LMFDB - Embedded newform 980.2.i.e.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(361,980)] 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("980.361"); 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, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-1,0,1,0,0,0,2,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	980.961
Dual form			980.2.i.e.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} -5.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{17} +(3.00000 - 5.19615i) q^{19} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{27} +3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{33} +(-4.00000 + 6.92820i) q^{37} +(2.50000 + 4.33013i) q^{39} -10.0000 q^{41} -2.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(3.50000 - 6.06218i) q^{47} +(-0.500000 + 0.866025i) q^{51} +(1.00000 + 1.73205i) q^{53} +1.00000 q^{55} -6.00000 q^{57} +(-7.00000 - 12.1244i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-2.50000 + 4.33013i) q^{65} +(-7.00000 - 12.1244i) q^{67} -4.00000 q^{69} +(5.00000 + 8.66025i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} -1.00000 q^{85} +(-1.50000 - 2.59808i) q^{87} +(-2.00000 + 3.46410i) q^{89} +(-1.00000 + 1.73205i) q^{93} +(-3.00000 - 5.19615i) q^{95} -3.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + q^{5} + 2 q^{9} + q^{11} - 10 q^{13} - 2 q^{15} - q^{17} + 6 q^{19} + 4 q^{23} - q^{25} - 10 q^{27} + 6 q^{29} - 2 q^{31} + q^{33} - 8 q^{37} + 5 q^{39} - 20 q^{41} - 4 q^{43} - 2 q^{45}+ \cdots + 4 q^{99}+O(q^{100}) $ 2 * q - q^3 + q^5 + 2 * q^9 + q^11 - 10 * q^13 - 2 * q^15 - q^17 + 6 * q^19 + 4 * q^23 - q^25 - 10 * q^27 + 6 * q^29 - 2 * q^31 + q^33 - 8 * q^37 + 5 * q^39 - 20 * q^41 - 4 * q^43 - 2 * q^45 + 7 * q^47 - q^51 + 2 * q^53 + 2 * q^55 - 12 * q^57 - 14 * q^59 + 8 * q^61 - 5 * q^65 - 14 * q^67 - 8 * q^69 + 10 * q^73 - q^75 + 11 * q^79 - q^81 - 8 * q^83 - 2 * q^85 - 3 * q^87 - 4 * q^89 - 2 * q^93 - 6 * q^95 - 6 * q^97 + 4 * q^99

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$	2.50000	+	4.33013i	0.400320	+	0.693375i
$40$		0			0
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$		0			0
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	−0.489398	−	0.872060i	$-0.662783\pi$
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	0.999926	−	0.0121990i	$-0.00388317\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.500000	+	0.866025i	−0.0700140	+	0.121268i
$52$		0			0
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$	−6.00000			−0.794719
$58$		0			0
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.812198	−	0.583382i	$-0.801729\pi$
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.0991242	−	0.995075i	$-0.531604\pi$
$60$		0			0
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$		0			0
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	−1.00000			−0.108465
$86$		0			0
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$		0			0
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	−0.952340	−	0.305038i	$-0.901331\pi$
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	0.740341	+	0.672232i	$0.234664\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$		0			0
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$		0			0
$97$	−3.00000			−0.304604			−0.152302	−	0.988334i	$-0.548669\pi$
$97$	−3.00000			−0.304604			−0.152302	+	0.988334i	$0.548669\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$		0			0
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$		0			0
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	0.999512	+	0.0312328i	$0.00994332\pi$
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	−0.472708	+	0.881219i	$0.656723\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$		0			0
$113$	16.0000			1.50515			0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000			1.50515			0.752577	+	0.658505i	$0.228811\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	−5.00000	+	8.66025i	−0.462250	+	0.800641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	−0.973910	−	0.226935i	$-0.927130\pi$
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	0.290424	−	0.956898i	$-0.406204\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$	−7.00000			−0.589506
$142$		0			0
$143$	−2.50000	−	4.33013i	−0.209061	−	0.362103i
$144$		0			0
$145$	1.50000	−	2.59808i	0.124568	−	0.215758i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.0751583	−	0.997172i	$-0.476054\pi$
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.825997	−	0.563675i	$-0.190613\pi$
$150$		0			0
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	0.920583	−	0.390547i	$-0.127714\pi$
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	−0.798515	+	0.601975i	$0.794381\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−2.00000			−0.160644
$156$		0			0
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$		0			0
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$		0			0
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−6.00000	−	10.3923i	−0.458831	−	0.794719i
$172$		0			0
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.00000	+	12.1244i	−0.526152	+	0.911322i
$178$		0			0
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	0.949048	+	0.315130i	$0.102048\pi$
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	−0.201613	+	0.979465i	$0.564618\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	−8.00000			−0.591377
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$	0.500000	−	0.866025i	0.0365636	−	0.0633300i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$		0			0
$193$	6.00000	+	10.3923i	0.431889	+	0.748054i	0.997036	−	0.0769360i	$-0.0245137\pi$
$193$	6.00000	+	10.3923i	0.431889	+	0.748054i	−0.565147	+	0.824991i	$0.691180\pi$
$194$		0			0
$195$	5.00000			0.358057
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$		0			0
$201$	−7.00000	+	12.1244i	−0.493742	+	0.855186i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$		0			0
$207$	−4.00000	−	6.92820i	−0.278019	−	0.481543i
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	17.0000			1.17033			0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000			1.17033			0.585164	+	0.810915i	$0.301030\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$	2.50000	+	4.33013i	0.168168	+	0.291276i
$222$		0			0
$223$	29.0000			1.94198			0.970992	−	0.239113i	$-0.0768565\pi$
$223$	29.0000			1.94198			0.970992	+	0.239113i	$0.0768565\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		0			0
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$		0			0
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	−0.897173	−	0.441679i	$-0.854383\pi$
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	0.831092	+	0.556136i	$0.187717\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.00000	−	6.92820i	0.262049	−	0.453882i	−0.704737	−	0.709468i	$-0.748935\pi$
$233$	4.00000	−	6.92820i	0.262049	−	0.453882i	0.966786	+	0.255586i	$0.0822686\pi$
$234$		0			0
$235$	−3.50000	−	6.06218i	−0.228315	−	0.395453i
$236$		0			0
$237$	−11.0000			−0.714527
$238$		0			0
$239$	13.0000			0.840900			0.420450	−	0.907316i	$-0.361872\pi$
$239$	13.0000			0.840900			0.420450	+	0.907316i	$0.361872\pi$
$240$		0			0
$241$	8.00000	+	13.8564i	0.515325	+	0.892570i	0.999842	+	0.0177875i	$0.00566223\pi$
$241$	8.00000	+	13.8564i	0.515325	+	0.892570i	−0.484516	+	0.874782i	$0.661004\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−15.0000	+	25.9808i	−0.954427	+	1.65312i
$248$		0			0
$249$	2.00000	+	3.46410i	0.126745	+	0.219529i
$250$		0			0
$251$	−4.00000			−0.252478			−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000			−0.252478			−0.126239	+	0.992000i	$0.540291\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$		0			0
$255$	0.500000	+	0.866025i	0.0313112	+	0.0542326i
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$		0			0
$267$	4.00000			0.244796
$268$		0			0
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	0.961817	−	0.273692i	$-0.0882449\pi$
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	−0.717933	+	0.696112i	$0.754912\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	−10.0000	−	17.3205i	−0.600842	−	1.04069i	−0.992694	−	0.120660i	$-0.961499\pi$
$277$	−10.0000	−	17.3205i	−0.600842	−	1.04069i	0.391852	−	0.920028i	$-0.371834\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−13.0000			−0.775515			−0.387757	−	0.921761i	$-0.626750\pi$
$281$	−13.0000			−0.775515			−0.387757	+	0.921761i	$0.626750\pi$
$282$		0			0
$283$	0.500000	+	0.866025i	0.0297219	+	0.0514799i	0.880504	−	0.474039i	$-0.157204\pi$
$283$	0.500000	+	0.866025i	0.0297219	+	0.0514799i	−0.850782	+	0.525519i	$0.823871\pi$
$284$		0			0
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$	1.50000	+	2.59808i	0.0879316	+	0.152302i
$292$		0			0
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$	−14.0000			−0.815112
$296$		0			0
$297$	−2.50000	−	4.33013i	−0.145065	−	0.251259i
$298$		0			0
$299$	−10.0000	+	17.3205i	−0.578315	+	1.00167i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	5.00000	−	8.66025i	0.287242	−	0.497519i
$304$		0			0
$305$	−4.00000	−	6.92820i	−0.229039	−	0.396708i
$306$		0			0
$307$	23.0000			1.31268			0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000			1.31268			0.656340	+	0.754466i	$0.272104\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$		0			0
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	0.596412	−	0.802678i	$-0.296592\pi$
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	−0.993346	+	0.115169i	$0.963259\pi$
$312$		0			0
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	−0.259590	−	0.965719i	$-0.583588\pi$
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	0.966132	−	0.258047i	$-0.0830791\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	1.50000	+	2.59808i	0.0839839	+	0.145464i
$320$		0			0
$321$	18.0000			1.00466
$322$		0			0
$323$	−6.00000			−0.333849
$324$		0			0
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$		0			0
$327$	5.50000	−	9.52628i	0.304151	−	0.526804i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$		0			0
$333$	8.00000	+	13.8564i	0.438397	+	0.759326i
$334$		0			0
$335$	−14.0000			−0.764902
$336$		0			0
$337$	−8.00000			−0.435788			−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000			−0.435788			−0.217894	+	0.975972i	$0.569919\pi$
$338$		0			0
$339$	−8.00000	−	13.8564i	−0.434500	−	0.752577i
$340$		0			0
$341$	1.00000	−	1.73205i	0.0541530	−	0.0937958i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$		0			0
$347$	−4.00000	−	6.92820i	−0.214731	−	0.371925i	0.738458	−	0.674299i	$-0.235554\pi$
$347$	−4.00000	−	6.92820i	−0.214731	−	0.371925i	−0.953189	+	0.302374i	$0.902221\pi$
$348$		0			0
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	25.0000			1.33440
$352$		0			0
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	−0.740951	−	0.671559i	$-0.765625\pi$
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	0.952063	+	0.305903i	$0.0989582\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$		0			0
$363$	−10.0000			−0.524864
$364$		0			0
$365$	10.0000			0.523424
$366$		0			0
$367$	11.5000	+	19.9186i	0.600295	+	1.03974i	0.992776	+	0.119982i	$0.0382835\pi$
$367$	11.5000	+	19.9186i	0.600295	+	1.03974i	−0.392481	+	0.919760i	$0.628383\pi$
$368$		0			0
$369$	−10.0000	+	17.3205i	−0.520579	+	0.901670i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	−0.978507	−	0.206213i	$-0.933886\pi$
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	0.667839	+	0.744306i	$0.267219\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−15.0000			−0.772539
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$	3.00000	+	5.19615i	0.153695	+	0.266207i
$382$		0			0
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$		0			0
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$		0			0
$393$	12.0000			0.605320
$394$		0			0
$395$	−5.50000	−	9.52628i	−0.276735	−	0.479319i
$396$		0			0
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	−0.418634	−	0.908155i	$-0.637491\pi$
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	0.995802	−	0.0915300i	$-0.0291757\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.50000	−	9.52628i	0.274657	−	0.475720i	−0.695392	−	0.718631i	$-0.744769\pi$
$401$	5.50000	−	9.52628i	0.274657	−	0.475720i	0.970049	+	0.242911i	$0.0781024\pi$
$402$		0			0
$403$	5.00000	+	8.66025i	0.249068	+	0.431398i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$	−8.00000	+	13.8564i	−0.394611	+	0.683486i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.00000	+	3.46410i	−0.0981761	+	0.170046i
$416$		0			0
$417$	−8.00000	−	13.8564i	−0.391762	−	0.678551i
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$		0			0
$423$	−7.00000	−	12.1244i	−0.340352	−	0.589506i
$424$		0			0
$425$	−0.500000	+	0.866025i	−0.0242536	+	0.0420084i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.50000	+	4.33013i	−0.120701	+	0.209061i
$430$		0			0
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	0.922981	+	0.384846i	$0.125746\pi$
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	−0.128204	+	0.991748i	$0.540921\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−3.00000			−0.143839
$436$		0			0
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	−0.372265	−	0.928126i	$-0.621419\pi$
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	0.989914	−	0.141672i	$-0.0452479\pi$
$444$		0			0
$445$	2.00000	+	3.46410i	0.0948091	+	0.164214i
$446$		0			0
$447$	−22.0000			−1.04056
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−5.00000	−	8.66025i	−0.235441	−	0.407795i
$452$		0			0
$453$	1.50000	−	2.59808i	0.0704761	−	0.122068i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$		0			0
$459$	2.50000	+	4.33013i	0.116690	+	0.202113i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$		0			0
$465$	1.00000	+	1.73205i	0.0463739	+	0.0803219i
$466$		0			0
$467$	−9.50000	+	16.4545i	−0.439608	+	0.761423i	−0.997659	−	0.0683836i	$-0.978216\pi$
$467$	−9.50000	+	16.4545i	−0.439608	+	0.761423i	0.558052	+	0.829806i	$0.311549\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.00000	−	12.1244i	0.322543	−	0.558661i
$472$		0			0
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$		0			0
$475$	−6.00000			−0.275299
$476$		0			0
$477$	4.00000			0.183147
$478$		0			0
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$		0			0
$481$	20.0000	−	34.6410i	0.911922	−	1.57949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.50000	+	2.59808i	−0.0681115	+	0.117973i
$486$		0			0
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	0.998579	−	0.0532853i	$-0.0169693\pi$
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	−0.545436	+	0.838152i	$0.683636\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$		0			0
$491$	−15.0000			−0.676941			−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000			−0.676941			−0.338470	+	0.940977i	$0.609909\pi$
$492$		0			0
$493$	−1.50000	−	2.59808i	−0.0675566	−	0.117011i
$494$		0			0
$495$	1.00000	−	1.73205i	0.0449467	−	0.0778499i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$		0			0
$501$	−10.5000	−	18.1865i	−0.469105	−	0.812514i
$502$		0			0
$503$	−9.00000			−0.401290			−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000			−0.401290			−0.200645	+	0.979664i	$0.564304\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−15.0000	+	25.9808i	−0.662266	+	1.14708i
$514$		0			0
$515$	−3.50000	−	6.06218i	−0.154228	−	0.267131i
$516$		0			0
$517$	7.00000			0.307860
$518$		0			0
$519$	21.0000			0.921798
$520$		0			0
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$		0			0
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.00000	+	1.73205i	−0.0435607	+	0.0754493i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−28.0000			−1.21510
$532$		0			0
$533$	50.0000			2.16574
$534$		0			0
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	10.0000	−	17.3205i	0.431532	−	0.747435i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$		0			0
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$		0			0
$545$	11.0000			0.471188
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$		0			0
$549$	−8.00000	−	13.8564i	−0.341432	−	0.591377i
$550$		0			0
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.00000	−	6.92820i	0.169791	−	0.294086i
$556$		0			0
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$		0			0
$561$	−1.00000			−0.0422200
$562$		0			0
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$	8.00000	−	13.8564i	0.336563	−	0.582943i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$		0			0
$573$	3.00000			0.125327
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$		0			0
$579$	6.00000	−	10.3923i	0.249351	−	0.431889i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$		0			0
$585$	5.00000	+	8.66025i	0.206725	+	0.358057i
$586$		0			0
$587$	−44.0000			−1.81607			−0.908037	−	0.418890i	$-0.862419\pi$
$587$	−44.0000			−1.81607			−0.908037	+	0.418890i	$0.862419\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$		0			0
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$		0			0
$593$	−11.5000	+	19.9186i	−0.472248	+	0.817958i	−0.999496	−	0.0317536i	$-0.989891\pi$
$593$	−11.5000	+	19.9186i	−0.472248	+	0.817958i	0.527247	+	0.849712i	$0.323224\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.0000	−	19.0526i	0.450200	−	0.779769i
$598$		0			0
$599$	−17.5000	−	30.3109i	−0.715031	−	1.23847i	−0.962948	−	0.269688i	$-0.913079\pi$
$599$	−17.5000	−	30.3109i	−0.715031	−	1.23847i	0.247917	−	0.968781i	$-0.420254\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	−28.0000			−1.14025
$604$		0			0
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	14.5000	−	25.1147i	0.588537	−	1.01938i	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	14.5000	−	25.1147i	0.588537	−	1.01938i	0.994424	−	0.105453i	$-0.0336291\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.5000	+	30.3109i	−0.707974	+	1.22625i
$612$		0			0
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	0.999574	+	0.0291886i	$0.00929235\pi$
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	−0.474509	+	0.880251i	$0.657374\pi$
$614$		0			0
$615$	10.0000			0.403239
$616$		0			0
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$		0			0
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$	−10.0000	+	17.3205i	−0.401286	+	0.695048i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$		0			0
$629$	8.00000			0.318981
$630$		0			0
$631$	31.0000			1.23409			0.617045	−	0.786928i	$-0.288330\pi$
$631$	31.0000			1.23409			0.617045	+	0.786928i	$0.288330\pi$
$632$		0			0
$633$	−8.50000	−	14.7224i	−0.337845	−	0.585164i
$634$		0			0
$635$	−3.00000	+	5.19615i	−0.119051	+	0.206203i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	−15.0000			−0.591542			−0.295771	−	0.955259i	$-0.595577\pi$
$643$	−15.0000			−0.591542			−0.295771	+	0.955259i	$0.595577\pi$
$644$		0			0
$645$	2.00000			0.0787499
$646$		0			0
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	0.998246	+	0.0592060i	$0.0188569\pi$
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	−0.447849	+	0.894109i	$0.647810\pi$
$648$		0			0
$649$	7.00000	−	12.1244i	0.274774	−	0.475923i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$		0			0
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$		0			0
$657$	20.0000			0.780274
$658$		0			0
$659$	−37.0000			−1.44132			−0.720658	−	0.693291i	$-0.756160\pi$
$659$	−37.0000			−1.44132			−0.720658	+	0.693291i	$0.756160\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$		0			0
$663$	2.50000	−	4.33013i	0.0970920	−	0.168168i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.00000	−	10.3923i	0.232321	−	0.402392i
$668$		0			0
$669$	−14.5000	−	25.1147i	−0.560602	−	0.970992i
$670$		0			0
$671$	8.00000			0.308837
$672$		0			0
$673$	4.00000			0.154189			0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000			0.154189			0.0770943	+	0.997024i	$0.475436\pi$
$674$		0			0
$675$	2.50000	+	4.33013i	0.0962250	+	0.166667i
$676$		0			0
$677$	−15.5000	+	26.8468i	−0.595713	+	1.03181i	0.397732	+	0.917501i	$0.369797\pi$
$677$	−15.5000	+	26.8468i	−0.595713	+	1.03181i	−0.993446	+	0.114304i	$0.963536\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−4.50000	+	7.79423i	−0.172440	+	0.298675i
$682$		0			0
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.801945	−	0.597398i	$-0.796201\pi$
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.116390	−	0.993204i	$-0.537132\pi$
$684$		0			0
$685$	−16.0000			−0.611329
$686$		0			0
$687$	2.00000			0.0763048
$688$		0			0
$689$	−5.00000	−	8.66025i	−0.190485	−	0.329929i
$690$		0			0
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	0.466691	+	0.884420i	$0.345446\pi$
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	−0.999276	+	0.0380440i	$0.987887\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$		0			0
$697$	5.00000	+	8.66025i	0.189389	+	0.328031i
$698$		0			0
$699$	−8.00000			−0.302588
$700$		0			0
$701$	−29.0000			−1.09531			−0.547657	−	0.836703i	$-0.684480\pi$
$701$	−29.0000			−1.09531			−0.547657	+	0.836703i	$0.684480\pi$
$702$		0			0
$703$	24.0000	+	41.5692i	0.905177	+	1.56781i
$704$		0			0
$705$	−3.50000	+	6.06218i	−0.131818	+	0.228315i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−13.5000	+	23.3827i	−0.507003	+	0.878155i	0.492964	+	0.870050i	$0.335913\pi$
$709$	−13.5000	+	23.3827i	−0.507003	+	0.878155i	−0.999967	+	0.00810550i	$0.997420\pi$
$710$		0			0
$711$	−11.0000	−	19.0526i	−0.412532	−	0.714527i
$712$		0			0
$713$	−8.00000			−0.299602
$714$		0			0
$715$	−5.00000			−0.186989
$716$		0			0
$717$	−6.50000	−	11.2583i	−0.242747	−	0.420450i
$718$		0			0
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	−0.955947	−	0.293538i	$-0.905167\pi$
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	0.732185	+	0.681106i	$0.238501\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8.00000	−	13.8564i	0.297523	−	0.515325i
$724$		0			0
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$		0			0
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$		0			0
$733$	16.5000	−	28.5788i	0.609441	−	1.05558i	−0.381891	−	0.924207i	$-0.624727\pi$
$733$	16.5000	−	28.5788i	0.609441	−	1.05558i	0.991333	−	0.131376i	$-0.0419396\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.00000	−	12.1244i	0.257848	−	0.446606i
$738$		0			0
$739$	−1.50000	−	2.59808i	−0.0551784	−	0.0955718i	0.837117	−	0.547024i	$-0.184239\pi$
$739$	−1.50000	−	2.59808i	−0.0551784	−	0.0955718i	−0.892295	+	0.451452i	$0.850906\pi$
$740$		0			0
$741$	30.0000			1.10208
$742$		0			0
$743$	−18.0000			−0.660356			−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000			−0.660356			−0.330178	+	0.943919i	$0.607109\pi$
$744$		0			0
$745$	−11.0000	−	19.0526i	−0.403009	−	0.698032i
$746$		0			0
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	−0.959906	−	0.280321i	$-0.909559\pi$
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	0.722718	+	0.691143i	$0.242893\pi$
$752$		0			0
$753$	2.00000	+	3.46410i	0.0728841	+	0.126239i
$754$		0			0
$755$	3.00000			0.109181
$756$		0			0
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$		0			0
$759$	−2.00000	−	3.46410i	−0.0725954	−	0.125739i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$		0			0
$767$	35.0000	+	60.6218i	1.26378	+	2.18893i
$768$		0			0
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$		0			0
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−30.0000	+	51.9615i	−1.07486	+	1.86171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−15.0000			−0.536056
$784$		0			0
$785$	14.0000			0.499681
$786$		0			0
$787$	1.50000	+	2.59808i	0.0534692	+	0.0926114i	0.891521	−	0.452979i	$-0.149639\pi$
$787$	1.50000	+	2.59808i	0.0534692	+	0.0926114i	−0.838052	+	0.545590i	$0.816305\pi$
$788$		0			0
$789$	−9.00000	+	15.5885i	−0.320408	+	0.554964i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−20.0000	+	34.6410i	−0.710221	+	1.23014i
$794$		0			0
$795$	−1.00000	−	1.73205i	−0.0354663	−	0.0614295i
$796$		0			0
$797$	37.0000			1.31061			0.655304	−	0.755366i	$-0.272541\pi$
$797$	37.0000			1.31061			0.655304	+	0.755366i	$0.272541\pi$
$798$		0			0
$799$	−7.00000			−0.247642
$800$		0			0
$801$	4.00000	+	6.92820i	0.141333	+	0.244796i
$802$		0			0
$803$	−5.00000	+	8.66025i	−0.176446	+	0.305614i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.00000	−	6.92820i	0.140807	−	0.243884i
$808$		0			0
$809$	−2.50000	−	4.33013i	−0.0878953	−	0.152239i	0.818726	−	0.574184i	$-0.194681\pi$
$809$	−2.50000	−	4.33013i	−0.0878953	−	0.152239i	−0.906621	+	0.421945i	$0.861347\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$		0			0
$817$	−6.00000	+	10.3923i	−0.209913	+	0.363581i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.50000	−	2.59808i	0.0523504	−	0.0906735i	−0.838663	−	0.544651i	$-0.816662\pi$
$821$	1.50000	−	2.59808i	0.0523504	−	0.0906735i	0.891013	+	0.453978i	$0.149995\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$		0			0
$825$	−1.00000			−0.0348155
$826$		0			0
$827$	32.0000			1.11275			0.556375	−	0.830932i	$-0.312192\pi$
$827$	32.0000			1.11275			0.556375	+	0.830932i	$0.312192\pi$
$828$		0			0
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	0.121560	−	0.992584i	$-0.461210\pi$
$830$		0			0
$831$	−10.0000	+	17.3205i	−0.346896	+	0.600842i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	10.5000	−	18.1865i	0.363367	−	0.629371i
$836$		0			0
$837$	5.00000	+	8.66025i	0.172825	+	0.299342i
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	6.50000	+	11.2583i	0.223872	+	0.387757i
$844$		0			0
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.500000	−	0.866025i	0.0171600	−	0.0297219i
$850$		0			0
$851$	16.0000	+	27.7128i	0.548473	+	0.949983i
$852$		0			0
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	−26.0000	+	45.0333i	−0.887109	+	1.53652i	−0.0438309	+	0.999039i	$0.513956\pi$
$859$	−26.0000	+	45.0333i	−0.887109	+	1.53652i	−0.843278	+	0.537478i	$0.819377\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.0000	−	25.9808i	0.510606	−	0.884395i	−0.489319	−	0.872105i	$-0.662754\pi$
$863$	15.0000	−	25.9808i	0.510606	−	0.884395i	0.999924	−	0.0122903i	$-0.00391222\pi$
$864$		0			0
$865$	10.5000	+	18.1865i	0.357011	+	0.618361i
$866$		0			0
$867$	−16.0000			−0.543388
$868$		0			0
$869$	11.0000			0.373149
$870$		0			0
$871$	35.0000	+	60.6218i	1.18593	+	2.05409i
$872$		0			0
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	27.0000	−	46.7654i	0.911725	−	1.57915i	0.100099	−	0.994977i	$-0.468084\pi$
$877$	27.0000	−	46.7654i	0.911725	−	1.57915i	0.811626	−	0.584177i	$-0.198583\pi$
$878$		0			0
$879$	−4.50000	−	7.79423i	−0.151781	−	0.262893i
$880$		0			0
$881$	16.0000			0.539054			0.269527	−	0.962993i	$-0.413133\pi$
$881$	16.0000			0.539054			0.269527	+	0.962993i	$0.413133\pi$
$882$		0			0
$883$	−56.0000			−1.88455			−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000			−1.88455			−0.942275	+	0.334840i	$0.891318\pi$
$884$		0			0
$885$	7.00000	+	12.1244i	0.235302	+	0.407556i
$886$		0			0
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	−0.925332	−	0.379157i	$-0.876214\pi$
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	0.791026	+	0.611783i	$0.209547\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$		0			0
$893$	−21.0000	−	36.3731i	−0.702738	−	1.21718i
$894$		0			0
$895$	20.0000			0.668526
$896$		0			0
$897$	20.0000			0.667781
$898$		0			0
$899$	−3.00000	−	5.19615i	−0.100056	−	0.173301i
$900$		0			0
$901$	1.00000	−	1.73205i	0.0333148	−	0.0577030i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$		0			0
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	0.702094	−	0.712084i	$-0.252248\pi$
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	−0.967730	+	0.251990i	$0.918915\pi$
$908$		0			0
$909$	20.0000			0.663358
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$		0			0
$915$	−4.00000	+	6.92820i	−0.132236	+	0.229039i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	0.521380	+	0.853325i	$0.325417\pi$
$920$		0			0
$921$	−11.5000	−	19.9186i	−0.378938	−	0.656340i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	8.00000			0.263038
$926$		0			0
$927$	−7.00000	−	12.1244i	−0.229910	−	0.398216i
$928$		0			0
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−7.00000	+	12.1244i	−0.229170	+	0.396934i
$934$		0			0
$935$	−0.500000	−	0.866025i	−0.0163517	−	0.0283221i
$936$		0			0
$937$	9.00000			0.294017			0.147009	−	0.989135i	$-0.453036\pi$
$937$	9.00000			0.294017			0.147009	+	0.989135i	$0.453036\pi$
$938$		0			0
$939$	−25.0000			−0.815844
$940$		0			0
$941$	−20.0000	−	34.6410i	−0.651981	−	1.12926i	−0.982641	−	0.185515i	$-0.940605\pi$
$941$	−20.0000	−	34.6410i	−0.651981	−	1.12926i	0.330660	−	0.943750i	$-0.392729\pi$
$942$		0			0
$943$	−20.0000	+	34.6410i	−0.651290	+	1.12807i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.0000	−	46.7654i	0.877382	−	1.51967i	0.0231788	−	0.999731i	$-0.492621\pi$
$947$	27.0000	−	46.7654i	0.877382	−	1.51967i	0.854203	−	0.519939i	$-0.174045\pi$
$948$		0			0
$949$	−25.0000	−	43.3013i	−0.811534	−	1.40562i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	50.0000			1.61966			0.809829	−	0.586665i	$-0.199560\pi$
$953$	50.0000			1.61966			0.809829	+	0.586665i	$0.199560\pi$
$954$		0			0
$955$	1.50000	+	2.59808i	0.0485389	+	0.0840718i
$956$		0			0
$957$	1.50000	−	2.59808i	0.0484881	−	0.0839839i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$		0			0
$965$	12.0000			0.386294
$966$		0			0
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$		0			0
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$		0			0
$971$	−1.00000	+	1.73205i	−0.0320915	+	0.0555842i	−0.881625	−	0.471950i	$-0.843550\pi$
$971$	−1.00000	+	1.73205i	−0.0320915	+	0.0555842i	0.849534	+	0.527535i	$0.176883\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.50000	−	4.33013i	0.0800641	−	0.138675i
$976$		0			0
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	0.868227	+	0.496167i	$0.165259\pi$
$977$	27.0000	+	46.7654i	0.863807	+	1.49616i	−0.00442082	+	0.999990i	$0.501407\pi$
$978$		0			0
$979$	−4.00000			−0.127841
$980$		0			0
$981$	22.0000			0.702406
$982$		0			0
$983$	26.5000	+	45.8993i	0.845219	+	1.46396i	0.885431	+	0.464771i	$0.153863\pi$
$983$	26.5000	+	45.8993i	0.845219	+	1.46396i	−0.0402124	+	0.999191i	$0.512803\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$		0			0
$991$	−6.00000	−	10.3923i	−0.190596	−	0.330122i	0.754852	−	0.655895i	$-0.227709\pi$
$991$	−6.00000	−	10.3923i	−0.190596	−	0.330122i	−0.945448	+	0.325773i	$0.894375\pi$
$992$		0			0
$993$	20.0000			0.634681
$994$		0			0
$995$	22.0000			0.697447
$996$		0			0
$997$	1.50000	+	2.59808i	0.0475055	+	0.0822819i	0.888800	−	0.458295i	$-0.151540\pi$
$997$	1.50000	+	2.59808i	0.0475055	+	0.0822819i	−0.841295	+	0.540576i	$0.818206\pi$
$998$		0			0
$999$	20.0000	−	34.6410i	0.632772	−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.i.e.961.1		2
7.2	even	3		980.2.a.f.1.1	yes	1
7.3	odd	6		980.2.i.g.361.1		2
7.4	even	3	inner	980.2.i.e.361.1		2
7.5	odd	6		980.2.a.d.1.1	✓	1
7.6	odd	2		980.2.i.g.961.1		2
21.2	odd	6		8820.2.a.v.1.1		1
21.5	even	6		8820.2.a.i.1.1		1
28.19	even	6		3920.2.a.z.1.1		1
28.23	odd	6		3920.2.a.n.1.1		1
35.2	odd	12		4900.2.e.k.2549.1		2
35.9	even	6		4900.2.a.h.1.1		1
35.12	even	12		4900.2.e.j.2549.2		2
35.19	odd	6		4900.2.a.o.1.1		1
35.23	odd	12		4900.2.e.k.2549.2		2
35.33	even	12		4900.2.e.j.2549.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.a.d.1.1	✓	1	7.5	odd	6
980.2.a.f.1.1	yes	1	7.2	even	3
980.2.i.e.361.1		2	7.4	even	3	inner
980.2.i.e.961.1		2	1.1	even	1	trivial
980.2.i.g.361.1		2	7.3	odd	6
980.2.i.g.961.1		2	7.6	odd	2
3920.2.a.n.1.1		1	28.23	odd	6
3920.2.a.z.1.1		1	28.19	even	6
4900.2.a.h.1.1		1	35.9	even	6
4900.2.a.o.1.1		1	35.19	odd	6
4900.2.e.j.2549.1		2	35.33	even	12
4900.2.e.j.2549.2		2	35.12	even	12
4900.2.e.k.2549.1		2	35.2	odd	12
4900.2.e.k.2549.2		2	35.23	odd	12
8820.2.a.i.1.1		1	21.5	even	6
8820.2.a.v.1.1		1	21.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} -5.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{17} +(3.00000 - 5.19615i) q^{19} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{27} +3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{33} +(-4.00000 + 6.92820i) q^{37} +(2.50000 + 4.33013i) q^{39} -10.0000 q^{41} -2.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(3.50000 - 6.06218i) q^{47} +(-0.500000 + 0.866025i) q^{51} +(1.00000 + 1.73205i) q^{53} +1.00000 q^{55} -6.00000 q^{57} +(-7.00000 - 12.1244i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-2.50000 + 4.33013i) q^{65} +(-7.00000 - 12.1244i) q^{67} -4.00000 q^{69} +(5.00000 + 8.66025i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} -1.00000 q^{85} +(-1.50000 - 2.59808i) q^{87} +(-2.00000 + 3.46410i) q^{89} +(-1.00000 + 1.73205i) q^{93} +(-3.00000 - 5.19615i) q^{95} -3.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + q^{5} + 2 q^{9} + q^{11} - 10 q^{13} - 2 q^{15} - q^{17} + 6 q^{19} + 4 q^{23} - q^{25} - 10 q^{27} + 6 q^{29} - 2 q^{31} + q^{33} - 8 q^{37} + 5 q^{39} - 20 q^{41} - 4 q^{43} - 2 q^{45}+ \cdots + 4 q^{99}+O(q^{100}) \) 2 * q - q^3 + q^5 + 2 * q^9 + q^11 - 10 * q^13 - 2 * q^15 - q^17 + 6 * q^19 + 4 * q^23 - q^25 - 10 * q^27 + 6 * q^29 - 2 * q^31 + q^33 - 8 * q^37 + 5 * q^39 - 20 * q^41 - 4 * q^43 - 2 * q^45 + 7 * q^47 - q^51 + 2 * q^53 + 2 * q^55 - 12 * q^57 - 14 * q^59 + 8 * q^61 - 5 * q^65 - 14 * q^67 - 8 * q^69 + 10 * q^73 - q^75 + 11 * q^79 - q^81 - 8 * q^83 - 2 * q^85 - 3 * q^87 - 4 * q^89 - 2 * q^93 - 6 * q^95 - 6 * q^97 + 4 * q^99

Introduction

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