LMFDB - Embedded newform 1512.2.s.k.865.2

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			865.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.k.1297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.119562 - 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +O(q^{10})$	$q+(-0.119562 - 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-1.21053 + 2.09671i) q^{11} +0.760877 q^{13} +(1.71053 - 2.96273i) q^{17} +(-0.590972 - 1.02359i) q^{19} +(1.09097 + 1.88962i) q^{23} +(2.47141 - 4.28061i) q^{25} -2.89931 q^{29} +(2.32326 - 4.02400i) q^{31} +(-0.612725 + 0.157568i) q^{35} +(-2.89248 - 5.00992i) q^{37} +8.54583 q^{41} -3.37756 q^{43} +(-2.58414 - 4.47585i) q^{47} +(-5.99028 - 3.62167i) q^{49} +(1.56238 - 2.70612i) q^{53} +0.578933 q^{55} +(-3.11273 + 5.39140i) q^{59} +(-0.681943 - 1.18116i) q^{61} +(-0.0909717 - 0.157568i) q^{65} +(7.03379 - 12.1829i) q^{67} -8.02408 q^{71} +(3.91423 - 6.77965i) q^{73} +(4.48345 + 4.57489i) q^{77} +(-2.27292 - 3.93680i) q^{79} -12.0104 q^{83} -0.818057 q^{85} +(2.73912 + 4.74430i) q^{89} +(0.540628 - 1.93914i) q^{91} +(-0.141315 + 0.244765i) q^{95} +10.3639 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−0.119562	−	0.207087i	−0.0534696	−	0.0926120i	0.838052	−	0.545591i	$-0.183695\pi$
$5$	−0.119562	−	0.207087i	−0.0534696	−	0.0926120i	−0.891521	+	0.452979i	$0.850361\pi$
$6$		0			0
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.21053	+	2.09671i	−0.364990	+	0.632180i	−0.988774	−	0.149416i	$-0.952261\pi$
$11$	−1.21053	+	2.09671i	−0.364990	+	0.632180i	0.623785	+	0.781596i	$0.285594\pi$
$12$		0			0
$13$	0.760877			0.211029			0.105515	−	0.994418i	$-0.466351\pi$
$13$	0.760877			0.211029			0.105515	+	0.994418i	$0.466351\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.71053	−	2.96273i	0.414865	−	0.718568i	−0.580549	−	0.814225i	$-0.697162\pi$
$17$	1.71053	−	2.96273i	0.414865	−	0.718568i	0.995414	+	0.0956576i	$0.0304954\pi$
$18$		0			0
$19$	−0.590972	−	1.02359i	−0.135578	−	0.234828i	0.790240	−	0.612797i	$-0.209956\pi$
$19$	−0.590972	−	1.02359i	−0.135578	−	0.234828i	−0.925818	+	0.377969i	$0.876623\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.09097	+	1.88962i	0.227483	+	0.394013i	0.957062	−	0.289885i	$-0.0936169\pi$
$23$	1.09097	+	1.88962i	0.227483	+	0.394013i	−0.729578	+	0.683897i	$0.760284\pi$
$24$		0			0
$25$	2.47141	−	4.28061i	0.494282	−	0.856122i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.89931			−0.538389			−0.269194	−	0.963086i	$-0.586757\pi$
$29$	−2.89931			−0.538389			−0.269194	+	0.963086i	$0.586757\pi$
$30$		0			0
$31$	2.32326	−	4.02400i	0.417270	−	0.722732i	−0.578394	−	0.815757i	$-0.696320\pi$
$31$	2.32326	−	4.02400i	0.417270	−	0.722732i	0.995664	+	0.0930254i	$0.0296538\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.612725	+	0.157568i	−0.103569	+	0.0266338i
$36$		0			0
$37$	−2.89248	−	5.00992i	−0.475520	−	0.823625i	0.524087	−	0.851665i	$-0.324407\pi$
$37$	−2.89248	−	5.00992i	−0.475520	−	0.823625i	−0.999607	+	0.0280398i	$0.991073\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.54583			1.33463			0.667317	−	0.744774i	$-0.267443\pi$
$41$	8.54583			1.33463			0.667317	+	0.744774i	$0.267443\pi$
$42$		0			0
$43$	−3.37756			−0.515073			−0.257537	−	0.966269i	$-0.582911\pi$
$43$	−3.37756			−0.515073			−0.257537	+	0.966269i	$0.582911\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.58414	−	4.47585i	−0.376935	−	0.652870i	0.613680	−	0.789555i	$-0.289689\pi$
$47$	−2.58414	−	4.47585i	−0.376935	−	0.652870i	−0.990615	+	0.136685i	$0.956355\pi$
$48$		0			0
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.56238	−	2.70612i	0.214610	−	0.371715i	−0.738542	−	0.674207i	$-0.764485\pi$
$53$	1.56238	−	2.70612i	0.214610	−	0.371715i	0.953152	+	0.302493i	$0.0978187\pi$
$54$		0			0
$55$	0.578933			0.0780634
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.11273	+	5.39140i	−0.405242	+	0.701900i	−0.994350	−	0.106155i	$-0.966146\pi$
$59$	−3.11273	+	5.39140i	−0.405242	+	0.701900i	0.589107	+	0.808055i	$0.299480\pi$
$60$		0			0
$61$	−0.681943	−	1.18116i	−0.0873139	−	0.151232i	0.819061	−	0.573706i	$-0.194495\pi$
$61$	−0.681943	−	1.18116i	−0.0873139	−	0.151232i	−0.906375	+	0.422474i	$0.861162\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0909717	−	0.157568i	−0.0112836	−	0.0195438i
$66$		0			0
$67$	7.03379	−	12.1829i	0.859314	−	1.48838i	−0.0132695	−	0.999912i	$-0.504224\pi$
$67$	7.03379	−	12.1829i	0.859314	−	1.48838i	0.872584	−	0.488464i	$-0.162443\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.02408			−0.952283			−0.476141	−	0.879369i	$-0.657965\pi$
$71$	−8.02408			−0.952283			−0.476141	+	0.879369i	$0.657965\pi$
$72$		0			0
$73$	3.91423	−	6.77965i	0.458126	−	0.793497i	−0.540736	−	0.841192i	$-0.681854\pi$
$73$	3.91423	−	6.77965i	0.458126	−	0.793497i	0.998862	+	0.0476949i	$0.0151875\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.48345	+	4.57489i	0.510936	+	0.521357i
$78$		0			0
$79$	−2.27292	−	3.93680i	−0.255723	−	0.442925i	0.709369	−	0.704838i	$-0.248980\pi$
$79$	−2.27292	−	3.93680i	−0.255723	−	0.442925i	−0.965092	+	0.261913i	$0.915647\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−12.0104			−1.31831			−0.659157	−	0.752006i	$-0.729087\pi$
$83$	−12.0104			−1.31831			−0.659157	+	0.752006i	$0.729087\pi$
$84$		0			0
$85$	−0.818057			−0.0887307
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.73912	+	4.74430i	0.290346	+	0.502895i	0.973892	−	0.227013i	$-0.0728961\pi$
$89$	2.73912	+	4.74430i	0.290346	+	0.502895i	−0.683545	+	0.729908i	$0.739563\pi$
$90$		0			0
$91$	0.540628	−	1.93914i	0.0566732	−	0.203277i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.141315	+	0.244765i	−0.0144986	+	0.0251123i
$96$		0			0
$97$	10.3639			1.05229			0.526147	−	0.850394i	$-0.323636\pi$
$97$	10.3639			1.05229			0.526147	+	0.850394i	$0.323636\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.06238	−	8.76830i	0.503726	−	0.872479i	−0.496265	−	0.868171i	$-0.665296\pi$
$101$	5.06238	−	8.76830i	0.503726	−	0.872479i	0.999991	−	0.00430755i	$-0.00137114\pi$
$102$		0			0
$103$	1.31806	+	2.28294i	0.129872	+	0.224945i	0.923627	−	0.383293i	$-0.125210\pi$
$103$	1.31806	+	2.28294i	0.129872	+	0.224945i	−0.793755	+	0.608238i	$0.791877\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.16991	−	3.75839i	−0.209773	−	0.363337i	0.741870	−	0.670544i	$-0.233939\pi$
$107$	−2.16991	−	3.75839i	−0.209773	−	0.363337i	−0.951643	+	0.307207i	$0.900606\pi$
$108$		0			0
$109$	6.46457	−	11.1970i	0.619194	−	1.07248i	−0.370439	−	0.928857i	$-0.620793\pi$
$109$	6.46457	−	11.1970i	0.619194	−	1.07248i	0.989633	−	0.143619i	$-0.0458738\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	13.1352			1.23565			0.617826	−	0.786315i	$-0.288013\pi$
$113$	13.1352			1.23565			0.617826	+	0.786315i	$0.288013\pi$
$114$		0			0
$115$	0.260877	−	0.451852i	0.0243269	−	0.0421354i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.33530	−	6.46451i	−0.580756	−	0.592601i
$120$		0			0
$121$	2.56922	+	4.45002i	0.233565	+	0.404547i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.37756			−0.212655
$126$		0			0
$127$	−3.86156			−0.342658			−0.171329	−	0.985214i	$-0.554806\pi$
$127$	−3.86156			−0.342658			−0.171329	+	0.985214i	$0.554806\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.25636	+	12.5684i	0.633991	+	1.09811i	0.986728	+	0.162383i	$0.0519179\pi$
$131$	7.25636	+	12.5684i	0.633991	+	1.09811i	−0.352736	+	0.935723i	$0.614749\pi$
$132$		0			0
$133$	−3.02859	+	0.778828i	−0.262612	+	0.0675330i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.70370	−	9.87909i	0.487300	−	0.844028i	−0.512594	−	0.858631i	$-0.671315\pi$
$137$	5.70370	−	9.87909i	0.487300	−	0.844028i	0.999893	+	0.0146035i	$0.00464860\pi$
$138$		0			0
$139$	1.91874			0.162746			0.0813728	−	0.996684i	$-0.474070\pi$
$139$	1.91874			0.162746			0.0813728	+	0.996684i	$0.474070\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.921067	+	1.59533i	−0.0770235	+	0.133409i
$144$		0			0
$145$	0.346647	+	0.600410i	0.0287874	+	0.0498613i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.57730	+	13.1243i	0.620756	+	1.07518i	0.989345	+	0.145589i	$0.0465078\pi$
$149$	7.57730	+	13.1243i	0.620756	+	1.07518i	−0.368589	+	0.929593i	$0.620159\pi$
$150$		0			0
$151$	5.94966	−	10.3051i	0.484176	−	0.838618i	−0.515659	−	0.856794i	$-0.672453\pi$
$151$	5.94966	−	10.3051i	0.484176	−	0.838618i	0.999835	+	0.0181764i	$0.00578604\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.11109			−0.0892449
$156$		0			0
$157$	−1.92395	+	3.33237i	−0.153548	+	0.265952i	−0.932529	−	0.361095i	$-0.882403\pi$
$157$	−1.92395	+	3.33237i	−0.153548	+	0.265952i	0.778982	+	0.627047i	$0.215736\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.59097	−	1.43777i	0.440630	−	0.113312i
$162$		0			0
$163$	4.47661	+	7.75372i	0.350635	+	0.607318i	0.986361	−	0.164597i	$-0.0526323\pi$
$163$	4.47661	+	7.75372i	0.350635	+	0.607318i	−0.635726	+	0.771915i	$0.719299\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.19562			−0.169902			−0.0849509	−	0.996385i	$-0.527073\pi$
$167$	−2.19562			−0.169902			−0.0849509	+	0.996385i	$0.527073\pi$
$168$		0			0
$169$	−12.4211			−0.955467
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.15335	−	12.3900i	−0.543859	−	0.941992i	−0.998678	−	0.0514079i	$-0.983629\pi$
$173$	−7.15335	−	12.3900i	−0.543859	−	0.941992i	0.454818	−	0.890584i	$-0.349704\pi$
$174$		0			0
$175$	−9.15335	−	9.34004i	−0.691928	−	0.706041i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.66539	+	16.7409i	−0.722425	+	1.25128i	0.237600	+	0.971363i	$0.423639\pi$
$179$	−9.66539	+	16.7409i	−0.722425	+	1.25128i	−0.960025	+	0.279914i	$0.909694\pi$
$180$		0			0
$181$	1.32614			0.0985710			0.0492855	−	0.998785i	$-0.484306\pi$
$181$	1.32614			0.0985710			0.0492855	+	0.998785i	$0.484306\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.691658	+	1.19799i	−0.0508517	+	0.0880778i
$186$		0			0
$187$	4.14132	+	7.17297i	0.302843	+	0.524539i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.5172	−	21.6805i	−0.905716	−	1.56875i	−0.819954	−	0.572430i	$-0.806001\pi$
$191$	−12.5172	−	21.6805i	−0.905716	−	1.56875i	−0.0857621	−	0.996316i	$-0.527332\pi$
$192$		0			0
$193$	−1.97661	+	3.42359i	−0.142280	+	0.246436i	−0.928355	−	0.371695i	$-0.878777\pi$
$193$	−1.97661	+	3.42359i	−0.142280	+	0.246436i	0.786075	+	0.618131i	$0.212110\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.51135			−0.107679			−0.0538396	−	0.998550i	$-0.517146\pi$
$197$	−1.51135			−0.107679			−0.0538396	+	0.998550i	$0.517146\pi$
$198$		0			0
$199$	−13.5241	+	23.4244i	−0.958696	+	1.66051i	−0.233023	+	0.972471i	$0.574862\pi$
$199$	−13.5241	+	23.4244i	−0.958696	+	1.66051i	−0.725673	+	0.688040i	$0.758471\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.06006	+	7.38906i	−0.144588	+	0.518611i
$204$		0			0
$205$	−1.02175	−	1.76973i	−0.0713624	−	0.123603i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.86156			0.197938
$210$		0			0
$211$	−9.42107			−0.648573			−0.324286	−	0.945959i	$-0.605124\pi$
$211$	−9.42107			−0.648573			−0.324286	+	0.945959i	$0.605124\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.403827	+	0.699448i	0.0275407	+	0.0477020i
$216$		0			0
$217$	−8.60464	−	8.78014i	−0.584121	−	0.596035i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.30150	−	2.25427i	0.0875487	−	0.151639i
$222$		0			0
$223$	7.03775			0.471283			0.235641	−	0.971840i	$-0.424281\pi$
$223$	7.03775			0.471283			0.235641	+	0.971840i	$0.424281\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.3759	+	21.4357i	−0.821419	+	1.42274i	0.0832066	+	0.996532i	$0.473484\pi$
$227$	−12.3759	+	21.4357i	−0.821419	+	1.42274i	−0.904626	+	0.426207i	$0.859849\pi$
$228$		0			0
$229$	13.8542	+	23.9961i	0.915509	+	1.58571i	0.806154	+	0.591706i	$0.201545\pi$
$229$	13.8542	+	23.9961i	0.915509	+	1.58571i	0.109356	+	0.994003i	$0.465121\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.86389	−	6.69245i	−0.253132	−	0.438437i	0.711255	−	0.702934i	$-0.248127\pi$
$233$	−3.86389	−	6.69245i	−0.253132	−	0.438437i	−0.964386	+	0.264497i	$0.914794\pi$
$234$		0			0
$235$	−0.617927	+	1.07028i	−0.0403091	+	0.0698174i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	27.3880			1.77158			0.885790	−	0.464086i	$-0.153617\pi$
$239$	27.3880			1.77158			0.885790	+	0.464086i	$0.153617\pi$
$240$		0			0
$241$	−10.6683	+	18.4780i	−0.687204	+	1.19027i	0.285535	+	0.958368i	$0.407829\pi$
$241$	−10.6683	+	18.4780i	−0.687204	+	1.19027i	−0.972739	+	0.231903i	$0.925505\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.0337917	+	1.67352i	−0.00215887	+	0.106917i
$246$		0			0
$247$	−0.449657	−	0.778828i	−0.0286110	−	0.0495556i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.66595			−0.294512			−0.147256	−	0.989098i	$-0.547044\pi$
$251$	−4.66595			−0.294512			−0.147256	+	0.989098i	$0.547044\pi$
$252$		0			0
$253$	−5.28263			−0.332116
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.14652	+	1.98583i	0.0715178	+	0.123872i	0.899567	−	0.436783i	$-0.143882\pi$
$257$	1.14652	+	1.98583i	0.0715178	+	0.123872i	−0.828049	+	0.560656i	$0.810549\pi$
$258$		0			0
$259$	−14.8233	+	3.81193i	−0.921072	+	0.236862i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.39536	−	4.14888i	0.147704	−	0.255831i	−0.782675	−	0.622431i	$-0.786145\pi$
$263$	2.39536	−	4.14888i	0.147704	−	0.255831i	0.930378	+	0.366600i	$0.119478\pi$
$264$		0			0
$265$	−0.747204			−0.0459004
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.49316	−	16.4426i	0.578808	−	1.00253i	−0.416808	−	0.908995i	$-0.636851\pi$
$269$	9.49316	−	16.4426i	0.578808	−	1.00253i	0.995616	−	0.0935310i	$-0.0298154\pi$
$270$		0			0
$271$	14.0579	+	24.3489i	0.853955	+	1.47909i	0.877611	+	0.479373i	$0.159136\pi$
$271$	14.0579	+	24.3489i	0.853955	+	1.47909i	−0.0236567	+	0.999720i	$0.507531\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.98345	+	10.3636i	0.360816	+	0.624951i
$276$		0			0
$277$	4.08577	−	7.07676i	0.245490	−	0.425201i	−0.716779	−	0.697300i	$-0.754384\pi$
$277$	4.08577	−	7.07676i	0.245490	−	0.425201i	0.962269	+	0.272099i	$0.0877178\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−23.4315			−1.39780			−0.698902	−	0.715217i	$-0.746328\pi$
$281$	−23.4315			−1.39780			−0.698902	+	0.715217i	$0.746328\pi$
$282$		0			0
$283$	−1.10752	+	1.91829i	−0.0658354	+	0.114030i	−0.897064	−	0.441900i	$-0.854305\pi$
$283$	−1.10752	+	1.91829i	−0.0658354	+	0.114030i	0.831229	+	0.555930i	$0.187638\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.07210	−	21.7795i	0.358425	−	1.28561i
$288$		0			0
$289$	2.64815	+	4.58673i	0.155774	+	0.269808i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	22.1866			1.29615			0.648077	−	0.761575i	$-0.275573\pi$
$293$	22.1866			1.29615			0.648077	+	0.761575i	$0.275573\pi$
$294$		0			0
$295$	1.48865			0.0866726
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.830095	+	1.43777i	0.0480056	+	0.0831482i
$300$		0			0
$301$	−2.39987	+	8.60790i	−0.138326	+	0.496151i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.163069	+	0.282443i	−0.00933728	+	0.0161726i
$306$		0			0
$307$	16.0183			0.914214			0.457107	−	0.889412i	$-0.348886\pi$
$307$	16.0183			0.914214			0.457107	+	0.889412i	$0.348886\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.35348	+	5.80840i	−0.190159	+	0.329364i	−0.945303	−	0.326195i	$-0.894234\pi$
$311$	−3.35348	+	5.80840i	−0.190159	+	0.329364i	0.755144	+	0.655559i	$0.227567\pi$
$312$		0			0
$313$	14.0322	+	24.3044i	0.793144	+	1.37377i	0.924011	+	0.382366i	$0.124891\pi$
$313$	14.0322	+	24.3044i	0.793144	+	1.37377i	−0.130866	+	0.991400i	$0.541776\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.63323	+	2.82885i	0.0917316	+	0.158884i	0.908240	−	0.418450i	$-0.137426\pi$
$317$	1.63323	+	2.82885i	0.0917316	+	0.158884i	−0.816508	+	0.577334i	$0.804093\pi$
$318$		0			0
$319$	3.50972	−	6.07900i	0.196506	−	0.340359i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.04351			−0.224987
$324$		0			0
$325$	1.88044	−	3.25701i	0.104308	−	0.180667i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.2431	+	3.40557i	−0.730115	+	0.187755i
$330$		0			0
$331$	10.9617	+	18.9862i	0.602509	+	1.04358i	0.992440	+	0.122732i	$0.0391657\pi$
$331$	10.9617	+	18.9862i	0.602509	+	1.04358i	−0.389931	+	0.920844i	$0.627501\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.36389			−0.183789
$336$		0			0
$337$	−14.0733			−0.766624			−0.383312	−	0.923619i	$-0.625217\pi$
$337$	−14.0733			−0.766624			−0.383312	+	0.923619i	$0.625217\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.62476	+	9.74238i	0.304598	+	0.527579i
$342$		0			0
$343$	−13.4863	+	12.6933i	−0.728193	+	0.685372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.50808	+	4.34412i	−0.134641	+	0.233205i	−0.925460	−	0.378845i	$-0.876321\pi$
$347$	−2.50808	+	4.34412i	−0.134641	+	0.233205i	0.790819	+	0.612050i	$0.209655\pi$
$348$		0			0
$349$	−10.7382			−0.574801			−0.287401	−	0.957810i	$-0.592791\pi$
$349$	−10.7382			−0.574801			−0.287401	+	0.957810i	$0.592791\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.16307	−	2.01449i	0.0619039	−	0.107221i	−0.833413	−	0.552651i	$-0.813616\pi$
$353$	1.16307	−	2.01449i	0.0619039	−	0.107221i	0.895316	+	0.445431i	$0.146949\pi$
$354$		0			0
$355$	0.959372	+	1.66168i	0.0509182	+	0.0881928i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.97141	−	8.61073i	−0.262381	−	0.454457i	0.704493	−	0.709711i	$-0.251174\pi$
$359$	−4.97141	−	8.61073i	−0.262381	−	0.454457i	−0.966874	+	0.255254i	$0.917841\pi$
$360$		0			0
$361$	8.80150	−	15.2447i	0.463237	−	0.802350i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.87197			−0.0979832
$366$		0			0
$367$	−0.464574	+	0.804665i	−0.0242505	+	0.0420032i	−0.877896	−	0.478851i	$-0.841053\pi$
$367$	−0.464574	+	0.804665i	−0.0242505	+	0.0420032i	0.853645	+	0.520855i	$0.174387\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.78659	−	5.90461i	−0.300425	−	0.306552i
$372$		0			0
$373$	15.1352	+	26.2149i	0.783669	+	1.35735i	0.929791	+	0.368088i	$0.119988\pi$
$373$	15.1352	+	26.2149i	0.783669	+	1.35735i	−0.146122	+	0.989267i	$0.546679\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.20602			−0.113616
$378$		0			0
$379$	−28.5757			−1.46783			−0.733917	−	0.679240i	$-0.762310\pi$
$379$	−28.5757			−1.46783			−0.733917	+	0.679240i	$0.762310\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.8107	−	20.4567i	−0.603497	−	1.04529i	−0.992287	−	0.123961i	$-0.960440\pi$
$383$	−11.8107	−	20.4567i	−0.603497	−	1.04529i	0.388790	−	0.921326i	$-0.372893\pi$
$384$		0			0
$385$	0.411351	−	1.47544i	0.0209644	−	0.0751956i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.23749	+	14.2677i	−0.417657	+	0.723404i	−0.995703	−	0.0926005i	$-0.970482\pi$
$389$	−8.23749	+	14.2677i	−0.417657	+	0.723404i	0.578046	+	0.816004i	$0.303815\pi$
$390$		0			0
$391$	7.46457			0.377500
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.543507	+	0.941382i	−0.0273468	+	0.0473660i
$396$		0			0
$397$	6.41586	+	11.1126i	0.322003	+	0.557726i	0.980901	−	0.194507i	$-0.0623105\pi$
$397$	6.41586	+	11.1126i	0.322003	+	0.557726i	−0.658898	+	0.752232i	$0.728977\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.8187	+	27.3989i	0.789950	+	1.36823i	0.925997	+	0.377532i	$0.123227\pi$
$401$	15.8187	+	27.3989i	0.789950	+	1.36823i	−0.136046	+	0.990702i	$0.543440\pi$
$402$		0			0
$403$	1.76771	−	3.06177i	0.0880561	−	0.152518i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	14.0058			0.694240
$408$		0			0
$409$	−12.0144	+	20.8095i	−0.594072	+	1.02896i	0.399605	+	0.916687i	$0.369147\pi$
$409$	−12.0144	+	20.8095i	−0.594072	+	1.02896i	−0.993677	+	0.112275i	$0.964186\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	11.5286	+	11.7637i	0.567285	+	0.578855i
$414$		0			0
$415$	1.43598	+	2.48720i	0.0704897	+	0.122092i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.72777			0.0844073			0.0422036	−	0.999109i	$-0.486562\pi$
$419$	1.72777			0.0844073			0.0422036	+	0.999109i	$0.486562\pi$
$420$		0			0
$421$	−20.0949			−0.979367			−0.489683	−	0.871900i	$-0.662888\pi$
$421$	−20.0949			−0.979367			−0.489683	+	0.871900i	$0.662888\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.45486	−	14.6442i	−0.410121	−	0.710350i
$426$		0			0
$427$	−3.49480	+	0.898718i	−0.169125	+	0.0434920i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.4246	−	18.0560i	0.502137	−	0.869727i	−0.497860	−	0.867257i	$-0.665881\pi$
$431$	10.4246	−	18.0560i	0.502137	−	0.869727i	0.999997	−	0.00246928i	$-0.000785996\pi$
$432$		0			0
$433$	10.2255			0.491404			0.245702	−	0.969345i	$-0.420982\pi$
$433$	10.2255			0.491404			0.245702	+	0.969345i	$0.420982\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.28947	−	2.23342i	0.0616836	−	0.106839i
$438$		0			0
$439$	3.55718	+	6.16122i	0.169775	+	0.294059i	0.938341	−	0.345712i	$-0.112363\pi$
$439$	3.55718	+	6.16122i	0.169775	+	0.294059i	−0.768566	+	0.639771i	$0.779029\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.22094	+	9.04293i	0.248054	+	0.429642i	0.962986	−	0.269552i	$-0.0868756\pi$
$443$	5.22094	+	9.04293i	0.248054	+	0.429642i	−0.714932	+	0.699194i	$0.753542\pi$
$444$		0			0
$445$	0.654988	−	1.13447i	0.0310494	−	0.0537792i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−41.3502			−1.95144			−0.975719	−	0.219028i	$-0.929711\pi$
$449$	−41.3502			−1.95144			−0.975719	+	0.219028i	$0.929711\pi$
$450$		0			0
$451$	−10.3450	+	17.9181i	−0.487128	+	0.843730i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.466208	+	0.119889i	−0.0218562	+	0.00562051i
$456$		0			0
$457$	6.87592	+	11.9095i	0.321642	+	0.557101i	0.980827	−	0.194880i	$-0.0624318\pi$
$457$	6.87592	+	11.9095i	0.321642	+	0.557101i	−0.659185	+	0.751981i	$0.729099\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.54583			−0.304870			−0.152435	−	0.988314i	$-0.548711\pi$
$461$	−6.54583			−0.304870			−0.152435	+	0.988314i	$0.548711\pi$
$462$		0			0
$463$	−0.228720			−0.0106295			−0.00531475	−	0.999986i	$-0.501692\pi$
$463$	−0.228720			−0.0106295			−0.00531475	+	0.999986i	$0.501692\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.3788	+	30.1010i	0.804195	+	1.39291i	0.916833	+	0.399271i	$0.130737\pi$
$467$	17.3788	+	30.1010i	0.804195	+	1.39291i	−0.112638	+	0.993636i	$0.535930\pi$
$468$		0			0
$469$	−26.0510	−	26.5824i	−1.20292	−	1.22746i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.08865	−	7.08175i	0.187996	−	0.325619i
$474$		0			0
$475$	−5.84213			−0.268055
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.4721	−	21.6023i	0.569865	−	0.987035i	−0.426714	−	0.904387i	$-0.640329\pi$
$479$	12.4721	−	21.6023i	0.569865	−	0.987035i	0.996579	−	0.0826481i	$-0.0263377\pi$
$480$		0			0
$481$	−2.20082	−	3.81193i	−0.100349	−	0.173809i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.23912	−	2.14622i	−0.0562657	−	0.0974550i
$486$		0			0
$487$	3.88207	−	6.72395i	0.175914	−	0.304691i	−0.764564	−	0.644548i	$-0.777045\pi$
$487$	3.88207	−	6.72395i	0.175914	−	0.304691i	0.940477	+	0.339857i	$0.110379\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	24.6224			1.11120			0.555598	−	0.831451i	$-0.312490\pi$
$491$	24.6224			1.11120			0.555598	+	0.831451i	$0.312490\pi$
$492$		0			0
$493$	−4.95937	+	8.58988i	−0.223359	+	0.386869i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.70137	+	20.4498i	−0.255742	+	0.917300i
$498$		0			0
$499$	−12.3811	−	21.4447i	−0.554255	−	0.959998i	−0.997961	−	0.0638259i	$-0.979670\pi$
$499$	−12.3811	−	21.4447i	−0.554255	−	0.959998i	0.443706	−	0.896173i	$-0.353664\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.01367			−0.134373			−0.0671865	−	0.997740i	$-0.521402\pi$
$503$	−3.01367			−0.134373			−0.0671865	+	0.997740i	$0.521402\pi$
$504$		0			0
$505$	−2.42107			−0.107736
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.7323	−	30.7132i	−0.785970	−	1.36134i	−0.928418	−	0.371537i	$-0.878831\pi$
$509$	−17.7323	−	30.7132i	−0.785970	−	1.36134i	0.142448	−	0.989802i	$-0.454503\pi$
$510$		0			0
$511$	−14.4971	−	14.7928i	−0.641315	−	0.654395i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.315178	−	0.545904i	0.0138884	−	0.0240554i
$516$		0			0
$517$	12.5127			0.550309
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.48276	−	6.03232i	0.152582	−	0.264281i	−0.779594	−	0.626286i	$-0.784574\pi$
$521$	3.48276	−	6.03232i	0.152582	−	0.264281i	0.932176	+	0.362005i	$0.117908\pi$
$522$		0			0
$523$	16.6940	+	28.9148i	0.729977	+	1.26436i	0.956892	+	0.290443i	$0.0938025\pi$
$523$	16.6940	+	28.9148i	0.729977	+	1.26436i	−0.226916	+	0.973914i	$0.572864\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.94802	−	13.7664i	−0.346221	−	0.599673i
$528$		0			0
$529$	9.11956	−	15.7955i	0.396503	−	0.686763i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.50232			0.281647
$534$		0			0
$535$	−0.518875	+	0.898718i	−0.0224329	+	0.0388549i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	14.8450	−	8.17571i	0.639420	−	0.352153i
$540$		0			0
$541$	4.10752	+	7.11444i	0.176596	+	0.305874i	0.940713	−	0.339205i	$-0.110158\pi$
$541$	4.10752	+	7.11444i	0.176596	+	0.305874i	−0.764116	+	0.645079i	$0.776825\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.09166			−0.132432
$546$		0			0
$547$	−8.50232			−0.363533			−0.181767	−	0.983342i	$-0.558182\pi$
$547$	−8.50232			−0.363533			−0.181767	+	0.983342i	$0.558182\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.71341	+	2.96772i	0.0729938	+	0.126429i
$552$		0			0
$553$	−11.6482	+	2.99542i	−0.495330	+	0.127378i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.83009	+	13.5621i	−0.331772	+	0.574646i	−0.982859	−	0.184357i	$-0.940980\pi$
$557$	−7.83009	+	13.5621i	−0.331772	+	0.574646i	0.651088	+	0.759003i	$0.274313\pi$
$558$		0			0
$559$	−2.56991			−0.108695
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−21.2443	+	36.7963i	−0.895342	+	1.55078i	−0.0619602	+	0.998079i	$0.519735\pi$
$563$	−21.2443	+	36.7963i	−0.895342	+	1.55078i	−0.833381	+	0.552698i	$0.813598\pi$
$564$		0			0
$565$	−1.57046	−	2.72012i	−0.0660698	−	0.114436i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.422701	+	0.732140i	0.0177206	+	0.0306929i	0.874750	−	0.484575i	$-0.161026\pi$
$569$	0.422701	+	0.732140i	0.0177206	+	0.0306929i	−0.857029	+	0.515268i	$0.827692\pi$
$570$		0			0
$571$	14.8353	−	25.6955i	0.620838	−	1.07532i	−0.368492	−	0.929631i	$-0.620126\pi$
$571$	14.8353	−	25.6955i	0.620838	−	1.07532i	0.989330	−	0.145692i	$-0.0465408\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	10.7850			0.449764
$576$		0			0
$577$	6.04871	−	10.4767i	0.251811	−	0.436150i	−0.712213	−	0.701963i	$-0.752307\pi$
$577$	6.04871	−	10.4767i	0.251811	−	0.436150i	0.964024	+	0.265813i	$0.0856405\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.53379	+	30.6092i	−0.354041	+	1.26988i
$582$		0			0
$583$	3.78263	+	6.55171i	0.156661	+	0.271344i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.9338			0.575109			0.287555	−	0.957764i	$-0.407158\pi$
$587$	13.9338			0.575109			0.287555	+	0.957764i	$0.407158\pi$
$588$		0			0
$589$	−5.49192			−0.226291
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.77743	+	11.7389i	0.278316	+	0.482057i	0.970966	−	0.239216i	$-0.0768905\pi$
$593$	6.77743	+	11.7389i	0.278316	+	0.482057i	−0.692651	+	0.721273i	$0.743557\pi$
$594$		0			0
$595$	−0.581257	+	2.08486i	−0.0238292	+	0.0854711i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	20.3960	−	35.3270i	0.833360	−	1.44342i	−0.0619992	−	0.998076i	$-0.519748\pi$
$599$	20.3960	−	35.3270i	0.833360	−	1.44342i	0.895359	−	0.445345i	$-0.146919\pi$
$600$		0			0
$601$	30.2164			1.23255			0.616277	−	0.787530i	$-0.288640\pi$
$601$	30.2164			1.23255			0.616277	+	0.787530i	$0.288640\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.614360	−	1.06410i	0.0249773	−	0.0432619i
$606$		0			0
$607$	4.10752	+	7.11444i	0.166719	+	0.288766i	0.937264	−	0.348619i	$-0.113349\pi$
$607$	4.10752	+	7.11444i	0.166719	+	0.288766i	−0.770545	+	0.637385i	$0.780016\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.96621	−	3.40557i	−0.0795443	−	0.137775i
$612$		0			0
$613$	17.0224	−	29.4837i	0.687530	−	1.19084i	−0.285105	−	0.958496i	$-0.592028\pi$
$613$	17.0224	−	29.4837i	0.687530	−	1.19084i	0.972635	−	0.232340i	$-0.0746383\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−37.9064			−1.52606			−0.763028	−	0.646365i	$-0.776288\pi$
$617$	−37.9064			−1.52606			−0.763028	+	0.646365i	$0.776288\pi$
$618$		0			0
$619$	20.0293	−	34.6917i	0.805045	−	1.39438i	−0.111216	−	0.993796i	$-0.535475\pi$
$619$	20.0293	−	34.6917i	0.805045	−	1.39438i	0.916261	−	0.400582i	$-0.131192\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.0374	−	3.60983i	0.562395	−	0.144625i
$624$		0			0
$625$	−12.0728	−	20.9107i	−0.482911	−	0.836427i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−19.7907			−0.789107
$630$		0			0
$631$	3.44514			0.137149			0.0685745	−	0.997646i	$-0.478155\pi$
$631$	3.44514			0.137149			0.0685745	+	0.997646i	$0.478155\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.461695	+	0.799679i	0.0183218	+	0.0317343i
$636$		0			0
$637$	−4.55787	−	2.75564i	−0.180589	−	0.109183i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.47537	−	14.6798i	0.334757	−	0.579816i	−0.648681	−	0.761060i	$-0.724679\pi$
$641$	8.47537	−	14.6798i	0.334757	−	0.579816i	0.983438	+	0.181244i	$0.0580125\pi$
$642$		0			0
$643$	32.8090			1.29386			0.646931	−	0.762549i	$-0.276052\pi$
$643$	32.8090			1.29386			0.646931	+	0.762549i	$0.276052\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.5374	−	23.4474i	0.532208	−	0.921812i	−0.467084	−	0.884213i	$-0.654696\pi$
$647$	13.5374	−	23.4474i	0.532208	−	0.921812i	0.999293	−	0.0375994i	$-0.0119711\pi$
$648$		0			0
$649$	−7.53611	−	13.0529i	−0.295818	−	0.512372i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.9487	−	27.6240i	−0.624121	−	1.08101i	−0.988710	−	0.149841i	$-0.952124\pi$
$653$	−15.9487	−	27.6240i	−0.624121	−	1.08101i	0.364589	−	0.931169i	$-0.381210\pi$
$654$		0			0
$655$	1.73517	−	3.00539i	0.0677985	−	0.117430i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	33.9852			1.32388			0.661938	−	0.749559i	$-0.269734\pi$
$659$	33.9852			1.32388			0.661938	+	0.749559i	$0.269734\pi$
$660$		0			0
$661$	−7.58414	+	13.1361i	−0.294989	+	0.510935i	−0.974982	−	0.222283i	$-0.928649\pi$
$661$	−7.58414	+	13.1361i	−0.294989	+	0.510935i	0.679994	+	0.733218i	$0.261983\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.523388	+	0.534063i	0.0202961	+	0.0207101i
$666$		0			0
$667$	−3.16307	−	5.47860i	−0.122475	−	0.212132i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.30206			0.127475
$672$		0			0
$673$	17.7324			0.683535			0.341767	−	0.939785i	$-0.388975\pi$
$673$	17.7324			0.683535			0.341767	+	0.939785i	$0.388975\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.67154	−	2.89519i	−0.0642425	−	0.111271i	0.832115	−	0.554603i	$-0.187130\pi$
$677$	−1.67154	−	2.89519i	−0.0642425	−	0.111271i	−0.896358	+	0.443332i	$0.853796\pi$
$678$		0			0
$679$	7.36389	−	26.4130i	0.282600	−	1.01364i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−23.7427	+	41.1235i	−0.908489	+	1.57355i	−0.0923244	+	0.995729i	$0.529430\pi$
$683$	−23.7427	+	41.1235i	−0.908489	+	1.57355i	−0.816164	+	0.577820i	$0.803904\pi$
$684$		0			0
$685$	−2.72777			−0.104223
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.18878	−	2.05903i	0.0452889	−	0.0784427i
$690$		0			0
$691$	3.67674	+	6.36830i	0.139870	+	0.242262i	0.927447	−	0.373954i	$-0.121998\pi$
$691$	3.67674	+	6.36830i	0.139870	+	0.242262i	−0.787577	+	0.616216i	$0.788665\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.229408	−	0.397347i	−0.00870195	−	0.0150722i
$696$		0			0
$697$	14.6179	−	25.3190i	0.553693	−	0.959025i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−45.1729			−1.70616			−0.853079	−	0.521782i	$-0.825267\pi$
$701$	−45.1729			−1.70616			−0.853079	+	0.521782i	$0.825267\pi$
$702$		0			0
$703$	−3.41874	+	5.92144i	−0.128940	+	0.223331i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.7495	−	19.1319i	−0.705149	−	0.719531i
$708$		0			0
$709$	−19.9246	−	34.5105i	−0.748285	−	1.29607i	−0.948644	−	0.316346i	$-0.897544\pi$
$709$	−19.9246	−	34.5105i	−0.748285	−	1.29607i	0.200359	−	0.979723i	$-0.435789\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.1384			0.379687
$714$		0			0
$715$	0.440497			0.0164737
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.4211	+	35.3703i	0.761577	+	1.31909i	0.942037	+	0.335508i	$0.108908\pi$
$719$	20.4211	+	35.3703i	0.761577	+	1.31909i	−0.180460	+	0.983582i	$0.557759\pi$
$720$		0			0
$721$	6.75473	−	1.73704i	0.251559	−	0.0646906i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.16539	+	12.4108i	−0.266116	+	0.460926i
$726$		0			0
$727$	−6.42898			−0.238438			−0.119219	−	0.992868i	$-0.538039\pi$
$727$	−6.42898			−0.238438			−0.119219	+	0.992868i	$0.538039\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.77743	+	10.0068i	−0.213686	+	0.370115i
$732$		0			0
$733$	11.0773	+	19.1864i	0.409149	+	0.708667i	0.994795	−	0.101900i	$-0.0324922\pi$
$733$	11.0773	+	19.1864i	0.409149	+	0.708667i	−0.585645	+	0.810567i	$0.699159\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.0293	+	29.4956i	0.627282	+	1.08648i
$738$		0			0
$739$	9.62081	−	16.6637i	0.353907	−	0.612985i	−0.633023	−	0.774133i	$-0.718186\pi$
$739$	9.62081	−	16.6637i	0.353907	−	0.612985i	0.986930	+	0.161148i	$0.0515196\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	30.8616			1.13220			0.566100	−	0.824336i	$-0.308451\pi$
$743$	30.8616			1.13220			0.566100	+	0.824336i	$0.308451\pi$
$744$		0			0
$745$	1.81191	−	3.13832i	0.0663832	−	0.114979i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−11.1202	+	2.85967i	−0.406325	+	0.104490i
$750$		0			0
$751$	−2.12476	−	3.68020i	−0.0775337	−	0.134292i	0.824652	−	0.565641i	$-0.191371\pi$
$751$	−2.12476	−	3.68020i	−0.0775337	−	0.134292i	−0.902185	+	0.431349i	$0.858038\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.84540			−0.103555
$756$		0			0
$757$	2.69578			0.0979798			0.0489899	−	0.998799i	$-0.484400\pi$
$757$	2.69578			0.0979798			0.0489899	+	0.998799i	$0.484400\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.5064	−	33.7862i	−0.707108	−	1.22475i	−0.965925	−	0.258821i	$-0.916666\pi$
$761$	−19.5064	−	33.7862i	−0.707108	−	1.22475i	0.258817	−	0.965926i	$-0.416667\pi$
$762$		0			0
$763$	−23.9428	−	24.4312i	−0.866788	−	0.884467i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.36840	+	4.10219i	−0.0855180	+	0.148121i
$768$		0			0
$769$	−32.0930			−1.15730			−0.578652	−	0.815574i	$-0.696421\pi$
$769$	−32.0930			−1.15730			−0.578652	+	0.815574i	$0.696421\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.3873	−	21.4554i	0.445539	−	0.771697i	−0.552550	−	0.833480i	$-0.686345\pi$
$773$	12.3873	−	21.4554i	0.445539	−	0.771697i	0.998090	+	0.0617828i	$0.0196786\pi$
$774$		0			0
$775$	−11.4834	−	19.8899i	−0.412498	−	0.714467i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.05034	−	8.74745i	−0.180947	−	0.313410i
$780$		0			0
$781$	9.71341	−	16.8241i	0.347573	−	0.602014i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.920120			0.0328405
$786$		0			0
$787$	−4.03543	+	6.98956i	−0.143847	+	0.249151i	−0.928942	−	0.370224i	$-0.879281\pi$
$787$	−4.03543	+	6.98956i	−0.143847	+	0.249151i	0.785095	+	0.619375i	$0.212614\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.33297	−	33.4757i	0.331842	−	1.19026i
$792$		0			0
$793$	−0.518875	−	0.898718i	−0.0184258	−	0.0319144i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−32.6342			−1.15596			−0.577982	−	0.816050i	$-0.696160\pi$
$797$	−32.6342			−1.15596			−0.577982	+	0.816050i	$0.696160\pi$
$798$		0			0
$799$	−17.6810			−0.625509
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.47661	+	16.4140i	0.334422	+	0.579237i
$804$		0			0
$805$	−0.966208	−	0.985915i	−0.0340544	−	0.0347489i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	4.74200	−	8.21339i	0.166720	−	0.288767i	−0.770545	−	0.637386i	$-0.780016\pi$
$809$	4.74200	−	8.21339i	0.166720	−	0.288767i	0.937265	+	0.348618i	$0.113349\pi$
$810$		0			0
$811$	−6.95074			−0.244073			−0.122037	−	0.992526i	$-0.538943\pi$
$811$	−6.95074			−0.244073			−0.122037	+	0.992526i	$0.538943\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.07046	−	1.85409i	0.0374967	−	0.0649461i
$816$		0			0
$817$	1.99604	+	3.45725i	0.0698327	+	0.120954i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	23.7096	+	41.0662i	0.827470	+	1.43322i	0.900017	+	0.435856i	$0.143554\pi$
$821$	23.7096	+	41.0662i	0.827470	+	1.43322i	−0.0725464	+	0.997365i	$0.523113\pi$
$822$		0			0
$823$	14.6895	−	25.4429i	0.512043	−	0.886884i	−0.487860	−	0.872922i	$-0.662222\pi$
$823$	14.6895	−	25.4429i	0.512043	−	0.886884i	0.999903	−	0.0139620i	$-0.00444437\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	20.6238			0.717160			0.358580	−	0.933499i	$-0.383261\pi$
$827$	20.6238			0.717160			0.358580	+	0.933499i	$0.383261\pi$
$828$		0			0
$829$	19.4698	−	33.7226i	0.676213	−	1.17124i	−0.299899	−	0.953971i	$-0.596953\pi$
$829$	19.4698	−	33.7226i	0.676213	−	1.17124i	0.976113	−	0.217265i	$-0.0697135\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−20.9766	+	11.5526i	−0.726797	+	0.400274i
$834$		0			0
$835$	0.262511	+	0.454683i	0.00908458	+	0.0157350i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.3743			0.634351			0.317175	−	0.948367i	$-0.397266\pi$
$839$	18.3743			0.634351			0.317175	+	0.948367i	$0.397266\pi$
$840$		0			0
$841$	−20.5940			−0.710137
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.48508	+	2.57224i	0.0510884	+	0.0884877i
$846$		0			0
$847$	13.1666	−	3.38591i	0.452411	−	0.116341i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.31122	−	10.9314i	0.216346	−	0.374722i
$852$		0			0
$853$	28.1819			0.964931			0.482466	−	0.875915i	$-0.339741\pi$
$853$	28.1819			0.964931			0.482466	+	0.875915i	$0.339741\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.83762	+	15.3072i	−0.301887	+	0.522884i	−0.976563	−	0.215230i	$-0.930950\pi$
$857$	−8.83762	+	15.3072i	−0.301887	+	0.522884i	0.674676	+	0.738114i	$0.264283\pi$
$858$		0			0
$859$	−14.1449	−	24.4997i	−0.482617	−	0.835917i	0.517184	−	0.855874i	$-0.326980\pi$
$859$	−14.1449	−	24.4997i	−0.482617	−	0.835917i	−0.999801	+	0.0199570i	$0.993647\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.7821	−	42.9238i	−0.843592	−	1.46114i	−0.886839	−	0.462079i	$-0.847104\pi$
$863$	−24.7821	−	42.9238i	−0.843592	−	1.46114i	0.0432471	−	0.999064i	$-0.486230\pi$
$864$		0			0
$865$	−1.71053	+	2.96273i	−0.0581599	+	0.100736i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.0058			0.373345
$870$		0			0
$871$	5.35185	−	9.26967i	0.181340	−	0.314091i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.68934	+	6.05935i	−0.0571100	+	0.204843i
$876$		0			0
$877$	5.08701	+	8.81097i	0.171776	+	0.297525i	0.939041	−	0.343805i	$-0.111716\pi$
$877$	5.08701	+	8.81097i	0.171776	+	0.297525i	−0.767265	+	0.641331i	$0.778383\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.2919			1.22271			0.611353	−	0.791358i	$-0.290626\pi$
$881$	36.2919			1.22271			0.611353	+	0.791358i	$0.290626\pi$
$882$		0			0
$883$	−7.00327			−0.235679			−0.117839	−	0.993033i	$-0.537597\pi$
$883$	−7.00327			−0.235679			−0.117839	+	0.993033i	$0.537597\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.2930	−	40.3447i	−0.782104	−	1.35464i	−0.930714	−	0.365747i	$-0.880813\pi$
$887$	−23.2930	−	40.3447i	−0.782104	−	1.35464i	0.148611	−	0.988896i	$-0.452520\pi$
$888$		0			0
$889$	−2.74377	+	9.84141i	−0.0920231	+	0.330070i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.05430	+	5.29021i	−0.102208	+	0.177030i
$894$		0			0
$895$	4.62244			0.154511
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.73585	+	11.6668i	−0.224653	+	0.389111i
$900$		0			0
$901$	−5.34501	−	9.25783i	−0.178068	−	0.308423i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.158555	−	0.274626i	−0.00527055	−	0.00912886i
$906$		0			0
$907$	8.54583	−	14.8018i	0.283760	−	0.491486i	−0.688548	−	0.725191i	$-0.741752\pi$
$907$	8.54583	−	14.8018i	0.283760	−	0.491486i	0.972308	+	0.233705i	$0.0750849\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	26.7634			0.886710			0.443355	−	0.896346i	$-0.353788\pi$
$911$	26.7634			0.886710			0.443355	+	0.896346i	$0.353788\pi$
$912$		0			0
$913$	14.5390	−	25.1823i	0.481170	−	0.833412i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	37.1871	−	9.56300i	1.22803	−	0.315798i
$918$		0			0
$919$	−9.99441	−	17.3108i	−0.329685	−	0.571031i	0.652764	−	0.757561i	$-0.273609\pi$
$919$	−9.99441	−	17.3108i	−0.329685	−	0.571031i	−0.982449	+	0.186530i	$0.940276\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.10533			−0.200959
$924$		0			0
$925$	−28.5940			−0.940164
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.8126	+	46.4408i	0.879693	+	1.52367i	0.851678	+	0.524065i	$0.175585\pi$
$929$	26.8126	+	46.4408i	0.879693	+	1.52367i	0.0280145	+	0.999608i	$0.491082\pi$
$930$		0			0
$931$	−0.167026	+	8.27192i	−0.00547407	+	0.271101i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.990285	−	1.71522i	0.0323858	−	0.0560938i
$936$		0			0
$937$	−7.87524			−0.257273			−0.128636	−	0.991692i	$-0.541060\pi$
$937$	−7.87524			−0.257273			−0.128636	+	0.991692i	$0.541060\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.4406	+	30.2081i	−0.568548	+	0.984755i	0.428162	+	0.903702i	$0.359161\pi$
$941$	−17.4406	+	30.2081i	−0.568548	+	0.984755i	−0.996710	+	0.0810523i	$0.974172\pi$
$942$		0			0
$943$	9.32326	+	16.1484i	0.303607	+	0.525863i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.59905	+	2.76964i	0.0519622	+	0.0900012i	0.890837	−	0.454324i	$-0.150119\pi$
$947$	1.59905	+	2.76964i	0.0519622	+	0.0900012i	−0.838874	+	0.544325i	$0.816786\pi$
$948$		0			0
$949$	2.97825	−	5.15847i	0.0966780	−	0.167451i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−51.6465			−1.67299			−0.836497	−	0.547971i	$-0.815400\pi$
$953$	−51.6465			−1.67299			−0.836497	+	0.547971i	$0.815400\pi$
$954$		0			0
$955$	−2.99316	+	5.18431i	−0.0968565	+	0.167760i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.1248	−	21.5556i	−0.682154	−	0.696067i
$960$		0			0
$961$	4.70494	+	8.14920i	0.151772	+	0.262877i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.945308			0.0304305
$966$		0			0
$967$	−37.1021			−1.19312			−0.596561	−	0.802568i	$-0.703467\pi$
$967$	−37.1021			−1.19312			−0.596561	+	0.802568i	$0.703467\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.86320	+	15.3515i	0.284434	+	0.492653i	0.972472	−	0.233021i	$-0.0748611\pi$
$971$	8.86320	+	15.3515i	0.284434	+	0.492653i	−0.688038	+	0.725675i	$0.741528\pi$
$972$		0			0
$973$	1.36333	−	4.89003i	0.0437064	−	0.156767i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.4577	−	33.7018i	0.622508	−	1.07822i	−0.366509	−	0.930415i	$-0.619447\pi$
$977$	19.4577	−	33.7018i	0.622508	−	1.07822i	0.989017	−	0.147801i	$-0.0472196\pi$
$978$		0			0
$979$	−13.2632			−0.423894
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.6478	+	35.7630i	−0.658561	+	1.14066i	0.322427	+	0.946594i	$0.395501\pi$
$983$	−20.6478	+	35.7630i	−0.658561	+	1.14066i	−0.980988	+	0.194067i	$0.937832\pi$
$984$		0			0
$985$	0.180699	+	0.312981i	0.00575756	+	0.00997239i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.68482	−	6.38230i	−0.117171	−	0.202945i
$990$		0			0
$991$	9.72257	−	16.8400i	0.308848	−	0.534940i	−0.669263	−	0.743026i	$-0.733390\pi$
$991$	9.72257	−	16.8400i	0.308848	−	0.534940i	0.978111	+	0.208086i	$0.0667233\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.46784			0.205044
$996$		0			0
$997$	−17.1693	+	29.7382i	−0.543759	+	0.941818i	0.454925	+	0.890530i	$0.349666\pi$
$997$	−17.1693	+	29.7382i	−0.543759	+	0.941818i	−0.998684	+	0.0512881i	$0.983667\pi$
$998$		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.865.2	✓	6
3.2	odd	2		1512.2.s.l.865.2	yes	6
7.2	even	3	inner	1512.2.s.k.1297.2	yes	6
21.2	odd	6		1512.2.s.l.1297.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.k.865.2	✓	6	1.1	even	1	trivial
1512.2.s.k.1297.2	yes	6	7.2	even	3	inner
1512.2.s.l.865.2	yes	6	3.2	odd	2
1512.2.s.l.1297.2	yes	6	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.119562 - 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +O(q^{10})\)	\(q+(-0.119562 - 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-1.21053 + 2.09671i) q^{11} +0.760877 q^{13} +(1.71053 - 2.96273i) q^{17} +(-0.590972 - 1.02359i) q^{19} +(1.09097 + 1.88962i) q^{23} +(2.47141 - 4.28061i) q^{25} -2.89931 q^{29} +(2.32326 - 4.02400i) q^{31} +(-0.612725 + 0.157568i) q^{35} +(-2.89248 - 5.00992i) q^{37} +8.54583 q^{41} -3.37756 q^{43} +(-2.58414 - 4.47585i) q^{47} +(-5.99028 - 3.62167i) q^{49} +(1.56238 - 2.70612i) q^{53} +0.578933 q^{55} +(-3.11273 + 5.39140i) q^{59} +(-0.681943 - 1.18116i) q^{61} +(-0.0909717 - 0.157568i) q^{65} +(7.03379 - 12.1829i) q^{67} -8.02408 q^{71} +(3.91423 - 6.77965i) q^{73} +(4.48345 + 4.57489i) q^{77} +(-2.27292 - 3.93680i) q^{79} -12.0104 q^{83} -0.818057 q^{85} +(2.73912 + 4.74430i) q^{89} +(0.540628 - 1.93914i) q^{91} +(-0.141315 + 0.244765i) q^{95} +10.3639 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{5} - 4 q^{7}+O(q^{10}) \) 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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