LMFDB - Embedded newform 819.2.et.c.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.1
Character	$\chi$	$=$	819.145
Dual form			819.2.et.c.514.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92842 + 1.92842i) q^{2} -5.43762i q^{4} +(3.41458 - 0.914933i) q^{5} +(2.45097 - 0.996354i) q^{7} +(6.62917 + 6.62917i) q^{8} +O(q^{10})$	\(q+(-1.92842 + 1.92842i) q^{2} -5.43762i q^{4} +(3.41458 - 0.914933i) q^{5} +(2.45097 - 0.996354i) q^{7} +(6.62917 + 6.62917i) q^{8} +(-4.82036 + 8.34912i) q^{10} +(0.426935 - 0.114397i) q^{11} +(3.60449 - 0.0874303i) q^{13} +(-2.80512 + 6.64790i) q^{14} -14.6924 q^{16} -1.43104 q^{17} +(0.340943 - 1.27242i) q^{19} +(-4.97505 - 18.5671i) q^{20} +(-0.602706 + 1.04392i) q^{22} +7.18790i q^{23} +(6.49210 - 3.74822i) q^{25} +(-6.78237 + 7.11958i) q^{26} +(-5.41779 - 13.3275i) q^{28} +(-3.82097 - 6.61812i) q^{29} +(0.187215 - 0.698697i) q^{31} +(15.0748 - 15.0748i) q^{32} +(2.75965 - 2.75965i) q^{34} +(7.45744 - 5.64460i) q^{35} +(0.719109 + 0.719109i) q^{37} +(1.79627 + 3.11123i) q^{38} +(28.7010 + 16.5706i) q^{40} +(0.748673 - 2.79409i) q^{41} +(7.20261 + 4.15843i) q^{43} +(-0.622047 - 2.32151i) q^{44} +(-13.8613 - 13.8613i) q^{46} +(-0.242840 - 0.906290i) q^{47} +(5.01456 - 4.88408i) q^{49} +(-5.29136 + 19.7476i) q^{50} +(-0.475412 - 19.5998i) q^{52} +(-2.48381 - 4.30208i) q^{53} +(1.35314 - 0.781234i) q^{55} +(22.8529 + 9.64293i) q^{56} +(20.1310 + 5.39408i) q^{58} +(2.29996 - 2.29996i) q^{59} +(-11.2736 + 6.50883i) q^{61} +(0.986352 + 1.70841i) q^{62} +28.7565i q^{64} +(12.2278 - 3.59640i) q^{65} +(1.64481 + 6.13851i) q^{67} +7.78144i q^{68} +(-3.49591 + 25.2663i) q^{70} +(-0.487730 - 1.82023i) q^{71} +(-12.2890 - 3.29282i) q^{73} -2.77349 q^{74} +(-6.91890 - 1.85391i) q^{76} +(0.932428 - 0.705763i) q^{77} +(-1.77054 + 3.06666i) q^{79} +(-50.1684 + 13.4426i) q^{80} +(3.94442 + 6.83193i) q^{82} +(-2.33307 - 2.33307i) q^{83} +(-4.88639 + 1.30931i) q^{85} +(-21.9089 + 5.87046i) q^{86} +(3.58858 + 2.07187i) q^{88} +(-7.39789 + 7.39789i) q^{89} +(8.74741 - 3.80564i) q^{91} +39.0850 q^{92} +(2.21601 + 1.27941i) q^{94} -4.65670i q^{95} +(-2.51514 + 0.673929i) q^{97} +(-0.251615 + 19.0887i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.92842	+	1.92842i	−1.36360	+	1.36360i	−0.494319	+	0.869281i	$0.664583\pi$
$2$	−1.92842	+	1.92842i	−1.36360	+	1.36360i	−0.869281	+	0.494319i	$0.835417\pi$
$3$		0			0
$3$		0			0
$4$		−	5.43762i		−	2.71881i
$5$	3.41458	−	0.914933i	1.52704	−	0.409170i	0.604991	−	0.796232i	$-0.293177\pi$
$5$	3.41458	−	0.914933i	1.52704	−	0.409170i	0.922054	+	0.387062i	$0.126510\pi$
$6$		0			0
$7$	2.45097	−	0.996354i	0.926381	−	0.376587i
$7$	2.45097	−	0.996354i	0.926381	−	0.376587i
$8$	6.62917	+	6.62917i	2.34377	+	2.34377i
$9$		0			0
$10$	−4.82036	+	8.34912i	−1.52433	+	2.64022i
$11$	0.426935	−	0.114397i	0.128726	−	0.0344920i	−0.193881	−	0.981025i	$-0.562108\pi$
$11$	0.426935	−	0.114397i	0.128726	−	0.0344920i	0.322607	+	0.946533i	$0.395441\pi$
$12$		0			0
$13$	3.60449	−	0.0874303i	0.999706	−	0.0242488i
$13$	3.60449	−	0.0874303i	0.999706	−	0.0242488i
$14$	−2.80512	+	6.64790i	−0.749700	+	1.77673i
$15$		0			0
$16$	−14.6924			−3.67311
$17$	−1.43104			−0.347078			−0.173539	−	0.984827i	$-0.555520\pi$
$17$	−1.43104			−0.347078			−0.173539	+	0.984827i	$0.555520\pi$
$18$		0			0
$19$	0.340943	−	1.27242i	0.0782176	−	0.291912i	−0.915726	−	0.401803i	$-0.868384\pi$
$19$	0.340943	−	1.27242i	0.0782176	−	0.291912i	0.993944	+	0.109891i	$0.0350502\pi$
$20$	−4.97505	−	18.5671i	−1.11246	−	4.15174i
$21$		0			0
$22$	−0.602706	+	1.04392i	−0.128497	+	0.222564i
$23$			7.18790i			1.49878i	0.662129	+	0.749390i	$0.269653\pi$
$23$			7.18790i			1.49878i	−0.662129	+	0.749390i	$0.730347\pi$
$24$		0			0
$25$	6.49210	−	3.74822i	1.29842	−	0.749643i
$26$	−6.78237	+	7.11958i	−1.33013	+	1.39626i
$27$		0			0
$28$	−5.41779	−	13.3275i	−1.02387	−	2.51865i
$29$	−3.82097	−	6.61812i	−0.709537	−	1.22895i	−0.965029	−	0.262143i	$-0.915571\pi$
$29$	−3.82097	−	6.61812i	−0.709537	−	1.22895i	0.255492	−	0.966811i	$-0.417762\pi$
$30$		0			0
$31$	0.187215	−	0.698697i	0.0336249	−	0.125490i	−0.947073	−	0.321017i	$-0.895975\pi$
$31$	0.187215	−	0.698697i	0.0336249	−	0.125490i	0.980698	+	0.195528i	$0.0626419\pi$
$32$	15.0748	−	15.0748i	2.66488	−	2.66488i
$33$		0			0
$34$	2.75965	−	2.75965i	0.473276	−	0.473276i
$35$	7.45744	−	5.64460i	1.26054	−	0.954112i
$36$		0			0
$37$	0.719109	+	0.719109i	0.118221	+	0.118221i	0.763742	−	0.645521i	$-0.223360\pi$
$37$	0.719109	+	0.719109i	0.118221	+	0.118221i	−0.645521	+	0.763742i	$0.723360\pi$
$38$	1.79627	+	3.11123i	0.291394	+	0.504709i
$39$		0			0
$40$	28.7010	+	16.5706i	4.53803	+	2.62003i
$41$	0.748673	−	2.79409i	0.116923	−	0.436363i	−0.882500	−	0.470312i	$-0.844142\pi$
$41$	0.748673	−	2.79409i	0.116923	−	0.436363i	0.999424	+	0.0339485i	$0.0108082\pi$
$42$		0			0
$43$	7.20261	+	4.15843i	1.09839	+	0.634155i	0.935797	−	0.352539i	$-0.114682\pi$
$43$	7.20261	+	4.15843i	1.09839	+	0.634155i	0.162591	+	0.986694i	$0.448015\pi$
$44$	−0.622047	−	2.32151i	−0.0937771	−	0.349981i
$45$		0			0
$46$	−13.8613	−	13.8613i	−2.04374	−	2.04374i
$47$	−0.242840	−	0.906290i	−0.0354218	−	0.132196i	0.945951	−	0.324310i	$-0.105132\pi$
$47$	−0.242840	−	0.906290i	−0.0354218	−	0.132196i	−0.981373	+	0.192114i	$0.938466\pi$
$48$		0			0
$49$	5.01456	−	4.88408i	0.716365	−	0.697726i
$50$	−5.29136	+	19.7476i	−0.748312	+	2.79274i
$51$		0			0
$52$	−0.475412	−	19.5998i	−0.0659278	−	2.71801i
$53$	−2.48381	−	4.30208i	−0.341177	−	0.590936i	0.643474	−	0.765468i	$-0.277492\pi$
$53$	−2.48381	−	4.30208i	−0.341177	−	0.590936i	−0.984652	+	0.174531i	$0.944159\pi$
$54$		0			0
$55$	1.35314	−	0.781234i	0.182457	−	0.105342i
$56$	22.8529	+	9.64293i	3.05385	+	1.28859i
$57$		0			0
$58$	20.1310	+	5.39408i	2.64332	+	0.708277i
$59$	2.29996	−	2.29996i	0.299429	−	0.299429i	−0.541361	−	0.840790i	$-0.682091\pi$
$59$	2.29996	−	2.29996i	0.299429	−	0.299429i	0.840790	+	0.541361i	$0.182091\pi$
$60$		0			0
$61$	−11.2736	+	6.50883i	−1.44344	+	0.833370i	−0.998077	−	0.0619805i	$-0.980258\pi$
$61$	−11.2736	+	6.50883i	−1.44344	+	0.833370i	−0.445362	+	0.895351i	$0.646925\pi$
$62$	0.986352	+	1.70841i	0.125267	+	0.216969i
$63$		0			0
$64$			28.7565i			3.59456i
$65$	12.2278	−	3.59640i	1.51667	−	0.446079i
$66$		0			0
$67$	1.64481	+	6.13851i	0.200945	+	0.749939i	0.990647	+	0.136448i	$0.0435686\pi$
$67$	1.64481	+	6.13851i	0.200945	+	0.749939i	−0.789702	+	0.613491i	$0.789765\pi$
$68$			7.78144i			0.943639i
$69$		0			0
$70$	−3.49591	+	25.2663i	−0.417842	+	3.01990i
$71$	−0.487730	−	1.82023i	−0.0578829	−	0.216022i	0.930926	−	0.365207i	$-0.119002\pi$
$71$	−0.487730	−	1.82023i	−0.0578829	−	0.216022i	−0.988809	+	0.149185i	$0.952335\pi$
$72$		0			0
$73$	−12.2890	−	3.29282i	−1.43832	−	0.385396i	−0.546373	−	0.837542i	$-0.683992\pi$
$73$	−12.2890	−	3.29282i	−1.43832	−	0.385396i	−0.891944	+	0.452146i	$0.850659\pi$
$74$	−2.77349			−0.322412
$75$		0			0
$76$	−6.91890	−	1.85391i	−0.793653	−	0.212659i
$77$	0.932428	−	0.705763i	0.106260	−	0.0804292i
$78$		0			0
$79$	−1.77054	+	3.06666i	−0.199201	+	0.345026i	−0.948270	−	0.317466i	$-0.897168\pi$
$79$	−1.77054	+	3.06666i	−0.199201	+	0.345026i	0.749069	+	0.662493i	$0.230501\pi$
$80$	−50.1684	+	13.4426i	−5.60900	+	1.50293i
$81$		0			0
$82$	3.94442	+	6.83193i	0.435588	+	0.754461i
$83$	−2.33307	−	2.33307i	−0.256087	−	0.256087i	0.567373	−	0.823461i	$-0.307960\pi$
$83$	−2.33307	−	2.33307i	−0.256087	−	0.256087i	−0.823461	+	0.567373i	$0.807960\pi$
$84$		0			0
$85$	−4.88639	+	1.30931i	−0.530004	+	0.142014i
$86$	−21.9089	+	5.87046i	−2.36249	+	0.633028i
$87$		0			0
$88$	3.58858	+	2.07187i	0.382544	+	0.220862i
$89$	−7.39789	+	7.39789i	−0.784175	+	0.784175i	−0.980532	−	0.196357i	$-0.937089\pi$
$89$	−7.39789	+	7.39789i	−0.784175	+	0.784175i	0.196357	+	0.980532i	$0.437089\pi$
$90$		0			0
$91$	8.74741	−	3.80564i	0.916977	−	0.398939i
$92$	39.0850			4.07489
$93$		0			0
$94$	2.21601	+	1.27941i	0.228563	+	0.131961i
$95$		−	4.65670i		−	0.477767i
$96$		0			0
$97$	−2.51514	+	0.673929i	−0.255373	+	0.0684271i	−0.384234	−	0.923236i	$-0.625535\pi$
$97$	−2.51514	+	0.673929i	−0.255373	+	0.0684271i	0.128861	+	0.991663i	$0.458868\pi$
$98$	−0.251615	+	19.0887i	−0.0254170	+	1.92825i
$99$		0			0
$100$	−20.3814	−	35.3015i	−2.03814	−	3.53015i
$101$	−0.722867	+	1.25204i	−0.0719279	+	0.124583i	−0.899746	−	0.436413i	$-0.856248\pi$
$101$	−0.722867	+	1.25204i	−0.0719279	+	0.124583i	0.827818	+	0.560996i	$0.189582\pi$
$102$		0			0
$103$	6.70272	−	11.6095i	0.660439	−	1.14391i	−0.320061	−	0.947397i	$-0.603704\pi$
$103$	6.70272	−	11.6095i	0.660439	−	1.14391i	0.980500	−	0.196517i	$-0.0629631\pi$
$104$	24.4744	+	23.3152i	2.39991	+	2.28624i
$105$		0			0
$106$	13.0860	+	3.50640i	1.27103	+	0.340571i
$107$	−1.88975			−0.182689			−0.0913447	−	0.995819i	$-0.529117\pi$
$107$	−1.88975			−0.182689			−0.0913447	+	0.995819i	$0.529117\pi$
$108$		0			0
$109$	7.12442	+	1.90898i	0.682396	+	0.182847i	0.583332	−	0.812234i	$-0.301749\pi$
$109$	7.12442	+	1.90898i	0.682396	+	0.182847i	0.0990637	+	0.995081i	$0.468415\pi$
$110$	−1.10287	+	4.11597i	−0.105155	+	0.392442i
$111$		0			0
$112$	−36.0108	+	14.6389i	−3.40270	+	1.38324i
$113$	3.09382	−	5.35865i	0.291042	−	0.504100i	−0.683014	−	0.730405i	$-0.739331\pi$
$113$	3.09382	−	5.35865i	0.291042	−	0.504100i	0.974056	+	0.226305i	$0.0726647\pi$
$114$		0			0
$115$	6.57644	+	24.5436i	0.613256	+	2.28870i
$116$	−35.9868	+	20.7770i	−3.34129	+	1.92909i
$117$		0			0
$118$			8.87058i			0.816603i
$119$	−3.50744	+	1.42582i	−0.321527	+	0.130705i
$120$		0			0
$121$	−9.35709	+	5.40232i	−0.850645	+	0.491120i
$122$	9.18853	−	34.2921i	0.831890	−	3.10466i
$123$		0			0
$124$	−3.79925	−	1.01800i	−0.341182	−	0.0914195i
$125$	6.24018	−	6.24018i	0.558139	−	0.558139i
$126$		0			0
$127$	5.90231	−	3.40770i	0.523745	−	0.302384i	−0.214721	−	0.976676i	$-0.568884\pi$
$127$	5.90231	−	3.40770i	0.523745	−	0.302384i	0.738466	+	0.674291i	$0.235551\pi$
$128$	−25.3048	−	25.3048i	−2.23665	−	2.23665i
$129$		0			0
$130$	−16.6450	+	30.5158i	−1.45986	+	2.67641i
$131$	3.17967	+	1.83578i	0.277809	+	0.160393i	0.632431	−	0.774617i	$-0.282057\pi$
$131$	3.17967	+	1.83578i	0.277809	+	0.160393i	−0.354622	+	0.935010i	$0.615390\pi$
$132$		0			0
$133$	−0.432135	−	3.45836i	−0.0374708	−	0.299878i
$134$	−15.0095	−	8.66575i	−1.29662	−	0.748607i
$135$		0			0
$136$	−9.48660	−	9.48660i	−0.813470	−	0.813470i
$137$	5.57408	+	5.57408i	0.476225	+	0.476225i	0.903922	−	0.427697i	$-0.140675\pi$
$137$	5.57408	+	5.57408i	0.476225	+	0.476225i	−0.427697	+	0.903922i	$0.640675\pi$
$138$		0			0
$139$	10.3222	+	5.95952i	0.875517	+	0.505480i	0.869178	−	0.494500i	$-0.164649\pi$
$139$	10.3222	+	5.95952i	0.875517	+	0.505480i	0.00633943	+	0.999980i	$0.497982\pi$
$140$	−30.6932	−	40.5507i	−2.59405	−	3.42716i
$141$		0			0
$142$	4.45073	+	2.56963i	0.373497	+	0.215638i
$143$	1.52888	−	0.449670i	0.127852	−	0.0376033i
$144$		0			0
$145$	−19.1021	−	19.1021i	−1.58635	−	1.58635i
$146$	30.0483	−	17.3484i	2.48681	−	1.43576i
$147$		0			0
$148$	3.91024	−	3.91024i	0.321420	−	0.321420i
$149$	21.0304	+	5.63507i	1.72287	+	0.461643i	0.978522	−	0.206144i	$-0.0660914\pi$
$149$	21.0304	+	5.63507i	1.72287	+	0.461643i	0.744353	+	0.667787i	$0.232758\pi$
$150$		0			0
$151$	−3.61340	+	13.4854i	−0.294054	+	1.09742i	0.647912	+	0.761715i	$0.275643\pi$
$151$	−3.61340	+	13.4854i	−0.294054	+	1.09742i	−0.941966	+	0.335709i	$0.891024\pi$
$152$	10.6952	−	6.17489i	0.867497	−	0.500850i
$153$		0			0
$154$	−0.437105	+	3.15912i	−0.0352230	+	0.254569i
$155$		−	2.55704i		−	0.205387i
$156$		0			0
$157$	12.9689	−	7.48759i	1.03503	−	0.597574i	0.116608	−	0.993178i	$-0.462798\pi$
$157$	12.9689	−	7.48759i	1.03503	−	0.597574i	0.918421	+	0.395604i	$0.129465\pi$
$158$	−2.49947	−	9.32816i	−0.198847	−	0.742108i
$159$		0			0
$160$	37.6817	−	65.2667i	2.97900	−	5.15978i
$161$	7.16169	+	17.6174i	0.564420	+	1.38844i
$162$		0			0
$163$	−2.28941	+	8.54420i	−0.179320	+	0.669233i	0.816455	+	0.577409i	$0.195936\pi$
$163$	−2.28941	+	8.54420i	−0.179320	+	0.669233i	−0.995775	+	0.0918237i	$0.970730\pi$
$164$	−15.1932	−	4.07100i	−1.18639	−	0.317891i
$165$		0			0
$166$	8.99827			0.698401
$167$	0.331336	+	0.0887813i	0.0256396	+	0.00687010i	0.271616	−	0.962406i	$-0.412442\pi$
$167$	0.331336	+	0.0887813i	0.0256396	+	0.00687010i	−0.245976	+	0.969276i	$0.579109\pi$
$168$		0			0
$169$	12.9847	−	0.630284i	0.998824	−	0.0484833i
$170$	6.89813	−	11.9479i	0.529063	−	0.916363i
$171$		0			0
$172$	22.6119	−	39.1650i	1.72414	−	2.98631i
$173$	−4.62536	−	8.01137i	−0.351660	−	0.609093i	0.634880	−	0.772610i	$-0.281049\pi$
$173$	−4.62536	−	8.01137i	−0.351660	−	0.609093i	−0.986540	+	0.163517i	$0.947716\pi$
$174$		0			0
$175$	12.1774	−	15.6552i	0.920527	−	1.18342i
$176$	−6.27272	+	1.68077i	−0.472824	+	0.126693i
$177$		0			0
$178$		−	28.5325i		−	2.13860i
$179$	12.6486	+	7.30269i	0.945403	+	0.545829i	0.891650	−	0.452725i	$-0.149548\pi$
$179$	12.6486	+	7.30269i	0.945403	+	0.545829i	0.0537533	+	0.998554i	$0.482882\pi$
$180$		0			0
$181$	−8.63806			−0.642062			−0.321031	−	0.947069i	$-0.604029\pi$
$181$	−8.63806			−0.642062			−0.321031	+	0.947069i	$0.604029\pi$
$182$	−9.52981	+	24.2076i	−0.706396	+	1.79438i
$183$		0			0
$184$	−47.6498	+	47.6498i	−3.51279	+	3.51279i
$185$	3.11339	+	1.79752i	0.228901	+	0.132156i
$186$		0			0
$187$	−0.610962	+	0.163707i	−0.0446779	+	0.0119714i
$188$	−4.92806	+	1.32047i	−0.359415	+	0.0963051i
$189$		0			0
$190$	8.98007	+	8.98007i	0.651483	+	0.651483i
$191$	−3.52411	−	6.10394i	−0.254996	−	0.441666i	0.709899	−	0.704304i	$-0.248741\pi$
$191$	−3.52411	−	6.10394i	−0.254996	−	0.441666i	−0.964894	+	0.262638i	$0.915407\pi$
$192$		0			0
$193$	−22.3236	+	5.98160i	−1.60689	+	0.430565i	−0.947114	−	0.320897i	$-0.896016\pi$
$193$	−22.3236	+	5.98160i	−1.60689	+	0.430565i	−0.659776	+	0.751462i	$0.729349\pi$
$194$	3.55062	−	6.14986i	0.254920	−	0.441534i
$195$		0			0
$196$	−26.5577	−	27.2672i	−1.89698	−	1.94766i
$197$	18.7705	+	5.02954i	1.33734	+	0.358340i	0.855448	−	0.517889i	$-0.173282\pi$
$197$	18.7705	+	5.02954i	1.33734	+	0.358340i	0.481895	+	0.876229i	$0.339949\pi$
$198$		0			0
$199$	17.8108			1.26257			0.631285	−	0.775551i	$-0.282528\pi$
$199$	17.8108			1.26257			0.631285	+	0.775551i	$0.282528\pi$
$200$	67.8848	+	18.1897i	4.80018	+	1.28620i
$201$		0			0
$202$	−1.02047	−	3.80846i	−0.0718002	−	0.267962i
$203$	−15.9591	−	12.4138i	−1.12011	−	0.871278i
$204$		0			0
$205$		−	10.2256i		−	0.714187i
$206$	9.46225	+	35.3136i	0.659266	+	2.46041i
$207$		0			0
$208$	−52.9587	+	1.28456i	−3.67203	+	0.0890685i
$209$		−	0.582242i		−	0.0402745i
$210$		0			0
$211$	−5.03848	−	8.72690i	−0.346863	−	0.600785i	0.638827	−	0.769350i	$-0.279420\pi$
$211$	−5.03848	−	8.72690i	−0.346863	−	0.600785i	−0.985690	+	0.168565i	$0.946087\pi$
$212$	−23.3931	+	13.5060i	−1.60664	+	0.927595i
$213$		0			0
$214$	3.64424	−	3.64424i	0.249115	−	0.249115i
$215$	28.3985	+	7.60937i	1.93676	+	0.518955i
$216$		0			0
$217$	−0.237290	−	1.89902i	−0.0161083	−	0.128914i
$218$	−17.4202	+	10.0576i	−1.17985	+	0.681184i
$219$		0			0
$220$	−4.24805	−	7.35784i	−0.286404	−	0.496066i
$221$	−5.15817	+	0.125116i	−0.346976	+	0.00841623i
$222$		0			0
$223$	0.246185	−	0.918774i	0.0164857	−	0.0615256i	−0.957193	−	0.289451i	$-0.906527\pi$
$223$	0.246185	−	0.918774i	0.0164857	−	0.0615256i	0.973679	+	0.227925i	$0.0731941\pi$
$224$	21.9282	−	51.9680i	1.46514	−	3.47226i
$225$		0			0
$226$	4.36755	+	16.2999i	0.290525	+	1.08425i
$227$	−17.3431	−	17.3431i	−1.15110	−	1.15110i	−0.986333	−	0.164766i	$-0.947313\pi$
$227$	−17.3431	−	17.3431i	−1.15110	−	1.15110i	−0.164766	−	0.986333i	$-0.552687\pi$
$228$		0			0
$229$	−5.33978	−	19.9283i	−0.352863	−	1.31690i	−0.883153	−	0.469085i	$-0.844584\pi$
$229$	−5.33978	−	19.9283i	−0.352863	−	1.31690i	0.530290	−	0.847816i	$-0.322083\pi$
$230$	−60.0126	−	34.6483i	−3.95711	−	2.28464i
$231$		0			0
$232$	18.5428	−	69.2025i	1.21739	−	4.54337i
$233$	−19.6906	−	11.3684i	−1.28998	−	0.744768i	−0.311326	−	0.950303i	$-0.600773\pi$
$233$	−19.6906	−	11.3684i	−1.28998	−	0.744768i	−0.978650	+	0.205536i	$0.934106\pi$
$234$		0			0
$235$	−1.65839	−	2.87241i	−0.108181	−	0.187376i
$236$	−12.5063	−	12.5063i	−0.814091	−	0.814091i
$237$		0			0
$238$	4.01424	−	9.51341i	0.260205	−	0.616663i
$239$	−20.7640	+	20.7640i	−1.34311	+	1.34311i	−0.450171	+	0.892943i	$0.648637\pi$
$239$	−20.7640	+	20.7640i	−1.34311	+	1.34311i	−0.892943	+	0.450171i	$0.851363\pi$
$240$		0			0
$241$	−4.79541	+	4.79541i	−0.308900	+	0.308900i	−0.844483	−	0.535583i	$-0.820092\pi$
$241$	−4.79541	+	4.79541i	−0.308900	+	0.308900i	0.535583	+	0.844483i	$0.320092\pi$
$242$	7.62647	−	28.4624i	0.490248	−	1.82963i
$243$		0			0
$244$	35.3925	+	61.3016i	2.26577	+	3.92443i
$245$	12.6540	−	21.2650i	0.808433	−	1.35857i
$246$		0			0
$247$	1.11768	−	4.61622i	0.0711161	−	0.293723i
$248$	5.87286	−	3.39070i	0.372927	−	0.215310i
$249$		0			0
$250$			24.0674i			1.52216i
$251$	−2.83547	+	4.91118i	−0.178973	+	0.309991i	−0.941529	−	0.336932i	$-0.890611\pi$
$251$	−2.83547	+	4.91118i	−0.178973	+	0.309991i	0.762556	+	0.646922i	$0.223944\pi$
$252$		0			0
$253$	0.822274	+	3.06877i	0.0516959	+	0.192932i
$254$	−4.81065	+	17.9536i	−0.301847	+	1.12651i
$255$		0			0
$256$	40.0839			2.50524
$257$	−1.19397			−0.0744781			−0.0372390	−	0.999306i	$-0.511856\pi$
$257$	−1.19397			−0.0744781			−0.0372390	+	0.999306i	$0.511856\pi$
$258$		0			0
$259$	2.47901	+	1.04603i	0.154038	+	0.0649972i
$260$	−19.5559	−	66.4902i	−1.21280	−	4.12354i
$261$		0			0
$262$	−9.67191	+	2.59158i	−0.597533	+	0.160108i
$263$	−12.0587	+	20.8862i	−0.743569	+	1.28790i	0.207292	+	0.978279i	$0.433535\pi$
$263$	−12.0587	+	20.8862i	−0.743569	+	1.28790i	−0.950861	+	0.309619i	$0.899798\pi$
$264$		0			0
$265$	−12.4173	−	12.4173i	−0.762786	−	0.762786i
$266$	7.50251	+	5.83583i	0.460008	+	0.357818i
$267$		0			0
$268$	33.3789	−	8.94384i	2.03894	−	0.546332i
$269$			18.4510i			1.12498i	0.826804	+	0.562490i	$0.190156\pi$
$269$			18.4510i			1.12498i	−0.826804	+	0.562490i	$0.809844\pi$
$270$		0			0
$271$	0.695084	−	0.695084i	0.0422234	−	0.0422234i	−0.685680	−	0.727903i	$-0.740495\pi$
$271$	0.695084	−	0.695084i	0.0422234	−	0.0422234i	0.727903	+	0.685680i	$0.240495\pi$
$272$	21.0254			1.27486
$273$		0			0
$274$	−21.4983			−1.29876
$275$	2.34292	−	2.34292i	0.141284	−	0.141284i
$276$		0			0
$277$		−	18.0478i		−	1.08439i	−0.840254	−	0.542194i	$-0.817594\pi$
$277$		−	18.0478i		−	1.08439i	0.840254	−	0.542194i	$-0.182406\pi$
$278$	−31.3980	+	8.41307i	−1.88313	+	0.504582i
$279$		0			0
$280$	86.8557	+	12.0176i	5.19062	+	0.718189i
$281$	−15.4188	−	15.4188i	−0.919807	−	0.919807i	0.0772077	−	0.997015i	$-0.475400\pi$
$281$	−15.4188	−	15.4188i	−0.919807	−	0.919807i	−0.997015	+	0.0772077i	$0.975400\pi$
$282$		0			0
$283$	−13.7360	+	23.7915i	−0.816521	+	1.41426i	0.0917093	+	0.995786i	$0.470767\pi$
$283$	−13.7360	+	23.7915i	−0.816521	+	1.41426i	−0.908230	+	0.418470i	$0.862566\pi$
$284$	−9.89773	+	2.65209i	−0.587323	+	0.157373i
$285$		0			0
$286$	−2.08118	+	3.81548i	−0.123063	+	0.225614i
$287$	−0.948921	−	7.59418i	−0.0560130	−	0.448270i
$288$		0			0
$289$	−14.9521			−0.879537
$290$	73.6739			4.32628
$291$		0			0
$292$	−17.9051	+	66.8228i	−1.04782	+	3.91051i
$293$	−2.03171	−	7.58244i	−0.118694	−	0.442971i	0.880843	−	0.473409i	$-0.156977\pi$
$293$	−2.03171	−	7.58244i	−0.118694	−	0.442971i	−0.999537	+	0.0304377i	$0.990310\pi$
$294$		0			0
$295$	5.74908	−	9.95770i	0.334724	−	0.579760i
$296$			9.53419i			0.554163i
$297$		0			0
$298$	−51.4222	+	29.6886i	−2.97881	+	1.71982i
$299$	0.628440	+	25.9087i	0.0363436	+	1.49834i
$300$		0			0
$301$	21.7967	+	3.01585i	1.25634	+	0.173831i
$302$	−19.0373	−	32.9736i	−1.09548	−	1.89742i
$303$		0			0
$304$	−5.00927	+	18.6949i	−0.287302	+	1.07222i
$305$	−32.5395	+	32.5395i	−1.86321	+	1.86321i
$306$		0			0
$307$	−16.1223	+	16.1223i	−0.920147	+	0.920147i	−0.997039	−	0.0768923i	$-0.975500\pi$
$307$	−16.1223	+	16.1223i	−0.920147	+	0.920147i	0.0768923	+	0.997039i	$0.475500\pi$
$308$	−3.83767	−	5.07019i	−0.218671	−	0.288901i
$309$		0			0
$310$	4.93106	+	4.93106i	0.280065	+	0.280065i
$311$	2.75580	+	4.77319i	0.156267	+	0.270663i	0.933520	−	0.358526i	$-0.116721\pi$
$311$	2.75580	+	4.77319i	0.156267	+	0.270663i	−0.777253	+	0.629189i	$0.783387\pi$
$312$		0			0
$313$	16.8101	+	9.70534i	0.950165	+	0.548578i	0.893132	−	0.449794i	$-0.148503\pi$
$313$	16.8101	+	9.70534i	0.950165	+	0.548578i	0.0570329	+	0.998372i	$0.481836\pi$
$314$	−10.5702	+	39.4487i	−0.596513	+	2.22622i
$315$		0			0
$316$	16.6753	+	9.62750i	0.938060	+	0.541589i
$317$	−7.26716	−	27.1214i	−0.408164	−	1.52329i	−0.798144	−	0.602467i	$-0.794185\pi$
$317$	−7.26716	−	27.1214i	−0.408164	−	1.52329i	0.389980	−	0.920823i	$-0.372482\pi$
$318$		0			0
$319$	−2.38840	−	2.38840i	−0.133725	−	0.133725i
$320$	26.3102	+	98.1911i	1.47079	+	5.48905i
$321$		0			0
$322$	−47.7844	−	20.1629i	−2.66292	−	1.12364i
$323$	−0.487902	+	1.82088i	−0.0271476	+	0.101316i
$324$		0			0
$325$	23.0730	−	14.0780i	1.27986	−	0.780908i
$326$	−12.0619	−	20.8918i	−0.668045	−	1.15709i
$327$		0			0
$328$	23.4856	−	13.5594i	1.29677	−	0.748692i
$329$	−1.49818	−	1.97934i	−0.0825973	−	0.109125i
$330$		0			0
$331$	−7.33428	−	1.96521i	−0.403129	−	0.108018i	0.0515569	−	0.998670i	$-0.483582\pi$
$331$	−7.33428	−	1.96521i	−0.403129	−	0.108018i	−0.454685	+	0.890652i	$0.650248\pi$
$332$	−12.6863	+	12.6863i	−0.696252	+	0.696252i
$333$		0			0
$334$	−0.810163	+	0.467748i	−0.0443302	+	0.0255940i
$335$	11.2327	+	19.4555i	0.613705	+	1.06297i
$336$		0			0
$337$			3.26189i			0.177686i	0.996046	+	0.0888431i	$0.0283170\pi$
$337$			3.26189i			0.177686i	−0.996046	+	0.0888431i	$0.971683\pi$
$338$	−23.8245	+	26.2554i	−1.29588	+	1.42811i
$339$		0			0
$340$	7.11950	+	26.5703i	0.386109	+	1.44098i
$341$		−	0.319715i		−	0.0173136i
$342$		0			0
$343$	7.42428	−	16.9670i	0.400873	−	0.916133i
$344$	20.1804	+	75.3143i	1.08805	+	4.06067i
$345$		0			0
$346$	24.3689	+	6.52964i	1.31008	+	0.351035i
$347$	30.9665			1.66237			0.831185	−	0.555996i	$-0.187663\pi$
$347$	30.9665			1.66237			0.831185	+	0.555996i	$0.187663\pi$
$348$		0			0
$349$	−11.7105	−	3.13781i	−0.626847	−	0.167963i	−0.0686086	−	0.997644i	$-0.521856\pi$
$349$	−11.7105	−	3.13781i	−0.626847	−	0.167963i	−0.558239	+	0.829680i	$0.688523\pi$
$350$	6.70664	+	53.6730i	0.358485	+	2.86894i
$351$		0			0
$352$	4.71147	−	8.16050i	0.251122	−	0.434956i
$353$	28.4026	−	7.61046i	1.51172	−	0.405064i	0.594713	−	0.803938i	$-0.297266\pi$
$353$	28.4026	−	7.61046i	1.51172	−	0.405064i	0.917006	+	0.398874i	$0.130599\pi$
$354$		0			0
$355$	−3.33078	−	5.76909i	−0.176780	−	0.306191i
$356$	40.2269	+	40.2269i	2.13202	+	2.13202i
$357$		0			0
$358$	−38.4746	+	10.3092i	−2.03344	+	0.544860i
$359$	−8.99331	+	2.40975i	−0.474649	+	0.127182i	−0.488210	−	0.872726i	$-0.662350\pi$
$359$	−8.99331	+	2.40975i	−0.474649	+	0.127182i	0.0135610	+	0.999908i	$0.495683\pi$
$360$		0			0
$361$	14.9517	+	8.63236i	0.786931	+	0.454335i
$362$	16.6578	−	16.6578i	0.875516	−	0.875516i
$363$		0			0
$364$	−20.6936	−	47.5650i	−1.08464	−	2.49308i
$365$	−44.9744			−2.35407
$366$		0			0
$367$	21.8442	+	12.6118i	1.14026	+	0.658329i	0.946495	−	0.322720i	$-0.104597\pi$
$367$	21.8442	+	12.6118i	1.14026	+	0.658329i	0.193764	+	0.981048i	$0.437930\pi$
$368$		−	105.608i		−	5.50518i
$369$		0			0
$370$	−9.47029	+	2.53756i	−0.492337	+	0.131921i
$371$	−10.3741	−	8.06954i	−0.538599	−	0.418950i
$372$		0			0
$373$	0.524168	+	0.907886i	0.0271404	+	0.0470086i	0.879277	−	0.476312i	$-0.158027\pi$
$373$	0.524168	+	0.907886i	0.0271404	+	0.0470086i	−0.852136	+	0.523320i	$0.824693\pi$
$374$	0.862496	−	1.49389i	0.0445986	−	0.0772470i
$375$		0			0
$376$	4.39812	−	7.61777i	0.226816	−	0.392857i
$377$	−14.3513	−	23.5209i	−0.739129	−	1.21139i
$378$		0			0
$379$	−15.3006	−	4.09979i	−0.785941	−	0.210592i	−0.156539	−	0.987672i	$-0.550034\pi$
$379$	−15.3006	−	4.09979i	−0.785941	−	0.210592i	−0.629402	+	0.777080i	$0.716700\pi$
$380$	−25.3213			−1.29896
$381$		0			0
$382$	18.5669	+	4.97500i	0.949968	+	0.254543i
$383$	6.72323	−	25.0914i	0.343541	−	1.28211i	−0.550767	−	0.834659i	$-0.685665\pi$
$383$	6.72323	−	25.0914i	0.343541	−	1.28211i	0.894308	−	0.447453i	$-0.147669\pi$
$384$		0			0
$385$	2.53812	−	3.26299i	0.129355	−	0.166297i
$386$	31.5143	−	54.5844i	1.60404	−	2.77827i
$387$		0			0
$388$	3.66457	+	13.6763i	0.186040	+	0.694311i
$389$	−20.0494	+	11.5755i	−1.01655	+	0.586903i	−0.913102	−	0.407732i	$-0.866320\pi$
$389$	−20.0494	+	11.5755i	−1.01655	+	0.586903i	−0.103444	+	0.994635i	$0.532986\pi$
$390$		0			0
$391$		−	10.2862i		−	0.520194i
$392$	65.6197	+	0.864956i	3.31430	+	0.0436869i
$393$		0			0
$394$	−45.8965	+	26.4984i	−2.31223	+	1.33497i
$395$	−3.23985	+	12.0913i	−0.163014	+	0.608378i
$396$		0			0
$397$	−11.4194	−	3.05983i	−0.573125	−	0.153569i	−0.0393958	−	0.999224i	$-0.512543\pi$
$397$	−11.4194	−	3.05983i	−0.573125	−	0.153569i	−0.533730	+	0.845655i	$0.679210\pi$
$398$	−34.3466	+	34.3466i	−1.72164	+	1.72164i
$399$		0			0
$400$	−95.3847	+	55.0704i	−4.76923	+	2.75352i
$401$	−14.7302	−	14.7302i	−0.735592	−	0.735592i	0.236129	−	0.971722i	$-0.424121\pi$
$401$	−14.7302	−	14.7302i	−0.735592	−	0.735592i	−0.971722	+	0.236129i	$0.924121\pi$
$402$		0			0
$403$	0.613729	−	2.53482i	0.0305720	−	0.126268i
$404$	6.80812	+	3.93067i	0.338717	+	0.195558i
$405$		0			0
$406$	54.7149	−	6.83683i	2.71545	−	0.339306i
$407$	0.389277	+	0.224749i	0.0192957	+	0.0111404i
$408$		0			0
$409$	−11.2439	−	11.2439i	−0.555974	−	0.555974i	0.372185	−	0.928159i	$-0.378609\pi$
$409$	−11.2439	−	11.2439i	−0.555974	−	0.555974i	−0.928159	+	0.372185i	$0.878609\pi$
$410$	19.7193	+	19.7193i	0.973865	+	0.973865i
$411$		0			0
$412$	−63.1278	−	36.4468i	−3.11008	−	1.79561i
$413$	3.34557	−	7.92872i	0.164625	−	0.390147i
$414$		0			0
$415$	−10.1010	−	5.83183i	−0.495840	−	0.286274i
$416$	53.0192	−	55.6552i	2.59948	−	2.72872i
$417$		0			0
$418$	1.12281	+	1.12281i	0.0549183	+	0.0549183i
$419$	4.29128	−	2.47757i	0.209643	−	0.121037i	−0.391503	−	0.920177i	$-0.628045\pi$
$419$	4.29128	−	2.47757i	0.209643	−	0.121037i	0.601145	+	0.799140i	$0.294711\pi$
$420$		0			0
$421$	0.811225	−	0.811225i	0.0395367	−	0.0395367i	−0.687062	−	0.726599i	$-0.741100\pi$
$421$	0.811225	−	0.811225i	0.0395367	−	0.0395367i	0.726599	+	0.687062i	$0.241100\pi$
$422$	26.5455	+	7.11283i	1.29221	+	0.346247i
$423$		0			0
$424$	12.0536	−	44.9848i	0.585376	−	2.18465i
$425$	−9.29045	+	5.36385i	−0.450653	+	0.260185i
$426$		0			0
$427$	−21.1463	+	27.1855i	−1.02334	+	1.31560i
$428$			10.2758i			0.496697i
$429$		0			0
$430$	−69.4384	+	40.0903i	−3.34862	+	1.93333i
$431$	5.30567	+	19.8010i	0.255565	+	0.953783i	0.967775	+	0.251816i	$0.0810278\pi$
$431$	5.30567	+	19.8010i	0.255565	+	0.953783i	−0.712210	+	0.701967i	$0.752306\pi$
$432$		0			0
$433$	−0.246122	+	0.426295i	−0.0118279	+	0.0204864i	−0.871879	−	0.489722i	$-0.837098\pi$
$433$	−0.246122	+	0.426295i	−0.0118279	+	0.0204864i	0.860051	+	0.510208i	$0.170432\pi$
$434$	4.11971	+	3.20452i	0.197752	+	0.153822i
$435$		0			0
$436$	10.3803	−	38.7399i	0.497127	−	1.85530i
$437$	9.14599	+	2.45066i	0.437512	+	0.117231i
$438$		0			0
$439$	22.3782			1.06806			0.534028	−	0.845467i	$-0.320678\pi$
$439$	22.3782			1.06806			0.534028	+	0.845467i	$0.320678\pi$
$440$	14.1491	+	3.79124i	0.674533	+	0.180740i
$441$		0			0
$442$	9.70585	−	10.1884i	0.461660	−	0.484613i
$443$	−4.77420	+	8.26916i	−0.226829	+	0.392880i	−0.956867	−	0.290527i	$-0.906169\pi$
$443$	−4.77420	+	8.26916i	−0.226829	+	0.392880i	0.730038	+	0.683407i	$0.239503\pi$
$444$		0			0
$445$	−18.4921	+	32.0292i	−0.876609	+	1.51833i
$446$	1.29703	+	2.24653i	0.0614164	+	0.106376i
$447$		0			0
$448$	28.6516	+	70.4813i	1.35366	+	3.32993i
$449$	17.1874	−	4.60535i	0.811124	−	0.217340i	0.170662	−	0.985330i	$-0.445409\pi$
$449$	17.1874	−	4.60535i	0.811124	−	0.217340i	0.640462	+	0.767990i	$0.278743\pi$
$450$		0			0
$451$		−	1.27854i		−	0.0602041i
$452$	−29.1383	−	16.8230i	−1.37055	−	0.791287i
$453$		0			0
$454$	66.8894			3.13928
$455$	26.3868	−	20.9979i	1.23703	−	0.984398i
$456$		0			0
$457$	−19.4797	+	19.4797i	−0.911220	+	0.911220i	−0.996368	−	0.0851486i	$-0.972864\pi$
$457$	−19.4797	+	19.4797i	−0.911220	+	0.911220i	0.0851486	+	0.996368i	$0.472864\pi$
$458$	48.7276	+	28.1329i	2.27689	+	1.31456i
$459$		0			0
$460$	133.459	−	35.7602i	6.22255	−	1.66733i
$461$	10.0918	−	2.70408i	0.470021	−	0.125942i	−0.0160314	−	0.999871i	$-0.505103\pi$
$461$	10.0918	−	2.70408i	0.470021	−	0.125942i	0.486052	+	0.873930i	$0.338437\pi$
$462$		0			0
$463$	−10.7292	−	10.7292i	−0.498628	−	0.498628i	0.412382	−	0.911011i	$-0.364697\pi$
$463$	−10.7292	−	10.7292i	−0.498628	−	0.498628i	−0.911011	+	0.412382i	$0.864697\pi$
$464$	56.1394	+	97.2362i	2.60620	+	4.51408i
$465$		0			0
$466$	59.8948	−	16.0488i	2.77457	−	0.743445i
$467$	7.08987	−	12.2800i	0.328080	−	0.568251i	−0.654051	−	0.756451i	$-0.726932\pi$
$467$	7.08987	−	12.2800i	0.328080	−	0.568251i	0.982131	+	0.188199i	$0.0602651\pi$
$468$		0			0
$469$	10.1475	+	13.4065i	0.468569	+	0.619056i
$470$	8.73729	+	2.34115i	0.403021	+	0.107989i
$471$		0			0
$472$	30.4937			1.40358
$473$	3.55076	+	0.951424i	0.163264	+	0.0437465i
$474$		0			0
$475$	−2.55585	−	9.53857i	−0.117271	−	0.437660i
$476$	7.75308	+	19.0721i	0.355362	+	0.874169i
$477$		0			0
$478$		−	80.0836i		−	3.66294i
$479$	6.49544	+	24.2413i	0.296784	+	1.10761i	0.939790	+	0.341752i	$0.111020\pi$
$479$	6.49544	+	24.2413i	0.296784	+	1.10761i	−0.643006	+	0.765861i	$0.722313\pi$
$480$		0			0
$481$	2.65489	+	2.52915i	0.121053	+	0.115319i
$482$		−	18.4951i		−	0.842431i
$483$		0			0
$484$	29.3757	+	50.8803i	1.33526	+	2.31274i
$485$	−7.97153	+	4.60236i	−0.361968	+	0.208983i
$486$		0			0
$487$	−17.1606	+	17.1606i	−0.777620	+	0.777620i	−0.979426	−	0.201805i	$-0.935319\pi$
$487$	−17.1606	+	17.1606i	−0.777620	+	0.777620i	0.201805	+	0.979426i	$0.435319\pi$
$488$	−117.883	−	31.5866i	−5.33631	−	1.42986i
$489$		0			0
$490$	16.6058	+	65.4101i	0.750171	+	2.95493i
$491$	9.68019	−	5.58886i	0.436861	−	0.252222i	−0.265404	−	0.964137i	$-0.585505\pi$
$491$	9.68019	−	5.58886i	0.436861	−	0.252222i	0.702265	+	0.711915i	$0.252172\pi$
$492$		0			0
$493$	5.46796	+	9.47079i	0.246265	+	0.426543i
$494$	6.74666	+	11.0574i	0.303547	+	0.497494i
$495$		0			0
$496$	−2.75065	+	10.2656i	−0.123508	+	0.460937i
$497$	−3.00901	−	3.97540i	−0.134973	−	0.178321i
$498$		0			0
$499$	−10.2127	−	38.1144i	−0.457184	−	1.70623i	−0.681587	−	0.731737i	$-0.738710\pi$
$499$	−10.2127	−	38.1144i	−0.457184	−	1.70623i	0.224403	−	0.974496i	$-0.427957\pi$
$500$	−33.9317	−	33.9317i	−1.51747	−	1.51747i
$501$		0			0
$502$	−4.00284	−	14.9388i	−0.178655	−	0.666751i
$503$	7.48538	+	4.32169i	0.333757	+	0.192694i	0.657508	−	0.753448i	$-0.271611\pi$
$503$	7.48538	+	4.32169i	0.333757	+	0.192694i	−0.323751	+	0.946142i	$0.604944\pi$
$504$		0			0
$505$	−1.32275	+	4.93657i	−0.0588616	+	0.219674i
$506$	−7.50357	−	4.33219i	−0.333574	−	0.192589i
$507$		0			0
$508$	−18.5297	−	32.0945i	−0.822125	−	1.42396i
$509$	−3.95593	−	3.95593i	−0.175343	−	0.175343i	0.613979	−	0.789322i	$-0.289568\pi$
$509$	−3.95593	−	3.95593i	−0.175343	−	0.175343i	−0.789322	+	0.613979i	$0.789568\pi$
$510$		0			0
$511$	−33.4008	+	4.17355i	−1.47756	+	0.184627i
$512$	−26.6889	+	26.6889i	−1.17950	+	1.17950i
$513$		0			0
$514$	2.30249	−	2.30249i	0.101558	−	0.101558i
$515$	12.2651	−	45.7739i	0.540464	−	2.01704i
$516$		0			0
$517$	−0.207354	−	0.359147i	−0.00911940	−	0.0157953i
$518$	−6.79775	+	2.76338i	−0.298676	+	0.121416i
$519$		0			0
$520$	104.901	+	57.2191i	4.60023	+	2.50922i
$521$	−5.55782	+	3.20881i	−0.243493	+	0.140581i	−0.616781	−	0.787135i	$-0.711564\pi$
$521$	−5.55782	+	3.20881i	−0.243493	+	0.140581i	0.373288	+	0.927715i	$0.378230\pi$
$522$		0			0
$523$			31.6355i			1.38333i	0.722221	+	0.691663i	$0.243121\pi$
$523$			31.6355i			1.38333i	−0.722221	+	0.691663i	$0.756879\pi$
$524$	9.98229	−	17.2898i	0.436078	−	0.755310i
$525$		0			0
$526$	−17.0232	−	63.5316i	−0.742248	−	2.77011i
$527$	−0.267913	+	0.999863i	−0.0116705	+	0.0435547i
$528$		0			0
$529$	−28.6659			−1.24634
$530$	47.8914			2.08027
$531$		0			0
$532$	−18.8052	+	2.34978i	−0.815310	+	0.101876i
$533$	2.45430	−	10.1367i	0.106307	−	0.439070i
$534$		0			0
$535$	−6.45271	+	1.72900i	−0.278975	+	0.0747511i
$536$	−29.7895	+	51.5969i	−1.28671	+	2.22865i
$537$		0			0
$538$	−35.5814	−	35.5814i	−1.53402	−	1.53402i
$539$	1.58217	−	2.65884i	0.0681488	−	0.114524i
$540$		0			0
$541$	−18.2900	+	4.90078i	−0.786347	+	0.210701i	−0.629581	−	0.776935i	$-0.716773\pi$
$541$	−18.2900	+	4.90078i	−0.786347	+	0.210701i	−0.156766	+	0.987636i	$0.550107\pi$
$542$			2.68083i			0.115152i
$543$		0			0
$544$	−21.5727	+	21.5727i	−0.924922	+	0.924922i
$545$	26.0735			1.11686
$546$		0			0
$547$	−13.7543			−0.588091			−0.294046	−	0.955791i	$-0.595002\pi$
$547$	−13.7543			−0.588091			−0.294046	+	0.955791i	$0.595002\pi$
$548$	30.3097	−	30.3097i	1.29477	−	1.29477i
$549$		0			0
$550$			9.03628i			0.385308i
$551$	−9.72373	+	2.60546i	−0.414245	+	0.110997i
$552$		0			0
$553$	−1.28406	+	9.28039i	−0.0546039	+	0.394643i
$554$	34.8038	+	34.8038i	1.47867	+	1.47867i
$555$		0			0
$556$	32.4056	−	56.1281i	1.37430	−	2.38036i
$557$	−16.6591	+	4.46378i	−0.705867	+	0.189137i	−0.593857	−	0.804571i	$-0.702396\pi$
$557$	−16.6591	+	4.46378i	−0.705867	+	0.189137i	−0.112010	+	0.993707i	$0.535729\pi$
$558$		0			0
$559$	26.3253	+	14.3593i	1.11344	+	0.607334i
$560$	−109.568	+	82.9329i	−4.63009	+	3.50456i
$561$		0			0
$562$	59.4678			2.50850
$563$	−33.0554			−1.39312			−0.696559	−	0.717499i	$-0.745287\pi$
$563$	−33.0554			−1.39312			−0.696559	+	0.717499i	$0.745287\pi$
$564$		0			0
$565$	5.66127	−	21.1282i	0.238172	−	0.888868i
$566$	−19.3912	−	72.3688i	−0.815071	−	3.04189i
$567$		0			0
$568$	8.83340	−	15.2999i	0.370641	−	0.641969i
$569$		−	32.9428i		−	1.38104i	−0.723316	−	0.690518i	$-0.757383\pi$
$569$		−	32.9428i		−	1.38104i	0.723316	−	0.690518i	$-0.242617\pi$
$570$		0			0
$571$	6.40074	−	3.69547i	0.267862	−	0.154650i	−0.360053	−	0.932932i	$-0.617242\pi$
$571$	6.40074	−	3.69547i	0.267862	−	0.154650i	0.627916	+	0.778281i	$0.283908\pi$
$572$	−2.44513	−	8.31348i	−0.102236	−	0.347604i
$573$		0			0
$574$	16.4747	+	12.8149i	0.687640	+	0.534882i
$575$	26.9418	+	46.6645i	1.12355	+	1.94605i
$576$		0			0
$577$	−10.1455	+	37.8634i	−0.422362	+	1.57627i	0.347257	+	0.937770i	$0.387113\pi$
$577$	−10.1455	+	37.8634i	−0.422362	+	1.57627i	−0.769618	+	0.638505i	$0.779553\pi$
$578$	28.8340	−	28.8340i	1.19934	−	1.19934i
$579$		0			0
$580$	−103.870	+	103.870i	−4.31297	+	4.31297i
$581$	−8.04285	−	3.39373i	−0.333674	−	0.140796i
$582$		0			0
$583$	−1.55257	−	1.55257i	−0.0643009	−	0.0643009i
$584$	−59.6371	−	103.294i	−2.46780	−	4.27435i
$585$		0			0
$586$	18.5401	+	10.7041i	0.765886	+	0.442184i
$587$	−5.58839	+	20.8562i	−0.230658	+	0.860826i	0.749401	+	0.662117i	$0.230342\pi$
$587$	−5.58839	+	20.8562i	−0.230658	+	0.860826i	−0.980058	+	0.198709i	$0.936325\pi$
$588$		0			0
$589$	−0.825203	−	0.476431i	−0.0340019	−	0.0196310i
$590$	8.11599	+	30.2893i	0.334130	+	1.24699i
$591$		0			0
$592$	−10.5655	−	10.5655i	−0.434238	−	0.434238i
$593$	7.82600	+	29.2070i	0.321375	+	1.19939i	0.917906	+	0.396799i	$0.129879\pi$
$593$	7.82600	+	29.2070i	0.321375	+	1.19939i	−0.596530	+	0.802591i	$0.703454\pi$
$594$		0			0
$595$	−10.6719	+	8.07765i	−0.437505	+	0.331152i
$596$	30.6413	−	114.355i	1.25512	−	4.68416i
$597$		0			0
$598$	−51.1748	−	48.7510i	−2.09269	−	1.99358i
$599$	−9.06280	−	15.6972i	−0.370296	−	0.641371i	0.619315	−	0.785143i	$-0.287410\pi$
$599$	−9.06280	−	15.6972i	−0.370296	−	0.641371i	−0.989611	+	0.143771i	$0.954077\pi$
$600$		0			0
$601$	−30.9648	+	17.8775i	−1.26308	+	0.729240i	−0.973669	−	0.227965i	$-0.926793\pi$
$601$	−30.9648	+	17.8775i	−1.26308	+	0.729240i	−0.289411	+	0.957205i	$0.593459\pi$
$602$	−47.8490	+	36.2174i	−1.95018	+	1.47611i
$603$		0			0
$604$	73.3283	+	19.6483i	2.98369	+	0.799476i
$605$	−27.0077	+	27.0077i	−1.09802	+	1.09802i
$606$		0			0
$607$	3.30264	−	1.90678i	0.134050	−	0.0773937i	−0.431475	−	0.902125i	$-0.642007\pi$
$607$	3.30264	−	1.90678i	0.134050	−	0.0773937i	0.565525	+	0.824731i	$0.308673\pi$
$608$	−14.0418	−	24.3211i	−0.569470	−	0.986352i
$609$		0			0
$610$		−	125.500i		−	5.08133i
$611$	−0.954550	−	3.24548i	−0.0386170	−	0.131298i
$612$		0			0
$613$	1.06673	+	3.98111i	0.0430850	+	0.160795i	0.984117	−	0.177523i	$-0.0568085\pi$
$613$	1.06673	+	3.98111i	0.0430850	+	0.160795i	−0.941032	+	0.338319i	$0.890142\pi$
$614$		−	62.1811i		−	2.50942i
$615$		0			0
$616$	10.8598	+	1.50260i	0.437556	+	0.0605415i
$617$	−4.26184	−	15.9054i	−0.171575	−	0.640327i	−0.997110	−	0.0759754i	$-0.975793\pi$
$617$	−4.26184	−	15.9054i	−0.171575	−	0.640327i	0.825535	−	0.564351i	$-0.190874\pi$
$618$		0			0
$619$	9.82581	+	2.63282i	0.394933	+	0.105822i	0.450819	−	0.892615i	$-0.351132\pi$
$619$	9.82581	+	2.63282i	0.394933	+	0.105822i	−0.0558866	+	0.998437i	$0.517799\pi$
$620$	−13.9042			−0.558407
$621$		0			0
$622$	−14.5191	−	3.89037i	−0.582161	−	0.155990i
$623$	−10.7611	+	25.5030i	−0.431135	+	1.02176i
$624$		0			0
$625$	−3.14284	+	5.44356i	−0.125714	+	0.217743i
$626$	−51.1330	+	13.7010i	−2.04369	+	0.547604i
$627$		0			0
$628$	−40.7146	−	70.5198i	−1.62469	−	2.81405i
$629$	−1.02907	−	1.02907i	−0.0410318	−	0.0410318i
$630$		0			0
$631$	−35.7618	+	9.58236i	−1.42366	+	0.381468i	−0.886779	−	0.462193i	$-0.847063\pi$
$631$	−35.7618	+	9.58236i	−1.42366	+	0.381468i	−0.536877	+	0.843661i	$0.680396\pi$
$632$	−32.0666	+	8.59222i	−1.27554	+	0.341780i
$633$		0			0
$634$	66.3156	+	38.2873i	2.63373	+	1.52058i
$635$	17.0361	−	17.0361i	0.676055	−	0.676055i
$636$		0			0
$637$	17.6479	−	18.0430i	0.699236	−	0.714891i
$638$	9.21169			0.364694
$639$		0			0
$640$	−109.558	−	63.2531i	−4.33064	−	2.50030i
$641$			30.1425i			1.19056i	0.803520	+	0.595278i	$0.202958\pi$
$641$			30.1425i			1.19056i	−0.803520	+	0.595278i	$0.797042\pi$
$642$		0			0
$643$	36.7921	−	9.85840i	1.45094	−	0.388778i	0.554588	−	0.832125i	$-0.312876\pi$
$643$	36.7921	−	9.85840i	1.45094	−	0.388778i	0.896350	+	0.443348i	$0.146209\pi$
$644$	95.7964	−	38.9425i	3.77491	−	1.53455i
$645$		0			0
$646$	−2.57054	−	4.45230i	−0.101136	−	0.175173i
$647$	19.3901	−	33.5847i	0.762305	−	1.32035i	−0.179354	−	0.983785i	$-0.557401\pi$
$647$	19.3901	−	33.5847i	0.762305	−	1.32035i	0.941660	−	0.336567i	$-0.109266\pi$
$648$		0			0
$649$	0.718826	−	1.24504i	0.0282164	−	0.0488722i
$650$	−17.3461	+	71.6428i	−0.680371	+	2.81006i
$651$		0			0
$652$	46.4600	+	12.4489i	1.81952	+	0.487538i
$653$	13.0170			0.509396			0.254698	−	0.967021i	$-0.418024\pi$
$653$	13.0170			0.509396			0.254698	+	0.967021i	$0.418024\pi$
$654$		0			0
$655$	12.5368	+	3.35924i	0.489855	+	0.131256i
$656$	−10.9998	+	41.0519i	−0.429471	+	1.60281i
$657$		0			0
$658$	6.70612	+	0.927878i	0.261432	+	0.0361725i
$659$	−25.0015	+	43.3039i	−0.973921	+	1.68688i	−0.290470	+	0.956884i	$0.593812\pi$
$659$	−25.0015	+	43.3039i	−0.973921	+	1.68688i	−0.683451	+	0.729996i	$0.739522\pi$
$660$		0			0
$661$	3.33584	+	12.4495i	0.129749	+	0.484231i	0.999964	−	0.00844118i	$-0.00268694\pi$
$661$	3.33584	+	12.4495i	0.129749	+	0.484231i	−0.870215	+	0.492672i	$0.836020\pi$
$662$	17.9333	−	10.3538i	0.696999	−	0.402413i
$663$		0			0
$664$		−	30.9326i		−	1.20042i
$665$	−4.63972	−	11.4134i	−0.179921	−	0.442595i
$666$		0			0
$667$	47.5704	−	27.4648i	1.84193	−	1.06344i
$668$	0.482758	−	1.80168i	0.0186785	−	0.0697090i
$669$		0			0
$670$	−59.1797	−	15.8572i	−2.28631	−	0.612615i
$671$	−4.06852	+	4.06852i	−0.157063	+	0.157063i
$672$		0			0
$673$	34.5128	−	19.9259i	1.33037	−	0.768089i	0.345013	−	0.938598i	$-0.387875\pi$
$673$	34.5128	−	19.9259i	1.33037	−	0.768089i	0.985356	+	0.170509i	$0.0545413\pi$
$674$	−6.29029	−	6.29029i	−0.242293	−	0.242293i
$675$		0			0
$676$	−3.42724	−	70.6059i	−0.131817	−	2.71561i
$677$	3.61272	+	2.08580i	0.138848	+	0.0801640i	0.567815	−	0.823156i	$-0.307789\pi$
$677$	3.61272	+	2.08580i	0.138848	+	0.0801640i	−0.428967	+	0.903320i	$0.641122\pi$
$678$		0			0
$679$	−5.49307	+	4.15775i	−0.210805	+	0.159560i
$680$	−41.0723	−	23.7131i	−1.57505	−	0.909357i
$681$		0			0
$682$	0.616546	+	0.616546i	0.0236088	+	0.0236088i
$683$	−4.99136	−	4.99136i	−0.190989	−	0.190989i	0.605134	−	0.796123i	$-0.293119\pi$
$683$	−4.99136	−	4.99136i	−0.190989	−	0.190989i	−0.796123	+	0.605134i	$0.793119\pi$
$684$		0			0
$685$	24.1330	+	13.9332i	0.922075	+	0.532360i
$686$	18.4024	+	47.0367i	0.702609	+	1.79587i
$687$		0			0
$688$	−105.824	−	61.0974i	−4.03450	−	2.32932i
$689$	−9.32899	−	15.2896i	−0.355406	−	0.582489i
$690$		0			0
$691$	−15.9631	−	15.9631i	−0.607264	−	0.607264i	0.334966	−	0.942230i	$-0.391275\pi$
$691$	−15.9631	−	15.9631i	−0.607264	−	0.607264i	−0.942230	+	0.334966i	$0.891275\pi$
$692$	−43.5627	+	25.1510i	−1.65601	+	0.956096i
$693$		0			0
$694$	−59.7165	+	59.7165i	−2.26681	+	2.26681i
$695$	40.6985	+	10.9051i	1.54378	+	0.413655i
$696$		0			0
$697$	−1.07138	+	3.99845i	−0.0405815	+	0.151452i
$698$	28.6337	−	16.5317i	1.08380	−	0.625734i
$699$		0			0
$700$	−85.1270	−	66.2161i	−3.21750	−	2.50273i
$701$			38.0674i			1.43779i	0.695120	+	0.718894i	$0.255351\pi$
$701$			38.0674i			1.43779i	−0.695120	+	0.718894i	$0.744649\pi$
$702$		0			0
$703$	1.16018	−	0.669830i	0.0437570	−	0.0252631i
$704$	3.28965	+	12.2771i	0.123983	+	0.462712i
$705$		0			0
$706$	−40.0960	+	69.4484i	−1.50903	+	2.61372i
$707$	−0.524251	+	3.78896i	−0.0197165	+	0.142498i
$708$		0			0
$709$	−0.469956	+	1.75390i	−0.0176496	+	0.0658691i	−0.974189	−	0.225734i	$-0.927522\pi$
$709$	−0.469956	+	1.75390i	−0.0176496	+	0.0658691i	0.956539	+	0.291603i	$0.0941886\pi$
$710$	17.5484	+	4.70208i	0.658579	+	0.176466i
$711$		0			0
$712$	−98.0838			−3.67584
$713$	5.02216	+	1.34568i	0.188081	+	0.0503963i
$714$		0			0
$715$	4.80907	−	2.93426i	0.179849	−	0.109735i
$716$	39.7092	−	68.7784i	1.48400	−	2.57037i
$717$		0			0
$718$	12.6959	−	21.9899i	0.473806	−	0.820656i
$719$	−13.7958	−	23.8950i	−0.514496	−	0.891133i	−0.999859	−	0.0168198i	$-0.994646\pi$
$719$	−13.7958	−	23.8950i	−0.514496	−	0.891133i	0.485363	−	0.874313i	$-0.338688\pi$
$720$		0			0
$721$	4.86107	−	35.1328i	0.181036	−	1.30841i
$722$	−45.4800	+	12.1863i	−1.69259	+	0.453528i
$723$		0			0
$724$			46.9705i			1.74564i
$725$	−49.6123	−	28.6437i	−1.84255	−	1.06380i
$726$		0			0
$727$	1.57479			0.0584058			0.0292029	−	0.999574i	$-0.490703\pi$
$727$	1.57479			0.0584058			0.0292029	+	0.999574i	$0.490703\pi$
$728$	83.2163	+	32.7598i	3.08420	+	1.21416i
$729$		0			0
$730$	86.7295	−	86.7295i	3.21000	−	3.21000i
$731$	−10.3072	−	5.95088i	−0.381226	−	0.220101i
$732$		0			0
$733$	−37.5443	+	10.0600i	−1.38673	+	0.371574i	−0.873562	−	0.486713i	$-0.838196\pi$
$733$	−37.5443	+	10.0600i	−1.38673	+	0.371574i	−0.513170	+	0.858287i	$0.671529\pi$
$734$	−66.4456	+	17.8040i	−2.45255	+	0.657159i
$735$		0			0
$736$	108.356	+	108.356i	3.99407	+	3.99407i
$737$	1.40445	+	2.43259i	0.0517337	+	0.0896055i
$738$		0			0
$739$	−42.2979	+	11.3337i	−1.55595	+	0.416917i	−0.931380	−	0.364049i	$-0.881394\pi$
$739$	−42.2979	+	11.3337i	−1.55595	+	0.416917i	−0.624574	+	0.780966i	$0.714727\pi$
$740$	9.77420	−	16.9294i	0.359307	−	0.622337i
$741$		0			0
$742$	35.5672	−	4.44425i	1.30571	−	0.163154i
$743$	−18.3147	−	4.90740i	−0.671900	−	0.180035i	−0.0932893	−	0.995639i	$-0.529738\pi$
$743$	−18.3147	−	4.90740i	−0.671900	−	0.180035i	−0.578610	+	0.815604i	$0.696405\pi$
$744$		0			0
$745$	76.9655			2.81980
$746$	−2.76160	−	0.739970i	−0.101110	−	0.0270922i
$747$		0			0
$748$	0.890174	+	3.32217i	0.0325480	+	0.121471i
$749$	−4.63174	+	1.88286i	−0.169240	+	0.0687984i
$750$		0			0
$751$		−	11.4855i		−	0.419110i	−0.977797	−	0.209555i	$-0.932798\pi$
$751$		−	11.4855i		−	0.419110i	0.977797	−	0.209555i	$-0.0672016\pi$
$752$	3.56790	+	13.3156i	0.130108	+	0.485570i
$753$		0			0
$754$	73.0335	+	17.6828i	2.65972	+	0.643971i
$755$			49.3529i			1.79613i
$756$		0			0
$757$	0.505532	+	0.875607i	0.0183739	+	0.0318245i	0.875066	−	0.484003i	$-0.160818\pi$
$757$	0.505532	+	0.875607i	0.0183739	+	0.0318245i	−0.856692	+	0.515828i	$0.827484\pi$
$758$	37.4122	−	21.5999i	1.35887	−	0.784545i
$759$		0			0
$760$	30.8700	−	30.8700i	1.11977	−	1.11977i
$761$	−44.9154	−	12.0351i	−1.62818	−	0.436270i	−0.674792	−	0.738008i	$-0.735767\pi$
$761$	−44.9154	−	12.0351i	−1.62818	−	0.436270i	−0.953391	+	0.301737i	$0.902433\pi$
$762$		0			0
$763$	19.3638	−	2.41958i	0.701017	−	0.0875946i
$764$	−33.1909	+	19.1628i	−1.20080	+	0.693285i
$765$		0			0
$766$	35.4216	+	61.3520i	1.27983	+	2.21674i
$767$	8.08910	−	8.49127i	0.292080	−	0.306602i
$768$		0			0
$769$	10.0112	−	37.3624i	0.361014	−	1.34732i	−0.511730	−	0.859146i	$-0.670995\pi$
$769$	10.0112	−	37.3624i	0.361014	−	1.34732i	0.872745	−	0.488177i	$-0.162338\pi$
$770$	1.39786	+	11.1870i	0.0503752	+	0.403151i
$771$		0			0
$772$	32.5256	+	121.387i	1.17062	+	4.36882i
$773$	21.0972	+	21.0972i	0.758814	+	0.758814i	0.976107	−	0.217293i	$-0.0697226\pi$
$773$	21.0972	+	21.0972i	0.758814	+	0.758814i	−0.217293	+	0.976107i	$0.569723\pi$
$774$		0			0
$775$	−1.40345	−	5.23773i	−0.0504133	−	0.188145i
$776$	−21.1409	−	12.2057i	−0.758913	−	0.438158i
$777$		0			0
$778$	16.3412	−	60.9862i	0.585861	−	2.18646i
$779$	−3.29998	−	1.90525i	−0.118234	−	0.0682625i
$780$		0			0
$781$	−0.416459	−	0.721328i	−0.0149021	−	0.0258111i
$782$	19.8361	+	19.8361i	0.709336	+	0.709336i
$783$		0			0
$784$	−73.6760	+	71.7590i	−2.63129	+	2.56282i
$785$	37.4326	−	37.4326i	1.33603	−	1.33603i
$786$		0			0
$787$	3.12615	−	3.12615i	0.111435	−	0.111435i	−0.649191	−	0.760626i	$-0.724892\pi$
$787$	3.12615	−	3.12615i	0.111435	−	0.111435i	0.760626	+	0.649191i	$0.224892\pi$
$788$	27.3487	−	102.067i	0.974258	−	3.63598i
$789$		0			0
$790$	−17.0693	−	29.5649i	−0.607298	−	1.05187i
$791$	2.24376	−	16.2165i	0.0797788	−	0.576591i
$792$		0			0
$793$	−40.0666	+	24.4467i	−1.42281	+	0.868127i
$794$	27.9221	−	16.1209i	0.990920	−	0.572108i
$795$		0			0
$796$		−	96.8480i		−	3.43269i
$797$	8.62284	−	14.9352i	0.305437	−	0.529032i	−0.671922	−	0.740622i	$-0.734531\pi$
$797$	8.62284	−	14.9352i	0.305437	−	0.529032i	0.977358	+	0.211590i	$0.0678642\pi$
$798$		0			0
$799$	0.347513	+	1.29694i	0.0122941	+	0.0458823i
$800$	41.3636	−	154.371i	1.46243	−	5.45785i
$801$		0			0
$802$	56.8121			2.00611
$803$	−5.62329			−0.198442
$804$		0			0
$805$	40.5728	+	53.6033i	1.43000	+	1.88927i
$806$	3.70466	+	6.07172i	0.130491	+	0.213867i
$807$		0			0
$808$	−13.0920	+	3.50799i	−0.460575	+	0.123411i
$809$	11.7999	−	20.4380i	0.414862	−	0.718562i	−0.580552	−	0.814223i	$-0.697163\pi$
$809$	11.7999	−	20.4380i	0.414862	−	0.718562i	0.995414	+	0.0956610i	$0.0304965\pi$
$810$		0			0
$811$	16.8186	+	16.8186i	0.590582	+	0.590582i	0.937789	−	0.347207i	$-0.112870\pi$
$811$	16.8186	+	16.8186i	0.590582	+	0.590582i	−0.347207	+	0.937789i	$0.612870\pi$
$812$	−67.5015	+	86.7794i	−2.36884	+	3.04536i
$813$		0			0
$814$	−1.18410	+	0.317279i	−0.0415027	+	0.0111206i
$815$			31.2695i			1.09532i
$816$		0			0
$817$	7.74693	−	7.74693i	0.271031	−	0.271031i
$818$	43.3659			1.51625
$819$		0			0
$820$	−55.6029			−1.94174
$821$	−12.7007	+	12.7007i	−0.443259	+	0.443259i	−0.893106	−	0.449847i	$-0.851479\pi$
$821$	−12.7007	+	12.7007i	−0.443259	+	0.443259i	0.449847	+	0.893106i	$0.351479\pi$
$822$		0			0
$823$			27.7997i			0.969035i	0.874782	+	0.484518i	$0.161005\pi$
$823$			27.7997i			0.969035i	−0.874782	+	0.484518i	$0.838995\pi$
$824$	121.395	−	32.5276i	4.22898	−	1.13315i
$825$		0			0
$826$	8.83824	+	21.7416i	0.307522	+	0.756486i
$827$	19.2095	+	19.2095i	0.667980	+	0.667980i	0.957248	−	0.289268i	$-0.0934119\pi$
$827$	19.2095	+	19.2095i	0.667980	+	0.667980i	−0.289268	+	0.957248i	$0.593412\pi$
$828$		0			0
$829$	20.1884	−	34.9673i	0.701170	−	1.21446i	−0.266885	−	0.963728i	$-0.585995\pi$
$829$	20.1884	−	34.9673i	0.701170	−	1.21446i	0.968056	−	0.250735i	$-0.0806722\pi$
$830$	30.7253	−	8.23281i	1.06649	−	0.285765i
$831$		0			0
$832$	2.51419	+	103.652i	0.0871637	+	3.59350i
$833$	−7.17603	+	6.98931i	−0.248635	+	0.242165i
$834$		0			0
$835$	1.21260			0.0419638
$836$	−3.16601			−0.109499
$837$		0			0
$838$	−3.49759	+	13.0532i	−0.120822	+	0.450915i
$839$	3.20470	+	11.9601i	0.110638	+	0.412908i	0.998924	−	0.0463840i	$-0.0147698\pi$
$839$	3.20470	+	11.9601i	0.110638	+	0.412908i	−0.888285	+	0.459292i	$0.848103\pi$
$840$		0			0
$841$	−14.6997	+	25.4606i	−0.506885	+	0.877951i
$842$			3.12877i			0.107824i
$843$		0			0
$844$	−47.4535	+	27.3973i	−1.63342	+	0.943055i
$845$	43.7606	−	14.0323i	1.50541	−	0.482725i
$846$		0			0
$847$	−17.5514	+	22.5639i	−0.603072	+	0.775306i
$848$	36.4932	+	63.2080i	1.25318	+	2.17057i
$849$		0			0
$850$	7.57215	−	28.2597i	0.259723	−	0.969298i
$851$	−5.16888	+	5.16888i	−0.177187	+	0.177187i
$852$		0			0
$853$	30.9345	−	30.9345i	1.05918	−	1.05918i	0.0610421	−	0.998135i	$-0.480558\pi$
$853$	30.9345	−	30.9345i	1.05918	−	1.05918i	0.998135	−	0.0610421i	$-0.0194424\pi$
$854$	−11.6462	−	93.2040i	−0.398524	−	3.18937i
$855$		0			0
$856$	−12.5275	−	12.5275i	−0.428181	−	0.428181i
$857$	−4.46536	−	7.73423i	−0.152534	−	0.264196i	0.779624	−	0.626247i	$-0.215410\pi$
$857$	−4.46536	−	7.73423i	−0.152534	−	0.264196i	−0.932158	+	0.362051i	$0.882077\pi$
$858$		0			0
$859$	21.5650	+	12.4506i	0.735789	+	0.424808i	0.820536	−	0.571594i	$-0.193675\pi$
$859$	21.5650	+	12.4506i	0.735789	+	0.424808i	−0.0847471	+	0.996402i	$0.527008\pi$
$860$	41.3768	−	154.420i	1.41094	−	5.26569i
$861$		0			0
$862$	−48.4163	−	27.9532i	−1.64907	−	0.952089i
$863$	−4.57987	−	17.0923i	−0.155900	−	0.581829i	−0.999027	−	0.0441126i	$-0.985954\pi$
$863$	−4.57987	−	17.0923i	−0.155900	−	0.581829i	0.843126	−	0.537716i	$-0.180713\pi$
$864$		0			0
$865$	−23.1235	−	23.1235i	−0.786223	−	0.786223i
$866$	−0.347450	−	1.29670i	−0.0118068	−	0.0440638i
$867$		0			0
$868$	−10.3261	+	1.29029i	−0.350492	+	0.0437953i
$869$	−0.405088	+	1.51181i	−0.0137417	+	0.0512847i
$870$		0			0
$871$	6.46539	+	21.9824i	0.219071	+	0.744845i
$872$	34.5740	+	59.8840i	1.17082	+	2.02793i
$873$		0			0
$874$	−22.3632	+	12.9114i	−0.756447	+	0.436735i
$875$	9.07710	−	21.5120i	0.306862	−	0.727237i
$876$		0			0
$877$	−2.49405	−	0.668278i	−0.0842180	−	0.0225662i	0.216464	−	0.976291i	$-0.430548\pi$
$877$	−2.49405	−	0.668278i	−0.0842180	−	0.0225662i	−0.300682	+	0.953724i	$0.597214\pi$
$878$	−43.1547	+	43.1547i	−1.45640	+	1.45640i
$879$		0			0
$880$	−19.8809	+	11.4782i	−0.670184	+	0.386931i
$881$	5.24887	+	9.09131i	0.176839	+	0.306294i	0.940796	−	0.338973i	$-0.110079\pi$
$881$	5.24887	+	9.09131i	0.176839	+	0.306294i	−0.763957	+	0.645267i	$0.776746\pi$
$882$		0			0
$883$			0.987737i			0.0332400i	0.999862	+	0.0166200i	$0.00529056\pi$
$883$			0.987737i			0.0332400i	−0.999862	+	0.0166200i	$0.994709\pi$
$884$	0.680334	+	28.0481i	0.0228821	+	0.943361i
$885$		0			0
$886$	−6.73975	−	25.1531i	−0.226426	−	0.845035i
$887$			39.8664i			1.33858i	0.743001	+	0.669291i	$0.233402\pi$
$887$			39.8664i			1.33858i	−0.743001	+	0.669291i	$0.766598\pi$
$888$		0			0
$889$	11.0711	−	14.2330i	0.371314	−	0.477358i
$890$	−26.1053	−	97.4264i	−0.875052	−	3.26574i
$891$		0			0
$892$	−4.99594	−	1.33866i	−0.167276	−	0.0448216i
$893$	−1.23597			−0.0413602
$894$		0			0
$895$	49.8712	+	13.3629i	1.66701	+	0.446674i
$896$	−87.2341	−	36.8090i	−2.91429	−	1.22970i
$897$		0			0
$898$	−24.2635	+	42.0256i	−0.809684	+	1.40241i
$899$	−5.33940	+	1.43069i	−0.178079	+	0.0477162i
$900$		0			0
$901$	3.55443	+	6.15645i	0.118415	+	0.205101i
$902$	2.46556	+	2.46556i	0.0820943	+	0.0820943i
$903$		0			0
$904$	56.0329	−	15.0140i	1.86362	−	0.499357i
$905$	−29.4953	+	7.90325i	−0.980458	+	0.262713i
$906$		0			0
$907$	7.90175	+	4.56208i	0.262373	+	0.151481i	0.625417	−	0.780291i	$-0.284929\pi$
$907$	7.90175	+	4.56208i	0.262373	+	0.151481i	−0.363043	+	0.931772i	$0.618262\pi$
$908$	−94.3048	+	94.3048i	−3.12962	+	3.12962i
$909$		0			0
$910$	−10.3920	+	91.3777i	−0.344490	+	3.02914i
$911$	−28.0053			−0.927856			−0.463928	−	0.885873i	$-0.653560\pi$
$911$	−28.0053			−0.927856			−0.463928	+	0.885873i	$0.653560\pi$
$912$		0			0
$913$	−1.26296	−	0.729173i	−0.0417980	−	0.0241321i
$914$		−	75.1299i		−	2.48508i
$915$		0			0
$916$	−108.363	+	29.0357i	−3.58040	+	0.959366i
$917$	9.62239	+	1.33138i	0.317759	+	0.0439661i
$918$		0			0
$919$	−6.25029	−	10.8258i	−0.206178	−	0.357111i	0.744329	−	0.667813i	$-0.232769\pi$
$919$	−6.25029	−	10.8258i	−0.206178	−	0.357111i	−0.950507	+	0.310702i	$0.899436\pi$
$920$	−119.107	+	206.300i	−3.92686	+	6.80151i
$921$		0			0
$922$	−14.2466	+	24.6758i	−0.469186	+	0.812654i
$923$	−1.91716	−	6.51838i	−0.0631042	−	0.214555i
$924$		0			0
$925$	7.36390	+	1.97315i	0.242124	+	0.0648768i
$926$	41.3808			1.35986
$927$		0			0
$928$	−157.368	−	42.1666i	−5.16585	−	1.38418i
$929$	6.56236	−	24.4911i	0.215304	−	0.803525i	−0.770755	−	0.637131i	$-0.780121\pi$
$929$	6.56236	−	24.4911i	0.215304	−	0.803525i	0.986059	−	0.166394i	$-0.0532124\pi$
$930$		0			0
$931$	−4.50490	−	8.04579i	−0.147642	−	0.263690i
$932$	−61.8169	+	107.070i	−2.02488	+	3.50719i
$933$		0			0
$934$	10.0088	+	37.3533i	0.327497	+	1.22224i
$935$	−1.93639	+	1.11798i	−0.0633269	+	0.0365618i
$936$		0			0
$937$		−	27.8676i		−	0.910396i	−0.890390	−	0.455198i	$-0.849569\pi$
$937$		−	27.8676i		−	0.910396i	0.890390	−	0.455198i	$-0.150431\pi$
$938$	−45.4221	−	6.28474i	−1.48308	−	0.205204i
$939$		0			0
$940$	−15.6191	+	9.01768i	−0.509438	+	0.294124i
$941$	3.72461	−	13.9004i	0.121419	−	0.453141i	−0.878268	−	0.478169i	$-0.841301\pi$
$941$	3.72461	−	13.9004i	0.121419	−	0.453141i	0.999687	+	0.0250276i	$0.00796737\pi$
$942$		0			0
$943$	20.0836	+	5.38139i	0.654012	+	0.175242i
$944$	−33.7920	+	33.7920i	−1.09984	+	1.09984i
$945$		0			0
$946$	−8.68211	+	5.01262i	−0.282280	+	0.162974i
$947$	9.13292	+	9.13292i	0.296780	+	0.296780i	0.839751	−	0.542971i	$-0.182701\pi$
$947$	9.13292	+	9.13292i	0.296780	+	0.296780i	−0.542971	+	0.839751i	$0.682701\pi$
$948$		0			0
$949$	−44.5834	−	10.7945i	−1.44724	−	0.350405i
$950$	23.3231	+	13.4656i	0.756703	+	0.436882i
$951$		0			0
$952$	−32.7035	−	13.7994i	−1.05992	−	0.447241i
$953$	52.8130	+	30.4916i	1.71078	+	0.987720i	0.933507	+	0.358559i	$0.116732\pi$
$953$	52.8130	+	30.4916i	1.71078	+	0.987720i	0.777275	+	0.629161i	$0.216601\pi$
$954$		0			0
$955$	−17.6181	−	17.6181i	−0.570107	−	0.570107i
$956$	112.907	+	112.907i	3.65167	+	3.65167i
$957$		0			0
$958$	−59.2734	−	34.2215i	−1.91504	−	1.10565i
$959$	19.2157	+	8.10817i	0.620507	+	0.261826i
$960$		0			0
$961$	26.3937	+	15.2384i	0.851408	+	0.491561i
$962$	−9.99702	+	0.242487i	−0.322317	+	0.00781810i
$963$		0			0
$964$	26.0756	+	26.0756i	0.839838	+	0.839838i
$965$	−70.7530	+	40.8492i	−2.27762	+	1.31498i
$966$		0			0
$967$	33.5388	−	33.5388i	1.07853	−	1.07853i	0.0818928	−	0.996641i	$-0.473903\pi$
$967$	33.5388	−	33.5388i	1.07853	−	1.07853i	0.996641	−	0.0818928i	$-0.0260965\pi$
$968$	−97.8426	−	26.2169i	−3.14478	−	0.842642i
$969$		0			0
$970$	6.49717	−	24.2478i	0.208611	−	0.778548i
$971$	−11.8250	+	6.82715i	−0.379481	+	0.219094i	−0.677593	−	0.735437i	$-0.736977\pi$
$971$	−11.8250	+	6.82715i	−0.379481	+	0.219094i	0.298111	+	0.954531i	$0.403643\pi$
$972$		0			0
$973$	31.2372	+	4.32208i	1.00142	+	0.138559i
$974$		−	66.1857i		−	2.12073i
$975$		0			0
$976$	165.637	−	95.6305i	5.30191	−	3.06106i
$977$	7.88141	+	29.4138i	0.252149	+	0.941032i	0.969654	+	0.244479i	$0.0786170\pi$
$977$	7.88141	+	29.4138i	0.252149	+	0.941032i	−0.717506	+	0.696553i	$0.754716\pi$
$978$		0			0
$979$	−2.31213	+	4.00472i	−0.0738959	+	0.127991i
$980$	−115.631	−	68.8075i	−3.69370	−	2.19797i
$981$		0			0
$982$	−7.88981	+	29.4452i	−0.251774	+	0.939633i
$983$	3.36354	+	0.901257i	0.107280	+	0.0287456i	0.312060	−	0.950062i	$-0.398981\pi$
$983$	3.36354	+	0.901257i	0.107280	+	0.0287456i	−0.204780	+	0.978808i	$0.565648\pi$
$984$		0			0
$985$	68.6950			2.18881
$986$	−28.8082	−	7.71914i	−0.917440	−	0.245827i
$987$		0			0
$988$	−25.1012	−	6.07750i	−0.798576	−	0.193351i
$989$	−29.8904	+	51.7716i	−0.950458	+	1.64624i
$990$		0			0
$991$	13.5061	−	23.3933i	0.429036	−	0.743113i	−0.567751	−	0.823200i	$-0.692187\pi$
$991$	13.5061	−	23.3933i	0.429036	−	0.743113i	0.996788	+	0.0800871i	$0.0255199\pi$
$992$	−7.71051	−	13.3550i	−0.244809	−	0.424021i
$993$		0			0
$994$	13.4689	+	1.86359i	0.427207	+	0.0591096i
$995$	60.8162	−	16.2956i	1.92800	−	0.516607i
$996$		0			0
$997$			20.9195i			0.662526i	0.943538	+	0.331263i	$0.107475\pi$
$997$			20.9195i			0.662526i	−0.943538	+	0.331263i	$0.892525\pi$
$998$	93.1950	+	53.8061i	2.95004	+	1.70320i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.145.1		36
3.2	odd	2		273.2.bt.a.145.9	✓	36
7.3	odd	6		819.2.gh.c.262.1		36
13.7	odd	12		819.2.gh.c.397.1		36
21.17	even	6		273.2.cg.a.262.9	yes	36
39.20	even	12		273.2.cg.a.124.9	yes	36
91.59	even	12	inner	819.2.et.c.514.1		36
273.59	odd	12		273.2.bt.a.241.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.9	✓	36	3.2	odd	2
273.2.bt.a.241.9	yes	36	273.59	odd	12
273.2.cg.a.124.9	yes	36	39.20	even	12
273.2.cg.a.262.9	yes	36	21.17	even	6
819.2.et.c.145.1		36	1.1	even	1	trivial
819.2.et.c.514.1		36	91.59	even	12	inner
819.2.gh.c.262.1		36	7.3	odd	6
819.2.gh.c.397.1		36	13.7	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92842 + 1.92842i) q^{2} -5.43762i q^{4} +(3.41458 - 0.914933i) q^{5} +(2.45097 - 0.996354i) q^{7} +(6.62917 + 6.62917i) q^{8} +O(q^{10})\)	\(q+(-1.92842 + 1.92842i) q^{2} -5.43762i q^{4} +(3.41458 - 0.914933i) q^{5} +(2.45097 - 0.996354i) q^{7} +(6.62917 + 6.62917i) q^{8} +(-4.82036 + 8.34912i) q^{10} +(0.426935 - 0.114397i) q^{11} +(3.60449 - 0.0874303i) q^{13} +(-2.80512 + 6.64790i) q^{14} -14.6924 q^{16} -1.43104 q^{17} +(0.340943 - 1.27242i) q^{19} +(-4.97505 - 18.5671i) q^{20} +(-0.602706 + 1.04392i) q^{22} +7.18790i q^{23} +(6.49210 - 3.74822i) q^{25} +(-6.78237 + 7.11958i) q^{26} +(-5.41779 - 13.3275i) q^{28} +(-3.82097 - 6.61812i) q^{29} +(0.187215 - 0.698697i) q^{31} +(15.0748 - 15.0748i) q^{32} +(2.75965 - 2.75965i) q^{34} +(7.45744 - 5.64460i) q^{35} +(0.719109 + 0.719109i) q^{37} +(1.79627 + 3.11123i) q^{38} +(28.7010 + 16.5706i) q^{40} +(0.748673 - 2.79409i) q^{41} +(7.20261 + 4.15843i) q^{43} +(-0.622047 - 2.32151i) q^{44} +(-13.8613 - 13.8613i) q^{46} +(-0.242840 - 0.906290i) q^{47} +(5.01456 - 4.88408i) q^{49} +(-5.29136 + 19.7476i) q^{50} +(-0.475412 - 19.5998i) q^{52} +(-2.48381 - 4.30208i) q^{53} +(1.35314 - 0.781234i) q^{55} +(22.8529 + 9.64293i) q^{56} +(20.1310 + 5.39408i) q^{58} +(2.29996 - 2.29996i) q^{59} +(-11.2736 + 6.50883i) q^{61} +(0.986352 + 1.70841i) q^{62} +28.7565i q^{64} +(12.2278 - 3.59640i) q^{65} +(1.64481 + 6.13851i) q^{67} +7.78144i q^{68} +(-3.49591 + 25.2663i) q^{70} +(-0.487730 - 1.82023i) q^{71} +(-12.2890 - 3.29282i) q^{73} -2.77349 q^{74} +(-6.91890 - 1.85391i) q^{76} +(0.932428 - 0.705763i) q^{77} +(-1.77054 + 3.06666i) q^{79} +(-50.1684 + 13.4426i) q^{80} +(3.94442 + 6.83193i) q^{82} +(-2.33307 - 2.33307i) q^{83} +(-4.88639 + 1.30931i) q^{85} +(-21.9089 + 5.87046i) q^{86} +(3.58858 + 2.07187i) q^{88} +(-7.39789 + 7.39789i) q^{89} +(8.74741 - 3.80564i) q^{91} +39.0850 q^{92} +(2.21601 + 1.27941i) q^{94} -4.65670i q^{95} +(-2.51514 + 0.673929i) q^{97} +(-0.251615 + 19.0887i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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