LMFDB - Embedded newform 1512.2.s.l.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.l.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	0.891521	−	0.452979i	$-0.149639\pi$
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	−0.838052	+	0.545591i	$0.816305\pi$
$6$		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	−0.623785	−	0.781596i	$-0.714406\pi$
$11$	1.21053	−	2.09671i	0.364990	−	0.632180i	0.988774	+	0.149416i	$0.0477392\pi$
$12$		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	−0.995414	−	0.0956576i	$-0.969505\pi$
$17$	−1.71053	+	2.96273i	−0.414865	+	0.718568i	0.580549	+	0.814225i	$0.302838\pi$
$18$		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	0.729578	−	0.683897i	$-0.239716\pi$
$23$	−1.09097	−	1.88962i	−0.227483	−	0.394013i	−0.957062	+	0.289885i	$0.906383\pi$
$24$		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	$-0.413243\pi$
$29$	2.89931			0.538389			0.269194	+	0.963086i	$0.413243\pi$
$30$		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	$-0.732557\pi$
$41$	−8.54583			−1.33463			−0.667317	+	0.744774i	$0.732557\pi$
$42$		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	0.990615	−	0.136685i	$-0.0436447\pi$
$47$	2.58414	+	4.47585i	0.376935	+	0.652870i	−0.613680	+	0.789555i	$0.710311\pi$
$48$		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	−0.953152	−	0.302493i	$-0.902181\pi$
$53$	−1.56238	+	2.70612i	−0.214610	+	0.371715i	0.738542	+	0.674207i	$0.235515\pi$
$54$		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	−0.589107	−	0.808055i	$-0.700520\pi$
$59$	3.11273	−	5.39140i	0.405242	−	0.701900i	0.994350	+	0.106155i	$0.0338538\pi$
$60$		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	$-0.342035\pi$
$71$	8.02408			0.952283			0.476141	+	0.879369i	$0.342035\pi$
$72$		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	$-0.270913\pi$
$83$	12.0104			1.31831			0.659157	+	0.752006i	$0.270913\pi$
$84$		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	0.683545	−	0.729908i	$-0.260437\pi$
$89$	−2.73912	−	4.74430i	−0.290346	−	0.502895i	−0.973892	+	0.227013i	$0.927104\pi$
$90$		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	$0.334704\pi$
$101$	−5.06238	+	8.76830i	−0.503726	+	0.872479i	−0.999991	+	0.00430755i	$0.998629\pi$
$102$		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	0.951643	−	0.307207i	$-0.0993943\pi$
$107$	2.16991	+	3.75839i	0.209773	+	0.363337i	−0.741870	+	0.670544i	$0.766061\pi$
$108$		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	$-0.711987\pi$
$113$	−13.1352			−1.23565			−0.617826	+	0.786315i	$0.711987\pi$
$114$		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	$-0.948082\pi$
$131$	−7.25636	−	12.5684i	−0.633991	−	1.09811i	0.352736	−	0.935723i	$-0.385251\pi$
$132$		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	−0.999893	−	0.0146035i	$-0.995351\pi$
$137$	−5.70370	+	9.87909i	−0.487300	+	0.844028i	0.512594	+	0.858631i	$0.328685\pi$
$138$		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	$-0.953492\pi$
$149$	−7.57730	−	13.1243i	−0.620756	−	1.07518i	0.368589	−	0.929593i	$-0.379841\pi$
$150$		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	$-0.472927\pi$
$167$	2.19562			0.169902			0.0849509	+	0.996385i	$0.472927\pi$
$168$		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	$0.0163708\pi$
$173$	7.15335	+	12.3900i	0.543859	+	0.941992i	−0.454818	+	0.890584i	$0.650296\pi$
$174$		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	$-0.576361\pi$
$179$	9.66539	−	16.7409i	0.722425	−	1.25128i	0.960025	−	0.279914i	$-0.0903060\pi$
$180$		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	$0.193999\pi$
$191$	12.5172	+	21.6805i	0.905716	+	1.56875i	0.0857621	+	0.996316i	$0.472668\pi$
$192$		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	$-0.482854\pi$
$197$	1.51135			0.107679			0.0538396	+	0.998550i	$0.482854\pi$
$198$		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	$-0.526516\pi$
$227$	12.3759	−	21.4357i	0.821419	−	1.42274i	0.904626	−	0.426207i	$-0.140151\pi$
$228$		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	0.964386	−	0.264497i	$-0.0852061\pi$
$233$	3.86389	+	6.69245i	0.253132	+	0.438437i	−0.711255	+	0.702934i	$0.751873\pi$
$234$		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	$-0.846383\pi$
$239$	−27.3880			−1.77158			−0.885790	+	0.464086i	$0.846383\pi$
$240$		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	$-0.452956\pi$
$251$	4.66595			0.294512			0.147256	+	0.989098i	$0.452956\pi$
$252$		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	0.828049	−	0.560656i	$-0.189451\pi$
$257$	−1.14652	−	1.98583i	−0.0715178	−	0.123872i	−0.899567	+	0.436783i	$0.856118\pi$
$258$		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	−0.930378	−	0.366600i	$-0.880522\pi$
$263$	−2.39536	+	4.14888i	−0.147704	+	0.255831i	0.782675	+	0.622431i	$0.213855\pi$
$264$		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	$0.363149\pi$
$269$	−9.49316	+	16.4426i	−0.578808	+	1.00253i	−0.995616	+	0.0935310i	$0.970185\pi$
$270$		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	$-0.253672\pi$
$281$	23.4315			1.39780			0.698902	+	0.715217i	$0.253672\pi$
$282$		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	$-0.724427\pi$
$293$	−22.1866			−1.29615			−0.648077	+	0.761575i	$0.724427\pi$
$294$		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	−0.755144	−	0.655559i	$-0.772433\pi$
$311$	3.35348	−	5.80840i	0.190159	−	0.329364i	0.945303	+	0.326195i	$0.105766\pi$
$312$		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	0.816508	−	0.577334i	$-0.195907\pi$
$317$	−1.63323	−	2.82885i	−0.0917316	−	0.158884i	−0.908240	+	0.418450i	$0.862574\pi$
$318$		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	−0.790819	−	0.612050i	$-0.790345\pi$
$347$	2.50808	−	4.34412i	0.134641	−	0.233205i	0.925460	+	0.378845i	$0.123679\pi$
$348$		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	−0.895316	−	0.445431i	$-0.853051\pi$
$353$	−1.16307	+	2.01449i	−0.0619039	+	0.107221i	0.833413	+	0.552651i	$0.186384\pi$
$354$		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	0.966874	−	0.255254i	$-0.0821590\pi$
$359$	4.97141	+	8.61073i	0.262381	+	0.454457i	−0.704493	+	0.709711i	$0.748826\pi$
$360$		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	$0.0395597\pi$
$383$	11.8107	+	20.4567i	0.603497	+	1.04529i	−0.388790	+	0.921326i	$0.627107\pi$
$384$		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	−0.578046	−	0.816004i	$-0.696185\pi$
$389$	8.23749	−	14.2677i	0.417657	−	0.723404i	0.995703	+	0.0926005i	$0.0295180\pi$
$390$		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	$-0.876773\pi$
$401$	−15.8187	−	27.3989i	−0.789950	−	1.36823i	0.136046	−	0.990702i	$-0.456560\pi$
$402$		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	$-0.513438\pi$
$419$	−1.72777			−0.0844073			−0.0422036	+	0.999109i	$0.513438\pi$
$420$		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	$0.334119\pi$
$431$	−10.4246	+	18.0560i	−0.502137	+	0.869727i	−0.999997	+	0.00246928i	$0.999214\pi$
$432$		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	0.714932	−	0.699194i	$-0.246458\pi$
$443$	−5.22094	−	9.04293i	−0.248054	−	0.429642i	−0.962986	+	0.269552i	$0.913124\pi$
$444$		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	$-0.0702885\pi$
$449$	41.3502			1.95144			0.975719	+	0.219028i	$0.0702885\pi$
$450$		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	$-0.451289\pi$
$461$	6.54583			0.304870			0.152435	+	0.988314i	$0.451289\pi$
$462$		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	$-0.869263\pi$
$467$	−17.3788	−	30.1010i	−0.804195	−	1.39291i	0.112638	−	0.993636i	$-0.464070\pi$
$468$		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	$0.359671\pi$
$479$	−12.4721	+	21.6023i	−0.569865	+	0.987035i	−0.996579	+	0.0826481i	$0.973662\pi$
$480$		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	$-0.687510\pi$
$491$	−24.6224			−1.11120			−0.555598	+	0.831451i	$0.687510\pi$
$492$		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	$-0.478598\pi$
$503$	3.01367			0.134373			0.0671865	+	0.997740i	$0.478598\pi$
$504$		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	$0.121169\pi$
$509$	17.7323	+	30.7132i	0.785970	+	1.36134i	−0.142448	+	0.989802i	$0.545497\pi$
$510$		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	−0.932176	−	0.362005i	$-0.882092\pi$
$521$	−3.48276	+	6.03232i	−0.152582	+	0.264281i	0.779594	+	0.626286i	$0.215426\pi$
$522$		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	−0.651088	−	0.759003i	$-0.725687\pi$
$557$	7.83009	−	13.5621i	0.331772	−	0.574646i	0.982859	+	0.184357i	$0.0590203\pi$
$558$		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	$-0.480265\pi$
$563$	21.2443	−	36.7963i	0.895342	−	1.55078i	0.833381	−	0.552698i	$-0.186402\pi$
$564$		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	0.857029	−	0.515268i	$-0.172308\pi$
$569$	−0.422701	−	0.732140i	−0.0177206	−	0.0306929i	−0.874750	+	0.484575i	$0.838974\pi$
$570$		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	$-0.592842\pi$
$587$	−13.9338			−0.575109			−0.287555	+	0.957764i	$0.592842\pi$
$588$		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	0.692651	−	0.721273i	$-0.256443\pi$
$593$	−6.77743	−	11.7389i	−0.278316	−	0.482057i	−0.970966	+	0.239216i	$0.923109\pi$
$594$		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	$0.480252\pi$
$599$	−20.3960	+	35.3270i	−0.833360	+	1.44342i	−0.895359	+	0.445345i	$0.853081\pi$
$600$		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	$-0.223712\pi$
$617$	37.9064			1.52606			0.763028	+	0.646365i	$0.223712\pi$
$618$		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	−0.983438	−	0.181244i	$-0.941988\pi$
$641$	−8.47537	+	14.6798i	−0.334757	+	0.579816i	0.648681	+	0.761060i	$0.275321\pi$
$642$		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	$0.345304\pi$
$647$	−13.5374	+	23.4474i	−0.532208	+	0.921812i	−0.999293	+	0.0375994i	$0.988029\pi$
$648$		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	$0.0478762\pi$
$653$	15.9487	+	27.6240i	0.624121	+	1.08101i	−0.364589	+	0.931169i	$0.618790\pi$
$654$		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	$-0.730266\pi$
$659$	−33.9852			−1.32388			−0.661938	+	0.749559i	$0.730266\pi$
$660$		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	0.896358	−	0.443332i	$-0.146204\pi$
$677$	1.67154	+	2.89519i	0.0642425	+	0.111271i	−0.832115	+	0.554603i	$0.812870\pi$
$678$		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	$-0.470570\pi$
$683$	23.7427	−	41.1235i	0.908489	−	1.57355i	0.816164	−	0.577820i	$-0.196096\pi$
$684$		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	$-0.174733\pi$
$701$	45.1729			1.70616			0.853079	+	0.521782i	$0.174733\pi$
$702$		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	$-0.891092\pi$
$719$	−20.4211	−	35.3703i	−0.761577	−	1.31909i	0.180460	−	0.983582i	$-0.442241\pi$
$720$		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	$-0.691549\pi$
$743$	−30.8616			−1.13220			−0.566100	+	0.824336i	$0.691549\pi$
$744$		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	$0.0833339\pi$
$761$	19.5064	+	33.7862i	0.707108	+	1.22475i	−0.258817	+	0.965926i	$0.583333\pi$
$762$		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	−0.998090	−	0.0617828i	$-0.980321\pi$
$773$	−12.3873	+	21.4554i	−0.445539	+	0.771697i	0.552550	+	0.833480i	$0.313655\pi$
$774$		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	$-0.303840\pi$
$797$	32.6342			1.15596			0.577982	+	0.816050i	$0.303840\pi$
$798$		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	−0.937265	−	0.348618i	$-0.886651\pi$
$809$	−4.74200	+	8.21339i	−0.166720	+	0.288767i	0.770545	+	0.637386i	$0.219984\pi$
$810$		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	$-0.856446\pi$
$821$	−23.7096	−	41.0662i	−0.827470	−	1.43322i	0.0725464	−	0.997365i	$-0.476887\pi$
$822$		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	$-0.616739\pi$
$827$	−20.6238			−0.717160			−0.358580	+	0.933499i	$0.616739\pi$
$828$		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	$-0.602734\pi$
$839$	−18.3743			−0.634351			−0.317175	+	0.948367i	$0.602734\pi$
$840$		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	−0.674676	−	0.738114i	$-0.735717\pi$
$857$	8.83762	−	15.3072i	0.301887	−	0.522884i	0.976563	+	0.215230i	$0.0690500\pi$
$858$		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	$0.152896\pi$
$863$	24.7821	+	42.9238i	0.843592	+	1.46114i	−0.0432471	+	0.999064i	$0.513770\pi$
$864$		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	$-0.709374\pi$
$881$	−36.2919			−1.22271			−0.611353	+	0.791358i	$0.709374\pi$
$882$		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	$0.119187\pi$
$887$	23.2930	+	40.3447i	0.782104	+	1.35464i	−0.148611	+	0.988896i	$0.547480\pi$
$888$		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	$-0.646212\pi$
$911$	−26.7634			−0.886710			−0.443355	+	0.896346i	$0.646212\pi$
$912$		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	$-0.824415\pi$
$929$	−26.8126	−	46.4408i	−0.879693	−	1.52367i	−0.0280145	−	0.999608i	$-0.508918\pi$
$930$		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	$-0.640839\pi$
$941$	17.4406	−	30.2081i	0.568548	−	0.984755i	0.996710	−	0.0810523i	$-0.0258281\pi$
$942$		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	0.838874	−	0.544325i	$-0.183214\pi$
$947$	−1.59905	−	2.76964i	−0.0519622	−	0.0900012i	−0.890837	+	0.454324i	$0.849881\pi$
$948$		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	$-0.184600\pi$
$953$	51.6465			1.67299			0.836497	+	0.547971i	$0.184600\pi$
$954$		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	0.688038	−	0.725675i	$-0.258472\pi$
$971$	−8.86320	−	15.3515i	−0.284434	−	0.492653i	−0.972472	+	0.233021i	$0.925139\pi$
$972$		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	$0.380553\pi$
$977$	−19.4577	+	33.7018i	−0.622508	+	1.07822i	−0.989017	+	0.147801i	$0.952780\pi$
$978$		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	$-0.604499\pi$
$983$	20.6478	−	35.7630i	0.658561	−	1.14066i	0.980988	−	0.194067i	$-0.0621680\pi$
$984$		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.l.865.2	yes	6
3.2	odd	2		1512.2.s.k.865.2	✓	6
7.2	even	3	inner	1512.2.s.l.1297.2	yes	6
21.2	odd	6		1512.2.s.k.1297.2	yes	6

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

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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