LMFDB - Embedded newform 756.2.w.a.341.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(341,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("756.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
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			341.5
Root			$1.08696 + 1.34852i$ of defining polynomial
Character	$\chi$	$=$	756.341
Dual form			756.2.w.a.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0382122 - 0.0661855i) q^{5} +(0.232935 - 2.63548i) q^{7} +O(q^{10})$	$q+(-0.0382122 - 0.0661855i) q^{5} +(0.232935 - 2.63548i) q^{7} +(-4.66300 - 2.69219i) q^{11} +(4.60313 + 2.65762i) q^{13} +(-1.89092 - 3.27516i) q^{17} +(-4.33939 - 2.50535i) q^{19} +(2.02463 - 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(-8.84430 + 5.10626i) q^{29} -5.74620i q^{31} +(-0.183331 + 0.0852905i) q^{35} +(0.354486 - 0.613988i) q^{37} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +2.92385 q^{47} +(-6.89148 - 1.22779i) q^{49} +(10.4835 - 6.05264i) q^{53} +0.411498i q^{55} +0.579903 q^{59} -2.77868i q^{61} -0.406214i q^{65} +5.27185 q^{67} -3.32103i q^{71} +(-6.17326 + 3.56413i) q^{73} +(-8.18137 + 11.6621i) q^{77} +0.938245 q^{79} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-1.51794 + 2.62915i) q^{89} +(8.07632 - 11.5124i) q^{91} +0.382940i q^{95} +(-6.18183 + 3.56908i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85} - 21 q^{89} + 9 q^{91} - 3 q^{97}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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	$-0.172107\pi$
$5$	−0.0382122	−	0.0661855i	−0.0170890	−	0.0295991i	−0.874443	+	0.485127i	$0.838773\pi$
$6$		0			0
$7$	0.232935	−	2.63548i	0.0880412	−	0.996117i
$7$	0.232935	−	2.63548i	0.0880412	−	0.996117i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.66300	−	2.69219i	−1.40595	−	0.811725i	−0.410954	−	0.911656i	$-0.634804\pi$
$11$	−4.66300	−	2.69219i	−1.40595	−	0.811725i	−0.994994	+	0.0999316i	$0.968138\pi$
$12$		0			0
$13$	4.60313	+	2.65762i	1.27668	+	0.737091i	0.976236	−	0.216709i	$-0.0695324\pi$
$13$	4.60313	+	2.65762i	1.27668	+	0.737091i	0.300442	+	0.953800i	$0.402866\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.89092	−	3.27516i	−0.458615	−	0.794344i	0.540273	−	0.841490i	$-0.318321\pi$
$17$	−1.89092	−	3.27516i	−0.458615	−	0.794344i	−0.998888	+	0.0471458i	$0.984987\pi$
$18$		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	−0.273839	−	0.961776i	$-0.588293\pi$
$23$	2.02463	−	1.16892i	0.422164	−	0.243737i	0.696003	+	0.718039i	$0.254960\pi$
$24$		0			0
$25$	2.49708	−	4.32507i	0.499416	−	0.865014i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8.84430	+	5.10626i	−1.64235	+	0.948209i	−0.662349	+	0.749196i	$0.730440\pi$
$29$	−8.84430	+	5.10626i	−1.64235	+	0.948209i	−0.979997	+	0.199013i	$0.936226\pi$
$30$		0			0
$31$		−	5.74620i		−	1.03205i	−0.856574	−	0.516024i	$-0.827411\pi$
$31$		−	5.74620i		−	1.03205i	0.856574	−	0.516024i	$-0.172589\pi$
$32$		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
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	−0.484610	−	0.874730i	$-0.661039\pi$
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	0.999844	−	0.0176805i	$-0.00562816\pi$
$42$		0			0
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	0.915474	−	0.402377i	$-0.131816\pi$
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	−0.806206	+	0.591635i	$0.798483\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.92385			0.426487			0.213244	−	0.976999i	$-0.431597\pi$
$47$	2.92385			0.426487			0.213244	+	0.976999i	$0.431597\pi$
$48$		0			0
$49$	−6.89148	−	1.22779i	−0.984497	−	0.175399i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.4835	−	6.05264i	1.44002	−	0.831394i	0.442167	−	0.896933i	$-0.354210\pi$
$53$	10.4835	−	6.05264i	1.44002	−	0.831394i	0.997850	+	0.0655390i	$0.0208767\pi$
$54$		0			0
$55$			0.411498i			0.0554863i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.579903			0.0754969			0.0377484	−	0.999287i	$-0.487981\pi$
$59$	0.579903			0.0754969			0.0377484	+	0.999287i	$0.487981\pi$
$60$		0			0
$61$		−	2.77868i		−	0.355773i	−0.984051	−	0.177887i	$-0.943074\pi$
$61$		−	2.77868i		−	0.355773i	0.984051	−	0.177887i	$-0.0569261\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.406214i		−	0.0503847i
$66$		0			0
$67$	5.27185			0.644059			0.322030	−	0.946730i	$-0.395635\pi$
$67$	5.27185			0.644059			0.322030	+	0.946730i	$0.395635\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.32103i		−	0.394134i	−0.980390	−	0.197067i	$-0.936858\pi$
$71$		−	3.32103i		−	0.394134i	0.980390	−	0.197067i	$-0.0631416\pi$
$72$		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
$77$	−8.18137	+	11.6621i	−0.932354	+	1.32902i
$78$		0			0
$79$	0.938245			0.105561			0.0527804	−	0.998606i	$-0.483192\pi$
$79$	0.938245			0.105561			0.0527804	+	0.998606i	$0.483192\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	−0.963635	−	0.267221i	$-0.913895\pi$
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	0.250398	−	0.968143i	$-0.419439\pi$
$84$		0			0
$85$	−0.144512	+	0.250303i	−0.0156746	+	0.0271491i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.51794	+	2.62915i	−0.160901	+	0.278689i	−0.935192	−	0.354141i	$-0.884773\pi$
$89$	−1.51794	+	2.62915i	−0.160901	+	0.278689i	0.774291	+	0.632830i	$0.218107\pi$
$90$		0			0
$91$	8.07632	−	11.5124i	0.846629	−	1.20683i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			0.382940i			0.0392888i
$96$		0			0
$97$	−6.18183	+	3.56908i	−0.627670	+	0.362385i	−0.779849	−	0.625967i	$-0.784704\pi$
$97$	−6.18183	+	3.56908i	−0.627670	+	0.362385i	0.152179	+	0.988353i	$0.451371\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.08628	+	7.07765i	−0.406600	+	0.704252i	−0.994506	−	0.104677i	$-0.966619\pi$
$101$	−4.08628	+	7.07765i	−0.406600	+	0.704252i	0.587906	+	0.808929i	$0.299952\pi$
$102$		0			0
$103$	−6.46599	+	3.73314i	−0.637113	+	0.367837i	−0.783502	−	0.621390i	$-0.786568\pi$
$103$	−6.46599	+	3.73314i	−0.637113	+	0.367837i	0.146389	+	0.989227i	$0.453235\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.99991	+	2.30935i	0.386686	+	0.223253i	0.680723	−	0.732541i	$-0.261666\pi$
$107$	3.99991	+	2.30935i	0.386686	+	0.223253i	−0.294037	+	0.955794i	$0.594999\pi$
$108$		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
$113$	16.6379	+	9.60591i	1.56516	+	0.903648i	0.996720	+	0.0809270i	$0.0257881\pi$
$113$	16.6379	+	9.60591i	1.56516	+	0.903648i	0.568445	+	0.822721i	$0.307545\pi$
$114$		0			0
$115$	−0.154731	−	0.0893340i	−0.0144287	−	0.00833044i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.07208	+	4.22057i	−0.831636	+	0.386899i
$120$		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	0.986955	+	0.160998i	$0.0514714\pi$
$131$	7.24394	+	12.5469i	0.632906	+	1.09623i	−0.354049	+	0.935227i	$0.615195\pi$
$132$		0			0
$133$	−7.61359	+	10.8528i	−0.660182	+	0.941056i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.3414	+	7.70264i	1.13983	+	0.658081i	0.946389	−	0.323030i	$-0.104702\pi$
$137$	13.3414	+	7.70264i	1.13983	+	0.658081i	0.193442	+	0.981112i	$0.438035\pi$
$138$		0			0
$139$	0.374701	+	0.216333i	0.0317817	+	0.0183492i	0.515807	−	0.856705i	$-0.327492\pi$
$139$	0.374701	+	0.216333i	0.0317817	+	0.0183492i	−0.484025	+	0.875054i	$0.660826\pi$
$140$		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	−0.325058	−	0.945694i	$-0.605384\pi$
$149$	4.04535	−	2.33558i	0.331408	−	0.191338i	0.656466	+	0.754356i	$0.272051\pi$
$150$		0			0
$151$	4.12276	−	7.14083i	0.335506	−	0.581113i	−0.648076	−	0.761575i	$-0.724426\pi$
$151$	4.12276	−	7.14083i	0.335506	−	0.581113i	0.983582	+	0.180463i	$0.0577595\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.380316	+	0.219575i	−0.0305477	+	0.0176367i
$156$		0			0
$157$		−	17.5900i		−	1.40383i	−0.712258	−	0.701917i	$-0.752328\pi$
$157$		−	17.5900i		−	1.40383i	0.712258	−	0.701917i	$-0.247672\pi$
$158$		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
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	−0.987169	−	0.159679i	$-0.948954\pi$
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	0.631871	+	0.775074i	$0.282287\pi$
$168$		0			0
$169$	7.62587	+	13.2084i	0.586605	+	1.01603i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.44717			0.186055			0.0930274	−	0.995664i	$-0.470346\pi$
$173$	2.44717			0.186055			0.0930274	+	0.995664i	$0.470346\pi$
$174$		0			0
$175$	−10.8170	−	7.58846i	−0.817686	−	0.573633i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.05509	−	2.91856i	0.377835	−	0.218143i	−0.299041	−	0.954240i	$-0.596667\pi$
$179$	5.05509	−	2.91856i	0.377835	−	0.218143i	0.676876	+	0.736097i	$0.263333\pi$
$180$		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
$185$	−0.0541828			−0.00398360
$186$		0			0
$187$			20.3628i			1.48907i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	7.97223i		−	0.576850i	−0.957502	−	0.288425i	$-0.906868\pi$
$191$		−	7.97223i		−	0.576850i	0.957502	−	0.288425i	$-0.0931316\pi$
$192$		0			0
$193$	0.718054			0.0516867			0.0258433	−	0.999666i	$-0.491773\pi$
$193$	0.718054			0.0516867			0.0258433	+	0.999666i	$0.491773\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			13.5035i			0.962083i	0.876698	+	0.481042i	$0.159741\pi$
$197$			13.5035i			0.962083i	−0.876698	+	0.481042i	$0.840259\pi$
$198$		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
$203$	11.3973	+	24.4984i	0.799932	+	1.71945i
$204$		0			0
$205$	−0.504265			−0.0352194
$206$		0			0
$207$		0			0
$208$		0			0
$209$	13.4897	+	23.3649i	0.933105	+	1.61618i
$210$		0			0
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	0.100778	+	0.994909i	$0.467867\pi$
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	−0.912005	+	0.410178i	$0.865467\pi$
$212$		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
$221$		−	20.1013i		−	1.35216i
$222$		0			0
$223$	6.47489	−	3.73828i	0.433590	−	0.250334i	−0.267285	−	0.963618i	$-0.586126\pi$
$223$	6.47489	−	3.73828i	0.433590	−	0.250334i	0.700875	+	0.713284i	$0.252793\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.318701	+	0.552006i	−0.0211529	+	0.0366379i	−0.876408	−	0.481569i	$-0.840067\pi$
$227$	−0.318701	+	0.552006i	−0.0211529	+	0.0366379i	0.855255	+	0.518207i	$0.173400\pi$
$228$		0			0
$229$	−1.58351	+	0.914239i	−0.104641	+	0.0604146i	−0.551407	−	0.834236i	$-0.685909\pi$
$229$	−1.58351	+	0.914239i	−0.104641	+	0.0604146i	0.446766	+	0.894651i	$0.352576\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	17.4232	+	10.0593i	1.14143	+	0.659007i	0.946785	−	0.321866i	$-0.104310\pi$
$233$	17.4232	+	10.0593i	1.14143	+	0.659007i	0.194649	+	0.980873i	$0.437643\pi$
$234$		0			0
$235$	−0.111727	−	0.193516i	−0.00728825	−	0.0126236i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.41455	+	1.39404i	0.156184	+	0.0901730i	0.576055	−	0.817411i	$-0.304591\pi$
$239$	2.41455	+	1.39404i	0.156184	+	0.0901730i	−0.419871	+	0.907584i	$0.637925\pi$
$240$		0			0
$241$	−20.0304	−	11.5645i	−1.29027	−	0.744938i	−0.311568	−	0.950224i	$-0.600854\pi$
$241$	−20.0304	−	11.5645i	−1.29027	−	0.744938i	−0.978702	+	0.205286i	$0.934187\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.182077	+	0.503033i	0.0116325	+	0.0321376i
$246$		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	$-0.299633\pi$
$251$	18.6541			1.17743			0.588717	+	0.808339i	$0.299633\pi$
$252$		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	$-0.276804\pi$
$257$	−5.43687	−	9.41694i	−0.339143	−	0.587413i	−0.984272	+	0.176661i	$0.943470\pi$
$258$		0			0
$259$	−1.53558	−	1.07726i	−0.0954162	−	0.0669376i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−16.4519	−	9.49852i	−1.01447	−	0.585704i	−0.101972	−	0.994787i	$-0.532515\pi$
$263$	−16.4519	−	9.49852i	−1.01447	−	0.585704i	−0.912497	+	0.409083i	$0.865849\pi$
$264$		0			0
$265$	−0.801194	−	0.462570i	−0.0492170	−	0.0284154i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.29788	−	7.44415i	−0.262046	−	0.453878i	0.704739	−	0.709467i	$-0.251064\pi$
$269$	−4.29788	−	7.44415i	−0.262046	−	0.453878i	−0.966786	+	0.255589i	$0.917731\pi$
$270$		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	−0.999597	−	0.0283760i	$-0.990966\pi$
$277$	−7.90931	+	13.6993i	−0.475224	+	0.823113i	0.524373	+	0.851489i	$0.324300\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.95916	−	5.74992i	0.594114	−	0.343012i	−0.172609	−	0.984990i	$-0.555220\pi$
$281$	9.95916	−	5.74992i	0.594114	−	0.343012i	0.766722	+	0.641979i	$0.221886\pi$
$282$		0			0
$283$			9.92818i			0.590169i	0.955471	+	0.295085i	$0.0953478\pi$
$283$			9.92818i			0.590169i	−0.955471	+	0.295085i	$0.904652\pi$
$284$		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
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	−0.495467	−	0.868627i	$-0.665003\pi$
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	0.999986	−	0.00522664i	$-0.00166370\pi$
$294$		0			0
$295$	−0.0221594	−	0.0383812i	−0.00129017	−	0.00223464i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.4262			0.718624
$300$		0			0
$301$	3.43766	−	1.59929i	0.198143	−	0.0921815i
$302$		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
$311$	−20.2032			−1.14562			−0.572808	−	0.819690i	$-0.694146\pi$
$311$	−20.2032			−1.14562			−0.572808	+	0.819690i	$0.694146\pi$
$312$		0			0
$313$		−	21.8407i		−	1.23451i	−0.786764	−	0.617254i	$-0.788245\pi$
$313$		−	21.8407i		−	1.23451i	0.786764	−	0.617254i	$-0.211755\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	24.8594i		−	1.39624i	−0.715981	−	0.698120i	$-0.754020\pi$
$317$		−	24.8594i		−	1.39624i	0.715981	−	0.698120i	$-0.245980\pi$
$318$		0			0
$319$	54.9880			3.07874
$320$		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
$329$	0.681067	−	7.70574i	0.0375484	−	0.424831i
$330$		0			0
$331$	16.1444			0.887375			0.443688	−	0.896181i	$-0.353670\pi$
$331$	16.1444			0.887375			0.443688	+	0.896181i	$0.353670\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.201449	−	0.348920i	−0.0110063	−	0.0190635i
$336$		0			0
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	−0.996488	−	0.0837408i	$-0.973313\pi$
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	0.570765	+	0.821113i	$0.306647\pi$
$338$		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
$347$		−	32.3830i		−	1.73841i	−0.494451	−	0.869206i	$-0.664631\pi$
$347$		−	32.3830i		−	1.73841i	0.494451	−	0.869206i	$-0.335369\pi$
$348$		0			0
$349$	26.0421	−	15.0354i	1.39400	−	0.804827i	0.400246	−	0.916408i	$-0.368925\pi$
$349$	26.0421	−	15.0354i	1.39400	−	0.804827i	0.993755	+	0.111581i	$0.0355915\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.50607	+	14.7329i	−0.452733	+	0.784156i	−0.998555	−	0.0537453i	$-0.982884\pi$
$353$	−8.50607	+	14.7329i	−0.452733	+	0.784156i	0.545822	+	0.837901i	$0.316217\pi$
$354$		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	0.985858	−	0.167583i	$-0.0535962\pi$
$359$	25.2692	+	14.5892i	1.33366	+	0.769987i	0.347798	+	0.937570i	$0.386930\pi$
$360$		0			0
$361$	3.05356	+	5.28892i	0.160714	+	0.278364i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.471788	+	0.272387i	0.0246945	+	0.0142574i
$366$		0			0
$367$	−15.6981	−	9.06329i	−0.819433	−	0.473100i	0.0307880	−	0.999526i	$-0.490198\pi$
$367$	−15.6981	−	9.06329i	−0.819433	−	0.473100i	−0.850221	+	0.526426i	$0.823532\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−13.5096	−	29.0388i	−0.701385	−	1.50762i
$372$		0			0
$373$	10.1823	+	17.6362i	0.527219	+	0.913170i	0.999497	+	0.0317200i	$0.0100985\pi$
$373$	10.1823	+	17.6362i	0.527219	+	0.913170i	−0.472278	+	0.881450i	$0.656568\pi$
$374$		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	−0.895215	−	0.445634i	$-0.852978\pi$
$383$	−16.3127	−	28.2544i	−0.833538	−	1.44373i	0.0616774	−	0.998096i	$-0.480355\pi$
$384$		0			0
$385$	1.08449	+	0.0958523i	0.0552709	+	0.00488509i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.6400	+	7.87504i	0.691574	+	0.399280i	0.804201	−	0.594357i	$-0.202593\pi$
$389$	13.6400	+	7.87504i	0.691574	+	0.399280i	−0.112628	+	0.993637i	$0.535927\pi$
$390$		0			0
$391$	−7.65680	−	4.42066i	−0.387221	−	0.223562i
$392$		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	−0.478592	−	0.878037i	$-0.658853\pi$
$401$	0.851348	−	0.491526i	0.0425143	−	0.0245456i	0.521106	+	0.853492i	$0.325519\pi$
$402$		0			0
$403$	15.2712	−	26.4505i	0.760713	−	1.31759i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.30594	+	1.90868i	−0.163869	+	0.0946099i
$408$		0			0
$409$		−	28.8900i		−	1.42852i	−0.699880	−	0.714260i	$-0.746763\pi$
$409$		−	28.8900i		−	1.42852i	0.699880	−	0.714260i	$-0.253237\pi$
$410$		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
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	−0.670509	−	0.741901i	$-0.733924\pi$
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	0.977760	+	0.209727i	$0.0672577\pi$
$420$		0			0
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	−0.986576	−	0.163300i	$-0.947786\pi$
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	0.351866	−	0.936050i	$-0.385547\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.8871			−0.916158
$426$		0			0
$427$	−7.32315	−	0.647252i	−0.354392	−	0.0313227i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.28454	−	3.62838i	0.302716	−	0.174773i	−0.340947	−	0.940083i	$-0.610748\pi$
$431$	6.28454	−	3.62838i	0.302716	−	0.174773i	0.643662	+	0.765310i	$0.277414\pi$
$432$		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
$437$	−11.7142			−0.560367
$438$		0			0
$439$		−	3.27192i		−	0.156160i	−0.996947	−	0.0780802i	$-0.975121\pi$
$439$		−	3.27192i		−	0.156160i	0.996947	−	0.0780802i	$-0.0248790\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			2.84907i			0.135363i	0.997707	+	0.0676817i	$0.0215602\pi$
$443$			2.84907i			0.135363i	−0.997707	+	0.0676817i	$0.978440\pi$
$444$		0			0
$445$	0.232015			0.0109986
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	19.9802i		−	0.942925i	−0.881886	−	0.471463i	$-0.843726\pi$
$449$		−	19.9802i		−	0.942925i	0.881886	−	0.471463i	$-0.156274\pi$
$450$		0			0
$451$	−30.7675	+	17.7636i	−1.44878	+	0.836455i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.07057	−	0.0946216i	−0.0501890	−	0.00443593i
$456$		0			0
$457$	18.3002			0.856046			0.428023	−	0.903768i	$-0.359210\pi$
$457$	18.3002			0.856046			0.428023	+	0.903768i	$0.359210\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	0.952016	−	0.306049i	$-0.0990071\pi$
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	−0.741054	+	0.671445i	$0.765674\pi$
$462$		0			0
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	−0.497021	−	0.867739i	$-0.665573\pi$
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	0.999994	−	0.00343694i	$-0.00109401\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.7761	+	23.8610i	−0.637484	+	1.10415i	0.348500	+	0.937309i	$0.386691\pi$
$467$	−13.7761	+	23.8610i	−0.637484	+	1.10415i	−0.985983	+	0.166845i	$0.946642\pi$
$468$		0			0
$469$	1.22800	−	13.8938i	0.0567038	−	0.641558i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	7.71602i		−	0.354783i
$474$		0			0
$475$	−21.6716	+	12.5121i	−0.994362	+	0.574095i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.47325	+	4.28380i	−0.113006	+	0.195732i	−0.916981	−	0.398931i	$-0.869381\pi$
$479$	−2.47325	+	4.28380i	−0.113006	+	0.195732i	0.803975	+	0.594663i	$0.202715\pi$
$480$		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
$491$	33.0010	+	19.0531i	1.48931	+	0.859855i	0.999925	−	0.0122119i	$-0.00388725\pi$
$491$	33.0010	+	19.0531i	1.48931	+	0.859855i	0.489387	+	0.872067i	$0.337221\pi$
$492$		0			0
$493$	33.4477	+	19.3110i	1.50641	+	0.869725i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.75250	−	0.773585i	−0.392603	−	0.0347000i
$498$		0			0
$499$	12.4192	+	21.5107i	0.555960	+	0.962951i	0.997828	+	0.0658709i	$0.0209825\pi$
$499$	12.4192	+	21.5107i	0.555960	+	0.962951i	−0.441868	+	0.897080i	$0.645684\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.2820			1.21645			0.608223	−	0.793766i	$-0.291883\pi$
$503$	27.2820			1.21645			0.608223	+	0.793766i	$0.291883\pi$
$504$		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	−0.790338	−	0.612671i	$-0.790095\pi$
$509$	−20.8860	−	36.1757i	−0.925758	−	1.60346i	−0.135420	−	0.990788i	$-0.543238\pi$
$510$		0			0
$511$	7.95522	+	17.0997i	0.351918	+	0.756446i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.494160	+	0.285303i	0.0217753	+	0.0125720i
$516$		0			0
$517$	−13.6339	−	7.87154i	−0.599619	−	0.346190i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.02629	−	3.50963i	−0.0887732	−	0.153760i	0.818220	−	0.574906i	$-0.194961\pi$
$521$	−2.02629	−	3.50963i	−0.0887732	−	0.153760i	−0.906993	+	0.421146i	$0.861628\pi$
$522$		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
$533$	30.3724	−	17.5355i	1.31558	−	0.759548i
$534$		0			0
$535$		−	0.352982i		−	0.0152607i
$536$		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
$545$	0.399541	−	0.692026i	0.0171145	−	0.0296431i
$546$		0			0
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	0.815571	−	0.578657i	$-0.196423\pi$
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	−0.908917	+	0.416976i	$0.863090\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	51.1719			2.18000
$552$		0			0
$553$	0.218550	−	2.47272i	0.00929371	−	0.105151i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.7527	+	8.51750i	−0.625094	+	0.360898i	−0.778849	−	0.627211i	$-0.784196\pi$
$557$	−14.7527	+	8.51750i	−0.625094	+	0.360898i	0.153756	+	0.988109i	$0.450863\pi$
$558$		0			0
$559$			7.61695i			0.322163i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.9198			0.544507			0.272253	−	0.962226i	$-0.412231\pi$
$563$	12.9198			0.544507			0.272253	+	0.962226i	$0.412231\pi$
$564$		0			0
$565$		−	1.46825i		−	0.0617699i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	21.7408i		−	0.911420i	−0.890128	−	0.455710i	$-0.849385\pi$
$569$		−	21.7408i		−	0.911420i	0.890128	−	0.455710i	$-0.150615\pi$
$570$		0			0
$571$	−33.6508			−1.40824			−0.704122	−	0.710079i	$-0.748659\pi$
$571$	−33.6508			−1.40824			−0.704122	+	0.710079i	$0.748659\pi$
$572$		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
$581$	−31.1751	+	14.5035i	−1.29336	+	0.601705i
$582$		0			0
$583$	−65.1793			−2.69945
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	0.982179	+	0.187948i	$0.0601837\pi$
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	−0.328322	+	0.944566i	$0.606483\pi$
$588$		0			0
$589$	−14.3963	+	24.9350i	−0.593187	+	1.02743i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.54101	+	6.13320i	−0.145412	+	0.251860i	−0.929526	−	0.368755i	$-0.879784\pi$
$593$	−3.54101	+	6.13320i	−0.145412	+	0.251860i	0.784115	+	0.620616i	$0.213117\pi$
$594$		0			0
$595$	0.626005	+	0.439163i	0.0256637	+	0.0180039i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			6.00650i			0.245419i	0.992443	+	0.122709i	$0.0391583\pi$
$599$			6.00650i			0.245419i	−0.992443	+	0.122709i	$0.960842\pi$
$600$		0			0
$601$	0.530083	−	0.306043i	0.0216225	−	0.0124838i	−0.489150	−	0.872200i	$-0.662693\pi$
$601$	0.530083	−	0.306043i	0.0216225	−	0.0124838i	0.510772	+	0.859716i	$0.329360\pi$
$602$		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	$-0.653423\pi$
$607$	1.77500	−	1.02480i	0.0720450	−	0.0415952i	0.535590	+	0.844478i	$0.320089\pi$
$608$		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
$617$	−23.2143	−	13.4028i	−0.934571	−	0.539575i	−0.0463170	−	0.998927i	$-0.514748\pi$
$617$	−23.2143	−	13.4028i	−0.934571	−	0.539575i	−0.888254	+	0.459352i	$0.848082\pi$
$618$		0			0
$619$	0.0603011	+	0.0348148i	0.00242370	+	0.00139933i	0.501211	−	0.865325i	$-0.332888\pi$
$619$	0.0603011	+	0.0348148i	0.00242370	+	0.00139933i	−0.498788	+	0.866724i	$0.666221\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.57547	+	4.61291i	0.263441	+	0.184812i
$624$		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
$637$	−28.4594	−	23.9666i	−1.12760	−	0.949592i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.7673	+	10.2580i	0.701766	+	0.405165i	0.808005	−	0.589176i	$-0.200547\pi$
$641$	17.7673	+	10.2580i	0.701766	+	0.405165i	−0.106239	+	0.994341i	$0.533881\pi$
$642$		0			0
$643$	15.6081	+	9.01132i	0.615522	+	0.355372i	0.775123	−	0.631810i	$-0.217688\pi$
$643$	15.6081	+	9.01132i	0.615522	+	0.355372i	−0.159602	+	0.987182i	$0.551021\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.11827	−	15.7933i	−0.358476	−	0.620899i	0.629230	−	0.777219i	$-0.283370\pi$
$647$	−9.11827	−	15.7933i	−0.358476	−	0.620899i	−0.987706	+	0.156320i	$0.950037\pi$
$648$		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	−0.339651	−	0.940552i	$-0.610309\pi$
$653$	7.79559	−	4.50079i	0.305065	−	0.176129i	0.644716	+	0.764422i	$0.276976\pi$
$654$		0			0
$655$	0.553614	−	0.958888i	0.0216315	−	0.0374669i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−30.4806	+	17.5980i	−1.18735	+	0.685519i	−0.957704	−	0.287754i	$-0.907091\pi$
$659$	−30.4806	+	17.5980i	−1.18735	+	0.685519i	−0.229650	+	0.973273i	$0.573758\pi$
$660$		0			0
$661$			12.5628i			0.488637i	0.969695	+	0.244318i	$0.0785642\pi$
$661$			12.5628i			0.488637i	−0.969695	+	0.244318i	$0.921436\pi$
$662$		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
$671$	−7.48072	+	12.9570i	−0.288790	+	0.500199i
$672$		0			0
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.797960	+	0.602710i	$0.205913\pi$
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.122982	+	0.992409i	$0.460754\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	37.0471			1.42384			0.711918	−	0.702263i	$-0.247827\pi$
$677$	37.0471			1.42384			0.711918	+	0.702263i	$0.247827\pi$
$678$		0			0
$679$	7.96627	+	17.1234i	0.305717	+	0.657137i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.6844	+	12.5195i	−0.829732	+	0.479046i	−0.853761	−	0.520665i	$-0.825684\pi$
$683$	−21.6844	+	12.5195i	−0.829732	+	0.479046i	0.0240289	+	0.999711i	$0.492351\pi$
$684$		0			0
$685$		−	1.17734i		−	0.0449839i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	64.3424			2.45125
$690$		0			0
$691$			46.4946i			1.76874i	0.466787	+	0.884370i	$0.345411\pi$
$691$			46.4946i			1.76874i	−0.466787	+	0.884370i	$0.654589\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	0.0330663i		−	0.00125428i
$696$		0			0
$697$	−24.9533			−0.945174
$698$		0			0
$699$		0			0
$700$		0			0
$701$			36.0041i			1.35986i	0.733279	+	0.679928i	$0.237989\pi$
$701$			36.0041i			1.35986i	−0.733279	+	0.679928i	$0.762011\pi$
$702$		0			0
$703$	−3.07651	+	1.77622i	−0.116033	+	0.0669915i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	17.7011	+	12.4179i	0.665720	+	0.467025i
$708$		0			0
$709$	31.8316			1.19546			0.597731	−	0.801697i	$-0.296069\pi$
$709$	31.8316			1.19546			0.597731	+	0.801697i	$0.296069\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.71685	−	11.6339i	−0.251548	−	0.435694i
$714$		0			0
$715$	−1.09360	+	1.89418i	−0.0408985	+	0.0708382i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.0271	+	34.6879i	−0.746883	+	1.29364i	0.202427	+	0.979297i	$0.435117\pi$
$719$	−20.0271	+	34.6879i	−0.746883	+	1.29364i	−0.949310	+	0.314342i	$0.898216\pi$
$720$		0			0
$721$	8.33245	+	17.9106i	0.310317	+	0.667024i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			51.0030i			1.89420i
$726$		0			0
$727$	3.39242	−	1.95862i	0.125818	−	0.0726411i	−0.435770	−	0.900058i	$-0.643524\pi$
$727$	3.39242	−	1.95862i	0.125818	−	0.0726411i	0.561588	+	0.827417i	$0.310191\pi$
$728$		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	$-0.523224\pi$
$733$	20.4239	−	11.7918i	0.754376	−	0.435539i	0.827273	+	0.561800i	$0.189891\pi$
$734$		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
$743$	−29.4003	−	16.9743i	−1.07859	−	0.622725i	−0.148076	−	0.988976i	$-0.547308\pi$
$743$	−29.4003	−	16.9743i	−1.07859	−	0.622725i	−0.930516	+	0.366251i	$0.880641\pi$
$744$		0			0
$745$	−0.309164	−	0.178496i	−0.0113269	−	0.00653958i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.01796	−	10.0038i	0.256431	−	0.365529i
$750$		0			0
$751$	−1.69831	−	2.94157i	−0.0619724	−	0.107339i	0.833375	−	0.552709i	$-0.186406\pi$
$751$	−1.69831	−	2.94157i	−0.0619724	−	0.107339i	−0.895347	+	0.445369i	$0.853072\pi$
$752$		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	$-0.264706\pi$
$761$	−8.36288	−	14.4849i	−0.303154	−	0.525079i	−0.976849	+	0.213931i	$0.931373\pi$
$762$		0			0
$763$	25.0821	−	11.6688i	0.908032	−	0.422440i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.66937	+	1.54116i	0.0963852	+	0.0556480i
$768$		0			0
$769$	24.0816	+	13.9035i	0.868404	+	0.501373i	0.866818	−	0.498625i	$-0.166162\pi$
$769$	24.0816	+	13.9035i	0.868404	+	0.501373i	0.00158643	+	0.999999i	$0.499495\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.42238	−	11.1239i	−0.230997	−	0.400098i	0.727105	−	0.686526i	$-0.240865\pi$
$773$	−6.42238	−	11.1239i	−0.230997	−	0.400098i	−0.958102	+	0.286428i	$0.907532\pi$
$774$		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
$785$	−1.16420	+	0.672153i	−0.0415522	+	0.0239902i
$786$		0			0
$787$		−	7.56610i		−	0.269702i	−0.990866	−	0.134851i	$-0.956944\pi$
$787$		−	7.56610i		−	0.269702i	0.990866	−	0.134851i	$-0.0430556\pi$
$788$		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
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	−0.928579	−	0.371134i	$-0.878969\pi$
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	0.785701	+	0.618606i	$0.212302\pi$
$798$		0			0
$799$	−5.52875	−	9.57608i	−0.195593	−	0.338777i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	38.3812			1.35444
$804$		0			0
$805$	−0.271480	+	0.386981i	−0.00956842	+	0.0136393i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0849492	+	0.0490454i	−0.00298665	+	0.00172435i	−0.501493	−	0.865162i	$-0.667216\pi$
$809$	−0.0849492	+	0.0490454i	−0.00298665	+	0.00172435i	0.498506	+	0.866886i	$0.333882\pi$
$810$		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
$815$	0.805662			0.0282211
$816$		0			0
$817$		−	7.18054i		−	0.251215i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	22.5742i		−	0.787846i	−0.919143	−	0.393923i	$-0.871118\pi$
$821$		−	22.5742i		−	0.787846i	0.919143	−	0.393923i	$-0.128882\pi$
$822$		0			0
$823$	−24.5310			−0.855097			−0.427549	−	0.903992i	$-0.640623\pi$
$823$	−24.5310			−0.855097			−0.427549	+	0.903992i	$0.640623\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	40.3057i		−	1.40157i	−0.713375	−	0.700783i	$-0.752834\pi$
$827$		−	40.3057i		−	1.40157i	0.713375	−	0.700783i	$-0.247166\pi$
$828$		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
$833$	9.01000	+	24.8924i	0.312178	+	0.862470i
$834$		0			0
$835$	0.701801			0.0242868
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	0.585224	−	0.810872i	$-0.301007\pi$
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	−0.994847	+	0.101383i	$0.967673\pi$
$840$		0			0
$841$	37.6478	−	65.2079i	1.29820	−	2.24855i
$842$		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
$851$		−	1.65746i		−	0.0568170i
$852$		0			0
$853$	−48.0748	+	27.7560i	−1.64605	+	0.950347i	−0.667429	+	0.744673i	$0.732605\pi$
$853$	−48.0748	+	27.7560i	−1.64605	+	0.950347i	−0.978621	+	0.205674i	$0.934061\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.3048	+	26.5088i	−0.522803	+	0.905522i	0.476845	+	0.878988i	$0.341780\pi$
$857$	−15.3048	+	26.5088i	−0.522803	+	0.905522i	−0.999648	+	0.0265343i	$0.991553\pi$
$858$		0			0
$859$	−36.4944	+	21.0700i	−1.24517	+	0.718900i	−0.970143	−	0.242535i	$-0.922021\pi$
$859$	−36.4944	+	21.0700i	−1.24517	+	0.718900i	−0.275030	+	0.961436i	$0.588688\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	22.7782	+	13.1510i	0.775379	+	0.447665i	0.834790	−	0.550568i	$-0.185589\pi$
$863$	22.7782	+	13.1510i	0.775379	+	0.447665i	−0.0594112	+	0.998234i	$0.518922\pi$
$864$		0			0
$865$	−0.0935118	−	0.161967i	−0.00317950	−	0.00550705i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.37504	−	2.52593i	−0.148413	−	0.0856863i
$870$		0			0
$871$	24.2670	+	14.0106i	0.822256	+	0.474730i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.177916	+	2.01297i	−0.00601464	+	0.0680509i
$876$		0			0
$877$	−17.8533	−	30.9228i	−0.602863	−	1.04419i	−0.992385	−	0.123172i	$-0.960693\pi$
$877$	−17.8533	−	30.9228i	−0.602863	−	1.04419i	0.389522	−	0.921017i	$-0.372640\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−12.4482			−0.419392			−0.209696	−	0.977767i	$-0.567247\pi$
$881$	−12.4482			−0.419392			−0.209696	+	0.977767i	$0.567247\pi$
$882$		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	0.997345	+	0.0728170i	$0.0231989\pi$
$887$	16.7299	+	28.9770i	0.561734	+	0.972952i	−0.435611	+	0.900135i	$0.643468\pi$
$888$		0			0
$889$	0.294634	−	3.33355i	0.00988172	−	0.111804i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.6877	−	7.32526i	−0.424579	−	0.245131i
$894$		0			0
$895$	−0.386333	−	0.223049i	−0.0129137	−	0.00745572i
$896$		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	−0.858152	−	0.513396i	$-0.828387\pi$
$907$	0.467962	−	0.810535i	0.0155384	−	0.0269134i	0.873690	+	0.486483i	$0.161720\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−28.8739	+	16.6703i	−0.956634	+	0.552313i	−0.895136	−	0.445794i	$-0.852921\pi$
$911$	−28.8739	+	16.6703i	−0.956634	+	0.552313i	−0.0614988	+	0.998107i	$0.519588\pi$
$912$		0			0
$913$			69.9743i			2.31581i
$914$		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
$923$	8.82603	−	15.2871i	0.290512	−	0.503182i
$924$		0			0
$925$	−1.77036	−	3.06635i	−0.0582090	−	0.100821i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.1536			−0.497174			−0.248587	−	0.968610i	$-0.579966\pi$
$929$	−15.1536			−0.497174			−0.248587	+	0.968610i	$0.579966\pi$
$930$		0			0
$931$	26.8288	+	22.5934i	0.879279	+	0.740470i
$932$		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
$941$	37.7960			1.23212			0.616058	−	0.787701i	$-0.288729\pi$
$941$	37.7960			1.23212			0.616058	+	0.787701i	$0.288729\pi$
$942$		0			0
$943$		−	15.4255i		−	0.502325i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			10.9399i			0.355500i	0.984076	+	0.177750i	$0.0568818\pi$
$947$			10.9399i			0.355500i	−0.984076	+	0.177750i	$0.943118\pi$
$948$		0			0
$949$	−37.8884			−1.22991
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	11.0914i		−	0.359284i	−0.983732	−	0.179642i	$-0.942506\pi$
$953$		−	11.0914i		−	0.359284i	0.983732	−	0.179642i	$-0.0574939\pi$
$954$		0			0
$955$	−0.527646	+	0.304637i	−0.0170742	+	0.00985781i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	23.4078	−	33.3667i	0.755878	−	1.07747i
$960$		0			0
$961$	−2.01885			−0.0651242
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.0274384	−	0.0475248i	−0.000883275	−	0.00152988i
$966$		0			0
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	−0.335839	−	0.941920i	$-0.609020\pi$
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	0.983646	−	0.180115i	$-0.0576470\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.8458	−	41.3021i	0.765248	−	1.32545i	−0.174867	−	0.984592i	$-0.555950\pi$
$971$	23.8458	−	41.3021i	0.765248	−	1.32545i	0.940115	−	0.340856i	$-0.110717\pi$
$972$		0			0
$973$	0.657423	−	0.937123i	0.0210760	−	0.0300428i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			16.6901i			0.533963i	0.963702	+	0.266982i	$0.0860263\pi$
$977$			16.6901i			0.533963i	−0.963702	+	0.266982i	$0.913974\pi$
$978$		0			0
$979$	14.1563	−	8.17314i	0.452437	−	0.261215i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.9255	+	29.3157i	−0.539838	+	0.935027i	0.459074	+	0.888398i	$0.348181\pi$
$983$	−16.9255	+	29.3157i	−0.539838	+	0.935027i	−0.998912	+	0.0466291i	$0.985152\pi$
$984$		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
$995$	−1.62454	−	0.937928i	−0.0515014	−	0.0297343i
$996$		0			0
$997$	−18.7391	−	10.8190i	−0.593472	−	0.342641i	0.172997	−	0.984922i	$-0.444655\pi$
$997$	−18.7391	−	10.8190i	−0.593472	−	0.342641i	−0.766469	+	0.642281i	$0.777988\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.1	✓	16	3.2	odd	2
252.2.w.a.101.1	yes	16	63.52	odd	6
252.2.bm.a.173.3	yes	16	9.7	even	3
252.2.bm.a.185.3	yes	16	21.17	even	6
756.2.w.a.341.5		16	1.1	even	1	trivial
756.2.w.a.521.5		16	63.38	even	6	inner
756.2.bm.a.17.5		16	7.3	odd	6
756.2.bm.a.89.5		16	9.2	odd	6
1008.2.ca.d.257.8		16	12.11	even	2
1008.2.ca.d.353.8		16	252.115	even	6
1008.2.df.d.689.6		16	84.59	odd	6
1008.2.df.d.929.6		16	36.7	odd	6
1764.2.w.b.509.8		16	21.20	even	2
1764.2.w.b.1109.8		16	63.25	even	3
1764.2.x.a.293.5		16	21.2	odd	6
1764.2.x.a.1469.5		16	63.61	odd	6
1764.2.x.b.293.4		16	21.5	even	6
1764.2.x.b.1469.4		16	63.16	even	3
1764.2.bm.a.1685.6		16	63.34	odd	6
1764.2.bm.a.1697.6		16	21.11	odd	6
2268.2.t.a.1781.5		16	63.59	even	6
2268.2.t.a.2105.5		16	9.4	even	3
2268.2.t.b.1781.4		16	63.31	odd	6
2268.2.t.b.2105.4		16	9.5	odd	6
3024.2.ca.d.2033.5		16	252.227	odd	6
3024.2.ca.d.2609.5		16	4.3	odd	2
3024.2.df.d.17.5		16	28.3	even	6
3024.2.df.d.1601.5		16	36.11	even	6
5292.2.w.b.521.4		16	63.11	odd	6
5292.2.w.b.1097.4		16	7.6	odd	2
5292.2.x.a.881.5		16	7.2	even	3
5292.2.x.a.4409.5		16	63.47	even	6
5292.2.x.b.881.4		16	7.5	odd	6
5292.2.x.b.4409.4		16	63.2	odd	6
5292.2.bm.a.2285.4		16	7.4	even	3
5292.2.bm.a.4625.4		16	63.20	even	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0382122 - 0.0661855i) q^{5} +(0.232935 - 2.63548i) q^{7} +O(q^{10})\)	\(q+(-0.0382122 - 0.0661855i) q^{5} +(0.232935 - 2.63548i) q^{7} +(-4.66300 - 2.69219i) q^{11} +(4.60313 + 2.65762i) q^{13} +(-1.89092 - 3.27516i) q^{17} +(-4.33939 - 2.50535i) q^{19} +(2.02463 - 1.16892i) q^{23} +(2.49708 - 4.32507i) q^{25} +(-8.84430 + 5.10626i) q^{29} -5.74620i q^{31} +(-0.183331 + 0.0852905i) q^{35} +(0.354486 - 0.613988i) q^{37} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +2.92385 q^{47} +(-6.89148 - 1.22779i) q^{49} +(10.4835 - 6.05264i) q^{53} +0.411498i q^{55} +0.579903 q^{59} -2.77868i q^{61} -0.406214i q^{65} +5.27185 q^{67} -3.32103i q^{71} +(-6.17326 + 3.56413i) q^{73} +(-8.18137 + 11.6621i) q^{77} +0.938245 q^{79} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-1.51794 + 2.62915i) q^{89} +(8.07632 - 11.5124i) q^{91} +0.382940i q^{95} +(-6.18183 + 3.56908i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85} - 21 q^{89} + 9 q^{91} - 3 q^{97}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more