LMFDB - Embedded newform 2156.2.i.a.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2156,2,Mod(177,2156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2156.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2156, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$2156 = 2^{2} \cdot 7^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2156.i (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-1,0,-1,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$17.2157466758$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2156.177
Dual form			2156.2.i.a.1145.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{11} +4.00000 q^{13} +1.00000 q^{15} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} -5.00000 q^{27} +2.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(4.50000 - 7.79423i) q^{37} +(-2.00000 - 3.46410i) q^{39} -6.00000 q^{41} +8.00000 q^{43} +(1.00000 + 1.73205i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(-3.00000 + 5.19615i) q^{51} +(-5.00000 - 8.66025i) q^{53} +1.00000 q^{55} +2.00000 q^{57} +(0.500000 + 0.866025i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(-5.50000 - 9.52628i) q^{67} +1.00000 q^{69} +11.0000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(2.00000 - 3.46410i) q^{75} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +6.00000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(6.50000 - 11.2583i) q^{89} +(-0.500000 + 0.866025i) q^{93} +(-1.00000 - 1.73205i) q^{95} +9.00000 q^{97} -2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - q^{3} - q^{5} + 2 q^{9} - q^{11} + 8 q^{13} + 2 q^{15} - 6 q^{17} - 2 q^{19} - q^{23} + 4 q^{25} - 10 q^{27} + 4 q^{29} - q^{31} - q^{33} + 9 q^{37} - 4 q^{39} - 12 q^{41} + 16 q^{43} + 2 q^{45}+ \cdots - 4 q^{99}+O(q^{100})$ 2 * q - q^3 - q^5 + 2 * q^9 - q^11 + 8 * q^13 + 2 * q^15 - 6 * q^17 - 2 * q^19 - q^23 + 4 * q^25 - 10 * q^27 + 4 * q^29 - q^31 - q^33 + 9 * q^37 - 4 * q^39 - 12 * q^41 + 16 * q^43 + 2 * q^45 - 8 * q^47 - 6 * q^51 - 10 * q^53 + 2 * q^55 + 4 * q^57 + q^59 - 2 * q^61 - 4 * q^65 - 11 * q^67 + 2 * q^69 + 22 * q^71 - 14 * q^73 + 4 * q^75 + 14 * q^79 - q^81 - 8 * q^83 + 12 * q^85 - 2 * q^87 + 13 * q^89 - q^93 - 2 * q^95 + 18 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2156\mathbb{Z}\right)^\times$ .

$n$	$981$	$1079$	$1277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	0.817625	−	0.575751i	$-0.195290\pi$
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	−0.907428	+	0.420208i	$0.861957\pi$
$32$		0			0
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	−0.212792	−	0.977098i	$-0.568256\pi$
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	0.952587	−	0.304266i	$-0.0984111\pi$
$38$		0			0
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$		0			0
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	−0.972867	−	0.231367i	$-0.925680\pi$
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	0.286064	−	0.958211i	$-0.407653\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	0.500000	+	0.866025i	0.0650945	+	0.112747i	0.896736	−	0.442566i	$-0.145932\pi$
$59$	0.500000	+	0.866025i	0.0650945	+	0.112747i	−0.831641	+	0.555313i	$0.812598\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$		0			0
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	0.305424	−	0.952217i	$-0.401202\pi$
$68$		0			0
$69$	1.00000			0.120386
$70$		0			0
$71$	11.0000			1.30546			0.652730	−	0.757591i	$-0.273624\pi$
$71$	11.0000			1.30546			0.652730	+	0.757591i	$0.273624\pi$
$72$		0			0
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$		0			0
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$		0			0
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$		0			0
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	−0.283164	−	0.959072i	$-0.591384\pi$
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	0.972162	−	0.234309i	$-0.0752827\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.500000	+	0.866025i	−0.0518476	+	0.0898027i
$94$		0			0
$95$	−1.00000	−	1.73205i	−0.102598	−	0.177705i
$96$		0			0
$97$	9.00000			0.913812			0.456906	−	0.889515i	$-0.348958\pi$
$97$	9.00000			0.913812			0.456906	+	0.889515i	$0.348958\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$		0			0
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$		0			0
$111$	−9.00000			−0.854242
$112$		0			0
$113$	−11.0000			−1.03479			−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000			−1.03479			−0.517396	+	0.855746i	$0.673099\pi$
$114$		0			0
$115$	−0.500000	−	0.866025i	−0.0466252	−	0.0807573i
$116$		0			0
$117$	4.00000	−	6.92820i	0.369800	−	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−10.0000			−0.887357			−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000			−0.887357			−0.443678	+	0.896186i	$0.646327\pi$
$128$		0			0
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	−5.00000	+	8.66025i	−0.436852	+	0.756650i	−0.997445	−	0.0714417i	$-0.977240\pi$
$131$	−5.00000	+	8.66025i	−0.436852	+	0.756650i	0.560593	+	0.828092i	$0.310573\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		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
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$		0			0
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	0.996207	−	0.0870170i	$-0.0277334\pi$
$150$		0			0
$151$	7.00000	+	12.1244i	0.569652	+	0.986666i	0.996600	+	0.0823900i	$0.0262553\pi$
$151$	7.00000	+	12.1244i	0.569652	+	0.986666i	−0.426948	+	0.904276i	$0.640411\pi$
$152$		0			0
$153$	−12.0000			−0.970143
$154$		0			0
$155$	1.00000			0.0803219
$156$		0			0
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	−0.975470	−	0.220131i	$-0.929352\pi$
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	0.297097	−	0.954847i	$-0.403982\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$		0			0
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$		0			0
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$		0			0
$173$	8.00000	−	13.8564i	0.608229	−	1.05348i	−0.383304	−	0.923622i	$-0.625214\pi$
$173$	8.00000	−	13.8564i	0.608229	−	1.05348i	0.991532	−	0.129861i	$-0.0414530\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.500000	−	0.866025i	0.0375823	−	0.0650945i
$178$		0			0
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$		0			0
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	4.50000	+	7.79423i	0.330847	+	0.573043i
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.500000	−	0.866025i	0.0361787	−	0.0626634i	−0.847369	−	0.531004i	$-0.821815\pi$
$191$	0.500000	−	0.866025i	0.0361787	−	0.0626634i	0.883548	+	0.468341i	$0.155148\pi$
$192$		0			0
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$		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
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$	−5.50000	+	9.52628i	−0.387940	+	0.671932i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$		0			0
$207$	1.00000	+	1.73205i	0.0695048	+	0.120386i
$208$		0			0
$209$	2.00000			0.138343
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$		0			0
$213$	−5.50000	−	9.52628i	−0.376854	−	0.652730i
$214$		0			0
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		0			0
$221$	−12.0000	−	20.7846i	−0.807207	−	1.39812i
$222$		0			0
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$		0			0
$225$	8.00000			0.533333
$226$		0			0
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	0.791989	−	0.610535i	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$		0			0
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$		0			0
$237$	−14.0000			−0.909398
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	0.984496	+	0.175409i	$0.0561248\pi$
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.00000	+	6.92820i	−0.254514	+	0.440831i
$248$		0			0
$249$	2.00000	+	3.46410i	0.126745	+	0.219529i
$250$		0			0
$251$	−25.0000			−1.57799			−0.788993	−	0.614402i	$-0.789397\pi$
$251$	−25.0000			−1.57799			−0.788993	+	0.614402i	$0.789397\pi$
$252$		0			0
$253$	1.00000			0.0628695
$254$		0			0
$255$	−3.00000	−	5.19615i	−0.187867	−	0.325396i
$256$		0			0
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	−0.101305	−	0.994855i	$-0.532302\pi$
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	0.912222	−	0.409695i	$-0.134365\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2.00000	−	3.46410i	0.123797	−	0.214423i
$262$		0			0
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	0.758585	−	0.651575i	$-0.225891\pi$
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	−0.943572	+	0.331166i	$0.892558\pi$
$264$		0			0
$265$	10.0000			0.614295
$266$		0			0
$267$	−13.0000			−0.795587
$268$		0			0
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	16.0000	−	27.7128i	0.971931	−	1.68343i	0.282218	−	0.959350i	$-0.408930\pi$
$271$	16.0000	−	27.7128i	0.971931	−	1.68343i	0.689713	−	0.724083i	$-0.257737\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	12.0000	+	20.7846i	0.721010	+	1.24883i	0.960595	+	0.277951i	$0.0896552\pi$
$277$	12.0000	+	20.7846i	0.721010	+	1.24883i	−0.239585	+	0.970875i	$0.577011\pi$
$278$		0			0
$279$	−2.00000			−0.119737
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$	−1.00000	+	1.73205i	−0.0592349	+	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−4.50000	−	7.79423i	−0.263795	−	0.456906i
$292$		0			0
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	−1.00000			−0.0582223
$296$		0			0
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$		0			0
$299$	−2.00000	+	3.46410i	−0.115663	+	0.200334i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	10.5000	−	18.1865i	0.593495	−	1.02796i	−0.400262	−	0.916401i	$-0.631081\pi$
$313$	10.5000	−	18.1865i	0.593495	−	1.02796i	0.993757	−	0.111563i	$-0.0355857\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$		0			0
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$		0			0
$321$	−6.00000			−0.334887
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$		0			0
$327$	−2.00000	+	3.46410i	−0.110600	+	0.191565i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−12.5000	+	21.6506i	−0.687062	+	1.19003i	0.285722	+	0.958313i	$0.407767\pi$
$331$	−12.5000	+	21.6506i	−0.687062	+	1.19003i	−0.972784	+	0.231714i	$0.925567\pi$
$332$		0			0
$333$	−9.00000	−	15.5885i	−0.493197	−	0.854242i
$334$		0			0
$335$	11.0000			0.600994
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	5.50000	+	9.52628i	0.298719	+	0.517396i
$340$		0			0
$341$	−0.500000	+	0.866025i	−0.0270765	+	0.0468979i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.500000	+	0.866025i	−0.0269191	+	0.0466252i
$346$		0			0
$347$	15.0000	+	25.9808i	0.805242	+	1.39472i	0.916127	+	0.400887i	$0.131298\pi$
$347$	15.0000	+	25.9808i	0.805242	+	1.39472i	−0.110885	+	0.993833i	$0.535369\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−20.0000			−1.06752
$352$		0			0
$353$	2.50000	+	4.33013i	0.133062	+	0.230469i	0.924855	−	0.380319i	$-0.124186\pi$
$353$	2.50000	+	4.33013i	0.133062	+	0.230469i	−0.791794	+	0.610789i	$0.790853\pi$
$354$		0			0
$355$	−5.50000	+	9.52628i	−0.291910	+	0.505602i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	14.0000			0.732793
$366$		0			0
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	0.902516	−	0.430656i	$-0.141718\pi$
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	−0.824217	+	0.566274i	$0.808384\pi$
$368$		0			0
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	5.00000			0.256833			0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000			0.256833			0.128416	+	0.991720i	$0.459011\pi$
$380$		0			0
$381$	5.00000	+	8.66025i	0.256158	+	0.443678i
$382$		0			0
$383$	−12.5000	+	21.6506i	−0.638720	+	1.10630i	0.346994	+	0.937867i	$0.387203\pi$
$383$	−12.5000	+	21.6506i	−0.638720	+	1.10630i	−0.985714	+	0.168428i	$0.946131\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$		0			0
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	0.973601	+	0.228257i	$0.0733028\pi$
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	−0.289124	+	0.957292i	$0.593364\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$		0			0
$393$	10.0000			0.504433
$394$		0			0
$395$	7.00000	+	12.1244i	0.352208	+	0.610043i
$396$		0			0
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.0000	−	32.9090i	0.948815	−	1.64340i	0.200888	−	0.979614i	$-0.435617\pi$
$401$	19.0000	−	32.9090i	0.948815	−	1.64340i	0.747927	−	0.663781i	$-0.231049\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−9.00000			−0.446113
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$	1.50000	−	2.59808i	0.0739895	−	0.128154i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.00000	−	3.46410i	0.0981761	−	0.170046i
$416$		0			0
$417$	1.00000	+	1.73205i	0.0489702	+	0.0848189i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$		0			0
$423$	8.00000	+	13.8564i	0.388973	+	0.673722i
$424$		0			0
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$		0			0
$431$	−10.0000	−	17.3205i	−0.481683	−	0.834300i	0.518096	−	0.855323i	$-0.326641\pi$
$431$	−10.0000	−	17.3205i	−0.481683	−	0.834300i	−0.999779	+	0.0210230i	$0.993308\pi$
$432$		0			0
$433$	37.0000			1.77811			0.889053	−	0.457804i	$-0.151364\pi$
$433$	37.0000			1.77811			0.889053	+	0.457804i	$0.151364\pi$
$434$		0			0
$435$	2.00000			0.0958927
$436$		0			0
$437$	−1.00000	−	1.73205i	−0.0478365	−	0.0828552i
$438$		0			0
$439$	−17.0000	+	29.4449i	−0.811366	+	1.40533i	0.100543	+	0.994933i	$0.467942\pi$
$439$	−17.0000	+	29.4449i	−0.811366	+	1.40533i	−0.911908	+	0.410394i	$0.865391\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.5000	+	26.8468i	−0.736427	+	1.27553i	0.217667	+	0.976023i	$0.430155\pi$
$443$	−15.5000	+	26.8468i	−0.736427	+	1.27553i	−0.954094	+	0.299506i	$0.903178\pi$
$444$		0			0
$445$	6.50000	+	11.2583i	0.308130	+	0.533696i
$446$		0			0
$447$	−14.0000			−0.662177
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$		0			0
$453$	7.00000	−	12.1244i	0.328889	−	0.569652i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	−0.757174	−	0.653213i	$-0.773421\pi$
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	0.944286	+	0.329125i	$0.106754\pi$
$458$		0			0
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$		0			0
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$	−33.0000			−1.53364			−0.766820	−	0.641862i	$-0.778162\pi$
$463$	−33.0000			−1.53364			−0.766820	+	0.641862i	$0.778162\pi$
$464$		0			0
$465$	−0.500000	−	0.866025i	−0.0231869	−	0.0401610i
$466$		0			0
$467$	−3.50000	+	6.06218i	−0.161961	+	0.280524i	−0.935572	−	0.353137i	$-0.885115\pi$
$467$	−3.50000	+	6.06218i	−0.161961	+	0.280524i	0.773611	+	0.633661i	$0.218448\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−8.50000	+	14.7224i	−0.391659	+	0.678374i
$472$		0			0
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$		0			0
$475$	−8.00000			−0.367065
$476$		0			0
$477$	−20.0000			−0.915737
$478$		0			0
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	18.0000	−	31.1769i	0.820729	−	1.42154i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.50000	+	7.79423i	−0.204334	+	0.353918i
$486$		0			0
$487$	−16.5000	−	28.5788i	−0.747686	−	1.29503i	−0.948929	−	0.315489i	$-0.897831\pi$
$487$	−16.5000	−	28.5788i	−0.747686	−	1.29503i	0.201243	−	0.979541i	$-0.435502\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	−34.0000			−1.53440			−0.767199	−	0.641409i	$-0.778350\pi$
$491$	−34.0000			−1.53440			−0.767199	+	0.641409i	$0.778350\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$	1.00000	−	1.73205i	0.0449467	−	0.0778499i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$		0			0
$501$	−7.00000	−	12.1244i	−0.312737	−	0.541676i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$		0			0
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$		0			0
$509$	−15.5000	+	26.8468i	−0.687025	+	1.18996i	0.285770	+	0.958298i	$0.407751\pi$
$509$	−15.5000	+	26.8468i	−0.687025	+	1.18996i	−0.972796	+	0.231665i	$0.925583\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$		0			0
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$		0			0
$517$	8.00000			0.351840
$518$		0			0
$519$	−16.0000			−0.702322
$520$		0			0
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.00000	+	5.19615i	−0.130682	+	0.226348i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	2.00000			0.0867926
$532$		0			0
$533$	−24.0000			−1.03956
$534$		0			0
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$		0			0
$537$	−7.50000	+	12.9904i	−0.323649	+	0.560576i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.00000	+	13.8564i	−0.343947	+	0.595733i	−0.985162	−	0.171628i	$-0.945097\pi$
$541$	−8.00000	+	13.8564i	−0.343947	+	0.595733i	0.641215	+	0.767361i	$0.278431\pi$
$542$		0			0
$543$	2.50000	+	4.33013i	0.107285	+	0.185824i
$544$		0			0
$545$	4.00000			0.171341
$546$		0			0
$547$	40.0000			1.71028			0.855138	−	0.518400i	$-0.173472\pi$
$547$	40.0000			1.71028			0.855138	+	0.518400i	$0.173472\pi$
$548$		0			0
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$		0			0
$551$	−2.00000	+	3.46410i	−0.0852029	+	0.147576i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.50000	−	7.79423i	0.191014	−	0.330847i
$556$		0			0
$557$	21.0000	+	36.3731i	0.889799	+	1.54118i	0.840113	+	0.542411i	$0.182489\pi$
$557$	21.0000	+	36.3731i	0.889799	+	1.54118i	0.0496855	+	0.998765i	$0.484178\pi$
$558$		0			0
$559$	32.0000			1.35346
$560$		0			0
$561$	6.00000			0.253320
$562$		0			0
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	5.50000	−	9.52628i	0.231387	−	0.400774i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.00000	+	12.1244i	−0.293455	+	0.508279i	−0.974624	−	0.223847i	$-0.928139\pi$
$569$	−7.00000	+	12.1244i	−0.293455	+	0.508279i	0.681169	+	0.732126i	$0.261472\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$		0			0
$573$	−1.00000			−0.0417756
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	1.50000	+	2.59808i	0.0624458	+	0.108159i	0.895558	−	0.444945i	$-0.146777\pi$
$577$	1.50000	+	2.59808i	0.0624458	+	0.108159i	−0.833112	+	0.553104i	$0.813443\pi$
$578$		0			0
$579$	9.00000	−	15.5885i	0.374027	−	0.647834i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−5.00000	+	8.66025i	−0.207079	+	0.358671i
$584$		0			0
$585$	4.00000	+	6.92820i	0.165380	+	0.286446i
$586$		0			0
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$		0			0
$589$	2.00000			0.0824086
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$		0			0
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$		0			0
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$		0			0
$601$	24.0000			0.978980			0.489490	−	0.872009i	$-0.337183\pi$
$601$	24.0000			0.978980			0.489490	+	0.872009i	$0.337183\pi$
$602$		0			0
$603$	−22.0000			−0.895909
$604$		0			0
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$		0			0
$607$	21.0000	−	36.3731i	0.852364	−	1.47634i	−0.0267056	−	0.999643i	$-0.508502\pi$
$607$	21.0000	−	36.3731i	0.852364	−	1.47634i	0.879069	−	0.476694i	$-0.158165\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.0000	+	27.7128i	−0.647291	+	1.12114i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$		0			0
$619$	21.5000	+	37.2391i	0.864158	+	1.49677i	0.867881	+	0.496772i	$0.165482\pi$
$619$	21.5000	+	37.2391i	0.864158	+	1.49677i	−0.00372288	+	0.999993i	$0.501185\pi$
$620$		0			0
$621$	2.50000	−	4.33013i	0.100322	−	0.173762i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	−1.00000	−	1.73205i	−0.0399362	−	0.0691714i
$628$		0			0
$629$	−54.0000			−2.15312
$630$		0			0
$631$	41.0000			1.63218			0.816092	−	0.577922i	$-0.196136\pi$
$631$	41.0000			1.63218			0.816092	+	0.577922i	$0.196136\pi$
$632$		0			0
$633$	−1.00000	−	1.73205i	−0.0397464	−	0.0688428i
$634$		0			0
$635$	5.00000	−	8.66025i	0.198419	−	0.343672i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	11.0000	−	19.0526i	0.435153	−	0.753708i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$		0			0
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	0.995194	−	0.0979182i	$-0.0312184\pi$
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	−0.582397	+	0.812905i	$0.697885\pi$
$648$		0			0
$649$	0.500000	−	0.866025i	0.0196267	−	0.0339945i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	14.5000	−	25.1147i	0.567429	−	0.982816i	−0.429390	−	0.903119i	$-0.641272\pi$
$653$	14.5000	−	25.1147i	0.567429	−	0.982816i	0.996819	−	0.0796966i	$-0.0253951\pi$
$654$		0			0
$655$	−5.00000	−	8.66025i	−0.195366	−	0.338384i
$656$		0			0
$657$	−28.0000			−1.09238
$658$		0			0
$659$	−46.0000			−1.79191			−0.895953	−	0.444149i	$-0.853506\pi$
$659$	−46.0000			−1.79191			−0.895953	+	0.444149i	$0.853506\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		0			0
$663$	−12.0000	+	20.7846i	−0.466041	+	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.00000	+	1.73205i	−0.0387202	+	0.0670653i
$668$		0			0
$669$	−8.50000	−	14.7224i	−0.328629	−	0.569202i
$670$		0			0
$671$	2.00000			0.0772091
$672$		0			0
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$		0			0
$675$	−10.0000	−	17.3205i	−0.384900	−	0.666667i
$676$		0			0
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.00000	+	3.46410i	−0.0766402	+	0.132745i
$682$		0			0
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$		0			0
$685$	−3.00000			−0.114624
$686$		0			0
$687$	7.00000			0.267067
$688$		0			0
$689$	−20.0000	−	34.6410i	−0.761939	−	1.31972i
$690$		0			0
$691$	−1.50000	+	2.59808i	−0.0570627	+	0.0988355i	−0.893146	−	0.449768i	$-0.851507\pi$
$691$	−1.50000	+	2.59808i	−0.0570627	+	0.0988355i	0.836083	+	0.548603i	$0.184840\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.00000	−	1.73205i	0.0379322	−	0.0657004i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$	6.00000			0.226941
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	9.00000	+	15.5885i	0.339441	+	0.587930i
$704$		0			0
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$		0			0
$711$	−14.0000	−	24.2487i	−0.525041	−	0.909398i
$712$		0			0
$713$	1.00000			0.0374503
$714$		0			0
$715$	4.00000			0.149592
$716$		0			0
$717$	10.0000	+	17.3205i	0.373457	+	0.646846i
$718$		0			0
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	−0.496527	−	0.868021i	$-0.665392\pi$
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	0.999992	−	0.00400572i	$-0.00127506\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	10.0000	−	17.3205i	0.371904	−	0.644157i
$724$		0			0
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$		0			0
$727$	5.00000			0.185440			0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000			0.185440			0.0927199	+	0.995692i	$0.470444\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$		0			0
$733$	14.0000	−	24.2487i	0.517102	−	0.895647i	−0.482701	−	0.875785i	$-0.660344\pi$
$733$	14.0000	−	24.2487i	0.517102	−	0.895647i	0.999803	−	0.0198613i	$-0.00632248\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.50000	+	9.52628i	−0.202595	+	0.350905i
$738$		0			0
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	0.847046	−	0.531519i	$-0.178379\pi$
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	−0.883832	+	0.467804i	$0.845045\pi$
$740$		0			0
$741$	8.00000			0.293887
$742$		0			0
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$		0			0
$745$	7.00000	+	12.1244i	0.256460	+	0.444202i
$746$		0			0
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	0.347160	+	0.937806i	$0.387146\pi$
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	−0.985744	+	0.168254i	$0.946187\pi$
$752$		0			0
$753$	12.5000	+	21.6506i	0.455525	+	0.788993i
$754$		0			0
$755$	−14.0000			−0.509512
$756$		0			0
$757$	−42.0000			−1.52652			−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000			−1.52652			−0.763258	+	0.646094i	$0.776401\pi$
$758$		0			0
$759$	−0.500000	−	0.866025i	−0.0181489	−	0.0314347i
$760$		0			0
$761$	24.0000	−	41.5692i	0.869999	−	1.50688i	0.00800331	−	0.999968i	$-0.497452\pi$
$761$	24.0000	−	41.5692i	0.869999	−	1.50688i	0.861996	−	0.506915i	$-0.169214\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	6.00000	−	10.3923i	0.216930	−	0.375735i
$766$		0			0
$767$	2.00000	+	3.46410i	0.0722158	+	0.125081i
$768$		0			0
$769$	8.00000			0.288487			0.144244	−	0.989542i	$-0.453925\pi$
$769$	8.00000			0.288487			0.144244	+	0.989542i	$0.453925\pi$
$770$		0			0
$771$	−26.0000			−0.936367
$772$		0			0
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	0.999314	−	0.0370420i	$-0.0117935\pi$
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	−0.531736	+	0.846910i	$0.678460\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	−5.50000	−	9.52628i	−0.196805	−	0.340877i
$782$		0			0
$783$	−10.0000			−0.357371
$784$		0			0
$785$	17.0000			0.606756
$786$		0			0
$787$	−17.0000	−	29.4449i	−0.605985	−	1.04960i	−0.991895	−	0.127060i	$-0.959446\pi$
$787$	−17.0000	−	29.4449i	−0.605985	−	1.04960i	0.385911	−	0.922536i	$-0.373887\pi$
$788$		0			0
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−4.00000	+	6.92820i	−0.142044	+	0.246028i
$794$		0			0
$795$	−5.00000	−	8.66025i	−0.177332	−	0.307148i
$796$		0			0
$797$	−47.0000			−1.66483			−0.832413	−	0.554156i	$-0.813041\pi$
$797$	−47.0000			−1.66483			−0.832413	+	0.554156i	$0.813041\pi$
$798$		0			0
$799$	48.0000			1.69812
$800$		0			0
$801$	−13.0000	−	22.5167i	−0.459332	−	0.795587i
$802$		0			0
$803$	−7.00000	+	12.1244i	−0.247025	+	0.427859i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7.00000	−	12.1244i	0.246412	−	0.426798i
$808$		0			0
$809$	−7.00000	−	12.1244i	−0.246107	−	0.426270i	0.716335	−	0.697756i	$-0.245818\pi$
$809$	−7.00000	−	12.1244i	−0.246107	−	0.426270i	−0.962442	+	0.271487i	$0.912485\pi$
$810$		0			0
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$		0			0
$813$	−32.0000			−1.12229
$814$		0			0
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	−0.316691	−	0.948529i	$-0.602572\pi$
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	0.979795	−	0.200002i	$-0.0640949\pi$
$822$		0			0
$823$	−14.5000	−	25.1147i	−0.505438	−	0.875445i	−0.999980	−	0.00629095i	$-0.997998\pi$
$823$	−14.5000	−	25.1147i	−0.505438	−	0.875445i	0.494542	−	0.869154i	$-0.335336\pi$
$824$		0			0
$825$	−4.00000			−0.139262
$826$		0			0
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$		0			0
$829$	−2.50000	−	4.33013i	−0.0868286	−	0.150392i	0.819340	−	0.573307i	$-0.194340\pi$
$829$	−2.50000	−	4.33013i	−0.0868286	−	0.150392i	−0.906169	+	0.422916i	$0.861007\pi$
$830$		0			0
$831$	12.0000	−	20.7846i	0.416275	−	0.721010i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−7.00000	+	12.1244i	−0.242245	+	0.419581i
$836$		0			0
$837$	2.50000	+	4.33013i	0.0864126	+	0.149671i
$838$		0			0
$839$	−27.0000			−0.932144			−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000			−0.932144			−0.466072	+	0.884747i	$0.654331\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	−6.00000	−	10.3923i	−0.206651	−	0.357930i
$844$		0			0
$845$	−1.50000	+	2.59808i	−0.0516016	+	0.0893765i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.50000	+	7.79423i	0.154258	+	0.267183i
$852$		0			0
$853$	2.00000			0.0684787			0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000			0.0684787			0.0342393	+	0.999414i	$0.489099\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$		0			0
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$		0			0
$859$	−21.5000	+	37.2391i	−0.733571	+	1.27058i	0.221777	+	0.975097i	$0.428814\pi$
$859$	−21.5000	+	37.2391i	−0.733571	+	1.27058i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	−0.898056	−	0.439880i	$-0.855021\pi$
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	0.829976	+	0.557800i	$0.188354\pi$
$864$		0			0
$865$	8.00000	+	13.8564i	0.272008	+	0.471132i
$866$		0			0
$867$	19.0000			0.645274
$868$		0			0
$869$	−14.0000			−0.474917
$870$		0			0
$871$	−22.0000	−	38.1051i	−0.745442	−	1.29114i
$872$		0			0
$873$	9.00000	−	15.5885i	0.304604	−	0.527589i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.0000	−	39.8372i	0.776655	−	1.34521i	−0.157205	−	0.987566i	$-0.550248\pi$
$877$	23.0000	−	39.8372i	0.776655	−	1.34521i	0.933860	−	0.357640i	$-0.116418\pi$
$878$		0			0
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$	0.500000	+	0.866025i	0.0168073	+	0.0291111i
$886$		0			0
$887$	1.00000	−	1.73205i	0.0335767	−	0.0581566i	−0.848749	−	0.528796i	$-0.822644\pi$
$887$	1.00000	−	1.73205i	0.0335767	−	0.0581566i	0.882325	+	0.470640i	$0.155977\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$		0			0
$893$	−8.00000	−	13.8564i	−0.267710	−	0.463687i
$894$		0			0
$895$	15.0000			0.501395
$896$		0			0
$897$	4.00000			0.133556
$898$		0			0
$899$	−1.00000	−	1.73205i	−0.0333519	−	0.0577671i
$900$		0			0
$901$	−30.0000	+	51.9615i	−0.999445	+	1.73109i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.50000	−	4.33013i	0.0831028	−	0.143938i
$906$		0			0
$907$	12.0000	+	20.7846i	0.398453	+	0.690142i	0.993535	−	0.113523i	$-0.0362137\pi$
$907$	12.0000	+	20.7846i	0.398453	+	0.690142i	−0.595082	+	0.803665i	$0.702880\pi$
$908$		0			0
$909$	−24.0000			−0.796030
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$		0			0
$915$	−1.00000	+	1.73205i	−0.0330590	+	0.0572598i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$		0			0
$923$	44.0000			1.44828
$924$		0			0
$925$	36.0000			1.18367
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	−23.0000	+	39.8372i	−0.754606	+	1.30702i	0.190965	+	0.981597i	$0.438838\pi$
$929$	−23.0000	+	39.8372i	−0.754606	+	1.30702i	−0.945570	+	0.325418i	$0.894495\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		0			0
$935$	−3.00000	−	5.19615i	−0.0981105	−	0.169932i
$936$		0			0
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$		0			0
$939$	−21.0000			−0.685309
$940$		0			0
$941$	21.0000	+	36.3731i	0.684580	+	1.18573i	0.973568	+	0.228395i	$0.0733479\pi$
$941$	21.0000	+	36.3731i	0.684580	+	1.18573i	−0.288988	+	0.957333i	$0.593319\pi$
$942$		0			0
$943$	3.00000	−	5.19615i	0.0976934	−	0.169210i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.5000	−	38.9711i	0.731152	−	1.26639i	−0.225240	−	0.974303i	$-0.572316\pi$
$947$	22.5000	−	38.9711i	0.731152	−	1.26639i	0.956391	−	0.292089i	$-0.0943502\pi$
$948$		0			0
$949$	−28.0000	−	48.4974i	−0.908918	−	1.57429i
$950$		0			0
$951$	−3.00000			−0.0972817
$952$		0			0
$953$	28.0000			0.907009			0.453504	−	0.891254i	$-0.350174\pi$
$953$	28.0000			0.907009			0.453504	+	0.891254i	$0.350174\pi$
$954$		0			0
$955$	0.500000	+	0.866025i	0.0161796	+	0.0280239i
$956$		0			0
$957$	−1.00000	+	1.73205i	−0.0323254	+	0.0559893i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$		0			0
$965$	−18.0000			−0.579441
$966$		0			0
$967$	42.0000			1.35063			0.675314	−	0.737530i	$-0.264008\pi$
$967$	42.0000			1.35063			0.675314	+	0.737530i	$0.264008\pi$
$968$		0			0
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.107135	+	0.994244i	$0.534168\pi$
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.807473	+	0.589904i	$0.799166\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.00000	−	13.8564i	0.256205	−	0.443760i
$976$		0			0
$977$	−8.50000	−	14.7224i	−0.271939	−	0.471012i	0.697419	−	0.716663i	$-0.254332\pi$
$977$	−8.50000	−	14.7224i	−0.271939	−	0.471012i	−0.969358	+	0.245651i	$0.920998\pi$
$978$		0			0
$979$	−13.0000			−0.415482
$980$		0			0
$981$	−8.00000			−0.255420
$982$		0			0
$983$	5.50000	+	9.52628i	0.175423	+	0.303841i	0.940307	−	0.340326i	$-0.110537\pi$
$983$	5.50000	+	9.52628i	0.175423	+	0.303841i	−0.764885	+	0.644167i	$0.777204\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$		0			0
$993$	25.0000			0.793351
$994$		0			0
$995$	8.00000			0.253617
$996$		0			0
$997$	−30.0000	−	51.9615i	−0.950110	−	1.64564i	−0.745182	−	0.666861i	$-0.767638\pi$
$997$	−30.0000	−	51.9615i	−0.950110	−	1.64564i	−0.204927	−	0.978777i	$-0.565696\pi$
$998$		0			0
$999$	−22.5000	+	38.9711i	−0.711868	+	1.23299i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2156.2.i.a.177.1		2
7.2	even	3		2156.2.a.b.1.1		1
7.3	odd	6		2156.2.i.d.1145.1		2
7.4	even	3	inner	2156.2.i.a.1145.1		2
7.5	odd	6		308.2.a.a.1.1	✓	1
7.6	odd	2		2156.2.i.d.177.1		2
21.5	even	6		2772.2.a.e.1.1		1
28.19	even	6		1232.2.a.j.1.1		1
28.23	odd	6		8624.2.a.n.1.1		1
35.12	even	12		7700.2.e.f.1849.2		2
35.19	odd	6		7700.2.a.i.1.1		1
35.33	even	12		7700.2.e.f.1849.1		2
56.5	odd	6		4928.2.a.z.1.1		1
56.19	even	6		4928.2.a.l.1.1		1
77.54	even	6		3388.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.a.a.1.1	✓	1	7.5	odd	6
1232.2.a.j.1.1		1	28.19	even	6
2156.2.a.b.1.1		1	7.2	even	3
2156.2.i.a.177.1		2	1.1	even	1	trivial
2156.2.i.a.1145.1		2	7.4	even	3	inner
2156.2.i.d.177.1		2	7.6	odd	2
2156.2.i.d.1145.1		2	7.3	odd	6
2772.2.a.e.1.1		1	21.5	even	6
3388.2.a.e.1.1		1	77.54	even	6
4928.2.a.l.1.1		1	56.19	even	6
4928.2.a.z.1.1		1	56.5	odd	6
7700.2.a.i.1.1		1	35.19	odd	6
7700.2.e.f.1849.1		2	35.33	even	12
7700.2.e.f.1849.2		2	35.12	even	12
8624.2.a.n.1.1		1	28.23	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2156.2.i.a.177.1

Level	$2156$
Weight	$2$
Character	2156.177
Analytic conductor	$17.216$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$