LMFDB - Embedded newform 1674.2.g.b.1369.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(955,1674)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1674, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1674.955"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3669572984$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 558)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1369.12
Character	$\chi$	$=$	1674.1369
Dual form			1674.2.g.b.955.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.17303 - 2.03175i) q^{5} +(1.52021 + 2.63308i) q^{7} -1.00000 q^{8} +(-1.17303 - 2.03175i) q^{10} -5.84199 q^{11} +(-2.70313 + 4.68195i) q^{13} +3.04042 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.83888 + 3.18503i) q^{17} +(-2.58676 + 4.48039i) q^{19} -2.34606 q^{20} +(-2.92100 + 5.05931i) q^{22} +(2.63277 + 4.56010i) q^{23} +(-0.251992 - 0.436463i) q^{25} +(2.70313 + 4.68195i) q^{26} +(1.52021 - 2.63308i) q^{28} +(0.623172 - 1.07937i) q^{29} +(-4.74093 + 2.91951i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.83888 + 3.18503i) q^{34} +7.13300 q^{35} +(-2.03817 + 3.53022i) q^{37} +(2.58676 + 4.48039i) q^{38} +(-1.17303 + 2.03175i) q^{40} +(-1.47475 + 2.55433i) q^{41} +(-4.91997 - 8.52163i) q^{43} +(2.92100 + 5.05931i) q^{44} +5.26555 q^{46} +(4.27777 - 7.40932i) q^{47} +(-1.12208 + 1.94350i) q^{49} -0.503984 q^{50} +5.40625 q^{52} +(-5.39327 - 9.34142i) q^{53} +(-6.85282 + 11.8694i) q^{55} +(-1.52021 - 2.63308i) q^{56} +(-0.623172 - 1.07937i) q^{58} -4.76336 q^{59} +(7.03656 - 12.1877i) q^{61} +(0.157906 + 5.56552i) q^{62} +1.00000 q^{64} +(6.34169 + 10.9841i) q^{65} +(-5.06714 + 8.77655i) q^{67} +3.67775 q^{68} +(3.56650 - 6.17736i) q^{70} +(3.74130 + 6.48012i) q^{71} +(-2.09806 - 3.63394i) q^{73} +(2.03817 + 3.53022i) q^{74} +5.17351 q^{76} +(-8.88106 - 15.3824i) q^{77} +(-1.33943 - 2.31997i) q^{79} +(1.17303 + 2.03175i) q^{80} +(1.47475 + 2.55433i) q^{82} +8.77082 q^{83} +(4.31411 + 7.47226i) q^{85} -9.83993 q^{86} +5.84199 q^{88} -3.52297 q^{89} -16.4373 q^{91} +(2.63277 - 4.56010i) q^{92} +(-4.27777 - 7.40932i) q^{94} +(6.06868 + 10.5113i) q^{95} +(-1.79211 + 3.10403i) q^{97} +(1.12208 + 1.94350i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} + q^{5} + q^{7} - 32 q^{8} - q^{10} - 4 q^{11} - 10 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} - 2 q^{22} + q^{23} - 19 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 + q^5 + q^7 - 32 * q^8 - q^10 - 4 * q^11 - 10 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 - 2 * q^22 + q^23 - 19 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - q^31 + 16 * q^32 - 4 * q^34 - 19 * q^37 - 4 * q^38 - q^40 - 10 * q^41 - 13 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 - 13 * q^49 - 38 * q^50 + 20 * q^52 + 7 * q^53 - 11 * q^55 - q^56 - 3 * q^58 - 12 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 + 8 * q^65 - 8 * q^67 - 8 * q^68 - 7 * q^71 + 7 * q^73 + 19 * q^74 - 8 * q^76 + q^77 - 34 * q^79 + q^80 + 10 * q^82 + 28 * q^83 + 13 * q^85 - 26 * q^86 + 4 * q^88 - 2 * q^89 + 24 * q^91 + q^92 - 6 * q^94 - 21 * q^95 + 10 * q^97 + 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.17303	−	2.03175i	0.524594	−	0.908624i	−0.474996	−	0.879988i	$-0.657550\pi$
$5$	1.17303	−	2.03175i	0.524594	−	0.908624i	0.999590	−	0.0286358i	$-0.00911632\pi$
$6$		0			0
$7$	1.52021	+	2.63308i	0.574586	+	0.995211i	0.996087	+	0.0883835i	$0.0281701\pi$
$7$	1.52021	+	2.63308i	0.574586	+	0.995211i	−0.421501	+	0.906828i	$0.638497\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.17303	−	2.03175i	−0.370944	−	0.642494i
$11$	−5.84199			−1.76143			−0.880714	−	0.473649i	$-0.842936\pi$
$11$	−5.84199			−1.76143			−0.880714	+	0.473649i	$0.842936\pi$
$12$		0			0
$13$	−2.70313	+	4.68195i	−0.749712	+	1.29854i	0.198248	+	0.980152i	$0.436475\pi$
$13$	−2.70313	+	4.68195i	−0.749712	+	1.29854i	−0.947961	+	0.318388i	$0.896859\pi$
$14$	3.04042			0.812587
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.83888	+	3.18503i	−0.445993	+	0.772483i	−0.998121	−	0.0612767i	$-0.980483\pi$
$17$	−1.83888	+	3.18503i	−0.445993	+	0.772483i	0.552128	+	0.833760i	$0.313816\pi$
$18$		0			0
$19$	−2.58676	+	4.48039i	−0.593442	+	1.02787i	0.400322	+	0.916374i	$0.368898\pi$
$19$	−2.58676	+	4.48039i	−0.593442	+	1.02787i	−0.993765	+	0.111498i	$0.964435\pi$
$20$	−2.34606			−0.524594
$21$		0			0
$22$	−2.92100	+	5.05931i	−0.622759	+	1.07865i
$23$	2.63277	+	4.56010i	0.548971	+	0.950846i	0.998345	+	0.0575023i	$0.0183137\pi$
$23$	2.63277	+	4.56010i	0.548971	+	0.950846i	−0.449374	+	0.893344i	$0.648353\pi$
$24$		0			0
$25$	−0.251992	−	0.436463i	−0.0503984	−	0.0872926i
$26$	2.70313	+	4.68195i	0.530127	+	0.918206i
$27$		0			0
$28$	1.52021	−	2.63308i	0.287293	−	0.497606i
$29$	0.623172	−	1.07937i	0.115720	−	0.200433i	−0.802347	−	0.596857i	$-0.796416\pi$
$29$	0.623172	−	1.07937i	0.115720	−	0.200433i	0.918067	+	0.396424i	$0.129749\pi$
$30$		0			0
$31$	−4.74093	+	2.91951i	−0.851497	+	0.524360i
$31$	−4.74093	+	2.91951i	−0.851497	+	0.524360i
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.83888	+	3.18503i	0.315365	+	0.546228i
$35$	7.13300			1.20570
$36$		0			0
$37$	−2.03817	+	3.53022i	−0.335074	+	0.580365i	−0.983499	−	0.180914i	$-0.942095\pi$
$37$	−2.03817	+	3.53022i	−0.335074	+	0.580365i	0.648425	+	0.761278i	$0.275428\pi$
$38$	2.58676	+	4.48039i	0.419627	+	0.726815i
$39$		0			0
$40$	−1.17303	+	2.03175i	−0.185472	+	0.321247i
$41$	−1.47475	+	2.55433i	−0.230317	+	0.398920i	−0.957901	−	0.287098i	$-0.907309\pi$
$41$	−1.47475	+	2.55433i	−0.230317	+	0.398920i	0.727585	+	0.686018i	$0.240643\pi$
$42$		0			0
$43$	−4.91997	−	8.52163i	−0.750288	−	1.29954i	−0.947683	−	0.319213i	$-0.896582\pi$
$43$	−4.91997	−	8.52163i	−0.750288	−	1.29954i	0.197395	−	0.980324i	$-0.436752\pi$
$44$	2.92100	+	5.05931i	0.440357	+	0.762720i
$45$		0			0
$46$	5.26555			0.776362
$47$	4.27777	−	7.40932i	0.623977	−	1.08076i	−0.364760	−	0.931101i	$-0.618849\pi$
$47$	4.27777	−	7.40932i	0.623977	−	1.08076i	0.988738	−	0.149659i	$-0.0478176\pi$
$48$		0			0
$49$	−1.12208	+	1.94350i	−0.160297	+	0.277643i
$50$	−0.503984			−0.0712741
$51$		0			0
$52$	5.40625			0.749712
$53$	−5.39327	−	9.34142i	−0.740823	−	1.28314i	−0.952121	−	0.305721i	$-0.901102\pi$
$53$	−5.39327	−	9.34142i	−0.740823	−	1.28314i	0.211298	−	0.977422i	$-0.432231\pi$
$54$		0			0
$55$	−6.85282	+	11.8694i	−0.924035	+	1.60047i
$56$	−1.52021	−	2.63308i	−0.203147	−	0.351860i
$57$		0			0
$58$	−0.623172	−	1.07937i	−0.0818265	−	0.141728i
$59$	−4.76336			−0.620137			−0.310068	−	0.950714i	$-0.600352\pi$
$59$	−4.76336			−0.620137			−0.310068	+	0.950714i	$0.600352\pi$
$60$		0			0
$61$	7.03656	−	12.1877i	0.900939	−	1.56047i	0.0746624	−	0.997209i	$-0.476212\pi$
$61$	7.03656	−	12.1877i	0.900939	−	1.56047i	0.826277	−	0.563264i	$-0.190455\pi$
$62$	0.157906	+	5.56552i	0.0200541	+	0.706822i
$63$		0			0
$64$	1.00000			0.125000
$65$	6.34169	+	10.9841i	0.786589	+	1.36241i
$66$		0			0
$67$	−5.06714	+	8.77655i	−0.619050	+	1.07223i	0.370609	+	0.928789i	$0.379149\pi$
$67$	−5.06714	+	8.77655i	−0.619050	+	1.07223i	−0.989659	+	0.143438i	$0.954184\pi$
$68$	3.67775			0.445993
$69$		0			0
$70$	3.56650	−	6.17736i	0.426278	−	0.738336i
$71$	3.74130	+	6.48012i	0.444010	+	0.769049i	0.997983	−	0.0634865i	$-0.0202220\pi$
$71$	3.74130	+	6.48012i	0.444010	+	0.769049i	−0.553972	+	0.832535i	$0.686889\pi$
$72$		0			0
$73$	−2.09806	−	3.63394i	−0.245559	−	0.425321i	0.716730	−	0.697351i	$-0.245638\pi$
$73$	−2.09806	−	3.63394i	−0.245559	−	0.425321i	−0.962289	+	0.272030i	$0.912305\pi$
$74$	2.03817	+	3.53022i	0.236933	+	0.410380i
$75$		0			0
$76$	5.17351			0.593442
$77$	−8.88106	−	15.3824i	−1.01209	−	1.75299i
$78$		0			0
$79$	−1.33943	−	2.31997i	−0.150698	−	0.261017i	0.780786	−	0.624798i	$-0.214819\pi$
$79$	−1.33943	−	2.31997i	−0.150698	−	0.261017i	−0.931484	+	0.363782i	$0.881485\pi$
$80$	1.17303	+	2.03175i	0.131149	+	0.227156i
$81$		0			0
$82$	1.47475	+	2.55433i	0.162858	+	0.282079i
$83$	8.77082			0.962723			0.481362	−	0.876522i	$-0.340142\pi$
$83$	8.77082			0.962723			0.481362	+	0.876522i	$0.340142\pi$
$84$		0			0
$85$	4.31411	+	7.47226i	0.467931	+	0.810480i
$86$	−9.83993			−1.06107
$87$		0			0
$88$	5.84199			0.622759
$89$	−3.52297			−0.373434			−0.186717	−	0.982414i	$-0.559785\pi$
$89$	−3.52297			−0.373434			−0.186717	+	0.982414i	$0.559785\pi$
$90$		0			0
$91$	−16.4373			−1.72310
$92$	2.63277	−	4.56010i	0.274486	−	0.475423i
$93$		0			0
$94$	−4.27777	−	7.40932i	−0.441219	−	0.764213i
$95$	6.06868	+	10.5113i	0.622633	+	1.07843i
$96$		0			0
$97$	−1.79211	+	3.10403i	−0.181961	+	0.315166i	−0.942548	−	0.334070i	$-0.891578\pi$
$97$	−1.79211	+	3.10403i	−0.181961	+	0.315166i	0.760587	+	0.649236i	$0.224911\pi$
$98$	1.12208	+	1.94350i	0.113347	+	0.196323i
$99$		0			0
$100$	−0.251992	+	0.436463i	−0.0251992	+	0.0436463i
$101$	3.51439	−	6.08711i	0.349695	−	0.605690i	−0.636500	−	0.771277i	$-0.719619\pi$
$101$	3.51439	−	6.08711i	0.349695	−	0.605690i	0.986195	+	0.165587i	$0.0529519\pi$
$102$		0			0
$103$	−2.18966	+	3.79259i	−0.215753	+	0.373695i	−0.953505	−	0.301376i	$-0.902554\pi$
$103$	−2.18966	+	3.79259i	−0.215753	+	0.373695i	0.737752	+	0.675072i	$0.235887\pi$
$104$	2.70313	−	4.68195i	0.265063	−	0.459103i
$105$		0			0
$106$	−10.7865			−1.04768
$107$	−1.77681	+	3.07753i	−0.171771	+	0.297516i	−0.939039	−	0.343811i	$-0.888282\pi$
$107$	−1.77681	+	3.07753i	−0.171771	+	0.297516i	0.767268	+	0.641326i	$0.221616\pi$
$108$		0			0
$109$	18.3747			1.75998			0.879989	−	0.474993i	$-0.157550\pi$
$109$	18.3747			1.75998			0.879989	+	0.474993i	$0.157550\pi$
$110$	6.85282	+	11.8694i	0.653391	+	1.13171i
$111$		0			0
$112$	−3.04042			−0.287293
$113$	−1.84967	+	3.20372i	−0.174002	+	0.301380i	−0.939815	−	0.341683i	$-0.889003\pi$
$113$	−1.84967	+	3.20372i	−0.174002	+	0.301380i	0.765813	+	0.643063i	$0.222337\pi$
$114$		0			0
$115$	12.3533			1.15195
$116$	−1.24634			−0.115720
$117$		0			0
$118$	−2.38168	+	4.12519i	−0.219251	+	0.379755i
$119$	−11.1819			−1.02505
$120$		0			0
$121$	23.1289			2.10263
$122$	−7.03656	−	12.1877i	−0.637060	−	1.10342i
$123$		0			0
$124$	4.89884	+	2.64601i	0.439929	+	0.237619i
$125$	10.5479			0.943434
$126$		0			0
$127$	−1.95942	+	3.39381i	−0.173870	+	0.301152i	−0.939770	−	0.341808i	$-0.888961\pi$
$127$	−1.95942	+	3.39381i	−0.173870	+	0.301152i	0.765900	+	0.642960i	$0.222294\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	12.6834			1.11241
$131$	10.8084			0.944337			0.472169	−	0.881508i	$-0.343471\pi$
$131$	10.8084			0.944337			0.472169	+	0.881508i	$0.343471\pi$
$132$		0			0
$133$	−15.7297			−1.36393
$134$	5.06714	+	8.77655i	0.437735	+	0.758179i
$135$		0			0
$136$	1.83888	−	3.18503i	0.157682	−	0.273114i
$137$	−11.7047			−1.00000			−0.500001	−	0.866025i	$-0.666667\pi$
$137$	−11.7047			−1.00000			−0.500001	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	7.78289	+	13.4804i	0.660136	+	1.14339i	0.980580	+	0.196122i	$0.0628348\pi$
$139$	7.78289	+	13.4804i	0.660136	+	1.14339i	−0.320443	+	0.947268i	$0.603832\pi$
$140$	−3.56650	−	6.17736i	−0.301424	−	0.522082i
$141$		0			0
$142$	7.48260			0.627926
$143$	15.7916	−	27.3519i	1.32056	−	2.28728i
$144$		0			0
$145$	−1.46200	−	2.53225i	−0.121412	−	0.210292i
$146$	−4.19611			−0.347273
$147$		0			0
$148$	4.07635			0.335074
$149$	6.88872			0.564346			0.282173	−	0.959364i	$-0.408945\pi$
$149$	6.88872			0.564346			0.282173	+	0.959364i	$0.408945\pi$
$150$		0			0
$151$	−12.2302	+	21.1834i	−0.995283	+	1.72388i	−0.413623	+	0.910448i	$0.635737\pi$
$151$	−12.2302	+	21.1834i	−0.995283	+	1.72388i	−0.581660	+	0.813432i	$0.697597\pi$
$152$	2.58676	−	4.48039i	0.209814	−	0.363408i
$153$		0			0
$154$	−17.7621			−1.43131
$155$	0.370457	+	13.0570i	0.0297558	+	1.04877i
$156$		0			0
$157$	5.18717	+	8.98444i	0.413981	+	0.717036i	0.995321	−	0.0966246i	$-0.0308046\pi$
$157$	5.18717	+	8.98444i	0.413981	+	0.717036i	−0.581340	+	0.813661i	$0.697471\pi$
$158$	−2.67887			−0.213119
$159$		0			0
$160$	2.34606			0.185472
$161$	−8.00474	+	13.8646i	−0.630862	+	1.09268i
$162$		0			0
$163$	13.9787			1.09490			0.547448	−	0.836840i	$-0.315599\pi$
$163$	13.9787			1.09490			0.547448	+	0.836840i	$0.315599\pi$
$164$	2.94949			0.230317
$165$		0			0
$166$	4.38541	−	7.59576i	0.340374	−	0.589545i
$167$	−17.7304			−1.37202			−0.686011	−	0.727592i	$-0.740640\pi$
$167$	−17.7304			−1.37202			−0.686011	+	0.727592i	$0.740640\pi$
$168$		0			0
$169$	−8.11378	−	14.0535i	−0.624137	−	1.08104i
$170$	8.62822			0.661754
$171$		0			0
$172$	−4.91997	+	8.52163i	−0.375144	+	0.649768i
$173$	−5.49877			−0.418064			−0.209032	−	0.977909i	$-0.567031\pi$
$173$	−5.49877			−0.418064			−0.209032	+	0.977909i	$0.567031\pi$
$174$		0			0
$175$	0.766162	−	1.32703i	0.0579164	−	0.100314i
$176$	2.92100	−	5.05931i	0.220178	−	0.381360i
$177$		0			0
$178$	−1.76149	+	3.05098i	−0.132029	+	0.228681i
$179$	−11.6898	+	20.2473i	−0.873735	+	1.51335i	−0.0156315	+	0.999878i	$0.504976\pi$
$179$	−11.6898	+	20.2473i	−0.873735	+	1.51335i	−0.858104	+	0.513476i	$0.828357\pi$
$180$		0			0
$181$	−0.955580	−	1.65511i	−0.0710277	−	0.123024i	0.828324	−	0.560249i	$-0.189295\pi$
$181$	−0.955580	−	1.65511i	−0.0710277	−	0.123024i	−0.899352	+	0.437225i	$0.855961\pi$
$182$	−8.21864	+	14.2351i	−0.609206	+	1.05518i
$183$		0			0
$184$	−2.63277	−	4.56010i	−0.194091	−	0.336175i
$185$	4.78167	+	8.28210i	0.351555	+	0.608912i
$186$		0			0
$187$	10.7427	−	18.6069i	0.785585	−	1.36067i
$188$	−8.55555			−0.623977
$189$		0			0
$190$	12.1374			0.880536
$191$	16.8932			1.22235			0.611174	−	0.791496i	$-0.290698\pi$
$191$	16.8932			1.22235			0.611174	+	0.791496i	$0.290698\pi$
$192$		0			0
$193$	−12.3273			−0.887338			−0.443669	−	0.896191i	$-0.646323\pi$
$193$	−12.3273			−0.887338			−0.443669	+	0.896191i	$0.646323\pi$
$194$	1.79211	+	3.10403i	0.128666	+	0.222856i
$195$		0			0
$196$	2.24416			0.160297
$197$	−5.62507	−	9.74291i	−0.400770	−	0.694154i	0.593049	−	0.805166i	$-0.297924\pi$
$197$	−5.62507	−	9.74291i	−0.400770	−	0.694154i	−0.993819	+	0.111012i	$0.964591\pi$
$198$		0			0
$199$	−3.79423	−	6.57180i	−0.268966	−	0.465862i	0.699629	−	0.714506i	$-0.253348\pi$
$199$	−3.79423	−	6.57180i	−0.268966	−	0.465862i	−0.968595	+	0.248644i	$0.920015\pi$
$200$	0.251992	+	0.436463i	0.0178185	+	0.0308626i
$201$		0			0
$202$	−3.51439	−	6.08711i	−0.247272	−	0.428287i
$203$	3.78941			0.265964
$204$		0			0
$205$	3.45984	+	5.99261i	0.241645	+	0.418542i
$206$	2.18966	+	3.79259i	0.152561	+	0.264243i
$207$		0			0
$208$	−2.70313	−	4.68195i	−0.187428	−	0.324635i
$209$	15.1118	−	26.1744i	1.04531	−	1.81052i
$210$		0			0
$211$	−9.82384			−0.676301			−0.338151	−	0.941092i	$-0.609801\pi$
$211$	−9.82384			−0.676301			−0.338151	+	0.941092i	$0.609801\pi$
$212$	−5.39327	+	9.34142i	−0.370411	+	0.641571i
$213$		0			0
$214$	1.77681	+	3.07753i	0.121460	+	0.210375i
$215$	−23.0850			−1.57439
$216$		0			0
$217$	−14.8945	−	8.04499i	−1.01111	−	0.546130i
$218$	9.18736	−	15.9130i	0.622246	−	1.07776i
$219$		0			0
$220$	13.7056			0.924035
$221$	−9.94143	−	17.2191i	−0.668733	−	1.15828i
$222$		0			0
$223$	−5.12084	−	8.86956i	−0.342917	−	0.593950i	0.642056	−	0.766658i	$-0.278082\pi$
$223$	−5.12084	−	8.86956i	−0.342917	−	0.593950i	−0.984973	+	0.172708i	$0.944748\pi$
$224$	−1.52021	+	2.63308i	−0.101573	+	0.175930i
$225$		0			0
$226$	1.84967	+	3.20372i	0.123038	+	0.213108i
$227$	−17.2741			−1.14652			−0.573260	−	0.819374i	$-0.694321\pi$
$227$	−17.2741			−1.14652			−0.573260	+	0.819374i	$0.694321\pi$
$228$		0			0
$229$	2.33341			0.154196			0.0770982	−	0.997024i	$-0.475435\pi$
$229$	2.33341			0.154196			0.0770982	+	0.997024i	$0.475435\pi$
$230$	6.17664	−	10.6982i	0.407275	−	0.705422i
$231$		0			0
$232$	−0.623172	+	1.07937i	−0.0409132	+	0.0708638i
$233$	3.49547			0.228996			0.114498	−	0.993424i	$-0.463474\pi$
$233$	3.49547			0.228996			0.114498	+	0.993424i	$0.463474\pi$
$234$		0			0
$235$	−10.0359	−	17.3827i	−0.654670	−	1.13392i
$236$	2.38168	+	4.12519i	0.155034	+	0.268527i
$237$		0			0
$238$	−5.59096	+	9.68383i	−0.362408	+	0.627709i
$239$	2.85451	−	4.94415i	0.184643	−	0.319810i	−0.758813	−	0.651308i	$-0.774221\pi$
$239$	2.85451	−	4.94415i	0.184643	−	0.319810i	0.943456	+	0.331498i	$0.107554\pi$
$240$		0			0
$241$	8.88226	+	15.3845i	0.572157	+	0.991004i	0.996344	+	0.0854299i	$0.0272264\pi$
$241$	8.88226	+	15.3845i	0.572157	+	0.991004i	−0.424188	+	0.905574i	$0.639440\pi$
$242$	11.5644	−	20.0302i	0.743390	−	1.28759i
$243$		0			0
$244$	−14.0731			−0.900939
$245$	2.63247	+	4.55956i	0.168182	+	0.291300i
$246$		0			0
$247$	−13.9846	−	24.2221i	−0.889822	−	1.54122i
$248$	4.74093	−	2.91951i	0.301050	−	0.185389i
$249$		0			0
$250$	5.27396	−	9.13476i	0.333554	−	0.577733i
$251$	−1.50446	+	2.60581i	−0.0949609	+	0.164477i	−0.909592	−	0.415502i	$-0.863606\pi$
$251$	−1.50446	+	2.60581i	−0.0949609	+	0.164477i	0.814631	+	0.579979i	$0.196939\pi$
$252$		0			0
$253$	−15.3806	−	26.6401i	−0.966973	−	1.67485i
$254$	1.95942	+	3.39381i	0.122945	+	0.212947i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.94806	+	3.37414i	−0.121517	+	0.210473i	−0.920366	−	0.391058i	$-0.872109\pi$
$257$	−1.94806	+	3.37414i	−0.121517	+	0.210473i	0.798849	+	0.601531i	$0.205442\pi$
$258$		0			0
$259$	−12.3938			−0.770114
$260$	6.34169	−	10.9841i	0.393295	−	0.681206i
$261$		0			0
$262$	5.40422	−	9.36038i	0.333874	−	0.578286i
$263$	−7.02078	+	12.1603i	−0.432920	+	0.749839i	−0.997123	−	0.0757968i	$-0.975850\pi$
$263$	−7.02078	+	12.1603i	−0.432920	+	0.749839i	0.564204	+	0.825636i	$0.309183\pi$
$264$		0			0
$265$	−25.3058			−1.55453
$266$	−7.86483	+	13.6223i	−0.482223	+	0.835235i
$267$		0			0
$268$	10.1343			0.619050
$269$	2.44252	+	4.23057i	0.148923	+	0.257943i	0.930830	−	0.365453i	$-0.119086\pi$
$269$	2.44252	+	4.23057i	0.148923	+	0.257943i	−0.781907	+	0.623396i	$0.785753\pi$
$270$		0			0
$271$	13.2408			0.804323			0.402161	−	0.915569i	$-0.368259\pi$
$271$	13.2408			0.804323			0.402161	+	0.915569i	$0.368259\pi$
$272$	−1.83888	−	3.18503i	−0.111498	−	0.193121i
$273$		0			0
$274$	−5.85236	+	10.1366i	−0.353554	+	0.612374i
$275$	1.47214	+	2.54981i	0.0887731	+	0.153759i
$276$		0			0
$277$	9.95924	−	17.2499i	0.598393	−	1.03645i	−0.394666	−	0.918825i	$-0.629140\pi$
$277$	9.95924	−	17.2499i	0.598393	−	1.03645i	0.993058	−	0.117622i	$-0.0375270\pi$
$278$	15.5658			0.933574
$279$		0			0
$280$	−7.13300			−0.426278
$281$	−9.34766	+	16.1906i	−0.557635	+	0.965852i	0.440059	+	0.897969i	$0.354958\pi$
$281$	−9.34766	+	16.1906i	−0.557635	+	0.965852i	−0.997693	+	0.0678826i	$0.978376\pi$
$282$		0			0
$283$	−3.28581	−	5.69119i	−0.195321	−	0.338306i	0.751685	−	0.659523i	$-0.229242\pi$
$283$	−3.28581	−	5.69119i	−0.195321	−	0.338306i	−0.947006	+	0.321217i	$0.895908\pi$
$284$	3.74130	−	6.48012i	0.222005	−	0.384524i
$285$		0			0
$286$	−15.7916	−	27.3519i	−0.933779	−	1.61735i
$287$	−8.96769			−0.529346
$288$		0			0
$289$	1.73706	+	3.00868i	0.102180	+	0.176981i
$290$	−2.92399			−0.171703
$291$		0			0
$292$	−2.09806	+	3.63394i	−0.122780	+	0.212660i
$293$	15.4708			0.903812			0.451906	−	0.892066i	$-0.350744\pi$
$293$	15.4708			0.903812			0.451906	+	0.892066i	$0.350744\pi$
$294$		0			0
$295$	−5.58756	+	9.67793i	−0.325320	+	0.563471i
$296$	2.03817	−	3.53022i	0.118466	−	0.205190i
$297$		0			0
$298$	3.44436	−	5.96581i	0.199526	−	0.345590i
$299$	−28.4669			−1.64628
$300$		0			0
$301$	14.9588	−	25.9093i	0.862209	−	1.49339i
$302$	12.2302	+	21.1834i	0.703771	+	1.21897i
$303$		0			0
$304$	−2.58676	−	4.48039i	−0.148361	−	0.256968i
$305$	−16.5082	−	28.5930i	−0.945255	−	1.63723i
$306$		0			0
$307$	−7.91988	+	13.7176i	−0.452011	+	0.782907i	−0.998511	−	0.0545526i	$-0.982627\pi$
$307$	−7.91988	+	13.7176i	−0.452011	+	0.782907i	0.546499	+	0.837459i	$0.315960\pi$
$308$	−8.88106	+	15.3824i	−0.506045	+	0.876496i
$309$		0			0
$310$	11.4930	+	6.20769i	0.652756	+	0.352573i
$311$	2.91350	+	5.04633i	0.165209	+	0.286151i	0.936730	−	0.350054i	$-0.113837\pi$
$311$	2.91350	+	5.04633i	0.165209	+	0.286151i	−0.771520	+	0.636205i	$0.780503\pi$
$312$		0			0
$313$	1.69697	+	2.93925i	0.0959187	+	0.166136i	0.909992	−	0.414627i	$-0.136088\pi$
$313$	1.69697	+	2.93925i	0.0959187	+	0.166136i	−0.814073	+	0.580763i	$0.802754\pi$
$314$	10.3743			0.585458
$315$		0			0
$316$	−1.33943	+	2.31997i	−0.0753490	+	0.130508i
$317$	−10.0037	−	17.3269i	−0.561862	−	0.973174i	−0.997334	−	0.0729714i	$-0.976752\pi$
$317$	−10.0037	−	17.3269i	−0.561862	−	0.973174i	0.435472	−	0.900202i	$-0.356582\pi$
$318$		0			0
$319$	−3.64056	+	6.30564i	−0.203832	+	0.353048i
$320$	1.17303	−	2.03175i	0.0655743	−	0.113578i
$321$		0			0
$322$	8.00474	+	13.8646i	0.446087	+	0.772645i
$323$	−9.51345	−	16.4778i	−0.529343	−	0.916848i
$324$		0			0
$325$	2.72466			0.151137
$326$	6.98935	−	12.1059i	0.387104	−	0.670484i
$327$		0			0
$328$	1.47475	−	2.55433i	0.0814292	−	0.141039i
$329$	26.0125			1.43411
$330$		0			0
$331$	31.8747			1.75199			0.875996	−	0.482318i	$-0.160205\pi$
$331$	31.8747			1.75199			0.875996	+	0.482318i	$0.160205\pi$
$332$	−4.38541	−	7.59576i	−0.240681	−	0.416871i
$333$		0			0
$334$	−8.86521	+	15.3550i	−0.485083	+	0.840188i
$335$	11.8878	+	20.5903i	0.649500	+	1.12497i
$336$		0			0
$337$	11.3010	+	19.5740i	0.615606	+	1.06626i	0.990278	+	0.139104i	$0.0444221\pi$
$337$	11.3010	+	19.5740i	0.615606	+	1.06626i	−0.374672	+	0.927158i	$0.622245\pi$
$338$	−16.2276			−0.882662
$339$		0			0
$340$	4.31411	−	7.47226i	0.233966	−	0.405240i
$341$	27.6965	−	17.0558i	1.49985	−	0.923622i
$342$		0			0
$343$	14.4598			0.780753
$344$	4.91997	+	8.52163i	0.265267	+	0.459456i
$345$		0			0
$346$	−2.74939	+	4.76208i	−0.147808	+	0.256011i
$347$	13.9730			0.750112			0.375056	−	0.927002i	$-0.377624\pi$
$347$	13.9730			0.750112			0.375056	+	0.927002i	$0.377624\pi$
$348$		0			0
$349$	3.41690	−	5.91825i	0.182903	−	0.316796i	−0.759965	−	0.649964i	$-0.774784\pi$
$349$	3.41690	−	5.91825i	0.182903	−	0.316796i	0.942868	+	0.333167i	$0.108117\pi$
$350$	−0.766162	−	1.32703i	−0.0409531	−	0.0709328i
$351$		0			0
$352$	−2.92100	−	5.05931i	−0.155690	−	0.269662i
$353$	0.173175	+	0.299947i	0.00921715	+	0.0159646i	0.870597	−	0.491996i	$-0.163733\pi$
$353$	0.173175	+	0.299947i	0.00921715	+	0.0159646i	−0.861380	+	0.507961i	$0.830399\pi$
$354$		0			0
$355$	17.5546			0.931701
$356$	1.76149	+	3.05098i	0.0933585	+	0.161702i
$357$		0			0
$358$	11.6898	+	20.2473i	0.617824	+	1.07010i
$359$	10.8440	+	18.7823i	0.572324	+	0.991293i	0.996327	+	0.0856328i	$0.0272912\pi$
$359$	10.8440	+	18.7823i	0.572324	+	0.991293i	−0.424003	+	0.905661i	$0.639375\pi$
$360$		0			0
$361$	−3.88261	−	6.72487i	−0.204348	−	0.353941i
$362$	−1.91116			−0.100448
$363$		0			0
$364$	8.21864	+	14.2351i	0.430774	+	0.746122i
$365$	−9.84432			−0.515275
$366$		0			0
$367$	26.7415			1.39590			0.697948	−	0.716149i	$-0.254097\pi$
$367$	26.7415			1.39590			0.697948	+	0.716149i	$0.254097\pi$
$368$	−5.26555			−0.274486
$369$		0			0
$370$	9.56334			0.497175
$371$	16.3978	−	28.4019i	0.851332	−	1.47455i
$372$		0			0
$373$	1.69124	+	2.92931i	0.0875690	+	0.151674i	0.906483	−	0.422242i	$-0.138757\pi$
$373$	1.69124	+	2.92931i	0.0875690	+	0.151674i	−0.818914	+	0.573916i	$0.805424\pi$
$374$	−10.7427	−	18.6069i	−0.555492	−	0.962141i
$375$		0			0
$376$	−4.27777	+	7.40932i	−0.220609	+	0.382107i
$377$	3.36902	+	5.83532i	0.173514	+	0.300534i
$378$		0			0
$379$	−17.4095	+	30.1541i	−0.894264	+	1.54891i	−0.0595514	+	0.998225i	$0.518967\pi$
$379$	−17.4095	+	30.1541i	−0.894264	+	1.54891i	−0.834713	+	0.550686i	$0.814366\pi$
$380$	6.06868	−	10.5113i	0.311316	−	0.539216i
$381$		0			0
$382$	8.44659	−	14.6299i	0.432165	−	0.748532i
$383$	−14.8493	+	25.7198i	−0.758764	+	1.31422i	0.184717	+	0.982792i	$0.440863\pi$
$383$	−14.8493	+	25.7198i	−0.758764	+	1.31422i	−0.943481	+	0.331426i	$0.892470\pi$
$384$		0			0
$385$	−41.6709			−2.12375
$386$	−6.16365	+	10.6758i	−0.313721	+	0.543381i
$387$		0			0
$388$	3.58422			0.181961
$389$	−8.08558	−	14.0046i	−0.409955	−	0.710063i	0.584929	−	0.811084i	$-0.301122\pi$
$389$	−8.08558	−	14.0046i	−0.409955	−	0.710063i	−0.994884	+	0.101021i	$0.967789\pi$
$390$		0			0
$391$	−19.3654			−0.979350
$392$	1.12208	−	1.94350i	0.0566736	−	0.0981616i
$393$		0			0
$394$	−11.2501			−0.566774
$395$	−6.28477			−0.316221
$396$		0			0
$397$	3.08789	−	5.34838i	0.154977	−	0.268428i	−0.778074	−	0.628173i	$-0.783803\pi$
$397$	3.08789	−	5.34838i	0.154977	−	0.268428i	0.933051	+	0.359745i	$0.117136\pi$
$398$	−7.58846			−0.380375
$399$		0			0
$400$	0.503984			0.0251992
$401$	−8.67231	−	15.0209i	−0.433074	−	0.750107i	0.564062	−	0.825732i	$-0.309238\pi$
$401$	−8.67231	−	15.0209i	−0.433074	−	0.750107i	−0.997136	+	0.0756258i	$0.975905\pi$
$402$		0			0
$403$	−0.853680	−	30.0886i	−0.0425248	−	1.49882i
$404$	−7.02878			−0.349695
$405$		0			0
$406$	1.89470	−	3.28172i	0.0940326	−	0.162869i
$407$	11.9070	−	20.6235i	0.590208	−	1.02227i
$408$		0			0
$409$	24.3718			1.20511			0.602554	−	0.798078i	$-0.294150\pi$
$409$	24.3718			1.20511			0.602554	+	0.798078i	$0.294150\pi$
$410$	6.91967			0.341738
$411$		0			0
$412$	4.37931			0.215753
$413$	−7.24131	−	12.5423i	−0.356322	−	0.617167i
$414$		0			0
$415$	10.2884	−	17.8201i	0.505039	−	0.874753i
$416$	−5.40625			−0.265063
$417$		0			0
$418$	−15.1118	−	26.1744i	−0.739143	−	1.28023i
$419$	−11.3416	−	19.6442i	−0.554072	−	0.959681i	−0.997975	−	0.0636063i	$-0.979740\pi$
$419$	−11.3416	−	19.6442i	−0.554072	−	0.959681i	0.443903	−	0.896075i	$-0.353594\pi$
$420$		0			0
$421$	−4.96920			−0.242184			−0.121092	−	0.992641i	$-0.538640\pi$
$421$	−4.96920			−0.242184			−0.121092	+	0.992641i	$0.538640\pi$
$422$	−4.91192	+	8.50770i	−0.239109	+	0.414148i
$423$		0			0
$424$	5.39327	+	9.34142i	0.261920	+	0.453659i
$425$	1.85353			0.0899094
$426$		0			0
$427$	42.7882			2.07067
$428$	3.55362			0.171771
$429$		0			0
$430$	−11.5425	+	19.9922i	−0.556630	+	0.964111i
$431$	19.8668	−	34.4102i	0.956948	−	1.65748i	0.227103	−	0.973871i	$-0.427074\pi$
$431$	19.8668	−	34.4102i	0.956948	−	1.65748i	0.729845	−	0.683613i	$-0.239592\pi$
$432$		0			0
$433$	−26.3343			−1.26555			−0.632773	−	0.774338i	$-0.718083\pi$
$433$	−26.3343			−1.26555			−0.632773	+	0.774338i	$0.718083\pi$
$434$	−14.4144	+	8.87655i	−0.691915	+	0.426088i
$435$		0			0
$436$	−9.18736	−	15.9130i	−0.439995	−	0.762093i
$437$	−27.2414			−1.30313
$438$		0			0
$439$	27.0844			1.29267			0.646334	−	0.763054i	$-0.276301\pi$
$439$	27.0844			1.29267			0.646334	+	0.763054i	$0.276301\pi$
$440$	6.85282	−	11.8694i	0.326696	−	0.565853i
$441$		0			0
$442$	−19.8829			−0.945731
$443$	−3.41649			−0.162322			−0.0811611	−	0.996701i	$-0.525863\pi$
$443$	−3.41649			−0.162322			−0.0811611	+	0.996701i	$0.525863\pi$
$444$		0			0
$445$	−4.13255	+	7.15778i	−0.195901	+	0.339311i
$446$	−10.2417			−0.484958
$447$		0			0
$448$	1.52021	+	2.63308i	0.0718232	+	0.124401i
$449$	−36.5403			−1.72444			−0.862221	−	0.506532i	$-0.830927\pi$
$449$	−36.5403			−1.72444			−0.862221	+	0.506532i	$0.830927\pi$
$450$		0			0
$451$	8.61545	−	14.9224i	0.405686	−	0.702668i
$452$	3.69933			0.174002
$453$		0			0
$454$	−8.63703	+	14.9598i	−0.405356	+	0.702097i
$455$	−19.2814	+	33.3964i	−0.903926	+	1.56565i
$456$		0			0
$457$	−4.40598	+	7.63138i	−0.206103	+	0.356981i	−0.950484	−	0.310775i	$-0.899412\pi$
$457$	−4.40598	+	7.63138i	−0.206103	+	0.356981i	0.744381	+	0.667756i	$0.232745\pi$
$458$	1.16671	−	2.02080i	0.0545166	−	0.0944256i
$459$		0			0
$460$	−6.17664	−	10.6982i	−0.287987	−	0.498808i
$461$	6.69027	−	11.5879i	0.311597	−	0.539702i	−0.667111	−	0.744958i	$-0.732469\pi$
$461$	6.69027	−	11.5879i	0.311597	−	0.539702i	0.978708	+	0.205256i	$0.0658028\pi$
$462$		0			0
$463$	13.5432	+	23.4576i	0.629407	+	1.09016i	0.987671	+	0.156544i	$0.0500355\pi$
$463$	13.5432	+	23.4576i	0.629407	+	1.09016i	−0.358264	+	0.933620i	$0.616631\pi$
$464$	0.623172	+	1.07937i	0.0289300	+	0.0501083i
$465$		0			0
$466$	1.74773	−	3.02716i	0.0809622	−	0.140231i
$467$	−5.43494			−0.251499			−0.125750	−	0.992062i	$-0.540134\pi$
$467$	−5.43494			−0.251499			−0.125750	+	0.992062i	$0.540134\pi$
$468$		0			0
$469$	−30.8125			−1.42279
$470$	−20.0718			−0.925843
$471$		0			0
$472$	4.76336			0.219251
$473$	28.7424	+	49.7833i	1.32158	+	2.28904i
$474$		0			0
$475$	2.60737			0.119634
$476$	5.59096	+	9.68383i	0.256261	+	0.443858i
$477$		0			0
$478$	−2.85451	−	4.94415i	−0.130562	−	0.226140i
$479$	−1.78335	−	3.08885i	−0.0814833	−	0.141133i	0.822404	−	0.568904i	$-0.192632\pi$
$479$	−1.78335	−	3.08885i	−0.0814833	−	0.141133i	−0.903887	+	0.427771i	$0.859299\pi$
$480$		0			0
$481$	−11.0189	−	19.0853i	−0.502418	−	0.870213i
$482$	17.7645			0.809152
$483$		0			0
$484$	−11.5644	−	20.0302i	−0.525656	−	0.910463i
$485$	4.20439	+	7.28222i	0.190912	+	0.330669i
$486$		0			0
$487$	5.23602	+	9.06906i	0.237267	+	0.410958i	0.959929	−	0.280243i	$-0.0904151\pi$
$487$	5.23602	+	9.06906i	0.237267	+	0.410958i	−0.722662	+	0.691201i	$0.757082\pi$
$488$	−7.03656	+	12.1877i	−0.318530	+	0.551710i
$489$		0			0
$490$	5.26493			0.237845
$491$	8.32650	−	14.4219i	0.375770	−	0.650852i	−0.614672	−	0.788783i	$-0.710712\pi$
$491$	8.32650	−	14.4219i	0.375770	−	0.650852i	0.990442	+	0.137931i	$0.0440451\pi$
$492$		0			0
$493$	2.29187	+	3.96964i	0.103221	+	0.178784i
$494$	−27.9693			−1.25840
$495$		0			0
$496$	−0.157906	−	5.56552i	−0.00709020	−	0.249899i
$497$	−11.3751	+	19.7023i	−0.510244	+	0.883769i
$498$		0			0
$499$	−16.3686			−0.732759			−0.366380	−	0.930465i	$-0.619403\pi$
$499$	−16.3686			−0.732759			−0.366380	+	0.930465i	$0.619403\pi$
$500$	−5.27396	−	9.13476i	−0.235858	−	0.408519i
$501$		0			0
$502$	1.50446	+	2.60581i	0.0671475	+	0.116303i
$503$	−3.56017	+	6.16640i	−0.158740	+	0.274946i	−0.934415	−	0.356187i	$-0.884077\pi$
$503$	−3.56017	+	6.16640i	−0.158740	+	0.274946i	0.775674	+	0.631133i	$0.217410\pi$
$504$		0			0
$505$	−8.24496	−	14.2807i	−0.366896	−	0.635483i
$506$	−30.7613			−1.36751
$507$		0			0
$508$	3.91883			0.173870
$509$	−11.5784	+	20.0543i	−0.513202	+	0.888892i	0.486680	+	0.873580i	$0.338208\pi$
$509$	−11.5784	+	20.0543i	−0.513202	+	0.888892i	−0.999883	+	0.0153124i	$0.995126\pi$
$510$		0			0
$511$	6.37898	−	11.0487i	0.282189	−	0.488766i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	1.94806	+	3.37414i	0.0859252	+	0.148827i
$515$	5.13706	+	8.89764i	0.226366	+	0.392077i
$516$		0			0
$517$	−24.9907	+	43.2852i	−1.09909	+	1.90368i
$518$	−6.19691	+	10.7334i	−0.272276	+	0.471597i
$519$		0			0
$520$	−6.34169	−	10.9841i	−0.278101	−	0.481686i
$521$	−20.6348	+	35.7404i	−0.904025	+	1.56582i	−0.0818041	+	0.996648i	$0.526068\pi$
$521$	−20.6348	+	35.7404i	−0.904025	+	1.56582i	−0.822221	+	0.569169i	$0.807265\pi$
$522$		0			0
$523$	1.65720			0.0724643			0.0362322	−	0.999343i	$-0.488464\pi$
$523$	1.65720			0.0724643			0.0362322	+	0.999343i	$0.488464\pi$
$524$	−5.40422	−	9.36038i	−0.236084	−	0.408910i
$525$		0			0
$526$	7.02078	+	12.1603i	0.306120	+	0.530216i
$527$	−0.580740	−	20.4686i	−0.0252974	−	0.891628i
$528$		0			0
$529$	−2.36299	+	4.09282i	−0.102739	+	0.177949i
$530$	−12.6529	+	21.9155i	−0.549608	+	0.951949i
$531$		0			0
$532$	7.86483	+	13.6223i	0.340983	+	0.590601i
$533$	−7.97284	−	13.8094i	−0.345342	−	0.598150i
$534$		0			0
$535$	4.16850	+	7.22006i	0.180220	+	0.312150i
$536$	5.06714	−	8.77655i	0.218867	−	0.379089i
$537$		0			0
$538$	4.88504			0.210609
$539$	6.55519	−	11.3539i	0.282352	−	0.489048i
$540$		0			0
$541$	−5.52047	+	9.56173i	−0.237343	+	0.411091i	−0.959951	−	0.280167i	$-0.909610\pi$
$541$	−5.52047	+	9.56173i	−0.237343	+	0.411091i	0.722608	+	0.691258i	$0.242943\pi$
$542$	6.62041	−	11.4669i	0.284371	−	0.492545i
$543$		0			0
$544$	−3.67775			−0.157682
$545$	21.5541	−	37.3327i	0.923275	−	1.59916i
$546$		0			0
$547$	0.715421			0.0305892			0.0152946	−	0.999883i	$-0.495131\pi$
$547$	0.715421			0.0305892			0.0152946	+	0.999883i	$0.495131\pi$
$548$	5.85236	+	10.1366i	0.250001	+	0.433014i
$549$		0			0
$550$	2.94427			0.125544
$551$	3.22399	+	5.58411i	0.137346	+	0.237891i
$552$		0			0
$553$	4.07244	−	7.05368i	0.173178	−	0.299953i
$554$	−9.95924	−	17.2499i	−0.423127	−	0.732878i
$555$		0			0
$556$	7.78289	−	13.4804i	0.330068	−	0.571695i
$557$	−46.7111			−1.97921			−0.989607	−	0.143800i	$-0.954068\pi$
$557$	−46.7111			−1.97921			−0.989607	+	0.143800i	$0.954068\pi$
$558$		0			0
$559$	53.1971			2.25000
$560$	−3.56650	+	6.17736i	−0.150712	+	0.261041i
$561$		0			0
$562$	9.34766	+	16.1906i	0.394307	+	0.682960i
$563$	4.35465	−	7.54247i	0.183526	−	0.317877i	−0.759553	−	0.650446i	$-0.774582\pi$
$563$	4.35465	−	7.54247i	0.183526	−	0.317877i	0.943079	+	0.332569i	$0.107915\pi$
$564$		0			0
$565$	4.33942	+	7.51610i	0.182561	+	0.316205i
$566$	−6.57162			−0.276226
$567$		0			0
$568$	−3.74130	−	6.48012i	−0.156981	−	0.271900i
$569$	−18.1441			−0.760639			−0.380319	−	0.924855i	$-0.624186\pi$
$569$	−18.1441			−0.760639			−0.380319	+	0.924855i	$0.624186\pi$
$570$		0			0
$571$	20.0206	−	34.6767i	0.837836	−	1.45117i	−0.0538648	−	0.998548i	$-0.517154\pi$
$571$	20.0206	−	34.6767i	0.837836	−	1.45117i	0.891701	−	0.452626i	$-0.149513\pi$
$572$	−31.5833			−1.32056
$573$		0			0
$574$	−4.48385	+	7.76625i	−0.187152	+	0.324157i
$575$	1.32688	−	2.29822i	0.0553345	−	0.0958422i
$576$		0			0
$577$	18.0167	−	31.2059i	0.750047	−	1.29912i	−0.197753	−	0.980252i	$-0.563364\pi$
$577$	18.0167	−	31.2059i	0.750047	−	1.29912i	0.947799	−	0.318867i	$-0.103302\pi$
$578$	3.47412			0.144504
$579$		0			0
$580$	−1.46200	+	2.53225i	−0.0607061	+	0.105146i
$581$	13.3335	+	23.0943i	0.553167	+	0.958113i
$582$		0			0
$583$	31.5075	+	54.5725i	1.30491	+	2.26016i
$584$	2.09806	+	3.63394i	0.0868182	+	0.150374i
$585$		0			0
$586$	7.73539	−	13.3981i	0.319546	−	0.553470i
$587$	−8.45075	+	14.6371i	−0.348800	+	0.604139i	−0.986037	−	0.166529i	$-0.946744\pi$
$587$	−8.45075	+	14.6371i	−0.348800	+	0.604139i	0.637237	+	0.770668i	$0.280077\pi$
$588$		0			0
$589$	−0.816929	−	28.7933i	−0.0336610	−	1.18641i
$590$	5.58756	+	9.67793i	0.230036	+	0.398434i
$591$		0			0
$592$	−2.03817	−	3.53022i	−0.0837684	−	0.145091i
$593$	−29.7811			−1.22296			−0.611481	−	0.791259i	$-0.709426\pi$
$593$	−29.7811			−1.22296			−0.611481	+	0.791259i	$0.709426\pi$
$594$		0			0
$595$	−13.1167	+	22.7188i	−0.537733	+	0.931381i
$596$	−3.44436	−	5.96581i	−0.141087	−	0.244369i
$597$		0			0
$598$	−14.2334	+	24.6530i	−0.582048	+	1.00814i
$599$	−15.1054	+	26.1634i	−0.617191	+	1.06901i	0.372804	+	0.927910i	$0.378396\pi$
$599$	−15.1054	+	26.1634i	−0.617191	+	1.06901i	−0.989996	+	0.141097i	$0.954937\pi$
$600$		0			0
$601$	−13.4185	−	23.2415i	−0.547350	−	0.948039i	−0.998455	−	0.0555677i	$-0.982303\pi$
$601$	−13.4185	−	23.2415i	−0.547350	−	0.948039i	0.451104	−	0.892471i	$-0.351030\pi$
$602$	−14.9588	−	25.9093i	−0.609674	−	1.05599i
$603$		0			0
$604$	24.4605			0.995283
$605$	27.1308	−	46.9920i	1.10303	−	1.91050i
$606$		0			0
$607$	−11.2221	+	19.4373i	−0.455492	+	0.788936i	−0.998716	−	0.0506519i	$-0.983870\pi$
$607$	−11.2221	+	19.4373i	−0.455492	+	0.788936i	0.543224	+	0.839588i	$0.317203\pi$
$608$	−5.17351			−0.209814
$609$		0			0
$610$	−33.0164			−1.33679
$611$	23.1267	+	40.0567i	0.935607	+	1.62052i
$612$		0			0
$613$	−11.6053	+	20.1010i	−0.468734	+	0.811871i	−0.999361	−	0.0357343i	$-0.988623\pi$
$613$	−11.6053	+	20.1010i	−0.468734	+	0.811871i	0.530627	+	0.847605i	$0.321956\pi$
$614$	7.91988	+	13.7176i	0.319620	+	0.553599i
$615$		0			0
$616$	8.88106	+	15.3824i	0.357828	+	0.619776i
$617$	19.5805			0.788282			0.394141	−	0.919050i	$-0.371042\pi$
$617$	19.5805			0.788282			0.394141	+	0.919050i	$0.371042\pi$
$618$		0			0
$619$	−21.8791	+	37.8958i	−0.879396	+	1.52316i	−0.0273920	+	0.999625i	$0.508720\pi$
$619$	−21.8791	+	37.8958i	−0.879396	+	1.52316i	−0.852004	+	0.523535i	$0.824613\pi$
$620$	11.1225	−	6.84934i	0.446690	−	0.275076i
$621$		0			0
$622$	5.82700			0.233641
$623$	−5.35566	−	9.27627i	−0.214570	−	0.371646i
$624$		0			0
$625$	13.6330	−	23.6130i	0.545318	−	0.944519i
$626$	3.39395			0.135649
$627$		0			0
$628$	5.18717	−	8.98444i	0.206991	−	0.358518i
$629$	−7.49590	−	12.9833i	−0.298881	−	0.517677i
$630$		0			0
$631$	2.46804	+	4.27478i	0.0982513	+	0.170176i	0.910961	−	0.412493i	$-0.135342\pi$
$631$	2.46804	+	4.27478i	0.0982513	+	0.170176i	−0.812710	+	0.582669i	$0.802008\pi$
$632$	1.33943	+	2.31997i	0.0532798	+	0.0922833i
$633$		0			0
$634$	−20.0073			−0.794593
$635$	4.59690	+	7.96207i	0.182423	+	0.315965i
$636$		0			0
$637$	−6.06625	−	10.5071i	−0.240354	−	0.416305i
$638$	3.64056	+	6.30564i	0.144131	+	0.249643i
$639$		0			0
$640$	−1.17303	−	2.03175i	−0.0463680	−	0.0803118i
$641$	34.3824			1.35802			0.679012	−	0.734127i	$-0.262408\pi$
$641$	34.3824			1.35802			0.679012	+	0.734127i	$0.262408\pi$
$642$		0			0
$643$	10.3052	+	17.8491i	0.406397	+	0.703900i	0.994483	−	0.104899i	$-0.0334518\pi$
$643$	10.3052	+	17.8491i	0.406397	+	0.703900i	−0.588086	+	0.808798i	$0.700118\pi$
$644$	16.0095			0.630862
$645$		0			0
$646$	−19.0269			−0.748603
$647$	31.8242			1.25114			0.625570	−	0.780168i	$-0.284866\pi$
$647$	31.8242			1.25114			0.625570	+	0.780168i	$0.284866\pi$
$648$		0			0
$649$	27.8275			1.09233
$650$	1.36233	−	2.35963i	0.0534350	−	0.0925522i
$651$		0			0
$652$	−6.98935	−	12.1059i	−0.273724	−	0.474104i
$653$	5.79092	+	10.0302i	0.226616	+	0.392511i	0.956803	−	0.290737i	$-0.0939004\pi$
$653$	5.79092	+	10.0302i	0.226616	+	0.392511i	−0.730187	+	0.683247i	$0.760567\pi$
$654$		0			0
$655$	12.6786	−	21.9600i	0.495394	−	0.858047i
$656$	−1.47475	−	2.55433i	−0.0575791	−	0.0997300i
$657$		0			0
$658$	13.0062	−	22.5275i	0.507036	−	0.878212i
$659$	15.8445	−	27.4434i	0.617213	−	1.06904i	−0.372779	−	0.927920i	$-0.621595\pi$
$659$	15.8445	−	27.4434i	0.617213	−	1.06904i	0.989992	−	0.141124i	$-0.0450716\pi$
$660$		0			0
$661$	8.71653	−	15.0975i	0.339034	−	0.587223i	−0.645218	−	0.763999i	$-0.723233\pi$
$661$	8.71653	−	15.0975i	0.339034	−	0.587223i	0.984251	+	0.176775i	$0.0565666\pi$
$662$	15.9374	−	27.6043i	0.619423	−	1.07287i
$663$		0			0
$664$	−8.77082			−0.340374
$665$	−18.4513	+	31.9586i	−0.715512	+	1.23930i
$666$		0			0
$667$	6.56268			0.254108
$668$	8.86521	+	15.3550i	0.343005	+	0.594103i
$669$		0			0
$670$	23.7756			0.918532
$671$	−41.1075	+	71.2004i	−1.58694	+	2.74866i
$672$		0			0
$673$	12.8271			0.494450			0.247225	−	0.968958i	$-0.420481\pi$
$673$	12.8271			0.494450			0.247225	+	0.968958i	$0.420481\pi$
$674$	22.6021			0.870599
$675$		0			0
$676$	−8.11378	+	14.0535i	−0.312068	+	0.540518i
$677$	20.5857			0.791174			0.395587	−	0.918429i	$-0.370541\pi$
$677$	20.5857			0.791174			0.395587	+	0.918429i	$0.370541\pi$
$678$		0			0
$679$	−10.8975			−0.418209
$680$	−4.31411	−	7.47226i	−0.165439	−	0.286548i
$681$		0			0
$682$	−0.922487	−	32.5138i	−0.0353238	−	1.24502i
$683$	6.13838			0.234879			0.117439	−	0.993080i	$-0.462531\pi$
$683$	6.13838			0.234879			0.117439	+	0.993080i	$0.462531\pi$
$684$		0			0
$685$	−13.7300	+	23.7810i	−0.524596	+	0.908626i
$686$	7.22988	−	12.5225i	0.276038	−	0.478112i
$687$		0			0
$688$	9.83993			0.375144
$689$	58.3148			2.22162
$690$		0			0
$691$	−20.0938			−0.764404			−0.382202	−	0.924079i	$-0.624834\pi$
$691$	−20.0938			−0.764404			−0.382202	+	0.924079i	$0.624834\pi$
$692$	2.74939	+	4.76208i	0.104516	+	0.181027i
$693$		0			0
$694$	6.98652	−	12.1010i	0.265205	−	0.459348i
$695$	36.5182			1.38521
$696$		0			0
$697$	−5.42375	−	9.39421i	−0.205439	−	0.355831i
$698$	−3.41690	−	5.91825i	−0.129332	−	0.224009i
$699$		0			0
$700$	−1.53232			−0.0579164
$701$	5.99187	−	10.3782i	0.226310	−	0.391980i	−0.730402	−	0.683018i	$-0.760667\pi$
$701$	5.99187	−	10.3782i	0.226310	−	0.391980i	0.956712	+	0.291038i	$0.0940005\pi$
$702$		0			0
$703$	−10.5445	−	18.2636i	−0.397694	−	0.688826i
$704$	−5.84199			−0.220178
$705$		0			0
$706$	0.346349			0.0130350
$707$	21.3705			0.803719
$708$		0			0
$709$	−22.1973	+	38.4469i	−0.833638	+	1.44390i	0.0614959	+	0.998107i	$0.480413\pi$
$709$	−22.1973	+	38.4469i	−0.833638	+	1.44390i	−0.895134	+	0.445797i	$0.852920\pi$
$710$	8.77730	−	15.2027i	0.329406	−	0.570548i
$711$		0			0
$712$	3.52297			0.132029
$713$	−25.7951	−	13.9327i	−0.966033	−	0.521784i
$714$		0			0
$715$	−37.0481	−	64.1692i	−1.38552	−	2.39979i
$716$	23.3796			0.873735
$717$		0			0
$718$	21.6880			0.809388
$719$	−14.2308	+	24.6485i	−0.530720	+	0.919234i	0.468637	+	0.883391i	$0.344745\pi$
$719$	−14.2308	+	24.6485i	−0.530720	+	0.919234i	−0.999357	+	0.0358436i	$0.988588\pi$
$720$		0			0
$721$	−13.3149			−0.495875
$722$	−7.76521			−0.288991
$723$		0			0
$724$	−0.955580	+	1.65511i	−0.0355139	+	0.0615118i
$725$	−0.628137			−0.0233284
$726$		0			0
$727$	−8.17180	−	14.1540i	−0.303075	−	0.524942i	0.673756	−	0.738954i	$-0.264680\pi$
$727$	−8.17180	−	14.1540i	−0.303075	−	0.524942i	−0.976831	+	0.214012i	$0.931347\pi$
$728$	16.4373			0.609206
$729$		0			0
$730$	−4.92216	+	8.52543i	−0.182177	+	0.315540i
$731$	36.1889			1.33849
$732$		0			0
$733$	3.48532	−	6.03675i	0.128733	−	0.222973i	−0.794453	−	0.607326i	$-0.792242\pi$
$733$	3.48532	−	6.03675i	0.128733	−	0.222973i	0.923186	+	0.384353i	$0.125576\pi$
$734$	13.3708	−	23.1588i	0.493523	−	0.854808i
$735$		0			0
$736$	−2.63277	+	4.56010i	−0.0970453	+	0.168087i
$737$	29.6022	−	51.2726i	1.09041	−	1.88865i
$738$		0			0
$739$	−9.65514	−	16.7232i	−0.355170	−	0.615173i	0.631977	−	0.774987i	$-0.282244\pi$
$739$	−9.65514	−	16.7232i	−0.355170	−	0.615173i	−0.987147	+	0.159814i	$0.948910\pi$
$740$	4.78167	−	8.28210i	0.175778	−	0.304456i
$741$		0			0
$742$	−16.3978	−	28.4019i	−0.601983	−	1.04266i
$743$	−7.75132	−	13.4257i	−0.284368	−	0.492540i	0.688088	−	0.725628i	$-0.258451\pi$
$743$	−7.75132	−	13.4257i	−0.284368	−	0.492540i	−0.972456	+	0.233087i	$0.925117\pi$
$744$		0			0
$745$	8.08067	−	13.9961i	0.296053	−	0.512778i
$746$	3.38248			0.123841
$747$		0			0
$748$	−21.4854			−0.785585
$749$	−10.8045			−0.394788
$750$		0			0
$751$	−33.7537			−1.23169			−0.615844	−	0.787868i	$-0.711185\pi$
$751$	−33.7537			−1.23169			−0.615844	+	0.787868i	$0.711185\pi$
$752$	4.27777	+	7.40932i	0.155994	+	0.270190i
$753$		0			0
$754$	6.73805			0.245385
$755$	28.6928	+	49.6975i	1.04424	+	1.80868i
$756$		0			0
$757$	−2.29901	−	3.98200i	−0.0835588	−	0.144728i	0.821217	−	0.570615i	$-0.193295\pi$
$757$	−2.29901	−	3.98200i	−0.0835588	−	0.144728i	−0.904776	+	0.425887i	$0.859962\pi$
$758$	17.4095	+	30.1541i	0.632340	+	1.09525i
$759$		0			0
$760$	−6.06868	−	10.5113i	−0.220134	−	0.381283i
$761$	−1.95845			−0.0709938			−0.0354969	−	0.999370i	$-0.511301\pi$
$761$	−1.95845			−0.0709938			−0.0354969	+	0.999370i	$0.511301\pi$
$762$		0			0
$763$	27.9334	+	48.3821i	1.01126	+	1.75155i
$764$	−8.44659	−	14.6299i	−0.305587	−	0.529292i
$765$		0			0
$766$	14.8493	+	25.7198i	0.536527	+	0.929293i
$767$	12.8760	−	22.3018i	0.464924	−	0.805272i
$768$		0			0
$769$	7.03396			0.253651			0.126826	−	0.991925i	$-0.459521\pi$
$769$	7.03396			0.253651			0.126826	+	0.991925i	$0.459521\pi$
$770$	−20.8355	+	36.0881i	−0.750858	+	1.30052i
$771$		0			0
$772$	6.16365	+	10.6758i	0.221835	+	0.384229i
$773$	15.5206			0.558239			0.279119	−	0.960256i	$-0.409957\pi$
$773$	15.5206			0.558239			0.279119	+	0.960256i	$0.409957\pi$
$774$		0			0
$775$	2.46894	+	1.33355i	0.0886868	+	0.0479024i
$776$	1.79211	−	3.10403i	0.0643330	−	0.111428i
$777$		0			0
$778$	−16.1712			−0.579764
$779$	−7.62961	−	13.2149i	−0.273359	−	0.473472i
$780$		0			0
$781$	−21.8566	−	37.8568i	−0.782092	−	1.35462i
$782$	−9.68269	+	16.7709i	−0.346252	+	0.599727i
$783$		0			0
$784$	−1.12208	−	1.94350i	−0.0400743	−	0.0694107i
$785$	24.3388			0.868688
$786$		0			0
$787$	18.1468			0.646864			0.323432	−	0.946251i	$-0.395163\pi$
$787$	18.1468			0.646864			0.323432	+	0.946251i	$0.395163\pi$
$788$	−5.62507	+	9.74291i	−0.200385	+	0.347077i
$789$		0			0
$790$	−3.14239	+	5.44277i	−0.111801	+	0.193645i
$791$	−11.2475			−0.399916
$792$		0			0
$793$	38.0414	+	65.8897i	1.35089	+	2.33981i
$794$	−3.08789	−	5.34838i	−0.109585	−	0.189807i
$795$		0			0
$796$	−3.79423	+	6.57180i	−0.134483	+	0.232931i
$797$	18.2696	−	31.6439i	0.647144	−	1.12089i	−0.336658	−	0.941627i	$-0.609297\pi$
$797$	18.2696	−	31.6439i	0.647144	−	1.12089i	0.983802	−	0.179259i	$-0.0573700\pi$
$798$		0			0
$799$	15.7326	+	27.2497i	0.556579	+	0.964024i
$800$	0.251992	−	0.436463i	0.00890926	−	0.0154313i
$801$		0			0
$802$	−17.3446			−0.612459
$803$	12.2568	+	21.2295i	0.432534	+	0.749171i
$804$		0			0
$805$	18.7796	+	32.5272i	0.661893	+	1.14643i
$806$	−26.4844	−	14.3050i	−0.932872	−	0.503872i
$807$		0			0
$808$	−3.51439	+	6.08711i	−0.123636	+	0.214144i
$809$	6.75139	−	11.6938i	0.237366	−	0.411130i	−0.722591	−	0.691275i	$-0.757049\pi$
$809$	6.75139	−	11.6938i	0.237366	−	0.411130i	0.959958	+	0.280145i	$0.0903825\pi$
$810$		0			0
$811$	−7.93579	−	13.7452i	−0.278663	−	0.482659i	0.692390	−	0.721524i	$-0.256558\pi$
$811$	−7.93579	−	13.7452i	−0.278663	−	0.482659i	−0.971053	+	0.238865i	$0.923225\pi$
$812$	−1.89470	−	3.28172i	−0.0664911	−	0.115166i
$813$		0			0
$814$	−11.9070	−	20.6235i	−0.417340	−	0.722854i
$815$	16.3974	−	28.4011i	0.574376	−	0.994848i
$816$		0			0
$817$	50.9070			1.78101
$818$	12.1859	−	21.1066i	0.426070	−	0.737975i
$819$		0			0
$820$	3.45984	−	5.99261i	0.120823	−	0.209271i
$821$	−8.83187	+	15.2973i	−0.308235	+	0.533878i	−0.977976	−	0.208716i	$-0.933071\pi$
$821$	−8.83187	+	15.2973i	−0.308235	+	0.533878i	0.669742	+	0.742594i	$0.266405\pi$
$822$		0			0
$823$	−26.6917			−0.930412			−0.465206	−	0.885202i	$-0.654020\pi$
$823$	−26.6917			−0.930412			−0.465206	+	0.885202i	$0.654020\pi$
$824$	2.18966	−	3.79259i	0.0762803	−	0.132121i
$825$		0			0
$826$	−14.4826			−0.503915
$827$	6.36247	+	11.0201i	0.221245	+	0.383207i	0.955186	−	0.296006i	$-0.0956547\pi$
$827$	6.36247	+	11.0201i	0.221245	+	0.383207i	−0.733941	+	0.679213i	$0.762321\pi$
$828$		0			0
$829$	−35.0188			−1.21625			−0.608126	−	0.793840i	$-0.708079\pi$
$829$	−35.0188			−1.21625			−0.608126	+	0.793840i	$0.708079\pi$
$830$	−10.2884	−	17.8201i	−0.357117	−	0.618544i
$831$		0			0
$832$	−2.70313	+	4.68195i	−0.0937140	+	0.162317i
$833$	−4.12674	−	7.14772i	−0.142983	−	0.247654i
$834$		0			0
$835$	−20.7983	+	36.0237i	−0.719755	+	1.24665i
$836$	−30.2236			−1.04531
$837$		0			0
$838$	−22.6831			−0.783576
$839$	3.33440	−	5.77534i	0.115116	−	0.199387i	−0.802710	−	0.596370i	$-0.796609\pi$
$839$	3.33440	−	5.77534i	0.115116	−	0.199387i	0.917826	+	0.396983i	$0.129943\pi$
$840$		0			0
$841$	13.7233	+	23.7695i	0.473218	+	0.819637i
$842$	−2.48460	+	4.30346i	−0.0856250	+	0.148307i
$843$		0			0
$844$	4.91192	+	8.50770i	0.169075	+	0.292847i
$845$	−38.0708			−1.30967
$846$		0			0
$847$	35.1608	+	60.9002i	1.20814	+	2.09256i
$848$	10.7865			0.370411
$849$		0			0
$850$	0.926764	−	1.60520i	0.0317878	−	0.0550580i
$851$	−21.4642			−0.735783
$852$		0			0
$853$	−6.45115	+	11.1737i	−0.220883	+	0.382581i	−0.955076	−	0.296360i	$-0.904227\pi$
$853$	−6.45115	+	11.1737i	−0.220883	+	0.382581i	0.734193	+	0.678941i	$0.237561\pi$
$854$	21.3941	−	37.0557i	0.732091	−	1.26802i
$855$		0			0
$856$	1.77681	−	3.07753i	0.0607302	−	0.105188i
$857$	17.3374			0.592236			0.296118	−	0.955151i	$-0.404308\pi$
$857$	17.3374			0.592236			0.296118	+	0.955151i	$0.404308\pi$
$858$		0			0
$859$	4.59838	−	7.96462i	0.156895	−	0.271749i	−0.776853	−	0.629682i	$-0.783185\pi$
$859$	4.59838	−	7.96462i	0.156895	−	0.271749i	0.933747	+	0.357933i	$0.116518\pi$
$860$	11.5425	+	19.9922i	0.393597	+	0.681730i
$861$		0			0
$862$	−19.8668	−	34.4102i	−0.676665	−	1.17202i
$863$	23.8716	+	41.3468i	0.812598	+	1.40746i	0.911040	+	0.412317i	$0.135281\pi$
$863$	23.8716	+	41.3468i	0.812598	+	1.40746i	−0.0984427	+	0.995143i	$0.531386\pi$
$864$		0			0
$865$	−6.45022	+	11.1721i	−0.219314	+	0.379863i
$866$	−13.1671	+	22.8062i	−0.447438	+	0.774985i
$867$		0			0
$868$	0.480101	+	16.9215i	0.0162957	+	0.574354i
$869$	7.82496	+	13.5532i	0.265444	+	0.459762i
$870$		0			0
$871$	−27.3943	−	47.4482i	−0.928219	−	1.60772i
$872$	−18.3747			−0.622246
$873$		0			0
$874$	−13.6207	+	23.5917i	−0.460726	+	0.798001i
$875$	16.0350	+	27.7735i	0.542083	+	0.938916i
$876$		0			0
$877$	16.6409	−	28.8229i	0.561923	−	0.973280i	−0.435405	−	0.900234i	$-0.643395\pi$
$877$	16.6409	−	28.8229i	0.561923	−	0.973280i	0.997329	−	0.0730451i	$-0.0232717\pi$
$878$	13.5422	−	23.4558i	0.457027	−	0.791595i
$879$		0			0
$880$	−6.85282	−	11.8694i	−0.231009	−	0.400119i
$881$	16.4234	+	28.4461i	0.553317	+	0.958374i	0.998032	+	0.0627018i	$0.0199717\pi$
$881$	16.4234	+	28.4461i	0.553317	+	0.958374i	−0.444715	+	0.895672i	$0.646695\pi$
$882$		0			0
$883$	−19.1572			−0.644691			−0.322346	−	0.946622i	$-0.604471\pi$
$883$	−19.1572			−0.644691			−0.322346	+	0.946622i	$0.604471\pi$
$884$	−9.94143	+	17.2191i	−0.334367	+	0.579140i
$885$		0			0
$886$	−1.70824	+	2.95877i	−0.0573896	+	0.0994017i
$887$	4.33508			0.145558			0.0727788	−	0.997348i	$-0.476813\pi$
$887$	4.33508			0.145558			0.0727788	+	0.997348i	$0.476813\pi$
$888$		0			0
$889$	−11.9149			−0.399613
$890$	4.13255	+	7.15778i	0.138523	+	0.239929i
$891$		0			0
$892$	−5.12084	+	8.86956i	−0.171459	+	0.296975i
$893$	22.1311	+	38.3322i	0.740589	+	1.28274i
$894$		0			0
$895$	27.4249	+	47.5013i	0.916713	+	1.58779i
$896$	3.04042			0.101573
$897$		0			0
$898$	−18.2701	+	31.6448i	−0.609683	+	1.05600i
$899$	0.196805	+	6.93656i	0.00656382	+	0.231347i
$900$		0			0
$901$	39.6703			1.32161
$902$	−8.61545	−	14.9224i	−0.286863	−	0.496862i
$903$		0			0
$904$	1.84967	−	3.20372i	0.0615190	−	0.106554i
$905$	−4.48369			−0.149043
$906$		0			0
$907$	10.7856	−	18.6812i	0.358131	−	0.620301i	−0.629518	−	0.776986i	$-0.716748\pi$
$907$	10.7856	−	18.6812i	0.358131	−	0.620301i	0.987649	+	0.156685i	$0.0500809\pi$
$908$	8.63703	+	14.9598i	0.286630	+	0.496457i
$909$		0			0
$910$	19.2814	+	33.3964i	0.639172	+	1.10708i
$911$	1.35817	+	2.35243i	0.0449983	+	0.0779394i	0.887647	−	0.460524i	$-0.152338\pi$
$911$	1.35817	+	2.35243i	0.0449983	+	0.0779394i	−0.842649	+	0.538463i	$0.819005\pi$
$912$		0			0
$913$	−51.2391			−1.69577
$914$	4.40598	+	7.63138i	0.145737	+	0.252424i
$915$		0			0
$916$	−1.16671	−	2.02080i	−0.0385491	−	0.0667690i
$917$	16.4311	+	28.4595i	0.542602	+	0.939815i
$918$		0			0
$919$	15.9728	+	27.6657i	0.526894	+	0.912607i	0.999509	+	0.0313382i	$0.00997689\pi$
$919$	15.9728	+	27.6657i	0.526894	+	0.912607i	−0.472615	+	0.881269i	$0.656690\pi$
$920$	−12.3533			−0.407275
$921$		0			0
$922$	−6.69027	−	11.5879i	−0.220332	−	0.381627i
$923$	−40.4528			−1.33152
$924$		0			0
$925$	2.05441			0.0675487
$926$	27.0864			0.890116
$927$		0			0
$928$	1.24634			0.0409132
$929$	22.6243	−	39.1864i	0.742279	−	1.28567i	−0.209176	−	0.977878i	$-0.567078\pi$
$929$	22.6243	−	39.1864i	0.742279	−	1.28567i	0.951455	−	0.307787i	$-0.0995885\pi$
$930$		0			0
$931$	−5.80510	−	10.0547i	−0.190254	−	0.329530i
$932$	−1.74773	−	3.02716i	−0.0572489	−	0.0991580i
$933$		0			0
$934$	−2.71747	+	4.70680i	−0.0889184	+	0.154011i
$935$	−25.2030	−	43.6529i	−0.824226	−	1.42760i
$936$		0			0
$937$	15.7775	−	27.3274i	0.515427	−	0.892746i	−0.484413	−	0.874840i	$-0.660967\pi$
$937$	15.7775	−	27.3274i	0.515427	−	0.892746i	0.999840	−	0.0179062i	$-0.00570004\pi$
$938$	−15.4063	+	26.6844i	−0.503032	+	0.871277i
$939$		0			0
$940$	−10.0359	+	17.3827i	−0.327335	+	0.566961i
$941$	9.28506	−	16.0822i	0.302684	−	0.524264i	−0.674059	−	0.738678i	$-0.735451\pi$
$941$	9.28506	−	16.0822i	0.302684	−	0.524264i	0.976743	+	0.214413i	$0.0687839\pi$
$942$		0			0
$943$	−15.5307			−0.505749
$944$	2.38168	−	4.12519i	0.0775171	−	0.134264i
$945$		0			0
$946$	57.4848			1.86899
$947$	20.2488	+	35.0720i	0.657999	+	1.13969i	0.981133	+	0.193334i	$0.0619302\pi$
$947$	20.2488	+	35.0720i	0.657999	+	1.13969i	−0.323134	+	0.946353i	$0.604736\pi$
$948$		0			0
$949$	22.6852			0.736394
$950$	1.30368	−	2.25805i	0.0422971	−	0.0732607i
$951$		0			0
$952$	11.1819			0.362408
$953$	−28.2571			−0.915336			−0.457668	−	0.889123i	$-0.651315\pi$
$953$	−28.2571			−0.915336			−0.457668	+	0.889123i	$0.651315\pi$
$954$		0			0
$955$	19.8162	−	34.3226i	0.641237	−	1.11065i
$956$	−5.70901			−0.184643
$957$		0			0
$958$	−3.56670			−0.115235
$959$	−17.7937	−	30.8195i	−0.574587	−	0.995214i
$960$		0			0
$961$	13.9529	−	27.6824i	0.450093	−	0.892982i
$962$	−22.0378			−0.710526
$963$		0			0
$964$	8.88226	−	15.3845i	0.286078	−	0.495502i
$965$	−14.4603	+	25.0459i	−0.465493	+	0.806257i
$966$		0			0
$967$	4.86983			0.156603			0.0783016	−	0.996930i	$-0.475050\pi$
$967$	4.86983			0.156603			0.0783016	+	0.996930i	$0.475050\pi$
$968$	−23.1289			−0.743390
$969$		0			0
$970$	8.40879			0.269990
$971$	−14.1457	−	24.5011i	−0.453957	−	0.786277i	0.544670	−	0.838650i	$-0.316655\pi$
$971$	−14.1457	−	24.5011i	−0.453957	−	0.786277i	−0.998628	+	0.0523734i	$0.983321\pi$
$972$		0			0
$973$	−23.6633	+	40.9860i	−0.758609	+	1.31395i
$974$	10.4720			0.335546
$975$		0			0
$976$	7.03656	+	12.1877i	0.225235	+	0.390118i
$977$	14.5551	+	25.2102i	0.465659	+	0.806545i	0.999231	−	0.0392095i	$-0.0124840\pi$
$977$	14.5551	+	25.2102i	0.465659	+	0.806545i	−0.533572	+	0.845755i	$0.679151\pi$
$978$		0			0
$979$	20.5812			0.657777
$980$	2.63247	−	4.55956i	0.0840910	−	0.145650i
$981$		0			0
$982$	−8.32650	−	14.4219i	−0.265709	−	0.460222i
$983$	−54.9593			−1.75293			−0.876465	−	0.481465i	$-0.840105\pi$
$983$	−54.9593			−1.75293			−0.876465	+	0.481465i	$0.840105\pi$
$984$		0			0
$985$	−26.3935			−0.840966
$986$	4.58374			0.145976
$987$		0			0
$988$	−13.9846	+	24.2221i	−0.444911	+	0.770608i
$989$	25.9063	−	44.8710i	0.823773	−	1.42682i
$990$		0			0
$991$	50.0331			1.58935			0.794677	−	0.607033i	$-0.207640\pi$
$991$	50.0331			1.58935			0.794677	+	0.607033i	$0.207640\pi$
$992$	−4.89884	−	2.64601i	−0.155538	−	0.0840110i
$993$		0			0
$994$	11.3751	+	19.7023i	0.360797	+	0.624919i
$995$	−17.8030			−0.564392
$996$		0			0
$997$	−1.30768			−0.0414146			−0.0207073	−	0.999786i	$-0.506592\pi$
$997$	−1.30768			−0.0414146			−0.0207073	+	0.999786i	$0.506592\pi$
$998$	−8.18430	+	14.1756i	−0.259070	+	0.448722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.g.b.1369.12		32
3.2	odd	2		558.2.g.a.439.1	yes	32
9.4	even	3		1674.2.h.b.253.5		32
9.5	odd	6		558.2.h.a.67.11	yes	32
31.25	even	3		1674.2.h.b.397.5		32
93.56	odd	6		558.2.h.a.25.11	yes	32
279.149	odd	6		558.2.g.a.211.1	✓	32
279.211	even	3	inner	1674.2.g.b.955.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.1	✓	32	279.149	odd	6
558.2.g.a.439.1	yes	32	3.2	odd	2
558.2.h.a.25.11	yes	32	93.56	odd	6
558.2.h.a.67.11	yes	32	9.5	odd	6
1674.2.g.b.955.12		32	279.211	even	3	inner
1674.2.g.b.1369.12		32	1.1	even	1	trivial
1674.2.h.b.253.5		32	9.4	even	3
1674.2.h.b.397.5		32	31.25	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1674 = 2 \cdot 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1674.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.17303 - 2.03175i) q^{5} +(1.52021 + 2.63308i) q^{7} -1.00000 q^{8} +(-1.17303 - 2.03175i) q^{10} -5.84199 q^{11} +(-2.70313 + 4.68195i) q^{13} +3.04042 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.83888 + 3.18503i) q^{17} +(-2.58676 + 4.48039i) q^{19} -2.34606 q^{20} +(-2.92100 + 5.05931i) q^{22} +(2.63277 + 4.56010i) q^{23} +(-0.251992 - 0.436463i) q^{25} +(2.70313 + 4.68195i) q^{26} +(1.52021 - 2.63308i) q^{28} +(0.623172 - 1.07937i) q^{29} +(-4.74093 + 2.91951i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.83888 + 3.18503i) q^{34} +7.13300 q^{35} +(-2.03817 + 3.53022i) q^{37} +(2.58676 + 4.48039i) q^{38} +(-1.17303 + 2.03175i) q^{40} +(-1.47475 + 2.55433i) q^{41} +(-4.91997 - 8.52163i) q^{43} +(2.92100 + 5.05931i) q^{44} +5.26555 q^{46} +(4.27777 - 7.40932i) q^{47} +(-1.12208 + 1.94350i) q^{49} -0.503984 q^{50} +5.40625 q^{52} +(-5.39327 - 9.34142i) q^{53} +(-6.85282 + 11.8694i) q^{55} +(-1.52021 - 2.63308i) q^{56} +(-0.623172 - 1.07937i) q^{58} -4.76336 q^{59} +(7.03656 - 12.1877i) q^{61} +(0.157906 + 5.56552i) q^{62} +1.00000 q^{64} +(6.34169 + 10.9841i) q^{65} +(-5.06714 + 8.77655i) q^{67} +3.67775 q^{68} +(3.56650 - 6.17736i) q^{70} +(3.74130 + 6.48012i) q^{71} +(-2.09806 - 3.63394i) q^{73} +(2.03817 + 3.53022i) q^{74} +5.17351 q^{76} +(-8.88106 - 15.3824i) q^{77} +(-1.33943 - 2.31997i) q^{79} +(1.17303 + 2.03175i) q^{80} +(1.47475 + 2.55433i) q^{82} +8.77082 q^{83} +(4.31411 + 7.47226i) q^{85} -9.83993 q^{86} +5.84199 q^{88} -3.52297 q^{89} -16.4373 q^{91} +(2.63277 - 4.56010i) q^{92} +(-4.27777 - 7.40932i) q^{94} +(6.06868 + 10.5113i) q^{95} +(-1.79211 + 3.10403i) q^{97} +(1.12208 + 1.94350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} + q^{5} + q^{7} - 32 q^{8} - q^{10} - 4 q^{11} - 10 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} - 2 q^{22} + q^{23} - 19 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 + q^5 + q^7 - 32 * q^8 - q^10 - 4 * q^11 - 10 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 - 2 * q^22 + q^23 - 19 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - q^31 + 16 * q^32 - 4 * q^34 - 19 * q^37 - 4 * q^38 - q^40 - 10 * q^41 - 13 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 - 13 * q^49 - 38 * q^50 + 20 * q^52 + 7 * q^53 - 11 * q^55 - q^56 - 3 * q^58 - 12 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 + 8 * q^65 - 8 * q^67 - 8 * q^68 - 7 * q^71 + 7 * q^73 + 19 * q^74 - 8 * q^76 + q^77 - 34 * q^79 + q^80 + 10 * q^82 + 28 * q^83 + 13 * q^85 - 26 * q^86 + 4 * q^88 - 2 * q^89 + 24 * q^91 + q^92 - 6 * q^94 - 21 * q^95 + 10 * q^97 + 13 * q^98

Introduction

L-functions

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