LMFDB - Embedded newform 2016.2.s.j.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2016,2,Mod(289,2016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2016, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2016.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.s (of order $3$, degree $2$, 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:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2016.289
Dual form			2016.2.s.j.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{11} +(-4.00000 - 6.92820i) q^{17} +(2.00000 - 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{29} +(-3.50000 - 6.06218i) q^{31} +(2.00000 - 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{41} +10.0000 q^{43} +(3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{53} +1.00000 q^{55} +(4.50000 + 7.79423i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-1.00000 - 1.73205i) q^{67} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(0.500000 + 2.59808i) q^{77} +(4.50000 - 7.79423i) q^{79} +3.00000 q^{83} -8.00000 q^{85} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 - 3.46410i) q^{95} -1.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{5} + 5 q^{7}+O(q^{10}) $ 2 * q + q^5 + 5 * q^7	$ 2 q + q^{5} + 5 q^{7} + q^{11} - 8 q^{17} + 4 q^{19} + 4 q^{23} + 4 q^{25} + 10 q^{29} - 7 q^{31} + 4 q^{35} - 8 q^{37} - 8 q^{41} + 20 q^{43} + 6 q^{47} + 11 q^{49} - q^{53} + 2 q^{55} + 9 q^{59} + 2 q^{61} - 2 q^{67} - 12 q^{71} - 2 q^{73} + q^{77} + 9 q^{79} + 6 q^{83} - 16 q^{85} - 6 q^{89} - 4 q^{95} - 2 q^{97}+O(q^{100}) $ 2 * q + q^5 + 5 * q^7 + q^11 - 8 * q^17 + 4 * q^19 + 4 * q^23 + 4 * q^25 + 10 * q^29 - 7 * q^31 + 4 * q^35 - 8 * q^37 - 8 * q^41 + 20 * q^43 + 6 * q^47 + 11 * q^49 - q^53 + 2 * q^55 + 9 * q^59 + 2 * q^61 - 2 * q^67 - 12 * q^71 - 2 * q^73 + q^77 + 9 * q^79 + 6 * q^83 - 16 * q^85 - 6 * q^89 - 4 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.275029	−	0.961436i	$-0.588688\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		0			0
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.500000	+	2.59808i	0.0569803	+	0.296078i
$78$		0			0
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	−0.493684	−	0.869641i	$-0.664350\pi$
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	0.999974	−	0.00727784i	$-0.00231663\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	−0.233900	−	0.972261i	$-0.575149\pi$
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	0.958952	−	0.283567i	$-0.0915178\pi$
$108$		0			0
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.00000	−	20.7846i	−0.366679	−	1.90532i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.50000	+	16.4545i	−0.830019	+	1.43763i	0.0680035	+	0.997685i	$0.478337\pi$
$131$	−9.50000	+	16.4545i	−0.830019	+	1.43763i	−0.898022	+	0.439950i	$0.854996\pi$
$132$		0			0
$133$	8.00000	−	6.92820i	0.693688	−	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$		0			0
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	2.50000	−	4.33013i	0.207614	−	0.359597i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	0.687741	−	0.725956i	$-0.258602\pi$
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	−0.972567	+	0.232623i	$0.925269\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.00000			−0.562254
$156$		0			0
$157$	−10.0000	−	17.3205i	−0.798087	−	1.38233i	−0.920860	−	0.389892i	$-0.872512\pi$
$157$	−10.0000	−	17.3205i	−0.798087	−	1.38233i	0.122774	−	0.992435i	$-0.460821\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.00000	−	6.92820i	0.630488	−	0.546019i
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$	2.00000	+	10.3923i	0.151186	+	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	0.949048	+	0.315130i	$0.102048\pi$
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	−0.201613	+	0.979465i	$0.564618\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.5000	+	4.33013i	0.877328	+	0.303915i
$204$		0			0
$205$	−2.00000	+	3.46410i	−0.139686	+	0.241943i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$	−3.50000	−	18.1865i	−0.237595	−	1.23458i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.50000	+	6.06218i	0.232303	+	0.402361i	0.958485	−	0.285141i	$-0.0920405\pi$
$227$	3.50000	+	6.06218i	0.232303	+	0.402361i	−0.726182	+	0.687502i	$0.758707\pi$
$228$		0			0
$229$	−12.0000	+	20.7846i	−0.792982	+	1.37349i	0.131130	+	0.991365i	$0.458139\pi$
$229$	−12.0000	+	20.7846i	−0.792982	+	1.37349i	−0.924113	+	0.382121i	$0.875194\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.00000	+	6.92820i	−0.262049	+	0.453882i	−0.966786	−	0.255586i	$-0.917731\pi$
$233$	−4.00000	+	6.92820i	−0.262049	+	0.453882i	0.704737	+	0.709468i	$0.251065\pi$
$234$		0			0
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.00000			−0.0631194			−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000			−0.0631194			−0.0315597	+	0.999502i	$0.510047\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$		0			0
$259$	−16.0000	+	13.8564i	−0.994192	+	0.860995i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.791658	−	0.610964i	$-0.790782\pi$
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.133281	−	0.991078i	$-0.542551\pi$
$264$		0			0
$265$	−1.00000			−0.0614295
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.50000	−	14.7224i	−0.518254	−	0.897643i	−0.999775	−	0.0212079i	$-0.993249\pi$
$269$	−8.50000	−	14.7224i	−0.518254	−	0.897643i	0.481521	−	0.876435i	$-0.340085\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	12.0000	+	20.7846i	0.721010	+	1.24883i	0.960595	+	0.277951i	$0.0896552\pi$
$277$	12.0000	+	20.7846i	0.721010	+	1.24883i	−0.239585	+	0.970875i	$0.577011\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	3.00000	+	5.19615i	0.178331	+	0.308879i	0.941309	−	0.337546i	$-0.109597\pi$
$283$	3.00000	+	5.19615i	0.178331	+	0.308879i	−0.762978	+	0.646425i	$0.776263\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.0000	−	3.46410i	−0.590281	−	0.204479i
$288$		0			0
$289$	−23.5000	+	40.7032i	−1.38235	+	2.39431i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.00000			−0.175262			−0.0876309	−	0.996153i	$-0.527930\pi$
$293$	−3.00000			−0.175262			−0.0876309	+	0.996153i	$0.527930\pi$
$294$		0			0
$295$	9.00000			0.524000
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	25.0000	+	8.66025i	1.44098	+	0.499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.0000	+	24.2487i	0.793867	+	1.37502i	0.923556	+	0.383464i	$0.125269\pi$
$311$	14.0000	+	24.2487i	0.793867	+	1.37502i	−0.129689	+	0.991555i	$0.541398\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.50000	+	4.33013i	−0.140414	+	0.243204i	−0.927653	−	0.373444i	$-0.878177\pi$
$317$	−2.50000	+	4.33013i	−0.140414	+	0.243204i	0.787239	+	0.616649i	$0.211510\pi$
$318$		0			0
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−32.0000			−1.78053
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000	−	10.3923i	0.661581	−	0.572946i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.00000			−0.109272
$336$		0			0
$337$	1.00000			0.0544735			0.0272367	−	0.999629i	$-0.491329\pi$
$337$	1.00000			0.0544735			0.0272367	+	0.999629i	$0.491329\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.50000	−	6.06218i	0.189536	−	0.328285i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	0.902516	−	0.430656i	$-0.141718\pi$
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	−0.824217	+	0.566274i	$0.808384\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.500000	−	2.59808i	−0.0259587	−	0.134885i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.0000	+	29.4449i	−0.868659	+	1.50456i	−0.00529229	+	0.999986i	$0.501685\pi$
$383$	−17.0000	+	29.4449i	−0.868659	+	1.50456i	−0.863367	+	0.504576i	$0.831649\pi$
$384$		0			0
$385$	2.50000	+	0.866025i	0.127412	+	0.0441367i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	−0.870059	−	0.492947i	$-0.835920\pi$
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	0.00812520	−	0.999967i	$-0.497414\pi$
$390$		0			0
$391$	−32.0000			−1.61831
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.50000	−	7.79423i	−0.226420	−	0.392170i
$396$		0			0
$397$	−2.00000	+	3.46410i	−0.100377	+	0.173858i	−0.911840	−	0.410546i	$-0.865338\pi$
$397$	−2.00000	+	3.46410i	−0.100377	+	0.173858i	0.811463	+	0.584404i	$0.198672\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−16.0000	+	27.7128i	−0.799002	+	1.38391i	0.121265	+	0.992620i	$0.461305\pi$
$401$	−16.0000	+	27.7128i	−0.799002	+	1.38391i	−0.920267	+	0.391292i	$0.872028\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	−0.996701	−	0.0811615i	$-0.974137\pi$
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	0.428063	−	0.903749i	$-0.359196\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.50000	+	23.3827i	0.221431	+	1.15059i
$414$		0			0
$415$	1.50000	−	2.59808i	0.0736321	−	0.127535i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	16.0000	−	27.7128i	0.776114	−	1.34427i
$426$		0			0
$427$	4.00000	−	3.46410i	0.193574	−	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$	30.0000			1.44171			0.720854	−	0.693087i	$-0.243750\pi$
$433$	30.0000			1.44171			0.720854	+	0.693087i	$0.243750\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.00000	−	13.8564i	−0.382692	−	0.662842i
$438$		0			0
$439$	−9.50000	+	16.4545i	−0.453410	+	0.785330i	−0.998595	−	0.0529862i	$-0.983126\pi$
$439$	−9.50000	+	16.4545i	−0.453410	+	0.785330i	0.545185	+	0.838316i	$0.316459\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.5000	−	25.1147i	0.688916	−	1.19324i	−0.283273	−	0.959039i	$-0.591420\pi$
$443$	14.5000	−	25.1147i	0.688916	−	1.19324i	0.972189	−	0.234198i	$-0.0752464\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$		0			0
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	−0.986396	−	0.164386i	$-0.947436\pi$
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	0.635561	+	0.772051i	$0.280769\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$		0			0
$469$	−1.00000	−	5.19615i	−0.0461757	−	0.239936i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$		0			0
$475$	16.0000			0.734130
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.500000	+	0.866025i	−0.0227038	+	0.0393242i
$486$		0			0
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	0.967632	+	0.252367i	$0.0812090\pi$
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	−0.265260	+	0.964177i	$0.585458\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$		0			0
$493$	−20.0000	−	34.6410i	−0.900755	−	1.56015i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$		0			0
$499$	−17.0000	+	29.4449i	−0.761025	+	1.31813i	0.181298	+	0.983428i	$0.441970\pi$
$499$	−17.0000	+	29.4449i	−0.761025	+	1.31813i	−0.942323	+	0.334705i	$0.891363\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$		0			0
$511$	−1.00000	−	5.19615i	−0.0442374	−	0.229864i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$		0			0
$517$	6.00000			0.263880
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.00000	+	12.1244i	0.306676	+	0.531178i	0.977633	−	0.210318i	$-0.0674500\pi$
$521$	7.00000	+	12.1244i	0.306676	+	0.531178i	−0.670957	+	0.741496i	$0.734117\pi$
$522$		0			0
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	0.765222	+	0.643767i	$0.222629\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−28.0000	+	48.4974i	−1.21970	+	2.11258i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−7.50000	−	12.9904i	−0.324253	−	0.561623i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.00000	+	6.92820i	−0.0430730	+	0.298419i
$540$		0			0
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	−0.999520	−	0.0309841i	$-0.990136\pi$
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	0.526593	+	0.850118i	$0.323469\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−10.0000			−0.428353
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.0000	−	17.3205i	0.426014	−	0.737878i
$552$		0			0
$553$	18.0000	−	15.5885i	0.765438	−	0.662889i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	0.945473	−	0.325701i	$-0.105600\pi$
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	−0.754802	+	0.655953i	$0.772267\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.5000	+	25.1147i	0.611102	+	1.05846i	0.991055	+	0.133454i	$0.0426069\pi$
$563$	14.5000	+	25.1147i	0.611102	+	1.05846i	−0.379953	+	0.925006i	$0.624060\pi$
$564$		0			0
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	−0.963948	−	0.266090i	$-0.914268\pi$
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	0.712415	+	0.701758i	$0.247601\pi$
$570$		0			0
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	0.681563	−	0.731760i	$-0.261301\pi$
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	−0.974504	+	0.224371i	$0.927967\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.0000			0.667246
$576$		0			0
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	0.520952	−	0.853586i	$-0.325577\pi$
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	−0.999703	+	0.0243645i	$0.992244\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.50000	+	2.59808i	0.311152	+	0.107786i
$582$		0			0
$583$	0.500000	−	0.866025i	0.0207079	−	0.0358671i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.0000			−0.619116			−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000			−0.619116			−0.309558	+	0.950881i	$0.600181\pi$
$588$		0			0
$589$	−28.0000			−1.15372
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$	−20.0000	−	6.92820i	−0.819920	−	0.284029i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	−12.5000	+	21.6506i	−0.507359	+	0.878772i	0.492604	+	0.870253i	$0.336045\pi$
$607$	−12.5000	+	21.6506i	−0.507359	+	0.878772i	−0.999964	+	0.00851879i	$0.997288\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−22.0000	−	38.1051i	−0.888572	−	1.53905i	−0.841564	−	0.540157i	$-0.818365\pi$
$613$	−22.0000	−	38.1051i	−0.888572	−	1.53905i	−0.0470071	−	0.998895i	$-0.514968\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.0000	+	10.3923i	−0.480770	+	0.416359i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	64.0000			2.55185
$630$		0			0
$631$	33.0000			1.31371			0.656855	−	0.754017i	$-0.271887\pi$
$631$	33.0000			1.31371			0.656855	+	0.754017i	$0.271887\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.50000	−	11.2583i	0.257945	−	0.446773i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.0000	+	32.9090i	0.750455	+	1.29983i	0.947602	+	0.319452i	$0.103499\pi$
$641$	19.0000	+	32.9090i	0.750455	+	1.29983i	−0.197148	+	0.980374i	$0.563168\pi$
$642$		0			0
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.00000	+	8.66025i	0.196570	+	0.340470i	0.947414	−	0.320010i	$-0.103686\pi$
$647$	5.00000	+	8.66025i	0.196570	+	0.340470i	−0.750844	+	0.660480i	$0.770353\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.5000	+	26.8468i	−0.606562	+	1.05060i	0.385241	+	0.922816i	$0.374118\pi$
$653$	−15.5000	+	26.8468i	−0.606562	+	1.05060i	−0.991803	+	0.127780i	$0.959215\pi$
$654$		0			0
$655$	9.50000	+	16.4545i	0.371196	+	0.642930i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.0000			−0.623272			−0.311636	−	0.950202i	$-0.600877\pi$
$659$	−16.0000			−0.623272			−0.311636	+	0.950202i	$0.600877\pi$
$660$		0			0
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	0.636200	−	0.771524i	$-0.280505\pi$
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	−0.986260	+	0.165203i	$0.947172\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.00000	−	10.3923i	−0.0775567	−	0.402996i
$666$		0			0
$667$	10.0000	−	17.3205i	0.387202	−	0.670653i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.00000			0.0772091
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	0.480913	+	0.876768i	$0.340305\pi$
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	−0.999760	+	0.0219013i	$0.993028\pi$
$678$		0			0
$679$	−2.50000	−	0.866025i	−0.0959412	−	0.0332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−18.5000	−	32.0429i	−0.707883	−	1.22609i	−0.965641	−	0.259880i	$-0.916317\pi$
$683$	−18.5000	−	32.0429i	−0.707883	−	1.22609i	0.257758	−	0.966209i	$-0.417016\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$		0			0
$697$	16.0000	+	27.7128i	0.606043	+	1.04970i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.00000	+	5.19615i	0.0376089	+	0.195421i
$708$		0			0
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−28.0000			−1.04861
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.00000	−	8.66025i	0.186469	−	0.322973i	−0.757602	−	0.652717i	$-0.773629\pi$
$719$	5.00000	−	8.66025i	0.186469	−	0.322973i	0.944070	+	0.329744i	$0.106962\pi$
$720$		0			0
$721$	32.0000	−	27.7128i	1.19174	−	1.03208i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.0000	+	17.3205i	0.371391	+	0.643268i
$726$		0			0
$727$	19.0000			0.704671			0.352335	−	0.935874i	$-0.385388\pi$
$727$	19.0000			0.704671			0.352335	+	0.935874i	$0.385388\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−40.0000	−	69.2820i	−1.47945	−	2.56249i
$732$		0			0
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.00000	−	1.73205i	0.0368355	−	0.0638009i
$738$		0			0
$739$	−17.0000	−	29.4449i	−0.625355	−	1.08315i	−0.988472	−	0.151403i	$-0.951621\pi$
$739$	−17.0000	−	29.4449i	−0.625355	−	1.08315i	0.363117	−	0.931744i	$-0.381713\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	38.0000			1.39408			0.697042	−	0.717030i	$-0.254499\pi$
$743$	38.0000			1.39408			0.697042	+	0.717030i	$0.254499\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	30.0000	−	25.9808i	1.09618	−	0.949316i
$750$		0			0
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	−0.795075	−	0.606511i	$-0.792568\pi$
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	0.922792	+	0.385299i	$0.125902\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.00000			−0.254756
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$		0			0
$763$	−5.00000	−	25.9808i	−0.181012	−	0.940567i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−19.0000			−0.685158			−0.342579	−	0.939489i	$-0.611300\pi$
$769$	−19.0000			−0.685158			−0.342579	+	0.939489i	$0.611300\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$		0			0
$775$	14.0000	−	24.2487i	0.502895	−	0.871039i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.00000	+	13.8564i	−0.286630	+	0.496457i
$780$		0			0
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−20.0000			−0.713831
$786$		0			0
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	0.975798	+	0.218675i	$0.0701734\pi$
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	−0.298521	+	0.954403i	$0.596493\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.0000	−	3.46410i	−0.355559	−	0.123169i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	51.0000			1.80651			0.903256	−	0.429101i	$-0.141170\pi$
$797$	51.0000			1.80651			0.903256	+	0.429101i	$0.141170\pi$
$798$		0			0
$799$	−48.0000			−1.69812
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$		0			0
$805$	−2.00000	−	10.3923i	−0.0704907	−	0.366281i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.0000	−	27.7128i	−0.562530	−	0.974331i	−0.997275	−	0.0737769i	$-0.976495\pi$
$809$	−16.0000	−	27.7128i	−0.562530	−	0.974331i	0.434745	−	0.900554i	$-0.356839\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$		0			0
$817$	20.0000	−	34.6410i	0.699711	−	1.21194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.500000	+	0.866025i	−0.0174501	+	0.0302245i	−0.874619	−	0.484812i	$-0.838888\pi$
$821$	−0.500000	+	0.866025i	−0.0174501	+	0.0302245i	0.857168	+	0.515036i	$0.172221\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	43.0000			1.49526			0.747628	−	0.664117i	$-0.231193\pi$
$827$	43.0000			1.49526			0.747628	+	0.664117i	$0.231193\pi$
$828$		0			0
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	−0.638457	+	0.769657i	$0.720427\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.00000	−	55.4256i	0.277184	−	1.92038i
$834$		0			0
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.00000			0.276191			0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000			0.276191			0.138095	+	0.990419i	$0.455902\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.50000	+	11.2583i	−0.223607	+	0.387298i
$846$		0			0
$847$	20.0000	−	17.3205i	0.687208	−	0.595140i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	16.0000	+	27.7128i	0.548473	+	0.949983i
$852$		0			0
$853$	42.0000			1.43805			0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000			1.43805			0.719026	+	0.694983i	$0.244588\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$		0			0
$859$	9.00000	−	15.5885i	0.307076	−	0.531871i	−0.670645	−	0.741778i	$-0.733983\pi$
$859$	9.00000	−	15.5885i	0.307076	−	0.531871i	0.977721	+	0.209907i	$0.0673161\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23.0000	+	39.8372i	−0.782929	+	1.35607i	0.147299	+	0.989092i	$0.452942\pi$
$863$	−23.0000	+	39.8372i	−0.782929	+	1.35607i	−0.930228	+	0.366981i	$0.880391\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.00000			0.305304
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	22.5000	+	7.79423i	0.760639	+	0.263493i
$876$		0			0
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	0.458606	+	0.888640i	$0.348349\pi$
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	−0.998888	+	0.0471555i	$0.984984\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.00000	−	3.46410i	0.0671534	−	0.116313i	−0.830494	−	0.557028i	$-0.811942\pi$
$887$	2.00000	−	3.46410i	0.0671534	−	0.116313i	0.897647	+	0.440715i	$0.145275\pi$
$888$		0			0
$889$	32.5000	+	11.2583i	1.09002	+	0.377592i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.0000	−	20.7846i	−0.401565	−	0.695530i
$894$		0			0
$895$	20.0000			0.668526
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.5000	−	30.3109i	−0.583658	−	1.01092i
$900$		0			0
$901$	−4.00000	+	6.92820i	−0.133259	+	0.230812i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.0000	−	17.3205i	0.332411	−	0.575753i
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	1.50000	+	2.59808i	0.0496428	+	0.0859838i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−38.0000	+	32.9090i	−1.25487	+	1.08675i
$918$		0			0
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−32.0000			−1.05215
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	−0.439932	−	0.898031i	$-0.644997\pi$
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	0.997684	−	0.0680235i	$-0.0216693\pi$
$930$		0			0
$931$	26.0000	−	10.3923i	0.852116	−	0.340594i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.00000	−	6.92820i	−0.130814	−	0.226576i
$936$		0			0
$937$	−29.0000			−0.947389			−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000			−0.947389			−0.473694	+	0.880689i	$0.657080\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−25.5000	−	44.1673i	−0.831276	−	1.43981i	−0.897027	−	0.441977i	$-0.854277\pi$
$941$	−25.5000	−	44.1673i	−0.831276	−	1.43981i	0.0657503	−	0.997836i	$-0.479056\pi$
$942$		0			0
$943$	−8.00000	+	13.8564i	−0.260516	+	0.451227i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.0000	−	34.6410i	0.649913	−	1.12568i	−0.333231	−	0.942845i	$-0.608139\pi$
$947$	20.0000	−	34.6410i	0.649913	−	1.12568i	0.983143	−	0.182836i	$-0.0585279\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.00000	+	46.7654i	0.290625	+	1.51013i
$960$		0			0
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.0000			0.354103
$966$		0			0
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	29.5000	−	51.0955i	0.946700	−	1.63973i	0.194389	−	0.980925i	$-0.437728\pi$
$971$	29.5000	−	51.0955i	0.946700	−	1.63973i	0.752311	−	0.658808i	$-0.228939\pi$
$972$		0			0
$973$	25.0000	+	8.66025i	0.801463	+	0.277635i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.0000	+	43.3013i	0.799821	+	1.38533i	0.919732	+	0.392546i	$0.128406\pi$
$977$	25.0000	+	43.3013i	0.799821	+	1.38533i	−0.119912	+	0.992785i	$0.538261\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	20.0000	−	34.6410i	0.635963	−	1.10152i
$990$		0			0
$991$	2.50000	+	4.33013i	0.0794151	+	0.137551i	0.902998	−	0.429645i	$-0.141361\pi$
$991$	2.50000	+	4.33013i	0.0794151	+	0.137551i	−0.823583	+	0.567196i	$0.808028\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.0000			−0.634043
$996$		0			0
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.s.j.289.1		2
3.2	odd	2		672.2.q.g.289.1	yes	2
4.3	odd	2		2016.2.s.i.289.1		2
7.4	even	3	inner	2016.2.s.j.865.1		2
12.11	even	2		672.2.q.b.289.1	yes	2
21.2	odd	6		4704.2.a.l.1.1		1
21.5	even	6		4704.2.a.w.1.1		1
21.11	odd	6		672.2.q.g.193.1	yes	2
24.5	odd	2		1344.2.q.h.961.1		2
24.11	even	2		1344.2.q.r.961.1		2
28.11	odd	6		2016.2.s.i.865.1		2
84.11	even	6		672.2.q.b.193.1	✓	2
84.23	even	6		4704.2.a.bc.1.1		1
84.47	odd	6		4704.2.a.f.1.1		1
168.5	even	6		9408.2.a.bb.1.1		1
168.11	even	6		1344.2.q.r.193.1		2
168.53	odd	6		1344.2.q.h.193.1		2
168.107	even	6		9408.2.a.o.1.1		1
168.131	odd	6		9408.2.a.cp.1.1		1
168.149	odd	6		9408.2.a.cg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.b.193.1	✓	2	84.11	even	6
672.2.q.b.289.1	yes	2	12.11	even	2
672.2.q.g.193.1	yes	2	21.11	odd	6
672.2.q.g.289.1	yes	2	3.2	odd	2
1344.2.q.h.193.1		2	168.53	odd	6
1344.2.q.h.961.1		2	24.5	odd	2
1344.2.q.r.193.1		2	168.11	even	6
1344.2.q.r.961.1		2	24.11	even	2
2016.2.s.i.289.1		2	4.3	odd	2
2016.2.s.i.865.1		2	28.11	odd	6
2016.2.s.j.289.1		2	1.1	even	1	trivial
2016.2.s.j.865.1		2	7.4	even	3	inner
4704.2.a.f.1.1		1	84.47	odd	6
4704.2.a.l.1.1		1	21.2	odd	6
4704.2.a.w.1.1		1	21.5	even	6
4704.2.a.bc.1.1		1	84.23	even	6
9408.2.a.o.1.1		1	168.107	even	6
9408.2.a.bb.1.1		1	168.5	even	6
9408.2.a.cg.1.1		1	168.149	odd	6
9408.2.a.cp.1.1		1	168.131	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:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{11} +(-4.00000 - 6.92820i) q^{17} +(2.00000 - 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{29} +(-3.50000 - 6.06218i) q^{31} +(2.00000 - 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{41} +10.0000 q^{43} +(3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{53} +1.00000 q^{55} +(4.50000 + 7.79423i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-1.00000 - 1.73205i) q^{67} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(0.500000 + 2.59808i) q^{77} +(4.50000 - 7.79423i) q^{79} +3.00000 q^{83} -8.00000 q^{85} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 - 3.46410i) q^{95} -1.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5} + 5 q^{7}+O(q^{10}) \) 2 * q + q^5 + 5 * q^7	\( 2 q + q^{5} + 5 q^{7} + q^{11} - 8 q^{17} + 4 q^{19} + 4 q^{23} + 4 q^{25} + 10 q^{29} - 7 q^{31} + 4 q^{35} - 8 q^{37} - 8 q^{41} + 20 q^{43} + 6 q^{47} + 11 q^{49} - q^{53} + 2 q^{55} + 9 q^{59} + 2 q^{61} - 2 q^{67} - 12 q^{71} - 2 q^{73} + q^{77} + 9 q^{79} + 6 q^{83} - 16 q^{85} - 6 q^{89} - 4 q^{95} - 2 q^{97}+O(q^{100}) \) 2 * q + q^5 + 5 * q^7 + q^11 - 8 * q^17 + 4 * q^19 + 4 * q^23 + 4 * q^25 + 10 * q^29 - 7 * q^31 + 4 * q^35 - 8 * q^37 - 8 * q^41 + 20 * q^43 + 6 * q^47 + 11 * q^49 - q^53 + 2 * q^55 + 9 * q^59 + 2 * q^61 - 2 * q^67 - 12 * q^71 - 2 * q^73 + q^77 + 9 * q^79 + 6 * q^83 - 16 * q^85 - 6 * q^89 - 4 * q^95 - 2 * q^97

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