LMFDB - Embedded newform 2268.2.l.n.541.1

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			541.1
Root			$-1.04556 + 0.339889i$ of defining polynomial
Character	$\chi$	$=$	2268.541
Dual form			2268.2.l.n.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.67687 q^{5} +(-1.07542 + 2.41733i) q^{7} +O(q^{10})$	$q-3.67687 q^{5} +(-1.07542 + 2.41733i) q^{7} -0.603143 q^{11} +(2.62851 + 4.55271i) q^{13} +(2.12557 + 3.68159i) q^{17} +(3.68426 - 6.38133i) q^{19} -1.15778 q^{23} +8.51937 q^{25} +(-3.98826 + 6.90786i) q^{29} +(-1.57542 + 2.72871i) q^{31} +(3.95419 - 8.88819i) q^{35} +(0.00266923 - 0.00462323i) q^{37} +(-2.00937 - 3.48033i) q^{41} +(-3.66193 + 6.34264i) q^{43} +(-6.10863 - 10.5805i) q^{47} +(-4.68693 - 5.19930i) q^{49} +(-4.64928 - 8.05279i) q^{53} +2.21768 q^{55} +(-3.30760 + 5.72894i) q^{59} +(0.969252 + 1.67879i) q^{61} +(-9.66468 - 16.7397i) q^{65} +(-4.31544 + 7.47456i) q^{67} +1.13815 q^{71} +(-5.33511 - 9.24068i) q^{73} +(0.648634 - 1.45799i) q^{77} +(-2.07275 - 3.59011i) q^{79} +(6.24088 - 10.8095i) q^{83} +(-7.81544 - 13.5367i) q^{85} +(-4.09464 + 7.09212i) q^{89} +(-13.8321 + 1.45787i) q^{91} +(-13.5466 + 23.4633i) q^{95} +(6.77935 - 11.7422i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.67687			−1.64435			−0.822173	−	0.569238i	$-0.807238\pi$
$5$	−3.67687			−1.64435			−0.822173	+	0.569238i	$0.807238\pi$
$6$		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
$11$	−0.603143			−0.181855			−0.0909273	−	0.995858i	$-0.528983\pi$
$11$	−0.603143			−0.181855			−0.0909273	+	0.995858i	$0.528983\pi$
$12$		0			0
$13$	2.62851	+	4.55271i	0.729017	+	1.26269i	0.957299	+	0.289099i	$0.0933558\pi$
$13$	2.62851	+	4.55271i	0.729017	+	1.26269i	−0.228282	+	0.973595i	$0.573311\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.12557	+	3.68159i	0.515526	+	0.892918i	0.999838	+	0.0180219i	$0.00573685\pi$
$17$	2.12557	+	3.68159i	0.515526	+	0.892918i	−0.484311	+	0.874896i	$0.660930\pi$
$18$		0			0
$19$	3.68426	−	6.38133i	0.845228	−	1.46398i	−0.0401954	−	0.999192i	$-0.512798\pi$
$19$	3.68426	−	6.38133i	0.845228	−	1.46398i	0.885423	−	0.464786i	$-0.153869\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.15778			−0.241414			−0.120707	−	0.992688i	$-0.538516\pi$
$23$	−1.15778			−0.241414			−0.120707	+	0.992688i	$0.538516\pi$
$24$		0			0
$25$	8.51937			1.70387
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.98826	+	6.90786i	−0.740601	+	1.28276i	0.211622	+	0.977352i	$0.432126\pi$
$29$	−3.98826	+	6.90786i	−0.740601	+	1.28276i	−0.952222	+	0.305406i	$0.901208\pi$
$30$		0			0
$31$	−1.57542	+	2.72871i	−0.282954	+	0.490091i	−0.972111	−	0.234521i	$-0.924648\pi$
$31$	−1.57542	+	2.72871i	−0.282954	+	0.490091i	0.689157	+	0.724612i	$0.257981\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.95419	−	8.88819i	0.668380	−	1.50238i
$36$		0			0
$37$	0.00266923	−	0.00462323i	0.000438818	−	0.000760055i	−0.865806	−	0.500380i	$-0.833194\pi$
$37$	0.00266923	−	0.00462323i	0.000438818	−	0.000760055i	0.866245	+	0.499620i	$0.166527\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.00937	−	3.48033i	−0.313811	−	0.543537i	0.665373	−	0.746511i	$-0.268272\pi$
$41$	−2.00937	−	3.48033i	−0.313811	−	0.543537i	−0.979184	+	0.202974i	$0.934939\pi$
$42$		0			0
$43$	−3.66193	+	6.34264i	−0.558438	+	0.967244i	0.439189	+	0.898395i	$0.355266\pi$
$43$	−3.66193	+	6.34264i	−0.558438	+	0.967244i	−0.997627	+	0.0688488i	$0.978067\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.10863	−	10.5805i	−0.891036	−	1.54332i	−0.838635	−	0.544693i	$-0.816646\pi$
$47$	−6.10863	−	10.5805i	−0.891036	−	1.54332i	−0.0524003	−	0.998626i	$-0.516687\pi$
$48$		0			0
$49$	−4.68693	−	5.19930i	−0.669562	−	0.742756i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.64928	−	8.05279i	−0.638628	−	1.10614i	−0.985734	−	0.168310i	$-0.946169\pi$
$53$	−4.64928	−	8.05279i	−0.638628	−	1.10614i	0.347107	−	0.937826i	$-0.387164\pi$
$54$		0			0
$55$	2.21768			0.299032
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.30760	+	5.72894i	−0.430613	+	0.745844i	−0.996926	−	0.0783462i	$-0.975036\pi$
$59$	−3.30760	+	5.72894i	−0.430613	+	0.745844i	0.566313	+	0.824190i	$0.308369\pi$
$60$		0			0
$61$	0.969252	+	1.67879i	0.124100	+	0.214948i	0.921381	−	0.388661i	$-0.127062\pi$
$61$	0.969252	+	1.67879i	0.124100	+	0.214948i	−0.797281	+	0.603609i	$0.793729\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.66468	−	16.7397i	−1.19876	−	2.07631i
$66$		0			0
$67$	−4.31544	+	7.47456i	−0.527215	+	0.913163i	0.472282	+	0.881447i	$0.343430\pi$
$67$	−4.31544	+	7.47456i	−0.527215	+	0.913163i	−0.999497	+	0.0317155i	$0.989903\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.13815			0.135074			0.0675370	−	0.997717i	$-0.478486\pi$
$71$	1.13815			0.135074			0.0675370	+	0.997717i	$0.478486\pi$
$72$		0			0
$73$	−5.33511	−	9.24068i	−0.624427	−	1.08154i	−0.988651	−	0.150228i	$-0.951999\pi$
$73$	−5.33511	−	9.24068i	−0.624427	−	1.08154i	0.364224	−	0.931311i	$-0.381334\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.648634	−	1.45799i	0.0739187	−	0.166154i
$78$		0			0
$79$	−2.07275	−	3.59011i	−0.233203	−	0.403919i	0.725546	−	0.688174i	$-0.241587\pi$
$79$	−2.07275	−	3.59011i	−0.233203	−	0.403919i	−0.958749	+	0.284254i	$0.908254\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.24088	−	10.8095i	0.685026	−	1.18650i	−0.288403	−	0.957509i	$-0.593124\pi$
$83$	6.24088	−	10.8095i	0.685026	−	1.18650i	0.973429	−	0.228990i	$-0.0735423\pi$
$84$		0			0
$85$	−7.81544	−	13.5367i	−0.847703	−	1.46827i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.09464	+	7.09212i	−0.434031	+	0.751764i	−0.997216	−	0.0745672i	$-0.976242\pi$
$89$	−4.09464	+	7.09212i	−0.434031	+	0.751764i	0.563185	+	0.826331i	$0.309576\pi$
$90$		0			0
$91$	−13.8321	+	1.45787i	−1.45000	+	0.152827i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−13.5466	+	23.4633i	−1.38985	+	2.40729i
$96$		0			0
$97$	6.77935	−	11.7422i	0.688339	−	1.19224i	−0.284036	−	0.958814i	$-0.591673\pi$
$97$	6.77935	−	11.7422i	0.688339	−	1.19224i	0.972375	−	0.233425i	$-0.0749932\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−15.3395			−1.52634			−0.763169	−	0.646200i	$-0.776357\pi$
$101$	−15.3395			−1.52634			−0.763169	+	0.646200i	$0.776357\pi$
$102$		0			0
$103$	−4.96066			−0.488789			−0.244394	−	0.969676i	$-0.578589\pi$
$103$	−4.96066			−0.488789			−0.244394	+	0.969676i	$0.578589\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.41399	−	5.91320i	0.330043	−	0.571651i	−0.652477	−	0.757808i	$-0.726270\pi$
$107$	3.41399	−	5.91320i	0.330043	−	0.571651i	0.982520	+	0.186158i	$0.0596035\pi$
$108$		0			0
$109$	8.90194	+	15.4186i	0.852651	+	1.47684i	0.878807	+	0.477178i	$0.158340\pi$
$109$	8.90194	+	15.4186i	0.852651	+	1.47684i	−0.0261554	+	0.999658i	$0.508326\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.63946	−	8.03579i	−0.436444	−	0.755943i	0.560968	−	0.827837i	$-0.310429\pi$
$113$	−4.63946	−	8.03579i	−0.436444	−	0.755943i	−0.997412	+	0.0718940i	$0.977096\pi$
$114$		0			0
$115$	4.25702			0.396969
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.1855	+	1.17892i	−1.02537	+	0.108072i
$120$		0			0
$121$	−10.6362			−0.966929
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.9403			−1.15741
$126$		0			0
$127$	−14.9941			−1.33051			−0.665254	−	0.746617i	$-0.731677\pi$
$127$	−14.9941			−1.33051			−0.665254	+	0.746617i	$0.731677\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	22.8327			1.99490			0.997452	−	0.0713394i	$-0.0227273\pi$
$131$	22.8327			1.99490			0.997452	+	0.0713394i	$0.0227273\pi$
$132$		0			0
$133$	11.4636	+	15.7687i	0.994022	+	1.36732i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.52557			0.130338			0.0651690	−	0.997874i	$-0.479241\pi$
$137$	1.52557			0.130338			0.0651690	+	0.997874i	$0.479241\pi$
$138$		0			0
$139$	−3.31277	−	5.73789i	−0.280986	−	0.486681i	0.690642	−	0.723197i	$-0.257328\pi$
$139$	−3.31277	−	5.73789i	−0.280986	−	0.486681i	−0.971628	+	0.236515i	$0.923995\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.58537	−	2.74594i	−0.132575	−	0.229627i
$144$		0			0
$145$	14.6643	−	25.3993i	1.21780	−	2.10930i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.7749			−1.45618			−0.728089	−	0.685483i	$-0.759591\pi$
$149$	−17.7749			−1.45618			−0.728089	+	0.685483i	$0.759591\pi$
$150$		0			0
$151$	4.63622			0.377290			0.188645	−	0.982045i	$-0.439590\pi$
$151$	4.63622			0.377290			0.188645	+	0.982045i	$0.439590\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.79262	−	10.0331i	0.465275	−	0.805880i
$156$		0			0
$157$	−1.70660	+	2.95592i	−0.136202	+	0.235908i	−0.926056	−	0.377387i	$-0.876823\pi$
$157$	−1.70660	+	2.95592i	−0.136202	+	0.235908i	0.789854	+	0.613295i	$0.210156\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.24511	−	2.79874i	0.0981281	−	0.220571i
$162$		0			0
$163$	7.55012	−	13.0772i	0.591371	−	1.02428i	−0.402677	−	0.915342i	$-0.631920\pi$
$163$	7.55012	−	13.0772i	0.591371	−	1.02428i	0.994048	−	0.108942i	$-0.0347464\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.85782	−	4.94988i	−0.221144	−	0.383033i	0.734011	−	0.679137i	$-0.237646\pi$
$167$	−2.85782	−	4.94988i	−0.221144	−	0.383033i	−0.955156	+	0.296104i	$0.904313\pi$
$168$		0			0
$169$	−7.31811	+	12.6753i	−0.562931	+	0.975026i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.948157	−	1.64226i	−0.0720871	−	0.124858i	0.827729	−	0.561128i	$-0.189633\pi$
$173$	−0.948157	−	1.64226i	−0.0720871	−	0.124858i	−0.899816	+	0.436270i	$0.856299\pi$
$174$		0			0
$175$	−9.16193	+	20.5941i	−0.692576	+	1.55677i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.29747	+	12.6396i	0.545438	+	0.944727i	0.998579	+	0.0532881i	$0.0169702\pi$
$179$	7.29747	+	12.6396i	0.545438	+	0.944727i	−0.453141	+	0.891439i	$0.649696\pi$
$180$		0			0
$181$	7.89857			0.587096			0.293548	−	0.955944i	$-0.405164\pi$
$181$	7.89857			0.587096			0.293548	+	0.955944i	$0.405164\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.00981439	+	0.0169990i	−0.000721569	+	0.00124979i
$186$		0			0
$187$	−1.28202	−	2.22053i	−0.0937508	−	0.162381i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.23670	+	7.33818i	0.306557	+	0.530972i	0.977607	−	0.210440i	$-0.0674897\pi$
$191$	4.23670	+	7.33818i	0.306557	+	0.530972i	−0.671050	+	0.741412i	$0.734156\pi$
$192$		0			0
$193$	3.48300	−	6.03273i	0.250712	−	0.434246i	−0.713010	−	0.701154i	$-0.752669\pi$
$193$	3.48300	−	6.03273i	0.250712	−	0.434246i	0.963722	+	0.266908i	$0.0860020\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.2371			1.15685			0.578424	−	0.815736i	$-0.303668\pi$
$197$	16.2371			1.15685			0.578424	+	0.815736i	$0.303668\pi$
$198$		0			0
$199$	−7.35153	−	12.7332i	−0.521136	−	0.902634i	−0.999698	−	0.0245800i	$-0.992175\pi$
$199$	−7.35153	−	12.7332i	−0.521136	−	0.902634i	0.478562	−	0.878054i	$-0.341158\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.4095	−	17.0698i	−0.870976	−	1.19806i
$204$		0			0
$205$	7.38819	+	12.7967i	0.516014	+	0.893762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.22214	+	3.84886i	−0.153709	+	0.266231i
$210$		0			0
$211$	8.41053	+	14.5675i	0.579005	+	1.00287i	0.995594	+	0.0937708i	$0.0298921\pi$
$211$	8.41053	+	14.5675i	0.579005	+	1.00287i	−0.416589	+	0.909095i	$0.636775\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.4644	−	23.3211i	0.918266	−	1.59048i
$216$		0			0
$217$	−4.90194	−	6.74283i	−0.332766	−	0.457733i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.1741	+	19.3542i	−0.751655	+	1.30190i
$222$		0			0
$223$	3.45799	−	5.98942i	0.231564	−	0.401081i	−0.726704	−	0.686950i	$-0.758949\pi$
$223$	3.45799	−	5.98942i	0.231564	−	0.401081i	0.958269	+	0.285869i	$0.0922823\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.99634			−0.464363			−0.232182	−	0.972672i	$-0.574586\pi$
$227$	−6.99634			−0.464363			−0.232182	+	0.972672i	$0.574586\pi$
$228$		0			0
$229$	−2.82700			−0.186813			−0.0934066	−	0.995628i	$-0.529776\pi$
$229$	−2.82700			−0.186813			−0.0934066	+	0.995628i	$0.529776\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.1679	+	19.3434i	−0.731635	+	1.26723i	0.224550	+	0.974463i	$0.427909\pi$
$233$	−11.1679	+	19.3434i	−0.731635	+	1.26723i	−0.956184	+	0.292766i	$0.905424\pi$
$234$		0			0
$235$	22.4606	+	38.9030i	1.46517	+	2.53775i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.954829	+	1.65381i	0.0617628	+	0.106976i	0.895253	−	0.445557i	$-0.146994\pi$
$239$	0.954829	+	1.65381i	0.0617628	+	0.106976i	−0.833491	+	0.552534i	$0.813661\pi$
$240$		0			0
$241$	−19.6870			−1.26815			−0.634077	−	0.773270i	$-0.718620\pi$
$241$	−19.6870			−1.26815			−0.634077	+	0.773270i	$0.718620\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	17.2332	+	19.1171i	1.10099	+	1.22135i
$246$		0			0
$247$	38.7365			2.46474
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.2990			−0.776306			−0.388153	−	0.921595i	$-0.626887\pi$
$251$	−12.2990			−0.776306			−0.388153	+	0.921595i	$0.626887\pi$
$252$		0			0
$253$	0.698309			0.0439023
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.4242			0.712622			0.356311	−	0.934367i	$-0.384034\pi$
$257$	11.4242			0.712622			0.356311	+	0.934367i	$0.384034\pi$
$258$		0			0
$259$	0.00830532	+	0.0114243i	0.000516067	+	0.000709873i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.3109			−1.19076			−0.595380	−	0.803445i	$-0.702998\pi$
$263$	−19.3109			−1.19076			−0.595380	+	0.803445i	$0.702998\pi$
$264$		0			0
$265$	17.0948	+	29.6091i	1.05012	+	1.81887i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.00745	−	6.94110i	−0.244338	−	0.423206i	0.717607	−	0.696448i	$-0.245237\pi$
$269$	−4.00745	−	6.94110i	−0.244338	−	0.423206i	−0.961945	+	0.273242i	$0.911904\pi$
$270$		0			0
$271$	2.96658	−	5.13827i	0.180207	−	0.312128i	−0.761744	−	0.647878i	$-0.775657\pi$
$271$	2.96658	−	5.13827i	0.180207	−	0.312128i	0.941951	+	0.335750i	$0.108990\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.13840			−0.309857
$276$		0			0
$277$	−12.0554			−0.724336			−0.362168	−	0.932113i	$-0.617963\pi$
$277$	−12.0554			−0.724336			−0.362168	+	0.932113i	$0.617963\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.73700	+	16.8650i	−0.580861	+	1.00608i	0.414517	+	0.910042i	$0.363951\pi$
$281$	−9.73700	+	16.8650i	−0.580861	+	1.00608i	−0.995378	+	0.0960386i	$0.969383\pi$
$282$		0			0
$283$	14.3518	−	24.8581i	0.853127	−	1.47766i	−0.0252457	−	0.999681i	$-0.508037\pi$
$283$	14.3518	−	24.8581i	0.853127	−	1.47766i	0.878372	−	0.477977i	$-0.158630\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.5740	−	1.11448i	0.624165	−	0.0657854i
$288$		0			0
$289$	−0.536086	+	0.928529i	−0.0315345	+	0.0546193i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−11.3503	−	19.6593i	−0.663090	−	1.14851i	−0.979799	−	0.199983i	$-0.935911\pi$
$293$	−11.3503	−	19.6593i	−0.663090	−	1.14851i	0.316709	−	0.948523i	$-0.397422\pi$
$294$		0			0
$295$	12.1616	−	21.0646i	0.708077	−	1.22643i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.04324	−	5.27105i	−0.175995	−	0.304833i
$300$		0			0
$301$	−11.3941	−	15.6731i	−0.656746	−	0.903382i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.56381	−	6.17271i	−0.204063	−	0.353448i
$306$		0			0
$307$	−27.9486			−1.59511			−0.797555	−	0.603246i	$-0.793874\pi$
$307$	−27.9486			−1.59511			−0.797555	+	0.603246i	$0.793874\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.64908	−	13.2486i	0.433739	−	0.751259i	−0.563452	−	0.826149i	$-0.690527\pi$
$311$	7.64908	−	13.2486i	0.433739	−	0.751259i	0.997192	+	0.0748898i	$0.0238605\pi$
$312$		0			0
$313$	−1.67051	−	2.89341i	−0.0944230	−	0.163545i	0.814945	−	0.579539i	$-0.196767\pi$
$313$	−1.67051	−	2.89341i	−0.0944230	−	0.163545i	−0.909368	+	0.415993i	$0.863434\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.50722	+	7.80673i	0.253151	+	0.438470i	0.964392	−	0.264479i	$-0.0851998\pi$
$317$	4.50722	+	7.80673i	0.253151	+	0.438470i	−0.711241	+	0.702948i	$0.751867\pi$
$318$		0			0
$319$	2.40549	−	4.16643i	0.134682	−	0.233275i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	31.3246			1.74295
$324$		0			0
$325$	22.3932	+	38.7862i	1.24215	+	2.15147i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	32.1458	−	3.38809i	1.77226	−	0.186791i
$330$		0			0
$331$	−9.14760	−	15.8441i	−0.502797	−	0.870870i	−0.999995	−	0.00323307i	$-0.998971\pi$
$331$	−9.14760	−	15.8441i	−0.502797	−	0.870870i	0.497197	−	0.867637i	$-0.334362\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	15.8673	−	27.4830i	0.866924	−	1.50156i
$336$		0			0
$337$	−0.868823	−	1.50485i	−0.0473278	−	0.0819741i	0.841391	−	0.540427i	$-0.181737\pi$
$337$	−0.868823	−	1.50485i	−0.0473278	−	0.0819741i	−0.888719	+	0.458453i	$0.848404\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.950206	−	1.64580i	0.0514565	−	0.0891253i
$342$		0			0
$343$	17.6088	−	5.73840i	0.950787	−	0.309845i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.546358	−	0.946319i	0.0293300	−	0.0508011i	−0.850988	−	0.525185i	$-0.823996\pi$
$347$	0.546358	−	0.946319i	0.0293300	−	0.0508011i	0.880318	+	0.474384i	$0.157329\pi$
$348$		0			0
$349$	−4.70096	+	8.14231i	−0.251637	+	0.435848i	−0.963977	−	0.265987i	$-0.914302\pi$
$349$	−4.70096	+	8.14231i	−0.251637	+	0.435848i	0.712340	+	0.701835i	$0.247636\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	19.2910			1.02676			0.513378	−	0.858163i	$-0.328394\pi$
$353$	19.2910			1.02676			0.513378	+	0.858163i	$0.328394\pi$
$354$		0			0
$355$	−4.18484			−0.222108
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.94976	+	5.10914i	−0.155682	+	0.269650i	−0.933307	−	0.359079i	$-0.883091\pi$
$359$	−2.94976	+	5.10914i	−0.155682	+	0.269650i	0.777625	+	0.628729i	$0.216424\pi$
$360$		0			0
$361$	−17.6476	−	30.5665i	−0.928820	−	1.60876i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	19.6165	+	33.9768i	1.02677	+	1.77843i
$366$		0			0
$367$	10.9660			0.572421			0.286210	−	0.958167i	$-0.407604\pi$
$367$	10.9660			0.572421			0.286210	+	0.958167i	$0.407604\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	24.4662	−	2.57867i	1.27022	−	0.133878i
$372$		0			0
$373$	−31.9381			−1.65369			−0.826847	−	0.562428i	$-0.809868\pi$
$373$	−31.9381			−1.65369			−0.826847	+	0.562428i	$0.809868\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−41.9326			−2.15964
$378$		0			0
$379$	−14.4354			−0.741495			−0.370747	−	0.928734i	$-0.620898\pi$
$379$	−14.4354			−0.741495			−0.370747	+	0.928734i	$0.620898\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.7201			0.905456			0.452728	−	0.891649i	$-0.350451\pi$
$383$	17.7201			0.905456			0.452728	+	0.891649i	$0.350451\pi$
$384$		0			0
$385$	−2.38494	+	5.36085i	−0.121548	+	0.273214i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	18.9750			0.962072			0.481036	−	0.876701i	$-0.340261\pi$
$389$	18.9750			0.962072			0.481036	+	0.876701i	$0.340261\pi$
$390$		0			0
$391$	−2.46095	−	4.26249i	−0.124455	−	0.215563i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.62124	+	13.2004i	0.383466	+	0.664183i
$396$		0			0
$397$	−10.5889	+	18.3405i	−0.531440	+	0.920482i	0.467886	+	0.883789i	$0.345016\pi$
$397$	−10.5889	+	18.3405i	−0.531440	+	0.920482i	−0.999327	+	0.0366930i	$0.988318\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.7808			0.738116			0.369058	−	0.929406i	$-0.379680\pi$
$401$	14.7808			0.738116			0.369058	+	0.929406i	$0.379680\pi$
$402$		0			0
$403$	−16.5640			−0.825114
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.00160993	+	0.00278847i	−7.98011e−5	+	0.000138219i
$408$		0			0
$409$	1.86575	−	3.23158i	0.0922554	−	0.159791i	−0.816204	−	0.577763i	$-0.803926\pi$
$409$	1.86575	−	3.23158i	0.0922554	−	0.159791i	0.908460	+	0.417972i	$0.137259\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.2916	−	14.1566i	−0.506418	−	0.696600i
$414$		0			0
$415$	−22.9469	+	39.7452i	−1.12642	+	1.95102i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.1678	−	24.5393i	−0.692142	−	1.19883i	−0.971135	−	0.238532i	$-0.923334\pi$
$419$	−14.1678	−	24.5393i	−0.692142	−	1.19883i	0.278993	−	0.960293i	$-0.409999\pi$
$420$		0			0
$421$	−8.09776	+	14.0257i	−0.394661	+	0.683572i	−0.993058	−	0.117627i	$-0.962471\pi$
$421$	−8.09776	+	14.0257i	−0.394661	+	0.683572i	0.598397	+	0.801200i	$0.295805\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.1085	+	31.3649i	0.878392	+	1.52142i
$426$		0			0
$427$	−5.10055	+	0.537585i	−0.246833	+	0.0260156i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.5528	+	23.4741i	0.652815	+	1.13071i	0.982437	+	0.186595i	$0.0597453\pi$
$431$	13.5528	+	23.4741i	0.652815	+	1.13071i	−0.329622	+	0.944113i	$0.606921\pi$
$432$		0			0
$433$	−11.5028			−0.552789			−0.276394	−	0.961044i	$-0.589140\pi$
$433$	−11.5028			−0.552789			−0.276394	+	0.961044i	$0.589140\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.26558	+	7.38819i	−0.204050	+	0.353425i
$438$		0			0
$439$	1.43357	+	2.48301i	0.0684205	+	0.118508i	0.898206	−	0.439574i	$-0.144871\pi$
$439$	1.43357	+	2.48301i	0.0684205	+	0.118508i	−0.829786	+	0.558082i	$0.811537\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.42151	+	7.65827i	0.210072	+	0.363855i	0.951737	−	0.306915i	$-0.0992968\pi$
$443$	4.42151	+	7.65827i	0.210072	+	0.363855i	−0.741665	+	0.670771i	$0.765963\pi$
$444$		0			0
$445$	15.0555	−	26.0768i	0.713697	−	1.23616i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−40.5033			−1.91147			−0.955735	−	0.294229i	$-0.904937\pi$
$449$	−40.5033			−1.91147			−0.955735	+	0.294229i	$0.904937\pi$
$450$		0			0
$451$	1.21194	+	2.09914i	0.0570680	+	0.0988446i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	50.8590	−	5.36041i	2.38431	−	0.251300i
$456$		0			0
$457$	−19.4049	−	33.6103i	−0.907723	−	1.57222i	−0.817220	−	0.576326i	$-0.804486\pi$
$457$	−19.4049	−	33.6103i	−0.907723	−	1.57222i	−0.0905025	−	0.995896i	$-0.528847\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.1328	+	27.9428i	−0.751378	+	1.30142i	0.195777	+	0.980648i	$0.437277\pi$
$461$	−16.1328	+	27.9428i	−0.751378	+	1.30142i	−0.947155	+	0.320776i	$0.896056\pi$
$462$		0			0
$463$	−16.7430	−	28.9997i	−0.778112	−	1.34773i	−0.933029	−	0.359802i	$-0.882844\pi$
$463$	−16.7430	−	28.9997i	−0.778112	−	1.34773i	0.154917	−	0.987927i	$-0.450489\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.04280	+	8.73438i	−0.233353	+	0.404179i	−0.958793	−	0.284107i	$-0.908303\pi$
$467$	−5.04280	+	8.73438i	−0.233353	+	0.404179i	0.725440	+	0.688286i	$0.241636\pi$
$468$		0			0
$469$	−13.4275	−	18.4701i	−0.620026	−	0.852872i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.20867	−	3.82552i	0.101555	−	0.175898i
$474$		0			0
$475$	31.3876	−	54.3649i	1.44016	−	2.49443i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.59519			0.392724			0.196362	−	0.980531i	$-0.437087\pi$
$479$	8.59519			0.392724			0.196362	+	0.980531i	$0.437087\pi$
$480$		0			0
$481$	0.0280643			0.00127962
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.9268	+	43.1745i	−1.13187	+	1.96045i
$486$		0			0
$487$	−0.298843	−	0.517612i	−0.0135419	−	0.0234552i	0.859175	−	0.511682i	$-0.170977\pi$
$487$	−0.298843	−	0.517612i	−0.0135419	−	0.0234552i	−0.872717	+	0.488227i	$0.837644\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.1521	+	29.7084i	0.774066	+	1.34072i	0.935318	+	0.353808i	$0.115113\pi$
$491$	17.1521	+	29.7084i	0.774066	+	1.34072i	−0.161253	+	0.986913i	$0.551553\pi$
$492$		0			0
$493$	−33.9092			−1.52720
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.22400	+	2.75129i	−0.0549038	+	0.123412i
$498$		0			0
$499$	30.0494			1.34520			0.672598	−	0.740008i	$-0.265178\pi$
$499$	30.0494			1.34520			0.672598	+	0.740008i	$0.265178\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.5650			0.827773			0.413887	−	0.910328i	$-0.364171\pi$
$503$	18.5650			0.827773			0.413887	+	0.910328i	$0.364171\pi$
$504$		0			0
$505$	56.4013			2.50983
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.01815			−0.311074			−0.155537	−	0.987830i	$-0.549711\pi$
$509$	−7.01815			−0.311074			−0.155537	+	0.987830i	$0.549711\pi$
$510$		0			0
$511$	28.0752	−	2.95906i	1.24198	−	0.130901i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	18.2397			0.803738
$516$		0			0
$517$	3.68438	+	6.38154i	0.162039	+	0.280660i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.0742	+	26.1092i	0.660411	+	1.14387i	0.980508	+	0.196481i	$0.0629514\pi$
$521$	15.0742	+	26.1092i	0.660411	+	1.14387i	−0.320096	+	0.947385i	$0.603715\pi$
$522$		0			0
$523$	−14.1726	+	24.5476i	−0.619724	+	1.07339i	0.369812	+	0.929107i	$0.379422\pi$
$523$	−14.1726	+	24.5476i	−0.619724	+	1.07339i	−0.989536	+	0.144287i	$0.953911\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.3947			−0.583481
$528$		0			0
$529$	−21.6595			−0.941719
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.5633	−	18.2962i	0.457547	−	0.792495i
$534$		0			0
$535$	−12.5528	+	21.7421i	−0.542704	+	0.939991i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.82689	+	3.13592i	0.121763	+	0.135074i
$540$		0			0
$541$	−14.5245	+	25.1572i	−0.624458	+	1.08159i	0.364187	+	0.931326i	$0.381347\pi$
$541$	−14.5245	+	25.1572i	−0.624458	+	1.08159i	−0.988645	+	0.150268i	$0.951986\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−32.7313	−	56.6922i	−1.40205	−	2.42843i
$546$		0			0
$547$	−8.68455	+	15.0421i	−0.371324	+	0.643153i	−0.989770	−	0.142675i	$-0.954430\pi$
$547$	−8.68455	+	15.0421i	−0.371324	+	0.643153i	0.618445	+	0.785828i	$0.287763\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	29.3876	+	50.9008i	1.25195	+	2.16844i
$552$		0			0
$553$	10.9076	−	1.14963i	0.463837	−	0.0488873i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.5927	+	33.9355i	0.830169	+	1.43789i	0.897904	+	0.440191i	$0.145089\pi$
$557$	19.5927	+	33.9355i	0.830169	+	1.43789i	−0.0677355	+	0.997703i	$0.521577\pi$
$558$		0			0
$559$	−38.5016			−1.62844
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.2039	+	33.2622i	−0.809349	+	1.40183i	0.103967	+	0.994581i	$0.466846\pi$
$563$	−19.2039	+	33.2622i	−0.809349	+	1.40183i	−0.913316	+	0.407252i	$0.866487\pi$
$564$		0			0
$565$	17.0587	+	29.5465i	0.717665	+	1.24303i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.54032	−	7.86407i	−0.190340	−	0.329679i	0.755023	−	0.655698i	$-0.227626\pi$
$569$	−4.54032	−	7.86407i	−0.190340	−	0.329679i	−0.945363	+	0.326020i	$0.894292\pi$
$570$		0			0
$571$	18.5274	−	32.0904i	0.775347	−	1.34294i	−0.159253	−	0.987238i	$-0.550908\pi$
$571$	18.5274	−	32.0904i	0.775347	−	1.34294i	0.934599	−	0.355702i	$-0.115758\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.86358			−0.411340
$576$		0			0
$577$	1.04241	+	1.80550i	0.0433960	+	0.0751641i	0.886908	−	0.461947i	$-0.152849\pi$
$577$	1.04241	+	1.80550i	0.0433960	+	0.0751641i	−0.843512	+	0.537111i	$0.819516\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	19.4186	+	26.7110i	0.805617	+	1.10816i
$582$		0			0
$583$	2.80418	+	4.85699i	0.116137	+	0.201156i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.75919	−	8.24316i	0.196433	−	0.340232i	−0.750936	−	0.660374i	$-0.770398\pi$
$587$	4.75919	−	8.24316i	0.196433	−	0.340232i	0.947369	+	0.320143i	$0.103731\pi$
$588$		0			0
$589$	11.6085	+	20.1066i	0.478322	+	0.828477i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.63267	−	13.2202i	0.313436	−	0.542887i	−0.665668	−	0.746248i	$-0.731853\pi$
$593$	7.63267	−	13.2202i	0.313436	−	0.542887i	0.979104	+	0.203361i	$0.0651865\pi$
$594$		0			0
$595$	41.1276	−	4.33475i	1.68607	−	0.177707i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.0597	−	17.4240i	0.411030	−	0.711924i	−0.583973	−	0.811773i	$-0.698503\pi$
$599$	10.0597	−	17.4240i	0.411030	−	0.711924i	0.995003	+	0.0998490i	$0.0318360\pi$
$600$		0			0
$601$	−10.1529	+	17.5854i	−0.414146	+	0.717322i	−0.995338	−	0.0964440i	$-0.969253\pi$
$601$	−10.1529	+	17.5854i	−0.414146	+	0.717322i	0.581192	+	0.813766i	$0.302586\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	39.1080			1.58997
$606$		0			0
$607$	−2.07298			−0.0841396			−0.0420698	−	0.999115i	$-0.513395\pi$
$607$	−2.07298			−0.0841396			−0.0420698	+	0.999115i	$0.513395\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	32.1132	−	55.6217i	1.29916	−	2.25021i
$612$		0			0
$613$	−1.10053	−	1.90618i	−0.0444502	−	0.0769900i	0.842944	−	0.538001i	$-0.180820\pi$
$613$	−1.10053	−	1.90618i	−0.0444502	−	0.0769900i	−0.887395	+	0.461011i	$0.847487\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.1904	−	36.7029i	−0.853095	−	1.47760i	−0.878401	−	0.477924i	$-0.841389\pi$
$617$	−21.1904	−	36.7029i	−0.853095	−	1.47760i	0.0253061	−	0.999680i	$-0.491944\pi$
$618$		0			0
$619$	13.8707			0.557511			0.278756	−	0.960362i	$-0.410078\pi$
$619$	13.8707			0.557511			0.278756	+	0.960362i	$0.410078\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.7405	−	17.5251i	−0.510438	−	0.702129i
$624$		0			0
$625$	4.98282			0.199313
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.0226945			0.000904889
$630$		0			0
$631$	45.1845			1.79876			0.899382	−	0.437163i	$-0.144017\pi$
$631$	45.1845			1.79876			0.899382	+	0.437163i	$0.144017\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	55.1312			2.18782
$636$		0			0
$637$	11.3512	−	35.0046i	0.449753	−	1.38693i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−26.5128			−1.04719			−0.523597	−	0.851966i	$-0.675410\pi$
$641$	−26.5128			−1.04719			−0.523597	+	0.851966i	$0.675410\pi$
$642$		0			0
$643$	24.3184	+	42.1207i	0.959024	+	1.66108i	0.724879	+	0.688876i	$0.241896\pi$
$643$	24.3184	+	42.1207i	0.959024	+	1.66108i	0.234145	+	0.972202i	$0.424771\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.7224	−	18.5717i	−0.421540	−	0.730128i	0.574551	−	0.818469i	$-0.305177\pi$
$647$	−10.7224	−	18.5717i	−0.421540	−	0.730128i	−0.996090	+	0.0883409i	$0.971844\pi$
$648$		0			0
$649$	1.99496	−	3.45537i	0.0783090	−	0.135635i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.48991			−0.136571			−0.0682854	−	0.997666i	$-0.521753\pi$
$653$	−3.48991			−0.136571			−0.0682854	+	0.997666i	$0.521753\pi$
$654$		0			0
$655$	−83.9529			−3.28031
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.2754	+	31.6539i	−0.711908	+	1.23306i	0.252232	+	0.967667i	$0.418835\pi$
$659$	−18.2754	+	31.6539i	−0.711908	+	1.23306i	−0.964140	+	0.265394i	$0.914498\pi$
$660$		0			0
$661$	2.78748	−	4.82806i	0.108420	−	0.187790i	−0.806710	−	0.590947i	$-0.798754\pi$
$661$	2.78748	−	4.82806i	0.108420	−	0.187790i	0.915131	+	0.403158i	$0.132087\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−42.1502	−	57.9794i	−1.63452	−	2.24835i
$666$		0			0
$667$	4.61753	−	7.99780i	0.178792	−	0.309676i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.584598	−	1.01255i	−0.0225682	−	0.0390892i
$672$		0			0
$673$	1.25661	−	2.17652i	0.0484389	−	0.0838986i	−0.840789	−	0.541362i	$-0.817909\pi$
$673$	1.25661	−	2.17652i	0.0484389	−	0.0838986i	0.889228	+	0.457464i	$0.151242\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.8606	+	27.4714i	0.609574	+	1.05581i	0.991311	+	0.131542i	$0.0419928\pi$
$677$	15.8606	+	27.4714i	0.609574	+	1.05581i	−0.381737	+	0.924271i	$0.624674\pi$
$678$		0			0
$679$	21.0940	+	29.0157i	0.809514	+	1.11352i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.4275	+	37.1136i	0.819902	+	1.42011i	0.905754	+	0.423804i	$0.139305\pi$
$683$	21.4275	+	37.1136i	0.819902	+	1.42011i	−0.0858521	+	0.996308i	$0.527361\pi$
$684$		0			0
$685$	−5.60932			−0.214321
$686$		0			0
$687$		0			0
$688$		0			0
$689$	24.4413	−	42.3336i	0.931141	−	1.61278i
$690$		0			0
$691$	7.38187	+	12.7858i	0.280820	+	0.486394i	0.971587	−	0.236683i	$-0.0760604\pi$
$691$	7.38187	+	12.7858i	0.280820	+	0.486394i	−0.690767	+	0.723077i	$0.742727\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.1806	+	21.0975i	0.462037	+	0.800272i
$696$		0			0
$697$	8.54211	−	14.7954i	0.323556	−	0.560415i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	19.8352			0.749167			0.374583	−	0.927193i	$-0.377786\pi$
$701$	19.8352			0.749167			0.374583	+	0.927193i	$0.377786\pi$
$702$		0			0
$703$	−0.0196683	−	0.0340664i	−0.000741802	−	0.00128484i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.4964	−	37.0806i	0.620413	−	1.39456i
$708$		0			0
$709$	−5.10292	−	8.83852i	−0.191644	−	0.331937i	0.754151	−	0.656701i	$-0.228049\pi$
$709$	−5.10292	−	8.83852i	−0.191644	−	0.331937i	−0.945795	+	0.324763i	$0.894715\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.82400	−	3.15926i	0.0683092	−	0.118315i
$714$		0			0
$715$	5.82919	+	10.0965i	0.217999	+	0.377586i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.2769	−	28.1924i	0.607025	−	1.05140i	−0.384703	−	0.923040i	$-0.625696\pi$
$719$	16.2769	−	28.1924i	0.607025	−	1.05140i	0.991728	−	0.128358i	$-0.0409706\pi$
$720$		0			0
$721$	5.33481	−	11.9915i	0.198679	−	0.446588i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−33.9774	+	58.8506i	−1.26189	+	2.18566i
$726$		0			0
$727$	−7.65095	+	13.2518i	−0.283758	+	0.491483i	−0.972307	−	0.233706i	$-0.924915\pi$
$727$	−7.65095	+	13.2518i	−0.283758	+	0.491483i	0.688549	+	0.725190i	$0.258248\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−31.1347			−1.15156
$732$		0			0
$733$	−8.69354			−0.321103			−0.160552	−	0.987027i	$-0.551327\pi$
$733$	−8.69354			−0.321103			−0.160552	+	0.987027i	$0.551327\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.60283	−	4.50823i	0.0958764	−	0.166063i
$738$		0			0
$739$	−6.61922	−	11.4648i	−0.243492	−	0.421740i	0.718215	−	0.695822i	$-0.244960\pi$
$739$	−6.61922	−	11.4648i	−0.243492	−	0.421740i	−0.961707	+	0.274081i	$0.911626\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.7693	+	18.6530i	0.395089	+	0.684314i	0.993112	−	0.117165i	$-0.0373805\pi$
$743$	10.7693	+	18.6530i	0.395089	+	0.684314i	−0.598024	+	0.801478i	$0.704047\pi$
$744$		0			0
$745$	65.3561			2.39446
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.6227	+	14.6119i	0.388143	+	0.533908i
$750$		0			0
$751$	39.6483			1.44679			0.723393	−	0.690437i	$-0.242582\pi$
$751$	39.6483			1.44679			0.723393	+	0.690437i	$0.242582\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.0468			−0.620395
$756$		0			0
$757$	13.0719			0.475108			0.237554	−	0.971374i	$-0.423654\pi$
$757$	13.0719			0.475108			0.237554	+	0.971374i	$0.423654\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.3429			0.664930			0.332465	−	0.943116i	$-0.392120\pi$
$761$	18.3429			0.664930			0.332465	+	0.943116i	$0.392120\pi$
$762$		0			0
$763$	−46.8452	+	4.93737i	−1.69591	+	0.178745i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−34.7763			−1.25570
$768$		0			0
$769$	7.46351	+	12.9272i	0.269141	+	0.466166i	0.968640	−	0.248467i	$-0.0799269\pi$
$769$	7.46351	+	12.9272i	0.269141	+	0.466166i	−0.699499	+	0.714633i	$0.746594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	14.7818	+	25.6029i	0.531666	+	0.920873i	0.999317	+	0.0369592i	$0.0117672\pi$
$773$	14.7818	+	25.6029i	0.531666	+	0.920873i	−0.467651	+	0.883913i	$0.654900\pi$
$774$		0			0
$775$	−13.4216	+	23.2469i	−0.482118	+	0.835054i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−29.6122			−1.06097
$780$		0			0
$781$	−0.686470			−0.0245638
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.27495	−	10.8685i	0.223962	−	0.387914i
$786$		0			0
$787$	4.66430	−	8.07880i	0.166264	−	0.287978i	−0.770839	−	0.637030i	$-0.780163\pi$
$787$	4.66430	−	8.07880i	0.166264	−	0.287978i	0.937104	+	0.349052i	$0.113496\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.4145	−	2.57323i	0.868080	−	0.0914935i
$792$		0			0
$793$	−5.09537	+	8.82545i	−0.180942	+	0.313401i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.9334	−	20.6692i	−0.422701	−	0.732140i	0.573502	−	0.819204i	$-0.305585\pi$
$797$	−11.9334	−	20.6692i	−0.422701	−	0.732140i	−0.996203	+	0.0870647i	$0.972251\pi$
$798$		0			0
$799$	25.9686	−	44.9790i	0.918705	−	1.59124i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.21784	+	5.57345i	0.113555	+	0.196683i
$804$		0			0
$805$	−4.57809	+	10.2906i	−0.161357	+	0.362696i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	17.9594	+	31.1066i	0.631418	+	1.09365i	0.987262	+	0.159103i	$0.0508602\pi$
$809$	17.9594	+	31.1066i	0.631418	+	1.09365i	−0.355844	+	0.934545i	$0.615806\pi$
$810$		0			0
$811$	−36.5589			−1.28376			−0.641879	−	0.766806i	$-0.721845\pi$
$811$	−36.5589			−1.28376			−0.641879	+	0.766806i	$0.721845\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−27.7608	+	48.0831i	−0.972418	+	1.68428i
$816$		0			0
$817$	26.9830	+	46.7359i	0.944015	+	1.63508i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.97582	−	15.5466i	−0.313258	−	0.542580i	0.665807	−	0.746124i	$-0.268087\pi$
$821$	−8.97582	−	15.5466i	−0.313258	−	0.542580i	−0.979066	+	0.203544i	$0.934754\pi$
$822$		0			0
$823$	−0.969357	+	1.67898i	−0.0337897	+	0.0585254i	−0.882426	−	0.470452i	$-0.844091\pi$
$823$	−0.969357	+	1.67898i	−0.0337897	+	0.0585254i	0.848636	+	0.528977i	$0.177424\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.4779			−1.19891			−0.599457	−	0.800407i	$-0.704617\pi$
$827$	−34.4779			−1.19891			−0.599457	+	0.800407i	$0.704617\pi$
$828$		0			0
$829$	15.6165	+	27.0487i	0.542385	+	0.939439i	0.998766	+	0.0496544i	$0.0158120\pi$
$829$	15.6165	+	27.0487i	0.542385	+	0.939439i	−0.456381	+	0.889784i	$0.650855\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.17929	−	28.3068i	0.318044	−	0.980774i
$834$		0			0
$835$	10.5078	+	18.2001i	0.363638	+	0.629839i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	28.2433	−	48.9187i	0.975065	−	1.68886i	0.295346	−	0.955390i	$-0.404565\pi$
$839$	28.2433	−	48.9187i	0.975065	−	1.68886i	0.679719	−	0.733472i	$-0.262102\pi$
$840$		0			0
$841$	−17.3124	−	29.9859i	−0.596978	−	1.03400i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	26.9077	−	46.6056i	0.925654	−	1.60328i
$846$		0			0
$847$	11.4384	−	25.7112i	0.393029	−	0.883448i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.00309038	+	0.00535270i	−0.000105937	+	0.000183488i
$852$		0			0
$853$	5.83541	−	10.1072i	0.199800	−	0.346065i	−0.748663	−	0.662951i	$-0.769304\pi$
$853$	5.83541	−	10.1072i	0.199800	−	0.346065i	0.948464	+	0.316886i	$0.102637\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.9633			0.408659			0.204329	−	0.978902i	$-0.434499\pi$
$857$	11.9633			0.408659			0.204329	+	0.978902i	$0.434499\pi$
$858$		0			0
$859$	−57.4008			−1.95849			−0.979244	−	0.202683i	$-0.935034\pi$
$859$	−57.4008			−1.95849			−0.979244	+	0.202683i	$0.935034\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.1871	+	43.6253i	−0.857379	+	1.48502i	0.0170411	+	0.999855i	$0.494575\pi$
$863$	−25.1871	+	43.6253i	−0.857379	+	1.48502i	−0.874420	+	0.485169i	$0.838758\pi$
$864$		0			0
$865$	3.48625	+	6.03836i	0.118536	+	0.205311i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.25017	+	2.16535i	0.0424090	+	0.0734546i
$870$		0			0
$871$	−45.3727			−1.53739
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.9163	−	31.2808i	0.470455	−	1.05749i
$876$		0			0
$877$	−8.45137			−0.285383			−0.142691	−	0.989767i	$-0.545576\pi$
$877$	−8.45137			−0.285383			−0.142691	+	0.989767i	$0.545576\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.99396			−0.134560			−0.0672800	−	0.997734i	$-0.521432\pi$
$881$	−3.99396			−0.134560			−0.0672800	+	0.997734i	$0.521432\pi$
$882$		0			0
$883$	−6.72637			−0.226360			−0.113180	−	0.993574i	$-0.536104\pi$
$883$	−6.72637			−0.226360			−0.113180	+	0.993574i	$0.536104\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−46.3449			−1.55611			−0.778055	−	0.628196i	$-0.783794\pi$
$887$	−46.3449			−1.55611			−0.778055	+	0.628196i	$0.783794\pi$
$888$		0			0
$889$	16.1250	−	36.2455i	0.540814	−	1.21564i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−90.0232			−3.01251
$894$		0			0
$895$	−26.8318	−	46.4741i	−0.896890	−	1.55346i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.5664	−	21.7656i	−0.419112	−	0.725924i
$900$		0			0
$901$	19.7647	−	34.2335i	0.658458	−	1.14048i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−29.0420			−0.965389
$906$		0			0
$907$	4.27244			0.141864			0.0709320	−	0.997481i	$-0.477403\pi$
$907$	4.27244			0.141864			0.0709320	+	0.997481i	$0.477403\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.26635	−	14.3177i	0.273876	−	0.474368i	−0.695975	−	0.718066i	$-0.745027\pi$
$911$	8.26635	−	14.3177i	0.273876	−	0.474368i	0.969851	+	0.243699i	$0.0783607\pi$
$912$		0			0
$913$	−3.76415	+	6.51969i	−0.124575	+	0.215770i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.5548	+	55.1941i	−0.810872	+	1.82267i
$918$		0			0
$919$	2.48862	−	4.31042i	0.0820921	−	0.142188i	−0.822056	−	0.569406i	$-0.807173\pi$
$919$	2.48862	−	4.31042i	0.0820921	−	0.142188i	0.904148	+	0.427219i	$0.140507\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.99165	+	5.18168i	0.0984713	+	0.170557i
$924$		0			0
$925$	0.0227401	−	0.0393870i	0.000747691	−	0.00129504i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.9815	−	31.1448i	−0.589952	−	1.02183i	−0.994238	−	0.107195i	$-0.965813\pi$
$929$	−17.9815	−	31.1448i	−0.589952	−	1.02183i	0.404286	−	0.914633i	$-0.367520\pi$
$930$		0			0
$931$	−50.4463	+	10.7533i	−1.65331	+	0.352425i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.71383	+	8.16459i	0.154159	+	0.267011i
$936$		0			0
$937$	−24.5419			−0.801748			−0.400874	−	0.916133i	$-0.631294\pi$
$937$	−24.5419			−0.801748			−0.400874	+	0.916133i	$0.631294\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.16454	+	5.48114i	−0.103161	+	0.178680i	−0.912985	−	0.407992i	$-0.866229\pi$
$941$	−3.16454	+	5.48114i	−0.103161	+	0.178680i	0.809824	+	0.586672i	$0.199562\pi$
$942$		0			0
$943$	2.32641	+	4.02947i	0.0757585	+	0.131218i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.6043	−	23.5633i	−0.442080	−	0.765706i	0.555763	−	0.831341i	$-0.312426\pi$
$947$	−13.6043	−	23.5633i	−0.442080	−	0.765706i	−0.997844	+	0.0656348i	$0.979093\pi$
$948$		0			0
$949$	28.0467	−	48.5784i	0.910436	−	1.57692i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−24.9963			−0.809711			−0.404855	−	0.914381i	$-0.632678\pi$
$953$	−24.9963			−0.809711			−0.404855	+	0.914381i	$0.632678\pi$
$954$		0			0
$955$	−15.5778	−	26.9815i	−0.504086	−	0.873102i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.64063	+	3.68780i	−0.0529787	+	0.119085i
$960$		0			0
$961$	10.5361	+	18.2490i	0.339874	+	0.588679i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.8065	+	22.1816i	−0.412257	+	0.714050i
$966$		0			0
$967$	6.11169	+	10.5858i	0.196539	+	0.340415i	0.947404	−	0.320041i	$-0.103697\pi$
$967$	6.11169	+	10.5858i	0.196539	+	0.340415i	−0.750865	+	0.660455i	$0.770363\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.137437	+	0.238048i	−0.00441057	+	0.00763933i	−0.868222	−	0.496175i	$-0.834737\pi$
$971$	−0.137437	+	0.238048i	−0.00441057	+	0.00763933i	0.863812	+	0.503815i	$0.168071\pi$
$972$		0			0
$973$	17.4330	−	1.83739i	0.558875	−	0.0589041i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.5084	+	26.8614i	−0.496159	+	0.859372i	−0.999990	−	0.00443011i	$-0.998590\pi$
$977$	−15.5084	+	26.8614i	−0.496159	+	0.859372i	0.503832	+	0.863802i	$0.331923\pi$
$978$		0			0
$979$	2.46965	−	4.27757i	0.0789305	−	0.136712i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	36.0139			1.14866			0.574332	−	0.818623i	$-0.305262\pi$
$983$	36.0139			1.14866			0.574332	+	0.818623i	$0.305262\pi$
$984$		0			0
$985$	−59.7019			−1.90226
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.23971	−	7.34340i	0.134815	−	0.233507i
$990$		0			0
$991$	−2.19313	−	3.79862i	−0.0696672	−	0.120667i	0.829088	−	0.559119i	$-0.188860\pi$
$991$	−2.19313	−	3.79862i	−0.0696672	−	0.120667i	−0.898755	+	0.438452i	$0.855527\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	27.0306	+	46.8184i	0.856928	+	1.48424i
$996$		0			0
$997$	−24.7764			−0.784676			−0.392338	−	0.919821i	$-0.628334\pi$
$997$	−24.7764			−0.784676			−0.392338	+	0.919821i	$0.628334\pi$
$998$		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.541.1		16
3.2	odd	2	inner	2268.2.l.n.541.8		16
7.4	even	3		2268.2.i.n.865.8		16
9.2	odd	6		2268.2.k.g.1297.1	✓	16
9.4	even	3		2268.2.i.n.2053.8		16
9.5	odd	6		2268.2.i.n.2053.1		16
9.7	even	3		2268.2.k.g.1297.8	yes	16
21.11	odd	6		2268.2.i.n.865.1		16
63.4	even	3	inner	2268.2.l.n.109.1		16
63.11	odd	6		2268.2.k.g.1621.1	yes	16
63.25	even	3		2268.2.k.g.1621.8	yes	16
63.32	odd	6	inner	2268.2.l.n.109.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.1		16	21.11	odd	6
2268.2.i.n.865.8		16	7.4	even	3
2268.2.i.n.2053.1		16	9.5	odd	6
2268.2.i.n.2053.8		16	9.4	even	3
2268.2.k.g.1297.1	✓	16	9.2	odd	6
2268.2.k.g.1297.8	yes	16	9.7	even	3
2268.2.k.g.1621.1	yes	16	63.11	odd	6
2268.2.k.g.1621.8	yes	16	63.25	even	3
2268.2.l.n.109.1		16	63.4	even	3	inner
2268.2.l.n.109.8		16	63.32	odd	6	inner
2268.2.l.n.541.1		16	1.1	even	1	trivial
2268.2.l.n.541.8		16	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-3.67687 q^{5} +(-1.07542 + 2.41733i) q^{7} +O(q^{10})\)	\(q-3.67687 q^{5} +(-1.07542 + 2.41733i) q^{7} -0.603143 q^{11} +(2.62851 + 4.55271i) q^{13} +(2.12557 + 3.68159i) q^{17} +(3.68426 - 6.38133i) q^{19} -1.15778 q^{23} +8.51937 q^{25} +(-3.98826 + 6.90786i) q^{29} +(-1.57542 + 2.72871i) q^{31} +(3.95419 - 8.88819i) q^{35} +(0.00266923 - 0.00462323i) q^{37} +(-2.00937 - 3.48033i) q^{41} +(-3.66193 + 6.34264i) q^{43} +(-6.10863 - 10.5805i) q^{47} +(-4.68693 - 5.19930i) q^{49} +(-4.64928 - 8.05279i) q^{53} +2.21768 q^{55} +(-3.30760 + 5.72894i) q^{59} +(0.969252 + 1.67879i) q^{61} +(-9.66468 - 16.7397i) q^{65} +(-4.31544 + 7.47456i) q^{67} +1.13815 q^{71} +(-5.33511 - 9.24068i) q^{73} +(0.648634 - 1.45799i) q^{77} +(-2.07275 - 3.59011i) q^{79} +(6.24088 - 10.8095i) q^{83} +(-7.81544 - 13.5367i) q^{85} +(-4.09464 + 7.09212i) q^{89} +(-13.8321 + 1.45787i) q^{91} +(-13.5466 + 23.4633i) q^{95} +(6.77935 - 11.7422i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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