LMFDB - Embedded newform 588.2.e.e.491.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
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			491.2
Root			$-1.38193 + 0.300427i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.e.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38193 + 0.300427i) q^{2} +(-1.24483 + 1.20432i) q^{3} +(1.81949 - 0.830342i) q^{4} +2.72774i q^{5} +(1.35846 - 2.03828i) q^{6} +(-2.26495 + 1.69410i) q^{8} +(0.0992110 - 2.99836i) q^{9} +O(q^{10})$	\(q+(-1.38193 + 0.300427i) q^{2} +(-1.24483 + 1.20432i) q^{3} +(1.81949 - 0.830342i) q^{4} +2.72774i q^{5} +(1.35846 - 2.03828i) q^{6} +(-2.26495 + 1.69410i) q^{8} +(0.0992110 - 2.99836i) q^{9} +(-0.819487 - 3.76955i) q^{10} -2.04025 q^{11} +(-1.26495 + 3.22489i) q^{12} -4.44055 q^{13} +(-3.28508 - 3.39557i) q^{15} +(2.62106 - 3.02159i) q^{16} +0.660466i q^{17} +(0.763686 + 4.17334i) q^{18} +2.93921i q^{19} +(2.26495 + 4.96308i) q^{20} +(2.81949 - 0.612946i) q^{22} -1.04242 q^{23} +(0.779241 - 4.83661i) q^{24} -2.44055 q^{25} +(6.13655 - 1.33406i) q^{26} +(3.48749 + 3.85193i) q^{27} -2.06727i q^{29} +(5.55989 + 3.70553i) q^{30} -3.10397i q^{31} +(-2.71437 + 4.96308i) q^{32} +(2.53976 - 2.45712i) q^{33} +(-0.198422 - 0.912721i) q^{34} +(-2.30915 - 5.53785i) 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} +(0.376190 + 6.91798i) q^{48} +(3.37268 - 0.733208i) q^{50} +(-0.795415 - 0.822169i) q^{51} +(-8.07953 + 3.68718i) q^{52} -10.5866i q^{53} +(-5.97671 - 4.27538i) q^{54} -5.56526i q^{55} +(-3.53976 - 3.65883i) q^{57} +(0.621065 + 2.85683i) q^{58} -3.48749 q^{59} +(-8.79664 - 3.45046i) q^{60} -0.198422 q^{61} +(0.932518 + 4.28949i) q^{62} +(2.26004 - 7.67413i) q^{64} -12.1127i q^{65} +(-2.77160 + 4.15859i) q^{66} +4.76465i q^{67} +(0.548413 + 1.20171i) q^{68} +(1.29763 - 1.25541i) q^{69} +5.52774 q^{71} +(4.85482 + 6.95922i) q^{72} -3.03582 q^{73} +(13.1561 - 2.86009i) q^{74} +(3.03808 - 2.93921i) q^{75} +(2.44055 + 5.34786i) q^{76} +(-6.03233 + 9.05108i) 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} +(-11.3838 + 2.08313i) q^{90} +(-1.89666 + 0.865562i) q^{92} +(3.73818 + 3.86392i) q^{93} +(-1.44055 + 0.313170i) q^{94} -8.01740 q^{95} +(-2.59822 - 9.44718i) 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}+O(q^{10}) $ 12 * q + 2 * q^4 + 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38193	+	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	$0.208807\pi$
$5$			2.72774i			1.21988i	−0.792447	+	0.609941i	$0.791193\pi$
$6$	1.35846	−	2.03828i	0.554591	−	0.832123i
$7$		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	$-0.599519\pi$
$11$	−2.04025			−0.615157			−0.307579	+	0.951523i	$0.599519\pi$
$12$	−1.26495	+	3.22489i	−0.365161	+	0.930944i
$13$	−4.44055			−1.23159			−0.615794	−	0.787907i	$-0.711165\pi$
$13$	−4.44055			−1.23159			−0.615794	+	0.787907i	$0.711165\pi$
$14$		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	$0.0255218\pi$
$17$			0.660466i			0.160187i	−0.996787	+	0.0800933i	$0.974478\pi$
$18$	0.763686	+	4.17334i	0.180002	+	0.983666i
$19$			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	$-0.534662\pi$
$23$	−1.04242			−0.217359			−0.108679	+	0.994077i	$0.534662\pi$
$24$	0.779241	−	4.83661i	0.159062	−	0.987269i
$25$	−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	$-0.0614783\pi$
$30$	5.55989	+	3.70553i	1.01509	+	0.676535i
$31$		−	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
$36$	−2.30915	−	5.53785i	−0.384858	−	0.922976i
$37$	−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	$-0.789690\pi$
$41$		−	7.85889i		−	1.22735i	0.789558	−	0.613676i	$-0.210310\pi$
$42$		0			0
$43$		−	0.530567i		−	0.0809106i	−0.999181	−	0.0404553i	$-0.987119\pi$
$43$		−	0.530567i		−	0.0809106i	0.999181	−	0.0404553i	$-0.0128808\pi$
$44$	−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	$0.475777\pi$
$48$	0.376190	+	6.91798i	0.0542983	+	0.998525i
$49$		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	$-0.259129\pi$
$54$	−5.97671	−	4.27538i	−0.813328	−	0.581806i
$55$		−	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	$0.572897\pi$
$60$	−8.79664	−	3.45046i	−1.13564	−	0.445453i
$61$	−0.198422			−0.0254053			−0.0127027	−	0.999919i	$-0.504043\pi$
$61$	−0.198422			−0.0254053			−0.0127027	+	0.999919i	$0.504043\pi$
$62$	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
$66$	−2.77160	+	4.15859i	−0.341161	+	0.511887i
$67$			4.76465i			0.582095i	0.956709	+	0.291048i	$0.0940038\pi$
$67$			4.76465i			0.582095i	−0.956709	+	0.291048i	$0.905996\pi$
$68$	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	$-0.393622\pi$
$71$	5.52774			0.656022			0.328011	+	0.944674i	$0.393622\pi$
$72$	4.85482	+	6.95922i	0.572146	+	0.820152i
$73$	−3.03582			−0.355316			−0.177658	−	0.984092i	$-0.556852\pi$
$73$	−3.03582			−0.355316			−0.177658	+	0.984092i	$0.556852\pi$
$74$	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
$78$	−6.03233	+	9.05108i	−0.683027	+	1.02483i
$79$		−	10.9131i		−	1.22782i	−0.789375	−	0.613911i	$-0.789595\pi$
$79$		−	10.9131i		−	1.22782i	0.789375	−	0.613911i	$-0.210405\pi$
$80$	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	$-0.990868\pi$
$89$		−	0.541243i		−	0.0573717i	0.999588	−	0.0286858i	$-0.00913224\pi$
$90$	−11.3838	+	2.08313i	−1.19996	+	0.219582i
$91$		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
$96$	−2.59822	−	9.44718i	−0.265180	−	0.964199i
$97$	−6.91692			−0.702307			−0.351153	−	0.936318i	$-0.614210\pi$
$97$	−6.91692			−0.702307			−0.351153	+	0.936318i	$0.614210\pi$
$98$		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	$0.168157\pi$
$101$			10.1313i			1.00810i	−0.863675	+	0.504049i	$0.831843\pi$
$102$	1.34621	+	0.897219i	0.133295	+	0.0888380i
$103$		−	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	$-0.178297\pi$
$107$	17.5266			1.69436			0.847182	+	0.531303i	$0.178297\pi$
$108$	9.54387	+	4.11273i	0.918359	+	0.395748i
$109$	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	$0.830533\pi$
$114$	5.99093	+	3.99282i	0.561102	+	0.373961i
$115$		−	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
$120$	13.1930	+	2.12556i	1.20435	+	0.194037i
$121$	−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	$0.161583\pi$
$127$			10.9563i			0.972210i	−0.873900	+	0.486105i	$0.838417\pi$
$128$	−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	$0.919091\pi$
$132$	2.58082	−	6.57956i	0.224631	−	0.572677i
$133$		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	$0.787299\pi$
$138$	−1.41609	+	2.12473i	−0.120545	+	0.180869i
$139$			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
$144$	−8.79978	−	8.15867i	−0.733315	−	0.679889i
$145$	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	$0.807892\pi$
$150$	−3.31540	+	4.97452i	−0.270701	+	0.406168i
$151$		−	11.7732i		−	0.958089i	−0.877791	−	0.479045i	$-0.840983\pi$
$151$		−	11.7732i		−	0.958089i	0.877791	−	0.479045i	$-0.159017\pi$
$152$	−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
$156$	5.61710	−	14.3203i	0.449728	−	1.14654i
$157$	−10.6827			−0.852571			−0.426285	−	0.904589i	$-0.640178\pi$
$157$	−10.6827			−0.852571			−0.426285	+	0.904589i	$0.640178\pi$
$158$	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
$162$	12.5889	−	1.87576i	0.989081	−	0.147374i
$163$			20.4787i			1.60402i	0.597313	+	0.802008i	$0.296235\pi$
$163$			20.4787i			1.60402i	−0.597313	+	0.802008i	$0.703765\pi$
$164$	−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	$-0.735473\pi$
$173$		−	19.4303i		−	1.47726i	0.674112	−	0.738630i	$-0.264527\pi$
$174$	−4.21367	−	2.80831i	−0.319438	−	0.212898i
$175$		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	$-0.560239\pi$
$179$	−5.03373			−0.376239			−0.188119	+	0.982146i	$0.560239\pi$
$180$	15.1058	−	6.29875i	1.12592	−	0.469481i
$181$	5.71850			0.425053			0.212526	−	0.977155i	$-0.431831\pi$
$181$	5.71850			0.425053			0.212526	+	0.977155i	$0.431831\pi$
$182$		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
$186$	−6.32675	−	4.21663i	−0.463900	−	0.309179i
$187$		−	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	$-0.615552\pi$
$191$	−9.81507			−0.710193			−0.355097	+	0.934830i	$0.615552\pi$
$192$	6.42876	+	12.2748i	0.463956	+	0.885858i
$193$	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	$-0.128540\pi$
$198$	−1.55811	−	8.51464i	−0.110730	−	0.605109i
$199$			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
$204$	−2.12993	−	0.835460i	−0.149125	−	0.0584939i
$205$	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	$-0.787792\pi$
$211$		−	17.9648i		−	1.23675i	0.785884	−	0.618374i	$-0.212208\pi$
$212$	−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
$216$	−14.4246	−	2.81629i	−0.981468	−	0.191624i
$217$		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
$222$	−12.9327	+	19.4046i	−0.867985	+	1.30235i
$223$			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	$0.705949\pi$
$228$	−9.47863	−	3.71797i	−0.627737	−	0.246229i
$229$	−9.84529			−0.650595			−0.325297	−	0.945612i	$-0.605464\pi$
$229$	−9.84529			−0.650595			−0.325297	+	0.945612i	$0.605464\pi$
$230$	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	$0.671441\pi$
$234$	−3.39119	−	18.5319i	−0.221689	−	1.21147i
$235$			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	$-0.684486\pi$
$239$	−16.9336			−1.09535			−0.547673	+	0.836692i	$0.684486\pi$
$240$	−18.8704	+	1.02615i	−1.21808	+	0.0662375i
$241$	5.83740			0.376020			0.188010	−	0.982167i	$-0.439796\pi$
$241$	5.83740			0.376020			0.188010	+	0.982167i	$0.439796\pi$
$242$	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
$246$	−16.0186	−	10.6760i	−1.02131	−	0.680679i
$247$		−	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	$0.121910\pi$
$257$			11.9816i			0.747392i	−0.927551	+	0.373696i	$0.878090\pi$
$258$	−1.08144	−	0.720756i	−0.0673276	−	0.0448723i
$259$		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	$-0.646912\pi$
$263$	−14.4440			−0.890654			−0.445327	+	0.895368i	$0.646912\pi$
$264$	−1.58984	+	9.86787i	−0.0978481	+	0.607326i
$265$	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	$0.0642014\pi$
$269$			6.57131i			0.400660i	−0.979728	+	0.200330i	$0.935799\pi$
$270$	11.6621	−	16.3029i	0.709734	−	0.992163i
$271$			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
$276$	1.31861	−	3.36167i	0.0793710	−	0.202349i
$277$	−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	$-0.0153099\pi$
$282$	1.41609	−	2.12473i	0.0843267	−	0.126526i
$283$		−	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
$288$	14.6118	+	8.63105i	0.861009	+	0.508590i
$289$	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	$0.110601\pi$
$293$			11.6573i			0.681026i	−0.940240	+	0.340513i	$0.889399\pi$
$294$		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
$300$	3.08719	−	7.87050i	0.178239	−	0.454404i
$301$		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
$306$	−2.75635	+	0.504389i	−0.157570	+	0.0288340i
$307$			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	$0.608084\pi$
$312$	−3.46026	+	21.4772i	−0.195899	+	1.21591i
$313$	−14.8338			−0.838458			−0.419229	−	0.907880i	$-0.637700\pi$
$313$	−14.8338			−0.838458			−0.419229	+	0.907880i	$0.637700\pi$
$314$	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	$-0.0749052\pi$
$318$	−21.5785	−	14.3816i	−1.21006	−	0.806478i
$319$			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
$324$	−16.8336	+	6.37424i	−0.935198	+	0.354125i
$325$	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
$330$	−11.3435	−	7.56020i	−0.624441	−	0.416175i
$331$			15.2688i			0.839251i	0.907697	+	0.419625i	$0.137839\pi$
$331$			15.2688i			0.839251i	−0.907697	+	0.419625i	$0.862161\pi$
$332$	−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
$342$	−12.2663	+	2.24464i	−0.663288	+	0.121376i
$343$		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	$-0.298327\pi$
$347$	22.0565			1.18406			0.592029	+	0.805917i	$0.298327\pi$
$348$	6.66671	+	2.61500i	0.357373	+	0.140179i
$349$	−17.6748			−0.946110			−0.473055	−	0.881033i	$-0.656849\pi$
$349$	−17.6748			−0.946110			−0.473055	+	0.881033i	$0.656849\pi$
$350$		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	$0.00357499\pi$
$353$			0.422020i			0.0224619i	−0.999937	+	0.0112309i	$0.996425\pi$
$354$	−4.73763	+	7.10848i	−0.251802	+	0.377811i
$355$			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	$-0.624476\pi$
$359$	−14.4440			−0.762324			−0.381162	+	0.924508i	$0.624476\pi$
$360$	−18.9829	+	13.2427i	−1.00049	+	0.697950i
$361$	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
$366$	−0.269549	+	0.404439i	−0.0140896	+	0.0211404i
$367$		−	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
$372$	10.0100	+	3.92638i	0.518992	+	0.203573i
$373$	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	$0.339897\pi$
$379$			34.1136i			1.75230i	−0.482038	+	0.876150i	$0.660103\pi$
$380$	−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	$0.567312\pi$
$384$	−12.5718	−	15.0316i	−0.641553	−	0.767079i
$385$		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	$0.961211\pi$
$390$	−24.6890	−	16.4546i	−1.25017	−	0.833212i
$391$		−	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
$396$	4.71123	+	11.2986i	0.236748	+	0.567775i
$397$	10.4012			0.522020			0.261010	−	0.965336i	$-0.415944\pi$
$397$	10.4012			0.522020			0.261010	+	0.965336i	$0.415944\pi$
$398$	−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	$-0.0932976\pi$
$402$	9.71169	+	6.47261i	0.484375	+	0.322825i
$403$			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
$408$	3.19442	+	0.514662i	0.158147	+	0.0254796i
$409$	20.4370			1.01054			0.505272	−	0.862960i	$-0.331392\pi$
$409$	20.4370			1.01054			0.505272	+	0.862960i	$0.331392\pi$
$410$	−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
$414$	−0.796079	−	4.35036i	−0.0391251	−	0.213809i
$415$		−	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
$426$	7.50924	−	11.2671i	0.363824	−	0.545891i
$427$		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	$-0.747418\pi$
$431$	−29.1207			−1.40270			−0.701348	+	0.712820i	$0.747418\pi$
$432$	20.7799	−	0.441611i	0.999774	−	0.0212470i
$433$	26.1153			1.25502			0.627512	−	0.778607i	$-0.284073\pi$
$433$	26.1153			1.25502			0.627512	+	0.778607i	$0.284073\pi$
$434$		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
$438$	−4.12405	+	6.18784i	−0.197055	+	0.295666i
$439$			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	$-0.437065\pi$
$443$	8.26883			0.392864			0.196432	+	0.980517i	$0.437065\pi$
$444$	12.0425	−	30.7012i	0.571510	−	1.45701i
$445$	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	$0.807401\pi$
$450$	−1.86381	−	10.1853i	−0.0878611	−	0.480138i
$451$			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
$456$	14.2158	+	2.29035i	0.665717	+	0.107256i
$457$	−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	$-0.875535\pi$
$461$		−	16.3664i		−	0.762260i	0.924521	−	0.381130i	$-0.124465\pi$
$462$		0			0
$463$		−	11.3643i		−	0.528142i	−0.964503	−	0.264071i	$-0.914935\pi$
$463$		−	11.3643i		−	0.528142i	0.964503	−	0.264071i	$-0.0850653\pi$
$464$	−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	$0.182710\pi$
$468$	10.2539	+	24.5911i	0.473987	+	1.13673i
$469$		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
$474$	−22.2440	−	14.8251i	−1.02170	−	0.680938i
$475$		−	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	$0.417645\pi$
$480$	25.7694	−	7.08726i	1.17621	−	0.323488i
$481$	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
$486$	−13.4121	+	17.4962i	−0.608385	+	0.793642i
$487$			9.93825i			0.450345i	0.974319	+	0.225173i	$0.0722946\pi$
$487$			9.93825i			0.450345i	−0.974319	+	0.225173i	$0.927705\pi$
$488$	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	$-0.518995\pi$
$491$	−2.64307			−0.119280			−0.0596400	+	0.998220i	$0.518995\pi$
$492$	25.3440	+	9.94114i	1.14260	+	0.448181i
$493$	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
$498$	−12.4419	+	18.6682i	−0.557536	+	0.836542i
$499$			19.8429i			0.888289i	0.895955	+	0.444145i	$0.146492\pi$
$499$			19.8429i			0.888289i	−0.895955	+	0.444145i	$0.853508\pi$
$500$	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	$-0.877906\pi$
$509$		−	16.8861i		−	0.748465i	0.927335	−	0.374233i	$-0.122094\pi$
$510$	−2.44738	+	3.67212i	−0.108372	+	0.162604i
$511$		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
$516$	1.71102	+	0.671143i	0.0753233	+	0.0295454i
$517$	−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	$0.242812\pi$
$521$			31.5430i			1.38192i	−0.722892	+	0.690961i	$0.757188\pi$
$522$	8.62743	−	1.57875i	0.377612	−	0.0690998i
$523$		−	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
$528$	−0.767519	−	14.1144i	−0.0334020	−	0.614250i
$529$	−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
$534$	−1.10320	−	0.735260i	−0.0477403	−	0.0318178i
$535$			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
$540$	−11.2185	+	26.0332i	−0.482765	+	1.12029i
$541$	−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	$-0.925094\pi$
$547$		−	10.9063i		−	0.466318i	0.972439	−	0.233159i	$-0.0749063\pi$
$548$	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
$552$	−0.812293	+	5.04176i	−0.0345735	+	0.214592i
$553$		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	$-0.0744819\pi$
$558$	12.9539	−	2.37046i	0.548384	−	0.100350i
$559$			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	$0.703341\pi$
$564$	−1.31861	+	3.36167i	−0.0555235	+	0.141552i
$565$	−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	$0.993651\pi$
$570$	−10.8914	+	16.3417i	−0.456189	+	0.684478i
$571$		−	16.3835i		−	0.685630i	−0.939403	−	0.342815i	$-0.888620\pi$
$571$		−	16.3835i		−	0.685630i	0.939403	−	0.342815i	$-0.111380\pi$
$572$	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
$576$	−22.7856	−	7.53776i	−0.949399	−	0.314074i
$577$	−9.96852			−0.414995			−0.207497	−	0.978236i	$-0.566532\pi$
$577$	−9.96852			−0.414995			−0.207497	+	0.978236i	$0.566532\pi$
$578$	−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
$582$	−9.39639	+	14.0986i	−0.389493	+	0.584406i
$583$			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	$0.142381\pi$
$593$			21.0659i			0.865071i	−0.901617	+	0.432536i	$0.857619\pi$
$594$	12.1940	+	8.72283i	0.500324	+	0.357902i
$595$		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	$-0.198490\pi$
$599$	39.7366			1.62359			0.811796	+	0.583940i	$0.198490\pi$
$600$	−1.90178	+	11.8040i	−0.0776397	+	0.481896i
$601$	−36.5567			−1.49118			−0.745589	−	0.666406i	$-0.767832\pi$
$601$	−36.5567			−1.49118			−0.745589	+	0.666406i	$0.767832\pi$
$602$		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
$606$	20.6503	+	13.7630i	0.838862	+	0.559082i
$607$			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
$612$	3.65756	−	1.52512i	0.147848	−	0.0616491i
$613$	−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	$-0.317062\pi$
$618$	−14.9237	−	9.94629i	−0.600319	−	0.400098i
$619$			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
$624$	−1.67049	−	30.7197i	−0.0668731	−	1.22977i
$625$	−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	$-0.931537\pi$
$631$		−	10.7225i		−	0.426856i	0.976959	−	0.213428i	$-0.0684629\pi$
$632$	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
$636$	34.1407	+	13.3916i	1.35377	+	0.531012i
$637$		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	$-0.157002\pi$
$642$	23.8093	−	35.7241i	0.939678	−	1.40992i
$643$			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	$0.185983\pi$
$648$	21.3479	−	13.8661i	0.838624	−	0.544710i
$649$	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	$-0.137374\pi$
$654$	0.868023	−	1.30241i	0.0339424	−	0.0509281i
$655$		−	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	$-0.494819\pi$
$659$	0.835578			0.0325495			0.0162748	+	0.999868i	$0.494819\pi$
$660$	17.9473	+	7.03980i	0.698598	+	0.274024i
$661$	18.0043			0.700288			0.350144	−	0.936696i	$-0.386133\pi$
$661$	18.0043			0.700288			0.350144	+	0.936696i	$0.386133\pi$
$662$	−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
$666$	−7.27035	−	39.7305i	−0.281720	−	1.53953i
$667$			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	$0.250528\pi$
$677$			36.8577i			1.41656i	−0.705933	+	0.708278i	$0.749472\pi$
$678$	21.9965	+	14.6602i	0.844772	+	0.563021i
$679$		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	$-0.473256\pi$
$683$	4.38633			0.167838			0.0839191	+	0.996473i	$0.473256\pi$
$684$	16.2769	−	6.78708i	0.622364	−	0.259511i
$685$	−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
$690$	−5.79572	−	3.86271i	−0.220639	−	0.147051i
$691$		−	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
$696$	−9.99858	−	1.61090i	−0.378995	−	0.0610611i
$697$	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	$-0.161575\pi$
$702$	26.5399	+	18.9851i	1.00168	+	0.716545i
$703$		−	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
$708$	4.41152	−	11.2468i	0.165795	−	0.422679i
$709$	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	$0.244670\pi$
$720$	22.2547	−	24.0035i	0.829384	−	0.894557i
$721$		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
$726$	−9.28836	+	13.9365i	−0.344723	+	0.517232i
$727$		−	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
$732$	0.250995	−	0.639888i	0.00927704	−	0.0236510i
$733$	−12.5516			−0.463602			−0.231801	−	0.972763i	$-0.574462\pi$
$733$	−12.5516			−0.463602			−0.231801	+	0.972763i	$0.574462\pi$
$734$	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
$738$	32.7979	−	6.00173i	1.20731	−	0.220927i
$739$			6.26058i			0.230299i	0.993348	+	0.115150i	$0.0367347\pi$
$739$			6.26058i			0.230299i	−0.993348	+	0.115150i	$0.963265\pi$
$740$	−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	$-0.716330\pi$
$743$	−34.2633			−1.25700			−0.628498	+	0.777811i	$0.716330\pi$
$744$	−15.0127	−	2.41874i	−0.550392	−	0.0886753i
$745$	−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
$750$	14.2302	+	9.48412i	0.519615	+	0.346311i
$751$		−	29.0159i		−	1.05880i	−0.848371	−	0.529402i	$-0.822416\pi$
$751$		−	29.0159i		−	1.05880i	0.848371	−	0.529402i	$-0.177584\pi$
$752$	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	$-0.751143\pi$
$761$		−	38.8724i		−	1.40913i	0.709642	−	0.704563i	$-0.248857\pi$
$762$	22.3319	+	14.8837i	0.808999	+	0.539179i
$763$		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
$768$	21.8893	+	16.9958i	0.789863	+	0.613283i
$769$	25.5953			0.922989			0.461494	−	0.887143i	$-0.347313\pi$
$769$	25.5953			0.922989			0.461494	+	0.887143i	$0.347313\pi$
$770$		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	$-0.828924\pi$
$773$		−	28.4673i		−	1.02390i	0.859016	−	0.511948i	$-0.171076\pi$
$774$	2.21424	−	0.405186i	0.0795891	−	0.0145641i
$775$			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
$780$	39.0619	+	15.3220i	1.39864	+	0.548614i
$781$	−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
$786$	−30.0975	+	45.1591i	−1.07354	+	1.61077i
$787$		−	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
$792$	−9.90502	−	14.1985i	−0.351960	−	0.504523i
$793$	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	$-0.767029\pi$
$797$		−	37.7330i		−	1.33657i	0.743905	−	0.668285i	$-0.232971\pi$
$798$		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
$804$	−15.3655	−	6.02707i	−0.541898	−	0.212558i
$805$		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	$0.847602\pi$
$810$	5.11659	+	34.3393i	0.179779	+	1.20656i
$811$			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
$816$	−4.56909	+	0.248460i	−0.159950	+	0.00869786i
$817$	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	$0.872262\pi$
$822$	29.5637	+	19.7035i	1.03115	+	0.687239i
$823$			32.8946i			1.14663i	0.819334	+	0.573317i	$0.194344\pi$
$823$			32.8946i			1.14663i	−0.819334	+	0.573317i	$0.805656\pi$
$824$	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	$-0.405963\pi$
$827$	16.7455			0.582297			0.291148	+	0.956678i	$0.405963\pi$
$828$	2.40710	+	5.77275i	0.0836524	+	0.200617i
$829$	−0.948403			−0.0329394			−0.0164697	−	0.999864i	$-0.505243\pi$
$829$	−0.948403			−0.0329394			−0.0164697	+	0.999864i	$0.505243\pi$
$830$	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
$834$	11.7866	+	7.85553i	0.408138	+	0.272015i
$835$		−	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
$846$	0.796079	+	4.35036i	0.0273698	+	0.149568i
$847$		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
$852$	−6.99234	+	17.8263i	−0.239554	+	0.610720i
$853$	−35.8618			−1.22788			−0.613942	−	0.789351i	$-0.710417\pi$
$853$	−35.8618			−1.22788			−0.613942	+	0.789351i	$0.710417\pi$
$854$		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	$-0.774766\pi$
$857$		−	38.0573i		−	1.30001i	0.759929	−	0.650006i	$-0.225234\pi$
$858$	12.3074	−	18.4664i	0.420169	−	0.630433i
$859$			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	$-0.686411\pi$
$863$	−32.4744			−1.10544			−0.552721	+	0.833366i	$0.686411\pi$
$864$	−28.5838	+	6.85313i	−0.972441	+	0.233148i
$865$	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
$870$	7.66034	−	11.4938i	0.259710	−	0.389676i
$871$		−	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
$876$	3.84017	−	9.79017i	0.129747	−	0.330779i
$877$	−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	$-0.968780\pi$
$881$		−	5.81314i		−	0.195850i	0.995194	−	0.0979249i	$-0.0312205\pi$
$882$		0			0
$883$		−	47.2938i		−	1.59156i	−0.605583	−	0.795782i	$-0.707060\pi$
$883$		−	47.2938i		−	1.59156i	0.605583	−	0.795782i	$-0.292940\pi$
$884$	−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	$0.670425\pi$
$888$	−7.41843	+	46.0449i	−0.248946	+	1.54517i
$889$		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
$894$	28.2416	+	18.8224i	0.944540	+	0.629514i
$895$		−	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
$900$	5.63560	+	13.5154i	0.187853	+	0.450514i
$901$	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
$906$	−23.9970	−	15.9935i	−0.797248	−	0.531347i
$907$			42.6975i			1.41775i	0.705335	+	0.708874i	$0.250797\pi$
$907$			42.6975i			1.41775i	−0.705335	+	0.708874i	$0.749203\pi$
$908$	−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	$-0.748386\pi$
$911$	−42.4679			−1.40702			−0.703511	+	0.710684i	$0.748386\pi$
$912$	−20.3334	+	1.10570i	−0.673307	+	0.0366134i
$913$	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
$918$	2.82375	−	3.94742i	0.0931975	−	0.130284i
$919$			21.2198i			0.699978i	0.936754	+	0.349989i	$0.113815\pi$
$919$			21.2198i			0.699978i	−0.936754	+	0.349989i	$0.886185\pi$
$920$	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	$0.146353\pi$
$929$			27.0508i			0.887507i	−0.896149	+	0.443753i	$0.853647\pi$
$930$	11.5019	−	17.2577i	0.377161	−	0.565903i
$931$		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
$936$	−21.5581	−	30.9028i	−0.704647	−	1.01009i
$937$	47.2071			1.54219			0.771094	−	0.636721i	$-0.219710\pi$
$937$	47.2071			1.54219			0.771094	+	0.636721i	$0.219710\pi$
$938$		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	$-0.915663\pi$
$941$		−	16.0658i		−	0.523729i	0.965105	−	0.261864i	$-0.0843373\pi$
$942$	−14.5120	+	21.7743i	−0.472828	+	0.709444i
$943$			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	$-0.636484\pi$
$947$	−25.5886			−0.831519			−0.415759	+	0.909475i	$0.636484\pi$
$948$	35.1936	+	13.8046i	1.14303	+	0.448352i
$949$	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	$0.867206\pi$
$954$	44.1816	−	8.08486i	1.43043	−	0.261757i
$955$		−	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
$960$	−33.4825	+	17.5360i	−1.08064	+	0.565971i
$961$	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	$0.134144\pi$
$967$			25.4408i			0.818122i	−0.912507	+	0.409061i	$0.865856\pi$
$968$	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	$0.466330\pi$
$972$	13.2783	−	28.2079i	0.425902	−	0.904769i
$973$		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	$-0.0262663\pi$
$978$	41.7413	+	27.8196i	1.33474	+	0.889573i
$979$			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	$0.327739\pi$
$984$	−38.0104	−	6.12397i	−1.21173	−	0.195225i
$985$	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
$990$	23.2257	−	4.25011i	0.738162	−	0.135077i
$991$			2.58291i			0.0820487i	0.999158	+	0.0410244i	$0.0130621\pi$
$991$			2.58291i			0.0820487i	−0.999158	+	0.0410244i	$0.986938\pi$
$992$	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
$996$	11.5855	−	29.5361i	0.367100	−	0.935888i
$997$	−42.8067			−1.35570			−0.677851	−	0.735199i	$-0.737088\pi$
$997$	−42.8067			−1.35570			−0.677851	+	0.735199i	$0.737088\pi$
$998$	−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.e.491.2		12
3.2	odd	2	inner	588.2.e.e.491.11		12
4.3	odd	2	inner	588.2.e.e.491.12		12
7.2	even	3		84.2.n.a.11.9	yes	24
7.3	odd	6		588.2.n.e.275.8		24
7.4	even	3		84.2.n.a.23.8	yes	24
7.5	odd	6		588.2.n.e.263.9		24
7.6	odd	2		588.2.e.d.491.2		12
12.11	even	2	inner	588.2.e.e.491.1		12
21.2	odd	6		84.2.n.a.11.4	✓	24
21.5	even	6		588.2.n.e.263.4		24
21.11	odd	6		84.2.n.a.23.5	yes	24
21.17	even	6		588.2.n.e.275.5		24
21.20	even	2		588.2.e.d.491.11		12
28.3	even	6		588.2.n.e.275.4		24
28.11	odd	6		84.2.n.a.23.4	yes	24
28.19	even	6		588.2.n.e.263.5		24
28.23	odd	6		84.2.n.a.11.5	yes	24
28.27	even	2		588.2.e.d.491.12		12
84.11	even	6		84.2.n.a.23.9	yes	24
84.23	even	6		84.2.n.a.11.8	yes	24
84.47	odd	6		588.2.n.e.263.8		24
84.59	odd	6		588.2.n.e.275.9		24
84.83	odd	2		588.2.e.d.491.1		12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.38193 + 0.300427i) q^{2} +(-1.24483 + 1.20432i) q^{3} +(1.81949 - 0.830342i) q^{4} +2.72774i q^{5} +(1.35846 - 2.03828i) q^{6} +(-2.26495 + 1.69410i) q^{8} +(0.0992110 - 2.99836i) q^{9} +O(q^{10})\)	\(q+(-1.38193 + 0.300427i) q^{2} +(-1.24483 + 1.20432i) q^{3} +(1.81949 - 0.830342i) q^{4} +2.72774i q^{5} +(1.35846 - 2.03828i) q^{6} +(-2.26495 + 1.69410i) q^{8} +(0.0992110 - 2.99836i) q^{9} +(-0.819487 - 3.76955i) q^{10} -2.04025 q^{11} +(-1.26495 + 3.22489i) q^{12} -4.44055 q^{13} +(-3.28508 - 3.39557i) q^{15} +(2.62106 - 3.02159i) q^{16} +0.660466i q^{17} +(0.763686 + 4.17334i) q^{18} +2.93921i q^{19} +(2.26495 + 4.96308i) q^{20} +(2.81949 - 0.612946i) q^{22} -1.04242 q^{23} +(0.779241 - 4.83661i) q^{24} -2.44055 q^{25} +(6.13655 - 1.33406i) q^{26} +(3.48749 + 3.85193i) q^{27} -2.06727i q^{29} +(5.55989 + 3.70553i) q^{30} -3.10397i q^{31} +(-2.71437 + 4.96308i) q^{32} +(2.53976 - 2.45712i) q^{33} +(-0.198422 - 0.912721i) q^{34} +(-2.30915 - 5.53785i) 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} +(0.376190 + 6.91798i) q^{48} +(3.37268 - 0.733208i) q^{50} +(-0.795415 - 0.822169i) q^{51} +(-8.07953 + 3.68718i) q^{52} -10.5866i q^{53} +(-5.97671 - 4.27538i) q^{54} -5.56526i q^{55} +(-3.53976 - 3.65883i) q^{57} +(0.621065 + 2.85683i) q^{58} -3.48749 q^{59} +(-8.79664 - 3.45046i) q^{60} -0.198422 q^{61} +(0.932518 + 4.28949i) q^{62} +(2.26004 - 7.67413i) q^{64} -12.1127i q^{65} +(-2.77160 + 4.15859i) q^{66} +4.76465i q^{67} +(0.548413 + 1.20171i) q^{68} +(1.29763 - 1.25541i) q^{69} +5.52774 q^{71} +(4.85482 + 6.95922i) q^{72} -3.03582 q^{73} +(13.1561 - 2.86009i) q^{74} +(3.03808 - 2.93921i) q^{75} +(2.44055 + 5.34786i) q^{76} +(-6.03233 + 9.05108i) 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} +(-11.3838 + 2.08313i) q^{90} +(-1.89666 + 0.865562i) q^{92} +(3.73818 + 3.86392i) q^{93} +(-1.44055 + 0.313170i) q^{94} -8.01740 q^{95} +(-2.59822 - 9.44718i) q^{96} -6.91692 q^{97} +(-0.202415 + 6.11739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{9}+O(q^{10}) \) 12 * q + 2 * q^4 + 2 * q^9	\( 12 q + 2 q^{4} + 2 q^{9} + 10 q^{10} + 12 q^{12} - 12 q^{13} + 10 q^{16} + 10 q^{18} + 14 q^{22} + 14 q^{24} + 12 q^{25} + 14 q^{30} - 10 q^{33} - 4 q^{34} + 22 q^{36} + 8 q^{37} - 34 q^{40} + 18 q^{45} - 24 q^{46} + 4 q^{48} - 16 q^{52} - 38 q^{54} - 2 q^{57} - 14 q^{58} - 14 q^{60} - 4 q^{61} - 34 q^{64} - 30 q^{66} + 18 q^{69} - 20 q^{72} - 12 q^{76} - 52 q^{78} - 26 q^{81} + 68 q^{82} - 20 q^{85} + 34 q^{88} - 20 q^{90} + 6 q^{93} + 24 q^{94} + 62 q^{96} + 36 q^{97}+O(q^{100}) \) 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

Introduction

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