LMFDB - Embedded newform 1512.2.cx.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(17,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.cx (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	1512.17
Dual form			1512.2.cx.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04899 q^{5} +(1.41312 - 2.23676i) q^{7} +O(q^{10})$	$q-2.04899 q^{5} +(1.41312 - 2.23676i) q^{7} -5.90703i q^{11} +(-0.139269 - 0.0804071i) q^{13} +(-2.77904 + 4.81345i) q^{17} +(-4.02056 + 2.32127i) q^{19} -0.433237i q^{23} -0.801659 q^{25} +(1.95524 - 1.12886i) q^{29} +(-2.57823 + 1.48854i) q^{31} +(-2.89547 + 4.58308i) q^{35} +(2.17904 + 3.77422i) q^{37} +(-2.35740 + 4.08313i) q^{41} +(1.82369 + 3.15873i) q^{43} +(-0.0650477 + 0.112666i) q^{47} +(-3.00617 - 6.32162i) q^{49} +(-10.7936 - 6.23170i) q^{53} +12.1034i q^{55} +(3.22405 + 5.58421i) q^{59} +(-5.98415 - 3.45495i) q^{61} +(0.285360 + 0.164753i) q^{65} +(-7.64596 - 13.2432i) q^{67} -1.48027i q^{71} +(-2.60881 - 1.50620i) q^{73} +(-13.2126 - 8.34735i) q^{77} +(-8.69257 + 15.0560i) q^{79} +(-7.62399 - 13.2051i) q^{83} +(5.69422 - 9.86268i) q^{85} +(-4.04757 - 7.01059i) q^{89} +(-0.376655 + 0.197886i) q^{91} +(8.23808 - 4.75626i) q^{95} +(2.61123 - 1.50759i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	−2.04899			−0.916334			−0.458167	−	0.888866i	$-0.651494\pi$
$5$	−2.04899			−0.916334			−0.458167	+	0.888866i	$0.651494\pi$
$6$		0			0
$7$	1.41312	−	2.23676i	0.534110	−	0.845415i
$7$	1.41312	−	2.23676i	0.534110	−	0.845415i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	5.90703i		−	1.78104i	−0.454947	−	0.890518i	$-0.650342\pi$
$11$		−	5.90703i		−	1.78104i	0.454947	−	0.890518i	$-0.349658\pi$
$12$		0			0
$13$	−0.139269	−	0.0804071i	−0.0386263	−	0.0223009i	0.480562	−	0.876960i	$-0.340433\pi$
$13$	−0.139269	−	0.0804071i	−0.0386263	−	0.0223009i	−0.519189	+	0.854660i	$0.673766\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.77904	+	4.81345i	−0.674017	+	1.16743i	0.302738	+	0.953074i	$0.402099\pi$
$17$	−2.77904	+	4.81345i	−0.674017	+	1.16743i	−0.976755	+	0.214358i	$0.931234\pi$
$18$		0			0
$19$	−4.02056	+	2.32127i	−0.922381	+	0.532537i	−0.884394	−	0.466741i	$-0.845428\pi$
$19$	−4.02056	+	2.32127i	−0.922381	+	0.532537i	−0.0379869	+	0.999278i	$0.512095\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	0.433237i		−	0.0903361i	−0.998979	−	0.0451681i	$-0.985618\pi$
$23$		−	0.433237i		−	0.0903361i	0.998979	−	0.0451681i	$-0.0143823\pi$
$24$		0			0
$25$	−0.801659			−0.160332
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.95524	−	1.12886i	0.363079	−	0.209623i	−0.307352	−	0.951596i	$-0.599443\pi$
$29$	1.95524	−	1.12886i	0.363079	−	0.209623i	0.670430	+	0.741972i	$0.266110\pi$
$30$		0			0
$31$	−2.57823	+	1.48854i	−0.463064	+	0.267350i	−0.713332	−	0.700827i	$-0.752815\pi$
$31$	−2.57823	+	1.48854i	−0.463064	+	0.267350i	0.250268	+	0.968177i	$0.419481\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.89547	+	4.58308i	−0.489423	+	0.774683i
$36$		0			0
$37$	2.17904	+	3.77422i	0.358233	+	0.620477i	0.987666	−	0.156578i	$-0.0500461\pi$
$37$	2.17904	+	3.77422i	0.358233	+	0.620477i	−0.629433	+	0.777055i	$0.716713\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.35740	+	4.08313i	−0.368163	+	0.637678i	−0.989278	−	0.146042i	$-0.953347\pi$
$41$	−2.35740	+	4.08313i	−0.368163	+	0.637678i	0.621115	+	0.783719i	$0.286680\pi$
$42$		0			0
$43$	1.82369	+	3.15873i	0.278111	+	0.481702i	0.970915	−	0.239424i	$-0.0769585\pi$
$43$	1.82369	+	3.15873i	0.278111	+	0.481702i	−0.692805	+	0.721125i	$0.743625\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0650477	+	0.112666i	−0.00948818	+	0.0164340i	−0.870731	−	0.491760i	$-0.836354\pi$
$47$	−0.0650477	+	0.112666i	−0.00948818	+	0.0164340i	0.861242	+	0.508194i	$0.169687\pi$
$48$		0			0
$49$	−3.00617	−	6.32162i	−0.429453	−	0.903089i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.7936	−	6.23170i	−1.48262	−	0.855990i	−0.482813	−	0.875723i	$-0.660385\pi$
$53$	−10.7936	−	6.23170i	−1.48262	−	0.855990i	−0.999805	+	0.0197331i	$0.993718\pi$
$54$		0			0
$55$			12.1034i			1.63202i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.22405	+	5.58421i	0.419735	+	0.727003i	0.995913	−	0.0903220i	$-0.0287896\pi$
$59$	3.22405	+	5.58421i	0.419735	+	0.727003i	−0.576177	+	0.817325i	$0.695456\pi$
$60$		0			0
$61$	−5.98415	−	3.45495i	−0.766192	−	0.442361i	0.0653228	−	0.997864i	$-0.479192\pi$
$61$	−5.98415	−	3.45495i	−0.766192	−	0.442361i	−0.831514	+	0.555503i	$0.812526\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.285360	+	0.164753i	0.0353946	+	0.0204351i
$66$		0			0
$67$	−7.64596	−	13.2432i	−0.934102	−	1.61791i	−0.776227	−	0.630453i	$-0.782869\pi$
$67$	−7.64596	−	13.2432i	−0.934102	−	1.61791i	−0.157875	−	0.987459i	$-0.550464\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.48027i		−	0.175675i	−0.996135	−	0.0878376i	$-0.972004\pi$
$71$		−	1.48027i		−	0.175675i	0.996135	−	0.0878376i	$-0.0279957\pi$
$72$		0			0
$73$	−2.60881	−	1.50620i	−0.305339	−	0.176287i	0.339500	−	0.940606i	$-0.389742\pi$
$73$	−2.60881	−	1.50620i	−0.305339	−	0.176287i	−0.644839	+	0.764319i	$0.723075\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−13.2126	−	8.34735i	−1.50572	−	0.951269i
$78$		0			0
$79$	−8.69257	+	15.0560i	−0.977991	+	1.69393i	−0.308301	+	0.951289i	$0.599760\pi$
$79$	−8.69257	+	15.0560i	−0.977991	+	1.69393i	−0.669690	+	0.742641i	$0.733573\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.62399	−	13.2051i	−0.836841	−	1.44945i	−0.892522	−	0.451003i	$-0.851066\pi$
$83$	−7.62399	−	13.2051i	−0.836841	−	1.44945i	0.0556811	−	0.998449i	$-0.482267\pi$
$84$		0			0
$85$	5.69422	−	9.86268i	0.617625	−	1.06976i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.04757	−	7.01059i	−0.429041	−	0.743121i	0.567747	−	0.823203i	$-0.307815\pi$
$89$	−4.04757	−	7.01059i	−0.429041	−	0.743121i	−0.996788	+	0.0800819i	$0.974482\pi$
$90$		0			0
$91$	−0.376655	+	0.197886i	−0.0394842	+	0.0207441i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.23808	−	4.75626i	0.845209	−	0.487982i
$96$		0			0
$97$	2.61123	−	1.50759i	0.265130	−	0.153073i	−0.361542	−	0.932356i	$-0.617750\pi$
$97$	2.61123	−	1.50759i	0.265130	−	0.153073i	0.626673	+	0.779283i	$0.284416\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−15.1360			−1.50608			−0.753042	−	0.657972i	$-0.771414\pi$
$101$	−15.1360			−1.50608			−0.753042	+	0.657972i	$0.771414\pi$
$102$		0			0
$103$			10.7182i			1.05609i	0.849215	+	0.528047i	$0.177075\pi$
$103$			10.7182i			1.05609i	−0.849215	+	0.528047i	$0.822925\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.19081	−	4.72896i	0.791835	−	0.457166i	−0.0487731	−	0.998810i	$-0.515531\pi$
$107$	8.19081	−	4.72896i	0.791835	−	0.457166i	0.840608	+	0.541644i	$0.182198\pi$
$108$		0			0
$109$	−7.18065	+	12.4373i	−0.687782	+	1.19127i	0.284772	+	0.958595i	$0.408082\pi$
$109$	−7.18065	+	12.4373i	−0.687782	+	1.19127i	−0.972554	+	0.232678i	$0.925251\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.15594	+	0.667384i	0.108742	+	0.0627822i	0.553385	−	0.832926i	$-0.313336\pi$
$113$	1.15594	+	0.667384i	0.108742	+	0.0627822i	−0.444643	+	0.895708i	$0.646669\pi$
$114$		0			0
$115$			0.887696i			0.0827781i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.83939	+	13.0180i	0.626966	+	1.19336i
$120$		0			0
$121$	−23.8930			−2.17209
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.8875			1.06325
$126$		0			0
$127$	−0.715218			−0.0634653			−0.0317326	−	0.999496i	$-0.510103\pi$
$127$	−0.715218			−0.0634653			−0.0317326	+	0.999496i	$0.510103\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	18.2871			1.59775			0.798875	−	0.601497i	$-0.205429\pi$
$131$	18.2871			1.59775			0.798875	+	0.601497i	$0.205429\pi$
$132$		0			0
$133$	−0.489419	+	12.2733i	−0.0424380	+	1.06423i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			3.05364i			0.260890i	0.991456	+	0.130445i	$0.0416406\pi$
$137$			3.05364i			0.260890i	−0.991456	+	0.130445i	$0.958359\pi$
$138$		0			0
$139$	12.6377	+	7.29638i	1.07192	+	0.618871i	0.928704	−	0.370821i	$-0.120924\pi$
$139$	12.6377	+	7.29638i	1.07192	+	0.618871i	0.143211	+	0.989692i	$0.454257\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.474967	+	0.822667i	−0.0397187	+	0.0687949i
$144$		0			0
$145$	−4.00625	+	2.31301i	−0.332701	+	0.192085i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	3.99065i		−	0.326927i	−0.986549	−	0.163463i	$-0.947733\pi$
$149$		−	3.99065i		−	0.326927i	0.986549	−	0.163463i	$-0.0522665\pi$
$150$		0			0
$151$	8.14006			0.662429			0.331214	−	0.943556i	$-0.392542\pi$
$151$	8.14006			0.662429			0.331214	+	0.943556i	$0.392542\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.28275	−	3.05000i	0.424321	−	0.244982i
$156$		0			0
$157$	6.24025	−	3.60281i	0.498026	−	0.287536i	−0.229872	−	0.973221i	$-0.573831\pi$
$157$	6.24025	−	3.60281i	0.498026	−	0.287536i	0.727898	+	0.685685i	$0.240497\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.969046	−	0.612216i	−0.0763715	−	0.0482494i
$162$		0			0
$163$	−10.5854	−	18.3344i	−0.829111	−	1.43606i	−0.898736	−	0.438490i	$-0.855514\pi$
$163$	−10.5854	−	18.3344i	−0.829111	−	1.43606i	0.0696247	−	0.997573i	$-0.477820\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.90489	+	13.6917i	−0.611699	+	1.05949i	0.379256	+	0.925292i	$0.376180\pi$
$167$	−7.90489	+	13.6917i	−0.611699	+	1.05949i	−0.990954	+	0.134201i	$0.957153\pi$
$168$		0			0
$169$	−6.48707	−	11.2359i	−0.499005	−	0.864303i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.2911	−	19.5568i	0.858449	−	1.48688i	−0.0149584	−	0.999888i	$-0.504762\pi$
$173$	11.2911	−	19.5568i	0.858449	−	1.48688i	0.873408	−	0.486990i	$-0.161905\pi$
$174$		0			0
$175$	−1.13284	+	1.79312i	−0.0856348	+	0.135547i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.88911	−	4.55478i	−0.589660	−	0.340440i	0.175303	−	0.984515i	$-0.443909\pi$
$179$	−7.88911	−	4.55478i	−0.589660	−	0.340440i	−0.764963	+	0.644074i	$0.777243\pi$
$180$		0			0
$181$			7.60134i			0.565003i	0.959267	+	0.282501i	$0.0911642\pi$
$181$			7.60134i			0.565003i	−0.959267	+	0.282501i	$0.908836\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.46483	−	7.73331i	−0.328261	−	0.568564i
$186$		0			0
$187$	28.4332	+	16.4159i	2.07924	+	1.20045i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.95614	−	5.17083i	−0.648043	−	0.374148i	0.139663	−	0.990199i	$-0.455398\pi$
$191$	−8.95614	−	5.17083i	−0.648043	−	0.374148i	−0.787706	+	0.616051i	$0.788731\pi$
$192$		0			0
$193$	−5.65843	−	9.80068i	−0.407302	−	0.705468i	0.587284	−	0.809381i	$-0.300197\pi$
$193$	−5.65843	−	9.80068i	−0.407302	−	0.705468i	−0.994586	+	0.103912i	$0.966864\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			22.1012i			1.57464i	0.616543	+	0.787321i	$0.288533\pi$
$197$			22.1012i			1.57464i	−0.616543	+	0.787321i	$0.711467\pi$
$198$		0			0
$199$	12.6214	+	7.28696i	0.894706	+	0.516559i	0.875479	−	0.483257i	$-0.160546\pi$
$199$	12.6214	+	7.28696i	0.894706	+	0.516559i	0.0192269	+	0.999815i	$0.493879\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.238009	−	5.96861i	0.0167050	−	0.418914i
$204$		0			0
$205$	4.83027	−	8.36627i	0.337361	−	0.584326i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	13.7118	+	23.7496i	0.948468	+	1.64279i
$210$		0			0
$211$	11.4970	−	19.9135i	0.791489	−	1.37090i	−0.133556	−	0.991041i	$-0.542640\pi$
$211$	11.4970	−	19.9135i	0.791489	−	1.37090i	0.925045	−	0.379858i	$-0.124027\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.73672	−	6.47219i	−0.254842	−	0.441400i
$216$		0			0
$217$	−0.313845	+	7.87036i	−0.0213052	+	0.534275i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.774070	−	0.446910i	0.0520696	−	0.0300624i
$222$		0			0
$223$	16.8616	−	9.73506i	1.12914	−	0.651908i	0.185420	−	0.982659i	$-0.440636\pi$
$223$	16.8616	−	9.73506i	1.12914	−	0.651908i	0.943718	+	0.330751i	$0.107302\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.0147			−0.930191			−0.465095	−	0.885261i	$-0.653980\pi$
$227$	−14.0147			−0.930191			−0.465095	+	0.885261i	$0.653980\pi$
$228$		0			0
$229$		−	18.7560i		−	1.23943i	−0.784827	−	0.619714i	$-0.787248\pi$
$229$		−	18.7560i		−	1.23943i	0.784827	−	0.619714i	$-0.212752\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.05734	−	1.76516i	0.200293	−	0.115639i	−0.396499	−	0.918035i	$-0.629775\pi$
$233$	3.05734	−	1.76516i	0.200293	−	0.115639i	0.596792	+	0.802396i	$0.296442\pi$
$234$		0			0
$235$	0.133282	−	0.230851i	0.00869434	−	0.0150590i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.9732	+	9.79950i	1.09791	+	0.633877i	0.935670	−	0.352875i	$-0.114796\pi$
$239$	16.9732	+	9.79950i	1.09791	+	0.633877i	0.162236	+	0.986752i	$0.448129\pi$
$240$		0			0
$241$		−	12.2233i		−	0.787373i	−0.919245	−	0.393687i	$-0.871199\pi$
$241$		−	12.2233i		−	0.787373i	0.919245	−	0.393687i	$-0.128801\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.15961	+	12.9529i	0.393523	+	0.827531i
$246$		0			0
$247$	0.746587			0.0475042
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.48303			−0.535444			−0.267722	−	0.963496i	$-0.586271\pi$
$251$	−8.48303			−0.535444			−0.267722	+	0.963496i	$0.586271\pi$
$252$		0			0
$253$	−2.55914			−0.160892
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.8226			−1.04936			−0.524682	−	0.851298i	$-0.675816\pi$
$257$	−16.8226			−1.04936			−0.524682	+	0.851298i	$0.675816\pi$
$258$		0			0
$259$	11.5213	+	0.459431i	0.715896	+	0.0285477i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			27.0829i			1.67001i	0.550246	+	0.835003i	$0.314534\pi$
$263$			27.0829i			1.67001i	−0.550246	+	0.835003i	$0.685466\pi$
$264$		0			0
$265$	22.1160	+	12.7687i	1.35857	+	0.784373i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.61318	+	4.52615i	−0.159328	+	0.275964i	−0.934627	−	0.355631i	$-0.884266\pi$
$269$	−2.61318	+	4.52615i	−0.159328	+	0.275964i	0.775298	+	0.631595i	$0.217599\pi$
$270$		0			0
$271$	−10.6766	+	6.16413i	−0.648557	+	0.374444i	−0.787903	−	0.615799i	$-0.788833\pi$
$271$	−10.6766	+	6.16413i	−0.648557	+	0.374444i	0.139346	+	0.990244i	$0.455500\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			4.73543i			0.285557i
$276$		0			0
$277$	21.6742			1.30228			0.651138	−	0.758959i	$-0.274292\pi$
$277$	21.6742			1.30228			0.651138	+	0.758959i	$0.274292\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.39885	−	5.42643i	0.560688	−	0.323714i	−0.192733	−	0.981251i	$-0.561735\pi$
$281$	9.39885	−	5.42643i	0.560688	−	0.323714i	0.753422	+	0.657538i	$0.228402\pi$
$282$		0			0
$283$	−26.3386	+	15.2066i	−1.56567	+	0.903939i	−0.569003	+	0.822336i	$0.692671\pi$
$283$	−26.3386	+	15.2066i	−1.56567	+	0.903939i	−0.996665	+	0.0816032i	$0.973996\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.80168	+	11.0429i	0.342463	+	0.651841i
$288$		0			0
$289$	−6.94618	−	12.0311i	−0.408599	−	0.707714i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.22993	+	3.86235i	−0.130274	+	0.225641i	−0.923782	−	0.382919i	$-0.874919\pi$
$293$	−2.22993	+	3.86235i	−0.130274	+	0.225641i	0.793508	+	0.608559i	$0.208252\pi$
$294$		0			0
$295$	−6.60602	−	11.4420i	−0.384618	−	0.666177i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0348353	+	0.0603365i	−0.00201458	+	0.00348935i
$300$		0			0
$301$	9.64241	+	0.384509i	0.555779	+	0.0221627i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.2614	+	7.07914i	0.702087	+	0.405350i
$306$		0			0
$307$		−	9.43048i		−	0.538226i	−0.963109	−	0.269113i	$-0.913269\pi$
$307$		−	9.43048i		−	0.538226i	0.963109	−	0.269113i	$-0.0867305\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.48354	−	6.03367i	−0.197533	−	0.342138i	0.750195	−	0.661217i	$-0.229960\pi$
$311$	−3.48354	−	6.03367i	−0.197533	−	0.342138i	−0.947728	+	0.319079i	$0.896626\pi$
$312$		0			0
$313$	−5.74395	−	3.31627i	−0.324667	−	0.187447i	0.328804	−	0.944398i	$-0.393355\pi$
$313$	−5.74395	−	3.31627i	−0.324667	−	0.187447i	−0.653471	+	0.756951i	$0.726688\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.0283	−	7.52187i	−0.731740	−	0.422470i	0.0873185	−	0.996180i	$-0.472170\pi$
$317$	−13.0283	−	7.52187i	−0.731740	−	0.422470i	−0.819058	+	0.573710i	$0.805504\pi$
$318$		0			0
$319$	−6.66819	−	11.5497i	−0.373347	−	0.646656i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	25.8037i		−	1.43576i
$324$		0			0
$325$	0.111646	+	0.0644591i	0.00619303	+	0.00357555i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.160086	+	0.304707i	0.00882583	+	0.0167990i
$330$		0			0
$331$	15.1501	−	26.2407i	0.832722	−	1.44232i	−0.0631495	−	0.998004i	$-0.520114\pi$
$331$	15.1501	−	26.2407i	0.832722	−	1.44232i	0.895872	−	0.444313i	$-0.146552\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	15.6665	+	27.1351i	0.855950	+	1.48255i
$336$		0			0
$337$	−3.02011	+	5.23099i	−0.164516	+	0.284950i	−0.936483	−	0.350712i	$-0.885940\pi$
$337$	−3.02011	+	5.23099i	−0.164516	+	0.284950i	0.771967	+	0.635662i	$0.219273\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.79286	+	15.2297i	0.476160	+	0.824733i
$342$		0			0
$343$	−18.3880	−	2.20914i	−0.992860	−	0.119282i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.62925	−	3.25005i	0.302194	−	0.174472i	−0.341234	−	0.939978i	$-0.610845\pi$
$347$	5.62925	−	3.25005i	0.302194	−	0.174472i	0.643428	+	0.765506i	$0.277512\pi$
$348$		0			0
$349$	10.6732	−	6.16218i	0.571324	−	0.329854i	−0.186354	−	0.982483i	$-0.559667\pi$
$349$	10.6732	−	6.16218i	0.571324	−	0.329854i	0.757678	+	0.652629i	$0.226334\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.69397			0.515958			0.257979	−	0.966151i	$-0.416944\pi$
$353$	9.69397			0.515958			0.257979	+	0.966151i	$0.416944\pi$
$354$		0			0
$355$			3.03304i			0.160977i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.8975	−	12.0652i	1.10293	−	0.636776i	0.165940	−	0.986136i	$-0.446934\pi$
$359$	20.8975	−	12.0652i	1.10293	−	0.636776i	0.936989	+	0.349360i	$0.113601\pi$
$360$		0			0
$361$	1.27663	−	2.21118i	0.0671908	−	0.116378i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.34542	+	3.08618i	0.279792	+	0.161538i
$366$		0			0
$367$		−	4.89237i		−	0.255380i	−0.991814	−	0.127690i	$-0.959244\pi$
$367$		−	4.89237i		−	0.255380i	0.991814	−	0.127690i	$-0.0407562\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−29.1915	+	15.3366i	−1.51555	+	0.796235i
$372$		0			0
$373$	−30.7947			−1.59449			−0.797245	−	0.603656i	$-0.793710\pi$
$373$	−30.7947			−1.59449			−0.797245	+	0.603656i	$0.793710\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.363072			−0.0186992
$378$		0			0
$379$	8.36682			0.429775			0.214887	−	0.976639i	$-0.431062\pi$
$379$	8.36682			0.429775			0.214887	+	0.976639i	$0.431062\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.51462			−0.179589			−0.0897944	−	0.995960i	$-0.528621\pi$
$383$	−3.51462			−0.179589			−0.0897944	+	0.995960i	$0.528621\pi$
$384$		0			0
$385$	27.0724	+	17.1036i	1.37974	+	0.871681i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	26.5264i		−	1.34494i	−0.740123	−	0.672472i	$-0.765233\pi$
$389$		−	26.5264i		−	1.34494i	0.740123	−	0.672472i	$-0.234767\pi$
$390$		0			0
$391$	2.08536	+	1.20398i	0.105461	+	0.0608881i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	17.8110	−	30.8495i	0.896166	−	1.55221i
$396$		0			0
$397$	19.9734	−	11.5317i	1.00244	−	0.578758i	0.0934690	−	0.995622i	$-0.470204\pi$
$397$	19.9734	−	11.5317i	1.00244	−	0.578758i	0.908969	+	0.416865i	$0.136871\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	1.45936i		−	0.0728769i	−0.999336	−	0.0364385i	$-0.988399\pi$
$401$		−	1.45936i		−	0.0728769i	0.999336	−	0.0364385i	$-0.0116013\pi$
$402$		0			0
$403$	0.478757			0.0238486
$404$		0			0
$405$		0			0
$406$		0			0
$407$	22.2944	−	12.8717i	1.10509	−	0.638026i
$408$		0			0
$409$	22.3585	−	12.9087i	1.10556	−	0.638293i	0.167882	−	0.985807i	$-0.446307\pi$
$409$	22.3585	−	12.9087i	1.10556	−	0.638293i	0.937675	+	0.347514i	$0.112974\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.0465	+	0.679760i	0.838804	+	0.0334488i
$414$		0			0
$415$	15.6214	+	27.0571i	0.766826	+	1.32818i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.15180	+	7.19113i	−0.202829	+	0.351310i	−0.949439	−	0.313952i	$-0.898347\pi$
$419$	−4.15180	+	7.19113i	−0.202829	+	0.351310i	0.746610	+	0.665262i	$0.231680\pi$
$420$		0			0
$421$	8.28977	+	14.3583i	0.404019	+	0.699781i	0.994207	−	0.107485i	$-0.0342798\pi$
$421$	8.28977	+	14.3583i	0.404019	+	0.699781i	−0.590188	+	0.807266i	$0.700946\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.22785	−	3.85874i	0.108066	−	0.187177i
$426$		0			0
$427$	−16.1842	+	8.50283i	−0.783209	+	0.411481i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.7217	+	7.92225i	0.660953	+	0.381601i	0.792640	−	0.609690i	$-0.208706\pi$
$431$	13.7217	+	7.92225i	0.660953	+	0.381601i	−0.131687	+	0.991291i	$0.542039\pi$
$432$		0			0
$433$		−	12.0650i		−	0.579808i	−0.957056	−	0.289904i	$-0.906377\pi$
$433$		−	12.0650i		−	0.579808i	0.957056	−	0.289904i	$-0.0936233\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.00566	+	1.74186i	0.0481073	+	0.0833243i
$438$		0			0
$439$	−17.4438	−	10.0712i	−0.832548	−	0.480672i	0.0221764	−	0.999754i	$-0.492940\pi$
$439$	−17.4438	−	10.0712i	−0.832548	−	0.480672i	−0.854724	+	0.519082i	$0.826274\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.6613	−	6.73264i	−0.554044	−	0.319877i	0.196708	−	0.980462i	$-0.436975\pi$
$443$	−11.6613	−	6.73264i	−0.554044	−	0.319877i	−0.750751	+	0.660585i	$0.770308\pi$
$444$		0			0
$445$	8.29340	+	14.3646i	0.393145	+	0.680947i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	7.63121i		−	0.360139i	−0.983654	−	0.180069i	$-0.942368\pi$
$449$		−	7.63121i		−	0.360139i	0.983654	−	0.180069i	$-0.0576323\pi$
$450$		0			0
$451$	24.1192	+	13.9252i	1.13573	+	0.655712i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.771762	−	0.405466i	0.0361807	−	0.0190086i
$456$		0			0
$457$	−12.9351	+	22.4043i	−0.605079	+	1.04803i	0.386960	+	0.922096i	$0.373525\pi$
$457$	−12.9351	+	22.4043i	−0.605079	+	1.04803i	−0.992039	+	0.125931i	$0.959808\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.4048	+	19.7537i	0.531176	+	0.920023i	0.999338	+	0.0363806i	$0.0115829\pi$
$461$	11.4048	+	19.7537i	0.531176	+	0.920023i	−0.468162	+	0.883642i	$0.655084\pi$
$462$		0			0
$463$	10.7397	−	18.6017i	0.499116	−	0.864494i	−0.500884	−	0.865515i	$-0.666992\pi$
$463$	10.7397	−	18.6017i	0.499116	−	0.864494i	0.999999	+	0.00102063i	$0.000324876\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.8577	+	29.1984i	0.780081	+	1.35114i	0.931894	+	0.362730i	$0.118155\pi$
$467$	16.8577	+	29.1984i	0.780081	+	1.35114i	−0.151813	+	0.988409i	$0.548511\pi$
$468$		0			0
$469$	−40.4265	−	1.61208i	−1.86672	−	0.0744389i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.6587	−	10.7726i	0.857928	−	0.495325i
$474$		0			0
$475$	3.22312	−	1.86087i	0.147887	−	0.0853826i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.116088			0.00530421			0.00265211	−	0.999996i	$-0.499156\pi$
$479$	0.116088			0.00530421			0.00265211	+	0.999996i	$0.499156\pi$
$480$		0			0
$481$		−	0.700842i		−	0.0319557i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.35037	+	3.08904i	−0.242948	+	0.140266i
$486$		0			0
$487$	−3.60826	+	6.24968i	−0.163506	+	0.283200i	−0.936124	−	0.351671i	$-0.885614\pi$
$487$	−3.60826	+	6.24968i	−0.163506	+	0.283200i	0.772618	+	0.634871i	$0.218947\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.2127	+	7.62833i	0.596279	+	0.344262i	0.767576	−	0.640958i	$-0.221463\pi$
$491$	13.2127	+	7.62833i	0.596279	+	0.344262i	−0.171298	+	0.985219i	$0.554796\pi$
$492$		0			0
$493$			12.5486i			0.565159i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.31100	−	2.09180i	−0.148519	−	0.0938299i
$498$		0			0
$499$	16.4831			0.737884			0.368942	−	0.929452i	$-0.379720\pi$
$499$	16.4831			0.737884			0.368942	+	0.929452i	$0.379720\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.95709			−0.310201			−0.155101	−	0.987899i	$-0.549570\pi$
$503$	−6.95709			−0.310201			−0.155101	+	0.987899i	$0.549570\pi$
$504$		0			0
$505$	31.0134			1.38008
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−26.2690			−1.16435			−0.582177	−	0.813062i	$-0.697799\pi$
$509$	−26.2690			−1.16435			−0.582177	+	0.813062i	$0.697799\pi$
$510$		0			0
$511$	−7.05558	+	3.70684i	−0.312120	+	0.163981i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	21.9614i		−	0.967735i
$516$		0			0
$517$	0.665521	+	0.384239i	0.0292696	+	0.0168988i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.46686	+	16.3971i	−0.414750	+	0.718369i	−0.995402	−	0.0957832i	$-0.969464\pi$
$521$	−9.46686	+	16.3971i	−0.414750	+	0.718369i	0.580652	+	0.814152i	$0.302798\pi$
$522$		0			0
$523$	−8.19679	+	4.73242i	−0.358421	+	0.206934i	−0.668388	−	0.743813i	$-0.733015\pi$
$523$	−8.19679	+	4.73242i	−0.358421	+	0.206934i	0.309967	+	0.950747i	$0.399682\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	16.5469i		−	0.720794i
$528$		0			0
$529$	22.8123			0.991839
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.656625	−	0.379103i	0.0284416	−	0.0164208i
$534$		0			0
$535$	−16.7828	+	9.68958i	−0.725585	+	0.418917i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−37.3420	+	17.7576i	−1.60843	+	0.764872i
$540$		0			0
$541$	−9.96877	−	17.2664i	−0.428591	−	0.742341i	0.568157	−	0.822920i	$-0.307656\pi$
$541$	−9.96877	−	17.2664i	−0.428591	−	0.742341i	−0.996748	+	0.0805787i	$0.974323\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.7131	−	25.4838i	0.630238	−	1.09160i
$546$		0			0
$547$	−9.19529	−	15.9267i	−0.393162	−	0.680977i	0.599702	−	0.800223i	$-0.295286\pi$
$547$	−9.19529	−	15.9267i	−0.393162	−	0.680977i	−0.992865	+	0.119246i	$0.961952\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.24077	+	9.07729i	−0.223264	+	0.386705i
$552$		0			0
$553$	21.3929	+	40.7191i	0.909719	+	1.73155i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.1334	+	9.89198i	0.725966	+	0.419137i	0.816945	−	0.576716i	$-0.195666\pi$
$557$	17.1334	+	9.89198i	0.725966	+	0.419137i	−0.0909787	+	0.995853i	$0.529000\pi$
$558$		0			0
$559$		−	0.586551i		−	0.0248085i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.8204	−	20.4736i	−0.498171	−	0.862857i	0.501827	−	0.864968i	$-0.332661\pi$
$563$	−11.8204	−	20.4736i	−0.498171	−	0.862857i	−0.999998	+	0.00211070i	$0.999328\pi$
$564$		0			0
$565$	−2.36851	−	1.36746i	−0.0996440	−	0.0575295i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.215598	+	0.124476i	0.00903834	+	0.00521829i	0.504512	−	0.863404i	$-0.331672\pi$
$569$	0.215598	+	0.124476i	0.00903834	+	0.00521829i	−0.495474	+	0.868623i	$0.665006\pi$
$570$		0			0
$571$	−10.7047	−	18.5412i	−0.447979	−	0.775923i	0.550275	−	0.834983i	$-0.314523\pi$
$571$	−10.7047	−	18.5412i	−0.447979	−	0.775923i	−0.998254	+	0.0590604i	$0.981190\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.347308i			0.0144838i
$576$		0			0
$577$	−15.1856	−	8.76740i	−0.632184	−	0.364991i	0.149414	−	0.988775i	$-0.452261\pi$
$577$	−15.1856	−	8.76740i	−0.632184	−	0.364991i	−0.781597	+	0.623783i	$0.785595\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−40.3103	−	1.60745i	−1.67235	−	0.0666881i
$582$		0			0
$583$	−36.8109	+	63.7583i	−1.52455	+	2.64060i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.868296	+	1.50393i	0.0358384	+	0.0620739i	0.883388	−	0.468642i	$-0.155257\pi$
$587$	0.868296	+	1.50393i	0.0358384	+	0.0620739i	−0.847550	+	0.530716i	$0.821923\pi$
$588$		0			0
$589$	6.91062	−	11.9696i	0.284747	−	0.493197i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.20172	−	2.08145i	−0.0493489	−	0.0854749i	0.840296	−	0.542128i	$-0.182381\pi$
$593$	−1.20172	−	2.08145i	−0.0493489	−	0.0854749i	−0.889645	+	0.456653i	$0.849048\pi$
$594$		0			0
$595$	−14.0138	−	26.6738i	−0.574510	−	1.09352i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.0792419	+	0.0457503i	−0.00323774	+	0.00186931i	−0.501618	−	0.865089i	$-0.667262\pi$
$599$	−0.0792419	+	0.0457503i	−0.00323774	+	0.00186931i	0.498380	+	0.866959i	$0.333928\pi$
$600$		0			0
$601$	−23.2642	+	13.4316i	−0.948968	+	0.547887i	−0.892760	−	0.450532i	$-0.851234\pi$
$601$	−23.2642	+	13.4316i	−0.948968	+	0.547887i	−0.0562081	+	0.998419i	$0.517901\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	48.9564			1.99036
$606$		0			0
$607$		−	19.8891i		−	0.807275i	−0.914919	−	0.403637i	$-0.867746\pi$
$607$		−	19.8891i		−	0.807275i	0.914919	−	0.403637i	$-0.132254\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0181183	−	0.0104606i	0.000732987	−	0.000423190i
$612$		0			0
$613$	−21.2209	+	36.7558i	−0.857106	+	1.48455i	0.0175716	+	0.999846i	$0.494406\pi$
$613$	−21.2209	+	36.7558i	−0.857106	+	1.48455i	−0.874678	+	0.484705i	$0.838927\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.9907	+	8.07756i	0.563246	+	0.325190i	0.754447	−	0.656361i	$-0.227905\pi$
$617$	13.9907	+	8.07756i	0.563246	+	0.325190i	−0.191201	+	0.981551i	$0.561238\pi$
$618$		0			0
$619$		−	35.0821i		−	1.41007i	−0.709174	−	0.705034i	$-0.750932\pi$
$619$		−	35.0821i		−	1.41007i	0.709174	−	0.705034i	$-0.249068\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.4007	−	0.853392i	−0.857401	−	0.0341904i
$624$		0			0
$625$	−20.3490			−0.813962
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−24.2226			−0.965820
$630$		0			0
$631$	13.0916			0.521170			0.260585	−	0.965451i	$-0.416085\pi$
$631$	13.0916			0.521170			0.260585	+	0.965451i	$0.416085\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.46547			0.0581554
$636$		0			0
$637$	−0.0896361	+	1.12212i	−0.00355151	+	0.0444602i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	3.98448i		−	0.157377i	−0.996899	−	0.0786887i	$-0.974927\pi$
$641$		−	3.98448i		−	0.157377i	0.996899	−	0.0786887i	$-0.0250733\pi$
$642$		0			0
$643$	24.9128	+	14.3834i	0.982467	+	0.567227i	0.903014	−	0.429611i	$-0.141349\pi$
$643$	24.9128	+	14.3834i	0.982467	+	0.567227i	0.0794528	+	0.996839i	$0.474683\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.4786	−	19.8815i	0.451270	−	0.781623i	−0.547195	−	0.837005i	$-0.684304\pi$
$647$	11.4786	−	19.8815i	0.451270	−	0.781623i	0.998465	+	0.0553822i	$0.0176377\pi$
$648$		0			0
$649$	32.9861	−	19.0445i	1.29482	−	0.747564i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			1.85999i			0.0727871i	0.999338	+	0.0363936i	$0.0115870\pi$
$653$			1.85999i			0.0727871i	−0.999338	+	0.0363936i	$0.988413\pi$
$654$		0			0
$655$	−37.4700			−1.46407
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.04167	−	5.22021i	0.352213	−	0.203351i	−0.313446	−	0.949606i	$-0.601484\pi$
$659$	9.04167	−	5.22021i	0.352213	−	0.203351i	0.665660	+	0.746255i	$0.268150\pi$
$660$		0			0
$661$	−34.6227	+	19.9894i	−1.34667	+	0.777498i	−0.987776	−	0.155881i	$-0.950178\pi$
$661$	−34.6227	+	19.9894i	−1.34667	+	0.777498i	−0.358891	+	0.933380i	$0.616845\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.00281	−	25.1478i	0.0388874	−	0.975188i
$666$		0			0
$667$	−0.489063	−	0.847081i	−0.0189366	−	0.0327991i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−20.4085	+	35.3485i	−0.787861	+	1.36462i
$672$		0			0
$673$	−17.1038	−	29.6247i	−0.659303	−	1.14195i	−0.980796	−	0.195035i	$-0.937518\pi$
$673$	−17.1038	−	29.6247i	−0.659303	−	1.14195i	0.321493	−	0.946912i	$-0.395815\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.0112	−	19.0720i	0.423195	−	0.732995i	−0.573055	−	0.819517i	$-0.694242\pi$
$677$	11.0112	−	19.0720i	0.423195	−	0.732995i	0.996250	+	0.0865220i	$0.0275753\pi$
$678$		0			0
$679$	0.317862	−	7.97110i	0.0121984	−	0.305903i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−28.8171	−	16.6375i	−1.10265	−	0.636618i	−0.165737	−	0.986170i	$-0.553000\pi$
$683$	−28.8171	−	16.6375i	−1.10265	−	0.636618i	−0.936917	+	0.349552i	$0.886334\pi$
$684$		0			0
$685$		−	6.25687i		−	0.239063i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.00215	+	1.73577i	0.0381787	+	0.0661275i
$690$		0			0
$691$	−38.0659	−	21.9774i	−1.44810	−	0.836058i	−0.449727	−	0.893166i	$-0.648479\pi$
$691$	−38.0659	−	21.9774i	−1.44810	−	0.836058i	−0.998368	+	0.0571078i	$0.981812\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−25.8945	−	14.9502i	−0.982233	−	0.567092i
$696$		0			0
$697$	−13.1026	−	22.6944i	−0.496297	−	0.859611i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	20.6866i		−	0.781321i	−0.920535	−	0.390661i	$-0.872247\pi$
$701$		−	20.6866i		−	0.781321i	0.920535	−	0.390661i	$-0.127753\pi$
$702$		0			0
$703$	−17.5220	−	10.1163i	−0.660854	−	0.381544i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−21.3890	+	33.8555i	−0.804414	+	1.27327i
$708$		0			0
$709$	1.75655	−	3.04244i	0.0659688	−	0.114261i	−0.831155	−	0.556041i	$-0.812320\pi$
$709$	1.75655	−	3.04244i	0.0659688	−	0.114261i	0.897123	+	0.441780i	$0.145653\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.644891	+	1.11698i	0.0241514	+	0.0418314i
$714$		0			0
$715$	0.973201	−	1.68563i	0.0363956	−	0.0630391i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.36853	−	11.0306i	−0.237506	−	0.411372i	0.722492	−	0.691379i	$-0.242997\pi$
$719$	−6.36853	−	11.0306i	−0.237506	−	0.411372i	−0.959998	+	0.280007i	$0.909663\pi$
$720$		0			0
$721$	23.9740	+	15.1461i	0.892838	+	0.564070i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.56743	+	0.904959i	−0.0582131	+	0.0336093i
$726$		0			0
$727$	−17.7538	+	10.2502i	−0.658454	+	0.380158i	−0.791687	−	0.610926i	$-0.790797\pi$
$727$	−17.7538	+	10.2502i	−0.658454	+	0.380158i	0.133234	+	0.991085i	$0.457464\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−20.2725			−0.749805
$732$		0			0
$733$			19.0863i			0.704969i	0.935818	+	0.352484i	$0.114663\pi$
$733$			19.0863i			0.704969i	−0.935818	+	0.352484i	$0.885337\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−78.2279	+	45.1649i	−2.88156	+	1.66367i
$738$		0			0
$739$	17.3600	−	30.0685i	0.638599	−	1.10609i	−0.347141	−	0.937813i	$-0.612847\pi$
$739$	17.3600	−	30.0685i	0.638599	−	1.10609i	0.985740	−	0.168274i	$-0.0538193\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.7742	−	12.5713i	−0.798816	−	0.461197i	0.0442408	−	0.999021i	$-0.485913\pi$
$743$	−21.7742	−	12.5713i	−0.798816	−	0.461197i	−0.843057	+	0.537824i	$0.819246\pi$
$744$		0			0
$745$			8.17678i			0.299574i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.997058	−	25.0035i	0.0364317	−	0.913606i
$750$		0			0
$751$	45.2696			1.65191			0.825955	−	0.563736i	$-0.190636\pi$
$751$	45.2696			1.65191			0.825955	+	0.563736i	$0.190636\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.6789			−0.607006
$756$		0			0
$757$	−5.73623			−0.208487			−0.104243	−	0.994552i	$-0.533242\pi$
$757$	−5.73623			−0.208487			−0.104243	+	0.994552i	$0.533242\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.4200			0.595225			0.297613	−	0.954687i	$-0.403810\pi$
$761$	16.4200			0.595225			0.297613	+	0.954687i	$0.403810\pi$
$762$		0			0
$763$	17.6720	+	33.6367i	0.639769	+	1.21773i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	1.03694i		−	0.0374419i
$768$		0			0
$769$	45.8286	+	26.4592i	1.65262	+	0.954142i	0.975989	+	0.217822i	$0.0698951\pi$
$769$	45.8286	+	26.4592i	1.65262	+	0.954142i	0.676633	+	0.736320i	$0.263438\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.1328	+	24.4788i	−0.508322	+	0.880440i	0.491631	+	0.870803i	$0.336401\pi$
$773$	−14.1328	+	24.4788i	−0.508322	+	0.880440i	−0.999954	+	0.00963659i	$0.996933\pi$
$774$		0			0
$775$	2.06686	−	1.19330i	0.0742438	−	0.0428647i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	21.8886i		−	0.784242i
$780$		0			0
$781$	−8.74398			−0.312884
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.7862	+	7.38211i	−0.456359	+	0.263479i
$786$		0			0
$787$	−9.89388	+	5.71224i	−0.352679	+	0.203619i	−0.665864	−	0.746073i	$-0.731937\pi$
$787$	−9.89388	+	5.71224i	−0.352679	+	0.203619i	0.313186	+	0.949692i	$0.398604\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.12627	−	1.64247i	0.111157	−	0.0583995i
$792$		0			0
$793$	0.555605	+	0.962336i	0.0197301	+	0.0341735i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.29457	+	3.97432i	−0.0812780	+	0.140778i	−0.903799	−	0.427957i	$-0.859233\pi$
$797$	−2.29457	+	3.97432i	−0.0812780	+	0.140778i	0.822521	+	0.568735i	$0.192567\pi$
$798$		0			0
$799$	−0.361541	−	0.626207i	−0.0127904	−	0.0221536i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.89717	+	15.4103i	−0.313974	+	0.543819i
$804$		0			0
$805$	1.98556	+	1.25442i	0.0699818	+	0.0442126i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.1693	+	7.02597i	0.427851	+	0.247020i	0.698431	−	0.715678i	$-0.253882\pi$
$809$	12.1693	+	7.02597i	0.427851	+	0.247020i	−0.270579	+	0.962698i	$0.587215\pi$
$810$		0			0
$811$		−	33.6468i		−	1.18150i	−0.806855	−	0.590749i	$-0.798832\pi$
$811$		−	33.6468i		−	1.18150i	0.806855	−	0.590749i	$-0.201168\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	21.6893	+	37.5670i	0.759743	+	1.31591i
$816$		0			0
$817$	−14.6646	−	8.46658i	−0.513048	−	0.296208i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−41.8521	−	24.1633i	−1.46065	−	0.843306i	−0.461608	−	0.887084i	$-0.652727\pi$
$821$	−41.8521	−	24.1633i	−1.46065	−	0.843306i	−0.999041	+	0.0437777i	$0.986061\pi$
$822$		0			0
$823$	−16.0664	−	27.8278i	−0.560040	−	0.970017i	−0.997492	−	0.0707757i	$-0.977453\pi$
$823$	−16.0664	−	27.8278i	−0.560040	−	0.970017i	0.437453	−	0.899241i	$-0.355881\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	4.51801i		−	0.157107i	−0.996910	−	0.0785533i	$-0.974970\pi$
$827$		−	4.51801i		−	0.157107i	0.996910	−	0.0785533i	$-0.0250301\pi$
$828$		0			0
$829$	33.6077	+	19.4034i	1.16724	+	0.673909i	0.953029	−	0.302878i	$-0.0979475\pi$
$829$	33.6077	+	19.4034i	1.16724	+	0.673909i	0.214215	+	0.976787i	$0.431281\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	38.7831	+	3.09802i	1.34375	+	0.107340i
$834$		0			0
$835$	16.1970	−	28.0540i	0.560520	−	0.970849i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.38179	+	14.5177i	0.289372	+	0.501206i	0.973660	−	0.228005i	$-0.0732203\pi$
$839$	8.38179	+	14.5177i	0.289372	+	0.501206i	−0.684288	+	0.729212i	$0.739887\pi$
$840$		0			0
$841$	−11.9514	+	20.7004i	−0.412116	+	0.713806i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	13.2919	+	23.0223i	0.457256	+	0.791990i
$846$		0			0
$847$	−33.7637	+	53.4429i	−1.16014	+	1.83632i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.63513	−	0.944042i	0.0560515	−	0.0323614i
$852$		0			0
$853$	−14.0552	+	8.11477i	−0.481241	+	0.277844i	−0.720933	−	0.693004i	$-0.756287\pi$
$853$	−14.0552	+	8.11477i	−0.481241	+	0.277844i	0.239693	+	0.970849i	$0.422953\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−46.7556			−1.59714			−0.798570	−	0.601902i	$-0.794410\pi$
$857$	−46.7556			−1.59714			−0.798570	+	0.601902i	$0.794410\pi$
$858$		0			0
$859$			8.82915i			0.301247i	0.988591	+	0.150623i	$0.0481281\pi$
$859$			8.82915i			0.301247i	−0.988591	+	0.150623i	$0.951872\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.96721	−	5.17722i	0.305247	−	0.176235i	−0.339550	−	0.940588i	$-0.610275\pi$
$863$	8.96721	−	5.17722i	0.305247	−	0.176235i	0.644798	+	0.764353i	$0.276942\pi$
$864$		0			0
$865$	−23.1354	+	40.0716i	−0.786626	+	1.36248i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	88.9361	+	51.3473i	3.01695	+	1.74184i
$870$		0			0
$871$			2.45916i			0.0833253i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	16.7985	−	26.5895i	0.567893	−	0.898889i
$876$		0			0
$877$	39.4814			1.33319			0.666597	−	0.745418i	$-0.267750\pi$
$877$	39.4814			1.33319			0.666597	+	0.745418i	$0.267750\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−14.9886			−0.504980			−0.252490	−	0.967599i	$-0.581250\pi$
$881$	−14.9886			−0.504980			−0.252490	+	0.967599i	$0.581250\pi$
$882$		0			0
$883$	−0.888235			−0.0298915			−0.0149458	−	0.999888i	$-0.504758\pi$
$883$	−0.888235			−0.0298915			−0.0149458	+	0.999888i	$0.504758\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.09806			0.0368693			0.0184347	−	0.999830i	$-0.494132\pi$
$887$	1.09806			0.0368693			0.0184347	+	0.999830i	$0.494132\pi$
$888$		0			0
$889$	−1.01069	+	1.59977i	−0.0338974	+	0.0536545i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	0.603974i		−	0.0202112i
$894$		0			0
$895$	16.1647	+	9.33268i	0.540326	+	0.311957i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.36070	+	5.82090i	−0.112086	+	0.194138i
$900$		0			0
$901$	59.9919	−	34.6364i	1.99862	−	1.15390i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	15.5750i		−	0.517731i
$906$		0			0
$907$	−25.8584			−0.858613			−0.429307	−	0.903159i	$-0.641242\pi$
$907$	−25.8584			−0.858613			−0.429307	+	0.903159i	$0.641242\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−32.9640	+	19.0318i	−1.09215	+	0.630551i	−0.934147	−	0.356888i	$-0.883838\pi$
$911$	−32.9640	+	19.0318i	−1.09215	+	0.630551i	−0.157999	+	0.987439i	$0.550504\pi$
$912$		0			0
$913$	−78.0031	+	45.0351i	−2.58153	+	1.49045i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.8419	−	40.9038i	0.853374	−	1.35076i
$918$		0			0
$919$	−4.90995	−	8.50428i	−0.161964	−	0.280530i	0.773609	−	0.633663i	$-0.218450\pi$
$919$	−4.90995	−	8.50428i	−0.161964	−	0.280530i	−0.935573	+	0.353133i	$0.885116\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.119024	+	0.206155i	−0.00391772	+	0.00678569i
$924$		0			0
$925$	−1.74685	−	3.02563i	−0.0574361	−	0.0994823i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.99715	−	10.3874i	0.196760	−	0.340799i	−0.750716	−	0.660625i	$-0.770291\pi$
$929$	5.99715	−	10.3874i	0.196760	−	0.340799i	0.947476	+	0.319827i	$0.103625\pi$
$930$		0			0
$931$	26.7607	+	18.4383i	0.877048	+	0.604292i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−58.2592	−	33.6359i	−1.90528	−	1.10001i
$936$		0			0
$937$			36.5712i			1.19473i	0.801970	+	0.597364i	$0.203785\pi$
$937$			36.5712i			1.19473i	−0.801970	+	0.597364i	$0.796215\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−12.0155	−	20.8114i	−0.391693	−	0.678431i	0.600980	−	0.799264i	$-0.294777\pi$
$941$	−12.0155	−	20.8114i	−0.391693	−	0.678431i	−0.992673	+	0.120832i	$0.961444\pi$
$942$		0			0
$943$	1.76896	+	1.02131i	0.0576053	+	0.0332585i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.85426	−	4.53466i	−0.255229	−	0.147357i	0.366927	−	0.930250i	$-0.380410\pi$
$947$	−7.85426	−	4.53466i	−0.255229	−	0.147357i	−0.622156	+	0.782893i	$0.713743\pi$
$948$		0			0
$949$	0.242218	+	0.419534i	0.00786274	+	0.0136187i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	26.8728i		−	0.870495i	−0.900311	−	0.435247i	$-0.856661\pi$
$953$		−	26.8728i		−	0.870495i	0.900311	−	0.435247i	$-0.143339\pi$
$954$		0			0
$955$	18.3510	+	10.5949i	0.593824	+	0.342845i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.83026	+	4.31517i	0.220560	+	0.139344i
$960$		0			0
$961$	−11.0685	+	19.1712i	−0.357048	+	0.618425i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.5940	+	20.0815i	0.373225	+	0.646445i
$966$		0			0
$967$	0.193927	−	0.335892i	0.00623628	−	0.0108015i	−0.862890	−	0.505391i	$-0.831348\pi$
$967$	0.193927	−	0.335892i	0.00623628	−	0.0108015i	0.869127	+	0.494590i	$0.164682\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.5732	−	21.7775i	−0.403494	−	0.698872i	0.590651	−	0.806927i	$-0.298871\pi$
$971$	−12.5732	−	21.7775i	−0.403494	−	0.698872i	−0.994145	+	0.108055i	$0.965538\pi$
$972$		0			0
$973$	34.1788	−	17.9568i	1.09572	−	0.575669i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.3898	−	5.99857i	0.332400	−	0.191911i	−0.324506	−	0.945884i	$-0.605198\pi$
$977$	10.3898	−	5.99857i	0.332400	−	0.191911i	0.656906	+	0.753972i	$0.271865\pi$
$978$		0			0
$979$	−41.4118	+	23.9091i	−1.32353	+	0.764138i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	35.4781			1.13157			0.565787	−	0.824551i	$-0.308572\pi$
$983$	35.4781			1.13157			0.565787	+	0.824551i	$0.308572\pi$
$984$		0			0
$985$		−	45.2850i		−	1.44290i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.36848	−	0.790091i	0.0435151	−	0.0251234i
$990$		0			0
$991$	4.77487	−	8.27032i	0.151679	−	0.262715i	−0.780166	−	0.625573i	$-0.784865\pi$
$991$	4.77487	−	8.27032i	0.151679	−	0.262715i	0.931845	+	0.362857i	$0.118199\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−25.8610	−	14.9309i	−0.819849	−	0.473340i
$996$		0			0
$997$		−	26.1828i		−	0.829218i	−0.910000	−	0.414609i	$-0.863918\pi$
$997$		−	26.1828i		−	0.829218i	0.910000	−	0.414609i	$-0.136082\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.cx.a.17.8		48
3.2	odd	2		504.2.cx.a.185.19	yes	48
4.3	odd	2		3024.2.df.e.17.8		48
7.5	odd	6		1512.2.bs.a.1097.8		48
9.2	odd	6		1512.2.bs.a.521.8		48
9.7	even	3		504.2.bs.a.353.11	yes	48
12.11	even	2		1008.2.df.e.689.6		48
21.5	even	6		504.2.bs.a.257.11	✓	48
28.19	even	6		3024.2.ca.e.2609.8		48
36.7	odd	6		1008.2.ca.e.353.14		48
36.11	even	6		3024.2.ca.e.2033.8		48
63.47	even	6	inner	1512.2.cx.a.89.8		48
63.61	odd	6		504.2.cx.a.425.19	yes	48
84.47	odd	6		1008.2.ca.e.257.14		48
252.47	odd	6		3024.2.df.e.1601.8		48
252.187	even	6		1008.2.df.e.929.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.11	✓	48	21.5	even	6
504.2.bs.a.353.11	yes	48	9.7	even	3
504.2.cx.a.185.19	yes	48	3.2	odd	2
504.2.cx.a.425.19	yes	48	63.61	odd	6
1008.2.ca.e.257.14		48	84.47	odd	6
1008.2.ca.e.353.14		48	36.7	odd	6
1008.2.df.e.689.6		48	12.11	even	2
1008.2.df.e.929.6		48	252.187	even	6
1512.2.bs.a.521.8		48	9.2	odd	6
1512.2.bs.a.1097.8		48	7.5	odd	6
1512.2.cx.a.17.8		48	1.1	even	1	trivial
1512.2.cx.a.89.8		48	63.47	even	6	inner
3024.2.ca.e.2033.8		48	36.11	even	6
3024.2.ca.e.2609.8		48	28.19	even	6
3024.2.df.e.17.8		48	4.3	odd	2
3024.2.df.e.1601.8		48	252.47	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.04899 q^{5} +(1.41312 - 2.23676i) q^{7} +O(q^{10})\)	\(q-2.04899 q^{5} +(1.41312 - 2.23676i) q^{7} -5.90703i q^{11} +(-0.139269 - 0.0804071i) q^{13} +(-2.77904 + 4.81345i) q^{17} +(-4.02056 + 2.32127i) q^{19} -0.433237i q^{23} -0.801659 q^{25} +(1.95524 - 1.12886i) q^{29} +(-2.57823 + 1.48854i) q^{31} +(-2.89547 + 4.58308i) q^{35} +(2.17904 + 3.77422i) q^{37} +(-2.35740 + 4.08313i) q^{41} +(1.82369 + 3.15873i) q^{43} +(-0.0650477 + 0.112666i) q^{47} +(-3.00617 - 6.32162i) q^{49} +(-10.7936 - 6.23170i) q^{53} +12.1034i q^{55} +(3.22405 + 5.58421i) q^{59} +(-5.98415 - 3.45495i) q^{61} +(0.285360 + 0.164753i) q^{65} +(-7.64596 - 13.2432i) q^{67} -1.48027i q^{71} +(-2.60881 - 1.50620i) q^{73} +(-13.2126 - 8.34735i) q^{77} +(-8.69257 + 15.0560i) q^{79} +(-7.62399 - 13.2051i) q^{83} +(5.69422 - 9.86268i) q^{85} +(-4.04757 - 7.01059i) q^{89} +(-0.376655 + 0.197886i) q^{91} +(8.23808 - 4.75626i) q^{95} +(2.61123 - 1.50759i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more