LMFDB - Embedded newform 1512.2.s.l.1297.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(865,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1512.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1512.1297
Dual form			1512.2.s.l.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849814 + 1.47192i) q^{5} +(-2.64400 + 0.0963576i) q^{7} +O(q^{10})$	$q+(-0.849814 + 1.47192i) q^{5} +(-2.64400 + 0.0963576i) q^{7} +(-2.14400 - 3.71351i) q^{11} +2.69963 q^{13} +(1.64400 + 2.84748i) q^{17} +(1.79418 - 3.10761i) q^{19} +(1.29418 - 2.24159i) q^{23} +(1.05563 + 1.82841i) q^{25} -7.68725 q^{29} +(0.461078 + 0.798611i) q^{31} +(2.10507 - 3.97364i) q^{35} +(5.23236 - 9.06271i) q^{37} +5.76509 q^{41} +11.0865 q^{43} +(2.66071 - 4.60848i) q^{47} +(6.98143 - 0.509538i) q^{49} +(2.23855 + 3.87728i) q^{53} +7.28799 q^{55} +(4.60507 + 7.97622i) q^{59} +(4.08836 - 7.08125i) q^{61} +(-2.29418 + 3.97364i) q^{65} +(1.81708 + 3.14728i) q^{67} -10.1643 q^{71} +(-0.333104 - 0.576953i) q^{73} +(6.02654 + 9.61192i) q^{77} +(4.88255 - 8.45682i) q^{79} -1.25457 q^{83} -5.58836 q^{85} +(-0.800372 + 1.38628i) q^{89} +(-7.13781 + 0.260130i) q^{91} +(3.04944 + 5.28179i) q^{95} +0.823272 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q + q^5 - 4 * q^7	$ 6 q + q^{5} - 4 q^{7} - q^{11} + 4 q^{13} - 2 q^{17} + 5 q^{19} + 2 q^{23} + 6 q^{25} + 2 q^{29} - 4 q^{31} - 6 q^{35} + 8 q^{37} - 6 q^{43} - 3 q^{47} - 12 q^{49} + 8 q^{53} + 20 q^{55} + 9 q^{59} + 13 q^{61} - 8 q^{65} + 16 q^{67} - 2 q^{71} - 3 q^{73} + 7 q^{77} + 12 q^{79} + 2 q^{83} - 22 q^{85} - 17 q^{89} - 13 q^{91} + 28 q^{97}+O(q^{100}) $ 6 * q + q^5 - 4 * q^7 - q^11 + 4 * q^13 - 2 * q^17 + 5 * q^19 + 2 * q^23 + 6 * q^25 + 2 * q^29 - 4 * q^31 - 6 * q^35 + 8 * q^37 - 6 * q^43 - 3 * q^47 - 12 * q^49 + 8 * q^53 + 20 * q^55 + 9 * q^59 + 13 * q^61 - 8 * q^65 + 16 * q^67 - 2 * q^71 - 3 * q^73 + 7 * q^77 + 12 * q^79 + 2 * q^83 - 22 * q^85 - 17 * q^89 - 13 * q^91 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	−0.849814	+	1.47192i	−0.380048	+	0.658263i	−0.991069	−	0.133352i	$-0.957426\pi$
$5$	−0.849814	+	1.47192i	−0.380048	+	0.658263i	0.611020	+	0.791615i	$0.290759\pi$
$6$		0			0
$7$	−2.64400	+	0.0963576i	−0.999337	+	0.0364197i
$7$	−2.64400	+	0.0963576i	−0.999337	+	0.0364197i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.14400	−	3.71351i	−0.646439	−	1.11967i	−0.983967	−	0.178350i	$-0.942924\pi$
$11$	−2.14400	−	3.71351i	−0.646439	−	1.11967i	0.337528	−	0.941315i	$-0.390409\pi$
$12$		0			0
$13$	2.69963			0.748742			0.374371	−	0.927279i	$-0.377859\pi$
$13$	2.69963			0.748742			0.374371	+	0.927279i	$0.377859\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.64400	+	2.84748i	0.398728	+	0.690616i	0.993569	−	0.113226i	$-0.0361186\pi$
$17$	1.64400	+	2.84748i	0.398728	+	0.690616i	−0.594842	+	0.803843i	$0.702785\pi$
$18$		0			0
$19$	1.79418	−	3.10761i	0.411614	−	0.712936i	−0.583453	−	0.812147i	$-0.698299\pi$
$19$	1.79418	−	3.10761i	0.411614	−	0.712936i	0.995066	+	0.0992114i	$0.0316320\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.29418	−	2.24159i	0.269856	−	0.467404i	−0.698969	−	0.715152i	$-0.746357\pi$
$23$	1.29418	−	2.24159i	0.269856	−	0.467404i	0.968824	+	0.247749i	$0.0796907\pi$
$24$		0			0
$25$	1.05563	+	1.82841i	0.211126	+	0.365682i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.68725			−1.42749			−0.713743	−	0.700408i	$-0.753002\pi$
$29$	−7.68725			−1.42749			−0.713743	+	0.700408i	$0.753002\pi$
$30$		0			0
$31$	0.461078	+	0.798611i	0.0828121	+	0.143435i	0.904457	−	0.426565i	$-0.140277\pi$
$31$	0.461078	+	0.798611i	0.0828121	+	0.143435i	−0.821645	+	0.570000i	$0.806943\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.10507	−	3.97364i	0.355823	−	0.671668i
$36$		0			0
$37$	5.23236	−	9.06271i	0.860195	−	1.48990i	−0.0115460	−	0.999933i	$-0.503675\pi$
$37$	5.23236	−	9.06271i	0.860195	−	1.48990i	0.871741	−	0.489968i	$-0.162991\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.76509			0.900356			0.450178	−	0.892939i	$-0.351361\pi$
$41$	5.76509			0.900356			0.450178	+	0.892939i	$0.351361\pi$
$42$		0			0
$43$	11.0865			1.69068			0.845338	−	0.534232i	$-0.179399\pi$
$43$	11.0865			1.69068			0.845338	+	0.534232i	$0.179399\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.66071	−	4.60848i	0.388104	−	0.672216i	−0.604091	−	0.796916i	$-0.706463\pi$
$47$	2.66071	−	4.60848i	0.388104	−	0.672216i	0.992194	+	0.124700i	$0.0397968\pi$
$48$		0			0
$49$	6.98143	−	0.509538i	0.997347	−	0.0727912i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.23855	+	3.87728i	0.307488	+	0.532586i	0.977812	−	0.209483i	$-0.0671781\pi$
$53$	2.23855	+	3.87728i	0.307488	+	0.532586i	−0.670324	+	0.742069i	$0.733845\pi$
$54$		0			0
$55$	7.28799			0.982713
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.60507	+	7.97622i	0.599530	+	1.03842i	0.992890	+	0.119032i	$0.0379790\pi$
$59$	4.60507	+	7.97622i	0.599530	+	1.03842i	−0.393361	+	0.919384i	$0.628688\pi$
$60$		0			0
$61$	4.08836	−	7.08125i	0.523461	−	0.906662i	−0.476166	−	0.879356i	$-0.657974\pi$
$61$	4.08836	−	7.08125i	0.523461	−	0.906662i	0.999627	−	0.0273061i	$-0.00869289\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.29418	+	3.97364i	−0.284558	+	0.492869i
$66$		0			0
$67$	1.81708	+	3.14728i	0.221992	+	0.384501i	0.955413	−	0.295274i	$-0.0954108\pi$
$67$	1.81708	+	3.14728i	0.221992	+	0.384501i	−0.733421	+	0.679775i	$0.762077\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.1643			−1.20629			−0.603143	−	0.797633i	$-0.706085\pi$
$71$	−10.1643			−1.20629			−0.603143	+	0.797633i	$0.706085\pi$
$72$		0			0
$73$	−0.333104	−	0.576953i	−0.0389868	−	0.0675272i	0.845874	−	0.533383i	$-0.179080\pi$
$73$	−0.333104	−	0.576953i	−0.0389868	−	0.0675272i	−0.884860	+	0.465856i	$0.845746\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.02654	+	9.61192i	0.686788	+	1.09538i
$78$		0			0
$79$	4.88255	−	8.45682i	0.549329	−	0.951466i	−0.448991	−	0.893536i	$-0.648217\pi$
$79$	4.88255	−	8.45682i	0.549329	−	0.951466i	0.998321	−	0.0579302i	$-0.0184501\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.25457			−0.137707			−0.0688536	−	0.997627i	$-0.521934\pi$
$83$	−1.25457			−0.137707			−0.0688536	+	0.997627i	$0.521934\pi$
$84$		0			0
$85$	−5.58836			−0.606143
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.800372	+	1.38628i	−0.0848392	+	0.146946i	−0.905323	−	0.424724i	$-0.860371\pi$
$89$	−0.800372	+	1.38628i	−0.0848392	+	0.146946i	0.820483	+	0.571670i	$0.193704\pi$
$90$		0			0
$91$	−7.13781	+	0.260130i	−0.748245	+	0.0272690i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.04944	+	5.28179i	0.312866	+	0.541900i
$96$		0			0
$97$	0.823272			0.0835906			0.0417953	−	0.999126i	$-0.486692\pi$
$97$	0.823272			0.0835906			0.0417953	+	0.999126i	$0.486692\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.26145	−	2.18490i	−0.125519	−	0.217405i	0.796417	−	0.604748i	$-0.206726\pi$
$101$	−1.26145	−	2.18490i	−0.125519	−	0.217405i	−0.921936	+	0.387343i	$0.873393\pi$
$102$		0			0
$103$	6.08836	−	10.5454i	0.599904	−	1.03906i	−0.392930	−	0.919568i	$-0.628539\pi$
$103$	6.08836	−	10.5454i	0.599904	−	1.03906i	0.992835	−	0.119497i	$-0.0381280\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.49381	−	11.2476i	0.627780	−	1.08735i	−0.360216	−	0.932869i	$-0.617297\pi$
$107$	6.49381	−	11.2476i	0.627780	−	1.08735i	0.987996	−	0.154478i	$-0.0493697\pi$
$108$		0			0
$109$	7.51052	+	13.0086i	0.719377	+	1.24600i	0.961247	+	0.275689i	$0.0889061\pi$
$109$	7.51052	+	13.0086i	0.719377	+	1.24600i	−0.241869	+	0.970309i	$0.577761\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.73167			0.727334			0.363667	−	0.931529i	$-0.381525\pi$
$113$	7.73167			0.727334			0.363667	+	0.931529i	$0.381525\pi$
$114$		0			0
$115$	2.19963	+	3.80987i	0.205116	+	0.355272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.62110	−	7.37033i	−0.423615	−	0.675637i
$120$		0			0
$121$	−3.69344	+	6.39722i	−0.335767	+	0.581566i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0865			−1.08105
$126$		0			0
$127$	−16.3869			−1.45410			−0.727050	−	0.686584i	$-0.759109\pi$
$127$	−16.3869			−1.45410			−0.727050	+	0.686584i	$0.759109\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.4091	−	18.0291i	0.909446	−	1.57521i	0.0946111	−	0.995514i	$-0.469839\pi$
$131$	10.4091	−	18.0291i	0.909446	−	1.57521i	0.814835	−	0.579693i	$-0.196827\pi$
$132$		0			0
$133$	−4.44437	+	8.38940i	−0.385376	+	0.727454i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.81089	−	8.33271i	−0.411022	−	0.711911i	0.583980	−	0.811768i	$-0.301495\pi$
$137$	−4.81089	−	8.33271i	−0.411022	−	0.711911i	−0.995002	+	0.0998569i	$0.968161\pi$
$138$		0			0
$139$	17.2756			1.46530			0.732649	−	0.680606i	$-0.238284\pi$
$139$	17.2756			1.46530			0.732649	+	0.680606i	$0.238284\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.78799	−	10.0251i	−0.484016	−	0.838341i
$144$		0			0
$145$	6.53273	−	11.3150i	0.542514	−	0.939662i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.1156	+	17.5207i	−0.828702	+	1.43535i	0.0703552	+	0.997522i	$0.477587\pi$
$149$	−10.1156	+	17.5207i	−0.828702	+	1.43535i	−0.899057	+	0.437832i	$0.855747\pi$
$150$		0			0
$151$	0.656376	+	1.13688i	0.0534151	+	0.0925177i	0.891497	−	0.453027i	$-0.149656\pi$
$151$	0.656376	+	1.13688i	0.0534151	+	0.0925177i	−0.838082	+	0.545545i	$0.816323\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.56732			−0.125890
$156$		0			0
$157$	−10.6483	−	18.4434i	−0.849829	−	1.47195i	−0.881361	−	0.472444i	$-0.843372\pi$
$157$	−10.6483	−	18.4434i	−0.849829	−	1.47195i	0.0315316	−	0.999503i	$-0.489962\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.20582	+	6.05146i	−0.252654	+	0.476922i
$162$		0			0
$163$	−3.57165	+	6.18629i	−0.279754	+	0.484547i	−0.971323	−	0.237762i	$-0.923586\pi$
$163$	−3.57165	+	6.18629i	−0.279754	+	0.484547i	0.691570	+	0.722310i	$0.256919\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.49814			−0.580224			−0.290112	−	0.956993i	$-0.593692\pi$
$167$	−7.49814			−0.580224			−0.290112	+	0.956993i	$0.593692\pi$
$168$		0			0
$169$	−5.71201			−0.439385
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.967268	−	1.67536i	0.0735400	−	0.127375i	−0.826910	−	0.562334i	$-0.809904\pi$
$173$	0.967268	−	1.67536i	0.0735400	−	0.127375i	0.900450	+	0.434959i	$0.143237\pi$
$174$		0			0
$175$	−2.96727	−	4.73259i	−0.224304	−	0.357750i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.61491	−	9.72530i	−0.419678	−	0.726903i	0.576229	−	0.817288i	$-0.304524\pi$
$179$	−5.61491	−	9.72530i	−0.419678	−	0.726903i	−0.995907	+	0.0903850i	$0.971190\pi$
$180$		0			0
$181$	14.8974			1.10731			0.553657	−	0.832745i	$-0.313232\pi$
$181$	14.8974			1.10731			0.553657	+	0.832745i	$0.313232\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.89307	+	15.4032i	0.653831	+	1.13247i
$186$		0			0
$187$	7.04944	−	12.2100i	0.515506	−	0.892883i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.20946	+	5.55895i	−0.232228	+	0.402231i	−0.958464	−	0.285215i	$-0.907935\pi$
$191$	−3.20946	+	5.55895i	−0.232228	+	0.402231i	0.726235	+	0.687446i	$0.241268\pi$
$192$		0			0
$193$	6.07165	+	10.5164i	0.437047	+	0.756988i	0.997460	−	0.0712253i	$-0.0226909\pi$
$193$	6.07165	+	10.5164i	0.437047	+	0.756988i	−0.560413	+	0.828213i	$0.689358\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.6538			1.32903			0.664515	−	0.747275i	$-0.268638\pi$
$197$	18.6538			1.32903			0.664515	+	0.747275i	$0.268638\pi$
$198$		0			0
$199$	4.66435	+	8.07889i	0.330647	+	0.572697i	0.982639	−	0.185529i	$-0.0593998\pi$
$199$	4.66435	+	8.07889i	0.330647	+	0.572697i	−0.651992	+	0.758226i	$0.726066\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	20.3251	−	0.740725i	1.42654	−	0.0519887i
$204$		0			0
$205$	−4.89926	+	8.48576i	−0.342179	+	0.592671i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−15.3869			−1.06433
$210$		0			0
$211$	−2.71201			−0.186702			−0.0933512	−	0.995633i	$-0.529758\pi$
$211$	−2.71201			−0.186702			−0.0933512	+	0.995633i	$0.529758\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−9.42147	+	16.3185i	−0.642539	+	1.11291i
$216$		0			0
$217$	−1.29604	−	2.06710i	−0.0879810	−	0.140324i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.43818	+	7.68715i	0.298544	+	0.517094i
$222$		0			0
$223$	−16.0741			−1.07640			−0.538202	−	0.842816i	$-0.680896\pi$
$223$	−16.0741			−1.07640			−0.538202	+	0.842816i	$0.680896\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.25890	−	10.8407i	−0.415418	−	0.719525i	0.580054	−	0.814578i	$-0.303031\pi$
$227$	−6.25890	−	10.8407i	−0.415418	−	0.719525i	−0.995472	+	0.0950529i	$0.969698\pi$
$228$		0			0
$229$	−8.65816	+	14.9964i	−0.572147	+	0.990988i	0.424198	+	0.905569i	$0.360556\pi$
$229$	−8.65816	+	14.9964i	−0.572147	+	0.990988i	−0.996345	+	0.0854185i	$0.972777\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.67673	+	9.83238i	−0.371895	+	0.644141i	−0.989857	−	0.142067i	$-0.954625\pi$
$233$	−5.67673	+	9.83238i	−0.371895	+	0.644141i	0.617962	+	0.786208i	$0.287958\pi$
$234$		0			0
$235$	4.52221	+	7.83270i	0.294997	+	0.510949i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.341076			0.0220624			0.0110312	−	0.999939i	$-0.496489\pi$
$239$	0.341076			0.0220624			0.0110312	+	0.999939i	$0.496489\pi$
$240$		0			0
$241$	−10.8214	−	18.7432i	−0.697068	−	1.20736i	−0.969478	−	0.245177i	$-0.921154\pi$
$241$	−10.8214	−	18.7432i	−0.697068	−	1.20736i	0.272410	−	0.962181i	$-0.412179\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.18292	+	10.7091i	−0.331124	+	0.684181i
$246$		0			0
$247$	4.84362	−	8.38940i	0.308192	−	0.533805i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	26.8850			1.69697			0.848484	−	0.529222i	$-0.177516\pi$
$251$	26.8850			1.69697			0.848484	+	0.529222i	$0.177516\pi$
$252$		0			0
$253$	−11.0989			−0.697781
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.57784	−	4.46496i	0.160801	−	0.278516i	−0.774355	−	0.632752i	$-0.781925\pi$
$257$	2.57784	−	4.46496i	0.160801	−	0.278516i	0.935156	+	0.354235i	$0.115259\pi$
$258$		0			0
$259$	−12.9611	+	24.4660i	−0.805362	+	1.52024i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.70396	−	16.8077i	−0.598372	−	1.03641i	−0.993062	−	0.117596i	$-0.962481\pi$
$263$	−9.70396	−	16.8077i	−0.598372	−	1.03641i	0.394690	−	0.918814i	$-0.370852\pi$
$264$		0			0
$265$	−7.60940			−0.467442
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.9549	−	20.7065i	−0.728902	−	1.26250i	−0.957347	−	0.288939i	$-0.906697\pi$
$269$	−11.9549	−	20.7065i	−0.728902	−	1.26250i	0.228445	−	0.973557i	$-0.426636\pi$
$270$		0			0
$271$	−9.34727	+	16.1899i	−0.567806	+	0.983469i	0.428977	+	0.903316i	$0.358874\pi$
$271$	−9.34727	+	16.1899i	−0.567806	+	0.983469i	−0.996783	+	0.0801532i	$0.974459\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.52654	−	7.84020i	0.272961	−	0.472782i
$276$		0			0
$277$	8.33310	+	14.4334i	0.500688	+	0.867217i	1.00000		0.000794246i	$0.000252817\pi$
$277$	8.33310	+	14.4334i	0.500688	+	0.867217i	−0.499312	+	0.866422i	$0.666414\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.45744			0.206253			0.103127	−	0.994668i	$-0.467115\pi$
$281$	3.45744			0.206253			0.103127	+	0.994668i	$0.467115\pi$
$282$		0			0
$283$	−9.23236	−	15.9909i	−0.548807	−	0.950561i	−0.998357	−	0.0573061i	$-0.981749\pi$
$283$	−9.23236	−	15.9909i	−0.548807	−	0.950561i	0.449550	−	0.893255i	$-0.351584\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−15.2429	+	0.555510i	−0.899759	+	0.0327907i
$288$		0			0
$289$	3.09455	−	5.35992i	0.182033	−	0.315290i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	26.7156			1.56074			0.780370	−	0.625318i	$-0.215031\pi$
$293$	26.7156			1.56074			0.780370	+	0.625318i	$0.215031\pi$
$294$		0			0
$295$	−15.6538			−0.911401
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.49381	−	6.05146i	0.202052	−	0.349965i
$300$		0			0
$301$	−29.3127	+	1.06827i	−1.68955	+	0.0615740i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.94870	+	12.0355i	0.397881	+	0.689151i
$306$		0			0
$307$	−33.0370			−1.88552			−0.942760	−	0.333471i	$-0.891780\pi$
$307$	−33.0370			−1.88552			−0.942760	+	0.333471i	$0.891780\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.07784	+	12.2592i	0.401348	+	0.695155i	0.993889	−	0.110386i	$-0.0352086\pi$
$311$	7.07784	+	12.2592i	0.401348	+	0.695155i	−0.592541	+	0.805540i	$0.701875\pi$
$312$		0			0
$313$	4.64468	−	8.04483i	0.262533	−	0.454721i	−0.704381	−	0.709822i	$-0.748775\pi$
$313$	4.64468	−	8.04483i	0.262533	−	0.454721i	0.966914	+	0.255101i	$0.0821088\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.25959	−	7.37783i	0.239242	−	0.414380i	−0.721255	−	0.692670i	$-0.756434\pi$
$317$	4.25959	−	7.37783i	0.239242	−	0.414380i	0.960497	+	0.278290i	$0.0897676\pi$
$318$		0			0
$319$	16.4814	+	28.5467i	0.922783	+	1.59831i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	11.7985			0.656487
$324$		0			0
$325$	2.84981	+	4.93602i	0.158079	+	0.273801i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.59084	+	12.4412i	−0.363365	+	0.685904i
$330$		0			0
$331$	−3.42580	+	5.93366i	−0.188299	+	0.326143i	−0.944683	−	0.327984i	$-0.893631\pi$
$331$	−3.42580	+	5.93366i	−0.188299	+	0.326143i	0.756384	+	0.654128i	$0.226964\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.17673			−0.337471
$336$		0			0
$337$	−34.5068			−1.87971			−0.939853	−	0.341580i	$-0.889038\pi$
$337$	−34.5068			−1.87971			−0.939853	+	0.341580i	$0.889038\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.97710	−	3.42444i	0.107066	−	0.185444i
$342$		0			0
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.3090	+	19.5878i	0.607101	+	1.05153i	0.991716	+	0.128452i	$0.0410009\pi$
$347$	11.3090	+	19.5878i	0.607101	+	1.05153i	−0.384615	+	0.923077i	$0.625666\pi$
$348$		0			0
$349$	21.6080			1.15665			0.578326	−	0.815806i	$-0.303706\pi$
$349$	21.6080			1.15665			0.578326	+	0.815806i	$0.303706\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.94870	−	13.7675i	−0.423067	−	0.732773i	0.573171	−	0.819436i	$-0.305713\pi$
$353$	−7.94870	−	13.7675i	−0.423067	−	0.732773i	−0.996238	+	0.0866629i	$0.972380\pi$
$354$		0			0
$355$	8.63781	−	14.9611i	0.458447	−	0.794054i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.55563	−	6.15854i	0.187659	−	0.325035i	−0.756810	−	0.653635i	$-0.773243\pi$
$359$	3.55563	−	6.15854i	0.187659	−	0.325035i	0.944469	+	0.328600i	$0.106577\pi$
$360$		0			0
$361$	3.06182	+	5.30323i	0.161149	+	0.279117i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.13231			0.0592676
$366$		0			0
$367$	−1.51052	−	2.61630i	−0.0788485	−	0.136570i	0.823905	−	0.566728i	$-0.191791\pi$
$367$	−1.51052	−	2.61630i	−0.0788485	−	0.136570i	−0.902753	+	0.430158i	$0.858458\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.29232	−	10.0358i	−0.326681	−	0.521034i
$372$		0			0
$373$	−5.73167	+	9.92755i	−0.296775	+	0.514029i	−0.975396	−	0.220459i	$-0.929244\pi$
$373$	−5.73167	+	9.92755i	−0.296775	+	0.514029i	0.678621	+	0.734488i	$0.262578\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−20.7527			−1.06882
$378$		0			0
$379$	−26.9432			−1.38398			−0.691990	−	0.721908i	$-0.743266\pi$
$379$	−26.9432			−1.38398			−0.691990	+	0.721908i	$0.743266\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.4567	+	31.9679i	−0.943092	+	1.63348i	−0.183564	+	0.983008i	$0.558764\pi$
$383$	−18.4567	+	31.9679i	−0.943092	+	1.63348i	−0.759527	+	0.650475i	$0.774570\pi$
$384$		0			0
$385$	−19.2694	+	0.702253i	−0.982061	+	0.0357901i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.12797	+	3.68576i	0.107893	+	0.186875i	0.914916	−	0.403644i	$-0.132256\pi$
$389$	2.12797	+	3.68576i	0.107893	+	0.186875i	−0.807024	+	0.590519i	$0.798923\pi$
$390$		0			0
$391$	8.51052			0.430396
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.29851	+	14.3734i	0.417543	+	0.723207i
$396$		0			0
$397$	6.33929	−	10.9800i	0.318160	−	0.551069i	−0.661944	−	0.749553i	$-0.730268\pi$
$397$	6.33929	−	10.9800i	0.318160	−	0.551069i	0.980104	+	0.198484i	$0.0636017\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.64764	−	9.78200i	0.282030	−	0.488490i	−0.689855	−	0.723948i	$-0.742326\pi$
$401$	5.64764	−	9.78200i	0.282030	−	0.488490i	0.971885	+	0.235458i	$0.0756590\pi$
$402$		0			0
$403$	1.24474	+	2.15595i	0.0620049	+	0.107396i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−44.8726			−2.22425
$408$		0			0
$409$	19.1458	+	33.1615i	0.946698	+	1.63973i	0.752316	+	0.658803i	$0.228937\pi$
$409$	19.1458	+	33.1615i	0.946698	+	1.63973i	0.194382	+	0.980926i	$0.437730\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−12.9444	−	20.6454i	−0.636951	−	1.01589i
$414$		0			0
$415$	1.06615	−	1.84663i	0.0523354	−	0.0906475i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.3535			0.847772			0.423886	−	0.905716i	$-0.360666\pi$
$419$	17.3535			0.847772			0.423886	+	0.905716i	$0.360666\pi$
$420$		0			0
$421$	0.185389			0.00903532			0.00451766	−	0.999990i	$-0.498562\pi$
$421$	0.185389			0.00903532			0.00451766	+	0.999990i	$0.498562\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.47091	+	6.01179i	−0.168364	+	0.291615i
$426$		0			0
$427$	−10.1273	+	19.1168i	−0.490094	+	0.925125i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.08768	+	12.2762i	0.341401	+	0.591324i	0.984693	−	0.174297i	$-0.0557652\pi$
$431$	7.08768	+	12.2762i	0.341401	+	0.591324i	−0.643292	+	0.765621i	$0.722432\pi$
$432$		0			0
$433$	13.2101			0.634839			0.317420	−	0.948285i	$-0.397184\pi$
$433$	13.2101			0.634839			0.317420	+	0.948285i	$0.397184\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.64400	−	8.04364i	−0.222152	−	0.384779i
$438$		0			0
$439$	6.38874	−	11.0656i	0.304918	−	0.528133i	−0.672325	−	0.740256i	$-0.734704\pi$
$439$	6.38874	−	11.0656i	0.304918	−	0.528133i	0.977243	+	0.212123i	$0.0680377\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.3986	−	19.7429i	0.541562	−	0.938013i	−0.457252	−	0.889337i	$-0.651166\pi$
$443$	11.3986	−	19.7429i	0.541562	−	0.938013i	0.998815	−	0.0486764i	$-0.0155003\pi$
$444$		0			0
$445$	−1.36033	−	2.35617i	−0.0644860	−	0.111693i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	36.7330			1.73354			0.866770	−	0.498708i	$-0.166192\pi$
$449$	36.7330			1.73354			0.866770	+	0.498708i	$0.166192\pi$
$450$		0			0
$451$	−12.3603	−	21.4087i	−0.582025	−	1.00810i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.68292	−	10.7273i	0.266419	−	0.502906i
$456$		0			0
$457$	−11.7589	+	20.3670i	−0.550058	+	0.952729i	0.448211	+	0.893928i	$0.352061\pi$
$457$	−11.7589	+	20.3670i	−0.550058	+	0.952729i	−0.998270	+	0.0588013i	$0.981272\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.76509			−0.361656			−0.180828	−	0.983515i	$-0.557878\pi$
$461$	−7.76509			−0.361656			−0.180828	+	0.983515i	$0.557878\pi$
$462$		0			0
$463$	−11.5549			−0.537004			−0.268502	−	0.963279i	$-0.586529\pi$
$463$	−11.5549			−0.537004			−0.268502	+	0.963279i	$0.586529\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.1774	+	24.5560i	−0.656053	+	1.13632i	0.325576	+	0.945516i	$0.394442\pi$
$467$	−14.1774	+	24.5560i	−0.656053	+	1.13632i	−0.981629	+	0.190801i	$0.938892\pi$
$468$		0			0
$469$	−5.10762	−	8.14630i	−0.235848	−	0.376161i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−23.7694	−	41.1698i	−1.09292	−	1.89299i
$474$		0			0
$475$	7.57598			0.347610
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.1804	+	26.2932i	0.693609	+	1.20137i	0.970647	+	0.240507i	$0.0773137\pi$
$479$	15.1804	+	26.2932i	0.693609	+	1.20137i	−0.277039	+	0.960859i	$0.589353\pi$
$480$		0			0
$481$	14.1254	−	24.4660i	0.644064	−	1.11555i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.699628	+	1.21179i	−0.0317685	+	0.0550246i
$486$		0			0
$487$	9.02221	+	15.6269i	0.408835	+	0.708124i	0.994760	−	0.102242i	$-0.0326017\pi$
$487$	9.02221	+	15.6269i	0.408835	+	0.708124i	−0.585924	+	0.810366i	$0.699268\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−39.0865			−1.76395			−0.881975	−	0.471297i	$-0.843786\pi$
$491$	−39.0865			−1.76395			−0.881975	+	0.471297i	$0.843786\pi$
$492$		0			0
$493$	−12.6378	−	21.8893i	−0.569178	−	0.985846i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	26.8745	−	0.979412i	1.20549	−	0.0439326i
$498$		0			0
$499$	12.8862	−	22.3195i	0.576865	−	0.999159i	−0.418971	−	0.907999i	$-0.637609\pi$
$499$	12.8862	−	22.3195i	0.576865	−	0.999159i	0.995836	−	0.0911600i	$-0.0290575\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.90978			−0.0851527			−0.0425764	−	0.999093i	$-0.513557\pi$
$503$	−1.90978			−0.0851527			−0.0425764	+	0.999093i	$0.513557\pi$
$504$		0			0
$505$	4.28799			0.190813
$506$		0			0
$507$		0			0
$508$		0			0
$509$	18.2553	−	31.6190i	0.809150	−	1.40149i	−0.104303	−	0.994546i	$-0.533261\pi$
$509$	18.2553	−	31.6190i	0.809150	−	1.40149i	0.913453	−	0.406944i	$-0.133405\pi$
$510$		0			0
$511$	0.936319	+	1.49336i	0.0414203	+	0.0660625i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.3480	+	17.9232i	0.455985	+	0.789790i
$516$		0			0
$517$	−22.8182			−1.00354
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.2095	−	33.2718i	−0.841582	−	1.45766i	−0.888557	−	0.458766i	$-0.848292\pi$
$521$	−19.2095	−	33.2718i	−0.841582	−	1.45766i	0.0469753	−	0.998896i	$-0.485042\pi$
$522$		0			0
$523$	2.82946	−	4.90077i	0.123724	−	0.214296i	−0.797510	−	0.603306i	$-0.793850\pi$
$523$	2.82946	−	4.90077i	0.123724	−	0.214296i	0.921233	+	0.389010i	$0.127183\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.51602	+	2.62583i	−0.0660389	+	0.114383i
$528$		0			0
$529$	8.15019	+	14.1165i	0.354356	+	0.613762i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	15.5636			0.674135
$534$		0			0
$535$	11.0371	+	19.1168i	0.477174	+	0.826489i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−16.8603	−	24.8332i	−0.726226	−	1.06964i
$540$		0			0
$541$	12.2324	−	21.1871i	0.525910	−	0.910903i	−0.473634	−	0.880722i	$-0.657058\pi$
$541$	12.2324	−	21.1871i	0.525910	−	0.910903i	0.999544	−	0.0301816i	$-0.00960856\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−25.5302			−1.09359
$546$		0			0
$547$	13.5636			0.579938			0.289969	−	0.957036i	$-0.406355\pi$
$547$	13.5636			0.579938			0.289969	+	0.957036i	$0.406355\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.7923	+	23.8890i	−0.587573	+	1.01771i
$552$		0			0
$553$	−12.0946	+	22.8303i	−0.514313	+	0.970842i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.50619	+	6.07290i	0.148562	+	0.257317i	0.930696	−	0.365793i	$-0.119202\pi$
$557$	3.50619	+	6.07290i	0.148562	+	0.257317i	−0.782134	+	0.623110i	$0.785869\pi$
$558$		0			0
$559$	29.9294			1.26588
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.6731	+	21.9504i	0.534107	+	0.925100i	0.999206	+	0.0398417i	$0.0126854\pi$
$563$	12.6731	+	21.9504i	0.534107	+	0.925100i	−0.465099	+	0.885259i	$0.653981\pi$
$564$		0			0
$565$	−6.57048	+	11.3804i	−0.276422	+	0.478777i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.11559	−	3.66432i	0.0886903	−	0.153616i	−0.818267	−	0.574838i	$-0.805065\pi$
$569$	2.11559	−	3.66432i	0.0886903	−	0.153616i	0.906958	+	0.421222i	$0.138399\pi$
$570$		0			0
$571$	3.87890	+	6.71846i	0.162327	+	0.281159i	0.935703	−	0.352789i	$-0.114767\pi$
$571$	3.87890	+	6.71846i	0.162327	+	0.281159i	−0.773376	+	0.633948i	$0.781433\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	5.46472			0.227895
$576$		0			0
$577$	7.17123	+	12.4209i	0.298542	+	0.517090i	0.975803	−	0.218653i	$-0.0701663\pi$
$577$	7.17123	+	12.4209i	0.298542	+	0.517090i	−0.677261	+	0.735743i	$0.736833\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.31708	−	0.120887i	0.137616	−	0.00501526i
$582$		0			0
$583$	9.59888	−	16.6258i	0.397545	−	0.688568i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.1062			1.16007			0.580033	−	0.814593i	$-0.303040\pi$
$587$	28.1062			1.16007			0.580033	+	0.814593i	$0.303040\pi$
$588$		0			0
$589$	3.30903			0.136346
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.2262	+	33.3007i	−0.789524	+	1.36750i	0.136735	+	0.990608i	$0.456339\pi$
$593$	−19.2262	+	33.3007i	−0.789524	+	1.36750i	−0.926259	+	0.376888i	$0.876994\pi$
$594$		0			0
$595$	14.7756	−	0.538481i	0.605741	−	0.0220756i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.46796	−	2.54258i	−0.0599791	−	0.103887i	0.834477	−	0.551043i	$-0.185770\pi$
$599$	−1.46796	−	2.54258i	−0.0599791	−	0.103887i	−0.894456	+	0.447156i	$0.852437\pi$
$600$		0			0
$601$	−6.00728			−0.245042			−0.122521	−	0.992466i	$-0.539098\pi$
$601$	−6.00728			−0.245042			−0.122521	+	0.992466i	$0.539098\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.27747	−	10.8729i	−0.255216	−	0.442046i
$606$		0			0
$607$	12.2324	−	21.1871i	0.496496	−	0.859957i	−0.503496	−	0.863998i	$-0.667953\pi$
$607$	12.2324	−	21.1871i	0.496496	−	0.859957i	0.999992	+	0.00404115i	$0.00128634\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.18292	−	12.4412i	0.290590	−	0.503316i
$612$		0			0
$613$	−5.33675	−	9.24351i	−0.215549	−	0.373342i	0.737893	−	0.674918i	$-0.235821\pi$
$613$	−5.33675	−	9.24351i	−0.215549	−	0.373342i	−0.953442	+	0.301575i	$0.902487\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.71339			0.230012			0.115006	−	0.993365i	$-0.463311\pi$
$617$	5.71339			0.230012			0.115006	+	0.993365i	$0.463311\pi$
$618$		0			0
$619$	−4.79163	−	8.29935i	−0.192592	−	0.333579i	0.753516	−	0.657429i	$-0.228356\pi$
$619$	−4.79163	−	8.29935i	−0.192592	−	0.333579i	−0.946108	+	0.323850i	$0.895023\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.98260	−	3.74245i	0.0794312	−	0.149938i
$624$		0			0
$625$	4.99312	−	8.64834i	0.199725	−	0.345934i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	34.4079			1.37193
$630$		0			0
$631$	−21.4523			−0.854004			−0.427002	−	0.904251i	$-0.640430\pi$
$631$	−21.4523			−0.854004			−0.427002	+	0.904251i	$0.640430\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.9258	−	24.1202i	0.552628	−	0.957181i
$636$		0			0
$637$	18.8473	−	1.37556i	0.746756	−	0.0545018i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.8356	+	18.7678i	0.427979	+	0.741282i	0.996693	−	0.0812531i	$-0.0258922\pi$
$641$	10.8356	+	18.7678i	0.427979	+	0.741282i	−0.568714	+	0.822535i	$0.692559\pi$
$642$		0			0
$643$	−1.62907			−0.0642442			−0.0321221	−	0.999484i	$-0.510227\pi$
$643$	−1.62907			−0.0642442			−0.0321221	+	0.999484i	$0.510227\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.48260	+	4.29999i	0.0976011	+	0.169050i	0.910691	−	0.413088i	$-0.135550\pi$
$647$	2.48260	+	4.29999i	0.0976011	+	0.169050i	−0.813090	+	0.582138i	$0.802216\pi$
$648$		0			0
$649$	19.7465	−	34.2020i	0.775119	−	1.34255i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.7520	+	34.2115i	−0.772956	+	1.33880i	0.162980	+	0.986629i	$0.447890\pi$
$653$	−19.7520	+	34.2115i	−0.772956	+	1.33880i	−0.935936	+	0.352170i	$0.885444\pi$
$654$		0			0
$655$	17.6916	+	30.6427i	0.691267	+	1.19731i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	36.0901			1.40587			0.702935	−	0.711254i	$-0.251873\pi$
$659$	36.0901			1.40587			0.702935	+	0.711254i	$0.251873\pi$
$660$		0			0
$661$	−7.66071	−	13.2687i	−0.297967	−	0.516094i	0.677704	−	0.735335i	$-0.262975\pi$
$661$	−7.66071	−	13.2687i	−0.297967	−	0.516094i	−0.975671	+	0.219241i	$0.929642\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.57165	−	13.6712i	−0.332394	−	0.530146i
$666$		0			0
$667$	−9.94870	+	17.2317i	−0.385215	+	0.667212i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−35.0617			−1.35354
$672$		0			0
$673$	−45.4807			−1.75315			−0.876575	−	0.481265i	$-0.840178\pi$
$673$	−45.4807			−1.75315			−0.876575	+	0.481265i	$0.840178\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.1662	−	17.6084i	0.390719	−	0.676745i	−0.601825	−	0.798628i	$-0.705560\pi$
$677$	10.1662	−	17.6084i	0.390719	−	0.676745i	0.992545	+	0.121882i	$0.0388930\pi$
$678$		0			0
$679$	−2.17673	+	0.0793285i	−0.0835352	+	0.00304435i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	11.0007	+	19.0538i	0.420930	+	0.729072i	0.996031	−	0.0890109i	$-0.0283706\pi$
$683$	11.0007	+	19.0538i	0.420930	+	0.729072i	−0.575101	+	0.818082i	$0.695037\pi$
$684$		0			0
$685$	16.3535			0.624833
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.04325	+	10.4672i	0.230230	+	0.398769i
$690$		0			0
$691$	5.53892	−	9.59369i	0.210711	−	0.364961i	−0.741227	−	0.671255i	$-0.765756\pi$
$691$	5.53892	−	9.59369i	0.210711	−	0.364961i	0.951937	+	0.306294i	$0.0990889\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.6811	+	25.4283i	−0.556884	+	0.964552i
$696$		0			0
$697$	9.47779	+	16.4160i	0.358997	+	0.621801i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.19420			0.0451044			0.0225522	−	0.999746i	$-0.492821\pi$
$701$	1.19420			0.0451044			0.0225522	+	0.999746i	$0.492821\pi$
$702$		0			0
$703$	−18.7756	−	32.5203i	−0.708136	−	1.22653i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.54580	+	5.65531i	0.133354	+	0.212690i
$708$		0			0
$709$	−2.41232	+	4.17827i	−0.0905968	+	0.156918i	−0.907762	−	0.419485i	$-0.862211\pi$
$709$	−2.41232	+	4.17827i	−0.0905968	+	0.156918i	0.817166	+	0.576403i	$0.195544\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.38688			0.0893892
$714$		0			0
$715$	19.6749			0.735798
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.7120	+	23.7499i	−0.511372	+	0.885722i	0.488542	+	0.872541i	$0.337529\pi$
$719$	−13.7120	+	23.7499i	−0.511372	+	0.885722i	−0.999913	+	0.0131810i	$0.995804\pi$
$720$		0			0
$721$	−15.0815	+	28.4685i	−0.561664	+	1.06022i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.11491	−	14.0554i	−0.301380	−	0.522006i
$726$		0			0
$727$	36.0704			1.33778			0.668889	−	0.743363i	$-0.266770\pi$
$727$	36.0704			1.33778			0.668889	+	0.743363i	$0.266770\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	18.2262	+	31.5687i	0.674119	+	1.16761i
$732$		0			0
$733$	13.6156	−	23.5829i	0.502903	−	0.871054i	−0.497091	−	0.867698i	$-0.665598\pi$
$733$	13.6156	−	23.5829i	0.502903	−	0.871054i	0.999994	−	0.00335589i	$-0.00106821\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.79163	−	13.4955i	0.287009	−	0.497113i
$738$		0			0
$739$	19.9141	+	34.4922i	0.732552	+	1.26882i	0.955789	+	0.294053i	$0.0950044\pi$
$739$	19.9141	+	34.4922i	0.732552	+	1.26882i	−0.223237	+	0.974764i	$0.571662\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−43.3869			−1.59171			−0.795855	−	0.605487i	$-0.792978\pi$
$743$	−43.3869			−1.59171			−0.795855	+	0.605487i	$0.792978\pi$
$744$		0			0
$745$	−17.1927	−	29.7787i	−0.629894	−	1.09101i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.0858	+	30.3644i	−0.587763	+	1.10949i
$750$		0			0
$751$	5.47710	−	9.48662i	0.199862	−	0.346172i	−0.748621	−	0.662998i	$-0.769284\pi$
$751$	5.47710	−	9.48662i	0.199862	−	0.346172i	0.948484	+	0.316826i	$0.102617\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.23119			−0.0812013
$756$		0			0
$757$	37.5933			1.36635			0.683176	−	0.730254i	$-0.260598\pi$
$757$	37.5933			1.36635			0.683176	+	0.730254i	$0.260598\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	24.1366	−	41.8059i	0.874952	−	1.51546i	0.0181389	−	0.999835i	$-0.494226\pi$
$761$	24.1366	−	41.8059i	0.874952	−	1.51546i	0.856813	−	0.515626i	$-0.172441\pi$
$762$		0			0
$763$	−21.1113	−	33.6710i	−0.764279	−	1.21897i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.4320	+	21.5328i	0.448893	+	0.777506i
$768$		0			0
$769$	49.0022			1.76706			0.883532	−	0.468371i	$-0.155159\pi$
$769$	49.0022			1.76706			0.883532	+	0.468371i	$0.155159\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.8949	−	18.8706i	−0.391863	−	0.678727i	0.600832	−	0.799375i	$-0.294836\pi$
$773$	−10.8949	−	18.8706i	−0.391863	−	0.678727i	−0.992695	+	0.120648i	$0.961503\pi$
$774$		0			0
$775$	−0.973458	+	1.68608i	−0.0349676	+	0.0605657i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.3436	−	17.9157i	0.370599	−	0.641896i
$780$		0			0
$781$	21.7923	+	37.7454i	0.779791	+	1.35064i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	36.1964			1.29190
$786$		0			0
$787$	−2.98948	−	5.17793i	−0.106563	−	0.184573i	0.807812	−	0.589440i	$-0.200651\pi$
$787$	−2.98948	−	5.17793i	−0.106563	−	0.184573i	−0.914376	+	0.404866i	$0.867318\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−20.4425	+	0.745005i	−0.726852	+	0.0264893i
$792$		0			0
$793$	11.0371	−	19.1168i	0.391938	−	0.678856i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.6401			−0.660265			−0.330133	−	0.943935i	$-0.607093\pi$
$797$	−18.6401			−0.660265			−0.330133	+	0.943935i	$0.607093\pi$
$798$		0			0
$799$	17.4968			0.618991
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.42835	+	2.47397i	−0.0504052	+	0.0873044i
$804$		0			0
$805$	−6.18292	−	9.86132i	−0.217919	−	0.347566i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−18.2367	−	31.5869i	−0.641168	−	1.11054i	−0.985172	−	0.171567i	$-0.945117\pi$
$809$	−18.2367	−	31.5869i	−0.641168	−	1.11054i	0.344004	−	0.938968i	$-0.388216\pi$
$810$		0			0
$811$	31.6712			1.11212			0.556062	−	0.831141i	$-0.312312\pi$
$811$	31.6712			1.11212			0.556062	+	0.831141i	$0.312312\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.07048	−	10.5144i	−0.212640	−	0.368303i
$816$		0			0
$817$	19.8912	−	34.4526i	0.695905	−	1.20534i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.0524	−	17.4113i	0.350831	−	0.607657i	−0.635564	−	0.772048i	$-0.719232\pi$
$821$	10.0524	−	17.4113i	0.350831	−	0.607657i	0.986395	+	0.164391i	$0.0525658\pi$
$822$		0			0
$823$	−18.7793	−	32.5266i	−0.654604	−	1.13381i	−0.981993	−	0.188917i	$-0.939502\pi$
$823$	−18.7793	−	32.5266i	−0.654604	−	1.13381i	0.327389	−	0.944890i	$-0.393831\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	17.3855			0.604553			0.302277	−	0.953220i	$-0.402253\pi$
$827$	17.3855			0.604553			0.302277	+	0.953220i	$0.402253\pi$
$828$		0			0
$829$	13.8832	+	24.0465i	0.482185	+	0.835168i	0.999791	−	0.0204506i	$-0.00651009\pi$
$829$	13.8832	+	24.0465i	0.482185	+	0.835168i	−0.517606	+	0.855619i	$0.673177\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.9283	+	19.0418i	0.447941	+	0.659761i
$834$		0			0
$835$	6.37203	−	11.0367i	0.220513	−	0.381940i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.43130			0.152985			0.0764927	−	0.997070i	$-0.475628\pi$
$839$	4.43130			0.152985			0.0764927	+	0.997070i	$0.475628\pi$
$840$		0			0
$841$	30.0938			1.03772
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.85414	−	8.40763i	0.166988	−	0.289231i
$846$		0			0
$847$	9.14902	−	17.2701i	0.314364	−	0.593408i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.5433	−	23.4576i	−0.464257	−	0.804116i
$852$		0			0
$853$	23.4116			0.801599			0.400800	−	0.916166i	$-0.368732\pi$
$853$	23.4116			0.801599			0.400800	+	0.916166i	$0.368732\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.1847	−	41.8891i	−0.826134	−	1.43091i	−0.901050	−	0.433716i	$-0.857202\pi$
$857$	−24.1847	−	41.8891i	−0.826134	−	1.43091i	0.0749162	−	0.997190i	$-0.476131\pi$
$858$		0			0
$859$	−6.24976	+	10.8249i	−0.213239	+	0.369341i	−0.952726	−	0.303830i	$-0.901735\pi$
$859$	−6.24976	+	10.8249i	−0.213239	+	0.369341i	0.739487	+	0.673170i	$0.235068\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.90104	+	11.9530i	−0.234914	+	0.406883i	−0.959248	−	0.282566i	$-0.908814\pi$
$863$	−6.90104	+	11.9530i	−0.234914	+	0.406883i	0.724334	+	0.689450i	$0.242148\pi$
$864$		0			0
$865$	1.64400	+	2.84748i	0.0558975	+	0.0968174i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−41.8726			−1.42043
$870$		0			0
$871$	4.90545	+	8.49648i	0.166215	+	0.287892i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	31.9567	−	1.16463i	1.08033	−	0.0393716i
$876$		0			0
$877$	20.5970	−	35.6751i	0.695512	−	1.20466i	−0.274496	−	0.961588i	$-0.588511\pi$
$877$	20.5970	−	35.6751i	0.695512	−	1.20466i	0.970008	−	0.243074i	$-0.0781558\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	46.1555			1.55502			0.777510	−	0.628871i	$-0.216483\pi$
$881$	46.1555			1.55502			0.777510	+	0.628871i	$0.216483\pi$
$882$		0			0
$883$	−15.3448			−0.516393			−0.258197	−	0.966092i	$-0.583128\pi$
$883$	−15.3448			−0.516393			−0.258197	+	0.966092i	$0.583128\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.8443	−	27.4432i	0.532000	−	0.921451i	−0.467302	−	0.884098i	$-0.654774\pi$
$887$	15.8443	−	27.4432i	0.532000	−	0.921451i	0.999302	−	0.0373533i	$-0.0118927\pi$
$888$		0			0
$889$	43.3268	−	1.57900i	1.45314	−	0.0529580i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.54758	−	16.5369i	−0.319498	−	0.553386i
$894$		0			0
$895$	19.0865			0.637991
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.54442	−	6.13912i	−0.118213	−	0.204751i
$900$		0			0
$901$	−7.36033	+	12.7485i	−0.245208	+	0.424713i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.6600	+	21.9278i	−0.420833	+	0.728905i
$906$		0			0
$907$	−5.76509	−	9.98543i	−0.191427	−	0.331561i	0.754297	−	0.656534i	$-0.227978\pi$
$907$	−5.76509	−	9.98543i	−0.191427	−	0.331561i	−0.945723	+	0.324973i	$0.894645\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−51.2275			−1.69724			−0.848621	−	0.529001i	$-0.822567\pi$
$911$	−51.2275			−1.69724			−0.848621	+	0.529001i	$0.822567\pi$
$912$		0			0
$913$	2.68980	+	4.65886i	0.0890193	+	0.154186i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−25.7844	+	48.6718i	−0.851474	+	1.60728i
$918$		0			0
$919$	−23.7188	+	41.0822i	−0.782411	+	1.35518i	0.148122	+	0.988969i	$0.452677\pi$
$919$	−23.7188	+	41.0822i	−0.782411	+	1.35518i	−0.930533	+	0.366207i	$0.880656\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−27.4400			−0.903197
$924$		0			0
$925$	22.0938			0.726439
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.4288	−	31.9195i	0.604628	−	1.04725i	−0.387482	−	0.921877i	$-0.626655\pi$
$929$	18.4288	−	31.9195i	0.604628	−	1.04725i	0.992110	−	0.125369i	$-0.0400114\pi$
$930$		0			0
$931$	10.9425	−	22.6098i	0.358626	−	0.741006i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11.9814	+	20.7524i	0.391835	+	0.678678i
$936$		0			0
$937$	−15.4771			−0.505615			−0.252807	−	0.967517i	$-0.581354\pi$
$937$	−15.4771			−0.505615			−0.252807	+	0.967517i	$0.581354\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.0611	−	46.8711i	−0.882165	−	1.52796i	−0.848929	−	0.528507i	$-0.822752\pi$
$941$	−27.0611	−	46.8711i	−0.882165	−	1.52796i	−0.0332366	−	0.999448i	$-0.510581\pi$
$942$		0			0
$943$	7.46108	−	12.9230i	0.242966	−	0.420830i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.01485	+	13.8821i	−0.260448	+	0.451109i	−0.966361	−	0.257190i	$-0.917203\pi$
$947$	−8.01485	+	13.8821i	−0.260448	+	0.451109i	0.705913	+	0.708298i	$0.250537\pi$
$948$		0			0
$949$	−0.899256	−	1.55756i	−0.0291911	−	0.0505605i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	47.9222			1.55235			0.776175	−	0.630517i	$-0.217157\pi$
$953$	47.9222			1.55235			0.776175	+	0.630517i	$0.217157\pi$
$954$		0			0
$955$	−5.45489	−	9.44814i	−0.176516	−	0.305735i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	13.5229	+	21.5681i	0.436677	+	0.696470i
$960$		0			0
$961$	15.0748	−	26.1103i	0.486284	−	0.842269i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−20.6391			−0.664396
$966$		0			0
$967$	4.78476			0.153867			0.0769337	−	0.997036i	$-0.475487\pi$
$967$	4.78476			0.153867			0.0769337	+	0.997036i	$0.475487\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−25.5593	+	44.2700i	−0.820236	+	1.42069i	0.0852702	+	0.996358i	$0.472825\pi$
$971$	−25.5593	+	44.2700i	−0.820236	+	1.42069i	−0.905506	+	0.424333i	$0.860509\pi$
$972$		0			0
$973$	−45.6767	+	1.66464i	−1.46433	+	0.0533658i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.9654	−	39.7773i	−0.734729	−	1.27259i	−0.954842	−	0.297113i	$-0.903976\pi$
$977$	−22.9654	−	39.7773i	−0.734729	−	1.27259i	0.220114	−	0.975474i	$-0.429357\pi$
$978$		0			0
$979$	6.86398			0.219374
$980$		0			0
$981$		0			0
$982$		0			0
$983$	28.1861	+	48.8197i	0.898996	+	1.55711i	0.828779	+	0.559575i	$0.189036\pi$
$983$	28.1861	+	48.8197i	0.898996	+	1.55711i	0.0702169	+	0.997532i	$0.477631\pi$
$984$		0			0
$985$	−15.8523	+	27.4570i	−0.505096	+	0.874852i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.3480	−	24.8514i	0.456238	−	0.790228i
$990$		0			0
$991$	−2.72617	−	4.72187i	−0.0865997	−	0.149995i	0.819472	−	0.573119i	$-0.194267\pi$
$991$	−2.72617	−	4.72187i	−0.0865997	−	0.149995i	−0.906072	+	0.423124i	$0.860933\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−15.8553			−0.502647
$996$		0			0
$997$	16.0061	+	27.7234i	0.506919	+	0.878009i	0.999968	+	0.00800753i	$0.00254890\pi$
$997$	16.0061	+	27.7234i	0.506919	+	0.878009i	−0.493049	+	0.870001i	$0.664118\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.l.1297.1	yes	6
3.2	odd	2		1512.2.s.k.1297.3	yes	6
7.4	even	3	inner	1512.2.s.l.865.1	yes	6
21.11	odd	6		1512.2.s.k.865.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.k.865.3	✓	6	21.11	odd	6
1512.2.s.k.1297.3	yes	6	3.2	odd	2
1512.2.s.l.865.1	yes	6	7.4	even	3	inner
1512.2.s.l.1297.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849814 + 1.47192i) q^{5} +(-2.64400 + 0.0963576i) q^{7} +O(q^{10})\)	\(q+(-0.849814 + 1.47192i) q^{5} +(-2.64400 + 0.0963576i) q^{7} +(-2.14400 - 3.71351i) q^{11} +2.69963 q^{13} +(1.64400 + 2.84748i) q^{17} +(1.79418 - 3.10761i) q^{19} +(1.29418 - 2.24159i) q^{23} +(1.05563 + 1.82841i) q^{25} -7.68725 q^{29} +(0.461078 + 0.798611i) q^{31} +(2.10507 - 3.97364i) q^{35} +(5.23236 - 9.06271i) q^{37} +5.76509 q^{41} +11.0865 q^{43} +(2.66071 - 4.60848i) q^{47} +(6.98143 - 0.509538i) q^{49} +(2.23855 + 3.87728i) q^{53} +7.28799 q^{55} +(4.60507 + 7.97622i) q^{59} +(4.08836 - 7.08125i) q^{61} +(-2.29418 + 3.97364i) q^{65} +(1.81708 + 3.14728i) q^{67} -10.1643 q^{71} +(-0.333104 - 0.576953i) q^{73} +(6.02654 + 9.61192i) q^{77} +(4.88255 - 8.45682i) q^{79} -1.25457 q^{83} -5.58836 q^{85} +(-0.800372 + 1.38628i) q^{89} +(-7.13781 + 0.260130i) q^{91} +(3.04944 + 5.28179i) q^{95} +0.823272 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q + q^5 - 4 * q^7	\( 6 q + q^{5} - 4 q^{7} - q^{11} + 4 q^{13} - 2 q^{17} + 5 q^{19} + 2 q^{23} + 6 q^{25} + 2 q^{29} - 4 q^{31} - 6 q^{35} + 8 q^{37} - 6 q^{43} - 3 q^{47} - 12 q^{49} + 8 q^{53} + 20 q^{55} + 9 q^{59} + 13 q^{61} - 8 q^{65} + 16 q^{67} - 2 q^{71} - 3 q^{73} + 7 q^{77} + 12 q^{79} + 2 q^{83} - 22 q^{85} - 17 q^{89} - 13 q^{91} + 28 q^{97}+O(q^{100}) \) 6 * q + q^5 - 4 * q^7 - q^11 + 4 * q^13 - 2 * q^17 + 5 * q^19 + 2 * q^23 + 6 * q^25 + 2 * q^29 - 4 * q^31 - 6 * q^35 + 8 * q^37 - 6 * q^43 - 3 * q^47 - 12 * q^49 + 8 * q^53 + 20 * q^55 + 9 * q^59 + 13 * q^61 - 8 * q^65 + 16 * q^67 - 2 * q^71 - 3 * q^73 + 7 * q^77 + 12 * q^79 + 2 * q^83 - 22 * q^85 - 17 * q^89 - 13 * q^91 + 28 * q^97

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