LMFDB - Embedded newform 2268.2.l.n.109.7

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			109.7
Root			$-1.30887 - 2.01944i$ of defining polynomial
Character	$\chi$	$=$	2268.109
Dual form			2268.2.l.n.541.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30201 q^{5} +(-2.14324 + 1.55130i) q^{7} +O(q^{10})$	$q+2.30201 q^{5} +(-2.14324 + 1.55130i) q^{7} -4.46291 q^{11} +(1.42148 - 2.46208i) q^{13} +(0.115312 - 0.199726i) q^{17} +(-1.49360 - 2.58700i) q^{19} +0.800587 q^{23} +0.299269 q^{25} +(-3.82751 - 6.62944i) q^{29} +(-2.64324 - 4.57822i) q^{31} +(-4.93376 + 3.57112i) q^{35} +(-1.69333 - 2.93293i) q^{37} +(0.899697 - 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +(2.88818 - 5.00247i) q^{47} +(2.18693 - 6.64961i) q^{49} +(4.31905 - 7.48081i) q^{53} -10.2737 q^{55} +(-4.17793 - 7.23638i) q^{59} +(6.58675 - 11.4086i) q^{61} +(3.27227 - 5.66774i) q^{65} +(3.76545 + 6.52195i) q^{67} -8.59672 q^{71} +(-2.29287 + 3.97137i) q^{73} +(9.56507 - 6.92331i) q^{77} +(-4.83657 + 8.37718i) q^{79} +(-8.46521 - 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(-0.944450 - 1.63584i) q^{89} +(0.772852 + 7.48196i) q^{91} +(-3.43829 - 5.95530i) q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

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

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
$5$	2.30201			1.02949			0.514746	−	0.857343i	$-0.327886\pi$
$5$	2.30201			1.02949			0.514746	+	0.857343i	$0.327886\pi$
$6$		0			0
$7$	−2.14324	+	1.55130i	−0.810068	+	0.586337i
$7$	−2.14324	+	1.55130i	−0.810068	+	0.586337i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.46291			−1.34562			−0.672809	−	0.739816i	$-0.734912\pi$
$11$	−4.46291			−1.34562			−0.672809	+	0.739816i	$0.734912\pi$
$12$		0			0
$13$	1.42148	−	2.46208i	0.394248	−	0.682858i	−0.598757	−	0.800931i	$-0.704338\pi$
$13$	1.42148	−	2.46208i	0.394248	−	0.682858i	0.993005	+	0.118073i	$0.0376717\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.115312	−	0.199726i	0.0279673	−	0.0484408i	−0.851703	−	0.524025i	$-0.824430\pi$
$17$	0.115312	−	0.199726i	0.0279673	−	0.0484408i	0.879670	+	0.475584i	$0.157763\pi$
$18$		0			0
$19$	−1.49360	−	2.58700i	−0.342656	−	0.593498i	0.642269	−	0.766479i	$-0.277993\pi$
$19$	−1.49360	−	2.58700i	−0.342656	−	0.593498i	−0.984925	+	0.172982i	$0.944660\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.800587			0.166934			0.0834670	−	0.996511i	$-0.473401\pi$
$23$	0.800587			0.166934			0.0834670	+	0.996511i	$0.473401\pi$
$24$		0			0
$25$	0.299269			0.0598538
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.82751	−	6.62944i	−0.710750	−	1.23106i	−0.964576	−	0.263806i	$-0.915022\pi$
$29$	−3.82751	−	6.62944i	−0.710750	−	1.23106i	0.253825	−	0.967250i	$-0.418311\pi$
$30$		0			0
$31$	−2.64324	−	4.57822i	−0.474739	−	0.822273i	0.524842	−	0.851200i	$-0.324124\pi$
$31$	−2.64324	−	4.57822i	−0.474739	−	0.822273i	−0.999582	+	0.0289268i	$0.990791\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.93376	+	3.57112i	−0.833958	+	0.603629i
$36$		0			0
$37$	−1.69333	−	2.93293i	−0.278382	−	0.482171i	0.692601	−	0.721321i	$-0.256465\pi$
$37$	−1.69333	−	2.93293i	−0.278382	−	0.482171i	−0.970983	+	0.239150i	$0.923131\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.899697	−	1.55832i	0.140509	−	0.243369i	−0.787179	−	0.616724i	$-0.788459\pi$
$41$	0.899697	−	1.55832i	0.140509	−	0.243369i	0.927688	+	0.373355i	$0.121793\pi$
$42$		0			0
$43$	4.85860	+	8.41533i	0.740929	+	1.28333i	0.952073	+	0.305871i	$0.0989478\pi$
$43$	4.85860	+	8.41533i	0.740929	+	1.28333i	−0.211144	+	0.977455i	$0.567719\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.88818	−	5.00247i	0.421284	−	0.729686i	−0.574781	−	0.818307i	$-0.694913\pi$
$47$	2.88818	−	5.00247i	0.421284	−	0.729686i	0.996065	+	0.0886214i	$0.0282461\pi$
$48$		0			0
$49$	2.18693	−	6.64961i	0.312419	−	0.949944i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.31905	−	7.48081i	0.593267	−	1.02757i	−0.400522	−	0.916287i	$-0.631171\pi$
$53$	4.31905	−	7.48081i	0.593267	−	1.02757i	0.993789	−	0.111281i	$-0.0354954\pi$
$54$		0			0
$55$	−10.2737			−1.38530
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.17793	−	7.23638i	−0.543920	−	0.942097i	−0.998674	−	0.0514798i	$-0.983606\pi$
$59$	−4.17793	−	7.23638i	−0.543920	−	0.942097i	0.454754	−	0.890617i	$-0.349727\pi$
$60$		0			0
$61$	6.58675	−	11.4086i	0.843347	−	1.46072i	−0.0437026	−	0.999045i	$-0.513915\pi$
$61$	6.58675	−	11.4086i	0.843347	−	1.46072i	0.887049	−	0.461675i	$-0.152751\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.27227	−	5.66774i	0.405875	−	0.702997i
$66$		0			0
$67$	3.76545	+	6.52195i	0.460023	+	0.796783i	0.998962	−	0.0455620i	$-0.0145078\pi$
$67$	3.76545	+	6.52195i	0.460023	+	0.796783i	−0.538939	+	0.842345i	$0.681175\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.59672			−1.02024			−0.510122	−	0.860102i	$-0.670400\pi$
$71$	−8.59672			−1.02024			−0.510122	+	0.860102i	$0.670400\pi$
$72$		0			0
$73$	−2.29287	+	3.97137i	−0.268360	+	0.464814i	−0.968439	−	0.249252i	$-0.919815\pi$
$73$	−2.29287	+	3.97137i	−0.268360	+	0.464814i	0.700078	+	0.714066i	$0.253148\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.56507	−	6.92331i	1.09004	−	0.788985i
$78$		0			0
$79$	−4.83657	+	8.37718i	−0.544156	+	0.942506i	0.454503	+	0.890745i	$0.349817\pi$
$79$	−4.83657	+	8.37718i	−0.544156	+	0.942506i	−0.998659	+	0.0517612i	$0.983517\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.46521	−	14.6622i	−0.929177	−	1.60938i	−0.784701	−	0.619874i	$-0.787184\pi$
$83$	−8.46521	−	14.6622i	−0.929177	−	1.60938i	−0.144476	−	0.989508i	$-0.546150\pi$
$84$		0			0
$85$	0.265450	−	0.459773i	0.0287921	−	0.0498694i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.944450	−	1.63584i	−0.100111	−	0.173398i	0.811619	−	0.584187i	$-0.198587\pi$
$89$	−0.944450	−	1.63584i	−0.100111	−	0.173398i	−0.911730	+	0.410789i	$0.865253\pi$
$90$		0			0
$91$	0.772852	+	7.48196i	0.0810169	+	0.784323i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.43829	−	5.95530i	−0.352762	−	0.611001i
$96$		0			0
$97$	7.70796	+	13.3506i	0.782624	+	1.35555i	0.930408	+	0.366525i	$0.119453\pi$
$97$	7.70796	+	13.3506i	0.782624	+	1.35555i	−0.147784	+	0.989020i	$0.547214\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.81488			0.280091			0.140045	−	0.990145i	$-0.455275\pi$
$101$	2.81488			0.280091			0.140045	+	0.990145i	$0.455275\pi$
$102$		0			0
$103$	5.11664			0.504158			0.252079	−	0.967707i	$-0.418886\pi$
$103$	5.11664			0.504158			0.252079	+	0.967707i	$0.418886\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.29487	+	2.24278i	0.125180	+	0.216818i	0.921803	−	0.387658i	$-0.126716\pi$
$107$	1.29487	+	2.24278i	0.125180	+	0.216818i	−0.796623	+	0.604476i	$0.793383\pi$
$108$		0			0
$109$	−8.76728	+	15.1854i	−0.839753	+	1.45450i	0.0503474	+	0.998732i	$0.483967\pi$
$109$	−8.76728	+	15.1854i	−0.839753	+	1.45450i	−0.890101	+	0.455764i	$0.849366\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.21711	−	14.2325i	0.773001	−	1.33888i	−0.162910	−	0.986641i	$-0.552088\pi$
$113$	8.21711	−	14.2325i	0.773001	−	1.33888i	0.935911	−	0.352236i	$-0.114579\pi$
$114$		0			0
$115$	1.84296			0.171857
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.0626945	+	0.606945i	0.00574720	+	0.0556385i
$120$		0			0
$121$	8.91756			0.810687
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.8211			−0.967873
$126$		0			0
$127$	8.13145			0.721549			0.360775	−	0.932653i	$-0.382512\pi$
$127$	8.13145			0.721549			0.360775	+	0.932653i	$0.382512\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	12.5118			1.09316			0.546582	−	0.837406i	$-0.315929\pi$
$131$	12.5118			1.09316			0.546582	+	0.837406i	$0.315929\pi$
$132$		0			0
$133$	7.21435	+	3.22752i	0.625564	+	0.279861i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.1934			−1.38349			−0.691746	−	0.722141i	$-0.743158\pi$
$137$	−16.1934			−1.38349			−0.691746	+	0.722141i	$0.743158\pi$
$138$		0			0
$139$	3.07212	−	5.32107i	0.260574	−	0.451327i	−0.705821	−	0.708391i	$-0.749422\pi$
$139$	3.07212	−	5.32107i	0.260574	−	0.451327i	0.966395	+	0.257063i	$0.0827549\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.34394	+	10.9880i	−0.530507	+	0.918866i
$144$		0			0
$145$	−8.81098	−	15.2611i	−0.731712	−	1.26736i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.71855			−0.632328			−0.316164	−	0.948705i	$-0.602395\pi$
$149$	−7.71855			−0.632328			−0.316164	+	0.948705i	$0.602395\pi$
$150$		0			0
$151$	−14.9176			−1.21397			−0.606987	−	0.794712i	$-0.707622\pi$
$151$	−14.9176			−1.21397			−0.606987	+	0.794712i	$0.707622\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.08477	−	10.5391i	−0.488740	−	0.846523i
$156$		0			0
$157$	0.128610	+	0.222759i	0.0102642	+	0.0177781i	0.871112	−	0.491085i	$-0.163399\pi$
$157$	0.128610	+	0.222759i	0.0102642	+	0.0177781i	−0.860848	+	0.508863i	$0.830066\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.71585	+	1.24195i	−0.135228	+	0.0978795i
$162$		0			0
$163$	−6.28748	−	10.8902i	−0.492473	−	0.852989i	0.507489	−	0.861658i	$-0.330574\pi$
$163$	−6.28748	−	10.8902i	−0.492473	−	0.852989i	−0.999962	+	0.00866931i	$0.997240\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.8470	+	18.7875i	−0.839363	+	1.45382i	0.0510657	+	0.998695i	$0.483738\pi$
$167$	−10.8470	+	18.7875i	−0.839363	+	1.45382i	−0.890428	+	0.455123i	$0.849595\pi$
$168$		0			0
$169$	2.45878	+	4.25873i	0.189137	+	0.327595i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.88024	−	11.9169i	0.523095	−	0.906026i	−0.476544	−	0.879151i	$-0.658111\pi$
$173$	6.88024	−	11.9169i	0.523095	−	0.906026i	0.999639	−	0.0268759i	$-0.00855590\pi$
$174$		0			0
$175$	−0.641405	+	0.464256i	−0.0484856	+	0.0350945i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.448262	−	0.776412i	0.0335046	−	0.0580317i	−0.848787	−	0.528735i	$-0.822666\pi$
$179$	0.448262	−	0.776412i	0.0335046	−	0.0580317i	0.882292	+	0.470703i	$0.156000\pi$
$180$		0			0
$181$	−17.4613			−1.29788			−0.648942	−	0.760838i	$-0.724788\pi$
$181$	−17.4613			−1.29788			−0.648942	+	0.760838i	$0.724788\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.89807	−	6.75165i	−0.286592	−	0.496391i
$186$		0			0
$187$	−0.514627	+	0.891361i	−0.0376333	+	0.0651827i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.734511	+	1.27221i	−0.0531474	+	0.0920540i	−0.891375	−	0.453266i	$-0.850259\pi$
$191$	−0.734511	+	1.27221i	−0.0531474	+	0.0920540i	0.838228	+	0.545320i	$0.183592\pi$
$192$		0			0
$193$	−3.25165	−	5.63202i	−0.234059	−	0.405402i	0.724940	−	0.688812i	$-0.241868\pi$
$193$	−3.25165	−	5.63202i	−0.234059	−	0.405402i	−0.958999	+	0.283410i	$0.908534\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.9521			0.851552			0.425776	−	0.904828i	$-0.360001\pi$
$197$	11.9521			0.851552			0.425776	+	0.904828i	$0.360001\pi$
$198$		0			0
$199$	9.73886	−	16.8682i	0.690369	−	1.19575i	−0.281348	−	0.959606i	$-0.590781\pi$
$199$	9.73886	−	16.8682i	0.690369	−	1.19575i	0.971717	−	0.236149i	$-0.0758852\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	18.4875	+	8.27084i	1.29757	+	0.580499i
$204$		0			0
$205$	2.07112	−	3.58728i	0.144653	−	0.250546i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.66581	+	11.5455i	0.461084	+	0.798621i
$210$		0			0
$211$	6.43611	−	11.1477i	0.443080	−	0.767437i	−0.554836	−	0.831960i	$-0.687219\pi$
$211$	6.43611	−	11.1477i	0.443080	−	0.767437i	0.997916	+	0.0645225i	$0.0205524\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.1846	+	19.3722i	0.762780	+	1.32117i
$216$		0			0
$217$	12.7673	+	5.71176i	0.866700	+	0.387739i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.327828	−	0.567815i	−0.0220521	−	0.0381954i
$222$		0			0
$223$	−4.92331	−	8.52743i	−0.329690	−	0.571039i	0.652761	−	0.757564i	$-0.273611\pi$
$223$	−4.92331	−	8.52743i	−0.329690	−	0.571039i	−0.982450	+	0.186525i	$0.940277\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−24.4507			−1.62285			−0.811426	−	0.584455i	$-0.801309\pi$
$227$	−24.4507			−1.62285			−0.811426	+	0.584455i	$0.801309\pi$
$228$		0			0
$229$	−22.0037			−1.45404			−0.727022	−	0.686615i	$-0.759096\pi$
$229$	−22.0037			−1.45404			−0.727022	+	0.686615i	$0.759096\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.8179	−	18.7372i	−0.708706	−	1.22752i	−0.965337	−	0.261006i	$-0.915946\pi$
$233$	−10.8179	−	18.7372i	−0.708706	−	1.22752i	0.256631	−	0.966510i	$-0.417388\pi$
$234$		0			0
$235$	6.64863	−	11.5158i	0.433709	−	0.751206i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.86360	−	15.3522i	0.573338	−	0.993051i	−0.422882	−	0.906185i	$-0.638981\pi$
$239$	8.86360	−	15.3522i	0.573338	−	0.993051i	0.996220	−	0.0868662i	$-0.0276853\pi$
$240$		0			0
$241$	4.31774			0.278130			0.139065	−	0.990283i	$-0.455590\pi$
$241$	4.31774			0.278130			0.139065	+	0.990283i	$0.455590\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.03435	−	15.3075i	0.321633	−	0.977960i
$246$		0			0
$247$	−8.49252			−0.540366
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.2938			−0.649741			−0.324870	−	0.945759i	$-0.605321\pi$
$251$	−10.2938			−0.649741			−0.324870	+	0.945759i	$0.605321\pi$
$252$		0			0
$253$	−3.57295			−0.224629
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.7914			−0.735525			−0.367763	−	0.929920i	$-0.619876\pi$
$257$	−11.7914			−0.735525			−0.367763	+	0.929920i	$0.619876\pi$
$258$		0			0
$259$	8.17907	+	3.65911i	0.508222	+	0.227366i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.18719			−0.319856			−0.159928	−	0.987129i	$-0.551126\pi$
$263$	−5.18719			−0.319856			−0.159928	+	0.987129i	$0.551126\pi$
$264$		0			0
$265$	9.94251	−	17.2209i	0.610763	−	1.05787i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.6103	−	25.3058i	0.890805	−	1.54292i	0.0518936	−	0.998653i	$-0.483474\pi$
$269$	14.6103	−	25.3058i	0.890805	−	1.54292i	0.838912	−	0.544268i	$-0.183192\pi$
$270$		0			0
$271$	10.2801	+	17.8056i	0.624470	+	1.08161i	0.988643	+	0.150283i	$0.0480184\pi$
$271$	10.2801	+	17.8056i	0.624470	+	1.08161i	−0.364173	+	0.931331i	$0.618648\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.33561			−0.0805403
$276$		0			0
$277$	−11.9567			−0.718407			−0.359203	−	0.933259i	$-0.616952\pi$
$277$	−11.9567			−0.718407			−0.359203	+	0.933259i	$0.616952\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.9166	+	25.8363i	0.889850	+	1.54126i	0.840052	+	0.542506i	$0.182524\pi$
$281$	14.9166	+	25.8363i	0.889850	+	1.54126i	0.0497975	+	0.998759i	$0.484142\pi$
$282$		0			0
$283$	4.78547	+	8.28868i	0.284467	+	0.492711i	0.972480	−	0.232988i	$-0.0748502\pi$
$283$	4.78547	+	8.28868i	0.284467	+	0.492711i	−0.688013	+	0.725698i	$0.741517\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.489161	+	4.73555i	0.0288742	+	0.279531i
$288$		0			0
$289$	8.47341	+	14.6764i	0.498436	+	0.863316i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.41014	+	12.8347i	−0.432905	+	0.749813i	−0.997122	−	0.0758132i	$-0.975845\pi$
$293$	−7.41014	+	12.8347i	−0.432905	+	0.749813i	0.564217	+	0.825626i	$0.309178\pi$
$294$		0			0
$295$	−9.61765	−	16.6583i	−0.559961	−	0.969881i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.13802	−	1.97111i	0.0658134	−	0.113992i
$300$		0			0
$301$	−23.4678	−	10.4989i	−1.35266	−	0.605147i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.1628	−	26.2627i	0.868219	−	1.50380i
$306$		0			0
$307$	−5.88207			−0.335708			−0.167854	−	0.985812i	$-0.553684\pi$
$307$	−5.88207			−0.335708			−0.167854	+	0.985812i	$0.553684\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.11753	+	14.0600i	0.460303	+	0.797268i	0.998976	−	0.0452468i	$-0.0144074\pi$
$311$	8.11753	+	14.0600i	0.460303	+	0.797268i	−0.538673	+	0.842515i	$0.681074\pi$
$312$		0			0
$313$	−8.84480	+	15.3196i	−0.499937	+	0.865917i	−1.00000		7.22344e-5i	$-0.999977\pi$
$313$	−8.84480	+	15.3196i	−0.499937	+	0.865917i	0.500063	+	0.865989i	$0.333310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.64009	+	4.57276i	−0.148282	+	0.256832i	−0.930593	−	0.366057i	$-0.880708\pi$
$317$	−2.64009	+	4.57276i	−0.148282	+	0.256832i	0.782311	+	0.622889i	$0.214041\pi$
$318$		0			0
$319$	17.0818	+	29.5866i	0.956398	+	1.65653i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.688922			−0.0383326
$324$		0			0
$325$	0.425406	−	0.736824i	0.0235973	−	0.0408716i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.57029	+	15.2019i	0.0865727	+	0.838109i
$330$		0			0
$331$	7.80358	−	13.5162i	0.428923	−	0.742917i	−0.567855	−	0.823129i	$-0.692226\pi$
$331$	7.80358	−	13.5162i	0.428923	−	0.742917i	0.996778	+	0.0802120i	$0.0255597\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.66812	+	15.0136i	0.473590	+	0.820282i
$336$		0			0
$337$	−3.77185	+	6.53303i	−0.205466	+	0.355877i	−0.950281	−	0.311394i	$-0.899204\pi$
$337$	−3.77185	+	6.53303i	−0.205466	+	0.355877i	0.744815	+	0.667271i	$0.232538\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.7965	+	20.4322i	0.638818	+	1.10646i
$342$		0			0
$343$	5.62843	+	17.6443i	0.303907	+	0.952702i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.4502	−	23.2963i	−0.722042	−	1.25061i	−0.960180	−	0.279382i	$-0.909870\pi$
$347$	−13.4502	−	23.2963i	−0.722042	−	1.25061i	0.238138	−	0.971231i	$-0.423463\pi$
$348$		0			0
$349$	7.00100	+	12.1261i	0.374755	+	0.649095i	0.990290	−	0.139014i	$-0.0443934\pi$
$349$	7.00100	+	12.1261i	0.374755	+	0.649095i	−0.615535	+	0.788109i	$0.711060\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	30.3311			1.61436			0.807180	−	0.590306i	$-0.200993\pi$
$353$	30.3311			1.61436			0.807180	+	0.590306i	$0.200993\pi$
$354$		0			0
$355$	−19.7898			−1.05033
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.99876	−	12.1222i	−0.369381	−	0.639786i	0.620088	−	0.784532i	$-0.287097\pi$
$359$	−6.99876	−	12.1222i	−0.369381	−	0.639786i	−0.989469	+	0.144746i	$0.953763\pi$
$360$		0			0
$361$	5.03830	−	8.72659i	0.265174	−	0.459294i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.27822	+	9.14215i	−0.276275	+	0.478522i
$366$		0			0
$367$	−2.50330			−0.130671			−0.0653356	−	0.997863i	$-0.520812\pi$
$367$	−2.50330			−0.130671			−0.0653356	+	0.997863i	$0.520812\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.34824	+	22.7333i	0.121915	+	1.18025i
$372$		0			0
$373$	17.6062			0.911616			0.455808	−	0.890078i	$-0.349350\pi$
$373$	17.6062			0.911616			0.455808	+	0.890078i	$0.349350\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.7629			−1.12085
$378$		0			0
$379$	10.5474			0.541781			0.270891	−	0.962610i	$-0.412682\pi$
$379$	10.5474			0.541781			0.270891	+	0.962610i	$0.412682\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	21.6837			1.10798			0.553992	−	0.832522i	$-0.313104\pi$
$383$	21.6837			1.10798			0.553992	+	0.832522i	$0.313104\pi$
$384$		0			0
$385$	22.0189	−	15.9376i	1.12219	−	0.812254i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.9330			0.706434			0.353217	−	0.935541i	$-0.385088\pi$
$389$	13.9330			0.706434			0.353217	+	0.935541i	$0.385088\pi$
$390$		0			0
$391$	0.0923174	−	0.159898i	0.00466869	−	0.00808641i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.1338	+	19.2844i	−0.560204	+	0.970303i
$396$		0			0
$397$	13.9542	+	24.1694i	0.700342	+	1.21303i	0.968346	+	0.249610i	$0.0803025\pi$
$397$	13.9542	+	24.1694i	0.700342	+	1.21303i	−0.268004	+	0.963418i	$0.586364\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−34.9049			−1.74307			−0.871534	−	0.490335i	$-0.836874\pi$
$401$	−34.9049			−1.74307			−0.871534	+	0.490335i	$0.836874\pi$
$402$		0			0
$403$	−15.0293			−0.748660
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.55717	+	13.0894i	0.374595	+	0.648818i
$408$		0			0
$409$	10.3369	+	17.9041i	0.511128	+	0.885300i	0.999917	+	0.0128979i	$0.00410563\pi$
$409$	10.3369	+	17.9041i	0.511128	+	0.885300i	−0.488789	+	0.872402i	$0.662561\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	20.1801	+	9.02806i	0.992998	+	0.444242i
$414$		0			0
$415$	−19.4870	−	33.7525i	−0.956581	−	1.65685i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.9859	+	34.6166i	−0.976376	+	1.69113i	−0.301061	+	0.953605i	$0.597341\pi$
$419$	−19.9859	+	34.6166i	−0.976376	+	1.69113i	−0.675316	+	0.737529i	$0.735993\pi$
$420$		0			0
$421$	−12.5082	−	21.6649i	−0.609614	−	1.05588i	−0.991304	−	0.131592i	$-0.957991\pi$
$421$	−12.5082	−	21.6649i	−0.609614	−	1.05588i	0.381690	−	0.924290i	$-0.375342\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.0345093	−	0.0597719i	0.00167395	−	0.00289936i
$426$		0			0
$427$	3.58118	+	34.6693i	0.173305	+	1.67777i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.05181	+	12.2141i	−0.339674	+	0.588332i	−0.984371	−	0.176106i	$-0.943650\pi$
$431$	−7.05181	+	12.2141i	−0.339674	+	0.588332i	0.644698	+	0.764438i	$0.276983\pi$
$432$		0			0
$433$	1.58941			0.0763821			0.0381911	−	0.999270i	$-0.487840\pi$
$433$	1.58941			0.0763821			0.0381911	+	0.999270i	$0.487840\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.19576	−	2.07112i	−0.0572009	−	0.0990749i
$438$		0			0
$439$	12.1884	−	21.1109i	0.581721	−	1.00757i	−0.413555	−	0.910479i	$-0.635713\pi$
$439$	12.1884	−	21.1109i	0.581721	−	1.00757i	0.995276	−	0.0970905i	$-0.0309536\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.28200	+	16.0769i	−0.441001	+	0.763836i	−0.997764	−	0.0668352i	$-0.978710\pi$
$443$	−9.28200	+	16.0769i	−0.441001	+	0.763836i	0.556763	+	0.830671i	$0.312043\pi$
$444$		0			0
$445$	−2.17414	−	3.76572i	−0.103064	−	0.178512i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.4616			1.01284			0.506418	−	0.862288i	$-0.330969\pi$
$449$	21.4616			1.01284			0.506418	+	0.862288i	$0.330969\pi$
$450$		0			0
$451$	−4.01527	+	6.95465i	−0.189072	+	0.327482i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.77912	+	17.2236i	0.0834062	+	0.807454i
$456$		0			0
$457$	−7.56371	+	13.1007i	−0.353816	+	0.612827i	−0.986915	−	0.161244i	$-0.948449\pi$
$457$	−7.56371	+	13.1007i	−0.353816	+	0.612827i	0.633099	+	0.774071i	$0.281783\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.5385	+	28.6455i	0.770273	+	1.33415i	0.937413	+	0.348219i	$0.113213\pi$
$461$	16.5385	+	28.6455i	0.770273	+	1.33415i	−0.167140	+	0.985933i	$0.553453\pi$
$462$		0			0
$463$	−13.4223	+	23.2481i	−0.623788	+	1.08043i	0.364986	+	0.931013i	$0.381074\pi$
$463$	−13.4223	+	23.2481i	−0.623788	+	1.08043i	−0.988774	+	0.149419i	$0.952260\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.93579	+	10.2811i	0.274675	+	0.475752i	0.970053	−	0.242893i	$-0.0780963\pi$
$467$	5.93579	+	10.2811i	0.274675	+	0.475752i	−0.695378	+	0.718644i	$0.744763\pi$
$468$		0			0
$469$	−18.1878	−	8.13674i	−0.839833	−	0.375720i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−21.6835	−	37.5569i	−0.997007	−	1.72687i
$474$		0			0
$475$	−0.446989	−	0.774208i	−0.0205093	−	0.0355231i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.4395			−0.796830			−0.398415	−	0.917205i	$-0.630440\pi$
$479$	−17.4395			−0.796830			−0.398415	+	0.917205i	$0.630440\pi$
$480$		0			0
$481$	−9.62815			−0.439006
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.7438	+	30.7332i	0.805706	+	1.39552i
$486$		0			0
$487$	18.3889	−	31.8504i	0.833279	−	1.44328i	−0.0621458	−	0.998067i	$-0.519794\pi$
$487$	18.3889	−	31.8504i	0.833279	−	1.44328i	0.895424	−	0.445214i	$-0.146872\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.54050	+	7.86437i	−0.204910	+	0.354914i	−0.950104	−	0.311933i	$-0.899023\pi$
$491$	−4.54050	+	7.86437i	−0.204910	+	0.354914i	0.745194	+	0.666847i	$0.232357\pi$
$492$		0			0
$493$	−1.76543			−0.0795110
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.4248	−	13.3361i	0.826466	−	0.598206i
$498$		0			0
$499$	6.82522			0.305539			0.152769	−	0.988262i	$-0.451181\pi$
$499$	6.82522			0.305539			0.152769	+	0.988262i	$0.451181\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.09211			−0.182458			−0.0912291	−	0.995830i	$-0.529080\pi$
$503$	−4.09211			−0.182458			−0.0912291	+	0.995830i	$0.529080\pi$
$504$		0			0
$505$	6.47989			0.288351
$506$		0			0
$507$		0			0
$508$		0			0
$509$	28.7982			1.27646			0.638228	−	0.769847i	$-0.279668\pi$
$509$	28.7982			1.27646			0.638228	+	0.769847i	$0.279668\pi$
$510$		0			0
$511$	−1.24662	−	12.0685i	−0.0551473	−	0.533880i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.7786			0.519026
$516$		0			0
$517$	−12.8897	+	22.3256i	−0.566888	+	0.981878i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.92170	−	10.2567i	0.259434	−	0.449353i	−0.706656	−	0.707557i	$-0.749797\pi$
$521$	5.92170	−	10.2567i	0.259434	−	0.449353i	0.966090	+	0.258204i	$0.0831306\pi$
$522$		0			0
$523$	6.86664	+	11.8934i	0.300257	+	0.520061i	0.976194	−	0.216899i	$-0.0695942\pi$
$523$	6.86664	+	11.8934i	0.300257	+	0.520061i	−0.675937	+	0.736959i	$0.736261\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.21919			−0.0531087
$528$		0			0
$529$	−22.3591			−0.972133
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.55781	−	4.43025i	−0.110791	−	0.191896i
$534$		0			0
$535$	2.98081	+	5.16291i	0.128872	+	0.223212i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.76008	+	29.6766i	−0.420396	+	1.27826i
$540$		0			0
$541$	21.7425	+	37.6592i	0.934784	+	1.61909i	0.775019	+	0.631938i	$0.217740\pi$
$541$	21.7425	+	37.6592i	0.934784	+	1.61909i	0.159765	+	0.987155i	$0.448926\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−20.1824	+	34.9570i	−0.864519	+	1.49739i
$546$		0			0
$547$	−11.0307	−	19.1058i	−0.471640	−	0.816904i	0.527834	−	0.849348i	$-0.323004\pi$
$547$	−11.0307	−	19.1058i	−0.471640	−	0.816904i	−0.999474	+	0.0324437i	$0.989671\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−11.4336	+	19.8035i	−0.487086	+	0.843657i
$552$		0			0
$553$	−2.62961	−	25.4573i	−0.111823	−	1.08255i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.0925	−	27.8730i	0.681862	−	1.18102i	−0.292551	−	0.956250i	$-0.594504\pi$
$557$	16.0925	−	27.8730i	0.681862	−	1.18102i	0.974412	−	0.224769i	$-0.0721627\pi$
$558$		0			0
$559$	27.6256			1.16844
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.69369	+	2.93355i	0.0713804	+	0.123635i	0.899507	−	0.436907i	$-0.143926\pi$
$563$	1.69369	+	2.93355i	0.0713804	+	0.123635i	−0.828126	+	0.560542i	$0.810593\pi$
$564$		0			0
$565$	18.9159	−	32.7633i	0.795798	−	1.37836i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.1737	+	34.9419i	−0.845726	+	1.46484i	0.0392637	+	0.999229i	$0.487499\pi$
$569$	−20.1737	+	34.9419i	−0.845726	+	1.46484i	−0.884989	+	0.465611i	$0.845835\pi$
$570$		0			0
$571$	5.21928	+	9.04006i	0.218420	+	0.378315i	0.954325	−	0.298770i	$-0.0965763\pi$
$571$	5.21928	+	9.04006i	0.218420	+	0.378315i	−0.735905	+	0.677085i	$0.763243\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.239591			0.00999164
$576$		0			0
$577$	5.55156	−	9.61559i	0.231114	−	0.400302i	−0.727022	−	0.686614i	$-0.759096\pi$
$577$	5.55156	−	9.61559i	0.231114	−	0.400302i	0.958136	+	0.286312i	$0.0924295\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	40.8884	+	18.2924i	1.69634	+	0.758898i
$582$		0			0
$583$	−19.2755	+	33.3862i	−0.798310	+	1.38271i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.3875	+	35.3122i	0.841482	+	1.45749i	0.888642	+	0.458602i	$0.151650\pi$
$587$	20.3875	+	35.3122i	0.841482	+	1.45749i	−0.0471601	+	0.998887i	$0.515017\pi$
$588$		0			0
$589$	−7.89589	+	13.6761i	−0.325345	+	0.563513i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.7930	−	25.6221i	−0.607474	−	1.05218i	−0.991655	−	0.128918i	$-0.958850\pi$
$593$	−14.7930	−	25.6221i	−0.607474	−	1.05218i	0.384182	−	0.923258i	$-0.374484\pi$
$594$		0			0
$595$	0.144324	+	1.39720i	0.00591669	+	0.0572794i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.17760	−	15.8961i	−0.374987	−	0.649496i	0.615338	−	0.788263i	$-0.289019\pi$
$599$	−9.17760	−	15.8961i	−0.374987	−	0.649496i	−0.990325	+	0.138767i	$0.955686\pi$
$600$		0			0
$601$	15.9250	+	27.5828i	0.649593	+	1.12513i	0.983220	+	0.182423i	$0.0583939\pi$
$601$	15.9250	+	27.5828i	0.649593	+	1.12513i	−0.333628	+	0.942705i	$0.608273\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	20.5283			0.834596
$606$		0			0
$607$	23.6903			0.961560			0.480780	−	0.876841i	$-0.340353\pi$
$607$	23.6903			0.961560			0.480780	+	0.876841i	$0.340353\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.21099	−	14.2219i	−0.332181	−	0.575354i
$612$		0			0
$613$	13.3159	−	23.0638i	0.537824	−	0.931539i	−0.461197	−	0.887298i	$-0.652580\pi$
$613$	13.3159	−	23.0638i	0.537824	−	0.931539i	0.999021	−	0.0442411i	$-0.0140870\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.72483	+	8.18364i	−0.190214	+	0.329461i	−0.945321	−	0.326141i	$-0.894252\pi$
$617$	−4.72483	+	8.18364i	−0.190214	+	0.329461i	0.755107	+	0.655602i	$0.227585\pi$
$618$		0			0
$619$	−36.0947			−1.45077			−0.725385	−	0.688344i	$-0.758338\pi$
$619$	−36.0947			−1.45077			−0.725385	+	0.688344i	$0.758338\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.56185	+	2.04086i	0.182767	+	0.0817652i
$624$		0			0
$625$	−26.4068			−1.05627
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.781045			−0.0311423
$630$		0			0
$631$	0.0100579			0.000400401			0.000200200	−	1.00000i	$-0.499936\pi$
$631$	0.0100579			0.000400401			0.000200200		1.00000i	$0.499936\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	18.7187			0.742829
$636$		0			0
$637$	−13.2632	−	14.8367i	−0.525506	−	0.587851i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.90453			0.193717			0.0968587	−	0.995298i	$-0.469121\pi$
$641$	4.90453			0.193717			0.0968587	+	0.995298i	$0.469121\pi$
$642$		0			0
$643$	22.0655	−	38.2186i	0.870180	−	1.50720i	0.00837033	−	0.999965i	$-0.497336\pi$
$643$	22.0655	−	38.2186i	0.870180	−	1.50720i	0.861810	−	0.507231i	$-0.169331\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.8813	−	43.0957i	0.978186	−	1.69427i	0.309192	−	0.950999i	$-0.399941\pi$
$647$	24.8813	−	43.0957i	0.978186	−	1.69427i	0.668993	−	0.743268i	$-0.266725\pi$
$648$		0			0
$649$	18.6457	+	32.2953i	0.731908	+	1.26770i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.9716			−0.546749			−0.273375	−	0.961908i	$-0.588140\pi$
$653$	−13.9716			−0.546749			−0.273375	+	0.961908i	$0.588140\pi$
$654$		0			0
$655$	28.8024			1.12540
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.9827	−	22.4867i	−0.505733	−	0.875956i	−0.999978	−	0.00663317i	$-0.997889\pi$
$659$	−12.9827	−	22.4867i	−0.505733	−	0.875956i	0.494245	−	0.869323i	$-0.335445\pi$
$660$		0			0
$661$	−12.7681	−	22.1150i	−0.496622	−	0.860174i	0.503370	−	0.864071i	$-0.332093\pi$
$661$	−12.7681	−	22.1150i	−0.496622	−	0.860174i	−0.999992	+	0.00389626i	$0.998760\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	16.6075	+	7.42979i	0.644013	+	0.288115i
$666$		0			0
$667$	−3.06425	−	5.30744i	−0.118648	−	0.205505i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−29.3961	+	50.9155i	−1.13482	+	1.96557i
$672$		0			0
$673$	2.71472	+	4.70203i	0.104645	+	0.181250i	0.913593	−	0.406630i	$-0.133296\pi$
$673$	2.71472	+	4.70203i	0.104645	+	0.181250i	−0.808948	+	0.587880i	$0.799963\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.07571	+	12.2555i	−0.271942	+	0.471017i	−0.969359	−	0.245648i	$-0.920999\pi$
$677$	−7.07571	+	12.2555i	−0.271942	+	0.471017i	0.697417	+	0.716665i	$0.254332\pi$
$678$		0			0
$679$	−37.2307	−	16.6561i	−1.42878	−	0.639202i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.553330	−	0.958397i	0.0211726	−	0.0366720i	−0.855245	−	0.518224i	$-0.826593\pi$
$683$	0.553330	−	0.958397i	0.0211726	−	0.0366720i	0.876418	+	0.481552i	$0.159927\pi$
$684$		0			0
$685$	−37.2773			−1.42429
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−12.2789	−	21.2677i	−0.467789	−	0.810234i
$690$		0			0
$691$	−11.4539	+	19.8387i	−0.435725	+	0.754698i	−0.997355	−	0.0726910i	$-0.976841\pi$
$691$	−11.4539	+	19.8387i	−0.435725	+	0.754698i	0.561629	+	0.827389i	$0.310175\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.07207	−	12.2492i	0.268259	−	0.464638i
$696$		0			0
$697$	−0.207492	−	0.359387i	−0.00785932	−	0.0136127i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	11.4056			0.430782			0.215391	−	0.976528i	$-0.430897\pi$
$701$	11.4056			0.430782			0.215391	+	0.976528i	$0.430897\pi$
$702$		0			0
$703$	−5.05832	+	8.76127i	−0.190778	+	0.330438i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.03295	+	4.36672i	−0.226892	+	0.164227i
$708$		0			0
$709$	18.5336	−	32.1011i	0.696042	−	1.20558i	−0.273786	−	0.961791i	$-0.588276\pi$
$709$	18.5336	−	32.1011i	0.696042	−	1.20558i	0.969828	−	0.243790i	$-0.0783908\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.11614	−	3.66527i	−0.0792502	−	0.137265i
$714$		0			0
$715$	−14.6038	+	25.2946i	−0.546153	+	0.945965i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.459342	+	0.795604i	0.0171306	+	0.0296710i	0.874464	−	0.485091i	$-0.161214\pi$
$719$	0.459342	+	0.795604i	0.0171306	+	0.0296710i	−0.857333	+	0.514762i	$0.827880\pi$
$720$		0			0
$721$	−10.9662	+	7.93745i	−0.408402	+	0.295606i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.14545	−	1.98399i	−0.0425411	−	0.0736834i
$726$		0			0
$727$	7.34433	+	12.7208i	0.272386	+	0.471787i	0.969472	−	0.245201i	$-0.0788538\pi$
$727$	7.34433	+	12.7208i	0.272386	+	0.471787i	−0.697086	+	0.716987i	$0.745521\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.24102			0.0828871
$732$		0			0
$733$	−22.8624			−0.844441			−0.422220	−	0.906493i	$-0.638749\pi$
$733$	−22.8624			−0.844441			−0.422220	+	0.906493i	$0.638749\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.8049	−	29.1069i	−0.619015	−	1.07217i
$738$		0			0
$739$	19.6692	−	34.0681i	0.723544	−	1.25321i	−0.236027	−	0.971746i	$-0.575845\pi$
$739$	19.6692	−	34.0681i	0.723544	−	1.25321i	0.959571	−	0.281468i	$-0.0908212\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.8663	+	18.8210i	−0.398647	+	0.690477i	−0.993559	−	0.113314i	$-0.963853\pi$
$743$	−10.8663	+	18.8210i	−0.398647	+	0.690477i	0.594912	+	0.803791i	$0.297187\pi$
$744$		0			0
$745$	−17.7682			−0.650977
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.25444	−	2.79808i	−0.228532	−	0.102240i
$750$		0			0
$751$	20.6143			0.752225			0.376113	−	0.926574i	$-0.377261\pi$
$751$	20.6143			0.752225			0.376113	+	0.926574i	$0.377261\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−34.3404			−1.24978
$756$		0			0
$757$	17.8453			0.648600			0.324300	−	0.945954i	$-0.394871\pi$
$757$	17.8453			0.648600			0.324300	+	0.945954i	$0.394871\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	33.9427			1.23042			0.615211	−	0.788362i	$-0.289071\pi$
$761$	33.9427			1.23042			0.615211	+	0.788362i	$0.289071\pi$
$762$		0			0
$763$	−4.76672	−	46.1466i	−0.172567	−	1.67062i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.7554			−0.857757
$768$		0			0
$769$	20.3452	−	35.2389i	0.733665	−	1.27075i	−0.221641	−	0.975128i	$-0.571141\pi$
$769$	20.3452	−	35.2389i	0.733665	−	1.27075i	0.955306	−	0.295617i	$-0.0955253\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.17562	+	3.76829i	−0.0782517	+	0.135536i	−0.902496	−	0.430699i	$-0.858267\pi$
$773$	−2.17562	+	3.76829i	−0.0782517	+	0.135536i	0.824244	+	0.566235i	$0.191600\pi$
$774$		0			0
$775$	−0.791039	−	1.37012i	−0.0284150	−	0.0492162i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.37516			−0.192585
$780$		0			0
$781$	38.3664			1.37286
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.296062	+	0.512795i	0.0105669	+	0.0183024i
$786$		0			0
$787$	−18.8110	−	32.5816i	−0.670539	−	1.16141i	−0.977751	−	0.209767i	$-0.932730\pi$
$787$	−18.8110	−	32.5816i	−0.670539	−	1.16141i	0.307213	−	0.951641i	$-0.400604\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.46760	+	43.2508i	0.158850	+	1.53782i
$792$		0			0
$793$	−18.7259	−	32.4342i	−0.664976	−	1.15177i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.1570	−	38.3771i	0.784842	−	1.35939i	−0.144251	−	0.989541i	$-0.546077\pi$
$797$	22.1570	−	38.3771i	0.784842	−	1.35939i	0.929093	−	0.369845i	$-0.120589\pi$
$798$		0			0
$799$	−0.666084	−	1.15369i	−0.0235644	−	0.0408147i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.2329	−	17.7239i	0.361110	−	0.625462i
$804$		0			0
$805$	−3.94991	+	2.85899i	−0.139216	+	0.100766i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.78609	−	16.9500i	0.344061	−	0.595931i	−0.641122	−	0.767439i	$-0.721531\pi$
$809$	9.78609	−	16.9500i	0.344061	−	0.595931i	0.985183	+	0.171508i	$0.0548641\pi$
$810$		0			0
$811$	−4.15430			−0.145877			−0.0729386	−	0.997336i	$-0.523238\pi$
$811$	−4.15430			−0.145877			−0.0729386	+	0.997336i	$0.523238\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.4739	−	25.0695i	−0.506997	−	0.878145i
$816$		0			0
$817$	14.5136	−	25.1383i	0.507767	−	0.879479i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.3771	−	24.9019i	0.501764	−	0.869081i	−0.498234	−	0.867043i	$-0.666018\pi$
$821$	14.3771	−	24.9019i	0.501764	−	0.869081i	0.999998	−	0.00203808i	$-0.000648743\pi$
$822$		0			0
$823$	10.5441	+	18.2628i	0.367543	+	0.636603i	0.989181	−	0.146702i	$-0.0468658\pi$
$823$	10.5441	+	18.2628i	0.367543	+	0.636603i	−0.621638	+	0.783305i	$0.713532\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	56.8422			1.97660			0.988299	−	0.152530i	$-0.0487420\pi$
$827$	56.8422			1.97660			0.988299	+	0.152530i	$0.0487420\pi$
$828$		0			0
$829$	−8.97588	+	15.5467i	−0.311745	+	0.539959i	−0.978740	−	0.205104i	$-0.934247\pi$
$829$	−8.97588	+	15.5467i	−0.311745	+	0.539959i	0.666995	+	0.745062i	$0.267580\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.07592	−	1.20357i	−0.0372785	−	0.0417012i
$834$		0			0
$835$	−24.9698	+	43.2490i	−0.864117	+	1.49669i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.38469	+	7.59451i	0.151376	+	0.262192i	0.931734	−	0.363142i	$-0.118296\pi$
$839$	4.38469	+	7.59451i	0.151376	+	0.262192i	−0.780357	+	0.625334i	$0.784963\pi$
$840$		0			0
$841$	−14.7996	+	25.6337i	−0.510332	+	0.883921i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.66014	+	9.80366i	0.194715	+	0.337256i
$846$		0			0
$847$	−19.1124	+	13.8338i	−0.656711	+	0.475336i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.35566	−	2.34807i	−0.0464714	−	0.0804908i
$852$		0			0
$853$	16.0519	+	27.8027i	0.549607	+	0.951948i	0.998301	+	0.0582625i	$0.0185560\pi$
$853$	16.0519	+	27.8027i	0.549607	+	0.951948i	−0.448694	+	0.893686i	$0.648111\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.5025			0.427078			0.213539	−	0.976935i	$-0.431501\pi$
$857$	12.5025			0.427078			0.213539	+	0.976935i	$0.431501\pi$
$858$		0			0
$859$	7.56877			0.258243			0.129121	−	0.991629i	$-0.458784\pi$
$859$	7.56877			0.258243			0.129121	+	0.991629i	$0.458784\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.268987	−	0.465899i	−0.00915642	−	0.0158594i	0.861411	−	0.507909i	$-0.169581\pi$
$863$	−0.268987	−	0.465899i	−0.00915642	−	0.0158594i	−0.870567	+	0.492049i	$0.836248\pi$
$864$		0			0
$865$	15.8384	−	27.4329i	0.538522	−	0.932747i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	21.5852	−	37.3866i	0.732226	−	1.26825i
$870$		0			0
$871$	21.4101			0.725453
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23.1923	−	16.7869i	0.784042	−	0.567499i
$876$		0			0
$877$	26.7073			0.901843			0.450921	−	0.892564i	$-0.351096\pi$
$877$	26.7073			0.901843			0.450921	+	0.892564i	$0.351096\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−33.6239			−1.13282			−0.566408	−	0.824125i	$-0.691667\pi$
$881$	−33.6239			−1.13282			−0.566408	+	0.824125i	$0.691667\pi$
$882$		0			0
$883$	7.20109			0.242336			0.121168	−	0.992632i	$-0.461336\pi$
$883$	7.20109			0.242336			0.121168	+	0.992632i	$0.461336\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.78746			0.160747			0.0803736	−	0.996765i	$-0.474389\pi$
$887$	4.78746			0.160747			0.0803736	+	0.996765i	$0.474389\pi$
$888$		0			0
$889$	−17.4276	+	12.6143i	−0.584504	+	0.423071i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−17.2552			−0.577422
$894$		0			0
$895$	1.03190	−	1.78731i	0.0344928	−	0.0597432i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−20.2340	+	35.0464i	−0.674842	+	1.16886i
$900$		0			0
$901$	−0.996076	−	1.72525i	−0.0331841	−	0.0574766i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−40.1961			−1.33616
$906$		0			0
$907$	−34.8351			−1.15668			−0.578341	−	0.815795i	$-0.696299\pi$
$907$	−34.8351			−1.15668			−0.578341	+	0.815795i	$0.696299\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−29.1584	−	50.5038i	−0.966060	−	1.67326i	−0.706740	−	0.707473i	$-0.749835\pi$
$911$	−29.1584	−	50.5038i	−0.966060	−	1.67326i	−0.259319	−	0.965792i	$-0.583498\pi$
$912$		0			0
$913$	37.7795	+	65.4359i	1.25032	+	2.16561i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−26.8158	+	19.4096i	−0.885536	+	0.640962i
$918$		0			0
$919$	−0.113983	−	0.197424i	−0.00375995	−	0.00651242i	0.864139	−	0.503253i	$-0.167863\pi$
$919$	−0.113983	−	0.197424i	−0.00375995	−	0.00651242i	−0.867899	+	0.496740i	$0.834530\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−12.2201	+	21.1658i	−0.402229	+	0.696681i
$924$		0			0
$925$	−0.506761	−	0.877736i	−0.0166622	−	0.0288598i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.4425	+	21.5511i	−0.408226	+	0.707069i	−0.994691	−	0.102906i	$-0.967186\pi$
$929$	−12.4425	+	21.5511i	−0.408226	+	0.707069i	0.586465	+	0.809975i	$0.300519\pi$
$930$		0			0
$931$	−20.4689	+	4.27429i	−0.670842	+	0.140084i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.18468	+	2.05192i	−0.0387432	+	0.0671051i
$936$		0			0
$937$	−44.3194			−1.44785			−0.723926	−	0.689878i	$-0.757664\pi$
$937$	−44.3194			−1.44785			−0.723926	+	0.689878i	$0.757664\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.1410	+	52.2057i	0.982568	+	1.70186i	0.652282	+	0.757977i	$0.273812\pi$
$941$	30.1410	+	52.2057i	0.982568	+	1.70186i	0.330286	+	0.943881i	$0.392855\pi$
$942$		0			0
$943$	0.720286	−	1.24757i	0.0234558	−	0.0406266i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.29884	+	12.6420i	−0.237180	+	0.410808i	−0.959904	−	0.280329i	$-0.909557\pi$
$947$	−7.29884	+	12.6420i	−0.237180	+	0.410808i	0.722724	+	0.691137i	$0.242890\pi$
$948$		0			0
$949$	6.51855	+	11.2905i	0.211601	+	0.366504i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−11.9601			−0.387427			−0.193713	−	0.981058i	$-0.562053\pi$
$953$	−11.9601			−0.387427			−0.193713	+	0.981058i	$0.562053\pi$
$954$		0			0
$955$	−1.69086	+	2.92865i	−0.0547148	+	0.0947688i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	34.7062	−	25.1208i	1.12072	−	0.811192i
$960$		0			0
$961$	1.52659	−	2.64414i	0.0492450	−	0.0852948i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.48535	−	12.9650i	−0.240962	−	0.417358i
$966$		0			0
$967$	22.8250	−	39.5340i	0.734001	−	1.27133i	−0.221159	−	0.975238i	$-0.570984\pi$
$967$	22.8250	−	39.5340i	0.734001	−	1.27133i	0.955160	−	0.296090i	$-0.0956828\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.25397	−	2.17194i	−0.0402418	−	0.0697009i	0.845203	−	0.534445i	$-0.179479\pi$
$971$	−1.25397	−	2.17194i	−0.0402418	−	0.0697009i	−0.885445	+	0.464745i	$0.846146\pi$
$972$		0			0
$973$	1.67030	+	16.1701i	0.0535472	+	0.518390i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.8101	−	49.9005i	−0.921715	−	1.59646i	−0.796760	−	0.604296i	$-0.793455\pi$
$977$	−28.8101	−	49.9005i	−0.921715	−	1.59646i	−0.124955	−	0.992162i	$-0.539879\pi$
$978$		0			0
$979$	4.21499	+	7.30058i	0.134712	+	0.233328i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−59.3736			−1.89372			−0.946862	−	0.321641i	$-0.895765\pi$
$983$	−59.3736			−1.89372			−0.946862	+	0.321641i	$0.895765\pi$
$984$		0			0
$985$	27.5139			0.876666
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.88973	+	6.73721i	0.123686	+	0.214231i
$990$		0			0
$991$	−20.2341	+	35.0465i	−0.642758	+	1.11329i	0.342057	+	0.939679i	$0.388877\pi$
$991$	−20.2341	+	35.0465i	−0.642758	+	1.11329i	−0.984814	+	0.173610i	$0.944457\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	22.4190	−	38.8308i	0.710730	−	1.23102i
$996$		0			0
$997$	−14.1422			−0.447889			−0.223945	−	0.974602i	$-0.571893\pi$
$997$	−14.1422			−0.447889			−0.223945	+	0.974602i	$0.571893\pi$
$998$		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.109.7		16
3.2	odd	2	inner	2268.2.l.n.109.2		16
7.2	even	3		2268.2.i.n.2053.2		16
9.2	odd	6		2268.2.i.n.865.7		16
9.4	even	3		2268.2.k.g.1621.2	yes	16
9.5	odd	6		2268.2.k.g.1621.7	yes	16
9.7	even	3		2268.2.i.n.865.2		16
21.2	odd	6		2268.2.i.n.2053.7		16
63.2	odd	6	inner	2268.2.l.n.541.2		16
63.16	even	3	inner	2268.2.l.n.541.7		16
63.23	odd	6		2268.2.k.g.1297.7	yes	16
63.58	even	3		2268.2.k.g.1297.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.2		16	9.7	even	3
2268.2.i.n.865.7		16	9.2	odd	6
2268.2.i.n.2053.2		16	7.2	even	3
2268.2.i.n.2053.7		16	21.2	odd	6
2268.2.k.g.1297.2	✓	16	63.58	even	3
2268.2.k.g.1297.7	yes	16	63.23	odd	6
2268.2.k.g.1621.2	yes	16	9.4	even	3
2268.2.k.g.1621.7	yes	16	9.5	odd	6
2268.2.l.n.109.2		16	3.2	odd	2	inner
2268.2.l.n.109.7		16	1.1	even	1	trivial
2268.2.l.n.541.2		16	63.2	odd	6	inner
2268.2.l.n.541.7		16	63.16	even	3	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)

\(f(q)\)	\(=\)	\(q+2.30201 q^{5} +(-2.14324 + 1.55130i) q^{7} +O(q^{10})\)	\(q+2.30201 q^{5} +(-2.14324 + 1.55130i) q^{7} -4.46291 q^{11} +(1.42148 - 2.46208i) q^{13} +(0.115312 - 0.199726i) q^{17} +(-1.49360 - 2.58700i) q^{19} +0.800587 q^{23} +0.299269 q^{25} +(-3.82751 - 6.62944i) q^{29} +(-2.64324 - 4.57822i) q^{31} +(-4.93376 + 3.57112i) q^{35} +(-1.69333 - 2.93293i) q^{37} +(0.899697 - 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +(2.88818 - 5.00247i) q^{47} +(2.18693 - 6.64961i) q^{49} +(4.31905 - 7.48081i) q^{53} -10.2737 q^{55} +(-4.17793 - 7.23638i) q^{59} +(6.58675 - 11.4086i) q^{61} +(3.27227 - 5.66774i) q^{65} +(3.76545 + 6.52195i) q^{67} -8.59672 q^{71} +(-2.29287 + 3.97137i) q^{73} +(9.56507 - 6.92331i) q^{77} +(-4.83657 + 8.37718i) q^{79} +(-8.46521 - 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(-0.944450 - 1.63584i) q^{89} +(0.772852 + 7.48196i) q^{91} +(-3.43829 - 5.95530i) q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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

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