LMFDB - Embedded newform 1156.2.e.d.829.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1156,2,Mod(829,1156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1156, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1156.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1156 = 2^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1156.e (of order $4$, 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:	$9.23070647366$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1156.829
Dual form			1156.2.e.d.905.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.93185 - 1.93185i) q^{3} +(-2.44949 - 2.44949i) q^{5} +(-1.93185 + 1.93185i) q^{7} +4.46410i q^{9} +(0.896575 - 0.896575i) q^{11} -5.46410 q^{13} +9.46410i q^{15} +1.46410i q^{19} +7.46410 q^{21} +(0.896575 - 0.896575i) q^{23} +7.00000i q^{25} +(2.82843 - 2.82843i) q^{27} +(2.44949 + 2.44949i) q^{29} +(-2.96713 - 2.96713i) q^{31} -3.46410 q^{33} +9.46410 q^{35} +(-3.20736 - 3.20736i) q^{37} +(10.5558 + 10.5558i) q^{39} +(-4.24264 + 4.24264i) q^{41} -8.39230i q^{43} +(10.9348 - 10.9348i) q^{45} +6.92820 q^{47} -0.464102i q^{49} -12.9282i q^{53} -4.39230 q^{55} +(2.82843 - 2.82843i) q^{57} +2.53590i q^{59} +(-0.378937 + 0.378937i) q^{61} +(-8.62398 - 8.62398i) q^{63} +(13.3843 + 13.3843i) q^{65} +14.9282 q^{67} -3.46410 q^{69} +(5.79555 + 5.79555i) q^{71} +(1.41421 + 1.41421i) q^{73} +(13.5230 - 13.5230i) q^{75} +3.46410i q^{77} +(8.62398 - 8.62398i) q^{79} +2.46410 q^{81} +2.53590i q^{83} -9.46410i q^{87} -2.53590 q^{89} +(10.5558 - 10.5558i) q^{91} +11.4641i q^{93} +(3.58630 - 3.58630i) q^{95} +(-3.48477 - 3.48477i) q^{97} +(4.00240 + 4.00240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{13} + 32 q^{21} + 48 q^{35} + 48 q^{55} + 64 q^{67} - 8 q^{81} - 48 q^{89}+O(q^{100}) $ 8 * q - 16 * q^13 + 32 * q^21 + 48 * q^35 + 48 * q^55 + 64 * q^67 - 8 * q^81 - 48 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.93185	−	1.93185i	−1.11536	−	1.11536i	−0.992414	−	0.122941i	$-0.960767\pi$
$3$	−1.93185	−	1.93185i	−1.11536	−	1.11536i	−0.122941	−	0.992414i	$-0.539233\pi$
$4$		0			0
$5$	−2.44949	−	2.44949i	−1.09545	−	1.09545i	−0.994936	−	0.100509i	$-0.967953\pi$
$5$	−2.44949	−	2.44949i	−1.09545	−	1.09545i	−0.100509	−	0.994936i	$-0.532047\pi$
$6$		0			0
$7$	−1.93185	+	1.93185i	−0.730171	+	0.730171i	−0.970654	−	0.240482i	$-0.922694\pi$
$7$	−1.93185	+	1.93185i	−0.730171	+	0.730171i	0.240482	+	0.970654i	$0.422694\pi$
$8$		0			0
$9$			4.46410i			1.48803i
$10$		0			0
$11$	0.896575	−	0.896575i	0.270328	−	0.270328i	−0.558904	−	0.829232i	$-0.688778\pi$
$11$	0.896575	−	0.896575i	0.270328	−	0.270328i	0.829232	+	0.558904i	$0.188778\pi$
$12$		0			0
$13$	−5.46410			−1.51547			−0.757735	−	0.652563i	$-0.773694\pi$
$13$	−5.46410			−1.51547			−0.757735	+	0.652563i	$0.773694\pi$
$14$		0			0
$15$			9.46410i			2.44362i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$			1.46410i			0.335888i	0.985797	+	0.167944i	$0.0537128\pi$
$19$			1.46410i			0.335888i	−0.985797	+	0.167944i	$0.946287\pi$
$20$		0			0
$21$	7.46410			1.62880
$22$		0			0
$23$	0.896575	−	0.896575i	0.186949	−	0.186949i	−0.607427	−	0.794376i	$-0.707798\pi$
$23$	0.896575	−	0.896575i	0.186949	−	0.186949i	0.794376	+	0.607427i	$0.207798\pi$
$24$		0			0
$25$			7.00000i			1.40000i
$26$		0			0
$27$	2.82843	−	2.82843i	0.544331	−	0.544331i
$28$		0			0
$29$	2.44949	+	2.44949i	0.454859	+	0.454859i	0.896963	−	0.442105i	$-0.145768\pi$
$29$	2.44949	+	2.44949i	0.454859	+	0.454859i	−0.442105	+	0.896963i	$0.645768\pi$
$30$		0			0
$31$	−2.96713	−	2.96713i	−0.532912	−	0.532912i	0.388526	−	0.921438i	$-0.372984\pi$
$31$	−2.96713	−	2.96713i	−0.532912	−	0.532912i	−0.921438	+	0.388526i	$0.872984\pi$
$32$		0			0
$33$	−3.46410			−0.603023
$34$		0			0
$35$	9.46410			1.59973
$36$		0			0
$37$	−3.20736	−	3.20736i	−0.527287	−	0.527287i	0.392475	−	0.919763i	$-0.371619\pi$
$37$	−3.20736	−	3.20736i	−0.527287	−	0.527287i	−0.919763	+	0.392475i	$0.871619\pi$
$38$		0			0
$39$	10.5558	+	10.5558i	1.69029	+	1.69029i
$40$		0			0
$41$	−4.24264	+	4.24264i	−0.662589	+	0.662589i	−0.955990	−	0.293400i	$-0.905213\pi$
$41$	−4.24264	+	4.24264i	−0.662589	+	0.662589i	0.293400	+	0.955990i	$0.405213\pi$
$42$		0			0
$43$		−	8.39230i		−	1.27981i	−0.768452	−	0.639907i	$-0.778973\pi$
$43$		−	8.39230i		−	1.27981i	0.768452	−	0.639907i	$-0.221027\pi$
$44$		0			0
$45$	10.9348	−	10.9348i	1.63006	−	1.63006i
$46$		0			0
$47$	6.92820			1.01058			0.505291	−	0.862949i	$-0.331385\pi$
$47$	6.92820			1.01058			0.505291	+	0.862949i	$0.331385\pi$
$48$		0			0
$49$		−	0.464102i		−	0.0663002i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	12.9282i		−	1.77583i	−0.460012	−	0.887913i	$-0.652155\pi$
$53$		−	12.9282i		−	1.77583i	0.460012	−	0.887913i	$-0.347845\pi$
$54$		0			0
$55$	−4.39230			−0.592258
$56$		0			0
$57$	2.82843	−	2.82843i	0.374634	−	0.374634i
$58$		0			0
$59$			2.53590i			0.330146i	0.986281	+	0.165073i	$0.0527859\pi$
$59$			2.53590i			0.330146i	−0.986281	+	0.165073i	$0.947214\pi$
$60$		0			0
$61$	−0.378937	+	0.378937i	−0.0485180	+	0.0485180i	−0.730950	−	0.682432i	$-0.760923\pi$
$61$	−0.378937	+	0.378937i	−0.0485180	+	0.0485180i	0.682432	+	0.730950i	$0.260923\pi$
$62$		0			0
$63$	−8.62398	−	8.62398i	−1.08652	−	1.08652i
$64$		0			0
$65$	13.3843	+	13.3843i	1.66011	+	1.66011i
$66$		0			0
$67$	14.9282			1.82377			0.911885	−	0.410445i	$-0.134627\pi$
$67$	14.9282			1.82377			0.911885	+	0.410445i	$0.134627\pi$
$68$		0			0
$69$	−3.46410			−0.417029
$70$		0			0
$71$	5.79555	+	5.79555i	0.687806	+	0.687806i	0.961747	−	0.273941i	$-0.0883272\pi$
$71$	5.79555	+	5.79555i	0.687806	+	0.687806i	−0.273941	+	0.961747i	$0.588327\pi$
$72$		0			0
$73$	1.41421	+	1.41421i	0.165521	+	0.165521i	0.785007	−	0.619486i	$-0.212659\pi$
$73$	1.41421	+	1.41421i	0.165521	+	0.165521i	−0.619486	+	0.785007i	$0.712659\pi$
$74$		0			0
$75$	13.5230	−	13.5230i	1.56150	−	1.56150i
$76$		0			0
$77$			3.46410i			0.394771i
$78$		0			0
$79$	8.62398	−	8.62398i	0.970274	−	0.970274i	−0.0292970	−	0.999571i	$-0.509327\pi$
$79$	8.62398	−	8.62398i	0.970274	−	0.970274i	0.999571	+	0.0292970i	$0.00932685\pi$
$80$		0			0
$81$	2.46410			0.273789
$82$		0			0
$83$			2.53590i			0.278351i	0.990268	+	0.139176i	$0.0444452\pi$
$83$			2.53590i			0.278351i	−0.990268	+	0.139176i	$0.955555\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	9.46410i		−	1.01466i
$88$		0			0
$89$	−2.53590			−0.268805			−0.134402	−	0.990927i	$-0.542911\pi$
$89$	−2.53590			−0.268805			−0.134402	+	0.990927i	$0.542911\pi$
$90$		0			0
$91$	10.5558	−	10.5558i	1.10655	−	1.10655i
$92$		0			0
$93$			11.4641i			1.18877i
$94$		0			0
$95$	3.58630	−	3.58630i	0.367947	−	0.367947i
$96$		0			0
$97$	−3.48477	−	3.48477i	−0.353824	−	0.353824i	0.507706	−	0.861530i	$-0.330494\pi$
$97$	−3.48477	−	3.48477i	−0.353824	−	0.353824i	−0.861530	+	0.507706i	$0.830494\pi$
$98$		0			0
$99$	4.00240	+	4.00240i	0.402257	+	0.402257i
$100$		0			0
$101$	−2.53590			−0.252331			−0.126166	−	0.992009i	$-0.540267\pi$
$101$	−2.53590			−0.252331			−0.126166	+	0.992009i	$0.540267\pi$
$102$		0			0
$103$	−10.9282			−1.07679			−0.538394	−	0.842693i	$-0.680969\pi$
$103$	−10.9282			−1.07679			−0.538394	+	0.842693i	$0.680969\pi$
$104$		0			0
$105$	−18.2832	−	18.2832i	−1.78426	−	1.78426i
$106$		0			0
$107$	7.58871	+	7.58871i	0.733628	+	0.733628i	0.971337	−	0.237709i	$-0.0763963\pi$
$107$	7.58871	+	7.58871i	0.733628	+	0.733628i	−0.237709	+	0.971337i	$0.576396\pi$
$108$		0			0
$109$	−10.1769	+	10.1769i	−0.974770	+	0.974770i	−0.999689	−	0.0249196i	$-0.992067\pi$
$109$	−10.1769	+	10.1769i	−0.974770	+	0.974770i	0.0249196	+	0.999689i	$0.492067\pi$
$110$		0			0
$111$			12.3923i			1.17623i
$112$		0			0
$113$	−14.0406	+	14.0406i	−1.32083	+	1.32083i	−0.407723	+	0.913106i	$0.633677\pi$
$113$	−14.0406	+	14.0406i	−1.32083	+	1.32083i	−0.913106	+	0.407723i	$0.866323\pi$
$114$		0			0
$115$	−4.39230			−0.409585
$116$		0			0
$117$		−	24.3923i		−	2.25507i
$118$		0			0
$119$		0			0
$120$		0			0
$121$			9.39230i			0.853846i
$122$		0			0
$123$	16.3923			1.47804
$124$		0			0
$125$	4.89898	−	4.89898i	0.438178	−	0.438178i
$126$		0			0
$127$			0.392305i			0.0348114i	0.999849	+	0.0174057i	$0.00554069\pi$
$127$			0.392305i			0.0348114i	−0.999849	+	0.0174057i	$0.994459\pi$
$128$		0			0
$129$	−16.2127	+	16.2127i	−1.42745	+	1.42745i
$130$		0			0
$131$	4.00240	+	4.00240i	0.349692	+	0.349692i	0.859995	−	0.510303i	$-0.170467\pi$
$131$	4.00240	+	4.00240i	0.349692	+	0.349692i	−0.510303	+	0.859995i	$0.670467\pi$
$132$		0			0
$133$	−2.82843	−	2.82843i	−0.245256	−	0.245256i
$134$		0			0
$135$	−13.8564			−1.19257
$136$		0			0
$137$	2.53590			0.216656			0.108328	−	0.994115i	$-0.465450\pi$
$137$	2.53590			0.216656			0.108328	+	0.994115i	$0.465450\pi$
$138$		0			0
$139$	10.4171	+	10.4171i	0.883570	+	0.883570i	0.993895	−	0.110326i	$-0.0351894\pi$
$139$	10.4171	+	10.4171i	0.883570	+	0.883570i	−0.110326	+	0.993895i	$0.535189\pi$
$140$		0			0
$141$	−13.3843	−	13.3843i	−1.12716	−	1.12716i
$142$		0			0
$143$	−4.89898	+	4.89898i	−0.409673	+	0.409673i
$144$		0			0
$145$		−	12.0000i		−	0.996546i
$146$		0			0
$147$	−0.896575	+	0.896575i	−0.0739483	+	0.0739483i
$148$		0			0
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$		0			0
$151$			13.4641i			1.09569i	0.836579	+	0.547847i	$0.184552\pi$
$151$			13.4641i			1.09569i	−0.836579	+	0.547847i	$0.815448\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			14.5359i			1.16755i
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	−24.9754	+	24.9754i	−1.98068	+	1.98068i
$160$		0			0
$161$			3.46410i			0.273009i
$162$		0			0
$163$	14.5582	−	14.5582i	1.14029	−	1.14029i	0.151892	−	0.988397i	$-0.451463\pi$
$163$	14.5582	−	14.5582i	1.14029	−	1.14029i	0.988397	−	0.151892i	$-0.0485366\pi$
$164$		0			0
$165$	8.48528	+	8.48528i	0.660578	+	0.660578i
$166$		0			0
$167$	−4.00240	−	4.00240i	−0.309715	−	0.309715i	0.535084	−	0.844799i	$-0.320280\pi$
$167$	−4.00240	−	4.00240i	−0.309715	−	0.309715i	−0.844799	+	0.535084i	$0.820280\pi$
$168$		0			0
$169$	16.8564			1.29665
$170$		0			0
$171$	−6.53590			−0.499813
$172$		0			0
$173$	10.9348	+	10.9348i	0.831355	+	0.831355i	0.987702	−	0.156347i	$-0.0499718\pi$
$173$	10.9348	+	10.9348i	0.831355	+	0.831355i	−0.156347	+	0.987702i	$0.549972\pi$
$174$		0			0
$175$	−13.5230	−	13.5230i	−1.02224	−	1.02224i
$176$		0			0
$177$	4.89898	−	4.89898i	0.368230	−	0.368230i
$178$		0			0
$179$			14.5359i			1.08646i	0.839583	+	0.543232i	$0.182800\pi$
$179$			14.5359i			1.08646i	−0.839583	+	0.543232i	$0.817200\pi$
$180$		0			0
$181$	−3.20736	+	3.20736i	−0.238402	+	0.238402i	−0.816188	−	0.577786i	$-0.803917\pi$
$181$	−3.20736	+	3.20736i	−0.238402	+	0.238402i	0.577786	+	0.816188i	$0.303917\pi$
$182$		0			0
$183$	1.46410			0.108230
$184$		0			0
$185$			15.7128i			1.15523i
$186$		0			0
$187$		0			0
$188$		0			0
$189$			10.9282i			0.794910i
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	−14.7985	+	14.7985i	−1.06522	+	1.06522i	−0.0674981	+	0.997719i	$0.521502\pi$
$193$	−14.7985	+	14.7985i	−1.06522	+	1.06522i	−0.997719	+	0.0674981i	$0.978498\pi$
$194$		0			0
$195$		−	51.7128i		−	3.70323i
$196$		0			0
$197$	2.44949	−	2.44949i	0.174519	−	0.174519i	−0.614443	−	0.788962i	$-0.710619\pi$
$197$	2.44949	−	2.44949i	0.174519	−	0.174519i	0.788962	+	0.614443i	$0.210619\pi$
$198$		0			0
$199$	2.96713	+	2.96713i	0.210334	+	0.210334i	0.804409	−	0.594075i	$-0.202482\pi$
$199$	2.96713	+	2.96713i	0.210334	+	0.210334i	−0.594075	+	0.804409i	$0.702482\pi$
$200$		0			0
$201$	−28.8391	−	28.8391i	−2.03415	−	2.03415i
$202$		0			0
$203$	−9.46410			−0.664250
$204$		0			0
$205$	20.7846			1.45166
$206$		0			0
$207$	4.00240	+	4.00240i	0.278186	+	0.278186i
$208$		0			0
$209$	1.31268	+	1.31268i	0.0907998	+	0.0907998i
$210$		0			0
$211$	1.65445	−	1.65445i	0.113897	−	0.113897i	−0.647861	−	0.761758i	$-0.724336\pi$
$211$	1.65445	−	1.65445i	0.113897	−	0.113897i	0.761758	+	0.647861i	$0.224336\pi$
$212$		0			0
$213$		−	22.3923i		−	1.53430i
$214$		0			0
$215$	−20.5569	+	20.5569i	−1.40197	+	1.40197i
$216$		0			0
$217$	11.4641			0.778234
$218$		0			0
$219$		−	5.46410i		−	0.369230i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	12.3923i		−	0.829850i	−0.909856	−	0.414925i	$-0.863808\pi$
$223$		−	12.3923i		−	0.829850i	0.909856	−	0.414925i	$-0.136192\pi$
$224$		0			0
$225$	−31.2487			−2.08325
$226$		0			0
$227$	14.2808	−	14.2808i	0.947852	−	0.947852i	−0.0508537	−	0.998706i	$-0.516194\pi$
$227$	14.2808	−	14.2808i	0.947852	−	0.947852i	0.998706	+	0.0508537i	$0.0161942\pi$
$228$		0			0
$229$		−	20.3923i		−	1.34756i	−0.738931	−	0.673781i	$-0.764669\pi$
$229$		−	20.3923i		−	1.34756i	0.738931	−	0.673781i	$-0.235331\pi$
$230$		0			0
$231$	6.69213	−	6.69213i	0.440310	−	0.440310i
$232$		0			0
$233$	4.24264	+	4.24264i	0.277945	+	0.277945i	0.832288	−	0.554343i	$-0.187031\pi$
$233$	4.24264	+	4.24264i	0.277945	+	0.277945i	−0.554343	+	0.832288i	$0.687031\pi$
$234$		0			0
$235$	−16.9706	−	16.9706i	−1.10704	−	1.10704i
$236$		0			0
$237$	−33.3205			−2.16440
$238$		0			0
$239$	20.7846			1.34444			0.672222	−	0.740349i	$-0.265340\pi$
$239$	20.7846			1.34444			0.672222	+	0.740349i	$0.265340\pi$
$240$		0			0
$241$	−1.41421	−	1.41421i	−0.0910975	−	0.0910975i	0.660089	−	0.751187i	$-0.270518\pi$
$241$	−1.41421	−	1.41421i	−0.0910975	−	0.0910975i	−0.751187	+	0.660089i	$0.770518\pi$
$242$		0			0
$243$	−13.2456	−	13.2456i	−0.849703	−	0.849703i
$244$		0			0
$245$	−1.13681	+	1.13681i	−0.0726283	+	0.0726283i
$246$		0			0
$247$		−	8.00000i		−	0.509028i
$248$		0			0
$249$	4.89898	−	4.89898i	0.310460	−	0.310460i
$250$		0			0
$251$	−6.92820			−0.437304			−0.218652	−	0.975803i	$-0.570166\pi$
$251$	−6.92820			−0.437304			−0.218652	+	0.975803i	$0.570166\pi$
$252$		0			0
$253$		−	1.60770i		−	0.101075i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			28.3923i			1.77106i	0.464579	+	0.885532i	$0.346206\pi$
$257$			28.3923i			1.77106i	−0.464579	+	0.885532i	$0.653794\pi$
$258$		0			0
$259$	12.3923			0.770020
$260$		0			0
$261$	−10.9348	+	10.9348i	−0.676845	+	0.676845i
$262$		0			0
$263$			11.3205i			0.698052i	0.937113	+	0.349026i	$0.113488\pi$
$263$			11.3205i			0.698052i	−0.937113	+	0.349026i	$0.886512\pi$
$264$		0			0
$265$	−31.6675	+	31.6675i	−1.94532	+	1.94532i
$266$		0			0
$267$	4.89898	+	4.89898i	0.299813	+	0.299813i
$268$		0			0
$269$	19.4201	+	19.4201i	1.18406	+	1.18406i	0.978683	+	0.205379i	$0.0658427\pi$
$269$	19.4201	+	19.4201i	1.18406	+	1.18406i	0.205379	+	0.978683i	$0.434157\pi$
$270$		0			0
$271$	1.07180			0.0651070			0.0325535	−	0.999470i	$-0.489636\pi$
$271$	1.07180			0.0651070			0.0325535	+	0.999470i	$0.489636\pi$
$272$		0			0
$273$	−40.7846			−2.46840
$274$		0			0
$275$	6.27603	+	6.27603i	0.378459	+	0.378459i
$276$		0			0
$277$	4.52004	+	4.52004i	0.271583	+	0.271583i	0.829737	−	0.558154i	$-0.188490\pi$
$277$	4.52004	+	4.52004i	0.271583	+	0.271583i	−0.558154	+	0.829737i	$0.688490\pi$
$278$		0			0
$279$	13.2456	−	13.2456i	0.792991	−	0.792991i
$280$		0			0
$281$		−	19.8564i		−	1.18453i	−0.805742	−	0.592267i	$-0.798233\pi$
$281$		−	19.8564i		−	1.18453i	0.805742	−	0.592267i	$-0.201767\pi$
$282$		0			0
$283$	−14.5582	+	14.5582i	−0.865397	+	0.865397i	−0.991959	−	0.126561i	$-0.959606\pi$
$283$	−14.5582	+	14.5582i	−0.865397	+	0.865397i	0.126561	+	0.991959i	$0.459606\pi$
$284$		0			0
$285$	−13.8564			−0.820783
$286$		0			0
$287$		−	16.3923i		−	0.967607i
$288$		0			0
$289$		0			0
$290$		0			0
$291$			13.4641i			0.789280i
$292$		0			0
$293$	−30.0000			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		0			0
$295$	6.21166	−	6.21166i	0.361657	−	0.361657i
$296$		0			0
$297$		−	5.07180i		−	0.294295i
$298$		0			0
$299$	−4.89898	+	4.89898i	−0.283315	+	0.283315i
$300$		0			0
$301$	16.2127	+	16.2127i	0.934484	+	0.934484i
$302$		0			0
$303$	4.89898	+	4.89898i	0.281439	+	0.281439i
$304$		0			0
$305$	1.85641			0.106298
$306$		0			0
$307$	−24.7846			−1.41453			−0.707266	−	0.706947i	$-0.750072\pi$
$307$	−24.7846			−1.41453			−0.707266	+	0.706947i	$0.750072\pi$
$308$		0			0
$309$	21.1117	+	21.1117i	1.20100	+	1.20100i
$310$		0			0
$311$	−2.20925	−	2.20925i	−0.125275	−	0.125275i	0.641689	−	0.766965i	$-0.278234\pi$
$311$	−2.20925	−	2.20925i	−0.125275	−	0.125275i	−0.766965	+	0.641689i	$0.778234\pi$
$312$		0			0
$313$	14.7985	−	14.7985i	0.836459	−	0.836459i	−0.151932	−	0.988391i	$-0.548549\pi$
$313$	14.7985	−	14.7985i	0.836459	−	0.836459i	0.988391	+	0.151932i	$0.0485494\pi$
$314$		0			0
$315$			42.2487i			2.38045i
$316$		0			0
$317$	−6.03579	+	6.03579i	−0.339004	+	0.339004i	−0.855992	−	0.516989i	$-0.827053\pi$
$317$	−6.03579	+	6.03579i	−0.339004	+	0.339004i	0.516989	+	0.855992i	$0.327053\pi$
$318$		0			0
$319$	4.39230			0.245922
$320$		0			0
$321$		−	29.3205i		−	1.63651i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		−	38.2487i		−	2.12166i
$326$		0			0
$327$	39.3205			2.17443
$328$		0			0
$329$	−13.3843	+	13.3843i	−0.737898	+	0.737898i
$330$		0			0
$331$			19.3205i			1.06195i	0.847387	+	0.530976i	$0.178174\pi$
$331$			19.3205i			1.06195i	−0.847387	+	0.530976i	$0.821826\pi$
$332$		0			0
$333$	14.3180	−	14.3180i	0.784622	−	0.784622i
$334$		0			0
$335$	−36.5665	−	36.5665i	−1.99784	−	1.99784i
$336$		0			0
$337$	4.79744	+	4.79744i	0.261333	+	0.261333i	0.825596	−	0.564262i	$-0.190839\pi$
$337$	4.79744	+	4.79744i	0.261333	+	0.261333i	−0.564262	+	0.825596i	$0.690839\pi$
$338$		0			0
$339$	54.2487			2.94639
$340$		0			0
$341$	−5.32051			−0.288122
$342$		0			0
$343$	−12.6264	−	12.6264i	−0.681761	−	0.681761i
$344$		0			0
$345$	8.48528	+	8.48528i	0.456832	+	0.456832i
$346$		0			0
$347$	−24.0788	+	24.0788i	−1.29262	+	1.29262i	−0.359455	+	0.933162i	$0.617037\pi$
$347$	−24.0788	+	24.0788i	−1.29262	+	1.29262i	−0.933162	+	0.359455i	$0.882963\pi$
$348$		0			0
$349$			10.7846i			0.577287i	0.957437	+	0.288643i	$0.0932042\pi$
$349$			10.7846i			0.577287i	−0.957437	+	0.288643i	$0.906796\pi$
$350$		0			0
$351$	−15.4548	+	15.4548i	−0.824917	+	0.824917i
$352$		0			0
$353$	19.8564			1.05685			0.528425	−	0.848980i	$-0.322783\pi$
$353$	19.8564			1.05685			0.528425	+	0.848980i	$0.322783\pi$
$354$		0			0
$355$		−	28.3923i		−	1.50691i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			23.3205i			1.23081i	0.788211	+	0.615405i	$0.211007\pi$
$359$			23.3205i			1.23081i	−0.788211	+	0.615405i	$0.788993\pi$
$360$		0			0
$361$	16.8564			0.887179
$362$		0			0
$363$	18.1445	−	18.1445i	0.952341	−	0.952341i
$364$		0			0
$365$		−	6.92820i		−	0.362639i
$366$		0			0
$367$	1.65445	−	1.65445i	0.0863616	−	0.0863616i	−0.662606	−	0.748968i	$-0.730550\pi$
$367$	1.65445	−	1.65445i	0.0863616	−	0.0863616i	0.748968	+	0.662606i	$0.230550\pi$
$368$		0			0
$369$	−18.9396	−	18.9396i	−0.985955	−	0.985955i
$370$		0			0
$371$	24.9754	+	24.9754i	1.29666	+	1.29666i
$372$		0			0
$373$	−8.39230			−0.434537			−0.217269	−	0.976112i	$-0.569715\pi$
$373$	−8.39230			−0.434537			−0.217269	+	0.976112i	$0.569715\pi$
$374$		0			0
$375$	−18.9282			−0.977448
$376$		0			0
$377$	−13.3843	−	13.3843i	−0.689325	−	0.689325i
$378$		0			0
$379$	−3.72500	−	3.72500i	−0.191341	−	0.191341i	0.604935	−	0.796275i	$-0.293199\pi$
$379$	−3.72500	−	3.72500i	−0.191341	−	0.191341i	−0.796275	+	0.604935i	$0.793199\pi$
$380$		0			0
$381$	0.757875	−	0.757875i	0.0388271	−	0.0388271i
$382$		0			0
$383$		−	2.53590i		−	0.129578i	−0.997899	−	0.0647892i	$-0.979363\pi$
$383$		−	2.53590i		−	0.129578i	0.997899	−	0.0647892i	$-0.0206375\pi$
$384$		0			0
$385$	8.48528	−	8.48528i	0.432450	−	0.432450i
$386$		0			0
$387$	37.4641			1.90441
$388$		0			0
$389$		−	37.1769i		−	1.88494i	−0.334285	−	0.942472i	$-0.608495\pi$
$389$		−	37.1769i		−	1.88494i	0.334285	−	0.942472i	$-0.391505\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		−	15.4641i		−	0.780061i
$394$		0			0
$395$	−42.2487			−2.12576
$396$		0			0
$397$	3.96524	−	3.96524i	0.199010	−	0.199010i	−0.600566	−	0.799575i	$-0.705058\pi$
$397$	3.96524	−	3.96524i	0.199010	−	0.199010i	0.799575	+	0.600566i	$0.205058\pi$
$398$		0			0
$399$			10.9282i			0.547094i
$400$		0			0
$401$	22.5259	−	22.5259i	1.12489	−	1.12489i	0.133893	−	0.990996i	$-0.457252\pi$
$401$	22.5259	−	22.5259i	1.12489	−	1.12489i	0.990996	−	0.133893i	$-0.0427479\pi$
$402$		0			0
$403$	16.2127	+	16.2127i	0.807612	+	0.807612i
$404$		0			0
$405$	−6.03579	−	6.03579i	−0.299921	−	0.299921i
$406$		0			0
$407$	−5.75129			−0.285081
$408$		0			0
$409$	17.7128			0.875842			0.437921	−	0.899013i	$-0.355715\pi$
$409$	17.7128			0.875842			0.437921	+	0.899013i	$0.355715\pi$
$410$		0			0
$411$	−4.89898	−	4.89898i	−0.241649	−	0.241649i
$412$		0			0
$413$	−4.89898	−	4.89898i	−0.241063	−	0.241063i
$414$		0			0
$415$	6.21166	−	6.21166i	0.304918	−	0.304918i
$416$		0			0
$417$		−	40.2487i		−	1.97099i
$418$		0			0
$419$	17.3867	−	17.3867i	0.849394	−	0.849394i	−0.140663	−	0.990057i	$-0.544924\pi$
$419$	17.3867	−	17.3867i	0.849394	−	0.849394i	0.990057	+	0.140663i	$0.0449235\pi$
$420$		0			0
$421$	22.2487			1.08434			0.542168	−	0.840270i	$-0.317604\pi$
$421$	22.2487			1.08434			0.542168	+	0.840270i	$0.317604\pi$
$422$		0			0
$423$			30.9282i			1.50378i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	1.46410i		−	0.0708528i
$428$		0			0
$429$	18.9282			0.913862
$430$		0			0
$431$	−12.4877	+	12.4877i	−0.601511	+	0.601511i	−0.940713	−	0.339203i	$-0.889843\pi$
$431$	−12.4877	+	12.4877i	−0.601511	+	0.601511i	0.339203	+	0.940713i	$0.389843\pi$
$432$		0			0
$433$			3.60770i			0.173375i	0.996236	+	0.0866874i	$0.0276281\pi$
$433$			3.60770i			0.173375i	−0.996236	+	0.0866874i	$0.972372\pi$
$434$		0			0
$435$	−23.1822	+	23.1822i	−1.11150	+	1.11150i
$436$		0			0
$437$	1.31268	+	1.31268i	0.0627939	+	0.0627939i
$438$		0			0
$439$	17.1093	+	17.1093i	0.816581	+	0.816581i	0.985611	−	0.169030i	$-0.0540636\pi$
$439$	17.1093	+	17.1093i	0.816581	+	0.816581i	−0.169030	+	0.985611i	$0.554064\pi$
$440$		0			0
$441$	2.07180			0.0986570
$442$		0			0
$443$	−20.7846			−0.987507			−0.493753	−	0.869602i	$-0.664375\pi$
$443$	−20.7846			−0.987507			−0.493753	+	0.869602i	$0.664375\pi$
$444$		0			0
$445$	6.21166	+	6.21166i	0.294461	+	0.294461i
$446$		0			0
$447$	11.5911	+	11.5911i	0.548241	+	0.548241i
$448$		0			0
$449$	4.24264	−	4.24264i	0.200223	−	0.200223i	−0.599873	−	0.800095i	$-0.704782\pi$
$449$	4.24264	−	4.24264i	0.200223	−	0.200223i	0.800095	+	0.599873i	$0.204782\pi$
$450$		0			0
$451$			7.60770i			0.358232i
$452$		0			0
$453$	26.0106	−	26.0106i	1.22209	−	1.22209i
$454$		0			0
$455$	−51.7128			−2.42433
$456$		0			0
$457$			20.3923i			0.953912i	0.878927	+	0.476956i	$0.158260\pi$
$457$			20.3923i			0.953912i	−0.878927	+	0.476956i	$0.841740\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	26.7846i		−	1.24748i	−0.781630	−	0.623742i	$-0.785612\pi$
$461$		−	26.7846i		−	1.24748i	0.781630	−	0.623742i	$-0.214388\pi$
$462$		0			0
$463$	2.14359			0.0996212			0.0498106	−	0.998759i	$-0.484138\pi$
$463$	2.14359			0.0996212			0.0498106	+	0.998759i	$0.484138\pi$
$464$		0			0
$465$	28.0812	−	28.0812i	1.30223	−	1.30223i
$466$		0			0
$467$			14.5359i			0.672641i	0.941748	+	0.336321i	$0.109183\pi$
$467$			14.5359i			0.672641i	−0.941748	+	0.336321i	$0.890817\pi$
$468$		0			0
$469$	−28.8391	+	28.8391i	−1.33166	+	1.33166i
$470$		0			0
$471$	3.86370	+	3.86370i	0.178030	+	0.178030i
$472$		0			0
$473$	−7.52433	−	7.52433i	−0.345969	−	0.345969i
$474$		0			0
$475$	−10.2487			−0.470243
$476$		0			0
$477$	57.7128			2.64249
$478$		0			0
$479$	12.4877	+	12.4877i	0.570577	+	0.570577i	0.932290	−	0.361713i	$-0.117808\pi$
$479$	12.4877	+	12.4877i	0.570577	+	0.570577i	−0.361713	+	0.932290i	$0.617808\pi$
$480$		0			0
$481$	17.5254	+	17.5254i	0.799088	+	0.799088i
$482$		0			0
$483$	6.69213	−	6.69213i	0.304502	−	0.304502i
$484$		0			0
$485$			17.0718i			0.775190i
$486$		0			0
$487$	−4.27981	+	4.27981i	−0.193936	+	0.193936i	−0.797395	−	0.603458i	$-0.793789\pi$
$487$	−4.27981	+	4.27981i	−0.193936	+	0.193936i	0.603458	+	0.797395i	$0.293789\pi$
$488$		0			0
$489$	−56.2487			−2.54365
$490$		0			0
$491$			37.1769i			1.67777i	0.544308	+	0.838885i	$0.316792\pi$
$491$			37.1769i			1.67777i	−0.544308	+	0.838885i	$0.683208\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		−	19.6077i		−	0.881300i
$496$		0			0
$497$	−22.3923			−1.00443
$498$		0			0
$499$	−17.6641	+	17.6641i	−0.790752	+	0.790752i	−0.981616	−	0.190864i	$-0.938871\pi$
$499$	−17.6641	+	17.6641i	−0.790752	+	0.790752i	0.190864	+	0.981616i	$0.438871\pi$
$500$		0			0
$501$			15.4641i			0.690885i
$502$		0			0
$503$	19.1798	−	19.1798i	0.855186	−	0.855186i	−0.135581	−	0.990766i	$-0.543290\pi$
$503$	19.1798	−	19.1798i	0.855186	−	0.855186i	0.990766	+	0.135581i	$0.0432900\pi$
$504$		0			0
$505$	6.21166	+	6.21166i	0.276415	+	0.276415i
$506$		0			0
$507$	−32.5641	−	32.5641i	−1.44622	−	1.44622i
$508$		0			0
$509$	−21.7128			−0.962404			−0.481202	−	0.876610i	$-0.659800\pi$
$509$	−21.7128			−0.962404			−0.481202	+	0.876610i	$0.659800\pi$
$510$		0			0
$511$	−5.46410			−0.241718
$512$		0			0
$513$	4.14110	+	4.14110i	0.182834	+	0.182834i
$514$		0			0
$515$	26.7685	+	26.7685i	1.17956	+	1.17956i
$516$		0			0
$517$	6.21166	−	6.21166i	0.273188	−	0.273188i
$518$		0			0
$519$		−	42.2487i		−	1.85451i
$520$		0			0
$521$	4.24264	−	4.24264i	0.185873	−	0.185873i	−0.608036	−	0.793909i	$-0.708042\pi$
$521$	4.24264	−	4.24264i	0.185873	−	0.185873i	0.793909	+	0.608036i	$0.208042\pi$
$522$		0			0
$523$	12.7846			0.559032			0.279516	−	0.960141i	$-0.409826\pi$
$523$	12.7846			0.559032			0.279516	+	0.960141i	$0.409826\pi$
$524$		0			0
$525$			52.2487i			2.28032i
$526$		0			0
$527$		0			0
$528$		0			0
$529$			21.3923i			0.930100i
$530$		0			0
$531$	−11.3205			−0.491268
$532$		0			0
$533$	23.1822	−	23.1822i	1.00413	−	1.00413i
$534$		0			0
$535$		−	37.1769i		−	1.60730i
$536$		0			0
$537$	28.0812	−	28.0812i	1.21179	−	1.21179i
$538$		0			0
$539$	−0.416102	−	0.416102i	−0.0179228	−	0.0179228i
$540$		0			0
$541$	−13.0053	−	13.0053i	−0.559143	−	0.559143i	0.369921	−	0.929063i	$-0.379385\pi$
$541$	−13.0053	−	13.0053i	−0.559143	−	0.559143i	−0.929063	+	0.369921i	$0.879385\pi$
$542$		0			0
$543$	12.3923			0.531805
$544$		0			0
$545$	49.8564			2.13561
$546$		0			0
$547$	−30.2161	−	30.2161i	−1.29195	−	1.29195i	−0.933581	−	0.358368i	$-0.883333\pi$
$547$	−30.2161	−	30.2161i	−1.29195	−	1.29195i	−0.358368	−	0.933581i	$-0.616667\pi$
$548$		0			0
$549$	−1.69161	−	1.69161i	−0.0721964	−	0.0721964i
$550$		0			0
$551$	−3.58630	+	3.58630i	−0.152782	+	0.152782i
$552$		0			0
$553$			33.3205i			1.41693i
$554$		0			0
$555$	30.3548	−	30.3548i	1.28849	−	1.28849i
$556$		0			0
$557$	26.5359			1.12436			0.562181	−	0.827014i	$-0.309962\pi$
$557$	26.5359			1.12436			0.562181	+	0.827014i	$0.309962\pi$
$558$		0			0
$559$			45.8564i			1.93952i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			35.3205i			1.48858i	0.667855	+	0.744291i	$0.267212\pi$
$563$			35.3205i			1.48858i	−0.667855	+	0.744291i	$0.732788\pi$
$564$		0			0
$565$	68.7846			2.89379
$566$		0			0
$567$	−4.76028	+	4.76028i	−0.199913	+	0.199913i
$568$		0			0
$569$		−	7.85641i		−	0.329358i	−0.986347	−	0.164679i	$-0.947341\pi$
$569$		−	7.85641i		−	0.329358i	0.986347	−	0.164679i	$-0.0526588\pi$
$570$		0			0
$571$	7.86611	−	7.86611i	0.329186	−	0.329186i	−0.523091	−	0.852277i	$-0.675221\pi$
$571$	7.86611	−	7.86611i	0.329186	−	0.329186i	0.852277	+	0.523091i	$0.175221\pi$
$572$		0			0
$573$	23.1822	+	23.1822i	0.968451	+	0.968451i
$574$		0			0
$575$	6.27603	+	6.27603i	0.261728	+	0.261728i
$576$		0			0
$577$	−13.4641			−0.560518			−0.280259	−	0.959924i	$-0.590420\pi$
$577$	−13.4641			−0.560518			−0.280259	+	0.959924i	$0.590420\pi$
$578$		0			0
$579$	57.1769			2.37619
$580$		0			0
$581$	−4.89898	−	4.89898i	−0.203244	−	0.203244i
$582$		0			0
$583$	−11.5911	−	11.5911i	−0.480055	−	0.480055i
$584$		0			0
$585$	−59.7487	+	59.7487i	−2.47030	+	2.47030i
$586$		0			0
$587$			28.3923i			1.17188i	0.810356	+	0.585938i	$0.199274\pi$
$587$			28.3923i			1.17188i	−0.810356	+	0.585938i	$0.800726\pi$
$588$		0			0
$589$	4.34418	−	4.34418i	0.178999	−	0.178999i
$590$		0			0
$591$	−9.46410			−0.389301
$592$		0			0
$593$			4.14359i			0.170157i	0.996374	+	0.0850785i	$0.0271141\pi$
$593$			4.14359i			0.170157i	−0.996374	+	0.0850785i	$0.972886\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	11.4641i		−	0.469194i
$598$		0			0
$599$	27.7128			1.13231			0.566157	−	0.824297i	$-0.308429\pi$
$599$	27.7128			1.13231			0.566157	+	0.824297i	$0.308429\pi$
$600$		0			0
$601$	−7.62587	+	7.62587i	−0.311066	+	0.311066i	−0.845322	−	0.534257i	$-0.820592\pi$
$601$	−7.62587	+	7.62587i	−0.311066	+	0.311066i	0.534257	+	0.845322i	$0.320592\pi$
$602$		0			0
$603$			66.6410i			2.71383i
$604$		0			0
$605$	23.0064	−	23.0064i	0.935341	−	0.935341i
$606$		0			0
$607$	−27.3877	−	27.3877i	−1.11163	−	1.11163i	−0.992930	−	0.118702i	$-0.962127\pi$
$607$	−27.3877	−	27.3877i	−1.11163	−	1.11163i	−0.118702	−	0.992930i	$-0.537873\pi$
$608$		0			0
$609$	18.2832	+	18.2832i	0.740874	+	0.740874i
$610$		0			0
$611$	−37.8564			−1.53151
$612$		0			0
$613$	−47.8564			−1.93290			−0.966451	−	0.256851i	$-0.917315\pi$
$613$	−47.8564			−1.93290			−0.966451	+	0.256851i	$0.917315\pi$
$614$		0			0
$615$	−40.1528	−	40.1528i	−1.61912	−	1.61912i
$616$		0			0
$617$	−25.1512	−	25.1512i	−1.01255	−	1.01255i	−0.999920	−	0.0126304i	$-0.995980\pi$
$617$	−25.1512	−	25.1512i	−1.01255	−	1.01255i	−0.0126304	−	0.999920i	$-0.504020\pi$
$618$		0			0
$619$	8.34658	−	8.34658i	0.335477	−	0.335477i	−0.519185	−	0.854662i	$-0.673764\pi$
$619$	8.34658	−	8.34658i	0.335477	−	0.335477i	0.854662	+	0.519185i	$0.173764\pi$
$620$		0			0
$621$		−	5.07180i		−	0.203524i
$622$		0			0
$623$	4.89898	−	4.89898i	0.196273	−	0.196273i
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$		−	5.07180i		−	0.202548i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		−	41.4641i		−	1.65066i	−0.564651	−	0.825330i	$-0.690989\pi$
$631$		−	41.4641i		−	1.65066i	0.564651	−	0.825330i	$-0.309011\pi$
$632$		0			0
$633$	−6.39230			−0.254071
$634$		0			0
$635$	0.960947	−	0.960947i	0.0381340	−	0.0381340i
$636$		0			0
$637$			2.53590i			0.100476i
$638$		0			0
$639$	−25.8719	+	25.8719i	−1.02348	+	1.02348i
$640$		0			0
$641$	−9.14162	−	9.14162i	−0.361072	−	0.361072i	0.503135	−	0.864208i	$-0.332180\pi$
$641$	−9.14162	−	9.14162i	−0.361072	−	0.361072i	−0.864208	+	0.503135i	$0.832180\pi$
$642$		0			0
$643$	−23.0435	−	23.0435i	−0.908748	−	0.908748i	0.0874235	−	0.996171i	$-0.472137\pi$
$643$	−23.0435	−	23.0435i	−0.908748	−	0.908748i	−0.996171	+	0.0874235i	$0.972137\pi$
$644$		0			0
$645$	79.4256			3.12738
$646$		0			0
$647$	17.0718			0.671162			0.335581	−	0.942011i	$-0.391067\pi$
$647$	17.0718			0.671162			0.335581	+	0.942011i	$0.391067\pi$
$648$		0			0
$649$	2.27362	+	2.27362i	0.0892476	+	0.0892476i
$650$		0			0
$651$	−22.1469	−	22.1469i	−0.868007	−	0.868007i
$652$		0			0
$653$	−7.34847	+	7.34847i	−0.287568	+	0.287568i	−0.836118	−	0.548550i	$-0.815180\pi$
$653$	−7.34847	+	7.34847i	−0.287568	+	0.287568i	0.548550	+	0.836118i	$0.315180\pi$
$654$		0			0
$655$		−	19.6077i		−	0.766136i
$656$		0			0
$657$	−6.31319	+	6.31319i	−0.246301	+	0.246301i
$658$		0			0
$659$	−42.9282			−1.67225			−0.836123	−	0.548542i	$-0.815183\pi$
$659$	−42.9282			−1.67225			−0.836123	+	0.548542i	$0.815183\pi$
$660$		0			0
$661$			15.0718i			0.586225i	0.956078	+	0.293112i	$0.0946910\pi$
$661$			15.0718i			0.586225i	−0.956078	+	0.293112i	$0.905309\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			13.8564i			0.537328i
$666$		0			0
$667$	4.39230			0.170071
$668$		0			0
$669$	−23.9401	+	23.9401i	−0.925578	+	0.925578i
$670$		0			0
$671$			0.679492i			0.0262315i
$672$		0			0
$673$	0.101536	−	0.101536i	0.00391392	−	0.00391392i	−0.705147	−	0.709061i	$-0.749119\pi$
$673$	0.101536	−	0.101536i	0.00391392	−	0.00391392i	0.709061	+	0.705147i	$0.249119\pi$
$674$		0			0
$675$	19.7990	+	19.7990i	0.762063	+	0.762063i
$676$		0			0
$677$	17.1464	+	17.1464i	0.658991	+	0.658991i	0.955141	−	0.296151i	$-0.0957030\pi$
$677$	17.1464	+	17.1464i	0.658991	+	0.658991i	−0.296151	+	0.955141i	$0.595703\pi$
$678$		0			0
$679$	13.4641			0.516705
$680$		0			0
$681$	−55.1769			−2.11438
$682$		0			0
$683$	32.5641	+	32.5641i	1.24603	+	1.24603i	0.957458	+	0.288571i	$0.0931803\pi$
$683$	32.5641	+	32.5641i	1.24603	+	1.24603i	0.288571	+	0.957458i	$0.406820\pi$
$684$		0			0
$685$	−6.21166	−	6.21166i	−0.237335	−	0.237335i
$686$		0			0
$687$	−39.3949	+	39.3949i	−1.50301	+	1.50301i
$688$		0			0
$689$			70.6410i			2.69121i
$690$		0			0
$691$	25.5945	−	25.5945i	0.973662	−	0.973662i	−0.0259996	−	0.999662i	$-0.508277\pi$
$691$	25.5945	−	25.5945i	0.973662	−	0.973662i	0.999662	+	0.0259996i	$0.00827686\pi$
$692$		0			0
$693$	−15.4641			−0.587433
$694$		0			0
$695$		−	51.0333i		−	1.93580i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	16.3923i		−	0.620014i
$700$		0			0
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$		0			0
$703$	4.69591	−	4.69591i	0.177110	−	0.177110i
$704$		0			0
$705$			65.5692i			2.46948i
$706$		0			0
$707$	4.89898	−	4.89898i	0.184245	−	0.184245i
$708$		0			0
$709$	−11.4896	−	11.4896i	−0.431500	−	0.431500i	0.457638	−	0.889138i	$-0.348695\pi$
$709$	−11.4896	−	11.4896i	−0.431500	−	0.431500i	−0.889138	+	0.457638i	$0.848695\pi$
$710$		0			0
$711$	38.4983	+	38.4983i	1.44380	+	1.44380i
$712$		0			0
$713$	−5.32051			−0.199255
$714$		0			0
$715$	24.0000			0.897549
$716$		0			0
$717$	−40.1528	−	40.1528i	−1.49953	−	1.49953i
$718$		0			0
$719$	30.7709	+	30.7709i	1.14756	+	1.14756i	0.987031	+	0.160531i	$0.0513207\pi$
$719$	30.7709	+	30.7709i	1.14756	+	1.14756i	0.160531	+	0.987031i	$0.448679\pi$
$720$		0			0
$721$	21.1117	−	21.1117i	0.786240	−	0.786240i
$722$		0			0
$723$			5.46410i			0.203212i
$724$		0			0
$725$	−17.1464	+	17.1464i	−0.636802	+	0.636802i
$726$		0			0
$727$	−4.78461			−0.177451			−0.0887257	−	0.996056i	$-0.528279\pi$
$727$	−4.78461			−0.177451			−0.0887257	+	0.996056i	$0.528279\pi$
$728$		0			0
$729$			43.7846i			1.62165i
$730$		0			0
$731$		0			0
$732$		0			0
$733$			18.7846i			0.693825i	0.937897	+	0.346913i	$0.112770\pi$
$733$			18.7846i			0.693825i	−0.937897	+	0.346913i	$0.887230\pi$
$734$		0			0
$735$	4.39230			0.162013
$736$		0			0
$737$	13.3843	−	13.3843i	0.493016	−	0.493016i
$738$		0			0
$739$			12.3923i			0.455858i	0.973678	+	0.227929i	$0.0731955\pi$
$739$			12.3923i			0.455858i	−0.973678	+	0.227929i	$0.926805\pi$
$740$		0			0
$741$	−15.4548	+	15.4548i	−0.567747	+	0.567747i
$742$		0			0
$743$	16.9062	+	16.9062i	0.620228	+	0.620228i	0.945590	−	0.325362i	$-0.105486\pi$
$743$	16.9062	+	16.9062i	0.620228	+	0.620228i	−0.325362	+	0.945590i	$0.605486\pi$
$744$		0			0
$745$	14.6969	+	14.6969i	0.538454	+	0.538454i
$746$		0			0
$747$	−11.3205			−0.414196
$748$		0			0
$749$	−29.3205			−1.07135
$750$		0			0
$751$	−13.2456	−	13.2456i	−0.483337	−	0.483337i	0.422858	−	0.906196i	$-0.361027\pi$
$751$	−13.2456	−	13.2456i	−0.483337	−	0.483337i	−0.906196	+	0.422858i	$0.861027\pi$
$752$		0			0
$753$	13.3843	+	13.3843i	0.487750	+	0.487750i
$754$		0			0
$755$	32.9802	−	32.9802i	1.20027	−	1.20027i
$756$		0			0
$757$			17.4641i			0.634744i	0.948301	+	0.317372i	$0.102800\pi$
$757$			17.4641i			0.634744i	−0.948301	+	0.317372i	$0.897200\pi$
$758$		0			0
$759$	−3.10583	+	3.10583i	−0.112734	+	0.112734i
$760$		0			0
$761$	−16.3923			−0.594221			−0.297110	−	0.954843i	$-0.596023\pi$
$761$	−16.3923			−0.594221			−0.297110	+	0.954843i	$0.596023\pi$
$762$		0			0
$763$		−	39.3205i		−	1.42350i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	13.8564i		−	0.500326i
$768$		0			0
$769$	−0.392305			−0.0141469			−0.00707344	−	0.999975i	$-0.502252\pi$
$769$	−0.392305			−0.0141469			−0.00707344	+	0.999975i	$0.502252\pi$
$770$		0			0
$771$	54.8497	−	54.8497i	1.97536	−	1.97536i
$772$		0			0
$773$		−	0.679492i		−	0.0244396i	−0.999925	−	0.0122198i	$-0.996110\pi$
$773$		−	0.679492i		−	0.0244396i	0.999925	−	0.0122198i	$-0.00388978\pi$
$774$		0			0
$775$	20.7699	−	20.7699i	0.746077	−	0.746077i
$776$		0			0
$777$	−23.9401	−	23.9401i	−0.858846	−	0.858846i
$778$		0			0
$779$	−6.21166	−	6.21166i	−0.222556	−	0.222556i
$780$		0			0
$781$	10.3923			0.371866
$782$		0			0
$783$	13.8564			0.495188
$784$		0			0
$785$	4.89898	+	4.89898i	0.174852	+	0.174852i
$786$		0			0
$787$	16.3514	+	16.3514i	0.582864	+	0.582864i	0.935689	−	0.352825i	$-0.114779\pi$
$787$	16.3514	+	16.3514i	0.582864	+	0.582864i	−0.352825	+	0.935689i	$0.614779\pi$
$788$		0			0
$789$	21.8695	−	21.8695i	0.778576	−	0.778576i
$790$		0			0
$791$		−	54.2487i		−	1.92886i
$792$		0			0
$793$	2.07055	−	2.07055i	0.0735275	−	0.0735275i
$794$		0			0
$795$	122.354			4.33944
$796$		0			0
$797$			2.78461i			0.0986359i	0.998783	+	0.0493180i	$0.0157048\pi$
$797$			2.78461i			0.0986359i	−0.998783	+	0.0493180i	$0.984295\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		−	11.3205i		−	0.399990i
$802$		0			0
$803$	2.53590			0.0894899
$804$		0			0
$805$	8.48528	−	8.48528i	0.299067	−	0.299067i
$806$		0			0
$807$		−	75.0333i		−	2.64130i
$808$		0			0
$809$	−5.55532	+	5.55532i	−0.195315	+	0.195315i	−0.797988	−	0.602673i	$-0.794102\pi$
$809$	−5.55532	+	5.55532i	−0.195315	+	0.195315i	0.602673	+	0.797988i	$0.294102\pi$
$810$		0			0
$811$	−26.4267	−	26.4267i	−0.927969	−	0.927969i	0.0696059	−	0.997575i	$-0.477826\pi$
$811$	−26.4267	−	26.4267i	−0.927969	−	0.927969i	−0.997575	+	0.0696059i	$0.977826\pi$
$812$		0			0
$813$	−2.07055	−	2.07055i	−0.0726174	−	0.0726174i
$814$		0			0
$815$	−71.3205			−2.49825
$816$		0			0
$817$	12.2872			0.429874
$818$		0			0
$819$	47.1223	+	47.1223i	1.64659	+	1.64659i
$820$		0			0
$821$	31.8434	+	31.8434i	1.11134	+	1.11134i	0.992969	+	0.118372i	$0.0377675\pi$
$821$	31.8434	+	31.8434i	1.11134	+	1.11134i	0.118372	+	0.992969i	$0.462233\pi$
$822$		0			0
$823$	1.17398	−	1.17398i	0.0409223	−	0.0409223i	−0.686350	−	0.727272i	$-0.740788\pi$
$823$	1.17398	−	1.17398i	0.0409223	−	0.0409223i	0.727272	+	0.686350i	$0.240788\pi$
$824$		0			0
$825$		−	24.2487i		−	0.844232i
$826$		0			0
$827$	13.8004	−	13.8004i	0.479886	−	0.479886i	−0.425209	−	0.905095i	$-0.639800\pi$
$827$	13.8004	−	13.8004i	0.479886	−	0.479886i	0.905095	+	0.425209i	$0.139800\pi$
$828$		0			0
$829$	−39.8564			−1.38427			−0.692135	−	0.721768i	$-0.743330\pi$
$829$	−39.8564			−1.38427			−0.692135	+	0.721768i	$0.743330\pi$
$830$		0			0
$831$		−	17.4641i		−	0.605823i
$832$		0			0
$833$		0			0
$834$		0			0
$835$			19.6077i			0.678552i
$836$		0			0
$837$	−16.7846			−0.580161
$838$		0			0
$839$	−3.17020	+	3.17020i	−0.109447	+	0.109447i	−0.759710	−	0.650262i	$-0.774659\pi$
$839$	−3.17020	+	3.17020i	−0.109447	+	0.109447i	0.650262	+	0.759710i	$0.274659\pi$
$840$		0			0
$841$		−	17.0000i		−	0.586207i
$842$		0			0
$843$	−38.3596	+	38.3596i	−1.32118	+	1.32118i
$844$		0			0
$845$	−41.2896	−	41.2896i	−1.42041	−	1.42041i
$846$		0			0
$847$	−18.1445	−	18.1445i	−0.623454	−	0.623454i
$848$		0			0
$849$	56.2487			1.93045
$850$		0			0
$851$	−5.75129			−0.197152
$852$		0			0
$853$	−5.83272	−	5.83272i	−0.199709	−	0.199709i	0.600167	−	0.799875i	$-0.295101\pi$
$853$	−5.83272	−	5.83272i	−0.199709	−	0.199709i	−0.799875	+	0.600167i	$0.795101\pi$
$854$		0			0
$855$	16.0096	+	16.0096i	0.547517	+	0.547517i
$856$		0			0
$857$	11.7670	−	11.7670i	0.401952	−	0.401952i	−0.476968	−	0.878921i	$-0.658264\pi$
$857$	11.7670	−	11.7670i	0.401952	−	0.401952i	0.878921	+	0.476968i	$0.158264\pi$
$858$		0			0
$859$		−	27.3205i		−	0.932164i	−0.884742	−	0.466082i	$-0.845665\pi$
$859$		−	27.3205i		−	0.932164i	0.884742	−	0.466082i	$-0.154335\pi$
$860$		0			0
$861$	−31.6675	+	31.6675i	−1.07923	+	1.07923i
$862$		0			0
$863$	−10.1436			−0.345292			−0.172646	−	0.984984i	$-0.555232\pi$
$863$	−10.1436			−0.345292			−0.172646	+	0.984984i	$0.555232\pi$
$864$		0			0
$865$		−	53.5692i		−	1.82141i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	15.4641i		−	0.524584i
$870$		0			0
$871$	−81.5692			−2.76387
$872$		0			0
$873$	15.5563	−	15.5563i	0.526503	−	0.526503i
$874$		0			0
$875$			18.9282i			0.639890i
$876$		0			0
$877$	6.79367	−	6.79367i	0.229406	−	0.229406i	−0.583039	−	0.812444i	$-0.698136\pi$
$877$	6.79367	−	6.79367i	0.229406	−	0.229406i	0.812444	+	0.583039i	$0.198136\pi$
$878$		0			0
$879$	57.9555	+	57.9555i	1.95479	+	1.95479i
$880$		0			0
$881$	27.4249	+	27.4249i	0.923967	+	0.923967i	0.997307	−	0.0733400i	$-0.0233658\pi$
$881$	27.4249	+	27.4249i	0.923967	+	0.923967i	−0.0733400	+	0.997307i	$0.523366\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$		0			0
$887$	−8.06918	−	8.06918i	−0.270937	−	0.270937i	0.558541	−	0.829477i	$-0.311361\pi$
$887$	−8.06918	−	8.06918i	−0.270937	−	0.270937i	−0.829477	+	0.558541i	$0.811361\pi$
$888$		0			0
$889$	−0.757875	−	0.757875i	−0.0254183	−	0.0254183i
$890$		0			0
$891$	2.20925	−	2.20925i	0.0740128	−	0.0740128i
$892$		0			0
$893$			10.1436i			0.339442i
$894$		0			0
$895$	35.6055	−	35.6055i	1.19016	−	1.19016i
$896$		0			0
$897$	18.9282			0.631994
$898$		0			0
$899$		−	14.5359i		−	0.484799i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		−	62.6410i		−	2.08456i
$904$		0			0
$905$	15.7128			0.522312
$906$		0			0
$907$	−24.3562	+	24.3562i	−0.808734	+	0.808734i	−0.984442	−	0.175708i	$-0.943779\pi$
$907$	−24.3562	+	24.3562i	−0.808734	+	0.808734i	0.175708	+	0.984442i	$0.443779\pi$
$908$		0			0
$909$		−	11.3205i		−	0.375478i
$910$		0			0
$911$	−11.1750	+	11.1750i	−0.370245	+	0.370245i	−0.867566	−	0.497322i	$-0.834317\pi$
$911$	−11.1750	+	11.1750i	−0.370245	+	0.370245i	0.497322	+	0.867566i	$0.334317\pi$
$912$		0			0
$913$	2.27362	+	2.27362i	0.0752460	+	0.0752460i
$914$		0			0
$915$	−3.58630	−	3.58630i	−0.118559	−	0.118559i
$916$		0			0
$917$	−15.4641			−0.510670
$918$		0			0
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$		0			0
$921$	47.8802	+	47.8802i	1.57771	+	1.57771i
$922$		0			0
$923$	−31.6675	−	31.6675i	−1.04235	−	1.04235i
$924$		0			0
$925$	22.4516	−	22.4516i	0.738202	−	0.738202i
$926$		0			0
$927$		−	48.7846i		−	1.60230i
$928$		0			0
$929$	6.86800	−	6.86800i	0.225332	−	0.225332i	−0.585408	−	0.810739i	$-0.699065\pi$
$929$	6.86800	−	6.86800i	0.225332	−	0.225332i	0.810739	+	0.585408i	$0.199065\pi$
$930$		0			0
$931$	0.679492			0.0222694
$932$		0			0
$933$			8.53590i			0.279453i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	0.143594i		−	0.00469100i	−0.999997	−	0.00234550i	$-0.999253\pi$
$937$		−	0.143594i		−	0.00469100i	0.999997	−	0.00234550i	$-0.000746596\pi$
$938$		0			0
$939$	−57.1769			−1.86590
$940$		0			0
$941$	−29.2180	+	29.2180i	−0.952480	+	0.952480i	−0.998921	−	0.0464411i	$-0.985212\pi$
$941$	−29.2180	+	29.2180i	−0.952480	+	0.952480i	0.0464411	+	0.998921i	$0.485212\pi$
$942$		0			0
$943$			7.60770i			0.247741i
$944$		0			0
$945$	26.7685	−	26.7685i	0.870780	−	0.870780i
$946$		0			0
$947$	34.8377	+	34.8377i	1.13207	+	1.13207i	0.989832	+	0.142241i	$0.0454308\pi$
$947$	34.8377	+	34.8377i	1.13207	+	1.13207i	0.142241	+	0.989832i	$0.454569\pi$
$948$		0			0
$949$	−7.72741	−	7.72741i	−0.250842	−	0.250842i
$950$		0			0
$951$	23.3205			0.756219
$952$		0			0
$953$	6.24871			0.202416			0.101208	−	0.994865i	$-0.467729\pi$
$953$	6.24871			0.202416			0.101208	+	0.994865i	$0.467729\pi$
$954$		0			0
$955$	29.3939	+	29.3939i	0.951164	+	0.951164i
$956$		0			0
$957$	−8.48528	−	8.48528i	−0.274290	−	0.274290i
$958$		0			0
$959$	−4.89898	+	4.89898i	−0.158196	+	0.158196i
$960$		0			0
$961$		−	13.3923i		−	0.432010i
$962$		0			0
$963$	−33.8768	+	33.8768i	−1.09166	+	1.09166i
$964$		0			0
$965$	72.4974			2.33377
$966$		0			0
$967$		−	27.6077i		−	0.887804i	−0.896075	−	0.443902i	$-0.853594\pi$
$967$		−	27.6077i		−	0.887804i	0.896075	−	0.443902i	$-0.146406\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	20.1051i		−	0.645204i	−0.946535	−	0.322602i	$-0.895442\pi$
$971$		−	20.1051i		−	0.645204i	0.946535	−	0.322602i	$-0.104558\pi$
$972$		0			0
$973$	−40.2487			−1.29031
$974$		0			0
$975$	−73.8908	+	73.8908i	−2.36640	+	2.36640i
$976$		0			0
$977$		−	42.0000i		−	1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$		−	42.0000i		−	1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$		0			0
$979$	−2.27362	+	2.27362i	−0.0726653	+	0.0726653i
$980$		0			0
$981$	−45.4307	−	45.4307i	−1.45049	−	1.45049i
$982$		0			0
$983$	25.3915	+	25.3915i	0.809862	+	0.809862i	0.984613	−	0.174751i	$-0.0559119\pi$
$983$	25.3915	+	25.3915i	0.809862	+	0.809862i	−0.174751	+	0.984613i	$0.555912\pi$
$984$		0			0
$985$	−12.0000			−0.382352
$986$		0			0
$987$	51.7128			1.64604
$988$		0			0
$989$	−7.52433	−	7.52433i	−0.239260	−	0.239260i
$990$		0			0
$991$	−0.138701	−	0.138701i	−0.00440597	−	0.00440597i	0.704900	−	0.709306i	$-0.250992\pi$
$991$	−0.138701	−	0.138701i	−0.00440597	−	0.00440597i	−0.709306	+	0.704900i	$0.750992\pi$
$992$		0			0
$993$	37.3244	−	37.3244i	1.18445	−	1.18445i
$994$		0			0
$995$		−	14.5359i		−	0.460819i
$996$		0			0
$997$	−15.2789	+	15.2789i	−0.483889	+	0.483889i	−0.906371	−	0.422482i	$-0.861159\pi$
$997$	−15.2789	+	15.2789i	−0.483889	+	0.483889i	0.422482	+	0.906371i	$0.361159\pi$
$998$		0			0
$999$	−18.1436			−0.574038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.e.d.829.1		8
17.2	even	8		1156.2.a.a.1.1		2
17.3	odd	16		1156.2.h.f.1001.1		16
17.4	even	4	inner	1156.2.e.d.905.1		8
17.5	odd	16		1156.2.h.f.733.4		16
17.6	odd	16		1156.2.h.f.757.1		16
17.7	odd	16		1156.2.h.f.977.1		16
17.8	even	8		1156.2.b.c.577.4		4
17.9	even	8		1156.2.b.c.577.1		4
17.10	odd	16		1156.2.h.f.977.4		16
17.11	odd	16		1156.2.h.f.757.4		16
17.12	odd	16		1156.2.h.f.733.1		16
17.13	even	4	inner	1156.2.e.d.905.4		8
17.14	odd	16		1156.2.h.f.1001.4		16
17.15	even	8		68.2.a.a.1.2	✓	2
17.16	even	2	inner	1156.2.e.d.829.4		8
51.32	odd	8		612.2.a.e.1.2		2
68.15	odd	8		272.2.a.e.1.1		2
68.19	odd	8		4624.2.a.x.1.2		2
85.32	odd	8		1700.2.e.c.749.1		4
85.49	even	8		1700.2.a.d.1.1		2
85.83	odd	8		1700.2.e.c.749.4		4
119.83	odd	8		3332.2.a.h.1.1		2
136.83	odd	8		1088.2.a.t.1.2		2
136.117	even	8		1088.2.a.p.1.1		2
187.32	odd	8		8228.2.a.k.1.2		2
204.83	even	8		2448.2.a.y.1.2		2
340.219	odd	8		6800.2.a.bh.1.2		2
408.83	even	8		9792.2.a.cs.1.1		2
408.389	odd	8		9792.2.a.cr.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.a.a.1.2	✓	2	17.15	even	8
272.2.a.e.1.1		2	68.15	odd	8
612.2.a.e.1.2		2	51.32	odd	8
1088.2.a.p.1.1		2	136.117	even	8
1088.2.a.t.1.2		2	136.83	odd	8
1156.2.a.a.1.1		2	17.2	even	8
1156.2.b.c.577.1		4	17.9	even	8
1156.2.b.c.577.4		4	17.8	even	8
1156.2.e.d.829.1		8	1.1	even	1	trivial
1156.2.e.d.829.4		8	17.16	even	2	inner
1156.2.e.d.905.1		8	17.4	even	4	inner
1156.2.e.d.905.4		8	17.13	even	4	inner
1156.2.h.f.733.1		16	17.12	odd	16
1156.2.h.f.733.4		16	17.5	odd	16
1156.2.h.f.757.1		16	17.6	odd	16
1156.2.h.f.757.4		16	17.11	odd	16
1156.2.h.f.977.1		16	17.7	odd	16
1156.2.h.f.977.4		16	17.10	odd	16
1156.2.h.f.1001.1		16	17.3	odd	16
1156.2.h.f.1001.4		16	17.14	odd	16
1700.2.a.d.1.1		2	85.49	even	8
1700.2.e.c.749.1		4	85.32	odd	8
1700.2.e.c.749.4		4	85.83	odd	8
2448.2.a.y.1.2		2	204.83	even	8
3332.2.a.h.1.1		2	119.83	odd	8
4624.2.a.x.1.2		2	68.19	odd	8
6800.2.a.bh.1.2		2	340.219	odd	8
8228.2.a.k.1.2		2	187.32	odd	8
9792.2.a.cr.1.1		2	408.389	odd	8
9792.2.a.cs.1.1		2	408.83	even	8

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:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93185 - 1.93185i) q^{3} +(-2.44949 - 2.44949i) q^{5} +(-1.93185 + 1.93185i) q^{7} +4.46410i q^{9} +(0.896575 - 0.896575i) q^{11} -5.46410 q^{13} +9.46410i q^{15} +1.46410i q^{19} +7.46410 q^{21} +(0.896575 - 0.896575i) q^{23} +7.00000i q^{25} +(2.82843 - 2.82843i) q^{27} +(2.44949 + 2.44949i) q^{29} +(-2.96713 - 2.96713i) q^{31} -3.46410 q^{33} +9.46410 q^{35} +(-3.20736 - 3.20736i) q^{37} +(10.5558 + 10.5558i) q^{39} +(-4.24264 + 4.24264i) q^{41} -8.39230i q^{43} +(10.9348 - 10.9348i) q^{45} +6.92820 q^{47} -0.464102i q^{49} -12.9282i q^{53} -4.39230 q^{55} +(2.82843 - 2.82843i) q^{57} +2.53590i q^{59} +(-0.378937 + 0.378937i) q^{61} +(-8.62398 - 8.62398i) q^{63} +(13.3843 + 13.3843i) q^{65} +14.9282 q^{67} -3.46410 q^{69} +(5.79555 + 5.79555i) q^{71} +(1.41421 + 1.41421i) q^{73} +(13.5230 - 13.5230i) q^{75} +3.46410i q^{77} +(8.62398 - 8.62398i) q^{79} +2.46410 q^{81} +2.53590i q^{83} -9.46410i q^{87} -2.53590 q^{89} +(10.5558 - 10.5558i) q^{91} +11.4641i q^{93} +(3.58630 - 3.58630i) q^{95} +(-3.48477 - 3.48477i) q^{97} +(4.00240 + 4.00240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{13} + 32 q^{21} + 48 q^{35} + 48 q^{55} + 64 q^{67} - 8 q^{81} - 48 q^{89}+O(q^{100}) \) 8 * q - 16 * q^13 + 32 * q^21 + 48 * q^35 + 48 * q^55 + 64 * q^67 - 8 * q^81 - 48 * q^89

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