LMFDB - Embedded newform 792.2.r.g.433.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(289,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

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

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

chi := DirichletCharacter("792.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.r (of order $5$, degree $4$, 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:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			433.2
Root			$-0.390899 + 1.20306i$ of defining polynomial
Character	$\chi$	$=$	792.433
Dual form			792.2.r.g.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44151 - 1.04732i) q^{5} +(0.109101 + 0.335777i) q^{7} +O(q^{10})$	$q+(1.44151 - 1.04732i) q^{5} +(0.109101 + 0.335777i) q^{7} +(-2.91429 - 1.58333i) q^{11} +(4.48828 + 3.26093i) q^{13} +(3.08462 - 2.24111i) q^{17} +(1.42705 - 4.39201i) q^{19} +7.00209 q^{23} +(-0.564016 + 1.73586i) q^{25} +(-0.654831 - 2.01536i) q^{29} +(-2.79456 - 2.03037i) q^{31} +(0.508933 + 0.369762i) q^{35} +(-0.537843 - 1.65531i) q^{37} +(0.458327 - 1.41059i) q^{41} -3.92979 q^{43} +(0.374078 - 1.15129i) q^{47} +(5.56228 - 4.04123i) q^{49} +(6.41260 + 4.65902i) q^{53} +(-5.85921 + 0.769801i) q^{55} +(0.954915 + 2.93893i) q^{59} +(6.15309 - 4.47048i) q^{61} +9.88510 q^{65} +1.17352 q^{67} +(-1.91702 + 1.39280i) q^{71} +(1.20648 + 3.71317i) q^{73} +(0.213695 - 1.15129i) q^{77} +(-3.32452 - 2.41540i) q^{79} +(0.662074 - 0.481025i) q^{83} +(2.09935 - 6.46114i) q^{85} +1.92979 q^{89} +(-0.605270 + 1.86283i) q^{91} +(-2.54272 - 7.82568i) q^{95} +(7.66755 + 5.57080i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} + 7 q^{7}+O(q^{10}) $ 8 * q + 3 * q^5 + 7 * q^7	$ 8 q + 3 q^{5} + 7 q^{7} - 7 q^{11} + 7 q^{13} - q^{17} - 2 q^{19} + 4 q^{23} - 33 q^{25} - 17 q^{29} - 13 q^{31} - 11 q^{35} + q^{37} - 9 q^{41} + 6 q^{43} + q^{47} + 3 q^{49} + 33 q^{53} + 13 q^{55} + 30 q^{59} - 9 q^{61} + 10 q^{65} - 10 q^{67} + 25 q^{71} - 7 q^{73} + 7 q^{77} - q^{79} + 39 q^{85} - 22 q^{89} + 7 q^{91} - 7 q^{95} + 8 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 + 7 * q^7 - 7 * q^11 + 7 * q^13 - q^17 - 2 * q^19 + 4 * q^23 - 33 * q^25 - 17 * q^29 - 13 * q^31 - 11 * q^35 + q^37 - 9 * q^41 + 6 * q^43 + q^47 + 3 * q^49 + 33 * q^53 + 13 * q^55 + 30 * q^59 - 9 * q^61 + 10 * q^65 - 10 * q^67 + 25 * q^71 - 7 * q^73 + 7 * q^77 - q^79 + 39 * q^85 - 22 * q^89 + 7 * q^91 - 7 * q^95 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.44151	−	1.04732i	0.644661	−	0.468374i	−0.216787	−	0.976219i	$-0.569558\pi$
$5$	1.44151	−	1.04732i	0.644661	−	0.468374i	0.861448	+	0.507845i	$0.169558\pi$
$6$		0			0
$7$	0.109101	+	0.335777i	0.0412361	+	0.126912i	0.969555	−	0.244873i	$-0.0787461\pi$
$7$	0.109101	+	0.335777i	0.0412361	+	0.126912i	−0.928319	+	0.371784i	$0.878746\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.91429	−	1.58333i	−0.878691	−	0.477391i
$11$	−2.91429	−	1.58333i	−0.878691	−	0.477391i
$12$		0			0
$13$	4.48828	+	3.26093i	1.24483	+	0.904419i	0.997910	−	0.0646185i	$-0.0205831\pi$
$13$	4.48828	+	3.26093i	1.24483	+	0.904419i	0.246915	+	0.969037i	$0.420583\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.08462	−	2.24111i	0.748130	−	0.543548i	−0.147117	−	0.989119i	$-0.546999\pi$
$17$	3.08462	−	2.24111i	0.748130	−	0.543548i	0.895247	+	0.445571i	$0.146999\pi$
$18$		0			0
$19$	1.42705	−	4.39201i	0.327388	−	1.00760i	−0.642963	−	0.765897i	$-0.722295\pi$
$19$	1.42705	−	4.39201i	0.327388	−	1.00760i	0.970351	−	0.241699i	$-0.0777048\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.00209			1.46004			0.730018	−	0.683428i	$-0.239511\pi$
$23$	7.00209			1.46004			0.730018	+	0.683428i	$0.239511\pi$
$24$		0			0
$25$	−0.564016	+	1.73586i	−0.112803	+	0.347172i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.654831	−	2.01536i	−0.121599	−	0.374244i	0.871667	−	0.490099i	$-0.163039\pi$
$29$	−0.654831	−	2.01536i	−0.121599	−	0.374244i	−0.993266	+	0.115855i	$0.963039\pi$
$30$		0			0
$31$	−2.79456	−	2.03037i	−0.501918	−	0.364665i	0.307831	−	0.951441i	$-0.400397\pi$
$31$	−2.79456	−	2.03037i	−0.501918	−	0.364665i	−0.809749	+	0.586776i	$0.800397\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.508933	+	0.369762i	0.0860254	+	0.0625011i
$36$		0			0
$37$	−0.537843	−	1.65531i	−0.0884208	−	0.272131i	0.897063	−	0.441904i	$-0.145697\pi$
$37$	−0.537843	−	1.65531i	−0.0884208	−	0.272131i	−0.985483	+	0.169773i	$0.945697\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.458327	−	1.41059i	0.0715787	−	0.220297i	−0.908867	−	0.417086i	$-0.863051\pi$
$41$	0.458327	−	1.41059i	0.0715787	−	0.220297i	0.980446	+	0.196789i	$0.0630515\pi$
$42$		0			0
$43$	−3.92979			−0.599287			−0.299643	−	0.954051i	$-0.596868\pi$
$43$	−3.92979			−0.599287			−0.299643	+	0.954051i	$0.596868\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.374078	−	1.15129i	0.0545648	−	0.167933i	−0.920060	−	0.391777i	$-0.871860\pi$
$47$	0.374078	−	1.15129i	0.0545648	−	0.167933i	0.974625	+	0.223844i	$0.0718605\pi$
$48$		0			0
$49$	5.56228	−	4.04123i	0.794611	−	0.577319i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.41260	+	4.65902i	0.880838	+	0.639966i	0.933473	−	0.358648i	$-0.116762\pi$
$53$	6.41260	+	4.65902i	0.880838	+	0.639966i	−0.0526352	+	0.998614i	$0.516762\pi$
$54$		0			0
$55$	−5.85921	+	0.769801i	−0.790055	+	0.103800i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.954915	+	2.93893i	0.124319	+	0.382616i	0.993776	−	0.111393i	$-0.0355312\pi$
$59$	0.954915	+	2.93893i	0.124319	+	0.382616i	−0.869457	+	0.494008i	$0.835531\pi$
$60$		0			0
$61$	6.15309	−	4.47048i	0.787823	−	0.572387i	−0.119494	−	0.992835i	$-0.538127\pi$
$61$	6.15309	−	4.47048i	0.787823	−	0.572387i	0.907317	+	0.420448i	$0.138127\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.88510			1.22610
$66$		0			0
$67$	1.17352			0.143368			0.0716839	−	0.997427i	$-0.477163\pi$
$67$	1.17352			0.143368			0.0716839	+	0.997427i	$0.477163\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.91702	+	1.39280i	−0.227509	+	0.165295i	−0.695700	−	0.718332i	$-0.744906\pi$
$71$	−1.91702	+	1.39280i	−0.227509	+	0.165295i	0.468191	+	0.883627i	$0.344906\pi$
$72$		0			0
$73$	1.20648	+	3.71317i	0.141208	+	0.434594i	0.996504	−	0.0835461i	$-0.0266246\pi$
$73$	1.20648	+	3.71317i	0.141208	+	0.434594i	−0.855296	+	0.518140i	$0.826625\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.213695	−	1.15129i	0.0243528	−	0.131202i
$78$		0			0
$79$	−3.32452	−	2.41540i	−0.374037	−	0.271754i	0.384846	−	0.922981i	$-0.374255\pi$
$79$	−3.32452	−	2.41540i	−0.374037	−	0.271754i	−0.758883	+	0.651227i	$0.774255\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.662074	−	0.481025i	0.0726720	−	0.0527993i	−0.550856	−	0.834600i	$-0.685699\pi$
$83$	0.662074	−	0.481025i	0.0726720	−	0.0527993i	0.623528	+	0.781801i	$0.285699\pi$
$84$		0			0
$85$	2.09935	−	6.46114i	0.227706	−	0.700809i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.92979			0.204557			0.102279	−	0.994756i	$-0.467387\pi$
$89$	1.92979			0.204557			0.102279	+	0.994756i	$0.467387\pi$
$90$		0			0
$91$	−0.605270	+	1.86283i	−0.0634496	+	0.195278i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.54272	−	7.82568i	−0.260877	−	0.802898i
$96$		0			0
$97$	7.66755	+	5.57080i	0.778521	+	0.565629i	0.904535	−	0.426400i	$-0.140218\pi$
$97$	7.66755	+	5.57080i	0.778521	+	0.565629i	−0.126014	+	0.992029i	$0.540218\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.6541	−	8.46723i	−1.15963	−	0.842520i	−0.169899	−	0.985462i	$-0.554344\pi$
$101$	−11.6541	−	8.46723i	−1.15963	−	0.842520i	−0.989731	+	0.142941i	$0.954344\pi$
$102$		0			0
$103$	2.48002	+	7.63273i	0.244364	+	0.752075i	0.995740	+	0.0922013i	$0.0293903\pi$
$103$	2.48002	+	7.63273i	0.244364	+	0.752075i	−0.751376	+	0.659874i	$0.770610\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.41364	+	4.35074i	−0.136662	+	0.420602i	−0.995845	−	0.0910665i	$-0.970972\pi$
$107$	−1.41364	+	4.35074i	−0.136662	+	0.420602i	0.859183	+	0.511669i	$0.170972\pi$
$108$		0			0
$109$	−20.6592			−1.97880			−0.989398	−	0.145228i	$-0.953608\pi$
$109$	−20.6592			−1.97880			−0.989398	+	0.145228i	$0.953608\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.72094	+	8.37418i	−0.255964	+	0.787777i	0.737674	+	0.675157i	$0.235924\pi$
$113$	−2.72094	+	8.37418i	−0.255964	+	0.787777i	−0.993638	+	0.112620i	$0.964076\pi$
$114$		0			0
$115$	10.0936	−	7.33339i	0.941229	−	0.683843i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.08905	+	0.791238i	0.0998327	+	0.0725327i
$120$		0			0
$121$	5.98614	+	9.22855i	0.544195	+	0.838959i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.75799	+	11.5659i	0.336125	+	1.03449i
$126$		0			0
$127$	−14.3946	+	10.4583i	−1.27732	+	0.928025i	−0.999468	−	0.0325998i	$-0.989621\pi$
$127$	−14.3946	+	10.4583i	−1.27732	+	0.928025i	−0.277849	+	0.960625i	$0.589621\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−18.3585			−1.60399			−0.801996	−	0.597329i	$-0.796229\pi$
$131$	−18.3585			−1.60399			−0.801996	+	0.597329i	$0.796229\pi$
$132$		0			0
$133$	1.63043			0.141376
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.9036	+	7.92194i	−0.931559	+	0.676817i	−0.946374	−	0.323073i	$-0.895284\pi$
$137$	−10.9036	+	7.92194i	−0.931559	+	0.676817i	0.0148153	+	0.999890i	$0.495284\pi$
$138$		0			0
$139$	4.40981	+	13.5720i	0.374035	+	1.15116i	0.944127	+	0.329581i	$0.106908\pi$
$139$	4.40981	+	13.5720i	0.374035	+	1.15116i	−0.570092	+	0.821581i	$0.693092\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.91702	−	16.6097i	−0.662055	−	1.38897i
$144$		0			0
$145$	−3.05466	−	2.21934i	−0.253676	−	0.184306i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.25430	+	5.99710i	−0.676219	+	0.491302i	−0.872101	−	0.489326i	$-0.837243\pi$
$149$	−8.25430	+	5.99710i	−0.676219	+	0.491302i	0.195882	+	0.980627i	$0.437243\pi$
$150$		0			0
$151$	1.35621	−	4.17399i	0.110367	−	0.339674i	−0.880586	−	0.473887i	$-0.842851\pi$
$151$	1.35621	−	4.17399i	0.110367	−	0.339674i	0.990953	+	0.134213i	$0.0428505\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.15481			−0.494366
$156$		0			0
$157$	6.85433	−	21.0955i	0.547035	−	1.68360i	−0.169066	−	0.985605i	$-0.554075\pi$
$157$	6.85433	−	21.0955i	0.547035	−	1.68360i	0.716101	−	0.697996i	$-0.245925\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.763932	+	2.35114i	0.0602063	+	0.185296i
$162$		0			0
$163$	−15.9621	−	11.5971i	−1.25025	−	0.908356i	−0.252009	−	0.967725i	$-0.581091\pi$
$163$	−15.9621	−	11.5971i	−1.25025	−	0.908356i	−0.998236	+	0.0593688i	$0.981091\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.800035	−	0.581259i	−0.0619085	−	0.0449792i	0.556401	−	0.830914i	$-0.312182\pi$
$167$	−0.800035	−	0.581259i	−0.0619085	−	0.0449792i	−0.618309	+	0.785935i	$0.712182\pi$
$168$		0			0
$169$	5.49380	+	16.9082i	0.422600	+	1.30063i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.40772	−	16.6433i	0.411141	−	1.26536i	−0.504516	−	0.863403i	$-0.668329\pi$
$173$	5.40772	−	16.6433i	0.411141	−	1.26536i	0.915657	−	0.401961i	$-0.131671\pi$
$174$		0			0
$175$	−0.644397			−0.0487118
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.881320	−	2.71242i	0.0658730	−	0.202736i	−0.912702	−	0.408625i	$-0.866008\pi$
$179$	0.881320	−	2.71242i	0.0658730	−	0.202736i	0.978575	+	0.205889i	$0.0660085\pi$
$180$		0			0
$181$	1.70101	−	1.23586i	0.126435	−	0.0918605i	−0.522770	−	0.852474i	$-0.675102\pi$
$181$	1.70101	−	1.23586i	0.126435	−	0.0918605i	0.649206	+	0.760613i	$0.275102\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.50893	−	1.82285i	−0.184460	−	0.134018i
$186$		0			0
$187$	−12.5379	+	1.64726i	−0.916860	+	0.120460i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.29073	+	16.2832i	0.382824	+	1.17821i	0.938047	+	0.346509i	$0.112633\pi$
$191$	5.29073	+	16.2832i	0.382824	+	1.17821i	−0.555223	+	0.831702i	$0.687367\pi$
$192$		0			0
$193$	−16.2846	+	11.8314i	−1.17219	+	0.851645i	−0.991269	−	0.131853i	$-0.957907\pi$
$193$	−16.2846	+	11.8314i	−1.17219	+	0.851645i	−0.180919	+	0.983498i	$0.557907\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.5589			−0.894786			−0.447393	−	0.894337i	$-0.647648\pi$
$197$	−12.5589			−0.894786			−0.447393	+	0.894337i	$0.647648\pi$
$198$		0			0
$199$	−3.32962			−0.236031			−0.118015	−	0.993012i	$-0.537653\pi$
$199$	−3.32962			−0.236031			−0.118015	+	0.993012i	$0.537653\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.605270	−	0.439755i	0.0424817	−	0.0308647i
$204$		0			0
$205$	−0.816647	−	2.51338i	−0.0570371	−	0.175542i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.1128	+	10.5401i	−0.768691	+	0.729073i
$210$		0			0
$211$	19.4927	+	14.1623i	1.34194	+	0.974973i	0.999370	+	0.0354791i	$0.0112957\pi$
$211$	19.4927	+	14.1623i	1.34194	+	0.974973i	0.342565	+	0.939494i	$0.388704\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.66481	+	4.11573i	−0.386337	+	0.280690i
$216$		0			0
$217$	0.376863	−	1.15986i	0.0255831	−	0.0787367i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	21.1527			1.42289
$222$		0			0
$223$	0.163537	−	0.503315i	0.0109512	−	0.0337044i	−0.945432	−	0.325821i	$-0.894359\pi$
$223$	0.163537	−	0.503315i	0.0109512	−	0.0337044i	0.956383	+	0.292116i	$0.0943594\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.91835	+	12.0594i	0.260070	+	0.800412i	0.992788	+	0.119881i	$0.0382512\pi$
$227$	3.91835	+	12.0594i	0.260070	+	0.800412i	−0.732719	+	0.680532i	$0.761749\pi$
$228$		0			0
$229$	4.93708	+	3.58700i	0.326251	+	0.237035i	0.738838	−	0.673883i	$-0.235375\pi$
$229$	4.93708	+	3.58700i	0.326251	+	0.237035i	−0.412587	+	0.910918i	$0.635375\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.01513	−	1.46408i	−0.132016	−	0.0959149i	0.519818	−	0.854277i	$-0.326000\pi$
$233$	−2.01513	−	1.46408i	−0.132016	−	0.0959149i	−0.651833	+	0.758362i	$0.726000\pi$
$234$		0			0
$235$	−0.666531	−	2.05137i	−0.0434797	−	0.133817i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.91215	+	21.2734i	−0.447110	+	1.37606i	0.433044	+	0.901373i	$0.357440\pi$
$239$	−6.91215	+	21.2734i	−0.447110	+	1.37606i	−0.880153	+	0.474689i	$0.842560\pi$
$240$		0			0
$241$	−24.1025			−1.55258			−0.776288	−	0.630378i	$-0.782900\pi$
$241$	−24.1025			−1.55258			−0.776288	+	0.630378i	$0.782900\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.78561	−	11.6509i	0.241854	−	0.744349i
$246$		0			0
$247$	20.7270	−	15.0591i	1.31883	−	0.958186i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.60736	−	4.07399i	−0.353933	−	0.257148i	0.396584	−	0.917999i	$-0.370196\pi$
$251$	−5.60736	−	4.07399i	−0.353933	−	0.257148i	−0.750517	+	0.660851i	$0.770196\pi$
$252$		0			0
$253$	−20.4061	−	11.0866i	−1.28292	−	0.697009i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.52799	+	13.9357i	0.282448	+	0.869286i	0.987152	+	0.159784i	$0.0510798\pi$
$257$	4.52799	+	13.9357i	0.282448	+	0.869286i	−0.704704	+	0.709501i	$0.748920\pi$
$258$		0			0
$259$	0.497136	−	0.361190i	0.0308905	−	0.0224433i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.9868			1.41742			0.708712	−	0.705497i	$-0.249276\pi$
$263$	22.9868			1.41742			0.708712	+	0.705497i	$0.249276\pi$
$264$		0			0
$265$	14.1233			0.867585
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.48828	+	3.26093i	−0.273655	+	0.198822i	−0.716145	−	0.697951i	$-0.754095\pi$
$269$	−4.48828	+	3.26093i	−0.273655	+	0.198822i	0.442490	+	0.896773i	$0.354095\pi$
$270$		0			0
$271$	−4.18270	−	12.8730i	−0.254081	−	0.781980i	−0.994009	−	0.109295i	$-0.965141\pi$
$271$	−4.18270	−	12.8730i	−0.254081	−	0.781980i	0.739929	−	0.672685i	$-0.234859\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.39214	−	4.16578i	0.264856	−	0.251206i
$276$		0			0
$277$	2.39473	+	1.73987i	0.143885	+	0.104539i	0.657399	−	0.753542i	$-0.271657\pi$
$277$	2.39473	+	1.73987i	0.143885	+	0.104539i	−0.513514	+	0.858081i	$0.671657\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.25120	+	5.26830i	−0.432570	+	0.314281i	−0.782676	−	0.622430i	$-0.786146\pi$
$281$	−7.25120	+	5.26830i	−0.432570	+	0.314281i	0.350106	+	0.936710i	$0.386146\pi$
$282$		0			0
$283$	5.57487	−	17.1577i	0.331392	−	1.01992i	−0.637081	−	0.770797i	$-0.719858\pi$
$283$	5.57487	−	17.1577i	0.331392	−	1.01992i	0.968472	−	0.249121i	$-0.0801417\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.523646			0.0309099
$288$		0			0
$289$	−0.760976	+	2.34204i	−0.0447633	+	0.137767i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.54122	−	26.2872i	−0.498984	−	1.53571i	−0.810655	−	0.585524i	$-0.800889\pi$
$293$	−8.54122	−	26.2872i	−0.498984	−	1.53571i	0.311671	−	0.950190i	$-0.399111\pi$
$294$		0			0
$295$	4.45450	+	3.23638i	0.259351	+	0.188429i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	31.4274	+	22.8333i	1.81749	+	1.32048i
$300$		0			0
$301$	−0.428742	−	1.31953i	−0.0247123	−	0.0760566i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.18771	−	12.8885i	0.239788	−	0.737991i
$306$		0			0
$307$	0.662166			0.0377918			0.0188959	−	0.999821i	$-0.493985\pi$
$307$	0.662166			0.0377918			0.0188959	+	0.999821i	$0.493985\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.03889	−	12.4304i	0.229024	−	0.704864i	−0.768834	−	0.639449i	$-0.779163\pi$
$311$	4.03889	−	12.4304i	0.229024	−	0.704864i	0.997858	−	0.0654157i	$-0.0208373\pi$
$312$		0			0
$313$	−16.0289	+	11.6457i	−0.906006	+	0.658252i	−0.940002	−	0.341170i	$-0.889177\pi$
$313$	−16.0289	+	11.6457i	−0.906006	+	0.658252i	0.0339952	+	0.999422i	$0.489177\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.9693	−	11.6024i	−0.896924	−	0.651653i	0.0407503	−	0.999169i	$-0.487025\pi$
$317$	−15.9693	−	11.6024i	−0.896924	−	0.651653i	−0.937674	+	0.347516i	$0.887025\pi$
$318$		0			0
$319$	−1.28262	+	6.91016i	−0.0718127	+	0.386895i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.44106	−	16.7459i	−0.302749	−	0.931764i
$324$		0			0
$325$	−8.19198	+	5.95182i	−0.454409	+	0.330148i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.427390			0.0235628
$330$		0			0
$331$	21.0860			1.15899			0.579494	−	0.814976i	$-0.303250\pi$
$331$	21.0860			1.15899			0.579494	+	0.814976i	$0.303250\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.69163	−	1.22904i	0.0924236	−	0.0671496i
$336$		0			0
$337$	−0.428343	−	1.31830i	−0.0233333	−	0.0718126i	0.938712	−	0.344703i	$-0.112020\pi$
$337$	−0.428343	−	1.31830i	−0.0233333	−	0.0718126i	−0.962045	+	0.272890i	$0.912020\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.92942	+	10.3418i	0.266943	+	0.560039i
$342$		0			0
$343$	3.96320	+	2.87944i	0.213993	+	0.155475i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.4653	−	11.2362i	0.830220	−	0.603190i	−0.0894013	−	0.995996i	$-0.528495\pi$
$347$	15.4653	−	11.2362i	0.830220	−	0.603190i	0.919622	+	0.392805i	$0.128495\pi$
$348$		0			0
$349$	6.40170	−	19.7024i	0.342675	−	1.05464i	−0.620142	−	0.784490i	$-0.712925\pi$
$349$	6.40170	−	19.7024i	0.342675	−	1.05464i	0.962817	−	0.270155i	$-0.0870750\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.09091			−0.270962			−0.135481	−	0.990780i	$-0.543258\pi$
$353$	−5.09091			−0.270962			−0.135481	+	0.990780i	$0.543258\pi$
$354$		0			0
$355$	−1.30470	+	4.01546i	−0.0692463	+	0.213118i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.27450	+	3.92251i	0.0672655	+	0.207022i	0.979040	−	0.203670i	$-0.0652871\pi$
$359$	1.27450	+	3.92251i	0.0672655	+	0.207022i	−0.911774	+	0.410692i	$0.865287\pi$
$360$		0			0
$361$	−1.88197	−	1.36733i	−0.0990508	−	0.0719646i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.62801	+	4.08899i	0.294584	+	0.214028i
$366$		0			0
$367$	11.2797	+	34.7153i	0.588795	+	1.81212i	0.583464	+	0.812139i	$0.301697\pi$
$367$	11.2797	+	34.7153i	0.588795	+	1.81212i	0.00533096	+	0.999986i	$0.498303\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.864775	+	2.66150i	−0.0448969	+	0.138178i
$372$		0			0
$373$	−5.01741			−0.259792			−0.129896	−	0.991528i	$-0.541464\pi$
$373$	−5.01741			−0.259792			−0.129896	+	0.991528i	$0.541464\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.63289	−	11.1809i	0.187103	−	0.575845i
$378$		0			0
$379$	−16.3812	+	11.9017i	−0.841447	+	0.611347i	−0.922774	−	0.385340i	$-0.874084\pi$
$379$	−16.3812	+	11.9017i	−0.841447	+	0.611347i	0.0813276	+	0.996687i	$0.474084\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.60736	−	5.52707i	−0.388718	−	0.282420i	0.376212	−	0.926534i	$-0.377226\pi$
$383$	−7.60736	−	5.52707i	−0.388718	−	0.282420i	−0.764930	+	0.644113i	$0.777226\pi$
$384$		0			0
$385$	−0.897724	−	1.88340i	−0.0457522	−	0.0959870i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.09040	−	6.43358i	−0.105987	−	0.326196i	0.883974	−	0.467537i	$-0.154859\pi$
$389$	−2.09040	−	6.43358i	−0.105987	−	0.326196i	−0.989961	+	0.141341i	$0.954859\pi$
$390$		0			0
$391$	21.5988	−	15.6924i	1.09230	−	0.793600i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.32200			−0.368410
$396$		0			0
$397$	−5.18919			−0.260438			−0.130219	−	0.991485i	$-0.541568\pi$
$397$	−5.18919			−0.260438			−0.130219	+	0.991485i	$0.541568\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.76448	−	3.46160i	0.237927	−	0.172864i	−0.462432	−	0.886655i	$-0.653023\pi$
$401$	4.76448	−	3.46160i	0.237927	−	0.172864i	0.700359	+	0.713791i	$0.253023\pi$
$402$		0			0
$403$	−5.92190	−	18.2257i	−0.294991	−	0.907888i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.05347	+	5.67563i	−0.0522186	+	0.281330i
$408$		0			0
$409$	27.9425	+	20.3014i	1.38167	+	1.00384i	0.996722	+	0.0808983i	$0.0257789\pi$
$409$	27.9425	+	20.3014i	1.38167	+	1.00384i	0.384943	+	0.922940i	$0.374221\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.882642	+	0.641277i	−0.0434320	+	0.0315552i
$414$		0			0
$415$	0.450599	−	1.38680i	0.0221190	−	0.0680753i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.32141			0.357674			0.178837	−	0.983879i	$-0.442767\pi$
$419$	7.32141			0.357674			0.178837	+	0.983879i	$0.442767\pi$
$420$		0			0
$421$	10.1601	−	31.2694i	0.495171	−	1.52398i	−0.321519	−	0.946903i	$-0.604194\pi$
$421$	10.1601	−	31.2694i	0.495171	−	1.52398i	0.816690	−	0.577076i	$-0.195806\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.15048	+	6.61849i	0.104313	+	0.321044i
$426$		0			0
$427$	2.17239	+	1.57833i	0.105129	+	0.0763810i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.21992	−	3.06595i	−0.203267	−	0.147682i	0.481495	−	0.876449i	$-0.340094\pi$
$431$	−4.21992	−	3.06595i	−0.203267	−	0.147682i	−0.684762	+	0.728767i	$0.740094\pi$
$432$		0			0
$433$	3.40789	+	10.4884i	0.163773	+	0.504041i	0.998944	−	0.0459495i	$-0.0146313\pi$
$433$	3.40789	+	10.4884i	0.163773	+	0.504041i	−0.835171	+	0.549990i	$0.814631\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.99234	−	30.7533i	0.477998	−	1.47113i
$438$		0			0
$439$	22.5808			1.07772			0.538862	−	0.842394i	$-0.318855\pi$
$439$	22.5808			1.07772			0.538862	+	0.842394i	$0.318855\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.9139	−	33.5895i	0.518534	−	1.59589i	−0.258223	−	0.966085i	$-0.583137\pi$
$443$	10.9139	−	33.5895i	0.518534	−	1.59589i	0.776758	−	0.629800i	$-0.216863\pi$
$444$		0			0
$445$	2.78180	−	2.02110i	0.131870	−	0.0958091i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	29.9820	+	21.7832i	1.41494	+	1.02801i	0.992581	+	0.121584i	$0.0387974\pi$
$449$	29.9820	+	21.7832i	1.41494	+	1.02801i	0.422358	+	0.906429i	$0.361203\pi$
$450$		0			0
$451$	−3.56912	+	3.38517i	−0.168063	+	0.159401i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.07847	+	3.31919i	0.0505595	+	0.155606i
$456$		0			0
$457$	−0.285580	+	0.207486i	−0.0133589	+	0.00970579i	−0.594445	−	0.804137i	$-0.702628\pi$
$457$	−0.285580	+	0.207486i	−0.0133589	+	0.00970579i	0.581086	+	0.813842i	$0.302628\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.2449			−0.570303			−0.285151	−	0.958482i	$-0.592044\pi$
$461$	−12.2449			−0.570303			−0.285151	+	0.958482i	$0.592044\pi$
$462$		0			0
$463$	20.9578			0.973992			0.486996	−	0.873404i	$-0.338093\pi$
$463$	20.9578			0.973992			0.486996	+	0.873404i	$0.338093\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.9281	−	17.3848i	1.10726	−	0.804473i	0.125031	−	0.992153i	$-0.460097\pi$
$467$	23.9281	−	17.3848i	1.10726	−	0.804473i	0.982230	+	0.187680i	$0.0600968\pi$
$468$		0			0
$469$	0.128031	+	0.394039i	0.00591193	+	0.0181951i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.4525	+	6.22214i	0.526588	+	0.286094i
$474$		0			0
$475$	6.81904	+	4.95433i	0.312879	+	0.227320i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.71340	+	3.42449i	−0.215361	+	0.156469i	−0.690236	−	0.723584i	$-0.742493\pi$
$479$	−4.71340	+	3.42449i	−0.215361	+	0.156469i	0.474875	+	0.880053i	$0.342493\pi$
$480$		0			0
$481$	2.98385	−	9.18336i	0.136052	−	0.418725i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.8872			0.766808
$486$		0			0
$487$	9.56462	−	29.4369i	0.433414	−	1.33391i	−0.461288	−	0.887250i	$-0.652613\pi$
$487$	9.56462	−	29.4369i	0.433414	−	1.33391i	0.894703	−	0.446662i	$-0.147387\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.30431	−	10.1696i	−0.149122	−	0.458949i	0.848396	−	0.529361i	$-0.177568\pi$
$491$	−3.30431	−	10.1696i	−0.149122	−	0.458949i	−0.997518	+	0.0704125i	$0.977568\pi$
$492$		0			0
$493$	−6.53655	−	4.74908i	−0.294391	−	0.213888i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.676818	−	0.491737i	−0.0303595	−	0.0220574i
$498$		0			0
$499$	7.93548	+	24.4229i	0.355241	+	1.09332i	0.955870	+	0.293791i	$0.0949169\pi$
$499$	7.93548	+	24.4229i	0.355241	+	1.09332i	−0.600629	+	0.799528i	$0.705083\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.33277	−	16.4126i	0.237777	−	0.731801i	−0.758964	−	0.651132i	$-0.774294\pi$
$503$	5.33277	−	16.4126i	0.237777	−	0.731801i	0.996741	−	0.0806690i	$-0.0257057\pi$
$504$		0			0
$505$	−25.6674			−1.14218
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.7918	+	33.2137i	−0.478337	+	1.47217i	0.363067	+	0.931763i	$0.381730\pi$
$509$	−10.7918	+	33.2137i	−0.478337	+	1.47217i	−0.841404	+	0.540407i	$0.818270\pi$
$510$		0			0
$511$	−1.11517	+	0.810218i	−0.0493322	+	0.0358419i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.5688	+	8.40526i	0.509784	+	0.370380i
$516$		0			0
$517$	−2.91304	+	2.76291i	−0.128116	+	0.121513i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.46282	+	7.57979i	0.107898	+	0.332076i	0.990400	−	0.138233i	$-0.0441423\pi$
$521$	2.46282	+	7.57979i	0.107898	+	0.332076i	−0.882502	+	0.470310i	$0.844142\pi$
$522$		0			0
$523$	−18.4741	+	13.4223i	−0.807818	+	0.586914i	−0.913197	−	0.407518i	$-0.866394\pi$
$523$	−18.4741	+	13.4223i	−0.807818	+	0.586914i	0.105379	+	0.994432i	$0.466394\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.1704			−0.573713
$528$		0			0
$529$	26.0293			1.13171
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.65692	−	4.83654i	0.288343	−	0.209494i
$534$		0			0
$535$	2.51882	+	7.75215i	0.108898	+	0.335154i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−22.6087	+	2.97040i	−0.973824	+	0.127944i
$540$		0			0
$541$	−32.3265	−	23.4866i	−1.38983	−	1.00977i	−0.995885	−	0.0906312i	$-0.971112\pi$
$541$	−32.3265	−	23.4866i	−1.38983	−	1.00977i	−0.393941	−	0.919136i	$-0.628888\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−29.7804	+	21.6367i	−1.27565	+	0.926816i
$546$		0			0
$547$	−5.14156	+	15.8241i	−0.219837	+	0.676590i	0.778937	+	0.627102i	$0.215759\pi$
$547$	−5.14156	+	15.8241i	−0.219837	+	0.676590i	−0.998775	+	0.0494881i	$0.984241\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.78598			−0.416897
$552$		0			0
$553$	0.448330	−	1.37982i	0.0190649	−	0.0586758i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.10617	+	18.7929i	0.258727	+	0.796280i	0.993072	+	0.117504i	$0.0374892\pi$
$557$	6.10617	+	18.7929i	0.258727	+	0.796280i	−0.734346	+	0.678776i	$0.762511\pi$
$558$		0			0
$559$	−17.6380	−	12.8148i	−0.746008	−	0.542006i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.6319	+	14.2634i	0.827385	+	0.601130i	0.918818	−	0.394681i	$-0.129145\pi$
$563$	19.6319	+	14.2634i	0.827385	+	0.601130i	−0.0914334	+	0.995811i	$0.529145\pi$
$564$		0			0
$565$	4.84816	+	14.9211i	0.203964	+	0.627736i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.79195	−	27.0588i	0.368578	−	1.13437i	−0.579133	−	0.815233i	$-0.696609\pi$
$569$	8.79195	−	27.0588i	0.368578	−	1.13437i	0.947710	−	0.319132i	$-0.103391\pi$
$570$		0			0
$571$	−26.9485			−1.12776			−0.563879	−	0.825858i	$-0.690692\pi$
$571$	−26.9485			−1.12776			−0.563879	+	0.825858i	$0.690692\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.94929	+	12.1547i	−0.164697	+	0.506884i
$576$		0			0
$577$	−8.80048	+	6.39392i	−0.366369	+	0.266183i	−0.755704	−	0.654914i	$-0.772705\pi$
$577$	−8.80048	+	6.39392i	−0.366369	+	0.266183i	0.389335	+	0.921096i	$0.372705\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.233750	+	0.169829i	0.00969757	+	0.00704570i
$582$		0			0
$583$	−11.3114	−	23.7310i	−0.468470	−	0.982837i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.35893	+	25.7261i	0.345010	+	1.06183i	0.961579	+	0.274530i	$0.0885223\pi$
$587$	8.35893	+	25.7261i	0.345010	+	1.06183i	−0.616569	+	0.787301i	$0.711478\pi$
$588$		0			0
$589$	−12.9054	+	9.37631i	−0.531757	+	0.386344i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.72088			−0.275993			−0.137997	−	0.990433i	$-0.544066\pi$
$593$	−6.72088			−0.275993			−0.137997	+	0.990433i	$0.544066\pi$
$594$		0			0
$595$	2.39854			0.0983306
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.6797	−	16.4777i	0.926666	−	0.673262i	−0.0185083	−	0.999829i	$-0.505892\pi$
$599$	22.6797	−	16.4777i	0.926666	−	0.673262i	0.945174	+	0.326566i	$0.105892\pi$
$600$		0			0
$601$	−5.29192	−	16.2868i	−0.215862	−	0.664354i	−0.999091	−	0.0426217i	$-0.986429\pi$
$601$	−5.29192	−	16.2868i	−0.215862	−	0.664354i	0.783229	−	0.621733i	$-0.213571\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	18.2943	+	7.03363i	0.743767	+	0.285958i
$606$		0			0
$607$	−30.3423	−	22.0450i	−1.23156	−	0.894777i	−0.234550	−	0.972104i	$-0.575362\pi$
$607$	−30.3423	−	22.0450i	−1.23156	−	0.894777i	−0.997006	+	0.0773268i	$0.975362\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.43325	−	3.94749i	0.219806	−	0.159698i
$612$		0			0
$613$	8.22609	−	25.3173i	0.332249	−	1.02256i	−0.635813	−	0.771843i	$-0.719335\pi$
$613$	8.22609	−	25.3173i	0.332249	−	1.02256i	0.968061	−	0.250713i	$-0.0806650\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.8616			−0.558047			−0.279024	−	0.960284i	$-0.590011\pi$
$617$	−13.8616			−0.558047			−0.279024	+	0.960284i	$0.590011\pi$
$618$		0			0
$619$	2.53801	−	7.81120i	0.102011	−	0.313959i	−0.887006	−	0.461758i	$-0.847219\pi$
$619$	2.53801	−	7.81120i	0.102011	−	0.313959i	0.989017	+	0.147799i	$0.0472189\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.210541	+	0.647978i	0.00843514	+	0.0259607i
$624$		0			0
$625$	10.1473	+	7.37242i	0.405891	+	0.294897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.36876	−	3.90064i	−0.214067	−	0.155529i
$630$		0			0
$631$	12.1950	+	37.5323i	0.485475	+	1.49414i	0.831292	+	0.555836i	$0.187602\pi$
$631$	12.1950	+	37.5323i	0.485475	+	1.49414i	−0.345817	+	0.938302i	$0.612398\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.79679	+	30.1514i	−0.388774	+	1.19652i
$636$		0			0
$637$	38.1432			1.51129
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.1686	−	34.3735i	0.441134	−	1.35767i	−0.445534	−	0.895265i	$-0.646986\pi$
$641$	11.1686	−	34.3735i	0.441134	−	1.35767i	0.886668	−	0.462406i	$-0.153014\pi$
$642$		0			0
$643$	19.4047	−	14.0983i	0.765245	−	0.555983i	−0.135270	−	0.990809i	$-0.543190\pi$
$643$	19.4047	−	14.0983i	0.765245	−	0.555983i	0.900515	+	0.434826i	$0.143190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−33.6307	−	24.4341i	−1.32216	−	0.960605i	−0.999903	−	0.0139526i	$-0.995559\pi$
$647$	−33.6307	−	24.4341i	−1.32216	−	0.960605i	−0.322257	−	0.946652i	$-0.604441\pi$
$648$		0			0
$649$	1.87039	−	10.0768i	0.0734192	−	0.395550i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.28600	−	28.5794i	−0.363389	−	1.11840i	−0.950984	−	0.309241i	$-0.899925\pi$
$653$	−9.28600	−	28.5794i	−0.363389	−	1.11840i	0.587594	−	0.809156i	$-0.300075\pi$
$654$		0			0
$655$	−26.4639	+	19.2272i	−1.03403	+	0.751267i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−25.2450			−0.983405			−0.491702	−	0.870763i	$-0.663625\pi$
$659$	−25.2450			−0.983405			−0.491702	+	0.870763i	$0.663625\pi$
$660$		0			0
$661$	9.51852			0.370227			0.185114	−	0.982717i	$-0.440735\pi$
$661$	9.51852			0.370227			0.185114	+	0.982717i	$0.440735\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.35027	−	1.70757i	0.0911396	−	0.0662168i
$666$		0			0
$667$	−4.58519	−	14.1118i	−0.177539	−	0.546410i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−25.0101	+	3.28591i	−0.965505	+	0.126851i
$672$		0			0
$673$	−9.13567	−	6.63745i	−0.352154	−	0.255855i	0.397618	−	0.917551i	$-0.369837\pi$
$673$	−9.13567	−	6.63745i	−0.352154	−	0.255855i	−0.749772	+	0.661696i	$0.769837\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.7064	+	20.8564i	−1.10328	+	0.801577i	−0.981592	−	0.190992i	$-0.938830\pi$
$677$	−28.7064	+	20.8564i	−1.10328	+	0.801577i	−0.121684	+	0.992569i	$0.538830\pi$
$678$		0			0
$679$	−1.03401	+	3.18236i	−0.0396818	+	0.122128i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.8947			−0.952569			−0.476284	−	0.879291i	$-0.658017\pi$
$683$	−24.8947			−0.952569			−0.476284	+	0.879291i	$0.658017\pi$
$684$		0			0
$685$	−7.42085	+	22.8390i	−0.283536	+	0.872635i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	13.5888	+	41.8220i	0.517692	+	1.59329i
$690$		0			0
$691$	0.513361	+	0.372978i	0.0195292	+	0.0141888i	0.597507	−	0.801864i	$-0.296158\pi$
$691$	0.513361	+	0.372978i	0.0195292	+	0.0141888i	−0.577978	+	0.816052i	$0.696158\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	20.5709	+	14.9457i	0.780300	+	0.566921i
$696$		0			0
$697$	−1.74751	−	5.37828i	−0.0661916	−	0.203717i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−5.39612	+	16.6076i	−0.203809	+	0.627259i	0.795951	+	0.605361i	$0.206971\pi$
$701$	−5.39612	+	16.6076i	−0.203809	+	0.627259i	−0.999760	+	0.0218985i	$0.993029\pi$
$702$		0			0
$703$	−8.03767			−0.303146
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.57163	−	4.83697i	0.0591071	−	0.181913i
$708$		0			0
$709$	−26.3781	+	19.1648i	−0.990651	+	0.719750i	−0.960064	−	0.279782i	$-0.909738\pi$
$709$	−26.3781	+	19.1648i	−0.990651	+	0.719750i	−0.0305874	+	0.999532i	$0.509738\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−19.5678	−	14.2168i	−0.732819	−	0.532424i
$714$		0			0
$715$	−28.8080	−	15.6514i	−1.07736	−	0.585328i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.8109	+	33.2726i	0.403180	+	1.24086i	0.922405	+	0.386223i	$0.126220\pi$
$719$	10.8109	+	33.2726i	0.403180	+	1.24086i	−0.519226	+	0.854637i	$0.673780\pi$
$720$		0			0
$721$	−2.29232	+	1.66547i	−0.0853706	+	0.0620254i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.86773			0.143644
$726$		0			0
$727$	−16.2644			−0.603214			−0.301607	−	0.953432i	$-0.597523\pi$
$727$	−16.2644			−0.603214			−0.301607	+	0.953432i	$0.597523\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.1219	+	8.80707i	−0.448344	+	0.325741i
$732$		0			0
$733$	13.9308	+	42.8746i	0.514546	+	1.58361i	0.784106	+	0.620627i	$0.213122\pi$
$733$	13.9308	+	42.8746i	0.514546	+	1.58361i	−0.269560	+	0.962984i	$0.586878\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.41996	−	1.85806i	−0.125976	−	0.0684425i
$738$		0			0
$739$	11.8506	+	8.60999i	0.435933	+	0.316724i	0.784017	−	0.620740i	$-0.213168\pi$
$739$	11.8506	+	8.60999i	0.435933	+	0.316724i	−0.348084	+	0.937463i	$0.613168\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.42499	−	2.48840i	0.125651	−	0.0912906i	−0.523185	−	0.852219i	$-0.675256\pi$
$743$	3.42499	−	2.48840i	0.125651	−	0.0912906i	0.648836	+	0.760929i	$0.275256\pi$
$744$		0			0
$745$	−5.61777	+	17.2897i	−0.205819	+	0.633446i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.61511			−0.0590148
$750$		0			0
$751$	−7.05755	+	21.7209i	−0.257534	+	0.792607i	0.735786	+	0.677214i	$0.236813\pi$
$751$	−7.05755	+	21.7209i	−0.257534	+	0.792607i	−0.993320	+	0.115393i	$0.963187\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.41649	−	7.43721i	−0.0879453	−	0.270668i
$756$		0			0
$757$	25.0773	+	18.2197i	0.911450	+	0.662207i	0.941381	−	0.337345i	$-0.109529\pi$
$757$	25.0773	+	18.2197i	0.911450	+	0.662207i	−0.0299310	+	0.999552i	$0.509529\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.3917	−	16.9951i	−0.847948	−	0.616071i	0.0766312	−	0.997060i	$-0.475584\pi$
$761$	−23.3917	−	16.9951i	−0.847948	−	0.616071i	−0.924580	+	0.380989i	$0.875584\pi$
$762$		0			0
$763$	−2.25393	−	6.93690i	−0.0815979	−	0.251133i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.29770	+	16.3046i	−0.191289	+	0.588726i
$768$		0			0
$769$	5.37741			0.193914			0.0969571	−	0.995289i	$-0.469089\pi$
$769$	5.37741			0.193914			0.0969571	+	0.995289i	$0.469089\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.7820	+	42.4167i	−0.495705	+	1.52562i	0.320150	+	0.947367i	$0.396267\pi$
$773$	−13.7820	+	42.4167i	−0.495705	+	1.52562i	−0.815855	+	0.578256i	$0.803733\pi$
$774$		0			0
$775$	5.10062	−	3.70581i	0.183220	−	0.133117i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.54125	−	4.02596i	−0.198536	−	0.144245i
$780$		0			0
$781$	7.79202	−	1.02374i	0.278820	−	0.0366323i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.2130	−	37.5879i	−0.435902	−	1.34157i
$786$		0			0
$787$	33.6779	−	24.4684i	1.20049	−	0.872206i	0.206156	−	0.978519i	$-0.433905\pi$
$787$	33.6779	−	24.4684i	1.20049	−	0.872206i	0.994333	+	0.106313i	$0.0339047\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.10871			−0.110533
$792$		0			0
$793$	42.1947			1.49838
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.07959	+	2.96400i	−0.144507	+	0.104990i	−0.657690	−	0.753289i	$-0.728466\pi$
$797$	−4.07959	+	2.96400i	−0.144507	+	0.104990i	0.513183	+	0.858279i	$0.328466\pi$
$798$		0			0
$799$	−1.42628	−	4.38965i	−0.0504583	−	0.155295i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.36313	−	12.7315i	0.0833932	−	0.449285i
$804$		0			0
$805$	3.56360	+	2.58911i	0.125600	+	0.0912540i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	22.6592	−	16.4628i	0.796654	−	0.578803i	−0.113277	−	0.993563i	$-0.536135\pi$
$809$	22.6592	−	16.4628i	0.796654	−	0.578803i	0.909931	+	0.414761i	$0.136135\pi$
$810$		0			0
$811$	−10.3208	+	31.7642i	−0.362413	+	1.11539i	0.589172	+	0.808008i	$0.299454\pi$
$811$	−10.3208	+	31.7642i	−0.362413	+	1.11539i	−0.951585	+	0.307386i	$0.900546\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−35.1552			−1.23143
$816$		0			0
$817$	−5.60801	+	17.2597i	−0.196199	+	0.603839i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.37955	−	28.8673i	−0.327349	−	1.00748i	−0.970369	−	0.241627i	$-0.922319\pi$
$821$	−9.37955	−	28.8673i	−0.327349	−	1.00748i	0.643021	−	0.765849i	$-0.277681\pi$
$822$		0			0
$823$	−5.46823	−	3.97290i	−0.190610	−	0.138487i	0.488387	−	0.872627i	$-0.337585\pi$
$823$	−5.46823	−	3.97290i	−0.190610	−	0.138487i	−0.678998	+	0.734140i	$0.737585\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−26.5609	−	19.2976i	−0.923614	−	0.671045i	0.0208068	−	0.999784i	$-0.493377\pi$
$827$	−26.5609	−	19.2976i	−0.923614	−	0.671045i	−0.944421	+	0.328739i	$0.893377\pi$
$828$		0			0
$829$	4.77520	+	14.6966i	0.165850	+	0.510433i	0.999098	−	0.0424663i	$-0.0135215\pi$
$829$	4.77520	+	14.6966i	0.165850	+	0.510433i	−0.833248	+	0.552899i	$0.813522\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.10067	−	24.9313i	0.280672	−	0.863819i
$834$		0			0
$835$	−1.76202			−0.0609771
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.63951	+	26.5897i	−0.298269	+	0.917978i	0.683835	+	0.729637i	$0.260311\pi$
$839$	−8.63951	+	26.5897i	−0.298269	+	0.917978i	−0.982104	+	0.188341i	$0.939689\pi$
$840$		0			0
$841$	19.8286	−	14.4063i	0.683745	−	0.496770i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	25.6275	+	18.6195i	0.881614	+	0.640530i
$846$		0			0
$847$	−2.44564	+	3.01685i	−0.0840333	+	0.103660i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.76602	−	11.5906i	−0.129098	−	0.397321i
$852$		0			0
$853$	−11.3899	+	8.27524i	−0.389983	+	0.283339i	−0.765448	−	0.643497i	$-0.777483\pi$
$853$	−11.3899	+	8.27524i	−0.389983	+	0.283339i	0.375466	+	0.926836i	$0.377483\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.4776			−0.904457			−0.452228	−	0.891902i	$-0.649371\pi$
$857$	−26.4776			−0.904457			−0.452228	+	0.891902i	$0.649371\pi$
$858$		0			0
$859$	−47.5614			−1.62277			−0.811387	−	0.584510i	$-0.801287\pi$
$859$	−47.5614			−1.62277			−0.811387	+	0.584510i	$0.801287\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.1250	−	25.5198i	1.19567	−	0.868704i	0.201817	−	0.979423i	$-0.435316\pi$
$863$	35.1250	−	25.5198i	1.19567	−	0.868704i	0.993852	+	0.110720i	$0.0353155\pi$
$864$		0			0
$865$	−9.63547	−	29.6549i	−0.327616	−	1.00830i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.86422	+	12.3030i	0.198930	+	0.417350i
$870$		0			0
$871$	5.26707	+	3.82675i	0.178468	+	0.129664i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.47357	+	2.52370i	−0.117428	+	0.0853165i
$876$		0			0
$877$	4.05884	−	12.4918i	0.137057	−	0.421819i	−0.858847	−	0.512232i	$-0.828819\pi$
$877$	4.05884	−	12.4918i	0.137057	−	0.421819i	0.995904	+	0.0904129i	$0.0288187\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.3388			1.22429			0.612143	−	0.790747i	$-0.290308\pi$
$881$	36.3388			1.22429			0.612143	+	0.790747i	$0.290308\pi$
$882$		0			0
$883$	10.3944	−	31.9907i	0.349800	−	1.07657i	−0.609163	−	0.793045i	$-0.708495\pi$
$883$	10.3944	−	31.9907i	0.349800	−	1.07657i	0.958964	−	0.283529i	$-0.0915054\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.8199	+	33.3001i	0.363295	+	1.11811i	0.951042	+	0.309062i	$0.100015\pi$
$887$	10.8199	+	33.3001i	0.363295	+	1.11811i	−0.587747	+	0.809045i	$0.699985\pi$
$888$		0			0
$889$	−5.08212	−	3.69238i	−0.170449	−	0.123838i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.52266	−	3.28591i	−0.151345	−	0.109959i
$894$		0			0
$895$	−1.57034	−	4.83299i	−0.0524905	−	0.161549i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.26196	+	6.96161i	−0.0754407	+	0.232183i
$900$		0			0
$901$	30.2218			1.00683
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.15768	−	3.56299i	0.0384827	−	0.118438i
$906$		0			0
$907$	−41.9407	+	30.4717i	−1.39262	+	1.01180i	−0.397046	+	0.917799i	$0.629965\pi$
$907$	−41.9407	+	30.4717i	−1.39262	+	1.01180i	−0.995572	+	0.0939979i	$0.970035\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.9715	−	17.4163i	−0.794212	−	0.577029i	0.114998	−	0.993366i	$-0.463314\pi$
$911$	−23.9715	−	17.4163i	−0.794212	−	0.577029i	−0.909210	+	0.416337i	$0.863314\pi$
$912$		0			0
$913$	−2.69109	+	0.353564i	−0.0890622	+	0.0117013i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.00293	−	6.16437i	−0.0661424	−	0.203566i
$918$		0			0
$919$	24.3567	−	17.6962i	0.803454	−	0.583743i	−0.108472	−	0.994100i	$-0.534596\pi$
$919$	24.3567	−	17.6962i	0.803454	−	0.583743i	0.911925	+	0.410356i	$0.134596\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13.1460			−0.432704
$924$		0			0
$925$	3.17674			0.104451
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−41.3186	+	30.0197i	−1.35562	+	0.984914i	−0.356908	+	0.934140i	$0.616169\pi$
$929$	−41.3186	+	30.0197i	−1.35562	+	0.984914i	−0.998710	+	0.0507745i	$0.983831\pi$
$930$		0			0
$931$	−9.81148	−	30.1966i	−0.321558	−	0.989654i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.3482	+	15.5056i	−0.534644	+	0.507089i
$936$		0			0
$937$	6.75635	+	4.90878i	0.220720	+	0.160363i	0.692651	−	0.721273i	$-0.256443\pi$
$937$	6.75635	+	4.90878i	0.220720	+	0.160363i	−0.471931	+	0.881636i	$0.656443\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	43.1964	−	31.3840i	1.40816	−	1.02309i	0.414576	−	0.910015i	$-0.363930\pi$
$941$	43.1964	−	31.3840i	1.40816	−	1.02309i	0.993586	−	0.113075i	$-0.0360699\pi$
$942$		0			0
$943$	3.20925	−	9.87705i	0.104508	−	0.321641i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.2532			0.625646			0.312823	−	0.949811i	$-0.398725\pi$
$947$	19.2532			0.625646			0.312823	+	0.949811i	$0.398725\pi$
$948$		0			0
$949$	−6.69335	+	20.6000i	−0.217275	+	0.668705i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.3253	+	34.8556i	0.366862	+	1.12908i	0.948807	+	0.315857i	$0.102292\pi$
$953$	11.3253	+	34.8556i	0.366862	+	1.12908i	−0.581945	+	0.813228i	$0.697708\pi$
$954$		0			0
$955$	24.6803	+	17.9313i	0.798634	+	0.580242i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.84960	−	2.79689i	−0.124310	−	0.0903164i
$960$		0			0
$961$	−5.89234	−	18.1348i	−0.190076	−	0.584993i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.0831	+	34.1101i	−0.356776	+	1.09804i
$966$		0			0
$967$	−45.6501			−1.46801			−0.734004	−	0.679146i	$-0.762351\pi$
$967$	−45.6501			−1.46801			−0.734004	+	0.679146i	$0.762351\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.2715	+	43.9232i	−0.457995	+	1.40956i	0.409588	+	0.912270i	$0.365672\pi$
$971$	−14.2715	+	43.9232i	−0.457995	+	1.40956i	−0.867583	+	0.497292i	$0.834328\pi$
$972$		0			0
$973$	−4.07605	+	2.96143i	−0.130672	+	0.0949390i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	43.1572	+	31.3555i	1.38072	+	1.00315i	0.996812	+	0.0797806i	$0.0254220\pi$
$977$	43.1572	+	31.3555i	1.38072	+	1.00315i	0.383908	+	0.923371i	$0.374578\pi$
$978$		0			0
$979$	−5.62395	−	3.05549i	−0.179742	−	0.0976538i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−3.73470	−	11.4942i	−0.119118	−	0.366609i	0.873665	−	0.486527i	$-0.161737\pi$
$983$	−3.73470	−	11.4942i	−0.119118	−	0.366609i	−0.992784	+	0.119919i	$0.961737\pi$
$984$		0			0
$985$	−18.1038	+	13.1532i	−0.576834	+	0.419094i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−27.5167			−0.874981
$990$		0			0
$991$	−36.0620			−1.14555			−0.572774	−	0.819714i	$-0.694133\pi$
$991$	−36.0620			−1.14555			−0.572774	+	0.819714i	$0.694133\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.79967	+	3.48716i	−0.152160	+	0.110550i
$996$		0			0
$997$	−2.88069	−	8.86586i	−0.0912325	−	0.280785i	0.895021	−	0.446024i	$-0.147160\pi$
$997$	−2.88069	−	8.86586i	−0.0912325	−	0.280785i	−0.986254	+	0.165239i	$0.947160\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.r.g.433.2		8
3.2	odd	2		88.2.i.b.81.2	yes	8
11.3	even	5	inner	792.2.r.g.289.2		8
11.5	even	5		8712.2.a.ce.1.2		4
11.6	odd	10		8712.2.a.cd.1.2		4
12.11	even	2		176.2.m.d.81.1		8
24.5	odd	2		704.2.m.l.257.1		8
24.11	even	2		704.2.m.i.257.2		8
33.2	even	10		968.2.i.t.753.1		8
33.5	odd	10		968.2.a.n.1.4		4
33.8	even	10		968.2.i.p.729.2		8
33.14	odd	10		88.2.i.b.25.2	✓	8
33.17	even	10		968.2.a.m.1.4		4
33.20	odd	10		968.2.i.s.753.1		8
33.26	odd	10		968.2.i.s.9.1		8
33.29	even	10		968.2.i.t.9.1		8
33.32	even	2		968.2.i.p.81.2		8
132.47	even	10		176.2.m.d.113.1		8
132.71	even	10		1936.2.a.bb.1.1		4
132.83	odd	10		1936.2.a.bc.1.1		4
264.5	odd	10		7744.2.a.di.1.1		4
264.83	odd	10		7744.2.a.ds.1.4		4
264.149	even	10		7744.2.a.dh.1.1		4
264.179	even	10		704.2.m.i.641.2		8
264.203	even	10		7744.2.a.dr.1.4		4
264.245	odd	10		704.2.m.l.641.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.25.2	✓	8	33.14	odd	10
88.2.i.b.81.2	yes	8	3.2	odd	2
176.2.m.d.81.1		8	12.11	even	2
176.2.m.d.113.1		8	132.47	even	10
704.2.m.i.257.2		8	24.11	even	2
704.2.m.i.641.2		8	264.179	even	10
704.2.m.l.257.1		8	24.5	odd	2
704.2.m.l.641.1		8	264.245	odd	10
792.2.r.g.289.2		8	11.3	even	5	inner
792.2.r.g.433.2		8	1.1	even	1	trivial
968.2.a.m.1.4		4	33.17	even	10
968.2.a.n.1.4		4	33.5	odd	10
968.2.i.p.81.2		8	33.32	even	2
968.2.i.p.729.2		8	33.8	even	10
968.2.i.s.9.1		8	33.26	odd	10
968.2.i.s.753.1		8	33.20	odd	10
968.2.i.t.9.1		8	33.29	even	10
968.2.i.t.753.1		8	33.2	even	10
1936.2.a.bb.1.1		4	132.71	even	10
1936.2.a.bc.1.1		4	132.83	odd	10
7744.2.a.dh.1.1		4	264.149	even	10
7744.2.a.di.1.1		4	264.5	odd	10
7744.2.a.dr.1.4		4	264.203	even	10
7744.2.a.ds.1.4		4	264.83	odd	10
8712.2.a.cd.1.2		4	11.6	odd	10
8712.2.a.ce.1.2		4	11.5	even	5

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44151 - 1.04732i) q^{5} +(0.109101 + 0.335777i) q^{7} +O(q^{10})\)	\(q+(1.44151 - 1.04732i) q^{5} +(0.109101 + 0.335777i) q^{7} +(-2.91429 - 1.58333i) q^{11} +(4.48828 + 3.26093i) q^{13} +(3.08462 - 2.24111i) q^{17} +(1.42705 - 4.39201i) q^{19} +7.00209 q^{23} +(-0.564016 + 1.73586i) q^{25} +(-0.654831 - 2.01536i) q^{29} +(-2.79456 - 2.03037i) q^{31} +(0.508933 + 0.369762i) q^{35} +(-0.537843 - 1.65531i) q^{37} +(0.458327 - 1.41059i) q^{41} -3.92979 q^{43} +(0.374078 - 1.15129i) q^{47} +(5.56228 - 4.04123i) q^{49} +(6.41260 + 4.65902i) q^{53} +(-5.85921 + 0.769801i) q^{55} +(0.954915 + 2.93893i) q^{59} +(6.15309 - 4.47048i) q^{61} +9.88510 q^{65} +1.17352 q^{67} +(-1.91702 + 1.39280i) q^{71} +(1.20648 + 3.71317i) q^{73} +(0.213695 - 1.15129i) q^{77} +(-3.32452 - 2.41540i) q^{79} +(0.662074 - 0.481025i) q^{83} +(2.09935 - 6.46114i) q^{85} +1.92979 q^{89} +(-0.605270 + 1.86283i) q^{91} +(-2.54272 - 7.82568i) q^{95} +(7.66755 + 5.57080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} + 7 q^{7}+O(q^{10}) \) 8 * q + 3 * q^5 + 7 * q^7	\( 8 q + 3 q^{5} + 7 q^{7} - 7 q^{11} + 7 q^{13} - q^{17} - 2 q^{19} + 4 q^{23} - 33 q^{25} - 17 q^{29} - 13 q^{31} - 11 q^{35} + q^{37} - 9 q^{41} + 6 q^{43} + q^{47} + 3 q^{49} + 33 q^{53} + 13 q^{55} + 30 q^{59} - 9 q^{61} + 10 q^{65} - 10 q^{67} + 25 q^{71} - 7 q^{73} + 7 q^{77} - q^{79} + 39 q^{85} - 22 q^{89} + 7 q^{91} - 7 q^{95} + 8 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 + 7 * q^7 - 7 * q^11 + 7 * q^13 - q^17 - 2 * q^19 + 4 * q^23 - 33 * q^25 - 17 * q^29 - 13 * q^31 - 11 * q^35 + q^37 - 9 * q^41 + 6 * q^43 + q^47 + 3 * q^49 + 33 * q^53 + 13 * q^55 + 30 * q^59 - 9 * q^61 + 10 * q^65 - 10 * q^67 + 25 * q^71 - 7 * q^73 + 7 * q^77 - q^79 + 39 * q^85 - 22 * q^89 + 7 * q^91 - 7 * q^95 + 8 * q^97

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