LMFDB - Embedded newform 980.2.i.h.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:	$0$
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:	no (minimal twist has level 140)
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.h.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000 q^{13} +1.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} -9.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(1.50000 + 2.59808i) q^{33} +(5.00000 + 8.66025i) q^{37} +(0.500000 - 0.866025i) q^{39} +2.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{47} +(1.50000 + 2.59808i) q^{51} -3.00000 q^{55} +2.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(4.00000 + 6.92820i) q^{61} +(0.500000 + 0.866025i) q^{65} +(-4.00000 + 6.92820i) q^{67} +6.00000 q^{69} +(7.00000 - 12.1244i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} -3.00000 q^{85} +(-4.50000 + 7.79423i) q^{87} +(6.00000 + 10.3923i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-1.00000 + 1.73205i) q^{95} -17.0000 q^{97} -6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + q^{5} + 2 q^{9} - 3 q^{11} + 2 q^{13} + 2 q^{15} - 3 q^{17} + 2 q^{19} + 6 q^{23} - q^{25} + 10 q^{27} - 18 q^{29} + 8 q^{31} + 3 q^{33} + 10 q^{37} + q^{39} + 4 q^{43} - 2 q^{45} - 3 q^{47}+ \cdots - 12 q^{99}+O(q^{100}) $ 2 * q + q^3 + q^5 + 2 * q^9 - 3 * q^11 + 2 * q^13 + 2 * q^15 - 3 * q^17 + 2 * q^19 + 6 * q^23 - q^25 + 10 * q^27 - 18 * q^29 + 8 * q^31 + 3 * q^33 + 10 * q^37 + q^39 + 4 * q^43 - 2 * q^45 - 3 * q^47 + 3 * q^51 - 6 * q^55 + 4 * q^57 + 12 * q^59 + 8 * q^61 + q^65 - 8 * q^67 + 12 * q^69 + 14 * q^73 + q^75 - 5 * q^79 - q^81 + 24 * q^83 - 6 * q^85 - 9 * q^87 + 12 * q^89 - 8 * q^93 - 2 * q^95 - 34 * q^97 - 12 * q^99

Character values

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

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

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		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
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$		0			0
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$		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
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$		0			0
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$		0			0
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	0.986303	+	0.164946i	$0.0527450\pi$
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	−0.350304	+	0.936636i	$0.613922\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$		0			0
$97$	−17.0000			−1.72609			−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000			−1.72609			−0.863044	+	0.505128i	$0.831445\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		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
$109$	9.50000	−	16.4545i	0.909935	−	1.57605i	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	9.50000	−	16.4545i	0.909935	−	1.57605i	0.814152	−	0.580651i	$-0.197202\pi$
$110$		0			0
$111$	10.0000			0.949158
$112$		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
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$		0			0
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.50000	+	4.33013i	0.215166	+	0.372678i
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$		0			0
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	0.935857	−	0.352381i	$-0.114628\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	8.00000			0.642575
$156$		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
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$		0			0
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$		0			0
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$		0			0
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	0.803354	−	0.595502i	$-0.203047\pi$
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	−0.917397	+	0.397974i	$0.869713\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$		0			0
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−5.00000	+	8.66025i	−0.367607	+	0.636715i
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$		0			0
$195$	1.00000			0.0716115
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$		0			0
$201$	4.00000	+	6.92820i	0.282138	+	0.488678i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$		0			0
$209$	−6.00000			−0.415029
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$		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
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$		0			0
$221$	−1.50000	+	2.59808i	−0.100901	+	0.174766i
$222$		0			0
$223$	−17.0000			−1.13840			−0.569202	−	0.822198i	$-0.692748\pi$
$223$	−17.0000			−1.13840			−0.569202	+	0.822198i	$0.692748\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		0			0
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.0634974	+	0.997982i	$0.520225\pi$
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.832529	+	0.553981i	$0.813108\pi$
$228$		0			0
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$		0			0
$237$	−5.00000			−0.324785
$238$		0			0
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$		0			0
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$		0			0
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$		0			0
$255$	−1.50000	+	2.59808i	−0.0939336	+	0.162698i
$256$		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
$261$	−9.00000	−	15.5885i	−0.557086	−	0.964901i
$262$		0			0
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.133281	−	0.991078i	$-0.457449\pi$
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.791658	−	0.610964i	$-0.209218\pi$
$264$		0			0
$265$		0			0
$266$		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
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$		0			0
$279$	16.0000			0.957895
$280$		0			0
$281$	−21.0000			−1.25275			−0.626377	−	0.779520i	$-0.715463\pi$
$281$	−21.0000			−1.25275			−0.626377	+	0.779520i	$0.715463\pi$
$282$		0			0
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	−0.654962	−	0.755662i	$-0.727315\pi$
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	0.981903	+	0.189383i	$0.0606488\pi$
$284$		0			0
$285$	1.00000	+	1.73205i	0.0592349	+	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−8.50000	+	14.7224i	−0.498279	+	0.863044i
$292$		0			0
$293$	15.0000			0.876309			0.438155	−	0.898900i	$-0.355632\pi$
$293$	15.0000			0.876309			0.438155	+	0.898900i	$0.355632\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$		0			0
$297$	−7.50000	+	12.9904i	−0.435194	+	0.753778i
$298$		0			0
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$		0			0
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$		0			0
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$		0			0
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	−0.989158	+	0.146852i	$0.953086\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	13.5000	−	23.3827i	0.755855	−	1.30918i
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$	−6.00000			−0.333849
$324$		0			0
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$		0			0
$327$	−9.50000	−	16.4545i	−0.525351	−	0.909935i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$		0			0
$333$	−10.0000	+	17.3205i	−0.547997	+	0.949158i
$334$		0			0
$335$	−8.00000			−0.437087
$336$		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
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$		0			0
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$		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
$351$	5.00000			0.266880
$352$		0			0
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	14.0000			0.732793
$366$		0			0
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	−0.793370	−	0.608740i	$-0.791675\pi$
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	0.923869	+	0.382709i	$0.125009\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$		0			0
$381$	10.0000	−	17.3205i	0.512316	−	0.887357i
$382$		0			0
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$		0			0
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	−0.957263	−	0.289220i	$-0.906604\pi$
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	0.729103	+	0.684403i	$0.239937\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−18.0000			−0.907980
$394$		0			0
$395$	2.50000	−	4.33013i	0.125789	−	0.217872i
$396$		0			0
$397$	2.50000	+	4.33013i	0.125471	+	0.217323i	0.921917	−	0.387387i	$-0.126622\pi$
$397$	2.50000	+	4.33013i	0.125471	+	0.217323i	−0.796446	+	0.604710i	$0.793289\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−30.0000			−1.48704
$408$		0			0
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$		0			0
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$		0			0
$417$	−1.00000	+	1.73205i	−0.0489702	+	0.0848189i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	29.0000			1.41337			0.706687	−	0.707527i	$-0.250189\pi$
$421$	29.0000			1.41337			0.706687	+	0.707527i	$0.250189\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	−1.50000	−	2.59808i	−0.0727607	−	0.126025i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.50000	+	2.59808i	0.0724207	+	0.125436i
$430$		0			0
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	−0.988169	−	0.153370i	$-0.950987\pi$
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	0.626907	+	0.779094i	$0.284321\pi$
$432$		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
$435$	−9.00000			−0.431517
$436$		0			0
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.00000	+	5.19615i	0.142534	+	0.246877i	0.928450	−	0.371457i	$-0.121142\pi$
$443$	3.00000	+	5.19615i	0.142534	+	0.246877i	−0.785916	+	0.618333i	$0.787808\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$		0			0
$447$	−18.0000			−0.851371
$448$		0			0
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−9.50000	−	16.4545i	−0.446349	−	0.773099i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	0.981921	+	0.189292i	$0.0606194\pi$
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	−0.327028	+	0.945015i	$0.606047\pi$
$458$		0			0
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		0			0
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$		0			0
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	0.985726	−	0.168360i	$-0.0538472\pi$
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	−0.638667	+	0.769483i	$0.720514\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	11.0000	+	19.0526i	0.506853	+	0.877896i
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	5.00000	+	8.66025i	0.227980	+	0.394874i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.50000	−	14.7224i	−0.385965	−	0.668511i
$486$		0			0
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	−0.730218	−	0.683214i	$-0.760582\pi$
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	0.956790	+	0.290780i	$0.0939149\pi$
$488$		0			0
$489$	−2.00000			−0.0904431
$490$		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
$493$	13.5000	−	23.3827i	0.608009	−	1.05310i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$		0			0
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$		0			0
$503$	33.0000			1.47140			0.735699	−	0.677309i	$-0.236854\pi$
$503$	33.0000			1.47140			0.735699	+	0.677309i	$0.236854\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.00000	+	8.66025i	0.220755	+	0.382360i
$514$		0			0
$515$	3.50000	−	6.06218i	0.154228	−	0.267131i
$516$		0			0
$517$	9.00000			0.395820
$518$		0			0
$519$	−3.00000			−0.131685
$520$		0			0
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$		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
$531$	24.0000			1.04151
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$		0			0
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	−4.00000	+	6.92820i	−0.171656	+	0.297318i
$544$		0			0
$545$	19.0000			0.813871
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		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
$555$	5.00000	+	8.66025i	0.212238	+	0.367607i
$556$		0			0
$557$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$557$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$		0			0
$561$	−9.00000			−0.379980
$562$		0			0
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$		0			0
$573$	−3.00000			−0.125327
$574$		0			0
$575$	−6.00000			−0.250217
$576$		0			0
$577$	23.5000	−	40.7032i	0.978318	−	1.69450i	0.309797	−	0.950803i	$-0.399739\pi$
$577$	23.5000	−	40.7032i	0.978318	−	1.69450i	0.668521	−	0.743693i	$-0.266928\pi$
$578$		0			0
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$		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
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$		0			0
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$		0			0
$593$	−16.5000	−	28.5788i	−0.677574	−	1.17359i	−0.975709	−	0.219069i	$-0.929698\pi$
$593$	−16.5000	−	28.5788i	−0.677574	−	1.17359i	0.298136	−	0.954524i	$-0.403635\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.0000	−	17.3205i	−0.409273	−	0.708881i
$598$		0			0
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$	−16.0000			−0.651570
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	0.855700	−	0.517472i	$-0.173127\pi$
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	−0.875994	+	0.482322i	$0.839794\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.50000	−	2.59808i	−0.0606835	−	0.105107i
$612$		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
$615$		0			0
$616$		0			0
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$		0			0
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$		0			0
$621$	15.0000	+	25.9808i	0.601929	+	1.04257i
$622$		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
$629$	−30.0000			−1.19618
$630$		0			0
$631$	−25.0000			−0.995234			−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000			−0.995234			−0.497617	+	0.867397i	$0.665792\pi$
$632$		0			0
$633$	2.50000	−	4.33013i	0.0993661	−	0.172107i
$634$		0			0
$635$	10.0000	+	17.3205i	0.396838	+	0.687343i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	−41.0000			−1.61688			−0.808441	−	0.588577i	$-0.799688\pi$
$643$	−41.0000			−1.61688			−0.808441	+	0.588577i	$0.799688\pi$
$644$		0			0
$645$	2.00000			0.0787499
$646$		0			0
$647$	24.0000	−	41.5692i	0.943537	−	1.63425i	0.184884	−	0.982760i	$-0.440809\pi$
$647$	24.0000	−	41.5692i	0.943537	−	1.63425i	0.758654	−	0.651494i	$-0.225858\pi$
$648$		0			0
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$		0			0
$657$	28.0000			1.09238
$658$		0			0
$659$	−33.0000			−1.28550			−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000			−1.28550			−0.642749	+	0.766077i	$0.722206\pi$
$660$		0			0
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	−0.777689	−	0.628649i	$-0.783608\pi$
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	0.933271	+	0.359174i	$0.116941\pi$
$662$		0			0
$663$	1.50000	+	2.59808i	0.0582552	+	0.100901i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−27.0000	−	46.7654i	−1.04544	−	1.81076i
$668$		0			0
$669$	−8.50000	+	14.7224i	−0.328629	+	0.569202i
$670$		0			0
$671$	−24.0000			−0.926510
$672$		0			0
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$		0			0
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$		0			0
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	0.973392	−	0.229147i	$-0.0735938\pi$
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	−0.685143	+	0.728408i	$0.740260\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	13.5000	+	23.3827i	0.517321	+	0.896026i
$682$		0			0
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	−0.998917	−	0.0465244i	$-0.985185\pi$
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	0.539750	+	0.841825i	$0.318519\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−16.0000			−0.610438
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.00000	−	1.73205i	−0.0379322	−	0.0657004i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−24.0000			−0.907763
$700$		0			0
$701$	3.00000			0.113308			0.0566542	−	0.998394i	$-0.481957\pi$
$701$	3.00000			0.113308			0.0566542	+	0.998394i	$0.481957\pi$
$702$		0			0
$703$	−10.0000	+	17.3205i	−0.377157	+	0.653255i
$704$		0			0
$705$	−1.50000	−	2.59808i	−0.0564933	−	0.0978492i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$		0			0
$713$	48.0000			1.79761
$714$		0			0
$715$	−3.00000			−0.112194
$716$		0			0
$717$	4.50000	−	7.79423i	0.168056	−	0.291081i
$718$		0			0
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.00000	+	8.66025i	0.185952	+	0.322078i
$724$		0			0
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$		0			0
$733$	−6.50000	−	11.2583i	−0.240083	−	0.415836i	0.720655	−	0.693294i	$-0.243841\pi$
$733$	−6.50000	−	11.2583i	−0.240083	−	0.415836i	−0.960738	+	0.277458i	$0.910508\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$		0			0
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	0.746955	+	0.664875i	$0.231515\pi$
$740$		0			0
$741$	2.00000			0.0734718
$742$		0			0
$743$	48.0000			1.76095			0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000			1.76095			0.880475	+	0.474093i	$0.157224\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$	12.0000	+	20.7846i	0.439057	+	0.760469i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−26.5000	−	45.8993i	−0.966999	−	1.67489i	−0.704146	−	0.710055i	$-0.748670\pi$
$751$	−26.5000	−	45.8993i	−0.966999	−	1.67489i	−0.262852	−	0.964836i	$-0.584663\pi$
$752$		0			0
$753$	−3.00000	+	5.19615i	−0.109326	+	0.189358i
$754$		0			0
$755$	19.0000			0.691481
$756$		0			0
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$		0			0
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$		0			0
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$		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
$771$	−6.00000			−0.216085
$772$		0			0
$773$	7.50000	−	12.9904i	0.269756	−	0.467232i	−0.699043	−	0.715080i	$-0.746390\pi$
$773$	7.50000	−	12.9904i	0.269756	−	0.467232i	0.968799	+	0.247849i	$0.0797235\pi$
$774$		0			0
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−45.0000			−1.60817
$784$		0			0
$785$	−22.0000			−0.785214
$786$		0			0
$787$	2.50000	−	4.33013i	0.0891154	−	0.154352i	−0.818022	−	0.575187i	$-0.804929\pi$
$787$	2.50000	−	4.33013i	0.0891154	−	0.154352i	0.907137	+	0.420834i	$0.138263\pi$
$788$		0			0
$789$	−15.0000	−	25.9808i	−0.534014	−	0.924940i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.00000			0.106265			0.0531327	−	0.998587i	$-0.483079\pi$
$797$	3.00000			0.106265			0.0531327	+	0.998587i	$0.483079\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	−12.0000	+	20.7846i	−0.423999	+	0.734388i
$802$		0			0
$803$	21.0000	+	36.3731i	0.741074	+	1.28358i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.00000	−	15.5885i	−0.316815	−	0.548740i
$808$		0			0
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	1.00000	−	1.73205i	0.0350285	−	0.0606711i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$		0			0
$825$	−3.00000			−0.104447
$826$		0			0
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$		0			0
$829$	−20.0000	+	34.6410i	−0.694629	+	1.20313i	0.275677	+	0.961250i	$0.411098\pi$
$829$	−20.0000	+	34.6410i	−0.694629	+	1.20313i	−0.970306	+	0.241882i	$0.922235\pi$
$830$		0			0
$831$	−11.0000	−	19.0526i	−0.381586	−	0.660926i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$		0			0
$837$	20.0000	−	34.6410i	0.691301	−	1.19737i
$838$		0			0
$839$	−18.0000			−0.621429			−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000			−0.621429			−0.310715	+	0.950503i	$0.600568\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	−10.5000	+	18.1865i	−0.361639	+	0.626377i
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−5.50000	−	9.52628i	−0.188760	−	0.326941i
$850$		0			0
$851$	−30.0000	+	51.9615i	−1.02839	+	1.78122i
$852$		0			0
$853$	22.0000			0.753266			0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000			0.753266			0.376633	+	0.926363i	$0.377082\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$		0			0
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$		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
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	0.745649	−	0.666339i	$-0.232140\pi$
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	−0.949891	+	0.312581i	$0.898806\pi$
$864$		0			0
$865$	1.50000	−	2.59808i	0.0510015	−	0.0883372i
$866$		0			0
$867$	8.00000			0.271694
$868$		0			0
$869$	15.0000			0.508840
$870$		0			0
$871$	−4.00000	+	6.92820i	−0.135535	+	0.234753i
$872$		0			0
$873$	−17.0000	−	29.4449i	−0.575363	−	0.996558i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	7.50000	−	12.9904i	0.252969	−	0.438155i
$880$		0			0
$881$	−48.0000			−1.61716			−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000			−1.61716			−0.808581	+	0.588386i	$0.799764\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	6.00000	−	10.3923i	0.201688	−	0.349334i
$886$		0			0
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		0			0
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$	6.00000			0.200334
$898$		0			0
$899$	−36.0000	+	62.3538i	−1.20067	+	2.07962i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.00000	−	6.92820i	−0.132964	−	0.230301i
$906$		0			0
$907$	11.0000	−	19.0526i	0.365249	−	0.632630i	−0.623567	−	0.781770i	$-0.714317\pi$
$907$	11.0000	−	19.0526i	0.365249	−	0.632630i	0.988816	+	0.149140i	$0.0476505\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$		0			0
$915$	4.00000	+	6.92820i	0.132236	+	0.229039i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−20.5000	−	35.5070i	−0.676233	−	1.17127i	−0.976107	−	0.217291i	$-0.930278\pi$
$919$	−20.5000	−	35.5070i	−0.676233	−	1.17127i	0.299874	−	0.953979i	$-0.403055\pi$
$920$		0			0
$921$	6.50000	−	11.2583i	0.214182	−	0.370975i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$		0			0
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$		0			0
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	0.599228	−	0.800578i	$-0.295474\pi$
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	−0.992935	+	0.118657i	$0.962141\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$		0			0
$935$	4.50000	−	7.79423i	0.147166	−	0.254899i
$936$		0			0
$937$	7.00000			0.228680			0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000			0.228680			0.114340	+	0.993442i	$0.463525\pi$
$938$		0			0
$939$	−13.0000			−0.424239
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.0000	−	31.1769i	−0.584921	−	1.01311i	−0.994885	−	0.101012i	$-0.967792\pi$
$947$	−18.0000	−	31.1769i	−0.584921	−	1.01311i	0.409964	−	0.912102i	$-0.365541\pi$
$948$		0			0
$949$	7.00000	−	12.1244i	0.227230	−	0.393573i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	1.50000	−	2.59808i	0.0485389	−	0.0840718i
$956$		0			0
$957$	−13.5000	−	23.3827i	−0.436393	−	0.755855i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$		0			0
$965$	4.00000			0.128765
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$		0			0
$969$	−3.00000	+	5.19615i	−0.0963739	+	0.166924i
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$	38.0000			1.21325
$982$		0			0
$983$	−16.5000	+	28.5788i	−0.526268	+	0.911523i	0.473263	+	0.880921i	$0.343076\pi$
$983$	−16.5000	+	28.5788i	−0.526268	+	0.911523i	−0.999532	+	0.0306024i	$0.990257\pi$
$984$		0			0
$985$	6.00000	+	10.3923i	0.191176	+	0.331126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	6.00000	+	10.3923i	0.190789	+	0.330456i
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$		0			0
$993$	−20.0000			−0.634681
$994$		0			0
$995$	20.0000			0.634043
$996$		0			0
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$		0			0
$999$	25.0000	+	43.3013i	0.790965	+	1.36999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.i.h.361.1		2
7.2	even	3	inner	980.2.i.h.961.1		2
7.3	odd	6		140.2.a.a.1.1	✓	1
7.4	even	3		980.2.a.c.1.1		1
7.5	odd	6		980.2.i.d.961.1		2
7.6	odd	2		980.2.i.d.361.1		2
21.11	odd	6		8820.2.a.r.1.1		1
21.17	even	6		1260.2.a.c.1.1		1
28.3	even	6		560.2.a.c.1.1		1
28.11	odd	6		3920.2.a.u.1.1		1
35.3	even	12		700.2.e.c.449.2		2
35.4	even	6		4900.2.a.p.1.1		1
35.17	even	12		700.2.e.c.449.1		2
35.18	odd	12		4900.2.e.l.2549.1		2
35.24	odd	6		700.2.a.d.1.1		1
35.32	odd	12		4900.2.e.l.2549.2		2
56.3	even	6		2240.2.a.r.1.1		1
56.45	odd	6		2240.2.a.g.1.1		1
84.59	odd	6		5040.2.a.h.1.1		1
105.17	odd	12		6300.2.k.c.6049.2		2
105.38	odd	12		6300.2.k.c.6049.1		2
105.59	even	6		6300.2.a.d.1.1		1
140.3	odd	12		2800.2.g.j.449.1		2
140.59	even	6		2800.2.a.y.1.1		1
140.87	odd	12		2800.2.g.j.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.a.a.1.1	✓	1	7.3	odd	6
560.2.a.c.1.1		1	28.3	even	6
700.2.a.d.1.1		1	35.24	odd	6
700.2.e.c.449.1		2	35.17	even	12
700.2.e.c.449.2		2	35.3	even	12
980.2.a.c.1.1		1	7.4	even	3
980.2.i.d.361.1		2	7.6	odd	2
980.2.i.d.961.1		2	7.5	odd	6
980.2.i.h.361.1		2	1.1	even	1	trivial
980.2.i.h.961.1		2	7.2	even	3	inner
1260.2.a.c.1.1		1	21.17	even	6
2240.2.a.g.1.1		1	56.45	odd	6
2240.2.a.r.1.1		1	56.3	even	6
2800.2.a.y.1.1		1	140.59	even	6
2800.2.g.j.449.1		2	140.3	odd	12
2800.2.g.j.449.2		2	140.87	odd	12
3920.2.a.u.1.1		1	28.11	odd	6
4900.2.a.p.1.1		1	35.4	even	6
4900.2.e.l.2549.1		2	35.18	odd	12
4900.2.e.l.2549.2		2	35.32	odd	12
5040.2.a.h.1.1		1	84.59	odd	6
6300.2.a.d.1.1		1	105.59	even	6
6300.2.k.c.6049.1		2	105.38	odd	12
6300.2.k.c.6049.2		2	105.17	odd	12
8820.2.a.r.1.1		1	21.11	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000 q^{13} +1.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} -9.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(1.50000 + 2.59808i) q^{33} +(5.00000 + 8.66025i) q^{37} +(0.500000 - 0.866025i) q^{39} +2.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{47} +(1.50000 + 2.59808i) q^{51} -3.00000 q^{55} +2.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(4.00000 + 6.92820i) q^{61} +(0.500000 + 0.866025i) q^{65} +(-4.00000 + 6.92820i) q^{67} +6.00000 q^{69} +(7.00000 - 12.1244i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} -3.00000 q^{85} +(-4.50000 + 7.79423i) q^{87} +(6.00000 + 10.3923i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-1.00000 + 1.73205i) q^{95} -17.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + q^{5} + 2 q^{9} - 3 q^{11} + 2 q^{13} + 2 q^{15} - 3 q^{17} + 2 q^{19} + 6 q^{23} - q^{25} + 10 q^{27} - 18 q^{29} + 8 q^{31} + 3 q^{33} + 10 q^{37} + q^{39} + 4 q^{43} - 2 q^{45} - 3 q^{47}+ \cdots - 12 q^{99}+O(q^{100}) \) 2 * q + q^3 + q^5 + 2 * q^9 - 3 * q^11 + 2 * q^13 + 2 * q^15 - 3 * q^17 + 2 * q^19 + 6 * q^23 - q^25 + 10 * q^27 - 18 * q^29 + 8 * q^31 + 3 * q^33 + 10 * q^37 + q^39 + 4 * q^43 - 2 * q^45 - 3 * q^47 + 3 * q^51 - 6 * q^55 + 4 * q^57 + 12 * q^59 + 8 * q^61 + q^65 - 8 * q^67 + 12 * q^69 + 14 * q^73 + q^75 - 5 * q^79 - q^81 + 24 * q^83 - 6 * q^85 - 9 * q^87 + 12 * q^89 - 8 * q^93 - 2 * q^95 - 34 * q^97 - 12 * q^99

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