LMFDB - Embedded newform 2268.2.l.n.541.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(109,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("2268.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.l (of order $3$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 $ x^16 - 9x^14 + 31x^12 - 282x^10 + 1695x^8 - 3318x^6 + 4606x^4 - 4116*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.6
Root			$0.817131 - 0.735533i$ of defining polynomial
Character	$\chi$	$=$	2268.541
Dual form			2268.2.l.n.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.03112 q^{5} +(1.07542 + 2.41733i) q^{7} +O(q^{10})$	$q+1.03112 q^{5} +(1.07542 + 2.41733i) q^{7} -1.58576 q^{11} +(-2.52415 - 4.37196i) q^{13} +(-2.58242 - 4.47288i) q^{17} +(-0.392975 + 0.680652i) q^{19} -5.86577 q^{23} -3.93679 q^{25} +(4.44511 - 7.69915i) q^{29} +(0.575423 - 0.996661i) q^{31} +(1.10889 + 2.49255i) q^{35} +(4.07991 - 7.06661i) q^{37} +(-3.87206 - 6.70660i) q^{41} +(1.26628 - 2.19326i) q^{43} +(-4.24595 - 7.35420i) q^{47} +(-4.68693 + 5.19930i) q^{49} +(2.41270 + 4.17892i) q^{53} -1.63510 q^{55} +(-1.93622 + 3.35364i) q^{59} +(4.82204 + 8.35201i) q^{61} +(-2.60270 - 4.50801i) q^{65} +(0.837220 - 1.45011i) q^{67} +14.2795 q^{71} +(3.04382 + 5.27205i) q^{73} +(-1.70536 - 3.83329i) q^{77} +(4.15533 + 7.19724i) q^{79} +(7.12095 - 12.3339i) q^{83} +(-2.66278 - 4.61207i) q^{85} +(6.69272 - 11.5921i) q^{89} +(7.85392 - 10.8034i) q^{91} +(-0.405203 + 0.701833i) q^{95} +(-2.67500 + 4.63323i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 10 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} - 10 q^{43} - 20 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) $ 16 * q + 10 * q^13 + 8 * q^19 - 8 * q^31 - 4 * q^37 - 10 * q^43 - 20 * q^49 - 32 * q^55 + 28 * q^61 + 18 * q^67 - 20 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.03112			0.461130			0.230565	−	0.973057i	$-0.425943\pi$
$5$	1.03112			0.461130			0.230565	+	0.973057i	$0.425943\pi$
$6$		0			0
$7$	1.07542	+	2.41733i	0.406472	+	0.913663i
$7$	1.07542	+	2.41733i	0.406472	+	0.913663i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.58576			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$11$	−1.58576			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$12$		0			0
$13$	−2.52415	−	4.37196i	−0.700074	−	1.21256i	−0.968440	−	0.249246i	$-0.919817\pi$
$13$	−2.52415	−	4.37196i	−0.700074	−	1.21256i	0.268366	−	0.963317i	$-0.413516\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.58242	−	4.47288i	−0.626329	−	1.08483i	−0.988282	−	0.152637i	$-0.951223\pi$
$17$	−2.58242	−	4.47288i	−0.626329	−	1.08483i	0.361954	−	0.932196i	$-0.382110\pi$
$18$		0			0
$19$	−0.392975	+	0.680652i	−0.0901546	+	0.156152i	−0.907576	−	0.419888i	$-0.862069\pi$
$19$	−0.392975	+	0.680652i	−0.0901546	+	0.156152i	0.817421	+	0.576040i	$0.195403\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.86577			−1.22310			−0.611549	−	0.791207i	$-0.709453\pi$
$23$	−5.86577			−1.22310			−0.611549	+	0.791207i	$0.709453\pi$
$24$		0			0
$25$	−3.93679			−0.787359
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.44511	−	7.69915i	0.825435	−	1.42970i	−0.0761506	−	0.997096i	$-0.524263\pi$
$29$	4.44511	−	7.69915i	0.825435	−	1.42970i	0.901586	−	0.432600i	$-0.142404\pi$
$30$		0			0
$31$	0.575423	−	0.996661i	0.103349	−	0.179006i	−0.809713	−	0.586825i	$-0.800377\pi$
$31$	0.575423	−	0.996661i	0.103349	−	0.179006i	0.913062	+	0.407820i	$0.133711\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.10889	+	2.49255i	0.187436	+	0.421318i
$36$		0			0
$37$	4.07991	−	7.06661i	0.670732	−	1.16174i	−0.306964	−	0.951721i	$-0.599313\pi$
$37$	4.07991	−	7.06661i	0.670732	−	1.16174i	0.977697	−	0.210022i	$-0.0673535\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.87206	−	6.70660i	−0.604714	−	1.04739i	−0.992097	−	0.125476i	$-0.959954\pi$
$41$	−3.87206	−	6.70660i	−0.604714	−	1.04739i	0.387383	−	0.921919i	$-0.373379\pi$
$42$		0			0
$43$	1.26628	−	2.19326i	0.193106	−	0.334470i	−0.753172	−	0.657824i	$-0.771477\pi$
$43$	1.26628	−	2.19326i	0.193106	−	0.334470i	0.946278	+	0.323354i	$0.104811\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.24595	−	7.35420i	−0.619335	−	1.07272i	−0.989607	−	0.143796i	$-0.954069\pi$
$47$	−4.24595	−	7.35420i	−0.619335	−	1.07272i	0.370272	−	0.928923i	$-0.379264\pi$
$48$		0			0
$49$	−4.68693	+	5.19930i	−0.669562	+	0.742756i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.41270	+	4.17892i	0.331410	+	0.574019i	0.982789	−	0.184734i	$-0.0591423\pi$
$53$	2.41270	+	4.17892i	0.331410	+	0.574019i	−0.651378	+	0.758753i	$0.725809\pi$
$54$		0			0
$55$	−1.63510			−0.220477
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.93622	+	3.35364i	−0.252075	+	0.436607i	−0.964097	−	0.265551i	$-0.914446\pi$
$59$	−1.93622	+	3.35364i	−0.252075	+	0.436607i	0.712022	+	0.702157i	$0.247780\pi$
$60$		0			0
$61$	4.82204	+	8.35201i	0.617398	+	1.06937i	0.989959	+	0.141357i	$0.0451467\pi$
$61$	4.82204	+	8.35201i	0.617398	+	1.06937i	−0.372560	+	0.928008i	$0.621520\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.60270	−	4.50801i	−0.322825	−	0.559150i
$66$		0			0
$67$	0.837220	−	1.45011i	0.102283	−	0.177159i	−0.810342	−	0.585957i	$-0.800719\pi$
$67$	0.837220	−	1.45011i	0.102283	−	0.177159i	0.912625	+	0.408798i	$0.134052\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	14.2795			1.69467			0.847333	−	0.531062i	$-0.178207\pi$
$71$	14.2795			1.69467			0.847333	+	0.531062i	$0.178207\pi$
$72$		0			0
$73$	3.04382	+	5.27205i	0.356252	+	0.617047i	0.987331	−	0.158671i	$-0.0507211\pi$
$73$	3.04382	+	5.27205i	0.356252	+	0.617047i	−0.631079	+	0.775718i	$0.717388\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.70536	−	3.83329i	−0.194344	−	0.436844i
$78$		0			0
$79$	4.15533	+	7.19724i	0.467511	+	0.809753i	0.999311	−	0.0371172i	$-0.0118175\pi$
$79$	4.15533	+	7.19724i	0.467511	+	0.809753i	−0.531800	+	0.846870i	$0.678484\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.12095	−	12.3339i	0.781626	−	1.35382i	−0.149368	−	0.988782i	$-0.547724\pi$
$83$	7.12095	−	12.3339i	0.781626	−	1.35382i	0.930994	−	0.365034i	$-0.118943\pi$
$84$		0			0
$85$	−2.66278	−	4.61207i	−0.288819	−	0.500249i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.69272	−	11.5921i	0.709426	−	1.22876i	−0.255644	−	0.966771i	$-0.582287\pi$
$89$	6.69272	−	11.5921i	0.709426	−	1.22876i	0.965070	−	0.261992i	$-0.0843793\pi$
$90$		0			0
$91$	7.85392	−	10.8034i	0.823315	−	1.13250i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.405203	+	0.701833i	−0.0415730	+	0.0720065i
$96$		0			0
$97$	−2.67500	+	4.63323i	−0.271605	+	0.470433i	−0.969273	−	0.245988i	$-0.920888\pi$
$97$	−2.67500	+	4.63323i	−0.271605	+	0.470433i	0.697668	+	0.716421i	$0.254221\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.18076			−0.316498			−0.158249	−	0.987399i	$-0.550585\pi$
$101$	−3.18076			−0.316498			−0.158249	+	0.987399i	$0.550585\pi$
$102$		0			0
$103$	−11.4132			−1.12458			−0.562288	−	0.826941i	$-0.690079\pi$
$103$	−11.4132			−1.12458			−0.562288	+	0.826941i	$0.690079\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.311386	+	0.539337i	−0.0301028	+	0.0521396i	−0.880684	−	0.473704i	$-0.842917\pi$
$107$	−0.311386	+	0.539337i	−0.0301028	+	0.0521396i	0.850582	+	0.525843i	$0.176250\pi$
$108$		0			0
$109$	0.971921	+	1.68342i	0.0930932	+	0.161242i	0.908811	−	0.417208i	$-0.136991\pi$
$109$	0.971921	+	1.68342i	0.0930932	+	0.161242i	−0.815718	+	0.578450i	$0.803658\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.79416	−	3.10758i	−0.168781	−	0.292337i	0.769211	−	0.638995i	$-0.220650\pi$
$113$	−1.79416	−	3.10758i	−0.168781	−	0.292337i	−0.937991	+	0.346658i	$0.887316\pi$
$114$		0			0
$115$	−6.04830			−0.564007
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.03522	−	11.0528i	0.736587	−	1.01321i
$120$		0			0
$121$	−8.48537			−0.771398
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.21489			−0.824205
$126$		0			0
$127$	11.6202			1.03113			0.515563	−	0.856852i	$-0.327583\pi$
$127$	11.6202			1.03113			0.515563	+	0.856852i	$0.327583\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.15797			−0.712765			−0.356382	−	0.934340i	$-0.615990\pi$
$131$	−8.15797			−0.712765			−0.356382	+	0.934340i	$0.615990\pi$
$132$		0			0
$133$	−2.06797	−	0.217959i	−0.179316	−	0.0188995i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.5636			−1.24425			−0.622127	−	0.782916i	$-0.713731\pi$
$137$	−14.5636			−1.24425			−0.622127	+	0.782916i	$0.713731\pi$
$138$		0			0
$139$	5.91713	+	10.2488i	0.501884	+	0.869289i	0.999998	+	0.00217698i	$0.000692954\pi$
$139$	5.91713	+	10.2488i	0.501884	+	0.869289i	−0.498113	+	0.867112i	$0.665974\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.00269	+	6.93287i	0.334722	+	0.579756i
$144$		0			0
$145$	4.58343	−	7.93873i	0.380633	−	0.659276i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−14.0495			−1.15098			−0.575492	−	0.817808i	$-0.695189\pi$
$149$	−14.0495			−1.15098			−0.575492	+	0.817808i	$0.695189\pi$
$150$		0			0
$151$	2.48537			0.202257			0.101128	−	0.994873i	$-0.467755\pi$
$151$	2.48537			0.202257			0.101128	+	0.994873i	$0.467755\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.593329	−	1.02768i	0.0476573	−	0.0825449i
$156$		0			0
$157$	1.51967	−	2.63214i	0.121283	−	0.210068i	−0.798991	−	0.601343i	$-0.794633\pi$
$157$	1.51967	−	2.63214i	0.121283	−	0.210068i	0.920274	+	0.391275i	$0.127966\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.30818	−	14.1795i	−0.497154	−	1.11750i
$162$		0			0
$163$	−8.75883	+	15.1707i	−0.686045	+	1.18826i	0.287063	+	0.957912i	$0.407321\pi$
$163$	−8.75883	+	15.1707i	−0.686045	+	1.18826i	−0.973107	+	0.230352i	$0.926012\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.2738	−	21.2588i	−0.949775	−	1.64506i	−0.745897	−	0.666061i	$-0.767979\pi$
$167$	−12.2738	−	21.2588i	−0.949775	−	1.64506i	−0.203877	−	0.978996i	$-0.565354\pi$
$168$		0			0
$169$	−6.24269	+	10.8126i	−0.480207	+	0.831742i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.0344569	+	0.0596811i	0.00261971	+	0.00453747i	0.867332	−	0.497730i	$-0.165833\pi$
$173$	0.0344569	+	0.0596811i	0.00261971	+	0.00453747i	−0.864713	+	0.502267i	$0.832499\pi$
$174$		0			0
$175$	−4.23372	−	9.51652i	−0.320039	−	0.719381i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.96086	+	6.86041i	0.296049	+	0.512771i	0.975228	−	0.221201i	$-0.0709976\pi$
$179$	3.96086	+	6.86041i	0.296049	+	0.512771i	−0.679180	+	0.733972i	$0.737664\pi$
$180$		0			0
$181$	3.59688			0.267354			0.133677	−	0.991025i	$-0.457322\pi$
$181$	3.59688			0.267354			0.133677	+	0.991025i	$0.457322\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.20687	−	7.28651i	0.309295	−	0.535715i
$186$		0			0
$187$	4.09509	+	7.09291i	0.299463	+	0.518685i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.02458	−	13.8990i	−0.580638	−	1.00569i	−0.995404	−	0.0957664i	$-0.969470\pi$
$191$	−8.02458	−	13.8990i	−0.580638	−	1.00569i	0.414766	−	0.909928i	$-0.363864\pi$
$192$		0			0
$193$	10.7865	−	18.6828i	0.776430	−	1.34482i	−0.157558	−	0.987510i	$-0.550362\pi$
$193$	10.7865	−	18.6828i	0.776430	−	1.34482i	0.933987	−	0.357306i	$-0.116305\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−20.4441			−1.45659			−0.728293	−	0.685266i	$-0.759686\pi$
$197$	−20.4441			−1.45659			−0.728293	+	0.685266i	$0.759686\pi$
$198$		0			0
$199$	−6.50056	−	11.2593i	−0.460812	−	0.798150i	0.538189	−	0.842824i	$-0.319109\pi$
$199$	−6.50056	−	11.2593i	−0.460812	−	0.798150i	−0.999002	+	0.0446737i	$0.985775\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	23.3917	+	2.46543i	1.64178	+	0.173039i
$204$		0			0
$205$	−3.99255	−	6.91530i	−0.278852	−	0.482985i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.623163	−	1.07935i	0.0431051	−	0.0746602i
$210$		0			0
$211$	−2.11924	−	3.67064i	−0.145895	−	0.252697i	0.783812	−	0.620999i	$-0.213273\pi$
$211$	−2.11924	−	3.67064i	−0.145895	−	0.252697i	−0.929706	+	0.368302i	$0.879939\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.30569	−	2.26151i	0.0890470	−	0.154234i
$216$		0			0
$217$	3.02808	+	0.319152i	0.205559	+	0.0216655i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−13.0368	+	22.5805i	−0.876953	+	1.51893i
$222$		0			0
$223$	5.83329	−	10.1036i	0.390626	−	0.676584i	−0.601906	−	0.798567i	$-0.705592\pi$
$223$	5.83329	−	10.1036i	0.390626	−	0.676584i	0.992532	+	0.121982i	$0.0389252\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.17979			0.277422			0.138711	−	0.990333i	$-0.455704\pi$
$227$	4.17979			0.277422			0.138711	+	0.990333i	$0.455704\pi$
$228$		0			0
$229$	−8.38172			−0.553879			−0.276940	−	0.960887i	$-0.589320\pi$
$229$	−8.38172			−0.553879			−0.276940	+	0.960887i	$0.589320\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.499512	−	0.865180i	0.0327241	−	0.0566798i	−0.849200	−	0.528072i	$-0.822915\pi$
$233$	0.499512	−	0.865180i	0.0327241	−	0.0566798i	0.881924	+	0.471392i	$0.156248\pi$
$234$		0			0
$235$	−4.37807	−	7.58305i	−0.285594	−	0.494663i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.15412	+	10.6593i	0.398077	+	0.689490i	0.993489	−	0.113931i	$-0.0363443\pi$
$239$	6.15412	+	10.6593i	0.398077	+	0.689490i	−0.595411	+	0.803421i	$0.703011\pi$
$240$		0			0
$241$	6.47832			0.417306			0.208653	−	0.977990i	$-0.433092\pi$
$241$	6.47832			0.417306			0.208653	+	0.977990i	$0.433092\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.83278	+	5.36109i	−0.308755	+	0.342507i
$246$		0			0
$247$	3.96771			0.252459
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.2236			0.771544			0.385772	−	0.922594i	$-0.373935\pi$
$251$	12.2236			0.771544			0.385772	+	0.922594i	$0.373935\pi$
$252$		0			0
$253$	9.30169			0.584792
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.9271			0.993506			0.496753	−	0.867892i	$-0.334526\pi$
$257$	15.9271			0.993506			0.496753	+	0.867892i	$0.334526\pi$
$258$		0			0
$259$	21.4699	+	2.26288i	1.33408	+	0.140608i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	23.0610			1.42200			0.711002	−	0.703190i	$-0.248242\pi$
$263$	23.0610			1.42200			0.711002	+	0.703190i	$0.248242\pi$
$264$		0			0
$265$	2.48778	+	4.30897i	0.152823	+	0.264698i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.51107	+	9.54546i	0.336016	+	0.581997i	0.983679	−	0.179930i	$-0.0575871\pi$
$269$	5.51107	+	9.54546i	0.336016	+	0.581997i	−0.647663	+	0.761927i	$0.724254\pi$
$270$		0			0
$271$	2.74213	−	4.74951i	0.166572	−	0.288512i	−0.770640	−	0.637271i	$-0.780063\pi$
$271$	2.74213	−	4.74951i	0.166572	−	0.288512i	0.937213	+	0.348759i	$0.113397\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.24280			0.376455
$276$		0			0
$277$	−30.0662			−1.80651			−0.903253	−	0.429109i	$-0.858828\pi$
$277$	−30.0662			−1.80651			−0.903253	+	0.429109i	$0.858828\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.90908	+	10.2348i	−0.352506	+	0.610559i	−0.986688	−	0.162625i	$-0.948004\pi$
$281$	−5.90908	+	10.2348i	−0.352506	+	0.610559i	0.634182	+	0.773184i	$0.281337\pi$
$282$		0			0
$283$	−10.5605	+	18.2914i	−0.627758	+	1.08731i	0.360243	+	0.932859i	$0.382694\pi$
$283$	−10.5605	+	18.2914i	−0.627758	+	1.08731i	−0.988001	+	0.154450i	$0.950639\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0479	−	16.5725i	0.711167	−	0.978241i
$288$		0			0
$289$	−4.83778	+	8.37928i	−0.284575	+	0.492899i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.15098	−	10.6538i	−0.359344	−	0.622402i	0.628507	−	0.777804i	$-0.283666\pi$
$293$	−6.15098	−	10.6538i	−0.359344	−	0.622402i	−0.987851	+	0.155401i	$0.950333\pi$
$294$		0			0
$295$	−1.99648	+	3.45800i	−0.116239	+	0.201332i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	14.8061	+	25.6449i	0.856259	+	1.48308i
$300$		0			0
$301$	6.66362	+	0.702329i	0.384085	+	0.0404816i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.97209	+	8.61191i	0.284701	+	0.493117i
$306$		0			0
$307$	−33.5033			−1.91213			−0.956067	−	0.293147i	$-0.905297\pi$
$307$	−33.5033			−1.91213			−0.956067	+	0.293147i	$0.905297\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.8057	+	25.6442i	−0.839555	+	1.45415i	0.0507130	+	0.998713i	$0.483851\pi$
$311$	−14.8057	+	25.6442i	−0.839555	+	1.45415i	−0.890268	+	0.455438i	$0.849483\pi$
$312$		0			0
$313$	5.85745	+	10.1454i	0.331082	+	0.573452i	0.982724	−	0.185075i	$-0.0592529\pi$
$313$	5.85745	+	10.1454i	0.331082	+	0.573452i	−0.651642	+	0.758527i	$0.725920\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.08084	−	1.87207i	−0.0607061	−	0.105146i	0.834075	−	0.551651i	$-0.186002\pi$
$317$	−1.08084	−	1.87207i	−0.0607061	−	0.105146i	−0.894781	+	0.446505i	$0.852669\pi$
$318$		0			0
$319$	−7.04886	+	12.2090i	−0.394660	+	0.683572i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.05930			0.225866
$324$		0			0
$325$	9.93707	+	17.2115i	0.551209	+	0.954723i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.2113	−	18.1727i	0.728363	−	1.00189i
$330$		0			0
$331$	−15.6001	−	27.0202i	−0.857461	−	1.48517i	−0.874343	−	0.485308i	$-0.838707\pi$
$331$	−15.6001	−	27.0202i	−0.857461	−	1.48517i	0.0168824	−	0.999857i	$-0.494626\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.863273	−	1.49523i	0.0471656	−	0.0816933i
$336$		0			0
$337$	−1.94425	−	3.36753i	−0.105910	−	0.183441i	0.808200	−	0.588908i	$-0.200442\pi$
$337$	−1.94425	−	3.36753i	−0.105910	−	0.183441i	−0.914110	+	0.405467i	$0.867109\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.912481	+	1.58046i	−0.0494136	+	0.0855869i
$342$		0			0
$343$	−17.6088	−	5.73840i	−0.950787	−	0.309845i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.37831	+	14.5117i	−0.449771	+	0.779027i	−0.998371	−	0.0570585i	$-0.981828\pi$
$347$	−8.37831	+	14.5117i	−0.449771	+	0.779027i	0.548600	+	0.836085i	$0.315161\pi$
$348$		0			0
$349$	15.9097	−	27.5564i	0.851625	−	1.47506i	−0.0281152	−	0.999605i	$-0.508951\pi$
$349$	15.9097	−	27.5564i	0.851625	−	1.47506i	0.879741	−	0.475454i	$-0.157716\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.33733			0.390527			0.195263	−	0.980751i	$-0.437444\pi$
$353$	7.33733			0.390527			0.195263	+	0.980751i	$0.437444\pi$
$354$		0			0
$355$	14.7239			0.781461
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.16644	+	12.4126i	−0.378230	+	0.655114i	−0.990805	−	0.135299i	$-0.956801\pi$
$359$	−7.16644	+	12.4126i	−0.378230	+	0.655114i	0.612574	+	0.790413i	$0.290134\pi$
$360$		0			0
$361$	9.19114	+	15.9195i	0.483744	+	0.837870i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.13854	+	5.43611i	0.164279	+	0.284539i
$366$		0			0
$367$	25.5730			1.33490			0.667450	−	0.744654i	$-0.267386\pi$
$367$	25.5730			1.33490			0.667450	+	0.744654i	$0.267386\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.50715	+	10.3264i	−0.389752	+	0.536120i
$372$		0			0
$373$	31.1468			1.61272			0.806361	−	0.591424i	$-0.201434\pi$
$373$	31.1468			1.61272			0.806361	+	0.591424i	$0.201434\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−44.8805			−2.31146
$378$		0			0
$379$	−6.72979			−0.345686			−0.172843	−	0.984949i	$-0.555295\pi$
$379$	−6.72979			−0.345686			−0.172843	+	0.984949i	$0.555295\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	37.5347			1.91793			0.958967	−	0.283519i	$-0.0915018\pi$
$383$	37.5347			1.91793			0.958967	+	0.283519i	$0.0915018\pi$
$384$		0			0
$385$	−1.75843	−	3.95258i	−0.0896178	−	0.201442i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−30.6425			−1.55364			−0.776819	−	0.629724i	$-0.783168\pi$
$389$	−30.6425			−1.55364			−0.776819	+	0.629724i	$0.783168\pi$
$390$		0			0
$391$	15.1479	+	26.2369i	0.766061	+	1.32686i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.28464	+	7.42121i	0.215583	+	0.373401i
$396$		0			0
$397$	−2.65885	+	4.60527i	−0.133444	+	0.231132i	−0.925002	−	0.379962i	$-0.875937\pi$
$397$	−2.65885	+	4.60527i	−0.133444	+	0.231132i	0.791558	+	0.611094i	$0.209270\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.656797			0.0327989			0.0163994	−	0.999866i	$-0.494780\pi$
$401$	0.656797			0.0327989			0.0163994	+	0.999866i	$0.494780\pi$
$402$		0			0
$403$	−5.80982			−0.289408
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.46974	+	11.2059i	−0.320693	+	0.555457i
$408$		0			0
$409$	15.7994	−	27.3654i	0.781230	−	1.35313i	−0.149995	−	0.988687i	$-0.547926\pi$
$409$	15.7994	−	27.3654i	0.781230	−	1.35313i	0.931226	−	0.364443i	$-0.118741\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.1891	−	1.07391i	−0.501373	−	0.0528435i
$414$		0			0
$415$	7.34254	−	12.7177i	0.360431	−	0.624285i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.4424	−	18.0868i	−0.510146	−	0.883598i	−0.999931	−	0.0117550i	$-0.996258\pi$
$419$	−10.4424	−	18.0868i	−0.510146	−	0.883598i	0.489785	−	0.871843i	$-0.337075\pi$
$420$		0			0
$421$	−6.79788	+	11.7743i	−0.331309	+	0.573843i	−0.982769	−	0.184840i	$-0.940823\pi$
$421$	−6.79788	+	11.7743i	−0.331309	+	0.573843i	0.651460	+	0.758683i	$0.274157\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.1665	+	17.6088i	0.493145	+	0.854153i
$426$		0			0
$427$	−15.0038	+	20.6384i	−0.726085	+	0.998761i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.9416	+	24.1475i	0.671541	+	1.16314i	0.977467	+	0.211088i	$0.0677006\pi$
$431$	13.9416	+	24.1475i	0.671541	+	1.16314i	−0.305926	+	0.952055i	$0.598966\pi$
$432$		0			0
$433$	−22.7059			−1.09118			−0.545589	−	0.838053i	$-0.683694\pi$
$433$	−22.7059			−1.09118			−0.545589	+	0.838053i	$0.683694\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.30510	−	3.99255i	0.110268	−	0.190990i
$438$		0			0
$439$	−15.9508	−	27.6276i	−0.761290	−	1.31859i	−0.942186	−	0.335091i	$-0.891233\pi$
$439$	−15.9508	−	27.6276i	−0.761290	−	1.31859i	0.180895	−	0.983502i	$-0.442100\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.5629	+	30.4198i	0.834436	+	1.44529i	0.894488	+	0.447091i	$0.147540\pi$
$443$	17.5629	+	30.4198i	0.834436	+	1.44529i	−0.0600520	+	0.998195i	$0.519127\pi$
$444$		0			0
$445$	6.90098	−	11.9529i	0.327138	−	0.566620i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0966532			−0.00456135			−0.00228067	−	0.999997i	$-0.500726\pi$
$449$	−0.0966532			−0.00456135			−0.00228067	+	0.999997i	$0.500726\pi$
$450$		0			0
$451$	6.14014	+	10.6350i	0.289128	+	0.500785i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.09832	−	11.1396i	0.379655	−	0.522232i
$456$		0			0
$457$	8.50925	+	14.7385i	0.398046	+	0.689436i	0.993485	−	0.113965i	$-0.0363551\pi$
$457$	8.50925	+	14.7385i	0.398046	+	0.689436i	−0.595439	+	0.803401i	$0.703022\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.08817	+	14.0091i	−0.376704	+	0.652470i	−0.990580	−	0.136932i	$-0.956276\pi$
$461$	−8.08817	+	14.0091i	−0.376704	+	0.652470i	0.613877	+	0.789402i	$0.289609\pi$
$462$		0			0
$463$	6.24297	+	10.8131i	0.290135	+	0.502529i	0.973842	−	0.227228i	$-0.0729663\pi$
$463$	6.24297	+	10.8131i	0.290135	+	0.502529i	−0.683706	+	0.729757i	$0.739633\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.72717	−	11.6518i	0.311296	−	0.539181i	−0.667347	−	0.744747i	$-0.732570\pi$
$467$	6.72717	−	11.6518i	0.311296	−	0.539181i	0.978643	+	0.205566i	$0.0659035\pi$
$468$		0			0
$469$	4.40575	+	0.464355i	0.203439	+	0.0214419i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.00802	+	3.47798i	−0.0923286	+	0.159918i
$474$		0			0
$475$	1.54706	−	2.67959i	0.0709840	−	0.122948i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.9621			−0.637946			−0.318973	−	0.947764i	$-0.603338\pi$
$479$	−13.9621			−0.637946			−0.318973	+	0.947764i	$0.603338\pi$
$480$		0			0
$481$	−41.1932			−1.87825
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.75824	+	4.77741i	−0.125245	+	0.216931i
$486$		0			0
$487$	14.4858	+	25.0901i	0.656413	+	1.13694i	0.981538	+	0.191270i	$0.0612605\pi$
$487$	14.4858	+	25.0901i	0.656413	+	1.13694i	−0.325124	+	0.945671i	$0.605406\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.8775	+	36.1609i	0.942189	+	1.63192i	0.761283	+	0.648419i	$0.224570\pi$
$491$	20.8775	+	36.1609i	0.942189	+	1.63192i	0.180906	+	0.983500i	$0.442097\pi$
$492$		0			0
$493$	−45.9165			−2.06798
$494$		0			0
$495$		0			0
$496$		0			0
$497$	15.3565	+	34.5182i	0.688833	+	1.54835i
$498$		0			0
$499$	21.4460			0.960056			0.480028	−	0.877253i	$-0.340626\pi$
$499$	21.4460			0.960056			0.480028	+	0.877253i	$0.340626\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−28.3098			−1.26227			−0.631135	−	0.775673i	$-0.717411\pi$
$503$	−28.3098			−1.26227			−0.631135	+	0.775673i	$0.717411\pi$
$504$		0			0
$505$	−3.27974			−0.145947
$506$		0			0
$507$		0			0
$508$		0			0
$509$	31.6284			1.40190			0.700951	−	0.713209i	$-0.252759\pi$
$509$	31.6284			1.40190			0.700951	+	0.713209i	$0.252759\pi$
$510$		0			0
$511$	−9.47087	+	13.0276i	−0.418967	+	0.576307i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.7684			−0.518576
$516$		0			0
$517$	6.73304	+	11.6620i	0.296119	+	0.512893i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.0364	−	26.0439i	−0.658759	−	1.14100i	−0.980937	−	0.194325i	$-0.937749\pi$
$521$	−15.0364	−	26.0439i	−0.658759	−	1.14100i	0.322179	−	0.946679i	$-0.395585\pi$
$522$		0			0
$523$	7.73793	−	13.4025i	0.338356	−	0.586050i	−0.645768	−	0.763534i	$-0.723463\pi$
$523$	7.73793	−	13.4025i	0.338356	−	0.586050i	0.984124	+	0.177484i	$0.0567959\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.94393			−0.258922
$528$		0			0
$529$	11.4073			0.495968
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.5473	+	33.8570i	−0.846689	+	1.46651i
$534$		0			0
$535$	−0.321076	+	0.556120i	−0.0138813	+	0.0240432i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.43234	−	8.24482i	0.320133	−	0.355130i
$540$		0			0
$541$	−8.11884	+	14.0622i	−0.349056	+	0.604583i	−0.986082	−	0.166259i	$-0.946831\pi$
$541$	−8.11884	+	14.0622i	−0.349056	+	0.604583i	0.637026	+	0.770842i	$0.280164\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.00217	+	1.73580i	0.0429281	+	0.0743536i
$546$		0			0
$547$	19.4541	−	33.6954i	0.831795	−	1.44071i	−0.0648180	−	0.997897i	$-0.520647\pi$
$547$	19.4541	−	33.6954i	0.831795	−	1.44071i	0.896613	−	0.442815i	$-0.146020\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.49363	+	6.05114i	0.148834	+	0.257787i
$552$		0			0
$553$	−12.9293	+	17.7849i	−0.549812	+	0.756289i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.86210	−	4.95730i	−0.121271	−	0.210048i	0.798998	−	0.601334i	$-0.205364\pi$
$557$	−2.86210	−	4.95730i	−0.121271	−	0.210048i	−0.920269	+	0.391286i	$0.872030\pi$
$558$		0			0
$559$	−12.7851			−0.540754
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.47334	−	4.28394i	0.104239	−	0.180547i	−0.809188	−	0.587549i	$-0.800093\pi$
$563$	2.47334	−	4.28394i	0.104239	−	0.180547i	0.913427	+	0.407003i	$0.133426\pi$
$564$		0			0
$565$	−1.84999	−	3.20429i	−0.0778299	−	0.134805i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.10972	+	14.0465i	0.339977	+	0.588858i	0.984428	−	0.175788i	$-0.0562473\pi$
$569$	8.10972	+	14.0465i	0.339977	+	0.588858i	−0.644451	+	0.764646i	$0.722914\pi$
$570$		0			0
$571$	18.3029	−	31.7016i	0.765954	−	1.32667i	−0.173787	−	0.984783i	$-0.555601\pi$
$571$	18.3029	−	31.7016i	0.765954	−	1.32667i	0.939741	−	0.341887i	$-0.111066\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	23.0923			0.963017
$576$		0			0
$577$	−18.2684	−	31.6417i	−0.760522	−	1.31726i	−0.942582	−	0.333975i	$-0.891610\pi$
$577$	−18.2684	−	31.6417i	−0.760522	−	1.31726i	0.182060	−	0.983287i	$-0.441723\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	37.4730	+	3.94956i	1.55464	+	0.163855i
$582$		0			0
$583$	−3.82596	−	6.62676i	−0.158455	−	0.274452i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.9237	−	20.6525i	0.492144	−	0.852419i	−0.507815	−	0.861466i	$-0.669547\pi$
$587$	11.9237	−	20.6525i	0.492144	−	0.852419i	0.999959	+	0.00904721i	$0.00287986\pi$
$588$		0			0
$589$	0.452253	+	0.783325i	0.0186348	+	0.0322764i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.54751	−	11.3406i	0.268874	−	0.465704i	−0.699697	−	0.714439i	$-0.746682\pi$
$593$	6.54751	−	11.3406i	0.268874	−	0.465704i	0.968571	+	0.248736i	$0.0800151\pi$
$594$		0			0
$595$	8.28526	−	11.3967i	0.339663	−	0.467220i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.5770	+	32.1762i	−0.759034	+	1.31469i	0.184310	+	0.982868i	$0.440995\pi$
$599$	−18.5770	+	32.1762i	−0.759034	+	1.31469i	−0.943344	+	0.331817i	$0.892338\pi$
$600$		0			0
$601$	8.53133	−	14.7767i	0.348000	−	0.602754i	−0.637894	−	0.770124i	$-0.720194\pi$
$601$	8.53133	−	14.7767i	0.348000	−	0.602754i	0.985894	+	0.167370i	$0.0535275\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.74942			−0.355715
$606$		0			0
$607$	23.1946			0.941438			0.470719	−	0.882283i	$-0.343994\pi$
$607$	23.1946			0.941438			0.470719	+	0.882283i	$0.343994\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−21.4348	+	37.1262i	−0.867160	+	1.50197i
$612$		0			0
$613$	22.2875	+	38.6030i	0.900182	+	1.55916i	0.827257	+	0.561824i	$0.189900\pi$
$613$	22.2875	+	38.6030i	0.900182	+	1.55916i	0.0729255	+	0.997337i	$0.476766\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.12703	+	5.41618i	0.125890	+	0.218047i	0.922080	−	0.386999i	$-0.126488\pi$
$617$	3.12703	+	5.41618i	0.125890	+	0.218047i	−0.796191	+	0.605046i	$0.793155\pi$
$618$		0			0
$619$	−1.54042			−0.0619145			−0.0309573	−	0.999521i	$-0.509856\pi$
$619$	−1.54042			−0.0619145			−0.0309573	+	0.999521i	$0.509856\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	35.2194	+	3.71204i	1.41104	+	0.148720i
$624$		0			0
$625$	10.1823			0.407293
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−42.1441			−1.68040
$630$		0			0
$631$	−44.5148			−1.77210			−0.886052	−	0.463585i	$-0.846563\pi$
$631$	−44.5148			−1.77210			−0.886052	+	0.463585i	$0.846563\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	11.9818			0.475483
$636$		0			0
$637$	34.5616	+	7.36726i	1.36938	+	0.291902i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.75040			−0.148132			−0.0740660	−	0.997253i	$-0.523598\pi$
$641$	−3.75040			−0.148132			−0.0740660	+	0.997253i	$0.523598\pi$
$642$		0			0
$643$	−0.818392	−	1.41750i	−0.0322742	−	0.0559006i	0.849437	−	0.527690i	$-0.176942\pi$
$643$	−0.818392	−	1.41750i	−0.0322742	−	0.0559006i	−0.881711	+	0.471789i	$0.843608\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.0748	+	17.4501i	0.396082	+	0.686034i	0.993239	−	0.116091i	$-0.0370363\pi$
$647$	10.0748	+	17.4501i	0.396082	+	0.686034i	−0.597157	+	0.802125i	$0.703703\pi$
$648$		0			0
$649$	3.07038	−	5.31806i	0.120523	−	0.208752i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−42.9140			−1.67935			−0.839677	−	0.543087i	$-0.817255\pi$
$653$	−42.9140			−1.67935			−0.839677	+	0.543087i	$0.817255\pi$
$654$		0			0
$655$	−8.41183			−0.328677
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.8526	−	18.7973i	0.422758	−	0.732238i	−0.573450	−	0.819240i	$-0.694395\pi$
$659$	10.8526	−	18.7973i	0.422758	−	0.732238i	0.996208	+	0.0870025i	$0.0277288\pi$
$660$		0			0
$661$	12.6907	−	21.9810i	0.493613	−	0.854962i	−0.506360	−	0.862322i	$-0.669009\pi$
$661$	12.6907	−	21.9810i	0.493613	−	0.854962i	0.999973	+	0.00735996i	$0.00234277\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.13232	−	0.224742i	−0.0826880	−	0.00871511i
$666$		0			0
$667$	−26.0740	+	45.1614i	−1.00959	+	1.74866i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.64658	−	13.2443i	−0.295193	−	0.511289i
$672$		0			0
$673$	7.88676	−	13.6603i	0.304012	−	0.526565i	−0.673029	−	0.739616i	$-0.735007\pi$
$673$	7.88676	−	13.6603i	0.304012	−	0.526565i	0.977041	+	0.213052i	$0.0683403\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.32531	−	9.22370i	−0.204668	−	0.354496i	0.745359	−	0.666664i	$-0.232278\pi$
$677$	−5.32531	−	9.22370i	−0.204668	−	0.354496i	−0.950027	+	0.312168i	$0.898945\pi$
$678$		0			0
$679$	−14.0768	−	1.48366i	−0.540217	−	0.0569376i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.3656	+	24.8819i	0.549683	+	0.952078i	0.998296	+	0.0583524i	$0.0185847\pi$
$683$	14.3656	+	24.8819i	0.549683	+	0.952078i	−0.448613	+	0.893726i	$0.648082\pi$
$684$		0			0
$685$	−15.0168			−0.573763
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.1801	−	21.0965i	0.464023	−	0.803712i
$690$		0			0
$691$	19.6136	+	33.9717i	0.746136	+	1.29235i	0.949662	+	0.313276i	$0.101426\pi$
$691$	19.6136	+	33.9717i	0.746136	+	1.29235i	−0.203526	+	0.979069i	$0.565240\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.10126	+	10.5677i	0.231434	+	0.400855i
$696$		0			0
$697$	−19.9985	+	34.6385i	−0.757499	+	1.31203i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	34.1643			1.29037			0.645184	−	0.764028i	$-0.276781\pi$
$701$	34.1643			1.29037			0.645184	+	0.764028i	$0.276781\pi$
$702$		0			0
$703$	3.20660	+	5.55399i	0.120939	+	0.209473i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.42066	−	7.68894i	−0.128647	−	0.289172i
$708$		0			0
$709$	−9.85352	−	17.0668i	−0.370057	−	0.640957i	0.619517	−	0.784983i	$-0.287328\pi$
$709$	−9.85352	−	17.0668i	−0.370057	−	0.640957i	−0.989574	+	0.144026i	$0.953995\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.37530	+	5.84619i	−0.126406	+	0.218941i
$714$		0			0
$715$	4.12725	+	7.14861i	0.154350	+	0.267343i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.87829	−	10.1815i	0.219223	−	0.379705i	−0.735348	−	0.677690i	$-0.762981\pi$
$719$	5.87829	−	10.1815i	0.219223	−	0.379705i	0.954571	+	0.297985i	$0.0963144\pi$
$720$		0			0
$721$	−12.2740	−	27.5894i	−0.457108	−	1.02748i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−17.4995	+	30.3100i	−0.649914	+	1.12568i
$726$		0			0
$727$	22.8161	−	39.5186i	0.846202	−	1.46567i	−0.0383705	−	0.999264i	$-0.512217\pi$
$727$	22.8161	−	39.5186i	0.846202	−	1.46567i	0.884573	−	0.466402i	$-0.154450\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.0803			−0.483791
$732$		0			0
$733$	38.9803			1.43977			0.719885	−	0.694094i	$-0.244195\pi$
$733$	38.9803			1.43977			0.719885	+	0.694094i	$0.244195\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.32763	+	2.29952i	−0.0489038	+	0.0847039i
$738$		0			0
$739$	−11.7719	−	20.3895i	−0.433036	−	0.750040i	0.564097	−	0.825708i	$-0.309224\pi$
$739$	−11.7719	−	20.3895i	−0.433036	−	0.750040i	−0.997133	+	0.0756686i	$0.975891\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.09612	+	7.09469i	0.150272	+	0.260279i	0.931327	−	0.364183i	$-0.118652\pi$
$743$	4.09612	+	7.09469i	0.150272	+	0.260279i	−0.781055	+	0.624462i	$0.785318\pi$
$744$		0			0
$745$	−14.4867			−0.530753
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.63862	−	0.172707i	−0.0598740	−	0.00631058i
$750$		0			0
$751$	−28.1873			−1.02857			−0.514284	−	0.857620i	$-0.671942\pi$
$751$	−28.1873			−1.02857			−0.514284	+	0.857620i	$0.671942\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.56271			0.0932667
$756$		0			0
$757$	7.42352			0.269812			0.134906	−	0.990858i	$-0.456927\pi$
$757$	7.42352			0.269812			0.134906	+	0.990858i	$0.456927\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	30.7067			1.11312			0.556559	−	0.830808i	$-0.312121\pi$
$761$	30.7067			1.11312			0.556559	+	0.830808i	$0.312121\pi$
$762$		0			0
$763$	−3.02414	+	4.15984i	−0.109481	+	0.150596i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	19.5493			0.705884
$768$		0			0
$769$	20.0973	+	34.8095i	0.724727	+	1.25526i	0.959086	+	0.283113i	$0.0913673\pi$
$769$	20.0973	+	34.8095i	0.724727	+	1.25526i	−0.234360	+	0.972150i	$0.575299\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.69611	−	2.93775i	−0.0610050	−	0.105664i	0.833910	−	0.551901i	$-0.186097\pi$
$773$	−1.69611	−	2.93775i	−0.0610050	−	0.105664i	−0.894915	+	0.446237i	$0.852764\pi$
$774$		0			0
$775$	−2.26532	+	3.92365i	−0.0813727	+	0.140942i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.08648			0.218071
$780$		0			0
$781$	−22.6438			−0.810260
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.56696	−	2.71405i	0.0559271	−	0.0968686i
$786$		0			0
$787$	−5.41657	+	9.38177i	−0.193080	+	0.334424i	−0.946269	−	0.323379i	$-0.895181\pi$
$787$	−5.41657	+	9.38177i	−0.193080	+	0.334424i	0.753190	+	0.657804i	$0.228514\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.58256	−	7.67904i	0.198493	−	0.273035i
$792$		0			0
$793$	24.3431	−	42.1635i	0.864449	−	1.49727i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.4982	−	40.7001i	−0.832350	−	1.44167i	−0.896170	−	0.443712i	$-0.853661\pi$
$797$	−23.4982	−	40.7001i	−0.832350	−	1.44167i	0.0638193	−	0.997961i	$-0.479672\pi$
$798$		0			0
$799$	−21.9296	+	37.9832i	−0.775814	+	1.34375i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.82676	−	8.36020i	−0.170333	−	0.295025i
$804$		0			0
$805$	−6.50448	−	14.6207i	−0.229253	−	0.515313i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.5052	−	25.1238i	−0.509977	−	0.883306i	−0.999933	−	0.0115587i	$-0.996321\pi$
$809$	−14.5052	−	25.1238i	−0.509977	−	0.883306i	0.489957	−	0.871747i	$-0.337013\pi$
$810$		0			0
$811$	34.6805			1.21780			0.608899	−	0.793248i	$-0.291612\pi$
$811$	34.6805			1.21780			0.608899	+	0.793248i	$0.291612\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.03139	+	15.6428i	−0.316356	+	0.547944i
$816$		0			0
$817$	0.995233	+	1.72379i	0.0348188	+	0.0603079i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.6606	−	34.0532i	−0.686161	−	1.18847i	−0.973070	−	0.230508i	$-0.925961\pi$
$821$	−19.6606	−	34.0532i	−0.686161	−	1.18847i	0.286909	−	0.957958i	$-0.407372\pi$
$822$		0			0
$823$	21.3432	−	36.9675i	0.743978	−	1.28861i	−0.206693	−	0.978406i	$-0.566270\pi$
$823$	21.3432	−	36.9675i	0.743978	−	1.28861i	0.950671	−	0.310202i	$-0.100397\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.5672			0.506551			0.253276	−	0.967394i	$-0.418492\pi$
$827$	14.5672			0.506551			0.253276	+	0.967394i	$0.418492\pi$
$828$		0			0
$829$	16.6920	+	28.9113i	0.579736	+	1.00413i	0.995509	+	0.0946641i	$0.0301777\pi$
$829$	16.6920	+	28.9113i	0.579736	+	1.00413i	−0.415773	+	0.909468i	$0.636489\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	35.3595	+	7.53733i	1.22513	+	0.261153i
$834$		0			0
$835$	−12.6557	−	21.9204i	−0.437970	−	0.758586i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.987290	+	1.71004i	−0.0340850	+	0.0590370i	−0.882565	−	0.470191i	$-0.844185\pi$
$839$	−0.987290	+	1.71004i	−0.0340850	+	0.0590370i	0.848480	+	0.529228i	$0.177518\pi$
$840$		0			0
$841$	−25.0179	−	43.3323i	−0.862687	−	1.49422i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.43695	+	11.1491i	−0.221438	+	0.383541i
$846$		0			0
$847$	−9.12536	−	20.5119i	−0.313551	−	0.704798i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−23.9318	+	41.4511i	−0.820371	+	1.42092i
$852$		0			0
$853$	6.68637	−	11.5811i	0.228937	−	0.396531i	−0.728556	−	0.684986i	$-0.759808\pi$
$853$	6.68637	−	11.5811i	0.228937	−	0.396531i	0.957493	+	0.288455i	$0.0931417\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.8648			0.917684			0.458842	−	0.888518i	$-0.348264\pi$
$857$	26.8648			0.917684			0.458842	+	0.888518i	$0.348264\pi$
$858$		0			0
$859$	−45.8424			−1.56412			−0.782062	−	0.623201i	$-0.785832\pi$
$859$	−45.8424			−1.56412			−0.782062	+	0.623201i	$0.785832\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.90612	−	10.2297i	0.201047	−	0.348223i	−0.747819	−	0.663902i	$-0.768899\pi$
$863$	5.90612	−	10.2297i	0.201047	−	0.348223i	0.948866	+	0.315679i	$0.102232\pi$
$864$		0			0
$865$	0.0355291	+	0.0615383i	0.00120803	+	0.00209236i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.58935	−	11.4131i	−0.223528	−	0.387162i
$870$		0			0
$871$	−8.45308			−0.286422
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−9.90991	−	22.2754i	−0.335016	−	0.753046i
$876$		0			0
$877$	−25.2092			−0.851255			−0.425628	−	0.904898i	$-0.639947\pi$
$877$	−25.2092			−0.851255			−0.425628	+	0.904898i	$0.639947\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.268589			−0.00904898			−0.00452449	−	0.999990i	$-0.501440\pi$
$881$	−0.268589			−0.00904898			−0.00452449	+	0.999990i	$0.501440\pi$
$882$		0			0
$883$	25.8915			0.871319			0.435660	−	0.900112i	$-0.356515\pi$
$883$	25.8915			0.871319			0.435660	+	0.900112i	$0.356515\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	43.6793			1.46661			0.733303	−	0.679902i	$-0.237977\pi$
$887$	43.6793			1.46661			0.733303	+	0.679902i	$0.237977\pi$
$888$		0			0
$889$	12.4966	+	28.0898i	0.419124	+	0.942102i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.67420			0.223344
$894$		0			0
$895$	4.08412	+	7.07390i	0.136517	+	0.236454i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.11563	−	8.86053i	−0.170616	−	0.295515i
$900$		0			0
$901$	12.4612	−	21.5835i	0.415143	−	0.719050i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.70881			0.123285
$906$		0			0
$907$	−0.0292549			−0.000971393			−0.000485696	−	1.00000i	$-0.500155\pi$
$907$	−0.0292549			−0.000971393			−0.000485696		1.00000i	$0.500155\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.0048	+	24.2569i	−0.463998	+	0.803668i	−0.999156	−	0.0410839i	$-0.986919\pi$
$911$	−14.0048	+	24.2569i	−0.463998	+	0.803668i	0.535158	+	0.844752i	$0.320252\pi$
$912$		0			0
$913$	−11.2921	+	19.5585i	−0.373714	+	0.647292i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.77326	−	19.7205i	−0.289719	−	0.651227i
$918$		0			0
$919$	−6.11476	+	10.5911i	−0.201707	+	0.349367i	−0.949079	−	0.315039i	$-0.897982\pi$
$919$	−6.11476	+	10.5911i	−0.201707	+	0.349367i	0.747371	+	0.664407i	$0.231316\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−36.0436	−	62.4294i	−1.18639	−	2.05489i
$924$		0			0
$925$	−16.0618	+	27.8198i	−0.528107	+	0.914709i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.98202	+	6.89707i	0.130646	+	0.226285i	0.923926	−	0.382572i	$-0.124962\pi$
$929$	3.98202	+	6.89707i	0.130646	+	0.226285i	−0.793280	+	0.608857i	$0.791628\pi$
$930$		0			0
$931$	−1.69707	−	5.23336i	−0.0556191	−	0.171516i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.22252	+	7.31363i	0.138091	+	0.239181i
$936$		0			0
$937$	−15.0407			−0.491358			−0.245679	−	0.969351i	$-0.579011\pi$
$937$	−15.0407			−0.491358			−0.245679	+	0.969351i	$0.579011\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−28.9559	+	50.1531i	−0.943936	+	1.63495i	−0.186069	+	0.982537i	$0.559575\pi$
$941$	−28.9559	+	50.1531i	−0.943936	+	1.63495i	−0.757867	+	0.652409i	$0.773758\pi$
$942$		0			0
$943$	22.7126	+	39.3394i	0.739624	+	1.28107i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.8442	−	20.5147i	−0.384883	−	0.666638i	0.606870	−	0.794801i	$-0.292425\pi$
$947$	−11.8442	−	20.5147i	−0.384883	−	0.666638i	−0.991753	+	0.128164i	$0.959092\pi$
$948$		0			0
$949$	15.3661	−	26.6149i	0.498806	−	0.863957i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.2226			0.460716			0.230358	−	0.973106i	$-0.426010\pi$
$953$	14.2226			0.460716			0.230358	+	0.973106i	$0.426010\pi$
$954$		0			0
$955$	−8.27429	−	14.3315i	−0.267750	−	0.463756i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−15.6621	−	35.2050i	−0.505754	−	1.13683i
$960$		0			0
$961$	14.8378	+	25.6998i	0.478638	+	0.829025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.1222	−	19.2642i	0.358035	−	0.620135i
$966$		0			0
$967$	10.3665	+	17.9554i	0.333365	+	0.577405i	0.983169	−	0.182696i	$-0.0584825\pi$
$967$	10.3665	+	17.9554i	0.333365	+	0.577405i	−0.649804	+	0.760102i	$0.725149\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.39847	−	14.5466i	0.269520	−	0.466822i	−0.699218	−	0.714908i	$-0.746468\pi$
$971$	8.39847	−	14.5466i	0.269520	−	0.466822i	0.968738	+	0.248087i	$0.0798018\pi$
$972$		0			0
$973$	−18.4112	+	25.3254i	−0.590236	+	0.811894i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.7163	−	32.4176i	0.598788	−	1.03713i	−0.394212	−	0.919020i	$-0.628982\pi$
$977$	18.7163	−	32.4176i	0.598788	−	1.03713i	0.993000	−	0.118112i	$-0.0376843\pi$
$978$		0			0
$979$	−10.6130	+	18.3823i	−0.339194	+	0.587501i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−51.6778			−1.64826			−0.824132	−	0.566397i	$-0.808337\pi$
$983$	−51.6778			−1.64826			−0.824132	+	0.566397i	$0.808337\pi$
$984$		0			0
$985$	−21.0803			−0.671675
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.42771	+	12.8652i	−0.236188	+	0.409089i
$990$		0			0
$991$	28.5452	+	49.4418i	0.906769	+	1.57057i	0.818525	+	0.574471i	$0.194792\pi$
$991$	28.5452	+	49.4418i	0.906769	+	1.57057i	0.0882435	+	0.996099i	$0.471875\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.70284	−	11.6097i	−0.212494	−	0.368051i
$996$		0			0
$997$	−2.01490			−0.0638126			−0.0319063	−	0.999491i	$-0.510158\pi$
$997$	−2.01490			−0.0638126			−0.0319063	+	0.999491i	$0.510158\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.l.n.541.6		16
3.2	odd	2	inner	2268.2.l.n.541.3		16
7.4	even	3		2268.2.i.n.865.3		16
9.2	odd	6		2268.2.k.g.1297.6	yes	16
9.4	even	3		2268.2.i.n.2053.3		16
9.5	odd	6		2268.2.i.n.2053.6		16
9.7	even	3		2268.2.k.g.1297.3	✓	16
21.11	odd	6		2268.2.i.n.865.6		16
63.4	even	3	inner	2268.2.l.n.109.6		16
63.11	odd	6		2268.2.k.g.1621.6	yes	16
63.25	even	3		2268.2.k.g.1621.3	yes	16
63.32	odd	6	inner	2268.2.l.n.109.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.3		16	7.4	even	3
2268.2.i.n.865.6		16	21.11	odd	6
2268.2.i.n.2053.3		16	9.4	even	3
2268.2.i.n.2053.6		16	9.5	odd	6
2268.2.k.g.1297.3	✓	16	9.7	even	3
2268.2.k.g.1297.6	yes	16	9.2	odd	6
2268.2.k.g.1621.3	yes	16	63.25	even	3
2268.2.k.g.1621.6	yes	16	63.11	odd	6
2268.2.l.n.109.3		16	63.32	odd	6	inner
2268.2.l.n.109.6		16	63.4	even	3	inner
2268.2.l.n.541.3		16	3.2	odd	2	inner
2268.2.l.n.541.6		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.03112 q^{5} +(1.07542 + 2.41733i) q^{7} +O(q^{10})\)	\(q+1.03112 q^{5} +(1.07542 + 2.41733i) q^{7} -1.58576 q^{11} +(-2.52415 - 4.37196i) q^{13} +(-2.58242 - 4.47288i) q^{17} +(-0.392975 + 0.680652i) q^{19} -5.86577 q^{23} -3.93679 q^{25} +(4.44511 - 7.69915i) q^{29} +(0.575423 - 0.996661i) q^{31} +(1.10889 + 2.49255i) q^{35} +(4.07991 - 7.06661i) q^{37} +(-3.87206 - 6.70660i) q^{41} +(1.26628 - 2.19326i) q^{43} +(-4.24595 - 7.35420i) q^{47} +(-4.68693 + 5.19930i) q^{49} +(2.41270 + 4.17892i) q^{53} -1.63510 q^{55} +(-1.93622 + 3.35364i) q^{59} +(4.82204 + 8.35201i) q^{61} +(-2.60270 - 4.50801i) q^{65} +(0.837220 - 1.45011i) q^{67} +14.2795 q^{71} +(3.04382 + 5.27205i) q^{73} +(-1.70536 - 3.83329i) q^{77} +(4.15533 + 7.19724i) q^{79} +(7.12095 - 12.3339i) q^{83} +(-2.66278 - 4.61207i) q^{85} +(6.69272 - 11.5921i) q^{89} +(7.85392 - 10.8034i) q^{91} +(-0.405203 + 0.701833i) q^{95} +(-2.67500 + 4.63323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 10 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} - 10 q^{43} - 20 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) 16 * q + 10 * q^13 + 8 * q^19 - 8 * q^31 - 4 * q^37 - 10 * q^43 - 20 * q^49 - 32 * q^55 + 28 * q^61 + 18 * q^67 - 20 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

Introduction

L-functions

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