LMFDB - Embedded newform 1152.2.v.a.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(145,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("1152.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.v (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			433.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1152.433
Dual form			1152.2.v.a.721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12132 + 2.70711i) q^{5} +(-1.00000 - 1.00000i) q^{7} +O(q^{10})$	$q+(-1.12132 + 2.70711i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-4.12132 - 1.70711i) q^{11} +(0.292893 + 0.707107i) q^{13} -2.82843i q^{17} +(-1.53553 - 3.70711i) q^{19} +(5.82843 - 5.82843i) q^{23} +(-2.53553 - 2.53553i) q^{25} +(3.12132 - 1.29289i) q^{29} +4.00000 q^{31} +(3.82843 - 1.58579i) q^{35} +(0.292893 - 0.707107i) q^{37} +(0.171573 - 0.171573i) q^{41} +(-4.70711 - 1.94975i) q^{43} +0.343146i q^{47} -5.00000i q^{49} +(1.12132 + 0.464466i) q^{53} +(9.24264 - 9.24264i) q^{55} +(-1.87868 + 4.53553i) q^{59} +(1.70711 - 0.707107i) q^{61} -2.24264 q^{65} +(5.53553 - 2.29289i) q^{67} +(-5.82843 - 5.82843i) q^{71} +(7.00000 - 7.00000i) q^{73} +(2.41421 + 5.82843i) q^{77} +6.00000i q^{79} +(1.87868 + 4.53553i) q^{83} +(7.65685 + 3.17157i) q^{85} +(-8.65685 - 8.65685i) q^{89} +(0.414214 - 1.00000i) q^{91} +11.7574 q^{95} -18.4853 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q + 4 * q^5 - 4 * q^7	$ 4 q + 4 q^{5} - 4 q^{7} - 8 q^{11} + 4 q^{13} + 8 q^{19} + 12 q^{23} + 4 q^{25} + 4 q^{29} + 16 q^{31} + 4 q^{35} + 4 q^{37} + 12 q^{41} - 16 q^{43} - 4 q^{53} + 20 q^{55} - 16 q^{59} + 4 q^{61} + 8 q^{65} + 8 q^{67} - 12 q^{71} + 28 q^{73} + 4 q^{77} + 16 q^{83} + 8 q^{85} - 12 q^{89} - 4 q^{91} + 64 q^{95} - 40 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 - 4 * q^7 - 8 * q^11 + 4 * q^13 + 8 * q^19 + 12 * q^23 + 4 * q^25 + 4 * q^29 + 16 * q^31 + 4 * q^35 + 4 * q^37 + 12 * q^41 - 16 * q^43 - 4 * q^53 + 20 * q^55 - 16 * q^59 + 4 * q^61 + 8 * q^65 + 8 * q^67 - 12 * q^71 + 28 * q^73 + 4 * q^77 + 16 * q^83 + 8 * q^85 - 12 * q^89 - 4 * q^91 + 64 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.12132	+	2.70711i	−0.501470	+	1.21065i	0.447214	+	0.894427i	$0.352416\pi$
$5$	−1.12132	+	2.70711i	−0.501470	+	1.21065i	−0.948683	+	0.316228i	$0.897584\pi$
$6$		0			0
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.12132	−	1.70711i	−1.24262	−	0.514712i	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	−4.12132	−	1.70711i	−1.24262	−	0.514712i	−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	0.292893	+	0.707107i	0.0812340	+	0.196116i	0.959278	−	0.282464i	$-0.0911517\pi$
$13$	0.292893	+	0.707107i	0.0812340	+	0.196116i	−0.878044	+	0.478580i	$0.841152\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	2.82843i		−	0.685994i	−0.939336	−	0.342997i	$-0.888558\pi$
$17$		−	2.82843i		−	0.685994i	0.939336	−	0.342997i	$-0.111442\pi$
$18$		0			0
$19$	−1.53553	−	3.70711i	−0.352276	−	0.850469i	−0.996339	−	0.0854961i	$-0.972752\pi$
$19$	−1.53553	−	3.70711i	−0.352276	−	0.850469i	0.644063	−	0.764973i	$-0.277248\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.82843	−	5.82843i	1.21531	−	1.21531i	0.246055	−	0.969256i	$-0.420866\pi$
$23$	5.82843	−	5.82843i	1.21531	−	1.21531i	0.969256	−	0.246055i	$-0.0791345\pi$
$24$		0			0
$25$	−2.53553	−	2.53553i	−0.507107	−	0.507107i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.12132	−	1.29289i	0.579615	−	0.240084i	−0.0735609	−	0.997291i	$-0.523436\pi$
$29$	3.12132	−	1.29289i	0.579615	−	0.240084i	0.653176	+	0.757206i	$0.273436\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.82843	−	1.58579i	0.647122	−	0.268047i
$36$		0			0
$37$	0.292893	−	0.707107i	0.0481513	−	0.116248i	−0.897974	−	0.440049i	$-0.854961\pi$
$37$	0.292893	−	0.707107i	0.0481513	−	0.116248i	0.946125	+	0.323802i	$0.104961\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.171573	−	0.171573i	0.0267952	−	0.0267952i	−0.693582	−	0.720377i	$-0.743969\pi$
$41$	0.171573	−	0.171573i	0.0267952	−	0.0267952i	0.720377	+	0.693582i	$0.243969\pi$
$42$		0			0
$43$	−4.70711	−	1.94975i	−0.717827	−	0.297334i	−0.00628798	−	0.999980i	$-0.502002\pi$
$43$	−4.70711	−	1.94975i	−0.717827	−	0.297334i	−0.711539	+	0.702647i	$0.752002\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			0.343146i			0.0500530i	0.999687	+	0.0250265i	$0.00796701\pi$
$47$			0.343146i			0.0500530i	−0.999687	+	0.0250265i	$0.992033\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.12132	+	0.464466i	0.154025	+	0.0637993i	0.458364	−	0.888764i	$-0.348436\pi$
$53$	1.12132	+	0.464466i	0.154025	+	0.0637993i	−0.304339	+	0.952564i	$0.598436\pi$
$54$		0			0
$55$	9.24264	−	9.24264i	1.24628	−	1.24628i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.87868	+	4.53553i	−0.244583	+	0.590476i	−0.997727	−	0.0673793i	$-0.978536\pi$
$59$	−1.87868	+	4.53553i	−0.244583	+	0.590476i	0.753144	+	0.657855i	$0.228536\pi$
$60$		0			0
$61$	1.70711	−	0.707107i	0.218573	−	0.0905357i	−0.270710	−	0.962661i	$-0.587259\pi$
$61$	1.70711	−	0.707107i	0.218573	−	0.0905357i	0.489283	+	0.872125i	$0.337259\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.24264			−0.278165
$66$		0			0
$67$	5.53553	−	2.29289i	0.676273	−	0.280121i	−0.0179949	−	0.999838i	$-0.505728\pi$
$67$	5.53553	−	2.29289i	0.676273	−	0.280121i	0.694268	+	0.719717i	$0.255728\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.82843	−	5.82843i	−0.691707	−	0.691707i	0.270900	−	0.962607i	$-0.412679\pi$
$71$	−5.82843	−	5.82843i	−0.691707	−	0.691707i	−0.962607	+	0.270900i	$0.912679\pi$
$72$		0			0
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	−0.166717	−	0.986005i	$-0.553317\pi$
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	0.986005	+	0.166717i	$0.0533166\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.41421	+	5.82843i	0.275125	+	0.664211i
$78$		0			0
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.87868	+	4.53553i	0.206212	+	0.497840i	0.992821	−	0.119612i	$-0.0381651\pi$
$83$	1.87868	+	4.53553i	0.206212	+	0.497840i	−0.786609	+	0.617452i	$0.788165\pi$
$84$		0			0
$85$	7.65685	+	3.17157i	0.830502	+	0.344005i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.65685	−	8.65685i	−0.917625	−	0.917625i	0.0792315	−	0.996856i	$-0.474753\pi$
$89$	−8.65685	−	8.65685i	−0.917625	−	0.917625i	−0.996856	+	0.0792315i	$0.974753\pi$
$90$		0			0
$91$	0.414214	−	1.00000i	0.0434214	−	0.104828i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11.7574			1.20628
$96$		0			0
$97$	−18.4853			−1.87690			−0.938448	−	0.345421i	$-0.887736\pi$
$97$	−18.4853			−1.87690			−0.938448	+	0.345421i	$0.887736\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.36396	−	3.29289i	0.135719	−	0.327655i	−0.841379	−	0.540446i	$-0.818255\pi$
$101$	1.36396	−	3.29289i	0.135719	−	0.327655i	0.977098	+	0.212791i	$0.0682554\pi$
$102$		0			0
$103$	−9.48528	−	9.48528i	−0.934613	−	0.934613i	0.0633771	−	0.997990i	$-0.479813\pi$
$103$	−9.48528	−	9.48528i	−0.934613	−	0.934613i	−0.997990	+	0.0633771i	$0.979813\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.12132	−	1.70711i	−0.398423	−	0.165032i	0.174470	−	0.984663i	$-0.444179\pi$
$107$	−4.12132	−	1.70711i	−0.398423	−	0.165032i	−0.572893	+	0.819630i	$0.694179\pi$
$108$		0			0
$109$	−5.70711	−	13.7782i	−0.546642	−	1.31971i	−0.919962	−	0.392007i	$-0.871781\pi$
$109$	−5.70711	−	13.7782i	−0.546642	−	1.31971i	0.373320	−	0.927702i	$-0.378219\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	6.34315i		−	0.596713i	−0.954455	−	0.298356i	$-0.903562\pi$
$113$		−	6.34315i		−	0.596713i	0.954455	−	0.298356i	$-0.0964384\pi$
$114$		0			0
$115$	9.24264	+	22.3137i	0.861881	+	2.08076i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.82843	+	2.82843i	−0.259281	+	0.259281i
$120$		0			0
$121$	6.29289	+	6.29289i	0.572081	+	0.572081i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.82843	+	1.58579i	−0.342425	+	0.141837i
$126$		0			0
$127$	−12.9706			−1.15095			−0.575476	−	0.817819i	$-0.695183\pi$
$127$	−12.9706			−1.15095			−0.575476	+	0.817819i	$0.695183\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−16.3640	+	6.77817i	−1.42973	+	0.592212i	−0.957284	−	0.289150i	$-0.906627\pi$
$131$	−16.3640	+	6.77817i	−1.42973	+	0.592212i	−0.472442	+	0.881362i	$0.656627\pi$
$132$		0			0
$133$	−2.17157	+	5.24264i	−0.188299	+	0.454595i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.65685	−	8.65685i	0.739605	−	0.739605i	−0.232897	−	0.972502i	$-0.574820\pi$
$137$	8.65685	−	8.65685i	0.739605	−	0.739605i	0.972502	+	0.232897i	$0.0748204\pi$
$138$		0			0
$139$	−13.1924	−	5.46447i	−1.11896	−	0.463490i	−0.254948	−	0.966955i	$-0.582058\pi$
$139$	−13.1924	−	5.46447i	−1.11896	−	0.463490i	−0.864016	+	0.503465i	$0.832058\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	3.41421i		−	0.285511i
$144$		0			0
$145$			9.89949i			0.822108i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.6066	+	6.46447i	1.27854	+	0.529590i	0.915551	−	0.402203i	$-0.131755\pi$
$149$	15.6066	+	6.46447i	1.27854	+	0.529590i	0.362992	+	0.931792i	$0.381755\pi$
$150$		0			0
$151$	1.48528	−	1.48528i	0.120870	−	0.120870i	−0.644084	−	0.764955i	$-0.722761\pi$
$151$	1.48528	−	1.48528i	0.120870	−	0.120870i	0.764955	+	0.644084i	$0.222761\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.48528	+	10.8284i	−0.360266	+	0.869760i
$156$		0			0
$157$	1.70711	−	0.707107i	0.136242	−	0.0564333i	−0.313521	−	0.949581i	$-0.601509\pi$
$157$	1.70711	−	0.707107i	0.136242	−	0.0564333i	0.449763	+	0.893148i	$0.351509\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.6569			−0.918689
$162$		0			0
$163$	−0.464466	+	0.192388i	−0.0363798	+	0.0150690i	−0.400799	−	0.916166i	$-0.631267\pi$
$163$	−0.464466	+	0.192388i	−0.0363798	+	0.0150690i	0.364419	+	0.931235i	$0.381267\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.6569	+	14.6569i	1.13418	+	1.13418i	0.989475	+	0.144707i	$0.0462239\pi$
$167$	14.6569	+	14.6569i	1.13418	+	1.13418i	0.144707	+	0.989475i	$0.453776\pi$
$168$		0			0
$169$	8.77817	−	8.77817i	0.675244	−	0.675244i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.12132	−	7.53553i	−0.237310	−	0.572916i	0.759693	−	0.650282i	$-0.225349\pi$
$173$	−3.12132	−	7.53553i	−0.237310	−	0.572916i	−0.997003	+	0.0773656i	$0.975349\pi$
$174$		0			0
$175$			5.07107i			0.383337i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.63604	−	3.94975i	−0.122283	−	0.295218i	0.850870	−	0.525377i	$-0.176076\pi$
$179$	−1.63604	−	3.94975i	−0.122283	−	0.295218i	−0.973153	+	0.230159i	$0.926076\pi$
$180$		0			0
$181$	16.1924	+	6.70711i	1.20357	+	0.498535i	0.892151	−	0.451737i	$-0.149196\pi$
$181$	16.1924	+	6.70711i	1.20357	+	0.498535i	0.311420	+	0.950272i	$0.399196\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.58579	+	1.58579i	0.116589	+	0.116589i
$186$		0			0
$187$	−4.82843	+	11.6569i	−0.353090	+	0.852434i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	−1.51472			−0.109032			−0.0545159	−	0.998513i	$-0.517362\pi$
$193$	−1.51472			−0.109032			−0.0545159	+	0.998513i	$0.517362\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.63604	+	11.1924i	−0.330304	+	0.797425i	0.668264	+	0.743924i	$0.267038\pi$
$197$	−4.63604	+	11.1924i	−0.330304	+	0.797425i	−0.998568	+	0.0535002i	$0.982962\pi$
$198$		0			0
$199$	15.9706	+	15.9706i	1.13212	+	1.13212i	0.989824	+	0.142300i	$0.0454496\pi$
$199$	15.9706	+	15.9706i	1.13212	+	1.13212i	0.142300	+	0.989824i	$0.454550\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.41421	−	1.82843i	−0.309817	−	0.128330i
$204$		0			0
$205$	0.272078	+	0.656854i	0.0190027	+	0.0458767i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			17.8995i			1.23813i
$210$		0			0
$211$	−7.53553	−	18.1924i	−0.518768	−	1.25242i	−0.938661	−	0.344842i	$-0.887932\pi$
$211$	−7.53553	−	18.1924i	−0.518768	−	1.25242i	0.419893	−	0.907574i	$-0.362068\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	10.5563	−	10.5563i	0.719937	−	0.719937i
$216$		0			0
$217$	−4.00000	−	4.00000i	−0.271538	−	0.271538i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.00000	−	0.828427i	0.134535	−	0.0557260i
$222$		0			0
$223$	20.9706			1.40429			0.702146	−	0.712033i	$-0.252225\pi$
$223$	20.9706			1.40429			0.702146	+	0.712033i	$0.252225\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.6066	−	7.70711i	1.23496	−	0.511539i	0.332826	−	0.942988i	$-0.391998\pi$
$227$	18.6066	−	7.70711i	1.23496	−	0.511539i	0.902137	+	0.431449i	$0.141998\pi$
$228$		0			0
$229$	−9.22183	+	22.2635i	−0.609395	+	1.47121i	0.254264	+	0.967135i	$0.418167\pi$
$229$	−9.22183	+	22.2635i	−0.609395	+	1.47121i	−0.863659	+	0.504076i	$0.831833\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.65685	−	2.65685i	0.174056	−	0.174056i	−0.614703	−	0.788759i	$-0.710724\pi$
$233$	2.65685	−	2.65685i	0.174056	−	0.174056i	0.788759	+	0.614703i	$0.210724\pi$
$234$		0			0
$235$	−0.928932	−	0.384776i	−0.0605969	−	0.0251000i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			5.31371i			0.343715i	0.985122	+	0.171858i	$0.0549769\pi$
$239$			5.31371i			0.343715i	−0.985122	+	0.171858i	$0.945023\pi$
$240$		0			0
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.5355	+	5.60660i	0.864754	+	0.358193i
$246$		0			0
$247$	2.17157	−	2.17157i	0.138174	−	0.138174i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.60660	−	15.9497i	0.417005	−	1.00674i	−0.566205	−	0.824264i	$-0.691589\pi$
$251$	6.60660	−	15.9497i	0.417005	−	1.00674i	0.983210	−	0.182475i	$-0.0584109\pi$
$252$		0			0
$253$	−33.9706	+	14.0711i	−2.13571	+	0.884640i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	−1.00000	+	0.414214i	−0.0621370	+	0.0257380i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.82843	−	5.82843i	−0.359396	−	0.359396i	0.504194	−	0.863590i	$-0.331790\pi$
$263$	−5.82843	−	5.82843i	−0.359396	−	0.359396i	−0.863590	+	0.504194i	$0.831790\pi$
$264$		0			0
$265$	−2.51472	+	2.51472i	−0.154478	+	0.154478i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.12132	−	22.0208i	−0.556137	−	1.34263i	−0.912803	−	0.408401i	$-0.866087\pi$
$269$	−9.12132	−	22.0208i	−0.556137	−	1.34263i	0.356666	−	0.934232i	$-0.383913\pi$
$270$		0			0
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.12132	+	14.7782i	0.369130	+	0.891157i
$276$		0			0
$277$	1.70711	+	0.707107i	0.102570	+	0.0424859i	0.433378	−	0.901212i	$-0.357321\pi$
$277$	1.70711	+	0.707107i	0.102570	+	0.0424859i	−0.330808	+	0.943698i	$0.607321\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.8284	+	11.8284i	0.705625	+	0.705625i	0.965612	−	0.259987i	$-0.0837184\pi$
$281$	11.8284	+	11.8284i	0.705625	+	0.705625i	−0.259987	+	0.965612i	$0.583718\pi$
$282$		0			0
$283$	−5.77817	+	13.9497i	−0.343477	+	0.829226i	0.653882	+	0.756596i	$0.273139\pi$
$283$	−5.77817	+	13.9497i	−0.343477	+	0.829226i	−0.997359	+	0.0726300i	$0.976861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.343146			−0.0202553
$288$		0			0
$289$	9.00000			0.529412
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.60660	+	23.1924i	−0.561224	+	1.35491i	0.347565	+	0.937656i	$0.387009\pi$
$293$	−9.60660	+	23.1924i	−0.561224	+	1.35491i	−0.908788	+	0.417258i	$0.862991\pi$
$294$		0			0
$295$	−10.1716	−	10.1716i	−0.592212	−	0.592212i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.82843	+	2.41421i	0.337067	+	0.139618i
$300$		0			0
$301$	2.75736	+	6.65685i	0.158932	+	0.383695i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			5.41421i			0.310017i
$306$		0			0
$307$	6.94975	+	16.7782i	0.396643	+	0.957581i	0.988456	+	0.151506i	$0.0484123\pi$
$307$	6.94975	+	16.7782i	0.396643	+	0.957581i	−0.591813	+	0.806075i	$0.701588\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.65685	+	2.65685i	−0.150656	+	0.150656i	−0.778411	−	0.627755i	$-0.783974\pi$
$311$	−2.65685	+	2.65685i	−0.150656	+	0.150656i	0.627755	+	0.778411i	$0.283974\pi$
$312$		0			0
$313$	−7.48528	−	7.48528i	−0.423093	−	0.423093i	0.463174	−	0.886267i	$-0.346710\pi$
$313$	−7.48528	−	7.48528i	−0.423093	−	0.423093i	−0.886267	+	0.463174i	$0.846710\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.3640	+	7.19239i	−0.975257	+	0.403965i	−0.812667	−	0.582729i	$-0.801985\pi$
$317$	−17.3640	+	7.19239i	−0.975257	+	0.403965i	−0.162591	+	0.986694i	$0.551985\pi$
$318$		0			0
$319$	−15.0711			−0.843818
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.4853	+	4.34315i	−0.583417	+	0.241659i
$324$		0			0
$325$	1.05025	−	2.53553i	0.0582575	−	0.140646i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.343146	−	0.343146i	0.0189182	−	0.0189182i
$330$		0			0
$331$	1.29289	+	0.535534i	0.0710638	+	0.0294356i	0.417932	−	0.908478i	$-0.362755\pi$
$331$	1.29289	+	0.535534i	0.0710638	+	0.0294356i	−0.346868	+	0.937914i	$0.612755\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			17.5563i			0.959206i
$336$		0			0
$337$			16.9706i			0.924445i	0.886764	+	0.462223i	$0.152948\pi$
$337$			16.9706i			0.924445i	−0.886764	+	0.462223i	$0.847052\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−16.4853	−	6.82843i	−0.892728	−	0.369780i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.63604	−	3.94975i	0.0878272	−	0.212034i	−0.873863	−	0.486172i	$-0.838393\pi$
$347$	1.63604	−	3.94975i	0.0878272	−	0.212034i	0.961690	+	0.274139i	$0.0883927\pi$
$348$		0			0
$349$	24.6777	−	10.2218i	1.32097	−	0.547162i	0.392901	−	0.919581i	$-0.371472\pi$
$349$	24.6777	−	10.2218i	1.32097	−	0.547162i	0.928065	+	0.372419i	$0.121472\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	22.3137	−	9.24264i	1.18429	−	0.490548i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.8284	−	17.8284i	−0.940948	−	0.940948i	0.0574027	−	0.998351i	$-0.481718\pi$
$359$	−17.8284	−	17.8284i	−0.940948	−	0.940948i	−0.998351	+	0.0574027i	$0.981718\pi$
$360$		0			0
$361$	2.05025	−	2.05025i	0.107908	−	0.107908i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.1005	+	26.7990i	0.581027	+	1.40272i
$366$		0			0
$367$		−	6.00000i		−	0.313197i	−0.987662	−	0.156599i	$-0.949947\pi$
$367$		−	6.00000i		−	0.313197i	0.987662	−	0.156599i	$-0.0500529\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.656854	−	1.58579i	−0.0341022	−	0.0823299i
$372$		0			0
$373$	−10.2929	−	4.26346i	−0.532946	−	0.220753i	0.0999471	−	0.994993i	$-0.468133\pi$
$373$	−10.2929	−	4.26346i	−0.532946	−	0.220753i	−0.632893	+	0.774239i	$0.718133\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.82843	+	1.82843i	0.0941688	+	0.0941688i
$378$		0			0
$379$	13.6777	−	33.0208i	0.702575	−	1.69617i	−0.0151948	−	0.999885i	$-0.504837\pi$
$379$	13.6777	−	33.0208i	0.702575	−	1.69617i	0.717769	−	0.696281i	$-0.245163\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−16.9706			−0.867155			−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$		0			0
$385$	−18.4853			−0.942097
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.39340	−	20.2635i	0.425562	−	1.02740i	−0.555117	−	0.831773i	$-0.687326\pi$
$389$	8.39340	−	20.2635i	0.425562	−	1.02740i	0.980679	−	0.195625i	$-0.0626737\pi$
$390$		0			0
$391$	−16.4853	−	16.4853i	−0.833697	−	0.833697i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−16.2426	−	6.72792i	−0.817256	−	0.338518i
$396$		0			0
$397$	−9.22183	−	22.2635i	−0.462830	−	1.11737i	−0.967230	−	0.253901i	$-0.918286\pi$
$397$	−9.22183	−	22.2635i	−0.462830	−	1.11737i	0.504400	−	0.863470i	$-0.331714\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$		0			0
$403$	1.17157	+	2.82843i	0.0583602	+	0.140894i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.41421	+	2.41421i	−0.119668	+	0.119668i
$408$		0			0
$409$	21.4853	+	21.4853i	1.06238	+	1.06238i	0.997920	+	0.0644584i	$0.0205320\pi$
$409$	21.4853	+	21.4853i	1.06238	+	1.06238i	0.0644584	+	0.997920i	$0.479468\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.41421	−	2.65685i	0.315623	−	0.130735i
$414$		0			0
$415$	−14.3848			−0.706121
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.6066	−	5.22183i	0.615873	−	0.255103i	−0.0528644	−	0.998602i	$-0.516835\pi$
$419$	12.6066	−	5.22183i	0.615873	−	0.255103i	0.668737	+	0.743499i	$0.266835\pi$
$420$		0			0
$421$	6.29289	−	15.1924i	0.306697	−	0.740432i	−0.693111	−	0.720831i	$-0.743760\pi$
$421$	6.29289	−	15.1924i	0.306697	−	0.740432i	0.999808	−	0.0196009i	$-0.00623955\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.17157	+	7.17157i	−0.347872	+	0.347872i
$426$		0			0
$427$	−2.41421	−	1.00000i	−0.116832	−	0.0483934i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			12.3431i			0.594548i	0.954792	+	0.297274i	$0.0960775\pi$
$431$			12.3431i			0.594548i	−0.954792	+	0.297274i	$0.903922\pi$
$432$		0			0
$433$			15.5147i			0.745590i	0.927914	+	0.372795i	$0.121600\pi$
$433$			15.5147i			0.745590i	−0.927914	+	0.372795i	$0.878400\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.5563	−	12.6569i	−1.46171	−	0.605459i
$438$		0			0
$439$	17.0000	−	17.0000i	0.811366	−	0.811366i	−0.173473	−	0.984839i	$-0.555499\pi$
$439$	17.0000	−	17.0000i	0.811366	−	0.811366i	0.984839	+	0.173473i	$0.0554989\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.606602	−	1.46447i	0.0288205	−	0.0695789i	−0.908814	−	0.417201i	$-0.863011\pi$
$443$	0.606602	−	1.46447i	0.0288205	−	0.0695789i	0.937635	+	0.347623i	$0.113011\pi$
$444$		0			0
$445$	33.1421	−	13.7279i	1.57109	−	0.650766i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	19.4558			0.918178			0.459089	−	0.888390i	$-0.348176\pi$
$449$	19.4558			0.918178			0.459089	+	0.888390i	$0.348176\pi$
$450$		0			0
$451$	−1.00000	+	0.414214i	−0.0470882	+	0.0195046i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.24264	+	2.24264i	0.105137	+	0.105137i
$456$		0			0
$457$	−7.48528	+	7.48528i	−0.350147	+	0.350147i	−0.860164	−	0.510017i	$-0.829639\pi$
$457$	−7.48528	+	7.48528i	−0.350147	+	0.350147i	0.510017	+	0.860164i	$0.329639\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.636039	−	1.53553i	−0.0296233	−	0.0715169i	0.908376	−	0.418155i	$-0.137323\pi$
$461$	−0.636039	−	1.53553i	−0.0296233	−	0.0715169i	−0.937999	+	0.346638i	$0.887323\pi$
$462$		0			0
$463$			22.9706i			1.06753i	0.845632	+	0.533766i	$0.179224\pi$
$463$			22.9706i			1.06753i	−0.845632	+	0.533766i	$0.820776\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.09188	−	21.9497i	−0.420722	−	1.01571i	−0.982135	−	0.188177i	$-0.939742\pi$
$467$	−9.09188	−	21.9497i	−0.420722	−	1.01571i	0.561413	−	0.827536i	$-0.310258\pi$
$468$		0			0
$469$	−7.82843	−	3.24264i	−0.361483	−	0.149731i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	16.0711	+	16.0711i	0.738948	+	0.738948i
$474$		0			0
$475$	−5.50610	+	13.2929i	−0.252637	+	0.609920i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	28.9706			1.32370			0.661849	−	0.749637i	$-0.269772\pi$
$479$	28.9706			1.32370			0.661849	+	0.749637i	$0.269772\pi$
$480$		0			0
$481$	0.585786			0.0267096
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.7279	−	50.0416i	0.941206	−	2.27227i
$486$		0			0
$487$	11.0000	+	11.0000i	0.498458	+	0.498458i	0.910958	−	0.412500i	$-0.135344\pi$
$487$	11.0000	+	11.0000i	0.498458	+	0.498458i	−0.412500	+	0.910958i	$0.635344\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	39.3345	+	16.2929i	1.77514	+	0.735288i	0.993800	+	0.111186i	$0.0354648\pi$
$491$	39.3345	+	16.2929i	1.77514	+	0.735288i	0.781343	+	0.624102i	$0.214535\pi$
$492$		0			0
$493$	−3.65685	−	8.82843i	−0.164696	−	0.397612i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			11.6569i			0.522881i
$498$		0			0
$499$	0.949747	+	2.29289i	0.0425165	+	0.102644i	0.943711	−	0.330771i	$-0.107309\pi$
$499$	0.949747	+	2.29289i	0.0425165	+	0.102644i	−0.901195	+	0.433415i	$0.857309\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.1421	+	11.1421i	−0.496803	+	0.496803i	−0.910441	−	0.413638i	$-0.864258\pi$
$503$	−11.1421	+	11.1421i	−0.496803	+	0.496803i	0.413638	+	0.910441i	$0.364258\pi$
$504$		0			0
$505$	7.38478	+	7.38478i	0.328618	+	0.328618i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	26.0919	−	10.8076i	1.15650	−	0.479039i	0.279793	−	0.960060i	$-0.409734\pi$
$509$	26.0919	−	10.8076i	1.15650	−	0.479039i	0.876709	+	0.481021i	$0.159734\pi$
$510$		0			0
$511$	−14.0000			−0.619324
$512$		0			0
$513$		0			0
$514$		0			0
$515$	36.3137	−	15.0416i	1.60017	−	0.662813i
$516$		0			0
$517$	0.585786	−	1.41421i	0.0257629	−	0.0621970i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.34315	+	3.34315i	−0.146466	+	0.146466i	−0.776537	−	0.630071i	$-0.783026\pi$
$521$	−3.34315	+	3.34315i	−0.146466	+	0.146466i	0.630071	+	0.776537i	$0.283026\pi$
$522$		0			0
$523$	−19.1924	−	7.94975i	−0.839225	−	0.347618i	−0.0786768	−	0.996900i	$-0.525070\pi$
$523$	−19.1924	−	7.94975i	−0.839225	−	0.347618i	−0.760548	+	0.649282i	$0.775070\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	11.3137i		−	0.492833i
$528$		0			0
$529$		−	44.9411i		−	1.95396i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.171573	+	0.0710678i	0.00743165	+	0.00307829i
$534$		0			0
$535$	9.24264	−	9.24264i	0.399594	−	0.399594i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.53553	+	20.6066i	−0.367651	+	0.887589i
$540$		0			0
$541$	−27.2635	+	11.2929i	−1.17215	+	0.485519i	−0.881902	−	0.471433i	$-0.843737\pi$
$541$	−27.2635	+	11.2929i	−1.17215	+	0.485519i	−0.290246	+	0.956952i	$0.593737\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	43.6985			1.87184
$546$		0			0
$547$	17.5355	−	7.26346i	0.749765	−	0.310563i	0.0251195	−	0.999684i	$-0.492003\pi$
$547$	17.5355	−	7.26346i	0.749765	−	0.310563i	0.724646	+	0.689122i	$0.242003\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.58579	−	9.58579i	−0.408368	−	0.408368i
$552$		0			0
$553$	6.00000	−	6.00000i	0.255146	−	0.255146i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.1213	−	36.5061i	−0.640711	−	1.54681i	−0.825722	−	0.564077i	$-0.809232\pi$
$557$	−15.1213	−	36.5061i	−0.640711	−	1.54681i	0.185012	−	0.982736i	$-0.440768\pi$
$558$		0			0
$559$		−	3.89949i		−	0.164931i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.87868	+	19.0208i	0.332047	+	0.801632i	0.998430	+	0.0560220i	$0.0178417\pi$
$563$	7.87868	+	19.0208i	0.332047	+	0.801632i	−0.666383	+	0.745610i	$0.732158\pi$
$564$		0			0
$565$	17.1716	+	7.11270i	0.722414	+	0.299233i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.6569	−	14.6569i	−0.614447	−	0.614447i	0.329654	−	0.944102i	$-0.393068\pi$
$569$	−14.6569	−	14.6569i	−0.614447	−	0.614447i	−0.944102	+	0.329654i	$0.893068\pi$
$570$		0			0
$571$	2.70711	−	6.53553i	0.113289	−	0.273504i	−0.857058	−	0.515220i	$-0.827710\pi$
$571$	2.70711	−	6.53553i	0.113289	−	0.273504i	0.970347	+	0.241716i	$0.0777103\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−29.5563			−1.23258
$576$		0			0
$577$	18.9706			0.789755			0.394877	−	0.918734i	$-0.370787\pi$
$577$	18.9706			0.789755			0.394877	+	0.918734i	$0.370787\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.65685	−	6.41421i	0.110225	−	0.266106i
$582$		0			0
$583$	−3.82843	−	3.82843i	−0.158557	−	0.158557i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.6066	−	5.22183i	−0.520330	−	0.215528i	0.107032	−	0.994256i	$-0.465865\pi$
$587$	−12.6066	−	5.22183i	−0.520330	−	0.215528i	−0.627362	+	0.778728i	$0.715865\pi$
$588$		0			0
$589$	−6.14214	−	14.8284i	−0.253082	−	0.610995i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	28.2843i		−	1.16150i	−0.814083	−	0.580748i	$-0.802760\pi$
$593$		−	28.2843i		−	1.16150i	0.814083	−	0.580748i	$-0.197240\pi$
$594$		0			0
$595$	−4.48528	−	10.8284i	−0.183879	−	0.443922i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.6569	+	26.6569i	−1.08917	+	1.08917i	−0.0935555	+	0.995614i	$0.529823\pi$
$599$	−26.6569	+	26.6569i	−1.08917	+	1.08917i	−0.995614	+	0.0935555i	$0.970177\pi$
$600$		0			0
$601$	−21.9706	−	21.9706i	−0.896198	−	0.896198i	0.0988995	−	0.995097i	$-0.468468\pi$
$601$	−21.9706	−	21.9706i	−0.896198	−	0.896198i	−0.995097	+	0.0988995i	$0.968468\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.0919	+	9.97918i	−0.979474	+	0.405712i
$606$		0			0
$607$	32.9706			1.33823			0.669117	−	0.743157i	$-0.266673\pi$
$607$	32.9706			1.33823			0.669117	+	0.743157i	$0.266673\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.242641	+	0.100505i	−0.00981619	+	0.00406600i
$612$		0			0
$613$	1.32233	−	3.19239i	0.0534084	−	0.128939i	−0.894923	−	0.446220i	$-0.852770\pi$
$613$	1.32233	−	3.19239i	0.0534084	−	0.128939i	0.948332	+	0.317281i	$0.102770\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.7990	+	22.7990i	−0.917853	+	0.917853i	−0.996873	−	0.0790202i	$-0.974821\pi$
$617$	−22.7990	+	22.7990i	−0.917853	+	0.917853i	0.0790202	+	0.996873i	$0.474821\pi$
$618$		0			0
$619$	21.7782	+	9.02082i	0.875339	+	0.362577i	0.774687	−	0.632345i	$-0.217907\pi$
$619$	21.7782	+	9.02082i	0.875339	+	0.362577i	0.100651	+	0.994922i	$0.467907\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			17.3137i			0.693659i
$624$		0			0
$625$		−	30.0711i		−	1.20284i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.00000	−	0.828427i	−0.0797452	−	0.0330316i
$630$		0			0
$631$	−32.4558	+	32.4558i	−1.29205	+	1.29205i	−0.358528	+	0.933519i	$0.616721\pi$
$631$	−32.4558	+	32.4558i	−1.29205	+	1.29205i	−0.933519	+	0.358528i	$0.883279\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.5442	−	35.1127i	0.577167	−	1.39340i
$636$		0			0
$637$	3.53553	−	1.46447i	0.140083	−	0.0580243i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.45584			−0.294488			−0.147244	−	0.989100i	$-0.547040\pi$
$641$	−7.45584			−0.294488			−0.147244	+	0.989100i	$0.547040\pi$
$642$		0			0
$643$	−11.4350	+	4.73654i	−0.450954	+	0.186791i	−0.596588	−	0.802547i	$-0.703478\pi$
$643$	−11.4350	+	4.73654i	−0.450954	+	0.186791i	0.145635	+	0.989338i	$0.453478\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.17157	+	6.17157i	0.242630	+	0.242630i	0.817937	−	0.575308i	$-0.195118\pi$
$647$	6.17157	+	6.17157i	0.242630	+	0.242630i	−0.575308	+	0.817937i	$0.695118\pi$
$648$		0			0
$649$	15.4853	−	15.4853i	0.607850	−	0.607850i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.09188	−	5.05025i	−0.0818617	−	0.197632i	0.877649	−	0.479304i	$-0.159111\pi$
$653$	−2.09188	−	5.05025i	−0.0818617	−	0.197632i	−0.959511	+	0.281672i	$0.909111\pi$
$654$		0			0
$655$		−	51.8995i		−	2.02788i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.1213	−	24.4350i	−0.394271	−	0.951854i	−0.988998	−	0.147926i	$-0.952740\pi$
$659$	−10.1213	−	24.4350i	−0.394271	−	0.951854i	0.594728	−	0.803927i	$-0.297260\pi$
$660$		0			0
$661$	−41.7487	−	17.2929i	−1.62384	−	0.672616i	−0.629316	−	0.777149i	$-0.716665\pi$
$661$	−41.7487	−	17.2929i	−1.62384	−	0.672616i	−0.994521	+	0.104534i	$0.966665\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−11.7574	−	11.7574i	−0.455931	−	0.455931i
$666$		0			0
$667$	10.6569	−	25.7279i	0.412635	−	0.996189i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−8.24264			−0.318204
$672$		0			0
$673$	22.4853			0.866744			0.433372	−	0.901215i	$-0.357324\pi$
$673$	22.4853			0.866744			0.433372	+	0.901215i	$0.357324\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.6066	+	37.6777i	−0.599810	+	1.44807i	0.273964	+	0.961740i	$0.411665\pi$
$677$	−15.6066	+	37.6777i	−0.599810	+	1.44807i	−0.873775	+	0.486331i	$0.838335\pi$
$678$		0			0
$679$	18.4853	+	18.4853i	0.709400	+	0.709400i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.1213	−	4.19239i	−0.387282	−	0.160417i	0.180543	−	0.983567i	$-0.442215\pi$
$683$	−10.1213	−	4.19239i	−0.387282	−	0.160417i	−0.567824	+	0.823150i	$0.692215\pi$
$684$		0			0
$685$	13.7279	+	33.1421i	0.524517	+	1.26630i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			0.928932i			0.0353895i
$690$		0			0
$691$	−12.5061	−	30.1924i	−0.475754	−	1.14857i	−0.961582	−	0.274518i	$-0.911482\pi$
$691$	−12.5061	−	30.1924i	−0.475754	−	1.14857i	0.485828	−	0.874055i	$-0.338518\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	29.5858	−	29.5858i	1.12225	−	1.12225i
$696$		0			0
$697$	−0.485281	−	0.485281i	−0.0183813	−	0.0183813i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.87868	+	1.19239i	−0.108726	+	0.0450359i	−0.436383	−	0.899761i	$-0.643741\pi$
$701$	−2.87868	+	1.19239i	−0.108726	+	0.0450359i	0.327657	+	0.944797i	$0.393741\pi$
$702$		0			0
$703$	−3.07107			−0.115828
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.65685	+	1.92893i	−0.175139	+	0.0725450i
$708$		0			0
$709$	8.77817	−	21.1924i	0.329671	−	0.795897i	−0.668945	−	0.743312i	$-0.733254\pi$
$709$	8.77817	−	21.1924i	0.329671	−	0.795897i	0.998616	−	0.0525851i	$-0.0167461\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	23.3137	−	23.3137i	0.873105	−	0.873105i
$714$		0			0
$715$	9.24264	+	3.82843i	0.345655	+	0.143175i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	35.6569i		−	1.32978i	−0.746943	−	0.664888i	$-0.768479\pi$
$719$		−	35.6569i		−	1.32978i	0.746943	−	0.664888i	$-0.231521\pi$
$720$		0			0
$721$			18.9706i			0.706501i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.1924	−	4.63604i	−0.415675	−	0.172178i
$726$		0			0
$727$	9.97056	−	9.97056i	0.369788	−	0.369788i	−0.497612	−	0.867400i	$-0.665790\pi$
$727$	9.97056	−	9.97056i	0.369788	−	0.369788i	0.867400	+	0.497612i	$0.165790\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.51472	+	13.3137i	−0.203969	+	0.492425i
$732$		0			0
$733$	−33.2635	+	13.7782i	−1.22861	+	0.508908i	−0.900138	−	0.435604i	$-0.856535\pi$
$733$	−33.2635	+	13.7782i	−1.22861	+	0.508908i	−0.328475	+	0.944513i	$0.606535\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−26.7279			−0.984536
$738$		0			0
$739$	−0.464466	+	0.192388i	−0.0170857	+	0.00707711i	−0.391210	−	0.920301i	$-0.627943\pi$
$739$	−0.464466	+	0.192388i	−0.0170857	+	0.00707711i	0.374124	+	0.927379i	$0.377943\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.6274	+	31.6274i	1.16030	+	1.16030i	0.984410	+	0.175887i	$0.0562793\pi$
$743$	31.6274	+	31.6274i	1.16030	+	1.16030i	0.175887	+	0.984410i	$0.443721\pi$
$744$		0			0
$745$	−35.0000	+	35.0000i	−1.28230	+	1.28230i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.41421	+	5.82843i	0.0882134	+	0.212966i
$750$		0			0
$751$		−	10.9706i		−	0.400322i	−0.979763	−	0.200161i	$-0.935854\pi$
$751$		−	10.9706i		−	0.400322i	0.979763	−	0.200161i	$-0.0641464\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.35534	+	5.68629i	0.0857196	+	0.206945i
$756$		0			0
$757$	−33.2635	−	13.7782i	−1.20898	−	0.500776i	−0.315090	−	0.949062i	$-0.602035\pi$
$757$	−33.2635	−	13.7782i	−1.20898	−	0.500776i	−0.893890	+	0.448285i	$0.852035\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	29.8284	+	29.8284i	1.08128	+	1.08128i	0.996390	+	0.0848892i	$0.0270536\pi$
$761$	29.8284	+	29.8284i	1.08128	+	1.08128i	0.0848892	+	0.996390i	$0.472946\pi$
$762$		0			0
$763$	−8.07107	+	19.4853i	−0.292192	+	0.705415i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.75736			−0.135670
$768$		0			0
$769$	5.51472			0.198866			0.0994329	−	0.995044i	$-0.468297\pi$
$769$	5.51472			0.198866			0.0994329	+	0.995044i	$0.468297\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.0919	+	29.1924i	−0.434915	+	1.04998i	0.542766	+	0.839884i	$0.317377\pi$
$773$	−12.0919	+	29.1924i	−0.434915	+	1.04998i	−0.977681	+	0.210094i	$0.932623\pi$
$774$		0			0
$775$	−10.1421	−	10.1421i	−0.364316	−	0.364316i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.899495	−	0.372583i	−0.0322278	−	0.0133492i
$780$		0			0
$781$	14.0711	+	33.9706i	0.503502	+	1.21556i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			5.41421i			0.193242i
$786$		0			0
$787$	0.949747	+	2.29289i	0.0338548	+	0.0817328i	0.939903	−	0.341442i	$-0.110915\pi$
$787$	0.949747	+	2.29289i	0.0338548	+	0.0817328i	−0.906048	+	0.423175i	$0.860915\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.34315	+	6.34315i	−0.225536	+	0.225536i
$792$		0			0
$793$	1.00000	+	1.00000i	0.0355110	+	0.0355110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	26.0919	−	10.8076i	0.924222	−	0.382825i	0.130738	−	0.991417i	$-0.458265\pi$
$797$	26.0919	−	10.8076i	0.924222	−	0.382825i	0.793484	+	0.608592i	$0.208265\pi$
$798$		0			0
$799$	0.970563			0.0343360
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−40.7990	+	16.8995i	−1.43977	+	0.596370i
$804$		0			0
$805$	13.0711	−	31.5563i	0.460695	−	1.11222i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	29.1421	−	29.1421i	1.02458	−	1.02458i	0.0248928	−	0.999690i	$-0.492076\pi$
$809$	29.1421	−	29.1421i	1.02458	−	1.02458i	0.999690	−	0.0248928i	$-0.00792444\pi$
$810$		0			0
$811$	42.2635	+	17.5061i	1.48407	+	0.614722i	0.970017	−	0.243036i	$-0.0781433\pi$
$811$	42.2635	+	17.5061i	1.48407	+	0.614722i	0.514053	+	0.857758i	$0.328143\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	1.47309i		−	0.0516000i
$816$		0			0
$817$			20.4437i			0.715233i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.6066	+	8.94975i	0.754076	+	0.312348i	0.726403	−	0.687269i	$-0.241191\pi$
$821$	21.6066	+	8.94975i	0.754076	+	0.312348i	0.0276723	+	0.999617i	$0.491191\pi$
$822$		0			0
$823$	−35.9706	+	35.9706i	−1.25385	+	1.25385i	−0.299877	+	0.953978i	$0.596946\pi$
$823$	−35.9706	+	35.9706i	−1.25385	+	1.25385i	−0.953978	+	0.299877i	$0.903054\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.1213	−	38.9203i	0.560593	−	1.35339i	−0.348699	−	0.937235i	$-0.613377\pi$
$827$	16.1213	−	38.9203i	0.560593	−	1.35339i	0.909293	−	0.416157i	$-0.136623\pi$
$828$		0			0
$829$	34.1924	−	14.1630i	1.18755	−	0.491900i	0.300594	−	0.953752i	$-0.402815\pi$
$829$	34.1924	−	14.1630i	1.18755	−	0.491900i	0.886957	+	0.461853i	$0.152815\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−14.1421			−0.489996
$834$		0			0
$835$	−56.1127	+	23.2426i	−1.94186	+	0.804345i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.68629	+	9.68629i	0.334408	+	0.334408i	0.854258	−	0.519850i	$-0.174012\pi$
$839$	9.68629	+	9.68629i	0.334408	+	0.334408i	−0.519850	+	0.854258i	$0.674012\pi$
$840$		0			0
$841$	−12.4350	+	12.4350i	−0.428794	+	0.428794i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	13.9203	+	33.6066i	0.478873	+	1.15610i
$846$		0			0
$847$		−	12.5858i		−	0.432453i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.41421	−	5.82843i	−0.0827582	−	0.199796i
$852$		0			0
$853$	51.1630	+	21.1924i	1.75179	+	0.725614i	0.997622	+	0.0689279i	$0.0219579\pi$
$853$	51.1630	+	21.1924i	1.75179	+	0.725614i	0.754164	+	0.656686i	$0.228042\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.68629	−	9.68629i	−0.330877	−	0.330877i	0.522042	−	0.852920i	$-0.325170\pi$
$857$	−9.68629	−	9.68629i	−0.330877	−	0.330877i	−0.852920	+	0.522042i	$0.825170\pi$
$858$		0			0
$859$	1.67767	−	4.05025i	0.0572413	−	0.138193i	−0.892671	−	0.450708i	$-0.851172\pi$
$859$	1.67767	−	4.05025i	0.0572413	−	0.138193i	0.949913	+	0.312515i	$0.101172\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	21.9411			0.746885			0.373442	−	0.927653i	$-0.378177\pi$
$863$	21.9411			0.746885			0.373442	+	0.927653i	$0.378177\pi$
$864$		0			0
$865$	23.8995			0.812607
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.2426	−	24.7279i	0.347458	−	0.838837i
$870$		0			0
$871$	3.24264	+	3.24264i	0.109873	+	0.109873i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.41421	+	2.24264i	0.183034	+	0.0758151i
$876$		0			0
$877$	−0.736544	−	1.77817i	−0.0248713	−	0.0600447i	0.910956	−	0.412504i	$-0.135346\pi$
$877$	−0.736544	−	1.77817i	−0.0248713	−	0.0600447i	−0.935827	+	0.352459i	$0.885346\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$		0			0
$883$	−20.5650	−	49.6482i	−0.692066	−	1.67080i	−0.740575	−	0.671973i	$-0.765447\pi$
$883$	−20.5650	−	49.6482i	−0.692066	−	1.67080i	0.0485090	−	0.998823i	$-0.484553\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.31371	−	2.31371i	0.0776867	−	0.0776867i	−0.667196	−	0.744882i	$-0.732506\pi$
$887$	2.31371	−	2.31371i	0.0776867	−	0.0776867i	0.744882	+	0.667196i	$0.232506\pi$
$888$		0			0
$889$	12.9706	+	12.9706i	0.435019	+	0.435019i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.27208	−	0.526912i	0.0425685	−	0.0176324i
$894$		0			0
$895$	12.5269			0.418728
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.4853	−	5.17157i	0.416407	−	0.172482i
$900$		0			0
$901$	1.31371	−	3.17157i	0.0437660	−	0.105660i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−36.3137	+	36.3137i	−1.20711	+	1.20711i
$906$		0			0
$907$	15.7782	+	6.53553i	0.523906	+	0.217009i	0.628932	−	0.777461i	$-0.283493\pi$
$907$	15.7782	+	6.53553i	0.523906	+	0.217009i	−0.105026	+	0.994469i	$0.533493\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	33.5980i		−	1.11315i	−0.830797	−	0.556575i	$-0.812115\pi$
$911$		−	33.5980i		−	1.11315i	0.830797	−	0.556575i	$-0.187885\pi$
$912$		0			0
$913$		−	21.8995i		−	0.724767i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23.1421	+	9.58579i	0.764221	+	0.316551i
$918$		0			0
$919$	8.51472	−	8.51472i	0.280875	−	0.280875i	−0.552583	−	0.833458i	$-0.686358\pi$
$919$	8.51472	−	8.51472i	0.280875	−	0.280875i	0.833458	+	0.552583i	$0.186358\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.41421	−	5.82843i	0.0794648	−	0.191845i
$924$		0			0
$925$	−2.53553	+	1.05025i	−0.0833678	+	0.0345321i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.51472			0.312168			0.156084	−	0.987744i	$-0.450113\pi$
$929$	9.51472			0.312168			0.156084	+	0.987744i	$0.450113\pi$
$930$		0			0
$931$	−18.5355	+	7.67767i	−0.607478	+	0.251625i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−26.1421	−	26.1421i	−0.854939	−	0.854939i
$936$		0			0
$937$	19.0000	−	19.0000i	0.620703	−	0.620703i	−0.325008	−	0.945711i	$-0.605367\pi$
$937$	19.0000	−	19.0000i	0.620703	−	0.620703i	0.945711	+	0.325008i	$0.105367\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.636039	−	1.53553i	−0.0207343	−	0.0500570i	0.913173	−	0.407571i	$-0.133624\pi$
$941$	−0.636039	−	1.53553i	−0.0207343	−	0.0500570i	−0.933908	+	0.357514i	$0.883624\pi$
$942$		0			0
$943$		−	2.00000i		−	0.0651290i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.33452	+	22.5355i	0.303331	+	0.732306i	0.999890	+	0.0148070i	$0.00471340\pi$
$947$	9.33452	+	22.5355i	0.303331	+	0.732306i	−0.696559	+	0.717499i	$0.745287\pi$
$948$		0			0
$949$	7.00000	+	2.89949i	0.227230	+	0.0941216i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.6569	−	14.6569i	−0.474782	−	0.474782i	0.428676	−	0.903458i	$-0.358980\pi$
$953$	−14.6569	−	14.6569i	−0.474782	−	0.474782i	−0.903458	+	0.428676i	$0.858980\pi$
$954$		0			0
$955$	13.4558	−	32.4853i	0.435421	−	1.05120i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.3137			−0.559089
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.69848	−	4.10051i	0.0546762	−	0.132000i
$966$		0			0
$967$	6.02944	+	6.02944i	0.193894	+	0.193894i	0.797376	−	0.603483i	$-0.206221\pi$
$967$	6.02944	+	6.02944i	0.193894	+	0.193894i	−0.603483	+	0.797376i	$0.706221\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.3640	+	9.26346i	0.717694	+	0.297278i	0.711484	−	0.702702i	$-0.248023\pi$
$971$	22.3640	+	9.26346i	0.717694	+	0.297278i	0.00620964	+	0.999981i	$0.498023\pi$
$972$		0			0
$973$	7.72792	+	18.6569i	0.247746	+	0.598111i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$		0			0
$979$	20.8995	+	50.4558i	0.667951	+	1.61258i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.6274	+	19.6274i	−0.626017	+	0.626017i	−0.947064	−	0.321046i	$-0.895966\pi$
$983$	−19.6274	+	19.6274i	−0.626017	+	0.626017i	0.321046	+	0.947064i	$0.395966\pi$
$984$		0			0
$985$	−25.1005	−	25.1005i	−0.799769	−	0.799769i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−38.7990	+	16.0711i	−1.23374	+	0.511030i
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−61.1421	+	25.3259i	−1.93834	+	0.802885i
$996$		0			0
$997$	−20.1924	+	48.7487i	−0.639499	+	1.54389i	0.187848	+	0.982198i	$0.439849\pi$
$997$	−20.1924	+	48.7487i	−0.639499	+	1.54389i	−0.827348	+	0.561690i	$0.810151\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.v.a.433.1		4
3.2	odd	2		128.2.g.a.49.1		4
4.3	odd	2		288.2.v.a.181.1		4
12.11	even	2		32.2.g.a.21.1	✓	4
24.5	odd	2		256.2.g.a.97.1		4
24.11	even	2		256.2.g.b.97.1		4
32.3	odd	8		288.2.v.a.253.1		4
32.29	even	8	inner	1152.2.v.a.721.1		4
48.5	odd	4		512.2.g.b.449.1		4
48.11	even	4		512.2.g.d.449.1		4
48.29	odd	4		512.2.g.c.449.1		4
48.35	even	4		512.2.g.a.449.1		4
60.23	odd	4		800.2.ba.a.149.1		4
60.47	odd	4		800.2.ba.b.149.1		4
60.59	even	2		800.2.y.a.501.1		4
96.5	odd	8		512.2.g.b.65.1		4
96.11	even	8		512.2.g.a.65.1		4
96.29	odd	8		128.2.g.a.81.1		4
96.35	even	8		32.2.g.a.29.1	yes	4
96.53	odd	8		512.2.g.c.65.1		4
96.59	even	8		512.2.g.d.65.1		4
96.77	odd	8		256.2.g.a.161.1		4
96.83	even	8		256.2.g.b.161.1		4
192.29	odd	16		4096.2.a.f.1.3		4
192.35	even	16		4096.2.a.e.1.2		4
192.125	odd	16		4096.2.a.f.1.2		4
192.131	even	16		4096.2.a.e.1.3		4
480.227	odd	8		800.2.ba.a.349.1		4
480.323	odd	8		800.2.ba.b.349.1		4
480.419	even	8		800.2.y.a.701.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.21.1	✓	4	12.11	even	2
32.2.g.a.29.1	yes	4	96.35	even	8
128.2.g.a.49.1		4	3.2	odd	2
128.2.g.a.81.1		4	96.29	odd	8
256.2.g.a.97.1		4	24.5	odd	2
256.2.g.a.161.1		4	96.77	odd	8
256.2.g.b.97.1		4	24.11	even	2
256.2.g.b.161.1		4	96.83	even	8
288.2.v.a.181.1		4	4.3	odd	2
288.2.v.a.253.1		4	32.3	odd	8
512.2.g.a.65.1		4	96.11	even	8
512.2.g.a.449.1		4	48.35	even	4
512.2.g.b.65.1		4	96.5	odd	8
512.2.g.b.449.1		4	48.5	odd	4
512.2.g.c.65.1		4	96.53	odd	8
512.2.g.c.449.1		4	48.29	odd	4
512.2.g.d.65.1		4	96.59	even	8
512.2.g.d.449.1		4	48.11	even	4
800.2.y.a.501.1		4	60.59	even	2
800.2.y.a.701.1		4	480.419	even	8
800.2.ba.a.149.1		4	60.23	odd	4
800.2.ba.a.349.1		4	480.227	odd	8
800.2.ba.b.149.1		4	60.47	odd	4
800.2.ba.b.349.1		4	480.323	odd	8
1152.2.v.a.433.1		4	1.1	even	1	trivial
1152.2.v.a.721.1		4	32.29	even	8	inner
4096.2.a.e.1.2		4	192.35	even	16
4096.2.a.e.1.3		4	192.131	even	16
4096.2.a.f.1.2		4	192.125	odd	16
4096.2.a.f.1.3		4	192.29	odd	16

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.v (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12132 + 2.70711i) q^{5} +(-1.00000 - 1.00000i) q^{7} +O(q^{10})\)	\(q+(-1.12132 + 2.70711i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-4.12132 - 1.70711i) q^{11} +(0.292893 + 0.707107i) q^{13} -2.82843i q^{17} +(-1.53553 - 3.70711i) q^{19} +(5.82843 - 5.82843i) q^{23} +(-2.53553 - 2.53553i) q^{25} +(3.12132 - 1.29289i) q^{29} +4.00000 q^{31} +(3.82843 - 1.58579i) q^{35} +(0.292893 - 0.707107i) q^{37} +(0.171573 - 0.171573i) q^{41} +(-4.70711 - 1.94975i) q^{43} +0.343146i q^{47} -5.00000i q^{49} +(1.12132 + 0.464466i) q^{53} +(9.24264 - 9.24264i) q^{55} +(-1.87868 + 4.53553i) q^{59} +(1.70711 - 0.707107i) q^{61} -2.24264 q^{65} +(5.53553 - 2.29289i) q^{67} +(-5.82843 - 5.82843i) q^{71} +(7.00000 - 7.00000i) q^{73} +(2.41421 + 5.82843i) q^{77} +6.00000i q^{79} +(1.87868 + 4.53553i) q^{83} +(7.65685 + 3.17157i) q^{85} +(-8.65685 - 8.65685i) q^{89} +(0.414214 - 1.00000i) q^{91} +11.7574 q^{95} -18.4853 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q + 4 * q^5 - 4 * q^7	\( 4 q + 4 q^{5} - 4 q^{7} - 8 q^{11} + 4 q^{13} + 8 q^{19} + 12 q^{23} + 4 q^{25} + 4 q^{29} + 16 q^{31} + 4 q^{35} + 4 q^{37} + 12 q^{41} - 16 q^{43} - 4 q^{53} + 20 q^{55} - 16 q^{59} + 4 q^{61} + 8 q^{65} + 8 q^{67} - 12 q^{71} + 28 q^{73} + 4 q^{77} + 16 q^{83} + 8 q^{85} - 12 q^{89} - 4 q^{91} + 64 q^{95} - 40 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 - 4 * q^7 - 8 * q^11 + 4 * q^13 + 8 * q^19 + 12 * q^23 + 4 * q^25 + 4 * q^29 + 16 * q^31 + 4 * q^35 + 4 * q^37 + 12 * q^41 - 16 * q^43 - 4 * q^53 + 20 * q^55 - 16 * q^59 + 4 * q^61 + 8 * q^65 + 8 * q^67 - 12 * q^71 + 28 * q^73 + 4 * q^77 + 16 * q^83 + 8 * q^85 - 12 * q^89 - 4 * q^91 + 64 * q^95 - 40 * q^97

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