LMFDB - Embedded newform 588.2.e.e.491.5

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			491.5
Root			$-0.225298 - 1.39615i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.e.491.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.225298 - 1.39615i) q^{2} +(-0.687941 - 1.58957i) q^{3} +(-1.89848 + 0.629100i) q^{4} +2.07605i q^{5} +(-2.06429 + 1.31860i) q^{6} +(1.30604 + 2.50883i) q^{8} +(-2.05347 + 2.18706i) q^{9} +O(q^{10})$	\(q+(-0.225298 - 1.39615i) q^{2} +(-0.687941 - 1.58957i) q^{3} +(-1.89848 + 0.629100i) q^{4} +2.07605i q^{5} +(-2.06429 + 1.31860i) q^{6} +(1.30604 + 2.50883i) q^{8} +(-2.05347 + 2.18706i) q^{9} +(2.89848 - 0.467730i) q^{10} +3.98797 q^{11} +(2.30604 + 2.58499i) q^{12} -1.30998 q^{13} +(3.30003 - 1.42820i) q^{15} +(3.20847 - 2.38867i) q^{16} +2.94162i q^{17} +(3.51612 + 2.37422i) q^{18} +1.09683i q^{19} +(-1.30604 - 3.94134i) q^{20} +(-0.898482 - 5.56781i) q^{22} +7.50125 q^{23} +(3.08949 - 3.80198i) q^{24} +0.690016 q^{25} +(0.295137 + 1.82894i) q^{26} +(4.88916 + 1.75957i) q^{27} +0.865568i q^{29} +(-2.73748 - 4.28557i) q^{30} -3.68051i q^{31} +(-4.05781 - 3.94134i) q^{32} +(-2.74349 - 6.33916i) q^{33} +(4.10695 - 0.662741i) q^{34} +(2.52260 - 5.44394i) q^{36} +4.17700 q^{37} +(1.53134 - 0.247114i) q^{38} +(0.901192 + 2.08231i) q^{39} +(-5.20847 + 2.71141i) q^{40} +7.01712i q^{41} -4.27597i q^{43} +(-7.57109 + 2.50883i) q^{44} +(-4.54045 - 4.26311i) q^{45} +(-1.69002 - 10.4729i) q^{46} -7.50125 q^{47} +(-6.00420 - 3.45682i) q^{48} +(-0.155459 - 0.963368i) q^{50} +(4.67591 - 2.02366i) q^{51} +(2.48698 - 0.824111i) q^{52} +4.94107i q^{53} +(1.35511 - 7.22244i) q^{54} +8.27923i q^{55} +(1.74349 - 0.754555i) q^{57} +(1.20847 - 0.195011i) q^{58} -4.88916 q^{59} +(-5.36656 + 4.78746i) q^{60} +4.10695 q^{61} +(-5.13856 + 0.829212i) q^{62} +(-4.58850 + 6.55330i) q^{64} -2.71959i q^{65} +(-8.23233 + 5.25853i) q^{66} +2.42231i q^{67} +(-1.85057 - 5.58461i) q^{68} +(-5.16042 - 11.9238i) q^{69} +0.901192 q^{71} +(-8.16891 - 2.29542i) q^{72} +13.0109 q^{73} +(-0.941069 - 5.83172i) q^{74} +(-0.474691 - 1.09683i) q^{75} +(-0.690016 - 2.08231i) q^{76} +(2.70419 - 1.72734i) q^{78} +10.3615i q^{79} +(4.95900 + 6.66093i) q^{80} +(-0.566494 - 8.98215i) q^{81} +(9.79696 - 1.58094i) q^{82} +12.4386 q^{83} -6.10695 q^{85} +(-5.96991 + 0.963368i) q^{86} +(1.37588 - 0.595460i) q^{87} +(5.20847 + 10.0052i) q^{88} +8.52623i q^{89} +(-4.92900 + 7.29963i) q^{90} +(-14.2410 + 4.71904i) q^{92} +(-5.85044 + 2.53198i) q^{93} +(1.69002 + 10.4729i) q^{94} -2.27707 q^{95} +(-3.47351 + 9.16159i) q^{96} +15.3909 q^{97} +(-8.18919 + 8.72195i) 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 $

$2$	−0.225298	−	1.39615i	−0.159310	−	0.987229i
$2$	−0.225298	−	1.39615i	−0.159310	−	0.987229i
$3$	−0.687941	−	1.58957i	−0.397183	−	0.917739i
$3$	−0.687941	−	1.58957i	−0.397183	−	0.917739i
$4$	−1.89848	+	0.629100i	−0.949241	+	0.314550i
$5$			2.07605i			0.928438i	0.885721	+	0.464219i	$0.153665\pi$
$5$			2.07605i			0.928438i	−0.885721	+	0.464219i	$0.846335\pi$
$6$	−2.06429	+	1.31860i	−0.842743	+	0.538315i
$7$		0			0
$7$		0			0
$8$	1.30604	+	2.50883i	0.461756	+	0.887007i
$9$	−2.05347	+	2.18706i	−0.684491	+	0.729021i
$10$	2.89848	−	0.467730i	0.916580	−	0.147909i
$11$	3.98797			1.20242			0.601209	−	0.799092i	$-0.294686\pi$
$11$	3.98797			1.20242			0.601209	+	0.799092i	$0.294686\pi$
$12$	2.30604	+	2.58499i	0.665698	+	0.746222i
$13$	−1.30998			−0.363324			−0.181662	−	0.983361i	$-0.558148\pi$
$13$	−1.30998			−0.363324			−0.181662	+	0.983361i	$0.558148\pi$
$14$		0			0
$15$	3.30003	−	1.42820i	0.852064	−	0.368760i
$16$	3.20847	−	2.38867i	0.802116	−	0.597168i
$17$			2.94162i			0.713447i	0.934210	+	0.356724i	$0.116106\pi$
$17$			2.94162i			0.713447i	−0.934210	+	0.356724i	$0.883894\pi$
$18$	3.51612	+	2.37422i	0.828757	+	0.559609i
$19$			1.09683i			0.251630i	0.992054	+	0.125815i	$0.0401546\pi$
$19$			1.09683i			0.251630i	−0.992054	+	0.125815i	$0.959845\pi$
$20$	−1.30604	−	3.94134i	−0.292040	−	0.881311i
$21$		0			0
$22$	−0.898482	−	5.56781i	−0.191557	−	1.18706i
$23$	7.50125			1.56412			0.782059	−	0.623204i	$-0.214169\pi$
$23$	7.50125			1.56412			0.782059	+	0.623204i	$0.214169\pi$
$24$	3.08949	−	3.80198i	0.630639	−	0.776076i
$25$	0.690016			0.138003
$26$	0.295137	+	1.82894i	0.0578811	+	0.358684i
$27$	4.88916	+	1.75957i	0.940920	+	0.338630i
$28$		0			0
$29$			0.865568i			0.160732i	0.996765	+	0.0803660i	$0.0256089\pi$
$29$			0.865568i			0.160732i	−0.996765	+	0.0803660i	$0.974391\pi$
$30$	−2.73748	−	4.28557i	−0.499792	−	0.782435i
$31$		−	3.68051i		−	0.661040i	−0.943799	−	0.330520i	$-0.892776\pi$
$31$		−	3.68051i		−	0.661040i	0.943799	−	0.330520i	$-0.107224\pi$
$32$	−4.05781	−	3.94134i	−0.717326	−	0.696738i
$33$	−2.74349	−	6.33916i	−0.477580	−	1.10351i
$34$	4.10695	−	0.662741i	0.704336	−	0.113659i
$35$		0			0
$36$	2.52260	−	5.44394i	0.420433	−	0.907324i
$37$	4.17700			0.686694			0.343347	−	0.939209i	$-0.388439\pi$
$37$	4.17700			0.686694			0.343347	+	0.939209i	$0.388439\pi$
$38$	1.53134	−	0.247114i	0.248416	−	0.0400871i
$39$	0.901192	+	2.08231i	0.144306	+	0.333437i
$40$	−5.20847	+	2.71141i	−0.823531	+	0.428712i
$41$			7.01712i			1.09589i	0.836514	+	0.547945i	$0.184590\pi$
$41$			7.01712i			1.09589i	−0.836514	+	0.547945i	$0.815410\pi$
$42$		0			0
$43$		−	4.27597i		−	0.652080i	−0.945356	−	0.326040i	$-0.894286\pi$
$43$		−	4.27597i		−	0.652080i	0.945356	−	0.326040i	$-0.105714\pi$
$44$	−7.57109	+	2.50883i	−1.14138	+	0.378221i
$45$	−4.54045	−	4.26311i	−0.676851	−	0.635507i
$46$	−1.69002	−	10.4729i	−0.249179	−	1.54414i
$47$	−7.50125			−1.09417			−0.547085	−	0.837077i	$-0.684263\pi$
$47$	−7.50125			−1.09417			−0.547085	+	0.837077i	$0.684263\pi$
$48$	−6.00420	−	3.45682i	−0.866632	−	0.498949i
$49$		0			0
$50$	−0.155459	−	0.963368i	−0.0219853	−	0.136241i
$51$	4.67591	−	2.02366i	0.654759	−	0.283369i
$52$	2.48698	−	0.824111i	0.344882	−	0.114284i
$53$			4.94107i			0.678708i	0.940659	+	0.339354i	$0.110208\pi$
$53$			4.94107i			0.678708i	−0.940659	+	0.339354i	$0.889792\pi$
$54$	1.35511	−	7.22244i	0.184407	−	0.982850i
$55$			8.27923i			1.11637i
$56$		0			0
$57$	1.74349	−	0.754555i	0.230931	−	0.0999432i
$58$	1.20847	−	0.195011i	0.158679	−	0.0256062i
$59$	−4.88916			−0.636515			−0.318257	−	0.948004i	$-0.603098\pi$
$59$	−4.88916			−0.636515			−0.318257	+	0.948004i	$0.603098\pi$
$60$	−5.36656	+	4.78746i	−0.692820	+	0.618059i
$61$	4.10695			0.525841			0.262920	−	0.964818i	$-0.415314\pi$
$61$	4.10695			0.525841			0.262920	+	0.964818i	$0.415314\pi$
$62$	−5.13856	+	0.829212i	−0.652597	+	0.105310i
$63$		0			0
$64$	−4.58850	+	6.55330i	−0.573562	+	0.819162i
$65$		−	2.71959i		−	0.337324i
$66$	−8.23233	+	5.25853i	−1.01333	+	0.647280i
$67$			2.42231i			0.295932i	0.988992	+	0.147966i	$0.0472727\pi$
$67$			2.42231i			0.295932i	−0.988992	+	0.147966i	$0.952727\pi$
$68$	−1.85057	−	5.58461i	−0.224415	−	0.677233i
$69$	−5.16042	−	11.9238i	−0.621242	−	1.43545i
$70$		0			0
$71$	0.901192			0.106952			0.0534759	−	0.998569i	$-0.482970\pi$
$71$	0.901192			0.106952			0.0534759	+	0.998569i	$0.482970\pi$
$72$	−8.16891	−	2.29542i	−0.962715	−	0.270518i
$73$	13.0109			1.52281			0.761403	−	0.648279i	$-0.224511\pi$
$73$	13.0109			1.52281			0.761403	+	0.648279i	$0.224511\pi$
$74$	−0.941069	−	5.83172i	−0.109397	−	0.677924i
$75$	−0.474691	−	1.09683i	−0.0548126	−	0.126651i
$76$	−0.690016	−	2.08231i	−0.0791503	−	0.238858i
$77$		0			0
$78$	2.70419	−	1.72734i	0.306189	−	0.195583i
$79$			10.3615i			1.16576i	0.812557	+	0.582882i	$0.198075\pi$
$79$			10.3615i			1.16576i	−0.812557	+	0.582882i	$0.801925\pi$
$80$	4.95900	+	6.66093i	0.554433	+	0.744715i
$81$	−0.566494	−	8.98215i	−0.0629437	−	0.998017i
$82$	9.79696	−	1.58094i	1.08189	−	0.174586i
$83$	12.4386			1.36531			0.682657	−	0.730739i	$-0.260824\pi$
$83$	12.4386			1.36531			0.682657	+	0.730739i	$0.260824\pi$
$84$		0			0
$85$	−6.10695			−0.662391
$86$	−5.96991	+	0.963368i	−0.643752	+	0.103883i
$87$	1.37588	−	0.595460i	0.147510	−	0.0638400i
$88$	5.20847	+	10.0052i	0.555224	+	1.06655i
$89$			8.52623i			0.903778i	0.892074	+	0.451889i	$0.149250\pi$
$89$			8.52623i			0.903778i	−0.892074	+	0.451889i	$0.850750\pi$
$90$	−4.92900	+	7.29963i	−0.519562	+	0.769449i
$91$		0			0
$92$	−14.2410	+	4.71904i	−1.48473	+	0.491994i
$93$	−5.85044	+	2.53198i	−0.606662	+	0.262554i
$94$	1.69002	+	10.4729i	0.174312	+	1.08020i
$95$	−2.27707			−0.233623
$96$	−3.47351	+	9.16159i	−0.354514	+	0.935051i
$97$	15.3909			1.56271			0.781354	−	0.624088i	$-0.214529\pi$
$97$	15.3909			1.56271			0.781354	+	0.624088i	$0.214529\pi$
$98$		0			0
$99$	−8.18919	+	8.72195i	−0.823045	+	0.876588i
$100$	−1.30998	+	0.434090i	−0.130998	+	0.0434090i
$101$		−	6.10526i		−	0.607496i	−0.952752	−	0.303748i	$-0.901762\pi$
$101$		−	6.10526i		−	0.607496i	0.952752	−	0.303748i	$-0.0982382\pi$
$102$	−3.87881	−	6.07236i	−0.384060	−	0.601253i
$103$		−	7.13237i		−	0.702774i	−0.936230	−	0.351387i	$-0.885710\pi$
$103$		−	7.13237i		−	0.702774i	0.936230	−	0.351387i	$-0.114290\pi$
$104$	−1.71090	−	3.28653i	−0.167767	−	0.322271i
$105$		0			0
$106$	6.89848	−	1.11321i	0.670040	−	0.108125i
$107$	2.41675			0.233636			0.116818	−	0.993153i	$-0.462731\pi$
$107$	2.41675			0.233636			0.116818	+	0.993153i	$0.462731\pi$
$108$	−10.3889	−	0.264739i	−0.999675	−	0.0254745i
$109$	−6.79696			−0.651031			−0.325516	−	0.945537i	$-0.605538\pi$
$109$	−6.79696			−0.651031			−0.325516	+	0.945537i	$0.605538\pi$
$110$	11.5591	−	1.86529i	1.10211	−	0.177849i
$111$	−2.87353	−	6.63963i	−0.272743	−	0.630206i
$112$		0			0
$113$		−	3.16365i		−	0.297611i	−0.988867	−	0.148805i	$-0.952457\pi$
$113$		−	3.16365i		−	0.297611i	0.988867	−	0.148805i	$-0.0475428\pi$
$114$	−1.44628	−	2.26418i	−0.135456	−	0.212060i
$115$			15.5730i			1.45219i
$116$	−0.544529	−	1.64327i	−0.0505583	−	0.152573i
$117$	2.69002	−	2.86502i	0.248692	−	0.264871i
$118$	1.10152	+	6.82601i	0.101403	+	0.628386i
$119$		0			0
$120$	7.89310	+	6.41393i	0.720538	+	0.585509i
$121$	4.90391			0.445810
$122$	−0.925287	−	5.73392i	−0.0837715	−	0.519125i
$123$	11.1542	−	4.82736i	1.00574	−	0.435269i
$124$	2.31541	+	6.98739i	0.207930	+	0.627486i
$125$			11.8128i			1.05657i
$126$		0			0
$127$			15.0889i			1.33892i	0.742848	+	0.669460i	$0.233474\pi$
$127$			15.0889i			1.33892i	−0.742848	+	0.669460i	$0.766526\pi$
$128$	10.1832	+	4.92980i	0.900074	+	0.435737i
$129$	−6.79696	+	2.94162i	−0.598439	+	0.258995i
$130$	−3.79696	+	0.612718i	−0.333016	+	0.0537390i
$131$	7.40976			0.647394			0.323697	−	0.946161i	$-0.395074\pi$
$131$	7.40976			0.647394			0.323697	+	0.946161i	$0.395074\pi$
$132$	9.19644	+	10.3089i	0.800447	+	0.897271i
$133$		0			0
$134$	3.38192	−	0.545742i	0.292153	−	0.0471449i
$135$	−3.65296	+	10.1501i	−0.314396	+	0.873585i
$136$	−7.38003	+	3.84188i	−0.632833	+	0.329439i
$137$			15.0993i			1.29002i	0.764174	+	0.645010i	$0.223147\pi$
$137$			15.0993i			1.29002i	−0.764174	+	0.645010i	$0.776853\pi$
$138$	−15.4848	+	9.89113i	−1.31815	+	0.841989i
$139$		−	14.4761i		−	1.22785i	−0.789364	−	0.613925i	$-0.789590\pi$
$139$		−	14.4761i		−	1.22785i	0.789364	−	0.613925i	$-0.210410\pi$
$140$		0			0
$141$	5.16042	+	11.9238i	0.434586	+	1.00416i
$142$	−0.203037	−	1.25820i	−0.0170385	−	0.105586i
$143$	−5.22418			−0.436868
$144$	−1.36432	+	11.9222i	−0.113694	+	0.993516i
$145$	−1.79696			−0.149230
$146$	−2.93132	−	18.1651i	−0.242598	−	1.50336i
$147$		0			0
$148$	−7.92995	+	2.62775i	−0.651838	+	0.216000i
$149$		−	11.3912i		−	0.933207i	−0.884467	−	0.466604i	$-0.845477\pi$
$149$		−	11.3912i		−	0.933207i	0.884467	−	0.466604i	$-0.154523\pi$
$150$	−1.42440	+	0.909854i	−0.116301	+	0.0742893i
$151$			0.918202i			0.0747222i	0.999302	+	0.0373611i	$0.0118952\pi$
$151$			0.918202i			0.0747222i	−0.999302	+	0.0373611i	$0.988105\pi$
$152$	−2.75177	+	1.43251i	−0.223198	+	0.116192i
$153$	−6.43351	−	6.04054i	−0.520118	−	0.488348i
$154$		0			0
$155$	7.64093			0.613734
$156$	−3.02088	−	3.38629i	−0.241864	−	0.271120i
$157$	−8.72691			−0.696484			−0.348242	−	0.937405i	$-0.613221\pi$
$157$	−8.72691			−0.696484			−0.348242	+	0.937405i	$0.613221\pi$
$158$	14.4663	−	2.33443i	1.15088	−	0.185718i
$159$	7.85418	−	3.39916i	0.622877	−	0.269571i
$160$	8.18242	−	8.42422i	0.646877	−	0.665993i
$161$		0			0
$162$	−12.4128	+	2.81457i	−0.975244	+	0.221134i
$163$		−	8.99199i		−	0.704307i	−0.935942	−	0.352153i	$-0.885450\pi$
$163$		−	8.99199i		−	0.704307i	0.935942	−	0.352153i	$-0.114550\pi$
$164$	−4.41447	−	13.3219i	−0.344712	−	1.04026i
$165$	13.1604	−	5.69562i	1.02454	−	0.443404i
$166$	−2.80239	−	17.3662i	−0.217508	−	1.34788i
$167$	−16.1830			−1.25228			−0.626141	−	0.779710i	$-0.715367\pi$
$167$	−16.1830			−1.25228			−0.626141	+	0.779710i	$0.715367\pi$
$168$		0			0
$169$	−11.2839			−0.867996
$170$	1.37588	+	8.52623i	0.105525	+	0.653932i
$171$	−2.39884	−	2.25231i	−0.183444	−	0.172239i
$172$	2.69002	+	8.11786i	0.205112	+	0.618981i
$173$		−	4.22870i		−	0.321502i	−0.986995	−	0.160751i	$-0.948608\pi$
$173$		−	4.22870i		−	0.321502i	0.986995	−	0.160751i	$-0.0513916\pi$
$174$	−1.14134	−	1.78679i	−0.0865245	−	0.135456i
$175$		0			0
$176$	12.7953	−	9.52595i	0.964479	−	0.718046i
$177$	3.36346	+	7.77167i	0.252813	+	0.584155i
$178$	11.9039	−	1.92094i	0.892236	−	0.143981i
$179$	−6.55187			−0.489710			−0.244855	−	0.969560i	$-0.578740\pi$
$179$	−6.55187			−0.489710			−0.244855	+	0.969560i	$0.578740\pi$
$180$	11.3019	+	5.23704i	0.842393	+	0.390346i
$181$	−12.2839			−0.913058			−0.456529	−	0.889708i	$-0.650908\pi$
$181$	−12.2839			−0.913058			−0.456529	+	0.889708i	$0.650908\pi$
$182$		0			0
$183$	−2.82534	−	6.52828i	−0.208855	−	0.482585i
$184$	9.79696	+	18.8194i	0.722242	+	1.38738i
$185$			8.67165i			0.637553i
$186$	4.85312	+	7.59765i	0.355848	+	0.557087i
$187$			11.7311i			0.857862i
$188$	14.2410	−	4.71904i	1.03863	−	0.344171i
$189$		0			0
$190$	0.513020	+	3.17914i	0.0372184	+	0.230639i
$191$	−23.7325			−1.71722			−0.858611	−	0.512627i	$-0.828672\pi$
$191$	−23.7325			−1.71722			−0.858611	+	0.512627i	$0.828672\pi$
$192$	13.5735	+	2.78546i	0.979586	+	0.201023i
$193$	−3.97396			−0.286052			−0.143026	−	0.989719i	$-0.545683\pi$
$193$	−3.97396			−0.286052			−0.143026	+	0.989719i	$0.545683\pi$
$194$	−3.46754	−	21.4880i	−0.248955	−	1.54275i
$195$	−4.32298	+	1.87092i	−0.309575	+	0.133979i
$196$		0			0
$197$		−	19.7720i		−	1.40870i	−0.709853	−	0.704350i	$-0.751239\pi$
$197$		−	19.7720i		−	1.40870i	0.709853	−	0.704350i	$-0.248761\pi$
$198$	14.0222	+	9.46832i	0.996512	+	0.672884i
$199$		−	7.66651i		−	0.543464i	−0.962373	−	0.271732i	$-0.912404\pi$
$199$		−	7.66651i		−	0.543464i	0.962373	−	0.271732i	$-0.0875965\pi$
$200$	0.901192	+	1.73114i	0.0637239	+	0.122410i
$201$	3.85044	−	1.66641i	0.271589	−	0.117539i
$202$	−8.52388	+	1.37550i	−0.599738	+	0.0967801i
$203$		0			0
$204$	−7.60405	+	6.78350i	−0.532390	+	0.474940i
$205$	−14.5679			−1.01747
$206$	−9.95788	+	1.60691i	−0.693798	+	0.111959i
$207$	−15.4036	+	16.4057i	−1.07063	+	1.14028i
$208$	−4.20304	+	3.12912i	−0.291428	+	0.216965i
$209$			4.37413i			0.302565i
$210$		0			0
$211$		−	11.7483i		−	0.808789i	−0.914585	−	0.404395i	$-0.867482\pi$
$211$		−	11.7483i		−	0.808789i	0.914585	−	0.404395i	$-0.132518\pi$
$212$	−3.10843	−	9.38053i	−0.213488	−	0.644257i
$213$	−0.619967	−	1.43251i	−0.0424794	−	0.0981539i
$214$	−0.544489	−	3.37415i	−0.0372205	−	0.230652i
$215$	8.87713			0.605415
$216$	1.97099	+	14.5642i	0.134109	+	0.990967i
$217$		0			0
$218$	1.53134	+	9.48959i	0.103716	+	0.642716i
$219$	−8.95071	−	20.6817i	−0.604833	−	1.39754i
$220$	−5.20847	−	15.7180i	−0.351155	−	1.05970i
$221$		−	3.85347i		−	0.259213i
$222$	−8.62254	+	5.50778i	−0.578707	+	0.369658i
$223$			14.5202i			0.972345i	0.873863	+	0.486173i	$0.161607\pi$
$223$			14.5202i			0.972345i	−0.873863	+	0.486173i	$0.838393\pi$
$224$		0			0
$225$	−1.41693	+	1.50911i	−0.0944620	+	0.100607i
$226$	−4.41693	+	0.712763i	−0.293810	+	0.0474123i
$227$	21.4629			1.42454			0.712271	−	0.701905i	$-0.247667\pi$
$227$	21.4629			1.42454			0.712271	+	0.701905i	$0.247667\pi$
$228$	−2.83529	+	2.52934i	−0.187772	+	0.167510i
$229$	−19.6308			−1.29724			−0.648621	−	0.761112i	$-0.724654\pi$
$229$	−19.6308			−1.29724			−0.648621	+	0.761112i	$0.724654\pi$
$230$	21.7422	−	3.50856i	1.43364	−	0.231348i
$231$		0			0
$232$	−2.17157	+	1.13047i	−0.142570	+	0.0742190i
$233$			14.2640i			0.934468i	0.884134	+	0.467234i	$0.154749\pi$
$233$			14.2640i			0.934468i	−0.884134	+	0.467234i	$0.845251\pi$
$234$	−4.60606	−	3.11019i	−0.301107	−	0.203319i
$235$		−	15.5730i		−	1.01587i
$236$	9.28199	−	3.07577i	0.604206	−	0.200216i
$237$	16.4704	−	7.12813i	1.06987	−	0.463022i
$238$		0			0
$239$	−15.2819			−0.988501			−0.494251	−	0.869320i	$-0.664557\pi$
$239$	−15.2819			−0.988501			−0.494251	+	0.869320i	$0.664557\pi$
$240$	7.17653	−	12.4650i	0.463243	−	0.804613i
$241$	−5.90391			−0.380304			−0.190152	−	0.981755i	$-0.560898\pi$
$241$	−5.90391			−0.380304			−0.190152	+	0.981755i	$0.560898\pi$
$242$	−1.10484	−	6.84660i	−0.0710219	−	0.440116i
$243$	−13.8881	+	7.07968i	−0.890919	+	0.454161i
$244$	−7.79696	+	2.58368i	−0.499149	+	0.165403i
$245$		0			0
$246$	−9.25276	−	14.4854i	−0.589934	−	0.923554i
$247$		−	1.43683i		−	0.0914233i
$248$	9.23380	−	4.80691i	0.586347	−	0.305239i
$249$	−8.55703	−	19.7720i	−0.542280	−	1.25300i
$250$	16.4924	−	2.66139i	1.04307	−	0.168321i
$251$	−23.7400			−1.49845			−0.749226	−	0.662314i	$-0.769575\pi$
$251$	−23.7400			−1.49845			−0.749226	+	0.662314i	$0.769575\pi$
$252$		0			0
$253$	29.9148			1.88073
$254$	21.0663	−	3.39949i	1.32182	−	0.213303i
$255$	4.20122	+	9.70743i	0.263091	+	0.607903i
$256$	4.58850	−	15.3279i	0.286781	−	0.957996i
$257$			14.8007i			0.923240i	0.887078	+	0.461620i	$0.152732\pi$
$257$			14.8007i			0.923240i	−0.887078	+	0.461620i	$0.847268\pi$
$258$	5.63829	+	8.82685i	0.351025	+	0.549536i
$259$		0			0
$260$	1.71090	+	5.16309i	0.106105	+	0.320202i
$261$	−1.89305	−	1.77742i	−0.117177	−	0.110020i
$262$	−1.66940	−	10.3452i	−0.103136	−	0.639126i
$263$	−13.9060			−0.857479			−0.428740	−	0.903428i	$-0.641042\pi$
$263$	−13.9060			−0.857479			−0.428740	+	0.903428i	$0.641042\pi$
$264$	12.3208	−	15.1622i	0.758292	−	0.933168i
$265$	−10.2579			−0.630138
$266$		0			0
$267$	13.5530	−	5.86554i	0.829433	−	0.358965i
$268$	−1.52388	−	4.59871i	−0.0930856	−	0.280911i
$269$			8.25792i			0.503494i	0.967793	+	0.251747i	$0.0810051\pi$
$269$			8.25792i			0.503494i	−0.967793	+	0.251747i	$0.918995\pi$
$270$	14.9942	+	2.81328i	0.912515	+	0.171211i
$271$		−	5.30552i		−	0.322288i	−0.986931	−	0.161144i	$-0.948482\pi$
$271$		−	5.30552i		−	0.322288i	0.986931	−	0.161144i	$-0.0515183\pi$
$272$	7.02656	+	9.43808i	0.426048	+	0.572268i
$273$		0			0
$274$	21.0809	−	3.40184i	1.27354	−	0.205513i
$275$	2.75177			0.165938
$276$	17.2982	+	19.3906i	1.04123	+	1.16718i
$277$	12.6048			0.757348			0.378674	−	0.925530i	$-0.376380\pi$
$277$	12.6048			0.757348			0.378674	+	0.925530i	$0.376380\pi$
$278$	−20.2109	+	3.26144i	−1.21217	+	0.195608i
$279$	8.04951	+	7.55783i	0.481912	+	0.452476i
$280$		0			0
$281$			2.02977i			0.121086i	0.998166	+	0.0605428i	$0.0192832\pi$
$281$			2.02977i			0.121086i	−0.998166	+	0.0605428i	$0.980717\pi$
$282$	15.4848	−	9.89113i	0.922105	−	0.589008i
$283$		−	7.67781i		−	0.456399i	−0.973614	−	0.228199i	$-0.926716\pi$
$283$		−	7.67781i		−	0.456399i	0.973614	−	0.228199i	$-0.0732838\pi$
$284$	−1.71090	+	0.566940i	−0.101523	+	0.0336417i
$285$	1.56649	+	3.61957i	0.0927911	+	0.214405i
$286$	1.17700	+	7.29374i	0.0695972	+	0.431288i
$287$		0			0
$288$	16.9526	−	0.781244i	0.998940	−	0.0460352i
$289$	8.34688			0.490993
$290$	0.404852	+	2.50883i	0.0237737	+	0.147324i
$291$	−10.5880	−	24.4649i	−0.620681	−	1.43416i
$292$	−24.7009	+	8.18514i	−1.44551	+	0.478999i
$293$			1.55539i			0.0908671i	0.998967	+	0.0454336i	$0.0144669\pi$
$293$			1.55539i			0.0908671i	−0.998967	+	0.0454336i	$0.985533\pi$
$294$		0			0
$295$		−	10.1501i		−	0.590964i
$296$	5.45534	+	10.4794i	0.317085	+	0.609102i
$297$	19.4978	+	7.01712i	1.13138	+	0.407174i
$298$	−15.9039	+	2.56642i	−0.921289	+	0.148669i
$299$	−9.82651			−0.568282
$300$	1.59121	+	1.78368i	0.0918685	+	0.102981i
$301$		0			0
$302$	1.28195	−	0.206869i	0.0737679	−	0.0119040i
$303$	−9.70475	+	4.20006i	−0.557523	+	0.241287i
$304$	2.61997	+	3.51914i	0.150265	+	0.201837i
$305$			8.52623i			0.488210i
$306$	−6.98405	+	10.3431i	−0.399252	+	0.591274i
$307$		−	31.5800i		−	1.80237i	−0.433437	−	0.901184i	$-0.642699\pi$
$307$		−	31.5800i		−	1.80237i	0.433437	−	0.901184i	$-0.357301\pi$
$308$		0			0
$309$	−11.3374	+	4.90665i	−0.644963	+	0.279130i
$310$	−1.72149	−	10.6679i	−0.0977738	−	0.605896i
$311$	18.2771			1.03640			0.518201	−	0.855259i	$-0.326602\pi$
$311$	18.2771			1.03640			0.518201	+	0.855259i	$0.326602\pi$
$312$	−4.04718	+	4.98053i	−0.229126	+	0.281967i
$313$	29.7818			1.68337			0.841683	−	0.539972i	$-0.181565\pi$
$313$	29.7818			1.68337			0.841683	+	0.539972i	$0.181565\pi$
$314$	1.96616	+	12.1841i	0.110957	+	0.687589i
$315$		0			0
$316$	−6.51845	−	19.6712i	−0.366691	−	1.10659i
$317$		−	17.6960i		−	0.993906i	−0.867777	−	0.496953i	$-0.834452\pi$
$317$		−	17.6960i		−	0.993906i	0.867777	−	0.496953i	$-0.165548\pi$
$318$	−6.51528	−	10.1998i	−0.365359	−	0.571977i
$319$			3.45186i			0.193267i
$320$	−13.6050	−	9.52595i	−0.760541	−	0.532517i
$321$	−1.66258	−	3.84160i	−0.0927964	−	0.214417i
$322$		0			0
$323$	−3.22646			−0.179525
$324$	6.72615	+	16.6961i	0.373675	+	0.927560i
$325$	−0.903910			−0.0501399
$326$	−12.5542	+	2.02588i	−0.695312	+	0.112203i
$327$	4.67591	+	10.8043i	0.258579	+	0.597477i
$328$	−17.6048	+	9.16466i	−0.972062	+	0.506034i
$329$		0			0
$330$	−10.9170	−	17.0907i	−0.600959	−	0.940814i
$331$		−	35.0819i		−	1.92828i	−0.265401	−	0.964138i	$-0.585504\pi$
$331$		−	35.0819i		−	1.92828i	0.265401	−	0.964138i	$-0.414496\pi$
$332$	−23.6145	+	7.82513i	−1.29601	+	0.429460i
$333$	−8.57735	+	9.13536i	−0.470036	+	0.500614i
$334$	3.64601	+	22.5940i	0.199501	+	1.23629i
$335$	−5.02884			−0.274755
$336$		0			0
$337$	−0.132987			−0.00724428			−0.00362214	−	0.999993i	$-0.501153\pi$
$337$	−0.132987			−0.00724428			−0.00362214	+	0.999993i	$0.501153\pi$
$338$	2.54225	+	15.7541i	0.138280	+	0.856910i
$339$	−5.02884	+	2.17640i	−0.273129	+	0.118206i
$340$	11.5939	−	3.84188i	0.628769	−	0.208355i
$341$		−	14.6778i		−	0.794846i
$342$	−2.60412	+	3.85658i	−0.140815	+	0.208540i
$343$		0			0
$344$	10.7277	−	5.58461i	0.578399	−	0.301102i
$345$	24.7543	−	10.7133i	1.33273	−	0.576784i
$346$	−5.90391	+	0.952718i	−0.317396	+	0.0512184i
$347$	−0.195336			−0.0104862			−0.00524310	−	0.999986i	$-0.501669\pi$
$347$	−0.195336			−0.0104862			−0.00524310	+	0.999986i	$0.501669\pi$
$348$	−2.23748	+	1.99604i	−0.119942	+	0.106999i
$349$	5.80782			0.310885			0.155443	−	0.987845i	$-0.450320\pi$
$349$	5.80782			0.310885			0.155443	+	0.987845i	$0.450320\pi$
$350$		0			0
$351$	−6.40472	−	2.30501i	−0.341859	−	0.123032i
$352$	−16.1824	−	15.7180i	−0.862526	−	0.837770i
$353$		−	19.9941i		−	1.06418i	−0.846689	−	0.532089i	$-0.821407\pi$
$353$		−	19.9941i		−	1.06418i	0.846689	−	0.532089i	$-0.178593\pi$
$354$	10.0927	−	6.44684i	0.536419	−	0.342646i
$355$			1.87092i			0.0992981i
$356$	−5.36385	−	16.1869i	−0.284284	−	0.857903i
$357$		0			0
$358$	1.47612	+	9.14741i	0.0780155	+	0.483455i
$359$	−13.9060			−0.733929			−0.366965	−	0.930235i	$-0.619603\pi$
$359$	−13.9060			−0.733929			−0.366965	+	0.930235i	$0.619603\pi$
$360$	4.76541	−	16.9591i	0.251159	−	0.893821i
$361$	17.7970			0.936682
$362$	2.76755	+	17.1503i	0.145459	+	0.901397i
$363$	−3.37360	−	7.79511i	−0.177068	−	0.409137i
$364$		0			0
$365$			27.0112i			1.41383i
$366$	−8.47794	+	5.41541i	−0.443149	+	0.283068i
$367$		−	18.8134i		−	0.982054i	−0.871144	−	0.491027i	$-0.836622\pi$
$367$		−	18.8134i		−	0.982054i	0.871144	−	0.491027i	$-0.163378\pi$
$368$	24.0675	−	17.9180i	1.25461	−	0.934041i
$369$	−15.3469	−	14.4095i	−0.798927	−	0.750127i
$370$	12.1069	−	1.95371i	0.629410	−	0.101568i
$371$		0			0
$372$	9.51408	−	8.48742i	0.493282	−	0.440052i
$373$	5.82300			0.301504			0.150752	−	0.988572i	$-0.451831\pi$
$373$	5.82300			0.301504			0.150752	+	0.988572i	$0.451831\pi$
$374$	16.3784	−	2.64299i	0.846906	−	0.136666i
$375$	18.7772	−	8.12648i	0.969652	−	0.419650i
$376$	−9.79696	−	18.8194i	−0.505240	−	0.970536i
$377$		−	1.13388i		−	0.0583978i
$378$		0			0
$379$		−	12.0598i		−	0.619469i	−0.950823	−	0.309735i	$-0.899760\pi$
$379$		−	12.0598i		−	0.619469i	0.950823	−	0.309735i	$-0.100240\pi$
$380$	4.32298	−	1.43251i	0.221764	−	0.0734861i
$381$	23.9848	−	10.3802i	1.22878	−	0.531796i
$382$	5.34688	+	33.1342i	0.273570	+	1.69529i
$383$	12.1518			0.620927			0.310463	−	0.950585i	$-0.399516\pi$
$383$	12.1518			0.620927			0.310463	+	0.950585i	$0.399516\pi$
$384$	0.830836	−	19.5783i	0.0423984	−	0.999101i
$385$		0			0
$386$	0.895325	+	5.54825i	0.0455708	+	0.282399i
$387$	9.35182	+	8.78060i	0.475380	+	0.446343i
$388$	−29.2193	+	9.68242i	−1.48339	+	0.491550i
$389$			1.21048i			0.0613739i	0.999529	+	0.0306869i	$0.00976949\pi$
$389$			1.21048i			0.0613739i	−0.999529	+	0.0306869i	$0.990231\pi$
$390$	3.58605	+	5.61403i	0.181587	+	0.284277i
$391$			22.0658i			1.11592i
$392$		0			0
$393$	−5.09748	−	11.7783i	−0.257134	−	0.594139i
$394$	−27.6048	+	4.45460i	−1.39071	+	0.224420i
$395$	−21.5111			−1.08234
$396$	10.0601	−	21.7103i	0.505537	−	1.09098i
$397$	−9.55703			−0.479654			−0.239827	−	0.970816i	$-0.577091\pi$
$397$	−9.55703			−0.479654			−0.239827	+	0.970816i	$0.577091\pi$
$398$	−10.7036	+	1.72725i	−0.536524	+	0.0865792i
$399$		0			0
$400$	2.21389	−	1.64822i	0.110695	−	0.0824111i
$401$		−	11.2458i		−	0.561589i	−0.959768	−	0.280795i	$-0.909402\pi$
$401$		−	11.2458i		−	0.561589i	0.959768	−	0.280795i	$-0.0905980\pi$
$402$	−3.19405	−	5.00036i	−0.159305	−	0.249395i
$403$			4.82141i			0.240172i
$404$	3.84082	+	11.5907i	0.191088	+	0.576660i
$405$	18.6474	−	1.17607i	0.926597	−	0.0584393i
$406$		0			0
$407$	16.6577			0.825693
$408$	11.1840	+	9.08810i	0.553689	+	0.449928i
$409$	−15.5679			−0.769782			−0.384891	−	0.922962i	$-0.625761\pi$
$409$	−15.5679			−0.769782			−0.384891	+	0.922962i	$0.625761\pi$
$410$	3.28212	+	20.3390i	0.162092	+	1.00447i
$411$	24.0014	−	10.3874i	1.18390	−	0.512374i
$412$	4.48698	+	13.5407i	0.221058	+	0.667101i
$413$		0			0
$414$	26.3753	+	17.8096i	1.29627	+	0.875295i
$415$			25.8232i			1.26761i
$416$	5.31566	+	5.16309i	0.260622	+	0.253142i
$417$	−23.0109	+	9.95874i	−1.12685	+	0.487681i
$418$	6.10695	−	0.985482i	0.298701	−	0.0482015i
$419$	18.0336			0.881000			0.440500	−	0.897753i	$-0.354801\pi$
$419$	18.0336			0.881000			0.440500	+	0.897753i	$0.354801\pi$
$420$		0			0
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	−16.4025	+	2.64688i	−0.798460	+	0.128848i
$423$	15.4036	−	16.4057i	0.748950	−	0.797673i
$424$	−12.3963	+	6.45325i	−0.602018	+	0.313398i
$425$			2.02977i			0.0984581i
$426$	−1.86032	+	1.18831i	−0.0901329	+	0.0575738i
$427$		0			0
$428$	−4.58816	+	1.52038i	−0.221777	+	0.0734903i
$429$	3.59393	+	8.30420i	0.173516	+	0.400931i
$430$	−2.00000	−	12.3938i	−0.0964486	−	0.597683i
$431$	12.4461			0.599506			0.299753	−	0.954017i	$-0.403096\pi$
$431$	12.4461			0.599506			0.299753	+	0.954017i	$0.403096\pi$
$432$	19.8897	−	6.03308i	0.956946	−	0.290267i
$433$	−0.497837			−0.0239245			−0.0119623	−	0.999928i	$-0.503808\pi$
$433$	−0.497837			−0.0239245			−0.0119623	+	0.999928i	$0.503808\pi$
$434$		0			0
$435$	1.23621	+	2.85640i	0.0592715	+	0.136954i
$436$	12.9039	−	4.27597i	0.617985	−	0.204782i
$437$			8.22760i			0.393579i
$438$	−26.8582	+	17.1561i	−1.28333	+	0.819750i
$439$			4.66004i			0.222412i	0.993797	+	0.111206i	$0.0354713\pi$
$439$			4.66004i			0.222412i	−0.993797	+	0.111206i	$0.964529\pi$
$440$	−20.7712	+	10.8130i	−0.990228	+	0.515491i
$441$		0			0
$442$	−5.38003	+	0.868179i	−0.255902	+	0.0412951i
$443$	22.0698			1.04857			0.524283	−	0.851544i	$-0.324333\pi$
$443$	22.0698			1.04857			0.524283	+	0.851544i	$0.324333\pi$
$444$	9.63234	+	10.7975i	0.457130	+	0.512426i
$445$	−17.7009			−0.839102
$446$	20.2724	−	3.27137i	0.959927	−	0.154904i
$447$	−18.1072	+	7.83651i	−0.856441	+	0.370654i
$448$		0			0
$449$		−	6.02866i		−	0.284510i	−0.989830	−	0.142255i	$-0.954565\pi$
$449$		−	6.02866i		−	0.284510i	0.989830	−	0.142255i	$-0.0454353\pi$
$450$	2.42618	+	1.63825i	0.114371	+	0.0772279i
$451$			27.9841i			1.31772i
$452$	1.99025	+	6.00612i	0.0936135	+	0.282504i
$453$	1.45955	−	0.631669i	0.0685755	−	0.0296784i
$454$	−4.83554	−	29.9654i	−0.226943	−	1.40635i
$455$		0			0
$456$	4.17013	+	3.38865i	0.195284	+	0.158688i
$457$	−38.2616			−1.78980			−0.894902	−	0.446262i	$-0.852755\pi$
$457$	−38.2616			−1.78980			−0.894902	+	0.446262i	$0.852755\pi$
$458$	4.42278	+	27.4076i	0.206663	+	1.28067i
$459$	−5.17599	+	14.3821i	−0.241594	+	0.671297i
$460$	−9.79696	−	29.5650i	−0.456786	−	1.37848i
$461$		−	12.4563i		−	0.580148i	−0.957004	−	0.290074i	$-0.906320\pi$
$461$		−	12.4563i		−	0.580148i	0.957004	−	0.290074i	$-0.0936799\pi$
$462$		0			0
$463$			28.0609i			1.30410i	0.758176	+	0.652050i	$0.226091\pi$
$463$			28.0609i			1.30410i	−0.758176	+	0.652050i	$0.773909\pi$
$464$	2.06756	+	2.77715i	0.0959840	+	0.128926i
$465$	−5.25651	−	12.1458i	−0.243765	−	0.563248i
$466$	19.9148	−	3.21366i	0.922534	−	0.148870i
$467$	−17.0966			−0.791136			−0.395568	−	0.918437i	$-0.629452\pi$
$467$	−17.0966			−0.791136			−0.395568	+	0.918437i	$0.629452\pi$
$468$	−3.30456	+	7.13147i	−0.152753	+	0.329652i
$469$		0			0
$470$	−21.7422	+	3.50856i	−1.00289	+	0.161838i
$471$	6.00360	+	13.8721i	0.276632	+	0.639190i
$472$	−6.38546	−	12.2661i	−0.293915	−	0.564593i
$473$		−	17.0525i		−	0.784073i
$474$	−13.6627	−	21.3892i	−0.627549	−	0.982440i
$475$			0.756831i			0.0347258i
$476$		0			0
$477$	−10.8064	−	10.1464i	−0.494792	−	0.464569i
$478$	3.44297	+	21.3358i	0.157478	+	0.975877i
$479$	−16.4266			−0.750549			−0.375275	−	0.926914i	$-0.622452\pi$
$479$	−16.4266			−0.750549			−0.375275	+	0.926914i	$0.622452\pi$
$480$	−19.0199	−	7.21118i	−0.868137	−	0.329144i
$481$	−5.47180			−0.249492
$482$	1.33014	+	8.24276i	0.0605862	+	0.375447i
$483$		0			0
$484$	−9.30998	+	3.08505i	−0.423181	+	0.140230i
$485$			31.9523i			1.45088i
$486$	13.0133	+	17.7948i	0.590293	+	0.807189i
$487$			31.9873i			1.44948i	0.689021	+	0.724742i	$0.258041\pi$
$487$			31.9873i			1.44948i	−0.689021	+	0.724742i	$0.741959\pi$
$488$	5.36385	+	10.3036i	0.242810	+	0.466424i
$489$	−14.2934	+	6.18596i	−0.646370	+	0.279739i
$490$		0			0
$491$	2.03844			0.0919935			0.0459968	−	0.998942i	$-0.485354\pi$
$491$	2.03844			0.0919935			0.0459968	+	0.998942i	$0.485354\pi$
$492$	−18.1392	+	16.1818i	−0.817777	+	0.729531i
$493$	−2.54617			−0.114674
$494$	−2.00603	+	0.323715i	−0.0902557	+	0.0145646i
$495$	−18.1072	−	17.0012i	−0.813858	−	0.764146i
$496$	−8.79153	−	11.8088i	−0.394752	−	0.530231i
$497$		0			0
$498$	−25.6769	+	16.4015i	−1.15061	+	0.734970i
$499$			4.29323i			0.192191i	0.995372	+	0.0960957i	$0.0306355\pi$
$499$			4.29323i			0.192191i	−0.995372	+	0.0960957i	$0.969365\pi$
$500$	−7.43141	−	22.4263i	−0.332343	−	1.00293i
$501$	11.1330	+	25.7241i	0.497385	+	1.14927i
$502$	5.34856	+	33.1446i	0.238718	+	1.47932i
$503$	26.3039			1.17283			0.586415	−	0.810010i	$-0.300539\pi$
$503$	26.3039			1.17283			0.586415	+	0.810010i	$0.300539\pi$
$504$		0			0
$505$	12.6748			0.564023
$506$	−6.73974	−	41.7656i	−0.299618	−	1.85671i
$507$	7.76269	+	17.9366i	0.344753	+	0.796594i
$508$	−9.49241	−	28.6459i	−0.421158	−	1.27096i
$509$			40.7771i			1.80741i	0.428152	+	0.903707i	$0.359165\pi$
$509$			40.7771i			1.80741i	−0.428152	+	0.903707i	$0.640835\pi$
$510$	12.6065	−	8.05261i	0.558226	−	0.356575i
$511$		0			0
$512$	−22.4339	−	2.95289i	−0.991448	−	0.130500i
$513$	−1.92995	+	5.36258i	−0.0852094	+	0.236764i
$514$	20.6640	−	3.33456i	0.911449	−	0.147081i
$515$	14.8072			0.652482
$516$	11.0533	−	9.86058i	0.486596	−	0.434088i
$517$	−29.9148			−1.31565
$518$		0			0
$519$	−6.72182	+	2.90910i	−0.295055	+	0.127695i
$520$	6.82300	−	3.55191i	0.299209	−	0.155761i
$521$			6.94829i			0.304410i	0.988349	+	0.152205i	$0.0486374\pi$
$521$			6.94829i			0.304410i	−0.988349	+	0.152205i	$0.951363\pi$
$522$	−2.05505	+	3.04344i	−0.0899471	+	0.133208i
$523$			7.55516i			0.330364i	0.986263	+	0.165182i	$0.0528212\pi$
$523$			7.55516i			0.330364i	−0.986263	+	0.165182i	$0.947179\pi$
$524$	−14.0673	+	4.66149i	−0.614533	+	0.203638i
$525$		0			0
$526$	3.13299	+	19.4149i	0.136605	+	0.846528i
$527$	10.8267			0.471617
$528$	−23.9446	−	13.7857i	−1.04205	−	0.599945i
$529$	33.2688			1.44647
$530$	2.31108	+	14.3216i	0.100387	+	0.622090i
$531$	10.0398	−	10.6929i	0.435689	−	0.464033i
$532$		0			0
$533$		−	9.19231i		−	0.398163i
$534$	−11.2427	−	17.6006i	−0.486518	−	0.761653i
$535$			5.01730i			0.216917i
$536$	−6.07718	+	3.16365i	−0.262494	+	0.136649i
$537$	4.50730	+	10.4147i	0.194504	+	0.449426i
$538$	11.5293	−	1.86049i	0.497064	−	0.0802115i
$539$		0			0
$540$	0.549611	−	21.5679i	0.0236515	−	0.928136i
$541$	11.1510			0.479417			0.239709	−	0.970845i	$-0.422948\pi$
$541$	11.1510			0.479417			0.239709	+	0.970845i	$0.422948\pi$
$542$	−7.40732	+	1.19532i	−0.318172	+	0.0513435i
$543$	8.45063	+	19.5262i	0.362651	+	0.837950i
$544$	11.5939	−	11.9365i	0.497086	−	0.511774i
$545$		−	14.1108i		−	0.604442i
$546$		0			0
$547$			39.2870i			1.67979i	0.542748	+	0.839896i	$0.317384\pi$
$547$			39.2870i			1.67979i	−0.542748	+	0.839896i	$0.682616\pi$
$548$	−9.49897	−	28.6657i	−0.405776	−	1.22454i
$549$	−8.43351	+	8.98215i	−0.359933	+	0.383349i
$550$	−0.619967	−	3.84188i	−0.0264355	−	0.163818i
$551$	−0.949382			−0.0404450
$552$	23.1750	−	28.5196i	0.986395	−	1.21388i
$553$		0			0
$554$	−2.83983	−	17.5982i	−0.120653	−	0.747676i
$555$	13.7842	−	5.96559i	0.585107	−	0.253225i
$556$	9.10695	+	27.4827i	0.386221	+	1.16553i
$557$		−	29.4625i		−	1.24836i	−0.781279	−	0.624182i	$-0.785432\pi$
$557$		−	29.4625i		−	1.24836i	0.781279	−	0.624182i	$-0.214568\pi$
$558$	8.73835	−	12.9411i	0.369924	−	0.547841i
$559$			5.60145i			0.236916i
$560$		0			0
$561$	18.6474	−	8.07030i	0.787294	−	0.340728i
$562$	2.83386	−	0.457302i	0.119539	−	0.0192901i
$563$	−40.6771			−1.71433			−0.857167	−	0.515039i	$-0.827777\pi$
$563$	−40.6771			−1.71433			−0.857167	+	0.515039i	$0.827777\pi$
$564$	−17.2982	−	19.3906i	−0.728386	−	0.816493i
$565$	6.56789			0.276313
$566$	−10.7194	+	1.72980i	−0.450570	+	0.0727087i
$567$		0			0
$568$	1.17700	+	2.26094i	0.0493857	+	0.0948670i
$569$		−	4.97138i		−	0.208411i	−0.994556	−	0.104206i	$-0.966770\pi$
$569$		−	4.97138i		−	0.208411i	0.994556	−	0.104206i	$-0.0332300\pi$
$570$	4.70055	−	3.00255i	0.196884	−	0.125763i
$571$		−	34.9819i		−	1.46395i	−0.681334	−	0.731973i	$-0.738600\pi$
$571$		−	34.9819i		−	1.46395i	0.681334	−	0.731973i	$-0.261400\pi$
$572$	9.91800	−	3.28653i	0.414693	−	0.137417i
$573$	16.3266	+	37.7245i	0.682052	+	1.57596i
$574$		0			0
$575$	5.17599			0.215854
$576$	−4.91012	−	23.4924i	−0.204588	−	0.978848i
$577$	−14.6677			−0.610625			−0.305313	−	0.952252i	$-0.598761\pi$
$577$	−14.6677			−0.610625			−0.305313	+	0.952252i	$0.598761\pi$
$578$	−1.88054	−	11.6535i	−0.0782200	−	0.484722i
$579$	2.73385	+	6.31689i	0.113615	+	0.262521i
$580$	3.41150	−	1.13047i	0.141655	−	0.0469402i
$581$		0			0
$582$	−31.7713	+	20.2944i	−1.31696	+	0.841230i
$583$			19.7048i			0.816091i
$584$	16.9928	+	32.6421i	0.703165	+	1.35074i
$585$	5.94792	+	5.58461i	0.245916	+	0.230895i
$586$	2.17157	−	0.350427i	0.0897066	−	0.0144760i
$587$	18.7469			0.773769			0.386885	−	0.922128i	$-0.373551\pi$
$587$	18.7469			0.773769			0.386885	+	0.922128i	$0.373551\pi$
$588$		0			0
$589$	4.03690			0.166337
$590$	−14.1711	+	2.28681i	−0.583417	+	0.0941464i
$591$	−31.4291	+	13.6020i	−1.29282	+	0.559512i
$592$	13.4017	−	9.97747i	0.550808	−	0.410072i
$593$		−	44.8989i		−	1.84378i	−0.387456	−	0.921888i	$-0.626646\pi$
$593$		−	44.8989i		−	1.84378i	0.387456	−	0.921888i	$-0.373354\pi$
$594$	5.40414	−	28.8029i	0.221735	−	1.18180i
$595$		0			0
$596$	7.16624	+	21.6261i	0.293541	+	0.885838i
$597$	−12.1865	+	5.27411i	−0.498759	+	0.215855i
$598$	2.21389	+	13.7193i	0.0905328	+	0.561024i
$599$	−1.19291			−0.0487409			−0.0243704	−	0.999703i	$-0.507758\pi$
$599$	−1.19291			−0.0487409			−0.0243704	+	0.999703i	$0.507758\pi$
$600$	2.13180	−	2.62343i	0.0870303	−	0.107101i
$601$	37.4089			1.52594			0.762970	−	0.646434i	$-0.223741\pi$
$601$	37.4089			1.52594			0.762970	+	0.646434i	$0.223741\pi$
$602$		0			0
$603$	−5.29775	−	4.97415i	−0.215741	−	0.202563i
$604$	−0.577641	−	1.74319i	−0.0235039	−	0.0709293i
$605$			10.1808i			0.413907i
$606$	8.05039	+	12.6030i	0.327025	+	0.511964i
$607$		−	21.4299i		−	0.869812i	−0.900476	−	0.434906i	$-0.856782\pi$
$607$		−	21.4299i		−	0.869812i	0.900476	−	0.434906i	$-0.143218\pi$
$608$	4.32298	−	4.45073i	0.175320	−	0.180501i
$609$		0			0
$610$	11.9039	−	1.92094i	0.481975	−	0.0777766i
$611$	9.82651			0.397538
$612$	16.0140	+	7.42052i	0.647327	+	0.299957i
$613$	−40.5347			−1.63718			−0.818591	−	0.574377i	$-0.805245\pi$
$613$	−40.5347			−1.63718			−0.818591	+	0.574377i	$0.805245\pi$
$614$	−44.0905	+	7.11492i	−1.77935	+	0.287135i
$615$	10.0219	+	23.1567i	0.404120	+	0.933768i
$616$		0			0
$617$			46.2548i			1.86215i	0.364830	+	0.931074i	$0.381127\pi$
$617$			46.2548i			1.86215i	−0.364830	+	0.931074i	$0.618873\pi$
$618$	9.40473	+	14.7233i	0.378314	+	0.592258i
$619$		−	25.7964i		−	1.03684i	−0.855125	−	0.518421i	$-0.826520\pi$
$619$		−	25.7964i		−	1.03684i	0.855125	−	0.518421i	$-0.173480\pi$
$620$	−14.5062	+	4.80691i	−0.582581	+	0.193050i
$621$	36.6748	+	13.1990i	1.47171	+	0.529657i
$622$	−4.11780	−	25.5177i	−0.165109	−	1.02317i
$623$		0			0
$624$	7.86540	+	4.52838i	0.314868	+	0.181280i
$625$	−21.0738			−0.842952
$626$	−6.70977	−	41.5799i	−0.268177	−	1.66187i
$627$	6.95299	−	3.00914i	0.277676	−	0.120174i
$628$	16.5679	−	5.49011i	0.661131	−	0.219079i
$629$			12.2871i			0.489920i
$630$		0			0
$631$		−	26.5913i		−	1.05858i	−0.848440	−	0.529291i	$-0.822458\pi$
$631$		−	26.5913i		−	1.05858i	0.848440	−	0.529291i	$-0.177542\pi$
$632$	−25.9954	+	13.5326i	−1.03404	+	0.538299i
$633$	−18.6748	+	8.08217i	−0.742258	+	0.321238i
$634$	−24.7063	+	3.98687i	−0.981213	+	0.158339i
$635$	−31.3252			−1.24310
$636$	−12.7726	+	11.3943i	−0.506466	+	0.451814i
$637$		0			0
$638$	4.81932	−	0.777697i	0.190799	−	0.0307893i
$639$	−1.85057	+	1.97096i	−0.0732076	+	0.0779701i
$640$	−10.2345	+	21.1408i	−0.404554	+	0.835663i
$641$		−	6.05241i		−	0.239056i	−0.992831	−	0.119528i	$-0.961862\pi$
$641$		−	6.05241i		−	0.239056i	0.992831	−	0.119528i	$-0.0381381\pi$
$642$	−4.98888	+	3.18672i	−0.196895	+	0.125770i
$643$		−	9.95426i		−	0.392558i	−0.980548	−	0.196279i	$-0.937114\pi$
$643$		−	9.95426i		−	0.392558i	0.980548	−	0.196279i	$-0.0628858\pi$
$644$		0			0
$645$	−6.10695	−	14.1108i	−0.240461	−	0.555614i
$646$	0.726914	+	4.50462i	0.0286000	+	0.177232i
$647$	30.9902			1.21835			0.609175	−	0.793035i	$-0.291501\pi$
$647$	30.9902			1.21835			0.609175	+	0.793035i	$0.291501\pi$
$648$	21.7949	−	13.1523i	0.856183	−	0.516672i
$649$	−19.4978			−0.765357
$650$	0.203649	+	1.26200i	0.00798778	+	0.0494996i
$651$		0			0
$652$	5.65686	+	17.0711i	0.221540	+	0.668557i
$653$			8.10471i			0.317162i	0.987346	+	0.158581i	$0.0506919\pi$
$653$			8.10471i			0.317162i	−0.987346	+	0.158581i	$0.949308\pi$
$654$	14.0309	−	8.96246i	0.548652	−	0.350460i
$655$			15.3830i			0.601065i
$656$	16.7616	+	22.5142i	0.654430	+	0.879031i
$657$	−26.7174	+	28.4556i	−1.04235	+	1.11016i
$658$		0			0
$659$	−38.3085			−1.49229			−0.746143	−	0.665785i	$-0.768097\pi$
$659$	−38.3085			−1.49229			−0.746143	+	0.665785i	$0.768097\pi$
$660$	−21.4017	+	19.0923i	−0.833060	+	0.743165i
$661$	6.65686			0.258922			0.129461	−	0.991585i	$-0.458675\pi$
$661$	6.65686			0.258922			0.129461	+	0.991585i	$0.458675\pi$
$662$	−48.9797	+	7.90388i	−1.90365	+	0.307193i
$663$	−6.12537	+	2.65096i	−0.237890	+	0.102955i
$664$	16.2454	+	31.2064i	0.630442	+	1.21104i
$665$		0			0
$666$	14.6868	+	9.91711i	0.569102	+	0.384280i
$667$			6.49285i			0.251404i
$668$	30.7232	−	10.1808i	1.18872	−	0.393906i
$669$	23.0809	−	9.98905i	0.892359	−	0.386199i
$670$	1.13299	+	7.02103i	0.0437711	+	0.271246i
$671$	16.3784			0.632280
$672$		0			0
$673$	−22.0809			−0.851156			−0.425578	−	0.904922i	$-0.639929\pi$
$673$	−22.0809			−0.851156			−0.425578	+	0.904922i	$0.639929\pi$
$674$	0.0299618	+	0.185671i	0.00115408	+	0.00715176i
$675$	3.37360	+	1.21413i	0.129850	+	0.0467320i
$676$	21.4224	−	7.09873i	0.823937	−	0.273028i
$677$		−	45.0746i		−	1.73236i	−0.499733	−	0.866180i	$-0.666569\pi$
$677$		−	45.0746i		−	1.73236i	0.499733	−	0.866180i	$-0.333431\pi$
$678$	4.17158	+	6.53069i	0.160208	+	0.250810i
$679$		0			0
$680$	−7.97594	−	15.3213i	−0.305863	−	0.587546i
$681$	−14.7652	−	34.1168i	−0.565804	−	1.30736i
$682$	−20.4924	+	3.30687i	−0.784695	+	0.126627i
$683$	15.6169			0.597563			0.298781	−	0.954322i	$-0.403420\pi$
$683$	15.6169			0.597563			0.298781	+	0.954322i	$0.403420\pi$
$684$	5.97108	+	2.76686i	0.228310	+	0.105794i
$685$	−31.3469			−1.19770
$686$		0			0
$687$	13.5049	+	31.2046i	0.515242	+	1.19053i
$688$	−10.2139	−	13.7193i	−0.389401	−	0.523044i
$689$		−	6.47272i		−	0.246591i
$690$	−20.5345	−	32.1472i	−0.781735	−	1.22382i
$691$		−	38.3128i		−	1.45749i	−0.684786	−	0.728744i	$-0.740104\pi$
$691$		−	38.3128i		−	1.45749i	0.684786	−	0.728744i	$-0.259896\pi$
$692$	2.66028	+	8.02811i	0.101129	+	0.305183i
$693$		0			0
$694$	0.0440088	+	0.272719i	0.00167055	+	0.0103523i
$695$	30.0532			1.13998
$696$	3.29087	+	2.67416i	0.124740	+	0.101364i
$697$	−20.6417			−0.781859
$698$	−1.30849	−	8.10860i	−0.0495271	−	0.306915i
$699$	22.6737	−	9.81282i	0.857598	−	0.371155i
$700$		0			0
$701$		−	36.6488i		−	1.38420i	−0.721799	−	0.692102i	$-0.756685\pi$
$701$		−	36.6488i		−	1.38420i	0.721799	−	0.692102i	$-0.243315\pi$
$702$	−1.77517	+	9.46128i	−0.0669996	+	0.357093i
$703$			4.58146i			0.172793i
$704$	−18.2988	+	26.1344i	−0.689662	+	0.984975i
$705$	−24.7543	+	10.7133i	−0.932303	+	0.403486i
$706$	−27.9148	+	4.50462i	−1.05059	+	0.169534i
$707$		0			0
$708$	−11.2746	−	12.6384i	−0.423726	−	0.474981i
$709$	36.5347			1.37209			0.686045	−	0.727559i	$-0.259345\pi$
$709$	36.5347			1.37209			0.686045	+	0.727559i	$0.259345\pi$
$710$	2.61209	−	0.421514i	0.0980299	−	0.0158191i
$711$	−22.6613	−	21.2771i	−0.849867	−	0.797955i
$712$	−21.3909	+	11.1356i	−0.801657	+	0.417325i
$713$		−	27.6084i		−	1.03394i
$714$		0			0
$715$		−	10.8457i		−	0.405604i
$716$	12.4386	−	4.12178i	0.464852	−	0.154038i
$717$	10.5130	+	24.2916i	0.392616	+	0.907186i
$718$	3.13299	+	19.4149i	0.116922	+	0.724556i
$719$	24.5373			0.915087			0.457543	−	0.889187i	$-0.348729\pi$
$719$	24.5373			0.915087			0.457543	+	0.889187i	$0.348729\pi$
$720$	−24.7511	−	2.83240i	−0.922418	−	0.105557i
$721$		0			0
$722$	−4.00962	−	24.8473i	−0.149223	−	0.924720i
$723$	4.06154	+	9.38469i	0.151050	+	0.349020i
$724$	23.3208	−	7.72783i	0.866712	−	0.287203i
$725$			0.597256i			0.0221815i
$726$	−10.1231	+	6.46629i	−0.375703	+	0.239986i
$727$		−	7.89691i		−	0.292880i	−0.989220	−	0.146440i	$-0.953218\pi$
$727$		−	7.89691i		−	0.292880i	0.989220	−	0.146440i	$-0.0467816\pi$
$728$		0			0
$729$	20.8078	+	17.2057i	0.770660	+	0.637247i
$730$	37.7117	−	6.08557i	1.39577	−	0.225237i
$731$	12.5783			0.465224
$732$	9.47080	+	10.6164i	0.350051	+	0.392394i
$733$	5.84472			0.215880			0.107940	−	0.994157i	$-0.465575\pi$
$733$	5.84472			0.215880			0.107940	+	0.994157i	$0.465575\pi$
$734$	−26.2664	+	4.23863i	−0.969511	+	0.156451i
$735$		0			0
$736$	−30.4386	−	29.5650i	−1.12198	−	1.08978i
$737$			9.66011i			0.355835i
$738$	−16.6602	+	24.6730i	−0.613270	+	0.908226i
$739$		−	1.41957i		−	0.0522198i	−0.999659	−	0.0261099i	$-0.991688\pi$
$739$		−	1.41957i		−	0.0522198i	0.999659	−	0.0261099i	$-0.00831198\pi$
$740$	−5.45534	−	16.4630i	−0.200542	−	0.605191i
$741$	−2.28394	+	0.988455i	−0.0839027	+	0.0363118i
$742$		0			0
$743$	−1.70600			−0.0625872			−0.0312936	−	0.999510i	$-0.509963\pi$
$743$	−1.70600			−0.0625872			−0.0312936	+	0.999510i	$0.509963\pi$
$744$	−13.9932	−	11.3709i	−0.513017	−	0.416878i
$745$	23.6488			0.866425
$746$	−1.31191	−	8.12980i	−0.0480325	−	0.297653i
$747$	−25.5423	+	27.2040i	−0.934545	+	0.995343i
$748$	−7.38003	−	22.2713i	−0.269841	−	0.814318i
$749$		0			0
$750$	−15.5763	−	24.3850i	−0.568765	−	0.890413i
$751$			26.7854i			0.977414i	0.872448	+	0.488707i	$0.162531\pi$
$751$			26.7854i			0.977414i	−0.872448	+	0.488707i	$0.837469\pi$
$752$	−24.0675	+	17.9180i	−0.877651	+	0.653403i
$753$	16.3317	+	37.7364i	0.595160	+	1.37519i
$754$	−1.58307	+	0.255461i	−0.0576520	+	0.00930334i
$755$	−1.90623			−0.0693749
$756$		0			0
$757$	−23.8816			−0.867992			−0.433996	−	0.900915i	$-0.642897\pi$
$757$	−23.8816			−0.867992			−0.433996	+	0.900915i	$0.642897\pi$
$758$	−16.8373	+	2.71704i	−0.611558	+	0.0986875i
$759$	−20.5796	−	47.5517i	−0.746992	−	1.72602i
$760$	−2.97396	−	5.71280i	−0.107877	−	0.207225i
$761$			15.0915i			0.547067i	0.961862	+	0.273533i	$0.0881924\pi$
$761$			15.0915i			0.547067i	−0.961862	+	0.273533i	$0.911808\pi$
$762$	−19.8961	−	31.1478i	−0.720761	−	1.12837i
$763$		0			0
$764$	45.0557	−	14.9301i	1.63006	−	0.540153i
$765$	12.5405	−	13.3563i	0.453401	−	0.482897i
$766$	−2.73777	−	16.9657i	−0.0989197	−	0.612997i
$767$	6.40472			0.231261
$768$	−27.5215	+	3.25098i	−0.993095	+	0.117310i
$769$	12.6792			0.457222			0.228611	−	0.973518i	$-0.426582\pi$
$769$	12.6792			0.457222			0.228611	+	0.973518i	$0.426582\pi$
$770$		0			0
$771$	23.5267	−	10.1820i	0.847294	−	0.366695i
$772$	7.54449	−	2.50002i	0.271532	−	0.0899777i
$773$		−	38.7248i		−	1.39283i	−0.717637	−	0.696417i	$-0.754776\pi$
$773$		−	38.7248i		−	1.39283i	0.717637	−	0.696417i	$-0.245224\pi$
$774$	10.1521	−	15.0348i	0.364910	−	0.540415i
$775$		−	2.53961i		−	0.0912256i
$776$	20.1012	+	38.6132i	0.721590	+	1.38613i
$777$		0			0
$778$	1.69002	−	0.272719i	0.0605900	−	0.00977745i
$779$	−7.69659			−0.275759
$780$	7.03011	−	6.27150i	0.251718	−	0.224556i
$781$	3.59393			0.128601
$782$	30.8072	−	4.97138i	1.10166	−	0.177776i
$783$	−1.52303	+	4.23190i	−0.0544286	+	0.151236i
$784$		0			0
$785$		−	18.1175i		−	0.646642i
$786$	−15.2959	+	9.77050i	−0.545587	+	0.348502i
$787$			20.3831i			0.726578i	0.931676	+	0.363289i	$0.118346\pi$
$787$			20.3831i			0.726578i	−0.931676	+	0.363289i	$0.881654\pi$
$788$	12.4386	+	37.5369i	0.443107	+	1.33720i
$789$	9.56649	+	22.1045i	0.340576	+	0.786942i
$790$	4.84640	+	30.0327i	0.172427	+	1.06852i
$791$		0			0
$792$	−32.5774	−	9.15408i	−1.15759	−	0.325276i
$793$	−5.38003			−0.191051
$794$	2.15318	+	13.3431i	0.0764135	+	0.473528i
$795$	7.05684	+	16.3057i	0.250280	+	0.578302i
$796$	4.82300	+	14.5547i	0.170947	+	0.515879i
$797$		−	27.9005i		−	0.988287i	−0.869380	−	0.494143i	$-0.835482\pi$
$797$		−	27.9005i		−	0.988287i	0.869380	−	0.494143i	$-0.164518\pi$
$798$		0			0
$799$		−	22.0658i		−	0.780632i
$800$	−2.79996	−	2.71959i	−0.0989934	−	0.0961521i
$801$	−18.6474	−	17.5084i	−0.658873	−	0.618628i
$802$	−15.7009	+	2.53366i	−0.554417	+	0.0894666i
$803$	51.8869			1.83105
$804$	−6.26165	+	5.58596i	−0.220831	+	0.197002i
$805$		0			0
$806$	6.73142	−	1.08625i	0.237104	−	0.0382617i
$807$	13.1265	−	5.68096i	0.462076	−	0.199979i
$808$	15.3171	−	7.97374i	0.538854	−	0.280515i
$809$			14.2640i			0.501497i	0.968052	+	0.250748i	$0.0806767\pi$
$809$			14.2640i			0.501497i	−0.968052	+	0.250748i	$0.919323\pi$
$810$	−5.84319	−	25.7696i	−0.205309	−	0.905453i
$811$			38.4069i			1.34865i	0.738435	+	0.674325i	$0.235565\pi$
$811$			38.4069i			1.34865i	−0.738435	+	0.674325i	$0.764435\pi$
$812$		0			0
$813$	−8.43351	+	3.64989i	−0.295776	+	0.128007i
$814$	−3.75295	−	23.2567i	−0.131541	−	0.815148i
$815$	18.6678			0.653905
$816$	10.1686	−	17.6621i	0.355974	−	0.618296i
$817$	4.69002			0.164083
$818$	3.50741	+	21.7351i	0.122634	+	0.759951i
$819$		0			0
$820$	27.6569	−	9.16466i	0.965820	−	0.320044i
$821$			52.7894i			1.84236i	0.389135	+	0.921181i	$0.372774\pi$
$821$			52.7894i			1.84236i	−0.389135	+	0.921181i	$0.627226\pi$
$822$	−19.9099	−	31.1693i	−0.694437	−	1.08716i
$823$			5.73006i			0.199737i	0.995001	+	0.0998687i	$0.0318423\pi$
$823$			5.73006i			0.199737i	−0.995001	+	0.0998687i	$0.968158\pi$
$824$	17.8939	−	9.31519i	0.623365	−	0.324510i
$825$	−1.89305	−	4.37413i	−0.0659077	−	0.152288i
$826$		0			0
$827$	44.5253			1.54830			0.774149	−	0.633003i	$-0.218178\pi$
$827$	44.5253			1.54830			0.774149	+	0.633003i	$0.218178\pi$
$828$	18.9226	−	40.8364i	0.657607	−	1.41916i
$829$	26.0586			0.905053			0.452526	−	0.891751i	$-0.350523\pi$
$829$	26.0586			0.905053			0.452526	+	0.891751i	$0.350523\pi$
$830$	36.0531	−	5.81791i	1.25142	−	0.201942i
$831$	−8.67135	−	20.0362i	−0.300806	−	0.695048i
$832$	6.01086	−	8.58471i	0.208389	−	0.297621i
$833$		0			0
$834$	19.0882	+	29.8830i	0.660971	+	1.03476i
$835$		−	33.5968i		−	1.16267i
$836$	−2.75177	−	8.30420i	−0.0951718	−	0.287207i
$837$	6.47612	−	17.9946i	0.223848	−	0.621985i
$838$	−4.06294	−	25.1777i	−0.140352	−	0.869748i
$839$	−46.0533			−1.58994			−0.794968	−	0.606652i	$-0.792512\pi$
$839$	−46.0533			−1.58994			−0.794968	+	0.606652i	$0.792512\pi$
$840$		0			0
$841$	28.2508			0.974165
$842$	2.81574	+	17.4489i	0.0970367	+	0.601328i
$843$	3.22646	−	1.39636i	0.111125	−	0.0480932i
$844$	7.39089	+	22.3040i	0.254405	+	0.767736i
$845$		−	23.4260i		−	0.805880i
$846$	−26.3753	−	17.8096i	−0.906801	−	0.612307i
$847$		0			0
$848$	11.8026	+	15.8532i	0.405302	+	0.544403i
$849$	−12.2044	+	5.28188i	−0.418855	+	0.181274i
$850$	2.83386	−	0.457302i	0.0972006	−	0.0156853i
$851$	31.3327			1.07407
$852$	2.07819	+	2.32957i	0.0711975	+	0.0798097i
$853$	46.3274			1.58622			0.793109	−	0.609079i	$-0.208461\pi$
$853$	46.3274			1.58622			0.793109	+	0.609079i	$0.208461\pi$
$854$		0			0
$855$	4.67591	−	4.98011i	0.159913	−	0.170316i
$856$	3.15638	+	6.06323i	0.107883	+	0.207237i
$857$		−	41.1458i		−	1.40551i	−0.711431	−	0.702756i	$-0.751952\pi$
$857$		−	41.1458i		−	1.40551i	0.711431	−	0.702756i	$-0.248048\pi$
$858$	10.7842	−	6.88859i	0.368167	−	0.235173i
$859$			57.4109i			1.95883i	0.201846	+	0.979417i	$0.435306\pi$
$859$			57.4109i			1.95883i	−0.201846	+	0.979417i	$0.564694\pi$
$860$	−16.8531	+	5.58461i	−0.574685	+	0.190434i
$861$		0			0
$862$	−2.80407	−	17.3766i	−0.0955072	−	0.591850i
$863$	−25.4867			−0.867577			−0.433788	−	0.901015i	$-0.642823\pi$
$863$	−25.4867			−0.867577			−0.433788	+	0.901015i	$0.642823\pi$
$864$	−12.9042	−	26.4099i	−0.439010	−	0.898482i
$865$	8.77899			0.298495
$866$	0.112162	+	0.695056i	0.00381141	+	0.0236190i
$867$	−5.74216	−	13.2680i	−0.195014	−	0.450604i
$868$		0			0
$869$			41.3215i			1.40174i
$870$	3.70946	−	2.36947i	0.125762	−	0.0803326i
$871$		−	3.17319i		−	0.107519i
$872$	−8.87713	−	17.0525i	−0.300618	−	0.577469i
$873$	−31.6048	+	33.6609i	−1.06966	+	1.13925i
$874$	11.4870	−	1.85366i	0.388553	−	0.0627010i
$875$		0			0
$876$	30.0036	+	33.6329i	1.01373	+	1.13635i
$877$	41.8627			1.41360			0.706801	−	0.707412i	$-0.250138\pi$
$877$	41.8627			1.41360			0.706801	+	0.707412i	$0.250138\pi$
$878$	6.50613	−	1.04990i	0.219571	−	0.0354323i
$879$	2.47241	−	1.07002i	0.0833923	−	0.0360909i
$880$	19.7764	+	26.5636i	0.666661	+	0.895459i
$881$		−	38.5556i		−	1.29897i	−0.760373	−	0.649486i	$-0.774984\pi$
$881$		−	38.5556i		−	1.29897i	0.760373	−	0.649486i	$-0.225016\pi$
$882$		0			0
$883$			4.56420i			0.153597i	0.997047	+	0.0767987i	$0.0244699\pi$
$883$			4.56420i			0.153597i	−0.997047	+	0.0767987i	$0.975530\pi$
$884$	2.42422	+	7.31575i	0.0815354	+	0.246055i
$885$	−16.1344	+	6.98270i	−0.542351	+	0.234721i
$886$	−4.97228	−	30.8128i	−0.167047	−	1.03518i
$887$	−40.4892			−1.35949			−0.679747	−	0.733447i	$-0.737910\pi$
$887$	−40.4892			−1.35949			−0.679747	+	0.733447i	$0.737910\pi$
$888$	12.9048	−	15.8809i	0.433056	−	0.532927i
$889$		0			0
$890$	3.98797	+	24.7131i	0.133677	+	0.828385i
$891$	−2.25916	−	35.8206i	−0.0756847	−	1.20003i
$892$	−9.13467	−	27.5664i	−0.305851	−	0.922990i
$893$		−	8.22760i		−	0.275326i
$894$	15.0205	+	23.5148i	0.502360	+	0.786454i
$895$		−	13.6020i		−	0.454665i
$896$		0			0
$897$	6.76007	+	15.6199i	0.225712	+	0.521535i
$898$	−8.41693	+	1.35825i	−0.280877	+	0.0453252i
$899$	3.18574			0.106250
$900$	1.74063	−	3.75641i	0.0580212	−	0.125214i
$901$	−14.5347			−0.484222
$902$	39.0700	−	6.30475i	1.30089	−	0.209925i
$903$		0			0
$904$	7.93706	−	4.13186i	0.263983	−	0.137424i
$905$		−	25.5021i		−	0.847718i
$906$	−1.21074	−	1.89544i	−0.0402241	−	0.0629716i
$907$			2.73314i			0.0907526i	0.998970	+	0.0453763i	$0.0144487\pi$
$907$			2.73314i			0.0907526i	−0.998970	+	0.0453763i	$0.985551\pi$
$908$	−40.7469	+	13.5023i	−1.35223	+	0.448090i
$909$	13.3526	+	12.5370i	0.442878	+	0.415826i
$910$		0			0
$911$	−5.16105			−0.170993			−0.0854966	−	0.996338i	$-0.527248\pi$
$911$	−5.16105			−0.170993			−0.0854966	+	0.996338i	$0.527248\pi$
$912$	3.79154	−	6.58559i	0.125551	−	0.218071i
$913$	49.6048			1.64168
$914$	8.62027	+	53.4191i	0.285133	+	1.76695i
$915$	13.5530	−	5.86554i	0.448050	−	0.193909i
$916$	37.2688	−	12.3498i	1.23139	−	0.408048i
$917$		0			0
$918$	21.2457	+	3.98622i	0.701212	+	0.131565i
$919$		−	39.8384i		−	1.31415i	−0.753826	−	0.657074i	$-0.771794\pi$
$919$		−	39.8384i		−	1.31415i	0.753826	−	0.657074i	$-0.228206\pi$
$920$	−39.0700	+	20.3390i	−1.28810	+	0.670556i
$921$	−50.1987	+	21.7252i	−1.65410	+	0.715870i
$922$	−17.3909	+	2.80638i	−0.572738	+	0.0924232i
$923$	−1.18055			−0.0388582
$924$		0			0
$925$	2.88220			0.0947660
$926$	39.1773	−	6.32206i	1.28745	−	0.207756i
$927$	15.5990	+	14.6461i	0.512337	+	0.481042i
$928$	3.41150	−	3.51231i	0.111988	−	0.115297i
$929$		−	25.7241i		−	0.843981i	−0.906600	−	0.421990i	$-0.861332\pi$
$929$		−	25.7241i		−	0.843981i	0.906600	−	0.421990i	$-0.138668\pi$
$930$	−15.7731	+	10.0753i	−0.517220	+	0.330382i
$931$		0			0
$932$	−8.97351	−	27.0800i	−0.293937	−	0.887035i
$933$	−12.5736	−	29.0528i	−0.411641	−	0.951147i
$934$	3.85183	+	23.8695i	0.126036	+	0.781032i
$935$	−24.3543			−0.796472
$936$	10.7011	+	3.00697i	0.349777	+	0.0982858i
$937$	20.2068			0.660127			0.330063	−	0.943959i	$-0.392930\pi$
$937$	20.2068			0.660127			0.330063	+	0.943959i	$0.392930\pi$
$938$		0			0
$939$	−20.4881	−	47.3403i	−0.668604	−	1.54489i
$940$	9.79696	+	29.5650i	0.319542	+	0.964304i
$941$			47.8868i			1.56107i	0.625115	+	0.780533i	$0.285052\pi$
$941$			47.8868i			1.56107i	−0.625115	+	0.780533i	$0.714948\pi$
$942$	18.0149	−	11.5073i	0.586957	−	0.374928i
$943$			52.6372i			1.71410i
$944$	−15.6867	+	11.6786i	−0.510559	+	0.380106i
$945$		0			0
$946$	−23.8078	+	3.84188i	−0.774059	+	0.124910i
$947$	6.32070			0.205395			0.102698	−	0.994713i	$-0.467253\pi$
$947$	6.32070			0.205395			0.102698	+	0.994713i	$0.467253\pi$
$948$	−26.7844	+	23.8942i	−0.869918	+	0.776046i
$949$	−17.0440			−0.553272
$950$	1.05665	−	0.170512i	0.0342823	−	0.00553215i
$951$	−28.1290	+	12.1738i	−0.912147	+	0.394763i
$952$		0			0
$953$		−	3.70027i		−	0.119863i	−0.998202	−	0.0599317i	$-0.980912\pi$
$953$		−	3.70027i		−	0.119863i	0.998202	−	0.0599317i	$-0.0190883\pi$
$954$	−11.7312	+	17.3734i	−0.379811	+	0.562484i
$955$		−	49.2698i		−	1.59433i
$956$	29.0123	−	9.61382i	0.938326	−	0.310933i
$957$	5.48698	−	2.37468i	0.177369	−	0.0767624i
$958$	3.70087	+	22.9340i	0.119570	+	0.740964i
$959$		0			0
$960$	−5.78276	+	28.1794i	−0.186638	+	0.909485i
$961$	17.4538			0.563027
$962$	1.23278	+	7.63946i	0.0397466	+	0.246306i
$963$	−4.96274	+	5.28559i	−0.159922	+	0.170326i
$964$	11.2085	−	3.71415i	0.361000	−	0.119625i
$965$		−	8.25014i		−	0.265581i
$966$		0			0
$967$		−	14.5970i		−	0.469409i	−0.972067	−	0.234705i	$-0.924588\pi$
$967$		−	14.5970i		−	0.469409i	0.972067	−	0.234705i	$-0.0754123\pi$
$968$	6.40472	+	12.3031i	0.205856	+	0.395437i
$969$	2.21961	+	5.12868i	0.0713042	+	0.164757i
$970$	44.6102	−	7.19878i	1.43235	−	0.231139i
$971$	8.21458			0.263618			0.131809	−	0.991275i	$-0.457921\pi$
$971$	8.21458			0.263618			0.131809	+	0.991275i	$0.457921\pi$
$972$	21.9124	−	22.1776i	0.702840	−	0.711348i
$973$		0			0
$974$	44.6592	−	7.20668i	1.43097	−	0.230917i
$975$	0.621837	+	1.43683i	0.0199147	+	0.0460154i
$976$	13.1770	−	9.81015i	0.421785	−	0.314015i
$977$		−	35.6140i		−	1.13939i	−0.821855	−	0.569697i	$-0.807061\pi$
$977$		−	35.6140i		−	1.13939i	0.821855	−	0.569697i	$-0.192939\pi$
$978$	11.8568	+	18.5621i	0.379139	+	0.593550i
$979$			34.0023i			1.08672i
$980$		0			0
$981$	13.9574	−	14.8654i	0.445625	−	0.474615i
$982$	−0.459257	−	2.84597i	−0.0146555	−	0.0908187i
$983$	−31.1497			−0.993522			−0.496761	−	0.867887i	$-0.665477\pi$
$983$	−31.1497			−0.993522			−0.496761	+	0.867887i	$0.665477\pi$
$984$	26.6789	+	21.6793i	0.850494	+	0.691111i
$985$	41.0478			1.30789
$986$	0.573647	+	3.55484i	0.0182687	+	0.113209i
$987$		0			0
$988$	0.903910	+	2.72779i	0.0287572	+	0.0867827i
$989$		−	32.0751i		−	1.01993i
$990$	−19.6567	+	29.1107i	−0.624731	+	0.925200i
$991$		−	34.8265i		−	1.10630i	−0.833082	−	0.553149i	$-0.813426\pi$
$991$		−	34.8265i		−	1.10630i	0.833082	−	0.553149i	$-0.186574\pi$
$992$	−14.5062	+	14.9348i	−0.460571	+	0.474181i
$993$	−55.7652	+	24.1343i	−1.76966	+	0.765879i
$994$		0			0
$995$	15.9161			0.504573
$996$	28.6840	+	32.1536i	0.908886	+	1.01883i
$997$	8.45719			0.267842			0.133921	−	0.990992i	$-0.457243\pi$
$997$	8.45719			0.267842			0.133921	+	0.990992i	$0.457243\pi$
$998$	5.99400	−	0.967256i	0.189737	−	0.0306180i
$999$	20.4220	+	7.34972i	0.646124	+	0.232535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.e.491.5		12
3.2	odd	2	inner	588.2.e.e.491.8		12
4.3	odd	2	inner	588.2.e.e.491.7		12
7.2	even	3		84.2.n.a.11.3	yes	24
7.3	odd	6		588.2.n.e.275.12		24
7.4	even	3		84.2.n.a.23.12	yes	24
7.5	odd	6		588.2.n.e.263.3		24
7.6	odd	2		588.2.e.d.491.5		12
12.11	even	2	inner	588.2.e.e.491.6		12
21.2	odd	6		84.2.n.a.11.10	yes	24
21.5	even	6		588.2.n.e.263.10		24
21.11	odd	6		84.2.n.a.23.1	yes	24
21.17	even	6		588.2.n.e.275.1		24
21.20	even	2		588.2.e.d.491.8		12
28.3	even	6		588.2.n.e.275.10		24
28.11	odd	6		84.2.n.a.23.10	yes	24
28.19	even	6		588.2.n.e.263.1		24
28.23	odd	6		84.2.n.a.11.1	✓	24
28.27	even	2		588.2.e.d.491.7		12
84.11	even	6		84.2.n.a.23.3	yes	24
84.23	even	6		84.2.n.a.11.12	yes	24
84.47	odd	6		588.2.n.e.263.12		24
84.59	odd	6		588.2.n.e.275.3		24
84.83	odd	2		588.2.e.d.491.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.1	✓	24	28.23	odd	6
84.2.n.a.11.3	yes	24	7.2	even	3
84.2.n.a.11.10	yes	24	21.2	odd	6
84.2.n.a.11.12	yes	24	84.23	even	6
84.2.n.a.23.1	yes	24	21.11	odd	6
84.2.n.a.23.3	yes	24	84.11	even	6
84.2.n.a.23.10	yes	24	28.11	odd	6
84.2.n.a.23.12	yes	24	7.4	even	3
588.2.e.d.491.5		12	7.6	odd	2
588.2.e.d.491.6		12	84.83	odd	2
588.2.e.d.491.7		12	28.27	even	2
588.2.e.d.491.8		12	21.20	even	2
588.2.e.e.491.5		12	1.1	even	1	trivial
588.2.e.e.491.6		12	12.11	even	2	inner
588.2.e.e.491.7		12	4.3	odd	2	inner
588.2.e.e.491.8		12	3.2	odd	2	inner
588.2.n.e.263.1		24	28.19	even	6
588.2.n.e.263.3		24	7.5	odd	6
588.2.n.e.263.10		24	21.5	even	6
588.2.n.e.263.12		24	84.47	odd	6
588.2.n.e.275.1		24	21.17	even	6
588.2.n.e.275.3		24	84.59	odd	6
588.2.n.e.275.10		24	28.3	even	6
588.2.n.e.275.12		24	7.3	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)

\(f(q)\)	\(=\)	\(q+(-0.225298 - 1.39615i) q^{2} +(-0.687941 - 1.58957i) q^{3} +(-1.89848 + 0.629100i) q^{4} +2.07605i q^{5} +(-2.06429 + 1.31860i) q^{6} +(1.30604 + 2.50883i) q^{8} +(-2.05347 + 2.18706i) q^{9} +O(q^{10})\)	\(q+(-0.225298 - 1.39615i) q^{2} +(-0.687941 - 1.58957i) q^{3} +(-1.89848 + 0.629100i) q^{4} +2.07605i q^{5} +(-2.06429 + 1.31860i) q^{6} +(1.30604 + 2.50883i) q^{8} +(-2.05347 + 2.18706i) q^{9} +(2.89848 - 0.467730i) q^{10} +3.98797 q^{11} +(2.30604 + 2.58499i) q^{12} -1.30998 q^{13} +(3.30003 - 1.42820i) q^{15} +(3.20847 - 2.38867i) q^{16} +2.94162i q^{17} +(3.51612 + 2.37422i) q^{18} +1.09683i q^{19} +(-1.30604 - 3.94134i) q^{20} +(-0.898482 - 5.56781i) q^{22} +7.50125 q^{23} +(3.08949 - 3.80198i) q^{24} +0.690016 q^{25} +(0.295137 + 1.82894i) q^{26} +(4.88916 + 1.75957i) q^{27} +0.865568i q^{29} +(-2.73748 - 4.28557i) q^{30} -3.68051i q^{31} +(-4.05781 - 3.94134i) q^{32} +(-2.74349 - 6.33916i) q^{33} +(4.10695 - 0.662741i) q^{34} +(2.52260 - 5.44394i) q^{36} +4.17700 q^{37} +(1.53134 - 0.247114i) q^{38} +(0.901192 + 2.08231i) q^{39} +(-5.20847 + 2.71141i) q^{40} +7.01712i q^{41} -4.27597i q^{43} +(-7.57109 + 2.50883i) q^{44} +(-4.54045 - 4.26311i) q^{45} +(-1.69002 - 10.4729i) q^{46} -7.50125 q^{47} +(-6.00420 - 3.45682i) q^{48} +(-0.155459 - 0.963368i) q^{50} +(4.67591 - 2.02366i) q^{51} +(2.48698 - 0.824111i) q^{52} +4.94107i q^{53} +(1.35511 - 7.22244i) q^{54} +8.27923i q^{55} +(1.74349 - 0.754555i) q^{57} +(1.20847 - 0.195011i) q^{58} -4.88916 q^{59} +(-5.36656 + 4.78746i) q^{60} +4.10695 q^{61} +(-5.13856 + 0.829212i) q^{62} +(-4.58850 + 6.55330i) q^{64} -2.71959i q^{65} +(-8.23233 + 5.25853i) q^{66} +2.42231i q^{67} +(-1.85057 - 5.58461i) q^{68} +(-5.16042 - 11.9238i) q^{69} +0.901192 q^{71} +(-8.16891 - 2.29542i) q^{72} +13.0109 q^{73} +(-0.941069 - 5.83172i) q^{74} +(-0.474691 - 1.09683i) q^{75} +(-0.690016 - 2.08231i) q^{76} +(2.70419 - 1.72734i) q^{78} +10.3615i q^{79} +(4.95900 + 6.66093i) q^{80} +(-0.566494 - 8.98215i) q^{81} +(9.79696 - 1.58094i) q^{82} +12.4386 q^{83} -6.10695 q^{85} +(-5.96991 + 0.963368i) q^{86} +(1.37588 - 0.595460i) q^{87} +(5.20847 + 10.0052i) q^{88} +8.52623i q^{89} +(-4.92900 + 7.29963i) q^{90} +(-14.2410 + 4.71904i) q^{92} +(-5.85044 + 2.53198i) q^{93} +(1.69002 + 10.4729i) q^{94} -2.27707 q^{95} +(-3.47351 + 9.16159i) q^{96} +15.3909 q^{97} +(-8.18919 + 8.72195i) 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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