LMFDB - Embedded newform 588.2.e.f.491.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.19
Character	$\chi$	$=$	588.491
Dual form			588.2.e.f.491.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05533 + 0.941421i) q^{2} +(-0.406768 + 1.68361i) q^{3} +(0.227452 + 1.98702i) q^{4} +1.25365i q^{5} +(-2.01426 + 1.39383i) q^{6} +(-1.63059 + 2.31110i) q^{8} +(-2.66908 - 1.36968i) q^{9} +O(q^{10})$	\(q+(1.05533 + 0.941421i) q^{2} +(-0.406768 + 1.68361i) q^{3} +(0.227452 + 1.98702i) q^{4} +1.25365i q^{5} +(-2.01426 + 1.39383i) q^{6} +(-1.63059 + 2.31110i) q^{8} +(-2.66908 - 1.36968i) q^{9} +(-1.18022 + 1.32302i) q^{10} +5.05827 q^{11} +(-3.43789 - 0.425318i) q^{12} -4.41798 q^{13} +(-2.11066 - 0.509947i) q^{15} +(-3.89653 + 0.903905i) q^{16} +5.85341i q^{17} +(-1.52732 - 3.95819i) q^{18} -1.53176i q^{19} +(-2.49104 + 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +0.313570 q^{23} +(-3.22771 - 3.68536i) q^{24} +3.42835 q^{25} +(-4.66244 - 4.15918i) q^{26} +(3.39170 - 3.93654i) q^{27} -5.53862i q^{29} +(-1.74738 - 2.52519i) q^{30} -4.89898i q^{31} +(-4.96309 - 2.71436i) q^{32} +(-2.05755 + 8.51615i) q^{33} +(-5.51053 + 6.17729i) q^{34} +(2.11450 - 5.61506i) q^{36} -5.33816 q^{37} +(1.44203 - 1.61652i) q^{38} +(1.79709 - 7.43815i) q^{39} +(-2.89732 - 2.04420i) q^{40} +1.97938i q^{41} +3.18613i q^{43} +(1.15051 + 10.0509i) q^{44} +(1.71710 - 3.34610i) q^{45} +(0.330921 + 0.295202i) q^{46} +11.4963 q^{47} +(0.0631619 - 6.92792i) q^{48} +(3.61805 + 3.22752i) q^{50} +(-9.85486 - 2.38098i) q^{51} +(-1.00488 - 8.77863i) q^{52} +12.7903i q^{53} +(7.28532 - 0.961345i) q^{54} +6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(5.21417 - 5.84508i) q^{58} +7.96701 q^{59} +(0.533202 - 4.30993i) q^{60} +0.302889 q^{61} +(4.61200 - 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} -5.53862i q^{65} +(-10.1887 + 7.05035i) q^{66} +10.5438i q^{67} +(-11.6309 + 1.33137i) q^{68} +(-0.127550 + 0.527930i) q^{69} +4.53490 q^{71} +(7.51763 - 3.93512i) q^{72} -1.41421 q^{73} +(-5.63353 - 5.02546i) q^{74} +(-1.39454 + 5.77200i) q^{75} +(3.04365 - 0.348402i) q^{76} +(8.89896 - 6.15790i) q^{78} +6.92820i q^{79} +(-1.13319 - 4.88490i) q^{80} +(5.24797 + 7.31156i) q^{81} +(-1.86343 + 2.08890i) q^{82} -6.78340 q^{83} -7.33816 q^{85} +(-2.99949 + 3.36243i) q^{86} +(9.32487 + 2.25294i) q^{87} +(-8.24797 + 11.6902i) q^{88} -4.79755i q^{89} +(4.96221 - 1.91473i) q^{90} +(0.0713222 + 0.623072i) q^{92} +(8.24797 + 1.99275i) q^{93} +(12.1324 + 10.8228i) q^{94} +1.92030 q^{95} +(6.58874 - 7.25179i) q^{96} +13.6844 q^{97} +(-13.5009 - 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) $ 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.05533	+	0.941421i	0.746233	+	0.665685i
$2$	1.05533	+	0.941421i	0.746233	+	0.665685i
$3$	−0.406768	+	1.68361i	−0.234848	+	0.972032i
$3$	−0.406768	+	1.68361i	−0.234848	+	0.972032i
$4$	0.227452	+	1.98702i	0.113726	+	0.993512i
$5$			1.25365i			0.560651i	0.959905	+	0.280326i	$0.0904425\pi$
$5$			1.25365i			0.560651i	−0.959905	+	0.280326i	$0.909558\pi$
$6$	−2.01426	+	1.39383i	−0.822319	+	0.569027i
$7$		0			0
$7$		0			0
$8$	−1.63059	+	2.31110i	−0.576500	+	0.817097i
$9$	−2.66908	−	1.36968i	−0.889693	−	0.456559i
$10$	−1.18022	+	1.32302i	−0.373217	+	0.418376i
$11$	5.05827			1.52513			0.762563	−	0.646914i	$-0.223941\pi$
$11$	5.05827			1.52513			0.762563	+	0.646914i	$0.223941\pi$
$12$	−3.43789	−	0.425318i	−0.992434	−	0.122779i
$13$	−4.41798			−1.22533			−0.612664	−	0.790344i	$-0.709902\pi$
$13$	−4.41798			−1.22533			−0.612664	+	0.790344i	$0.709902\pi$
$14$		0			0
$15$	−2.11066	−	0.509947i	−0.544971	−	0.131668i
$16$	−3.89653	+	0.903905i	−0.974133	+	0.225976i
$17$			5.85341i			1.41966i	0.704372	+	0.709831i	$0.251229\pi$
$17$			5.85341i			1.41966i	−0.704372	+	0.709831i	$0.748771\pi$
$18$	−1.52732	−	3.95819i	−0.359993	−	0.932955i
$19$		−	1.53176i		−	0.351410i	−0.984443	−	0.175705i	$-0.943779\pi$
$19$		−	1.53176i		−	0.351410i	0.984443	−	0.175705i	$-0.0562205\pi$
$20$	−2.49104	+	0.285146i	−0.557014	+	0.0637607i
$21$		0			0
$22$	5.33816	+	4.76197i	1.13810	+	1.01525i
$23$	0.313570			0.0653839			0.0326920	−	0.999465i	$-0.489592\pi$
$23$	0.313570			0.0653839			0.0326920	+	0.999465i	$0.489592\pi$
$24$	−3.22771	−	3.68536i	−0.658855	−	0.752270i
$25$	3.42835			0.685670
$26$	−4.66244	−	4.15918i	−0.914379	−	0.815682i
$27$	3.39170	−	3.93654i	0.652733	−	0.757588i
$28$		0			0
$29$		−	5.53862i		−	1.02850i	−0.857642	−	0.514248i	$-0.828071\pi$
$29$		−	5.53862i		−	1.02850i	0.857642	−	0.514248i	$-0.171929\pi$
$30$	−1.74738	−	2.52519i	−0.319026	−	0.461034i
$31$		−	4.89898i		−	0.879883i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$		−	4.89898i		−	0.879883i	0.898027	−	0.439941i	$-0.145001\pi$
$32$	−4.96309	−	2.71436i	−0.877359	−	0.479835i
$33$	−2.05755	+	8.51615i	−0.358173	+	1.48247i
$34$	−5.51053	+	6.17729i	−0.945048	+	1.05940i
$35$		0			0
$36$	2.11450	−	5.61506i	0.352416	−	0.935843i
$37$	−5.33816			−0.877588			−0.438794	−	0.898588i	$-0.644594\pi$
$37$	−5.33816			−0.877588			−0.438794	+	0.898588i	$0.644594\pi$
$38$	1.44203	−	1.61652i	0.233929	−	0.262234i
$39$	1.79709	−	7.43815i	0.287765	−	1.19106i
$40$	−2.89732	−	2.04420i	−0.458106	−	0.323216i
$41$			1.97938i			0.309127i	0.987983	+	0.154564i	$0.0493971\pi$
$41$			1.97938i			0.309127i	−0.987983	+	0.154564i	$0.950603\pi$
$42$		0			0
$43$			3.18613i			0.485881i	0.970041	+	0.242940i	$0.0781119\pi$
$43$			3.18613i			0.485881i	−0.970041	+	0.242940i	$0.921888\pi$
$44$	1.15051	+	10.0509i	0.173447	+	1.51523i
$45$	1.71710	−	3.34610i	0.255971	−	0.498808i
$46$	0.330921	+	0.295202i	0.0487916	+	0.0435251i
$47$	11.4963			1.67690			0.838451	−	0.544977i	$-0.183461\pi$
$47$	11.4963			1.67690			0.838451	+	0.544977i	$0.183461\pi$
$48$	0.0631619	−	6.92792i	0.00911663	−	0.999958i
$49$		0			0
$50$	3.61805	+	3.22752i	0.511669	+	0.456440i
$51$	−9.85486	−	2.38098i	−1.37996	−	0.333404i
$52$	−1.00488	−	8.77863i	−0.139352	−	1.21738i
$53$			12.7903i			1.75688i	0.477854	+	0.878439i	$0.341415\pi$
$53$			12.7903i			1.75688i	−0.477854	+	0.878439i	$0.658585\pi$
$54$	7.28532	−	0.961345i	0.991406	−	0.130822i
$55$			6.34133i			0.855064i
$56$		0			0
$57$	2.57889	+	0.623072i	0.341582	+	0.0825279i
$58$	5.21417	−	5.84508i	0.684655	−	0.767497i
$59$	7.96701			1.03722			0.518608	−	0.855012i	$-0.326450\pi$
$59$	7.96701			1.03722			0.518608	+	0.855012i	$0.326450\pi$
$60$	0.533202	−	4.30993i	0.0688361	−	0.556410i
$61$	0.302889			0.0387810			0.0193905	−	0.999812i	$-0.493827\pi$
$61$	0.302889			0.0387810			0.0193905	+	0.999812i	$0.493827\pi$
$62$	4.61200	−	5.17005i	0.585725	−	0.656597i
$63$		0			0
$64$	−2.68236	−	7.53691i	−0.335295	−	0.942113i
$65$		−	5.53862i		−	0.686981i
$66$	−10.1887	+	7.05035i	−1.25414	+	0.867839i
$67$			10.5438i			1.28813i	0.764969	+	0.644067i	$0.222754\pi$
$67$			10.5438i			1.28813i	−0.764969	+	0.644067i	$0.777246\pi$
$68$	−11.6309	+	1.33137i	−1.41045	+	0.161452i
$69$	−0.127550	+	0.527930i	−0.0153553	+	0.0635553i
$70$		0			0
$71$	4.53490			0.538194			0.269097	−	0.963113i	$-0.413275\pi$
$71$	4.53490			0.538194			0.269097	+	0.963113i	$0.413275\pi$
$72$	7.51763	−	3.93512i	0.885962	−	0.463759i
$73$	−1.41421			−0.165521			−0.0827606	−	0.996569i	$-0.526374\pi$
$73$	−1.41421			−0.165521			−0.0827606	+	0.996569i	$0.526374\pi$
$74$	−5.63353	−	5.02546i	−0.654885	−	0.584197i
$75$	−1.39454	+	5.77200i	−0.161028	+	0.666493i
$76$	3.04365	−	0.348402i	0.349130	−	0.0399645i
$77$		0			0
$78$	8.89896	−	6.15790i	1.00761	−	0.697245i
$79$			6.92820i			0.779484i	0.920924	+	0.389742i	$0.127436\pi$
$79$			6.92820i			0.779484i	−0.920924	+	0.389742i	$0.872564\pi$
$80$	−1.13319	−	4.88490i	−0.126694	−	0.546149i
$81$	5.24797	+	7.31156i	0.583107	+	0.812395i
$82$	−1.86343	+	2.08890i	−0.205781	+	0.230681i
$83$	−6.78340			−0.744575			−0.372287	−	0.928118i	$-0.621426\pi$
$83$	−6.78340			−0.744575			−0.372287	+	0.928118i	$0.621426\pi$
$84$		0			0
$85$	−7.33816			−0.795935
$86$	−2.99949	+	3.36243i	−0.323444	+	0.362580i
$87$	9.32487	+	2.25294i	0.999731	+	0.241540i
$88$	−8.24797	+	11.6902i	−0.879236	+	1.24618i
$89$		−	4.79755i		−	0.508540i	−0.967133	−	0.254270i	$-0.918165\pi$
$89$		−	4.79755i		−	0.508540i	0.967133	−	0.254270i	$-0.0818351\pi$
$90$	4.96221	−	1.91473i	0.523063	−	0.201831i
$91$		0			0
$92$	0.0713222	+	0.623072i	0.00743586	+	0.0649597i
$93$	8.24797	+	1.99275i	0.855274	+	0.206639i
$94$	12.1324	+	10.8228i	1.25136	+	1.11629i
$95$	1.92030			0.197019
$96$	6.58874	−	7.25179i	0.672461	−	0.740133i
$97$	13.6844			1.38944			0.694719	−	0.719281i	$-0.255529\pi$
$97$	13.6844			1.38944			0.694719	+	0.719281i	$0.255529\pi$
$98$		0			0
$99$	−13.5009	−	6.92820i	−1.35689	−	0.696311i
$100$	0.779785	+	6.81221i	0.0779785	+	0.681221i
$101$			4.07183i			0.405162i	0.979266	+	0.202581i	$0.0649329\pi$
$101$			4.07183i			0.405162i	−0.979266	+	0.202581i	$0.935067\pi$
$102$	−8.15864	−	11.7903i	−0.807826	−	1.16741i
$103$		−	13.0758i		−	1.28839i	−0.764860	−	0.644197i	$-0.777192\pi$
$103$		−	13.0758i		−	1.28839i	0.764860	−	0.644197i	$-0.222808\pi$
$104$	7.20391	−	10.2104i	0.706402	−	1.00121i
$105$		0			0
$106$	−12.0410	+	13.4980i	−1.16953	+	1.31104i
$107$	3.90776			0.377777			0.188889	−	0.981999i	$-0.439511\pi$
$107$	3.90776			0.377777			0.188889	+	0.981999i	$0.439511\pi$
$108$	8.59346	+	5.84401i	0.826906	+	0.562340i
$109$	−8.24797			−0.790012			−0.395006	−	0.918679i	$-0.629257\pi$
$109$	−8.24797			−0.790012			−0.395006	+	0.918679i	$0.629257\pi$
$110$	−5.96986	+	6.69221i	−0.569204	+	0.638077i
$111$	2.17139	−	8.98737i	0.206100	−	0.853044i
$112$		0			0
$113$		−	6.72485i		−	0.632621i	−0.948656	−	0.316311i	$-0.897556\pi$
$113$		−	6.72485i		−	0.632621i	0.948656	−	0.316311i	$-0.102444\pi$
$114$	2.13501	+	3.08537i	0.199962	+	0.288971i
$115$			0.393109i			0.0366576i
$116$	11.0054	−	1.25977i	1.02182	−	0.116967i
$117$	11.7919	+	6.05121i	1.09016	+	0.559434i
$118$	8.40785	+	7.50032i	0.774005	+	0.690460i
$119$		0			0
$120$	4.62016	−	4.04644i	0.421761	−	0.369388i
$121$	14.5861			1.32601
$122$	0.319649	+	0.285146i	0.0289396	+	0.0258159i
$123$	−3.33250	−	0.805149i	−0.300482	−	0.0725978i
$124$	9.73439	−	1.11428i	0.874174	−	0.100066i
$125$			10.5662i			0.945073i
$126$		0			0
$127$			8.50404i			0.754611i	0.926089	+	0.377306i	$0.123149\pi$
$127$			8.50404i			0.754611i	−0.926089	+	0.377306i	$0.876851\pi$
$128$	4.26463	−	10.4792i	0.376943	−	0.926236i
$129$	−5.36420	−	1.29602i	−0.472291	−	0.114108i
$130$	5.21417	−	5.84508i	0.457313	−	0.512648i
$131$	8.41047			0.734826			0.367413	−	0.930058i	$-0.380244\pi$
$131$	8.41047			0.734826			0.367413	+	0.930058i	$0.380244\pi$
$132$	−17.3898	−	2.15138i	−1.51359	−	0.187253i
$133$		0			0
$134$	−9.92618	+	11.1272i	−0.857491	+	0.961247i
$135$	4.93507	+	4.25202i	0.424743	+	0.365955i
$136$	−13.5278	−	9.54451i	−1.16000	−	0.818435i
$137$		−	13.7567i		−	1.17531i	−0.809111	−	0.587657i	$-0.800051\pi$
$137$		−	13.7567i		−	1.17531i	0.809111	−	0.587657i	$-0.199949\pi$
$138$	−0.631613	+	0.437063i	−0.0537664	+	0.0372052i
$139$			13.1652i			1.11666i	0.829620	+	0.558328i	$0.188557\pi$
$139$			13.1652i			1.11666i	−0.829620	+	0.558328i	$0.811443\pi$
$140$		0			0
$141$	−4.67632	+	19.3552i	−0.393817	+	1.63000i
$142$	4.78583	+	4.26925i	0.401618	+	0.358268i
$143$	−22.3473			−1.86878
$144$	11.6382	+	2.92440i	0.969851	+	0.243700i
$145$	6.94352			0.576628
$146$	−1.49247	−	1.33137i	−0.123517	−	0.110185i
$147$		0			0
$148$	−1.21417	−	10.6071i	−0.0998046	−	0.871894i
$149$		−	11.2971i		−	0.925491i	−0.886491	−	0.462745i	$-0.846864\pi$
$149$		−	11.2971i		−	0.925491i	0.886491	−	0.462745i	$-0.153136\pi$
$150$	−6.90559	+	4.77853i	−0.563839	+	0.390165i
$151$		−	11.0998i		−	0.903286i	−0.892199	−	0.451643i	$-0.850838\pi$
$151$		−	11.0998i		−	0.903286i	0.892199	−	0.451643i	$-0.149162\pi$
$152$	3.54005	+	2.49767i	0.287136	+	0.202588i
$153$	8.01729	−	15.6232i	0.648159	−	1.26306i
$154$		0			0
$155$	6.14163			0.493307
$156$	15.1885	+	1.87905i	1.21606	+	0.150444i
$157$	14.7957			1.18083			0.590413	−	0.807101i	$-0.298965\pi$
$157$	14.7957			1.18083			0.590413	+	0.807101i	$0.298965\pi$
$158$	−6.52236	+	7.31156i	−0.518891	+	0.581676i
$159$	−21.5338	−	5.20268i	−1.70774	−	0.412599i
$160$	3.40287	−	6.22200i	0.269020	−	0.491892i
$161$		0			0
$162$	−1.34491	+	12.6567i	−0.105666	+	0.994402i
$163$		−	13.2660i		−	1.03907i	−0.854448	−	0.519537i	$-0.826105\pi$
$163$		−	13.2660i		−	1.03907i	0.854448	−	0.519537i	$-0.173895\pi$
$164$	−3.93307	+	0.450214i	−0.307122	+	0.0351558i
$165$	−10.6763	−	2.57945i	−0.831150	−	0.200810i
$166$	−7.15874	−	6.38603i	−0.555626	−	0.495652i
$167$	−4.78624			−0.370371			−0.185185	−	0.982704i	$-0.559289\pi$
$167$	−4.78624			−0.370371			−0.185185	+	0.982704i	$0.559289\pi$
$168$		0			0
$169$	6.51854			0.501426
$170$	−7.74419	−	6.90830i	−0.593953	−	0.529842i
$171$	−2.09802	+	4.08839i	−0.160440	+	0.312647i
$172$	−6.33092	+	0.724692i	−0.482728	+	0.0552573i
$173$		−	14.4119i		−	1.09572i	−0.836570	−	0.547859i	$-0.815443\pi$
$173$		−	14.4119i		−	1.09572i	0.836570	−	0.547859i	$-0.184557\pi$
$174$	7.71988	+	11.1562i	0.585242	+	0.845751i
$175$		0			0
$176$	−19.7097	+	4.57220i	−1.48568	+	0.344643i
$177$	−3.24073	+	13.4133i	−0.243588	+	1.00821i
$178$	4.51652	−	5.06301i	0.338527	−	0.379489i
$179$	0.694300			0.0518944			0.0259472	−	0.999663i	$-0.491740\pi$
$179$	0.694300			0.0518944			0.0259472	+	0.999663i	$0.491740\pi$
$180$	7.03935	+	2.65085i	0.524682	+	0.197582i
$181$	−6.31042			−0.469050			−0.234525	−	0.972110i	$-0.575353\pi$
$181$	−6.31042			−0.469050			−0.234525	+	0.972110i	$0.575353\pi$
$182$		0			0
$183$	−0.123206	+	0.509947i	−0.00910763	+	0.0376964i
$184$	−0.511305	+	0.724692i	−0.0376939	+	0.0534250i
$185$		−	6.69221i		−	0.492021i
$186$	6.82833	+	9.86782i	0.500677	+	0.723544i
$187$			29.6082i			2.16516i
$188$	2.61485	+	22.8434i	0.190707	+	1.66602i
$189$		0			0
$190$	2.02655	+	1.80781i	0.147022	+	0.131152i
$191$	3.90776			0.282755			0.141378	−	0.989956i	$-0.454847\pi$
$191$	3.90776			0.282755			0.141378	+	0.989956i	$0.454847\pi$
$192$	13.7803	−	1.45026i	0.994508	−	0.104664i
$193$	1.57165			0.113130			0.0565649	−	0.998399i	$-0.481985\pi$
$193$	1.57165			0.113130			0.0565649	+	0.998399i	$0.481985\pi$
$194$	14.4416	+	12.8828i	1.03684	+	0.924929i
$195$	9.32487	+	2.25294i	0.667768	+	0.161336i
$196$		0			0
$197$		−	1.83285i		−	0.130585i	−0.997866	−	0.0652924i	$-0.979202\pi$
$197$		−	1.83285i		−	0.130585i	0.997866	−	0.0652924i	$-0.0207980\pi$
$198$	−7.72561	−	20.0216i	−0.549035	−	1.42287i
$199$		−	3.67091i		−	0.260224i	−0.991499	−	0.130112i	$-0.958466\pi$
$199$		−	3.67091i		−	0.260224i	0.991499	−	0.130112i	$-0.0415337\pi$
$200$	−5.59023	+	7.92326i	−0.395289	+	0.560259i
$201$	−17.7517	−	4.28889i	−1.25211	−	0.302515i
$202$	−3.83331	+	4.29713i	−0.269710	+	0.302345i
$203$		0			0
$204$	2.48956	−	20.1234i	0.174304	−	1.40892i
$205$	−2.48146			−0.173313
$206$	12.3098	−	13.7993i	0.857665	−	0.961441i
$207$	−0.836944	−	0.429490i	−0.0581716	−	0.0298516i
$208$	17.2148	−	3.99344i	1.19363	−	0.276895i
$209$		−	7.74807i		−	0.535945i
$210$		0			0
$211$		−	14.8763i		−	1.02413i	−0.858948	−	0.512063i	$-0.828881\pi$
$211$		−	14.8763i		−	1.02413i	0.858948	−	0.512063i	$-0.171119\pi$
$212$	−25.4146	+	2.90917i	−1.74548	+	0.199803i
$213$	−1.84465	+	7.63500i	−0.126394	+	0.523141i
$214$	4.12398	+	3.67885i	0.281910	+	0.251481i
$215$	−3.99431			−0.272410
$216$	3.56728	+	14.2574i	0.242722	+	0.970096i
$217$		0			0
$218$	−8.70434	−	7.76481i	−0.589533	−	0.525899i
$219$	0.575257	−	2.38098i	0.0388723	−	0.160892i
$220$	−12.6004	+	1.44235i	−0.849517	+	0.0972431i
$221$		−	25.8603i		−	1.73955i
$222$	10.7524	−	7.44047i	0.721657	−	0.499371i
$223$		−	19.4171i		−	1.30026i	−0.759821	−	0.650132i	$-0.774713\pi$
$223$		−	19.4171i		−	1.30026i	0.759821	−	0.650132i	$-0.225287\pi$
$224$		0			0
$225$	−9.15054	−	4.69573i	−0.610036	−	0.313049i
$226$	6.33092	−	7.09696i	0.421127	−	0.472082i
$227$	−10.6827			−0.709038			−0.354519	−	0.935049i	$-0.615355\pi$
$227$	−10.6827			−0.709038			−0.354519	+	0.935049i	$0.615355\pi$
$228$	−0.651486	+	5.26603i	−0.0431457	+	0.348751i
$229$	−7.50151			−0.495714			−0.247857	−	0.968797i	$-0.579726\pi$
$229$	−7.50151			−0.495714			−0.247857	+	0.968797i	$0.579726\pi$
$230$	−0.370081	+	0.414861i	−0.0244024	+	0.0273551i
$231$		0			0
$232$	12.8003	+	9.03122i	0.840381	+	0.592928i
$233$			2.79927i			0.183386i	0.995787	+	0.0916930i	$0.0292278\pi$
$233$			2.79927i			0.183386i	−0.995787	+	0.0916930i	$0.970772\pi$
$234$	6.74767	+	17.4872i	0.441109	+	1.14317i
$235$			14.4123i			0.940158i
$236$	1.81211	+	15.8307i	0.117959	+	1.03049i
$237$	−11.6644	−	2.81817i	−0.757683	−	0.183060i
$238$		0			0
$239$	20.5467			1.32905			0.664527	−	0.747265i	$-0.268633\pi$
$239$	20.5467			1.32905			0.664527	+	0.747265i	$0.268633\pi$
$240$	8.68521	+	0.0791832i	0.560628	+	0.00511125i
$241$	−18.0546			−1.16300			−0.581499	−	0.813547i	$-0.697533\pi$
$241$	−18.0546			−1.16300			−0.581499	+	0.813547i	$0.697533\pi$
$242$	15.3932	+	13.7317i	0.989513	+	0.882706i
$243$	−14.4445	+	5.86141i	−0.926616	+	0.376010i
$244$	0.0688928	+	0.601848i	0.00441041	+	0.0385294i
$245$		0			0
$246$	−2.75891	−	3.98699i	−0.175902	−	0.254201i
$247$			6.76729i			0.430592i
$248$	11.3220	+	7.98822i	0.718949	+	0.507253i
$249$	2.75927	−	11.4206i	0.174862	−	0.723750i
$250$	−9.94728	+	11.1509i	−0.629121	+	0.705244i
$251$	10.4810			0.661555			0.330777	−	0.943709i	$-0.392689\pi$
$251$	10.4810			0.661555			0.330777	+	0.943709i	$0.392689\pi$
$252$		0			0
$253$	1.58612			0.0997188
$254$	−8.00588	+	8.97458i	−0.502334	+	0.563115i
$255$	2.98493	−	12.3546i	0.186924	−	0.773674i
$256$	14.3659	−	7.04419i	0.897869	−	0.440262i
$257$		−	8.36072i		−	0.521528i	−0.965403	−	0.260764i	$-0.916026\pi$
$257$		−	8.36072i		−	0.521528i	0.965403	−	0.260764i	$-0.0839744\pi$
$258$	−4.44091	−	6.41770i	−0.276479	−	0.399549i
$259$		0			0
$260$	11.0054	−	1.25977i	0.682524	−	0.0781277i
$261$	−7.58612	+	14.7830i	−0.469569	+	0.915046i
$262$	8.87584	+	7.91780i	0.548351	+	0.489163i
$263$	−29.3700			−1.81103			−0.905517	−	0.424309i	$-0.860517\pi$
$263$	−29.3700			−1.81103			−0.905517	+	0.424309i	$0.860517\pi$
$264$	−16.3267	−	18.6415i	−1.00484	−	1.14731i
$265$	−16.0346			−0.984996
$266$		0			0
$267$	8.07720	+	1.95149i	0.494317	+	0.119429i
$268$	−20.9508	+	2.39821i	−1.27978	+	0.146494i
$269$		−	20.3977i		−	1.24367i	−0.783149	−	0.621834i	$-0.786388\pi$
$269$		−	20.3977i		−	1.24367i	0.783149	−	0.621834i	$-0.213612\pi$
$270$	1.20519	+	9.13327i	0.0733458	+	0.555833i
$271$		−	20.5964i		−	1.25114i	−0.780167	−	0.625572i	$-0.784866\pi$
$271$		−	20.5964i		−	1.25114i	0.780167	−	0.625572i	$-0.215134\pi$
$272$	−5.29093	−	22.8080i	−0.320810	−	1.38294i
$273$		0			0
$274$	12.9508	−	14.5179i	0.782389	−	0.877057i
$275$	17.3415			1.04573
$276$	−1.07802	−	0.133367i	−0.0648893	−	0.00802776i
$277$	−3.94689			−0.237146			−0.118573	−	0.992945i	$-0.537832\pi$
$277$	−3.94689			−0.237146			−0.118573	+	0.992945i	$0.537832\pi$
$278$	−12.3940	+	13.8936i	−0.743341	+	0.833285i
$279$	−6.71002	+	13.0758i	−0.401719	+	0.782825i
$280$		0			0
$281$		−	1.18623i		−	0.0707648i	−0.999374	−	0.0353824i	$-0.988735\pi$
$281$		−	1.18623i		−	0.0707648i	0.999374	−	0.0353824i	$-0.0112649\pi$
$282$	−23.1565	+	16.0238i	−1.37895	+	0.954203i
$283$			27.6833i			1.64560i	0.568331	+	0.822800i	$0.307590\pi$
$283$			27.6833i			1.64560i	−0.568331	+	0.822800i	$0.692410\pi$
$284$	1.03147	+	9.01095i	0.0612066	+	0.534702i
$285$	−0.781117	+	3.23303i	−0.0462694	+	0.191508i
$286$	−23.5839	−	21.0383i	−1.39454	−	1.24402i
$287$		0			0
$288$	9.52909	+	14.0427i	0.561507	+	0.827472i
$289$	−17.2624			−1.01544
$290$	7.32772	+	6.53677i	0.430298	+	0.383853i
$291$	−5.56637	+	23.0391i	−0.326306	+	1.35058i
$292$	−0.321666	−	2.81008i	−0.0188241	−	0.164447i
$293$			0.197795i			0.0115553i	0.999983	+	0.00577765i	$0.00183909\pi$
$293$			0.197795i			0.0115553i	−0.999983	+	0.00577765i	$0.998161\pi$
$294$		0			0
$295$			9.98789i			0.581517i
$296$	8.70434	−	12.3370i	0.505930	−	0.717074i
$297$	17.1561	−	19.9121i	0.995500	−	1.15542i
$298$	10.6353	−	11.9221i	0.616086	−	0.690631i
$299$	−1.38535			−0.0801167
$300$	−11.7863	−	1.45814i	−0.680482	−	0.0841857i
$301$		0			0
$302$	10.4496	−	11.7139i	0.601304	−	0.674061i
$303$	−6.85537	−	1.65629i	−0.393831	−	0.0951514i
$304$	1.38457	+	5.96856i	0.0794104	+	0.342320i
$305$			0.379718i			0.0217426i
$306$	23.1689	−	8.94004i	1.32448	−	0.511068i
$307$		−	16.6218i		−	0.948657i	−0.880348	−	0.474328i	$-0.842691\pi$
$307$		−	16.6218i		−	0.948657i	0.880348	−	0.474328i	$-0.157309\pi$
$308$		0			0
$309$	22.0145	+	5.31881i	1.25236	+	0.302576i
$310$	6.48146	+	5.78186i	0.368122	+	0.328388i
$311$	10.7561			0.609923			0.304961	−	0.952365i	$-0.401356\pi$
$311$	10.7561			0.609923			0.304961	+	0.952365i	$0.401356\pi$
$312$	14.2600	+	16.2818i	0.807312	+	0.921777i
$313$	−4.94400			−0.279451			−0.139726	−	0.990190i	$-0.544622\pi$
$313$	−4.94400			−0.279451			−0.139726	+	0.990190i	$0.544622\pi$
$314$	15.6144	+	13.9290i	0.881170	+	0.786058i
$315$		0			0
$316$	−13.7665	+	1.57583i	−0.774427	+	0.0886476i
$317$			21.9347i			1.23197i	0.787756	+	0.615987i	$0.211243\pi$
$317$			21.9347i			1.23197i	−0.787756	+	0.615987i	$0.788757\pi$
$318$	−17.8274	−	25.7629i	−0.999712	−	1.44471i
$319$		−	28.0159i		−	1.56859i
$320$	9.44868	−	3.36275i	0.528197	−	0.187983i
$321$	−1.58955	+	6.57914i	−0.0887202	+	0.367212i
$322$		0			0
$323$	8.96603			0.498883
$324$	−13.3346	+	12.0909i	−0.740810	+	0.671715i
$325$	−15.1464			−0.840170
$326$	12.4889	−	14.0000i	0.691696	−	0.775390i
$327$	3.35501	−	13.8864i	0.185533	−	0.767917i
$328$	−4.57454	−	3.22756i	−0.252587	−	0.178212i
$329$		0			0
$330$	−8.83871	−	12.7731i	−0.486555	−	0.703135i
$331$			3.74207i			0.205683i	0.994698	+	0.102841i	$0.0327934\pi$
$331$			3.74207i			0.205683i	−0.994698	+	0.102841i	$0.967207\pi$
$332$	−1.54290	−	13.4788i	−0.0846775	−	0.739744i
$333$	14.2480	+	7.31156i	0.780784	+	0.400671i
$334$	−5.05108	−	4.50587i	−0.276383	−	0.246550i
$335$	−13.2183			−0.722194
$336$		0			0
$337$	22.9774			1.25166			0.625829	−	0.779960i	$-0.284761\pi$
$337$	22.9774			1.25166			0.625829	+	0.779960i	$0.284761\pi$
$338$	6.87923	+	6.13669i	0.374181	+	0.333792i
$339$	11.3220	+	2.73546i	0.614928	+	0.148570i
$340$	−1.66908	−	14.5811i	−0.0905185	−	0.790771i
$341$		−	24.7804i		−	1.34193i
$342$	−6.06301	+	2.33949i	−0.327850	+	0.126505i
$343$		0			0
$344$	−7.36347	−	5.19527i	−0.397011	−	0.280110i
$345$	−0.661842	−	0.159904i	−0.0356324	−	0.00860896i
$346$	13.5677	−	15.2094i	0.729404	−	0.817661i
$347$	−2.13010			−0.114350			−0.0571750	−	0.998364i	$-0.518209\pi$
$347$	−2.13010			−0.114350			−0.0571750	+	0.998364i	$0.518209\pi$
$348$	−2.35568	+	19.0412i	−0.126277	+	1.02071i
$349$	3.55710			0.190407			0.0952036	−	0.995458i	$-0.469650\pi$
$349$	3.55710			0.190407			0.0952036	+	0.995458i	$0.469650\pi$
$350$		0			0
$351$	−14.9845	+	17.3916i	−0.799811	+	0.928293i
$352$	−25.1047	−	13.7300i	−1.33808	−	0.731809i
$353$			18.9270i			1.00738i	0.863884	+	0.503690i	$0.168025\pi$
$353$			18.9270i			1.00738i	−0.863884	+	0.503690i	$0.831975\pi$
$354$	−16.0476	+	11.1046i	−0.852923	+	0.590205i
$355$			5.68520i			0.301739i
$356$	9.53285	−	1.09121i	0.505240	−	0.0578342i
$357$		0			0
$358$	0.732717	+	0.653628i	0.0387253	+	0.0345453i
$359$	−1.22600			−0.0647058			−0.0323529	−	0.999477i	$-0.510300\pi$
$359$	−1.22600			−0.0647058			−0.0323529	+	0.999477i	$0.510300\pi$
$360$	4.93329	+	9.42452i	0.260007	+	0.496716i
$361$	16.6537			0.876511
$362$	−6.65959	−	5.94076i	−0.350020	−	0.312240i
$363$	−5.93317	+	24.5573i	−0.311411	+	1.28893i
$364$		0			0
$365$		−	1.77294i		−	0.0927997i
$366$	−0.610098	+	0.422175i	−0.0318903	+	0.0220674i
$367$		−	20.2033i		−	1.05460i	−0.849678	−	0.527302i	$-0.823204\pi$
$367$		−	20.2033i		−	1.05460i	0.849678	−	0.527302i	$-0.176796\pi$
$368$	−1.22184	+	0.283438i	−0.0636926	+	0.0147752i
$369$	2.71111	−	5.28312i	0.141135	−	0.275028i
$370$	6.30019	−	7.06250i	0.327531	−	0.367162i
$371$		0			0
$372$	−2.08363	+	16.8422i	−0.108031	+	0.873226i
$373$	−8.18038			−0.423564			−0.211782	−	0.977317i	$-0.567927\pi$
$373$	−8.18038			−0.423564			−0.211782	+	0.977317i	$0.567927\pi$
$374$	−27.8738	+	31.2464i	−1.44132	+	1.61572i
$375$	−17.7894	−	4.29801i	−0.918642	−	0.221948i
$376$	−18.7457	+	26.5690i	−0.966735	+	1.37019i
$377$			24.4695i			1.26024i
$378$		0			0
$379$		−	31.2020i		−	1.60274i	−0.598170	−	0.801369i	$-0.704105\pi$
$379$		−	31.2020i		−	1.60274i	0.598170	−	0.801369i	$-0.295895\pi$
$380$	0.436776	+	3.81568i	0.0224061	+	0.195740i
$381$	−14.3175	−	3.45917i	−0.733506	−	0.177219i
$382$	4.12398	+	3.67885i	0.211001	+	0.188226i
$383$	−24.4179			−1.24770			−0.623848	−	0.781546i	$-0.714431\pi$
$383$	−24.4179			−1.24770			−0.623848	+	0.781546i	$0.714431\pi$
$384$	15.9081	+	11.4426i	0.811807	+	0.583926i
$385$		0			0
$386$	1.65861	+	1.47958i	0.0844212	+	0.0753089i
$387$	4.36397	−	8.50404i	0.221833	−	0.432285i
$388$	3.11254	+	27.1912i	0.158015	+	1.38042i
$389$			9.08449i			0.460602i	0.973119	+	0.230301i	$0.0739711\pi$
$389$			9.08449i			0.460602i	−0.973119	+	0.230301i	$0.926029\pi$
$390$	7.71988	+	11.1562i	0.390911	+	0.564918i
$391$			1.83546i			0.0928230i
$392$		0			0
$393$	−3.42111	+	14.1599i	−0.172572	+	0.714275i
$394$	1.72548	−	1.93426i	0.0869284	−	0.0974466i
$395$	−8.68557			−0.437019
$396$	10.6957	−	28.4025i	0.537479	−	1.42728i
$397$	−23.2810			−1.16844			−0.584220	−	0.811596i	$-0.698599\pi$
$397$	−23.2810			−1.16844			−0.584220	+	0.811596i	$0.698599\pi$
$398$	3.45588	−	3.87403i	0.173227	−	0.194188i
$399$		0			0
$400$	−13.3587	+	3.09890i	−0.667934	+	0.154945i
$401$		−	7.59128i		−	0.379090i	−0.981872	−	0.189545i	$-0.939299\pi$
$401$		−	7.59128i		−	0.379090i	0.981872	−	0.189545i	$-0.0607014\pi$
$402$	−14.6963	−	21.2380i	−0.732983	−	1.05926i
$403$			21.6436i			1.07814i
$404$	−8.09082	+	0.926146i	−0.402533	+	0.0460775i
$405$	−9.16617	+	6.57914i	−0.455470	+	0.326920i
$406$		0			0
$407$	−27.0019			−1.33843
$408$	21.5719	−	18.8931i	1.06797	−	0.935350i
$409$	6.39018			0.315974			0.157987	−	0.987441i	$-0.449500\pi$
$409$	6.39018			0.315974			0.157987	+	0.987441i	$0.449500\pi$
$410$	−2.61876	−	2.33610i	−0.129331	−	0.115372i
$411$	23.1609	+	5.59578i	1.14244	+	0.276020i
$412$	25.9819	−	2.97411i	1.28003	−	0.146524i
$413$		0			0
$414$	−0.478923	−	1.24117i	−0.0235378	−	0.0610003i
$415$		−	8.50404i		−	0.417447i
$416$	21.9268	+	11.9920i	1.07505	+	0.587955i
$417$	−22.1650	−	5.35518i	−1.08543	−	0.262244i
$418$	7.29419	−	8.17678i	0.356771	−	0.399940i
$419$	−29.1307			−1.42313			−0.711565	−	0.702620i	$-0.752013\pi$
$419$	−29.1307			−1.42313			−0.711565	+	0.702620i	$0.752013\pi$
$420$		0			0
$421$	−32.0821			−1.56358			−0.781792	−	0.623539i	$-0.785694\pi$
$421$	−32.0821			−1.56358			−0.781792	+	0.623539i	$0.785694\pi$
$422$	14.0049	−	15.6994i	0.681746	−	0.764237i
$423$	−30.6844	−	15.7462i	−1.49193	−	0.765605i
$424$	−29.5596	−	20.8557i	−1.43554	−	1.01284i
$425$			20.0675i			0.973419i
$426$	−9.13447	+	6.32086i	−0.442567	+	0.306247i
$427$		0			0
$428$	0.888828	+	7.76481i	0.0429631	+	0.375326i
$429$	9.09019	−	37.6242i	0.438879	−	1.81651i
$430$	−4.21532	−	3.76033i	−0.203281	−	0.181339i
$431$	18.2456			0.878861			0.439431	−	0.898277i	$-0.355180\pi$
$431$	18.2456			0.878861			0.439431	+	0.898277i	$0.355180\pi$
$432$	−9.65759	+	18.4046i	−0.464651	+	0.885494i
$433$	−4.84842			−0.233000			−0.116500	−	0.993191i	$-0.537168\pi$
$433$	−4.84842			−0.233000			−0.116500	+	0.993191i	$0.537168\pi$
$434$		0			0
$435$	−2.82440	+	11.6902i	−0.135420	+	0.560501i
$436$	−1.87602	−	16.3889i	−0.0898449	−	0.784886i
$437$		−	0.480315i		−	0.0229766i
$438$	2.84860	−	1.97117i	0.136111	−	0.0941861i
$439$			20.2520i			0.966578i	0.875461	+	0.483289i	$0.160558\pi$
$439$			20.2520i			0.966578i	−0.875461	+	0.483289i	$0.839442\pi$
$440$	−14.6554	−	10.3401i	−0.698670	−	0.492945i
$441$		0			0
$442$	24.3454	−	27.2912i	1.15799	−	1.29811i
$443$	−22.4670			−1.06744			−0.533719	−	0.845662i	$-0.679206\pi$
$443$	−22.4670			−1.06744			−0.533719	+	0.845662i	$0.679206\pi$
$444$	18.3520	+	2.27042i	0.870948	+	0.107749i
$445$	6.01447			0.285113
$446$	18.2797	−	20.4915i	0.865567	−	0.970300i
$447$	19.0198	+	4.59528i	0.899607	+	0.217349i
$448$		0			0
$449$			29.5660i			1.39531i	0.716435	+	0.697654i	$0.245773\pi$
$449$			29.5660i			1.39531i	−0.716435	+	0.697654i	$0.754227\pi$
$450$	−5.23619	−	13.5701i	−0.246836	−	0.639699i
$451$			10.0122i			0.471458i
$452$	13.3624	−	1.52958i	0.628517	−	0.0719455i
$453$	18.6877	+	4.51503i	0.878023	+	0.212135i
$454$	−11.2738	−	10.0569i	−0.529107	−	0.471996i
$455$		0			0
$456$	−5.64509	+	4.94409i	−0.264355	+	0.231528i
$457$	18.1949			0.851120			0.425560	−	0.904930i	$-0.360077\pi$
$457$	18.1949			0.851120			0.425560	+	0.904930i	$0.360077\pi$
$458$	−7.91658	−	7.06208i	−0.369918	−	0.329989i
$459$	23.0422	+	19.8530i	1.07552	+	0.926659i
$460$	−0.781117	+	0.0894134i	−0.0364198	+	0.00416892i
$461$		−	24.9782i		−	1.16335i	−0.813422	−	0.581675i	$-0.802398\pi$
$461$		−	24.9782i		−	1.16335i	0.813422	−	0.581675i	$-0.197602\pi$
$462$		0			0
$463$		−	6.37226i		−	0.296144i	−0.988977	−	0.148072i	$-0.952693\pi$
$463$		−	6.37226i		−	0.296144i	0.988977	−	0.148072i	$-0.0473068\pi$
$464$	5.00639	+	21.5814i	0.232416	+	1.00189i
$465$	−2.49822	+	10.3401i	−0.115852	+	0.479511i
$466$	−2.63529	+	2.95415i	−0.122077	+	0.136849i
$467$	27.3569			1.26593			0.632964	−	0.774182i	$-0.281838\pi$
$467$	27.3569			1.26593			0.632964	+	0.774182i	$0.281838\pi$
$468$	−9.34180	+	24.8072i	−0.431825	+	1.14671i
$469$		0			0
$470$	−13.5681	+	15.2098i	−0.625849	+	0.701576i
$471$	−6.01842	+	24.9102i	−0.277314	+	1.14780i
$472$	−12.9909	+	18.4126i	−0.597956	+	0.847507i
$473$			16.1163i			0.741029i
$474$	−9.65671	−	13.9552i	−0.443548	−	0.640984i
$475$		−	5.25141i		−	0.240951i
$476$		0			0
$477$	17.5185	−	34.1382i	0.802119	−	1.56308i
$478$	21.6836	+	19.3431i	0.991783	+	0.884731i
$479$	19.8334			0.906209			0.453105	−	0.891457i	$-0.350316\pi$
$479$	19.8334			0.906209			0.453105	+	0.891457i	$0.350316\pi$
$480$	9.09124	+	8.26001i	0.414956	+	0.377016i
$481$	23.5839			1.07533
$482$	−19.0536	−	16.9970i	−0.867866	−	0.774190i
$483$		0			0
$484$	3.31764	+	28.9830i	0.150802	+	1.31741i
$485$			17.1555i			0.778990i
$486$	−20.7618	−	7.41263i	−0.941775	−	0.336244i
$487$		−	40.8524i		−	1.85120i	−0.378506	−	0.925599i	$-0.623562\pi$
$487$		−	40.8524i		−	1.85120i	0.378506	−	0.925599i	$-0.376438\pi$
$488$	−0.493888	+	0.700007i	−0.0223573	+	0.0316878i
$489$	22.3348	+	5.39619i	1.01001	+	0.244024i
$490$		0			0
$491$	−20.3003			−0.916137			−0.458069	−	0.888917i	$-0.651459\pi$
$491$	−20.3003			−0.916137			−0.458069	+	0.888917i	$0.651459\pi$
$492$	0.841866	−	6.80489i	0.0379543	−	0.306788i
$493$	32.4198			1.46012
$494$	−6.37087	+	7.14174i	−0.286639	+	0.321322i
$495$	8.68557	−	16.9255i	0.390388	−	0.760745i
$496$	4.42821	+	19.0890i	0.198833	+	0.857123i
$497$		0			0
$498$	13.6635	−	9.45488i	0.612278	−	0.423683i
$499$		−	34.2272i		−	1.53222i	−0.642709	−	0.766110i	$-0.722190\pi$
$499$		−	34.2272i		−	1.53222i	0.642709	−	0.766110i	$-0.277810\pi$
$500$	−20.9954	+	2.40331i	−0.938942	+	0.107479i
$501$	1.94689	−	8.05816i	0.0869807	−	0.360012i
$502$	11.0609	+	9.86704i	0.493674	+	0.440387i
$503$	31.1279			1.38792			0.693962	−	0.720011i	$-0.255863\pi$
$503$	31.1279			1.38792			0.693962	+	0.720011i	$0.255863\pi$
$504$		0			0
$505$	−5.10467			−0.227155
$506$	1.67389	+	1.49321i	0.0744134	+	0.0663813i
$507$	−2.65154	+	10.9747i	−0.117759	+	0.487402i
$508$	−16.8977	+	1.93426i	−0.749715	+	0.0858189i
$509$			39.5032i			1.75095i	0.483266	+	0.875474i	$0.339450\pi$
$509$			39.5032i			1.75095i	−0.483266	+	0.875474i	$0.660550\pi$
$510$	14.7810	−	10.2281i	0.654512	−	0.452909i
$511$		0			0
$512$	21.7924	+	6.09041i	0.963095	+	0.269161i
$513$	−6.02985	−	5.19527i	−0.266224	−	0.229377i
$514$	7.87096	−	8.82334i	0.347173	−	0.389181i
$515$	16.3925			0.722340
$516$	1.35512	−	10.9536i	0.0596558	−	0.482204i
$517$	58.1512			2.55749
$518$		0			0
$519$	24.2641	+	5.86232i	1.06507	+	0.257327i
$520$	12.8003	+	9.03122i	0.561330	+	0.396045i
$521$			24.1110i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$521$			24.1110i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$522$	−21.9229	+	8.45925i	−0.959540	+	0.370251i
$523$			9.26670i			0.405204i	0.979261	+	0.202602i	$0.0649398\pi$
$523$			9.26670i			0.405204i	−0.979261	+	0.202602i	$0.935060\pi$
$524$	1.91298	+	16.7118i	0.0835689	+	0.730059i
$525$		0			0
$526$	−30.9952	−	27.6496i	−1.35145	−	1.20558i
$527$	28.6757			1.24914
$528$	0.319490	−	35.0433i	0.0139040	−	1.52506i
$529$	−22.9017			−0.995725
$530$	−16.9218	−	15.0953i	−0.735036	−	0.655698i
$531$	−21.2646	−	10.9122i	−0.922805	−	0.473551i
$532$		0			0
$533$		−	8.74486i		−	0.378782i
$534$	6.68696	+	9.66352i	0.289373	+	0.418182i
$535$			4.89898i			0.211801i
$536$	−24.3678	−	17.1926i	−1.05253	−	0.742609i
$537$	−0.282419	+	1.16893i	−0.0121873	+	0.0504430i
$538$	19.2028	−	21.5263i	0.827892	−	0.928066i
$539$		0			0
$540$	−7.32637	+	10.7732i	−0.315277	+	0.463606i
$541$	25.9017			1.11360			0.556800	−	0.830647i	$-0.312029\pi$
$541$	25.9017			1.11360			0.556800	+	0.830647i	$0.312029\pi$
$542$	19.3899	−	21.7361i	0.832868	−	0.933644i
$543$	2.56688	−	10.6243i	0.110155	−	0.455932i
$544$	15.8882	−	29.0510i	0.681203	−	1.24555i
$545$		−	10.3401i		−	0.442921i
$546$		0			0
$547$			32.9387i			1.40836i	0.710022	+	0.704179i	$0.248685\pi$
$547$			32.9387i			1.40836i	−0.710022	+	0.704179i	$0.751315\pi$
$548$	27.3349	−	3.12899i	1.16769	−	0.133664i
$549$	−0.808435	−	0.414861i	−0.0345032	−	0.0177058i
$550$	18.3011	+	16.3257i	0.780360	+	0.696130i
$551$	−8.48384			−0.361424
$552$	−1.01212	−	1.15562i	−0.0430785	−	0.0491864i
$553$		0			0
$554$	−4.16528	−	3.71569i	−0.176966	−	0.157864i
$555$	11.2671	+	2.72218i	0.478260	+	0.115550i
$556$	−26.1595	+	2.99445i	−1.10941	+	0.126993i
$557$			29.9057i			1.26714i	0.773684	+	0.633572i	$0.218412\pi$
$557$			29.9057i			1.26714i	−0.773684	+	0.633572i	$0.781588\pi$
$558$	−19.3911	+	7.48232i	−0.820891	+	0.316752i
$559$		−	14.0763i		−	0.595363i
$560$		0			0
$561$	−49.8486	−	12.0437i	−2.10461	−	0.508484i
$562$	1.11675	−	1.25187i	0.0471071	−	0.0528070i
$563$	31.1063			1.31097			0.655487	−	0.755206i	$-0.272463\pi$
$563$	31.1063			1.31097			0.655487	+	0.755206i	$0.272463\pi$
$564$	−39.5229	−	4.88957i	−1.66422	−	0.205888i
$565$	8.43065			0.354680
$566$	−26.0616	+	29.2151i	−1.09545	+	1.22800i
$567$		0			0
$568$	−7.39456	+	10.4806i	−0.310269	+	0.439756i
$569$		−	17.6694i		−	0.740742i	−0.928884	−	0.370371i	$-0.879231\pi$
$569$		−	17.6694i		−	0.740742i	0.928884	−	0.370371i	$-0.120769\pi$
$570$	−3.86798	+	2.67656i	−0.162012	+	0.112109i
$571$		−	7.51861i		−	0.314644i	−0.987547	−	0.157322i	$-0.949714\pi$
$571$		−	7.51861i		−	0.314644i	0.987547	−	0.157322i	$-0.0502860\pi$
$572$	−5.08295	−	44.4047i	−0.212529	−	1.85665i
$573$	−1.58955	+	6.57914i	−0.0664045	+	0.274847i
$574$		0			0
$575$	1.07503			0.0448318
$576$	−3.16371	+	23.7906i	−0.131821	+	0.991273i
$577$	4.26311			0.177476			0.0887378	−	0.996055i	$-0.471717\pi$
$577$	4.26311			0.177476			0.0887378	+	0.996055i	$0.471717\pi$
$578$	−18.2176	−	16.2512i	−0.757753	−	0.675962i
$579$	−0.639297	+	2.64604i	−0.0265683	+	0.109966i
$580$	1.57932	+	13.7969i	0.0655776	+	0.572887i
$581$		0			0
$582$	−27.5639	+	19.0736i	−1.14256	+	0.790628i
$583$			64.6967i			2.67946i
$584$	2.30600	−	3.26839i	0.0954230	−	0.135247i
$585$	−7.58612	+	14.7830i	−0.313648	+	0.611202i
$586$	−0.186208	+	0.208739i	−0.00769219	+	0.00862294i
$587$	43.2909			1.78681			0.893404	−	0.449253i	$-0.148310\pi$
$587$	43.2909			1.78681			0.893404	+	0.449253i	$0.148310\pi$
$588$		0			0
$589$	−7.50407			−0.309200
$590$	−9.40281	+	10.5405i	−0.387107	+	0.433947i
$591$	3.08580	+	0.745543i	0.126933	+	0.0306676i
$592$	20.8003	−	4.82519i	0.854887	−	0.198314i
$593$		−	5.76869i		−	0.236892i	−0.992961	−	0.118446i	$-0.962209\pi$
$593$		−	5.76869i		−	0.236892i	0.992961	−	0.118446i	$-0.0377912\pi$
$594$	36.8511	−	4.86274i	1.51202	−	0.199521i
$595$		0			0
$596$	22.4475	−	2.56954i	0.919486	−	0.105252i
$597$	6.18038	+	1.49321i	0.252946	+	0.0611131i
$598$	−1.46200	−	1.30420i	−0.0597857	−	0.0533325i
$599$	35.7970			1.46262			0.731312	−	0.682043i	$-0.238908\pi$
$599$	35.7970			1.46262			0.731312	+	0.682043i	$0.238908\pi$
$600$	−11.0657	−	12.6347i	−0.451757	−	0.515809i
$601$	−42.3193			−1.72624			−0.863121	−	0.504998i	$-0.831493\pi$
$601$	−42.3193			−1.72624			−0.863121	+	0.504998i	$0.831493\pi$
$602$		0			0
$603$	14.4416	−	28.1423i	0.588109	−	1.14604i
$604$	22.0555	−	2.52466i	0.897426	−	0.102727i
$605$			18.2860i			0.743430i
$606$	−5.67542	−	8.20172i	−0.230548	−	0.333172i
$607$		−	47.3686i		−	1.92263i	−0.275446	−	0.961316i	$-0.588826\pi$
$607$		−	47.3686i		−	1.92263i	0.275446	−	0.961316i	$-0.411174\pi$
$608$	−4.15775	+	7.60227i	−0.168619	+	0.308313i
$609$		0			0
$610$	−0.357475	+	0.400729i	−0.0144737	+	0.0162250i
$611$	−50.7903			−2.05475
$612$	32.8673	+	12.3770i	1.32858	+	0.500311i
$613$	2.78912			0.112651			0.0563257	−	0.998412i	$-0.482061\pi$
$613$	2.78912			0.112651			0.0563257	+	0.998412i	$0.482061\pi$
$614$	15.6481	−	17.5415i	0.631507	−	0.707919i
$615$	1.00938	−	4.17781i	0.0407021	−	0.168465i
$616$		0			0
$617$		−	21.6549i		−	0.871795i	−0.899996	−	0.435898i	$-0.856431\pi$
$617$		−	21.6549i		−	0.871795i	0.899996	−	0.435898i	$-0.143569\pi$
$618$	18.2253	+	26.3380i	0.733131	+	1.05947i
$619$		−	5.64452i		−	0.226873i	−0.993545	−	0.113436i	$-0.963814\pi$
$619$		−	5.64452i		−	0.226873i	0.993545	−	0.113436i	$-0.0361858\pi$
$620$	1.39693	+	12.2036i	0.0561019	+	0.490107i
$621$	1.06354	−	1.23438i	0.0426782	−	0.0495341i
$622$	11.3513	+	10.1260i	0.455144	+	0.406017i
$623$		0			0
$624$	−0.279048	+	30.6074i	−0.0111709	+	1.22528i
$625$	3.89533			0.155813
$626$	−5.21756	−	4.65438i	−0.208536	−	0.186027i
$627$	13.0447	+	3.15167i	0.520956	+	0.125865i
$628$	3.36531	+	29.3994i	0.134291	+	1.17316i
$629$		−	31.2464i		−	1.24588i
$630$		0			0
$631$		−	6.37226i		−	0.253676i	−0.991923	−	0.126838i	$-0.959517\pi$
$631$		−	6.37226i		−	0.253676i	0.991923	−	0.126838i	$-0.0404828\pi$
$632$	−16.0118	−	11.2971i	−0.636914	−	0.449373i
$633$	25.0459	+	6.05121i	0.995484	+	0.240514i
$634$	−20.6498	+	23.1484i	−0.820107	+	0.919339i
$635$	−10.6611			−0.423074
$636$	5.43993	−	43.9716i	0.215707	−	1.74359i
$637$		0			0
$638$	26.3747	−	29.5660i	1.04419	−	1.17053i
$639$	−12.1040	−	6.21135i	−0.478827	−	0.245717i
$640$	13.1373	+	5.34637i	0.519296	+	0.211334i
$641$			16.4960i			0.651554i	0.945447	+	0.325777i	$0.105626\pi$
$641$			16.4960i			0.651554i	−0.945447	+	0.325777i	$0.894374\pi$
$642$	−7.87125	+	5.44674i	−0.310653	+	0.214966i
$643$			2.36672i			0.0933343i	0.998910	+	0.0466671i	$0.0148600\pi$
$643$			2.36672i			0.0933343i	−0.998910	+	0.0466671i	$0.985140\pi$
$644$		0			0
$645$	1.62476	−	6.72485i	0.0639748	−	0.264791i
$646$	9.46214	+	8.44081i	0.372283	+	0.332099i
$647$	11.3495			0.446196			0.223098	−	0.974796i	$-0.428383\pi$
$647$	11.3495			0.446196			0.223098	+	0.974796i	$0.428383\pi$
$648$	−25.4550	+	0.206423i	−0.999967	+	0.00810908i
$649$	40.2993			1.58189
$650$	−15.9845	−	14.2591i	−0.626962	−	0.559289i
$651$		0			0
$652$	26.3599	−	3.01738i	1.03233	−	0.118170i
$653$		−	44.5689i		−	1.74411i	−0.489404	−	0.872057i	$-0.662786\pi$
$653$		−	44.5689i		−	1.74411i	0.489404	−	0.872057i	$-0.337214\pi$
$654$	16.6136	−	11.4962i	0.649642	−	0.449538i
$655$			10.5438i			0.411981i
$656$	−1.78917	−	7.71271i	−0.0698554	−	0.301131i
$657$	3.77465	+	1.93702i	0.147263	+	0.0755702i
$658$		0			0
$659$	0.590533			0.0230039			0.0115019	−	0.999934i	$-0.496339\pi$
$659$	0.590533			0.0230039			0.0115019	+	0.999934i	$0.496339\pi$
$660$	2.69708	−	21.8008i	0.104984	−	0.848595i
$661$	−43.1004			−1.67641			−0.838206	−	0.545353i	$-0.816396\pi$
$661$	−43.1004			−1.67641			−0.838206	+	0.545353i	$0.816396\pi$
$662$	−3.52287	+	3.94913i	−0.136920	+	0.153487i
$663$	43.5386	+	10.5191i	1.69090	+	0.408529i
$664$	11.0609	−	15.6771i	0.429248	−	0.608390i
$665$		0			0
$666$	8.15308	+	21.1295i	0.315926	+	0.818750i
$667$		−	1.73675i		−	0.0672471i
$668$	−1.08864	−	9.51038i	−0.0421208	−	0.367968i
$669$	32.6908	+	7.89826i	1.26390	+	0.305364i
$670$	−13.9497	−	12.4440i	−0.538924	−	0.480754i
$671$	1.53210			0.0591459
$672$		0			0
$673$	15.2706			0.588637			0.294319	−	0.955707i	$-0.404907\pi$
$673$	15.2706			0.588637			0.294319	+	0.955707i	$0.404907\pi$
$674$	24.2488	+	21.6314i	0.934028	+	0.833211i
$675$	11.6279	−	13.4959i	0.447559	−	0.519456i
$676$	1.48266	+	12.9525i	0.0570252	+	0.498173i
$677$			41.3887i			1.59070i	0.606151	+	0.795349i	$0.292713\pi$
$677$			41.3887i			1.59070i	−0.606151	+	0.795349i	$0.707287\pi$
$678$	9.37328	+	13.5456i	0.359979	+	0.520216i
$679$		0			0
$680$	11.9655	−	16.9592i	0.458857	−	0.650356i
$681$	4.34540	−	17.9855i	0.166516	−	0.689207i
$682$	23.3288	−	26.1515i	0.893305	−	1.00139i
$683$	−4.53490			−0.173523			−0.0867615	−	0.996229i	$-0.527652\pi$
$683$	−4.53490			−0.173523			−0.0867615	+	0.996229i	$0.527652\pi$
$684$	−8.60093	−	3.23890i	−0.328865	−	0.123843i
$685$	17.2461			0.658941
$686$		0			0
$687$	3.05138	−	12.6296i	0.116417	−	0.481850i
$688$	−2.87996	−	12.4149i	−0.109798	−	0.473312i
$689$		−	56.5071i		−	2.15275i
$690$	−0.547926	−	0.791824i	−0.0208592	−	0.0301442i
$691$			27.2902i			1.03817i	0.854723	+	0.519084i	$0.173727\pi$
$691$			27.2902i			1.03817i	−0.854723	+	0.519084i	$0.826273\pi$
$692$	28.6369	−	3.27802i	1.08861	−	0.124612i
$693$		0			0
$694$	−2.24797	−	2.00532i	−0.0853316	−	0.0761211i
$695$	−16.5046			−0.626055
$696$	−20.4118	+	17.8771i	−0.773707	+	0.677629i
$697$	−11.5861			−0.438856
$698$	3.75392	+	3.34873i	0.142088	+	0.126751i
$699$	−4.71287	−	1.13865i	−0.178257	−	0.0430678i
$700$		0			0
$701$			9.20431i			0.347642i	0.984777	+	0.173821i	$0.0556114\pi$
$701$			9.20431i			0.347642i	−0.984777	+	0.173821i	$0.944389\pi$
$702$	−32.1864	+	4.24720i	−1.21480	+	0.160300i
$703$			8.17678i			0.308393i
$704$	−13.5681	−	38.1237i	−0.511367	−	1.43684i
$705$	−24.2648	−	5.86249i	−0.913864	−	0.220794i
$706$	−17.8182	+	19.9742i	−0.670598	+	0.751740i
$707$		0			0
$708$	−27.3897	−	3.38852i	−1.02937	−	0.127348i
$709$	−29.6006			−1.11167			−0.555837	−	0.831291i	$-0.687602\pi$
$709$	−29.6006			−1.11167			−0.555837	+	0.831291i	$0.687602\pi$
$710$	−5.35217	+	5.99977i	−0.200863	+	0.225167i
$711$	9.48941	−	18.4919i	0.355880	−	0.693501i
$712$	11.0876	+	7.82284i	0.415526	+	0.293173i
$713$		−	1.53617i		−	0.0575302i
$714$		0			0
$715$		−	28.0159i		−	1.04773i
$716$	0.157920	+	1.37959i	0.00590174	+	0.0515577i
$717$	−8.35773	+	34.5925i	−0.312125	+	1.29188i
$718$	−1.29384	−	1.15418i	−0.0482856	−	0.0430737i
$719$	2.71571			0.101279			0.0506395	−	0.998717i	$-0.483874\pi$
$719$	2.71571			0.101279			0.0506395	+	0.998717i	$0.483874\pi$
$720$	−3.66618	+	14.5903i	−0.136631	+	0.543748i
$721$		0			0
$722$	17.5752	+	15.6782i	0.654081	+	0.583480i
$723$	7.34403	−	30.3968i	0.273127	−	1.13047i
$724$	−1.43532	−	12.5390i	−0.0533432	−	0.466007i
$725$		−	18.9883i		−	0.705209i
$726$	−29.3803	+	20.3305i	−1.09040	+	0.754537i
$727$			18.9752i			0.703753i	0.936046	+	0.351876i	$0.114456\pi$
$727$			18.9752i			0.703753i	−0.936046	+	0.351876i	$0.885544\pi$
$728$		0			0
$729$	−3.99276	−	26.7031i	−0.147880	−	0.989005i
$730$	1.66908	−	1.87104i	0.0617754	−	0.0692501i
$731$	−18.6497			−0.689786
$732$	−1.04130	−	0.128824i	−0.0384876	−	0.00476148i
$733$	−15.3059			−0.565336			−0.282668	−	0.959218i	$-0.591220\pi$
$733$	−15.3059			−0.565336			−0.282668	+	0.959218i	$0.591220\pi$
$734$	19.0198	−	21.3212i	0.702035	−	0.786980i
$735$		0			0
$736$	−1.55628	−	0.851142i	−0.0573652	−	0.0313735i
$737$			53.3335i			1.96457i
$738$	7.83476	−	3.02315i	0.288402	−	0.111284i
$739$			26.8695i			0.988411i	0.869345	+	0.494205i	$0.164541\pi$
$739$			26.8695i			0.988411i	−0.869345	+	0.494205i	$0.835459\pi$
$740$	13.2976	−	1.52216i	0.488829	−	0.0559556i
$741$	−11.3935	−	2.75272i	−0.418550	−	0.101124i
$742$		0			0
$743$	−23.4748			−0.861208			−0.430604	−	0.902541i	$-0.641699\pi$
$743$	−23.4748			−0.861208			−0.430604	+	0.902541i	$0.641699\pi$
$744$	−18.0545	+	15.8125i	−0.661910	+	0.579715i
$745$	14.1626			0.518878
$746$	−8.63302	−	7.70119i	−0.316077	−	0.281960i
$747$	18.1054	+	9.29107i	0.662443	+	0.339942i
$748$	−58.8321	+	6.73444i	−2.15112	+	0.246235i
$749$		0			0
$750$	−14.7275	−	21.2832i	−0.537772	−	0.777151i
$751$		−	35.9640i		−	1.31234i	−0.754612	−	0.656172i	$-0.772175\pi$
$751$		−	35.9640i		−	1.31234i	0.754612	−	0.656172i	$-0.227825\pi$
$752$	−44.7956	+	10.3915i	−1.63353	+	0.378940i
$753$	−4.26334	+	17.6459i	−0.155365	+	0.643053i
$754$	−23.0361	+	25.8235i	−0.838926	+	0.940435i
$755$	13.9153			0.506429
$756$		0			0
$757$	23.4202			0.851222			0.425611	−	0.904906i	$-0.360059\pi$
$757$	23.4202			0.851222			0.425611	+	0.904906i	$0.360059\pi$
$758$	29.3742	−	32.9285i	1.06692	−	1.19602i
$759$	−0.645185	+	2.67041i	−0.0234187	+	0.0969299i
$760$	−3.13122	+	4.43800i	−0.113581	+	0.160983i
$761$			40.3136i			1.46137i	0.682716	+	0.730684i	$0.260799\pi$
$761$			40.3136i			1.46137i	−0.682716	+	0.730684i	$0.739201\pi$
$762$	−11.8532	−	17.1294i	−0.429394	−	0.620531i
$763$		0			0
$764$	0.888828	+	7.76481i	0.0321567	+	0.280921i
$765$	19.5861	+	10.0509i	0.708138	+	0.363391i
$766$	−25.7690	−	22.9875i	−0.931071	−	0.830572i
$767$	−35.1981			−1.27093
$768$	6.01607	+	27.0519i	0.217086	+	0.976152i
$769$	−20.6279			−0.743861			−0.371930	−	0.928261i	$-0.621304\pi$
$769$	−20.6279			−0.743861			−0.371930	+	0.928261i	$0.621304\pi$
$770$		0			0
$771$	14.0762	+	3.40088i	0.506942	+	0.122480i
$772$	0.357475	+	3.12291i	0.0128658	+	0.112396i
$773$			23.3006i			0.838064i	0.907972	+	0.419032i	$0.137630\pi$
$773$			23.3006i			0.838064i	−0.907972	+	0.419032i	$0.862370\pi$
$774$	12.6113	−	4.86625i	0.453305	−	0.174914i
$775$		−	16.7954i		−	0.603309i
$776$	−22.3136	+	31.6260i	−0.801012	+	1.13531i
$777$		0			0
$778$	−8.55233	+	9.58716i	−0.306616	+	0.343716i
$779$	3.03194			0.108630
$780$	−2.35568	+	19.0412i	−0.0843467	+	0.681784i
$781$	22.9388			0.820813
$782$	−1.72794	+	1.93702i	−0.0617909	+	0.0692676i
$783$	−21.8030	−	18.7853i	−0.779177	−	0.671333i
$784$		0			0
$785$			18.5487i			0.662032i
$786$	−16.9409	+	11.7227i	−0.604261	+	0.418136i
$787$		−	3.18839i		−	0.113654i	−0.998384	−	0.0568269i	$-0.981902\pi$
$787$		−	3.18839i		−	0.113654i	0.998384	−	0.0568269i	$-0.0180983\pi$
$788$	3.64191	−	0.416884i	0.129738	−	0.0148509i
$789$	11.9468	−	49.4477i	0.425318	−	1.76038i
$790$	−9.16617	−	8.17678i	−0.326118	−	0.290917i
$791$		0			0
$792$	38.0262	−	19.9049i	1.35120	−	0.707291i
$793$	−1.33816			−0.0475194
$794$	−24.5692	−	21.9172i	−0.871927	−	0.777813i
$795$	6.52236	−	26.9960i	0.231324	−	0.957448i
$796$	7.29419	−	0.834957i	0.258536	−	0.0295943i
$797$			55.9985i			1.98357i	0.127925	+	0.991784i	$0.459168\pi$
$797$			55.9985i			1.98357i	−0.127925	+	0.991784i	$0.540832\pi$
$798$		0			0
$799$			67.2924i			2.38063i
$800$	−17.0152	−	9.30576i	−0.601579	−	0.329008i
$801$	−6.57110	+	12.8050i	−0.232178	+	0.452444i
$802$	7.14659	−	8.01132i	0.252355	−	0.282890i
$803$	−7.15348			−0.252441
$804$	4.48448	−	36.2485i	0.158155	−	1.27839i
$805$		0			0
$806$	−20.3757	+	22.8412i	−0.717705	+	0.804546i
$807$	34.3417	+	8.29713i	1.20889	+	0.292073i
$808$	−9.41040	−	6.63948i	−0.331057	−	0.233576i
$809$			21.3480i			0.750555i	0.926913	+	0.375277i	$0.122453\pi$
$809$			21.3480i			0.750555i	−0.926913	+	0.375277i	$0.877547\pi$
$810$	−15.8671	−	1.68605i	−0.557513	−	0.0592417i
$811$			52.7856i			1.85355i	0.375614	+	0.926776i	$0.377432\pi$
$811$			52.7856i			1.85355i	−0.375614	+	0.926776i	$0.622568\pi$
$812$		0			0
$813$	34.6763	+	8.37797i	1.21615	+	0.293828i
$814$	−28.4959	−	25.4201i	−0.998782	−	0.890975i
$815$	16.6310			0.582558
$816$	40.5519	+	0.369713i	1.41960	+	0.0129425i
$817$	4.88039			0.170743
$818$	6.74377	+	6.01585i	0.235790	+	0.210339i
$819$		0			0
$820$	−0.564413	−	4.93072i	−0.0197101	−	0.172188i
$821$			5.81834i			0.203062i	0.994832	+	0.101531i	$0.0323740\pi$
$821$			5.81834i			0.203062i	−0.994832	+	0.101531i	$0.967626\pi$
$822$	19.1744	+	27.7096i	0.668785	+	0.966482i
$823$			10.1488i			0.353765i	0.984232	+	0.176882i	$0.0566012\pi$
$823$			10.1488i			0.353765i	−0.984232	+	0.176882i	$0.943399\pi$
$824$	30.2194	+	21.3212i	1.05274	+	0.742759i
$825$	−7.05398	+	29.1964i	−0.245588	+	1.01649i
$826$		0			0
$827$	−53.0241			−1.84383			−0.921915	−	0.387393i	$-0.873376\pi$
$827$	−53.0241			−1.84383			−0.921915	+	0.387393i	$0.873376\pi$
$828$	0.663043	−	1.76072i	0.0230423	−	0.0611891i
$829$	32.7023			1.13580			0.567898	−	0.823099i	$-0.307757\pi$
$829$	32.7023			1.13580			0.567898	+	0.823099i	$0.307757\pi$
$830$	8.00588	−	8.97458i	0.277888	−	0.311512i
$831$	1.60547	−	6.64502i	0.0556932	−	0.230513i
$832$	11.8506	+	33.2979i	0.410845	+	1.15440i
$833$		0			0
$834$	−18.3500	−	26.5181i	−0.635408	−	0.918247i
$835$		−	6.00030i		−	0.207649i
$836$	15.3956	−	1.76231i	0.532468	−	0.0609509i
$837$	−19.2850	−	16.6159i	−0.666589	−	0.574328i
$838$	−30.7426	−	27.4243i	−1.06199	−	0.947357i
$839$	−37.5962			−1.29796			−0.648982	−	0.760803i	$-0.724805\pi$
$839$	−37.5962			−1.29796			−0.648982	+	0.760803i	$0.724805\pi$
$840$		0			0
$841$	−1.67632			−0.0578040
$842$	−33.8572	−	30.2027i	−1.16680	−	1.04085i
$843$	1.99715	+	0.482522i	0.0687857	+	0.0166190i
$844$	29.5596	−	3.38364i	1.01748	−	0.116470i
$845$			8.17200i			0.281125i
$846$	−17.5585	−	45.5044i	−0.603673	−	1.56447i
$847$		0			0
$848$	−11.5612	−	49.8377i	−0.397013	−	1.71143i
$849$	−46.6078	−	11.2607i	−1.59958	−	0.386466i
$850$	−18.8920	+	21.1779i	−0.647991	+	0.726397i
$851$	−1.67389			−0.0573802
$852$	−15.5905	−	1.92878i	−0.534122	−	0.0660787i
$853$	5.68417			0.194622			0.0973112	−	0.995254i	$-0.468976\pi$
$853$	5.68417			0.194622			0.0973112	+	0.995254i	$0.468976\pi$
$854$		0			0
$855$	−5.12543	−	2.63019i	−0.175286	−	0.0899507i
$856$	−6.37195	+	9.03122i	−0.217789	+	0.308681i
$857$		−	31.6896i		−	1.08250i	−0.840862	−	0.541249i	$-0.817952\pi$
$857$		−	31.6896i		−	1.08250i	0.840862	−	0.541249i	$-0.182048\pi$
$858$	45.0134	−	31.1483i	1.53673	−	1.06339i
$859$		−	6.03763i		−	0.206001i	−0.994681	−	0.103001i	$-0.967156\pi$
$859$		−	6.03763i		−	0.206001i	0.994681	−	0.103001i	$-0.0328444\pi$
$860$	−0.908514	−	7.93679i	−0.0309801	−	0.270642i
$861$		0			0
$862$	19.2552	+	17.1768i	0.655835	+	0.585045i
$863$	−40.1137			−1.36549			−0.682744	−	0.730658i	$-0.739213\pi$
$863$	−40.1137			−1.36549			−0.682744	+	0.730658i	$0.739213\pi$
$864$	−27.5185	+	10.3311i	−0.936198	+	0.351473i
$865$	18.0676			0.614316
$866$	−5.11669	−	4.56440i	−0.173872	−	0.155105i
$867$	7.02181	−	29.0632i	0.238473	−	0.987038i
$868$		0			0
$869$			35.0447i			1.18881i
$870$	−13.9861	+	9.67806i	−0.474172	+	0.328117i
$871$		−	46.5824i		−	1.57838i
$872$	13.4490	−	19.0619i	0.455442	−	0.645516i
$873$	−36.5247	−	18.7432i	−1.23617	−	0.634361i
$874$	0.452179	−	0.506892i	0.0152952	−	0.0171459i
$875$		0			0
$876$	4.86191	+	0.601491i	0.164269	+	0.0203225i
$877$	−43.8872			−1.48197			−0.740983	−	0.671524i	$-0.765640\pi$
$877$	−43.8872			−1.48197			−0.740983	+	0.671524i	$0.765640\pi$
$878$	−19.0657	+	21.3726i	−0.643436	+	0.721292i
$879$	−0.333009	−	0.0804567i	−0.0112321	−	0.00271374i
$880$	−5.73196	−	24.7092i	−0.193224	−	0.832946i
$881$			1.27293i			0.0428860i	0.999770	+	0.0214430i	$0.00682603\pi$
$881$			1.27293i			0.0428860i	−0.999770	+	0.0214430i	$0.993174\pi$
$882$		0			0
$883$			19.5118i			0.656625i	0.944569	+	0.328312i	$0.106480\pi$
$883$			19.5118i			0.656625i	−0.944569	+	0.328312i	$0.893520\pi$
$884$	51.3850	−	5.88197i	1.72826	−	0.197832i
$885$	−16.8157	−	4.06276i	−0.565253	−	0.136568i
$886$	−23.7101	−	21.1509i	−0.796557	−	0.710578i
$887$	−26.8919			−0.902940			−0.451470	−	0.892286i	$-0.649100\pi$
$887$	−26.8919			−0.902940			−0.451470	+	0.892286i	$0.649100\pi$
$888$	17.2301	+	19.6730i	0.578203	+	0.660183i
$889$		0			0
$890$	6.34727	+	5.66215i	0.212761	+	0.189796i
$891$	26.5456	+	36.9838i	0.889313	+	1.23901i
$892$	38.5822	−	4.41646i	1.29183	−	0.147874i
$893$		−	17.6095i		−	0.589281i
$894$	15.7461	+	22.7552i	0.526630	+	0.761048i
$895$			0.870412i			0.0290947i
$896$		0			0
$897$	0.563515	−	2.33238i	0.0188152	−	0.0778760i
$898$	−27.8341	+	31.2020i	−0.928836	+	1.04122i
$899$	−27.1336			−0.904956
$900$	7.24923	−	19.2504i	0.241641	−	0.641680i
$901$	−74.8667			−2.49417
$902$	−9.42574	+	10.5662i	−0.313843	+	0.351817i
$903$		0			0
$904$	15.5418	+	10.9655i	0.516913	+	0.364706i
$905$		−	7.91109i		−	0.262973i
$906$	15.4711	+	22.3578i	0.513994	+	0.742789i
$907$			18.6528i			0.619357i	0.950841	+	0.309679i	$0.100221\pi$
$907$			18.6528i			0.619357i	−0.950841	+	0.309679i	$0.899779\pi$
$908$	−2.42981	−	21.2268i	−0.0806360	−	0.704437i
$909$	5.57709	−	10.8680i	0.184980	−	0.360470i
$910$		0			0
$911$	8.12909			0.269329			0.134664	−	0.990891i	$-0.457004\pi$
$911$	8.12909			0.269329			0.134664	+	0.990891i	$0.457004\pi$
$912$	−10.6119	−	0.0967489i	−0.351396	−	0.00320368i
$913$	−34.3123			−1.13557
$914$	19.2016	+	17.1290i	0.635133	+	0.566578i
$915$	−0.639297	−	0.154457i	−0.0211345	−	0.00510621i
$916$	−1.70623	−	14.9057i	−0.0563755	−	0.492497i
$917$		0			0
$918$	5.62715	+	42.6440i	0.185724	+	1.40746i
$919$			17.5640i			0.579383i	0.957120	+	0.289692i	$0.0935528\pi$
$919$			17.5640i			0.579383i	−0.957120	+	0.289692i	$0.906447\pi$
$920$	−0.908514	−	0.640999i	−0.0299528	−	0.0211331i
$921$	27.9846	+	6.76123i	0.922125	+	0.222790i
$922$	23.5150	−	26.3603i	0.774425	−	0.868129i
$923$	−20.0351			−0.659463
$924$		0			0
$925$	−18.3011			−0.601736
$926$	5.99898	−	6.72485i	0.197139	−	0.220992i
$927$	−17.9096	+	34.9002i	−0.588228	+	1.14627i
$928$	−15.0338	+	27.4887i	−0.493508	+	0.902360i
$929$		−	38.9854i		−	1.27907i	−0.768762	−	0.639535i	$-0.779127\pi$
$929$		−	38.9854i		−	1.27907i	0.768762	−	0.639535i	$-0.220873\pi$
$930$	−12.3708	+	8.56036i	−0.405656	+	0.280705i
$931$		0			0
$932$	−5.56221	+	0.636699i	−0.182196	+	0.0208558i
$933$	−4.37524	+	18.1091i	−0.143239	+	0.592864i
$934$	28.8706	+	25.7544i	0.944676	+	0.842709i
$935$	−37.1184			−1.21390
$936$	−33.2127	+	17.3853i	−1.08559	+	0.568256i
$937$	−23.7865			−0.777072			−0.388536	−	0.921434i	$-0.627019\pi$
$937$	−23.7865			−0.777072			−0.388536	+	0.921434i	$0.627019\pi$
$938$		0			0
$939$	2.01106	−	8.32376i	0.0656285	−	0.271636i
$940$	−28.6377	+	3.27812i	−0.934058	+	0.106920i
$941$		−	30.6145i		−	0.998005i	−0.866601	−	0.499002i	$-0.833700\pi$
$941$		−	30.6145i		−	0.998005i	0.866601	−	0.499002i	$-0.166300\pi$
$942$	−29.8024	+	20.6226i	−0.971015	+	0.671922i
$943$			0.620675i			0.0202120i
$944$	−31.0437	+	7.20143i	−1.01039	+	0.234387i
$945$		0			0
$946$	−15.1722	+	17.0081i	−0.493292	+	0.552980i
$947$	15.4601			0.502386			0.251193	−	0.967937i	$-0.419177\pi$
$947$	15.4601			0.502386			0.251193	+	0.967937i	$0.419177\pi$
$948$	2.94669	−	23.8184i	0.0957041	−	0.773586i
$949$	6.24797			0.202818
$950$	4.94379	−	5.54199i	0.160398	−	0.179806i
$951$	−36.9294	−	8.92233i	−1.19752	−	0.289326i
$952$		0			0
$953$			13.4497i			0.435679i	0.975985	+	0.217839i	$0.0699009\pi$
$953$			13.4497i			0.435679i	−0.975985	+	0.217839i	$0.930099\pi$
$954$	50.6263	−	19.5348i	1.63909	−	0.632464i
$955$			4.89898i			0.158527i
$956$	4.67338	+	40.8267i	0.151148	+	1.32043i
$957$	47.1677	+	11.3960i	1.52472	+	0.368379i
$958$	20.9308	+	18.6715i	0.676243	+	0.603250i
$959$		0			0
$960$	1.81813	+	17.2757i	0.0586799	+	0.557572i
$961$	7.00000			0.225806
$962$	24.8888	+	22.2024i	0.802448	+	0.715833i
$963$	−10.4301	−	5.35237i	−0.336106	−	0.172478i
$964$	−4.10655	−	35.8749i	−0.132263	−	1.15545i
$965$			1.97031i			0.0634264i
$966$		0			0
$967$		−	41.1554i		−	1.32347i	−0.749738	−	0.661734i	$-0.769821\pi$
$967$		−	41.1554i		−	1.32347i	0.749738	−	0.661734i	$-0.230179\pi$
$968$	−23.7840	+	33.7100i	−0.764446	+	1.08348i
$969$	−3.64710	+	15.0953i	−0.117162	+	0.484931i
$970$	−16.1505	+	18.1047i	−0.518562	+	0.581308i
$971$	−28.8890			−0.927093			−0.463546	−	0.886073i	$-0.653423\pi$
$971$	−28.8890			−0.927093			−0.463546	+	0.886073i	$0.653423\pi$
$972$	−14.9322	−	27.3684i	−0.478951	−	0.877842i
$973$		0			0
$974$	38.4593	−	43.1128i	1.23232	−	1.38142i
$975$	6.16107	−	25.5006i	0.197312	−	0.816672i
$976$	−1.18022	+	0.273783i	−0.0377778	+	0.00876359i
$977$		−	46.9884i		−	1.50329i	−0.659567	−	0.751646i	$-0.729260\pi$
$977$		−	46.9884i		−	1.50329i	0.659567	−	0.751646i	$-0.270740\pi$
$978$	18.4905	+	26.7212i	0.591261	+	0.854450i
$979$		−	24.2673i		−	0.775587i
$980$		0			0
$981$	22.0145	+	11.2971i	0.702868	+	0.360687i
$982$	−21.4235	−	19.1111i	−0.683652	−	0.609859i
$983$	−27.3353			−0.871861			−0.435931	−	0.899980i	$-0.643581\pi$
$983$	−27.3353			−0.871861			−0.435931	+	0.899980i	$0.643581\pi$
$984$	7.29472	−	6.38887i	0.232547	−	0.203670i
$985$	2.29776			0.0732126
$986$	34.2137	+	30.5207i	1.08959	+	0.971978i
$987$		0			0
$988$	−13.4468	+	1.53923i	−0.427799	+	0.0489696i
$989$			0.999076i			0.0317688i
$990$	25.1002	−	9.68525i	0.797737	−	0.307817i
$991$			20.7846i			0.660245i	0.943938	+	0.330122i	$0.107090\pi$
$991$			20.7846i			0.660245i	−0.943938	+	0.330122i	$0.892910\pi$
$992$	−13.2976	+	24.3141i	−0.422199	+	0.771973i
$993$	−6.30019	−	1.52216i	−0.199930	−	0.0483042i
$994$		0			0
$995$	4.60206			0.145895
$996$	23.3206	+	2.88510i	0.738941	+	0.0914180i
$997$	12.0424			0.381386			0.190693	−	0.981650i	$-0.438926\pi$
$997$	12.0424			0.381386			0.190693	+	0.981650i	$0.438926\pi$
$998$	32.2222	−	36.1211i	1.01998	−	1.14339i
$999$	−18.1054	+	21.0139i	−0.572830	+	0.664850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.f.491.19	yes	24
3.2	odd	2	inner	588.2.e.f.491.6	yes	24
4.3	odd	2	inner	588.2.e.f.491.8	yes	24
7.2	even	3		588.2.n.d.263.7		24
7.3	odd	6		588.2.n.h.275.3		24
7.4	even	3		588.2.n.h.275.4		24
7.5	odd	6		588.2.n.d.263.8		24
7.6	odd	2	inner	588.2.e.f.491.20	yes	24
12.11	even	2	inner	588.2.e.f.491.17	yes	24
21.2	odd	6		588.2.n.d.263.5		24
21.5	even	6		588.2.n.d.263.6		24
21.11	odd	6		588.2.n.h.275.10		24
21.17	even	6		588.2.n.h.275.9		24
21.20	even	2	inner	588.2.e.f.491.5	✓	24
28.3	even	6		588.2.n.d.275.6		24
28.11	odd	6		588.2.n.d.275.5		24
28.19	even	6		588.2.n.h.263.9		24
28.23	odd	6		588.2.n.h.263.10		24
28.27	even	2	inner	588.2.e.f.491.7	yes	24
84.11	even	6		588.2.n.d.275.7		24
84.23	even	6		588.2.n.h.263.4		24
84.47	odd	6		588.2.n.h.263.3		24
84.59	odd	6		588.2.n.d.275.8		24
84.83	odd	2	inner	588.2.e.f.491.18	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.5	✓	24	21.20	even	2	inner
588.2.e.f.491.6	yes	24	3.2	odd	2	inner
588.2.e.f.491.7	yes	24	28.27	even	2	inner
588.2.e.f.491.8	yes	24	4.3	odd	2	inner
588.2.e.f.491.17	yes	24	12.11	even	2	inner
588.2.e.f.491.18	yes	24	84.83	odd	2	inner
588.2.e.f.491.19	yes	24	1.1	even	1	trivial
588.2.e.f.491.20	yes	24	7.6	odd	2	inner
588.2.n.d.263.5		24	21.2	odd	6
588.2.n.d.263.6		24	21.5	even	6
588.2.n.d.263.7		24	7.2	even	3
588.2.n.d.263.8		24	7.5	odd	6
588.2.n.d.275.5		24	28.11	odd	6
588.2.n.d.275.6		24	28.3	even	6
588.2.n.d.275.7		24	84.11	even	6
588.2.n.d.275.8		24	84.59	odd	6
588.2.n.h.263.3		24	84.47	odd	6
588.2.n.h.263.4		24	84.23	even	6
588.2.n.h.263.9		24	28.19	even	6
588.2.n.h.263.10		24	28.23	odd	6
588.2.n.h.275.3		24	7.3	odd	6
588.2.n.h.275.4		24	7.4	even	3
588.2.n.h.275.9		24	21.17	even	6
588.2.n.h.275.10		24	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05533 + 0.941421i) q^{2} +(-0.406768 + 1.68361i) q^{3} +(0.227452 + 1.98702i) q^{4} +1.25365i q^{5} +(-2.01426 + 1.39383i) q^{6} +(-1.63059 + 2.31110i) q^{8} +(-2.66908 - 1.36968i) q^{9} +O(q^{10})\)	\(q+(1.05533 + 0.941421i) q^{2} +(-0.406768 + 1.68361i) q^{3} +(0.227452 + 1.98702i) q^{4} +1.25365i q^{5} +(-2.01426 + 1.39383i) q^{6} +(-1.63059 + 2.31110i) q^{8} +(-2.66908 - 1.36968i) q^{9} +(-1.18022 + 1.32302i) q^{10} +5.05827 q^{11} +(-3.43789 - 0.425318i) q^{12} -4.41798 q^{13} +(-2.11066 - 0.509947i) q^{15} +(-3.89653 + 0.903905i) q^{16} +5.85341i q^{17} +(-1.52732 - 3.95819i) q^{18} -1.53176i q^{19} +(-2.49104 + 0.285146i) q^{20} +(5.33816 + 4.76197i) q^{22} +0.313570 q^{23} +(-3.22771 - 3.68536i) q^{24} +3.42835 q^{25} +(-4.66244 - 4.15918i) q^{26} +(3.39170 - 3.93654i) q^{27} -5.53862i q^{29} +(-1.74738 - 2.52519i) q^{30} -4.89898i q^{31} +(-4.96309 - 2.71436i) q^{32} +(-2.05755 + 8.51615i) q^{33} +(-5.51053 + 6.17729i) q^{34} +(2.11450 - 5.61506i) q^{36} -5.33816 q^{37} +(1.44203 - 1.61652i) q^{38} +(1.79709 - 7.43815i) q^{39} +(-2.89732 - 2.04420i) q^{40} +1.97938i q^{41} +3.18613i q^{43} +(1.15051 + 10.0509i) q^{44} +(1.71710 - 3.34610i) q^{45} +(0.330921 + 0.295202i) q^{46} +11.4963 q^{47} +(0.0631619 - 6.92792i) q^{48} +(3.61805 + 3.22752i) q^{50} +(-9.85486 - 2.38098i) q^{51} +(-1.00488 - 8.77863i) q^{52} +12.7903i q^{53} +(7.28532 - 0.961345i) q^{54} +6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(5.21417 - 5.84508i) q^{58} +7.96701 q^{59} +(0.533202 - 4.30993i) q^{60} +0.302889 q^{61} +(4.61200 - 5.17005i) q^{62} +(-2.68236 - 7.53691i) q^{64} -5.53862i q^{65} +(-10.1887 + 7.05035i) q^{66} +10.5438i q^{67} +(-11.6309 + 1.33137i) q^{68} +(-0.127550 + 0.527930i) q^{69} +4.53490 q^{71} +(7.51763 - 3.93512i) q^{72} -1.41421 q^{73} +(-5.63353 - 5.02546i) q^{74} +(-1.39454 + 5.77200i) q^{75} +(3.04365 - 0.348402i) q^{76} +(8.89896 - 6.15790i) q^{78} +6.92820i q^{79} +(-1.13319 - 4.88490i) q^{80} +(5.24797 + 7.31156i) q^{81} +(-1.86343 + 2.08890i) q^{82} -6.78340 q^{83} -7.33816 q^{85} +(-2.99949 + 3.36243i) q^{86} +(9.32487 + 2.25294i) q^{87} +(-8.24797 + 11.6902i) q^{88} -4.79755i q^{89} +(4.96221 - 1.91473i) q^{90} +(0.0713222 + 0.623072i) q^{92} +(8.24797 + 1.99275i) q^{93} +(12.1324 + 10.8228i) q^{94} +1.92030 q^{95} +(6.58874 - 7.25179i) q^{96} +13.6844 q^{97} +(-13.5009 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) \) 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

Introduction

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