LMFDB - Embedded newform 588.2.e.d.491.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(491,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [12,0,0,2,0,0,0,0,2,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.312013725601644544.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} - 2x^{8} + 8x^{6} - 8x^{4} - 16x^{2} + 64 $ x^12 - x^10 - 2x^8 + 8x^6 - 8x^4 - 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.12
Root			$1.38193 + 0.300427i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.d.491.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38193 + 0.300427i) q^{2} +(-1.24483 + 1.20432i) q^{3} +(1.81949 + 0.830342i) q^{4} -2.72774i q^{5} +(-2.08209 + 1.29031i) q^{6} +(2.26495 + 1.69410i) q^{8} +(0.0992110 - 2.99836i) q^{9} +(0.819487 - 3.76955i) q^{10} +2.04025 q^{11} +(-3.26495 + 1.15761i) q^{12} +4.44055 q^{13} +(3.28508 + 3.39557i) q^{15} +(2.62106 + 3.02159i) q^{16} -0.660466i q^{17} +(1.03789 - 4.11373i) q^{18} +2.93921i q^{19} +(2.26495 - 4.96308i) q^{20} +(2.81949 + 0.612946i) q^{22} +1.04242 q^{23} +(-4.85973 + 0.618866i) q^{24} -2.44055 q^{25} +(6.13655 + 1.33406i) q^{26} +(3.48749 + 3.85193i) q^{27} -2.06727i q^{29} +(3.51964 + 5.67939i) q^{30} -3.10397i q^{31} +(2.71437 + 4.96308i) q^{32} +(-2.53976 + 2.45712i) q^{33} +(0.198422 - 0.912721i) q^{34} +(2.67018 - 5.37310i) q^{36} -9.52008 q^{37} +(-0.883020 + 4.06180i) q^{38} +(-5.52774 + 5.34786i) q^{39} +(4.62106 - 6.17820i) q^{40} +7.85889i q^{41} +0.530567i q^{43} +(3.71220 + 1.69410i) q^{44} +(-8.17874 - 0.270622i) q^{45} +(1.44055 + 0.313170i) q^{46} +1.04242 q^{47} +(-6.90176 - 0.604764i) q^{48} +(-3.37268 - 0.733208i) q^{50} +(0.795415 + 0.822169i) q^{51} +(8.07953 + 3.68718i) q^{52} -10.5866i q^{53} +(3.66226 + 6.37086i) q^{54} -5.56526i q^{55} +(-3.53976 - 3.65883i) q^{57} +(0.621065 - 2.85683i) q^{58} -3.48749 q^{59} +(3.15767 + 8.90594i) q^{60} +0.198422 q^{61} +(0.932518 - 4.28949i) q^{62} +(2.26004 + 7.67413i) q^{64} -12.1127i q^{65} +(-4.24797 + 2.63256i) q^{66} -4.76465i q^{67} +(0.548413 - 1.20171i) q^{68} +(-1.29763 + 1.25541i) q^{69} -5.52774 q^{71} +(5.30423 - 6.62307i) q^{72} +3.03582 q^{73} +(-13.1561 - 2.86009i) q^{74} +(3.03808 - 2.93921i) q^{75} +(-2.44055 + 5.34786i) q^{76} +(-9.24562 + 5.72971i) q^{78} +10.9131i q^{79} +(8.24211 - 7.14958i) q^{80} +(-8.98031 - 0.594941i) q^{81} +(-2.36103 + 10.8605i) q^{82} -9.15881 q^{83} -1.80158 q^{85} +(-0.159397 + 0.733208i) q^{86} +(2.48966 + 2.57340i) q^{87} +(4.62106 + 3.45638i) q^{88} +0.541243i q^{89} +(-11.2212 - 2.83110i) q^{90} +(1.89666 + 0.865562i) q^{92} +(3.73818 + 3.86392i) q^{93} +(1.44055 + 0.313170i) q^{94} +8.01740 q^{95} +(-9.35609 - 2.90922i) q^{96} +6.91692 q^{97} +(0.202415 - 6.11739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} + 2 q^{9} - 10 q^{10} - 12 q^{12} + 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} - 14 q^{24} + 12 q^{25} + 14 q^{30} + 10 q^{33} + 4 q^{34} + 22 q^{36} + 8 q^{37} + 34 q^{40} - 18 q^{45}+ \cdots - 36 q^{97}+O(q^{100}) $ 12 * q + 2 * q^4 + 2 * q^9 - 10 * q^10 - 12 * q^12 + 12 * q^13 + 10 * q^16 + 10 * q^18 + 14 * q^22 - 14 * q^24 + 12 * q^25 + 14 * q^30 + 10 * q^33 + 4 * q^34 + 22 * q^36 + 8 * q^37 + 34 * q^40 - 18 * q^45 - 24 * q^46 - 4 * q^48 + 16 * q^52 + 38 * q^54 - 2 * q^57 - 14 * q^58 - 14 * q^60 + 4 * q^61 - 34 * q^64 + 30 * q^66 - 18 * q^69 - 20 * q^72 + 12 * q^76 - 52 * q^78 - 26 * q^81 - 68 * q^82 - 20 * q^85 + 34 * q^88 + 20 * q^90 + 6 * q^93 - 24 * q^94 - 62 * q^96 - 36 * q^97

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 $

$2$	1.38193	+	0.300427i	0.977175	+	0.212434i
$2$	1.38193	+	0.300427i	0.977175	+	0.212434i
$3$	−1.24483	+	1.20432i	−0.718704	+	0.695316i
$3$	−1.24483	+	1.20432i	−0.718704	+	0.695316i
$4$	1.81949	+	0.830342i	0.909743	+	0.415171i
$5$		−	2.72774i		−	1.21988i	−0.792447	−	0.609941i	$-0.791193\pi$
$5$		−	2.72774i		−	1.21988i	0.792447	−	0.609941i	$-0.208807\pi$
$6$	−2.08209	+	1.29031i	−0.850009	+	0.526769i
$7$		0			0
$7$		0			0
$8$	2.26495	+	1.69410i	0.800782	+	0.598955i
$9$	0.0992110	−	2.99836i	0.0330703	−	0.999453i
$10$	0.819487	−	3.76955i	0.259144	−	1.19204i
$11$	2.04025			0.615157			0.307579	−	0.951523i	$-0.400481\pi$
$11$	2.04025			0.615157			0.307579	+	0.951523i	$0.400481\pi$
$12$	−3.26495	+	1.15761i	−0.942511	+	0.334175i
$13$	4.44055			1.23159			0.615794	−	0.787907i	$-0.288835\pi$
$13$	4.44055			1.23159			0.615794	+	0.787907i	$0.288835\pi$
$14$		0			0
$15$	3.28508	+	3.39557i	0.848203	+	0.876733i
$16$	2.62106	+	3.02159i	0.655266	+	0.755398i
$17$		−	0.660466i		−	0.160187i	−0.996787	−	0.0800933i	$-0.974478\pi$
$17$		−	0.660466i		−	0.160187i	0.996787	−	0.0800933i	$-0.0255218\pi$
$18$	1.03789	−	4.11373i	0.244634	−	0.969616i
$19$			2.93921i			0.674302i	0.941451	+	0.337151i	$0.109463\pi$
$19$			2.93921i			0.674302i	−0.941451	+	0.337151i	$0.890537\pi$
$20$	2.26495	−	4.96308i	0.506459	−	1.10978i
$21$		0			0
$22$	2.81949	+	0.612946i	0.601117	+	0.130680i
$23$	1.04242			0.217359			0.108679	−	0.994077i	$-0.465338\pi$
$23$	1.04242			0.217359			0.108679	+	0.994077i	$0.465338\pi$
$24$	−4.85973	+	0.618866i	−0.991989	+	0.126326i
$25$	−2.44055			−0.488110
$26$	6.13655	+	1.33406i	1.20348	+	0.261631i
$27$	3.48749	+	3.85193i	0.671168	+	0.741305i
$28$		0			0
$29$		−	2.06727i		−	0.383883i	−0.981406	−	0.191941i	$-0.938522\pi$
$29$		−	2.06727i		−	0.383883i	0.981406	−	0.191941i	$-0.0614783\pi$
$30$	3.51964	+	5.67939i	0.642595	+	1.03691i
$31$		−	3.10397i		−	0.557490i	−0.960365	−	0.278745i	$-0.910082\pi$
$31$		−	3.10397i		−	0.557490i	0.960365	−	0.278745i	$-0.0899184\pi$
$32$	2.71437	+	4.96308i	0.479838	+	0.877357i
$33$	−2.53976	+	2.45712i	−0.442116	+	0.427729i
$34$	0.198422	−	0.912721i	0.0340291	−	0.156530i
$35$		0			0
$36$	2.67018	−	5.37310i	0.445029	−	0.895516i
$37$	−9.52008			−1.56509			−0.782546	−	0.622593i	$-0.786079\pi$
$37$	−9.52008			−1.56509			−0.782546	+	0.622593i	$0.786079\pi$
$38$	−0.883020	+	4.06180i	−0.143245	+	0.658911i
$39$	−5.52774	+	5.34786i	−0.885147	+	0.856343i
$40$	4.62106	−	6.17820i	0.730655	−	0.976859i
$41$			7.85889i			1.22735i	0.789558	+	0.613676i	$0.210310\pi$
$41$			7.85889i			1.22735i	−0.789558	+	0.613676i	$0.789690\pi$
$42$		0			0
$43$			0.530567i			0.0809106i	0.999181	+	0.0404553i	$0.0128808\pi$
$43$			0.530567i			0.0809106i	−0.999181	+	0.0404553i	$0.987119\pi$
$44$	3.71220	+	1.69410i	0.559635	+	0.255395i
$45$	−8.17874	−	0.270622i	−1.21921	−	0.0403419i
$46$	1.44055	+	0.313170i	0.212398	+	0.0461745i
$47$	1.04242			0.152052			0.0760260	−	0.997106i	$-0.475777\pi$
$47$	1.04242			0.152052			0.0760260	+	0.997106i	$0.475777\pi$
$48$	−6.90176	−	0.604764i	−0.996183	−	0.0872901i
$49$		0			0
$50$	−3.37268	−	0.733208i	−0.476969	−	0.103691i
$51$	0.795415	+	0.822169i	0.111380	+	0.115127i
$52$	8.07953	+	3.68718i	1.12043	+	0.511319i
$53$		−	10.5866i		−	1.45419i	−0.686539	−	0.727093i	$-0.740871\pi$
$53$		−	10.5866i		−	1.45419i	0.686539	−	0.727093i	$-0.259129\pi$
$54$	3.66226	+	6.37086i	0.498371	+	0.866964i
$55$		−	5.56526i		−	0.750419i
$56$		0			0
$57$	−3.53976	−	3.65883i	−0.468853	−	0.484623i
$58$	0.621065	−	2.85683i	0.0815498	−	0.375121i
$59$	−3.48749			−0.454033			−0.227016	−	0.973891i	$-0.572897\pi$
$59$	−3.48749			−0.454033			−0.227016	+	0.973891i	$0.572897\pi$
$60$	3.15767	+	8.90594i	0.407653	+	1.14975i
$61$	0.198422			0.0254053			0.0127027	−	0.999919i	$-0.495957\pi$
$61$	0.198422			0.0254053			0.0127027	+	0.999919i	$0.495957\pi$
$62$	0.932518	−	4.28949i	0.118430	−	0.544765i
$63$		0			0
$64$	2.26004	+	7.67413i	0.282505	+	0.959266i
$65$		−	12.1127i		−	1.50239i
$66$	−4.24797	+	2.63256i	−0.522889	+	0.324046i
$67$		−	4.76465i		−	0.582095i	−0.956709	−	0.291048i	$-0.905996\pi$
$67$		−	4.76465i		−	0.582095i	0.956709	−	0.291048i	$-0.0940038\pi$
$68$	0.548413	−	1.20171i	0.0665048	−	0.145729i
$69$	−1.29763	+	1.25541i	−0.156217	+	0.151133i
$70$		0			0
$71$	−5.52774			−0.656022			−0.328011	−	0.944674i	$-0.606378\pi$
$71$	−5.52774			−0.656022			−0.328011	+	0.944674i	$0.606378\pi$
$72$	5.30423	−	6.62307i	0.625110	−	0.780537i
$73$	3.03582			0.355316			0.177658	−	0.984092i	$-0.443148\pi$
$73$	3.03582			0.355316			0.177658	+	0.984092i	$0.443148\pi$
$74$	−13.1561	−	2.86009i	−1.52937	−	0.332479i
$75$	3.03808	−	2.93921i	0.350807	−	0.339391i
$76$	−2.44055	+	5.34786i	−0.279950	+	0.613442i
$77$		0			0
$78$	−9.24562	+	5.72971i	−1.04686	+	0.648762i
$79$			10.9131i			1.22782i	0.789375	+	0.613911i	$0.210405\pi$
$79$			10.9131i			1.22782i	−0.789375	+	0.613911i	$0.789595\pi$
$80$	8.24211	−	7.14958i	0.921496	−	0.799347i
$81$	−8.98031	−	0.594941i	−0.997813	−	0.0661045i
$82$	−2.36103	+	10.8605i	−0.260732	+	1.19934i
$83$	−9.15881			−1.00531			−0.502655	−	0.864487i	$-0.667643\pi$
$83$	−9.15881			−1.00531			−0.502655	+	0.864487i	$0.667643\pi$
$84$		0			0
$85$	−1.80158			−0.195409
$86$	−0.159397	+	0.733208i	−0.0171882	+	0.0790639i
$87$	2.48966	+	2.57340i	0.266920	+	0.275898i
$88$	4.62106	+	3.45638i	0.492607	+	0.368452i
$89$			0.541243i			0.0573717i	0.999588	+	0.0286858i	$0.00913224\pi$
$89$			0.541243i			0.0573717i	−0.999588	+	0.0286858i	$0.990868\pi$
$90$	−11.2212	−	2.83110i	−1.18282	−	0.298424i
$91$		0			0
$92$	1.89666	+	0.865562i	0.197741	+	0.0902411i
$93$	3.73818	+	3.86392i	0.387632	+	0.400670i
$94$	1.44055	+	0.313170i	0.148582	+	0.0323011i
$95$	8.01740			0.822568
$96$	−9.35609	−	2.90922i	−0.954902	−	0.296921i
$97$	6.91692			0.702307			0.351153	−	0.936318i	$-0.385790\pi$
$97$	6.91692			0.702307			0.351153	+	0.936318i	$0.385790\pi$
$98$		0			0
$99$	0.202415	−	6.11739i	0.0203435	−	0.614821i
$100$	−4.44055	−	2.02649i	−0.444055	−	0.202649i
$101$		−	10.1313i		−	1.00810i	−0.863675	−	0.504049i	$-0.831843\pi$
$101$		−	10.1313i		−	1.00810i	0.863675	−	0.504049i	$-0.168157\pi$
$102$	0.852209	+	1.37515i	0.0843813	+	0.136160i
$103$		−	7.32171i		−	0.721430i	−0.932676	−	0.360715i	$-0.882533\pi$
$103$		−	7.32171i		−	0.721430i	0.932676	−	0.360715i	$-0.117467\pi$
$104$	10.0576	+	7.52275i	0.986234	+	0.737666i
$105$		0			0
$106$	3.18051	−	14.6300i	0.308919	−	1.42099i
$107$	−17.5266			−1.69436			−0.847182	−	0.531303i	$-0.821703\pi$
$107$	−17.5266			−1.69436			−0.847182	+	0.531303i	$0.821703\pi$
$108$	3.14702	+	9.90435i	0.302823	+	0.953047i
$109$	0.638974			0.0612026			0.0306013	−	0.999532i	$-0.490258\pi$
$109$	0.638974			0.0612026			0.0306013	+	0.999532i	$0.490258\pi$
$110$	1.67195	−	7.69082i	0.159415	−	0.733291i
$111$	11.8509	−	11.4653i	1.12484	−	1.08823i
$112$		0			0
$113$			10.7917i			1.01520i	0.861593	+	0.507600i	$0.169467\pi$
$113$			10.7917i			1.01520i	−0.861593	+	0.507600i	$0.830533\pi$
$114$	−3.79251	−	6.11970i	−0.355201	−	0.573162i
$115$		−	2.84344i		−	0.265152i
$116$	1.71654	−	3.76137i	0.159377	−	0.349235i
$117$	0.440552	−	13.3144i	0.0407290	−	1.23091i
$118$	−4.81949	−	1.04774i	−0.443670	−	0.0964521i
$119$		0			0
$120$	1.68810	+	13.2561i	0.154102	+	1.21011i
$121$	−6.83740			−0.621581
$122$	0.274206	+	0.0596114i	0.0248255	+	0.00539696i
$123$	−9.46465	−	9.78300i	−0.853399	−	0.882103i
$124$	2.57736	−	5.64763i	0.231454	−	0.507173i
$125$		−	6.98150i		−	0.624445i
$126$		0			0
$127$		−	10.9563i		−	0.972210i	−0.873900	−	0.486105i	$-0.838417\pi$
$127$		−	10.9563i		−	0.972210i	0.873900	−	0.486105i	$-0.161583\pi$
$128$	0.817708	+	11.2841i	0.0722759	+	0.997385i
$129$	−0.638974	−	0.660466i	−0.0562585	−	0.0581508i
$130$	3.63897	−	16.7389i	0.319159	−	1.46810i
$131$	−22.1555			−1.93574			−0.967869	−	0.251454i	$-0.919091\pi$
$131$	−22.1555			−1.93574			−0.967869	+	0.251454i	$0.919091\pi$
$132$	−6.66131	+	2.36182i	−0.579793	+	0.205570i
$133$		0			0
$134$	1.43143	−	6.58444i	0.123657	−	0.568809i
$135$	10.5071	−	9.51296i	0.904304	−	0.818746i
$136$	1.11890	−	1.49593i	0.0959446	−	0.128275i
$137$			14.5042i			1.23918i	0.784925	+	0.619591i	$0.212701\pi$
$137$			14.5042i			1.23918i	−0.784925	+	0.619591i	$0.787299\pi$
$138$	−2.17040	+	1.34505i	−0.184757	+	0.114498i
$139$			5.78265i			0.490478i	0.969463	+	0.245239i	$0.0788665\pi$
$139$			5.78265i			0.490478i	−0.969463	+	0.245239i	$0.921134\pi$
$140$		0			0
$141$	−1.29763	+	1.25541i	−0.109280	+	0.105724i
$142$	−7.63897	−	1.66068i	−0.641048	−	0.139361i
$143$	9.05982			0.757620
$144$	9.31986	−	7.55912i	0.776655	−	0.629927i
$145$	−5.63897			−0.468291
$146$	4.19530	+	0.912043i	0.347206	+	0.0754812i
$147$		0			0
$148$	−17.3217	−	7.90492i	−1.42383	−	0.649780i
$149$			13.8556i			1.13510i	0.823340	+	0.567548i	$0.192108\pi$
$149$			13.8556i			1.13510i	−0.823340	+	0.567548i	$0.807892\pi$
$150$	5.08144	−	3.14908i	0.414898	−	0.257121i
$151$			11.7732i			0.958089i	0.877791	+	0.479045i	$0.159017\pi$
$151$			11.7732i			0.958089i	−0.877791	+	0.479045i	$0.840983\pi$
$152$	−4.97933	+	6.65718i	−0.403877	+	0.539969i
$153$	−1.98031	−	0.0655255i	−0.160099	−	0.00529742i
$154$		0			0
$155$	−8.46682			−0.680071
$156$	−14.4982	+	5.14045i	−1.16078	+	0.411565i
$157$	10.6827			0.852571			0.426285	−	0.904589i	$-0.359822\pi$
$157$	10.6827			0.852571			0.426285	+	0.904589i	$0.359822\pi$
$158$	−3.27860	+	15.0812i	−0.260831	+	1.19980i
$159$	12.7497	+	13.1786i	1.01112	+	1.04513i
$160$	13.5380	−	7.40409i	1.07027	−	0.585345i
$161$		0			0
$162$	−12.2315	−	3.52010i	−0.960995	−	0.276565i
$163$		−	20.4787i		−	1.60402i	−0.597313	−	0.802008i	$-0.703765\pi$
$163$		−	20.4787i		−	1.60402i	0.597313	−	0.802008i	$-0.296235\pi$
$164$	−6.52557	+	14.2992i	−0.509561	+	1.11658i
$165$	6.70237	+	6.92781i	0.521779	+	0.539329i
$166$	−12.6569	−	2.75156i	−0.982365	−	0.213562i
$167$	−22.4614			−1.73811			−0.869057	−	0.494712i	$-0.835273\pi$
$167$	−22.4614			−1.73811			−0.869057	+	0.494712i	$0.835273\pi$
$168$		0			0
$169$	6.71850			0.516808
$170$	−2.48966	−	0.541243i	−0.190948	−	0.0415115i
$171$	8.81282	+	0.291602i	0.673933	+	0.0222994i
$172$	−0.440552	+	0.965359i	−0.0335917	+	0.0736079i
$173$			19.4303i			1.47726i	0.674112	+	0.738630i	$0.264527\pi$
$173$			19.4303i			1.47726i	−0.674112	+	0.738630i	$0.735473\pi$
$174$	2.66743	+	4.30424i	0.202217	+	0.326304i
$175$		0			0
$176$	5.34762	+	6.16479i	0.403092	+	0.464689i
$177$	4.34134	−	4.20007i	0.326315	−	0.315696i
$178$	−0.162604	+	0.747963i	−0.0121877	+	0.0560622i
$179$	5.03373			0.376239			0.188119	−	0.982146i	$-0.439761\pi$
$179$	5.03373			0.376239			0.188119	+	0.982146i	$0.439761\pi$
$180$	−14.6564	−	7.28354i	−1.09242	−	0.542883i
$181$	−5.71850			−0.425053			−0.212526	−	0.977155i	$-0.568169\pi$
$181$	−5.71850			−0.425053			−0.212526	+	0.977155i	$0.568169\pi$
$182$		0			0
$183$	−0.247002	+	0.238964i	−0.0182589	+	0.0176647i
$184$	2.36103	+	1.76596i	0.174057	+	0.130188i
$185$			25.9683i			1.90923i
$186$	4.00510	+	6.46274i	0.293668	+	0.473871i
$187$		−	1.34751i		−	0.0985399i
$188$	1.89666	+	0.865562i	0.138328	+	0.0631276i
$189$		0			0
$190$	11.0795	+	2.40865i	0.803793	+	0.174742i
$191$	9.81507			0.710193			0.355097	−	0.934830i	$-0.384448\pi$
$191$	9.81507			0.710193			0.355097	+	0.934830i	$0.384448\pi$
$192$	−12.0555	−	6.83118i	−0.870031	−	0.492998i
$193$	17.1591			1.23514			0.617568	−	0.786518i	$-0.288118\pi$
$193$	17.1591			1.23514			0.617568	+	0.786518i	$0.288118\pi$
$194$	9.55873	+	2.07803i	0.686277	+	0.149194i
$195$	14.5876	+	15.0782i	1.04464	+	1.07977i
$196$		0			0
$197$		−	11.0302i		−	0.785867i	−0.919567	−	0.392934i	$-0.871460\pi$
$197$		−	11.0302i		−	0.785867i	0.919567	−	0.392934i	$-0.128540\pi$
$198$	2.11756	−	8.39302i	0.150488	−	0.596466i
$199$			22.3042i			1.58110i	0.612398	+	0.790550i	$0.290205\pi$
$199$			22.3042i			1.58110i	−0.612398	+	0.790550i	$0.709795\pi$
$200$	−5.52774	−	4.13454i	−0.390870	−	0.292356i
$201$	5.73818	+	5.93119i	0.404740	+	0.418354i
$202$	3.04371	−	14.0007i	0.214155	−	0.985089i
$203$		0			0
$204$	0.764565	+	2.15639i	0.0535303	+	0.150978i
$205$	21.4370			1.49722
$206$	2.19964	−	10.1181i	0.153256	−	0.704964i
$207$	0.103419	−	3.12554i	0.00718813	−	0.217240i
$208$	11.6390	+	13.4175i	0.807018	+	0.930339i
$209$			5.99672i			0.414802i
$210$		0			0
$211$			17.9648i			1.23675i	0.785884	+	0.618374i	$0.212208\pi$
$211$			17.9648i			1.23675i	−0.785884	+	0.618374i	$0.787792\pi$
$212$	8.79052	−	19.2622i	0.603736	−	1.32294i
$213$	6.88110	−	6.65718i	0.471485	−	0.456143i
$214$	−24.2207	−	5.26548i	−1.65569	−	0.359941i
$215$	1.44725			0.0987014
$216$	1.37344	+	14.6326i	0.0934510	+	0.995624i
$217$		0			0
$218$	0.883020	+	0.191965i	0.0598057	+	0.0130015i
$219$	−3.77908	+	3.65611i	−0.255367	+	0.247057i
$220$	4.62106	−	10.1259i	0.311552	−	0.682689i
$221$		−	2.93283i		−	0.197284i
$222$	19.8216	−	12.2839i	1.33034	−	0.824441i
$223$			1.95751i			0.131084i	0.997850	+	0.0655422i	$0.0208777\pi$
$223$			1.95751i			0.131084i	−0.997850	+	0.0655422i	$0.979122\pi$
$224$		0			0
$225$	−0.242130	+	7.31765i	−0.0161420	+	0.487843i
$226$	−3.24213	+	14.9135i	−0.215663	+	0.992029i
$227$	−18.1642			−1.20560			−0.602801	−	0.797892i	$-0.705949\pi$
$227$	−18.1642			−1.20560			−0.602801	+	0.797892i	$0.705949\pi$
$228$	−3.40248	−	9.59640i	−0.225334	−	0.635537i
$229$	9.84529			0.650595			0.325297	−	0.945612i	$-0.394536\pi$
$229$	9.84529			0.650595			0.325297	+	0.945612i	$0.394536\pi$
$230$	0.854247	−	3.92945i	0.0563274	−	0.259100i
$231$		0			0
$232$	3.50217	−	4.68228i	0.229929	−	0.307406i
$233$			26.2067i			1.71686i	0.512932	+	0.858430i	$0.328559\pi$
$233$			26.2067i			1.71686i	−0.512932	+	0.858430i	$0.671441\pi$
$234$	4.60881	−	18.2672i	0.301288	−	1.19417i
$235$		−	2.84344i		−	0.185485i
$236$	−6.34545	−	2.89581i	−0.413053	−	0.188501i
$237$	−13.1429	−	13.5850i	−0.853724	−	0.882440i
$238$		0			0
$239$	16.9336			1.09535			0.547673	−	0.836692i	$-0.315514\pi$
$239$	16.9336			1.09535			0.547673	+	0.836692i	$0.315514\pi$
$240$	−1.64964	+	18.8262i	−0.106484	+	1.21522i
$241$	−5.83740			−0.376020			−0.188010	−	0.982167i	$-0.560204\pi$
$241$	−5.83740			−0.376020			−0.188010	+	0.982167i	$0.560204\pi$
$242$	−9.44883	−	2.05414i	−0.607394	−	0.132045i
$243$	11.8955	−	10.0746i	0.763095	−	0.646286i
$244$	0.361026	+	0.164758i	0.0231123	+	0.0105476i
$245$		0			0
$246$	−10.1404	−	16.3629i	−0.646531	−	1.04326i
$247$			13.0517i			0.830462i
$248$	5.25844	−	7.03035i	0.333911	−	0.446428i
$249$	11.4012	−	11.0302i	0.722520	−	0.699009i
$250$	2.09743	−	9.64798i	0.132653	−	0.610192i
$251$	10.1468			0.640462			0.320231	−	0.947340i	$-0.396240\pi$
$251$	10.1468			0.640462			0.320231	+	0.947340i	$0.396240\pi$
$252$		0			0
$253$	2.12679			0.133710
$254$	3.29156	−	15.1408i	0.206531	−	0.950020i
$255$	2.24266	−	2.16968i	0.140441	−	0.135871i
$256$	−2.26004	+	15.8396i	−0.141252	+	0.989974i
$257$		−	11.9816i		−	0.747392i	−0.927551	−	0.373696i	$-0.878090\pi$
$257$		−	11.9816i		−	0.747392i	0.927551	−	0.373696i	$-0.121910\pi$
$258$	−0.684598	−	1.10469i	−0.0426212	−	0.0687748i
$259$		0			0
$260$	10.0576	−	22.0388i	0.623749	−	1.36679i
$261$	−6.19842	−	0.205096i	−0.383673	−	0.0126951i
$262$	−30.6175	−	6.65613i	−1.89156	−	0.411217i
$263$	14.4440			0.890654			0.445327	−	0.895368i	$-0.353088\pi$
$263$	14.4440			0.890654			0.445327	+	0.895368i	$0.353088\pi$
$264$	−9.91505	+	1.26264i	−0.610229	+	0.0777101i
$265$	−28.8775			−1.77393
$266$		0			0
$267$	−0.651832	−	0.673757i	−0.0398915	−	0.0412332i
$268$	3.95629	−	8.66923i	0.241669	−	0.529557i
$269$		−	6.57131i		−	0.400660i	−0.979728	−	0.200330i	$-0.935799\pi$
$269$		−	6.57131i		−	0.400660i	0.979728	−	0.200330i	$-0.0642014\pi$
$270$	17.3780	−	9.98969i	1.05759	−	0.607953i
$271$			0.0163458i			0.000992938i	1.00000		0.000496469i	$0.000158031\pi$
$271$			0.0163458i			0.000992938i	−1.00000		0.000496469i	$0.999842\pi$
$272$	1.99566	−	1.73112i	0.121005	−	0.104965i
$273$		0			0
$274$	−4.35747	+	20.0439i	−0.263245	+	1.21090i
$275$	−4.97933			−0.300265
$276$	−3.40344	+	1.20672i	−0.204863	+	0.0726358i
$277$	−18.3138			−1.10037			−0.550184	−	0.835044i	$-0.685442\pi$
$277$	−18.3138			−1.10037			−0.550184	+	0.835044i	$0.685442\pi$
$278$	−1.73727	+	7.99125i	−0.104194	+	0.479283i
$279$	−9.30682	−	0.307948i	−0.557185	−	0.0184364i
$280$		0			0
$281$		−	1.61190i		−	0.0961580i	−0.998844	−	0.0480790i	$-0.984690\pi$
$281$		−	1.61190i		−	0.0961580i	0.998844	−	0.0480790i	$-0.0153099\pi$
$282$	−2.17040	+	1.34505i	−0.129246	+	0.0800963i
$283$		−	20.5745i		−	1.22303i	−0.791234	−	0.611513i	$-0.790561\pi$
$283$		−	20.5745i		−	1.22303i	0.791234	−	0.611513i	$-0.209439\pi$
$284$	−10.0576	−	4.58991i	−0.596812	−	0.272361i
$285$	−9.98031	+	9.65554i	−0.591183	+	0.571945i
$286$	12.5201	+	2.72182i	0.740328	+	0.160944i
$287$		0			0
$288$	15.1504	−	7.64627i	0.892746	−	0.450561i
$289$	16.5638			0.974340
$290$	−7.79269	−	1.69410i	−0.457603	−	0.0994811i
$291$	−8.61040	+	8.33021i	−0.504751	+	0.488325i
$292$	5.52363	+	2.52077i	0.323246	+	0.147517i
$293$		−	11.6573i		−	0.681026i	−0.940240	−	0.340513i	$-0.889399\pi$
$293$		−	11.6573i		−	0.681026i	0.940240	−	0.340513i	$-0.110601\pi$
$294$		0			0
$295$			9.51296i			0.553866i
$296$	−21.5625	−	16.1280i	−1.25330	−	0.937420i
$297$	7.11534	+	7.85889i	0.412874	+	0.456019i
$298$	−4.16260	+	19.1476i	−0.241133	+	1.10919i
$299$	4.62890			0.267696
$300$	7.96829	−	2.82522i	0.460049	−	0.163114i
$301$		0			0
$302$	−3.53699	+	16.2698i	−0.203531	+	0.936221i
$303$	12.2013	+	12.6117i	0.700947	+	0.724524i
$304$	−8.88110	+	7.70387i	−0.509366	+	0.441847i
$305$		−	0.541243i		−	0.0309915i
$306$	−2.71698	−	0.685493i	−0.155319	−	0.0391870i
$307$			3.66039i			0.208909i	0.994530	+	0.104455i	$0.0333097\pi$
$307$			3.66039i			0.208909i	−0.994530	+	0.104455i	$0.966690\pi$
$308$		0			0
$309$	8.81771	+	9.11430i	0.501622	+	0.518494i
$310$	−11.7006	−	2.54366i	−0.664549	−	0.144470i
$311$	−11.7475			−0.666138			−0.333069	−	0.942902i	$-0.608084\pi$
$311$	−11.7475			−0.666138			−0.333069	+	0.942902i	$0.608084\pi$
$312$	−21.5799	+	2.74811i	−1.22172	+	0.155581i
$313$	14.8338			0.838458			0.419229	−	0.907880i	$-0.362300\pi$
$313$	14.8338			0.838458			0.419229	+	0.907880i	$0.362300\pi$
$314$	14.7628	+	3.20937i	0.833111	+	0.181115i
$315$		0			0
$316$	−9.06162	+	19.8563i	−0.509756	+	1.11700i
$317$		−	8.30244i		−	0.466311i	−0.972439	−	0.233156i	$-0.925095\pi$
$317$		−	8.30244i		−	0.466311i	0.972439	−	0.233156i	$-0.0749052\pi$
$318$	13.6601	+	22.0423i	0.766020	+	1.23607i
$319$		−	4.21774i		−	0.236148i
$320$	20.9330	−	6.16479i	1.17019	−	0.344622i
$321$	21.8177	−	21.1077i	1.21775	−	1.17812i
$322$		0			0
$323$	1.94125			0.108014
$324$	−15.8456	−	8.53922i	−0.880309	−	0.474401i
$325$	−10.8374			−0.601151
$326$	6.15237	−	28.3002i	0.340748	−	1.56741i
$327$	−0.795415	+	0.769531i	−0.0439865	+	0.0425552i
$328$	−13.3138	+	17.8000i	−0.735130	+	0.982843i
$329$		0			0
$330$	7.18093	+	11.5873i	0.395297	+	0.637863i
$331$		−	15.2688i		−	0.839251i	−0.907697	−	0.419625i	$-0.862161\pi$
$331$		−	15.2688i		−	0.839251i	0.907697	−	0.419625i	$-0.137839\pi$
$332$	−16.6643	−	7.60495i	−0.914575	−	0.417376i
$333$	−0.944497	+	28.5446i	−0.0517581	+	1.56423i
$334$	−31.0402	−	6.74801i	−1.69844	−	0.369235i
$335$	−12.9967			−0.710087
$336$		0			0
$337$	−16.9606			−0.923904			−0.461952	−	0.886905i	$-0.652851\pi$
$337$	−16.9606			−0.923904			−0.461952	+	0.886905i	$0.652851\pi$
$338$	9.28453	+	2.01842i	0.505012	+	0.109788i
$339$	−12.9967	−	13.4339i	−0.705885	−	0.729628i
$340$	−3.27795	−	1.49593i	−0.177772	−	0.0811280i
$341$		−	6.33287i		−	0.342944i
$342$	12.0911	+	3.05059i	0.653813	+	0.164957i
$343$		0			0
$344$	−0.898834	+	1.20171i	−0.0484619	+	0.0647918i
$345$	3.42442	+	3.53960i	0.184365	+	0.190566i
$346$	−5.83740	+	26.8514i	−0.313820	+	1.44354i
$347$	−22.0565			−1.18406			−0.592029	−	0.805917i	$-0.701673\pi$
$347$	−22.0565			−1.18406			−0.592029	+	0.805917i	$0.701673\pi$
$348$	2.39310	+	6.74955i	0.128284	+	0.361814i
$349$	17.6748			0.946110			0.473055	−	0.881033i	$-0.343151\pi$
$349$	17.6748			0.946110			0.473055	+	0.881033i	$0.343151\pi$
$350$		0			0
$351$	15.4864	+	17.1047i	0.826602	+	0.912982i
$352$	5.53799	+	10.1259i	0.295176	+	0.539713i
$353$		−	0.422020i		−	0.0224619i	−0.999937	−	0.0112309i	$-0.996425\pi$
$353$		−	0.422020i		−	0.0224619i	0.999937	−	0.0112309i	$-0.00357499\pi$
$354$	7.26126	−	4.49996i	0.385932	−	0.239170i
$355$			15.0782i			0.800269i
$356$	−0.449417	+	0.984785i	−0.0238190	+	0.0521935i
$357$		0			0
$358$	6.95629	+	1.51227i	0.367651	+	0.0799260i
$359$	14.4440			0.762324			0.381162	−	0.924508i	$-0.375524\pi$
$359$	14.4440			0.762324			0.381162	+	0.924508i	$0.375524\pi$
$360$	−18.0660	−	14.4686i	−0.952162	−	0.762560i
$361$	10.3610			0.545317
$362$	−7.90259	−	1.71799i	−0.415351	−	0.0902957i
$363$	8.51141	−	8.23443i	0.446733	−	0.432196i
$364$		0			0
$365$		−	8.28091i		−	0.433443i
$366$	−0.413132	+	0.256027i	−0.0215948	+	0.0133827i
$367$		−	21.8004i		−	1.13797i	−0.822348	−	0.568985i	$-0.807336\pi$
$367$		−	21.8004i		−	1.13797i	0.822348	−	0.568985i	$-0.192664\pi$
$368$	2.73224	+	3.14976i	0.142428	+	0.164192i
$369$	23.5638	+	0.779689i	1.22668	+	0.0405890i
$370$	−7.80158	+	35.8865i	−0.405585	+	1.86565i
$371$		0			0
$372$	3.59320	+	10.1343i	0.186299	+	0.525440i
$373$	19.5201			1.01071			0.505356	−	0.862911i	$-0.331361\pi$
$373$	19.5201			1.01071			0.505356	+	0.862911i	$0.331361\pi$
$374$	0.404830	−	1.86218i	0.0209333	−	0.0962908i
$375$	8.40799	+	8.69080i	0.434187	+	0.448791i
$376$	2.36103	+	1.76596i	0.121761	+	0.0910724i
$377$		−	9.17983i		−	0.472785i
$378$		0			0
$379$		−	34.1136i		−	1.75230i	−0.482038	−	0.876150i	$-0.660103\pi$
$379$		−	34.1136i		−	1.75230i	0.482038	−	0.876150i	$-0.339897\pi$
$380$	14.5876	+	6.65718i	0.748326	+	0.341506i
$381$	13.1949	+	13.6387i	0.675994	+	0.698731i
$382$	13.5638	+	2.94871i	0.693984	+	0.150869i
$383$	−8.21539			−0.419787			−0.209893	−	0.977724i	$-0.567312\pi$
$383$	−8.21539			−0.419787			−0.209893	+	0.977724i	$0.567312\pi$
$384$	−14.6076	−	13.0620i	−0.745443	−	0.666570i
$385$		0			0
$386$	23.7127	+	5.15505i	1.20694	+	0.262385i
$387$	1.59083	+	0.0526381i	0.0808664	+	0.00267574i
$388$	12.5852	+	5.74341i	0.638919	+	0.291577i
$389$			4.79501i			0.243117i	0.992584	+	0.121558i	$0.0387891\pi$
$389$			4.79501i			0.243117i	−0.992584	+	0.121558i	$0.961211\pi$
$390$	15.6291	+	25.2196i	0.791412	+	1.27704i
$391$		−	0.688481i		−	0.0348180i
$392$		0			0
$393$	27.5799	−	26.6824i	1.39122	−	1.34595i
$394$	3.31377	−	15.2430i	0.166945	−	0.767930i
$395$	29.7681			1.49780
$396$	5.44782	−	10.9624i	0.273763	−	0.550883i
$397$	−10.4012			−0.522020			−0.261010	−	0.965336i	$-0.584056\pi$
$397$	−10.4012			−0.522020			−0.261010	+	0.965336i	$0.584056\pi$
$398$	−6.70078	+	30.8229i	−0.335880	+	1.54501i
$399$		0			0
$400$	−6.39684	−	7.37435i	−0.319842	−	0.368718i
$401$		−	11.5714i		−	0.577849i	−0.957352	−	0.288924i	$-0.906702\pi$
$401$		−	11.5714i		−	0.577849i	0.957352	−	0.288924i	$-0.0932976\pi$
$402$	6.14790	+	9.92043i	0.306630	+	0.494786i
$403$		−	13.7833i		−	0.686597i
$404$	8.41241	−	18.4337i	0.418533	−	0.917111i
$405$	−1.62284	+	24.4959i	−0.0806396	+	1.21721i
$406$		0			0
$407$	−19.4233			−0.962777
$408$	0.408740	+	3.20969i	0.0202357	+	0.158903i
$409$	−20.4370			−1.01054			−0.505272	−	0.862960i	$-0.668608\pi$
$409$	−20.4370			−1.01054			−0.505272	+	0.862960i	$0.668608\pi$
$410$	29.6245	+	6.44026i	1.46305	+	0.318062i
$411$	−17.4678	−	18.0553i	−0.861623	−	0.890605i
$412$	6.07953	−	13.3218i	0.299517	−	0.656316i
$413$		0			0
$414$	1.08192	−	4.28822i	0.0531733	−	0.210755i
$415$			24.9828i			1.22636i
$416$	12.0533	+	22.0388i	0.590962	+	1.08054i
$417$	−6.96418	−	7.19843i	−0.341037	−	0.352509i
$418$	−1.80158	+	8.28707i	−0.0881181	+	0.405334i
$419$	21.9130			1.07052			0.535259	−	0.844688i	$-0.320214\pi$
$419$	21.9130			1.07052			0.535259	+	0.844688i	$0.320214\pi$
$420$		0			0
$421$	14.1153			0.687940			0.343970	−	0.938981i	$-0.388228\pi$
$421$	14.1153			0.687940			0.343970	+	0.938981i	$0.388228\pi$
$422$	−5.39712	+	24.8262i	−0.262727	+	1.20852i
$423$	0.103419	−	3.12554i	0.00502841	−	0.151969i
$424$	17.9348	−	23.9782i	0.870992	−	1.16449i
$425$			1.61190i			0.0781887i
$426$	11.5092	−	7.13252i	0.557624	−	0.345572i
$427$		0			0
$428$	−31.8895	−	14.5531i	−1.54144	−	0.703451i
$429$	−11.2779	+	10.9109i	−0.544504	+	0.526786i
$430$	2.00000	+	0.434792i	0.0964486	+	0.0209675i
$431$	29.1207			1.40270			0.701348	−	0.712820i	$-0.252582\pi$
$431$	29.1207			1.40270			0.701348	+	0.712820i	$0.252582\pi$
$432$	−2.49803	+	20.6339i	−0.120187	+	0.992751i
$433$	−26.1153			−1.25502			−0.627512	−	0.778607i	$-0.715927\pi$
$433$	−26.1153			−1.25502			−0.627512	+	0.778607i	$0.715927\pi$
$434$		0			0
$435$	7.01957	−	6.79115i	0.336563	−	0.325611i
$436$	1.16260	+	0.530567i	0.0556786	+	0.0254095i
$437$			3.06388i			0.146565i
$438$	−6.32084	+	3.91716i	−0.302021	+	0.187169i
$439$			18.3832i			0.877384i	0.898637	+	0.438692i	$0.144558\pi$
$439$			18.3832i			0.877384i	−0.898637	+	0.438692i	$0.855442\pi$
$440$	9.42811	−	12.6051i	0.449467	−	0.600922i
$441$		0			0
$442$	0.881103	−	4.05298i	0.0419098	−	0.192781i
$443$	−8.26883			−0.392864			−0.196432	−	0.980517i	$-0.562935\pi$
$443$	−8.26883			−0.392864			−0.196432	+	0.980517i	$0.562935\pi$
$444$	31.0826	−	11.0206i	1.47512	−	0.523014i
$445$	1.47637			0.0699866
$446$	−0.588089	+	2.70515i	−0.0278468	+	0.128092i
$447$	−16.6866	−	17.2479i	−0.789251	−	0.815798i
$448$		0			0
$449$			24.1061i			1.13764i	0.822463	+	0.568818i	$0.192599\pi$
$449$			24.1061i			1.13764i	−0.822463	+	0.568818i	$0.807401\pi$
$450$	−2.53303	+	10.0398i	−0.119408	+	0.473279i
$451$			16.0341i			0.755015i
$452$	−8.96082	+	19.6354i	−0.421482	+	0.923572i
$453$	−14.1787	−	14.6556i	−0.666175	−	0.688582i
$454$	−25.1018	−	5.45703i	−1.17808	−	0.256111i
$455$		0			0
$456$	−1.81898	−	14.2838i	−0.0851815	−	0.668900i
$457$	−18.6906			−0.874308			−0.437154	−	0.899387i	$-0.644014\pi$
$457$	−18.6906			−0.874308			−0.437154	+	0.899387i	$0.644014\pi$
$458$	13.6055	+	2.95779i	0.635745	+	0.138209i
$459$	2.54407	−	2.30337i	0.118747	−	0.107512i
$460$	2.36103	−	5.17360i	0.110083	−	0.241220i
$461$			16.3664i			0.762260i	0.924521	+	0.381130i	$0.124465\pi$
$461$			16.3664i			0.762260i	−0.924521	+	0.381130i	$0.875535\pi$
$462$		0			0
$463$			11.3643i			0.528142i	0.964503	+	0.264071i	$0.0850653\pi$
$463$			11.3643i			0.528142i	−0.964503	+	0.264071i	$0.914935\pi$
$464$	6.24645	−	5.41845i	0.289984	−	0.251545i
$465$	10.5398	−	10.1968i	0.488770	−	0.472865i
$466$	−7.87321	+	36.2160i	−0.364720	+	1.67767i
$467$	36.2937			1.67947			0.839736	−	0.542995i	$-0.182710\pi$
$467$	36.2937			1.67947			0.839736	+	0.542995i	$0.182710\pi$
$468$	11.8571	−	23.8595i	0.548093	−	1.10291i
$469$		0			0
$470$	0.854247	−	3.92945i	0.0394035	−	0.181252i
$471$	−13.2981	+	12.8654i	−0.612746	+	0.592806i
$472$	−7.89901	−	5.90817i	−0.363582	−	0.271945i
$473$			1.08249i			0.0497728i
$474$	−14.0814	−	22.7221i	−0.646778	−	1.04366i
$475$		−	7.17330i		−	0.329134i
$476$		0			0
$477$	−31.7425	−	1.05031i	−1.45339	−	0.0480904i
$478$	23.4012	+	5.08733i	1.07035	+	0.232689i
$479$	11.1991			0.511698			0.255849	−	0.966717i	$-0.417645\pi$
$479$	11.1991			0.511698			0.255849	+	0.966717i	$0.417645\pi$
$480$	−7.93559	+	25.5210i	−0.362208	+	1.16487i
$481$	−42.2744			−1.92755
$482$	−8.06690	−	1.75371i	−0.367437	−	0.0798794i
$483$		0			0
$484$	−12.4406	−	5.67738i	−0.565480	−	0.258063i
$485$		−	18.8675i		−	0.856731i
$486$	19.4655	−	10.3487i	0.882971	−	0.469427i
$487$		−	9.93825i		−	0.450345i	−0.974319	−	0.225173i	$-0.927705\pi$
$487$		−	9.93825i		−	0.450345i	0.974319	−	0.225173i	$-0.0722946\pi$
$488$	0.449417	+	0.336147i	0.0203441	+	0.0152167i
$489$	24.6630	+	25.4926i	1.11530	+	1.15281i
$490$		0			0
$491$	2.64307			0.119280			0.0596400	−	0.998220i	$-0.481005\pi$
$491$	2.64307			0.119280			0.0596400	+	0.998220i	$0.481005\pi$
$492$	−9.09757	−	25.6589i	−0.410150	−	1.15679i
$493$	−1.36536			−0.0614928
$494$	−3.92110	+	18.0366i	−0.176418	+	0.811507i
$495$	−16.6866	−	0.552135i	−0.750008	−	0.0248166i
$496$	9.37894	−	8.13571i	0.421127	−	0.365304i
$497$		0			0
$498$	19.0695	−	11.8178i	0.854523	−	0.529566i
$499$		−	19.8429i		−	0.888289i	−0.895955	−	0.444145i	$-0.853508\pi$
$499$		−	19.8429i		−	0.888289i	0.895955	−	0.444145i	$-0.146492\pi$
$500$	5.79703	−	12.7028i	0.259251	−	0.568084i
$501$	27.9606	−	27.0508i	1.24919	−	1.20854i
$502$	14.0222	+	3.04838i	0.625843	+	0.136056i
$503$	−3.07284			−0.137011			−0.0685056	−	0.997651i	$-0.521823\pi$
$503$	−3.07284			−0.137011			−0.0685056	+	0.997651i	$0.521823\pi$
$504$		0			0
$505$	−27.6354			−1.22976
$506$	2.93908	+	0.638945i	0.130658	+	0.0284046i
$507$	−8.36340	+	8.09124i	−0.371432	+	0.359345i
$508$	9.09743	−	19.9348i	0.403633	−	0.884462i
$509$			16.8861i			0.748465i	0.927335	+	0.374233i	$0.122094\pi$
$509$			16.8861i			0.748465i	−0.927335	+	0.374233i	$0.877906\pi$
$510$	3.75104	−	2.32460i	0.166099	−	0.102935i
$511$		0			0
$512$	−7.88187	+	21.2103i	−0.348333	+	0.937371i
$513$	−11.3217	+	10.2505i	−0.499863	+	0.452570i
$514$	3.59960	−	16.5578i	0.158772	−	0.730333i
$515$	−19.9717			−0.880059
$516$	−0.614192	−	1.73228i	−0.0270383	−	0.0762592i
$517$	2.12679			0.0935360
$518$		0			0
$519$	−23.4004	−	24.1875i	−1.02716	−	1.06171i
$520$	20.5201	−	27.4346i	0.899865	−	1.20309i
$521$		−	31.5430i		−	1.38192i	−0.722892	−	0.690961i	$-0.757188\pi$
$521$		−	31.5430i		−	1.38192i	0.722892	−	0.690961i	$-0.242812\pi$
$522$	−8.50420	−	2.14560i	−0.372219	−	0.0939106i
$523$		−	33.5304i		−	1.46618i	−0.680129	−	0.733092i	$-0.738076\pi$
$523$		−	33.5304i		−	1.46618i	0.680129	−	0.733092i	$-0.261924\pi$
$524$	−40.3117	−	18.3967i	−1.76103	−	0.803662i
$525$		0			0
$526$	19.9606	+	4.33936i	0.870325	+	0.189205i
$527$	−2.05007			−0.0893023
$528$	−14.0813	−	1.23387i	−0.612809	−	0.0536972i
$529$	−21.9134			−0.952755
$530$	−39.9069	−	8.67560i	−1.73344	−	0.376844i
$531$	−0.345998	+	10.4568i	−0.0150150	+	0.453785i
$532$		0			0
$533$			34.8978i			1.51159i
$534$	−0.698374	−	1.12692i	−0.0302216	−	0.0487664i
$535$			47.8081i			2.06692i
$536$	8.07181	−	10.7917i	0.348649	−	0.466132i
$537$	−6.26615	+	6.06224i	−0.270404	+	0.261605i
$538$	1.97420	−	9.08112i	0.0851139	−	0.391515i
$539$		0			0
$540$	27.0165	−	8.58426i	1.16260	−	0.369408i
$541$	−23.6791			−1.01805			−0.509023	−	0.860753i	$-0.669993\pi$
$541$	−23.6791			−1.01805			−0.509023	+	0.860753i	$0.669993\pi$
$542$	−0.00491073	+	0.0225889i	−0.000210934	+	0.000970275i
$543$	7.11857	−	6.88692i	0.305487	−	0.295546i
$544$	3.27795	−	1.79275i	0.140541	−	0.0768635i
$545$		−	1.74295i		−	0.0746599i
$546$		0			0
$547$			10.9063i			0.466318i	0.972439	+	0.233159i	$0.0749063\pi$
$547$			10.9063i			0.466318i	−0.972439	+	0.233159i	$0.925094\pi$
$548$	−12.0435	+	26.3903i	−0.514472	+	1.12734i
$549$	0.0196857	−	0.594941i	0.000840163	−	0.0253914i
$550$	−6.88110	−	1.49593i	−0.293411	−	0.0637865i
$551$	6.07615			0.258853
$552$	−5.06587	+	0.645116i	−0.215618	+	0.0274580i
$553$		0			0
$554$	−25.3084	−	5.50196i	−1.07525	−	0.233756i
$555$	−31.2742	−	32.3261i	−1.32752	−	1.37217i
$556$	−4.80158	+	10.5215i	−0.203632	+	0.446209i
$557$		−	10.9443i		−	0.463725i	−0.972749	−	0.231862i	$-0.925518\pi$
$557$		−	10.9443i		−	0.463725i	0.972749	−	0.231862i	$-0.0744819\pi$
$558$	−12.7689	−	3.22159i	−0.540551	−	0.136381i
$559$			2.35601i			0.0996485i
$560$		0			0
$561$	1.62284	+	1.67743i	0.0685164	+	0.0708210i
$562$	0.484259	−	2.22754i	0.0204272	−	0.0939632i
$563$	−28.2949			−1.19249			−0.596245	−	0.802803i	$-0.703341\pi$
$563$	−28.2949			−1.19249			−0.596245	+	0.802803i	$0.703341\pi$
$564$	−3.40344	+	1.20672i	−0.143311	+	0.0508119i
$565$	29.4370			1.23842
$566$	6.18114	−	28.4326i	0.259813	−	1.19511i
$567$		0			0
$568$	−12.5201	−	9.36455i	−0.525331	−	0.392928i
$569$			0.951435i			0.0398862i	0.999801	+	0.0199431i	$0.00634851\pi$
$569$			0.951435i			0.0398862i	−0.999801	+	0.0199431i	$0.993651\pi$
$570$	−16.6929	+	10.3450i	−0.699190	+	0.433303i
$571$			16.3835i			0.685630i	0.939403	+	0.342815i	$0.111380\pi$
$571$			16.3835i			0.685630i	−0.939403	+	0.342815i	$0.888620\pi$
$572$	16.4842	+	7.52275i	0.689240	+	0.314542i
$573$	−12.2181	+	11.8205i	−0.510419	+	0.493809i
$574$		0			0
$575$	−2.54407			−0.106095
$576$	23.2340	−	6.01505i	0.968084	−	0.250627i
$577$	9.96852			0.414995			0.207497	−	0.978236i	$-0.433468\pi$
$577$	9.96852			0.414995			0.207497	+	0.978236i	$0.433468\pi$
$578$	22.8901	+	4.97621i	0.952101	+	0.206983i
$579$	−21.3601	+	20.6650i	−0.887697	+	0.858810i
$580$	−10.2600	−	4.68228i	−0.426025	−	0.194421i
$581$		0			0
$582$	−14.4016	+	8.92500i	−0.596967	+	0.369953i
$583$		−	21.5993i		−	0.894553i
$584$	6.87599	+	5.14298i	0.284530	+	0.212818i
$585$	−36.3181	−	1.20171i	−1.50157	−	0.0496846i
$586$	3.50217	−	16.1096i	0.144673	−	0.665482i
$587$	29.5354			1.21905			0.609527	−	0.792765i	$-0.291359\pi$
$587$	29.5354			1.21905			0.609527	+	0.792765i	$0.291359\pi$
$588$		0			0
$589$	9.12323			0.375916
$590$	−2.85795	+	13.1463i	−0.117660	+	0.541224i
$591$	13.2839	+	13.7307i	0.546426	+	0.564806i
$592$	−24.9527	−	28.7658i	−1.02555	−	1.18227i
$593$		−	21.0659i		−	0.865071i	−0.901617	−	0.432536i	$-0.857619\pi$
$593$		−	21.0659i		−	0.865071i	0.901617	−	0.432536i	$-0.142381\pi$
$594$	7.47191	+	12.9981i	0.306576	+	0.533319i
$595$		0			0
$596$	−11.5049	+	25.2101i	−0.471259	+	1.03265i
$597$	−26.8614	−	27.7649i	−1.09936	−	1.13634i
$598$	6.39684	+	1.39065i	0.261586	+	0.0568679i
$599$	−39.7366			−1.62359			−0.811796	−	0.583940i	$-0.801510\pi$
$599$	−39.7366			−1.62359			−0.811796	+	0.583940i	$0.801510\pi$
$600$	11.8604	−	1.51037i	0.484200	−	0.0616608i
$601$	36.5567			1.49118			0.745589	−	0.666406i	$-0.232168\pi$
$601$	36.5567			1.49118			0.745589	+	0.666406i	$0.232168\pi$
$602$		0			0
$603$	−14.2861	−	0.472706i	−0.581777	−	0.0192501i
$604$	−9.77578	+	21.4212i	−0.397771	+	0.871615i
$605$			18.6506i			0.758256i
$606$	13.0725	+	21.0942i	0.531035	+	0.856892i
$607$			13.1733i			0.534690i	0.963601	+	0.267345i	$0.0861463\pi$
$607$			13.1733i			0.534690i	−0.963601	+	0.267345i	$0.913854\pi$
$608$	−14.5876	+	7.97812i	−0.591604	+	0.323555i
$609$		0			0
$610$	0.162604	−	0.747963i	0.00658365	−	0.0302841i
$611$	4.62890			0.187265
$612$	−3.54875	−	1.76356i	−0.143450	−	0.0712877i
$613$	−19.0079			−0.767721			−0.383861	−	0.923391i	$-0.625406\pi$
$613$	−19.0079			−0.767721			−0.383861	+	0.923391i	$0.625406\pi$
$614$	−1.09968	+	5.05841i	−0.0443795	+	0.204141i
$615$	−26.6855	+	25.8171i	−1.07606	+	1.04104i
$616$		0			0
$617$		−	41.6979i		−	1.67869i	−0.543596	−	0.839347i	$-0.682938\pi$
$617$		−	41.6979i		−	1.67869i	0.543596	−	0.839347i	$-0.317062\pi$
$618$	9.44731	+	15.2444i	0.380027	+	0.613222i
$619$			13.4107i			0.539021i	0.962997	+	0.269511i	$0.0868619\pi$
$619$			13.4107i			0.539021i	−0.962997	+	0.269511i	$0.913138\pi$
$620$	−15.4053	−	7.03035i	−0.618690	−	0.282346i
$621$	3.63542	+	4.01532i	0.145884	+	0.161129i
$622$	−16.2342	−	3.52926i	−0.650934	−	0.141511i
$623$		0			0
$624$	−30.6476	−	2.68549i	−1.22689	−	0.107505i
$625$	−31.2465			−1.24986
$626$	20.4994	+	4.45649i	0.819321	+	0.178117i
$627$	−7.22199	−	7.46490i	−0.288418	−	0.298120i
$628$	19.4370	+	8.87028i	0.775621	+	0.353963i
$629$			6.28769i			0.250707i
$630$		0			0
$631$			10.7225i			0.426856i	0.976959	+	0.213428i	$0.0684629\pi$
$631$			10.7225i			0.426856i	−0.976959	+	0.213428i	$0.931537\pi$
$632$	−18.4879	+	24.7177i	−0.735410	+	0.983218i
$633$	−21.6354	−	22.3631i	−0.859931	−	0.888855i
$634$	2.49428	−	11.4734i	0.0990604	−	0.455668i
$635$	−29.8858			−1.18598
$636$	12.2552	+	34.5649i	0.485952	+	1.37059i
$637$		0			0
$638$	1.26713	−	5.82864i	0.0501660	−	0.230758i
$639$	−0.548413	+	16.5741i	−0.0216949	+	0.655663i
$640$	30.7801	−	2.23049i	1.21669	−	0.0881680i
$641$		−	23.9750i		−	0.946957i	−0.880805	−	0.473479i	$-0.842998\pi$
$641$		−	23.9750i		−	0.946957i	0.880805	−	0.473479i	$-0.157002\pi$
$642$	36.4920	−	22.6149i	1.44022	−	0.892538i
$643$			24.5118i			0.966649i	0.875441	+	0.483325i	$0.160571\pi$
$643$			24.5118i			0.966649i	−0.875441	+	0.483325i	$0.839429\pi$
$644$		0			0
$645$	−1.80158	+	1.74295i	−0.0709371	+	0.0686287i
$646$	2.68268	+	0.583205i	0.105549	+	0.0229459i
$647$	42.4331			1.66822			0.834108	−	0.551601i	$-0.185983\pi$
$647$	42.4331			1.66822			0.834108	+	0.551601i	$0.185983\pi$
$648$	−19.3321	−	16.5611i	−0.759437	−	0.650581i
$649$	−7.11534			−0.279302
$650$	−14.9766	−	3.25585i	−0.587430	−	0.127705i
$651$		0			0
$652$	17.0043	−	37.2608i	0.665941	−	1.45924i
$653$		−	21.3784i		−	0.836600i	−0.908309	−	0.418300i	$-0.862626\pi$
$653$		−	21.3784i		−	0.836600i	0.908309	−	0.418300i	$-0.137374\pi$
$654$	−1.33040	+	0.824477i	−0.0520227	+	0.0322396i
$655$			60.4345i			2.36137i
$656$	−23.7464	+	20.5987i	−0.927140	+	0.804243i
$657$	0.301187	−	9.10247i	0.0117504	−	0.355121i
$658$		0			0
$659$	−0.835578			−0.0325495			−0.0162748	−	0.999868i	$-0.505181\pi$
$659$	−0.835578			−0.0325495			−0.0162748	+	0.999868i	$0.505181\pi$
$660$	6.44242	+	18.1703i	0.250771	+	0.707278i
$661$	−18.0043			−0.700288			−0.350144	−	0.936696i	$-0.613867\pi$
$661$	−18.0043			−0.700288			−0.350144	+	0.936696i	$0.613867\pi$
$662$	4.58717	−	21.1005i	0.178286	−	0.820095i
$663$	3.53208	+	3.65088i	0.137175	+	0.141789i
$664$	−20.7443	−	15.5160i	−0.805035	−	0.602136i
$665$		0			0
$666$	−9.88081	+	39.1630i	−0.382874	+	1.51754i
$667$		−	2.15496i		−	0.0834403i
$668$	−40.8682	−	18.6506i	−1.58124	−	0.721614i
$669$	−2.35747	−	2.43677i	−0.0911452	−	0.0942109i
$670$	−17.9606	−	3.90457i	−0.693880	−	0.150847i
$671$	0.404830			0.0156283
$672$		0			0
$673$	3.35747			0.129421			0.0647105	−	0.997904i	$-0.479388\pi$
$673$	3.35747			0.129421			0.0647105	+	0.997904i	$0.479388\pi$
$674$	−23.4385	−	5.09544i	−0.902817	−	0.196269i
$675$	−8.51141	−	9.40084i	−0.327604	−	0.361839i
$676$	12.2242	+	5.57865i	0.470162	+	0.214563i
$677$		−	36.8577i		−	1.41656i	−0.705933	−	0.708278i	$-0.749472\pi$
$677$		−	36.8577i		−	1.41656i	0.705933	−	0.708278i	$-0.250528\pi$
$678$	−13.9247	−	22.4693i	−0.534776	−	0.862929i
$679$		0			0
$680$	−4.08049	−	3.05206i	−0.156480	−	0.117041i
$681$	22.6114	−	21.8756i	0.866471	−	0.838275i
$682$	1.90257	−	8.75161i	0.0728530	−	0.335116i
$683$	−4.38633			−0.167838			−0.0839191	−	0.996473i	$-0.526744\pi$
$683$	−4.38633			−0.167838			−0.0839191	+	0.996473i	$0.526744\pi$
$684$	15.7927	+	7.84822i	0.603848	+	0.300084i
$685$	39.5638			1.51165
$686$		0			0
$687$	−12.2557	+	11.8569i	−0.467585	+	0.452369i
$688$	−1.60316	+	1.39065i	−0.0611197	+	0.0530180i
$689$		−	47.0105i		−	1.79096i
$690$	3.66893	+	5.92029i	0.139674	+	0.225382i
$691$		−	40.2595i		−	1.53154i	−0.643113	−	0.765771i	$-0.722358\pi$
$691$		−	40.2595i		−	1.53154i	0.643113	−	0.765771i	$-0.277642\pi$
$692$	−16.1338	+	35.3532i	−0.613315	+	1.34393i
$693$		0			0
$694$	−30.4807	−	6.62639i	−1.15703	−	0.251534i
$695$	15.7736			0.598325
$696$	1.27936	+	10.0464i	0.0484942	+	0.380807i
$697$	5.19053			0.196605
$698$	24.4254	+	5.30999i	0.924515	+	0.200986i
$699$	−31.5614	−	32.6229i	−1.19376	−	1.23391i
$700$		0			0
$701$		−	25.7395i		−	0.972168i	−0.873912	−	0.486084i	$-0.838425\pi$
$701$		−	25.7395i		−	0.972168i	0.873912	−	0.486084i	$-0.161575\pi$
$702$	16.2625	+	28.2901i	0.613787	+	1.06774i
$703$		−	27.9815i		−	1.05534i
$704$	4.61103	+	15.6571i	0.173785	+	0.590099i
$705$	3.42442	+	3.53960i	0.128971	+	0.133309i
$706$	0.126786	−	0.583205i	0.00477167	−	0.0219492i
$707$		0			0
$708$	11.3865	−	4.03717i	0.427931	−	0.151726i
$709$	15.0079			0.563633			0.281817	−	0.959468i	$-0.409063\pi$
$709$	15.0079			0.563633			0.281817	+	0.959468i	$0.409063\pi$
$710$	−4.52991	+	20.8371i	−0.170004	+	0.782003i
$711$	32.7214	+	1.08270i	1.22715	+	0.0406045i
$712$	−0.916921	+	1.22589i	−0.0343631	+	0.0459422i
$713$		−	3.23563i		−	0.121175i
$714$		0			0
$715$		−	24.7128i		−	0.924207i
$716$	9.15881	+	4.17972i	0.342281	+	0.156203i
$717$	−21.0795	+	20.3936i	−0.787229	+	0.761612i
$718$	19.9606	+	4.33936i	0.744924	+	0.161944i
$719$	38.5506			1.43769			0.718847	−	0.695168i	$-0.244670\pi$
$719$	38.5506			1.43769			0.718847	+	0.695168i	$0.244670\pi$
$720$	−20.6193	−	25.4221i	−0.768436	−	0.947427i
$721$		0			0
$722$	14.3183	+	3.11274i	0.532871	+	0.115844i
$723$	7.26657	−	7.03011i	0.270247	−	0.261453i
$724$	−10.4047	−	4.74831i	−0.386689	−	0.176470i
$725$			5.04528i			0.187377i
$726$	14.2361	−	8.82239i	0.528350	−	0.327430i
$727$		−	50.3452i		−	1.86720i	−0.358318	−	0.933600i	$-0.616650\pi$
$727$		−	50.3452i		−	1.86720i	0.358318	−	0.933600i	$-0.383350\pi$
$728$		0			0
$729$	−2.67479	+	26.8672i	−0.0990664	+	0.995081i
$730$	2.48781	−	11.4437i	0.0920781	−	0.423550i
$731$	0.350421			0.0129608
$732$	−0.647839	+	0.229696i	−0.0239448	+	0.00848982i
$733$	12.5516			0.463602			0.231801	−	0.972763i	$-0.425538\pi$
$733$	12.5516			0.463602			0.231801	+	0.972763i	$0.425538\pi$
$734$	6.54943	−	30.1267i	0.241744	−	1.11200i
$735$		0			0
$736$	2.82951	+	5.17360i	0.104297	+	0.190701i
$737$		−	9.72107i		−	0.358080i
$738$	32.3294	+	8.15668i	1.19006	+	0.300252i
$739$		−	6.26058i		−	0.230299i	−0.993348	−	0.115150i	$-0.963265\pi$
$739$		−	6.26058i		−	0.230299i	0.993348	−	0.115150i	$-0.0367347\pi$
$740$	−21.5625	+	47.2489i	−0.792655	+	1.73691i
$741$	−15.7185	−	16.2472i	−0.577433	−	0.596856i
$742$		0			0
$743$	34.2633			1.25700			0.628498	−	0.777811i	$-0.283670\pi$
$743$	34.2633			1.25700			0.628498	+	0.777811i	$0.283670\pi$
$744$	1.92094	+	15.0845i	0.0704252	+	0.553024i
$745$	37.7945			1.38468
$746$	26.9755	+	5.86436i	0.987642	+	0.214710i
$747$	−0.908655	+	27.4614i	−0.0332460	+	1.00476i
$748$	1.11890	−	2.45178i	0.0409109	−	0.0896461i
$749$		0			0
$750$	9.00834	+	14.5361i	0.328938	+	0.530783i
$751$			29.0159i			1.05880i	0.848371	+	0.529402i	$0.177584\pi$
$751$			29.0159i			1.05880i	−0.848371	+	0.529402i	$0.822416\pi$
$752$	2.73224	+	3.14976i	0.0996346	+	0.114860i
$753$	−12.6311	+	12.2201i	−0.460302	+	0.445324i
$754$	2.75787	−	12.6859i	0.100436	−	0.461994i
$755$	32.1142			1.16876
$756$		0			0
$757$	−10.5717			−0.384234			−0.192117	−	0.981372i	$-0.561535\pi$
$757$	−10.5717			−0.384234			−0.192117	+	0.981372i	$0.561535\pi$
$758$	10.2487	−	47.1428i	0.372249	−	1.71230i
$759$	−2.64749	+	2.56134i	−0.0960978	+	0.0929707i
$760$	18.1591	+	13.5823i	0.658698	+	0.492682i
$761$			38.8724i			1.40913i	0.709642	+	0.704563i	$0.248857\pi$
$761$			38.8724i			1.40913i	−0.709642	+	0.704563i	$0.751143\pi$
$762$	14.1370	+	22.8119i	0.512130	+	0.826387i
$763$		0			0
$764$	17.8584	+	8.14986i	0.646094	+	0.294852i
$765$	−0.178736	+	5.40178i	−0.00646223	+	0.195302i
$766$	−11.3531	−	2.46813i	−0.410205	−	0.0891771i
$767$	−15.4864			−0.559181
$768$	−16.2626	−	22.4394i	−0.586826	−	0.809713i
$769$	−25.5953			−0.922989			−0.461494	−	0.887143i	$-0.652687\pi$
$769$	−25.5953			−0.922989			−0.461494	+	0.887143i	$0.652687\pi$
$770$		0			0
$771$	14.4297	+	14.9151i	0.519674	+	0.537154i
$772$	31.2207	+	14.2479i	1.12366	+	0.512792i
$773$			28.4673i			1.02390i	0.859016	+	0.511948i	$0.171076\pi$
$773$			28.4673i			1.02390i	−0.859016	+	0.511948i	$0.828924\pi$
$774$	2.18261	+	0.550671i	0.0784522	+	0.0197935i
$775$			7.57540i			0.272116i
$776$	15.6665	+	11.7180i	0.562395	+	0.420651i
$777$		0			0
$778$	−1.44055	+	6.62639i	−0.0516463	+	0.237568i
$779$	−23.0990			−0.827606
$780$	14.0218	+	39.5473i	0.502061	+	1.41602i
$781$	−11.2779			−0.403557
$782$	0.206838	−	0.951435i	0.00739653	−	0.0340233i
$783$	7.96299	−	7.20959i	0.284574	−	0.257650i
$784$		0			0
$785$		−	29.1395i		−	1.04004i
$786$	46.1298	−	28.5876i	1.64539	−	1.01969i
$787$		−	31.9387i		−	1.13849i	−0.822167	−	0.569247i	$-0.807235\pi$
$787$		−	31.9387i		−	1.13849i	0.822167	−	0.569247i	$-0.192765\pi$
$788$	9.15881	−	20.0693i	0.326269	−	0.714938i
$789$	−17.9803	+	17.3952i	−0.640116	+	0.619286i
$790$	41.1376	+	8.94315i	1.46361	+	0.318183i
$791$		0			0
$792$	10.8219	−	13.5127i	0.384541	−	0.480153i
$793$	0.881103			0.0312889
$794$	−14.3738	−	3.12480i	−0.510105	−	0.110895i
$795$	35.9477	−	34.7779i	1.27493	−	1.23345i
$796$	−18.5201	+	40.5821i	−0.656427	+	1.43840i
$797$			37.7330i			1.33657i	0.743905	+	0.668285i	$0.232971\pi$
$797$			37.7330i			1.33657i	−0.743905	+	0.668285i	$0.767029\pi$
$798$		0			0
$799$		−	0.688481i		−	0.0243567i
$800$	−6.62456	−	12.1127i	−0.234214	−	0.428247i
$801$	1.62284	+	0.0536973i	0.0573403	+	0.00189730i
$802$	3.47637	−	15.9909i	0.122755	−	0.564660i
$803$	6.19382			0.218575
$804$	5.51563	+	15.5564i	0.194521	+	0.548631i
$805$		0			0
$806$	4.14089	−	19.0477i	0.145857	−	0.670926i
$807$	7.91398	+	8.18017i	0.278585	+	0.287956i
$808$	17.1634	−	22.9468i	0.603806	−	0.807267i
$809$			26.2067i			0.921379i	0.887561	+	0.460690i	$0.152398\pi$
$809$			26.2067i			0.921379i	−0.887561	+	0.460690i	$0.847602\pi$
$810$	−9.60191	+	33.3642i	−0.337377	+	1.17230i
$811$			32.1734i			1.12976i	0.825172	+	0.564881i	$0.191078\pi$
$811$			32.1734i			1.12976i	−0.825172	+	0.564881i	$0.808922\pi$
$812$		0			0
$813$	−0.0196857	−	0.0203478i	−0.000690406	−	0.000713628i
$814$	−26.8417	−	5.83529i	−0.940802	−	0.204527i
$815$	−55.8606			−1.95671
$816$	−0.399426	+	4.55838i	−0.0139827	+	0.159575i
$817$	−1.55945			−0.0545582
$818$	−28.2426	−	6.13983i	−0.987479	−	0.214674i
$819$		0			0
$820$	39.0043	+	17.8000i	1.36209	+	0.621604i
$821$			22.3847i			0.781230i	0.920554	+	0.390615i	$0.127738\pi$
$821$			22.3847i			0.781230i	−0.920554	+	0.390615i	$0.872262\pi$
$822$	−18.7150	−	30.1991i	−0.652762	−	1.05332i
$823$		−	32.8946i		−	1.14663i	−0.819334	−	0.573317i	$-0.805656\pi$
$823$		−	32.8946i		−	1.14663i	0.819334	−	0.573317i	$-0.194344\pi$
$824$	12.4037	−	16.5833i	0.432104	−	0.577708i
$825$	6.19842	−	5.99672i	0.215801	−	0.208779i
$826$		0			0
$827$	−16.7455			−0.582297			−0.291148	−	0.956678i	$-0.594037\pi$
$827$	−16.7455			−0.582297			−0.291148	+	0.956678i	$0.594037\pi$
$828$	2.78344	−	5.60100i	0.0967311	−	0.194648i
$829$	0.948403			0.0329394			0.0164697	−	0.999864i	$-0.494757\pi$
$829$	0.948403			0.0329394			0.0164697	+	0.999864i	$0.494757\pi$
$830$	−7.50553	+	34.5247i	−0.260521	+	1.19837i
$831$	22.7976	−	22.0557i	0.790838	−	0.765104i
$832$	10.0358	+	34.0774i	0.347929	+	1.18142i
$833$		0			0
$834$	−7.46144	−	12.0400i	−0.258369	−	0.416911i
$835$			61.2687i			2.12029i
$836$	−4.97933	+	10.9109i	−0.172214	+	0.377363i
$837$	11.9563	−	10.8251i	0.413270	−	0.374169i
$838$	30.2823	+	6.58325i	1.04608	+	0.227415i
$839$	35.5384			1.22692			0.613461	−	0.789725i	$-0.289777\pi$
$839$	35.5384			1.22692			0.613461	+	0.789725i	$0.289777\pi$
$840$		0			0
$841$	24.7264			0.852634
$842$	19.5065	+	4.24063i	0.672238	+	0.146142i
$843$	1.94125	+	2.00655i	0.0668602	+	0.0691091i
$844$	−14.9169	+	32.6867i	−0.513462	+	1.12512i
$845$		−	18.3263i		−	0.630444i
$846$	1.08192	−	4.28822i	0.0371970	−	0.147432i
$847$		0			0
$848$	31.9885	−	27.7482i	1.09849	−	0.952879i
$849$	24.7783	+	25.6118i	0.850390	+	0.878994i
$850$	−0.484259	+	2.22754i	−0.0166100	+	0.0764041i
$851$	−9.92389			−0.340186
$852$	18.0478	−	6.39899i	0.618308	−	0.219226i
$853$	35.8618			1.22788			0.613942	−	0.789351i	$-0.289583\pi$
$853$	35.8618			1.22788			0.613942	+	0.789351i	$0.289583\pi$
$854$		0			0
$855$	0.795415	−	24.0390i	0.0272026	−	0.822118i
$856$	−39.6970	−	29.6919i	−1.35682	−	1.01485i
$857$			38.0573i			1.30001i	0.759929	+	0.650006i	$0.225234\pi$
$857$			38.0573i			1.30001i	−0.759929	+	0.650006i	$0.774766\pi$
$858$	−18.8633	+	11.6900i	−0.643984	+	0.399091i
$859$			21.5535i			0.735397i	0.929945	+	0.367699i	$0.119854\pi$
$859$			21.5535i			0.735397i	−0.929945	+	0.367699i	$0.880146\pi$
$860$	2.63325	+	1.20171i	0.0897929	+	0.0409779i
$861$		0			0
$862$	40.2429	+	8.74866i	1.37068	+	0.297980i
$863$	32.4744			1.10544			0.552721	−	0.833366i	$-0.313589\pi$
$863$	32.4744			1.10544			0.552721	+	0.833366i	$0.313589\pi$
$864$	−9.65112	+	27.7643i	−0.328338	+	0.944560i
$865$	53.0008			1.80208
$866$	−36.0897	−	7.84576i	−1.22638	−	0.266610i
$867$	−20.6191	+	19.9482i	−0.700262	+	0.677475i
$868$		0			0
$869$			22.2654i			0.755303i
$870$	11.7408	−	7.27605i	0.398052	−	0.246681i
$871$		−	21.1577i		−	0.716901i
$872$	1.44725	+	1.08249i	0.0490099	+	0.0366576i
$873$	0.686235	−	20.7394i	0.0232255	−	0.701923i
$874$	−0.920475	+	4.23409i	−0.0311355	+	0.143220i
$875$		0			0
$876$	−9.91181	+	3.51431i	−0.334889	+	0.118737i
$877$	−28.1913			−0.951953			−0.475977	−	0.879458i	$-0.657905\pi$
$877$	−28.1913			−0.951953			−0.475977	+	0.879458i	$0.657905\pi$
$878$	−5.52283	+	25.4044i	−0.186386	+	0.857358i
$879$	14.0391	+	14.5114i	0.473529	+	0.489456i
$880$	16.8159	−	14.5869i	0.566865	−	0.491724i
$881$			5.81314i			0.195850i	0.995194	+	0.0979249i	$0.0312205\pi$
$881$			5.81314i			0.195850i	−0.995194	+	0.0979249i	$0.968780\pi$
$882$		0			0
$883$			47.2938i			1.59156i	0.605583	+	0.795782i	$0.292940\pi$
$883$			47.2938i			1.59156i	−0.605583	+	0.795782i	$0.707060\pi$
$884$	2.43525	−	5.33625i	0.0819065	−	0.179478i
$885$	−11.4567	−	11.8420i	−0.385112	−	0.398066i
$886$	−11.4270	−	2.48418i	−0.383897	−	0.0834577i
$887$	−30.3896			−1.02038			−0.510192	−	0.860061i	$-0.670425\pi$
$887$	−30.3896			−1.02038			−0.510192	+	0.860061i	$0.670425\pi$
$888$	46.2650	−	5.89165i	1.55255	−	0.197711i
$889$		0			0
$890$	2.04025	+	0.443542i	0.0683892	+	0.0148676i
$891$	−18.3221	−	1.21383i	−0.613812	−	0.0406647i
$892$	−1.62540	+	3.56166i	−0.0544225	+	0.119253i
$893$			3.06388i			0.102529i
$894$	−17.8781	−	28.8486i	−0.597933	−	0.964841i
$895$		−	13.7307i		−	0.458967i
$896$		0			0
$897$	−5.76221	+	5.57470i	−0.192394	+	0.186134i
$898$	−7.24213	+	33.3130i	−0.241673	+	1.11167i
$899$	−6.41675			−0.214011
$900$	−6.51670	+	13.1133i	−0.217223	+	0.437111i
$901$	−6.99211			−0.232941
$902$	−4.81707	+	22.1580i	−0.160391	+	0.737782i
$903$		0			0
$904$	−18.2823	+	24.4428i	−0.608060	+	0.812954i
$905$			15.5986i			0.518514i
$906$	−15.1911	−	24.5128i	−0.504691	−	0.814384i
$907$		−	42.6975i		−	1.41775i	−0.705335	−	0.708874i	$-0.749203\pi$
$907$		−	42.6975i		−	1.41775i	0.705335	−	0.708874i	$-0.250797\pi$
$908$	−33.0496	−	15.0825i	−1.09679	−	0.500531i
$909$	−30.3772	−	1.00513i	−1.00755	−	0.0333381i
$910$		0			0
$911$	42.4679			1.40702			0.703511	−	0.710684i	$-0.251614\pi$
$911$	42.4679			1.40702			0.703511	+	0.710684i	$0.251614\pi$
$912$	1.77753	−	20.2857i	0.0588599	−	0.671728i
$913$	−18.6862			−0.618424
$914$	−25.8291	−	5.61516i	−0.854352	−	0.185733i
$915$	0.651832	+	0.673757i	0.0215489	+	0.0222737i
$916$	17.9134	+	8.17495i	0.591874	+	0.270108i
$917$		0			0
$918$	4.20774	−	2.41880i	0.138876	−	0.0798323i
$919$		−	21.2198i		−	0.699978i	−0.936754	−	0.349989i	$-0.886185\pi$
$919$		−	21.2198i		−	0.699978i	0.936754	−	0.349989i	$-0.113815\pi$
$920$	4.81707	−	6.44026i	0.158814	−	0.212329i
$921$	−4.40829	−	4.55656i	−0.145258	−	0.150144i
$922$	−4.91692	+	22.6173i	−0.161930	+	0.744862i
$923$	−24.5462			−0.807948
$924$		0			0
$925$	23.2342			0.763937
$926$	−3.41413	+	15.7047i	−0.112195	+	0.516087i
$927$	−21.9531	−	0.726395i	−0.721035	−	0.0238579i
$928$	10.2600	−	5.61134i	0.336802	−	0.184201i
$929$		−	27.0508i		−	0.887507i	−0.896149	−	0.443753i	$-0.853647\pi$
$929$		−	27.0508i		−	0.887507i	0.896149	−	0.443753i	$-0.146353\pi$
$930$	17.6287	−	10.9249i	0.578066	−	0.358240i
$931$		0			0
$932$	−21.7605	+	47.6828i	−0.712790	+	1.56190i
$933$	14.6236	−	14.1478i	0.478756	−	0.463177i
$934$	50.1555	+	10.9036i	1.64114	+	0.356777i
$935$	−3.67566			−0.120207
$936$	23.5537	−	29.4101i	0.769878	−	0.961299i
$937$	−47.2071			−1.54219			−0.771094	−	0.636721i	$-0.780290\pi$
$937$	−47.2071			−1.54219			−0.771094	+	0.636721i	$0.780290\pi$
$938$		0			0
$939$	−18.4656	+	17.8647i	−0.602603	+	0.582994i
$940$	2.36103	−	5.17360i	0.0770082	−	0.168744i
$941$			16.0658i			0.523729i	0.965105	+	0.261864i	$0.0843373\pi$
$941$			16.0658i			0.523729i	−0.965105	+	0.261864i	$0.915663\pi$
$942$	−22.2423	+	13.7840i	−0.724693	+	0.449108i
$943$			8.19224i			0.266776i
$944$	−9.14094	−	10.5378i	−0.297512	−	0.342976i
$945$		0			0
$946$	−0.325209	+	1.49593i	−0.0105734	+	0.0486367i
$947$	25.5886			0.831519			0.415759	−	0.909475i	$-0.363516\pi$
$947$	25.5886			0.831519			0.415759	+	0.909475i	$0.363516\pi$
$948$	−12.6332	−	35.6308i	−0.410307	−	1.15724i
$949$	13.4807			0.437602
$950$	2.15506	−	9.91303i	0.0699192	−	0.321621i
$951$	9.99882	+	10.3351i	0.324234	+	0.335140i
$952$		0			0
$953$			25.0168i			0.810375i	0.914234	+	0.405187i	$0.132794\pi$
$953$			25.0168i			0.810375i	−0.914234	+	0.405187i	$0.867206\pi$
$954$	−43.5505	−	10.9878i	−1.41000	−	0.355743i
$955$		−	26.7729i		−	0.866352i
$956$	30.8105	+	14.0607i	0.996484	+	0.454756i
$957$	5.07953	+	5.25038i	0.164198	+	0.169721i
$958$	15.4764	+	3.36450i	0.500019	+	0.108702i
$959$		0			0
$960$	−18.6337	+	32.8842i	−0.601399	+	1.06133i
$961$	21.3654			0.689205
$962$	−58.4205	−	12.7004i	−1.88355	−	0.409477i
$963$	−1.73884	+	52.5512i	−0.0560332	+	1.69344i
$964$	−10.6211	−	4.84703i	−0.342081	−	0.156112i
$965$		−	46.8054i		−	1.50672i
$966$		0			0
$967$		−	25.4408i		−	0.818122i	−0.912507	−	0.409061i	$-0.865856\pi$
$967$		−	25.4408i		−	0.818122i	0.912507	−	0.409061i	$-0.134144\pi$
$968$	−15.4864	−	11.5832i	−0.497751	−	0.372300i
$969$	−2.41653	+	2.33789i	−0.0776301	+	0.0751039i
$970$	5.66833	−	26.0737i	0.181999	−	0.837177i
$971$	6.57998			0.211162			0.105581	−	0.994411i	$-0.466330\pi$
$971$	6.57998			0.211162			0.105581	+	0.994411i	$0.466330\pi$
$972$	30.0090	−	8.45329i	0.962540	−	0.271139i
$973$		0			0
$974$	2.98572	−	13.7340i	0.0956687	−	0.440066i
$975$	13.4907	−	13.0517i	0.432049	−	0.417990i
$976$	0.520077	+	0.599550i	0.0166473	+	0.0191911i
$977$		−	5.15268i		−	0.164849i	−0.996597	−	0.0824244i	$-0.973734\pi$
$977$		−	5.15268i		−	0.164849i	0.996597	−	0.0824244i	$-0.0262663\pi$
$978$	26.4240	+	42.6385i	0.844946	+	1.36343i
$979$			1.10427i			0.0352926i
$980$		0			0
$981$	0.0633932	−	1.91587i	0.00202399	−	0.0611691i
$982$	3.65255	+	0.794050i	0.116557	+	0.0253391i
$983$	32.3024			1.03029			0.515143	−	0.857104i	$-0.327739\pi$
$983$	32.3024			1.03029			0.515143	+	0.857104i	$0.327739\pi$
$984$	−4.86360	−	38.1921i	−0.155046	−	1.21752i
$985$	−30.0874			−0.958665
$986$	−1.88684	−	0.410192i	−0.0600893	−	0.0130632i
$987$		0			0
$988$	−10.8374	+	23.7474i	−0.344783	+	0.755507i
$989$			0.553071i			0.0175866i
$990$	−22.8940	−	5.77614i	−0.727618	−	0.183578i
$991$		−	2.58291i		−	0.0820487i	−0.999158	−	0.0410244i	$-0.986938\pi$
$991$		−	2.58291i		−	0.0820487i	0.999158	−	0.0410244i	$-0.0130621\pi$
$992$	15.4053	−	8.42533i	0.489118	−	0.267505i
$993$	18.3886	+	19.0071i	0.583545	+	0.603173i
$994$		0			0
$995$	60.8399			1.92875
$996$	29.9031	−	10.6024i	0.947516	−	0.335949i
$997$	42.8067			1.35570			0.677851	−	0.735199i	$-0.262912\pi$
$997$	42.8067			1.35570			0.677851	+	0.735199i	$0.262912\pi$
$998$	5.96134	−	27.4216i	0.188703	−	0.868014i
$999$	−33.2012	−	36.6707i	−1.05044	−	1.16021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.d.491.12		12
3.2	odd	2	inner	588.2.e.d.491.1		12
4.3	odd	2	inner	588.2.e.d.491.2		12
7.2	even	3		588.2.n.e.263.5		24
7.3	odd	6		84.2.n.a.23.4	yes	24
7.4	even	3		588.2.n.e.275.4		24
7.5	odd	6		84.2.n.a.11.5	yes	24
7.6	odd	2		588.2.e.e.491.12		12
12.11	even	2	inner	588.2.e.d.491.11		12
21.2	odd	6		588.2.n.e.263.8		24
21.5	even	6		84.2.n.a.11.8	yes	24
21.11	odd	6		588.2.n.e.275.9		24
21.17	even	6		84.2.n.a.23.9	yes	24
21.20	even	2		588.2.e.e.491.1		12
28.3	even	6		84.2.n.a.23.8	yes	24
28.11	odd	6		588.2.n.e.275.8		24
28.19	even	6		84.2.n.a.11.9	yes	24
28.23	odd	6		588.2.n.e.263.9		24
28.27	even	2		588.2.e.e.491.2		12
84.11	even	6		588.2.n.e.275.5		24
84.23	even	6		588.2.n.e.263.4		24
84.47	odd	6		84.2.n.a.11.4	✓	24
84.59	odd	6		84.2.n.a.23.5	yes	24
84.83	odd	2		588.2.e.e.491.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.4	✓	24	84.47	odd	6
84.2.n.a.11.5	yes	24	7.5	odd	6
84.2.n.a.11.8	yes	24	21.5	even	6
84.2.n.a.11.9	yes	24	28.19	even	6
84.2.n.a.23.4	yes	24	7.3	odd	6
84.2.n.a.23.5	yes	24	84.59	odd	6
84.2.n.a.23.8	yes	24	28.3	even	6
84.2.n.a.23.9	yes	24	21.17	even	6
588.2.e.d.491.1		12	3.2	odd	2	inner
588.2.e.d.491.2		12	4.3	odd	2	inner
588.2.e.d.491.11		12	12.11	even	2	inner
588.2.e.d.491.12		12	1.1	even	1	trivial
588.2.e.e.491.1		12	21.20	even	2
588.2.e.e.491.2		12	28.27	even	2
588.2.e.e.491.11		12	84.83	odd	2
588.2.e.e.491.12		12	7.6	odd	2
588.2.n.e.263.4		24	84.23	even	6
588.2.n.e.263.5		24	7.2	even	3
588.2.n.e.263.8		24	21.2	odd	6
588.2.n.e.263.9		24	28.23	odd	6
588.2.n.e.275.4		24	7.4	even	3
588.2.n.e.275.5		24	84.11	even	6
588.2.n.e.275.8		24	28.11	odd	6
588.2.n.e.275.9		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 $\F_{q}$
Belyi maps

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+(1.38193 + 0.300427i) q^{2} +(-1.24483 + 1.20432i) q^{3} +(1.81949 + 0.830342i) q^{4} -2.72774i q^{5} +(-2.08209 + 1.29031i) q^{6} +(2.26495 + 1.69410i) q^{8} +(0.0992110 - 2.99836i) q^{9} +(0.819487 - 3.76955i) q^{10} +2.04025 q^{11} +(-3.26495 + 1.15761i) q^{12} +4.44055 q^{13} +(3.28508 + 3.39557i) q^{15} +(2.62106 + 3.02159i) q^{16} -0.660466i q^{17} +(1.03789 - 4.11373i) q^{18} +2.93921i q^{19} +(2.26495 - 4.96308i) q^{20} +(2.81949 + 0.612946i) q^{22} +1.04242 q^{23} +(-4.85973 + 0.618866i) q^{24} -2.44055 q^{25} +(6.13655 + 1.33406i) q^{26} +(3.48749 + 3.85193i) q^{27} -2.06727i q^{29} +(3.51964 + 5.67939i) q^{30} -3.10397i q^{31} +(2.71437 + 4.96308i) q^{32} +(-2.53976 + 2.45712i) q^{33} +(0.198422 - 0.912721i) q^{34} +(2.67018 - 5.37310i) q^{36} -9.52008 q^{37} +(-0.883020 + 4.06180i) q^{38} +(-5.52774 + 5.34786i) q^{39} +(4.62106 - 6.17820i) q^{40} +7.85889i q^{41} +0.530567i q^{43} +(3.71220 + 1.69410i) q^{44} +(-8.17874 - 0.270622i) q^{45} +(1.44055 + 0.313170i) q^{46} +1.04242 q^{47} +(-6.90176 - 0.604764i) q^{48} +(-3.37268 - 0.733208i) q^{50} +(0.795415 + 0.822169i) q^{51} +(8.07953 + 3.68718i) q^{52} -10.5866i q^{53} +(3.66226 + 6.37086i) q^{54} -5.56526i q^{55} +(-3.53976 - 3.65883i) q^{57} +(0.621065 - 2.85683i) q^{58} -3.48749 q^{59} +(3.15767 + 8.90594i) q^{60} +0.198422 q^{61} +(0.932518 - 4.28949i) q^{62} +(2.26004 + 7.67413i) q^{64} -12.1127i q^{65} +(-4.24797 + 2.63256i) q^{66} -4.76465i q^{67} +(0.548413 - 1.20171i) q^{68} +(-1.29763 + 1.25541i) q^{69} -5.52774 q^{71} +(5.30423 - 6.62307i) q^{72} +3.03582 q^{73} +(-13.1561 - 2.86009i) q^{74} +(3.03808 - 2.93921i) q^{75} +(-2.44055 + 5.34786i) q^{76} +(-9.24562 + 5.72971i) q^{78} +10.9131i q^{79} +(8.24211 - 7.14958i) q^{80} +(-8.98031 - 0.594941i) q^{81} +(-2.36103 + 10.8605i) q^{82} -9.15881 q^{83} -1.80158 q^{85} +(-0.159397 + 0.733208i) q^{86} +(2.48966 + 2.57340i) q^{87} +(4.62106 + 3.45638i) q^{88} +0.541243i q^{89} +(-11.2212 - 2.83110i) q^{90} +(1.89666 + 0.865562i) q^{92} +(3.73818 + 3.86392i) q^{93} +(1.44055 + 0.313170i) q^{94} +8.01740 q^{95} +(-9.35609 - 2.90922i) q^{96} +6.91692 q^{97} +(0.202415 - 6.11739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{9} - 10 q^{10} - 12 q^{12} + 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} - 14 q^{24} + 12 q^{25} + 14 q^{30} + 10 q^{33} + 4 q^{34} + 22 q^{36} + 8 q^{37} + 34 q^{40} - 18 q^{45}+ \cdots - 36 q^{97}+O(q^{100}) \) 12 * q + 2 * q^4 + 2 * q^9 - 10 * q^10 - 12 * q^12 + 12 * q^13 + 10 * q^16 + 10 * q^18 + 14 * q^22 - 14 * q^24 + 12 * q^25 + 14 * q^30 + 10 * q^33 + 4 * q^34 + 22 * q^36 + 8 * q^37 + 34 * q^40 - 18 * q^45 - 24 * q^46 - 4 * q^48 + 16 * q^52 + 38 * q^54 - 2 * q^57 - 14 * q^58 - 14 * q^60 + 4 * q^61 - 34 * q^64 + 30 * q^66 - 18 * q^69 - 20 * q^72 + 12 * q^76 - 52 * q^78 - 26 * q^81 - 68 * q^82 - 20 * q^85 + 34 * q^88 + 20 * q^90 + 6 * q^93 - 24 * q^94 - 62 * q^96 - 36 * q^97

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