LMFDB - Embedded newform 637.2.g.i.263.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.100088711424.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 $ x^8 - 13x^6 + 130x^4 - 507*x^2 + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.2
Root			$-2.49541 - 1.44073i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.i.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15139 + 1.99426i) q^{2} +2.16731 q^{3} +(-1.65139 - 2.86029i) q^{4} +(-1.08365 - 1.87694i) q^{5} +(-2.49541 + 4.32218i) q^{6} +3.00000 q^{8} +1.69722 q^{9} +4.99082 q^{10} +4.90833 q^{11} +(-3.57907 - 6.19912i) q^{12} +(-1.41176 - 3.31767i) q^{13} +(-2.34861 - 4.06792i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(-3.57907 - 6.19912i) q^{17} +(-1.95416 + 3.38471i) q^{18} +2.16731 q^{19} +(-3.57907 + 6.19912i) q^{20} +(-5.65139 + 9.78849i) q^{22} +(0.302776 - 0.524423i) q^{23} +6.50192 q^{24} +(0.151388 - 0.262211i) q^{25} +(8.24179 + 1.00451i) q^{26} -2.82352 q^{27} +(1.15139 + 1.99426i) q^{29} +10.8167 q^{30} +(3.57907 - 6.19912i) q^{31} +(2.65139 + 4.59234i) q^{32} +10.6379 q^{33} +16.4836 q^{34} +(-2.80278 - 4.85455i) q^{36} +(-4.30278 + 7.45263i) q^{37} +(-2.49541 + 4.32218i) q^{38} +(-3.05971 - 7.19041i) q^{39} +(-3.25096 - 5.63083i) q^{40} +(4.99082 + 8.64436i) q^{41} +(6.25694 - 10.8373i) q^{43} +(-8.10555 - 14.0392i) q^{44} +(-1.83920 - 3.18559i) q^{45} +(0.697224 + 1.20763i) q^{46} +(0.755550 + 1.30865i) q^{47} +(-0.328104 + 0.568293i) q^{48} +(0.348612 + 0.603814i) q^{50} +(-7.75694 - 13.4354i) q^{51} +(-7.15813 + 9.51680i) q^{52} +(-1.19722 + 2.07365i) q^{53} +(3.25096 - 5.63083i) q^{54} +(-5.31893 - 9.21265i) q^{55} +4.69722 q^{57} -5.30278 q^{58} +(1.41176 + 2.44524i) q^{59} +(-7.75694 + 13.4354i) q^{60} +4.33462 q^{61} +(8.24179 + 14.2752i) q^{62} -12.8167 q^{64} +(-4.69722 + 6.24500i) q^{65} +(-12.2483 + 21.2147i) q^{66} +1.00000 q^{67} +(-11.8209 + 20.4743i) q^{68} +(0.656208 - 1.13659i) q^{69} +(-2.00000 + 3.46410i) q^{71} +5.09167 q^{72} +(2.16731 - 3.75389i) q^{73} +(-9.90833 - 17.1617i) q^{74} +(0.328104 - 0.568293i) q^{75} +(-3.57907 - 6.19912i) q^{76} +(17.8625 + 2.17708i) q^{78} +(3.30278 + 5.72058i) q^{79} +0.656208 q^{80} -11.2111 q^{81} -22.9855 q^{82} +2.82352 q^{83} +(-7.75694 + 13.4354i) q^{85} +(14.4083 + 24.9560i) q^{86} +(2.49541 + 4.32218i) q^{87} +14.7250 q^{88} +(-3.25096 + 5.63083i) q^{89} +8.47055 q^{90} -2.00000 q^{92} +(7.75694 - 13.4354i) q^{93} -3.47972 q^{94} +(-2.34861 - 4.06792i) q^{95} +(5.74637 + 9.95301i) q^{96} +(6.83003 - 11.8300i) q^{97} +8.33053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9} - 4 q^{11} - 26 q^{15} + 6 q^{16} + 6 q^{18} - 38 q^{22} - 12 q^{23} - 6 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44}+ \cdots - 92 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 28 * q^9 - 4 * q^11 - 26 * q^15 + 6 * q^16 + 6 * q^18 - 38 * q^22 - 12 * q^23 - 6 * q^25 + 2 * q^29 + 14 * q^32 - 8 * q^36 - 20 * q^37 + 26 * q^39 + 14 * q^43 - 36 * q^44 + 20 * q^46 + 10 * q^50 - 26 * q^51 - 24 * q^53 + 52 * q^57 - 28 * q^58 - 26 * q^60 - 16 * q^64 - 52 * q^65 + 8 * q^67 - 16 * q^71 + 84 * q^72 - 36 * q^74 + 78 * q^78 + 12 * q^79 - 32 * q^81 - 26 * q^85 + 72 * q^86 - 12 * q^88 - 16 * q^92 + 26 * q^93 - 26 * q^95 - 92 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.15139	+	1.99426i	−0.814154	+	1.41016i	0.0957796	+	0.995403i	$0.469466\pi$
$2$	−1.15139	+	1.99426i	−0.814154	+	1.41016i	−0.909934	+	0.414754i	$0.863868\pi$
$3$	2.16731			1.25130			0.625648	−	0.780106i	$-0.284835\pi$
$3$	2.16731			1.25130			0.625648	+	0.780106i	$0.284835\pi$
$4$	−1.65139	−	2.86029i	−0.825694	−	1.43014i
$5$	−1.08365	−	1.87694i	−0.484625	−	0.839395i	0.515219	−	0.857058i	$-0.327711\pi$
$5$	−1.08365	−	1.87694i	−0.484625	−	0.839395i	−0.999844	+	0.0176637i	$0.994377\pi$
$6$	−2.49541	+	4.32218i	−1.01875	+	1.76452i
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	1.69722			0.565741
$10$	4.99082			1.57824
$11$	4.90833			1.47992			0.739958	−	0.672653i	$-0.234845\pi$
$11$	4.90833			1.47992			0.739958	+	0.672653i	$0.234845\pi$
$12$	−3.57907	−	6.19912i	−1.03319	−	1.78953i
$13$	−1.41176	−	3.31767i	−0.391551	−	0.920156i
$13$	−1.41176	−	3.31767i	−0.391551	−	0.920156i
$14$		0			0
$15$	−2.34861	−	4.06792i	−0.606409	−	1.05033i
$16$	−0.151388	+	0.262211i	−0.0378470	+	0.0655528i
$17$	−3.57907	−	6.19912i	−0.868051	−	1.50351i	−0.863985	−	0.503517i	$-0.832039\pi$
$17$	−3.57907	−	6.19912i	−0.868051	−	1.50351i	−0.00406561	−	0.999992i	$-0.501294\pi$
$18$	−1.95416	+	3.38471i	−0.460601	+	0.797784i
$19$	2.16731			0.497215			0.248607	−	0.968604i	$-0.420027\pi$
$19$	2.16731			0.497215			0.248607	+	0.968604i	$0.420027\pi$
$20$	−3.57907	+	6.19912i	−0.800304	+	1.38617i
$21$		0			0
$22$	−5.65139	+	9.78849i	−1.20488	+	2.08691i
$23$	0.302776	−	0.524423i	0.0631331	−	0.109350i	−0.832731	−	0.553677i	$-0.813224\pi$
$23$	0.302776	−	0.524423i	0.0631331	−	0.109350i	0.895864	+	0.444328i	$0.146557\pi$
$24$	6.50192			1.32720
$25$	0.151388	−	0.262211i	0.0302776	−	0.0524423i
$26$	8.24179	+	1.00451i	1.61635	+	0.197001i
$27$	−2.82352			−0.543386
$28$		0			0
$29$	1.15139	+	1.99426i	0.213807	+	0.370325i	0.952903	−	0.303275i	$-0.0980802\pi$
$29$	1.15139	+	1.99426i	0.213807	+	0.370325i	−0.739096	+	0.673601i	$0.764747\pi$
$30$	10.8167			1.97484
$31$	3.57907	−	6.19912i	0.642819	−	1.11340i	−0.341981	−	0.939707i	$-0.611098\pi$
$31$	3.57907	−	6.19912i	0.642819	−	1.11340i	0.984801	−	0.173689i	$-0.0555687\pi$
$32$	2.65139	+	4.59234i	0.468704	+	0.811818i
$33$	10.6379			1.85181
$34$	16.4836			2.82691
$35$		0			0
$36$	−2.80278	−	4.85455i	−0.467129	−	0.809092i
$37$	−4.30278	+	7.45263i	−0.707372	+	1.22520i	0.258457	+	0.966023i	$0.416786\pi$
$37$	−4.30278	+	7.45263i	−0.707372	+	1.22520i	−0.965829	+	0.259181i	$0.916547\pi$
$38$	−2.49541	+	4.32218i	−0.404809	+	0.701150i
$39$	−3.05971	−	7.19041i	−0.489946	−	1.15139i
$40$	−3.25096	−	5.63083i	−0.514022	−	0.890313i
$41$	4.99082	+	8.64436i	0.779436	+	1.35002i	0.932267	+	0.361770i	$0.117827\pi$
$41$	4.99082	+	8.64436i	0.779436	+	1.35002i	−0.152832	+	0.988252i	$0.548839\pi$
$42$		0			0
$43$	6.25694	−	10.8373i	0.954174	−	1.65268i	0.217928	−	0.975965i	$-0.430070\pi$
$43$	6.25694	−	10.8373i	0.954174	−	1.65268i	0.736247	−	0.676713i	$-0.236596\pi$
$44$	−8.10555	−	14.0392i	−1.22196	−	2.11649i
$45$	−1.83920	−	3.18559i	−0.274172	−	0.474880i
$46$	0.697224	+	1.20763i	0.102800	+	0.178055i
$47$	0.755550	+	1.30865i	0.110208	+	0.190886i	0.915854	−	0.401511i	$-0.131515\pi$
$47$	0.755550	+	1.30865i	0.110208	+	0.190886i	−0.805646	+	0.592397i	$0.798182\pi$
$48$	−0.328104	+	0.568293i	−0.0473577	+	0.0820260i
$49$		0			0
$50$	0.348612	+	0.603814i	0.0493012	+	0.0853922i
$51$	−7.75694	−	13.4354i	−1.08619	−	1.88133i
$52$	−7.15813	+	9.51680i	−0.992654	+	1.31974i
$53$	−1.19722	+	2.07365i	−0.164451	+	0.284838i	−0.936460	−	0.350773i	$-0.885919\pi$
$53$	−1.19722	+	2.07365i	−0.164451	+	0.284838i	0.772009	+	0.635612i	$0.219252\pi$
$54$	3.25096	−	5.63083i	0.442400	−	0.766259i
$55$	−5.31893	−	9.21265i	−0.717204	−	1.24223i
$56$		0			0
$57$	4.69722			0.622163
$58$	−5.30278			−0.696289
$59$	1.41176	+	2.44524i	0.183795	+	0.318343i	0.943170	−	0.332311i	$-0.107828\pi$
$59$	1.41176	+	2.44524i	0.183795	+	0.318343i	−0.759375	+	0.650654i	$0.774495\pi$
$60$	−7.75694	+	13.4354i	−1.00142	+	1.73450i
$61$	4.33462			0.554991			0.277495	−	0.960727i	$-0.410496\pi$
$61$	4.33462			0.554991			0.277495	+	0.960727i	$0.410496\pi$
$62$	8.24179	+	14.2752i	1.04671	+	1.81295i
$63$		0			0
$64$	−12.8167			−1.60208
$65$	−4.69722	+	6.24500i	−0.582619	+	0.774597i
$66$	−12.2483	+	21.2147i	−1.50766	+	2.61135i
$67$	1.00000			0.122169			0.0610847	−	0.998133i	$-0.480544\pi$
$67$	1.00000			0.122169			0.0610847	+	0.998133i	$0.480544\pi$
$68$	−11.8209	+	20.4743i	−1.43349	+	2.48288i
$69$	0.656208	−	1.13659i	0.0789982	−	0.136829i
$70$		0			0
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	−0.959955	−	0.280155i	$-0.909614\pi$
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	0.722599	+	0.691268i	$0.242948\pi$
$72$	5.09167			0.600059
$73$	2.16731	−	3.75389i	0.253664	−	0.439359i	−0.710868	−	0.703326i	$-0.751698\pi$
$73$	2.16731	−	3.75389i	0.253664	−	0.439359i	0.964532	+	0.263967i	$0.0850308\pi$
$74$	−9.90833	−	17.1617i	−1.15182	−	1.99501i
$75$	0.328104	−	0.568293i	0.0378862	−	0.0656208i
$76$	−3.57907	−	6.19912i	−0.410547	−	0.711088i
$77$		0			0
$78$	17.8625	+	2.17708i	2.02253	+	0.246506i
$79$	3.30278	+	5.72058i	0.371591	+	0.643615i	0.989811	−	0.142391i	$-0.0454789\pi$
$79$	3.30278	+	5.72058i	0.371591	+	0.643615i	−0.618219	+	0.786006i	$0.712146\pi$
$80$	0.656208			0.0733663
$81$	−11.2111			−1.24568
$82$	−22.9855			−2.53832
$83$	2.82352			0.309921			0.154961	−	0.987921i	$-0.450475\pi$
$83$	2.82352			0.309921			0.154961	+	0.987921i	$0.450475\pi$
$84$		0			0
$85$	−7.75694	+	13.4354i	−0.841358	+	1.45728i
$86$	14.4083	+	24.9560i	1.55369	+	2.69107i
$87$	2.49541	+	4.32218i	0.267536	+	0.463386i
$88$	14.7250			1.56969
$89$	−3.25096	+	5.63083i	−0.344601	+	0.596867i	−0.985281	−	0.170941i	$-0.945319\pi$
$89$	−3.25096	+	5.63083i	−0.344601	+	0.596867i	0.640680	+	0.767808i	$0.278653\pi$
$90$	8.47055			0.892874
$91$		0			0
$92$	−2.00000			−0.208514
$93$	7.75694	−	13.4354i	0.804357	−	1.39319i
$94$	−3.47972			−0.358906
$95$	−2.34861	−	4.06792i	−0.240963	−	0.417359i
$96$	5.74637	+	9.95301i	0.586487	+	1.01583i
$97$	6.83003	−	11.8300i	0.693484	−	1.20115i	−0.277205	−	0.960811i	$-0.589408\pi$
$97$	6.83003	−	11.8300i	0.693484	−	1.20115i	0.970689	−	0.240339i	$-0.0772587\pi$
$98$		0			0
$99$	8.33053			0.837250
$100$	−1.00000			−0.100000
$101$	−6.50192			−0.646966			−0.323483	−	0.946234i	$-0.604854\pi$
$101$	−6.50192			−0.646966			−0.323483	+	0.946234i	$0.604854\pi$
$102$	35.7250			3.53730
$103$	−5.74637	−	9.95301i	−0.566207	−	0.980699i	−0.996936	−	0.0782182i	$-0.975077\pi$
$103$	−5.74637	−	9.95301i	−0.566207	−	0.980699i	0.430729	−	0.902481i	$-0.358256\pi$
$104$	−4.23527	−	9.95301i	−0.415303	−	0.975973i
$105$		0			0
$106$	−2.75694	−	4.77516i	−0.267778	−	0.463804i
$107$	−2.84861	+	4.93394i	−0.275386	+	0.476982i	−0.970232	−	0.242176i	$-0.922139\pi$
$107$	−2.84861	+	4.93394i	−0.275386	+	0.476982i	0.694847	+	0.719158i	$0.255472\pi$
$108$	4.66272	+	8.07607i	0.448670	+	0.777120i
$109$	−4.10555	+	7.11102i	−0.393240	+	0.681113i	−0.992875	−	0.119162i	$-0.961979\pi$
$109$	−4.10555	+	7.11102i	−0.393240	+	0.681113i	0.599634	+	0.800274i	$0.295313\pi$
$110$	24.4966			2.33566
$111$	−9.32544	+	16.1521i	−0.885132	+	1.53309i
$112$		0			0
$113$	−3.40833	+	5.90340i	−0.320628	+	0.555345i	−0.980618	−	0.195930i	$-0.937227\pi$
$113$	−3.40833	+	5.90340i	−0.320628	+	0.555345i	0.659989	+	0.751275i	$0.270561\pi$
$114$	−5.40833	+	9.36750i	−0.506536	+	0.877346i
$115$	−1.31242			−0.122383
$116$	3.80278	−	6.58660i	0.353079	−	0.611551i
$117$	−2.39607	−	5.63083i	−0.221517	−	0.520571i
$118$	−6.50192			−0.598551
$119$		0			0
$120$	−7.04584	−	12.2037i	−0.643194	−	1.11404i
$121$	13.0917			1.19015
$122$	−4.99082	+	8.64436i	−0.451848	+	0.782624i
$123$	10.8167	+	18.7350i	0.975305	+	1.68928i
$124$	−23.6417			−2.12309
$125$	−11.4927			−1.02794
$126$		0			0
$127$	−3.95416	−	6.84881i	−0.350875	−	0.607734i	0.635528	−	0.772078i	$-0.280783\pi$
$127$	−3.95416	−	6.84881i	−0.350875	−	0.607734i	−0.986403	+	0.164344i	$0.947449\pi$
$128$	9.45416	−	16.3751i	0.835638	−	1.44737i
$129$	13.5607	−	23.4878i	1.19395	−	2.06799i
$130$	−7.04584	−	16.5579i	−0.617961	−	1.45222i
$131$	5.31893	+	9.21265i	0.464717	+	0.804913i	0.999189	−	0.0402730i	$-0.0128228\pi$
$131$	5.31893	+	9.21265i	0.464717	+	0.804913i	−0.534472	+	0.845186i	$0.679489\pi$
$132$	−17.5672	−	30.4273i	−1.52903	−	2.64836i
$133$		0			0
$134$	−1.15139	+	1.99426i	−0.0994648	+	0.172278i
$135$	3.05971	+	5.29958i	0.263338	+	0.456115i
$136$	−10.7372	−	18.5974i	−0.920707	−	1.59471i
$137$	−3.15139	−	5.45836i	−0.269241	−	0.466339i	0.699425	−	0.714706i	$-0.253440\pi$
$137$	−3.15139	−	5.45836i	−0.269241	−	0.466339i	−0.968666	+	0.248367i	$0.920106\pi$
$138$	1.51110	+	2.61730i	0.128633	+	0.222800i
$139$	5.31893	−	9.21265i	0.451146	−	0.781407i	−0.547312	−	0.836929i	$-0.684349\pi$
$139$	5.31893	−	9.21265i	0.451146	−	0.781407i	0.998457	+	0.0555216i	$0.0176822\pi$
$140$		0			0
$141$	1.63751	+	2.83625i	0.137903	+	0.238855i
$142$	−4.60555	−	7.97705i	−0.386489	−	0.669419i
$143$	−6.92937	−	16.2842i	−0.579463	−	1.36175i
$144$	−0.256939	+	0.445032i	−0.0214116	+	0.0370860i
$145$	2.49541	−	4.32218i	0.207233	−	0.358938i
$146$	4.99082	+	8.64436i	0.413044	+	0.715412i
$147$		0			0
$148$	28.4222			2.33629
$149$	−17.5139			−1.43479			−0.717396	−	0.696665i	$-0.754666\pi$
$149$	−17.5139			−1.43479			−0.717396	+	0.696665i	$0.754666\pi$
$150$	0.755550	+	1.30865i	0.0616904	+	0.106851i
$151$	−4.10555	+	7.11102i	−0.334105	+	0.578687i	−0.983313	−	0.181924i	$-0.941767\pi$
$151$	−4.10555	+	7.11102i	−0.334105	+	0.578687i	0.649207	+	0.760611i	$0.275101\pi$
$152$	6.50192			0.527376
$153$	−6.07448	−	10.5213i	−0.491092	−	0.850597i
$154$		0			0
$155$	−15.5139			−1.24610
$156$	−15.5139	+	20.6258i	−1.24210	+	1.65139i
$157$	0.328104	−	0.568293i	0.0261856	−	0.0453547i	−0.852636	−	0.522506i	$-0.824997\pi$
$157$	0.328104	−	0.568293i	0.0261856	−	0.0453547i	0.878821	+	0.477151i	$0.158331\pi$
$158$	−15.2111			−1.21013
$159$	−2.59475	+	4.49425i	−0.205777	+	0.356417i
$160$	5.74637	−	9.95301i	0.454291	−	0.786855i
$161$		0			0
$162$	12.9083	−	22.3579i	1.01417	−	1.75660i
$163$	−2.78890			−0.218443			−0.109222	−	0.994017i	$-0.534836\pi$
$163$	−2.78890			−0.218443			−0.109222	+	0.994017i	$0.534836\pi$
$164$	16.4836	−	28.5504i	1.28715	−	2.22941i
$165$	−11.5278	−	19.9667i	−0.897435	−	1.55440i
$166$	−3.25096	+	5.63083i	−0.252324	+	0.437037i
$167$	−5.74637	−	9.95301i	−0.444668	−	0.770187i	0.553361	−	0.832941i	$-0.313345\pi$
$167$	−5.74637	−	9.95301i	−0.444668	−	0.770187i	−0.998029	+	0.0627542i	$0.980012\pi$
$168$		0			0
$169$	−9.01388	+	9.36750i	−0.693375	+	0.720577i
$170$	−17.8625	−	30.9387i	−1.36999	−	2.37289i
$171$	3.67841			0.281295
$172$	−41.3305			−3.15142
$173$	10.1803			0.773996			0.386998	−	0.922080i	$-0.373512\pi$
$173$	10.1803			0.773996			0.386998	+	0.922080i	$0.373512\pi$
$174$	−11.4927			−0.871263
$175$		0			0
$176$	−0.743061	+	1.28702i	−0.0560103	+	0.0970127i
$177$	3.05971	+	5.29958i	0.229982	+	0.398341i
$178$	−7.48624	−	12.9665i	−0.561117	−	0.971883i
$179$	21.6056			1.61487			0.807437	−	0.589953i	$-0.200854\pi$
$179$	21.6056			1.61487			0.807437	+	0.589953i	$0.200854\pi$
$180$	−6.07448	+	10.5213i	−0.452765	+	0.784212i
$181$	−24.2979			−1.80605			−0.903025	−	0.429588i	$-0.858659\pi$
$181$	−24.2979			−1.80605			−0.903025	+	0.429588i	$0.858659\pi$
$182$		0			0
$183$	9.39445			0.694458
$184$	0.908327	−	1.57327i	0.0669627	−	0.115983i
$185$	18.6509			1.37124
$186$	17.8625	+	30.9387i	1.30974	+	2.26854i
$187$	−17.5672	−	30.4273i	−1.28464	−	2.22507i
$188$	2.49541	−	4.32218i	0.181997	−	0.315227i
$189$		0			0
$190$	10.8167			0.784723
$191$	15.6972			1.13581			0.567906	−	0.823094i	$-0.307754\pi$
$191$	15.6972			1.13581			0.567906	+	0.823094i	$0.307754\pi$
$192$	−27.7776			−2.00468
$193$	19.8167			1.42643			0.713217	−	0.700943i	$-0.247237\pi$
$193$	19.8167			1.42643			0.713217	+	0.700943i	$0.247237\pi$
$194$	15.7280	+	27.2417i	1.12921	+	1.95584i
$195$	−10.1803	+	13.5348i	−0.729029	+	0.969250i
$196$		0			0
$197$	0.545837	+	0.945417i	0.0388892	+	0.0673581i	0.884815	−	0.465943i	$-0.154285\pi$
$197$	0.545837	+	0.945417i	0.0388892	+	0.0673581i	−0.845926	+	0.533301i	$0.820951\pi$
$198$	−9.59167	+	16.6133i	−0.681651	+	1.18065i
$199$	3.57907	+	6.19912i	0.253713	+	0.439444i	0.964545	−	0.263918i	$-0.0850147\pi$
$199$	3.57907	+	6.19912i	0.253713	+	0.439444i	−0.710832	+	0.703362i	$0.751681\pi$
$200$	0.454163	−	0.786634i	0.0321142	−	0.0556234i
$201$	2.16731			0.152870
$202$	7.48624	−	12.9665i	0.526730	−	0.912323i
$203$		0			0
$204$	−25.6194	+	44.3742i	−1.79372	+	3.10681i
$205$	10.8167	−	18.7350i	0.755468	−	1.30851i
$206$	26.4652			1.84392
$207$	0.513878	−	0.890063i	0.0357170	−	0.0618637i
$208$	1.08365	+	0.132076i	0.0751379	+	0.00915781i
$209$	10.6379			0.735836
$210$		0			0
$211$	−7.50000	−	12.9904i	−0.516321	−	0.894295i	−0.999820	−	0.0189499i	$-0.993968\pi$
$211$	−7.50000	−	12.9904i	−0.516321	−	0.894295i	0.483499	−	0.875345i	$-0.339366\pi$
$212$	7.90833			0.543146
$213$	−4.33462	+	7.50778i	−0.297003	+	0.514424i
$214$	−6.55971	−	11.3618i	−0.448413	−	0.776674i
$215$	−27.1214			−1.84967
$216$	−8.47055			−0.576348
$217$		0			0
$218$	−9.45416	−	16.3751i	−0.640317	−	1.10906i
$219$	4.69722	−	8.13583i	0.317409	−	0.549769i
$220$	−17.5672	+	30.4273i	−1.18438	+	2.05141i
$221$	−15.5139	+	20.6258i	−1.04358	+	1.38744i
$222$	−21.4744	−	37.1947i	−1.44127	−	2.49635i
$223$	8.99734	+	15.5838i	0.602506	+	1.04357i	0.992440	+	0.122729i	$0.0391645\pi$
$223$	8.99734	+	15.5838i	0.602506	+	1.04357i	−0.389934	+	0.920843i	$0.627502\pi$
$224$		0			0
$225$	0.256939	−	0.445032i	0.0171293	−	0.0296688i
$226$	−7.84861	−	13.5942i	−0.522082	−	0.904272i
$227$	9.22610	+	15.9801i	0.612358	+	1.06063i	0.990842	+	0.135027i	$0.0431121\pi$
$227$	9.22610	+	15.9801i	0.612358	+	1.06063i	−0.378484	+	0.925608i	$0.623555\pi$
$228$	−7.75694	−	13.4354i	−0.513716	−	0.889782i
$229$	7.81434	+	13.5348i	0.516386	+	0.894407i	0.999819	+	0.0190256i	$0.00605640\pi$
$229$	7.81434	+	13.5348i	0.516386	+	0.894407i	−0.483433	+	0.875381i	$0.660610\pi$
$230$	1.51110	−	2.61730i	0.0996390	−	0.172580i
$231$		0			0
$232$	3.45416	+	5.98279i	0.226777	+	0.392789i
$233$	6.54584	+	11.3377i	0.428832	+	0.742759i	0.996770	−	0.0803127i	$-0.0255919\pi$
$233$	6.54584	+	11.3377i	0.428832	+	0.742759i	−0.567938	+	0.823072i	$0.692259\pi$
$234$	13.9882	+	1.70488i	0.914435	+	0.111451i
$235$	1.63751	−	2.83625i	0.106819	−	0.185017i
$236$	4.66272	−	8.07607i	0.303517	−	0.525707i
$237$	7.15813	+	12.3982i	0.464971	+	0.805353i
$238$		0			0
$239$	4.39445			0.284253			0.142127	−	0.989848i	$-0.454606\pi$
$239$	4.39445			0.284253			0.142127	+	0.989848i	$0.454606\pi$
$240$	1.42221			0.0918029
$241$	4.66272	+	8.07607i	0.300352	+	0.520225i	0.976216	−	0.216802i	$-0.0695624\pi$
$241$	4.66272	+	8.07607i	0.300352	+	0.520225i	−0.675863	+	0.737027i	$0.736229\pi$
$242$	−15.0736	+	26.1082i	−0.968967	+	1.67830i
$243$	−15.8274			−1.01533
$244$	−7.15813	−	12.3982i	−0.458252	−	0.793717i
$245$		0			0
$246$	−49.8167			−3.17619
$247$	−3.05971	−	7.19041i	−0.194685	−	0.457515i
$248$	10.7372	−	18.5974i	0.681813	−	1.18093i
$249$	6.11943			0.387803
$250$	13.2326	−	22.9196i	0.836904	−	1.44956i
$251$	−14.9725	+	25.9331i	−0.945054	+	1.63688i	−0.189411	+	0.981898i	$0.560658\pi$
$251$	−14.9725	+	25.9331i	−0.945054	+	1.63688i	−0.755643	+	0.654984i	$0.772675\pi$
$252$		0			0
$253$	1.48612	−	2.57404i	0.0934317	−	0.161828i
$254$	18.2111			1.14267
$255$	−16.8117	+	29.1187i	−1.05279	+	1.82348i
$256$	8.95416	+	15.5091i	0.559635	+	0.969317i
$257$	−3.15162	+	5.45877i	−0.196593	+	0.340508i	−0.947421	−	0.319988i	$-0.896321\pi$
$257$	−3.15162	+	5.45877i	−0.196593	+	0.340508i	0.750829	+	0.660497i	$0.229654\pi$
$258$	31.2273	+	54.0872i	1.94413	+	3.36732i
$259$		0			0
$260$	25.6194	+	3.12250i	1.58885	+	0.193649i
$261$	1.95416	+	3.38471i	0.120960	+	0.209508i
$262$	−24.4966			−1.51340
$263$	15.4222			0.950974			0.475487	−	0.879723i	$-0.342272\pi$
$263$	15.4222			0.950974			0.475487	+	0.879723i	$0.342272\pi$
$264$	31.9136			1.96414
$265$	5.18951			0.318789
$266$		0			0
$267$	−7.04584	+	12.2037i	−0.431198	+	0.746857i
$268$	−1.65139	−	2.86029i	−0.100875	−	0.174720i
$269$	0.328104	+	0.568293i	0.0200049	+	0.0346494i	0.875855	−	0.482575i	$-0.160298\pi$
$269$	0.328104	+	0.568293i	0.0200049	+	0.0346494i	−0.855850	+	0.517225i	$0.826965\pi$
$270$	−14.0917			−0.857592
$271$	−7.25747	+	12.5703i	−0.440860	+	0.763592i	−0.997754	−	0.0669918i	$-0.978660\pi$
$271$	−7.25747	+	12.5703i	−0.440860	+	0.763592i	0.556893	+	0.830584i	$0.311993\pi$
$272$	2.16731			0.131412
$273$		0			0
$274$	14.5139			0.876815
$275$	0.743061	−	1.28702i	0.0448083	−	0.0776102i
$276$	−4.33462			−0.260913
$277$	0.105551	+	0.182820i	0.00634196	+	0.0109846i	0.869179	−	0.494498i	$-0.164648\pi$
$277$	0.105551	+	0.182820i	0.00634196	+	0.0109846i	−0.862837	+	0.505482i	$0.831315\pi$
$278$	12.2483	+	21.2147i	0.734604	+	1.27237i
$279$	6.07448	−	10.5213i	0.363670	−	0.629894i
$280$		0			0
$281$	23.8167			1.42078			0.710391	−	0.703807i	$-0.248518\pi$
$281$	23.8167			1.42078			0.710391	+	0.703807i	$0.248518\pi$
$282$	−7.54163			−0.449098
$283$	18.6509			1.10868			0.554340	−	0.832290i	$-0.312971\pi$
$283$	18.6509			1.10868			0.554340	+	0.832290i	$0.312971\pi$
$284$	13.2111			0.783935
$285$	−5.09017	−	8.81643i	−0.301515	−	0.522240i
$286$	40.4534	+	4.93046i	2.39206	+	0.291544i
$287$		0			0
$288$	4.50000	+	7.79423i	0.265165	+	0.459279i
$289$	−17.1194	+	29.6517i	−1.00703	+	1.74422i
$290$	5.74637	+	9.95301i	0.337439	+	0.584461i
$291$	14.8028	−	25.6392i	0.867754	−	1.50299i
$292$	−14.3163			−0.837796
$293$	14.3163	−	24.7965i	0.836365	−	1.44863i	−0.0565490	−	0.998400i	$-0.518010\pi$
$293$	14.3163	−	24.7965i	0.836365	−	1.44863i	0.892914	−	0.450227i	$-0.148657\pi$
$294$		0			0
$295$	3.05971	−	5.29958i	0.178143	−	0.308554i
$296$	−12.9083	+	22.3579i	−0.750281	+	1.29953i
$297$	−13.8587			−0.804166
$298$	20.1653	−	34.9273i	1.16814	−	2.02328i
$299$	−2.16731	−	0.264152i	−0.125339	−	0.0152763i
$300$	−2.16731			−0.125130
$301$		0			0
$302$	−9.45416	−	16.3751i	−0.544026	−	0.942281i
$303$	−14.0917			−0.809545
$304$	−0.328104	+	0.568293i	−0.0188181	+	0.0325938i
$305$	−4.69722	−	8.13583i	−0.268962	−	0.465856i
$306$	27.9763			1.59930
$307$	3.67841			0.209938			0.104969	−	0.994476i	$-0.466526\pi$
$307$	3.67841			0.209938			0.104969	+	0.994476i	$0.466526\pi$
$308$		0			0
$309$	−12.4542	−	21.5712i	−0.708493	−	1.22715i
$310$	17.8625	−	30.9387i	1.01452	−	1.75720i
$311$	−5.31893	+	9.21265i	−0.301609	+	0.522402i	−0.976501	−	0.215515i	$-0.930857\pi$
$311$	−5.31893	+	9.21265i	−0.301609	+	0.522402i	0.674892	+	0.737917i	$0.264190\pi$
$312$	−9.17914	−	21.5712i	−0.519667	−	1.22123i
$313$	2.82352	+	4.89047i	0.159595	+	0.276426i	0.934723	−	0.355378i	$-0.115648\pi$
$313$	2.82352	+	4.89047i	0.159595	+	0.276426i	−0.775128	+	0.631804i	$0.782315\pi$
$314$	0.755550	+	1.30865i	0.0426382	+	0.0738514i
$315$		0			0
$316$	10.9083	−	18.8938i	0.613641	−	1.06286i
$317$	3.10555	+	5.37897i	0.174425	+	0.302113i	0.939962	−	0.341279i	$-0.110860\pi$
$317$	3.10555	+	5.37897i	0.174425	+	0.302113i	−0.765537	+	0.643392i	$0.777527\pi$
$318$	−5.97514	−	10.3492i	−0.335069	−	0.580357i
$319$	5.65139	+	9.78849i	0.316417	+	0.548050i
$320$	13.8888	+	24.0561i	0.776409	+	1.34478i
$321$	−6.17382	+	10.6934i	−0.344589	+	0.596846i
$322$		0			0
$323$	−7.75694	−	13.4354i	−0.431608	−	0.747566i
$324$	18.5139	+	32.0670i	1.02855	+	1.78150i
$325$	−1.08365	−	0.132076i	−0.0601103	−	0.00732625i
$326$	3.21110	−	5.56179i	0.177847	−	0.308039i
$327$	−8.89799	+	15.4118i	−0.492060	+	0.852273i
$328$	14.9725	+	25.9331i	0.826717	+	1.43192i
$329$		0			0
$330$	53.0917			2.92260
$331$	4.30278			0.236502			0.118251	−	0.992984i	$-0.462271\pi$
$331$	4.30278			0.236502			0.118251	+	0.992984i	$0.462271\pi$
$332$	−4.66272	−	8.07607i	−0.255900	−	0.443232i
$333$	−7.30278	+	12.6488i	−0.400190	+	0.693149i
$334$	26.4652			1.44811
$335$	−1.08365	−	1.87694i	−0.0592063	−	0.102548i
$336$		0			0
$337$	18.1194			0.987028			0.493514	−	0.869738i	$-0.335712\pi$
$337$	18.1194			0.987028			0.493514	+	0.869738i	$0.335712\pi$
$338$	−8.30278	−	28.7617i	−0.451611	−	1.56443i
$339$	−7.38689	+	12.7945i	−0.401201	+	0.694901i
$340$	51.2389			2.77882
$341$	17.5672	−	30.4273i	0.951319	−	1.64773i
$342$	−4.23527	+	7.33571i	−0.229017	+	0.396670i
$343$		0			0
$344$	18.7708	−	32.5120i	1.01205	−	1.75293i
$345$	−2.84441			−0.153138
$346$	−11.7215	+	20.3023i	−0.630152	+	1.09146i
$347$	−7.60555	−	13.1732i	−0.408287	−	0.707174i	0.586411	−	0.810014i	$-0.300541\pi$
$347$	−7.60555	−	13.1732i	−0.408287	−	0.707174i	−0.994698	+	0.102839i	$0.967207\pi$
$348$	8.24179	−	14.2752i	0.441806	−	0.765231i
$349$	−5.09017	−	8.81643i	−0.272470	−	0.471932i	0.697023	−	0.717048i	$-0.254507\pi$
$349$	−5.09017	−	8.81643i	−0.272470	−	0.471932i	−0.969494	+	0.245116i	$0.921174\pi$
$350$		0			0
$351$	3.98612	+	9.36750i	0.212763	+	0.500000i
$352$	13.0139	+	22.5407i	0.693642	+	1.20142i
$353$	−26.4652			−1.40860			−0.704301	−	0.709902i	$-0.748739\pi$
$353$	−26.4652			−1.40860			−0.704301	+	0.709902i	$0.748739\pi$
$354$	−14.0917			−0.748964
$355$	8.66923			0.460115
$356$	21.4744			1.13814
$357$		0			0
$358$	−24.8764	+	43.0871i	−1.31476	+	2.27723i
$359$	6.04584	+	10.4717i	0.319087	+	0.552675i	0.980298	−	0.197525i	$-0.0632904\pi$
$359$	6.04584	+	10.4717i	0.319087	+	0.552675i	−0.661211	+	0.750200i	$0.729957\pi$
$360$	−5.51761	−	9.55678i	−0.290804	−	0.503687i
$361$	−14.3028			−0.752778
$362$	27.9763	−	48.4564i	1.47040	−	2.54681i
$363$	28.3737			1.48923
$364$		0			0
$365$	−9.39445			−0.491728
$366$	−10.8167	+	18.7350i	−0.565396	+	0.979294i
$367$	25.6103			1.33685			0.668424	−	0.743780i	$-0.266969\pi$
$367$	25.6103			1.33685			0.668424	+	0.743780i	$0.266969\pi$
$368$	0.0916731	+	0.158782i	0.00477879	+	0.00827711i
$369$	8.47055	+	14.6714i	0.440959	+	0.763764i
$370$	−21.4744	+	37.1947i	−1.11640	+	1.93366i
$371$		0			0
$372$	−51.2389			−2.65661
$373$	−12.6972			−0.657437			−0.328719	−	0.944428i	$-0.606617\pi$
$373$	−12.6972			−0.657437			−0.328719	+	0.944428i	$0.606617\pi$
$374$	80.9068			4.18359
$375$	−24.9083			−1.28626
$376$	2.26665	+	3.92595i	0.116894	+	0.202466i
$377$	4.99082	−	6.63534i	0.257041	−	0.341737i
$378$		0			0
$379$	6.05971	+	10.4957i	0.311267	+	0.539130i	0.978637	−	0.205596i	$-0.0659134\pi$
$379$	6.05971	+	10.4957i	0.311267	+	0.539130i	−0.667370	+	0.744726i	$0.732580\pi$
$380$	−7.75694	+	13.4354i	−0.397923	+	0.689222i
$381$	−8.56989	−	14.8435i	−0.439049	−	0.760455i
$382$	−18.0736	+	31.3044i	−0.924725	+	1.60167i
$383$	−22.3293			−1.14097			−0.570487	−	0.821307i	$-0.693245\pi$
$383$	−22.3293			−1.14097			−0.570487	+	0.821307i	$0.693245\pi$
$384$	20.4901	−	35.4899i	1.04563	−	1.81108i
$385$		0			0
$386$	−22.8167	+	39.5196i	−1.16134	+	2.01149i
$387$	10.6194	−	18.3934i	0.539816	−	0.934989i
$388$	−45.1161			−2.29042
$389$	−14.5139	+	25.1388i	−0.735883	+	1.27459i	0.218452	+	0.975848i	$0.429899\pi$
$389$	−14.5139	+	25.1388i	−0.735883	+	1.27459i	−0.954335	+	0.298739i	$0.903434\pi$
$390$	−15.2705	−	35.8861i	−0.773252	−	1.81716i
$391$	−4.33462			−0.219211
$392$		0			0
$393$	11.5278	+	19.9667i	0.581498	+	1.00718i
$394$	−2.51388			−0.126647
$395$	7.15813	−	12.3982i	0.360165	−	0.623824i
$396$	−13.7569	−	23.8277i	−0.691312	−	1.19739i
$397$	4.33462			0.217548			0.108774	−	0.994066i	$-0.465307\pi$
$397$	4.33462			0.217548			0.108774	+	0.994066i	$0.465307\pi$
$398$	−16.4836			−0.826247
$399$		0			0
$400$	0.0458365	+	0.0793912i	0.00229183	+	0.00396956i
$401$	5.05971	−	8.76368i	0.252670	−	0.437637i	−0.711590	−	0.702595i	$-0.752025\pi$
$401$	5.05971	−	8.76368i	0.252670	−	0.437637i	0.964260	+	0.264958i	$0.0853579\pi$
$402$	−2.49541	+	4.32218i	−0.124460	+	0.215571i
$403$	−25.6194	−	3.12250i	−1.27619	−	0.155543i
$404$	10.7372	+	18.5974i	0.534196	+	0.925254i
$405$	12.1490	+	21.0426i	0.603687	+	1.04562i
$406$		0			0
$407$	−21.1194	+	36.5799i	−1.04685	+	1.81320i
$408$	−23.2708	−	40.3062i	−1.15208	−	1.99546i
$409$	−1.73986	−	3.01353i	−0.0860306	−	0.149009i	0.819799	−	0.572651i	$-0.194085\pi$
$409$	−1.73986	−	3.01353i	−0.0860306	−	0.149009i	−0.905830	+	0.423642i	$0.860752\pi$
$410$	24.9083	+	43.1425i	1.23013	+	2.13066i
$411$	−6.83003	−	11.8300i	−0.336900	−	0.583529i
$412$	−18.9790	+	32.8726i	−0.935027	+	1.61952i
$413$		0			0
$414$	1.18335	+	2.04962i	0.0581583	+	0.100733i
$415$	−3.05971	−	5.29958i	−0.150195	−	0.260146i
$416$	11.4927	−	15.2797i	0.563478	−	0.749149i
$417$	11.5278	−	19.9667i	0.564517	−	0.977772i
$418$	−12.2483	+	21.2147i	−0.599084	+	1.03764i
$419$	8.56989	+	14.8435i	0.418667	+	0.725152i	0.995806	−	0.0914942i	$-0.0291643\pi$
$419$	8.56989	+	14.8435i	0.418667	+	0.725152i	−0.577139	+	0.816646i	$0.695831\pi$
$420$		0			0
$421$	5.02776			0.245038			0.122519	−	0.992466i	$-0.460903\pi$
$421$	5.02776			0.245038			0.122519	+	0.992466i	$0.460903\pi$
$422$	34.5416			1.68146
$423$	1.28234	+	2.22107i	0.0623494	+	0.107992i
$424$	−3.59167	+	6.22096i	−0.174427	+	0.302117i
$425$	−2.16731			−0.105130
$426$	−9.98165	−	17.2887i	−0.483612	−	0.837641i
$427$		0			0
$428$	18.8167			0.909537
$429$	−15.0181	−	35.2929i	−0.725080	−	1.70396i
$430$	31.2273	−	54.0872i	1.50591	−	2.60832i
$431$	−20.9361			−1.00846			−0.504228	−	0.863571i	$-0.668223\pi$
$431$	−20.9361			−1.00846			−0.504228	+	0.863571i	$0.668223\pi$
$432$	0.427446	−	0.740358i	0.0205655	−	0.0356205i
$433$	−8.56989	+	14.8435i	−0.411843	+	0.713332i	−0.995091	−	0.0989613i	$-0.968448\pi$
$433$	−8.56989	+	14.8435i	−0.411843	+	0.713332i	0.583249	+	0.812294i	$0.301781\pi$
$434$		0			0
$435$	5.40833	−	9.36750i	0.259309	−	0.449137i
$436$	27.1194			1.29879
$437$	0.656208	−	1.13659i	0.0313907	−	0.0543703i
$438$	10.8167	+	18.7350i	0.516840	+	0.895193i
$439$	1.83920	−	3.18559i	0.0877804	−	0.152040i	−0.818792	−	0.574090i	$-0.805356\pi$
$439$	1.83920	−	3.18559i	0.0877804	−	0.152040i	0.906573	+	0.422050i	$0.138689\pi$
$440$	−15.9568	−	27.6380i	−0.760710	−	1.31759i
$441$		0			0
$442$	−23.2708	−	54.6871i	−1.10688	−	2.60120i
$443$	10.1194	+	17.5274i	0.480789	+	0.832750i	0.999757	−	0.0220431i	$-0.00701711\pi$
$443$	10.1194	+	17.5274i	0.480789	+	0.832750i	−0.518968	+	0.854793i	$0.673684\pi$
$444$	61.5997			2.92339
$445$	14.0917			0.668009
$446$	−41.4377			−1.96213
$447$	−37.9580			−1.79535
$448$		0			0
$449$	10.2111	−	17.6861i	0.481892	−	0.834661i	−0.517892	−	0.855446i	$-0.673283\pi$
$449$	10.2111	−	17.6861i	0.481892	−	0.834661i	0.999784	+	0.0207849i	$0.00661652\pi$
$450$	0.591673	+	1.02481i	0.0278917	+	0.0483099i
$451$	24.4966	+	42.4294i	1.15350	+	1.99792i
$452$	22.5139			1.05896
$453$	−8.89799	+	15.4118i	−0.418064	+	0.724109i
$454$	−42.4913			−1.99421
$455$		0			0
$456$	14.0917			0.659903
$457$	−10.3028	+	17.8449i	−0.481944	+	0.834751i	−0.999785	−	0.0207258i	$-0.993402\pi$
$457$	−10.3028	+	17.8449i	−0.481944	+	0.834751i	0.517842	+	0.855476i	$0.326736\pi$
$458$	−35.9893			−1.68167
$459$	10.1056	+	17.5033i	0.471687	+	0.816985i
$460$	2.16731	+	3.75389i	0.101051	+	0.175026i
$461$	12.5764	−	21.7830i	0.585741	−	1.01453i	−0.409041	−	0.912516i	$-0.634137\pi$
$461$	12.5764	−	21.7830i	0.585741	−	1.01453i	0.994783	−	0.102018i	$-0.0325299\pi$
$462$		0			0
$463$	−13.7889			−0.640824			−0.320412	−	0.947278i	$-0.603821\pi$
$463$	−13.7889			−0.640824			−0.320412	+	0.947278i	$0.603821\pi$
$464$	−0.697224			−0.0323678
$465$	−33.6234			−1.55925
$466$	−30.1472			−1.39654
$467$	−6.40258	−	11.0896i	−0.296276	−	0.513165i	0.679005	−	0.734134i	$-0.262412\pi$
$467$	−6.40258	−	11.0896i	−0.296276	−	0.513165i	−0.975281	+	0.220968i	$0.929078\pi$
$468$	−12.1490	+	16.1521i	−0.561586	+	0.746633i
$469$		0			0
$470$	3.77082	+	6.53125i	0.173935	+	0.301264i
$471$	0.711103	−	1.23167i	0.0327659	−	0.0567522i
$472$	4.23527	+	7.33571i	0.194944	+	0.337653i
$473$	30.7111	−	53.1932i	1.41210	−	2.44583i
$474$	−32.9671			−1.51423
$475$	0.328104	−	0.568293i	0.0150544	−	0.0260751i
$476$		0			0
$477$	−2.03196	+	3.51946i	−0.0930370	+	0.161145i
$478$	−5.05971	+	8.76368i	−0.231426	+	0.400842i
$479$	−16.4836			−0.753154			−0.376577	−	0.926385i	$-0.622899\pi$
$479$	−16.4836			−0.753154			−0.376577	+	0.926385i	$0.622899\pi$
$480$	12.4542	−	21.5712i	0.568452	−	0.984588i
$481$	30.7998	+	3.75389i	1.40435	+	0.171163i
$482$	−21.4744			−0.978132
$483$		0			0
$484$	−21.6194	−	37.4460i	−0.982701	−	1.70209i
$485$	−29.6056			−1.34432
$486$	18.2234	−	31.5639i	0.826632	−	1.43177i
$487$	15.6514	+	27.1090i	0.709232	+	1.22843i	0.965142	+	0.261725i	$0.0842915\pi$
$487$	15.6514	+	27.1090i	0.709232	+	1.22843i	−0.255910	+	0.966701i	$0.582375\pi$
$488$	13.0038			0.588657
$489$	−6.04440			−0.273337
$490$		0			0
$491$	−9.86249	−	17.0823i	−0.445088	−	0.770915i	0.552970	−	0.833201i	$-0.313494\pi$
$491$	−9.86249	−	17.0823i	−0.445088	−	0.770915i	−0.998058	+	0.0622859i	$0.980161\pi$
$492$	35.7250	−	61.8775i	1.61061	−	2.78965i
$493$	8.24179	−	14.2752i	0.371191	−	0.642922i
$494$	17.8625	+	2.17708i	0.803671	+	0.0979516i
$495$	−9.02741	−	15.6359i	−0.405752	−	0.702783i
$496$	1.08365	+	1.87694i	0.0486575	+	0.0842773i
$497$		0			0
$498$	−7.04584	+	12.2037i	−0.315731	+	0.546863i
$499$	4.16527	+	7.21445i	0.186463	+	0.322963i	0.944069	−	0.329749i	$-0.106964\pi$
$499$	4.16527	+	7.21445i	0.186463	+	0.322963i	−0.757606	+	0.652713i	$0.773631\pi$
$500$	18.9790	+	32.8726i	0.848766	+	1.47011i
$501$	−12.4542	−	21.5712i	−0.556411	−	0.963732i
$502$	−34.4782	−	59.7181i	−1.53884	−	2.66535i
$503$	9.75289	−	16.8925i	0.434860	−	0.753199i	−0.562424	−	0.826849i	$-0.690131\pi$
$503$	9.75289	−	16.8925i	0.434860	−	0.753199i	0.997284	+	0.0736495i	$0.0234646\pi$
$504$		0			0
$505$	7.04584	+	12.2037i	0.313536	+	0.543060i
$506$	3.42221	+	5.92743i	0.152136	+	0.263507i
$507$	−19.5359	+	20.3023i	−0.867618	+	0.901655i
$508$	−13.0597	+	22.6201i	−0.579431	+	1.00360i
$509$	−10.7372	+	18.5974i	−0.475918	+	0.824314i	−0.999619	−	0.0275878i	$-0.991217\pi$
$509$	−10.7372	+	18.5974i	−0.475918	+	0.824314i	0.523701	+	0.851902i	$0.324551\pi$
$510$	−38.7135	−	67.0538i	−1.71426	−	2.96919i
$511$		0			0
$512$	−3.42221			−0.151242
$513$	−6.11943			−0.270179
$514$	−7.25747	−	12.5703i	−0.320113	−	0.554453i
$515$	−12.4542	+	21.5712i	−0.548796	+	0.950543i
$516$	−89.5760			−3.94336
$517$	3.70849	+	6.42329i	0.163099	+	0.282496i
$518$		0			0
$519$	22.0639			0.968498
$520$	−14.0917	+	18.7350i	−0.617961	+	0.821584i
$521$	10.8365	−	18.7694i	0.474757	−	0.822304i	−0.524825	−	0.851210i	$-0.675869\pi$
$521$	10.8365	−	18.7694i	0.474757	−	0.822304i	0.999582	+	0.0289063i	$0.00920245\pi$
$522$	−9.00000			−0.393919
$523$	−12.1490	+	21.0426i	−0.531237	+	0.920129i	0.468099	+	0.883676i	$0.344939\pi$
$523$	−12.1490	+	21.0426i	−0.531237	+	0.920129i	−0.999335	+	0.0364529i	$0.988394\pi$
$524$	17.5672	−	30.4273i	0.767428	−	1.32922i
$525$		0			0
$526$	−17.7569	+	30.7559i	−0.774239	+	1.34102i
$527$	−51.2389			−2.23200
$528$	−1.61044	+	2.78937i	−0.0700855	+	0.121392i
$529$	11.3167	+	19.6010i	0.492028	+	0.852218i
$530$	−5.97514	+	10.3492i	−0.259543	+	0.449542i
$531$	2.39607	+	4.15012i	0.103981	+	0.180100i
$532$		0			0
$533$	21.6333	−	28.7617i	0.937043	−	1.24581i
$534$	−16.2250	−	28.1025i	−0.702124	−	1.21611i
$535$	12.3476			0.533835
$536$	3.00000			0.129580
$537$	46.8259			2.02069
$538$	−1.51110			−0.0651481
$539$		0			0
$540$	10.1056	−	17.5033i	0.434874	−	0.753223i
$541$	−13.9680	−	24.1934i	−0.600533	−	1.04015i	−0.992740	−	0.120277i	$-0.961622\pi$
$541$	−13.9680	−	24.1934i	−0.600533	−	1.04015i	0.392207	−	0.919877i	$-0.371712\pi$
$542$	−16.7123	−	28.9466i	−0.717856	−	1.24336i
$543$	−52.6611			−2.25990
$544$	18.9790	−	32.8726i	0.813717	−	1.40940i
$545$	17.7960			0.762296
$546$		0			0
$547$	29.0000			1.23995			0.619975	−	0.784621i	$-0.287143\pi$
$547$	29.0000			1.23995			0.619975	+	0.784621i	$0.287143\pi$
$548$	−10.4083	+	18.0278i	−0.444622	+	0.770107i
$549$	7.35682			0.313981
$550$	1.71110	+	2.96372i	0.0729617	+	0.126373i
$551$	2.49541	+	4.32218i	0.106308	+	0.184131i
$552$	1.96862	−	3.40976i	0.0837902	−	0.145129i
$553$		0			0
$554$	−0.486122			−0.0206533
$555$	40.4222			1.71583
$556$	−35.1345			−1.49003
$557$	6.09167			0.258112			0.129056	−	0.991637i	$-0.458805\pi$
$557$	6.09167			0.258112			0.129056	+	0.991637i	$0.458805\pi$
$558$	13.9882	+	24.2282i	0.592166	+	1.02566i
$559$	−44.7880	−	5.45877i	−1.89433	−	0.230881i
$560$		0			0
$561$	−38.0736	−	65.9454i	−1.60747	−	2.78422i
$562$	−27.4222	+	47.4967i	−1.15674	+	2.00353i
$563$	−0.656208	−	1.13659i	−0.0276559	−	0.0479014i	0.851866	−	0.523759i	$-0.175471\pi$
$563$	−0.656208	−	1.13659i	−0.0276559	−	0.0479014i	−0.879522	+	0.475858i	$0.842138\pi$
$564$	5.40833	−	9.36750i	0.227732	−	0.394443i
$565$	14.7738			0.621538
$566$	−21.4744	+	37.1947i	−0.902636	+	1.56341i
$567$		0			0
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	17.3028	−	29.9693i	0.725370	−	1.25638i	−0.233451	−	0.972368i	$-0.575002\pi$
$569$	17.3028	−	29.9693i	0.725370	−	1.25638i	0.958822	−	0.284009i	$-0.0916647\pi$
$570$	23.4430			0.981920
$571$	5.36249	−	9.28811i	0.224413	−	0.388695i	−0.731730	−	0.681595i	$-0.761287\pi$
$571$	5.36249	−	9.28811i	0.224413	−	0.388695i	0.956143	+	0.292899i	$0.0946201\pi$
$572$	−35.1345	+	46.7115i	−1.46905	+	1.95311i
$573$	34.0207			1.42124
$574$		0			0
$575$	−0.0916731	−	0.158782i	−0.00382303	−	0.00662169i
$576$	−21.7527			−0.906364
$577$	−16.5829	+	28.7225i	−0.690356	+	1.19573i	0.281366	+	0.959601i	$0.409213\pi$
$577$	−16.5829	+	28.7225i	−0.690356	+	1.19573i	−0.971721	+	0.236131i	$0.924121\pi$
$578$	−39.4222	−	68.2813i	−1.63975	−	2.84013i
$579$	42.9488			1.78489
$580$	−16.4836			−0.684443
$581$		0			0
$582$	34.0875	+	59.0412i	1.41297	+	2.44734i
$583$	−5.87637	+	10.1782i	−0.243374	+	0.421537i
$584$	6.50192	−	11.2617i	0.269052	−	0.466011i
$585$	−7.97224	+	10.5992i	−0.329612	+	0.438221i
$586$	32.9671	+	57.1008i	1.36186	+	2.35881i
$587$	−0.984312	−	1.70488i	−0.0406269	−	0.0703679i	0.844997	−	0.534771i	$-0.179602\pi$
$587$	−0.984312	−	1.70488i	−0.0406269	−	0.0703679i	−0.885624	+	0.464403i	$0.846269\pi$
$588$		0			0
$589$	7.75694	−	13.4354i	0.319619	−	0.553597i
$590$	7.04584	+	12.2037i	0.290072	+	0.502420i
$591$	1.18300	+	2.04901i	0.0486620	+	0.0842850i
$592$	−1.30278	−	2.25647i	−0.0535437	−	0.0927405i
$593$	−3.15162	−	5.45877i	−0.129422	−	0.224165i	0.794031	−	0.607877i	$-0.207979\pi$
$593$	−3.15162	−	5.45877i	−0.129422	−	0.224165i	−0.923453	+	0.383712i	$0.874645\pi$
$594$	15.9568	−	27.6380i	0.654715	−	1.13400i
$595$		0			0
$596$	28.9222	+	50.0947i	1.18470	+	2.05196i
$597$	7.75694	+	13.4354i	0.317470	+	0.549875i
$598$	3.02220	−	4.01804i	0.123587	−	0.164310i
$599$	5.25694	−	9.10529i	0.214793	−	0.372032i	−0.738416	−	0.674346i	$-0.764426\pi$
$599$	5.25694	−	9.10529i	0.214793	−	0.372032i	0.953208	+	0.302314i	$0.0977591\pi$
$600$	0.984312	−	1.70488i	0.0401844	−	0.0696014i
$601$	−4.56338	−	7.90400i	−0.186144	−	0.322411i	0.757817	−	0.652467i	$-0.226266\pi$
$601$	−4.56338	−	7.90400i	−0.186144	−	0.322411i	−0.943961	+	0.330056i	$0.892932\pi$
$602$		0			0
$603$	1.69722			0.0691163
$604$	27.1194			1.10347
$605$	−14.1868	−	24.5723i	−0.576777	−	0.999008i
$606$	16.2250	−	28.1025i	0.659095	−	1.14159i
$607$	38.8129			1.57537			0.787683	−	0.616081i	$-0.211281\pi$
$607$	38.8129			1.57537			0.787683	+	0.616081i	$0.211281\pi$
$608$	5.74637	+	9.95301i	0.233046	+	0.403648i
$609$		0			0
$610$	21.6333			0.875907
$611$	3.27502	−	4.35416i	0.132493	−	0.176151i
$612$	−20.0626	+	34.7495i	−0.810984	+	1.40467i
$613$	31.9083			1.28877			0.644383	−	0.764703i	$-0.277114\pi$
$613$	31.9083			1.28877			0.644383	+	0.764703i	$0.277114\pi$
$614$	−4.23527	+	7.33571i	−0.170922	+	0.296045i
$615$	23.4430	−	40.6045i	0.945314	−	1.63733i
$616$		0			0
$617$	−7.92221	+	13.7217i	−0.318936	+	0.552413i	−0.980266	−	0.197681i	$-0.936659\pi$
$617$	−7.92221	+	13.7217i	−0.318936	+	0.552413i	0.661330	+	0.750095i	$0.269992\pi$
$618$	57.3583			2.30729
$619$	14.9725	−	25.9331i	0.601794	−	1.04234i	−0.390755	−	0.920495i	$-0.627786\pi$
$619$	14.9725	−	25.9331i	0.601794	−	1.04234i	0.992549	−	0.121844i	$-0.0388807\pi$
$620$	25.6194	+	44.3742i	1.02890	+	1.78211i
$621$	−0.854892	+	1.48072i	−0.0343056	+	0.0594191i
$622$	−12.2483	−	21.2147i	−0.491112	−	0.850631i
$623$		0			0
$624$	2.34861	+	0.286249i	0.0940197	+	0.0114591i
$625$	11.6972	+	20.2602i	0.467889	+	0.810407i
$626$	−13.0038			−0.519738
$627$	23.0555			0.920748
$628$	−2.16731			−0.0864850
$629$	61.5997			2.45614
$630$		0			0
$631$	−11.4542	+	19.8392i	−0.455983	+	0.789786i	−0.998744	−	0.0501013i	$-0.984046\pi$
$631$	−11.4542	+	19.8392i	−0.455983	+	0.789786i	0.542761	+	0.839887i	$0.317379\pi$
$632$	9.90833	+	17.1617i	0.394132	+	0.682657i
$633$	−16.2548	−	28.1542i	−0.646071	−	1.11903i
$634$	−14.3028			−0.568036
$635$	−8.56989	+	14.8435i	−0.340086	+	0.589046i
$636$	17.1398			0.679637
$637$		0			0
$638$	−26.0278			−1.03045
$639$	−3.39445	+	5.87936i	−0.134282	+	0.232584i
$640$	−40.9802			−1.61988
$641$	7.25694	+	12.5694i	0.286632	+	0.496461i	0.973004	−	0.230790i	$-0.0741310\pi$
$641$	7.25694	+	12.5694i	0.286632	+	0.496461i	−0.686372	+	0.727251i	$0.740798\pi$
$642$	−14.2169	−	24.6244i	−0.561097	−	0.971849i
$643$	−8.56989	+	14.8435i	−0.337963	+	0.585370i	−0.984050	−	0.177895i	$-0.943071\pi$
$643$	−8.56989	+	14.8435i	−0.337963	+	0.585370i	0.646086	+	0.763265i	$0.276405\pi$
$644$		0			0
$645$	−58.7805			−2.31448
$646$	35.7250			1.40558
$647$	−32.9671			−1.29607			−0.648036	−	0.761610i	$-0.724409\pi$
$647$	−32.9671			−1.29607			−0.648036	+	0.761610i	$0.724409\pi$
$648$	−33.6333			−1.32124
$649$	6.92937	+	12.0020i	0.272002	+	0.471121i
$650$	1.51110	−	2.00902i	0.0592702	−	0.0788002i
$651$		0			0
$652$	4.60555	+	7.97705i	0.180367	+	0.312405i
$653$	23.3764	−	40.4891i	0.914788	−	1.58446i	0.107577	−	0.994197i	$-0.465691\pi$
$653$	23.3764	−	40.4891i	0.914788	−	1.58446i	0.807211	−	0.590262i	$-0.200976\pi$
$654$	−20.4901	−	35.4899i	−0.801226	−	1.38776i
$655$	11.5278	−	19.9667i	0.450427	−	0.780162i
$656$	−3.02220			−0.117997
$657$	3.67841	−	6.37119i	0.143508	−	0.248564i
$658$		0			0
$659$	9.81665	−	17.0029i	0.382403	−	0.662341i	−0.609003	−	0.793168i	$-0.708430\pi$
$659$	9.81665	−	17.0029i	0.382403	−	0.662341i	0.991405	+	0.130828i	$0.0417634\pi$
$660$	−38.0736	+	65.9454i	−1.48201	+	2.56692i
$661$	−22.9855			−0.894032			−0.447016	−	0.894526i	$-0.647513\pi$
$661$	−22.9855			−0.894032			−0.447016	+	0.894526i	$0.647513\pi$
$662$	−4.95416	+	8.58086i	−0.192549	+	0.333505i
$663$	−33.6234	+	44.7025i	−1.30582	+	1.73610i
$664$	8.47055			0.328721
$665$		0			0
$666$	−16.8167	−	29.1273i	−0.651632	−	1.12866i
$667$	1.39445			0.0539933
$668$	−18.9790	+	32.8726i	−0.734319	+	1.27188i
$669$	19.5000	+	33.7750i	0.753914	+	1.30582i
$670$	4.99082			0.192812
$671$	21.2757			0.821340
$672$		0			0
$673$	1.10555	+	1.91487i	0.0426159	+	0.0738129i	0.886547	−	0.462639i	$-0.153098\pi$
$673$	1.10555	+	1.91487i	0.0426159	+	0.0738129i	−0.843931	+	0.536452i	$0.819764\pi$
$674$	−20.8625	+	36.1349i	−0.803593	+	1.39186i
$675$	−0.427446	+	0.740358i	−0.0164524	+	0.0284964i
$676$	41.6791	+	10.3129i	1.60304	+	0.396651i
$677$	13.2326	+	22.9196i	0.508571	+	0.880870i	0.999951	+	0.00992485i	$0.00315923\pi$
$677$	13.2326	+	22.9196i	0.508571	+	0.880870i	−0.491380	+	0.870945i	$0.663507\pi$
$678$	−17.0104	−	29.4628i	−0.653279	−	1.13151i
$679$		0			0
$680$	−23.2708	+	40.3062i	−0.892395	+	1.54567i
$681$	19.9958	+	34.6337i	0.766241	+	1.32717i
$682$	40.4534	+	70.0673i	1.54904	+	2.68302i
$683$	1.80278	+	3.12250i	0.0689813	+	0.119479i	0.898453	−	0.439069i	$-0.144692\pi$
$683$	1.80278	+	3.12250i	0.0689813	+	0.119479i	−0.829472	+	0.558549i	$0.811358\pi$
$684$	−6.07448	−	10.5213i	−0.232263	−	0.402292i
$685$	−6.83003	+	11.8300i	−0.260962	+	0.451999i
$686$		0			0
$687$	16.9361	+	29.3342i	0.646152	+	1.11917i
$688$	1.89445	+	3.28128i	0.0722252	+	0.125098i
$689$	8.56989	+	1.04450i	0.326487	+	0.0397923i
$690$	3.27502	−	5.67250i	0.124678	−	0.215948i
$691$	18.8796	−	32.7005i	0.718215	−	1.24399i	−0.243491	−	0.969903i	$-0.578293\pi$
$691$	18.8796	−	32.7005i	0.718215	−	1.24399i	0.961706	−	0.274082i	$-0.0883741\pi$
$692$	−16.8117	−	29.1187i	−0.639084	−	1.10693i
$693$		0			0
$694$	35.0278			1.32964
$695$	−23.0555			−0.874545
$696$	7.48624	+	12.9665i	0.283765	+	0.491495i
$697$	35.7250	−	61.8775i	1.35318	−	2.34378i
$698$	23.4430			0.887331
$699$	14.1868	+	24.5723i	0.536596	+	0.929411i
$700$		0			0
$701$	9.02776			0.340974			0.170487	−	0.985360i	$-0.445466\pi$
$701$	9.02776			0.340974			0.170487	+	0.985360i	$0.445466\pi$
$702$	−23.2708	−	2.83625i	−0.878300	−	0.107047i
$703$	−9.32544	+	16.1521i	−0.351716	+	0.609189i
$704$	−62.9083			−2.37095
$705$	3.54899	−	6.14703i	0.133663	−	0.231510i
$706$	30.4717	−	52.7786i	1.14682	−	1.98635i
$707$		0			0
$708$	10.1056	−	17.5033i	0.379790	−	0.657815i
$709$	32.7250			1.22901			0.614506	−	0.788912i	$-0.289355\pi$
$709$	32.7250			1.22901			0.614506	+	0.788912i	$0.289355\pi$
$710$	−9.98165	+	17.2887i	−0.374605	+	0.648834i
$711$	5.60555	+	9.70910i	0.210225	+	0.364120i
$712$	−9.75289	+	16.8925i	−0.365505	+	0.633073i
$713$	−2.16731	−	3.75389i	−0.0811663	−	0.140584i
$714$		0			0
$715$	−23.0555	+	30.6525i	−0.862227	+	1.14634i
$716$	−35.6791	−	61.7981i	−1.33339	−	2.30950i
$717$	9.52412			0.355685
$718$	−27.8444			−1.03914
$719$	−22.7868			−0.849805			−0.424902	−	0.905239i	$-0.639692\pi$
$719$	−22.7868			−0.849805			−0.424902	+	0.905239i	$0.639692\pi$
$720$	1.11373			0.0415064
$721$		0			0
$722$	16.4680	−	28.5235i	0.612877	−	1.06153i
$723$	10.1056	+	17.5033i	0.375829	+	0.650956i
$724$	40.1253	+	69.4990i	1.49124	+	2.58291i
$725$	0.697224			0.0258943
$726$	−32.6691	+	56.5846i	−1.21246	+	2.10005i
$727$	37.1031			1.37608			0.688038	−	0.725674i	$-0.258472\pi$
$727$	37.1031			1.37608			0.688038	+	0.725674i	$0.258472\pi$
$728$		0			0
$729$	−0.669468			−0.0247951
$730$	10.8167	−	18.7350i	0.400342	−	0.693413i
$731$	−89.5760			−3.31309
$732$	−15.5139	−	26.8708i	−0.573409	−	0.993174i
$733$	3.35030	+	5.80290i	0.123746	+	0.214335i	0.921242	−	0.388990i	$-0.127176\pi$
$733$	3.35030	+	5.80290i	0.123746	+	0.214335i	−0.797496	+	0.603324i	$0.793842\pi$
$734$	−29.4874	+	51.0737i	−1.08840	+	1.88517i
$735$		0			0
$736$	3.21110			0.118363
$737$	4.90833			0.180801
$738$	−39.0115			−1.43603
$739$	−33.2111			−1.22169			−0.610845	−	0.791750i	$-0.709170\pi$
$739$	−33.2111			−1.22169			−0.610845	+	0.791750i	$0.709170\pi$
$740$	−30.7998	−	53.3469i	−1.13222	−	1.96107i
$741$	−6.63134	−	15.5838i	−0.243609	−	0.572487i
$742$		0			0
$743$	20.6514	+	35.7693i	0.757626	+	1.31225i	0.944058	+	0.329779i	$0.106974\pi$
$743$	20.6514	+	35.7693i	0.757626	+	1.31225i	−0.186432	+	0.982468i	$0.559692\pi$
$744$	23.2708	−	40.3062i	0.853150	−	1.47770i
$745$	18.9790	+	32.8726i	0.695336	+	1.20436i
$746$	14.6194	−	25.3216i	0.535255	−	0.927089i
$747$	4.79214			0.175335
$748$	−58.0206	+	100.495i	−2.12144	+	3.67445i
$749$		0			0
$750$	28.6791	−	49.6737i	1.04721	−	1.81383i
$751$	5.80278	−	10.0507i	0.211746	−	0.366755i	−0.740515	−	0.672040i	$-0.765418\pi$
$751$	5.80278	−	10.0507i	0.211746	−	0.366755i	0.952261	+	0.305285i	$0.0987516\pi$
$752$	−0.457524			−0.0166842
$753$	−32.4500	+	56.2050i	−1.18254	+	2.04822i
$754$	7.48624	+	17.5929i	0.272633	+	0.640694i
$755$	17.7960			0.647662
$756$		0			0
$757$	−3.11943	−	5.40301i	−0.113378	−	0.196376i	0.803752	−	0.594964i	$-0.202834\pi$
$757$	−3.11943	−	5.40301i	−0.113378	−	0.196376i	−0.917130	+	0.398588i	$0.869500\pi$
$758$	−27.9083			−1.01368
$759$	3.22088	−	5.57873i	0.116911	−	0.202495i
$760$	−7.04584	−	12.2037i	−0.255579	−	0.442676i
$761$	−42.2926			−1.53311			−0.766553	−	0.642182i	$-0.778029\pi$
$761$	−42.2926			−1.53311			−0.766553	+	0.642182i	$0.778029\pi$
$762$	39.4691			1.42981
$763$		0			0
$764$	−25.9222	−	44.8986i	−0.937832	−	1.62437i
$765$	−13.1653	+	22.8029i	−0.475991	+	0.824441i
$766$	25.7097	−	44.5305i	0.928928	−	1.60895i
$767$	6.11943	−	8.13583i	0.220960	−	0.293768i
$768$	19.4064	+	33.6129i	0.700269	+	1.21290i
$769$	−23.5424	−	40.7766i	−0.848959	−	1.47044i	−0.882138	−	0.470991i	$-0.843896\pi$
$769$	−23.5424	−	40.7766i	−0.848959	−	1.47044i	0.0331785	−	0.999449i	$-0.489437\pi$
$770$		0			0
$771$	−6.83053	+	11.8308i	−0.245996	+	0.426077i
$772$	−32.7250	−	56.6813i	−1.17780	−	2.04001i
$773$	−14.2169	−	24.6244i	−0.511347	−	0.885679i	−0.999914	−	0.0131525i	$-0.995813\pi$
$773$	−14.2169	−	24.6244i	−0.511347	−	0.885679i	0.488566	−	0.872527i	$-0.337520\pi$
$774$	24.4542	+	42.3559i	0.878987	+	1.52245i
$775$	−1.08365	−	1.87694i	−0.0389260	−	0.0674218i
$776$	20.4901	−	35.4899i	0.735551	−	1.27401i
$777$		0			0
$778$	−33.4222	−	57.8890i	−1.19824	−	2.07542i
$779$	10.8167	+	18.7350i	0.387547	+	0.671251i
$780$	55.5252	+	6.76742i	1.98812	+	0.242312i
$781$	−9.81665	+	17.0029i	−0.351267	+	0.608413i
$782$	4.99082	−	8.64436i	0.178472	−	0.309122i
$783$	−3.25096	−	5.63083i	−0.116180	−	0.201230i
$784$		0			0
$785$	−1.42221			−0.0507607
$786$	−53.0917			−1.89372
$787$	15.6287	+	27.0697i	0.557102	+	0.964930i	0.997737	+	0.0672428i	$0.0214202\pi$
$787$	15.6287	+	27.0697i	0.557102	+	0.964930i	−0.440634	+	0.897687i	$0.645246\pi$
$788$	1.80278	−	3.12250i	0.0642212	−	0.111234i
$789$	33.4247			1.18995
$790$	16.4836	+	28.5504i	0.586459	+	1.01578i
$791$		0			0
$792$	24.9916			0.888038
$793$	−6.11943	−	14.3808i	−0.217307	−	0.510678i
$794$	−4.99082	+	8.64436i	−0.177118	+	0.306777i
$795$	11.2473			0.398899
$796$	11.8209	−	20.4743i	0.418979	−	0.725693i
$797$	−13.0038	+	22.5233i	−0.460620	+	0.797817i	−0.998992	−	0.0448902i	$-0.985706\pi$
$797$	−13.0038	+	22.5233i	−0.460620	+	0.797817i	0.538372	+	0.842707i	$0.319040\pi$
$798$		0			0
$799$	5.40833	−	9.36750i	0.191333	−	0.331398i
$800$	1.60555			0.0567648
$801$	−5.51761	+	9.55678i	−0.194955	+	0.337672i
$802$	11.6514	+	20.1808i	0.411425	+	0.712609i
$803$	10.6379	−	18.4253i	0.375402	−	0.650215i
$804$	−3.57907	−	6.19912i	−0.126224	−	0.218626i
$805$		0			0
$806$	35.7250	−	47.4967i	1.25836	−	1.67300i
$807$	0.711103	+	1.23167i	0.0250320	+	0.0433567i
$808$	−19.5058			−0.686211
$809$	20.0278			0.704138			0.352069	−	0.935974i	$-0.385478\pi$
$809$	20.0278			0.704138			0.352069	+	0.935974i	$0.385478\pi$
$810$	−55.9526			−1.96598
$811$	0.854892			0.0300193			0.0150097	−	0.999887i	$-0.495222\pi$
$811$	0.854892			0.0300193			0.0150097	+	0.999887i	$0.495222\pi$
$812$		0			0
$813$	−15.7292	+	27.2437i	−0.551647	+	0.955480i
$814$	−48.6333	−	84.2354i	−1.70460	−	2.95245i
$815$	3.02220	+	5.23460i	0.105863	+	0.183360i
$816$	4.69722			0.164436
$817$	13.5607	−	23.4878i	0.474429	−	0.821736i
$818$	8.01302			0.280169
$819$		0			0
$820$	−71.4500			−2.49514
$821$	27.9222	−	48.3627i	0.974492	−	1.68787i	0.292889	−	0.956146i	$-0.405383\pi$
$821$	27.9222	−	48.3627i	0.974492	−	1.68787i	0.681602	−	0.731723i	$-0.261283\pi$
$822$	31.4560			1.09716
$823$	−21.1333	−	36.6040i	−0.736661	−	1.27593i	−0.953991	−	0.299836i	$-0.903068\pi$
$823$	−21.1333	−	36.6040i	−0.736661	−	1.27593i	0.217330	−	0.976098i	$-0.430265\pi$
$824$	−17.2391	−	29.8590i	−0.600553	−	1.04019i
$825$	1.61044	−	2.78937i	0.0560684	−	0.0971133i
$826$		0			0
$827$	−16.7527			−0.582550			−0.291275	−	0.956639i	$-0.594079\pi$
$827$	−16.7527			−0.582550			−0.291275	+	0.956639i	$0.594079\pi$
$828$	−3.39445			−0.117965
$829$	50.7631			1.76308			0.881538	−	0.472113i	$-0.156508\pi$
$829$	50.7631			1.76308			0.881538	+	0.472113i	$0.156508\pi$
$830$	14.0917			0.489129
$831$	0.228762	+	0.396228i	0.00793567	+	0.0137450i
$832$	18.0940	+	42.5214i	0.627297	+	1.47417i
$833$		0			0
$834$	26.5458	+	45.9787i	0.919207	+	1.59211i
$835$	−12.4542	+	21.5712i	−0.430994	+	0.746504i
$836$	−17.5672	−	30.4273i	−0.607575	−	1.05235i
$837$	−10.1056	+	17.5033i	−0.349299	+	0.605004i
$838$	−39.4691			−1.36344
$839$	−6.73069	+	11.6579i	−0.232369	+	0.402475i	−0.958505	−	0.285076i	$-0.907981\pi$
$839$	−6.73069	+	11.6579i	−0.232369	+	0.402475i	0.726136	+	0.687551i	$0.241314\pi$
$840$		0			0
$841$	11.8486	−	20.5224i	0.408573	−	0.707669i
$842$	−5.78890	+	10.0267i	−0.199499	+	0.345542i
$843$	51.6180			1.77782
$844$	−24.7708	+	42.9043i	−0.852647	+	1.47683i
$845$	27.3502	+	6.76742i	0.940875	+	0.232806i
$846$	−5.90587			−0.203048
$847$		0			0
$848$	−0.362490	−	0.627852i	−0.0124480	−	0.0215605i
$849$	40.4222			1.38729
$850$	2.49541	−	4.32218i	0.0855919	−	0.148250i
$851$	2.60555	+	4.51295i	0.0893171	+	0.154702i
$852$	28.6325			0.980934
$853$	12.8052			0.438440			0.219220	−	0.975675i	$-0.429649\pi$
$853$	12.8052			0.438440			0.219220	+	0.975675i	$0.429649\pi$
$854$		0			0
$855$	−3.98612	−	6.90417i	−0.136322	−	0.236117i
$856$	−8.54584	+	14.8018i	−0.292091	+	0.505916i
$857$	−1.64052	+	2.84146i	−0.0560391	+	0.0970626i	−0.892684	−	0.450683i	$-0.851180\pi$
$857$	−1.64052	+	2.84146i	−0.0560391	+	0.0970626i	0.836645	+	0.547746i	$0.184514\pi$
$858$	87.6749	+	10.6858i	2.99317	+	0.364808i
$859$	−1.51110	−	2.61730i	−0.0515581	−	0.0893012i	0.839095	−	0.543986i	$-0.183085\pi$
$859$	−1.51110	−	2.61730i	−0.0515581	−	0.0893012i	−0.890653	+	0.454684i	$0.849752\pi$
$860$	44.7880	+	77.5751i	1.52726	+	2.64529i
$861$		0			0
$862$	24.1056	−	41.7520i	0.821038	−	1.42208i
$863$	−4.90833	−	8.50147i	−0.167081	−	0.289393i	0.770311	−	0.637668i	$-0.220101\pi$
$863$	−4.90833	−	8.50147i	−0.167081	−	0.289393i	−0.937392	+	0.348275i	$0.886768\pi$
$864$	−7.48624	−	12.9665i	−0.254687	−	0.441131i
$865$	−11.0320	−	19.1079i	−0.375098	−	0.649689i
$866$	−19.7345	−	34.1812i	−0.670607	−	1.16153i
$867$	−37.1031	+	64.2644i	−1.26009	+	2.18253i
$868$		0			0
$869$	16.2111	+	28.0785i	0.549924	+	0.952496i
$870$	12.4542	+	21.5712i	0.422236	+	0.731334i
$871$	−1.41176	−	3.31767i	−0.0478356	−	0.112415i
$872$	−12.3167	+	21.3331i	−0.417095	+	0.722429i
$873$	11.5921	−	20.0781i	0.392333	−	0.679540i
$874$	1.51110	+	2.61730i	0.0511137	+	0.0885316i
$875$		0			0
$876$	−31.0278			−1.04833
$877$	−45.6056			−1.53999			−0.769995	−	0.638050i	$-0.779741\pi$
$877$	−45.6056			−1.53999			−0.769995	+	0.638050i	$0.779741\pi$
$878$	4.23527	+	7.33571i	0.142934	+	0.247568i
$879$	31.0278	−	53.7417i	1.04654	−	1.81266i
$880$	3.22088			0.108576
$881$	−9.42478	−	16.3242i	−0.317529	−	0.549976i	0.662443	−	0.749112i	$-0.269520\pi$
$881$	−9.42478	−	16.3242i	−0.317529	−	0.549976i	−0.979972	+	0.199136i	$0.936186\pi$
$882$		0			0
$883$	−24.3944			−0.820939			−0.410469	−	0.911874i	$-0.634635\pi$
$883$	−24.3944			−0.820939			−0.410469	+	0.911874i	$0.634635\pi$
$884$	84.6152	+	10.3129i	2.84592	+	0.346861i
$885$	6.63134	−	11.4858i	0.222910	−	0.386092i
$886$	−46.6056			−1.56574
$887$	−17.3385	+	30.0311i	−0.582169	+	1.00835i	0.413053	+	0.910707i	$0.364462\pi$
$887$	−17.3385	+	30.0311i	−0.582169	+	1.00835i	−0.995222	+	0.0976388i	$0.968871\pi$
$888$	−27.9763	+	48.4564i	−0.938824	+	1.62609i
$889$		0			0
$890$	−16.2250	+	28.1025i	−0.543863	+	0.941998i
$891$	−55.0278			−1.84350
$892$	29.7162	−	51.4699i	0.994971	−	1.72334i
$893$	1.63751	+	2.83625i	0.0547972	+	0.0949115i
$894$	43.7043	−	75.6981i	1.46169	−	2.53172i
$895$	−23.4129	−	40.5524i	−0.782608	−	1.35552i
$896$		0			0
$897$	−4.69722	−	0.572498i	−0.156836	−	0.0191152i
$898$	23.5139	+	40.7272i	0.784668	+	1.35909i
$899$	16.4836			0.549758
$900$	−1.69722			−0.0565741
$901$	17.1398			0.571009
$902$	−112.820			−3.75651
$903$		0			0
$904$	−10.2250	+	17.7102i	−0.340078	+	0.589032i
$905$	26.3305	+	45.6058i	0.875256	+	1.51599i
$906$	−20.4901	−	35.4899i	−0.680737	−	1.17907i
$907$	−38.8444			−1.28981			−0.644904	−	0.764264i	$-0.723103\pi$
$907$	−38.8444			−1.28981			−0.644904	+	0.764264i	$0.723103\pi$
$908$	30.4717	−	52.7786i	1.01124	−	1.75152i
$909$	−11.0352			−0.366015
$910$		0			0
$911$	35.9361			1.19062			0.595308	−	0.803498i	$-0.297030\pi$
$911$	35.9361			1.19062			0.595308	+	0.803498i	$0.297030\pi$
$912$	−0.711103	+	1.23167i	−0.0235470	+	0.0407845i
$913$	13.8587			0.458657
$914$	−23.7250	−	41.0929i	−0.784753	−	1.35923i
$915$	−10.1803	−	17.6329i	−0.336551	−	0.582924i
$916$	25.8090	−	44.7025i	0.852754	−	1.47701i
$917$		0			0
$918$	−46.5416			−1.53610
$919$	53.4500			1.76315			0.881576	−	0.472043i	$-0.156483\pi$
$919$	53.4500			1.76315			0.881576	+	0.472043i	$0.156483\pi$
$920$	−3.93725			−0.129807
$921$	7.97224			0.262694
$922$	28.9606	+	50.1613i	0.953768	+	1.65197i
$923$	14.3163	+	1.74487i	0.471226	+	0.0574330i
$924$		0			0
$925$	1.30278	+	2.25647i	0.0428350	+	0.0741924i
$926$	15.8764	−	27.4987i	0.521730	−	0.903663i
$927$	−9.75289	−	16.8925i	−0.320327	−	0.554822i
$928$	−6.10555	+	10.5751i	−0.200425	+	0.347145i
$929$	−17.1398			−0.562338			−0.281169	−	0.959658i	$-0.590722\pi$
$929$	−17.1398			−0.562338			−0.281169	+	0.959658i	$0.590722\pi$
$930$	38.7135	−	67.0538i	1.26947	−	2.19878i
$931$		0			0
$932$	21.6194	−	37.4460i	0.708168	−	1.22658i
$933$	−11.5278	+	19.9667i	−0.377402	+	0.653679i
$934$	29.4874			0.964858
$935$	−38.0736	+	65.9454i	−1.24514	+	2.15665i
$936$	−7.18821	−	16.8925i	−0.234954	−	0.552148i
$937$	−19.7646			−0.645682			−0.322841	−	0.946453i	$-0.604638\pi$
$937$	−19.7646			−0.645682			−0.322841	+	0.946453i	$0.604638\pi$
$938$		0			0
$939$	6.11943	+	10.5992i	0.199700	+	0.345891i
$940$	−10.8167			−0.352800
$941$	2.72417	−	4.71841i	0.0888055	−	0.153816i	−0.818201	−	0.574932i	$-0.805028\pi$
$941$	2.72417	−	4.71841i	0.0888055	−	0.153816i	0.907006	+	0.421117i	$0.138362\pi$
$942$	1.63751	+	2.83625i	0.0533529	+	0.0924100i
$943$	6.04440			0.196833
$944$	−0.854892			−0.0278244
$945$		0			0
$946$	70.7208	+	122.492i	2.29933	+	3.98256i
$947$	−13.9403	+	24.1453i	−0.452998	+	0.784616i	−0.998571	−	0.0534475i	$-0.982979\pi$
$947$	−13.9403	+	24.1453i	−0.452998	+	0.784616i	0.545572	+	0.838064i	$0.316312\pi$
$948$	23.6417	−	40.9486i	0.767847	−	1.32995i
$949$	−15.5139	−	1.89083i	−0.503602	−	0.0613790i
$950$	0.755550	+	1.30865i	0.0245133	+	0.0424582i
$951$	6.73069	+	11.6579i	0.218257	+	0.378033i
$952$		0			0
$953$	−17.1972	+	29.7865i	−0.557073	+	0.964878i	0.440666	+	0.897671i	$0.354742\pi$
$953$	−17.1972	+	29.7865i	−0.557073	+	0.964878i	−0.997739	+	0.0672073i	$0.978591\pi$
$954$	−4.67914	−	8.10452i	−0.151493	−	0.262393i
$955$	−17.0104	−	29.4628i	−0.550442	−	0.953394i
$956$	−7.25694	−	12.5694i	−0.234706	−	0.406523i
$957$	12.2483	+	21.2147i	0.395931	+	0.685773i
$958$	18.9790	−	32.8726i	0.613183	−	1.06206i
$959$		0			0
$960$	30.1013	+	52.1371i	0.971517	+	1.68272i
$961$	−10.1194	−	17.5274i	−0.326433	−	0.565399i
$962$	−42.9488	+	57.1008i	−1.38472	+	1.84100i
$963$	−4.83473	+	8.37400i	−0.155797	+	0.269849i
$964$	15.3999	−	26.6734i	0.495998	−	0.859094i
$965$	−21.4744	−	37.1947i	−0.691285	−	1.19734i
$966$		0			0
$967$	−42.4500			−1.36510			−0.682549	−	0.730839i	$-0.739129\pi$
$967$	−42.4500			−1.36510			−0.682549	+	0.730839i	$0.739129\pi$
$968$	39.2750			1.26235
$969$	−16.8117	−	29.1187i	−0.540069	−	0.935427i
$970$	34.0875	−	59.0412i	1.09448	−	1.89570i
$971$	−31.4560			−1.00947			−0.504736	−	0.863274i	$-0.668410\pi$
$971$	−31.4560			−1.00947			−0.504736	+	0.863274i	$0.668410\pi$
$972$	26.1371	+	45.2708i	0.838348	+	1.45206i
$973$		0			0
$974$	−72.0833			−2.30970
$975$	−2.34861	−	0.286249i	−0.0752158	−	0.00916731i
$976$	−0.656208	+	1.13659i	−0.0210047	+	0.0363812i
$977$	−3.97224			−0.127083			−0.0635417	−	0.997979i	$-0.520240\pi$
$977$	−3.97224			−0.127083			−0.0635417	+	0.997979i	$0.520240\pi$
$978$	6.95945	−	12.0541i	0.222539	−	0.385448i
$979$	−15.9568	+	27.6380i	−0.509981	+	0.883313i
$980$		0			0
$981$	−6.96804	+	12.0690i	−0.222472	+	0.385334i
$982$	45.4222			1.44948
$983$	−14.6444	+	25.3648i	−0.467083	+	0.809011i	−0.999293	−	0.0376012i	$-0.988028\pi$
$983$	−14.6444	+	25.3648i	−0.467083	+	0.809011i	0.532210	+	0.846612i	$0.321362\pi$
$984$	32.4500	+	56.2050i	1.03447	+	1.79175i
$985$	1.18300	−	2.04901i	0.0376934	−	0.0652869i
$986$	18.9790	+	32.8726i	0.604414	+	1.04688i
$987$		0			0
$988$	−15.5139	+	20.6258i	−0.493562	+	0.656195i
$989$	−3.78890	−	6.56256i	−0.120480	−	0.208677i
$990$	41.5762			1.32138
$991$	−6.66947			−0.211863			−0.105931	−	0.994373i	$-0.533782\pi$
$991$	−6.66947			−0.211863			−0.105931	+	0.994373i	$0.533782\pi$
$992$	37.9580			1.20517
$993$	9.32544			0.295934
$994$		0			0
$995$	7.75694	−	13.4354i	0.245912	−	0.425931i
$996$	−10.1056	−	17.5033i	−0.320207	−	0.554614i
$997$	−26.3659	−	45.6670i	−0.835016	−	1.44629i	−0.894018	−	0.448032i	$-0.852125\pi$
$997$	−26.3659	−	45.6670i	−0.835016	−	1.44629i	0.0590018	−	0.998258i	$-0.481208\pi$
$998$	−19.1833			−0.607238
$999$	12.1490	−	21.0426i	0.384376	−	0.665759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.i.263.2		8
7.2	even	3		637.2.h.j.471.3		8
7.3	odd	6		637.2.f.h.393.2	yes	8
7.4	even	3		637.2.f.h.393.1	yes	8
7.5	odd	6		637.2.h.j.471.4		8
7.6	odd	2	inner	637.2.g.i.263.1		8
13.9	even	3		637.2.h.j.165.3		8
91.3	odd	6		8281.2.a.bu.1.3		4
91.9	even	3	inner	637.2.g.i.373.2		8
91.10	odd	6		8281.2.a.bo.1.1		4
91.48	odd	6		637.2.h.j.165.4		8
91.61	odd	6	inner	637.2.g.i.373.1		8
91.74	even	3		637.2.f.h.295.1	✓	8
91.81	even	3		8281.2.a.bu.1.4		4
91.87	odd	6		637.2.f.h.295.2	yes	8
91.88	even	6		8281.2.a.bo.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.h.295.1	✓	8	91.74	even	3
637.2.f.h.295.2	yes	8	91.87	odd	6
637.2.f.h.393.1	yes	8	7.4	even	3
637.2.f.h.393.2	yes	8	7.3	odd	6
637.2.g.i.263.1		8	7.6	odd	2	inner
637.2.g.i.263.2		8	1.1	even	1	trivial
637.2.g.i.373.1		8	91.61	odd	6	inner
637.2.g.i.373.2		8	91.9	even	3	inner
637.2.h.j.165.3		8	13.9	even	3
637.2.h.j.165.4		8	91.48	odd	6
637.2.h.j.471.3		8	7.2	even	3
637.2.h.j.471.4		8	7.5	odd	6
8281.2.a.bo.1.1		4	91.10	odd	6
8281.2.a.bo.1.2		4	91.88	even	6
8281.2.a.bu.1.3		4	91.3	odd	6
8281.2.a.bu.1.4		4	91.81	even	3

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15139 + 1.99426i) q^{2} +2.16731 q^{3} +(-1.65139 - 2.86029i) q^{4} +(-1.08365 - 1.87694i) q^{5} +(-2.49541 + 4.32218i) q^{6} +3.00000 q^{8} +1.69722 q^{9} +4.99082 q^{10} +4.90833 q^{11} +(-3.57907 - 6.19912i) q^{12} +(-1.41176 - 3.31767i) q^{13} +(-2.34861 - 4.06792i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(-3.57907 - 6.19912i) q^{17} +(-1.95416 + 3.38471i) q^{18} +2.16731 q^{19} +(-3.57907 + 6.19912i) q^{20} +(-5.65139 + 9.78849i) q^{22} +(0.302776 - 0.524423i) q^{23} +6.50192 q^{24} +(0.151388 - 0.262211i) q^{25} +(8.24179 + 1.00451i) q^{26} -2.82352 q^{27} +(1.15139 + 1.99426i) q^{29} +10.8167 q^{30} +(3.57907 - 6.19912i) q^{31} +(2.65139 + 4.59234i) q^{32} +10.6379 q^{33} +16.4836 q^{34} +(-2.80278 - 4.85455i) q^{36} +(-4.30278 + 7.45263i) q^{37} +(-2.49541 + 4.32218i) q^{38} +(-3.05971 - 7.19041i) q^{39} +(-3.25096 - 5.63083i) q^{40} +(4.99082 + 8.64436i) q^{41} +(6.25694 - 10.8373i) q^{43} +(-8.10555 - 14.0392i) q^{44} +(-1.83920 - 3.18559i) q^{45} +(0.697224 + 1.20763i) q^{46} +(0.755550 + 1.30865i) q^{47} +(-0.328104 + 0.568293i) q^{48} +(0.348612 + 0.603814i) q^{50} +(-7.75694 - 13.4354i) q^{51} +(-7.15813 + 9.51680i) q^{52} +(-1.19722 + 2.07365i) q^{53} +(3.25096 - 5.63083i) q^{54} +(-5.31893 - 9.21265i) q^{55} +4.69722 q^{57} -5.30278 q^{58} +(1.41176 + 2.44524i) q^{59} +(-7.75694 + 13.4354i) q^{60} +4.33462 q^{61} +(8.24179 + 14.2752i) q^{62} -12.8167 q^{64} +(-4.69722 + 6.24500i) q^{65} +(-12.2483 + 21.2147i) q^{66} +1.00000 q^{67} +(-11.8209 + 20.4743i) q^{68} +(0.656208 - 1.13659i) q^{69} +(-2.00000 + 3.46410i) q^{71} +5.09167 q^{72} +(2.16731 - 3.75389i) q^{73} +(-9.90833 - 17.1617i) q^{74} +(0.328104 - 0.568293i) q^{75} +(-3.57907 - 6.19912i) q^{76} +(17.8625 + 2.17708i) q^{78} +(3.30278 + 5.72058i) q^{79} +0.656208 q^{80} -11.2111 q^{81} -22.9855 q^{82} +2.82352 q^{83} +(-7.75694 + 13.4354i) q^{85} +(14.4083 + 24.9560i) q^{86} +(2.49541 + 4.32218i) q^{87} +14.7250 q^{88} +(-3.25096 + 5.63083i) q^{89} +8.47055 q^{90} -2.00000 q^{92} +(7.75694 - 13.4354i) q^{93} -3.47972 q^{94} +(-2.34861 - 4.06792i) q^{95} +(5.74637 + 9.95301i) q^{96} +(6.83003 - 11.8300i) q^{97} +8.33053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9} - 4 q^{11} - 26 q^{15} + 6 q^{16} + 6 q^{18} - 38 q^{22} - 12 q^{23} - 6 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44}+ \cdots - 92 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 28 * q^9 - 4 * q^11 - 26 * q^15 + 6 * q^16 + 6 * q^18 - 38 * q^22 - 12 * q^23 - 6 * q^25 + 2 * q^29 + 14 * q^32 - 8 * q^36 - 20 * q^37 + 26 * q^39 + 14 * q^43 - 36 * q^44 + 20 * q^46 + 10 * q^50 - 26 * q^51 - 24 * q^53 + 52 * q^57 - 28 * q^58 - 26 * q^60 - 16 * q^64 - 52 * q^65 + 8 * q^67 - 16 * q^71 + 84 * q^72 - 36 * q^74 + 78 * q^78 + 12 * q^79 - 32 * q^81 - 26 * q^85 + 72 * q^86 - 12 * q^88 - 16 * q^92 + 26 * q^93 - 26 * q^95 - 92 * q^99

Introduction

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