LMFDB - Embedded newform 980.2.i.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(361,980)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: 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:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	980.361
Dual form			980.2.i.c.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{13} +2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{39} -6.00000 q^{41} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.00000 - 10.3923i) q^{51} +(3.00000 - 5.19615i) q^{53} +8.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-1.00000 + 1.73205i) q^{67} +12.0000 q^{69} -12.0000 q^{71} +(1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-4.00000 - 6.92820i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{83} +6.00000 q^{85} +(-6.00000 + 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-2.00000 + 3.46410i) q^{95} -2.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - q^{5} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - q^5 - q^9	$ 2 q - 2 q^{3} - q^{5} - q^{9} - 4 q^{13} + 4 q^{15} - 6 q^{17} - 4 q^{19} - 6 q^{23} - q^{25} - 8 q^{27} + 12 q^{29} - 4 q^{31} - 2 q^{37} + 4 q^{39} - 12 q^{41} - 20 q^{43} - q^{45} - 6 q^{47} - 12 q^{51} + 6 q^{53} + 16 q^{57} + 12 q^{59} + 2 q^{61} + 2 q^{65} - 2 q^{67} + 24 q^{69} - 24 q^{71} + 2 q^{73} - 2 q^{75} - 8 q^{79} + 11 q^{81} - 12 q^{83} + 12 q^{85} - 12 q^{87} - 6 q^{89} - 8 q^{93} - 4 q^{95} - 4 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - q^5 - q^9 - 4 * q^13 + 4 * q^15 - 6 * q^17 - 4 * q^19 - 6 * q^23 - q^25 - 8 * q^27 + 12 * q^29 - 4 * q^31 - 2 * q^37 + 4 * q^39 - 12 * q^41 - 20 * q^43 - q^45 - 6 * q^47 - 12 * q^51 + 6 * q^53 + 16 * q^57 + 12 * q^59 + 2 * q^61 + 2 * q^65 - 2 * q^67 + 24 * q^69 - 24 * q^71 + 2 * q^73 - 2 * q^75 - 8 * q^79 + 11 * q^81 - 12 * q^83 + 12 * q^85 - 12 * q^87 - 6 * q^89 - 8 * q^93 - 4 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		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
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6.00000	−	10.3923i	−0.840168	−	1.45521i
$52$		0			0
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	8.00000			1.05963
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$	12.0000			1.44463
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$		0			0
$87$	−6.00000	+	10.3923i	−0.643268	+	1.11417i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$		0			0
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$		0			0
$123$	6.00000	−	10.3923i	0.541002	−	0.937043i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$	10.0000	−	17.3205i	0.880451	−	1.52499i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$		0			0
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.0242497	+	0.999706i	$0.507720\pi$
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.853646	+	0.520854i	$0.825614\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.0000			−1.39288			−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000			−1.39288			−0.696441	+	0.717614i	$0.745234\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.0000	+	20.7846i	0.901975	+	1.56227i
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		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
$183$	−4.00000			−0.295689
$184$		0			0
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.162488	+	0.986710i	$0.551952\pi$
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.773272	+	0.634074i	$0.781381\pi$
$194$		0			0
$195$	−4.00000			−0.286446
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		0			0
$201$	−2.00000	−	3.46410i	−0.141069	−	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$		0			0
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	12.0000	−	20.7846i	0.822226	−	1.42414i
$214$		0			0
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	10.0000			0.669650			0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000			0.669650			0.334825	+	0.942280i	$0.391323\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$		0			0
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−6.00000	+	10.3923i	−0.375735	+	0.650791i
$256$		0			0
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		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	−0.442943	−	0.896550i	$-0.646065\pi$
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	0.997906	−	0.0646755i	$-0.0206012\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	12.0000			0.734388
$268$		0			0
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	−4.00000	−	6.92820i	−0.236940	−	0.410391i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	2.00000	−	3.46410i	0.117242	−	0.203069i
$292$		0			0
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$		0			0
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	−28.0000			−1.59286
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−12.0000			−0.669775
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$		0			0
$327$	−2.00000	−	3.46410i	−0.110600	−	0.191565i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$		0			0
$335$	2.00000			0.109272
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−6.00000	−	10.3923i	−0.323029	−	0.559503i
$346$		0			0
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$	−22.0000			−1.15470
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	0.421933	+	0.906627i	$0.361352\pi$
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	−0.996129	+	0.0879086i	$0.971982\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$		0			0
$375$	−1.00000	+	1.73205i	−0.0516398	+	0.0894427i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		0			0
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.00000	+	8.66025i	0.254164	+	0.440225i
$388$		0			0
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	0.890028	−	0.455905i	$-0.150684\pi$
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	−0.839840	+	0.542834i	$0.817351\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$	−11.0000			−0.546594
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−17.0000	+	29.4449i	−0.840596	+	1.45595i	0.0487958	+	0.998809i	$0.484462\pi$
$409$	−17.0000	+	29.4449i	−0.840596	+	1.45595i	−0.889392	+	0.457146i	$0.848872\pi$
$410$		0			0
$411$	−18.0000	−	31.1769i	−0.887875	−	1.53784i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$		0			0
$417$	−4.00000	+	6.92820i	−0.195881	+	0.339276i
$418$		0			0
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.00201168	+	0.999998i	$0.500640\pi$
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.865018	+	0.501741i	$0.832693\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	12.0000			0.575356
$436$		0			0
$437$	−12.0000	+	20.7846i	−0.574038	+	0.994263i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$		0			0
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$		0			0
$447$	−12.0000			−0.567581
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−20.0000	−	34.6410i	−0.939682	−	1.62758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	0.383437	−	0.923567i	$-0.374740\pi$
$458$		0			0
$459$	12.0000	−	20.7846i	0.560112	−	0.970143i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$		0			0
$465$	−4.00000	+	6.92820i	−0.185496	+	0.321288i
$466$		0			0
$467$	−15.0000	−	25.9808i	−0.694117	−	1.20225i	−0.970477	−	0.241192i	$-0.922462\pi$
$467$	−15.0000	−	25.9808i	−0.694117	−	1.20225i	0.276360	−	0.961054i	$-0.410872\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−22.0000	−	38.1051i	−1.01371	−	1.75579i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	0.405266	+	0.914199i	$0.367179\pi$
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	−0.994352	+	0.106129i	$0.966154\pi$
$488$		0			0
$489$	−20.0000			−0.904431
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$		0			0
$501$	18.0000	−	31.1769i	0.804181	−	1.39288i
$502$		0			0
$503$	18.0000			0.802580			0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	9.00000	−	15.5885i	0.399704	−	0.692308i
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	8.00000	+	13.8564i	0.353209	+	0.611775i
$514$		0			0
$515$	7.00000	−	12.1244i	0.308457	−	0.534263i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$		0			0
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$		0			0
$537$	12.0000	+	20.7846i	0.517838	+	0.896922i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	0.675399	−	0.737453i	$-0.263972\pi$
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	−0.976352	+	0.216186i	$0.930638\pi$
$542$		0			0
$543$	−10.0000	+	17.3205i	−0.429141	+	0.743294i
$544$		0			0
$545$	2.00000			0.0856706
$546$		0			0
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$		0			0
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$		0			0
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$		0			0
$559$	20.0000			0.845910
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	−0.937503	−	0.347977i	$-0.886869\pi$
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	0.770108	+	0.637913i	$0.220202\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	6.00000			0.250217
$576$		0			0
$577$	−11.0000	+	19.0526i	−0.457936	+	0.793168i	−0.998852	−	0.0479084i	$-0.984744\pi$
$577$	−11.0000	+	19.0526i	−0.457936	+	0.793168i	0.540916	+	0.841077i	$0.318078\pi$
$578$		0			0
$579$	−26.0000	−	45.0333i	−1.08052	−	1.87152i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$		0			0
$587$	6.00000			0.247647			0.123823	−	0.992304i	$-0.460484\pi$
$587$	6.00000			0.247647			0.123823	+	0.992304i	$0.460484\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$		0			0
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	0.989501	−	0.144528i	$-0.0461663\pi$
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	−0.619915	+	0.784669i	$0.712833\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.00000	+	13.8564i	0.327418	+	0.567105i
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$		0			0
$605$	5.50000	−	9.52628i	0.223607	−	0.387298i
$606$		0			0
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	0.551678	−	0.834058i	$-0.313988\pi$
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	−0.998154	+	0.0607380i	$0.980655\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$		0			0
$615$	−12.0000			−0.483887
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$		0			0
$621$	12.0000	+	20.7846i	0.481543	+	0.834058i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$		0			0
$633$	16.0000	−	27.7128i	0.635943	−	1.10149i
$634$		0			0
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$		0			0
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$	−20.0000			−0.787499
$646$		0			0
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	−0.0758684	−	0.997118i	$-0.524173\pi$
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	0.901464	−	0.432855i	$-0.142494\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.00000			−0.0780274
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$		0			0
$663$	12.0000	+	20.7846i	0.466041	+	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−18.0000	−	31.1769i	−0.696963	−	1.20717i
$668$		0			0
$669$	−10.0000	+	17.3205i	−0.386622	+	0.669650i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−46.0000			−1.77317			−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000			−1.77317			−0.886585	+	0.462566i	$0.846929\pi$
$674$		0			0
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$		0			0
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$		0			0
$683$	21.0000	−	36.3731i	0.803543	−	1.39178i	−0.113728	−	0.993512i	$-0.536279\pi$
$683$	21.0000	−	36.3731i	0.803543	−	1.39178i	0.917270	−	0.398265i	$-0.130387\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$		0			0
$687$	−28.0000			−1.06827
$688$		0			0
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$		0			0
$699$	−12.0000			−0.453882
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$		0			0
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.0000	−	41.5692i	0.896296	−	1.55243i
$718$		0			0
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	0.550700	−	0.834703i	$-0.314361\pi$
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	−0.998224	+	0.0595683i	$0.981028\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	14.0000	+	24.2487i	0.520666	+	0.901819i
$724$		0			0
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	46.0000			1.70605			0.853023	−	0.521874i	$-0.174767\pi$
$727$	46.0000			1.70605			0.853023	+	0.521874i	$0.174767\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	30.0000	−	51.9615i	1.10959	−	1.92187i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$		0			0
$741$	−16.0000			−0.587775
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		0			0
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.0000			0.727875
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$		0			0
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	12.0000			0.432169
$772$		0			0
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	0.459418	+	0.888220i	$0.348058\pi$
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	−0.998930	+	0.0462427i	$0.985275\pi$
$774$		0			0
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−24.0000			−0.857690
$784$		0			0
$785$	22.0000			0.785214
$786$		0			0
$787$	13.0000	−	22.5167i	0.463400	−	0.802632i	−0.535728	−	0.844391i	$-0.679963\pi$
$787$	13.0000	−	22.5167i	0.463400	−	0.802632i	0.999128	+	0.0417585i	$0.0132960\pi$
$788$		0			0
$789$	18.0000	+	31.1769i	0.640817	+	1.10993i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.00000	−	3.46410i	−0.0710221	−	0.123014i
$794$		0			0
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$		0			0
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	18.0000	+	31.1769i	0.633630	+	1.09748i
$808$		0			0
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$		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
$813$	−40.0000			−1.40286
$814$		0			0
$815$	5.00000	−	8.66025i	0.175142	−	0.303355i
$816$		0			0
$817$	20.0000	+	34.6410i	0.699711	+	1.21194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.761056	+	0.648686i	$0.224681\pi$
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.181250	+	0.983437i	$0.441986\pi$
$822$		0			0
$823$	−19.0000	+	32.9090i	−0.662298	+	1.14713i	0.317712	+	0.948187i	$0.397086\pi$
$823$	−19.0000	+	32.9090i	−0.662298	+	1.14713i	−0.980010	+	0.198947i	$0.936248\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$		0			0
$831$	−26.0000	−	45.0333i	−0.901930	−	1.56219i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$		0			0
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$		0			0
$839$	48.0000			1.65714			0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000			1.65714			0.828572	+	0.559883i	$0.189154\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−6.00000	+	10.3923i	−0.206651	+	0.357930i
$844$		0			0
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	−50.0000			−1.71197			−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000			−1.71197			−0.855984	+	0.517003i	$0.827048\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	0.810437	−	0.585826i	$-0.199230\pi$
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	−0.912558	+	0.408946i	$0.865896\pi$
$864$		0			0
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$		0			0
$867$	38.0000			1.29055
$868$		0			0
$869$		0			0
$870$		0			0
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$		0			0
$873$	1.00000	+	1.73205i	0.0338449	+	0.0586210i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.0000	−	22.5167i	−0.438979	−	0.760334i	0.558632	−	0.829416i	$-0.311326\pi$
$877$	−13.0000	−	22.5167i	−0.438979	−	0.760334i	−0.997611	+	0.0690819i	$0.977993\pi$
$878$		0			0
$879$	−30.0000	+	51.9615i	−1.01187	+	1.75262i
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	14.0000			0.471138			0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000			0.471138			0.235569	+	0.971858i	$0.424305\pi$
$884$		0			0
$885$	12.0000	−	20.7846i	0.403376	−	0.698667i
$886$		0			0
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$	−24.0000			−0.801337
$898$		0			0
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.00000	−	8.66025i	−0.166206	−	0.287877i
$906$		0			0
$907$	23.0000	−	39.8372i	0.763702	−	1.32277i	−0.177227	−	0.984170i	$-0.556713\pi$
$907$	23.0000	−	39.8372i	0.763702	−	1.32277i	0.940930	−	0.338602i	$-0.109954\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	2.00000	+	3.46410i	0.0661180	+	0.114520i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$	2.00000			0.0657596
$926$		0			0
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$		0			0
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	44.0000			1.43589
$940$		0			0
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	6.00000	−	10.3923i	0.194155	−	0.336287i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	3.00000	−	5.19615i	0.0966736	−	0.167444i
$964$		0			0
$965$	26.0000			0.836970
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$	−24.0000	+	41.5692i	−0.770991	+	1.33540i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.00000	+	3.46410i	0.0640513	+	0.110940i
$976$		0			0
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	−0.973106	−	0.230360i	$-0.926010\pi$
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	0.686050	+	0.727554i	$0.259343\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30.0000	+	51.9615i	0.953945	+	1.65228i
$990$		0			0
$991$	2.00000	−	3.46410i	0.0635321	−	0.110041i	−0.832510	−	0.554010i	$-0.813097\pi$
$991$	2.00000	−	3.46410i	0.0635321	−	0.110041i	0.896042	+	0.443969i	$0.146430\pi$
$992$		0			0
$993$	16.0000			0.507745
$994$		0			0
$995$	−8.00000			−0.253617
$996$		0			0
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$		0			0
$999$	4.00000	+	6.92820i	0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.i.c.361.1		2
7.2	even	3	inner	980.2.i.c.961.1		2
7.3	odd	6		20.2.a.a.1.1	✓	1
7.4	even	3		980.2.a.h.1.1		1
7.5	odd	6		980.2.i.i.961.1		2
7.6	odd	2		980.2.i.i.361.1		2
21.11	odd	6		8820.2.a.g.1.1		1
21.17	even	6		180.2.a.a.1.1		1
28.3	even	6		80.2.a.b.1.1		1
28.11	odd	6		3920.2.a.h.1.1		1
35.3	even	12		100.2.c.a.49.1		2
35.4	even	6		4900.2.a.e.1.1		1
35.17	even	12		100.2.c.a.49.2		2
35.18	odd	12		4900.2.e.f.2549.2		2
35.24	odd	6		100.2.a.a.1.1		1
35.32	odd	12		4900.2.e.f.2549.1		2
56.3	even	6		320.2.a.a.1.1		1
56.45	odd	6		320.2.a.f.1.1		1
63.31	odd	6		1620.2.i.h.541.1		2
63.38	even	6		1620.2.i.b.1081.1		2
63.52	odd	6		1620.2.i.h.1081.1		2
63.59	even	6		1620.2.i.b.541.1		2
77.10	even	6		2420.2.a.a.1.1		1
84.59	odd	6		720.2.a.h.1.1		1
91.31	even	12		3380.2.f.b.3041.2		2
91.38	odd	6		3380.2.a.c.1.1		1
91.73	even	12		3380.2.f.b.3041.1		2
105.17	odd	12		900.2.d.c.649.2		2
105.38	odd	12		900.2.d.c.649.1		2
105.59	even	6		900.2.a.b.1.1		1
112.3	even	12		1280.2.d.g.641.2		2
112.45	odd	12		1280.2.d.c.641.1		2
112.59	even	12		1280.2.d.g.641.1		2
112.101	odd	12		1280.2.d.c.641.2		2
119.38	odd	12		5780.2.c.a.5201.2		2
119.101	odd	6		5780.2.a.f.1.1		1
119.115	odd	12		5780.2.c.a.5201.1		2
133.94	even	6		7220.2.a.f.1.1		1
140.3	odd	12		400.2.c.b.49.2		2
140.59	even	6		400.2.a.c.1.1		1
140.87	odd	12		400.2.c.b.49.1		2
168.59	odd	6		2880.2.a.f.1.1		1
168.101	even	6		2880.2.a.m.1.1		1
280.3	odd	12		1600.2.c.e.449.1		2
280.59	even	6		1600.2.a.w.1.1		1
280.157	even	12		1600.2.c.d.449.1		2
280.213	even	12		1600.2.c.d.449.2		2
280.227	odd	12		1600.2.c.e.449.2		2
280.269	odd	6		1600.2.a.c.1.1		1
308.87	odd	6		9680.2.a.ba.1.1		1
420.59	odd	6		3600.2.a.be.1.1		1
420.143	even	12		3600.2.f.j.2449.2		2
420.227	even	12		3600.2.f.j.2449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.2.a.a.1.1	✓	1	7.3	odd	6
80.2.a.b.1.1		1	28.3	even	6
100.2.a.a.1.1		1	35.24	odd	6
100.2.c.a.49.1		2	35.3	even	12
100.2.c.a.49.2		2	35.17	even	12
180.2.a.a.1.1		1	21.17	even	6
320.2.a.a.1.1		1	56.3	even	6
320.2.a.f.1.1		1	56.45	odd	6
400.2.a.c.1.1		1	140.59	even	6
400.2.c.b.49.1		2	140.87	odd	12
400.2.c.b.49.2		2	140.3	odd	12
720.2.a.h.1.1		1	84.59	odd	6
900.2.a.b.1.1		1	105.59	even	6
900.2.d.c.649.1		2	105.38	odd	12
900.2.d.c.649.2		2	105.17	odd	12
980.2.a.h.1.1		1	7.4	even	3
980.2.i.c.361.1		2	1.1	even	1	trivial
980.2.i.c.961.1		2	7.2	even	3	inner
980.2.i.i.361.1		2	7.6	odd	2
980.2.i.i.961.1		2	7.5	odd	6
1280.2.d.c.641.1		2	112.45	odd	12
1280.2.d.c.641.2		2	112.101	odd	12
1280.2.d.g.641.1		2	112.59	even	12
1280.2.d.g.641.2		2	112.3	even	12
1600.2.a.c.1.1		1	280.269	odd	6
1600.2.a.w.1.1		1	280.59	even	6
1600.2.c.d.449.1		2	280.157	even	12
1600.2.c.d.449.2		2	280.213	even	12
1600.2.c.e.449.1		2	280.3	odd	12
1600.2.c.e.449.2		2	280.227	odd	12
1620.2.i.b.541.1		2	63.59	even	6
1620.2.i.b.1081.1		2	63.38	even	6
1620.2.i.h.541.1		2	63.31	odd	6
1620.2.i.h.1081.1		2	63.52	odd	6
2420.2.a.a.1.1		1	77.10	even	6
2880.2.a.f.1.1		1	168.59	odd	6
2880.2.a.m.1.1		1	168.101	even	6
3380.2.a.c.1.1		1	91.38	odd	6
3380.2.f.b.3041.1		2	91.73	even	12
3380.2.f.b.3041.2		2	91.31	even	12
3600.2.a.be.1.1		1	420.59	odd	6
3600.2.f.j.2449.1		2	420.227	even	12
3600.2.f.j.2449.2		2	420.143	even	12
3920.2.a.h.1.1		1	28.11	odd	6
4900.2.a.e.1.1		1	35.4	even	6
4900.2.e.f.2549.1		2	35.32	odd	12
4900.2.e.f.2549.2		2	35.18	odd	12
5780.2.a.f.1.1		1	119.101	odd	6
5780.2.c.a.5201.1		2	119.115	odd	12
5780.2.c.a.5201.2		2	119.38	odd	12
7220.2.a.f.1.1		1	133.94	even	6
8820.2.a.g.1.1		1	21.11	odd	6
9680.2.a.ba.1.1		1	308.87	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{13} +2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{39} -6.00000 q^{41} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.00000 - 10.3923i) q^{51} +(3.00000 - 5.19615i) q^{53} +8.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-1.00000 + 1.73205i) q^{67} +12.0000 q^{69} -12.0000 q^{71} +(1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-4.00000 - 6.92820i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{83} +6.00000 q^{85} +(-6.00000 + 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-2.00000 + 3.46410i) q^{95} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - q^{5} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - q^5 - q^9	\( 2 q - 2 q^{3} - q^{5} - q^{9} - 4 q^{13} + 4 q^{15} - 6 q^{17} - 4 q^{19} - 6 q^{23} - q^{25} - 8 q^{27} + 12 q^{29} - 4 q^{31} - 2 q^{37} + 4 q^{39} - 12 q^{41} - 20 q^{43} - q^{45} - 6 q^{47} - 12 q^{51} + 6 q^{53} + 16 q^{57} + 12 q^{59} + 2 q^{61} + 2 q^{65} - 2 q^{67} + 24 q^{69} - 24 q^{71} + 2 q^{73} - 2 q^{75} - 8 q^{79} + 11 q^{81} - 12 q^{83} + 12 q^{85} - 12 q^{87} - 6 q^{89} - 8 q^{93} - 4 q^{95} - 4 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - q^5 - q^9 - 4 * q^13 + 4 * q^15 - 6 * q^17 - 4 * q^19 - 6 * q^23 - q^25 - 8 * q^27 + 12 * q^29 - 4 * q^31 - 2 * q^37 + 4 * q^39 - 12 * q^41 - 20 * q^43 - q^45 - 6 * q^47 - 12 * q^51 + 6 * q^53 + 16 * q^57 + 12 * q^59 + 2 * q^61 + 2 * q^65 - 2 * q^67 + 24 * q^69 - 24 * q^71 + 2 * q^73 - 2 * q^75 - 8 * q^79 + 11 * q^81 - 12 * q^83 + 12 * q^85 - 12 * q^87 - 6 * q^89 - 8 * q^93 - 4 * q^95 - 4 * q^97

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