LMFDB - Embedded newform 1512.2.t.c.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (of order $3$, degree $2$, not 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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	1512.361
Dual form			1512.2.t.c.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +O(q^{10})$	$q-2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +3.43944 q^{11} +(-0.429164 + 0.743335i) q^{13} +(0.405132 - 0.701710i) q^{17} +(0.750215 + 1.29941i) q^{19} -7.64930 q^{23} +2.68286 q^{25} +(-3.99696 - 6.92294i) q^{29} +(3.60578 + 6.24540i) q^{31} +(-2.37193 - 6.93931i) q^{35} +(0.458211 + 0.793644i) q^{37} +(-1.67577 + 2.90251i) q^{41} +(1.20465 + 2.08652i) q^{43} +(-0.307520 + 0.532640i) q^{47} +(-5.53543 + 4.28474i) q^{49} +(-6.31646 + 10.9404i) q^{53} -9.53342 q^{55} +(0.734690 + 1.27252i) q^{59} +(-5.71635 + 9.90101i) q^{61} +(1.18956 - 2.06037i) q^{65} +(-8.10061 - 14.0307i) q^{67} -14.4177 q^{71} +(-4.16893 + 7.22079i) q^{73} +(2.94325 + 8.61077i) q^{77} +(1.37586 - 2.38305i) q^{79} +(5.75814 + 9.97340i) q^{83} +(-1.12294 + 1.94500i) q^{85} +(5.11395 + 8.85763i) q^{89} +(-2.22822 - 0.438331i) q^{91} +(-2.07944 - 3.60170i) q^{95} +(3.82852 + 6.63119i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.77180			−1.23959			−0.619793	−	0.784766i	$-0.712783\pi$
$5$	−2.77180			−1.23959			−0.619793	+	0.784766i	$0.712783\pi$
$6$		0			0
$7$	0.855737	+	2.50354i	0.323438	+	0.946249i
$7$	0.855737	+	2.50354i	0.323438	+	0.946249i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.43944			1.03703			0.518515	−	0.855069i	$-0.326485\pi$
$11$	3.43944			1.03703			0.518515	+	0.855069i	$0.326485\pi$
$12$		0			0
$13$	−0.429164	+	0.743335i	−0.119029	+	0.206164i	−0.919383	−	0.393363i	$-0.871311\pi$
$13$	−0.429164	+	0.743335i	−0.119029	+	0.206164i	0.800354	+	0.599527i	$0.204645\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.405132	−	0.701710i	0.0982590	−	0.170190i	−0.812705	−	0.582675i	$-0.802006\pi$
$17$	0.405132	−	0.701710i	0.0982590	−	0.170190i	0.910964	+	0.412486i	$0.135339\pi$
$18$		0			0
$19$	0.750215	+	1.29941i	0.172111	+	0.298105i	0.939158	−	0.343486i	$-0.111608\pi$
$19$	0.750215	+	1.29941i	0.172111	+	0.298105i	−0.767047	+	0.641591i	$0.778275\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.64930			−1.59499			−0.797495	−	0.603326i	$-0.793842\pi$
$23$	−7.64930			−1.59499			−0.797495	+	0.603326i	$0.793842\pi$
$24$		0			0
$25$	2.68286			0.536572
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.99696	−	6.92294i	−0.742217	−	1.28556i	−0.951484	−	0.307700i	$-0.900441\pi$
$29$	−3.99696	−	6.92294i	−0.742217	−	1.28556i	0.209266	−	0.977859i	$-0.432893\pi$
$30$		0			0
$31$	3.60578	+	6.24540i	0.647618	+	1.12171i	0.983690	+	0.179871i	$0.0575679\pi$
$31$	3.60578	+	6.24540i	0.647618	+	1.12171i	−0.336073	+	0.941836i	$0.609099\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.37193	−	6.93931i	−0.400929	−	1.17296i
$36$		0			0
$37$	0.458211	+	0.793644i	0.0753294	+	0.130474i	0.901229	−	0.433342i	$-0.142666\pi$
$37$	0.458211	+	0.793644i	0.0753294	+	0.130474i	−0.825900	+	0.563817i	$0.809333\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.67577	+	2.90251i	−0.261711	+	0.453297i	−0.966697	−	0.255925i	$-0.917620\pi$
$41$	−1.67577	+	2.90251i	−0.261711	+	0.453297i	0.704986	+	0.709221i	$0.250953\pi$
$42$		0			0
$43$	1.20465	+	2.08652i	0.183708	+	0.318191i	0.943140	−	0.332395i	$-0.107857\pi$
$43$	1.20465	+	2.08652i	0.183708	+	0.318191i	−0.759433	+	0.650586i	$0.774523\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.307520	+	0.532640i	−0.0448564	+	0.0776935i	−0.887582	−	0.460650i	$-0.847616\pi$
$47$	−0.307520	+	0.532640i	−0.0448564	+	0.0776935i	0.842726	+	0.538343i	$0.180950\pi$
$48$		0			0
$49$	−5.53543	+	4.28474i	−0.790775	+	0.612106i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.31646	+	10.9404i	−0.867633	+	1.50278i	−0.00322332	+	0.999995i	$0.501026\pi$
$53$	−6.31646	+	10.9404i	−0.867633	+	1.50278i	−0.864409	+	0.502789i	$0.832307\pi$
$54$		0			0
$55$	−9.53342			−1.28549
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.734690	+	1.27252i	0.0956485	+	0.165668i	0.909879	−	0.414874i	$-0.136174\pi$
$59$	0.734690	+	1.27252i	0.0956485	+	0.165668i	−0.814231	+	0.580542i	$0.802841\pi$
$60$		0			0
$61$	−5.71635	+	9.90101i	−0.731904	+	1.26769i	0.224165	+	0.974551i	$0.428035\pi$
$61$	−5.71635	+	9.90101i	−0.731904	+	1.26769i	−0.956069	+	0.293143i	$0.905299\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.18956	−	2.06037i	0.147546	−	0.255558i
$66$		0			0
$67$	−8.10061	−	14.0307i	−0.989647	−	1.71412i	−0.619117	−	0.785299i	$-0.712509\pi$
$67$	−8.10061	−	14.0307i	−0.989647	−	1.71412i	−0.370530	−	0.928820i	$-0.620824\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.4177			−1.71106			−0.855532	−	0.517749i	$-0.826770\pi$
$71$	−14.4177			−1.71106			−0.855532	+	0.517749i	$0.826770\pi$
$72$		0			0
$73$	−4.16893	+	7.22079i	−0.487936	+	0.845130i	−0.999904	−	0.0138749i	$-0.995583\pi$
$73$	−4.16893	+	7.22079i	−0.487936	+	0.845130i	0.511968	+	0.859005i	$0.328917\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.94325	+	8.61077i	0.335415	+	0.981288i
$78$		0			0
$79$	1.37586	−	2.38305i	0.154796	−	0.268115i	−0.778189	−	0.628031i	$-0.783861\pi$
$79$	1.37586	−	2.38305i	0.154796	−	0.268115i	0.932985	+	0.359916i	$0.117195\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.75814	+	9.97340i	0.632038	+	1.09472i	0.987134	+	0.159893i	$0.0511148\pi$
$83$	5.75814	+	9.97340i	0.632038	+	1.09472i	−0.355096	+	0.934830i	$0.615552\pi$
$84$		0			0
$85$	−1.12294	+	1.94500i	−0.121800	+	0.210965i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.11395	+	8.85763i	0.542078	+	0.938907i	0.998785	+	0.0492892i	$0.0156956\pi$
$89$	5.11395	+	8.85763i	0.542078	+	0.938907i	−0.456707	+	0.889617i	$0.650971\pi$
$90$		0			0
$91$	−2.22822	−	0.438331i	−0.233581	−	0.0459496i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.07944	−	3.60170i	−0.213346	−	0.369527i
$96$		0			0
$97$	3.82852	+	6.63119i	0.388727	+	0.673296i	0.992279	−	0.124029i	$-0.0395814\pi$
$97$	3.82852	+	6.63119i	0.388727	+	0.673296i	−0.603551	+	0.797324i	$0.706248\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.68603			0.366774			0.183387	−	0.983041i	$-0.441294\pi$
$101$	3.68603			0.366774			0.183387	+	0.983041i	$0.441294\pi$
$102$		0			0
$103$	−16.1205			−1.58840			−0.794201	−	0.607656i	$-0.792110\pi$
$103$	−16.1205			−1.58840			−0.794201	+	0.607656i	$0.792110\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.16767	−	5.48656i	−0.306230	−	0.530405i	0.671305	−	0.741182i	$-0.265734\pi$
$107$	−3.16767	−	5.48656i	−0.306230	−	0.530405i	−0.977534	+	0.210776i	$0.932401\pi$
$108$		0			0
$109$	4.89477	−	8.47799i	0.468834	−	0.812044i	−0.530532	−	0.847665i	$-0.678008\pi$
$109$	4.89477	−	8.47799i	0.468834	−	0.812044i	0.999365	+	0.0356213i	$0.0113410\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.06963	+	7.04881i	−0.382839	+	0.663096i	−0.991467	−	0.130360i	$-0.958387\pi$
$113$	−4.06963	+	7.04881i	−0.382839	+	0.663096i	0.608628	+	0.793456i	$0.291720\pi$
$114$		0			0
$115$	21.2023			1.97713
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.10345	+	0.413786i	0.192823	+	0.0379317i
$120$		0			0
$121$	0.829725			0.0754295
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.42264			0.574459
$126$		0			0
$127$	−12.5658			−1.11504			−0.557518	−	0.830165i	$-0.688246\pi$
$127$	−12.5658			−1.11504			−0.557518	+	0.830165i	$0.688246\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.58550			−0.138526			−0.0692631	−	0.997598i	$-0.522065\pi$
$131$	−1.58550			−0.138526			−0.0692631	+	0.997598i	$0.522065\pi$
$132$		0			0
$133$	−2.61114	+	2.99015i	−0.226415	+	0.259279i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.92788			−0.421017			−0.210508	−	0.977592i	$-0.567512\pi$
$137$	−4.92788			−0.421017			−0.210508	+	0.977592i	$0.567512\pi$
$138$		0			0
$139$	4.12999	−	7.15336i	0.350301	−	0.606740i	−0.636001	−	0.771688i	$-0.719412\pi$
$139$	4.12999	−	7.15336i	0.350301	−	0.606740i	0.986302	+	0.164949i	$0.0527458\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.47608	+	2.55665i	−0.123436	+	0.213798i
$144$		0			0
$145$	11.0788	+	19.1890i	0.920042	+	1.59356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	13.9140			1.13988			0.569938	−	0.821688i	$-0.306967\pi$
$149$	13.9140			1.13988			0.569938	+	0.821688i	$0.306967\pi$
$150$		0			0
$151$	22.9927			1.87112			0.935561	−	0.353166i	$-0.114895\pi$
$151$	22.9927			1.87112			0.935561	+	0.353166i	$0.114895\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.99450	−	17.3110i	−0.802777	−	1.39045i
$156$		0			0
$157$	−9.29022	−	16.0911i	−0.741441	−	1.28421i	−0.951839	−	0.306597i	$-0.900810\pi$
$157$	−9.29022	−	16.0911i	−0.741441	−	1.28421i	0.210399	−	0.977616i	$-0.432524\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.54579	−	19.1503i	−0.515880	−	1.50926i
$162$		0			0
$163$	−2.45194	−	4.24688i	−0.192050	−	0.332641i	0.753879	−	0.657013i	$-0.228180\pi$
$163$	−2.45194	−	4.24688i	−0.192050	−	0.332641i	−0.945930	+	0.324372i	$0.894847\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.47493	−	9.48286i	0.423663	−	0.733805i	−0.572632	−	0.819813i	$-0.694077\pi$
$167$	5.47493	−	9.48286i	0.423663	−	0.733805i	0.996295	+	0.0860073i	$0.0274108\pi$
$168$		0			0
$169$	6.13164	+	10.6203i	0.471664	+	0.816947i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.70271	+	11.6094i	−0.509598	+	0.882649i	0.490340	+	0.871531i	$0.336873\pi$
$173$	−6.70271	+	11.6094i	−0.509598	+	0.882649i	−0.999938	+	0.0111184i	$0.996461\pi$
$174$		0			0
$175$	2.29582	+	6.71665i	0.173548	+	0.507731i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.64888	−	11.5162i	0.496961	−	0.860761i	−0.503033	−	0.864267i	$-0.667783\pi$
$179$	6.64888	−	11.5162i	0.496961	−	0.860761i	0.999994	+	0.00350600i	$0.00111600\pi$
$180$		0			0
$181$	−10.9190			−0.811601			−0.405801	−	0.913962i	$-0.633007\pi$
$181$	−10.9190			−0.811601			−0.405801	+	0.913962i	$0.633007\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.27007	−	2.19982i	−0.0933772	−	0.161734i
$186$		0			0
$187$	1.39343	−	2.41349i	0.101897	−	0.176492i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.30553	+	16.1177i	−0.673325	+	1.16623i	0.303631	+	0.952790i	$0.401801\pi$
$191$	−9.30553	+	16.1177i	−0.673325	+	1.16623i	−0.976956	+	0.213443i	$0.931532\pi$
$192$		0			0
$193$	−1.46470	−	2.53693i	−0.105431	−	0.182613i	0.808483	−	0.588520i	$-0.200289\pi$
$193$	−1.46470	−	2.53693i	−0.105431	−	0.182613i	−0.913914	+	0.405907i	$0.866956\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.5050			1.31843			0.659214	−	0.751956i	$-0.270889\pi$
$197$	18.5050			1.31843			0.659214	+	0.751956i	$0.270889\pi$
$198$		0			0
$199$	0.793836	−	1.37496i	0.0562736	−	0.0974687i	−0.836516	−	0.547942i	$-0.815411\pi$
$199$	0.793836	−	1.37496i	0.0562736	−	0.0974687i	0.892790	+	0.450473i	$0.148745\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	13.9115	−	15.9308i	0.976397	−	1.11812i
$204$		0			0
$205$	4.64489	−	8.04518i	0.324413	−	0.561900i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.58032	+	4.46924i	0.178484	+	0.309144i
$210$		0			0
$211$	12.3436	−	21.3798i	0.849770	−	1.47184i	−0.0316443	−	0.999499i	$-0.510074\pi$
$211$	12.3436	−	21.3798i	0.849770	−	1.47184i	0.881414	−	0.472345i	$-0.156592\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.33905	−	5.78340i	−0.227721	−	0.394425i
$216$		0			0
$217$	−12.5500	+	14.3716i	−0.851950	+	0.975611i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.347737	+	0.602298i	0.0233913	+	0.0405149i
$222$		0			0
$223$	−9.78468	−	16.9476i	−0.655231	−	1.13489i	−0.981836	−	0.189732i	$-0.939238\pi$
$223$	−9.78468	−	16.9476i	−0.655231	−	1.13489i	0.326605	−	0.945161i	$-0.394095\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.64808			−0.573993			−0.286996	−	0.957932i	$-0.592657\pi$
$227$	−8.64808			−0.573993			−0.286996	+	0.957932i	$0.592657\pi$
$228$		0			0
$229$	11.5427			0.762765			0.381382	−	0.924417i	$-0.375448\pi$
$229$	11.5427			0.762765			0.381382	+	0.924417i	$0.375448\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.12745	+	14.0772i	0.532447	+	0.922225i	0.999282	+	0.0378811i	$0.0120608\pi$
$233$	8.12745	+	14.0772i	0.532447	+	0.922225i	−0.466835	+	0.884344i	$0.654606\pi$
$234$		0			0
$235$	0.852382	−	1.47637i	0.0556033	−	0.0963077i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.4336	+	21.5355i	−0.804260	+	1.39302i	0.112530	+	0.993648i	$0.464105\pi$
$239$	−12.4336	+	21.5355i	−0.804260	+	1.39302i	−0.916790	+	0.399371i	$0.869229\pi$
$240$		0			0
$241$	−19.0363			−1.22623			−0.613117	−	0.789992i	$-0.710085\pi$
$241$	−19.0363			−1.22623			−0.613117	+	0.789992i	$0.710085\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	15.3431	−	11.8764i	0.980234	−	0.758758i
$246$		0			0
$247$	−1.28786			−0.0819447
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.980433			0.0618844			0.0309422	−	0.999521i	$-0.490149\pi$
$251$	0.980433			0.0618844			0.0309422	+	0.999521i	$0.490149\pi$
$252$		0			0
$253$	−26.3093			−1.65405
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.36725			−0.272421			−0.136211	−	0.990680i	$-0.543492\pi$
$257$	−4.36725			−0.272421			−0.136211	+	0.990680i	$0.543492\pi$
$258$		0			0
$259$	−1.59481	+	1.82630i	−0.0990968	+	0.113481i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.4842			0.769811			0.384905	−	0.922956i	$-0.374234\pi$
$263$	12.4842			0.769811			0.384905	+	0.922956i	$0.374234\pi$
$264$		0			0
$265$	17.5079	−	30.3247i	1.07550	−	1.86283i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.29270	+	14.3634i	−0.505615	+	0.875750i	0.494364	+	0.869255i	$0.335401\pi$
$269$	−8.29270	+	14.3634i	−0.505615	+	0.875750i	−0.999979	+	0.00649532i	$0.997932\pi$
$270$		0			0
$271$	12.9814	+	22.4845i	0.788566	+	1.36584i	0.926845	+	0.375444i	$0.122510\pi$
$271$	12.9814	+	22.4845i	0.788566	+	1.36584i	−0.138279	+	0.990393i	$0.544157\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.22753			0.556441
$276$		0			0
$277$	−1.96075			−0.117810			−0.0589049	−	0.998264i	$-0.518761\pi$
$277$	−1.96075			−0.117810			−0.0589049	+	0.998264i	$0.518761\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.42057	−	16.3169i	−0.561984	−	0.973385i	−0.997323	−	0.0731185i	$-0.976705\pi$
$281$	−9.42057	−	16.3169i	−0.561984	−	0.973385i	0.435339	−	0.900267i	$-0.356628\pi$
$282$		0			0
$283$	11.7422	+	20.3381i	0.698002	+	1.20898i	0.969158	+	0.246440i	$0.0792608\pi$
$283$	11.7422	+	20.3381i	0.698002	+	1.20898i	−0.271156	+	0.962536i	$0.587406\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.70058	−	1.71156i	−0.513579	−	0.101030i
$288$		0			0
$289$	8.17174	+	14.1539i	0.480690	+	0.832580i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.00384	−	1.73871i	0.0586452	−	0.101576i	−0.835212	−	0.549928i	$-0.814655\pi$
$293$	1.00384	−	1.73871i	0.0586452	−	0.101576i	0.893857	+	0.448351i	$0.147989\pi$
$294$		0			0
$295$	−2.03641	−	3.52717i	−0.118564	−	0.205360i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.28281	−	5.68599i	0.189850	−	0.328829i
$300$		0			0
$301$	−4.19282	+	4.80140i	−0.241670	+	0.276748i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.8446	−	27.4436i	0.907257	−	1.57142i
$306$		0			0
$307$	32.7633			1.86990			0.934951	−	0.354777i	$-0.115443\pi$
$307$	32.7633			1.86990			0.934951	+	0.354777i	$0.115443\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.04979	−	12.2106i	−0.399757	−	0.692400i	0.593939	−	0.804510i	$-0.297572\pi$
$311$	−7.04979	−	12.2106i	−0.399757	−	0.692400i	−0.993696	+	0.112111i	$0.964239\pi$
$312$		0			0
$313$	17.0769	−	29.5781i	0.965245	−	1.67185i	0.256291	−	0.966600i	$-0.417499\pi$
$313$	17.0769	−	29.5781i	0.965245	−	1.67185i	0.708954	−	0.705255i	$-0.249167\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.790586	+	1.36933i	−0.0444037	+	0.0769095i	−0.887373	−	0.461052i	$-0.847472\pi$
$317$	−0.790586	+	1.36933i	−0.0444037	+	0.0769095i	0.842969	+	0.537962i	$0.180805\pi$
$318$		0			0
$319$	−13.7473	−	23.8110i	−0.769701	−	1.33316i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.21575			0.0676459
$324$		0			0
$325$	−1.15139	+	1.99426i	−0.0638675	+	0.110622i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.59664	−	0.314088i	−0.0880257	−	0.0173163i
$330$		0			0
$331$	−6.86862	+	11.8968i	−0.377533	+	0.653907i	−0.990703	−	0.136044i	$-0.956561\pi$
$331$	−6.86862	+	11.8968i	−0.377533	+	0.653907i	0.613169	+	0.789951i	$0.289894\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	22.4533	+	38.8902i	1.22675	+	2.12480i
$336$		0			0
$337$	−8.72318	+	15.1090i	−0.475182	+	0.823039i	−0.999596	−	0.0284243i	$-0.990951\pi$
$337$	−8.72318	+	15.1090i	−0.475182	+	0.823039i	0.524414	+	0.851463i	$0.324284\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.4019	+	21.4807i	0.671598	+	1.16324i
$342$		0			0
$343$	−15.4639	−	10.1916i	−0.834972	−	0.550292i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.91552	+	3.31778i	0.102830	+	0.178108i	0.912850	−	0.408296i	$-0.133877\pi$
$347$	1.91552	+	3.31778i	0.102830	+	0.178108i	−0.810019	+	0.586403i	$0.800543\pi$
$348$		0			0
$349$	1.69984	+	2.94421i	0.0909903	+	0.157600i	0.907928	−	0.419126i	$-0.137663\pi$
$349$	1.69984	+	2.94421i	0.0909903	+	0.157600i	−0.816938	+	0.576726i	$0.804330\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.5568			−0.668332			−0.334166	−	0.942514i	$-0.608455\pi$
$353$	−12.5568			−0.668332			−0.334166	+	0.942514i	$0.608455\pi$
$354$		0			0
$355$	39.9629			2.12101
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.02209	+	10.4306i	0.317834	+	0.550504i	0.980036	−	0.198821i	$-0.0637113\pi$
$359$	6.02209	+	10.4306i	0.317834	+	0.550504i	−0.662202	+	0.749325i	$0.730378\pi$
$360$		0			0
$361$	8.37435	−	14.5048i	0.440756	−	0.763411i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.5554	−	20.0146i	0.604838	−	1.04761i
$366$		0			0
$367$	−2.02514			−0.105711			−0.0528557	−	0.998602i	$-0.516832\pi$
$367$	−2.02514			−0.105711			−0.0528557	+	0.998602i	$0.516832\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−32.7950	−	6.45138i	−1.70263	−	0.334939i
$372$		0			0
$373$	21.6259			1.11975			0.559874	−	0.828578i	$-0.310849\pi$
$373$	21.6259			1.11975			0.559874	+	0.828578i	$0.310849\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.86142			0.353381
$378$		0			0
$379$	−6.76701			−0.347598			−0.173799	−	0.984781i	$-0.555604\pi$
$379$	−6.76701			−0.347598			−0.173799	+	0.984781i	$0.555604\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.65645			0.391226			0.195613	−	0.980681i	$-0.437330\pi$
$383$	7.65645			0.391226			0.195613	+	0.980681i	$0.437330\pi$
$384$		0			0
$385$	−8.15810	−	23.8673i	−0.415775	−	1.21639i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	21.1561			1.07266			0.536329	−	0.844009i	$-0.319811\pi$
$389$	21.1561			1.07266			0.536329	+	0.844009i	$0.319811\pi$
$390$		0			0
$391$	−3.09898	+	5.36759i	−0.156722	+	0.271451i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.81360	+	6.60534i	−0.191883	+	0.332351i
$396$		0			0
$397$	4.02642	+	6.97396i	0.202080	+	0.350013i	0.949199	−	0.314678i	$-0.101896\pi$
$397$	4.02642	+	6.97396i	0.202080	+	0.350013i	−0.747118	+	0.664691i	$0.768563\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.77773			0.388401			0.194201	−	0.980962i	$-0.437789\pi$
$401$	7.77773			0.388401			0.194201	+	0.980962i	$0.437789\pi$
$402$		0			0
$403$	−6.18989			−0.308341
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.57599	+	2.72969i	0.0781188	+	0.135306i
$408$		0			0
$409$	−9.76327	−	16.9105i	−0.482763	−	0.836170i	0.517041	−	0.855960i	$-0.327033\pi$
$409$	−9.76327	−	16.9105i	−0.482763	−	0.836170i	−0.999804	+	0.0197907i	$0.993700\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.55710	+	2.92827i	−0.125827	+	0.144091i
$414$		0			0
$415$	−15.9604	−	27.6442i	−0.783466	−	1.35700i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.5259	−	21.6955i	0.611932	−	1.05990i	−0.378983	−	0.925404i	$-0.623726\pi$
$419$	12.5259	−	21.6955i	0.611932	−	1.05990i	0.990915	−	0.134493i	$-0.0429406\pi$
$420$		0			0
$421$	18.0746	+	31.3061i	0.880902	+	1.52577i	0.850340	+	0.526234i	$0.176396\pi$
$421$	18.0746	+	31.3061i	0.880902	+	1.52577i	0.0305620	+	0.999533i	$0.490270\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.08691	−	1.88259i	0.0527231	−	0.0913190i
$426$		0			0
$427$	−29.6793	−	5.83845i	−1.43628	−	0.282543i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.95636	−	3.38852i	0.0942346	−	0.163219i	−0.815054	−	0.579385i	$-0.803293\pi$
$431$	1.95636	−	3.38852i	0.0942346	−	0.163219i	0.909289	+	0.416165i	$0.136626\pi$
$432$		0			0
$433$	−14.2929			−0.686872			−0.343436	−	0.939176i	$-0.611591\pi$
$433$	−14.2929			−0.686872			−0.343436	+	0.939176i	$0.611591\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.73862	−	9.93958i	−0.274515	−	0.475475i
$438$		0			0
$439$	2.39235	−	4.14367i	0.114180	−	0.197766i	−0.803271	−	0.595613i	$-0.796909\pi$
$439$	2.39235	−	4.14367i	0.114180	−	0.197766i	0.917452	+	0.397847i	$0.130242\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.13213	+	7.15707i	−0.196324	+	0.340042i	−0.947334	−	0.320248i	$-0.896234\pi$
$443$	−4.13213	+	7.15707i	−0.196324	+	0.340042i	0.751010	+	0.660291i	$0.229567\pi$
$444$		0			0
$445$	−14.1748	−	24.5515i	−0.671952	−	1.16385i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.6036			0.972346			0.486173	−	0.873863i	$-0.338392\pi$
$449$	20.6036			0.972346			0.486173	+	0.873863i	$0.338392\pi$
$450$		0			0
$451$	−5.76370	+	9.98301i	−0.271402	+	0.470082i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.17617	+	1.21497i	0.289543	+	0.0569585i
$456$		0			0
$457$	8.98220	−	15.5576i	0.420170	−	0.727755i	−0.575786	−	0.817600i	$-0.695304\pi$
$457$	8.98220	−	15.5576i	0.420170	−	0.727755i	0.995956	+	0.0898451i	$0.0286372\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.03501	−	6.98885i	−0.187929	−	0.325503i	0.756630	−	0.653843i	$-0.226844\pi$
$461$	−4.03501	−	6.98885i	−0.187929	−	0.325503i	−0.944560	+	0.328340i	$0.893511\pi$
$462$		0			0
$463$	−2.50704	+	4.34232i	−0.116512	+	0.201805i	−0.918383	−	0.395692i	$-0.870505\pi$
$463$	−2.50704	+	4.34232i	−0.116512	+	0.201805i	0.801871	+	0.597497i	$0.203838\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.1673	+	22.8063i	0.609308	+	1.05535i	0.991355	+	0.131209i	$0.0418859\pi$
$467$	13.1673	+	22.8063i	0.609308	+	1.05535i	−0.382047	+	0.924143i	$0.624781\pi$
$468$		0			0
$469$	28.1944	−	32.2868i	1.30189	−	1.49086i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.14332	+	7.17645i	0.190510	+	0.329973i
$474$		0			0
$475$	2.01272	+	3.48614i	0.0923500	+	0.159955i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	25.2445			1.15345			0.576724	−	0.816939i	$-0.304331\pi$
$479$	25.2445			1.15345			0.576724	+	0.816939i	$0.304331\pi$
$480$		0			0
$481$	−0.786591			−0.0358655
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−10.6119	−	18.3803i	−0.481861	−	0.834608i
$486$		0			0
$487$	1.36124	−	2.35774i	0.0616837	−	0.106839i	−0.833534	−	0.552468i	$-0.813686\pi$
$487$	1.36124	−	2.35774i	0.0616837	−	0.106839i	0.895218	+	0.445628i	$0.147020\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.8020	−	27.3698i	0.713134	−	1.23518i	−0.250541	−	0.968106i	$-0.580609\pi$
$491$	15.8020	−	27.3698i	0.713134	−	1.23518i	0.963675	−	0.267078i	$-0.0860581\pi$
$492$		0			0
$493$	−6.47720			−0.291718
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.3377	−	36.0953i	−0.553424	−	1.61909i
$498$		0			0
$499$	5.94890			0.266309			0.133155	−	0.991095i	$-0.457489\pi$
$499$	5.94890			0.266309			0.133155	+	0.991095i	$0.457489\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.6905			1.23466			0.617329	−	0.786705i	$-0.288215\pi$
$503$	27.6905			1.23466			0.617329	+	0.786705i	$0.288215\pi$
$504$		0			0
$505$	−10.2169			−0.454647
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−37.2885			−1.65278			−0.826392	−	0.563095i	$-0.809611\pi$
$509$	−37.2885			−1.65278			−0.826392	+	0.563095i	$0.809611\pi$
$510$		0			0
$511$	−21.6450	−	4.25798i	−0.957521	−	0.188362i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	44.6828			1.96896
$516$		0			0
$517$	−1.05769	+	1.83198i	−0.0465174	+	0.0805704i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.1271	+	31.3971i	−0.794163	+	1.37553i	0.129207	+	0.991618i	$0.458757\pi$
$521$	−18.1271	+	31.3971i	−0.794163	+	1.37553i	−0.923370	+	0.383912i	$0.874577\pi$
$522$		0			0
$523$	10.2931	+	17.8282i	0.450086	+	0.779572i	0.998391	−	0.0567068i	$-0.0180600\pi$
$523$	10.2931	+	17.8282i	0.450086	+	0.779572i	−0.548305	+	0.836278i	$0.684727\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.84328			0.254537
$528$		0			0
$529$	35.5118			1.54399
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.43836	−	2.49131i	−0.0623023	−	0.107911i
$534$		0			0
$535$	8.78013	+	15.2076i	0.379598	+	0.657483i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.0388	+	14.7371i	−0.820057	+	0.634772i
$540$		0			0
$541$	−0.649192	−	1.12443i	−0.0279109	−	0.0483432i	0.851733	−	0.523977i	$-0.175552\pi$
$541$	−0.649192	−	1.12443i	−0.0279109	−	0.0483432i	−0.879643	+	0.475634i	$0.842219\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.5673	+	23.4993i	−0.581159	+	1.00660i
$546$		0			0
$547$	−13.8412	−	23.9736i	−0.591805	−	1.02504i	−0.993989	−	0.109478i	$-0.965082\pi$
$547$	−13.8412	−	23.9736i	−0.591805	−	1.02504i	0.402184	−	0.915559i	$-0.368251\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.99716	−	10.3874i	0.255488	−	0.442518i
$552$		0			0
$553$	7.14344	+	1.40525i	0.303770	+	0.0597571i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.72089	−	13.3730i	0.327145	−	0.566631i	−0.654799	−	0.755803i	$-0.727247\pi$
$557$	7.72089	−	13.3730i	0.327145	−	0.566631i	0.981944	+	0.189172i	$0.0605802\pi$
$558$		0			0
$559$	−2.06797			−0.0874660
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.956715	+	1.65708i	0.0403207	+	0.0698375i	0.885482	−	0.464675i	$-0.153829\pi$
$563$	0.956715	+	1.65708i	0.0403207	+	0.0698375i	−0.845161	+	0.534512i	$0.820495\pi$
$564$		0			0
$565$	11.2802	−	19.5379i	0.474561	−	0.821964i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.38138	+	12.7849i	−0.309444	+	0.535972i	−0.978241	−	0.207473i	$-0.933476\pi$
$569$	−7.38138	+	12.7849i	−0.309444	+	0.535972i	0.668797	+	0.743445i	$0.266809\pi$
$570$		0			0
$571$	−1.28208	−	2.22063i	−0.0536535	−	0.0929306i	0.837951	−	0.545745i	$-0.183753\pi$
$571$	−1.28208	−	2.22063i	−0.0536535	−	0.0929306i	−0.891605	+	0.452814i	$0.850420\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.5220			−0.855827
$576$		0			0
$577$	7.01283	−	12.1466i	0.291948	−	0.505669i	−0.682322	−	0.731052i	$-0.739030\pi$
$577$	7.01283	−	12.1466i	0.291948	−	0.505669i	0.974270	+	0.225383i	$0.0723632\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−20.0413	+	22.9504i	−0.831455	+	0.952141i
$582$		0			0
$583$	−21.7251	+	37.6289i	−0.899760	+	1.55843i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.7666	−	27.3085i	−0.650756	−	1.12714i	−0.982940	−	0.183928i	$-0.941119\pi$
$587$	−15.7666	−	27.3085i	−0.650756	−	1.12714i	0.332183	−	0.943215i	$-0.392215\pi$
$588$		0			0
$589$	−5.41022	+	9.37078i	−0.222924	+	0.386116i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.72311	+	9.91272i	0.235020	+	0.407067i	0.959279	−	0.282462i	$-0.0911511\pi$
$593$	5.72311	+	9.91272i	0.235020	+	0.407067i	−0.724258	+	0.689529i	$0.757818\pi$
$594$		0			0
$595$	−5.83033	−	1.14693i	−0.239020	−	0.0470196i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.80684	+	4.86159i	0.114684	+	0.198639i	0.917654	−	0.397381i	$-0.130081\pi$
$599$	2.80684	+	4.86159i	0.114684	+	0.198639i	−0.802969	+	0.596021i	$0.796748\pi$
$600$		0			0
$601$	19.2223	+	33.2940i	0.784094	+	1.35809i	0.929539	+	0.368725i	$0.120205\pi$
$601$	19.2223	+	33.2940i	0.784094	+	1.35809i	−0.145444	+	0.989366i	$0.546461\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.29983			−0.0935013
$606$		0			0
$607$	−16.3437			−0.663372			−0.331686	−	0.943390i	$-0.607617\pi$
$607$	−16.3437			−0.663372			−0.331686	+	0.943390i	$0.607617\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.263953	−	0.457180i	−0.0106784	−	0.0184955i
$612$		0			0
$613$	−6.19332	+	10.7272i	−0.250146	+	0.433266i	−0.963566	−	0.267471i	$-0.913812\pi$
$613$	−6.19332	+	10.7272i	−0.250146	+	0.433266i	0.713420	+	0.700737i	$0.247145\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.9853	+	36.3476i	−0.844836	+	1.46330i	0.0409280	+	0.999162i	$0.486969\pi$
$617$	−20.9853	+	36.3476i	−0.844836	+	1.46330i	−0.885764	+	0.464136i	$0.846365\pi$
$618$		0			0
$619$	−35.8945			−1.44272			−0.721361	−	0.692559i	$-0.756483\pi$
$619$	−35.8945			−1.44272			−0.721361	+	0.692559i	$0.756483\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−17.7992	+	20.3828i	−0.713111	+	0.816619i
$624$		0			0
$625$	−31.2166			−1.24866
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.742544			0.0296072
$630$		0			0
$631$	−19.5519			−0.778349			−0.389175	−	0.921164i	$-0.627240\pi$
$631$	−19.5519			−0.778349			−0.389175	+	0.921164i	$0.627240\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	34.8299			1.38218
$636$		0			0
$637$	−0.809390	−	5.95353i	−0.0320692	−	0.235888i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	14.6026			0.576769			0.288385	−	0.957515i	$-0.406882\pi$
$641$	14.6026			0.576769			0.288385	+	0.957515i	$0.406882\pi$
$642$		0			0
$643$	−5.96942	+	10.3393i	−0.235411	+	0.407744i	−0.959392	−	0.282076i	$-0.908977\pi$
$643$	−5.96942	+	10.3393i	−0.235411	+	0.407744i	0.723981	+	0.689820i	$0.242310\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.92060	−	3.32658i	0.0755067	−	0.130781i	−0.825800	−	0.563963i	$-0.809276\pi$
$647$	1.92060	−	3.32658i	0.0755067	−	0.130781i	0.901306	+	0.433182i	$0.142609\pi$
$648$		0			0
$649$	2.52692	+	4.37675i	0.0991903	+	0.171803i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−39.9918			−1.56500			−0.782501	−	0.622650i	$-0.786056\pi$
$653$	−39.9918			−1.56500			−0.782501	+	0.622650i	$0.786056\pi$
$654$		0			0
$655$	4.39469			0.171715
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.60101	−	2.77303i	−0.0623665	−	0.108022i	0.833156	−	0.553038i	$-0.186531\pi$
$659$	−1.60101	−	2.77303i	−0.0623665	−	0.108022i	−0.895523	+	0.445016i	$0.853198\pi$
$660$		0			0
$661$	21.6515	+	37.5015i	0.842146	+	1.45864i	0.888077	+	0.459695i	$0.152041\pi$
$661$	21.6515	+	37.5015i	0.842146	+	1.45864i	−0.0459311	+	0.998945i	$0.514625\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.23755	−	8.28808i	0.280660	−	0.321398i
$666$		0			0
$667$	30.5740	+	52.9557i	1.18383	+	2.05045i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−19.6610	+	34.0539i	−0.759006	+	1.31464i
$672$		0			0
$673$	12.2936	+	21.2931i	0.473883	+	0.820790i	0.999553	−	0.0298991i	$-0.00951859\pi$
$673$	12.2936	+	21.2931i	0.473883	+	0.820790i	−0.525670	+	0.850689i	$0.676185\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.2094	+	33.2716i	−0.738276	+	1.27873i	0.214994	+	0.976615i	$0.431027\pi$
$677$	−19.2094	+	33.2716i	−0.738276	+	1.27873i	−0.953271	+	0.302117i	$0.902307\pi$
$678$		0			0
$679$	−13.3253	+	15.2594i	−0.511376	+	0.585603i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.122464	−	0.212113i	0.00468594	−	0.00811629i	−0.863673	−	0.504053i	$-0.831842\pi$
$683$	0.122464	−	0.212113i	0.00468594	−	0.00811629i	0.868359	+	0.495936i	$0.165175\pi$
$684$		0			0
$685$	13.6591			0.521886
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.42160	−	9.39049i	−0.206547	−	0.357749i
$690$		0			0
$691$	3.65146	−	6.32452i	0.138908	−	0.240596i	−0.788175	−	0.615451i	$-0.788974\pi$
$691$	3.65146	−	6.32452i	0.138908	−	0.240596i	0.927084	+	0.374855i	$0.122307\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.4475	+	19.8277i	−0.434229	+	0.752106i
$696$		0			0
$697$	1.35782	+	2.35181i	0.0514309	+	0.0890810i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−32.3889			−1.22331			−0.611656	−	0.791124i	$-0.709496\pi$
$701$	−32.3889			−1.22331			−0.611656	+	0.791124i	$0.709496\pi$
$702$		0			0
$703$	−0.687513	+	1.19081i	−0.0259301	+	0.0449122i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.15427	+	9.22813i	0.118629	+	0.347059i
$708$		0			0
$709$	−1.46137	+	2.53116i	−0.0548828	+	0.0950599i	−0.892162	−	0.451716i	$-0.850812\pi$
$709$	−1.46137	+	2.53116i	−0.0548828	+	0.0950599i	0.837279	+	0.546776i	$0.184145\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−27.5817	−	47.7729i	−1.03294	−	1.78911i
$714$		0			0
$715$	4.09141	−	7.08652i	0.153010	−	0.265021i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.78527	−	15.2165i	−0.327635	−	0.567481i	0.654407	−	0.756143i	$-0.272918\pi$
$719$	−8.78527	−	15.2165i	−0.327635	−	0.567481i	−0.982042	+	0.188662i	$0.939585\pi$
$720$		0			0
$721$	−13.7949	−	40.3584i	−0.513750	−	1.50302i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.7233	−	18.5733i	−0.398253	−	0.689795i
$726$		0			0
$727$	20.0486	+	34.7252i	0.743561	+	1.28789i	0.950864	+	0.309609i	$0.100198\pi$
$727$	20.0486	+	34.7252i	0.743561	+	1.28789i	−0.207303	+	0.978277i	$0.566469\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.95217			0.0722037
$732$		0			0
$733$	−7.12469			−0.263156			−0.131578	−	0.991306i	$-0.542004\pi$
$733$	−7.12469			−0.263156			−0.131578	+	0.991306i	$0.542004\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−27.8615	−	48.2576i	−1.02629	−	1.77759i
$738$		0			0
$739$	−2.13570	+	3.69914i	−0.0785631	+	0.136075i	−0.902630	−	0.430417i	$-0.858367\pi$
$739$	−2.13570	+	3.69914i	−0.0785631	+	0.136075i	0.824067	+	0.566492i	$0.191700\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.108257	+	0.187507i	−0.00397157	+	0.00687896i	−0.868004	−	0.496557i	$-0.834598\pi$
$743$	−0.108257	+	0.187507i	−0.00397157	+	0.00687896i	0.864033	+	0.503436i	$0.167931\pi$
$744$		0			0
$745$	−38.5667			−1.41297
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.0251	−	12.6254i	0.402849	−	0.461323i
$750$		0			0
$751$	23.5840			0.860594			0.430297	−	0.902687i	$-0.358409\pi$
$751$	23.5840			0.860594			0.430297	+	0.902687i	$0.358409\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−63.7312			−2.31942
$756$		0			0
$757$	−22.0176			−0.800242			−0.400121	−	0.916462i	$-0.631032\pi$
$757$	−22.0176			−0.800242			−0.400121	+	0.916462i	$0.631032\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.1140			0.656631			0.328316	−	0.944568i	$-0.393519\pi$
$761$	18.1140			0.656631			0.328316	+	0.944568i	$0.393519\pi$
$762$		0			0
$763$	25.4136	+	4.99932i	0.920035	+	0.180988i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.26121			−0.0455397
$768$		0			0
$769$	3.16710	−	5.48558i	0.114209	−	0.197815i	−0.803255	−	0.595636i	$-0.796900\pi$
$769$	3.16710	−	5.48558i	0.114209	−	0.197815i	0.917463	+	0.397821i	$0.130233\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.10740	+	5.38218i	−0.111765	+	0.193584i	−0.916482	−	0.400076i	$-0.868984\pi$
$773$	−3.10740	+	5.38218i	−0.111765	+	0.193584i	0.804717	+	0.593659i	$0.202317\pi$
$774$		0			0
$775$	9.67381	+	16.7555i	0.347494	+	0.601876i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.02874			−0.180173
$780$		0			0
$781$	−49.5887			−1.77442
$782$		0			0
$783$		0			0
$784$		0			0
$785$	25.7506	+	44.6014i	0.919079	+	1.59189i
$786$		0			0
$787$	9.65916	+	16.7302i	0.344312	+	0.596366i	0.985229	−	0.171245i	$-0.0547789\pi$
$787$	9.65916	+	16.7302i	0.344312	+	0.596366i	−0.640917	+	0.767611i	$0.721446\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−21.1295	−	4.15656i	−0.751279	−	0.147790i
$792$		0			0
$793$	−4.90651	−	8.49832i	−0.174235	−	0.301784i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.09519	−	8.82513i	0.180481	−	0.312602i	−0.761563	−	0.648090i	$-0.775568\pi$
$797$	5.09519	−	8.82513i	0.180481	−	0.312602i	0.942044	+	0.335488i	$0.108901\pi$
$798$		0			0
$799$	0.249172	+	0.431579i	0.00881509	+	0.0152682i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−14.3388	+	24.8355i	−0.506004	+	0.876424i
$804$		0			0
$805$	18.1436	+	53.0808i	0.639478	+	1.87085i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	23.7068	−	41.0613i	0.833485	−	1.44364i	−0.0617729	−	0.998090i	$-0.519675\pi$
$809$	23.7068	−	41.0613i	0.833485	−	1.44364i	0.895258	−	0.445548i	$-0.146991\pi$
$810$		0			0
$811$	47.4177			1.66506			0.832531	−	0.553979i	$-0.186891\pi$
$811$	47.4177			1.66506			0.832531	+	0.553979i	$0.186891\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.79627	+	11.7715i	0.238063	+	0.412337i
$816$		0			0
$817$	−1.80750	+	3.13067i	−0.0632363	+	0.109528i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.8177	−	46.4495i	0.935943	−	1.62110i	0.162998	−	0.986626i	$-0.447883\pi$
$821$	26.8177	−	46.4495i	0.935943	−	1.62110i	0.772944	−	0.634474i	$-0.218783\pi$
$822$		0			0
$823$	0.475192	+	0.823057i	0.0165641	+	0.0286899i	0.874189	−	0.485586i	$-0.161394\pi$
$823$	0.475192	+	0.823057i	0.0165641	+	0.0286899i	−0.857625	+	0.514276i	$0.828061\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−20.7813			−0.722636			−0.361318	−	0.932443i	$-0.617673\pi$
$827$	−20.7813			−0.722636			−0.361318	+	0.932443i	$0.617673\pi$
$828$		0			0
$829$	12.1615	−	21.0644i	0.422387	−	0.731596i	−0.573785	−	0.819006i	$-0.694526\pi$
$829$	12.1615	−	21.0644i	0.422387	−	0.731596i	0.996172	+	0.0874096i	$0.0278589\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.764066	+	5.62015i	0.0264733	+	0.194727i
$834$		0			0
$835$	−15.1754	+	26.2846i	−0.525166	+	0.909615i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.7367	+	27.2567i	0.543290	+	0.941006i	0.998712	+	0.0507305i	$0.0161550\pi$
$839$	15.7367	+	27.2567i	0.543290	+	0.941006i	−0.455422	+	0.890276i	$0.650512\pi$
$840$		0			0
$841$	−17.4514	+	30.2268i	−0.601774	+	1.04230i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.9957	−	29.4373i	−0.584668	−	1.01268i
$846$		0			0
$847$	0.710026	+	2.07725i	0.0243968	+	0.0713751i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.50499	−	6.07082i	−0.120150	−	0.208105i
$852$		0			0
$853$	−26.6959	−	46.2386i	−0.914049	−	1.58318i	−0.808287	−	0.588788i	$-0.799605\pi$
$853$	−26.6959	−	46.2386i	−0.914049	−	1.58318i	−0.105762	−	0.994391i	$-0.533728\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.6297			−0.738857			−0.369428	−	0.929259i	$-0.620446\pi$
$857$	−21.6297			−0.738857			−0.369428	+	0.929259i	$0.620446\pi$
$858$		0			0
$859$	−34.4288			−1.17470			−0.587348	−	0.809334i	$-0.699828\pi$
$859$	−34.4288			−1.17470			−0.587348	+	0.809334i	$0.699828\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.4262	+	23.2548i	0.457033	+	0.791604i	0.998803	−	0.0489229i	$-0.0155789\pi$
$863$	13.4262	+	23.2548i	0.457033	+	0.791604i	−0.541770	+	0.840527i	$0.682246\pi$
$864$		0			0
$865$	18.5786	−	32.1790i	0.631690	−	1.09412i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.73217	−	8.19636i	0.160528	−	0.278043i
$870$		0			0
$871$	13.9060			0.471186
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.49609	+	16.0793i	0.185802	+	0.543581i
$876$		0			0
$877$	32.4068			1.09430			0.547150	−	0.837034i	$-0.315713\pi$
$877$	32.4068			1.09430			0.547150	+	0.837034i	$0.315713\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	39.0404			1.31530			0.657652	−	0.753322i	$-0.271550\pi$
$881$	39.0404			1.31530			0.657652	+	0.753322i	$0.271550\pi$
$882$		0			0
$883$	−13.8079			−0.464672			−0.232336	−	0.972636i	$-0.574637\pi$
$883$	−13.8079			−0.464672			−0.232336	+	0.972636i	$0.574637\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.9555			−0.804348			−0.402174	−	0.915563i	$-0.631745\pi$
$887$	−23.9555			−0.804348			−0.402174	+	0.915563i	$0.631745\pi$
$888$		0			0
$889$	−10.7530	−	31.4590i	−0.360645	−	1.05510i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.922824			−0.0308811
$894$		0			0
$895$	−18.4293	+	31.9206i	−0.616025	+	1.06699i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	28.8244	−	49.9253i	0.961346	−	1.66510i
$900$		0			0
$901$	5.11801	+	8.86465i	0.170505	+	0.295324i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	30.2652			1.00605
$906$		0			0
$907$	4.70128			0.156103			0.0780517	−	0.996949i	$-0.475130\pi$
$907$	4.70128			0.156103			0.0780517	+	0.996949i	$0.475130\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.0884	−	36.5262i	−0.698689	−	1.21017i	−0.968921	−	0.247370i	$-0.920434\pi$
$911$	−21.0884	−	36.5262i	−0.698689	−	1.21017i	0.270232	−	0.962795i	$-0.412900\pi$
$912$		0			0
$913$	19.8048	+	34.3029i	0.655442	+	1.13526i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.35677	−	3.96937i	−0.0448046	−	0.131080i
$918$		0			0
$919$	−20.1071	−	34.8265i	−0.663271	−	1.14882i	−0.979751	−	0.200220i	$-0.935834\pi$
$919$	−20.1071	−	34.8265i	−0.663271	−	1.14882i	0.316480	−	0.948599i	$-0.397499\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.18756	−	10.7172i	0.203666	−	0.352760i
$924$		0			0
$925$	1.22932	+	2.12924i	0.0404196	+	0.0700089i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.0712	+	26.1040i	−0.494469	+	0.856446i	−0.999980	−	0.00637464i	$-0.997971\pi$
$929$	−15.0712	+	26.1040i	−0.494469	+	0.856446i	0.505510	+	0.862820i	$0.331304\pi$
$930$		0			0
$931$	−9.72040	−	3.97831i	−0.318573	−	0.130384i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.86230	+	6.68970i	−0.126311	+	0.218776i
$936$		0			0
$937$	35.1550			1.14846			0.574231	−	0.818693i	$-0.305301\pi$
$937$	35.1550			1.14846			0.574231	+	0.818693i	$0.305301\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.52163	−	2.63554i	−0.0496038	−	0.0859162i	0.840157	−	0.542343i	$-0.182463\pi$
$941$	−1.52163	−	2.63554i	−0.0496038	−	0.0859162i	−0.889761	+	0.456426i	$0.849129\pi$
$942$		0			0
$943$	12.8184	−	22.2022i	0.417426	−	0.723003i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.33905	−	10.9796i	0.205991	−	0.356788i	−0.744457	−	0.667671i	$-0.767291\pi$
$947$	6.33905	−	10.9796i	0.205991	−	0.356788i	0.950448	+	0.310883i	$0.100625\pi$
$948$		0			0
$949$	−3.57831	−	6.19781i	−0.116157	−	0.201190i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−23.0052			−0.745212			−0.372606	−	0.927990i	$-0.621536\pi$
$953$	−23.0052			−0.745212			−0.372606	+	0.927990i	$0.621536\pi$
$954$		0			0
$955$	25.7930	−	44.6749i	0.834643	−	1.44564i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.21697	−	12.3371i	−0.136173	−	0.398387i
$960$		0			0
$961$	−10.5033	+	18.1923i	−0.338817	+	0.586849i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.05985	+	7.03187i	0.130691	+	0.226364i
$966$		0			0
$967$	−0.617767	+	1.07000i	−0.0198660	+	0.0344090i	−0.875788	−	0.482697i	$-0.839657\pi$
$967$	−0.617767	+	1.07000i	−0.0198660	+	0.0344090i	0.855921	+	0.517106i	$0.172991\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.01657	+	12.1530i	0.225172	+	0.390010i	0.956371	−	0.292155i	$-0.0943722\pi$
$971$	7.01657	+	12.1530i	0.225172	+	0.390010i	−0.731199	+	0.682164i	$0.761039\pi$
$972$		0			0
$973$	21.4429	+	4.21821i	0.687428	+	0.135230i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.1301	+	19.2780i	0.356084	+	0.616756i	0.987303	−	0.158849i	$-0.0507782\pi$
$977$	11.1301	+	19.2780i	0.356084	+	0.616756i	−0.631218	+	0.775605i	$0.717445\pi$
$978$		0			0
$979$	17.5891	+	30.4652i	0.562151	+	0.973673i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−33.7341			−1.07595			−0.537976	−	0.842960i	$-0.680811\pi$
$983$	−33.7341			−1.07595			−0.537976	+	0.842960i	$0.680811\pi$
$984$		0			0
$985$	−51.2921			−1.63430
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.21474	−	15.9604i	−0.293012	−	0.507511i
$990$		0			0
$991$	6.87364	−	11.9055i	0.218348	−	0.378191i	−0.735955	−	0.677031i	$-0.763266\pi$
$991$	6.87364	−	11.9055i	0.218348	−	0.378191i	0.954303	+	0.298840i	$0.0965997\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.20035	+	3.81112i	−0.0697559	+	0.120821i
$996$		0			0
$997$	37.2565			1.17993			0.589963	−	0.807430i	$-0.299142\pi$
$997$	37.2565			1.17993			0.589963	+	0.807430i	$0.299142\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.361.3		22
3.2	odd	2		504.2.t.c.193.2	yes	22
4.3	odd	2		3024.2.t.k.1873.3		22
7.2	even	3		1512.2.q.d.793.9		22
9.2	odd	6		504.2.q.c.25.8	✓	22
9.7	even	3		1512.2.q.d.1369.9		22
12.11	even	2		1008.2.t.l.193.10		22
21.2	odd	6		504.2.q.c.121.8	yes	22
28.23	odd	6		3024.2.q.l.2305.9		22
36.7	odd	6		3024.2.q.l.2881.9		22
36.11	even	6		1008.2.q.l.529.4		22
63.2	odd	6		504.2.t.c.457.2	yes	22
63.16	even	3	inner	1512.2.t.c.289.3		22
84.23	even	6		1008.2.q.l.625.4		22
252.79	odd	6		3024.2.t.k.289.3		22
252.191	even	6		1008.2.t.l.961.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.8	✓	22	9.2	odd	6
504.2.q.c.121.8	yes	22	21.2	odd	6
504.2.t.c.193.2	yes	22	3.2	odd	2
504.2.t.c.457.2	yes	22	63.2	odd	6
1008.2.q.l.529.4		22	36.11	even	6
1008.2.q.l.625.4		22	84.23	even	6
1008.2.t.l.193.10		22	12.11	even	2
1008.2.t.l.961.10		22	252.191	even	6
1512.2.q.d.793.9		22	7.2	even	3
1512.2.q.d.1369.9		22	9.7	even	3
1512.2.t.c.289.3		22	63.16	even	3	inner
1512.2.t.c.361.3		22	1.1	even	1	trivial
3024.2.q.l.2305.9		22	28.23	odd	6
3024.2.q.l.2881.9		22	36.7	odd	6
3024.2.t.k.289.3		22	252.79	odd	6
3024.2.t.k.1873.3		22	4.3	odd	2

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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.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +O(q^{10})\)	\(q-2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +3.43944 q^{11} +(-0.429164 + 0.743335i) q^{13} +(0.405132 - 0.701710i) q^{17} +(0.750215 + 1.29941i) q^{19} -7.64930 q^{23} +2.68286 q^{25} +(-3.99696 - 6.92294i) q^{29} +(3.60578 + 6.24540i) q^{31} +(-2.37193 - 6.93931i) q^{35} +(0.458211 + 0.793644i) q^{37} +(-1.67577 + 2.90251i) q^{41} +(1.20465 + 2.08652i) q^{43} +(-0.307520 + 0.532640i) q^{47} +(-5.53543 + 4.28474i) q^{49} +(-6.31646 + 10.9404i) q^{53} -9.53342 q^{55} +(0.734690 + 1.27252i) q^{59} +(-5.71635 + 9.90101i) q^{61} +(1.18956 - 2.06037i) q^{65} +(-8.10061 - 14.0307i) q^{67} -14.4177 q^{71} +(-4.16893 + 7.22079i) q^{73} +(2.94325 + 8.61077i) q^{77} +(1.37586 - 2.38305i) q^{79} +(5.75814 + 9.97340i) q^{83} +(-1.12294 + 1.94500i) q^{85} +(5.11395 + 8.85763i) q^{89} +(-2.22822 - 0.438331i) q^{91} +(-2.07944 - 3.60170i) q^{95} +(3.82852 + 6.63119i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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