LMFDB - Embedded newform 2268.2.t.b.2105.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1781,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("2268.1781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.t (of order $6$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2105.4
Root			$1.08696 + 1.34852i$ of defining polynomial
Character	$\chi$	$=$	2268.2105
Dual form			2268.2.t.b.1781.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0382122 - 0.0661855i) q^{5} +(2.16592 + 1.51947i) q^{7} +O(q^{10})$	$q+(0.0382122 - 0.0661855i) q^{5} +(2.16592 + 1.51947i) q^{7} +(-4.66300 + 2.69219i) q^{11} -5.31524i q^{13} +(1.89092 + 3.27516i) q^{17} +(-4.33939 - 2.50535i) q^{19} +(2.02463 + 1.16892i) q^{23} +(2.49708 + 4.32507i) q^{25} +10.2125i q^{29} +(-4.97636 + 2.87310i) q^{31} +(0.183331 - 0.0852905i) q^{35} +(0.354486 - 0.613988i) q^{37} +6.59821 q^{41} -1.43304 q^{43} +(1.46192 - 2.53213i) q^{47} +(2.38244 + 6.58209i) q^{49} +(-10.4835 + 6.05264i) q^{53} +0.411498i q^{55} +(0.289951 + 0.502210i) q^{59} +(2.40641 + 1.38934i) q^{61} +(-0.351792 - 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} +3.32103i q^{71} +(-6.17326 + 3.56413i) q^{73} +(-14.1904 - 1.25421i) q^{77} +(-0.469123 + 0.812544i) q^{79} -12.9958 q^{83} +0.289025 q^{85} +(1.51794 - 2.62915i) q^{89} +(8.07632 - 11.5124i) q^{91} +(-0.331636 + 0.191470i) q^{95} -7.13816i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{7}+O(q^{10}) $ 16 * q + 2 * q^7	$ 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95}+O(q^{100}) $ 16 * q + 2 * q^7 + 6 * q^11 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^31 - 15 * q^35 + q^37 + 12 * q^41 + 4 * q^43 + 18 * q^47 - 8 * q^49 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - 48 * q^77 - q^79 - 12 * q^85 + 21 * q^89 + 9 * q^91 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0382122	−	0.0661855i	0.0170890	−	0.0295991i	−0.857354	−	0.514727i	$-0.827893\pi$
$5$	0.0382122	−	0.0661855i	0.0170890	−	0.0295991i	0.874443	+	0.485127i	$0.161227\pi$
$6$		0			0
$7$	2.16592	+	1.51947i	0.818642	+	0.574304i
$7$	2.16592	+	1.51947i	0.818642	+	0.574304i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.66300	+	2.69219i	−1.40595	+	0.811725i	−0.994994	−	0.0999316i	$-0.968138\pi$
$11$	−4.66300	+	2.69219i	−1.40595	+	0.811725i	−0.410954	+	0.911656i	$0.634804\pi$
$12$		0			0
$13$		−	5.31524i		−	1.47418i	−0.675794	−	0.737091i	$-0.736199\pi$
$13$		−	5.31524i		−	1.47418i	0.675794	−	0.737091i	$-0.263801\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.89092	+	3.27516i	0.458615	+	0.794344i	0.998888	−	0.0471458i	$-0.0150125\pi$
$17$	1.89092	+	3.27516i	0.458615	+	0.794344i	−0.540273	+	0.841490i	$0.681679\pi$
$18$		0			0
$19$	−4.33939	−	2.50535i	−0.995525	−	0.574767i	−0.0886040	−	0.996067i	$-0.528241\pi$
$19$	−4.33939	−	2.50535i	−0.995525	−	0.574767i	−0.906921	+	0.421300i	$0.861574\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.02463	+	1.16892i	0.422164	+	0.243737i	0.696003	−	0.718039i	$-0.254960\pi$
$23$	2.02463	+	1.16892i	0.422164	+	0.243737i	−0.273839	+	0.961776i	$0.588293\pi$
$24$		0			0
$25$	2.49708	+	4.32507i	0.499416	+	0.865014i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			10.2125i			1.89642i	0.317648	+	0.948209i	$0.397107\pi$
$29$			10.2125i			1.89642i	−0.317648	+	0.948209i	$0.602893\pi$
$30$		0			0
$31$	−4.97636	+	2.87310i	−0.893780	+	0.516024i	−0.875177	−	0.483803i	$-0.839255\pi$
$31$	−4.97636	+	2.87310i	−0.893780	+	0.516024i	−0.0186031	+	0.999827i	$0.505922\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.183331	−	0.0852905i	0.0309887	−	0.0144167i
$36$		0			0
$37$	0.354486	−	0.613988i	0.0582771	−	0.100939i	−0.835415	−	0.549620i	$-0.814773\pi$
$37$	0.354486	−	0.613988i	0.0582771	−	0.100939i	0.893692	+	0.448681i	$0.148106\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.59821			1.03047			0.515234	−	0.857050i	$-0.327705\pi$
$41$	6.59821			1.03047			0.515234	+	0.857050i	$0.327705\pi$
$42$		0			0
$43$	−1.43304			−0.218537			−0.109268	−	0.994012i	$-0.534851\pi$
$43$	−1.43304			−0.218537			−0.109268	+	0.994012i	$0.534851\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.46192	−	2.53213i	0.213244	−	0.369349i	−0.739484	−	0.673174i	$-0.764931\pi$
$47$	1.46192	−	2.53213i	0.213244	−	0.369349i	0.952728	+	0.303825i	$0.0982639\pi$
$48$		0			0
$49$	2.38244	+	6.58209i	0.340349	+	0.940299i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.4835	+	6.05264i	−1.44002	+	0.831394i	−0.997850	−	0.0655390i	$-0.979123\pi$
$53$	−10.4835	+	6.05264i	−1.44002	+	0.831394i	−0.442167	+	0.896933i	$0.645790\pi$
$54$		0			0
$55$			0.411498i			0.0554863i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.289951	+	0.502210i	0.0377484	+	0.0653822i	0.884282	−	0.466953i	$-0.154648\pi$
$59$	0.289951	+	0.502210i	0.0377484	+	0.0653822i	−0.846534	+	0.532335i	$0.821315\pi$
$60$		0			0
$61$	2.40641	+	1.38934i	0.308109	+	0.177887i	0.646080	−	0.763270i	$-0.276407\pi$
$61$	2.40641	+	1.38934i	0.308109	+	0.177887i	−0.337971	+	0.941156i	$0.609741\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.351792	−	0.203107i	−0.0436344	−	0.0251923i
$66$		0			0
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	0.658877	−	0.752251i	$-0.271032\pi$
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	−0.980907	+	0.194479i	$0.937698\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			3.32103i			0.394134i	0.980390	+	0.197067i	$0.0631416\pi$
$71$			3.32103i			0.394134i	−0.980390	+	0.197067i	$0.936858\pi$
$72$		0			0
$73$	−6.17326	+	3.56413i	−0.722525	+	0.417150i	−0.815681	−	0.578502i	$-0.803638\pi$
$73$	−6.17326	+	3.56413i	−0.722525	+	0.417150i	0.0931564	+	0.995651i	$0.470304\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−14.1904	−	1.25421i	−1.61714	−	0.142930i
$78$		0			0
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	−0.891208	−	0.453594i	$-0.850142\pi$
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	0.838428	+	0.545012i	$0.183475\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−12.9958			−1.42648			−0.713238	−	0.700922i	$-0.752772\pi$
$83$	−12.9958			−1.42648			−0.713238	+	0.700922i	$0.752772\pi$
$84$		0			0
$85$	0.289025			0.0313491
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.51794	−	2.62915i	0.160901	−	0.278689i	−0.774291	−	0.632830i	$-0.781893\pi$
$89$	1.51794	−	2.62915i	0.160901	−	0.278689i	0.935192	+	0.354141i	$0.115227\pi$
$90$		0			0
$91$	8.07632	−	11.5124i	0.846629	−	1.20683i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.331636	+	0.191470i	−0.0340251	+	0.0196444i
$96$		0			0
$97$		−	7.13816i		−	0.724771i	−0.932028	−	0.362385i	$-0.881962\pi$
$97$		−	7.13816i		−	0.724771i	0.932028	−	0.362385i	$-0.118038\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.08628	+	7.07765i	0.406600	+	0.704252i	0.994506	−	0.104677i	$-0.0333808\pi$
$101$	4.08628	+	7.07765i	0.406600	+	0.704252i	−0.587906	+	0.808929i	$0.700048\pi$
$102$		0			0
$103$	6.46599	+	3.73314i	0.637113	+	0.367837i	0.783502	−	0.621390i	$-0.213432\pi$
$103$	6.46599	+	3.73314i	0.637113	+	0.367837i	−0.146389	+	0.989227i	$0.546765\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.99991	−	2.30935i	−0.386686	−	0.223253i	0.294037	−	0.955794i	$-0.405001\pi$
$107$	−3.99991	−	2.30935i	−0.386686	−	0.223253i	−0.680723	+	0.732541i	$0.738334\pi$
$108$		0			0
$109$	5.22792	+	9.05503i	0.500744	+	0.867314i	1.00000		0.000859385i	$0.000273551\pi$
$109$	5.22792	+	9.05503i	0.500744	+	0.867314i	−0.499256	+	0.866455i	$0.666393\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			19.2118i			1.80730i	0.428275	+	0.903648i	$0.359121\pi$
$113$			19.2118i			1.80730i	−0.428275	+	0.903648i	$0.640879\pi$
$114$		0			0
$115$	0.154731	−	0.0893340i	0.0144287	−	0.00833044i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.880922	+	9.96693i	−0.0807540	+	0.913667i
$120$		0			0
$121$	8.99573	−	15.5811i	0.817793	−	1.41646i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.763798			0.0683162
$126$		0			0
$127$	1.26488			0.112240			0.0561198	−	0.998424i	$-0.482127\pi$
$127$	1.26488			0.112240			0.0561198	+	0.998424i	$0.482127\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.24394	+	12.5469i	−0.632906	+	1.09623i	0.354049	+	0.935227i	$0.384805\pi$
$131$	−7.24394	+	12.5469i	−0.632906	+	1.09623i	−0.986955	+	0.160998i	$0.948529\pi$
$132$		0			0
$133$	−5.59200	−	12.0200i	−0.484888	−	1.04226i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.3414	−	7.70264i	1.13983	−	0.658081i	0.193442	−	0.981112i	$-0.438035\pi$
$137$	13.3414	−	7.70264i	1.13983	−	0.658081i	0.946389	+	0.323030i	$0.104702\pi$
$138$		0			0
$139$		−	0.432667i		−	0.0366983i	−0.999832	−	0.0183492i	$-0.994159\pi$
$139$		−	0.432667i		−	0.0366983i	0.999832	−	0.0183492i	$-0.00584105\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	14.3096	+	24.7850i	1.19663	+	2.07262i
$144$		0			0
$145$	0.675921	+	0.390243i	0.0561322	+	0.0324079i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.04535	+	2.33558i	0.331408	+	0.191338i	0.656466	−	0.754356i	$-0.272051\pi$
$149$	4.04535	+	2.33558i	0.331408	+	0.191338i	−0.325058	+	0.945694i	$0.605384\pi$
$150$		0			0
$151$	4.12276	+	7.14083i	0.335506	+	0.581113i	0.983582	−	0.180463i	$-0.0577595\pi$
$151$	4.12276	+	7.14083i	0.335506	+	0.581113i	−0.648076	+	0.761575i	$0.724426\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			0.439151i			0.0352734i
$156$		0			0
$157$	−15.2334	+	8.79500i	−1.21576	+	0.701917i	−0.964007	−	0.265875i	$-0.914339\pi$
$157$	−15.2334	+	8.79500i	−1.21576	+	0.701917i	−0.251749	+	0.967793i	$0.581006\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.60905	+	5.60814i	0.205622	+	0.441984i
$162$		0			0
$163$	−5.27097	+	9.12959i	−0.412854	+	0.715085i	−0.995201	−	0.0978563i	$-0.968801\pi$
$163$	−5.27097	+	9.12959i	−0.412854	+	0.715085i	0.582346	+	0.812941i	$0.302135\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.18293			−0.710596			−0.355298	−	0.934753i	$-0.615621\pi$
$167$	−9.18293			−0.710596			−0.355298	+	0.934753i	$0.615621\pi$
$168$		0			0
$169$	−15.2517			−1.17321
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.22358	−	2.11931i	0.0930274	−	0.161128i	−0.815756	−	0.578396i	$-0.803679\pi$
$173$	1.22358	−	2.11931i	0.0930274	−	0.161128i	0.908784	+	0.417268i	$0.137012\pi$
$174$		0			0
$175$	−1.16332	+	13.1620i	−0.0879384	+	0.994953i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.05509	+	2.91856i	−0.377835	+	0.218143i	−0.676876	−	0.736097i	$-0.736667\pi$
$179$	−5.05509	+	2.91856i	−0.377835	+	0.218143i	0.299041	+	0.954240i	$0.403333\pi$
$180$		0			0
$181$			16.0704i			1.19451i	0.802053	+	0.597253i	$0.203741\pi$
$181$			16.0704i			1.19451i	−0.802053	+	0.597253i	$0.796259\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.0270914	−	0.0469237i	−0.00199180	−	0.00344990i
$186$		0			0
$187$	−17.6347	−	10.1814i	−1.28958	−	0.744537i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.90415	−	3.98611i	−0.499567	−	0.288425i	0.228968	−	0.973434i	$-0.426465\pi$
$191$	−6.90415	−	3.98611i	−0.499567	−	0.288425i	−0.728535	+	0.685009i	$0.759798\pi$
$192$		0			0
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	0.852814	−	0.522214i	$-0.174894\pi$
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	−0.878658	+	0.477452i	$0.841560\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	13.5035i		−	0.962083i	−0.876698	−	0.481042i	$-0.840259\pi$
$197$		−	13.5035i		−	0.962083i	0.876698	−	0.481042i	$-0.159741\pi$
$198$		0			0
$199$	21.2568	−	12.2726i	1.50685	−	0.869983i	0.506886	−	0.862013i	$-0.330797\pi$
$199$	21.2568	−	12.2726i	1.50685	−	0.869983i	0.999968	−	0.00796947i	$-0.00253679\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−15.5176	+	22.1195i	−1.08912	+	1.55249i
$204$		0			0
$205$	0.252132	−	0.436706i	0.0176097	−	0.0305009i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	26.9795			1.86621
$210$		0			0
$211$	23.5675			1.62245			0.811227	−	0.584731i	$-0.198800\pi$
$211$	23.5675			1.62245			0.811227	+	0.584731i	$0.198800\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.0547597	+	0.0948465i	−0.00373458	+	0.00646848i
$216$		0			0
$217$	−15.1440	−	1.33849i	−1.02804	−	0.0908628i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.4083	−	10.0507i	1.17101	−	0.676081i
$222$		0			0
$223$			7.47655i			0.500667i	0.968160	+	0.250334i	$0.0805403\pi$
$223$			7.47655i			0.500667i	−0.968160	+	0.250334i	$0.919460\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.318701	+	0.552006i	0.0211529	+	0.0366379i	0.876408	−	0.481569i	$-0.159933\pi$
$227$	0.318701	+	0.552006i	0.0211529	+	0.0366379i	−0.855255	+	0.518207i	$0.826600\pi$
$228$		0			0
$229$	1.58351	+	0.914239i	0.104641	+	0.0604146i	0.551407	−	0.834236i	$-0.314091\pi$
$229$	1.58351	+	0.914239i	0.104641	+	0.0604146i	−0.446766	+	0.894651i	$0.647424\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.4232	−	10.0593i	−1.14143	−	0.659007i	−0.194649	−	0.980873i	$-0.562357\pi$
$233$	−17.4232	−	10.0593i	−1.14143	−	0.659007i	−0.946785	+	0.321866i	$0.895690\pi$
$234$		0			0
$235$	−0.111727	−	0.193516i	−0.00728825	−	0.0126236i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			2.78808i			0.180346i	0.995926	+	0.0901730i	$0.0287420\pi$
$239$			2.78808i			0.180346i	−0.995926	+	0.0901730i	$0.971258\pi$
$240$		0			0
$241$	20.0304	−	11.5645i	1.29027	−	0.744938i	0.311568	−	0.950224i	$-0.399146\pi$
$241$	20.0304	−	11.5645i	1.29027	−	0.744938i	0.978702	+	0.205286i	$0.0658126\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.526678	+	0.0938333i	0.0336482	+	0.00599479i
$246$		0			0
$247$	−13.3165	+	23.0649i	−0.847310	+	1.46758i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.6541			−1.17743			−0.588717	−	0.808339i	$-0.700367\pi$
$251$	−18.6541			−1.17743			−0.588717	+	0.808339i	$0.700367\pi$
$252$		0			0
$253$	−12.5878			−0.791388
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.43687	−	9.41694i	0.339143	−	0.587413i	−0.645129	−	0.764074i	$-0.723196\pi$
$257$	5.43687	−	9.41694i	0.339143	−	0.587413i	0.984272	+	0.176661i	$0.0565297\pi$
$258$		0			0
$259$	1.70072	−	0.791220i	0.105678	−	0.0491640i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−16.4519	+	9.49852i	−1.01447	+	0.585704i	−0.912497	−	0.409083i	$-0.865849\pi$
$263$	−16.4519	+	9.49852i	−1.01447	+	0.585704i	−0.101972	+	0.994787i	$0.532515\pi$
$264$		0			0
$265$			0.925140i			0.0568309i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.29788	+	7.44415i	0.262046	+	0.453878i	0.966786	−	0.255589i	$-0.0822693\pi$
$269$	4.29788	+	7.44415i	0.262046	+	0.453878i	−0.704739	+	0.709467i	$0.748936\pi$
$270$		0			0
$271$	1.58706	+	0.916292i	0.0964073	+	0.0556608i	0.547429	−	0.836852i	$-0.315607\pi$
$271$	1.58706	+	0.916292i	0.0964073	+	0.0556608i	−0.451021	+	0.892513i	$0.648940\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−23.2878	−	13.4452i	−1.40431	−	0.810776i
$276$		0			0
$277$	−7.90931	−	13.6993i	−0.475224	−	0.823113i	0.524373	−	0.851489i	$-0.324300\pi$
$277$	−7.90931	−	13.6993i	−0.475224	−	0.823113i	−0.999597	+	0.0283760i	$0.990966\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	11.4998i		−	0.686023i	−0.939331	−	0.343012i	$-0.888553\pi$
$281$		−	11.4998i		−	0.686023i	0.939331	−	0.343012i	$-0.111447\pi$
$282$		0			0
$283$	8.59806	−	4.96409i	0.511101	−	0.295085i	−0.222185	−	0.975005i	$-0.571319\pi$
$283$	8.59806	−	4.96409i	0.511101	−	0.295085i	0.733286	+	0.679920i	$0.237986\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.2912	+	10.0258i	0.843584	+	0.591802i
$288$		0			0
$289$	1.34887	−	2.33631i	0.0793454	−	0.137430i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	17.2720			1.00904			0.504520	−	0.863400i	$-0.331670\pi$
$293$	17.2720			1.00904			0.504520	+	0.863400i	$0.331670\pi$
$294$		0			0
$295$	0.0443187			0.00258034
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.21308	−	10.7614i	0.359312	−	0.622346i
$300$		0			0
$301$	−3.10385	−	2.17746i	−0.178903	−	0.125507i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.183908	−	0.106180i	0.0105306	−	0.00607982i
$306$		0			0
$307$		−	21.6425i		−	1.23520i	−0.786490	−	0.617602i	$-0.788104\pi$
$307$		−	21.6425i		−	1.23520i	0.786490	−	0.617602i	$-0.211896\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.1016	−	17.4964i	−0.572808	−	0.992133i	−0.996276	−	0.0862215i	$-0.972521\pi$
$311$	−10.1016	−	17.4964i	−0.572808	−	0.992133i	0.423468	−	0.905911i	$-0.360813\pi$
$312$		0			0
$313$	18.9146	+	10.9203i	1.06911	+	0.617254i	0.927939	−	0.372731i	$-0.121579\pi$
$313$	18.9146	+	10.9203i	1.06911	+	0.617254i	0.141175	+	0.989985i	$0.454912\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.5288	−	12.4297i	−1.20918	−	0.698120i	−0.246599	−	0.969117i	$-0.579313\pi$
$317$	−21.5288	−	12.4297i	−1.20918	−	0.698120i	−0.962580	+	0.270997i	$0.912647\pi$
$318$		0			0
$319$	−27.4940	−	47.6210i	−1.53937	−	2.66626i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	18.9496i		−	1.05439i
$324$		0			0
$325$	22.9888	−	13.2726i	1.27519	−	0.736230i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.01390	−	3.26305i	0.386689	−	0.179898i
$330$		0			0
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	−0.997960	−	0.0638459i	$-0.979663\pi$
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	0.554272	+	0.832336i	$0.312997\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.402898			−0.0220127
$336$		0			0
$337$	15.6304			0.851444			0.425722	−	0.904854i	$-0.360020\pi$
$337$	15.6304			0.851444			0.425722	+	0.904854i	$0.360020\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.4698	−	26.7946i	0.837739	−	1.45101i
$342$		0			0
$343$	−4.84108	+	17.8764i	−0.261394	+	0.965232i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	28.0445	−	16.1915i	1.50551	−	0.869206i	0.505529	−	0.862810i	$-0.331297\pi$
$347$	28.0445	−	16.1915i	1.50551	−	0.869206i	0.999980	−	0.00639573i	$-0.00203584\pi$
$348$		0			0
$349$			30.0708i			1.60965i	0.593510	+	0.804827i	$0.297742\pi$
$349$			30.0708i			1.60965i	−0.593510	+	0.804827i	$0.702258\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.50607	+	14.7329i	0.452733	+	0.784156i	0.998555	−	0.0537453i	$-0.0171159\pi$
$353$	8.50607	+	14.7329i	0.452733	+	0.784156i	−0.545822	+	0.837901i	$0.683783\pi$
$354$		0			0
$355$	0.219804	+	0.126904i	0.0116660	+	0.00673537i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−25.2692	−	14.5892i	−1.33366	−	0.769987i	−0.347798	−	0.937570i	$-0.613070\pi$
$359$	−25.2692	−	14.5892i	−1.33366	−	0.769987i	−0.985858	+	0.167583i	$0.946404\pi$
$360$		0			0
$361$	3.05356	+	5.28892i	0.160714	+	0.278364i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			0.544774i			0.0285148i
$366$		0			0
$367$	15.6981	−	9.06329i	0.819433	−	0.473100i	−0.0307880	−	0.999526i	$-0.509802\pi$
$367$	15.6981	−	9.06329i	0.819433	−	0.473100i	0.850221	+	0.526426i	$0.176468\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−31.9032	−	2.81975i	−1.65633	−	0.146394i
$372$		0			0
$373$	10.1823	−	17.6362i	0.527219	−	0.913170i	−0.472278	−	0.881450i	$-0.656568\pi$
$373$	10.1823	−	17.6362i	0.527219	−	0.913170i	0.999497	−	0.0317200i	$-0.0100985\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	54.2820			2.79566
$378$		0			0
$379$	−21.9961			−1.12986			−0.564931	−	0.825138i	$-0.691097\pi$
$379$	−21.9961			−1.12986			−0.564931	+	0.825138i	$0.691097\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.3127	−	28.2544i	0.833538	−	1.44373i	−0.0616774	−	0.998096i	$-0.519645\pi$
$383$	16.3127	−	28.2544i	0.833538	−	1.44373i	0.895215	−	0.445634i	$-0.147022\pi$
$384$		0			0
$385$	−0.625257	+	0.891272i	−0.0318660	+	0.0454234i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.6400	−	7.87504i	0.691574	−	0.399280i	−0.112628	−	0.993637i	$-0.535927\pi$
$389$	13.6400	−	7.87504i	0.691574	−	0.399280i	0.804201	+	0.594357i	$0.202593\pi$
$390$		0			0
$391$			8.84131i			0.447124i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.0358524	+	0.0620983i	0.00180393	+	0.00312450i
$396$		0			0
$397$	−2.95864	−	1.70817i	−0.148490	−	0.0857308i	0.423914	−	0.905702i	$-0.360656\pi$
$397$	−2.95864	−	1.70817i	−0.148490	−	0.0857308i	−0.572404	+	0.819972i	$0.693989\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.851348	+	0.491526i	0.0425143	+	0.0245456i	0.521106	−	0.853492i	$-0.325519\pi$
$401$	0.851348	+	0.491526i	0.0425143	+	0.0245456i	−0.478592	+	0.878037i	$0.658853\pi$
$402$		0			0
$403$	15.2712	+	26.4505i	0.760713	+	1.31759i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			3.81737i			0.189220i
$408$		0			0
$409$	−25.0195	+	14.4450i	−1.23714	+	0.714260i	−0.968508	−	0.248984i	$-0.919903\pi$
$409$	−25.0195	+	14.4450i	−1.23714	+	0.714260i	−0.268627	+	0.963244i	$0.586570\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.135080	+	1.52832i	−0.00664684	+	0.0752037i
$414$		0			0
$415$	−0.496599	+	0.860135i	−0.0243771	+	0.0422223i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.5785			0.614501			0.307251	−	0.951629i	$-0.400591\pi$
$419$	12.5785			0.614501			0.307251	+	0.951629i	$0.400591\pi$
$420$		0			0
$421$	26.0463			1.26942			0.634710	−	0.772750i	$-0.281120\pi$
$421$	26.0463			1.26942			0.634710	+	0.772750i	$0.281120\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9.44354	+	16.3567i	−0.458079	+	0.793416i
$426$		0			0
$427$	3.10104	+	6.66566i	0.150070	+	0.322574i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.28454	+	3.62838i	−0.302716	+	0.174773i	−0.643662	−	0.765310i	$-0.722586\pi$
$431$	−6.28454	+	3.62838i	−0.302716	+	0.174773i	0.340947	+	0.940083i	$0.389252\pi$
$432$		0			0
$433$		−	8.29113i		−	0.398446i	−0.979954	−	0.199223i	$-0.936158\pi$
$433$		−	8.29113i		−	0.398446i	0.979954	−	0.199223i	$-0.0638419\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.85710	−	10.1448i	−0.280183	−	0.485292i
$438$		0			0
$439$	2.83357	+	1.63596i	0.135239	+	0.0780802i	0.566093	−	0.824341i	$-0.308454\pi$
$439$	2.83357	+	1.63596i	0.135239	+	0.0780802i	−0.430854	+	0.902422i	$0.641788\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.46737	+	1.42454i	0.117228	+	0.0676817i	0.557468	−	0.830199i	$-0.311773\pi$
$443$	2.46737	+	1.42454i	0.117228	+	0.0676817i	−0.440239	+	0.897880i	$0.645106\pi$
$444$		0			0
$445$	−0.116008	−	0.200931i	−0.00549929	−	0.00952505i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			19.9802i			0.942925i	0.881886	+	0.471463i	$0.156274\pi$
$449$			19.9802i			0.942925i	−0.881886	+	0.471463i	$0.843726\pi$
$450$		0			0
$451$	−30.7675	+	17.7636i	−1.44878	+	0.836455i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.453339	−	0.974450i	−0.0212529	−	0.0456829i
$456$		0			0
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	−0.996697	−	0.0812053i	$-0.974123\pi$
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	0.568675	+	0.822563i	$0.307456\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.05908			0.421923			0.210962	−	0.977494i	$-0.432340\pi$
$461$	9.05908			0.421923			0.210962	+	0.977494i	$0.432340\pi$
$462$		0			0
$463$	−21.6454			−1.00595			−0.502974	−	0.864302i	$-0.667761\pi$
$463$	−21.6454			−1.00595			−0.502974	+	0.864302i	$0.667761\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.7761	−	23.8610i	0.637484	−	1.10415i	−0.348500	−	0.937309i	$-0.613309\pi$
$467$	13.7761	−	23.8610i	0.637484	−	1.10415i	0.985983	−	0.166845i	$-0.0533580\pi$
$468$		0			0
$469$	1.22800	−	13.8938i	0.0567038	−	0.641558i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.68227	−	3.85801i	0.307251	−	0.177392i
$474$		0			0
$475$		−	25.0242i		−	1.14819i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.47325	+	4.28380i	0.113006	+	0.195732i	0.916981	−	0.398931i	$-0.130619\pi$
$479$	2.47325	+	4.28380i	0.113006	+	0.195732i	−0.803975	+	0.594663i	$0.797285\pi$
$480$		0			0
$481$	−3.26349	−	1.88418i	−0.148802	−	0.0859110i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.472443	−	0.272765i	−0.0214525	−	0.0123856i
$486$		0			0
$487$	−4.78573	−	8.28913i	−0.216862	−	0.375616i	0.736985	−	0.675909i	$-0.236249\pi$
$487$	−4.78573	−	8.28913i	−0.216862	−	0.375616i	−0.953847	+	0.300293i	$0.902916\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			38.1062i			1.71971i	0.510538	+	0.859855i	$0.329446\pi$
$491$			38.1062i			1.71971i	−0.510538	+	0.859855i	$0.670554\pi$
$492$		0			0
$493$	−33.4477	+	19.3110i	−1.50641	+	0.869725i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.04620	+	7.19310i	−0.226353	+	0.322655i
$498$		0			0
$499$	12.4192	−	21.5107i	0.555960	−	0.962951i	−0.441868	−	0.897080i	$-0.645684\pi$
$499$	12.4192	−	21.5107i	0.555960	−	0.962951i	0.997828	−	0.0658709i	$-0.0209825\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.2820			−1.21645			−0.608223	−	0.793766i	$-0.708117\pi$
$503$	−27.2820			−1.21645			−0.608223	+	0.793766i	$0.708117\pi$
$504$		0			0
$505$	0.624584			0.0277936
$506$		0			0
$507$		0			0
$508$		0			0
$509$	20.8860	−	36.1757i	0.925758	−	1.60346i	0.135420	−	0.990788i	$-0.456762\pi$
$509$	20.8860	−	36.1757i	0.925758	−	1.60346i	0.790338	−	0.612671i	$-0.209905\pi$
$510$		0			0
$511$	−18.7864	−	1.66042i	−0.831060	−	0.0734528i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.494160	−	0.285303i	0.0217753	−	0.0125720i
$516$		0			0
$517$			15.7431i			0.692380i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.02629	+	3.50963i	0.0887732	+	0.153760i	0.906993	−	0.421146i	$-0.138372\pi$
$521$	2.02629	+	3.50963i	0.0887732	+	0.153760i	−0.818220	+	0.574906i	$0.805039\pi$
$522$		0			0
$523$	26.2429	+	15.1514i	1.14752	+	0.662523i	0.948282	−	0.317428i	$-0.102819\pi$
$523$	26.2429	+	15.1514i	1.14752	+	0.662523i	0.199241	+	0.979951i	$0.436152\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.8198	−	10.8656i	−0.819801	−	0.473312i
$528$		0			0
$529$	−8.76726	−	15.1853i	−0.381185	−	0.660232i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	35.0710i		−	1.51910i
$534$		0			0
$535$	−0.305691	+	0.176491i	−0.0132162	+	0.00763037i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−28.8296	−	24.2783i	−1.24178	−	1.04574i
$540$		0			0
$541$	8.82681	−	15.2885i	0.379494	−	0.657303i	−0.611495	−	0.791249i	$-0.709431\pi$
$541$	8.82681	−	15.2885i	0.379494	−	0.657303i	0.990989	+	0.133946i	$0.0427647\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.799082			0.0342289
$546$		0			0
$547$	4.36639			0.186693			0.0933466	−	0.995634i	$-0.470244\pi$
$547$	4.36639			0.186693			0.0933466	+	0.995634i	$0.470244\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	25.5859	−	44.3161i	1.09000	−	1.88793i
$552$		0			0
$553$	−2.25072	+	1.04709i	−0.0957102	+	0.0445269i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.7527	−	8.51750i	0.625094	−	0.360898i	−0.153756	−	0.988109i	$-0.549137\pi$
$557$	14.7527	−	8.51750i	0.625094	−	0.360898i	0.778849	+	0.627211i	$0.215804\pi$
$558$		0			0
$559$			7.61695i			0.322163i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.45992	+	11.1889i	0.272253	+	0.471556i	0.969438	−	0.245335i	$-0.0788978\pi$
$563$	6.45992	+	11.1889i	0.272253	+	0.471556i	−0.697185	+	0.716891i	$0.745564\pi$
$564$		0			0
$565$	1.27155	+	0.734127i	0.0534943	+	0.0308850i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.8280	−	10.8704i	−0.789313	−	0.455710i	0.0504079	−	0.998729i	$-0.483948\pi$
$569$	−18.8280	−	10.8704i	−0.789313	−	0.455710i	−0.839720	+	0.543019i	$0.817281\pi$
$570$		0			0
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	0.967007	+	0.254748i	$0.0819925\pi$
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	−0.262885	+	0.964827i	$0.584674\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			11.6755i			0.486904i
$576$		0			0
$577$	12.5598	−	7.25141i	0.522871	−	0.301880i	−0.215237	−	0.976562i	$-0.569052\pi$
$577$	12.5598	−	7.25141i	0.522871	−	0.301880i	0.738109	+	0.674682i	$0.235719\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−28.1479	−	19.7467i	−1.16777	−	0.819231i
$582$		0			0
$583$	32.5897	−	56.4469i	1.34973	−	2.33779i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	31.6834			1.30771			0.653857	−	0.756618i	$-0.273150\pi$
$587$	31.6834			1.30771			0.653857	+	0.756618i	$0.273150\pi$
$588$		0			0
$589$	28.7925			1.18637
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.54101	−	6.13320i	0.145412	−	0.251860i	−0.784115	−	0.620616i	$-0.786883\pi$
$593$	3.54101	−	6.13320i	0.145412	−	0.251860i	0.929526	+	0.368755i	$0.120216\pi$
$594$		0			0
$595$	0.626005	+	0.439163i	0.0256637	+	0.0180039i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.20178	+	3.00325i	−0.212539	+	0.122709i	−0.602491	−	0.798126i	$-0.705825\pi$
$599$	−5.20178	+	3.00325i	−0.212539	+	0.122709i	0.389952	+	0.920835i	$0.372492\pi$
$600$		0			0
$601$			0.612087i			0.0249675i	0.999922	+	0.0124838i	$0.00397381\pi$
$601$			0.612087i			0.0249675i	−0.999922	+	0.0124838i	$0.996026\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.687494	−	1.19077i	−0.0279506	−	0.0484119i
$606$		0			0
$607$	−1.77500	−	1.02480i	−0.0720450	−	0.0415952i	0.463545	−	0.886073i	$-0.346577\pi$
$607$	−1.77500	−	1.02480i	−0.0720450	−	0.0415952i	−0.535590	+	0.844478i	$0.679911\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.4588	−	7.77047i	−0.544487	−	0.314360i
$612$		0			0
$613$	−4.93166	−	8.54189i	−0.199188	−	0.345003i	0.749077	−	0.662482i	$-0.230497\pi$
$613$	−4.93166	−	8.54189i	−0.199188	−	0.345003i	−0.948265	+	0.317479i	$0.897164\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	26.8055i		−	1.07915i	−0.841937	−	0.539575i	$-0.818585\pi$
$617$		−	26.8055i		−	1.07915i	0.841937	−	0.539575i	$-0.181415\pi$
$618$		0			0
$619$	−0.0603011	+	0.0348148i	−0.00242370	+	0.00139933i	−0.501211	−	0.865325i	$-0.667112\pi$
$619$	−0.0603011	+	0.0348148i	−0.00242370	+	0.00139933i	0.498788	+	0.866724i	$0.333779\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.28264	−	3.38807i	0.291773	−	0.135740i
$624$		0			0
$625$	−12.4562	+	21.5748i	−0.498248	+	0.862992i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.68121			0.106907
$630$		0			0
$631$	11.8214			0.470603			0.235301	−	0.971922i	$-0.424392\pi$
$631$	11.8214			0.470603			0.235301	+	0.971922i	$0.424392\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.0483338	−	0.0837165i	0.00191807	−	0.00332219i
$636$		0			0
$637$	34.9854	−	12.6632i	1.38617	−	0.501736i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.7673	−	10.2580i	0.701766	−	0.405165i	−0.106239	−	0.994341i	$-0.533881\pi$
$641$	17.7673	−	10.2580i	0.701766	−	0.405165i	0.808005	+	0.589176i	$0.200547\pi$
$642$		0			0
$643$		−	18.0226i		−	0.710743i	−0.934725	−	0.355372i	$-0.884354\pi$
$643$		−	18.0226i		−	0.710743i	0.934725	−	0.355372i	$-0.115646\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.11827	+	15.7933i	0.358476	+	0.620899i	0.987706	−	0.156320i	$-0.0499631\pi$
$647$	9.11827	+	15.7933i	0.358476	+	0.620899i	−0.629230	+	0.777219i	$0.716630\pi$
$648$		0			0
$649$	−2.70409	−	1.56121i	−0.106145	−	0.0612827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.79559	+	4.50079i	0.305065	+	0.176129i	0.644716	−	0.764422i	$-0.276976\pi$
$653$	7.79559	+	4.50079i	0.305065	+	0.176129i	−0.339651	+	0.940552i	$0.610309\pi$
$654$		0			0
$655$	0.553614	+	0.958888i	0.0216315	+	0.0374669i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			35.1959i			1.37104i	0.728055	+	0.685519i	$0.240425\pi$
$659$			35.1959i			1.37104i	−0.728055	+	0.685519i	$0.759575\pi$
$660$		0			0
$661$	10.8797	−	6.28141i	0.423172	−	0.244318i	−0.273262	−	0.961940i	$-0.588102\pi$
$661$	10.8797	−	6.28141i	0.423172	−	0.244318i	0.696433	+	0.717621i	$0.254769\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.00923	−	0.0892002i	−0.0391363	−	0.00345904i
$666$		0			0
$667$	−11.9376	+	20.6765i	−0.462226	+	0.800599i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.9614			−0.577580
$672$		0			0
$673$	−47.7826			−1.84188			−0.920942	−	0.389699i	$-0.872579\pi$
$673$	−47.7826			−1.84188			−0.920942	+	0.389699i	$0.872579\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.5235	−	32.0837i	0.711918	−	1.23308i	−0.252219	−	0.967670i	$-0.581160\pi$
$677$	18.5235	−	32.0837i	0.711918	−	1.23308i	0.964136	−	0.265407i	$-0.0855064\pi$
$678$		0			0
$679$	10.8462	−	15.4607i	0.416239	−	0.593328i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.6844	−	12.5195i	0.829732	−	0.479046i	−0.0240289	−	0.999711i	$-0.507649\pi$
$683$	21.6844	−	12.5195i	0.829732	−	0.479046i	0.853761	+	0.520665i	$0.174316\pi$
$684$		0			0
$685$		−	1.17734i		−	0.0449839i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	32.1712	+	55.7222i	1.22563	+	2.12285i
$690$		0			0
$691$	−40.2655	−	23.2473i	−1.53177	−	0.884370i	−0.999280	−	0.0379352i	$-0.987922\pi$
$691$	−40.2655	−	23.2473i	−1.53177	−	0.884370i	−0.532493	−	0.846434i	$-0.678745\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.0286363	−	0.0165332i	−0.00108624	−	0.000627139i
$696$		0			0
$697$	12.4767	+	21.6102i	0.472587	+	0.818545i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	36.0041i		−	1.35986i	−0.733279	−	0.679928i	$-0.762011\pi$
$701$		−	36.0041i		−	1.35986i	0.733279	−	0.679928i	$-0.237989\pi$
$702$		0			0
$703$	−3.07651	+	1.77622i	−0.116033	+	0.0669915i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.90368	+	21.5386i	−0.0715952	+	0.810043i
$708$		0			0
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	0.395424	+	0.918499i	$0.370598\pi$
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	−0.993155	+	0.116802i	$0.962736\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.4337			−0.503096
$714$		0			0
$715$	2.18721			0.0817969
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.0271	−	34.6879i	0.746883	−	1.29364i	−0.202427	−	0.979297i	$-0.564883\pi$
$719$	20.0271	−	34.6879i	0.746883	−	1.29364i	0.949310	−	0.314342i	$-0.101784\pi$
$720$		0			0
$721$	8.33245	+	17.9106i	0.310317	+	0.667024i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−44.1699	+	25.5015i	−1.64043	+	0.947101i
$726$		0			0
$727$			3.91723i			0.145282i	0.997358	+	0.0726411i	$0.0231428\pi$
$727$			3.91723i			0.145282i	−0.997358	+	0.0726411i	$0.976857\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.70976	−	4.69344i	−0.100224	−	0.173593i
$732$		0			0
$733$	−20.4239	−	11.7918i	−0.754376	−	0.435539i	0.0728971	−	0.997339i	$-0.476776\pi$
$733$	−20.4239	−	11.7918i	−0.754376	−	0.435539i	−0.827273	+	0.561800i	$0.810109\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.5827	+	14.1928i	0.905514	+	0.522798i
$738$		0			0
$739$	16.8641	+	29.2094i	0.620355	+	1.07449i	0.989420	+	0.145083i	$0.0463448\pi$
$739$	16.8641	+	29.2094i	0.620355	+	1.07449i	−0.369065	+	0.929404i	$0.620322\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	33.9485i		−	1.24545i	−0.782441	−	0.622725i	$-0.786025\pi$
$743$		−	33.9485i		−	1.24545i	0.782441	−	0.622725i	$-0.213975\pi$
$744$		0			0
$745$	0.309164	−	0.178496i	0.0113269	−	0.00653958i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.15452	−	11.0796i	−0.188342	−	0.404840i
$750$		0			0
$751$	−1.69831	+	2.94157i	−0.0619724	+	0.107339i	−0.895347	−	0.445369i	$-0.853072\pi$
$751$	−1.69831	+	2.94157i	−0.0619724	+	0.107339i	0.833375	+	0.552709i	$0.186406\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.630160			0.0229339
$756$		0			0
$757$	29.1344			1.05891			0.529454	−	0.848339i	$-0.322397\pi$
$757$	29.1344			1.05891			0.529454	+	0.848339i	$0.322397\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.36288	−	14.4849i	0.303154	−	0.525079i	−0.673694	−	0.739010i	$-0.735294\pi$
$761$	8.36288	−	14.4849i	0.303154	−	0.525079i	0.976849	+	0.213931i	$0.0686269\pi$
$762$		0			0
$763$	−2.43553	+	27.5561i	−0.0881723	+	0.997599i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.66937	−	1.54116i	0.0963852	−	0.0556480i
$768$		0			0
$769$		−	27.8070i		−	1.00275i	−0.865231	−	0.501373i	$-0.832828\pi$
$769$		−	27.8070i		−	1.00275i	0.865231	−	0.501373i	$-0.167172\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.42238	+	11.1239i	0.230997	+	0.400098i	0.958102	−	0.286428i	$-0.0924679\pi$
$773$	6.42238	+	11.1239i	0.230997	+	0.400098i	−0.727105	+	0.686526i	$0.759135\pi$
$774$		0			0
$775$	−24.8527	−	14.3487i	−0.892736	−	0.515421i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−28.6322	−	16.5308i	−1.02586	−	0.592278i
$780$		0			0
$781$	−8.94083	−	15.4860i	−0.319928	−	0.554132i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			1.34431i			0.0479804i
$786$		0			0
$787$	−6.55243	+	3.78305i	−0.233569	+	0.134851i	−0.612217	−	0.790689i	$-0.709722\pi$
$787$	−6.55243	+	3.78305i	−0.233569	+	0.134851i	0.378648	+	0.925541i	$0.376389\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−29.1917	+	41.6113i	−1.03794	+	1.47953i
$792$		0			0
$793$	7.38467	−	12.7906i	0.262237	−	0.454208i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.06724			−0.285756			−0.142878	−	0.989740i	$-0.545636\pi$
$797$	−8.06724			−0.285756			−0.142878	+	0.989740i	$0.545636\pi$
$798$		0			0
$799$	11.0575			0.391186
$800$		0			0
$801$		0			0
$802$		0			0
$803$	19.1906	−	33.2391i	0.677222	−	1.17298i
$804$		0			0
$805$	0.470876	+	0.0416181i	0.0165962	+	0.00146684i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0849492	−	0.0490454i	0.00298665	−	0.00172435i	−0.498506	−	0.866886i	$-0.666118\pi$
$809$	0.0849492	−	0.0490454i	0.00298665	−	0.00172435i	0.501493	+	0.865162i	$0.332784\pi$
$810$		0			0
$811$			30.3085i			1.06428i	0.846658	+	0.532138i	$0.178611\pi$
$811$			30.3085i			1.06428i	−0.846658	+	0.532138i	$0.821389\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.402831	+	0.697724i	0.0141106	+	0.0244402i
$816$		0			0
$817$	6.21853	+	3.59027i	0.217559	+	0.125608i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.5499	−	11.2871i	−0.682295	−	0.393923i	0.118424	−	0.992963i	$-0.462216\pi$
$821$	−19.5499	−	11.2871i	−0.682295	−	0.393923i	−0.800719	+	0.599040i	$0.795549\pi$
$822$		0			0
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	0.996655	−	0.0817282i	$-0.0260439\pi$
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	−0.569106	+	0.822264i	$0.692711\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			40.3057i			1.40157i	0.713375	+	0.700783i	$0.247166\pi$
$827$			40.3057i			1.40157i	−0.713375	+	0.700783i	$0.752834\pi$
$828$		0			0
$829$	−46.8081	+	27.0247i	−1.62571	+	0.938605i	−0.640359	+	0.768076i	$0.721214\pi$
$829$	−46.8081	+	27.0247i	−1.62571	+	0.938605i	−0.985353	+	0.170529i	$0.945452\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−17.0524	+	20.2491i	−0.590832	+	0.701589i
$834$		0			0
$835$	−0.350900	+	0.607777i	−0.0121434	+	0.0210330i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−23.7299			−0.819247			−0.409624	−	0.912255i	$-0.634340\pi$
$839$	−23.7299			−0.819247			−0.409624	+	0.912255i	$0.634340\pi$
$840$		0			0
$841$	−75.2956			−2.59640
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.582803	+	1.00944i	−0.0200490	+	0.0347259i
$846$		0			0
$847$	43.1589	−	20.0787i	1.48296	−	0.689911i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.43540	−	0.828731i	0.0492050	−	0.0284085i
$852$		0			0
$853$		−	55.5120i		−	1.90069i	−0.311191	−	0.950347i	$-0.600728\pi$
$853$		−	55.5120i		−	1.90069i	0.311191	−	0.950347i	$-0.399272\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.3048	+	26.5088i	0.522803	+	0.905522i	0.999648	+	0.0265343i	$0.00844714\pi$
$857$	15.3048	+	26.5088i	0.522803	+	0.905522i	−0.476845	+	0.878988i	$0.658220\pi$
$858$		0			0
$859$	36.4944	+	21.0700i	1.24517	+	0.718900i	0.970143	−	0.242535i	$-0.0779790\pi$
$859$	36.4944	+	21.0700i	1.24517	+	0.718900i	0.275030	+	0.961436i	$0.411312\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−22.7782	−	13.1510i	−0.775379	−	0.447665i	0.0594112	−	0.998234i	$-0.481078\pi$
$863$	−22.7782	−	13.1510i	−0.775379	−	0.447665i	−0.834790	+	0.550568i	$0.814411\pi$
$864$		0			0
$865$	−0.0935118	−	0.161967i	−0.00317950	−	0.00550705i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	5.05186i		−	0.171373i
$870$		0			0
$871$	−24.2670	+	14.0106i	−0.822256	+	0.474730i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.65433	+	1.16057i	0.0559265	+	0.0392343i
$876$		0			0
$877$	−17.8533	+	30.9228i	−0.602863	+	1.04419i	0.389522	+	0.921017i	$0.372640\pi$
$877$	−17.8533	+	30.9228i	−0.602863	+	1.04419i	−0.992385	+	0.123172i	$0.960693\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.4482			0.419392			0.209696	−	0.977767i	$-0.432753\pi$
$881$	12.4482			0.419392			0.209696	+	0.977767i	$0.432753\pi$
$882$		0			0
$883$	2.35637			0.0792982			0.0396491	−	0.999214i	$-0.487376\pi$
$883$	2.35637			0.0792982			0.0396491	+	0.999214i	$0.487376\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.7299	+	28.9770i	−0.561734	+	0.972952i	0.435611	+	0.900135i	$0.356532\pi$
$887$	−16.7299	+	28.9770i	−0.561734	+	0.972952i	−0.997345	+	0.0728170i	$0.976801\pi$
$888$		0			0
$889$	2.73962	+	1.92194i	0.0918841	+	0.0644597i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.6877	+	7.32526i	−0.424579	+	0.245131i
$894$		0			0
$895$			0.446099i			0.0149114i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−29.3416	−	50.8212i	−0.978597	−	1.69498i
$900$		0			0
$901$	−39.6468	−	22.8901i	−1.32083	−	0.762579i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.06363	+	0.614087i	0.0353563	+	0.0204130i
$906$		0			0
$907$	0.467962	+	0.810535i	0.0155384	+	0.0269134i	0.873690	−	0.486483i	$-0.161720\pi$
$907$	0.467962	+	0.810535i	0.0155384	+	0.0269134i	−0.858152	+	0.513396i	$0.828387\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			33.3407i			1.10463i	0.833637	+	0.552313i	$0.186255\pi$
$911$			33.3407i			1.10463i	−0.833637	+	0.552313i	$0.813745\pi$
$912$		0			0
$913$	60.5995	−	34.9871i	2.00555	−	1.15791i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−34.7544	+	16.1686i	−1.14769	+	0.533935i
$918$		0			0
$919$	−1.73484	+	3.00483i	−0.0572270	+	0.0991200i	−0.893220	−	0.449621i	$-0.851559\pi$
$919$	−1.73484	+	3.00483i	−0.0572270	+	0.0991200i	0.835993	+	0.548741i	$0.184893\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	17.6521			0.581025
$924$		0			0
$925$	3.54072			0.116418
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.57680	+	13.1234i	−0.248587	+	0.430565i	−0.963134	−	0.269022i	$-0.913299\pi$
$929$	−7.57680	+	13.1234i	−0.248587	+	0.430565i	0.714547	+	0.699587i	$0.246633\pi$
$930$		0			0
$931$	6.15209	−	34.5312i	0.201627	−	1.13171i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.34772	+	0.778108i	−0.0440752	+	0.0254468i
$936$		0			0
$937$		−	33.6651i		−	1.09979i	−0.835233	−	0.549896i	$-0.814667\pi$
$937$		−	33.6651i		−	1.09979i	0.835233	−	0.549896i	$-0.185333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.8980	+	32.7323i	0.616058	+	1.06704i	0.990198	+	0.139671i	$0.0446045\pi$
$941$	18.8980	+	32.7323i	0.616058	+	1.06704i	−0.374140	+	0.927372i	$0.622062\pi$
$942$		0			0
$943$	13.3589	+	7.71277i	0.435026	+	0.251162i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.47426	+	5.46997i	0.307872	+	0.177750i	0.645974	−	0.763360i	$-0.276452\pi$
$947$	9.47426	+	5.46997i	0.307872	+	0.177750i	−0.338102	+	0.941110i	$0.609785\pi$
$948$		0			0
$949$	18.9442	+	32.8123i	0.614955	+	1.06513i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			11.0914i			0.359284i	0.983732	+	0.179642i	$0.0574939\pi$
$953$			11.0914i			0.359284i	−0.983732	+	0.179642i	$0.942506\pi$
$954$		0			0
$955$	−0.527646	+	0.304637i	−0.0170742	+	0.00985781i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	40.6003	+	3.58843i	1.31105	+	0.115877i
$960$		0			0
$961$	1.00942	−	1.74838i	0.0325621	−	0.0563992i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.0548769			−0.00176655
$966$		0			0
$967$	−40.2892			−1.29561			−0.647807	−	0.761805i	$-0.724314\pi$
$967$	−40.2892			−1.29561			−0.647807	+	0.761805i	$0.724314\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.8458	+	41.3021i	−0.765248	+	1.32545i	0.174867	+	0.984592i	$0.444050\pi$
$971$	−23.8458	+	41.3021i	−0.765248	+	1.32545i	−0.940115	+	0.340856i	$0.889283\pi$
$972$		0			0
$973$	0.657423	−	0.937123i	0.0210760	−	0.0300428i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.4540	+	8.34504i	−0.462426	+	0.266982i	−0.713064	−	0.701099i	$-0.752693\pi$
$977$	−14.4540	+	8.34504i	−0.462426	+	0.266982i	0.250638	+	0.968081i	$0.419360\pi$
$978$		0			0
$979$			16.3463i			0.522430i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.9255	+	29.3157i	0.539838	+	0.935027i	0.998912	+	0.0466291i	$0.0148479\pi$
$983$	16.9255	+	29.3157i	0.539838	+	0.935027i	−0.459074	+	0.888398i	$0.651819\pi$
$984$		0			0
$985$	−0.893735	−	0.515998i	−0.0284768	−	0.0164411i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.90137	−	1.67511i	−0.0922583	−	0.0532653i
$990$		0			0
$991$	−4.09775	−	7.09751i	−0.130169	−	0.225460i	0.793572	−	0.608476i	$-0.208219\pi$
$991$	−4.09775	−	7.09751i	−0.130169	−	0.225460i	−0.923742	+	0.383016i	$0.874885\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	1.87586i		−	0.0594686i
$996$		0			0
$997$	18.7391	−	10.8190i	0.593472	−	0.342641i	−0.172997	−	0.984922i	$-0.555345\pi$
$997$	18.7391	−	10.8190i	0.593472	−	0.342641i	0.766469	+	0.642281i	$0.222012\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.b.2105.4		16
3.2	odd	2		2268.2.t.a.2105.5		16
7.3	odd	6		2268.2.t.a.1781.5		16
9.2	odd	6		756.2.w.a.341.5		16
9.4	even	3		756.2.bm.a.89.5		16
9.5	odd	6		252.2.bm.a.173.3	yes	16
9.7	even	3		252.2.w.a.5.1	✓	16
21.17	even	6	inner	2268.2.t.b.1781.4		16
36.7	odd	6		1008.2.ca.d.257.8		16
36.11	even	6		3024.2.ca.d.2609.5		16
36.23	even	6		1008.2.df.d.929.6		16
36.31	odd	6		3024.2.df.d.1601.5		16
63.2	odd	6		5292.2.x.a.881.5		16
63.4	even	3		5292.2.w.b.521.4		16
63.5	even	6		1764.2.x.a.1469.5		16
63.11	odd	6		5292.2.bm.a.2285.4		16
63.13	odd	6		5292.2.bm.a.4625.4		16
63.16	even	3		1764.2.x.a.293.5		16
63.20	even	6		5292.2.w.b.1097.4		16
63.23	odd	6		1764.2.x.b.1469.4		16
63.25	even	3		1764.2.bm.a.1697.6		16
63.31	odd	6		756.2.w.a.521.5		16
63.32	odd	6		1764.2.w.b.1109.8		16
63.34	odd	6		1764.2.w.b.509.8		16
63.38	even	6		756.2.bm.a.17.5		16
63.40	odd	6		5292.2.x.a.4409.5		16
63.41	even	6		1764.2.bm.a.1685.6		16
63.47	even	6		5292.2.x.b.881.4		16
63.52	odd	6		252.2.bm.a.185.3	yes	16
63.58	even	3		5292.2.x.b.4409.4		16
63.59	even	6		252.2.w.a.101.1	yes	16
63.61	odd	6		1764.2.x.b.293.4		16
252.31	even	6		3024.2.ca.d.2033.5		16
252.59	odd	6		1008.2.ca.d.353.8		16
252.115	even	6		1008.2.df.d.689.6		16
252.227	odd	6		3024.2.df.d.17.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.1	✓	16	9.7	even	3
252.2.w.a.101.1	yes	16	63.59	even	6
252.2.bm.a.173.3	yes	16	9.5	odd	6
252.2.bm.a.185.3	yes	16	63.52	odd	6
756.2.w.a.341.5		16	9.2	odd	6
756.2.w.a.521.5		16	63.31	odd	6
756.2.bm.a.17.5		16	63.38	even	6
756.2.bm.a.89.5		16	9.4	even	3
1008.2.ca.d.257.8		16	36.7	odd	6
1008.2.ca.d.353.8		16	252.59	odd	6
1008.2.df.d.689.6		16	252.115	even	6
1008.2.df.d.929.6		16	36.23	even	6
1764.2.w.b.509.8		16	63.34	odd	6
1764.2.w.b.1109.8		16	63.32	odd	6
1764.2.x.a.293.5		16	63.16	even	3
1764.2.x.a.1469.5		16	63.5	even	6
1764.2.x.b.293.4		16	63.61	odd	6
1764.2.x.b.1469.4		16	63.23	odd	6
1764.2.bm.a.1685.6		16	63.41	even	6
1764.2.bm.a.1697.6		16	63.25	even	3
2268.2.t.a.1781.5		16	7.3	odd	6
2268.2.t.a.2105.5		16	3.2	odd	2
2268.2.t.b.1781.4		16	21.17	even	6	inner
2268.2.t.b.2105.4		16	1.1	even	1	trivial
3024.2.ca.d.2033.5		16	252.31	even	6
3024.2.ca.d.2609.5		16	36.11	even	6
3024.2.df.d.17.5		16	252.227	odd	6
3024.2.df.d.1601.5		16	36.31	odd	6
5292.2.w.b.521.4		16	63.4	even	3
5292.2.w.b.1097.4		16	63.20	even	6
5292.2.x.a.881.5		16	63.2	odd	6
5292.2.x.a.4409.5		16	63.40	odd	6
5292.2.x.b.881.4		16	63.47	even	6
5292.2.x.b.4409.4		16	63.58	even	3
5292.2.bm.a.2285.4		16	63.11	odd	6
5292.2.bm.a.4625.4		16	63.13	odd	6

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0382122 - 0.0661855i) q^{5} +(2.16592 + 1.51947i) q^{7} +O(q^{10})\)	\(q+(0.0382122 - 0.0661855i) q^{5} +(2.16592 + 1.51947i) q^{7} +(-4.66300 + 2.69219i) q^{11} -5.31524i q^{13} +(1.89092 + 3.27516i) q^{17} +(-4.33939 - 2.50535i) q^{19} +(2.02463 + 1.16892i) q^{23} +(2.49708 + 4.32507i) q^{25} +10.2125i q^{29} +(-4.97636 + 2.87310i) q^{31} +(0.183331 - 0.0852905i) q^{35} +(0.354486 - 0.613988i) q^{37} +6.59821 q^{41} -1.43304 q^{43} +(1.46192 - 2.53213i) q^{47} +(2.38244 + 6.58209i) q^{49} +(-10.4835 + 6.05264i) q^{53} +0.411498i q^{55} +(0.289951 + 0.502210i) q^{59} +(2.40641 + 1.38934i) q^{61} +(-0.351792 - 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} +3.32103i q^{71} +(-6.17326 + 3.56413i) q^{73} +(-14.1904 - 1.25421i) q^{77} +(-0.469123 + 0.812544i) q^{79} -12.9958 q^{83} +0.289025 q^{85} +(1.51794 - 2.62915i) q^{89} +(8.07632 - 11.5124i) q^{91} +(-0.331636 + 0.191470i) q^{95} -7.13816i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{7}+O(q^{10}) \) 16 * q + 2 * q^7	\( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95}+O(q^{100}) \) 16 * q + 2 * q^7 + 6 * q^11 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^31 - 15 * q^35 + q^37 + 12 * q^41 + 4 * q^43 + 18 * q^47 - 8 * q^49 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - 48 * q^77 - q^79 - 12 * q^85 + 21 * q^89 + 9 * q^91 + 6 * q^95

Introduction

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