LMFDB - Embedded newform 280.2.s.a.237.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(13,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.s (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40282095616.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 8x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 8x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label			237.2
Root			$-1.03179 - 1.39119i$ of defining polynomial
Character	$\chi$	$=$	280.237
Dual form			280.2.s.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-0.359404 + 0.359404i) q^{3} +2.00000i q^{4} +(1.39119 - 1.75060i) q^{5} +0.718808 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.74166i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.359404 + 0.359404i) q^{3} +2.00000i q^{4} +(1.39119 - 1.75060i) q^{5} +0.718808 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.74166i q^{9} +(-3.14179 + 0.359404i) q^{10} +(-0.718808 - 0.718808i) q^{12} +(4.48655 - 4.48655i) q^{13} +3.74166i q^{14} +(0.129171 + 1.12917i) q^{15} -4.00000 q^{16} +(2.74166 - 2.74166i) q^{18} -7.62834i q^{19} +(3.50119 + 2.78238i) q^{20} +1.34477 q^{21} +(0.741657 - 0.741657i) q^{23} +1.43762i q^{24} +(-1.12917 - 4.87083i) q^{25} -8.97311 q^{26} +(-2.06358 - 2.06358i) q^{27} +(3.74166 - 3.74166i) q^{28} +(1.00000 - 1.25834i) q^{30} +(4.00000 + 4.00000i) q^{32} +(-5.87775 + 0.672384i) q^{35} -5.48331 q^{36} +(-7.62834 + 7.62834i) q^{38} +3.22497i q^{39} +(-0.718808 - 6.28357i) q^{40} +(-1.34477 - 1.34477i) q^{42} +(4.79953 + 3.81417i) q^{45} -1.48331 q^{46} +(1.43762 - 1.43762i) q^{48} +7.00000i q^{49} +(-3.74166 + 6.00000i) q^{50} +(8.97311 + 8.97311i) q^{52} +4.12715i q^{54} -7.48331 q^{56} +(2.74166 + 2.74166i) q^{57} +15.3495i q^{59} +(-2.25834 + 0.258343i) q^{60} +14.6307 q^{61} +(5.12917 - 5.12917i) q^{63} -8.00000i q^{64} +(-1.61249 - 14.0958i) q^{65} +0.533109i q^{69} +(6.55013 + 5.20536i) q^{70} +7.22497 q^{71} +(5.48331 + 5.48331i) q^{72} +(2.15642 + 1.34477i) q^{75} +15.2567 q^{76} +(3.22497 - 3.22497i) q^{78} +15.7417i q^{79} +(-5.56477 + 7.00238i) q^{80} -6.74166 q^{81} +(-5.83132 + 5.83132i) q^{83} +2.68953i q^{84} +(-0.985363 - 8.61370i) q^{90} -16.7871 q^{91} +(1.48331 + 1.48331i) q^{92} +(-13.3541 - 10.6125i) q^{95} -2.87523 q^{96} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} + 16 q^{15} - 32 q^{16} - 8 q^{18} - 24 q^{23} - 24 q^{25} + 8 q^{30} + 32 q^{32} + 16 q^{36} + 48 q^{46} - 8 q^{57} - 48 q^{60} + 56 q^{63} + 32 q^{65} - 32 q^{71} - 16 q^{72} - 64 q^{78} - 24 q^{81} - 48 q^{92} - 32 q^{95} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 + 16 * q^15 - 32 * q^16 - 8 * q^18 - 24 * q^23 - 24 * q^25 + 8 * q^30 + 32 * q^32 + 16 * q^36 + 48 * q^46 - 8 * q^57 - 48 * q^60 + 56 * q^63 + 32 * q^65 - 32 * q^71 - 16 * q^72 - 64 * q^78 - 24 * q^81 - 48 * q^92 - 32 * q^95 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−0.359404	+	0.359404i	−0.207502	+	0.207502i	−0.803205	−	0.595703i	$-0.796874\pi$
$3$	−0.359404	+	0.359404i	−0.207502	+	0.207502i	0.595703	+	0.803205i	$0.296874\pi$
$4$			2.00000i			1.00000i
$5$	1.39119	−	1.75060i	0.622160	−	0.782890i
$5$	1.39119	−	1.75060i	0.622160	−	0.782890i
$6$	0.718808			0.293452
$7$	−1.87083	−	1.87083i	−0.707107	−	0.707107i
$7$	−1.87083	−	1.87083i	−0.707107	−	0.707107i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$			2.74166i			0.913886i
$10$	−3.14179	+	0.359404i	−0.993520	+	0.113654i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	−0.718808	−	0.718808i	−0.207502	−	0.207502i
$13$	4.48655	−	4.48655i	1.24435	−	1.24435i	0.286166	−	0.958180i	$-0.407619\pi$
$13$	4.48655	−	4.48655i	1.24435	−	1.24435i	0.958180	−	0.286166i	$-0.0923810\pi$
$14$			3.74166i			1.00000i
$15$	0.129171	+	1.12917i	0.0333519	+	0.291551i
$16$	−4.00000			−1.00000
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	2.74166	−	2.74166i	0.646215	−	0.646215i
$19$		−	7.62834i		−	1.75006i	−0.484067	−	0.875031i	$-0.660841\pi$
$19$		−	7.62834i		−	1.75006i	0.484067	−	0.875031i	$-0.339159\pi$
$20$	3.50119	+	2.78238i	0.782890	+	0.622160i
$21$	1.34477			0.293452
$22$		0			0
$23$	0.741657	−	0.741657i	0.154646	−	0.154646i	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	0.741657	−	0.741657i	0.154646	−	0.154646i	0.780189	+	0.625543i	$0.215123\pi$
$24$			1.43762i			0.293452i
$25$	−1.12917	−	4.87083i	−0.225834	−	0.974166i
$26$	−8.97311			−1.75977
$27$	−2.06358	−	2.06358i	−0.397135	−	0.397135i
$28$	3.74166	−	3.74166i	0.707107	−	0.707107i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.00000	−	1.25834i	0.182574	−	0.229741i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		0			0
$34$		0			0
$35$	−5.87775	+	0.672384i	−0.993520	+	0.113654i
$36$	−5.48331			−0.913886
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	−7.62834	+	7.62834i	−1.23748	+	1.23748i
$39$			3.22497i			0.516409i
$40$	−0.718808	−	6.28357i	−0.113654	−	0.993520i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	−1.34477	−	1.34477i	−0.207502	−	0.207502i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	4.79953	+	3.81417i	0.715472	+	0.568583i
$46$	−1.48331			−0.218703
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	1.43762	−	1.43762i	0.207502	−	0.207502i
$49$			7.00000i			1.00000i
$50$	−3.74166	+	6.00000i	−0.529150	+	0.848528i
$51$		0			0
$52$	8.97311	+	8.97311i	1.24435	+	1.24435i
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$			4.12715i			0.561634i
$55$		0			0
$56$	−7.48331			−1.00000
$57$	2.74166	+	2.74166i	0.363141	+	0.363141i
$58$		0			0
$59$			15.3495i			1.99834i	0.0407464	+	0.999170i	$0.487026\pi$
$59$			15.3495i			1.99834i	−0.0407464	+	0.999170i	$0.512974\pi$
$60$	−2.25834	+	0.258343i	−0.291551	+	0.0333519i
$61$	14.6307			1.87327			0.936636	−	0.350304i	$-0.113922\pi$
$61$	14.6307			1.87327			0.936636	+	0.350304i	$0.113922\pi$
$62$		0			0
$63$	5.12917	−	5.12917i	0.646215	−	0.646215i
$64$		−	8.00000i		−	1.00000i
$65$	−1.61249	−	14.0958i	−0.200004	−	1.74837i
$66$		0			0
$67$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$67$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$68$		0			0
$69$			0.533109i			0.0641788i
$70$	6.55013	+	5.20536i	0.782890	+	0.622160i
$71$	7.22497			0.857446			0.428723	−	0.903436i	$-0.358964\pi$
$71$	7.22497			0.857446			0.428723	+	0.903436i	$0.358964\pi$
$72$	5.48331	+	5.48331i	0.646215	+	0.646215i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$		0			0
$75$	2.15642	+	1.34477i	0.249002	+	0.155280i
$76$	15.2567			1.75006
$77$		0			0
$78$	3.22497	−	3.22497i	0.365156	−	0.365156i
$79$			15.7417i			1.77107i	0.464568	+	0.885537i	$0.346210\pi$
$79$			15.7417i			1.77107i	−0.464568	+	0.885537i	$0.653790\pi$
$80$	−5.56477	+	7.00238i	−0.622160	+	0.782890i
$81$	−6.74166			−0.749073
$82$		0			0
$83$	−5.83132	+	5.83132i	−0.640071	+	0.640071i	−0.950573	−	0.310502i	$-0.899503\pi$
$83$	−5.83132	+	5.83132i	−0.640071	+	0.640071i	0.310502	+	0.950573i	$0.399503\pi$
$84$			2.68953i			0.293452i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	−0.985363	−	8.61370i	−0.103866	−	0.907964i
$91$	−16.7871			−1.75977
$92$	1.48331	+	1.48331i	0.154646	+	0.154646i
$93$		0			0
$94$		0			0
$95$	−13.3541	−	10.6125i	−1.37011	−	1.08882i
$96$	−2.87523			−0.293452
$97$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$97$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$98$	7.00000	−	7.00000i	0.707107	−	0.707107i
$99$		0			0
$100$	9.74166	−	2.25834i	0.974166	−	0.225834i
$101$	−13.1931			−1.31276			−0.656382	−	0.754429i	$-0.727914\pi$
$101$	−13.1931			−1.31276			−0.656382	+	0.754429i	$0.727914\pi$
$102$		0			0
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$		−	17.9462i		−	1.75977i
$105$	1.87083	−	2.35414i	0.182574	−	0.229741i
$106$		0			0
$107$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$107$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$108$	4.12715	−	4.12715i	0.397135	−	0.397135i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	7.48331	+	7.48331i	0.707107	+	0.707107i
$113$	−11.2250	+	11.2250i	−1.05596	+	1.05596i	−0.0576178	+	0.998339i	$0.518350\pi$
$113$	−11.2250	+	11.2250i	−1.05596	+	1.05596i	−0.998339	+	0.0576178i	$0.981650\pi$
$114$		−	5.48331i		−	0.513559i
$115$	−0.266555	−	2.33013i	−0.0248564	−	0.217286i
$116$		0			0
$117$	12.3006	+	12.3006i	1.13719	+	1.13719i
$118$	15.3495	−	15.3495i	1.41304	−	1.41304i
$119$		0			0
$120$	2.51669	+	2.00000i	0.229741	+	0.182574i
$121$	11.0000			1.00000
$122$	−14.6307	−	14.6307i	−1.32460	−	1.32460i
$123$		0			0
$124$		0			0
$125$	−10.0977	−	4.79953i	−0.903170	−	0.429283i
$126$	−10.2583			−0.913886
$127$	−12.2250	−	12.2250i	−1.08479	−	1.08479i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$	−12.2250	−	12.2250i	−1.08479	−	1.08479i	−0.0887357	−	0.996055i	$-0.528283\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		0			0
$130$	−12.4833	+	15.7083i	−1.09486	+	1.37771i
$131$	4.93881			0.431506			0.215753	−	0.976448i	$-0.430779\pi$
$131$	4.93881			0.431506			0.215753	+	0.976448i	$0.430779\pi$
$132$		0			0
$133$	−14.2713	+	14.2713i	−1.23748	+	1.23748i
$134$		0			0
$135$	−6.48331	+	0.741657i	−0.557995	+	0.0638317i
$136$		0			0
$137$	16.4833	+	16.4833i	1.40826	+	1.40826i	0.768922	+	0.639343i	$0.220793\pi$
$137$	16.4833	+	16.4833i	1.40826	+	1.40826i	0.639343	+	0.768922i	$0.279207\pi$
$138$	0.533109	−	0.533109i	0.0453813	−	0.0453813i
$139$		−	12.4743i		−	1.05806i	−0.848604	−	0.529028i	$-0.822557\pi$
$139$		−	12.4743i		−	1.05806i	0.848604	−	0.529028i	$-0.177443\pi$
$140$	−1.34477	−	11.7555i	−0.113654	−	0.993520i
$141$		0			0
$142$	−7.22497	−	7.22497i	−0.606306	−	0.606306i
$143$		0			0
$144$		−	10.9666i		−	0.913886i
$145$		0			0
$146$		0			0
$147$	−2.51583	−	2.51583i	−0.207502	−	0.207502i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	−0.811658	−	3.50119i	−0.0662716	−	0.285871i
$151$	22.4499			1.82695			0.913475	−	0.406894i	$-0.133388\pi$
$151$	22.4499			1.82695			0.913475	+	0.406894i	$0.133388\pi$
$152$	−15.2567	−	15.2567i	−1.23748	−	1.23748i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−6.44994			−0.516409
$157$	−16.4277	−	16.4277i	−1.31108	−	1.31108i	−0.920622	−	0.390455i	$-0.872318\pi$
$157$	−16.4277	−	16.4277i	−1.31108	−	1.31108i	−0.390455	−	0.920622i	$-0.627682\pi$
$158$	15.7417	−	15.7417i	1.25234	−	1.25234i
$159$		0			0
$160$	12.5671	−	1.43762i	0.993520	−	0.113654i
$161$	−2.77503			−0.218703
$162$	6.74166	+	6.74166i	0.529675	+	0.529675i
$163$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$163$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$164$		0			0
$165$		0			0
$166$	11.6626			0.905197
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$	2.68953	−	2.68953i	0.207502	−	0.207502i
$169$		−	27.2583i		−	2.09680i
$170$		0			0
$171$	20.9143			1.59936
$172$		0			0
$173$	13.5525	−	13.5525i	1.03038	−	1.03038i	0.0308546	−	0.999524i	$-0.490177\pi$
$173$	13.5525	−	13.5525i	1.03038	−	1.03038i	0.999524	−	0.0308546i	$-0.00982288\pi$
$174$		0			0
$175$	−7.00000	+	11.2250i	−0.529150	+	0.848528i
$176$		0			0
$177$	−5.51669	−	5.51669i	−0.414659	−	0.414659i
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−7.62834	+	9.59907i	−0.568583	+	0.715472i
$181$	−19.2910			−1.43389			−0.716944	−	0.697131i	$-0.754460\pi$
$181$	−19.2910			−1.43389			−0.716944	+	0.697131i	$0.754460\pi$
$182$	16.7871	+	16.7871i	1.24435	+	1.24435i
$183$	−5.25834	+	5.25834i	−0.388708	+	0.388708i
$184$		−	2.96663i		−	0.218703i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$			7.72119i			0.561634i
$190$	2.74166	+	23.9666i	0.198901	+	1.73872i
$191$	27.2250			1.96993			0.984965	−	0.172754i	$-0.0552667\pi$
$191$	27.2250			1.96993			0.984965	+	0.172754i	$0.0552667\pi$
$192$	2.87523	+	2.87523i	0.207502	+	0.207502i
$193$	−6.00000	+	6.00000i	−0.431889	+	0.431889i	−0.889271	−	0.457381i	$-0.848787\pi$
$193$	−6.00000	+	6.00000i	−0.431889	+	0.431889i	0.457381	+	0.889271i	$0.348787\pi$
$194$		0			0
$195$	5.64562	+	4.48655i	0.404291	+	0.321289i
$196$	−14.0000			−1.00000
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−12.0000	−	7.48331i	−0.848528	−	0.529150i
$201$		0			0
$202$	13.1931	+	13.1931i	0.928264	+	0.928264i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.03337	+	2.03337i	0.141329	+	0.141329i
$208$	−17.9462	+	17.9462i	−1.24435	+	1.24435i
$209$		0			0
$210$	−4.22497	+	0.483315i	−0.291551	+	0.0333519i
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$		0			0
$213$	−2.59668	+	2.59668i	−0.177922	+	0.177922i
$214$		0			0
$215$		0			0
$216$	−8.25430			−0.561634
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$		−	14.9666i		−	1.00000i
$225$	13.3541	−	3.09580i	0.890276	−	0.206387i
$226$	22.4499			1.49335
$227$	21.0880	+	21.0880i	1.39966	+	1.39966i	0.801013	+	0.598647i	$0.204295\pi$
$227$	21.0880	+	21.0880i	1.39966	+	1.39966i	0.598647	+	0.801013i	$0.295705\pi$
$228$	−5.48331	+	5.48331i	−0.363141	+	0.363141i
$229$			18.9436i			1.25183i	0.779893	+	0.625913i	$0.215274\pi$
$229$			18.9436i			1.25183i	−0.779893	+	0.625913i	$0.784726\pi$
$230$	−2.06358	+	2.59668i	−0.136068	+	0.171220i
$231$		0			0
$232$		0			0
$233$	−17.9666	+	17.9666i	−1.17703	+	1.17703i	−0.196537	+	0.980497i	$0.562969\pi$
$233$	−17.9666	+	17.9666i	−1.17703	+	1.17703i	−0.980497	+	0.196537i	$0.937031\pi$
$234$		−	24.6012i		−	1.60823i
$235$		0			0
$236$	−30.6991			−1.99834
$237$	−5.65762	−	5.65762i	−0.367502	−	0.367502i
$238$		0			0
$239$			7.48331i			0.484055i	0.970269	+	0.242028i	$0.0778125\pi$
$239$			7.48331i			0.484055i	−0.970269	+	0.242028i	$0.922188\pi$
$240$	−0.516685	−	4.51669i	−0.0333519	−	0.291551i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−11.0000	−	11.0000i	−0.707107	−	0.707107i
$243$	8.61370	−	8.61370i	0.552569	−	0.552569i
$244$			29.2615i			1.87327i
$245$	12.2542	+	9.73834i	0.782890	+	0.622160i
$246$		0			0
$247$	−34.2250	−	34.2250i	−2.17768	−	2.17768i
$248$		0			0
$249$		−	4.19160i		−	0.265632i
$250$	5.29821	+	14.8973i	0.335088	+	0.942187i
$251$	11.0367			0.696629			0.348315	−	0.937378i	$-0.386754\pi$
$251$	11.0367			0.696629			0.348315	+	0.937378i	$0.386754\pi$
$252$	10.2583	+	10.2583i	0.646215	+	0.646215i
$253$		0			0
$254$			24.4499i			1.53413i
$255$		0			0
$256$	16.0000			1.00000
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$		0			0
$259$		0			0
$260$	28.1916	−	3.22497i	1.74837	−	0.200004i
$261$		0			0
$262$	−4.93881	−	4.93881i	−0.305121	−	0.305121i
$263$	−11.2250	+	11.2250i	−0.692161	+	0.692161i	−0.962707	−	0.270546i	$-0.912796\pi$
$263$	−11.2250	+	11.2250i	−0.692161	+	0.692161i	0.270546	+	0.962707i	$0.412796\pi$
$264$		0			0
$265$		0			0
$266$	28.5426			1.75006
$267$		0			0
$268$		0			0
$269$		−	31.8581i		−	1.94242i	−0.238215	−	0.971212i	$-0.576562\pi$
$269$		−	31.8581i		−	1.94242i	0.238215	−	0.971212i	$-0.423438\pi$
$270$	7.22497	+	5.74166i	0.439698	+	0.349426i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	6.03337	−	6.03337i	0.365156	−	0.365156i
$274$		−	32.9666i		−	1.99159i
$275$		0			0
$276$	−1.06622			−0.0641788
$277$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$277$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$278$	−12.4743	+	12.4743i	−0.748159	+	0.748159i
$279$		0			0
$280$	−10.4107	+	13.1003i	−0.622160	+	0.782890i
$281$	−14.9666			−0.892834			−0.446417	−	0.894825i	$-0.647300\pi$
$281$	−14.9666			−0.892834			−0.446417	+	0.894825i	$0.647300\pi$
$282$		0			0
$283$	18.3985	−	18.3985i	1.09368	−	1.09368i	0.0985428	−	0.995133i	$-0.468582\pi$
$283$	18.3985	−	18.3985i	1.09368	−	1.09368i	0.995133	−	0.0985428i	$-0.0314181\pi$
$284$			14.4499i			0.857446i
$285$	8.61370	−	0.985363i	0.510232	−	0.0583679i
$286$		0			0
$287$		0			0
$288$	−10.9666	+	10.9666i	−0.646215	+	0.646215i
$289$			17.0000i			1.00000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−17.8654	+	17.8654i	−1.04371	+	1.04371i	−0.0447054	+	0.999000i	$0.514235\pi$
$293$	−17.8654	+	17.8654i	−1.04371	+	1.04371i	−0.999000	+	0.0447054i	$0.985765\pi$
$294$			5.03166i			0.293452i
$295$	26.8708	+	21.3541i	1.56448	+	1.24329i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	6.65497i		−	0.384867i
$300$	−2.68953	+	4.31285i	−0.155280	+	0.249002i
$301$		0			0
$302$	−22.4499	−	22.4499i	−1.29185	−	1.29185i
$303$	4.74166	−	4.74166i	0.272401	−	0.272401i
$304$			30.5134i			1.75006i
$305$	20.3541	−	25.6125i	1.16547	−	1.46657i
$306$		0			0
$307$	0.452253	+	0.452253i	0.0258115	+	0.0258115i	0.719895	−	0.694083i	$-0.244190\pi$
$307$	0.452253	+	0.452253i	0.0258115	+	0.0258115i	−0.694083	+	0.719895i	$0.744190\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	6.44994	+	6.44994i	0.365156	+	0.365156i
$313$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$313$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$314$			32.8555i			1.85414i
$315$	−1.84345	−	16.1148i	−0.103866	−	0.907964i
$316$	−31.4833			−1.77107
$317$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$317$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$318$		0			0
$319$		0			0
$320$	−14.0048	−	11.1295i	−0.782890	−	0.622160i
$321$		0			0
$322$	2.77503	+	2.77503i	0.154646	+	0.154646i
$323$		0			0
$324$		−	13.4833i		−	0.749073i
$325$	−26.9193	−	16.7871i	−1.49322	−	0.931184i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−11.6626	−	11.6626i	−0.640071	−	0.640071i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−5.37907			−0.293452
$337$	18.0000	+	18.0000i	0.980522	+	0.980522i	0.999814	−	0.0192914i	$-0.00614103\pi$
$337$	18.0000	+	18.0000i	0.980522	+	0.980522i	−0.0192914	+	0.999814i	$0.506141\pi$
$338$	−27.2583	+	27.2583i	−1.48266	+	1.48266i
$339$		−	8.06860i		−	0.438226i
$340$		0			0
$341$		0			0
$342$	−20.9143	−	20.9143i	−1.13092	−	1.13092i
$343$	13.0958	−	13.0958i	0.707107	−	0.707107i
$344$		0			0
$345$	0.933259	+	0.741657i	0.0502450	+	0.0399295i
$346$	−27.1050			−1.45718
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$		−	11.2224i		−	0.600720i	−0.953826	−	0.300360i	$-0.902893\pi$
$349$		−	11.2224i		−	0.600720i	0.953826	−	0.300360i	$-0.0971069\pi$
$350$	18.2250	−	4.22497i	0.974166	−	0.225834i
$351$	−18.5167			−0.988348
$352$		0			0
$353$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$353$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$354$			11.0334i			0.586417i
$355$	10.0513	−	12.6480i	0.533469	−	0.671286i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$	17.2274	−	1.97073i	0.907964	−	0.103866i
$361$	−39.1916			−2.06272
$362$	19.2910	+	19.2910i	1.01391	+	1.01391i
$363$	−3.95345	+	3.95345i	−0.207502	+	0.207502i
$364$		−	33.5743i		−	1.75977i
$365$		0			0
$366$	10.5167			0.549716
$367$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$367$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$368$	−2.96663	+	2.96663i	−0.154646	+	0.154646i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$373$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$374$		0			0
$375$	5.35414	−	1.90420i	0.276487	−	0.0983324i
$376$		0			0
$377$		0			0
$378$	7.72119	−	7.72119i	0.397135	−	0.397135i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	21.2250	−	26.7083i	1.08882	−	1.37011i
$381$	8.78741			0.450193
$382$	−27.2250	−	27.2250i	−1.39295	−	1.39295i
$383$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$383$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$384$		−	5.75047i		−	0.293452i
$385$		0			0
$386$	12.0000			0.610784
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	−1.15907	−	10.1322i	−0.0586917	−	0.513063i
$391$		0			0
$392$	14.0000	+	14.0000i	0.707107	+	0.707107i
$393$	−1.77503	+	1.77503i	−0.0895383	+	0.0895383i
$394$		0			0
$395$	27.5573	+	21.8997i	1.38656	+	1.10189i
$396$		0			0
$397$	18.5842	+	18.5842i	0.932713	+	0.932713i	0.997875	−	0.0651619i	$-0.0207564\pi$
$397$	18.5842	+	18.5842i	0.932713	+	0.932713i	−0.0651619	+	0.997875i	$0.520756\pi$
$398$		0			0
$399$		−	10.2583i		−	0.513559i
$400$	4.51669	+	19.4833i	0.225834	+	0.974166i
$401$	37.2250			1.85893			0.929463	−	0.368915i	$-0.120271\pi$
$401$	37.2250			1.85893			0.929463	+	0.368915i	$0.120271\pi$
$402$		0			0
$403$		0			0
$404$		−	26.3862i		−	1.31276i
$405$	−9.37894	+	11.8019i	−0.466043	+	0.586442i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$		0			0
$411$	−11.8483			−0.584436
$412$		0			0
$413$	28.7163	−	28.7163i	1.41304	−	1.41304i
$414$		−	4.06674i		−	0.199869i
$415$	2.09580	+	18.3208i	0.102879	+	0.899331i
$416$	35.8924			1.75977
$417$	4.48331	+	4.48331i	0.219549	+	0.219549i
$418$		0			0
$419$			40.8312i			1.99474i	0.0725002	+	0.997368i	$0.476902\pi$
$419$			40.8312i			1.99474i	−0.0725002	+	0.997368i	$0.523098\pi$
$420$	4.70829	+	3.74166i	0.229741	+	0.182574i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	5.19337			0.251620
$427$	−27.3716	−	27.3716i	−1.32460	−	1.32460i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.0000			−0.867029			−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000			−0.867029			−0.433515	+	0.901146i	$0.642727\pi$
$432$	8.25430	+	8.25430i	0.397135	+	0.397135i
$433$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$433$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.65762	−	5.65762i	−0.270640	−	0.270640i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−19.1916			−0.913886
$442$		0			0
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−14.9666	+	14.9666i	−0.707107	+	0.707107i
$449$		−	29.9333i		−	1.41264i	−0.707894	−	0.706319i	$-0.750354\pi$
$449$		−	29.9333i		−	1.41264i	0.707894	−	0.706319i	$-0.249646\pi$
$450$	−16.4499	−	10.2583i	−0.775458	−	0.483583i
$451$		0			0
$452$	−22.4499	−	22.4499i	−1.05596	−	1.05596i
$453$	−8.06860	+	8.06860i	−0.379096	+	0.379096i
$454$		−	42.1760i		−	1.97942i
$455$	−23.3541	+	29.3875i	−1.09486	+	1.37771i
$456$	10.9666			0.513559
$457$	−3.74166	−	3.74166i	−0.175027	−	0.175027i	0.614157	−	0.789184i	$-0.289496\pi$
$457$	−3.74166	−	3.74166i	−0.175027	−	0.175027i	−0.789184	+	0.614157i	$0.789496\pi$
$458$	18.9436	−	18.9436i	0.885175	−	0.885175i
$459$		0			0
$460$	4.66026	−	0.533109i	0.217286	−	0.0248564i
$461$	21.9805			1.02373			0.511867	−	0.859064i	$-0.328954\pi$
$461$	21.9805			1.02373			0.511867	+	0.859064i	$0.328954\pi$
$462$		0			0
$463$	24.0000	−	24.0000i	1.11537	−	1.11537i	0.122963	−	0.992411i	$-0.460760\pi$
$463$	24.0000	−	24.0000i	1.11537	−	1.11537i	0.992411	−	0.122963i	$-0.0392398\pi$
$464$		0			0
$465$		0			0
$466$	35.9333			1.66458
$467$	−30.3397	−	30.3397i	−1.40395	−	1.40395i	−0.787003	−	0.616949i	$-0.788368\pi$
$467$	−30.3397	−	30.3397i	−1.40395	−	1.40395i	−0.616949	−	0.787003i	$-0.711632\pi$
$468$	−24.6012	+	24.6012i	−1.13719	+	1.13719i
$469$		0			0
$470$		0			0
$471$	11.8084			0.544102
$472$	30.6991	+	30.6991i	1.41304	+	1.41304i
$473$		0			0
$474$			11.3152i			0.519726i
$475$	−37.1563	+	8.61370i	−1.70485	+	0.395224i
$476$		0			0
$477$		0			0
$478$	7.48331	−	7.48331i	0.342279	−	0.342279i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	−4.00000	+	5.03337i	−0.182574	+	0.229741i
$481$		0			0
$482$		0			0
$483$	0.997356	−	0.997356i	0.0453813	−	0.0453813i
$484$			22.0000i			1.00000i
$485$		0			0
$486$	−17.2274			−0.781451
$487$	7.77503	+	7.77503i	0.352320	+	0.352320i	0.860972	−	0.508652i	$-0.169856\pi$
$487$	7.77503	+	7.77503i	0.352320	+	0.352320i	−0.508652	+	0.860972i	$0.669856\pi$
$488$	29.2615	−	29.2615i	1.32460	−	1.32460i
$489$		0			0
$490$	−2.51583	−	21.9925i	−0.113654	−	0.993520i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$			68.4499i			3.07971i
$495$		0			0
$496$		0			0
$497$	−13.5167	−	13.5167i	−0.606306	−	0.606306i
$498$	−4.19160	+	4.19160i	−0.187830	+	0.187830i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	9.59907	−	20.1955i	0.429283	−	0.903170i
$501$		0			0
$502$	−11.0367	−	11.0367i	−0.492591	−	0.492591i
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		−	20.5167i		−	0.913886i
$505$	−18.3541	+	23.0958i	−0.816749	+	1.02775i
$506$		0			0
$507$	9.79676	+	9.79676i	0.435089	+	0.435089i
$508$	24.4499	−	24.4499i	1.08479	−	1.08479i
$509$		−	8.88026i		−	0.393611i	−0.980443	−	0.196805i	$-0.936943\pi$
$509$		−	8.88026i		−	0.393611i	0.980443	−	0.196805i	$-0.0630567\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−15.7417	+	15.7417i	−0.695011	+	0.695011i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$			9.74166i			0.427611i
$520$	−31.4166	−	24.9666i	−1.37771	−	1.09486i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−31.7773	+	31.7773i	−1.38952	+	1.38952i	−0.563209	+	0.826315i	$0.690433\pi$
$523$	−31.7773	+	31.7773i	−1.38952	+	1.38952i	−0.826315	+	0.563209i	$0.809567\pi$
$524$			9.87762i			0.431506i
$525$	−1.51847	−	6.55013i	−0.0662716	−	0.285871i
$526$	22.4499			0.978864
$527$		0			0
$528$		0			0
$529$			21.8999i			0.952169i
$530$		0			0
$531$	−42.0832			−1.82625
$532$	−28.5426	−	28.5426i	−1.23748	−	1.23748i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−31.8581	+	31.8581i	−1.37350	+	1.37350i
$539$		0			0
$540$	−1.48331	−	12.9666i	−0.0638317	−	0.557995i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	6.93326	−	6.93326i	0.297535	−	0.297535i
$544$		0			0
$545$		0			0
$546$	−12.0667			−0.516409
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	−32.9666	+	32.9666i	−1.40826	+	1.40826i
$549$			40.1124i			1.71196i
$550$		0			0
$551$		0			0
$552$	1.06622	+	1.06622i	0.0453813	+	0.0453813i
$553$	29.4499	−	29.4499i	1.25234	−	1.25234i
$554$		0			0
$555$		0			0
$556$	24.9486			1.05806
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$		0			0
$559$		0			0
$560$	23.5110	−	2.68953i	0.993520	−	0.113654i
$561$		0			0
$562$	14.9666	+	14.9666i	0.631329	+	0.631329i
$563$	−28.1832	+	28.1832i	−1.18778	+	1.18778i	−0.210103	+	0.977679i	$0.567380\pi$
$563$	−28.1832	+	28.1832i	−1.18778	+	1.18778i	−0.977679	+	0.210103i	$0.932620\pi$
$564$		0			0
$565$	4.03430	+	35.2665i	0.169724	+	1.48367i
$566$	−36.7969			−1.54669
$567$	12.6125	+	12.6125i	0.529675	+	0.529675i
$568$	14.4499	−	14.4499i	0.606306	−	0.606306i
$569$		−	31.6749i		−	1.32788i	−0.747785	−	0.663941i	$-0.768883\pi$
$569$		−	31.6749i		−	1.32788i	0.747785	−	0.663941i	$-0.231117\pi$
$570$	−9.59907	−	7.62834i	−0.402061	−	0.319516i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−9.78477	+	9.78477i	−0.408764	+	0.408764i
$574$		0			0
$575$	−4.44994	−	2.77503i	−0.185576	−	0.115727i
$576$	21.9333			0.913886
$577$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$577$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$578$	17.0000	−	17.0000i	0.707107	−	0.707107i
$579$		−	4.31285i		−	0.179236i
$580$		0			0
$581$	21.8188			0.905197
$582$		0			0
$583$		0			0
$584$		0			0
$585$	38.6459	−	4.42088i	1.59781	−	0.182781i
$586$	35.7307			1.47602
$587$	32.4961	+	32.4961i	1.34126	+	1.34126i	0.894810	+	0.446447i	$0.147311\pi$
$587$	32.4961	+	32.4961i	1.34126	+	1.34126i	0.446447	+	0.894810i	$0.352689\pi$
$588$	5.03166	−	5.03166i	0.207502	−	0.207502i
$589$		0			0
$590$	−5.51669	−	48.2250i	−0.227118	−	1.98539i
$591$		0			0
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−6.65497	+	6.65497i	−0.272142	+	0.272142i
$599$		−	41.6749i		−	1.70279i	−0.524524	−	0.851395i	$-0.675757\pi$
$599$		−	41.6749i		−	1.70279i	0.524524	−	0.851395i	$-0.324243\pi$
$600$	7.00238	−	1.62332i	0.285871	−	0.0662716i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$			44.8999i			1.82695i
$605$	15.3031	−	19.2566i	0.622160	−	0.782890i
$606$	−9.48331			−0.385233
$607$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$607$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$608$	30.5134	−	30.5134i	1.23748	−	1.23748i
$609$		0			0
$610$	−45.9666	+	5.25834i	−1.86113	+	0.212904i
$611$		0			0
$612$		0			0
$613$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$613$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$614$		−	0.904507i		−	0.0365029i
$615$		0			0
$616$		0			0
$617$	33.6749	+	33.6749i	1.35570	+	1.35570i	0.879143	+	0.476558i	$0.158116\pi$
$617$	33.6749	+	33.6749i	1.35570	+	1.35570i	0.476558	+	0.879143i	$0.341884\pi$
$618$		0			0
$619$			8.16145i			0.328036i	0.986457	+	0.164018i	$0.0524456\pi$
$619$			8.16145i			0.328036i	−0.986457	+	0.164018i	$0.947554\pi$
$620$		0			0
$621$	−3.06093			−0.122831
$622$		0			0
$623$		0			0
$624$		−	12.8999i		−	0.516409i
$625$	−22.4499	+	11.0000i	−0.897998	+	0.440000i
$626$		0			0
$627$		0			0
$628$	32.8555	−	32.8555i	1.31108	−	1.31108i
$629$		0			0
$630$	−14.2713	+	17.9582i	−0.568583	+	0.715472i
$631$	−50.1916			−1.99810			−0.999048	−	0.0436231i	$-0.986110\pi$
$631$	−50.1916			−1.99810			−0.999048	+	0.0436231i	$0.986110\pi$
$632$	31.4833	+	31.4833i	1.25234	+	1.25234i
$633$		0			0
$634$		0			0
$635$	−38.4083	+	4.39371i	−1.52419	+	0.174359i
$636$		0			0
$637$	31.4059	+	31.4059i	1.24435	+	1.24435i
$638$		0			0
$639$			19.8084i			0.783608i
$640$	2.87523	+	25.1343i	0.113654	+	0.993520i
$641$	−22.7750			−0.899560			−0.449780	−	0.893140i	$-0.648498\pi$
$641$	−22.7750			−0.899560			−0.449780	+	0.893140i	$0.648498\pi$
$642$		0			0
$643$	27.4644	−	27.4644i	1.08309	−	1.08309i	0.0868719	−	0.996219i	$-0.472313\pi$
$643$	27.4644	−	27.4644i	1.08309	−	1.08309i	0.996219	−	0.0868719i	$-0.0276871\pi$
$644$		−	5.55006i		−	0.218703i
$645$		0			0
$646$		0			0
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$	−13.4833	+	13.4833i	−0.529675	+	0.529675i
$649$		0			0
$650$	10.1322	+	43.7065i	0.397417	+	1.71431i
$651$		0			0
$652$		0			0
$653$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$653$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$654$		0			0
$655$	6.87083	−	8.64586i	0.268465	−	0.337822i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−26.4791			−1.02992			−0.514958	−	0.857215i	$-0.672193\pi$
$661$	−26.4791			−1.02992			−0.514958	+	0.857215i	$0.672193\pi$
$662$		0			0
$663$		0			0
$664$			23.3253i			0.905197i
$665$	5.12917	+	44.8375i	0.198901	+	1.73872i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	5.37907	+	5.37907i	0.207502	+	0.207502i
$673$	9.44994	−	9.44994i	0.364269	−	0.364269i	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	9.44994	−	9.44994i	0.364269	−	0.364269i	0.865382	+	0.501113i	$0.167076\pi$
$674$		−	36.0000i		−	1.38667i
$675$	−7.72119	+	12.3815i	−0.297189	+	0.476562i
$676$	54.5167			2.09680
$677$	−20.0218	−	20.0218i	−0.769500	−	0.769500i	0.208519	−	0.978018i	$-0.433136\pi$
$677$	−20.0218	−	20.0218i	−0.769500	−	0.769500i	−0.978018	+	0.208519i	$0.933136\pi$
$678$	−8.06860	+	8.06860i	−0.309873	+	0.309873i
$679$		0			0
$680$		0			0
$681$	−15.1582			−0.580865
$682$		0			0
$683$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$683$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$684$			41.8286i			1.59936i
$685$	51.7871	−	5.92417i	1.97868	−	0.226351i
$686$	−26.1916			−1.00000
$687$	−6.80840	−	6.80840i	−0.259757	−	0.259757i
$688$		0			0
$689$		0			0
$690$	−0.191602	−	1.67492i	−0.00729415	−	0.0637630i
$691$	−15.6969			−0.597140			−0.298570	−	0.954388i	$-0.596510\pi$
$691$	−15.6969			−0.597140			−0.298570	+	0.954388i	$0.596510\pi$
$692$	27.1050	+	27.1050i	1.03038	+	1.03038i
$693$		0			0
$694$		0			0
$695$	−21.8375	−	17.3541i	−0.828342	−	0.658280i
$696$		0			0
$697$		0			0
$698$	−11.2224	+	11.2224i	−0.424773	+	0.424773i
$699$		−	12.9146i		−	0.488474i
$700$	−22.4499	−	14.0000i	−0.848528	−	0.529150i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	18.5167	+	18.5167i	0.698867	+	0.698867i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.6820	+	24.6820i	0.928264	+	0.928264i
$708$	11.0334	−	11.0334i	0.414659	−	0.414659i
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	−22.6993	+	2.59668i	−0.851891	+	0.0974518i
$711$	−43.1582			−1.61856
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.68953	−	2.68953i	−0.100442	−	0.100442i
$718$	−6.00000	+	6.00000i	−0.223918	+	0.223918i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−19.1981	−	15.2567i	−0.715472	−	0.568583i
$721$		0			0
$722$	39.1916	+	39.1916i	1.45856	+	1.45856i
$723$		0			0
$724$		−	38.5820i		−	1.43389i
$725$		0			0
$726$	7.90689			0.293452
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$	−33.5743	+	33.5743i	−1.24435	+	1.24435i
$729$		−	14.0334i		−	0.519754i
$730$		0			0
$731$		0			0
$732$	−10.5167	−	10.5167i	−0.388708	−	0.388708i
$733$	9.95847	−	9.95847i	0.367825	−	0.367825i	−0.498859	−	0.866683i	$-0.666247\pi$
$733$	9.95847	−	9.95847i	0.367825	−	0.367825i	0.866683	+	0.498859i	$0.166247\pi$
$734$		0			0
$735$	−7.90420	+	0.904199i	−0.291551	+	0.0333519i
$736$	5.93326			0.218703
$737$		0			0
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$		0			0
$741$	24.6012			0.903747
$742$		0			0
$743$	30.7417	−	30.7417i	1.12780	−	1.12780i	0.137268	−	0.990534i	$-0.456168\pi$
$743$	30.7417	−	30.7417i	1.12780	−	1.12780i	0.990534	−	0.137268i	$-0.0438322\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.9875	−	15.9875i	−0.584952	−	0.584952i
$748$		0			0
$749$		0			0
$750$	−7.25834	−	3.44994i	−0.265037	−	0.125974i
$751$	22.4499			0.819210			0.409605	−	0.912263i	$-0.365667\pi$
$751$	22.4499			0.819210			0.409605	+	0.912263i	$0.365667\pi$
$752$		0			0
$753$	−3.96663	+	3.96663i	−0.144552	+	0.144552i
$754$		0			0
$755$	31.2322	−	39.3008i	1.13666	−	1.43030i
$756$	−15.4424			−0.561634
$757$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$757$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$758$		0			0
$759$		0			0
$760$	−47.9333	+	5.48331i	−1.73872	+	0.198901i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	−8.78741	−	8.78741i	−0.318334	−	0.318334i
$763$		0			0
$764$			54.4499i			1.96993i
$765$		0			0
$766$		0			0
$767$	68.8665	+	68.8665i	2.48663	+	2.48663i
$768$	−5.75047	+	5.75047i	−0.207502	+	0.207502i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	−12.0000	−	12.0000i	−0.431889	−	0.431889i
$773$	25.1223	−	25.1223i	0.903587	−	0.903587i	−0.0921578	−	0.995744i	$-0.529376\pi$
$773$	25.1223	−	25.1223i	0.903587	−	0.903587i	0.995744	+	0.0921578i	$0.0293764\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−8.97311	+	11.2912i	−0.321289	+	0.404291i
$781$		0			0
$782$		0			0
$783$		0			0
$784$		−	28.0000i		−	1.00000i
$785$	−51.6125	+	5.90420i	−1.84213	+	0.210730i
$786$	3.55006			0.126626
$787$	−33.9337	−	33.9337i	−1.20961	−	1.20961i	−0.971154	−	0.238451i	$-0.923360\pi$
$787$	−33.9337	−	33.9337i	−1.20961	−	1.20961i	−0.238451	−	0.971154i	$-0.576640\pi$
$788$		0			0
$789$		−	8.06860i		−	0.287250i
$790$	−5.65762	−	49.4569i	−0.201289	−	1.75960i
$791$	42.0000			1.49335
$792$		0			0
$793$	65.6415	−	65.6415i	2.33100	−	2.33100i
$794$		−	37.1683i		−	1.31906i
$795$		0			0
$796$		0			0
$797$	−9.86562	−	9.86562i	−0.349458	−	0.349458i	0.510449	−	0.859908i	$-0.329479\pi$
$797$	−9.86562	−	9.86562i	−0.349458	−	0.349458i	−0.859908	+	0.510449i	$0.829479\pi$
$798$	−10.2583	+	10.2583i	−0.363141	+	0.363141i
$799$		0			0
$800$	14.9666	−	24.0000i	0.529150	−	0.848528i
$801$		0			0
$802$	−37.2250	−	37.2250i	−1.31446	−	1.31446i
$803$		0			0
$804$		0			0
$805$	−3.86060	+	4.85795i	−0.136068	+	0.171220i
$806$		0			0
$807$	11.4499	+	11.4499i	0.403057	+	0.403057i
$808$	−26.3862	+	26.3862i	−0.928264	+	0.928264i
$809$		−	11.6749i		−	0.410468i	−0.978713	−	0.205234i	$-0.934204\pi$
$809$		−	11.6749i		−	0.410468i	0.978713	−	0.205234i	$-0.0657956\pi$
$810$	21.1809	−	2.42298i	0.744219	−	0.0851348i
$811$	46.2103			1.62266			0.811332	−	0.584586i	$-0.198743\pi$
$811$	46.2103			1.62266			0.811332	+	0.584586i	$0.198743\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		−	46.0246i		−	1.60823i
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	11.8483	+	11.8483i	0.413258	+	0.413258i
$823$	−36.0000	+	36.0000i	−1.25488	+	1.25488i	−0.301376	+	0.953506i	$0.597446\pi$
$823$	−36.0000	+	36.0000i	−1.25488	+	1.25488i	−0.953506	+	0.301376i	$0.902554\pi$
$824$		0			0
$825$		0			0
$826$	−57.4327			−1.99834
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	−4.06674	+	4.06674i	−0.141329	+	0.141329i
$829$		−	23.2564i		−	0.807729i	−0.914819	−	0.403864i	$-0.867667\pi$
$829$		−	23.2564i		−	0.807729i	0.914819	−	0.403864i	$-0.132333\pi$
$830$	16.2250	−	20.4166i	0.563177	−	0.708670i
$831$		0			0
$832$	−35.8924	−	35.8924i	−1.24435	−	1.24435i
$833$		0			0
$834$		−	8.96663i		−	0.310489i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	40.8312	−	40.8312i	1.41049	−	1.41049i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−0.966630	−	8.44994i	−0.0333519	−	0.291551i
$841$	−29.0000			−1.00000
$842$		0			0
$843$	5.37907	−	5.37907i	0.185265	−	0.185265i
$844$		0			0
$845$	−47.7183	−	37.9216i	−1.64156	−	1.30454i
$846$		0			0
$847$	−20.5791	−	20.5791i	−0.707107	−	0.707107i
$848$		0			0
$849$			13.2250i			0.453880i
$850$		0			0
$851$		0			0
$852$	−5.19337	−	5.19337i	−0.177922	−	0.177922i
$853$	20.7406	−	20.7406i	0.710144	−	0.710144i	−0.256421	−	0.966565i	$-0.582543\pi$
$853$	20.7406	−	20.7406i	0.710144	−	0.710144i	0.966565	+	0.256421i	$0.0825433\pi$
$854$			54.7432i			1.87327i
$855$	29.0958	−	36.6125i	0.995055	−	1.25212i
$856$		0			0
$857$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$857$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$858$		0			0
$859$		−	0.440260i		−	0.0150215i	−0.999972	−	0.00751074i	$-0.997609\pi$
$859$		−	0.440260i		−	0.0150215i	0.999972	−	0.00751074i	$-0.00239076\pi$
$860$		0			0
$861$		0			0
$862$	18.0000	+	18.0000i	0.613082	+	0.613082i
$863$	−11.2250	+	11.2250i	−0.382102	+	0.382102i	−0.871859	−	0.489757i	$-0.837086\pi$
$863$	−11.2250	+	11.2250i	−0.382102	+	0.382102i	0.489757	+	0.871859i	$0.337086\pi$
$864$		−	16.5086i		−	0.561634i
$865$	−4.87083	−	42.5791i	−0.165613	−	1.44773i
$866$		0			0
$867$	−6.10987	−	6.10987i	−0.207502	−	0.207502i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$			11.3152i			0.382743i
$875$	9.91205	+	27.8703i	0.335088	+	0.942187i
$876$		0			0
$877$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$877$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$878$		0			0
$879$		−	12.8418i		−	0.433142i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	19.1916	+	19.1916i	0.646215	+	0.646215i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$		0			0
$885$	−17.3323	+	1.98272i	−0.582617	+	0.0666484i
$886$		0			0
$887$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$887$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$888$		0			0
$889$			45.7417i			1.53413i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	29.9333			1.00000
$897$	2.39182	+	2.39182i	0.0798607	+	0.0798607i
$898$	−29.9333	+	29.9333i	−0.998886	+	0.998886i
$899$		0			0
$900$	6.19160	+	26.7083i	0.206387	+	0.890276i
$901$		0			0
$902$		0			0
$903$		0			0
$904$			44.8999i			1.49335i
$905$	−26.8375	+	33.7707i	−0.892107	+	1.12258i
$906$	16.1372			0.536123
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$	−42.1760	+	42.1760i	−1.39966	+	1.39966i
$909$		−	36.1710i		−	1.19972i
$910$	52.7417	−	6.03337i	1.74837	−	0.200004i
$911$	−52.3832			−1.73553			−0.867766	−	0.496972i	$-0.834445\pi$
$911$	−52.3832			−1.73553			−0.867766	+	0.496972i	$0.834445\pi$
$912$	−10.9666	−	10.9666i	−0.363141	−	0.363141i
$913$		0			0
$914$			7.48331i			0.247526i
$915$	1.88987	+	16.5206i	0.0624772	+	0.546154i
$916$	−37.8871			−1.25183
$917$	−9.23966	−	9.23966i	−0.305121	−	0.305121i
$918$		0			0
$919$			53.1582i			1.75353i	0.480921	+	0.876764i	$0.340303\pi$
$919$			53.1582i			1.75353i	−0.480921	+	0.876764i	$0.659697\pi$
$920$	−5.19337	−	4.12715i	−0.171220	−	0.136068i
$921$	−0.325084			−0.0107119
$922$	−21.9805	−	21.9805i	−0.723890	−	0.723890i
$923$	32.4152	−	32.4152i	1.06696	−	1.06696i
$924$		0			0
$925$		0			0
$926$	−48.0000			−1.57738
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	53.3984			1.75006
$932$	−35.9333	−	35.9333i	−1.17703	−	1.17703i
$933$		0			0
$934$			60.6793i			1.98549i
$935$		0			0
$936$	49.2024			1.60823
$937$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.9267			−1.30157			−0.650787	−	0.759260i	$-0.725561\pi$
$941$	−39.9267			−1.30157			−0.650787	+	0.759260i	$0.725561\pi$
$942$	−11.8084	−	11.8084i	−0.384738	−	0.384738i
$943$		0			0
$944$		−	61.3981i		−	1.99834i
$945$	13.5167	+	10.7417i	0.439698	+	0.349426i
$946$		0			0
$947$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$947$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$948$	11.3152	−	11.3152i	0.367502	−	0.367502i
$949$		0			0
$950$	45.7701	+	28.5426i	1.48498	+	0.926046i
$951$		0			0
$952$		0			0
$953$	12.0334	−	12.0334i	0.389799	−	0.389799i	−0.484817	−	0.874616i	$-0.661114\pi$
$953$	12.0334	−	12.0334i	0.389799	−	0.389799i	0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	37.8752	−	47.6599i	1.22561	−	1.54224i
$956$	−14.9666			−0.484055
$957$		0			0
$958$		0			0
$959$		−	61.6749i		−	1.99159i
$960$	9.03337	−	1.03337i	0.291551	−	0.0333519i
$961$	31.0000			1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.15642	+	18.8507i	0.0694178	+	0.606826i
$966$	−1.99471			−0.0641788
$967$	17.7750	+	17.7750i	0.571606	+	0.571606i	0.932577	−	0.360971i	$-0.117555\pi$
$967$	17.7750	+	17.7750i	0.571606	+	0.571606i	−0.360971	+	0.932577i	$0.617555\pi$
$968$	22.0000	−	22.0000i	0.707107	−	0.707107i
$969$		0			0
$970$		0			0
$971$	−23.9752			−0.769402			−0.384701	−	0.923041i	$-0.625695\pi$
$971$	−23.9752			−0.769402			−0.384701	+	0.923041i	$0.625695\pi$
$972$	17.2274	+	17.2274i	0.552569	+	0.552569i
$973$	−23.3373	+	23.3373i	−0.748159	+	0.748159i
$974$		−	15.5501i		−	0.498256i
$975$	15.7083	−	3.64155i	0.503068	−	0.116623i
$976$	−58.5229			−1.87327
$977$	−20.9333	−	20.9333i	−0.669714	−	0.669714i	0.287936	−	0.957650i	$-0.407031\pi$
$977$	−20.9333	−	20.9333i	−0.669714	−	0.669714i	−0.957650	+	0.287936i	$0.907031\pi$
$978$		0			0
$979$		0			0
$980$	−19.4767	+	24.5083i	−0.622160	+	0.782890i
$981$		0			0
$982$		0			0
$983$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$983$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	68.4499	−	68.4499i	2.17768	−	2.17768i
$989$		0			0
$990$		0			0
$991$	9.80840			0.311574			0.155787	−	0.987791i	$-0.450209\pi$
$991$	9.80840			0.311574			0.155787	+	0.987791i	$0.450209\pi$
$992$		0			0
$993$		0			0
$994$			27.0334i			0.857446i
$995$		0			0
$996$	8.38320			0.265632
$997$	14.3642	+	14.3642i	0.454918	+	0.454918i	0.896983	−	0.442065i	$-0.145754\pi$
$997$	14.3642	+	14.3642i	0.454918	+	0.454918i	−0.442065	+	0.896983i	$0.645754\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.a.237.2	yes	8
4.3	odd	2		1120.2.w.a.657.3		8
5.3	odd	4	inner	280.2.s.a.13.2	✓	8
7.6	odd	2	inner	280.2.s.a.237.3	yes	8
8.3	odd	2		1120.2.w.a.657.2		8
8.5	even	2	inner	280.2.s.a.237.3	yes	8
20.3	even	4		1120.2.w.a.433.3		8
28.27	even	2		1120.2.w.a.657.2		8
35.13	even	4	inner	280.2.s.a.13.3	yes	8
40.3	even	4		1120.2.w.a.433.2		8
40.13	odd	4	inner	280.2.s.a.13.3	yes	8
56.13	odd	2	CM	280.2.s.a.237.2	yes	8
56.27	even	2		1120.2.w.a.657.3		8
140.83	odd	4		1120.2.w.a.433.2		8
280.13	even	4	inner	280.2.s.a.13.2	✓	8
280.83	odd	4		1120.2.w.a.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.a.13.2	✓	8	5.3	odd	4	inner
280.2.s.a.13.2	✓	8	280.13	even	4	inner
280.2.s.a.13.3	yes	8	35.13	even	4	inner
280.2.s.a.13.3	yes	8	40.13	odd	4	inner
280.2.s.a.237.2	yes	8	1.1	even	1	trivial
280.2.s.a.237.2	yes	8	56.13	odd	2	CM
280.2.s.a.237.3	yes	8	7.6	odd	2	inner
280.2.s.a.237.3	yes	8	8.5	even	2	inner
1120.2.w.a.433.2		8	40.3	even	4
1120.2.w.a.433.2		8	140.83	odd	4
1120.2.w.a.433.3		8	20.3	even	4
1120.2.w.a.433.3		8	280.83	odd	4
1120.2.w.a.657.2		8	8.3	odd	2
1120.2.w.a.657.2		8	28.27	even	2
1120.2.w.a.657.3		8	4.3	odd	2
1120.2.w.a.657.3		8	56.27	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.359404 + 0.359404i) q^{3} +2.00000i q^{4} +(1.39119 - 1.75060i) q^{5} +0.718808 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.74166i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.359404 + 0.359404i) q^{3} +2.00000i q^{4} +(1.39119 - 1.75060i) q^{5} +0.718808 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.74166i q^{9} +(-3.14179 + 0.359404i) q^{10} +(-0.718808 - 0.718808i) q^{12} +(4.48655 - 4.48655i) q^{13} +3.74166i q^{14} +(0.129171 + 1.12917i) q^{15} -4.00000 q^{16} +(2.74166 - 2.74166i) q^{18} -7.62834i q^{19} +(3.50119 + 2.78238i) q^{20} +1.34477 q^{21} +(0.741657 - 0.741657i) q^{23} +1.43762i q^{24} +(-1.12917 - 4.87083i) q^{25} -8.97311 q^{26} +(-2.06358 - 2.06358i) q^{27} +(3.74166 - 3.74166i) q^{28} +(1.00000 - 1.25834i) q^{30} +(4.00000 + 4.00000i) q^{32} +(-5.87775 + 0.672384i) q^{35} -5.48331 q^{36} +(-7.62834 + 7.62834i) q^{38} +3.22497i q^{39} +(-0.718808 - 6.28357i) q^{40} +(-1.34477 - 1.34477i) q^{42} +(4.79953 + 3.81417i) q^{45} -1.48331 q^{46} +(1.43762 - 1.43762i) q^{48} +7.00000i q^{49} +(-3.74166 + 6.00000i) q^{50} +(8.97311 + 8.97311i) q^{52} +4.12715i q^{54} -7.48331 q^{56} +(2.74166 + 2.74166i) q^{57} +15.3495i q^{59} +(-2.25834 + 0.258343i) q^{60} +14.6307 q^{61} +(5.12917 - 5.12917i) q^{63} -8.00000i q^{64} +(-1.61249 - 14.0958i) q^{65} +0.533109i q^{69} +(6.55013 + 5.20536i) q^{70} +7.22497 q^{71} +(5.48331 + 5.48331i) q^{72} +(2.15642 + 1.34477i) q^{75} +15.2567 q^{76} +(3.22497 - 3.22497i) q^{78} +15.7417i q^{79} +(-5.56477 + 7.00238i) q^{80} -6.74166 q^{81} +(-5.83132 + 5.83132i) q^{83} +2.68953i q^{84} +(-0.985363 - 8.61370i) q^{90} -16.7871 q^{91} +(1.48331 + 1.48331i) q^{92} +(-13.3541 - 10.6125i) q^{95} -2.87523 q^{96} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} + 16 q^{15} - 32 q^{16} - 8 q^{18} - 24 q^{23} - 24 q^{25} + 8 q^{30} + 32 q^{32} + 16 q^{36} + 48 q^{46} - 8 q^{57} - 48 q^{60} + 56 q^{63} + 32 q^{65} - 32 q^{71} - 16 q^{72} - 64 q^{78} - 24 q^{81} - 48 q^{92} - 32 q^{95} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 + 16 * q^15 - 32 * q^16 - 8 * q^18 - 24 * q^23 - 24 * q^25 + 8 * q^30 + 32 * q^32 + 16 * q^36 + 48 * q^46 - 8 * q^57 - 48 * q^60 + 56 * q^63 + 32 * q^65 - 32 * q^71 - 16 * q^72 - 64 * q^78 - 24 * q^81 - 48 * q^92 - 32 * q^95 + 56 * q^98

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