
$840$		0			0
$841$	−2.83870	+	2.83870i	−0.0978864	+	0.0978864i
$842$		0			0
$843$	−11.6531	−	11.6531i	−0.401353	−	0.401353i
$844$		0			0
$845$	2.01266	−	1.95135i	0.0692374	−	0.0671283i
$846$		0			0
$847$	3.68246	+	8.89025i	0.126531	+	0.305473i
$848$		0			0
$849$	−17.6615	+	7.31564i	−0.606142	+	0.251072i
$850$		0			0
$851$		−	61.6510i		−	2.11337i
$852$		0			0
$853$	2.72360			0.0932543			0.0466272	−	0.998912i	$-0.485153\pi$
$853$	2.72360			0.0932543			0.0466272	+	0.998912i	$0.485153\pi$
$854$		0			0
$855$	29.8723	−	11.8357i	1.02161	−	0.404771i
$856$		0			0
$857$	3.85361	+	3.85361i	0.131637	+	0.131637i	0.769855	−	0.638219i	$-0.220328\pi$
$857$	3.85361	+	3.85361i	0.131637	+	0.131637i	−0.638219	+	0.769855i	$0.720328\pi$
$858$		0			0
$859$	4.93558	+	4.93558i	0.168400	+	0.168400i	0.786276	−	0.617876i	$-0.212007\pi$
$859$	4.93558	+	4.93558i	0.168400	+	0.168400i	−0.617876	+	0.786276i	$0.712007\pi$
$860$		0			0
$861$	−4.61259	−	1.05385i	−0.157197	−	0.0359152i
$862$		0			0
$863$	11.5665			0.393728			0.196864	−	0.980431i	$-0.436924\pi$
$863$	11.5665			0.393728			0.196864	+	0.980431i	$0.436924\pi$
$864$		0			0
$865$	−37.1811	−	0.575068i	−1.26419	−	0.0195529i
$866$		0			0
$867$	11.4075	−	4.72516i	0.387420	−	0.160475i
$868$		0			0
$869$	−1.37684	−	1.37684i	−0.0467062	−	0.0467062i
$870$		0			0
$871$	26.0432			0.882442
$872$		0			0
$873$	−7.84703	+	18.9444i	−0.265582	+	0.641171i
$874$		0			0
$875$	−9.03336	−	4.24275i	−0.305383	−	0.143431i
$876$		0			0
$877$	24.5644	+	24.5644i	0.829482	+	0.829482i	0.987445	−	0.157963i	$-0.0504927\pi$
$877$	24.5644	+	24.5644i	0.829482	+	0.829482i	−0.157963	+	0.987445i	$0.550493\pi$
$878$		0			0
$879$		−	23.4047i		−	0.789420i
$880$		0			0
$881$	−16.7957	−	16.7957i	−0.565863	−	0.565863i	0.365104	−	0.930967i	$-0.381033\pi$
$881$	−16.7957	−	16.7957i	−0.565863	−	0.565863i	−0.930967	+	0.365104i	$0.881033\pi$
$882$		0			0
$883$	9.75916	−	4.04238i	0.328422	−	0.136037i	−0.212379	−	0.977187i	$-0.568121\pi$
$883$	9.75916	−	4.04238i	0.328422	−	0.136037i	0.540801	+	0.841151i	$0.318121\pi$
$884$		0			0
$885$	19.3923	+	8.38622i	0.651865	+	0.281900i
$886$		0			0
$887$	−0.00191650		0.000793840i	−6.43498e−5		2.66545e-5i	−0.382716	−	0.923866i	$-0.625011\pi$
$887$	−0.00191650		0.000793840i	−6.43498e−5		2.66545e-5i	0.382651	+	0.923893i	$0.375011\pi$
$888$		0			0
$889$	−5.27136	−	12.7262i	−0.176796	−	0.426822i
$890$		0			0
$891$	−0.592775	−	1.43109i	−0.0198587	−	0.0479432i
$892$		0			0
$893$	−62.3245			−2.08561
$894$		0			0
$895$	−37.5970	−	16.2589i	−1.25673	−	0.543474i
$896$		0			0
$897$		−	17.8049i		−	0.594488i
$898$		0			0
$899$	−16.4542	−	39.7240i	−0.548780	−	1.32487i
$900$		0			0
$901$			0.193038i			0.00643102i
$902$		0			0
$903$	−3.36684	+	3.36684i	−0.112041	+	0.112041i
$904$		0			0
$905$	33.9564	+	14.6845i	1.12875	+	0.488129i
$906$		0			0
$907$	−40.2351			−1.33599			−0.667993	−	0.744168i	$-0.732846\pi$
$907$	−40.2351			−1.33599			−0.667993	+	0.744168i	$0.732846\pi$
$908$		0			0
$909$	−11.4696	+	4.75085i	−0.380422	+	0.157576i
$910$		0			0
$911$	−5.54934	+	5.54934i	−0.183858	+	0.183858i	−0.793034	−	0.609177i	$-0.791500\pi$
$911$	−5.54934	+	5.54934i	−0.183858	+	0.183858i	0.609177	+	0.793034i	$0.291500\pi$
$912$		0			0
$913$	−0.579729	+	1.39959i	−0.0191862	+	0.0463197i
$914$		0			0
$915$	15.0023	−	5.94403i	0.495960	−	0.196503i
$916$		0			0
$917$	2.01310	+	4.86006i	0.0664785	+	0.160493i
$918$		0			0
$919$	−11.6319	−	4.81810i	−0.383702	−	0.158935i	0.182491	−	0.983208i	$-0.441584\pi$
$919$	−11.6319	−	4.81810i	−0.383702	−	0.158935i	−0.566192	+	0.824273i	$0.691584\pi$
$920$		0			0
$921$	1.84405	−	4.45193i	0.0607635	−	0.146696i
$922$		0			0
$923$		−	30.2238i		−	0.994830i
$924$		0			0
$925$	33.6411	+	35.7894i	1.10611	+	1.17675i
$926$		0			0
$927$	7.58873	−	7.58873i	0.249247	−	0.249247i
$928$		0			0
$929$	8.21197	−	19.8255i	0.269426	−	0.650452i	−0.730030	−	0.683415i	$-0.760494\pi$
$929$	8.21197	−	19.8255i	0.269426	−	0.650452i	0.999457	+	0.0329624i	$0.0104942\pi$
$930$		0			0
$931$	14.7365	+	35.5771i	0.482970	+	1.16599i
$932$		0			0
$933$	−5.92278	−	5.92278i	−0.193903	−	0.193903i
$934$		0			0
$935$	1.05392	+	1.08704i	0.0344670	+	0.0355500i
$936$		0			0
$937$	−0.647467	−	1.56312i	−0.0211518	−	0.0510650i	0.912951	−	0.408070i	$-0.133798\pi$
$937$	−0.647467	−	1.56312i	−0.0211518	−	0.0510650i	−0.934103	+	0.357005i	$0.883798\pi$
$938$		0			0
$939$			6.45478i			0.210644i
$940$		0			0
$941$	23.8797	−	23.8797i	0.778456	−	0.778456i	−0.201112	−	0.979568i	$-0.564456\pi$
$941$	23.8797	−	23.8797i	0.778456	−	0.778456i	0.979568	+	0.201112i	$0.0644556\pi$
$942$		0			0
$943$	−8.95045	+	39.1750i	−0.291467	+	1.27571i
$944$		0			0
$945$	−0.135805	+	8.78049i	−0.00441774	+	0.285629i
$946$		0			0
$947$	−1.52357	+	1.52357i	−0.0495092	+	0.0495092i	−0.731428	−	0.681919i	$-0.761146\pi$
$947$	−1.52357	+	1.52357i	−0.0495092	+	0.0495092i	0.681919	+	0.731428i	$0.261146\pi$
$948$		0			0
$949$	23.1625	+	9.59421i	0.751885	+	0.311441i
$950$		0			0
$951$	−10.7936	+	10.7936i	−0.350006	+	0.350006i
$952$		0			0
$953$	2.71670	−	2.71670i	0.0880026	−	0.0880026i	−0.661735	−	0.749738i	$-0.730180\pi$
$953$	2.71670	−	2.71670i	0.0880026	−	0.0880026i	0.749738	+	0.661735i	$0.230180\pi$
$954$		0			0
$955$	−22.0506	+	50.9897i	−0.713539	+	1.64999i
$956$		0			0
$957$	−1.79309	+	0.742724i	−0.0579625	+	0.0240088i
$958$		0			0
$959$		−	2.04972i		−	0.0661890i
$960$		0			0
$961$	−42.9927			−1.38686
$962$		0			0
$963$	−36.8515			−1.18752
$964$		0			0
$965$	−16.1915	+	37.4413i	−0.521224	+	1.20528i
$966$		0			0
$967$	16.7330	+	40.3971i	0.538098	+	1.29908i	0.926049	+	0.377403i	$0.123183\pi$
$967$	16.7330	+	40.3971i	0.538098	+	1.29908i	−0.387951	+	0.921680i	$0.626817\pi$
$968$		0			0
$969$	6.85357	+	2.83884i	0.220168	+	0.0911967i
$970$		0			0
$971$	1.04760	−	0.433931i	0.0336192	−	0.0139255i	−0.365810	−	0.930689i	$-0.619208\pi$
$971$	1.04760	−	0.433931i	0.0336192	−	0.0139255i	0.399430	+	0.916764i	$0.369208\pi$
$972$		0			0
$973$	−3.47592	−	1.43977i	−0.111433	−	0.0461570i
$974$		0			0
$975$	9.71561	+	10.3360i	0.311149	+	0.331018i
$976$		0			0
$977$	−18.6000	−	7.70437i	−0.595067	−	0.246485i	0.0647620	−	0.997901i	$-0.479371\pi$
$977$	−18.6000	−	7.70437i	−0.595067	−	0.246485i	−0.659829	+	0.751416i	$0.729371\pi$
$978$		0			0
$979$	−2.39812	+	2.39812i	−0.0766443	+	0.0766443i
$980$		0			0
$981$	8.65898	−	3.58667i	0.276460	−	0.114513i
$982$		0			0
$983$	−29.9555	−	29.9555i	−0.955431	−	0.955431i	0.0436173	−	0.999048i	$-0.486112\pi$
$983$	−29.9555	−	29.9555i	−0.955431	−	0.955431i	−0.999048	+	0.0436173i	$0.986112\pi$
$984$		0			0
$985$	−3.12637	−	0.0483545i	−0.0996143	−	0.00154070i
$986$		0			0
$987$	2.83896	−	6.85386i	0.0903651	−	0.218161i
$988$		0			0
$989$	28.5948	+	28.5948i	0.909262	+	0.909262i
$990$		0			0
$991$	6.70978	+	16.1988i	0.213143	+	0.514573i	0.993903	−	0.110258i	$-0.0351678\pi$
$991$	6.70978	+	16.1988i	0.213143	+	0.514573i	−0.780760	+	0.624831i	$0.785168\pi$
$992$		0			0
$993$		−	22.6702i		−	0.719417i
$994$		0			0
$995$	−22.9700	−	9.93338i	−0.728197	−	0.314909i
$996$		0			0
$997$	−14.0520	+	33.9245i	−0.445031	+	1.07440i	0.529129	+	0.848541i	$0.322519\pi$
$997$	−14.0520	+	33.9245i	−0.445031	+	1.07440i	−0.974160	+	0.225858i	$0.927481\pi$
$998$		0			0
$999$	16.5393	−	39.9295i	0.523281	−	1.26331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.137.8	yes	84
5.3	odd	4		820.2.x.a.793.14	yes	84
41.3	odd	8		820.2.x.a.577.14	✓	84
205.3	even	8	inner	820.2.y.a.413.8	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.14	✓	84	41.3	odd	8
820.2.x.a.793.14	yes	84	5.3	odd	4
820.2.y.a.137.8	yes	84	1.1	even	1	trivial
820.2.y.a.413.8	yes	84	205.3	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764781 - 0.316783i) q^{3} +(-0.0345804 + 2.23580i) q^{5} +(0.341602 - 0.824700i) q^{7} +(-1.63678 - 1.63678i) q^{9} +(-0.433349 + 0.179499i) q^{11} +(3.16640 + 1.31157i) q^{13} +(0.734709 - 1.69894i) q^{15} +(-1.33369 + 0.552431i) q^{17} +(5.73531 + 2.37564i) q^{19} +(-0.522501 + 0.522501i) q^{21} +(4.43764 + 4.43764i) q^{23} +(-4.99761 - 0.154630i) q^{25} +(1.68362 + 4.06463i) q^{27} +(-4.61805 + 1.91286i) q^{29} +8.60190i q^{31} +0.388279 q^{33} +(1.83205 + 0.792272i) q^{35} +(-6.94637 - 6.94637i) q^{37} +(-2.00612 - 2.00612i) q^{39} +(3.40548 + 5.42242i) q^{41} +6.44371 q^{43} +(3.71612 - 3.60292i) q^{45} +(-9.27541 + 3.84200i) q^{47} +(4.38631 + 4.38631i) q^{49} +1.19498 q^{51} +(0.0511732 - 0.123543i) q^{53} +(-0.386339 - 0.975089i) q^{55} +(-3.63369 - 3.63369i) q^{57} +11.4143i q^{59} +(6.16451 + 6.16451i) q^{61} +(-1.90898 + 0.790726i) q^{63} +(-3.04190 + 7.03409i) q^{65} +(7.02036 - 2.90793i) q^{67} +(-1.98805 - 4.79958i) q^{69} +(-3.37473 - 8.14731i) q^{71} +7.31507 q^{73} +(3.77309 + 1.70141i) q^{75} +0.418700i q^{77} +(1.58861 + 3.83524i) q^{79} +3.30239i q^{81} +(2.28375 - 2.28375i) q^{83} +(-1.18901 - 3.00096i) q^{85} +4.13776 q^{87} +(6.68004 - 2.76696i) q^{89} +(2.16330 - 2.16330i) q^{91} +(2.72493 - 6.57857i) q^{93} +(-5.50979 + 12.7408i) q^{95} +(-3.39000 - 8.18418i) q^{97} +(1.00310 + 0.415497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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