LMFDB - Embedded newform 637.2.g.i.263.3

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			263.3
Root			$-1.87694 - 1.08365i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.i.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.651388 - 1.12824i) q^{2} -2.88145 q^{3} +(0.151388 + 0.262211i) q^{4} +(1.44073 + 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +5.30278 q^{9} +O(q^{10})$	\(q+(0.651388 - 1.12824i) q^{2} -2.88145 q^{3} +(0.151388 + 0.262211i) q^{4} +(1.44073 + 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +5.30278 q^{9} +3.75389 q^{10} -5.90833 q^{11} +(-0.436217 - 0.755550i) q^{12} +(-3.31767 + 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} +(1.65139 - 2.86029i) q^{16} +(-0.436217 - 0.755550i) q^{17} +(3.45416 - 5.98279i) q^{18} -2.88145 q^{19} +(-0.436217 + 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +(-3.30278 + 5.72058i) q^{23} -8.64436 q^{24} +(-1.65139 + 2.86029i) q^{25} +(-0.568293 + 4.66272i) q^{26} -6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} -10.8167 q^{30} +(0.436217 - 0.755550i) q^{31} +(0.848612 + 1.46984i) q^{32} +17.0246 q^{33} -1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +(-0.697224 + 1.20763i) q^{37} +(-1.87694 + 3.25096i) q^{38} +(9.55971 - 4.06792i) q^{39} +(4.32218 + 7.48624i) q^{40} +(3.75389 + 6.50192i) q^{41} +(-2.75694 + 4.77516i) q^{43} +(-0.894449 - 1.54923i) q^{44} +(7.63985 + 13.2326i) q^{45} +(4.30278 + 7.45263i) q^{46} +(-6.19912 - 10.7372i) q^{47} +(-4.75840 + 8.24179i) q^{48} +(2.15139 + 3.72631i) q^{50} +(1.25694 + 2.17708i) q^{51} +(-0.872434 - 0.656208i) q^{52} +(-4.80278 + 8.31865i) q^{53} +(-4.32218 + 7.48624i) q^{54} +(-8.51229 - 14.7437i) q^{55} +8.30278 q^{57} -1.69722 q^{58} +(3.31767 + 5.74637i) q^{59} +(1.25694 - 2.17708i) q^{60} -5.76291 q^{61} +(-0.568293 - 0.984312i) q^{62} +8.81665 q^{64} +(-8.30278 - 6.24500i) q^{65} +(11.0896 - 19.2077i) q^{66} +1.00000 q^{67} +(0.132076 - 0.228762i) q^{68} +(9.51680 - 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +15.9083 q^{72} +(-2.88145 + 4.99082i) q^{73} +(0.908327 + 1.57327i) q^{74} +(4.75840 - 8.24179i) q^{75} +(-0.436217 - 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +(-0.302776 - 0.524423i) q^{79} +9.51680 q^{80} +3.21110 q^{81} +9.78095 q^{82} +6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} +(3.59167 + 6.22096i) q^{86} +(1.87694 + 3.25096i) q^{87} -17.7250 q^{88} +(4.32218 - 7.48624i) q^{89} +19.9060 q^{90} -2.00000 q^{92} +(-1.25694 + 2.17708i) q^{93} -16.1521 q^{94} +(-4.15139 - 7.19041i) q^{95} +(-2.44524 - 4.23527i) q^{96} +(-3.88596 + 6.73069i) q^{97} -31.3305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 28 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	0.651388	−	1.12824i	0.460601	−	0.797784i	−0.538390	−	0.842696i	$-0.680967\pi$
$2$	0.651388	−	1.12824i	0.460601	−	0.797784i	0.998991	+	0.0449118i	$0.0143007\pi$
$3$	−2.88145			−1.66361			−0.831804	−	0.555069i	$-0.812692\pi$
$3$	−2.88145			−1.66361			−0.831804	+	0.555069i	$0.812692\pi$
$4$	0.151388	+	0.262211i	0.0756939	+	0.131106i
$5$	1.44073	+	2.49541i	0.644313	+	1.11598i	0.984460	+	0.175610i	$0.0561898\pi$
$5$	1.44073	+	2.49541i	0.644313	+	1.11598i	−0.340147	+	0.940372i	$0.610477\pi$
$6$	−1.87694	+	3.25096i	−0.766259	+	1.32720i
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	5.30278			1.76759
$10$	3.75389			1.18708
$11$	−5.90833			−1.78143			−0.890714	−	0.454565i	$-0.849795\pi$
$11$	−5.90833			−1.78143			−0.890714	+	0.454565i	$0.849795\pi$
$12$	−0.436217	−	0.755550i	−0.125925	−	0.218108i
$13$	−3.31767	+	1.41176i	−0.920156	+	0.391551i
$13$	−3.31767	+	1.41176i	−0.920156	+	0.391551i
$14$		0			0
$15$	−4.15139	−	7.19041i	−1.07188	−	1.85656i
$16$	1.65139	−	2.86029i	0.412847	−	0.715072i
$17$	−0.436217	−	0.755550i	−0.105798	−	0.183248i	0.808266	−	0.588818i	$-0.200406\pi$
$17$	−0.436217	−	0.755550i	−0.105798	−	0.183248i	−0.914064	+	0.405570i	$0.867073\pi$
$18$	3.45416	−	5.98279i	0.814154	−	1.41016i
$19$	−2.88145			−0.661051			−0.330525	−	0.943797i	$-0.607226\pi$
$19$	−2.88145			−0.661051			−0.330525	+	0.943797i	$0.607226\pi$
$20$	−0.436217	+	0.755550i	−0.0975411	+	0.168946i
$21$		0			0
$22$	−3.84861	+	6.66599i	−0.820527	+	1.42119i
$23$	−3.30278	+	5.72058i	−0.688676	+	1.19282i	0.283590	+	0.958946i	$0.408475\pi$
$23$	−3.30278	+	5.72058i	−0.688676	+	1.19282i	−0.972266	+	0.233877i	$0.924859\pi$
$24$	−8.64436			−1.76452
$25$	−1.65139	+	2.86029i	−0.330278	+	0.572058i
$26$	−0.568293	+	4.66272i	−0.111451	+	0.914435i
$27$	−6.63534			−1.27697
$28$		0			0
$29$	−0.651388	−	1.12824i	−0.120960	−	0.209508i	0.799187	−	0.601083i	$-0.205264\pi$
$29$	−0.651388	−	1.12824i	−0.120960	−	0.209508i	−0.920146	+	0.391575i	$0.871931\pi$
$30$	−10.8167			−1.97484
$31$	0.436217	−	0.755550i	0.0783469	−	0.135701i	−0.824190	−	0.566313i	$-0.808369\pi$
$31$	0.436217	−	0.755550i	0.0783469	−	0.135701i	0.902537	+	0.430613i	$0.141702\pi$
$32$	0.848612	+	1.46984i	0.150015	+	0.259833i
$33$	17.0246			2.96360
$34$	−1.13659			−0.194923
$35$		0			0
$36$	0.802776	+	1.39045i	0.133796	+	0.231741i
$37$	−0.697224	+	1.20763i	−0.114623	+	0.198533i	−0.917629	−	0.397438i	$-0.869899\pi$
$37$	−0.697224	+	1.20763i	−0.114623	+	0.198533i	0.803006	+	0.595971i	$0.203233\pi$
$38$	−1.87694	+	3.25096i	−0.304481	+	0.527376i
$39$	9.55971	−	4.06792i	1.53078	−	0.651388i
$40$	4.32218	+	7.48624i	0.683397	+	1.18368i
$41$	3.75389	+	6.50192i	0.586259	+	1.01543i	0.994717	+	0.102653i	$0.0327331\pi$
$41$	3.75389	+	6.50192i	0.586259	+	1.01543i	−0.408458	+	0.912777i	$0.633934\pi$
$42$		0			0
$43$	−2.75694	+	4.77516i	−0.420429	+	0.728205i	−0.995981	−	0.0895602i	$-0.971454\pi$
$43$	−2.75694	+	4.77516i	−0.420429	+	0.728205i	0.575552	+	0.817765i	$0.304787\pi$
$44$	−0.894449	−	1.54923i	−0.134843	−	0.233555i
$45$	7.63985	+	13.2326i	1.13888	+	1.97260i
$46$	4.30278	+	7.45263i	0.634410	+	1.09883i
$47$	−6.19912	−	10.7372i	−0.904235	−	1.56618i	−0.821941	−	0.569573i	$-0.807108\pi$
$47$	−6.19912	−	10.7372i	−0.904235	−	1.56618i	−0.0822947	−	0.996608i	$-0.526225\pi$
$48$	−4.75840	+	8.24179i	−0.686816	+	1.18960i
$49$		0			0
$50$	2.15139	+	3.72631i	0.304252	+	0.526980i
$51$	1.25694	+	2.17708i	0.176007	+	0.304853i
$52$	−0.872434	−	0.656208i	−0.120985	−	0.0909997i
$53$	−4.80278	+	8.31865i	−0.659712	+	1.14265i	0.320978	+	0.947087i	$0.395988\pi$
$53$	−4.80278	+	8.31865i	−0.659712	+	1.14265i	−0.980690	+	0.195568i	$0.937345\pi$
$54$	−4.32218	+	7.48624i	−0.588174	+	1.01875i
$55$	−8.51229	−	14.7437i	−1.14780	−	1.98804i
$56$		0			0
$57$	8.30278			1.09973
$58$	−1.69722			−0.222856
$59$	3.31767	+	5.74637i	0.431924	+	0.748114i	0.997039	−	0.0768979i	$-0.0245016\pi$
$59$	3.31767	+	5.74637i	0.431924	+	0.748114i	−0.565115	+	0.825012i	$0.691168\pi$
$60$	1.25694	−	2.17708i	0.162270	−	0.281060i
$61$	−5.76291			−0.737865			−0.368932	−	0.929456i	$-0.620277\pi$
$61$	−5.76291			−0.737865			−0.368932	+	0.929456i	$0.620277\pi$
$62$	−0.568293	−	0.984312i	−0.0721733	−	0.125008i
$63$		0			0
$64$	8.81665			1.10208
$65$	−8.30278	−	6.24500i	−1.02983	−	0.774597i
$66$	11.0896	−	19.2077i	1.36504	−	2.36431i
$67$	1.00000			0.122169			0.0610847	−	0.998133i	$-0.480544\pi$
$67$	1.00000			0.122169			0.0610847	+	0.998133i	$0.480544\pi$
$68$	0.132076	−	0.228762i	0.0160166	−	0.0277415i
$69$	9.51680	−	16.4836i	1.14569	−	1.98439i
$70$		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	$0.242948\pi$
$72$	15.9083			1.87481
$73$	−2.88145	+	4.99082i	−0.337249	+	0.584132i	−0.983914	−	0.178642i	$-0.942830\pi$
$73$	−2.88145	+	4.99082i	−0.337249	+	0.584132i	0.646666	+	0.762774i	$0.276163\pi$
$74$	0.908327	+	1.57327i	0.105591	+	0.182889i
$75$	4.75840	−	8.24179i	0.549452	−	0.951680i
$76$	−0.436217	−	0.755550i	−0.0500375	−	0.0866675i
$77$		0			0
$78$	1.63751	−	13.4354i	0.185411	−	1.52126i
$79$	−0.302776	−	0.524423i	−0.0340649	−	0.0590022i	0.848490	−	0.529211i	$-0.177512\pi$
$79$	−0.302776	−	0.524423i	−0.0340649	−	0.0590022i	−0.882555	+	0.470209i	$0.844179\pi$
$80$	9.51680			1.06401
$81$	3.21110			0.356789
$82$	9.78095			1.08012
$83$	6.63534			0.728323			0.364162	−	0.931336i	$-0.381356\pi$
$83$	6.63534			0.728323			0.364162	+	0.931336i	$0.381356\pi$
$84$		0			0
$85$	1.25694	−	2.17708i	0.136334	−	0.236138i
$86$	3.59167	+	6.22096i	0.387300	+	0.670823i
$87$	1.87694	+	3.25096i	0.201230	+	0.348540i
$88$	−17.7250			−1.88949
$89$	4.32218	−	7.48624i	0.458150	−	0.793539i	−0.540713	−	0.841207i	$-0.681846\pi$
$89$	4.32218	−	7.48624i	0.458150	−	0.793539i	0.998863	+	0.0476677i	$0.0151788\pi$
$90$	19.9060			2.09828
$91$		0			0
$92$	−2.00000			−0.208514
$93$	−1.25694	+	2.17708i	−0.130339	+	0.225753i
$94$	−16.1521			−1.66597
$95$	−4.15139	−	7.19041i	−0.425923	−	0.737721i
$96$	−2.44524	−	4.23527i	−0.249566	−	0.432261i
$97$	−3.88596	+	6.73069i	−0.394560	+	0.683398i	−0.993045	−	0.117736i	$-0.962436\pi$
$97$	−3.88596	+	6.73069i	−0.394560	+	0.683398i	0.598485	+	0.801134i	$0.295770\pi$
$98$		0			0
$99$	−31.3305			−3.14884
$100$	−1.00000			−0.100000
$101$	8.64436			0.860146			0.430073	−	0.902794i	$-0.358488\pi$
$101$	8.64436			0.860146			0.430073	+	0.902794i	$0.358488\pi$
$102$	3.27502			0.324275
$103$	2.44524	+	4.23527i	0.240936	+	0.417314i	0.960981	−	0.276613i	$-0.0892122\pi$
$103$	2.44524	+	4.23527i	0.240936	+	0.417314i	−0.720045	+	0.693927i	$0.755879\pi$
$104$	−9.95301	+	4.23527i	−0.975973	+	0.415303i
$105$		0			0
$106$	6.25694	+	10.8373i	0.607728	+	1.05262i
$107$	−4.65139	+	8.05644i	−0.449667	+	0.778845i	−0.998364	−	0.0571755i	$-0.981791\pi$
$107$	−4.65139	+	8.05644i	−0.449667	+	0.778845i	0.548698	+	0.836021i	$0.315124\pi$
$108$	−1.00451	−	1.73986i	−0.0966590	−	0.167418i
$109$	3.10555	−	5.37897i	0.297458	−	0.515212i	−0.678096	−	0.734974i	$-0.737195\pi$
$109$	3.10555	−	5.37897i	0.297458	−	0.515212i	0.975554	+	0.219761i	$0.0705279\pi$
$110$	−22.1792			−2.11470
$111$	2.00902	−	3.47972i	0.190688	−	0.330281i
$112$		0			0
$113$	7.40833	−	12.8316i	0.696917	−	1.20710i	−0.272613	−	0.962124i	$-0.587888\pi$
$113$	7.40833	−	12.8316i	0.696917	−	1.20710i	0.969530	−	0.244972i	$-0.0787786\pi$
$114$	5.40833	−	9.36750i	0.506536	−	0.877346i
$115$	−19.0336			−1.77489
$116$	0.197224	−	0.341603i	0.0183118	−	0.0317170i
$117$	−17.5929	+	7.48624i	−1.62646	+	0.692103i
$118$	8.64436			0.795778
$119$		0			0
$120$	−12.4542	−	21.5712i	−1.13690	−	1.96918i
$121$	23.9083			2.17348
$122$	−3.75389	+	6.50192i	−0.339861	+	0.588657i
$123$	−10.8167	−	18.7350i	−0.975305	−	1.68928i
$124$	0.264152			0.0237215
$125$	4.89047			0.437417
$126$		0			0
$127$	1.45416	+	2.51868i	0.129036	+	0.223497i	0.923303	−	0.384071i	$-0.125478\pi$
$127$	1.45416	+	2.51868i	0.129036	+	0.223497i	−0.794267	+	0.607569i	$0.792145\pi$
$128$	4.04584	−	7.00759i	0.357605	−	0.619390i
$129$	7.94399	−	13.7594i	0.699430	−	1.21145i
$130$	−12.4542	+	5.29958i	−1.09230	+	0.464804i
$131$	8.51229	+	14.7437i	0.743722	+	1.28816i	0.950790	+	0.309837i	$0.100275\pi$
$131$	8.51229	+	14.7437i	0.743722	+	1.28816i	−0.207068	+	0.978327i	$0.566392\pi$
$132$	2.57731	+	4.46404i	0.224326	+	0.388544i
$133$		0			0
$134$	0.651388	−	1.12824i	0.0562713	−	0.0974648i
$135$	−9.55971	−	16.5579i	−0.822769	−	1.42508i
$136$	−1.30865	−	2.26665i	−0.112216	−	0.194364i
$137$	−1.34861	−	2.33586i	−0.115220	−	0.199566i	0.802648	−	0.596453i	$-0.203424\pi$
$137$	−1.34861	−	2.33586i	−0.115220	−	0.199566i	−0.917868	+	0.396887i	$0.870091\pi$
$138$	−12.3982	−	21.4744i	−1.05541	−	1.82802i
$139$	8.51229	−	14.7437i	0.722003	−	1.25055i	−0.238193	−	0.971218i	$-0.576555\pi$
$139$	8.51229	−	14.7437i	0.722003	−	1.25055i	0.960196	−	0.279327i	$-0.0901115\pi$
$140$		0			0
$141$	17.8625	+	30.9387i	1.50429	+	2.60551i
$142$	2.60555	+	4.51295i	0.218653	+	0.378718i
$143$	19.6019	−	8.34113i	1.63919	−	0.697520i
$144$	8.75694	−	15.1675i	0.729745	−	1.26396i
$145$	1.87694	−	3.25096i	0.155872	−	0.269978i
$146$	3.75389	+	6.50192i	0.310674	+	0.538103i
$147$		0			0
$148$	−0.422205			−0.0347050
$149$	0.513878			0.0420985			0.0210493	−	0.999778i	$-0.493299\pi$
$149$	0.513878			0.0420985			0.0210493	+	0.999778i	$0.493299\pi$
$150$	−6.19912	−	10.7372i	−0.506156	−	0.876689i
$151$	3.10555	−	5.37897i	0.252726	−	0.437735i	−0.711549	−	0.702636i	$-0.752006\pi$
$151$	3.10555	−	5.37897i	0.252726	−	0.437735i	0.964275	+	0.264902i	$0.0853395\pi$
$152$	−8.64436			−0.701150
$153$	−2.31316	−	4.00651i	−0.187008	−	0.323907i
$154$		0			0
$155$	2.51388			0.201920
$156$	2.51388	+	1.89083i	0.201271	+	0.151388i
$157$	4.75840	−	8.24179i	0.379761	−	0.657766i	−0.611266	−	0.791425i	$-0.709339\pi$
$157$	4.75840	−	8.24179i	0.379761	−	0.657766i	0.991027	+	0.133659i	$0.0426727\pi$
$158$	−0.788897			−0.0627613
$159$	13.8390	−	23.9698i	1.09750	−	1.90093i
$160$	−2.44524	+	4.23527i	−0.193313	+	0.334828i
$161$		0			0
$162$	2.09167	−	3.62288i	0.164337	−	0.284641i
$163$	−17.2111			−1.34808			−0.674039	−	0.738696i	$-0.735442\pi$
$163$	−17.2111			−1.34808			−0.674039	+	0.738696i	$0.735442\pi$
$164$	−1.13659	+	1.96862i	−0.0887524	+	0.153724i
$165$	24.5278	+	42.4833i	1.90948	+	3.30732i
$166$	4.32218	−	7.48624i	0.335466	−	0.581045i
$167$	2.44524	+	4.23527i	0.189218	+	0.327735i	0.944990	−	0.327100i	$-0.106071\pi$
$167$	2.44524	+	4.23527i	0.189218	+	0.327735i	−0.755772	+	0.654835i	$0.772738\pi$
$168$		0			0
$169$	9.01388	−	9.36750i	0.693375	−	0.720577i
$170$	−1.63751	−	2.83625i	−0.125591	−	0.217530i
$171$	−15.2797			−1.16847
$172$	−1.66947			−0.127296
$173$	−23.9241			−1.81891			−0.909456	−	0.415799i	$-0.863502\pi$
$173$	−23.9241			−1.81891			−0.909456	+	0.415799i	$0.863502\pi$
$174$	4.89047			0.370746
$175$		0			0
$176$	−9.75694	+	16.8995i	−0.735457	+	1.27385i
$177$	−9.55971	−	16.5579i	−0.718552	−	1.24457i
$178$	−5.63083	−	9.75289i	−0.422049	−	0.731010i
$179$	14.3944			1.07589			0.537946	−	0.842979i	$-0.319200\pi$
$179$	14.3944			1.07589			0.537946	+	0.842979i	$0.319200\pi$
$180$	−2.31316	+	4.00651i	−0.172413	+	0.298628i
$181$	−9.25264			−0.687744			−0.343872	−	0.939017i	$-0.611739\pi$
$181$	−9.25264			−0.687744			−0.343872	+	0.939017i	$0.611739\pi$
$182$		0			0
$183$	16.6056			1.22752
$184$	−9.90833	+	17.1617i	−0.730452	+	1.26518i
$185$	−4.01804			−0.295412
$186$	1.63751	+	2.83625i	0.120068	+	0.207964i
$187$	2.57731	+	4.46404i	0.188472	+	0.326443i
$188$	1.87694	−	3.25096i	0.136890	−	0.237101i
$189$		0			0
$190$	−10.8167			−0.784723
$191$	19.3028			1.39670			0.698350	−	0.715757i	$-0.253918\pi$
$191$	19.3028			1.39670			0.698350	+	0.715757i	$0.253918\pi$
$192$	−25.4048			−1.83343
$193$	−1.81665			−0.130766			−0.0653828	−	0.997860i	$-0.520827\pi$
$193$	−1.81665			−0.130766			−0.0653828	+	0.997860i	$0.520827\pi$
$194$	5.06254	+	8.76857i	0.363469	+	0.629547i
$195$	23.9241	+	17.9947i	1.71324	+	1.28863i
$196$		0			0
$197$	5.95416	+	10.3129i	0.424217	+	0.734765i	0.996347	−	0.0853980i	$-0.0272162\pi$
$197$	5.95416	+	10.3129i	0.424217	+	0.734765i	−0.572130	+	0.820163i	$0.693883\pi$
$198$	−20.4083	+	35.3483i	−1.45036	+	2.51209i
$199$	0.436217	+	0.755550i	0.0309226	+	0.0535595i	0.881073	−	0.472981i	$-0.156822\pi$
$199$	0.436217	+	0.755550i	0.0309226	+	0.0535595i	−0.850150	+	0.526541i	$0.823489\pi$
$200$	−4.95416	+	8.58086i	−0.350312	+	0.606759i
$201$	−2.88145			−0.203242
$202$	5.63083	−	9.75289i	0.396184	−	0.686211i
$203$		0			0
$204$	−0.380571	+	0.659168i	−0.0266453	+	0.0461510i
$205$	−10.8167	+	18.7350i	−0.755468	+	1.30851i
$206$	6.37119			0.443902
$207$	−17.5139	+	30.3349i	−1.21730	+	2.10842i
$208$	−1.44073	+	11.8209i	−0.0998964	+	0.819629i
$209$	17.0246			1.17761
$210$		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	$-0.339366\pi$
$212$	−2.90833			−0.199745
$213$	5.76291	−	9.98165i	0.394868	−	0.683931i
$214$	6.05971	+	10.4957i	0.414234	+	0.717474i
$215$	−15.8880			−1.08355
$216$	−19.9060			−1.35443
$217$		0			0
$218$	−4.04584	−	7.00759i	−0.274019	−	0.474614i
$219$	8.30278	−	14.3808i	0.561050	−	0.971766i
$220$	2.57731	−	4.46404i	0.173762	−	0.300965i
$221$	2.51388	+	1.89083i	0.169102	+	0.127191i
$222$	−2.61730	−	4.53330i	−0.175662	−	0.304255i
$223$	−6.76742	−	11.7215i	−0.453180	−	0.784930i	0.545402	−	0.838175i	$-0.316377\pi$
$223$	−6.76742	−	11.7215i	−0.453180	−	0.784930i	−0.998582	+	0.0532444i	$0.983044\pi$
$224$		0			0
$225$	−8.75694	+	15.1675i	−0.583796	+	1.01116i
$226$	−9.65139	−	16.7167i	−0.642001	−	1.11198i
$227$	13.7069	+	23.7410i	0.909759	+	1.57575i	0.814399	+	0.580306i	$0.197067\pi$
$227$	13.7069	+	23.7410i	0.909759	+	1.57575i	0.0953602	+	0.995443i	$0.469600\pi$
$228$	1.25694	+	2.17708i	0.0832428	+	0.144181i
$229$	10.3892	+	17.9947i	0.686540	+	1.18912i	0.972950	+	0.231015i	$0.0742045\pi$
$229$	10.3892	+	17.9947i	0.686540	+	1.18912i	−0.286411	+	0.958107i	$0.592462\pi$
$230$	−12.3982	+	21.4744i	−0.817516	+	1.41598i
$231$		0			0
$232$	−1.95416	−	3.38471i	−0.128297	−	0.222217i
$233$	11.9542	+	20.7052i	0.783143	+	1.35644i	0.930102	+	0.367301i	$0.119718\pi$
$233$	11.9542	+	20.7052i	0.783143	+	1.35644i	−0.146959	+	0.989143i	$0.546948\pi$
$234$	−3.01353	+	24.7254i	−0.197001	+	1.61635i
$235$	17.8625	−	30.9387i	1.16522	−	2.01822i
$236$	−1.00451	+	1.73986i	−0.0653880	+	0.113255i
$237$	0.872434	+	1.51110i	0.0566707	+	0.0981565i
$238$		0			0
$239$	11.6056			0.750701			0.375350	−	0.926883i	$-0.377522\pi$
$239$	11.6056			0.750701			0.375350	+	0.926883i	$0.377522\pi$
$240$	−27.4222			−1.77010
$241$	−1.00451	−	1.73986i	−0.0647062	−	0.112074i	0.831857	−	0.554989i	$-0.187278\pi$
$241$	−1.00451	−	1.73986i	−0.0647062	−	0.112074i	−0.896564	+	0.442915i	$0.853944\pi$
$242$	15.5736	−	26.9743i	1.00111	−	1.73397i
$243$	10.6534			0.683415
$244$	−0.872434	−	1.51110i	−0.0558519	−	0.0967383i
$245$		0			0
$246$	−28.1833			−1.79690
$247$	9.55971	−	4.06792i	0.608270	−	0.258835i
$248$	1.30865	−	2.26665i	0.0830994	−	0.143932i
$249$	−19.1194			−1.21164
$250$	3.18559	−	5.51761i	0.201475	−	0.348964i
$251$	−11.2617	+	19.5058i	−0.710830	+	1.23119i	0.253716	+	0.967279i	$0.418347\pi$
$251$	−11.2617	+	19.5058i	−0.710830	+	1.23119i	−0.964546	+	0.263915i	$0.914986\pi$
$252$		0			0
$253$	19.5139	−	33.7990i	1.22683	−	2.12493i
$254$	3.78890			0.237737
$255$	−3.62181	+	6.27316i	−0.226807	+	0.392841i
$256$	3.54584	+	6.14157i	0.221615	+	0.383848i
$257$	−11.3937	+	19.7345i	−0.710722	+	1.23101i	0.253865	+	0.967240i	$0.418298\pi$
$257$	−11.3937	+	19.7345i	−0.710722	+	1.23101i	−0.964587	+	0.263767i	$0.915035\pi$
$258$	−10.3492	−	17.9254i	−0.644316	−	1.11599i
$259$		0			0
$260$	0.380571	−	3.12250i	0.0236020	−	0.193649i
$261$	−3.45416	−	5.98279i	−0.213807	−	0.370325i
$262$	22.1792			1.37024
$263$	−13.4222			−0.827649			−0.413824	−	0.910357i	$-0.635807\pi$
$263$	−13.4222			−0.827649			−0.413824	+	0.910357i	$0.635807\pi$
$264$	51.0737			3.14337
$265$	−27.6780			−1.70024
$266$		0			0
$267$	−12.4542	+	21.5712i	−0.762182	+	1.32014i
$268$	0.151388	+	0.262211i	0.00924748	+	0.0160171i
$269$	4.75840	+	8.24179i	0.290125	+	0.502511i	0.973839	−	0.227239i	$-0.0729699\pi$
$269$	4.75840	+	8.24179i	0.290125	+	0.502511i	−0.683714	+	0.729750i	$0.739637\pi$
$270$	−24.9083			−1.51587
$271$	14.8435	−	25.7097i	0.901678	−	1.56175i	0.0763615	−	0.997080i	$-0.475670\pi$
$271$	14.8435	−	25.7097i	0.901678	−	1.56175i	0.825316	−	0.564671i	$-0.190997\pi$
$272$	−2.88145			−0.174714
$273$		0			0
$274$	−3.51388			−0.212281
$275$	9.75694	−	16.8995i	0.588366	−	1.01908i
$276$	5.76291			0.346886
$277$	−7.10555	−	12.3072i	−0.426931	−	0.739467i	0.569667	−	0.821875i	$-0.307072\pi$
$277$	−7.10555	−	12.3072i	−0.426931	−	0.739467i	−0.996599	+	0.0824088i	$0.973739\pi$
$278$	−11.0896	−	19.2077i	−0.665110	−	1.15200i
$279$	2.31316	−	4.00651i	0.138485	−	0.239864i
$280$		0			0
$281$	2.18335			0.130248			0.0651238	−	0.997877i	$-0.479256\pi$
$281$	2.18335			0.130248			0.0651238	+	0.997877i	$0.479256\pi$
$282$	46.5416			2.77151
$283$	−4.01804			−0.238848			−0.119424	−	0.992843i	$-0.538105\pi$
$283$	−4.01804			−0.238848			−0.119424	+	0.992843i	$0.538105\pi$
$284$	−1.21110			−0.0718657
$285$	11.9620	+	20.7188i	0.708570	+	1.22728i
$286$	3.35766	−	27.5489i	0.198543	−	1.62900i
$287$		0			0
$288$	4.50000	+	7.79423i	0.265165	+	0.459279i
$289$	8.11943	−	14.0633i	0.477613	−	0.827251i
$290$	−2.44524	−	4.23527i	−0.143589	−	0.248704i
$291$	11.1972	−	19.3942i	0.656393	−	1.13691i
$292$	−1.74487			−0.102111
$293$	1.74487	−	3.02220i	0.101936	−	0.176559i	−0.810546	−	0.585675i	$-0.800830\pi$
$293$	1.74487	−	3.02220i	0.101936	−	0.176559i	0.912482	+	0.409116i	$0.134163\pi$
$294$		0			0
$295$	−9.55971	+	16.5579i	−0.556588	+	0.964039i
$296$	−2.09167	+	3.62288i	−0.121576	+	0.210576i
$297$	39.2038			2.27483
$298$	0.334734	−	0.579776i	0.0193906	−	0.0335855i
$299$	2.88145	−	23.6417i	0.166639	−	1.36724i
$300$	2.88145			0.166361
$301$		0			0
$302$	−4.04584	−	7.00759i	−0.232812	−	0.403242i
$303$	−24.9083			−1.43095
$304$	−4.75840	+	8.24179i	−0.272913	+	0.472699i
$305$	−8.30278	−	14.3808i	−0.475416	−	0.823444i
$306$	−6.02706			−0.344544
$307$	−15.2797			−0.872059			−0.436029	−	0.899932i	$-0.643616\pi$
$307$	−15.2797			−0.872059			−0.436029	+	0.899932i	$0.643616\pi$
$308$		0			0
$309$	−7.04584	−	12.2037i	−0.400824	−	0.694247i
$310$	1.63751	−	2.83625i	0.0930043	−	0.161088i
$311$	−8.51229	+	14.7437i	−0.482687	+	0.836039i	−0.999802	−	0.0198768i	$-0.993673\pi$
$311$	−8.51229	+	14.7437i	−0.482687	+	0.836039i	0.517115	+	0.855916i	$0.327006\pi$
$312$	28.6791	−	12.2037i	1.62364	−	0.690901i
$313$	6.63534	+	11.4927i	0.375052	+	0.649609i	0.990335	−	0.138698i	$-0.0442916\pi$
$313$	6.63534	+	11.4927i	0.375052	+	0.649609i	−0.615283	+	0.788306i	$0.710958\pi$
$314$	−6.19912	−	10.7372i	−0.349837	−	0.605935i
$315$		0			0
$316$	0.0916731	−	0.158782i	0.00515701	−	0.00893221i
$317$	−4.10555	−	7.11102i	−0.230591	−	0.399395i	0.727391	−	0.686223i	$-0.240733\pi$
$317$	−4.10555	−	7.11102i	−0.230591	−	0.399395i	−0.957982	+	0.286828i	$0.907399\pi$
$318$	−18.0291	−	31.2273i	−1.01102	−	1.75114i
$319$	3.84861	+	6.66599i	0.215481	+	0.373224i
$320$	12.7024	+	22.0012i	0.710085	+	1.22990i
$321$	13.4028	−	23.2143i	0.748069	−	1.29569i
$322$		0			0
$323$	1.25694	+	2.17708i	0.0699380	+	0.121136i
$324$	0.486122	+	0.841988i	0.0270068	+	0.0467771i
$325$	1.44073	−	11.8209i	0.0799171	−	0.655703i
$326$	−11.2111	+	19.4182i	−0.620926	+	1.07547i
$327$	−8.94850	+	15.4993i	−0.494853	+	0.857111i
$328$	11.2617	+	19.5058i	0.621821	+	1.07703i
$329$		0			0
$330$	63.9083			3.51804
$331$	0.697224			0.0383229			0.0191615	−	0.999816i	$-0.493900\pi$
$331$	0.697224			0.0383229			0.0191615	+	0.999816i	$0.493900\pi$
$332$	1.00451	+	1.73986i	0.0551296	+	0.0954873i
$333$	−3.69722	+	6.40378i	−0.202607	+	0.350925i
$334$	6.37119			0.348616
$335$	1.44073	+	2.49541i	0.0787153	+	0.136339i
$336$		0			0
$337$	−7.11943			−0.387820			−0.193910	−	0.981019i	$-0.562117\pi$
$337$	−7.11943			−0.387820			−0.193910	+	0.981019i	$0.562117\pi$
$338$	−4.69722	−	16.2717i	−0.255495	−	0.885062i
$339$	−21.3468	+	36.9737i	−1.15940	+	2.00813i
$340$	0.761141			0.0412787
$341$	−2.57731	+	4.46404i	−0.139569	+	0.241741i
$342$	−9.95301	+	17.2391i	−0.538197	+	0.932185i
$343$		0			0
$344$	−8.27082	+	14.3255i	−0.445933	+	0.772378i
$345$	54.8444			2.95272
$346$	−15.5838	+	26.9920i	−0.837793	+	1.45110i
$347$	−0.394449	−	0.683205i	−0.0211751	−	0.0366764i	0.855244	−	0.518226i	$-0.173407\pi$
$347$	−0.394449	−	0.683205i	−0.0211751	−	0.0366764i	−0.876419	+	0.481550i	$0.840074\pi$
$348$	−0.568293	+	0.984312i	−0.0304637	+	0.0527647i
$349$	11.9620	+	20.7188i	0.640313	+	1.10905i	0.985363	+	0.170470i	$0.0545286\pi$
$349$	11.9620	+	20.7188i	0.640313	+	1.10905i	−0.345050	+	0.938584i	$0.612138\pi$
$350$		0			0
$351$	22.0139	−	9.36750i	1.17501	−	0.500000i
$352$	−5.01388	−	8.68429i	−0.267241	−	0.462874i
$353$	−6.37119			−0.339104			−0.169552	−	0.985521i	$-0.554232\pi$
$353$	−6.37119			−0.339104			−0.169552	+	0.985521i	$0.554232\pi$
$354$	−24.9083			−1.32386
$355$	−11.5258			−0.611727
$356$	2.61730			0.138717
$357$		0			0
$358$	9.37637	−	16.2403i	0.495556	−	0.858329i
$359$	11.4542	+	19.8392i	0.604528	+	1.04707i	0.992126	+	0.125244i	$0.0399714\pi$
$359$	11.4542	+	19.8392i	0.604528	+	1.04707i	−0.387598	+	0.921828i	$0.626695\pi$
$360$	22.9196	+	39.6978i	1.20797	+	2.09226i
$361$	−10.6972			−0.563012
$362$	−6.02706	+	10.4392i	−0.316775	+	0.548671i
$363$	−68.8907			−3.61583
$364$		0			0
$365$	−16.6056			−0.869174
$366$	10.8167	−	18.7350i	0.565396	−	0.979294i
$367$	28.2862			1.47653			0.738265	−	0.674511i	$-0.235646\pi$
$367$	28.2862			1.47653			0.738265	+	0.674511i	$0.235646\pi$
$368$	10.9083	+	18.8938i	0.568636	+	0.984906i
$369$	19.9060	+	34.4782i	1.03627	+	1.79487i
$370$	−2.61730	+	4.53330i	−0.136067	+	0.235675i
$371$		0			0
$372$	−0.761141			−0.0394633
$373$	−16.3028			−0.844126			−0.422063	−	0.906567i	$-0.638694\pi$
$373$	−16.3028			−0.844126			−0.422063	+	0.906567i	$0.638694\pi$
$374$	6.71532			0.347241
$375$	−14.0917			−0.727691
$376$	−18.5974	−	32.2116i	−0.959086	−	1.66119i
$377$	3.75389	+	2.82352i	0.193335	+	0.145418i
$378$		0			0
$379$	−6.55971	−	11.3618i	−0.336950	−	0.583614i	0.646908	−	0.762568i	$-0.276062\pi$
$379$	−6.55971	−	11.3618i	−0.336950	−	0.583614i	−0.983857	+	0.178954i	$0.942729\pi$
$380$	1.25694	−	2.17708i	0.0644796	−	0.111682i
$381$	−4.19010	−	7.25747i	−0.214666	−	0.371812i
$382$	12.5736	−	21.7781i	0.643321	−	1.11426i
$383$	19.2977			0.986069			0.493034	−	0.870010i	$-0.335888\pi$
$383$	19.2977			0.986069			0.493034	+	0.870010i	$0.335888\pi$
$384$	−11.6579	+	20.1921i	−0.594914	+	1.03042i
$385$		0			0
$386$	−1.18335	+	2.04962i	−0.0602307	+	0.104323i
$387$	−14.6194	+	25.3216i	−0.743147	+	1.28717i
$388$	−2.35315			−0.119463
$389$	3.51388	−	6.08622i	0.178161	−	0.308583i	−0.763090	−	0.646292i	$-0.776319\pi$
$389$	3.51388	−	6.08622i	0.178161	−	0.308583i	0.941251	+	0.337709i	$0.109652\pi$
$390$	35.8861	−	15.2705i	1.81716	−	0.773252i
$391$	5.76291			0.291443
$392$		0			0
$393$	−24.5278	−	42.4833i	−1.23726	−	2.14300i
$394$	15.5139			0.781578
$395$	0.872434	−	1.51110i	0.0438969	−	0.0760317i
$396$	−4.74306	−	8.21522i	−0.238348	−	0.412830i
$397$	−5.76291			−0.289232			−0.144616	−	0.989488i	$-0.546195\pi$
$397$	−5.76291			−0.289232			−0.144616	+	0.989488i	$0.546195\pi$
$398$	1.13659			0.0569719
$399$		0			0
$400$	5.45416	+	9.44689i	0.272708	+	0.472344i
$401$	−7.55971	+	13.0938i	−0.377514	+	0.653874i	−0.990700	−	0.136065i	$-0.956554\pi$
$401$	−7.55971	+	13.0938i	−0.377514	+	0.653874i	0.613186	+	0.789939i	$0.289888\pi$
$402$	−1.87694	+	3.25096i	−0.0936135	+	0.162143i
$403$	−0.380571	+	3.12250i	−0.0189576	+	0.155543i
$404$	1.30865	+	2.26665i	0.0651078	+	0.112770i
$405$	4.62632	+	8.01302i	0.229884	+	0.398170i
$406$		0			0
$407$	4.11943	−	7.13506i	0.204193	−	0.353672i
$408$	3.77082	+	6.53125i	0.186683	+	0.323345i
$409$	−8.07607	−	13.9882i	−0.399336	−	0.691670i	0.594308	−	0.804237i	$-0.297426\pi$
$409$	−8.07607	−	13.9882i	−0.399336	−	0.691670i	−0.993644	+	0.112567i	$0.964093\pi$
$410$	14.0917	+	24.4075i	0.695938	+	1.20540i
$411$	3.88596	+	6.73069i	0.191680	+	0.332000i
$412$	−0.740358	+	1.28234i	−0.0364748	+	0.0631763i
$413$		0			0
$414$	22.8167	+	39.5196i	1.12138	+	1.94228i
$415$	9.55971	+	16.5579i	0.469268	+	0.812796i
$416$	−4.89047	−	3.67841i	−0.239775	−	0.180349i
$417$	−24.5278	+	42.4833i	−1.20113	+	2.08042i
$418$	11.0896	−	19.2077i	0.542410	−	0.939482i
$419$	4.19010	+	7.25747i	0.204700	+	0.354551i	0.950037	−	0.312137i	$-0.101045\pi$
$419$	4.19010	+	7.25747i	0.204700	+	0.354551i	−0.745337	+	0.666688i	$0.767711\pi$
$420$		0			0
$421$	−31.0278			−1.51220			−0.756100	−	0.654456i	$-0.772898\pi$
$421$	−31.0278			−1.51220			−0.756100	+	0.654456i	$0.772898\pi$
$422$	−19.5416			−0.951272
$423$	−32.8726	−	56.9370i	−1.59832	−	2.76837i
$424$	−14.4083	+	24.9560i	−0.699730	+	1.21197i
$425$	2.88145			0.139771
$426$	−7.50778	−	13.0038i	−0.363753	−	0.630039i
$427$		0			0
$428$	−2.81665			−0.136148
$429$	−56.4819	+	24.0346i	−2.72697	+	1.16040i
$430$	−10.3492	+	17.9254i	−0.499085	+	0.864440i
$431$	25.9361			1.24930			0.624649	−	0.780906i	$-0.285242\pi$
$431$	25.9361			1.24930			0.624649	+	0.780906i	$0.285242\pi$
$432$	−10.9575	+	18.9790i	−0.527194	+	0.913127i
$433$	−4.19010	+	7.25747i	−0.201364	+	0.348772i	−0.948968	−	0.315372i	$-0.897871\pi$
$433$	−4.19010	+	7.25747i	−0.201364	+	0.348772i	0.747604	+	0.664144i	$0.231204\pi$
$434$		0			0
$435$	−5.40833	+	9.36750i	−0.259309	+	0.449137i
$436$	1.88057			0.0900630
$437$	9.51680	−	16.4836i	0.455250	−	0.788516i
$438$	−10.8167	−	18.7350i	−0.516840	−	0.895193i
$439$	−7.63985	+	13.2326i	−0.364630	+	0.631558i	−0.988717	−	0.149797i	$-0.952138\pi$
$439$	−7.63985	+	13.2326i	−0.364630	+	0.631558i	0.624087	+	0.781355i	$0.285471\pi$
$440$	−25.5369	−	44.2311i	−1.21742	−	2.10864i
$441$		0			0
$442$	3.77082	−	1.60458i	0.179359	−	0.0763223i
$443$	−15.1194	−	26.1876i	−0.718346	−	1.24421i	−0.961655	−	0.274263i	$-0.911566\pi$
$443$	−15.1194	−	26.1876i	−0.718346	−	1.24421i	0.243309	−	0.969949i	$-0.421767\pi$
$444$	1.21656			0.0577356
$445$	24.9083			1.18077
$446$	−17.6329			−0.834940
$447$	−1.48072			−0.0700355
$448$		0			0
$449$	−4.21110	+	7.29384i	−0.198734	+	0.344218i	−0.948118	−	0.317918i	$-0.897016\pi$
$449$	−4.21110	+	7.29384i	−0.198734	+	0.344218i	0.749384	+	0.662136i	$0.230350\pi$
$450$	11.4083	+	19.7598i	0.537794	+	0.931486i
$451$	−22.1792	−	38.4155i	−1.04438	−	1.80891i
$452$	4.48612			0.211009
$453$	−8.94850	+	15.4993i	−0.420437	+	0.728219i
$454$	35.7140			1.67614
$455$		0			0
$456$	24.9083			1.16644
$457$	−6.69722	+	11.5999i	−0.313283	+	0.542622i	−0.979071	−	0.203519i	$-0.934762\pi$
$457$	−6.69722	+	11.5999i	−0.313283	+	0.542622i	0.665788	+	0.746141i	$0.268095\pi$
$458$	27.0697			1.26488
$459$	2.89445	+	5.01333i	0.135101	+	0.234002i
$460$	−2.88145	−	4.99082i	−0.134348	−	0.232698i
$461$	−6.33120	+	10.9660i	−0.294873	+	0.510736i	−0.974955	−	0.222400i	$-0.928611\pi$
$461$	−6.33120	+	10.9660i	−0.294873	+	0.510736i	0.680082	+	0.733136i	$0.261944\pi$
$462$		0			0
$463$	−28.2111			−1.31108			−0.655541	−	0.755160i	$-0.727559\pi$
$463$	−28.2111			−1.31108			−0.655541	+	0.755160i	$0.727559\pi$
$464$	−4.30278			−0.199751
$465$	−7.24362			−0.335915
$466$	31.1472			1.44287
$467$	−7.07156	−	12.2483i	−0.327233	−	0.566784i	0.654729	−	0.755864i	$-0.272783\pi$
$467$	−7.07156	−	12.2483i	−0.327233	−	0.566784i	−0.981962	+	0.189080i	$0.939449\pi$
$468$	−4.62632	−	3.47972i	−0.213852	−	0.160850i
$469$		0			0
$470$	−23.2708	−	40.3062i	−1.07340	−	1.85919i
$471$	−13.7111	+	23.7483i	−0.631774	+	1.09427i
$472$	9.95301	+	17.2391i	0.458125	+	0.793495i
$473$	16.2889	−	28.2132i	0.748964	−	1.29724i
$474$	2.27317			0.104410
$475$	4.75840	−	8.24179i	0.218330	−	0.378159i
$476$		0			0
$477$	−25.4680	+	44.1119i	−1.16610	+	2.01975i
$478$	7.55971	−	13.0938i	0.345773	−	0.598897i
$479$	1.13659			0.0519319			0.0259660	−	0.999663i	$-0.491734\pi$
$479$	1.13659			0.0519319			0.0259660	+	0.999663i	$0.491734\pi$
$480$	7.04584	−	12.2037i	0.321597	−	0.557022i
$481$	0.608282	−	4.99082i	0.0277353	−	0.227562i
$482$	−2.61730			−0.119215
$483$		0			0
$484$	3.61943	+	6.26904i	0.164520	+	0.284956i
$485$	−22.3944			−1.01688
$486$	6.93948	−	12.0195i	0.314781	−	0.545217i
$487$	13.8486	+	23.9865i	0.627541	+	1.08693i	0.988044	+	0.154174i	$0.0492717\pi$
$487$	13.8486	+	23.9865i	0.627541	+	1.08693i	−0.360503	+	0.932758i	$0.617395\pi$
$488$	−17.2887			−0.782624
$489$	49.5930			2.24267
$490$		0			0
$491$	6.36249	+	11.0202i	0.287135	+	0.497333i	0.973125	−	0.230279i	$-0.0739638\pi$
$491$	6.36249	+	11.0202i	0.287135	+	0.497333i	−0.685990	+	0.727611i	$0.740630\pi$
$492$	3.27502	−	5.67250i	0.147649	−	0.255736i
$493$	−0.568293	+	0.984312i	−0.0255946	+	0.0443312i
$494$	1.63751	−	13.4354i	0.0736750	−	0.604488i
$495$	−45.1387	−	78.1826i	−2.02884	−	3.51405i
$496$	−1.44073	−	2.49541i	−0.0646905	−	0.112047i
$497$		0			0
$498$	−12.4542	+	21.5712i	−0.558084	+	0.966631i
$499$	−15.6653	−	27.1330i	−0.701274	−	1.21464i	−0.968020	−	0.250875i	$-0.919282\pi$
$499$	−15.6653	−	27.1330i	−0.701274	−	1.21464i	0.266746	−	0.963767i	$-0.414052\pi$
$500$	0.740358	+	1.28234i	0.0331098	+	0.0573479i
$501$	−7.04584	−	12.2037i	−0.314785	−	0.545223i
$502$	14.6714	+	25.4116i	0.654818	+	1.13418i
$503$	−12.9665	+	22.4587i	−0.578150	+	1.00138i	0.417542	+	0.908658i	$0.362892\pi$
$503$	−12.9665	+	22.4587i	−0.578150	+	1.00138i	−0.995692	+	0.0927268i	$0.970442\pi$
$504$		0			0
$505$	12.4542	+	21.5712i	0.554203	+	0.959908i
$506$	−25.4222	−	44.0326i	−1.13015	−	1.95749i
$507$	−25.9731	+	26.9920i	−1.15350	+	1.19876i
$508$	−0.440285	+	0.762596i	−0.0195345	+	0.0338347i
$509$	−1.30865	+	2.26665i	−0.0580049	+	0.100467i	−0.893570	−	0.448924i	$-0.851807\pi$
$509$	−1.30865	+	2.26665i	−0.0580049	+	0.100467i	0.835565	+	0.549392i	$0.185141\pi$
$510$	4.71841	+	8.17252i	0.208935	+	0.361885i
$511$		0			0
$512$	25.4222			1.12351
$513$	19.1194			0.844143
$514$	14.8435	+	25.7097i	0.654718	+	1.13400i
$515$	−7.04584	+	12.2037i	−0.310477	+	0.537761i
$516$	4.81049			0.211770
$517$	36.6265	+	63.4389i	1.61083	+	2.79004i
$518$		0			0
$519$	68.9361			3.02596
$520$	−24.9083	−	18.7350i	−1.09230	−	0.821584i
$521$	−14.4073	+	24.9541i	−0.631194	+	1.09326i	0.356114	+	0.934442i	$0.384101\pi$
$521$	−14.4073	+	24.9541i	−0.631194	+	1.09326i	−0.987308	+	0.158817i	$0.949232\pi$
$522$	−9.00000			−0.393919
$523$	−4.62632	+	8.01302i	−0.202295	+	0.350385i	−0.949267	−	0.314470i	$-0.898173\pi$
$523$	−4.62632	+	8.01302i	−0.202295	+	0.350385i	0.746973	+	0.664855i	$0.231507\pi$
$524$	−2.57731	+	4.46404i	−0.112590	+	0.195012i
$525$		0			0
$526$	−8.74306	+	15.1434i	−0.381216	+	0.660285i
$527$	−0.761141			−0.0331558
$528$	28.1142	−	48.6952i	1.22351	−	2.11919i
$529$	−10.3167	−	17.8690i	−0.448550	−	0.776912i
$530$	−18.0291	+	31.2273i	−0.783133	+	1.35643i
$531$	17.5929	+	30.4717i	0.763465	+	1.32236i
$532$		0			0
$533$	−21.6333	−	16.2717i	−0.937043	−	0.704804i
$534$	16.2250	+	28.1025i	0.702124	+	1.21611i
$535$	−26.8055			−1.15890
$536$	3.00000			0.129580
$537$	−41.4769			−1.78986
$538$	12.3982			0.534526
$539$		0			0
$540$	2.89445	−	5.01333i	0.124557	−	0.215739i
$541$	9.46804	+	16.3991i	0.407063	+	0.705054i	0.994559	−	0.104173i	$-0.0332196\pi$
$541$	9.46804	+	16.3991i	0.407063	+	0.705054i	−0.587496	+	0.809227i	$0.699886\pi$
$542$	−19.3377	−	33.4939i	−0.830627	−	1.43869i
$543$	26.6611			1.14414
$544$	0.740358	−	1.28234i	0.0317426	−	0.0549798i
$545$	17.8970			0.766623
$546$		0			0
$547$	29.0000			1.23995			0.619975	−	0.784621i	$-0.287143\pi$
$547$	29.0000			1.23995			0.619975	+	0.784621i	$0.287143\pi$
$548$	0.408327	−	0.707243i	0.0174429	−	0.0302119i
$549$	−30.5594			−1.30424
$550$	−12.7111	−	22.0163i	−0.542003	−	0.938777i
$551$	1.87694	+	3.25096i	0.0799605	+	0.138496i
$552$	28.5504	−	49.4507i	1.21519	−	2.10476i
$553$		0			0
$554$	−18.5139			−0.786579
$555$	11.5778			0.491450
$556$	5.15463			0.218605
$557$	16.9083			0.716429			0.358214	−	0.933639i	$-0.383386\pi$
$557$	16.9083			0.716429			0.358214	+	0.933639i	$0.383386\pi$
$558$	−3.01353	−	5.21959i	−0.127573	−	0.220963i
$559$	2.40525	−	19.7345i	0.101731	−	0.834682i
$560$		0			0
$561$	−7.42641	−	12.8629i	−0.313543	−	0.543073i
$562$	1.42221	−	2.46333i	0.0599921	−	0.103909i
$563$	−9.51680	−	16.4836i	−0.401085	−	0.694700i	0.592772	−	0.805370i	$-0.298034\pi$
$563$	−9.51680	−	16.4836i	−0.401085	−	0.694700i	−0.993857	+	0.110671i	$0.964700\pi$
$564$	−5.40833	+	9.36750i	−0.227732	+	0.394443i
$565$	42.6935			1.79613
$566$	−2.61730	+	4.53330i	−0.110013	+	0.190549i
$567$		0			0
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	13.6972	−	23.7243i	0.574218	−	0.994574i	−0.421909	−	0.906638i	$-0.638640\pi$
$569$	13.6972	−	23.7243i	0.574218	−	0.994574i	0.996126	−	0.0879356i	$-0.0280270\pi$
$570$	31.1677			1.30547
$571$	−10.8625	+	18.8144i	−0.454581	+	0.787358i	−0.998664	−	0.0516739i	$-0.983544\pi$
$571$	−10.8625	+	18.8144i	−0.454581	+	0.787358i	0.544083	+	0.839031i	$0.316878\pi$
$572$	5.15463	+	3.87709i	0.215526	+	0.162109i
$573$	−55.6201			−2.32356
$574$		0			0
$575$	−10.9083	−	18.8938i	−0.454909	−	0.787925i
$576$	46.7527			1.94803
$577$	16.8525	−	29.1894i	0.701579	−	1.21517i	−0.266333	−	0.963881i	$-0.585812\pi$
$577$	16.8525	−	29.1894i	0.701579	−	1.21517i	0.967912	−	0.251289i	$-0.0808546\pi$
$578$	−10.5778	−	18.3213i	−0.439978	−	0.762065i
$579$	5.23460			0.217543
$580$	1.13659			0.0471942
$581$		0			0
$582$	−14.5875	−	25.2662i	−0.604670	−	1.04732i
$583$	28.3764	−	49.1493i	1.17523	−	2.03556i
$584$	−8.64436	+	14.9725i	−0.357706	+	0.619565i
$585$	−44.0278	−	33.1158i	−1.82032	−	1.36917i
$586$	−2.27317	−	3.93725i	−0.0939038	−	0.162646i
$587$	−14.2752	−	24.7254i	−0.589200	−	1.02052i	−0.994337	−	0.106269i	$-0.966110\pi$
$587$	−14.2752	−	24.7254i	−0.589200	−	1.02052i	0.405137	−	0.914256i	$-0.367224\pi$
$588$		0			0
$589$	−1.25694	+	2.17708i	−0.0517913	+	0.0897051i
$590$	12.4542	+	21.5712i	0.512730	+	0.888074i
$591$	−17.1566	−	29.7162i	−0.705730	−	1.22236i
$592$	2.30278	+	3.98852i	0.0946435	+	0.163927i
$593$	−11.3937	−	19.7345i	−0.467885	−	0.810400i	0.531442	−	0.847095i	$-0.321650\pi$
$593$	−11.3937	−	19.7345i	−0.467885	−	0.810400i	−0.999327	+	0.0366946i	$0.988317\pi$
$594$	25.5369	−	44.2311i	1.04779	−	1.81483i
$595$		0			0
$596$	0.0777949	+	0.134745i	0.00318660	+	0.00551936i
$597$	−1.25694	−	2.17708i	−0.0514431	−	0.0891020i
$598$	−24.7965	−	18.6509i	−1.01400	−	0.762691i
$599$	−3.75694	+	6.50721i	−0.153504	+	0.265877i	−0.932513	−	0.361135i	$-0.882389\pi$
$599$	−3.75694	+	6.50721i	−0.153504	+	0.265877i	0.779009	+	0.627013i	$0.215723\pi$
$600$	14.2752	−	24.7254i	0.582782	−	1.00941i
$601$	−14.7114	−	25.4809i	−0.600091	−	1.03939i	−0.992807	−	0.119728i	$-0.961798\pi$
$601$	−14.7114	−	25.4809i	−0.600091	−	1.03939i	0.392716	−	0.919660i	$-0.371536\pi$
$602$		0			0
$603$	5.30278			0.215946
$604$	1.88057			0.0765193
$605$	34.4454	+	59.6611i	1.40040	+	2.42557i
$606$	−16.2250	+	28.1025i	−0.659095	+	1.14159i
$607$	−20.4343			−0.829404			−0.414702	−	0.909957i	$-0.636114\pi$
$607$	−20.4343			−0.829404			−0.414702	+	0.909957i	$0.636114\pi$
$608$	−2.44524	−	4.23527i	−0.0991674	−	0.171763i
$609$		0			0
$610$	−21.6333			−0.875907
$611$	35.7250	+	26.8708i	1.44528	+	1.08708i
$612$	0.700369	−	1.21307i	0.0283107	−	0.0490356i
$613$	21.0917			0.851885			0.425942	−	0.904750i	$-0.359943\pi$
$613$	21.0917			0.851885			0.425942	+	0.904750i	$0.359943\pi$
$614$	−9.95301	+	17.2391i	−0.401671	+	0.695714i
$615$	31.1677	−	53.9840i	1.25680	−	2.17685i
$616$		0			0
$617$	20.9222	−	36.2383i	0.842296	−	1.45890i	−0.0456524	−	0.998957i	$-0.514537\pi$
$617$	20.9222	−	36.2383i	0.842296	−	1.45890i	0.887949	−	0.459943i	$-0.152130\pi$
$618$	−18.3583			−0.738479
$619$	11.2617	−	19.5058i	0.452644	−	0.784003i	−0.545905	−	0.837847i	$-0.683814\pi$
$619$	11.2617	−	19.5058i	0.452644	−	0.784003i	0.998549	+	0.0538439i	$0.0171474\pi$
$620$	0.380571	+	0.659168i	0.0152841	+	0.0264728i
$621$	21.9150	−	37.9580i	0.879420	−	1.52320i
$622$	11.0896	+	19.2077i	0.444652	+	0.770160i
$623$		0			0
$624$	4.15139	−	34.0612i	0.166189	−	1.36354i
$625$	15.3028	+	26.5052i	0.612111	+	1.06021i
$626$	17.2887			0.690996
$627$	−49.0555			−1.95909
$628$	2.88145			0.114983
$629$	1.21656			0.0485076
$630$		0			0
$631$	−6.04584	+	10.4717i	−0.240681	+	0.416872i	−0.960908	−	0.276866i	$-0.910704\pi$
$631$	−6.04584	+	10.4717i	−0.240681	+	0.416872i	0.720227	+	0.693738i	$0.244037\pi$
$632$	−0.908327	−	1.57327i	−0.0361313	−	0.0625813i
$633$	21.6109	+	37.4312i	0.858956	+	1.48776i
$634$	−10.6972			−0.424841
$635$	−4.19010	+	7.25747i	−0.166279	+	0.288004i
$636$	8.38021			0.332297
$637$		0			0
$638$	10.0278			0.397003
$639$	−10.6056	+	18.3694i	−0.419549	+	0.726680i
$640$	23.3158			0.921637
$641$	−1.75694	−	3.04311i	−0.0693949	−	0.120196i	0.829240	−	0.558892i	$-0.188774\pi$
$641$	−1.75694	−	3.04311i	−0.0693949	−	0.120196i	−0.898635	+	0.438697i	$0.855440\pi$
$642$	−17.4608	−	30.2430i	−0.689122	−	1.19359i
$643$	−4.19010	+	7.25747i	−0.165242	+	0.286207i	−0.936741	−	0.350023i	$-0.886174\pi$
$643$	−4.19010	+	7.25747i	−0.165242	+	0.286207i	0.771499	+	0.636230i	$0.219507\pi$
$644$		0			0
$645$	45.7805			1.80261
$646$	3.27502			0.128854
$647$	2.27317			0.0893676			0.0446838	−	0.999001i	$-0.485772\pi$
$647$	2.27317			0.0893676			0.0446838	+	0.999001i	$0.485772\pi$
$648$	9.63331			0.378432
$649$	−19.6019	−	33.9515i	−0.769441	−	1.33271i
$650$	−12.3982	−	9.32544i	−0.486299	−	0.365774i
$651$		0			0
$652$	−2.60555	−	4.51295i	−0.102041	−	0.176741i
$653$	−10.8764	+	18.8384i	−0.425625	+	0.737204i	−0.996479	−	0.0838475i	$-0.973279\pi$
$653$	−10.8764	+	18.8384i	−0.425625	+	0.737204i	0.570853	+	0.821052i	$0.306612\pi$
$654$	11.6579	+	20.1921i	0.455860	+	0.789572i
$655$	−24.5278	+	42.4833i	−0.958379	+	1.65996i
$656$	24.7965			0.968141
$657$	−15.2797	+	26.4652i	−0.596118	+	1.03251i
$658$		0			0
$659$	−11.8167	+	20.4670i	−0.460311	+	0.797283i	−0.998976	−	0.0452373i	$-0.985596\pi$
$659$	−11.8167	+	20.4670i	−0.460311	+	0.797283i	0.538665	+	0.842520i	$0.318929\pi$
$660$	−7.42641	+	12.8629i	−0.289073	+	0.500688i
$661$	9.78095			0.380435			0.190217	−	0.981742i	$-0.439081\pi$
$661$	9.78095			0.380435			0.190217	+	0.981742i	$0.439081\pi$
$662$	0.454163	−	0.786634i	0.0176516	−	0.0305734i
$663$	−7.24362	−	5.44835i	−0.281319	−	0.211596i
$664$	19.9060			0.772504
$665$		0			0
$666$	4.81665	+	8.34269i	0.186642	+	0.323273i
$667$	8.60555			0.333208
$668$	−0.740358	+	1.28234i	−0.0286453	+	0.0496151i
$669$	19.5000	+	33.7750i	0.753914	+	1.30582i
$670$	3.75389			0.145025
$671$	34.0491			1.31445
$672$		0			0
$673$	−6.10555	−	10.5751i	−0.235352	−	0.407641i	0.724023	−	0.689776i	$-0.242291\pi$
$673$	−6.10555	−	10.5751i	−0.235352	−	0.407641i	−0.959375	+	0.282135i	$0.908958\pi$
$674$	−4.63751	+	8.03240i	−0.178630	+	0.309397i
$675$	10.9575	−	18.9790i	0.421755	−	0.730501i
$676$	3.82086	+	0.945417i	0.146956	+	0.0363622i
$677$	3.18559	+	5.51761i	0.122432	+	0.212059i	0.920726	−	0.390209i	$-0.127597\pi$
$677$	3.18559	+	5.51761i	0.122432	+	0.212059i	−0.798294	+	0.602268i	$0.794264\pi$
$678$	27.8100	+	48.1684i	1.06804	+	1.84990i
$679$		0			0
$680$	3.77082	−	6.53125i	0.144604	−	0.250462i
$681$	−39.4958	−	68.4087i	−1.51348	−	2.62143i
$682$	3.35766	+	5.81564i	0.128571	+	0.222692i
$683$	−1.80278	−	3.12250i	−0.0689813	−	0.119479i	0.829472	−	0.558549i	$-0.188642\pi$
$683$	−1.80278	−	3.12250i	−0.0689813	−	0.119479i	−0.898453	+	0.439069i	$0.855308\pi$
$684$	−2.31316	−	4.00651i	−0.0884459	−	0.153193i
$685$	3.88596	−	6.73069i	0.148475	−	0.257166i
$686$		0			0
$687$	−29.9361	−	51.8508i	−1.14213	−	1.97823i
$688$	9.10555	+	15.7713i	0.347146	+	0.601274i
$689$	4.19010	−	34.3789i	0.159630	−	1.30973i
$690$	35.7250	−	61.8775i	1.36003	−	2.35564i
$691$	16.4563	−	28.5031i	0.626026	−	1.08431i	−0.362315	−	0.932056i	$-0.618014\pi$
$691$	16.4563	−	28.5031i	0.626026	−	1.08431i	0.988341	−	0.152254i	$-0.0486531\pi$
$692$	−3.62181	−	6.27316i	−0.137681	−	0.238470i
$693$		0			0
$694$	−1.02776			−0.0390131
$695$	49.0555			1.86078
$696$	5.63083	+	9.75289i	0.213436	+	0.369682i
$697$	3.27502	−	5.67250i	0.124050	−	0.214861i
$698$	31.1677			1.17971
$699$	−34.4454	−	59.6611i	−1.30284	−	2.25659i
$700$		0			0
$701$	−27.0278			−1.02082			−0.510412	−	0.859930i	$-0.670507\pi$
$701$	−27.0278			−1.02082			−0.510412	+	0.859930i	$0.670507\pi$
$702$	3.77082	−	30.9387i	0.142320	−	1.16771i
$703$	2.00902	−	3.47972i	0.0757716	−	0.131240i
$704$	−52.0917			−1.96328
$705$	−51.4699	+	89.1486i	−1.93847	+	3.35753i
$706$	−4.15012	+	7.18821i	−0.156192	+	0.270532i
$707$		0			0
$708$	2.89445	−	5.01333i	0.108780	−	0.188413i
$709$	0.275019			0.0103286			0.00516428	−	0.999987i	$-0.498356\pi$
$709$	0.275019			0.0103286			0.00516428	+	0.999987i	$0.498356\pi$
$710$	−7.50778	+	13.0038i	−0.281762	+	0.488026i
$711$	−1.60555	−	2.78090i	−0.0602129	−	0.104292i
$712$	12.9665	−	22.4587i	0.485942	−	0.841676i
$713$	2.88145	+	4.99082i	0.107911	+	0.186908i
$714$		0			0
$715$	49.0555	+	36.8975i	1.83457	+	1.37989i
$716$	2.17914	+	3.77439i	0.0814384	+	0.141056i
$717$	−33.4409			−1.24887
$718$	29.8444			1.11378
$719$	−21.6509			−0.807442			−0.403721	−	0.914882i	$-0.632283\pi$
$719$	−21.6509			−0.807442			−0.403721	+	0.914882i	$0.632283\pi$
$720$	50.4654			1.88074
$721$		0			0
$722$	−6.96804	+	12.0690i	−0.259324	+	0.449162i
$723$	2.89445	+	5.01333i	0.107646	+	0.186448i
$724$	−1.40074	−	2.42615i	−0.0520580	−	0.0901671i
$725$	4.30278			0.159801
$726$	−44.8746	+	77.7251i	−1.66545	+	2.88465i
$727$	23.3958			0.867701			0.433850	−	0.900985i	$-0.357155\pi$
$727$	23.3958			0.867701			0.433850	+	0.900985i	$0.357155\pi$
$728$		0			0
$729$	−40.3305			−1.49372
$730$	−10.8167	+	18.7350i	−0.400342	+	0.693413i
$731$	4.81049			0.177923
$732$	2.51388	+	4.35416i	0.0929156	+	0.160935i
$733$	−20.0381	−	34.7070i	−0.740124	−	1.28193i	−0.952438	−	0.304731i	$-0.901433\pi$
$733$	−20.0381	−	34.7070i	−0.740124	−	1.28193i	0.212314	−	0.977201i	$-0.431900\pi$
$734$	18.4253	−	31.9136i	0.680091	−	1.17795i
$735$		0			0
$736$	−11.2111			−0.413247
$737$	−5.90833			−0.217636
$738$	51.8662			1.90922
$739$	−18.7889			−0.691161			−0.345580	−	0.938389i	$-0.612318\pi$
$739$	−18.7889			−0.691161			−0.345580	+	0.938389i	$0.612318\pi$
$740$	−0.608282	−	1.05358i	−0.0223609	−	0.0387302i
$741$	−27.5459	+	11.7215i	−1.01192	+	0.430600i
$742$		0			0
$743$	18.8486	+	32.6468i	0.691489	+	1.19769i	0.971350	+	0.237653i	$0.0763781\pi$
$743$	18.8486	+	32.6468i	0.691489	+	1.19769i	−0.279862	+	0.960040i	$0.590289\pi$
$744$	−3.77082	+	6.53125i	−0.138245	+	0.239447i
$745$	0.740358	+	1.28234i	0.0271246	+	0.0469812i
$746$	−10.6194	+	18.3934i	−0.388805	+	0.673430i
$747$	35.1857			1.28738
$748$	−0.780347	+	1.35160i	−0.0285323	+	0.0494194i
$749$		0			0
$750$	−9.17914	+	15.8987i	−0.335175	+	0.580540i
$751$	2.19722	−	3.80570i	0.0801779	−	0.138872i	−0.823148	−	0.567826i	$-0.807785\pi$
$751$	2.19722	−	3.80570i	0.0801779	−	0.138872i	0.903326	+	0.428954i	$0.141118\pi$
$752$	−40.9486			−1.49324
$753$	32.4500	−	56.2050i	1.18254	−	2.04822i
$754$	5.63083	−	2.39607i	0.205063	−	0.0872597i
$755$	17.8970			0.651339
$756$		0			0
$757$	22.1194	+	38.3120i	0.803944	+	1.39247i	0.917001	+	0.398884i	$0.130602\pi$
$757$	22.1194	+	38.3120i	0.803944	+	1.39247i	−0.113057	+	0.993588i	$0.536064\pi$
$758$	−17.0917			−0.620798
$759$	−56.2283	+	97.3903i	−2.04096	+	3.53505i
$760$	−12.4542	−	21.5712i	−0.451760	−	0.782471i
$761$	4.28219			0.155229			0.0776147	−	0.996983i	$-0.475270\pi$
$761$	4.28219			0.155229			0.0776147	+	0.996983i	$0.475270\pi$
$762$	−10.9175			−0.395500
$763$		0			0
$764$	2.92221	+	5.06141i	0.105722	+	0.183115i
$765$	6.66527	−	11.5446i	0.240983	−	0.417395i
$766$	12.5703	−	21.7724i	0.454184	−	0.786670i
$767$	−19.1194	−	14.3808i	−0.690363	−	0.519262i
$768$	−10.2172	−	17.6966i	−0.368680	−	0.638573i
$769$	−15.4518	−	26.7632i	−0.557205	−	0.965107i	−0.997728	−	0.0673662i	$-0.978540\pi$
$769$	−15.4518	−	26.7632i	−0.557205	−	0.965107i	0.440523	−	0.897741i	$-0.354793\pi$
$770$		0			0
$771$	32.8305	−	56.8641i	1.18236	−	2.04791i
$772$	−0.275019	−	0.476347i	−0.00989816	−	0.0171441i
$773$	−17.4608	−	30.2430i	−0.628021	−	1.08776i	−0.987948	−	0.154784i	$-0.950532\pi$
$773$	−17.4608	−	30.2430i	−0.628021	−	1.08776i	0.359927	−	0.932980i	$-0.382801\pi$
$774$	19.0458	+	32.9884i	0.684588	+	1.18574i
$775$	1.44073	+	2.49541i	0.0517524	+	0.0896379i
$776$	−11.6579	+	20.1921i	−0.418494	+	0.724853i
$777$		0			0
$778$	−4.57779	−	7.92897i	−0.164122	−	0.284267i
$779$	−10.8167	−	18.7350i	−0.387547	−	0.671251i
$780$	−1.09660	+	8.99734i	−0.0392644	+	0.322156i
$781$	11.8167	−	20.4670i	0.422833	−	0.732368i
$782$	3.75389	−	6.50192i	0.134239	−	0.232508i
$783$	4.32218	+	7.48624i	0.154462	+	0.267536i
$784$		0			0
$785$	27.4222			0.978740
$786$	−63.9083			−2.27953
$787$	20.7785	+	35.9893i	0.740672	+	1.28288i	0.952190	+	0.305507i	$0.0988261\pi$
$787$	20.7785	+	35.9893i	0.740672	+	1.28288i	−0.211518	+	0.977374i	$0.567841\pi$
$788$	−1.80278	+	3.12250i	−0.0642212	+	0.111234i
$789$	38.6755			1.37688
$790$	−1.13659	−	1.96862i	−0.0404379	−	0.0700405i
$791$		0			0
$792$	−93.9916			−3.33985
$793$	19.1194	−	8.13583i	0.678951	−	0.288912i
$794$	−3.75389	+	6.50192i	−0.133220	+	0.230745i
$795$	79.7527			2.82854
$796$	−0.132076	+	0.228762i	−0.00468131	+	0.00810826i
$797$	17.2887	−	29.9449i	0.612398	−	1.06070i	−0.378437	−	0.925627i	$-0.623538\pi$
$797$	17.2887	−	29.9449i	0.612398	−	1.06070i	0.990835	−	0.135077i	$-0.0431283\pi$
$798$		0			0
$799$	−5.40833	+	9.36750i	−0.191333	+	0.331398i
$800$	−5.60555			−0.198186
$801$	22.9196	−	39.6978i	0.809823	−	1.40265i
$802$	9.84861	+	17.0583i	0.347767	+	0.602349i
$803$	17.0246	−	29.4874i	0.600784	−	1.04059i
$804$	−0.436217	−	0.755550i	−0.0153842	−	0.0266462i
$805$		0			0
$806$	3.27502	+	2.46333i	0.115358	+	0.0867672i
$807$	−13.7111	−	23.7483i	−0.482654	−	0.835981i
$808$	25.9331			0.912323
$809$	−16.0278			−0.563506			−0.281753	−	0.959487i	$-0.590916\pi$
$809$	−16.0278			−0.563506			−0.281753	+	0.959487i	$0.590916\pi$
$810$	12.0541			0.423539
$811$	−21.9150			−0.769541			−0.384771	−	0.923012i	$-0.625719\pi$
$811$	−21.9150			−0.769541			−0.384771	+	0.923012i	$0.625719\pi$
$812$		0			0
$813$	−42.7708	+	74.0812i	−1.50004	+	2.59814i
$814$	−5.36669	−	9.29538i	−0.188102	−	0.325803i
$815$	−24.7965	−	42.9488i	−0.868583	−	1.50443i
$816$	8.30278			0.290655
$817$	7.94399	−	13.7594i	0.277925	−	0.481380i
$818$	−21.0426			−0.735738
$819$		0			0
$820$	−6.55004			−0.228737
$821$	−0.922205	+	1.59731i	−0.0321852	+	0.0557464i	−0.881669	−	0.471868i	$-0.843580\pi$
$821$	−0.922205	+	1.59731i	−0.0321852	+	0.0557464i	0.849484	+	0.527614i	$0.176913\pi$
$822$	10.1251			0.353153
$823$	22.1333	+	38.3360i	0.771519	+	1.33631i	0.936731	+	0.350051i	$0.113836\pi$
$823$	22.1333	+	38.3360i	0.771519	+	1.33631i	−0.165212	+	0.986258i	$0.552831\pi$
$824$	7.33571	+	12.7058i	0.255552	+	0.442628i
$825$	−28.1142	+	48.6952i	−0.978810	+	1.69535i
$826$		0			0
$827$	51.7527			1.79962			0.899809	−	0.436283i	$-0.143705\pi$
$827$	51.7527			1.79962			0.899809	+	0.436283i	$0.143705\pi$
$828$	−10.6056			−0.368568
$829$	15.6238			0.542638			0.271319	−	0.962489i	$-0.412540\pi$
$829$	15.6238			0.542638			0.271319	+	0.962489i	$0.412540\pi$
$830$	24.9083			0.864581
$831$	20.4743	+	35.4626i	0.710246	+	1.23018i
$832$	−29.2508	+	12.4470i	−1.01409	+	0.431521i
$833$		0			0
$834$	31.9542	+	55.3462i	1.10648	+	1.91648i
$835$	−7.04584	+	12.2037i	−0.243831	+	0.422328i
$836$	2.57731	+	4.46404i	0.0891382	+	0.154392i
$837$	−2.89445	+	5.01333i	−0.100047	+	0.173286i
$838$	10.9175			0.377140
$839$	−11.8300	+	20.4901i	−0.408415	+	0.707396i	−0.994712	−	0.102700i	$-0.967252\pi$
$839$	−11.8300	+	20.4901i	−0.408415	+	0.707396i	0.586297	+	0.810096i	$0.300585\pi$
$840$		0			0
$841$	13.6514	−	23.6449i	0.470738	−	0.815341i
$842$	−20.2111	+	35.0067i	−0.696521	+	1.20641i
$843$	−6.29121			−0.216681
$844$	2.27082	−	3.93317i	0.0781648	−	0.135385i
$845$	36.3623	+	8.99734i	1.25090	+	0.309518i
$846$	−85.6512			−2.94475
$847$		0			0
$848$	15.8625	+	27.4746i	0.544720	+	0.943483i
$849$	11.5778			0.397349
$850$	1.87694	−	3.25096i	0.0643786	−	0.111507i
$851$	−4.60555	−	7.97705i	−0.157876	−	0.273450i
$852$	3.48974			0.119556
$853$	14.1431			0.484251			0.242126	−	0.970245i	$-0.422155\pi$
$853$	14.1431			0.484251			0.242126	+	0.970245i	$0.422155\pi$
$854$		0			0
$855$	−22.0139	−	38.1292i	−0.752859	−	1.30399i
$856$	−13.9542	+	24.1693i	−0.476943	+	0.826090i
$857$	−23.7920	+	41.2089i	−0.812719	+	1.40767i	0.0982356	+	0.995163i	$0.468680\pi$
$857$	−23.7920	+	41.2089i	−0.812719	+	1.40767i	−0.910954	+	0.412507i	$0.864653\pi$
$858$	−9.67494	+	79.3808i	−0.330297	+	2.71002i
$859$	12.3982	+	21.4744i	0.423023	+	0.732697i	0.996234	−	0.0867110i	$-0.0276357\pi$
$859$	12.3982	+	21.4744i	0.423023	+	0.732697i	−0.573211	+	0.819408i	$0.694302\pi$
$860$	−2.40525	−	4.16601i	−0.0820183	−	0.142060i
$861$		0			0
$862$	16.8944	−	29.2620i	0.575427	−	0.996669i
$863$	5.90833	+	10.2335i	0.201122	+	0.348353i	0.948890	−	0.315607i	$-0.102208\pi$
$863$	5.90833	+	10.2335i	0.201122	+	0.348353i	−0.747768	+	0.663960i	$0.768875\pi$
$864$	−5.63083	−	9.75289i	−0.191565	−	0.331800i
$865$	−34.4680	−	59.7004i	−1.17195	−	2.02987i
$866$	5.45877	+	9.45486i	0.185496	+	0.321289i
$867$	−23.3958	+	40.5226i	−0.794562	+	1.37622i
$868$		0			0
$869$	1.78890	+	3.09846i	0.0606842	+	0.105108i
$870$	7.04584	+	12.2037i	0.238876	+	0.413746i
$871$	−3.31767	+	1.41176i	−0.112415	+	0.0478356i
$872$	9.31665	−	16.1369i	0.315502	−	0.546465i
$873$	−20.6064	+	35.6913i	−0.697421	+	1.20797i
$874$	−12.3982	−	21.4744i	−0.419377	−	0.726382i
$875$		0			0
$876$	5.02776			0.169872
$877$	−38.3944			−1.29649			−0.648244	−	0.761432i	$-0.724496\pi$
$877$	−38.3944			−1.29649			−0.648244	+	0.761432i	$0.724496\pi$
$878$	9.95301	+	17.2391i	0.335898	+	0.581792i
$879$	−5.02776	+	8.70833i	−0.169582	+	0.293725i
$880$	−56.2283			−1.89546
$881$	17.7249	+	30.7005i	0.597168	+	1.03433i	0.993237	+	0.116105i	$0.0370409\pi$
$881$	17.7249	+	30.7005i	0.597168	+	1.03433i	−0.396069	+	0.918221i	$0.629626\pi$
$882$		0			0
$883$	−31.6056			−1.06361			−0.531806	−	0.846866i	$-0.678486\pi$
$883$	−31.6056			−1.06361			−0.531806	+	0.846866i	$0.678486\pi$
$884$	−0.115227	+	0.945417i	−0.00387552	+	0.0317978i
$885$	27.5459	−	47.7109i	0.925944	−	1.60378i
$886$	−39.3944			−1.32348
$887$	23.0516	−	39.9266i	0.773998	−	1.34060i	−0.161358	−	0.986896i	$-0.551587\pi$
$887$	23.0516	−	39.9266i	0.773998	−	1.34060i	0.935356	−	0.353708i	$-0.115079\pi$
$888$	6.02706	−	10.4392i	0.202255	−	0.350316i
$889$		0			0
$890$	16.2250	−	28.1025i	0.543863	−	0.941998i
$891$	−18.9722			−0.635594
$892$	2.04901	−	3.54899i	0.0686059	−	0.118829i
$893$	17.8625	+	30.9387i	0.597745	+	1.03533i
$894$	−0.964521	+	1.67060i	−0.0322584	+	0.0558732i
$895$	20.7385	+	35.9201i	0.693211	+	1.20068i
$896$		0			0
$897$	−8.30278	+	68.1225i	−0.277222	+	2.27454i
$898$	5.48612	+	9.50224i	0.183074	+	0.317094i
$899$	−1.13659			−0.0379073
$900$	−5.30278			−0.176759
$901$	8.38021			0.279185
$902$	−57.7890			−1.92416
$903$		0			0
$904$	22.2250	−	38.4948i	0.739192	−	1.28032i
$905$	−13.3305	−	23.0892i	−0.443122	−	0.767510i
$906$	11.6579	+	20.1921i	0.387307	+	0.670836i
$907$	18.8444			0.625718			0.312859	−	0.949800i	$-0.398713\pi$
$907$	18.8444			0.625718			0.312859	+	0.949800i	$0.398713\pi$
$908$	−4.15012	+	7.18821i	−0.137726	+	0.238549i
$909$	45.8391			1.52039
$910$		0			0
$911$	−10.9361			−0.362329			−0.181164	−	0.983453i	$-0.557987\pi$
$911$	−10.9361			−0.362329			−0.181164	+	0.983453i	$0.557987\pi$
$912$	13.7111	−	23.7483i	0.454020	−	0.786386i
$913$	−39.2038			−1.29746
$914$	8.72498	+	15.1121i	0.288597	+	0.499864i
$915$	23.9241	+	41.4377i	0.790905	+	1.36989i
$916$	−3.14561	+	5.44835i	−0.103934	+	0.180019i
$917$		0			0
$918$	7.54163			0.248911
$919$	−11.4500			−0.377699			−0.188850	−	0.982006i	$-0.560476\pi$
$919$	−11.4500			−0.377699			−0.188850	+	0.982006i	$0.560476\pi$
$920$	−57.1008			−1.88256
$921$	44.0278			1.45076
$922$	8.24813	+	14.2862i	0.271638	+	0.470490i
$923$	1.74487	−	14.3163i	0.0574330	−	0.471226i
$924$		0			0
$925$	−2.30278	−	3.98852i	−0.0757148	−	0.131142i
$926$	−18.3764	+	31.8288i	−0.603885	+	1.04596i
$927$	12.9665	+	22.4587i	0.425877	+	0.737641i
$928$	1.10555	−	1.91487i	0.0362915	−	0.0628587i
$929$	−8.38021			−0.274946			−0.137473	−	0.990506i	$-0.543898\pi$
$929$	−8.38021			−0.274946			−0.137473	+	0.990506i	$0.543898\pi$
$930$	−4.71841	+	8.17252i	−0.154723	+	0.267988i
$931$		0			0
$932$	−3.61943	+	6.26904i	−0.118558	+	0.205349i
$933$	24.5278	−	42.4833i	0.803003	−	1.39084i
$934$	−18.4253			−0.602895
$935$	−7.42641	+	12.8629i	−0.242869	+	0.420662i
$936$	−52.7786	+	22.4587i	−1.72512	+	0.734086i
$937$	−46.4474			−1.51737			−0.758685	−	0.651458i	$-0.774158\pi$
$937$	−46.4474			−1.51737			−0.758685	+	0.651458i	$0.774158\pi$
$938$		0			0
$939$	−19.1194	−	33.1158i	−0.623939	−	1.08069i
$940$	10.8167			0.352800
$941$	22.3513	−	38.7135i	0.728630	−	1.26202i	−0.228832	−	0.973466i	$-0.573491\pi$
$941$	22.3513	−	38.7135i	0.728630	−	1.26202i	0.957462	−	0.288559i	$-0.0931760\pi$
$942$	17.8625	+	30.9387i	0.581991	+	1.00804i
$943$	−49.5930			−1.61497
$944$	21.9150			0.713274
$945$		0			0
$946$	−21.2208	−	36.7555i	−0.689947	−	1.19502i
$947$	−26.5597	+	46.0028i	−0.863075	+	1.49489i	0.00587143	+	0.999983i	$0.498131\pi$
$947$	−26.5597	+	46.0028i	−0.863075	+	1.49489i	−0.868946	+	0.494907i	$0.835202\pi$
$948$	−0.264152	+	0.457524i	−0.00857925	+	0.0148597i
$949$	2.51388	−	20.6258i	0.0816039	−	0.669543i
$950$	−6.19912	−	10.7372i	−0.201126	−	0.348361i
$951$	11.8300	+	20.4901i	0.383613	+	0.664437i
$952$		0			0
$953$	−20.8028	+	36.0315i	−0.673868	+	1.16717i	0.302930	+	0.953013i	$0.402035\pi$
$953$	−20.8028	+	36.0315i	−0.673868	+	1.16717i	−0.976798	+	0.214161i	$0.931298\pi$
$954$	33.1791	+	57.4680i	1.07421	+	1.86059i
$955$	27.8100	+	48.1684i	0.899911	+	1.55869i
$956$	1.75694	+	3.04311i	0.0568235	+	0.0984211i
$957$	−11.0896	−	19.2077i	−0.358476	−	0.620898i
$958$	0.740358	−	1.28234i	0.0239199	−	0.0414305i
$959$		0			0
$960$	−36.6013	−	63.3954i	−1.18130	−	2.04608i
$961$	15.1194	+	26.1876i	0.487724	+	0.844762i
$962$	−5.23460	−	3.93725i	−0.168770	−	0.126942i
$963$	−24.6653	+	42.7215i	−0.794827	+	1.37668i
$964$	0.304141	−	0.526788i	0.00979573	−	0.0169667i
$965$	−2.61730	−	4.53330i	−0.0842539	−	0.145932i
$966$		0			0
$967$	22.4500			0.721942			0.360971	−	0.932577i	$-0.382445\pi$
$967$	22.4500			0.721942			0.360971	+	0.932577i	$0.382445\pi$
$968$	71.7250			2.30533
$969$	−3.62181	−	6.27316i	−0.116349	−	0.201523i
$970$	−14.5875	+	25.2662i	−0.468375	+	0.811250i
$971$	−10.1251			−0.324929			−0.162465	−	0.986714i	$-0.551944\pi$
$971$	−10.1251			−0.324929			−0.162465	+	0.986714i	$0.551944\pi$
$972$	1.61279	+	2.79344i	0.0517303	+	0.0895996i
$973$		0			0
$974$	36.0833			1.15618
$975$	−4.15139	+	34.0612i	−0.132951	+	1.09083i
$976$	−9.51680	+	16.4836i	−0.304625	+	0.527626i
$977$	−40.0278			−1.28060			−0.640301	−	0.768124i	$-0.721190\pi$
$977$	−40.0278			−1.28060			−0.640301	+	0.768124i	$0.721190\pi$
$978$	32.3043	−	55.9526i	1.03298	−	1.78917i
$979$	−25.5369	+	44.2311i	−0.816161	+	1.41363i
$980$		0			0
$981$	16.4680	−	28.5235i	0.525784	−	0.910685i
$982$	16.5778			0.529019
$983$	−6.50327	+	11.2640i	−0.207422	+	0.359265i	−0.950902	−	0.309493i	$-0.899841\pi$
$983$	−6.50327	+	11.2640i	−0.207422	+	0.359265i	0.743480	+	0.668758i	$0.233174\pi$
$984$	−32.4500	−	56.2050i	−1.03447	−	1.79175i
$985$	−17.1566	+	29.7162i	−0.546656	+	0.946836i
$986$	0.740358	+	1.28234i	0.0235778	+	0.0408380i
$987$		0			0
$988$	2.51388	+	1.89083i	0.0799771	+	0.0601554i
$989$	−18.2111	−	31.5426i	−0.579079	−	1.00299i
$990$	−117.611			−3.73793
$991$	−46.3305			−1.47174			−0.735869	−	0.677124i	$-0.763226\pi$
$991$	−46.3305			−1.47174			−0.735869	+	0.677124i	$0.763226\pi$
$992$	1.48072			0.0470128
$993$	−2.00902			−0.0637543
$994$		0			0
$995$	−1.25694	+	2.17708i	−0.0398476	+	0.0690182i
$996$	−2.89445	−	5.01333i	−0.0917141	−	0.158854i
$997$	−22.0871	−	38.2560i	−0.699506	−	1.21158i	−0.968638	−	0.248476i	$-0.920070\pi$
$997$	−22.0871	−	38.2560i	−0.699506	−	1.21158i	0.269132	−	0.963103i	$-0.413263\pi$
$998$	−40.8167			−1.29203
$999$	4.62632	−	8.01302i	0.146370	−	0.253521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.i.263.3		8
7.2	even	3		637.2.h.j.471.2		8
7.3	odd	6		637.2.f.h.393.3	yes	8
7.4	even	3		637.2.f.h.393.4	yes	8
7.5	odd	6		637.2.h.j.471.1		8
7.6	odd	2	inner	637.2.g.i.263.4		8
13.9	even	3		637.2.h.j.165.2		8
91.3	odd	6		8281.2.a.bu.1.2		4
91.9	even	3	inner	637.2.g.i.373.3		8
91.10	odd	6		8281.2.a.bo.1.4		4
91.48	odd	6		637.2.h.j.165.1		8
91.61	odd	6	inner	637.2.g.i.373.4		8
91.74	even	3		637.2.f.h.295.4	yes	8
91.81	even	3		8281.2.a.bu.1.1		4
91.87	odd	6		637.2.f.h.295.3	✓	8
91.88	even	6		8281.2.a.bo.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.h.295.3	✓	8	91.87	odd	6
637.2.f.h.295.4	yes	8	91.74	even	3
637.2.f.h.393.3	yes	8	7.3	odd	6
637.2.f.h.393.4	yes	8	7.4	even	3
637.2.g.i.263.3		8	1.1	even	1	trivial
637.2.g.i.263.4		8	7.6	odd	2	inner
637.2.g.i.373.3		8	91.9	even	3	inner
637.2.g.i.373.4		8	91.61	odd	6	inner
637.2.h.j.165.1		8	91.48	odd	6
637.2.h.j.165.2		8	13.9	even	3
637.2.h.j.471.1		8	7.5	odd	6
637.2.h.j.471.2		8	7.2	even	3
8281.2.a.bo.1.3		4	91.88	even	6
8281.2.a.bo.1.4		4	91.10	odd	6
8281.2.a.bu.1.1		4	91.81	even	3
8281.2.a.bu.1.2		4	91.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.651388 - 1.12824i) q^{2} -2.88145 q^{3} +(0.151388 + 0.262211i) q^{4} +(1.44073 + 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +5.30278 q^{9} +O(q^{10})\)	\(q+(0.651388 - 1.12824i) q^{2} -2.88145 q^{3} +(0.151388 + 0.262211i) q^{4} +(1.44073 + 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +5.30278 q^{9} +3.75389 q^{10} -5.90833 q^{11} +(-0.436217 - 0.755550i) q^{12} +(-3.31767 + 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} +(1.65139 - 2.86029i) q^{16} +(-0.436217 - 0.755550i) q^{17} +(3.45416 - 5.98279i) q^{18} -2.88145 q^{19} +(-0.436217 + 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +(-3.30278 + 5.72058i) q^{23} -8.64436 q^{24} +(-1.65139 + 2.86029i) q^{25} +(-0.568293 + 4.66272i) q^{26} -6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} -10.8167 q^{30} +(0.436217 - 0.755550i) q^{31} +(0.848612 + 1.46984i) q^{32} +17.0246 q^{33} -1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +(-0.697224 + 1.20763i) q^{37} +(-1.87694 + 3.25096i) q^{38} +(9.55971 - 4.06792i) q^{39} +(4.32218 + 7.48624i) q^{40} +(3.75389 + 6.50192i) q^{41} +(-2.75694 + 4.77516i) q^{43} +(-0.894449 - 1.54923i) q^{44} +(7.63985 + 13.2326i) q^{45} +(4.30278 + 7.45263i) q^{46} +(-6.19912 - 10.7372i) q^{47} +(-4.75840 + 8.24179i) q^{48} +(2.15139 + 3.72631i) q^{50} +(1.25694 + 2.17708i) q^{51} +(-0.872434 - 0.656208i) q^{52} +(-4.80278 + 8.31865i) q^{53} +(-4.32218 + 7.48624i) q^{54} +(-8.51229 - 14.7437i) q^{55} +8.30278 q^{57} -1.69722 q^{58} +(3.31767 + 5.74637i) q^{59} +(1.25694 - 2.17708i) q^{60} -5.76291 q^{61} +(-0.568293 - 0.984312i) q^{62} +8.81665 q^{64} +(-8.30278 - 6.24500i) q^{65} +(11.0896 - 19.2077i) q^{66} +1.00000 q^{67} +(0.132076 - 0.228762i) q^{68} +(9.51680 - 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +15.9083 q^{72} +(-2.88145 + 4.99082i) q^{73} +(0.908327 + 1.57327i) q^{74} +(4.75840 - 8.24179i) q^{75} +(-0.436217 - 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +(-0.302776 - 0.524423i) q^{79} +9.51680 q^{80} +3.21110 q^{81} +9.78095 q^{82} +6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} +(3.59167 + 6.22096i) q^{86} +(1.87694 + 3.25096i) q^{87} -17.7250 q^{88} +(4.32218 - 7.48624i) q^{89} +19.9060 q^{90} -2.00000 q^{92} +(-1.25694 + 2.17708i) q^{93} -16.1521 q^{94} +(-4.15139 - 7.19041i) q^{95} +(-2.44524 - 4.23527i) q^{96} +(-3.88596 + 6.73069i) q^{97} -31.3305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 28 * q^9	\( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9} - 4 q^{11} - 26 q^{15} + 6 q^{16} + 6 q^{18} - 38 q^{22} - 12 q^{23} - 6 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44} + 20 q^{46} + 10 q^{50} - 26 q^{51} - 24 q^{53} + 52 q^{57} - 28 q^{58} - 26 q^{60} - 16 q^{64} - 52 q^{65} + 8 q^{67} - 16 q^{71} + 84 q^{72} - 36 q^{74} + 78 q^{78} + 12 q^{79} - 32 q^{81} - 26 q^{85} + 72 q^{86} - 12 q^{88} - 16 q^{92} + 26 q^{93} - 26 q^{95} - 92 q^{99}+O(q^{100}) \) 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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