LMFDB - Embedded newform 572.2.bc.a.197.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

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

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

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.6
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.425370 - 0.736762i) q^{3} +(2.35532 - 2.35532i) q^{5} +(0.337440 + 1.25934i) q^{7} +(1.13812 - 1.97128i) q^{9} +O(q^{10})$	\(q+(-0.425370 - 0.736762i) q^{3} +(2.35532 - 2.35532i) q^{5} +(0.337440 + 1.25934i) q^{7} +(1.13812 - 1.97128i) q^{9} +(-3.29233 - 0.400712i) q^{11} +(3.56676 + 0.527479i) q^{13} +(-2.73719 - 0.733429i) q^{15} +(1.12651 - 1.95118i) q^{17} +(1.77011 - 0.474299i) q^{19} +(0.784299 - 0.784299i) q^{21} +(-1.72379 + 0.995228i) q^{23} -6.09507i q^{25} -4.48871 q^{27} +(-6.89826 + 3.98271i) q^{29} +(1.52216 - 1.52216i) q^{31} +(1.10523 + 2.59611i) q^{33} +(3.76093 + 2.17138i) q^{35} +(1.36555 - 5.09629i) q^{37} +(-1.12856 - 2.85223i) q^{39} +(-0.255426 + 0.953263i) q^{41} +(5.50646 - 9.53747i) q^{43} +(-1.96237 - 7.32365i) q^{45} +(-0.190569 - 0.190569i) q^{47} +(4.59010 - 2.65010i) q^{49} -1.91674 q^{51} -1.82238 q^{53} +(-8.69830 + 6.81069i) q^{55} +(-1.10240 - 1.10240i) q^{57} +(1.64518 - 0.440824i) q^{59} +(2.51005 + 1.44918i) q^{61} +(2.86657 + 0.768095i) q^{63} +(9.64324 - 7.15848i) q^{65} +(5.43944 + 1.45749i) q^{67} +(1.46649 + 0.846680i) q^{69} +(2.24519 + 8.37918i) q^{71} +(-5.32332 + 5.32332i) q^{73} +(-4.49062 + 2.59266i) q^{75} +(-0.606329 - 4.28139i) q^{77} +9.18416i q^{79} +(-1.50500 - 2.60674i) q^{81} +(-1.51784 - 1.51784i) q^{83} +(-1.94235 - 7.24895i) q^{85} +(5.86862 + 3.38825i) q^{87} +(-2.08017 + 7.76328i) q^{89} +(0.539289 + 4.66976i) q^{91} +(-1.76895 - 0.473988i) q^{93} +(3.05204 - 5.28630i) q^{95} +(2.47736 + 9.24563i) q^{97} +(-4.53699 + 6.03406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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
$3$	−0.425370	−	0.736762i	−0.245587	−	0.425370i	0.716709	−	0.697372i	$-0.245647\pi$
$3$	−0.425370	−	0.736762i	−0.245587	−	0.425370i	−0.962297	+	0.272002i	$0.912314\pi$
$4$		0			0
$5$	2.35532	−	2.35532i	1.05333	−	1.05333i	0.0548361	−	0.998495i	$-0.482536\pi$
$5$	2.35532	−	2.35532i	1.05333	−	1.05333i	0.998495	−	0.0548361i	$-0.0174636\pi$
$6$		0			0
$7$	0.337440	+	1.25934i	0.127540	+	0.475987i	0.999917	−	0.0128466i	$-0.00408932\pi$
$7$	0.337440	+	1.25934i	0.127540	+	0.475987i	−0.872377	+	0.488833i	$0.837423\pi$
$8$		0			0
$9$	1.13812	−	1.97128i	0.379374	−	0.657095i
$10$		0			0
$11$	−3.29233	−	0.400712i	−0.992675	−	0.120819i
$11$	−3.29233	−	0.400712i	−0.992675	−	0.120819i
$12$		0			0
$13$	3.56676	+	0.527479i	0.989241	+	0.146296i
$13$	3.56676	+	0.527479i	0.989241	+	0.146296i
$14$		0			0
$15$	−2.73719	−	0.733429i	−0.706740	−	0.189370i
$16$		0			0
$17$	1.12651	−	1.95118i	0.273219	−	0.473230i	−0.696465	−	0.717591i	$-0.745245\pi$
$17$	1.12651	−	1.95118i	0.273219	−	0.473230i	0.969684	+	0.244361i	$0.0785781\pi$
$18$		0			0
$19$	1.77011	−	0.474299i	0.406091	−	0.108812i	−0.0499909	−	0.998750i	$-0.515919\pi$
$19$	1.77011	−	0.474299i	0.406091	−	0.108812i	0.456081	+	0.889938i	$0.349253\pi$
$20$		0			0
$21$	0.784299	−	0.784299i	0.171148	−	0.171148i
$22$		0			0
$23$	−1.72379	+	0.995228i	−0.359434	+	0.207519i	−0.668832	−	0.743413i	$-0.733206\pi$
$23$	−1.72379	+	0.995228i	−0.359434	+	0.207519i	0.309398	+	0.950932i	$0.399872\pi$
$24$		0			0
$25$		−	6.09507i		−	1.21901i
$26$		0			0
$27$	−4.48871			−0.863852
$28$		0			0
$29$	−6.89826	+	3.98271i	−1.28097	+	0.739571i	−0.977027	−	0.213117i	$-0.931638\pi$
$29$	−6.89826	+	3.98271i	−1.28097	+	0.739571i	−0.303948	+	0.952689i	$0.598305\pi$
$30$		0			0
$31$	1.52216	−	1.52216i	0.273388	−	0.273388i	−0.557075	−	0.830462i	$-0.688076\pi$
$31$	1.52216	−	1.52216i	0.273388	−	0.273388i	0.830462	+	0.557075i	$0.188076\pi$
$32$		0			0
$33$	1.10523	+	2.59611i	0.192395	+	0.451925i
$34$		0			0
$35$	3.76093	+	2.17138i	0.635714	+	0.367030i
$36$		0			0
$37$	1.36555	−	5.09629i	0.224494	−	0.837824i	−0.758112	−	0.652124i	$-0.773878\pi$
$37$	1.36555	−	5.09629i	0.224494	−	0.837824i	0.982606	−	0.185700i	$-0.0594553\pi$
$38$		0			0
$39$	−1.12856	−	2.85223i	−0.180715	−	0.456722i
$40$		0			0
$41$	−0.255426	+	0.953263i	−0.0398908	+	0.148875i	−0.982999	−	0.183612i	$-0.941221\pi$
$41$	−0.255426	+	0.953263i	−0.0398908	+	0.148875i	0.943108	+	0.332487i	$0.107888\pi$
$42$		0			0
$43$	5.50646	−	9.53747i	0.839728	−	1.45445i	−0.0503947	−	0.998729i	$-0.516048\pi$
$43$	5.50646	−	9.53747i	0.839728	−	1.45445i	0.890122	−	0.455722i	$-0.150619\pi$
$44$		0			0
$45$	−1.96237	−	7.32365i	−0.292532	−	1.09174i
$46$		0			0
$47$	−0.190569	−	0.190569i	−0.0277974	−	0.0277974i	0.693071	−	0.720869i	$-0.256257\pi$
$47$	−0.190569	−	0.190569i	−0.0277974	−	0.0277974i	−0.720869	+	0.693071i	$0.756257\pi$
$48$		0			0
$49$	4.59010	−	2.65010i	0.655729	−	0.378585i
$50$		0			0
$51$	−1.91674			−0.268397
$52$		0			0
$53$	−1.82238			−0.250323			−0.125162	−	0.992136i	$-0.539945\pi$
$53$	−1.82238			−0.250323			−0.125162	+	0.992136i	$0.539945\pi$
$54$		0			0
$55$	−8.69830	+	6.81069i	−1.17288	+	0.918353i
$56$		0			0
$57$	−1.10240	−	1.10240i	−0.146016	−	0.146016i
$58$		0			0
$59$	1.64518	−	0.440824i	0.214184	−	0.0573905i	−0.150131	−	0.988666i	$-0.547970\pi$
$59$	1.64518	−	0.440824i	0.214184	−	0.0573905i	0.364315	+	0.931276i	$0.381303\pi$
$60$		0			0
$61$	2.51005	+	1.44918i	0.321379	+	0.185548i	0.652007	−	0.758213i	$-0.273927\pi$
$61$	2.51005	+	1.44918i	0.321379	+	0.185548i	−0.330628	+	0.943761i	$0.607261\pi$
$62$		0			0
$63$	2.86657	+	0.768095i	0.361154	+	0.0967708i
$64$		0			0
$65$	9.64324	−	7.15848i	1.19610	−	0.887900i
$66$		0			0
$67$	5.43944	+	1.45749i	0.664533	+	0.178061i	0.575291	−	0.817949i	$-0.304889\pi$
$67$	5.43944	+	1.45749i	0.664533	+	0.178061i	0.0892424	+	0.996010i	$0.471555\pi$
$68$		0			0
$69$	1.46649	+	0.846680i	0.176545	+	0.101928i
$70$		0			0
$71$	2.24519	+	8.37918i	0.266456	+	0.994426i	0.961353	+	0.275317i	$0.0887829\pi$
$71$	2.24519	+	8.37918i	0.266456	+	0.994426i	−0.694898	+	0.719108i	$0.744550\pi$
$72$		0			0
$73$	−5.32332	+	5.32332i	−0.623048	+	0.623048i	−0.946310	−	0.323262i	$-0.895221\pi$
$73$	−5.32332	+	5.32332i	−0.623048	+	0.623048i	0.323262	+	0.946310i	$0.395221\pi$
$74$		0			0
$75$	−4.49062	+	2.59266i	−0.518532	+	0.299374i
$76$		0			0
$77$	−0.606329	−	4.28139i	−0.0690977	−	0.487909i
$78$		0			0
$79$			9.18416i			1.03330i	0.856197	+	0.516649i	$0.172821\pi$
$79$			9.18416i			1.03330i	−0.856197	+	0.516649i	$0.827179\pi$
$80$		0			0
$81$	−1.50500	−	2.60674i	−0.167223	−	0.289638i
$82$		0			0
$83$	−1.51784	−	1.51784i	−0.166604	−	0.166604i	0.618881	−	0.785485i	$-0.287586\pi$
$83$	−1.51784	−	1.51784i	−0.166604	−	0.166604i	−0.785485	+	0.618881i	$0.787586\pi$
$84$		0			0
$85$	−1.94235	−	7.24895i	−0.210677	−	0.786259i
$86$		0			0
$87$	5.86862	+	3.38825i	0.629182	+	0.363259i
$88$		0			0
$89$	−2.08017	+	7.76328i	−0.220497	+	0.822906i	0.763662	+	0.645617i	$0.223400\pi$
$89$	−2.08017	+	7.76328i	−0.220497	+	0.822906i	−0.984159	+	0.177290i	$0.943267\pi$
$90$		0			0
$91$	0.539289	+	4.66976i	0.0565329	+	0.489524i
$92$		0			0
$93$	−1.76895	−	0.473988i	−0.183431	−	0.0491503i
$94$		0			0
$95$	3.05204	−	5.28630i	0.313133	−	0.542363i
$96$		0			0
$97$	2.47736	+	9.24563i	0.251538	+	0.938751i	0.969984	+	0.243169i	$0.0781869\pi$
$97$	2.47736	+	9.24563i	0.251538	+	0.938751i	−0.718446	+	0.695582i	$0.755146\pi$
$98$		0			0
$99$	−4.53699	+	6.03406i	−0.455984	+	0.606445i
$100$		0			0
$101$	5.29946	+	9.17893i	0.527316	+	0.913338i	0.999493	+	0.0318341i	$0.0101348\pi$
$101$	5.29946	+	9.17893i	0.527316	+	0.913338i	−0.472177	+	0.881504i	$0.656532\pi$
$102$		0			0
$103$			19.3794i			1.90951i	0.297391	+	0.954756i	$0.403884\pi$
$103$			19.3794i			1.90951i	−0.297391	+	0.954756i	$0.596116\pi$
$104$		0			0
$105$		−	3.69455i		−	0.360551i
$106$		0			0
$107$	−8.94884	+	5.16662i	−0.865117	+	0.499476i	−0.865723	−	0.500524i	$-0.833141\pi$
$107$	−8.94884	+	5.16662i	−0.865117	+	0.499476i	0.000605486		1.00000i	$0.499807\pi$
$108$		0			0
$109$	−8.97324	−	8.97324i	−0.859481	−	0.859481i	0.131796	−	0.991277i	$-0.457926\pi$
$109$	−8.97324	−	8.97324i	−0.859481	−	0.859481i	−0.991277	+	0.131796i	$0.957926\pi$
$110$		0			0
$111$	−4.33561	+	1.16172i	−0.411518	+	0.110266i
$112$		0			0
$113$	−6.83614	+	11.8405i	−0.643090	+	1.11386i	0.341649	+	0.939828i	$0.389015\pi$
$113$	−6.83614	+	11.8405i	−0.643090	+	1.11386i	−0.984739	+	0.174037i	$0.944319\pi$
$114$		0			0
$115$	−1.71599	+	6.40415i	−0.160017	+	0.597190i
$116$		0			0
$117$	5.09921	−	6.43076i	0.471423	−	0.594524i
$118$		0			0
$119$	2.83733	+	0.760260i	0.260098	+	0.0696930i
$120$		0			0
$121$	10.6789	+	2.63855i	0.970805	+	0.239868i
$122$		0			0
$123$	0.810978	−	0.217301i	0.0731235	−	0.0195934i
$124$		0			0
$125$	−2.57924	−	2.57924i	−0.230695	−	0.230695i
$126$		0			0
$127$	−8.81504	−	15.2681i	−0.782208	−	1.35482i	−0.930653	−	0.365903i	$-0.880760\pi$
$127$	−8.81504	−	15.2681i	−0.782208	−	1.35482i	0.148445	−	0.988921i	$-0.452573\pi$
$128$		0			0
$129$	−9.36913			−0.824906
$130$		0			0
$131$		−	4.79234i		−	0.418709i	−0.977840	−	0.209354i	$-0.932864\pi$
$131$		−	4.79234i		−	0.418709i	0.977840	−	0.209354i	$-0.0671362\pi$
$132$		0			0
$133$	1.19461	+	2.06912i	0.103586	+	0.179416i
$134$		0			0
$135$	−10.5723	+	10.5723i	−0.909923	+	0.909923i
$136$		0			0
$137$	−1.80559	+	0.483806i	−0.154262	+	0.0413343i	−0.335123	−	0.942174i	$-0.608778\pi$
$137$	−1.80559	+	0.483806i	−0.154262	+	0.0413343i	0.180862	+	0.983509i	$0.442111\pi$
$138$		0			0
$139$	10.1020	+	5.83242i	0.856844	+	0.494699i	0.862954	−	0.505282i	$-0.168612\pi$
$139$	10.1020	+	5.83242i	0.856844	+	0.494699i	−0.00611025	+	0.999981i	$0.501945\pi$
$140$		0			0
$141$	−0.0593418	+	0.221467i	−0.00499748	+	0.0186509i
$142$		0			0
$143$	−11.5316	−	3.16588i	−0.964319	−	0.264744i
$144$		0			0
$145$	−6.86705	+	25.6282i	−0.570278	+	2.12830i
$146$		0			0
$147$	−3.90498	−	2.25454i	−0.322077	−	0.185951i
$148$		0			0
$149$	12.3285	−	3.30342i	1.00999	−	0.270626i	0.284366	−	0.958716i	$-0.408217\pi$
$149$	12.3285	−	3.30342i	1.00999	−	0.270626i	0.725626	+	0.688089i	$0.241550\pi$
$150$		0			0
$151$	−1.00976	+	1.00976i	−0.0821735	+	0.0821735i	−0.746999	−	0.664825i	$-0.768506\pi$
$151$	−1.00976	+	1.00976i	−0.0821735	+	0.0821735i	0.664825	+	0.746999i	$0.268506\pi$
$152$		0			0
$153$	−2.56422	−	4.44135i	−0.207305	−	0.359062i
$154$		0			0
$155$		−	7.17034i		−	0.575936i
$156$		0			0
$157$	16.1466			1.28864			0.644319	−	0.764757i	$-0.277141\pi$
$157$	16.1466			1.28864			0.644319	+	0.764757i	$0.277141\pi$
$158$		0			0
$159$	0.775186	+	1.34266i	0.0614763	+	0.106480i
$160$		0			0
$161$	−1.83501	−	1.83501i	−0.144619	−	0.144619i
$162$		0			0
$163$	1.89449	−	0.507626i	0.148388	−	0.0397604i	−0.183861	−	0.982952i	$-0.558859\pi$
$163$	1.89449	−	0.507626i	0.148388	−	0.0397604i	0.332248	+	0.943192i	$0.392193\pi$
$164$		0			0
$165$	8.71785	+	3.51151i	0.678683	+	0.273371i
$166$		0			0
$167$	3.50682	+	0.939648i	0.271366	+	0.0727122i	0.391936	−	0.919993i	$-0.371806\pi$
$167$	3.50682	+	0.939648i	0.271366	+	0.0727122i	−0.120570	+	0.992705i	$0.538472\pi$
$168$		0			0
$169$	12.4435	+	3.76278i	0.957195	+	0.289445i
$170$		0			0
$171$	1.07962	−	4.02919i	0.0825605	−	0.308120i
$172$		0			0
$173$	−7.82822	+	13.5589i	−0.595168	+	1.03086i	0.398355	+	0.917231i	$0.369581\pi$
$173$	−7.82822	+	13.5589i	−0.595168	+	1.03086i	−0.993523	+	0.113630i	$0.963752\pi$
$174$		0			0
$175$	7.67578	−	2.05672i	0.580234	−	0.155473i
$176$		0			0
$177$	−1.02459	−	1.02459i	−0.0770131	−	0.0770131i
$178$		0			0
$179$	11.2126	−	6.47359i	0.838068	−	0.483859i	−0.0185390	−	0.999828i	$-0.505901\pi$
$179$	11.2126	−	6.47359i	0.838068	−	0.483859i	0.856607	+	0.515969i	$0.172568\pi$
$180$		0			0
$181$			1.43232i			0.106463i	0.998582	+	0.0532317i	$0.0169522\pi$
$181$			1.43232i			0.106463i	−0.998582	+	0.0532317i	$0.983048\pi$
$182$		0			0
$183$		−	2.46575i		−	0.182273i
$184$		0			0
$185$	−8.78709	−	15.2197i	−0.646040	−	1.11897i
$186$		0			0
$187$	−4.49071	+	5.97251i	−0.328393	+	0.436753i
$188$		0			0
$189$	−1.51467	−	5.65282i	−0.110176	−	0.411182i
$190$		0			0
$191$	2.76875	−	4.79561i	0.200340	−	0.346998i	−0.748298	−	0.663362i	$-0.769129\pi$
$191$	2.76875	−	4.79561i	0.200340	−	0.346998i	0.948638	+	0.316364i	$0.102462\pi$
$192$		0			0
$193$	14.1165	+	3.78251i	1.01613	+	0.272271i	0.728188	−	0.685378i	$-0.240363\pi$
$193$	14.1165	+	3.78251i	1.01613	+	0.272271i	0.287940	+	0.957648i	$0.407030\pi$
$194$		0			0
$195$	−9.37604	−	4.05977i	−0.671432	−	0.290726i
$196$		0			0
$197$	0.448559	−	1.67404i	0.0319585	−	0.119271i	−0.948104	−	0.317961i	$-0.897002\pi$
$197$	0.448559	−	1.67404i	0.0319585	−	0.119271i	0.980062	+	0.198690i	$0.0636687\pi$
$198$		0			0
$199$	10.5093	+	6.06753i	0.744983	+	0.430116i	0.823878	−	0.566767i	$-0.191806\pi$
$199$	10.5093	+	6.06753i	0.744983	+	0.430116i	−0.0788956	+	0.996883i	$0.525139\pi$
$200$		0			0
$201$	−1.23995	−	4.62755i	−0.0874591	−	0.326402i
$202$		0			0
$203$	−7.34335	−	7.34335i	−0.515402	−	0.515402i
$204$		0			0
$205$	1.64363	+	2.84685i	0.114796	+	0.198833i
$206$		0			0
$207$			4.53076i			0.314910i
$208$		0			0
$209$	−6.01783	+	0.852245i	−0.416262	+	0.0589510i
$210$		0			0
$211$	−18.1711	+	10.4911i	−1.25095	+	0.722237i	−0.971299	−	0.237864i	$-0.923553\pi$
$211$	−18.1711	+	10.4911i	−1.25095	+	0.722237i	−0.279653	+	0.960101i	$0.590220\pi$
$212$		0			0
$213$	5.21842	−	5.21842i	0.357560	−	0.357560i
$214$		0			0
$215$	−9.49432	−	35.4333i	−0.647507	−	2.41653i
$216$		0			0
$217$	2.43055	+	1.40328i	0.164997	+	0.0952609i
$218$		0			0
$219$	6.18640	+	1.65764i	0.418038	+	0.112013i
$220$		0			0
$221$	5.04720	−	6.36517i	0.339512	−	0.428167i
$222$		0			0
$223$	−15.0234	−	4.02550i	−1.00604	−	0.269567i	−0.282065	−	0.959395i	$-0.591019\pi$
$223$	−15.0234	−	4.02550i	−1.00604	−	0.269567i	−0.723973	+	0.689828i	$0.757686\pi$
$224$		0			0
$225$	−12.0151	−	6.93693i	−0.801008	−	0.462462i
$226$		0			0
$227$	14.3793	−	3.85293i	0.954391	−	0.255728i	0.252166	−	0.967684i	$-0.418857\pi$
$227$	14.3793	−	3.85293i	0.954391	−	0.255728i	0.702224	+	0.711956i	$0.252190\pi$
$228$		0			0
$229$	16.4206	+	16.4206i	1.08511	+	1.08511i	0.996024	+	0.0890819i	$0.0283933\pi$
$229$	16.4206	+	16.4206i	1.08511	+	1.08511i	0.0890819	+	0.996024i	$0.471607\pi$
$230$		0			0
$231$	−2.89645	+	2.26789i	−0.190572	+	0.149216i
$232$		0			0
$233$	−22.3223			−1.46238			−0.731192	−	0.682172i	$-0.761036\pi$
$233$	−22.3223			−1.46238			−0.731192	+	0.682172i	$0.761036\pi$
$234$		0			0
$235$	−0.897704			−0.0585598
$236$		0			0
$237$	6.76654	−	3.90666i	0.439534	−	0.253765i
$238$		0			0
$239$	17.2343	+	17.2343i	1.11479	+	1.11479i	0.992493	+	0.122302i	$0.0390277\pi$
$239$	17.2343	+	17.2343i	1.11479	+	1.11479i	0.122302	+	0.992493i	$0.460972\pi$
$240$		0			0
$241$	−5.78938	−	21.6063i	−0.372927	−	1.39178i	−0.856350	−	0.516395i	$-0.827274\pi$
$241$	−5.78938	−	21.6063i	−0.372927	−	1.39178i	0.483424	−	0.875387i	$-0.339393\pi$
$242$		0			0
$243$	−8.01343	+	13.8797i	−0.514062	+	0.890381i
$244$		0			0
$245$	4.56933	−	17.0530i	0.291924	−	1.08948i
$246$		0			0
$247$	6.56373	−	0.758015i	0.417640	−	0.0482313i
$248$		0			0
$249$	−0.472643	+	1.76393i	−0.0299525	+	0.111784i
$250$		0			0
$251$	−26.6613	−	15.3929i	−1.68285	−	0.971593i	−0.959754	−	0.280843i	$-0.909386\pi$
$251$	−26.6613	−	15.3929i	−1.68285	−	0.971593i	−0.723094	−	0.690749i	$-0.757281\pi$
$252$		0			0
$253$	6.07407	−	2.58588i	0.381873	−	0.162573i
$254$		0			0
$255$	−4.51453	+	4.51453i	−0.282711	+	0.282711i
$256$		0			0
$257$	−17.0388	+	9.83734i	−1.06285	+	0.613636i	−0.926219	−	0.376986i	$-0.876961\pi$
$257$	−17.0388	+	9.83734i	−1.06285	+	0.613636i	−0.136630	+	0.990622i	$0.543627\pi$
$258$		0			0
$259$	6.87876			0.427425
$260$		0			0
$261$			18.1312i			1.12230i
$262$		0			0
$263$	−22.5690	+	13.0302i	−1.39166	+	0.803477i	−0.993499	−	0.113838i	$-0.963686\pi$
$263$	−22.5690	+	13.0302i	−1.39166	+	0.803477i	−0.398163	+	0.917315i	$0.630352\pi$
$264$		0			0
$265$	−4.29229	+	4.29229i	−0.263674	+	0.263674i
$266$		0			0
$267$	6.60453	−	1.76968i	0.404191	−	0.108303i
$268$		0			0
$269$	7.68975	−	13.3190i	0.468852	−	0.812076i	−0.530514	−	0.847676i	$-0.678001\pi$
$269$	7.68975	−	13.3190i	0.468852	−	0.812076i	0.999366	+	0.0356006i	$0.0113344\pi$
$270$		0			0
$271$	20.5357	+	5.50253i	1.24746	+	0.334255i	0.821353	−	0.570420i	$-0.193219\pi$
$271$	20.5357	+	5.50253i	1.24746	+	0.334255i	0.426103	+	0.904675i	$0.359886\pi$
$272$		0			0
$273$	3.21111	−	2.38370i	0.194345	−	0.144268i
$274$		0			0
$275$	−2.44237	+	20.0670i	−0.147280	+	1.21008i
$276$		0			0
$277$	−14.2317	+	24.6500i	−0.855100	+	1.48108i	0.0214521	+	0.999770i	$0.493171\pi$
$277$	−14.2317	+	24.6500i	−0.855100	+	1.48108i	−0.876552	+	0.481307i	$0.840162\pi$
$278$		0			0
$279$	−1.26821	−	4.73301i	−0.0759255	−	0.283358i
$280$		0			0
$281$	20.1079	−	20.1079i	1.19954	−	1.19954i	0.225231	−	0.974305i	$-0.427686\pi$
$281$	20.1079	−	20.1079i	1.19954	−	1.19954i	0.974305	−	0.225231i	$-0.0723137\pi$
$282$		0			0
$283$	−6.21048	−	10.7569i	−0.369175	−	0.639429i	0.620262	−	0.784395i	$-0.287026\pi$
$283$	−6.21048	−	10.7569i	−0.369175	−	0.639429i	−0.989437	+	0.144965i	$0.953693\pi$
$284$		0			0
$285$	−5.19299			−0.307606
$286$		0			0
$287$	−1.28668			−0.0759500
$288$		0			0
$289$	5.96194	+	10.3264i	0.350702	+	0.607434i
$290$		0			0
$291$	5.75803	−	5.75803i	0.337542	−	0.337542i
$292$		0			0
$293$	−8.07865	−	30.1499i	−0.471960	−	1.76138i	−0.632716	−	0.774384i	$-0.718060\pi$
$293$	−8.07865	−	30.1499i	−0.471960	−	1.76138i	0.160756	−	0.986994i	$-0.448607\pi$
$294$		0			0
$295$	2.83664	−	4.91321i	0.165156	−	0.286058i
$296$		0			0
$297$	14.7783	+	1.79868i	0.857524	+	0.104370i
$298$		0			0
$299$	−6.67329	+	2.64048i	−0.385926	+	0.152703i
$300$		0			0
$301$	13.8690	+	3.71620i	0.799398	+	0.214198i
$302$		0			0
$303$	4.50846	−	7.80888i	0.259004	−	0.448608i
$304$		0			0
$305$	9.32526	−	2.49870i	0.533963	−	0.143075i
$306$		0			0
$307$	−2.73282	+	2.73282i	−0.155970	+	0.155970i	−0.780778	−	0.624808i	$-0.785177\pi$
$307$	−2.73282	+	2.73282i	−0.155970	+	0.155970i	0.624808	+	0.780778i	$0.285177\pi$
$308$		0			0
$309$	14.2780	−	8.24342i	0.812248	−	0.468952i
$310$		0			0
$311$		−	27.0223i		−	1.53229i	−0.642667	−	0.766146i	$-0.722172\pi$
$311$		−	27.0223i		−	1.53229i	0.642667	−	0.766146i	$-0.277828\pi$
$312$		0			0
$313$	−9.41276			−0.532041			−0.266020	−	0.963967i	$-0.585709\pi$
$313$	−9.41276			−0.532041			−0.266020	+	0.963967i	$0.585709\pi$
$314$		0			0
$315$	8.56080	−	4.94258i	0.482346	−	0.278483i
$316$		0			0
$317$	19.6344	−	19.6344i	1.10278	−	1.10278i	0.108704	−	0.994074i	$-0.465330\pi$
$317$	19.6344	−	19.6344i	1.10278	−	1.10278i	0.994074	−	0.108704i	$-0.0346700\pi$
$318$		0			0
$319$	24.3073	−	10.3482i	1.36095	−	0.579387i
$320$		0			0
$321$	7.61313	+	4.39544i	0.424924	+	0.245330i
$322$		0			0
$323$	1.06861	−	3.98810i	0.0594589	−	0.221904i
$324$		0			0
$325$	3.21502	−	21.7396i	0.178337	−	1.20590i
$326$		0			0
$327$	−2.79420	+	10.4281i	−0.154520	+	0.576675i
$328$		0			0
$329$	0.175686	−	0.304298i	0.00968591	−	0.0167765i
$330$		0			0
$331$	−5.27309	−	19.6794i	−0.289835	−	1.08168i	−0.945233	−	0.326396i	$-0.894166\pi$
$331$	−5.27309	−	19.6794i	−0.289835	−	1.08168i	0.655398	−	0.755284i	$-0.272501\pi$
$332$		0			0
$333$	−8.49207	−	8.49207i	−0.465362	−	0.465362i
$334$		0			0
$335$	16.2445	−	9.37876i	0.887531	−	0.512417i
$336$		0			0
$337$	−13.3095			−0.725017			−0.362508	−	0.931981i	$-0.618080\pi$
$337$	−13.3095			−0.725017			−0.362508	+	0.931981i	$0.618080\pi$
$338$		0			0
$339$	11.6315			0.631739
$340$		0			0
$341$	−5.62139	+	4.40150i	−0.304415	+	0.238355i
$342$		0			0
$343$	11.3396	+	11.3396i	0.612280	+	0.612280i
$344$		0			0
$345$	5.44826	−	1.45986i	0.293324	−	0.0785961i
$346$		0			0
$347$	10.0919	+	5.82657i	0.541763	+	0.312787i	0.745793	−	0.666178i	$-0.232071\pi$
$347$	10.0919	+	5.82657i	0.541763	+	0.312787i	−0.204030	+	0.978965i	$0.565404\pi$
$348$		0			0
$349$	10.6872	+	2.86364i	0.572075	+	0.153287i	0.533248	−	0.845959i	$-0.320971\pi$
$349$	10.6872	+	2.86364i	0.572075	+	0.153287i	0.0388271	+	0.999246i	$0.487638\pi$
$350$		0			0
$351$	−16.0101	−	2.36770i	−0.854558	−	0.126378i
$352$		0			0
$353$	−27.1593	−	7.27732i	−1.44554	−	0.387333i	−0.551073	−	0.834457i	$-0.685781\pi$
$353$	−27.1593	−	7.27732i	−1.44554	−	0.387333i	−0.894472	+	0.447124i	$0.852448\pi$
$354$		0			0
$355$	25.0238	+	14.4475i	1.32813	+	0.766794i
$356$		0			0
$357$	−0.646783	−	2.41383i	−0.0342314	−	0.127753i
$358$		0			0
$359$	18.0346	−	18.0346i	0.951831	−	0.951831i	−0.0470606	−	0.998892i	$-0.514985\pi$
$359$	18.0346	−	18.0346i	0.951831	−	0.951831i	0.998892	+	0.0470606i	$0.0149854\pi$
$360$		0			0
$361$	−13.5462	+	7.82088i	−0.712956	+	0.411625i
$362$		0			0
$363$	−2.59848	−	8.99014i	−0.136385	−	0.471860i
$364$		0			0
$365$			25.0763i			1.31255i
$366$		0			0
$367$	−11.5716	−	20.0426i	−0.604033	−	1.04622i	−0.992203	−	0.124628i	$-0.960226\pi$
$367$	−11.5716	−	20.0426i	−0.604033	−	1.04622i	0.388170	−	0.921588i	$-0.373107\pi$
$368$		0			0
$369$	1.58845	+	1.58845i	0.0826912	+	0.0826912i
$370$		0			0
$371$	−0.614944	−	2.29500i	−0.0319263	−	0.119151i
$372$		0			0
$373$	−10.2469	−	5.91605i	−0.530564	−	0.306321i	0.210682	−	0.977555i	$-0.432432\pi$
$373$	−10.2469	−	5.91605i	−0.530564	−	0.306321i	−0.741246	+	0.671233i	$0.765765\pi$
$374$		0			0
$375$	−0.803156	+	2.99742i	−0.0414748	+	0.154786i
$376$		0			0
$377$	−26.7052	+	10.5667i	−1.37539	+	0.544212i
$378$		0			0
$379$	−0.613944	−	0.164506i	−0.0315362	−	0.00845010i	0.243016	−	0.970022i	$-0.421863\pi$
$379$	−0.613944	−	0.164506i	−0.0315362	−	0.00845010i	−0.274553	+	0.961572i	$0.588530\pi$
$380$		0			0
$381$	−7.49930	+	12.9892i	−0.384201	+	0.665455i
$382$		0			0
$383$	2.82017	+	10.5250i	0.144104	+	0.537803i	0.999794	+	0.0203137i	$0.00646651\pi$
$383$	2.82017	+	10.5250i	0.144104	+	0.537803i	−0.855690	+	0.517489i	$0.826867\pi$
$384$		0			0
$385$	−11.5121	−	8.65593i	−0.586713	−	0.441147i
$386$		0			0
$387$	−12.5340	−	21.7096i	−0.637141	−	1.10356i
$388$		0			0
$389$			8.15316i			0.413381i	0.978406	+	0.206691i	$0.0662694\pi$
$389$			8.15316i			0.413381i	−0.978406	+	0.206691i	$0.933731\pi$
$390$		0			0
$391$			4.48455i			0.226793i
$392$		0			0
$393$	−3.53081	+	2.03852i	−0.178106	+	0.102830i
$394$		0			0
$395$	21.6316	+	21.6316i	1.08841	+	1.08841i
$396$		0			0
$397$	9.78973	−	2.62315i	0.491333	−	0.131652i	−0.00464195	−	0.999989i	$-0.501478\pi$
$397$	9.78973	−	2.62315i	0.491333	−	0.131652i	0.495975	+	0.868337i	$0.334811\pi$
$398$		0			0
$399$	1.01630	−	1.76029i	0.0508787	−	0.0881245i
$400$		0			0
$401$	−5.86068	+	21.8724i	−0.292669	+	1.09225i	0.650383	+	0.759607i	$0.274609\pi$
$401$	−5.86068	+	21.8724i	−0.292669	+	1.09225i	−0.943051	+	0.332647i	$0.892058\pi$
$402$		0			0
$403$	6.23208	−	4.62626i	0.310442	−	0.230451i
$404$		0			0
$405$	−9.68448	−	2.59495i	−0.481226	−	0.128944i
$406$		0			0
$407$	−6.53797	+	16.2315i	−0.324075	+	0.804563i
$408$		0			0
$409$	−10.2938	+	2.75821i	−0.508995	+	0.136385i	−0.504171	−	0.863604i	$-0.668202\pi$
$409$	−10.2938	+	2.75821i	−0.508995	+	0.136385i	−0.00482332	+	0.999988i	$0.501535\pi$
$410$		0			0
$411$	1.12449	+	1.12449i	0.0554671	+	0.0554671i
$412$		0			0
$413$	1.11030	+	1.92309i	0.0546342	+	0.0946292i
$414$		0			0
$415$	−7.14999			−0.350979
$416$		0			0
$417$		−	9.92373i		−	0.485967i
$418$		0			0
$419$	6.62367	+	11.4725i	0.323587	+	0.560470i	0.981225	−	0.192864i	$-0.0617777\pi$
$419$	6.62367	+	11.4725i	0.323587	+	0.560470i	−0.657638	+	0.753334i	$0.728444\pi$
$420$		0			0
$421$	−12.2658	+	12.2658i	−0.597798	+	0.597798i	−0.939726	−	0.341928i	$-0.888920\pi$
$421$	−12.2658	+	12.2658i	−0.597798	+	0.597798i	0.341928	+	0.939726i	$0.388920\pi$
$422$		0			0
$423$	−0.592557	+	0.158775i	−0.0288111	+	0.00771992i
$424$		0			0
$425$	−11.8926	−	6.86618i	−0.576874	−	0.333058i
$426$		0			0
$427$	−0.978021	+	3.65002i	−0.0473298	+	0.176637i
$428$		0			0
$429$	2.57269	+	9.84269i	0.124210	+	0.475210i
$430$		0			0
$431$	0.933615	−	3.48430i	0.0449707	−	0.167833i	−0.939788	−	0.341757i	$-0.888978\pi$
$431$	0.933615	−	3.48430i	0.0449707	−	0.167833i	0.984759	+	0.173924i	$0.0556447\pi$
$432$		0			0
$433$	−21.3849	−	12.3466i	−1.02769	−	0.593338i	−0.111369	−	0.993779i	$-0.535523\pi$
$433$	−21.3849	−	12.3466i	−1.02769	−	0.593338i	−0.916322	+	0.400441i	$0.868857\pi$
$434$		0			0
$435$	21.8029	−	5.84207i	1.04537	−	0.280106i
$436$		0			0
$437$	−2.57925	+	2.57925i	−0.123382	+	0.123382i
$438$		0			0
$439$	−18.3260	−	31.7415i	−0.874650	−	1.51494i	−0.857135	−	0.515092i	$-0.827758\pi$
$439$	−18.3260	−	31.7415i	−0.874650	−	1.51494i	−0.0175150	−	0.999847i	$-0.505575\pi$
$440$		0			0
$441$		−	12.0645i		−	0.574501i
$442$		0			0
$443$	−14.7224			−0.699482			−0.349741	−	0.936846i	$-0.613730\pi$
$443$	−14.7224			−0.699482			−0.349741	+	0.936846i	$0.613730\pi$
$444$		0			0
$445$	13.3856	+	23.1845i	0.634537	+	1.09905i
$446$		0			0
$447$	−7.67801	−	7.67801i	−0.363157	−	0.363157i
$448$		0			0
$449$	−29.7484	+	7.97105i	−1.40391	+	0.376177i	−0.879748	−	0.475440i	$-0.842289\pi$
$449$	−29.7484	+	7.97105i	−1.40391	+	0.376177i	−0.524164	+	0.851617i	$0.675622\pi$
$450$		0			0
$451$	1.22293	−	3.03610i	0.0575855	−	0.142965i
$452$		0			0
$453$	1.17348	+	0.314433i	0.0551349	+	0.0147733i
$454$		0			0
$455$	12.2690	+	9.72859i	0.575179	+	0.456083i
$456$		0			0
$457$	1.61053	−	6.01059i	0.0753376	−	0.281164i	−0.917972	−	0.396645i	$-0.870174\pi$
$457$	1.61053	−	6.01059i	0.0753376	−	0.281164i	0.993310	+	0.115481i	$0.0368410\pi$
$458$		0			0
$459$	−5.05659	+	8.75826i	−0.236021	+	0.408801i
$460$		0			0
$461$	25.5259	−	6.83963i	1.18886	−	0.318553i	0.390423	−	0.920635i	$-0.372329\pi$
$461$	25.5259	−	6.83963i	1.18886	−	0.318553i	0.798434	+	0.602082i	$0.205662\pi$
$462$		0			0
$463$	−2.72391	−	2.72391i	−0.126591	−	0.126591i	0.640973	−	0.767564i	$-0.278531\pi$
$463$	−2.72391	−	2.72391i	−0.126591	−	0.126591i	−0.767564	+	0.640973i	$0.778531\pi$
$464$		0			0
$465$	−5.28283	+	3.05005i	−0.244986	+	0.141442i
$466$		0			0
$467$			14.5570i			0.673615i	0.941573	+	0.336808i	$0.109347\pi$
$467$			14.5570i			0.673615i	−0.941573	+	0.336808i	$0.890653\pi$
$468$		0			0
$469$			7.34193i			0.339019i
$470$		0			0
$471$	−6.86827	−	11.8962i	−0.316473	−	0.548148i
$472$		0			0
$473$	−21.9509	+	29.1940i	−1.00930	+	1.34234i
$474$		0			0
$475$	−2.89089	−	10.7889i	−0.132643	−	0.495030i
$476$		0			0
$477$	−2.07409	+	3.59243i	−0.0949661	+	0.164486i
$478$		0			0
$479$	−32.4291	−	8.68935i	−1.48172	−	0.397026i	−0.574790	−	0.818301i	$-0.694916\pi$
$479$	−32.4291	−	8.68935i	−1.48172	−	0.397026i	−0.906933	+	0.421275i	$0.861583\pi$
$480$		0			0
$481$	7.55875	−	17.4569i	0.344650	−	0.795967i
$482$		0			0
$483$	−0.571407	+	2.13252i	−0.0259999	+	0.0970330i
$484$		0			0
$485$	27.6114	+	15.9414i	1.25377	+	0.723864i
$486$		0			0
$487$	4.95078	+	18.4765i	0.224341	+	0.837252i	0.982667	+	0.185377i	$0.0593507\pi$
$487$	4.95078	+	18.4765i	0.224341	+	0.837252i	−0.758326	+	0.651875i	$0.773983\pi$
$488$		0			0
$489$	−1.17986	−	1.17986i	−0.0533550	−	0.0533550i
$490$		0			0
$491$	−6.13533	−	10.6267i	−0.276884	−	0.479577i	0.693725	−	0.720240i	$-0.255968\pi$
$491$	−6.13533	−	10.6267i	−0.276884	−	0.479577i	−0.970609	+	0.240663i	$0.922635\pi$
$492$		0			0
$493$			17.9463i			0.808261i
$494$		0			0
$495$	3.52608	+	24.8982i	0.158486	+	1.11909i
$496$		0			0
$497$	−9.79464	+	5.65494i	−0.439349	+	0.253659i
$498$		0			0
$499$	26.6447	−	26.6447i	1.19278	−	1.19278i	0.216498	−	0.976283i	$-0.430537\pi$
$499$	26.6447	−	26.6447i	1.19278	−	1.19278i	0.976283	−	0.216498i	$-0.0694634\pi$
$500$		0			0
$501$	−0.799396	−	2.98339i	−0.0357144	−	0.133288i
$502$		0			0
$503$	33.6811	+	19.4458i	1.50177	+	0.867044i	0.999998	+	0.00204172i	$0.000649901\pi$
$503$	33.6811	+	19.4458i	1.50177	+	0.867044i	0.501767	+	0.865003i	$0.332683\pi$
$504$		0			0
$505$	34.1012	+	9.13740i	1.51749	+	0.406609i
$506$		0			0
$507$	−2.52083	−	10.7685i	−0.111954	−	0.478246i
$508$		0			0
$509$	28.4307	+	7.61798i	1.26017	+	0.337661i	0.826256	−	0.563295i	$-0.190466\pi$
$509$	28.4307	+	7.61798i	1.26017	+	0.337661i	0.433911	+	0.900956i	$0.357133\pi$
$510$		0			0
$511$	−8.50019	−	4.90759i	−0.376026	−	0.217099i
$512$		0			0
$513$	−7.94549	+	2.12899i	−0.350802	+	0.0939972i
$514$		0			0
$515$	45.6448	+	45.6448i	2.01135	+	2.01135i
$516$		0			0
$517$	0.551054	+	0.703781i	0.0242353	+	0.0309522i
$518$		0			0
$519$	13.3195			0.584663
$520$		0			0
$521$	−32.5137			−1.42445			−0.712226	−	0.701950i	$-0.752313\pi$
$521$	−32.5137			−1.42445			−0.712226	+	0.701950i	$0.752313\pi$
$522$		0			0
$523$	2.72175	−	1.57140i	0.119014	−	0.0687127i	−0.439311	−	0.898335i	$-0.644777\pi$
$523$	2.72175	−	1.57140i	0.119014	−	0.0687127i	0.558325	+	0.829622i	$0.311444\pi$
$524$		0			0
$525$	−4.78036	−	4.78036i	−0.208632	−	0.208632i
$526$		0			0
$527$	−1.25527	−	4.68473i	−0.0546804	−	0.204070i
$528$		0			0
$529$	−9.51904	+	16.4875i	−0.413871	+	0.716846i
$530$		0			0
$531$	1.00342	−	3.74483i	0.0435449	−	0.162512i
$532$		0			0
$533$	−1.41387	+	3.26533i	−0.0612415	+	0.141437i
$534$		0			0
$535$	−8.90835	+	33.2464i	−0.385142	+	1.43737i
$536$		0			0
$537$	−9.53899	−	5.50734i	−0.411638	−	0.237659i
$538$		0			0
$539$	−16.1740	+	6.88568i	−0.696665	+	0.296587i
$540$		0			0
$541$	−15.3196	+	15.3196i	−0.658641	+	0.658641i	−0.955058	−	0.296417i	$-0.904208\pi$
$541$	−15.3196	+	15.3196i	−0.658641	+	0.658641i	0.296417	+	0.955058i	$0.404208\pi$
$542$		0			0
$543$	1.05528	−	0.609265i	0.0452863	−	0.0261460i
$544$		0			0
$545$	−42.2697			−1.81064
$546$		0			0
$547$			24.8203i			1.06124i	0.847610	+	0.530620i	$0.178041\pi$
$547$			24.8203i			1.06124i	−0.847610	+	0.530620i	$0.821959\pi$
$548$		0			0
$549$	5.71349	−	3.29868i	0.243846	−	0.140784i
$550$		0			0
$551$	−10.3217	+	10.3217i	−0.439718	+	0.439718i
$552$		0			0
$553$	−11.5660	+	3.09910i	−0.491836	+	0.131787i
$554$		0			0
$555$	−7.47552	+	12.9480i	−0.317318	+	0.549611i
$556$		0			0
$557$	−10.0888	−	2.70328i	−0.427475	−	0.114542i	0.0386655	−	0.999252i	$-0.487689\pi$
$557$	−10.0888	−	2.70328i	−0.427475	−	0.114542i	−0.466141	+	0.884711i	$0.654356\pi$
$558$		0			0
$559$	24.6710	−	31.1133i	1.04347	−	1.31595i
$560$		0			0
$561$	6.31053	+	0.768059i	0.266431	+	0.0324275i
$562$		0			0
$563$	12.5165	−	21.6792i	0.527507	−	0.913669i	−0.471979	−	0.881610i	$-0.656460\pi$
$563$	12.5165	−	21.6792i	0.527507	−	0.913669i	0.999486	−	0.0320595i	$-0.0102066\pi$
$564$		0			0
$565$	11.7870	+	43.9896i	0.495882	+	1.85066i
$566$		0			0
$567$	2.77493	−	2.77493i	0.116536	−	0.116536i
$568$		0			0
$569$	13.0072	+	22.5291i	0.545290	+	0.944471i	0.998589	+	0.0531117i	$0.0169140\pi$
$569$	13.0072	+	22.5291i	0.545290	+	0.944471i	−0.453298	+	0.891359i	$0.649753\pi$
$570$		0			0
$571$	10.7284			0.448969			0.224485	−	0.974478i	$-0.427930\pi$
$571$	10.7284			0.448969			0.224485	+	0.974478i	$0.427930\pi$
$572$		0			0
$573$	−4.71096			−0.196803
$574$		0			0
$575$	6.06598	+	10.5066i	0.252969	+	0.438155i
$576$		0			0
$577$	−11.7775	+	11.7775i	−0.490303	+	0.490303i	−0.908402	−	0.418099i	$-0.862697\pi$
$577$	−11.7775	+	11.7775i	−0.490303	+	0.490303i	0.418099	+	0.908402i	$0.362697\pi$
$578$		0			0
$579$	−3.21793	−	12.0095i	−0.133732	−	0.499096i
$580$		0			0
$581$	1.39930	−	2.42366i	0.0580527	−	0.100550i
$582$		0			0
$583$	5.99988	+	0.730250i	0.248490	+	0.0302439i
$584$		0			0
$585$	−3.13621	−	27.1568i	−0.129666	−	1.12279i
$586$		0			0
$587$	10.6926	+	2.86507i	0.441330	+	0.118254i	0.472640	−	0.881256i	$-0.343301\pi$
$587$	10.6926	+	2.86507i	0.441330	+	0.118254i	−0.0313096	+	0.999510i	$0.509968\pi$
$588$		0			0
$589$	1.97243	−	3.41634i	0.0812724	−	0.140768i
$590$		0			0
$591$	−1.42417	+	0.381606i	−0.0585827	+	0.0156972i
$592$		0			0
$593$	25.2426	−	25.2426i	1.03659	−	1.03659i	0.0372841	−	0.999305i	$-0.488129\pi$
$593$	25.2426	−	25.2426i	1.03659	−	1.03659i	0.999305	−	0.0372841i	$-0.0118707\pi$
$594$		0			0
$595$	8.47348	−	4.89217i	0.347379	−	0.200559i
$596$		0			0
$597$		−	10.3238i		−	0.422524i
$598$		0			0
$599$	12.6365			0.516313			0.258157	−	0.966103i	$-0.416885\pi$
$599$	12.6365			0.516313			0.258157	+	0.966103i	$0.416885\pi$
$600$		0			0
$601$	−25.2519	+	14.5792i	−1.03005	+	0.594698i	−0.916998	−	0.398892i	$-0.869395\pi$
$601$	−25.2519	+	14.5792i	−1.03005	+	0.594698i	−0.113049	+	0.993589i	$0.536062\pi$
$602$		0			0
$603$	9.06388	−	9.06388i	0.369110	−	0.369110i
$604$		0			0
$605$	31.3668	−	18.9375i	1.27524	−	0.769919i
$606$		0			0
$607$	11.8673	+	6.85161i	0.481680	+	0.278098i	0.721116	−	0.692814i	$-0.243629\pi$
$607$	11.8673	+	6.85161i	0.481680	+	0.278098i	−0.239436	+	0.970912i	$0.576963\pi$
$608$		0			0
$609$	−2.28666	+	8.53393i	−0.0926602	+	0.345812i
$610$		0			0
$611$	−0.579194	−	0.780236i	−0.0234317	−	0.0315650i
$612$		0			0
$613$	6.75784	−	25.2206i	0.272946	−	1.01865i	−0.684259	−	0.729239i	$-0.739874\pi$
$613$	6.75784	−	25.2206i	0.272946	−	1.01865i	0.957205	−	0.289411i	$-0.0934593\pi$
$614$		0			0
$615$	1.39830	−	2.42193i	0.0563849	−	0.0976615i
$616$		0			0
$617$	1.62323	+	6.05799i	0.0653489	+	0.243885i	0.990872	−	0.134806i	$-0.0430410\pi$
$617$	1.62323	+	6.05799i	0.0653489	+	0.243885i	−0.925523	+	0.378691i	$0.876374\pi$
$618$		0			0
$619$	−25.7346	−	25.7346i	−1.03436	−	1.03436i	−0.999388	−	0.0349708i	$-0.988866\pi$
$619$	−25.7346	−	25.7346i	−1.03436	−	1.03436i	−0.0349708	−	0.999388i	$-0.511134\pi$
$620$		0			0
$621$	7.73757	−	4.46729i	0.310498	−	0.179266i
$622$		0			0
$623$	−10.4786			−0.419815
$624$		0			0
$625$	18.3255			0.733019
$626$		0			0
$627$	3.18771	+	4.07119i	0.127305	+	0.162588i
$628$		0			0
$629$	−8.40545	−	8.40545i	−0.335147	−	0.335147i
$630$		0			0
$631$	−35.4237	+	9.49175i	−1.41019	+	0.377860i	−0.881994	−	0.471260i	$-0.843799\pi$
$631$	−35.4237	+	9.49175i	−1.41019	+	0.377860i	−0.528200	+	0.849120i	$0.677133\pi$
$632$		0			0
$633$	15.4589	+	8.92520i	0.614436	+	0.354745i
$634$		0			0
$635$	−56.7235	−	15.1990i	−2.25100	−	0.603154i
$636$		0			0
$637$	17.7696	−	7.03107i	0.704059	−	0.278581i
$638$		0			0
$639$	19.0730	+	5.11061i	0.754518	+	0.202172i
$640$		0			0
$641$	27.6323	+	15.9535i	1.09141	+	0.630125i	0.933951	−	0.357401i	$-0.116337\pi$
$641$	27.6323	+	15.9535i	1.09141	+	0.630125i	0.157458	+	0.987526i	$0.449670\pi$
$642$		0			0
$643$	−4.48792	−	16.7492i	−0.176986	−	0.660523i	−0.996205	−	0.0870407i	$-0.972259\pi$
$643$	−4.48792	−	16.7492i	−0.176986	−	0.660523i	0.819218	−	0.573482i	$-0.194408\pi$
$644$		0			0
$645$	−22.0673	+	22.0673i	−0.868899	+	0.868899i
$646$		0			0
$647$	−23.3562	+	13.4847i	−0.918226	+	0.530138i	−0.883069	−	0.469244i	$-0.844526\pi$
$647$	−23.3562	+	13.4847i	−0.918226	+	0.530138i	−0.0351571	+	0.999382i	$0.511193\pi$
$648$		0			0
$649$	−5.59311	+	0.792096i	−0.219549	+	0.0310925i
$650$		0			0
$651$		−	2.38765i		−	0.0935795i
$652$		0			0
$653$	−11.9838	−	20.7566i	−0.468963	−	0.812268i	0.530407	−	0.847743i	$-0.322039\pi$
$653$	−11.9838	−	20.7566i	−0.468963	−	0.812268i	−0.999371	+	0.0354749i	$0.988706\pi$
$654$		0			0
$655$	−11.2875	−	11.2875i	−0.441039	−	0.441039i
$656$		0			0
$657$	4.43519	+	16.5524i	0.173033	+	0.645769i
$658$		0			0
$659$	24.5922	+	14.1983i	0.957976	+	0.553088i	0.895549	−	0.444962i	$-0.146783\pi$
$659$	24.5922	+	14.1983i	0.957976	+	0.553088i	0.0624263	+	0.998050i	$0.480116\pi$
$660$		0			0
$661$	−6.87192	+	25.6464i	−0.267287	+	0.997528i	0.693549	+	0.720409i	$0.256046\pi$
$661$	−6.87192	+	25.6464i	−0.267287	+	0.997528i	−0.960836	+	0.277118i	$0.910621\pi$
$662$		0			0
$663$	−6.83654	−	1.01104i	−0.265509	−	0.0392655i
$664$		0			0
$665$	7.68714	+	2.05976i	0.298094	+	0.0798742i
$666$		0			0
$667$	7.92741	−	13.7307i	0.306951	−	0.531654i
$668$		0			0
$669$	3.42465	+	12.7810i	0.132405	+	0.494141i
$670$		0			0
$671$	−7.68321	−	5.77698i	−0.296607	−	0.223018i
$672$		0			0
$673$	10.2110	+	17.6859i	0.393604	+	0.681742i	0.992922	−	0.118769i	$-0.0378948\pi$
$673$	10.2110	+	17.6859i	0.393604	+	0.681742i	−0.599318	+	0.800511i	$0.704561\pi$
$674$		0			0
$675$			27.3590i			1.05305i
$676$		0			0
$677$			6.22223i			0.239140i	0.992826	+	0.119570i	$0.0381516\pi$
$677$			6.22223i			0.239140i	−0.992826	+	0.119570i	$0.961848\pi$
$678$		0			0
$679$	−10.8074	+	6.23968i	−0.414752	+	0.239457i
$680$		0			0
$681$	−8.95523	−	8.95523i	−0.343165	−	0.343165i
$682$		0			0
$683$	−31.5467	+	8.45291i	−1.20710	+	0.323442i	−0.805624	−	0.592427i	$-0.798170\pi$
$683$	−31.5467	+	8.45291i	−1.20710	+	0.323442i	−0.401477	+	0.915869i	$0.631503\pi$
$684$		0			0
$685$	−3.11322	+	5.39225i	−0.118950	+	0.206027i
$686$		0			0
$687$	5.11326	−	19.0829i	0.195083	−	0.728060i
$688$		0			0
$689$	−6.50000	−	0.961268i	−0.247630	−	0.0366214i
$690$		0			0
$691$	−38.2930	−	10.2606i	−1.45673	−	0.390331i	−0.558374	−	0.829590i	$-0.688574\pi$
$691$	−38.2930	−	10.2606i	−1.45673	−	0.390331i	−0.898360	+	0.439259i	$0.855241\pi$
$692$		0			0
$693$	−9.12990	−	3.67749i	−0.346816	−	0.139696i
$694$		0			0
$695$	37.5308	−	10.0563i	1.42362	−	0.381459i
$696$		0			0
$697$	1.57224	+	1.57224i	0.0595530	+	0.0595530i
$698$		0			0
$699$	9.49524	+	16.4462i	0.359143	+	0.622054i
$700$		0			0
$701$	−2.28042			−0.0861301			−0.0430651	−	0.999072i	$-0.513712\pi$
$701$	−2.28042			−0.0861301			−0.0430651	+	0.999072i	$0.513712\pi$
$702$		0			0
$703$		−	9.66865i		−	0.364660i
$704$		0			0
$705$	0.381856	+	0.661394i	0.0143815	+	0.0249095i
$706$		0			0
$707$	−9.77117	+	9.77117i	−0.367483	+	0.367483i
$708$		0			0
$709$	23.9911	−	6.42839i	0.901004	−	0.241423i	0.221557	−	0.975147i	$-0.428886\pi$
$709$	23.9911	−	6.42839i	0.901004	−	0.241423i	0.679448	+	0.733724i	$0.262220\pi$
$710$		0			0
$711$	18.1046	+	10.4527i	0.678975	+	0.392006i
$712$		0			0
$713$	−1.10898	+	4.13877i	−0.0415316	+	0.154998i
$714$		0			0
$715$	−34.6172	+	19.7039i	−1.29461	+	0.736884i
$716$		0			0
$717$	5.36663	−	20.0285i	0.200420	−	0.747979i
$718$		0			0
$719$	12.6090	+	7.27981i	0.470236	+	0.271491i	0.716339	−	0.697753i	$-0.245817\pi$
$719$	12.6090	+	7.27981i	0.470236	+	0.271491i	−0.246102	+	0.969244i	$0.579150\pi$
$720$		0			0
$721$	−24.4053	+	6.53939i	−0.908902	+	0.243540i
$722$		0			0
$723$	−13.4560	+	13.4560i	−0.500436	+	0.500436i
$724$		0			0
$725$	24.2749	+	42.0454i	0.901548	+	1.56153i
$726$		0			0
$727$		−	49.0752i		−	1.82010i	−0.414498	−	0.910050i	$-0.636043\pi$
$727$		−	49.0752i		−	1.82010i	0.414498	−	0.910050i	$-0.363957\pi$
$728$		0			0
$729$	4.60465			0.170543
$730$		0			0
$731$	−12.4062	−	21.4882i	−0.458860	−	0.794769i
$732$		0			0
$733$	14.5746	+	14.5746i	0.538327	+	0.538327i	0.923037	−	0.384711i	$-0.125699\pi$
$733$	14.5746	+	14.5746i	0.538327	+	0.538327i	−0.384711	+	0.923037i	$0.625699\pi$
$734$		0			0
$735$	−14.5076	+	3.88731i	−0.535123	+	0.143386i
$736$		0			0
$737$	−17.3244	−	6.97820i	−0.638152	−	0.257045i
$738$		0			0
$739$	−9.83259	−	2.63463i	−0.361698	−	0.0969166i	0.0733933	−	0.997303i	$-0.476617\pi$
$739$	−9.83259	−	2.63463i	−0.361698	−	0.0969166i	−0.435091	+	0.900386i	$0.643284\pi$
$740$		0			0
$741$	−3.35049	−	4.51347i	−0.123083	−	0.165806i
$742$		0			0
$743$	3.92786	−	14.6590i	0.144099	−	0.537785i	−0.855695	−	0.517481i	$-0.826870\pi$
$743$	3.92786	−	14.6590i	0.144099	−	0.537785i	0.999794	−	0.0203043i	$-0.00646349\pi$
$744$		0			0
$745$	21.2570	−	36.8182i	0.778797	−	1.34892i
$746$		0			0
$747$	−4.71958	+	1.26461i	−0.172680	+	0.0462695i
$748$		0			0
$749$	−9.52623	−	9.52623i	−0.348081	−	0.348081i
$750$		0			0
$751$	9.02621	−	5.21129i	0.329371	−	0.190163i	−0.326191	−	0.945304i	$-0.605765\pi$
$751$	9.02621	−	5.21129i	0.329371	−	0.190163i	0.655562	+	0.755141i	$0.272432\pi$
$752$		0			0
$753$			26.1907i			0.954443i
$754$		0			0
$755$			4.75664i			0.173112i
$756$		0			0
$757$	−14.7634	−	25.5710i	−0.536585	−	0.929392i	−0.999085	−	0.0427728i	$-0.986381\pi$
$757$	−14.7634	−	25.5710i	−0.536585	−	0.929392i	0.462500	−	0.886619i	$-0.346953\pi$
$758$		0			0
$759$	−4.48890	−	3.37519i	−0.162937	−	0.122512i
$760$		0			0
$761$	7.06369	+	26.3620i	0.256059	+	0.955623i	0.967499	+	0.252877i	$0.0813767\pi$
$761$	7.06369	+	26.3620i	0.256059	+	0.955623i	−0.711440	+	0.702747i	$0.751957\pi$
$762$		0			0
$763$	8.27246	−	14.3283i	0.299483	−	0.518720i
$764$		0			0
$765$	−16.5004	−	4.42126i	−0.596572	−	0.159851i
$766$		0			0
$767$	6.10048	−	0.704517i	0.220276	−	0.0254386i
$768$		0			0
$769$	0.529669	−	1.97675i	0.0191003	−	0.0712834i	−0.955718	−	0.294285i	$-0.904919\pi$
$769$	0.529669	−	1.97675i	0.0191003	−	0.0712834i	0.974818	+	0.223001i	$0.0715853\pi$
$770$		0			0
$771$	14.4956	+	8.36901i	0.522045	+	0.301403i
$772$		0			0
$773$	−13.1969	−	49.2516i	−0.474660	−	1.77146i	−0.622685	−	0.782473i	$-0.713958\pi$
$773$	−13.1969	−	49.2516i	−0.474660	−	1.77146i	0.148024	−	0.988984i	$-0.452709\pi$
$774$		0			0
$775$	−9.27766	−	9.27766i	−0.333263	−	0.333263i
$776$		0			0
$777$	−2.92601	−	5.06801i	−0.104970	−	0.181814i
$778$		0			0
$779$			1.80853i			0.0647972i
$780$		0			0
$781$	−4.03428	−	28.4867i	−0.144358	−	1.01933i
$782$		0			0
$783$	30.9643	−	17.8772i	1.10657	−	0.638880i
$784$		0			0
$785$	38.0304	−	38.0304i	1.35736	−	1.35736i
$786$		0			0
$787$	8.34148	+	31.1308i	0.297342	+	1.10969i	0.939340	+	0.342988i	$0.111439\pi$
$787$	8.34148	+	31.1308i	0.297342	+	1.10969i	−0.641998	+	0.766706i	$0.721894\pi$
$788$		0			0
$789$	19.2003	+	11.0853i	0.683549	+	0.394647i
$790$		0			0
$791$	−17.2181	−	4.61357i	−0.612205	−	0.164040i
$792$		0			0
$793$	8.18834	+	6.49287i	0.290776	+	0.230569i
$794$		0			0
$795$	4.98821	+	1.33659i	0.176914	+	0.0474039i
$796$		0			0
$797$	−38.4816	−	22.2174i	−1.36309	−	0.786979i	−0.373054	−	0.927810i	$-0.621689\pi$
$797$	−38.4816	−	22.2174i	−1.36309	−	0.786979i	−0.990034	+	0.140831i	$0.955023\pi$
$798$		0			0
$799$	−0.586514	+	0.157156i	−0.0207494	+	0.00555977i
$800$		0			0
$801$	12.9362	+	12.9362i	0.457077	+	0.457077i
$802$		0			0
$803$	19.6593	−	15.3930i	0.693760	−	0.543208i
$804$		0			0
$805$	−8.64406			−0.304663
$806$		0			0
$807$	−13.0839			−0.460576
$808$		0			0
$809$	−33.0435	+	19.0777i	−1.16175	+	0.670735i	−0.951722	−	0.306960i	$-0.900688\pi$
$809$	−33.0435	+	19.0777i	−1.16175	+	0.670735i	−0.210026	+	0.977696i	$0.567355\pi$
$810$		0			0
$811$	−28.0114	−	28.0114i	−0.983612	−	0.983612i	0.0162560	−	0.999868i	$-0.494825\pi$
$811$	−28.0114	−	28.0114i	−0.983612	−	0.983612i	−0.999868	+	0.0162560i	$0.994825\pi$
$812$		0			0
$813$	−4.68122	−	17.4706i	−0.164178	−	0.612719i
$814$		0			0
$815$	3.26650	−	5.65775i	0.114421	−	0.198182i
$816$		0			0
$817$	5.22342	−	19.4941i	0.182744	−	0.682011i
$818$		0			0
$819$	9.81920	+	4.25166i	0.343111	+	0.148565i
$820$		0			0
$821$	9.93329	−	37.0716i	0.346674	−	1.29381i	−0.543970	−	0.839105i	$-0.683079\pi$
$821$	9.93329	−	37.0716i	0.346674	−	1.29381i	0.890644	−	0.454701i	$-0.150254\pi$
$822$		0			0
$823$	−29.3415	−	16.9403i	−1.02278	−	0.590502i	−0.107872	−	0.994165i	$-0.534404\pi$
$823$	−29.3415	−	16.9403i	−1.02278	−	0.590502i	−0.914908	+	0.403662i	$0.867737\pi$
$824$		0			0
$825$	15.8235	−	6.73644i	0.550903	−	0.234533i
$826$		0			0
$827$	18.7312	−	18.7312i	0.651348	−	0.651348i	−0.301970	−	0.953318i	$-0.597644\pi$
$827$	18.7312	−	18.7312i	0.651348	−	0.651348i	0.953318	+	0.301970i	$0.0976441\pi$
$828$		0			0
$829$	7.29942	−	4.21432i	0.253519	−	0.146369i	−0.367855	−	0.929883i	$-0.619908\pi$
$829$	7.29942	−	4.21432i	0.253519	−	0.146369i	0.621375	+	0.783514i	$0.286574\pi$
$830$		0			0
$831$	24.2149			0.840007
$832$		0			0
$833$		−	11.9415i		−	0.413747i
$834$		0			0
$835$	10.4728	−	6.04650i	0.362428	−	0.209248i
$836$		0			0
$837$	−6.83252	+	6.83252i	−0.236167	+	0.236167i
$838$		0			0
$839$	40.4936	−	10.8502i	1.39800	−	0.374592i	0.520371	−	0.853940i	$-0.325794\pi$
$839$	40.4936	−	10.8502i	1.39800	−	0.374592i	0.877625	+	0.479348i	$0.159127\pi$
$840$		0			0
$841$	17.2240	−	29.8328i	0.593931	−	1.02872i
$842$		0			0
$843$	−23.3680	−	6.26144i	−0.804837	−	0.215656i
$844$		0			0
$845$	38.1711	−	20.4460i	1.31312	−	0.703362i
$846$		0			0
$847$	0.280635	+	14.3387i	0.00964272	+	0.492683i
$848$		0			0
$849$	−5.28350	+	9.15129i	−0.181329	+	0.314071i
$850$		0			0
$851$	2.71806	+	10.1439i	0.0931738	+	0.347729i
$852$		0			0
$853$	−39.8564	+	39.8564i	−1.36466	+	1.36466i	−0.496778	+	0.867877i	$0.665484\pi$
$853$	−39.8564	+	39.8564i	−1.36466	+	1.36466i	−0.867877	+	0.496778i	$0.834516\pi$
$854$		0			0
$855$	−6.94719	−	12.0329i	−0.237589	−	0.411516i
$856$		0			0
$857$	1.14977			0.0392753			0.0196376	−	0.999807i	$-0.493749\pi$
$857$	1.14977			0.0392753			0.0196376	+	0.999807i	$0.493749\pi$
$858$		0			0
$859$	21.7178			0.741003			0.370502	−	0.928832i	$-0.379186\pi$
$859$	21.7178			0.741003			0.370502	+	0.928832i	$0.379186\pi$
$860$		0			0
$861$	0.547313	+	0.947973i	0.0186524	+	0.0323068i
$862$		0			0
$863$	−5.73837	+	5.73837i	−0.195336	+	0.195336i	−0.797997	−	0.602661i	$-0.794107\pi$
$863$	−5.73837	+	5.73837i	−0.195336	+	0.195336i	0.602661	+	0.797997i	$0.294107\pi$
$864$		0			0
$865$	13.4975	+	50.3734i	0.458930	+	1.71275i
$866$		0			0
$867$	5.07206	−	8.78506i	0.172256	−	0.298356i
$868$		0			0
$869$	3.68020	−	30.2373i	0.124842	−	1.02573i
$870$		0			0
$871$	18.6324	+	8.06772i	0.631334	+	0.273364i
$872$		0			0
$873$	21.0453	+	5.63907i	0.712275	+	0.190854i
$874$		0			0
$875$	2.37781	−	4.11849i	0.0803847	−	0.139230i
$876$		0			0
$877$	22.1321	−	5.93027i	0.747347	−	0.200251i	0.135006	−	0.990845i	$-0.456895\pi$
$877$	22.1321	−	5.93027i	0.747347	−	0.200251i	0.612341	+	0.790594i	$0.290228\pi$
$878$		0			0
$879$	−18.7769	+	18.7769i	−0.633330	+	0.633330i
$880$		0			0
$881$	−3.31381	+	1.91323i	−0.111645	+	0.0644583i	−0.554783	−	0.831995i	$-0.687199\pi$
$881$	−3.31381	+	1.91323i	−0.111645	+	0.0644583i	0.443138	+	0.896454i	$0.353865\pi$
$882$		0			0
$883$		−	40.7711i		−	1.37206i	−0.727575	−	0.686028i	$-0.759353\pi$
$883$		−	40.7711i		−	1.37206i	0.727575	−	0.686028i	$-0.240647\pi$
$884$		0			0
$885$	−4.82649			−0.162241
$886$		0			0
$887$	−4.23262	+	2.44371i	−0.142118	+	0.0820516i	−0.569373	−	0.822079i	$-0.692814\pi$
$887$	−4.23262	+	2.44371i	−0.142118	+	0.0820516i	0.427255	+	0.904131i	$0.359481\pi$
$888$		0			0
$889$	16.2532	−	16.2532i	0.545115	−	0.545115i
$890$		0			0
$891$	3.91041	+	9.18533i	0.131004	+	0.307720i
$892$		0			0
$893$	−0.427715	−	0.246941i	−0.0143129	−	0.00826358i
$894$		0			0
$895$	11.1619	−	41.6566i	0.373100	−	1.39243i
$896$		0			0
$897$	4.78402	+	3.79345i	0.159734	+	0.126659i
$898$		0			0
$899$	−4.43793	+	16.5626i	−0.148013	+	0.552392i
$900$		0			0
$901$	−2.05294	+	3.55579i	−0.0683932	+	0.118461i
$902$		0			0
$903$	−3.16152	−	11.7989i	−0.105209	−	0.392644i
$904$		0			0
$905$	3.37357	+	3.37357i	0.112141	+	0.112141i
$906$		0			0
$907$	−12.7500	+	7.36123i	−0.423357	+	0.244426i	−0.696513	−	0.717544i	$-0.745266\pi$
$907$	−12.7500	+	7.36123i	−0.423357	+	0.244426i	0.273155	+	0.961970i	$0.411933\pi$
$908$		0			0
$909$	24.1257			0.800199
$910$		0			0
$911$	27.7740			0.920193			0.460096	−	0.887869i	$-0.347815\pi$
$911$	27.7740			0.920193			0.460096	+	0.887869i	$0.347815\pi$
$912$		0			0
$913$	4.38901	+	5.60544i	0.145255	+	0.185513i
$914$		0			0
$915$	−5.80763	−	5.80763i	−0.191994	−	0.191994i
$916$		0			0
$917$	6.03520	−	1.61713i	0.199300	−	0.0534022i
$918$		0			0
$919$	4.79012	+	2.76558i	0.158011	+	0.0912279i	0.576921	−	0.816800i	$-0.304254\pi$
$919$	4.79012	+	2.76558i	0.158011	+	0.0912279i	−0.418909	+	0.908028i	$0.637587\pi$
$920$		0			0
$921$	3.17590	+	0.850979i	0.104649	+	0.0280407i
$922$		0			0
$923$	3.58822	+	31.0708i	0.118108	+	1.02271i
$924$		0			0
$925$	−31.0622	−	8.32310i	−1.02132	−	0.273662i
$926$		0			0
$927$	38.2024	+	22.0561i	1.25473	+	0.724419i
$928$		0			0
$929$	−5.87990	−	21.9441i	−0.192913	−	0.719963i	−0.992797	−	0.119808i	$-0.961772\pi$
$929$	−5.87990	−	21.9441i	−0.192913	−	0.719963i	0.799884	−	0.600155i	$-0.204894\pi$
$930$		0			0
$931$	6.86803	−	6.86803i	0.225091	−	0.225091i
$932$		0			0
$933$	−19.9090	+	11.4944i	−0.651790	+	0.376311i
$934$		0			0
$935$	3.49012	+	24.6442i	0.114139	+	0.805953i
$936$		0			0
$937$		−	41.6793i		−	1.36160i	−0.732468	−	0.680801i	$-0.761632\pi$
$937$		−	41.6793i		−	1.36160i	0.732468	−	0.680801i	$-0.238368\pi$
$938$		0			0
$939$	4.00390	+	6.93496i	0.130662	+	0.226314i
$940$		0			0
$941$	24.4550	+	24.4550i	0.797211	+	0.797211i	0.982655	−	0.185444i	$-0.0593723\pi$
$941$	24.4550	+	24.4550i	0.797211	+	0.797211i	−0.185444	+	0.982655i	$0.559372\pi$
$942$		0			0
$943$	−0.508414	−	1.89743i	−0.0165562	−	0.0617887i
$944$		0			0
$945$	−16.8817	−	9.74667i	−0.549163	−	0.317059i
$946$		0			0
$947$	4.26863	−	15.9307i	0.138712	−	0.517679i	−0.861243	−	0.508193i	$-0.830314\pi$
$947$	4.26863	−	15.9307i	0.138712	−	0.517679i	0.999955	−	0.00948635i	$-0.00301964\pi$
$948$		0			0
$949$	−21.7950	+	16.1791i	−0.707494	+	0.525195i
$950$		0			0
$951$	−22.8178	−	6.11400i	−0.739917	−	0.198260i
$952$		0			0
$953$	0.733554	−	1.27055i	0.0237621	−	0.0411572i	−0.853900	−	0.520437i	$-0.825769\pi$
$953$	0.733554	−	1.27055i	0.0237621	−	0.0411572i	0.877662	+	0.479280i	$0.159102\pi$
$954$		0			0
$955$	−4.77391	−	17.8165i	−0.154480	−	0.576528i
$956$		0			0
$957$	−17.9637	−	13.5069i	−0.580685	−	0.436615i
$958$		0			0
$959$	−1.21855	−	2.11060i	−0.0393492	−	0.0681547i
$960$		0			0
$961$			26.3661i			0.850518i
$962$		0			0
$963$			23.5209i			0.757952i
$964$		0			0
$965$	42.1579	−	24.3399i	1.35711	−	0.783528i
$966$		0			0
$967$	−33.6688	−	33.6688i	−1.08272	−	1.08272i	−0.996255	−	0.0864611i	$-0.972444\pi$
$967$	−33.6688	−	33.6688i	−1.08272	−	1.08272i	−0.0864611	−	0.996255i	$-0.527556\pi$
$968$		0			0
$969$	−3.39283	+	0.909107i	−0.108993	+	0.0292047i
$970$		0			0
$971$	−27.0273	+	46.8126i	−0.867346	+	1.50229i	−0.00264743	+	0.999996i	$0.500843\pi$
$971$	−27.0273	+	46.8126i	−0.867346	+	1.50229i	−0.864699	+	0.502291i	$0.832491\pi$
$972$		0			0
$973$	−3.93618	+	14.6900i	−0.126188	+	0.470940i
$974$		0			0
$975$	−17.3845	+	6.87868i	−0.556750	+	0.220294i
$976$		0			0
$977$	−2.17510	−	0.582816i	−0.0695875	−	0.0186459i	0.223857	−	0.974622i	$-0.428135\pi$
$977$	−2.17510	−	0.582816i	−0.0695875	−	0.0186459i	−0.293445	+	0.955976i	$0.594802\pi$
$978$		0			0
$979$	9.95943	−	24.7257i	0.318305	−	0.790238i
$980$		0			0
$981$	−27.9014	+	7.47617i	−0.890825	+	0.238696i
$982$		0			0
$983$	−14.7853	−	14.7853i	−0.471578	−	0.471578i	0.430847	−	0.902425i	$-0.358215\pi$
$983$	−14.7853	−	14.7853i	−0.471578	−	0.471578i	−0.902425	+	0.430847i	$0.858215\pi$
$984$		0			0
$985$	−2.88641	−	4.99941i	−0.0919687	−	0.159294i
$986$		0			0
$987$	−0.298927			−0.00951494
$988$		0			0
$989$			21.9207i			0.697039i
$990$		0			0
$991$	17.6694	+	30.6043i	0.561286	+	0.972177i	0.997385	+	0.0722775i	$0.0230267\pi$
$991$	17.6694	+	30.6043i	0.561286	+	0.972177i	−0.436098	+	0.899899i	$0.643640\pi$
$992$		0			0
$993$	−12.2560	+	12.2560i	−0.388934	+	0.388934i
$994$		0			0
$995$	39.0437	−	10.4617i	1.23777	−	0.331659i
$996$		0			0
$997$	0.117556	+	0.0678713i	0.00372305	+	0.00214950i	0.501860	−	0.864949i	$-0.332649\pi$
$997$	0.117556	+	0.0678713i	0.00372305	+	0.00214950i	−0.498137	+	0.867098i	$0.665982\pi$
$998$		0			0
$999$	−6.12953	+	22.8757i	−0.193930	+	0.723756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.197.6	yes	56
11.10	odd	2	inner	572.2.bc.a.197.5	✓	56
13.7	odd	12	inner	572.2.bc.a.241.5	yes	56
143.98	even	12	inner	572.2.bc.a.241.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.5	✓	56	11.10	odd	2	inner
572.2.bc.a.197.6	yes	56	1.1	even	1	trivial
572.2.bc.a.241.5	yes	56	13.7	odd	12	inner
572.2.bc.a.241.6	yes	56	143.98	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.425370 - 0.736762i) q^{3} +(2.35532 - 2.35532i) q^{5} +(0.337440 + 1.25934i) q^{7} +(1.13812 - 1.97128i) q^{9} +O(q^{10})\)	\(q+(-0.425370 - 0.736762i) q^{3} +(2.35532 - 2.35532i) q^{5} +(0.337440 + 1.25934i) q^{7} +(1.13812 - 1.97128i) q^{9} +(-3.29233 - 0.400712i) q^{11} +(3.56676 + 0.527479i) q^{13} +(-2.73719 - 0.733429i) q^{15} +(1.12651 - 1.95118i) q^{17} +(1.77011 - 0.474299i) q^{19} +(0.784299 - 0.784299i) q^{21} +(-1.72379 + 0.995228i) q^{23} -6.09507i q^{25} -4.48871 q^{27} +(-6.89826 + 3.98271i) q^{29} +(1.52216 - 1.52216i) q^{31} +(1.10523 + 2.59611i) q^{33} +(3.76093 + 2.17138i) q^{35} +(1.36555 - 5.09629i) q^{37} +(-1.12856 - 2.85223i) q^{39} +(-0.255426 + 0.953263i) q^{41} +(5.50646 - 9.53747i) q^{43} +(-1.96237 - 7.32365i) q^{45} +(-0.190569 - 0.190569i) q^{47} +(4.59010 - 2.65010i) q^{49} -1.91674 q^{51} -1.82238 q^{53} +(-8.69830 + 6.81069i) q^{55} +(-1.10240 - 1.10240i) q^{57} +(1.64518 - 0.440824i) q^{59} +(2.51005 + 1.44918i) q^{61} +(2.86657 + 0.768095i) q^{63} +(9.64324 - 7.15848i) q^{65} +(5.43944 + 1.45749i) q^{67} +(1.46649 + 0.846680i) q^{69} +(2.24519 + 8.37918i) q^{71} +(-5.32332 + 5.32332i) q^{73} +(-4.49062 + 2.59266i) q^{75} +(-0.606329 - 4.28139i) q^{77} +9.18416i q^{79} +(-1.50500 - 2.60674i) q^{81} +(-1.51784 - 1.51784i) q^{83} +(-1.94235 - 7.24895i) q^{85} +(5.86862 + 3.38825i) q^{87} +(-2.08017 + 7.76328i) q^{89} +(0.539289 + 4.66976i) q^{91} +(-1.76895 - 0.473988i) q^{93} +(3.05204 - 5.28630i) q^{95} +(2.47736 + 9.24563i) q^{97} +(-4.53699 + 6.03406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more