LMFDB - Embedded newform 1512.2.r.e.505.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(505,1512)]

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, 0]))

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

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

chi := DirichletCharacter("1512.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.r (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2091141441.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 $ x^8 - x^7 + x^6 + 3x^5 - 15x^4 + 9x^3 + 9x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.1
Root			$1.65525 + 0.510048i$ of defining polynomial
Character	$\chi$	$=$	1512.505
Dual form			1512.2.r.e.1009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15525 - 2.00095i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-1.15525 - 2.00095i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.655250 - 1.13493i) q^{11} +(1.93281 + 3.34772i) q^{13} +0.326936 q^{17} +3.08232 q^{19} +(1.81872 + 3.15011i) q^{23} +(-0.169204 + 0.293069i) q^{25} +(4.75152 - 8.22988i) q^{29} +(-3.24904 - 5.62751i) q^{31} -2.31050 q^{35} -2.31050 q^{37} +(-4.74904 - 8.22558i) q^{41} +(-0.0493786 + 0.0855263i) q^{43} +(0.108354 - 0.187674i) q^{47} +(-0.500000 - 0.866025i) q^{49} -13.7921 q^{53} -3.02791 q^{55} +(-1.22493 - 2.12163i) q^{59} +(7.68433 - 13.3097i) q^{61} +(4.46575 - 7.73490i) q^{65} +(2.93529 + 5.08407i) q^{67} +1.77182 q^{71} -5.99504 q^{73} +(-0.655250 - 1.13493i) q^{77} +(7.29594 - 12.6369i) q^{79} +(-3.04116 + 5.26744i) q^{83} +(-0.377692 - 0.654183i) q^{85} -5.52224 q^{89} +3.86561 q^{91} +(-3.56085 - 6.16757i) q^{95} +(2.99178 - 5.18192i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q + 3 * q^5 + 4 * q^7	$ 8 q + 3 q^{5} + 4 q^{7} - 7 q^{11} + 3 q^{13} - 6 q^{17} - 8 q^{19} - 2 q^{23} - 5 q^{25} + 9 q^{29} + 3 q^{31} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 8 q^{43} - 3 q^{47} - 4 q^{49} - 12 q^{53} - 56 q^{55} - 10 q^{59} + 20 q^{61} - q^{65} + 11 q^{67} + 6 q^{71} - 48 q^{73} + 7 q^{77} + 21 q^{79} - 8 q^{83} + 9 q^{85} - 12 q^{89} + 6 q^{91} - 36 q^{95} + 16 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 + 4 * q^7 - 7 * q^11 + 3 * q^13 - 6 * q^17 - 8 * q^19 - 2 * q^23 - 5 * q^25 + 9 * q^29 + 3 * q^31 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 8 * q^43 - 3 * q^47 - 4 * q^49 - 12 * q^53 - 56 * q^55 - 10 * q^59 + 20 * q^61 - q^65 + 11 * q^67 + 6 * q^71 - 48 * q^73 + 7 * q^77 + 21 * q^79 - 8 * q^83 + 9 * q^85 - 12 * q^89 + 6 * q^91 - 36 * q^95 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.15525	−	2.00095i	−0.516643	−	0.894853i	−0.999813	−	0.0193259i	$-0.993848\pi$
$5$	−1.15525	−	2.00095i	−0.516643	−	0.894853i	0.483170	−	0.875527i	$-0.339485\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.655250	−	1.13493i	0.197565	−	0.342193i	−0.750173	−	0.661241i	$-0.770030\pi$
$11$	0.655250	−	1.13493i	0.197565	−	0.342193i	0.947738	+	0.319048i	$0.103363\pi$
$12$		0			0
$13$	1.93281	+	3.34772i	0.536064	+	0.928490i	0.999111	+	0.0421566i	$0.0134228\pi$
$13$	1.93281	+	3.34772i	0.536064	+	0.928490i	−0.463047	+	0.886334i	$0.653244\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.326936			0.0792936			0.0396468	−	0.999214i	$-0.487377\pi$
$17$	0.326936			0.0792936			0.0396468	+	0.999214i	$0.487377\pi$
$18$		0			0
$19$	3.08232			0.707133			0.353566	−	0.935409i	$-0.384969\pi$
$19$	3.08232			0.707133			0.353566	+	0.935409i	$0.384969\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.81872	+	3.15011i	0.379229	+	0.656844i	0.990950	−	0.134230i	$-0.0428560\pi$
$23$	1.81872	+	3.15011i	0.379229	+	0.656844i	−0.611721	+	0.791073i	$0.709523\pi$
$24$		0			0
$25$	−0.169204	+	0.293069i	−0.0338407	+	0.0586139i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.75152	−	8.22988i	0.882336	−	1.52825i	0.0335990	−	0.999435i	$-0.489303\pi$
$29$	4.75152	−	8.22988i	0.882336	−	1.52825i	0.848737	−	0.528815i	$-0.177364\pi$
$30$		0			0
$31$	−3.24904	−	5.62751i	−0.583545	−	1.01073i	−0.995055	−	0.0993246i	$-0.968332\pi$
$31$	−3.24904	−	5.62751i	−0.583545	−	1.01073i	0.411510	−	0.911405i	$-0.365002\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.31050			−0.390546
$36$		0			0
$37$	−2.31050			−0.379844			−0.189922	−	0.981799i	$-0.560823\pi$
$37$	−2.31050			−0.379844			−0.189922	+	0.981799i	$0.560823\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.74904	−	8.22558i	−0.741676	−	1.28462i	−0.951732	−	0.306931i	$-0.900698\pi$
$41$	−4.74904	−	8.22558i	−0.741676	−	1.28462i	0.210056	−	0.977689i	$-0.432635\pi$
$42$		0			0
$43$	−0.0493786	+	0.0855263i	−0.00753017	+	0.0130426i	−0.869766	−	0.493465i	$-0.835730\pi$
$43$	−0.0493786	+	0.0855263i	−0.00753017	+	0.0130426i	0.862236	+	0.506507i	$0.169064\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.108354	−	0.187674i	0.0158050	−	0.0273750i	−0.858015	−	0.513625i	$-0.828302\pi$
$47$	0.108354	−	0.187674i	0.0158050	−	0.0273750i	0.873820	+	0.486250i	$0.161636\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−13.7921			−1.89450			−0.947249	−	0.320500i	$-0.896149\pi$
$53$	−13.7921			−1.89450			−0.947249	+	0.320500i	$0.896149\pi$
$54$		0			0
$55$	−3.02791			−0.408283
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.22493	−	2.12163i	−0.159472	−	0.276213i	0.775207	−	0.631708i	$-0.217646\pi$
$59$	−1.22493	−	2.12163i	−0.159472	−	0.276213i	−0.934678	+	0.355495i	$0.884312\pi$
$60$		0			0
$61$	7.68433	−	13.3097i	0.983878	−	1.70413i	0.337057	−	0.941484i	$-0.390568\pi$
$61$	7.68433	−	13.3097i	0.983878	−	1.70413i	0.646821	−	0.762642i	$-0.276098\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.46575	−	7.73490i	0.553908	−	0.959397i
$66$		0			0
$67$	2.93529	+	5.08407i	0.358603	+	0.621118i	0.987728	−	0.156186i	$-0.0499200\pi$
$67$	2.93529	+	5.08407i	0.358603	+	0.621118i	−0.629125	+	0.777304i	$0.716587\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.77182			0.210277			0.105138	−	0.994458i	$-0.466471\pi$
$71$	1.77182			0.210277			0.105138	+	0.994458i	$0.466471\pi$
$72$		0			0
$73$	−5.99504			−0.701666			−0.350833	−	0.936438i	$-0.614101\pi$
$73$	−5.99504			−0.701666			−0.350833	+	0.936438i	$0.614101\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.655250	−	1.13493i	−0.0746726	−	0.129337i
$78$		0			0
$79$	7.29594	−	12.6369i	0.820857	−	1.42177i	−0.0841876	−	0.996450i	$-0.526829\pi$
$79$	7.29594	−	12.6369i	0.820857	−	1.42177i	0.905045	−	0.425316i	$-0.139837\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.04116	+	5.26744i	−0.333811	+	0.578177i	−0.983256	−	0.182231i	$-0.941668\pi$
$83$	−3.04116	+	5.26744i	−0.333811	+	0.578177i	0.649445	+	0.760409i	$0.275001\pi$
$84$		0			0
$85$	−0.377692	−	0.654183i	−0.0409665	−	0.0709561i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.52224			−0.585356			−0.292678	−	0.956211i	$-0.594546\pi$
$89$	−5.52224			−0.585356			−0.292678	+	0.956211i	$0.594546\pi$
$90$		0			0
$91$	3.86561			0.405226
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.56085	−	6.16757i	−0.365336	−	0.632780i
$96$		0			0
$97$	2.99178	−	5.18192i	0.303769	−	0.526144i	−0.673217	−	0.739445i	$-0.735088\pi$
$97$	2.99178	−	5.18192i	0.303769	−	0.526144i	0.976987	+	0.213301i	$0.0684214\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.85105	+	6.67022i	−0.383194	+	0.663712i	−0.991517	−	0.129978i	$-0.958509\pi$
$101$	−3.85105	+	6.67022i	−0.383194	+	0.663712i	0.608323	+	0.793690i	$0.291843\pi$
$102$		0			0
$103$	−2.03046	−	3.51686i	−0.200067	−	0.346526i	0.748483	−	0.663154i	$-0.230783\pi$
$103$	−2.03046	−	3.51686i	−0.200067	−	0.346526i	−0.948550	+	0.316628i	$0.897449\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.0774			1.36091			0.680455	−	0.732790i	$-0.261782\pi$
$107$	14.0774			1.36091			0.680455	+	0.732790i	$0.261782\pi$
$108$		0			0
$109$	−6.67306			−0.639164			−0.319582	−	0.947559i	$-0.603542\pi$
$109$	−6.67306			−0.639164			−0.319582	+	0.947559i	$0.603542\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.84918	−	6.66697i	−0.362100	−	0.627176i	0.626206	−	0.779658i	$-0.284607\pi$
$113$	−3.84918	−	6.66697i	−0.362100	−	0.627176i	−0.988306	+	0.152482i	$0.951273\pi$
$114$		0			0
$115$	4.20215	−	7.27833i	0.391852	−	0.678708i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.163468	−	0.283135i	0.0149851	−	0.0259549i
$120$		0			0
$121$	4.64130	+	8.03896i	0.421936	+	0.730815i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.7706			−0.963352
$126$		0			0
$127$	14.9847			1.32968			0.664838	−	0.746987i	$-0.268500\pi$
$127$	14.9847			1.32968			0.664838	+	0.746987i	$0.268500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.20788	+	9.02032i	0.455015	+	0.788109i	0.998689	−	0.0511876i	$-0.0163007\pi$
$131$	5.20788	+	9.02032i	0.455015	+	0.788109i	−0.543674	+	0.839296i	$0.682967\pi$
$132$		0			0
$133$	1.54116	−	2.66937i	0.133636	−	0.231464i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.13170	−	5.42426i	0.267559	−	0.463426i	−0.700672	−	0.713484i	$-0.747116\pi$
$137$	3.13170	−	5.42426i	0.267559	−	0.463426i	0.968231	+	0.250058i	$0.0804496\pi$
$138$		0			0
$139$	10.0798	+	17.4588i	0.854961	+	1.48084i	0.876681	+	0.481071i	$0.159752\pi$
$139$	10.0798	+	17.4588i	0.854961	+	1.48084i	−0.0217207	+	0.999764i	$0.506914\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.06588			0.423631
$144$		0			0
$145$	−21.9568			−1.82341
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.50878	+	14.7376i	0.697067	+	1.20736i	0.969479	+	0.245174i	$0.0788452\pi$
$149$	8.50878	+	14.7376i	0.697067	+	1.20736i	−0.272412	+	0.962181i	$0.587821\pi$
$150$		0			0
$151$	8.19641	−	14.1966i	0.667014	−	1.15530i	−0.311721	−	0.950174i	$-0.600905\pi$
$151$	8.19641	−	14.1966i	0.667014	−	1.15530i	0.978735	−	0.205129i	$-0.0657614\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.50691	+	13.0023i	−0.602969	+	1.04437i
$156$		0			0
$157$	−10.2274	−	17.7144i	−0.816238	−	1.41377i	−0.908435	−	0.418025i	$-0.862722\pi$
$157$	−10.2274	−	17.7144i	−0.816238	−	1.41377i	0.0921971	−	0.995741i	$-0.470611\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.63744			0.286670
$162$		0			0
$163$	16.8810			1.32222			0.661110	−	0.750289i	$-0.270086\pi$
$163$	16.8810			1.32222			0.661110	+	0.750289i	$0.270086\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.60587	−	2.78145i	−0.124266	−	0.215235i	0.797180	−	0.603742i	$-0.206324\pi$
$167$	−1.60587	−	2.78145i	−0.124266	−	0.215235i	−0.921446	+	0.388507i	$0.872991\pi$
$168$		0			0
$169$	−0.971485	+	1.68266i	−0.0747296	+	0.129435i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.306072	−	0.530133i	0.0232703	−	0.0403053i	−0.854156	−	0.520017i	$-0.825926\pi$
$173$	0.306072	−	0.530133i	0.0232703	−	0.0403053i	0.877426	+	0.479712i	$0.159259\pi$
$174$		0			0
$175$	0.169204	+	0.293069i	0.0127906	+	0.0221540i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.38135			−0.327477			−0.163739	−	0.986504i	$-0.552355\pi$
$179$	−4.38135			−0.327477			−0.163739	+	0.986504i	$0.552355\pi$
$180$		0			0
$181$	−3.50192			−0.260295			−0.130148	−	0.991495i	$-0.541545\pi$
$181$	−3.50192			−0.260295			−0.130148	+	0.991495i	$0.541545\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.66920	+	4.62320i	0.196244	+	0.339904i
$186$		0			0
$187$	0.214225	−	0.371048i	0.0156657	−	0.0271337i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.71533	+	4.70309i	−0.196474	+	0.340303i	−0.947383	−	0.320103i	$-0.896283\pi$
$191$	−2.71533	+	4.70309i	−0.196474	+	0.340303i	0.750909	+	0.660406i	$0.229616\pi$
$192$		0			0
$193$	4.54193	+	7.86686i	0.326935	+	0.566269i	0.981902	−	0.189389i	$-0.0606507\pi$
$193$	4.54193	+	7.86686i	0.326935	+	0.566269i	−0.654967	+	0.755658i	$0.727317\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.58040			0.611329			0.305664	−	0.952139i	$-0.401121\pi$
$197$	8.58040			0.611329			0.305664	+	0.952139i	$0.401121\pi$
$198$		0			0
$199$	−25.4905			−1.80697			−0.903487	−	0.428616i	$-0.859001\pi$
$199$	−25.4905			−1.80697			−0.903487	+	0.428616i	$0.859001\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.75152	−	8.22988i	−0.333492	−	0.577624i
$204$		0			0
$205$	−10.9727	+	19.0052i	−0.766364	+	1.32738i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.01969	−	3.49821i	0.139705	−	0.241976i
$210$		0			0
$211$	8.32066	+	14.4118i	0.572818	+	0.992150i	0.996275	+	0.0862336i	$0.0274832\pi$
$211$	8.32066	+	14.4118i	0.572818	+	0.992150i	−0.423457	+	0.905916i	$0.639184\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.228179			0.0155616
$216$		0			0
$217$	−6.49808			−0.441119
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.631904	+	1.09449i	0.0425064	+	0.0736233i
$222$		0			0
$223$	−9.28503	+	16.0821i	−0.621772	+	1.07694i	0.367384	+	0.930069i	$0.380254\pi$
$223$	−9.28503	+	16.0821i	−0.621772	+	1.07694i	−0.989156	+	0.146871i	$0.953080\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.84096	+	13.5809i	−0.520423	+	0.901399i	0.479295	+	0.877654i	$0.340892\pi$
$227$	−7.84096	+	13.5809i	−0.520423	+	0.901399i	−0.999718	+	0.0237449i	$0.992441\pi$
$228$		0			0
$229$	−5.57024	−	9.64794i	−0.368092	−	0.637554i	0.621175	−	0.783672i	$-0.286656\pi$
$229$	−5.57024	−	9.64794i	−0.368092	−	0.637554i	−0.989267	+	0.146118i	$0.953322\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	21.6831			1.42050			0.710252	−	0.703948i	$-0.248581\pi$
$233$	21.6831			1.42050			0.710252	+	0.703948i	$0.248581\pi$
$234$		0			0
$235$	−0.500702			−0.0326622
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.20271	−	10.7434i	−0.401220	−	0.694934i	0.592653	−	0.805458i	$-0.298080\pi$
$239$	−6.20271	−	10.7434i	−0.401220	−	0.694934i	−0.993873	+	0.110524i	$0.964747\pi$
$240$		0			0
$241$	8.35028	−	14.4631i	0.537889	−	0.931651i	−0.461129	−	0.887333i	$-0.652555\pi$
$241$	8.35028	−	14.4631i	0.537889	−	0.931651i	0.999017	−	0.0443176i	$-0.0141114\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.15525	+	2.00095i	−0.0738062	+	0.127836i
$246$		0			0
$247$	5.95753	+	10.3187i	0.379069	+	0.656566i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	27.0215			1.70558			0.852790	−	0.522255i	$-0.174909\pi$
$251$	27.0215			1.70558			0.852790	+	0.522255i	$0.174909\pi$
$252$		0			0
$253$	4.76686			0.299690
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.97645	−	17.2797i	−0.622314	−	1.07788i	−0.989054	−	0.147556i	$-0.952859\pi$
$257$	−9.97645	−	17.2797i	−0.622314	−	1.07788i	0.366740	−	0.930324i	$-0.380474\pi$
$258$		0			0
$259$	−1.15525	+	2.00095i	−0.0717837	+	0.124333i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.92841	−	13.7324i	0.488887	−	0.846776i	−0.511032	−	0.859562i	$-0.670737\pi$
$263$	7.92841	−	13.7324i	0.488887	−	0.846776i	0.999918	+	0.0127855i	$0.00406985\pi$
$264$		0			0
$265$	15.9334	+	27.5974i	0.978779	+	1.69530i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.694466			−0.0423423			−0.0211712	−	0.999776i	$-0.506739\pi$
$269$	−0.694466			−0.0423423			−0.0211712	+	0.999776i	$0.506739\pi$
$270$		0			0
$271$	−9.08883			−0.552107			−0.276053	−	0.961142i	$-0.589027\pi$
$271$	−9.08883			−0.552107			−0.276053	+	0.961142i	$0.589027\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.221741	+	0.384067i	0.0133715	+	0.0231601i
$276$		0			0
$277$	−7.20084	+	12.4722i	−0.432656	+	0.749383i	−0.997101	−	0.0760880i	$-0.975757\pi$
$277$	−7.20084	+	12.4722i	−0.432656	+	0.749383i	0.564445	+	0.825471i	$0.309090\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.68356	+	8.11216i	−0.279398	+	0.483931i	−0.971235	−	0.238122i	$-0.923468\pi$
$281$	−4.68356	+	8.11216i	−0.279398	+	0.483931i	0.691837	+	0.722053i	$0.256801\pi$
$282$		0			0
$283$	9.54310	+	16.5291i	0.567279	+	0.982556i	0.996834	+	0.0795148i	$0.0253371\pi$
$283$	9.54310	+	16.5291i	0.567279	+	0.982556i	−0.429555	+	0.903041i	$0.641330\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.49808			−0.560654
$288$		0			0
$289$	−16.8931			−0.993713
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.10262	+	15.7662i	0.531781	+	0.921071i	0.999312	+	0.0370944i	$0.0118102\pi$
$293$	9.10262	+	15.7662i	0.531781	+	0.921071i	−0.467531	+	0.883977i	$0.654856\pi$
$294$		0			0
$295$	−2.83019	+	4.90203i	−0.164780	+	0.285407i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.03046	+	12.1771i	−0.406582	+	0.704221i
$300$		0			0
$301$	0.0493786	+	0.0855263i	0.00284614	+	0.00492965i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−35.5093			−2.03326
$306$		0			0
$307$	−26.8537			−1.53262			−0.766312	−	0.642469i	$-0.777910\pi$
$307$	−26.8537			−1.53262			−0.766312	+	0.642469i	$0.777910\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.790243	−	1.36874i	−0.0448106	−	0.0776142i	0.842750	−	0.538305i	$-0.180935\pi$
$311$	−0.790243	−	1.36874i	−0.0448106	−	0.0776142i	−0.887561	+	0.460691i	$0.847602\pi$
$312$		0			0
$313$	−10.2617	+	17.7738i	−0.580025	+	1.00463i	0.415451	+	0.909616i	$0.363624\pi$
$313$	−10.2617	+	17.7738i	−0.580025	+	1.00463i	−0.995476	+	0.0950169i	$0.969709\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.9323	−	27.5955i	0.894845	−	1.54992i	0.0608495	−	0.998147i	$-0.480619\pi$
$317$	15.9323	−	27.5955i	0.894845	−	1.54992i	0.833996	−	0.551771i	$-0.186048\pi$
$318$		0			0
$319$	−6.22687	−	10.7853i	−0.348638	−	0.603858i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.00772			0.0560711
$324$		0			0
$325$	−1.30815			−0.0725632
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.108354	−	0.187674i	−0.00597372	−	0.0103468i
$330$		0			0
$331$	−17.0714	+	29.5686i	−0.938330	+	1.62524i	−0.169744	+	0.985488i	$0.554294\pi$
$331$	−17.0714	+	29.5686i	−0.938330	+	1.62524i	−0.768586	+	0.639747i	$0.779039\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.78198	−	11.7467i	0.370539	−	0.641793i
$336$		0			0
$337$	−0.252833	−	0.437920i	−0.0137727	−	0.0238550i	0.859057	−	0.511880i	$-0.171051\pi$
$337$	−0.252833	−	0.437920i	−0.0137727	−	0.0238550i	−0.872830	+	0.488025i	$0.837717\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.51573			−0.461153
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.2154	+	24.6217i	0.763120	+	1.32176i	0.941235	+	0.337753i	$0.109667\pi$
$347$	14.2154	+	24.6217i	0.763120	+	1.32176i	−0.178114	+	0.984010i	$0.557000\pi$
$348$		0			0
$349$	17.5804	−	30.4502i	0.941057	−	1.62996i	0.177599	−	0.984103i	$-0.443167\pi$
$349$	17.5804	−	30.4502i	0.941057	−	1.62996i	0.763459	−	0.645856i	$-0.223500\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.496139	−	0.859339i	0.0264068	−	0.0457380i	−0.852520	−	0.522695i	$-0.824927\pi$
$353$	0.496139	−	0.859339i	0.0264068	−	0.0457380i	0.878927	+	0.476957i	$0.158260\pi$
$354$		0			0
$355$	−2.04690	−	3.54533i	−0.108638	−	0.188166i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	23.2914			1.22928			0.614638	−	0.788810i	$-0.289302\pi$
$359$	23.2914			1.22928			0.614638	+	0.788810i	$0.289302\pi$
$360$		0			0
$361$	−9.49930			−0.499963
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.92576	+	11.9958i	0.362511	+	0.627887i
$366$		0			0
$367$	5.89144	−	10.2043i	0.307531	−	0.532659i	−0.670291	−	0.742099i	$-0.733831\pi$
$367$	5.89144	−	10.2043i	0.307531	−	0.532659i	0.977822	+	0.209440i	$0.0671640\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.89607	+	11.9443i	−0.358026	+	0.620120i
$372$		0			0
$373$	6.91714	+	11.9808i	0.358156	+	0.620344i	0.987653	−	0.156659i	$-0.0500723\pi$
$373$	6.91714	+	11.9808i	0.358156	+	0.620344i	−0.629497	+	0.777003i	$0.716739\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	36.7351			1.89195
$378$		0			0
$379$	−21.5877			−1.10889			−0.554443	−	0.832222i	$-0.687069\pi$
$379$	−21.5877			−1.10889			−0.554443	+	0.832222i	$0.687069\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.31989	+	14.4105i	0.425127	+	0.736341i	0.996432	−	0.0843965i	$-0.0268962\pi$
$383$	8.31989	+	14.4105i	0.425127	+	0.736341i	−0.571306	+	0.820737i	$0.693563\pi$
$384$		0			0
$385$	−1.51395	+	2.62225i	−0.0771582	+	0.133642i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.46709	+	16.3975i	−0.480000	+	0.831385i	−0.999737	−	0.0229417i	$-0.992697\pi$
$389$	−9.46709	+	16.3975i	−0.480000	+	0.831385i	0.519736	+	0.854327i	$0.326030\pi$
$390$		0			0
$391$	0.594604	+	1.02988i	0.0300704	+	0.0520835i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−33.7145			−1.69636
$396$		0			0
$397$	16.0746			0.806761			0.403381	−	0.915032i	$-0.367835\pi$
$397$	16.0746			0.806761			0.403381	+	0.915032i	$0.367835\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.4409	+	33.6726i	0.970832	+	1.68153i	0.693056	+	0.720884i	$0.256264\pi$
$401$	19.4409	+	33.6726i	0.970832	+	1.68153i	0.277776	+	0.960646i	$0.410403\pi$
$402$		0			0
$403$	12.5595	−	21.7538i	0.625635	−	1.08363i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.51395	+	2.62225i	−0.0750439	+	0.129980i
$408$		0			0
$409$	−6.39993	−	11.0850i	−0.316456	−	0.548119i	0.663290	−	0.748363i	$-0.269160\pi$
$409$	−6.39993	−	11.0850i	−0.316456	−	0.548119i	−0.979746	+	0.200244i	$0.935826\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.44985			−0.120549
$414$		0			0
$415$	14.0532			0.689844
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.597046	+	1.03411i	0.0291676	+	0.0505197i	0.880241	−	0.474527i	$-0.157381\pi$
$419$	0.597046	+	1.03411i	0.0291676	+	0.0505197i	−0.851073	+	0.525047i	$0.824048\pi$
$420$		0			0
$421$	−8.19067	+	14.1867i	−0.399189	+	0.691416i	−0.993626	−	0.112726i	$-0.964042\pi$
$421$	−8.19067	+	14.1867i	−0.399189	+	0.691416i	0.594437	+	0.804142i	$0.297375\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.0553187	+	0.0958149i	−0.00268335	+	0.00464770i
$426$		0			0
$427$	−7.68433	−	13.3097i	−0.371871	−	0.644099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	26.3928			1.27130			0.635649	−	0.771978i	$-0.280733\pi$
$431$	26.3928			1.27130			0.635649	+	0.771978i	$0.280733\pi$
$432$		0			0
$433$	23.7503			1.14137			0.570684	−	0.821170i	$-0.306678\pi$
$433$	23.7503			1.14137			0.570684	+	0.821170i	$0.306678\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.60587	+	9.70965i	0.268165	+	0.464476i
$438$		0			0
$439$	10.2431	−	17.7416i	0.488877	−	0.846759i	−0.511042	−	0.859556i	$-0.670740\pi$
$439$	10.2431	−	17.7416i	0.488877	−	0.846759i	0.999918	+	0.0127969i	$0.00407350\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.89909	+	6.75343i	−0.185252	+	0.320865i	−0.943661	−	0.330913i	$-0.892643\pi$
$443$	−3.89909	+	6.75343i	−0.185252	+	0.320865i	0.758410	+	0.651778i	$0.225977\pi$
$444$		0			0
$445$	6.37957	+	11.0497i	0.302421	+	0.523808i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.35981			−0.111366			−0.0556831	−	0.998448i	$-0.517734\pi$
$449$	−2.35981			−0.111366			−0.0556831	+	0.998448i	$0.517734\pi$
$450$		0			0
$451$	−12.4472			−0.586117
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.46575	−	7.73490i	−0.209358	−	0.362618i
$456$		0			0
$457$	−10.1012	+	17.4959i	−0.472516	+	0.818422i	−0.999505	−	0.0314501i	$-0.989987\pi$
$457$	−10.1012	+	17.4959i	−0.472516	+	0.818422i	0.526989	+	0.849872i	$0.323321\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.02197	+	10.4304i	−0.280471	+	0.485790i	−0.971501	−	0.237036i	$-0.923824\pi$
$461$	−6.02197	+	10.4304i	−0.280471	+	0.485790i	0.691030	+	0.722826i	$0.257157\pi$
$462$		0			0
$463$	11.6437	+	20.1675i	0.541130	+	0.937265i	0.998839	+	0.0481633i	$0.0153368\pi$
$463$	11.6437	+	20.1675i	0.541130	+	0.937265i	−0.457709	+	0.889102i	$0.651330\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−34.0682			−1.57649			−0.788243	−	0.615364i	$-0.789009\pi$
$467$	−34.0682			−1.57649			−0.788243	+	0.615364i	$0.789009\pi$
$468$		0			0
$469$	5.87058			0.271078
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.0647107	+	0.112082i	0.00297540	+	0.00515354i
$474$		0			0
$475$	−0.521540	+	0.903334i	−0.0239299	+	0.0414478i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.38477	+	16.2549i	−0.428801	+	0.742705i	−0.996767	−	0.0803471i	$-0.974397\pi$
$479$	−9.38477	+	16.2549i	−0.428801	+	0.742705i	0.567966	+	0.823052i	$0.307730\pi$
$480$		0			0
$481$	−4.46575	−	7.73490i	−0.203621	−	0.352681i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.8250			−0.627762
$486$		0			0
$487$	−13.8837			−0.629132			−0.314566	−	0.949236i	$-0.601859\pi$
$487$	−13.8837			−0.629132			−0.314566	+	0.949236i	$0.601859\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.54250	+	7.86784i	0.205000	+	0.355071i	0.950133	−	0.311846i	$-0.100947\pi$
$491$	4.54250	+	7.86784i	0.205000	+	0.355071i	−0.745133	+	0.666916i	$0.767614\pi$
$492$		0			0
$493$	1.55344	−	2.69064i	0.0699636	−	0.121180i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.885911	−	1.53444i	0.0397385	−	0.0688291i
$498$		0			0
$499$	11.8788	+	20.5747i	0.531769	+	0.921051i	0.999312	+	0.0370810i	$0.0118060\pi$
$499$	11.8788	+	20.5747i	0.531769	+	0.921051i	−0.467543	+	0.883970i	$0.654861\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.5612			1.00595			0.502977	−	0.864300i	$-0.332238\pi$
$503$	22.5612			1.00595			0.502977	+	0.864300i	$0.332238\pi$
$504$		0			0
$505$	17.7957			0.791899
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.94814	+	6.83838i	0.174998	+	0.303106i	0.940161	−	0.340732i	$-0.110675\pi$
$509$	3.94814	+	6.83838i	0.174998	+	0.303106i	−0.765162	+	0.643837i	$0.777341\pi$
$510$		0			0
$511$	−2.99752	+	5.19185i	−0.132602	+	0.229674i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.69138	+	8.12570i	−0.206727	+	0.358061i
$516$		0			0
$517$	−0.141997	−	0.245946i	−0.00624503	−	0.0108167i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.86440			−0.432167			−0.216084	−	0.976375i	$-0.569328\pi$
$521$	−9.86440			−0.432167			−0.216084	+	0.976375i	$0.569328\pi$
$522$		0			0
$523$	22.9097			1.00177			0.500885	−	0.865514i	$-0.333008\pi$
$523$	22.9097			1.00177			0.500885	+	0.865514i	$0.333008\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.06223	−	1.83983i	−0.0462714	−	0.0801444i
$528$		0			0
$529$	4.88453	−	8.46026i	0.212371	−	0.367837i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.3580	−	31.7969i	0.795172	−	1.37728i
$534$		0			0
$535$	−16.2629	−	28.1681i	−0.703105	−	1.21781i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.31050			−0.0564472
$540$		0			0
$541$	29.7187			1.27771			0.638853	−	0.769329i	$-0.279409\pi$
$541$	29.7187			1.27771			0.638853	+	0.769329i	$0.279409\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.70906	+	13.3525i	0.330220	+	0.571957i
$546$		0			0
$547$	1.30472	−	2.25985i	0.0557859	−	0.0966240i	−0.836784	−	0.547533i	$-0.815567\pi$
$547$	1.30472	−	2.25985i	0.0557859	−	0.0966240i	0.892570	+	0.450909i	$0.148900\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	14.6457	−	25.3671i	0.623929	−	1.08068i
$552$		0			0
$553$	−7.29594	−	12.6369i	−0.310255	−	0.537377i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.0406			−1.10338			−0.551688	−	0.834051i	$-0.686016\pi$
$557$	−26.0406			−1.10338			−0.551688	+	0.834051i	$0.686016\pi$
$558$		0			0
$559$	−0.381757			−0.0161466
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.3876	−	38.7765i	−0.943525	−	1.63423i	−0.758677	−	0.651467i	$-0.774154\pi$
$563$	−22.3876	−	38.7765i	−0.943525	−	1.63423i	−0.184848	−	0.982767i	$-0.559179\pi$
$564$		0			0
$565$	−8.89352	+	15.4040i	−0.374153	+	0.648052i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.6290	+	25.3382i	−0.613280	+	1.06223i	0.377404	+	0.926049i	$0.376817\pi$
$569$	−14.6290	+	25.3382i	−0.613280	+	1.06223i	−0.990684	+	0.136183i	$0.956516\pi$
$570$		0			0
$571$	−18.2628	−	31.6321i	−0.764275	−	1.32376i	−0.940629	−	0.339437i	$-0.889764\pi$
$571$	−18.2628	−	31.6321i	−0.764275	−	1.32376i	0.176354	−	0.984327i	$-0.443570\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.23093			−0.0513335
$576$		0			0
$577$	9.88205			0.411395			0.205698	−	0.978616i	$-0.434054\pi$
$577$	9.88205			0.411395			0.205698	+	0.978616i	$0.434054\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.04116	+	5.26744i	0.126169	+	0.218530i
$582$		0			0
$583$	−9.03730	+	15.6531i	−0.374287	+	0.648284i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.05954	+	7.03133i	−0.167555	+	0.290214i	−0.937560	−	0.347824i	$-0.886921\pi$
$587$	−4.05954	+	7.03133i	−0.167555	+	0.290214i	0.770005	+	0.638038i	$0.220254\pi$
$588$		0			0
$589$	−10.0146	−	17.3458i	−0.412644	−	0.714720i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−29.6969			−1.21950			−0.609752	−	0.792592i	$-0.708731\pi$
$593$	−29.6969			−1.21950			−0.609752	+	0.792592i	$0.708731\pi$
$594$		0			0
$595$	−0.755385			−0.0309678
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.19531	−	14.1947i	−0.334851	−	0.579979i	0.648605	−	0.761125i	$-0.275353\pi$
$599$	−8.19531	−	14.1947i	−0.334851	−	0.579979i	−0.983456	+	0.181146i	$0.942019\pi$
$600$		0			0
$601$	24.4424	−	42.3355i	0.997028	−	1.72690i	0.431790	−	0.901974i	$-0.357882\pi$
$601$	24.4424	−	42.3355i	0.997028	−	1.72690i	0.565237	−	0.824928i	$-0.308785\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.7237	−	18.5740i	0.435981	−	0.755141i
$606$		0			0
$607$	−23.6033	−	40.8820i	−0.958027	−	1.65935i	−0.727285	−	0.686335i	$-0.759218\pi$
$607$	−23.6033	−	40.8820i	−0.958027	−	1.65935i	−0.230741	−	0.973015i	$-0.574115\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.837706			0.0338899
$612$		0			0
$613$	−15.6396			−0.631679			−0.315840	−	0.948813i	$-0.602286\pi$
$613$	−15.6396			−0.631679			−0.315840	+	0.948813i	$0.602286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.7793	+	27.3305i	0.635251	+	1.10029i	0.986462	+	0.163990i	$0.0524365\pi$
$617$	15.7793	+	27.3305i	0.635251	+	1.10029i	−0.351211	+	0.936296i	$0.614230\pi$
$618$		0			0
$619$	−7.31619	+	12.6720i	−0.294063	+	0.509331i	−0.974766	−	0.223227i	$-0.928341\pi$
$619$	−7.31619	+	12.6720i	−0.294063	+	0.509331i	0.680704	+	0.732559i	$0.261674\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.76112	+	4.78240i	−0.110622	+	0.191603i
$624$		0			0
$625$	13.2888	+	23.0168i	0.531550	+	0.920672i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.755385			−0.0301192
$630$		0			0
$631$	−36.3101			−1.44548			−0.722742	−	0.691118i	$-0.757119\pi$
$631$	−36.3101			−1.44548			−0.722742	+	0.691118i	$0.757119\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.3111	−	29.9836i	−0.686969	−	1.18986i
$636$		0			0
$637$	1.93281	−	3.34772i	0.0765806	−	0.132641i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.40731	−	9.36574i	0.213576	−	0.369924i	−0.739255	−	0.673425i	$-0.764822\pi$
$641$	5.40731	−	9.36574i	0.213576	−	0.369924i	0.952831	+	0.303501i	$0.0981556\pi$
$642$		0			0
$643$	6.97535	+	12.0817i	0.275081	+	0.476454i	0.970155	−	0.242484i	$-0.0779621\pi$
$643$	6.97535	+	12.0817i	0.275081	+	0.476454i	−0.695075	+	0.718937i	$0.744629\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	34.5634			1.35883			0.679414	−	0.733755i	$-0.262234\pi$
$647$	34.5634			1.35883			0.679414	+	0.733755i	$0.262234\pi$
$648$		0			0
$649$	−3.21053			−0.126024
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.7927	−	23.8897i	−0.539751	−	0.934875i	−0.998917	−	0.0465252i	$-0.985185\pi$
$653$	−13.7927	−	23.8897i	−0.539751	−	0.934875i	0.459167	−	0.888350i	$-0.348148\pi$
$654$		0			0
$655$	12.0328	−	20.8414i	0.470161	−	0.814342i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.3059	−	17.8503i	0.401460	−	0.695348i	−0.592443	−	0.805613i	$-0.701836\pi$
$659$	10.3059	−	17.8503i	0.401460	−	0.695348i	0.993902	+	0.110264i	$0.0351697\pi$
$660$		0			0
$661$	13.5815	+	23.5239i	0.528259	+	0.914972i	0.999457	+	0.0329446i	$0.0104885\pi$
$661$	13.5815	+	23.5239i	0.528259	+	0.914972i	−0.471198	+	0.882028i	$0.656178\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.12170			−0.276168
$666$		0			0
$667$	34.5667			1.33843
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.0703	−	17.4423i	−0.388760	−	0.673352i
$672$		0			0
$673$	−9.52644	+	16.5003i	−0.367217	+	0.636039i	−0.989129	−	0.147048i	$-0.953023\pi$
$673$	−9.52644	+	16.5003i	−0.367217	+	0.636039i	0.621912	+	0.783087i	$0.286356\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.8695	+	18.8265i	−0.417748	+	0.723560i	−0.995713	−	0.0925013i	$-0.970514\pi$
$677$	−10.8695	+	18.8265i	−0.417748	+	0.723560i	0.577965	+	0.816062i	$0.303847\pi$
$678$		0			0
$679$	−2.99178	−	5.18192i	−0.114814	−	0.198864i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	41.0808			1.57191			0.785957	−	0.618281i	$-0.212171\pi$
$683$	41.0808			1.57191			0.785957	+	0.618281i	$0.212171\pi$
$684$		0			0
$685$	−14.4716			−0.552931
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−26.6576	−	46.1722i	−1.01557	−	1.75902i
$690$		0			0
$691$	−9.03599	+	15.6508i	−0.343745	+	0.595384i	−0.985125	−	0.171839i	$-0.945029\pi$
$691$	−9.03599	+	15.6508i	−0.343745	+	0.595384i	0.641380	+	0.767224i	$0.278362\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	23.2895	−	40.3385i	0.883420	−	1.53013i
$696$		0			0
$697$	−1.55263	−	2.68924i	−0.0588101	−	0.101862i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	41.5130			1.56793			0.783963	−	0.620808i	$-0.213195\pi$
$701$	41.5130			1.56793			0.783963	+	0.620808i	$0.213195\pi$
$702$		0			0
$703$	−7.12170			−0.268600
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.85105	+	6.67022i	0.144834	+	0.250859i
$708$		0			0
$709$	−0.684536	+	1.18565i	−0.0257083	+	0.0445280i	−0.878593	−	0.477571i	$-0.841517\pi$
$709$	−0.684536	+	1.18565i	−0.0257083	+	0.0445280i	0.852885	+	0.522099i	$0.174851\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	11.8182	−	20.4697i	0.442594	−	0.766596i
$714$		0			0
$715$	−5.85236	−	10.1366i	−0.218866	−	0.379087i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.1854			−0.752787			−0.376394	−	0.926460i	$-0.622836\pi$
$719$	−20.1854			−0.752787			−0.376394	+	0.926460i	$0.622836\pi$
$720$		0			0
$721$	−4.06092			−0.151237
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.60795	+	2.78505i	0.0597178	+	0.103434i
$726$		0			0
$727$	−1.69393	+	2.93397i	−0.0628243	+	0.108815i	−0.895727	−	0.444605i	$-0.853344\pi$
$727$	−1.69393	+	2.93397i	−0.0628243	+	0.108815i	0.832903	+	0.553420i	$0.186677\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.0161436	+	0.0279616i	−0.000597094	+	0.00103420i
$732$		0			0
$733$	8.90603	+	15.4257i	0.328952	+	0.569761i	0.982304	−	0.187293i	$-0.0599713\pi$
$733$	8.90603	+	15.4257i	0.328952	+	0.569761i	−0.653352	+	0.757054i	$0.726638\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.69339			0.283390
$738$		0			0
$739$	−1.15512			−0.0424918			−0.0212459	−	0.999774i	$-0.506763\pi$
$739$	−1.15512			−0.0424918			−0.0212459	+	0.999774i	$0.506763\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.5863	−	23.5322i	−0.498435	−	0.863314i	0.501564	−	0.865121i	$-0.332758\pi$
$743$	−13.5863	−	23.5322i	−0.498435	−	0.863314i	−0.999998	+	0.00180657i	$0.999425\pi$
$744$		0			0
$745$	19.6595	−	34.0513i	0.720270	−	1.24754i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.03868	−	12.1913i	0.257188	−	0.445462i
$750$		0			0
$751$	−11.2959	−	19.5651i	−0.412195	−	0.713942i	0.582935	−	0.812519i	$-0.301904\pi$
$751$	−11.2959	−	19.5651i	−0.412195	−	0.713942i	−0.995129	+	0.0985769i	$0.968571\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−37.8756			−1.37843
$756$		0			0
$757$	13.9989			0.508797			0.254399	−	0.967099i	$-0.418122\pi$
$757$	13.9989			0.508797			0.254399	+	0.967099i	$0.418122\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.252336	−	0.437059i	−0.00914718	−	0.0158434i	0.861416	−	0.507901i	$-0.169578\pi$
$761$	−0.252336	−	0.437059i	−0.00914718	−	0.0158434i	−0.870563	+	0.492057i	$0.836245\pi$
$762$		0			0
$763$	−3.33653	+	5.77904i	−0.120791	+	0.209215i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.73509	−	8.20141i	0.170974	−	0.296136i
$768$		0			0
$769$	4.89218	+	8.47351i	0.176417	+	0.305563i	0.940651	−	0.339376i	$-0.110216\pi$
$769$	4.89218	+	8.47351i	0.176417	+	0.305563i	−0.764234	+	0.644939i	$0.776883\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−26.5907			−0.956403			−0.478201	−	0.878250i	$-0.658711\pi$
$773$	−26.5907			−0.956403			−0.478201	+	0.878250i	$0.658711\pi$
$774$		0			0
$775$	2.19900			0.0789904
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14.6381	−	25.3539i	−0.524463	−	0.908397i
$780$		0			0
$781$	1.16099	−	2.01089i	0.0415433	−	0.0719551i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−23.6305	+	40.9292i	−0.843408	+	1.46083i
$786$		0			0
$787$	19.1108	+	33.1009i	0.681227	+	1.17992i	0.974607	+	0.223924i	$0.0718868\pi$
$787$	19.1108	+	33.1009i	0.681227	+	1.17992i	−0.293379	+	0.955996i	$0.594780\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.69835			−0.273722
$792$		0			0
$793$	59.4093			2.10969
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.1866	+	19.3758i	0.396250	+	0.686325i	0.993260	−	0.115909i	$-0.0369780\pi$
$797$	11.1866	+	19.3758i	0.396250	+	0.686325i	−0.597010	+	0.802234i	$0.703645\pi$
$798$		0			0
$799$	0.0354246	−	0.0613573i	0.00125323	−	0.00217066i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.92824	+	6.80392i	−0.138625	+	0.240105i
$804$		0			0
$805$	−4.20215	−	7.27833i	−0.148106	−	0.256527i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.50319			−0.193482			−0.0967409	−	0.995310i	$-0.530842\pi$
$809$	−5.50319			−0.193482			−0.0967409	+	0.995310i	$0.530842\pi$
$810$		0			0
$811$	−12.3713			−0.434414			−0.217207	−	0.976126i	$-0.569695\pi$
$811$	−12.3713			−0.434414			−0.217207	+	0.976126i	$0.569695\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−19.5017	−	33.7780i	−0.683116	−	1.18319i
$816$		0			0
$817$	−0.152201	+	0.263619i	−0.00532483	+	0.00922288i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.2767	−	36.8524i	0.742564	−	1.28616i	−0.208761	−	0.977967i	$-0.566943\pi$
$821$	21.2767	−	36.8524i	0.742564	−	1.28616i	0.951324	−	0.308191i	$-0.0997236\pi$
$822$		0			0
$823$	8.11754	+	14.0600i	0.282960	+	0.490101i	0.972112	−	0.234516i	$-0.0753504\pi$
$823$	8.11754	+	14.0600i	0.282960	+	0.490101i	−0.689153	+	0.724616i	$0.742017\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.0199			−1.18299			−0.591494	−	0.806309i	$-0.701462\pi$
$827$	−34.0199			−1.18299			−0.591494	+	0.806309i	$0.701462\pi$
$828$		0			0
$829$	38.6394			1.34200			0.671000	−	0.741457i	$-0.265865\pi$
$829$	38.6394			1.34200			0.671000	+	0.741457i	$0.265865\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.163468	−	0.283135i	−0.00566383	−	0.00981004i
$834$		0			0
$835$	−3.71036	+	6.42654i	−0.128402	+	0.222400i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.88612	+	6.73095i	−0.134164	+	0.232378i	−0.925278	−	0.379291i	$-0.876168\pi$
$839$	−3.88612	+	6.73095i	−0.134164	+	0.232378i	0.791114	+	0.611669i	$0.209501\pi$
$840$		0			0
$841$	−30.6540	−	53.0942i	−1.05703	−	1.83084i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.48923			0.154434
$846$		0			0
$847$	9.28259			0.318954
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.20215	−	7.27833i	−0.144048	−	0.249498i
$852$		0			0
$853$	−10.0272	+	17.3676i	−0.343324	+	0.594654i	−0.985048	−	0.172282i	$-0.944886\pi$
$853$	−10.0272	+	17.3676i	−0.343324	+	0.594654i	0.641724	+	0.766936i	$0.278219\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.837910	−	1.45130i	0.0286225	−	0.0495756i	−0.851359	−	0.524583i	$-0.824221\pi$
$857$	0.837910	−	1.45130i	0.0286225	−	0.0495756i	0.879982	+	0.475007i	$0.157555\pi$
$858$		0			0
$859$	−18.7256	−	32.4336i	−0.638908	−	1.10662i	−0.985673	−	0.168669i	$-0.946053\pi$
$859$	−18.7256	−	32.4336i	−0.638908	−	1.10662i	0.346765	−	0.937952i	$-0.387280\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.0265			1.02211			0.511057	−	0.859547i	$-0.329254\pi$
$863$	30.0265			1.02211			0.511057	+	0.859547i	$0.329254\pi$
$864$		0			0
$865$	−1.41436			−0.0480897
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.56132	−	16.5607i	−0.324346	−	0.561783i
$870$		0			0
$871$	−11.3467	+	19.6531i	−0.384468	+	0.665918i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.38530	+	9.32762i	−0.182056	+	0.315331i
$876$		0			0
$877$	−11.3517	−	19.6617i	−0.383318	−	0.663927i	0.608216	−	0.793772i	$-0.291885\pi$
$877$	−11.3517	−	19.6617i	−0.383318	−	0.663927i	−0.991534	+	0.129845i	$0.958552\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.0266			1.21377			0.606883	−	0.794791i	$-0.292420\pi$
$881$	36.0266			1.21377			0.606883	+	0.794791i	$0.292420\pi$
$882$		0			0
$883$	47.7159			1.60577			0.802884	−	0.596135i	$-0.203298\pi$
$883$	47.7159			1.60577			0.802884	+	0.596135i	$0.203298\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.70962	−	9.88935i	−0.191710	−	0.332052i	0.754107	−	0.656752i	$-0.228070\pi$
$887$	−5.70962	−	9.88935i	−0.191710	−	0.332052i	−0.945817	+	0.324700i	$0.894737\pi$
$888$		0			0
$889$	7.49235	−	12.9771i	0.251285	−	0.435239i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.333980	−	0.578471i	0.0111762	−	0.0193578i
$894$		0			0
$895$	5.06155	+	8.76686i	0.169189	+	0.293044i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−61.7516			−2.05953
$900$		0			0
$901$	−4.50915			−0.150221
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.04559	+	7.00716i	0.134480	+	0.232926i
$906$		0			0
$907$	−1.81546	+	3.14448i	−0.0602815	+	0.104411i	−0.894591	−	0.446885i	$-0.852533\pi$
$907$	−1.81546	+	3.14448i	−0.0602815	+	0.104411i	0.834310	+	0.551296i	$0.185867\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.24848	−	2.16242i	0.0413638	−	0.0716443i	−0.844602	−	0.535394i	$-0.820163\pi$
$911$	1.24848	−	2.16242i	0.0413638	−	0.0716443i	0.885966	+	0.463750i	$0.153496\pi$
$912$		0			0
$913$	3.98544	+	6.90298i	0.131899	+	0.228455i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.4158			0.343959
$918$		0			0
$919$	0.454816			0.0150030			0.00750149	−	0.999972i	$-0.497612\pi$
$919$	0.454816			0.0150030			0.00750149	+	0.999972i	$0.497612\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.42459	+	5.93156i	0.112722	+	0.195240i
$924$		0			0
$925$	0.390945	−	0.677137i	0.0128542	−	0.0222641i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.6846	+	28.8985i	−0.547403	+	0.948129i	0.451049	+	0.892499i	$0.351050\pi$
$929$	−16.6846	+	28.8985i	−0.547403	+	0.948129i	−0.998451	+	0.0556301i	$0.982283\pi$
$930$		0			0
$931$	−1.54116	−	2.66937i	−0.0505095	−	0.0874850i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.989932			−0.0323742
$936$		0			0
$937$	−5.28675			−0.172711			−0.0863553	−	0.996264i	$-0.527522\pi$
$937$	−5.28675			−0.172711			−0.0863553	+	0.996264i	$0.527522\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	22.3084	+	38.6393i	0.727234	+	1.25961i	0.958048	+	0.286608i	$0.0925277\pi$
$941$	22.3084	+	38.6393i	0.727234	+	1.25961i	−0.230814	+	0.972998i	$0.574139\pi$
$942$		0			0
$943$	17.2743	−	29.9200i	0.562530	−	0.974330i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.3695	+	24.8887i	−0.466945	+	0.808773i	−0.999287	−	0.0377568i	$-0.987979\pi$
$947$	−14.3695	+	24.8887i	−0.466945	+	0.808773i	0.532342	+	0.846530i	$0.321312\pi$
$948$		0			0
$949$	−11.5872	−	20.0697i	−0.376138	−	0.651490i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	52.6957			1.70698			0.853491	−	0.521107i	$-0.174481\pi$
$953$	52.6957			1.70698			0.853491	+	0.521107i	$0.174481\pi$
$954$		0			0
$955$	12.5475			0.406029
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.13170	−	5.42426i	−0.101128	−	0.175159i
$960$		0			0
$961$	−5.61255	+	9.72122i	−0.181050	+	0.313588i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.4941	−	18.1764i	0.337818	−	0.585118i
$966$		0			0
$967$	−22.1564	−	38.3759i	−0.712500	−	1.23409i	−0.963916	−	0.266207i	$-0.914229\pi$
$967$	−22.1564	−	38.3759i	−0.712500	−	1.23409i	0.251415	−	0.967879i	$-0.419104\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	49.8993			1.60134			0.800672	−	0.599103i	$-0.204476\pi$
$971$	49.8993			1.60134			0.800672	+	0.599103i	$0.204476\pi$
$972$		0			0
$973$	20.1597			0.646290
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.0981	−	27.8827i	−0.515022	−	0.892045i	−0.999848	−	0.0174342i	$-0.994450\pi$
$977$	−16.0981	−	27.8827i	−0.515022	−	0.892045i	0.484826	−	0.874611i	$-0.338883\pi$
$978$		0			0
$979$	−3.61845	+	6.26733i	−0.115646	+	0.200305i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.17356	+	10.6929i	−0.196906	+	0.341051i	−0.947524	−	0.319686i	$-0.896423\pi$
$983$	−6.17356	+	10.6929i	−0.196906	+	0.341051i	0.750618	+	0.660737i	$0.229756\pi$
$984$		0			0
$985$	−9.91251	−	17.1690i	−0.315839	−	0.547049i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.359223			−0.0114226
$990$		0			0
$991$	6.80483			0.216163			0.108081	−	0.994142i	$-0.465529\pi$
$991$	6.80483			0.216163			0.108081	+	0.994142i	$0.465529\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	29.4479	+	51.0052i	0.933561	+	1.61698i
$996$		0			0
$997$	−0.812415	+	1.40714i	−0.0257295	+	0.0445647i	−0.878603	−	0.477552i	$-0.841524\pi$
$997$	−0.812415	+	1.40714i	−0.0257295	+	0.0445647i	0.852874	+	0.522117i	$0.174858\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.r.e.505.1		8
3.2	odd	2		504.2.r.e.169.3	✓	8
4.3	odd	2		3024.2.r.m.2017.1		8
9.2	odd	6		4536.2.a.z.1.1		4
9.4	even	3	inner	1512.2.r.e.1009.1		8
9.5	odd	6		504.2.r.e.337.3	yes	8
9.7	even	3		4536.2.a.y.1.4		4
12.11	even	2		1008.2.r.l.673.2		8
36.7	odd	6		9072.2.a.cg.1.4		4
36.11	even	6		9072.2.a.cj.1.1		4
36.23	even	6		1008.2.r.l.337.2		8
36.31	odd	6		3024.2.r.m.1009.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.3	✓	8	3.2	odd	2
504.2.r.e.337.3	yes	8	9.5	odd	6
1008.2.r.l.337.2		8	36.23	even	6
1008.2.r.l.673.2		8	12.11	even	2
1512.2.r.e.505.1		8	1.1	even	1	trivial
1512.2.r.e.1009.1		8	9.4	even	3	inner
3024.2.r.m.1009.1		8	36.31	odd	6
3024.2.r.m.2017.1		8	4.3	odd	2
4536.2.a.y.1.4		4	9.7	even	3
4536.2.a.z.1.1		4	9.2	odd	6
9072.2.a.cg.1.4		4	36.7	odd	6
9072.2.a.cj.1.1		4	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15525 - 2.00095i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-1.15525 - 2.00095i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.655250 - 1.13493i) q^{11} +(1.93281 + 3.34772i) q^{13} +0.326936 q^{17} +3.08232 q^{19} +(1.81872 + 3.15011i) q^{23} +(-0.169204 + 0.293069i) q^{25} +(4.75152 - 8.22988i) q^{29} +(-3.24904 - 5.62751i) q^{31} -2.31050 q^{35} -2.31050 q^{37} +(-4.74904 - 8.22558i) q^{41} +(-0.0493786 + 0.0855263i) q^{43} +(0.108354 - 0.187674i) q^{47} +(-0.500000 - 0.866025i) q^{49} -13.7921 q^{53} -3.02791 q^{55} +(-1.22493 - 2.12163i) q^{59} +(7.68433 - 13.3097i) q^{61} +(4.46575 - 7.73490i) q^{65} +(2.93529 + 5.08407i) q^{67} +1.77182 q^{71} -5.99504 q^{73} +(-0.655250 - 1.13493i) q^{77} +(7.29594 - 12.6369i) q^{79} +(-3.04116 + 5.26744i) q^{83} +(-0.377692 - 0.654183i) q^{85} -5.52224 q^{89} +3.86561 q^{91} +(-3.56085 - 6.16757i) q^{95} +(2.99178 - 5.18192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q + 3 * q^5 + 4 * q^7	\( 8 q + 3 q^{5} + 4 q^{7} - 7 q^{11} + 3 q^{13} - 6 q^{17} - 8 q^{19} - 2 q^{23} - 5 q^{25} + 9 q^{29} + 3 q^{31} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 8 q^{43} - 3 q^{47} - 4 q^{49} - 12 q^{53} - 56 q^{55} - 10 q^{59} + 20 q^{61} - q^{65} + 11 q^{67} + 6 q^{71} - 48 q^{73} + 7 q^{77} + 21 q^{79} - 8 q^{83} + 9 q^{85} - 12 q^{89} + 6 q^{91} - 36 q^{95} + 16 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 + 4 * q^7 - 7 * q^11 + 3 * q^13 - 6 * q^17 - 8 * q^19 - 2 * q^23 - 5 * q^25 + 9 * q^29 + 3 * q^31 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 8 * q^43 - 3 * q^47 - 4 * q^49 - 12 * q^53 - 56 * q^55 - 10 * q^59 + 20 * q^61 - q^65 + 11 * q^67 + 6 * q^71 - 48 * q^73 + 7 * q^77 + 21 * q^79 - 8 * q^83 + 9 * q^85 - 12 * q^89 + 6 * q^91 - 36 * q^95 + 16 * q^97

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