LMFDB - Embedded newform 324.3.j.a.199.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.25
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22060 - 1.58434i) q^{2} +(-1.02026 - 3.86769i) q^{4} +(-4.29021 + 1.56151i) q^{5} +(11.3387 - 1.99932i) q^{7} +(-7.37308 - 3.10447i) q^{8} +O(q^{10})$	\(q+(1.22060 - 1.58434i) q^{2} +(-1.02026 - 3.86769i) q^{4} +(-4.29021 + 1.56151i) q^{5} +(11.3387 - 1.99932i) q^{7} +(-7.37308 - 3.10447i) q^{8} +(-2.76268 + 8.70313i) q^{10} +(2.79665 - 7.68375i) q^{11} +(-18.9359 - 15.8891i) q^{13} +(10.6724 - 20.4047i) q^{14} +(-13.9181 + 7.89213i) q^{16} +(6.56214 - 11.3660i) q^{17} +(8.74492 - 5.04888i) q^{19} +(10.4166 + 15.0001i) q^{20} +(-8.76006 - 13.8096i) q^{22} +(-20.3386 - 3.58624i) q^{23} +(-3.18352 + 2.67129i) q^{25} +(-48.2869 + 10.6066i) q^{26} +(-19.3012 - 41.8148i) q^{28} +(-6.33255 + 5.31364i) q^{29} +(-9.50040 - 1.67518i) q^{31} +(-4.48468 + 31.6842i) q^{32} +(-9.99778 - 24.2700i) q^{34} +(-45.5234 + 26.2830i) q^{35} +(21.4626 - 37.1743i) q^{37} +(2.67492 - 20.0176i) q^{38} +(36.4797 + 1.80572i) q^{40} +(33.7981 + 28.3600i) q^{41} +(-3.42972 + 9.42307i) q^{43} +(-32.5717 - 2.97717i) q^{44} +(-30.5071 + 27.8458i) q^{46} +(87.0515 - 15.3495i) q^{47} +(78.5238 - 28.5803i) q^{49} +(0.346420 + 8.30436i) q^{50} +(-42.1346 + 89.4493i) q^{52} -8.52710 q^{53} +37.3319i q^{55} +(-89.8079 - 20.4596i) q^{56} +(0.689087 + 16.5187i) q^{58} +(4.23230 + 11.6281i) q^{59} +(-5.96660 - 33.8383i) q^{61} +(-14.2502 + 13.0071i) q^{62} +(44.7245 + 45.7790i) q^{64} +(106.050 + 38.5990i) q^{65} +(38.0852 - 45.3881i) q^{67} +(-50.6552 - 13.7841i) q^{68} +(-13.9248 + 104.206i) q^{70} +(22.0271 + 12.7174i) q^{71} +(-9.11022 - 15.7794i) q^{73} +(-32.6995 - 79.3791i) q^{74} +(-28.4497 - 28.6715i) q^{76} +(16.3482 - 92.7151i) q^{77} +(48.7210 + 58.0634i) q^{79} +(47.3881 - 55.5922i) q^{80} +(86.1858 - 18.9314i) q^{82} +(-20.4415 - 24.3612i) q^{83} +(-10.4049 + 59.0092i) q^{85} +(10.7430 + 16.9357i) q^{86} +(-44.4739 + 47.9707i) q^{88} +(13.1160 + 22.7175i) q^{89} +(-246.476 - 142.303i) q^{91} +(6.88020 + 82.3223i) q^{92} +(81.9364 - 156.655i) q^{94} +(-29.6337 + 35.3160i) q^{95} +(-29.5430 - 10.7528i) q^{97} +(50.5654 - 159.294i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.22060	−	1.58434i	0.610301	−	0.792170i
$2$	1.22060	−	1.58434i	0.610301	−	0.792170i
$3$		0			0
$3$		0			0
$4$	−1.02026	−	3.86769i	−0.255066	−	0.966924i
$5$	−4.29021	+	1.56151i	−0.858042	+	0.312302i	−0.733315	−	0.679889i	$-0.762028\pi$
$5$	−4.29021	+	1.56151i	−0.858042	+	0.312302i	−0.124727	+	0.992191i	$0.539806\pi$
$6$		0			0
$7$	11.3387	−	1.99932i	1.61981	−	0.285617i	0.711117	−	0.703074i	$-0.248190\pi$
$7$	11.3387	−	1.99932i	1.61981	−	0.285617i	0.908697	+	0.417457i	$0.137079\pi$
$8$	−7.37308	−	3.10447i	−0.921634	−	0.388059i
$9$		0			0
$10$	−2.76268	+	8.70313i	−0.276268	+	0.870313i
$11$	2.79665	−	7.68375i	0.254241	−	0.698522i	−0.745255	−	0.666780i	$-0.767672\pi$
$11$	2.79665	−	7.68375i	0.254241	−	0.698522i	0.999496	−	0.0317425i	$-0.0101057\pi$
$12$		0			0
$13$	−18.9359	−	15.8891i	−1.45661	−	1.22224i	−0.927575	−	0.373637i	$-0.878111\pi$
$13$	−18.9359	−	15.8891i	−1.45661	−	1.22224i	−0.529032	−	0.848602i	$-0.677445\pi$
$14$	10.6724	−	20.4047i	0.762317	−	1.45748i
$15$		0			0
$16$	−13.9181	+	7.89213i	−0.869883	+	0.493258i
$17$	6.56214	−	11.3660i	0.386008	−	0.668586i	−0.605900	−	0.795541i	$-0.707187\pi$
$17$	6.56214	−	11.3660i	0.386008	−	0.668586i	0.991909	+	0.126955i	$0.0405203\pi$
$18$		0			0
$19$	8.74492	−	5.04888i	0.460259	−	0.265731i	−0.251894	−	0.967755i	$-0.581053\pi$
$19$	8.74492	−	5.04888i	0.460259	−	0.265731i	0.712153	+	0.702024i	$0.247720\pi$
$20$	10.4166	+	15.0001i	0.520829	+	0.750004i
$21$		0			0
$22$	−8.76006	−	13.8096i	−0.398185	−	0.627711i
$23$	−20.3386	−	3.58624i	−0.884286	−	0.155923i	−0.286980	−	0.957937i	$-0.592651\pi$
$23$	−20.3386	−	3.58624i	−0.884286	−	0.155923i	−0.597306	+	0.802013i	$0.703762\pi$
$24$		0			0
$25$	−3.18352	+	2.67129i	−0.127341	+	0.106852i
$26$	−48.2869	+	10.6066i	−1.85719	+	0.407947i
$27$		0			0
$28$	−19.3012	−	41.8148i	−0.689328	−	1.49339i
$29$	−6.33255	+	5.31364i	−0.218364	+	0.183229i	−0.745407	−	0.666609i	$-0.767745\pi$
$29$	−6.33255	+	5.31364i	−0.218364	+	0.183229i	0.527044	+	0.849838i	$0.323300\pi$
$30$		0			0
$31$	−9.50040	−	1.67518i	−0.306464	−	0.0540379i	0.0183011	−	0.999833i	$-0.494174\pi$
$31$	−9.50040	−	1.67518i	−0.306464	−	0.0540379i	−0.324765	+	0.945795i	$0.605285\pi$
$32$	−4.48468	+	31.6842i	−0.140146	+	0.990131i
$33$		0			0
$34$	−9.99778	−	24.2700i	−0.294052	−	0.713822i
$35$	−45.5234	+	26.2830i	−1.30067	+	0.750942i
$36$		0			0
$37$	21.4626	−	37.1743i	0.580071	−	1.00471i	−0.415400	−	0.909639i	$-0.636358\pi$
$37$	21.4626	−	37.1743i	0.580071	−	1.00471i	0.995470	−	0.0950729i	$-0.0303084\pi$
$38$	2.67492	−	20.0176i	0.0703927	−	0.526779i
$39$		0			0
$40$	36.4797	+	1.80572i	0.911993	+	0.0451430i
$41$	33.7981	+	28.3600i	0.824344	+	0.691707i	0.953985	−	0.299854i	$-0.0969381\pi$
$41$	33.7981	+	28.3600i	0.824344	+	0.691707i	−0.129641	+	0.991561i	$0.541383\pi$
$42$		0			0
$43$	−3.42972	+	9.42307i	−0.0797609	+	0.219141i	−0.973163	−	0.230117i	$-0.926089\pi$
$43$	−3.42972	+	9.42307i	−0.0797609	+	0.219141i	0.893402	+	0.449258i	$0.148311\pi$
$44$	−32.5717	−	2.97717i	−0.740266	−	0.0676630i
$45$		0			0
$46$	−30.5071	+	27.8458i	−0.663198	+	0.605344i
$47$	87.0515	−	15.3495i	1.85216	−	0.326586i	0.867011	−	0.498288i	$-0.166038\pi$
$47$	87.0515	−	15.3495i	1.85216	−	0.326586i	0.985149	+	0.171703i	$0.0549268\pi$
$48$		0			0
$49$	78.5238	−	28.5803i	1.60253	−	0.583272i
$50$	0.346420	+	8.30436i	0.00692841	+	0.166087i
$51$		0			0
$52$	−42.1346	+	89.4493i	−0.810281	+	1.72018i
$53$	−8.52710			−0.160889			−0.0804443	−	0.996759i	$-0.525634\pi$
$53$	−8.52710			−0.160889			−0.0804443	+	0.996759i	$0.525634\pi$
$54$		0			0
$55$			37.3319i			0.678762i
$56$	−89.8079	−	20.4596i	−1.60371	−	0.365349i
$57$		0			0
$58$	0.689087	+	16.5187i	0.0118808	+	0.284806i
$59$	4.23230	+	11.6281i	0.0717339	+	0.197087i	0.970378	−	0.241591i	$-0.0776691\pi$
$59$	4.23230	+	11.6281i	0.0717339	+	0.197087i	−0.898644	+	0.438678i	$0.855447\pi$
$60$		0			0
$61$	−5.96660	−	33.8383i	−0.0978132	−	0.554726i	−0.993849	−	0.110744i	$-0.964677\pi$
$61$	−5.96660	−	33.8383i	−0.0978132	−	0.554726i	0.896036	−	0.443982i	$-0.146435\pi$
$62$	−14.2502	+	13.0071i	−0.229843	+	0.209792i
$63$		0			0
$64$	44.7245	+	45.7790i	0.698820	+	0.715297i
$65$	106.050	+	38.5990i	1.63154	+	0.593831i
$66$		0			0
$67$	38.0852	−	45.3881i	0.568435	−	0.677435i	−0.402874	−	0.915256i	$-0.631989\pi$
$67$	38.0852	−	45.3881i	0.568435	−	0.677435i	0.971309	+	0.237821i	$0.0764331\pi$
$68$	−50.6552	−	13.7841i	−0.744929	−	0.202707i
$69$		0			0
$70$	−13.9248	+	104.206i	−0.198926	+	1.48865i
$71$	22.0271	+	12.7174i	0.310241	+	0.179118i	0.647034	−	0.762461i	$-0.276009\pi$
$71$	22.0271	+	12.7174i	0.310241	+	0.179118i	−0.336793	+	0.941579i	$0.609342\pi$
$72$		0			0
$73$	−9.11022	−	15.7794i	−0.124797	−	0.216156i	0.796856	−	0.604169i	$-0.206495\pi$
$73$	−9.11022	−	15.7794i	−0.124797	−	0.216156i	−0.921654	+	0.388013i	$0.873161\pi$
$74$	−32.6995	−	79.3791i	−0.441885	−	1.07269i
$75$		0			0
$76$	−28.4497	−	28.6715i	−0.374338	−	0.377257i
$77$	16.3482	−	92.7151i	0.212314	−	1.20409i
$78$		0			0
$79$	48.7210	+	58.0634i	0.616721	+	0.734980i	0.980503	−	0.196505i	$-0.0629591\pi$
$79$	48.7210	+	58.0634i	0.616721	+	0.734980i	−0.363782	+	0.931484i	$0.618515\pi$
$80$	47.3881	−	55.5922i	0.592351	−	0.694902i
$81$		0			0
$82$	86.1858	−	18.9314i	1.05105	−	0.230871i
$83$	−20.4415	−	24.3612i	−0.246283	−	0.293509i	0.628714	−	0.777636i	$-0.283582\pi$
$83$	−20.4415	−	24.3612i	−0.246283	−	0.293509i	−0.874997	+	0.484128i	$0.839137\pi$
$84$		0			0
$85$	−10.4049	+	59.0092i	−0.122411	+	0.694226i
$86$	10.7430	+	16.9357i	0.124919	+	0.196926i
$87$		0			0
$88$	−44.4739	+	47.9707i	−0.505386	+	0.545122i
$89$	13.1160	+	22.7175i	0.147371	+	0.255253i	0.930255	−	0.366914i	$-0.119586\pi$
$89$	13.1160	+	22.7175i	0.147371	+	0.255253i	−0.782884	+	0.622167i	$0.786252\pi$
$90$		0			0
$91$	−246.476	−	142.303i	−2.70852	−	1.56377i
$92$	6.88020	+	82.3223i	0.0747848	+	0.894808i
$93$		0			0
$94$	81.9364	−	156.655i	0.871664	−	1.66654i
$95$	−29.6337	+	35.3160i	−0.311933	+	0.371748i
$96$		0			0
$97$	−29.5430	−	10.7528i	−0.304567	−	0.110853i	0.185215	−	0.982698i	$-0.440702\pi$
$97$	−29.5430	−	10.7528i	−0.304567	−	0.110853i	−0.489783	+	0.871844i	$0.662924\pi$
$98$	50.5654	−	159.294i	0.515973	−	1.62544i
$99$		0			0
$100$	13.5798	+	9.58747i	0.135798	+	0.0958747i
$101$	7.75907	+	44.0039i	0.0768225	+	0.435682i	0.998823	+	0.0484945i	$0.0154423\pi$
$101$	7.75907	+	44.0039i	0.0768225	+	0.435682i	−0.922001	+	0.387188i	$0.873447\pi$
$102$		0			0
$103$	55.3396	+	152.044i	0.537278	+	1.47616i	0.850241	+	0.526393i	$0.176456\pi$
$103$	55.3396	+	152.044i	0.537278	+	1.47616i	−0.312963	+	0.949765i	$0.601322\pi$
$104$	90.2885	+	175.938i	0.868159	+	1.69171i
$105$		0			0
$106$	−10.4082	+	13.5098i	−0.0981905	+	0.127451i
$107$			130.167i			1.21651i	0.793741	+	0.608256i	$0.208131\pi$
$107$			130.167i			1.21651i	−0.793741	+	0.608256i	$0.791869\pi$
$108$		0			0
$109$	25.8218			0.236897			0.118449	−	0.992960i	$-0.462208\pi$
$109$	25.8218			0.236897			0.118449	+	0.992960i	$0.462208\pi$
$110$	59.1464	+	45.5674i	0.537694	+	0.414249i
$111$		0			0
$112$	−142.035	+	117.313i	−1.26817	+	1.04744i
$113$	−18.4582	+	6.71825i	−0.163347	+	0.0594535i	−0.422399	−	0.906410i	$-0.638812\pi$
$113$	−18.4582	+	6.71825i	−0.163347	+	0.0594535i	0.259052	+	0.965863i	$0.416590\pi$
$114$		0			0
$115$	92.8567	−	16.3731i	0.807449	−	0.142375i
$116$	27.0124	+	19.0711i	0.232865	+	0.164406i
$117$		0			0
$118$	23.5889	+	7.48793i	0.199906	+	0.0634571i
$119$	51.6819	−	141.995i	0.434302	−	1.19323i
$120$		0			0
$121$	41.4727	+	34.7997i	0.342750	+	0.287601i
$122$	−60.8942	−	31.8500i	−0.499133	−	0.261065i
$123$		0			0
$124$	3.21383	+	38.4538i	0.0259180	+	0.310111i
$125$	66.5561	−	115.278i	0.532448	−	0.922228i
$126$		0			0
$127$	−85.9709	+	49.6353i	−0.676936	+	0.390829i	−0.798700	−	0.601730i	$-0.794478\pi$
$127$	−85.9709	+	49.6353i	−0.676936	+	0.390829i	0.121763	+	0.992559i	$0.461145\pi$
$128$	127.120	−	14.9808i	0.993128	−	0.117037i
$129$		0			0
$130$	190.599	−	120.905i	1.46614	−	0.930039i
$131$	71.0230	+	12.5233i	0.542161	+	0.0955976i	0.438020	−	0.898965i	$-0.355680\pi$
$131$	71.0230	+	12.5233i	0.542161	+	0.0955976i	0.104140	+	0.994563i	$0.466791\pi$
$132$		0			0
$133$	89.0617	−	74.7316i	0.669637	−	0.561892i
$134$	−25.4234	−	115.741i	−0.189727	−	0.863736i
$135$		0			0
$136$	−83.6685	+	63.4301i	−0.615209	+	0.466398i
$137$	78.2241	−	65.6378i	0.570979	−	0.479108i	−0.310992	−	0.950413i	$-0.600661\pi$
$137$	78.2241	−	65.6378i	0.570979	−	0.479108i	0.881971	+	0.471304i	$0.156217\pi$
$138$		0			0
$139$	156.260	+	27.5528i	1.12417	+	0.198222i	0.704672	−	0.709533i	$-0.251094\pi$
$139$	156.260	+	27.5528i	1.12417	+	0.198222i	0.419500	+	0.907755i	$0.362205\pi$
$140$	148.100	+	149.255i	1.05786	+	1.06611i
$141$		0			0
$142$	47.0350	−	19.3756i	0.331232	−	0.136448i
$143$	−175.045	+	101.062i	−1.22409	+	0.706729i
$144$		0			0
$145$	18.8707	−	32.6850i	0.130143	−	0.225413i
$146$	−36.1198	−	4.82664i	−0.247396	−	0.0330592i
$147$		0			0
$148$	−165.677	−	45.0833i	−1.11944	−	0.304617i
$149$	13.9503	+	11.7057i	0.0936261	+	0.0785616i	0.688399	−	0.725332i	$-0.258314\pi$
$149$	13.9503	+	11.7057i	0.0936261	+	0.0785616i	−0.594773	+	0.803894i	$0.702758\pi$
$150$		0			0
$151$	58.6575	−	161.160i	0.388460	−	1.06729i	−0.579235	−	0.815161i	$-0.696648\pi$
$151$	58.6575	−	161.160i	0.388460	−	1.06729i	0.967695	−	0.252125i	$-0.0811293\pi$
$152$	−80.1511	+	10.0774i	−0.527310	+	0.0662988i
$153$		0			0
$154$	−126.938	−	139.069i	−0.824270	−	0.903047i
$155$	43.3745	−	7.64809i	0.279835	−	0.0493425i
$156$		0			0
$157$	−162.347	+	59.0894i	−1.03406	+	0.376365i	−0.802624	−	0.596486i	$-0.796563\pi$
$157$	−162.347	+	59.0894i	−1.03406	+	0.376365i	−0.231432	+	0.972851i	$0.574341\pi$
$158$	151.461	−	6.31827i	0.958614	−	0.0399891i
$159$		0			0
$160$	−30.2349	−	142.935i	−0.188968	−	0.893342i
$161$	−237.783			−1.47691
$162$		0			0
$163$		−	23.1683i		−	0.142137i	−0.997471	−	0.0710684i	$-0.977359\pi$
$163$		−	23.1683i		−	0.142137i	0.997471	−	0.0710684i	$-0.0226409\pi$
$164$	75.2048	−	159.655i	0.458566	−	0.973508i
$165$		0			0
$166$	−63.5474	+	2.65091i	−0.382816	+	0.0159693i
$167$	−81.2649	−	223.274i	−0.486616	−	1.33697i	−0.903726	−	0.428111i	$-0.859179\pi$
$167$	−81.2649	−	223.274i	−0.486616	−	1.33697i	0.417110	−	0.908856i	$-0.363043\pi$
$168$		0			0
$169$	76.7580	+	435.316i	0.454189	+	2.57584i
$170$	80.7903	+	88.5116i	0.475237	+	0.520657i
$171$		0			0
$172$	39.9448	+	3.65109i	0.232237	+	0.0212273i
$173$	−230.336	−	83.8353i	−1.33142	−	0.484597i	−0.424320	−	0.905512i	$-0.639487\pi$
$173$	−230.336	−	83.8353i	−1.33142	−	0.484597i	−0.907100	+	0.420915i	$0.861709\pi$
$174$		0			0
$175$	−30.7562	+	36.6538i	−0.175750	+	0.209450i
$176$	21.7169	+	129.015i	0.123392	+	0.733039i
$177$		0			0
$178$	52.0017	+	6.94891i	0.292144	+	0.0390388i
$179$	51.8077	+	29.9112i	0.289428	+	0.167102i	0.637684	−	0.770298i	$-0.279893\pi$
$179$	51.8077	+	29.9112i	0.289428	+	0.167102i	−0.348256	+	0.937400i	$0.613226\pi$
$180$		0			0
$181$	−33.9126	−	58.7384i	−0.187362	−	0.324521i	0.757008	−	0.653406i	$-0.226661\pi$
$181$	−33.9126	−	58.7384i	−0.187362	−	0.324521i	−0.944370	+	0.328885i	$0.893327\pi$
$182$	−526.305	+	216.806i	−2.89178	+	1.19124i
$183$		0			0
$184$	138.824	+	89.5822i	0.754481	+	0.486860i
$185$	−34.0311	+	193.000i	−0.183952	+	1.04324i
$186$		0			0
$187$	−68.9811	−	82.2085i	−0.368883	−	0.439617i
$188$	−148.183	−	321.028i	−0.788206	−	1.70760i
$189$		0			0
$190$	19.7817	+	90.0566i	0.104114	+	0.473982i
$191$	3.10621	+	3.70184i	0.0162629	+	0.0193814i	0.774115	−	0.633045i	$-0.218195\pi$
$191$	3.10621	+	3.70184i	0.0162629	+	0.0193814i	−0.757852	+	0.652427i	$0.773751\pi$
$192$		0			0
$193$	−19.2895	+	109.396i	−0.0999455	+	0.566819i	0.893174	+	0.449712i	$0.148473\pi$
$193$	−19.2895	+	109.396i	−0.0999455	+	0.566819i	−0.993119	+	0.117107i	$0.962638\pi$
$194$	−53.0964	+	33.6813i	−0.273693	+	0.173615i
$195$		0			0
$196$	−190.655	−	274.547i	−0.972729	−	1.40075i
$197$	103.487	+	179.244i	0.525314	+	0.909870i	0.999565	+	0.0294806i	$0.00938533\pi$
$197$	103.487	+	179.244i	0.525314	+	0.909870i	−0.474252	+	0.880389i	$0.657281\pi$
$198$		0			0
$199$	95.4698	+	55.1195i	0.479748	+	0.276982i	0.720311	−	0.693651i	$-0.243999\pi$
$199$	95.4698	+	55.1195i	0.479748	+	0.276982i	−0.240564	+	0.970633i	$0.577332\pi$
$200$	31.7653	−	9.81247i	0.158826	−	0.0490624i
$201$		0			0
$202$	79.1878	+	41.4182i	0.392019	+	0.205041i
$203$	−61.1792	+	72.9105i	−0.301375	+	0.359165i
$204$		0			0
$205$	−189.285	−	68.8942i	−0.923343	−	0.336069i
$206$	308.437	+	97.9089i	1.49727	+	0.475286i
$207$		0			0
$208$	388.951	+	71.7021i	1.86996	+	0.344722i
$209$	−14.3378	−	81.3137i	−0.0686019	−	0.389061i
$210$		0			0
$211$	61.7185	+	169.570i	0.292505	+	0.803651i	0.995699	+	0.0926522i	$0.0295345\pi$
$211$	61.7185	+	169.570i	0.292505	+	0.803651i	−0.703194	+	0.710998i	$0.748243\pi$
$212$	8.69988	+	32.9802i	0.0410372	+	0.155567i
$213$		0			0
$214$	206.229	+	158.882i	0.963685	+	0.742439i
$215$		−	45.7825i		−	0.212942i
$216$		0			0
$217$	−111.071			−0.511849
$218$	31.5181	−	40.9105i	0.144578	−	0.187663i
$219$		0			0
$220$	144.388	−	38.0883i	0.656311	−	0.173129i
$221$	−304.855	+	110.958i	−1.37943	+	0.502073i
$222$		0			0
$223$	−8.13269	+	1.43401i	−0.0364695	+	0.00643055i	−0.191853	−	0.981424i	$-0.561450\pi$
$223$	−8.13269	+	1.43401i	−0.0364695	+	0.00643055i	0.155384	+	0.987854i	$0.450339\pi$
$224$	12.4963	+	368.224i	0.0557870	+	1.64386i
$225$		0			0
$226$	−11.8862	+	37.4444i	−0.0525937	+	0.165683i
$227$	45.2829	−	124.414i	0.199484	−	0.548079i	−0.799104	−	0.601193i	$-0.794692\pi$
$227$	45.2829	−	124.414i	0.199484	−	0.548079i	0.998588	+	0.0531140i	$0.0169147\pi$
$228$		0			0
$229$	−286.648	−	240.527i	−1.25174	−	1.05033i	−0.996512	−	0.0834533i	$-0.973405\pi$
$229$	−286.648	−	240.527i	−1.25174	−	1.05033i	−0.255228	−	0.966881i	$-0.582150\pi$
$230$	87.4004	−	167.102i	0.380002	−	0.726529i
$231$		0			0
$232$	63.1864	−	19.5186i	0.272355	−	0.0841320i
$233$	48.4626	−	83.9396i	0.207994	−	0.360256i	−0.743089	−	0.669193i	$-0.766640\pi$
$233$	48.4626	−	83.9396i	0.207994	−	0.360256i	0.951082	+	0.308937i	$0.0999733\pi$
$234$		0			0
$235$	−349.501	+	201.784i	−1.48724	+	0.858657i
$236$	40.6560	−	28.2330i	0.172271	−	0.119631i
$237$		0			0
$238$	−161.885	−	255.201i	−0.680189	−	1.07227i
$239$	−461.201	−	81.3223i	−1.92971	−	0.340261i	−0.930080	−	0.367356i	$-0.880263\pi$
$239$	−461.201	−	81.3223i	−1.92971	−	0.340261i	−0.999633	+	0.0270953i	$0.991374\pi$
$240$		0			0
$241$	110.780	−	92.9556i	0.459669	−	0.385708i	−0.383341	−	0.923607i	$-0.625226\pi$
$241$	110.780	−	92.9556i	0.459669	−	0.385708i	0.843009	+	0.537899i	$0.180782\pi$
$242$	105.756	−	23.2302i	0.437009	−	0.0959926i
$243$		0			0
$244$	−124.789	+	57.6009i	−0.511429	+	0.236069i
$245$	−292.255	+	245.231i	−1.19288	+	1.00094i
$246$		0			0
$247$	−245.815	−	43.3438i	−0.995203	−	0.175481i
$248$	64.8466	+	41.8449i	0.261478	+	0.168730i
$249$		0			0
$250$	−101.402	−	246.156i	−0.405607	−	0.984626i
$251$	246.323	−	142.215i	0.981366	−	0.566592i	0.0786839	−	0.996900i	$-0.474928\pi$
$251$	246.323	−	142.215i	0.981366	−	0.566592i	0.902682	+	0.430308i	$0.141595\pi$
$252$		0			0
$253$	−84.4357	+	146.247i	−0.333738	+	0.578051i
$254$	−26.2970	+	196.792i	−0.103532	+	0.774772i
$255$		0			0
$256$	131.429	−	219.687i	0.513393	−	0.858154i
$257$	−164.184	−	137.767i	−0.638848	−	0.536057i	0.264816	−	0.964299i	$-0.414689\pi$
$257$	−164.184	−	137.767i	−0.638848	−	0.536057i	−0.903664	+	0.428242i	$0.859133\pi$
$258$		0			0
$259$	169.035	−	464.419i	0.652644	−	1.79312i
$260$	41.0905	−	449.550i	0.158040	−	1.72904i
$261$		0			0
$262$	106.532	−	97.2387i	0.406611	−	0.371140i
$263$	121.818	−	21.4798i	0.463187	−	0.0816723i	0.0628152	−	0.998025i	$-0.479992\pi$
$263$	121.818	−	21.4798i	0.463187	−	0.0816723i	0.400372	+	0.916353i	$0.368881\pi$
$264$		0			0
$265$	36.5830	−	13.3151i	0.138049	−	0.0502458i
$266$	−9.69140	−	232.321i	−0.0364338	−	0.873389i
$267$		0			0
$268$	−214.404	−	100.994i	−0.800016	−	0.376843i
$269$	−395.510			−1.47030			−0.735150	−	0.677905i	$-0.762888\pi$
$269$	−395.510			−1.47030			−0.735150	+	0.677905i	$0.762888\pi$
$270$		0			0
$271$		−	462.522i		−	1.70672i	−0.521320	−	0.853361i	$-0.674560\pi$
$271$		−	462.522i		−	1.70672i	0.521320	−	0.853361i	$-0.325440\pi$
$272$	−1.63110	+	209.982i	−0.00599670	+	0.771993i
$273$		0			0
$274$	−8.51209	−	204.051i	−0.0310660	−	0.744712i
$275$	11.6223	+	31.9320i	0.0422630	+	0.116117i
$276$		0			0
$277$	−6.18174	−	35.0584i	−0.0223168	−	0.126565i	0.971614	−	0.236572i	$-0.0760238\pi$
$277$	−6.18174	−	35.0584i	−0.0223168	−	0.126565i	−0.993931	+	0.110007i	$0.964913\pi$
$278$	234.384	−	213.938i	0.843109	−	0.769560i
$279$		0			0
$280$	417.242	−	52.4600i	1.49015	−	0.187357i
$281$	58.6385	+	21.3427i	0.208678	+	0.0759525i	0.444244	−	0.895906i	$-0.353472\pi$
$281$	58.6385	+	21.3427i	0.208678	+	0.0759525i	−0.235566	+	0.971858i	$0.575694\pi$
$282$		0			0
$283$	−177.070	+	211.024i	−0.625690	+	0.745668i	−0.982038	−	0.188685i	$-0.939577\pi$
$283$	−177.070	+	211.024i	−0.625690	+	0.745668i	0.356348	+	0.934353i	$0.384022\pi$
$284$	26.7134	−	98.1692i	0.0940614	−	0.345666i
$285$		0			0
$286$	−53.5433	+	400.688i	−0.187214	+	1.40101i
$287$	439.927	+	253.992i	1.53285	+	0.884989i
$288$		0			0
$289$	58.3767	+	101.111i	0.201995	+	0.349866i
$290$	−28.7505	−	69.7928i	−0.0991396	−	0.240665i
$291$		0			0
$292$	−51.7349	+	51.3346i	−0.177174	+	0.175804i
$293$	89.3427	−	506.688i	0.304924	−	1.72931i	−0.318938	−	0.947776i	$-0.603326\pi$
$293$	89.3427	−	506.688i	0.304924	−	1.72931i	0.623862	−	0.781534i	$-0.285563\pi$
$294$		0			0
$295$	−36.3149	−	43.2784i	−0.123101	−	0.146706i
$296$	−273.652	+	207.459i	−0.924501	+	0.700875i
$297$		0			0
$298$	35.5735	−	7.81401i	0.119374	−	0.0262215i
$299$	328.147	+	391.070i	1.09748	+	1.30793i
$300$		0			0
$301$	−20.0488	+	113.702i	−0.0666073	+	0.377749i
$302$	−183.735	−	289.646i	−0.608394	−	0.959092i
$303$		0			0
$304$	−81.8665	+	139.287i	−0.269298	+	0.458181i
$305$	78.4368	+	135.856i	0.257170	+	0.445431i
$306$		0			0
$307$	369.715	+	213.455i	1.20428	+	0.695294i	0.961505	−	0.274787i	$-0.0886075\pi$
$307$	369.715	+	213.455i	1.20428	+	0.695294i	0.242780	+	0.970081i	$0.421941\pi$
$308$	−375.273	+	31.3640i	−1.21842	+	0.101831i
$309$		0			0
$310$	40.8258	−	78.0552i	0.131696	−	0.251791i
$311$	303.936	−	362.217i	0.977287	−	1.16468i	−0.00905262	−	0.999959i	$-0.502882\pi$
$311$	303.936	−	362.217i	0.977287	−	1.16468i	0.986339	−	0.164726i	$-0.0526740\pi$
$312$		0			0
$313$	−271.635	−	98.8672i	−0.867845	−	0.315870i	−0.130551	−	0.991442i	$-0.541675\pi$
$313$	−271.635	−	98.8672i	−0.867845	−	0.315870i	−0.737294	+	0.675572i	$0.763897\pi$
$314$	−104.543	+	329.337i	−0.332940	+	1.04884i
$315$		0			0
$316$	174.863	−	247.678i	0.553365	−	0.783790i
$317$	45.4577	+	257.803i	0.143400	+	0.813260i	0.968638	+	0.248476i	$0.0799296\pi$
$317$	45.4577	+	257.803i	0.143400	+	0.813260i	−0.825238	+	0.564784i	$0.808959\pi$
$318$		0			0
$319$	23.1187	+	63.5181i	0.0724724	+	0.199116i
$320$	−263.362	−	126.564i	−0.823006	−	0.395512i
$321$		0			0
$322$	−290.238	+	376.729i	−0.901361	+	1.16997i
$323$		−	132.526i		−	0.410297i
$324$		0			0
$325$	102.727			0.316084
$326$	−36.7065	−	28.2793i	−0.112597	−	0.0867463i
$327$		0			0
$328$	−161.153	−	314.025i	−0.491321	−	0.957395i
$329$	956.362	−	348.087i	2.90688	−	1.05802i
$330$		0			0
$331$	63.1721	−	11.1389i	0.190852	−	0.0336524i	−0.0774050	−	0.997000i	$-0.524663\pi$
$331$	63.1721	−	11.1389i	0.190852	−	0.0336524i	0.268257	+	0.963347i	$0.413552\pi$
$332$	−73.3661	+	103.916i	−0.220982	+	0.313001i
$333$		0			0
$334$	−452.933	−	143.777i	−1.35609	−	0.430470i
$335$	−92.5194	+	254.195i	−0.276177	+	0.758791i
$336$		0			0
$337$	274.967	+	230.725i	0.815926	+	0.684644i	0.952014	−	0.306053i	$-0.0990086\pi$
$337$	274.967	+	230.725i	0.815926	+	0.684644i	−0.136088	+	0.990697i	$0.543453\pi$
$338$	783.380	+	409.737i	2.31769	+	1.21224i
$339$		0			0
$340$	238.845	−	19.9618i	0.702486	−	0.0587113i
$341$	−39.4410	+	68.3137i	−0.115663	+	0.200334i
$342$		0			0
$343$	344.633	−	198.974i	1.00476	−	0.580099i
$344$	54.5412	−	58.8295i	0.158550	−	0.171016i
$345$		0			0
$346$	−413.972	+	262.600i	−1.19645	+	0.758960i
$347$	−468.627	−	82.6316i	−1.35051	−	0.238131i	−0.548854	−	0.835918i	$-0.684936\pi$
$347$	−468.627	−	82.6316i	−1.35051	−	0.238131i	−0.801655	+	0.597787i	$0.796047\pi$
$348$		0			0
$349$	369.888	−	310.373i	1.05985	−	0.889320i	0.0657560	−	0.997836i	$-0.479054\pi$
$349$	369.888	−	310.373i	1.05985	−	0.889320i	0.994095	+	0.108515i	$0.0346097\pi$
$350$	20.5310	+	93.4680i	0.0586600	+	0.267051i
$351$		0			0
$352$	230.911	+	123.069i	0.655998	+	0.349628i
$353$	314.600	−	263.981i	0.891219	−	0.747822i	−0.0772349	−	0.997013i	$-0.524609\pi$
$353$	314.600	−	263.981i	0.891219	−	0.747822i	0.968454	+	0.249191i	$0.0801647\pi$
$354$		0			0
$355$	−114.359	−	20.1646i	−0.322139	−	0.0568017i
$356$	74.4828	−	73.9065i	0.209221	−	0.207602i
$357$		0			0
$358$	110.626	−	45.5713i	0.309011	−	0.127294i
$359$	−560.800	+	323.778i	−1.56212	+	0.901889i	−0.565074	+	0.825040i	$0.691152\pi$
$359$	−560.800	+	323.778i	−1.56212	+	0.901889i	−0.997043	+	0.0768487i	$0.975514\pi$
$360$		0			0
$361$	−129.518	+	224.331i	−0.358774	+	0.621416i
$362$	−134.455	−	17.9671i	−0.371423	−	0.0496328i
$363$		0			0
$364$	−298.914	+	1098.48i	−0.821192	+	3.01780i
$365$	63.7244	+	53.4711i	0.174587	+	0.146496i
$366$		0			0
$367$	−147.995	+	406.613i	−0.403256	+	1.10794i	0.557412	+	0.830236i	$0.311794\pi$
$367$	−147.995	+	406.613i	−0.403256	+	1.10794i	−0.960668	+	0.277700i	$0.910428\pi$
$368$	311.378	−	110.601i	0.846136	−	0.300546i
$369$		0			0
$370$	264.239	+	289.493i	0.714159	+	0.782413i
$371$	−96.6862	+	17.0484i	−0.260610	+	0.0459525i
$372$		0			0
$373$	442.492	−	161.054i	1.18630	−	0.431779i	0.327880	−	0.944719i	$-0.393666\pi$
$373$	442.492	−	161.054i	1.18630	−	0.431779i	0.858424	+	0.512940i	$0.171444\pi$
$374$	−214.445	+	8.94566i	−0.573381	+	0.0239189i
$375$		0			0
$376$	−689.490	−	157.076i	−1.83375	−	0.417755i
$377$	204.341			0.542020
$378$		0			0
$379$			387.390i			1.02214i	0.859540	+	0.511068i	$0.170750\pi$
$379$			387.390i			1.02214i	−0.859540	+	0.511068i	$0.829250\pi$
$380$	166.826	+	78.5824i	0.439015	+	0.206796i
$381$		0			0
$382$	9.65643	−	0.402823i	0.0252786	−	0.00105451i
$383$	−97.0070	−	266.524i	−0.253282	−	0.695886i	−0.999543	−	0.0302328i	$-0.990375\pi$
$383$	−97.0070	−	266.524i	−0.253282	−	0.695886i	0.746261	−	0.665653i	$-0.231847\pi$
$384$		0			0
$385$	74.6383	+	423.295i	0.193866	+	1.09947i
$386$	149.776	+	164.090i	0.388020	+	0.425104i
$387$		0			0
$388$	−11.4468	+	125.234i	−0.0295022	+	0.322768i
$389$	67.3782	+	24.5237i	0.173209	+	0.0630428i	0.427169	−	0.904172i	$-0.359511\pi$
$389$	67.3782	+	24.5237i	0.173209	+	0.0630428i	−0.253960	+	0.967215i	$0.581733\pi$
$390$		0			0
$391$	−174.226	+	207.634i	−0.445590	+	0.531033i
$392$	−667.689	−	33.0502i	−1.70329	−	0.0843116i
$393$		0			0
$394$	410.300	+	54.8278i	1.04137	+	0.139157i
$395$	−299.690	−	173.026i	−0.758708	−	0.438040i
$396$		0			0
$397$	66.7682	+	115.646i	0.168182	+	0.291300i	0.937781	−	0.347228i	$-0.112877\pi$
$397$	66.7682	+	115.646i	0.168182	+	0.291300i	−0.769599	+	0.638528i	$0.779544\pi$
$398$	203.859	−	83.9776i	0.512207	−	0.210999i
$399$		0			0
$400$	23.2265	−	62.3041i	0.0580662	−	0.155760i
$401$	−95.0909	+	539.287i	−0.237134	+	1.34486i	0.600937	+	0.799296i	$0.294794\pi$
$401$	−95.0909	+	539.287i	−0.237134	+	1.34486i	−0.838072	+	0.545560i	$0.816317\pi$
$402$		0			0
$403$	153.281	+	182.674i	0.380351	+	0.453285i
$404$	162.277	−	74.9053i	0.401677	−	0.185409i
$405$		0			0
$406$	40.8396	+	185.923i	0.100590	+	0.457939i
$407$	−225.615	−	268.877i	−0.554336	−	0.660632i
$408$		0			0
$409$	105.910	−	600.648i	0.258950	−	1.46858i	−0.526778	−	0.850003i	$-0.676600\pi$
$409$	105.910	−	600.648i	0.258950	−	1.46858i	0.785727	−	0.618573i	$-0.212289\pi$
$410$	−340.194	+	215.800i	−0.829741	+	0.526341i
$411$		0			0
$412$	531.600	−	369.162i	1.29029	−	0.896024i
$413$	71.2371	+	123.386i	0.172487	+	0.298756i
$414$		0			0
$415$	125.739	+	72.5952i	0.302985	+	0.174928i
$416$	588.355	−	528.711i	1.41431	−	1.27094i
$417$		0			0
$418$	−146.329	−	76.5357i	−0.350070	−	0.183100i
$419$	−271.624	+	323.708i	−0.648267	+	0.772574i	−0.985652	−	0.168793i	$-0.946013\pi$
$419$	−271.624	+	323.708i	−0.648267	+	0.772574i	0.337385	+	0.941367i	$0.390458\pi$
$420$		0			0
$421$	−158.812	−	57.8029i	−0.377226	−	0.137299i	0.146447	−	0.989219i	$-0.453216\pi$
$421$	−158.812	−	57.8029i	−0.377226	−	0.137299i	−0.523673	+	0.851920i	$0.675438\pi$
$422$	343.991	+	109.195i	0.815144	+	0.258755i
$423$		0			0
$424$	62.8709	+	26.4721i	0.148281	+	0.0624343i
$425$	9.47107	+	53.7131i	0.0222849	+	0.126384i
$426$		0			0
$427$	−135.307	−	371.753i	−0.316878	−	0.870616i
$428$	503.446	−	132.804i	1.17628	−	0.310291i
$429$		0			0
$430$	−72.5350	−	55.8822i	−0.168686	−	0.129959i
$431$			132.068i			0.306422i	0.988193	+	0.153211i	$0.0489614\pi$
$431$			132.068i			0.306422i	−0.988193	+	0.153211i	$0.951039\pi$
$432$		0			0
$433$	303.878			0.701797			0.350898	−	0.936414i	$-0.385876\pi$
$433$	303.878			0.701797			0.350898	+	0.936414i	$0.385876\pi$
$434$	−135.574	+	175.975i	−0.312382	+	0.405472i
$435$		0			0
$436$	−26.3450	−	99.8708i	−0.0604243	−	0.229061i
$437$	−195.966	+	71.3257i	−0.448434	+	0.163217i
$438$		0			0
$439$	−419.874	+	74.0352i	−0.956433	+	0.168645i	−0.630017	−	0.776581i	$-0.716952\pi$
$439$	−419.874	+	74.0352i	−0.956433	+	0.168645i	−0.326416	+	0.945226i	$0.605841\pi$
$440$	115.896	−	275.251i	0.263400	−	0.625570i
$441$		0			0
$442$	−196.311	+	618.429i	−0.444143	+	1.39916i
$443$	−101.688	+	279.386i	−0.229544	+	0.630667i	−0.999977	−	0.00685446i	$-0.997818\pi$
$443$	−101.688	+	279.386i	−0.229544	+	0.630667i	0.770432	+	0.637522i	$0.220040\pi$
$444$		0			0
$445$	−91.7440	−	76.9823i	−0.206166	−	0.172994i
$446$	−7.65481	+	14.6353i	−0.0171633	+	0.0328146i
$447$		0			0
$448$	598.644	+	429.656i	1.33626	+	0.959054i
$449$	344.212	−	596.193i	0.766620	−	1.32782i	−0.172766	−	0.984963i	$-0.555271\pi$
$449$	344.212	−	596.193i	0.766620	−	1.32782i	0.939386	−	0.342861i	$-0.111396\pi$
$450$		0			0
$451$	312.432	−	180.383i	0.692755	−	0.399962i
$452$	44.8164	+	64.5364i	0.0991513	+	0.142780i
$453$		0			0
$454$	−141.841	−	223.603i	−0.312426	−	0.492518i
$455$	1279.64	+	225.635i	2.81239	+	0.495901i
$456$		0			0
$457$	426.489	−	357.867i	0.933237	−	0.783079i	−0.0431589	−	0.999068i	$-0.513742\pi$
$457$	426.489	−	357.867i	0.933237	−	0.783079i	0.976396	+	0.215990i	$0.0692977\pi$
$458$	−730.959	+	160.561i	−1.59598	+	0.350570i
$459$		0			0
$460$	−158.064	−	342.436i	−0.343618	−	0.744427i
$461$	263.908	−	221.445i	0.572469	−	0.480358i	−0.309995	−	0.950738i	$-0.600328\pi$
$461$	263.908	−	221.445i	0.572469	−	0.480358i	0.882464	+	0.470380i	$0.155883\pi$
$462$		0			0
$463$	613.691	+	108.210i	1.32547	+	0.233715i	0.791177	−	0.611587i	$-0.209468\pi$
$463$	613.691	+	108.210i	1.32547	+	0.233715i	0.534289	+	0.845302i	$0.320580\pi$
$464$	46.2013	−	123.933i	0.0995718	−	0.267097i
$465$		0			0
$466$	−73.8354	−	179.238i	−0.158445	−	0.384631i
$467$	513.973	−	296.742i	1.10058	−	0.635422i	0.164210	−	0.986425i	$-0.447493\pi$
$467$	513.973	−	296.742i	1.10058	−	0.635422i	0.936374	+	0.351003i	$0.114159\pi$
$468$		0			0
$469$	341.091	−	590.787i	0.727272	−	1.25967i
$470$	−106.906	+	800.026i	−0.227460	+	1.70218i
$471$		0			0
$472$	4.89421	−	98.8742i	0.0103691	−	0.209479i
$473$	62.8127	+	52.7062i	0.132797	+	0.111429i
$474$		0			0
$475$	−14.3526	+	39.4334i	−0.0302160	+	0.0830178i
$476$	−601.922	−	55.0178i	−1.26454	−	0.115584i
$477$		0			0
$478$	−691.785	+	631.438i	−1.44725	+	1.32100i
$479$	−539.671	+	95.1586i	−1.12666	+	0.198661i	−0.705764	−	0.708447i	$-0.749396\pi$
$479$	−539.671	+	95.1586i	−1.12666	+	0.198661i	−0.420898	+	0.907108i	$0.638285\pi$
$480$		0			0
$481$	−997.081	+	362.908i	−2.07293	+	0.754486i
$482$	−12.0547	−	288.975i	−0.0250098	−	0.599533i
$483$		0			0
$484$	92.2817	−	195.909i	0.190665	−	0.404770i
$485$	143.536			0.295951
$486$		0			0
$487$			190.678i			0.391536i	0.980650	+	0.195768i	$0.0627199\pi$
$487$			190.678i			0.391536i	−0.980650	+	0.195768i	$0.937280\pi$
$488$	−61.0579	+	268.015i	−0.125119	+	0.549212i
$489$		0			0
$490$	31.8023	+	762.361i	0.0649026	+	1.55584i
$491$	117.631	+	323.189i	0.239575	+	0.658226i	0.999962	+	0.00875596i	$0.00278714\pi$
$491$	117.631	+	323.189i	0.239575	+	0.658226i	−0.760387	+	0.649470i	$0.774991\pi$
$492$		0			0
$493$	18.8395	+	106.844i	0.0382141	+	0.216723i
$494$	−368.714	+	336.549i	−0.746384	+	0.681273i
$495$		0			0
$496$	145.448	−	51.6630i	0.293243	−	0.104159i
$497$	275.185	+	100.159i	0.553692	+	0.201527i
$498$		0			0
$499$	286.634	−	341.597i	0.574417	−	0.684563i	−0.398114	−	0.917336i	$-0.630335\pi$
$499$	286.634	−	341.597i	0.574417	−	0.684563i	0.972531	+	0.232772i	$0.0747797\pi$
$500$	−513.767	−	139.804i	−1.02753	−	0.279608i
$501$		0			0
$502$	75.3460	−	563.847i	0.150092	−	1.12320i
$503$	756.960	+	437.031i	1.50489	+	0.868849i	0.999984	+	0.00567418i	$0.00180616\pi$
$503$	756.960	+	437.031i	1.50489	+	0.868849i	0.504906	+	0.863174i	$0.331527\pi$
$504$		0			0
$505$	−102.001	−	176.670i	−0.201981	−	0.349842i
$506$	128.642	+	312.284i	0.254234	+	0.617162i
$507$		0			0
$508$	279.687	+	281.868i	0.550565	+	0.554859i
$509$	−121.243	+	687.602i	−0.238198	+	1.35089i	0.597575	+	0.801813i	$0.296131\pi$
$509$	−121.243	+	687.602i	−0.238198	+	1.35089i	−0.835773	+	0.549075i	$0.814980\pi$
$510$		0			0
$511$	−134.846	−	160.703i	−0.263886	−	0.314488i
$512$	−187.637	−	476.378i	−0.366479	−	0.930426i
$513$		0			0
$514$	−418.672	+	91.9648i	−0.814538	+	0.178920i
$515$	−474.837	−	565.889i	−0.922014	−	1.09881i
$516$		0			0
$517$	125.511	−	711.809i	0.242768	−	1.37681i
$518$	−529.473	−	834.679i	−1.02215	−	1.61135i
$519$		0			0
$520$	−662.085	−	613.823i	−1.27324	−	1.18043i
$521$	198.852	+	344.421i	0.381673	+	0.661077i	0.991302	−	0.131610i	$-0.0420147\pi$
$521$	198.852	+	344.421i	0.381673	+	0.661077i	−0.609629	+	0.792687i	$0.708681\pi$
$522$		0			0
$523$	−732.018	−	422.631i	−1.39965	−	0.808089i	−0.405296	−	0.914186i	$-0.632831\pi$
$523$	−732.018	−	422.631i	−1.39965	−	0.808089i	−0.994356	+	0.106096i	$0.966165\pi$
$524$	−24.0259	−	287.473i	−0.0458510	−	0.548612i
$525$		0			0
$526$	114.660	−	219.220i	0.217985	−	0.416767i
$527$	−81.3829	+	96.9884i	−0.154427	+	0.184039i
$528$		0			0
$529$	−96.3010	−	35.0507i	−0.182044	−	0.0662584i
$530$	23.5576	−	74.2124i	0.0444484	−	0.140023i
$531$		0			0
$532$	−379.905	−	268.218i	−0.714108	−	0.504168i
$533$	−189.383	−	1074.04i	−0.355315	−	2.01509i
$534$		0			0
$535$	−203.257	−	558.443i	−0.379919	−	1.04382i
$536$	−421.711	+	216.416i	−0.786774	+	0.403761i
$537$		0			0
$538$	−482.761	+	626.623i	−0.897325	+	1.16473i
$539$		−	683.286i		−	1.26769i
$540$		0			0
$541$	−419.088			−0.774654			−0.387327	−	0.921942i	$-0.626602\pi$
$541$	−419.088			−0.774654			−0.387327	+	0.921942i	$0.626602\pi$
$542$	−732.791	−	564.555i	−1.35201	−	1.04161i
$543$		0			0
$544$	330.692	+	258.889i	0.607890	+	0.475898i
$545$	−110.781	+	40.3209i	−0.203268	+	0.0739834i
$546$		0			0
$547$	−360.585	+	63.5809i	−0.659205	+	0.116236i	−0.493236	−	0.869895i	$-0.664186\pi$
$547$	−360.585	+	63.5809i	−0.659205	+	0.116236i	−0.165969	+	0.986131i	$0.553075\pi$
$548$	−333.676	−	235.579i	−0.608898	−	0.429889i
$549$		0			0
$550$	64.7774	+	20.5626i	0.117777	+	0.0373866i
$551$	−28.5497	+	78.4396i	−0.0518143	+	0.142359i
$552$		0			0
$553$	668.519	+	560.954i	1.20890	+	1.01438i
$554$	−63.0899	−	32.9984i	−0.113881	−	0.0595638i
$555$		0			0
$556$	−52.8602	−	632.477i	−0.0950722	−	1.13755i
$557$	−96.4150	+	166.996i	−0.173097	+	0.299813i	−0.939501	−	0.342546i	$-0.888711\pi$
$557$	−96.4150	+	166.996i	−0.173097	+	0.299813i	0.766404	+	0.642359i	$0.222044\pi$
$558$		0			0
$559$	214.669	−	123.939i	0.384023	−	0.221716i
$560$	426.172	−	725.086i	0.761022	−	1.29480i
$561$		0			0
$562$	105.388	−	66.8524i	0.187524	−	0.118954i
$563$	413.192	+	72.8569i	0.733912	+	0.129408i	0.528099	−	0.849183i	$-0.322905\pi$
$563$	413.192	+	72.8569i	0.733912	+	0.129408i	0.205813	+	0.978591i	$0.434016\pi$
$564$		0			0
$565$	68.6991	−	57.6454i	0.121591	−	0.102027i
$566$	118.202	+	538.116i	0.208837	+	0.950735i
$567$		0			0
$568$	−122.927	−	162.149i	−0.216421	−	0.285473i
$569$	−787.303	+	660.626i	−1.38366	+	1.16103i	−0.415825	+	0.909445i	$0.636507\pi$
$569$	−787.303	+	660.626i	−1.38366	+	1.16103i	−0.967835	+	0.251584i	$0.919048\pi$
$570$		0			0
$571$	99.4864	+	17.5421i	0.174232	+	0.0307218i	0.260083	−	0.965586i	$-0.416250\pi$
$571$	99.4864	+	17.5421i	0.174232	+	0.0307218i	−0.0858515	+	0.996308i	$0.527361\pi$
$572$	569.470	+	573.911i	0.995577	+	1.00334i
$573$		0			0
$574$	939.385	−	386.970i	1.63656	−	0.674165i
$575$	74.3281	−	42.9134i	0.129266	−	0.0746319i
$576$		0			0
$577$	93.5986	−	162.118i	0.162216	−	0.280966i	−0.773447	−	0.633861i	$-0.781469\pi$
$577$	93.5986	−	162.118i	0.162216	−	0.280966i	0.935663	+	0.352894i	$0.114803\pi$
$578$	231.449	+	30.9283i	0.400431	+	0.0535091i
$579$		0			0
$580$	−145.668	−	39.6387i	−0.251153	−	0.0683427i
$581$	−280.486	−	235.356i	−0.482764	−	0.405087i
$582$		0			0
$583$	−23.8473	+	65.5201i	−0.0409045	+	0.112384i
$584$	18.1837	+	144.625i	0.0311365	+	0.247645i
$585$		0			0
$586$	−693.714	−	760.013i	−1.18381	−	1.29695i
$587$	408.972	−	72.1129i	0.696716	−	0.122850i	0.185937	−	0.982562i	$-0.440468\pi$
$587$	408.972	−	72.1129i	0.696716	−	0.122850i	0.510779	+	0.859712i	$0.329357\pi$
$588$		0			0
$589$	−91.5380	+	33.3171i	−0.155413	+	0.0565655i
$590$	−112.894	+	4.70942i	−0.191345	+	0.00798206i
$591$		0			0
$592$	−5.33480	+	686.783i	−0.00901149	+	1.16011i
$593$	598.860			1.00988			0.504941	−	0.863154i	$-0.331514\pi$
$593$	598.860			1.00988			0.504941	+	0.863154i	$0.331514\pi$
$594$		0			0
$595$			689.890i			1.15948i
$596$	31.0411	−	65.8983i	0.0520823	−	0.110568i
$597$		0			0
$598$	1020.12	−	42.5550i	1.70589	−	0.0711622i
$599$	346.568	+	952.189i	0.578578	+	1.58963i	0.790578	+	0.612361i	$0.209780\pi$
$599$	346.568	+	952.189i	0.578578	+	1.58963i	−0.212000	+	0.977270i	$0.567998\pi$
$600$		0			0
$601$	68.1551	+	386.527i	0.113403	+	0.643140i	0.987529	+	0.157440i	$0.0503241\pi$
$601$	68.1551	+	386.527i	0.113403	+	0.643140i	−0.874126	+	0.485700i	$0.838565\pi$
$602$	155.672	+	170.549i	0.258591	+	0.283305i
$603$		0			0
$604$	−683.164	−	62.4436i	−1.13107	−	0.103384i
$605$	−232.267	−	84.5381i	−0.383912	−	0.139732i
$606$		0			0
$607$	121.947	−	145.331i	0.200901	−	0.239424i	−0.656182	−	0.754602i	$-0.727830\pi$
$607$	121.947	−	145.331i	0.200901	−	0.239424i	0.857083	+	0.515178i	$0.172274\pi$
$608$	120.752	+	299.718i	0.198604	+	0.492958i
$609$		0			0
$610$	310.983	+	41.5562i	0.509808	+	0.0681249i
$611$	−1892.29	−	1092.51i	−3.09704	−	1.78807i
$612$		0			0
$613$	−373.608	−	647.108i	−0.609474	−	1.05564i	−0.991327	−	0.131418i	$-0.958047\pi$
$613$	−373.608	−	647.108i	−0.609474	−	1.05564i	0.381853	−	0.924223i	$-0.375286\pi$
$614$	789.461	−	325.211i	1.28577	−	0.529659i
$615$		0			0
$616$	−408.368	+	632.843i	−0.662935	+	1.02734i
$617$	117.557	−	666.700i	0.190530	−	1.08055i	−0.728111	−	0.685459i	$-0.759601\pi$
$617$	117.557	−	666.700i	0.190530	−	1.08055i	0.918641	−	0.395092i	$-0.129287\pi$
$618$		0			0
$619$	639.472	+	762.093i	1.03307	+	1.23117i	0.972475	+	0.233006i	$0.0748560\pi$
$619$	639.472	+	762.093i	1.03307	+	1.23117i	0.0605971	+	0.998162i	$0.480700\pi$
$620$	−73.8339	−	159.956i	−0.119087	−	0.257994i
$621$		0			0
$622$	−202.890	−	923.661i	−0.326189	−	1.48499i
$623$	194.138	+	231.364i	0.311618	+	0.371371i
$624$		0			0
$625$	−87.4900	+	496.180i	−0.139984	+	0.793888i
$626$	−488.198	+	309.685i	−0.779869	+	0.494705i
$627$		0			0
$628$	394.176	+	567.621i	0.627669	+	0.903855i
$629$	−281.681	−	487.886i	−0.447824	−	0.775654i
$630$		0			0
$631$	301.563	+	174.107i	0.477913	+	0.275923i	0.719546	−	0.694445i	$-0.244350\pi$
$631$	301.563	+	174.107i	0.477913	+	0.275923i	−0.241634	+	0.970368i	$0.577683\pi$
$632$	−178.967	−	579.359i	−0.283176	−	0.916707i
$633$		0			0
$634$	463.934	+	242.655i	0.731757	+	0.382737i
$635$	291.327	−	347.190i	0.458783	−	0.546756i
$636$		0			0
$637$	−1941.03	−	706.479i	−3.04715	−	1.10907i
$638$	128.853	+	40.9024i	0.201964	+	0.0641104i
$639$		0			0
$640$	−521.980	+	262.770i	−0.815594	+	0.410578i
$641$	34.7159	+	196.884i	0.0541589	+	0.307151i	0.999839	−	0.0179485i	$-0.00571348\pi$
$641$	34.7159	+	196.884i	0.0541589	+	0.307151i	−0.945680	+	0.325099i	$0.894602\pi$
$642$		0			0
$643$	−255.040	−	700.717i	−0.396641	−	1.08976i	−0.963910	−	0.266230i	$-0.914222\pi$
$643$	−255.040	−	700.717i	−0.396641	−	1.08976i	0.567269	−	0.823533i	$-0.308000\pi$
$644$	242.601	+	919.672i	0.376710	+	1.42806i
$645$		0			0
$646$	−209.966	−	161.761i	−0.325025	−	0.250405i
$647$		−	654.355i		−	1.01137i	−0.862719	−	0.505684i	$-0.831240\pi$
$647$		−	654.355i		−	1.01137i	0.862719	−	0.505684i	$-0.168760\pi$
$648$		0			0
$649$	101.184			0.155907
$650$	125.389	−	162.755i	0.192906	−	0.250392i
$651$		0			0
$652$	−89.6080	+	23.6378i	−0.137436	+	0.0362542i
$653$	−621.236	+	226.111i	−0.951357	+	0.346266i	−0.770641	−	0.637270i	$-0.780064\pi$
$653$	−621.236	+	226.111i	−0.951357	+	0.346266i	−0.180716	+	0.983535i	$0.557842\pi$
$654$		0			0
$655$	−324.259	+	57.1756i	−0.495052	+	0.0872910i
$656$	−694.227	−	127.979i	−1.05827	−	0.195090i
$657$		0			0
$658$	615.849	−	1940.08i	0.935940	−	2.94845i
$659$	−125.066	+	343.616i	−0.189782	+	0.521421i	−0.997693	−	0.0678827i	$-0.978376\pi$
$659$	−125.066	+	343.616i	−0.189782	+	0.521421i	0.807912	+	0.589304i	$0.200598\pi$
$660$		0			0
$661$	90.6624	+	76.0748i	0.137159	+	0.115090i	0.708786	−	0.705423i	$-0.249243\pi$
$661$	90.6624	+	76.0748i	0.137159	+	0.115090i	−0.571627	+	0.820514i	$0.693687\pi$
$662$	59.4601	−	113.682i	0.0898188	−	0.171725i
$663$		0			0
$664$	75.0879	+	243.077i	0.113084	+	0.366080i
$665$	−265.399	+	459.685i	−0.399097	+	0.691255i
$666$		0			0
$667$	147.851	−	85.3618i	0.221666	−	0.127979i
$668$	−780.642	+	542.105i	−1.16863	+	0.811535i
$669$		0			0
$670$	289.802	+	456.853i	0.432540	+	0.681870i
$671$	−276.691	−	48.7882i	−0.412357	−	0.0727096i
$672$		0			0
$673$	594.886	−	499.169i	0.883932	−	0.741707i	−0.0830516	−	0.996545i	$-0.526467\pi$
$673$	594.886	−	499.169i	0.883932	−	0.741707i	0.966984	+	0.254838i	$0.0820222\pi$
$674$	701.172	−	154.018i	1.04031	−	0.228514i
$675$		0			0
$676$	1605.36	−	741.014i	2.37479	−	1.09617i
$677$	149.055	−	125.072i	0.220170	−	0.184745i	−0.526031	−	0.850466i	$-0.676320\pi$
$677$	149.055	−	125.072i	0.220170	−	0.184745i	0.746201	+	0.665721i	$0.231876\pi$
$678$		0			0
$679$	−356.478	−	62.8567i	−0.525004	−	0.0925724i
$680$	259.909	−	402.777i	0.382219	−	0.592320i
$681$		0			0
$682$	60.0904	+	145.872i	0.0881092	+	0.213888i
$683$	420.466	−	242.756i	0.615617	−	0.355427i	−0.159544	−	0.987191i	$-0.551002\pi$
$683$	420.466	−	242.756i	0.615617	−	0.355427i	0.775161	+	0.631764i	$0.217669\pi$
$684$		0			0
$685$	−233.104	+	403.748i	−0.340297	+	0.589413i
$686$	105.417	−	788.884i	0.153670	−	1.14998i
$687$		0			0
$688$	−26.6328	−	158.219i	−0.0387105	−	0.229970i
$689$	161.468	+	135.488i	0.234352	+	0.196644i
$690$		0			0
$691$	−373.852	+	1027.15i	−0.541030	+	1.48647i	0.304485	+	0.952517i	$0.401516\pi$
$691$	−373.852	+	1027.15i	−0.541030	+	1.48647i	−0.845515	+	0.533951i	$0.820707\pi$
$692$	−89.2466	+	976.402i	−0.128969	+	1.41099i
$693$		0			0
$694$	−702.923	+	641.604i	−1.01286	+	0.924501i
$695$	−713.412	+	125.794i	−1.02649	+	0.180998i
$696$		0			0
$697$	544.126	−	198.046i	0.780669	−	0.284140i
$698$	−40.2500	−	964.870i	−0.0576648	−	1.38233i
$699$		0			0
$700$	173.145	+	81.5591i	0.247350	+	0.116513i
$701$	−933.794			−1.33209			−0.666044	−	0.745912i	$-0.732014\pi$
$701$	−933.794			−1.33209			−0.666044	+	0.745912i	$0.732014\pi$
$702$		0			0
$703$		−	433.449i		−	0.616570i
$704$	476.833	−	215.623i	0.677320	−	0.306283i
$705$		0			0
$706$	−34.2338	−	820.650i	−0.0484898	−	1.16239i
$707$	175.956	+	483.434i	0.248876	+	0.683782i
$708$		0			0
$709$	212.090	+	1202.82i	0.299139	+	1.69650i	0.649886	+	0.760032i	$0.274817\pi$
$709$	212.090	+	1202.82i	0.299139	+	1.69650i	−0.350746	+	0.936470i	$0.614072\pi$
$710$	−171.535	+	156.571i	−0.241598	+	0.220522i
$711$		0			0
$712$	−26.1791	−	208.216i	−0.0367684	−	0.292439i
$713$	187.217	+	68.1414i	0.262576	+	0.0955700i
$714$		0			0
$715$	593.170	−	706.913i	0.829609	−	0.988689i
$716$	62.8299	−	230.894i	0.0877512	−	0.322477i
$717$		0			0
$718$	−171.539	+	1283.70i	−0.238913	+	1.78789i
$719$	−392.348	−	226.522i	−0.545685	−	0.315052i	0.201695	−	0.979448i	$-0.435355\pi$
$719$	−392.348	−	226.522i	−0.545685	−	0.315052i	−0.747380	+	0.664397i	$0.768689\pi$
$720$		0			0
$721$	931.464	+	1613.34i	1.29191	+	2.23765i
$722$	197.327	+	479.019i	0.273306	+	0.663461i
$723$		0			0
$724$	−192.582	+	191.092i	−0.265998	+	0.263939i
$725$	5.96552	−	33.8321i	0.00822830	−	0.0466650i
$726$		0			0
$727$	−183.034	−	218.131i	−0.251766	−	0.300043i	0.625328	−	0.780362i	$-0.284965\pi$
$727$	−183.034	−	218.131i	−0.251766	−	0.300043i	−0.877094	+	0.480319i	$0.840521\pi$
$728$	1375.51	+	1814.39i	1.88944	+	2.49229i
$729$		0			0
$730$	162.498	−	35.6941i	0.222601	−	0.0488960i
$731$	84.5959	+	100.818i	0.115726	+	0.137917i
$732$		0			0
$733$	−127.118	+	720.924i	−0.173422	+	0.983525i	0.766528	+	0.642211i	$0.221983\pi$
$733$	−127.118	+	720.924i	−0.173422	+	0.983525i	−0.939950	+	0.341313i	$0.889128\pi$
$734$	463.570	+	730.786i	0.631566	+	0.995622i
$735$		0			0
$736$	204.839	−	628.328i	0.278314	−	0.853706i
$737$	−242.240	−	419.572i	−0.328684	−	0.569297i
$738$		0			0
$739$	266.611	+	153.928i	0.360772	+	0.208292i	0.669419	−	0.742885i	$-0.266543\pi$
$739$	266.611	+	153.928i	0.360772	+	0.208292i	−0.308647	+	0.951177i	$0.599876\pi$
$740$	781.185	−	65.2886i	1.05566	−	0.0882279i
$741$		0			0
$742$	−91.0049	+	173.993i	−0.122648	+	0.234492i
$743$	39.9815	−	47.6481i	0.0538109	−	0.0641294i	−0.738468	−	0.674289i	$-0.764450\pi$
$743$	39.9815	−	47.6481i	0.0538109	−	0.0641294i	0.792279	+	0.610160i	$0.208895\pi$
$744$		0			0
$745$	−78.1282	−	28.4363i	−0.104870	−	0.0381696i
$746$	284.942	−	897.639i	0.381960	−	1.20327i
$747$		0			0
$748$	−247.578	+	350.672i	−0.330987	+	0.468813i
$749$	260.245	+	1475.92i	0.347457	+	1.97052i
$750$		0			0
$751$	81.5013	+	223.923i	0.108524	+	0.298167i	0.982053	−	0.188605i	$-0.0603966\pi$
$751$	81.5013	+	223.923i	0.108524	+	0.298167i	−0.873529	+	0.486772i	$0.838174\pi$
$752$	−1090.45	+	900.659i	−1.45007	+	1.19768i
$753$		0			0
$754$	249.419	−	323.746i	0.330795	−	0.429372i
$755$			783.005i			1.03709i
$756$		0			0
$757$	−1178.31			−1.55655			−0.778276	−	0.627923i	$-0.783905\pi$
$757$	−1178.31			−1.55655			−0.778276	+	0.627923i	$0.783905\pi$
$758$	613.757	+	472.849i	0.809706	+	0.623811i
$759$		0			0
$760$	328.129	−	168.391i	0.431749	−	0.221567i
$761$	−1203.80	+	438.148i	−1.58187	+	0.575753i	−0.975610	−	0.219513i	$-0.929553\pi$
$761$	−1203.80	+	438.148i	−1.58187	+	0.575753i	−0.606260	+	0.795267i	$0.707331\pi$
$762$		0			0
$763$	292.785	−	51.6259i	0.383729	−	0.0676618i
$764$	11.1484	−	15.7907i	0.0145922	−	0.0206685i
$765$		0			0
$766$	−540.672	−	171.628i	−0.705838	−	0.224058i
$767$	104.618	−	287.437i	0.136399	−	0.374754i
$768$		0			0
$769$	−143.704	−	120.582i	−0.186871	−	0.156803i	0.544553	−	0.838726i	$-0.316699\pi$
$769$	−143.704	−	120.582i	−0.186871	−	0.156803i	−0.731424	+	0.681923i	$0.761144\pi$
$770$	761.746	+	398.422i	0.989281	+	0.517431i
$771$		0			0
$772$	442.791	−	37.0069i	0.573563	−	0.0479364i
$773$	−226.649	+	392.567i	−0.293207	+	0.507849i	−0.974566	−	0.224100i	$-0.928056\pi$
$773$	−226.649	+	392.567i	−0.293207	+	0.507849i	0.681359	+	0.731949i	$0.261389\pi$
$774$		0			0
$775$	34.7196	−	20.0454i	0.0447995	−	0.0258650i
$776$	184.441	+	170.997i	0.237682	+	0.220357i
$777$		0			0
$778$	121.096	−	76.8163i	0.155650	−	0.0987356i
$779$	438.748	+	77.3631i	0.563219	+	0.0993107i
$780$		0			0
$781$	159.319	−	133.685i	0.203994	−	0.171171i
$782$	116.303	+	529.471i	0.148725	+	0.677073i
$783$		0			0
$784$	−867.345	+	1017.50i	−1.10631	+	1.29784i
$785$	604.233	−	507.012i	0.769724	−	0.645875i
$786$		0			0
$787$	−817.303	−	144.113i	−1.03850	−	0.183116i	−0.371703	−	0.928352i	$-0.621226\pi$
$787$	−817.303	−	144.113i	−1.03850	−	0.183116i	−0.666802	+	0.745235i	$0.732337\pi$
$788$	587.679	−	583.132i	0.745785	−	0.740015i
$789$		0			0
$790$	−639.934	+	263.614i	−0.810042	+	0.333689i
$791$	−195.860	+	113.080i	−0.247611	+	0.142958i
$792$		0			0
$793$	−424.677	+	735.562i	−0.535532	+	0.927569i
$794$	264.720	+	35.3741i	0.333400	+	0.0445518i
$795$		0			0
$796$	115.781	−	425.484i	0.145454	−	0.534528i
$797$	418.325	+	351.017i	0.524875	+	0.440422i	0.866327	−	0.499477i	$-0.166474\pi$
$797$	418.325	+	351.017i	0.524875	+	0.440422i	−0.341452	+	0.939899i	$0.610919\pi$
$798$		0			0
$799$	396.782	−	1090.15i	0.496598	−	1.36439i
$800$	−70.3606	−	112.847i	−0.0879507	−	0.141059i
$801$		0			0
$802$	738.346	+	808.912i	0.920631	+	1.00862i
$803$	−146.723	+	25.8712i	−0.182718	+	0.0322182i
$804$		0			0
$805$	1020.14	−	371.300i	1.26725	−	0.461242i
$806$	476.513	−	19.8780i	0.591207	−	0.0246625i
$807$		0			0
$808$	79.4007	−	348.532i	0.0982682	−	0.431351i
$809$	1048.73			1.29633			0.648167	−	0.761499i	$-0.275536\pi$
$809$	1048.73			1.29633			0.648167	+	0.761499i	$0.275536\pi$
$810$		0			0
$811$			28.9928i			0.0357495i	0.999840	+	0.0178747i	$0.00569001\pi$
$811$			28.9928i			0.0357495i	−0.999840	+	0.0178747i	$0.994310\pi$
$812$	344.414	+	162.235i	0.424156	+	0.199796i
$813$		0			0
$814$	−701.378	+	29.2583i	−0.861644	+	0.0359439i
$815$	36.1775	+	99.3969i	0.0443896	+	0.121959i
$816$		0			0
$817$	17.5834	+	99.7202i	0.0215219	+	0.122057i
$818$	−822.355	−	900.950i	−1.00532	−	1.10141i
$819$		0			0
$820$	−73.3411	+	802.388i	−0.0894404	+	0.978522i
$821$	−687.233	−	250.132i	−0.837069	−	0.304668i	−0.112312	−	0.993673i	$-0.535826\pi$
$821$	−687.233	−	250.132i	−0.837069	−	0.304668i	−0.724757	+	0.689005i	$0.758048\pi$
$822$		0			0
$823$	−337.483	+	402.197i	−0.410065	+	0.488696i	−0.931061	−	0.364863i	$-0.881116\pi$
$823$	−337.483	+	402.197i	−0.410065	+	0.488696i	0.520997	+	0.853559i	$0.325560\pi$
$824$	63.9945	−	1292.83i	0.0776632	−	1.56897i
$825$		0			0
$826$	282.438	+	37.7418i	0.341934	+	0.0456922i
$827$	437.915	+	252.830i	0.529522	+	0.305720i	0.740822	−	0.671702i	$-0.234436\pi$
$827$	437.915	+	252.830i	0.529522	+	0.305720i	−0.211300	+	0.977421i	$0.567770\pi$
$828$		0			0
$829$	−334.899	−	580.062i	−0.403979	−	0.699712i	0.590223	−	0.807240i	$-0.299040\pi$
$829$	−334.899	−	580.062i	−0.403979	−	0.699712i	−0.994202	+	0.107528i	$0.965706\pi$
$830$	268.492	−	110.603i	0.323485	−	0.133256i
$831$		0			0
$832$	−119.510	−	1577.50i	−0.143642	−	1.89603i
$833$	190.441	−	1080.05i	0.228621	−	1.29657i
$834$		0			0
$835$	697.287	+	830.994i	0.835074	+	0.995203i
$836$	−299.868	+	138.416i	−0.358694	+	0.165569i
$837$		0			0
$838$	181.320	+	825.463i	0.216372	+	0.985040i
$839$	−402.854	−	480.103i	−0.480160	−	0.572233i	0.470526	−	0.882386i	$-0.344064\pi$
$839$	−402.854	−	480.103i	−0.480160	−	0.572233i	−0.950687	+	0.310153i	$0.899620\pi$
$840$		0			0
$841$	−134.172	+	760.926i	−0.159538	+	0.904787i
$842$	−285.426	+	181.058i	−0.338985	+	0.215033i
$843$		0			0
$844$	592.877	−	411.715i	0.702461	−	0.487814i
$845$	−1009.06	−	1747.74i	−1.19415	−	2.06833i
$846$		0			0
$847$	539.822	+	311.666i	0.637334	+	0.367965i
$848$	118.681	−	67.2969i	0.139954	−	0.0793596i
$849$		0			0
$850$	96.6602	+	50.5570i	0.113718	+	0.0594788i
$851$	−569.835	+	679.103i	−0.669606	+	0.798006i
$852$		0			0
$853$	774.167	+	281.774i	0.907582	+	0.330333i	0.753287	−	0.657692i	$-0.228467\pi$
$853$	774.167	+	281.774i	0.907582	+	0.330333i	0.154295	+	0.988025i	$0.450689\pi$
$854$	−754.139	−	239.390i	−0.883067	−	0.280316i
$855$		0			0
$856$	404.100	−	959.730i	0.472079	−	1.12118i
$857$	−131.996	−	748.584i	−0.154020	−	0.873494i	−0.959676	−	0.281109i	$-0.909298\pi$
$857$	−131.996	−	748.584i	−0.154020	−	0.873494i	0.805655	−	0.592385i	$-0.201813\pi$
$858$		0			0
$859$	−48.7050	−	133.816i	−0.0566997	−	0.155781i	0.908109	−	0.418734i	$-0.137526\pi$
$859$	−48.7050	−	133.816i	−0.0566997	−	0.155781i	−0.964809	+	0.262953i	$0.915304\pi$
$860$	−177.073	+	46.7101i	−0.205898	+	0.0543141i
$861$		0			0
$862$	209.240	+	161.202i	0.242738	+	0.187010i
$863$		−	507.425i		−	0.587978i	−0.955809	−	0.293989i	$-0.905017\pi$
$863$		−	507.425i		−	0.587978i	0.955809	−	0.293989i	$-0.0949830\pi$
$864$		0			0
$865$	1119.10			1.29375
$866$	370.914	−	481.446i	0.428307	−	0.555942i
$867$		0			0
$868$	113.322	+	429.590i	0.130555	+	0.494919i
$869$	582.400	−	211.976i	0.670196	−	0.243931i
$870$		0			0
$871$	−1442.35	+	254.326i	−1.65597	+	0.291993i
$872$	−190.386	−	80.1630i	−0.218332	−	0.0919301i
$873$		0			0
$874$	−126.192	+	397.536i	−0.144384	+	0.454847i
$875$	524.180	−	1440.17i	0.599063	−	1.64591i
$876$		0			0
$877$	−855.706	−	718.023i	−0.975720	−	0.818726i	0.00771826	−	0.999970i	$-0.497543\pi$
$877$	−855.706	−	718.023i	−0.975720	−	0.818726i	−0.983438	+	0.181244i	$0.941988\pi$
$878$	−395.202	+	755.591i	−0.450117	+	0.860582i
$879$		0			0
$880$	−294.628	−	519.590i	−0.334805	−	0.590443i
$881$	−220.266	+	381.511i	−0.250018	+	0.433044i	−0.963530	−	0.267599i	$-0.913770\pi$
$881$	−220.266	+	381.511i	−0.250018	+	0.433044i	0.713513	+	0.700642i	$0.247103\pi$
$882$		0			0
$883$	−513.152	+	296.269i	−0.581146	+	0.335525i	−0.761589	−	0.648060i	$-0.775580\pi$
$883$	−513.152	+	296.269i	−0.581146	+	0.335525i	0.180442	+	0.983586i	$0.442247\pi$
$884$	740.184	+	1065.88i	0.837312	+	1.20575i
$885$		0			0
$886$	318.521	+	502.127i	0.359504	+	0.566735i
$887$	447.779	+	78.9555i	0.504824	+	0.0890140i	0.420259	−	0.907404i	$-0.361939\pi$
$887$	447.779	+	78.9555i	0.504824	+	0.0890140i	0.0845643	+	0.996418i	$0.473050\pi$
$888$		0			0
$889$	−875.561	+	734.683i	−0.984883	+	0.826415i
$890$	−233.949	+	51.3888i	−0.262864	+	0.0577402i
$891$		0			0
$892$	13.8438	+	29.9917i	0.0155200	+	0.0336230i
$893$	683.761	−	573.743i	0.765689	−	0.642490i
$894$		0			0
$895$	−268.972	−	47.4271i	−0.300528	−	0.0529912i
$896$	1411.43	−	424.017i	1.57525	−	0.473233i
$897$		0			0
$898$	−524.426	−	1273.06i	−0.583993	−	1.41767i
$899$	69.0630	−	39.8735i	0.0768220	−	0.0443532i
$900$		0			0
$901$	−55.9560	+	96.9186i	−0.0621043	+	0.107568i
$902$	95.5678	−	715.175i	0.105951	−	0.792877i
$903$		0			0
$904$	156.951	+	7.76895i	0.173618	+	0.00859397i
$905$	237.213	+	199.045i	0.262113	+	0.219939i
$906$		0			0
$907$	−509.329	+	1399.37i	−0.561554	+	1.54286i	0.255806	+	0.966728i	$0.417659\pi$
$907$	−509.329	+	1399.37i	−0.561554	+	1.54286i	−0.817360	+	0.576128i	$0.804563\pi$
$908$	−527.395	−	48.2058i	−0.580832	−	0.0530901i
$909$		0			0
$910$	1919.41	−	1751.97i	2.10924	−	1.92525i
$911$	−372.965	+	65.7638i	−0.409402	+	0.0721886i	−0.374556	−	0.927204i	$-0.622205\pi$
$911$	−372.965	+	65.7638i	−0.409402	+	0.0721886i	−0.0348454	+	0.999393i	$0.511094\pi$
$912$		0			0
$913$	−244.353	+	88.9373i	−0.267638	+	0.0974122i
$914$	−46.4092	−	1112.52i	−0.0507759	−	1.21720i
$915$		0			0
$916$	−637.827	+	1354.07i	−0.696317	+	1.47824i
$917$	830.347			0.905503
$918$		0			0
$919$		−	235.053i		−	0.255771i	−0.991789	−	0.127885i	$-0.959181\pi$
$919$		−	235.053i		−	0.255771i	0.991789	−	0.127885i	$-0.0408190\pi$
$920$	−735.469	−	167.551i	−0.799423	−	0.182120i
$921$		0			0
$922$	−28.7176	−	688.416i	−0.0311471	−	0.746655i
$923$	−215.036	−	590.806i	−0.232975	−	0.640093i
$924$		0			0
$925$	30.9768	+	175.678i	0.0334884	+	0.189922i
$926$	920.514	−	840.213i	0.994075	−	0.907357i
$927$		0			0
$928$	−139.959	−	224.472i	−0.150818	−	0.241887i
$929$	−227.048	−	82.6386i	−0.244400	−	0.0889543i	0.216916	−	0.976190i	$-0.430400\pi$
$929$	−227.048	−	82.6386i	−0.244400	−	0.0889543i	−0.461316	+	0.887236i	$0.652622\pi$
$930$		0			0
$931$	542.386	−	646.390i	0.582584	−	0.694297i
$932$	−374.097	−	101.798i	−0.401392	−	0.109225i
$933$		0			0
$934$	157.216	−	1176.51i	0.168325	−	1.25965i
$935$	424.313	+	244.977i	0.453810	+	0.262007i
$936$		0			0
$937$	−244.489	−	423.467i	−0.260927	−	0.451939i	0.705561	−	0.708649i	$-0.250695\pi$
$937$	−244.489	−	423.467i	−0.260927	−	0.451939i	−0.966489	+	0.256710i	$0.917362\pi$
$938$	−519.670	−	1261.52i	−0.554020	−	1.34490i
$939$		0			0
$940$	1137.02	+	1145.89i	1.20960	+	1.21903i
$941$	−181.612	+	1029.97i	−0.192999	+	1.09455i	0.722242	+	0.691641i	$0.243112\pi$
$941$	−181.612	+	1029.97i	−0.192999	+	1.09455i	−0.915240	+	0.402909i	$0.867999\pi$
$942$		0			0
$943$	−585.699	−	698.009i	−0.621102	−	0.740201i
$944$	−150.676	−	128.440i	−0.159615	−	0.136059i
$945$		0			0
$946$	160.174	−	35.1835i	0.169317	−	0.0371918i
$947$	1167.17	+	1390.98i	1.23250	+	1.46883i	0.834097	+	0.551618i	$0.185989\pi$
$947$	1167.17	+	1390.98i	1.23250	+	1.46883i	0.398399	+	0.917212i	$0.369566\pi$
$948$		0			0
$949$	−78.2097	+	443.550i	−0.0824128	+	0.467386i
$950$	44.9571	+	70.8719i	0.0473233	+	0.0746020i
$951$		0			0
$952$	−821.874	+	886.494i	−0.863313	+	0.931191i
$953$	541.513	+	937.929i	0.568220	+	0.984185i	0.996742	+	0.0806543i	$0.0257010\pi$
$953$	541.513	+	937.929i	0.568220	+	0.984185i	−0.428522	+	0.903531i	$0.640966\pi$
$954$		0			0
$955$	−19.1068	−	11.0313i	−0.0200071	−	0.0115511i
$956$	156.017	+	1866.76i	0.163198	+	1.95267i
$957$		0			0
$958$	−507.960	+	971.173i	−0.530230	+	1.01375i
$959$	755.728	−	900.642i	0.788038	−	0.939147i
$960$		0			0
$961$	−815.593	−	296.852i	−0.848692	−	0.308899i
$962$	−642.070	+	2022.68i	−0.667432	+	2.10258i
$963$		0			0
$964$	−472.549	−	333.625i	−0.490196	−	0.346084i
$965$	−88.0670	−	499.453i	−0.0912611	−	0.517568i
$966$		0			0
$967$	93.2391	+	256.172i	0.0964210	+	0.264915i	0.978521	−	0.206148i	$-0.0660928\pi$
$967$	93.2391	+	256.172i	0.0964210	+	0.264915i	−0.882100	+	0.471063i	$0.843871\pi$
$968$	−197.747	−	385.332i	−0.204284	−	0.398070i
$969$		0			0
$970$	175.201	−	227.410i	0.180619	−	0.234444i
$971$			1287.81i			1.32627i	0.748498	+	0.663137i	$0.230775\pi$
$971$			1287.81i			1.32627i	−0.748498	+	0.663137i	$0.769225\pi$
$972$		0			0
$973$	1826.87			1.87756
$974$	302.099	+	232.742i	0.310163	+	0.238955i
$975$		0			0
$976$	350.100	+	423.877i	0.358709	+	0.434300i
$977$	286.009	−	104.099i	0.292742	−	0.106549i	−0.191475	−	0.981498i	$-0.561327\pi$
$977$	286.009	−	104.099i	0.292742	−	0.106549i	0.484216	+	0.874948i	$0.339105\pi$
$978$		0			0
$979$	211.237	−	37.2467i	0.215768	−	0.0380457i
$980$	1246.66	+	880.154i	1.27210	+	0.898116i
$981$		0			0
$982$	655.622	+	208.117i	0.667640	+	0.211932i
$983$	−368.108	+	1011.37i	−0.374474	+	1.02886i	0.599138	+	0.800646i	$0.295510\pi$
$983$	−368.108	+	1011.37i	−0.374474	+	1.02886i	−0.973611	+	0.228212i	$0.926712\pi$
$984$		0			0
$985$	−723.872	−	607.400i	−0.734895	−	0.616650i
$986$	192.273	+	100.566i	0.195003	+	0.101994i
$987$		0			0
$988$	83.1552	+	994.960i	0.0841652	+	1.00704i
$989$	103.549	−	179.352i	0.104701	−	0.181347i
$990$		0			0
$991$	616.046	−	355.674i	0.621641	−	0.358904i	−0.155867	−	0.987778i	$-0.549817\pi$
$991$	616.046	−	355.674i	0.621641	−	0.358904i	0.777508	+	0.628874i	$0.216484\pi$
$992$	95.6829	−	293.500i	0.0964545	−	0.295867i
$993$		0			0
$994$	494.577	−	313.732i	0.497563	−	0.315626i
$995$	−495.655	−	87.3973i	−0.498146	−	0.0878365i
$996$		0			0
$997$	−128.599	+	107.907i	−0.128985	+	0.108232i	−0.704998	−	0.709209i	$-0.749052\pi$
$997$	−128.599	+	107.907i	−0.128985	+	0.108232i	0.576013	+	0.817441i	$0.304608\pi$
$998$	−191.340	−	871.080i	−0.191723	−	0.872825i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.25		204
3.2	odd	2		108.3.j.a.103.10	yes	204
4.3	odd	2	inner	324.3.j.a.199.29		204
12.11	even	2		108.3.j.a.103.6	yes	204
27.11	odd	18		108.3.j.a.43.6	✓	204
27.16	even	9	inner	324.3.j.a.127.29		204
108.11	even	18		108.3.j.a.43.10	yes	204
108.43	odd	18	inner	324.3.j.a.127.25		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.6	✓	204	27.11	odd	18
108.3.j.a.43.10	yes	204	108.11	even	18
108.3.j.a.103.6	yes	204	12.11	even	2
108.3.j.a.103.10	yes	204	3.2	odd	2
324.3.j.a.127.25		204	108.43	odd	18	inner
324.3.j.a.127.29		204	27.16	even	9	inner
324.3.j.a.199.25		204	1.1	even	1	trivial
324.3.j.a.199.29		204	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22060 - 1.58434i) q^{2} +(-1.02026 - 3.86769i) q^{4} +(-4.29021 + 1.56151i) q^{5} +(11.3387 - 1.99932i) q^{7} +(-7.37308 - 3.10447i) q^{8} +O(q^{10})\)	\(q+(1.22060 - 1.58434i) q^{2} +(-1.02026 - 3.86769i) q^{4} +(-4.29021 + 1.56151i) q^{5} +(11.3387 - 1.99932i) q^{7} +(-7.37308 - 3.10447i) q^{8} +(-2.76268 + 8.70313i) q^{10} +(2.79665 - 7.68375i) q^{11} +(-18.9359 - 15.8891i) q^{13} +(10.6724 - 20.4047i) q^{14} +(-13.9181 + 7.89213i) q^{16} +(6.56214 - 11.3660i) q^{17} +(8.74492 - 5.04888i) q^{19} +(10.4166 + 15.0001i) q^{20} +(-8.76006 - 13.8096i) q^{22} +(-20.3386 - 3.58624i) q^{23} +(-3.18352 + 2.67129i) q^{25} +(-48.2869 + 10.6066i) q^{26} +(-19.3012 - 41.8148i) q^{28} +(-6.33255 + 5.31364i) q^{29} +(-9.50040 - 1.67518i) q^{31} +(-4.48468 + 31.6842i) q^{32} +(-9.99778 - 24.2700i) q^{34} +(-45.5234 + 26.2830i) q^{35} +(21.4626 - 37.1743i) q^{37} +(2.67492 - 20.0176i) q^{38} +(36.4797 + 1.80572i) q^{40} +(33.7981 + 28.3600i) q^{41} +(-3.42972 + 9.42307i) q^{43} +(-32.5717 - 2.97717i) q^{44} +(-30.5071 + 27.8458i) q^{46} +(87.0515 - 15.3495i) q^{47} +(78.5238 - 28.5803i) q^{49} +(0.346420 + 8.30436i) q^{50} +(-42.1346 + 89.4493i) q^{52} -8.52710 q^{53} +37.3319i q^{55} +(-89.8079 - 20.4596i) q^{56} +(0.689087 + 16.5187i) q^{58} +(4.23230 + 11.6281i) q^{59} +(-5.96660 - 33.8383i) q^{61} +(-14.2502 + 13.0071i) q^{62} +(44.7245 + 45.7790i) q^{64} +(106.050 + 38.5990i) q^{65} +(38.0852 - 45.3881i) q^{67} +(-50.6552 - 13.7841i) q^{68} +(-13.9248 + 104.206i) q^{70} +(22.0271 + 12.7174i) q^{71} +(-9.11022 - 15.7794i) q^{73} +(-32.6995 - 79.3791i) q^{74} +(-28.4497 - 28.6715i) q^{76} +(16.3482 - 92.7151i) q^{77} +(48.7210 + 58.0634i) q^{79} +(47.3881 - 55.5922i) q^{80} +(86.1858 - 18.9314i) q^{82} +(-20.4415 - 24.3612i) q^{83} +(-10.4049 + 59.0092i) q^{85} +(10.7430 + 16.9357i) q^{86} +(-44.4739 + 47.9707i) q^{88} +(13.1160 + 22.7175i) q^{89} +(-246.476 - 142.303i) q^{91} +(6.88020 + 82.3223i) q^{92} +(81.9364 - 156.655i) q^{94} +(-29.6337 + 35.3160i) q^{95} +(-29.5430 - 10.7528i) q^{97} +(50.5654 - 159.294i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

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