LMFDB - Embedded newform 637.2.h.j.165.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,4,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			165.1
Root			$1.87694 + 1.08365i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.j.471.1

$q$-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} +(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} + 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$	−1.30278			−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	−0.896606	−	0.442829i	$-0.853975\pi$
$3$	−1.44073	−	2.49541i	−0.831804	−	1.44073i	0.0648022	−	0.997898i	$-0.479358\pi$
$4$	−0.302776			−0.151388
$5$	−1.44073	−	2.49541i	−0.644313	−	1.11598i	−0.984460	−	0.175610i	$-0.943810\pi$
$5$	−1.44073	−	2.49541i	−0.644313	−	1.11598i	0.340147	−	0.940372i	$-0.389523\pi$
$6$	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	0.839021	+	0.544098i	$0.183128\pi$
$11$	2.95416	+	5.11676i	0.890714	+	1.54276i	0.0516924	+	0.998663i	$0.483538\pi$
$12$	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	$-0.533740\pi$
$17$	−0.872434			−0.211596			−0.105798	+	0.994388i	$0.533740\pi$
$18$	3.45416	−	5.98279i	0.814154	−	1.41016i
$19$	−1.44073	+	2.49541i	−0.330525	+	0.572487i	−0.982615	−	0.185655i	$-0.940559\pi$
$19$	−1.44073	+	2.49541i	−0.330525	+	0.572487i	0.652090	+	0.758142i	$0.273893\pi$
$20$	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	−0.920146	−	0.391575i	$-0.871931\pi$
$29$	−0.651388	+	1.12824i	−0.120960	+	0.209508i	0.799187	+	0.601083i	$0.205264\pi$
$30$	5.40833	−	9.36750i	0.987421	−	1.71026i
$31$	−0.436217	+	0.755550i	−0.0783469	+	0.135701i	−0.902537	−	0.430613i	$-0.858298\pi$
$31$	−0.436217	+	0.755550i	−0.0783469	+	0.135701i	0.824190	+	0.566313i	$0.191631\pi$
$32$	−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	0.408458	+	0.912777i	$0.366066\pi$
$41$	−3.75389	+	6.50192i	−0.586259	+	1.01543i	−0.994717	+	0.102653i	$0.967267\pi$
$42$		0			0
$43$	−2.75694	−	4.77516i	−0.420429	−	0.728205i	0.575552	−	0.817765i	$-0.304787\pi$
$43$	−2.75694	−	4.77516i	−0.420429	−	0.728205i	−0.995981	+	0.0895602i	$0.971454\pi$
$44$	−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	0.821941	+	0.569573i	$0.192892\pi$
$47$	6.19912	+	10.7372i	0.904235	+	1.56618i	0.0822947	+	0.996608i	$0.473775\pi$
$48$	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	0.320978	+	0.947087i	$0.395988\pi$
$53$	−4.80278	+	8.31865i	−0.659712	+	1.14265i	−0.980690	+	0.195568i	$0.937345\pi$
$54$	−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	$-0.357835\pi$
$59$	6.63534			0.863848			0.431924	+	0.901910i	$0.357835\pi$
$60$	1.25694	−	2.17708i	0.162270	−	0.281060i
$61$	−2.88145	+	4.99082i	−0.368932	+	0.639010i	−0.989399	−	0.145223i	$-0.953610\pi$
$61$	−2.88145	+	4.99082i	−0.368932	+	0.639010i	0.620467	+	0.784233i	$0.286943\pi$
$62$	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	0.833866	−	0.551967i	$-0.186123\pi$
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	−0.894951	+	0.446165i	$0.852789\pi$
$68$	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	0.722599	−	0.691268i	$-0.242948\pi$
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	−0.959955	+	0.280155i	$0.909614\pi$
$72$	−7.95416	+	13.7770i	−0.937407	+	1.62364i
$73$	2.88145	−	4.99082i	0.337249	−	0.584132i	−0.646666	−	0.762774i	$-0.723837\pi$
$73$	2.88145	−	4.99082i	0.337249	−	0.584132i	0.983914	+	0.178642i	$0.0571704\pi$
$74$	−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	0.848490	−	0.529211i	$-0.177512\pi$
$79$	−0.302776	−	0.524423i	−0.0340649	−	0.0590022i	−0.882555	+	0.470209i	$0.844179\pi$
$80$	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	$-0.618644\pi$
$83$	−6.63534			−0.728323			−0.364162	+	0.931336i	$0.618644\pi$
$84$		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	$-0.348512\pi$
$89$	8.64436			0.916300			0.458150	+	0.888875i	$0.348512\pi$
$90$	−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	$-0.0375638\pi$
$97$	3.88596	+	6.73069i	0.394560	+	0.683398i	−0.598485	+	0.801134i	$0.704230\pi$
$98$		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	$-0.0251545\pi$
$101$	4.32218	+	7.48624i	0.430073	+	0.744908i	−0.566806	+	0.823851i	$0.691821\pi$
$102$	−1.63751	−	2.83625i	−0.162138	−	0.280831i
$103$	−2.44524	−	4.23527i	−0.240936	−	0.417314i	0.720045	−	0.693927i	$-0.244121\pi$
$103$	−2.44524	−	4.23527i	−0.240936	−	0.417314i	−0.960981	+	0.276613i	$0.910788\pi$
$104$	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	−0.678096	−	0.734974i	$-0.737195\pi$
$109$	3.10555	−	5.37897i	0.297458	−	0.515212i	0.975554	+	0.219761i	$0.0705279\pi$
$110$	−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	0.969530	+	0.244972i	$0.0787786\pi$
$113$	7.40833	+	12.8316i	0.696917	+	1.20710i	−0.272613	+	0.962124i	$0.587888\pi$
$114$	−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	−0.794267	−	0.607569i	$-0.792145\pi$
$127$	1.45416	−	2.51868i	0.129036	−	0.223497i	0.923303	+	0.384071i	$0.125478\pi$
$128$	−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	−0.950790	−	0.309837i	$-0.899725\pi$
$131$	−8.51229	−	14.7437i	−0.743722	−	1.28816i	0.207068	−	0.978327i	$-0.433608\pi$
$132$	−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	−0.960196	−	0.279327i	$-0.909889\pi$
$139$	−8.51229	−	14.7437i	−0.722003	−	1.25055i	0.238193	−	0.971218i	$-0.423445\pi$
$140$		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	−0.876358	−	0.481660i	$-0.840034\pi$
$149$	−0.256939	+	0.445032i	−0.0210493	+	0.0364584i	0.855309	+	0.518118i	$0.173367\pi$
$150$	−12.3982			−1.01231
$151$	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	$0.0853395\pi$
$152$	−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	$-0.957327\pi$
$157$	−4.75840	+	8.24179i	−0.379761	+	0.657766i	0.611266	+	0.791425i	$0.290661\pi$
$158$	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	−0.302710	−	0.953083i	$-0.597891\pi$
$163$	8.60555	−	14.9053i	0.674039	−	1.16747i	0.976749	−	0.214387i	$-0.0687753\pi$
$164$	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	$-0.893929\pi$
$167$	−2.44524	+	4.23527i	−0.189218	+	0.327735i	0.755772	+	0.654835i	$0.227262\pi$
$168$		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	−0.0946356	+	0.995512i	$0.530169\pi$
$173$	−11.9620	+	20.7188i	−0.909456	+	1.57522i	−0.814821	+	0.579713i	$0.803165\pi$
$174$	−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	−0.999014	−	0.0443850i	$-0.985867\pi$
$179$	−7.19722	−	12.4660i	−0.537946	−	0.931749i	0.461069	−	0.887364i	$-0.347466\pi$
$180$	−4.62632			−0.344826
$181$	9.25264			0.687744			0.343872	−	0.939017i	$-0.388261\pi$
$181$	9.25264			0.687744			0.343872	+	0.939017i	$0.388261\pi$
$182$		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	0.270688	+	0.962667i	$0.412749\pi$
$191$	−9.65139	+	16.7167i	−0.698350	+	1.20958i	−0.969038	+	0.246911i	$0.920585\pi$
$192$	−12.7024	−	22.0012i	−0.916716	−	1.58780i
$193$	0.908327	+	1.57327i	0.0653828	+	0.113246i	0.896864	−	0.442307i	$-0.145840\pi$
$193$	0.908327	+	1.57327i	0.0653828	+	0.113246i	−0.831481	+	0.555553i	$0.812506\pi$
$194$	−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	−0.572130	−	0.820163i	$-0.693883\pi$
$197$	5.95416	−	10.3129i	0.424217	−	0.734765i	0.996347	+	0.0853980i	$0.0272162\pi$
$198$	40.8167			2.90071
$199$	0.872434			0.0618452			0.0309226	−	0.999522i	$-0.490155\pi$
$199$	0.872434			0.0618452			0.0309226	+	0.999522i	$0.490155\pi$
$200$	−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	0.483499	+	0.875345i	$0.339366\pi$
$211$	−7.50000	+	12.9904i	−0.516321	+	0.894295i	−0.999820	+	0.0189499i	$0.993968\pi$
$212$	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	$-0.683623\pi$
$223$	6.76742	−	11.7215i	0.453180	−	0.784930i	0.998582	+	0.0532444i	$0.0169562\pi$
$224$		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	$-0.136266\pi$
$227$	27.4138			1.81952			0.909759	+	0.415137i	$0.136266\pi$
$228$	−2.51388			−0.166486
$229$	−10.3892	−	17.9947i	−0.686540	−	1.18912i	−0.972950	−	0.231015i	$-0.925796\pi$
$229$	−10.3892	−	17.9947i	−0.686540	−	1.18912i	0.286411	−	0.958107i	$-0.407538\pi$
$230$	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	$0.546948\pi$
$234$	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	$-0.520611\pi$
$241$	−2.00902			−0.129412			−0.0647062	+	0.997904i	$0.520611\pi$
$242$	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	0.964546	+	0.263915i	$0.0850138\pi$
$251$	11.2617	+	19.5058i	0.710830	+	1.23119i	−0.253716	+	0.967279i	$0.581653\pi$
$252$		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	$-0.751632\pi$
$257$	−22.7875			−1.42144			−0.710722	+	0.703473i	$0.751632\pi$
$258$	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	0.995304	−	0.0967960i	$-0.0308594\pi$
$263$	6.71110	+	11.6240i	0.413824	+	0.716765i	−0.581480	+	0.813561i	$0.697526\pi$
$264$	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	$-0.406303\pi$
$269$	9.51680			0.580249			0.290125	+	0.956989i	$0.406303\pi$
$270$	12.4542	+	21.5712i	0.757936	+	1.31278i
$271$	29.6870			1.80336			0.901678	−	0.432409i	$-0.142336\pi$
$271$	29.6870			1.80336			0.901678	+	0.432409i	$0.142336\pi$
$272$	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	$-0.204771\pi$
$283$	−2.00902	−	3.47972i	−0.119424	−	0.206848i	−0.919539	+	0.392998i	$0.871438\pi$
$284$	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	$-0.199170\pi$
$293$	−1.74487	−	3.02220i	−0.101936	−	0.176559i	−0.912482	+	0.409116i	$0.865837\pi$
$294$		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	$-0.356384\pi$
$307$	15.2797			0.872059			0.436029	+	0.899932i	$0.356384\pi$
$308$		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	$-0.672994\pi$
$311$	8.51229	−	14.7437i	0.482687	−	0.836039i	0.999802	+	0.0198768i	$0.00632739\pi$
$312$	−3.77082	−	30.9387i	−0.213480	−	1.75156i
$313$	−6.63534	−	11.4927i	−0.375052	−	0.649609i	0.615283	−	0.788306i	$-0.289042\pi$
$313$	−6.63534	−	11.4927i	−0.375052	−	0.649609i	−0.990335	+	0.138698i	$0.955708\pi$
$314$	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	$0.907399\pi$
$318$	−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	−0.875447	−	0.483314i	$-0.839433\pi$
$331$	−0.348612	+	0.603814i	−0.0191615	+	0.0331886i	0.856286	+	0.516503i	$0.172766\pi$
$332$	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	0.345050	+	0.938584i	$0.387862\pi$
$349$	−11.9620	+	20.7188i	−0.640313	+	1.10905i	−0.985363	+	0.170470i	$0.945471\pi$
$350$		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	$-0.220899\pi$
$353$	−3.18559	−	5.51761i	−0.169552	−	0.293673i	−0.938262	+	0.345924i	$0.887565\pi$
$354$	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	0.992126	+	0.125244i	$0.0399714\pi$
$359$	11.4542	+	19.8392i	0.604528	+	1.04707i	−0.387598	+	0.921828i	$0.626695\pi$
$360$	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	0.953276	+	0.302100i	$0.0976878\pi$
$367$	14.1431	+	24.4966i	0.738265	+	1.27871i	−0.215011	+	0.976612i	$0.568979\pi$
$368$	−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	−0.574078	−	0.818800i	$-0.694639\pi$
$373$	8.15139	−	14.1186i	0.422063	−	0.731034i	0.996141	+	0.0877661i	$0.0279728\pi$
$374$	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	−0.983857	−	0.178954i	$-0.942729\pi$
$379$	−6.55971	+	11.3618i	−0.336950	+	0.583614i	0.646908	+	0.762568i	$0.276062\pi$
$380$	−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	$-0.669221\pi$
$383$	9.64887	−	16.7123i	0.493034	−	0.853960i	0.999968	+	0.00802473i	$0.00255438\pi$
$384$	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	−0.763090	−	0.646292i	$-0.776319\pi$
$389$	3.51388	−	6.08622i	0.178161	−	0.308583i	0.941251	+	0.337709i	$0.109652\pi$
$390$	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	$-0.879528\pi$
$397$	−2.88145	+	4.99082i	−0.144616	+	0.250482i	0.784614	+	0.619985i	$0.212861\pi$
$398$	−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	$-0.630759\pi$
$409$	−16.1521			−0.798672			−0.399336	+	0.916805i	$0.630759\pi$
$410$	−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	$-0.898955\pi$
$419$	−4.19010	+	7.25747i	−0.204700	+	0.354551i	0.745337	+	0.666688i	$0.232289\pi$
$420$		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	−0.988609	−	0.150509i	$-0.951909\pi$
$431$	−12.9680	−	22.4613i	−0.624649	−	1.08192i	0.363960	−	0.931415i	$-0.381424\pi$
$432$	−21.9150			−1.05439
$433$	4.19010	+	7.25747i	0.201364	+	0.348772i	0.948968	−	0.315372i	$-0.102129\pi$
$433$	4.19010	+	7.25747i	0.201364	+	0.348772i	−0.747604	+	0.664144i	$0.768796\pi$
$434$		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	$-0.618805\pi$
$439$	−15.2797			−0.729260			−0.364630	+	0.931152i	$0.618805\pi$
$440$	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	$-0.421767\pi$
$444$	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	0.749384	−	0.662136i	$-0.230350\pi$
$449$	−4.21110	−	7.29384i	−0.198734	−	0.344218i	−0.948118	+	0.317918i	$0.897016\pi$
$450$	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	$-0.0713892\pi$
$461$	6.33120	+	10.9660i	0.294873	+	0.510736i	−0.680082	+	0.733136i	$0.738056\pi$
$462$		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	$-0.0605506\pi$
$467$	7.07156	+	12.2483i	0.327233	+	0.566784i	−0.654729	+	0.755864i	$0.727217\pi$
$468$	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	$-0.158401\pi$
$479$	0.568293	+	0.984312i	0.0259660	+	0.0449744i	−0.852750	+	0.522319i	$0.825067\pi$
$480$	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	−0.685990	−	0.727611i	$-0.740630\pi$
$491$	6.36249	−	11.0202i	0.287135	−	0.497333i	0.973125	+	0.230279i	$0.0739638\pi$
$492$	−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	−0.968020	−	0.250875i	$-0.919282\pi$
$499$	−15.6653	−	27.1330i	−0.701274	−	1.21464i	0.266746	−	0.963767i	$-0.414052\pi$
$500$	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	0.995692	+	0.0927268i	$0.0295583\pi$
$503$	12.9665	+	22.4587i	0.578150	+	1.00138i	−0.417542	+	0.908658i	$0.637108\pi$
$504$		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	$-0.518474\pi$
$509$	−2.61730			−0.116010			−0.0580049	+	0.998316i	$0.518474\pi$
$510$	−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	−0.356114	−	0.934442i	$-0.615899\pi$
$521$	14.4073	−	24.9541i	0.631194	−	1.09326i	0.987308	−	0.158817i	$-0.0507681\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	−9.25264			−0.404590			−0.202295	−	0.979325i	$-0.564840\pi$
$523$	−9.25264			−0.404590			−0.202295	+	0.979325i	$0.564840\pi$
$524$	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	0.994559	−	0.104173i	$-0.0332196\pi$
$541$	9.46804	+	16.3991i	0.407063	+	0.705054i	−0.587496	+	0.809227i	$0.699886\pi$
$542$	−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	0.629448	−	0.777042i	$-0.283281\pi$
$557$	−8.45416	−	14.6430i	−0.358214	−	0.620446i	−0.987663	+	0.156597i	$0.949948\pi$
$558$	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	$-0.631367\pi$
$563$	−19.0336			−0.802170			−0.401085	+	0.916041i	$0.631367\pi$
$564$	−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	−0.998664	−	0.0516739i	$-0.983544\pi$
$571$	−10.8625	+	18.8144i	−0.454581	+	0.787358i	0.544083	+	0.839031i	$0.316878\pi$
$572$	−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	0.266333	+	0.963881i	$0.414188\pi$
$577$	−16.8525	+	29.1894i	−0.701579	+	1.21517i	−0.967912	+	0.251289i	$0.919145\pi$
$578$	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	−0.405137	−	0.914256i	$-0.632776\pi$
$587$	14.2752	−	24.7254i	0.589200	−	1.02052i	0.994337	−	0.106269i	$-0.0338904\pi$
$588$		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	$-0.0116829\pi$
$593$	11.3937	+	19.7345i	0.467885	+	0.810400i	−0.531442	+	0.847095i	$0.678350\pi$
$594$	−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	−0.932513	−	0.361135i	$-0.882389\pi$
$599$	−3.75694	+	6.50721i	−0.153504	+	0.265877i	0.779009	+	0.627013i	$0.215723\pi$
$600$	28.5504			1.16556
$601$	14.7114	−	25.4809i	0.600091	−	1.03939i	−0.392716	−	0.919660i	$-0.628464\pi$
$601$	14.7114	−	25.4809i	0.600091	−	1.03939i	0.992807	−	0.119728i	$-0.0382023\pi$
$602$		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	$-0.969447\pi$
$607$	−10.2172	+	17.6966i	−0.414702	+	0.718285i	0.580695	+	0.814121i	$0.302781\pi$
$608$	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	0.570566	−	0.821252i	$-0.306724\pi$
$613$	−10.5458	−	18.2659i	−0.425942	−	0.737754i	−0.996508	+	0.0834983i	$0.973391\pi$
$614$	−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	0.887949	+	0.459943i	$0.152130\pi$
$617$	20.9222	+	36.2383i	0.842296	+	1.45890i	−0.0456524	+	0.998957i	$0.514537\pi$
$618$	9.17914	−	15.8987i	0.369239	−	0.639541i
$619$	−11.2617	+	19.5058i	−0.452644	+	0.784003i	−0.998549	−	0.0538439i	$-0.982853\pi$
$619$	−11.2617	+	19.5058i	−0.452644	+	0.784003i	0.545905	+	0.837847i	$0.316186\pi$
$620$	−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	0.720227	−	0.693738i	$-0.244037\pi$
$631$	−6.04584	−	10.4717i	−0.240681	−	0.416872i	−0.960908	+	0.276866i	$0.910704\pi$
$632$	−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	$-0.113826\pi$
$643$	4.19010	+	7.25747i	0.165242	+	0.286207i	−0.771499	+	0.636230i	$0.780493\pi$
$644$		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	$-0.152439\pi$
$647$	1.13659	+	1.96862i	0.0446838	+	0.0773946i	−0.842819	+	0.538198i	$0.819105\pi$
$648$	−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	0.538665	−	0.842520i	$-0.318929\pi$
$659$	−11.8167	−	20.4670i	−0.460311	−	0.797283i	−0.998976	+	0.0452373i	$0.985596\pi$
$660$	14.8528			0.578145
$661$	4.89047	+	8.47055i	0.190217	+	0.329466i	0.945322	−	0.326138i	$-0.105747\pi$
$661$	4.89047	+	8.47055i	0.190217	+	0.329466i	−0.755105	+	0.655604i	$0.772414\pi$
$662$	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	−0.959375	−	0.282135i	$-0.908958\pi$
$673$	−6.10555	+	10.5751i	−0.235352	+	0.407641i	0.724023	+	0.689776i	$0.242291\pi$
$674$	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	$-0.205736\pi$
$677$	−3.18559	−	5.51761i	−0.122432	−	0.212059i	−0.920726	+	0.390209i	$0.872403\pi$
$678$	−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	$-0.284680\pi$
$691$	32.9126			1.25205			0.626026	+	0.779802i	$0.284680\pi$
$692$	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	−0.868596	−	0.495521i	$-0.834977\pi$
$709$	−0.137510	+	0.238174i	−0.00516428	+	0.00894480i	0.863432	+	0.504466i	$0.168311\pi$
$710$	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	$-0.965617\pi$
$719$	−10.8254	+	18.7502i	−0.403721	+	0.699265i	0.590451	+	0.807074i	$0.298950\pi$
$720$	−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	$-0.642845\pi$
$727$	−23.3958			−0.867701			−0.433850	+	0.900985i	$0.642845\pi$
$728$		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	0.952438	+	0.304731i	$0.0985666\pi$
$733$	20.0381	+	34.7070i	0.740124	+	1.28193i	−0.212314	+	0.977201i	$0.568100\pi$
$734$	−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	0.985459	−	0.169913i	$-0.0543487\pi$
$739$	9.39445	+	16.2717i	0.345580	+	0.598563i	−0.639879	+	0.768476i	$0.721015\pi$
$740$	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	−0.279862	−	0.960040i	$-0.590289\pi$
$743$	18.8486	−	32.6468i	0.691489	−	1.19769i	0.971350	−	0.237653i	$-0.0763781\pi$
$744$	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	−0.113057	−	0.993588i	$-0.536064\pi$
$757$	22.1194	−	38.3120i	0.803944	−	1.39247i	0.917001	−	0.398884i	$-0.130602\pi$
$758$	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	$-0.808603\pi$
$761$	2.14110	−	3.70849i	0.0776147	−	0.134433i	0.902220	+	0.431275i	$0.141936\pi$
$762$	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	−0.440523	−	0.897741i	$-0.645207\pi$
$769$	15.4518	−	26.7632i	0.557205	−	0.965107i	0.997728	−	0.0673662i	$-0.0214596\pi$
$770$		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	$-0.716135\pi$
$773$	−34.9216			−1.25604			−0.628021	+	0.778196i	$0.716135\pi$
$774$	−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	$-0.234507\pi$
$787$	41.5569			1.48134			0.740672	+	0.671867i	$0.234507\pi$
$788$	−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	−0.990835	−	0.135077i	$-0.956872\pi$
$797$	−17.2887	−	29.9449i	−0.612398	−	1.06070i	0.378437	−	0.925627i	$-0.376462\pi$
$798$		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	0.971817	−	0.235738i	$-0.0757508\pi$
$809$	8.01388	+	13.8804i	0.281753	+	0.488010i	−0.690064	+	0.723749i	$0.742417\pi$
$810$	6.02706	−	10.4392i	0.211769	−	0.366795i
$811$	21.9150			0.769541			0.384771	−	0.923012i	$-0.374281\pi$
$811$	21.9150			0.769541			0.384771	+	0.923012i	$0.374281\pi$
$812$		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	$-0.0792068\pi$
$829$	7.81192	+	13.5306i	0.271319	+	0.469938i	−0.697881	+	0.716214i	$0.745873\pi$
$830$	−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	$-0.0327481\pi$
$839$	11.8300	+	20.4901i	0.408415	+	0.707396i	−0.586297	+	0.810096i	$0.699415\pi$
$840$		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	$-0.577845\pi$
$853$	−14.1431			−0.484251			−0.242126	+	0.970245i	$0.577845\pi$
$854$		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	−0.0982356	−	0.995163i	$-0.531320\pi$
$857$	23.7920	−	41.2089i	0.812719	−	1.40767i	0.910954	−	0.412507i	$-0.135347\pi$
$858$	−63.9083	+	48.0692i	−2.18179	+	1.64105i
$859$	−12.3982	−	21.4744i	−0.423023	−	0.732697i	0.573211	−	0.819408i	$-0.305698\pi$
$859$	−12.3982	−	21.4744i	−0.423023	−	0.732697i	−0.996234	+	0.0867110i	$0.972364\pi$
$860$	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	$0.768875\pi$
$864$	−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	−0.335298	−	0.942112i	$-0.608837\pi$
$877$	19.1972	−	33.2506i	0.648244	−	1.12279i	0.983542	−	0.180680i	$-0.0578297\pi$
$878$	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	0.396069	+	0.918221i	$0.370374\pi$
$881$	−17.7249	+	30.7005i	−0.597168	+	1.03433i	−0.993237	+	0.116105i	$0.962959\pi$
$882$		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	$-0.218254\pi$
$887$	46.1033			1.54800			0.773998	+	0.633188i	$0.218254\pi$
$888$	−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	0.666121	−	0.745844i	$-0.267953\pi$
$907$	−9.42221	−	16.3197i	−0.312859	−	0.541888i	−0.978980	+	0.203956i	$0.934620\pi$
$908$	−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	−0.756017	−	0.654552i	$-0.772857\pi$
$919$	5.72498	−	9.91596i	0.188850	−	0.327097i	0.944867	+	0.327454i	$0.106191\pi$
$920$	−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	$-0.877231\pi$
$929$	−4.19010	+	7.25747i	−0.137473	+	0.238110i	0.789067	+	0.614308i	$0.210565\pi$
$930$	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	$-0.225842\pi$
$937$	46.4474			1.51737			0.758685	+	0.651458i	$0.225842\pi$
$938$		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	0.228832	+	0.973466i	$0.426509\pi$
$941$	−22.3513	+	38.7135i	−0.728630	+	1.26202i	−0.957462	+	0.288559i	$0.906824\pi$
$942$	−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	−0.976798	−	0.214161i	$-0.931298\pi$
$953$	−20.8028	−	36.0315i	−0.673868	−	1.16717i	0.302930	−	0.953013i	$-0.402035\pi$
$954$	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	$-0.885278\pi$
$971$	−5.06254	+	8.76857i	−0.162465	+	0.281397i	0.773287	+	0.634056i	$0.218611\pi$
$972$	−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	0.985366	+	0.170454i	$0.0545236\pi$
$977$	20.0139	+	34.6651i	0.640301	+	1.10903i	−0.345065	+	0.938579i	$0.612143\pi$
$978$	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	$-0.766826\pi$
$983$	6.50327	−	11.2640i	0.207422	−	0.359265i	0.950902	+	0.309493i	$0.100159\pi$
$984$	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	0.954341	+	0.298719i	$0.0965594\pi$
$991$	23.1653	+	40.1234i	0.735869	+	1.27456i	−0.218472	+	0.975843i	$0.570107\pi$
$992$	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	$-0.746596\pi$
$997$	−44.1742			−1.39901			−0.699506	+	0.714627i	$0.746596\pi$
$998$	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.165.1		8
7.2	even	3		637.2.g.i.373.4		8
7.3	odd	6		637.2.f.h.295.4	yes	8
7.4	even	3		637.2.f.h.295.3	✓	8
7.5	odd	6		637.2.g.i.373.3		8
7.6	odd	2	inner	637.2.h.j.165.2		8
13.3	even	3		637.2.g.i.263.4		8
91.3	odd	6		637.2.f.h.393.4	yes	8
91.4	even	6		8281.2.a.bo.1.4		4
91.16	even	3	inner	637.2.h.j.471.1		8
91.17	odd	6		8281.2.a.bo.1.3		4
91.55	odd	6		637.2.g.i.263.3		8
91.68	odd	6	inner	637.2.h.j.471.2		8
91.74	even	3		8281.2.a.bu.1.2		4
91.81	even	3		637.2.f.h.393.3	yes	8
91.87	odd	6		8281.2.a.bu.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.h.295.3	✓	8	7.4	even	3
637.2.f.h.295.4	yes	8	7.3	odd	6
637.2.f.h.393.3	yes	8	91.81	even	3
637.2.f.h.393.4	yes	8	91.3	odd	6
637.2.g.i.263.3		8	91.55	odd	6
637.2.g.i.263.4		8	13.3	even	3
637.2.g.i.373.3		8	7.5	odd	6
637.2.g.i.373.4		8	7.2	even	3
637.2.h.j.165.1		8	1.1	even	1	trivial
637.2.h.j.165.2		8	7.6	odd	2	inner
637.2.h.j.471.1		8	91.16	even	3	inner
637.2.h.j.471.2		8	91.68	odd	6	inner
8281.2.a.bo.1.3		4	91.17	odd	6
8281.2.a.bo.1.4		4	91.4	even	6
8281.2.a.bu.1.1		4	91.87	odd	6
8281.2.a.bu.1.2		4	91.74	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} - 12 q^{16} + 6 q^{18} - 38 q^{22} + 24 q^{23} - 6 q^{25} + 2 q^{29} - 28 q^{32} - 8 q^{36} + 40 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44}+ \cdots - 92 q^{99}+O(q^{100}) \) 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

Introduction

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