LMFDB - Embedded newform 2268.2.i.n.2053.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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, 4, 4]))

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (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			2053.7
Root			$2.40332 + 0.123797i$ of defining polynomial
Character	$\chi$	$=$	2268.2053
Dual form			2268.2.i.n.865.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +O(q^{10})$	$q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +(-2.23145 + 3.86499i) q^{11} +(1.42148 - 2.46208i) q^{13} +(-0.115312 - 0.199726i) q^{17} +(-1.49360 + 2.58700i) q^{19} +(0.400294 + 0.693329i) q^{23} +(-0.149635 + 0.259175i) q^{25} +(3.82751 + 6.62944i) q^{29} +5.28647 q^{31} +(4.93376 + 3.57112i) q^{35} +(-1.69333 + 2.93293i) q^{37} +(-0.899697 + 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +5.77636 q^{47} +(4.66527 - 5.21874i) q^{49} +(-4.31905 - 7.48081i) q^{53} -10.2737 q^{55} -8.35585 q^{59} -13.1735 q^{61} +6.54454 q^{65} -7.53090 q^{67} +8.59672 q^{71} +(-2.29287 - 3.97137i) q^{73} +(-1.21323 + 11.7453i) q^{77} +9.67313 q^{79} +(8.46521 + 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(0.944450 - 1.63584i) q^{89} +(0.772852 - 7.48196i) q^{91} -6.87659 q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) $ 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * 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 $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

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

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
$5$	1.15101	+	1.99360i	0.514746	+	0.891566i	0.999854	+	0.0171118i	$0.00544711\pi$
$5$	1.15101	+	1.99360i	0.514746	+	0.891566i	−0.485108	+	0.874454i	$0.661220\pi$
$6$		0			0
$7$	2.41508	−	1.08045i	0.912816	−	0.408371i
$7$	2.41508	−	1.08045i	0.912816	−	0.408371i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.23145	+	3.86499i	−0.672809	+	1.16534i	0.304295	+	0.952578i	$0.401579\pi$
$11$	−2.23145	+	3.86499i	−0.672809	+	1.16534i	−0.977104	+	0.212761i	$0.931754\pi$
$12$		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	$-0.175570\pi$
$17$	−0.115312	−	0.199726i	−0.0279673	−	0.0484408i	−0.879670	+	0.475584i	$0.842237\pi$
$18$		0			0
$19$	−1.49360	+	2.58700i	−0.342656	+	0.593498i	−0.984925	−	0.172982i	$-0.944660\pi$
$19$	−1.49360	+	2.58700i	−0.342656	+	0.593498i	0.642269	+	0.766479i	$0.277993\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.400294	+	0.693329i	0.0834670	+	0.144569i	0.904737	−	0.425971i	$-0.140067\pi$
$23$	0.400294	+	0.693329i	0.0834670	+	0.144569i	−0.821270	+	0.570540i	$0.806734\pi$
$24$		0			0
$25$	−0.149635	+	0.259175i	−0.0299269	+	0.0518349i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.82751	+	6.62944i	0.710750	+	1.23106i	0.964576	+	0.263806i	$0.0849778\pi$
$29$	3.82751	+	6.62944i	0.710750	+	1.23106i	−0.253825	+	0.967250i	$0.581689\pi$
$30$		0			0
$31$	5.28647			0.949479			0.474739	−	0.880126i	$-0.342542\pi$
$31$	5.28647			0.949479			0.474739	+	0.880126i	$0.342542\pi$
$32$		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	−0.970983	−	0.239150i	$-0.923131\pi$
$37$	−1.69333	+	2.93293i	−0.278382	+	0.482171i	0.692601	+	0.721321i	$0.256465\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.899697	+	1.55832i	−0.140509	+	0.243369i	−0.927688	−	0.373355i	$-0.878207\pi$
$41$	−0.899697	+	1.55832i	−0.140509	+	0.243369i	0.787179	+	0.616724i	$0.211541\pi$
$42$		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
$47$	5.77636			0.842569			0.421284	−	0.906929i	$-0.361579\pi$
$47$	5.77636			0.842569			0.421284	+	0.906929i	$0.361579\pi$
$48$		0			0
$49$	4.66527	−	5.21874i	0.666467	−	0.745535i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.31905	−	7.48081i	−0.593267	−	1.02757i	−0.993789	−	0.111281i	$-0.964505\pi$
$53$	−4.31905	−	7.48081i	−0.593267	−	1.02757i	0.400522	−	0.916287i	$-0.368829\pi$
$54$		0			0
$55$	−10.2737			−1.38530
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.35585			−1.08784			−0.543920	−	0.839137i	$-0.683060\pi$
$59$	−8.35585			−1.08784			−0.543920	+	0.839137i	$0.683060\pi$
$60$		0			0
$61$	−13.1735			−1.68669			−0.843347	−	0.537370i	$-0.819418\pi$
$61$	−13.1735			−1.68669			−0.843347	+	0.537370i	$0.819418\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.54454			0.811751
$66$		0			0
$67$	−7.53090			−0.920046			−0.460023	−	0.887907i	$-0.652159\pi$
$67$	−7.53090			−0.920046			−0.460023	+	0.887907i	$0.652159\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.59672			1.02024			0.510122	−	0.860102i	$-0.329600\pi$
$71$	8.59672			1.02024			0.510122	+	0.860102i	$0.329600\pi$
$72$		0			0
$73$	−2.29287	−	3.97137i	−0.268360	−	0.464814i	0.700078	−	0.714066i	$-0.253148\pi$
$73$	−2.29287	−	3.97137i	−0.268360	−	0.464814i	−0.968439	+	0.249252i	$0.919815\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.21323	+	11.7453i	−0.138260	+	1.33850i
$78$		0			0
$79$	9.67313			1.08831			0.544156	−	0.838984i	$-0.316850\pi$
$79$	9.67313			1.08831			0.544156	+	0.838984i	$0.316850\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.46521	+	14.6622i	0.929177	+	1.60938i	0.784701	+	0.619874i	$0.212816\pi$
$83$	8.46521	+	14.6622i	0.929177	+	1.60938i	0.144476	+	0.989508i	$0.453850\pi$
$84$		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	$-0.801413\pi$
$89$	0.944450	−	1.63584i	0.100111	−	0.173398i	0.911730	+	0.410789i	$0.134747\pi$
$90$		0			0
$91$	0.772852	−	7.48196i	0.0810169	−	0.784323i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.87659			−0.705523
$96$		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
$101$	1.40744	−	2.43775i	0.140045	−	0.242566i	−0.787468	−	0.616355i	$-0.788609\pi$
$101$	1.40744	−	2.43775i	0.140045	−	0.242566i	0.927513	+	0.373790i	$0.121942\pi$
$102$		0			0
$103$	−2.55832	−	4.43114i	−0.252079	−	0.436614i	0.712019	−	0.702160i	$-0.247781\pi$
$103$	−2.55832	−	4.43114i	−0.252079	−	0.436614i	−0.964098	+	0.265547i	$0.914448\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.29487	+	2.24278i	−0.125180	+	0.216818i	−0.921803	−	0.387658i	$-0.873284\pi$
$107$	−1.29487	+	2.24278i	−0.125180	+	0.216818i	0.796623	+	0.604476i	$0.206617\pi$
$108$		0			0
$109$	−8.76728	−	15.1854i	−0.839753	−	1.45450i	−0.890101	−	0.455764i	$-0.849366\pi$
$109$	−8.76728	−	15.1854i	−0.839753	−	1.45450i	0.0503474	−	0.998732i	$-0.483967\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−8.21711	+	14.2325i	−0.773001	+	1.33888i	0.162910	+	0.986641i	$0.447912\pi$
$113$	−8.21711	+	14.2325i	−0.773001	+	1.33888i	−0.935911	+	0.352236i	$0.885421\pi$
$114$		0			0
$115$	−0.921482	+	1.59605i	−0.0859286	+	0.148833i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.494282	−	0.357767i	−0.0453108	−	0.0327965i
$120$		0			0
$121$	−4.45878	−	7.72283i	−0.405344	−	0.702076i
$122$		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
$131$	6.25591	+	10.8356i	0.546582	+	0.946707i	0.998506	+	0.0546508i	$0.0174046\pi$
$131$	6.25591	+	10.8356i	0.546582	+	0.946707i	−0.451924	+	0.892057i	$0.649262\pi$
$132$		0			0
$133$	−0.812064	+	7.86157i	−0.0704148	+	0.681685i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.09668	+	14.0239i	−0.691746	+	1.19814i	0.279519	+	0.960140i	$0.409825\pi$
$137$	−8.09668	+	14.0239i	−0.691746	+	1.19814i	−0.971265	+	0.237999i	$0.923508\pi$
$138$		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
$149$	−3.85927	−	6.68446i	−0.316164	−	0.547612i	0.663520	−	0.748158i	$-0.269062\pi$
$149$	−3.85927	−	6.68446i	−0.316164	−	0.547612i	−0.979684	+	0.200546i	$0.935728\pi$
$150$		0			0
$151$	7.45878	−	12.9190i	0.606987	−	1.05133i	−0.384747	−	0.923022i	$-0.625711\pi$
$151$	7.45878	−	12.9190i	0.606987	−	1.05133i	0.991734	−	0.128310i	$-0.0409553\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.08477	+	10.5391i	0.488740	+	0.846523i
$156$		0			0
$157$	−0.257220			−0.0205284			−0.0102642	−	0.999947i	$-0.503267\pi$
$157$	−0.257220			−0.0205284			−0.0102642	+	0.999947i	$0.503267\pi$
$158$		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	−0.999962	−	0.00866931i	$-0.997240\pi$
$163$	−6.28748	+	10.8902i	−0.492473	+	0.852989i	0.507489	+	0.861658i	$0.330574\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.8470	−	18.7875i	0.839363	−	1.45382i	−0.0510657	−	0.998695i	$-0.516262\pi$
$167$	10.8470	−	18.7875i	0.839363	−	1.45382i	0.890428	−	0.455123i	$-0.150405\pi$
$168$		0			0
$169$	2.45878	+	4.25873i	0.189137	+	0.327595i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	13.7605			1.04619			0.523095	−	0.852275i	$-0.324777\pi$
$173$	13.7605			1.04619			0.523095	+	0.852275i	$0.324777\pi$
$174$		0			0
$175$	−0.0813555	+	0.787601i	−0.00614990	+	0.0595370i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.448262	−	0.776412i	−0.0335046	−	0.0580317i	0.848787	−	0.528735i	$-0.177334\pi$
$179$	−0.448262	−	0.776412i	−0.0335046	−	0.0580317i	−0.882292	+	0.470703i	$0.844000\pi$
$180$		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
$185$	−7.79613			−0.573183
$186$		0			0
$187$	1.02925			0.0752665
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.46902			−0.106295			−0.0531474	−	0.998587i	$-0.516925\pi$
$191$	−1.46902			−0.106295			−0.0531474	+	0.998587i	$0.516925\pi$
$192$		0			0
$193$	6.50330			0.468118			0.234059	−	0.972222i	$-0.424799\pi$
$193$	6.50330			0.468118			0.234059	+	0.972222i	$0.424799\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.9521			−0.851552			−0.425776	−	0.904828i	$-0.639999\pi$
$197$	−11.9521			−0.851552			−0.425776	+	0.904828i	$0.639999\pi$
$198$		0			0
$199$	9.73886	+	16.8682i	0.690369	+	1.19575i	0.971717	+	0.236149i	$0.0758852\pi$
$199$	9.73886	+	16.8682i	0.690369	+	1.19575i	−0.281348	+	0.959606i	$0.590781\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	16.4065	+	11.8752i	1.15151	+	0.833478i
$204$		0			0
$205$	−4.14223			−0.289306
$206$		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
$221$	−0.655656			−0.0441042
$222$		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
$227$	−12.2254	+	21.1750i	−0.811426	+	1.40543i	0.100439	+	0.994943i	$0.467975\pi$
$227$	−12.2254	+	21.1750i	−0.811426	+	1.40543i	−0.911866	+	0.410489i	$0.865358\pi$
$228$		0			0
$229$	11.0018	+	19.0557i	0.727022	+	1.25924i	0.958136	+	0.286312i	$0.0924293\pi$
$229$	11.0018	+	19.0557i	0.727022	+	1.25924i	−0.231115	+	0.972926i	$0.574237\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.8179	−	18.7372i	0.708706	−	1.22752i	−0.256631	−	0.966510i	$-0.582612\pi$
$233$	10.8179	−	18.7372i	0.708706	−	1.22752i	0.965337	−	0.261006i	$-0.0840542\pi$
$234$		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	$0.361019\pi$
$239$	−8.86360	+	15.3522i	−0.573338	+	0.993051i	−0.996220	+	0.0868662i	$0.972315\pi$
$240$		0			0
$241$	−2.15887	+	3.73927i	−0.139065	+	0.240868i	−0.927143	−	0.374708i	$-0.877743\pi$
$241$	−2.15887	+	3.73927i	−0.139065	+	0.240868i	0.788078	+	0.615575i	$0.211076\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	15.7739	+	3.29388i	1.00775	+	0.210438i
$246$		0			0
$247$	4.24626	+	7.35473i	0.270183	+	0.467971i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.2938			0.649741			0.324870	−	0.945759i	$-0.394679\pi$
$251$	10.2938			0.649741			0.324870	+	0.945759i	$0.394679\pi$
$252$		0			0
$253$	−3.57295			−0.224629
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.89568	−	10.2116i	−0.367763	−	0.636983i	0.621453	−	0.783452i	$-0.286543\pi$
$257$	−5.89568	−	10.2116i	−0.367763	−	0.636983i	−0.989215	+	0.146468i	$0.953209\pi$
$258$		0			0
$259$	−0.920654	+	8.91283i	−0.0572066	+	0.553816i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.59359	+	4.49223i	−0.159928	+	0.277003i	−0.934842	−	0.355063i	$-0.884459\pi$
$263$	−2.59359	+	4.49223i	−0.159928	+	0.277003i	0.774915	+	0.632066i	$0.217793\pi$
$264$		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	−0.838912	−	0.544268i	$-0.816808\pi$
$269$	−14.6103	−	25.3058i	−0.890805	−	1.54292i	−0.0518936	−	0.998653i	$-0.516526\pi$
$270$		0			0
$271$	10.2801	−	17.8056i	0.624470	−	1.08161i	−0.364173	−	0.931331i	$-0.618648\pi$
$271$	10.2801	−	17.8056i	0.624470	−	1.08161i	0.988643	−	0.150283i	$-0.0480184\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.667805	−	1.15667i	−0.0402702	−	0.0697500i
$276$		0			0
$277$	5.97833	−	10.3548i	0.359203	−	0.622158i	−0.628625	−	0.777709i	$-0.716382\pi$
$277$	5.97833	−	10.3548i	0.359203	−	0.622158i	0.987828	+	0.155550i	$0.0497151\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.9166	−	25.8363i	−0.889850	−	1.54126i	−0.840052	−	0.542506i	$-0.817476\pi$
$281$	−14.9166	−	25.8363i	−0.889850	−	1.54126i	−0.0497975	−	0.998759i	$-0.515858\pi$
$282$		0			0
$283$	−9.57094			−0.568933			−0.284467	−	0.958686i	$-0.591817\pi$
$283$	−9.57094			−0.568933			−0.284467	+	0.958686i	$0.591817\pi$
$284$		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	−0.564217	−	0.825626i	$-0.690822\pi$
$293$	7.41014	−	12.8347i	0.432905	−	0.749813i	0.997122	+	0.0758132i	$0.0241553\pi$
$294$		0			0
$295$	−9.61765	−	16.6583i	−0.559961	−	0.969881i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.27604			0.131627
$300$		0			0
$301$	20.8262	+	15.0743i	1.20040	+	0.868867i
$302$		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
$311$	16.2351			0.920606			0.460303	−	0.887762i	$-0.347741\pi$
$311$	16.2351			0.920606			0.460303	+	0.887762i	$0.347741\pi$
$312$		0			0
$313$	17.6896			0.999875			0.499937	−	0.866062i	$-0.333356\pi$
$313$	17.6896			0.999875			0.499937	+	0.866062i	$0.333356\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.28017			−0.296564			−0.148282	−	0.988945i	$-0.547374\pi$
$317$	−5.28017			−0.296564			−0.148282	+	0.988945i	$0.547374\pi$
$318$		0			0
$319$	−34.1636			−1.91280
$320$		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
$329$	13.9504	−	6.24105i	0.769110	−	0.344080i
$330$		0			0
$331$	−15.6072			−0.857847			−0.428923	−	0.903341i	$-0.641107\pi$
$331$	−15.6072			−0.857847			−0.428923	+	0.903341i	$0.641107\pi$
$332$		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
$347$	−26.9003			−1.44408			−0.722042	−	0.691849i	$-0.756796\pi$
$347$	−26.9003			−1.44408			−0.722042	+	0.691849i	$0.756796\pi$
$348$		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
$353$	15.1655	−	26.2675i	0.807180	−	1.39808i	−0.107630	−	0.994191i	$-0.534326\pi$
$353$	15.1655	−	26.2675i	0.807180	−	1.39808i	0.914810	−	0.403885i	$-0.132341\pi$
$354$		0			0
$355$	9.89489	+	17.1384i	0.525166	+	0.909614i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.99876	−	12.1222i	0.369381	−	0.639786i	−0.620088	−	0.784532i	$-0.712903\pi$
$359$	6.99876	−	12.1222i	0.369381	−	0.639786i	0.989469	+	0.144746i	$0.0462366\pi$
$360$		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
$367$	1.25165	−	2.16792i	0.0653356	−	0.113165i	−0.831507	−	0.555514i	$-0.812522\pi$
$367$	1.25165	−	2.16792i	0.0653356	−	0.113165i	0.896843	+	0.442349i	$0.145855\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.5135	−	13.4003i	−0.961172	−	0.695708i
$372$		0			0
$373$	−8.80311	−	15.2474i	−0.455808	−	0.789482i	0.542926	−	0.839780i	$-0.317316\pi$
$373$	−8.80311	−	15.2474i	−0.455808	−	0.789482i	−0.998734	+	0.0502980i	$0.983983\pi$
$374$		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
$383$	10.8418	+	18.7786i	0.553992	+	0.959542i	0.997981	+	0.0635100i	$0.0202295\pi$
$383$	10.8418	+	18.7786i	0.553992	+	0.959542i	−0.443989	+	0.896032i	$0.646437\pi$
$384$		0			0
$385$	−24.8118	+	11.1002i	−1.26453	+	0.565717i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.96652	−	12.0664i	0.353217	−	0.611790i	−0.633594	−	0.773665i	$-0.718421\pi$
$389$	6.96652	−	12.0664i	0.353217	−	0.611790i	0.986811	+	0.161876i	$0.0517545\pi$
$390$		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	−0.268004	−	0.963418i	$-0.586364\pi$
$397$	13.9542	−	24.1694i	0.700342	−	1.21303i	0.968346	−	0.249610i	$-0.0803025\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.4525	−	30.2285i	−0.871534	−	1.50954i	−0.860410	−	0.509603i	$-0.829792\pi$
$401$	−17.4525	−	30.2285i	−0.871534	−	1.50954i	−0.0111242	−	0.999938i	$-0.503541\pi$
$402$		0			0
$403$	7.51463	−	13.0157i	0.374330	−	0.648359i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.55717	−	13.0894i	−0.374595	−	0.648818i
$408$		0			0
$409$	−20.6739			−1.02226			−0.511128	−	0.859504i	$-0.670772\pi$
$409$	−20.6739			−1.02226			−0.511128	+	0.859504i	$0.670772\pi$
$410$		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	$-0.402659\pi$
$419$	19.9859	−	34.6166i	0.976376	−	1.69113i	0.675316	−	0.737529i	$-0.264007\pi$
$420$		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
$425$	0.0690187			0.00334790
$426$		0			0
$427$	−31.8151	+	14.2333i	−1.53964	+	0.688796i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.05181	+	12.2141i	0.339674	+	0.588332i	0.984371	−	0.176106i	$-0.0563500\pi$
$431$	7.05181	+	12.2141i	0.339674	+	0.588332i	−0.644698	+	0.764438i	$0.723017\pi$
$432$		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
$437$	−2.39152			−0.114402
$438$		0			0
$439$	−24.3768			−1.16344			−0.581721	−	0.813389i	$-0.697620\pi$
$439$	−24.3768			−1.16344			−0.581721	+	0.813389i	$0.697620\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.5640			−0.882002			−0.441001	−	0.897507i	$-0.645376\pi$
$443$	−18.5640			−0.882002			−0.441001	+	0.897507i	$0.645376\pi$
$444$		0			0
$445$	4.34827			0.206128
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−21.4616			−1.01284			−0.506418	−	0.862288i	$-0.669031\pi$
$449$	−21.4616			−1.01284			−0.506418	+	0.862288i	$0.669031\pi$
$450$		0			0
$451$	−4.01527	−	6.95465i	−0.189072	−	0.327482i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	15.8056	−	7.07103i	0.740979	−	0.331495i
$456$		0			0
$457$	15.1274			0.707631			0.353816	−	0.935315i	$-0.384884\pi$
$457$	15.1274			0.707631			0.353816	+	0.935315i	$0.384884\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.5385	−	28.6455i	−0.770273	−	1.33415i	−0.937413	−	0.348219i	$-0.886787\pi$
$461$	−16.5385	−	28.6455i	−0.770273	−	1.33415i	0.167140	−	0.985933i	$-0.446547\pi$
$462$		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	$-0.921904\pi$
$467$	−5.93579	+	10.2811i	−0.274675	+	0.475752i	0.695378	+	0.718644i	$0.255237\pi$
$468$		0			0
$469$	−18.1878	+	8.13674i	−0.839833	+	0.375720i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−43.3669			−1.99401
$474$		0			0
$475$	−0.446989	−	0.774208i	−0.0205093	−	0.0355231i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.71973	+	15.1030i	−0.398415	+	0.690075i	−0.993531	−	0.113565i	$-0.963773\pi$
$479$	−8.71973	+	15.1030i	−0.398415	+	0.690075i	0.595116	+	0.803640i	$0.297106\pi$
$480$		0			0
$481$	4.81407	+	8.33822i	0.219503	+	0.380190i
$482$		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	0.895424	+	0.445214i	$0.146872\pi$
$487$	18.3889	+	31.8504i	0.833279	+	1.44328i	−0.0621458	+	0.998067i	$0.519794\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.54050	−	7.86437i	0.204910	−	0.354914i	−0.745194	−	0.666847i	$-0.767643\pi$
$491$	4.54050	−	7.86437i	0.204910	−	0.354914i	0.950104	+	0.311933i	$0.100977\pi$
$492$		0			0
$493$	0.882716	−	1.52891i	0.0397555	−	0.0688586i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.7618	−	9.28831i	0.931294	−	0.416638i
$498$		0			0
$499$	−3.41261	−	5.91082i	−0.152769	−	0.264604i	0.779475	−	0.626433i	$-0.215486\pi$
$499$	−3.41261	−	5.91082i	−0.152769	−	0.264604i	−0.932245	+	0.361829i	$0.882153\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.09211			0.182458			0.0912291	−	0.995830i	$-0.470920\pi$
$503$	4.09211			0.182458			0.0912291	+	0.995830i	$0.470920\pi$
$504$		0			0
$505$	6.47989			0.288351
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.3991	+	24.9400i	0.638228	+	1.10544i	0.985821	+	0.167798i	$0.0536658\pi$
$509$	14.3991	+	24.9400i	0.638228	+	1.10544i	−0.347593	+	0.937646i	$0.613001\pi$
$510$		0			0
$511$	−9.82834	−	7.11387i	−0.434780	−	0.314699i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.88929	−	10.2006i	0.259513	−	0.449490i
$516$		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	$-0.250203\pi$
$521$	−5.92170	−	10.2567i	−0.259434	−	0.449353i	−0.966090	+	0.258204i	$0.916869\pi$
$522$		0			0
$523$	6.86664	−	11.8934i	0.300257	−	0.520061i	−0.675937	−	0.736959i	$-0.736261\pi$
$523$	6.86664	−	11.8934i	0.300257	−	0.520061i	0.976194	+	0.216899i	$0.0695942\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.609594	−	1.05585i	−0.0265543	−	0.0459935i
$528$		0			0
$529$	11.1795	−	19.3635i	0.486067	−	0.841892i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.55781	+	4.43025i	0.110791	+	0.191896i
$534$		0			0
$535$	−5.96162			−0.257743
$536$		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	0.159765	−	0.987155i	$-0.448926\pi$
$541$	21.7425	−	37.6592i	0.934784	−	1.61909i	0.775019	−	0.631938i	$-0.217740\pi$
$542$		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
$551$	−22.8671			−0.974171
$552$		0			0
$553$	23.3614	−	10.4513i	0.993429	−	0.444435i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.0925	−	27.8730i	−0.681862	−	1.18102i	−0.974412	−	0.224769i	$-0.927837\pi$
$557$	−16.0925	−	27.8730i	−0.681862	−	1.18102i	0.292551	−	0.956250i	$-0.405496\pi$
$558$		0			0
$559$	27.6256			1.16844
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.38738			0.142761			0.0713804	−	0.997449i	$-0.477260\pi$
$563$	3.38738			0.142761			0.0713804	+	0.997449i	$0.477260\pi$
$564$		0			0
$565$	−37.8318			−1.59160
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−40.3474			−1.69145			−0.845726	−	0.533618i	$-0.820832\pi$
$569$	−40.3474			−1.69145			−0.845726	+	0.533618i	$0.820832\pi$
$570$		0			0
$571$	−10.4386			−0.436840			−0.218420	−	0.975855i	$-0.570090\pi$
$571$	−10.4386			−0.436840			−0.218420	+	0.975855i	$0.570090\pi$
$572$		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	0.958136	−	0.286312i	$-0.0924295\pi$
$577$	5.55156	+	9.61559i	0.231114	+	0.400302i	−0.727022	+	0.686614i	$0.759096\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	36.2859	+	26.2642i	1.50539	+	1.08962i
$582$		0			0
$583$	38.5510			1.59662
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.3875	−	35.3122i	−0.841482	−	1.45749i	−0.888642	−	0.458602i	$-0.848350\pi$
$587$	−20.3875	−	35.3122i	−0.841482	−	1.45749i	0.0471601	−	0.998887i	$-0.484983\pi$
$588$		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	−0.384182	−	0.923258i	$-0.625516\pi$
$593$	14.7930	−	25.6221i	0.607474	−	1.05218i	0.991655	−	0.128918i	$-0.0411503\pi$
$594$		0			0
$595$	0.144324	−	1.39720i	0.00591669	−	0.0572794i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.3552			−0.749973			−0.374987	−	0.927030i	$-0.622353\pi$
$599$	−18.3552			−0.749973			−0.374987	+	0.927030i	$0.622353\pi$
$600$		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
$605$	10.2642	−	17.7781i	0.417298	−	0.722781i
$606$		0			0
$607$	−11.8452	−	20.5164i	−0.480780	−	0.832736i	0.518977	−	0.854788i	$-0.326313\pi$
$607$	−11.8452	−	20.5164i	−0.480780	−	0.832736i	−0.999757	+	0.0220527i	$0.992980\pi$
$608$		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	0.999021	+	0.0442411i	$0.0140870\pi$
$613$	13.3159	+	23.0638i	0.537824	+	0.931539i	−0.461197	+	0.887298i	$0.652580\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.72483	−	8.18364i	0.190214	−	0.329461i	−0.755107	−	0.655602i	$-0.772415\pi$
$617$	4.72483	−	8.18364i	0.190214	−	0.329461i	0.945321	+	0.326141i	$0.105748\pi$
$618$		0			0
$619$	18.0474	−	31.2589i	0.725385	−	1.25640i	−0.233431	−	0.972373i	$-0.574995\pi$
$619$	18.0474	−	31.2589i	0.725385	−	1.25640i	0.958815	−	0.284030i	$-0.0916714\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.513492	−	4.97111i	0.0205726	−	0.199163i
$624$		0			0
$625$	13.2034	+	22.8689i	0.528136	+	0.914758i
$626$		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
$635$	9.35935	+	16.2109i	0.371415	+	0.643309i
$636$		0			0
$637$	−6.21737	−	18.9046i	−0.246341	−	0.749028i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.45227	−	4.24745i	0.0968587	−	0.167764i	−0.813524	−	0.581531i	$-0.802454\pi$
$641$	2.45227	−	4.24745i	0.0968587	−	0.167764i	0.910383	+	0.413767i	$0.135787\pi$
$642$		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	−0.668993	−	0.743268i	$-0.733275\pi$
$647$	−24.8813	−	43.0957i	−0.978186	−	1.69427i	−0.309192	−	0.950999i	$-0.600059\pi$
$648$		0			0
$649$	18.6457	−	32.2953i	0.731908	−	1.26770i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.98578	−	12.0997i	−0.273375	−	0.473499i	0.696349	−	0.717703i	$-0.254807\pi$
$653$	−6.98578	−	12.0997i	−0.273375	−	0.473499i	−0.969724	+	0.244205i	$0.921473\pi$
$654$		0			0
$655$	−14.4012	+	24.9436i	−0.562702	+	0.974628i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.9827	+	22.4867i	0.505733	+	0.875956i	0.999978	+	0.00663317i	$0.00211142\pi$
$659$	12.9827	+	22.4867i	0.505733	+	0.875956i	−0.494245	+	0.869323i	$0.664555\pi$
$660$		0			0
$661$	25.5362			0.993244			0.496622	−	0.867967i	$-0.334574\pi$
$661$	25.5362			0.993244			0.496622	+	0.867967i	$0.334574\pi$
$662$		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
$677$	−14.1514			−0.543883			−0.271942	−	0.962314i	$-0.587666\pi$
$677$	−14.1514			−0.543883			−0.271942	+	0.962314i	$0.587666\pi$
$678$		0			0
$679$	33.0400	+	23.9147i	1.26796	+	0.917763i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.553330	−	0.958397i	−0.0211726	−	0.0366720i	0.855245	−	0.518224i	$-0.173407\pi$
$683$	−0.553330	−	0.958397i	−0.0211726	−	0.0366720i	−0.876418	+	0.481552i	$0.840073\pi$
$684$		0			0
$685$	−37.2773			−1.42429
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−24.5578			−0.935577
$690$		0			0
$691$	22.9077			0.871450			0.435725	−	0.900080i	$-0.356492\pi$
$691$	22.9077			0.871450			0.435725	+	0.900080i	$0.356492\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.1441			0.536517
$696$		0			0
$697$	0.414984			0.0157186
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11.4056			−0.430782			−0.215391	−	0.976528i	$-0.569103\pi$
$701$	−11.4056			−0.430782			−0.215391	+	0.976528i	$0.569103\pi$
$702$		0			0
$703$	−5.05832	−	8.76127i	−0.190778	−	0.330438i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.765216	−	7.40805i	0.0287789	−	0.278608i
$708$		0			0
$709$	−37.0671			−1.39208			−0.696042	−	0.718001i	$-0.745057\pi$
$709$	−37.0671			−1.39208			−0.696042	+	0.718001i	$0.745057\pi$
$710$		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	$-0.838786\pi$
$719$	−0.459342	+	0.795604i	−0.0171306	+	0.0296710i	0.857333	+	0.514762i	$0.172120\pi$
$720$		0			0
$721$	−10.9662	−	7.93745i	−0.408402	−	0.295606i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.29091			−0.0850822
$726$		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
$731$	1.12051	−	1.94078i	0.0414435	−	0.0717823i
$732$		0			0
$733$	11.4312	+	19.7994i	0.422220	+	0.731307i	0.996156	−	0.0875931i	$-0.0279175\pi$
$733$	11.4312	+	19.7994i	0.422220	+	0.731307i	−0.573936	+	0.818900i	$0.694584\pi$
$734$		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	0.959571	+	0.281468i	$0.0908212\pi$
$739$	19.6692	+	34.0681i	0.723544	+	1.25321i	−0.236027	+	0.971746i	$0.575845\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.8663	−	18.8210i	0.398647	−	0.690477i	−0.594912	−	0.803791i	$-0.702813\pi$
$743$	10.8663	−	18.8210i	0.398647	−	0.690477i	0.993559	+	0.113314i	$0.0361465\pi$
$744$		0			0
$745$	8.88410	−	15.3877i	0.325488	−	0.563762i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.704014	+	6.81554i	−0.0257241	+	0.249034i
$750$		0			0
$751$	−10.3071	−	17.8525i	−0.376113	−	0.651446i	0.614380	−	0.789010i	$-0.289406\pi$
$751$	−10.3071	−	17.8525i	−0.376113	−	0.651446i	−0.990493	+	0.137564i	$0.956073\pi$
$752$		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
$761$	16.9714	+	29.3953i	0.615211	+	1.06558i	0.990347	+	0.138607i	$0.0442626\pi$
$761$	16.9714	+	29.3953i	0.615211	+	1.06558i	−0.375136	+	0.926970i	$0.622404\pi$
$762$		0			0
$763$	−37.5807	−	27.2014i	−1.36051	−	0.984756i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.8777	+	20.5728i	−0.428879	+	0.742840i
$768$		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	$-0.141733\pi$
$773$	2.17562	+	3.76829i	0.0782517	+	0.135536i	−0.824244	+	0.566235i	$0.808400\pi$
$774$		0			0
$775$	−0.791039	+	1.37012i	−0.0284150	+	0.0492162i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.68758	−	4.65503i	−0.0962926	−	0.166784i
$780$		0			0
$781$	−19.1832	+	33.2263i	−0.686429	+	1.18893i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.296062	−	0.512795i	−0.0105669	−	0.0183024i
$786$		0			0
$787$	37.6220			1.34108			0.670539	−	0.741874i	$-0.266063\pi$
$787$	37.6220			1.34108			0.670539	+	0.741874i	$0.266063\pi$
$788$		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	$0.453923\pi$
$797$	−22.1570	+	38.3771i	−0.784842	+	1.35939i	−0.929093	+	0.369845i	$0.879411\pi$
$798$		0			0
$799$	−0.666084	−	1.15369i	−0.0235644	−	0.0408147i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	20.4658			0.722221
$804$		0			0
$805$	−0.501005	+	4.85022i	−0.0176581	+	0.170948i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.78609	−	16.9500i	−0.344061	−	0.595931i	0.641122	−	0.767439i	$-0.278469\pi$
$809$	−9.78609	−	16.9500i	−0.344061	−	0.595931i	−0.985183	+	0.171508i	$0.945136\pi$
$810$		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
$815$	−28.9477			−1.01399
$816$		0			0
$817$	−29.0272			−1.01553
$818$		0			0
$819$		0			0
$820$		0			0
$821$	28.7542			1.00353			0.501764	−	0.865005i	$-0.332685\pi$
$821$	28.7542			1.00353			0.501764	+	0.865005i	$0.332685\pi$
$822$		0			0
$823$	−21.0881			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$823$	−21.0881			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−56.8422			−1.97660			−0.988299	−	0.152530i	$-0.951258\pi$
$827$	−56.8422			−1.97660			−0.988299	+	0.152530i	$0.951258\pi$
$828$		0			0
$829$	−8.97588	−	15.5467i	−0.311745	−	0.539959i	0.666995	−	0.745062i	$-0.267580\pi$
$829$	−8.97588	−	15.5467i	−0.311745	−	0.539959i	−0.978740	+	0.205104i	$0.934247\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.58028	−	0.329992i	−0.0547535	−	0.0114336i
$834$		0			0
$835$	49.9397			1.72823
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.38469	−	7.59451i	−0.151376	−	0.262192i	0.780357	−	0.625334i	$-0.215037\pi$
$839$	−4.38469	−	7.59451i	−0.151376	−	0.262192i	−0.931734	+	0.363142i	$0.881704\pi$
$840$		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
$851$	−2.71132			−0.0929427
$852$		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
$857$	6.25126	−	10.8275i	0.213539	−	0.369861i	−0.739281	−	0.673398i	$-0.764834\pi$
$857$	6.25126	−	10.8275i	0.213539	−	0.369861i	0.952820	+	0.303537i	$0.0981676\pi$
$858$		0			0
$859$	−3.78438	−	6.55474i	−0.129121	−	0.223645i	0.794215	−	0.607637i	$-0.207882\pi$
$859$	−3.78438	−	6.55474i	−0.129121	−	0.223645i	−0.923336	+	0.383992i	$0.874549\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.268987	−	0.465899i	0.00915642	−	0.0158594i	−0.861411	−	0.507909i	$-0.830419\pi$
$863$	0.268987	−	0.465899i	0.00915642	−	0.0158594i	0.870567	+	0.492049i	$0.163752\pi$
$864$		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
$871$	−10.7050	+	18.5417i	−0.362726	+	0.628260i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	26.1340	−	11.6917i	0.883490	−	0.395251i
$876$		0			0
$877$	−13.3537	−	23.1292i	−0.450921	−	0.781019i	0.547522	−	0.836791i	$-0.315571\pi$
$877$	−13.3537	−	23.1292i	−0.450921	−	0.781019i	−0.998443	+	0.0557726i	$0.982238\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	33.6239			1.13282			0.566408	−	0.824125i	$-0.308333\pi$
$881$	33.6239			1.13282			0.566408	+	0.824125i	$0.308333\pi$
$882$		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
$887$	2.39373	+	4.14606i	0.0803736	+	0.139211i	0.903410	−	0.428777i	$-0.141055\pi$
$887$	2.39373	+	4.14606i	0.0803736	+	0.139211i	−0.823037	+	0.567988i	$0.807722\pi$
$888$		0			0
$889$	19.6381	−	8.78560i	0.658642	−	0.294660i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.62759	+	14.9434i	−0.288711	+	0.500062i
$894$		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
$905$	−20.0980	−	34.8108i	−0.668081	−	1.15715i
$906$		0			0
$907$	17.4176	−	30.1681i	0.578341	−	1.00172i	−0.417329	−	0.908755i	$-0.637034\pi$
$907$	17.4176	−	30.1681i	0.578341	−	1.00172i	0.995670	−	0.0929599i	$-0.0296328\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	29.1584	+	50.5038i	0.966060	+	1.67326i	0.706740	+	0.707473i	$0.250165\pi$
$911$	29.1584	+	50.5038i	0.966060	+	1.67326i	0.259319	+	0.965792i	$0.416502\pi$
$912$		0			0
$913$	−75.5589			−2.50063
$914$		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	−0.867899	−	0.496740i	$-0.834530\pi$
$919$	−0.113983	+	0.197424i	−0.00375995	+	0.00651242i	0.864139	+	0.503253i	$0.167863\pi$
$920$		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
$929$	−24.8851			−0.816453			−0.408226	−	0.912881i	$-0.633853\pi$
$929$	−24.8851			−0.816453			−0.408226	+	0.912881i	$0.633853\pi$
$930$		0			0
$931$	6.53281	+	19.8638i	0.214104	+	0.651008i
$932$		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
$941$	60.2820			1.96514			0.982568	−	0.185904i	$-0.0595215\pi$
$941$	60.2820			1.96514			0.982568	+	0.185904i	$0.0595215\pi$
$942$		0			0
$943$	−1.44057			−0.0469115
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.5977			−0.474361			−0.237180	−	0.971466i	$-0.576223\pi$
$947$	−14.5977			−0.474361			−0.237180	+	0.971466i	$0.576223\pi$
$948$		0			0
$949$	−13.0371			−0.423202
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.9601			0.387427			0.193713	−	0.981058i	$-0.437947\pi$
$953$	11.9601			0.387427			0.193713	+	0.981058i	$0.437947\pi$
$954$		0			0
$955$	−1.69086	−	2.92865i	−0.0547148	−	0.0947688i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.40212	+	42.6168i	−0.142152	+	1.37617i
$960$		0			0
$961$	−3.05319			−0.0984899
$962$		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	$-0.820521\pi$
$971$	1.25397	−	2.17194i	0.0402418	−	0.0697009i	0.885445	+	0.464745i	$0.153854\pi$
$972$		0			0
$973$	1.67030	−	16.1701i	0.0535472	−	0.518390i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−57.6201			−1.84343			−0.921715	−	0.387867i	$-0.873212\pi$
$977$	−57.6201			−1.84343			−0.921715	+	0.387867i	$0.873212\pi$
$978$		0			0
$979$	4.21499	+	7.30058i	0.134712	+	0.233328i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−29.6868	+	51.4190i	−0.946862	+	1.64001i	−0.194881	+	0.980827i	$0.562432\pi$
$983$	−29.6868	+	51.4190i	−0.946862	+	1.64001i	−0.751980	+	0.659186i	$0.770901\pi$
$984$		0			0
$985$	−13.7570	−	23.8278i	−0.438333	−	0.759215i
$986$		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	−0.984814	−	0.173610i	$-0.944457\pi$
$991$	−20.2341	−	35.0465i	−0.642758	−	1.11329i	0.342057	−	0.939679i	$-0.388877\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−22.4190	+	38.8308i	−0.710730	+	1.23102i
$996$		0			0
$997$	7.07112	−	12.2475i	0.223945	−	0.387883i	−0.732058	−	0.681243i	$-0.761440\pi$
$997$	7.07112	−	12.2475i	0.223945	−	0.387883i	0.956002	+	0.293359i	$0.0947732\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.n.2053.7		16
3.2	odd	2	inner	2268.2.i.n.2053.2		16
7.4	even	3		2268.2.l.n.109.2		16
9.2	odd	6		2268.2.l.n.541.7		16
9.4	even	3		2268.2.k.g.1297.7	yes	16
9.5	odd	6		2268.2.k.g.1297.2	✓	16
9.7	even	3		2268.2.l.n.541.2		16
21.11	odd	6		2268.2.l.n.109.7		16
63.4	even	3		2268.2.k.g.1621.7	yes	16
63.11	odd	6	inner	2268.2.i.n.865.2		16
63.25	even	3	inner	2268.2.i.n.865.7		16
63.32	odd	6		2268.2.k.g.1621.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.2		16	63.11	odd	6	inner
2268.2.i.n.865.7		16	63.25	even	3	inner
2268.2.i.n.2053.2		16	3.2	odd	2	inner
2268.2.i.n.2053.7		16	1.1	even	1	trivial
2268.2.k.g.1297.2	✓	16	9.5	odd	6
2268.2.k.g.1297.7	yes	16	9.4	even	3
2268.2.k.g.1621.2	yes	16	63.32	odd	6
2268.2.k.g.1621.7	yes	16	63.4	even	3
2268.2.l.n.109.2		16	7.4	even	3
2268.2.l.n.109.7		16	21.11	odd	6
2268.2.l.n.541.2		16	9.7	even	3
2268.2.l.n.541.7		16	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +O(q^{10})\)	\(q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +(-2.23145 + 3.86499i) q^{11} +(1.42148 - 2.46208i) q^{13} +(-0.115312 - 0.199726i) q^{17} +(-1.49360 + 2.58700i) q^{19} +(0.400294 + 0.693329i) q^{23} +(-0.149635 + 0.259175i) q^{25} +(3.82751 + 6.62944i) q^{29} +5.28647 q^{31} +(4.93376 + 3.57112i) q^{35} +(-1.69333 + 2.93293i) q^{37} +(-0.899697 + 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +5.77636 q^{47} +(4.66527 - 5.21874i) q^{49} +(-4.31905 - 7.48081i) q^{53} -10.2737 q^{55} -8.35585 q^{59} -13.1735 q^{61} +6.54454 q^{65} -7.53090 q^{67} +8.59672 q^{71} +(-2.29287 - 3.97137i) q^{73} +(-1.21323 + 11.7453i) q^{77} +9.67313 q^{79} +(8.46521 + 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(0.944450 - 1.63584i) q^{89} +(0.772852 - 7.48196i) q^{91} -6.87659 q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) 16 * q - 6 * q^7 + 10 * q^13 + 8 * q^19 + 16 * q^31 - 4 * q^37 - 10 * q^43 + 10 * q^49 - 32 * q^55 - 56 * q^61 - 36 * q^67 + 40 * q^79 - 38 * q^85 - 2 * q^91 + 42 * q^97

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