LMFDB - Embedded newform 640.2.o.i.63.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(63,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("640.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.o (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:	$5.11042572936$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.3
Root			$-0.437016 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	640.63
Dual form			640.2.o.i.447.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 + 1.41421i) q^{3} -2.23607i q^{5} +(-3.16228 - 3.16228i) q^{7} +1.00000i q^{9} -2.82843 q^{11} +(2.23607 - 2.23607i) q^{13} +(3.16228 - 3.16228i) q^{15} +(1.00000 - 1.00000i) q^{17} -5.65685i q^{19} -8.94427i q^{21} +(-3.16228 + 3.16228i) q^{23} -5.00000 q^{25} +(2.82843 - 2.82843i) q^{27} +4.47214 q^{29} +6.32456i q^{31} +(-4.00000 - 4.00000i) q^{33} +(-7.07107 + 7.07107i) q^{35} +(-6.70820 - 6.70820i) q^{37} +6.32456 q^{39} +4.00000 q^{41} +(7.07107 + 7.07107i) q^{43} +2.23607 q^{45} +(3.16228 + 3.16228i) q^{47} +13.0000i q^{49} +2.82843 q^{51} +(6.70820 - 6.70820i) q^{53} +6.32456i q^{55} +(8.00000 - 8.00000i) q^{57} +4.47214i q^{61} +(3.16228 - 3.16228i) q^{63} +(-5.00000 - 5.00000i) q^{65} +(4.24264 - 4.24264i) q^{67} -8.94427 q^{69} -6.32456i q^{71} +(3.00000 + 3.00000i) q^{73} +(-7.07107 - 7.07107i) q^{75} +(8.94427 + 8.94427i) q^{77} -12.6491 q^{79} +11.0000 q^{81} +(-1.41421 - 1.41421i) q^{83} +(-2.23607 - 2.23607i) q^{85} +(6.32456 + 6.32456i) q^{87} +8.00000i q^{89} -14.1421 q^{91} +(-8.94427 + 8.94427i) q^{93} -12.6491 q^{95} +(3.00000 - 3.00000i) q^{97} -2.82843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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
$5$		−	2.23607i		−	1.00000i
$5$		−	2.23607i		−	1.00000i
$6$		0			0
$7$	−3.16228	−	3.16228i	−1.19523	−	1.19523i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−3.16228	−	3.16228i	−1.19523	−	1.19523i	−0.219650	−	0.975579i	$-0.570491\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.82843			−0.852803			−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843			−0.852803			−0.426401	+	0.904534i	$0.640219\pi$
$12$		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	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$		0			0
$19$		−	5.65685i		−	1.29777i	−0.760886	−	0.648886i	$-0.775235\pi$
$19$		−	5.65685i		−	1.29777i	0.760886	−	0.648886i	$-0.224765\pi$
$20$		0			0
$21$		−	8.94427i		−	1.95180i
$22$		0			0
$23$	−3.16228	+	3.16228i	−0.659380	+	0.659380i	−0.955233	−	0.295853i	$-0.904396\pi$
$23$	−3.16228	+	3.16228i	−0.659380	+	0.659380i	0.295853	+	0.955233i	$0.404396\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$		0			0
$27$	2.82843	−	2.82843i	0.544331	−	0.544331i
$28$		0			0
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$		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	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	7.07107	+	7.07107i	1.07833	+	1.07833i	0.996660	+	0.0816682i	$0.0260248\pi$
$43$	7.07107	+	7.07107i	1.07833	+	1.07833i	0.0816682	+	0.996660i	$0.473975\pi$
$44$		0			0
$45$	2.23607			0.333333
$46$		0			0
$47$	3.16228	+	3.16228i	0.461266	+	0.461266i	0.899070	−	0.437805i	$-0.144244\pi$
$47$	3.16228	+	3.16228i	0.461266	+	0.461266i	−0.437805	+	0.899070i	$0.644244\pi$
$48$		0			0
$49$			13.0000i			1.85714i
$50$		0			0
$51$	2.82843			0.396059
$52$		0			0
$53$	6.70820	−	6.70820i	0.921443	−	0.921443i	−0.0756888	−	0.997131i	$-0.524116\pi$
$53$	6.70820	−	6.70820i	0.921443	−	0.921443i	0.997131	+	0.0756888i	$0.0241156\pi$
$54$		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		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$			4.47214i			0.572598i	0.958140	+	0.286299i	$0.0924251\pi$
$61$			4.47214i			0.572598i	−0.958140	+	0.286299i	$0.907575\pi$
$62$		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	−0.398742	−	0.917063i	$-0.630553\pi$
$67$	4.24264	−	4.24264i	0.518321	−	0.518321i	0.917063	+	0.398742i	$0.130553\pi$
$68$		0			0
$69$	−8.94427			−1.07676
$70$		0			0
$71$		−	6.32456i		−	0.750587i	−0.926906	−	0.375293i	$-0.877542\pi$
$71$		−	6.32456i		−	0.750587i	0.926906	−	0.375293i	$-0.122458\pi$
$72$		0			0
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	0.860527	−	0.509404i	$-0.170134\pi$
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	−0.509404	+	0.860527i	$0.670134\pi$
$74$		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	$-0.752015\pi$
$79$	−12.6491			−1.42314			−0.711568	+	0.702617i	$0.752015\pi$
$80$		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
$91$	−14.1421			−1.48250
$92$		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	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$		0			0
$99$		−	2.82843i		−	0.284268i
$100$		0			0
$101$			8.94427i			0.889988i	0.895533	+	0.444994i	$0.146794\pi$
$101$			8.94427i			0.889988i	−0.895533	+	0.444994i	$0.853206\pi$
$102$		0			0
$103$	9.48683	−	9.48683i	0.934765	−	0.934765i	−0.0632333	−	0.997999i	$-0.520141\pi$
$103$	9.48683	−	9.48683i	0.934765	−	0.934765i	0.997999	+	0.0632333i	$0.0201412\pi$
$104$		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			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		−	18.9737i		−	1.80090i
$112$		0			0
$113$	−13.0000	−	13.0000i	−1.22294	−	1.22294i	−0.966583	−	0.256354i	$-0.917479\pi$
$113$	−13.0000	−	13.0000i	−1.22294	−	1.22294i	−0.256354	−	0.966583i	$-0.582521\pi$
$114$		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
$125$			11.1803i			1.00000i
$126$		0			0
$127$	−3.16228	−	3.16228i	−0.280607	−	0.280607i	0.552744	−	0.833351i	$-0.313581\pi$
$127$	−3.16228	−	3.16228i	−0.280607	−	0.280607i	−0.833351	+	0.552744i	$0.813581\pi$
$128$		0			0
$129$			20.0000i			1.76090i
$130$		0			0
$131$	14.1421			1.23560			0.617802	−	0.786334i	$-0.288023\pi$
$131$	14.1421			1.23560			0.617802	+	0.786334i	$0.288023\pi$
$132$		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	$-0.567019\pi$
$137$	9.00000	−	9.00000i	0.768922	−	0.768922i	0.977917	+	0.208995i	$0.0670192\pi$
$138$		0			0
$139$			5.65685i			0.479808i	0.970797	+	0.239904i	$0.0771160\pi$
$139$			5.65685i			0.479808i	−0.970797	+	0.239904i	$0.922884\pi$
$140$		0			0
$141$			8.94427i			0.753244i
$142$		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
$149$	17.8885			1.46549			0.732743	−	0.680505i	$-0.238240\pi$
$149$	17.8885			1.46549			0.732743	+	0.680505i	$0.238240\pi$
$150$		0			0
$151$			6.32456i			0.514685i	0.966320	+	0.257343i	$0.0828469\pi$
$151$			6.32456i			0.514685i	−0.966320	+	0.257343i	$0.917153\pi$
$152$		0			0
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$		0			0
$155$	14.1421			1.13592
$156$		0			0
$157$	−2.23607	−	2.23607i	−0.178458	−	0.178458i	0.612226	−	0.790683i	$-0.290274\pi$
$157$	−2.23607	−	2.23607i	−0.178458	−	0.178458i	−0.790683	+	0.612226i	$0.790274\pi$
$158$		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	0.818793	−	0.574089i	$-0.194644\pi$
$167$	3.16228	+	3.16228i	0.244704	+	0.244704i	−0.574089	+	0.818793i	$0.694644\pi$
$168$		0			0
$169$			3.00000i			0.230769i
$170$		0			0
$171$	5.65685			0.432590
$172$		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
$179$		−	5.65685i		−	0.422813i	−0.977398	−	0.211407i	$-0.932196\pi$
$179$		−	5.65685i		−	0.422813i	0.977398	−	0.211407i	$-0.0678044\pi$
$180$		0			0
$181$			8.94427i			0.664822i	0.943135	+	0.332411i	$0.107862\pi$
$181$			8.94427i			0.664822i	−0.943135	+	0.332411i	$0.892138\pi$
$182$		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
$189$	−17.8885			−1.30120
$190$		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	0.408768	−	0.912639i	$-0.365959\pi$
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	−0.912639	+	0.408768i	$0.865959\pi$
$194$		0			0
$195$		−	14.1421i		−	1.01274i
$196$		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
$205$		−	8.94427i		−	0.624695i
$206$		0			0
$207$	−3.16228	−	3.16228i	−0.219793	−	0.219793i
$208$		0			0
$209$			16.0000i			1.10674i
$210$		0			0
$211$	−2.82843			−0.194717			−0.0973585	−	0.995249i	$-0.531039\pi$
$211$	−2.82843			−0.194717			−0.0973585	+	0.995249i	$0.531039\pi$
$212$		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
$219$			8.48528i			0.573382i
$220$		0			0
$221$		−	4.47214i		−	0.300828i
$222$		0			0
$223$	3.16228	−	3.16228i	0.211762	−	0.211762i	−0.593254	−	0.805016i	$-0.702157\pi$
$223$	3.16228	−	3.16228i	0.211762	−	0.211762i	0.805016	+	0.593254i	$0.202157\pi$
$224$		0			0
$225$		−	5.00000i		−	0.333333i
$226$		0			0
$227$	7.07107	−	7.07107i	0.469323	−	0.469323i	−0.432372	−	0.901695i	$-0.642323\pi$
$227$	7.07107	−	7.07107i	0.469323	−	0.469323i	0.901695	+	0.432372i	$0.142323\pi$
$228$		0			0
$229$	−22.3607			−1.47764			−0.738818	−	0.673905i	$-0.764616\pi$
$229$	−22.3607			−1.47764			−0.738818	+	0.673905i	$0.764616\pi$
$230$		0			0
$231$			25.2982i			1.66450i
$232$		0			0
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	0.937526	−	0.347916i	$-0.113111\pi$
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	−0.347916	+	0.937526i	$0.613111\pi$
$234$		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	$-0.194971\pi$
$239$	25.2982			1.63641			0.818203	+	0.574930i	$0.194971\pi$
$240$		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
$245$	29.0689			1.85714
$246$		0			0
$247$	−12.6491	−	12.6491i	−0.804844	−	0.804844i
$248$		0			0
$249$		−	4.00000i		−	0.253490i
$250$		0			0
$251$	2.82843			0.178529			0.0892644	−	0.996008i	$-0.471548\pi$
$251$	2.82843			0.178529			0.0892644	+	0.996008i	$0.471548\pi$
$252$		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	−0.984771	−	0.173854i	$-0.944378\pi$
$257$	−13.0000	+	13.0000i	−0.810918	+	0.810918i	0.173854	+	0.984771i	$0.444378\pi$
$258$		0			0
$259$			42.4264i			2.63625i
$260$		0			0
$261$			4.47214i			0.276818i
$262$		0			0
$263$	−9.48683	+	9.48683i	−0.584983	+	0.584983i	−0.936268	−	0.351285i	$-0.885745\pi$
$263$	−9.48683	+	9.48683i	−0.584983	+	0.584983i	0.351285	+	0.936268i	$0.385745\pi$
$264$		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
$269$	17.8885			1.09068			0.545342	−	0.838214i	$-0.316400\pi$
$269$	17.8885			1.09068			0.545342	+	0.838214i	$0.316400\pi$
$270$		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
$275$	14.1421			0.852803
$276$		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	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$		0			0
$283$	−12.7279	−	12.7279i	−0.756596	−	0.756596i	0.219105	−	0.975701i	$-0.429686\pi$
$283$	−12.7279	−	12.7279i	−0.756596	−	0.756596i	−0.975701	+	0.219105i	$0.929686\pi$
$284$		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
$291$	8.48528			0.497416
$292$		0			0
$293$	6.70820	−	6.70820i	0.391897	−	0.391897i	−0.483466	−	0.875363i	$-0.660622\pi$
$293$	6.70820	−	6.70820i	0.391897	−	0.391897i	0.875363	+	0.483466i	$0.160622\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8.00000	+	8.00000i	−0.464207	+	0.464207i
$298$		0			0
$299$			14.1421i			0.817861i
$300$		0			0
$301$		−	44.7214i		−	2.57770i
$302$		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	−0.365728	−	0.930722i	$-0.619180\pi$
$307$	9.89949	−	9.89949i	0.564994	−	0.564994i	0.930722	+	0.365728i	$0.119180\pi$
$308$		0			0
$309$	26.8328			1.52647
$310$		0			0
$311$		−	31.6228i		−	1.79316i	−0.442879	−	0.896582i	$-0.646043\pi$
$311$		−	31.6228i		−	1.79316i	0.442879	−	0.896582i	$-0.353957\pi$
$312$		0			0
$313$	11.0000	+	11.0000i	0.621757	+	0.621757i	0.945980	−	0.324224i	$-0.105103\pi$
$313$	11.0000	+	11.0000i	0.621757	+	0.621757i	−0.324224	+	0.945980i	$0.605103\pi$
$314$		0			0
$315$	−7.07107	−	7.07107i	−0.398410	−	0.398410i
$316$		0			0
$317$	−6.70820	−	6.70820i	−0.376770	−	0.376770i	0.493165	−	0.869936i	$-0.335840\pi$
$317$	−6.70820	−	6.70820i	−0.376770	−	0.376770i	−0.869936	+	0.493165i	$0.835840\pi$
$318$		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
$331$	25.4558			1.39918			0.699590	−	0.714545i	$-0.253366\pi$
$331$	25.4558			1.39918			0.699590	+	0.714545i	$0.253366\pi$
$332$		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	−0.418127	−	0.908388i	$-0.637313\pi$
$337$	9.00000	−	9.00000i	0.490261	−	0.490261i	0.908388	+	0.418127i	$0.137313\pi$
$338$		0			0
$339$		−	36.7696i		−	1.99705i
$340$		0			0
$341$		−	17.8885i		−	0.968719i
$342$		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
$349$	−4.47214			−0.239388			−0.119694	−	0.992811i	$-0.538191\pi$
$349$	−4.47214			−0.239388			−0.119694	+	0.992811i	$0.538191\pi$
$350$		0			0
$351$		−	12.6491i		−	0.675160i
$352$		0			0
$353$	1.00000	+	1.00000i	0.0532246	+	0.0532246i	0.733218	−	0.679994i	$-0.238017\pi$
$353$	1.00000	+	1.00000i	0.0532246	+	0.0532246i	−0.679994	+	0.733218i	$0.738017\pi$
$354$		0			0
$355$	−14.1421			−0.750587
$356$		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	$-0.136125\pi$
$367$	9.48683	+	9.48683i	0.495209	+	0.495209i	−0.414734	+	0.909943i	$0.636125\pi$
$368$		0			0
$369$			4.00000i			0.208232i
$370$		0			0
$371$	−42.4264			−2.20267
$372$		0			0
$373$	2.23607	−	2.23607i	0.115779	−	0.115779i	−0.646844	−	0.762623i	$-0.723911\pi$
$373$	2.23607	−	2.23607i	0.115779	−	0.115779i	0.762623	+	0.646844i	$0.223911\pi$
$374$		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
$379$		−	33.9411i		−	1.74344i	−0.490006	−	0.871719i	$-0.663005\pi$
$379$		−	33.9411i		−	1.74344i	0.490006	−	0.871719i	$-0.336995\pi$
$380$		0			0
$381$		−	8.94427i		−	0.458229i
$382$		0			0
$383$	15.8114	−	15.8114i	0.807924	−	0.807924i	−0.176395	−	0.984319i	$-0.556444\pi$
$383$	15.8114	−	15.8114i	0.807924	−	0.807924i	0.984319	+	0.176395i	$0.0564437\pi$
$384$		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
$389$	17.8885			0.906985			0.453493	−	0.891260i	$-0.350178\pi$
$389$	17.8885			0.906985			0.453493	+	0.891260i	$0.350178\pi$
$390$		0			0
$391$			6.32456i			0.319847i
$392$		0			0
$393$	20.0000	+	20.0000i	1.00887	+	1.00887i
$394$		0			0
$395$			28.2843i			1.42314i
$396$		0			0
$397$	−2.23607	−	2.23607i	−0.112225	−	0.112225i	0.648764	−	0.760989i	$-0.275286\pi$
$397$	−2.23607	−	2.23607i	−0.112225	−	0.112225i	−0.760989	+	0.648764i	$0.775286\pi$
$398$		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
$405$		−	24.5967i		−	1.22222i
$406$		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
$411$	25.4558			1.25564
$412$		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
$419$			22.6274i			1.10542i	0.833373	+	0.552711i	$0.186407\pi$
$419$			22.6274i			1.10542i	−0.833373	+	0.552711i	$0.813593\pi$
$420$		0			0
$421$			4.47214i			0.217959i	0.994044	+	0.108979i	$0.0347582\pi$
$421$			4.47214i			0.217959i	−0.994044	+	0.108979i	$0.965242\pi$
$422$		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
$429$	−17.8885			−0.863667
$430$		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	0.775508	−	0.631337i	$-0.217494\pi$
$433$	3.00000	+	3.00000i	0.144171	+	0.144171i	−0.631337	+	0.775508i	$0.717494\pi$
$434$		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	0.972405	−	0.233300i	$-0.0749525\pi$
$443$	15.5563	+	15.5563i	0.739104	+	0.739104i	−0.233300	+	0.972405i	$0.574953\pi$
$444$		0			0
$445$	17.8885			0.847998
$446$		0			0
$447$	25.2982	+	25.2982i	1.19656	+	1.19656i
$448$		0			0
$449$		−	22.0000i		−	1.03824i	−0.854700	−	0.519122i	$-0.826259\pi$
$449$		−	22.0000i		−	1.03824i	0.854700	−	0.519122i	$-0.173741\pi$
$450$		0			0
$451$	−11.3137			−0.532742
$452$		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	$-0.994427\pi$
$457$	−21.0000	+	21.0000i	−0.982339	+	0.982339i	0.0175082	+	0.999847i	$0.494427\pi$
$458$		0			0
$459$		−	5.65685i		−	0.264039i
$460$		0			0
$461$			26.8328i			1.24973i	0.780733	+	0.624864i	$0.214846\pi$
$461$			26.8328i			1.24973i	−0.780733	+	0.624864i	$0.785154\pi$
$462$		0			0
$463$	9.48683	−	9.48683i	0.440891	−	0.440891i	−0.451421	−	0.892311i	$-0.649083\pi$
$463$	9.48683	−	9.48683i	0.440891	−	0.440891i	0.892311	+	0.451421i	$0.149083\pi$
$464$		0			0
$465$	20.0000	+	20.0000i	0.927478	+	0.927478i
$466$		0			0
$467$	7.07107	−	7.07107i	0.327210	−	0.327210i	−0.524315	−	0.851525i	$-0.675678\pi$
$467$	7.07107	−	7.07107i	0.327210	−	0.327210i	0.851525	+	0.524315i	$0.175678\pi$
$468$		0			0
$469$	−26.8328			−1.23902
$470$		0			0
$471$		−	6.32456i		−	0.291420i
$472$		0			0
$473$	−20.0000	−	20.0000i	−0.919601	−	0.919601i
$474$		0			0
$475$			28.2843i			1.29777i
$476$		0			0
$477$	6.70820	+	6.70820i	0.307148	+	0.307148i
$478$		0			0
$479$	−12.6491			−0.577953			−0.288976	−	0.957336i	$-0.593315\pi$
$479$	−12.6491			−0.577953			−0.288976	+	0.957336i	$0.593315\pi$
$480$		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	0.888591	−	0.458701i	$-0.151685\pi$
$487$	9.48683	+	9.48683i	0.429889	+	0.429889i	−0.458701	+	0.888591i	$0.651685\pi$
$488$		0			0
$489$		−	44.0000i		−	1.98975i
$490$		0			0
$491$	−42.4264			−1.91468			−0.957338	−	0.288969i	$-0.906688\pi$
$491$	−42.4264			−1.91468			−0.957338	+	0.288969i	$0.906688\pi$
$492$		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		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$			8.94427i			0.399601i
$502$		0			0
$503$	−3.16228	+	3.16228i	−0.140999	+	0.140999i	−0.774083	−	0.633084i	$-0.781789\pi$
$503$	−3.16228	+	3.16228i	−0.140999	+	0.140999i	0.633084	+	0.774083i	$0.281789\pi$
$504$		0			0
$505$	20.0000			0.889988
$506$		0			0
$507$	−4.24264	+	4.24264i	−0.188422	+	0.188422i
$508$		0			0
$509$	−4.47214			−0.198224			−0.0991120	−	0.995076i	$-0.531600\pi$
$509$	−4.47214			−0.198224			−0.0991120	+	0.995076i	$0.531600\pi$
$510$		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	$-0.400783\pi$
$521$	14.0000			0.613351			0.306676	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$	−1.41421	−	1.41421i	−0.0618392	−	0.0618392i	0.675511	−	0.737350i	$-0.263923\pi$
$523$	−1.41421	−	1.41421i	−0.0618392	−	0.0618392i	−0.737350	+	0.675511i	$0.763923\pi$
$524$		0			0
$525$			44.7214i			1.95180i
$526$		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
$539$		−	36.7696i		−	1.58378i
$540$		0			0
$541$			26.8328i			1.15363i	0.816874	+	0.576816i	$0.195705\pi$
$541$			26.8328i			1.15363i	−0.816874	+	0.576816i	$0.804295\pi$
$542$		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	$-0.490975\pi$
$547$	24.0416	−	24.0416i	1.02795	−	1.02795i	0.999598	−	0.0283478i	$-0.00902459\pi$
$548$		0			0
$549$	−4.47214			−0.190866
$550$		0			0
$551$		−	25.2982i		−	1.07774i
$552$		0			0
$553$	40.0000	+	40.0000i	1.70097	+	1.70097i
$554$		0			0
$555$	−42.4264			−1.80090
$556$		0			0
$557$	11.1803	+	11.1803i	0.473726	+	0.473726i	0.903118	−	0.429392i	$-0.141272\pi$
$557$	11.1803	+	11.1803i	0.473726	+	0.473726i	−0.429392	+	0.903118i	$0.641272\pi$
$558$		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
$571$	−14.1421			−0.591830			−0.295915	−	0.955214i	$-0.595625\pi$
$571$	−14.1421			−0.591830			−0.295915	+	0.955214i	$0.595625\pi$
$572$		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	−0.992931	−	0.118690i	$-0.962131\pi$
$577$	−21.0000	+	21.0000i	−0.874241	+	0.874241i	0.118690	+	0.992931i	$0.462131\pi$
$578$		0			0
$579$		−	19.7990i		−	0.822818i
$580$		0			0
$581$			8.94427i			0.371071i
$582$		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
$589$	35.7771			1.47417
$590$		0			0
$591$			44.2719i			1.82110i
$592$		0			0
$593$	17.0000	+	17.0000i	0.698106	+	0.698106i	0.964002	−	0.265896i	$-0.0856676\pi$
$593$	17.0000	+	17.0000i	0.698106	+	0.698106i	−0.265896	+	0.964002i	$0.585668\pi$
$594$		0			0
$595$			14.1421i			0.579771i
$596$		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	$-0.854546\pi$
$601$	−44.0000			−1.79480			−0.897399	+	0.441221i	$0.854546\pi$
$602$		0			0
$603$	4.24264	+	4.24264i	0.172774	+	0.172774i
$604$		0			0
$605$			6.70820i			0.272727i
$606$		0			0
$607$	−9.48683	−	9.48683i	−0.385059	−	0.385059i	0.487862	−	0.872921i	$-0.337777\pi$
$607$	−9.48683	−	9.48683i	−0.385059	−	0.385059i	−0.872921	+	0.487862i	$0.837777\pi$
$608$		0			0
$609$		−	40.0000i		−	1.62088i
$610$		0			0
$611$	14.1421			0.572130
$612$		0			0
$613$	−15.6525	+	15.6525i	−0.632198	+	0.632198i	−0.948619	−	0.316421i	$-0.897519\pi$
$613$	−15.6525	+	15.6525i	−0.632198	+	0.632198i	0.316421	+	0.948619i	$0.397519\pi$
$614$		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	$-0.813857\pi$
$617$	−7.00000	+	7.00000i	−0.281809	+	0.281809i	0.552021	+	0.833830i	$0.313857\pi$
$618$		0			0
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$			17.8885i			0.717843i
$622$		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
$629$	−13.4164			−0.534947
$630$		0			0
$631$			18.9737i			0.755330i	0.925942	+	0.377665i	$0.123273\pi$
$631$			18.9737i			0.755330i	−0.925942	+	0.377665i	$0.876727\pi$
$632$		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
$645$	44.7214			1.76090
$646$		0			0
$647$	−28.4605	−	28.4605i	−1.11890	−	1.11890i	−0.991903	−	0.126994i	$-0.959467\pi$
$647$	−28.4605	−	28.4605i	−1.11890	−	1.11890i	−0.126994	−	0.991903i	$-0.540533\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	56.5685			2.21710
$652$		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
$659$			33.9411i			1.32216i	0.750316	+	0.661079i	$0.229901\pi$
$659$			33.9411i			1.32216i	−0.750316	+	0.661079i	$0.770099\pi$
$660$		0			0
$661$		−	4.47214i		−	0.173946i	−0.996211	−	0.0869730i	$-0.972281\pi$
$661$		−	4.47214i		−	0.173946i	0.996211	−	0.0869730i	$-0.0277194\pi$
$662$		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
$669$	8.94427			0.345806
$670$		0			0
$671$		−	12.6491i		−	0.488314i
$672$		0			0
$673$	19.0000	+	19.0000i	0.732396	+	0.732396i	0.971094	−	0.238698i	$-0.0767205\pi$
$673$	19.0000	+	19.0000i	0.732396	+	0.732396i	−0.238698	+	0.971094i	$0.576721\pi$
$674$		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	0.907365	−	0.420344i	$-0.138091\pi$
$683$	12.7279	+	12.7279i	0.487020	+	0.487020i	−0.420344	+	0.907365i	$0.638091\pi$
$684$		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
$691$	−25.4558			−0.968386			−0.484193	−	0.874961i	$-0.660887\pi$
$691$	−25.4558			−0.968386			−0.484193	+	0.874961i	$0.660887\pi$
$692$		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
$699$			25.4558i			0.962828i
$700$		0			0
$701$			31.3050i			1.18237i	0.806535	+	0.591186i	$0.201340\pi$
$701$			31.3050i			1.18237i	−0.806535	+	0.591186i	$0.798660\pi$
$702$		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
$709$	−13.4164			−0.503864			−0.251932	−	0.967745i	$-0.581066\pi$
$709$	−13.4164			−0.503864			−0.251932	+	0.967745i	$0.581066\pi$
$710$		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	$-0.343629\pi$
$719$	25.2982			0.943464			0.471732	+	0.881742i	$0.343629\pi$
$720$		0			0
$721$	−60.0000			−2.23452
$722$		0			0
$723$	−5.65685	−	5.65685i	−0.210381	−	0.210381i
$724$		0			0
$725$	−22.3607			−0.830455
$726$		0			0
$727$	9.48683	+	9.48683i	0.351847	+	0.351847i	0.860796	−	0.508949i	$-0.169966\pi$
$727$	9.48683	+	9.48683i	0.351847	+	0.351847i	−0.508949	+	0.860796i	$0.669966\pi$
$728$		0			0
$729$		−	13.0000i		−	0.481481i
$730$		0			0
$731$	14.1421			0.523066
$732$		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
$739$		−	28.2843i		−	1.04045i	−0.854028	−	0.520227i	$-0.825847\pi$
$739$		−	28.2843i		−	1.04045i	0.854028	−	0.520227i	$-0.174153\pi$
$740$		0			0
$741$		−	35.7771i		−	1.31430i
$742$		0			0
$743$	3.16228	−	3.16228i	0.116013	−	0.116013i	−0.646717	−	0.762730i	$-0.723859\pi$
$743$	3.16228	−	3.16228i	0.116013	−	0.116013i	0.762730	+	0.646717i	$0.223859\pi$
$744$		0			0
$745$		−	40.0000i		−	1.46549i
$746$		0			0
$747$	1.41421	−	1.41421i	0.0517434	−	0.0517434i
$748$		0			0
$749$	−26.8328			−0.980450
$750$		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
$755$	14.1421			0.514685
$756$		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	$-0.813810\pi$
$761$	−46.0000			−1.66750			−0.833749	+	0.552143i	$0.813810\pi$
$762$		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	$0.0460749\pi$
$769$			8.00000i			0.288487i	−0.989542	+	0.144244i	$0.953925\pi$
$770$		0			0
$771$	−36.7696			−1.32422
$772$		0			0
$773$	20.1246	−	20.1246i	0.723832	−	0.723832i	−0.245552	−	0.969384i	$-0.578969\pi$
$773$	20.1246	−	20.1246i	0.723832	−	0.723832i	0.969384	+	0.245552i	$0.0789691\pi$
$774$		0			0
$775$		−	31.6228i		−	1.13592i
$776$		0			0
$777$	−60.0000	+	60.0000i	−2.15249	+	2.15249i
$778$		0			0
$779$		−	22.6274i		−	0.810711i
$780$		0			0
$781$			17.8885i			0.640102i
$782$		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	−0.821813	−	0.569757i	$-0.807037\pi$
$787$	−7.07107	+	7.07107i	−0.252056	+	0.252056i	0.569757	+	0.821813i	$0.307037\pi$
$788$		0			0
$789$	−26.8328			−0.955274
$790$		0			0
$791$			82.2192i			2.92338i
$792$		0			0
$793$	10.0000	+	10.0000i	0.355110	+	0.355110i
$794$		0			0
$795$		−	42.4264i		−	1.50471i
$796$		0			0
$797$	−24.5967	−	24.5967i	−0.871262	−	0.871262i	0.121348	−	0.992610i	$-0.461278\pi$
$797$	−24.5967	−	24.5967i	−0.871262	−	0.871262i	−0.992610	+	0.121348i	$0.961278\pi$
$798$		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
$805$		−	44.7214i		−	1.57622i
$806$		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
$811$	−42.4264			−1.48979			−0.744896	−	0.667180i	$-0.767501\pi$
$811$	−42.4264			−1.48979			−0.744896	+	0.667180i	$0.767501\pi$
$812$		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
$819$		−	14.1421i		−	0.494166i
$820$		0			0
$821$		−	13.4164i		−	0.468236i	−0.972208	−	0.234118i	$-0.924780\pi$
$821$		−	13.4164i		−	0.468236i	0.972208	−	0.234118i	$-0.0752202\pi$
$822$		0			0
$823$	−28.4605	+	28.4605i	−0.992071	+	0.992071i	−0.999969	−	0.00789818i	$-0.997486\pi$
$823$	−28.4605	+	28.4605i	−0.992071	+	0.992071i	0.00789818	+	0.999969i	$0.497486\pi$
$824$		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
$829$	53.6656			1.86388			0.931942	−	0.362607i	$-0.118113\pi$
$829$	53.6656			1.86388			0.931942	+	0.362607i	$0.118113\pi$
$830$		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
$845$	6.70820			0.230769
$846$		0			0
$847$	9.48683	+	9.48683i	0.325971	+	0.325971i
$848$		0			0
$849$		−	36.0000i		−	1.23552i
$850$		0			0
$851$	42.4264			1.45436
$852$		0			0
$853$	−15.6525	+	15.6525i	−0.535931	+	0.535931i	−0.922331	−	0.386401i	$-0.873718\pi$
$853$	−15.6525	+	15.6525i	−0.535931	+	0.535931i	0.386401	+	0.922331i	$0.373718\pi$
$854$		0			0
$855$		−	12.6491i		−	0.432590i
$856$		0			0
$857$	9.00000	−	9.00000i	0.307434	−	0.307434i	−0.536479	−	0.843913i	$-0.680246\pi$
$857$	9.00000	−	9.00000i	0.307434	−	0.307434i	0.843913	+	0.536479i	$0.180246\pi$
$858$		0			0
$859$			33.9411i			1.15806i	0.815308	+	0.579028i	$0.196568\pi$
$859$			33.9411i			1.15806i	−0.815308	+	0.579028i	$0.803432\pi$
$860$		0			0
$861$		−	35.7771i		−	1.21928i
$862$		0			0
$863$	−15.8114	+	15.8114i	−0.538226	+	0.538226i	−0.923008	−	0.384782i	$-0.874277\pi$
$863$	−15.8114	+	15.8114i	−0.538226	+	0.538226i	0.384782	+	0.923008i	$0.374277\pi$
$864$		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
$869$	35.7771			1.21365
$870$		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	$-0.887873\pi$
$877$	−38.0132	−	38.0132i	−1.28361	−	1.28361i	−0.345016	−	0.938597i	$-0.612127\pi$
$878$		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	0.982685	+	0.185283i	$0.0593200\pi$
$887$	34.7851	+	34.7851i	1.16797	+	1.16797i	0.185283	+	0.982685i	$0.440680\pi$
$888$		0			0
$889$			20.0000i			0.670778i
$890$		0			0
$891$	−31.1127			−1.04231
$892$		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
$899$			28.2843i			0.943333i
$900$		0			0
$901$		−	13.4164i		−	0.446965i
$902$		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
$909$	−8.94427			−0.296663
$910$		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	$-0.859741\pi$
$929$		−	26.0000i		−	0.853032i	0.904480	−	0.426516i	$-0.140259\pi$
$930$		0			0
$931$	73.5391			2.41015
$932$		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	$-0.742646\pi$
$937$	1.00000	−	1.00000i	0.0326686	−	0.0326686i	0.723252	+	0.690584i	$0.242646\pi$
$938$		0			0
$939$			31.1127i			1.01532i
$940$		0			0
$941$		−	44.7214i		−	1.45787i	−0.684580	−	0.728937i	$-0.740015\pi$
$941$		−	44.7214i		−	1.45787i	0.684580	−	0.728937i	$-0.259985\pi$
$942$		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	−0.812600	−	0.582821i	$-0.801949\pi$
$947$	−7.07107	+	7.07107i	−0.229779	+	0.229779i	0.582821	+	0.812600i	$0.301949\pi$
$948$		0			0
$949$	13.4164			0.435515
$950$		0			0
$951$		−	18.9737i		−	0.615263i
$952$		0			0
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	0.464475	−	0.885586i	$-0.346243\pi$
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	−0.885586	+	0.464475i	$0.846243\pi$
$954$		0			0
$955$	42.4264			1.37289
$956$		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	0.996677	−	0.0814495i	$-0.0259549\pi$
$967$	28.4605	+	28.4605i	0.915228	+	0.915228i	−0.0814495	+	0.996677i	$0.525955\pi$
$968$		0			0
$969$		−	16.0000i		−	0.513994i
$970$		0			0
$971$	−2.82843			−0.0907685			−0.0453843	−	0.998970i	$-0.514451\pi$
$971$	−2.82843			−0.0907685			−0.0453843	+	0.998970i	$0.514451\pi$
$972$		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	−0.997563	−	0.0697708i	$-0.977773\pi$
$977$	−29.0000	+	29.0000i	−0.927792	+	0.927792i	0.0697708	+	0.997563i	$0.477773\pi$
$978$		0			0
$979$		−	22.6274i		−	0.723175i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	15.8114	−	15.8114i	0.504305	−	0.504305i	−0.408468	−	0.912773i	$-0.633937\pi$
$983$	15.8114	−	15.8114i	0.504305	−	0.504305i	0.912773	+	0.408468i	$0.133937\pi$
$984$		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
$989$	−44.7214			−1.42206
$990$		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
$995$			28.2843i			0.896672i
$996$		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	640.2.o.i.63.3	yes	8
4.3	odd	2	inner	640.2.o.i.63.1	✓	8
5.2	odd	4	inner	640.2.o.i.447.3	yes	8
8.3	odd	2	inner	640.2.o.i.63.4	yes	8
8.5	even	2	inner	640.2.o.i.63.2	yes	8
16.3	odd	4		1280.2.n.o.1023.3		8
16.5	even	4		1280.2.n.o.1023.4		8
16.11	odd	4		1280.2.n.o.1023.2		8
16.13	even	4		1280.2.n.o.1023.1		8
20.7	even	4	inner	640.2.o.i.447.1	yes	8
40.27	even	4	inner	640.2.o.i.447.4	yes	8
40.37	odd	4	inner	640.2.o.i.447.2	yes	8
80.27	even	4		1280.2.n.o.767.4		8
80.37	odd	4		1280.2.n.o.767.2		8
80.67	even	4		1280.2.n.o.767.1		8
80.77	odd	4		1280.2.n.o.767.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.o.i.63.1	✓	8	4.3	odd	2	inner
640.2.o.i.63.2	yes	8	8.5	even	2	inner
640.2.o.i.63.3	yes	8	1.1	even	1	trivial
640.2.o.i.63.4	yes	8	8.3	odd	2	inner
640.2.o.i.447.1	yes	8	20.7	even	4	inner
640.2.o.i.447.2	yes	8	40.37	odd	4	inner
640.2.o.i.447.3	yes	8	5.2	odd	4	inner
640.2.o.i.447.4	yes	8	40.27	even	4	inner
1280.2.n.o.767.1		8	80.67	even	4
1280.2.n.o.767.2		8	80.37	odd	4
1280.2.n.o.767.3		8	80.77	odd	4
1280.2.n.o.767.4		8	80.27	even	4
1280.2.n.o.1023.1		8	16.13	even	4
1280.2.n.o.1023.2		8	16.11	odd	4
1280.2.n.o.1023.3		8	16.3	odd	4
1280.2.n.o.1023.4		8	16.5	even	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.o (of order \(4\), degree \(2\), minimal)

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

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