LMFDB - Embedded newform 1872.2.t.r.1153.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,2,Mod(289,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1872.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.t (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:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1872.1153
Dual form			1872.2.t.r.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.561553 q^{5} +(-1.78078 - 3.08440i) q^{7} +O(q^{10})$	$q-0.561553 q^{5} +(-1.78078 - 3.08440i) q^{7} +(1.00000 - 1.73205i) q^{11} +(0.500000 - 3.57071i) q^{13} +(1.28078 + 2.21837i) q^{17} +(-0.561553 - 0.972638i) q^{19} +(-1.00000 + 1.73205i) q^{23} -4.68466 q^{25} +(-2.84233 + 4.92306i) q^{29} +1.56155 q^{31} +(1.00000 + 1.73205i) q^{35} +(-1.71922 + 2.97778i) q^{37} +(1.28078 - 2.21837i) q^{41} +(0.219224 + 0.379706i) q^{43} -8.24621 q^{47} +(-2.84233 + 4.92306i) q^{49} -11.6847 q^{53} +(-0.561553 + 0.972638i) q^{55} +(5.56155 + 9.63289i) q^{59} +(-6.06155 - 10.4989i) q^{61} +(-0.280776 + 2.00514i) q^{65} +(0.219224 - 0.379706i) q^{67} +(-7.00000 - 12.1244i) q^{71} -1.87689 q^{73} -7.12311 q^{77} -9.56155 q^{79} -9.12311 q^{83} +(-0.719224 - 1.24573i) q^{85} +(6.56155 - 11.3649i) q^{89} +(-11.9039 + 4.81645i) q^{91} +(0.315342 + 0.546188i) q^{95} +(2.21922 + 3.84381i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5} - 3 q^{7}+O(q^{10}) $ 4 * q + 6 * q^5 - 3 * q^7	$ 4 q + 6 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} + q^{17} + 6 q^{19} - 4 q^{23} + 6 q^{25} + q^{29} - 2 q^{31} + 4 q^{35} - 11 q^{37} + q^{41} + 5 q^{43} + q^{49} - 22 q^{53} + 6 q^{55} + 14 q^{59} - 16 q^{61} + 3 q^{65} + 5 q^{67} - 28 q^{71} - 24 q^{73} - 12 q^{77} - 30 q^{79} - 20 q^{83} - 7 q^{85} + 18 q^{89} - 27 q^{91} + 26 q^{95} + 13 q^{97}+O(q^{100}) $ 4 * q + 6 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 + q^17 + 6 * q^19 - 4 * q^23 + 6 * q^25 + q^29 - 2 * q^31 + 4 * q^35 - 11 * q^37 + q^41 + 5 * q^43 + q^49 - 22 * q^53 + 6 * q^55 + 14 * q^59 - 16 * q^61 + 3 * q^65 + 5 * q^67 - 28 * q^71 - 24 * q^73 - 12 * q^77 - 30 * q^79 - 20 * q^83 - 7 * q^85 + 18 * q^89 - 27 * q^91 + 26 * q^95 + 13 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	−0.561553			−0.251134			−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−0.561553			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	−0.977029	−	0.213107i	$-0.931642\pi$
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	0.303959	−	0.952685i	$-0.401692\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	0.500000	−	3.57071i	0.138675	−	0.990338i
$13$	0.500000	−	3.57071i	0.138675	−	0.990338i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.28078	+	2.21837i	0.310634	+	0.538034i	0.978500	−	0.206248i	$-0.0661254\pi$
$17$	1.28078	+	2.21837i	0.310634	+	0.538034i	−0.667866	+	0.744282i	$0.732792\pi$
$18$		0			0
$19$	−0.561553	−	0.972638i	−0.128829	−	0.223138i	0.794394	−	0.607403i	$-0.207789\pi$
$19$	−0.561553	−	0.972638i	−0.128829	−	0.223138i	−0.923223	+	0.384264i	$0.874455\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.84233	+	4.92306i	−0.527807	+	0.914189i	0.471667	+	0.881777i	$0.343652\pi$
$29$	−2.84233	+	4.92306i	−0.527807	+	0.914189i	−0.999475	+	0.0324124i	$0.989681\pi$
$30$		0			0
$31$	1.56155			0.280463			0.140232	−	0.990119i	$-0.455215\pi$
$31$	1.56155			0.280463			0.140232	+	0.990119i	$0.455215\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$		0			0
$37$	−1.71922	+	2.97778i	−0.282639	+	0.489544i	−0.972034	−	0.234841i	$-0.924543\pi$
$37$	−1.71922	+	2.97778i	−0.282639	+	0.489544i	0.689395	+	0.724385i	$0.257876\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.28078	−	2.21837i	0.200024	−	0.346451i	−0.748512	−	0.663121i	$-0.769231\pi$
$41$	1.28078	−	2.21837i	0.200024	−	0.346451i	0.948536	+	0.316670i	$0.102565\pi$
$42$		0			0
$43$	0.219224	+	0.379706i	0.0334313	+	0.0579047i	0.882257	−	0.470768i	$-0.156023\pi$
$43$	0.219224	+	0.379706i	0.0334313	+	0.0579047i	−0.848826	+	0.528673i	$0.822690\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.24621			−1.20283			−0.601417	−	0.798935i	$-0.705397\pi$
$47$	−8.24621			−1.20283			−0.601417	+	0.798935i	$0.705397\pi$
$48$		0			0
$49$	−2.84233	+	4.92306i	−0.406047	+	0.703294i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.6847			−1.60501			−0.802506	−	0.596645i	$-0.796500\pi$
$53$	−11.6847			−1.60501			−0.802506	+	0.596645i	$0.796500\pi$
$54$		0			0
$55$	−0.561553	+	0.972638i	−0.0757198	+	0.131150i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.56155	+	9.63289i	0.724053	+	1.25410i	0.959363	+	0.282175i	$0.0910560\pi$
$59$	5.56155	+	9.63289i	0.724053	+	1.25410i	−0.235310	+	0.971920i	$0.575611\pi$
$60$		0			0
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	−0.934173	−	0.356821i	$-0.883861\pi$
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	0.158071	−	0.987428i	$-0.449473\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.280776	+	2.00514i	−0.0348260	+	0.248708i
$66$		0			0
$67$	0.219224	−	0.379706i	0.0267824	−	0.0463885i	−0.852324	−	0.523015i	$-0.824807\pi$
$67$	0.219224	−	0.379706i	0.0267824	−	0.0463885i	0.879106	+	0.476626i	$0.158141\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	−0.897447	−	0.441123i	$-0.854580\pi$
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	0.0666994	−	0.997773i	$-0.478753\pi$
$72$		0			0
$73$	−1.87689			−0.219674			−0.109837	−	0.993950i	$-0.535033\pi$
$73$	−1.87689			−0.219674			−0.109837	+	0.993950i	$0.535033\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.12311			−0.811753
$78$		0			0
$79$	−9.56155			−1.07576			−0.537879	−	0.843022i	$-0.680774\pi$
$79$	−9.56155			−1.07576			−0.537879	+	0.843022i	$0.680774\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.12311			−1.00139			−0.500695	−	0.865624i	$-0.666922\pi$
$83$	−9.12311			−1.00139			−0.500695	+	0.865624i	$0.666922\pi$
$84$		0			0
$85$	−0.719224	−	1.24573i	−0.0780108	−	0.135119i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.56155	−	11.3649i	0.695523	−	1.20468i	−0.274481	−	0.961593i	$-0.588506\pi$
$89$	6.56155	−	11.3649i	0.695523	−	1.20468i	0.970004	−	0.243089i	$-0.0781607\pi$
$90$		0			0
$91$	−11.9039	+	4.81645i	−1.24787	+	0.504901i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.315342	+	0.546188i	0.0323534	+	0.0560377i
$96$		0			0
$97$	2.21922	+	3.84381i	0.225328	+	0.390280i	0.956418	−	0.292002i	$-0.0943213\pi$
$97$	2.21922	+	3.84381i	0.225328	+	0.390280i	−0.731090	+	0.682281i	$0.760988\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.71922	+	2.97778i	−0.171069	+	0.296300i	−0.938794	−	0.344479i	$-0.888055\pi$
$101$	−1.71922	+	2.97778i	−0.171069	+	0.296300i	0.767725	+	0.640780i	$0.221389\pi$
$102$		0			0
$103$	7.56155			0.745062			0.372531	−	0.928020i	$-0.378490\pi$
$103$	7.56155			0.745062			0.372531	+	0.928020i	$0.378490\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	−0.993553	−	0.113369i	$-0.963836\pi$
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	0.594957	+	0.803757i	$0.297169\pi$
$108$		0			0
$109$	17.8078			1.70567			0.852837	−	0.522177i	$-0.174880\pi$
$109$	17.8078			1.70567			0.852837	+	0.522177i	$0.174880\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.40388	−	12.8239i	−0.696499	−	1.20637i	−0.969673	−	0.244406i	$-0.921407\pi$
$113$	−7.40388	−	12.8239i	−0.696499	−	1.20637i	0.273174	−	0.961965i	$-0.411926\pi$
$114$		0			0
$115$	0.561553	−	0.972638i	0.0523651	−	0.0906990i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.56155	−	7.90084i	0.418157	−	0.724269i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.43845			0.486430
$126$		0			0
$127$	4.78078	−	8.28055i	0.424225	−	0.734780i	−0.572122	−	0.820168i	$-0.693880\pi$
$127$	4.78078	−	8.28055i	0.424225	−	0.734780i	0.996348	+	0.0853884i	$0.0272131\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−17.3693			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$131$	−17.3693			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.719224	−	1.24573i	−0.0614474	−	0.106430i	0.833665	−	0.552270i	$-0.186238\pi$
$137$	−0.719224	−	1.24573i	−0.0614474	−	0.106430i	−0.895113	+	0.445840i	$0.852905\pi$
$138$		0			0
$139$	5.46543	+	9.46641i	0.463572	+	0.802930i	0.999136	−	0.0415643i	$-0.0132342\pi$
$139$	5.46543	+	9.46641i	0.463572	+	0.802930i	−0.535564	+	0.844495i	$0.679901\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.68466	−	4.43674i	−0.475375	−	0.371019i
$144$		0			0
$145$	1.59612	−	2.76456i	0.132550	−	0.229584i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.28078	−	5.68247i	−0.268772	−	0.465526i	0.699773	−	0.714365i	$-0.253284\pi$
$149$	−3.28078	−	5.68247i	−0.268772	−	0.465526i	−0.968545	+	0.248839i	$0.919951\pi$
$150$		0			0
$151$	−15.3693			−1.25074			−0.625369	−	0.780329i	$-0.715051\pi$
$151$	−15.3693			−1.25074			−0.625369	+	0.780329i	$0.715051\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.876894			−0.0704339
$156$		0			0
$157$	−4.36932			−0.348709			−0.174355	−	0.984683i	$-0.555784\pi$
$157$	−4.36932			−0.348709			−0.174355	+	0.984683i	$0.555784\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.12311			0.561379
$162$		0			0
$163$	7.90388	+	13.6899i	0.619080	+	1.07228i	0.989654	+	0.143475i	$0.0458276\pi$
$163$	7.90388	+	13.6899i	0.619080	+	1.07228i	−0.370574	+	0.928803i	$0.620839\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.12311	−	5.40938i	0.241673	−	0.418590i	−0.719518	−	0.694474i	$-0.755637\pi$
$167$	3.12311	−	5.40938i	0.241673	−	0.418590i	0.961191	+	0.275884i	$0.0889705\pi$
$168$		0			0
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.87689	+	3.25088i	0.142698	+	0.247160i	0.928512	−	0.371303i	$-0.121089\pi$
$173$	1.87689	+	3.25088i	0.142698	+	0.247160i	−0.785814	+	0.618463i	$0.787756\pi$
$174$		0			0
$175$	8.34233	+	14.4493i	0.630621	+	1.09227i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.56155	−	11.3649i	0.490433	−	0.849456i	−0.509506	−	0.860467i	$-0.670172\pi$
$179$	6.56155	−	11.3649i	0.490433	−	0.849456i	0.999939	+	0.0110115i	$0.00350513\pi$
$180$		0			0
$181$	9.68466			0.719855			0.359927	−	0.932980i	$-0.382801\pi$
$181$	9.68466			0.719855			0.359927	+	0.932980i	$0.382801\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.965435	−	1.67218i	0.0709802	−	0.122941i
$186$		0			0
$187$	5.12311			0.374639
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	0.881452	−	0.472274i	$-0.156567\pi$
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	−0.849727	+	0.527223i	$0.823233\pi$
$192$		0			0
$193$	−9.74621	+	16.8809i	−0.701548	+	1.21512i	0.266375	+	0.963869i	$0.414174\pi$
$193$	−9.74621	+	16.8809i	−0.701548	+	1.21512i	−0.967923	+	0.251247i	$0.919159\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.68466	+	9.84612i	−0.405015	+	0.701507i	−0.994323	−	0.106402i	$-0.966067\pi$
$197$	−5.68466	+	9.84612i	−0.405015	+	0.701507i	0.589308	+	0.807908i	$0.299400\pi$
$198$		0			0
$199$	−11.5885	−	20.0719i	−0.821490	−	1.42286i	−0.904573	−	0.426320i	$-0.859810\pi$
$199$	−11.5885	−	20.0719i	−0.821490	−	1.42286i	0.0830828	−	0.996543i	$-0.473523\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	20.2462			1.42101
$204$		0			0
$205$	−0.719224	+	1.24573i	−0.0502328	+	0.0870057i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.24621			−0.155374
$210$		0			0
$211$	3.65767	−	6.33527i	0.251804	−	0.436138i	−0.712218	−	0.701958i	$-0.752309\pi$
$211$	3.65767	−	6.33527i	0.251804	−	0.436138i	0.964023	+	0.265820i	$0.0856427\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.123106	−	0.213225i	−0.00839573	−	0.0145418i
$216$		0			0
$217$	−2.78078	−	4.81645i	−0.188771	−	0.326962i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.56155	−	3.46410i	0.575912	−	0.233021i
$222$		0			0
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.561553	+	0.972638i	0.0372716	+	0.0645563i	0.884059	−	0.467374i	$-0.154800\pi$
$227$	0.561553	+	0.972638i	0.0372716	+	0.0645563i	−0.846788	+	0.531931i	$0.821467\pi$
$228$		0			0
$229$	0.246211			0.0162701			0.00813505	−	0.999967i	$-0.497411\pi$
$229$	0.246211			0.0162701			0.00813505	+	0.999967i	$0.497411\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	4.63068			0.302072
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.630683			−0.0407955			−0.0203977	−	0.999792i	$-0.506493\pi$
$239$	−0.630683			−0.0407955			−0.0203977	+	0.999792i	$0.506493\pi$
$240$		0			0
$241$	−1.40388	−	2.43160i	−0.0904320	−	0.156633i	0.817261	−	0.576268i	$-0.195491\pi$
$241$	−1.40388	−	2.43160i	−0.0904320	−	0.156633i	−0.907693	+	0.419635i	$0.862158\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.59612	−	2.76456i	0.101972	−	0.176621i
$246$		0			0
$247$	−3.75379	+	1.51883i	−0.238848	+	0.0966406i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.3693	+	26.6204i	0.970103	+	1.68027i	0.695231	+	0.718786i	$0.255302\pi$
$251$	15.3693	+	26.6204i	0.970103	+	1.68027i	0.274871	+	0.961481i	$0.411365\pi$
$252$		0			0
$253$	2.00000	+	3.46410i	0.125739	+	0.217786i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.08854	+	14.0098i	−0.504549	+	0.873905i	0.495437	+	0.868644i	$0.335008\pi$
$257$	−8.08854	+	14.0098i	−0.504549	+	0.873905i	−0.999986	+	0.00526106i	$0.998325\pi$
$258$		0			0
$259$	12.2462			0.760943
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.68466	−	13.3102i	0.473856	−	0.820743i	−0.525696	−	0.850673i	$-0.676195\pi$
$263$	7.68466	−	13.3102i	0.473856	−	0.820743i	0.999552	+	0.0299295i	$0.00952826\pi$
$264$		0			0
$265$	6.56155			0.403073
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.68466	+	2.91791i	0.102715	+	0.177908i	0.912803	−	0.408401i	$-0.133914\pi$
$269$	1.68466	+	2.91791i	0.102715	+	0.177908i	−0.810087	+	0.586310i	$0.800580\pi$
$270$		0			0
$271$	−0.534565	+	0.925894i	−0.0324725	+	0.0562441i	−0.881805	−	0.471614i	$-0.843671\pi$
$271$	−0.534565	+	0.925894i	−0.0324725	+	0.0562441i	0.849332	+	0.527858i	$0.177005\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.68466	+	8.11407i	−0.282496	+	0.489297i
$276$		0			0
$277$	−8.84233	−	15.3154i	−0.531284	−	0.920211i	−0.999333	−	0.0365086i	$-0.988376\pi$
$277$	−8.84233	−	15.3154i	−0.531284	−	0.920211i	0.468049	−	0.883702i	$-0.344957\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.80776			0.167497			0.0837486	−	0.996487i	$-0.473311\pi$
$281$	2.80776			0.167497			0.0837486	+	0.996487i	$0.473311\pi$
$282$		0			0
$283$	−0.657671	+	1.13912i	−0.0390945	+	0.0677136i	−0.884911	−	0.465761i	$-0.845781\pi$
$283$	−0.657671	+	1.13912i	−0.0390945	+	0.0677136i	0.845816	+	0.533475i	$0.179114\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.12311			−0.538520
$288$		0			0
$289$	5.21922	−	9.03996i	0.307013	−	0.531762i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.2808	+	21.2709i	0.717451	+	1.24266i	0.962007	+	0.273026i	$0.0880244\pi$
$293$	12.2808	+	21.2709i	0.717451	+	1.24266i	−0.244556	+	0.969635i	$0.578642\pi$
$294$		0			0
$295$	−3.12311	−	5.40938i	−0.181834	−	0.314946i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.68466	+	4.43674i	0.328752	+	0.256583i
$300$		0			0
$301$	0.780776	−	1.35234i	0.0450032	−	0.0779478i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.40388	+	5.89570i	0.194906	+	0.337587i
$306$		0			0
$307$	−10.1922			−0.581702			−0.290851	−	0.956768i	$-0.593938\pi$
$307$	−10.1922			−0.581702			−0.290851	+	0.956768i	$0.593938\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.8769			−0.616772			−0.308386	−	0.951261i	$-0.599789\pi$
$311$	−10.8769			−0.616772			−0.308386	+	0.951261i	$0.599789\pi$
$312$		0			0
$313$	−1.31534			−0.0743475			−0.0371738	−	0.999309i	$-0.511835\pi$
$313$	−1.31534			−0.0743475			−0.0371738	+	0.999309i	$0.511835\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	23.0540			1.29484			0.647420	−	0.762133i	$-0.275848\pi$
$317$	23.0540			1.29484			0.647420	+	0.762133i	$0.275848\pi$
$318$		0			0
$319$	5.68466	+	9.84612i	0.318280	+	0.551277i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.43845	−	2.49146i	0.0800373	−	0.138629i
$324$		0			0
$325$	−2.34233	+	16.7276i	−0.129929	+	0.927879i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	14.6847	+	25.4346i	0.809591	+	1.40225i
$330$		0			0
$331$	−11.9039	−	20.6181i	−0.654297	−	1.13327i	−0.982070	−	0.188518i	$-0.939631\pi$
$331$	−11.9039	−	20.6181i	−0.654297	−	1.13327i	0.327773	−	0.944756i	$-0.393702\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.123106	+	0.213225i	−0.00672598	+	0.0116497i
$336$		0			0
$337$	2.12311			0.115653			0.0578265	−	0.998327i	$-0.481583\pi$
$337$	2.12311			0.115653			0.0578265	+	0.998327i	$0.481583\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.56155	−	2.70469i	0.0845628	−	0.146467i
$342$		0			0
$343$	−4.68466			−0.252948
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.80776	+	11.7914i	0.365460	+	0.632995i	0.988850	−	0.148916i	$-0.0475784\pi$
$347$	6.80776	+	11.7914i	0.365460	+	0.632995i	−0.623390	+	0.781911i	$0.714245\pi$
$348$		0			0
$349$	6.90388	−	11.9579i	0.369556	−	0.640090i	−0.619940	−	0.784649i	$-0.712843\pi$
$349$	6.90388	−	11.9579i	0.369556	−	0.640090i	0.989496	+	0.144559i	$0.0461763\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.84233	−	15.3154i	0.470630	−	0.815155i	−0.528806	−	0.848743i	$-0.677360\pi$
$353$	8.84233	−	15.3154i	0.470630	−	0.815155i	0.999436	+	0.0335881i	$0.0106934\pi$
$354$		0			0
$355$	3.93087	+	6.80847i	0.208629	+	0.361356i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.3693			0.811162			0.405581	−	0.914059i	$-0.367069\pi$
$359$	15.3693			0.811162			0.405581	+	0.914059i	$0.367069\pi$
$360$		0			0
$361$	8.86932	−	15.3621i	0.466806	−	0.808532i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.05398			0.0551676
$366$		0			0
$367$	10.0270	−	17.3673i	0.523404	−	0.906563i	−0.476224	−	0.879324i	$-0.657995\pi$
$367$	10.0270	−	17.3673i	0.523404	−	0.906563i	0.999629	−	0.0272394i	$-0.00867165\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	20.8078	+	36.0401i	1.08029	+	1.87111i
$372$		0			0
$373$	−1.81534	−	3.14426i	−0.0939948	−	0.162804i	0.815194	−	0.579188i	$-0.196630\pi$
$373$	−1.81534	−	3.14426i	−0.0939948	−	0.162804i	−0.909189	+	0.416384i	$0.863297\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.1577	+	12.6107i	0.832162	+	0.649483i
$378$		0			0
$379$	5.65767	−	9.79937i	0.290615	−	0.503360i	−0.683340	−	0.730100i	$-0.739473\pi$
$379$	5.65767	−	9.79937i	0.290615	−	0.503360i	0.973955	+	0.226740i	$0.0728068\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.3693	−	23.1563i	−0.683140	−	1.18323i	−0.974017	−	0.226473i	$-0.927280\pi$
$383$	−13.3693	−	23.1563i	−0.683140	−	1.18323i	0.290877	−	0.956760i	$-0.406053\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.05398			0.154843			0.0774213	−	0.996998i	$-0.475331\pi$
$389$	3.05398			0.154843			0.0774213	+	0.996998i	$0.475331\pi$
$390$		0			0
$391$	−5.12311			−0.259087
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.36932			0.270160
$396$		0			0
$397$	6.02699	+	10.4390i	0.302486	+	0.523921i	0.976698	−	0.214617i	$-0.0688502\pi$
$397$	6.02699	+	10.4390i	0.302486	+	0.523921i	−0.674213	+	0.738537i	$0.735517\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.28078	−	16.0748i	0.463460	−	0.802736i	−0.535671	−	0.844427i	$-0.679941\pi$
$401$	9.28078	−	16.0748i	0.463460	−	0.802736i	0.999131	+	0.0416909i	$0.0132745\pi$
$402$		0			0
$403$	0.780776	−	5.57586i	0.0388932	−	0.277753i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.43845	+	5.95557i	0.170437	+	0.295206i
$408$		0			0
$409$	9.18466	+	15.9083i	0.454152	+	0.786615i	0.998639	−	0.0521548i	$-0.0166089\pi$
$409$	9.18466	+	15.9083i	0.454152	+	0.786615i	−0.544487	+	0.838769i	$0.683276\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	19.8078	−	34.3081i	0.974676	−	1.68819i
$414$		0			0
$415$	5.12311			0.251483
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	−0.563521	−	0.826102i	$-0.690554\pi$
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	0.997186	+	0.0749725i	$0.0238869\pi$
$420$		0			0
$421$	14.7538			0.719056			0.359528	−	0.933134i	$-0.382938\pi$
$421$	14.7538			0.719056			0.359528	+	0.933134i	$0.382938\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$	−21.5885	+	37.3924i	−1.04474	+	1.80955i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.43845	−	2.49146i	0.0692876	−	0.120010i	−0.829300	−	0.558803i	$-0.811261\pi$
$431$	1.43845	−	2.49146i	0.0692876	−	0.120010i	0.898588	+	0.438794i	$0.144594\pi$
$432$		0			0
$433$	−12.6231	−	21.8639i	−0.606628	−	1.05071i	−0.991792	−	0.127862i	$-0.959189\pi$
$433$	−12.6231	−	21.8639i	−0.606628	−	1.05071i	0.385164	−	0.922848i	$-0.374145\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.24621			0.107451
$438$		0			0
$439$	−0.657671	+	1.13912i	−0.0313889	+	0.0543672i	−0.881293	−	0.472570i	$-0.843326\pi$
$439$	−0.657671	+	1.13912i	−0.0313889	+	0.0543672i	0.849904	+	0.526937i	$0.176660\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.7386			0.700254			0.350127	−	0.936702i	$-0.386138\pi$
$443$	14.7386			0.700254			0.350127	+	0.936702i	$0.386138\pi$
$444$		0			0
$445$	−3.68466	+	6.38202i	−0.174670	+	0.302537i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.12311	+	7.14143i	0.194581	+	0.337025i	0.946763	−	0.321931i	$-0.104332\pi$
$449$	4.12311	+	7.14143i	0.194581	+	0.337025i	−0.752182	+	0.658956i	$0.770998\pi$
$450$		0			0
$451$	−2.56155	−	4.43674i	−0.120619	−	0.208918i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.68466	−	2.70469i	0.313382	−	0.126798i
$456$		0			0
$457$	14.3078	−	24.7818i	0.669289	−	1.15924i	−0.308814	−	0.951122i	$-0.599932\pi$
$457$	14.3078	−	24.7818i	0.669289	−	1.15924i	0.978103	−	0.208120i	$-0.0667345\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.4039	−	31.8765i	−0.857154	−	1.48463i	−0.874632	−	0.484787i	$-0.838897\pi$
$461$	−18.4039	−	31.8765i	−0.857154	−	1.48463i	0.0174778	−	0.999847i	$-0.494436\pi$
$462$		0			0
$463$	26.6847			1.24014			0.620071	−	0.784546i	$-0.287104\pi$
$463$	26.6847			1.24014			0.620071	+	0.784546i	$0.287104\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.0000			−1.20314			−0.601568	−	0.798821i	$-0.705457\pi$
$467$	−26.0000			−1.20314			−0.601568	+	0.798821i	$0.705457\pi$
$468$		0			0
$469$	−1.56155			−0.0721058
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.876894			0.0403196
$474$		0			0
$475$	2.63068	+	4.55648i	0.120704	+	0.209065i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.12311	−	5.40938i	0.142698	−	0.247161i	−0.785814	−	0.618463i	$-0.787755\pi$
$479$	3.12311	−	5.40938i	0.142698	−	0.247161i	0.928512	+	0.371303i	$0.121089\pi$
$480$		0			0
$481$	9.77320	+	7.62775i	0.445620	+	0.347795i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.24621	−	2.15850i	−0.0565875	−	0.0980125i
$486$		0			0
$487$	−0.561553	−	0.972638i	−0.0254464	−	0.0440744i	0.853022	−	0.521875i	$-0.174767\pi$
$487$	−0.561553	−	0.972638i	−0.0254464	−	0.0440744i	−0.878468	+	0.477801i	$0.841434\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.87689	−	17.1073i	0.445738	−	0.772041i	−0.552365	−	0.833602i	$-0.686275\pi$
$491$	9.87689	−	17.1073i	0.445738	−	0.772041i	0.998103	+	0.0615613i	$0.0196080\pi$
$492$		0			0
$493$	−14.5616			−0.655819
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−24.9309	+	43.1815i	−1.11830	+	1.93696i
$498$		0			0
$499$	28.4924			1.27550			0.637748	−	0.770245i	$-0.279866\pi$
$499$	28.4924			1.27550			0.637748	+	0.770245i	$0.279866\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.87689	+	10.1791i	0.262038	+	0.453863i	0.966783	−	0.255597i	$-0.0822722\pi$
$503$	5.87689	+	10.1791i	0.262038	+	0.453863i	−0.704746	+	0.709460i	$0.748939\pi$
$504$		0			0
$505$	0.965435	−	1.67218i	0.0429613	−	0.0744111i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.40388	−	5.89570i	0.150874	−	0.261322i	−0.780675	−	0.624938i	$-0.785124\pi$
$509$	3.40388	−	5.89570i	0.150874	−	0.261322i	0.931549	+	0.363615i	$0.118458\pi$
$510$		0			0
$511$	3.34233	+	5.78908i	0.147856	+	0.256094i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.24621			−0.187110
$516$		0			0
$517$	−8.24621	+	14.2829i	−0.362668	+	0.628159i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	37.9309			1.66178			0.830891	−	0.556436i	$-0.187831\pi$
$521$	37.9309			1.66178			0.830891	+	0.556436i	$0.187831\pi$
$522$		0			0
$523$	−11.9309	+	20.6649i	−0.521701	+	0.903612i	0.477981	+	0.878370i	$0.341369\pi$
$523$	−11.9309	+	20.6649i	−0.521701	+	0.903612i	−0.999681	+	0.0252415i	$0.991965\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.28078	−	5.68247i	−0.315365	−	0.246135i
$534$		0			0
$535$	2.31534	−	4.01029i	0.100101	−	0.173380i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.68466	+	9.84612i	0.244856	+	0.424102i
$540$		0			0
$541$	−29.7386			−1.27856			−0.639282	−	0.768972i	$-0.720768\pi$
$541$	−29.7386			−1.27856			−0.639282	+	0.768972i	$0.720768\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−10.0000			−0.428353
$546$		0			0
$547$	24.9309			1.06597			0.532984	−	0.846126i	$-0.321071\pi$
$547$	24.9309			1.06597			0.532984	+	0.846126i	$0.321071\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.38447			0.271988
$552$		0			0
$553$	17.0270	+	29.4916i	0.724061	+	1.25411i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.03457	+	12.1842i	−0.298064	+	0.516262i	−0.975693	−	0.219142i	$-0.929674\pi$
$557$	−7.03457	+	12.1842i	−0.298064	+	0.516262i	0.677629	+	0.735404i	$0.263008\pi$
$558$		0			0
$559$	1.46543	−	0.592932i	0.0619813	−	0.0250783i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.684658	−	1.18586i	−0.0288549	−	0.0499782i	0.851237	−	0.524781i	$-0.175853\pi$
$563$	−0.684658	−	1.18586i	−0.0288549	−	0.0499782i	−0.880092	+	0.474803i	$0.842519\pi$
$564$		0			0
$565$	4.15767	+	7.20130i	0.174915	+	0.302961i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	20.3693	−	35.2807i	0.853926	−	1.47904i	−0.0237115	−	0.999719i	$-0.507548\pi$
$569$	20.3693	−	35.2807i	0.853926	−	1.47904i	0.877638	−	0.479325i	$-0.159118\pi$
$570$		0			0
$571$	−19.3693			−0.810581			−0.405290	−	0.914188i	$-0.632830\pi$
$571$	−19.3693			−0.810581			−0.405290	+	0.914188i	$0.632830\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.68466	−	8.11407i	0.195364	−	0.338380i
$576$		0			0
$577$	−29.6847			−1.23579			−0.617894	−	0.786261i	$-0.712014\pi$
$577$	−29.6847			−1.23579			−0.617894	+	0.786261i	$0.712014\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.2462	+	28.1393i	0.674006	+	1.16741i
$582$		0			0
$583$	−11.6847	+	20.2384i	−0.483929	+	0.838190i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.31534	+	12.6705i	−0.301936	+	0.522969i	−0.976575	−	0.215179i	$-0.930966\pi$
$587$	−7.31534	+	12.6705i	−0.301936	+	0.522969i	0.674638	+	0.738149i	$0.264300\pi$
$588$		0			0
$589$	−0.876894	−	1.51883i	−0.0361318	−	0.0625821i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−44.4233			−1.82425			−0.912123	−	0.409917i	$-0.865558\pi$
$593$	−44.4233			−1.82425			−0.912123	+	0.409917i	$0.865558\pi$
$594$		0			0
$595$	−2.56155	+	4.43674i	−0.105013	+	0.181889i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.384472			−0.0157091			−0.00785455	−	0.999969i	$-0.502500\pi$
$599$	−0.384472			−0.0157091			−0.00785455	+	0.999969i	$0.502500\pi$
$600$		0			0
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	−0.222846	−	0.974854i	$-0.571535\pi$
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	0.955671	−	0.294437i	$-0.0951321\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.96543	−	3.40423i	−0.0799063	−	0.138402i
$606$		0			0
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.12311	+	29.4449i	−0.166803	+	1.19121i
$612$		0			0
$613$	−11.4309	+	19.7988i	−0.461688	+	0.799668i	−0.999045	−	0.0436871i	$-0.986090\pi$
$613$	−11.4309	+	19.7988i	−0.461688	+	0.799668i	0.537357	+	0.843355i	$0.319423\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.40388	−	9.35980i	−0.217552	−	0.376811i	0.736507	−	0.676430i	$-0.236474\pi$
$617$	−5.40388	−	9.35980i	−0.217552	−	0.376811i	−0.954059	+	0.299619i	$0.903141\pi$
$618$		0			0
$619$	24.3002			0.976707			0.488353	−	0.872646i	$-0.337598\pi$
$619$	24.3002			0.976707			0.488353	+	0.872646i	$0.337598\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−46.7386			−1.87254
$624$		0			0
$625$	20.3693			0.814773
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−8.80776			−0.351189
$630$		0			0
$631$	−7.21922	−	12.5041i	−0.287393	−	0.497779i	0.685794	−	0.727796i	$-0.259455\pi$
$631$	−7.21922	−	12.5041i	−0.287393	−	0.497779i	−0.973187	+	0.230017i	$0.926122\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.68466	+	4.64996i	−0.106537	+	0.184528i
$636$		0			0
$637$	16.1577	+	12.6107i	0.640190	+	0.499653i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.0885	+	22.6700i	0.516966	+	0.895412i	0.999806	+	0.0197030i	$0.00627208\pi$
$641$	13.0885	+	22.6700i	0.516966	+	0.895412i	−0.482840	+	0.875709i	$0.660395\pi$
$642$		0			0
$643$	19.2732	+	33.3822i	0.760061	+	1.31646i	0.942819	+	0.333306i	$0.108164\pi$
$643$	19.2732	+	33.3822i	0.760061	+	1.31646i	−0.182758	+	0.983158i	$0.558502\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.8078	−	41.2363i	0.935980	−	1.62116i	0.163102	−	0.986609i	$-0.447850\pi$
$647$	23.8078	−	41.2363i	0.935980	−	1.62116i	0.772877	−	0.634555i	$-0.218817\pi$
$648$		0			0
$649$	22.2462			0.873240
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.43845	−	12.8838i	0.291089	−	0.504181i	−0.682979	−	0.730438i	$-0.739316\pi$
$653$	7.43845	−	12.8838i	0.291089	−	0.504181i	0.974068	+	0.226258i	$0.0726491\pi$
$654$		0			0
$655$	9.75379			0.381112
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	0.693280	−	0.720668i	$-0.256165\pi$
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	−0.970757	+	0.240064i	$0.922831\pi$
$660$		0			0
$661$	−15.1847	+	26.3006i	−0.590615	+	1.02297i	0.403535	+	0.914964i	$0.367781\pi$
$661$	−15.1847	+	26.3006i	−0.590615	+	1.02297i	−0.994150	+	0.108011i	$0.965552\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.12311	−	1.94528i	0.0435522	−	0.0754346i
$666$		0			0
$667$	−5.68466	−	9.84612i	−0.220111	−	0.381243i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−24.2462			−0.936015
$672$		0			0
$673$	3.37689	−	5.84895i	0.130170	−	0.225461i	−0.793572	−	0.608476i	$-0.791781\pi$
$673$	3.37689	−	5.84895i	0.130170	−	0.225461i	0.923742	+	0.383016i	$0.125114\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−25.6155			−0.984485			−0.492242	−	0.870458i	$-0.663823\pi$
$677$	−25.6155			−0.984485			−0.492242	+	0.870458i	$0.663823\pi$
$678$		0			0
$679$	7.90388	−	13.6899i	0.303323	−	0.525371i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−18.0540	−	31.2704i	−0.690816	−	1.19653i	−0.971571	−	0.236749i	$-0.923918\pi$
$683$	−18.0540	−	31.2704i	−0.690816	−	1.19653i	0.280755	−	0.959780i	$-0.409415\pi$
$684$		0			0
$685$	0.403882	+	0.699544i	0.0154315	+	0.0267282i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.84233	+	41.7226i	−0.222575	+	1.58950i
$690$		0			0
$691$	1.15009	−	1.99202i	0.0437516	−	0.0757800i	−0.843320	−	0.537411i	$-0.819402\pi$
$691$	1.15009	−	1.99202i	0.0437516	−	0.0757800i	0.887072	+	0.461631i	$0.152736\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.06913	−	5.31589i	−0.116419	−	0.201643i
$696$		0			0
$697$	6.56155			0.248537
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.3693			−0.731569			−0.365785	−	0.930700i	$-0.619199\pi$
$701$	−19.3693			−0.731569			−0.365785	+	0.930700i	$0.619199\pi$
$702$		0			0
$703$	3.86174			0.145648
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.2462			0.460566
$708$		0			0
$709$	−12.7462	−	22.0771i	−0.478694	−	0.829122i	0.521008	−	0.853552i	$-0.325556\pi$
$709$	−12.7462	−	22.0771i	−0.478694	−	0.829122i	−0.999702	+	0.0244297i	$0.992223\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.56155	+	2.70469i	−0.0584806	+	0.101291i
$714$		0			0
$715$	3.19224	+	2.49146i	0.119383	+	0.0931755i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.684658	−	1.18586i	−0.0255335	−	0.0442252i	0.852976	−	0.521950i	$-0.174795\pi$
$719$	−0.684658	−	1.18586i	−0.0255335	−	0.0442252i	−0.878510	+	0.477724i	$0.841462\pi$
$720$		0			0
$721$	−13.4654	−	23.3228i	−0.501479	−	0.868587i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.3153	−	23.0628i	0.494519	−	0.856533i
$726$		0			0
$727$	−39.6695			−1.47126			−0.735630	−	0.677383i	$-0.763114\pi$
$727$	−39.6695			−1.47126			−0.735630	+	0.677383i	$0.763114\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.561553	+	0.972638i	−0.0207698	+	0.0359743i
$732$		0			0
$733$	53.4924			1.97579			0.987894	−	0.155131i	$-0.0495801\pi$
$733$	53.4924			1.97579			0.987894	+	0.155131i	$0.0495801\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.438447	−	0.759413i	−0.0161504	−	0.0279733i
$738$		0			0
$739$	−3.12311	+	5.40938i	−0.114885	+	0.198987i	−0.917734	−	0.397196i	$-0.869983\pi$
$739$	−3.12311	+	5.40938i	−0.114885	+	0.198987i	0.802849	+	0.596183i	$0.203317\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18.6847	−	32.3628i	0.685474	−	1.18728i	−0.287814	−	0.957686i	$-0.592929\pi$
$743$	18.6847	−	32.3628i	0.685474	−	1.18728i	0.973288	−	0.229589i	$-0.0737382\pi$
$744$		0			0
$745$	1.84233	+	3.19101i	0.0674977	+	0.116909i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	29.3693			1.07313
$750$		0			0
$751$	−15.0540	+	26.0743i	−0.549327	+	0.951463i	0.448993	+	0.893535i	$0.351783\pi$
$751$	−15.0540	+	26.0743i	−0.549327	+	0.951463i	−0.998321	+	0.0579278i	$0.981551\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.63068			0.314103
$756$		0			0
$757$	−15.0000	+	25.9808i	−0.545184	+	0.944287i	0.453411	+	0.891302i	$0.350207\pi$
$757$	−15.0000	+	25.9808i	−0.545184	+	0.944287i	−0.998595	+	0.0529853i	$0.983126\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.68466	−	13.3102i	−0.278569	−	0.482495i	0.692461	−	0.721456i	$-0.256527\pi$
$761$	−7.68466	−	13.3102i	−0.278569	−	0.482495i	−0.971029	+	0.238961i	$0.923193\pi$
$762$		0			0
$763$	−31.7116	−	54.9262i	−1.14804	−	1.98846i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	37.1771	−	15.0423i	1.34239	−	0.543145i
$768$		0			0
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	−0.656873	−	0.754002i	$-0.728121\pi$
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	0.981421	+	0.191867i	$0.0614544\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.87689	−	6.71498i	−0.139442	−	0.241521i	0.787843	−	0.615876i	$-0.211198\pi$
$773$	−3.87689	−	6.71498i	−0.139442	−	0.241521i	−0.927286	+	0.374355i	$0.877864\pi$
$774$		0			0
$775$	−7.31534			−0.262775
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.87689			−0.103075
$780$		0			0
$781$	−28.0000			−1.00192
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.45360			0.0875728
$786$		0			0
$787$	−0.588540	−	1.01938i	−0.0209792	−	0.0363370i	0.855345	−	0.518058i	$-0.173345\pi$
$787$	−0.588540	−	1.01938i	−0.0209792	−	0.0363370i	−0.876324	+	0.481721i	$0.840012\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−26.3693	+	45.6730i	−0.937585	+	1.62394i
$792$		0			0
$793$	−40.5194	+	16.3946i	−1.43889	+	0.582190i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−20.8078	−	36.0401i	−0.737049	−	1.27661i	−0.953819	−	0.300383i	$-0.902885\pi$
$797$	−20.8078	−	36.0401i	−0.737049	−	1.27661i	0.216770	−	0.976223i	$-0.430448\pi$
$798$		0			0
$799$	−10.5616	−	18.2931i	−0.373641	−	0.647165i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.87689	+	3.25088i	−0.0662342	+	0.114721i
$804$		0			0
$805$	−4.00000			−0.140981
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.6501	−	32.3029i	0.655702	−	1.13571i	−0.326015	−	0.945365i	$-0.605706\pi$
$809$	18.6501	−	32.3029i	0.655702	−	1.13571i	0.981717	−	0.190345i	$-0.0609607\pi$
$810$		0			0
$811$	1.56155			0.0548335			0.0274168	−	0.999624i	$-0.491272\pi$
$811$	1.56155			0.0548335			0.0274168	+	0.999624i	$0.491272\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.43845	−	7.68762i	−0.155472	−	0.269285i
$816$		0			0
$817$	0.246211	−	0.426450i	0.00861384	−	0.0149196i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.2462	+	22.9431i	−0.462296	+	0.800720i	−0.999075	−	0.0430028i	$-0.986308\pi$
$821$	−13.2462	+	22.9431i	−0.462296	+	0.800720i	0.536779	+	0.843723i	$0.319641\pi$
$822$		0			0
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	34.7386			1.20798			0.603990	−	0.796992i	$-0.293577\pi$
$827$	34.7386			1.20798			0.603990	+	0.796992i	$0.293577\pi$
$828$		0			0
$829$	9.74621	−	16.8809i	0.338500	−	0.586299i	−0.645651	−	0.763633i	$-0.723414\pi$
$829$	9.74621	−	16.8809i	0.338500	−	0.586299i	0.984151	+	0.177334i	$0.0567472\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−14.5616			−0.504528
$834$		0			0
$835$	−1.75379	+	3.03765i	−0.0606924	+	0.105122i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.80776	+	16.9875i	0.338602	+	0.586475i	0.984170	−	0.177227i	$-0.0567128\pi$
$839$	9.80776	+	16.9875i	0.338602	+	0.586475i	−0.645568	+	0.763703i	$0.723379\pi$
$840$		0			0
$841$	−1.65767	−	2.87117i	−0.0571611	−	0.0990059i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.01941	+	2.00514i	0.241475	+	0.0689791i
$846$		0			0
$847$	12.4654	−	21.5908i	0.428317	−	0.741868i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.43845	−	5.95557i	−0.117868	−	0.204154i
$852$		0			0
$853$	−6.12311			−0.209651			−0.104826	−	0.994491i	$-0.533428\pi$
$853$	−6.12311			−0.209651			−0.104826	+	0.994491i	$0.533428\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.4384			−1.07392			−0.536958	−	0.843609i	$-0.680427\pi$
$857$	−31.4384			−1.07392			−0.536958	+	0.843609i	$0.680427\pi$
$858$		0			0
$859$	−20.4384			−0.697351			−0.348675	−	0.937244i	$-0.613368\pi$
$859$	−20.4384			−0.697351			−0.348675	+	0.937244i	$0.613368\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.49242			−0.0848430			−0.0424215	−	0.999100i	$-0.513507\pi$
$863$	−2.49242			−0.0848430			−0.0424215	+	0.999100i	$0.513507\pi$
$864$		0			0
$865$	−1.05398	−	1.82554i	−0.0358362	−	0.0620702i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.56155	+	16.5611i	−0.324353	+	0.561797i
$870$		0			0
$871$	−1.24621	−	0.972638i	−0.0422263	−	0.0329566i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−9.68466	−	16.7743i	−0.327401	−	0.567076i
$876$		0			0
$877$	−9.71922	−	16.8342i	−0.328195	−	0.568450i	0.653959	−	0.756530i	$-0.273107\pi$
$877$	−9.71922	−	16.8342i	−0.328195	−	0.568450i	−0.982154	+	0.188080i	$0.939774\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.9654	+	32.8491i	−0.638962	+	1.10671i	0.346699	+	0.937976i	$0.387302\pi$
$881$	−18.9654	+	32.8491i	−0.638962	+	1.10671i	−0.985661	+	0.168738i	$0.946031\pi$
$882$		0			0
$883$	11.8078			0.397363			0.198681	−	0.980064i	$-0.436334\pi$
$883$	11.8078			0.397363			0.198681	+	0.980064i	$0.436334\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.6847	+	42.7551i	−0.828830	+	1.43558i	0.0701272	+	0.997538i	$0.477659\pi$
$887$	−24.6847	+	42.7551i	−0.828830	+	1.43558i	−0.898957	+	0.438037i	$0.855674\pi$
$888$		0			0
$889$	−34.0540			−1.14213
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.63068	+	8.02058i	0.154960	+	0.268398i
$894$		0			0
$895$	−3.68466	+	6.38202i	−0.123165	+	0.213327i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.43845	+	7.68762i	−0.148031	+	0.256396i
$900$		0			0
$901$	−14.9654	−	25.9209i	−0.498571	−	0.863550i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.43845			−0.180780
$906$		0			0
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10.7386			−0.355787			−0.177893	−	0.984050i	$-0.556928\pi$
$911$	−10.7386			−0.355787			−0.177893	+	0.984050i	$0.556928\pi$
$912$		0			0
$913$	−9.12311	+	15.8017i	−0.301931	+	0.522959i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.9309	+	53.5738i	1.02143	+	1.76916i
$918$		0			0
$919$	22.2462	+	38.5316i	0.733835	+	1.27104i	0.955233	+	0.295856i	$0.0956047\pi$
$919$	22.2462	+	38.5316i	0.733835	+	1.27104i	−0.221398	+	0.975184i	$0.571062\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−46.7926	+	18.9328i	−1.54020	+	0.623181i
$924$		0			0
$925$	8.05398	−	13.9499i	0.264813	−	0.458670i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.40388	+	11.0918i	0.210105	+	0.363912i	0.951747	−	0.306884i	$-0.0992862\pi$
$929$	6.40388	+	11.0918i	0.210105	+	0.363912i	−0.741643	+	0.670795i	$0.765953\pi$
$930$		0			0
$931$	6.38447			0.209243
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.87689			−0.0940845
$936$		0			0
$937$	−3.43845			−0.112329			−0.0561646	−	0.998422i	$-0.517887\pi$
$937$	−3.43845			−0.112329			−0.0561646	+	0.998422i	$0.517887\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.49242			0.0812507			0.0406253	−	0.999174i	$-0.487065\pi$
$941$	2.49242			0.0812507			0.0406253	+	0.999174i	$0.487065\pi$
$942$		0			0
$943$	2.56155	+	4.43674i	0.0834156	+	0.144480i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.36932	+	9.29993i	−0.174479	+	0.302207i	−0.939981	−	0.341227i	$-0.889158\pi$
$947$	−5.36932	+	9.29993i	−0.174479	+	0.302207i	0.765502	+	0.643434i	$0.222491\pi$
$948$		0			0
$949$	−0.938447	+	6.70185i	−0.0304633	+	0.217551i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−17.4924	−	30.2978i	−0.566635	−	0.981441i	−0.996896	−	0.0787360i	$-0.974912\pi$
$953$	−17.4924	−	30.2978i	−0.566635	−	0.981441i	0.430260	−	0.902705i	$-0.358422\pi$
$954$		0			0
$955$	−0.246211	−	0.426450i	−0.00796721	−	0.0137996i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.56155	+	4.43674i	−0.0827169	+	0.143270i
$960$		0			0
$961$	−28.5616			−0.921340
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.47301	−	9.47954i	0.176183	−	0.305157i
$966$		0			0
$967$	9.12311			0.293379			0.146690	−	0.989183i	$-0.453138\pi$
$967$	9.12311			0.293379			0.146690	+	0.989183i	$0.453138\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	−0.881043	−	0.473035i	$-0.843158\pi$
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	0.0308612	−	0.999524i	$-0.490175\pi$
$972$		0			0
$973$	19.4654	−	33.7151i	0.624033	−	1.08086i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.91146	−	13.7030i	0.253110	−	0.438399i	−0.711270	−	0.702918i	$-0.751880\pi$
$977$	7.91146	−	13.7030i	0.253110	−	0.438399i	0.964380	+	0.264519i	$0.0852132\pi$
$978$		0			0
$979$	−13.1231	−	22.7299i	−0.419416	−	0.726450i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−27.6155			−0.880799			−0.440399	−	0.897802i	$-0.645163\pi$
$983$	−27.6155			−0.880799			−0.440399	+	0.897802i	$0.645163\pi$
$984$		0			0
$985$	3.19224	−	5.52911i	0.101713	−	0.176172i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.876894			−0.0278836
$990$		0			0
$991$	20.1771	−	34.9477i	0.640946	−	1.11015i	−0.344276	−	0.938869i	$-0.611876\pi$
$991$	20.1771	−	34.9477i	0.640946	−	1.11015i	0.985222	−	0.171283i	$-0.0547911\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.50758	+	11.2715i	0.206304	+	0.357329i
$996$		0			0
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	0.655355	−	0.755321i	$-0.272519\pi$
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	−0.981805	+	0.189893i	$0.939186\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.t.r.1153.1		4
3.2	odd	2		624.2.q.h.529.2		4
4.3	odd	2		117.2.g.c.100.2		4
12.11	even	2		39.2.e.b.22.1	yes	4
13.3	even	3	inner	1872.2.t.r.289.1		4
39.17	odd	6		8112.2.a.bo.1.1		2
39.29	odd	6		624.2.q.h.289.2		4
39.35	odd	6		8112.2.a.bk.1.2		2
52.3	odd	6		117.2.g.c.55.2		4
52.7	even	12		1521.2.b.h.1351.1		4
52.19	even	12		1521.2.b.h.1351.4		4
52.35	odd	6		1521.2.a.g.1.1		2
52.43	odd	6		1521.2.a.m.1.2		2
60.23	odd	4		975.2.bb.i.724.4		8
60.47	odd	4		975.2.bb.i.724.1		8
60.59	even	2		975.2.i.k.451.2		4
156.11	odd	12		507.2.j.g.361.4		8
156.23	even	6		507.2.e.g.484.2		4
156.35	even	6		507.2.a.g.1.2		2
156.47	odd	4		507.2.j.g.316.1		8
156.59	odd	12		507.2.b.d.337.4		4
156.71	odd	12		507.2.b.d.337.1		4
156.83	odd	4		507.2.j.g.316.4		8
156.95	even	6		507.2.a.d.1.1		2
156.107	even	6		39.2.e.b.16.1	✓	4
156.119	odd	12		507.2.j.g.361.1		8
156.155	even	2		507.2.e.g.22.2		4
780.107	odd	12		975.2.bb.i.874.4		8
780.263	odd	12		975.2.bb.i.874.1		8
780.419	even	6		975.2.i.k.601.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.1	✓	4	156.107	even	6
39.2.e.b.22.1	yes	4	12.11	even	2
117.2.g.c.55.2		4	52.3	odd	6
117.2.g.c.100.2		4	4.3	odd	2
507.2.a.d.1.1		2	156.95	even	6
507.2.a.g.1.2		2	156.35	even	6
507.2.b.d.337.1		4	156.71	odd	12
507.2.b.d.337.4		4	156.59	odd	12
507.2.e.g.22.2		4	156.155	even	2
507.2.e.g.484.2		4	156.23	even	6
507.2.j.g.316.1		8	156.47	odd	4
507.2.j.g.316.4		8	156.83	odd	4
507.2.j.g.361.1		8	156.119	odd	12
507.2.j.g.361.4		8	156.11	odd	12
624.2.q.h.289.2		4	39.29	odd	6
624.2.q.h.529.2		4	3.2	odd	2
975.2.i.k.451.2		4	60.59	even	2
975.2.i.k.601.2		4	780.419	even	6
975.2.bb.i.724.1		8	60.47	odd	4
975.2.bb.i.724.4		8	60.23	odd	4
975.2.bb.i.874.1		8	780.263	odd	12
975.2.bb.i.874.4		8	780.107	odd	12
1521.2.a.g.1.1		2	52.35	odd	6
1521.2.a.m.1.2		2	52.43	odd	6
1521.2.b.h.1351.1		4	52.7	even	12
1521.2.b.h.1351.4		4	52.19	even	12
1872.2.t.r.289.1		4	13.3	even	3	inner
1872.2.t.r.1153.1		4	1.1	even	1	trivial
8112.2.a.bk.1.2		2	39.35	odd	6
8112.2.a.bo.1.1		2	39.17	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:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.561553 q^{5} +(-1.78078 - 3.08440i) q^{7} +O(q^{10})\)	\(q-0.561553 q^{5} +(-1.78078 - 3.08440i) q^{7} +(1.00000 - 1.73205i) q^{11} +(0.500000 - 3.57071i) q^{13} +(1.28078 + 2.21837i) q^{17} +(-0.561553 - 0.972638i) q^{19} +(-1.00000 + 1.73205i) q^{23} -4.68466 q^{25} +(-2.84233 + 4.92306i) q^{29} +1.56155 q^{31} +(1.00000 + 1.73205i) q^{35} +(-1.71922 + 2.97778i) q^{37} +(1.28078 - 2.21837i) q^{41} +(0.219224 + 0.379706i) q^{43} -8.24621 q^{47} +(-2.84233 + 4.92306i) q^{49} -11.6847 q^{53} +(-0.561553 + 0.972638i) q^{55} +(5.56155 + 9.63289i) q^{59} +(-6.06155 - 10.4989i) q^{61} +(-0.280776 + 2.00514i) q^{65} +(0.219224 - 0.379706i) q^{67} +(-7.00000 - 12.1244i) q^{71} -1.87689 q^{73} -7.12311 q^{77} -9.56155 q^{79} -9.12311 q^{83} +(-0.719224 - 1.24573i) q^{85} +(6.56155 - 11.3649i) q^{89} +(-11.9039 + 4.81645i) q^{91} +(0.315342 + 0.546188i) q^{95} +(2.21922 + 3.84381i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} - 3 q^{7}+O(q^{10}) \) 4 * q + 6 * q^5 - 3 * q^7	\( 4 q + 6 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} + q^{17} + 6 q^{19} - 4 q^{23} + 6 q^{25} + q^{29} - 2 q^{31} + 4 q^{35} - 11 q^{37} + q^{41} + 5 q^{43} + q^{49} - 22 q^{53} + 6 q^{55} + 14 q^{59} - 16 q^{61} + 3 q^{65} + 5 q^{67} - 28 q^{71} - 24 q^{73} - 12 q^{77} - 30 q^{79} - 20 q^{83} - 7 q^{85} + 18 q^{89} - 27 q^{91} + 26 q^{95} + 13 q^{97}+O(q^{100}) \) 4 * q + 6 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 + q^17 + 6 * q^19 - 4 * q^23 + 6 * q^25 + q^29 - 2 * q^31 + 4 * q^35 - 11 * q^37 + q^41 + 5 * q^43 + q^49 - 22 * q^53 + 6 * q^55 + 14 * q^59 - 16 * q^61 + 3 * q^65 + 5 * q^67 - 28 * q^71 - 24 * q^73 - 12 * q^77 - 30 * q^79 - 20 * q^83 - 7 * q^85 + 18 * q^89 - 27 * q^91 + 26 * q^95 + 13 * q^97

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