LMFDB - Embedded newform 288.2.v.d.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 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("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	288.37
Dual form			288.2.v.d.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.605567 + 1.27800i) q^{2} +(-1.26658 - 1.54783i) q^{4} +(-1.60930 - 0.666593i) q^{5} +(-0.589445 - 0.589445i) q^{7} +(2.74513 - 0.681373i) q^{8} +O(q^{10})$	\(q+(-0.605567 + 1.27800i) q^{2} +(-1.26658 - 1.54783i) q^{4} +(-1.60930 - 0.666593i) q^{5} +(-0.589445 - 0.589445i) q^{7} +(2.74513 - 0.681373i) q^{8} +(1.82644 - 1.65302i) q^{10} +(0.657053 - 1.58627i) q^{11} +(3.87213 - 1.60389i) q^{13} +(1.11026 - 0.396364i) q^{14} +(-0.791564 + 3.92090i) q^{16} -7.96502i q^{17} +(3.97306 - 1.64569i) q^{19} +(1.00653 + 3.33521i) q^{20} +(1.62936 + 1.80031i) q^{22} +(0.452012 - 0.452012i) q^{23} +(-1.39004 - 1.39004i) q^{25} +(-0.295061 + 5.91986i) q^{26} +(-0.165784 + 1.65894i) q^{28} +(1.69130 + 4.08316i) q^{29} -9.32808 q^{31} +(-4.53157 - 3.38598i) q^{32} +(10.1793 + 4.82335i) q^{34} +(0.555673 + 1.34151i) q^{35} +(0.810329 + 0.335649i) q^{37} +(-0.302752 + 6.07415i) q^{38} +(-4.87193 - 0.733351i) q^{40} +(6.65023 - 6.65023i) q^{41} +(-2.22413 + 5.36952i) q^{43} +(-3.28748 + 0.992122i) q^{44} +(0.303949 + 0.851396i) q^{46} +8.50500i q^{47} -6.30511i q^{49} +(2.61824 - 0.934713i) q^{50} +(-7.38691 - 3.96196i) q^{52} +(-1.10759 + 2.67397i) q^{53} +(-2.11479 + 2.11479i) q^{55} +(-2.01974 - 1.21647i) q^{56} +(-6.24248 - 0.311142i) q^{58} +(1.92200 + 0.796118i) q^{59} +(-4.70435 - 11.3573i) q^{61} +(5.64878 - 11.9213i) q^{62} +(7.07146 - 3.74091i) q^{64} -7.30055 q^{65} +(4.54765 + 10.9790i) q^{67} +(-12.3285 + 10.0883i) q^{68} +(-2.05095 - 0.102225i) q^{70} +(-9.09946 - 9.09946i) q^{71} +(1.65052 - 1.65052i) q^{73} +(-0.919668 + 0.832343i) q^{74} +(-7.57944 - 4.06522i) q^{76} +(-1.32231 + 0.547721i) q^{77} -0.580469i q^{79} +(3.88750 - 5.78224i) q^{80} +(4.47185 + 12.5262i) q^{82} +(-3.33576 + 1.38172i) q^{83} +(-5.30942 + 12.8181i) q^{85} +(-5.51540 - 6.09404i) q^{86} +(0.722857 - 4.80220i) q^{88} +(4.91488 + 4.91488i) q^{89} +(-3.22782 - 1.33701i) q^{91} +(-1.27215 - 0.127130i) q^{92} +(-10.8694 - 5.15035i) q^{94} -7.49083 q^{95} -3.30926 q^{97} +(8.05794 + 3.81817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

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 $

$2$	−0.605567	+	1.27800i	−0.428200	+	0.903684i
$2$	−0.605567	+	1.27800i	−0.428200	+	0.903684i
$3$		0			0
$3$		0			0
$4$	−1.26658	−	1.54783i	−0.633289	−	0.773916i
$5$	−1.60930	−	0.666593i	−0.719700	−	0.298109i	−0.00738796	−	0.999973i	$-0.502352\pi$
$5$	−1.60930	−	0.666593i	−0.719700	−	0.298109i	−0.712312	+	0.701863i	$0.752352\pi$
$6$		0			0
$7$	−0.589445	−	0.589445i	−0.222789	−	0.222789i	0.586883	−	0.809672i	$-0.300355\pi$
$7$	−0.589445	−	0.589445i	−0.222789	−	0.222789i	−0.809672	+	0.586883i	$0.800355\pi$
$8$	2.74513	−	0.681373i	0.970550	−	0.240902i
$9$		0			0
$10$	1.82644	−	1.65302i	0.577572	−	0.522730i
$11$	0.657053	−	1.58627i	0.198109	−	0.478277i	−0.793339	−	0.608780i	$-0.791659\pi$
$11$	0.657053	−	1.58627i	0.198109	−	0.478277i	0.991448	+	0.130503i	$0.0416591\pi$
$12$		0			0
$13$	3.87213	−	1.60389i	1.07394	−	0.444839i	0.225558	−	0.974230i	$-0.427579\pi$
$13$	3.87213	−	1.60389i	1.07394	−	0.444839i	0.848378	+	0.529391i	$0.177579\pi$
$14$	1.11026	−	0.396364i	0.296730	−	0.105933i
$15$		0			0
$16$	−0.791564	+	3.92090i	−0.197891	+	0.980224i
$17$		−	7.96502i		−	1.93180i	−0.258913	−	0.965901i	$-0.583364\pi$
$17$		−	7.96502i		−	1.93180i	0.258913	−	0.965901i	$-0.416636\pi$
$18$		0			0
$19$	3.97306	−	1.64569i	0.911481	−	0.377548i	0.122858	−	0.992424i	$-0.460794\pi$
$19$	3.97306	−	1.64569i	0.911481	−	0.377548i	0.788624	+	0.614876i	$0.210794\pi$
$20$	1.00653	+	3.33521i	0.225066	+	0.745776i
$21$		0			0
$22$	1.62936	+	1.80031i	0.347381	+	0.383827i
$23$	0.452012	−	0.452012i	0.0942511	−	0.0942511i	−0.658409	−	0.752660i	$-0.728770\pi$
$23$	0.452012	−	0.452012i	0.0942511	−	0.0942511i	0.752660	+	0.658409i	$0.228770\pi$
$24$		0			0
$25$	−1.39004	−	1.39004i	−0.278009	−	0.278009i
$26$	−0.295061	+	5.91986i	−0.0578663	+	1.16098i
$27$		0			0
$28$	−0.165784	+	1.65894i	−0.0313302	+	0.313510i
$29$	1.69130	+	4.08316i	0.314067	+	0.758224i	0.999546	+	0.0301318i	$0.00959270\pi$
$29$	1.69130	+	4.08316i	0.314067	+	0.758224i	−0.685479	+	0.728092i	$0.740407\pi$
$30$		0			0
$31$	−9.32808			−1.67537			−0.837686	−	0.546152i	$-0.816092\pi$
$31$	−9.32808			−1.67537			−0.837686	+	0.546152i	$0.816092\pi$
$32$	−4.53157	−	3.38598i	−0.801076	−	0.598563i
$33$		0			0
$34$	10.1793	+	4.82335i	1.74574	+	0.827198i
$35$	0.555673	+	1.34151i	0.0939258	+	0.226757i
$36$		0			0
$37$	0.810329	+	0.335649i	0.133217	+	0.0551804i	0.448296	−	0.893885i	$-0.352031\pi$
$37$	0.810329	+	0.335649i	0.133217	+	0.0551804i	−0.315079	+	0.949065i	$0.602031\pi$
$38$	−0.302752	+	6.07415i	−0.0491128	+	0.985357i
$39$		0			0
$40$	−4.87193	−	0.733351i	−0.770319	−	0.115953i
$41$	6.65023	−	6.65023i	1.03859	−	1.03859i	0.0393665	−	0.999225i	$-0.487466\pi$
$41$	6.65023	−	6.65023i	1.03859	−	1.03859i	0.999225	−	0.0393665i	$-0.0125340\pi$
$42$		0			0
$43$	−2.22413	+	5.36952i	−0.339176	+	0.818844i	0.658619	+	0.752477i	$0.271141\pi$
$43$	−2.22413	+	5.36952i	−0.339176	+	0.818844i	−0.997795	+	0.0663675i	$0.978859\pi$
$44$	−3.28748	+	0.992122i	−0.495607	+	0.149568i
$45$		0			0
$46$	0.303949	+	0.851396i	0.0448148	+	0.125532i
$47$			8.50500i			1.24058i	0.784372	+	0.620291i	$0.212985\pi$
$47$			8.50500i			1.24058i	−0.784372	+	0.620291i	$0.787015\pi$
$48$		0			0
$49$		−	6.30511i		−	0.900730i
$50$	2.61824	−	0.934713i	0.370275	−	0.132188i
$51$		0			0
$52$	−7.38691	−	3.96196i	−1.02438	−	0.549425i
$53$	−1.10759	+	2.67397i	−0.152140	+	0.367298i	−0.981513	−	0.191398i	$-0.938698\pi$
$53$	−1.10759	+	2.67397i	−0.152140	+	0.367298i	0.829373	+	0.558696i	$0.188698\pi$
$54$		0			0
$55$	−2.11479	+	2.11479i	−0.285158	+	0.285158i
$56$	−2.01974	−	1.21647i	−0.269898	−	0.162558i
$57$		0			0
$58$	−6.24248	−	0.311142i	−0.819678	−	0.0408549i
$59$	1.92200	+	0.796118i	0.250223	+	0.103646i	0.504270	−	0.863546i	$-0.331762\pi$
$59$	1.92200	+	0.796118i	0.250223	+	0.103646i	−0.254047	+	0.967192i	$0.581762\pi$
$60$		0			0
$61$	−4.70435	−	11.3573i	−0.602331	−	1.45416i	−0.871176	−	0.490972i	$-0.836642\pi$
$61$	−4.70435	−	11.3573i	−0.602331	−	1.45416i	0.268845	−	0.963183i	$-0.413358\pi$
$62$	5.64878	−	11.9213i	0.717395	−	1.51401i
$63$		0			0
$64$	7.07146	−	3.74091i	0.883933	−	0.467614i
$65$	−7.30055			−0.905522
$66$		0			0
$67$	4.54765	+	10.9790i	0.555583	+	1.34130i	0.913232	+	0.407441i	$0.133579\pi$
$67$	4.54765	+	10.9790i	0.555583	+	1.34130i	−0.357648	+	0.933856i	$0.616421\pi$
$68$	−12.3285	+	10.0883i	−1.49505	+	1.22339i
$69$		0			0
$70$	−2.05095	−	0.102225i	−0.245136	−	0.0122182i
$71$	−9.09946	−	9.09946i	−1.07991	−	1.07991i	−0.996517	−	0.0833896i	$-0.973425\pi$
$71$	−9.09946	−	9.09946i	−1.07991	−	1.07991i	−0.0833896	−	0.996517i	$-0.526575\pi$
$72$		0			0
$73$	1.65052	−	1.65052i	0.193179	−	0.193179i	−0.603889	−	0.797068i	$-0.706383\pi$
$73$	1.65052	−	1.65052i	0.193179	−	0.193179i	0.797068	+	0.603889i	$0.206383\pi$
$74$	−0.919668	+	0.832343i	−0.106909	+	0.0967580i
$75$		0			0
$76$	−7.57944	−	4.06522i	−0.869421	−	0.466313i
$77$	−1.32231	+	0.547721i	−0.150692	+	0.0624186i
$78$		0			0
$79$		−	0.580469i		−	0.0653079i	−0.999467	−	0.0326540i	$-0.989604\pi$
$79$		−	0.580469i		−	0.0653079i	0.999467	−	0.0326540i	$-0.0103959\pi$
$80$	3.88750	−	5.78224i	0.434636	−	0.646474i
$81$		0			0
$82$	4.47185	+	12.5262i	0.493833	+	1.38328i
$83$	−3.33576	+	1.38172i	−0.366147	+	0.151663i	−0.558168	−	0.829728i	$-0.688496\pi$
$83$	−3.33576	+	1.38172i	−0.366147	+	0.151663i	0.192021	+	0.981391i	$0.438496\pi$
$84$		0			0
$85$	−5.30942	+	12.8181i	−0.575888	+	1.39032i
$86$	−5.51540	−	6.09404i	−0.594741	−	0.657138i
$87$		0			0
$88$	0.722857	−	4.80220i	0.0770568	−	0.511917i
$89$	4.91488	+	4.91488i	0.520976	+	0.520976i	0.917866	−	0.396890i	$-0.129911\pi$
$89$	4.91488	+	4.91488i	0.520976	+	0.520976i	−0.396890	+	0.917866i	$0.629911\pi$
$90$		0			0
$91$	−3.22782	−	1.33701i	−0.338367	−	0.140156i
$92$	−1.27215	−	0.127130i	−0.132630	−	0.0132542i
$93$		0			0
$94$	−10.8694	−	5.15035i	−1.12109	−	0.531218i
$95$	−7.49083			−0.768543
$96$		0			0
$97$	−3.30926			−0.336005			−0.168002	−	0.985787i	$-0.553732\pi$
$97$	−3.30926			−0.336005			−0.168002	+	0.985787i	$0.553732\pi$
$98$	8.05794	+	3.81817i	0.813975	+	0.385693i
$99$		0			0
$100$	−0.390955	+	3.91215i	−0.0390955	+	0.391215i
$101$	2.59134	+	1.07337i	0.257848	+	0.106804i	0.507863	−	0.861438i	$-0.330436\pi$
$101$	2.59134	+	1.07337i	0.257848	+	0.106804i	−0.250015	+	0.968242i	$0.580436\pi$
$102$		0			0
$103$	12.7576	+	12.7576i	1.25705	+	1.25705i	0.952496	+	0.304550i	$0.0985061\pi$
$103$	12.7576	+	12.7576i	1.25705	+	1.25705i	0.304550	+	0.952496i	$0.401494\pi$
$104$	9.53666	−	7.04125i	0.935146	−	0.690451i
$105$		0			0
$106$	−2.74661	−	3.03477i	−0.266775	−	0.294763i
$107$	3.17275	−	7.65969i	0.306721	−	0.740490i	−0.693086	−	0.720855i	$-0.743750\pi$
$107$	3.17275	−	7.65969i	0.306721	−	0.740490i	0.999807	−	0.0196351i	$-0.00625046\pi$
$108$		0			0
$109$	10.8733	−	4.50386i	1.04147	−	0.431391i	0.204631	−	0.978839i	$-0.434401\pi$
$109$	10.8733	−	4.50386i	1.04147	−	0.431391i	0.836840	+	0.547448i	$0.184401\pi$
$110$	−1.42206	−	3.98335i	−0.135588	−	0.379797i
$111$		0			0
$112$	2.77774	−	1.84457i	0.262472	−	0.174296i
$113$			1.05718i			0.0994515i	0.998763	+	0.0497257i	$0.0158347\pi$
$113$			1.05718i			0.0994515i	−0.998763	+	0.0497257i	$0.984165\pi$
$114$		0			0
$115$	−1.02873	+	0.426114i	−0.0959296	+	0.0397353i
$116$	4.17788	−	7.78949i	0.387907	−	0.723236i
$117$		0			0
$118$	−2.18134	+	1.97422i	−0.200809	+	0.181741i
$119$	−4.69494	+	4.69494i	−0.430385	+	0.430385i
$120$		0			0
$121$	5.69365	+	5.69365i	0.517605	+	0.517605i
$122$	17.3635	+	0.865441i	1.57201	+	0.0783534i
$123$		0			0
$124$	11.8147	+	14.4383i	1.06099	+	1.29660i
$125$	4.64336	+	11.2101i	0.415315	+	1.00266i
$126$		0			0
$127$	−7.93736			−0.704327			−0.352163	−	0.935939i	$-0.614554\pi$
$127$	−7.93736			−0.704327			−0.352163	+	0.935939i	$0.614554\pi$
$128$	0.498648	+	11.3027i	0.0440747	+	0.999028i
$129$		0			0
$130$	4.42097	−	9.33012i	0.387745	−	0.818306i
$131$	7.20756	+	17.4006i	0.629727	+	1.52030i	0.839962	+	0.542645i	$0.182577\pi$
$131$	7.20756	+	17.4006i	0.629727	+	1.52030i	−0.210234	+	0.977651i	$0.567423\pi$
$132$		0			0
$133$	−3.31195	−	1.37185i	−0.287182	−	0.118955i
$134$	−16.7851	−	0.836613i	−1.45001	−	0.0722723i
$135$		0			0
$136$	−5.42715	−	21.8650i	−0.465374	−	1.87491i
$137$	−0.305733	+	0.305733i	−0.0261205	+	0.0261205i	−0.720046	−	0.693926i	$-0.755880\pi$
$137$	−0.305733	+	0.305733i	−0.0261205	+	0.0261205i	0.693926	+	0.720046i	$0.255880\pi$
$138$		0			0
$139$	6.72200	−	16.2283i	0.570153	−	1.37647i	−0.331273	−	0.943535i	$-0.607478\pi$
$139$	6.72200	−	16.2283i	0.570153	−	1.37647i	0.901425	−	0.432935i	$-0.142522\pi$
$140$	1.37263	−	2.55922i	0.116009	−	0.216293i
$141$		0			0
$142$	17.1394	−	6.11879i	1.43831	−	0.513478i
$143$		−	7.19608i		−	0.601766i
$144$		0			0
$145$		−	7.69843i		−	0.639320i
$146$	1.10987	+	3.10887i	0.0918534	+	0.257292i
$147$		0			0
$148$	−0.506816	−	1.67938i	−0.0416600	−	0.138044i
$149$	−2.14465	+	5.17765i	−0.175697	+	0.424170i	−0.987056	−	0.160379i	$-0.948728\pi$
$149$	−2.14465	+	5.17765i	−0.175697	+	0.424170i	0.811359	+	0.584549i	$0.198728\pi$
$150$		0			0
$151$	10.2384	−	10.2384i	0.833193	−	0.833193i	−0.154759	−	0.987952i	$-0.549460\pi$
$151$	10.2384	−	10.2384i	0.833193	−	0.833193i	0.987952	+	0.154759i	$0.0494603\pi$
$152$	9.78522	−	7.22477i	0.793686	−	0.586006i
$153$		0			0
$154$	0.100762	−	2.02160i	0.00811963	−	0.162905i
$155$	15.0116	+	6.21803i	1.20576	+	0.499444i
$156$		0			0
$157$	4.64097	+	11.2043i	0.370389	+	0.894199i	0.993684	+	0.112212i	$0.0357936\pi$
$157$	4.64097	+	11.2043i	0.370389	+	0.894199i	−0.623295	+	0.781987i	$0.714206\pi$
$158$	0.741841	+	0.351513i	0.0590177	+	0.0279649i
$159$		0			0
$160$	5.03557	+	8.46977i	0.398096	+	0.669594i
$161$	−0.532873			−0.0419963
$162$		0			0
$163$	0.981891	+	2.37049i	0.0769076	+	0.185671i	0.957657	−	0.287911i	$-0.0929607\pi$
$163$	0.981891	+	2.37049i	0.0769076	+	0.185671i	−0.880750	+	0.473582i	$0.842961\pi$
$164$	−18.7165	−	1.87040i	−1.46151	−	0.146054i
$165$		0			0
$166$	0.254189	−	5.09983i	0.0197289	−	0.395823i
$167$	6.83087	+	6.83087i	0.528588	+	0.528588i	0.920151	−	0.391563i	$-0.128066\pi$
$167$	6.83087	+	6.83087i	0.528588	+	0.528588i	−0.391563	+	0.920151i	$0.628066\pi$
$168$		0			0
$169$	3.22856	−	3.22856i	0.248351	−	0.248351i
$170$	−13.1663	−	14.5477i	−1.00981	−	1.11575i
$171$		0			0
$172$	11.1281	−	3.35834i	0.848513	−	0.256071i
$173$	−2.76667	+	1.14599i	−0.210346	+	0.0871282i	−0.485369	−	0.874310i	$-0.661315\pi$
$173$	−2.76667	+	1.14599i	−0.210346	+	0.0871282i	0.275023	+	0.961438i	$0.411315\pi$
$174$		0			0
$175$			1.63871i			0.123875i
$176$	5.69949	+	3.83187i	0.429615	+	0.288838i
$177$		0			0
$178$	−9.25751	+	3.30494i	−0.693880	+	0.247715i
$179$	13.3854	−	5.54441i	1.00047	−	0.414409i	0.178501	−	0.983940i	$-0.442875\pi$
$179$	13.3854	−	5.54441i	1.00047	−	0.414409i	0.821970	+	0.569531i	$0.192875\pi$
$180$		0			0
$181$	−9.03488	+	21.8121i	−0.671557	+	1.62128i	0.107407	+	0.994215i	$0.465745\pi$
$181$	−9.03488	+	21.8121i	−0.671557	+	1.62128i	−0.778965	+	0.627068i	$0.784255\pi$
$182$	3.66335	−	3.31551i	0.271546	−	0.245762i
$183$		0			0
$184$	0.932843	−	1.54882i	0.0687701	−	0.114181i
$185$	−1.08032	−	1.08032i	−0.0794266	−	0.0794266i
$186$		0			0
$187$	−12.6346	−	5.23344i	−0.923937	−	0.382707i
$188$	13.1643	−	10.7722i	0.960105	−	0.785646i
$189$		0			0
$190$	4.53620	−	9.57330i	0.329091	−	0.694520i
$191$	−15.9720			−1.15570			−0.577848	−	0.816144i	$-0.696107\pi$
$191$	−15.9720			−1.15570			−0.577848	+	0.816144i	$0.696107\pi$
$192$		0			0
$193$	0.411129			0.0295937			0.0147968	−	0.999891i	$-0.495290\pi$
$193$	0.411129			0.0295937			0.0147968	+	0.999891i	$0.495290\pi$
$194$	2.00398	−	4.22924i	0.143877	−	0.303642i
$195$		0			0
$196$	−9.75924	+	7.98591i	−0.697089	+	0.570422i
$197$	4.09727	+	1.69715i	0.291919	+	0.120917i	0.523837	−	0.851819i	$-0.324500\pi$
$197$	4.09727	+	1.69715i	0.291919	+	0.120917i	−0.231918	+	0.972735i	$0.574500\pi$
$198$		0			0
$199$	−8.65705	−	8.65705i	−0.613682	−	0.613682i	0.330221	−	0.943904i	$-0.392877\pi$
$199$	−8.65705	−	8.65705i	−0.613682	−	0.613682i	−0.943904	+	0.330221i	$0.892877\pi$
$200$	−4.76298	−	2.86871i	−0.336794	−	0.202848i
$201$		0			0
$202$	−2.94100	+	2.66174i	−0.206928	+	0.187280i
$203$	1.40987	−	3.40373i	0.0989535	−	0.238895i
$204$		0			0
$205$	−15.1352	+	6.26920i	−1.05709	+	0.437860i
$206$	−24.0299	+	8.57867i	−1.67424	+	0.597705i
$207$		0			0
$208$	3.22365	+	16.4518i	0.223520	+	1.14073i
$209$		−	7.38363i		−	0.510737i
$210$		0			0
$211$	−4.51505	+	1.87019i	−0.310829	+	0.128749i	−0.532644	−	0.846339i	$-0.678802\pi$
$211$	−4.51505	+	1.87019i	−0.310829	+	0.128749i	0.221816	+	0.975089i	$0.428802\pi$
$212$	5.54171	−	1.67242i	0.380606	−	0.114862i
$213$		0			0
$214$	7.86778	+	8.69323i	0.537831	+	0.594257i
$215$	7.15857	−	7.15857i	0.488210	−	0.488210i
$216$		0			0
$217$	5.49839	+	5.49839i	0.373255	+	0.373255i
$218$	−0.828557	+	16.6234i	−0.0561170	+	1.12588i
$219$		0			0
$220$	5.95188	+	0.594792i	0.401275	+	0.0401009i
$221$	−12.7750	−	30.8416i	−0.859341	−	2.07463i
$222$		0			0
$223$	−8.07183			−0.540530			−0.270265	−	0.962786i	$-0.587111\pi$
$223$	−8.07183			−0.540530			−0.270265	+	0.962786i	$0.587111\pi$
$224$	0.675259	+	4.66696i	0.0451176	+	0.311825i
$225$		0			0
$226$	−1.35108	−	0.640196i	−0.0898727	−	0.0425852i
$227$	0.993337	+	2.39813i	0.0659301	+	0.159169i	0.953410	−	0.301676i	$-0.0975462\pi$
$227$	0.993337	+	2.39813i	0.0659301	+	0.159169i	−0.887480	+	0.460846i	$0.847546\pi$
$228$		0			0
$229$	9.46203	+	3.91930i	0.625269	+	0.258995i	0.672741	−	0.739878i	$-0.265117\pi$
$229$	9.46203	+	3.91930i	0.625269	+	0.258995i	−0.0474727	+	0.998873i	$0.515117\pi$
$230$	0.0783905	−	1.57276i	0.00516892	−	0.103705i
$231$		0			0
$232$	7.42499	+	10.0564i	0.487475	+	0.660235i
$233$	−5.94847	+	5.94847i	−0.389698	+	0.389698i	−0.874580	−	0.484882i	$-0.838863\pi$
$233$	−5.94847	+	5.94847i	−0.389698	+	0.389698i	0.484882	+	0.874580i	$0.338863\pi$
$234$		0			0
$235$	5.66937	−	13.6871i	0.369829	−	0.892846i
$236$	−1.20210	−	3.98327i	−0.0782503	−	0.259289i
$237$		0			0
$238$	−3.15704	−	8.84325i	−0.204641	−	0.573223i
$239$		−	2.07158i		−	0.134000i	−0.997753	−	0.0669998i	$-0.978657\pi$
$239$		−	2.07158i		−	0.134000i	0.997753	−	0.0669998i	$-0.0213427\pi$
$240$		0			0
$241$		−	5.10031i		−	0.328540i	−0.986415	−	0.164270i	$-0.947473\pi$
$241$		−	5.10031i		−	0.328540i	0.986415	−	0.164270i	$-0.0525268\pi$
$242$	−10.7244	+	3.82861i	−0.689389	+	0.246112i
$243$		0			0
$244$	−11.6208	+	21.6665i	−0.743944	+	1.38705i
$245$	−4.20294	+	10.1468i	−0.268516	+	0.648255i
$246$		0			0
$247$	12.7447	−	12.7447i	0.810925	−	0.810925i
$248$	−25.6068	+	6.35590i	−1.62603	+	0.403600i
$249$		0			0
$250$	−17.1384	−	0.854221i	−1.08392	−	0.0540257i
$251$	−15.6741	−	6.49243i	−0.989341	−	0.409798i	−0.171463	−	0.985191i	$-0.554849\pi$
$251$	−15.6741	−	6.49243i	−0.989341	−	0.409798i	−0.817878	+	0.575392i	$0.804849\pi$
$252$		0			0
$253$	−0.420016	−	1.01401i	−0.0264062	−	0.0637501i
$254$	4.80660	−	10.1440i	0.301593	−	0.636489i
$255$		0			0
$256$	−14.7469	−	6.20728i	−0.921678	−	0.387955i
$257$	−12.7920			−0.797942			−0.398971	−	0.916964i	$-0.630633\pi$
$257$	−12.7920			−0.797942			−0.398971	+	0.916964i	$0.630633\pi$
$258$		0			0
$259$	−0.279798	−	0.675491i	−0.0173858	−	0.0419730i
$260$	9.24672	+	11.3000i	0.573457	+	0.700798i
$261$		0			0
$262$	−26.6026	−	1.32595i	−1.64352	−	0.0819172i
$263$	5.06752	+	5.06752i	0.312477	+	0.312477i	0.845868	−	0.533392i	$-0.179083\pi$
$263$	5.06752	+	5.06752i	0.312477	+	0.312477i	−0.533392	+	0.845868i	$0.679083\pi$
$264$		0			0
$265$	3.56490	−	3.56490i	0.218990	−	0.218990i
$266$	3.75883	−	3.40192i	0.230469	−	0.208585i
$267$		0			0
$268$	11.2337	−	20.9447i	0.686206	−	1.27940i
$269$	16.4527	−	6.81494i	1.00314	−	0.415514i	0.180192	−	0.983631i	$-0.442328\pi$
$269$	16.4527	−	6.81494i	1.00314	−	0.415514i	0.822948	+	0.568117i	$0.192328\pi$
$270$		0			0
$271$			6.40145i			0.388860i	0.980916	+	0.194430i	$0.0622857\pi$
$271$			6.40145i			0.388860i	−0.980916	+	0.194430i	$0.937714\pi$
$272$	31.2300	+	6.30482i	1.89360	+	0.382286i
$273$		0			0
$274$	−0.205586	−	0.575869i	−0.0124199	−	0.0347895i
$275$	−3.11831	+	1.29165i	−0.188041	+	0.0778892i
$276$		0			0
$277$	2.00777	−	4.84718i	0.120635	−	0.291239i	−0.852014	−	0.523519i	$-0.824619\pi$
$277$	2.00777	−	4.84718i	0.120635	−	0.291239i	0.972649	+	0.232281i	$0.0746187\pi$
$278$	16.6692	+	18.4181i	0.999754	+	1.10464i
$279$		0			0
$280$	2.43946	+	3.30400i	0.145786	+	0.197452i
$281$	−9.02739	−	9.02739i	−0.538529	−	0.538529i	0.384568	−	0.923097i	$-0.374351\pi$
$281$	−9.02739	−	9.02739i	−0.538529	−	0.538529i	−0.923097	+	0.384568i	$0.874351\pi$
$282$		0			0
$283$	7.91426	+	3.27819i	0.470454	+	0.194868i	0.605299	−	0.795998i	$-0.293054\pi$
$283$	7.91426	+	3.27819i	0.470454	+	0.194868i	−0.134845	+	0.990867i	$0.543054\pi$
$284$	−2.55926	+	25.6096i	−0.151864	+	1.51965i
$285$		0			0
$286$	9.19660	+	4.35771i	0.543806	+	0.257677i
$287$	−7.83989			−0.462774
$288$		0			0
$289$	−46.4416			−2.73186
$290$	9.83860	+	4.66191i	0.577743	+	0.273757i
$291$		0			0
$292$	−4.64524	−	0.464216i	−0.271842	−	0.0271662i
$293$	1.10609	+	0.458156i	0.0646183	+	0.0267658i	0.414758	−	0.909932i	$-0.363866\pi$
$293$	1.10609	+	0.458156i	0.0646183	+	0.0267658i	−0.350140	+	0.936697i	$0.613866\pi$
$294$		0			0
$295$	−2.56238	−	2.56238i	−0.149188	−	0.149188i
$296$	2.45316	+	0.369264i	0.142587	+	0.0214630i
$297$		0			0
$298$	−5.31832	−	5.87628i	−0.308082	−	0.340404i
$299$	1.02527	−	2.47523i	0.0592931	−	0.143146i
$300$		0			0
$301$	4.47604	−	1.85404i	0.257995	−	0.106865i
$302$	6.88469	+	19.2848i	0.396169	+	1.10972i
$303$		0			0
$304$	3.30767	+	16.8806i	0.189708	+	0.968169i
$305$			21.4132i			1.22612i
$306$		0			0
$307$	10.0335	−	4.15602i	0.572643	−	0.237197i	−0.0775205	−	0.996991i	$-0.524700\pi$
$307$	10.0335	−	4.15602i	0.572643	−	0.237197i	0.650164	+	0.759794i	$0.274700\pi$
$308$	2.52259	+	1.35299i	0.143738	+	0.0770937i
$309$		0			0
$310$	−17.0372	+	15.4195i	−0.967649	+	0.875768i
$311$	11.1912	−	11.1912i	0.634595	−	0.634595i	−0.314622	−	0.949217i	$-0.601878\pi$
$311$	11.1912	−	11.1912i	0.634595	−	0.634595i	0.949217	+	0.314622i	$0.101878\pi$
$312$		0			0
$313$	15.1491	+	15.1491i	0.856279	+	0.856279i	0.990897	−	0.134619i	$-0.0429809\pi$
$313$	15.1491	+	15.1491i	0.856279	+	0.856279i	−0.134619	+	0.990897i	$0.542981\pi$
$314$	−17.1295	−	0.853780i	−0.966674	−	0.0481816i
$315$		0			0
$316$	−0.898469	+	0.735209i	−0.0505428	+	0.0413588i
$317$	2.50910	+	6.05751i	0.140925	+	0.340223i	0.978546	−	0.206029i	$-0.0660540\pi$
$317$	2.50910	+	6.05751i	0.140925	+	0.340223i	−0.837621	+	0.546252i	$0.816054\pi$
$318$		0			0
$319$	7.58826			0.424861
$320$	−13.8737	+	1.30645i	−0.775566	+	0.0730329i
$321$		0			0
$322$	0.322690	−	0.681013i	0.0179828	−	0.0379514i
$323$	−13.1080	−	31.6455i	−0.729348	−	1.76080i
$324$		0			0
$325$	−7.61191	−	3.15295i	−0.422233	−	0.174894i
$326$	−3.62410	−	0.180635i	−0.200720	−	0.0100044i
$327$		0			0
$328$	13.7245	−	22.7870i	0.757806	−	1.25820i
$329$	5.01323	−	5.01323i	0.276388	−	0.276388i
$330$		0			0
$331$	7.52873	−	18.1760i	0.413817	−	0.999042i	−0.570287	−	0.821446i	$-0.693168\pi$
$331$	7.52873	−	18.1760i	0.413817	−	0.999042i	0.984103	−	0.177596i	$-0.0568321\pi$
$332$	6.36366	+	3.41314i	0.349251	+	0.187320i
$333$		0			0
$334$	−12.8664	+	4.59331i	−0.704018	+	0.251335i
$335$		−	20.6999i		−	1.13096i
$336$		0			0
$337$			29.9155i			1.62960i	0.579741	+	0.814801i	$0.303154\pi$
$337$			29.9155i			1.62960i	−0.579741	+	0.814801i	$0.696846\pi$
$338$	2.17100	+	6.08122i	0.118087	+	0.330775i
$339$		0			0
$340$	26.5650	−	8.01700i	1.44069	−	0.434783i
$341$	−6.12904	+	14.7968i	−0.331906	+	0.801293i
$342$		0			0
$343$	−7.84263	+	7.84263i	−0.423462	+	0.423462i
$344$	−2.44687	+	16.2555i	−0.131927	+	0.876437i
$345$		0			0
$346$	0.210824	−	4.22978i	0.0113340	−	0.227395i
$347$	−18.9783	−	7.86106i	−1.01881	−	0.422004i	−0.190147	−	0.981756i	$-0.560897\pi$
$347$	−18.9783	−	7.86106i	−1.01881	−	0.422004i	−0.828660	+	0.559752i	$0.810897\pi$
$348$		0			0
$349$	−2.93498	−	7.08568i	−0.157106	−	0.379288i	0.825653	−	0.564178i	$-0.190807\pi$
$349$	−2.93498	−	7.08568i	−0.157106	−	0.379288i	−0.982759	+	0.184891i	$0.940807\pi$
$350$	−2.09427	−	0.992348i	−0.111944	−	0.0530432i
$351$		0			0
$352$	−8.34856	+	4.96350i	−0.444980	+	0.264556i
$353$	28.6693			1.52591			0.762956	−	0.646450i	$-0.223747\pi$
$353$	28.6693			1.52591			0.762956	+	0.646450i	$0.223747\pi$
$354$		0			0
$355$	8.57810	+	20.7094i	0.455278	+	1.09914i
$356$	1.38233	−	13.8325i	0.0732633	−	0.733120i
$357$		0			0
$358$	−1.01998	+	20.4641i	−0.0539078	+	1.08156i
$359$	13.9965	+	13.9965i	0.738709	+	0.738709i	0.972328	−	0.233619i	$-0.0750569\pi$
$359$	13.9965	+	13.9965i	0.738709	+	0.738709i	−0.233619	+	0.972328i	$0.575057\pi$
$360$		0			0
$361$	−0.358168	+	0.358168i	−0.0188510	+	0.0188510i
$362$	−22.4047	−	24.7553i	−1.17757	−	1.30111i
$363$		0			0
$364$	2.01882	+	6.68954i	0.105815	+	0.350627i
$365$	−3.75641	+	1.55595i	−0.196619	+	0.0814424i
$366$		0			0
$367$		−	11.6706i		−	0.609203i	−0.952480	−	0.304601i	$-0.901477\pi$
$367$		−	11.6706i		−	0.609203i	0.952480	−	0.304601i	$-0.0985232\pi$
$368$	1.41450	+	2.13009i	0.0737357	+	0.111039i
$369$		0			0
$370$	2.03485	−	0.726444i	0.105787	−	0.0377660i
$371$	2.22902	−	0.923292i	0.115725	−	0.0479350i
$372$		0			0
$373$	10.5778	−	25.5370i	0.547697	−	1.32226i	−0.371491	−	0.928437i	$-0.621153\pi$
$373$	10.5778	−	25.5370i	0.547697	−	1.32226i	0.919187	−	0.393820i	$-0.128847\pi$
$374$	14.3395	−	12.9779i	0.741477	−	0.671071i
$375$		0			0
$376$	5.79507	+	23.3473i	0.298858	+	1.20405i
$377$	13.0979	+	13.0979i	0.674575	+	0.674575i
$378$		0			0
$379$	11.2755	+	4.67048i	0.579185	+	0.239906i	0.652990	−	0.757366i	$-0.273514\pi$
$379$	11.2755	+	4.67048i	0.579185	+	0.239906i	−0.0738049	+	0.997273i	$0.523514\pi$
$380$	9.48772	+	11.5945i	0.486710	+	0.594788i
$381$		0			0
$382$	9.67214	−	20.4123i	0.494870	−	1.04438i
$383$	14.2648			0.728897			0.364448	−	0.931224i	$-0.381258\pi$
$383$	14.2648			0.728897			0.364448	+	0.931224i	$0.381258\pi$
$384$		0			0
$385$	2.49310			0.127060
$386$	−0.248966	+	0.525423i	−0.0126720	+	0.0267433i
$387$		0			0
$388$	4.19144	+	5.12218i	0.212788	+	0.260039i
$389$	−16.9675	−	7.02815i	−0.860284	−	0.356341i	−0.0914656	−	0.995808i	$-0.529155\pi$
$389$	−16.9675	−	7.02815i	−0.860284	−	0.356341i	−0.768819	+	0.639467i	$0.779155\pi$
$390$		0			0
$391$	−3.60029	−	3.60029i	−0.182074	−	0.182074i
$392$	−4.29613	−	17.3083i	−0.216987	−	0.874203i
$393$		0			0
$394$	−4.65013	+	4.20859i	−0.234270	+	0.212026i
$395$	−0.386937	+	0.934148i	−0.0194689	+	0.0470021i
$396$		0			0
$397$	12.7413	−	5.27761i	0.639466	−	0.264875i	−0.0393030	−	0.999227i	$-0.512514\pi$
$397$	12.7413	−	5.27761i	0.639466	−	0.264875i	0.678769	+	0.734352i	$0.262514\pi$
$398$	16.3062	−	5.82131i	0.817354	−	0.291796i
$399$		0			0
$400$	6.55052	−	4.34991i	0.327526	−	0.217495i
$401$		−	20.6525i		−	1.03134i	−0.856788	−	0.515669i	$-0.827543\pi$
$401$		−	20.6525i		−	1.03134i	0.856788	−	0.515669i	$-0.172457\pi$
$402$		0			0
$403$	−36.1196	+	14.9612i	−1.79924	+	0.745271i
$404$	−1.62074	−	5.37047i	−0.0806349	−	0.267191i
$405$		0			0
$406$	3.49620	+	3.86300i	0.173514	+	0.191718i
$407$	1.06486	−	1.06486i	0.0527831	−	0.0527831i
$408$		0			0
$409$	6.38072	+	6.38072i	0.315506	+	0.315506i	0.847038	−	0.531532i	$-0.178383\pi$
$409$	6.38072	+	6.38072i	0.315506	+	0.315506i	−0.531532	+	0.847038i	$0.678383\pi$
$410$	1.15332	−	23.1392i	0.0569584	−	1.14276i
$411$		0			0
$412$	3.58813	−	35.9052i	0.176775	−	1.76892i
$413$	−0.663645	−	1.60218i	−0.0326558	−	0.0788382i
$414$		0			0
$415$	6.28927			0.308728
$416$	−22.9776	−	5.84285i	−1.12657	−	0.286469i
$417$		0			0
$418$	9.43630	+	4.47128i	0.461544	+	0.218698i
$419$	8.46204	+	20.4292i	0.413398	+	0.998030i	0.984219	+	0.176956i	$0.0566250\pi$
$419$	8.46204	+	20.4292i	0.413398	+	0.998030i	−0.570821	+	0.821075i	$0.693375\pi$
$420$		0			0
$421$	−28.2742	−	11.7116i	−1.37800	−	0.570786i	−0.434054	−	0.900887i	$-0.642917\pi$
$421$	−28.2742	−	11.7116i	−1.37800	−	0.570786i	−0.943946	+	0.330100i	$0.892917\pi$
$422$	0.344052	−	6.90277i	0.0167482	−	0.336021i
$423$		0			0
$424$	−1.21852	+	8.09507i	−0.0591765	+	0.393132i
$425$	−11.0717	+	11.0717i	−0.537057	+	0.537057i
$426$		0			0
$427$	−3.92156	+	9.46748i	−0.189777	+	0.458163i
$428$	−15.8744	+	4.79071i	−0.767319	+	0.231568i
$429$		0			0
$430$	4.81367	+	13.4837i	0.232136	+	0.650239i
$431$		−	8.30038i		−	0.399815i	−0.979815	−	0.199908i	$-0.935936\pi$
$431$		−	8.30038i		−	0.399815i	0.979815	−	0.199908i	$-0.0640642\pi$
$432$		0			0
$433$		−	29.4261i		−	1.41413i	−0.707150	−	0.707063i	$-0.750020\pi$
$433$		−	29.4261i		−	1.41413i	0.707150	−	0.707063i	$-0.249980\pi$
$434$	−10.3566	+	3.69731i	−0.497133	+	0.177477i
$435$		0			0
$436$	−20.7431	−	11.1255i	−0.993412	−	0.532815i
$437$	1.05200	−	2.53974i	0.0503238	−	0.121492i
$438$		0			0
$439$	20.3138	−	20.3138i	0.969524	−	0.969524i	−0.0300252	−	0.999549i	$-0.509559\pi$
$439$	20.3138	−	20.3138i	0.969524	−	0.969524i	0.999549	+	0.0300252i	$0.00955876\pi$
$440$	−4.36441	+	7.24632i	−0.208065	+	0.345455i
$441$		0			0
$442$	47.1518	+	2.35017i	2.24278	+	0.111786i
$443$	−18.1169	−	7.50428i	−0.860762	−	0.356539i	−0.0917565	−	0.995781i	$-0.529248\pi$
$443$	−18.1169	−	7.50428i	−0.860762	−	0.356539i	−0.769005	+	0.639242i	$0.779248\pi$
$444$		0			0
$445$	−4.63328	−	11.1857i	−0.219638	−	0.530254i
$446$	4.88803	−	10.3158i	0.231455	−	0.488468i
$447$		0			0
$448$	−6.37330	−	1.96318i	−0.301110	−	0.0927514i
$449$	8.20853			0.387384			0.193692	−	0.981062i	$-0.437954\pi$
$449$	8.20853			0.387384			0.193692	+	0.981062i	$0.437954\pi$
$450$		0			0
$451$	−6.17948	−	14.9186i	−0.290981	−	0.702489i
$452$	1.63634	−	1.33901i	0.0769671	−	0.0629815i
$453$		0			0
$454$	−3.66634	−	0.182740i	−0.172070	−	0.00857643i
$455$	4.30328	+	4.30328i	0.201741	+	0.201741i
$456$		0			0
$457$	−12.2056	+	12.2056i	−0.570953	+	0.570953i	−0.932395	−	0.361442i	$-0.882285\pi$
$457$	−12.2056	+	12.2056i	−0.570953	+	0.570953i	0.361442	+	0.932395i	$0.382285\pi$
$458$	−10.7388	+	9.71909i	−0.501790	+	0.454143i
$459$		0			0
$460$	1.96252	+	1.05259i	0.0915029	+	0.0490775i
$461$	28.6007	−	11.8468i	1.33207	−	0.551761i	0.400824	−	0.916155i	$-0.368724\pi$
$461$	28.6007	−	11.8468i	1.33207	−	0.551761i	0.931245	+	0.364394i	$0.118724\pi$
$462$		0			0
$463$			22.9354i			1.06590i	0.846148	+	0.532948i	$0.178916\pi$
$463$			22.9354i			1.06590i	−0.846148	+	0.532948i	$0.821084\pi$
$464$	−17.3484	+	3.39933i	−0.805380	+	0.157810i
$465$		0			0
$466$	−3.99996	−	11.2044i	−0.185295	−	0.519032i
$467$	−20.6535	+	8.55495i	−0.955729	+	0.395876i	−0.805381	−	0.592757i	$-0.798039\pi$
$467$	−20.6535	+	8.55495i	−0.955729	+	0.395876i	−0.150348	+	0.988633i	$0.548039\pi$
$468$		0			0
$469$	3.79093	−	9.15210i	0.175049	−	0.422605i
$470$	14.0589	+	15.5339i	0.648489	+	0.716525i
$471$		0			0
$472$	5.81859	+	0.875849i	0.267822	+	0.0403142i
$473$	7.05612	+	7.05612i	0.324441	+	0.324441i
$474$		0			0
$475$	−7.81030	−	3.23513i	−0.358361	−	0.148438i
$476$	13.2135	+	1.32047i	0.605639	+	0.0605237i
$477$		0			0
$478$	2.64749	+	1.25448i	0.121093	+	0.0573787i
$479$	41.8313			1.91132			0.955661	−	0.294468i	$-0.0951424\pi$
$479$	41.8313			1.91132			0.955661	+	0.294468i	$0.0951424\pi$
$480$		0			0
$481$	3.67604			0.167613
$482$	6.51820	+	3.08858i	0.296896	+	0.140681i
$483$		0			0
$484$	1.60136	−	16.0243i	0.0727892	−	0.728376i
$485$	5.32559	+	2.20593i	0.241822	+	0.100166i
$486$		0			0
$487$	4.02796	+	4.02796i	0.182524	+	0.182524i	0.792455	−	0.609931i	$-0.208803\pi$
$487$	4.02796	+	4.02796i	0.182524	+	0.182524i	−0.609931	+	0.792455i	$0.708803\pi$
$488$	−20.6526	−	27.9719i	−0.934900	−	1.26623i
$489$		0			0
$490$	−10.4225	−	11.5159i	−0.470839	−	0.520236i
$491$	−15.7614	+	38.0514i	−0.711301	+	1.71723i	−0.0145778	+	0.999894i	$0.504640\pi$
$491$	−15.7614	+	38.0514i	−0.711301	+	1.71723i	−0.696724	+	0.717340i	$0.745360\pi$
$492$		0			0
$493$	32.5225	−	13.4712i	1.46474	−	0.606714i
$494$	8.56997	+	24.0055i	0.385581	+	1.08006i
$495$		0			0
$496$	7.38377	−	36.5744i	0.331541	−	1.64224i
$497$			10.7273i			0.481184i
$498$		0			0
$499$	7.53276	−	3.12017i	0.337213	−	0.139678i	−0.207650	−	0.978203i	$-0.566582\pi$
$499$	7.53276	−	3.12017i	0.337213	−	0.139678i	0.544863	+	0.838525i	$0.316582\pi$
$500$	11.4701	−	21.3856i	0.512959	−	0.956391i
$501$		0			0
$502$	17.7891	−	16.0999i	0.793964	−	0.718575i
$503$	−10.0612	+	10.0612i	−0.448607	+	0.448607i	−0.894891	−	0.446284i	$-0.852747\pi$
$503$	−10.0612	+	10.0612i	−0.448607	+	0.448607i	0.446284	+	0.894891i	$0.352747\pi$
$504$		0			0
$505$	−3.45474	−	3.45474i	−0.153734	−	0.153734i
$506$	1.55025	+	0.0772687i	0.0689171	+	0.00343501i
$507$		0			0
$508$	10.0533	+	12.2857i	0.446042	+	0.545090i
$509$	−5.89292	−	14.2268i	−0.261199	−	0.630590i	0.737814	−	0.675004i	$-0.235858\pi$
$509$	−5.89292	−	14.2268i	−0.261199	−	0.630590i	−0.999013	+	0.0444138i	$0.985858\pi$
$510$		0			0
$511$	−1.94578			−0.0860765
$512$	16.8631	−	15.0876i	0.745252	−	0.666783i
$513$		0			0
$514$	7.74640	−	16.3482i	0.341679	−	0.721087i
$515$	−12.0267	−	29.0350i	−0.529958	−	1.27943i
$516$		0			0
$517$	13.4912	+	5.58824i	0.593342	+	0.245770i
$518$	1.03272	+	0.0514733i	0.0453749	+	0.00226161i
$519$		0			0
$520$	−20.0410	+	4.97440i	−0.878854	+	0.218142i
$521$	−11.9481	+	11.9481i	−0.523456	+	0.523456i	−0.918613	−	0.395158i	$-0.870690\pi$
$521$	−11.9481	+	11.9481i	−0.523456	+	0.523456i	0.395158	+	0.918613i	$0.370690\pi$
$522$		0			0
$523$	−6.15336	+	14.8555i	−0.269068	+	0.649587i	−0.999440	−	0.0334625i	$-0.989347\pi$
$523$	−6.15336	+	14.8555i	−0.269068	+	0.649587i	0.730372	+	0.683049i	$0.239347\pi$
$524$	17.8042	−	33.1953i	0.777782	−	1.45014i
$525$		0			0
$526$	−9.54503	+	3.40758i	−0.416183	+	0.148577i
$527$			74.2983i			3.23649i
$528$		0			0
$529$			22.5914i			0.982233i
$530$	2.39716	+	6.71473i	0.104126	+	0.291669i
$531$		0			0
$532$	2.07144	+	6.86389i	0.0898082	+	0.297587i
$533$	15.0843	−	36.4168i	0.653375	−	1.57739i
$534$		0			0
$535$	−10.2118	+	10.2118i	−0.441494	+	0.441494i
$536$	19.9647	+	27.0401i	0.862342	+	1.16795i
$537$		0			0
$538$	−1.25372	+	25.1535i	−0.0540516	+	1.08444i
$539$	−10.0016	−	4.14279i	−0.430799	−	0.178443i
$540$		0			0
$541$	8.64537	+	20.8718i	0.371693	+	0.897347i	0.993464	+	0.114148i	$0.0364137\pi$
$541$	8.64537	+	20.8718i	0.371693	+	0.897347i	−0.621770	+	0.783200i	$0.713586\pi$
$542$	−8.18106	−	3.87650i	−0.351407	−	0.166510i
$543$		0			0
$544$	−26.9694	+	36.0940i	−1.15631	+	1.54752i
$545$	−20.5006			−0.878148
$546$		0			0
$547$	10.1653	+	24.5412i	0.434637	+	1.04931i	0.977774	+	0.209662i	$0.0672363\pi$
$547$	10.1653	+	24.5412i	0.434637	+	1.04931i	−0.543137	+	0.839644i	$0.682764\pi$
$548$	0.860458	+	0.0859886i	0.0367569	+	0.00367325i
$549$		0			0
$550$	0.237619	−	4.76738i	0.0101321	−	0.203282i
$551$	13.4393	+	13.4393i	0.572532	+	0.572532i
$552$		0			0
$553$	−0.342155	+	0.342155i	−0.0145499	+	0.0145499i
$554$	4.97887	+	5.50122i	0.211532	+	0.233725i
$555$		0			0
$556$	−33.6327	+	10.1499i	−1.42634	+	0.430453i
$557$	−40.0425	+	16.5861i	−1.69666	+	0.702778i	−0.999894	−	0.0145256i	$-0.995376\pi$
$557$	−40.0425	+	16.5861i	−1.69666	+	0.702778i	−0.696761	+	0.717303i	$0.745376\pi$
$558$		0			0
$559$			24.3588i			1.03027i
$560$	−5.69978	+	1.11684i	−0.240860	+	0.0471952i
$561$		0			0
$562$	17.0037	−	6.07034i	0.717259	−	0.256062i
$563$	18.6724	−	7.73435i	0.786947	−	0.325964i	0.0472316	−	0.998884i	$-0.484960\pi$
$563$	18.6724	−	7.73435i	0.786947	−	0.325964i	0.739715	+	0.672920i	$0.234960\pi$
$564$		0			0
$565$	0.704711	−	1.70132i	0.0296474	−	0.0715752i
$566$	−8.98215	+	8.12927i	−0.377548	+	0.341699i
$567$		0			0
$568$	−31.1793	−	18.7791i	−1.30825	−	0.787952i
$569$	−8.77986	−	8.77986i	−0.368071	−	0.368071i	0.498702	−	0.866773i	$-0.333810\pi$
$569$	−8.77986	−	8.77986i	−0.368071	−	0.368071i	−0.866773	+	0.498702i	$0.833810\pi$
$570$		0			0
$571$	−23.2136	−	9.61539i	−0.971459	−	0.402392i	−0.160204	−	0.987084i	$-0.551215\pi$
$571$	−23.2136	−	9.61539i	−0.971459	−	0.402392i	−0.811255	+	0.584692i	$0.801215\pi$
$572$	−11.1383	+	9.11439i	−0.465716	+	0.381092i
$573$		0			0
$574$	4.74758	−	10.0194i	0.198160	−	0.418202i
$575$	−1.25663			−0.0524052
$576$		0			0
$577$	32.9671			1.37244			0.686220	−	0.727394i	$-0.259269\pi$
$577$	32.9671			1.37244			0.686220	+	0.727394i	$0.259269\pi$
$578$	28.1235	−	59.3524i	1.16978	−	2.46873i
$579$		0			0
$580$	−11.9159	+	9.75065i	−0.494779	+	0.404874i
$581$	2.78069	+	1.15180i	0.115363	+	0.0477848i
$582$		0			0
$583$	3.51388	+	3.51388i	0.145530	+	0.145530i
$584$	3.40627	−	5.65552i	0.140953	−	0.234027i
$585$		0			0
$586$	−1.25533	+	1.13614i	−0.0518574	+	0.0469334i
$587$	−6.05934	+	14.6285i	−0.250096	+	0.603785i	−0.998211	−	0.0597837i	$-0.980959\pi$
$587$	−6.05934	+	14.6285i	−0.250096	+	0.603785i	0.748115	+	0.663569i	$0.230959\pi$
$588$		0			0
$589$	−37.0610	+	15.3512i	−1.52707	+	0.632533i
$590$	4.82642	−	1.72303i	0.198701	−	0.0709362i
$591$		0			0
$592$	−1.95747	+	2.91153i	−0.0804516	+	0.119663i
$593$			21.5942i			0.886767i	0.896332	+	0.443384i	$0.146222\pi$
$593$			21.5942i			0.886767i	−0.896332	+	0.443384i	$0.853778\pi$
$594$		0			0
$595$	10.6852	−	4.42595i	0.438050	−	0.181446i
$596$	10.7305	−	3.23833i	0.439538	−	0.132647i
$597$		0			0
$598$	2.54248	+	2.80922i	0.103970	+	0.114877i
$599$	16.6522	−	16.6522i	0.680392	−	0.680392i	−0.279696	−	0.960089i	$-0.590234\pi$
$599$	16.6522	−	16.6522i	0.680392	−	0.680392i	0.960089	+	0.279696i	$0.0902338\pi$
$600$		0			0
$601$	17.8090	+	17.8090i	0.726445	+	0.726445i	0.969910	−	0.243465i	$-0.0782840\pi$
$601$	17.8090	+	17.8090i	0.726445	+	0.726445i	−0.243465	+	0.969910i	$0.578284\pi$
$602$	−0.341080	+	6.84313i	−0.0139014	+	0.278905i
$603$		0			0
$604$	−28.8152	−	2.87960i	−1.17247	−	0.117169i
$605$	−5.36743	−	12.9581i	−0.218217	−	0.526823i
$606$		0			0
$607$	−2.08575			−0.0846579			−0.0423289	−	0.999104i	$-0.513478\pi$
$607$	−2.08575			−0.0846579			−0.0423289	+	0.999104i	$0.513478\pi$
$608$	−23.5765	−	5.99513i	−0.956152	−	0.243135i
$609$		0			0
$610$	−27.3661	−	12.9671i	−1.10802	−	0.525023i
$611$	13.6411	+	32.9325i	0.551859	+	1.33231i
$612$		0			0
$613$	23.3947	+	9.69039i	0.944902	+	0.391391i	0.801312	−	0.598246i	$-0.204135\pi$
$613$	23.3947	+	9.69039i	0.944902	+	0.391391i	0.143590	+	0.989637i	$0.454135\pi$
$614$	−0.764567	+	15.3396i	−0.0308554	+	0.619056i
$615$		0			0
$616$	−3.25672	+	2.40455i	−0.131217	+	0.0968822i
$617$	3.94760	−	3.94760i	0.158924	−	0.158924i	−0.623166	−	0.782090i	$-0.714154\pi$
$617$	3.94760	−	3.94760i	0.158924	−	0.158924i	0.782090	+	0.623166i	$0.214154\pi$
$618$		0			0
$619$	−13.7586	+	33.2161i	−0.553004	+	1.33507i	0.362208	+	0.932097i	$0.382023\pi$
$619$	−13.7586	+	33.2161i	−0.553004	+	1.33507i	−0.915212	+	0.402972i	$0.867977\pi$
$620$	−9.38896	−	31.1111i	−0.377070	−	1.24945i
$621$		0			0
$622$	7.52536	+	21.0794i	0.301740	+	0.845208i
$623$		−	5.79410i		−	0.232136i
$624$		0			0
$625$		−	11.3065i		−	0.452259i
$626$	−28.5344	+	10.1868i	−1.14046	+	0.407146i
$627$		0			0
$628$	11.4642	−	21.3745i	0.457471	−	0.852936i
$629$	2.67345	−	6.45428i	0.106598	−	0.257349i
$630$		0			0
$631$	−28.2524	+	28.2524i	−1.12471	+	1.12471i	−0.133687	+	0.991024i	$0.542682\pi$
$631$	−28.2524	+	28.2524i	−1.12471	+	1.12471i	−0.991024	+	0.133687i	$0.957318\pi$
$632$	−0.395516	−	1.59346i	−0.0157328	−	0.0633846i
$633$		0			0
$634$	−9.26093	−	0.461590i	−0.367799	−	0.0183321i
$635$	12.7736	+	5.29099i	0.506904	+	0.209966i
$636$		0			0
$637$	−10.1127	−	24.4142i	−0.400680	−	0.967326i
$638$	−4.59520	+	9.69781i	−0.181926	+	0.383940i
$639$		0			0
$640$	6.73183	−	18.5218i	0.266099	−	0.732139i
$641$	−9.34587			−0.369140			−0.184570	−	0.982819i	$-0.559089\pi$
$641$	−9.34587			−0.369140			−0.184570	+	0.982819i	$0.559089\pi$
$642$		0			0
$643$	−14.3013	−	34.5265i	−0.563989	−	1.36159i	−0.906551	−	0.422096i	$-0.861295\pi$
$643$	−14.3013	−	34.5265i	−0.563989	−	1.36159i	0.342562	−	0.939495i	$-0.388705\pi$
$644$	0.674925	+	0.824798i	0.0265958	+	0.0325016i
$645$		0			0
$646$	48.3807	+	2.41142i	1.90351	+	0.0948762i
$647$	−29.8159	−	29.8159i	−1.17218	−	1.17218i	−0.981688	−	0.190496i	$-0.938990\pi$
$647$	−29.8159	−	29.8159i	−1.17218	−	1.17218i	−0.190496	−	0.981688i	$-0.561010\pi$
$648$		0			0
$649$	2.52571	−	2.52571i	0.0991428	−	0.0991428i
$650$	8.63900	−	7.81870i	0.338849	−	0.306675i
$651$		0			0
$652$	2.42548	−	4.52222i	0.0949893	−	0.177104i
$653$	30.3070	−	12.5536i	1.18600	−	0.491259i	0.299552	−	0.954080i	$-0.403163\pi$
$653$	30.3070	−	12.5536i	1.18600	−	0.491259i	0.886452	+	0.462821i	$0.153163\pi$
$654$		0			0
$655$		−	32.8072i		−	1.28188i
$656$	20.8108	+	31.3389i	0.812524	+	1.22358i
$657$		0			0
$658$	3.37107	+	9.44277i	0.131418	+	0.368117i
$659$	−23.8281	+	9.86994i	−0.928212	+	0.384478i	−0.795000	−	0.606609i	$-0.792529\pi$
$659$	−23.8281	+	9.86994i	−0.928212	+	0.384478i	−0.133212	+	0.991088i	$0.542529\pi$
$660$		0			0
$661$	−1.40604	+	3.39448i	−0.0546886	+	0.132030i	−0.948862	−	0.315690i	$-0.897764\pi$
$661$	−1.40604	+	3.39448i	−0.0546886	+	0.132030i	0.894174	+	0.447720i	$0.147764\pi$
$662$	18.6698	+	20.6285i	0.725621	+	0.801750i
$663$		0			0
$664$	−8.21563	+	6.06589i	−0.318828	+	0.235402i
$665$	4.41544	+	4.41544i	0.171223	+	0.171223i
$666$		0			0
$667$	2.61013	+	1.08115i	0.101065	+	0.0418623i
$668$	1.92121	−	19.2248i	0.0743338	−	0.743832i
$669$		0			0
$670$	26.4545	+	12.5352i	1.02203	+	0.484276i
$671$	−21.1067			−0.814817
$672$		0			0
$673$	19.4796			0.750885			0.375442	−	0.926846i	$-0.377491\pi$
$673$	19.4796			0.750885			0.375442	+	0.926846i	$0.377491\pi$
$674$	−38.2321	−	18.1158i	−1.47264	−	0.697796i
$675$		0			0
$676$	−9.08649	−	0.908045i	−0.349480	−	0.0349248i
$677$	−19.1189	−	7.91933i	−0.734801	−	0.304364i	−0.0162777	−	0.999868i	$-0.505182\pi$
$677$	−19.1189	−	7.91933i	−0.734801	−	0.304364i	−0.718523	+	0.695503i	$0.755182\pi$
$678$		0			0
$679$	1.95063	+	1.95063i	0.0748583	+	0.0748583i
$680$	−5.84116	+	38.8050i	−0.223998	+	1.48810i
$681$		0			0
$682$	−15.1988	−	16.7934i	−0.581993	−	0.643052i
$683$	8.46056	−	20.4256i	0.323734	−	0.781564i	−0.675296	−	0.737547i	$-0.735984\pi$
$683$	8.46056	−	20.4256i	0.323734	−	0.781564i	0.999031	−	0.0440175i	$-0.0140157\pi$
$684$		0			0
$685$	0.695815	−	0.288216i	0.0265857	−	0.0110122i
$686$	−5.27366	−	14.7721i	−0.201349	−	0.564003i
$687$		0			0
$688$	−19.2928	−	12.9709i	−0.735531	−	0.494511i
$689$			12.1304i			0.462132i
$690$		0			0
$691$	−14.6182	+	6.05507i	−0.556104	+	0.230346i	−0.642993	−	0.765872i	$-0.722307\pi$
$691$	−14.6182	+	6.05507i	−0.556104	+	0.230346i	0.0868889	+	0.996218i	$0.472307\pi$
$692$	5.27800	+	2.83085i	0.200640	+	0.107613i
$693$		0			0
$694$	21.5391	−	19.4939i	0.817612	−	0.739978i
$695$	−21.6354	+	21.6354i	−0.820677	+	0.820677i
$696$		0			0
$697$	−52.9692	−	52.9692i	−2.00635	−	2.00635i
$698$	10.8328	+	0.539937i	0.410029	+	0.0204369i
$699$		0			0
$700$	2.53644	−	2.07555i	0.0958686	−	0.0784485i
$701$	9.53654	+	23.0232i	0.360190	+	0.869576i	0.995272	+	0.0971307i	$0.0309665\pi$
$701$	9.53654	+	23.0232i	0.360190	+	0.869576i	−0.635082	+	0.772445i	$0.719034\pi$
$702$		0			0
$703$	3.77186			0.142258
$704$	−1.28776	−	13.6752i	−0.0485342	−	0.515404i
$705$		0			0
$706$	−17.3612	+	36.6394i	−0.653396	+	1.37894i
$707$	−0.894763	−	2.16015i	−0.0336510	−	0.0812407i
$708$		0			0
$709$	−4.53151	−	1.87701i	−0.170184	−	0.0704927i	0.295965	−	0.955199i	$-0.404359\pi$
$709$	−4.53151	−	1.87701i	−0.170184	−	0.0704927i	−0.466149	+	0.884706i	$0.654359\pi$
$710$	−31.6612	−	1.57808i	−1.18822	−	0.0592242i
$711$		0			0
$712$	16.8408	+	10.1431i	0.631137	+	0.380129i
$713$	−4.21641	+	4.21641i	−0.157906	+	0.157906i
$714$		0			0
$715$	−4.79685	+	11.5806i	−0.179392	+	0.433091i
$716$	−25.5354	−	13.6959i	−0.954304	−	0.511840i
$717$		0			0
$718$	−26.3634	+	9.41176i	−0.983875	+	0.351244i
$719$		−	39.7315i		−	1.48173i	−0.671652	−	0.740867i	$-0.734415\pi$
$719$		−	39.7315i		−	1.48173i	0.671652	−	0.740867i	$-0.265585\pi$
$720$		0			0
$721$		−	15.0398i		−	0.560113i
$722$	−0.240845	−	0.674634i	−0.00896332	−	0.0251073i
$723$		0			0
$724$	45.2049	−	13.6423i	1.68003	−	0.507011i
$725$	3.32479	−	8.02675i	0.123480	−	0.298106i
$726$		0			0
$727$	−6.99691	+	6.99691i	−0.259501	+	0.259501i	−0.824851	−	0.565350i	$-0.808741\pi$
$727$	−6.99691	+	6.99691i	−0.259501	+	0.259501i	0.565350	+	0.824851i	$0.308741\pi$
$728$	−9.77177	−	1.47091i	−0.362166	−	0.0545154i
$729$		0			0
$730$	0.286243	−	5.74293i	0.0105943	−	0.212555i
$731$	42.7683	+	17.7152i	1.58184	+	0.655221i
$732$		0			0
$733$	1.40532	+	3.39275i	0.0519068	+	0.125314i	0.947706	−	0.319145i	$-0.103396\pi$
$733$	1.40532	+	3.39275i	0.0519068	+	0.125314i	−0.895799	+	0.444459i	$0.853396\pi$
$734$	14.9151	+	7.06736i	0.550527	+	0.260861i
$735$		0			0
$736$	−3.57883	+	0.517818i	−0.131917	+	0.0190870i
$737$	20.4037			0.751578
$738$		0			0
$739$	−8.11566	−	19.5929i	−0.298539	−	0.720738i	−0.999968	−	0.00799797i	$-0.997454\pi$
$739$	−8.11566	−	19.5929i	−0.298539	−	0.720738i	0.701429	−	0.712740i	$-0.252546\pi$
$740$	−0.303844	+	3.04046i	−0.0111695	+	0.111769i
$741$		0			0
$742$	−0.169854	+	3.40781i	−0.00623555	+	0.125105i
$743$	−5.67248	−	5.67248i	−0.208103	−	0.208103i	0.595358	−	0.803461i	$-0.297010\pi$
$743$	−5.67248	−	5.67248i	−0.208103	−	0.208103i	−0.803461	+	0.595358i	$0.797010\pi$
$744$		0			0
$745$	6.90277	−	6.90277i	0.252898	−	0.252898i
$746$	26.2308	+	28.9828i	0.960378	+	1.06114i
$747$		0			0
$748$	7.90227	+	26.1849i	0.288936	+	0.957413i
$749$	−6.38513	+	2.64481i	−0.233307	+	0.0966391i
$750$		0			0
$751$		−	14.2209i		−	0.518930i	−0.965753	−	0.259465i	$-0.916454\pi$
$751$		−	14.2209i		−	0.518930i	0.965753	−	0.259465i	$-0.0835462\pi$
$752$	−33.3472	−	6.73225i	−1.21605	−	0.245500i
$753$		0			0
$754$	−24.6708	+	8.80747i	−0.898456	+	0.320749i
$755$	−23.3016	+	9.65183i	−0.848031	+	0.351266i
$756$		0			0
$757$	−6.45206	+	15.5767i	−0.234504	+	0.566143i	−0.996697	−	0.0812065i	$-0.974123\pi$
$757$	−6.45206	+	15.5767i	−0.234504	+	0.566143i	0.762193	+	0.647350i	$0.224123\pi$
$758$	−12.7970	+	11.5819i	−0.464807	+	0.420672i
$759$		0			0
$760$	−20.5633	+	5.10405i	−0.745909	+	0.185143i
$761$	8.62429	+	8.62429i	0.312630	+	0.312630i	0.845928	−	0.533298i	$-0.179047\pi$
$761$	8.62429	+	8.62429i	0.312630	+	0.312630i	−0.533298	+	0.845928i	$0.679047\pi$
$762$		0			0
$763$	−9.06398	−	3.75442i	−0.328138	−	0.135919i
$764$	20.2298	+	24.7220i	0.731889	+	0.894411i
$765$		0			0
$766$	−8.63828	+	18.2304i	−0.312114	+	0.658692i
$767$	8.71912			0.314829
$768$		0			0
$769$	13.1949			0.475821			0.237911	−	0.971287i	$-0.423537\pi$
$769$	13.1949			0.475821			0.237911	+	0.971287i	$0.423537\pi$
$770$	−1.50974	+	3.18619i	−0.0544073	+	0.114822i
$771$		0			0
$772$	−0.520726	−	0.636358i	−0.0187413	−	0.0229030i
$773$	23.3275	+	9.66257i	0.839032	+	0.347538i	0.760472	−	0.649371i	$-0.224968\pi$
$773$	23.3275	+	9.66257i	0.839032	+	0.347538i	0.0785601	+	0.996909i	$0.474968\pi$
$774$		0			0
$775$	12.9664	+	12.9664i	0.465768	+	0.465768i
$776$	−9.08435	+	2.25484i	−0.326109	+	0.0809441i
$777$		0			0
$778$	19.2569	−	17.4284i	0.690394	−	0.624839i
$779$	15.4775	−	37.3660i	0.554539	−	1.33877i
$780$		0			0
$781$	−20.4130	+	8.45534i	−0.730434	+	0.302556i
$782$	6.78139	−	2.42096i	0.242502	−	0.0865733i
$783$		0			0
$784$	24.7217	+	4.99089i	0.882917	+	0.178246i
$785$		−	21.1247i		−	0.753971i
$786$		0			0
$787$	12.3210	−	5.10352i	0.439196	−	0.181921i	−0.152118	−	0.988362i	$-0.548609\pi$
$787$	12.3210	−	5.10352i	0.439196	−	0.181921i	0.591314	+	0.806442i	$0.298609\pi$
$788$	−2.56262	−	8.49146i	−0.0912895	−	0.302496i
$789$		0			0
$790$	−0.959527	−	1.06019i	−0.0341384	−	0.0377200i
$791$	0.623152	−	0.623152i	0.0221567	−	0.0221567i
$792$		0			0
$793$	−36.4318	−	36.4318i	−1.29373	−	1.29373i
$794$	−0.970901	+	19.4793i	−0.0344560	+	0.691295i
$795$		0			0
$796$	−2.43483	+	24.3645i	−0.0863003	+	0.863576i
$797$	0.0303911	+	0.0733705i	0.00107651	+	0.00259892i	0.924417	−	0.381384i	$-0.124552\pi$
$797$	0.0303911	+	0.0733705i	0.00107651	+	0.00259892i	−0.923340	+	0.383983i	$0.874552\pi$
$798$		0			0
$799$	67.7425			2.39656
$800$	1.59241	+	11.0057i	0.0563002	+	0.389112i
$801$		0			0
$802$	26.3940	+	12.5065i	0.932004	+	0.441620i
$803$	−1.53369	−	3.70265i	−0.0541226	−	0.130664i
$804$		0			0
$805$	0.857551	+	0.355209i	0.0302247	+	0.0125195i
$806$	2.75236	−	55.2209i	0.0969476	−	1.94507i
$807$		0			0
$808$	7.84494	+	1.18087i	0.275984	+	0.0415428i
$809$	6.49942	−	6.49942i	0.228507	−	0.228507i	−0.583562	−	0.812069i	$-0.698341\pi$
$809$	6.49942	−	6.49942i	0.228507	−	0.228507i	0.812069	+	0.583562i	$0.198341\pi$
$810$		0			0
$811$	6.45066	−	15.5733i	0.226513	−	0.546852i	−0.769235	−	0.638966i	$-0.779362\pi$
$811$	6.45066	−	15.5733i	0.226513	−	0.546852i	0.995748	+	0.0921142i	$0.0293625\pi$
$812$	−7.05411	+	2.12884i	−0.247551	+	0.0747078i
$813$		0			0
$814$	0.716048	+	2.00573i	0.0250975	+	0.0703009i
$815$		−	4.46935i		−	0.156555i
$816$		0			0
$817$			24.9936i			0.874417i
$818$	−12.0185	+	4.29062i	−0.420218	+	0.150018i
$819$		0			0
$820$	28.8736	+	15.4863i	1.00831	+	0.540805i
$821$	20.6508	−	49.8554i	0.720717	−	1.73996i	0.0494163	−	0.998778i	$-0.484264\pi$
$821$	20.6508	−	49.8554i	0.720717	−	1.73996i	0.671300	−	0.741185i	$-0.265736\pi$
$822$		0			0
$823$	−22.2511	+	22.2511i	−0.775623	+	0.775623i	−0.979083	−	0.203460i	$-0.934781\pi$
$823$	−22.2511	+	22.2511i	−0.775623	+	0.775623i	0.203460	+	0.979083i	$0.434781\pi$
$824$	43.7140	+	26.3286i	1.52285	+	0.917201i
$825$		0			0
$826$	2.44947	+	0.122088i	0.0852280	+	0.00424799i
$827$	34.4764	+	14.2806i	1.19886	+	0.496584i	0.890631	−	0.454728i	$-0.150263\pi$
$827$	34.4764	+	14.2806i	1.19886	+	0.496584i	0.308230	+	0.951312i	$0.400263\pi$
$828$		0			0
$829$	−0.158799	−	0.383374i	−0.00551531	−	0.0133151i	0.921098	−	0.389331i	$-0.127294\pi$
$829$	−0.158799	−	0.383374i	−0.00551531	−	0.0133151i	−0.926613	+	0.376016i	$0.877294\pi$
$830$	−3.80857	+	8.03770i	−0.132198	+	0.278993i
$831$		0			0
$832$	21.3816	−	25.8272i	0.741275	−	0.895395i
$833$	−50.2203			−1.74003
$834$		0			0
$835$	−6.43949	−	15.5463i	−0.222848	−	0.538002i
$836$	−11.4286	+	9.35194i	−0.395267	+	0.323444i
$837$		0			0
$838$	−31.2329	−	1.55673i	−1.07892	−	0.0537763i
$839$	−19.2723	−	19.2723i	−0.665353	−	0.665353i	0.291284	−	0.956637i	$-0.405918\pi$
$839$	−19.2723	−	19.2723i	−0.665353	−	0.665353i	−0.956637	+	0.291284i	$0.905918\pi$
$840$		0			0
$841$	6.69439	−	6.69439i	0.230841	−	0.230841i
$842$	32.0893	−	29.0424i	1.10587	−	1.00087i
$843$		0			0
$844$	8.61340	+	4.61979i	0.296486	+	0.159020i
$845$	−7.34785	+	3.04358i	−0.252774	+	0.104702i
$846$		0			0
$847$		−	6.71219i		−	0.230634i
$848$	−9.60762	−	6.45938i	−0.329927	−	0.221816i
$849$		0			0
$850$	−7.44501	−	20.8543i	−0.255362	−	0.715298i
$851$	0.517996	−	0.214561i	0.0177567	−	0.00735505i
$852$		0			0
$853$	11.9556	−	28.8634i	0.409352	−	0.988263i	−0.575957	−	0.817480i	$-0.695370\pi$
$853$	11.9556	−	28.8634i	0.409352	−	0.988263i	0.985309	−	0.170783i	$-0.0546297\pi$
$854$	−9.72469	−	10.7449i	−0.332772	−	0.367685i
$855$		0			0
$856$	3.49049	−	23.1886i	0.119303	−	0.792572i
$857$	7.59541	+	7.59541i	0.259454	+	0.259454i	0.824832	−	0.565378i	$-0.191270\pi$
$857$	7.59541	+	7.59541i	0.259454	+	0.259454i	−0.565378	+	0.824832i	$0.691270\pi$
$858$		0			0
$859$	31.8605	+	13.1970i	1.08707	+	0.450277i	0.852983	−	0.521939i	$-0.174791\pi$
$859$	31.8605	+	13.1970i	1.08707	+	0.450277i	0.234083	+	0.972217i	$0.424791\pi$
$860$	−20.1471	−	2.01337i	−0.687011	−	0.0686555i
$861$		0			0
$862$	10.6079	+	5.02643i	0.361306	+	0.171201i
$863$	10.7216			0.364968			0.182484	−	0.983209i	$-0.441586\pi$
$863$	10.7216			0.364968			0.182484	+	0.983209i	$0.441586\pi$
$864$		0			0
$865$	5.21630			0.177360
$866$	37.6066	+	17.8194i	1.27792	+	0.605530i
$867$		0			0
$868$	1.54644	−	15.4747i	0.0524898	−	0.525246i
$869$	−0.920779	−	0.381399i	−0.0312353	−	0.0129381i
$870$		0			0
$871$	35.2182	+	35.2182i	1.19332	+	1.19332i
$872$	26.7797	−	19.7724i	0.906876	−	0.669579i
$873$		0			0
$874$	2.60874	+	2.88244i	0.0882420	+	0.0974999i
$875$	3.87071	−	9.34473i	0.130854	−	0.315910i
$876$		0			0
$877$	8.29027	−	3.43394i	0.279943	−	0.115956i	−0.238295	−	0.971193i	$-0.576588\pi$
$877$	8.29027	−	3.43394i	0.279943	−	0.115956i	0.518237	+	0.855237i	$0.326588\pi$
$878$	13.6597	+	38.2624i	0.460992	+	1.29129i
$879$		0			0
$880$	−6.61787	−	9.96585i	−0.223088	−	0.335949i
$881$			13.4623i			0.453557i	0.973946	+	0.226779i	$0.0728194\pi$
$881$			13.4623i			0.453557i	−0.973946	+	0.226779i	$0.927181\pi$
$882$		0			0
$883$	28.1854	−	11.6748i	0.948513	−	0.392887i	0.145841	−	0.989308i	$-0.453411\pi$
$883$	28.1854	−	11.6748i	0.948513	−	0.392887i	0.802672	+	0.596421i	$0.203411\pi$
$884$	−31.5571	+	58.8369i	−1.06138	+	1.97890i
$885$		0			0
$886$	20.5615	−	18.6091i	0.690777	−	0.625186i
$887$	−12.7798	+	12.7798i	−0.429102	+	0.429102i	−0.888322	−	0.459220i	$-0.848129\pi$
$887$	−12.7798	+	12.7798i	−0.429102	+	0.429102i	0.459220	+	0.888322i	$0.348129\pi$
$888$		0			0
$889$	4.67864	+	4.67864i	0.156917	+	0.156917i
$890$	17.1011	+	0.852366i	0.573231	+	0.0285714i
$891$		0			0
$892$	10.2236	+	12.4938i	0.342311	+	0.418324i
$893$	13.9966	+	33.7908i	0.468379	+	1.13077i
$894$		0			0
$895$	−25.2369			−0.843578
$896$	6.36841	−	6.95626i	0.212754	−	0.232392i
$897$		0			0
$898$	−4.97081	+	10.4905i	−0.165878	+	0.350073i
$899$	−15.7766	−	38.0880i	−0.526179	−	1.27031i
$900$		0			0
$901$	21.2982	+	8.82201i	0.709547	+	0.293904i
$902$	22.8081	+	1.13682i	0.759426	+	0.0378518i
$903$		0			0
$904$	0.720336	+	2.90211i	0.0239580	+	0.0965226i
$905$	29.0796	−	29.0796i	0.966639	−	0.966639i
$906$		0			0
$907$	−20.4543	+	49.3811i	−0.679175	+	1.63967i	0.0863491	+	0.996265i	$0.472480\pi$
$907$	−20.4543	+	49.3811i	−0.679175	+	1.63967i	−0.765524	+	0.643408i	$0.777520\pi$
$908$	2.45376	−	4.57493i	0.0814308	−	0.151824i
$909$		0			0
$910$	−8.10552	+	2.89367i	−0.268695	+	0.0959243i
$911$		−	19.5928i		−	0.649138i	−0.945862	−	0.324569i	$-0.894781\pi$
$911$		−	19.5928i		−	0.649138i	0.945862	−	0.324569i	$-0.105219\pi$
$912$		0			0
$913$			6.19927i			0.205166i
$914$	−8.20746	−	22.9900i	−0.271479	−	0.760443i
$915$		0			0
$916$	−5.91798	−	19.6097i	−0.195535	−	0.647924i
$917$	6.00823	−	14.5052i	0.198409	−	0.479003i
$918$		0			0
$919$	33.9389	−	33.9389i	1.11954	−	1.11954i	0.127732	−	0.991809i	$-0.459230\pi$
$919$	33.9389	−	33.9389i	1.11954	−	1.11954i	0.991809	−	0.127732i	$-0.0407696\pi$
$920$	−2.53365	+	1.87069i	−0.0835321	+	0.0616747i
$921$		0			0
$922$	−2.17941	+	43.7258i	−0.0717751	+	1.44003i
$923$	−49.8288	−	20.6398i	−1.64014	−	0.679366i
$924$		0			0
$925$	−0.659825	−	1.59296i	−0.0216949	−	0.0523761i
$926$	−29.3114	−	13.8889i	−0.963233	−	0.456417i
$927$		0			0
$928$	6.16128	−	24.2298i	0.202254	−	0.795383i
$929$	42.5730			1.39678			0.698388	−	0.715720i	$-0.253901\pi$
$929$	42.5730			1.39678			0.698388	+	0.715720i	$0.253901\pi$
$930$		0			0
$931$	−10.3763	−	25.0505i	−0.340069	−	0.820998i
$932$	16.7414	+	1.67303i	0.548384	+	0.0548020i
$933$		0			0
$934$	1.57382	−	31.5758i	0.0514970	−	1.03319i
$935$	16.8443	+	16.8443i	0.550868	+	0.550868i
$936$		0			0
$937$	−13.0124	+	13.0124i	−0.425098	+	0.425098i	−0.886954	−	0.461857i	$-0.847183\pi$
$937$	−13.0124	+	13.0124i	−0.425098	+	0.425098i	0.461857	+	0.886954i	$0.347183\pi$
$938$	9.40075	+	10.3870i	0.306945	+	0.339148i
$939$		0			0
$940$	−28.3660	+	8.56050i	−0.925196	+	0.279213i
$941$	−12.9144	+	5.34932i	−0.420998	+	0.174383i	−0.583117	−	0.812388i	$-0.698167\pi$
$941$	−12.9144	+	5.34932i	−0.420998	+	0.174383i	0.162119	+	0.986771i	$0.448167\pi$
$942$		0			0
$943$		−	6.01197i		−	0.195777i
$944$	−4.64288	+	6.90578i	−0.151113	+	0.224764i
$945$		0			0
$946$	−13.2907	+	4.74478i	−0.432118	+	0.154266i
$947$	−1.72532	+	0.714653i	−0.0560655	+	0.0232231i	−0.410540	−	0.911843i	$-0.634660\pi$
$947$	−1.72532	+	0.714653i	−0.0560655	+	0.0232231i	0.354474	+	0.935066i	$0.384660\pi$
$948$		0			0
$949$	3.74378	−	9.03829i	0.121528	−	0.293395i
$950$	8.86416	−	8.02249i	0.287591	−	0.260284i
$951$		0			0
$952$	−9.68922	+	16.0872i	−0.314029	+	0.521390i
$953$	−19.2732	−	19.2732i	−0.624321	−	0.624321i	0.322312	−	0.946633i	$-0.395540\pi$
$953$	−19.2732	−	19.2732i	−0.624321	−	0.624321i	−0.946633	+	0.322312i	$0.895540\pi$
$954$		0			0
$955$	25.7038	+	10.6468i	0.831754	+	0.344524i
$956$	−3.20646	+	2.62382i	−0.103704	+	0.0848605i
$957$		0			0
$958$	−25.3317	+	53.4605i	−0.818429	+	1.72723i
$959$	0.360426			0.0116388
$960$		0			0
$961$	56.0131			1.80687
$962$	−2.22609	+	4.69799i	−0.0717720	+	0.151469i
$963$		0			0
$964$	−7.89441	+	6.45993i	−0.254262	+	0.208060i
$965$	−0.661628	−	0.274055i	−0.0212986	−	0.00882215i
$966$		0			0
$967$	−39.5173	−	39.5173i	−1.27079	−	1.27079i	−0.945674	−	0.325118i	$-0.894596\pi$
$967$	−39.5173	−	39.5173i	−1.27079	−	1.27079i	−0.325118	−	0.945674i	$-0.605404\pi$
$968$	19.5093	+	11.7503i	0.627053	+	0.377669i
$969$		0			0
$970$	−6.04418	+	5.47027i	−0.194067	+	0.175640i
$971$	1.47350	−	3.55734i	0.0472868	−	0.114161i	−0.898471	−	0.439033i	$-0.855321\pi$
$971$	1.47350	−	3.55734i	0.0472868	−	0.114161i	0.945758	+	0.324872i	$0.105321\pi$
$972$		0			0
$973$	−13.5280	+	5.60347i	−0.433687	+	0.179639i
$974$	−7.58694	+	2.70854i	−0.243101	+	0.0867872i
$975$		0			0
$976$	48.2546	−	9.45525i	1.54459	−	0.302655i
$977$		−	11.1620i		−	0.357103i	−0.983931	−	0.178551i	$-0.942859\pi$
$977$		−	11.1620i		−	0.357103i	0.983931	−	0.178551i	$-0.0571410\pi$
$978$		0			0
$979$	11.0256	−	4.56697i	0.352381	−	0.145961i
$980$	21.0289	−	6.34626i	0.671743	−	0.202724i
$981$		0			0
$982$	−39.0851	−	43.1857i	−1.24726	−	1.37811i
$983$	14.2055	−	14.2055i	0.453085	−	0.453085i	−0.443292	−	0.896377i	$-0.646190\pi$
$983$	14.2055	−	14.2055i	0.453085	−	0.453085i	0.896377	+	0.443292i	$0.146190\pi$
$984$		0			0
$985$	−5.46242	−	5.46242i	−0.174047	−	0.174047i
$986$	−2.47825	+	49.7215i	−0.0789236	+	1.58346i
$987$		0			0
$988$	−35.8688	−	3.58449i	−1.14114	−	0.114038i
$989$	1.42176	+	3.43242i	0.0452092	+	0.109145i
$990$		0			0
$991$	−31.5264			−1.00147			−0.500734	−	0.865601i	$-0.666937\pi$
$991$	−31.5264			−1.00147			−0.500734	+	0.865601i	$0.666937\pi$
$992$	42.2708	+	31.5847i	1.34210	+	1.00282i
$993$		0			0
$994$	−13.7095	−	6.49608i	−0.434838	−	0.206043i
$995$	8.16104	+	19.7025i	0.258722	+	0.624611i
$996$		0			0
$997$	−25.5314	−	10.5755i	−0.808588	−	0.334928i	−0.0601976	−	0.998186i	$-0.519173\pi$
$997$	−25.5314	−	10.5755i	−0.808588	−	0.334928i	−0.748391	+	0.663258i	$0.769173\pi$
$998$	−0.574006	+	11.5164i	−0.0181698	+	0.364544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.37.4		32
3.2	odd	2		96.2.n.a.37.5	yes	32
4.3	odd	2		1152.2.v.c.1009.3		32
12.11	even	2		384.2.n.a.241.7		32
24.5	odd	2		768.2.n.a.481.6		32
24.11	even	2		768.2.n.b.481.2		32
32.13	even	8	inner	288.2.v.d.109.4		32
32.19	odd	8		1152.2.v.c.145.3		32
96.29	odd	8		768.2.n.a.289.6		32
96.35	even	8		768.2.n.b.289.2		32
96.77	odd	8		96.2.n.a.13.5	✓	32
96.83	even	8		384.2.n.a.145.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.5	✓	32	96.77	odd	8
96.2.n.a.37.5	yes	32	3.2	odd	2
288.2.v.d.37.4		32	1.1	even	1	trivial
288.2.v.d.109.4		32	32.13	even	8	inner
384.2.n.a.145.7		32	96.83	even	8
384.2.n.a.241.7		32	12.11	even	2
768.2.n.a.289.6		32	96.29	odd	8
768.2.n.a.481.6		32	24.5	odd	2
768.2.n.b.289.2		32	96.35	even	8
768.2.n.b.481.2		32	24.11	even	2
1152.2.v.c.145.3		32	32.19	odd	8
1152.2.v.c.1009.3		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.605567 + 1.27800i) q^{2} +(-1.26658 - 1.54783i) q^{4} +(-1.60930 - 0.666593i) q^{5} +(-0.589445 - 0.589445i) q^{7} +(2.74513 - 0.681373i) q^{8} +O(q^{10})\)	\(q+(-0.605567 + 1.27800i) q^{2} +(-1.26658 - 1.54783i) q^{4} +(-1.60930 - 0.666593i) q^{5} +(-0.589445 - 0.589445i) q^{7} +(2.74513 - 0.681373i) q^{8} +(1.82644 - 1.65302i) q^{10} +(0.657053 - 1.58627i) q^{11} +(3.87213 - 1.60389i) q^{13} +(1.11026 - 0.396364i) q^{14} +(-0.791564 + 3.92090i) q^{16} -7.96502i q^{17} +(3.97306 - 1.64569i) q^{19} +(1.00653 + 3.33521i) q^{20} +(1.62936 + 1.80031i) q^{22} +(0.452012 - 0.452012i) q^{23} +(-1.39004 - 1.39004i) q^{25} +(-0.295061 + 5.91986i) q^{26} +(-0.165784 + 1.65894i) q^{28} +(1.69130 + 4.08316i) q^{29} -9.32808 q^{31} +(-4.53157 - 3.38598i) q^{32} +(10.1793 + 4.82335i) q^{34} +(0.555673 + 1.34151i) q^{35} +(0.810329 + 0.335649i) q^{37} +(-0.302752 + 6.07415i) q^{38} +(-4.87193 - 0.733351i) q^{40} +(6.65023 - 6.65023i) q^{41} +(-2.22413 + 5.36952i) q^{43} +(-3.28748 + 0.992122i) q^{44} +(0.303949 + 0.851396i) q^{46} +8.50500i q^{47} -6.30511i q^{49} +(2.61824 - 0.934713i) q^{50} +(-7.38691 - 3.96196i) q^{52} +(-1.10759 + 2.67397i) q^{53} +(-2.11479 + 2.11479i) q^{55} +(-2.01974 - 1.21647i) q^{56} +(-6.24248 - 0.311142i) q^{58} +(1.92200 + 0.796118i) q^{59} +(-4.70435 - 11.3573i) q^{61} +(5.64878 - 11.9213i) q^{62} +(7.07146 - 3.74091i) q^{64} -7.30055 q^{65} +(4.54765 + 10.9790i) q^{67} +(-12.3285 + 10.0883i) q^{68} +(-2.05095 - 0.102225i) q^{70} +(-9.09946 - 9.09946i) q^{71} +(1.65052 - 1.65052i) q^{73} +(-0.919668 + 0.832343i) q^{74} +(-7.57944 - 4.06522i) q^{76} +(-1.32231 + 0.547721i) q^{77} -0.580469i q^{79} +(3.88750 - 5.78224i) q^{80} +(4.47185 + 12.5262i) q^{82} +(-3.33576 + 1.38172i) q^{83} +(-5.30942 + 12.8181i) q^{85} +(-5.51540 - 6.09404i) q^{86} +(0.722857 - 4.80220i) q^{88} +(4.91488 + 4.91488i) q^{89} +(-3.22782 - 1.33701i) q^{91} +(-1.27215 - 0.127130i) q^{92} +(-10.8694 - 5.15035i) q^{94} -7.49083 q^{95} -3.30926 q^{97} +(8.05794 + 3.81817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Introduction

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