LMFDB - Embedded newform 637.2.r.g.116.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.2
Character	$\chi$	$=$	637.116
Dual form			637.2.r.g.324.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36789 + 1.36710i) q^{2} +(0.577975 - 1.00108i) q^{3} +(2.73793 - 4.74223i) q^{4} +(1.62576 - 0.938635i) q^{5} +3.16060i q^{6} +9.50370i q^{8} +(0.831889 + 1.44087i) q^{9} +O(q^{10})$	\(q+(-2.36789 + 1.36710i) q^{2} +(0.577975 - 1.00108i) q^{3} +(2.73793 - 4.74223i) q^{4} +(1.62576 - 0.938635i) q^{5} +3.16060i q^{6} +9.50370i q^{8} +(0.831889 + 1.44087i) q^{9} +(-2.56642 + 4.44516i) q^{10} +(1.99163 + 1.14987i) q^{11} +(-3.16491 - 5.48179i) q^{12} +(0.574228 + 3.55953i) q^{13} -2.17003i q^{15} +(-7.51666 - 13.0192i) q^{16} +(-3.03578 + 5.25812i) q^{17} +(-3.93964 - 2.27455i) q^{18} +(-4.46010 + 2.57504i) q^{19} -10.2797i q^{20} -6.28794 q^{22} +(2.20891 + 3.82595i) q^{23} +(9.51399 + 5.49290i) q^{24} +(-0.737930 + 1.27813i) q^{25} +(-6.22595 - 7.64354i) q^{26} +5.39110 q^{27} +7.50488 q^{29} +(2.96665 + 5.13839i) q^{30} +(-3.75139 - 2.16586i) q^{31} +(19.1363 + 11.0484i) q^{32} +(2.30222 - 1.32919i) q^{33} -16.6009i q^{34} +9.11062 q^{36} +(2.74415 - 1.58433i) q^{37} +(7.04068 - 12.1948i) q^{38} +(3.89527 + 1.48247i) q^{39} +(8.92050 + 15.4508i) q^{40} +2.45446i q^{41} -2.17732 q^{43} +(10.9059 - 6.29651i) q^{44} +(2.70491 + 1.56168i) q^{45} +(-10.4609 - 6.03961i) q^{46} +(7.71162 - 4.45231i) q^{47} -17.3778 q^{48} -4.03530i q^{50} +(3.50921 + 6.07813i) q^{51} +(18.4523 + 7.02262i) q^{52} +(-4.05001 + 7.01482i) q^{53} +(-12.7655 + 7.37017i) q^{54} +4.31722 q^{55} +5.95323i q^{57} +(-17.7707 + 10.2599i) q^{58} +(-6.18303 - 3.56978i) q^{59} +(-10.2908 - 5.94139i) q^{60} +(-4.00490 - 6.93668i) q^{61} +11.8438 q^{62} -30.3503 q^{64} +(4.27466 + 5.24796i) q^{65} +(-3.63427 + 6.29475i) q^{66} +(1.00227 + 0.578661i) q^{67} +(16.6235 + 28.7927i) q^{68} +5.10678 q^{69} -5.11328i q^{71} +(-13.6936 + 7.90603i) q^{72} +(-1.70519 - 0.984492i) q^{73} +(-4.33189 + 7.50305i) q^{74} +(0.853010 + 1.47746i) q^{75} +28.2011i q^{76} +(-11.2503 + 1.81491i) q^{78} +(-1.90604 - 3.30136i) q^{79} +(-24.4406 - 14.1108i) q^{80} +(0.620251 - 1.07431i) q^{81} +(-3.35549 - 5.81188i) q^{82} +2.49170i q^{83} +11.3980i q^{85} +(5.15565 - 2.97662i) q^{86} +(4.33763 - 7.51300i) q^{87} +(-10.9280 + 18.9279i) q^{88} +(9.03187 - 5.21456i) q^{89} -8.53990 q^{90} +24.1914 q^{92} +(-4.33642 + 2.50363i) q^{93} +(-12.1735 + 21.0851i) q^{94} +(-4.83404 + 8.37280i) q^{95} +(22.1206 - 12.7714i) q^{96} -2.51219i q^{97} +3.82625i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 16 * q^9	$ 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.36789	+	1.36710i	−1.67435	+	0.966686i	−0.709193	+	0.705014i	$0.750941\pi$
$2$	−2.36789	+	1.36710i	−1.67435	+	0.966686i	−0.965157	+	0.261672i	$0.915726\pi$
$3$	0.577975	−	1.00108i	0.333694	−	0.577975i	−0.649539	−	0.760328i	$-0.725038\pi$
$3$	0.577975	−	1.00108i	0.333694	−	0.577975i	0.983233	+	0.182353i	$0.0583714\pi$
$4$	2.73793	−	4.74223i	1.36896	−	2.37112i
$5$	1.62576	−	0.938635i	0.727063	−	0.419770i	−0.0902836	−	0.995916i	$-0.528777\pi$
$5$	1.62576	−	0.938635i	0.727063	−	0.419770i	0.817347	+	0.576146i	$0.195444\pi$
$6$			3.16060i			1.29031i
$7$		0			0
$7$		0			0
$8$			9.50370i			3.36007i
$9$	0.831889	+	1.44087i	0.277296	+	0.480292i
$10$	−2.56642	+	4.44516i	−0.811572	+	1.40568i
$11$	1.99163	+	1.14987i	0.600499	+	0.346698i	0.769238	−	0.638963i	$-0.220636\pi$
$11$	1.99163	+	1.14987i	0.600499	+	0.346698i	−0.168739	+	0.985661i	$0.553969\pi$
$12$	−3.16491	−	5.48179i	−0.913631	−	1.58246i
$13$	0.574228	+	3.55953i	0.159262	+	0.987236i
$13$	0.574228	+	3.55953i	0.159262	+	0.987236i
$14$		0			0
$15$		−	2.17003i		−	0.560299i
$16$	−7.51666	−	13.0192i	−1.87917	−	3.25481i
$17$	−3.03578	+	5.25812i	−0.736285	+	1.27528i	0.217873	+	0.975977i	$0.430088\pi$
$17$	−3.03578	+	5.25812i	−0.736285	+	1.27528i	−0.954157	+	0.299305i	$0.903245\pi$
$18$	−3.93964	−	2.27455i	−0.928583	−	0.536117i
$19$	−4.46010	+	2.57504i	−1.02322	+	0.590754i	−0.915034	−	0.403377i	$-0.867836\pi$
$19$	−4.46010	+	2.57504i	−1.02322	+	0.590754i	−0.108183	+	0.994131i	$0.534503\pi$
$20$		−	10.2797i		−	2.29860i
$21$		0			0
$22$	−6.28794			−1.34059
$23$	2.20891	+	3.82595i	0.460590	+	0.797765i	0.998990	−	0.0449240i	$-0.0143046\pi$
$23$	2.20891	+	3.82595i	0.460590	+	0.797765i	−0.538401	+	0.842689i	$0.680971\pi$
$24$	9.51399	+	5.49290i	1.94203	+	1.12123i
$25$	−0.737930	+	1.27813i	−0.147586	+	0.255626i
$26$	−6.22595	−	7.64354i	−1.22101	−	1.49902i
$27$	5.39110			1.03752
$28$		0			0
$29$	7.50488			1.39362			0.696810	−	0.717255i	$-0.254602\pi$
$29$	7.50488			1.39362			0.696810	+	0.717255i	$0.254602\pi$
$30$	2.96665	+	5.13839i	0.541634	+	0.938137i
$31$	−3.75139	−	2.16586i	−0.673769	−	0.389001i	0.123734	−	0.992315i	$-0.460513\pi$
$31$	−3.75139	−	2.16586i	−0.673769	−	0.389001i	−0.797503	+	0.603315i	$0.793846\pi$
$32$	19.1363	+	11.0484i	3.38286	+	1.95309i
$33$	2.30222	−	1.32919i	0.400766	−	0.231382i
$34$		−	16.6009i		−	2.84703i
$35$		0			0
$36$	9.11062			1.51844
$37$	2.74415	−	1.58433i	0.451135	−	0.260463i	−0.257174	−	0.966365i	$-0.582791\pi$
$37$	2.74415	−	1.58433i	0.451135	−	0.260463i	0.708309	+	0.705902i	$0.249458\pi$
$38$	7.04068	−	12.1948i	1.14215	−	1.97826i
$39$	3.89527	+	1.48247i	0.623743	+	0.237385i
$40$	8.92050	+	15.4508i	1.41046	+	2.44298i
$41$			2.45446i			0.383322i	0.981461	+	0.191661i	$0.0613874\pi$
$41$			2.45446i			0.383322i	−0.981461	+	0.191661i	$0.938613\pi$
$42$		0			0
$43$	−2.17732			−0.332038			−0.166019	−	0.986123i	$-0.553091\pi$
$43$	−2.17732			−0.332038			−0.166019	+	0.986123i	$0.553091\pi$
$44$	10.9059	−	6.29651i	1.64412	−	0.949235i
$45$	2.70491	+	1.56168i	0.403224	+	0.232802i
$46$	−10.4609	−	6.03961i	−1.54238	−	0.890492i
$47$	7.71162	−	4.45231i	1.12486	−	0.649436i	0.182220	−	0.983258i	$-0.441672\pi$
$47$	7.71162	−	4.45231i	1.12486	−	0.649436i	0.942636	+	0.333822i	$0.108338\pi$
$48$	−17.3778			−2.50827
$49$		0			0
$50$		−	4.03530i		−	0.570677i
$51$	3.50921	+	6.07813i	0.491388	+	0.851108i
$52$	18.4523	+	7.02262i	2.55888	+	0.973863i
$53$	−4.05001	+	7.01482i	−0.556312	+	0.963560i	0.441488	+	0.897267i	$0.354451\pi$
$53$	−4.05001	+	7.01482i	−0.556312	+	0.963560i	−0.997800	+	0.0662933i	$0.978883\pi$
$54$	−12.7655	+	7.37017i	−1.73717	+	1.00295i
$55$	4.31722			0.582134
$56$		0			0
$57$			5.95323i			0.788525i
$58$	−17.7707	+	10.2599i	−2.33341	+	1.34719i
$59$	−6.18303	−	3.56978i	−0.804963	−	0.464745i	0.0402409	−	0.999190i	$-0.487187\pi$
$59$	−6.18303	−	3.56978i	−0.804963	−	0.464745i	−0.845203	+	0.534445i	$0.820521\pi$
$60$	−10.2908	−	5.94139i	−1.32854	−	0.767030i
$61$	−4.00490	−	6.93668i	−0.512774	−	0.888151i	−0.999890	−	0.0148140i	$-0.995284\pi$
$61$	−4.00490	−	6.93668i	−0.512774	−	0.888151i	0.487116	−	0.873337i	$-0.338049\pi$
$62$	11.8438			1.50417
$63$		0			0
$64$	−30.3503			−3.79379
$65$	4.27466	+	5.24796i	0.530206	+	0.650930i
$66$	−3.63427	+	6.29475i	−0.447348	+	0.774830i
$67$	1.00227	+	0.578661i	0.122447	+	0.0706947i	0.559972	−	0.828511i	$-0.310812\pi$
$67$	1.00227	+	0.578661i	0.122447	+	0.0706947i	−0.437526	+	0.899206i	$0.644145\pi$
$68$	16.6235	+	28.7927i	2.01590	+	3.49163i
$69$	5.10678			0.614785
$70$		0			0
$71$		−	5.11328i		−	0.606835i	−0.952858	−	0.303417i	$-0.901872\pi$
$71$		−	5.11328i		−	0.606835i	0.952858	−	0.303417i	$-0.0981276\pi$
$72$	−13.6936	+	7.90603i	−1.61381	+	0.931735i
$73$	−1.70519	−	0.984492i	−0.199578	−	0.115226i	0.396881	−	0.917870i	$-0.370093\pi$
$73$	−1.70519	−	0.984492i	−0.199578	−	0.115226i	−0.596458	+	0.802644i	$0.703426\pi$
$74$	−4.33189	+	7.50305i	−0.503572	+	0.872212i
$75$	0.853010	+	1.47746i	0.0984971	+	0.170602i
$76$			28.2011i			3.23489i
$77$		0			0
$78$	−11.2503	+	1.81491i	−1.27384	+	0.205498i
$79$	−1.90604	−	3.30136i	−0.214446	−	0.371432i	0.738655	−	0.674084i	$-0.235461\pi$
$79$	−1.90604	−	3.30136i	−0.214446	−	0.371432i	−0.953101	+	0.302652i	$0.902128\pi$
$80$	−24.4406	−	14.1108i	−2.73254	−	1.57764i
$81$	0.620251	−	1.07431i	0.0689168	−	0.119367i
$82$	−3.35549	−	5.81188i	−0.370552	−	0.641815i
$83$			2.49170i			0.273499i	0.990606	+	0.136750i	$0.0436656\pi$
$83$			2.49170i			0.273499i	−0.990606	+	0.136750i	$0.956334\pi$
$84$		0			0
$85$			11.3980i			1.23628i
$86$	5.15565	−	2.97662i	0.555948	−	0.320977i
$87$	4.33763	−	7.51300i	0.465043	−	0.805478i
$88$	−10.9280	+	18.9279i	−1.16493	+	2.01772i
$89$	9.03187	−	5.21456i	0.957377	−	0.552742i	0.0620121	−	0.998075i	$-0.480248\pi$
$89$	9.03187	−	5.21456i	0.957377	−	0.552742i	0.895365	+	0.445334i	$0.146915\pi$
$90$	−8.53990			−0.900185
$91$		0			0
$92$	24.1914			2.52213
$93$	−4.33642	+	2.50363i	−0.449665	+	0.259614i
$94$	−12.1735	+	21.0851i	−1.25560	+	2.17477i
$95$	−4.83404	+	8.37280i	−0.495962	+	0.859032i
$96$	22.1206	−	12.7714i	2.25768	−	1.30347i
$97$		−	2.51219i		−	0.255074i	−0.991834	−	0.127537i	$-0.959293\pi$
$97$		−	2.51219i		−	0.255074i	0.991834	−	0.127537i	$-0.0407072\pi$
$98$		0			0
$99$			3.82625i			0.384553i
$100$	4.04080	+	6.99887i	0.404080	+	0.699887i
$101$	5.34019	−	9.24947i	0.531368	−	0.920357i	−0.467961	−	0.883749i	$-0.655011\pi$
$101$	5.34019	−	9.24947i	0.531368	−	0.920357i	0.999330	−	0.0366080i	$-0.0116553\pi$
$102$	−16.6188	−	9.59489i	−1.64551	−	0.950035i
$103$	−5.90150	−	10.2217i	−0.581492	−	1.00717i	−0.995303	−	0.0968106i	$-0.969136\pi$
$103$	−5.90150	−	10.2217i	−0.581492	−	1.00717i	0.413811	−	0.910363i	$-0.364197\pi$
$104$	−33.8287	+	5.45729i	−3.31718	+	0.535131i
$105$		0			0
$106$		−	22.1471i		−	2.15112i
$107$	2.13867	+	3.70429i	0.206753	+	0.358107i	0.950690	−	0.310143i	$-0.100377\pi$
$107$	2.13867	+	3.70429i	0.206753	+	0.358107i	−0.743937	+	0.668250i	$0.767044\pi$
$108$	14.7604	−	25.5658i	1.42032	−	2.46007i
$109$	1.74188	+	1.00567i	0.166842	+	0.0963260i	0.581096	−	0.813835i	$-0.302624\pi$
$109$	1.74188	+	1.00567i	0.166842	+	0.0963260i	−0.414254	+	0.910161i	$0.635958\pi$
$110$	−10.2227	+	5.90208i	−0.974696	+	0.562741i
$111$		−	3.66282i		−	0.347660i
$112$		0			0
$113$	−4.16866			−0.392154			−0.196077	−	0.980588i	$-0.562820\pi$
$113$	−4.16866			−0.392154			−0.196077	+	0.980588i	$0.562820\pi$
$114$	−8.13867	−	14.0966i	−0.762256	−	1.32027i
$115$	7.18233	+	4.14672i	0.669756	+	0.386684i
$116$	20.5478	−	35.5899i	1.90782	−	3.30444i
$117$	−4.65114	+	3.78853i	−0.429998	+	0.350249i
$118$	19.5210			1.79705
$119$		0			0
$120$	20.6233			1.88264
$121$	−2.85561	−	4.94606i	−0.259601	−	0.449642i
$122$	18.9663	+	10.9502i	1.71713	+	0.991384i
$123$	2.45711	+	1.41862i	0.221551	+	0.127912i
$124$	−20.5421	+	11.8600i	−1.84473	+	1.06506i
$125$			12.1569i			1.08735i
$126$		0			0
$127$	15.1922			1.34809			0.674046	−	0.738689i	$-0.264555\pi$
$127$	15.1922			1.34809			0.674046	+	0.738689i	$0.264555\pi$
$128$	33.5934	−	19.3952i	2.96927	−	1.71431i
$129$	−1.25844	+	2.17968i	−0.110799	+	0.191910i
$130$	−17.2964	−	6.58270i	−1.51700	−	0.577341i
$131$	0.475488	+	0.823570i	0.0415436	+	0.0719556i	0.886050	−	0.463591i	$-0.153439\pi$
$131$	0.475488	+	0.823570i	0.0415436	+	0.0719556i	−0.844506	+	0.535546i	$0.820106\pi$
$132$		−	14.5569i		−	1.26702i
$133$		0			0
$134$	−3.16435			−0.273359
$135$	8.76464	−	5.06027i	0.754341	−	0.435519i
$136$	−49.9716	−	28.8511i	−4.28503	−	2.47397i
$137$	10.5983	+	6.11895i	0.905477	+	0.522777i	0.878973	−	0.476871i	$-0.158229\pi$
$137$	10.5983	+	6.11895i	0.905477	+	0.522777i	0.0265039	+	0.999649i	$0.491563\pi$
$138$	−12.0923	+	6.98149i	−1.02936	+	0.594304i
$139$	5.24824			0.445150			0.222575	−	0.974916i	$-0.428554\pi$
$139$	5.24824			0.445150			0.222575	+	0.974916i	$0.428554\pi$
$140$		0			0
$141$		−	10.2933i		−	0.866852i
$142$	6.99037	+	12.1077i	0.586619	+	1.01605i
$143$	−2.94934	+	7.74955i	−0.246636	+	0.648050i
$144$	12.5061	−	21.6611i	1.04217	−	1.80509i
$145$	12.2012	−	7.04434i	1.01325	−	0.585001i
$146$	5.38360			0.445550
$147$		0			0
$148$		−	17.3512i		−	1.42626i
$149$	−2.06234	+	1.19069i	−0.168953	+	0.0975451i	−0.582092	−	0.813123i	$-0.697766\pi$
$149$	−2.06234	+	1.19069i	−0.168953	+	0.0975451i	0.413139	+	0.910668i	$0.364432\pi$
$150$	−4.03967	−	2.33230i	−0.329837	−	0.190432i
$151$	17.5877	+	10.1543i	1.43127	+	0.826341i	0.997217	−	0.0745487i	$-0.0237516\pi$
$151$	17.5877	+	10.1543i	1.43127	+	0.826341i	0.434048	+	0.900890i	$0.357085\pi$
$152$	−24.4724	−	42.3874i	−1.98497	−	3.43808i
$153$	−10.1017			−0.816677
$154$		0			0
$155$	−8.13182			−0.653163
$156$	17.6952	−	14.4134i	1.41675	−	1.15400i
$157$	−5.52023	+	9.56132i	−0.440562	+	0.763076i	−0.997731	−	0.0673230i	$-0.978554\pi$
$157$	−5.52023	+	9.56132i	−0.440562	+	0.763076i	0.557169	+	0.830399i	$0.311888\pi$
$158$	9.02658	+	5.21150i	0.718116	+	0.414605i
$159$	4.68161	+	8.10879i	0.371276	+	0.643069i
$160$	41.4815			3.27940
$161$		0			0
$162$			3.39178i			0.266484i
$163$	16.4358	−	9.48921i	1.28735	−	0.743253i	0.309170	−	0.951007i	$-0.399949\pi$
$163$	16.4358	−	9.48921i	1.28735	−	0.743253i	0.978181	+	0.207754i	$0.0666154\pi$
$164$	11.6396	+	6.72013i	0.908901	+	0.524754i
$165$	2.49525	−	4.32190i	0.194255	−	0.336459i
$166$	−3.40640	−	5.90006i	−0.264388	−	0.457934i
$167$		−	21.7305i		−	1.68155i	−0.541382	−	0.840776i	$-0.682099\pi$
$167$		−	21.7305i		−	1.68155i	0.541382	−	0.840776i	$-0.317901\pi$
$168$		0			0
$169$	−12.3405	+	4.08796i	−0.949271	+	0.314459i
$170$	−15.5821	−	26.9891i	−1.19510	−	2.06997i
$171$	−7.42062	−	4.28430i	−0.567469	−	0.327628i
$172$	−5.96135	+	10.3254i	−0.454549	+	0.787301i
$173$	1.45150	+	2.51408i	0.110356	+	0.191142i	0.915914	−	0.401375i	$-0.131468\pi$
$173$	1.45150	+	2.51408i	0.110356	+	0.191142i	−0.805558	+	0.592517i	$0.798134\pi$
$174$			23.7199i			1.79820i
$175$		0			0
$176$		−	34.5727i		−	2.60601i
$177$	−7.14728	+	4.12648i	−0.537223	+	0.310166i
$178$	−14.2576	+	24.6950i	−1.06866	+	1.85097i
$179$	9.67514	−	16.7578i	0.723154	−	1.25254i	−0.236575	−	0.971613i	$-0.576025\pi$
$179$	9.67514	−	16.7578i	0.723154	−	1.25254i	0.959729	−	0.280926i	$-0.0906416\pi$
$180$	14.8117	−	8.55154i	1.10400	−	0.637394i
$181$	−9.98016			−0.741820			−0.370910	−	0.928669i	$-0.620954\pi$
$181$	−9.98016			−0.741820			−0.370910	+	0.928669i	$0.620954\pi$
$182$		0			0
$183$	−9.25892			−0.684439
$184$	−36.3607	+	20.9928i	−2.68054	+	1.54761i
$185$	2.97422	−	5.15150i	0.218669	−	0.378746i
$186$	6.84543	−	11.8566i	0.501931	−	0.869371i
$187$	−12.0923	+	6.98149i	−0.884276	+	0.510537i
$188$		−	48.7604i		−	3.55622i
$189$		0			0
$190$		−	26.4345i		−	1.91776i
$191$	−2.70243	−	4.68074i	−0.195541	−	0.338687i	0.751537	−	0.659691i	$-0.229313\pi$
$191$	−2.70243	−	4.68074i	−0.195541	−	0.338687i	−0.947078	+	0.321004i	$0.895980\pi$
$192$	−17.5417	+	30.3831i	−1.26596	+	2.19271i
$193$	−12.6151	−	7.28331i	−0.908052	−	0.524264i	−0.0282481	−	0.999601i	$-0.508993\pi$
$193$	−12.6151	−	7.28331i	−0.908052	−	0.524264i	−0.879804	+	0.475337i	$0.842326\pi$
$194$	3.43442	+	5.94858i	0.246577	+	0.427083i
$195$	7.72429	−	1.24609i	0.553148	−	0.0892345i
$196$		0			0
$197$			15.9055i			1.13322i	0.823987	+	0.566609i	$0.191745\pi$
$197$			15.9055i			1.13322i	−0.823987	+	0.566609i	$0.808255\pi$
$198$	−5.23087	−	9.06014i	−0.371742	−	0.643876i
$199$	−0.186833	+	0.323604i	−0.0132442	+	0.0229397i	−0.872572	−	0.488486i	$-0.837549\pi$
$199$	−0.186833	+	0.323604i	−0.0132442	+	0.0229397i	0.859327	+	0.511426i	$0.170883\pi$
$200$	−12.1470	−	7.01307i	−0.858922	−	0.495899i
$201$	1.15858	−	0.668904i	0.0817196	−	0.0471808i
$202$			29.2023i			2.05467i
$203$		0			0
$204$	38.4319			2.69077
$205$	2.30384	+	3.99037i	0.160907	+	0.278699i
$206$	27.9482	+	16.1359i	1.94724	+	1.12424i
$207$	−3.67514	+	6.36553i	−0.255440	+	0.442435i
$208$	42.0261	−	34.2318i	2.91399	−	2.37355i
$209$	−11.8438			−0.819254
$210$		0			0
$211$	6.05258			0.416677			0.208339	−	0.978057i	$-0.433194\pi$
$211$	6.05258			0.416677			0.208339	+	0.978057i	$0.433194\pi$
$212$	22.1773	+	38.4122i	1.52314	+	2.63816i
$213$	−5.11881	−	2.95535i	−0.350735	−	0.202497i
$214$	−10.1283	−	5.84756i	−0.692354	−	0.399731i
$215$	−3.53981	+	2.04371i	−0.241413	+	0.139380i
$216$			51.2354i			3.48613i
$217$		0			0
$218$	−5.49943			−0.372468
$219$	−1.97112	+	1.13802i	−0.133196	+	0.0769006i
$220$	11.8203	−	20.4733i	0.796921	−	1.38031i
$221$	−20.4597	−	7.78659i	−1.37627	−	0.523783i
$222$	5.00745	+	8.67316i	0.336078	+	0.582104i
$223$		−	7.30624i		−	0.489262i	−0.969616	−	0.244631i	$-0.921333\pi$
$223$		−	7.30624i		−	0.489262i	0.969616	−	0.244631i	$-0.0786668\pi$
$224$		0			0
$225$	−2.45550			−0.163700
$226$	9.87091	−	5.69898i	0.656603	−	0.379090i
$227$	−13.5891	−	7.84570i	−0.901943	−	0.520737i	−0.0241132	−	0.999709i	$-0.507676\pi$
$227$	−13.5891	−	7.84570i	−0.901943	−	0.520737i	−0.877830	+	0.478972i	$0.841010\pi$
$228$	28.2316	+	16.2995i	1.86969	+	1.07946i
$229$	22.1384	−	12.7816i	1.46295	−	0.844632i	0.463800	−	0.885940i	$-0.346486\pi$
$229$	22.1384	−	12.7816i	1.46295	−	0.844632i	0.999146	+	0.0413077i	$0.0131524\pi$
$230$	−22.6759			−1.49521
$231$		0			0
$232$			71.3241i			4.68266i
$233$	−8.17026	−	14.1513i	−0.535252	−	0.927083i	−0.999151	−	0.0411952i	$-0.986883\pi$
$233$	−8.17026	−	14.1513i	−0.535252	−	0.927083i	0.463899	−	0.885888i	$-0.346450\pi$
$234$	5.83409	−	15.3294i	0.381387	−	1.00211i
$235$	8.35818	−	14.4768i	0.545228	−	0.944362i
$236$	−33.8574	+	19.5476i	−2.20393	+	1.27244i
$237$	−4.40658			−0.286238
$238$		0			0
$239$			17.2505i			1.11584i	0.829895	+	0.557920i	$0.188400\pi$
$239$			17.2505i			1.11584i	−0.829895	+	0.557920i	$0.811600\pi$
$240$	−28.2521	+	16.3114i	−1.82367	+	1.05290i
$241$	−8.75810	−	5.05649i	−0.564159	−	0.325717i	0.190654	−	0.981657i	$-0.438939\pi$
$241$	−8.75810	−	5.05649i	−0.564159	−	0.325717i	−0.754813	+	0.655940i	$0.772272\pi$
$242$	13.5235	+	7.80781i	0.869325	+	0.501905i
$243$	7.36967	+	12.7646i	0.472764	+	0.818852i
$244$	−43.8605			−2.80788
$245$		0			0
$246$	−7.75756			−0.494604
$247$	−11.7270	−	14.3972i	−0.746174	−	0.916072i
$248$	20.5837	−	35.6521i	1.30707	−	2.26391i
$249$	2.49439	+	1.44014i	0.158076	+	0.0912651i
$250$	−16.6198	−	28.7863i	−1.05113	−	1.82060i
$251$	−20.8184			−1.31404			−0.657022	−	0.753871i	$-0.728184\pi$
$251$	−20.8184			−1.31404			−0.657022	+	0.753871i	$0.728184\pi$
$252$		0			0
$253$			10.1598i			0.638743i
$254$	−35.9735	+	20.7693i	−2.25718	+	1.30318i
$255$	11.4103	+	6.58773i	0.714540	+	0.412540i
$256$	−22.6800	+	39.2829i	−1.41750	+	2.45518i
$257$	14.1148	+	24.4475i	0.880456	+	1.52499i	0.850835	+	0.525434i	$0.176097\pi$
$257$	14.1148	+	24.4475i	0.880456	+	1.52499i	0.0296216	+	0.999561i	$0.490570\pi$
$258$		−	6.88164i		−	0.428432i
$259$		0			0
$260$	36.5908	−	5.90287i	2.26926	−	0.366080i
$261$	6.24323	+	10.8136i	0.386446	+	0.669344i
$262$	−2.25181	−	1.30008i	−0.139117	−	0.0803193i
$263$	−3.05434	+	5.29028i	−0.188339	+	0.326212i	−0.944697	−	0.327946i	$-0.893644\pi$
$263$	−3.05434	+	5.29028i	−0.188339	+	0.326212i	0.756358	+	0.654158i	$0.226977\pi$
$264$	12.6322	+	21.8797i	0.777460	+	1.34660i
$265$			15.2059i			0.934092i
$266$		0			0
$267$		−	12.0555i		−	0.737787i
$268$	5.48829	−	3.16867i	0.335251	−	0.193557i
$269$	2.42062	−	4.19264i	0.147588	−	0.255630i	−0.782748	−	0.622339i	$-0.786182\pi$
$269$	2.42062	−	4.19264i	0.147588	−	0.255630i	0.930335	+	0.366710i	$0.119516\pi$
$270$	−13.8358	+	23.9643i	−0.842020	+	1.45842i
$271$	0.258850	−	0.149447i	0.0157240	−	0.00907826i	−0.492117	−	0.870529i	$-0.663777\pi$
$271$	0.258850	−	0.149447i	0.0157240	−	0.00907826i	0.507841	+	0.861451i	$0.330444\pi$
$272$	91.2757			5.53440
$273$		0			0
$274$	−33.4609			−2.02145
$275$	−2.93937	+	1.69704i	−0.177250	+	0.102336i
$276$	13.9820	−	24.2176i	0.841618	−	1.45773i
$277$	4.36348	−	7.55777i	0.262176	−	0.454102i	−0.704644	−	0.709561i	$-0.748893\pi$
$277$	4.36348	−	7.55777i	0.262176	−	0.454102i	0.966820	+	0.255459i	$0.0822265\pi$
$278$	−12.4272	+	7.17487i	−0.745336	+	0.430320i
$279$		−	7.20704i		−	0.431474i
$280$		0			0
$281$		−	24.7012i		−	1.47355i	−0.676137	−	0.736776i	$-0.736347\pi$
$281$		−	24.7012i		−	1.47355i	0.676137	−	0.736776i	$-0.263653\pi$
$282$	14.0720	+	24.3734i	0.837974	+	1.45141i
$283$	−6.12622	+	10.6109i	−0.364166	+	0.630754i	−0.988642	−	0.150290i	$-0.951979\pi$
$283$	−6.12622	+	10.6109i	−0.364166	+	0.630754i	0.624476	+	0.781044i	$0.285313\pi$
$284$	−24.2484	−	13.9998i	−1.43888	−	0.830735i
$285$	5.58791	+	9.67855i	0.330999	+	0.573308i
$286$	−3.61071	−	22.3821i	−0.213506	−	1.32348i
$287$		0			0
$288$			36.7641i			2.16634i
$289$	−9.93191	−	17.2026i	−0.584230	−	1.01192i
$290$	−19.2606	+	33.3604i	−1.13102	+	1.95899i
$291$	−2.51491	−	1.45198i	−0.147427	−	0.0851167i
$292$	−9.33739	+	5.39094i	−0.546429	+	0.315481i
$293$			14.6524i			0.856001i	0.903779	+	0.428000i	$0.140782\pi$
$293$			14.6524i			0.856001i	−0.903779	+	0.428000i	$0.859218\pi$
$294$		0			0
$295$	−13.4029			−0.780345
$296$	15.0570	+	26.0796i	0.875173	+	1.51584i
$297$	10.7371	+	6.19905i	0.623028	+	0.359705i
$298$	3.25559	−	5.63884i	0.188591	−	0.326649i
$299$	−12.3502	+	10.0597i	−0.714228	+	0.581765i
$300$	9.34193			0.539357
$301$		0			0
$302$	−55.5275			−3.19525
$303$	−6.17299	−	10.6919i	−0.354629	−	0.614235i
$304$	67.0501	+	38.7114i	3.84559	+	2.22025i
$305$	−13.0220	−	7.51827i	−0.745639	−	0.430495i
$306$	23.9198	−	13.8101i	1.36740	−	0.789470i
$307$		−	18.8687i		−	1.07690i	−0.842659	−	0.538448i	$-0.819011\pi$
$307$		−	18.8687i		−	1.07690i	0.842659	−	0.538448i	$-0.180989\pi$
$308$		0			0
$309$	−13.6437			−0.776162
$310$	19.2552	−	11.1170i	1.09362	−	0.631404i
$311$	2.85269	−	4.94101i	0.161761	−	0.280179i	−0.773739	−	0.633504i	$-0.781616\pi$
$311$	2.85269	−	4.94101i	0.161761	−	0.280179i	0.935500	+	0.353325i	$0.114949\pi$
$312$	−14.0890	+	37.0195i	−0.797631	+	2.09582i
$313$	−1.97167	−	3.41503i	−0.111445	−	0.193029i	0.804908	−	0.593400i	$-0.202215\pi$
$313$	−1.97167	−	3.41503i	−0.111445	−	0.193029i	−0.916353	+	0.400371i	$0.868881\pi$
$314$		−	30.1868i		−	1.70354i
$315$		0			0
$316$	−20.8744			−1.17428
$317$	3.32654	−	1.92058i	0.186837	−	0.107871i	−0.403664	−	0.914907i	$-0.632263\pi$
$317$	3.32654	−	1.92058i	0.186837	−	0.107871i	0.590501	+	0.807037i	$0.298930\pi$
$318$	−22.1711	−	12.8005i	−1.24329	−	0.717815i
$319$	14.9469	+	8.62962i	0.836868	+	0.483166i
$320$	−49.3424	+	28.4878i	−2.75832	+	1.59252i
$321$	4.94439			0.275969
$322$		0			0
$323$		−	31.2690i		−	1.73985i
$324$	−3.39641	−	5.88275i	−0.188689	−	0.326820i
$325$	−4.97329	−	1.89275i	−0.275869	−	0.104991i
$326$	−25.9454	+	44.9388i	−1.43698	+	2.48893i
$327$	2.01352	−	1.16251i	0.111348	−	0.0642868i
$328$	−23.3264			−1.28799
$329$		0			0
$330$			13.6450i			0.751134i
$331$	5.30526	−	3.06299i	0.291603	−	0.168357i	−0.347061	−	0.937842i	$-0.612820\pi$
$331$	5.30526	−	3.06299i	0.291603	−	0.168357i	0.638665	+	0.769485i	$0.279487\pi$
$332$	11.8162	+	6.82209i	0.648499	+	0.374411i
$333$	4.56565	+	2.63598i	0.250196	+	0.144451i
$334$	29.7077	+	51.4553i	1.62553	+	2.81551i
$335$	2.17261			0.118702
$336$		0			0
$337$	20.8026			1.13319			0.566594	−	0.823997i	$-0.308261\pi$
$337$	20.8026			1.13319			0.566594	+	0.823997i	$0.308261\pi$
$338$	23.6323	−	26.5506i	1.28543	−	1.44416i
$339$	−2.40938	+	4.17317i	−0.130860	+	0.226655i
$340$	54.0517	+	31.2068i	2.93137	+	1.69243i
$341$	−4.98091	−	8.62719i	−0.269732	−	0.467189i
$342$	23.4283			1.26686
$343$		0			0
$344$		−	20.6926i		−	1.11567i
$345$	8.30242	−	4.79340i	0.446987	−	0.258068i
$346$	−6.87400	−	3.96871i	−0.369549	−	0.213359i
$347$	−8.87542	+	15.3727i	−0.476457	+	0.825248i	−0.999636	−	0.0269746i	$-0.991413\pi$
$347$	−8.87542	+	15.3727i	−0.476457	+	0.825248i	0.523179	+	0.852223i	$0.324746\pi$
$348$	−23.7523	−	41.1401i	−1.27326	−	2.20534i
$349$			1.00552i			0.0538245i	0.999638	+	0.0269122i	$0.00856746\pi$
$349$			1.00552i			0.0538245i	−0.999638	+	0.0269122i	$0.991433\pi$
$350$		0			0
$351$	3.09572	+	19.1898i	0.165237	+	1.02427i
$352$	25.4083	+	44.0085i	1.35427	+	2.34566i
$353$	10.9309	+	6.31096i	0.581793	+	0.335898i	0.761846	−	0.647759i	$-0.224293\pi$
$353$	10.9309	+	6.31096i	0.581793	+	0.335898i	−0.180053	+	0.983657i	$0.557627\pi$
$354$	11.2826	−	19.5421i	0.599666	−	1.03865i
$355$	−4.79950	−	8.31298i	−0.254731	−	0.441207i
$356$		−	57.1083i		−	3.02674i
$357$		0			0
$358$			52.9076i			2.79625i
$359$	9.93763	−	5.73750i	0.524488	−	0.302813i	−0.214281	−	0.976772i	$-0.568741\pi$
$359$	9.93763	−	5.73750i	0.524488	−	0.302813i	0.738769	+	0.673959i	$0.235407\pi$
$360$	−14.8417	+	25.7067i	−0.782229	+	1.35486i
$361$	3.76165	−	6.51537i	0.197982	−	0.342914i
$362$	23.6319	−	13.6439i	1.24207	−	0.717107i
$363$	−6.60188			−0.346509
$364$		0			0
$365$	−3.69631			−0.193474
$366$	21.9241	−	12.6579i	1.14599	−	0.661638i
$367$	14.4557	−	25.0380i	0.754583	−	1.30698i	−0.190999	−	0.981590i	$-0.561173\pi$
$367$	14.4557	−	25.0380i	0.754583	−	1.30698i	0.945582	−	0.325385i	$-0.105494\pi$
$368$	33.2073	−	57.5167i	1.73105	−	2.99826i
$369$	−3.53657	+	2.04184i	−0.184106	+	0.106294i
$370$			16.2642i			0.845538i
$371$		0			0
$372$			27.4191i			1.42161i
$373$	−11.7444	−	20.3419i	−0.608103	−	1.05326i	−0.991553	−	0.129703i	$-0.958598\pi$
$373$	−11.7444	−	20.3419i	−0.608103	−	1.05326i	0.383450	−	0.923562i	$-0.374736\pi$
$374$	19.0888	−	33.0628i	0.987058	−	1.70964i
$375$	12.1701	+	7.02641i	0.628461	+	0.362842i
$376$	42.3134	+	73.2890i	2.18215	+	3.77959i
$377$	4.30951	+	26.7138i	0.221951	+	1.37583i
$378$		0			0
$379$		−	37.6063i		−	1.93171i	−0.259088	−	0.965854i	$-0.583422\pi$
$379$		−	37.6063i		−	1.93171i	0.259088	−	0.965854i	$-0.416578\pi$
$380$	26.4705	+	45.8483i	1.35791	+	2.35197i
$381$	8.78073	−	15.2087i	0.449850	−	0.779164i
$382$	12.7981	+	7.38898i	0.654808	+	0.378053i
$383$	−21.9263	+	12.6592i	−1.12038	+	0.646853i	−0.941498	−	0.337018i	$-0.890582\pi$
$383$	−21.9263	+	12.6592i	−1.12038	+	0.646853i	−0.178883	+	0.983870i	$0.557248\pi$
$384$		−	44.8397i		−	2.28822i
$385$		0			0
$386$	39.8281			2.02720
$387$	−1.81129	−	3.13725i	−0.0920730	−	0.159475i
$388$	−11.9134	−	6.87820i	−0.604811	−	0.349188i
$389$	−0.659447	+	1.14220i	−0.0334353	+	0.0579117i	−0.882259	−	0.470765i	$-0.843978\pi$
$389$	−0.659447	+	1.14220i	−0.0334353	+	0.0579117i	0.848824	+	0.528676i	$0.177311\pi$
$390$	−16.5867	+	13.5105i	−0.839901	+	0.684130i
$391$	−26.8231			−1.35650
$392$		0			0
$393$	1.09928			0.0554514
$394$	−21.7444	−	37.6624i	−1.09547	−	1.89740i
$395$	−6.19754	−	3.57815i	−0.311832	−	0.180036i
$396$	18.1450	+	10.4760i	0.911819	+	0.526439i
$397$	−32.3466	+	18.6753i	−1.62343	+	0.937287i	−0.637435	+	0.770504i	$0.720005\pi$
$397$	−32.3466	+	18.6753i	−1.62343	+	0.937287i	−0.985994	+	0.166783i	$0.946662\pi$
$398$		−	1.02168i		−	0.0512121i
$399$		0			0
$400$	22.1871			1.10935
$401$	−23.6584	+	13.6592i	−1.18144	+	0.682106i	−0.956348	−	0.292231i	$-0.905602\pi$
$401$	−23.6584	+	13.6592i	−1.18144	+	0.682106i	−0.225095	+	0.974337i	$0.572269\pi$
$402$	−1.82892	+	3.16778i	−0.0912181	+	0.157994i
$403$	5.55531	−	14.5969i	0.276730	−	0.727122i
$404$	−29.2421	−	50.6488i	−1.45485	−	2.51987i
$405$		−	2.32876i		−	0.115717i
$406$		0			0
$407$	7.28710			0.361208
$408$	−57.7647	+	33.3505i	−2.85978	+	1.65110i
$409$	20.7042	+	11.9536i	1.02375	+	0.591065i	0.915189	−	0.403024i	$-0.132041\pi$
$409$	20.7042	+	11.9536i	1.02375	+	0.591065i	0.108565	+	0.994089i	$0.465374\pi$
$410$	−10.9105	−	6.29916i	−0.538830	−	0.311093i
$411$	12.2511	−	7.07320i	0.604305	−	0.348895i
$412$	−64.6315			−3.18417
$413$		0			0
$414$		−	20.0972i		−	0.987721i
$415$	2.33879	+	4.05091i	0.114807	+	0.198851i
$416$	−28.3384	+	74.4606i	−1.38940	+	3.65073i
$417$	3.03335	−	5.25392i	0.148544	−	0.257285i
$418$	28.0448	−	16.1917i	1.37172	−	0.791962i
$419$	−16.4726			−0.804739			−0.402369	−	0.915477i	$-0.631813\pi$
$419$	−16.4726			−0.804739			−0.402369	+	0.915477i	$0.631813\pi$
$420$		0			0
$421$			23.9857i			1.16899i	0.811397	+	0.584495i	$0.198708\pi$
$421$			23.9857i			1.16899i	−0.811397	+	0.584495i	$0.801292\pi$
$422$	−14.3318	+	8.27449i	−0.697663	+	0.402796i
$423$	12.8304	+	7.40766i	0.623837	+	0.360173i
$424$	−66.6668	−	38.4901i	−3.23763	−	1.86924i
$425$	−4.48038	−	7.76025i	−0.217331	−	0.376428i
$426$	16.1610			0.783005
$427$		0			0
$428$	23.4221			1.13215
$429$	6.05329	+	7.43158i	0.292256	+	0.358800i
$430$	5.58791	−	9.67855i	0.269473	−	0.466741i
$431$	−19.6500	−	11.3449i	−0.946508	−	0.546467i	−0.0545135	−	0.998513i	$-0.517361\pi$
$431$	−19.6500	−	11.3449i	−0.946508	−	0.546467i	−0.891994	+	0.452046i	$0.850694\pi$
$432$	−40.5230	−	70.1880i	−1.94967	−	3.37692i
$433$	17.0937			0.821470			0.410735	−	0.911755i	$-0.365272\pi$
$433$	17.0937			0.821470			0.410735	+	0.911755i	$0.365272\pi$
$434$		0			0
$435$		−	16.2858i		−	0.780845i
$436$	9.53827	−	5.50692i	0.456800	−	0.263734i
$437$	−19.7039	−	11.3761i	−0.942566	−	0.544191i
$438$	3.11159	−	5.38943i	0.148677	−	0.257517i
$439$	−17.7006	−	30.6584i	−0.844805	−	1.46325i	−0.885790	−	0.464086i	$-0.846383\pi$
$439$	−17.7006	−	30.6584i	−0.844805	−	1.46325i	0.0409849	−	0.999160i	$-0.486950\pi$
$440$			41.0296i			1.95601i
$441$		0			0
$442$	59.0913	−	9.53268i	2.81069	−	0.453423i
$443$	8.13161	+	14.0844i	0.386345	+	0.669168i	0.991955	−	0.126593i	$-0.0404042\pi$
$443$	8.13161	+	14.0844i	0.386345	+	0.669168i	−0.605610	+	0.795761i	$0.707071\pi$
$444$	−17.3700	−	10.0286i	−0.824342	−	0.475934i
$445$	9.78912	−	16.9553i	0.464049	−	0.803756i
$446$	9.98836	+	17.3003i	0.472963	+	0.819195i
$447$			2.75276i			0.130201i
$448$		0			0
$449$			15.1472i			0.714839i	0.933944	+	0.357419i	$0.116343\pi$
$449$			15.1472i			0.714839i	−0.933944	+	0.357419i	$0.883657\pi$
$450$	5.81436	−	3.35692i	0.274092	−	0.158247i
$451$	−2.82230	+	4.88837i	−0.132897	+	0.230184i
$452$	−11.4135	+	19.7687i	−0.536845	+	0.929844i
$453$	20.3305	−	11.7378i	0.955209	−	0.551490i
$454$	42.9034			2.01356
$455$		0			0
$456$	−56.5778			−2.64950
$457$	−34.2065	+	19.7491i	−1.60011	+	0.923826i	−0.608650	+	0.793439i	$0.708289\pi$
$457$	−34.2065	+	19.7491i	−1.60011	+	0.923826i	−0.991463	+	0.130387i	$0.958378\pi$
$458$	−34.9475	+	60.5308i	−1.63299	+	2.82842i
$459$	−16.3662	+	28.3471i	−0.763908	+	1.32313i
$460$	39.3294	−	22.7069i	1.83375	−	1.05871i
$461$			19.0149i			0.885614i	0.896617	+	0.442807i	$0.146017\pi$
$461$			19.0149i			0.885614i	−0.896617	+	0.442807i	$0.853983\pi$
$462$		0			0
$463$		−	2.48740i		−	0.115599i	−0.998328	−	0.0577996i	$-0.981592\pi$
$463$		−	2.48740i		−	0.115599i	0.998328	−	0.0577996i	$-0.0184084\pi$
$464$	−56.4116	−	97.7078i	−2.61884	−	4.53597i
$465$	−4.69999	+	8.14062i	−0.217957	+	0.377512i
$466$	38.6925	+	22.3391i	1.79240	+	1.03484i
$467$	7.43931	+	12.8853i	0.344250	+	0.596259i	0.985217	−	0.171309i	$-0.0547998\pi$
$467$	7.43931	+	12.8853i	0.344250	+	0.596259i	−0.640967	+	0.767568i	$0.721466\pi$
$468$	5.23157	+	32.4295i	0.241830	+	1.49906i
$469$		0			0
$470$			45.7059i			2.10826i
$471$	6.38111	+	11.0524i	0.294026	+	0.509268i
$472$	33.9261	−	58.7617i	1.56158	−	2.70473i
$473$	−4.33642	−	2.50363i	−0.199389	−	0.115117i
$474$	10.4343	−	6.02423i	0.479262	−	0.276702i
$475$		−	7.60079i		−	0.348748i
$476$		0			0
$477$	−13.4766			−0.617053
$478$	−23.5831	−	40.8472i	−1.07867	−	1.86831i
$479$	14.6183	+	8.43988i	0.667927	+	0.385628i	0.795291	−	0.606228i	$-0.207318\pi$
$479$	14.6183	+	8.43988i	0.667927	+	0.385628i	−0.127364	+	0.991856i	$0.540652\pi$
$480$	23.9753	−	41.5264i	1.09432	−	1.89541i
$481$	7.21525	+	8.85811i	0.328987	+	0.403895i
$482$	27.6509			1.25947
$483$		0			0
$484$	−31.2738			−1.42154
$485$	−2.35803	−	4.08422i	−0.107073	−	0.185455i
$486$	−34.9011	−	20.1502i	−1.58315	−	0.914029i
$487$	−3.84982	−	2.22270i	−0.174452	−	0.100720i	0.410231	−	0.911981i	$-0.365448\pi$
$487$	−3.84982	−	2.22270i	−0.174452	−	0.100720i	−0.584683	+	0.811262i	$0.698781\pi$
$488$	65.9242	−	38.0613i	2.98425	−	1.72296i
$489$		−	21.9381i		−	0.992076i
$490$		0			0
$491$	−16.9816			−0.766368			−0.383184	−	0.923672i	$-0.625172\pi$
$491$	−16.9816			−0.766368			−0.383184	+	0.923672i	$0.625172\pi$
$492$	13.4548	−	7.76814i	0.606590	−	0.350215i
$493$	−22.7832	+	39.4616i	−1.02610	+	1.77726i
$494$	47.4508	+	18.0589i	2.13491	+	0.812509i
$495$	3.59145	+	6.22058i	0.161424	+	0.279594i
$496$			65.1202i			2.92399i
$497$		0			0
$498$	−7.87526			−0.352899
$499$	35.5080	−	20.5006i	1.58956	−	0.917731i	0.596177	−	0.802853i	$-0.296686\pi$
$499$	35.5080	−	20.5006i	1.58956	−	0.917731i	0.993380	−	0.114878i	$-0.0366476\pi$
$500$	57.6510	+	33.2848i	2.57823	+	1.48854i
$501$	−21.7540	−	12.5597i	−0.971896	−	0.561124i
$502$	49.2956	−	28.4608i	2.20017	−	1.27027i
$503$	37.2910			1.66272			0.831361	−	0.555732i	$-0.187562\pi$
$503$	37.2910			1.66272			0.831361	+	0.555732i	$0.187562\pi$
$504$		0			0
$505$		−	20.0499i		−	0.892210i
$506$	−13.8895	−	24.0573i	−0.617464	−	1.06948i
$507$	−3.04013	+	14.7166i	−0.135017	+	0.653588i
$508$	41.5952	−	72.0451i	1.84549	−	3.19648i
$509$	−7.11501	+	4.10785i	−0.315367	+	0.182077i	−0.649326	−	0.760510i	$-0.724949\pi$
$509$	−7.11501	+	4.10785i	−0.315367	+	0.182077i	0.333958	+	0.942588i	$0.391615\pi$
$510$	−36.0244			−1.59519
$511$		0			0
$512$		−	46.4428i		−	2.05250i
$513$	−24.0448	+	13.8823i	−1.06160	+	0.612918i
$514$	−66.8445	−	38.5927i	−2.94838	−	1.70225i
$515$	−19.1889	−	11.0787i	−0.845563	−	0.488186i
$516$	6.89103	+	11.9356i	0.303360	+	0.525436i
$517$	20.4783			0.900633
$518$		0			0
$519$	3.35573			0.147300
$520$	−49.8751	+	40.6251i	−2.18717	+	1.78153i
$521$	16.9997	−	29.4443i	0.744768	−	1.28998i	−0.205534	−	0.978650i	$-0.565893\pi$
$521$	16.9997	−	29.4443i	0.744768	−	1.28998i	0.950303	−	0.311327i	$-0.100773\pi$
$522$	−29.5665	−	17.0702i	−1.29409	−	0.747145i
$523$	−11.4391	−	19.8131i	−0.500197	−	0.866366i	−1.00000		0.000227041i	$-0.999928\pi$
$523$	−11.4391	−	19.8131i	−0.500197	−	0.866366i	0.499803	−	0.866139i	$-0.333406\pi$
$524$	5.20742			0.227487
$525$		0			0
$526$		−	16.7024i		−	0.728258i
$527$	22.7768	−	13.1502i	0.992171	−	0.572830i
$528$	−34.6101	−	19.9821i	−1.50621	−	0.869611i
$529$	1.74142	−	3.01623i	0.0757139	−	0.131140i
$530$	−20.7880	−	36.0059i	−0.902974	−	1.56400i
$531$		−	11.8786i		−	0.515489i
$532$		0			0
$533$	−8.73672	+	1.40942i	−0.378429	+	0.0610487i
$534$	16.4811	+	28.5462i	0.713208	+	1.23531i
$535$	6.95394	+	4.01486i	0.300645	+	0.173578i
$536$	−5.49943	+	9.52528i	−0.237539	+	0.411430i
$537$	−11.1840	−	19.3712i	−0.482624	−	0.835930i
$538$			13.2369i			0.570685i
$539$		0			0
$540$		−	55.4187i		−	2.38484i
$541$	−34.2065	+	19.7491i	−1.47065	+	0.849082i	−0.999457	−	0.0329468i	$-0.989511\pi$
$541$	−34.2065	+	19.7491i	−1.47065	+	0.849082i	−0.471196	+	0.882029i	$0.656177\pi$
$542$	−0.408618	+	0.707747i	−0.0175517	+	0.0304004i
$543$	−5.76829	+	9.99096i	−0.247541	+	0.428753i
$544$	−116.187	+	67.0808i	−4.98149	+	2.87607i
$545$	3.77584			0.161739
$546$		0			0
$547$	37.0129			1.58256			0.791279	−	0.611455i	$-0.209416\pi$
$547$	37.0129			1.58256			0.791279	+	0.611455i	$0.209416\pi$
$548$	58.0350	−	33.5065i	2.47913	−	1.43133i
$549$	6.66326	−	11.5411i	0.284381	−	0.492563i
$550$	4.64006	−	8.03682i	0.197853	−	0.342691i
$551$	−33.4725	+	19.3254i	−1.42598	+	0.823288i
$552$			48.5334i			2.06572i
$553$		0			0
$554$			23.8613i			1.01377i
$555$	−3.43805	−	5.95488i	−0.145937	−	0.252771i
$556$	14.3693	−	24.8884i	0.609394	−	1.05550i
$557$	20.8597	+	12.0433i	0.883853	+	0.510293i	0.871927	−	0.489636i	$-0.162870\pi$
$557$	20.8597	+	12.0433i	0.883853	+	0.510293i	0.0119264	+	0.999929i	$0.496204\pi$
$558$	9.85275	+	17.0655i	0.417100	+	0.722438i
$559$	−1.25028	−	7.75024i	−0.0528811	−	0.327800i
$560$		0			0
$561$			16.1405i			0.681453i
$562$	33.7691	+	58.4897i	1.42446	+	2.46724i
$563$	−3.24699	+	5.62395i	−0.136844	+	0.237021i	−0.926300	−	0.376786i	$-0.877029\pi$
$563$	−3.24699	+	5.62395i	−0.136844	+	0.237021i	0.789456	+	0.613807i	$0.210363\pi$
$564$	−48.8132	−	28.1823i	−2.05541	−	1.18669i
$565$	−6.77725	+	3.91285i	−0.285121	+	0.164615i
$566$		−	33.5006i		−	1.40814i
$567$		0			0
$568$	48.5951			2.03900
$569$	14.3819	+	24.9102i	0.602921	+	1.04429i	0.992376	+	0.123244i	$0.0393298\pi$
$569$	14.3819	+	24.9102i	0.602921	+	1.04429i	−0.389456	+	0.921045i	$0.627337\pi$
$570$	−26.4631	−	15.2785i	−1.10842	−	0.639945i
$571$	−1.24308	+	2.15307i	−0.0520211	+	0.0901032i	−0.890863	−	0.454271i	$-0.849900\pi$
$571$	−1.24308	+	2.15307i	−0.0520211	+	0.0901032i	0.838842	+	0.544375i	$0.183233\pi$
$572$	28.6751	+	35.2042i	1.19897	+	1.47196i
$573$	−6.24775			−0.261003
$574$		0			0
$575$	−6.52009			−0.271906
$576$	−25.2481	−	43.7310i	−1.05200	−	1.82212i
$577$	−12.6221	−	7.28737i	−0.525465	−	0.303377i	0.213703	−	0.976899i	$-0.431448\pi$
$577$	−12.6221	−	7.28737i	−0.525465	−	0.303377i	−0.739168	+	0.673521i	$0.764781\pi$
$578$	47.0353	+	27.1559i	1.95641	+	1.12953i
$579$	−14.5824	+	8.41914i	−0.606023	+	0.349888i
$580$		−	77.1476i		−	3.20338i
$581$		0			0
$582$	7.94003			0.329125
$583$	−16.1322	+	9.31395i	−0.668129	+	0.385745i
$584$	9.35632	−	16.2056i	0.387167	−	0.670594i
$585$	−4.00562	+	10.5250i	−0.165612	+	0.435154i
$586$	−20.0313	−	34.6952i	−0.827484	−	1.43324i
$587$			8.69744i			0.358982i	0.983760	+	0.179491i	$0.0574450\pi$
$587$			8.69744i			0.358982i	−0.983760	+	0.179491i	$0.942555\pi$
$588$		0			0
$589$	22.3087			0.919215
$590$	31.7365	−	18.3231i	1.30657	−	0.754349i
$591$	15.9227	+	9.19297i	0.654972	+	0.378148i
$592$	−41.2536	−	23.8178i	−1.69551	−	0.978906i
$593$	15.6144	−	9.01495i	0.641205	−	0.370200i	−0.143874	−	0.989596i	$-0.545956\pi$
$593$	15.6144	−	9.01495i	0.641205	−	0.370200i	0.785078	+	0.619396i	$0.212623\pi$
$594$	−33.8989			−1.39089
$595$		0			0
$596$			13.0401i			0.534143i
$597$	0.215970	+	0.374070i	0.00883905	+	0.0153097i
$598$	15.4912	−	40.7041i	0.633484	−	1.66451i
$599$	−0.00705812	+	0.0122250i	−0.000288387	+	0.000499501i	−0.866170	−	0.499750i	$-0.833425\pi$
$599$	−0.00705812	+	0.0122250i	−0.000288387	+	0.000499501i	0.865881	+	0.500250i	$0.166758\pi$
$600$	−14.0413	+	8.10676i	−0.573234	+	0.330957i
$601$	13.7533			0.561007			0.280504	−	0.959853i	$-0.409499\pi$
$601$	13.7533			0.561007			0.280504	+	0.959853i	$0.409499\pi$
$602$		0			0
$603$			1.92553i			0.0784136i
$604$	96.3077	−	55.6033i	3.91870	−	2.26246i
$605$	−9.28508	−	5.36075i	−0.377492	−	0.217945i
$606$	29.2339	+	16.8782i	1.18755	+	0.685630i
$607$	−11.8742	−	20.5667i	−0.481959	−	0.834778i	0.517826	−	0.855486i	$-0.326741\pi$
$607$	−11.8742	−	20.5667i	−0.481959	−	0.834778i	−0.999786	+	0.0207079i	$0.993408\pi$
$608$	−113.800			−4.61519
$609$		0			0
$610$	41.1129			1.66461
$611$	20.2764	+	24.8931i	0.820294	+	1.00707i
$612$	−27.6578	+	47.9048i	−1.11800	+	1.93644i
$613$	−1.89149	−	1.09205i	−0.0763964	−	0.0441075i	0.461315	−	0.887236i	$-0.347378\pi$
$613$	−1.89149	−	1.09205i	−0.0763964	−	0.0441075i	−0.537712	+	0.843129i	$0.680711\pi$
$614$	25.7955	+	44.6791i	1.04102	+	1.80310i
$615$	5.32625			0.214775
$616$		0			0
$617$		−	14.6673i		−	0.590485i	−0.955422	−	0.295243i	$-0.904600\pi$
$617$		−	14.6673i		−	0.590485i	0.955422	−	0.295243i	$-0.0954005\pi$
$618$	32.3067	−	18.6523i	1.29957	−	0.750305i
$619$	18.4159	+	10.6324i	0.740198	+	0.427354i	0.822141	−	0.569283i	$-0.192779\pi$
$619$	18.4159	+	10.6324i	0.740198	+	0.427354i	−0.0819430	+	0.996637i	$0.526113\pi$
$620$	−22.2643	+	38.5630i	−0.894158	+	1.54873i
$621$	11.9085	+	20.6261i	0.477870	+	0.827695i
$622$			15.5997i			0.625490i
$623$		0			0
$624$	−9.97880	−	61.8567i	−0.399472	−	2.47625i
$625$	7.72127	+	13.3736i	0.308851	+	0.534945i
$626$	9.33739	+	5.39094i	0.373197	+	0.215465i
$627$	−6.84543	+	11.8566i	−0.273380	+	0.473508i
$628$	30.2280	+	52.3564i	1.20623	+	2.08925i
$629$			19.2388i			0.767099i
$630$		0			0
$631$			34.4910i			1.37307i	0.727099	+	0.686533i	$0.240868\pi$
$631$			34.4910i			1.37307i	−0.727099	+	0.686533i	$0.759132\pi$
$632$	31.3751	−	18.1144i	1.24804	−	0.720554i
$633$	3.49824	−	6.05913i	0.139043	−	0.240829i
$634$	−5.25126	+	9.09544i	−0.208554	+	0.361226i
$635$	24.6990	−	14.2599i	0.980148	−	0.565889i
$636$	51.2717			2.03305
$637$		0			0
$638$	−47.1902			−1.86828
$639$	7.36760	−	4.25368i	0.291458	−	0.168273i
$640$	36.4100	−	63.0639i	1.43923	−	2.49282i
$641$	10.8972	−	18.8745i	0.430414	−	0.745500i	−0.566494	−	0.824066i	$-0.691701\pi$
$641$	10.8972	−	18.8745i	0.430414	−	0.745500i	0.996909	+	0.0785658i	$0.0250341\pi$
$642$	−11.7078	+	6.75949i	−0.462069	+	0.266776i
$643$		−	5.81898i		−	0.229478i	−0.993396	−	0.114739i	$-0.963397\pi$
$643$		−	5.81898i		−	0.229478i	0.993396	−	0.114739i	$-0.0366032\pi$
$644$		0			0
$645$			4.72485i			0.186041i
$646$	42.7479	+	74.0415i	1.68189	+	2.91312i
$647$	−16.5354	+	28.6402i	−0.650074	+	1.12596i	0.333031	+	0.942916i	$0.391929\pi$
$647$	−16.5354	+	28.6402i	−0.650074	+	1.12596i	−0.983105	+	0.183045i	$0.941405\pi$
$648$	10.2099	+	5.89468i	0.401082	+	0.231565i
$649$	−8.20954	−	14.2193i	−0.322253	−	0.558158i
$650$	14.3638	−	2.31718i	0.563394	−	0.0908873i
$651$		0			0
$652$		−	103.923i		−	4.06995i
$653$	0.869964	+	1.50682i	0.0340443	+	0.0589665i	0.882546	−	0.470227i	$-0.155828\pi$
$653$	0.869964	+	1.50682i	0.0340443	+	0.0589665i	−0.848501	+	0.529193i	$0.822495\pi$
$654$	−3.17853	+	5.50538i	−0.124290	+	0.215277i
$655$	1.54606	+	0.892620i	0.0604097	+	0.0348775i
$656$	31.9552	−	18.4493i	1.24764	−	0.720325i
$657$		−	3.27596i		−	0.127807i
$658$		0			0
$659$	27.9823			1.09003			0.545017	−	0.838425i	$-0.316523\pi$
$659$	27.9823			1.09003			0.545017	+	0.838425i	$0.316523\pi$
$660$	−13.6636	−	23.6661i	−0.531856	−	0.921201i
$661$	18.0422	+	10.4167i	0.701762	+	0.405163i	0.808003	−	0.589178i	$-0.200548\pi$
$661$	18.0422	+	10.4167i	0.701762	+	0.405163i	−0.106241	+	0.994340i	$0.533882\pi$
$662$	−8.37484	+	14.5057i	−0.325497	+	0.563778i
$663$	−19.6202	+	15.9814i	−0.761986	+	0.620665i
$664$	−23.6804			−0.918976
$665$		0			0
$666$	−14.4146			−0.558555
$667$	16.5776	+	28.7133i	0.641888	+	1.11178i
$668$	−103.051	−	59.4965i	−3.98716	−	2.30199i
$669$	−7.31414	−	4.22282i	−0.282781	−	0.163264i
$670$	−5.14449	+	2.97017i	−0.198749	+	0.114748i
$671$		−	18.4204i		−	0.711112i
$672$		0			0
$673$	−7.06203			−0.272221			−0.136111	−	0.990694i	$-0.543460\pi$
$673$	−7.06203			−0.272221			−0.136111	+	0.990694i	$0.543460\pi$
$674$	−49.2582	+	28.4392i	−1.89735	+	1.09544i
$675$	−3.97825	+	6.89053i	−0.153123	+	0.265217i
$676$	−14.4014	+	69.7142i	−0.553900	+	2.68132i
$677$	−2.61495	−	4.52922i	−0.100501	−	0.174072i	0.811390	−	0.584505i	$-0.198711\pi$
$677$	−2.61495	−	4.52922i	−0.100501	−	0.174072i	−0.911891	+	0.410432i	$0.865378\pi$
$678$		−	13.1755i		−	0.506001i
$679$		0			0
$680$	−108.323			−4.15399
$681$	−15.7084	+	9.06924i	−0.601946	+	0.347534i
$682$	23.5885	+	13.6188i	0.903250	+	0.521492i
$683$	−24.1982	−	13.9708i	−0.925917	−	0.534579i	−0.0403993	−	0.999184i	$-0.512863\pi$
$683$	−24.1982	−	13.9708i	−0.925917	−	0.534579i	−0.885518	+	0.464605i	$0.846196\pi$
$684$	−40.6343	+	23.4602i	−1.55369	+	0.897023i
$685$	22.9738			0.877785
$686$		0			0
$687$		−	29.5498i		−	1.12740i
$688$	16.3662	+	28.3471i	0.623955	+	1.08072i
$689$	−27.2951	−	10.3880i	−1.03986	−	0.395752i
$690$	−13.1061	+	22.7005i	−0.498942	+	0.864193i
$691$	22.0416	−	12.7257i	0.838503	−	0.484110i	−0.0182518	−	0.999833i	$-0.505810\pi$
$691$	22.0416	−	12.7257i	0.838503	−	0.484110i	0.856755	+	0.515723i	$0.172477\pi$
$692$	15.8965			0.604293
$693$		0			0
$694$		−	48.5344i		−	1.84234i
$695$	8.53239	−	4.92618i	0.323652	−	0.186861i
$696$	71.4013	+	41.2236i	2.70646	+	1.56258i
$697$	−12.9058	−	7.45119i	−0.488844	−	0.282234i
$698$	−1.37465	−	2.38097i	−0.0520314	−	0.0901210i
$699$	−18.8888			−0.714441
$700$		0			0
$701$	−17.9541			−0.678117			−0.339058	−	0.940765i	$-0.610108\pi$
$701$	−17.9541			−0.678117			−0.339058	+	0.940765i	$0.610108\pi$
$702$	−33.5647	−	41.2071i	−1.26682	−	1.55526i
$703$	−8.15944	+	14.1326i	−0.307739	+	0.533020i
$704$	−60.4465	−	34.8988i	−2.27816	−	1.31530i
$705$	−9.66164	−	16.7345i	−0.363878	−	0.630256i
$706$	−34.5109			−1.29883
$707$		0			0
$708$			45.1921i			1.69842i
$709$	−25.3044	+	14.6095i	−0.950328	+	0.548672i	−0.893183	−	0.449694i	$-0.851533\pi$
$709$	−25.3044	+	14.6095i	−0.950328	+	0.548672i	−0.0571454	+	0.998366i	$0.518200\pi$
$710$	22.7294	+	13.1228i	0.853018	+	0.492490i
$711$	3.17123	−	5.49273i	0.118930	−	0.205994i
$712$	49.5576	+	85.8363i	1.85725	+	3.21685i
$713$		−	19.1368i		−	0.716679i
$714$		0			0
$715$	2.47907	+	15.3673i	0.0927120	+	0.574704i
$716$	−52.9797	−	91.7636i	−1.97994	−	3.42937i
$717$	17.2691	+	9.97034i	0.644927	+	0.372349i
$718$	−15.6875	+	27.1715i	−0.585451	+	1.01403i
$719$	19.3600	+	33.5325i	0.722005	+	1.25055i	0.960195	+	0.279331i	$0.0901128\pi$
$719$	19.3600	+	33.5325i	0.722005	+	1.25055i	−0.238189	+	0.971219i	$0.576554\pi$
$720$		−	46.9545i		−	1.74989i
$721$		0			0
$722$			20.5702i			0.765544i
$723$	−10.1239	+	5.84505i	−0.376513	+	0.217380i
$724$	−27.3250	+	47.3283i	−1.01553	+	1.75894i
$725$	−5.53807	+	9.59223i	−0.205679	+	0.356246i
$726$	15.6325	−	9.02544i	0.580177	−	0.334966i
$727$	27.9441			1.03639			0.518194	−	0.855263i	$-0.326604\pi$
$727$	27.9441			1.03639			0.518194	+	0.855263i	$0.326604\pi$
$728$		0			0
$729$	20.7594			0.768868
$730$	8.75246	−	5.05324i	0.323943	−	0.187029i
$731$	6.60986	−	11.4486i	0.244475	−	0.423443i
$732$	−25.3503	+	43.9080i	−0.936973	+	1.62289i
$733$	−37.8831	+	21.8718i	−1.39924	+	0.807854i	−0.994313	−	0.106493i	$-0.966038\pi$
$733$	−37.8831	+	21.8718i	−1.39924	+	0.807854i	−0.404931	+	0.914347i	$0.632704\pi$
$734$			79.0497i			2.91778i
$735$		0			0
$736$			97.6195i			3.59830i
$737$	1.33077	+	2.30496i	0.0490195	+	0.0849042i
$738$	5.58280	−	9.66969i	0.205506	−	0.355946i
$739$	−6.27411	−	3.62236i	−0.230797	−	0.133251i	0.380143	−	0.924928i	$-0.375875\pi$
$739$	−6.27411	−	3.62236i	−0.230797	−	0.133251i	−0.610940	+	0.791677i	$0.709208\pi$
$740$	−16.2864	−	28.2089i	−0.598701	−	1.03698i
$741$	−21.1907	+	3.41851i	−0.778461	+	0.125582i
$742$		0			0
$743$		−	33.9142i		−	1.24419i	−0.782941	−	0.622096i	$-0.786281\pi$
$743$		−	33.9142i		−	1.24419i	0.782941	−	0.622096i	$-0.213719\pi$
$744$	−23.7938	−	41.2120i	−0.872322	−	1.51091i
$745$	−2.23525	+	3.87156i	−0.0818931	+	0.141843i
$746$	55.6189	+	32.1116i	2.03635	+	1.17569i
$747$	−3.59022	+	2.07282i	−0.131359	+	0.0758404i
$748$			76.4593i			2.79563i
$749$		0			0
$750$	−38.4232			−1.40302
$751$	19.2487	+	33.3396i	0.702393	+	1.21658i	0.967624	+	0.252396i	$0.0812186\pi$
$751$	19.2487	+	33.3396i	0.702393	+	1.21658i	−0.265231	+	0.964185i	$0.585448\pi$
$752$	−115.931	−	66.9330i	−4.22758	−	2.44079i
$753$	−12.0325	+	20.8409i	−0.438489	+	0.759485i
$754$	−46.7250	−	57.3639i	−1.70162	−	2.08907i
$755$	38.1245			1.38749
$756$		0			0
$757$	8.18792			0.297595			0.148797	−	0.988868i	$-0.452460\pi$
$757$	8.18792			0.297595			0.148797	+	0.988868i	$0.452460\pi$
$758$	51.4117	+	89.0476i	1.86736	+	3.23435i
$759$	10.1708	+	5.87213i	0.369177	+	0.213145i
$760$	−79.5726	−	45.9413i	−2.88640	−	1.66647i
$761$	8.71186	−	5.02979i	0.315805	−	0.182330i	−0.333716	−	0.942674i	$-0.608303\pi$
$761$	8.71186	−	5.02979i	0.315805	−	0.182330i	0.649521	+	0.760344i	$0.274969\pi$
$762$			48.0166i			1.73946i
$763$		0			0
$764$	−29.5962			−1.07075
$765$	−16.4230	+	9.48184i	−0.593776	+	0.342816i
$766$	34.6127	−	59.9509i	1.25061	−	2.16612i
$767$	9.15626	−	24.0586i	0.330613	−	0.868705i
$768$	26.2170	+	45.4091i	0.946024	+	1.63856i
$769$			2.53594i			0.0914482i	0.998954	+	0.0457241i	$0.0145595\pi$
$769$			2.53594i			0.0914482i	−0.998954	+	0.0457241i	$0.985440\pi$
$770$		0			0
$771$	32.6320			1.17521
$772$	−69.0783	+	39.8824i	−2.48618	+	1.43540i
$773$	−25.3049	−	14.6098i	−0.910152	−	0.525477i	−0.0296721	−	0.999560i	$-0.509446\pi$
$773$	−25.3049	−	14.6098i	−0.910152	−	0.525477i	−0.880480	+	0.474083i	$0.842780\pi$
$774$	8.57786	+	4.95243i	0.308325	+	0.178012i
$775$	5.53652	−	3.19651i	0.198878	−	0.114822i
$776$	23.8751			0.857066
$777$		0			0
$778$		−	3.60612i		−	0.129286i
$779$	−6.32032	−	10.9471i	−0.226449	−	0.392221i
$780$	15.2393	−	40.0421i	0.545655	−	1.43374i
$781$	5.87959	−	10.1838i	0.210388	−	0.364403i
$782$	63.5140	−	36.6698i	2.27126	−	1.31131i
$783$	40.4595			1.44591
$784$		0			0
$785$			20.7259i			0.739739i
$786$	−2.60298	+	1.50283i	−0.0928451	+	0.0536041i
$787$	−0.129425	−	0.0747235i	−0.00461350	−	0.00266360i	0.497691	−	0.867354i	$-0.334181\pi$
$787$	−0.129425	−	0.0747235i	−0.00461350	−	0.00266360i	−0.502305	+	0.864691i	$0.667515\pi$
$788$	75.4275	+	43.5481i	2.68699	+	1.55134i
$789$	3.53067	+	6.11530i	0.125695	+	0.217710i
$790$	19.5668			0.696155
$791$		0			0
$792$	−36.3636			−1.29212
$793$	22.3916	−	18.2388i	0.795150	−	0.647678i
$794$	51.0621	−	88.4421i	1.81213	−	3.13869i
$795$	15.2224	+	8.78865i	0.539882	+	0.311701i
$796$	1.02307	+	1.77201i	0.0362618	+	0.0628073i
$797$	−29.7429			−1.05355			−0.526773	−	0.850006i	$-0.676598\pi$
$797$	−29.7429			−1.05355			−0.526773	+	0.850006i	$0.676598\pi$
$798$		0			0
$799$			54.0649i			1.91268i
$800$	−28.2425	+	16.3058i	−0.998525	+	0.576499i
$801$	15.0270	+	8.67587i	0.530954	+	0.306547i
$802$	37.3469	−	64.6868i	1.31877	−	2.28417i
$803$	−2.26407	−	3.92149i	−0.0798974	−	0.138386i
$804$		−	7.32565i		−	0.258356i
$805$		0			0
$806$	6.80105	+	42.1584i	0.239557	+	1.48497i
$807$	−2.79812	−	4.84648i	−0.0984984	−	0.170604i
$808$	87.9042	+	50.7515i	3.09246	+	1.78543i
$809$	−17.4451	+	30.2158i	−0.613336	+	1.06233i	0.377337	+	0.926076i	$0.376840\pi$
$809$	−17.4451	+	30.2158i	−0.613336	+	1.06233i	−0.990674	+	0.136254i	$0.956494\pi$
$810$	3.18365	+	5.51424i	0.111862	+	0.193751i
$811$			31.6196i			1.11031i	0.831745	+	0.555157i	$0.187342\pi$
$811$			31.6196i			1.11031i	−0.831745	+	0.555157i	$0.812658\pi$
$812$		0			0
$813$		−	0.345507i		−	0.0121174i
$814$	−17.2550	+	9.96220i	−0.604789	+	0.349175i
$815$	17.8138	−	30.8544i	0.623991	−	1.08078i
$816$	52.7551	−	91.3745i	1.84680	−	3.19875i
$817$	9.71106	−	5.60668i	0.339747	−	0.196153i
$818$	−65.3668			−2.28550
$819$		0			0
$820$	25.2310			0.881105
$821$	4.94391	−	2.85437i	0.172544	−	0.0996181i	−0.411241	−	0.911527i	$-0.634905\pi$
$821$	4.94391	−	2.85437i	0.172544	−	0.0996181i	0.583785	+	0.811909i	$0.301571\pi$
$822$	−19.3396	+	33.4971i	−0.674545	+	1.16835i
$823$	0.00433157	−	0.00750250i	0.000150989	−	0.000261521i	−0.865950	−	0.500131i	$-0.833285\pi$
$823$	0.00433157	−	0.00750250i	0.000150989	−	0.000261521i	0.866101	+	0.499869i	$0.166619\pi$
$824$	97.1439	−	56.0861i	3.38417	−	1.95385i
$825$			3.92340i			0.136595i
$826$		0			0
$827$		−	52.4236i		−	1.82295i	−0.411359	−	0.911473i	$-0.634946\pi$
$827$		−	52.4236i		−	1.82295i	0.411359	−	0.911473i	$-0.365054\pi$
$828$	20.1246	+	34.8568i	0.699377	+	1.21136i
$829$	−8.73616	+	15.1315i	−0.303419	+	0.525538i	−0.976908	−	0.213660i	$-0.931462\pi$
$829$	−8.73616	+	15.1315i	−0.303419	+	0.525538i	0.673489	+	0.739197i	$0.264795\pi$
$830$	−11.0760	−	6.39473i	−0.384454	−	0.221964i
$831$	−5.04397	−	8.73641i	−0.174973	−	0.303063i
$832$	−17.4280	−	108.033i	−0.604206	−	3.74536i
$833$		0			0
$834$			16.5876i			0.574381i
$835$	−20.3970	−	35.3286i	−0.705866	−	1.22260i
$836$	−32.4275	+	56.1661i	−1.12153	+	1.94255i
$837$	−20.2241	−	11.6764i	−0.699047	−	0.403595i
$838$	39.0053	−	22.5197i	1.34741	−	0.777930i
$839$			19.7237i			0.680939i	0.940256	+	0.340470i	$0.110586\pi$
$839$			19.7237i			0.680939i	−0.940256	+	0.340470i	$0.889414\pi$
$840$		0			0
$841$	27.3232			0.942179
$842$	−32.7909	−	56.7954i	−1.13005	−	1.95730i
$843$	−24.7280	−	14.2767i	−0.851676	−	0.491716i
$844$	16.5716	−	28.7028i	0.570416	−	0.987990i
$845$	−16.2257	+	18.2293i	−0.558180	+	0.627107i
$846$	−40.5081			−1.39270
$847$		0			0
$848$	121.770			4.18161
$849$	7.08160	+	12.2657i	0.243040	+	0.420958i
$850$	21.2181	+	12.2503i	0.727775	+	0.420181i
$851$	12.1232	+	6.99931i	0.415576	+	0.239933i
$852$	−28.0299	+	16.1831i	−0.960289	+	0.554423i
$853$		−	1.74842i		−	0.0598648i	−0.999552	−	0.0299324i	$-0.990471\pi$
$853$		−	1.74842i		−	0.0598648i	0.999552	−	0.0299324i	$-0.00952921\pi$
$854$		0			0
$855$	−16.0856			−0.550114
$856$	−35.2044	+	20.3253i	−1.20326	+	0.694704i
$857$	1.67801	−	2.90639i	0.0573196	−	0.0992805i	−0.835942	−	0.548818i	$-0.815078\pi$
$857$	1.67801	−	2.90639i	0.0573196	−	0.0992805i	0.893261	+	0.449538i	$0.148411\pi$
$858$	−24.4932	−	9.32169i	−0.836186	−	0.318237i
$859$	14.9108	+	25.8263i	0.508750	+	0.881181i	0.999949	+	0.0101332i	$0.00322555\pi$
$859$	14.9108	+	25.8263i	0.508750	+	0.881181i	−0.491199	+	0.871048i	$0.663441\pi$
$860$			22.3821i			0.763224i
$861$		0			0
$862$	62.0387			2.11305
$863$	0.340244	−	0.196440i	0.0115820	−	0.00668690i	−0.494198	−	0.869349i	$-0.664538\pi$
$863$	0.340244	−	0.196440i	0.0115820	−	0.00668690i	0.505780	+	0.862663i	$0.331205\pi$
$864$	103.166	+	59.5628i	3.50977	+	2.02637i
$865$	4.71960	+	2.72487i	0.160471	+	0.0926482i
$866$	−40.4759	+	23.3688i	−1.37543	+	0.794104i
$867$	−22.9616			−0.779817
$868$		0			0
$869$		−	8.76678i		−	0.297393i
$870$	22.2643	+	38.5630i	0.754832	+	1.30741i
$871$	−1.48423	+	3.89990i	−0.0502913	+	0.132143i
$872$	−9.55762	+	16.5543i	−0.323662	+	0.560599i
$873$	3.61975	−	2.08986i	0.122510	−	0.0707312i
$874$	62.2089			2.10425
$875$		0			0
$876$			12.4633i			0.421097i
$877$	44.9539	−	25.9541i	1.51798	−	0.876409i	0.518208	−	0.855255i	$-0.326599\pi$
$877$	44.9539	−	25.9541i	1.51798	−	0.876409i	0.999776	−	0.0211538i	$-0.00673397\pi$
$878$	83.8263	+	48.3971i	2.82900	+	1.63332i
$879$	14.6682	+	8.46871i	0.494747	+	0.285642i
$880$	−32.4511	−	56.2070i	−1.09393	−	1.89474i
$881$	10.0487			0.338548			0.169274	−	0.985569i	$-0.445858\pi$
$881$	10.0487			0.338548			0.169274	+	0.985569i	$0.445858\pi$
$882$		0			0
$883$	−57.1835			−1.92438			−0.962189	−	0.272383i	$-0.912188\pi$
$883$	−57.1835			−1.92438			−0.962189	+	0.272383i	$0.912188\pi$
$884$	−92.9430	+	75.7055i	−3.12601	+	2.54625i
$885$	−7.74652	+	13.4174i	−0.260397	+	0.451020i
$886$	−38.5095	−	22.2335i	−1.29375	−	0.746948i
$887$	0.353960	+	0.613076i	0.0118848	+	0.0205851i	0.871907	−	0.489672i	$-0.162884\pi$
$887$	0.353960	+	0.613076i	0.0118848	+	0.0205851i	−0.860022	+	0.510257i	$0.829550\pi$
$888$	34.8104			1.16816
$889$		0			0
$890$			53.5309i			1.79436i
$891$	2.47062	−	1.42641i	0.0827689	−	0.0477867i
$892$	−34.6479	−	20.0040i	−1.16010	−	0.669782i
$893$	−22.9297	+	39.7155i	−0.767314	+	1.32903i
$894$	−3.76330	−	6.51822i	−0.125863	−	0.218002i
$895$		−	36.3257i		−	1.21423i
$896$		0			0
$897$	2.93246	+	18.1778i	0.0979119	+	0.606938i
$898$	−20.7077	−	35.8668i	−0.691025	−	1.19689i
$899$	−28.1537	−	16.2545i	−0.938978	−	0.542119i
$900$	−6.72300	+	11.6446i	−0.224100	+	0.388153i
$901$	−24.5899	−	42.5909i	−0.819208	−	1.41891i
$902$		−	15.4335i		−	0.513879i
$903$		0			0
$904$		−	39.6177i		−	1.31766i
$905$	−16.2254	+	9.36773i	−0.539350	+	0.311394i
$906$	−32.0935	+	55.5876i	−1.06624	+	1.84678i
$907$	22.1896	−	38.4336i	0.736795	−	1.27617i	−0.217136	−	0.976141i	$-0.569672\pi$
$907$	22.1896	−	38.4336i	0.736795	−	1.27617i	0.953931	−	0.300025i	$-0.0969952\pi$
$908$	−74.4123	+	42.9619i	−2.46946	+	1.42574i
$909$	17.7698			0.589386
$910$		0			0
$911$	28.9184			0.958109			0.479055	−	0.877785i	$-0.340980\pi$
$911$	28.9184			0.958109			0.479055	+	0.877785i	$0.340980\pi$
$912$	77.5066	−	44.7484i	2.56650	−	1.48177i
$913$	−2.86512	+	4.96254i	−0.0948217	+	0.164236i
$914$	53.9981	−	93.5275i	1.78610	−	3.09362i
$915$	−15.0528	+	8.69075i	−0.497631	+	0.287307i
$916$		−	139.981i		−	4.62509i
$917$		0			0
$918$		−	89.4969i		−	2.95384i
$919$	−12.8806	−	22.3098i	−0.424891	−	0.735932i	0.571520	−	0.820588i	$-0.306354\pi$
$919$	−12.8806	−	22.3098i	−0.424891	−	0.735932i	−0.996410	+	0.0846563i	$0.973021\pi$
$920$	−39.4092	+	68.2588i	−1.29928	+	2.25042i
$921$	−18.8892	−	10.9057i	−0.622419	−	0.359354i
$922$	−25.9953	−	45.0252i	−0.856111	−	1.48283i
$923$	18.2009	−	2.93619i	0.599089	−	0.0966458i
$924$		0			0
$925$			4.67651i			0.153763i
$926$	3.40052	+	5.88988i	0.111748	+	0.193554i
$927$	9.81879	−	17.0066i	0.322491	−	0.558571i
$928$	143.616	+	82.9166i	4.71442	+	2.72187i
$929$	47.5549	−	27.4558i	1.56023	−	0.900797i	0.562993	−	0.826462i	$-0.309650\pi$
$929$	47.5549	−	27.4558i	1.56023	−	0.900797i	0.997233	−	0.0743356i	$-0.0236836\pi$
$930$		−	25.7014i		−	0.842783i
$931$		0			0
$932$	−89.4784			−2.93096
$933$	−3.29757	−	5.71156i	−0.107958	−	0.186988i
$934$	−35.2309	−	20.3406i	−1.15279	−	0.665564i
$935$	−13.1061	+	22.7005i	−0.428616	+	0.742385i
$936$	−36.0050	−	44.2031i	−1.17686	−	1.44482i
$937$	−23.1364			−0.755835			−0.377917	−	0.925839i	$-0.623360\pi$
$937$	−23.1364			−0.755835			−0.377917	+	0.925839i	$0.623360\pi$
$938$		0			0
$939$	−4.55830			−0.148755
$940$	−45.7682	−	79.2729i	−1.49280	−	2.58560i
$941$	0.302692	+	0.174759i	0.00986748	+	0.00569699i	0.504926	−	0.863163i	$-0.331520\pi$
$941$	0.302692	+	0.174759i	0.00986748	+	0.00569699i	−0.495058	+	0.868860i	$0.664853\pi$
$942$	−30.2195	−	17.4472i	−0.984605	−	0.568462i
$943$	−9.39062	+	5.42168i	−0.305801	+	0.176554i
$944$			107.331i			3.49333i
$945$		0			0
$946$	13.6909			0.445128
$947$	15.1884	−	8.76900i	0.493555	−	0.284954i	−0.232493	−	0.972598i	$-0.574688\pi$
$947$	15.1884	−	8.76900i	0.493555	−	0.284954i	0.726048	+	0.687644i	$0.241355\pi$
$948$	−12.0649	+	20.8970i	−0.391850	+	0.678703i
$949$	2.52516	−	6.63500i	0.0819703	−	0.215381i
$950$	10.3911	+	17.9978i	0.337130	+	0.583927i
$951$		−	4.44019i		−	0.143983i
$952$		0			0
$953$	−47.8790			−1.55095			−0.775477	−	0.631376i	$-0.782491\pi$
$953$	−47.8790			−1.55095			−0.775477	+	0.631376i	$0.782491\pi$
$954$	31.9112	−	18.4239i	1.03316	−	0.596497i
$955$	−8.78702	−	5.07319i	−0.284341	−	0.164164i
$956$	81.8057	+	47.2305i	2.64579	+	1.52754i
$957$	17.2779	−	9.97541i	0.558516	−	0.322459i
$958$	−46.1527			−1.49112
$959$		0			0
$960$			65.8610i			2.12566i
$961$	−6.11807	−	10.5968i	−0.197357	−	0.341833i
$962$	−29.1948	−	11.1110i	−0.941279	−	0.358234i
$963$	−3.55828	+	6.16311i	−0.114664	+	0.198604i
$964$	−47.9581	+	27.6886i	−1.54463	+	0.891791i
$965$	−27.3455			−0.880282
$966$		0			0
$967$			12.4683i			0.400955i	0.979698	+	0.200477i	$0.0642493\pi$
$967$			12.4683i			0.400955i	−0.979698	+	0.200477i	$0.935751\pi$
$968$	47.0059	−	27.1389i	1.51083	−	0.872276i
$969$	−31.3028	−	18.0727i	−1.00559	−	0.580579i
$970$	11.1671	+	6.44732i	0.358554	+	0.207011i
$971$	−19.6189	−	33.9810i	−0.629602	−	1.09050i	−0.987632	−	0.156792i	$-0.949885\pi$
$971$	−19.6189	−	33.9810i	−0.629602	−	1.09050i	0.358030	−	0.933710i	$-0.383449\pi$
$972$	80.7105			2.58879
$973$		0			0
$974$	12.1546			0.389458
$975$	−4.76923	+	3.88471i	−0.152738	+	0.124410i
$976$	−60.2069	+	104.281i	−1.92718	+	3.33797i
$977$	21.1382	+	12.2041i	0.676269	+	0.390444i	0.798448	−	0.602064i	$-0.205655\pi$
$977$	21.1382	+	12.2041i	0.676269	+	0.390444i	−0.122179	+	0.992508i	$0.538988\pi$
$978$	29.9916	+	51.9470i	0.959026	+	1.66108i
$979$	23.9842			0.766538
$980$		0			0
$981$			3.34643i			0.106843i
$982$	40.2105	−	23.2155i	1.28317	−	0.740837i
$983$	47.4783	+	27.4116i	1.51432	+	0.874295i	0.999859	+	0.0167828i	$0.00534238\pi$
$983$	47.4783	+	27.4116i	1.51432	+	0.874295i	0.514464	+	0.857512i	$0.327991\pi$
$984$	−13.4821	+	23.3517i	−0.429794	+	0.744424i
$985$	14.9294	+	25.8585i	0.475691	+	0.823921i
$986$		−	124.587i		−	3.96767i
$987$		0			0
$988$	−100.383	+	16.1939i	−3.19360	+	0.515195i
$989$	−4.80951	−	8.33031i	−0.152933	−	0.264889i
$990$	−17.0083	−	9.81976i	−0.540560	−	0.312092i
$991$	19.0686	−	33.0278i	0.605734	−	1.04916i	−0.386201	−	0.922415i	$-0.626213\pi$
$991$	19.0686	−	33.0278i	0.605734	−	1.04916i	0.991935	−	0.126748i	$-0.0404539\pi$
$992$	−47.8585	−	82.8934i	−1.51951	−	2.63187i
$993$		−	7.08134i		−	0.224719i
$994$		0			0
$995$			0.701472i			0.0222382i
$996$	13.6590	−	7.88600i	0.432801	−	0.249878i
$997$	26.5130	−	45.9219i	0.839676	−	1.45436i	−0.0504904	−	0.998725i	$-0.516078\pi$
$997$	26.5130	−	45.9219i	0.839676	−	1.45436i	0.890166	−	0.455636i	$-0.150588\pi$
$998$	−56.0527	+	97.0860i	−1.77432	+	3.07321i
$999$	14.7940	−	8.54130i	0.468060	−	0.270235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.g.116.2		32
7.2	even	3	inner	637.2.r.g.324.16		32
7.3	odd	6		637.2.c.g.246.2	yes	16
7.4	even	3		637.2.c.g.246.1	✓	16
7.5	odd	6	inner	637.2.r.g.324.15		32
7.6	odd	2	inner	637.2.r.g.116.1		32
13.12	even	2	inner	637.2.r.g.116.16		32
91.12	odd	6	inner	637.2.r.g.324.1		32
91.18	odd	12		8281.2.a.cs.1.1		16
91.25	even	6		637.2.c.g.246.15	yes	16
91.31	even	12		8281.2.a.cs.1.2		16
91.38	odd	6		637.2.c.g.246.16	yes	16
91.51	even	6	inner	637.2.r.g.324.2		32
91.60	odd	12		8281.2.a.cs.1.15		16
91.73	even	12		8281.2.a.cs.1.16		16
91.90	odd	2	inner	637.2.r.g.116.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.1	✓	16	7.4	even	3
637.2.c.g.246.2	yes	16	7.3	odd	6
637.2.c.g.246.15	yes	16	91.25	even	6
637.2.c.g.246.16	yes	16	91.38	odd	6
637.2.r.g.116.1		32	7.6	odd	2	inner
637.2.r.g.116.2		32	1.1	even	1	trivial
637.2.r.g.116.15		32	91.90	odd	2	inner
637.2.r.g.116.16		32	13.12	even	2	inner
637.2.r.g.324.1		32	91.12	odd	6	inner
637.2.r.g.324.2		32	91.51	even	6	inner
637.2.r.g.324.15		32	7.5	odd	6	inner
637.2.r.g.324.16		32	7.2	even	3	inner
8281.2.a.cs.1.1		16	91.18	odd	12
8281.2.a.cs.1.2		16	91.31	even	12
8281.2.a.cs.1.15		16	91.60	odd	12
8281.2.a.cs.1.16		16	91.73	even	12

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.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.36789 + 1.36710i) q^{2} +(0.577975 - 1.00108i) q^{3} +(2.73793 - 4.74223i) q^{4} +(1.62576 - 0.938635i) q^{5} +3.16060i q^{6} +9.50370i q^{8} +(0.831889 + 1.44087i) q^{9} +O(q^{10})\)	\(q+(-2.36789 + 1.36710i) q^{2} +(0.577975 - 1.00108i) q^{3} +(2.73793 - 4.74223i) q^{4} +(1.62576 - 0.938635i) q^{5} +3.16060i q^{6} +9.50370i q^{8} +(0.831889 + 1.44087i) q^{9} +(-2.56642 + 4.44516i) q^{10} +(1.99163 + 1.14987i) q^{11} +(-3.16491 - 5.48179i) q^{12} +(0.574228 + 3.55953i) q^{13} -2.17003i q^{15} +(-7.51666 - 13.0192i) q^{16} +(-3.03578 + 5.25812i) q^{17} +(-3.93964 - 2.27455i) q^{18} +(-4.46010 + 2.57504i) q^{19} -10.2797i q^{20} -6.28794 q^{22} +(2.20891 + 3.82595i) q^{23} +(9.51399 + 5.49290i) q^{24} +(-0.737930 + 1.27813i) q^{25} +(-6.22595 - 7.64354i) q^{26} +5.39110 q^{27} +7.50488 q^{29} +(2.96665 + 5.13839i) q^{30} +(-3.75139 - 2.16586i) q^{31} +(19.1363 + 11.0484i) q^{32} +(2.30222 - 1.32919i) q^{33} -16.6009i q^{34} +9.11062 q^{36} +(2.74415 - 1.58433i) q^{37} +(7.04068 - 12.1948i) q^{38} +(3.89527 + 1.48247i) q^{39} +(8.92050 + 15.4508i) q^{40} +2.45446i q^{41} -2.17732 q^{43} +(10.9059 - 6.29651i) q^{44} +(2.70491 + 1.56168i) q^{45} +(-10.4609 - 6.03961i) q^{46} +(7.71162 - 4.45231i) q^{47} -17.3778 q^{48} -4.03530i q^{50} +(3.50921 + 6.07813i) q^{51} +(18.4523 + 7.02262i) q^{52} +(-4.05001 + 7.01482i) q^{53} +(-12.7655 + 7.37017i) q^{54} +4.31722 q^{55} +5.95323i q^{57} +(-17.7707 + 10.2599i) q^{58} +(-6.18303 - 3.56978i) q^{59} +(-10.2908 - 5.94139i) q^{60} +(-4.00490 - 6.93668i) q^{61} +11.8438 q^{62} -30.3503 q^{64} +(4.27466 + 5.24796i) q^{65} +(-3.63427 + 6.29475i) q^{66} +(1.00227 + 0.578661i) q^{67} +(16.6235 + 28.7927i) q^{68} +5.10678 q^{69} -5.11328i q^{71} +(-13.6936 + 7.90603i) q^{72} +(-1.70519 - 0.984492i) q^{73} +(-4.33189 + 7.50305i) q^{74} +(0.853010 + 1.47746i) q^{75} +28.2011i q^{76} +(-11.2503 + 1.81491i) q^{78} +(-1.90604 - 3.30136i) q^{79} +(-24.4406 - 14.1108i) q^{80} +(0.620251 - 1.07431i) q^{81} +(-3.35549 - 5.81188i) q^{82} +2.49170i q^{83} +11.3980i q^{85} +(5.15565 - 2.97662i) q^{86} +(4.33763 - 7.51300i) q^{87} +(-10.9280 + 18.9279i) q^{88} +(9.03187 - 5.21456i) q^{89} -8.53990 q^{90} +24.1914 q^{92} +(-4.33642 + 2.50363i) q^{93} +(-12.1735 + 21.0851i) q^{94} +(-4.83404 + 8.37280i) q^{95} +(22.1206 - 12.7714i) q^{96} -2.51219i q^{97} +3.82625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 16 * q^9	\( 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Introduction

L-functions

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