LMFDB - Embedded newform 637.2.h.j.471.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (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			471.2
Root			$-1.87694 + 1.08365i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.j.165.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30278 q^{2} +(1.44073 - 2.49541i) q^{3} -0.302776 q^{4} +(1.44073 - 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 - 4.59234i) q^{9} +O(q^{10})$	\(q-1.30278 q^{2} +(1.44073 - 2.49541i) q^{3} -0.302776 q^{4} +(1.44073 - 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 - 4.59234i) q^{9} +(-1.87694 + 3.25096i) q^{10} +(2.95416 - 5.11676i) q^{11} +(-0.436217 + 0.755550i) q^{12} +(-3.31767 + 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} -3.30278 q^{16} +0.872434 q^{17} +(3.45416 + 5.98279i) q^{18} +(1.44073 + 2.49541i) q^{19} +(-0.436217 + 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +6.60555 q^{23} +(4.32218 - 7.48624i) q^{24} +(-1.65139 - 2.86029i) q^{25} +(4.32218 - 1.83920i) q^{26} -6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} +(5.40833 + 9.36750i) q^{30} +(0.436217 + 0.755550i) q^{31} -1.69722 q^{32} +(-8.51229 - 14.7437i) q^{33} -1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +1.39445 q^{37} +(-1.87694 - 3.25096i) q^{38} +(-1.25694 + 10.3129i) 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} -15.2797 q^{45} -8.60555 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} +(1.00451 - 0.427446i) q^{52} +(-4.80278 - 8.31865i) q^{53} +8.64436 q^{54} +(-8.51229 - 14.7437i) q^{55} +8.30278 q^{57} +(0.848612 + 1.46984i) q^{58} -6.63534 q^{59} +(1.25694 + 2.17708i) q^{60} +(2.88145 + 4.99082i) q^{61} +(-0.568293 - 0.984312i) q^{62} +8.81665 q^{64} +(-1.25694 + 10.3129i) q^{65} +(11.0896 + 19.2077i) q^{66} +(-0.500000 + 0.866025i) q^{67} -0.264152 q^{68} +(9.51680 - 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +(-7.95416 - 13.7770i) q^{72} +(-2.88145 - 4.99082i) q^{73} -1.81665 q^{74} -9.51680 q^{75} +(-0.436217 - 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +(-0.302776 + 0.524423i) q^{79} +(-4.75840 + 8.24179i) q^{80} +(-1.60555 + 2.78090i) q^{81} +(-4.89047 - 8.47055i) q^{82} +6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} +(3.59167 - 6.22096i) q^{86} -3.75389 q^{87} +(8.86249 - 15.3503i) q^{88} -8.64436 q^{89} +19.9060 q^{90} -2.00000 q^{92} +2.51388 q^{93} +(8.07607 - 13.9882i) q^{94} +8.30278 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 + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 14 * q^9	$ 8 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} - 12 q^{16} + 6 q^{18} - 38 q^{22} + 24 q^{23} - 6 q^{25} + 2 q^{29} - 28 q^{32} - 8 q^{36} + 40 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44} - 40 q^{46} + 10 q^{50} - 26 q^{51} - 24 q^{53} + 52 q^{57} + 14 q^{58} - 26 q^{60} - 16 q^{64} + 26 q^{65} - 4 q^{67} - 16 q^{71} - 42 q^{72} + 72 q^{74} + 78 q^{78} + 12 q^{79} + 16 q^{81} - 26 q^{85} + 72 q^{86} + 6 q^{88} - 16 q^{92} - 52 q^{93} + 52 q^{95} - 92 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 14 * q^9 + 2 * q^11 - 26 * q^15 - 12 * q^16 + 6 * q^18 - 38 * q^22 + 24 * q^23 - 6 * q^25 + 2 * q^29 - 28 * q^32 - 8 * q^36 + 40 * q^37 + 26 * q^39 + 14 * q^43 - 36 * q^44 - 40 * q^46 + 10 * q^50 - 26 * q^51 - 24 * q^53 + 52 * q^57 + 14 * q^58 - 26 * q^60 - 16 * q^64 + 26 * q^65 - 4 * q^67 - 16 * q^71 - 42 * q^72 + 72 * q^74 + 78 * q^78 + 12 * q^79 + 16 * q^81 - 26 * q^85 + 72 * q^86 + 6 * q^88 - 16 * q^92 - 52 * q^93 + 52 * q^95 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.30278			−0.921201			−0.460601	−	0.887607i	$-0.652366\pi$
$2$	−1.30278			−0.921201			−0.460601	+	0.887607i	$0.652366\pi$
$3$	1.44073	−	2.49541i	0.831804	−	1.44073i	−0.0648022	−	0.997898i	$-0.520642\pi$
$3$	1.44073	−	2.49541i	0.831804	−	1.44073i	0.896606	−	0.442829i	$-0.146025\pi$
$4$	−0.302776			−0.151388
$5$	1.44073	−	2.49541i	0.644313	−	1.11598i	−0.340147	−	0.940372i	$-0.610477\pi$
$5$	1.44073	−	2.49541i	0.644313	−	1.11598i	0.984460	−	0.175610i	$-0.0561898\pi$
$6$	−1.87694	+	3.25096i	−0.766259	+	1.32720i
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	−2.65139	−	4.59234i	−0.883796	−	1.53078i
$10$	−1.87694	+	3.25096i	−0.593542	+	1.02804i
$11$	2.95416	−	5.11676i	0.890714	−	1.54276i	0.0516924	−	0.998663i	$-0.483538\pi$
$11$	2.95416	−	5.11676i	0.890714	−	1.54276i	0.839021	−	0.544098i	$-0.183128\pi$
$12$	−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
$16$	−3.30278			−0.825694
$17$	0.872434			0.211596			0.105798	−	0.994388i	$-0.466260\pi$
$17$	0.872434			0.211596			0.105798	+	0.994388i	$0.466260\pi$
$18$	3.45416	+	5.98279i	0.814154	+	1.41016i
$19$	1.44073	+	2.49541i	0.330525	+	0.572487i	0.982615	−	0.185655i	$-0.0594407\pi$
$19$	1.44073	+	2.49541i	0.330525	+	0.572487i	−0.652090	+	0.758142i	$0.726107\pi$
$20$	−0.436217	+	0.755550i	−0.0975411	+	0.168946i
$21$		0			0
$22$	−3.84861	+	6.66599i	−0.820527	+	1.42119i
$23$	6.60555			1.37735			0.688676	−	0.725069i	$-0.258192\pi$
$23$	6.60555			1.37735			0.688676	+	0.725069i	$0.258192\pi$
$24$	4.32218	−	7.48624i	0.882261	−	1.52812i
$25$	−1.65139	−	2.86029i	−0.330278	−	0.572058i
$26$	4.32218	−	1.83920i	0.847649	−	0.360698i
$27$	−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	$0.871931\pi$
$30$	5.40833	+	9.36750i	0.987421	+	1.71026i
$31$	0.436217	+	0.755550i	0.0783469	+	0.135701i	0.902537	−	0.430613i	$-0.141702\pi$
$31$	0.436217	+	0.755550i	0.0783469	+	0.135701i	−0.824190	+	0.566313i	$0.808369\pi$
$32$	−1.69722			−0.300030
$33$	−8.51229	−	14.7437i	−1.48180	−	2.56655i
$34$	−1.13659			−0.194923
$35$		0			0
$36$	0.802776	+	1.39045i	0.133796	+	0.231741i
$37$	1.39445			0.229246			0.114623	−	0.993409i	$-0.463434\pi$
$37$	1.39445			0.229246			0.114623	+	0.993409i	$0.463434\pi$
$38$	−1.87694	−	3.25096i	−0.304481	−	0.527376i
$39$	−1.25694	+	10.3129i	−0.201271	+	1.65139i
$40$	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
$45$	−15.2797			−2.27776
$46$	−8.60555			−1.26882
$47$	−6.19912	+	10.7372i	−0.904235	+	1.56618i	−0.0822947	+	0.996608i	$0.526225\pi$
$47$	−6.19912	+	10.7372i	−0.904235	+	1.56618i	−0.821941	+	0.569573i	$0.807108\pi$
$48$	−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
$52$	1.00451	−	0.427446i	0.139300	−	0.0592761i
$53$	−4.80278	−	8.31865i	−0.659712	−	1.14265i	−0.980690	−	0.195568i	$-0.937345\pi$
$53$	−4.80278	−	8.31865i	−0.659712	−	1.14265i	0.320978	−	0.947087i	$-0.395988\pi$
$54$	8.64436			1.17635
$55$	−8.51229	−	14.7437i	−1.14780	−	1.98804i
$56$		0			0
$57$	8.30278			1.09973
$58$	0.848612	+	1.46984i	0.111428	+	0.192999i
$59$	−6.63534			−0.863848			−0.431924	−	0.901910i	$-0.642165\pi$
$59$	−6.63534			−0.863848			−0.431924	+	0.901910i	$0.642165\pi$
$60$	1.25694	+	2.17708i	0.162270	+	0.281060i
$61$	2.88145	+	4.99082i	0.368932	+	0.639010i	0.989399	−	0.145223i	$-0.0463901\pi$
$61$	2.88145	+	4.99082i	0.368932	+	0.639010i	−0.620467	+	0.784233i	$0.713057\pi$
$62$	−0.568293	−	0.984312i	−0.0721733	−	0.125008i
$63$		0			0
$64$	8.81665			1.10208
$65$	−1.25694	+	10.3129i	−0.155904	+	1.27916i
$66$	11.0896	+	19.2077i	1.36504	+	2.36431i
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i	−0.894951	−	0.446165i	$-0.852789\pi$
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i	0.833866	+	0.551967i	$0.186123\pi$
$68$	−0.264152			−0.0320331
$69$	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	$0.242948\pi$
$72$	−7.95416	−	13.7770i	−0.937407	−	1.62364i
$73$	−2.88145	−	4.99082i	−0.337249	−	0.584132i	0.646666	−	0.762774i	$-0.276163\pi$
$73$	−2.88145	−	4.99082i	−0.337249	−	0.584132i	−0.983914	+	0.178642i	$0.942830\pi$
$74$	−1.81665			−0.211182
$75$	−9.51680			−1.09890
$76$	−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	−0.882555	−	0.470209i	$-0.844179\pi$
$79$	−0.302776	+	0.524423i	−0.0340649	+	0.0590022i	0.848490	+	0.529211i	$0.177512\pi$
$80$	−4.75840	+	8.24179i	−0.532005	+	0.921460i
$81$	−1.60555	+	2.78090i	−0.178395	+	0.308988i
$82$	−4.89047	−	8.47055i	−0.540062	−	0.935416i
$83$	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
$87$	−3.75389			−0.402459
$88$	8.86249	−	15.3503i	0.944745	−	1.63635i
$89$	−8.64436			−0.916300			−0.458150	−	0.888875i	$-0.651488\pi$
$89$	−8.64436			−0.916300			−0.458150	+	0.888875i	$0.651488\pi$
$90$	19.9060			2.09828
$91$		0			0
$92$	−2.00000			−0.208514
$93$	2.51388			0.260677
$94$	8.07607	−	13.9882i	0.832983	−	1.44277i
$95$	8.30278			0.851847
$96$	−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
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−4.32218	+	7.48624i	−0.430073	+	0.744908i	−0.996879	−	0.0789429i	$-0.974846\pi$
$101$	−4.32218	+	7.48624i	−0.430073	+	0.744908i	0.566806	+	0.823851i	$0.308179\pi$
$102$	−1.63751	+	2.83625i	−0.162138	+	0.280831i
$103$	2.44524	−	4.23527i	0.240936	−	0.417314i	−0.720045	−	0.693927i	$-0.755879\pi$
$103$	2.44524	−	4.23527i	0.240936	−	0.417314i	0.960981	+	0.276613i	$0.0892122\pi$
$104$	−9.95301	+	4.23527i	−0.975973	+	0.415303i
$105$		0			0
$106$	6.25694	+	10.8373i	0.607728	+	1.05262i
$107$	9.30278			0.899333			0.449667	−	0.893196i	$-0.351543\pi$
$107$	9.30278			0.899333			0.449667	+	0.893196i	$0.351543\pi$
$108$	2.00902			0.193318
$109$	3.10555	+	5.37897i	0.297458	+	0.515212i	0.975554	−	0.219761i	$-0.0705279\pi$
$109$	3.10555	+	5.37897i	0.297458	+	0.515212i	−0.678096	+	0.734974i	$0.737195\pi$
$110$	11.0896	+	19.2077i	1.05735	+	1.83139i
$111$	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	$-0.0787786\pi$
$114$	−10.8167			−1.01307
$115$	9.51680	−	16.4836i	0.887446	−	1.53710i
$116$	0.197224	+	0.341603i	0.0183118	+	0.0317170i
$117$	15.2797	+	11.4927i	1.41261	+	1.06250i
$118$	8.64436			0.795778
$119$		0			0
$120$	−12.4542	−	21.5712i	−1.13690	−	1.96918i
$121$	−11.9542	−	20.7052i	−1.08674	−	1.88229i
$122$	−3.75389	−	6.50192i	−0.339861	−	0.588657i
$123$	21.6333			1.95061
$124$	−0.132076	−	0.228762i	−0.0118608	−	0.0205434i
$125$	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	$0.792145\pi$
$128$	−8.09167			−0.715210
$129$	7.94399	+	13.7594i	0.699430	+	1.21145i
$130$	1.63751	−	13.4354i	0.143619	−	1.17836i
$131$	8.51229	−	14.7437i	0.743722	−	1.28816i	−0.207068	−	0.978327i	$-0.566392\pi$
$131$	8.51229	−	14.7437i	0.743722	−	1.28816i	0.950790	−	0.309837i	$-0.100275\pi$
$132$	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
$136$	2.61730			0.224432
$137$	2.69722			0.230439			0.115220	−	0.993340i	$-0.463243\pi$
$137$	2.69722			0.230439			0.115220	+	0.993340i	$0.463243\pi$
$138$	−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
$143$	−2.57731	+	21.1463i	−0.215526	+	1.76834i
$144$	8.75694	+	15.1675i	0.729745	+	1.26396i
$145$	−3.75389			−0.311743
$146$	3.75389	+	6.50192i	0.310674	+	0.538103i
$147$		0			0
$148$	−0.422205			−0.0347050
$149$	−0.256939	−	0.445032i	−0.0210493	−	0.0364584i	0.855309	−	0.518118i	$-0.173367\pi$
$149$	−0.256939	−	0.445032i	−0.0210493	−	0.0364584i	−0.876358	+	0.481660i	$0.840034\pi$
$150$	12.3982			1.01231
$151$	3.10555	+	5.37897i	0.252726	+	0.437735i	0.964275	−	0.264902i	$-0.0853395\pi$
$151$	3.10555	+	5.37897i	0.252726	+	0.437735i	−0.711549	+	0.702636i	$0.752006\pi$
$152$	4.32218	+	7.48624i	0.350575	+	0.607214i
$153$	−2.31316	−	4.00651i	−0.187008	−	0.323907i
$154$		0			0
$155$	2.51388			0.201920
$156$	0.380571	−	3.12250i	0.0304700	−	0.250000i
$157$	4.75840	+	8.24179i	0.379761	+	0.657766i	0.991027	−	0.133659i	$-0.0426727\pi$
$157$	4.75840	+	8.24179i	0.379761	+	0.657766i	−0.611266	+	0.791425i	$0.709339\pi$
$158$	0.394449	−	0.683205i	0.0313807	−	0.0543529i
$159$	−27.6780			−2.19500
$160$	−2.44524	+	4.23527i	−0.193313	+	0.334828i
$161$		0			0
$162$	2.09167	−	3.62288i	0.164337	−	0.284641i
$163$	8.60555	+	14.9053i	0.674039	+	1.16747i	0.976749	+	0.214387i	$0.0687753\pi$
$163$	8.60555	+	14.9053i	0.674039	+	1.16747i	−0.302710	+	0.953083i	$0.597891\pi$
$164$	−1.13659	−	1.96862i	−0.0887524	−	0.153724i
$165$	−49.0555			−3.81897
$166$	−8.64436			−0.670933
$167$	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
$171$	7.63985	−	13.2326i	0.584234	−	1.01192i
$172$	0.834734	−	1.44580i	0.0636479	−	0.110241i
$173$	11.9620	+	20.7188i	0.909456	+	1.57522i	0.814821	+	0.579713i	$0.196835\pi$
$173$	11.9620	+	20.7188i	0.909456	+	1.57522i	0.0946356	+	0.995512i	$0.469831\pi$
$174$	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
$178$	11.2617			0.844097
$179$	−7.19722	+	12.4660i	−0.537946	+	0.931749i	0.461069	+	0.887364i	$0.347466\pi$
$179$	−7.19722	+	12.4660i	−0.537946	+	0.931749i	−0.999014	+	0.0443850i	$0.985867\pi$
$180$	4.62632			0.344826
$181$	−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
$184$	19.8167			1.46090
$185$	2.00902	−	3.47972i	0.147706	−	0.255834i
$186$	−3.27502			−0.240136
$187$	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
$191$	−9.65139	−	16.7167i	−0.698350	−	1.20958i	−0.969038	−	0.246911i	$-0.920585\pi$
$191$	−9.65139	−	16.7167i	−0.698350	−	1.20958i	0.270688	−	0.962667i	$-0.412749\pi$
$192$	12.7024	−	22.0012i	0.916716	−	1.58780i
$193$	0.908327	−	1.57327i	0.0653828	−	0.113246i	−0.831481	−	0.555553i	$-0.812506\pi$
$193$	0.908327	−	1.57327i	0.0653828	−	0.113246i	0.896864	+	0.442307i	$0.145840\pi$
$194$	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	$0.693883\pi$
$198$	40.8167			2.90071
$199$	−0.872434			−0.0618452			−0.0309226	−	0.999522i	$-0.509845\pi$
$199$	−0.872434			−0.0618452			−0.0309226	+	0.999522i	$0.509845\pi$
$200$	−4.95416	−	8.58086i	−0.350312	−	0.606759i
$201$	1.44073	+	2.49541i	0.101621	+	0.176013i
$202$	5.63083	−	9.75289i	0.396184	−	0.686211i
$203$		0			0
$204$	−0.380571	+	0.659168i	−0.0266453	+	0.0461510i
$205$	21.6333			1.51094
$206$	−3.18559	+	5.51761i	−0.221951	+	0.384430i
$207$	−17.5139	−	30.3349i	−1.21730	−	2.10842i
$208$	10.9575	−	4.66272i	0.759767	−	0.323301i
$209$	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	$-0.339366\pi$
$212$	1.45416	+	2.51868i	0.0998724	+	0.172984i
$213$	5.76291	+	9.98165i	0.394868	+	0.683931i
$214$	−12.1194			−0.828467
$215$	7.94399	+	13.7594i	0.541776	+	0.938383i
$216$	−19.9060			−1.35443
$217$		0			0
$218$	−4.04584	−	7.00759i	−0.274019	−	0.474614i
$219$	−16.6056			−1.12210
$220$	2.57731	+	4.46404i	0.173762	+	0.300965i
$221$	−2.89445	+	1.23167i	−0.194702	+	0.0828508i
$222$	−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
$227$	−27.4138			−1.81952			−0.909759	−	0.415137i	$-0.863734\pi$
$227$	−27.4138			−1.81952			−0.909759	+	0.415137i	$0.863734\pi$
$228$	−2.51388			−0.166486
$229$	10.3892	−	17.9947i	0.686540	−	1.18912i	−0.286411	−	0.958107i	$-0.592462\pi$
$229$	10.3892	−	17.9947i	0.686540	−	1.18912i	0.972950	−	0.231015i	$-0.0742045\pi$
$230$	−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	−0.146959	−	0.989143i	$-0.546948\pi$
$233$	11.9542	−	20.7052i	0.783143	−	1.35644i	0.930102	−	0.367301i	$-0.119718\pi$
$234$	−19.9060	−	14.9725i	−1.30130	−	0.978781i
$235$	17.8625	+	30.9387i	1.16522	+	2.01822i
$236$	2.00902			0.130776
$237$	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	$0.377522\pi$
$240$	13.7111	+	23.7483i	0.885048	+	1.53295i
$241$	2.00902			0.129412			0.0647062	−	0.997904i	$-0.479389\pi$
$241$	2.00902			0.129412			0.0647062	+	0.997904i	$0.479389\pi$
$242$	15.5736	+	26.9743i	1.00111	+	1.73397i
$243$	−5.32669	−	9.22610i	−0.341707	−	0.591854i
$244$	−0.872434	−	1.51110i	−0.0558519	−	0.0967383i
$245$		0			0
$246$	−28.1833			−1.79690
$247$	−8.30278	−	6.24500i	−0.528293	−	0.397360i
$248$	1.30865	+	2.26665i	0.0830994	+	0.143932i
$249$	9.55971	−	16.5579i	0.605822	−	1.04932i
$250$	−6.37119			−0.402949
$251$	−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
$254$	−1.89445	−	3.28128i	−0.118868	−	0.205886i
$255$	−3.62181	−	6.27316i	−0.226807	−	0.392841i
$256$	−7.09167			−0.443230
$257$	22.7875			1.42144			0.710722	−	0.703473i	$-0.248368\pi$
$257$	22.7875			1.42144			0.710722	+	0.703473i	$0.248368\pi$
$258$	−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
$262$	−11.0896	+	19.2077i	−0.685118	+	1.18666i
$263$	6.71110	−	11.6240i	0.413824	−	0.716765i	−0.581480	−	0.813561i	$-0.697526\pi$
$263$	6.71110	−	11.6240i	0.413824	−	0.716765i	0.995304	+	0.0967960i	$0.0308594\pi$
$264$	−25.5369	−	44.2311i	−1.57168	−	2.72224i
$265$	−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
$269$	−9.51680			−0.580249			−0.290125	−	0.956989i	$-0.593697\pi$
$269$	−9.51680			−0.580249			−0.290125	+	0.956989i	$0.593697\pi$
$270$	12.4542	−	21.5712i	0.757936	−	1.31278i
$271$	−29.6870			−1.80336			−0.901678	−	0.432409i	$-0.857664\pi$
$271$	−29.6870			−1.80336			−0.901678	+	0.432409i	$0.857664\pi$
$272$	−2.88145			−0.174714
$273$		0			0
$274$	−3.51388			−0.212281
$275$	−19.5139			−1.17673
$276$	−2.88145	+	4.99082i	−0.173443	+	0.300412i
$277$	14.2111			0.853862			0.426931	−	0.904284i	$-0.359595\pi$
$277$	14.2111			0.853862			0.426931	+	0.904284i	$0.359595\pi$
$278$	−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	$0.479256\pi$
$282$	−23.2708	−	40.3062i	−1.38576	−	2.40020i
$283$	2.00902	−	3.47972i	0.119424	−	0.206848i	−0.800116	−	0.599846i	$-0.795229\pi$
$283$	2.00902	−	3.47972i	0.119424	−	0.206848i	0.919539	+	0.392998i	$0.128562\pi$
$284$	0.605551	−	1.04885i	0.0359329	−	0.0622375i
$285$	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
$289$	−16.2389			−0.955227
$290$	4.89047			0.287178
$291$	11.1972	+	19.3942i	0.656393	+	1.13691i
$292$	0.872434	+	1.51110i	0.0510553	+	0.0884304i
$293$	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
$296$	4.18335			0.243152
$297$	−19.6019	+	33.9515i	−1.13742	+	1.97006i
$298$	0.334734	+	0.579776i	0.0193906	+	0.0335855i
$299$	−21.9150	+	9.32544i	−1.26738	+	0.539304i
$300$	2.88145			0.166361
$301$		0			0
$302$	−4.04584	−	7.00759i	−0.232812	−	0.403242i
$303$	12.4542	+	21.5712i	0.715473	+	1.23924i
$304$	−4.75840	−	8.24179i	−0.272913	−	0.472699i
$305$	16.6056			0.950831
$306$	3.01353	+	5.21959i	0.172272	+	0.298384i
$307$	−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
$310$	−3.27502			−0.186009
$311$	−8.51229	−	14.7437i	−0.482687	−	0.836039i	0.517115	−	0.855916i	$-0.327006\pi$
$311$	−8.51229	−	14.7437i	−0.482687	−	0.836039i	−0.999802	+	0.0198768i	$0.993673\pi$
$312$	−3.77082	+	30.9387i	−0.213480	+	1.75156i
$313$	6.63534	−	11.4927i	0.375052	−	0.649609i	−0.615283	−	0.788306i	$-0.710958\pi$
$313$	6.63534	−	11.4927i	0.375052	−	0.649609i	0.990335	+	0.138698i	$0.0442916\pi$
$314$	−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	−0.957982	−	0.286828i	$-0.907399\pi$
$317$	−4.10555	+	7.11102i	−0.230591	+	0.399395i	0.727391	+	0.686223i	$0.240733\pi$
$318$	36.0582			2.02204
$319$	−7.69722			−0.430962
$320$	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
$325$	9.51680	+	7.15813i	0.527897	+	0.397062i
$326$	−11.2111	−	19.4182i	−0.620926	−	1.07547i
$327$	17.8970			0.989707
$328$	11.2617	+	19.5058i	0.621821	+	1.07703i
$329$		0			0
$330$	63.9083			3.51804
$331$	−0.348612	−	0.603814i	−0.0191615	−	0.0331886i	0.856286	−	0.516503i	$-0.172766\pi$
$331$	−0.348612	−	0.603814i	−0.0191615	−	0.0331886i	−0.875447	+	0.483314i	$0.839433\pi$
$332$	−2.00902			−0.110259
$333$	−3.69722	−	6.40378i	−0.202607	−	0.350925i
$334$	−3.18559	−	5.51761i	−0.174308	−	0.301910i
$335$	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	$0.562117\pi$
$338$	−11.7431	+	12.2037i	−0.638738	+	0.663796i
$339$	−21.3468	−	36.9737i	−1.15940	−	2.00813i
$340$	−0.380571	+	0.659168i	−0.0206393	+	0.0357484i
$341$	5.15463			0.279139
$342$	−9.95301	+	17.2391i	−0.538197	+	0.932185i
$343$		0			0
$344$	−8.27082	+	14.3255i	−0.445933	+	0.772378i
$345$	−27.4222	−	47.4967i	−1.47636	−	2.55713i
$346$	−15.5838	−	26.9920i	−0.837793	−	1.45110i
$347$	0.788897			0.0423502			0.0211751	−	0.999776i	$-0.493259\pi$
$347$	0.788897			0.0423502			0.0211751	+	0.999776i	$0.493259\pi$
$348$	1.13659			0.0609274
$349$	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
$353$	3.18559	−	5.51761i	0.169552	−	0.293673i	−0.768710	−	0.639597i	$-0.779101\pi$
$353$	3.18559	−	5.51761i	0.169552	−	0.293673i	0.938262	+	0.345924i	$0.112435\pi$
$354$	12.4542	−	21.5712i	0.661931	−	1.14650i
$355$	5.76291	+	9.98165i	0.305863	+	0.529771i
$356$	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	−0.387598	−	0.921828i	$-0.626695\pi$
$359$	11.4542	−	19.8392i	0.604528	−	1.04707i	0.992126	−	0.125244i	$-0.0399714\pi$
$360$	−45.8391			−2.41593
$361$	5.34861	−	9.26407i	0.281506	−	0.487583i
$362$	12.0541			0.633550
$363$	−68.8907			−3.61583
$364$		0			0
$365$	−16.6056			−0.869174
$366$	−21.6333			−1.13079
$367$	−14.1431	+	24.4966i	−0.738265	+	1.27871i	0.215011	+	0.976612i	$0.431021\pi$
$367$	−14.1431	+	24.4966i	−0.738265	+	1.27871i	−0.953276	+	0.302100i	$0.902312\pi$
$368$	−21.8167			−1.13727
$369$	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
$373$	8.15139	+	14.1186i	0.422063	+	0.731034i	0.996141	−	0.0877661i	$-0.0279728\pi$
$373$	8.15139	+	14.1186i	0.422063	+	0.731034i	−0.574078	+	0.818800i	$0.694639\pi$
$374$	−3.35766	+	5.81564i	−0.173620	+	0.300719i
$375$	7.04584	−	12.2037i	0.363845	−	0.630199i
$376$	−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	$0.942729\pi$
$380$	−2.51388			−0.128959
$381$	8.38021			0.429331
$382$	12.5736	+	21.7781i	0.643321	+	1.11426i
$383$	−9.64887	−	16.7123i	−0.493034	−	0.853960i	0.506934	−	0.861985i	$-0.330779\pi$
$383$	−9.64887	−	16.7123i	−0.493034	−	0.853960i	−0.999968	+	0.00802473i	$0.997446\pi$
$384$	−11.6579	+	20.1921i	−0.594914	+	1.03042i
$385$		0			0
$386$	−1.18335	+	2.04962i	−0.0602307	+	0.104323i
$387$	29.2389			1.48629
$388$	1.17658	−	2.03789i	0.0597316	−	0.103458i
$389$	3.51388	+	6.08622i	0.178161	+	0.308583i	0.941251	−	0.337709i	$-0.109652\pi$
$389$	3.51388	+	6.08622i	0.178161	+	0.308583i	−0.763090	+	0.646292i	$0.776319\pi$
$390$	−31.1677	−	23.4430i	−1.57824	−	1.18708i
$391$	5.76291			0.291443
$392$		0			0
$393$	−24.5278	−	42.4833i	−1.23726	−	2.14300i
$394$	−7.75694	−	13.4354i	−0.390789	−	0.676866i
$395$	0.872434	+	1.51110i	0.0438969	+	0.0760317i
$396$	9.48612			0.476696
$397$	2.88145	+	4.99082i	0.144616	+	0.250482i	0.929230	−	0.369503i	$-0.120472\pi$
$397$	2.88145	+	4.99082i	0.144616	+	0.250482i	−0.784614	+	0.619985i	$0.787139\pi$
$398$	1.13659			0.0569719
$399$		0			0
$400$	5.45416	+	9.44689i	0.272708	+	0.472344i
$401$	15.1194			0.755028			0.377514	−	0.926004i	$-0.376779\pi$
$401$	15.1194			0.755028			0.377514	+	0.926004i	$0.376779\pi$
$402$	−1.87694	−	3.25096i	−0.0936135	−	0.162143i
$403$	−2.51388	−	1.89083i	−0.125225	−	0.0941891i
$404$	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
$409$	16.1521			0.798672			0.399336	−	0.916805i	$-0.369241\pi$
$409$	16.1521			0.798672			0.399336	+	0.916805i	$0.369241\pi$
$410$	−28.1833			−1.39188
$411$	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
$416$	5.63083	−	2.39607i	0.276074	−	0.117477i
$417$	−24.5278	−	42.4833i	−1.20113	−	2.08042i
$418$	−22.1792			−1.08482
$419$	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	$0.772898\pi$
$422$	9.77082	+	16.9236i	0.475636	+	0.823826i
$423$	65.7451			3.19664
$424$	−14.4083	−	24.9560i	−0.699730	−	1.21197i
$425$	−1.44073	−	2.49541i	−0.0698855	−	0.121045i
$426$	−7.50778	−	13.0038i	−0.363753	−	0.630039i
$427$		0			0
$428$	−2.81665			−0.136148
$429$	49.0555	+	36.8975i	2.36842	+	1.78143i
$430$	−10.3492	−	17.9254i	−0.499085	−	0.864440i
$431$	−12.9680	+	22.4613i	−0.624649	+	1.08192i	0.363960	+	0.931415i	$0.381424\pi$
$431$	−12.9680	+	22.4613i	−0.624649	+	1.08192i	−0.988609	+	0.150509i	$0.951909\pi$
$432$	21.9150			1.05439
$433$	−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
$436$	−0.940285	−	1.62862i	−0.0450315	−	0.0779968i
$437$	9.51680	+	16.4836i	0.455250	+	0.788516i
$438$	21.6333			1.03368
$439$	15.2797			0.729260			0.364630	−	0.931152i	$-0.381195\pi$
$439$	15.2797			0.729260			0.364630	+	0.931152i	$0.381195\pi$
$440$	−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	0.243309	+	0.969949i	$0.421767\pi$
$443$	−15.1194	+	26.1876i	−0.718346	+	1.24421i	−0.961655	+	0.274263i	$0.911566\pi$
$444$	−0.608282	+	1.05358i	−0.0288678	+	0.0500005i
$445$	−12.4542	+	21.5712i	−0.590384	+	1.02258i
$446$	8.81643	+	15.2705i	0.417470	+	0.723079i
$447$	−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
$451$	44.3584			2.08876
$452$	−2.24306	+	3.88510i	−0.105505	+	0.182740i
$453$	17.8970			0.840875
$454$	35.7140			1.67614
$455$		0			0
$456$	24.9083			1.16644
$457$	13.3944			0.626566			0.313283	−	0.949660i	$-0.398571\pi$
$457$	13.3944			0.626566			0.313283	+	0.949660i	$0.398571\pi$
$458$	−13.5348	+	23.4430i	−0.632441	+	1.09542i
$459$	−5.78890			−0.270203
$460$	−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	$0.727559\pi$
$464$	2.15139	+	3.72631i	0.0998757	+	0.172990i
$465$	3.62181	−	6.27316i	0.167958	−	0.290911i
$466$	−15.5736	+	26.9743i	−0.721433	+	1.24956i
$467$	−7.07156	+	12.2483i	−0.327233	+	0.566784i	−0.981962	−	0.189080i	$-0.939449\pi$
$467$	−7.07156	+	12.2483i	−0.327233	+	0.566784i	0.654729	+	0.755864i	$0.272783\pi$
$468$	−4.62632	−	3.47972i	−0.213852	−	0.160850i
$469$		0			0
$470$	−23.2708	−	40.3062i	−1.07340	−	1.85919i
$471$	27.4222			1.26355
$472$	−19.9060			−0.916249
$473$	16.2889	+	28.2132i	0.748964	+	1.29724i
$474$	−1.13659	−	1.96862i	−0.0522051	−	0.0904219i
$475$	4.75840	−	8.24179i	0.218330	−	0.378159i
$476$		0			0
$477$	−25.4680	+	44.1119i	−1.16610	+	2.01975i
$478$	−15.1194			−0.691547
$479$	−0.568293	+	0.984312i	−0.0259660	+	0.0449744i	−0.878716	−	0.477344i	$-0.841599\pi$
$479$	−0.568293	+	0.984312i	−0.0259660	+	0.0449744i	0.852750	+	0.522319i	$0.174933\pi$
$480$	7.04584	+	12.2037i	0.321597	+	0.557022i
$481$	−4.62632	+	1.96862i	−0.210942	+	0.0897615i
$482$	−2.61730			−0.119215
$483$		0			0
$484$	3.61943	+	6.26904i	0.164520	+	0.284956i
$485$	11.1972	+	19.3942i	0.508440	+	0.880644i
$486$	6.93948	+	12.0195i	0.314781	+	0.545217i
$487$	−27.6972			−1.25508			−0.627541	−	0.778584i	$-0.715938\pi$
$487$	−27.6972			−1.25508			−0.627541	+	0.778584i	$0.715938\pi$
$488$	8.64436	+	14.9725i	0.391312	+	0.677772i
$489$	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	$0.740630\pi$
$492$	−6.55004			−0.295299
$493$	−0.568293	−	0.984312i	−0.0255946	−	0.0443312i
$494$	10.8167	+	8.13583i	0.486664	+	0.366048i
$495$	−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	0.266746	+	0.963767i	$0.414052\pi$
$499$	−15.6653	+	27.1330i	−0.701274	+	1.21464i	−0.968020	+	0.250875i	$0.919282\pi$
$500$	−1.48072			−0.0662196
$501$	14.0917			0.629570
$502$	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
$507$	−10.3892	−	35.9893i	−0.461402	−	1.59834i
$508$	−0.440285	−	0.762596i	−0.0195345	−	0.0338347i
$509$	2.61730			0.116010			0.0580049	−	0.998316i	$-0.481526\pi$
$509$	2.61730			0.116010			0.0580049	+	0.998316i	$0.481526\pi$
$510$	4.71841	+	8.17252i	0.208935	+	0.361885i
$511$		0			0
$512$	25.4222			1.12351
$513$	−9.55971	−	16.5579i	−0.422072	−	0.731050i
$514$	−29.6870			−1.30944
$515$	−7.04584	−	12.2037i	−0.310477	−	0.537761i
$516$	−2.40525	−	4.16601i	−0.105885	−	0.183398i
$517$	36.6265	+	63.4389i	1.61083	+	2.79004i
$518$		0			0
$519$	68.9361			3.02596
$520$	−3.77082	+	30.9387i	−0.165361	+	1.35675i
$521$	−14.4073	−	24.9541i	−0.631194	−	1.09326i	−0.987308	−	0.158817i	$-0.949232\pi$
$521$	−14.4073	−	24.9541i	−0.631194	−	1.09326i	0.356114	−	0.934442i	$-0.384101\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	9.25264			0.404590			0.202295	−	0.979325i	$-0.435160\pi$
$523$	9.25264			0.404590			0.202295	+	0.979325i	$0.435160\pi$
$524$	−2.57731	+	4.46404i	−0.112590	+	0.195012i
$525$		0			0
$526$	−8.74306	+	15.1434i	−0.381216	+	0.660285i
$527$	0.380571	+	0.659168i	0.0165779	+	0.0287138i
$528$	28.1142	+	48.6952i	1.22351	+	2.11919i
$529$	20.6333			0.897100
$530$	36.0582			1.56627
$531$	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
$535$	13.4028	−	23.2143i	0.579452	−	1.00364i
$536$	−1.50000	+	2.59808i	−0.0647901	+	0.112220i
$537$	20.7385	+	35.9201i	0.894931	+	1.55007i
$538$	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	−0.587496	−	0.809227i	$-0.699886\pi$
$541$	9.46804	−	16.3991i	0.407063	−	0.705054i	0.994559	+	0.104173i	$0.0332196\pi$
$542$	38.6755			1.66125
$543$	−13.3305	+	23.0892i	−0.572068	+	0.990851i
$544$	−1.48072			−0.0634852
$545$	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	$0.287143\pi$
$548$	−0.816654			−0.0348857
$549$	15.2797	−	26.4652i	0.652122	−	1.12951i
$550$	25.4222			1.08401
$551$	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
$555$	−5.78890	−	10.0267i	−0.245725	−	0.425608i
$556$	−2.57731	+	4.46404i	−0.109302	+	0.189317i
$557$	−8.45416	+	14.6430i	−0.358214	+	0.620446i	−0.987663	−	0.156597i	$-0.949948\pi$
$557$	−8.45416	+	14.6430i	−0.358214	+	0.620446i	0.629448	+	0.777042i	$0.283281\pi$
$558$	−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
$562$	−2.84441			−0.119984
$563$	19.0336			0.802170			0.401085	−	0.916041i	$-0.368633\pi$
$563$	19.0336			0.802170			0.401085	+	0.916041i	$0.368633\pi$
$564$	−5.40833	−	9.36750i	−0.227732	−	0.394443i
$565$	−21.3468	−	36.9737i	−0.898065	−	1.55549i
$566$	−2.61730	+	4.53330i	−0.110013	+	0.190549i
$567$		0			0
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	−27.3944			−1.14844			−0.574218	−	0.818703i	$-0.694694\pi$
$569$	−27.3944			−1.14844			−0.574218	+	0.818703i	$0.694694\pi$
$570$	−15.5838	+	26.9920i	−0.652735	+	1.13057i
$571$	−10.8625	−	18.8144i	−0.454581	−	0.787358i	0.544083	−	0.839031i	$-0.316878\pi$
$571$	−10.8625	−	18.8144i	−0.454581	−	0.787358i	−0.998664	+	0.0516739i	$0.983544\pi$
$572$	0.780347	−	6.40258i	0.0326280	−	0.267705i
$573$	−55.6201			−2.32356
$574$		0			0
$575$	−10.9083	−	18.8938i	−0.454909	−	0.787925i
$576$	−23.3764	−	40.4891i	−0.974015	−	1.68704i
$577$	16.8525	+	29.1894i	0.701579	+	1.21517i	0.967912	+	0.251289i	$0.0808546\pi$
$577$	16.8525	+	29.1894i	0.701579	+	1.21517i	−0.266333	+	0.963881i	$0.585812\pi$
$578$	21.1556			0.879957
$579$	−2.61730	−	4.53330i	−0.108771	−	0.188398i
$580$	1.13659			0.0471942
$581$		0			0
$582$	−14.5875	−	25.2662i	−0.604670	−	1.04732i
$583$	−56.7527			−2.35046
$584$	−8.64436	−	14.9725i	−0.357706	−	0.619565i
$585$	50.6930	−	21.5712i	2.09590	−	0.891861i
$586$	−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
$591$	34.3133			1.41146
$592$	−4.60555			−0.189287
$593$	−11.3937	+	19.7345i	−0.467885	+	0.810400i	−0.999327	−	0.0366946i	$-0.988317\pi$
$593$	−11.3937	+	19.7345i	−0.467885	+	0.810400i	0.531442	+	0.847095i	$0.321650\pi$
$594$	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
$598$	28.5504	−	12.1490i	1.16751	−	0.496808i
$599$	−3.75694	−	6.50721i	−0.153504	−	0.265877i	0.779009	−	0.627013i	$-0.215723\pi$
$599$	−3.75694	−	6.50721i	−0.153504	−	0.265877i	−0.932513	+	0.361135i	$0.882389\pi$
$600$	−28.5504			−1.16556
$601$	−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
$604$	−0.940285	−	1.62862i	−0.0382597	−	0.0662677i
$605$	−68.8907			−2.80081
$606$	−16.2250	−	28.1025i	−0.659095	−	1.14159i
$607$	10.2172	+	17.6966i	0.414702	+	0.718285i	0.995397	−	0.0958363i	$-0.0305525\pi$
$607$	10.2172	+	17.6966i	0.414702	+	0.718285i	−0.580695	+	0.814121i	$0.697219\pi$
$608$	−2.44524	−	4.23527i	−0.0991674	−	0.171763i
$609$		0			0
$610$	−21.6333			−0.875907
$611$	5.40833	−	44.3742i	0.218797	−	1.79519i
$612$	0.700369	+	1.21307i	0.0283107	+	0.0490356i
$613$	−10.5458	+	18.2659i	−0.425942	+	0.737754i	−0.996508	−	0.0834983i	$-0.973391\pi$
$613$	−10.5458	+	18.2659i	−0.425942	+	0.737754i	0.570566	+	0.821252i	$0.306724\pi$
$614$	19.9060			0.803342
$615$	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	$-0.152130\pi$
$618$	9.17914	+	15.8987i	0.369239	+	0.639541i
$619$	11.2617	+	19.5058i	0.452644	+	0.784003i	0.998549	−	0.0538439i	$-0.0171474\pi$
$619$	11.2617	+	19.5058i	0.452644	+	0.784003i	−0.545905	+	0.837847i	$0.683814\pi$
$620$	−0.761141			−0.0305682
$621$	−43.8301			−1.75884
$622$	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
$626$	−8.64436	+	14.9725i	−0.345498	+	0.598420i
$627$	24.5278	−	42.4833i	0.979544	−	1.69662i
$628$	−1.44073	−	2.49541i	−0.0574913	−	0.0995778i
$629$	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
$633$	−43.2218			−1.71791
$634$	5.34861	−	9.26407i	0.212421	−	0.367923i
$635$	8.38021			0.332558
$636$	8.38021			0.332297
$637$		0			0
$638$	10.0278			0.397003
$639$	21.2111			0.839098
$640$	−11.6579	+	20.1921i	−0.460819	+	0.798161i
$641$	3.51388			0.138790			0.0693949	−	0.997589i	$-0.477893\pi$
$641$	3.51388			0.138790			0.0693949	+	0.997589i	$0.477893\pi$
$642$	−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
$646$	−1.63751	−	2.83625i	−0.0644270	−	0.111591i
$647$	−1.13659	+	1.96862i	−0.0446838	+	0.0773946i	−0.887502	−	0.460803i	$-0.847561\pi$
$647$	−1.13659	+	1.96862i	−0.0446838	+	0.0773946i	0.842819	+	0.538198i	$0.180895\pi$
$648$	−4.81665	+	8.34269i	−0.189216	+	0.327732i
$649$	−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
$653$	21.7527			0.851250			0.425625	−	0.904900i	$-0.360054\pi$
$653$	21.7527			0.851250			0.425625	+	0.904900i	$0.360054\pi$
$654$	−23.3158			−0.911719
$655$	−24.5278	−	42.4833i	−0.958379	−	1.65996i
$656$	−12.3982	−	21.4744i	−0.484070	−	0.838434i
$657$	−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	$0.318929\pi$
$660$	14.8528			0.578145
$661$	−4.89047	+	8.47055i	−0.190217	+	0.329466i	−0.945322	−	0.326138i	$-0.894253\pi$
$661$	−4.89047	+	8.47055i	−0.190217	+	0.329466i	0.755105	+	0.655604i	$0.227586\pi$
$662$	0.454163	+	0.786634i	0.0176516	+	0.0305734i
$663$	−1.09660	+	8.99734i	−0.0425883	+	0.349428i
$664$	19.9060			0.772504
$665$		0			0
$666$	4.81665	+	8.34269i	0.186642	+	0.323273i
$667$	−4.30278	−	7.45263i	−0.166604	−	0.288567i
$668$	−0.740358	−	1.28234i	−0.0286453	−	0.0496151i
$669$	−39.0000			−1.50783
$670$	−1.87694	−	3.25096i	−0.0725127	−	0.125596i
$671$	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	$0.908958\pi$
$674$	9.27502			0.357260
$675$	10.9575	+	18.9790i	0.421755	+	0.730501i
$676$	−2.72918	+	2.83625i	−0.104969	+	0.109087i
$677$	3.18559	−	5.51761i	0.122432	−	0.212059i	−0.798294	−	0.602268i	$-0.794264\pi$
$677$	3.18559	−	5.51761i	0.122432	−	0.212059i	0.920726	+	0.390209i	$0.127597\pi$
$678$	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
$682$	−6.71532			−0.257143
$683$	3.60555			0.137963			0.0689813	−	0.997618i	$-0.478025\pi$
$683$	3.60555			0.137963			0.0689813	+	0.997618i	$0.478025\pi$
$684$	−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
$689$	27.6780	+	20.8182i	1.05445	+	0.793110i
$690$	35.7250	+	61.8775i	1.36003	+	2.35564i
$691$	−32.9126			−1.25205			−0.626026	−	0.779802i	$-0.715320\pi$
$691$	−32.9126			−1.25205			−0.626026	+	0.779802i	$0.715320\pi$
$692$	−3.62181	−	6.27316i	−0.137681	−	0.238470i
$693$		0			0
$694$	−1.02776			−0.0390131
$695$	−24.5278	−	42.4833i	−0.930391	−	1.61148i
$696$	−11.2617			−0.426872
$697$	3.27502	+	5.67250i	0.124050	+	0.214861i
$698$	−15.5838	−	26.9920i	−0.589857	−	1.02166i
$699$	−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	$0.670507\pi$
$702$	−28.6791	+	12.2037i	−1.08242	+	0.460601i
$703$	2.00902	+	3.47972i	0.0757716	+	0.131240i
$704$	26.0458	−	45.1127i	0.981639	−	1.70025i
$705$	102.940			3.87694
$706$	−4.15012	+	7.18821i	−0.156192	+	0.270532i
$707$		0			0
$708$	2.89445	−	5.01333i	0.108780	−	0.188413i
$709$	−0.137510	−	0.238174i	−0.00516428	−	0.00894480i	0.863432	−	0.504466i	$-0.168311\pi$
$709$	−0.137510	−	0.238174i	−0.00516428	−	0.00894480i	−0.868596	+	0.495521i	$0.834977\pi$
$710$	−7.50778	−	13.0038i	−0.281762	−	0.488026i
$711$	3.21110			0.120426
$712$	−25.9331			−0.971883
$713$	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
$717$	16.7204	−	28.9606i	0.624436	−	1.08155i
$718$	−14.9222	+	25.8460i	−0.556892	+	0.964565i
$719$	10.8254	+	18.7502i	0.403721	+	0.699265i	0.994172	−	0.107808i	$-0.0343833\pi$
$719$	10.8254	+	18.7502i	0.403721	+	0.699265i	−0.590451	+	0.807074i	$0.701050\pi$
$720$	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
$724$	2.80148			0.104116
$725$	−2.15139	+	3.72631i	−0.0799005	+	0.138392i
$726$	89.7492			3.33090
$727$	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
$730$	21.6333			0.800685
$731$	−2.40525	+	4.16601i	−0.0889613	+	0.154085i
$732$	−5.02776			−0.185831
$733$	−20.0381	+	34.7070i	−0.740124	+	1.28193i	0.212314	+	0.977201i	$0.431900\pi$
$733$	−20.0381	+	34.7070i	−0.740124	+	1.28193i	−0.952438	+	0.304731i	$0.901433\pi$
$734$	18.4253	−	31.9136i	0.680091	−	1.17795i
$735$		0			0
$736$	−11.2111			−0.413247
$737$	2.95416	+	5.11676i	0.108818	+	0.188478i
$738$	−25.9331	+	44.9174i	−0.954610	+	1.65343i
$739$	9.39445	−	16.2717i	0.345580	−	0.598563i	−0.639879	−	0.768476i	$-0.721015\pi$
$739$	9.39445	−	16.2717i	0.345580	−	0.598563i	0.985459	+	0.169913i	$0.0543487\pi$
$740$	−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	$0.590289\pi$
$744$	7.54163			0.276490
$745$	−1.48072			−0.0542492
$746$	−10.6194	−	18.3934i	−0.388805	−	0.673430i
$747$	−17.5929	−	30.4717i	−0.643689	−	1.11490i
$748$	−0.780347	+	1.35160i	−0.0285323	+	0.0494194i
$749$		0			0
$750$	−9.17914	+	15.8987i	−0.335175	+	0.580540i
$751$	−4.39445			−0.160356			−0.0801779	−	0.996781i	$-0.525549\pi$
$751$	−4.39445			−0.160356			−0.0801779	+	0.996781i	$0.525549\pi$
$752$	20.4743	−	35.4626i	0.746622	−	1.29319i
$753$	32.4500	+	56.2050i	1.18254	+	2.04822i
$754$	−4.89047	−	3.67841i	−0.178101	−	0.133960i
$755$	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	$0.536064\pi$
$758$	8.54584	+	14.8018i	0.310399	+	0.537626i
$759$	−56.2283	−	97.3903i	−2.04096	−	3.53505i
$760$	24.9083			0.903520
$761$	−2.14110	−	3.70849i	−0.0776147	−	0.134433i	0.824606	−	0.565708i	$-0.191397\pi$
$761$	−2.14110	−	3.70849i	−0.0776147	−	0.134433i	−0.902220	+	0.431275i	$0.858064\pi$
$762$	−10.9175			−0.395500
$763$		0			0
$764$	2.92221	+	5.06141i	0.105722	+	0.183115i
$765$	−13.3305			−0.481966
$766$	12.5703	+	21.7724i	0.454184	+	0.786670i
$767$	22.0139	−	9.36750i	0.794875	−	0.338241i
$768$	−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
$773$	34.9216			1.25604			0.628021	−	0.778196i	$-0.283865\pi$
$773$	34.9216			1.25604			0.628021	+	0.778196i	$0.283865\pi$
$774$	−38.0917			−1.36918
$775$	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
$780$	−7.24362	−	5.44835i	−0.259363	−	0.195082i
$781$	11.8167	+	20.4670i	0.422833	+	0.732368i
$782$	−7.50778			−0.268478
$783$	4.32218	+	7.48624i	0.154462	+	0.267536i
$784$		0			0
$785$	27.4222			0.978740
$786$	31.9542	+	55.3462i	1.13977	+	1.97413i
$787$	−41.5569			−1.48134			−0.740672	−	0.671867i	$-0.765493\pi$
$787$	−41.5569			−1.48134			−0.740672	+	0.671867i	$0.765493\pi$
$788$	−1.80278	−	3.12250i	−0.0642212	−	0.111234i
$789$	−19.3377	−	33.4939i	−0.688441	−	1.19242i
$790$	−1.13659	−	1.96862i	−0.0404379	−	0.0700405i
$791$		0			0
$792$	−93.9916			−3.33985
$793$	−16.6056	−	12.4900i	−0.589680	−	0.443533i
$794$	−3.75389	−	6.50192i	−0.133220	−	0.230745i
$795$	−39.8764	+	69.0679i	−1.41427	+	2.44959i
$796$	0.264152			0.00936261
$797$	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
$800$	2.80278	+	4.85455i	0.0990931	+	0.171634i
$801$	22.9196	+	39.6978i	0.809823	+	1.40265i
$802$	−19.6972			−0.695533
$803$	−34.0491			−1.20157
$804$	−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
$808$	−12.9665	+	22.4587i	−0.456161	+	0.790095i
$809$	8.01388	−	13.8804i	0.281753	−	0.488010i	−0.690064	−	0.723749i	$-0.742417\pi$
$809$	8.01388	−	13.8804i	0.281753	−	0.488010i	0.971817	+	0.235738i	$0.0757508\pi$
$810$	−6.02706	−	10.4392i	−0.211769	−	0.366795i
$811$	−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
$815$	49.5930			1.73717
$816$	−4.15139	+	7.19041i	−0.145328	+	0.251715i
$817$	−15.8880			−0.555850
$818$	−21.0426			−0.735738
$819$		0			0
$820$	−6.55004			−0.228737
$821$	1.84441			0.0643704			0.0321852	−	0.999482i	$-0.489753\pi$
$821$	1.84441			0.0643704			0.0321852	+	0.999482i	$0.489753\pi$
$822$	−5.06254	+	8.76857i	−0.176576	+	0.305839i
$823$	−44.2666			−1.54304			−0.771519	−	0.636207i	$-0.780503\pi$
$823$	−44.2666			−1.54304			−0.771519	+	0.636207i	$0.780503\pi$
$824$	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	$0.143705\pi$
$828$	5.30278	+	9.18468i	0.184284	+	0.319190i
$829$	−7.81192	+	13.5306i	−0.271319	+	0.469938i	−0.969200	−	0.246276i	$-0.920793\pi$
$829$	−7.81192	+	13.5306i	−0.271319	+	0.469938i	0.697881	+	0.716214i	$0.254127\pi$
$830$	−12.4542	+	21.5712i	−0.432290	+	0.748749i
$831$	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
$835$	14.0917			0.487662
$836$	−5.15463			−0.178276
$837$	−2.89445	−	5.01333i	−0.100047	−	0.173286i
$838$	−5.45877	−	9.45486i	−0.188570	−	0.326613i
$839$	−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
$842$	40.4222			1.39304
$843$	3.14561	−	5.44835i	0.108340	−	0.187651i
$844$	2.27082	+	3.93317i	0.0781648	+	0.135385i
$845$	−10.3892	−	35.9893i	−0.357400	−	1.23807i
$846$	−85.6512			−2.94475
$847$		0			0
$848$	15.8625	+	27.4746i	0.544720	+	0.943483i
$849$	−5.78890	−	10.0267i	−0.198674	−	0.344114i
$850$	1.87694	+	3.25096i	0.0643786	+	0.111507i
$851$	9.21110			0.315753
$852$	−1.74487	−	3.02220i	−0.0597782	−	0.103539i
$853$	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
$856$	27.9083			0.953887
$857$	−23.7920	−	41.2089i	−0.812719	−	1.40767i	−0.910954	−	0.412507i	$-0.864653\pi$
$857$	−23.7920	−	41.2089i	−0.812719	−	1.40767i	0.0982356	−	0.995163i	$-0.468680\pi$
$858$	−63.9083	−	48.0692i	−2.18179	−	1.64105i
$859$	12.3982	−	21.4744i	0.423023	−	0.732697i	−0.573211	−	0.819408i	$-0.694302\pi$
$859$	12.3982	−	21.4744i	0.423023	−	0.732697i	0.996234	+	0.0867110i	$0.0276357\pi$
$860$	−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	−0.747768	−	0.663960i	$-0.768875\pi$
$863$	5.90833	−	10.2335i	0.201122	−	0.348353i	0.948890	+	0.315607i	$0.102208\pi$
$864$	11.2617			0.383130
$865$	68.9361			2.34390
$866$	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
$871$	0.436217	−	3.57907i	0.0147806	−	0.121272i
$872$	9.31665	+	16.1369i	0.315502	+	0.546465i
$873$	41.2128			1.39484
$874$	−12.3982	−	21.4744i	−0.419377	−	0.726382i
$875$		0			0
$876$	5.02776			0.169872
$877$	19.1972	+	33.2506i	0.648244	+	1.12279i	0.983542	+	0.180680i	$0.0578297\pi$
$877$	19.1972	+	33.2506i	0.648244	+	1.12279i	−0.335298	+	0.942112i	$0.608837\pi$
$878$	−19.9060			−0.671796
$879$	−5.02776	−	8.70833i	−0.169582	−	0.293725i
$880$	28.1142	+	48.6952i	0.947728	+	1.64151i
$881$	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	$0.678486\pi$
$884$	0.876369	−	0.372918i	0.0294755	−	0.0125426i
$885$	27.5459	+	47.7109i	0.925944	+	1.60378i
$886$	19.6972	−	34.1166i	0.661741	−	1.14617i
$887$	−46.1033			−1.54800			−0.773998	−	0.633188i	$-0.781746\pi$
$887$	−46.1033			−1.54800			−0.773998	+	0.633188i	$0.781746\pi$
$888$	6.02706	−	10.4392i	0.202255	−	0.350316i
$889$		0			0
$890$	16.2250	−	28.1025i	0.543863	−	0.941998i
$891$	9.48612	+	16.4304i	0.317797	+	0.550441i
$892$	2.04901	+	3.54899i	0.0686059	+	0.118829i
$893$	−35.7250			−1.19549
$894$	1.92904			0.0645168
$895$	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
$899$	0.568293	−	0.984312i	0.0189536	−	0.0328286i
$900$	2.65139	−	4.59234i	0.0883796	−	0.153078i
$901$	−4.19010	−	7.25747i	−0.139593	−	0.241782i
$902$	−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
$906$	−23.3158			−0.774615
$907$	−9.42221	+	16.3197i	−0.312859	+	0.541888i	−0.978980	−	0.203956i	$-0.934620\pi$
$907$	−9.42221	+	16.3197i	−0.312859	+	0.541888i	0.666121	+	0.745844i	$0.267953\pi$
$908$	8.30023			0.275453
$909$	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	$0.557987\pi$
$912$	−27.4222			−0.908040
$913$	19.6019	−	33.9515i	0.648728	−	1.12363i
$914$	−17.4500			−0.577193
$915$	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
$919$	5.72498	+	9.91596i	0.188850	+	0.327097i	0.944867	−	0.327454i	$-0.106191\pi$
$919$	5.72498	+	9.91596i	0.188850	+	0.327097i	−0.756017	+	0.654552i	$0.772857\pi$
$920$	28.5504	−	49.4507i	0.941278	−	1.63034i
$921$	−22.0139	+	38.1292i	−0.725382	+	1.25640i
$922$	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
$926$	36.7527			1.20777
$927$	−25.9331			−0.851754
$928$	1.10555	+	1.91487i	0.0362915	+	0.0628587i
$929$	4.19010	+	7.25747i	0.137473	+	0.238110i	0.926539	−	0.376198i	$-0.122769\pi$
$929$	4.19010	+	7.25747i	0.137473	+	0.238110i	−0.789067	+	0.614308i	$0.789435\pi$
$930$	−4.71841	+	8.17252i	−0.154723	+	0.267988i
$931$		0			0
$932$	−3.61943	+	6.26904i	−0.118558	+	0.205349i
$933$	−49.0555			−1.60601
$934$	9.21265	−	15.9568i	0.301447	−	0.522122i
$935$	−7.42641	−	12.8629i	−0.242869	−	0.420662i
$936$	45.8391	+	34.4782i	1.49830	+	1.12696i
$937$	−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
$940$	−5.40833	−	9.36750i	−0.176400	−	0.305534i
$941$	22.3513	+	38.7135i	0.728630	+	1.26202i	0.957462	+	0.288559i	$0.0931760\pi$
$941$	22.3513	+	38.7135i	0.728630	+	1.26202i	−0.228832	+	0.973466i	$0.573491\pi$
$942$	−35.7250			−1.16398
$943$	24.7965	+	42.9488i	0.807485	+	1.39861i
$944$	21.9150			0.713274
$945$		0			0
$946$	−21.2208	−	36.7555i	−0.689947	−	1.19502i
$947$	53.1194			1.72615			0.863075	−	0.505076i	$-0.168536\pi$
$947$	53.1194			1.72615			0.863075	+	0.505076i	$0.168536\pi$
$948$	−0.264152	−	0.457524i	−0.00857925	−	0.0148597i
$949$	16.6056	+	12.4900i	0.539039	+	0.405442i
$950$	−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
$955$	−55.6201			−1.79982
$956$	−3.51388			−0.113647
$957$	−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
$962$	6.02706	−	2.56468i	0.194320	−	0.0826885i
$963$	−24.6653	−	42.7215i	−0.794827	−	1.37668i
$964$	−0.608282			−0.0195915
$965$	−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	$0.382445\pi$
$968$	−35.8625	−	62.1157i	−1.15266	−	1.99647i
$969$	7.24362			0.232699
$970$	−14.5875	−	25.2662i	−0.468375	−	0.811250i
$971$	5.06254	+	8.76857i	0.162465	+	0.281397i	0.935752	−	0.352659i	$-0.114722\pi$
$971$	5.06254	+	8.76857i	0.162465	+	0.281397i	−0.773287	+	0.634056i	$0.781389\pi$
$972$	1.61279	+	2.79344i	0.0517303	+	0.0895996i
$973$		0			0
$974$	36.0833			1.15618
$975$	31.5736	−	13.4354i	1.01116	−	0.430278i
$976$	−9.51680	−	16.4836i	−0.304625	−	0.527626i
$977$	20.0139	−	34.6651i	0.640301	−	1.10903i	−0.345065	−	0.938579i	$-0.612143\pi$
$977$	20.0139	−	34.6651i	0.640301	−	1.10903i	0.985366	−	0.170454i	$-0.0545236\pi$
$978$	−64.6085			−2.06595
$979$	−25.5369	+	44.2311i	−0.816161	+	1.41363i
$980$		0			0
$981$	16.4680	−	28.5235i	0.525784	−	0.910685i
$982$	−8.28890	−	14.3568i	−0.264509	−	0.458144i
$983$	−6.50327	−	11.2640i	−0.207422	−	0.359265i	0.743480	−	0.668758i	$-0.233174\pi$
$983$	−6.50327	−	11.2640i	−0.207422	−	0.359265i	−0.950902	+	0.309493i	$0.899841\pi$
$984$	64.8999			2.06893
$985$	34.3133			1.09331
$986$	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
$990$	58.8056	−	101.854i	1.86897	−	3.23714i
$991$	23.1653	−	40.1234i	0.735869	−	1.27456i	−0.218472	−	0.975843i	$-0.570107\pi$
$991$	23.1653	−	40.1234i	0.735869	−	1.27456i	0.954341	−	0.298719i	$-0.0965594\pi$
$992$	−0.740358	−	1.28234i	−0.0235064	−	0.0407143i
$993$	−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
$997$	44.1742			1.39901			0.699506	−	0.714627i	$-0.253404\pi$
$997$	44.1742			1.39901			0.699506	+	0.714627i	$0.253404\pi$
$998$	20.4083	−	35.3483i	0.646014	−	1.11893i
$999$	−9.25264			−0.292741

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.h.295.3	✓	8	91.61	odd	6
637.2.f.h.295.4	yes	8	91.9	even	3
637.2.f.h.393.3	yes	8	7.5	odd	6
637.2.f.h.393.4	yes	8	7.2	even	3
637.2.g.i.263.3		8	7.4	even	3
637.2.g.i.263.4		8	7.3	odd	6
637.2.g.i.373.3		8	13.9	even	3
637.2.g.i.373.4		8	91.48	odd	6
637.2.h.j.165.1		8	91.87	odd	6	inner
637.2.h.j.165.2		8	91.74	even	3	inner
637.2.h.j.471.1		8	7.6	odd	2	inner
637.2.h.j.471.2		8	1.1	even	1	trivial
8281.2.a.bo.1.3		4	91.23	even	6
8281.2.a.bo.1.4		4	91.75	odd	6
8281.2.a.bu.1.1		4	91.16	even	3
8281.2.a.bu.1.2		4	91.68	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.30278 q^{2} +(1.44073 - 2.49541i) q^{3} -0.302776 q^{4} +(1.44073 - 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 - 4.59234i) q^{9} +O(q^{10})\)	\(q-1.30278 q^{2} +(1.44073 - 2.49541i) q^{3} -0.302776 q^{4} +(1.44073 - 2.49541i) q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 - 4.59234i) q^{9} +(-1.87694 + 3.25096i) q^{10} +(2.95416 - 5.11676i) q^{11} +(-0.436217 + 0.755550i) q^{12} +(-3.31767 + 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} -3.30278 q^{16} +0.872434 q^{17} +(3.45416 + 5.98279i) q^{18} +(1.44073 + 2.49541i) q^{19} +(-0.436217 + 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +6.60555 q^{23} +(4.32218 - 7.48624i) q^{24} +(-1.65139 - 2.86029i) q^{25} +(4.32218 - 1.83920i) q^{26} -6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} +(5.40833 + 9.36750i) q^{30} +(0.436217 + 0.755550i) q^{31} -1.69722 q^{32} +(-8.51229 - 14.7437i) q^{33} -1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +1.39445 q^{37} +(-1.87694 - 3.25096i) q^{38} +(-1.25694 + 10.3129i) 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} -15.2797 q^{45} -8.60555 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} +(1.00451 - 0.427446i) q^{52} +(-4.80278 - 8.31865i) q^{53} +8.64436 q^{54} +(-8.51229 - 14.7437i) q^{55} +8.30278 q^{57} +(0.848612 + 1.46984i) q^{58} -6.63534 q^{59} +(1.25694 + 2.17708i) q^{60} +(2.88145 + 4.99082i) q^{61} +(-0.568293 - 0.984312i) q^{62} +8.81665 q^{64} +(-1.25694 + 10.3129i) q^{65} +(11.0896 + 19.2077i) q^{66} +(-0.500000 + 0.866025i) q^{67} -0.264152 q^{68} +(9.51680 - 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +(-7.95416 - 13.7770i) q^{72} +(-2.88145 - 4.99082i) q^{73} -1.81665 q^{74} -9.51680 q^{75} +(-0.436217 - 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +(-0.302776 + 0.524423i) q^{79} +(-4.75840 + 8.24179i) q^{80} +(-1.60555 + 2.78090i) q^{81} +(-4.89047 - 8.47055i) q^{82} +6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} +(3.59167 - 6.22096i) q^{86} -3.75389 q^{87} +(8.86249 - 15.3503i) q^{88} -8.64436 q^{89} +19.9060 q^{90} -2.00000 q^{92} +2.51388 q^{93} +(8.07607 - 13.9882i) q^{94} +8.30278 q^{95} +(-2.44524 + 4.23527i) q^{96} +(-3.88596 + 6.73069i) q^{97} -31.3305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 14 * q^9	\( 8 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} - 12 q^{16} + 6 q^{18} - 38 q^{22} + 24 q^{23} - 6 q^{25} + 2 q^{29} - 28 q^{32} - 8 q^{36} + 40 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44} - 40 q^{46} + 10 q^{50} - 26 q^{51} - 24 q^{53} + 52 q^{57} + 14 q^{58} - 26 q^{60} - 16 q^{64} + 26 q^{65} - 4 q^{67} - 16 q^{71} - 42 q^{72} + 72 q^{74} + 78 q^{78} + 12 q^{79} + 16 q^{81} - 26 q^{85} + 72 q^{86} + 6 q^{88} - 16 q^{92} - 52 q^{93} + 52 q^{95} - 92 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 12 * q^4 + 24 * q^8 - 14 * q^9 + 2 * q^11 - 26 * q^15 - 12 * q^16 + 6 * q^18 - 38 * q^22 + 24 * q^23 - 6 * q^25 + 2 * q^29 - 28 * q^32 - 8 * q^36 + 40 * q^37 + 26 * q^39 + 14 * q^43 - 36 * q^44 - 40 * q^46 + 10 * q^50 - 26 * q^51 - 24 * q^53 + 52 * q^57 + 14 * q^58 - 26 * q^60 - 16 * q^64 + 26 * q^65 - 4 * q^67 - 16 * q^71 - 42 * q^72 + 72 * q^74 + 78 * q^78 + 12 * q^79 + 16 * q^81 - 26 * q^85 + 72 * q^86 + 6 * q^88 - 16 * q^92 - 52 * q^93 + 52 * q^95 - 92 * q^99

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