LMFDB - Embedded newform 980.2.q.g.569.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(569,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.569"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,6,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	980.569
Dual form			980.2.q.g.949.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} +(-2.13746 + 0.656712i) q^{5} +(2.63746 + 4.56821i) q^{11} +2.62685i q^{13} +(-2.63746 + 2.83616i) q^{15} +(-0.362541 + 0.209313i) q^{17} +(-1.63746 + 2.83616i) q^{19} +(-6.77492 - 3.91150i) q^{23} +(4.13746 - 2.80739i) q^{25} +5.19615i q^{27} -4.27492 q^{29} +(1.63746 + 2.83616i) q^{31} +(7.91238 + 4.56821i) q^{33} +(8.63746 + 4.98684i) q^{37} +(2.27492 + 3.94027i) q^{39} +3.72508 q^{41} +2.15068i q^{43} +(5.63746 + 3.25479i) q^{47} +(-0.362541 + 0.627940i) q^{51} +(4.91238 - 2.83616i) q^{53} +(-8.63746 - 8.03231i) q^{55} +5.67232i q^{57} +(1.63746 + 2.83616i) q^{59} +(-6.77492 + 11.7345i) q^{61} +(-1.72508 - 5.61478i) q^{65} +(3.04983 - 1.76082i) q^{67} -13.5498 q^{69} -4.54983 q^{71} +(5.63746 - 3.25479i) q^{73} +(3.77492 - 7.79423i) q^{75} +(3.63746 - 6.30026i) q^{79} +(4.50000 + 7.79423i) q^{81} -7.40437i q^{83} +(0.637459 - 0.685484i) q^{85} +(-6.41238 + 3.70219i) q^{87} +(3.50000 - 6.06218i) q^{89} +(4.91238 + 2.83616i) q^{93} +(1.63746 - 7.13752i) q^{95} +6.92820i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - q^{5} + 3 q^{11} - 3 q^{15} - 9 q^{17} + q^{19} - 12 q^{23} + 9 q^{25} - 2 q^{29} - q^{31} + 9 q^{33} + 27 q^{37} - 6 q^{39} + 30 q^{41} + 15 q^{47} - 9 q^{51} - 3 q^{53} - 27 q^{55}+ \cdots - q^{95}+O(q^{100}) $ 4 * q + 6 * q^3 - q^5 + 3 * q^11 - 3 * q^15 - 9 * q^17 + q^19 - 12 * q^23 + 9 * q^25 - 2 * q^29 - q^31 + 9 * q^33 + 27 * q^37 - 6 * q^39 + 30 * q^41 + 15 * q^47 - 9 * q^51 - 3 * q^53 - 27 * q^55 - q^59 - 12 * q^61 - 22 * q^65 - 18 * q^67 - 24 * q^69 + 12 * q^71 + 15 * q^73 + 7 * q^79 + 18 * q^81 - 5 * q^85 - 3 * q^87 + 14 * q^89 - 3 * q^93 - q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$4$		0			0
$5$	−2.13746	+	0.656712i	−0.955901	+	0.293691i
$5$	−2.13746	+	0.656712i	−0.955901	+	0.293691i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.63746	+	4.56821i	0.795224	+	1.37737i	0.922697	+	0.385526i	$0.125980\pi$
$11$	2.63746	+	4.56821i	0.795224	+	1.37737i	−0.127473	+	0.991842i	$0.540687\pi$
$12$		0			0
$13$			2.62685i			0.728557i	0.931290	+	0.364278i	$0.118684\pi$
$13$			2.62685i			0.728557i	−0.931290	+	0.364278i	$0.881316\pi$
$14$		0			0
$15$	−2.63746	+	2.83616i	−0.680989	+	0.732294i
$16$		0			0
$17$	−0.362541	+	0.209313i	−0.0879292	+	0.0507659i	−0.543320	−	0.839526i	$-0.682833\pi$
$17$	−0.362541	+	0.209313i	−0.0879292	+	0.0507659i	0.455391	+	0.890292i	$0.349500\pi$
$18$		0			0
$19$	−1.63746	+	2.83616i	−0.375659	+	0.650660i	−0.990425	−	0.138049i	$-0.955917\pi$
$19$	−1.63746	+	2.83616i	−0.375659	+	0.650660i	0.614767	+	0.788709i	$0.289250\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.77492	−	3.91150i	−1.41267	−	0.815604i	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−6.77492	−	3.91150i	−1.41267	−	0.815604i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	4.13746	−	2.80739i	0.827492	−	0.561478i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−4.27492			−0.793832			−0.396916	−	0.917855i	$-0.629920\pi$
$29$	−4.27492			−0.793832			−0.396916	+	0.917855i	$0.629920\pi$
$30$		0			0
$31$	1.63746	+	2.83616i	0.294096	+	0.509390i	0.974774	−	0.223193i	$-0.0716480\pi$
$31$	1.63746	+	2.83616i	0.294096	+	0.509390i	−0.680678	+	0.732583i	$0.738315\pi$
$32$		0			0
$33$	7.91238	+	4.56821i	1.37737	+	0.795224i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.63746	+	4.98684i	1.41999	+	0.819831i	0.996297	−	0.0859750i	$-0.0274005\pi$
$37$	8.63746	+	4.98684i	1.41999	+	0.819831i	0.423692	+	0.905806i	$0.360734\pi$
$38$		0			0
$39$	2.27492	+	3.94027i	0.364278	+	0.630949i
$40$		0			0
$41$	3.72508			0.581760			0.290880	−	0.956760i	$-0.406052\pi$
$41$	3.72508			0.581760			0.290880	+	0.956760i	$0.406052\pi$
$42$		0			0
$43$			2.15068i			0.327975i	0.986462	+	0.163988i	$0.0524357\pi$
$43$			2.15068i			0.327975i	−0.986462	+	0.163988i	$0.947564\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.63746	+	3.25479i	0.822308	+	0.474760i	0.851212	−	0.524823i	$-0.175868\pi$
$47$	5.63746	+	3.25479i	0.822308	+	0.474760i	−0.0289038	+	0.999582i	$0.509202\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.362541	+	0.627940i	−0.0507659	+	0.0879292i
$52$		0			0
$53$	4.91238	−	2.83616i	0.674767	−	0.389577i	−0.123114	−	0.992393i	$-0.539288\pi$
$53$	4.91238	−	2.83616i	0.674767	−	0.389577i	0.797880	+	0.602816i	$0.205955\pi$
$54$		0			0
$55$	−8.63746	−	8.03231i	−1.16467	−	1.08308i
$56$		0			0
$57$			5.67232i			0.751318i
$58$		0			0
$59$	1.63746	+	2.83616i	0.213179	+	0.369237i	0.952708	−	0.303888i	$-0.0982849\pi$
$59$	1.63746	+	2.83616i	0.213179	+	0.369237i	−0.739529	+	0.673125i	$0.764952\pi$
$60$		0			0
$61$	−6.77492	+	11.7345i	−0.867439	+	1.50245i	−0.00283468	+	0.999996i	$0.500902\pi$
$61$	−6.77492	+	11.7345i	−0.867439	+	1.50245i	−0.864605	+	0.502453i	$0.832431\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.72508	−	5.61478i	−0.213970	−	0.696428i
$66$		0			0
$67$	3.04983	−	1.76082i	0.372597	−	0.215119i	−0.301996	−	0.953309i	$-0.597653\pi$
$67$	3.04983	−	1.76082i	0.372597	−	0.215119i	0.674592	+	0.738191i	$0.264319\pi$
$68$		0			0
$69$	−13.5498			−1.63121
$70$		0			0
$71$	−4.54983			−0.539966			−0.269983	−	0.962865i	$-0.587018\pi$
$71$	−4.54983			−0.539966			−0.269983	+	0.962865i	$0.587018\pi$
$72$		0			0
$73$	5.63746	−	3.25479i	0.659815	−	0.380944i	−0.132392	−	0.991197i	$-0.542266\pi$
$73$	5.63746	−	3.25479i	0.659815	−	0.380944i	0.792206	+	0.610253i	$0.208932\pi$
$74$		0			0
$75$	3.77492	−	7.79423i	0.435890	−	0.900000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.63746	−	6.30026i	0.409246	−	0.708835i	−0.585559	−	0.810630i	$-0.699125\pi$
$79$	3.63746	−	6.30026i	0.409246	−	0.708835i	0.994805	+	0.101795i	$0.0324584\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$		−	7.40437i		−	0.812736i	−0.913710	−	0.406368i	$-0.866795\pi$
$83$		−	7.40437i		−	0.812736i	0.913710	−	0.406368i	$-0.133205\pi$
$84$		0			0
$85$	0.637459	−	0.685484i	0.0691421	−	0.0743512i
$86$		0			0
$87$	−6.41238	+	3.70219i	−0.687479	+	0.396916i
$88$		0			0
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.91238	+	2.83616i	0.509390	+	0.294096i
$94$		0			0
$95$	1.63746	−	7.13752i	0.168000	−	0.732294i
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.77492	−	11.7345i	−0.674129	−	1.16763i	−0.976723	−	0.214507i	$-0.931186\pi$
$101$	−6.77492	−	11.7345i	−0.674129	−	1.16763i	0.302593	−	0.953120i	$-0.402148\pi$
$102$		0			0
$103$	−9.77492	−	5.64355i	−0.963151	−	0.556076i	−0.0660098	−	0.997819i	$-0.521027\pi$
$103$	−9.77492	−	5.64355i	−0.963151	−	0.556076i	−0.897141	+	0.441743i	$0.854360\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.04983	−	1.76082i	−0.294839	−	0.170225i	0.345283	−	0.938499i	$-0.387783\pi$
$107$	−3.04983	−	1.76082i	−0.294839	−	0.170225i	−0.640122	+	0.768273i	$0.721116\pi$
$108$		0			0
$109$	−5.77492	−	10.0025i	−0.553137	−	0.958061i	−0.998046	−	0.0624852i	$-0.980097\pi$
$109$	−5.77492	−	10.0025i	−0.553137	−	0.958061i	0.444909	−	0.895576i	$-0.353236\pi$
$110$		0			0
$111$	17.2749			1.63966
$112$		0			0
$113$		−	4.30136i		−	0.404637i	−0.979320	−	0.202319i	$-0.935152\pi$
$113$		−	4.30136i		−	0.404637i	0.979320	−	0.202319i	$-0.0648477\pi$
$114$		0			0
$115$	17.0498	+	3.91150i	1.58991	+	0.364749i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−8.41238	+	14.5707i	−0.764761	+	1.32461i
$122$		0			0
$123$	5.58762	−	3.22602i	0.503819	−	0.290880i
$124$		0			0
$125$	−7.00000	+	8.71780i	−0.626099	+	0.779744i
$126$		0			0
$127$		−	15.6460i		−	1.38836i	−0.719802	−	0.694179i	$-0.755768\pi$
$127$		−	15.6460i		−	1.38836i	0.719802	−	0.694179i	$-0.244232\pi$
$128$		0			0
$129$	1.86254	+	3.22602i	0.163988	+	0.284035i
$130$		0			0
$131$	−5.36254	+	9.28819i	−0.468527	+	0.811513i	−0.999353	−	0.0359678i	$-0.988549\pi$
$131$	−5.36254	+	9.28819i	−0.468527	+	0.811513i	0.530826	+	0.847481i	$0.321882\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.41238	−	11.1066i	−0.293691	−	0.955901i
$136$		0			0
$137$	−18.4622	+	10.6592i	−1.57733	+	0.910674i	−0.582103	+	0.813115i	$0.697770\pi$
$137$	−18.4622	+	10.6592i	−1.57733	+	0.910674i	−0.995230	+	0.0975588i	$0.968897\pi$
$138$		0			0
$139$	13.0997			1.11110			0.555550	−	0.831483i	$-0.312508\pi$
$139$	13.0997			1.11110			0.555550	+	0.831483i	$0.312508\pi$
$140$		0			0
$141$	11.2749			0.949519
$142$		0			0
$143$	−12.0000	+	6.92820i	−1.00349	+	0.579365i
$144$		0			0
$145$	9.13746	−	2.80739i	0.758825	−	0.233141i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.77492	+	6.53835i	−0.309253	+	0.535642i	−0.978199	−	0.207669i	$-0.933412\pi$
$149$	−3.77492	+	6.53835i	−0.309253	+	0.535642i	0.668946	+	0.743311i	$0.266746\pi$
$150$		0			0
$151$	6.36254	+	11.0202i	0.517776	+	0.896815i	0.999787	+	0.0206494i	$0.00657337\pi$
$151$	6.36254	+	11.0202i	0.517776	+	0.896815i	−0.482011	+	0.876165i	$0.660093\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.36254	−	4.98684i	−0.430730	−	0.400553i
$156$		0			0
$157$	1.91238	−	1.10411i	0.152624	−	0.0881176i	−0.421743	−	0.906715i	$-0.638582\pi$
$157$	1.91238	−	1.10411i	0.152624	−	0.0881176i	0.574367	+	0.818598i	$0.305248\pi$
$158$		0			0
$159$	4.91238	−	8.50848i	0.389577	−	0.674767i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.91238	+	2.83616i	0.384767	+	0.222145i	0.679890	−	0.733314i	$-0.262027\pi$
$163$	4.91238	+	2.83616i	0.384767	+	0.222145i	−0.295123	+	0.955459i	$0.595361\pi$
$164$		0			0
$165$	−19.9124	−	4.56821i	−1.55018	−	0.355635i
$166$		0			0
$167$			0.476171i			0.0368472i	0.999830	+	0.0184236i	$0.00586474\pi$
$167$			0.476171i			0.0368472i	−0.999830	+	0.0184236i	$0.994135\pi$
$168$		0			0
$169$	6.09967			0.469205
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.7371	−	10.2405i	−1.34853	−	0.778573i	−0.360488	−	0.932764i	$-0.617390\pi$
$173$	−17.7371	−	10.2405i	−1.34853	−	0.778573i	−0.988041	+	0.154190i	$0.950723\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.91238	+	2.83616i	0.369237	+	0.213179i
$178$		0			0
$179$	−3.63746	−	6.30026i	−0.271876	−	0.470904i	0.697466	−	0.716618i	$-0.254311\pi$
$179$	−3.63746	−	6.30026i	−0.271876	−	0.470904i	−0.969342	+	0.245714i	$0.920978\pi$
$180$		0			0
$181$	24.2749			1.80434			0.902170	−	0.431380i	$-0.141973\pi$
$181$	24.2749			1.80434			0.902170	+	0.431380i	$0.141973\pi$
$182$		0			0
$183$			23.4690i			1.73488i
$184$		0			0
$185$	−21.7371	−	4.98684i	−1.59815	−	0.366640i
$186$		0			0
$187$	−1.91238	−	1.10411i	−0.139847	−	0.0807406i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.0876242	+	0.151770i	−0.00634026	+	0.0109817i	−0.869178	−	0.494499i	$-0.835352\pi$
$191$	−0.0876242	+	0.151770i	−0.00634026	+	0.0109817i	0.862838	+	0.505481i	$0.168685\pi$
$192$		0			0
$193$	−18.4622	+	10.6592i	−1.32894	+	0.767263i	−0.985136	−	0.171778i	$-0.945049\pi$
$193$	−18.4622	+	10.6592i	−1.32894	+	0.767263i	−0.343803	+	0.939042i	$0.611715\pi$
$194$		0			0
$195$	−7.45017	−	6.92820i	−0.533517	−	0.496139i
$196$		0			0
$197$			8.60271i			0.612918i	0.951884	+	0.306459i	$0.0991442\pi$
$197$			8.60271i			0.612918i	−0.951884	+	0.306459i	$0.900856\pi$
$198$		0			0
$199$	−8.63746	−	14.9605i	−0.612293	−	1.06052i	−0.990853	−	0.134946i	$-0.956914\pi$
$199$	−8.63746	−	14.9605i	−0.612293	−	1.06052i	0.378560	−	0.925577i	$-0.376419\pi$
$200$		0			0
$201$	3.04983	−	5.28247i	0.215119	−	0.372597i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−7.96221	+	2.44631i	−0.556105	+	0.170857i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−17.2749			−1.19493
$210$		0			0
$211$	25.6495			1.76578			0.882892	−	0.469576i	$-0.155593\pi$
$211$	25.6495			1.76578			0.882892	+	0.469576i	$0.155593\pi$
$212$		0			0
$213$	−6.82475	+	3.94027i	−0.467624	+	0.269983i
$214$		0			0
$215$	−1.41238	−	4.59698i	−0.0963232	−	0.313512i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.63746	−	9.76436i	0.380944	−	0.659815i
$220$		0			0
$221$	−0.549834	−	0.952341i	−0.0369859	−	0.0640614i
$222$		0			0
$223$		−	8.71780i		−	0.583787i	−0.956451	−	0.291893i	$-0.905715\pi$
$223$		−	8.71780i		−	0.583787i	0.956451	−	0.291893i	$-0.0942853\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.9124	−	9.76436i	1.12251	−	0.648084i	0.180472	−	0.983580i	$-0.442237\pi$
$227$	16.9124	−	9.76436i	1.12251	−	0.648084i	0.942041	+	0.335496i	$0.108904\pi$
$228$		0			0
$229$	−1.63746	+	2.83616i	−0.108206	+	0.187419i	−0.915044	−	0.403355i	$-0.867844\pi$
$229$	−1.63746	+	2.83616i	−0.108206	+	0.187419i	0.806837	+	0.590774i	$0.201177\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.3625	+	7.13752i	0.809897	+	0.467594i	0.846920	−	0.531720i	$-0.178454\pi$
$233$	12.3625	+	7.13752i	0.809897	+	0.467594i	−0.0370231	+	0.999314i	$0.511788\pi$
$234$		0			0
$235$	−14.1873	−	3.25479i	−0.925477	−	0.212319i
$236$		0			0
$237$		−	12.6005i		−	0.818492i
$238$		0			0
$239$	−0.549834			−0.0355658			−0.0177829	−	0.999842i	$-0.505661\pi$
$239$	−0.549834			−0.0355658			−0.0177829	+	0.999842i	$0.505661\pi$
$240$		0			0
$241$	4.91238	+	8.50848i	0.316434	+	0.548080i	0.979741	−	0.200267i	$-0.0641811\pi$
$241$	4.91238	+	8.50848i	0.316434	+	0.548080i	−0.663307	+	0.748347i	$0.730848\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.45017	−	4.30136i	−0.474043	−	0.273689i
$248$		0			0
$249$	−6.41238	−	11.1066i	−0.406368	−	0.703850i
$250$		0			0
$251$	20.5498			1.29709			0.648547	−	0.761175i	$-0.275377\pi$
$251$	20.5498			1.29709			0.648547	+	0.761175i	$0.275377\pi$
$252$		0			0
$253$		−	41.2657i		−	2.59435i
$254$		0			0
$255$	0.362541	−	1.58028i	0.0227032	−	0.0989611i
$256$		0			0
$257$	−10.0876	−	5.82409i	−0.629249	−	0.363297i	0.151212	−	0.988501i	$-0.451682\pi$
$257$	−10.0876	−	5.82409i	−0.629249	−	0.363297i	−0.780461	+	0.625204i	$0.785016\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.675248	+	0.389855i	−0.0416376	+	0.0240395i	−0.520674	−	0.853755i	$-0.674319\pi$
$263$	−0.675248	+	0.389855i	−0.0416376	+	0.0240395i	0.479037	+	0.877795i	$0.340986\pi$
$264$		0			0
$265$	−8.63746	+	9.28819i	−0.530595	+	0.570569i
$266$		0			0
$267$		−	12.1244i		−	0.741999i
$268$		0			0
$269$	7.22508	+	12.5142i	0.440521	+	0.763005i	0.997728	−	0.0673687i	$-0.0214604\pi$
$269$	7.22508	+	12.5142i	0.440521	+	0.763005i	−0.557207	+	0.830374i	$0.688127\pi$
$270$		0			0
$271$	4.91238	−	8.50848i	0.298406	−	0.516854i	−0.677366	−	0.735646i	$-0.736879\pi$
$271$	4.91238	−	8.50848i	0.298406	−	0.516854i	0.975771	+	0.218793i	$0.0702119\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	23.7371	+	11.4964i	1.43140	+	0.693260i
$276$		0			0
$277$	12.3625	−	7.13752i	0.742793	−	0.428852i	−0.0802909	−	0.996771i	$-0.525585\pi$
$277$	12.3625	−	7.13752i	0.742793	−	0.428852i	0.823084	+	0.567920i	$0.192252\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	9.46221	−	5.46301i	0.562470	−	0.324742i	−0.191666	−	0.981460i	$-0.561389\pi$
$283$	9.46221	−	5.46301i	0.562470	−	0.324742i	0.754136	+	0.656718i	$0.228056\pi$
$284$		0			0
$285$	−3.72508	−	12.1244i	−0.220655	−	0.718185i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.41238	+	14.5707i	−0.494846	+	0.857098i
$290$		0			0
$291$	6.00000	+	10.3923i	0.351726	+	0.609208i
$292$		0			0
$293$			6.92820i			0.404750i	0.979308	+	0.202375i	$0.0648660\pi$
$293$			6.92820i			0.404750i	−0.979308	+	0.202375i	$0.935134\pi$
$294$		0			0
$295$	−5.36254	−	4.98684i	−0.312219	−	0.290345i
$296$		0			0
$297$	−23.7371	+	13.7046i	−1.37737	+	0.795224i
$298$		0			0
$299$	10.2749	−	17.7967i	0.594214	−	1.02921i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−20.3248	−	11.7345i	−1.16763	−	0.674129i
$304$		0			0
$305$	6.77492	−	29.5312i	0.387931	−	1.69095i
$306$		0			0
$307$		−	26.5145i		−	1.51326i	−0.653843	−	0.756631i	$-0.726844\pi$
$307$		−	26.5145i		−	1.51326i	0.653843	−	0.756631i	$-0.273156\pi$
$308$		0			0
$309$	−19.5498			−1.11215
$310$		0			0
$311$	−4.91238	−	8.50848i	−0.278555	−	0.482472i	0.692471	−	0.721446i	$-0.256522\pi$
$311$	−4.91238	−	8.50848i	−0.278555	−	0.482472i	−0.971026	+	0.238974i	$0.923189\pi$
$312$		0			0
$313$	29.0120	+	16.7501i	1.63986	+	0.946772i	0.980881	+	0.194609i	$0.0623438\pi$
$313$	29.0120	+	16.7501i	1.63986	+	0.946772i	0.658977	+	0.752163i	$0.270990\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.1873	−	12.8098i	−1.24616	−	0.719472i	−0.275821	−	0.961209i	$-0.588950\pi$
$317$	−22.1873	−	12.8098i	−1.24616	−	0.719472i	−0.970342	+	0.241737i	$0.922283\pi$
$318$		0			0
$319$	−11.2749	−	19.5287i	−0.631274	−	1.09340i
$320$		0			0
$321$	−6.09967			−0.340450
$322$		0			0
$323$		−	1.37097i		−	0.0762827i
$324$		0			0
$325$	7.37459	+	10.8685i	0.409068	+	0.602875i
$326$		0			0
$327$	−17.3248	−	10.0025i	−0.958061	−	0.553137i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.91238	+	15.4367i	−0.489868	+	0.848477i	−0.999932	−	0.0116596i	$-0.996289\pi$
$331$	−8.91238	+	15.4367i	−0.489868	+	0.848477i	0.510064	+	0.860137i	$0.329622\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.36254	+	5.76655i	−0.292987	+	0.315060i
$336$		0			0
$337$		−	4.30136i		−	0.234310i	−0.993114	−	0.117155i	$-0.962623\pi$
$337$		−	4.30136i		−	0.234310i	0.993114	−	0.117155i	$-0.0373774\pi$
$338$		0			0
$339$	−3.72508	−	6.45203i	−0.202319	−	0.350426i
$340$		0			0
$341$	−8.63746	+	14.9605i	−0.467745	+	0.810157i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	28.9622	−	8.89834i	1.55927	−	0.479070i
$346$		0			0
$347$	10.5000	−	6.06218i	0.563670	−	0.325435i	−0.190947	−	0.981600i	$-0.561156\pi$
$347$	10.5000	−	6.06218i	0.563670	−	0.325435i	0.754617	+	0.656165i	$0.227823\pi$
$348$		0			0
$349$	−3.72508			−0.199399			−0.0996996	−	0.995018i	$-0.531788\pi$
$349$	−3.72508			−0.199399			−0.0996996	+	0.995018i	$0.531788\pi$
$350$		0			0
$351$	−13.6495			−0.728557
$352$		0			0
$353$	7.08762	−	4.09204i	0.377236	−	0.217797i	−0.299379	−	0.954134i	$-0.596779\pi$
$353$	7.08762	−	4.09204i	0.377236	−	0.217797i	0.676615	+	0.736337i	$0.263446\pi$
$354$		0			0
$355$	9.72508	−	2.98793i	0.516154	−	0.158583i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.1873	−	31.5013i	0.959889	−	1.66258i	0.237127	−	0.971479i	$-0.423794\pi$
$359$	18.1873	−	31.5013i	0.959889	−	1.66258i	0.722762	−	0.691097i	$-0.242872\pi$
$360$		0			0
$361$	4.13746	+	7.16629i	0.217761	+	0.377173i
$362$		0			0
$363$			29.1413i			1.52952i
$364$		0			0
$365$	−9.91238	+	10.6592i	−0.518837	+	0.557926i
$366$		0			0
$367$	5.22508	−	3.01670i	0.272747	−	0.157471i	−0.357388	−	0.933956i	$-0.616333\pi$
$367$	5.22508	−	3.01670i	0.272747	−	0.157471i	0.630135	+	0.776485i	$0.282999\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	8.63746	+	4.98684i	0.447231	+	0.258209i	0.706660	−	0.707553i	$-0.250201\pi$
$373$	8.63746	+	4.98684i	0.447231	+	0.258209i	−0.259429	+	0.965762i	$0.583534\pi$
$374$		0			0
$375$	−2.95017	+	19.1389i	−0.152346	+	0.988327i
$376$		0			0
$377$		−	11.2296i		−	0.578352i
$378$		0			0
$379$	21.6495			1.11206			0.556030	−	0.831162i	$-0.312324\pi$
$379$	21.6495			1.11206			0.556030	+	0.831162i	$0.312324\pi$
$380$		0			0
$381$	−13.5498	−	23.4690i	−0.694179	−	1.20235i
$382$		0			0
$383$	5.32475	+	3.07425i	0.272082	+	0.157087i	0.629833	−	0.776730i	$-0.283123\pi$
$383$	5.32475	+	3.07425i	0.272082	+	0.157087i	−0.357751	+	0.933817i	$0.616456\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.1873	+	28.0372i	0.820728	+	1.42154i	0.905141	+	0.425112i	$0.139765\pi$
$389$	16.1873	+	28.0372i	0.820728	+	1.42154i	−0.0844123	+	0.996431i	$0.526901\pi$
$390$		0			0
$391$	3.27492			0.165620
$392$		0			0
$393$			18.5764i			0.937055i
$394$		0			0
$395$	−3.63746	+	15.8553i	−0.183020	+	0.797767i
$396$		0			0
$397$	9.36254	+	5.40547i	0.469892	+	0.271293i	0.716195	−	0.697901i	$-0.245882\pi$
$397$	9.36254	+	5.40547i	0.469892	+	0.271293i	−0.246302	+	0.969193i	$0.579216\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	−7.45017	+	4.30136i	−0.371119	+	0.214266i
$404$		0			0
$405$	−14.7371	−	13.7046i	−0.732294	−	0.680989i
$406$		0			0
$407$			52.6103i			2.60780i
$408$		0			0
$409$	10.0498	+	17.4068i	0.496932	+	0.860712i	0.999994	−	0.00353862i	$-0.00112638\pi$
$409$	10.0498	+	17.4068i	0.496932	+	0.860712i	−0.503061	+	0.864251i	$0.667793\pi$
$410$		0			0
$411$	−18.4622	+	31.9775i	−0.910674	+	1.57733i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.86254	+	15.8265i	0.238693	+	0.776894i
$416$		0			0
$417$	19.6495	−	11.3446i	0.962240	−	0.555550i
$418$		0			0
$419$	−13.0997			−0.639961			−0.319980	−	0.947424i	$-0.603676\pi$
$419$	−13.0997			−0.639961			−0.319980	+	0.947424i	$0.603676\pi$
$420$		0			0
$421$	−4.27492			−0.208347			−0.104173	−	0.994559i	$-0.533220\pi$
$421$	−4.27492			−0.208347			−0.104173	+	0.994559i	$0.533220\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.912376	+	1.88382i	−0.0442567	+	0.0913787i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−12.0000	+	20.7846i	−0.579365	+	1.00349i
$430$		0			0
$431$	9.18729	+	15.9129i	0.442536	+	0.766495i	0.997877	−	0.0651276i	$-0.0207454\pi$
$431$	9.18729	+	15.9129i	0.442536	+	0.766495i	−0.555341	+	0.831623i	$0.687412\pi$
$432$		0			0
$433$		−	18.1578i		−	0.872606i	−0.899800	−	0.436303i	$-0.856288\pi$
$433$		−	18.1578i		−	0.872606i	0.899800	−	0.436303i	$-0.143712\pi$
$434$		0			0
$435$	11.2749	−	12.1244i	0.540591	−	0.581318i
$436$		0			0
$437$	22.1873	−	12.8098i	1.06136	−	0.612778i
$438$		0			0
$439$	−11.9124	+	20.6328i	−0.568547	+	0.984752i	0.428163	+	0.903701i	$0.359161\pi$
$439$	−11.9124	+	20.6328i	−0.568547	+	0.984752i	−0.996710	+	0.0810504i	$0.974173\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	0.229377	−	0.973338i	$-0.426331\pi$
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	−0.728247	+	0.685315i	$0.759665\pi$
$444$		0			0
$445$	−3.50000	+	15.2561i	−0.165916	+	0.723211i
$446$		0			0
$447$			13.0767i			0.618507i
$448$		0			0
$449$	3.17525			0.149849			0.0749246	−	0.997189i	$-0.476128\pi$
$449$	3.17525			0.149849			0.0749246	+	0.997189i	$0.476128\pi$
$450$		0			0
$451$	9.82475	+	17.0170i	0.462629	+	0.801298i
$452$		0			0
$453$	19.0876	+	11.0202i	0.896815	+	0.517776i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.18729	+	0.685484i	0.0555392	+	0.0320656i	0.527512	−	0.849547i	$-0.323125\pi$
$457$	1.18729	+	0.685484i	0.0555392	+	0.0320656i	−0.471973	+	0.881613i	$0.656458\pi$
$458$		0			0
$459$	−1.08762	−	1.88382i	−0.0507659	−	0.0879292i
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$		−	2.15068i		−	0.0999505i	−0.998750	−	0.0499752i	$-0.984086\pi$
$463$		−	2.15068i		−	0.0999505i	0.998750	−	0.0499752i	$-0.0159142\pi$
$464$		0			0
$465$	−12.3625	−	2.83616i	−0.573299	−	0.131524i
$466$		0			0
$467$	13.5997	+	7.85177i	0.629318	+	0.363337i	0.780488	−	0.625171i	$-0.214971\pi$
$467$	13.5997	+	7.85177i	0.629318	+	0.363337i	−0.151170	+	0.988508i	$0.548304\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.91238	−	3.31233i	0.0881176	−	0.152624i
$472$		0			0
$473$	−9.82475	+	5.67232i	−0.451743	+	0.260814i
$474$		0			0
$475$	1.18729	+	16.3315i	0.0544767	+	0.749340i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.91238	−	8.50848i	−0.224452	−	0.388763i	0.731703	−	0.681624i	$-0.238726\pi$
$479$	−4.91238	−	8.50848i	−0.224452	−	0.388763i	−0.956155	+	0.292861i	$0.905393\pi$
$480$		0			0
$481$	−13.0997	+	22.6893i	−0.597293	+	1.03454i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.54983	−	14.8087i	−0.206597	−	0.672431i
$486$		0			0
$487$	2.53779	−	1.46519i	0.114998	−	0.0663943i	−0.441398	−	0.897312i	$-0.645517\pi$
$487$	2.53779	−	1.46519i	0.114998	−	0.0663943i	0.556396	+	0.830917i	$0.312184\pi$
$488$		0			0
$489$	9.82475			0.444291
$490$		0			0
$491$	−28.5498			−1.28844			−0.644218	−	0.764842i	$-0.722817\pi$
$491$	−28.5498			−1.28844			−0.644218	+	0.764842i	$0.722817\pi$
$492$		0			0
$493$	1.54983	−	0.894797i	0.0698010	−	0.0402996i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.812707	−	1.40765i	0.0363818	−	0.0630151i	−0.847261	−	0.531177i	$-0.821750\pi$
$499$	0.812707	−	1.40765i	0.0363818	−	0.0630151i	0.883643	+	0.468161i	$0.155083\pi$
$500$		0			0
$501$	0.412376	+	0.714256i	0.0184236	+	0.0319106i
$502$		0			0
$503$			31.7682i			1.41647i	0.705975	+	0.708236i	$0.250509\pi$
$503$			31.7682i			1.41647i	−0.705975	+	0.708236i	$0.749491\pi$
$504$		0			0
$505$	22.1873	+	20.6328i	0.987322	+	0.918149i
$506$		0			0
$507$	9.14950	−	5.28247i	0.406344	−	0.234603i
$508$		0			0
$509$	7.22508	−	12.5142i	0.320246	−	0.554683i	−0.660293	−	0.751008i	$-0.729568\pi$
$509$	7.22508	−	12.5142i	0.320246	−	0.554683i	0.980539	+	0.196326i	$0.0629010\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−14.7371	−	8.50848i	−0.650660	−	0.375659i
$514$		0			0
$515$	24.5997	+	5.64355i	1.08399	+	0.248685i
$516$		0			0
$517$			34.3375i			1.51016i
$518$		0			0
$519$	−35.4743			−1.55715
$520$		0			0
$521$	4.91238	+	8.50848i	0.215215	+	0.372763i	0.953339	−	0.301902i	$-0.0976214\pi$
$521$	4.91238	+	8.50848i	0.215215	+	0.372763i	−0.738124	+	0.674665i	$0.764288\pi$
$522$		0			0
$523$	−6.36254	−	3.67341i	−0.278215	−	0.160627i	0.354400	−	0.935094i	$-0.384685\pi$
$523$	−6.36254	−	3.67341i	−0.278215	−	0.160627i	−0.632615	+	0.774467i	$0.718018\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.18729	−	0.685484i	−0.0517193	−	0.0298602i
$528$		0			0
$529$	19.0997	+	33.0816i	0.830420	+	1.43833i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			9.78523i			0.423845i
$534$		0			0
$535$	7.67525	+	1.76082i	0.331830	+	0.0761270i
$536$		0			0
$537$	−10.9124	−	6.30026i	−0.470904	−	0.271876i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.77492	−	15.1986i	0.377263	−	0.653439i	−0.613400	−	0.789773i	$-0.710199\pi$
$541$	8.77492	−	15.1986i	0.377263	−	0.653439i	0.990663	+	0.136334i	$0.0435319\pi$
$542$		0			0
$543$	36.4124	−	21.0227i	1.56260	−	0.902170i
$544$		0			0
$545$	18.9124	+	17.5874i	0.810117	+	0.753360i
$546$		0			0
$547$		−	20.5386i		−	0.878168i	−0.898446	−	0.439084i	$-0.855303\pi$
$547$		−	20.5386i		−	0.878168i	0.898446	−	0.439084i	$-0.144697\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−36.9244	+	11.3446i	−1.56735	+	0.481553i
$556$		0			0
$557$	8.63746	−	4.98684i	0.365981	−	0.211299i	−0.305720	−	0.952121i	$-0.598897\pi$
$557$	8.63746	−	4.98684i	0.365981	−	0.211299i	0.671701	+	0.740822i	$0.265564\pi$
$558$		0			0
$559$	−5.64950			−0.238949
$560$		0			0
$561$	−3.82475			−0.161481
$562$		0			0
$563$	−19.5997	+	11.3159i	−0.826028	+	0.476907i	−0.852491	−	0.522743i	$-0.824909\pi$
$563$	−19.5997	+	11.3159i	−0.826028	+	0.476907i	0.0264630	+	0.999650i	$0.491576\pi$
$564$		0			0
$565$	2.82475	+	9.19397i	0.118838	+	0.386793i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.18729	−	7.25260i	0.175540	−	0.304045i	−0.764808	−	0.644259i	$-0.777166\pi$
$569$	4.18729	−	7.25260i	0.175540	−	0.304045i	0.940348	+	0.340214i	$0.110499\pi$
$570$		0			0
$571$	−3.63746	−	6.30026i	−0.152223	−	0.263658i	0.779821	−	0.626002i	$-0.215310\pi$
$571$	−3.63746	−	6.30026i	−0.152223	−	0.263658i	−0.932044	+	0.362344i	$0.881976\pi$
$572$		0			0
$573$			0.303539i			0.0126805i
$574$		0			0
$575$	−39.0120	+	2.83616i	−1.62691	+	0.118276i
$576$		0			0
$577$	3.36254	−	1.94136i	0.139984	−	0.0808200i	−0.428372	−	0.903602i	$-0.640913\pi$
$577$	3.36254	−	1.94136i	0.139984	−	0.0808200i	0.568357	+	0.822782i	$0.307579\pi$
$578$		0			0
$579$	−18.4622	+	31.9775i	−0.767263	+	1.32894i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	25.9124	+	14.9605i	1.07318	+	0.619601i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	20.8997i		−	0.862623i	−0.902203	−	0.431311i	$-0.858051\pi$
$587$		−	20.8997i		−	0.862623i	0.902203	−	0.431311i	$-0.141949\pi$
$588$		0			0
$589$	−10.7251			−0.441919
$590$		0			0
$591$	7.45017	+	12.9041i	0.306459	+	0.530802i
$592$		0			0
$593$	−28.9124	−	16.6926i	−1.18729	−	0.685482i	−0.229600	−	0.973285i	$-0.573742\pi$
$593$	−28.9124	−	16.6926i	−1.18729	−	0.685482i	−0.957689	+	0.287804i	$0.907075\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−25.9124	−	14.9605i	−1.06052	−	0.612293i
$598$		0			0
$599$	2.63746	+	4.56821i	0.107764	+	0.186652i	0.914864	−	0.403762i	$-0.132298\pi$
$599$	2.63746	+	4.56821i	0.107764	+	0.186652i	−0.807100	+	0.590414i	$0.798964\pi$
$600$		0			0
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.41238	−	36.6687i	0.342012	−	1.49079i
$606$		0			0
$607$	9.87459	+	5.70109i	0.400797	+	0.231400i	0.686828	−	0.726820i	$-0.259003\pi$
$607$	9.87459	+	5.70109i	0.400797	+	0.231400i	−0.286031	+	0.958220i	$0.592336\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.54983	+	14.8087i	−0.345889	+	0.599098i
$612$		0			0
$613$	24.5619	−	14.1808i	0.992045	−	0.572757i	0.0861600	−	0.996281i	$-0.472540\pi$
$613$	24.5619	−	14.1808i	0.992045	−	0.572757i	0.905885	+	0.423524i	$0.139207\pi$
$614$		0			0
$615$	−9.82475	+	10.5649i	−0.396172	+	0.426019i
$616$		0			0
$617$		−	31.2920i		−	1.25977i	−0.776689	−	0.629884i	$-0.783102\pi$
$617$		−	31.2920i		−	1.25977i	0.776689	−	0.629884i	$-0.216898\pi$
$618$		0			0
$619$	4.46221	+	7.72877i	0.179351	+	0.310646i	0.941659	−	0.336570i	$-0.109267\pi$
$619$	4.46221	+	7.72877i	0.179351	+	0.310646i	−0.762307	+	0.647215i	$0.775933\pi$
$620$		0			0
$621$	20.3248	−	35.2035i	0.815604	−	1.41267i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.23713	−	23.2309i	0.369485	−	0.929237i
$626$		0			0
$627$	−25.9124	+	14.9605i	−1.03484	+	0.597466i
$628$		0			0
$629$	−4.17525			−0.166478
$630$		0			0
$631$	33.0997			1.31768			0.658839	−	0.752284i	$-0.271048\pi$
$631$	33.0997			1.31768			0.658839	+	0.752284i	$0.271048\pi$
$632$		0			0
$633$	38.4743	−	22.2131i	1.52921	−	0.882892i
$634$		0			0
$635$	10.2749	+	33.4427i	0.407748	+	1.32713i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.04983	+	1.81837i	0.0414660	+	0.0718212i	0.886014	−	0.463659i	$-0.153464\pi$
$641$	1.04983	+	1.81837i	0.0414660	+	0.0718212i	−0.844548	+	0.535481i	$0.820131\pi$
$642$		0			0
$643$		−	31.4071i		−	1.23857i	−0.785164	−	0.619287i	$-0.787422\pi$
$643$		−	31.4071i		−	1.23857i	0.785164	−	0.619287i	$-0.212578\pi$
$644$		0			0
$645$	−6.09967	−	5.67232i	−0.240174	−	0.223348i
$646$		0			0
$647$	−23.3248	+	13.4666i	−0.916991	+	0.529425i	−0.882674	−	0.469986i	$-0.844259\pi$
$647$	−23.3248	+	13.4666i	−0.916991	+	0.529425i	−0.0343169	+	0.999411i	$0.510926\pi$
$648$		0			0
$649$	−8.63746	+	14.9605i	−0.339050	+	0.587252i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	24.5619	+	14.1808i	0.961181	+	0.554938i	0.896536	−	0.442970i	$-0.146075\pi$
$653$	24.5619	+	14.1808i	0.961181	+	0.554938i	0.0646444	+	0.997908i	$0.479409\pi$
$654$		0			0
$655$	5.36254	−	23.3748i	0.209532	−	0.913328i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	40.5498			1.57960			0.789799	−	0.613366i	$-0.210185\pi$
$659$	40.5498			1.57960			0.789799	+	0.613366i	$0.210185\pi$
$660$		0			0
$661$	−0.225083	−	0.389855i	−0.00875471	−	0.0151636i	0.861615	−	0.507563i	$-0.169453\pi$
$661$	−0.225083	−	0.389855i	−0.00875471	−	0.0151636i	−0.870370	+	0.492399i	$0.836120\pi$
$662$		0			0
$663$	−1.64950	−	0.952341i	−0.0640614	−	0.0369859i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	28.9622	+	16.7213i	1.12142	+	0.647453i
$668$		0			0
$669$	−7.54983	−	13.0767i	−0.291893	−	0.505574i
$670$		0			0
$671$	−71.4743			−2.75923
$672$		0			0
$673$			31.2920i			1.20622i	0.797659	+	0.603109i	$0.206072\pi$
$673$			31.2920i			1.20622i	−0.797659	+	0.603109i	$0.793928\pi$
$674$		0			0
$675$	14.5876	+	21.4989i	0.561478	+	0.827492i
$676$		0			0
$677$	40.1873	+	23.2021i	1.54452	+	0.891731i	0.998545	+	0.0539317i	$0.0171753\pi$
$677$	40.1873	+	23.2021i	1.54452	+	0.891731i	0.545979	+	0.837799i	$0.316158\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	16.9124	−	29.2931i	0.648084	−	1.12251i
$682$		0			0
$683$	−16.5997	+	9.58382i	−0.635169	+	0.366715i	−0.782751	−	0.622335i	$-0.786184\pi$
$683$	−16.5997	+	9.58382i	−0.635169	+	0.366715i	0.147582	+	0.989050i	$0.452851\pi$
$684$		0			0
$685$	32.4622	−	34.9079i	1.24032	−	1.33376i
$686$		0			0
$687$			5.67232i			0.216413i
$688$		0			0
$689$	7.45017	+	12.9041i	0.283829	+	0.491606i
$690$		0			0
$691$	15.1873	−	26.3052i	0.577752	−	1.00070i	−0.417985	−	0.908454i	$-0.637263\pi$
$691$	15.1873	−	26.3052i	0.577752	−	1.00070i	0.995737	−	0.0922416i	$-0.0294032\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.0000	+	8.60271i	−1.06210	+	0.326319i
$696$		0			0
$697$	−1.35050	+	0.779710i	−0.0511537	+	0.0295336i
$698$		0			0
$699$	24.7251			0.935189
$700$		0			0
$701$	8.82475			0.333306			0.166653	−	0.986016i	$-0.446704\pi$
$701$	8.82475			0.333306			0.166653	+	0.986016i	$0.446704\pi$
$702$		0			0
$703$	−28.2870	+	16.3315i	−1.06686	+	0.615954i
$704$		0			0
$705$	−24.0997	+	7.40437i	−0.907646	+	0.278865i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.22508	+	9.05011i	−0.196232	+	0.339884i	−0.947304	−	0.320337i	$-0.896204\pi$
$709$	−5.22508	+	9.05011i	−0.196232	+	0.339884i	0.751072	+	0.660221i	$0.229537\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	25.6197i		−	0.959465i
$714$		0			0
$715$	21.0997	−	22.6893i	0.789083	−	0.848531i
$716$		0			0
$717$	−0.824752	+	0.476171i	−0.0308009	+	0.0177829i
$718$		0			0
$719$	15.1873	−	26.3052i	0.566390	−	0.981017i	−0.430528	−	0.902577i	$-0.641673\pi$
$719$	15.1873	−	26.3052i	0.566390	−	0.981017i	0.996919	−	0.0784400i	$-0.0249939\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	14.7371	+	8.50848i	0.548080	+	0.316434i
$724$		0			0
$725$	−17.6873	+	12.0014i	−0.656890	+	0.445719i
$726$		0			0
$727$		−	3.10302i		−	0.115085i	−0.998343	−	0.0575423i	$-0.981674\pi$
$727$		−	3.10302i		−	0.115085i	0.998343	−	0.0575423i	$-0.0183264\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−0.450166	−	0.779710i	−0.0166500	−	0.0288386i
$732$		0			0
$733$	−32.6375	−	18.8432i	−1.20549	−	0.695991i	−0.243721	−	0.969845i	$-0.578368\pi$
$733$	−32.6375	−	18.8432i	−1.20549	−	0.695991i	−0.961771	+	0.273854i	$0.911701\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.0876	+	9.28819i	0.592595	+	0.342135i
$738$		0			0
$739$	−10.4622	−	18.1211i	−0.384859	−	0.666595i	0.606891	−	0.794785i	$-0.292416\pi$
$739$	−10.4622	−	18.1211i	−0.384859	−	0.666595i	−0.991750	+	0.128190i	$0.959083\pi$
$740$		0			0
$741$	−14.9003			−0.547377
$742$		0			0
$743$			6.45203i			0.236702i	0.992972	+	0.118351i	$0.0377608\pi$
$743$			6.45203i			0.236702i	−0.992972	+	0.118351i	$0.962239\pi$
$744$		0			0
$745$	3.77492	−	16.4545i	0.138302	−	0.602846i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.36254	−	12.7523i	0.268663	−	0.465338i	−0.699854	−	0.714286i	$-0.746752\pi$
$751$	7.36254	−	12.7523i	0.268663	−	0.465338i	0.968517	+	0.248948i	$0.0800849\pi$
$752$		0			0
$753$	30.8248	−	17.7967i	1.12332	−	0.648547i
$754$		0			0
$755$	−20.8368	−	19.3770i	−0.758329	−	0.705200i
$756$		0			0
$757$			35.5934i			1.29366i	0.762633	+	0.646831i	$0.223906\pi$
$757$			35.5934i			1.29366i	−0.762633	+	0.646831i	$0.776094\pi$
$758$		0			0
$759$	−35.7371	−	61.8985i	−1.29718	−	2.24677i
$760$		0			0
$761$	11.4622	−	19.8531i	0.415505	−	0.719675i	−0.579977	−	0.814633i	$-0.696938\pi$
$761$	11.4622	−	19.8531i	0.415505	−	0.719675i	0.995481	+	0.0949578i	$0.0302716\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.45017	+	4.30136i	−0.269010	+	0.155313i
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−20.1752			−0.726594
$772$		0			0
$773$	−34.9124	+	20.1567i	−1.25571	+	0.724985i	−0.972238	−	0.233995i	$-0.924820\pi$
$773$	−34.9124	+	20.1567i	−1.25571	+	0.724985i	−0.283473	+	0.958980i	$0.591487\pi$
$774$		0			0
$775$	14.7371	+	7.13752i	0.529373	+	0.256387i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.09967	+	10.5649i	−0.218543	+	0.378528i
$780$		0			0
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$		0			0
$783$		−	22.2131i		−	0.793832i
$784$		0			0
$785$	−3.36254	+	3.61587i	−0.120014	+	0.129056i
$786$		0			0
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	−0.473027	−	0.881048i	$-0.656839\pi$
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	0.526496	+	0.850177i	$0.323505\pi$
$788$		0			0
$789$	−0.675248	+	1.16956i	−0.0240395	+	0.0416376i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−30.8248	−	17.7967i	−1.09462	−	0.631979i
$794$		0			0
$795$	−4.91238	+	21.4125i	−0.174224	+	0.759425i
$796$		0			0
$797$			46.8229i			1.65855i	0.558839	+	0.829276i	$0.311247\pi$
$797$			46.8229i			1.65855i	−0.558839	+	0.829276i	$0.688753\pi$
$798$		0			0
$799$	−2.72508			−0.0964065
$800$		0			0
$801$		0			0
$802$		0			0
$803$	29.7371	+	17.1687i	1.04940	+	0.605872i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	21.6752	+	12.5142i	0.763005	+	0.440521i
$808$		0			0
$809$	−8.59967	−	14.8951i	−0.302348	−	0.523683i	0.674319	−	0.738440i	$-0.264437\pi$
$809$	−8.59967	−	14.8951i	−0.302348	−	0.523683i	−0.976667	+	0.214757i	$0.931104\pi$
$810$		0			0
$811$	−7.45017			−0.261611			−0.130805	−	0.991408i	$-0.541756\pi$
$811$	−7.45017			−0.261611			−0.130805	+	0.991408i	$0.541756\pi$
$812$		0			0
$813$		−	17.0170i		−	0.596811i
$814$		0			0
$815$	−12.3625	−	2.83616i	−0.433041	−	0.0993464i
$816$		0			0
$817$	−6.09967	−	3.52165i	−0.213400	−	0.123207i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.1873	−	17.6449i	0.355539	−	0.615812i	−0.631671	−	0.775237i	$-0.717631\pi$
$821$	10.1873	−	17.6449i	0.355539	−	0.615812i	0.987210	+	0.159425i	$0.0509640\pi$
$822$		0			0
$823$	−39.9743	+	23.0791i	−1.39341	+	0.804488i	−0.993692	−	0.112147i	$-0.964227\pi$
$823$	−39.9743	+	23.0791i	−1.39341	+	0.804488i	−0.399723	+	0.916636i	$0.630894\pi$
$824$		0			0
$825$	45.5619	−	3.31233i	1.58626	−	0.115321i
$826$		0			0
$827$		−	15.0547i		−	0.523505i	−0.965135	−	0.261752i	$-0.915700\pi$
$827$		−	15.0547i		−	0.523505i	0.965135	−	0.261752i	$-0.0843004\pi$
$828$		0			0
$829$	25.4622	+	44.1018i	0.884339	+	1.53172i	0.846469	+	0.532438i	$0.178724\pi$
$829$	25.4622	+	44.1018i	0.884339	+	1.53172i	0.0378699	+	0.999283i	$0.487943\pi$
$830$		0			0
$831$	12.3625	−	21.4125i	0.428852	−	0.742793i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.312707	−	1.01779i	−0.0108217	−	0.0352222i
$836$		0			0
$837$	−14.7371	+	8.50848i	−0.509390	+	0.294096i
$838$		0			0
$839$	41.0997			1.41892			0.709459	−	0.704747i	$-0.248939\pi$
$839$	41.0997			1.41892			0.709459	+	0.704747i	$0.248939\pi$
$840$		0			0
$841$	−10.7251			−0.369830
$842$		0			0
$843$	9.00000	−	5.19615i	0.309976	−	0.178965i
$844$		0			0
$845$	−13.0378	+	4.00573i	−0.448514	+	0.137801i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	9.46221	−	16.3890i	0.324742	−	0.562470i
$850$		0			0
$851$	−39.0120	−	67.5708i	−1.33732	−	2.31630i
$852$		0			0
$853$			13.1342i			0.449708i	0.974392	+	0.224854i	$0.0721905\pi$
$853$			13.1342i			0.449708i	−0.974392	+	0.224854i	$0.927810\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−32.6375	+	18.8432i	−1.11487	+	0.643673i	−0.940087	−	0.340933i	$-0.889257\pi$
$857$	−32.6375	+	18.8432i	−1.11487	+	0.643673i	−0.174787	+	0.984606i	$0.555924\pi$
$858$		0			0
$859$	1.18729	−	2.05645i	0.0405099	−	0.0701652i	−0.845060	−	0.534672i	$-0.820435\pi$
$859$	1.18729	−	2.05645i	0.0405099	−	0.0701652i	0.885569	+	0.464507i	$0.153768\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.2251	−	8.21286i	−0.484227	−	0.279569i	0.237949	−	0.971278i	$-0.423525\pi$
$863$	−14.2251	−	8.21286i	−0.484227	−	0.279569i	−0.722177	+	0.691709i	$0.756858\pi$
$864$		0			0
$865$	44.6375	+	10.2405i	1.51772	+	0.348189i
$866$		0			0
$867$			29.1413i			0.989691i
$868$		0			0
$869$	38.3746			1.30177
$870$		0			0
$871$	4.62541	+	8.01145i	0.156726	+	0.271458i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.8127	+	11.4389i	0.669028	+	0.386263i	0.795708	−	0.605680i	$-0.207099\pi$
$877$	19.8127	+	11.4389i	0.669028	+	0.386263i	−0.126681	+	0.991944i	$0.540432\pi$
$878$		0			0
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	43.0241			1.44952			0.724759	−	0.689002i	$-0.241951\pi$
$881$	43.0241			1.44952			0.724759	+	0.689002i	$0.241951\pi$
$882$		0			0
$883$		−	55.5407i		−	1.86909i	−0.355840	−	0.934547i	$-0.615805\pi$
$883$		−	55.5407i		−	1.86909i	0.355840	−	0.934547i	$-0.384195\pi$
$884$		0			0
$885$	−12.3625	−	2.83616i	−0.415562	−	0.0953365i
$886$		0			0
$887$	−33.9743	−	19.6150i	−1.14074	−	0.658609i	−0.194129	−	0.980976i	$-0.562188\pi$
$887$	−33.9743	−	19.6150i	−1.14074	−	0.658609i	−0.946615	+	0.322367i	$0.895521\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−23.7371	+	41.1139i	−0.795224	+	1.37737i
$892$		0			0
$893$	−18.4622	+	10.6592i	−0.617814	+	0.356695i
$894$		0			0
$895$	11.9124	+	11.0778i	0.398187	+	0.370290i
$896$		0			0
$897$		−	35.5934i		−	1.18843i
$898$		0			0
$899$	−7.00000	−	12.1244i	−0.233463	−	0.404370i
$900$		0			0
$901$	−1.18729	+	2.05645i	−0.0395545	+	0.0685103i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−51.8866	+	15.9416i	−1.72477	+	0.529918i
$906$		0			0
$907$	−36.2492	+	20.9285i	−1.20363	+	0.694918i	−0.961361	−	0.275290i	$-0.911226\pi$
$907$	−36.2492	+	20.9285i	−1.20363	+	0.694918i	−0.242273	+	0.970208i	$0.577893\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.0997			−0.831589			−0.415795	−	0.909459i	$-0.636496\pi$
$911$	−25.0997			−0.831589			−0.415795	+	0.909459i	$0.636496\pi$
$912$		0			0
$913$	33.8248	−	19.5287i	1.11944	−	0.646307i
$914$		0			0
$915$	−15.4124	−	50.1640i	−0.509517	−	1.65837i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−23.4622	+	40.6377i	−0.773947	+	1.34052i	0.161438	+	0.986883i	$0.448387\pi$
$919$	−23.4622	+	40.6377i	−0.773947	+	1.34052i	−0.935384	+	0.353632i	$0.884946\pi$
$920$		0			0
$921$	−22.9622	−	39.7717i	−0.756631	−	1.31052i
$922$		0			0
$923$		−	11.9517i		−	0.393396i
$924$		0			0
$925$	49.7371	−	3.61587i	1.63535	−	0.118889i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.0498	−	41.6555i	0.789049	−	1.36667i	−0.137500	−	0.990502i	$-0.543907\pi$
$929$	24.0498	−	41.6555i	0.789049	−	1.36667i	0.926550	−	0.376172i	$-0.122760\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−14.7371	−	8.50848i	−0.482472	−	0.278555i
$934$		0			0
$935$	4.81271	+	1.10411i	0.157392	+	0.0361083i
$936$		0			0
$937$		−	24.3638i		−	0.795931i	−0.917400	−	0.397965i	$-0.869716\pi$
$937$		−	24.3638i		−	0.795931i	0.917400	−	0.397965i	$-0.130284\pi$
$938$		0			0
$939$	58.0241			1.89354
$940$		0			0
$941$	−1.63746	−	2.83616i	−0.0533796	−	0.0924562i	0.838101	−	0.545515i	$-0.183666\pi$
$941$	−1.63746	−	2.83616i	−0.0533796	−	0.0924562i	−0.891481	+	0.453059i	$0.850333\pi$
$942$		0			0
$943$	−25.2371	−	14.5707i	−0.821834	−	0.474486i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.14950	+	5.28247i	0.297319	+	0.171657i	0.641238	−	0.767342i	$-0.278421\pi$
$947$	9.14950	+	5.28247i	0.297319	+	0.171657i	−0.343919	+	0.938999i	$0.611755\pi$
$948$		0			0
$949$	8.54983	+	14.8087i	0.277539	+	0.480712i
$950$		0			0
$951$	−44.3746			−1.43894
$952$		0			0
$953$		−	22.6893i		−	0.734978i	−0.930028	−	0.367489i	$-0.880218\pi$
$953$		−	22.6893i		−	0.734978i	0.930028	−	0.367489i	$-0.119782\pi$
$954$		0			0
$955$	0.0876242	−	0.381945i	0.00283545	−	0.0123594i
$956$		0			0
$957$	−33.8248	−	19.5287i	−1.09340	−	0.631274i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	10.1375	−	17.5586i	0.327015	−	0.566406i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	32.4622	−	34.9079i	1.04500	−	1.12372i
$966$		0			0
$967$		−	2.15068i		−	0.0691611i	−0.999402	−	0.0345806i	$-0.988990\pi$
$967$		−	2.15068i		−	0.0691611i	0.999402	−	0.0345806i	$-0.0110095\pi$
$968$		0			0
$969$	−1.18729	−	2.05645i	−0.0381413	−	0.0660628i
$970$		0			0
$971$	−18.4622	+	31.9775i	−0.592481	+	1.02621i	0.401417	+	0.915896i	$0.368518\pi$
$971$	−18.4622	+	31.9775i	−0.592481	+	1.02621i	−0.993897	+	0.110311i	$0.964815\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	20.4743	+	9.91613i	0.655701	+	0.317570i
$976$		0			0
$977$	−25.9124	+	14.9605i	−0.829010	+	0.478629i	−0.853514	−	0.521070i	$-0.825533\pi$
$977$	−25.9124	+	14.9605i	−0.829010	+	0.478629i	0.0245034	+	0.999700i	$0.492200\pi$
$978$		0			0
$979$	36.9244			1.18011
$980$		0			0
$981$		0			0
$982$		0			0
$983$	39.7749	−	22.9641i	1.26862	−	0.732440i	0.293895	−	0.955838i	$-0.405048\pi$
$983$	39.7749	−	22.9641i	1.26862	−	0.732440i	0.974727	+	0.223398i	$0.0717149\pi$
$984$		0			0
$985$	−5.64950	−	18.3879i	−0.180008	−	0.585888i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.41238	−	14.5707i	0.267498	−	0.463320i
$990$		0			0
$991$	−16.7371	−	28.9896i	−0.531672	−	0.920884i	−0.999316	−	0.0369667i	$-0.988230\pi$
$991$	−16.7371	−	28.9896i	−0.531672	−	0.920884i	0.467644	−	0.883917i	$-0.345103\pi$
$992$		0			0
$993$			30.8734i			0.979737i
$994$		0			0
$995$	28.2870	+	26.3052i	0.896757	+	0.833930i
$996$		0			0
$997$	−0.362541	+	0.209313i	−0.0114818	+	0.00662902i	−0.505730	−	0.862692i	$-0.668777\pi$
$997$	−0.362541	+	0.209313i	−0.0114818	+	0.00662902i	0.494248	+	0.869321i	$0.335443\pi$
$998$		0			0
$999$	−25.9124	+	44.8816i	−0.819831	+	1.41999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.q.g.569.1		4
5.4	even	2		980.2.q.b.569.2		4
7.2	even	3		980.2.e.c.589.4		4
7.3	odd	6		140.2.q.b.109.2	yes	4
7.4	even	3		980.2.q.b.949.1		4
7.5	odd	6		980.2.e.f.589.1		4
7.6	odd	2		140.2.q.a.9.2	✓	4
21.17	even	6		1260.2.bm.b.109.1		4
21.20	even	2		1260.2.bm.a.289.1		4
28.3	even	6		560.2.bw.a.529.2		4
28.27	even	2		560.2.bw.e.289.2		4
35.2	odd	12		4900.2.a.bf.1.3		4
35.3	even	12		700.2.i.f.501.2		8
35.4	even	6	inner	980.2.q.g.949.1		4
35.9	even	6		980.2.e.c.589.2		4
35.12	even	12		4900.2.a.be.1.1		4
35.13	even	4		700.2.i.f.401.2		8
35.17	even	12		700.2.i.f.501.3		8
35.19	odd	6		980.2.e.f.589.3		4
35.23	odd	12		4900.2.a.bf.1.1		4
35.24	odd	6		140.2.q.a.109.2	yes	4
35.27	even	4		700.2.i.f.401.3		8
35.33	even	12		4900.2.a.be.1.3		4
35.34	odd	2		140.2.q.b.9.1	yes	4
105.59	even	6		1260.2.bm.a.109.1		4
105.104	even	2		1260.2.bm.b.289.2		4
140.59	even	6		560.2.bw.e.529.2		4
140.139	even	2		560.2.bw.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.2	✓	4	7.6	odd	2
140.2.q.a.109.2	yes	4	35.24	odd	6
140.2.q.b.9.1	yes	4	35.34	odd	2
140.2.q.b.109.2	yes	4	7.3	odd	6
560.2.bw.a.289.1		4	140.139	even	2
560.2.bw.a.529.2		4	28.3	even	6
560.2.bw.e.289.2		4	28.27	even	2
560.2.bw.e.529.2		4	140.59	even	6
700.2.i.f.401.2		8	35.13	even	4
700.2.i.f.401.3		8	35.27	even	4
700.2.i.f.501.2		8	35.3	even	12
700.2.i.f.501.3		8	35.17	even	12
980.2.e.c.589.2		4	35.9	even	6
980.2.e.c.589.4		4	7.2	even	3
980.2.e.f.589.1		4	7.5	odd	6
980.2.e.f.589.3		4	35.19	odd	6
980.2.q.b.569.2		4	5.4	even	2
980.2.q.b.949.1		4	7.4	even	3
980.2.q.g.569.1		4	1.1	even	1	trivial
980.2.q.g.949.1		4	35.4	even	6	inner
1260.2.bm.a.109.1		4	105.59	even	6
1260.2.bm.a.289.1		4	21.20	even	2
1260.2.bm.b.109.1		4	21.17	even	6
1260.2.bm.b.289.2		4	105.104	even	2
4900.2.a.be.1.1		4	35.12	even	12
4900.2.a.be.1.3		4	35.33	even	12
4900.2.a.bf.1.1		4	35.23	odd	12
4900.2.a.bf.1.3		4	35.2	odd	12

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-2.13746 + 0.656712i) q^{5} +(2.63746 + 4.56821i) q^{11} +2.62685i q^{13} +(-2.63746 + 2.83616i) q^{15} +(-0.362541 + 0.209313i) q^{17} +(-1.63746 + 2.83616i) q^{19} +(-6.77492 - 3.91150i) q^{23} +(4.13746 - 2.80739i) q^{25} +5.19615i q^{27} -4.27492 q^{29} +(1.63746 + 2.83616i) q^{31} +(7.91238 + 4.56821i) q^{33} +(8.63746 + 4.98684i) q^{37} +(2.27492 + 3.94027i) q^{39} +3.72508 q^{41} +2.15068i q^{43} +(5.63746 + 3.25479i) q^{47} +(-0.362541 + 0.627940i) q^{51} +(4.91238 - 2.83616i) q^{53} +(-8.63746 - 8.03231i) q^{55} +5.67232i q^{57} +(1.63746 + 2.83616i) q^{59} +(-6.77492 + 11.7345i) q^{61} +(-1.72508 - 5.61478i) q^{65} +(3.04983 - 1.76082i) q^{67} -13.5498 q^{69} -4.54983 q^{71} +(5.63746 - 3.25479i) q^{73} +(3.77492 - 7.79423i) q^{75} +(3.63746 - 6.30026i) q^{79} +(4.50000 + 7.79423i) q^{81} -7.40437i q^{83} +(0.637459 - 0.685484i) q^{85} +(-6.41238 + 3.70219i) q^{87} +(3.50000 - 6.06218i) q^{89} +(4.91238 + 2.83616i) q^{93} +(1.63746 - 7.13752i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - q^{5} + 3 q^{11} - 3 q^{15} - 9 q^{17} + q^{19} - 12 q^{23} + 9 q^{25} - 2 q^{29} - q^{31} + 9 q^{33} + 27 q^{37} - 6 q^{39} + 30 q^{41} + 15 q^{47} - 9 q^{51} - 3 q^{53} - 27 q^{55}+ \cdots - q^{95}+O(q^{100}) \) 4 * q + 6 * q^3 - q^5 + 3 * q^11 - 3 * q^15 - 9 * q^17 + q^19 - 12 * q^23 + 9 * q^25 - 2 * q^29 - q^31 + 9 * q^33 + 27 * q^37 - 6 * q^39 + 30 * q^41 + 15 * q^47 - 9 * q^51 - 3 * q^53 - 27 * q^55 - q^59 - 12 * q^61 - 22 * q^65 - 18 * q^67 - 24 * q^69 + 12 * q^71 + 15 * q^73 + 7 * q^79 + 18 * q^81 - 5 * q^85 - 3 * q^87 + 14 * q^89 - 3 * q^93 - q^95

Introduction

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