LMFDB - Embedded newform 1536.2.j.c.385.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1536,2,Mod(385,1536)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1536, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1536.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1536 = 2^{9} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1536.j (of order $4$, degree $2$, 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:	$12.2650217505$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			385.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1536.385
Dual form			1536.2.j.c.1153.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.82843i q^{7} -1.00000i q^{9} +O(q^{10})$	$q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.82843i q^{7} -1.00000i q^{9} +(-3.00000 + 3.00000i) q^{13} +1.41421 q^{15} -4.00000 q^{17} +(-5.65685 + 5.65685i) q^{19} +(2.00000 + 2.00000i) q^{21} +5.65685i q^{23} -3.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(1.00000 - 1.00000i) q^{29} -2.82843 q^{31} +(-2.82843 + 2.82843i) q^{35} +(-3.00000 - 3.00000i) q^{37} +4.24264i q^{39} +4.00000i q^{41} +(1.00000 - 1.00000i) q^{45} +11.3137 q^{47} -1.00000 q^{49} +(-2.82843 + 2.82843i) q^{51} +(-5.00000 - 5.00000i) q^{53} +8.00000i q^{57} +(-8.48528 - 8.48528i) q^{59} +(1.00000 - 1.00000i) q^{61} +2.82843 q^{63} -6.00000 q^{65} +(-2.82843 + 2.82843i) q^{67} +(4.00000 + 4.00000i) q^{69} +11.3137i q^{71} -14.0000i q^{73} +(-2.12132 - 2.12132i) q^{75} +8.48528 q^{79} -1.00000 q^{81} +(-11.3137 + 11.3137i) q^{83} +(-4.00000 - 4.00000i) q^{85} -1.41421i q^{87} +6.00000i q^{89} +(-8.48528 - 8.48528i) q^{91} +(-2.00000 + 2.00000i) q^{93} -11.3137 q^{95} +16.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5}+O(q^{10}) $ 4 * q + 4 * q^5	$ 4 q + 4 q^{5} - 12 q^{13} - 16 q^{17} + 8 q^{21} + 4 q^{29} - 12 q^{37} + 4 q^{45} - 4 q^{49} - 20 q^{53} + 4 q^{61} - 24 q^{65} + 16 q^{69} - 4 q^{81} - 16 q^{85} - 8 q^{93} + 64 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 - 12 * q^13 - 16 * q^17 + 8 * q^21 + 4 * q^29 - 12 * q^37 + 4 * q^45 - 4 * q^49 - 20 * q^53 + 4 * q^61 - 24 * q^65 + 16 * q^69 - 4 * q^81 - 16 * q^85 - 8 * q^93 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times$.

$n$	$511$	$517$	$1025$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$			2.82843i			1.06904i	0.845154	+	0.534522i	$0.179509\pi$
$7$			2.82843i			1.06904i	−0.845154	+	0.534522i	$0.820491\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$11$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$12$		0			0
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	0.155747	+	0.987797i	$0.450222\pi$
$14$		0			0
$15$	1.41421			0.365148
$16$		0			0
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	−5.65685	+	5.65685i	−1.29777	+	1.29777i	−0.367910	+	0.929861i	$0.619927\pi$
$19$	−5.65685	+	5.65685i	−1.29777	+	1.29777i	−0.929861	+	0.367910i	$0.880073\pi$
$20$		0			0
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$		0			0
$23$			5.65685i			1.17954i	0.807573	+	0.589768i	$0.200781\pi$
$23$			5.65685i			1.17954i	−0.807573	+	0.589768i	$0.799219\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	−0.608137	−	0.793832i	$-0.708083\pi$
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	0.793832	+	0.608137i	$0.208083\pi$
$30$		0			0
$31$	−2.82843			−0.508001			−0.254000	−	0.967204i	$-0.581746\pi$
$31$	−2.82843			−0.508001			−0.254000	+	0.967204i	$0.581746\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.82843	+	2.82843i	−0.478091	+	0.478091i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$			4.24264i			0.679366i
$40$		0			0
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	1.00000	−	1.00000i	0.149071	−	0.149071i
$46$		0			0
$47$	11.3137			1.65027			0.825137	−	0.564933i	$-0.191098\pi$
$47$	11.3137			1.65027			0.825137	+	0.564933i	$0.191098\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−2.82843	+	2.82843i	−0.396059	+	0.396059i
$52$		0			0
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	0.274721	−	0.961524i	$-0.411414\pi$
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	−0.961524	+	0.274721i	$0.911414\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			8.00000i			1.05963i
$58$		0			0
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.993837	−	0.110853i	$-0.964642\pi$
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.110853	−	0.993837i	$-0.535358\pi$
$60$		0			0
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	0.768221	+	0.640184i	$0.221142\pi$
$62$		0			0
$63$	2.82843			0.356348
$64$		0			0
$65$	−6.00000			−0.744208
$66$		0			0
$67$	−2.82843	+	2.82843i	−0.345547	+	0.345547i	−0.858448	−	0.512901i	$-0.828571\pi$
$67$	−2.82843	+	2.82843i	−0.345547	+	0.345547i	0.512901	+	0.858448i	$0.328571\pi$
$68$		0			0
$69$	4.00000	+	4.00000i	0.481543	+	0.481543i
$70$		0			0
$71$			11.3137i			1.34269i	0.741145	+	0.671345i	$0.234283\pi$
$71$			11.3137i			1.34269i	−0.741145	+	0.671345i	$0.765717\pi$
$72$		0			0
$73$		−	14.0000i		−	1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$		−	14.0000i		−	1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$		0			0
$75$	−2.12132	−	2.12132i	−0.244949	−	0.244949i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.48528			0.954669			0.477334	−	0.878722i	$-0.341603\pi$
$79$	8.48528			0.954669			0.477334	+	0.878722i	$0.341603\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−11.3137	+	11.3137i	−1.24184	+	1.24184i	−0.282604	+	0.959237i	$0.591198\pi$
$83$	−11.3137	+	11.3137i	−1.24184	+	1.24184i	−0.959237	+	0.282604i	$0.908802\pi$
$84$		0			0
$85$	−4.00000	−	4.00000i	−0.433861	−	0.433861i
$86$		0			0
$87$		−	1.41421i		−	0.151620i
$88$		0			0
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$		0			0
$91$	−8.48528	−	8.48528i	−0.889499	−	0.889499i
$92$		0			0
$93$	−2.00000	+	2.00000i	−0.207390	+	0.207390i
$94$		0			0
$95$	−11.3137			−1.16076
$96$		0			0
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.0000	+	11.0000i	1.09454	+	1.09454i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$	11.0000	+	11.0000i	1.09454	+	1.09454i	0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$			19.7990i			1.95085i	0.220326	+	0.975426i	$0.429288\pi$
$103$			19.7990i			1.95085i	−0.220326	+	0.975426i	$0.570712\pi$
$104$		0			0
$105$			4.00000i			0.390360i
$106$		0			0
$107$	8.48528	+	8.48528i	0.820303	+	0.820303i	0.986151	−	0.165848i	$-0.0530362\pi$
$107$	8.48528	+	8.48528i	0.820303	+	0.820303i	−0.165848	+	0.986151i	$0.553036\pi$
$108$		0			0
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	−0.548683	−	0.836031i	$-0.684871\pi$
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	0.836031	+	0.548683i	$0.184871\pi$
$110$		0			0
$111$	−4.24264			−0.402694
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	−5.65685	+	5.65685i	−0.527504	+	0.527504i
$116$		0			0
$117$	3.00000	+	3.00000i	0.277350	+	0.277350i
$118$		0			0
$119$		−	11.3137i		−	1.03713i
$120$		0			0
$121$		−	11.0000i		−	1.00000i
$122$		0			0
$123$	2.82843	+	2.82843i	0.255031	+	0.255031i
$124$		0			0
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$		0			0
$127$	8.48528			0.752947			0.376473	−	0.926427i	$-0.377137\pi$
$127$	8.48528			0.752947			0.376473	+	0.926427i	$0.377137\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.82843	−	2.82843i	0.247121	−	0.247121i	−0.572667	−	0.819788i	$-0.694091\pi$
$131$	2.82843	−	2.82843i	0.247121	−	0.247121i	0.819788	+	0.572667i	$0.194091\pi$
$132$		0			0
$133$	−16.0000	−	16.0000i	−1.38738	−	1.38738i
$134$		0			0
$135$		−	1.41421i		−	0.121716i
$136$		0			0
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		0			0
$139$	2.82843	+	2.82843i	0.239904	+	0.239904i	0.816810	−	0.576906i	$-0.195740\pi$
$139$	2.82843	+	2.82843i	0.239904	+	0.239904i	−0.576906	+	0.816810i	$0.695740\pi$
$140$		0			0
$141$	8.00000	−	8.00000i	0.673722	−	0.673722i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	2.00000			0.166091
$146$		0			0
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$		0			0
$149$	9.00000	+	9.00000i	0.737309	+	0.737309i	0.972056	−	0.234748i	$-0.0754264\pi$
$149$	9.00000	+	9.00000i	0.737309	+	0.737309i	−0.234748	+	0.972056i	$0.575426\pi$
$150$		0			0
$151$			2.82843i			0.230174i	0.993355	+	0.115087i	$0.0367147\pi$
$151$			2.82843i			0.230174i	−0.993355	+	0.115087i	$0.963285\pi$
$152$		0			0
$153$			4.00000i			0.323381i
$154$		0			0
$155$	−2.82843	−	2.82843i	−0.227185	−	0.227185i
$156$		0			0
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$		0			0
$159$	−7.07107			−0.560772
$160$		0			0
$161$	−16.0000			−1.26098
$162$		0			0
$163$	11.3137	−	11.3137i	0.886158	−	0.886158i	−0.107994	−	0.994152i	$-0.534443\pi$
$163$	11.3137	−	11.3137i	0.886158	−	0.886158i	0.994152	+	0.107994i	$0.0344426\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			11.3137i			0.875481i	0.899101	+	0.437741i	$0.144221\pi$
$167$			11.3137i			0.875481i	−0.899101	+	0.437741i	$0.855779\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	5.65685	+	5.65685i	0.432590	+	0.432590i
$172$		0			0
$173$	−5.00000	+	5.00000i	−0.380143	+	0.380143i	−0.871154	−	0.491011i	$-0.836628\pi$
$173$	−5.00000	+	5.00000i	−0.380143	+	0.380143i	0.491011	+	0.871154i	$0.336628\pi$
$174$		0			0
$175$	8.48528			0.641427
$176$		0			0
$177$	−12.0000			−0.901975
$178$		0			0
$179$	2.82843	−	2.82843i	0.211407	−	0.211407i	−0.593458	−	0.804865i	$-0.702238\pi$
$179$	2.82843	−	2.82843i	0.211407	−	0.211407i	0.804865	+	0.593458i	$0.202238\pi$
$180$		0			0
$181$	−9.00000	−	9.00000i	−0.668965	−	0.668965i	0.288512	−	0.957476i	$-0.406840\pi$
$181$	−9.00000	−	9.00000i	−0.668965	−	0.668965i	−0.957476	+	0.288512i	$0.906840\pi$
$182$		0			0
$183$		−	1.41421i		−	0.104542i
$184$		0			0
$185$		−	6.00000i		−	0.441129i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.00000	−	2.00000i	0.145479	−	0.145479i
$190$		0			0
$191$	5.65685			0.409316			0.204658	−	0.978834i	$-0.434392\pi$
$191$	5.65685			0.409316			0.204658	+	0.978834i	$0.434392\pi$
$192$		0			0
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$		0			0
$195$	−4.24264	+	4.24264i	−0.303822	+	0.303822i
$196$		0			0
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	0.862423	−	0.506188i	$-0.168946\pi$
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	−0.506188	+	0.862423i	$0.668946\pi$
$198$		0			0
$199$		−	8.48528i		−	0.601506i	−0.953702	−	0.300753i	$-0.902762\pi$
$199$		−	8.48528i		−	0.601506i	0.953702	−	0.300753i	$-0.0972379\pi$
$200$		0			0
$201$			4.00000i			0.282138i
$202$		0			0
$203$	2.82843	+	2.82843i	0.198517	+	0.198517i
$204$		0			0
$205$	−4.00000	+	4.00000i	−0.279372	+	0.279372i
$206$		0			0
$207$	5.65685			0.393179
$208$		0			0
$209$		0			0
$210$		0			0
$211$	8.48528	−	8.48528i	0.584151	−	0.584151i	−0.351890	−	0.936041i	$-0.614461\pi$
$211$	8.48528	−	8.48528i	0.584151	−	0.584151i	0.936041	+	0.351890i	$0.114461\pi$
$212$		0			0
$213$	8.00000	+	8.00000i	0.548151	+	0.548151i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	8.00000i		−	0.543075i
$218$		0			0
$219$	−9.89949	−	9.89949i	−0.668946	−	0.668946i
$220$		0			0
$221$	12.0000	−	12.0000i	0.807207	−	0.807207i
$222$		0			0
$223$	−25.4558			−1.70465			−0.852325	−	0.523013i	$-0.824808\pi$
$223$	−25.4558			−1.70465			−0.852325	+	0.523013i	$0.824808\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	5.65685	−	5.65685i	0.375459	−	0.375459i	−0.494002	−	0.869461i	$-0.664466\pi$
$227$	5.65685	−	5.65685i	0.375459	−	0.375459i	0.869461	+	0.494002i	$0.164466\pi$
$228$		0			0
$229$	−17.0000	−	17.0000i	−1.12339	−	1.12339i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−17.0000	−	17.0000i	−1.12339	−	1.12339i	−0.132164	−	0.991228i	$-0.542192\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$		0			0
$235$	11.3137	+	11.3137i	0.738025	+	0.738025i
$236$		0			0
$237$	6.00000	−	6.00000i	0.389742	−	0.389742i
$238$		0			0
$239$	−5.65685			−0.365911			−0.182956	−	0.983121i	$-0.558567\pi$
$239$	−5.65685			−0.365911			−0.182956	+	0.983121i	$0.558567\pi$
$240$		0			0
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.00000	−	1.00000i	−0.0638877	−	0.0638877i
$246$		0			0
$247$		−	33.9411i		−	2.15962i
$248$		0			0
$249$			16.0000i			1.01396i
$250$		0			0
$251$	5.65685	+	5.65685i	0.357057	+	0.357057i	0.862727	−	0.505670i	$-0.168755\pi$
$251$	5.65685	+	5.65685i	0.357057	+	0.357057i	−0.505670	+	0.862727i	$0.668755\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−5.65685			−0.354246
$256$		0			0
$257$	2.00000			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$258$		0			0
$259$	8.48528	−	8.48528i	0.527250	−	0.527250i
$260$		0			0
$261$	−1.00000	−	1.00000i	−0.0618984	−	0.0618984i
$262$		0			0
$263$		−	28.2843i		−	1.74408i	−0.489432	−	0.872041i	$-0.662796\pi$
$263$		−	28.2843i		−	1.74408i	0.489432	−	0.872041i	$-0.337204\pi$
$264$		0			0
$265$		−	10.0000i		−	0.614295i
$266$		0			0
$267$	4.24264	+	4.24264i	0.259645	+	0.259645i
$268$		0			0
$269$	−15.0000	+	15.0000i	−0.914566	+	0.914566i	−0.996627	−	0.0820612i	$-0.973850\pi$
$269$	−15.0000	+	15.0000i	−0.914566	+	0.914566i	0.0820612	+	0.996627i	$0.473850\pi$
$270$		0			0
$271$	−8.48528			−0.515444			−0.257722	−	0.966219i	$-0.582972\pi$
$271$	−8.48528			−0.515444			−0.257722	+	0.966219i	$0.582972\pi$
$272$		0			0
$273$	−12.0000			−0.726273
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.00000	+	1.00000i	0.0600842	+	0.0600842i	0.736510	−	0.676426i	$-0.236472\pi$
$277$	1.00000	+	1.00000i	0.0600842	+	0.0600842i	−0.676426	+	0.736510i	$0.736472\pi$
$278$		0			0
$279$			2.82843i			0.169334i
$280$		0			0
$281$		−	22.0000i		−	1.31241i	−0.754583	−	0.656205i	$-0.772161\pi$
$281$		−	22.0000i		−	1.31241i	0.754583	−	0.656205i	$-0.227839\pi$
$282$		0			0
$283$	−2.82843	−	2.82843i	−0.168133	−	0.168133i	0.618026	−	0.786158i	$-0.287933\pi$
$283$	−2.82843	−	2.82843i	−0.168133	−	0.168133i	−0.786158	+	0.618026i	$0.787933\pi$
$284$		0			0
$285$	−8.00000	+	8.00000i	−0.473879	+	0.473879i
$286$		0			0
$287$	−11.3137			−0.667827
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	11.3137	−	11.3137i	0.663221	−	0.663221i
$292$		0			0
$293$	13.0000	+	13.0000i	0.759468	+	0.759468i	0.976226	−	0.216757i	$-0.0695481\pi$
$293$	13.0000	+	13.0000i	0.759468	+	0.759468i	−0.216757	+	0.976226i	$0.569548\pi$
$294$		0			0
$295$		−	16.9706i		−	0.988064i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−16.9706	−	16.9706i	−0.981433	−	0.981433i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	15.5563			0.893689
$304$		0			0
$305$	2.00000			0.114520
$306$		0			0
$307$	−2.82843	+	2.82843i	−0.161427	+	0.161427i	−0.783199	−	0.621772i	$-0.786413\pi$
$307$	−2.82843	+	2.82843i	−0.161427	+	0.161427i	0.621772	+	0.783199i	$0.286413\pi$
$308$		0			0
$309$	14.0000	+	14.0000i	0.796432	+	0.796432i
$310$		0			0
$311$		−	28.2843i		−	1.60385i	−0.597422	−	0.801927i	$-0.703808\pi$
$311$		−	28.2843i		−	1.60385i	0.597422	−	0.801927i	$-0.296192\pi$
$312$		0			0
$313$		−	16.0000i		−	0.904373i	−0.891923	−	0.452187i	$-0.850644\pi$
$313$		−	16.0000i		−	0.904373i	0.891923	−	0.452187i	$-0.149356\pi$
$314$		0			0
$315$	2.82843	+	2.82843i	0.159364	+	0.159364i
$316$		0			0
$317$	−15.0000	+	15.0000i	−0.842484	+	0.842484i	−0.989181	−	0.146697i	$-0.953136\pi$
$317$	−15.0000	+	15.0000i	−0.842484	+	0.842484i	0.146697	+	0.989181i	$0.453136\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	22.6274	−	22.6274i	1.25902	−	1.25902i
$324$		0			0
$325$	9.00000	+	9.00000i	0.499230	+	0.499230i
$326$		0			0
$327$		−	4.24264i		−	0.234619i
$328$		0			0
$329$			32.0000i			1.76422i
$330$		0			0
$331$	−2.82843	−	2.82843i	−0.155464	−	0.155464i	0.625089	−	0.780553i	$-0.285063\pi$
$331$	−2.82843	−	2.82843i	−0.155464	−	0.155464i	−0.780553	+	0.625089i	$0.785063\pi$
$332$		0			0
$333$	−3.00000	+	3.00000i	−0.164399	+	0.164399i
$334$		0			0
$335$	−5.65685			−0.309067
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$		0			0
$339$	12.7279	−	12.7279i	0.691286	−	0.691286i
$340$		0			0
$341$		0			0
$342$		0			0
$343$			16.9706i			0.916324i
$344$		0			0
$345$			8.00000i			0.430706i
$346$		0			0
$347$	22.6274	+	22.6274i	1.21470	+	1.21470i	0.969462	+	0.245241i	$0.0788672\pi$
$347$	22.6274	+	22.6274i	1.21470	+	1.21470i	0.245241	+	0.969462i	$0.421133\pi$
$348$		0			0
$349$	−9.00000	+	9.00000i	−0.481759	+	0.481759i	−0.905693	−	0.423934i	$-0.860649\pi$
$349$	−9.00000	+	9.00000i	−0.481759	+	0.481759i	0.423934	+	0.905693i	$0.360649\pi$
$350$		0			0
$351$	4.24264			0.226455
$352$		0			0
$353$	−18.0000			−0.958043			−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000			−0.958043			−0.479022	+	0.877803i	$0.659008\pi$
$354$		0			0
$355$	−11.3137	+	11.3137i	−0.600469	+	0.600469i
$356$		0			0
$357$	−8.00000	−	8.00000i	−0.423405	−	0.423405i
$358$		0			0
$359$			11.3137i			0.597115i	0.954392	+	0.298557i	$0.0965054\pi$
$359$			11.3137i			0.597115i	−0.954392	+	0.298557i	$0.903495\pi$
$360$		0			0
$361$		−	45.0000i		−	2.36842i
$362$		0			0
$363$	−7.77817	−	7.77817i	−0.408248	−	0.408248i
$364$		0			0
$365$	14.0000	−	14.0000i	0.732793	−	0.732793i
$366$		0			0
$367$	2.82843			0.147643			0.0738213	−	0.997271i	$-0.476481\pi$
$367$	2.82843			0.147643			0.0738213	+	0.997271i	$0.476481\pi$
$368$		0			0
$369$	4.00000			0.208232
$370$		0			0
$371$	14.1421	−	14.1421i	0.734223	−	0.734223i
$372$		0			0
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	0.625161	−	0.780496i	$-0.285033\pi$
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	−0.780496	+	0.625161i	$0.785033\pi$
$374$		0			0
$375$		−	11.3137i		−	0.584237i
$376$		0			0
$377$			6.00000i			0.309016i
$378$		0			0
$379$	11.3137	+	11.3137i	0.581146	+	0.581146i	0.935218	−	0.354072i	$-0.115203\pi$
$379$	11.3137	+	11.3137i	0.581146	+	0.581146i	−0.354072	+	0.935218i	$0.615203\pi$
$380$		0			0
$381$	6.00000	−	6.00000i	0.307389	−	0.307389i
$382$		0			0
$383$	28.2843			1.44526			0.722629	−	0.691236i	$-0.242933\pi$
$383$	28.2843			1.44526			0.722629	+	0.691236i	$0.242933\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.00000	+	7.00000i	0.354914	+	0.354914i	0.861934	−	0.507020i	$-0.169253\pi$
$389$	7.00000	+	7.00000i	0.354914	+	0.354914i	−0.507020	+	0.861934i	$0.669253\pi$
$390$		0			0
$391$		−	22.6274i		−	1.14432i
$392$		0			0
$393$		−	4.00000i		−	0.201773i
$394$		0			0
$395$	8.48528	+	8.48528i	0.426941	+	0.426941i
$396$		0			0
$397$	15.0000	−	15.0000i	0.752828	−	0.752828i	−0.222178	−	0.975006i	$-0.571317\pi$
$397$	15.0000	−	15.0000i	0.752828	−	0.752828i	0.975006	+	0.222178i	$0.0713165\pi$
$398$		0			0
$399$	−22.6274			−1.13279
$400$		0			0
$401$	20.0000			0.998752			0.499376	−	0.866385i	$-0.333563\pi$
$401$	20.0000			0.998752			0.499376	+	0.866385i	$0.333563\pi$
$402$		0			0
$403$	8.48528	−	8.48528i	0.422682	−	0.422682i
$404$		0			0
$405$	−1.00000	−	1.00000i	−0.0496904	−	0.0496904i
$406$		0			0
$407$		0			0
$408$		0			0
$409$			32.0000i			1.58230i	0.611623	+	0.791149i	$0.290517\pi$
$409$			32.0000i			1.58230i	−0.611623	+	0.791149i	$0.709483\pi$
$410$		0			0
$411$	8.48528	+	8.48528i	0.418548	+	0.418548i
$412$		0			0
$413$	24.0000	−	24.0000i	1.18096	−	1.18096i
$414$		0			0
$415$	−22.6274			−1.11074
$416$		0			0
$417$	4.00000			0.195881
$418$		0			0
$419$	5.65685	−	5.65685i	0.276355	−	0.276355i	−0.555297	−	0.831652i	$-0.687395\pi$
$419$	5.65685	−	5.65685i	0.276355	−	0.276355i	0.831652	+	0.555297i	$0.187395\pi$
$420$		0			0
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	0.452919	−	0.891552i	$-0.350383\pi$
$421$	−9.00000	−	9.00000i	−0.438633	−	0.438633i	−0.891552	+	0.452919i	$0.850383\pi$
$422$		0			0
$423$		−	11.3137i		−	0.550091i
$424$		0			0
$425$			12.0000i			0.582086i
$426$		0			0
$427$	2.82843	+	2.82843i	0.136877	+	0.136877i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.3137			−0.544962			−0.272481	−	0.962161i	$-0.587844\pi$
$431$	−11.3137			−0.544962			−0.272481	+	0.962161i	$0.587844\pi$
$432$		0			0
$433$	−8.00000			−0.384455			−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000			−0.384455			−0.192228	+	0.981350i	$0.561571\pi$
$434$		0			0
$435$	1.41421	−	1.41421i	0.0678064	−	0.0678064i
$436$		0			0
$437$	−32.0000	−	32.0000i	−1.53077	−	1.53077i
$438$		0			0
$439$		−	2.82843i		−	0.134993i	−0.997719	−	0.0674967i	$-0.978499\pi$
$439$		−	2.82843i		−	0.134993i	0.997719	−	0.0674967i	$-0.0215012\pi$
$440$		0			0
$441$			1.00000i			0.0476190i
$442$		0			0
$443$	−16.9706	−	16.9706i	−0.806296	−	0.806296i	0.177775	−	0.984071i	$-0.443110\pi$
$443$	−16.9706	−	16.9706i	−0.806296	−	0.806296i	−0.984071	+	0.177775i	$0.943110\pi$
$444$		0			0
$445$	−6.00000	+	6.00000i	−0.284427	+	0.284427i
$446$		0			0
$447$	12.7279			0.602010
$448$		0			0
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	2.00000	+	2.00000i	0.0939682	+	0.0939682i
$454$		0			0
$455$		−	16.9706i		−	0.795592i
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$		0			0
$459$	2.82843	+	2.82843i	0.132020	+	0.132020i
$460$		0			0
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	−0.915237	−	0.402916i	$-0.867997\pi$
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	0.402916	+	0.915237i	$0.367997\pi$
$462$		0			0
$463$	−31.1127			−1.44593			−0.722965	−	0.690885i	$-0.757221\pi$
$463$	−31.1127			−1.44593			−0.722965	+	0.690885i	$0.757221\pi$
$464$		0			0
$465$	−4.00000			−0.185496
$466$		0			0
$467$	5.65685	−	5.65685i	0.261768	−	0.261768i	−0.564004	−	0.825772i	$-0.690740\pi$
$467$	5.65685	−	5.65685i	0.261768	−	0.261768i	0.825772	+	0.564004i	$0.190740\pi$
$468$		0			0
$469$	−8.00000	−	8.00000i	−0.369406	−	0.369406i
$470$		0			0
$471$			21.2132i			0.977453i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	16.9706	+	16.9706i	0.778663	+	0.778663i
$476$		0			0
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$		0			0
$479$	−28.2843			−1.29234			−0.646171	−	0.763193i	$-0.723631\pi$
$479$	−28.2843			−1.29234			−0.646171	+	0.763193i	$0.723631\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$	−11.3137	+	11.3137i	−0.514792	+	0.514792i
$484$		0			0
$485$	16.0000	+	16.0000i	0.726523	+	0.726523i
$486$		0			0
$487$		−	2.82843i		−	0.128168i	−0.997944	−	0.0640841i	$-0.979587\pi$
$487$		−	2.82843i		−	0.128168i	0.997944	−	0.0640841i	$-0.0204126\pi$
$488$		0			0
$489$		−	16.0000i		−	0.723545i
$490$		0			0
$491$	8.48528	+	8.48528i	0.382935	+	0.382935i	0.872159	−	0.489223i	$-0.162720\pi$
$491$	8.48528	+	8.48528i	0.382935	+	0.382935i	−0.489223	+	0.872159i	$0.662720\pi$
$492$		0			0
$493$	−4.00000	+	4.00000i	−0.180151	+	0.180151i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−32.0000			−1.43540
$498$		0			0
$499$	19.7990	−	19.7990i	0.886325	−	0.886325i	−0.107843	−	0.994168i	$-0.534395\pi$
$499$	19.7990	−	19.7990i	0.886325	−	0.886325i	0.994168	+	0.107843i	$0.0343945\pi$
$500$		0			0
$501$	8.00000	+	8.00000i	0.357414	+	0.357414i
$502$		0			0
$503$			11.3137i			0.504453i	0.967668	+	0.252227i	$0.0811629\pi$
$503$			11.3137i			0.504453i	−0.967668	+	0.252227i	$0.918837\pi$
$504$		0			0
$505$			22.0000i			0.978987i
$506$		0			0
$507$	−3.53553	−	3.53553i	−0.157019	−	0.157019i
$508$		0			0
$509$	23.0000	−	23.0000i	1.01946	−	1.01946i	0.0196502	−	0.999807i	$-0.493745\pi$
$509$	23.0000	−	23.0000i	1.01946	−	1.01946i	0.999807	−	0.0196502i	$-0.00625524\pi$
$510$		0			0
$511$	39.5980			1.75171
$512$		0			0
$513$	8.00000			0.353209
$514$		0			0
$515$	−19.7990	+	19.7990i	−0.872448	+	0.872448i
$516$		0			0
$517$		0			0
$518$		0			0
$519$			7.07107i			0.310385i
$520$		0			0
$521$		−	12.0000i		−	0.525730i	−0.964833	−	0.262865i	$-0.915333\pi$
$521$		−	12.0000i		−	0.525730i	0.964833	−	0.262865i	$-0.0846673\pi$
$522$		0			0
$523$	−5.65685	−	5.65685i	−0.247357	−	0.247357i	0.572528	−	0.819885i	$-0.305963\pi$
$523$	−5.65685	−	5.65685i	−0.247357	−	0.247357i	−0.819885	+	0.572528i	$0.805963\pi$
$524$		0			0
$525$	6.00000	−	6.00000i	0.261861	−	0.261861i
$526$		0			0
$527$	11.3137			0.492833
$528$		0			0
$529$	−9.00000			−0.391304
$530$		0			0
$531$	−8.48528	+	8.48528i	−0.368230	+	0.368230i
$532$		0			0
$533$	−12.0000	−	12.0000i	−0.519778	−	0.519778i
$534$		0			0
$535$			16.9706i			0.733701i
$536$		0			0
$537$		−	4.00000i		−	0.172613i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−3.00000	+	3.00000i	−0.128980	+	0.128980i	−0.768650	−	0.639670i	$-0.779071\pi$
$541$	−3.00000	+	3.00000i	−0.128980	+	0.128980i	0.639670	+	0.768650i	$0.279071\pi$
$542$		0			0
$543$	−12.7279			−0.546207
$544$		0			0
$545$	6.00000			0.257012
$546$		0			0
$547$	5.65685	−	5.65685i	0.241870	−	0.241870i	−0.575754	−	0.817623i	$-0.695291\pi$
$547$	5.65685	−	5.65685i	0.241870	−	0.241870i	0.817623	+	0.575754i	$0.195291\pi$
$548$		0			0
$549$	−1.00000	−	1.00000i	−0.0426790	−	0.0426790i
$550$		0			0
$551$			11.3137i			0.481980i
$552$		0			0
$553$			24.0000i			1.02058i
$554$		0			0
$555$	−4.24264	−	4.24264i	−0.180090	−	0.180090i
$556$		0			0
$557$	−21.0000	+	21.0000i	−0.889799	+	0.889799i	−0.994503	−	0.104705i	$-0.966610\pi$
$557$	−21.0000	+	21.0000i	−0.889799	+	0.889799i	0.104705	+	0.994503i	$0.466610\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.65685	+	5.65685i	−0.238408	+	0.238408i	−0.816191	−	0.577783i	$-0.803918\pi$
$563$	−5.65685	+	5.65685i	−0.238408	+	0.238408i	0.577783	+	0.816191i	$0.303918\pi$
$564$		0			0
$565$	18.0000	+	18.0000i	0.757266	+	0.757266i
$566$		0			0
$567$		−	2.82843i		−	0.118783i
$568$		0			0
$569$		−	20.0000i		−	0.838444i	−0.907884	−	0.419222i	$-0.862303\pi$
$569$		−	20.0000i		−	0.838444i	0.907884	−	0.419222i	$-0.137697\pi$
$570$		0			0
$571$	−14.1421	−	14.1421i	−0.591830	−	0.591830i	0.346296	−	0.938125i	$-0.387439\pi$
$571$	−14.1421	−	14.1421i	−0.591830	−	0.591830i	−0.938125	+	0.346296i	$0.887439\pi$
$572$		0			0
$573$	4.00000	−	4.00000i	0.167102	−	0.167102i
$574$		0			0
$575$	16.9706			0.707721
$576$		0			0
$577$	22.0000			0.915872			0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000			0.915872			0.457936	+	0.888985i	$0.348589\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−32.0000	−	32.0000i	−1.32758	−	1.32758i
$582$		0			0
$583$		0			0
$584$		0			0
$585$			6.00000i			0.248069i
$586$		0			0
$587$	−2.82843	−	2.82843i	−0.116742	−	0.116742i	0.646323	−	0.763064i	$-0.276306\pi$
$587$	−2.82843	−	2.82843i	−0.116742	−	0.116742i	−0.763064	+	0.646323i	$0.776306\pi$
$588$		0			0
$589$	16.0000	−	16.0000i	0.659269	−	0.659269i
$590$		0			0
$591$	7.07107			0.290865
$592$		0			0
$593$	34.0000			1.39621			0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000			1.39621			0.698106	+	0.715994i	$0.254026\pi$
$594$		0			0
$595$	11.3137	−	11.3137i	0.463817	−	0.463817i
$596$		0			0
$597$	−6.00000	−	6.00000i	−0.245564	−	0.245564i
$598$		0			0
$599$			39.5980i			1.61793i	0.587857	+	0.808965i	$0.299972\pi$
$599$			39.5980i			1.61793i	−0.587857	+	0.808965i	$0.700028\pi$
$600$		0			0
$601$			14.0000i			0.571072i	0.958368	+	0.285536i	$0.0921716\pi$
$601$			14.0000i			0.571072i	−0.958368	+	0.285536i	$0.907828\pi$
$602$		0			0
$603$	2.82843	+	2.82843i	0.115182	+	0.115182i
$604$		0			0
$605$	11.0000	−	11.0000i	0.447214	−	0.447214i
$606$		0			0
$607$	42.4264			1.72203			0.861017	−	0.508576i	$-0.169828\pi$
$607$	42.4264			1.72203			0.861017	+	0.508576i	$0.169828\pi$
$608$		0			0
$609$	4.00000			0.162088
$610$		0			0
$611$	−33.9411	+	33.9411i	−1.37311	+	1.37311i
$612$		0			0
$613$	11.0000	+	11.0000i	0.444286	+	0.444286i	0.893449	−	0.449164i	$-0.148278\pi$
$613$	11.0000	+	11.0000i	0.444286	+	0.444286i	−0.449164	+	0.893449i	$0.648278\pi$
$614$		0			0
$615$			5.65685i			0.228106i
$616$		0			0
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$		0			0
$619$	−31.1127	−	31.1127i	−1.25052	−	1.25052i	−0.955485	−	0.295040i	$-0.904667\pi$
$619$	−31.1127	−	31.1127i	−1.25052	−	1.25052i	−0.295040	−	0.955485i	$-0.595333\pi$
$620$		0			0
$621$	4.00000	−	4.00000i	0.160514	−	0.160514i
$622$		0			0
$623$	−16.9706			−0.679911
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.0000	+	12.0000i	0.478471	+	0.478471i
$630$		0			0
$631$		−	8.48528i		−	0.337794i	−0.985634	−	0.168897i	$-0.945980\pi$
$631$		−	8.48528i		−	0.337794i	0.985634	−	0.168897i	$-0.0540205\pi$
$632$		0			0
$633$		−	12.0000i		−	0.476957i
$634$		0			0
$635$	8.48528	+	8.48528i	0.336728	+	0.336728i
$636$		0			0
$637$	3.00000	−	3.00000i	0.118864	−	0.118864i
$638$		0			0
$639$	11.3137			0.447563
$640$		0			0
$641$	−12.0000			−0.473972			−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000			−0.473972			−0.236986	+	0.971513i	$0.576159\pi$
$642$		0			0
$643$	−11.3137	+	11.3137i	−0.446169	+	0.446169i	−0.894079	−	0.447910i	$-0.852169\pi$
$643$	−11.3137	+	11.3137i	−0.446169	+	0.446169i	0.447910	+	0.894079i	$0.352169\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	39.5980i		−	1.55676i	−0.627795	−	0.778379i	$-0.716042\pi$
$647$		−	39.5980i		−	1.55676i	0.627795	−	0.778379i	$-0.283958\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−5.65685	−	5.65685i	−0.221710	−	0.221710i
$652$		0			0
$653$	−3.00000	+	3.00000i	−0.117399	+	0.117399i	−0.763366	−	0.645967i	$-0.776455\pi$
$653$	−3.00000	+	3.00000i	−0.117399	+	0.117399i	0.645967	+	0.763366i	$0.276455\pi$
$654$		0			0
$655$	5.65685			0.221032
$656$		0			0
$657$	−14.0000			−0.546192
$658$		0			0
$659$	14.1421	−	14.1421i	0.550899	−	0.550899i	−0.375801	−	0.926700i	$-0.622632\pi$
$659$	14.1421	−	14.1421i	0.550899	−	0.550899i	0.926700	+	0.375801i	$0.122632\pi$
$660$		0			0
$661$	19.0000	+	19.0000i	0.739014	+	0.739014i	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	19.0000	+	19.0000i	0.739014	+	0.739014i	−0.233373	+	0.972387i	$0.574976\pi$
$662$		0			0
$663$		−	16.9706i		−	0.659082i
$664$		0			0
$665$		−	32.0000i		−	1.24091i
$666$		0			0
$667$	5.65685	+	5.65685i	0.219034	+	0.219034i
$668$		0			0
$669$	−18.0000	+	18.0000i	−0.695920	+	0.695920i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.00000			−0.308377			−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000			−0.308377			−0.154189	+	0.988041i	$0.549276\pi$
$674$		0			0
$675$	−2.12132	+	2.12132i	−0.0816497	+	0.0816497i
$676$		0			0
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	0.993935	−	0.109973i	$-0.0350764\pi$
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	−0.109973	+	0.993935i	$0.535076\pi$
$678$		0			0
$679$			45.2548i			1.73672i
$680$		0			0
$681$		−	8.00000i		−	0.306561i
$682$		0			0
$683$	−22.6274	−	22.6274i	−0.865814	−	0.865814i	0.126192	−	0.992006i	$-0.459725\pi$
$683$	−22.6274	−	22.6274i	−0.865814	−	0.865814i	−0.992006	+	0.126192i	$0.959725\pi$
$684$		0			0
$685$	−12.0000	+	12.0000i	−0.458496	+	0.458496i
$686$		0			0
$687$	−24.0416			−0.917245
$688$		0			0
$689$	30.0000			1.14291
$690$		0			0
$691$	−28.2843	+	28.2843i	−1.07598	+	1.07598i	−0.0791192	+	0.996865i	$0.525211\pi$
$691$	−28.2843	+	28.2843i	−1.07598	+	1.07598i	−0.996865	+	0.0791192i	$0.974789\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			5.65685i			0.214577i
$696$		0			0
$697$		−	16.0000i		−	0.606043i
$698$		0			0
$699$	7.07107	+	7.07107i	0.267452	+	0.267452i
$700$		0			0
$701$	−33.0000	+	33.0000i	−1.24639	+	1.24639i	−0.289091	+	0.957302i	$0.593353\pi$
$701$	−33.0000	+	33.0000i	−1.24639	+	1.24639i	−0.957302	+	0.289091i	$0.906647\pi$
$702$		0			0
$703$	33.9411			1.28011
$704$		0			0
$705$	16.0000			0.602595
$706$		0			0
$707$	−31.1127	+	31.1127i	−1.17011	+	1.17011i
$708$		0			0
$709$	25.0000	+	25.0000i	0.938895	+	0.938895i	0.998238	−	0.0593429i	$-0.0189006\pi$
$709$	25.0000	+	25.0000i	0.938895	+	0.938895i	−0.0593429	+	0.998238i	$0.518901\pi$
$710$		0			0
$711$		−	8.48528i		−	0.318223i
$712$		0			0
$713$		−	16.0000i		−	0.599205i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−4.00000	+	4.00000i	−0.149383	+	0.149383i
$718$		0			0
$719$	−16.9706			−0.632895			−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$		0			0
$721$	−56.0000			−2.08555
$722$		0			0
$723$	−5.65685	+	5.65685i	−0.210381	+	0.210381i
$724$		0			0
$725$	−3.00000	−	3.00000i	−0.111417	−	0.111417i
$726$		0			0
$727$			42.4264i			1.57351i	0.617266	+	0.786754i	$0.288240\pi$
$727$			42.4264i			1.57351i	−0.617266	+	0.786754i	$0.711760\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	3.00000	−	3.00000i	0.110808	−	0.110808i	−0.649529	−	0.760337i	$-0.725034\pi$
$733$	3.00000	−	3.00000i	0.110808	−	0.110808i	0.760337	+	0.649529i	$0.225034\pi$
$734$		0			0
$735$	−1.41421			−0.0521641
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−25.4558	+	25.4558i	−0.936408	+	0.936408i	−0.998096	−	0.0616872i	$-0.980352\pi$
$739$	−25.4558	+	25.4558i	−0.936408	+	0.936408i	0.0616872	+	0.998096i	$0.480352\pi$
$740$		0			0
$741$	−24.0000	−	24.0000i	−0.881662	−	0.881662i
$742$		0			0
$743$		−	11.3137i		−	0.415060i	−0.978229	−	0.207530i	$-0.933458\pi$
$743$		−	11.3137i		−	0.415060i	0.978229	−	0.207530i	$-0.0665424\pi$
$744$		0			0
$745$			18.0000i			0.659469i
$746$		0			0
$747$	11.3137	+	11.3137i	0.413947	+	0.413947i
$748$		0			0
$749$	−24.0000	+	24.0000i	−0.876941	+	0.876941i
$750$		0			0
$751$	−8.48528			−0.309632			−0.154816	−	0.987943i	$-0.549479\pi$
$751$	−8.48528			−0.309632			−0.154816	+	0.987943i	$0.549479\pi$
$752$		0			0
$753$	8.00000			0.291536
$754$		0			0
$755$	−2.82843	+	2.82843i	−0.102937	+	0.102937i
$756$		0			0
$757$	15.0000	+	15.0000i	0.545184	+	0.545184i	0.925044	−	0.379860i	$-0.124028\pi$
$757$	15.0000	+	15.0000i	0.545184	+	0.545184i	−0.379860	+	0.925044i	$0.624028\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			36.0000i			1.30500i	0.757789	+	0.652499i	$0.226280\pi$
$761$			36.0000i			1.30500i	−0.757789	+	0.652499i	$0.773720\pi$
$762$		0			0
$763$	8.48528	+	8.48528i	0.307188	+	0.307188i
$764$		0			0
$765$	−4.00000	+	4.00000i	−0.144620	+	0.144620i
$766$		0			0
$767$	50.9117			1.83831
$768$		0			0
$769$	−32.0000			−1.15395			−0.576975	−	0.816762i	$-0.695767\pi$
$769$	−32.0000			−1.15395			−0.576975	+	0.816762i	$0.695767\pi$
$770$		0			0
$771$	1.41421	−	1.41421i	0.0509317	−	0.0509317i
$772$		0			0
$773$	−13.0000	−	13.0000i	−0.467578	−	0.467578i	0.433551	−	0.901129i	$-0.357260\pi$
$773$	−13.0000	−	13.0000i	−0.467578	−	0.467578i	−0.901129	+	0.433551i	$0.857260\pi$
$774$		0			0
$775$			8.48528i			0.304800i
$776$		0			0
$777$		−	12.0000i		−	0.430498i
$778$		0			0
$779$	−22.6274	−	22.6274i	−0.810711	−	0.810711i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.41421			−0.0505399
$784$		0			0
$785$	−30.0000			−1.07075
$786$		0			0
$787$	−22.6274	+	22.6274i	−0.806580	+	0.806580i	−0.984115	−	0.177534i	$-0.943188\pi$
$787$	−22.6274	+	22.6274i	−0.806580	+	0.806580i	0.177534	+	0.984115i	$0.443188\pi$
$788$		0			0
$789$	−20.0000	−	20.0000i	−0.712019	−	0.712019i
$790$		0			0
$791$			50.9117i			1.81021i
$792$		0			0
$793$			6.00000i			0.213066i
$794$		0			0
$795$	−7.07107	−	7.07107i	−0.250785	−	0.250785i
$796$		0			0
$797$	35.0000	−	35.0000i	1.23976	−	1.23976i	0.279666	−	0.960097i	$-0.409776\pi$
$797$	35.0000	−	35.0000i	1.23976	−	1.23976i	0.960097	−	0.279666i	$-0.0902238\pi$
$798$		0			0
$799$	−45.2548			−1.60100
$800$		0			0
$801$	6.00000			0.212000
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−16.0000	−	16.0000i	−0.563926	−	0.563926i
$806$		0			0
$807$			21.2132i			0.746740i
$808$		0			0
$809$		−	4.00000i		−	0.140633i	−0.997525	−	0.0703163i	$-0.977599\pi$
$809$		−	4.00000i		−	0.140633i	0.997525	−	0.0703163i	$-0.0224008\pi$
$810$		0			0
$811$	−28.2843	−	28.2843i	−0.993195	−	0.993195i	0.00678191	−	0.999977i	$-0.497841\pi$
$811$	−28.2843	−	28.2843i	−0.993195	−	0.993195i	−0.999977	+	0.00678191i	$0.997841\pi$
$812$		0			0
$813$	−6.00000	+	6.00000i	−0.210429	+	0.210429i
$814$		0			0
$815$	22.6274			0.792604
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−8.48528	+	8.48528i	−0.296500	+	0.296500i
$820$		0			0
$821$	−5.00000	−	5.00000i	−0.174501	−	0.174501i	0.614453	−	0.788954i	$-0.289377\pi$
$821$	−5.00000	−	5.00000i	−0.174501	−	0.174501i	−0.788954	+	0.614453i	$0.789377\pi$
$822$		0			0
$823$			25.4558i			0.887335i	0.896191	+	0.443667i	$0.146323\pi$
$823$			25.4558i			0.887335i	−0.896191	+	0.443667i	$0.853677\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.1421	+	14.1421i	0.491770	+	0.491770i	0.908864	−	0.417093i	$-0.136951\pi$
$827$	14.1421	+	14.1421i	0.491770	+	0.491770i	−0.417093	+	0.908864i	$0.636951\pi$
$828$		0			0
$829$	37.0000	−	37.0000i	1.28506	−	1.28506i	0.347314	−	0.937749i	$-0.387094\pi$
$829$	37.0000	−	37.0000i	1.28506	−	1.28506i	0.937749	−	0.347314i	$-0.112906\pi$
$830$		0			0
$831$	1.41421			0.0490585
$832$		0			0
$833$	4.00000			0.138592
$834$		0			0
$835$	−11.3137	+	11.3137i	−0.391527	+	0.391527i
$836$		0			0
$837$	2.00000	+	2.00000i	0.0691301	+	0.0691301i
$838$		0			0
$839$			45.2548i			1.56237i	0.624299	+	0.781185i	$0.285385\pi$
$839$			45.2548i			1.56237i	−0.624299	+	0.781185i	$0.714615\pi$
$840$		0			0
$841$			27.0000i			0.931034i
$842$		0			0
$843$	−15.5563	−	15.5563i	−0.535789	−	0.535789i
$844$		0			0
$845$	5.00000	−	5.00000i	0.172005	−	0.172005i
$846$		0			0
$847$	31.1127			1.06904
$848$		0			0
$849$	−4.00000			−0.137280
$850$		0			0
$851$	16.9706	−	16.9706i	0.581743	−	0.581743i
$852$		0			0
$853$	−11.0000	−	11.0000i	−0.376633	−	0.376633i	0.493253	−	0.869886i	$-0.335808\pi$
$853$	−11.0000	−	11.0000i	−0.376633	−	0.376633i	−0.869886	+	0.493253i	$0.835808\pi$
$854$		0			0
$855$			11.3137i			0.386921i
$856$		0			0
$857$		−	20.0000i		−	0.683187i	−0.939848	−	0.341593i	$-0.889033\pi$
$857$		−	20.0000i		−	0.683187i	0.939848	−	0.341593i	$-0.110967\pi$
$858$		0			0
$859$	−5.65685	−	5.65685i	−0.193009	−	0.193009i	0.603986	−	0.796995i	$-0.293578\pi$
$859$	−5.65685	−	5.65685i	−0.193009	−	0.193009i	−0.796995	+	0.603986i	$0.793578\pi$
$860$		0			0
$861$	−8.00000	+	8.00000i	−0.272639	+	0.272639i
$862$		0			0
$863$	−5.65685			−0.192562			−0.0962808	−	0.995354i	$-0.530695\pi$
$863$	−5.65685			−0.192562			−0.0962808	+	0.995354i	$0.530695\pi$
$864$		0			0
$865$	−10.0000			−0.340010
$866$		0			0
$867$	−0.707107	+	0.707107i	−0.0240146	+	0.0240146i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	16.9706i		−	0.575026i
$872$		0			0
$873$		−	16.0000i		−	0.541518i
$874$		0			0
$875$	22.6274	+	22.6274i	0.764946	+	0.764946i
$876$		0			0
$877$	23.0000	−	23.0000i	0.776655	−	0.776655i	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	23.0000	−	23.0000i	0.776655	−	0.776655i	0.979260	+	0.202606i	$0.0649409\pi$
$878$		0			0
$879$	18.3848			0.620103
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	16.9706	−	16.9706i	0.571105	−	0.571105i	−0.361332	−	0.932437i	$-0.617678\pi$
$883$	16.9706	−	16.9706i	0.571105	−	0.571105i	0.932437	+	0.361332i	$0.117678\pi$
$884$		0			0
$885$	−12.0000	−	12.0000i	−0.403376	−	0.403376i
$886$		0			0
$887$			16.9706i			0.569816i	0.958555	+	0.284908i	$0.0919630\pi$
$887$			16.9706i			0.569816i	−0.958555	+	0.284908i	$0.908037\pi$
$888$		0			0
$889$			24.0000i			0.804934i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−64.0000	+	64.0000i	−2.14168	+	2.14168i
$894$		0			0
$895$	5.65685			0.189088
$896$		0			0
$897$	−24.0000			−0.801337
$898$		0			0
$899$	−2.82843	+	2.82843i	−0.0943333	+	0.0943333i
$900$		0			0
$901$	20.0000	+	20.0000i	0.666297	+	0.666297i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	18.0000i		−	0.598340i
$906$		0			0
$907$	22.6274	+	22.6274i	0.751331	+	0.751331i	0.974728	−	0.223397i	$-0.0717145\pi$
$907$	22.6274	+	22.6274i	0.751331	+	0.751331i	−0.223397	+	0.974728i	$0.571714\pi$
$908$		0			0
$909$	11.0000	−	11.0000i	0.364847	−	0.364847i
$910$		0			0
$911$	−5.65685			−0.187420			−0.0937100	−	0.995600i	$-0.529873\pi$
$911$	−5.65685			−0.187420			−0.0937100	+	0.995600i	$0.529873\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.41421	−	1.41421i	0.0467525	−	0.0467525i
$916$		0			0
$917$	8.00000	+	8.00000i	0.264183	+	0.264183i
$918$		0			0
$919$			2.82843i			0.0933012i	0.998911	+	0.0466506i	$0.0148547\pi$
$919$			2.82843i			0.0933012i	−0.998911	+	0.0466506i	$0.985145\pi$
$920$		0			0
$921$			4.00000i			0.131804i
$922$		0			0
$923$	−33.9411	−	33.9411i	−1.11719	−	1.11719i
$924$		0			0
$925$	−9.00000	+	9.00000i	−0.295918	+	0.295918i
$926$		0			0
$927$	19.7990			0.650284
$928$		0			0
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	5.65685	−	5.65685i	0.185396	−	0.185396i
$932$		0			0
$933$	−20.0000	−	20.0000i	−0.654771	−	0.654771i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			42.0000i			1.37208i	0.727564	+	0.686040i	$0.240653\pi$
$937$			42.0000i			1.37208i	−0.727564	+	0.686040i	$0.759347\pi$
$938$		0			0
$939$	−11.3137	−	11.3137i	−0.369209	−	0.369209i
$940$		0			0
$941$	37.0000	−	37.0000i	1.20617	−	1.20617i	0.233906	−	0.972259i	$-0.424849\pi$
$941$	37.0000	−	37.0000i	1.20617	−	1.20617i	0.972259	−	0.233906i	$-0.0751509\pi$
$942$		0			0
$943$	−22.6274			−0.736850
$944$		0			0
$945$	4.00000			0.130120
$946$		0			0
$947$	−36.7696	+	36.7696i	−1.19485	+	1.19485i	−0.219161	+	0.975689i	$0.570332\pi$
$947$	−36.7696	+	36.7696i	−1.19485	+	1.19485i	−0.975689	+	0.219161i	$0.929668\pi$
$948$		0			0
$949$	42.0000	+	42.0000i	1.36338	+	1.36338i
$950$		0			0
$951$			21.2132i			0.687885i
$952$		0			0
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$		0			0
$955$	5.65685	+	5.65685i	0.183052	+	0.183052i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−33.9411			−1.09602
$960$		0			0
$961$	−23.0000			−0.741935
$962$		0			0
$963$	8.48528	−	8.48528i	0.273434	−	0.273434i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	42.4264i		−	1.36434i	−0.731193	−	0.682171i	$-0.761036\pi$
$967$		−	42.4264i		−	1.36434i	0.731193	−	0.682171i	$-0.238964\pi$
$968$		0			0
$969$		−	32.0000i		−	1.02799i
$970$		0			0
$971$	−16.9706	−	16.9706i	−0.544611	−	0.544611i	0.380266	−	0.924877i	$-0.375832\pi$
$971$	−16.9706	−	16.9706i	−0.544611	−	0.544611i	−0.924877	+	0.380266i	$0.875832\pi$
$972$		0			0
$973$	−8.00000	+	8.00000i	−0.256468	+	0.256468i
$974$		0			0
$975$	12.7279			0.407620
$976$		0			0
$977$	36.0000			1.15174			0.575871	−	0.817541i	$-0.304663\pi$
$977$	36.0000			1.15174			0.575871	+	0.817541i	$0.304663\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−3.00000	−	3.00000i	−0.0957826	−	0.0957826i
$982$		0			0
$983$			16.9706i			0.541277i	0.962681	+	0.270638i	$0.0872348\pi$
$983$			16.9706i			0.541277i	−0.962681	+	0.270638i	$0.912765\pi$
$984$		0			0
$985$			10.0000i			0.318626i
$986$		0			0
$987$	22.6274	+	22.6274i	0.720239	+	0.720239i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−25.4558			−0.808632			−0.404316	−	0.914619i	$-0.632490\pi$
$991$	−25.4558			−0.808632			−0.404316	+	0.914619i	$0.632490\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$	8.48528	−	8.48528i	0.269002	−	0.269002i
$996$		0			0
$997$	5.00000	+	5.00000i	0.158352	+	0.158352i	0.781836	−	0.623484i	$-0.214283\pi$
$997$	5.00000	+	5.00000i	0.158352	+	0.158352i	−0.623484	+	0.781836i	$0.714283\pi$
$998$		0			0
$999$			4.24264i			0.134231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1536.2.j.c.385.2	yes	4
3.2	odd	2		4608.2.k.y.3457.2		4
4.3	odd	2	inner	1536.2.j.c.385.1	yes	4
8.3	odd	2		1536.2.j.b.385.2	yes	4
8.5	even	2		1536.2.j.b.385.1	✓	4
12.11	even	2		4608.2.k.y.3457.1		4
16.3	odd	4	inner	1536.2.j.c.1153.1	yes	4
16.5	even	4		1536.2.j.b.1153.1	yes	4
16.11	odd	4		1536.2.j.b.1153.2	yes	4
16.13	even	4	inner	1536.2.j.c.1153.2	yes	4
24.5	odd	2		4608.2.k.bb.3457.2		4
24.11	even	2		4608.2.k.bb.3457.1		4
32.3	odd	8		3072.2.a.b.1.1		2
32.5	even	8		3072.2.d.c.1537.4		4
32.11	odd	8		3072.2.d.c.1537.3		4
32.13	even	8		3072.2.a.b.1.2		2
32.19	odd	8		3072.2.a.h.1.2		2
32.21	even	8		3072.2.d.c.1537.1		4
32.27	odd	8		3072.2.d.c.1537.2		4
32.29	even	8		3072.2.a.h.1.1		2
48.5	odd	4		4608.2.k.bb.1153.1		4
48.11	even	4		4608.2.k.bb.1153.2		4
48.29	odd	4		4608.2.k.y.1153.1		4
48.35	even	4		4608.2.k.y.1153.2		4
96.29	odd	8		9216.2.a.i.1.2		2
96.35	even	8		9216.2.a.h.1.2		2
96.77	odd	8		9216.2.a.h.1.1		2
96.83	even	8		9216.2.a.i.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1536.2.j.b.385.1	✓	4	8.5	even	2
1536.2.j.b.385.2	yes	4	8.3	odd	2
1536.2.j.b.1153.1	yes	4	16.5	even	4
1536.2.j.b.1153.2	yes	4	16.11	odd	4
1536.2.j.c.385.1	yes	4	4.3	odd	2	inner
1536.2.j.c.385.2	yes	4	1.1	even	1	trivial
1536.2.j.c.1153.1	yes	4	16.3	odd	4	inner
1536.2.j.c.1153.2	yes	4	16.13	even	4	inner
3072.2.a.b.1.1		2	32.3	odd	8
3072.2.a.b.1.2		2	32.13	even	8
3072.2.a.h.1.1		2	32.29	even	8
3072.2.a.h.1.2		2	32.19	odd	8
3072.2.d.c.1537.1		4	32.21	even	8
3072.2.d.c.1537.2		4	32.27	odd	8
3072.2.d.c.1537.3		4	32.11	odd	8
3072.2.d.c.1537.4		4	32.5	even	8
4608.2.k.y.1153.1		4	48.29	odd	4
4608.2.k.y.1153.2		4	48.35	even	4
4608.2.k.y.3457.1		4	12.11	even	2
4608.2.k.y.3457.2		4	3.2	odd	2
4608.2.k.bb.1153.1		4	48.5	odd	4
4608.2.k.bb.1153.2		4	48.11	even	4
4608.2.k.bb.3457.1		4	24.11	even	2
4608.2.k.bb.3457.2		4	24.5	odd	2
9216.2.a.h.1.1		2	96.77	odd	8
9216.2.a.h.1.2		2	96.35	even	8
9216.2.a.i.1.1		2	96.83	even	8
9216.2.a.i.1.2		2	96.29	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1536 = 2^{9} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1536.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.82843i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{5} +2.82843i q^{7} -1.00000i q^{9} +(-3.00000 + 3.00000i) q^{13} +1.41421 q^{15} -4.00000 q^{17} +(-5.65685 + 5.65685i) q^{19} +(2.00000 + 2.00000i) q^{21} +5.65685i q^{23} -3.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(1.00000 - 1.00000i) q^{29} -2.82843 q^{31} +(-2.82843 + 2.82843i) q^{35} +(-3.00000 - 3.00000i) q^{37} +4.24264i q^{39} +4.00000i q^{41} +(1.00000 - 1.00000i) q^{45} +11.3137 q^{47} -1.00000 q^{49} +(-2.82843 + 2.82843i) q^{51} +(-5.00000 - 5.00000i) q^{53} +8.00000i q^{57} +(-8.48528 - 8.48528i) q^{59} +(1.00000 - 1.00000i) q^{61} +2.82843 q^{63} -6.00000 q^{65} +(-2.82843 + 2.82843i) q^{67} +(4.00000 + 4.00000i) q^{69} +11.3137i q^{71} -14.0000i q^{73} +(-2.12132 - 2.12132i) q^{75} +8.48528 q^{79} -1.00000 q^{81} +(-11.3137 + 11.3137i) q^{83} +(-4.00000 - 4.00000i) q^{85} -1.41421i q^{87} +6.00000i q^{89} +(-8.48528 - 8.48528i) q^{91} +(-2.00000 + 2.00000i) q^{93} -11.3137 q^{95} +16.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5}+O(q^{10}) \) 4 * q + 4 * q^5	\( 4 q + 4 q^{5} - 12 q^{13} - 16 q^{17} + 8 q^{21} + 4 q^{29} - 12 q^{37} + 4 q^{45} - 4 q^{49} - 20 q^{53} + 4 q^{61} - 24 q^{65} + 16 q^{69} - 4 q^{81} - 16 q^{85} - 8 q^{93} + 64 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 - 12 * q^13 - 16 * q^17 + 8 * q^21 + 4 * q^29 - 12 * q^37 + 4 * q^45 - 4 * q^49 - 20 * q^53 + 4 * q^61 - 24 * q^65 + 16 * q^69 - 4 * q^81 - 16 * q^85 - 8 * q^93 + 64 * q^97

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