LMFDB - Embedded newform 1156.2.e.f.829.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1156,2,Mod(829,1156)] 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("1156.829"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [8,0,0,0,0,0,0,0,0,0,0,0,32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	1156.829
Dual form			1156.2.e.f.905.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30656 - 1.30656i) q^{3} +(-1.30656 - 1.30656i) q^{5} +(0.541196 - 0.541196i) q^{7} +0.414214i q^{9} +(2.38896 - 2.38896i) q^{11} +6.82843 q^{13} +3.41421i q^{15} +2.58579i q^{19} -1.41421 q^{21} +(5.00208 - 5.00208i) q^{23} -1.58579i q^{25} +(-3.37849 + 3.37849i) q^{27} +(2.83730 + 2.83730i) q^{29} +(-4.55374 - 4.55374i) q^{31} -6.24264 q^{33} -1.41421 q^{35} +(-4.68506 - 4.68506i) q^{37} +(-8.92177 - 8.92177i) q^{39} +(0.858221 - 0.858221i) q^{41} +4.24264i q^{43} +(0.541196 - 0.541196i) q^{45} -3.65685 q^{47} +6.41421i q^{49} -5.89949i q^{53} -6.24264 q^{55} +(3.37849 - 3.37849i) q^{57} -13.8995i q^{59} +(1.30656 - 1.30656i) q^{61} +(0.224171 + 0.224171i) q^{63} +(-8.92177 - 8.92177i) q^{65} -11.3137 q^{67} -13.0711 q^{69} +(0.858221 + 0.858221i) q^{71} +(6.08447 + 6.08447i) q^{73} +(-2.07193 + 2.07193i) q^{75} -2.58579i q^{77} +(-8.06355 + 8.06355i) q^{79} +10.0711 q^{81} -0.242641i q^{83} -7.41421i q^{87} +10.8284 q^{89} +(3.69552 - 3.69552i) q^{91} +11.8995i q^{93} +(3.37849 - 3.37849i) q^{95} +(0.672512 + 0.672512i) q^{97} +(0.989538 + 0.989538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{13} - 16 q^{33} + 16 q^{47} - 16 q^{55} - 48 q^{69} + 24 q^{81} + 64 q^{89}+O(q^{100}) $ 8 * q + 32 * q^13 - 16 * q^33 + 16 * q^47 - 16 * q^55 - 48 * q^69 + 24 * q^81 + 64 * 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
$3$	−1.30656	−	1.30656i	−0.754344	−	0.754344i	0.220942	−	0.975287i	$-0.429087\pi$
$3$	−1.30656	−	1.30656i	−0.754344	−	0.754344i	−0.975287	+	0.220942i	$0.929087\pi$
$4$		0			0
$5$	−1.30656	−	1.30656i	−0.584313	−	0.584313i	0.351773	−	0.936085i	$-0.385579\pi$
$5$	−1.30656	−	1.30656i	−0.584313	−	0.584313i	−0.936085	+	0.351773i	$0.885579\pi$
$6$		0			0
$7$	0.541196	−	0.541196i	0.204553	−	0.204553i	−0.597395	−	0.801947i	$-0.703797\pi$
$7$	0.541196	−	0.541196i	0.204553	−	0.204553i	0.801947	+	0.597395i	$0.203797\pi$
$8$		0			0
$9$			0.414214i			0.138071i
$10$		0			0
$11$	2.38896	−	2.38896i	0.720297	−	0.720297i	−0.248369	−	0.968666i	$-0.579894\pi$
$11$	2.38896	−	2.38896i	0.720297	−	0.720297i	0.968666	+	0.248369i	$0.0798944\pi$
$12$		0			0
$13$	6.82843			1.89386			0.946932	−	0.321433i	$-0.104164\pi$
$13$	6.82843			1.89386			0.946932	+	0.321433i	$0.104164\pi$
$14$		0			0
$15$			3.41421i			0.881546i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$			2.58579i			0.593220i	0.954999	+	0.296610i	$0.0958562\pi$
$19$			2.58579i			0.593220i	−0.954999	+	0.296610i	$0.904144\pi$
$20$		0			0
$21$	−1.41421			−0.308607
$22$		0			0
$23$	5.00208	−	5.00208i	1.04301	−	1.04301i	0.0439733	−	0.999033i	$-0.485998\pi$
$23$	5.00208	−	5.00208i	1.04301	−	1.04301i	0.999033	−	0.0439733i	$-0.0140017\pi$
$24$		0			0
$25$		−	1.58579i		−	0.317157i
$26$		0			0
$27$	−3.37849	+	3.37849i	−0.650191	+	0.650191i
$28$		0			0
$29$	2.83730	+	2.83730i	0.526873	+	0.526873i	0.919639	−	0.392766i	$-0.128482\pi$
$29$	2.83730	+	2.83730i	0.526873	+	0.526873i	−0.392766	+	0.919639i	$0.628482\pi$
$30$		0			0
$31$	−4.55374	−	4.55374i	−0.817876	−	0.817876i	0.167924	−	0.985800i	$-0.446294\pi$
$31$	−4.55374	−	4.55374i	−0.817876	−	0.817876i	−0.985800	+	0.167924i	$0.946294\pi$
$32$		0			0
$33$	−6.24264			−1.08670
$34$		0			0
$35$	−1.41421			−0.239046
$36$		0			0
$37$	−4.68506	−	4.68506i	−0.770218	−	0.770218i	0.207926	−	0.978145i	$-0.433329\pi$
$37$	−4.68506	−	4.68506i	−0.770218	−	0.770218i	−0.978145	+	0.207926i	$0.933329\pi$
$38$		0			0
$39$	−8.92177	−	8.92177i	−1.42863	−	1.42863i
$40$		0			0
$41$	0.858221	−	0.858221i	0.134032	−	0.134032i	−0.636908	−	0.770940i	$-0.719787\pi$
$41$	0.858221	−	0.858221i	0.134032	−	0.134032i	0.770940	+	0.636908i	$0.219787\pi$
$42$		0			0
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$	0.541196	−	0.541196i	0.0806768	−	0.0806768i
$46$		0			0
$47$	−3.65685			−0.533407			−0.266704	−	0.963779i	$-0.585934\pi$
$47$	−3.65685			−0.533407			−0.266704	+	0.963779i	$0.585934\pi$
$48$		0			0
$49$			6.41421i			0.916316i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	5.89949i		−	0.810358i	−0.914237	−	0.405179i	$-0.867209\pi$
$53$		−	5.89949i		−	0.810358i	0.914237	−	0.405179i	$-0.132791\pi$
$54$		0			0
$55$	−6.24264			−0.841757
$56$		0			0
$57$	3.37849	−	3.37849i	0.447492	−	0.447492i
$58$		0			0
$59$		−	13.8995i		−	1.80956i	−0.425879	−	0.904780i	$-0.640035\pi$
$59$		−	13.8995i		−	1.80956i	0.425879	−	0.904780i	$-0.359965\pi$
$60$		0			0
$61$	1.30656	−	1.30656i	0.167288	−	0.167288i	−0.618498	−	0.785786i	$-0.712259\pi$
$61$	1.30656	−	1.30656i	0.167288	−	0.167288i	0.785786	+	0.618498i	$0.212259\pi$
$62$		0			0
$63$	0.224171	+	0.224171i	0.0282429	+	0.0282429i
$64$		0			0
$65$	−8.92177	−	8.92177i	−1.10661	−	1.10661i
$66$		0			0
$67$	−11.3137			−1.38219			−0.691095	−	0.722764i	$-0.742871\pi$
$67$	−11.3137			−1.38219			−0.691095	+	0.722764i	$0.742871\pi$
$68$		0			0
$69$	−13.0711			−1.57357
$70$		0			0
$71$	0.858221	+	0.858221i	0.101852	+	0.101852i	0.756197	−	0.654344i	$-0.227055\pi$
$71$	0.858221	+	0.858221i	0.101852	+	0.101852i	−0.654344	+	0.756197i	$0.727055\pi$
$72$		0			0
$73$	6.08447	+	6.08447i	0.712134	+	0.712134i	0.966981	−	0.254848i	$-0.0820253\pi$
$73$	6.08447	+	6.08447i	0.712134	+	0.712134i	−0.254848	+	0.966981i	$0.582025\pi$
$74$		0			0
$75$	−2.07193	+	2.07193i	−0.239246	+	0.239246i
$76$		0			0
$77$		−	2.58579i		−	0.294678i
$78$		0			0
$79$	−8.06355	+	8.06355i	−0.907220	+	0.907220i	−0.996047	−	0.0888270i	$-0.971688\pi$
$79$	−8.06355	+	8.06355i	−0.907220	+	0.907220i	0.0888270	+	0.996047i	$0.471688\pi$
$80$		0			0
$81$	10.0711			1.11901
$82$		0			0
$83$		−	0.242641i		−	0.0266333i	−0.999911	−	0.0133166i	$-0.995761\pi$
$83$		−	0.242641i		−	0.0266333i	0.999911	−	0.0133166i	$-0.00423894\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	7.41421i		−	0.794887i
$88$		0			0
$89$	10.8284			1.14781			0.573905	−	0.818922i	$-0.305428\pi$
$89$	10.8284			1.14781			0.573905	+	0.818922i	$0.305428\pi$
$90$		0			0
$91$	3.69552	−	3.69552i	0.387396	−	0.387396i
$92$		0			0
$93$			11.8995i			1.23392i
$94$		0			0
$95$	3.37849	−	3.37849i	0.346626	−	0.346626i
$96$		0			0
$97$	0.672512	+	0.672512i	0.0682833	+	0.0682833i	0.740424	−	0.672140i	$-0.234625\pi$
$97$	0.672512	+	0.672512i	0.0682833	+	0.0682833i	−0.672140	+	0.740424i	$0.734625\pi$
$98$		0			0
$99$	0.989538	+	0.989538i	0.0994523	+	0.0994523i
$100$		0			0
$101$	−12.8284			−1.27648			−0.638238	−	0.769839i	$-0.720336\pi$
$101$	−12.8284			−1.27648			−0.638238	+	0.769839i	$0.720336\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	1.84776	+	1.84776i	0.180323	+	0.180323i
$106$		0			0
$107$	−2.70598	−	2.70598i	−0.261597	−	0.261597i	0.564106	−	0.825703i	$-0.309221\pi$
$107$	−2.70598	−	2.70598i	−0.261597	−	0.261597i	−0.825703	+	0.564106i	$0.809221\pi$
$108$		0			0
$109$	−3.47135	+	3.47135i	−0.332495	+	0.332495i	−0.853533	−	0.521038i	$-0.825545\pi$
$109$	−3.47135	+	3.47135i	−0.332495	+	0.332495i	0.521038	+	0.853533i	$0.325545\pi$
$110$		0			0
$111$			12.2426i			1.16202i
$112$		0			0
$113$	0.989538	−	0.989538i	0.0930879	−	0.0930879i	−0.659029	−	0.752117i	$-0.729033\pi$
$113$	0.989538	−	0.989538i	0.0930879	−	0.0930879i	0.752117	+	0.659029i	$0.229033\pi$
$114$		0			0
$115$	−13.0711			−1.21888
$116$		0			0
$117$			2.82843i			0.261488i
$118$		0			0
$119$		0			0
$120$		0			0
$121$		−	0.414214i		−	0.0376558i
$122$		0			0
$123$	−2.24264			−0.202212
$124$		0			0
$125$	−8.60474	+	8.60474i	−0.769632	+	0.769632i
$126$		0			0
$127$		−	0.242641i		−	0.0215309i	−0.999942	−	0.0107654i	$-0.996573\pi$
$127$		−	0.242641i		−	0.0215309i	0.999942	−	0.0107654i	$-0.00342681\pi$
$128$		0			0
$129$	5.54328	−	5.54328i	0.488058	−	0.488058i
$130$		0			0
$131$	−7.74652	−	7.74652i	−0.676817	−	0.676817i	0.282462	−	0.959279i	$-0.408849\pi$
$131$	−7.74652	−	7.74652i	−0.676817	−	0.676817i	−0.959279	+	0.282462i	$0.908849\pi$
$132$		0			0
$133$	1.39942	+	1.39942i	0.121345	+	0.121345i
$134$		0			0
$135$	8.82843			0.759830
$136$		0			0
$137$	12.1421			1.03737			0.518686	−	0.854965i	$-0.326421\pi$
$137$	12.1421			1.03737			0.518686	+	0.854965i	$0.326421\pi$
$138$		0			0
$139$	−12.3931	−	12.3931i	−1.05117	−	1.05117i	−0.998618	−	0.0525523i	$-0.983264\pi$
$139$	−12.3931	−	12.3931i	−1.05117	−	1.05117i	−0.0525523	−	0.998618i	$-0.516736\pi$
$140$		0			0
$141$	4.77791	+	4.77791i	0.402373	+	0.402373i
$142$		0			0
$143$	16.3128	−	16.3128i	1.36415	−	1.36415i
$144$		0			0
$145$		−	7.41421i		−	0.615717i
$146$		0			0
$147$	8.38057	−	8.38057i	0.691218	−	0.691218i
$148$		0			0
$149$	9.65685			0.791120			0.395560	−	0.918440i	$-0.370550\pi$
$149$	9.65685			0.791120			0.395560	+	0.918440i	$0.370550\pi$
$150$		0			0
$151$		−	14.5858i		−	1.18697i	−0.804843	−	0.593487i	$-0.797751\pi$
$151$		−	14.5858i		−	1.18697i	0.804843	−	0.593487i	$-0.202249\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			11.8995i			0.955790i
$156$		0			0
$157$	−2.34315			−0.187003			−0.0935017	−	0.995619i	$-0.529806\pi$
$157$	−2.34315			−0.187003			−0.0935017	+	0.995619i	$0.529806\pi$
$158$		0			0
$159$	−7.70806	+	7.70806i	−0.611289	+	0.611289i
$160$		0			0
$161$		−	5.41421i		−	0.426700i
$162$		0			0
$163$	−5.13340	+	5.13340i	−0.402079	+	0.402079i	−0.878965	−	0.476886i	$-0.841765\pi$
$163$	−5.13340	+	5.13340i	−0.402079	+	0.402079i	0.476886	+	0.878965i	$0.341765\pi$
$164$		0			0
$165$	8.15640	+	8.15640i	0.634975	+	0.634975i
$166$		0			0
$167$	8.69760	+	8.69760i	0.673040	+	0.673040i	0.958416	−	0.285375i	$-0.0921183\pi$
$167$	8.69760	+	8.69760i	0.673040	+	0.673040i	−0.285375	+	0.958416i	$0.592118\pi$
$168$		0			0
$169$	33.6274			2.58672
$170$		0			0
$171$	−1.07107			−0.0819066
$172$		0			0
$173$	17.7507	+	17.7507i	1.34956	+	1.34956i	0.886138	+	0.463422i	$0.153379\pi$
$173$	17.7507	+	17.7507i	1.34956	+	1.34956i	0.463422	+	0.886138i	$0.346621\pi$
$174$		0			0
$175$	−0.858221	−	0.858221i	−0.0648754	−	0.0648754i
$176$		0			0
$177$	−18.1606	+	18.1606i	−1.36503	+	1.36503i
$178$		0			0
$179$		−	18.3848i		−	1.37414i	−0.726590	−	0.687071i	$-0.758896\pi$
$179$		−	18.3848i		−	1.37414i	0.726590	−	0.687071i	$-0.241104\pi$
$180$		0			0
$181$	−2.70598	+	2.70598i	−0.201134	+	0.201134i	−0.800486	−	0.599352i	$-0.795425\pi$
$181$	−2.70598	+	2.70598i	−0.201134	+	0.201134i	0.599352	+	0.800486i	$0.295425\pi$
$182$		0			0
$183$	−3.41421			−0.252386
$184$		0			0
$185$			12.2426i			0.900097i
$186$		0			0
$187$		0			0
$188$		0			0
$189$			3.65685i			0.265997i
$190$		0			0
$191$	−0.343146			−0.0248292			−0.0124146	−	0.999923i	$-0.503952\pi$
$191$	−0.343146			−0.0248292			−0.0124146	+	0.999923i	$0.503952\pi$
$192$		0			0
$193$	10.9937	−	10.9937i	0.791344	−	0.791344i	−0.190369	−	0.981713i	$-0.560968\pi$
$193$	10.9937	−	10.9937i	0.791344	−	0.791344i	0.981713	+	0.190369i	$0.0609684\pi$
$194$		0			0
$195$			23.3137i			1.66953i
$196$		0			0
$197$	−8.88331	+	8.88331i	−0.632910	+	0.632910i	−0.948797	−	0.315887i	$-0.897698\pi$
$197$	−8.88331	+	8.88331i	−0.632910	+	0.632910i	0.315887	+	0.948797i	$0.397698\pi$
$198$		0			0
$199$	1.17525	+	1.17525i	0.0833110	+	0.0833110i	0.747534	−	0.664223i	$-0.231238\pi$
$199$	1.17525	+	1.17525i	0.0833110	+	0.0833110i	−0.664223	+	0.747534i	$0.731238\pi$
$200$		0			0
$201$	14.7821	+	14.7821i	1.04265	+	1.04265i
$202$		0			0
$203$	3.07107			0.215547
$204$		0			0
$205$	−2.24264			−0.156633
$206$		0			0
$207$	2.07193	+	2.07193i	0.144009	+	0.144009i
$208$		0			0
$209$	6.17733	+	6.17733i	0.427295	+	0.427295i
$210$		0			0
$211$	1.43788	−	1.43788i	0.0989877	−	0.0989877i	−0.655879	−	0.754866i	$-0.727702\pi$
$211$	1.43788	−	1.43788i	0.0989877	−	0.0989877i	0.754866	+	0.655879i	$0.227702\pi$
$212$		0			0
$213$		−	2.24264i		−	0.153663i
$214$		0			0
$215$	5.54328	−	5.54328i	0.378048	−	0.378048i
$216$		0			0
$217$	−4.92893			−0.334598
$218$		0			0
$219$		−	15.8995i		−	1.07439i
$220$		0			0
$221$		0			0
$222$		0			0
$223$			17.2132i			1.15268i	0.817210	+	0.576341i	$0.195520\pi$
$223$			17.2132i			1.15268i	−0.817210	+	0.576341i	$0.804480\pi$
$224$		0			0
$225$	0.656854			0.0437903
$226$		0			0
$227$	−13.7381	+	13.7381i	−0.911833	+	0.911833i	−0.996416	−	0.0845839i	$-0.973044\pi$
$227$	−13.7381	+	13.7381i	−0.911833	+	0.911833i	0.0845839	+	0.996416i	$0.473044\pi$
$228$		0			0
$229$		−	3.75736i		−	0.248293i	−0.992264	−	0.124147i	$-0.960381\pi$
$229$		−	3.75736i		−	0.248293i	0.992264	−	0.124147i	$-0.0396193\pi$
$230$		0			0
$231$	−3.37849	+	3.37849i	−0.222289	+	0.222289i
$232$		0			0
$233$	−6.34711	−	6.34711i	−0.415813	−	0.415813i	0.467945	−	0.883758i	$-0.344995\pi$
$233$	−6.34711	−	6.34711i	−0.415813	−	0.415813i	−0.883758	+	0.467945i	$0.844995\pi$
$234$		0			0
$235$	4.77791	+	4.77791i	0.311677	+	0.311677i
$236$		0			0
$237$	21.0711			1.36871
$238$		0			0
$239$	22.6274			1.46365			0.731823	−	0.681495i	$-0.238670\pi$
$239$	22.6274			1.46365			0.731823	+	0.681495i	$0.238670\pi$
$240$		0			0
$241$	14.0552	+	14.0552i	0.905373	+	0.905373i	0.995894	−	0.0905216i	$-0.0288534\pi$
$241$	14.0552	+	14.0552i	0.905373	+	0.905373i	−0.0905216	+	0.995894i	$0.528853\pi$
$242$		0			0
$243$	−3.02301	−	3.02301i	−0.193926	−	0.193926i
$244$		0			0
$245$	8.38057	−	8.38057i	0.535415	−	0.535415i
$246$		0			0
$247$			17.6569i			1.12348i
$248$		0			0
$249$	−0.317025	+	0.317025i	−0.0200907	+	0.0200907i
$250$		0			0
$251$	−22.9706			−1.44989			−0.724945	−	0.688807i	$-0.758135\pi$
$251$	−22.9706			−1.44989			−0.724945	+	0.688807i	$0.758135\pi$
$252$		0			0
$253$		−	23.8995i		−	1.50255i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	3.75736i		−	0.234378i	−0.993110	−	0.117189i	$-0.962612\pi$
$257$		−	3.75736i		−	0.234378i	0.993110	−	0.117189i	$-0.0373883\pi$
$258$		0			0
$259$	−5.07107			−0.315101
$260$		0			0
$261$	−1.17525	+	1.17525i	−0.0727459	+	0.0727459i
$262$		0			0
$263$		−	13.2132i		−	0.814761i	−0.913259	−	0.407381i	$-0.866442\pi$
$263$		−	13.2132i		−	0.814761i	0.913259	−	0.407381i	$-0.133558\pi$
$264$		0			0
$265$	−7.70806	+	7.70806i	−0.473502	+	0.473502i
$266$		0			0
$267$	−14.1480	−	14.1480i	−0.865845	−	0.865845i
$268$		0			0
$269$	5.95316	+	5.95316i	0.362970	+	0.362970i	0.864905	−	0.501935i	$-0.167378\pi$
$269$	5.95316	+	5.95316i	0.362970	+	0.362970i	−0.501935	+	0.864905i	$0.667378\pi$
$270$		0			0
$271$	11.3137			0.687259			0.343629	−	0.939105i	$-0.388344\pi$
$271$	11.3137			0.687259			0.343629	+	0.939105i	$0.388344\pi$
$272$		0			0
$273$	−9.65685			−0.584459
$274$		0			0
$275$	−3.78837	−	3.78837i	−0.228447	−	0.228447i
$276$		0			0
$277$	10.6767	+	10.6767i	0.641499	+	0.641499i	0.950924	−	0.309425i	$-0.100136\pi$
$277$	10.6767	+	10.6767i	0.641499	+	0.641499i	−0.309425	+	0.950924i	$0.600136\pi$
$278$		0			0
$279$	1.88622	−	1.88622i	0.112925	−	0.112925i
$280$		0			0
$281$		−	15.0711i		−	0.899065i	−0.893264	−	0.449532i	$-0.851591\pi$
$281$		−	15.0711i		−	0.899065i	0.893264	−	0.449532i	$-0.148409\pi$
$282$		0			0
$283$	−5.00208	+	5.00208i	−0.297343	+	0.297343i	−0.839972	−	0.542629i	$-0.817429\pi$
$283$	−5.00208	+	5.00208i	−0.297343	+	0.297343i	0.542629	+	0.839972i	$0.317429\pi$
$284$		0			0
$285$	−8.82843			−0.522951
$286$		0			0
$287$		−	0.928932i		−	0.0548331i
$288$		0			0
$289$		0			0
$290$		0			0
$291$		−	1.75736i		−	0.103018i
$292$		0			0
$293$	8.00000			0.467365			0.233682	−	0.972313i	$-0.424922\pi$
$293$	8.00000			0.467365			0.233682	+	0.972313i	$0.424922\pi$
$294$		0			0
$295$	−18.1606	+	18.1606i	−1.05735	+	1.05735i
$296$		0			0
$297$			16.1421i			0.936662i
$298$		0			0
$299$	34.1563	−	34.1563i	1.97531	−	1.97531i
$300$		0			0
$301$	2.29610	+	2.29610i	0.132345	+	0.132345i
$302$		0			0
$303$	16.7611	+	16.7611i	0.962903	+	0.962903i
$304$		0			0
$305$	−3.41421			−0.195497
$306$		0			0
$307$	6.34315			0.362022			0.181011	−	0.983481i	$-0.442063\pi$
$307$	6.34315			0.362022			0.181011	+	0.983481i	$0.442063\pi$
$308$		0			0
$309$	−5.22625	−	5.22625i	−0.297311	−	0.297311i
$310$		0			0
$311$	9.01462	+	9.01462i	0.511172	+	0.511172i	0.914886	−	0.403713i	$-0.132281\pi$
$311$	9.01462	+	9.01462i	0.511172	+	0.511172i	−0.403713	+	0.914886i	$0.632281\pi$
$312$		0			0
$313$	−16.0886	+	16.0886i	−0.909383	+	0.909383i	−0.996222	−	0.0868389i	$-0.972323\pi$
$313$	−16.0886	+	16.0886i	−0.909383	+	0.909383i	0.0868389	+	0.996222i	$0.472323\pi$
$314$		0			0
$315$		−	0.585786i		−	0.0330053i
$316$		0			0
$317$	−0.278564	+	0.278564i	−0.0156457	+	0.0156457i	−0.714886	−	0.699241i	$-0.753522\pi$
$317$	−0.278564	+	0.278564i	−0.0156457	+	0.0156457i	0.699241	+	0.714886i	$0.253522\pi$
$318$		0			0
$319$	13.5563			0.759010
$320$		0			0
$321$			7.07107i			0.394669i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		−	10.8284i		−	0.600653i
$326$		0			0
$327$	9.07107			0.501631
$328$		0			0
$329$	−1.97908	+	1.97908i	−0.109110	+	0.109110i
$330$		0			0
$331$			28.7279i			1.57903i	0.613732	+	0.789515i	$0.289668\pi$
$331$			28.7279i			1.57903i	−0.613732	+	0.789515i	$0.710332\pi$
$332$		0			0
$333$	1.94061	−	1.94061i	0.106345	−	0.106345i
$334$		0			0
$335$	14.7821	+	14.7821i	0.807631	+	0.807631i
$336$		0			0
$337$	−18.3847	−	18.3847i	−1.00148	−	1.00148i	−0.999999	−	0.00148149i	$-0.999528\pi$
$337$	−18.3847	−	18.3847i	−1.00148	−	1.00148i	−0.00148149	−	0.999999i	$-0.500472\pi$
$338$		0			0
$339$	−2.58579			−0.140441
$340$		0			0
$341$	−21.7574			−1.17823
$342$		0			0
$343$	7.25972	+	7.25972i	0.391988	+	0.391988i
$344$		0			0
$345$	17.0782	+	17.0782i	0.919458	+	0.919458i
$346$		0			0
$347$	5.50482	−	5.50482i	0.295514	−	0.295514i	−0.543740	−	0.839254i	$-0.682992\pi$
$347$	5.50482	−	5.50482i	0.295514	−	0.295514i	0.839254	+	0.543740i	$0.182992\pi$
$348$		0			0
$349$		−	28.0416i		−	1.50103i	−0.660851	−	0.750517i	$-0.729805\pi$
$349$		−	28.0416i		−	1.50103i	0.660851	−	0.750517i	$-0.270195\pi$
$350$		0			0
$351$	−23.0698	+	23.0698i	−1.23137	+	1.23137i
$352$		0			0
$353$	−15.3137			−0.815066			−0.407533	−	0.913190i	$-0.633611\pi$
$353$	−15.3137			−0.815066			−0.407533	+	0.913190i	$0.633611\pi$
$354$		0			0
$355$		−	2.24264i		−	0.119027i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	30.3848i		−	1.60365i	−0.597561	−	0.801824i	$-0.703863\pi$
$359$		−	30.3848i		−	1.60365i	0.597561	−	0.801824i	$-0.296137\pi$
$360$		0			0
$361$	12.3137			0.648090
$362$		0			0
$363$	−0.541196	+	0.541196i	−0.0284054	+	0.0284054i
$364$		0			0
$365$		−	15.8995i		−	0.832218i
$366$		0			0
$367$	−2.70598	+	2.70598i	−0.141251	+	0.141251i	−0.774196	−	0.632945i	$-0.781846\pi$
$367$	−2.70598	+	2.70598i	−0.141251	+	0.141251i	0.632945	+	0.774196i	$0.281846\pi$
$368$		0			0
$369$	0.355487	+	0.355487i	0.0185059	+	0.0185059i
$370$		0			0
$371$	−3.19278	−	3.19278i	−0.165761	−	0.165761i
$372$		0			0
$373$	−18.4853			−0.957132			−0.478566	−	0.878052i	$-0.658843\pi$
$373$	−18.4853			−0.957132			−0.478566	+	0.878052i	$0.658843\pi$
$374$		0			0
$375$	22.4853			1.16113
$376$		0			0
$377$	19.3743	+	19.3743i	0.997826	+	0.997826i
$378$		0			0
$379$	7.74652	+	7.74652i	0.397912	+	0.397912i	0.877496	−	0.479584i	$-0.159212\pi$
$379$	7.74652	+	7.74652i	0.397912	+	0.397912i	−0.479584	+	0.877496i	$0.659212\pi$
$380$		0			0
$381$	−0.317025	+	0.317025i	−0.0162417	+	0.0162417i
$382$		0			0
$383$			25.8995i			1.32340i	0.749768	+	0.661701i	$0.230165\pi$
$383$			25.8995i			1.32340i	−0.749768	+	0.661701i	$0.769835\pi$
$384$		0			0
$385$	−3.37849	+	3.37849i	−0.172184	+	0.172184i
$386$		0			0
$387$	−1.75736			−0.0893316
$388$		0			0
$389$			2.10051i			0.106500i	0.998581	+	0.0532499i	$0.0169580\pi$
$389$			2.10051i			0.106500i	−0.998581	+	0.0532499i	$0.983042\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$			20.2426i			1.02111i
$394$		0			0
$395$	21.0711			1.06020
$396$		0			0
$397$	−13.3442	+	13.3442i	−0.669726	+	0.669726i	−0.957652	−	0.287927i	$-0.907034\pi$
$397$	−13.3442	+	13.3442i	−0.669726	+	0.669726i	0.287927	+	0.957652i	$0.407034\pi$
$398$		0			0
$399$		−	3.65685i		−	0.183072i
$400$		0			0
$401$	6.53281	−	6.53281i	0.326233	−	0.326233i	−0.524919	−	0.851152i	$-0.675904\pi$
$401$	6.53281	−	6.53281i	0.326233	−	0.326233i	0.851152	+	0.524919i	$0.175904\pi$
$402$		0			0
$403$	−31.0949	−	31.0949i	−1.54895	−	1.54895i
$404$		0			0
$405$	−13.1585	−	13.1585i	−0.653850	−	0.653850i
$406$		0			0
$407$	−22.3848			−1.10957
$408$		0			0
$409$	−11.6569			−0.576394			−0.288197	−	0.957571i	$-0.593056\pi$
$409$	−11.6569			−0.576394			−0.288197	+	0.957571i	$0.593056\pi$
$410$		0			0
$411$	−15.8645	−	15.8645i	−0.782536	−	0.782536i
$412$		0			0
$413$	−7.52235	−	7.52235i	−0.370151	−	0.370151i
$414$		0			0
$415$	−0.317025	+	0.317025i	−0.0155622	+	0.0155622i
$416$		0			0
$417$			32.3848i			1.58589i
$418$		0			0
$419$	25.1961	−	25.1961i	1.23091	−	1.23091i	0.267296	−	0.963614i	$-0.413870\pi$
$419$	25.1961	−	25.1961i	1.23091	−	1.23091i	0.963614	−	0.267296i	$-0.0861303\pi$
$420$		0			0
$421$	1.17157			0.0570990			0.0285495	−	0.999592i	$-0.490911\pi$
$421$	1.17157			0.0570990			0.0285495	+	0.999592i	$0.490911\pi$
$422$		0			0
$423$		−	1.51472i		−	0.0736481i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	1.41421i		−	0.0684386i
$428$		0			0
$429$	−42.6274			−2.05807
$430$		0			0
$431$	14.5579	−	14.5579i	0.701229	−	0.701229i	−0.263445	−	0.964674i	$-0.584859\pi$
$431$	14.5579	−	14.5579i	0.701229	−	0.701229i	0.964674	+	0.263445i	$0.0848587\pi$
$432$		0			0
$433$			8.24264i			0.396116i	0.980190	+	0.198058i	$0.0634634\pi$
$433$			8.24264i			0.396116i	−0.980190	+	0.198058i	$0.936537\pi$
$434$		0			0
$435$	−9.68714	+	9.68714i	−0.464463	+	0.464463i
$436$		0			0
$437$	12.9343	+	12.9343i	0.618732	+	0.618732i
$438$		0			0
$439$	10.4910	+	10.4910i	0.500706	+	0.500706i	0.911657	−	0.410951i	$-0.134803\pi$
$439$	10.4910	+	10.4910i	0.500706	+	0.500706i	−0.410951	+	0.911657i	$0.634803\pi$
$440$		0			0
$441$	−2.65685			−0.126517
$442$		0			0
$443$	−21.6569			−1.02895			−0.514474	−	0.857506i	$-0.672013\pi$
$443$	−21.6569			−1.02895			−0.514474	+	0.857506i	$0.672013\pi$
$444$		0			0
$445$	−14.1480	−	14.1480i	−0.670681	−	0.670681i
$446$		0			0
$447$	−12.6173	−	12.6173i	−0.596777	−	0.596777i
$448$		0			0
$449$	15.0062	−	15.0062i	0.708188	−	0.708188i	−0.257966	−	0.966154i	$-0.583052\pi$
$449$	15.0062	−	15.0062i	0.708188	−	0.708188i	0.966154	+	0.257966i	$0.0830521\pi$
$450$		0			0
$451$		−	4.10051i		−	0.193085i
$452$		0			0
$453$	−19.0572	+	19.0572i	−0.895388	+	0.895388i
$454$		0			0
$455$	−9.65685			−0.452720
$456$		0			0
$457$		−	4.24264i		−	0.198462i	−0.995064	−	0.0992312i	$-0.968362\pi$
$457$		−	4.24264i		−	0.198462i	0.995064	−	0.0992312i	$-0.0316383\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			7.75736i			0.361296i	0.983548	+	0.180648i	$0.0578195\pi$
$461$			7.75736i			0.361296i	−0.983548	+	0.180648i	$0.942180\pi$
$462$		0			0
$463$	−7.65685			−0.355844			−0.177922	−	0.984045i	$-0.556938\pi$
$463$	−7.65685			−0.355844			−0.177922	+	0.984045i	$0.556938\pi$
$464$		0			0
$465$	15.5474	−	15.5474i	0.720995	−	0.720995i
$466$		0			0
$467$		−	28.2426i		−	1.30691i	−0.756964	−	0.653457i	$-0.773318\pi$
$467$		−	28.2426i		−	1.30691i	0.756964	−	0.653457i	$-0.226682\pi$
$468$		0			0
$469$	−6.12293	+	6.12293i	−0.282731	+	0.282731i
$470$		0			0
$471$	3.06147	+	3.06147i	0.141065	+	0.141065i
$472$		0			0
$473$	10.1355	+	10.1355i	0.466030	+	0.466030i
$474$		0			0
$475$	4.10051			0.188144
$476$		0			0
$477$	2.44365			0.111887
$478$		0			0
$479$	5.82184	+	5.82184i	0.266007	+	0.266007i	0.827489	−	0.561482i	$-0.189769\pi$
$479$	5.82184	+	5.82184i	0.266007	+	0.266007i	−0.561482	+	0.827489i	$0.689769\pi$
$480$		0			0
$481$	−31.9916	−	31.9916i	−1.45869	−	1.45869i
$482$		0			0
$483$	−7.07401	+	7.07401i	−0.321879	+	0.321879i
$484$		0			0
$485$		−	1.75736i		−	0.0797976i
$486$		0			0
$487$	−2.57466	+	2.57466i	−0.116669	+	0.116669i	−0.763031	−	0.646362i	$-0.776290\pi$
$487$	−2.57466	+	2.57466i	−0.116669	+	0.116669i	0.646362	+	0.763031i	$0.276290\pi$
$488$		0			0
$489$	13.4142			0.606612
$490$		0			0
$491$			23.7574i			1.07215i	0.844169	+	0.536077i	$0.180094\pi$
$491$			23.7574i			1.07215i	−0.844169	+	0.536077i	$0.819906\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		−	2.58579i		−	0.116222i
$496$		0			0
$497$	0.928932			0.0416683
$498$		0			0
$499$	26.5411	−	26.5411i	1.18814	−	1.18814i	0.210565	−	0.977580i	$-0.432470\pi$
$499$	26.5411	−	26.5411i	1.18814	−	1.18814i	0.977580	−	0.210565i	$-0.0675302\pi$
$500$		0			0
$501$		−	22.7279i		−	1.01541i
$502$		0			0
$503$	5.58174	−	5.58174i	0.248877	−	0.248877i	−0.571632	−	0.820510i	$-0.693690\pi$
$503$	5.58174	−	5.58174i	0.248877	−	0.248877i	0.820510	+	0.571632i	$0.193690\pi$
$504$		0			0
$505$	16.7611	+	16.7611i	0.745861	+	0.745861i
$506$		0			0
$507$	−43.9363	−	43.9363i	−1.95128	−	1.95128i
$508$		0			0
$509$	−6.68629			−0.296365			−0.148182	−	0.988960i	$-0.547342\pi$
$509$	−6.68629			−0.296365			−0.148182	+	0.988960i	$0.547342\pi$
$510$		0			0
$511$	6.58579			0.291338
$512$		0			0
$513$	−8.73606	−	8.73606i	−0.385707	−	0.385707i
$514$		0			0
$515$	−5.22625	−	5.22625i	−0.230296	−	0.230296i
$516$		0			0
$517$	−8.73606	+	8.73606i	−0.384212	+	0.384212i
$518$		0			0
$519$		−	46.3848i		−	2.03607i
$520$		0			0
$521$	19.4671	−	19.4671i	0.852870	−	0.852870i	−0.137615	−	0.990486i	$-0.543944\pi$
$521$	19.4671	−	19.4671i	0.852870	−	0.852870i	0.990486	+	0.137615i	$0.0439438\pi$
$522$		0			0
$523$	34.0000			1.48672			0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000			1.48672			0.743358	+	0.668894i	$0.233232\pi$
$524$		0			0
$525$			2.24264i			0.0978769i
$526$		0			0
$527$		0			0
$528$		0			0
$529$		−	27.0416i		−	1.17572i
$530$		0			0
$531$	5.75736			0.249848
$532$		0			0
$533$	5.86030	−	5.86030i	0.253838	−	0.253838i
$534$		0			0
$535$			7.07107i			0.305709i
$536$		0			0
$537$	−24.0209	+	24.0209i	−1.03658	+	1.03658i
$538$		0			0
$539$	15.3233	+	15.3233i	0.660020	+	0.660020i
$540$		0			0
$541$	5.58174	+	5.58174i	0.239978	+	0.239978i	0.816841	−	0.576863i	$-0.195723\pi$
$541$	5.58174	+	5.58174i	0.239978	+	0.239978i	−0.576863	+	0.816841i	$0.695723\pi$
$542$		0			0
$543$	7.07107			0.303449
$544$		0			0
$545$	9.07107			0.388562
$546$		0			0
$547$	−17.3567	−	17.3567i	−0.742120	−	0.742120i	0.230865	−	0.972986i	$-0.425844\pi$
$547$	−17.3567	−	17.3567i	−0.742120	−	0.742120i	−0.972986	+	0.230865i	$0.925844\pi$
$548$		0			0
$549$	0.541196	+	0.541196i	0.0230977	+	0.0230977i
$550$		0			0
$551$	−7.33664	+	7.33664i	−0.312552	+	0.312552i
$552$		0			0
$553$			8.72792i			0.371149i
$554$		0			0
$555$	15.9958	−	15.9958i	0.678983	−	0.678983i
$556$		0			0
$557$	22.8284			0.967272			0.483636	−	0.875269i	$-0.339316\pi$
$557$	22.8284			0.967272			0.483636	+	0.875269i	$0.339316\pi$
$558$		0			0
$559$			28.9706i			1.22532i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			38.5858i			1.62620i	0.582126	+	0.813099i	$0.302221\pi$
$563$			38.5858i			1.62620i	−0.582126	+	0.813099i	$0.697779\pi$
$564$		0			0
$565$	−2.58579			−0.108785
$566$		0			0
$567$	5.45042	−	5.45042i	0.228896	−	0.228896i
$568$		0			0
$569$		−	27.5563i		−	1.15522i	−0.816312	−	0.577611i	$-0.803985\pi$
$569$		−	27.5563i		−	1.15522i	0.816312	−	0.577611i	$-0.196015\pi$
$570$		0			0
$571$	−18.0133	+	18.0133i	−0.753834	+	0.753834i	−0.975192	−	0.221359i	$-0.928951\pi$
$571$	−18.0133	+	18.0133i	−0.753834	+	0.753834i	0.221359	+	0.975192i	$0.428951\pi$
$572$		0			0
$573$	0.448342	+	0.448342i	0.0187297	+	0.0187297i
$574$		0			0
$575$	−7.93223	−	7.93223i	−0.330797	−	0.330797i
$576$		0			0
$577$	−1.79899			−0.0748929			−0.0374465	−	0.999299i	$-0.511922\pi$
$577$	−1.79899			−0.0748929			−0.0374465	+	0.999299i	$0.511922\pi$
$578$		0			0
$579$	−28.7279			−1.19389
$580$		0			0
$581$	−0.131316	−	0.131316i	−0.00544791	−	0.00544791i
$582$		0			0
$583$	−14.0936	−	14.0936i	−0.583698	−	0.583698i
$584$		0			0
$585$	3.69552	−	3.69552i	0.152791	−	0.152791i
$586$		0			0
$587$			29.2132i			1.20576i	0.797833	+	0.602879i	$0.205980\pi$
$587$			29.2132i			1.20576i	−0.797833	+	0.602879i	$0.794020\pi$
$588$		0			0
$589$	11.7750	−	11.7750i	0.485180	−	0.485180i
$590$		0			0
$591$	23.2132			0.954864
$592$		0			0
$593$			33.2132i			1.36390i	0.731397	+	0.681951i	$0.238868\pi$
$593$			33.2132i			1.36390i	−0.731397	+	0.681951i	$0.761132\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	3.07107i		−	0.125690i
$598$		0			0
$599$	−37.3137			−1.52460			−0.762298	−	0.647226i	$-0.775929\pi$
$599$	−37.3137			−1.52460			−0.762298	+	0.647226i	$0.775929\pi$
$600$		0			0
$601$	3.60266	−	3.60266i	0.146956	−	0.146956i	−0.629801	−	0.776757i	$-0.716864\pi$
$601$	3.60266	−	3.60266i	0.146956	−	0.146956i	0.776757	+	0.629801i	$0.216864\pi$
$602$		0			0
$603$		−	4.68629i		−	0.190841i
$604$		0			0
$605$	−0.541196	+	0.541196i	−0.0220028	+	0.0220028i
$606$		0			0
$607$	11.2563	+	11.2563i	0.456880	+	0.456880i	0.897630	−	0.440750i	$-0.145287\pi$
$607$	11.2563	+	11.2563i	0.456880	+	0.456880i	−0.440750	+	0.897630i	$0.645287\pi$
$608$		0			0
$609$	−4.01254	−	4.01254i	−0.162596	−	0.162596i
$610$		0			0
$611$	−24.9706			−1.01020
$612$		0			0
$613$	0.343146			0.0138595			0.00692976	−	0.999976i	$-0.497794\pi$
$613$	0.343146			0.0138595			0.00692976	+	0.999976i	$0.497794\pi$
$614$		0			0
$615$	2.93015	+	2.93015i	0.118155	+	0.118155i
$616$		0			0
$617$	−24.1137	−	24.1137i	−0.970782	−	0.970782i	0.0288032	−	0.999585i	$-0.490830\pi$
$617$	−24.1137	−	24.1137i	−0.970782	−	0.970782i	−0.999585	+	0.0288032i	$0.990830\pi$
$618$		0			0
$619$	9.46297	−	9.46297i	0.380349	−	0.380349i	−0.490879	−	0.871228i	$-0.663324\pi$
$619$	9.46297	−	9.46297i	0.380349	−	0.380349i	0.871228	+	0.490879i	$0.163324\pi$
$620$		0			0
$621$			33.7990i			1.35631i
$622$		0			0
$623$	5.86030	−	5.86030i	0.234788	−	0.234788i
$624$		0			0
$625$	14.5563			0.582254
$626$		0			0
$627$		−	16.1421i		−	0.644655i
$628$		0			0
$629$		0			0
$630$		0			0
$631$			14.5858i			0.580651i	0.956928	+	0.290325i	$0.0937636\pi$
$631$			14.5858i			0.580651i	−0.956928	+	0.290325i	$0.906236\pi$
$632$		0			0
$633$	−3.75736			−0.149342
$634$		0			0
$635$	−0.317025	+	0.317025i	−0.0125808	+	0.0125808i
$636$		0			0
$637$			43.7990i			1.73538i
$638$		0			0
$639$	−0.355487	+	0.355487i	−0.0140628	+	0.0140628i
$640$		0			0
$641$	−32.8498	−	32.8498i	−1.29749	−	1.29749i	−0.930046	−	0.367442i	$-0.880234\pi$
$641$	−32.8498	−	32.8498i	−1.29749	−	1.29749i	−0.367442	−	0.930046i	$-0.619766\pi$
$642$		0			0
$643$	−3.91969	−	3.91969i	−0.154577	−	0.154577i	0.625581	−	0.780159i	$-0.284862\pi$
$643$	−3.91969	−	3.91969i	−0.154577	−	0.154577i	−0.780159	+	0.625581i	$0.784862\pi$
$644$		0			0
$645$	−14.4853			−0.570357
$646$		0			0
$647$	32.9706			1.29621			0.648103	−	0.761552i	$-0.275563\pi$
$647$	32.9706			1.29621			0.648103	+	0.761552i	$0.275563\pi$
$648$		0			0
$649$	−33.2053	−	33.2053i	−1.30342	−	1.30342i
$650$		0			0
$651$	6.43996	+	6.43996i	0.252402	+	0.252402i
$652$		0			0
$653$	31.9531	−	31.9531i	1.25042	−	1.25042i	0.294890	−	0.955531i	$-0.404717\pi$
$653$	31.9531	−	31.9531i	1.25042	−	1.25042i	0.955531	−	0.294890i	$-0.0952831\pi$
$654$		0			0
$655$			20.2426i			0.790945i
$656$		0			0
$657$	−2.52027	+	2.52027i	−0.0983252	+	0.0983252i
$658$		0			0
$659$	2.68629			0.104643			0.0523215	−	0.998630i	$-0.483338\pi$
$659$	2.68629			0.104643			0.0523215	+	0.998630i	$0.483338\pi$
$660$		0			0
$661$		−	12.7279i		−	0.495059i	−0.968880	−	0.247529i	$-0.920381\pi$
$661$		−	12.7279i		−	0.495059i	0.968880	−	0.247529i	$-0.0796187\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	3.65685i		−	0.141807i
$666$		0			0
$667$	28.3848			1.09906
$668$		0			0
$669$	22.4901	−	22.4901i	0.869519	−	0.869519i
$670$		0			0
$671$		−	6.24264i		−	0.240994i
$672$		0			0
$673$	21.9489	−	21.9489i	0.846069	−	0.846069i	−0.143571	−	0.989640i	$-0.545858\pi$
$673$	21.9489	−	21.9489i	0.846069	−	0.846069i	0.989640	+	0.143571i	$0.0458584\pi$
$674$		0			0
$675$	5.35757	+	5.35757i	0.206213	+	0.206213i
$676$		0			0
$677$	−1.17525	−	1.17525i	−0.0451684	−	0.0451684i	0.684162	−	0.729330i	$-0.260168\pi$
$677$	−1.17525	−	1.17525i	−0.0451684	−	0.0451684i	−0.729330	+	0.684162i	$0.760168\pi$
$678$		0			0
$679$	0.727922			0.0279351
$680$		0			0
$681$	35.8995			1.37567
$682$		0			0
$683$	3.02301	+	3.02301i	0.115672	+	0.115672i	0.762574	−	0.646901i	$-0.223936\pi$
$683$	3.02301	+	3.02301i	0.115672	+	0.115672i	−0.646901	+	0.762574i	$0.723936\pi$
$684$		0			0
$685$	−15.8645	−	15.8645i	−0.606150	−	0.606150i
$686$		0			0
$687$	−4.90923	+	4.90923i	−0.187299	+	0.187299i
$688$		0			0
$689$		−	40.2843i		−	1.53471i
$690$		0			0
$691$	−5.00208	+	5.00208i	−0.190288	+	0.190288i	−0.795821	−	0.605532i	$-0.792960\pi$
$691$	−5.00208	+	5.00208i	−0.190288	+	0.190288i	0.605532	+	0.795821i	$0.292960\pi$
$692$		0			0
$693$	1.07107			0.0406865
$694$		0			0
$695$			32.3848i			1.22842i
$696$		0			0
$697$		0			0
$698$		0			0
$699$			16.5858i			0.627332i
$700$		0			0
$701$	19.5147			0.737061			0.368530	−	0.929616i	$-0.379861\pi$
$701$	19.5147			0.737061			0.368530	+	0.929616i	$0.379861\pi$
$702$		0			0
$703$	12.1146	−	12.1146i	0.456909	−	0.456909i
$704$		0			0
$705$		−	12.4853i		−	0.470223i
$706$		0			0
$707$	−6.94269	+	6.94269i	−0.261107	+	0.261107i
$708$		0			0
$709$	−2.38896	−	2.38896i	−0.0897191	−	0.0897191i	0.660823	−	0.750542i	$-0.270207\pi$
$709$	−2.38896	−	2.38896i	−0.0897191	−	0.0897191i	−0.750542	+	0.660823i	$0.770207\pi$
$710$		0			0
$711$	−3.34003	−	3.34003i	−0.125261	−	0.125261i
$712$		0			0
$713$	−45.5563			−1.70610
$714$		0			0
$715$	−42.6274			−1.59418
$716$		0			0
$717$	−29.5641	−	29.5641i	−1.10409	−	1.10409i
$718$		0			0
$719$	−10.6223	−	10.6223i	−0.396144	−	0.396144i	0.480726	−	0.876871i	$-0.340373\pi$
$719$	−10.6223	−	10.6223i	−0.396144	−	0.396144i	−0.876871	+	0.480726i	$0.840373\pi$
$720$		0			0
$721$	2.16478	−	2.16478i	0.0806208	−	0.0806208i
$722$		0			0
$723$		−	36.7279i		−	1.36593i
$724$		0			0
$725$	4.49935	−	4.49935i	0.167102	−	0.167102i
$726$		0			0
$727$	−19.6569			−0.729032			−0.364516	−	0.931197i	$-0.618766\pi$
$727$	−19.6569			−0.729032			−0.364516	+	0.931197i	$0.618766\pi$
$728$		0			0
$729$		−	22.3137i		−	0.826434i
$730$		0			0
$731$		0			0
$732$		0			0
$733$			4.72792i			0.174630i	0.996181	+	0.0873149i	$0.0278286\pi$
$733$			4.72792i			0.174630i	−0.996181	+	0.0873149i	$0.972171\pi$
$734$		0			0
$735$	−21.8995			−0.807775
$736$		0			0
$737$	−27.0279	+	27.0279i	−0.995587	+	0.995587i
$738$		0			0
$739$		−	16.9289i		−	0.622741i	−0.950289	−	0.311370i	$-0.899212\pi$
$739$		−	16.9289i		−	0.622741i	0.950289	−	0.311370i	$-0.100788\pi$
$740$		0			0
$741$	23.0698	−	23.0698i	0.847490	−	0.847490i
$742$		0			0
$743$	19.9155	+	19.9155i	0.730628	+	0.730628i	0.970744	−	0.240116i	$-0.0771856\pi$
$743$	19.9155	+	19.9155i	0.730628	+	0.730628i	−0.240116	+	0.970744i	$0.577186\pi$
$744$		0			0
$745$	−12.6173	−	12.6173i	−0.462262	−	0.462262i
$746$		0			0
$747$	0.100505			0.00367729
$748$		0			0
$749$	−2.92893			−0.107021
$750$		0			0
$751$	32.5872	+	32.5872i	1.18912	+	1.18912i	0.977311	+	0.211811i	$0.0679363\pi$
$751$	32.5872	+	32.5872i	1.18912	+	1.18912i	0.211811	+	0.977311i	$0.432064\pi$
$752$		0			0
$753$	30.0125	+	30.0125i	1.09372	+	1.09372i
$754$		0			0
$755$	−19.0572	+	19.0572i	−0.693564	+	0.693564i
$756$		0			0
$757$			46.6690i			1.69622i	0.529824	+	0.848108i	$0.322258\pi$
$757$			46.6690i			1.69622i	−0.529824	+	0.848108i	$0.677742\pi$
$758$		0			0
$759$	−31.2262	+	31.2262i	−1.13344	+	1.13344i
$760$		0			0
$761$	17.8579			0.647347			0.323674	−	0.946169i	$-0.395082\pi$
$761$	17.8579			0.647347			0.323674	+	0.946169i	$0.395082\pi$
$762$		0			0
$763$			3.75736i			0.136026i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	94.9117i		−	3.42706i
$768$		0			0
$769$	−3.79899			−0.136995			−0.0684975	−	0.997651i	$-0.521821\pi$
$769$	−3.79899			−0.136995			−0.0684975	+	0.997651i	$0.521821\pi$
$770$		0			0
$771$	−4.90923	+	4.90923i	−0.176801	+	0.176801i
$772$		0			0
$773$			20.9289i			0.752761i	0.926465	+	0.376381i	$0.122832\pi$
$773$			20.9289i			0.752761i	−0.926465	+	0.376381i	$0.877168\pi$
$774$		0			0
$775$	−7.22126	+	7.22126i	−0.259395	+	0.259395i
$776$		0			0
$777$	6.62567	+	6.62567i	0.237695	+	0.237695i
$778$		0			0
$779$	2.21918	+	2.21918i	0.0795103	+	0.0795103i
$780$		0			0
$781$	4.10051			0.146728
$782$		0			0
$783$	−19.1716			−0.685136
$784$		0			0
$785$	3.06147	+	3.06147i	0.109268	+	0.109268i
$786$		0			0
$787$	24.9560	+	24.9560i	0.889586	+	0.889586i	0.994483	−	0.104897i	$-0.0334514\pi$
$787$	24.9560	+	24.9560i	0.889586	+	0.889586i	−0.104897	+	0.994483i	$0.533451\pi$
$788$		0			0
$789$	−17.2639	+	17.2639i	−0.614610	+	0.614610i
$790$		0			0
$791$		−	1.07107i		−	0.0380828i
$792$		0			0
$793$	8.92177	−	8.92177i	0.316821	−	0.316821i
$794$		0			0
$795$	20.1421			0.714368
$796$		0			0
$797$			48.5269i			1.71891i	0.511210	+	0.859456i	$0.329197\pi$
$797$			48.5269i			1.71891i	−0.511210	+	0.859456i	$0.670803\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			4.48528i			0.158480i
$802$		0			0
$803$	29.0711			1.02590
$804$		0			0
$805$	−7.07401	+	7.07401i	−0.249326	+	0.249326i
$806$		0			0
$807$		−	15.5563i		−	0.547609i
$808$		0			0
$809$	21.0523	−	21.0523i	0.740158	−	0.740158i	−0.232450	−	0.972608i	$-0.574674\pi$
$809$	21.0523	−	21.0523i	0.740158	−	0.740158i	0.972608	+	0.232450i	$0.0746743\pi$
$810$		0			0
$811$	16.8540	+	16.8540i	0.591824	+	0.591824i	0.938124	−	0.346300i	$-0.112562\pi$
$811$	16.8540	+	16.8540i	0.591824	+	0.591824i	−0.346300	+	0.938124i	$0.612562\pi$
$812$		0			0
$813$	−14.7821	−	14.7821i	−0.518430	−	0.518430i
$814$		0			0
$815$	13.4142			0.469879
$816$		0			0
$817$	−10.9706			−0.383811
$818$		0			0
$819$	1.53073	+	1.53073i	0.0534882	+	0.0534882i
$820$		0			0
$821$	4.18232	+	4.18232i	0.145964	+	0.145964i	0.776312	−	0.630348i	$-0.217088\pi$
$821$	4.18232	+	4.18232i	0.145964	+	0.145964i	−0.630348	+	0.776312i	$0.717088\pi$
$822$		0			0
$823$	−21.3693	+	21.3693i	−0.744886	+	0.744886i	−0.973514	−	0.228628i	$-0.926576\pi$
$823$	−21.3693	+	21.3693i	−0.744886	+	0.744886i	0.228628	+	0.973514i	$0.426576\pi$
$824$		0			0
$825$			9.89949i			0.344656i
$826$		0			0
$827$	−2.57466	+	2.57466i	−0.0895299	+	0.0895299i	−0.750453	−	0.660923i	$-0.770165\pi$
$827$	−2.57466	+	2.57466i	−0.0895299	+	0.0895299i	0.660923	+	0.750453i	$0.270165\pi$
$828$		0			0
$829$	−29.6569			−1.03003			−0.515013	−	0.857183i	$-0.672213\pi$
$829$	−29.6569			−1.03003			−0.515013	+	0.857183i	$0.672213\pi$
$830$		0			0
$831$		−	27.8995i		−	0.967823i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		−	22.7279i		−	0.786532i
$836$		0			0
$837$	30.7696			1.06355
$838$		0			0
$839$	−4.29111	+	4.29111i	−0.148145	+	0.148145i	−0.777289	−	0.629144i	$-0.783406\pi$
$839$	−4.29111	+	4.29111i	−0.148145	+	0.148145i	0.629144	+	0.777289i	$0.283406\pi$
$840$		0			0
$841$		−	12.8995i		−	0.444810i
$842$		0			0
$843$	−19.6913	+	19.6913i	−0.678204	+	0.678204i
$844$		0			0
$845$	−43.9363	−	43.9363i	−1.51146	−	1.51146i
$846$		0			0
$847$	−0.224171	−	0.224171i	−0.00770260	−	0.00770260i
$848$		0			0
$849$	13.0711			0.448598
$850$		0			0
$851$	−46.8701			−1.60668
$852$		0			0
$853$	15.3233	+	15.3233i	0.524659	+	0.524659i	0.918975	−	0.394316i	$-0.129018\pi$
$853$	15.3233	+	15.3233i	0.524659	+	0.524659i	−0.394316	+	0.918975i	$0.629018\pi$
$854$		0			0
$855$	1.39942	+	1.39942i	0.0478591	+	0.0478591i
$856$		0			0
$857$	9.14594	−	9.14594i	0.312419	−	0.312419i	−0.533427	−	0.845846i	$-0.679096\pi$
$857$	9.14594	−	9.14594i	0.312419	−	0.312419i	0.845846	+	0.533427i	$0.179096\pi$
$858$		0			0
$859$		−	16.7279i		−	0.570749i	−0.958416	−	0.285375i	$-0.907882\pi$
$859$		−	16.7279i		−	0.570749i	0.958416	−	0.285375i	$-0.0921180\pi$
$860$		0			0
$861$	−1.21371	+	1.21371i	−0.0413631	+	0.0413631i
$862$		0			0
$863$	−14.0000			−0.476566			−0.238283	−	0.971196i	$-0.576585\pi$
$863$	−14.0000			−0.476566			−0.238283	+	0.971196i	$0.576585\pi$
$864$		0			0
$865$		−	46.3848i		−	1.57713i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			38.5269i			1.30694i
$870$		0			0
$871$	−77.2548			−2.61768
$872$		0			0
$873$	−0.278564	+	0.278564i	−0.00942795	+	0.00942795i
$874$		0			0
$875$			9.31371i			0.314861i
$876$		0			0
$877$	−6.08447	+	6.08447i	−0.205458	+	0.205458i	−0.802334	−	0.596876i	$-0.796409\pi$
$877$	−6.08447	+	6.08447i	−0.205458	+	0.205458i	0.596876	+	0.802334i	$0.296409\pi$
$878$		0			0
$879$	−10.4525	−	10.4525i	−0.352554	−	0.352554i
$880$		0			0
$881$	6.84984	+	6.84984i	0.230777	+	0.230777i	0.813017	−	0.582240i	$-0.197824\pi$
$881$	6.84984	+	6.84984i	0.230777	+	0.230777i	−0.582240	+	0.813017i	$0.697824\pi$
$882$		0			0
$883$	−14.3431			−0.482685			−0.241343	−	0.970440i	$-0.577588\pi$
$883$	−14.3431			−0.482685			−0.241343	+	0.970440i	$0.577588\pi$
$884$		0			0
$885$	47.4558			1.59521
$886$		0			0
$887$	25.0873	+	25.0873i	0.842350	+	0.842350i	0.989164	−	0.146814i	$-0.0469019\pi$
$887$	25.0873	+	25.0873i	0.842350	+	0.842350i	−0.146814	+	0.989164i	$0.546902\pi$
$888$		0			0
$889$	−0.131316	−	0.131316i	−0.00440420	−	0.00440420i
$890$		0			0
$891$	24.0593	−	24.0593i	0.806018	−	0.806018i
$892$		0			0
$893$		−	9.45584i		−	0.316428i
$894$		0			0
$895$	−24.0209	+	24.0209i	−0.802929	+	0.802929i
$896$		0			0
$897$	−89.2548			−2.98013
$898$		0			0
$899$		−	25.8406i		−	0.861833i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		−	6.00000i		−	0.199667i
$904$		0			0
$905$	7.07107			0.235050
$906$		0			0
$907$	5.37350	−	5.37350i	0.178424	−	0.178424i	−0.612244	−	0.790669i	$-0.709733\pi$
$907$	5.37350	−	5.37350i	0.178424	−	0.178424i	0.790669	+	0.612244i	$0.209733\pi$
$908$		0			0
$909$		−	5.31371i		−	0.176245i
$910$		0			0
$911$	2.14885	−	2.14885i	0.0711947	−	0.0711947i	−0.670613	−	0.741808i	$-0.733969\pi$
$911$	2.14885	−	2.14885i	0.0711947	−	0.0711947i	0.741808	+	0.670613i	$0.233969\pi$
$912$		0			0
$913$	−0.579658	−	0.579658i	−0.0191839	−	0.0191839i
$914$		0			0
$915$	4.46088	+	4.46088i	0.147472	+	0.147472i
$916$		0			0
$917$	−8.38478			−0.276890
$918$		0			0
$919$	−14.3431			−0.473137			−0.236568	−	0.971615i	$-0.576023\pi$
$919$	−14.3431			−0.473137			−0.236568	+	0.971615i	$0.576023\pi$
$920$		0			0
$921$	−8.28772	−	8.28772i	−0.273090	−	0.273090i
$922$		0			0
$923$	5.86030	+	5.86030i	0.192894	+	0.192894i
$924$		0			0
$925$	−7.42950	+	7.42950i	−0.244280	+	0.244280i
$926$		0			0
$927$			1.65685i			0.0544182i
$928$		0			0
$929$	−34.9602	+	34.9602i	−1.14701	+	1.14701i	−0.159868	+	0.987138i	$0.551107\pi$
$929$	−34.9602	+	34.9602i	−1.14701	+	1.14701i	−0.987138	+	0.159868i	$0.948893\pi$
$930$		0			0
$931$	−16.5858			−0.543577
$932$		0			0
$933$		−	23.5563i		−	0.771200i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			23.3553i			0.762986i	0.924372	+	0.381493i	$0.124590\pi$
$937$			23.3553i			0.762986i	−0.924372	+	0.381493i	$0.875410\pi$
$938$		0			0
$939$	42.0416			1.37198
$940$		0			0
$941$	1.17525	−	1.17525i	0.0383119	−	0.0383119i	−0.687691	−	0.726003i	$-0.741376\pi$
$941$	1.17525	−	1.17525i	0.0383119	−	0.0383119i	0.726003	+	0.687691i	$0.241376\pi$
$942$		0			0
$943$		−	8.58579i		−	0.279592i
$944$		0			0
$945$	4.77791	−	4.77791i	0.155425	−	0.155425i
$946$		0			0
$947$	6.40150	+	6.40150i	0.208021	+	0.208021i	0.803426	−	0.595405i	$-0.203008\pi$
$947$	6.40150	+	6.40150i	0.208021	+	0.208021i	−0.595405	+	0.803426i	$0.703008\pi$
$948$		0			0
$949$	41.5474	+	41.5474i	1.34869	+	1.34869i
$950$		0			0
$951$	0.727922			0.0236045
$952$		0			0
$953$	12.1421			0.393322			0.196661	−	0.980472i	$-0.436990\pi$
$953$	12.1421			0.393322			0.196661	+	0.980472i	$0.436990\pi$
$954$		0			0
$955$	0.448342	+	0.448342i	0.0145080	+	0.0145080i
$956$		0			0
$957$	−17.7122	−	17.7122i	−0.572555	−	0.572555i
$958$		0			0
$959$	6.57128	−	6.57128i	0.212198	−	0.212198i
$960$		0			0
$961$			10.4731i			0.337842i
$962$		0			0
$963$	1.12085	−	1.12085i	0.0361190	−	0.0361190i
$964$		0			0
$965$	−28.7279			−0.924785
$966$		0			0
$967$			33.0122i			1.06160i	0.847497	+	0.530800i	$0.178109\pi$
$967$			33.0122i			1.06160i	−0.847497	+	0.530800i	$0.821891\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			37.2132i			1.19423i	0.802156	+	0.597114i	$0.203686\pi$
$971$			37.2132i			1.19423i	−0.802156	+	0.597114i	$0.796314\pi$
$972$		0			0
$973$	−13.4142			−0.430040
$974$		0			0
$975$	−14.1480	+	14.1480i	−0.453099	+	0.453099i
$976$		0			0
$977$			38.3848i			1.22804i	0.789291	+	0.614019i	$0.210448\pi$
$977$			38.3848i			1.22804i	−0.789291	+	0.614019i	$0.789552\pi$
$978$		0			0
$979$	25.8686	−	25.8686i	0.826765	−	0.826765i
$980$		0			0
$981$	−1.43788	−	1.43788i	−0.0459079	−	0.0459079i
$982$		0			0
$983$	27.8092	+	27.8092i	0.886977	+	0.886977i	0.994232	−	0.107255i	$-0.0342060\pi$
$983$	27.8092	+	27.8092i	0.886977	+	0.886977i	−0.107255	+	0.994232i	$0.534206\pi$
$984$		0			0
$985$	23.2132			0.739634
$986$		0			0
$987$	5.17157			0.164613
$988$		0			0
$989$	21.2220	+	21.2220i	0.674821	+	0.674821i
$990$		0			0
$991$	32.0844	+	32.0844i	1.01920	+	1.01920i	0.999812	+	0.0193829i	$0.00617017\pi$
$991$	32.0844	+	32.0844i	1.01920	+	1.01920i	0.0193829	+	0.999812i	$0.493830\pi$
$992$		0			0
$993$	37.5348	−	37.5348i	1.19113	−	1.19113i
$994$		0			0
$995$		−	3.07107i		−	0.0973594i
$996$		0			0
$997$	21.8945	−	21.8945i	0.693407	−	0.693407i	−0.269573	−	0.962980i	$-0.586882\pi$
$997$	21.8945	−	21.8945i	0.693407	−	0.693407i	0.962980	+	0.269573i	$0.0868825\pi$
$998$		0			0
$999$	31.6569			1.00158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.e.f.829.1		8
17.2	even	8		1156.2.a.g.1.1		4
17.3	odd	16		68.2.h.a.49.1	yes	4
17.4	even	4	inner	1156.2.e.f.905.1		8
17.5	odd	16		1156.2.h.c.733.1		4
17.6	odd	16		1156.2.h.a.757.1		4
17.7	odd	16		68.2.h.a.25.1	✓	4
17.8	even	8		1156.2.b.d.577.4		4
17.9	even	8		1156.2.b.d.577.1		4
17.10	odd	16		1156.2.h.b.977.1		4
17.11	odd	16		1156.2.h.c.757.1		4
17.12	odd	16		1156.2.h.a.733.1		4
17.13	even	4	inner	1156.2.e.f.905.4		8
17.14	odd	16		1156.2.h.b.1001.1		4
17.15	even	8		1156.2.a.g.1.4		4
17.16	even	2	inner	1156.2.e.f.829.4		8
51.20	even	16		612.2.w.a.253.1		4
51.41	even	16		612.2.w.a.433.1		4
68.3	even	16		272.2.v.c.49.1		4
68.7	even	16		272.2.v.c.161.1		4
68.15	odd	8		4624.2.a.bl.1.1		4
68.19	odd	8		4624.2.a.bl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.h.a.25.1	✓	4	17.7	odd	16
68.2.h.a.49.1	yes	4	17.3	odd	16
272.2.v.c.49.1		4	68.3	even	16
272.2.v.c.161.1		4	68.7	even	16
612.2.w.a.253.1		4	51.20	even	16
612.2.w.a.433.1		4	51.41	even	16
1156.2.a.g.1.1		4	17.2	even	8
1156.2.a.g.1.4		4	17.15	even	8
1156.2.b.d.577.1		4	17.9	even	8
1156.2.b.d.577.4		4	17.8	even	8
1156.2.e.f.829.1		8	1.1	even	1	trivial
1156.2.e.f.829.4		8	17.16	even	2	inner
1156.2.e.f.905.1		8	17.4	even	4	inner
1156.2.e.f.905.4		8	17.13	even	4	inner
1156.2.h.a.733.1		4	17.12	odd	16
1156.2.h.a.757.1		4	17.6	odd	16
1156.2.h.b.977.1		4	17.10	odd	16
1156.2.h.b.1001.1		4	17.14	odd	16
1156.2.h.c.733.1		4	17.5	odd	16
1156.2.h.c.757.1		4	17.11	odd	16
4624.2.a.bl.1.1		4	68.15	odd	8
4624.2.a.bl.1.4		4	68.19	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.30656 - 1.30656i) q^{3} +(-1.30656 - 1.30656i) q^{5} +(0.541196 - 0.541196i) q^{7} +0.414214i q^{9} +(2.38896 - 2.38896i) q^{11} +6.82843 q^{13} +3.41421i q^{15} +2.58579i q^{19} -1.41421 q^{21} +(5.00208 - 5.00208i) q^{23} -1.58579i q^{25} +(-3.37849 + 3.37849i) q^{27} +(2.83730 + 2.83730i) q^{29} +(-4.55374 - 4.55374i) q^{31} -6.24264 q^{33} -1.41421 q^{35} +(-4.68506 - 4.68506i) q^{37} +(-8.92177 - 8.92177i) q^{39} +(0.858221 - 0.858221i) q^{41} +4.24264i q^{43} +(0.541196 - 0.541196i) q^{45} -3.65685 q^{47} +6.41421i q^{49} -5.89949i q^{53} -6.24264 q^{55} +(3.37849 - 3.37849i) q^{57} -13.8995i q^{59} +(1.30656 - 1.30656i) q^{61} +(0.224171 + 0.224171i) q^{63} +(-8.92177 - 8.92177i) q^{65} -11.3137 q^{67} -13.0711 q^{69} +(0.858221 + 0.858221i) q^{71} +(6.08447 + 6.08447i) q^{73} +(-2.07193 + 2.07193i) q^{75} -2.58579i q^{77} +(-8.06355 + 8.06355i) q^{79} +10.0711 q^{81} -0.242641i q^{83} -7.41421i q^{87} +10.8284 q^{89} +(3.69552 - 3.69552i) q^{91} +11.8995i q^{93} +(3.37849 - 3.37849i) q^{95} +(0.672512 + 0.672512i) q^{97} +(0.989538 + 0.989538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{13} - 16 q^{33} + 16 q^{47} - 16 q^{55} - 48 q^{69} + 24 q^{81} + 64 q^{89}+O(q^{100}) \) 8 * q + 32 * q^13 - 16 * q^33 + 16 * q^47 - 16 * q^55 - 48 * q^69 + 24 * q^81 + 64 * q^89

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