LMFDB - Embedded newform 1280.2.n.o.767.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(767,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("1280.767");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			767.3
Root			$0.437016 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	1280.767
Dual form			1280.2.n.o.1023.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 + 1.41421i) q^{3} -2.23607 q^{5} +(-3.16228 + 3.16228i) q^{7} +1.00000i q^{9} +2.82843i q^{11} +(2.23607 - 2.23607i) q^{13} +(-3.16228 - 3.16228i) q^{15} +(1.00000 + 1.00000i) q^{17} -5.65685 q^{19} -8.94427 q^{21} +(-3.16228 - 3.16228i) q^{23} +5.00000 q^{25} +(2.82843 - 2.82843i) q^{27} -4.47214i q^{29} +6.32456i q^{31} +(-4.00000 + 4.00000i) q^{33} +(7.07107 - 7.07107i) q^{35} +(-6.70820 - 6.70820i) q^{37} +6.32456 q^{39} -4.00000 q^{41} +(-7.07107 - 7.07107i) q^{43} -2.23607i q^{45} +(-3.16228 + 3.16228i) q^{47} -13.0000i q^{49} +2.82843i q^{51} +(-6.70820 + 6.70820i) q^{53} -6.32456i q^{55} +(-8.00000 - 8.00000i) q^{57} -4.47214 q^{61} +(-3.16228 - 3.16228i) q^{63} +(-5.00000 + 5.00000i) q^{65} +(-4.24264 + 4.24264i) q^{67} -8.94427i q^{69} +6.32456i q^{71} +(-3.00000 + 3.00000i) q^{73} +(7.07107 + 7.07107i) q^{75} +(-8.94427 - 8.94427i) q^{77} +12.6491 q^{79} +11.0000 q^{81} +(-1.41421 - 1.41421i) q^{83} +(-2.23607 - 2.23607i) q^{85} +(6.32456 - 6.32456i) q^{87} +8.00000i q^{89} +14.1421i q^{91} +(-8.94427 + 8.94427i) q^{93} +12.6491 q^{95} +(3.00000 + 3.00000i) q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{17} + 40 q^{25} - 32 q^{33} - 32 q^{41} - 64 q^{57} - 40 q^{65} - 24 q^{73} + 88 q^{81} + 24 q^{97}+O(q^{100}) $ 8 * q + 8 * q^17 + 40 * q^25 - 32 * q^33 - 32 * q^41 - 64 * q^57 - 40 * q^65 - 24 * q^73 + 88 * q^81 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.41421	+	1.41421i	0.816497	+	0.816497i	0.985599	−	0.169102i	$-0.0540867\pi$
$3$	1.41421	+	1.41421i	0.816497	+	0.816497i	−0.169102	+	0.985599i	$0.554087\pi$
$4$		0			0
$5$	−2.23607			−1.00000
$5$	−2.23607			−1.00000
$6$		0			0
$7$	−3.16228	+	3.16228i	−1.19523	+	1.19523i	−0.219650	+	0.975579i	$0.570491\pi$
$7$	−3.16228	+	3.16228i	−1.19523	+	1.19523i	−0.975579	+	0.219650i	$0.929509\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	2.23607	−	2.23607i	0.620174	−	0.620174i	−0.325402	−	0.945576i	$-0.605500\pi$
$13$	2.23607	−	2.23607i	0.620174	−	0.620174i	0.945576	+	0.325402i	$0.105500\pi$
$14$		0			0
$15$	−3.16228	−	3.16228i	−0.816497	−	0.816497i
$16$		0			0
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$		0			0
$19$	−5.65685			−1.29777			−0.648886	−	0.760886i	$-0.724765\pi$
$19$	−5.65685			−1.29777			−0.648886	+	0.760886i	$0.724765\pi$
$20$		0			0
$21$	−8.94427			−1.95180
$22$		0			0
$23$	−3.16228	−	3.16228i	−0.659380	−	0.659380i	0.295853	−	0.955233i	$-0.404396\pi$
$23$	−3.16228	−	3.16228i	−0.659380	−	0.659380i	−0.955233	+	0.295853i	$0.904396\pi$
$24$		0			0
$25$	5.00000			1.00000
$26$		0			0
$27$	2.82843	−	2.82843i	0.544331	−	0.544331i
$28$		0			0
$29$		−	4.47214i		−	0.830455i	−0.909718	−	0.415227i	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$		0			0
$31$			6.32456i			1.13592i	0.823055	+	0.567962i	$0.192268\pi$
$31$			6.32456i			1.13592i	−0.823055	+	0.567962i	$0.807732\pi$
$32$		0			0
$33$	−4.00000	+	4.00000i	−0.696311	+	0.696311i
$34$		0			0
$35$	7.07107	−	7.07107i	1.19523	−	1.19523i
$36$		0			0
$37$	−6.70820	−	6.70820i	−1.10282	−	1.10282i	−0.994069	−	0.108753i	$-0.965314\pi$
$37$	−6.70820	−	6.70820i	−1.10282	−	1.10282i	−0.108753	−	0.994069i	$-0.534686\pi$
$38$		0			0
$39$	6.32456			1.01274
$40$		0			0
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$	−7.07107	−	7.07107i	−1.07833	−	1.07833i	−0.996660	−	0.0816682i	$-0.973975\pi$
$43$	−7.07107	−	7.07107i	−1.07833	−	1.07833i	−0.0816682	−	0.996660i	$-0.526025\pi$
$44$		0			0
$45$		−	2.23607i		−	0.333333i
$46$		0			0
$47$	−3.16228	+	3.16228i	−0.461266	+	0.461266i	−0.899070	−	0.437805i	$-0.855756\pi$
$47$	−3.16228	+	3.16228i	−0.461266	+	0.461266i	0.437805	+	0.899070i	$0.355756\pi$
$48$		0			0
$49$		−	13.0000i		−	1.85714i
$50$		0			0
$51$			2.82843i			0.396059i
$52$		0			0
$53$	−6.70820	+	6.70820i	−0.921443	+	0.921443i	−0.997131	−	0.0756888i	$-0.975884\pi$
$53$	−6.70820	+	6.70820i	−0.921443	+	0.921443i	0.0756888	+	0.997131i	$0.475884\pi$
$54$		0			0
$55$		−	6.32456i		−	0.852803i
$56$		0			0
$57$	−8.00000	−	8.00000i	−1.05963	−	1.05963i
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	−4.47214			−0.572598			−0.286299	−	0.958140i	$-0.592425\pi$
$61$	−4.47214			−0.572598			−0.286299	+	0.958140i	$0.592425\pi$
$62$		0			0
$63$	−3.16228	−	3.16228i	−0.398410	−	0.398410i
$64$		0			0
$65$	−5.00000	+	5.00000i	−0.620174	+	0.620174i
$66$		0			0
$67$	−4.24264	+	4.24264i	−0.518321	+	0.518321i	−0.917063	−	0.398742i	$-0.869447\pi$
$67$	−4.24264	+	4.24264i	−0.518321	+	0.518321i	0.398742	+	0.917063i	$0.369447\pi$
$68$		0			0
$69$		−	8.94427i		−	1.07676i
$70$		0			0
$71$			6.32456i			0.750587i	0.926906	+	0.375293i	$0.122458\pi$
$71$			6.32456i			0.750587i	−0.926906	+	0.375293i	$0.877542\pi$
$72$		0			0
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$		0			0
$75$	7.07107	+	7.07107i	0.816497	+	0.816497i
$76$		0			0
$77$	−8.94427	−	8.94427i	−1.01929	−	1.01929i
$78$		0			0
$79$	12.6491			1.42314			0.711568	−	0.702617i	$-0.247985\pi$
$79$	12.6491			1.42314			0.711568	+	0.702617i	$0.247985\pi$
$80$		0			0
$81$	11.0000			1.22222
$82$		0			0
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	0.625219	−	0.780449i	$-0.285010\pi$
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	−0.780449	+	0.625219i	$0.785010\pi$
$84$		0			0
$85$	−2.23607	−	2.23607i	−0.242536	−	0.242536i
$86$		0			0
$87$	6.32456	−	6.32456i	0.678064	−	0.678064i
$88$		0			0
$89$			8.00000i			0.847998i	0.905663	+	0.423999i	$0.139374\pi$
$89$			8.00000i			0.847998i	−0.905663	+	0.423999i	$0.860626\pi$
$90$		0			0
$91$			14.1421i			1.48250i
$92$		0			0
$93$	−8.94427	+	8.94427i	−0.927478	+	0.927478i
$94$		0			0
$95$	12.6491			1.29777
$96$		0			0
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$		0			0
$101$	8.94427			0.889988			0.444994	−	0.895533i	$-0.353206\pi$
$101$	8.94427			0.889988			0.444994	+	0.895533i	$0.353206\pi$
$102$		0			0
$103$	9.48683	+	9.48683i	0.934765	+	0.934765i	0.997999	−	0.0632333i	$-0.0201412\pi$
$103$	9.48683	+	9.48683i	0.934765	+	0.934765i	−0.0632333	+	0.997999i	$0.520141\pi$
$104$		0			0
$105$	20.0000			1.95180
$106$		0			0
$107$	4.24264	−	4.24264i	0.410152	−	0.410152i	−0.471640	−	0.881791i	$-0.656338\pi$
$107$	4.24264	−	4.24264i	0.410152	−	0.410152i	0.881791	+	0.471640i	$0.156338\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		−	18.9737i		−	1.80090i
$112$		0			0
$113$	−13.0000	+	13.0000i	−1.22294	+	1.22294i	−0.256354	+	0.966583i	$0.582521\pi$
$113$	−13.0000	+	13.0000i	−1.22294	+	1.22294i	−0.966583	+	0.256354i	$0.917479\pi$
$114$		0			0
$115$	7.07107	+	7.07107i	0.659380	+	0.659380i
$116$		0			0
$117$	2.23607	+	2.23607i	0.206725	+	0.206725i
$118$		0			0
$119$	−6.32456			−0.579771
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$	−5.65685	−	5.65685i	−0.510061	−	0.510061i
$124$		0			0
$125$	−11.1803			−1.00000
$126$		0			0
$127$	3.16228	−	3.16228i	0.280607	−	0.280607i	−0.552744	−	0.833351i	$-0.686419\pi$
$127$	3.16228	−	3.16228i	0.280607	−	0.280607i	0.833351	+	0.552744i	$0.186419\pi$
$128$		0			0
$129$		−	20.0000i		−	1.76090i
$130$		0			0
$131$			14.1421i			1.23560i	0.786334	+	0.617802i	$0.211977\pi$
$131$			14.1421i			1.23560i	−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$	17.8885	−	17.8885i	1.55113	−	1.55113i
$134$		0			0
$135$	−6.32456	+	6.32456i	−0.544331	+	0.544331i
$136$		0			0
$137$	−9.00000	−	9.00000i	−0.768922	−	0.768922i	0.208995	−	0.977917i	$-0.432981\pi$
$137$	−9.00000	−	9.00000i	−0.768922	−	0.768922i	−0.977917	+	0.208995i	$0.932981\pi$
$138$		0			0
$139$	−5.65685			−0.479808			−0.239904	−	0.970797i	$-0.577116\pi$
$139$	−5.65685			−0.479808			−0.239904	+	0.970797i	$0.577116\pi$
$140$		0			0
$141$	−8.94427			−0.753244
$142$		0			0
$143$	6.32456	+	6.32456i	0.528886	+	0.528886i
$144$		0			0
$145$			10.0000i			0.830455i
$146$		0			0
$147$	18.3848	−	18.3848i	1.51635	−	1.51635i
$148$		0			0
$149$			17.8885i			1.46549i	0.680505	+	0.732743i	$0.261760\pi$
$149$			17.8885i			1.46549i	−0.680505	+	0.732743i	$0.738240\pi$
$150$		0			0
$151$		−	6.32456i		−	0.514685i	−0.966320	−	0.257343i	$-0.917153\pi$
$151$		−	6.32456i		−	0.514685i	0.966320	−	0.257343i	$-0.0828469\pi$
$152$		0			0
$153$	−1.00000	+	1.00000i	−0.0808452	+	0.0808452i
$154$		0			0
$155$		−	14.1421i		−	1.13592i
$156$		0			0
$157$	2.23607	+	2.23607i	0.178458	+	0.178458i	0.790683	−	0.612226i	$-0.209726\pi$
$157$	2.23607	+	2.23607i	0.178458	+	0.178458i	−0.612226	+	0.790683i	$0.709726\pi$
$158$		0			0
$159$	−18.9737			−1.50471
$160$		0			0
$161$	20.0000			1.57622
$162$		0			0
$163$	−15.5563	−	15.5563i	−1.21847	−	1.21847i	−0.968169	−	0.250299i	$-0.919471\pi$
$163$	−15.5563	−	15.5563i	−1.21847	−	1.21847i	−0.250299	−	0.968169i	$-0.580529\pi$
$164$		0			0
$165$	8.94427	−	8.94427i	0.696311	−	0.696311i
$166$		0			0
$167$	3.16228	−	3.16228i	0.244704	−	0.244704i	−0.574089	−	0.818793i	$-0.694644\pi$
$167$	3.16228	−	3.16228i	0.244704	−	0.244704i	0.818793	+	0.574089i	$0.194644\pi$
$168$		0			0
$169$			3.00000i			0.230769i
$170$		0			0
$171$		−	5.65685i		−	0.432590i
$172$		0			0
$173$	2.23607	−	2.23607i	0.170005	−	0.170005i	−0.616976	−	0.786982i	$-0.711643\pi$
$173$	2.23607	−	2.23607i	0.170005	−	0.170005i	0.786982	+	0.616976i	$0.211643\pi$
$174$		0			0
$175$	−15.8114	+	15.8114i	−1.19523	+	1.19523i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.65685			−0.422813			−0.211407	−	0.977398i	$-0.567804\pi$
$179$	−5.65685			−0.422813			−0.211407	+	0.977398i	$0.567804\pi$
$180$		0			0
$181$	8.94427			0.664822			0.332411	−	0.943135i	$-0.392138\pi$
$181$	8.94427			0.664822			0.332411	+	0.943135i	$0.392138\pi$
$182$		0			0
$183$	−6.32456	−	6.32456i	−0.467525	−	0.467525i
$184$		0			0
$185$	15.0000	+	15.0000i	1.10282	+	1.10282i
$186$		0			0
$187$	−2.82843	+	2.82843i	−0.206835	+	0.206835i
$188$		0			0
$189$			17.8885i			1.30120i
$190$		0			0
$191$			18.9737i			1.37289i	0.727183	+	0.686443i	$0.240829\pi$
$191$			18.9737i			1.37289i	−0.727183	+	0.686443i	$0.759171\pi$
$192$		0			0
$193$	−7.00000	+	7.00000i	−0.503871	+	0.503871i	−0.912639	−	0.408768i	$-0.865959\pi$
$193$	−7.00000	+	7.00000i	−0.503871	+	0.503871i	0.408768	+	0.912639i	$0.365959\pi$
$194$		0			0
$195$	−14.1421			−1.01274
$196$		0			0
$197$	15.6525	+	15.6525i	1.11519	+	1.11519i	0.992437	+	0.122756i	$0.0391732\pi$
$197$	15.6525	+	15.6525i	1.11519	+	1.11519i	0.122756	+	0.992437i	$0.460827\pi$
$198$		0			0
$199$	−12.6491			−0.896672			−0.448336	−	0.893865i	$-0.647983\pi$
$199$	−12.6491			−0.896672			−0.448336	+	0.893865i	$0.647983\pi$
$200$		0			0
$201$	−12.0000			−0.846415
$202$		0			0
$203$	14.1421	+	14.1421i	0.992583	+	0.992583i
$204$		0			0
$205$	8.94427			0.624695
$206$		0			0
$207$	3.16228	−	3.16228i	0.219793	−	0.219793i
$208$		0			0
$209$		−	16.0000i		−	1.10674i
$210$		0			0
$211$		−	2.82843i		−	0.194717i	−0.995249	−	0.0973585i	$-0.968961\pi$
$211$		−	2.82843i		−	0.194717i	0.995249	−	0.0973585i	$-0.0310393\pi$
$212$		0			0
$213$	−8.94427	+	8.94427i	−0.612851	+	0.612851i
$214$		0			0
$215$	15.8114	+	15.8114i	1.07833	+	1.07833i
$216$		0			0
$217$	−20.0000	−	20.0000i	−1.35769	−	1.35769i
$218$		0			0
$219$	−8.48528			−0.573382
$220$		0			0
$221$	4.47214			0.300828
$222$		0			0
$223$	−3.16228	−	3.16228i	−0.211762	−	0.211762i	0.593254	−	0.805016i	$-0.297843\pi$
$223$	−3.16228	−	3.16228i	−0.211762	−	0.211762i	−0.805016	+	0.593254i	$0.797843\pi$
$224$		0			0
$225$			5.00000i			0.333333i
$226$		0			0
$227$	−7.07107	+	7.07107i	−0.469323	+	0.469323i	−0.901695	−	0.432372i	$-0.857677\pi$
$227$	−7.07107	+	7.07107i	−0.469323	+	0.469323i	0.432372	+	0.901695i	$0.357677\pi$
$228$		0			0
$229$		−	22.3607i		−	1.47764i	−0.673905	−	0.738818i	$-0.735384\pi$
$229$		−	22.3607i		−	1.47764i	0.673905	−	0.738818i	$-0.264616\pi$
$230$		0			0
$231$		−	25.2982i		−	1.66450i
$232$		0			0
$233$	−9.00000	+	9.00000i	−0.589610	+	0.589610i	−0.937526	−	0.347916i	$-0.886889\pi$
$233$	−9.00000	+	9.00000i	−0.589610	+	0.589610i	0.347916	+	0.937526i	$0.386889\pi$
$234$		0			0
$235$	7.07107	−	7.07107i	0.461266	−	0.461266i
$236$		0			0
$237$	17.8885	+	17.8885i	1.16199	+	1.16199i
$238$		0			0
$239$	−25.2982			−1.63641			−0.818203	−	0.574930i	$-0.805029\pi$
$239$	−25.2982			−1.63641			−0.818203	+	0.574930i	$0.805029\pi$
$240$		0			0
$241$	−4.00000			−0.257663			−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000			−0.257663			−0.128831	+	0.991667i	$0.541123\pi$
$242$		0			0
$243$	7.07107	+	7.07107i	0.453609	+	0.453609i
$244$		0			0
$245$			29.0689i			1.85714i
$246$		0			0
$247$	−12.6491	+	12.6491i	−0.804844	+	0.804844i
$248$		0			0
$249$		−	4.00000i		−	0.253490i
$250$		0			0
$251$		−	2.82843i		−	0.178529i	−0.996008	−	0.0892644i	$-0.971548\pi$
$251$		−	2.82843i		−	0.178529i	0.996008	−	0.0892644i	$-0.0284516\pi$
$252$		0			0
$253$	8.94427	−	8.94427i	0.562322	−	0.562322i
$254$		0			0
$255$		−	6.32456i		−	0.396059i
$256$		0			0
$257$	−13.0000	−	13.0000i	−0.810918	−	0.810918i	0.173854	−	0.984771i	$-0.444378\pi$
$257$	−13.0000	−	13.0000i	−0.810918	−	0.810918i	−0.984771	+	0.173854i	$0.944378\pi$
$258$		0			0
$259$	42.4264			2.63625
$260$		0			0
$261$	4.47214			0.276818
$262$		0			0
$263$	−9.48683	−	9.48683i	−0.584983	−	0.584983i	0.351285	−	0.936268i	$-0.385745\pi$
$263$	−9.48683	−	9.48683i	−0.584983	−	0.584983i	−0.936268	+	0.351285i	$0.885745\pi$
$264$		0			0
$265$	15.0000	−	15.0000i	0.921443	−	0.921443i
$266$		0			0
$267$	−11.3137	+	11.3137i	−0.692388	+	0.692388i
$268$		0			0
$269$		−	17.8885i		−	1.09068i	−0.838214	−	0.545342i	$-0.816400\pi$
$269$		−	17.8885i		−	1.09068i	0.838214	−	0.545342i	$-0.183600\pi$
$270$		0			0
$271$		−	6.32456i		−	0.384189i	−0.981376	−	0.192095i	$-0.938472\pi$
$271$		−	6.32456i		−	0.384189i	0.981376	−	0.192095i	$-0.0615281\pi$
$272$		0			0
$273$	−20.0000	+	20.0000i	−1.21046	+	1.21046i
$274$		0			0
$275$			14.1421i			0.852803i
$276$		0			0
$277$	−2.23607	−	2.23607i	−0.134352	−	0.134352i	0.636732	−	0.771085i	$-0.280286\pi$
$277$	−2.23607	−	2.23607i	−0.134352	−	0.134352i	−0.771085	+	0.636732i	$0.780286\pi$
$278$		0			0
$279$	−6.32456			−0.378641
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	12.7279	+	12.7279i	0.756596	+	0.756596i	0.975701	−	0.219105i	$-0.0703137\pi$
$283$	12.7279	+	12.7279i	0.756596	+	0.756596i	−0.219105	+	0.975701i	$0.570314\pi$
$284$		0			0
$285$	17.8885	+	17.8885i	1.05963	+	1.05963i
$286$		0			0
$287$	12.6491	−	12.6491i	0.746653	−	0.746653i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$			8.48528i			0.497416i
$292$		0			0
$293$	−6.70820	+	6.70820i	−0.391897	+	0.391897i	−0.875363	−	0.483466i	$-0.839378\pi$
$293$	−6.70820	+	6.70820i	−0.391897	+	0.391897i	0.483466	+	0.875363i	$0.339378\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	8.00000	+	8.00000i	0.464207	+	0.464207i
$298$		0			0
$299$	−14.1421			−0.817861
$300$		0			0
$301$	44.7214			2.57770
$302$		0			0
$303$	12.6491	+	12.6491i	0.726672	+	0.726672i
$304$		0			0
$305$	10.0000			0.572598
$306$		0			0
$307$	−9.89949	+	9.89949i	−0.564994	+	0.564994i	−0.930722	−	0.365728i	$-0.880820\pi$
$307$	−9.89949	+	9.89949i	−0.564994	+	0.564994i	0.365728	+	0.930722i	$0.380820\pi$
$308$		0			0
$309$			26.8328i			1.52647i
$310$		0			0
$311$			31.6228i			1.79316i	0.442879	+	0.896582i	$0.353957\pi$
$311$			31.6228i			1.79316i	−0.442879	+	0.896582i	$0.646043\pi$
$312$		0			0
$313$	−11.0000	+	11.0000i	−0.621757	+	0.621757i	−0.945980	−	0.324224i	$-0.894897\pi$
$313$	−11.0000	+	11.0000i	−0.621757	+	0.621757i	0.324224	+	0.945980i	$0.394897\pi$
$314$		0			0
$315$	7.07107	+	7.07107i	0.398410	+	0.398410i
$316$		0			0
$317$	6.70820	+	6.70820i	0.376770	+	0.376770i	0.869936	−	0.493165i	$-0.164160\pi$
$317$	6.70820	+	6.70820i	0.376770	+	0.376770i	−0.493165	+	0.869936i	$0.664160\pi$
$318$		0			0
$319$	12.6491			0.708214
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	−5.65685	−	5.65685i	−0.314756	−	0.314756i
$324$		0			0
$325$	11.1803	−	11.1803i	0.620174	−	0.620174i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		−	20.0000i		−	1.10264i
$330$		0			0
$331$		−	25.4558i		−	1.39918i	−0.714545	−	0.699590i	$-0.753366\pi$
$331$		−	25.4558i		−	1.39918i	0.714545	−	0.699590i	$-0.246634\pi$
$332$		0			0
$333$	6.70820	−	6.70820i	0.367607	−	0.367607i
$334$		0			0
$335$	9.48683	−	9.48683i	0.518321	−	0.518321i
$336$		0			0
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$		0			0
$339$	−36.7696			−1.99705
$340$		0			0
$341$	−17.8885			−0.968719
$342$		0			0
$343$	18.9737	+	18.9737i	1.02448	+	1.02448i
$344$		0			0
$345$			20.0000i			1.07676i
$346$		0			0
$347$	−9.89949	+	9.89949i	−0.531433	+	0.531433i	−0.920999	−	0.389566i	$-0.872625\pi$
$347$	−9.89949	+	9.89949i	−0.531433	+	0.531433i	0.389566	+	0.920999i	$0.372625\pi$
$348$		0			0
$349$			4.47214i			0.239388i	0.992811	+	0.119694i	$0.0381913\pi$
$349$			4.47214i			0.239388i	−0.992811	+	0.119694i	$0.961809\pi$
$350$		0			0
$351$		−	12.6491i		−	0.675160i
$352$		0			0
$353$	1.00000	−	1.00000i	0.0532246	−	0.0532246i	−0.679994	−	0.733218i	$-0.738017\pi$
$353$	1.00000	−	1.00000i	0.0532246	−	0.0532246i	0.733218	+	0.679994i	$0.238017\pi$
$354$		0			0
$355$		−	14.1421i		−	0.750587i
$356$		0			0
$357$	−8.94427	−	8.94427i	−0.473381	−	0.473381i
$358$		0			0
$359$	12.6491			0.667595			0.333797	−	0.942645i	$-0.391670\pi$
$359$	12.6491			0.667595			0.333797	+	0.942645i	$0.391670\pi$
$360$		0			0
$361$	13.0000			0.684211
$362$		0			0
$363$	4.24264	+	4.24264i	0.222681	+	0.222681i
$364$		0			0
$365$	6.70820	−	6.70820i	0.351123	−	0.351123i
$366$		0			0
$367$	−9.48683	+	9.48683i	−0.495209	+	0.495209i	−0.909943	−	0.414734i	$-0.863875\pi$
$367$	−9.48683	+	9.48683i	−0.495209	+	0.495209i	0.414734	+	0.909943i	$0.363875\pi$
$368$		0			0
$369$		−	4.00000i		−	0.208232i
$370$		0			0
$371$		−	42.4264i		−	2.20267i
$372$		0			0
$373$	−2.23607	+	2.23607i	−0.115779	+	0.115779i	−0.762623	−	0.646844i	$-0.776089\pi$
$373$	−2.23607	+	2.23607i	−0.115779	+	0.115779i	0.646844	+	0.762623i	$0.276089\pi$
$374$		0			0
$375$	−15.8114	−	15.8114i	−0.816497	−	0.816497i
$376$		0			0
$377$	−10.0000	−	10.0000i	−0.515026	−	0.515026i
$378$		0			0
$379$	33.9411			1.74344			0.871719	−	0.490006i	$-0.163005\pi$
$379$	33.9411			1.74344			0.871719	+	0.490006i	$0.163005\pi$
$380$		0			0
$381$	8.94427			0.458229
$382$		0			0
$383$	−15.8114	−	15.8114i	−0.807924	−	0.807924i	0.176395	−	0.984319i	$-0.443556\pi$
$383$	−15.8114	−	15.8114i	−0.807924	−	0.807924i	−0.984319	+	0.176395i	$0.943556\pi$
$384$		0			0
$385$	20.0000	+	20.0000i	1.01929	+	1.01929i
$386$		0			0
$387$	7.07107	−	7.07107i	0.359443	−	0.359443i
$388$		0			0
$389$			17.8885i			0.906985i	0.891260	+	0.453493i	$0.149822\pi$
$389$			17.8885i			0.906985i	−0.891260	+	0.453493i	$0.850178\pi$
$390$		0			0
$391$		−	6.32456i		−	0.319847i
$392$		0			0
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$		0			0
$395$	−28.2843			−1.42314
$396$		0			0
$397$	2.23607	+	2.23607i	0.112225	+	0.112225i	0.760989	−	0.648764i	$-0.224714\pi$
$397$	2.23607	+	2.23607i	0.112225	+	0.112225i	−0.648764	+	0.760989i	$0.724714\pi$
$398$		0			0
$399$	50.5964			2.53299
$400$		0			0
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$		0			0
$403$	14.1421	+	14.1421i	0.704470	+	0.704470i
$404$		0			0
$405$	−24.5967			−1.22222
$406$		0			0
$407$	18.9737	−	18.9737i	0.940490	−	0.940490i
$408$		0			0
$409$			2.00000i			0.0988936i	0.998777	+	0.0494468i	$0.0157458\pi$
$409$			2.00000i			0.0988936i	−0.998777	+	0.0494468i	$0.984254\pi$
$410$		0			0
$411$		−	25.4558i		−	1.25564i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3.16228	+	3.16228i	0.155230	+	0.155230i
$416$		0			0
$417$	−8.00000	−	8.00000i	−0.391762	−	0.391762i
$418$		0			0
$419$	22.6274			1.10542			0.552711	−	0.833373i	$-0.313593\pi$
$419$	22.6274			1.10542			0.552711	+	0.833373i	$0.313593\pi$
$420$		0			0
$421$	4.47214			0.217959			0.108979	−	0.994044i	$-0.465242\pi$
$421$	4.47214			0.217959			0.108979	+	0.994044i	$0.465242\pi$
$422$		0			0
$423$	−3.16228	−	3.16228i	−0.153755	−	0.153755i
$424$		0			0
$425$	5.00000	+	5.00000i	0.242536	+	0.242536i
$426$		0			0
$427$	14.1421	−	14.1421i	0.684386	−	0.684386i
$428$		0			0
$429$			17.8885i			0.863667i
$430$		0			0
$431$			18.9737i			0.913929i	0.889485	+	0.456965i	$0.151063\pi$
$431$			18.9737i			0.913929i	−0.889485	+	0.456965i	$0.848937\pi$
$432$		0			0
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	−0.631337	−	0.775508i	$-0.717494\pi$
$433$	3.00000	−	3.00000i	0.144171	−	0.144171i	0.775508	+	0.631337i	$0.217494\pi$
$434$		0			0
$435$	−14.1421	+	14.1421i	−0.678064	+	0.678064i
$436$		0			0
$437$	17.8885	+	17.8885i	0.855725	+	0.855725i
$438$		0			0
$439$	37.9473			1.81113			0.905564	−	0.424210i	$-0.139448\pi$
$439$	37.9473			1.81113			0.905564	+	0.424210i	$0.139448\pi$
$440$		0			0
$441$	13.0000			0.619048
$442$		0			0
$443$	−15.5563	−	15.5563i	−0.739104	−	0.739104i	0.233300	−	0.972405i	$-0.425047\pi$
$443$	−15.5563	−	15.5563i	−0.739104	−	0.739104i	−0.972405	+	0.233300i	$0.925047\pi$
$444$		0			0
$445$		−	17.8885i		−	0.847998i
$446$		0			0
$447$	−25.2982	+	25.2982i	−1.19656	+	1.19656i
$448$		0			0
$449$			22.0000i			1.03824i	0.854700	+	0.519122i	$0.173741\pi$
$449$			22.0000i			1.03824i	−0.854700	+	0.519122i	$0.826259\pi$
$450$		0			0
$451$		−	11.3137i		−	0.532742i
$452$		0			0
$453$	8.94427	−	8.94427i	0.420239	−	0.420239i
$454$		0			0
$455$		−	31.6228i		−	1.48250i
$456$		0			0
$457$	21.0000	+	21.0000i	0.982339	+	0.982339i	0.999847	−	0.0175082i	$-0.00557330\pi$
$457$	21.0000	+	21.0000i	0.982339	+	0.982339i	−0.0175082	+	0.999847i	$0.505573\pi$
$458$		0			0
$459$	5.65685			0.264039
$460$		0			0
$461$	−26.8328			−1.24973			−0.624864	−	0.780733i	$-0.714846\pi$
$461$	−26.8328			−1.24973			−0.624864	+	0.780733i	$0.714846\pi$
$462$		0			0
$463$	−9.48683	−	9.48683i	−0.440891	−	0.440891i	0.451421	−	0.892311i	$-0.350917\pi$
$463$	−9.48683	−	9.48683i	−0.440891	−	0.440891i	−0.892311	+	0.451421i	$0.850917\pi$
$464$		0			0
$465$	20.0000	−	20.0000i	0.927478	−	0.927478i
$466$		0			0
$467$	−7.07107	+	7.07107i	−0.327210	+	0.327210i	−0.851525	−	0.524315i	$-0.824322\pi$
$467$	−7.07107	+	7.07107i	−0.327210	+	0.327210i	0.524315	+	0.851525i	$0.324322\pi$
$468$		0			0
$469$		−	26.8328i		−	1.23902i
$470$		0			0
$471$			6.32456i			0.291420i
$472$		0			0
$473$	20.0000	−	20.0000i	0.919601	−	0.919601i
$474$		0			0
$475$	−28.2843			−1.29777
$476$		0			0
$477$	−6.70820	−	6.70820i	−0.307148	−	0.307148i
$478$		0			0
$479$	12.6491			0.577953			0.288976	−	0.957336i	$-0.406685\pi$
$479$	12.6491			0.577953			0.288976	+	0.957336i	$0.406685\pi$
$480$		0			0
$481$	−30.0000			−1.36788
$482$		0			0
$483$	28.2843	+	28.2843i	1.28698	+	1.28698i
$484$		0			0
$485$	−6.70820	−	6.70820i	−0.304604	−	0.304604i
$486$		0			0
$487$	9.48683	−	9.48683i	0.429889	−	0.429889i	−0.458701	−	0.888591i	$-0.651685\pi$
$487$	9.48683	−	9.48683i	0.429889	−	0.429889i	0.888591	+	0.458701i	$0.151685\pi$
$488$		0			0
$489$		−	44.0000i		−	1.98975i
$490$		0			0
$491$			42.4264i			1.91468i	0.288969	+	0.957338i	$0.406688\pi$
$491$			42.4264i			1.91468i	−0.288969	+	0.957338i	$0.593312\pi$
$492$		0			0
$493$	4.47214	−	4.47214i	0.201415	−	0.201415i
$494$		0			0
$495$	6.32456			0.284268
$496$		0			0
$497$	−20.0000	−	20.0000i	−0.897123	−	0.897123i
$498$		0			0
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$		0			0
$501$	8.94427			0.399601
$502$		0			0
$503$	−3.16228	−	3.16228i	−0.140999	−	0.140999i	0.633084	−	0.774083i	$-0.281789\pi$
$503$	−3.16228	−	3.16228i	−0.140999	−	0.140999i	−0.774083	+	0.633084i	$0.781789\pi$
$504$		0			0
$505$	−20.0000			−0.889988
$506$		0			0
$507$	−4.24264	+	4.24264i	−0.188422	+	0.188422i
$508$		0			0
$509$			4.47214i			0.198224i	0.995076	+	0.0991120i	$0.0316002\pi$
$509$			4.47214i			0.198224i	−0.995076	+	0.0991120i	$0.968400\pi$
$510$		0			0
$511$		−	18.9737i		−	0.839346i
$512$		0			0
$513$	−16.0000	+	16.0000i	−0.706417	+	0.706417i
$514$		0			0
$515$	−21.2132	−	21.2132i	−0.934765	−	0.934765i
$516$		0			0
$517$	−8.94427	−	8.94427i	−0.393369	−	0.393369i
$518$		0			0
$519$	6.32456			0.277617
$520$		0			0
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$		0			0
$523$	1.41421	+	1.41421i	0.0618392	+	0.0618392i	0.737350	−	0.675511i	$-0.236077\pi$
$523$	1.41421	+	1.41421i	0.0618392	+	0.0618392i	−0.675511	+	0.737350i	$0.736077\pi$
$524$		0			0
$525$	−44.7214			−1.95180
$526$		0			0
$527$	−6.32456	+	6.32456i	−0.275502	+	0.275502i
$528$		0			0
$529$		−	3.00000i		−	0.130435i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.94427	+	8.94427i	−0.387419	+	0.387419i
$534$		0			0
$535$	−9.48683	+	9.48683i	−0.410152	+	0.410152i
$536$		0			0
$537$	−8.00000	−	8.00000i	−0.345225	−	0.345225i
$538$		0			0
$539$	36.7696			1.58378
$540$		0			0
$541$	−26.8328			−1.15363			−0.576816	−	0.816874i	$-0.695705\pi$
$541$	−26.8328			−1.15363			−0.576816	+	0.816874i	$0.695705\pi$
$542$		0			0
$543$	12.6491	+	12.6491i	0.542825	+	0.542825i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−24.0416	+	24.0416i	−1.02795	+	1.02795i	−0.0283478	+	0.999598i	$0.509025\pi$
$547$	−24.0416	+	24.0416i	−1.02795	+	1.02795i	−0.999598	+	0.0283478i	$0.990975\pi$
$548$		0			0
$549$		−	4.47214i		−	0.190866i
$550$		0			0
$551$			25.2982i			1.07774i
$552$		0			0
$553$	−40.0000	+	40.0000i	−1.70097	+	1.70097i
$554$		0			0
$555$			42.4264i			1.80090i
$556$		0			0
$557$	−11.1803	−	11.1803i	−0.473726	−	0.473726i	0.429392	−	0.903118i	$-0.358728\pi$
$557$	−11.1803	−	11.1803i	−0.473726	−	0.473726i	−0.903118	+	0.429392i	$0.858728\pi$
$558$		0			0
$559$	−31.6228			−1.33750
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	7.07107	+	7.07107i	0.298010	+	0.298010i	0.840234	−	0.542224i	$-0.182418\pi$
$563$	7.07107	+	7.07107i	0.298010	+	0.298010i	−0.542224	+	0.840234i	$0.682418\pi$
$564$		0			0
$565$	29.0689	−	29.0689i	1.22294	−	1.22294i
$566$		0			0
$567$	−34.7851	+	34.7851i	−1.46083	+	1.46083i
$568$		0			0
$569$		−	18.0000i		−	0.754599i	−0.926091	−	0.377300i	$-0.876853\pi$
$569$		−	18.0000i		−	0.754599i	0.926091	−	0.377300i	$-0.123147\pi$
$570$		0			0
$571$			14.1421i			0.591830i	0.955214	+	0.295915i	$0.0956245\pi$
$571$			14.1421i			0.591830i	−0.955214	+	0.295915i	$0.904375\pi$
$572$		0			0
$573$	−26.8328	+	26.8328i	−1.12096	+	1.12096i
$574$		0			0
$575$	−15.8114	−	15.8114i	−0.659380	−	0.659380i
$576$		0			0
$577$	−21.0000	−	21.0000i	−0.874241	−	0.874241i	0.118690	−	0.992931i	$-0.462131\pi$
$577$	−21.0000	−	21.0000i	−0.874241	−	0.874241i	−0.992931	+	0.118690i	$0.962131\pi$
$578$		0			0
$579$	−19.7990			−0.822818
$580$		0			0
$581$	8.94427			0.371071
$582$		0			0
$583$	−18.9737	−	18.9737i	−0.785809	−	0.785809i
$584$		0			0
$585$	−5.00000	−	5.00000i	−0.206725	−	0.206725i
$586$		0			0
$587$	24.0416	−	24.0416i	0.992304	−	0.992304i	−0.00766632	−	0.999971i	$-0.502440\pi$
$587$	24.0416	−	24.0416i	0.992304	−	0.992304i	0.999971	+	0.00766632i	$0.00244029\pi$
$588$		0			0
$589$		−	35.7771i		−	1.47417i
$590$		0			0
$591$			44.2719i			1.82110i
$592$		0			0
$593$	17.0000	−	17.0000i	0.698106	−	0.698106i	−0.265896	−	0.964002i	$-0.585668\pi$
$593$	17.0000	−	17.0000i	0.698106	−	0.698106i	0.964002	+	0.265896i	$0.0856676\pi$
$594$		0			0
$595$	14.1421			0.579771
$596$		0			0
$597$	−17.8885	−	17.8885i	−0.732129	−	0.732129i
$598$		0			0
$599$	−37.9473			−1.55049			−0.775243	−	0.631663i	$-0.782373\pi$
$599$	−37.9473			−1.55049			−0.775243	+	0.631663i	$0.782373\pi$
$600$		0			0
$601$	44.0000			1.79480			0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000			1.79480			0.897399	+	0.441221i	$0.145454\pi$
$602$		0			0
$603$	−4.24264	−	4.24264i	−0.172774	−	0.172774i
$604$		0			0
$605$	−6.70820			−0.272727
$606$		0			0
$607$	9.48683	−	9.48683i	0.385059	−	0.385059i	−0.487862	−	0.872921i	$-0.662223\pi$
$607$	9.48683	−	9.48683i	0.385059	−	0.385059i	0.872921	+	0.487862i	$0.162223\pi$
$608$		0			0
$609$			40.0000i			1.62088i
$610$		0			0
$611$			14.1421i			0.572130i
$612$		0			0
$613$	15.6525	−	15.6525i	0.632198	−	0.632198i	−0.316421	−	0.948619i	$-0.602481\pi$
$613$	15.6525	−	15.6525i	0.632198	−	0.632198i	0.948619	+	0.316421i	$0.102481\pi$
$614$		0			0
$615$	12.6491	+	12.6491i	0.510061	+	0.510061i
$616$		0			0
$617$	7.00000	+	7.00000i	0.281809	+	0.281809i	0.833830	−	0.552021i	$-0.186143\pi$
$617$	7.00000	+	7.00000i	0.281809	+	0.281809i	−0.552021	+	0.833830i	$0.686143\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$	−17.8885			−0.717843
$622$		0			0
$623$	−25.2982	−	25.2982i	−1.01355	−	1.01355i
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	22.6274	−	22.6274i	0.903652	−	0.903652i
$628$		0			0
$629$		−	13.4164i		−	0.534947i
$630$		0			0
$631$		−	18.9737i		−	0.755330i	−0.925942	−	0.377665i	$-0.876727\pi$
$631$		−	18.9737i		−	0.755330i	0.925942	−	0.377665i	$-0.123273\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	−7.07107	+	7.07107i	−0.280607	+	0.280607i
$636$		0			0
$637$	−29.0689	−	29.0689i	−1.15175	−	1.15175i
$638$		0			0
$639$	−6.32456			−0.250196
$640$		0			0
$641$	28.0000			1.10593			0.552967	−	0.833203i	$-0.313496\pi$
$641$	28.0000			1.10593			0.552967	+	0.833203i	$0.313496\pi$
$642$		0			0
$643$	−7.07107	−	7.07107i	−0.278856	−	0.278856i	0.553796	−	0.832652i	$-0.313179\pi$
$643$	−7.07107	−	7.07107i	−0.278856	−	0.278856i	−0.832652	+	0.553796i	$0.813179\pi$
$644$		0			0
$645$			44.7214i			1.76090i
$646$		0			0
$647$	−28.4605	+	28.4605i	−1.11890	+	1.11890i	−0.126994	+	0.991903i	$0.540533\pi$
$647$	−28.4605	+	28.4605i	−1.11890	+	1.11890i	−0.991903	+	0.126994i	$0.959467\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		−	56.5685i		−	2.21710i
$652$		0			0
$653$	−29.0689	+	29.0689i	−1.13755	+	1.13755i	−0.148666	+	0.988887i	$0.547498\pi$
$653$	−29.0689	+	29.0689i	−1.13755	+	1.13755i	−0.988887	+	0.148666i	$0.952502\pi$
$654$		0			0
$655$		−	31.6228i		−	1.23560i
$656$		0			0
$657$	−3.00000	−	3.00000i	−0.117041	−	0.117041i
$658$		0			0
$659$	33.9411			1.32216			0.661079	−	0.750316i	$-0.270099\pi$
$659$	33.9411			1.32216			0.661079	+	0.750316i	$0.270099\pi$
$660$		0			0
$661$	−4.47214			−0.173946			−0.0869730	−	0.996211i	$-0.527719\pi$
$661$	−4.47214			−0.173946			−0.0869730	+	0.996211i	$0.527719\pi$
$662$		0			0
$663$	6.32456	+	6.32456i	0.245625	+	0.245625i
$664$		0			0
$665$	−40.0000	+	40.0000i	−1.55113	+	1.55113i
$666$		0			0
$667$	−14.1421	+	14.1421i	−0.547586	+	0.547586i
$668$		0			0
$669$		−	8.94427i		−	0.345806i
$670$		0			0
$671$		−	12.6491i		−	0.488314i
$672$		0			0
$673$	19.0000	−	19.0000i	0.732396	−	0.732396i	−0.238698	−	0.971094i	$-0.576721\pi$
$673$	19.0000	−	19.0000i	0.732396	−	0.732396i	0.971094	+	0.238698i	$0.0767205\pi$
$674$		0			0
$675$	14.1421	−	14.1421i	0.544331	−	0.544331i
$676$		0			0
$677$	−20.1246	−	20.1246i	−0.773452	−	0.773452i	0.205257	−	0.978708i	$-0.434197\pi$
$677$	−20.1246	−	20.1246i	−0.773452	−	0.773452i	−0.978708	+	0.205257i	$0.934197\pi$
$678$		0			0
$679$	−18.9737			−0.728142
$680$		0			0
$681$	−20.0000			−0.766402
$682$		0			0
$683$	−12.7279	−	12.7279i	−0.487020	−	0.487020i	0.420344	−	0.907365i	$-0.361909\pi$
$683$	−12.7279	−	12.7279i	−0.487020	−	0.487020i	−0.907365	+	0.420344i	$0.861909\pi$
$684$		0			0
$685$	20.1246	+	20.1246i	0.768922	+	0.768922i
$686$		0			0
$687$	31.6228	−	31.6228i	1.20648	−	1.20648i
$688$		0			0
$689$			30.0000i			1.14291i
$690$		0			0
$691$		−	25.4558i		−	0.968386i	−0.874961	−	0.484193i	$-0.839113\pi$
$691$		−	25.4558i		−	0.968386i	0.874961	−	0.484193i	$-0.160887\pi$
$692$		0			0
$693$	8.94427	−	8.94427i	0.339765	−	0.339765i
$694$		0			0
$695$	12.6491			0.479808
$696$		0			0
$697$	−4.00000	−	4.00000i	−0.151511	−	0.151511i
$698$		0			0
$699$	−25.4558			−0.962828
$700$		0			0
$701$	−31.3050			−1.18237			−0.591186	−	0.806535i	$-0.701340\pi$
$701$	−31.3050			−1.18237			−0.591186	+	0.806535i	$0.701340\pi$
$702$		0			0
$703$	37.9473	+	37.9473i	1.43121	+	1.43121i
$704$		0			0
$705$	20.0000			0.753244
$706$		0			0
$707$	−28.2843	+	28.2843i	−1.06374	+	1.06374i
$708$		0			0
$709$		−	13.4164i		−	0.503864i	−0.967745	−	0.251932i	$-0.918934\pi$
$709$		−	13.4164i		−	0.503864i	0.967745	−	0.251932i	$-0.0810659\pi$
$710$		0			0
$711$			12.6491i			0.474379i
$712$		0			0
$713$	20.0000	−	20.0000i	0.749006	−	0.749006i
$714$		0			0
$715$	−14.1421	−	14.1421i	−0.528886	−	0.528886i
$716$		0			0
$717$	−35.7771	−	35.7771i	−1.33612	−	1.33612i
$718$		0			0
$719$	−25.2982			−0.943464			−0.471732	−	0.881742i	$-0.656371\pi$
$719$	−25.2982			−0.943464			−0.471732	+	0.881742i	$0.656371\pi$
$720$		0			0
$721$	−60.0000			−2.23452
$722$		0			0
$723$	−5.65685	−	5.65685i	−0.210381	−	0.210381i
$724$		0			0
$725$		−	22.3607i		−	0.830455i
$726$		0			0
$727$	9.48683	−	9.48683i	0.351847	−	0.351847i	−0.508949	−	0.860796i	$-0.669966\pi$
$727$	9.48683	−	9.48683i	0.351847	−	0.351847i	0.860796	+	0.508949i	$0.169966\pi$
$728$		0			0
$729$		−	13.0000i		−	0.481481i
$730$		0			0
$731$		−	14.1421i		−	0.523066i
$732$		0			0
$733$	20.1246	−	20.1246i	0.743319	−	0.743319i	−0.229896	−	0.973215i	$-0.573839\pi$
$733$	20.1246	−	20.1246i	0.743319	−	0.743319i	0.973215	+	0.229896i	$0.0738385\pi$
$734$		0			0
$735$	−41.1096	+	41.1096i	−1.51635	+	1.51635i
$736$		0			0
$737$	−12.0000	−	12.0000i	−0.442026	−	0.442026i
$738$		0			0
$739$	−28.2843			−1.04045			−0.520227	−	0.854028i	$-0.674153\pi$
$739$	−28.2843			−1.04045			−0.520227	+	0.854028i	$0.674153\pi$
$740$		0			0
$741$	−35.7771			−1.31430
$742$		0			0
$743$	3.16228	+	3.16228i	0.116013	+	0.116013i	0.762730	−	0.646717i	$-0.223859\pi$
$743$	3.16228	+	3.16228i	0.116013	+	0.116013i	−0.646717	+	0.762730i	$0.723859\pi$
$744$		0			0
$745$		−	40.0000i		−	1.46549i
$746$		0			0
$747$	1.41421	−	1.41421i	0.0517434	−	0.0517434i
$748$		0			0
$749$			26.8328i			0.980450i
$750$		0			0
$751$		−	6.32456i		−	0.230786i	−0.993320	−	0.115393i	$-0.963187\pi$
$751$		−	6.32456i		−	0.230786i	0.993320	−	0.115393i	$-0.0368128\pi$
$752$		0			0
$753$	4.00000	−	4.00000i	0.145768	−	0.145768i
$754$		0			0
$755$			14.1421i			0.514685i
$756$		0			0
$757$	15.6525	+	15.6525i	0.568899	+	0.568899i	0.931820	−	0.362921i	$-0.118221\pi$
$757$	15.6525	+	15.6525i	0.568899	+	0.568899i	−0.362921	+	0.931820i	$0.618221\pi$
$758$		0			0
$759$	25.2982			0.918267
$760$		0			0
$761$	46.0000			1.66750			0.833749	−	0.552143i	$-0.186190\pi$
$761$	46.0000			1.66750			0.833749	+	0.552143i	$0.186190\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.23607	−	2.23607i	0.0808452	−	0.0808452i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	8.00000i		−	0.288487i	−0.989542	−	0.144244i	$-0.953925\pi$
$769$		−	8.00000i		−	0.288487i	0.989542	−	0.144244i	$-0.0460749\pi$
$770$		0			0
$771$		−	36.7696i		−	1.32422i
$772$		0			0
$773$	−20.1246	+	20.1246i	−0.723832	+	0.723832i	−0.969384	−	0.245552i	$-0.921031\pi$
$773$	−20.1246	+	20.1246i	−0.723832	+	0.723832i	0.245552	+	0.969384i	$0.421031\pi$
$774$		0			0
$775$			31.6228i			1.13592i
$776$		0			0
$777$	60.0000	+	60.0000i	2.15249	+	2.15249i
$778$		0			0
$779$	22.6274			0.810711
$780$		0			0
$781$	−17.8885			−0.640102
$782$		0			0
$783$	−12.6491	−	12.6491i	−0.452042	−	0.452042i
$784$		0			0
$785$	−5.00000	−	5.00000i	−0.178458	−	0.178458i
$786$		0			0
$787$	7.07107	−	7.07107i	0.252056	−	0.252056i	−0.569757	−	0.821813i	$-0.692963\pi$
$787$	7.07107	−	7.07107i	0.252056	−	0.252056i	0.821813	+	0.569757i	$0.192963\pi$
$788$		0			0
$789$		−	26.8328i		−	0.955274i
$790$		0			0
$791$		−	82.2192i		−	2.92338i
$792$		0			0
$793$	−10.0000	+	10.0000i	−0.355110	+	0.355110i
$794$		0			0
$795$	42.4264			1.50471
$796$		0			0
$797$	24.5967	+	24.5967i	0.871262	+	0.871262i	0.992610	−	0.121348i	$-0.0387218\pi$
$797$	24.5967	+	24.5967i	0.871262	+	0.871262i	−0.121348	+	0.992610i	$0.538722\pi$
$798$		0			0
$799$	−6.32456			−0.223747
$800$		0			0
$801$	−8.00000			−0.282666
$802$		0			0
$803$	−8.48528	−	8.48528i	−0.299439	−	0.299439i
$804$		0			0
$805$	−44.7214			−1.57622
$806$		0			0
$807$	25.2982	−	25.2982i	0.890540	−	0.890540i
$808$		0			0
$809$		−	24.0000i		−	0.843795i	−0.906644	−	0.421898i	$-0.861364\pi$
$809$		−	24.0000i		−	0.843795i	0.906644	−	0.421898i	$-0.138636\pi$
$810$		0			0
$811$			42.4264i			1.48979i	0.667180	+	0.744896i	$0.267501\pi$
$811$			42.4264i			1.48979i	−0.667180	+	0.744896i	$0.732499\pi$
$812$		0			0
$813$	8.94427	−	8.94427i	0.313689	−	0.313689i
$814$		0			0
$815$	34.7851	+	34.7851i	1.21847	+	1.21847i
$816$		0			0
$817$	40.0000	+	40.0000i	1.39942	+	1.39942i
$818$		0			0
$819$	−14.1421			−0.494166
$820$		0			0
$821$	−13.4164			−0.468236			−0.234118	−	0.972208i	$-0.575220\pi$
$821$	−13.4164			−0.468236			−0.234118	+	0.972208i	$0.575220\pi$
$822$		0			0
$823$	−28.4605	−	28.4605i	−0.992071	−	0.992071i	0.00789818	−	0.999969i	$-0.497486\pi$
$823$	−28.4605	−	28.4605i	−0.992071	−	0.992071i	−0.999969	+	0.00789818i	$0.997486\pi$
$824$		0			0
$825$	−20.0000	+	20.0000i	−0.696311	+	0.696311i
$826$		0			0
$827$	−4.24264	+	4.24264i	−0.147531	+	0.147531i	−0.777014	−	0.629483i	$-0.783267\pi$
$827$	−4.24264	+	4.24264i	−0.147531	+	0.147531i	0.629483	+	0.777014i	$0.283267\pi$
$828$		0			0
$829$		−	53.6656i		−	1.86388i	−0.362607	−	0.931942i	$-0.618113\pi$
$829$		−	53.6656i		−	1.86388i	0.362607	−	0.931942i	$-0.381887\pi$
$830$		0			0
$831$		−	6.32456i		−	0.219396i
$832$		0			0
$833$	13.0000	−	13.0000i	0.450423	−	0.450423i
$834$		0			0
$835$	−7.07107	+	7.07107i	−0.244704	+	0.244704i
$836$		0			0
$837$	17.8885	+	17.8885i	0.618319	+	0.618319i
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$		0			0
$843$	16.9706	+	16.9706i	0.584497	+	0.584497i
$844$		0			0
$845$		−	6.70820i		−	0.230769i
$846$		0			0
$847$	−9.48683	+	9.48683i	−0.325971	+	0.325971i
$848$		0			0
$849$			36.0000i			1.23552i
$850$		0			0
$851$			42.4264i			1.45436i
$852$		0			0
$853$	15.6525	−	15.6525i	0.535931	−	0.535931i	−0.386401	−	0.922331i	$-0.626282\pi$
$853$	15.6525	−	15.6525i	0.535931	−	0.535931i	0.922331	+	0.386401i	$0.126282\pi$
$854$		0			0
$855$			12.6491i			0.432590i
$856$		0			0
$857$	−9.00000	−	9.00000i	−0.307434	−	0.307434i	0.536479	−	0.843913i	$-0.319754\pi$
$857$	−9.00000	−	9.00000i	−0.307434	−	0.307434i	−0.843913	+	0.536479i	$0.819754\pi$
$858$		0			0
$859$	−33.9411			−1.15806			−0.579028	−	0.815308i	$-0.696568\pi$
$859$	−33.9411			−1.15806			−0.579028	+	0.815308i	$0.696568\pi$
$860$		0			0
$861$	35.7771			1.21928
$862$		0			0
$863$	15.8114	+	15.8114i	0.538226	+	0.538226i	0.923008	−	0.384782i	$-0.125723\pi$
$863$	15.8114	+	15.8114i	0.538226	+	0.538226i	−0.384782	+	0.923008i	$0.625723\pi$
$864$		0			0
$865$	−5.00000	+	5.00000i	−0.170005	+	0.170005i
$866$		0			0
$867$	21.2132	−	21.2132i	0.720438	−	0.720438i
$868$		0			0
$869$			35.7771i			1.21365i
$870$		0			0
$871$			18.9737i			0.642898i
$872$		0			0
$873$	−3.00000	+	3.00000i	−0.101535	+	0.101535i
$874$		0			0
$875$	35.3553	−	35.3553i	1.19523	−	1.19523i
$876$		0			0
$877$	38.0132	+	38.0132i	1.28361	+	1.28361i	0.938597	+	0.345016i	$0.112127\pi$
$877$	38.0132	+	38.0132i	1.28361	+	1.28361i	0.345016	+	0.938597i	$0.387873\pi$
$878$		0			0
$879$	−18.9737			−0.639966
$880$		0			0
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$	1.41421	+	1.41421i	0.0475921	+	0.0475921i	0.730502	−	0.682910i	$-0.239286\pi$
$883$	1.41421	+	1.41421i	0.0475921	+	0.0475921i	−0.682910	+	0.730502i	$0.739286\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	34.7851	−	34.7851i	1.16797	−	1.16797i	0.185283	−	0.982685i	$-0.440680\pi$
$887$	34.7851	−	34.7851i	1.16797	−	1.16797i	0.982685	−	0.185283i	$-0.0593200\pi$
$888$		0			0
$889$			20.0000i			0.670778i
$890$		0			0
$891$			31.1127i			1.04231i
$892$		0			0
$893$	17.8885	−	17.8885i	0.598617	−	0.598617i
$894$		0			0
$895$	12.6491			0.422813
$896$		0			0
$897$	−20.0000	−	20.0000i	−0.667781	−	0.667781i
$898$		0			0
$899$	28.2843			0.943333
$900$		0			0
$901$	−13.4164			−0.446965
$902$		0			0
$903$	63.2456	+	63.2456i	2.10468	+	2.10468i
$904$		0			0
$905$	−20.0000			−0.664822
$906$		0			0
$907$	−35.3553	+	35.3553i	−1.17395	+	1.17395i	−0.192696	+	0.981258i	$0.561723\pi$
$907$	−35.3553	+	35.3553i	−1.17395	+	1.17395i	−0.981258	+	0.192696i	$0.938277\pi$
$908$		0			0
$909$			8.94427i			0.296663i
$910$		0			0
$911$		−	18.9737i		−	0.628626i	−0.949319	−	0.314313i	$-0.898226\pi$
$911$		−	18.9737i		−	0.628626i	0.949319	−	0.314313i	$-0.101774\pi$
$912$		0			0
$913$	4.00000	−	4.00000i	0.132381	−	0.132381i
$914$		0			0
$915$	14.1421	+	14.1421i	0.467525	+	0.467525i
$916$		0			0
$917$	−44.7214	−	44.7214i	−1.47683	−	1.47683i
$918$		0			0
$919$	−12.6491			−0.417256			−0.208628	−	0.977995i	$-0.566900\pi$
$919$	−12.6491			−0.417256			−0.208628	+	0.977995i	$0.566900\pi$
$920$		0			0
$921$	−28.0000			−0.922631
$922$		0			0
$923$	14.1421	+	14.1421i	0.465494	+	0.465494i
$924$		0			0
$925$	−33.5410	−	33.5410i	−1.10282	−	1.10282i
$926$		0			0
$927$	−9.48683	+	9.48683i	−0.311588	+	0.311588i
$928$		0			0
$929$			26.0000i			0.853032i	0.904480	+	0.426516i	$0.140259\pi$
$929$			26.0000i			0.853032i	−0.904480	+	0.426516i	$0.859741\pi$
$930$		0			0
$931$			73.5391i			2.41015i
$932$		0			0
$933$	−44.7214	+	44.7214i	−1.46411	+	1.46411i
$934$		0			0
$935$	6.32456	−	6.32456i	0.206835	−	0.206835i
$936$		0			0
$937$	−1.00000	−	1.00000i	−0.0326686	−	0.0326686i	0.690584	−	0.723252i	$-0.257354\pi$
$937$	−1.00000	−	1.00000i	−0.0326686	−	0.0326686i	−0.723252	+	0.690584i	$0.757354\pi$
$938$		0			0
$939$	−31.1127			−1.01532
$940$		0			0
$941$	44.7214			1.45787			0.728937	−	0.684580i	$-0.240015\pi$
$941$	44.7214			1.45787			0.728937	+	0.684580i	$0.240015\pi$
$942$		0			0
$943$	12.6491	+	12.6491i	0.411912	+	0.411912i
$944$		0			0
$945$		−	40.0000i		−	1.30120i
$946$		0			0
$947$	7.07107	−	7.07107i	0.229779	−	0.229779i	−0.582821	−	0.812600i	$-0.698051\pi$
$947$	7.07107	−	7.07107i	0.229779	−	0.229779i	0.812600	+	0.582821i	$0.198051\pi$
$948$		0			0
$949$			13.4164i			0.435515i
$950$		0			0
$951$			18.9737i			0.615263i
$952$		0			0
$953$	13.0000	−	13.0000i	0.421111	−	0.421111i	−0.464475	−	0.885586i	$-0.653757\pi$
$953$	13.0000	−	13.0000i	0.421111	−	0.421111i	0.885586	+	0.464475i	$0.153757\pi$
$954$		0			0
$955$		−	42.4264i		−	1.37289i
$956$		0			0
$957$	17.8885	+	17.8885i	0.578254	+	0.578254i
$958$		0			0
$959$	56.9210			1.83807
$960$		0			0
$961$	−9.00000			−0.290323
$962$		0			0
$963$	4.24264	+	4.24264i	0.136717	+	0.136717i
$964$		0			0
$965$	15.6525	−	15.6525i	0.503871	−	0.503871i
$966$		0			0
$967$	28.4605	−	28.4605i	0.915228	−	0.915228i	−0.0814495	−	0.996677i	$-0.525955\pi$
$967$	28.4605	−	28.4605i	0.915228	−	0.915228i	0.996677	+	0.0814495i	$0.0259549\pi$
$968$		0			0
$969$		−	16.0000i		−	0.513994i
$970$		0			0
$971$			2.82843i			0.0907685i	0.998970	+	0.0453843i	$0.0144512\pi$
$971$			2.82843i			0.0907685i	−0.998970	+	0.0453843i	$0.985549\pi$
$972$		0			0
$973$	17.8885	−	17.8885i	0.573480	−	0.573480i
$974$		0			0
$975$	31.6228			1.01274
$976$		0			0
$977$	−29.0000	−	29.0000i	−0.927792	−	0.927792i	0.0697708	−	0.997563i	$-0.477773\pi$
$977$	−29.0000	−	29.0000i	−0.927792	−	0.927792i	−0.997563	+	0.0697708i	$0.977773\pi$
$978$		0			0
$979$	−22.6274			−0.723175
$980$		0			0
$981$		0			0
$982$		0			0
$983$	15.8114	+	15.8114i	0.504305	+	0.504305i	0.912773	−	0.408468i	$-0.133937\pi$
$983$	15.8114	+	15.8114i	0.504305	+	0.504305i	−0.408468	+	0.912773i	$0.633937\pi$
$984$		0			0
$985$	−35.0000	−	35.0000i	−1.11519	−	1.11519i
$986$		0			0
$987$	28.2843	−	28.2843i	0.900298	−	0.900298i
$988$		0			0
$989$			44.7214i			1.42206i
$990$		0			0
$991$		−	44.2719i		−	1.40634i	−0.711020	−	0.703171i	$-0.751767\pi$
$991$		−	44.2719i		−	1.40634i	0.711020	−	0.703171i	$-0.248233\pi$
$992$		0			0
$993$	36.0000	−	36.0000i	1.14243	−	1.14243i
$994$		0			0
$995$	28.2843			0.896672
$996$		0			0
$997$	11.1803	+	11.1803i	0.354085	+	0.354085i	0.861627	−	0.507542i	$-0.169446\pi$
$997$	11.1803	+	11.1803i	0.354085	+	0.354085i	−0.507542	+	0.861627i	$0.669446\pi$
$998$		0			0
$999$	−37.9473			−1.20060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.o.767.3		8
4.3	odd	2	inner	1280.2.n.o.767.1		8
5.3	odd	4	inner	1280.2.n.o.1023.1		8
8.3	odd	2	inner	1280.2.n.o.767.4		8
8.5	even	2	inner	1280.2.n.o.767.2		8
16.3	odd	4		640.2.o.i.447.4	yes	8
16.5	even	4		640.2.o.i.447.3	yes	8
16.11	odd	4		640.2.o.i.447.1	yes	8
16.13	even	4		640.2.o.i.447.2	yes	8
20.3	even	4	inner	1280.2.n.o.1023.3		8
40.3	even	4	inner	1280.2.n.o.1023.2		8
40.13	odd	4	inner	1280.2.n.o.1023.4		8
80.3	even	4		640.2.o.i.63.4	yes	8
80.13	odd	4		640.2.o.i.63.2	yes	8
80.43	even	4		640.2.o.i.63.1	✓	8
80.53	odd	4		640.2.o.i.63.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.o.i.63.1	✓	8	80.43	even	4
640.2.o.i.63.2	yes	8	80.13	odd	4
640.2.o.i.63.3	yes	8	80.53	odd	4
640.2.o.i.63.4	yes	8	80.3	even	4
640.2.o.i.447.1	yes	8	16.11	odd	4
640.2.o.i.447.2	yes	8	16.13	even	4
640.2.o.i.447.3	yes	8	16.5	even	4
640.2.o.i.447.4	yes	8	16.3	odd	4
1280.2.n.o.767.1		8	4.3	odd	2	inner
1280.2.n.o.767.2		8	8.5	even	2	inner
1280.2.n.o.767.3		8	1.1	even	1	trivial
1280.2.n.o.767.4		8	8.3	odd	2	inner
1280.2.n.o.1023.1		8	5.3	odd	4	inner
1280.2.n.o.1023.2		8	40.3	even	4	inner
1280.2.n.o.1023.3		8	20.3	even	4	inner
1280.2.n.o.1023.4		8	40.13	odd	4	inner

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 1.41421i) q^{3} -2.23607 q^{5} +(-3.16228 + 3.16228i) q^{7} +1.00000i q^{9} +2.82843i q^{11} +(2.23607 - 2.23607i) q^{13} +(-3.16228 - 3.16228i) q^{15} +(1.00000 + 1.00000i) q^{17} -5.65685 q^{19} -8.94427 q^{21} +(-3.16228 - 3.16228i) q^{23} +5.00000 q^{25} +(2.82843 - 2.82843i) q^{27} -4.47214i q^{29} +6.32456i q^{31} +(-4.00000 + 4.00000i) q^{33} +(7.07107 - 7.07107i) q^{35} +(-6.70820 - 6.70820i) q^{37} +6.32456 q^{39} -4.00000 q^{41} +(-7.07107 - 7.07107i) q^{43} -2.23607i q^{45} +(-3.16228 + 3.16228i) q^{47} -13.0000i q^{49} +2.82843i q^{51} +(-6.70820 + 6.70820i) q^{53} -6.32456i q^{55} +(-8.00000 - 8.00000i) q^{57} -4.47214 q^{61} +(-3.16228 - 3.16228i) q^{63} +(-5.00000 + 5.00000i) q^{65} +(-4.24264 + 4.24264i) q^{67} -8.94427i q^{69} +6.32456i q^{71} +(-3.00000 + 3.00000i) q^{73} +(7.07107 + 7.07107i) q^{75} +(-8.94427 - 8.94427i) q^{77} +12.6491 q^{79} +11.0000 q^{81} +(-1.41421 - 1.41421i) q^{83} +(-2.23607 - 2.23607i) q^{85} +(6.32456 - 6.32456i) q^{87} +8.00000i q^{89} +14.1421i q^{91} +(-8.94427 + 8.94427i) q^{93} +12.6491 q^{95} +(3.00000 + 3.00000i) q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{17} + 40 q^{25} - 32 q^{33} - 32 q^{41} - 64 q^{57} - 40 q^{65} - 24 q^{73} + 88 q^{81} + 24 q^{97}+O(q^{100}) \) 8 * q + 8 * q^17 + 40 * q^25 - 32 * q^33 - 32 * q^41 - 64 * q^57 - 40 * q^65 - 24 * q^73 + 88 * q^81 + 24 * q^97

Introduction

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