LMFDB - Embedded newform 280.2.s.b.13.3

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:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label			13.3
Root			$1.71331 + 0.254137i$ of defining polynomial
Character	$\chi$	$=$	280.13
Dual form			280.2.s.b.237.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.45917 + 1.45917i) q^{3} -2.00000i q^{4} +(2.22158 - 0.254137i) q^{5} +2.91834 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +1.25834i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.45917 + 1.45917i) q^{3} -2.00000i q^{4} +(2.22158 - 0.254137i) q^{5} +2.91834 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +1.25834i q^{9} +(1.96744 - 2.47572i) q^{10} +(2.91834 - 2.91834i) q^{12} +(-1.45917 - 1.45917i) q^{13} +3.74166i q^{14} +(3.61249 + 2.87083i) q^{15} -4.00000 q^{16} +(1.25834 + 1.25834i) q^{18} +8.37804i q^{19} +(-0.508274 - 4.44316i) q^{20} -5.45971 q^{21} +(-6.74166 - 6.74166i) q^{23} -5.83667i q^{24} +(4.87083 - 1.12917i) q^{25} -2.91834 q^{26} +(2.54137 - 2.54137i) q^{27} +(3.74166 + 3.74166i) q^{28} +(6.48331 - 0.741657i) q^{30} +(-4.00000 + 4.00000i) q^{32} +(-3.68075 + 4.63164i) q^{35} +2.51669 q^{36} +(8.37804 + 8.37804i) q^{38} -4.25834i q^{39} +(-4.95143 - 3.93488i) q^{40} +(-5.45971 + 5.45971i) q^{42} +(0.319792 + 2.79551i) q^{45} -13.4833 q^{46} +(-5.83667 - 5.83667i) q^{48} -7.00000i q^{49} +(3.74166 - 6.00000i) q^{50} +(-2.91834 + 2.91834i) q^{52} -5.08274i q^{54} +7.48331 q^{56} +(-12.2250 + 12.2250i) q^{57} +11.2964i q^{59} +(5.74166 - 7.22497i) q^{60} -14.2147 q^{61} +(-2.35414 - 2.35414i) q^{63} +8.00000i q^{64} +(-3.61249 - 2.87083i) q^{65} -19.6744i q^{69} +(0.950894 + 8.31239i) q^{70} +15.2250 q^{71} +(2.51669 - 2.51669i) q^{72} +(8.75501 + 5.45971i) q^{75} +16.7561 q^{76} +(-4.25834 - 4.25834i) q^{78} +8.25834i q^{79} +(-8.88632 + 1.01655i) q^{80} +11.1916 q^{81} +(-4.00054 - 4.00054i) q^{83} +10.9194i q^{84} +(3.11530 + 2.47572i) q^{90} +5.45971 q^{91} +(-13.4833 + 13.4833i) q^{92} +(2.12917 + 18.6125i) q^{95} -11.6733 q^{96} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 40 q^{18} - 24 q^{23} + 24 q^{25} - 8 q^{30} - 32 q^{32} + 80 q^{36} - 48 q^{46} - 8 q^{57} + 16 q^{60} + 56 q^{63} + 16 q^{65} + 32 q^{71} + 80 q^{72} - 64 q^{78} - 120 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 + 40 * q^18 - 24 * q^23 + 24 * q^25 - 8 * q^30 - 32 * q^32 + 80 * q^36 - 48 * q^46 - 8 * q^57 + 16 * q^60 + 56 * q^63 + 16 * q^65 + 32 * q^71 + 80 * q^72 - 64 * q^78 - 120 * 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

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
$3$	1.45917	+	1.45917i	0.842451	+	0.842451i	0.989177	−	0.146726i	$-0.0468736\pi$
$3$	1.45917	+	1.45917i	0.842451	+	0.842451i	−0.146726	+	0.989177i	$0.546874\pi$
$4$		−	2.00000i		−	1.00000i
$5$	2.22158	−	0.254137i	0.993520	−	0.113654i
$5$	2.22158	−	0.254137i	0.993520	−	0.113654i
$6$	2.91834			1.19141
$7$	−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
$9$			1.25834i			0.419448i
$10$	1.96744	−	2.47572i	0.622160	−	0.782890i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	2.91834	−	2.91834i	0.842451	−	0.842451i
$13$	−1.45917	−	1.45917i	−0.404700	−	0.404700i	0.475185	−	0.879886i	$-0.342381\pi$
$13$	−1.45917	−	1.45917i	−0.404700	−	0.404700i	−0.879886	+	0.475185i	$0.842381\pi$
$14$			3.74166i			1.00000i
$15$	3.61249	+	2.87083i	0.932740	+	0.741245i
$16$	−4.00000			−1.00000
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	1.25834	+	1.25834i	0.296594	+	0.296594i
$19$			8.37804i			1.92205i	0.276453	+	0.961027i	$0.410841\pi$
$19$			8.37804i			1.92205i	−0.276453	+	0.961027i	$0.589159\pi$
$20$	−0.508274	−	4.44316i	−0.113654	−	0.993520i
$21$	−5.45971			−1.19141
$22$		0			0
$23$	−6.74166	−	6.74166i	−1.40573	−	1.40573i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$	−6.74166	−	6.74166i	−1.40573	−	1.40573i	−0.625543	−	0.780189i	$-0.715123\pi$
$24$		−	5.83667i		−	1.19141i
$25$	4.87083	−	1.12917i	0.974166	−	0.225834i
$26$	−2.91834			−0.572333
$27$	2.54137	−	2.54137i	0.489087	−	0.489087i
$28$	3.74166	+	3.74166i	0.707107	+	0.707107i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	6.48331	−	0.741657i	1.18369	−	0.135407i
$31$		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
$35$	−3.68075	+	4.63164i	−0.622160	+	0.782890i
$36$	2.51669			0.419448
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	8.37804	+	8.37804i	1.35910	+	1.35910i
$39$		−	4.25834i		−	0.681881i
$40$	−4.95143	−	3.93488i	−0.782890	−	0.622160i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	−5.45971	+	5.45971i	−0.842451	+	0.842451i
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	0.319792	+	2.79551i	0.0476717	+	0.416730i
$46$	−13.4833			−1.98801
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$	−5.83667	−	5.83667i	−0.842451	−	0.842451i
$49$		−	7.00000i		−	1.00000i
$50$	3.74166	−	6.00000i	0.529150	−	0.848528i
$51$		0			0
$52$	−2.91834	+	2.91834i	−0.404700	+	0.404700i
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$		−	5.08274i		−	0.691674i
$55$		0			0
$56$	7.48331			1.00000
$57$	−12.2250	+	12.2250i	−1.61924	+	1.61924i
$58$		0			0
$59$			11.2964i			1.47066i	0.677707	+	0.735332i	$0.262974\pi$
$59$			11.2964i			1.47066i	−0.677707	+	0.735332i	$0.737026\pi$
$60$	5.74166	−	7.22497i	0.741245	−	0.932740i
$61$	−14.2147			−1.82001			−0.910004	−	0.414600i	$-0.863922\pi$
$61$	−14.2147			−1.82001			−0.910004	+	0.414600i	$0.863922\pi$
$62$		0			0
$63$	−2.35414	−	2.35414i	−0.296594	−	0.296594i
$64$			8.00000i			1.00000i
$65$	−3.61249	−	2.87083i	−0.448074	−	0.356082i
$66$		0			0
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$		0			0
$69$		−	19.6744i		−	2.36852i
$70$	0.950894	+	8.31239i	0.113654	+	0.993520i
$71$	15.2250			1.80687			0.903436	−	0.428723i	$-0.141036\pi$
$71$	15.2250			1.80687			0.903436	+	0.428723i	$0.141036\pi$
$72$	2.51669	−	2.51669i	0.296594	−	0.296594i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	8.75501	+	5.45971i	1.01094	+	0.630433i
$76$	16.7561			1.92205
$77$		0			0
$78$	−4.25834	−	4.25834i	−0.482162	−	0.482162i
$79$			8.25834i			0.929136i	0.885537	+	0.464568i	$0.153790\pi$
$79$			8.25834i			0.929136i	−0.885537	+	0.464568i	$0.846210\pi$
$80$	−8.88632	+	1.01655i	−0.993520	+	0.113654i
$81$	11.1916			1.24351
$82$		0			0
$83$	−4.00054	−	4.00054i	−0.439116	−	0.439116i	0.452598	−	0.891715i	$-0.350497\pi$
$83$	−4.00054	−	4.00054i	−0.439116	−	0.439116i	−0.891715	+	0.452598i	$0.850497\pi$
$84$			10.9194i			1.19141i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	3.11530	+	2.47572i	0.328381	+	0.260963i
$91$	5.45971			0.572333
$92$	−13.4833	+	13.4833i	−1.40573	+	1.40573i
$93$		0			0
$94$		0			0
$95$	2.12917	+	18.6125i	0.218448	+	1.90960i
$96$	−11.6733			−1.19141
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	−7.00000	−	7.00000i	−0.707107	−	0.707107i
$99$		0			0
$100$	−2.25834	−	9.74166i	−0.225834	−	0.974166i
$101$	20.0514			1.99519			0.997594	−	0.0693299i	$-0.0220861\pi$
$101$	20.0514			1.99519			0.997594	+	0.0693299i	$0.0220861\pi$
$102$		0			0
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$			5.83667i			0.572333i
$105$	−12.1292	+	1.38751i	−1.18369	+	0.135407i
$106$		0			0
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	−5.08274	−	5.08274i	−0.489087	−	0.489087i
$109$		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	−0.998339	−	0.0576178i	$-0.981650\pi$
$113$	−11.2250	−	11.2250i	−1.05596	−	1.05596i	−0.0576178	−	0.998339i	$-0.518350\pi$
$114$			24.4499i			2.28995i
$115$	−16.6904	−	13.2638i	−1.55639	−	1.23686i
$116$		0			0
$117$	1.83613	−	1.83613i	0.169751	−	0.169751i
$118$	11.2964	+	11.2964i	1.03992	+	1.03992i
$119$		0			0
$120$	−1.48331	−	12.9666i	−0.135407	−	1.18369i
$121$	11.0000			1.00000
$122$	−14.2147	+	14.2147i	−1.28694	+	1.28694i
$123$		0			0
$124$		0			0
$125$	10.5340	−	3.74640i	0.942187	−	0.335088i
$126$	−4.70829			−0.419448
$127$	10.2250	−	10.2250i	0.907320	−	0.907320i	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	10.2250	−	10.2250i	0.907320	−	0.907320i	0.996055	+	0.0887357i	$0.0282826\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$		0			0
$130$	−6.48331	+	0.741657i	−0.568624	+	0.0650477i
$131$	19.2975			1.68603			0.843013	−	0.537893i	$-0.180779\pi$
$131$	19.2975			1.68603			0.843013	+	0.537893i	$0.180779\pi$
$132$		0			0
$133$	−15.6739	−	15.6739i	−1.35910	−	1.35910i
$134$		0			0
$135$	5.00000	−	6.29171i	0.430331	−	0.541504i
$136$		0			0
$137$	1.51669	−	1.51669i	0.129579	−	0.129579i	−0.639343	−	0.768922i	$-0.720793\pi$
$137$	1.51669	−	1.51669i	0.129579	−	0.129579i	0.768922	+	0.639343i	$0.220793\pi$
$138$	−19.6744	−	19.6744i	−1.67480	−	1.67480i
$139$		−	22.9697i		−	1.94827i	−0.225974	−	0.974133i	$-0.572557\pi$
$139$		−	22.9697i		−	1.94827i	0.225974	−	0.974133i	$-0.427443\pi$
$140$	9.26328	+	7.36149i	0.782890	+	0.622160i
$141$		0			0
$142$	15.2250	−	15.2250i	1.27765	−	1.27765i
$143$		0			0
$144$		−	5.03337i		−	0.419448i
$145$		0			0
$146$		0			0
$147$	10.2142	−	10.2142i	0.842451	−	0.842451i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	14.2147	−	3.29530i	1.16063	−	0.269060i
$151$	−22.4499			−1.82695			−0.913475	−	0.406894i	$-0.866612\pi$
$151$	−22.4499			−1.82695			−0.913475	+	0.406894i	$0.866612\pi$
$152$	16.7561	−	16.7561i	1.35910	−	1.35910i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−8.51669			−0.681881
$157$	−6.91887	+	6.91887i	−0.552186	+	0.552186i	−0.927071	−	0.374885i	$-0.877682\pi$
$157$	−6.91887	+	6.91887i	−0.552186	+	0.552186i	0.374885	+	0.927071i	$0.377682\pi$
$158$	8.25834	+	8.25834i	0.656998	+	0.656998i
$159$		0			0
$160$	−7.86977	+	9.90287i	−0.622160	+	0.782890i
$161$	25.2250			1.98801
$162$	11.1916	−	11.1916i	0.879295	−	0.879295i
$163$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$163$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$164$		0			0
$165$		0			0
$166$	−8.00108			−0.621004
$167$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$167$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$168$	10.9194	+	10.9194i	0.842451	+	0.842451i
$169$		−	8.74166i		−	0.672435i
$170$		0			0
$171$	−10.5424			−0.806201
$172$		0			0
$173$	18.5922	+	18.5922i	1.41354	+	1.41354i	0.728588	+	0.684953i	$0.240177\pi$
$173$	18.5922	+	18.5922i	1.41354	+	1.41354i	0.684953	+	0.728588i	$0.259823\pi$
$174$		0			0
$175$	−7.00000	+	11.2250i	−0.529150	+	0.848528i
$176$		0			0
$177$	−16.4833	+	16.4833i	−1.23896	+	1.23896i
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	5.59102	−	0.639583i	0.416730	−	0.0476717i
$181$	−0.376965			−0.0280196			−0.0140098	−	0.999902i	$-0.504460\pi$
$181$	−0.376965			−0.0280196			−0.0140098	+	0.999902i	$0.504460\pi$
$182$	5.45971	−	5.45971i	0.404700	−	0.404700i
$183$	−20.7417	−	20.7417i	−1.53327	−	1.53327i
$184$			26.9666i			1.98801i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$			9.50894i			0.691674i
$190$	20.7417	+	16.4833i	1.50476	+	1.19583i
$191$	−4.77503			−0.345509			−0.172754	−	0.984965i	$-0.555267\pi$
$191$	−4.77503			−0.345509			−0.172754	+	0.984965i	$0.555267\pi$
$192$	−11.6733	+	11.6733i	−0.842451	+	0.842451i
$193$	6.00000	+	6.00000i	0.431889	+	0.431889i	0.889271	−	0.457381i	$-0.151213\pi$
$193$	6.00000	+	6.00000i	0.431889	+	0.431889i	−0.457381	+	0.889271i	$0.651213\pi$
$194$		0			0
$195$	−1.08220	−	9.46025i	−0.0774981	−	0.677462i
$196$	−14.0000			−1.00000
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$		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
$202$	20.0514	−	20.0514i	1.41081	−	1.41081i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.48331	−	8.48331i	0.589631	−	0.589631i
$208$	5.83667	+	5.83667i	0.404700	+	0.404700i
$209$		0			0
$210$	−10.7417	+	13.5167i	−0.741245	+	0.932740i
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$		0			0
$213$	22.2158	+	22.2158i	1.52220	+	1.52220i
$214$		0			0
$215$		0			0
$216$	−10.1655			−0.691674
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		−	14.9666i		−	1.00000i
$225$	1.42088	+	6.12917i	0.0947256	+	0.408611i
$226$	−22.4499			−1.49335
$227$	−12.7555	+	12.7555i	−0.846615	+	0.846615i	−0.989709	−	0.143094i	$-0.954295\pi$
$227$	−12.7555	+	12.7555i	−0.846615	+	0.846615i	0.143094	+	0.989709i	$0.454295\pi$
$228$	24.4499	+	24.4499i	1.61924	+	1.61924i
$229$		−	3.29530i		−	0.217760i	−0.994055	−	0.108880i	$-0.965274\pi$
$229$		−	3.29530i		−	0.217760i	0.994055	−	0.108880i	$-0.0347264\pi$
$230$	−29.9543	+	3.42661i	−1.97512	+	0.225944i
$231$		0			0
$232$		0			0
$233$	11.9666	+	11.9666i	0.783960	+	0.783960i	0.980497	−	0.196537i	$-0.0629694\pi$
$233$	11.9666	+	11.9666i	0.783960	+	0.783960i	−0.196537	+	0.980497i	$0.562969\pi$
$234$		−	3.67227i		−	0.240064i
$235$		0			0
$236$	22.5928			1.47066
$237$	−12.0503	+	12.0503i	−0.782752	+	0.782752i
$238$		0			0
$239$			7.48331i			0.484055i	0.970269	+	0.242028i	$0.0778125\pi$
$239$			7.48331i			0.484055i	−0.970269	+	0.242028i	$0.922188\pi$
$240$	−14.4499	−	11.4833i	−0.932740	−	0.741245i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	11.0000	−	11.0000i	0.707107	−	0.707107i
$243$	8.70632	+	8.70632i	0.558510	+	0.558510i
$244$			28.4294i			1.82001i
$245$	−1.77896	−	15.5511i	−0.113654	−	0.993520i
$246$		0			0
$247$	12.2250	−	12.2250i	0.777856	−	0.777856i
$248$		0			0
$249$		−	11.6749i		−	0.739868i
$250$	6.78757	−	14.2804i	0.429283	−	0.903170i
$251$	−28.8064			−1.81824			−0.909122	−	0.416530i	$-0.863246\pi$
$251$	−28.8064			−1.81824			−0.909122	+	0.416530i	$0.863246\pi$
$252$	−4.70829	+	4.70829i	−0.296594	+	0.296594i
$253$		0			0
$254$		−	20.4499i		−	1.28314i
$255$		0			0
$256$	16.0000			1.00000
$257$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$257$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$258$		0			0
$259$		0			0
$260$	−5.74166	+	7.22497i	−0.356082	+	0.448074i
$261$		0			0
$262$	19.2975	−	19.2975i	1.19220	−	1.19220i
$263$	−11.2250	−	11.2250i	−0.692161	−	0.692161i	0.270546	−	0.962707i	$-0.412796\pi$
$263$	−11.2250	−	11.2250i	−0.692161	−	0.692161i	−0.962707	+	0.270546i	$0.912796\pi$
$264$		0			0
$265$		0			0
$266$	−31.3478			−1.92205
$267$		0			0
$268$		0			0
$269$			28.0525i			1.71039i	0.518307	+	0.855194i	$0.326562\pi$
$269$			28.0525i			1.71039i	−0.518307	+	0.855194i	$0.673438\pi$
$270$	−1.29171	−	11.2917i	−0.0786112	−	0.687192i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	7.96663	+	7.96663i	0.482162	+	0.482162i
$274$		−	3.03337i		−	0.183253i
$275$		0			0
$276$	−39.3488			−2.36852
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	−22.9697	−	22.9697i	−1.37763	−	1.37763i
$279$		0			0
$280$	16.6248	−	1.90179i	0.993520	−	0.113654i
$281$	14.9666			0.892834			0.446417	−	0.894825i	$-0.352700\pi$
$281$	14.9666			0.892834			0.446417	+	0.894825i	$0.352700\pi$
$282$		0			0
$283$	−23.6750	−	23.6750i	−1.40733	−	1.40733i	−0.773345	−	0.633985i	$-0.781418\pi$
$283$	−23.6750	−	23.6750i	−1.40733	−	1.40733i	−0.633985	−	0.773345i	$-0.718582\pi$
$284$		−	30.4499i		−	1.80687i
$285$	−24.0519	+	30.2656i	−1.42471	+	1.79278i
$286$		0			0
$287$		0			0
$288$	−5.03337	−	5.03337i	−0.296594	−	0.296594i
$289$		−	17.0000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.08220	−	1.08220i	−0.0632230	−	0.0632230i	0.674788	−	0.738011i	$-0.264235\pi$
$293$	−1.08220	−	1.08220i	−0.0632230	−	0.0632230i	−0.738011	+	0.674788i	$0.764235\pi$
$294$		−	20.4284i		−	1.19141i
$295$	2.87083	+	25.0958i	0.167146	+	1.46113i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			19.6744i			1.13780i
$300$	10.9194	−	17.5100i	0.630433	−	1.01094i
$301$		0			0
$302$	−22.4499	+	22.4499i	−1.29185	+	1.29185i
$303$	29.2583	+	29.2583i	1.68085	+	1.68085i
$304$		−	33.5122i		−	1.92205i
$305$	−31.5791	+	3.61249i	−1.80821	+	0.206850i
$306$		0			0
$307$	−17.8383	+	17.8383i	−1.01808	+	1.01808i	−0.0182515	+	0.999833i	$0.505810\pi$
$307$	−17.8383	+	17.8383i	−1.01808	+	1.01808i	−0.999833	+	0.0182515i	$0.994190\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	−8.51669	+	8.51669i	−0.482162	+	0.482162i
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$			13.8377i			0.780909i
$315$	−5.82819	−	4.63164i	−0.328381	−	0.260963i
$316$	16.5167			0.929136
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$		0			0
$320$	2.03310	+	17.7726i	0.113654	+	0.993520i
$321$		0			0
$322$	25.2250	−	25.2250i	1.40573	−	1.40573i
$323$		0			0
$324$		−	22.3832i		−	1.24351i
$325$	−8.75501	−	5.45971i	−0.485640	−	0.302850i
$326$		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			$\pi$
$332$	−8.00108	+	8.00108i	−0.439116	+	0.439116i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	21.8388			1.19141
$337$	−18.0000	+	18.0000i	−0.980522	+	0.980522i	−0.999814	−	0.0192914i	$-0.993859\pi$
$337$	−18.0000	+	18.0000i	−0.980522	+	0.980522i	0.0192914	+	0.999814i	$0.493859\pi$
$338$	−8.74166	−	8.74166i	−0.475483	−	0.475483i
$339$		−	32.7582i		−	1.77918i
$340$		0			0
$341$		0			0
$342$	−10.5424	+	10.5424i	−0.570070	+	0.570070i
$343$	13.0958	+	13.0958i	0.707107	+	0.707107i
$344$		0			0
$345$	−5.00000	−	43.7083i	−0.269191	−	2.35318i
$346$	37.1844			1.99905
$347$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$347$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$348$		0			0
$349$			33.1352i			1.77369i	0.462070	+	0.886843i	$0.347107\pi$
$349$			33.1352i			1.77369i	−0.462070	+	0.886843i	$0.652893\pi$
$350$	4.22497	+	18.2250i	0.225834	+	0.974166i
$351$	−7.41657			−0.395867
$352$		0			0
$353$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$353$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$354$			32.9666i			1.75216i
$355$	33.8235	−	3.86923i	1.79516	−	0.205357i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$	4.95143	−	6.23060i	0.260963	−	0.328381i
$361$	−51.1916			−2.69429
$362$	−0.376965	+	0.376965i	−0.0198129	+	0.0198129i
$363$	16.0508	+	16.0508i	0.842451	+	0.842451i
$364$		−	10.9194i		−	0.572333i
$365$		0			0
$366$	−41.4833			−2.16837
$367$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$367$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$368$	26.9666	+	26.9666i	1.40573	+	1.40573i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$373$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$374$		0			0
$375$	20.8375	+	9.90420i	1.07604	+	0.511451i
$376$		0			0
$377$		0			0
$378$	9.50894	+	9.50894i	0.489087	+	0.489087i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	37.2250	−	4.25834i	1.90960	−	0.218448i
$381$	29.8399			1.52874
$382$	−4.77503	+	4.77503i	−0.244312	+	0.244312i
$383$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$383$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$384$			23.3467i			1.19141i
$385$		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	$0.5\pi$
$390$	−10.5424	−	8.37804i	−0.533838	−	0.424239i
$391$		0			0
$392$	−14.0000	+	14.0000i	−0.707107	+	0.707107i
$393$	28.1582	+	28.1582i	1.42039	+	1.42039i
$394$		0			0
$395$	2.09875	+	18.3466i	0.105600	+	0.923116i
$396$		0			0
$397$	−1.83613	+	1.83613i	−0.0921529	+	0.0921529i	−0.751680	−	0.659528i	$-0.770756\pi$
$397$	−1.83613	+	1.83613i	−0.0921529	+	0.0921529i	0.659528	+	0.751680i	$0.270756\pi$
$398$		0			0
$399$		−	45.7417i		−	2.28995i
$400$	−19.4833	+	4.51669i	−0.974166	+	0.225834i
$401$	−14.7750			−0.737830			−0.368915	−	0.929463i	$-0.620271\pi$
$401$	−14.7750			−0.737830			−0.368915	+	0.929463i	$0.620271\pi$
$402$		0			0
$403$		0			0
$404$		−	40.1028i		−	1.99519i
$405$	24.8630	−	2.84420i	1.23545	−	0.141329i
$406$		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
$411$	4.42620			0.218328
$412$		0			0
$413$	−21.1336	−	21.1336i	−1.03992	−	1.03992i
$414$		−	16.9666i		−	0.833864i
$415$	−9.90420	−	7.87083i	−0.486178	−	0.386364i
$416$	11.6733			0.572333
$417$	33.5167	−	33.5167i	1.64132	−	1.64132i
$418$		0			0
$419$		−	30.9708i		−	1.51302i	−0.653981	−	0.756511i	$-0.726902\pi$
$419$		−	30.9708i		−	1.51302i	0.653981	−	0.756511i	$-0.273098\pi$
$420$	2.77503	+	24.2583i	0.135407	+	1.18369i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	44.4316			2.15272
$427$	26.5933	−	26.5933i	1.28694	−	1.28694i
$428$		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	$0.642727\pi$
$432$	−10.1655	+	10.1655i	−0.489087	+	0.489087i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	56.4819	−	56.4819i	2.70190	−	2.70190i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	8.80840			0.419448
$442$		0			0
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		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	$-0.249646\pi$
$450$	7.55006	+	4.70829i	0.355913	+	0.221951i
$451$		0			0
$452$	−22.4499	+	22.4499i	−1.05596	+	1.05596i
$453$	−32.7582	−	32.7582i	−1.53912	−	1.53912i
$454$			25.5111i			1.19729i
$455$	12.1292	−	1.38751i	0.568624	−	0.0650477i
$456$	48.8999			2.28995
$457$	−3.74166	+	3.74166i	−0.175027	+	0.175027i	−0.789184	−	0.614157i	$-0.789496\pi$
$457$	−3.74166	+	3.74166i	−0.175027	+	0.175027i	0.614157	+	0.789184i	$0.289496\pi$
$458$	−3.29530	−	3.29530i	−0.153979	−	0.153979i
$459$		0			0
$460$	−26.5276	+	33.3809i	−1.23686	+	1.55639i
$461$	−10.5424			−0.491011			−0.245505	−	0.969395i	$-0.578954\pi$
$461$	−10.5424			−0.491011			−0.245505	+	0.969395i	$0.578954\pi$
$462$		0			0
$463$	−24.0000	−	24.0000i	−1.11537	−	1.11537i	−0.992411	−	0.122963i	$-0.960760\pi$
$463$	−24.0000	−	24.0000i	−1.11537	−	1.11537i	−0.122963	−	0.992411i	$-0.539240\pi$
$464$		0			0
$465$		0			0
$466$	23.9333			1.10869
$467$	−24.0519	+	24.0519i	−1.11299	+	1.11299i	−0.120246	+	0.992744i	$0.538368\pi$
$467$	−24.0519	+	24.0519i	−1.11299	+	1.11299i	−0.992744	+	0.120246i	$0.961632\pi$
$468$	−3.67227	−	3.67227i	−0.169751	−	0.169751i
$469$		0			0
$470$		0			0
$471$	−20.1916			−0.930380
$472$	22.5928	−	22.5928i	1.03992	−	1.03992i
$473$		0			0
$474$			24.1006i			1.10698i
$475$	9.46025	+	40.8080i	0.434066	+	1.87240i
$476$		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	$0.5\pi$
$480$	−25.9333	+	2.96663i	−1.18369	+	0.135407i
$481$		0			0
$482$		0			0
$483$	36.8075	+	36.8075i	1.67480	+	1.67480i
$484$		−	22.0000i		−	1.00000i
$485$		0			0
$486$	17.4126			0.789853
$487$	30.2250	−	30.2250i	1.36962	−	1.36962i	0.508652	−	0.860972i	$-0.330144\pi$
$487$	30.2250	−	30.2250i	1.36962	−	1.36962i	0.860972	−	0.508652i	$-0.169856\pi$
$488$	28.4294	+	28.4294i	1.28694	+	1.28694i
$489$		0			0
$490$	−17.3300	−	13.7721i	−0.782890	−	0.622160i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		−	24.4499i		−	1.10006i
$495$		0			0
$496$		0			0
$497$	−28.4833	+	28.4833i	−1.27765	+	1.27765i
$498$	−11.6749	−	11.6749i	−0.523166	−	0.523166i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−7.49280	−	21.0679i	−0.335088	−	0.942187i
$501$		0			0
$502$	−28.8064	+	28.8064i	−1.28569	+	1.28569i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$			9.41657i			0.419448i
$505$	44.5457	−	5.09580i	1.98226	−	0.226760i
$506$		0			0
$507$	12.7555	−	12.7555i	0.566494	−	0.566494i
$508$	−20.4499	−	20.4499i	−0.907320	−	0.907320i
$509$		−	37.5614i		−	1.66488i	−0.554115	−	0.832440i	$-0.686943\pi$
$509$		−	37.5614i		−	1.66488i	0.554115	−	0.832440i	$-0.313057\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	21.2917	+	21.2917i	0.940052	+	0.940052i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$			54.2583i			2.38168i
$520$	1.48331	+	12.9666i	0.0650477	+	0.568624i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−18.2153	−	18.2153i	−0.796497	−	0.796497i	0.186044	−	0.982541i	$-0.440433\pi$
$523$	−18.2153	−	18.2153i	−0.796497	−	0.796497i	−0.982541	+	0.186044i	$0.940433\pi$
$524$		−	38.5949i		−	1.68603i
$525$	−26.5933	+	6.16494i	−1.16063	+	0.269060i
$526$	−22.4499			−0.978864
$527$		0			0
$528$		0			0
$529$			67.8999i			2.95217i
$530$		0			0
$531$	−14.2147			−0.616866
$532$	−31.3478	+	31.3478i	−1.35910	+	1.35910i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	28.0525	+	28.0525i	1.20943	+	1.20943i
$539$		0			0
$540$	−12.5834	−	10.0000i	−0.541504	−	0.430331i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−0.550056	−	0.550056i	−0.0236051	−	0.0236051i
$544$		0			0
$545$		0			0
$546$	15.9333			0.681881
$547$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$547$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$548$	−3.03337	−	3.03337i	−0.129579	−	0.129579i
$549$		−	17.8870i		−	0.763398i
$550$		0			0
$551$		0			0
$552$	−39.3488	+	39.3488i	−1.67480	+	1.67480i
$553$	−15.4499	−	15.4499i	−0.656998	−	0.656998i
$554$		0			0
$555$		0			0
$556$	−45.9394			−1.94827
$557$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$557$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$558$		0			0
$559$		0			0
$560$	14.7230	−	18.5266i	0.622160	−	0.782890i
$561$		0			0
$562$	14.9666	−	14.9666i	0.631329	−	0.631329i
$563$	−32.8069	−	32.8069i	−1.38265	−	1.38265i	−0.839889	−	0.542759i	$-0.817380\pi$
$563$	−32.8069	−	32.8069i	−1.38265	−	1.38265i	−0.542759	−	0.839889i	$-0.682620\pi$
$564$		0			0
$565$	−27.7898	−	22.0845i	−1.16913	−	0.929101i
$566$	−47.3499			−1.99027
$567$	−20.9376	+	20.9376i	−0.879295	+	0.879295i
$568$	−30.4499	−	30.4499i	−1.27765	−	1.27765i
$569$			35.6749i			1.49557i	0.663941	+	0.747785i	$0.268883\pi$
$569$			35.6749i			1.49557i	−0.663941	+	0.747785i	$0.731117\pi$
$570$	6.21364	+	54.3175i	0.260261	+	2.27511i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−6.96757	−	6.96757i	−0.291074	−	0.291074i
$574$		0			0
$575$	−40.4499	−	25.2250i	−1.68688	−	1.05195i
$576$	−10.0667			−0.419448
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−17.0000	−	17.0000i	−0.707107	−	0.707107i
$579$			17.5100i			0.727691i
$580$		0			0
$581$	14.9686			0.621004
$582$		0			0
$583$		0			0
$584$		0			0
$585$	3.61249	−	4.54575i	0.149358	−	0.187943i
$586$	−2.16441			−0.0894108
$587$	15.2969	−	15.2969i	0.631371	−	0.631371i	−0.317041	−	0.948412i	$-0.602689\pi$
$587$	15.2969	−	15.2969i	0.631371	−	0.631371i	0.948412	+	0.317041i	$0.102689\pi$
$588$	−20.4284	−	20.4284i	−0.842451	−	0.842451i
$589$		0			0
$590$	27.9666	+	22.2250i	1.15137	+	0.914988i
$591$		0			0
$592$		0			0
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	19.6744	+	19.6744i	0.804547	+	0.804547i
$599$			25.6749i			1.04905i	0.851395	+	0.524524i	$0.175757\pi$
$599$			25.6749i			1.04905i	−0.851395	+	0.524524i	$0.824243\pi$
$600$	−6.59060	−	28.4294i	−0.269060	−	1.16063i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$			44.8999i			1.82695i
$605$	24.4374	−	2.79551i	0.993520	−	0.113654i
$606$	58.5167			2.37708
$607$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$607$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$608$	−33.5122	−	33.5122i	−1.35910	−	1.35910i
$609$		0			0
$610$	−27.9666	+	35.1916i	−1.13234	+	1.42487i
$611$		0			0
$612$		0			0
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$			35.6766i			1.43979i
$615$		0			0
$616$		0			0
$617$	33.6749	−	33.6749i	1.35570	−	1.35570i	0.476558	−	0.879143i	$-0.341884\pi$
$617$	33.6749	−	33.6749i	1.35570	−	1.35570i	0.879143	−	0.476558i	$-0.158116\pi$
$618$		0			0
$619$			40.4797i			1.62702i	0.581552	+	0.813509i	$0.302446\pi$
$619$			40.4797i			1.62702i	−0.581552	+	0.813509i	$0.697554\pi$
$620$		0			0
$621$	−34.2661			−1.37505
$622$		0			0
$623$		0			0
$624$			17.0334i			0.681881i
$625$	22.4499	−	11.0000i	0.897998	−	0.440000i
$626$		0			0
$627$		0			0
$628$	13.8377	+	13.8377i	0.552186	+	0.552186i
$629$		0			0
$630$	−10.4598	+	1.19655i	−0.416730	+	0.0476717i
$631$	−2.19160			−0.0872463			−0.0436231	−	0.999048i	$-0.513890\pi$
$631$	−2.19160			−0.0872463			−0.0436231	+	0.999048i	$0.513890\pi$
$632$	16.5167	−	16.5167i	0.656998	−	0.656998i
$633$		0			0
$634$		0			0
$635$	20.1170	−	25.3141i	0.798320	−	1.00456i
$636$		0			0
$637$	−10.2142	+	10.2142i	−0.404700	+	0.404700i
$638$		0			0
$639$			19.1582i			0.757888i
$640$	19.8057	+	15.7395i	0.782890	+	0.622160i
$641$	45.2250			1.78628			0.893140	−	0.449780i	$-0.148498\pi$
$641$	45.2250			1.78628			0.893140	+	0.449780i	$0.148498\pi$
$642$		0			0
$643$	35.7253	+	35.7253i	1.40887	+	1.40887i	0.765861	+	0.643006i	$0.222313\pi$
$643$	35.7253	+	35.7253i	1.40887	+	1.40887i	0.643006	+	0.765861i	$0.277687\pi$
$644$		−	50.4499i		−	1.98801i
$645$		0			0
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−22.3832	−	22.3832i	−0.879295	−	0.879295i
$649$		0			0
$650$	−14.2147	+	3.29530i	−0.557547	+	0.129252i
$651$		0			0
$652$		0			0
$653$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$653$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$654$		0			0
$655$	42.8708	−	4.90420i	1.67510	−	0.191623i
$656$		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
$661$	−49.8913			−1.94055			−0.970273	−	0.242012i	$-0.922193\pi$
$661$	−49.8913			−1.94055			−0.970273	+	0.242012i	$0.922193\pi$
$662$		0			0
$663$		0			0
$664$			16.0022i			0.621004i
$665$	−38.8041	−	30.8375i	−1.50476	−	1.19583i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	21.8388	−	21.8388i	0.842451	−	0.842451i
$673$	−35.4499	−	35.4499i	−1.36649	−	1.36649i	−0.865382	−	0.501113i	$-0.832924\pi$
$673$	−35.4499	−	35.4499i	−1.36649	−	1.36649i	−0.501113	−	0.865382i	$-0.667076\pi$
$674$			36.0000i			1.38667i
$675$	9.50894	−	15.2482i	0.365999	−	0.586904i
$676$	−17.4833			−0.672435
$677$	7.67281	−	7.67281i	0.294890	−	0.294890i	−0.544119	−	0.839008i	$-0.683136\pi$
$677$	7.67281	−	7.67281i	0.294890	−	0.294890i	0.839008	+	0.544119i	$0.183136\pi$
$678$	−32.7582	−	32.7582i	−1.25807	−	1.25807i
$679$		0			0
$680$		0			0
$681$	−37.2250			−1.42646
$682$		0			0
$683$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$683$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$684$			21.0849i			0.806201i
$685$	2.98399	−	3.75488i	0.114012	−	0.143467i
$686$	26.1916			1.00000
$687$	4.80840	−	4.80840i	0.183452	−	0.183452i
$688$		0			0
$689$		0			0
$690$	−48.7083	−	38.7083i	−1.85429	−	1.47360i
$691$	24.3802			0.927466			0.463733	−	0.885975i	$-0.346510\pi$
$691$	24.3802			0.927466			0.463733	+	0.885975i	$0.346510\pi$
$692$	37.1844	−	37.1844i	1.41354	−	1.41354i
$693$		0			0
$694$		0			0
$695$	−5.83746	−	51.0291i	−0.221427	−	1.93564i
$696$		0			0
$697$		0			0
$698$	33.1352	+	33.1352i	1.25419	+	1.25419i
$699$			34.9226i			1.32090i
$700$	22.4499	+	14.0000i	0.848528	+	0.529150i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−7.41657	+	7.41657i	−0.279921	+	0.279921i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−37.5127	+	37.5127i	−1.41081	+	1.41081i
$708$	32.9666	+	32.9666i	1.23896	+	1.23896i
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	29.9543	−	37.6927i	1.12416	−	1.41458i
$711$	−10.3918			−0.389724
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.9194	+	10.9194i	−0.407793	+	0.407793i
$718$	6.00000	+	6.00000i	0.223918	+	0.223918i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−1.27917	−	11.1820i	−0.0476717	−	0.416730i
$721$		0			0
$722$	−51.1916	+	51.1916i	−1.90515	+	1.90515i
$723$		0			0
$724$			0.753931i			0.0280196i
$725$		0			0
$726$	32.1017			1.19141
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$	−10.9194	−	10.9194i	−0.404700	−	0.404700i
$729$		−	8.16685i		−	0.302476i
$730$		0			0
$731$		0			0
$732$	−41.4833	+	41.4833i	−1.53327	+	1.53327i
$733$	33.1839	+	33.1839i	1.22568	+	1.22568i	0.965584	+	0.260091i	$0.0837526\pi$
$733$	33.1839	+	33.1839i	1.22568	+	1.22568i	0.260091	+	0.965584i	$0.416247\pi$
$734$		0			0
$735$	20.0958	−	25.2874i	0.741245	−	0.932740i
$736$	53.9333			1.98801
$737$		0			0
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$		0			0
$741$	35.6766			1.31061
$742$		0			0
$743$	23.2583	+	23.2583i	0.853266	+	0.853266i	0.990534	−	0.137268i	$-0.0438322\pi$
$743$	23.2583	+	23.2583i	0.853266	+	0.853266i	−0.137268	+	0.990534i	$0.543832\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.03405	−	5.03405i	0.184186	−	0.184186i
$748$		0			0
$749$		0			0
$750$	30.7417	−	10.9333i	1.12253	−	0.399226i
$751$	−22.4499			−0.819210			−0.409605	−	0.912263i	$-0.634333\pi$
$751$	−22.4499			−0.819210			−0.409605	+	0.912263i	$0.634333\pi$
$752$		0			0
$753$	−42.0334	−	42.0334i	−1.53178	−	1.53178i
$754$		0			0
$755$	−49.8743	+	5.70536i	−1.81511	+	0.207639i
$756$	19.0179			0.691674
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$		0			0
$760$	32.9666	−	41.4833i	1.19583	−	1.50476i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	29.8399	−	29.8399i	1.08099	−	1.08099i
$763$		0			0
$764$			9.55006i			0.345509i
$765$		0			0
$766$		0			0
$767$	16.4833	−	16.4833i	0.595178	−	0.595178i
$768$	23.3467	+	23.3467i	0.842451	+	0.842451i
$769$		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
$773$	3.62357	+	3.62357i	0.130331	+	0.130331i	0.769263	−	0.638932i	$-0.220624\pi$
$773$	3.62357	+	3.62357i	0.130331	+	0.130331i	−0.638932	+	0.769263i	$0.720624\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−18.9205	+	2.16441i	−0.677462	+	0.0774981i
$781$		0			0
$782$		0			0
$783$		0			0
$784$			28.0000i			1.00000i
$785$	−13.6125	+	17.1292i	−0.485850	+	0.611366i
$786$	56.3165			2.00874
$787$	−9.46025	+	9.46025i	−0.337221	+	0.337221i	−0.855321	−	0.518099i	$-0.826640\pi$
$787$	−9.46025	+	9.46025i	−0.337221	+	0.337221i	0.518099	+	0.855321i	$0.326640\pi$
$788$		0			0
$789$		−	32.7582i		−	1.16622i
$790$	20.4453	+	16.2478i	0.727412	+	0.578071i
$791$	42.0000			1.49335
$792$		0			0
$793$	20.7417	+	20.7417i	0.736558	+	0.736558i
$794$			3.67227i			0.130324i
$795$		0			0
$796$		0			0
$797$	−20.3797	+	20.3797i	−0.721885	+	0.721885i	−0.968989	−	0.247104i	$-0.920521\pi$
$797$	−20.3797	+	20.3797i	−0.721885	+	0.721885i	0.247104	+	0.968989i	$0.420521\pi$
$798$	−45.7417	−	45.7417i	−1.61924	−	1.61924i
$799$		0			0
$800$	−14.9666	+	24.0000i	−0.529150	+	0.848528i
$801$		0			0
$802$	−14.7750	+	14.7750i	−0.521724	+	0.521724i
$803$		0			0
$804$		0			0
$805$	56.0393	−	6.41060i	1.97512	−	0.225944i
$806$		0			0
$807$	−40.9333	+	40.9333i	−1.44092	+	1.44092i
$808$	−40.1028	−	40.1028i	−1.41081	−	1.41081i
$809$			55.6749i			1.95743i	0.205234	+	0.978713i	$0.434204\pi$
$809$			55.6749i			1.95743i	−0.205234	+	0.978713i	$0.565796\pi$
$810$	22.0188	−	27.7072i	0.773663	−	0.973533i
$811$	9.13197			0.320667			0.160333	−	0.987063i	$-0.448743\pi$
$811$	9.13197			0.320667			0.160333	+	0.987063i	$0.448743\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$			6.87018i			0.240064i
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	4.42620	−	4.42620i	0.154381	−	0.154381i
$823$	36.0000	+	36.0000i	1.25488	+	1.25488i	0.953506	+	0.301376i	$0.0974458\pi$
$823$	36.0000	+	36.0000i	1.25488	+	1.25488i	0.301376	+	0.953506i	$0.402554\pi$
$824$		0			0
$825$		0			0
$826$	−42.2672			−1.47066
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$	−16.9666	−	16.9666i	−0.589631	−	0.589631i
$829$			20.8053i			0.722599i	0.932450	+	0.361299i	$0.117667\pi$
$829$			20.8053i			0.722599i	−0.932450	+	0.361299i	$0.882333\pi$
$830$	−17.7750	+	2.03337i	−0.616980	+	0.0705793i
$831$		0			0
$832$	11.6733	−	11.6733i	0.404700	−	0.404700i
$833$		0			0
$834$		−	67.0334i		−	2.32118i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−30.9708	−	30.9708i	−1.06987	−	1.06987i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	27.0334	+	21.4833i	0.932740	+	0.741245i
$841$	−29.0000			−1.00000
$842$		0			0
$843$	21.8388	+	21.8388i	0.752169	+	0.752169i
$844$		0			0
$845$	−2.22158	−	19.4203i	−0.0764246	−	0.668078i
$846$		0			0
$847$	−20.5791	+	20.5791i	−0.707107	+	0.707107i
$848$		0			0
$849$		−	69.0915i		−	2.37121i
$850$		0			0
$851$		0			0
$852$	44.4316	−	44.4316i	1.52220	−	1.52220i
$853$	−10.5911	−	10.5911i	−0.362634	−	0.362634i	0.502148	−	0.864782i	$-0.332543\pi$
$853$	−10.5911	−	10.5911i	−0.362634	−	0.362634i	−0.864782	+	0.502148i	$0.832543\pi$
$854$		−	53.1866i		−	1.82001i
$855$	−23.4209	+	2.67923i	−0.800977	+	0.0916276i
$856$		0			0
$857$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$857$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$858$		0			0
$859$		−	41.1363i		−	1.40355i	−0.712398	−	0.701776i	$-0.752391\pi$
$859$		−	41.1363i		−	1.40355i	0.712398	−	0.701776i	$-0.247609\pi$
$860$		0			0
$861$		0			0
$862$	−18.0000	+	18.0000i	−0.613082	+	0.613082i
$863$	−11.2250	−	11.2250i	−0.382102	−	0.382102i	0.489757	−	0.871859i	$-0.337086\pi$
$863$	−11.2250	−	11.2250i	−0.382102	−	0.382102i	−0.871859	+	0.489757i	$0.837086\pi$
$864$			20.3310i			0.691674i
$865$	46.0291	+	36.5791i	1.56503	+	1.24373i
$866$		0			0
$867$	24.8059	−	24.8059i	0.842451	−	0.842451i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		−	112.964i		−	3.82106i
$875$	−12.6984	+	26.7161i	−0.429283	+	0.903170i
$876$		0			0
$877$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$877$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$878$		0			0
$879$		−	3.15823i		−	0.106524i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	8.80840	−	8.80840i	0.296594	−	0.296594i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$	−32.4300	+	40.8080i	−1.09012	+	1.37175i
$886$		0			0
$887$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$887$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$			38.2583i			1.28314i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−29.9333			−1.00000
$897$	−28.7083	+	28.7083i	−0.958542	+	0.958542i
$898$	−29.9333	−	29.9333i	−0.998886	−	0.998886i
$899$		0			0
$900$	12.2583	−	2.84177i	0.408611	−	0.0947256i
$901$		0			0
$902$		0			0
$903$		0			0
$904$			44.8999i			1.49335i
$905$	−0.837458	+	0.0958009i	−0.0278381	+	0.00318453i
$906$	−65.5165			−2.17664
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$	25.5111	+	25.5111i	0.846615	+	0.846615i
$909$			25.2315i			0.836877i
$910$	10.7417	−	13.5167i	0.356082	−	0.448074i
$911$	52.3832			1.73553			0.867766	−	0.496972i	$-0.165555\pi$
$911$	52.3832			1.73553			0.867766	+	0.496972i	$0.165555\pi$
$912$	48.8999	−	48.8999i	1.61924	−	1.61924i
$913$		0			0
$914$			7.48331i			0.247526i
$915$	−51.3505	−	40.8080i	−1.69759	−	1.34907i
$916$	−6.59060			−0.217760
$917$	−36.1022	+	36.1022i	−1.19220	+	1.19220i
$918$		0			0
$919$		−	29.1582i		−	0.961841i	−0.876764	−	0.480921i	$-0.840303\pi$
$919$		−	29.1582i		−	0.961841i	0.876764	−	0.480921i	$-0.159697\pi$
$920$	6.85322	+	59.9085i	0.225944	+	1.97512i
$921$	−52.0581			−1.71537
$922$	−10.5424	+	10.5424i	−0.347197	+	0.347197i
$923$	−22.2158	−	22.2158i	−0.731242	−	0.731242i
$924$		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
$931$	58.6463			1.92205
$932$	23.9333	−	23.9333i	0.783960	−	0.783960i
$933$		0			0
$934$			48.1039i			1.57401i
$935$		0			0
$936$	−7.34453			−0.240064
$937$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$937$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.70578			0.153404			0.0767020	−	0.997054i	$-0.475561\pi$
$941$	4.70578			0.153404			0.0767020	+	0.997054i	$0.475561\pi$
$942$	−20.1916	+	20.1916i	−0.657878	+	0.657878i
$943$		0			0
$944$		−	45.1855i		−	1.47066i
$945$	2.41657	+	21.1249i	0.0786112	+	0.687192i
$946$		0			0
$947$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$947$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$948$	24.1006	+	24.1006i	0.782752	+	0.782752i
$949$		0			0
$950$	50.2683	+	31.3478i	1.63092	+	1.01706i
$951$		0			0
$952$		0			0
$953$	41.9666	+	41.9666i	1.35943	+	1.35943i	0.874616	+	0.484817i	$0.161114\pi$
$953$	41.9666	+	41.9666i	1.35943	+	1.35943i	0.484817	+	0.874616i	$0.338886\pi$
$954$		0			0
$955$	−10.6081	+	1.21351i	−0.343270	+	0.0392683i
$956$	14.9666			0.484055
$957$		0			0
$958$		0			0
$959$			5.67492i			0.183253i
$960$	−22.9666	+	28.8999i	−0.741245	+	0.932740i
$961$	31.0000			1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	14.8543	+	11.8047i	0.478177	+	0.380005i
$966$	73.6149			2.36852
$967$	40.2250	−	40.2250i	1.29355	−	1.29355i	0.360971	−	0.932577i	$-0.382445\pi$
$967$	40.2250	−	40.2250i	1.29355	−	1.29355i	0.932577	−	0.360971i	$-0.117555\pi$
$968$	−22.0000	−	22.0000i	−0.707107	−	0.707107i
$969$		0			0
$970$		0			0
$971$	−23.7237			−0.761328			−0.380664	−	0.924713i	$-0.624305\pi$
$971$	−23.7237			−0.761328			−0.380664	+	0.924713i	$0.624305\pi$
$972$	17.4126	−	17.4126i	0.558510	−	0.558510i
$973$	42.9724	+	42.9724i	1.37763	+	1.37763i
$974$		−	60.4499i		−	1.93694i
$975$	−4.80840	−	20.7417i	−0.153992	−	0.664265i
$976$	56.8589			1.82001
$977$	38.9333	−	38.9333i	1.24559	−	1.24559i	0.287936	−	0.957650i	$-0.407031\pi$
$977$	38.9333	−	38.9333i	1.24559	−	1.24559i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$		0			0
$979$		0			0
$980$	−31.1021	+	3.55792i	−0.993520	+	0.113654i
$981$		0			0
$982$		0			0
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−24.4499	−	24.4499i	−0.777856	−	0.777856i
$989$		0			0
$990$		0			0
$991$	−62.1916			−1.97558			−0.987791	−	0.155787i	$-0.950209\pi$
$991$	−62.1916			−1.97558			−0.987791	+	0.155787i	$0.950209\pi$
$992$		0			0
$993$		0			0
$994$			56.9666i			1.80687i
$995$		0			0
$996$	−23.3498			−0.739868
$997$	−40.0541	+	40.0541i	−1.26853	+	1.26853i	−0.321675	+	0.946850i	$0.604246\pi$
$997$	−40.0541	+	40.0541i	−1.26853	+	1.26853i	−0.946850	+	0.321675i	$0.895754\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.b.13.3	yes	8
4.3	odd	2		1120.2.w.b.433.2		8
5.2	odd	4	inner	280.2.s.b.237.3	yes	8
7.6	odd	2	inner	280.2.s.b.13.2	✓	8
8.3	odd	2		1120.2.w.b.433.3		8
8.5	even	2	inner	280.2.s.b.13.2	✓	8
20.7	even	4		1120.2.w.b.657.2		8
28.27	even	2		1120.2.w.b.433.3		8
35.27	even	4	inner	280.2.s.b.237.2	yes	8
40.27	even	4		1120.2.w.b.657.3		8
40.37	odd	4	inner	280.2.s.b.237.2	yes	8
56.13	odd	2	CM	280.2.s.b.13.3	yes	8
56.27	even	2		1120.2.w.b.433.2		8
140.27	odd	4		1120.2.w.b.657.3		8
280.27	odd	4		1120.2.w.b.657.2		8
280.237	even	4	inner	280.2.s.b.237.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.b.13.2	✓	8	7.6	odd	2	inner
280.2.s.b.13.2	✓	8	8.5	even	2	inner
280.2.s.b.13.3	yes	8	1.1	even	1	trivial
280.2.s.b.13.3	yes	8	56.13	odd	2	CM
280.2.s.b.237.2	yes	8	35.27	even	4	inner
280.2.s.b.237.2	yes	8	40.37	odd	4	inner
280.2.s.b.237.3	yes	8	5.2	odd	4	inner
280.2.s.b.237.3	yes	8	280.237	even	4	inner
1120.2.w.b.433.2		8	4.3	odd	2
1120.2.w.b.433.2		8	56.27	even	2
1120.2.w.b.433.3		8	8.3	odd	2
1120.2.w.b.433.3		8	28.27	even	2
1120.2.w.b.657.2		8	20.7	even	4
1120.2.w.b.657.2		8	280.27	odd	4
1120.2.w.b.657.3		8	40.27	even	4
1120.2.w.b.657.3		8	140.27	odd	4

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.45917 + 1.45917i) q^{3} -2.00000i q^{4} +(2.22158 - 0.254137i) q^{5} +2.91834 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +1.25834i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.45917 + 1.45917i) q^{3} -2.00000i q^{4} +(2.22158 - 0.254137i) q^{5} +2.91834 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +1.25834i q^{9} +(1.96744 - 2.47572i) q^{10} +(2.91834 - 2.91834i) q^{12} +(-1.45917 - 1.45917i) q^{13} +3.74166i q^{14} +(3.61249 + 2.87083i) q^{15} -4.00000 q^{16} +(1.25834 + 1.25834i) q^{18} +8.37804i q^{19} +(-0.508274 - 4.44316i) q^{20} -5.45971 q^{21} +(-6.74166 - 6.74166i) q^{23} -5.83667i q^{24} +(4.87083 - 1.12917i) q^{25} -2.91834 q^{26} +(2.54137 - 2.54137i) q^{27} +(3.74166 + 3.74166i) q^{28} +(6.48331 - 0.741657i) q^{30} +(-4.00000 + 4.00000i) q^{32} +(-3.68075 + 4.63164i) q^{35} +2.51669 q^{36} +(8.37804 + 8.37804i) q^{38} -4.25834i q^{39} +(-4.95143 - 3.93488i) q^{40} +(-5.45971 + 5.45971i) q^{42} +(0.319792 + 2.79551i) q^{45} -13.4833 q^{46} +(-5.83667 - 5.83667i) q^{48} -7.00000i q^{49} +(3.74166 - 6.00000i) q^{50} +(-2.91834 + 2.91834i) q^{52} -5.08274i q^{54} +7.48331 q^{56} +(-12.2250 + 12.2250i) q^{57} +11.2964i q^{59} +(5.74166 - 7.22497i) q^{60} -14.2147 q^{61} +(-2.35414 - 2.35414i) q^{63} +8.00000i q^{64} +(-3.61249 - 2.87083i) q^{65} -19.6744i q^{69} +(0.950894 + 8.31239i) q^{70} +15.2250 q^{71} +(2.51669 - 2.51669i) q^{72} +(8.75501 + 5.45971i) q^{75} +16.7561 q^{76} +(-4.25834 - 4.25834i) q^{78} +8.25834i q^{79} +(-8.88632 + 1.01655i) q^{80} +11.1916 q^{81} +(-4.00054 - 4.00054i) q^{83} +10.9194i q^{84} +(3.11530 + 2.47572i) q^{90} +5.45971 q^{91} +(-13.4833 + 13.4833i) q^{92} +(2.12917 + 18.6125i) q^{95} -11.6733 q^{96} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 16 * q^8	\( 8 q + 8 q^{2} - 16 q^{8} - 16 q^{15} - 32 q^{16} + 40 q^{18} - 24 q^{23} + 24 q^{25} - 8 q^{30} - 32 q^{32} + 80 q^{36} - 48 q^{46} - 8 q^{57} + 16 q^{60} + 56 q^{63} + 16 q^{65} + 32 q^{71} + 80 q^{72} - 64 q^{78} - 120 q^{81} - 48 q^{92} + 32 q^{95} - 56 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^8 - 16 * q^15 - 32 * q^16 + 40 * q^18 - 24 * q^23 + 24 * q^25 - 8 * q^30 - 32 * q^32 + 80 * q^36 - 48 * q^46 - 8 * q^57 + 16 * q^60 + 56 * q^63 + 16 * q^65 + 32 * q^71 + 80 * q^72 - 64 * q^78 - 120 * q^81 - 48 * q^92 + 32 * q^95 - 56 * q^98

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