LMFDB - Embedded newform 1512.2.s.k.1297.3

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			1297.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1512.1297
Dual form			1512.2.s.k.865.3

$q$-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	−0.611020	−	0.791615i	$-0.709241\pi$
$5$	0.849814	−	1.47192i	0.380048	−	0.658263i	0.991069	+	0.133352i	$0.0425740\pi$
$6$		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	$0.0570759\pi$
$11$	2.14400	+	3.71351i	0.646439	+	1.11967i	−0.337528	+	0.941315i	$0.609591\pi$
$12$		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	0.594842	−	0.803843i	$-0.297215\pi$
$17$	−1.64400	−	2.84748i	−0.398728	−	0.690616i	−0.993569	+	0.113226i	$0.963881\pi$
$18$		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	−0.968824	−	0.247749i	$-0.920309\pi$
$23$	−1.29418	+	2.24159i	−0.269856	+	0.467404i	0.698969	+	0.715152i	$0.253643\pi$
$24$		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	$-0.246998\pi$
$29$	7.68725			1.42749			0.713743	+	0.700408i	$0.246998\pi$
$30$		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	$-0.648639\pi$
$41$	−5.76509			−0.900356			−0.450178	+	0.892939i	$0.648639\pi$
$42$		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	−0.992194	−	0.124700i	$-0.960203\pi$
$47$	−2.66071	+	4.60848i	−0.388104	+	0.672216i	0.604091	+	0.796916i	$0.293537\pi$
$48$		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	0.670324	−	0.742069i	$-0.266155\pi$
$53$	−2.23855	−	3.87728i	−0.307488	−	0.532586i	−0.977812	+	0.209483i	$0.932822\pi$
$54$		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	$-0.962021\pi$
$59$	−4.60507	−	7.97622i	−0.599530	−	1.03842i	0.393361	−	0.919384i	$-0.371312\pi$
$60$		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	$-0.293915\pi$
$71$	10.1643			1.20629			0.603143	+	0.797633i	$0.293915\pi$
$72$		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	$-0.478066\pi$
$83$	1.25457			0.137707			0.0688536	+	0.997627i	$0.478066\pi$
$84$		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	−0.820483	−	0.571670i	$-0.806296\pi$
$89$	0.800372	−	1.38628i	0.0848392	−	0.146946i	0.905323	+	0.424724i	$0.139629\pi$
$90$		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	0.921936	−	0.387343i	$-0.126607\pi$
$101$	1.26145	+	2.18490i	0.125519	+	0.217405i	−0.796417	+	0.604748i	$0.793274\pi$
$102$		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	$0.382703\pi$
$107$	−6.49381	+	11.2476i	−0.627780	+	1.08735i	−0.987996	+	0.154478i	$0.950630\pi$
$108$		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	$-0.618475\pi$
$113$	−7.73167			−0.727334			−0.363667	+	0.931529i	$0.618475\pi$
$114$		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	$0.530161\pi$
$131$	−10.4091	+	18.0291i	−0.909446	+	1.57521i	−0.814835	+	0.579693i	$0.803173\pi$
$132$		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	0.995002	−	0.0998569i	$-0.0318385\pi$
$137$	4.81089	+	8.33271i	0.411022	+	0.711911i	−0.583980	+	0.811768i	$0.698505\pi$
$138$		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	$-0.522413\pi$
$149$	10.1156	−	17.5207i	0.828702	−	1.43535i	0.899057	−	0.437832i	$-0.144253\pi$
$150$		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	$-0.406308\pi$
$167$	7.49814			0.580224			0.290112	+	0.956993i	$0.406308\pi$
$168$		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	−0.900450	−	0.434959i	$-0.856763\pi$
$173$	−0.967268	+	1.67536i	−0.0735400	+	0.127375i	0.826910	+	0.562334i	$0.190096\pi$
$174$		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	0.995907	−	0.0903850i	$-0.0288097\pi$
$179$	5.61491	+	9.72530i	0.419678	+	0.726903i	−0.576229	+	0.817288i	$0.695476\pi$
$180$		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	−0.726235	−	0.687446i	$-0.758732\pi$
$191$	3.20946	−	5.55895i	0.232228	−	0.402231i	0.958464	+	0.285215i	$0.0920650\pi$
$192$		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	$-0.731362\pi$
$197$	−18.6538			−1.32903			−0.664515	+	0.747275i	$0.731362\pi$
$198$		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	0.995472	−	0.0950529i	$-0.0303020\pi$
$227$	6.25890	+	10.8407i	0.415418	+	0.719525i	−0.580054	+	0.814578i	$0.696969\pi$
$228$		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	−0.617962	−	0.786208i	$-0.712042\pi$
$233$	5.67673	−	9.83238i	0.371895	−	0.644141i	0.989857	+	0.142067i	$0.0453749\pi$
$234$		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	$-0.503511\pi$
$239$	−0.341076			−0.0220624			−0.0110312	+	0.999939i	$0.503511\pi$
$240$		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	$-0.822484\pi$
$251$	−26.8850			−1.69697			−0.848484	+	0.529222i	$0.822484\pi$
$252$		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	−0.935156	−	0.354235i	$-0.884741\pi$
$257$	−2.57784	+	4.46496i	−0.160801	+	0.278516i	0.774355	+	0.632752i	$0.218075\pi$
$258$		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	$0.0375187\pi$
$263$	9.70396	+	16.8077i	0.598372	+	1.03641i	−0.394690	+	0.918814i	$0.629148\pi$
$264$		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	$0.0933025\pi$
$269$	11.9549	+	20.7065i	0.728902	+	1.26250i	−0.228445	+	0.973557i	$0.573364\pi$
$270$		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	$-0.532885\pi$
$281$	−3.45744			−0.206253			−0.103127	+	0.994668i	$0.532885\pi$
$282$		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	$-0.784969\pi$
$293$	−26.7156			−1.56074			−0.780370	+	0.625318i	$0.784969\pi$
$294$		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	0.592541	−	0.805540i	$-0.298125\pi$
$311$	−7.07784	−	12.2592i	−0.401348	−	0.695155i	−0.993889	+	0.110386i	$0.964791\pi$
$312$		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	−0.960497	−	0.278290i	$-0.910232\pi$
$317$	−4.25959	+	7.37783i	−0.239242	+	0.414380i	0.721255	+	0.692670i	$0.243566\pi$
$318$		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	$-0.958999\pi$
$347$	−11.3090	−	19.5878i	−0.607101	−	1.05153i	0.384615	−	0.923077i	$-0.374334\pi$
$348$		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	0.996238	−	0.0866629i	$-0.0276203\pi$
$353$	7.94870	+	13.7675i	0.423067	+	0.732773i	−0.573171	+	0.819436i	$0.694287\pi$
$354$		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	−0.944469	−	0.328600i	$-0.893423\pi$
$359$	−3.55563	+	6.15854i	−0.187659	+	0.325035i	0.756810	+	0.653635i	$0.226757\pi$
$360$		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	$-0.441236\pi$
$383$	18.4567	−	31.9679i	0.943092	−	1.63348i	0.759527	−	0.650475i	$-0.225430\pi$
$384$		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	0.807024	−	0.590519i	$-0.201077\pi$
$389$	−2.12797	−	3.68576i	−0.107893	−	0.186875i	−0.914916	+	0.403644i	$0.867744\pi$
$390$		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	−0.971885	−	0.235458i	$-0.924341\pi$
$401$	−5.64764	+	9.78200i	−0.282030	+	0.488490i	0.689855	+	0.723948i	$0.257674\pi$
$402$		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	$-0.639334\pi$
$419$	−17.3535			−0.847772			−0.423886	+	0.905716i	$0.639334\pi$
$420$		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	0.643292	−	0.765621i	$-0.277568\pi$
$431$	−7.08768	−	12.2762i	−0.341401	−	0.591324i	−0.984693	+	0.174297i	$0.944235\pi$
$432$		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	$0.348834\pi$
$443$	−11.3986	+	19.7429i	−0.541562	+	0.938013i	−0.998815	+	0.0486764i	$0.984500\pi$
$444$		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	$-0.833808\pi$
$449$	−36.7330			−1.73354			−0.866770	+	0.498708i	$0.833808\pi$
$450$		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	$-0.442122\pi$
$461$	7.76509			0.361656			0.180828	+	0.983515i	$0.442122\pi$
$462$		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	$-0.605558\pi$
$467$	14.1774	−	24.5560i	0.656053	−	1.13632i	0.981629	−	0.190801i	$-0.0611084\pi$
$468$		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	$-0.922686\pi$
$479$	−15.1804	−	26.2932i	−0.693609	−	1.20137i	0.277039	−	0.960859i	$-0.410647\pi$
$480$		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	$-0.156214\pi$
$491$	39.0865			1.76395			0.881975	+	0.471297i	$0.156214\pi$
$492$		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	$-0.486443\pi$
$503$	1.90978			0.0851527			0.0425764	+	0.999093i	$0.486443\pi$
$504$		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	$0.466739\pi$
$509$	−18.2553	+	31.6190i	−0.809150	+	1.40149i	−0.913453	+	0.406944i	$0.866595\pi$
$510$		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	$0.151708\pi$
$521$	19.2095	+	33.2718i	0.841582	+	1.45766i	−0.0469753	+	0.998896i	$0.514958\pi$
$522$		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	0.782134	−	0.623110i	$-0.214131\pi$
$557$	−3.50619	−	6.07290i	−0.148562	−	0.257317i	−0.930696	+	0.365793i	$0.880798\pi$
$558$		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	$-0.987315\pi$
$563$	−12.6731	−	21.9504i	−0.534107	−	0.925100i	0.465099	−	0.885259i	$-0.346019\pi$
$564$		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	−0.906958	−	0.421222i	$-0.861601\pi$
$569$	−2.11559	+	3.66432i	−0.0886903	+	0.153616i	0.818267	+	0.574838i	$0.194935\pi$
$570$		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	$-0.696960\pi$
$587$	−28.1062			−1.16007			−0.580033	+	0.814593i	$0.696960\pi$
$588$		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	$-0.543661\pi$
$593$	19.2262	−	33.3007i	0.789524	−	1.36750i	0.926259	−	0.376888i	$-0.123006\pi$
$594$		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	0.894456	−	0.447156i	$-0.147563\pi$
$599$	1.46796	+	2.54258i	0.0599791	+	0.103887i	−0.834477	+	0.551043i	$0.814230\pi$
$600$		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	$-0.536689\pi$
$617$	−5.71339			−0.230012			−0.115006	+	0.993365i	$0.536689\pi$
$618$		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	0.568714	−	0.822535i	$-0.307441\pi$
$641$	−10.8356	−	18.7678i	−0.427979	−	0.741282i	−0.996693	+	0.0812531i	$0.974108\pi$
$642$		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	0.813090	−	0.582138i	$-0.197784\pi$
$647$	−2.48260	−	4.29999i	−0.0976011	−	0.169050i	−0.910691	+	0.413088i	$0.864450\pi$
$648$		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	$-0.552110\pi$
$653$	19.7520	−	34.2115i	0.772956	−	1.33880i	0.935936	−	0.352170i	$-0.114556\pi$
$654$		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	$-0.748127\pi$
$659$	−36.0901			−1.40587			−0.702935	+	0.711254i	$0.748127\pi$
$660$		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	−0.992545	−	0.121882i	$-0.961107\pi$
$677$	−10.1662	+	17.6084i	−0.390719	+	0.676745i	0.601825	+	0.798628i	$0.294440\pi$
$678$		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	0.575101	−	0.818082i	$-0.304963\pi$
$683$	−11.0007	−	19.0538i	−0.420930	−	0.729072i	−0.996031	+	0.0890109i	$0.971629\pi$
$684$		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	$-0.507179\pi$
$701$	−1.19420			−0.0451044			−0.0225522	+	0.999746i	$0.507179\pi$
$702$		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	$-0.662471\pi$
$719$	13.7120	−	23.7499i	0.511372	−	0.885722i	0.999913	−	0.0131810i	$-0.00419575\pi$
$720$		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	$-0.207022\pi$
$743$	43.3869			1.59171			0.795855	+	0.605487i	$0.207022\pi$
$744$		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	$0.505774\pi$
$761$	−24.1366	+	41.8059i	−0.874952	+	1.51546i	−0.856813	+	0.515626i	$0.827559\pi$
$762$		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	0.992695	−	0.120648i	$-0.0384973\pi$
$773$	10.8949	+	18.8706i	0.391863	+	0.678727i	−0.600832	+	0.799375i	$0.705164\pi$
$774$		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	$-0.392907\pi$
$797$	18.6401			0.660265			0.330133	+	0.943935i	$0.392907\pi$
$798$		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	$0.0548831\pi$
$809$	18.2367	+	31.5869i	0.641168	+	1.11054i	−0.344004	+	0.938968i	$0.611784\pi$
$810$		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	−0.986395	−	0.164391i	$-0.947434\pi$
$821$	−10.0524	+	17.4113i	−0.350831	+	0.607657i	0.635564	+	0.772048i	$0.280768\pi$
$822$		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	$-0.597747\pi$
$827$	−17.3855			−0.604553			−0.302277	+	0.953220i	$0.597747\pi$
$828$		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	$-0.524372\pi$
$839$	−4.43130			−0.152985			−0.0764927	+	0.997070i	$0.524372\pi$
$840$		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	$0.142798\pi$
$857$	24.1847	+	41.8891i	0.826134	+	1.43091i	−0.0749162	+	0.997190i	$0.523869\pi$
$858$		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	−0.724334	−	0.689450i	$-0.757852\pi$
$863$	6.90104	−	11.9530i	0.234914	−	0.406883i	0.959248	+	0.282566i	$0.0911858\pi$
$864$		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	$-0.783517\pi$
$881$	−46.1555			−1.55502			−0.777510	+	0.628871i	$0.783517\pi$
$882$		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	$0.345226\pi$
$887$	−15.8443	+	27.4432i	−0.532000	+	0.921451i	−0.999302	+	0.0373533i	$0.988107\pi$
$888$		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	$-0.177433\pi$
$911$	51.2275			1.69724			0.848621	+	0.529001i	$0.177433\pi$
$912$		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	$0.373345\pi$
$929$	−18.4288	+	31.9195i	−0.604628	+	1.04725i	−0.992110	+	0.125369i	$0.959989\pi$
$930$		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	$0.177248\pi$
$941$	27.0611	+	46.8711i	0.882165	+	1.52796i	0.0332366	+	0.999448i	$0.489419\pi$
$942$		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	−0.705913	−	0.708298i	$-0.749463\pi$
$947$	8.01485	−	13.8821i	0.260448	−	0.451109i	0.966361	+	0.257190i	$0.0827965\pi$
$948$		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	$-0.782843\pi$
$953$	−47.9222			−1.55235			−0.776175	+	0.630517i	$0.782843\pi$
$954$		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	$-0.527175\pi$
$971$	25.5593	−	44.2700i	0.820236	−	1.42069i	0.905506	−	0.424333i	$-0.139491\pi$
$972$		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	$0.0960238\pi$
$977$	22.9654	+	39.7773i	0.734729	+	1.27259i	−0.220114	+	0.975474i	$0.570643\pi$
$978$		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	$-0.810964\pi$
$983$	−28.1861	−	48.8197i	−0.898996	−	1.55711i	−0.0702169	−	0.997532i	$-0.522369\pi$
$984$		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.k.1297.3	yes	6
3.2	odd	2		1512.2.s.l.1297.1	yes	6
7.4	even	3	inner	1512.2.s.k.865.3	✓	6
21.11	odd	6		1512.2.s.l.865.1	yes	6

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

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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