LMFDB - Embedded newform 980.2.m.a.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(97,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("980.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 802x^12 - 2264x^11 + 5402x^10 - 10642x^9 + 17766x^8 - 24680x^7 + 28682x^6 - 27248x^5 + 20861x^4 - 12338x^3 + 5322x^2 - 1484*x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.6
Root			$0.500000 + 1.61777i$ of defining polynomial
Character	$\chi$	$=$	980.293
Dual form			980.2.m.a.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11777 - 1.11777i) q^{3} +(0.524151 + 2.17377i) q^{5} +0.501168i q^{9} +O(q^{10})$	\(q+(1.11777 - 1.11777i) q^{3} +(0.524151 + 2.17377i) q^{5} +0.501168i q^{9} +0.685455 q^{11} +(-1.04830 + 1.04830i) q^{13} +(3.01566 + 1.84390i) q^{15} +(0.965868 + 0.965868i) q^{17} +3.11898 q^{19} +(3.25058 + 3.25058i) q^{23} +(-4.45053 + 2.27877i) q^{25} +(3.91351 + 3.91351i) q^{27} -7.90106i q^{29} +8.81863i q^{31} +(0.766183 - 0.766183i) q^{33} +(6.35839 - 6.35839i) q^{37} +2.34353i q^{39} +10.2469i q^{41} +(3.73689 + 3.73689i) q^{43} +(-1.08942 + 0.262688i) q^{45} +(-4.93346 - 4.93346i) q^{47} +2.15924 q^{51} +(-6.54501 - 6.54501i) q^{53} +(0.359282 + 1.49002i) q^{55} +(3.48631 - 3.48631i) q^{57} -4.20860 q^{59} +4.13247i q^{61} +(-2.82824 - 1.72930i) q^{65} +(-2.93604 + 2.93604i) q^{67} +7.26683 q^{69} +12.5889 q^{71} +(9.08131 - 9.08131i) q^{73} +(-2.42754 + 7.52182i) q^{75} -14.0313i q^{79} +7.24532 q^{81} +(-3.99595 + 3.99595i) q^{83} +(-1.59331 + 2.60583i) q^{85} +(-8.83159 - 8.83159i) q^{87} -11.5990 q^{89} +(9.85722 + 9.85722i) q^{93} +(1.63482 + 6.77993i) q^{95} +(2.60010 + 2.60010i) q^{97} +0.343528i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 20 q^{15} + 32 q^{23} - 12 q^{25} + 28 q^{37} + 28 q^{43} - 40 q^{51} + 20 q^{53} + 44 q^{57} - 68 q^{65} - 16 q^{67} - 8 q^{71} - 48 q^{81} + 124 q^{93} - 4 q^{95}+O(q^{100}) $ 16 * q - 20 * q^15 + 32 * q^23 - 12 * q^25 + 28 * q^37 + 28 * q^43 - 40 * q^51 + 20 * q^53 + 44 * q^57 - 68 * q^65 - 16 * q^67 - 8 * q^71 - 48 * q^81 + 124 * q^93 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.11777	−	1.11777i	0.645346	−	0.645346i	−0.306518	−	0.951865i	$-0.599164\pi$
$3$	1.11777	−	1.11777i	0.645346	−	0.645346i	0.951865	+	0.306518i	$0.0991641\pi$
$4$		0			0
$5$	0.524151	+	2.17377i	0.234408	+	0.972138i
$5$	0.524151	+	2.17377i	0.234408	+	0.972138i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$			0.501168i			0.167056i
$10$		0			0
$11$	0.685455			0.206672			0.103336	−	0.994646i	$-0.467048\pi$
$11$	0.685455			0.206672			0.103336	+	0.994646i	$0.467048\pi$
$12$		0			0
$13$	−1.04830	+	1.04830i	−0.290747	+	0.290747i	−0.837375	−	0.546628i	$-0.815911\pi$
$13$	−1.04830	+	1.04830i	−0.290747	+	0.290747i	0.546628	+	0.837375i	$0.315911\pi$
$14$		0			0
$15$	3.01566	+	1.84390i	0.778640	+	0.476092i
$16$		0			0
$17$	0.965868	+	0.965868i	0.234257	+	0.234257i	0.814467	−	0.580210i	$-0.197029\pi$
$17$	0.965868	+	0.965868i	0.234257	+	0.234257i	−0.580210	+	0.814467i	$0.697029\pi$
$18$		0			0
$19$	3.11898			0.715543			0.357771	−	0.933809i	$-0.383537\pi$
$19$	3.11898			0.715543			0.357771	+	0.933809i	$0.383537\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.25058	+	3.25058i	0.677794	+	0.677794i	0.959501	−	0.281707i	$-0.0909006\pi$
$23$	3.25058	+	3.25058i	0.677794	+	0.677794i	−0.281707	+	0.959501i	$0.590901\pi$
$24$		0			0
$25$	−4.45053	+	2.27877i	−0.890106	+	0.455753i
$26$		0			0
$27$	3.91351	+	3.91351i	0.753155	+	0.753155i
$28$		0			0
$29$		−	7.90106i		−	1.46719i	−0.679587	−	0.733595i	$-0.737841\pi$
$29$		−	7.90106i		−	1.46719i	0.679587	−	0.733595i	$-0.262159\pi$
$30$		0			0
$31$			8.81863i			1.58387i	0.610604	+	0.791936i	$0.290927\pi$
$31$			8.81863i			1.58387i	−0.610604	+	0.791936i	$0.709073\pi$
$32$		0			0
$33$	0.766183	−	0.766183i	0.133375	−	0.133375i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.35839	−	6.35839i	1.04531	−	1.04531i	0.0463890	−	0.998923i	$-0.485229\pi$
$37$	6.35839	−	6.35839i	1.04531	−	1.04531i	0.998923	−	0.0463890i	$-0.0147714\pi$
$38$		0			0
$39$			2.34353i			0.375265i
$40$		0			0
$41$			10.2469i			1.60029i	0.599805	+	0.800146i	$0.295245\pi$
$41$			10.2469i			1.60029i	−0.599805	+	0.800146i	$0.704755\pi$
$42$		0			0
$43$	3.73689	+	3.73689i	0.569871	+	0.569871i	0.932092	−	0.362221i	$-0.117982\pi$
$43$	3.73689	+	3.73689i	0.569871	+	0.569871i	−0.362221	+	0.932092i	$0.617982\pi$
$44$		0			0
$45$	−1.08942	+	0.262688i	−0.162402	+	0.0391592i
$46$		0			0
$47$	−4.93346	−	4.93346i	−0.719620	−	0.719620i	0.248908	−	0.968527i	$-0.419928\pi$
$47$	−4.93346	−	4.93346i	−0.719620	−	0.719620i	−0.968527	+	0.248908i	$0.919928\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.15924			0.302354
$52$		0			0
$53$	−6.54501	−	6.54501i	−0.899026	−	0.899026i	0.0963237	−	0.995350i	$-0.469292\pi$
$53$	−6.54501	−	6.54501i	−0.899026	−	0.899026i	−0.995350	+	0.0963237i	$0.969292\pi$
$54$		0			0
$55$	0.359282	+	1.49002i	0.0484456	+	0.200914i
$56$		0			0
$57$	3.48631	−	3.48631i	0.461773	−	0.461773i
$58$		0			0
$59$	−4.20860			−0.547912			−0.273956	−	0.961742i	$-0.588332\pi$
$59$	−4.20860			−0.547912			−0.273956	+	0.961742i	$0.588332\pi$
$60$		0			0
$61$			4.13247i			0.529108i	0.964371	+	0.264554i	$0.0852247\pi$
$61$			4.13247i			0.529108i	−0.964371	+	0.264554i	$0.914775\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.82824	−	1.72930i	−0.350799	−	0.214493i
$66$		0			0
$67$	−2.93604	+	2.93604i	−0.358694	+	0.358694i	−0.863331	−	0.504637i	$-0.831626\pi$
$67$	−2.93604	+	2.93604i	−0.358694	+	0.358694i	0.504637	+	0.863331i	$0.331626\pi$
$68$		0			0
$69$	7.26683			0.874823
$70$		0			0
$71$	12.5889			1.49402			0.747011	−	0.664812i	$-0.231488\pi$
$71$	12.5889			1.49402			0.747011	+	0.664812i	$0.231488\pi$
$72$		0			0
$73$	9.08131	−	9.08131i	1.06289	−	1.06289i	0.0650023	−	0.997885i	$-0.479295\pi$
$73$	9.08131	−	9.08131i	1.06289	−	1.06289i	0.997885	−	0.0650023i	$-0.0207055\pi$
$74$		0			0
$75$	−2.42754	+	7.52182i	−0.280308	+	0.868545i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		−	14.0313i		−	1.57865i	−0.613978	−	0.789323i	$-0.710432\pi$
$79$		−	14.0313i		−	1.57865i	0.613978	−	0.789323i	$-0.289568\pi$
$80$		0			0
$81$	7.24532			0.805036
$82$		0			0
$83$	−3.99595	+	3.99595i	−0.438612	+	0.438612i	−0.891545	−	0.452933i	$-0.850378\pi$
$83$	−3.99595	+	3.99595i	−0.438612	+	0.438612i	0.452933	+	0.891545i	$0.350378\pi$
$84$		0			0
$85$	−1.59331	+	2.60583i	−0.172819	+	0.282642i
$86$		0			0
$87$	−8.83159	−	8.83159i	−0.946846	−	0.946846i
$88$		0			0
$89$	−11.5990			−1.22949			−0.614745	−	0.788726i	$-0.710741\pi$
$89$	−11.5990			−1.22949			−0.614745	+	0.788726i	$0.710741\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	9.85722	+	9.85722i	1.02215	+	1.02215i
$94$		0			0
$95$	1.63482	+	6.77993i	0.167729	+	0.695607i
$96$		0			0
$97$	2.60010	+	2.60010i	0.264000	+	0.264000i	0.826677	−	0.562677i	$-0.190228\pi$
$97$	2.60010	+	2.60010i	0.264000	+	0.264000i	−0.562677	+	0.826677i	$0.690228\pi$
$98$		0			0
$99$			0.343528i			0.0345259i
$100$		0			0
$101$			3.06878i			0.305355i	0.988276	+	0.152677i	$0.0487896\pi$
$101$			3.06878i			0.305355i	−0.988276	+	0.152677i	$0.951210\pi$
$102$		0			0
$103$	11.7098	−	11.7098i	1.15380	−	1.15380i	0.168012	−	0.985785i	$-0.446265\pi$
$103$	11.7098	−	11.7098i	1.15380	−	1.15380i	0.985785	−	0.168012i	$-0.0537348\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.74942	−	3.74942i	0.362470	−	0.362470i	−0.502252	−	0.864721i	$-0.667495\pi$
$107$	3.74942	−	3.74942i	0.362470	−	0.362470i	0.864721	+	0.502252i	$0.167495\pi$
$108$		0			0
$109$		−	16.5615i		−	1.58630i	−0.609025	−	0.793151i	$-0.708439\pi$
$109$		−	16.5615i		−	1.58630i	0.609025	−	0.793151i	$-0.291561\pi$
$110$		0			0
$111$		−	14.2145i		−	1.34918i
$112$		0			0
$113$	−7.21561	−	7.21561i	−0.678787	−	0.678787i	0.280939	−	0.959726i	$-0.409354\pi$
$113$	−7.21561	−	7.21561i	−0.678787	−	0.678787i	−0.959726	+	0.280939i	$0.909354\pi$
$114$		0			0
$115$	−5.36222	+	8.76981i	−0.500029	+	0.817789i
$116$		0			0
$117$	−0.525376	−	0.525376i	−0.0485711	−	0.0485711i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.5302			−0.957287
$122$		0			0
$123$	11.4537	+	11.4537i	1.03274	+	1.03274i
$124$		0			0
$125$	−7.28626	−	8.48000i	−0.651703	−	0.758474i
$126$		0			0
$127$	−2.13026	+	2.13026i	−0.189030	+	0.189030i	−0.795277	−	0.606247i	$-0.792674\pi$
$127$	−2.13026	+	2.13026i	−0.189030	+	0.189030i	0.606247	+	0.795277i	$0.292674\pi$
$128$		0			0
$129$	8.35400			0.735528
$130$		0			0
$131$			10.9460i			0.956356i	0.878263	+	0.478178i	$0.158703\pi$
$131$			10.9460i			0.956356i	−0.878263	+	0.478178i	$0.841297\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−6.45579	+	10.5583i	−0.555626	+	0.908717i
$136$		0			0
$137$	0.956158	−	0.956158i	0.0816901	−	0.0816901i	−0.665081	−	0.746771i	$-0.731603\pi$
$137$	0.956158	−	0.956158i	0.0816901	−	0.0816901i	0.746771	+	0.665081i	$0.231603\pi$
$138$		0			0
$139$	−0.703180			−0.0596429			−0.0298215	−	0.999555i	$-0.509494\pi$
$139$	−0.703180			−0.0596429			−0.0298215	+	0.999555i	$0.509494\pi$
$140$		0			0
$141$	−11.0290			−0.928808
$142$		0			0
$143$	−0.718564	+	0.718564i	−0.0600894	+	0.0600894i
$144$		0			0
$145$	17.1751	−	4.14135i	1.42631	−	0.343921i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			11.3033i			0.926002i	0.886358	+	0.463001i	$0.153227\pi$
$149$			11.3033i			0.926002i	−0.886358	+	0.463001i	$0.846773\pi$
$150$		0			0
$151$	−7.90340			−0.643169			−0.321585	−	0.946881i	$-0.604215\pi$
$151$	−7.90340			−0.643169			−0.321585	+	0.946881i	$0.604215\pi$
$152$		0			0
$153$	−0.484063	+	0.484063i	−0.0391341	+	0.0391341i
$154$		0			0
$155$	−19.1696	+	4.62229i	−1.53974	+	0.371272i
$156$		0			0
$157$	−1.64962	−	1.64962i	−0.131654	−	0.131654i	0.638209	−	0.769863i	$-0.279675\pi$
$157$	−1.64962	−	1.64962i	−0.131654	−	0.131654i	−0.769863	+	0.638209i	$0.779675\pi$
$158$		0			0
$159$	−14.6317			−1.16037
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.799253	+	0.799253i	0.0626023	+	0.0626023i	0.737715	−	0.675112i	$-0.235905\pi$
$163$	0.799253	+	0.799253i	0.0626023	+	0.0626023i	−0.675112	+	0.737715i	$0.735905\pi$
$164$		0			0
$165$	2.06710	+	1.26391i	0.160923	+	0.0983951i
$166$		0			0
$167$	−5.76281	−	5.76281i	−0.445940	−	0.445940i	0.448062	−	0.894002i	$-0.352114\pi$
$167$	−5.76281	−	5.76281i	−0.445940	−	0.445940i	−0.894002	+	0.448062i	$0.852114\pi$
$168$		0			0
$169$			10.8021i			0.830933i
$170$		0			0
$171$			1.56313i			0.119536i
$172$		0			0
$173$	12.3652	−	12.3652i	0.940106	−	0.940106i	−0.0581991	−	0.998305i	$-0.518536\pi$
$173$	12.3652	−	12.3652i	0.940106	−	0.940106i	0.998305	+	0.0581991i	$0.0185358\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.70425	+	4.70425i	−0.353593	+	0.353593i
$178$		0			0
$179$			1.07389i			0.0802666i	0.999194	+	0.0401333i	$0.0127783\pi$
$179$			1.07389i			0.0802666i	−0.999194	+	0.0401333i	$0.987222\pi$
$180$		0			0
$181$		−	8.93607i		−	0.664213i	−0.943242	−	0.332106i	$-0.892241\pi$
$181$		−	8.93607i		−	0.664213i	0.943242	−	0.332106i	$-0.107759\pi$
$182$		0			0
$183$	4.61916	+	4.61916i	0.341458	+	0.341458i
$184$		0			0
$185$	17.1544	+	10.4889i	1.26122	+	0.771159i
$186$		0			0
$187$	0.662059	+	0.662059i	0.0484145	+	0.0484145i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−24.3795			−1.76404			−0.882020	−	0.471212i	$-0.843817\pi$
$191$	−24.3795			−1.76404			−0.882020	+	0.471212i	$0.843817\pi$
$192$		0			0
$193$	−6.38737	−	6.38737i	−0.459773	−	0.459773i	0.438808	−	0.898581i	$-0.355401\pi$
$193$	−6.38737	−	6.38737i	−0.459773	−	0.459773i	−0.898581	+	0.438808i	$0.855401\pi$
$194$		0			0
$195$	−5.09429	+	1.22836i	−0.364809	+	0.0879649i
$196$		0			0
$197$	1.78673	−	1.78673i	0.127299	−	0.127299i	−0.640587	−	0.767886i	$-0.721309\pi$
$197$	1.78673	−	1.78673i	0.127299	−	0.127299i	0.767886	+	0.640587i	$0.221309\pi$
$198$		0			0
$199$	−9.34400			−0.662379			−0.331189	−	0.943564i	$-0.607450\pi$
$199$	−9.34400			−0.662379			−0.331189	+	0.943564i	$0.607450\pi$
$200$		0			0
$201$			6.56365i			0.462964i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−22.2743	+	5.37091i	−1.55571	+	0.375121i
$206$		0			0
$207$	−1.62909	+	1.62909i	−0.113230	+	0.113230i
$208$		0			0
$209$	2.13792			0.147883
$210$		0			0
$211$	−9.84703			−0.677898			−0.338949	−	0.940805i	$-0.610071\pi$
$211$	−9.84703			−0.677898			−0.338949	+	0.940805i	$0.610071\pi$
$212$		0			0
$213$	14.0715	−	14.0715i	0.964162	−	0.964162i
$214$		0			0
$215$	−6.16444	+	10.0818i	−0.420411	+	0.687575i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		−	20.3017i		−	1.37186i
$220$		0			0
$221$	−2.02504			−0.136219
$222$		0			0
$223$	−0.338625	+	0.338625i	−0.0226760	+	0.0226760i	−0.718354	−	0.695678i	$-0.755104\pi$
$223$	−0.338625	+	0.338625i	−0.0226760	+	0.0226760i	0.695678	+	0.718354i	$0.255104\pi$
$224$		0			0
$225$	−1.14205	−	2.23047i	−0.0761364	−	0.148698i
$226$		0			0
$227$	−9.80638	−	9.80638i	−0.650872	−	0.650872i	0.302331	−	0.953203i	$-0.402235\pi$
$227$	−9.80638	−	9.80638i	−0.650872	−	0.650872i	−0.953203	+	0.302331i	$0.902235\pi$
$228$		0			0
$229$	−2.66291			−0.175970			−0.0879850	−	0.996122i	$-0.528043\pi$
$229$	−2.66291			−0.175970			−0.0879850	+	0.996122i	$0.528043\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.3874	+	13.3874i	0.877036	+	0.877036i	0.993227	−	0.116191i	$-0.0370685\pi$
$233$	13.3874	+	13.3874i	0.877036	+	0.877036i	−0.116191	+	0.993227i	$0.537068\pi$
$234$		0			0
$235$	8.13832	−	13.3101i	0.530886	−	0.868254i
$236$		0			0
$237$	−15.6838	−	15.6838i	−1.01877	−	1.01877i
$238$		0			0
$239$			5.74416i			0.371559i	0.982591	+	0.185779i	$0.0594809\pi$
$239$			5.74416i			0.371559i	−0.982591	+	0.185779i	$0.940519\pi$
$240$		0			0
$241$		−	10.1861i		−	0.656146i	−0.944652	−	0.328073i	$-0.893601\pi$
$241$		−	10.1861i		−	0.656146i	0.944652	−	0.328073i	$-0.106399\pi$
$242$		0			0
$243$	−3.64191	+	3.64191i	−0.233628	+	0.233628i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.26963	+	3.26963i	−0.208042	+	0.208042i
$248$		0			0
$249$			8.93312i			0.566113i
$250$		0			0
$251$		−	7.28871i		−	0.460059i	−0.973184	−	0.230030i	$-0.926118\pi$
$251$		−	7.28871i		−	0.460059i	0.973184	−	0.230030i	$-0.0738823\pi$
$252$		0			0
$253$	2.22813	+	2.22813i	0.140081	+	0.140081i
$254$		0			0
$255$	1.13177	+	4.69369i	0.0708742	+	0.293930i
$256$		0			0
$257$	−8.63856	−	8.63856i	−0.538859	−	0.538859i	0.384335	−	0.923194i	$-0.374431\pi$
$257$	−8.63856	−	8.63856i	−0.538859	−	0.538859i	−0.923194	+	0.384335i	$0.874431\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.95976			0.245103
$262$		0			0
$263$	15.2080	+	15.2080i	0.937766	+	0.937766i	0.998174	−	0.0604077i	$-0.0192401\pi$
$263$	15.2080	+	15.2080i	0.937766	+	0.937766i	−0.0604077	+	0.998174i	$0.519240\pi$
$264$		0			0
$265$	10.7968	−	17.6579i	0.663239	−	1.08472i
$266$		0			0
$267$	−12.9650	+	12.9650i	−0.793446	+	0.793446i
$268$		0			0
$269$	−26.4753			−1.61423			−0.807114	−	0.590396i	$-0.798972\pi$
$269$	−26.4753			−1.61423			−0.807114	+	0.590396i	$0.798972\pi$
$270$		0			0
$271$		−	17.8483i		−	1.08421i	−0.840312	−	0.542103i	$-0.817628\pi$
$271$		−	17.8483i		−	1.08421i	0.840312	−	0.542103i	$-0.182372\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.05064	+	1.56199i	−0.183960	+	0.0941916i
$276$		0			0
$277$	18.7630	−	18.7630i	1.12736	−	1.12736i	0.136751	−	0.990605i	$-0.456334\pi$
$277$	18.7630	−	18.7630i	1.12736	−	1.12736i	0.990605	−	0.136751i	$-0.0436661\pi$
$278$		0			0
$279$	−4.41962			−0.264596
$280$		0			0
$281$	−18.7465			−1.11832			−0.559161	−	0.829059i	$-0.688877\pi$
$281$	−18.7465			−1.11832			−0.559161	+	0.829059i	$0.688877\pi$
$282$		0			0
$283$	0.462374	−	0.462374i	0.0274853	−	0.0274853i	−0.693231	−	0.720716i	$-0.743813\pi$
$283$	0.462374	−	0.462374i	0.0274853	−	0.0274853i	0.720716	+	0.693231i	$0.243813\pi$
$284$		0			0
$285$	9.40578	+	5.75107i	0.557150	+	0.340664i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	15.1342i		−	0.890247i
$290$		0			0
$291$	5.81264			0.340743
$292$		0			0
$293$	1.72555	−	1.72555i	0.100808	−	0.100808i	−0.654904	−	0.755712i	$-0.727291\pi$
$293$	1.72555	−	1.72555i	0.100808	−	0.100808i	0.755712	+	0.654904i	$0.227291\pi$
$294$		0			0
$295$	−2.20594	−	9.14851i	−0.128435	−	0.532647i
$296$		0			0
$297$	2.68253	+	2.68253i	0.155656	+	0.155656i
$298$		0			0
$299$	−6.81519			−0.394133
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3.43020	+	3.43020i	0.197060	+	0.197060i
$304$		0			0
$305$	−8.98302	+	2.16604i	−0.514366	+	0.124027i
$306$		0			0
$307$	18.5555	+	18.5555i	1.05902	+	1.05902i	0.998145	+	0.0608747i	$0.0193890\pi$
$307$	18.5555	+	18.5555i	1.05902	+	1.05902i	0.0608747	+	0.998145i	$0.480611\pi$
$308$		0			0
$309$		−	26.1777i		−	1.48920i
$310$		0			0
$311$		−	4.96809i		−	0.281714i	−0.990030	−	0.140857i	$-0.955014\pi$
$311$		−	4.96809i		−	0.281714i	0.990030	−	0.140857i	$-0.0449858\pi$
$312$		0			0
$313$	8.65395	−	8.65395i	0.489150	−	0.489150i	−0.418888	−	0.908038i	$-0.637580\pi$
$313$	8.65395	−	8.65395i	0.489150	−	0.489150i	0.908038	+	0.418888i	$0.137580\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.3182	−	18.3182i	1.02885	−	1.02885i	0.0292785	−	0.999571i	$-0.490679\pi$
$317$	18.3182	−	18.3182i	1.02885	−	1.02885i	0.999571	−	0.0292785i	$-0.00932098\pi$
$318$		0			0
$319$		−	5.41582i		−	0.303228i
$320$		0			0
$321$		−	8.38199i		−	0.467837i
$322$		0			0
$323$	3.01252	+	3.01252i	0.167621	+	0.167621i
$324$		0			0
$325$	2.27667	−	7.05434i	0.126287	−	0.391304i
$326$		0			0
$327$	−18.5120	−	18.5120i	−1.02371	−	1.02371i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	15.1663			0.833613			0.416806	−	0.908995i	$-0.363149\pi$
$331$	15.1663			0.833613			0.416806	+	0.908995i	$0.363149\pi$
$332$		0			0
$333$	3.18662	+	3.18662i	0.174626	+	0.174626i
$334$		0			0
$335$	−7.92120	−	4.84334i	−0.432781	−	0.264620i
$336$		0			0
$337$	12.7442	−	12.7442i	0.694218	−	0.694218i	−0.268939	−	0.963157i	$-0.586673\pi$
$337$	12.7442	−	12.7442i	0.694218	−	0.694218i	0.963157	+	0.268939i	$0.0866729\pi$
$338$		0			0
$339$	−16.1308			−0.876106
$340$		0			0
$341$			6.04477i			0.327343i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.80892	+	15.7964i	0.205065	+	0.850449i
$346$		0			0
$347$	4.27723	−	4.27723i	0.229614	−	0.229614i	−0.582918	−	0.812531i	$-0.698089\pi$
$347$	4.27723	−	4.27723i	0.229614	−	0.229614i	0.812531	+	0.582918i	$0.198089\pi$
$348$		0			0
$349$	5.80171			0.310558			0.155279	−	0.987871i	$-0.450372\pi$
$349$	5.80171			0.310558			0.155279	+	0.987871i	$0.450372\pi$
$350$		0			0
$351$	−8.20509			−0.437955
$352$		0			0
$353$	−8.37164	+	8.37164i	−0.445577	+	0.445577i	−0.893881	−	0.448304i	$-0.852028\pi$
$353$	−8.37164	+	8.37164i	−0.445577	+	0.445577i	0.448304	+	0.893881i	$0.352028\pi$
$354$		0			0
$355$	6.59846	+	27.3652i	0.350210	+	1.45240i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			4.87602i			0.257346i	0.991687	+	0.128673i	$0.0410718\pi$
$359$			4.87602i			0.257346i	−0.991687	+	0.128673i	$0.958928\pi$
$360$		0			0
$361$	−9.27197			−0.487998
$362$		0			0
$363$	−11.7703	+	11.7703i	−0.617781	+	0.617781i
$364$		0			0
$365$	24.5006	+	14.9807i	1.28242	+	0.784125i
$366$		0			0
$367$	4.37569	+	4.37569i	0.228409	+	0.228409i	0.812028	−	0.583619i	$-0.198364\pi$
$367$	4.37569	+	4.37569i	0.228409	+	0.228409i	−0.583619	+	0.812028i	$0.698364\pi$
$368$		0			0
$369$	−5.13541			−0.267339
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−23.2192	−	23.2192i	−1.20225	−	1.20225i	−0.973482	−	0.228763i	$-0.926532\pi$
$373$	−23.2192	−	23.2192i	−1.20225	−	1.20225i	−0.228763	−	0.973482i	$-0.573468\pi$
$374$		0			0
$375$	−17.6231	−	1.33433i	−0.910053	−	0.0689045i
$376$		0			0
$377$	8.28270	+	8.28270i	0.426581	+	0.426581i
$378$		0			0
$379$			6.53089i			0.335469i	0.985832	+	0.167735i	$0.0536452\pi$
$379$			6.53089i			0.335469i	−0.985832	+	0.167735i	$0.946355\pi$
$380$		0			0
$381$			4.76229i			0.243980i
$382$		0			0
$383$	−0.607781	+	0.607781i	−0.0310561	+	0.0310561i	−0.722464	−	0.691408i	$-0.756991\pi$
$383$	−0.607781	+	0.607781i	−0.0310561	+	0.0310561i	0.691408	+	0.722464i	$0.256991\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.87281	+	1.87281i	−0.0952004	+	0.0952004i
$388$		0			0
$389$			26.3550i			1.33625i	0.744049	+	0.668125i	$0.232903\pi$
$389$			26.3550i			1.33625i	−0.744049	+	0.668125i	$0.767097\pi$
$390$		0			0
$391$			6.27927i			0.317556i
$392$		0			0
$393$	12.2351	+	12.2351i	0.617181	+	0.617181i
$394$		0			0
$395$	30.5008	−	7.35454i	1.53466	−	0.370047i
$396$		0			0
$397$	−7.66846	−	7.66846i	−0.384869	−	0.384869i	0.487984	−	0.872853i	$-0.337732\pi$
$397$	−7.66846	−	7.66846i	−0.384869	−	0.384869i	−0.872853	+	0.487984i	$0.837732\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$		0			0
$403$	−9.24459	−	9.24459i	−0.460506	−	0.460506i
$404$		0			0
$405$	3.79765	+	15.7497i	0.188707	+	0.782606i
$406$		0			0
$407$	4.35839	−	4.35839i	0.216037	−	0.216037i
$408$		0			0
$409$	3.39075			0.167662			0.0838308	−	0.996480i	$-0.473284\pi$
$409$	3.39075			0.167662			0.0838308	+	0.996480i	$0.473284\pi$
$410$		0			0
$411$		−	2.13753i		−	0.105437i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−10.7807	−	6.59178i	−0.529206	−	0.323578i
$416$		0			0
$417$	−0.785995	+	0.785995i	−0.0384904	+	0.0384904i
$418$		0			0
$419$	1.03776			0.0506978			0.0253489	−	0.999679i	$-0.491930\pi$
$419$	1.03776			0.0506978			0.0253489	+	0.999679i	$0.491930\pi$
$420$		0			0
$421$	−0.683118			−0.0332931			−0.0166466	−	0.999861i	$-0.505299\pi$
$421$	−0.683118			−0.0332931			−0.0166466	+	0.999861i	$0.505299\pi$
$422$		0			0
$423$	2.47250	−	2.47250i	0.120217	−	0.120217i
$424$		0			0
$425$	−6.49961	−	2.09764i	−0.315278	−	0.101750i
$426$		0			0
$427$		0			0
$428$		0			0
$429$			1.60638i			0.0775569i
$430$		0			0
$431$	−18.6855			−0.900047			−0.450023	−	0.893017i	$-0.648584\pi$
$431$	−18.6855			−0.900047			−0.450023	+	0.893017i	$0.648584\pi$
$432$		0			0
$433$	−7.43170	+	7.43170i	−0.357145	+	0.357145i	−0.862759	−	0.505615i	$-0.831266\pi$
$433$	−7.43170	+	7.43170i	−0.357145	+	0.357145i	0.505615	+	0.862759i	$0.331266\pi$
$434$		0			0
$435$	14.5687	−	23.8269i	0.698517	−	1.14241i
$436$		0			0
$437$	10.1385	+	10.1385i	0.484990	+	0.484990i
$438$		0			0
$439$	27.1027			1.29354			0.646772	−	0.762684i	$-0.276119\pi$
$439$	27.1027			1.29354			0.646772	+	0.762684i	$0.276119\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.5312	+	26.5312i	1.26053	+	1.26053i	0.950835	+	0.309699i	$0.100228\pi$
$443$	26.5312	+	26.5312i	1.26053	+	1.26053i	0.309699	+	0.950835i	$0.399772\pi$
$444$		0			0
$445$	−6.07962	−	25.2135i	−0.288202	−	1.19523i
$446$		0			0
$447$	12.6345	+	12.6345i	0.597592	+	0.597592i
$448$		0			0
$449$			6.36931i			0.300586i	0.988641	+	0.150293i	$0.0480217\pi$
$449$			6.36931i			0.300586i	−0.988641	+	0.150293i	$0.951978\pi$
$450$		0			0
$451$			7.02376i			0.330736i
$452$		0			0
$453$	−8.83420	+	8.83420i	−0.415067	+	0.415067i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.5160	−	10.5160i	0.491919	−	0.491919i	−0.416991	−	0.908910i	$-0.636915\pi$
$457$	10.5160	−	10.5160i	0.491919	−	0.491919i	0.908910	+	0.416991i	$0.136915\pi$
$458$		0			0
$459$			7.55987i			0.352865i
$460$		0			0
$461$			41.8860i			1.95082i	0.220390	+	0.975412i	$0.429267\pi$
$461$			41.8860i			1.95082i	−0.220390	+	0.975412i	$0.570733\pi$
$462$		0			0
$463$	17.8985	+	17.8985i	0.831813	+	0.831813i	0.987765	−	0.155952i	$-0.0498445\pi$
$463$	17.8985	+	17.8985i	0.831813	+	0.831813i	−0.155952	+	0.987765i	$0.549845\pi$
$464$		0			0
$465$	−16.2606	+	26.5940i	−0.754069	+	1.23327i
$466$		0			0
$467$	28.8630	+	28.8630i	1.33562	+	1.33562i	0.900255	+	0.435363i	$0.143380\pi$
$467$	28.8630	+	28.8630i	1.33562	+	1.33562i	0.435363	+	0.900255i	$0.356620\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−3.68779			−0.169924
$472$		0			0
$473$	2.56147	+	2.56147i	0.117777	+	0.117777i
$474$		0			0
$475$	−13.8811	+	7.10742i	−0.636909	+	0.326111i
$476$		0			0
$477$	3.28015	−	3.28015i	0.150188	−	0.150188i
$478$		0			0
$479$	4.88101			0.223019			0.111509	−	0.993763i	$-0.464431\pi$
$479$	4.88101			0.223019			0.111509	+	0.993763i	$0.464431\pi$
$480$		0			0
$481$			13.3310i			0.607843i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.28917	+	7.01486i	−0.194761	+	0.318528i
$486$		0			0
$487$	−25.0326	+	25.0326i	−1.13433	+	1.13433i	−0.144887	+	0.989448i	$0.546282\pi$
$487$	−25.0326	+	25.0326i	−1.13433	+	1.13433i	−0.989448	+	0.144887i	$0.953718\pi$
$488$		0			0
$489$	1.78677			0.0808003
$490$		0			0
$491$	25.8068			1.16464			0.582322	−	0.812958i	$-0.302144\pi$
$491$	25.8068			1.16464			0.582322	+	0.812958i	$0.302144\pi$
$492$		0			0
$493$	7.63138	−	7.63138i	0.343700	−	0.343700i
$494$		0			0
$495$	−0.746751	+	0.180061i	−0.0335640	+	0.00809313i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	13.0869i		−	0.585852i	−0.956135	−	0.292926i	$-0.905371\pi$
$499$		−	13.0869i		−	0.585852i	0.956135	−	0.292926i	$-0.0946290\pi$
$500$		0			0
$501$	−12.8830			−0.575571
$502$		0			0
$503$	15.2498	−	15.2498i	0.679955	−	0.679955i	−0.280035	−	0.959990i	$-0.590346\pi$
$503$	15.2498	−	15.2498i	0.679955	−	0.679955i	0.959990	+	0.280035i	$0.0903460\pi$
$504$		0			0
$505$	−6.67081	+	1.60850i	−0.296847	+	0.0715775i
$506$		0			0
$507$	12.0743	+	12.0743i	0.536239	+	0.536239i
$508$		0			0
$509$	−0.529424			−0.0234663			−0.0117332	−	0.999931i	$-0.503735\pi$
$509$	−0.529424			−0.0234663			−0.0117332	+	0.999931i	$0.503735\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	12.2062	+	12.2062i	0.538915	+	0.538915i
$514$		0			0
$515$	31.5920	+	19.3166i	1.39211	+	0.851192i
$516$		0			0
$517$	−3.38167	−	3.38167i	−0.148726	−	0.148726i
$518$		0			0
$519$		−	27.6429i		−	1.21339i
$520$		0			0
$521$		−	3.62652i		−	0.158881i	−0.996840	−	0.0794404i	$-0.974687\pi$
$521$		−	3.62652i		−	0.158881i	0.996840	−	0.0794404i	$-0.0253133\pi$
$522$		0			0
$523$	14.5942	−	14.5942i	0.638160	−	0.638160i	−0.311941	−	0.950101i	$-0.600979\pi$
$523$	14.5942	−	14.5942i	0.638160	−	0.638160i	0.950101	+	0.311941i	$0.100979\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.51763	+	8.51763i	−0.371034	+	0.371034i
$528$		0			0
$529$		−	1.86740i		−	0.0811915i
$530$		0			0
$531$		−	2.10922i		−	0.0915321i
$532$		0			0
$533$	−10.7418	−	10.7418i	−0.465280	−	0.465280i
$534$		0			0
$535$	10.1156	+	6.18510i	0.437336	+	0.267405i
$536$		0			0
$537$	1.20037	+	1.20037i	0.0517998	+	0.0517998i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	27.5486			1.18441			0.592204	−	0.805788i	$-0.298258\pi$
$541$	27.5486			1.18441			0.592204	+	0.805788i	$0.298258\pi$
$542$		0			0
$543$	−9.98849	−	9.98849i	−0.428647	−	0.428647i
$544$		0			0
$545$	36.0008	−	8.68072i	1.54210	−	0.371841i
$546$		0			0
$547$	5.00886	−	5.00886i	0.214164	−	0.214164i	−0.591870	−	0.806034i	$-0.701610\pi$
$547$	5.00886	−	5.00886i	0.214164	−	0.214164i	0.806034	+	0.591870i	$0.201610\pi$
$548$		0			0
$549$	−2.07106			−0.0883907
$550$		0			0
$551$		−	24.6432i		−	1.04984i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	30.8989	−	7.45053i	1.31159	−	0.316257i
$556$		0			0
$557$	7.38343	−	7.38343i	0.312846	−	0.312846i	−0.533165	−	0.846011i	$-0.678998\pi$
$557$	7.38343	−	7.38343i	0.312846	−	0.312846i	0.846011	+	0.533165i	$0.178998\pi$
$558$		0			0
$559$	−7.83479			−0.331376
$560$		0			0
$561$	1.48006			0.0624883
$562$		0			0
$563$	−19.5473	+	19.5473i	−0.823822	+	0.823822i	−0.986654	−	0.162832i	$-0.947937\pi$
$563$	−19.5473	+	19.5473i	−0.823822	+	0.823822i	0.162832	+	0.986654i	$0.447937\pi$
$564$		0			0
$565$	11.9030	−	19.4671i	0.500762	−	0.818988i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			11.1287i			0.466538i	0.972412	+	0.233269i	$0.0749422\pi$
$569$			11.1287i			0.466538i	−0.972412	+	0.233269i	$0.925058\pi$
$570$		0			0
$571$	20.6948			0.866051			0.433025	−	0.901382i	$-0.357446\pi$
$571$	20.6948			0.866051			0.433025	+	0.901382i	$0.357446\pi$
$572$		0			0
$573$	−27.2508	+	27.2508i	−1.13842	+	1.13842i
$574$		0			0
$575$	−21.8741	−	7.05950i	−0.912215	−	0.294402i
$576$		0			0
$577$	−5.12665	−	5.12665i	−0.213425	−	0.213425i	0.592295	−	0.805721i	$-0.298222\pi$
$577$	−5.12665	−	5.12665i	−0.213425	−	0.213425i	−0.805721	+	0.592295i	$0.798222\pi$
$578$		0			0
$579$	−14.2793			−0.593426
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.48631	−	4.48631i	−0.185804	−	0.185804i
$584$		0			0
$585$	0.866669	−	1.41742i	0.0358324	−	0.0586032i
$586$		0			0
$587$	−5.87340	−	5.87340i	−0.242421	−	0.242421i	0.575430	−	0.817851i	$-0.304835\pi$
$587$	−5.87340	−	5.87340i	−0.242421	−	0.242421i	−0.817851	+	0.575430i	$0.804835\pi$
$588$		0			0
$589$			27.5051i			1.13333i
$590$		0			0
$591$		−	3.99432i		−	0.164304i
$592$		0			0
$593$	−19.3128	+	19.3128i	−0.793082	+	0.793082i	−0.981994	−	0.188912i	$-0.939504\pi$
$593$	−19.3128	+	19.3128i	−0.793082	+	0.793082i	0.188912	+	0.981994i	$0.439504\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.4445	+	10.4445i	−0.427464	+	0.427464i
$598$		0			0
$599$		−	25.3620i		−	1.03626i	−0.855301	−	0.518131i	$-0.826628\pi$
$599$		−	25.3620i		−	1.03626i	0.855301	−	0.518131i	$-0.173372\pi$
$600$		0			0
$601$		−	13.8045i		−	0.563099i	−0.959547	−	0.281550i	$-0.909152\pi$
$601$		−	13.8045i		−	0.563099i	0.959547	−	0.281550i	$-0.0908484\pi$
$602$		0			0
$603$	−1.47145	−	1.47145i	−0.0599221	−	0.0599221i
$604$		0			0
$605$	−5.51939	−	22.8901i	−0.224395	−	0.930615i
$606$		0			0
$607$	15.8422	+	15.8422i	0.643016	+	0.643016i	0.951296	−	0.308280i	$-0.0997532\pi$
$607$	15.8422	+	15.8422i	0.643016	+	0.643016i	−0.308280	+	0.951296i	$0.599753\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	10.3435			0.418454
$612$		0			0
$613$	23.5361	+	23.5361i	0.950614	+	0.950614i	0.998837	−	0.0482227i	$-0.0153557\pi$
$613$	23.5361	+	23.5361i	0.950614	+	0.950614i	−0.0482227	+	0.998837i	$0.515356\pi$
$614$		0			0
$615$	−18.8942	+	30.9011i	−0.761886	+	1.24605i
$616$		0			0
$617$	21.1167	−	21.1167i	0.850125	−	0.850125i	−0.140023	−	0.990148i	$-0.544718\pi$
$617$	21.1167	−	21.1167i	0.850125	−	0.850125i	0.990148	+	0.140023i	$0.0447177\pi$
$618$		0			0
$619$	36.4621			1.46554			0.732768	−	0.680478i	$-0.238228\pi$
$619$	36.4621			1.46554			0.732768	+	0.680478i	$0.238228\pi$
$620$		0			0
$621$			25.4424i			1.02097i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.6144	−	20.2834i	0.584578	−	0.811338i
$626$		0			0
$627$	2.38971	−	2.38971i	0.0954357	−	0.0954357i
$628$		0			0
$629$	12.2827			0.489744
$630$		0			0
$631$	47.0247			1.87203			0.936013	−	0.351966i	$-0.114487\pi$
$631$	47.0247			1.87203			0.936013	+	0.351966i	$0.114487\pi$
$632$		0			0
$633$	−11.0067	+	11.0067i	−0.437479	+	0.437479i
$634$		0			0
$635$	−5.74727	−	3.51411i	−0.228073	−	0.139453i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			6.30914i			0.249586i
$640$		0			0
$641$	−16.1052			−0.636118			−0.318059	−	0.948071i	$-0.603031\pi$
$641$	−16.1052			−0.636118			−0.318059	+	0.948071i	$0.603031\pi$
$642$		0			0
$643$	29.1021	−	29.1021i	1.14768	−	1.14768i	0.160667	−	0.987009i	$-0.448635\pi$
$643$	29.1021	−	29.1021i	1.14768	−	1.14768i	0.987009	−	0.160667i	$-0.0513646\pi$
$644$		0			0
$645$	4.37876	+	18.1596i	0.172413	+	0.715035i
$646$		0			0
$647$	−30.1956	−	30.1956i	−1.18711	−	1.18711i	−0.977862	−	0.209251i	$-0.932898\pi$
$647$	−30.1956	−	30.1956i	−1.18711	−	1.18711i	−0.209251	−	0.977862i	$-0.567102\pi$
$648$		0			0
$649$	−2.88480			−0.113238
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−23.5747	−	23.5747i	−0.922550	−	0.922550i	0.0746587	−	0.997209i	$-0.476213\pi$
$653$	−23.5747	−	23.5747i	−0.922550	−	0.922550i	−0.997209	+	0.0746587i	$0.976213\pi$
$654$		0			0
$655$	−23.7941	+	5.73736i	−0.929711	+	0.224177i
$656$		0			0
$657$	4.55127	+	4.55127i	0.177562	+	0.177562i
$658$		0			0
$659$			2.01773i			0.0785996i	0.999227	+	0.0392998i	$0.0125127\pi$
$659$			2.01773i			0.0785996i	−0.999227	+	0.0392998i	$0.987487\pi$
$660$		0			0
$661$		−	0.473111i		−	0.0184019i	−0.999958	−	0.00920095i	$-0.997071\pi$
$661$		−	0.473111i		−	0.0184019i	0.999958	−	0.00920095i	$-0.00292879\pi$
$662$		0			0
$663$	−2.26354	+	2.26354i	−0.0879086	+	0.0879086i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	25.6831	−	25.6831i	0.994452	−	0.994452i
$668$		0			0
$669$			0.757012i			0.0292678i
$670$		0			0
$671$			2.83262i			0.109352i
$672$		0			0
$673$	−15.1663	−	15.1663i	−0.584616	−	0.584616i	0.351552	−	0.936168i	$-0.385654\pi$
$673$	−15.1663	−	15.1663i	−0.584616	−	0.584616i	−0.936168	+	0.351552i	$0.885654\pi$
$674$		0			0
$675$	−26.3352	−	8.49922i	−1.01364	−	0.327135i
$676$		0			0
$677$	−10.0449	−	10.0449i	−0.386058	−	0.386058i	0.487221	−	0.873279i	$-0.338011\pi$
$677$	−10.0449	−	10.0449i	−0.386058	−	0.386058i	−0.873279	+	0.487221i	$0.838011\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−21.9226			−0.840076
$682$		0			0
$683$	−14.8058	−	14.8058i	−0.566527	−	0.566527i	0.364626	−	0.931154i	$-0.381197\pi$
$683$	−14.8058	−	14.8058i	−0.566527	−	0.566527i	−0.931154	+	0.364626i	$0.881197\pi$
$684$		0			0
$685$	2.57964	+	1.57729i	0.0985628	+	0.0602653i
$686$		0			0
$687$	−2.97653	+	2.97653i	−0.113562	+	0.113562i
$688$		0			0
$689$	13.7223			0.522778
$690$		0			0
$691$			6.47007i			0.246133i	0.992398	+	0.123067i	$0.0392729\pi$
$691$			6.47007i			0.246133i	−0.992398	+	0.123067i	$0.960727\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.368573	−	1.52855i	−0.0139808	−	0.0579812i
$696$		0			0
$697$	−9.89712	+	9.89712i	−0.374880	+	0.374880i
$698$		0			0
$699$	29.9281			1.13198
$700$		0			0
$701$	15.5423			0.587026			0.293513	−	0.955955i	$-0.405176\pi$
$701$	15.5423			0.587026			0.293513	+	0.955955i	$0.405176\pi$
$702$		0			0
$703$	19.8317	−	19.8317i	0.747966	−	0.747966i
$704$		0			0
$705$	−5.78086	−	23.9744i	−0.217720	−	0.902930i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		−	8.97963i		−	0.337237i	−0.985681	−	0.168619i	$-0.946069\pi$
$709$		−	8.97963i		−	0.337237i	0.985681	−	0.168619i	$-0.0539306\pi$
$710$		0			0
$711$	7.03206			0.263723
$712$		0			0
$713$	−28.6657	+	28.6657i	−1.07354	+	1.07354i
$714$		0			0
$715$	−1.93863	−	1.18536i	−0.0725006	−	0.0443298i
$716$		0			0
$717$	6.42066	+	6.42066i	0.239784	+	0.239784i
$718$		0			0
$719$	−40.5516			−1.51232			−0.756160	−	0.654387i	$-0.772927\pi$
$719$	−40.5516			−1.51232			−0.756160	+	0.654387i	$0.772927\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−11.3858	−	11.3858i	−0.423441	−	0.423441i
$724$		0			0
$725$	18.0047	+	35.1639i	0.668677	+	1.30596i
$726$		0			0
$727$	11.9052	+	11.9052i	0.441540	+	0.441540i	0.892529	−	0.450990i	$-0.148929\pi$
$727$	11.9052	+	11.9052i	0.441540	+	0.441540i	−0.450990	+	0.892529i	$0.648929\pi$
$728$		0			0
$729$			29.8776i			1.10658i
$730$		0			0
$731$			7.21869i			0.266993i
$732$		0			0
$733$	−4.37977	+	4.37977i	−0.161770	+	0.161770i	−0.783351	−	0.621580i	$-0.786491\pi$
$733$	−4.37977	+	4.37977i	−0.161770	+	0.161770i	0.621580	+	0.783351i	$0.286491\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.01252	+	2.01252i	−0.0741322	+	0.0741322i
$738$		0			0
$739$		−	39.6402i		−	1.45819i	−0.684413	−	0.729095i	$-0.739941\pi$
$739$		−	39.6402i		−	1.45819i	0.684413	−	0.729095i	$-0.260059\pi$
$740$		0			0
$741$			7.30942i			0.268518i
$742$		0			0
$743$	−15.7507	−	15.7507i	−0.577837	−	0.577837i	0.356470	−	0.934307i	$-0.383980\pi$
$743$	−15.7507	−	15.7507i	−0.577837	−	0.577837i	−0.934307	+	0.356470i	$0.883980\pi$
$744$		0			0
$745$	−24.5707	+	5.92464i	−0.900202	+	0.217062i
$746$		0			0
$747$	−2.00264	−	2.00264i	−0.0732728	−	0.0732728i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−18.3346			−0.669039			−0.334520	−	0.942389i	$-0.608574\pi$
$751$	−18.3346			−0.669039			−0.334520	+	0.942389i	$0.608574\pi$
$752$		0			0
$753$	−8.14712	−	8.14712i	−0.296898	−	0.296898i
$754$		0			0
$755$	−4.14258	−	17.1802i	−0.150764	−	0.625250i
$756$		0			0
$757$	−14.1143	+	14.1143i	−0.512994	+	0.512994i	−0.915443	−	0.402449i	$-0.868159\pi$
$757$	−14.1143	+	14.1143i	−0.512994	+	0.512994i	0.402449	+	0.915443i	$0.368159\pi$
$758$		0			0
$759$	4.98108			0.180802
$760$		0			0
$761$			11.6443i			0.422107i	0.977475	+	0.211054i	$0.0676894\pi$
$761$			11.6443i			0.422107i	−0.977475	+	0.211054i	$0.932311\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.30596	−	0.798518i	−0.0472171	−	0.0288705i
$766$		0			0
$767$	4.41188	−	4.41188i	0.159304	−	0.159304i
$768$		0			0
$769$	−45.3371			−1.63490			−0.817448	−	0.576002i	$-0.804612\pi$
$769$	−45.3371			−1.63490			−0.817448	+	0.576002i	$0.804612\pi$
$770$		0			0
$771$	−19.3119			−0.695501
$772$		0			0
$773$	−5.16153	+	5.16153i	−0.185647	+	0.185647i	−0.793811	−	0.608164i	$-0.791906\pi$
$773$	−5.16153	+	5.16153i	−0.185647	+	0.185647i	0.608164	+	0.793811i	$0.291906\pi$
$774$		0			0
$775$	−20.0956	−	39.2476i	−0.721855	−	1.40981i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			31.9598i			1.14508i
$780$		0			0
$781$	8.62909			0.308773
$782$		0			0
$783$	30.9209	−	30.9209i	1.10502	−	1.10502i
$784$		0			0
$785$	2.72123	−	4.45053i	0.0971250	−	0.158846i
$786$		0			0
$787$	21.6593	+	21.6593i	0.772071	+	0.772071i	0.978468	−	0.206397i	$-0.0661738\pi$
$787$	21.6593	+	21.6593i	0.772071	+	0.772071i	−0.206397	+	0.978468i	$0.566174\pi$
$788$		0			0
$789$	33.9982			1.21037
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−4.33207	−	4.33207i	−0.153836	−	0.153836i
$794$		0			0
$795$	−7.66921	−	31.8058i	−0.271999	−	1.12804i
$796$		0			0
$797$	−30.7751	−	30.7751i	−1.09011	−	1.09011i	−0.995516	−	0.0945938i	$-0.969845\pi$
$797$	−30.7751	−	30.7751i	−1.09011	−	1.09011i	−0.0945938	−	0.995516i	$-0.530155\pi$
$798$		0			0
$799$		−	9.53015i		−	0.337153i
$800$		0			0
$801$		−	5.81304i		−	0.205394i
$802$		0			0
$803$	6.22483	−	6.22483i	0.219670	−	0.219670i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−29.5934	+	29.5934i	−1.04174	+	1.04174i
$808$		0			0
$809$			14.6597i			0.515407i	0.966224	+	0.257703i	$0.0829657\pi$
$809$			14.6597i			0.515407i	−0.966224	+	0.257703i	$0.917034\pi$
$810$		0			0
$811$		−	0.360507i		−	0.0126591i	−0.999980	−	0.00632956i	$-0.997985\pi$
$811$		−	0.360507i		−	0.0126591i	0.999980	−	0.00632956i	$-0.00201477\pi$
$812$		0			0
$813$	−19.9503	−	19.9503i	−0.699688	−	0.699688i
$814$		0			0
$815$	−1.31846	+	2.15632i	−0.0461836	+	0.0755326i
$816$		0			0
$817$	11.6553	+	11.6553i	0.407767	+	0.407767i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.2813			0.777623			0.388812	−	0.921317i	$-0.372886\pi$
$821$	22.2813			0.777623			0.388812	+	0.921317i	$0.372886\pi$
$822$		0			0
$823$	−8.18136	−	8.18136i	−0.285184	−	0.285184i	0.549988	−	0.835173i	$-0.314632\pi$
$823$	−8.18136	−	8.18136i	−0.285184	−	0.285184i	−0.835173	+	0.549988i	$0.814632\pi$
$824$		0			0
$825$	−1.66397	+	5.15587i	−0.0579319	+	0.179504i
$826$		0			0
$827$	−24.7972	+	24.7972i	−0.862283	+	0.862283i	−0.991603	−	0.129320i	$-0.958721\pi$
$827$	−24.7972	+	24.7972i	−0.862283	+	0.862283i	0.129320	+	0.991603i	$0.458721\pi$
$828$		0			0
$829$	−25.3974			−0.882089			−0.441044	−	0.897485i	$-0.645392\pi$
$829$	−25.3974			−0.882089			−0.441044	+	0.897485i	$0.645392\pi$
$830$		0			0
$831$		−	41.9454i		−	1.45507i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.50643	−	15.5476i	0.328984	−	0.538047i
$836$		0			0
$837$	−34.5118	+	34.5118i	−1.19290	+	1.19290i
$838$		0			0
$839$	−4.36253			−0.150611			−0.0753057	−	0.997160i	$-0.523993\pi$
$839$	−4.36253			−0.150611			−0.0753057	+	0.997160i	$0.523993\pi$
$840$		0			0
$841$	−33.4268			−1.15265
$842$		0			0
$843$	−20.9543	+	20.9543i	−0.721705	+	0.721705i
$844$		0			0
$845$	−23.4813	+	5.66195i	−0.807781	+	0.194777i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		−	1.03366i		−	0.0354750i
$850$		0			0
$851$	41.3369			1.41701
$852$		0			0
$853$	36.8935	−	36.8935i	1.26321	−	1.26321i	0.313683	−	0.949528i	$-0.398437\pi$
$853$	36.8935	−	36.8935i	1.26321	−	1.26321i	0.949528	−	0.313683i	$-0.101563\pi$
$854$		0			0
$855$	−3.39789	+	0.819319i	−0.116205	+	0.0280201i
$856$		0			0
$857$	−18.0587	−	18.0587i	−0.616873	−	0.616873i	0.327855	−	0.944728i	$-0.393674\pi$
$857$	−18.0587	−	18.0587i	−0.616873	−	0.616873i	−0.944728	+	0.327855i	$0.893674\pi$
$858$		0			0
$859$	32.7639			1.11789			0.558944	−	0.829205i	$-0.311207\pi$
$859$	32.7639			1.11789			0.558944	+	0.829205i	$0.311207\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−17.0139	−	17.0139i	−0.579159	−	0.579159i	0.355513	−	0.934672i	$-0.384306\pi$
$863$	−17.0139	−	17.0139i	−0.579159	−	0.579159i	−0.934672	+	0.355513i	$0.884306\pi$
$864$		0			0
$865$	33.3602	+	20.3978i	1.13428	+	0.693545i
$866$		0			0
$867$	−16.9166	−	16.9166i	−0.574518	−	0.574518i
$868$		0			0
$869$		−	9.61784i		−	0.326263i
$870$		0			0
$871$		−	6.15572i		−	0.208578i
$872$		0			0
$873$	−1.30309	+	1.30309i	−0.0441029	+	0.0441029i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−34.1895	+	34.1895i	−1.15450	+	1.15450i	−0.168857	+	0.985641i	$0.554007\pi$
$877$	−34.1895	+	34.1895i	−1.15450	+	1.15450i	−0.985641	+	0.168857i	$0.945993\pi$
$878$		0			0
$879$		−	3.85755i		−	0.130112i
$880$		0			0
$881$		−	3.63541i		−	0.122480i	−0.998123	−	0.0612400i	$-0.980494\pi$
$881$		−	3.63541i		−	0.122480i	0.998123	−	0.0612400i	$-0.0195055\pi$
$882$		0			0
$883$	−7.50117	−	7.50117i	−0.252434	−	0.252434i	0.569534	−	0.821968i	$-0.307124\pi$
$883$	−7.50117	−	7.50117i	−0.252434	−	0.252434i	−0.821968	+	0.569534i	$0.807124\pi$
$884$		0			0
$885$	−12.6917	−	7.76021i	−0.426627	−	0.260857i
$886$		0			0
$887$	7.98966	+	7.98966i	0.268267	+	0.268267i	0.828401	−	0.560135i	$-0.189251\pi$
$887$	7.98966	+	7.98966i	0.268267	+	0.268267i	−0.560135	+	0.828401i	$0.689251\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.96634			0.166379
$892$		0			0
$893$	−15.3874	−	15.3874i	−0.514919	−	0.514919i
$894$		0			0
$895$	−2.33440	+	0.562883i	−0.0780303	+	0.0188151i
$896$		0			0
$897$	−7.61784	+	7.61784i	−0.254352	+	0.254352i
$898$		0			0
$899$	69.6765			2.32384
$900$		0			0
$901$		−	12.6432i		−	0.421207i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	19.4249	−	4.68385i	0.645707	−	0.155697i
$906$		0			0
$907$	11.4009	−	11.4009i	0.378561	−	0.378561i	−0.492022	−	0.870583i	$-0.663742\pi$
$907$	11.4009	−	11.4009i	0.378561	−	0.378561i	0.870583	+	0.492022i	$0.163742\pi$
$908$		0			0
$909$	−1.53798			−0.0510114
$910$		0			0
$911$	−31.2211			−1.03440			−0.517201	−	0.855864i	$-0.673026\pi$
$911$	−31.2211			−1.03440			−0.517201	+	0.855864i	$0.673026\pi$
$912$		0			0
$913$	−2.73904	+	2.73904i	−0.0906490	+	0.0906490i
$914$		0			0
$915$	−7.61984	+	12.4621i	−0.251904	+	0.411985i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			49.3844i			1.62904i	0.580135	+	0.814520i	$0.303000\pi$
$919$			49.3844i			1.62904i	−0.580135	+	0.814520i	$0.697000\pi$
$920$		0			0
$921$	41.4817			1.36687
$922$		0			0
$923$	−13.1969	+	13.1969i	−0.434382	+	0.434382i
$924$		0			0
$925$	−13.8089	+	42.7875i	−0.454034	+	1.40684i
$926$		0			0
$927$	5.86856	+	5.86856i	0.192749	+	0.192749i
$928$		0			0
$929$	52.9421			1.73697			0.868487	−	0.495711i	$-0.165093\pi$
$929$	52.9421			1.73697			0.868487	+	0.495711i	$0.165093\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−5.55319	−	5.55319i	−0.181803	−	0.181803i
$934$		0			0
$935$	−1.09214	+	1.78618i	−0.0357169	+	0.0584144i
$936$		0			0
$937$	−28.9004	−	28.9004i	−0.944134	−	0.944134i	0.0543857	−	0.998520i	$-0.482680\pi$
$937$	−28.9004	−	28.9004i	−0.944134	−	0.944134i	−0.998520	+	0.0543857i	$0.982680\pi$
$938$		0			0
$939$		−	19.3463i		−	0.631343i
$940$		0			0
$941$			35.9805i			1.17293i	0.809975	+	0.586465i	$0.199481\pi$
$941$			35.9805i			1.17293i	−0.809975	+	0.586465i	$0.800519\pi$
$942$		0			0
$943$	−33.3083	+	33.3083i	−1.08467	+	1.08467i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.6841	+	13.6841i	−0.444675	+	0.444675i	−0.893580	−	0.448905i	$-0.851814\pi$
$947$	−13.6841	+	13.6841i	−0.444675	+	0.444675i	0.448905	+	0.893580i	$0.351814\pi$
$948$		0			0
$949$			19.0399i			0.618062i
$950$		0			0
$951$		−	40.9511i		−	1.32793i
$952$		0			0
$953$	13.7055	+	13.7055i	0.443965	+	0.443965i	0.893342	−	0.449377i	$-0.148354\pi$
$953$	13.7055	+	13.7055i	0.443965	+	0.443965i	−0.449377	+	0.893342i	$0.648354\pi$
$954$		0			0
$955$	−12.7786	−	52.9954i	−0.413504	−	1.71489i
$956$		0			0
$957$	−6.05366	−	6.05366i	−0.195687	−	0.195687i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−46.7682			−1.50865
$962$		0			0
$963$	1.87909	+	1.87909i	0.0605528	+	0.0605528i
$964$		0			0
$965$	10.5367	−	17.2326i	0.339189	−	0.554737i
$966$		0			0
$967$	−26.8117	+	26.8117i	−0.862207	+	0.862207i	−0.991594	−	0.129387i	$-0.958699\pi$
$967$	−26.8117	+	26.8117i	−0.862207	+	0.862207i	0.129387	+	0.991594i	$0.458699\pi$
$968$		0			0
$969$	6.73463			0.216347
$970$		0			0
$971$			2.20717i			0.0708313i	0.999373	+	0.0354157i	$0.0112755\pi$
$971$			2.20717i			0.0708313i	−0.999373	+	0.0354157i	$0.988724\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.34035	−	10.4299i	−0.171028	−	0.334026i
$976$		0			0
$977$	38.3487	−	38.3487i	1.22688	−	1.22688i	0.261749	−	0.965136i	$-0.415701\pi$
$977$	38.3487	−	38.3487i	1.22688	−	1.22688i	0.965136	−	0.261749i	$-0.0842992\pi$
$978$		0			0
$979$	−7.95058			−0.254102
$980$		0			0
$981$	8.30009			0.265001
$982$		0			0
$983$	24.9302	−	24.9302i	0.795149	−	0.795149i	−0.187177	−	0.982326i	$-0.559934\pi$
$983$	24.9302	−	24.9302i	0.795149	−	0.795149i	0.982326	+	0.187177i	$0.0599339\pi$
$984$		0			0
$985$	4.82045	+	2.94742i	0.153592	+	0.0939126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			24.2942i			0.772510i
$990$		0			0
$991$	8.32206			0.264359			0.132179	−	0.991226i	$-0.457802\pi$
$991$	8.32206			0.264359			0.132179	+	0.991226i	$0.457802\pi$
$992$		0			0
$993$	16.9524	−	16.9524i	0.537969	−	0.537969i
$994$		0			0
$995$	−4.89767	−	20.3117i	−0.155267	−	0.643924i
$996$		0			0
$997$	22.3341	+	22.3341i	0.707330	+	0.707330i	0.965973	−	0.258643i	$-0.0832754\pi$
$997$	22.3341	+	22.3341i	0.707330	+	0.707330i	−0.258643	+	0.965973i	$0.583275\pi$
$998$		0			0
$999$	49.7672			1.57457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.m.a.293.6		16
5.2	odd	4	inner	980.2.m.a.97.3		16
7.2	even	3		140.2.u.a.73.3	yes	16
7.3	odd	6		140.2.u.a.33.3	yes	16
7.4	even	3		980.2.v.a.313.2		16
7.5	odd	6		980.2.v.a.913.2		16
7.6	odd	2	inner	980.2.m.a.293.3		16
21.2	odd	6		1260.2.dq.a.73.2		16
21.17	even	6		1260.2.dq.a.1153.1		16
28.3	even	6		560.2.ci.d.33.2		16
28.23	odd	6		560.2.ci.d.353.2		16
35.2	odd	12		140.2.u.a.17.3	✓	16
35.3	even	12		700.2.bc.b.257.2		16
35.9	even	6		700.2.bc.b.493.2		16
35.12	even	12		980.2.v.a.717.2		16
35.17	even	12		140.2.u.a.117.3	yes	16
35.23	odd	12		700.2.bc.b.157.2		16
35.24	odd	6		700.2.bc.b.593.2		16
35.27	even	4	inner	980.2.m.a.97.6		16
35.32	odd	12		980.2.v.a.117.2		16
105.2	even	12		1260.2.dq.a.577.1		16
105.17	odd	12		1260.2.dq.a.397.2		16
140.87	odd	12		560.2.ci.d.257.2		16
140.107	even	12		560.2.ci.d.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.3	✓	16	35.2	odd	12
140.2.u.a.33.3	yes	16	7.3	odd	6
140.2.u.a.73.3	yes	16	7.2	even	3
140.2.u.a.117.3	yes	16	35.17	even	12
560.2.ci.d.17.2		16	140.107	even	12
560.2.ci.d.33.2		16	28.3	even	6
560.2.ci.d.257.2		16	140.87	odd	12
560.2.ci.d.353.2		16	28.23	odd	6
700.2.bc.b.157.2		16	35.23	odd	12
700.2.bc.b.257.2		16	35.3	even	12
700.2.bc.b.493.2		16	35.9	even	6
700.2.bc.b.593.2		16	35.24	odd	6
980.2.m.a.97.3		16	5.2	odd	4	inner
980.2.m.a.97.6		16	35.27	even	4	inner
980.2.m.a.293.3		16	7.6	odd	2	inner
980.2.m.a.293.6		16	1.1	even	1	trivial
980.2.v.a.117.2		16	35.32	odd	12
980.2.v.a.313.2		16	7.4	even	3
980.2.v.a.717.2		16	35.12	even	12
980.2.v.a.913.2		16	7.5	odd	6
1260.2.dq.a.73.2		16	21.2	odd	6
1260.2.dq.a.397.2		16	105.17	odd	12
1260.2.dq.a.577.1		16	105.2	even	12
1260.2.dq.a.1153.1		16	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11777 - 1.11777i) q^{3} +(0.524151 + 2.17377i) q^{5} +0.501168i q^{9} +O(q^{10})\)	\(q+(1.11777 - 1.11777i) q^{3} +(0.524151 + 2.17377i) q^{5} +0.501168i q^{9} +0.685455 q^{11} +(-1.04830 + 1.04830i) q^{13} +(3.01566 + 1.84390i) q^{15} +(0.965868 + 0.965868i) q^{17} +3.11898 q^{19} +(3.25058 + 3.25058i) q^{23} +(-4.45053 + 2.27877i) q^{25} +(3.91351 + 3.91351i) q^{27} -7.90106i q^{29} +8.81863i q^{31} +(0.766183 - 0.766183i) q^{33} +(6.35839 - 6.35839i) q^{37} +2.34353i q^{39} +10.2469i q^{41} +(3.73689 + 3.73689i) q^{43} +(-1.08942 + 0.262688i) q^{45} +(-4.93346 - 4.93346i) q^{47} +2.15924 q^{51} +(-6.54501 - 6.54501i) q^{53} +(0.359282 + 1.49002i) q^{55} +(3.48631 - 3.48631i) q^{57} -4.20860 q^{59} +4.13247i q^{61} +(-2.82824 - 1.72930i) q^{65} +(-2.93604 + 2.93604i) q^{67} +7.26683 q^{69} +12.5889 q^{71} +(9.08131 - 9.08131i) q^{73} +(-2.42754 + 7.52182i) q^{75} -14.0313i q^{79} +7.24532 q^{81} +(-3.99595 + 3.99595i) q^{83} +(-1.59331 + 2.60583i) q^{85} +(-8.83159 - 8.83159i) q^{87} -11.5990 q^{89} +(9.85722 + 9.85722i) q^{93} +(1.63482 + 6.77993i) q^{95} +(2.60010 + 2.60010i) q^{97} +0.343528i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 20 q^{15} + 32 q^{23} - 12 q^{25} + 28 q^{37} + 28 q^{43} - 40 q^{51} + 20 q^{53} + 44 q^{57} - 68 q^{65} - 16 q^{67} - 8 q^{71} - 48 q^{81} + 124 q^{93} - 4 q^{95}+O(q^{100}) \) 16 * q - 20 * q^15 + 32 * q^23 - 12 * q^25 + 28 * q^37 + 28 * q^43 - 40 * q^51 + 20 * q^53 + 44 * q^57 - 68 * q^65 - 16 * q^67 - 8 * q^71 - 48 * q^81 + 124 * q^93 - 4 * q^95

Introduction

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