LMFDB - Embedded newform 820.2.bq.a.49.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05623 + 1.05623i) q^{3} +(2.03080 - 0.935877i) q^{5} +(0.269596 - 1.70217i) q^{7} +0.768736i q^{9} +(2.98613 - 1.52151i) q^{11} +(0.0489169 - 0.00774768i) q^{13} +(-1.15649 + 3.13350i) q^{15} +(-2.41624 + 1.23114i) q^{17} +(0.213336 - 1.34695i) q^{19} +(1.51313 + 2.08264i) q^{21} +(4.22431 - 5.81426i) q^{23} +(3.24827 - 3.80115i) q^{25} +(-3.98067 - 3.98067i) q^{27} +(-0.765424 + 1.50223i) q^{29} +(1.81286 - 5.57941i) q^{31} +(-1.54698 + 4.76112i) q^{33} +(-1.04552 - 3.70906i) q^{35} +(-0.311494 + 0.101211i) q^{37} +(-0.0434844 + 0.0598511i) q^{39} +(4.30013 + 4.74435i) q^{41} +(7.60719 + 5.52695i) q^{43} +(0.719443 + 1.56115i) q^{45} +(0.914242 + 5.77229i) q^{47} +(3.83271 + 1.24532i) q^{49} +(1.25175 - 3.85249i) q^{51} +(12.1868 + 6.20947i) q^{53} +(4.64027 - 5.88452i) q^{55} +(1.19736 + 1.64803i) q^{57} +(-7.12083 - 5.17359i) q^{59} +(0.0274724 + 0.0378125i) q^{61} +(1.30852 + 0.207249i) q^{63} +(0.0920895 - 0.0615142i) q^{65} +(0.417773 - 0.819926i) q^{67} +(1.67936 + 10.6031i) q^{69} +(0.506397 - 0.258022i) q^{71} -5.65011 q^{73} +(0.583974 + 7.44584i) q^{75} +(-1.78481 - 5.49308i) q^{77} +(-1.10490 - 1.10490i) q^{79} +6.10284 q^{81} -13.0918i q^{83} +(-3.75470 + 4.76149i) q^{85} +(-0.778239 - 2.39517i) q^{87} +(2.33573 + 0.369944i) q^{89} -0.0853535i q^{91} +(3.97836 + 7.80797i) q^{93} +(-0.827339 - 2.93504i) q^{95} +(-0.686286 + 1.34691i) q^{97} +(1.16964 + 2.29554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

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
$3$	−1.05623	+	1.05623i	−0.609817	+	0.609817i	−0.942898	−	0.333081i	$-0.891912\pi$
$3$	−1.05623	+	1.05623i	−0.609817	+	0.609817i	0.333081	+	0.942898i	$0.391912\pi$
$4$		0			0
$5$	2.03080	−	0.935877i	0.908200	−	0.418537i
$5$	2.03080	−	0.935877i	0.908200	−	0.418537i
$6$		0			0
$7$	0.269596	−	1.70217i	0.101898	−	0.643358i	−0.882888	−	0.469584i	$-0.844404\pi$
$7$	0.269596	−	1.70217i	0.101898	−	0.643358i	0.984786	−	0.173774i	$-0.0555962\pi$
$8$		0			0
$9$			0.768736i			0.256245i
$10$		0			0
$11$	2.98613	−	1.52151i	0.900351	−	0.458752i	0.0583924	−	0.998294i	$-0.481403\pi$
$11$	2.98613	−	1.52151i	0.900351	−	0.458752i	0.841959	+	0.539542i	$0.181403\pi$
$12$		0			0
$13$	0.0489169	−	0.00774768i	0.0135671	−	0.00214882i	−0.149647	−	0.988739i	$-0.547814\pi$
$13$	0.0489169	−	0.00774768i	0.0135671	−	0.00214882i	0.163214	+	0.986591i	$0.447814\pi$
$14$		0			0
$15$	−1.15649	+	3.13350i	−0.298605	+	0.809067i
$16$		0			0
$17$	−2.41624	+	1.23114i	−0.586024	+	0.298594i	−0.721752	−	0.692152i	$-0.756663\pi$
$17$	−2.41624	+	1.23114i	−0.586024	+	0.298594i	0.135727	+	0.990746i	$0.456663\pi$
$18$		0			0
$19$	0.213336	−	1.34695i	0.0489427	−	0.309012i	−0.951057	−	0.309015i	$-0.900001\pi$
$19$	0.213336	−	1.34695i	0.0489427	−	0.309012i	1.00000		2.53092e-6i	$8.05616e-7\pi$
$20$		0			0
$21$	1.51313	+	2.08264i	0.330192	+	0.454470i
$22$		0			0
$23$	4.22431	−	5.81426i	0.880829	−	1.21236i	−0.0953614	−	0.995443i	$-0.530401\pi$
$23$	4.22431	−	5.81426i	0.880829	−	1.21236i	0.976191	−	0.216915i	$-0.0695993\pi$
$24$		0			0
$25$	3.24827	−	3.80115i	0.649654	−	0.760230i
$26$		0			0
$27$	−3.98067	−	3.98067i	−0.766080	−	0.766080i
$28$		0			0
$29$	−0.765424	+	1.50223i	−0.142136	+	0.278957i	−0.951090	−	0.308915i	$-0.900034\pi$
$29$	−0.765424	+	1.50223i	−0.142136	+	0.278957i	0.808954	+	0.587872i	$0.200034\pi$
$30$		0			0
$31$	1.81286	−	5.57941i	0.325599	−	1.00209i	−0.645570	−	0.763701i	$-0.723380\pi$
$31$	1.81286	−	5.57941i	0.325599	−	1.00209i	0.971169	−	0.238390i	$-0.0766197\pi$
$32$		0			0
$33$	−1.54698	+	4.76112i	−0.269295	+	0.828805i
$34$		0			0
$35$	−1.04552	−	3.70906i	−0.176725	−	0.626946i
$36$		0			0
$37$	−0.311494	+	0.101211i	−0.0512094	+	0.0166389i	−0.334510	−	0.942392i	$-0.608571\pi$
$37$	−0.311494	+	0.101211i	−0.0512094	+	0.0166389i	0.283300	+	0.959031i	$0.408571\pi$
$38$		0			0
$39$	−0.0434844	+	0.0598511i	−0.00696308	+	0.00958385i
$40$		0			0
$41$	4.30013	+	4.74435i	0.671568	+	0.740943i
$41$	4.30013	+	4.74435i	0.671568	+	0.740943i
$42$		0			0
$43$	7.60719	+	5.52695i	1.16009	+	0.842852i	0.989789	−	0.142541i	$-0.0455273\pi$
$43$	7.60719	+	5.52695i	1.16009	+	0.842852i	0.170297	+	0.985393i	$0.445527\pi$
$44$		0			0
$45$	0.719443	+	1.56115i	0.107248	+	0.232722i
$46$		0			0
$47$	0.914242	+	5.77229i	0.133356	+	0.841976i	0.960153	+	0.279475i	$0.0901605\pi$
$47$	0.914242	+	5.77229i	0.133356	+	0.841976i	−0.826797	+	0.562500i	$0.809840\pi$
$48$		0			0
$49$	3.83271	+	1.24532i	0.547530	+	0.177903i
$50$		0			0
$51$	1.25175	−	3.85249i	0.175280	−	0.539456i
$52$		0			0
$53$	12.1868	+	6.20947i	1.67398	+	0.852936i	0.992658	+	0.120954i	$0.0385953\pi$
$53$	12.1868	+	6.20947i	1.67398	+	0.852936i	0.681324	+	0.731982i	$0.261405\pi$
$54$		0			0
$55$	4.64027	−	5.88452i	0.625694	−	0.793469i
$56$		0			0
$57$	1.19736	+	1.64803i	0.158595	+	0.218287i
$58$		0			0
$59$	−7.12083	−	5.17359i	−0.927054	−	0.673544i	0.0182159	−	0.999834i	$-0.494201\pi$
$59$	−7.12083	−	5.17359i	−0.927054	−	0.673544i	−0.945270	+	0.326290i	$0.894201\pi$
$60$		0			0
$61$	0.0274724	+	0.0378125i	0.00351748	+	0.00484140i	0.810772	−	0.585362i	$-0.199048\pi$
$61$	0.0274724	+	0.0378125i	0.00351748	+	0.00484140i	−0.807255	+	0.590203i	$0.799048\pi$
$62$		0			0
$63$	1.30852	+	0.207249i	0.164858	+	0.0261109i
$64$		0			0
$65$	0.0920895	−	0.0615142i	0.0114223	−	0.00762990i
$66$		0			0
$67$	0.417773	−	0.819926i	0.0510391	−	0.100170i	−0.864078	−	0.503358i	$-0.832098\pi$
$67$	0.417773	−	0.819926i	0.0510391	−	0.100170i	0.915117	+	0.403188i	$0.132098\pi$
$68$		0			0
$69$	1.67936	+	10.6031i	0.202172	+	1.27646i
$70$		0			0
$71$	0.506397	−	0.258022i	0.0600983	−	0.0306216i	−0.423683	−	0.905810i	$-0.639263\pi$
$71$	0.506397	−	0.258022i	0.0600983	−	0.0306216i	0.483781	+	0.875189i	$0.339263\pi$
$72$		0			0
$73$	−5.65011			−0.661295			−0.330648	−	0.943754i	$-0.607267\pi$
$73$	−5.65011			−0.661295			−0.330648	+	0.943754i	$0.607267\pi$
$74$		0			0
$75$	0.583974	+	7.44584i	0.0674315	+	0.859772i
$76$		0			0
$77$	−1.78481	−	5.49308i	−0.203398	−	0.625994i
$78$		0			0
$79$	−1.10490	−	1.10490i	−0.124311	−	0.124311i	0.642214	−	0.766525i	$-0.278016\pi$
$79$	−1.10490	−	1.10490i	−0.124311	−	0.124311i	−0.766525	+	0.642214i	$0.778016\pi$
$80$		0			0
$81$	6.10284			0.678093
$82$		0			0
$83$		−	13.0918i		−	1.43701i	−0.695523	−	0.718504i	$-0.744827\pi$
$83$		−	13.0918i		−	1.43701i	0.695523	−	0.718504i	$-0.255173\pi$
$84$		0			0
$85$	−3.75470	+	4.76149i	−0.407255	+	0.516456i
$86$		0			0
$87$	−0.778239	−	2.39517i	−0.0834360	−	0.256790i
$88$		0			0
$89$	2.33573	+	0.369944i	0.247587	+	0.0392140i	0.278995	−	0.960293i	$-0.409999\pi$
$89$	2.33573	+	0.369944i	0.247587	+	0.0392140i	−0.0314072	+	0.999507i	$0.509999\pi$
$90$		0			0
$91$		−	0.0853535i		−	0.00894747i
$92$		0			0
$93$	3.97836	+	7.80797i	0.412537	+	0.809649i
$94$		0			0
$95$	−0.827339	−	2.93504i	−0.0848832	−	0.301129i
$96$		0			0
$97$	−0.686286	+	1.34691i	−0.0696818	+	0.136758i	−0.923220	−	0.384272i	$-0.874452\pi$
$97$	−0.686286	+	1.34691i	−0.0696818	+	0.136758i	0.853538	+	0.521031i	$0.174452\pi$
$98$		0			0
$99$	1.16964	+	2.29554i	0.117553	+	0.230711i
$100$		0			0
$101$	0.826260	−	5.21680i	0.0822159	−	0.519091i	−0.911869	−	0.410482i	$-0.865360\pi$
$101$	0.826260	−	5.21680i	0.0822159	−	0.519091i	0.994085	−	0.108609i	$-0.0346396\pi$
$102$		0			0
$103$	2.71672	−	1.97382i	0.267687	−	0.194486i	−0.445842	−	0.895112i	$-0.647096\pi$
$103$	2.71672	−	1.97382i	0.267687	−	0.194486i	0.713529	+	0.700626i	$0.247096\pi$
$104$		0			0
$105$	5.02195	+	2.81332i	0.490093	+	0.274552i
$106$		0			0
$107$	9.00432	+	12.3934i	0.870481	+	1.19811i	0.978968	+	0.204016i	$0.0653994\pi$
$107$	9.00432	+	12.3934i	0.870481	+	1.19811i	−0.108487	+	0.994098i	$0.534601\pi$
$108$		0			0
$109$	−8.15603	+	8.15603i	−0.781206	+	0.781206i	−0.980034	−	0.198828i	$-0.936286\pi$
$109$	−8.15603	+	8.15603i	−0.781206	+	0.781206i	0.198828	+	0.980034i	$0.436286\pi$
$110$		0			0
$111$	0.222109	−	0.435913i	0.0210817	−	0.0413751i
$112$		0			0
$113$	−12.3238	−	4.00426i	−1.15933	−	0.376689i	−0.334679	−	0.942332i	$-0.608628\pi$
$113$	−12.3238	−	4.00426i	−1.15933	−	0.376689i	−0.824650	+	0.565643i	$0.808628\pi$
$114$		0			0
$115$	3.13728	−	15.7610i	0.292553	−	1.46972i
$116$		0			0
$117$	0.00595592	+	0.0376042i	0.000550625	+	0.00347651i
$118$		0			0
$119$	1.44419	+	4.44475i	0.132388	+	0.407450i
$120$		0			0
$121$	0.136331	−	0.187644i	0.0123938	−	0.0170586i
$122$		0			0
$123$	−9.55310	−	0.469195i	−0.861374	−	0.0423059i
$124$		0			0
$125$	3.03916	−	10.7593i	0.271831	−	0.962345i
$126$		0			0
$127$	7.41147	−	2.40813i	0.657662	−	0.213687i	0.0388724	−	0.999244i	$-0.487623\pi$
$127$	7.41147	−	2.40813i	0.657662	−	0.213687i	0.618789	+	0.785557i	$0.287623\pi$
$128$		0			0
$129$	−13.8727	+	2.19723i	−1.22143	+	0.193455i
$130$		0			0
$131$	−15.1163	−	4.91158i	−1.32072	−	0.429127i	−0.437975	−	0.898987i	$-0.644304\pi$
$131$	−15.1163	−	4.91158i	−1.32072	−	0.429127i	−0.882741	+	0.469861i	$0.844304\pi$
$132$		0			0
$133$	−2.23522	−	0.726267i	−0.193818	−	0.0629754i
$134$		0			0
$135$	−11.8093	−	4.35851i	−1.01639	−	0.375121i
$136$		0			0
$137$	−8.43563	−	8.43563i	−0.720704	−	0.720704i	0.248044	−	0.968749i	$-0.420212\pi$
$137$	−8.43563	−	8.43563i	−0.720704	−	0.720704i	−0.968749	+	0.248044i	$0.920212\pi$
$138$		0			0
$139$	−11.8160	+	8.58481i	−1.00222	+	0.728154i	−0.962563	−	0.271060i	$-0.912626\pi$
$139$	−11.8160	+	8.58481i	−1.00222	+	0.728154i	−0.0396552	+	0.999213i	$0.512626\pi$
$140$		0			0
$141$	−7.06255	−	5.13124i	−0.594774	−	0.432129i
$142$		0			0
$143$	0.134284	−	0.0975631i	0.0112294	−	0.00815863i
$144$		0			0
$145$	−0.148519	+	3.76706i	−0.0123338	+	0.312838i
$146$		0			0
$147$	−5.36360	+	2.73289i	−0.442382	+	0.225405i
$148$		0			0
$149$	−6.39865	−	3.26027i	−0.524198	−	0.267092i	0.171805	−	0.985131i	$-0.445040\pi$
$149$	−6.39865	−	3.26027i	−0.524198	−	0.267092i	−0.696003	+	0.718039i	$0.745040\pi$
$150$		0			0
$151$	1.77132	+	11.1837i	0.144148	+	0.910117i	0.948687	+	0.316217i	$0.102413\pi$
$151$	1.77132	+	11.1837i	0.144148	+	0.910117i	−0.804539	+	0.593900i	$0.797587\pi$
$152$		0			0
$153$	−0.946419	−	1.85745i	−0.0765134	−	0.150166i
$154$		0			0
$155$	−1.54009	−	13.0273i	−0.123703	−	1.04637i
$156$		0			0
$157$	1.02618	−	6.47906i	0.0818983	−	0.517086i	−0.912300	−	0.409523i	$-0.865695\pi$
$157$	1.02618	−	6.47906i	0.0818983	−	0.517086i	0.994198	−	0.107563i	$-0.0343047\pi$
$158$		0			0
$159$	−19.4307	+	6.31343i	−1.54096	+	0.500688i
$160$		0			0
$161$	−8.75798	−	8.75798i	−0.690225	−	0.690225i
$162$		0			0
$163$		−	5.62570i		−	0.440639i	−0.975428	−	0.220319i	$-0.929290\pi$
$163$		−	5.62570i		−	0.440639i	0.975428	−	0.220319i	$-0.0707099\pi$
$164$		0			0
$165$	1.31422	+	11.1167i	0.102312	+	0.865430i
$166$		0			0
$167$	−13.0643	+	13.0643i	−1.01095	+	1.01095i	−0.0110070	+	0.999939i	$0.503504\pi$
$167$	−13.0643	+	13.0643i	−1.01095	+	1.01095i	−0.999939	+	0.0110070i	$0.996496\pi$
$168$		0			0
$169$	−12.3614	+	4.01646i	−0.950877	+	0.308959i
$170$		0			0
$171$	1.03545	+	0.163999i	0.0791829	+	0.0125413i
$172$		0			0
$173$	19.3413			1.47049			0.735245	−	0.677801i	$-0.237067\pi$
$173$	19.3413			1.47049			0.735245	+	0.677801i	$0.237067\pi$
$174$		0			0
$175$	−5.59447	−	6.55387i	−0.422902	−	0.495426i
$176$		0			0
$177$	12.9858	−	2.05675i	0.976072	−	0.154595i
$178$		0			0
$179$	−12.1999	−	6.21616i	−0.911863	−	0.464617i	−0.0658801	−	0.997828i	$-0.520985\pi$
$179$	−12.1999	−	6.21616i	−0.911863	−	0.464617i	−0.845983	+	0.533210i	$0.820985\pi$
$180$		0			0
$181$	6.66341	+	13.0777i	0.495287	+	0.972056i	0.994416	+	0.105528i	$0.0336533\pi$
$181$	6.66341	+	13.0777i	0.495287	+	0.972056i	−0.499129	+	0.866528i	$0.666347\pi$
$182$		0			0
$183$	−0.0689562	−	0.0109216i	−0.00509739	−	0.000807347i
$184$		0			0
$185$	−0.537861	+	0.497059i	−0.0395443	+	0.0365445i
$186$		0			0
$187$	−5.34202	+	7.35266i	−0.390647	+	0.537680i
$188$		0			0
$189$	−7.84893	+	5.70258i	−0.570926	+	0.414802i
$190$		0			0
$191$	1.52242	−	1.52242i	0.110158	−	0.110158i	−0.649879	−	0.760037i	$-0.725181\pi$
$191$	1.52242	−	1.52242i	0.110158	−	0.110158i	0.760037	+	0.649879i	$0.225181\pi$
$192$		0			0
$193$	0.407418	+	0.207590i	0.0293266	+	0.0149426i	0.468592	−	0.883415i	$-0.344761\pi$
$193$	0.407418	+	0.207590i	0.0293266	+	0.0149426i	−0.439266	+	0.898357i	$0.644761\pi$
$194$		0			0
$195$	−0.0322947	+	0.162242i	−0.00231267	+	0.0116184i
$196$		0			0
$197$	4.86268	−	14.9658i	0.346451	−	1.06627i	−0.614351	−	0.789033i	$-0.710582\pi$
$197$	4.86268	−	14.9658i	0.346451	−	1.06627i	0.960802	−	0.277235i	$-0.0894180\pi$
$198$		0			0
$199$	−17.7318	+	2.80844i	−1.25697	+	0.199085i	−0.749164	−	0.662384i	$-0.769545\pi$
$199$	−17.7318	+	2.80844i	−1.25697	+	0.199085i	−0.507810	+	0.861469i	$0.669545\pi$
$200$		0			0
$201$	0.424768	+	1.30730i	0.0299608	+	0.0922099i
$202$		0			0
$203$	2.35069	+	1.70787i	0.164986	+	0.119869i
$204$		0			0
$205$	13.1728	+	5.61041i	0.920030	+	0.391848i
$206$		0			0
$207$	4.46963	+	3.24738i	0.310661	+	0.225708i
$208$		0			0
$209$	−1.41235	−	4.34676i	−0.0976942	−	0.300672i
$210$		0			0
$211$	8.60558	−	1.36299i	0.592432	−	0.0938321i	0.146983	−	0.989139i	$-0.453044\pi$
$211$	8.60558	−	1.36299i	0.592432	−	0.0938321i	0.445450	+	0.895307i	$0.353044\pi$
$212$		0			0
$213$	−0.262342	+	0.807407i	−0.0179754	+	0.0553226i
$214$		0			0
$215$	20.6212	+	4.10471i	1.40635	+	0.279939i
$216$		0			0
$217$	−9.00833	−	4.58997i	−0.611525	−	0.311588i
$218$		0			0
$219$	5.96784	−	5.96784i	0.403269	−	0.403269i
$220$		0			0
$221$	−0.108657	+	0.0789437i	−0.00730904	+	0.00531033i
$222$		0			0
$223$	−13.2324	+	18.2129i	−0.886108	+	1.21962i	0.0885836	+	0.996069i	$0.471766\pi$
$223$	−13.2324	+	18.2129i	−0.886108	+	1.21962i	−0.974692	+	0.223554i	$0.928234\pi$
$224$		0			0
$225$	2.92208	+	2.49706i	0.194806	+	0.166471i
$226$		0			0
$227$	7.47786	+	1.18438i	0.496323	+	0.0786098i	0.399578	−	0.916699i	$-0.369157\pi$
$227$	7.47786	+	1.18438i	0.496323	+	0.0786098i	0.0967452	+	0.995309i	$0.469157\pi$
$228$		0			0
$229$	7.01373	+	13.7652i	0.463480	+	0.909631i	0.997922	+	0.0644262i	$0.0205217\pi$
$229$	7.01373	+	13.7652i	0.463480	+	0.909631i	−0.534442	+	0.845205i	$0.679478\pi$
$230$		0			0
$231$	7.68715	+	3.91680i	0.505778	+	0.257707i
$232$		0			0
$233$	−26.6486	+	4.22072i	−1.74581	+	0.276509i	−0.946099	−	0.323878i	$-0.895013\pi$
$233$	−26.6486	+	4.22072i	−1.74581	+	0.276509i	−0.799709	+	0.600387i	$0.795013\pi$
$234$		0			0
$235$	7.25880	+	10.8667i	0.473512	+	0.708868i
$236$		0			0
$237$	2.33407			0.151614
$238$		0			0
$239$	−28.7274	−	4.54997i	−1.85822	−	0.294313i	−0.876038	−	0.482242i	$-0.839823\pi$
$239$	−28.7274	−	4.54997i	−1.85822	−	0.294313i	−0.982183	+	0.187929i	$0.939823\pi$
$240$		0			0
$241$	−4.54916	+	1.47811i	−0.293037	+	0.0952135i	−0.451846	−	0.892096i	$-0.649235\pi$
$241$	−4.54916	+	1.47811i	−0.293037	+	0.0952135i	0.158809	+	0.987309i	$0.449235\pi$
$242$		0			0
$243$	5.49598	−	5.49598i	0.352568	−	0.352568i
$244$		0			0
$245$	8.94893	−	1.05795i	0.571726	−	0.0675898i
$246$		0			0
$247$		−	0.0675416i		−	0.00429757i
$248$		0			0
$249$	13.8280	+	13.8280i	0.876312	+	0.876312i
$250$		0			0
$251$	8.52149	−	2.76880i	0.537872	−	0.174765i	−0.0274690	−	0.999623i	$-0.508745\pi$
$251$	8.52149	−	2.76880i	0.537872	−	0.174765i	0.565341	+	0.824858i	$0.308745\pi$
$252$		0			0
$253$	3.76788	−	23.7894i	0.236884	−	1.49563i
$254$		0			0
$255$	−1.06341	−	8.99510i	−0.0665931	−	0.563295i
$256$		0			0
$257$	−2.24185	−	4.39988i	−0.139843	−	0.274457i	0.810454	−	0.585802i	$-0.199220\pi$
$257$	−2.24185	−	4.39988i	−0.139843	−	0.274457i	−0.950297	+	0.311345i	$0.899220\pi$
$258$		0			0
$259$	0.0882995	+	0.557501i	0.00548666	+	0.0346414i
$260$		0			0
$261$	−1.15482	−	0.588409i	−0.0714815	−	0.0364216i
$262$		0			0
$263$	−6.08759	+	3.10178i	−0.375377	+	0.191264i	−0.631492	−	0.775382i	$-0.717557\pi$
$263$	−6.08759	+	3.10178i	−0.375377	+	0.191264i	0.256115	+	0.966646i	$0.417557\pi$
$264$		0			0
$265$	30.5602	+	1.20485i	1.87730	+	0.0740135i
$266$		0			0
$267$	−2.85783	+	2.07634i	−0.174896	+	0.127070i
$268$		0			0
$269$	1.67349	+	1.21586i	0.102034	+	0.0741322i	0.637632	−	0.770341i	$-0.279914\pi$
$269$	1.67349	+	1.21586i	0.102034	+	0.0741322i	−0.535598	+	0.844473i	$0.679914\pi$
$270$		0			0
$271$	−0.633741	+	0.460440i	−0.0384970	+	0.0279697i	−0.606867	−	0.794803i	$-0.707574\pi$
$271$	−0.633741	+	0.460440i	−0.0384970	+	0.0279697i	0.568370	+	0.822773i	$0.307574\pi$
$272$		0			0
$273$	0.0901533	+	0.0901533i	0.00545632	+	0.00545632i
$274$		0			0
$275$	3.91626	−	16.2930i	0.236159	−	0.982504i
$276$		0			0
$277$	28.0611	+	9.11759i	1.68603	+	0.547823i	0.986065	−	0.166358i	$-0.0532008\pi$
$277$	28.0611	+	9.11759i	1.68603	+	0.547823i	0.699961	+	0.714181i	$0.253201\pi$
$278$		0			0
$279$	4.28909	+	1.39361i	0.256781	+	0.0834333i
$280$		0			0
$281$	−6.85665	+	1.08599i	−0.409034	+	0.0647846i	−0.357561	−	0.933890i	$-0.616392\pi$
$281$	−6.85665	+	1.08599i	−0.409034	+	0.0647846i	−0.0514727	+	0.998674i	$0.516392\pi$
$282$		0			0
$283$	−6.26856	+	2.03678i	−0.372627	+	0.121074i	−0.489343	−	0.872091i	$-0.662763\pi$
$283$	−6.26856	+	2.03678i	−0.372627	+	0.121074i	0.116716	+	0.993165i	$0.462763\pi$
$284$		0			0
$285$	3.97396	+	2.22623i	0.235397	+	0.131870i
$286$		0			0
$287$	9.23497	−	6.04048i	0.545123	−	0.356558i
$288$		0			0
$289$	−5.66983	+	7.80385i	−0.333519	+	0.459050i
$290$		0			0
$291$	−0.697777	−	2.14754i	−0.0409044	−	0.125891i
$292$		0			0
$293$	−3.24760	−	20.5045i	−0.189727	−	1.19789i	−0.880226	−	0.474554i	$-0.842609\pi$
$293$	−3.24760	−	20.5045i	−0.189727	−	1.19789i	0.690499	−	0.723333i	$-0.257391\pi$
$294$		0			0
$295$	−19.3028	−	3.84228i	−1.12385	−	0.223706i
$296$		0			0
$297$	−17.9434	−	5.83017i	−1.04118	−	0.338301i
$298$		0			0
$299$	0.161593	−	0.317144i	0.00934517	−	0.0183409i
$300$		0			0
$301$	11.4587	−	11.4587i	0.660466	−	0.660466i
$302$		0			0
$303$	4.63744	+	6.38289i	0.266414	+	0.366687i
$304$		0			0
$305$	0.0911787	+	0.0510787i	0.00522088	+	0.00292476i
$306$		0			0
$307$	−10.2392	+	7.43922i	−0.584383	+	0.424579i	−0.840301	−	0.542120i	$-0.817622\pi$
$307$	−10.2392	+	7.43922i	−0.584383	+	0.424579i	0.255919	+	0.966698i	$0.417622\pi$
$308$		0			0
$309$	−0.784686	+	4.95431i	−0.0446392	+	0.281841i
$310$		0			0
$311$	−3.15059	−	6.18337i	−0.178653	−	0.350627i	0.784262	−	0.620429i	$-0.213042\pi$
$311$	−3.15059	−	6.18337i	−0.178653	−	0.350627i	−0.962916	+	0.269802i	$0.913042\pi$
$312$		0			0
$313$	−13.6761	+	26.8408i	−0.773018	+	1.51713i	0.0808973	+	0.996722i	$0.474221\pi$
$313$	−13.6761	+	26.8408i	−0.773018	+	1.51713i	−0.853916	+	0.520411i	$0.825779\pi$
$314$		0			0
$315$	2.85129	−	0.803730i	0.160652	−	0.0452851i
$316$		0			0
$317$	9.53349	+	18.7105i	0.535454	+	1.05089i	0.987311	+	0.158798i	$0.0507618\pi$
$317$	9.53349	+	18.7105i	0.535454	+	1.05089i	−0.451857	+	0.892091i	$0.649238\pi$
$318$		0			0
$319$			5.65045i			0.316364i
$320$		0			0
$321$	−22.6010	−	3.57965i	−1.26146	−	0.199796i
$322$		0			0
$323$	1.14281	+	3.51721i	0.0635876	+	0.195703i
$324$		0			0
$325$	0.129445	−	0.211107i	0.00718033	−	0.0117101i
$326$		0			0
$327$		−	17.2294i		−	0.952786i
$328$		0			0
$329$	10.0719			0.555280
$330$		0			0
$331$	15.0474	+	15.0474i	0.827078	+	0.827078i	0.987112	−	0.160034i	$-0.0511603\pi$
$331$	15.0474	+	15.0474i	0.827078	+	0.827078i	−0.160034	+	0.987112i	$0.551160\pi$
$332$		0			0
$333$	−0.0778043	−	0.239457i	−0.00426365	−	0.0131222i
$334$		0			0
$335$	0.0810624	−	2.05609i	0.00442891	−	0.112336i
$336$		0			0
$337$	−11.4441			−0.623399			−0.311700	−	0.950181i	$-0.600898\pi$
$337$	−11.4441			−0.623399			−0.311700	+	0.950181i	$0.600898\pi$
$338$		0			0
$339$	17.2463	−	8.78743i	0.936691	−	0.477268i
$340$		0			0
$341$	−3.07568	−	19.4191i	−0.166558	−	1.05160i
$342$		0			0
$343$	8.62983	−	16.9370i	0.465967	−	0.914512i
$344$		0			0
$345$	13.3336	+	19.9610i	0.717858	+	1.07467i
$346$		0			0
$347$	18.4132	+	2.91636i	0.988472	+	0.156559i	0.629676	−	0.776858i	$-0.283188\pi$
$347$	18.4132	+	2.91636i	0.988472	+	0.156559i	0.358796	+	0.933416i	$0.383188\pi$
$348$		0			0
$349$	7.38263	+	10.1613i	0.395183	+	0.543923i	0.959527	−	0.281617i	$-0.0908707\pi$
$349$	7.38263	+	10.1613i	0.395183	+	0.543923i	−0.564344	+	0.825540i	$0.690871\pi$
$350$		0			0
$351$	−0.225563	−	0.163881i	−0.0120397	−	0.00874733i
$352$		0			0
$353$	4.58895	+	6.31615i	0.244245	+	0.336175i	0.913486	−	0.406871i	$-0.133380\pi$
$353$	4.58895	+	6.31615i	0.244245	+	0.336175i	−0.669240	+	0.743046i	$0.733380\pi$
$354$		0			0
$355$	0.786913	−	0.997917i	0.0417650	−	0.0529639i
$356$		0			0
$357$	−6.22010	−	3.16930i	−0.329203	−	0.167737i
$358$		0			0
$359$	−1.06775	+	3.28620i	−0.0563537	+	0.173439i	−0.975271	−	0.221010i	$-0.929065\pi$
$359$	−1.06775	+	3.28620i	−0.0563537	+	0.173439i	0.918918	+	0.394449i	$0.129065\pi$
$360$		0			0
$361$	16.3013	+	5.29662i	0.857963	+	0.278769i
$362$		0			0
$363$	0.0541982	+	0.342194i	0.00284467	+	0.0179605i
$364$		0			0
$365$	−11.4742	+	5.28781i	−0.600588	+	0.276777i
$366$		0			0
$367$	−5.34005	−	3.87977i	−0.278748	−	0.202522i	0.439623	−	0.898182i	$-0.355112\pi$
$367$	−5.34005	−	3.87977i	−0.278748	−	0.202522i	−0.718371	+	0.695660i	$0.755112\pi$
$368$		0			0
$369$	−3.64715	+	3.30567i	−0.189863	+	0.172086i
$370$		0			0
$371$	13.8551	−	19.0698i	0.719319	−	0.990057i
$372$		0			0
$373$	−16.2236	+	5.27137i	−0.840027	+	0.272941i	−0.697263	−	0.716815i	$-0.745599\pi$
$373$	−16.2236	+	5.27137i	−0.840027	+	0.272941i	−0.142764	+	0.989757i	$0.545599\pi$
$374$		0			0
$375$	8.15432	+	14.5745i	0.421087	+	0.752622i
$376$		0			0
$377$	−0.0258034	+	0.0794147i	−0.00132894	+	0.00409007i
$378$		0			0
$379$	5.90337	−	18.1687i	0.303236	−	0.933264i	−0.677094	−	0.735897i	$-0.736761\pi$
$379$	5.90337	−	18.1687i	0.303236	−	0.933264i	0.980330	−	0.197367i	$-0.0632391\pi$
$380$		0			0
$381$	−5.28470	+	10.3718i	−0.270743	+	0.531364i
$382$		0			0
$383$	−6.14689	−	6.14689i	−0.314091	−	0.314091i	0.532401	−	0.846492i	$-0.321290\pi$
$383$	−6.14689	−	6.14689i	−0.314091	−	0.314091i	−0.846492	+	0.532401i	$0.821290\pi$
$384$		0			0
$385$	−8.76542	−	9.48496i	−0.446727	−	0.483398i
$386$		0			0
$387$	−4.24877	+	5.84792i	−0.215977	+	0.297267i
$388$		0			0
$389$	−10.2865	−	14.1582i	−0.521546	−	0.717847i	0.464267	−	0.885696i	$-0.346318\pi$
$389$	−10.2865	−	14.1582i	−0.521546	−	0.717847i	−0.985813	+	0.167849i	$0.946318\pi$
$390$		0			0
$391$	−3.04880	+	19.2494i	−0.154184	+	0.973482i
$392$		0			0
$393$	21.1541	−	10.7786i	1.06708	−	0.543707i
$394$		0			0
$395$	−3.27788	−	1.20978i	−0.164928	−	0.0608705i
$396$		0			0
$397$	−7.99784	+	1.26673i	−0.401400	+	0.0635756i	−0.353871	−	0.935294i	$-0.615135\pi$
$397$	−7.99784	+	1.26673i	−0.401400	+	0.0635756i	−0.0475294	+	0.998870i	$0.515135\pi$
$398$		0			0
$399$	3.12803	−	1.59381i	0.156597	−	0.0797903i
$400$		0			0
$401$		−	24.7028i		−	1.23360i	−0.787121	−	0.616799i	$-0.788429\pi$
$401$		−	24.7028i		−	1.23360i	0.787121	−	0.616799i	$-0.211571\pi$
$402$		0			0
$403$	0.0454520	−	0.286973i	0.00226413	−	0.0142951i
$404$		0			0
$405$	12.3936	−	5.71150i	0.615844	−	0.283807i
$406$		0			0
$407$	−0.776169	+	0.776169i	−0.0384733	+	0.0384733i
$408$		0			0
$409$	25.5028			1.26103			0.630516	−	0.776176i	$-0.282843\pi$
$409$	25.5028			1.26103			0.630516	+	0.776176i	$0.282843\pi$
$410$		0			0
$411$	17.8200			0.878996
$412$		0			0
$413$	−10.7261	+	10.7261i	−0.527795	+	0.527795i
$414$		0			0
$415$	−12.2523	−	26.5867i	−0.601441	−	1.30509i
$416$		0			0
$417$	3.41287	−	21.5480i	0.167129	−	1.05521i
$418$		0			0
$419$		−	33.0764i		−	1.61589i	−0.589260	−	0.807944i	$-0.700581\pi$
$419$		−	33.0764i		−	1.61589i	0.589260	−	0.807944i	$-0.299419\pi$
$420$		0			0
$421$	−12.8768	+	6.56105i	−0.627577	+	0.319766i	−0.738694	−	0.674041i	$-0.764557\pi$
$421$	−12.8768	+	6.56105i	−0.627577	+	0.319766i	0.111117	+	0.993807i	$0.464557\pi$
$422$		0			0
$423$	−4.43737	+	0.702811i	−0.215752	+	0.0341718i
$424$		0			0
$425$	−3.16886	+	13.1836i	−0.153712	+	0.639496i
$426$		0			0
$427$	0.0717696	−	0.0365685i	0.00347318	−	0.00176967i
$428$		0			0
$429$	−0.0387860	+	0.244885i	−0.00187260	+	0.0118232i
$430$		0			0
$431$	13.9507	+	19.2014i	0.671979	+	0.924900i	0.999803	−	0.0198386i	$-0.00631524\pi$
$431$	13.9507	+	19.2014i	0.671979	+	0.924900i	−0.327824	+	0.944739i	$0.606315\pi$
$432$		0			0
$433$	0.882448	−	1.21459i	0.0424077	−	0.0583692i	−0.787287	−	0.616587i	$-0.788515\pi$
$433$	0.882448	−	1.21459i	0.0424077	−	0.0583692i	0.829694	+	0.558218i	$0.188515\pi$
$434$		0			0
$435$	−3.82203	−	4.13578i	−0.183253	−	0.198295i
$436$		0			0
$437$	−6.93033	−	6.93033i	−0.331523	−	0.331523i
$438$		0			0
$439$	−0.785443	+	1.54152i	−0.0374871	+	0.0735727i	−0.908990	−	0.416817i	$-0.863146\pi$
$439$	−0.785443	+	1.54152i	−0.0374871	+	0.0735727i	0.871503	+	0.490390i	$0.163146\pi$
$440$		0			0
$441$	−0.957325	+	2.94634i	−0.0455869	+	0.140302i
$442$		0			0
$443$	−4.52313	+	13.9208i	−0.214900	+	0.661395i	0.784260	+	0.620432i	$0.213043\pi$
$443$	−4.52313	+	13.9208i	−0.214900	+	0.661395i	−0.999161	+	0.0409634i	$0.986957\pi$
$444$		0			0
$445$	5.08962	−	1.43468i	0.241271	−	0.0680103i
$446$		0			0
$447$	10.2021	−	3.31486i	0.482542	−	0.156787i
$448$		0			0
$449$	14.3965	−	19.8151i	0.679415	−	0.935134i	−0.320512	−	0.947244i	$-0.603855\pi$
$449$	14.3965	−	19.8151i	0.679415	−	0.935134i	0.999927	+	0.0121104i	$0.00385496\pi$
$450$		0			0
$451$	20.0593	+	7.62454i	0.944556	+	0.359026i
$452$		0			0
$453$	−13.6835	−	9.94168i	−0.642909	−	0.467101i
$454$		0			0
$455$	−0.0798803	−	0.173335i	−0.00374485	−	0.00812609i
$456$		0			0
$457$	1.03077	+	6.50801i	0.0482173	+	0.304432i	0.999997	−	0.00234961i	$-0.000747904\pi$
$457$	1.03077	+	6.50801i	0.0482173	+	0.304432i	−0.951780	+	0.306782i	$0.900748\pi$
$458$		0			0
$459$	14.5190	+	4.71751i	0.677689	+	0.220195i
$460$		0			0
$461$	6.95363	−	21.4011i	0.323863	−	0.996748i	−0.648088	−	0.761565i	$-0.724431\pi$
$461$	6.95363	−	21.4011i	0.323863	−	0.996748i	0.971951	−	0.235183i	$-0.0755688\pi$
$462$		0			0
$463$	−29.2737	−	14.9157i	−1.36046	−	0.693190i	−0.387009	−	0.922076i	$-0.626492\pi$
$463$	−29.2737	−	14.9157i	−1.36046	−	0.693190i	−0.973453	+	0.228886i	$0.926492\pi$
$464$		0			0
$465$	15.3865	+	12.1331i	0.713533	+	0.562661i
$466$		0			0
$467$	−13.6458	−	18.7818i	−0.631453	−	0.869120i	0.366671	−	0.930351i	$-0.380498\pi$
$467$	−13.6458	−	18.7818i	−0.631453	−	0.869120i	−0.998124	+	0.0612305i	$0.980498\pi$
$468$		0			0
$469$	−1.28302	−	0.932168i	−0.0592443	−	0.0430435i
$470$		0			0
$471$	5.75952	+	7.92730i	0.265385	+	0.365271i
$472$		0			0
$473$	31.1253	+	4.92977i	1.43114	+	0.226671i
$474$		0			0
$475$	−4.42700	−	5.18619i	−0.203125	−	0.237959i
$476$		0			0
$477$	−4.77345	+	9.36841i	−0.218561	+	0.428950i
$478$		0			0
$479$	6.11320	+	38.5972i	0.279319	+	1.76355i	0.584631	+	0.811300i	$0.301239\pi$
$479$	6.11320	+	38.5972i	0.279319	+	1.76355i	−0.305311	+	0.952253i	$0.598761\pi$
$480$		0			0
$481$	−0.0144532	+	0.00736428i	−0.000659009	+	0.000335782i
$482$		0			0
$483$	18.5010			0.841823
$484$		0			0
$485$	−0.133163	+	3.37759i	−0.00604663	+	0.153368i
$486$		0			0
$487$	11.0318	+	33.9524i	0.499899	+	1.53853i	0.809181	+	0.587560i	$0.199911\pi$
$487$	11.0318	+	33.9524i	0.499899	+	1.53853i	−0.309282	+	0.950970i	$0.600089\pi$
$488$		0			0
$489$	5.94206	+	5.94206i	0.268709	+	0.268709i
$490$		0			0
$491$	−8.54660			−0.385702			−0.192851	−	0.981228i	$-0.561773\pi$
$491$	−8.54660			−0.385702			−0.192851	+	0.981228i	$0.561773\pi$
$492$		0			0
$493$		−	4.57209i		−	0.205917i
$494$		0			0
$495$	4.52364	+	3.56715i	0.203323	+	0.160331i
$496$		0			0
$497$	−0.302674	−	0.931534i	−0.0135768	−	0.0417850i
$498$		0			0
$499$	25.5882	+	4.05278i	1.14549	+	0.181427i	0.700190	−	0.713956i	$-0.253099\pi$
$499$	25.5882	+	4.05278i	1.14549	+	0.181427i	0.445296	+	0.895384i	$0.353099\pi$
$500$		0			0
$501$		−	27.5980i		−	1.23299i
$502$		0			0
$503$	1.17328	+	2.30270i	0.0523141	+	0.102672i	0.915683	−	0.401900i	$-0.131650\pi$
$503$	1.17328	+	2.30270i	0.0523141	+	0.102672i	−0.863369	+	0.504572i	$0.831650\pi$
$504$		0			0
$505$	−3.20432	−	11.3675i	−0.142590	−	0.505849i
$506$		0			0
$507$	8.81421	−	17.2989i	0.391453	−	0.768270i
$508$		0			0
$509$	−0.516698	−	1.01408i	−0.0229022	−	0.0449482i	0.879272	−	0.476320i	$-0.158030\pi$
$509$	−0.516698	−	1.01408i	−0.0229022	−	0.0449482i	−0.902174	+	0.431372i	$0.858030\pi$
$510$		0			0
$511$	−1.52325	+	9.61742i	−0.0673846	+	0.425450i
$512$		0			0
$513$	−6.21099	+	4.51255i	−0.274222	+	0.199234i
$514$		0			0
$515$	3.66987	−	6.55094i	0.161714	−	0.288669i
$516$		0			0
$517$	11.5126	+	15.8458i	0.506325	+	0.696896i
$518$		0			0
$519$	−20.4289	+	20.4289i	−0.896731	+	0.896731i
$520$		0			0
$521$	10.7340	−	21.0667i	0.470266	−	0.922949i	−0.527057	−	0.849830i	$-0.676705\pi$
$521$	10.7340	−	21.0667i	0.470266	−	0.922949i	0.997323	−	0.0731194i	$-0.0232954\pi$
$522$		0			0
$523$	−11.0380	−	3.58646i	−0.482658	−	0.156825i	0.0575740	−	0.998341i	$-0.481663\pi$
$523$	−11.0380	−	3.58646i	−0.482658	−	0.156825i	−0.540232	+	0.841516i	$0.681663\pi$
$524$		0			0
$525$	12.8315	+	1.01335i	0.560012	+	0.0442264i
$526$		0			0
$527$	2.48870	+	15.7131i	0.108410	+	0.684472i
$528$		0			0
$529$	−8.85346	−	27.2482i	−0.384933	−	1.18470i
$530$		0			0
$531$	3.97713	−	5.47404i	0.172593	−	0.237553i
$532$		0			0
$533$	0.247107	+	0.198763i	0.0107034	+	0.00860938i
$534$		0			0
$535$	29.8846	+	16.7415i	1.29203	+	0.723798i
$536$		0			0
$537$	19.4517	−	6.32023i	0.839402	−	0.272738i
$538$		0			0
$539$	13.3397	−	2.11281i	0.574583	−	0.0910050i
$540$		0			0
$541$	5.18660	+	1.68523i	0.222989	+	0.0724536i	0.418381	−	0.908272i	$-0.362598\pi$
$541$	5.18660	+	1.68523i	0.222989	+	0.0724536i	−0.195392	+	0.980725i	$0.562598\pi$
$542$		0			0
$543$	−20.8512	−	6.77497i	−0.894811	−	0.290742i
$544$		0			0
$545$	−8.93020	+	24.1963i	−0.382528	+	1.03645i
$546$		0			0
$547$	5.94877	+	5.94877i	0.254351	+	0.254351i	0.822752	−	0.568401i	$-0.192438\pi$
$547$	5.94877	+	5.94877i	0.254351	+	0.254351i	−0.568401	+	0.822752i	$0.692438\pi$
$548$		0			0
$549$	−0.0290679	+	0.0211190i	−0.00124059	+	0.000901339i
$550$		0			0
$551$	1.86014	+	1.35147i	0.0792446	+	0.0575745i
$552$		0			0
$553$	−2.17860	+	1.58285i	−0.0926435	+	0.0673095i
$554$		0			0
$555$	0.0430968	−	1.09312i	0.00182936	−	0.0464003i
$556$		0			0
$557$	−41.5768	+	21.1844i	−1.76166	+	0.897613i	−0.812420	+	0.583072i	$0.801850\pi$
$557$	−41.5768	+	21.1844i	−1.76166	+	0.897613i	−0.949244	+	0.314540i	$0.898150\pi$
$558$		0			0
$559$	0.414942	+	0.211423i	0.0175502	+	0.00894225i
$560$		0			0
$561$	−2.12371	−	13.4086i	−0.0896630	−	0.566110i
$562$		0			0
$563$	2.44411	+	4.79684i	0.103007	+	0.202163i	0.936758	−	0.349978i	$-0.113811\pi$
$563$	2.44411	+	4.79684i	0.103007	+	0.202163i	−0.833751	+	0.552141i	$0.813811\pi$
$564$		0			0
$565$	−28.7747	+	3.40176i	−1.21056	+	0.143113i
$566$		0			0
$567$	1.64530	−	10.3880i	0.0690962	−	0.436256i
$568$		0			0
$569$	29.9795	−	9.74094i	1.25681	−	0.408362i	0.396452	−	0.918055i	$-0.370241\pi$
$569$	29.9795	−	9.74094i	1.25681	−	0.408362i	0.860356	+	0.509694i	$0.170241\pi$
$570$		0			0
$571$	26.7167	+	26.7167i	1.11806	+	1.11806i	0.992026	+	0.126033i	$0.0402244\pi$
$571$	26.7167	+	26.7167i	1.11806	+	1.11806i	0.126033	+	0.992026i	$0.459776\pi$
$572$		0			0
$573$			3.21606i			0.134353i
$574$		0			0
$575$	−8.37920	−	34.9435i	−0.349437	−	1.45725i
$576$		0			0
$577$	−11.7622	+	11.7622i	−0.489668	+	0.489668i	−0.908201	−	0.418534i	$-0.862544\pi$
$577$	−11.7622	+	11.7622i	−0.489668	+	0.489668i	0.418534	+	0.908201i	$0.362544\pi$
$578$		0			0
$579$	−0.649593	+	0.211065i	−0.0269961	+	0.00877158i
$580$		0			0
$581$	−22.2843	−	3.52949i	−0.924510	−	0.146428i
$582$		0			0
$583$	45.8390			1.89846
$584$		0			0
$585$	0.0472882	+	0.0707925i	0.00195513	+	0.00292691i
$586$		0			0
$587$	−4.10563	+	0.650268i	−0.169458	+	0.0268394i	−0.240587	−	0.970628i	$-0.577340\pi$
$587$	−4.10563	+	0.650268i	−0.169458	+	0.0268394i	0.0711290	+	0.997467i	$0.477340\pi$
$588$		0			0
$589$	−7.12845	−	3.63212i	−0.293722	−	0.149659i
$590$		0			0
$591$	10.6713	+	20.9435i	0.438957	+	0.861501i
$592$		0			0
$593$	38.1825	+	6.04752i	1.56797	+	0.248342i	0.879133	−	0.476576i	$-0.158122\pi$
$593$	38.1825	+	6.04752i	1.56797	+	0.248342i	0.688835	+	0.724918i	$0.258122\pi$
$594$		0			0
$595$	7.09259	+	7.67480i	0.290768	+	0.314636i
$596$		0			0
$597$	15.7626	−	21.6953i	0.645119	−	0.887930i
$598$		0			0
$599$	−20.9617	+	15.2295i	−0.856470	+	0.622262i	−0.926922	−	0.375253i	$-0.877556\pi$
$599$	−20.9617	+	15.2295i	−0.856470	+	0.622262i	0.0704524	+	0.997515i	$0.477556\pi$
$600$		0			0
$601$	−31.8591	+	31.8591i	−1.29956	+	1.29956i	−0.370877	+	0.928682i	$0.620943\pi$
$601$	−31.8591	+	31.8591i	−1.29956	+	1.29956i	−0.928682	+	0.370877i	$0.879057\pi$
$602$		0			0
$603$	0.630307	+	0.321157i	0.0256681	+	0.0130785i
$604$		0			0
$605$	0.101250	−	0.508656i	0.00411638	−	0.0206798i
$606$		0			0
$607$	−1.27025	+	3.90944i	−0.0515580	+	0.158679i	−0.973520	−	0.228600i	$-0.926585\pi$
$607$	−1.27025	+	3.90944i	−0.0515580	+	0.158679i	0.921962	+	0.387279i	$0.126585\pi$
$608$		0			0
$609$	−4.28679	+	0.678961i	−0.173710	+	0.0275129i
$610$		0			0
$611$	0.0894438	+	0.275280i	0.00361851	+	0.0111366i
$612$		0			0
$613$	26.9194	+	19.5581i	1.08726	+	0.789943i	0.978935	−	0.204173i	$-0.0654504\pi$
$613$	26.9194	+	19.5581i	1.08726	+	0.789943i	0.108328	+	0.994115i	$0.465450\pi$
$614$		0			0
$615$	−19.8395	+	7.98768i	−0.800006	+	0.322094i
$616$		0			0
$617$	38.7720	+	28.1695i	1.56090	+	1.13406i	0.935266	+	0.353945i	$0.115160\pi$
$617$	38.7720	+	28.1695i	1.56090	+	1.13406i	0.625635	+	0.780116i	$0.284840\pi$
$618$		0			0
$619$	−8.95735	−	27.5679i	−0.360026	−	1.10805i	−0.953037	−	0.302853i	$-0.902061\pi$
$619$	−8.95735	−	27.5679i	−0.360026	−	1.10805i	0.593011	−	0.805194i	$-0.297939\pi$
$620$		0			0
$621$	−39.9602	+	6.32908i	−1.60355	+	0.253977i
$622$		0			0
$623$	1.25941	−	3.87607i	0.0504572	−	0.155291i
$624$		0			0
$625$	−3.89750	−	24.6943i	−0.155900	−	0.987773i
$626$		0			0
$627$	6.08297	+	3.09943i	0.242931	+	0.123779i
$628$		0			0
$629$	0.628041	−	0.628041i	0.0250417	−	0.0250417i
$630$		0			0
$631$	−20.6466	+	15.0006i	−0.821928	+	0.597165i	−0.917264	−	0.398280i	$-0.869607\pi$
$631$	−20.6466	+	15.0006i	−0.821928	+	0.597165i	0.0953363	+	0.995445i	$0.469607\pi$
$632$		0			0
$633$	−7.64987	+	10.5291i	−0.304055	+	0.418496i
$634$		0			0
$635$	12.7975	−	11.8267i	0.507852	−	0.469326i
$636$		0			0
$637$	0.197133	+	0.0312228i	0.00781069	+	0.00123709i
$638$		0			0
$639$	0.198351	+	0.389286i	0.00784665	+	0.0153999i
$640$		0			0
$641$	−34.5696	−	17.6141i	−1.36542	−	0.695715i	−0.390985	−	0.920397i	$-0.627866\pi$
$641$	−34.5696	−	17.6141i	−1.36542	−	0.695715i	−0.974432	+	0.224682i	$0.927866\pi$
$642$		0			0
$643$	−3.21315	+	0.508912i	−0.126714	+	0.0200695i	−0.219469	−	0.975619i	$-0.570433\pi$
$643$	−3.21315	+	0.508912i	−0.126714	+	0.0200695i	0.0927552	+	0.995689i	$0.470433\pi$
$644$		0			0
$645$	−26.1164	+	17.4453i	−1.02833	+	0.686908i
$646$		0			0
$647$	−20.1395			−0.791766			−0.395883	−	0.918301i	$-0.629561\pi$
$647$	−20.1395			−0.791766			−0.395883	+	0.918301i	$0.629561\pi$
$648$		0			0
$649$	−29.1354	−	4.61459i	−1.14366	−	0.181139i
$650$		0			0
$651$	14.3630	−	4.66682i	0.562930	−	0.182907i
$652$		0			0
$653$	15.4321	−	15.4321i	0.603904	−	0.603904i	−0.337442	−	0.941346i	$-0.609562\pi$
$653$	15.4321	−	15.4321i	0.603904	−	0.603904i	0.941346	+	0.337442i	$0.109562\pi$
$654$		0			0
$655$	−35.2947	+	4.17257i	−1.37908	+	0.163036i
$656$		0			0
$657$		−	4.34345i		−	0.169454i
$658$		0			0
$659$	−9.57918	−	9.57918i	−0.373152	−	0.373152i	0.495472	−	0.868624i	$-0.334995\pi$
$659$	−9.57918	−	9.57918i	−0.373152	−	0.373152i	−0.868624	+	0.495472i	$0.834995\pi$
$660$		0			0
$661$	9.64409	−	3.13355i	0.375111	−	0.121881i	−0.115393	−	0.993320i	$-0.536813\pi$
$661$	9.64409	−	3.13355i	0.375111	−	0.121881i	0.490504	+	0.871439i	$0.336813\pi$
$662$		0			0
$663$	0.0313839	−	0.198150i	0.00121885	−	0.00769551i
$664$		0			0
$665$	−5.21898	+	0.616991i	−0.202383	+	0.0239259i
$666$		0			0
$667$	5.50097	+	10.7963i	0.212998	+	0.418033i
$668$		0			0
$669$	−5.26051	−	33.2136i	−0.203383	−	1.28411i
$670$		0			0
$671$	0.139568	+	0.0711135i	0.00538797	+	0.00274531i
$672$		0			0
$673$	10.6918	−	5.44773i	0.412137	−	0.209994i	−0.235613	−	0.971847i	$-0.575710\pi$
$673$	10.6918	−	5.44773i	0.412137	−	0.209994i	0.647751	+	0.761852i	$0.275710\pi$
$674$		0			0
$675$	−28.0614	+	2.20084i	−1.08008	+	0.0847105i
$676$		0			0
$677$	1.56643	−	1.13807i	0.0602026	−	0.0437398i	−0.557277	−	0.830327i	$-0.688154\pi$
$677$	1.56643	−	1.13807i	0.0602026	−	0.0437398i	0.617480	+	0.786587i	$0.288154\pi$
$678$		0			0
$679$	2.10765	+	1.53130i	0.0808841	+	0.0587657i
$680$		0			0
$681$	−9.14935	+	6.64739i	−0.350604	+	0.254729i
$682$		0			0
$683$	10.4676	+	10.4676i	0.400532	+	0.400532i	0.878421	−	0.477888i	$-0.158598\pi$
$683$	10.4676	+	10.4676i	0.400532	+	0.400532i	−0.477888	+	0.878421i	$0.658598\pi$
$684$		0			0
$685$	−25.0258	−	9.23633i	−0.956185	−	0.352902i
$686$		0			0
$687$	−21.9474	−	7.13116i	−0.837347	−	0.272071i
$688$		0			0
$689$	0.644248	+	0.209329i	0.0245439	+	0.00797480i
$690$		0			0
$691$	−9.03606	+	1.43117i	−0.343748	+	0.0544443i	−0.325922	−	0.945397i	$-0.605675\pi$
$691$	−9.03606	+	1.43117i	−0.343748	+	0.0544443i	−0.0178262	+	0.999841i	$0.505675\pi$
$692$		0			0
$693$	4.22273	−	1.37205i	0.160408	−	0.0521198i
$694$		0			0
$695$	−15.9615	+	28.4923i	−0.605455	+	1.08077i
$696$		0			0
$697$	−16.2311	−	6.16944i	−0.614797	−	0.233684i
$698$		0			0
$699$	23.6891	−	32.6053i	0.896004	−	1.23324i
$700$		0			0
$701$	−1.66990	−	5.13942i	−0.0630712	−	0.194113i	0.914556	−	0.404460i	$-0.132541\pi$
$701$	−1.66990	−	5.13942i	−0.0630712	−	0.194113i	−0.977627	+	0.210347i	$0.932541\pi$
$702$		0			0
$703$	0.0698729	+	0.441160i	0.00263531	+	0.0166387i
$704$		0			0
$705$	−19.1448	−	3.81083i	−0.721035	−	0.143524i
$706$		0			0
$707$	−8.65710	−	2.81286i	−0.325584	−	0.105789i
$708$		0			0
$709$	−10.4586	+	20.5262i	−0.392781	+	0.770877i	−0.999715	−	0.0238757i	$-0.992399\pi$
$709$	−10.4586	+	20.5262i	−0.392781	+	0.770877i	0.606934	+	0.794753i	$0.292399\pi$
$710$		0			0
$711$	0.849377	−	0.849377i	0.0318541	−	0.0318541i
$712$		0			0
$713$	−24.7821	−	34.1096i	−0.928095	−	1.27741i
$714$		0			0
$715$	0.181397	−	0.323804i	0.00678384	−	0.0121096i
$716$		0			0
$717$	35.1487	−	25.5370i	1.31265	−	0.953698i
$718$		0			0
$719$	−2.55030	+	16.1020i	−0.0951101	+	0.600501i	0.893390	+	0.449282i	$0.148320\pi$
$719$	−2.55030	+	16.1020i	−0.0951101	+	0.600501i	−0.988500	+	0.151220i	$0.951680\pi$
$720$		0			0
$721$	−2.62734	−	5.15645i	−0.0978473	−	0.192036i
$722$		0			0
$723$	3.24375	−	6.36621i	0.120636	−	0.236762i
$724$		0			0
$725$	3.22390	+	7.78914i	0.119733	+	0.289281i
$726$		0			0
$727$	−19.9076	−	39.0709i	−0.738333	−	1.44906i	−0.887769	−	0.460288i	$-0.847746\pi$
$727$	−19.9076	−	39.0709i	−0.738333	−	1.44906i	0.149437	−	0.988771i	$-0.452254\pi$
$728$		0			0
$729$			29.9186i			1.10810i
$730$		0			0
$731$	−25.1852	−	3.98895i	−0.931509	−	0.147537i
$732$		0			0
$733$	2.39043	+	7.35699i	0.0882926	+	0.271737i	0.985448	−	0.169979i	$-0.0543700\pi$
$733$	2.39043	+	7.35699i	0.0882926	+	0.271737i	−0.897155	+	0.441716i	$0.854370\pi$
$734$		0			0
$735$	−8.33473	+	10.5696i	−0.307431	+	0.389866i
$736$		0			0
$737$		−	3.08405i		−	0.113602i
$738$		0			0
$739$	32.4190			1.19255			0.596275	−	0.802780i	$-0.296647\pi$
$739$	32.4190			1.19255			0.596275	+	0.802780i	$0.296647\pi$
$740$		0			0
$741$	0.0713398	+	0.0713398i	0.00262073	+	0.00262073i
$742$		0			0
$743$	4.24905	+	13.0772i	0.155882	+	0.479757i	0.998249	−	0.0591477i	$-0.0188383\pi$
$743$	4.24905	+	13.0772i	0.155882	+	0.479757i	−0.842367	+	0.538905i	$0.818838\pi$
$744$		0			0
$745$	−16.0456	−	0.632606i	−0.587864	−	0.0231769i
$746$		0			0
$747$	10.0641			0.368227
$748$		0			0
$749$	23.5231	−	11.9856i	0.859516	−	0.437945i
$750$		0			0
$751$	2.11056	+	13.3255i	0.0770153	+	0.486255i	0.995804	+	0.0915067i	$0.0291683\pi$
$751$	2.11056	+	13.3255i	0.0770153	+	0.486255i	−0.918789	+	0.394749i	$0.870832\pi$
$752$		0			0
$753$	−6.07619	+	11.9252i	−0.221429	+	0.434578i
$754$		0			0
$755$	14.0638	+	21.0541i	0.511833	+	0.766236i
$756$		0			0
$757$	−45.2505	−	7.16698i	−1.64466	−	0.260488i	−0.735679	−	0.677330i	$-0.763137\pi$
$757$	−45.2505	−	7.16698i	−1.64466	−	0.260488i	−0.908979	+	0.416842i	$0.863137\pi$
$758$		0			0
$759$	21.1475	+	29.1070i	0.767605	+	1.05652i
$760$		0			0
$761$	−9.58644	−	6.96496i	−0.347508	−	0.252479i	0.400315	−	0.916378i	$-0.368901\pi$
$761$	−9.58644	−	6.96496i	−0.347508	−	0.252479i	−0.747823	+	0.663898i	$0.768901\pi$
$762$		0			0
$763$	11.6841	+	16.0818i	0.422992	+	0.582198i
$764$		0			0
$765$	−3.66033	−	2.88638i	−0.132340	−	0.104357i
$766$		0			0
$767$	−0.388413	−	0.197906i	−0.0140248	−	0.00714598i
$768$		0			0
$769$	6.31637	−	19.4398i	0.227774	−	0.701017i	−0.770224	−	0.637773i	$-0.779856\pi$
$769$	6.31637	−	19.4398i	0.227774	−	0.701017i	0.997998	−	0.0632433i	$-0.0201444\pi$
$770$		0			0
$771$	7.01523	+	2.27939i	0.252647	+	0.0820901i
$772$		0			0
$773$	1.12679	+	7.11429i	0.0405279	+	0.255883i	0.999631	−	0.0271748i	$-0.00865106\pi$
$773$	1.12679	+	7.11429i	0.0405279	+	0.255883i	−0.959103	+	0.283058i	$0.908651\pi$
$774$		0			0
$775$	−15.3195	−	25.0144i	−0.550293	−	0.898542i
$776$		0			0
$777$	−0.682117	−	0.495587i	−0.0244708	−	0.0177791i
$778$		0			0
$779$	7.30779	−	4.77993i	0.261829	−	0.171259i
$780$		0			0
$781$	1.11958	−	1.54098i	0.0400619	−	0.0551404i
$782$		0			0
$783$	9.02678	−	2.93298i	0.322591	−	0.104816i
$784$		0			0
$785$	−3.97964	−	14.1180i	−0.142039	−	0.503894i
$786$		0			0
$787$	2.68864	−	8.27479i	0.0958397	−	0.294964i	−0.891632	−	0.452761i	$-0.850439\pi$
$787$	2.68864	−	8.27479i	0.0958397	−	0.294964i	0.987472	+	0.157797i	$0.0504391\pi$
$788$		0			0
$789$	3.15371	−	9.70613i	0.112275	−	0.345547i
$790$		0			0
$791$	−10.1384	+	19.8977i	−0.360479	+	0.707480i
$792$		0			0
$793$	0.00163683	+	0.00163683i	5.81254e−5	+	5.81254e-5i
$794$		0			0
$795$	−33.5513	+	31.0061i	−1.18994	+	1.09967i
$796$		0			0
$797$	15.7085	−	21.6209i	0.556424	−	0.765852i	−0.434442	−	0.900700i	$-0.643054\pi$
$797$	15.7085	−	21.6209i	0.556424	−	0.765852i	0.990866	+	0.134847i	$0.0430544\pi$
$798$		0			0
$799$	−9.31551	−	12.8217i	−0.329559	−	0.453599i
$800$		0			0
$801$	−0.284389	+	1.79556i	−0.0100484	+	0.0634431i
$802$		0			0
$803$	−16.8719	+	8.59669i	−0.595398	+	0.303370i
$804$		0			0
$805$	−25.9821	−	9.58928i	−0.915747	−	0.337978i
$806$		0			0
$807$	−3.05182	+	0.483362i	−0.107429	+	0.0170151i
$808$		0			0
$809$	39.9883	−	20.3750i	1.40591	−	0.716348i	0.423996	−	0.905664i	$-0.360627\pi$
$809$	39.9883	−	20.3750i	1.40591	−	0.716348i	0.981916	+	0.189316i	$0.0606270\pi$
$810$		0			0
$811$			24.6580i			0.865859i	0.901428	+	0.432930i	$0.142520\pi$
$811$			24.6580i			0.865859i	−0.901428	+	0.432930i	$0.857480\pi$
$812$		0			0
$813$	0.183047	−	1.15571i	0.00641973	−	0.0405326i
$814$		0			0
$815$	−5.26496	−	11.4246i	−0.184423	−	0.400188i
$816$		0			0
$817$	9.06743	−	9.06743i	0.317229	−	0.317229i
$818$		0			0
$819$	0.0656143			0.00229275
$820$		0			0
$821$	−10.6531			−0.371794			−0.185897	−	0.982569i	$-0.559519\pi$
$821$	−10.6531			−0.371794			−0.185897	+	0.982569i	$0.559519\pi$
$822$		0			0
$823$	1.08650	−	1.08650i	0.0378729	−	0.0378729i	−0.687917	−	0.725790i	$-0.741475\pi$
$823$	1.08650	−	1.08650i	0.0378729	−	0.0378729i	0.725790	+	0.687917i	$0.241475\pi$
$824$		0			0
$825$	13.0727	+	21.3457i	0.455134	+	0.743162i
$826$		0			0
$827$	−0.500186	+	3.15805i	−0.0173932	+	0.109816i	−0.994858	−	0.101284i	$-0.967705\pi$
$827$	−0.500186	+	3.15805i	−0.0173932	+	0.109816i	0.977464	+	0.211101i	$0.0677048\pi$
$828$		0			0
$829$		−	24.0797i		−	0.836321i	−0.908373	−	0.418161i	$-0.862675\pi$
$829$		−	24.0797i		−	0.836321i	0.908373	−	0.418161i	$-0.137325\pi$
$830$		0			0
$831$	−39.2694	+	20.0088i	−1.36224	+	0.694096i
$832$		0			0
$833$	−10.7939	+	1.70959i	−0.373987	+	0.0592337i
$834$		0			0
$835$	−14.3044	+	38.7575i	−0.495023	+	1.34126i
$836$		0			0
$837$	−29.4262	+	14.9934i	−1.01712	+	0.518247i
$838$		0			0
$839$	−5.09989	+	32.1994i	−0.176068	+	1.11165i	0.728415	+	0.685136i	$0.240257\pi$
$839$	−5.09989	+	32.1994i	−0.176068	+	1.11165i	−0.904482	+	0.426511i	$0.859743\pi$
$840$		0			0
$841$	15.3750	+	21.1618i	0.530171	+	0.729718i
$842$		0			0
$843$	6.09518	−	8.38929i	0.209929	−	0.288943i
$844$		0			0
$845$	−21.3446	+	19.7254i	−0.734276	+	0.678573i
$846$		0			0
$847$	−0.282647	−	0.282647i	−0.00971186	−	0.00971186i
$848$		0			0
$849$	4.46976	−	8.77239i	0.153402	−	0.301068i
$850$		0			0
$851$	−0.727383	+	2.23866i	−0.0249344	+	0.0767401i
$852$		0			0
$853$	4.30659	−	13.2543i	0.147455	−	0.453819i	−0.849864	−	0.527003i	$-0.823316\pi$
$853$	4.30659	−	13.2543i	0.147455	−	0.453819i	0.997319	+	0.0731834i	$0.0233158\pi$
$854$		0			0
$855$	2.25627	−	0.636006i	0.0771629	−	0.0217509i
$856$		0			0
$857$	−40.4192	+	13.1330i	−1.38069	+	0.448614i	−0.902897	−	0.429856i	$-0.858564\pi$
$857$	−40.4192	+	13.1330i	−1.38069	+	0.448614i	−0.477796	+	0.878471i	$0.658564\pi$
$858$		0			0
$859$	26.8872	−	37.0071i	0.917380	−	1.26266i	−0.0472035	−	0.998885i	$-0.515031\pi$
$859$	26.8872	−	37.0071i	0.917380	−	1.26266i	0.964583	−	0.263779i	$-0.0849691\pi$
$860$		0			0
$861$	−3.37413	+	16.1345i	−0.114990	+	0.549861i
$862$		0			0
$863$	−35.7162	−	25.9494i	−1.21579	−	0.883327i	−0.220051	−	0.975488i	$-0.570622\pi$
$863$	−35.7162	−	25.9494i	−1.21579	−	0.883327i	−0.995744	+	0.0921617i	$0.970622\pi$
$864$		0			0
$865$	39.2782	−	18.1011i	1.33550	−	0.615454i
$866$		0			0
$867$	−2.25403	−	14.2314i	−0.0765507	−	0.483322i
$868$		0			0
$869$	−4.98049	−	1.61826i	−0.168952	−	0.0548957i
$870$		0			0
$871$	0.0140837	−	0.0433450i	0.000477206	−	0.00146869i
$872$		0			0
$873$	−1.03542	−	0.527573i	−0.0350437	−	0.0178556i
$874$		0			0
$875$	−17.4948	−	8.07384i	−0.591433	−	0.272946i
$876$		0			0
$877$	29.7795	+	40.9880i	1.00558	+	1.38407i	0.921837	+	0.387578i	$0.126688\pi$
$877$	29.7795	+	40.9880i	1.00558	+	1.38407i	0.0837458	+	0.996487i	$0.473312\pi$
$878$		0			0
$879$	25.0878	+	18.2274i	0.846191	+	0.614794i
$880$		0			0
$881$	−22.4363	−	30.8810i	−0.755900	−	1.04041i	−0.997544	−	0.0700418i	$-0.977687\pi$
$881$	−22.4363	−	30.8810i	−0.755900	−	1.04041i	0.241644	−	0.970365i	$-0.422313\pi$
$882$		0			0
$883$	9.81600	+	1.55470i	0.330335	+	0.0523199i	0.319399	−	0.947620i	$-0.396519\pi$
$883$	9.81600	+	1.55470i	0.330335	+	0.0523199i	0.0109357	+	0.999940i	$0.496519\pi$
$884$		0			0
$885$	24.4466	−	16.3299i	0.821765	−	0.548925i
$886$		0			0
$887$	−11.5197	+	22.6087i	−0.386795	+	0.759127i	−0.999514	−	0.0311735i	$-0.990076\pi$
$887$	−11.5197	+	22.6087i	−0.386795	+	0.759127i	0.612719	+	0.790300i	$0.290076\pi$
$888$		0			0
$889$	−2.10093	−	13.2648i	−0.0704631	−	0.444886i
$890$		0			0
$891$	18.2238	−	9.28551i	0.610522	−	0.311076i
$892$		0			0
$893$	7.97005			0.266707
$894$		0			0
$895$	−30.5931	−	1.20615i	−1.02261	−	0.0403171i
$896$		0			0
$897$	0.164299	+	0.505659i	0.00548577	+	0.0168835i
$898$		0			0
$899$	6.99394	+	6.99394i	0.233261	+	0.233261i
$900$		0			0
$901$	−37.0909			−1.23568
$902$		0			0
$903$			24.2061i			0.805527i
$904$		0			0
$905$	25.7711	+	20.3220i	0.856661	+	0.675525i
$906$		0			0
$907$	−3.74460	−	11.5247i	−0.124337	−	0.382671i	0.869442	−	0.494034i	$-0.164478\pi$
$907$	−3.74460	−	11.5247i	−0.124337	−	0.382671i	−0.993780	+	0.111363i	$0.964478\pi$
$908$		0			0
$909$	4.01034	+	0.635176i	0.133015	+	0.0210675i
$910$		0			0
$911$		−	27.7200i		−	0.918404i	−0.888332	−	0.459202i	$-0.848135\pi$
$911$		−	27.7200i		−	0.918404i	0.888332	−	0.459202i	$-0.151865\pi$
$912$		0			0
$913$	−19.9192	−	39.0937i	−0.659230	−	1.29381i
$914$		0			0
$915$	−0.150257	+	0.0423550i	−0.00496735	+	0.00140021i
$916$		0			0
$917$	−12.4356	+	24.4063i	−0.410660	+	0.805966i
$918$		0			0
$919$	−3.55757	−	6.98213i	−0.117354	−	0.230319i	0.824856	−	0.565342i	$-0.191256\pi$
$919$	−3.55757	−	6.98213i	−0.117354	−	0.230319i	−0.942210	+	0.335023i	$0.891256\pi$
$920$		0			0
$921$	2.95744	−	18.6726i	0.0974511	−	0.615282i
$922$		0			0
$923$	0.0227723	−	0.0165451i	0.000749561	−	0.000544588i
$924$		0			0
$925$	−0.627101	+	1.51280i	−0.0206189	+	0.0497405i
$926$		0			0
$927$	1.51734	+	2.08844i	0.0498361	+	0.0685935i
$928$		0			0
$929$	−25.8285	+	25.8285i	−0.847404	+	0.847404i	−0.989809	−	0.142404i	$-0.954517\pi$
$929$	−25.8285	+	25.8285i	−0.847404	+	0.847404i	0.142404	+	0.989809i	$0.454517\pi$
$930$		0			0
$931$	2.49505	−	4.89681i	0.0817719	−	0.160486i
$932$		0			0
$933$	9.85885	+	3.20334i	0.322764	+	0.104873i
$934$		0			0
$935$	−3.96737	+	19.9312i	−0.129747	+	0.651821i
$936$		0			0
$937$	−8.31846	−	52.5207i	−0.271752	−	1.71578i	−0.625321	−	0.780368i	$-0.715032\pi$
$937$	−8.31846	−	52.5207i	−0.271752	−	1.71578i	0.353569	−	0.935409i	$-0.384968\pi$
$938$		0			0
$939$	−13.9051	−	42.7954i	−0.453775	−	1.39657i
$940$		0			0
$941$	−29.2577	+	40.2697i	−0.953773	+	1.31276i	−0.00394143	+	0.999992i	$0.501255\pi$
$941$	−29.2577	+	40.2697i	−0.953773	+	1.31276i	−0.949831	+	0.312763i	$0.898745\pi$
$942$		0			0
$943$	45.7500	−	4.96051i	1.48982	−	0.161536i
$944$		0			0
$945$	−10.6027	+	18.9264i	−0.344905	+	0.615677i
$946$		0			0
$947$	27.6204	−	8.97440i	0.897541	−	0.291629i	0.176319	−	0.984333i	$-0.443581\pi$
$947$	27.6204	−	8.97440i	0.897541	−	0.291629i	0.721222	+	0.692704i	$0.243581\pi$
$948$		0			0
$949$	−0.276386	+	0.0437753i	−0.00897187	+	0.00142100i
$950$		0			0
$951$	−29.8323	−	9.69311i	−0.967379	−	0.314321i
$952$		0			0
$953$	−0.698306	−	0.226893i	−0.0226204	−	0.00734980i	0.297685	−	0.954664i	$-0.403786\pi$
$953$	−0.698306	−	0.226893i	−0.0226204	−	0.00734980i	−0.320305	+	0.947314i	$0.603786\pi$
$954$		0			0
$955$	1.66692	−	4.51651i	0.0539404	−	0.146151i
$956$		0			0
$957$	−5.96820	−	5.96820i	−0.192924	−	0.192924i
$958$		0			0
$959$	−16.6331	+	12.0846i	−0.537109	+	0.390233i
$960$		0			0
$961$	−2.76379	−	2.00801i	−0.0891546	−	0.0647746i
$962$		0			0
$963$	−9.52725	+	6.92195i	−0.307011	+	0.223057i
$964$		0			0
$965$	1.02166	+	0.0402796i	0.0328884	+	0.00129665i
$966$		0			0
$967$	15.1542	−	7.72147i	0.487327	−	0.248306i	−0.193021	−	0.981195i	$-0.561829\pi$
$967$	15.1542	−	7.72147i	0.487327	−	0.248306i	0.680348	+	0.732889i	$0.261829\pi$
$968$		0			0
$969$	−4.92207	−	2.50792i	−0.158120	−	0.0805660i
$970$		0			0
$971$	1.84360	+	11.6400i	0.0591639	+	0.373546i	0.999450	+	0.0331612i	$0.0105575\pi$
$971$	1.84360	+	11.6400i	0.0591639	+	0.373546i	−0.940286	+	0.340385i	$0.889443\pi$
$972$		0			0
$973$	11.4272	+	22.4272i	0.366340	+	0.718982i
$974$		0			0
$975$	0.0862542	+	0.359703i	0.00276235	+	0.0115197i
$976$		0			0
$977$	−4.28186	+	27.0346i	−0.136989	+	0.864913i	0.819486	+	0.573099i	$0.194259\pi$
$977$	−4.28186	+	27.0346i	−0.136989	+	0.864913i	−0.956475	+	0.291814i	$0.905741\pi$
$978$		0			0
$979$	7.53767	−	2.44914i	0.240905	−	0.0782748i
$980$		0			0
$981$	−6.26984	−	6.26984i	−0.200181	−	0.200181i
$982$		0			0
$983$			13.4689i			0.429590i	0.976659	+	0.214795i	$0.0689084\pi$
$983$			13.4689i			0.429590i	−0.976659	+	0.214795i	$0.931092\pi$
$984$		0			0
$985$	−4.13102	−	34.9433i	−0.131625	−	1.11339i
$986$		0			0
$987$	−10.6383	+	10.6383i	−0.338620	+	0.338620i
$988$		0			0
$989$	64.2702	−	20.8827i	2.04367	−	0.664030i
$990$		0			0
$991$	60.3413	+	9.55712i	1.91680	+	0.303592i	0.996214	−	0.0869389i	$-0.0277085\pi$
$991$	60.3413	+	9.55712i	1.91680	+	0.303592i	0.920590	+	0.390531i	$0.127708\pi$
$992$		0			0
$993$	−31.7871			−1.00873
$994$		0			0
$995$	−33.3813	+	22.2982i	−1.05826	+	0.706899i
$996$		0			0
$997$	−12.9392	+	2.04937i	−0.409789	+	0.0649042i	−0.357926	−	0.933750i	$-0.616516\pi$
$997$	−12.9392	+	2.04937i	−0.409789	+	0.0649042i	−0.0518631	+	0.998654i	$0.516516\pi$
$998$		0			0
$999$	1.64284	+	0.837070i	0.0519773	+	0.0264837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.8	✓	176
5.4	even	2	inner	820.2.bq.a.49.15	yes	176
41.36	even	20	inner	820.2.bq.a.569.15	yes	176
205.159	even	20	inner	820.2.bq.a.569.8	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.8	✓	176	1.1	even	1	trivial
820.2.bq.a.49.15	yes	176	5.4	even	2	inner
820.2.bq.a.569.8	yes	176	205.159	even	20	inner
820.2.bq.a.569.15	yes	176	41.36	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05623 + 1.05623i) q^{3} +(2.03080 - 0.935877i) q^{5} +(0.269596 - 1.70217i) q^{7} +0.768736i q^{9} +(2.98613 - 1.52151i) q^{11} +(0.0489169 - 0.00774768i) q^{13} +(-1.15649 + 3.13350i) q^{15} +(-2.41624 + 1.23114i) q^{17} +(0.213336 - 1.34695i) q^{19} +(1.51313 + 2.08264i) q^{21} +(4.22431 - 5.81426i) q^{23} +(3.24827 - 3.80115i) q^{25} +(-3.98067 - 3.98067i) q^{27} +(-0.765424 + 1.50223i) q^{29} +(1.81286 - 5.57941i) q^{31} +(-1.54698 + 4.76112i) q^{33} +(-1.04552 - 3.70906i) q^{35} +(-0.311494 + 0.101211i) q^{37} +(-0.0434844 + 0.0598511i) q^{39} +(4.30013 + 4.74435i) q^{41} +(7.60719 + 5.52695i) q^{43} +(0.719443 + 1.56115i) q^{45} +(0.914242 + 5.77229i) q^{47} +(3.83271 + 1.24532i) q^{49} +(1.25175 - 3.85249i) q^{51} +(12.1868 + 6.20947i) q^{53} +(4.64027 - 5.88452i) q^{55} +(1.19736 + 1.64803i) q^{57} +(-7.12083 - 5.17359i) q^{59} +(0.0274724 + 0.0378125i) q^{61} +(1.30852 + 0.207249i) q^{63} +(0.0920895 - 0.0615142i) q^{65} +(0.417773 - 0.819926i) q^{67} +(1.67936 + 10.6031i) q^{69} +(0.506397 - 0.258022i) q^{71} -5.65011 q^{73} +(0.583974 + 7.44584i) q^{75} +(-1.78481 - 5.49308i) q^{77} +(-1.10490 - 1.10490i) q^{79} +6.10284 q^{81} -13.0918i q^{83} +(-3.75470 + 4.76149i) q^{85} +(-0.778239 - 2.39517i) q^{87} +(2.33573 + 0.369944i) q^{89} -0.0853535i q^{91} +(3.97836 + 7.80797i) q^{93} +(-0.827339 - 2.93504i) q^{95} +(-0.686286 + 1.34691i) q^{97} +(1.16964 + 2.29554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more