LMFDB - Embedded newform 637.2.r.g.324.1

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			324.1
Character	$\chi$	$=$	637.324
Dual form			637.2.r.g.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36789 - 1.36710i) q^{2} +(-0.577975 - 1.00108i) q^{3} +(2.73793 + 4.74223i) q^{4} +(-1.62576 - 0.938635i) q^{5} +3.16060i q^{6} -9.50370i q^{8} +(0.831889 - 1.44087i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.36789	−	1.36710i	−1.67435	−	0.966686i	−0.965157	−	0.261672i	$-0.915726\pi$
$2$	−2.36789	−	1.36710i	−1.67435	−	0.966686i	−0.709193	−	0.705014i	$-0.750941\pi$
$3$	−0.577975	−	1.00108i	−0.333694	−	0.577975i	0.649539	−	0.760328i	$-0.274962\pi$
$3$	−0.577975	−	1.00108i	−0.333694	−	0.577975i	−0.983233	+	0.182353i	$0.941629\pi$
$4$	2.73793	+	4.74223i	1.36896	+	2.37112i
$5$	−1.62576	−	0.938635i	−0.727063	−	0.419770i	0.0902836	−	0.995916i	$-0.471223\pi$
$5$	−1.62576	−	0.938635i	−0.727063	−	0.419770i	−0.817347	+	0.576146i	$0.804556\pi$
$6$			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	−0.168739	−	0.985661i	$-0.553969\pi$
$11$	1.99163	−	1.14987i	0.600499	−	0.346698i	0.769238	+	0.638963i	$0.220636\pi$
$12$	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	0.954157	+	0.299305i	$0.0967549\pi$
$17$	3.03578	+	5.25812i	0.736285	+	1.27528i	−0.217873	+	0.975977i	$0.569912\pi$
$18$	−3.93964	+	2.27455i	−0.928583	+	0.536117i
$19$	4.46010	+	2.57504i	1.02322	+	0.590754i	0.915034	−	0.403377i	$-0.132164\pi$
$19$	4.46010	+	2.57504i	1.02322	+	0.590754i	0.108183	+	0.994131i	$0.465497\pi$
$20$		−	10.2797i		−	2.29860i
$21$		0			0
$22$	−6.28794			−1.34059
$23$	2.20891	−	3.82595i	0.460590	−	0.797765i	−0.538401	−	0.842689i	$-0.680971\pi$
$23$	2.20891	−	3.82595i	0.460590	−	0.797765i	0.998990	+	0.0449240i	$0.0143046\pi$
$24$	−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	$-0.539487\pi$
$31$	3.75139	−	2.16586i	0.673769	−	0.389001i	0.797503	+	0.603315i	$0.206154\pi$
$32$	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	0.708309	−	0.705902i	$-0.249458\pi$
$37$	2.74415	+	1.58433i	0.451135	+	0.260463i	−0.257174	+	0.966365i	$0.582791\pi$
$38$	−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	$-0.558328\pi$
$47$	−7.71162	−	4.45231i	−1.12486	−	0.649436i	−0.942636	+	0.333822i	$0.891662\pi$
$48$	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	−0.997800	−	0.0662933i	$-0.978883\pi$
$53$	−4.05001	−	7.01482i	−0.556312	−	0.963560i	0.441488	−	0.897267i	$-0.354451\pi$
$54$	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	$-0.512813\pi$
$59$	6.18303	−	3.56978i	0.804963	−	0.464745i	0.845203	+	0.534445i	$0.179479\pi$
$60$	−10.2908	+	5.94139i	−1.32854	+	0.767030i
$61$	4.00490	−	6.93668i	0.512774	−	0.888151i	−0.487116	−	0.873337i	$-0.661951\pi$
$61$	4.00490	−	6.93668i	0.512774	−	0.888151i	0.999890	−	0.0148140i	$-0.00471562\pi$
$62$	−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	−0.437526	−	0.899206i	$-0.644145\pi$
$67$	1.00227	−	0.578661i	0.122447	−	0.0706947i	0.559972	+	0.828511i	$0.310812\pi$
$68$	−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	$0.0981276\pi$
$71$			5.11328i			0.606835i	−0.952858	+	0.303417i	$0.901872\pi$
$72$	−13.6936	−	7.90603i	−1.61381	−	0.931735i
$73$	1.70519	−	0.984492i	0.199578	−	0.115226i	−0.396881	−	0.917870i	$-0.629907\pi$
$73$	1.70519	−	0.984492i	0.199578	−	0.115226i	0.596458	+	0.802644i	$0.296574\pi$
$74$	−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	−0.953101	−	0.302652i	$-0.902128\pi$
$79$	−1.90604	+	3.30136i	−0.214446	+	0.371432i	0.738655	+	0.674084i	$0.235461\pi$
$80$	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	$-0.519752\pi$
$89$	−9.03187	−	5.21456i	−0.957377	−	0.552742i	−0.895365	+	0.445334i	$0.853085\pi$
$90$	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	−0.999330	−	0.0366080i	$-0.988345\pi$
$101$	−5.34019	−	9.24947i	−0.531368	−	0.920357i	0.467961	−	0.883749i	$-0.344989\pi$
$102$	−16.6188	+	9.59489i	−1.64551	+	0.950035i
$103$	5.90150	−	10.2217i	0.581492	−	1.00717i	−0.413811	−	0.910363i	$-0.635803\pi$
$103$	5.90150	−	10.2217i	0.581492	−	1.00717i	0.995303	−	0.0968106i	$-0.0308641\pi$
$104$	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	−0.743937	−	0.668250i	$-0.767044\pi$
$107$	2.13867	−	3.70429i	0.206753	−	0.358107i	0.950690	+	0.310143i	$0.100377\pi$
$108$	−14.7604	−	25.5658i	−1.42032	−	2.46007i
$109$	1.74188	−	1.00567i	0.166842	−	0.0963260i	−0.414254	−	0.910161i	$-0.635958\pi$
$109$	1.74188	−	1.00567i	0.166842	−	0.0963260i	0.581096	+	0.813835i	$0.302624\pi$
$110$	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	$-0.846561\pi$
$131$	−0.475488	+	0.823570i	−0.0415436	+	0.0719556i	0.844506	+	0.535546i	$0.179894\pi$
$132$		−	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	0.0265039	−	0.999649i	$-0.491563\pi$
$137$	10.5983	−	6.11895i	0.905477	−	0.522777i	0.878973	+	0.476871i	$0.158229\pi$
$138$	12.0923	+	6.98149i	1.02936	+	0.594304i
$139$	−5.24824			−0.445150			−0.222575	−	0.974916i	$-0.571446\pi$
$139$	−5.24824			−0.445150			−0.222575	+	0.974916i	$0.571446\pi$
$140$		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	0.413139	−	0.910668i	$-0.364432\pi$
$149$	−2.06234	−	1.19069i	−0.168953	−	0.0975451i	−0.582092	+	0.813123i	$0.697766\pi$
$150$	4.03967	−	2.33230i	0.329837	−	0.190432i
$151$	17.5877	−	10.1543i	1.43127	−	0.826341i	0.434048	−	0.900890i	$-0.357085\pi$
$151$	17.5877	−	10.1543i	1.43127	−	0.826341i	0.997217	+	0.0745487i	$0.0237516\pi$
$152$	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	$-0.0214458\pi$
$157$	5.52023	+	9.56132i	0.440562	+	0.763076i	−0.557169	+	0.830399i	$0.688112\pi$
$158$	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	0.978181	−	0.207754i	$-0.0666154\pi$
$163$	16.4358	+	9.48921i	1.28735	+	0.743253i	0.309170	+	0.951007i	$0.399949\pi$
$164$	−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	$-0.868532\pi$
$173$	−1.45150	+	2.51408i	−0.110356	+	0.191142i	0.805558	+	0.592517i	$0.201866\pi$
$174$			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	0.959729	+	0.280926i	$0.0906416\pi$
$179$	9.67514	+	16.7578i	0.723154	+	1.25254i	−0.236575	+	0.971613i	$0.576025\pi$
$180$	−14.8117	−	8.55154i	−1.10400	−	0.637394i
$181$	9.98016			0.741820			0.370910	−	0.928669i	$-0.379046\pi$
$181$	9.98016			0.741820			0.370910	+	0.928669i	$0.379046\pi$
$182$		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	−0.947078	−	0.321004i	$-0.895980\pi$
$191$	−2.70243	+	4.68074i	−0.195541	+	0.338687i	0.751537	+	0.659691i	$0.229313\pi$
$192$	17.5417	+	30.3831i	1.26596	+	2.19271i
$193$	−12.6151	+	7.28331i	−0.908052	+	0.524264i	−0.879804	−	0.475337i	$-0.842326\pi$
$193$	−12.6151	+	7.28331i	−0.908052	+	0.524264i	−0.0282481	+	0.999601i	$0.508993\pi$
$194$	−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	$-0.808255\pi$
$197$		−	15.9055i		−	1.13322i	0.823987	−	0.566609i	$-0.191745\pi$
$198$	−5.23087	+	9.06014i	−0.371742	+	0.643876i
$199$	0.186833	+	0.323604i	0.0132442	+	0.0229397i	0.872572	−	0.488486i	$-0.162451\pi$
$199$	0.186833	+	0.323604i	0.0132442	+	0.0229397i	−0.859327	+	0.511426i	$0.829117\pi$
$200$	−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	$-0.492324\pi$
$227$	13.5891	−	7.84570i	0.901943	−	0.520737i	0.877830	+	0.478972i	$0.158990\pi$
$228$	28.2316	−	16.2995i	1.86969	−	1.07946i
$229$	−22.1384	−	12.7816i	−1.46295	−	0.844632i	−0.463800	−	0.885940i	$-0.653514\pi$
$229$	−22.1384	−	12.7816i	−1.46295	−	0.844632i	−0.999146	+	0.0413077i	$0.986848\pi$
$230$	22.6759			1.49521
$231$		0			0
$232$		−	71.3241i		−	4.68266i
$233$	−8.17026	+	14.1513i	−0.535252	+	0.927083i	0.463899	+	0.885888i	$0.346450\pi$
$233$	−8.17026	+	14.1513i	−0.535252	+	0.927083i	−0.999151	+	0.0411952i	$0.986883\pi$
$234$	−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	$-0.811600\pi$
$239$		−	17.2505i		−	1.11584i	0.829895	−	0.557920i	$-0.188400\pi$
$240$	−28.2521	−	16.3114i	−1.82367	−	1.05290i
$241$	8.75810	−	5.05649i	0.564159	−	0.325717i	−0.190654	−	0.981657i	$-0.561061\pi$
$241$	8.75810	−	5.05649i	0.564159	−	0.325717i	0.754813	+	0.655940i	$0.227728\pi$
$242$	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	$-0.271816\pi$
$251$	20.8184			1.31404			0.657022	+	0.753871i	$0.271816\pi$
$252$		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	−0.0296216	+	0.999561i	$0.509430\pi$
$257$	−14.1148	+	24.4475i	−0.880456	+	1.52499i	−0.850835	+	0.525434i	$0.823903\pi$
$258$		−	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	0.756358	−	0.654158i	$-0.226977\pi$
$263$	−3.05434	−	5.29028i	−0.188339	−	0.326212i	−0.944697	+	0.327946i	$0.893644\pi$
$264$	−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	$-0.213818\pi$
$269$	−2.42062	−	4.19264i	−0.147588	−	0.255630i	−0.930335	+	0.366710i	$0.880484\pi$
$270$	−13.8358	−	23.9643i	−0.842020	−	1.45842i
$271$	−0.258850	−	0.149447i	−0.0157240	−	0.00907826i	0.492117	−	0.870529i	$-0.336223\pi$
$271$	−0.258850	−	0.149447i	−0.0157240	−	0.00907826i	−0.507841	+	0.861451i	$0.669556\pi$
$272$	−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	0.966820	−	0.255459i	$-0.0822265\pi$
$277$	4.36348	+	7.55777i	0.262176	+	0.454102i	−0.704644	+	0.709561i	$0.748893\pi$
$278$	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	$0.263653\pi$
$281$			24.7012i			1.47355i	−0.676137	+	0.736776i	$0.736347\pi$
$282$	14.0720	−	24.3734i	0.837974	−	1.45141i
$283$	6.12622	+	10.6109i	0.364166	+	0.630754i	0.988642	−	0.150290i	$-0.0480208\pi$
$283$	6.12622	+	10.6109i	0.364166	+	0.630754i	−0.624476	+	0.781044i	$0.714687\pi$
$284$	−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	$-0.218384\pi$
$311$	−2.85269	−	4.94101i	−0.161761	−	0.280179i	−0.935500	+	0.353325i	$0.885051\pi$
$312$	−14.0890	−	37.0195i	−0.797631	−	2.09582i
$313$	1.97167	−	3.41503i	0.111445	−	0.193029i	−0.804908	−	0.593400i	$-0.797785\pi$
$313$	1.97167	−	3.41503i	0.111445	−	0.193029i	0.916353	+	0.400371i	$0.131119\pi$
$314$		−	30.1868i		−	1.70354i
$315$		0			0
$316$	−20.8744			−1.17428
$317$	3.32654	+	1.92058i	0.186837	+	0.107871i	0.590501	−	0.807037i	$-0.298930\pi$
$317$	3.32654	+	1.92058i	0.186837	+	0.107871i	−0.403664	+	0.914907i	$0.632263\pi$
$318$	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	0.638665	−	0.769485i	$-0.279487\pi$
$331$	5.30526	+	3.06299i	0.291603	+	0.168357i	−0.347061	+	0.937842i	$0.612820\pi$
$332$	−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	0.523179	−	0.852223i	$-0.324746\pi$
$347$	−8.87542	−	15.3727i	−0.476457	−	0.825248i	−0.999636	+	0.0269746i	$0.991413\pi$
$348$	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	$-0.775707\pi$
$353$	−10.9309	+	6.31096i	−0.581793	+	0.335898i	0.180053	+	0.983657i	$0.442373\pi$
$354$	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	0.738769	−	0.673959i	$-0.235407\pi$
$359$	9.93763	+	5.73750i	0.524488	+	0.302813i	−0.214281	+	0.976772i	$0.568741\pi$
$360$	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	−0.945582	−	0.325385i	$-0.894506\pi$
$367$	−14.4557	−	25.0380i	−0.754583	−	1.30698i	0.190999	−	0.981590i	$-0.438827\pi$
$368$	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	0.383450	+	0.923562i	$0.374736\pi$
$373$	−11.7444	+	20.3419i	−0.608103	+	1.05326i	−0.991553	+	0.129703i	$0.958598\pi$
$374$	−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	$0.416578\pi$
$379$			37.6063i			1.93171i	−0.259088	+	0.965854i	$0.583422\pi$
$380$	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	$-0.109418\pi$
$383$	21.9263	+	12.6592i	1.12038	+	0.646853i	0.178883	+	0.983870i	$0.442752\pi$
$384$		−	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	0.848824	−	0.528676i	$-0.177311\pi$
$389$	−0.659447	−	1.14220i	−0.0334353	−	0.0579117i	−0.882259	+	0.470765i	$0.843978\pi$
$390$	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	0.985994	+	0.166783i	$0.0533379\pi$
$397$	32.3466	+	18.6753i	1.62343	+	0.937287i	0.637435	+	0.770504i	$0.279995\pi$
$398$		−	1.02168i		−	0.0512121i
$399$		0			0
$400$	22.1871			1.10935
$401$	−23.6584	−	13.6592i	−1.18144	−	0.682106i	−0.225095	−	0.974337i	$-0.572269\pi$
$401$	−23.6584	−	13.6592i	−1.18144	−	0.682106i	−0.956348	+	0.292231i	$0.905602\pi$
$402$	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	$-0.867959\pi$
$409$	−20.7042	+	11.9536i	−1.02375	+	0.591065i	−0.108565	+	0.994089i	$0.534626\pi$
$410$	−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	$-0.368187\pi$
$419$	16.4726			0.804739			0.402369	+	0.915477i	$0.368187\pi$
$420$		0			0
$421$		−	23.9857i		−	1.16899i	−0.811397	−	0.584495i	$-0.801292\pi$
$421$		−	23.9857i		−	1.16899i	0.811397	−	0.584495i	$-0.198708\pi$
$422$	−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	−0.891994	−	0.452046i	$-0.850694\pi$
$431$	−19.6500	+	11.3449i	−0.946508	+	0.546467i	−0.0545135	+	0.998513i	$0.517361\pi$
$432$	40.5230	−	70.1880i	1.94967	−	3.37692i
$433$	−17.0937			−0.821470			−0.410735	−	0.911755i	$-0.634728\pi$
$433$	−17.0937			−0.821470			−0.410735	+	0.911755i	$0.634728\pi$
$434$		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	−0.0409849	−	0.999160i	$-0.513050\pi$
$439$	17.7006	−	30.6584i	0.844805	−	1.46325i	0.885790	−	0.464086i	$-0.153617\pi$
$440$			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	−0.605610	−	0.795761i	$-0.707071\pi$
$443$	8.13161	−	14.0844i	0.386345	−	0.669168i	0.991955	+	0.126593i	$0.0404042\pi$
$444$	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	$-0.883657\pi$
$449$		−	15.1472i		−	0.714839i	0.933944	−	0.357419i	$-0.116343\pi$
$450$	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	−0.991463	−	0.130387i	$-0.958378\pi$
$457$	−34.2065	−	19.7491i	−1.60011	−	0.923826i	−0.608650	−	0.793439i	$-0.708289\pi$
$458$	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	$0.0184084\pi$
$463$			2.48740i			0.115599i	−0.998328	+	0.0577996i	$0.981592\pi$
$464$	−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	$-0.945200\pi$
$467$	−7.43931	+	12.8853i	−0.344250	+	0.596259i	0.640967	+	0.767568i	$0.278534\pi$
$468$	−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	$-0.792682\pi$
$479$	−14.6183	+	8.43988i	−0.667927	+	0.385628i	0.127364	+	0.991856i	$0.459348\pi$
$480$	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	−0.584683	−	0.811262i	$-0.698781\pi$
$487$	−3.84982	+	2.22270i	−0.174452	+	0.100720i	0.410231	+	0.911981i	$0.365448\pi$
$488$	−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	0.993380	+	0.114878i	$0.0366476\pi$
$499$	35.5080	+	20.5006i	1.58956	+	0.917731i	0.596177	+	0.802853i	$0.296686\pi$
$500$	−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	$-0.812438\pi$
$503$	−37.2910			−1.66272			−0.831361	+	0.555732i	$0.812438\pi$
$504$		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	$-0.275051\pi$
$509$	7.11501	+	4.10785i	0.315367	+	0.182077i	−0.333958	+	0.942588i	$0.608385\pi$
$510$	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	−0.950303	−	0.311327i	$-0.899227\pi$
$521$	−16.9997	−	29.4443i	−0.744768	−	1.28998i	0.205534	−	0.978650i	$-0.434107\pi$
$522$	−29.5665	+	17.0702i	−1.29409	+	0.747145i
$523$	11.4391	−	19.8131i	0.500197	−	0.866366i	−0.499803	−	0.866139i	$-0.666594\pi$
$523$	11.4391	−	19.8131i	0.500197	−	0.866366i	1.00000		0.000227041i	$-7.22694e-5\pi$
$524$	−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	−0.471196	−	0.882029i	$-0.656177\pi$
$541$	−34.2065	−	19.7491i	−1.47065	−	0.849082i	−0.999457	+	0.0329468i	$0.989511\pi$
$542$	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	0.0119264	−	0.999929i	$-0.496204\pi$
$557$	20.8597	−	12.0433i	0.883853	−	0.510293i	0.871927	+	0.489636i	$0.162870\pi$
$558$	−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	$-0.122971\pi$
$563$	3.24699	+	5.62395i	0.136844	+	0.237021i	−0.789456	+	0.613807i	$0.789637\pi$
$564$	−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	−0.389456	−	0.921045i	$-0.627337\pi$
$569$	14.3819	−	24.9102i	0.602921	−	1.04429i	0.992376	−	0.123244i	$-0.0393298\pi$
$570$	26.4631	−	15.2785i	1.10842	−	0.639945i
$571$	−1.24308	−	2.15307i	−0.0520211	−	0.0901032i	0.838842	−	0.544375i	$-0.183233\pi$
$571$	−1.24308	−	2.15307i	−0.0520211	−	0.0901032i	−0.890863	+	0.454271i	$0.849900\pi$
$572$	−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	$-0.568552\pi$
$577$	12.6221	−	7.28737i	0.525465	−	0.303377i	0.739168	+	0.673521i	$0.235219\pi$
$578$	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	$-0.454044\pi$
$593$	−15.6144	−	9.01495i	−0.641205	−	0.370200i	−0.785078	+	0.619396i	$0.787377\pi$
$594$	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	0.865881	−	0.500250i	$-0.166758\pi$
$599$	−0.00705812	−	0.0122250i	−0.000288387	−	0.000499501i	−0.866170	+	0.499750i	$0.833425\pi$
$600$	14.0413	+	8.10676i	0.573234	+	0.330957i
$601$	−13.7533			−0.561007			−0.280504	−	0.959853i	$-0.590501\pi$
$601$	−13.7533			−0.561007			−0.280504	+	0.959853i	$0.590501\pi$
$602$		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	$-0.673259\pi$
$607$	11.8742	−	20.5667i	0.481959	−	0.834778i	0.999786	+	0.0207079i	$0.00659200\pi$
$608$	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	−0.537712	−	0.843129i	$-0.680711\pi$
$613$	−1.89149	+	1.09205i	−0.0763964	+	0.0441075i	0.461315	+	0.887236i	$0.347378\pi$
$614$	−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	$0.0954005\pi$
$617$			14.6673i			0.590485i	−0.955422	+	0.295243i	$0.904600\pi$
$618$	32.3067	+	18.6523i	1.29957	+	0.750305i
$619$	−18.4159	+	10.6324i	−0.740198	+	0.427354i	−0.822141	−	0.569283i	$-0.807221\pi$
$619$	−18.4159	+	10.6324i	−0.740198	+	0.427354i	0.0819430	+	0.996637i	$0.473887\pi$
$620$	−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	$-0.759132\pi$
$631$		−	34.4910i		−	1.37307i	0.727099	−	0.686533i	$-0.240868\pi$
$632$	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	0.996909	−	0.0785658i	$-0.0250341\pi$
$641$	10.8972	+	18.8745i	0.430414	+	0.745500i	−0.566494	+	0.824066i	$0.691701\pi$
$642$	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	0.983105	+	0.183045i	$0.0585954\pi$
$647$	16.5354	+	28.6402i	0.650074	+	1.12596i	−0.333031	+	0.942916i	$0.608071\pi$
$648$	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	−0.848501	−	0.529193i	$-0.822495\pi$
$653$	0.869964	−	1.50682i	0.0340443	−	0.0589665i	0.882546	+	0.470227i	$0.155828\pi$
$654$	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	$-0.799452\pi$
$661$	−18.0422	+	10.4167i	−0.701762	+	0.405163i	0.106241	+	0.994340i	$0.466118\pi$
$662$	−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	$-0.801289\pi$
$677$	2.61495	−	4.52922i	0.100501	−	0.174072i	0.911891	+	0.410432i	$0.134622\pi$
$678$		−	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	−0.885518	−	0.464605i	$-0.846196\pi$
$683$	−24.1982	+	13.9708i	−0.925917	+	0.534579i	−0.0403993	+	0.999184i	$0.512863\pi$
$684$	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	$-0.494190\pi$
$691$	−22.0416	−	12.7257i	−0.838503	−	0.484110i	−0.856755	+	0.515723i	$0.827523\pi$
$692$	−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	−0.0571454	−	0.998366i	$-0.518200\pi$
$709$	−25.3044	−	14.6095i	−0.950328	−	0.548672i	−0.893183	+	0.449694i	$0.851533\pi$
$710$	−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	0.238189	+	0.971219i	$0.423446\pi$
$719$	−19.3600	+	33.5325i	−0.722005	+	1.25055i	−0.960195	+	0.279331i	$0.909887\pi$
$720$		−	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	$-0.673396\pi$
$727$	−27.9441			−1.03639			−0.518194	+	0.855263i	$0.673396\pi$
$728$		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	$-0.0339622\pi$
$733$	37.8831	+	21.8718i	1.39924	+	0.807854i	0.404931	+	0.914347i	$0.367296\pi$
$734$			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	−0.610940	−	0.791677i	$-0.709208\pi$
$739$	−6.27411	+	3.62236i	−0.230797	+	0.133251i	0.380143	+	0.924928i	$0.375875\pi$
$740$	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	$0.213719\pi$
$743$			33.9142i			1.24419i	−0.782941	+	0.622096i	$0.786281\pi$
$744$	−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	−0.265231	−	0.964185i	$-0.585448\pi$
$751$	19.2487	−	33.3396i	0.702393	−	1.21658i	0.967624	−	0.252396i	$-0.0812186\pi$
$752$	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	$-0.391697\pi$
$761$	−8.71186	−	5.02979i	−0.315805	−	0.182330i	−0.649521	+	0.760344i	$0.725031\pi$
$762$			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	$-0.490554\pi$
$773$	25.3049	−	14.6098i	0.910152	−	0.525477i	0.880480	+	0.474083i	$0.157220\pi$
$774$	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	$-0.665819\pi$
$787$	0.129425	−	0.0747235i	0.00461350	−	0.00266360i	0.502305	+	0.864691i	$0.332485\pi$
$788$	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	$-0.323402\pi$
$797$	29.7429			1.05355			0.526773	+	0.850006i	$0.323402\pi$
$798$		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	−0.990674	−	0.136254i	$-0.956494\pi$
$809$	−17.4451	−	30.2158i	−0.613336	−	1.06233i	0.377337	−	0.926076i	$-0.376840\pi$
$810$	−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	0.583785	−	0.811909i	$-0.301571\pi$
$821$	4.94391	+	2.85437i	0.172544	+	0.0996181i	−0.411241	+	0.911527i	$0.634905\pi$
$822$	19.3396	+	33.4971i	0.674545	+	1.16835i
$823$	0.00433157	+	0.00750250i	0.000150989	+	0.000261521i	0.866101	−	0.499869i	$-0.166619\pi$
$823$	0.00433157	+	0.00750250i	0.000150989	+	0.000261521i	−0.865950	+	0.500131i	$0.833285\pi$
$824$	−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	$0.365054\pi$
$827$			52.4236i			1.82295i	−0.411359	+	0.911473i	$0.634946\pi$
$828$	20.1246	−	34.8568i	0.699377	−	1.21136i
$829$	8.73616	+	15.1315i	0.303419	+	0.525538i	0.976908	−	0.213660i	$-0.0685384\pi$
$829$	8.73616	+	15.1315i	0.303419	+	0.525538i	−0.673489	+	0.739197i	$0.735205\pi$
$830$	−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	$-0.184922\pi$
$857$	−1.67801	−	2.90639i	−0.0573196	−	0.0992805i	−0.893261	+	0.449538i	$0.851589\pi$
$858$	−24.4932	+	9.32169i	−0.836186	+	0.318237i
$859$	−14.9108	+	25.8263i	−0.508750	+	0.881181i	0.491199	+	0.871048i	$0.336559\pi$
$859$	−14.9108	+	25.8263i	−0.508750	+	0.881181i	−0.999949	+	0.0101332i	$0.996774\pi$
$860$			22.3821i			0.763224i
$861$		0			0
$862$	62.0387			2.11305
$863$	0.340244	+	0.196440i	0.0115820	+	0.00668690i	0.505780	−	0.862663i	$-0.331205\pi$
$863$	0.340244	+	0.196440i	0.0115820	+	0.00668690i	−0.494198	+	0.869349i	$0.664538\pi$
$864$	−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	0.999776	+	0.0211538i	$0.00673397\pi$
$877$	44.9539	+	25.9541i	1.51798	+	0.876409i	0.518208	+	0.855255i	$0.326599\pi$
$878$	−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	$-0.554142\pi$
$881$	−10.0487			−0.338548			−0.169274	+	0.985569i	$0.554142\pi$
$882$		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	$-0.837116\pi$
$887$	−0.353960	+	0.613076i	−0.0118848	+	0.0205851i	0.860022	+	0.510257i	$0.170450\pi$
$888$	−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	0.953931	+	0.300025i	$0.0969952\pi$
$907$	22.1896	+	38.4336i	0.736795	+	1.27617i	−0.217136	+	0.976141i	$0.569672\pi$
$908$	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	−0.996410	−	0.0846563i	$-0.973021\pi$
$919$	−12.8806	+	22.3098i	−0.424891	+	0.735932i	0.571520	+	0.820588i	$0.306354\pi$
$920$	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	−0.997233	−	0.0743356i	$-0.976316\pi$
$929$	−47.5549	−	27.4558i	−1.56023	−	0.900797i	−0.562993	−	0.826462i	$-0.690350\pi$
$930$		−	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	$-0.376640\pi$
$937$	23.1364			0.755835			0.377917	+	0.925839i	$0.376640\pi$
$938$		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	$-0.668480\pi$
$941$	−0.302692	+	0.174759i	−0.00986748	+	0.00569699i	0.495058	+	0.868860i	$0.335147\pi$
$942$	−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	0.726048	−	0.687644i	$-0.241355\pi$
$947$	15.1884	+	8.76900i	0.493555	+	0.284954i	−0.232493	+	0.972598i	$0.574688\pi$
$948$	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	$-0.935751\pi$
$967$		−	12.4683i		−	0.400955i	0.979698	−	0.200477i	$-0.0642493\pi$
$968$	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	−0.358030	−	0.933710i	$-0.616551\pi$
$971$	19.6189	−	33.9810i	0.629602	−	1.09050i	0.987632	−	0.156792i	$-0.0501153\pi$
$972$	−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	−0.122179	−	0.992508i	$-0.538988\pi$
$977$	21.1382	−	12.2041i	0.676269	−	0.390444i	0.798448	+	0.602064i	$0.205655\pi$
$978$	−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	−0.514464	+	0.857512i	$0.672009\pi$
$983$	−47.4783	+	27.4116i	−1.51432	+	0.874295i	−0.999859	+	0.0167828i	$0.994658\pi$
$984$	−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	0.991935	+	0.126748i	$0.0404539\pi$
$991$	19.0686	+	33.0278i	0.605734	+	1.04916i	−0.386201	+	0.922415i	$0.626213\pi$
$992$	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	−0.890166	−	0.455636i	$-0.849412\pi$
$997$	−26.5130	−	45.9219i	−0.839676	−	1.45436i	0.0504904	−	0.998725i	$-0.483922\pi$
$998$	−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.324.1		32
7.2	even	3		637.2.c.g.246.16	yes	16
7.3	odd	6	inner	637.2.r.g.116.16		32
7.4	even	3	inner	637.2.r.g.116.15		32
7.5	odd	6		637.2.c.g.246.15	yes	16
7.6	odd	2	inner	637.2.r.g.324.2		32
13.12	even	2	inner	637.2.r.g.324.15		32
91.5	even	12		8281.2.a.cs.1.15		16
91.12	odd	6		637.2.c.g.246.1	✓	16
91.25	even	6	inner	637.2.r.g.116.1		32
91.38	odd	6	inner	637.2.r.g.116.2		32
91.44	odd	12		8281.2.a.cs.1.16		16
91.47	even	12		8281.2.a.cs.1.1		16
91.51	even	6		637.2.c.g.246.2	yes	16
91.86	odd	12		8281.2.a.cs.1.2		16
91.90	odd	2	inner	637.2.r.g.324.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.1	✓	16	91.12	odd	6
637.2.c.g.246.2	yes	16	91.51	even	6
637.2.c.g.246.15	yes	16	7.5	odd	6
637.2.c.g.246.16	yes	16	7.2	even	3
637.2.r.g.116.1		32	91.25	even	6	inner
637.2.r.g.116.2		32	91.38	odd	6	inner
637.2.r.g.116.15		32	7.4	even	3	inner
637.2.r.g.116.16		32	7.3	odd	6	inner
637.2.r.g.324.1		32	1.1	even	1	trivial
637.2.r.g.324.2		32	7.6	odd	2	inner
637.2.r.g.324.15		32	13.12	even	2	inner
637.2.r.g.324.16		32	91.90	odd	2	inner
8281.2.a.cs.1.1		16	91.47	even	12
8281.2.a.cs.1.2		16	91.86	odd	12
8281.2.a.cs.1.15		16	91.5	even	12
8281.2.a.cs.1.16		16	91.44	odd	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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