LMFDB - Embedded newform 1960.2.q.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (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:	$15.6506787962$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.b.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(-1.00000 - 1.73205i) q^{19} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +10.0000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-4.00000 - 6.92820i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{39} -12.0000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-2.00000 - 3.46410i) q^{47} +(-1.00000 + 1.73205i) q^{53} +4.00000 q^{55} +4.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-1.00000 - 1.73205i) q^{65} +(-2.00000 + 3.46410i) q^{67} -8.00000 q^{69} -12.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(2.00000 + 3.46410i) q^{79} +(5.50000 - 9.52628i) q^{81} +14.0000 q^{83} +(-10.0000 + 17.3205i) q^{87} +(-4.00000 - 6.92820i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-1.00000 + 1.73205i) q^{95} -8.00000 q^{97} +4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{11} + 4 q^{13} + 4 q^{15} - 2 q^{19} + 4 q^{23} - q^{25} - 8 q^{27} + 20 q^{29} - 4 q^{31} - 8 q^{33} + 2 q^{37} - 4 q^{39} - 24 q^{41} - 8 q^{43} - q^{45} - 4 q^{47} - 2 q^{53} + 8 q^{55} + 8 q^{57} - 10 q^{59} - 6 q^{61} - 2 q^{65} - 4 q^{67} - 16 q^{69} - 24 q^{71} + 4 q^{73} - 2 q^{75} + 4 q^{79} + 11 q^{81} + 28 q^{83} - 20 q^{87} - 8 q^{89} - 8 q^{93} - 2 q^{95} - 16 q^{97} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - q^5 - q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 - 2 * q^19 + 4 * q^23 - q^25 - 8 * q^27 + 20 * q^29 - 4 * q^31 - 8 * q^33 + 2 * q^37 - 4 * q^39 - 24 * q^41 - 8 * q^43 - q^45 - 4 * q^47 - 2 * q^53 + 8 * q^55 + 8 * q^57 - 10 * q^59 - 6 * q^61 - 2 * q^65 - 4 * q^67 - 16 * q^69 - 24 * q^71 + 4 * q^73 - 2 * q^75 + 4 * q^79 + 11 * q^81 + 28 * q^83 - 20 * q^87 - 8 * q^89 - 8 * q^93 - 2 * q^95 - 16 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$		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
$33$	−4.00000	−	6.92820i	−0.696311	−	1.20605i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	−12.0000			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−2.00000	−	3.46410i	−0.291730	−	0.505291i	0.682489	−	0.730896i	$-0.260898\pi$
$47$	−2.00000	−	3.46410i	−0.291730	−	0.505291i	−0.974219	+	0.225605i	$0.927564\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		0			0
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$	−8.00000			−0.963087
$70$		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
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−10.0000	+	17.3205i	−1.07211	+	1.85695i
$88$		0			0
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	0.572327	−	0.820025i	$-0.306041\pi$
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	−0.996326	+	0.0856373i	$0.972707\pi$
$90$		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
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$		0			0
$103$	−10.0000	−	17.3205i	−0.985329	−	1.70664i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−10.0000	−	17.3205i	−0.985329	−	1.70664i	−0.344865	−	0.938652i	$-0.612075\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	−0.999708	−	0.0241802i	$-0.992302\pi$
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	0.520794	+	0.853682i	$0.325636\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$		0			0
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	12.0000	−	20.7846i	1.08200	−	1.87409i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$		0			0
$129$	4.00000	−	6.92820i	0.352180	−	0.609994i
$130$		0			0
$131$	11.0000	+	19.0526i	0.961074	+	1.66463i	0.719811	+	0.694170i	$0.244228\pi$
$131$	11.0000	+	19.0526i	0.961074	+	1.66463i	0.241264	+	0.970460i	$0.422438\pi$
$132$		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	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		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
$141$	8.00000			0.673722
$142$		0			0
$143$	−4.00000	+	6.92820i	−0.334497	+	0.579365i
$144$		0			0
$145$	−5.00000	−	8.66025i	−0.415227	−	0.719195i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		0			0
$159$	−2.00000	−	3.46410i	−0.158610	−	0.274721i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$		0			0
$165$	−4.00000	+	6.92820i	−0.311400	+	0.539360i
$166$		0			0
$167$	−4.00000			−0.309529			−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000			−0.309529			−0.154765	+	0.987951i	$0.549462\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.0000	−	17.3205i	−0.751646	−	1.30189i
$178$		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
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	12.0000			0.887066
$184$		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
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	−0.335805	−	0.941932i	$-0.609008\pi$
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	0.983639	−	0.180150i	$-0.0576584\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$		0			0
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$		0			0
$209$	8.00000			0.553372
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	12.0000	−	20.7846i	0.822226	−	1.42414i
$214$		0			0
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	−0.999184	−	0.0403978i	$-0.987137\pi$
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	0.534577	+	0.845120i	$0.320471\pi$
$228$		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
$233$	5.00000	+	8.66025i	0.327561	+	0.567352i	0.982027	−	0.188739i	$-0.0604400\pi$
$233$	5.00000	+	8.66025i	0.327561	+	0.567352i	−0.654466	+	0.756091i	$0.727107\pi$
$234$		0			0
$235$	−2.00000	+	3.46410i	−0.130466	+	0.225973i
$236$		0			0
$237$	−8.00000			−0.519656
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	−0.923224	−	0.384262i	$-0.874456\pi$
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	0.794393	+	0.607404i	$0.207789\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$		0			0
$249$	−14.0000	+	24.2487i	−0.887214	+	1.53670i
$250$		0			0
$251$	14.0000			0.883672			0.441836	−	0.897096i	$-0.354327\pi$
$251$	14.0000			0.883672			0.441836	+	0.897096i	$0.354327\pi$
$252$		0			0
$253$	−16.0000			−1.00591
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.858567	+	0.512702i	$0.171355\pi$
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.0147291	+	0.999892i	$0.495311\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−5.00000	−	8.66025i	−0.309492	−	0.536056i
$262$		0			0
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$		0			0
$267$	16.0000			0.979184
$268$		0			0
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		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
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$		0			0
$285$	−2.00000	−	3.46410i	−0.118470	−	0.205196i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	8.00000	−	13.8564i	0.468968	−	0.812277i
$292$		0			0
$293$	22.0000			1.28525			0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000			1.28525			0.642627	+	0.766179i	$0.277845\pi$
$294$		0			0
$295$	10.0000			0.582223
$296$		0			0
$297$	8.00000	−	13.8564i	0.464207	−	0.804030i
$298$		0			0
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−14.0000	−	24.2487i	−0.804279	−	1.39305i
$304$		0			0
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$		0			0
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$		0			0
$309$	40.0000			2.27552
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	0.998522	−	0.0543564i	$-0.0173107\pi$
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	−0.546335	+	0.837567i	$0.683977\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0000	+	19.0526i	0.617822	+	1.07010i	0.989882	+	0.141890i	$0.0453179\pi$
$317$	11.0000	+	19.0526i	0.617822	+	1.07010i	−0.372061	+	0.928208i	$0.621349\pi$
$318$		0			0
$319$	−20.0000	+	34.6410i	−1.11979	+	1.93952i
$320$		0			0
$321$	−8.00000			−0.446516
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$		0			0
$327$	−10.0000	−	17.3205i	−0.553001	−	0.957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$		0			0
$335$	4.00000			0.218543
$336$		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
$339$	18.0000	−	31.1769i	0.977626	−	1.69330i
$340$		0			0
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.00000	+	6.92820i	0.215353	+	0.373002i
$346$		0			0
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$		0			0
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	−8.00000			−0.427008
$352$		0			0
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	−0.980352	−	0.197256i	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	10.0000			0.524864
$364$		0			0
$365$	−4.00000			−0.209370
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$	6.00000	+	10.3923i	0.312348	+	0.541002i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	15.0000	+	25.9808i	0.776671	+	1.34523i	0.933851	+	0.357663i	$0.116426\pi$
$373$	15.0000	+	25.9808i	0.776671	+	1.34523i	−0.157180	+	0.987570i	$0.550240\pi$
$374$		0			0
$375$	−1.00000	+	1.73205i	−0.0516398	+	0.0894427i
$376$		0			0
$377$	20.0000			1.03005
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$	12.0000	−	20.7846i	0.614779	−	1.06483i
$382$		0			0
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$		0			0
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−44.0000			−2.21951
$394$		0			0
$395$	2.00000	−	3.46410i	0.100631	−	0.174298i
$396$		0			0
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$		0			0
$405$	−11.0000			−0.546594
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	10.0000	−	17.3205i	0.494468	−	0.856444i	−0.505511	−	0.862820i	$-0.668696\pi$
$409$	10.0000	−	17.3205i	0.494468	−	0.856444i	0.999980	+	0.00637586i	$0.00202951\pi$
$410$		0			0
$411$	18.0000	+	31.1769i	0.887875	+	1.53784i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−7.00000	−	12.1244i	−0.343616	−	0.595161i
$416$		0			0
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$		0			0
$419$	14.0000			0.683945			0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000			0.683945			0.341972	+	0.939710i	$0.388905\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$		0			0
$423$	−2.00000	+	3.46410i	−0.0972433	+	0.168430i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−8.00000	−	13.8564i	−0.386244	−	0.668994i
$430$		0			0
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	−32.0000			−1.53782			−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000			−1.53782			−0.768911	+	0.639356i	$0.779201\pi$
$434$		0			0
$435$	20.0000			0.958927
$436$		0			0
$437$	4.00000	−	6.92820i	0.191346	−	0.331421i
$438$		0			0
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	−0.979242	−	0.202695i	$-0.935030\pi$
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	0.314082	−	0.949396i	$-0.398303\pi$
$444$		0			0
$445$	−4.00000	+	6.92820i	−0.189618	+	0.328428i
$446$		0			0
$447$	−20.0000			−0.945968
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	24.0000	−	41.5692i	1.13012	−	1.95742i
$452$		0			0
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	0.787288	−	0.616585i	$-0.211484\pi$
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	−0.927622	+	0.373519i	$0.878151\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	42.0000			1.95614			0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000			1.95614			0.978068	+	0.208288i	$0.0667892\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	−4.00000	+	6.92820i	−0.185496	+	0.321288i
$466$		0			0
$467$	13.0000	+	22.5167i	0.601568	+	1.04195i	0.992584	+	0.121563i	$0.0387905\pi$
$467$	13.0000	+	22.5167i	0.601568	+	1.04195i	−0.391015	+	0.920384i	$0.627876\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	14.0000	+	24.2487i	0.645086	+	1.11732i
$472$		0			0
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$		0			0
$475$	2.00000			0.0917663
$476$		0			0
$477$	2.00000			0.0915737
$478$		0			0
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$		0			0
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	−0.352241	−	0.935909i	$-0.614580\pi$
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	0.986642	−	0.162905i	$-0.0520863\pi$
$488$		0			0
$489$	40.0000			1.80886
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−2.00000	−	3.46410i	−0.0898933	−	0.155700i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	4.00000	−	6.92820i	0.178707	−	0.309529i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	14.0000			0.622992
$506$		0			0
$507$	9.00000	−	15.5885i	0.399704	−	0.692308i
$508$		0			0
$509$	11.0000	+	19.0526i	0.487566	+	0.844490i	0.999898	−	0.0142980i	$-0.00455136\pi$
$509$	11.0000	+	19.0526i	0.487566	+	0.844490i	−0.512331	+	0.858788i	$0.671218\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.00000	+	6.92820i	0.176604	+	0.305888i
$514$		0			0
$515$	−10.0000	+	17.3205i	−0.440653	+	0.763233i
$516$		0			0
$517$	16.0000			0.703679
$518$		0			0
$519$	36.0000			1.58022
$520$		0			0
$521$	−10.0000	+	17.3205i	−0.438108	+	0.758825i	−0.997544	−	0.0700486i	$-0.977685\pi$
$521$	−10.0000	+	17.3205i	−0.438108	+	0.758825i	0.559436	+	0.828874i	$0.311018\pi$
$522$		0			0
$523$	9.00000	+	15.5885i	0.393543	+	0.681636i	0.992914	−	0.118835i	$-0.0379161\pi$
$523$	9.00000	+	15.5885i	0.393543	+	0.681636i	−0.599371	+	0.800471i	$0.704583\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	10.0000			0.433963
$532$		0			0
$533$	−24.0000			−1.03956
$534$		0			0
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$		0			0
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−15.0000	−	25.9808i	−0.644900	−	1.11700i	−0.984325	−	0.176367i	$-0.943566\pi$
$541$	−15.0000	−	25.9808i	−0.644900	−	1.11700i	0.339424	−	0.940633i	$-0.389768\pi$
$542$		0			0
$543$	22.0000	−	38.1051i	0.944110	−	1.63525i
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	−44.0000			−1.88130			−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000			−1.88130			−0.940652	+	0.339372i	$0.889785\pi$
$548$		0			0
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	−10.0000	−	17.3205i	−0.426014	−	0.737878i
$552$		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
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.00000	+	1.73205i	−0.0421450	+	0.0729972i	−0.886328	−	0.463057i	$-0.846752\pi$
$563$	−1.00000	+	1.73205i	−0.0421450	+	0.0729972i	0.844183	+	0.536054i	$0.180086\pi$
$564$		0			0
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$		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
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	6.00000	−	10.3923i	0.249783	−	0.432637i	−0.713682	−	0.700470i	$-0.752974\pi$
$577$	6.00000	−	10.3923i	0.249783	−	0.432637i	0.963466	+	0.267832i	$0.0863073\pi$
$578$		0			0
$579$	18.0000	+	31.1769i	0.748054	+	1.29567i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$		0			0
$585$	−1.00000	+	1.73205i	−0.0413449	+	0.0716115i
$586$		0			0
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	8.00000			0.329634
$590$		0			0
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$		0			0
$593$	22.0000	+	38.1051i	0.903432	+	1.56479i	0.823009	+	0.568029i	$0.192294\pi$
$593$	22.0000	+	38.1051i	0.903432	+	1.56479i	0.0804231	+	0.996761i	$0.474373\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−20.0000	−	34.6410i	−0.818546	−	1.41776i
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	−2.50000	+	4.33013i	−0.101639	+	0.176045i
$606$		0			0
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$		0			0
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	−0.474509	−	0.880251i	$-0.657374\pi$
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	0.999574	−	0.0291886i	$-0.00929235\pi$
$614$		0			0
$615$	−24.0000			−0.967773
$616$		0			0
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$		0			0
$619$	15.0000	−	25.9808i	0.602901	−	1.04425i	−0.389479	−	0.921036i	$-0.627345\pi$
$619$	15.0000	−	25.9808i	0.602901	−	1.04425i	0.992379	−	0.123219i	$-0.0393219\pi$
$620$		0			0
$621$	−8.00000	−	13.8564i	−0.321029	−	0.556038i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−8.00000	+	13.8564i	−0.319489	+	0.553372i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		0			0
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$		0			0
$635$	6.00000	+	10.3923i	0.238103	+	0.412406i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	−0.694025	−	0.719951i	$-0.744164\pi$
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	0.970508	+	0.241068i	$0.0774976\pi$
$642$		0			0
$643$	−30.0000			−1.18308			−0.591542	−	0.806274i	$-0.701481\pi$
$643$	−30.0000			−1.18308			−0.591542	+	0.806274i	$0.701481\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$		0			0
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$		0			0
$649$	−20.0000	−	34.6410i	−0.785069	−	1.35978i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$		0			0
$655$	11.0000	−	19.0526i	0.429806	−	0.744445i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	−28.0000			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.0000	+	34.6410i	0.774403	+	1.34131i
$668$		0			0
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$		0			0
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$		0			0
$677$	7.00000	+	12.1244i	0.269032	+	0.465977i	0.968612	−	0.248577i	$-0.0799630\pi$
$677$	7.00000	+	12.1244i	0.269032	+	0.465977i	−0.699580	+	0.714554i	$0.746630\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−14.0000	−	24.2487i	−0.536481	−	0.929213i
$682$		0			0
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	−0.283491	−	0.958975i	$-0.591493\pi$
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	0.972242	−	0.233977i	$-0.0751739\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$	−28.0000			−1.06827
$688$		0			0
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	−0.920348	−	0.391102i	$-0.872094\pi$
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	0.121470	−	0.992595i	$-0.461239\pi$
$692$		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
$699$	−20.0000			−0.756469
$700$		0			0
$701$	10.0000			0.377695			0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000			0.377695			0.188847	+	0.982006i	$0.439525\pi$
$702$		0			0
$703$	2.00000	−	3.46410i	0.0754314	−	0.130651i
$704$		0			0
$705$	−4.00000	−	6.92820i	−0.150649	−	0.260931i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	0.916845	−	0.399244i	$-0.130727\pi$
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	−0.804178	+	0.594389i	$0.797394\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$		0			0
$713$	−16.0000			−0.599205
$714$		0			0
$715$	8.00000			0.299183
$716$		0			0
$717$	−16.0000	+	27.7128i	−0.597531	+	1.03495i
$718$		0			0
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−4.00000	−	6.92820i	−0.148762	−	0.257663i
$724$		0			0
$725$	−5.00000	+	8.66025i	−0.185695	+	0.321634i
$726$		0			0
$727$	4.00000			0.148352			0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000			0.148352			0.0741759	+	0.997245i	$0.476367\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.00000	−	13.8564i	−0.294684	−	0.510407i
$738$		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
$741$	8.00000			0.293887
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$		0			0
$747$	−7.00000	−	12.1244i	−0.256117	−	0.443607i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	0.682341	−	0.731034i	$-0.260962\pi$
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	−0.974265	+	0.225407i	$0.927629\pi$
$752$		0			0
$753$	−14.0000	+	24.2487i	−0.510188	+	0.883672i
$754$		0			0
$755$	−8.00000			−0.291150
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$		0			0
$759$	16.0000	−	27.7128i	0.580763	−	1.00591i
$760$		0			0
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.0000	+	17.3205i	−0.361079	+	0.625407i
$768$		0			0
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$		0			0
$771$	−56.0000			−2.01679
$772$		0			0
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	0.0729331	+	0.997337i	$0.476764\pi$
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	−0.900186	+	0.435507i	$0.856569\pi$
$774$		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
$781$	24.0000	−	41.5692i	0.858788	−	1.48746i
$782$		0			0
$783$	−40.0000			−1.42948
$784$		0			0
$785$	−14.0000			−0.499681
$786$		0			0
$787$	21.0000	−	36.3731i	0.748569	−	1.29656i	−0.199939	−	0.979808i	$-0.564075\pi$
$787$	21.0000	−	36.3731i	0.748569	−	1.29656i	0.948509	−	0.316752i	$-0.102592\pi$
$788$		0			0
$789$	16.0000	+	27.7128i	0.569615	+	0.986602i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.00000	−	10.3923i	−0.213066	−	0.369042i
$794$		0			0
$795$	−2.00000	+	3.46410i	−0.0709327	+	0.122859i
$796$		0			0
$797$	50.0000			1.77109			0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000			1.77109			0.885545	+	0.464553i	$0.153785\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−4.00000	+	6.92820i	−0.141333	+	0.244796i
$802$		0			0
$803$	8.00000	+	13.8564i	0.282314	+	0.488982i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.00000	+	10.3923i	0.211210	+	0.365826i
$808$		0			0
$809$	−11.0000	+	19.0526i	−0.386739	+	0.669852i	−0.992009	−	0.126168i	$-0.959732\pi$
$809$	−11.0000	+	19.0526i	−0.386739	+	0.669852i	0.605269	+	0.796021i	$0.293065\pi$
$810$		0			0
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$		0			0
$813$	−32.0000			−1.12229
$814$		0			0
$815$	−10.0000	+	17.3205i	−0.350285	+	0.606711i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$	8.00000			0.278524
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	−23.0000	+	39.8372i	−0.798823	+	1.38360i	0.121560	+	0.992584i	$0.461210\pi$
$829$	−23.0000	+	39.8372i	−0.798823	+	1.38360i	−0.920383	+	0.391018i	$0.872123\pi$
$830$		0			0
$831$	−26.0000	−	45.0333i	−0.901930	−	1.56219i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.00000	+	3.46410i	0.0692129	+	0.119880i
$836$		0			0
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$		0			0
$839$	−20.0000			−0.690477			−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$		0			0
$843$	10.0000	−	17.3205i	0.344418	−	0.596550i
$844$		0			0
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	10.0000	+	17.3205i	0.343199	+	0.594438i
$850$		0			0
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$		0			0
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$	2.00000			0.0683986
$856$		0			0
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	0.451958	+	0.892039i	$0.350726\pi$
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	−0.998508	+	0.0546125i	$0.982608\pi$
$858$		0			0
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$		0			0
$865$	−9.00000	+	15.5885i	−0.306009	+	0.530023i
$866$		0			0
$867$	−34.0000			−1.15470
$868$		0			0
$869$	−16.0000			−0.542763
$870$		0			0
$871$	−4.00000	+	6.92820i	−0.135535	+	0.234753i
$872$		0			0
$873$	4.00000	+	6.92820i	0.135379	+	0.234484i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	0.977018	−	0.213158i	$-0.0683750\pi$
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	−0.673109	+	0.739543i	$0.735042\pi$
$878$		0			0
$879$	−22.0000	+	38.1051i	−0.742042	+	1.28525i
$880$		0			0
$881$	8.00000			0.269527			0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000			0.269527			0.134763	+	0.990878i	$0.456973\pi$
$882$		0			0
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$		0			0
$885$	−10.0000	+	17.3205i	−0.336146	+	0.582223i
$886$		0			0
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	22.0000	+	38.1051i	0.737028	+	1.27657i
$892$		0			0
$893$	−4.00000	+	6.92820i	−0.133855	+	0.231843i
$894$		0			0
$895$	12.0000			0.401116
$896$		0			0
$897$	−16.0000			−0.534224
$898$		0			0
$899$	−20.0000	+	34.6410i	−0.667037	+	1.15534i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.0000	+	19.0526i	0.365652	+	0.633328i
$906$		0			0
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$		0			0
$909$	14.0000			0.464351
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−28.0000	+	48.4974i	−0.926665	+	1.60503i
$914$		0			0
$915$	−6.00000	−	10.3923i	−0.198354	−	0.343559i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$		0			0
$921$	−14.0000	+	24.2487i	−0.461316	+	0.799022i
$922$		0			0
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−2.00000			−0.0657596
$926$		0			0
$927$	−10.0000	+	17.3205i	−0.328443	+	0.568880i
$928$		0			0
$929$	−18.0000	−	31.1769i	−0.590561	−	1.02288i	−0.994157	−	0.107944i	$-0.965573\pi$
$929$	−18.0000	−	31.1769i	−0.590561	−	1.02288i	0.403596	−	0.914937i	$-0.367760\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−12.0000			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$938$		0			0
$939$	−32.0000			−1.04428
$940$		0			0
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	−0.772946	−	0.634472i	$-0.781218\pi$
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	0.935942	+	0.352155i	$0.114551\pi$
$942$		0			0
$943$	−24.0000	−	41.5692i	−0.781548	−	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.0000	−	24.2487i	−0.454939	−	0.787977i	0.543746	−	0.839250i	$-0.317006\pi$
$947$	−14.0000	−	24.2487i	−0.454939	−	0.787977i	−0.998685	+	0.0512727i	$0.983672\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$	−44.0000			−1.42680
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$		0			0
$955$	−2.00000	+	3.46410i	−0.0647185	+	0.112096i
$956$		0			0
$957$	−40.0000	−	69.2820i	−1.29302	−	2.23957i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	2.00000	−	3.46410i	0.0644491	−	0.111629i
$964$		0			0
$965$	−18.0000			−0.579441
$966$		0			0
$967$	−20.0000			−0.643157			−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000			−0.643157			−0.321578	+	0.946883i	$0.604213\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	0.910140	−	0.414301i	$-0.135974\pi$
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	−0.813865	+	0.581054i	$0.802641\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−2.00000	−	3.46410i	−0.0640513	−	0.110940i
$976$		0			0
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$978$		0			0
$979$	32.0000			1.02272
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.00000	−	13.8564i	−0.254385	−	0.440608i
$990$		0			0
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	0.424594	+	0.905384i	$0.360417\pi$
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	−0.996382	+	0.0849833i	$0.972916\pi$
$992$		0			0
$993$	−40.0000			−1.26936
$994$		0			0
$995$	20.0000			0.634043
$996$		0			0
$997$	−3.00000	+	5.19615i	−0.0950110	+	0.164564i	−0.909613	−	0.415456i	$-0.863622\pi$
$997$	−3.00000	+	5.19615i	−0.0950110	+	0.164564i	0.814602	+	0.580020i	$0.196955\pi$
$998$		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	1960.2.q.b.361.1		2
7.2	even	3	inner	1960.2.q.b.961.1		2
7.3	odd	6		1960.2.a.b.1.1	✓	1
7.4	even	3		1960.2.a.n.1.1	yes	1
7.5	odd	6		1960.2.q.n.961.1		2
7.6	odd	2		1960.2.q.n.361.1		2
28.3	even	6		3920.2.a.bd.1.1		1
28.11	odd	6		3920.2.a.f.1.1		1
35.4	even	6		9800.2.a.i.1.1		1
35.24	odd	6		9800.2.a.bn.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.b.1.1	✓	1	7.3	odd	6
1960.2.a.n.1.1	yes	1	7.4	even	3
1960.2.q.b.361.1		2	1.1	even	1	trivial
1960.2.q.b.961.1		2	7.2	even	3	inner
1960.2.q.n.361.1		2	7.6	odd	2
1960.2.q.n.961.1		2	7.5	odd	6
3920.2.a.f.1.1		1	28.11	odd	6
3920.2.a.bd.1.1		1	28.3	even	6
9800.2.a.i.1.1		1	35.4	even	6
9800.2.a.bn.1.1		1	35.24	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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(-1.00000 - 1.73205i) q^{19} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} +10.0000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-4.00000 - 6.92820i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{39} -12.0000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-2.00000 - 3.46410i) q^{47} +(-1.00000 + 1.73205i) q^{53} +4.00000 q^{55} +4.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-1.00000 - 1.73205i) q^{65} +(-2.00000 + 3.46410i) q^{67} -8.00000 q^{69} -12.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(2.00000 + 3.46410i) q^{79} +(5.50000 - 9.52628i) q^{81} +14.0000 q^{83} +(-10.0000 + 17.3205i) q^{87} +(-4.00000 - 6.92820i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-1.00000 + 1.73205i) q^{95} -8.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - q^{5} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - q^5 - q^9	\( 2 q - 2 q^{3} - q^{5} - q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} - 2 q^{19} + 4 q^{23} - q^{25} - 8 q^{27} + 20 q^{29} - 4 q^{31} - 8 q^{33} + 2 q^{37} - 4 q^{39} - 24 q^{41} - 8 q^{43} - q^{45} - 4 q^{47} - 2 q^{53} + 8 q^{55} + 8 q^{57} - 10 q^{59} - 6 q^{61} - 2 q^{65} - 4 q^{67} - 16 q^{69} - 24 q^{71} + 4 q^{73} - 2 q^{75} + 4 q^{79} + 11 q^{81} + 28 q^{83} - 20 q^{87} - 8 q^{89} - 8 q^{93} - 2 q^{95} - 16 q^{97} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - q^5 - q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 - 2 * q^19 + 4 * q^23 - q^25 - 8 * q^27 + 20 * q^29 - 4 * q^31 - 8 * q^33 + 2 * q^37 - 4 * q^39 - 24 * q^41 - 8 * q^43 - q^45 - 4 * q^47 - 2 * q^53 + 8 * q^55 + 8 * q^57 - 10 * q^59 - 6 * q^61 - 2 * q^65 - 4 * q^67 - 16 * q^69 - 24 * q^71 + 4 * q^73 - 2 * q^75 + 4 * q^79 + 11 * q^81 + 28 * q^83 - 20 * q^87 - 8 * q^89 - 8 * q^93 - 2 * q^95 - 16 * q^97 + 8 * q^99

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