LMFDB - Embedded newform 588.2.e.c.491.4

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:	12.0.2593100598870016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + x^8 + 4x^6 + 4x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.4
Root			$1.19877 + 0.750295i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.c.491.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 - 1.79887i) q^{4} +3.56257i q^{5} +(-2.34202 - 0.717607i) q^{6} +(2.81228 + 0.301817i) q^{8} +(-2.59774 + 1.50059i) q^{9} +O(q^{10})$	\(q+(-0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 - 1.79887i) q^{4} +3.56257i q^{5} +(-2.34202 - 0.717607i) q^{6} +(2.81228 + 0.301817i) q^{8} +(-2.59774 + 1.50059i) q^{9} +(-4.27072 - 2.67298i) q^{10} +0.335564 q^{11} +(2.61745 - 2.26913i) q^{12} -3.34596 q^{13} +(-5.96012 + 1.59774i) q^{15} +(-2.47185 + 3.14483i) q^{16} +0.335564i q^{17} +(0.150201 - 4.23998i) q^{18} +1.84951i q^{19} +(6.40860 - 3.11410i) q^{20} +(-0.251772 + 0.402265i) q^{22} +4.45953 q^{23} +(0.756309 + 4.84025i) q^{24} -7.69193 q^{25} +(2.51046 - 4.01105i) q^{26} +(-3.67549 - 3.67298i) q^{27} +5.91788i q^{29} +(2.55653 - 8.34360i) q^{30} -5.19547i q^{31} +(-1.91532 - 5.32274i) q^{32} +(0.150493 + 0.561392i) q^{33} +(-0.402265 - 0.251772i) q^{34} +(4.97008 + 3.36129i) q^{36} +3.19547 q^{37} +(-2.21714 - 1.38768i) q^{38} +(-1.50059 - 5.59774i) q^{39} +(-1.07525 + 10.0189i) q^{40} +1.45835i q^{41} -7.49646i q^{43} +(-0.293321 - 0.603635i) q^{44} +(-5.34596 - 9.25462i) q^{45} +(-3.34596 + 5.34596i) q^{46} -8.91906 q^{47} +(-6.36981 - 2.72497i) q^{48} +(5.77122 - 9.22087i) q^{50} +(-0.561392 + 0.150493i) q^{51} +(2.92475 + 6.01894i) q^{52} +4.79509i q^{53} +(7.16077 - 1.65025i) q^{54} +1.19547i q^{55} +(-3.09419 + 0.829463i) q^{57} +(-7.09419 - 4.44015i) q^{58} +14.0245 q^{59} +(8.08394 + 9.32486i) q^{60} +0.353051 q^{61} +(6.22819 + 3.89814i) q^{62} +(7.81781 + 1.69759i) q^{64} -11.9202i q^{65} +(-0.785896 - 0.240803i) q^{66} +3.19547i q^{67} +(0.603635 - 0.293321i) q^{68} +(2.00000 + 7.46071i) q^{69} -10.3774 q^{71} +(-7.75846 + 3.43604i) q^{72} +4.69193 q^{73} +(-2.39755 + 3.83064i) q^{74} +(-3.44966 - 12.8685i) q^{75} +(3.32702 - 1.61668i) q^{76} +(7.83630 + 2.40109i) q^{78} +4.00000i q^{79} +(-11.2037 - 8.80614i) q^{80} +(4.49646 - 7.79627i) q^{81} +(-1.74823 - 1.09419i) q^{82} -6.89932 q^{83} -1.19547 q^{85} +(8.98655 + 5.62456i) q^{86} +(-9.90050 + 2.65404i) q^{87} +(0.943698 + 0.101279i) q^{88} -3.87289i q^{89} +(15.1052 + 0.535101i) q^{90} +(-3.89814 - 8.02210i) q^{92} +(8.69193 - 2.33005i) q^{93} +(6.69193 - 10.6919i) q^{94} -6.58900 q^{95} +(8.04586 - 5.59143i) q^{96} +2.00000 q^{97} +(-0.871706 + 0.503544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9	$ 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} - 2 q^{24} - 12 q^{25} + 20 q^{30} + 16 q^{33} - 32 q^{34} - 20 q^{36} - 16 q^{37} - 20 q^{40} - 24 q^{45} - 46 q^{48} + 28 q^{52} - 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} + 16 q^{61} + 20 q^{64} + 12 q^{66} + 24 q^{69} - 32 q^{72} - 24 q^{73} + 60 q^{76} + 20 q^{78} + 28 q^{81} - 8 q^{82} + 40 q^{85} - 56 q^{88} + 80 q^{90} + 24 q^{93} + 34 q^{96} + 24 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 - 2 * q^24 - 12 * q^25 + 20 * q^30 + 16 * q^33 - 32 * q^34 - 20 * q^36 - 16 * q^37 - 20 * q^40 - 24 * q^45 - 46 * q^48 + 28 * q^52 - 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 + 16 * q^61 + 20 * q^64 + 12 * q^66 + 24 * q^69 - 32 * q^72 - 24 * q^73 + 60 * q^76 + 20 * q^78 + 28 * q^81 - 8 * q^82 + 40 * q^85 - 56 * q^88 + 80 * q^90 + 24 * q^93 + 34 * q^96 + 24 * 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 $

$2$	−0.750295	+	1.19877i	−0.530539	+	0.847661i
$2$	−0.750295	+	1.19877i	−0.530539	+	0.847661i
$3$	0.448478	+	1.67298i	0.258929	+	0.965896i
$3$	0.448478	+	1.67298i	0.258929	+	0.965896i
$4$	−0.874114	−	1.79887i	−0.437057	−	0.899434i
$5$			3.56257i			1.59323i	0.604486	+	0.796616i	$0.293378\pi$
$5$			3.56257i			1.59323i	−0.604486	+	0.796616i	$0.706622\pi$
$6$	−2.34202	−	0.717607i	−0.956124	−	0.292962i
$7$		0			0
$7$		0			0
$8$	2.81228	+	0.301817i	0.994290	+	0.106709i
$9$	−2.59774	+	1.50059i	−0.865912	+	0.500197i
$10$	−4.27072	−	2.67298i	−1.35052	−	0.845271i
$11$	0.335564			0.101176			0.0505881	−	0.998720i	$-0.483890\pi$
$11$	0.335564			0.101176			0.0505881	+	0.998720i	$0.483890\pi$
$12$	2.61745	−	2.26913i	0.755593	−	0.655041i
$13$	−3.34596			−0.928003			−0.464002	−	0.885834i	$-0.653587\pi$
$13$	−3.34596			−0.928003			−0.464002	+	0.885834i	$0.653587\pi$
$14$		0			0
$15$	−5.96012	+	1.59774i	−1.53890	+	0.412533i
$16$	−2.47185	+	3.14483i	−0.617962	+	0.786208i
$17$			0.335564i			0.0813862i	0.999172	+	0.0406931i	$0.0129566\pi$
$17$			0.335564i			0.0813862i	−0.999172	+	0.0406931i	$0.987043\pi$
$18$	0.150201	−	4.23998i	0.0354027	−	0.999373i
$19$			1.84951i			0.424306i	0.977236	+	0.212153i	$0.0680475\pi$
$19$			1.84951i			0.424306i	−0.977236	+	0.212153i	$0.931952\pi$
$20$	6.40860	−	3.11410i	1.43301	−	0.696333i
$21$		0			0
$22$	−0.251772	+	0.402265i	−0.0536779	+	0.0857631i
$23$	4.45953			0.929876			0.464938	−	0.885343i	$-0.346077\pi$
$23$	4.45953			0.929876			0.464938	+	0.885343i	$0.346077\pi$
$24$	0.756309	+	4.84025i	0.154381	+	0.988011i
$25$	−7.69193			−1.53839
$26$	2.51046	−	4.01105i	0.492342	−	0.786632i
$27$	−3.67549	−	3.67298i	−0.707348	−	0.706866i
$28$		0			0
$29$			5.91788i			1.09892i	0.835519	+	0.549461i	$0.185167\pi$
$29$			5.91788i			1.09892i	−0.835519	+	0.549461i	$0.814833\pi$
$30$	2.55653	−	8.34360i	0.466756	−	1.52333i
$31$		−	5.19547i		−	0.933134i	−0.884486	−	0.466567i	$-0.845491\pi$
$31$		−	5.19547i		−	0.933134i	0.884486	−	0.466567i	$-0.154509\pi$
$32$	−1.91532	−	5.32274i	−0.338584	−	0.940936i
$33$	0.150493	+	0.561392i	0.0261975	+	0.0977258i
$34$	−0.402265	−	0.251772i	−0.0689878	−	0.0431785i
$35$		0			0
$36$	4.97008	+	3.36129i	0.828347	+	0.560216i
$37$	3.19547			0.525332			0.262666	−	0.964887i	$-0.415398\pi$
$37$	3.19547			0.525332			0.262666	+	0.964887i	$0.415398\pi$
$38$	−2.21714	−	1.38768i	−0.359668	−	0.225111i
$39$	−1.50059	−	5.59774i	−0.240287	−	0.896355i
$40$	−1.07525	+	10.0189i	−0.170011	+	1.58413i
$41$			1.45835i			0.227756i	0.993495	+	0.113878i	$0.0363272\pi$
$41$			1.45835i			0.227756i	−0.993495	+	0.113878i	$0.963673\pi$
$42$		0			0
$43$		−	7.49646i		−	1.14320i	−0.820533	−	0.571599i	$-0.806323\pi$
$43$		−	7.49646i		−	1.14320i	0.820533	−	0.571599i	$-0.193677\pi$
$44$	−0.293321	−	0.603635i	−0.0442198	−	0.0910014i
$45$	−5.34596	−	9.25462i	−0.796929	−	1.37960i
$46$	−3.34596	+	5.34596i	−0.493335	+	0.788219i
$47$	−8.91906			−1.30098			−0.650489	−	0.759516i	$-0.725436\pi$
$47$	−8.91906			−1.30098			−0.650489	+	0.759516i	$0.725436\pi$
$48$	−6.36981	−	2.72497i	−0.919403	−	0.393316i
$49$		0			0
$50$	5.77122	−	9.22087i	0.816173	−	1.30403i
$51$	−0.561392	+	0.150493i	−0.0786106	+	0.0210732i
$52$	2.92475	+	6.01894i	0.405590	+	0.834677i
$53$			4.79509i			0.658657i	0.944215	+	0.329328i	$0.106822\pi$
$53$			4.79509i			0.658657i	−0.944215	+	0.329328i	$0.893178\pi$
$54$	7.16077	−	1.65025i	0.974458	−	0.224571i
$55$			1.19547i			0.161197i
$56$		0			0
$57$	−3.09419	+	0.829463i	−0.409836	+	0.109865i
$58$	−7.09419	−	4.44015i	−0.931513	−	0.583021i
$59$	14.0245			1.82583			0.912915	−	0.408150i	$-0.133826\pi$
$59$	14.0245			1.82583			0.912915	+	0.408150i	$0.133826\pi$
$60$	8.08394	+	9.32486i	1.04363	+	1.20383i
$61$	0.353051			0.0452035			0.0226018	−	0.999745i	$-0.492805\pi$
$61$	0.353051			0.0452035			0.0226018	+	0.999745i	$0.492805\pi$
$62$	6.22819	+	3.89814i	0.790981	+	0.495064i
$63$		0			0
$64$	7.81781	+	1.69759i	0.977227	+	0.212199i
$65$		−	11.9202i		−	1.47852i
$66$	−0.785896	−	0.240803i	−0.0967371	−	0.0296408i
$67$			3.19547i			0.390389i	0.980765	+	0.195194i	$0.0625338\pi$
$67$			3.19547i			0.390389i	−0.980765	+	0.195194i	$0.937466\pi$
$68$	0.603635	−	0.293321i	0.0732015	−	0.0355704i
$69$	2.00000	+	7.46071i	0.240772	+	0.898164i
$70$		0			0
$71$	−10.3774			−1.23157			−0.615786	−	0.787914i	$-0.711161\pi$
$71$	−10.3774			−1.23157			−0.615786	+	0.787914i	$0.711161\pi$
$72$	−7.75846	+	3.43604i	−0.914343	+	0.404941i
$73$	4.69193			0.549148			0.274574	−	0.961566i	$-0.411463\pi$
$73$	4.69193			0.549148			0.274574	+	0.961566i	$0.411463\pi$
$74$	−2.39755	+	3.83064i	−0.278709	+	0.445303i
$75$	−3.44966	−	12.8685i	−0.398332	−	1.48592i
$76$	3.32702	−	1.61668i	0.381635	−	0.185446i
$77$		0			0
$78$	7.83630	+	2.40109i	0.887286	+	0.271870i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	−11.2037	−	8.80614i	−1.25261	−	0.984557i
$81$	4.49646	−	7.79627i	0.499606	−	0.866253i
$82$	−1.74823	−	1.09419i	−0.193059	−	0.120833i
$83$	−6.89932			−0.757299			−0.378649	−	0.925540i	$-0.623611\pi$
$83$	−6.89932			−0.757299			−0.378649	+	0.925540i	$0.623611\pi$
$84$		0			0
$85$	−1.19547			−0.129667
$86$	8.98655	+	5.62456i	0.969045	+	0.606511i
$87$	−9.90050	+	2.65404i	−1.06144	+	0.284543i
$88$	0.943698	+	0.101279i	0.100599	+	0.0107964i
$89$		−	3.87289i		−	0.410525i	−0.978707	−	0.205263i	$-0.934195\pi$
$89$		−	3.87289i		−	0.410525i	0.978707	−	0.205263i	$-0.0658048\pi$
$90$	15.1052	+	0.535101i	1.59223	+	0.0564046i
$91$		0			0
$92$	−3.89814	−	8.02210i	−0.406409	−	0.836362i
$93$	8.69193	−	2.33005i	0.901311	−	0.241615i
$94$	6.69193	−	10.6919i	0.690220	−	1.10279i
$95$	−6.58900			−0.676018
$96$	8.04586	−	5.59143i	0.821178	−	0.570673i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−0.871706	+	0.503544i	−0.0876097	+	0.0506081i
$100$	6.72362	+	13.8368i	0.672362	+	1.38368i
$101$			13.1528i			1.30875i	0.756171	+	0.654374i	$0.227068\pi$
$101$			13.1528i			1.30875i	−0.756171	+	0.654374i	$0.772932\pi$
$102$	0.240803	−	0.785896i	0.0238430	−	0.0778153i
$103$			7.88740i			0.777168i	0.921413	+	0.388584i	$0.127036\pi$
$103$			7.88740i			0.777168i	−0.921413	+	0.388584i	$0.872964\pi$
$104$	−9.40978	−	1.00987i	−0.922705	−	0.0990259i
$105$		0			0
$106$	−5.74823	−	3.59774i	−0.558317	−	0.349443i
$107$	−8.13184			−0.786134			−0.393067	−	0.919510i	$-0.628586\pi$
$107$	−8.13184			−0.786134			−0.393067	+	0.919510i	$0.628586\pi$
$108$	−3.39441	+	9.82232i	−0.326628	+	0.945153i
$109$	19.0829			1.82781			0.913904	−	0.405931i	$-0.133053\pi$
$109$	19.0829			1.82781			0.913904	+	0.405931i	$0.133053\pi$
$110$	−1.43310	−	0.896956i	−0.136641	−	0.0855214i
$111$	1.43310	+	5.34596i	0.136024	+	0.507416i
$112$		0			0
$113$			12.5914i			1.18450i	0.805756	+	0.592248i	$0.201759\pi$
$113$			12.5914i			1.18450i	−0.805756	+	0.592248i	$0.798241\pi$
$114$	1.32722	−	4.33158i	0.124305	−	0.405689i
$115$			15.8874i			1.48151i
$116$	10.6455	−	5.17290i	0.988408	−	0.480292i
$117$	8.69193	−	5.02092i	0.803569	−	0.464184i
$118$	−10.5225	+	16.8122i	−0.968674	+	1.54768i
$119$		0			0
$120$	−17.2437	+	2.69441i	−1.57413	+	0.245965i
$121$	−10.8874			−0.989763
$122$	−0.264892	+	0.423228i	−0.0239822	+	0.0383173i
$123$	−2.43979	+	0.654037i	−0.219988	+	0.0589725i
$124$	−9.34596	+	4.54143i	−0.839292	+	0.407833i
$125$		−	9.59019i		−	0.857772i
$126$		0			0
$127$			10.1884i			0.904073i	0.891999	+	0.452036i	$0.149302\pi$
$127$			10.1884i			0.904073i	−0.891999	+	0.452036i	$0.850698\pi$
$128$	−7.90069	+	8.09809i	−0.698329	+	0.715777i
$129$	12.5414	−	3.36199i	1.10421	−	0.296007i
$130$	14.2897	+	8.94370i	1.25329	+	0.784414i
$131$	10.4871			0.916266			0.458133	−	0.888884i	$-0.348518\pi$
$131$	10.4871			0.916266			0.458133	+	0.888884i	$0.348518\pi$
$132$	0.878322	−	0.761437i	0.0764481	−	0.0662746i
$133$		0			0
$134$	−3.83064	−	2.39755i	−0.330917	−	0.207116i
$135$	13.0853	−	13.0942i	1.12620	−	1.12697i
$136$	−0.101279	+	0.943698i	−0.00868460	+	0.0809215i
$137$			8.91906i			0.762007i	0.924574	+	0.381003i	$0.124421\pi$
$137$			8.91906i			0.762007i	−0.924574	+	0.381003i	$0.875579\pi$
$138$	−10.4443	−	3.20019i	−0.889077	−	0.272418i
$139$		−	2.03789i		−	0.172852i	−0.996258	−	0.0864258i	$-0.972455\pi$
$139$		−	2.03789i		−	0.172852i	0.996258	−	0.0864258i	$-0.0275445\pi$
$140$		0			0
$141$	−4.00000	−	14.9214i	−0.336861	−	1.25661i
$142$	7.78612	−	12.4402i	0.653397	−	1.04395i
$143$	−1.12278			−0.0938919
$144$	1.70211	−	11.8787i	0.141842	−	0.989889i
$145$	−21.0829			−1.75084
$146$	−3.52033	+	5.62456i	−0.291345	+	0.465492i
$147$		0			0
$148$	−2.79321	−	5.74823i	−0.229600	−	0.472501i
$149$			15.4576i			1.26633i	0.774016	+	0.633166i	$0.218245\pi$
$149$			15.4576i			1.26633i	−0.774016	+	0.633166i	$0.781755\pi$
$150$	18.0146	+	5.51978i	1.47089	+	0.450688i
$151$			15.1955i			1.23659i	0.785946	+	0.618295i	$0.212176\pi$
$151$			15.1955i			1.23659i	−0.785946	+	0.618295i	$0.787824\pi$
$152$	−0.558213	+	5.20133i	−0.0452771	+	0.421883i
$153$	−0.503544	−	0.871706i	−0.0407091	−	0.0704732i
$154$		0			0
$155$	18.5092			1.48670
$156$	−8.75790	+	7.59242i	−0.701193	+	0.607880i
$157$	0.955023			0.0762191			0.0381095	−	0.999274i	$-0.487866\pi$
$157$	0.955023			0.0762191			0.0381095	+	0.999274i	$0.487866\pi$
$158$	−4.79509	−	3.00118i	−0.381477	−	0.238761i
$159$	−8.02210	+	2.15049i	−0.636194	+	0.170545i
$160$	18.9626	−	6.82347i	1.49913	−	0.539443i
$161$		0			0
$162$	5.97229	+	11.2397i	0.469228	+	0.883077i
$163$			9.88740i			0.774441i	0.921987	+	0.387220i	$0.126565\pi$
$163$			9.88740i			0.774441i	−0.921987	+	0.387220i	$0.873435\pi$
$164$	2.62337	−	1.27476i	0.204851	−	0.0995422i
$165$	−2.00000	+	0.536142i	−0.155700	+	0.0417386i
$166$	5.17653	−	8.27072i	0.401776	−	0.641932i
$167$	−1.12278			−0.0868836			−0.0434418	−	0.999056i	$-0.513832\pi$
$167$	−1.12278			−0.0868836			−0.0434418	+	0.999056i	$0.513832\pi$
$168$		0			0
$169$	−1.80453			−0.138810
$170$	0.896956	−	1.43310i	0.0687934	−	0.109914i
$171$	−2.77535	−	4.80453i	−0.212237	−	0.367412i
$172$	−13.4851	+	6.55276i	−1.02823	+	0.499643i
$173$			15.5673i			1.18356i	0.806100	+	0.591780i	$0.201575\pi$
$173$			15.5673i			1.18356i	−0.806100	+	0.591780i	$0.798425\pi$
$174$	4.24671	−	13.8598i	0.321942	−	1.05071i
$175$		0			0
$176$	−0.829463	+	1.05529i	−0.0625231	+	0.0795456i
$177$	6.28966	+	23.4627i	0.472760	+	1.76356i
$178$	4.64271	+	2.90581i	0.347986	+	0.217800i
$179$	21.7110			1.62276			0.811378	−	0.584521i	$-0.198718\pi$
$179$	21.7110			1.62276			0.811378	+	0.584521i	$0.198718\pi$
$180$	−11.9749	+	17.7063i	−0.892553	+	1.31975i
$181$	16.4288			1.22115			0.610573	−	0.791960i	$-0.290939\pi$
$181$	16.4288			1.22115			0.610573	+	0.791960i	$0.290939\pi$
$182$		0			0
$183$	0.158336	+	0.590648i	0.0117045	+	0.0436619i
$184$	12.5414	+	1.34596i	0.924567	+	0.0992257i
$185$			11.3841i			0.836975i
$186$	−3.72831	+	12.1679i	−0.273373	+	0.892192i
$187$			0.112603i			0.00823435i
$188$	7.79627	+	16.0442i	0.568602	+	1.17014i
$189$		0			0
$190$	4.94370	−	7.89872i	0.358654	−	0.573033i
$191$	−12.1208			−0.877032			−0.438516	−	0.898723i	$-0.644496\pi$
$191$	−12.1208			−0.877032			−0.438516	+	0.898723i	$0.644496\pi$
$192$	0.666081	+	13.8404i	0.0480703	+	0.998844i
$193$	−7.69901			−0.554187			−0.277094	−	0.960843i	$-0.589371\pi$
$193$	−7.69901			−0.554187			−0.277094	+	0.960843i	$0.589371\pi$
$194$	−1.50059	+	2.39755i	−0.107736	+	0.172134i
$195$	19.9423	−	5.34596i	1.42810	−	0.382832i
$196$		0			0
$197$		−	7.04066i		−	0.501626i	−0.968036	−	0.250813i	$-0.919302\pi$
$197$		−	7.04066i		−	0.501626i	0.968036	−	0.250813i	$-0.0806980\pi$
$198$	0.0504019	−	1.42278i	0.00358191	−	0.101113i
$199$		−	21.3839i		−	1.51586i	−0.652335	−	0.757931i	$-0.726211\pi$
$199$		−	21.3839i		−	1.51586i	0.652335	−	0.757931i	$-0.273789\pi$
$200$	−21.6318	−	2.32156i	−1.52960	−	0.164159i
$201$	−5.34596	+	1.43310i	−0.377075	+	0.101083i
$202$	−15.7672	−	9.86845i	−1.10937	−	0.694342i
$203$		0			0
$204$	0.761437	+	0.878322i	0.0533113	+	0.0614948i
$205$	−5.19547			−0.362867
$206$	−9.45520	−	5.91788i	−0.658775	−	0.412318i
$207$	−11.5847	+	6.69193i	−0.805191	+	0.465121i
$208$	8.27072	−	10.5225i	0.573471	−	0.729603i
$209$			0.620628i			0.0429297i
$210$		0			0
$211$		−	22.9703i		−	1.58134i	−0.612244	−	0.790669i	$-0.709733\pi$
$211$		−	22.9703i		−	1.58134i	0.612244	−	0.790669i	$-0.290267\pi$
$212$	8.62574	−	4.19146i	0.592418	−	0.287871i
$213$	−4.65404	−	17.3612i	−0.318889	−	1.18957i
$214$	6.10128	−	9.74823i	0.417075	−	0.666375i
$215$	26.7067			1.82138
$216$	−9.22792	−	11.4388i	−0.627881	−	0.778310i
$217$		0			0
$218$	−14.3178	+	22.8760i	−0.969723	+	1.54936i
$219$	2.10423	+	7.84951i	0.142190	+	0.530421i
$220$	2.15049	−	1.04498i	0.144986	−	0.0704524i
$221$		−	1.12278i		−	0.0755266i
$222$	−7.48384	−	2.29309i	−0.502283	−	0.153902i
$223$			9.68484i			0.648545i	0.945964	+	0.324272i	$0.105119\pi$
$223$			9.68484i			0.648545i	−0.945964	+	0.324272i	$0.894881\pi$
$224$		0			0
$225$	19.9816	−	11.5424i	1.33211	−	0.769495i
$226$	−15.0942	−	9.44724i	−1.00405	−	0.628421i
$227$	−13.4038			−0.889644			−0.444822	−	0.895619i	$-0.646733\pi$
$227$	−13.4038			−0.889644			−0.444822	+	0.895619i	$0.646733\pi$
$228$	4.19677	+	4.84100i	0.277938	+	0.320603i
$229$	16.7298			1.10554			0.552769	−	0.833335i	$-0.313571\pi$
$229$	16.7298			1.10554			0.552769	+	0.833335i	$0.313571\pi$
$230$	−19.0454	−	11.9202i	−1.25582	−	0.785997i
$231$		0			0
$232$	−1.78612	+	16.6427i	−0.117264	+	1.09265i
$233$		−	20.9238i		−	1.37076i	−0.728184	−	0.685381i	$-0.759636\pi$
$233$		−	20.9238i		−	1.37076i	0.728184	−	0.685381i	$-0.240364\pi$
$234$	−0.502566	+	14.1868i	−0.0328538	+	0.927422i
$235$		−	31.7748i		−	2.07276i
$236$	−12.2590	−	25.2282i	−0.797992	−	1.64221i
$237$	−6.69193	+	1.79391i	−0.434687	+	0.116527i
$238$		0			0
$239$	21.1244			1.36642			0.683211	−	0.730221i	$-0.260583\pi$
$239$	21.1244			1.36642			0.683211	+	0.730221i	$0.260583\pi$
$240$	9.70791	−	22.6929i	0.626643	−	1.46482i
$241$	−26.3768			−1.69908			−0.849538	−	0.527527i	$-0.823119\pi$
$241$	−26.3768			−1.69908			−0.849538	+	0.527527i	$0.823119\pi$
$242$	8.16876	−	13.0515i	0.525108	−	0.838983i
$243$	15.0596	+	4.02603i	0.966073	+	0.258270i
$244$	−0.308607	−	0.635092i	−0.0197565	−	0.0406576i
$245$		0			0
$246$	1.04652	−	3.41547i	0.0667237	−	0.217763i
$247$		−	6.18838i		−	0.393757i
$248$	1.56808	−	14.6111i	0.0995734	−	0.927806i
$249$	−3.09419	−	11.5424i	−0.196086	−	0.731472i
$250$	11.4965	+	7.19547i	0.727100	+	0.455082i
$251$	5.60756			0.353946			0.176973	−	0.984216i	$-0.443369\pi$
$251$	5.60756			0.353946			0.176973	+	0.984216i	$0.443369\pi$
$252$		0			0
$253$	1.49646			0.0940814
$254$	−12.2136	−	7.64430i	−0.766347	−	0.479646i
$255$	−0.536142	−	2.00000i	−0.0335745	−	0.125245i
$256$	−3.77992	−	15.5471i	−0.236245	−	0.971693i
$257$		−	18.1737i		−	1.13364i	−0.823841	−	0.566821i	$-0.808173\pi$
$257$		−	18.1737i		−	1.13364i	0.823841	−	0.566821i	$-0.191827\pi$
$258$	−5.37951	+	17.5568i	−0.334914	+	1.09304i
$259$		0			0
$260$	−21.4429	+	10.4196i	−1.32983	+	0.646199i
$261$	−8.88031	−	15.3731i	−0.549677	−	0.951570i
$262$	−7.86845	+	12.5717i	−0.486115	+	0.776682i
$263$	17.7220			1.09279			0.546393	−	0.837529i	$-0.316000\pi$
$263$	17.7220			1.09279			0.546393	+	0.837529i	$0.316000\pi$
$264$	0.253790	+	1.62421i	0.0156197	+	0.0999633i
$265$	−17.0829			−1.04939
$266$		0			0
$267$	6.47927	−	1.73690i	0.396525	−	0.106297i
$268$	5.74823	−	2.79321i	0.351129	−	0.170622i
$269$			12.4816i			0.761018i	0.924777	+	0.380509i	$0.124251\pi$
$269$			12.4816i			0.761018i	−0.924777	+	0.380509i	$0.875749\pi$
$270$	5.87915	+	25.5108i	0.357794	+	1.55254i
$271$			1.79744i			0.109187i	0.998509	+	0.0545934i	$0.0173863\pi$
$271$			1.79744i			0.109187i	−0.998509	+	0.0545934i	$0.982614\pi$
$272$	−1.05529	−	0.829463i	−0.0639864	−	0.0502936i
$273$		0			0
$274$	−10.6919	−	6.69193i	−0.645923	−	0.404274i
$275$	−2.58113			−0.155648
$276$	11.6726	−	10.1192i	0.702608	−	0.609107i
$277$	−23.2713			−1.39823			−0.699117	−	0.715007i	$-0.746423\pi$
$277$	−23.2713			−1.39823			−0.699117	+	0.715007i	$0.746423\pi$
$278$	2.44297	+	1.52902i	0.146519	+	0.0917045i
$279$	7.79627	+	13.4965i	0.466751	+	0.808012i
$280$		0			0
$281$		−	23.1693i		−	1.38217i	−0.722775	−	0.691084i	$-0.757134\pi$
$281$		−	23.1693i		−	1.38217i	0.722775	−	0.691084i	$-0.242866\pi$
$282$	20.8886	+	6.40038i	1.24390	+	0.381137i
$283$		−	1.84951i		−	0.109942i	−0.998488	−	0.0549709i	$-0.982493\pi$
$283$		−	1.84951i		−	0.109942i	0.998488	−	0.0549709i	$-0.0175066\pi$
$284$	9.07104	+	18.6676i	0.538267	+	1.10772i
$285$	−2.95502	−	11.0233i	−0.175040	−	0.652963i
$286$	0.842420	−	1.34596i	0.0498133	−	0.0795885i
$287$		0			0
$288$	12.9627	+	10.9530i	0.763837	+	0.645409i
$289$	16.8874			0.993376
$290$	15.8184	−	25.2736i	0.928887	−	1.48412i
$291$	0.896956	+	3.34596i	0.0525805	+	0.196144i
$292$	−4.10128	−	8.44015i	−0.240009	−	0.493923i
$293$		−	1.54919i		−	0.0905047i	−0.998976	−	0.0452523i	$-0.985591\pi$
$293$		−	1.54919i		−	0.0905047i	0.998976	−	0.0452523i	$-0.0144092\pi$
$294$		0			0
$295$			49.9632i			2.90897i
$296$	8.98655	+	0.964448i	0.522333	+	0.0560574i
$297$	−1.23336	−	1.23252i	−0.0715668	−	0.0715180i
$298$	−18.5301	−	11.5977i	−1.07342	−	0.671839i
$299$	−14.9214			−0.862928
$300$	−20.1332	+	17.4540i	−1.16239	+	1.00771i
$301$		0			0
$302$	−18.2159	−	11.4011i	−1.04821	−	0.656059i
$303$	−22.0043	+	5.89872i	−1.26412	+	0.338873i
$304$	−5.81639	−	4.57170i	−0.333593	−	0.262205i
$305$			1.25777i			0.0720197i
$306$	1.42278	+	0.0504019i	0.0813351	+	0.00288129i
$307$		−	12.5414i		−	0.715777i	−0.933764	−	0.357889i	$-0.883497\pi$
$307$		−	12.5414i		−	0.715777i	0.933764	−	0.357889i	$-0.116503\pi$
$308$		0			0
$309$	−13.1955	+	3.53732i	−0.750664	+	0.201231i
$310$	−13.8874	+	22.1884i	−0.788751	+	1.26022i
$311$	12.0552			0.683589			0.341795	−	0.939775i	$-0.388965\pi$
$311$	12.0552			0.683589			0.341795	+	0.939775i	$0.388965\pi$
$312$	−2.53058	−	16.1953i	−0.143266	−	0.916878i
$313$	22.0758			1.24780			0.623898	−	0.781505i	$-0.285548\pi$
$313$	22.0758			1.24780			0.623898	+	0.781505i	$0.285548\pi$
$314$	−0.716549	+	1.14486i	−0.0404372	+	0.0646079i
$315$		0			0
$316$	7.19547	−	3.49646i	0.404777	−	0.196691i
$317$			3.45284i			0.193931i	0.995288	+	0.0969653i	$0.0309136\pi$
$317$			3.45284i			0.193931i	−0.995288	+	0.0969653i	$0.969086\pi$
$318$	3.44099	−	11.2302i	0.192961	−	0.629757i
$319$			1.98582i			0.111185i
$320$	−6.04778	+	27.8515i	−0.338081	+	1.55695i
$321$	−3.64695	−	13.6044i	−0.203553	−	0.759324i
$322$		0			0
$323$	−0.620628			−0.0345326
$324$	−17.9549	−	1.27370i	−0.997493	−	0.0707609i
$325$	25.7369			1.42763
$326$	−11.8527	−	7.41847i	−0.656463	−	0.410871i
$327$	8.55824	+	31.9253i	0.473272	+	1.76547i
$328$	−0.440155	+	4.10128i	−0.0243035	+	0.226455i
$329$		0			0
$330$	0.857878	−	2.79981i	0.0472246	−	0.154125i
$331$		−	26.8945i		−	1.47825i	−0.673566	−	0.739127i	$-0.735238\pi$
$331$		−	26.8945i		−	1.47825i	0.673566	−	0.739127i	$-0.264762\pi$
$332$	6.03079	+	12.4110i	0.330983	+	0.681140i
$333$	−8.30099	+	4.79509i	−0.454891	+	0.262769i
$334$	0.842420	−	1.34596i	0.0460951	−	0.0736478i
$335$	−11.3841			−0.621980
$336$		0			0
$337$	10.5793			0.576292			0.288146	−	0.957586i	$-0.406961\pi$
$337$	10.5793			0.576292			0.288146	+	0.957586i	$0.406961\pi$
$338$	1.35393	−	2.16322i	0.0736441	−	0.117664i
$339$	−21.0651	+	5.64695i	−1.14410	+	0.306700i
$340$	1.04498	+	2.15049i	0.0566719	+	0.116627i
$341$		−	1.74341i		−	0.0944110i
$342$	7.84188	+	0.277797i	0.424040	+	0.0150216i
$343$		0			0
$344$	2.26256	−	21.0821i	0.121989	−	1.13667i
$345$	−26.5793	+	7.12515i	−1.43098	+	0.383605i
$346$	−18.6617	−	11.6801i	−1.00326	−	0.627924i
$347$	−25.2483			−1.35540			−0.677701	−	0.735338i	$-0.737023\pi$
$347$	−25.2483			−1.35540			−0.677701	+	0.735338i	$0.737023\pi$
$348$	13.4284	+	15.4898i	0.719839	+	0.830338i
$349$	−21.4359			−1.14744			−0.573719	−	0.819052i	$-0.694500\pi$
$349$	−21.4359			−1.14744			−0.573719	+	0.819052i	$0.694500\pi$
$350$		0			0
$351$	12.2980	+	12.2897i	0.656421	+	0.655974i
$352$	−0.642713	−	1.78612i	−0.0342567	−	0.0952004i
$353$		−	8.58349i		−	0.456853i	−0.973561	−	0.228427i	$-0.926642\pi$
$353$		−	8.58349i		−	0.456853i	0.973561	−	0.228427i	$-0.0733581\pi$
$354$	−32.8455	−	10.0641i	−1.74572	−	0.534898i
$355$		−	36.9703i		−	1.96218i
$356$	−6.96681	+	3.38534i	−0.369240	+	0.179423i
$357$		0			0
$358$	−16.2897	+	26.0266i	−0.860935	+	1.37555i
$359$	6.70510			0.353881			0.176941	−	0.984222i	$-0.443380\pi$
$359$	6.70510			0.353881			0.176941	+	0.984222i	$0.443380\pi$
$360$	−12.2411	−	27.6401i	−0.645164	−	1.45676i
$361$	15.5793			0.819964
$362$	−12.3265	+	19.6944i	−0.647865	+	1.03512i
$363$	−4.88276	−	18.2144i	−0.256278	−	0.956009i
$364$		0			0
$365$			16.7153i			0.874920i
$366$	−0.826851	−	0.253352i	−0.0432202	−	0.0132429i
$367$			24.4809i			1.27789i	0.769251	+	0.638946i	$0.220629\pi$
$367$			24.4809i			1.27789i	−0.769251	+	0.638946i	$0.779371\pi$
$368$	−11.0233	+	14.0245i	−0.574628	+	0.731076i
$369$	−2.18838	−	3.78840i	−0.113923	−	0.197216i
$370$	−13.6469	−	8.54143i	−0.709471	−	0.444048i
$371$		0			0
$372$	−11.7892	−	13.5989i	−0.611241	−	0.705070i
$373$	4.39094			0.227354			0.113677	−	0.993518i	$-0.463737\pi$
$373$	4.39094			0.227354			0.113677	+	0.993518i	$0.463737\pi$
$374$	−0.134985	−	0.0844855i	−0.00697993	−	0.00436864i
$375$	16.0442	−	4.30099i	0.828519	−	0.222102i
$376$	−25.0829	−	2.69193i	−1.29355	−	0.138826i
$377$		−	19.8010i		−	1.01980i
$378$		0			0
$379$		−	16.8803i		−	0.867083i	−0.901134	−	0.433542i	$-0.857264\pi$
$379$		−	16.8803i		−	0.867083i	0.901134	−	0.433542i	$-0.142736\pi$
$380$	5.75954	+	11.8527i	0.295458	+	0.608033i
$381$	−17.0450	+	4.56926i	−0.873241	+	0.234091i
$382$	9.09419	−	14.5301i	0.465299	−	0.743425i
$383$	−23.8405			−1.21819			−0.609096	−	0.793097i	$-0.708467\pi$
$383$	−23.8405			−1.21819			−0.609096	+	0.793097i	$0.708467\pi$
$384$	−17.0912	−	9.58590i	−0.872184	−	0.489178i
$385$		0			0
$386$	5.77653	−	9.22937i	0.294018	−	0.469763i
$387$	11.2491	+	19.4738i	0.571824	+	0.989909i
$388$	−1.74823	−	3.59774i	−0.0887528	−	0.182647i
$389$		−	20.1682i		−	1.02257i	−0.859412	−	0.511283i	$-0.829170\pi$
$389$		−	20.1682i		−	1.02257i	0.859412	−	0.511283i	$-0.170830\pi$
$390$	−8.55405	+	27.9174i	−0.433151	+	1.41365i
$391$			1.49646i			0.0756790i
$392$		0			0
$393$	4.70325	+	17.5448i	0.237248	+	0.885018i
$394$	8.44015	+	5.28257i	0.425209	+	0.266132i
$395$	−14.2503			−0.717010
$396$	1.66778	+	1.12793i	0.0838090	+	0.0566805i
$397$	18.3389			0.920402			0.460201	−	0.887815i	$-0.347777\pi$
$397$	18.3389			0.920402			0.460201	+	0.887815i	$0.347777\pi$
$398$	25.6344	+	16.0442i	1.28494	+	0.804223i
$399$		0			0
$400$	19.0133	−	24.1898i	0.950664	−	1.20949i
$401$			8.60239i			0.429583i	0.976660	+	0.214791i	$0.0689071\pi$
$401$			8.60239i			0.429583i	−0.976660	+	0.214791i	$0.931093\pi$
$402$	2.29309	−	7.48384i	0.114369	−	0.373260i
$403$			17.3839i			0.865951i
$404$	23.6601	−	11.4970i	1.17713	−	0.571998i
$405$	27.7748	+	16.0190i	1.38014	+	0.795988i
$406$		0			0
$407$	1.07228			0.0531511
$408$	−1.62421	+	0.253790i	−0.0804105	+	0.0125645i
$409$	−4.31516			−0.213371			−0.106685	−	0.994293i	$-0.534024\pi$
$409$	−4.31516			−0.213371			−0.106685	+	0.994293i	$0.534024\pi$
$410$	3.89814	−	6.22819i	0.192515	−	0.307588i
$411$	−14.9214	+	4.00000i	−0.736019	+	0.197305i
$412$	14.1884	−	6.89448i	0.699011	−	0.339667i
$413$		0			0
$414$	0.669825	−	18.9083i	0.0329201	−	0.929293i
$415$		−	24.5793i		−	1.20655i
$416$	6.40860	+	17.8097i	0.314207	+	0.873192i
$417$	3.40935	−	0.913949i	0.166957	−	0.0447563i
$418$	−0.743992	−	0.465654i	−0.0363898	−	0.0227759i
$419$	37.4133			1.82776			0.913879	−	0.405986i	$-0.133072\pi$
$419$	37.4133			1.82776			0.913879	+	0.405986i	$0.133072\pi$
$420$		0			0
$421$	11.9016			0.580047			0.290024	−	0.957020i	$-0.406337\pi$
$421$	11.9016			0.580047			0.290024	+	0.957020i	$0.406337\pi$
$422$	27.5361	+	17.2345i	1.34044	+	0.838961i
$423$	23.1693	−	13.3839i	1.12653	−	0.650745i
$424$	−1.44724	+	13.4851i	−0.0702843	+	0.654896i
$425$		−	2.58113i		−	0.125203i
$426$	24.3041	+	7.44690i	1.17754	+	0.360803i
$427$		0			0
$428$	7.10815	+	14.6281i	0.343586	+	0.707076i
$429$	−0.503544	−	1.87840i	−0.0243113	−	0.0906899i
$430$	−20.0379	+	32.0152i	−0.966313	+	1.54391i
$431$	−3.38724			−0.163158			−0.0815789	−	0.996667i	$-0.525996\pi$
$431$	−3.38724			−0.163158			−0.0815789	+	0.996667i	$0.525996\pi$
$432$	20.6362	−	2.47973i	0.992858	−	0.119306i
$433$	26.7819			1.28706			0.643528	−	0.765423i	$-0.277470\pi$
$433$	26.7819			1.28706			0.643528	+	0.765423i	$0.277470\pi$
$434$		0			0
$435$	−9.45520	−	35.2713i	−0.453342	−	1.69113i
$436$	−16.6806	−	34.3276i	−0.798856	−	1.64399i
$437$			8.24793i			0.394552i
$438$	−10.9886	−	3.36696i	−0.525054	−	0.160880i
$439$			3.77479i			0.180161i	0.995934	+	0.0900805i	$0.0287124\pi$
$439$			3.77479i			0.180161i	−0.995934	+	0.0900805i	$0.971288\pi$
$440$	−0.360814	+	3.36199i	−0.0172011	+	0.160277i
$441$		0			0
$442$	1.34596	+	0.842420i	0.0640209	+	0.0400698i
$443$	6.78958			0.322583			0.161291	−	0.986907i	$-0.448434\pi$
$443$	6.78958			0.322583			0.161291	+	0.986907i	$0.448434\pi$
$444$	8.36399	−	7.25093i	0.396937	−	0.344114i
$445$	13.7974			0.654061
$446$	−11.6099	−	7.26649i	−0.549746	−	0.344078i
$447$	−25.8602	+	6.93237i	−1.22315	+	0.327890i
$448$		0			0
$449$			12.9080i			0.609168i	0.952485	+	0.304584i	$0.0985174\pi$
$449$			12.9080i			0.609168i	−0.952485	+	0.304584i	$0.901483\pi$
$450$	−1.15533	+	32.6136i	−0.0544629	+	1.53742i
$451$			0.489369i			0.0230435i
$452$	22.6502	−	11.0063i	1.06538	−	0.517692i
$453$	−25.4217	+	6.81483i	−1.19442	+	0.320189i
$454$	10.0568	−	16.0682i	0.471991	−	0.754116i
$455$		0			0
$456$	−8.95207	+	1.39880i	−0.419219	+	0.0655048i
$457$	27.1813			1.27149			0.635744	−	0.771900i	$-0.280694\pi$
$457$	27.1813			1.27149			0.635744	+	0.771900i	$0.280694\pi$
$458$	−12.5523	+	20.0553i	−0.586531	+	0.937121i
$459$	1.23252	−	1.23336i	0.0575291	−	0.0575683i
$460$	28.5793	−	13.8874i	1.33252	−	0.647503i
$461$		−	7.31937i		−	0.340897i	−0.985367	−	0.170448i	$-0.945478\pi$
$461$		−	7.31937i		−	0.340897i	0.985367	−	0.170448i	$-0.0545216\pi$
$462$		0			0
$463$			3.77479i			0.175430i	0.996146	+	0.0877148i	$0.0279564\pi$
$463$			3.77479i			0.175430i	−0.996146	+	0.0877148i	$0.972044\pi$
$464$	−18.6107	−	14.6281i	−0.863981	−	0.679092i
$465$	8.30099	+	30.9656i	0.384949	+	1.43600i
$466$	25.0829	+	15.6990i	1.16194	+	0.727243i
$467$	29.4480			1.36269			0.681346	−	0.731961i	$-0.261395\pi$
$467$	29.4480			1.36269			0.681346	+	0.731961i	$0.261395\pi$
$468$	−16.6297	−	11.2468i	−0.768708	−	0.519882i
$469$		0			0
$470$	38.0908	+	23.8405i	1.75700	+	1.09968i
$471$	0.428306	+	1.59774i	0.0197353	+	0.0736198i
$472$	39.4407	+	4.23283i	1.81540	+	0.194832i
$473$		−	2.51554i		−	0.115665i
$474$	2.87043	−	9.36807i	0.131843	−	0.430289i
$475$		−	14.2263i		−	0.652746i
$476$		0			0
$477$	−7.19547	−	12.4564i	−0.329458	−	0.570338i
$478$	−15.8495	+	25.3233i	−0.724940	+	1.15826i
$479$	33.6628			1.53809			0.769047	−	0.639192i	$-0.220731\pi$
$479$	33.6628			1.53809			0.769047	+	0.639192i	$0.220731\pi$
$480$	19.9199	+	28.6640i	0.909214	+	1.30833i
$481$	−10.6919			−0.487510
$482$	19.7904	−	31.6198i	0.901426	−	1.44024i
$483$		0			0
$484$	9.51683	+	19.5850i	0.432583	+	0.890227i
$485$			7.12515i			0.323536i
$486$	−16.1254	+	15.0323i	−0.731465	+	0.681879i
$487$		−	21.1813i		−	0.959816i	−0.877319	−	0.479908i	$-0.840670\pi$
$487$		−	21.1813i		−	0.959816i	0.877319	−	0.479908i	$-0.159330\pi$
$488$	0.992877	+	0.106557i	0.0449454	+	0.00482360i
$489$	−16.5414	+	4.43428i	−0.748029	+	0.200525i
$490$		0			0
$491$	−12.1208			−0.547005			−0.273502	−	0.961871i	$-0.588182\pi$
$491$	−12.1208			−0.547005			−0.273502	+	0.961871i	$0.588182\pi$
$492$	3.30918	+	3.81715i	0.149189	+	0.172091i
$493$	−1.98582			−0.0894371
$494$	7.41847	+	4.64311i	0.333773	+	0.208904i
$495$	−1.79391	−	3.10552i	−0.0806303	−	0.139583i
$496$	16.3389	+	12.8424i	0.733637	+	0.576642i
$497$		0			0
$498$	16.1583	+	4.95100i	0.724071	+	0.221860i
$499$			36.5793i			1.63752i	0.574139	+	0.818758i	$0.305337\pi$
$499$			36.5793i			1.63752i	−0.574139	+	0.818758i	$0.694663\pi$
$500$	−17.2515	+	8.38292i	−0.771509	+	0.374895i
$501$	−0.503544	−	1.87840i	−0.0224967	−	0.0839206i
$502$	−4.20733	+	6.72220i	−0.187782	+	0.300026i
$503$	−0.890599			−0.0397098			−0.0198549	−	0.999803i	$-0.506320\pi$
$503$	−0.890599			−0.0397098			−0.0198549	+	0.999803i	$0.506320\pi$
$504$		0			0
$505$	−46.8577			−2.08514
$506$	−1.12278	+	1.79391i	−0.0499138	+	0.0797491i
$507$	−0.809292	−	3.01894i	−0.0359419	−	0.134076i
$508$	18.3276	−	8.90581i	0.813154	−	0.395131i
$509$			1.54919i			0.0686667i	0.999410	+	0.0343333i	$0.0109308\pi$
$509$			1.54919i			0.0686667i	−0.999410	+	0.0343333i	$0.989069\pi$
$510$	2.79981	+	0.857878i	0.123978	+	0.0379875i
$511$		0			0
$512$	21.4735	+	7.13364i	0.949004	+	0.315265i
$513$	6.79321	−	6.79784i	0.299927	−	0.300132i
$514$	21.7861	+	13.6356i	0.960944	+	0.601442i
$515$	−28.0994			−1.23821
$516$	−17.0104	−	19.6216i	−0.748842	−	0.863793i
$517$	−2.99291			−0.131628
$518$		0			0
$519$	−26.0438	+	6.98159i	−1.14320	+	0.306458i
$520$	3.59774	−	33.5230i	0.157771	−	1.47008i
$521$		−	35.5601i		−	1.55792i	−0.627075	−	0.778959i	$-0.715748\pi$
$521$		−	35.5601i		−	1.55792i	0.627075	−	0.778959i	$-0.284252\pi$
$522$	25.0917	+	0.888870i	1.09823	+	0.0389048i
$523$		−	14.0379i		−	0.613834i	−0.951736	−	0.306917i	$-0.900703\pi$
$523$		−	14.0379i		−	0.613834i	0.951736	−	0.306917i	$-0.0992974\pi$
$524$	−9.16696	−	18.8650i	−0.400460	−	0.824120i
$525$		0			0
$526$	−13.2967	+	21.2447i	−0.579766	+	0.926312i
$527$	1.74341			0.0759442
$528$	−2.13748	−	0.914402i	−0.0930218	−	0.0397942i
$529$	−3.11260			−0.135331
$530$	12.8172	−	20.4785i	0.556743	−	0.889528i
$531$	−36.4318	+	21.0450i	−1.58101	+	0.913274i
$532$		0			0
$533$		−	4.87958i		−	0.211358i
$534$	−2.77921	+	9.07036i	−0.120268	+	0.392513i
$535$		−	28.9703i		−	1.25249i
$536$	−0.964448	+	8.98655i	−0.0416578	+	0.388160i
$537$	9.73690	+	36.3221i	0.420178	+	1.56741i
$538$	−14.9626	−	9.36491i	−0.645085	−	0.403750i
$539$		0			0
$540$	−34.9927	−	12.0928i	−1.50585	−	0.520393i
$541$	−32.2783			−1.38775			−0.693877	−	0.720093i	$-0.744099\pi$
$541$	−32.2783			−1.38775			−0.693877	+	0.720093i	$0.744099\pi$
$542$	−2.15473	−	1.34861i	−0.0925534	−	0.0579279i
$543$	7.36797	+	27.4851i	0.316190	+	1.17950i
$544$	1.78612	−	0.642713i	0.0765792	−	0.0275561i
$545$			67.9841i			2.91212i
$546$		0			0
$547$		−	19.8732i		−	0.849718i	−0.905260	−	0.424859i	$-0.860324\pi$
$547$		−	19.8732i		−	0.849718i	0.905260	−	0.424859i	$-0.139676\pi$
$548$	16.0442	−	7.79627i	0.685374	−	0.333040i
$549$	−0.917133	+	0.529785i	−0.0391423	+	0.0226107i
$550$	1.93661	−	3.09419i	0.0825774	−	0.131937i
$551$	−10.9452			−0.466279
$552$	3.37278	+	21.5852i	0.143555	+	0.918728i
$553$		0			0
$554$	17.4603	−	27.8969i	0.741817	−	1.18523i
$555$	−19.0454	+	5.10552i	−0.808432	+	0.216717i
$556$	−3.66589	+	1.78135i	−0.155469	+	0.0755460i
$557$			29.5389i			1.25160i	0.779983	+	0.625801i	$0.215228\pi$
$557$			29.5389i			1.25160i	−0.779983	+	0.625801i	$0.784772\pi$
$558$	−22.0287	−	0.780364i	−0.932549	−	0.0330354i
$559$			25.0829i			1.06089i
$560$		0			0
$561$	−0.188383	+	0.0505000i	−0.00795353	+	0.00213211i
$562$	27.7748	+	17.3839i	1.17161	+	0.733294i
$563$	−20.7485			−0.874443			−0.437222	−	0.899354i	$-0.644037\pi$
$563$	−20.7485			−0.874443			−0.437222	+	0.899354i	$0.644037\pi$
$564$	−23.3452	+	20.2385i	−0.983010	+	0.852194i
$565$	−44.8577			−1.88718
$566$	2.21714	+	1.38768i	0.0931933	+	0.0583284i
$567$		0			0
$568$	−29.1841	−	3.13208i	−1.22454	−	0.131419i
$569$			4.74459i			0.198904i	0.995042	+	0.0994518i	$0.0317089\pi$
$569$			4.74459i			0.198904i	−0.995042	+	0.0994518i	$0.968291\pi$
$570$	15.4316	+	4.72832i	0.646357	+	0.198047i
$571$		−	18.2642i		−	0.764331i	−0.924094	−	0.382166i	$-0.875178\pi$
$571$		−	18.2642i		−	0.764331i	0.924094	−	0.382166i	$-0.124822\pi$
$572$	0.981441	+	2.01974i	0.0410361	+	0.0844496i
$573$	−5.43592	−	20.2779i	−0.227089	−	0.847122i
$574$		0			0
$575$	−34.3024			−1.43051
$576$	−22.8560	+	7.32145i	−0.952333	+	0.305060i
$577$	6.37677			0.265468			0.132734	−	0.991152i	$-0.457624\pi$
$577$	6.37677			0.265468			0.132734	+	0.991152i	$0.457624\pi$
$578$	−12.6705	+	20.2442i	−0.527025	+	0.842046i
$579$	−3.45284	−	12.8803i	−0.143495	−	0.535287i
$580$	18.4288	+	37.9253i	0.765216	+	1.57476i
$581$		0			0
$582$	−4.68403	−	1.43521i	−0.194159	−	0.0594915i
$583$			1.60906i			0.0666404i
$584$	13.1950	+	1.41610i	0.546013	+	0.0585988i
$585$	17.8874	+	30.9656i	0.739553	+	1.28027i
$586$	1.85713	+	1.16235i	0.0767172	+	0.0480162i
$587$	−16.8907			−0.697152			−0.348576	−	0.937280i	$-0.613335\pi$
$587$	−16.8907			−0.697152			−0.348576	+	0.937280i	$0.613335\pi$
$588$		0			0
$589$	9.60906			0.395934
$590$	−59.8945	−	37.4871i	−2.46582	−	1.54332i
$591$	11.7789	−	3.15758i	0.484519	−	0.129886i
$592$	−7.89872	+	10.0492i	−0.324635	+	0.413020i
$593$			40.6719i			1.67019i	0.550102	+	0.835097i	$0.314589\pi$
$593$			40.6719i			1.67019i	−0.550102	+	0.835097i	$0.685411\pi$
$594$	2.40290	−	0.553766i	0.0985920	−	0.0227213i
$595$		0			0
$596$	27.8061	−	13.5117i	1.13898	−	0.553460i
$597$	35.7748	−	9.59019i	1.46416	−	0.392500i
$598$	11.1955	−	17.8874i	0.457817	−	0.731470i
$599$	7.29174			0.297932			0.148966	−	0.988842i	$-0.452405\pi$
$599$	7.29174			0.297932			0.148966	+	0.988842i	$0.452405\pi$
$600$	−5.81748	−	37.2308i	−0.237497	−	1.51994i
$601$	30.6778			1.25137			0.625686	−	0.780075i	$-0.284819\pi$
$601$	30.6778			1.25137			0.625686	+	0.780075i	$0.284819\pi$
$602$		0			0
$603$	−4.79509	−	8.30099i	−0.195271	−	0.338042i
$604$	27.3346	−	13.2826i	1.11223	−	0.540460i
$605$		−	38.7871i		−	1.57692i
$606$	9.43851	−	30.8040i	0.383413	−	1.25133i
$607$			13.3081i			0.540158i	0.962838	+	0.270079i	$0.0870498\pi$
$607$			13.3081i			0.540158i	−0.962838	+	0.270079i	$0.912950\pi$
$608$	9.84444	−	3.54240i	0.399245	−	0.143663i
$609$		0			0
$610$	−1.50778	−	0.943698i	−0.0610482	−	0.0382092i
$611$	29.8428			1.20731
$612$	−1.12793	+	1.66778i	−0.0455938	+	0.0674160i
$613$	19.6848			0.795063			0.397532	−	0.917588i	$-0.369867\pi$
$613$	19.6848			0.795063			0.397532	+	0.917588i	$0.369867\pi$
$614$	15.0343	+	9.40978i	0.606736	+	0.379748i
$615$	−2.33005	−	8.69193i	−0.0939568	−	0.350492i
$616$		0			0
$617$		−	10.7470i		−	0.432656i	−0.976321	−	0.216328i	$-0.930592\pi$
$617$		−	10.7470i		−	0.432656i	0.976321	−	0.216328i	$-0.0694081\pi$
$618$	5.66005	−	18.4724i	0.227681	−	0.743069i
$619$			45.7369i			1.83832i	0.393883	+	0.919161i	$0.371132\pi$
$619$			45.7369i			1.83832i	−0.393883	+	0.919161i	$0.628868\pi$
$620$	−16.1792	−	33.2957i	−0.649772	−	1.33719i
$621$	−16.3909	−	16.3798i	−0.657746	−	0.657297i
$622$	−9.04498	+	14.4515i	−0.362671	+	0.579452i
$623$		0			0
$624$	21.3132	+	9.11765i	0.853209	+	0.364998i
$625$	−4.29390			−0.171756
$626$	−16.5634	+	26.4639i	−0.662005	+	1.05771i
$627$	−1.03830	+	0.278338i	−0.0414656	+	0.0111157i
$628$	−0.834799	−	1.71796i	−0.0333121	−	0.0685540i
$629$			1.07228i			0.0427548i
$630$		0			0
$631$		−	2.61615i		−	0.104147i	−0.998643	−	0.0520736i	$-0.983417\pi$
$631$		−	2.61615i		−	0.104147i	0.998643	−	0.0520736i	$-0.0165830\pi$
$632$	−1.20727	+	11.2491i	−0.0480226	+	0.447466i
$633$	38.4288	−	10.3017i	1.52741	−	0.409454i
$634$	−4.13917	−	2.59065i	−0.164387	−	0.102888i
$635$	−36.2969			−1.44040
$636$	10.8807	+	12.5509i	0.431447	+	0.497676i
$637$		0			0
$638$	−2.38055	−	1.48995i	−0.0942470	−	0.0589879i
$639$	26.9578	−	15.5722i	1.06643	−	0.616028i
$640$	−28.8500	−	28.1468i	−1.14040	−	1.11260i
$641$			22.5827i			0.891963i	0.895042	+	0.445982i	$0.147145\pi$
$641$			22.5827i			0.891963i	−0.895042	+	0.445982i	$0.852855\pi$
$642$	19.0449	+	5.83546i	0.751642	+	0.230307i
$643$			9.32332i			0.367676i	0.982957	+	0.183838i	$0.0588521\pi$
$643$			9.32332i			0.367676i	−0.982957	+	0.183838i	$0.941148\pi$
$644$		0			0
$645$	11.9774	+	44.6798i	0.471608	+	1.75926i
$646$	0.465654	−	0.743992i	0.0183209	−	0.0292720i
$647$	−15.5420			−0.611021			−0.305510	−	0.952189i	$-0.598827\pi$
$647$	−15.5420			−0.611021			−0.305510	+	0.952189i	$0.598827\pi$
$648$	14.9983	−	20.5682i	0.589190	−	0.807994i
$649$	4.70610			0.184731
$650$	−19.3103	+	30.8527i	−0.757411	+	1.21014i
$651$		0			0
$652$	17.7861	−	8.64271i	0.696558	−	0.338475i
$653$		−	9.40470i		−	0.368034i	−0.982923	−	0.184017i	$-0.941090\pi$
$653$		−	9.40470i		−	0.368034i	0.982923	−	0.184017i	$-0.0589102\pi$
$654$	−44.6924	−	13.6940i	−1.74761	−	0.535478i
$655$			37.3612i			1.45982i
$656$	−4.58626	−	3.60482i	−0.179063	−	0.140744i
$657$	−12.1884	+	7.04066i	−0.475514	+	0.274682i
$658$		0			0
$659$	−31.2507			−1.21735			−0.608677	−	0.793418i	$-0.708299\pi$
$659$	−31.2507			−1.21735			−0.608677	+	0.793418i	$0.708299\pi$
$660$	2.71268	+	3.12909i	0.105591	+	0.121800i
$661$	23.9479			0.931467			0.465733	−	0.884925i	$-0.345791\pi$
$661$	23.9479			0.931467			0.465733	+	0.884925i	$0.345791\pi$
$662$	32.2404	+	20.1788i	1.25306	+	0.784271i
$663$	1.87840	−	0.503544i	0.0729509	−	0.0195560i
$664$	−19.4028	−	2.08233i	−0.752975	−	0.0808102i
$665$		0			0
$666$	0.479962	−	13.5487i	0.0185982	−	0.525003i
$667$			26.3909i			1.02186i
$668$	0.981441	+	2.01974i	0.0379731	+	0.0781461i
$669$	−16.2026	+	4.34344i	−0.626427	+	0.167927i
$670$	8.54143	−	13.6469i	0.329984	−	0.527228i
$671$	0.118471			0.00457353
$672$		0			0
$673$	−23.8732			−0.920245			−0.460123	−	0.887855i	$-0.652195\pi$
$673$	−23.8732			−0.920245			−0.460123	+	0.887855i	$0.652195\pi$
$674$	−7.93762	+	12.6822i	−0.305746	+	0.488500i
$675$	28.2716	+	28.2523i	1.08817	+	1.08743i
$676$	1.57736	+	3.24611i	0.0606679	+	0.124850i
$677$		−	26.9514i		−	1.03583i	−0.855433	−	0.517913i	$-0.826709\pi$
$677$		−	26.9514i		−	1.03583i	0.855433	−	0.517913i	$-0.173291\pi$
$678$	9.03565	−	29.4892i	0.347012	−	1.13253i
$679$		0			0
$680$	−3.36199	−	0.360814i	−0.128927	−	0.0138366i
$681$	−6.01132	−	22.4244i	−0.230354	−	0.859304i
$682$	2.08995	+	1.30807i	0.0800285	+	0.0500887i
$683$	23.5554			0.901323			0.450661	−	0.892695i	$-0.351188\pi$
$683$	23.5554			0.901323			0.450661	+	0.892695i	$0.351188\pi$
$684$	−6.21674	+	9.19220i	−0.237703	+	0.351473i
$685$	−31.7748			−1.21405
$686$		0			0
$687$	7.50295	+	27.9887i	0.286255	+	1.06783i
$688$	23.5751	+	18.5301i	0.898792	+	0.706454i
$689$		−	16.0442i		−	0.611235i
$690$	11.4009	−	37.2085i	0.434025	−	1.41650i
$691$		−	4.24892i		−	0.161637i	−0.996729	−	0.0808183i	$-0.974247\pi$
$691$		−	4.24892i		−	0.161637i	0.996729	−	0.0808183i	$-0.0257533\pi$
$692$	28.0035	−	13.6076i	1.06453	−	0.517283i
$693$		0			0
$694$	18.9437	−	30.2670i	0.719093	−	1.14892i
$695$	7.26013			0.275392
$696$	−28.6440	+	4.47575i	−1.08575	+	0.169653i
$697$	−0.489369			−0.0185362
$698$	16.0833	−	25.6968i	0.608761	−	0.972638i
$699$	35.0051	−	9.38385i	1.32401	−	0.354930i
$700$		0			0
$701$		−	8.60239i		−	0.324908i	−0.986716	−	0.162454i	$-0.948059\pi$
$701$		−	8.60239i		−	0.324908i	0.986716	−	0.162454i	$-0.0519409\pi$
$702$	−23.9597	+	5.52169i	−0.904300	+	0.208403i
$703$			5.91005i			0.222902i
$704$	2.62337	+	0.569649i	0.0988721	+	0.0214695i
$705$	53.1586	−	14.2503i	2.00207	−	0.536697i
$706$	10.2897	+	6.44015i	0.387257	+	0.242378i
$707$		0			0
$708$	36.7084	−	31.8233i	1.37958	−	1.19599i
$709$	−14.7061			−0.552299			−0.276150	−	0.961115i	$-0.589059\pi$
$709$	−14.7061			−0.552299			−0.276150	+	0.961115i	$0.589059\pi$
$710$	44.3190	+	27.7386i	1.66326	+	1.04101i
$711$	−6.00236	−	10.3909i	−0.225106	−	0.389691i
$712$	1.16890	−	10.8916i	0.0438066	−	0.408181i
$713$		−	23.1693i		−	0.867699i
$714$		0			0
$715$		−	4.00000i		−	0.149592i
$716$	−18.9779	−	39.0552i	−0.709237	−	1.45956i
$717$	9.47381	+	35.3407i	0.353806	+	1.31982i
$718$	−5.03080	+	8.03789i	−0.187748	+	0.299971i
$719$	−10.9324			−0.407711			−0.203856	−	0.979001i	$-0.565347\pi$
$719$	−10.9324			−0.407711			−0.203856	+	0.979001i	$0.565347\pi$
$720$	42.3186	+	6.06388i	1.57712	+	0.225987i
$721$		0			0
$722$	−11.6891	+	18.6761i	−0.435023	+	0.695052i
$723$	−11.8294	−	44.1278i	−0.439940	−	1.64113i
$724$	−14.3607	−	29.5533i	−0.533710	−	1.09834i
$725$		−	45.5199i		−	1.69057i
$726$	25.4985	+	7.81287i	0.946337	+	0.289963i
$727$		−	38.8803i		−	1.44199i	−0.692940	−	0.720995i	$-0.743685\pi$
$727$		−	38.8803i		−	1.44199i	0.692940	−	0.720995i	$-0.256315\pi$
$728$		0			0
$729$	0.0184116	+	27.0000i	0.000681912	+	1.00000i
$730$	−20.0379	−	12.5414i	−0.741636	−	0.464179i
$731$	2.51554			0.0930406
$732$	0.924094	−	0.801118i	0.0341555	−	0.0296102i
$733$	−11.1208			−0.410755			−0.205377	−	0.978683i	$-0.565842\pi$
$733$	−11.1208			−0.410755			−0.205377	+	0.978683i	$0.565842\pi$
$734$	−29.3470	−	18.3679i	−1.08322	−	0.677972i
$735$		0			0
$736$	−8.54143	−	23.7369i	−0.314841	−	0.874954i
$737$			1.07228i			0.0394981i
$738$	6.18337	+	0.219045i	0.227613	+	0.00806316i
$739$			31.8732i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$739$			31.8732i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$740$	20.4785	−	9.95100i	0.752804	−	0.365806i
$741$	10.3531	−	2.77535i	0.380329	−	0.101955i
$742$		0			0
$743$	−24.5432			−0.900403			−0.450202	−	0.892927i	$-0.648648\pi$
$743$	−24.5432			−0.900403			−0.450202	+	0.892927i	$0.648648\pi$
$744$	25.1474	−	3.92938i	0.921947	−	0.144058i
$745$	−55.0687			−2.01756
$746$	−3.29450	+	5.26374i	−0.120620	+	0.192719i
$747$	17.9226	−	10.3531i	0.655754	−	0.378798i
$748$	0.202558	−	0.0984279i	0.00740625	−	0.00359888i
$749$		0			0
$750$	−6.88198	+	22.4604i	−0.251295	+	0.820137i
$751$		−	0.427764i		−	0.0156093i	−0.999970	−	0.00780467i	$-0.997516\pi$
$751$		−	0.427764i		−	0.0156093i	0.999970	−	0.00780467i	$-0.00248433\pi$
$752$	22.0466	−	28.0489i	0.803956	−	1.02284i
$753$	2.51487	+	9.38135i	0.0916469	+	0.341875i
$754$	23.7369	+	14.8566i	0.864447	+	0.541045i
$755$	−54.1350			−1.97017
$756$		0			0
$757$	51.4596			1.87033			0.935166	−	0.354210i	$-0.115250\pi$
$757$	51.4596			1.87033			0.935166	+	0.354210i	$0.115250\pi$
$758$	20.2357	+	12.6652i	0.734992	+	0.460021i
$759$	0.671128	+	2.50354i	0.0243604	+	0.0908729i
$760$	−18.5301	−	1.98868i	−0.672158	−	0.0721369i
$761$		−	9.03515i		−	0.327524i	−0.986500	−	0.163762i	$-0.947637\pi$
$761$		−	9.03515i		−	0.327524i	0.986500	−	0.163762i	$-0.0523629\pi$
$762$	7.31125	−	23.8614i	0.264859	−	0.864406i
$763$		0			0
$764$	10.5950	+	21.8037i	0.383313	+	0.788832i
$765$	3.10552	−	1.79391i	0.112280	−	0.0648590i
$766$	17.8874	−	28.5793i	0.646298	−	1.03261i
$767$	−46.9253			−1.69438
$768$	24.3148	−	13.2963i	0.877385	−	0.479788i
$769$	21.1728			0.763511			0.381756	−	0.924263i	$-0.375320\pi$
$769$	21.1728			0.763511			0.381756	+	0.924263i	$0.375320\pi$
$770$		0			0
$771$	30.4042	−	8.15049i	1.09498	−	0.293533i
$772$	6.72982	+	13.8495i	0.242211	+	0.498455i
$773$		−	4.11523i		−	0.148015i	−0.997258	−	0.0740073i	$-0.976421\pi$
$773$		−	4.11523i		−	0.148015i	0.997258	−	0.0740073i	$-0.0235788\pi$
$774$	−31.7848	−	1.12597i	−1.14248	−	0.0404723i
$775$			39.9632i			1.43552i
$776$	5.62456	+	0.603635i	0.201910	+	0.0216692i
$777$		0			0
$778$	24.1771	+	15.1321i	0.866790	+	0.542511i
$779$	−2.69722			−0.0966381
$780$	−27.0486	−	31.2006i	−0.968494	−	1.11716i
$781$	−3.48228			−0.124606
$782$	−1.79391	−	1.12278i	−0.0641501	−	0.0401507i
$783$	21.7363	−	21.7511i	0.776790	−	0.777320i
$784$		0			0
$785$			3.40234i			0.121435i
$786$	−24.5611	−	7.52565i	−0.876064	−	0.268431i
$787$		−	29.9621i		−	1.06803i	−0.845474	−	0.534017i	$-0.820682\pi$
$787$		−	29.9621i		−	1.06803i	0.845474	−	0.534017i	$-0.179318\pi$
$788$	−12.6652	+	6.15434i	−0.451180	+	0.219239i
$789$	7.94793	+	29.6486i	0.282954	+	1.05552i
$790$	10.6919	−	17.0829i	0.380402	−	0.607781i
$791$		0			0
$792$	−2.60346	+	1.15301i	−0.0925098	+	0.0409704i
$793$	−1.18130			−0.0419490
$794$	−13.7596	+	21.9842i	−0.488309	+	0.780188i
$795$	−7.66129	−	28.5793i	−0.271718	−	1.01360i
$796$	−38.4667	+	18.6919i	−1.36342	+	0.662518i
$797$			49.0485i			1.73739i	0.495351	+	0.868693i	$0.335039\pi$
$797$			49.0485i			1.73739i	−0.495351	+	0.868693i	$0.664961\pi$
$798$		0			0
$799$		−	2.99291i		−	0.105882i
$800$	14.7325	+	40.9421i	0.520873	+	1.44752i
$801$	5.81162	+	10.0607i	0.205343	+	0.355479i
$802$	−10.3123	−	6.45433i	−0.364140	−	0.227910i
$803$	1.57444			0.0555608
$804$	7.25093	+	8.36399i	0.255721	+	0.294975i
$805$		0			0
$806$	−20.8393	−	13.0430i	−0.734033	−	0.459421i
$807$	−20.8815	+	5.59774i	−0.735065	+	0.197050i
$808$	−3.96973	+	36.9892i	−0.139655	+	1.30128i
$809$		−	52.6577i		−	1.85135i	−0.378323	−	0.925674i	$-0.623499\pi$
$809$		−	52.6577i		−	1.85135i	0.378323	−	0.925674i	$-0.376501\pi$
$810$	−40.0424	+	21.2767i	−1.40695	+	0.747588i
$811$		−	37.5117i		−	1.31721i	−0.752487	−	0.658607i	$-0.771146\pi$
$811$		−	37.5117i		−	1.31721i	0.752487	−	0.658607i	$-0.228854\pi$
$812$		0			0
$813$	−3.00709	+	0.806113i	−0.105463	+	0.0282716i
$814$	−0.804530	+	1.28543i	−0.0281987	+	0.0450541i
$815$	−35.2246			−1.23386
$816$	0.914402	−	2.13748i	0.0320105	−	0.0748267i
$817$	13.8647			0.485066
$818$	3.23764	−	5.17290i	0.113202	−	0.180866i
$819$		0			0
$820$	4.54143	+	9.34596i	0.158594	+	0.326375i
$821$		−	2.11058i		−	0.0736598i	−0.999322	−	0.0368299i	$-0.988274\pi$
$821$		−	2.11058i		−	0.0736598i	0.999322	−	0.0368299i	$-0.0117260\pi$
$822$	6.40038	−	20.8886i	0.223239	−	0.728573i
$823$		−	52.5567i		−	1.83201i	−0.401166	−	0.916005i	$-0.631395\pi$
$823$		−	52.5567i		−	1.83201i	0.401166	−	0.916005i	$-0.368605\pi$
$824$	−2.38055	+	22.1816i	−0.0829305	+	0.772731i
$825$	−1.15758	−	4.31819i	−0.0403018	−	0.150340i
$826$		0			0
$827$	10.3774			0.360858			0.180429	−	0.983588i	$-0.442251\pi$
$827$	10.3774			0.360858			0.180429	+	0.983588i	$0.442251\pi$
$828$	22.1642	+	14.9898i	0.770260	+	0.520931i
$829$	−1.43592			−0.0498715			−0.0249358	−	0.999689i	$-0.507938\pi$
$829$	−1.43592			−0.0498715			−0.0249358	+	0.999689i	$0.507938\pi$
$830$	29.4650	+	18.4417i	1.02275	+	0.640122i
$831$	−10.4366	−	38.9324i	−0.362043	−	1.35055i
$832$	−26.1581	−	5.68007i	−0.906869	−	0.196921i
$833$		0			0
$834$	−1.46240	+	4.77277i	−0.0506389	+	0.165268i
$835$		−	4.00000i		−	0.138426i
$836$	1.11643	−	0.542499i	0.0386124	−	0.0187627i
$837$	−19.0829	+	19.0959i	−0.659600	+	0.660050i
$838$	−28.0710	+	44.8500i	−0.969697	+	1.54932i
$839$	1.39275			0.0480832			0.0240416	−	0.999711i	$-0.492347\pi$
$839$	1.39275			0.0480832			0.0240416	+	0.999711i	$0.492347\pi$
$840$		0			0
$841$	−6.02126			−0.207630
$842$	−8.92969	+	14.2673i	−0.307738	+	0.491683i
$843$	38.7619	−	10.3909i	1.33503	−	0.357883i
$844$	−41.3205	+	20.0786i	−1.42231	+	0.691135i
$845$		−	6.42877i		−	0.221156i
$846$	−1.33965	+	37.8166i	−0.0460581	+	1.30016i
$847$		0			0
$848$	−15.0798	−	11.8527i	−0.517841	−	0.407025i
$849$	3.09419	−	0.829463i	0.106192	−	0.0284671i
$850$	3.09419	+	1.93661i	0.106130	+	0.0664252i
$851$	14.2503			0.488494
$852$	−27.1624	+	23.5477i	−0.930567	+	0.806730i
$853$	−18.6399			−0.638217			−0.319108	−	0.947718i	$-0.603383\pi$
$853$	−18.6399			−0.638217			−0.319108	+	0.947718i	$0.603383\pi$
$854$		0			0
$855$	17.1165	−	9.88740i	0.585372	−	0.338142i
$856$	−22.8690	−	2.45433i	−0.781646	−	0.0838873i
$857$			30.8622i			1.05423i	0.849793	+	0.527117i	$0.176727\pi$
$857$			30.8622i			1.05423i	−0.849793	+	0.527117i	$0.823273\pi$
$858$	2.62958	+	0.805718i	0.0897723	+	0.0275067i
$859$			17.9253i			0.611603i	0.952095	+	0.305801i	$0.0989244\pi$
$859$			17.9253i			0.611603i	−0.952095	+	0.305801i	$0.901076\pi$
$860$	−23.3447	−	48.0418i	−0.796047	−	1.63821i
$861$		0			0
$862$	2.54143	−	4.06054i	0.0865616	−	0.138302i
$863$	5.04617			0.171774			0.0858868	−	0.996305i	$-0.472628\pi$
$863$	5.04617			0.171774			0.0858868	+	0.996305i	$0.472628\pi$
$864$	−12.5106	+	26.5986i	−0.425619	+	0.904903i
$865$	−55.4596			−1.88568
$866$	−20.0943	+	32.1054i	−0.682833	+	1.09099i
$867$	7.57362	+	28.2523i	0.257214	+	0.959499i
$868$		0			0
$869$			1.34226i			0.0455329i
$870$	49.3764	+	15.1292i	1.67402	+	0.512928i
$871$		−	10.6919i		−	0.362282i
$872$	53.6663	+	5.75954i	1.81737	+	0.195043i
$873$	−5.19547	+	3.00118i	−0.175840	+	0.101575i
$874$	−9.88740	−	6.18838i	−0.334446	−	0.209325i
$875$		0			0
$876$	12.2809	−	10.6466i	0.414933	−	0.359715i
$877$	−0.691927			−0.0233647			−0.0116824	−	0.999932i	$-0.503719\pi$
$877$	−0.691927			−0.0233647			−0.0116824	+	0.999932i	$0.503719\pi$
$878$	−4.52512	−	2.83221i	−0.152715	−	0.0955825i
$879$	2.59177	−	0.694778i	0.0874181	−	0.0234343i
$880$	−3.75955	−	2.95502i	−0.126734	−	0.0996138i
$881$		−	38.2574i		−	1.28892i	−0.764637	−	0.644462i	$-0.777082\pi$
$881$		−	38.2574i		−	1.28892i	0.764637	−	0.644462i	$-0.222918\pi$
$882$		0			0
$883$			3.42068i			0.115115i	0.998342	+	0.0575575i	$0.0183312\pi$
$883$			3.42068i			0.115115i	−0.998342	+	0.0575575i	$0.981669\pi$
$884$	−2.01974	+	0.981441i	−0.0679312	+	0.0330094i
$885$	−83.5875	+	22.4074i	−2.80976	+	0.753216i
$886$	−5.09419	+	8.13917i	−0.171143	+	0.273441i
$887$	−17.1543			−0.575984			−0.287992	−	0.957633i	$-0.592988\pi$
$887$	−17.1543			−0.575984			−0.287992	+	0.957633i	$0.592988\pi$
$888$	2.41676	+	15.4669i	0.0811013	+	0.519034i
$889$		0			0
$890$	−10.3522	+	16.5400i	−0.347005	+	0.554422i
$891$	1.50885	−	2.61615i	0.0505483	−	0.0876442i
$892$	17.4217	−	8.46565i	0.583323	−	0.283451i
$893$		−	16.4959i		−	0.552013i
$894$	11.0925	−	36.2019i	0.370987	−	1.21077i
$895$			77.3470i			2.58543i
$896$		0			0
$897$	−6.69193	−	24.9633i	−0.223437	−	0.833499i
$898$	−15.4738	−	9.68484i	−0.516368	−	0.323187i
$899$	30.7462			1.02544
$900$	−38.2295	−	25.8548i	−1.27432	−	0.861828i
$901$	−1.60906			−0.0536055
$902$	−0.586642	−	0.367171i	−0.0195330	−	0.0122255i
$903$		0			0
$904$	−3.80029	+	35.4104i	−0.126396	+	1.17773i
$905$			58.5289i			1.94557i
$906$	10.9044	−	35.5880i	0.362274	−	1.18233i
$907$		−	30.7904i		−	1.02238i	−0.859469	−	0.511188i	$-0.829205\pi$
$907$		−	30.7904i		−	1.02238i	0.859469	−	0.511188i	$-0.170795\pi$
$908$	11.7165	+	24.1117i	0.388825	+	0.800176i
$909$	−19.7369	−	34.1674i	−0.654632	−	1.13326i
$910$		0			0
$911$	−14.8898			−0.493321			−0.246661	−	0.969102i	$-0.579333\pi$
$911$	−14.8898			−0.493321			−0.246661	+	0.969102i	$0.579333\pi$
$912$	5.03985	−	11.7810i	0.166886	−	0.390108i
$913$	−2.31516			−0.0766206
$914$	−20.3940	+	32.5842i	−0.674573	+	1.07779i
$915$	−2.10423	+	0.564082i	−0.0695635	+	0.0186480i
$916$	−14.6238	−	30.0947i	−0.483183	−	0.994358i
$917$		0			0
$918$	0.553766	+	2.40290i	0.0182770	+	0.0793074i
$919$		−	2.99291i		−	0.0987271i	−0.998781	−	0.0493635i	$-0.984281\pi$
$919$		−	2.99291i		−	0.0987271i	0.998781	−	0.0493635i	$-0.0157193\pi$
$920$	−4.79509	+	44.6798i	−0.158090	+	1.47305i
$921$	20.9816	−	5.62456i	0.691367	−	0.185335i
$922$	8.77426	+	5.49169i	0.288965	+	0.180859i
$923$	34.7224			1.14290
$924$		0			0
$925$	−24.5793			−0.808163
$926$	−4.52512	−	2.83221i	−0.148705	−	0.0930722i
$927$	−11.8358	−	20.4894i	−0.388737	−	0.672959i
$928$	31.4993	−	11.3346i	1.03402	−	0.372078i
$929$			11.5002i			0.377309i	0.982044	+	0.188654i	$0.0604126\pi$
$929$			11.5002i			0.377309i	−0.982044	+	0.188654i	$0.939587\pi$
$930$	−43.3489	−	13.2824i	−1.42147	−	0.435546i
$931$		0			0
$932$	−37.6391	+	18.2898i	−1.23291	+	0.599101i
$933$	5.40650	+	20.1682i	0.177001	+	0.660276i
$934$	−22.0947	+	35.3015i	−0.722961	+	1.15510i
$935$	−0.401157			−0.0131192
$936$	25.9595	−	11.4968i	0.848513	−	0.375786i
$937$	−49.6254			−1.62119			−0.810595	−	0.585607i	$-0.800856\pi$
$937$	−49.6254			−1.62119			−0.810595	+	0.585607i	$0.800856\pi$
$938$		0			0
$939$	9.90050	+	36.9324i	0.323091	+	1.20524i
$940$	−57.1586	+	27.7748i	−1.86431	+	0.905914i
$941$		−	33.1859i		−	1.08183i	−0.841077	−	0.540915i	$-0.818078\pi$
$941$		−	33.1859i		−	1.08183i	0.841077	−	0.540915i	$-0.181922\pi$
$942$	−2.23668	−	0.685331i	−0.0728749	−	0.0223293i
$943$			6.50354i			0.211785i
$944$	−34.6664	+	44.1046i	−1.12829	+	1.43548i
$945$		0			0
$946$	3.01556	+	1.88740i	0.0980443	+	0.0613646i
$947$	−50.0299			−1.62575			−0.812877	−	0.582436i	$-0.802100\pi$
$947$	−50.0299			−1.62575			−0.812877	+	0.582436i	$0.802100\pi$
$948$	9.07652	+	10.4698i	0.294792	+	0.340044i
$949$	−15.6990			−0.509612
$950$	17.0541	+	10.6739i	0.553307	+	0.346307i
$951$	−5.77653	+	1.54852i	−0.187317	+	0.0502142i
$952$		0			0
$953$		−	45.2664i		−	1.46632i	−0.680055	−	0.733162i	$-0.738044\pi$
$953$		−	45.2664i		−	1.46632i	0.680055	−	0.733162i	$-0.261956\pi$
$954$	20.3311	+	0.720227i	0.658244	+	0.0233182i
$955$		−	43.1813i		−	1.39731i
$956$	−18.4651	−	37.9999i	−0.597204	−	1.22901i
$957$	−3.32225	+	0.890599i	−0.107393	+	0.0287890i
$958$	−25.2571	+	40.3541i	−0.816019	+	1.30378i
$959$		0			0
$960$	−49.3074	+	2.37296i	−1.59139	+	0.0765871i
$961$	4.00709			0.129261
$962$	8.02210	−	12.8172i	0.258643	−	0.413243i
$963$	21.1244	−	12.2026i	0.680723	−	0.393222i
$964$	23.0563	+	47.4483i	0.742593	+	1.52821i
$965$		−	27.4283i		−	0.882948i
$966$		0			0
$967$		−	3.60059i		−	0.115787i	−0.998323	−	0.0578935i	$-0.981562\pi$
$967$		−	3.60059i		−	0.115787i	0.998323	−	0.0578935i	$-0.0184384\pi$
$968$	−30.6184	−	3.28601i	−0.984112	−	0.105616i
$969$	−0.278338	−	1.03830i	−0.00894150	−	0.0333550i
$970$	−8.54143	−	5.34596i	−0.274249	−	0.171649i
$971$	32.7027			1.04948			0.524739	−	0.851263i	$-0.324163\pi$
$971$	32.7027			1.04948			0.524739	+	0.851263i	$0.324163\pi$
$972$	−5.92149	−	30.6094i	−0.189932	−	0.981797i
$973$		0			0
$974$	25.3916	+	15.8922i	0.813598	+	0.509220i
$975$	11.5424	+	43.0574i	0.369654	+	1.37894i
$976$	−0.872689	+	1.11029i	−0.0279341	+	0.0355394i
$977$		−	17.6059i		−	0.563264i	−0.959523	−	0.281632i	$-0.909124\pi$
$977$		−	17.6059i		−	0.563264i	0.959523	−	0.281632i	$-0.0908757\pi$
$978$	7.09526	−	23.1564i	0.226882	−	0.740461i
$979$		−	1.29960i		−	0.0415354i
$980$		0			0
$981$	−49.5722	+	28.6356i	−1.58272	+	0.914263i
$982$	9.09419	−	14.5301i	0.290207	−	0.463674i
$983$	−45.6171			−1.45496			−0.727479	−	0.686130i	$-0.759308\pi$
$983$	−45.6171			−1.45496			−0.727479	+	0.686130i	$0.759308\pi$
$984$	−7.05876	+	1.10296i	−0.225025	+	0.0351611i
$985$	25.0829			0.799207
$986$	1.48995	−	2.38055i	0.0474498	−	0.0758123i
$987$		0			0
$988$	−11.1321	+	5.40935i	−0.354159	+	0.172094i
$989$		−	33.4307i		−	1.06303i
$990$	5.06877	+	0.179561i	0.161096	+	0.00570681i
$991$			49.5354i			1.57354i	0.617244	+	0.786772i	$0.288249\pi$
$991$			49.5354i			1.57354i	−0.617244	+	0.786772i	$0.711751\pi$
$992$	−27.6541	+	9.95100i	−0.878019	+	0.315945i
$993$	44.9940	−	12.0616i	1.42784	−	0.382763i
$994$		0			0
$995$	76.1815			2.41512
$996$	−18.0586	+	15.6554i	−0.572210	+	0.496062i
$997$	55.5259			1.75852			0.879261	−	0.476340i	$-0.158037\pi$
$997$	55.5259			1.75852			0.879261	+	0.476340i	$0.158037\pi$
$998$	−43.8503	−	27.4453i	−1.38806	−	0.868766i
$999$	−11.7449	−	11.7369i	−0.371593	−	0.371339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.c.491.4		12
3.2	odd	2	inner	588.2.e.c.491.9		12
4.3	odd	2	inner	588.2.e.c.491.10		12
7.2	even	3		588.2.n.g.263.12		24
7.3	odd	6		588.2.n.f.275.5		24
7.4	even	3		588.2.n.g.275.5		24
7.5	odd	6		588.2.n.f.263.12		24
7.6	odd	2		84.2.e.a.71.4	yes	12
12.11	even	2	inner	588.2.e.c.491.3		12
21.2	odd	6		588.2.n.g.263.1		24
21.5	even	6		588.2.n.f.263.1		24
21.11	odd	6		588.2.n.g.275.8		24
21.17	even	6		588.2.n.f.275.8		24
21.20	even	2		84.2.e.a.71.9	yes	12
28.3	even	6		588.2.n.f.275.1		24
28.11	odd	6		588.2.n.g.275.1		24
28.19	even	6		588.2.n.f.263.8		24
28.23	odd	6		588.2.n.g.263.8		24
28.27	even	2		84.2.e.a.71.10	yes	12
56.13	odd	2		1344.2.h.h.575.8		12
56.27	even	2		1344.2.h.h.575.5		12
84.11	even	6		588.2.n.g.275.12		24
84.23	even	6		588.2.n.g.263.5		24
84.47	odd	6		588.2.n.f.263.5		24
84.59	odd	6		588.2.n.f.275.12		24
84.83	odd	2		84.2.e.a.71.3	✓	12
168.83	odd	2		1344.2.h.h.575.7		12
168.125	even	2		1344.2.h.h.575.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.3	✓	12	84.83	odd	2
84.2.e.a.71.4	yes	12	7.6	odd	2
84.2.e.a.71.9	yes	12	21.20	even	2
84.2.e.a.71.10	yes	12	28.27	even	2
588.2.e.c.491.3		12	12.11	even	2	inner
588.2.e.c.491.4		12	1.1	even	1	trivial
588.2.e.c.491.9		12	3.2	odd	2	inner
588.2.e.c.491.10		12	4.3	odd	2	inner
588.2.n.f.263.1		24	21.5	even	6
588.2.n.f.263.5		24	84.47	odd	6
588.2.n.f.263.8		24	28.19	even	6
588.2.n.f.263.12		24	7.5	odd	6
588.2.n.f.275.1		24	28.3	even	6
588.2.n.f.275.5		24	7.3	odd	6
588.2.n.f.275.8		24	21.17	even	6
588.2.n.f.275.12		24	84.59	odd	6
588.2.n.g.263.1		24	21.2	odd	6
588.2.n.g.263.5		24	84.23	even	6
588.2.n.g.263.8		24	28.23	odd	6
588.2.n.g.263.12		24	7.2	even	3
588.2.n.g.275.1		24	28.11	odd	6
588.2.n.g.275.5		24	7.4	even	3
588.2.n.g.275.8		24	21.11	odd	6
588.2.n.g.275.12		24	84.11	even	6
1344.2.h.h.575.5		12	56.27	even	2
1344.2.h.h.575.6		12	168.125	even	2
1344.2.h.h.575.7		12	168.83	odd	2
1344.2.h.h.575.8		12	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 - 1.79887i) q^{4} +3.56257i q^{5} +(-2.34202 - 0.717607i) q^{6} +(2.81228 + 0.301817i) q^{8} +(-2.59774 + 1.50059i) q^{9} +O(q^{10})\)	\(q+(-0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 - 1.79887i) q^{4} +3.56257i q^{5} +(-2.34202 - 0.717607i) q^{6} +(2.81228 + 0.301817i) q^{8} +(-2.59774 + 1.50059i) q^{9} +(-4.27072 - 2.67298i) q^{10} +0.335564 q^{11} +(2.61745 - 2.26913i) q^{12} -3.34596 q^{13} +(-5.96012 + 1.59774i) q^{15} +(-2.47185 + 3.14483i) q^{16} +0.335564i q^{17} +(0.150201 - 4.23998i) q^{18} +1.84951i q^{19} +(6.40860 - 3.11410i) q^{20} +(-0.251772 + 0.402265i) q^{22} +4.45953 q^{23} +(0.756309 + 4.84025i) q^{24} -7.69193 q^{25} +(2.51046 - 4.01105i) q^{26} +(-3.67549 - 3.67298i) q^{27} +5.91788i q^{29} +(2.55653 - 8.34360i) q^{30} -5.19547i q^{31} +(-1.91532 - 5.32274i) q^{32} +(0.150493 + 0.561392i) q^{33} +(-0.402265 - 0.251772i) q^{34} +(4.97008 + 3.36129i) q^{36} +3.19547 q^{37} +(-2.21714 - 1.38768i) q^{38} +(-1.50059 - 5.59774i) q^{39} +(-1.07525 + 10.0189i) q^{40} +1.45835i q^{41} -7.49646i q^{43} +(-0.293321 - 0.603635i) q^{44} +(-5.34596 - 9.25462i) q^{45} +(-3.34596 + 5.34596i) q^{46} -8.91906 q^{47} +(-6.36981 - 2.72497i) q^{48} +(5.77122 - 9.22087i) q^{50} +(-0.561392 + 0.150493i) q^{51} +(2.92475 + 6.01894i) q^{52} +4.79509i q^{53} +(7.16077 - 1.65025i) q^{54} +1.19547i q^{55} +(-3.09419 + 0.829463i) q^{57} +(-7.09419 - 4.44015i) q^{58} +14.0245 q^{59} +(8.08394 + 9.32486i) q^{60} +0.353051 q^{61} +(6.22819 + 3.89814i) q^{62} +(7.81781 + 1.69759i) q^{64} -11.9202i q^{65} +(-0.785896 - 0.240803i) q^{66} +3.19547i q^{67} +(0.603635 - 0.293321i) q^{68} +(2.00000 + 7.46071i) q^{69} -10.3774 q^{71} +(-7.75846 + 3.43604i) q^{72} +4.69193 q^{73} +(-2.39755 + 3.83064i) q^{74} +(-3.44966 - 12.8685i) q^{75} +(3.32702 - 1.61668i) q^{76} +(7.83630 + 2.40109i) q^{78} +4.00000i q^{79} +(-11.2037 - 8.80614i) q^{80} +(4.49646 - 7.79627i) q^{81} +(-1.74823 - 1.09419i) q^{82} -6.89932 q^{83} -1.19547 q^{85} +(8.98655 + 5.62456i) q^{86} +(-9.90050 + 2.65404i) q^{87} +(0.943698 + 0.101279i) q^{88} -3.87289i q^{89} +(15.1052 + 0.535101i) q^{90} +(-3.89814 - 8.02210i) q^{92} +(8.69193 - 2.33005i) q^{93} +(6.69193 - 10.6919i) q^{94} -6.58900 q^{95} +(8.04586 - 5.59143i) q^{96} +2.00000 q^{97} +(-0.871706 + 0.503544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9	\( 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} - 2 q^{24} - 12 q^{25} + 20 q^{30} + 16 q^{33} - 32 q^{34} - 20 q^{36} - 16 q^{37} - 20 q^{40} - 24 q^{45} - 46 q^{48} + 28 q^{52} - 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} + 16 q^{61} + 20 q^{64} + 12 q^{66} + 24 q^{69} - 32 q^{72} - 24 q^{73} + 60 q^{76} + 20 q^{78} + 28 q^{81} - 8 q^{82} + 40 q^{85} - 56 q^{88} + 80 q^{90} + 24 q^{93} + 34 q^{96} + 24 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 - 2 * q^24 - 12 * q^25 + 20 * q^30 + 16 * q^33 - 32 * q^34 - 20 * q^36 - 16 * q^37 - 20 * q^40 - 24 * q^45 - 46 * q^48 + 28 * q^52 - 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 + 16 * q^61 + 20 * q^64 + 12 * q^66 + 24 * q^69 - 32 * q^72 - 24 * q^73 + 60 * q^76 + 20 * q^78 + 28 * q^81 - 8 * q^82 + 40 * q^85 - 56 * q^88 + 80 * q^90 + 24 * q^93 + 34 * q^96 + 24 * q^97

Introduction

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