LMFDB - Embedded newform 572.2.bc.a.241.6

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			241.6
Character	$\chi$	$=$	572.241
Dual form			572.2.bc.a.197.6

$q$-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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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	−0.962297	−	0.272002i	$-0.912314\pi$
$3$	−0.425370	+	0.736762i	−0.245587	+	0.425370i	0.716709	+	0.697372i	$0.245647\pi$
$4$		0			0
$5$	2.35532	+	2.35532i	1.05333	+	1.05333i	0.998495	+	0.0548361i	$0.0174636\pi$
$5$	2.35532	+	2.35532i	1.05333	+	1.05333i	0.0548361	+	0.998495i	$0.482536\pi$
$6$		0			0
$7$	0.337440	−	1.25934i	0.127540	−	0.475987i	−0.872377	−	0.488833i	$-0.837423\pi$
$7$	0.337440	−	1.25934i	0.127540	−	0.475987i	0.999917	+	0.0128466i	$0.00408932\pi$
$8$		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	0.969684	−	0.244361i	$-0.0785781\pi$
$17$	1.12651	+	1.95118i	0.273219	+	0.473230i	−0.696465	+	0.717591i	$0.745245\pi$
$18$		0			0
$19$	1.77011	+	0.474299i	0.406091	+	0.108812i	0.456081	−	0.889938i	$-0.349253\pi$
$19$	1.77011	+	0.474299i	0.406091	+	0.108812i	−0.0499909	+	0.998750i	$0.515919\pi$
$20$		0			0
$21$	0.784299	+	0.784299i	0.171148	+	0.171148i
$22$		0			0
$23$	−1.72379	−	0.995228i	−0.359434	−	0.207519i	0.309398	−	0.950932i	$-0.399872\pi$
$23$	−1.72379	−	0.995228i	−0.359434	−	0.207519i	−0.668832	+	0.743413i	$0.733206\pi$
$24$		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	−0.303948	−	0.952689i	$-0.598305\pi$
$29$	−6.89826	−	3.98271i	−1.28097	−	0.739571i	−0.977027	+	0.213117i	$0.931638\pi$
$30$		0			0
$31$	1.52216	+	1.52216i	0.273388	+	0.273388i	0.830462	−	0.557075i	$-0.188076\pi$
$31$	1.52216	+	1.52216i	0.273388	+	0.273388i	−0.557075	+	0.830462i	$0.688076\pi$
$32$		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	0.982606	+	0.185700i	$0.0594553\pi$
$37$	1.36555	+	5.09629i	0.224494	+	0.837824i	−0.758112	+	0.652124i	$0.773878\pi$
$38$		0			0
$39$	−1.12856	+	2.85223i	−0.180715	+	0.456722i
$40$		0			0
$41$	−0.255426	−	0.953263i	−0.0398908	−	0.148875i	0.943108	−	0.332487i	$-0.107888\pi$
$41$	−0.255426	−	0.953263i	−0.0398908	−	0.148875i	−0.982999	+	0.183612i	$0.941221\pi$
$42$		0			0
$43$	5.50646	+	9.53747i	0.839728	+	1.45445i	0.890122	+	0.455722i	$0.150619\pi$
$43$	5.50646	+	9.53747i	0.839728	+	1.45445i	−0.0503947	+	0.998729i	$0.516048\pi$
$44$		0			0
$45$	−1.96237	+	7.32365i	−0.292532	+	1.09174i
$46$		0			0
$47$	−0.190569	+	0.190569i	−0.0277974	+	0.0277974i	−0.720869	−	0.693071i	$-0.756257\pi$
$47$	−0.190569	+	0.190569i	−0.0277974	+	0.0277974i	0.693071	+	0.720869i	$0.256257\pi$
$48$		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	0.364315	−	0.931276i	$-0.381303\pi$
$59$	1.64518	+	0.440824i	0.214184	+	0.0573905i	−0.150131	+	0.988666i	$0.547970\pi$
$60$		0			0
$61$	2.51005	−	1.44918i	0.321379	−	0.185548i	−0.330628	−	0.943761i	$-0.607261\pi$
$61$	2.51005	−	1.44918i	0.321379	−	0.185548i	0.652007	+	0.758213i	$0.273927\pi$
$62$		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	0.0892424	−	0.996010i	$-0.471555\pi$
$67$	5.43944	−	1.45749i	0.664533	−	0.178061i	0.575291	+	0.817949i	$0.304889\pi$
$68$		0			0
$69$	1.46649	−	0.846680i	0.176545	−	0.101928i
$70$		0			0
$71$	2.24519	−	8.37918i	0.266456	−	0.994426i	−0.694898	−	0.719108i	$-0.744550\pi$
$71$	2.24519	−	8.37918i	0.266456	−	0.994426i	0.961353	−	0.275317i	$-0.0887829\pi$
$72$		0			0
$73$	−5.32332	−	5.32332i	−0.623048	−	0.623048i	0.323262	−	0.946310i	$-0.395221\pi$
$73$	−5.32332	−	5.32332i	−0.623048	−	0.623048i	−0.946310	+	0.323262i	$0.895221\pi$
$74$		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	$-0.827179\pi$
$79$		−	9.18416i		−	1.03330i	0.856197	−	0.516649i	$-0.172821\pi$
$80$		0			0
$81$	−1.50500	+	2.60674i	−0.167223	+	0.289638i
$82$		0			0
$83$	−1.51784	+	1.51784i	−0.166604	+	0.166604i	−0.785485	−	0.618881i	$-0.787586\pi$
$83$	−1.51784	+	1.51784i	−0.166604	+	0.166604i	0.618881	+	0.785485i	$0.287586\pi$
$84$		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	−0.984159	−	0.177290i	$-0.943267\pi$
$89$	−2.08017	−	7.76328i	−0.220497	−	0.822906i	0.763662	−	0.645617i	$-0.223400\pi$
$90$		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	−0.718446	−	0.695582i	$-0.755146\pi$
$97$	2.47736	−	9.24563i	0.251538	−	0.938751i	0.969984	−	0.243169i	$-0.0781869\pi$
$98$		0			0
$99$	−4.53699	−	6.03406i	−0.455984	−	0.606445i
$100$		0			0
$101$	5.29946	−	9.17893i	0.527316	−	0.913338i	−0.472177	−	0.881504i	$-0.656532\pi$
$101$	5.29946	−	9.17893i	0.527316	−	0.913338i	0.999493	−	0.0318341i	$-0.0101348\pi$
$102$		0			0
$103$		−	19.3794i		−	1.90951i	−0.297391	−	0.954756i	$-0.596116\pi$
$103$		−	19.3794i		−	1.90951i	0.297391	−	0.954756i	$-0.403884\pi$
$104$		0			0
$105$			3.69455i			0.360551i
$106$		0			0
$107$	−8.94884	−	5.16662i	−0.865117	−	0.499476i	0.000605486	−	1.00000i	$-0.499807\pi$
$107$	−8.94884	−	5.16662i	−0.865117	−	0.499476i	−0.865723	+	0.500524i	$0.833141\pi$
$108$		0			0
$109$	−8.97324	+	8.97324i	−0.859481	+	0.859481i	−0.991277	−	0.131796i	$-0.957926\pi$
$109$	−8.97324	+	8.97324i	−0.859481	+	0.859481i	0.131796	+	0.991277i	$0.457926\pi$
$110$		0			0
$111$	−4.33561	−	1.16172i	−0.411518	−	0.110266i
$112$		0			0
$113$	−6.83614	−	11.8405i	−0.643090	−	1.11386i	−0.984739	−	0.174037i	$-0.944319\pi$
$113$	−6.83614	−	11.8405i	−0.643090	−	1.11386i	0.341649	−	0.939828i	$-0.389015\pi$
$114$		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	0.148445	+	0.988921i	$0.452573\pi$
$127$	−8.81504	+	15.2681i	−0.782208	+	1.35482i	−0.930653	+	0.365903i	$0.880760\pi$
$128$		0			0
$129$	−9.36913			−0.824906
$130$		0			0
$131$			4.79234i			0.418709i	0.977840	+	0.209354i	$0.0671362\pi$
$131$			4.79234i			0.418709i	−0.977840	+	0.209354i	$0.932864\pi$
$132$		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	0.180862	−	0.983509i	$-0.442111\pi$
$137$	−1.80559	−	0.483806i	−0.154262	−	0.0413343i	−0.335123	+	0.942174i	$0.608778\pi$
$138$		0			0
$139$	10.1020	−	5.83242i	0.856844	−	0.494699i	−0.00611025	−	0.999981i	$-0.501945\pi$
$139$	10.1020	−	5.83242i	0.856844	−	0.494699i	0.862954	+	0.505282i	$0.168612\pi$
$140$		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	0.725626	−	0.688089i	$-0.241550\pi$
$149$	12.3285	+	3.30342i	1.00999	+	0.270626i	0.284366	+	0.958716i	$0.408217\pi$
$150$		0			0
$151$	−1.00976	−	1.00976i	−0.0821735	−	0.0821735i	0.664825	−	0.746999i	$-0.268506\pi$
$151$	−1.00976	−	1.00976i	−0.0821735	−	0.0821735i	−0.746999	+	0.664825i	$0.768506\pi$
$152$		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	0.332248	−	0.943192i	$-0.392193\pi$
$163$	1.89449	+	0.507626i	0.148388	+	0.0397604i	−0.183861	+	0.982952i	$0.558859\pi$
$164$		0			0
$165$	8.71785	−	3.51151i	0.678683	−	0.273371i
$166$		0			0
$167$	3.50682	−	0.939648i	0.271366	−	0.0727122i	−0.120570	−	0.992705i	$-0.538472\pi$
$167$	3.50682	−	0.939648i	0.271366	−	0.0727122i	0.391936	+	0.919993i	$0.371806\pi$
$168$		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	−0.993523	−	0.113630i	$-0.963752\pi$
$173$	−7.82822	−	13.5589i	−0.595168	−	1.03086i	0.398355	−	0.917231i	$-0.369581\pi$
$174$		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	0.856607	−	0.515969i	$-0.172568\pi$
$179$	11.2126	+	6.47359i	0.838068	+	0.483859i	−0.0185390	+	0.999828i	$0.505901\pi$
$180$		0			0
$181$		−	1.43232i		−	0.106463i	−0.998582	−	0.0532317i	$-0.983048\pi$
$181$		−	1.43232i		−	0.106463i	0.998582	−	0.0532317i	$-0.0169522\pi$
$182$		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	0.948638	−	0.316364i	$-0.102462\pi$
$191$	2.76875	+	4.79561i	0.200340	+	0.346998i	−0.748298	+	0.663362i	$0.769129\pi$
$192$		0			0
$193$	14.1165	−	3.78251i	1.01613	−	0.272271i	0.287940	−	0.957648i	$-0.407030\pi$
$193$	14.1165	−	3.78251i	1.01613	−	0.272271i	0.728188	+	0.685378i	$0.240363\pi$
$194$		0			0
$195$	−9.37604	+	4.05977i	−0.671432	+	0.290726i
$196$		0			0
$197$	0.448559	+	1.67404i	0.0319585	+	0.119271i	0.980062	−	0.198690i	$-0.0636687\pi$
$197$	0.448559	+	1.67404i	0.0319585	+	0.119271i	−0.948104	+	0.317961i	$0.897002\pi$
$198$		0			0
$199$	10.5093	−	6.06753i	0.744983	−	0.430116i	−0.0788956	−	0.996883i	$-0.525139\pi$
$199$	10.5093	−	6.06753i	0.744983	−	0.430116i	0.823878	+	0.566767i	$0.191806\pi$
$200$		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	−0.279653	−	0.960101i	$-0.590220\pi$
$211$	−18.1711	−	10.4911i	−1.25095	−	0.722237i	−0.971299	+	0.237864i	$0.923553\pi$
$212$		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	−0.723973	−	0.689828i	$-0.757686\pi$
$223$	−15.0234	+	4.02550i	−1.00604	+	0.269567i	−0.282065	+	0.959395i	$0.591019\pi$
$224$		0			0
$225$	−12.0151	+	6.93693i	−0.801008	+	0.462462i
$226$		0			0
$227$	14.3793	+	3.85293i	0.954391	+	0.255728i	0.702224	−	0.711956i	$-0.252190\pi$
$227$	14.3793	+	3.85293i	0.954391	+	0.255728i	0.252166	+	0.967684i	$0.418857\pi$
$228$		0			0
$229$	16.4206	−	16.4206i	1.08511	−	1.08511i	0.0890819	−	0.996024i	$-0.471607\pi$
$229$	16.4206	−	16.4206i	1.08511	−	1.08511i	0.996024	−	0.0890819i	$-0.0283933\pi$
$230$		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	0.122302	−	0.992493i	$-0.460972\pi$
$239$	17.2343	−	17.2343i	1.11479	−	1.11479i	0.992493	−	0.122302i	$-0.0390277\pi$
$240$		0			0
$241$	−5.78938	+	21.6063i	−0.372927	+	1.39178i	0.483424	+	0.875387i	$0.339393\pi$
$241$	−5.78938	+	21.6063i	−0.372927	+	1.39178i	−0.856350	+	0.516395i	$0.827274\pi$
$242$		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	−0.723094	+	0.690749i	$0.757281\pi$
$251$	−26.6613	+	15.3929i	−1.68285	+	0.971593i	−0.959754	+	0.280843i	$0.909386\pi$
$252$		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	−0.136630	−	0.990622i	$-0.543627\pi$
$257$	−17.0388	−	9.83734i	−1.06285	−	0.613636i	−0.926219	+	0.376986i	$0.876961\pi$
$258$		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	−0.398163	−	0.917315i	$-0.630352\pi$
$263$	−22.5690	−	13.0302i	−1.39166	−	0.803477i	−0.993499	+	0.113838i	$0.963686\pi$
$264$		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	0.999366	−	0.0356006i	$-0.0113344\pi$
$269$	7.68975	+	13.3190i	0.468852	+	0.812076i	−0.530514	+	0.847676i	$0.678001\pi$
$270$		0			0
$271$	20.5357	−	5.50253i	1.24746	−	0.334255i	0.426103	−	0.904675i	$-0.359886\pi$
$271$	20.5357	−	5.50253i	1.24746	−	0.334255i	0.821353	+	0.570420i	$0.193219\pi$
$272$		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	−0.876552	−	0.481307i	$-0.840162\pi$
$277$	−14.2317	−	24.6500i	−0.855100	−	1.48108i	0.0214521	−	0.999770i	$-0.493171\pi$
$278$		0			0
$279$	−1.26821	+	4.73301i	−0.0759255	+	0.283358i
$280$		0			0
$281$	20.1079	+	20.1079i	1.19954	+	1.19954i	0.974305	+	0.225231i	$0.0723137\pi$
$281$	20.1079	+	20.1079i	1.19954	+	1.19954i	0.225231	+	0.974305i	$0.427686\pi$
$282$		0			0
$283$	−6.21048	+	10.7569i	−0.369175	+	0.639429i	−0.989437	−	0.144965i	$-0.953693\pi$
$283$	−6.21048	+	10.7569i	−0.369175	+	0.639429i	0.620262	+	0.784395i	$0.287026\pi$
$284$		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	0.160756	+	0.986994i	$0.448607\pi$
$293$	−8.07865	+	30.1499i	−0.471960	+	1.76138i	−0.632716	+	0.774384i	$0.718060\pi$
$294$		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	0.624808	−	0.780778i	$-0.285177\pi$
$307$	−2.73282	−	2.73282i	−0.155970	−	0.155970i	−0.780778	+	0.624808i	$0.785177\pi$
$308$		0			0
$309$	14.2780	+	8.24342i	0.812248	+	0.468952i
$310$		0			0
$311$			27.0223i			1.53229i	0.642667	+	0.766146i	$0.277828\pi$
$311$			27.0223i			1.53229i	−0.642667	+	0.766146i	$0.722172\pi$
$312$		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	0.994074	+	0.108704i	$0.0346700\pi$
$317$	19.6344	+	19.6344i	1.10278	+	1.10278i	0.108704	+	0.994074i	$0.465330\pi$
$318$		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	0.655398	+	0.755284i	$0.272501\pi$
$331$	−5.27309	+	19.6794i	−0.289835	+	1.08168i	−0.945233	+	0.326396i	$0.894166\pi$
$332$		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	−0.204030	−	0.978965i	$-0.565404\pi$
$347$	10.0919	−	5.82657i	0.541763	−	0.312787i	0.745793	+	0.666178i	$0.232071\pi$
$348$		0			0
$349$	10.6872	−	2.86364i	0.572075	−	0.153287i	0.0388271	−	0.999246i	$-0.487638\pi$
$349$	10.6872	−	2.86364i	0.572075	−	0.153287i	0.533248	+	0.845959i	$0.320971\pi$
$350$		0			0
$351$	−16.0101	+	2.36770i	−0.854558	+	0.126378i
$352$		0			0
$353$	−27.1593	+	7.27732i	−1.44554	+	0.387333i	−0.894472	−	0.447124i	$-0.852448\pi$
$353$	−27.1593	+	7.27732i	−1.44554	+	0.387333i	−0.551073	+	0.834457i	$0.685781\pi$
$354$		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	0.998892	−	0.0470606i	$-0.0149854\pi$
$359$	18.0346	+	18.0346i	0.951831	+	0.951831i	−0.0470606	+	0.998892i	$0.514985\pi$
$360$		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	0.388170	+	0.921588i	$0.373107\pi$
$367$	−11.5716	+	20.0426i	−0.604033	+	1.04622i	−0.992203	+	0.124628i	$0.960226\pi$
$368$		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	−0.741246	−	0.671233i	$-0.765765\pi$
$373$	−10.2469	+	5.91605i	−0.530564	+	0.306321i	0.210682	+	0.977555i	$0.432432\pi$
$374$		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	−0.274553	−	0.961572i	$-0.588530\pi$
$379$	−0.613944	+	0.164506i	−0.0315362	+	0.00845010i	0.243016	+	0.970022i	$0.421863\pi$
$380$		0			0
$381$	−7.49930	−	12.9892i	−0.384201	−	0.665455i
$382$		0			0
$383$	2.82017	−	10.5250i	0.144104	−	0.537803i	−0.855690	−	0.517489i	$-0.826867\pi$
$383$	2.82017	−	10.5250i	0.144104	−	0.537803i	0.999794	−	0.0203137i	$-0.00646651\pi$
$384$		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	$-0.933731\pi$
$389$		−	8.15316i		−	0.413381i	0.978406	−	0.206691i	$-0.0662694\pi$
$390$		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	0.495975	−	0.868337i	$-0.334811\pi$
$397$	9.78973	+	2.62315i	0.491333	+	0.131652i	−0.00464195	+	0.999989i	$0.501478\pi$
$398$		0			0
$399$	1.01630	+	1.76029i	0.0508787	+	0.0881245i
$400$		0			0
$401$	−5.86068	−	21.8724i	−0.292669	−	1.09225i	−0.943051	−	0.332647i	$-0.892058\pi$
$401$	−5.86068	−	21.8724i	−0.292669	−	1.09225i	0.650383	−	0.759607i	$-0.274609\pi$
$402$		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	−0.00482332	−	0.999988i	$-0.501535\pi$
$409$	−10.2938	−	2.75821i	−0.508995	−	0.136385i	−0.504171	+	0.863604i	$0.668202\pi$
$410$		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	−0.657638	−	0.753334i	$-0.728444\pi$
$419$	6.62367	−	11.4725i	0.323587	−	0.560470i	0.981225	+	0.192864i	$0.0617777\pi$
$420$		0			0
$421$	−12.2658	−	12.2658i	−0.597798	−	0.597798i	0.341928	−	0.939726i	$-0.388920\pi$
$421$	−12.2658	−	12.2658i	−0.597798	−	0.597798i	−0.939726	+	0.341928i	$0.888920\pi$
$422$		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	0.984759	−	0.173924i	$-0.0556447\pi$
$431$	0.933615	+	3.48430i	0.0449707	+	0.167833i	−0.939788	+	0.341757i	$0.888978\pi$
$432$		0			0
$433$	−21.3849	+	12.3466i	−1.02769	+	0.593338i	−0.916322	−	0.400441i	$-0.868857\pi$
$433$	−21.3849	+	12.3466i	−1.02769	+	0.593338i	−0.111369	+	0.993779i	$0.535523\pi$
$434$		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	−0.0175150	+	0.999847i	$0.505575\pi$
$439$	−18.3260	+	31.7415i	−0.874650	+	1.51494i	−0.857135	+	0.515092i	$0.827758\pi$
$440$		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	−0.524164	−	0.851617i	$-0.675622\pi$
$449$	−29.7484	−	7.97105i	−1.40391	−	0.376177i	−0.879748	+	0.475440i	$0.842289\pi$
$450$		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	0.993310	−	0.115481i	$-0.0368410\pi$
$457$	1.61053	+	6.01059i	0.0753376	+	0.281164i	−0.917972	+	0.396645i	$0.870174\pi$
$458$		0			0
$459$	−5.05659	−	8.75826i	−0.236021	−	0.408801i
$460$		0			0
$461$	25.5259	+	6.83963i	1.18886	+	0.318553i	0.798434	−	0.602082i	$-0.205662\pi$
$461$	25.5259	+	6.83963i	1.18886	+	0.318553i	0.390423	+	0.920635i	$0.372329\pi$
$462$		0			0
$463$	−2.72391	+	2.72391i	−0.126591	+	0.126591i	−0.767564	−	0.640973i	$-0.778531\pi$
$463$	−2.72391	+	2.72391i	−0.126591	+	0.126591i	0.640973	+	0.767564i	$0.278531\pi$
$464$		0			0
$465$	−5.28283	−	3.05005i	−0.244986	−	0.141442i
$466$		0			0
$467$		−	14.5570i		−	0.673615i	−0.941573	−	0.336808i	$-0.890653\pi$
$467$		−	14.5570i		−	0.673615i	0.941573	−	0.336808i	$-0.109347\pi$
$468$		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	−0.906933	−	0.421275i	$-0.861583\pi$
$479$	−32.4291	+	8.68935i	−1.48172	+	0.397026i	−0.574790	+	0.818301i	$0.694916\pi$
$480$		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	−0.758326	−	0.651875i	$-0.773983\pi$
$487$	4.95078	−	18.4765i	0.224341	−	0.837252i	0.982667	−	0.185377i	$-0.0593507\pi$
$488$		0			0
$489$	−1.17986	+	1.17986i	−0.0533550	+	0.0533550i
$490$		0			0
$491$	−6.13533	+	10.6267i	−0.276884	+	0.479577i	−0.970609	−	0.240663i	$-0.922635\pi$
$491$	−6.13533	+	10.6267i	−0.276884	+	0.479577i	0.693725	+	0.720240i	$0.255968\pi$
$492$		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	0.976283	+	0.216498i	$0.0694634\pi$
$499$	26.6447	+	26.6447i	1.19278	+	1.19278i	0.216498	+	0.976283i	$0.430537\pi$
$500$		0			0
$501$	−0.799396	+	2.98339i	−0.0357144	+	0.133288i
$502$		0			0
$503$	33.6811	−	19.4458i	1.50177	−	0.867044i	0.501767	−	0.865003i	$-0.332683\pi$
$503$	33.6811	−	19.4458i	1.50177	−	0.867044i	0.999998	−	0.00204172i	$-0.000649901\pi$
$504$		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	0.433911	−	0.900956i	$-0.357133\pi$
$509$	28.4307	−	7.61798i	1.26017	−	0.337661i	0.826256	+	0.563295i	$0.190466\pi$
$510$		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	0.558325	−	0.829622i	$-0.311444\pi$
$523$	2.72175	+	1.57140i	0.119014	+	0.0687127i	−0.439311	+	0.898335i	$0.644777\pi$
$524$		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	0.296417	−	0.955058i	$-0.404208\pi$
$541$	−15.3196	−	15.3196i	−0.658641	−	0.658641i	−0.955058	+	0.296417i	$0.904208\pi$
$542$		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	$-0.821959\pi$
$547$		−	24.8203i		−	1.06124i	0.847610	−	0.530620i	$-0.178041\pi$
$548$		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	−0.466141	−	0.884711i	$-0.654356\pi$
$557$	−10.0888	+	2.70328i	−0.427475	+	0.114542i	0.0386655	+	0.999252i	$0.487689\pi$
$558$		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	0.999486	+	0.0320595i	$0.0102066\pi$
$563$	12.5165	+	21.6792i	0.527507	+	0.913669i	−0.471979	+	0.881610i	$0.656460\pi$
$564$		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	−0.453298	−	0.891359i	$-0.649753\pi$
$569$	13.0072	−	22.5291i	0.545290	−	0.944471i	0.998589	−	0.0531117i	$-0.0169140\pi$
$570$		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	0.418099	−	0.908402i	$-0.362697\pi$
$577$	−11.7775	−	11.7775i	−0.490303	−	0.490303i	−0.908402	+	0.418099i	$0.862697\pi$
$578$		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	−0.0313096	−	0.999510i	$-0.509968\pi$
$587$	10.6926	−	2.86507i	0.441330	−	0.118254i	0.472640	+	0.881256i	$0.343301\pi$
$588$		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	0.999305	+	0.0372841i	$0.0118707\pi$
$593$	25.2426	+	25.2426i	1.03659	+	1.03659i	0.0372841	+	0.999305i	$0.488129\pi$
$594$		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	−0.113049	−	0.993589i	$-0.536062\pi$
$601$	−25.2519	−	14.5792i	−1.03005	−	0.594698i	−0.916998	+	0.398892i	$0.869395\pi$
$602$		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	−0.239436	−	0.970912i	$-0.576963\pi$
$607$	11.8673	−	6.85161i	0.481680	−	0.278098i	0.721116	+	0.692814i	$0.243629\pi$
$608$		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	0.957205	+	0.289411i	$0.0934593\pi$
$613$	6.75784	+	25.2206i	0.272946	+	1.01865i	−0.684259	+	0.729239i	$0.739874\pi$
$614$		0			0
$615$	1.39830	+	2.42193i	0.0563849	+	0.0976615i
$616$		0			0
$617$	1.62323	−	6.05799i	0.0653489	−	0.243885i	−0.925523	−	0.378691i	$-0.876374\pi$
$617$	1.62323	−	6.05799i	0.0653489	−	0.243885i	0.990872	+	0.134806i	$0.0430410\pi$
$618$		0			0
$619$	−25.7346	+	25.7346i	−1.03436	+	1.03436i	−0.0349708	+	0.999388i	$0.511134\pi$
$619$	−25.7346	+	25.7346i	−1.03436	+	1.03436i	−0.999388	+	0.0349708i	$0.988866\pi$
$620$		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	−0.528200	−	0.849120i	$-0.677133\pi$
$631$	−35.4237	−	9.49175i	−1.41019	−	0.377860i	−0.881994	+	0.471260i	$0.843799\pi$
$632$		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	0.157458	−	0.987526i	$-0.449670\pi$
$641$	27.6323	−	15.9535i	1.09141	−	0.630125i	0.933951	+	0.357401i	$0.116337\pi$
$642$		0			0
$643$	−4.48792	+	16.7492i	−0.176986	+	0.660523i	0.819218	+	0.573482i	$0.194408\pi$
$643$	−4.48792	+	16.7492i	−0.176986	+	0.660523i	−0.996205	+	0.0870407i	$0.972259\pi$
$644$		0			0
$645$	−22.0673	−	22.0673i	−0.868899	−	0.868899i
$646$		0			0
$647$	−23.3562	−	13.4847i	−0.918226	−	0.530138i	−0.0351571	−	0.999382i	$-0.511193\pi$
$647$	−23.3562	−	13.4847i	−0.918226	−	0.530138i	−0.883069	+	0.469244i	$0.844526\pi$
$648$		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	−0.999371	−	0.0354749i	$-0.988706\pi$
$653$	−11.9838	+	20.7566i	−0.468963	+	0.812268i	0.530407	+	0.847743i	$0.322039\pi$
$654$		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	0.0624263	−	0.998050i	$-0.480116\pi$
$659$	24.5922	−	14.1983i	0.957976	−	0.553088i	0.895549	+	0.444962i	$0.146783\pi$
$660$		0			0
$661$	−6.87192	−	25.6464i	−0.267287	−	0.997528i	−0.960836	−	0.277118i	$-0.910621\pi$
$661$	−6.87192	−	25.6464i	−0.267287	−	0.997528i	0.693549	−	0.720409i	$-0.256046\pi$
$662$		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	−0.599318	−	0.800511i	$-0.704561\pi$
$673$	10.2110	−	17.6859i	0.393604	−	0.681742i	0.992922	+	0.118769i	$0.0378948\pi$
$674$		0			0
$675$		−	27.3590i		−	1.05305i
$676$		0			0
$677$		−	6.22223i		−	0.239140i	−0.992826	−	0.119570i	$-0.961848\pi$
$677$		−	6.22223i		−	0.239140i	0.992826	−	0.119570i	$-0.0381516\pi$
$678$		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	−0.401477	−	0.915869i	$-0.631503\pi$
$683$	−31.5467	−	8.45291i	−1.20710	−	0.323442i	−0.805624	+	0.592427i	$0.798170\pi$
$684$		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	−0.898360	−	0.439259i	$-0.855241\pi$
$691$	−38.2930	+	10.2606i	−1.45673	+	0.390331i	−0.558374	+	0.829590i	$0.688574\pi$
$692$		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	0.679448	−	0.733724i	$-0.262220\pi$
$709$	23.9911	+	6.42839i	0.901004	+	0.241423i	0.221557	+	0.975147i	$0.428886\pi$
$710$		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	−0.246102	−	0.969244i	$-0.579150\pi$
$719$	12.6090	−	7.27981i	0.470236	−	0.271491i	0.716339	+	0.697753i	$0.245817\pi$
$720$		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	$0.363957\pi$
$727$			49.0752i			1.82010i	−0.414498	+	0.910050i	$0.636043\pi$
$728$		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	−0.384711	−	0.923037i	$-0.625699\pi$
$733$	14.5746	−	14.5746i	0.538327	−	0.538327i	0.923037	+	0.384711i	$0.125699\pi$
$734$		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	−0.435091	−	0.900386i	$-0.643284\pi$
$739$	−9.83259	+	2.63463i	−0.361698	+	0.0969166i	0.0733933	+	0.997303i	$0.476617\pi$
$740$		0			0
$741$	−3.35049	+	4.51347i	−0.123083	+	0.165806i
$742$		0			0
$743$	3.92786	+	14.6590i	0.144099	+	0.537785i	0.999794	+	0.0203043i	$0.00646349\pi$
$743$	3.92786	+	14.6590i	0.144099	+	0.537785i	−0.855695	+	0.517481i	$0.826870\pi$
$744$		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	0.655562	−	0.755141i	$-0.272432\pi$
$751$	9.02621	+	5.21129i	0.329371	+	0.190163i	−0.326191	+	0.945304i	$0.605765\pi$
$752$		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	0.462500	+	0.886619i	$0.346953\pi$
$757$	−14.7634	+	25.5710i	−0.536585	+	0.929392i	−0.999085	+	0.0427728i	$0.986381\pi$
$758$		0			0
$759$	−4.48890	+	3.37519i	−0.162937	+	0.122512i
$760$		0			0
$761$	7.06369	−	26.3620i	0.256059	−	0.955623i	−0.711440	−	0.702747i	$-0.751957\pi$
$761$	7.06369	−	26.3620i	0.256059	−	0.955623i	0.967499	−	0.252877i	$-0.0813767\pi$
$762$		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	0.974818	−	0.223001i	$-0.0715853\pi$
$769$	0.529669	+	1.97675i	0.0191003	+	0.0712834i	−0.955718	+	0.294285i	$0.904919\pi$
$770$		0			0
$771$	14.4956	−	8.36901i	0.522045	−	0.301403i
$772$		0			0
$773$	−13.1969	+	49.2516i	−0.474660	+	1.77146i	0.148024	+	0.988984i	$0.452709\pi$
$773$	−13.1969	+	49.2516i	−0.474660	+	1.77146i	−0.622685	+	0.782473i	$0.713958\pi$
$774$		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	−0.641998	−	0.766706i	$-0.721894\pi$
$787$	8.34148	−	31.1308i	0.297342	−	1.10969i	0.939340	−	0.342988i	$-0.111439\pi$
$788$		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	−0.990034	−	0.140831i	$-0.955023\pi$
$797$	−38.4816	+	22.2174i	−1.36309	+	0.786979i	−0.373054	+	0.927810i	$0.621689\pi$
$798$		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	−0.210026	−	0.977696i	$-0.567355\pi$
$809$	−33.0435	−	19.0777i	−1.16175	−	0.670735i	−0.951722	+	0.306960i	$0.900688\pi$
$810$		0			0
$811$	−28.0114	+	28.0114i	−0.983612	+	0.983612i	−0.999868	−	0.0162560i	$-0.994825\pi$
$811$	−28.0114	+	28.0114i	−0.983612	+	0.983612i	0.0162560	+	0.999868i	$0.494825\pi$
$812$		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	0.890644	+	0.454701i	$0.150254\pi$
$821$	9.93329	+	37.0716i	0.346674	+	1.29381i	−0.543970	+	0.839105i	$0.683079\pi$
$822$		0			0
$823$	−29.3415	+	16.9403i	−1.02278	+	0.590502i	−0.914908	−	0.403662i	$-0.867737\pi$
$823$	−29.3415	+	16.9403i	−1.02278	+	0.590502i	−0.107872	+	0.994165i	$0.534404\pi$
$824$		0			0
$825$	15.8235	+	6.73644i	0.550903	+	0.234533i
$826$		0			0
$827$	18.7312	+	18.7312i	0.651348	+	0.651348i	0.953318	−	0.301970i	$-0.0976441\pi$
$827$	18.7312	+	18.7312i	0.651348	+	0.651348i	−0.301970	+	0.953318i	$0.597644\pi$
$828$		0			0
$829$	7.29942	+	4.21432i	0.253519	+	0.146369i	0.621375	−	0.783514i	$-0.286574\pi$
$829$	7.29942	+	4.21432i	0.253519	+	0.146369i	−0.367855	+	0.929883i	$0.619908\pi$
$830$		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	0.877625	−	0.479348i	$-0.159127\pi$
$839$	40.4936	+	10.8502i	1.39800	+	0.374592i	0.520371	+	0.853940i	$0.325794\pi$
$840$		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	−0.867877	−	0.496778i	$-0.834516\pi$
$853$	−39.8564	−	39.8564i	−1.36466	−	1.36466i	−0.496778	−	0.867877i	$-0.665484\pi$
$854$		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	0.602661	−	0.797997i	$-0.294107\pi$
$863$	−5.73837	−	5.73837i	−0.195336	−	0.195336i	−0.797997	+	0.602661i	$0.794107\pi$
$864$		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	0.612341	−	0.790594i	$-0.290228\pi$
$877$	22.1321	+	5.93027i	0.747347	+	0.200251i	0.135006	+	0.990845i	$0.456895\pi$
$878$		0			0
$879$	−18.7769	−	18.7769i	−0.633330	−	0.633330i
$880$		0			0
$881$	−3.31381	−	1.91323i	−0.111645	−	0.0644583i	0.443138	−	0.896454i	$-0.353865\pi$
$881$	−3.31381	−	1.91323i	−0.111645	−	0.0644583i	−0.554783	+	0.831995i	$0.687199\pi$
$882$		0			0
$883$			40.7711i			1.37206i	0.727575	+	0.686028i	$0.240647\pi$
$883$			40.7711i			1.37206i	−0.727575	+	0.686028i	$0.759353\pi$
$884$		0			0
$885$	−4.82649			−0.162241
$886$		0			0
$887$	−4.23262	−	2.44371i	−0.142118	−	0.0820516i	0.427255	−	0.904131i	$-0.359481\pi$
$887$	−4.23262	−	2.44371i	−0.142118	−	0.0820516i	−0.569373	+	0.822079i	$0.692814\pi$
$888$		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	0.273155	−	0.961970i	$-0.411933\pi$
$907$	−12.7500	−	7.36123i	−0.423357	−	0.244426i	−0.696513	+	0.717544i	$0.745266\pi$
$908$		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	−0.418909	−	0.908028i	$-0.637587\pi$
$919$	4.79012	−	2.76558i	0.158011	−	0.0912279i	0.576921	+	0.816800i	$0.304254\pi$
$920$		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	0.799884	+	0.600155i	$0.204894\pi$
$929$	−5.87990	+	21.9441i	−0.192913	+	0.719963i	−0.992797	+	0.119808i	$0.961772\pi$
$930$		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	$0.238368\pi$
$937$			41.6793i			1.36160i	−0.732468	+	0.680801i	$0.761632\pi$
$938$		0			0
$939$	4.00390	−	6.93496i	0.130662	−	0.226314i
$940$		0			0
$941$	24.4550	−	24.4550i	0.797211	−	0.797211i	−0.185444	−	0.982655i	$-0.559372\pi$
$941$	24.4550	−	24.4550i	0.797211	−	0.797211i	0.982655	+	0.185444i	$0.0593723\pi$
$942$		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	0.999955	+	0.00948635i	$0.00301964\pi$
$947$	4.26863	+	15.9307i	0.138712	+	0.517679i	−0.861243	+	0.508193i	$0.830314\pi$
$948$		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	0.877662	−	0.479280i	$-0.159102\pi$
$953$	0.733554	+	1.27055i	0.0237621	+	0.0411572i	−0.853900	+	0.520437i	$0.825769\pi$
$954$		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	−0.0864611	+	0.996255i	$0.527556\pi$
$967$	−33.6688	+	33.6688i	−1.08272	+	1.08272i	−0.996255	+	0.0864611i	$0.972444\pi$
$968$		0			0
$969$	−3.39283	−	0.909107i	−0.108993	−	0.0292047i
$970$		0			0
$971$	−27.0273	−	46.8126i	−0.867346	−	1.50229i	−0.864699	−	0.502291i	$-0.832491\pi$
$971$	−27.0273	−	46.8126i	−0.867346	−	1.50229i	−0.00264743	−	0.999996i	$-0.500843\pi$
$972$		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	−0.293445	−	0.955976i	$-0.594802\pi$
$977$	−2.17510	+	0.582816i	−0.0695875	+	0.0186459i	0.223857	+	0.974622i	$0.428135\pi$
$978$		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	−0.902425	−	0.430847i	$-0.858215\pi$
$983$	−14.7853	+	14.7853i	−0.471578	+	0.471578i	0.430847	+	0.902425i	$0.358215\pi$
$984$		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	−0.436098	−	0.899899i	$-0.643640\pi$
$991$	17.6694	−	30.6043i	0.561286	−	0.972177i	0.997385	−	0.0722775i	$-0.0230267\pi$
$992$		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	−0.498137	−	0.867098i	$-0.665982\pi$
$997$	0.117556	−	0.0678713i	0.00372305	−	0.00214950i	0.501860	+	0.864949i	$0.332649\pi$
$998$		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.241.6	yes	56
11.10	odd	2	inner	572.2.bc.a.241.5	yes	56
13.2	odd	12	inner	572.2.bc.a.197.5	✓	56
143.54	even	12	inner	572.2.bc.a.197.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.5	✓	56	13.2	odd	12	inner
572.2.bc.a.197.6	yes	56	143.54	even	12	inner
572.2.bc.a.241.5	yes	56	11.10	odd	2	inner
572.2.bc.a.241.6	yes	56	1.1	even	1	trivial

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

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