LMFDB - Embedded newform 288.2.w.a.179.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			179.6
Character	$\chi$	$=$	288.179
Dual form			288.2.w.a.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.450008 - 1.34071i) q^{2} +(-1.59499 - 1.20666i) q^{4} +(-0.739921 - 1.78633i) q^{5} +(0.385417 + 0.385417i) q^{7} +(-2.33553 + 1.59540i) q^{8} +O(q^{10})$	\(q+(0.450008 - 1.34071i) q^{2} +(-1.59499 - 1.20666i) q^{4} +(-0.739921 - 1.78633i) q^{5} +(0.385417 + 0.385417i) q^{7} +(-2.33553 + 1.59540i) q^{8} +(-2.72791 + 0.188155i) q^{10} +(-2.36398 - 5.70716i) q^{11} +(-2.30916 - 0.956485i) q^{13} +(0.690171 - 0.343290i) q^{14} +(1.08796 + 3.84920i) q^{16} +5.05518 q^{17} +(-1.27305 + 3.07341i) q^{19} +(-0.975320 + 3.74200i) q^{20} +(-8.71543 + 0.601139i) q^{22} +(-2.28291 - 2.28291i) q^{23} +(0.892052 - 0.892052i) q^{25} +(-2.32151 + 2.66548i) q^{26} +(-0.149669 - 1.07980i) q^{28} +(0.735171 + 0.304518i) q^{29} +3.40740i q^{31} +(5.65024 + 0.273536i) q^{32} +(2.27487 - 6.77751i) q^{34} +(0.403302 - 0.973658i) q^{35} +(9.56094 - 3.96027i) q^{37} +(3.54766 + 3.08984i) q^{38} +(4.57802 + 2.99155i) q^{40} +(5.27801 - 5.27801i) q^{41} +(2.53597 - 1.05043i) q^{43} +(-3.11606 + 11.9553i) q^{44} +(-4.08804 + 2.03338i) q^{46} +6.85609i q^{47} -6.70291i q^{49} +(-0.794549 - 1.59741i) q^{50} +(2.52893 + 4.31194i) q^{52} +(-7.45793 + 3.08917i) q^{53} +(-8.44569 + 8.44569i) q^{55} +(-1.51505 - 0.285257i) q^{56} +(0.739101 - 0.848613i) q^{58} +(6.14066 - 2.54355i) q^{59} +(2.67989 - 6.46983i) q^{61} +(4.56833 + 1.53336i) q^{62} +(2.90938 - 7.45221i) q^{64} +4.83264i q^{65} +(10.2890 + 4.26184i) q^{67} +(-8.06294 - 6.09987i) q^{68} +(-1.12390 - 0.978864i) q^{70} +(-6.37064 + 6.37064i) q^{71} +(9.03739 + 9.03739i) q^{73} +(-1.00706 - 14.6006i) q^{74} +(5.73905 - 3.36592i) q^{76} +(1.28852 - 3.11075i) q^{77} +1.22095 q^{79} +(6.07093 - 4.79156i) q^{80} +(-4.70112 - 9.45141i) q^{82} +(-14.8416 - 6.14761i) q^{83} +(-3.74043 - 9.03021i) q^{85} +(-0.267116 - 3.87270i) q^{86} +(14.6264 + 9.55772i) q^{88} +(4.97492 + 4.97492i) q^{89} +(-0.521343 - 1.25863i) q^{91} +(0.886520 + 6.39590i) q^{92} +(9.19200 + 3.08529i) q^{94} +6.43208 q^{95} +1.23680 q^{97} +(-8.98663 - 3.01636i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 - 4 * q^8	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$

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 $

$2$	0.450008	−	1.34071i	0.318204	−	0.948022i
$2$	0.450008	−	1.34071i	0.318204	−	0.948022i
$3$		0			0
$3$		0			0
$4$	−1.59499	−	1.20666i	−0.797493	−	0.603328i
$5$	−0.739921	−	1.78633i	−0.330903	−	0.798870i	−0.998521	−	0.0543661i	$-0.982686\pi$
$5$	−0.739921	−	1.78633i	−0.330903	−	0.798870i	0.667618	−	0.744504i	$-0.267314\pi$
$6$		0			0
$7$	0.385417	+	0.385417i	0.145674	+	0.145674i	0.776182	−	0.630509i	$-0.217154\pi$
$7$	0.385417	+	0.385417i	0.145674	+	0.145674i	−0.630509	+	0.776182i	$0.717154\pi$
$8$	−2.33553	+	1.59540i	−0.825734	+	0.564060i
$9$		0			0
$10$	−2.72791	+	0.188155i	−0.862641	+	0.0594999i
$11$	−2.36398	−	5.70716i	−0.712767	−	1.72077i	−0.692968	−	0.720969i	$-0.743697\pi$
$11$	−2.36398	−	5.70716i	−0.712767	−	1.72077i	−0.0197998	−	0.999804i	$-0.506303\pi$
$12$		0			0
$13$	−2.30916	−	0.956485i	−0.640446	−	0.265281i	0.0387383	−	0.999249i	$-0.487666\pi$
$13$	−2.30916	−	0.956485i	−0.640446	−	0.265281i	−0.679184	+	0.733968i	$0.737666\pi$
$14$	0.690171	−	0.343290i	0.184456	−	0.0917481i
$15$		0			0
$16$	1.08796	+	3.84920i	0.271990	+	0.962300i
$17$	5.05518			1.22606			0.613031	−	0.790059i	$-0.289950\pi$
$17$	5.05518			1.22606			0.613031	+	0.790059i	$0.289950\pi$
$18$		0			0
$19$	−1.27305	+	3.07341i	−0.292057	+	0.705089i	−0.999999	−	0.00118164i	$-0.999624\pi$
$19$	−1.27305	+	3.07341i	−0.292057	+	0.705089i	0.707942	+	0.706271i	$0.249624\pi$
$20$	−0.975320	+	3.74200i	−0.218088	+	0.836736i
$21$		0			0
$22$	−8.71543	+	0.601139i	−1.85814	+	0.128163i
$23$	−2.28291	−	2.28291i	−0.476020	−	0.476020i	0.427837	−	0.903856i	$-0.359276\pi$
$23$	−2.28291	−	2.28291i	−0.476020	−	0.476020i	−0.903856	+	0.427837i	$0.859276\pi$
$24$		0			0
$25$	0.892052	−	0.892052i	0.178410	−	0.178410i
$26$	−2.32151	+	2.66548i	−0.455285	+	0.522743i
$27$		0			0
$28$	−0.149669	−	1.07980i	−0.0282847	−	0.204063i
$29$	0.735171	+	0.304518i	0.136518	+	0.0565475i	0.449896	−	0.893081i	$-0.351461\pi$
$29$	0.735171	+	0.304518i	0.136518	+	0.0565475i	−0.313379	+	0.949628i	$0.601461\pi$
$30$		0			0
$31$			3.40740i			0.611988i	0.952033	+	0.305994i	$0.0989887\pi$
$31$			3.40740i			0.611988i	−0.952033	+	0.305994i	$0.901011\pi$
$32$	5.65024	+	0.273536i	0.998830	+	0.0483549i
$33$		0			0
$34$	2.27487	−	6.77751i	0.390137	−	1.16233i
$35$	0.403302	−	0.973658i	0.0681705	−	0.164578i
$36$		0			0
$37$	9.56094	−	3.96027i	1.57181	−	0.651065i	0.584720	−	0.811235i	$-0.301204\pi$
$37$	9.56094	−	3.96027i	1.57181	−	0.651065i	0.987089	+	0.160170i	$0.0512043\pi$
$38$	3.54766	+	3.08984i	0.575507	+	0.501239i
$39$		0			0
$40$	4.57802	+	2.99155i	0.723848	+	0.473005i
$41$	5.27801	−	5.27801i	0.824287	−	0.824287i	−0.162432	−	0.986720i	$-0.551934\pi$
$41$	5.27801	−	5.27801i	0.824287	−	0.824287i	0.986720	+	0.162432i	$0.0519340\pi$
$42$		0			0
$43$	2.53597	−	1.05043i	0.386732	−	0.160190i	−0.180842	−	0.983512i	$-0.557882\pi$
$43$	2.53597	−	1.05043i	0.386732	−	0.160190i	0.567574	+	0.823323i	$0.307882\pi$
$44$	−3.11606	+	11.9553i	−0.469764	+	1.80234i
$45$		0			0
$46$	−4.08804	+	2.03338i	−0.602748	+	0.299806i
$47$			6.85609i			1.00006i	0.866007	+	0.500031i	$0.166678\pi$
$47$			6.85609i			1.00006i	−0.866007	+	0.500031i	$0.833322\pi$
$48$		0			0
$49$		−	6.70291i		−	0.957558i
$50$	−0.794549	−	1.59741i	−0.112366	−	0.225908i
$51$		0			0
$52$	2.52893	+	4.31194i	0.350699	+	0.597959i
$53$	−7.45793	+	3.08917i	−1.02442	+	0.424331i	−0.830697	−	0.556725i	$-0.812058\pi$
$53$	−7.45793	+	3.08917i	−1.02442	+	0.424331i	−0.193728	+	0.981055i	$0.562058\pi$
$54$		0			0
$55$	−8.44569	+	8.44569i	−1.13882	+	1.13882i
$56$	−1.51505	−	0.285257i	−0.202456	−	0.0381190i
$57$		0			0
$58$	0.739101	−	0.848613i	0.0970488	−	0.111428i
$59$	6.14066	−	2.54355i	0.799446	−	0.331142i	0.0547117	−	0.998502i	$-0.482576\pi$
$59$	6.14066	−	2.54355i	0.799446	−	0.331142i	0.744735	+	0.667361i	$0.232576\pi$
$60$		0			0
$61$	2.67989	−	6.46983i	0.343125	−	0.828376i	−0.654272	−	0.756260i	$-0.727025\pi$
$61$	2.67989	−	6.46983i	0.343125	−	0.828376i	0.997396	−	0.0721165i	$-0.0229753\pi$
$62$	4.56833	+	1.53336i	0.580178	+	0.194737i
$63$		0			0
$64$	2.90938	−	7.45221i	0.363673	−	0.931527i
$65$			4.83264i			0.599415i
$66$		0			0
$67$	10.2890	+	4.26184i	1.25700	+	0.520666i	0.908987	−	0.416824i	$-0.136857\pi$
$67$	10.2890	+	4.26184i	1.25700	+	0.520666i	0.348012	+	0.937490i	$0.386857\pi$
$68$	−8.06294	−	6.09987i	−0.977775	−	0.739718i
$69$		0			0
$70$	−1.12390	−	0.978864i	−0.134332	−	0.116997i
$71$	−6.37064	+	6.37064i	−0.756056	+	0.756056i	−0.975602	−	0.219546i	$-0.929542\pi$
$71$	−6.37064	+	6.37064i	−0.756056	+	0.756056i	0.219546	+	0.975602i	$0.429542\pi$
$72$		0			0
$73$	9.03739	+	9.03739i	1.05775	+	1.05775i	0.998227	+	0.0595198i	$0.0189570\pi$
$73$	9.03739	+	9.03739i	1.05775	+	1.05775i	0.0595198	+	0.998227i	$0.481043\pi$
$74$	−1.00706	−	14.6006i	−0.117069	−	1.69728i
$75$		0			0
$76$	5.73905	−	3.36592i	0.658314	−	0.386097i
$77$	1.28852	−	3.11075i	0.146840	−	0.354503i
$78$		0			0
$79$	1.22095			0.137367			0.0686837	−	0.997638i	$-0.478120\pi$
$79$	1.22095			0.137367			0.0686837	+	0.997638i	$0.478120\pi$
$80$	6.07093	−	4.79156i	0.678750	−	0.535712i
$81$		0			0
$82$	−4.70112	−	9.45141i	−0.519152	−	1.04373i
$83$	−14.8416	−	6.14761i	−1.62908	−	0.674788i	−0.633953	−	0.773372i	$-0.718569\pi$
$83$	−14.8416	−	6.14761i	−1.62908	−	0.674788i	−0.995129	+	0.0985841i	$0.968569\pi$
$84$		0			0
$85$	−3.74043	−	9.03021i	−0.405707	−	0.979464i
$86$	−0.267116	−	3.87270i	−0.0288038	−	0.417603i
$87$		0			0
$88$	14.6264	+	9.55772i	1.55918	+	1.01886i
$89$	4.97492	+	4.97492i	0.527340	+	0.527340i	0.919778	−	0.392438i	$-0.128368\pi$
$89$	4.97492	+	4.97492i	0.527340	+	0.527340i	−0.392438	+	0.919778i	$0.628368\pi$
$90$		0			0
$91$	−0.521343	−	1.25863i	−0.0546516	−	0.131941i
$92$	0.886520	+	6.39590i	0.0924261	+	0.666818i
$93$		0			0
$94$	9.19200	+	3.08529i	0.948082	+	0.318224i
$95$	6.43208			0.659917
$96$		0			0
$97$	1.23680			0.125579			0.0627893	−	0.998027i	$-0.480000\pi$
$97$	1.23680			0.125579			0.0627893	+	0.998027i	$0.480000\pi$
$98$	−8.98663	−	3.01636i	−0.907787	−	0.304699i
$99$		0			0
$100$	−2.49921	+	0.346410i	−0.249921	+	0.0346410i
$101$	5.61006	+	13.5439i	0.558222	+	1.34767i	0.911172	+	0.412025i	$0.135179\pi$
$101$	5.61006	+	13.5439i	0.558222	+	1.34767i	−0.352950	+	0.935642i	$0.614821\pi$
$102$		0			0
$103$	−13.0799	−	13.0799i	−1.28880	−	1.28880i	−0.935518	−	0.353279i	$-0.885067\pi$
$103$	−13.0799	−	13.0799i	−1.28880	−	1.28880i	−0.353279	−	0.935518i	$-0.614933\pi$
$104$	6.91909	−	1.45014i	0.678472	−	0.142198i
$105$		0			0
$106$	0.785549	+	11.3890i	0.0762993	+	1.10620i
$107$	−1.16330	−	2.80844i	−0.112460	−	0.271502i	0.857622	−	0.514281i	$-0.171941\pi$
$107$	−1.16330	−	2.80844i	−0.112460	−	0.271502i	−0.970082	+	0.242779i	$0.921941\pi$
$108$		0			0
$109$	−13.5958	−	5.63158i	−1.30225	−	0.539408i	−0.379634	−	0.925137i	$-0.623950\pi$
$109$	−13.5958	−	5.63158i	−1.30225	−	0.539408i	−0.922612	+	0.385729i	$0.873950\pi$
$110$	7.52256	+	15.1238i	0.717248	+	1.44200i
$111$		0			0
$112$	−1.06423	+	1.90286i	−0.100560	+	0.179804i
$113$	13.6829			1.28718			0.643591	−	0.765369i	$-0.277444\pi$
$113$	13.6829			1.28718			0.643591	+	0.765369i	$0.277444\pi$
$114$		0			0
$115$	−2.38885	+	5.76720i	−0.222761	+	0.537794i
$116$	−0.805139	−	1.37280i	−0.0747552	−	0.127461i
$117$		0			0
$118$	−0.646801	−	9.37744i	−0.0595429	−	0.863264i
$119$	1.94835	+	1.94835i	0.178605	+	0.178605i
$120$		0			0
$121$	−19.2051	+	19.2051i	−1.74591	+	1.74591i
$122$	−7.46816	−	6.50442i	−0.676136	−	0.588882i
$123$		0			0
$124$	4.11157	−	5.43476i	0.369230	−	0.488056i
$125$	−11.1852	−	4.63305i	−1.00043	−	0.414393i
$126$		0			0
$127$		−	8.19707i		−	0.727372i	−0.931522	−	0.363686i	$-0.881518\pi$
$127$		−	8.19707i		−	0.727372i	0.931522	−	0.363686i	$-0.118482\pi$
$128$	−8.68198	−	7.25418i	−0.767386	−	0.641185i
$129$		0			0
$130$	6.47915	+	2.17473i	0.568259	+	0.190736i
$131$	−1.61003	+	3.88695i	−0.140669	+	0.339604i	−0.978476	−	0.206362i	$-0.933837\pi$
$131$	−1.61003	+	3.88695i	−0.140669	+	0.339604i	0.837807	+	0.545967i	$0.183837\pi$
$132$		0			0
$133$	−1.67520	+	0.693890i	−0.145258	+	0.0601679i
$134$	10.3440	−	11.8766i	0.893585	−	1.02599i
$135$		0			0
$136$	−11.8065	+	8.06505i	−1.01240	+	0.691572i
$137$	−6.79006	+	6.79006i	−0.580114	+	0.580114i	−0.934934	−	0.354821i	$-0.884542\pi$
$137$	−6.79006	+	6.79006i	−0.580114	+	0.580114i	0.354821	+	0.934934i	$0.384542\pi$
$138$		0			0
$139$	−3.08589	+	1.27822i	−0.261742	+	0.108417i	−0.509695	−	0.860355i	$-0.670242\pi$
$139$	−3.08589	+	1.27822i	−0.261742	+	0.108417i	0.247954	+	0.968772i	$0.420242\pi$
$140$	−1.81813	+	1.06632i	−0.153660	+	0.0901208i
$141$		0			0
$142$	5.67432	+	11.4080i	0.476178	+	0.957338i
$143$			15.4399i			1.29115i
$144$		0			0
$145$		−	1.53857i		−	0.127772i
$146$	16.1834	−	8.04959i	1.33935	−	0.666189i
$147$		0			0
$148$	−20.0283	−	5.22020i	−1.64631	−	0.429098i
$149$	−8.40712	+	3.48234i	−0.688738	+	0.285285i	−0.699474	−	0.714658i	$-0.746582\pi$
$149$	−8.40712	+	3.48234i	−0.688738	+	0.285285i	0.0107364	+	0.999942i	$0.496582\pi$
$150$		0			0
$151$	−13.7649	+	13.7649i	−1.12017	+	1.12017i	−0.128459	+	0.991715i	$0.541003\pi$
$151$	−13.7649	+	13.7649i	−1.12017	+	1.12017i	−0.991715	+	0.128459i	$0.958997\pi$
$152$	−1.93009	−	9.20907i	−0.156551	−	0.746954i
$153$		0			0
$154$	−3.59076	−	3.12738i	−0.289352	−	0.252012i
$155$	6.08674	−	2.52121i	0.488899	−	0.202508i
$156$		0			0
$157$	1.16741	−	2.81838i	0.0931694	−	0.224931i	−0.870424	−	0.492303i	$-0.836155\pi$
$157$	1.16741	−	2.81838i	0.0931694	−	0.224931i	0.963593	+	0.267372i	$0.0861553\pi$
$158$	0.549436	−	1.63693i	0.0437108	−	0.130227i
$159$		0			0
$160$	−3.69210	−	10.2956i	−0.291886	−	0.813936i
$161$		−	1.75974i		−	0.138687i
$162$		0			0
$163$	11.1679	+	4.62591i	0.874740	+	0.362329i	0.774455	−	0.632630i	$-0.218024\pi$
$163$	11.1679	+	4.62591i	0.874740	+	0.362329i	0.100285	+	0.994959i	$0.468024\pi$
$164$	−14.7871	+	2.04961i	−1.15468	+	0.160047i
$165$		0			0
$166$	−14.9210	+	17.1318i	−1.15809	+	1.32969i
$167$	2.51551	−	2.51551i	0.194656	−	0.194656i	−0.603049	−	0.797704i	$-0.706048\pi$
$167$	2.51551	−	2.51551i	0.194656	−	0.194656i	0.797704	+	0.603049i	$0.206048\pi$
$168$		0			0
$169$	−4.77503	−	4.77503i	−0.367310	−	0.367310i
$170$	−13.7901	+	0.951159i	−1.05765	+	0.0729506i
$171$		0			0
$172$	−5.31235	−	1.38462i	−0.405063	−	0.105576i
$173$	0.737563	−	1.78063i	0.0560759	−	0.135379i	−0.893359	−	0.449344i	$-0.851658\pi$
$173$	0.737563	−	1.78063i	0.0560759	−	0.135379i	0.949434	+	0.313965i	$0.101658\pi$
$174$		0			0
$175$	0.687623			0.0519794
$176$	19.3961	−	15.3086i	1.46203	−	1.15393i
$177$		0			0
$178$	8.90866	−	4.43115i	0.667732	−	0.332129i
$179$	9.47042	+	3.92278i	0.707852	+	0.293202i	0.707416	−	0.706798i	$-0.249861\pi$
$179$	9.47042	+	3.92278i	0.707852	+	0.293202i	0.000436715		1.00000i	$0.499861\pi$
$180$		0			0
$181$	9.91984	+	23.9486i	0.737336	+	1.78009i	0.616410	+	0.787426i	$0.288587\pi$
$181$	9.91984	+	23.9486i	0.737336	+	1.78009i	0.120927	+	0.992661i	$0.461413\pi$
$182$	−1.92207	+	0.132573i	−0.142473	+	0.00982696i
$183$		0			0
$184$	8.97396	+	1.68964i	0.661569	+	0.124562i
$185$	−14.1487	−	14.1487i	−1.04023	−	1.04023i
$186$		0			0
$187$	−11.9504	−	28.8507i	−0.873897	−	2.10977i
$188$	8.27294	−	10.9354i	0.603366	−	0.797543i
$189$		0			0
$190$	2.89448	−	8.62352i	0.209988	−	0.625616i
$191$	−3.03200			−0.219388			−0.109694	−	0.993965i	$-0.534987\pi$
$191$	−3.03200			−0.219388			−0.109694	+	0.993965i	$0.534987\pi$
$192$		0			0
$193$	4.75813			0.342498			0.171249	−	0.985228i	$-0.445220\pi$
$193$	4.75813			0.342498			0.171249	+	0.985228i	$0.445220\pi$
$194$	0.556572	−	1.65819i	0.0399595	−	0.119051i
$195$		0			0
$196$	−8.08811	+	10.6910i	−0.577722	+	0.763646i
$197$	−3.20309	−	7.73295i	−0.228211	−	0.550950i	0.767749	−	0.640751i	$-0.221377\pi$
$197$	−3.20309	−	7.73295i	−0.228211	−	0.550950i	−0.995960	+	0.0898012i	$0.971377\pi$
$198$		0			0
$199$	15.9060	+	15.9060i	1.12755	+	1.12755i	0.990575	+	0.136973i	$0.0437372\pi$
$199$	15.9060	+	15.9060i	1.12755	+	1.12755i	0.136973	+	0.990575i	$0.456263\pi$
$200$	−0.660231	+	3.50659i	−0.0466854	+	0.247954i
$201$		0			0
$202$	20.6830	−	1.42659i	1.45525	−	0.100374i
$203$	0.165981	+	0.400713i	0.0116496	+	0.0281245i
$204$		0			0
$205$	−13.3336	−	5.52295i	−0.931257	−	0.385739i
$206$	−23.4223	+	11.6502i	−1.63191	+	0.811708i
$207$		0			0
$208$	1.16943	−	9.92904i	0.0810855	−	0.688455i
$209$	20.5499			1.42147
$210$		0			0
$211$	2.38241	−	5.75165i	0.164012	−	0.395960i	−0.820412	−	0.571773i	$-0.806256\pi$
$211$	2.38241	−	5.75165i	0.164012	−	0.395960i	0.984423	+	0.175814i	$0.0562557\pi$
$212$	15.6229	+	4.07197i	1.07298	+	0.279664i
$213$		0			0
$214$	−4.28879	+	0.295816i	−0.293176	+	0.0202215i
$215$	−3.75284	−	3.75284i	−0.255941	−	0.255941i
$216$		0			0
$217$	−1.31327	+	1.31327i	−0.0891506	+	0.0891506i
$218$	−13.6685	+	15.6938i	−0.925750	+	1.06292i
$219$		0			0
$220$	23.6618	−	3.27971i	1.59528	−	0.221118i
$221$	−11.6732	−	4.83521i	−0.785226	−	0.325251i
$222$		0			0
$223$		−	24.2829i		−	1.62611i	−0.582190	−	0.813053i	$-0.697804\pi$
$223$		−	24.2829i		−	1.62611i	0.582190	−	0.813053i	$-0.302196\pi$
$224$	2.07227	+	2.28312i	0.138459	+	0.152547i
$225$		0			0
$226$	6.15743	−	18.3448i	0.409586	−	1.22028i
$227$	3.57334	−	8.62682i	0.237171	−	0.572582i	−0.759817	−	0.650137i	$-0.774711\pi$
$227$	3.57334	−	8.62682i	0.237171	−	0.572582i	0.996988	+	0.0775552i	$0.0247114\pi$
$228$		0			0
$229$	14.4317	−	5.97779i	0.953672	−	0.395024i	0.149062	−	0.988828i	$-0.452375\pi$
$229$	14.4317	−	5.97779i	0.953672	−	0.395024i	0.804610	+	0.593804i	$0.202375\pi$
$230$	6.65711	+	5.79803i	0.438957	+	0.382311i
$231$		0			0
$232$	−2.20284	+	0.461683i	−0.144624	+	0.0303110i
$233$	−6.50138	+	6.50138i	−0.425920	+	0.425920i	−0.887236	−	0.461316i	$-0.847377\pi$
$233$	−6.50138	+	6.50138i	−0.425920	+	0.425920i	0.461316	+	0.887236i	$0.347377\pi$
$234$		0			0
$235$	12.2472	−	5.07296i	0.798920	−	0.330923i
$236$	−12.8635	−	3.35275i	−0.837340	−	0.218246i
$237$		0			0
$238$	3.48894	−	1.73539i	0.226154	−	0.112489i
$239$			19.9787i			1.29232i	0.763203	+	0.646159i	$0.223626\pi$
$239$			19.9787i			1.29232i	−0.763203	+	0.646159i	$0.776374\pi$
$240$		0			0
$241$			0.606349i			0.0390584i	0.999809	+	0.0195292i	$0.00621673\pi$
$241$			0.606349i			0.0390584i	−0.999809	+	0.0195292i	$0.993783\pi$
$242$	17.1059	+	34.3908i	1.09961	+	2.21072i
$243$		0			0
$244$	−12.0812	+	7.08557i	−0.773422	+	0.453607i
$245$	−11.9736	+	4.95962i	−0.764964	+	0.316859i
$246$		0			0
$247$	5.87935	−	5.87935i	0.374094	−	0.374094i
$248$	−5.43618	−	7.95809i	−0.345198	−	0.505339i
$249$		0			0
$250$	−11.2450	+	12.9111i	−0.711195	+	0.816572i
$251$	14.5988	−	6.04703i	0.921470	−	0.381685i	0.129034	−	0.991640i	$-0.458813\pi$
$251$	14.5988	−	6.04703i	0.921470	−	0.381685i	0.792436	+	0.609955i	$0.208813\pi$
$252$		0			0
$253$	−7.63217	+	18.4257i	−0.479830	+	1.15841i
$254$	−10.9899	−	3.68874i	−0.689565	−	0.231452i
$255$		0			0
$256$	−13.6327	+	8.37555i	−0.852043	+	0.523472i
$257$		−	10.5962i		−	0.660974i	−0.943811	−	0.330487i	$-0.892787\pi$
$257$		−	10.5962i		−	0.660974i	0.943811	−	0.330487i	$-0.107213\pi$
$258$		0			0
$259$	5.21130	+	2.15859i	0.323815	+	0.134128i
$260$	5.83134	−	7.70799i	0.361644	−	0.478029i
$261$		0			0
$262$	4.48673	+	3.90773i	0.277191	+	0.241420i
$263$	19.2991	−	19.2991i	1.19004	−	1.19004i	0.212979	−	0.977057i	$-0.431683\pi$
$263$	19.2991	−	19.2991i	1.19004	−	1.19004i	0.977057	−	0.212979i	$-0.0683166\pi$
$264$		0			0
$265$	11.0366	+	11.0366i	0.677970	+	0.677970i
$266$	0.176450	+	2.55820i	0.0108188	+	0.156854i
$267$		0			0
$268$	−11.2682	−	19.2128i	−0.688315	−	1.17361i
$269$	4.57782	−	11.0518i	0.279114	−	0.673842i	−0.720697	−	0.693250i	$-0.756178\pi$
$269$	4.57782	−	11.0518i	0.279114	−	0.673842i	0.999812	+	0.0194081i	$0.00617818\pi$
$270$		0			0
$271$	29.0069			1.76204			0.881022	−	0.473075i	$-0.156856\pi$
$271$	29.0069			1.76204			0.881022	+	0.473075i	$0.156856\pi$
$272$	5.49983	+	19.4584i	0.333476	+	1.17984i
$273$		0			0
$274$	6.04789	+	12.1591i	0.365367	+	0.734555i
$275$	−7.19988	−	2.98229i	−0.434169	−	0.179839i
$276$		0			0
$277$	3.29625	+	7.95785i	0.198053	+	0.478141i	0.991438	−	0.130578i	$-0.0416834\pi$
$277$	3.29625	+	7.95785i	0.198053	+	0.478141i	−0.793385	+	0.608720i	$0.791683\pi$
$278$	0.325039	+	4.71248i	0.0194946	+	0.282636i
$279$		0			0
$280$	0.611452	+	2.91743i	0.0365413	+	0.174350i
$281$	−6.61069	−	6.61069i	−0.394361	−	0.394361i	0.481878	−	0.876238i	$-0.339955\pi$
$281$	−6.61069	−	6.61069i	−0.394361	−	0.394361i	−0.876238	+	0.481878i	$0.839955\pi$
$282$		0			0
$283$	−0.300555	−	0.725605i	−0.0178662	−	0.0431327i	0.914695	−	0.404146i	$-0.132431\pi$
$283$	−0.300555	−	0.725605i	−0.0178662	−	0.0431327i	−0.932561	+	0.361013i	$0.882431\pi$
$284$	17.8483	−	2.47391i	1.05910	−	0.146799i
$285$		0			0
$286$	20.7003	+	6.94805i	1.22403	+	0.410847i
$287$	4.06847			0.240154
$288$		0			0
$289$	8.55486			0.503227
$290$	−2.06278	−	0.692371i	−0.121130	−	0.0406574i
$291$		0			0
$292$	−3.50948	−	25.3195i	−0.205377	−	1.48171i
$293$	0.400806	+	0.967632i	0.0234154	+	0.0565297i	0.935155	−	0.354239i	$-0.115260\pi$
$293$	0.400806	+	0.967632i	0.0234154	+	0.0565297i	−0.911739	+	0.410769i	$0.865260\pi$
$294$		0			0
$295$	−9.08721	−	9.08721i	−0.529078	−	0.529078i
$296$	−16.0116	+	24.5029i	−0.930657	+	1.42420i
$297$		0			0
$298$	0.885528	+	12.8386i	0.0512973	+	0.743717i
$299$	3.08803	+	7.45517i	0.178586	+	0.431144i
$300$		0			0
$301$	1.38226	+	0.572551i	0.0796721	+	0.0330013i
$302$	12.2604	+	24.6491i	0.705507	+	1.41839i
$303$		0			0
$304$	−13.2152	−	1.55647i	−0.757944	−	0.0892698i
$305$	−13.5401			−0.775306
$306$		0			0
$307$	−3.22266	+	7.78018i	−0.183927	+	0.444038i	−0.988769	−	0.149450i	$-0.952250\pi$
$307$	−3.22266	+	7.78018i	−0.183927	+	0.444038i	0.804843	+	0.593488i	$0.202250\pi$
$308$	−5.80877	+	3.40681i	−0.330985	+	0.194121i
$309$		0			0
$310$	−0.641121	−	9.29509i	−0.0364132	−	0.527926i
$311$	7.17660	+	7.17660i	0.406948	+	0.406948i	0.880673	−	0.473725i	$-0.157091\pi$
$311$	7.17660	+	7.17660i	0.406948	+	0.406948i	−0.473725	+	0.880673i	$0.657091\pi$
$312$		0			0
$313$	0.108611	−	0.108611i	0.00613907	−	0.00613907i	−0.704031	−	0.710170i	$-0.748618\pi$
$313$	0.108611	−	0.108611i	0.00613907	−	0.00613907i	0.710170	+	0.704031i	$0.248618\pi$
$314$	−3.25327	−	2.83344i	−0.183593	−	0.159901i
$315$		0			0
$316$	−1.94740	−	1.47327i	−0.109550	−	0.0828776i
$317$	9.89983	+	4.10065i	0.556030	+	0.230315i	0.642961	−	0.765899i	$-0.277706\pi$
$317$	9.89983	+	4.10065i	0.556030	+	0.230315i	−0.0869307	+	0.996214i	$0.527706\pi$
$318$		0			0
$319$		−	4.91561i		−	0.275221i
$320$	−15.4648	+	0.316939i	−0.864509	+	0.0177174i
$321$		0			0
$322$	−2.35930	−	0.791898i	−0.131479	−	0.0441307i
$323$	−6.43549	+	15.5367i	−0.358080	+	0.864483i
$324$		0			0
$325$	−2.91312	+	1.20666i	−0.161591	+	0.0669332i
$326$	11.2276	−	12.8912i	0.621842	−	0.713979i
$327$		0			0
$328$	−3.90639	+	20.7475i	−0.215695	+	1.14559i
$329$	−2.64245	+	2.64245i	−0.145683	+	0.145683i
$330$		0			0
$331$	−14.7254	+	6.09946i	−0.809381	+	0.335257i	−0.748707	−	0.662901i	$-0.769325\pi$
$331$	−14.7254	+	6.09946i	−0.809381	+	0.335257i	−0.0606740	+	0.998158i	$0.519325\pi$
$332$	16.2542	+	27.7141i	0.892062	+	1.52101i
$333$		0			0
$334$	−2.24056	−	4.50455i	−0.122598	−	0.246478i
$335$		−	21.5329i		−	1.17647i
$336$		0			0
$337$		−	15.5033i		−	0.844517i	−0.906475	−	0.422259i	$-0.861237\pi$
$337$		−	15.5033i		−	0.844517i	0.906475	−	0.422259i	$-0.138763\pi$
$338$	−8.55072	+	4.25311i	−0.465098	+	0.231339i
$339$		0			0
$340$	−4.93042	+	18.9165i	−0.267390	+	1.02589i
$341$	19.4466	−	8.05504i	1.05309	−	0.436205i
$342$		0			0
$343$	5.28133	−	5.28133i	0.285165	−	0.285165i
$344$	−4.24697	+	6.49921i	−0.228981	+	0.350414i
$345$		0			0
$346$	−2.05540	−	1.79015i	−0.110499	−	0.0962393i
$347$	0.714667	−	0.296025i	0.0383654	−	0.0158914i	−0.363418	−	0.931626i	$-0.618390\pi$
$347$	0.714667	−	0.296025i	0.0383654	−	0.0158914i	0.401784	+	0.915735i	$0.368390\pi$
$348$		0			0
$349$	−3.21246	+	7.75558i	−0.171959	+	0.415146i	−0.986239	−	0.165326i	$-0.947132\pi$
$349$	−3.21246	+	7.75558i	−0.171959	+	0.415146i	0.814280	+	0.580473i	$0.197132\pi$
$350$	0.309436	−	0.921901i	0.0165400	−	0.0492777i
$351$		0			0
$352$	−11.7959	−	32.8934i	−0.628726	−	1.75323i
$353$			11.9668i			0.636927i	0.947935	+	0.318463i	$0.103167\pi$
$353$			11.9668i			0.636927i	−0.947935	+	0.318463i	$0.896833\pi$
$354$		0			0
$355$	16.0938	+	6.66628i	0.854171	+	0.353809i
$356$	−1.93191	−	13.9379i	−0.102391	−	0.738710i
$357$		0			0
$358$	9.52105	−	10.9318i	0.503203	−	0.577762i
$359$	−10.0179	+	10.0179i	−0.528723	+	0.528723i	−0.920191	−	0.391469i	$-0.871967\pi$
$359$	−10.0179	+	10.0179i	−0.528723	+	0.528723i	0.391469	+	0.920191i	$0.371967\pi$
$360$		0			0
$361$	5.60982	+	5.60982i	0.295254	+	0.295254i
$362$	36.5721	−	2.52253i	1.92219	−	0.132581i
$363$		0			0
$364$	−0.687204	+	2.63659i	−0.0360193	+	0.138195i
$365$	9.45679	−	22.8307i	0.494991	−	1.19501i
$366$		0			0
$367$	26.0524			1.35992			0.679961	−	0.733248i	$-0.261996\pi$
$367$	26.0524			1.35992			0.679961	+	0.733248i	$0.261996\pi$
$368$	6.30366	−	11.2711i	0.328601	−	0.587546i
$369$		0			0
$370$	−25.3363	+	12.6022i	−1.31717	+	0.655158i
$371$	−4.06503	−	1.68379i	−0.211046	−	0.0874180i
$372$		0			0
$373$	1.11398	+	2.68939i	0.0576797	+	0.139251i	0.950092	−	0.311970i	$-0.100989\pi$
$373$	1.11398	+	2.68939i	0.0576797	+	0.139251i	−0.892412	+	0.451221i	$0.850989\pi$
$374$	−44.0581	+	3.03887i	−2.27819	+	0.157136i
$375$		0			0
$376$	−10.9382	−	16.0126i	−0.564095	−	0.825786i
$377$	−1.40636	−	1.40636i	−0.0724312	−	0.0724312i
$378$		0			0
$379$	−2.87476	−	6.94029i	−0.147667	−	0.356499i	0.832688	−	0.553743i	$-0.186801\pi$
$379$	−2.87476	−	6.94029i	−0.147667	−	0.356499i	−0.980354	+	0.197244i	$0.936801\pi$
$380$	−10.2591	−	7.76131i	−0.526279	−	0.398147i
$381$		0			0
$382$	−1.36442	+	4.06502i	−0.0698099	+	0.207984i
$383$	18.2355			0.931792			0.465896	−	0.884839i	$-0.345732\pi$
$383$	18.2355			0.931792			0.465896	+	0.884839i	$0.345732\pi$
$384$		0			0
$385$	−6.51022			−0.331791
$386$	2.14120	−	6.37926i	0.108984	−	0.324696i
$387$		0			0
$388$	−1.97269	−	1.49240i	−0.100148	−	0.0757651i
$389$	9.18501	+	22.1746i	0.465699	+	1.12430i	0.966023	+	0.258458i	$0.0832143\pi$
$389$	9.18501	+	22.1746i	0.465699	+	1.12430i	−0.500324	+	0.865838i	$0.666786\pi$
$390$		0			0
$391$	−11.5405	−	11.5405i	−0.583629	−	0.583629i
$392$	10.6938	+	15.6548i	0.540120	+	0.790688i
$393$		0			0
$394$	−11.8090	+	0.814517i	−0.594930	+	0.0410348i
$395$	−0.903405	−	2.18101i	−0.0454552	−	0.109739i
$396$		0			0
$397$	3.77144	+	1.56218i	0.189283	+	0.0784037i	0.475312	−	0.879817i	$-0.342335\pi$
$397$	3.77144	+	1.56218i	0.189283	+	0.0784037i	−0.286029	+	0.958221i	$0.592335\pi$
$398$	28.4831	−	14.1675i	1.42773	−	0.710150i
$399$		0			0
$400$	4.40420	+	2.46317i	0.220210	+	0.123159i
$401$	−32.5110			−1.62352			−0.811761	−	0.583990i	$-0.801491\pi$
$401$	−32.5110			−1.62352			−0.811761	+	0.583990i	$0.801491\pi$
$402$		0			0
$403$	3.25913	−	7.86824i	0.162349	−	0.391945i
$404$	7.39485	−	28.3717i	0.367908	−	1.41155i
$405$		0			0
$406$	0.611931	−	0.0422074i	0.0303696	−	0.00209472i
$407$	−45.2038	−	45.2038i	−2.24067	−	2.24067i
$408$		0			0
$409$	−15.0850	+	15.0850i	−0.745903	+	0.745903i	−0.973707	−	0.227804i	$-0.926845\pi$
$409$	−15.0850	+	15.0850i	−0.745903	+	0.745903i	0.227804	+	0.973707i	$0.426845\pi$
$410$	−13.4049	+	15.3910i	−0.662019	+	0.760109i
$411$		0			0
$412$	5.07929	+	36.6451i	0.250239	+	1.80537i
$413$	3.34704	+	1.38639i	0.164697	+	0.0682197i
$414$		0			0
$415$			31.0608i			1.52471i
$416$	−12.7857	−	6.03601i	−0.626869	−	0.295940i
$417$		0			0
$418$	9.24762	−	27.5514i	0.452316	−	1.34758i
$419$	−6.41529	+	15.4879i	−0.313407	+	0.756632i	0.686167	+	0.727444i	$0.259292\pi$
$419$	−6.41529	+	15.4879i	−0.313407	+	0.756632i	−0.999574	+	0.0291878i	$0.990708\pi$
$420$		0			0
$421$	−13.8675	+	5.74412i	−0.675863	+	0.279951i	−0.694096	−	0.719882i	$-0.744196\pi$
$421$	−13.8675	+	5.74412i	−0.675863	+	0.279951i	0.0182335	+	0.999834i	$0.494196\pi$
$422$	−6.63916	−	5.78240i	−0.323189	−	0.281483i
$423$		0			0
$424$	12.4897	−	19.1132i	0.606554	−	0.928221i
$425$	4.50948	−	4.50948i	0.218742	−	0.218742i
$426$		0			0
$427$	3.52645	−	1.46070i	0.170657	−	0.0706884i
$428$	−1.53339	+	5.88312i	−0.0741191	+	0.284372i
$429$		0			0
$430$	−6.72026	+	3.34264i	−0.324080	+	0.161197i
$431$		−	39.1679i		−	1.88665i	−0.331870	−	0.943325i	$-0.607680\pi$
$431$		−	39.1679i		−	1.88665i	0.331870	−	0.943325i	$-0.392320\pi$
$432$		0			0
$433$		−	20.6897i		−	0.994283i	−0.867669	−	0.497142i	$-0.834383\pi$
$433$		−	20.6897i		−	0.994283i	0.867669	−	0.497142i	$-0.165617\pi$
$434$	1.16973	+	2.35169i	0.0561487	+	0.112885i
$435$		0			0
$436$	14.8898	+	25.3878i	0.713092	+	1.21586i
$437$	9.92258	−	4.11007i	0.474661	−	0.196611i
$438$		0			0
$439$	−7.49686	+	7.49686i	−0.357805	+	0.357805i	−0.863003	−	0.505198i	$-0.831419\pi$
$439$	−7.49686	+	7.49686i	−0.357805	+	0.357805i	0.505198	+	0.863003i	$0.331419\pi$
$440$	6.25087	−	33.1994i	0.297999	−	1.58272i
$441$		0			0
$442$	−11.7356	+	13.4745i	−0.558207	+	0.640916i
$443$	5.58792	−	2.31459i	0.265490	−	0.109970i	−0.245968	−	0.969278i	$-0.579106\pi$
$443$	5.58792	−	2.31459i	0.265490	−	0.109970i	0.511458	+	0.859308i	$0.329106\pi$
$444$		0			0
$445$	5.20579	−	12.5679i	0.246778	−	0.595775i
$446$	−32.5563	−	10.9275i	−1.54158	−	0.517433i
$447$		0			0
$448$	3.99353	−	1.75088i	0.188677	−	0.0827214i
$449$		−	9.22927i		−	0.435556i	−0.975998	−	0.217778i	$-0.930119\pi$
$449$		−	9.22927i		−	0.435556i	0.975998	−	0.217778i	$-0.0698809\pi$
$450$		0			0
$451$	−42.5996	−	17.6453i	−2.00594	−	0.830886i
$452$	−21.8241	−	16.5106i	−1.02652	−	0.776594i
$453$		0			0
$454$	−9.95799	−	8.67294i	−0.467352	−	0.407041i
$455$	−1.86258	+	1.86258i	−0.0873190	+	0.0873190i
$456$		0			0
$457$	−15.0540	−	15.0540i	−0.704197	−	0.704197i	0.261112	−	0.965309i	$-0.415911\pi$
$457$	−15.0540	−	15.0540i	−0.704197	−	0.704197i	−0.965309	+	0.261112i	$0.915911\pi$
$458$	−1.52010	−	22.0387i	−0.0710296	−	1.02980i
$459$		0			0
$460$	10.7692	−	6.31607i	0.502117	−	0.294488i
$461$	−2.11682	+	5.11046i	−0.0985902	+	0.238018i	−0.965478	−	0.260486i	$-0.916117\pi$
$461$	−2.11682	+	5.11046i	−0.0985902	+	0.238018i	0.866887	+	0.498504i	$0.166117\pi$
$462$		0			0
$463$	−30.2844			−1.40743			−0.703717	−	0.710481i	$-0.748478\pi$
$463$	−30.2844			−1.40743			−0.703717	+	0.710481i	$0.748478\pi$
$464$	−0.372314	+	3.16112i	−0.0172842	+	0.146751i
$465$		0			0
$466$	5.79077	+	11.6421i	0.268252	+	0.539311i
$467$	12.9725	+	5.37338i	0.600295	+	0.248650i	0.662073	−	0.749439i	$-0.269677\pi$
$467$	12.9725	+	5.37338i	0.600295	+	0.248650i	−0.0617775	+	0.998090i	$0.519677\pi$
$468$		0			0
$469$	2.32296	+	5.60813i	0.107264	+	0.258959i
$470$	−1.29001	−	18.7028i	−0.0595037	−	0.862695i
$471$		0			0
$472$	−10.2837	+	15.7374i	−0.473346	+	0.724370i
$473$	−11.9900	−	11.9900i	−0.551300	−	0.551300i
$474$		0			0
$475$	1.60602	+	3.87727i	0.0736891	+	0.177901i
$476$	−0.756601	−	5.45858i	−0.0346788	−	0.250194i
$477$		0			0
$478$	26.7856	+	8.99059i	1.22515	+	0.411220i
$479$	−2.51607			−0.114962			−0.0574810	−	0.998347i	$-0.518307\pi$
$479$	−2.51607			−0.114962			−0.0574810	+	0.998347i	$0.518307\pi$
$480$		0			0
$481$	−25.8657			−1.17937
$482$	0.812936	+	0.272862i	0.0370282	+	0.0124285i
$483$		0			0
$484$	53.8057	−	7.45789i	2.44571	−	0.338995i
$485$	−0.915138	−	2.20934i	−0.0415543	−	0.100321i
$486$		0			0
$487$	1.66386	+	1.66386i	0.0753965	+	0.0753965i	0.743799	−	0.668403i	$-0.233022\pi$
$487$	1.66386	+	1.66386i	0.0753965	+	0.0753965i	−0.668403	+	0.743799i	$0.733022\pi$
$488$	4.06302	+	19.3860i	0.183924	+	0.877561i
$489$		0			0
$490$	1.26119	+	18.2849i	0.0569746	+	0.826029i
$491$	12.2708	+	29.6244i	0.553775	+	1.33693i	0.914624	+	0.404306i	$0.132487\pi$
$491$	12.2708	+	29.6244i	0.553775	+	1.33693i	−0.360849	+	0.932624i	$0.617513\pi$
$492$		0			0
$493$	3.71642	+	1.53939i	0.167379	+	0.0693307i
$494$	−5.23672	−	10.5282i	−0.235611	−	0.473687i
$495$		0			0
$496$	−13.1158	+	3.70712i	−0.588916	+	0.166454i
$497$	−4.91070			−0.220275
$498$		0			0
$499$	−13.7034	+	33.0830i	−0.613450	+	1.48100i	0.245736	+	0.969337i	$0.420971\pi$
$499$	−13.7034	+	33.0830i	−0.613450	+	1.48100i	−0.859186	+	0.511663i	$0.829029\pi$
$500$	12.2497	+	20.8863i	0.547823	+	0.934065i
$501$		0			0
$502$	−1.53771	−	22.2939i	−0.0686312	−	0.995027i
$503$	23.6161	+	23.6161i	1.05299	+	1.05299i	0.998515	+	0.0544742i	$0.0173483\pi$
$503$	23.6161	+	23.6161i	1.05299	+	1.05299i	0.0544742	+	0.998515i	$0.482652\pi$
$504$		0			0
$505$	20.0428	−	20.0428i	0.891894	−	0.891894i
$506$	21.2689	+	18.5242i	0.945517	+	0.823501i
$507$		0			0
$508$	−9.89104	+	13.0742i	−0.438844	+	0.580074i
$509$	33.8424	+	14.0180i	1.50004	+	0.621336i	0.973474	−	0.228798i	$-0.0734797\pi$
$509$	33.8424	+	14.0180i	1.50004	+	0.621336i	0.526565	+	0.850135i	$0.323480\pi$
$510$		0			0
$511$			6.96632i			0.308172i
$512$	5.09433	+	22.0465i	0.225140	+	0.974326i
$513$		0			0
$514$	−14.2064	−	4.76838i	−0.626618	−	0.210324i
$515$	−13.6868	+	33.0430i	−0.603115	+	1.45605i
$516$		0			0
$517$	39.1288	−	16.2077i	1.72088	−	0.712812i
$518$	5.23916	−	6.01544i	0.230196	−	0.264303i
$519$		0			0
$520$	−7.71000	−	11.2868i	−0.338106	−	0.494957i
$521$	1.30745	−	1.30745i	0.0572804	−	0.0572804i	−0.677886	−	0.735167i	$-0.737104\pi$
$521$	1.30745	−	1.30745i	0.0572804	−	0.0572804i	0.735167	+	0.677886i	$0.237104\pi$
$522$		0			0
$523$	−21.7896	+	9.02554i	−0.952792	+	0.394660i	−0.804280	−	0.594251i	$-0.797449\pi$
$523$	−21.7896	+	9.02554i	−0.952792	+	0.394660i	−0.148513	+	0.988911i	$0.547449\pi$
$524$	7.25818	−	4.25688i	0.317075	−	0.185963i
$525$		0			0
$526$	−17.1897	−	34.5592i	−0.749507	−	1.50685i
$527$			17.2250i			0.750335i
$528$		0			0
$529$		−	12.5766i		−	0.546811i
$530$	19.7633	−	9.83024i	0.858463	−	0.426998i
$531$		0			0
$532$	3.50920	+	0.914645i	0.152143	+	0.0396549i
$533$	−17.2361	+	7.13943i	−0.746579	+	0.309243i
$534$		0			0
$535$	−4.15605	+	4.15605i	−0.179682	+	0.179682i
$536$	−30.8296	+	6.46143i	−1.33163	+	0.279091i
$537$		0			0
$538$	−12.7572	−	11.1109i	−0.550002	−	0.479026i
$539$	−38.2546	+	15.8456i	−1.64774	+	0.682516i
$540$		0			0
$541$	−3.04512	+	7.35157i	−0.130920	+	0.316069i	−0.975723	−	0.219009i	$-0.929718\pi$
$541$	−3.04512	+	7.35157i	−0.130920	+	0.316069i	0.844803	+	0.535078i	$0.179718\pi$
$542$	13.0533	−	38.8897i	0.560689	−	1.67046i
$543$		0			0
$544$	28.5630	+	1.38278i	1.22463	+	0.0592860i
$545$			28.4536i			1.21882i
$546$		0			0
$547$	5.38090	+	2.22884i	0.230071	+	0.0952984i	0.494741	−	0.869041i	$-0.335263\pi$
$547$	5.38090	+	2.22884i	0.230071	+	0.0952984i	−0.264670	+	0.964339i	$0.585263\pi$
$548$	19.0233	−	2.63678i	0.812636	−	0.112638i
$549$		0			0
$550$	−7.23837	+	8.31086i	−0.308645	+	0.354376i
$551$	−1.87182	+	1.87182i	−0.0797421	+	0.0797421i
$552$		0			0
$553$	0.470574	+	0.470574i	0.0200108	+	0.0200108i
$554$	12.1525	−	0.838207i	0.516310	−	0.0356120i
$555$		0			0
$556$	6.46432	+	1.68487i	0.274148	+	0.0714544i
$557$	−8.63425	+	20.8449i	−0.365845	+	0.883228i	0.628576	+	0.777748i	$0.283638\pi$
$557$	−8.63425	+	20.8449i	−0.365845	+	0.883228i	−0.994421	+	0.105480i	$0.966362\pi$
$558$		0			0
$559$	−6.86069			−0.290176
$560$	4.18658	+	0.493091i	0.176915	+	0.0208369i
$561$		0			0
$562$	−11.8379	+	5.88813i	−0.499350	+	0.248376i
$563$	17.1318	+	7.09624i	0.722021	+	0.299071i	0.713268	−	0.700891i	$-0.247214\pi$
$563$	17.1318	+	7.09624i	0.722021	+	0.299071i	0.00875227	+	0.999962i	$0.497214\pi$
$564$		0			0
$565$	−10.1243	−	24.4422i	−0.425932	−	1.02829i
$566$	−1.10807	+	0.0764285i	−0.0465759	+	0.00321253i
$567$		0			0
$568$	4.71508	−	25.0425i	0.197840	−	1.05076i
$569$	15.5020	+	15.5020i	0.649877	+	0.649877i	0.952963	−	0.303086i	$-0.0980169\pi$
$569$	15.5020	+	15.5020i	0.649877	+	0.649877i	−0.303086	+	0.952963i	$0.598017\pi$
$570$		0			0
$571$	11.3574	+	27.4193i	0.475294	+	1.14746i	0.961793	+	0.273779i	$0.0882737\pi$
$571$	11.3574	+	27.4193i	0.475294	+	1.14746i	−0.486499	+	0.873681i	$0.661726\pi$
$572$	18.6306	−	24.6263i	0.778985	−	1.02968i
$573$		0			0
$574$	1.83084	−	5.45462i	0.0764179	−	0.227671i
$575$	−4.07295			−0.169854
$576$		0			0
$577$	19.6105			0.816396			0.408198	−	0.912893i	$-0.366157\pi$
$577$	19.6105			0.816396			0.408198	+	0.912893i	$0.366157\pi$
$578$	3.84975	−	11.4695i	0.160129	−	0.477070i
$579$		0			0
$580$	−1.85653	+	2.45400i	−0.0770883	+	0.101897i
$581$	−3.35082	−	8.08960i	−0.139016	−	0.335613i
$582$		0			0
$583$	35.2608	+	35.2608i	1.46035	+	1.46035i
$584$	−35.5254	−	6.68881i	−1.47005	−	0.276785i
$585$		0			0
$586$	1.47768	−	0.101921i	0.0610422	−	0.00421034i
$587$	−6.56890	−	15.8587i	−0.271128	−	0.654560i	0.728404	−	0.685147i	$-0.240262\pi$
$587$	−6.56890	−	15.8587i	−0.271128	−	0.654560i	−0.999532	+	0.0305874i	$0.990262\pi$
$588$		0			0
$589$	−10.4724	−	4.33779i	−0.431506	−	0.178736i
$590$	−16.2726	+	8.09396i	−0.669932	+	0.333223i
$591$		0			0
$592$	25.6458	+	32.4934i	1.05404	+	1.33547i
$593$	0.287201			0.0117939			0.00589697	−	0.999983i	$-0.498123\pi$
$593$	0.287201			0.0117939			0.00589697	+	0.999983i	$0.498123\pi$
$594$		0			0
$595$	2.03877	−	4.92202i	0.0835813	−	0.201783i
$596$	17.6112	+	4.59022i	0.721384	+	0.188023i
$597$		0			0
$598$	11.3848	−	0.785259i	0.465560	−	0.0321116i
$599$	−12.5596	−	12.5596i	−0.513170	−	0.513170i	0.402326	−	0.915496i	$-0.368202\pi$
$599$	−12.5596	−	12.5596i	−0.513170	−	0.513170i	−0.915496	+	0.402326i	$0.868202\pi$
$600$		0			0
$601$	23.9708	−	23.9708i	0.977791	−	0.977791i	−0.0219673	−	0.999759i	$-0.506993\pi$
$601$	23.9708	−	23.9708i	0.977791	−	0.977791i	0.999759	+	0.0219673i	$0.00699298\pi$
$602$	1.38965	−	1.59555i	0.0566379	−	0.0650298i
$603$		0			0
$604$	38.5644	−	5.34532i	1.56916	−	0.217498i
$605$	48.5168	+	20.0963i	1.97249	+	0.817031i
$606$		0			0
$607$		−	27.9757i		−	1.13550i	−0.823202	−	0.567749i	$-0.807815\pi$
$607$		−	27.9757i		−	1.13550i	0.823202	−	0.567749i	$-0.192185\pi$
$608$	−8.03372	+	17.0173i	−0.325810	+	0.690142i
$609$		0			0
$610$	−6.09317	+	18.1533i	−0.246705	+	0.735007i
$611$	6.55774	−	15.8318i	0.265298	−	0.640486i
$612$		0			0
$613$	−30.2175	+	12.5165i	−1.22047	+	0.505537i	−0.897560	−	0.440892i	$-0.854662\pi$
$613$	−30.2175	+	12.5165i	−1.22047	+	0.505537i	−0.322913	+	0.946429i	$0.604662\pi$
$614$	8.98071	+	7.82177i	0.362432	+	0.315661i
$615$		0			0
$616$	1.95354	+	9.32095i	0.0787102	+	0.375552i
$617$	−23.4695	+	23.4695i	−0.944848	+	0.944848i	−0.998557	−	0.0537086i	$-0.982896\pi$
$617$	−23.4695	+	23.4695i	−0.944848	+	0.944848i	0.0537086	+	0.998557i	$0.482896\pi$
$618$		0			0
$619$	−16.2802	+	6.74349i	−0.654357	+	0.271044i	−0.685062	−	0.728485i	$-0.740225\pi$
$619$	−16.2802	+	6.74349i	−0.654357	+	0.271044i	0.0307046	+	0.999529i	$0.490225\pi$
$620$	−12.7505	−	3.32331i	−0.512072	−	0.133467i
$621$		0			0
$622$	12.8512	−	6.39218i	0.515288	−	0.256303i
$623$			3.83483i			0.153639i
$624$		0			0
$625$			17.1007i			0.684029i
$626$	−0.0967398	−	0.194492i	−0.00386650	−	0.00777345i
$627$		0			0
$628$	−5.26281	+	3.08661i	−0.210009	+	0.123169i
$629$	48.3323	−	20.0199i	1.92714	−	0.798246i
$630$		0			0
$631$	18.7206	−	18.7206i	0.745256	−	0.745256i	−0.228328	−	0.973584i	$-0.573326\pi$
$631$	18.7206	−	18.7206i	0.745256	−	0.745256i	0.973584	+	0.228328i	$0.0733259\pi$
$632$	−2.85156	+	1.94790i	−0.113429	+	0.0774834i
$633$		0			0
$634$	9.95276	−	11.4274i	0.395275	−	0.453842i
$635$	−14.6426	+	6.06518i	−0.581076	+	0.240689i
$636$		0			0
$637$	−6.41123	+	15.4781i	−0.254022	+	0.613264i
$638$	−6.59039	−	2.21206i	−0.260916	−	0.0875764i
$639$		0			0
$640$	−6.53436	+	20.8764i	−0.258293	+	0.825212i
$641$			39.5671i			1.56281i	0.624026	+	0.781404i	$0.285496\pi$
$641$			39.5671i			1.56281i	−0.624026	+	0.781404i	$0.714504\pi$
$642$		0			0
$643$	−32.9323	−	13.6410i	−1.29872	−	0.537949i	−0.377149	−	0.926153i	$-0.623096\pi$
$643$	−32.9323	−	13.6410i	−1.29872	−	0.537949i	−0.921573	+	0.388204i	$0.873096\pi$
$644$	−2.12340	+	2.80676i	−0.0836739	+	0.110602i
$645$		0			0
$646$	17.9341	+	15.6197i	0.705606	+	0.614550i
$647$	15.1226	−	15.1226i	0.594532	−	0.594532i	−0.344320	−	0.938852i	$-0.611891\pi$
$647$	15.1226	−	15.1226i	0.594532	−	0.594532i	0.938852	+	0.344320i	$0.111891\pi$
$648$		0			0
$649$	−29.0328	−	29.0328i	−1.13964	−	1.13964i
$650$	0.306842	+	4.44865i	0.0120353	+	0.174490i
$651$		0			0
$652$	−12.2308	−	20.8541i	−0.478995	−	0.816710i
$653$	−5.76633	+	13.9212i	−0.225654	+	0.544777i	−0.995640	−	0.0932843i	$-0.970263\pi$
$653$	−5.76633	+	13.9212i	−0.225654	+	0.544777i	0.769985	+	0.638061i	$0.220263\pi$
$654$		0			0
$655$	8.13465			0.317847
$656$	26.0584	+	14.5739i	1.01741	+	0.569014i
$657$		0			0
$658$	2.35362	+	4.73187i	0.0917538	+	0.184467i
$659$	−21.9719	−	9.10108i	−0.855905	−	0.354528i	−0.0888005	−	0.996049i	$-0.528303\pi$
$659$	−21.9719	−	9.10108i	−0.855905	−	0.354528i	−0.767105	+	0.641522i	$0.778303\pi$
$660$		0			0
$661$	6.04221	+	14.5872i	0.235015	+	0.567376i	0.996754	−	0.0805079i	$-0.0256542\pi$
$661$	6.04221	+	14.5872i	0.235015	+	0.567376i	−0.761739	+	0.647884i	$0.775654\pi$
$662$	1.55104	+	22.4872i	0.0602828	+	0.873991i
$663$		0			0
$664$	44.4710	−	9.32047i	1.72581	−	0.361704i
$665$	2.47903	+	2.47903i	0.0961326	+	0.0961326i
$666$		0			0
$667$	−0.983142	−	2.37351i	−0.0380674	−	0.0919029i
$668$	−7.04755	+	0.976844i	−0.272678	+	0.0377952i
$669$		0			0
$670$	−28.8693	−	9.68998i	−1.11532	−	0.374357i
$671$	−43.2595			−1.67002
$672$		0			0
$673$	23.2501			0.896225			0.448113	−	0.893977i	$-0.352096\pi$
$673$	23.2501			0.896225			0.448113	+	0.893977i	$0.352096\pi$
$674$	−20.7853	−	6.97659i	−0.800621	−	0.268728i
$675$		0			0
$676$	1.85429	+	13.3779i	0.0713187	+	0.514536i
$677$	−8.28073	−	19.9914i	−0.318254	−	0.768333i	−0.999347	−	0.0361363i	$-0.988495\pi$
$677$	−8.28073	−	19.9914i	−0.318254	−	0.768333i	0.681093	−	0.732197i	$-0.261505\pi$
$678$		0			0
$679$	0.476685	+	0.476685i	0.0182935	+	0.0182935i
$680$	23.1427	+	15.1228i	0.887482	+	0.579933i
$681$		0			0
$682$	−2.04832	−	29.6970i	−0.0784344	−	1.13716i
$683$	−6.09927	−	14.7249i	−0.233382	−	0.563434i	0.763189	−	0.646175i	$-0.223633\pi$
$683$	−6.09927	−	14.7249i	−0.233382	−	0.563434i	−0.996571	+	0.0827411i	$0.973633\pi$
$684$		0			0
$685$	17.1534	+	7.10516i	0.655397	+	0.271474i
$686$	−4.70407	−	9.45735i	−0.179602	−	0.361083i
$687$		0			0
$688$	6.80236	+	8.61863i	0.259338	+	0.328582i
$689$	20.1763			0.768655
$690$		0			0
$691$	−6.28104	+	15.1638i	−0.238942	+	0.576857i	−0.997174	−	0.0751281i	$-0.976063\pi$
$691$	−6.28104	+	15.1638i	−0.238942	+	0.576857i	0.758232	+	0.651985i	$0.226063\pi$
$692$	−3.32502	+	1.95010i	−0.126398	+	0.0741317i
$693$		0			0
$694$	−0.0752765	−	1.09137i	−0.00285746	−	0.0414279i
$695$	4.56663	+	4.56663i	0.173222	+	0.173222i
$696$		0			0
$697$	26.6813	−	26.6813i	1.01063	−	1.01063i
$698$	8.95231	+	7.79704i	0.338850	+	0.295122i
$699$		0			0
$700$	−1.09675	−	0.829725i	−0.0414532	−	0.0313607i
$701$	−24.6746	−	10.2205i	−0.931946	−	0.386025i	−0.135529	−	0.990773i	$-0.543274\pi$
$701$	−24.6746	−	10.2205i	−0.931946	−	0.386025i	−0.796416	+	0.604749i	$0.793274\pi$
$702$		0			0
$703$			34.4263i			1.29841i
$704$	−49.4087	+	1.01259i	−1.86216	+	0.0381635i
$705$		0			0
$706$	16.0439	+	5.38514i	0.603821	+	0.202672i
$707$	−3.05783	+	7.38225i	−0.115001	+	0.277638i
$708$		0			0
$709$	−11.4821	+	4.75606i	−0.431221	+	0.178617i	−0.587727	−	0.809060i	$-0.699977\pi$
$709$	−11.4821	+	4.75606i	−0.431221	+	0.178617i	0.156506	+	0.987677i	$0.449977\pi$
$710$	16.1799	−	18.5772i	0.607220	−	0.697190i
$711$		0			0
$712$	−19.5561	−	3.68207i	−0.732895	−	0.137991i
$713$	7.77879	−	7.77879i	0.291318	−	0.291318i
$714$		0			0
$715$	27.5806	−	11.4243i	1.03146	−	0.427243i
$716$	−10.3717	−	17.6843i	−0.387610	−	0.660894i
$717$		0			0
$718$	8.92289	+	17.9391i	0.332999	+	0.669482i
$719$		−	24.1182i		−	0.899455i	−0.893166	−	0.449728i	$-0.851521\pi$
$719$		−	24.1182i		−	0.899455i	0.893166	−	0.449728i	$-0.148479\pi$
$720$		0			0
$721$		−	10.0824i		−	0.375488i
$722$	10.0456	−	4.99666i	0.373858	−	0.185956i
$723$		0			0
$724$	13.0758	−	50.1676i	0.485957	−	1.86446i
$725$	0.927456	−	0.384165i	0.0344449	−	0.0142675i
$726$		0			0
$727$	23.8328	−	23.8328i	0.883909	−	0.883909i	−0.110020	−	0.993929i	$-0.535092\pi$
$727$	23.8328	−	23.8328i	0.883909	−	0.883909i	0.993929	+	0.110020i	$0.0350915\pi$
$728$	3.22564	+	2.10782i	0.119550	+	0.0781211i
$729$		0			0
$730$	−26.3536	−	22.9528i	−0.975392	−	0.849520i
$731$	12.8198	−	5.31013i	0.474157	−	0.196402i
$732$		0			0
$733$	7.22918	−	17.4528i	0.267016	−	0.644633i	−0.732324	−	0.680956i	$-0.761564\pi$
$733$	7.22918	−	17.4528i	0.267016	−	0.644633i	0.999340	+	0.0363227i	$0.0115644\pi$
$734$	11.7238	−	34.9286i	0.432732	−	1.28924i
$735$		0			0
$736$	−12.2745	−	13.5234i	−0.452445	−	0.498481i
$737$		−	68.7958i		−	2.53412i
$738$		0			0
$739$	2.37240	+	0.982682i	0.0872703	+	0.0361485i	0.425892	−	0.904774i	$-0.359961\pi$
$739$	2.37240	+	0.982682i	0.0872703	+	0.0361485i	−0.338621	+	0.940923i	$0.609961\pi$
$740$	5.49435	+	39.6396i	0.201976	+	1.45718i
$741$		0			0
$742$	−4.08676	+	4.69229i	−0.150030	+	0.172259i
$743$	−9.84906	+	9.84906i	−0.361327	+	0.361327i	−0.864301	−	0.502974i	$-0.832239\pi$
$743$	−9.84906	+	9.84906i	−0.361327	+	0.361327i	0.502974	+	0.864301i	$0.332239\pi$
$744$		0			0
$745$	12.4412	+	12.4412i	0.455810	+	0.455810i
$746$	4.10698	−	0.283275i	0.150367	−	0.0103714i
$747$		0			0
$748$	−15.7523	+	60.4365i	−0.575960	+	2.20978i
$749$	0.634067	−	1.53077i	0.0231683	−	0.0559333i
$750$		0			0
$751$	−14.4324			−0.526644			−0.263322	−	0.964708i	$-0.584818\pi$
$751$	−14.4324			−0.526644			−0.263322	+	0.964708i	$0.584818\pi$
$752$	−26.3904	+	7.45914i	−0.962361	+	0.272007i
$753$		0			0
$754$	−2.51839	+	1.25264i	−0.0917143	+	0.0456185i
$755$	34.7736	+	14.4037i	1.26554	+	0.524205i
$756$		0			0
$757$	−12.5839	−	30.3803i	−0.457371	−	1.10419i	−0.969458	−	0.245257i	$-0.921128\pi$
$757$	−12.5839	−	30.3803i	−0.457371	−	1.10419i	0.512088	−	0.858933i	$-0.328872\pi$
$758$	−10.5986	+	0.731026i	−0.384957	+	0.0265521i
$759$		0			0
$760$	−15.0223	+	10.2617i	−0.544916	+	0.372233i
$761$	10.8012	+	10.8012i	0.391543	+	0.391543i	0.875237	−	0.483694i	$-0.160705\pi$
$761$	10.8012	+	10.8012i	0.391543	+	0.391543i	−0.483694	+	0.875237i	$0.660705\pi$
$762$		0			0
$763$	−3.06956	−	7.41057i	−0.111125	−	0.268281i
$764$	4.83599	+	3.65858i	0.174960	+	0.132363i
$765$		0			0
$766$	8.20613	−	24.4485i	0.296500	−	0.883360i
$767$	−16.6126			−0.599848
$768$		0			0
$769$	−31.6614			−1.14174			−0.570869	−	0.821041i	$-0.693394\pi$
$769$	−31.6614			−1.14174			−0.570869	+	0.821041i	$0.693394\pi$
$770$	−2.92965	+	8.72829i	−0.105577	+	0.314546i
$771$		0			0
$772$	−7.58916	−	5.74143i	−0.273140	−	0.206639i
$773$	7.73399	+	18.6715i	0.278172	+	0.671567i	0.999785	−	0.0207297i	$-0.00659894\pi$
$773$	7.73399	+	18.6715i	0.278172	+	0.671567i	−0.721613	+	0.692297i	$0.756599\pi$
$774$		0			0
$775$	3.03958	+	3.03958i	0.109185	+	0.109185i
$776$	−2.88859	+	1.97320i	−0.103694	+	0.0708338i
$777$		0			0
$778$	33.8629	−	2.33567i	1.21404	−	0.0837377i
$779$	9.50234	+	22.9407i	0.340457	+	0.821935i
$780$		0			0
$781$	51.4183	+	21.2982i	1.83989	+	0.762108i
$782$	−20.6658	+	10.2791i	−0.739007	+	0.367581i
$783$		0			0
$784$	25.8008	−	7.29249i	0.921458	−	0.260446i
$785$	−5.89833			−0.210520
$786$		0			0
$787$	7.03017	−	16.9723i	0.250598	−	0.604998i	−0.747654	−	0.664088i	$-0.768820\pi$
$787$	7.03017	−	16.9723i	0.250598	−	0.604998i	0.998253	+	0.0590900i	$0.0188199\pi$
$788$	−4.22213	+	16.1990i	−0.150407	+	0.577065i
$789$		0			0
$790$	−3.33064	+	0.229728i	−0.118499	+	0.00817335i
$791$	5.27363	+	5.27363i	0.187509	+	0.187509i
$792$		0			0
$793$	−12.3766	+	12.3766i	−0.439505	+	0.439505i
$794$	3.79161	−	4.35340i	0.134559	−	0.154496i
$795$		0			0
$796$	−6.17677	−	44.5630i	−0.218930	−	1.57949i
$797$	−43.7568	−	18.1246i	−1.54994	−	0.642008i	−0.566638	−	0.823967i	$-0.691756\pi$
$797$	−43.7568	−	18.1246i	−1.54994	−	0.642008i	−0.983306	+	0.181959i	$0.941756\pi$
$798$		0			0
$799$			34.6588i			1.22614i
$800$	5.28431	−	4.79630i	0.186829	−	0.169575i
$801$		0			0
$802$	−14.6302	+	43.5877i	−0.516611	+	1.53914i
$803$	30.2136	−	72.9421i	1.06621	−	2.57407i
$804$		0			0
$805$	−3.14348	+	1.30207i	−0.110793	+	0.0458919i
$806$	−9.08236	−	7.91031i	−0.319913	−	0.278629i
$807$		0			0
$808$	−34.7104	−	22.6818i	−1.22111	−	0.797944i
$809$	6.34143	−	6.34143i	0.222953	−	0.222953i	−0.586788	−	0.809741i	$-0.699608\pi$
$809$	6.34143	−	6.34143i	0.222953	−	0.222953i	0.809741	+	0.586788i	$0.199608\pi$
$810$		0			0
$811$	−12.8711	+	5.33139i	−0.451966	+	0.187210i	−0.597042	−	0.802210i	$-0.703657\pi$
$811$	−12.8711	+	5.33139i	−0.451966	+	0.187210i	0.145076	+	0.989421i	$0.453657\pi$
$812$	0.218786	−	0.839414i	0.00767789	−	0.0294576i
$813$		0			0
$814$	−80.9471	+	40.2629i	−2.83719	+	1.41122i
$815$		−	23.3724i		−	0.818699i
$816$		0			0
$817$			9.13134i			0.319465i
$818$	13.4361	+	27.0128i	0.469784	+	0.944482i
$819$		0			0
$820$	14.6026	+	24.8981i	0.509943	+	0.869478i
$821$	12.6767	−	5.25088i	0.442421	−	0.183257i	−0.150341	−	0.988634i	$-0.548037\pi$
$821$	12.6767	−	5.25088i	0.442421	−	0.183257i	0.592763	+	0.805377i	$0.298037\pi$
$822$		0			0
$823$	−21.6528	+	21.6528i	−0.754770	+	0.754770i	−0.975365	−	0.220596i	$-0.929200\pi$
$823$	−21.6528	+	21.6528i	−0.754770	+	0.754770i	0.220596	+	0.975365i	$0.429200\pi$
$824$	51.4160	+	9.68074i	1.79116	+	0.337245i
$825$		0			0
$826$	3.36493	−	3.86351i	0.117081	−	0.134429i
$827$	−26.0418	+	10.7869i	−0.905563	+	0.375096i	−0.786356	−	0.617773i	$-0.788035\pi$
$827$	−26.0418	+	10.7869i	−0.905563	+	0.375096i	−0.119206	+	0.992869i	$0.538035\pi$
$828$		0			0
$829$	5.29036	−	12.7721i	0.183742	−	0.443592i	−0.804990	−	0.593288i	$-0.797830\pi$
$829$	5.29036	−	12.7721i	0.183742	−	0.443592i	0.988732	+	0.149696i	$0.0478295\pi$
$830$	41.6434	+	13.9776i	1.44546	+	0.485169i
$831$		0			0
$832$	−13.8462	+	14.4256i	−0.480029	+	0.500117i
$833$		−	33.8844i		−	1.17403i
$834$		0			0
$835$	−6.35479	−	2.63224i	−0.219917	−	0.0910924i
$836$	−32.7768	−	24.7967i	−1.13361	−	0.857611i
$837$		0			0
$838$	17.8778	+	15.5707i	0.617577	+	0.537880i
$839$	14.9362	−	14.9362i	0.515654	−	0.515654i	−0.400600	−	0.916253i	$-0.631198\pi$
$839$	14.9362	−	14.9362i	0.515654	−	0.515654i	0.916253	+	0.400600i	$0.131198\pi$
$840$		0			0
$841$	−20.0584	−	20.0584i	−0.691667	−	0.691667i
$842$	1.46068	+	21.1772i	0.0503383	+	0.729815i
$843$		0			0
$844$	−10.7402	+	6.29904i	−0.369692	+	0.216822i
$845$	−4.99663	+	12.0629i	−0.171889	+	0.414977i
$846$		0			0
$847$	−14.8039			−0.508668
$848$	−20.0048	−	25.3462i	−0.686967	−	0.870391i
$849$		0			0
$850$	−4.01659	−	8.07520i	−0.137768	−	0.276977i
$851$	−30.8677	−	12.7858i	−1.05813	−	0.438292i
$852$		0			0
$853$	10.9239	+	26.3725i	0.374026	+	0.902978i	0.993059	+	0.117613i	$0.0375243\pi$
$853$	10.9239	+	26.3725i	0.374026	+	0.902978i	−0.619034	+	0.785364i	$0.712476\pi$
$854$	−0.371444	−	5.38526i	−0.0127105	−	0.184280i
$855$		0			0
$856$	7.19751	+	4.70327i	0.246006	+	0.160755i
$857$	−2.77666	−	2.77666i	−0.0948488	−	0.0948488i	0.658090	−	0.752939i	$-0.271365\pi$
$857$	−2.77666	−	2.77666i	−0.0948488	−	0.0948488i	−0.752939	+	0.658090i	$0.771365\pi$
$858$		0			0
$859$	21.8775	+	52.8170i	0.746452	+	1.80209i	0.577352	+	0.816495i	$0.304086\pi$
$859$	21.8775	+	52.8170i	0.746452	+	1.80209i	0.169100	+	0.985599i	$0.445914\pi$
$860$	1.45734	+	10.5141i	0.0496947	+	0.358528i
$861$		0			0
$862$	−52.5126	−	17.6259i	−1.78859	−	0.600339i
$863$	35.8729			1.22113			0.610564	−	0.791967i	$-0.290943\pi$
$863$	35.8729			1.22113			0.610564	+	0.791967i	$0.290943\pi$
$864$		0			0
$865$	−3.72653			−0.126706
$866$	−27.7388	−	9.31053i	−0.942603	−	0.316385i
$867$		0			0
$868$	3.67931	−	0.509981i	0.124884	−	0.0173099i
$869$	−2.88630	−	6.96814i	−0.0979110	−	0.236378i
$870$		0			0
$871$	−19.6825	−	19.6825i	−0.666917	−	0.666917i
$872$	40.7381	−	8.53812i	1.37957	−	0.289137i
$873$		0			0
$874$	−1.04515	−	15.1528i	−0.0353528	−	0.512552i
$875$	−2.52530	−	6.09661i	−0.0853707	−	0.206103i
$876$		0			0
$877$	14.2190	+	5.88971i	0.480142	+	0.198882i	0.609609	−	0.792702i	$-0.291326\pi$
$877$	14.2190	+	5.88971i	0.480142	+	0.198882i	−0.129466	+	0.991584i	$0.541326\pi$
$878$	6.67744	+	13.4247i	0.225353	+	0.453063i
$879$		0			0
$880$	−41.6977	−	23.3206i	−1.40563	−	0.786137i
$881$	−51.9652			−1.75075			−0.875377	−	0.483442i	$-0.839386\pi$
$881$	−51.9652			−1.75075			−0.875377	+	0.483442i	$0.839386\pi$
$882$		0			0
$883$	20.6623	−	49.8832i	0.695342	−	1.67870i	−0.0383892	−	0.999263i	$-0.512223\pi$
$883$	20.6623	−	49.8832i	0.695342	−	1.67870i	0.733731	−	0.679440i	$-0.237777\pi$
$884$	12.7842	+	21.7977i	0.429979	+	0.733134i
$885$		0			0
$886$	−0.588580	−	8.53334i	−0.0197737	−	0.286683i
$887$	24.4215	+	24.4215i	0.819994	+	0.819994i	0.986107	−	0.166112i	$-0.0531215\pi$
$887$	24.4215	+	24.4215i	0.819994	+	0.819994i	−0.166112	+	0.986107i	$0.553121\pi$
$888$		0			0
$889$	3.15928	−	3.15928i	0.105959	−	0.105959i
$890$	−14.5072	−	12.6351i	−0.486282	−	0.423529i
$891$		0			0
$892$	−29.3012	+	38.7309i	−0.981075	+	1.29681i
$893$	−21.0716	−	8.72813i	−0.705133	−	0.292076i
$894$		0			0
$895$		−	19.8198i		−	0.662503i
$896$	−0.550298	−	6.14206i	−0.0183842	−	0.205192i
$897$		0			0
$898$	−12.3737	−	4.15324i	−0.412917	−	0.138595i
$899$	−1.03761	+	2.50502i	−0.0346064	+	0.0835472i
$900$		0			0
$901$	−37.7012	+	15.6163i	−1.25601	+	0.520256i
$902$	−42.8273	+	49.1730i	−1.42599	+	1.63728i
$903$		0			0
$904$	−31.9569	+	21.8298i	−1.06287	+	0.726048i
$905$	35.4402	−	35.4402i	1.17807	−	1.17807i
$906$		0			0
$907$	−1.89537	+	0.785090i	−0.0629349	+	0.0260685i	−0.413929	−	0.910309i	$-0.635844\pi$
$907$	−1.89537	+	0.785090i	−0.0629349	+	0.0260685i	0.350994	+	0.936378i	$0.385844\pi$
$908$	−16.1090	+	9.44785i	−0.534597	+	0.313538i
$909$		0			0
$910$	1.65900	+	3.33535i	0.0549952	+	0.110566i
$911$		−	1.10306i		−	0.0365460i	−0.999833	−	0.0182730i	$-0.994183\pi$
$911$		−	1.10306i		−	0.0365460i	0.999833	−	0.0182730i	$-0.00581679\pi$
$912$		0			0
$913$			99.2364i			3.28425i
$914$	−26.9574	+	13.4086i	−0.891673	+	0.443516i
$915$		0			0
$916$	−30.2315	−	7.87957i	−0.998875	−	0.260348i
$917$	−2.11862	+	0.877563i	−0.0699632	+	0.0289797i
$918$		0			0
$919$	21.1448	−	21.1448i	0.697501	−	0.697501i	−0.266370	−	0.963871i	$-0.585824\pi$
$919$	21.1448	−	21.1448i	0.697501	−	0.697501i	0.963871	+	0.266370i	$0.0858242\pi$
$920$	−3.62177	−	17.2806i	−0.119406	−	0.569725i
$921$		0			0
$922$	5.89904	+	5.13778i	0.194275	+	0.169204i
$923$	20.8042	−	8.61740i	0.684780	−	0.283645i
$924$		0			0
$925$	4.99609	−	12.0616i	0.164270	−	0.396584i
$926$	−13.6282	+	40.6024i	−0.447851	+	1.33428i
$927$		0			0
$928$	4.07059	+	1.92169i	0.133624	+	0.0630827i
$929$			8.59550i			0.282009i	0.990009	+	0.141005i	$0.0450332\pi$
$929$			8.59550i			0.282009i	−0.990009	+	0.141005i	$0.954967\pi$
$930$		0			0
$931$	20.6008	+	8.53313i	0.675164	+	0.279662i
$932$	18.2145	−	2.52468i	0.596637	−	0.0826985i
$933$		0			0
$934$	13.0418	−	14.9742i	0.426742	−	0.489972i
$935$	−42.6945	+	42.6945i	−1.39626	+	1.39626i
$936$		0			0
$937$	5.50940	+	5.50940i	0.179984	+	0.179984i	0.791349	−	0.611365i	$-0.209379\pi$
$937$	5.50940	+	5.50940i	0.179984	+	0.179984i	−0.611365	+	0.791349i	$0.709379\pi$
$938$	8.56420	−	0.590708i	0.279631	−	0.0192873i
$939$		0			0
$940$	−25.6555	−	6.68688i	−0.836789	−	0.218102i
$941$	7.60686	−	18.3646i	0.247977	−	0.598669i	−0.750055	−	0.661375i	$-0.769973\pi$
$941$	7.60686	−	18.3646i	0.247977	−	0.598669i	0.998032	+	0.0627064i	$0.0199732\pi$
$942$		0			0
$943$	−24.0985			−0.784754
$944$	16.4714	+	20.8694i	0.536099	+	0.679240i
$945$		0			0
$946$	−21.4706	+	10.6795i	−0.698070	+	0.347219i
$947$	−0.912836	−	0.378109i	−0.0296632	−	0.0122869i	0.367803	−	0.929904i	$-0.380110\pi$
$947$	−0.912836	−	0.378109i	−0.0296632	−	0.0122869i	−0.397466	+	0.917617i	$0.630110\pi$
$948$		0			0
$949$	−12.2247	−	29.5129i	−0.396829	−	0.958030i
$950$	5.92100	−	0.408396i	0.192103	−	0.0132501i
$951$		0			0
$952$	−7.65883	−	1.44202i	−0.248224	−	0.0467363i
$953$	32.2689	+	32.2689i	1.04529	+	1.04529i	0.998924	+	0.0463673i	$0.0147645\pi$
$953$	32.2689	+	32.2689i	1.04529	+	1.04529i	0.0463673	+	0.998924i	$0.485236\pi$
$954$		0			0
$955$	2.24344	+	5.41614i	0.0725960	+	0.175262i
$956$	24.1075	−	31.8658i	0.779692	−	1.03061i
$957$		0			0
$958$	−1.13225	+	3.37331i	−0.0365813	+	0.108987i
$959$	−5.23400			−0.169015
$960$		0			0
$961$	19.3896			0.625471
$962$	−11.6398	+	34.6783i	−0.375281	+	1.11807i
$963$		0			0
$964$	0.731656	−	0.967119i	0.0235650	−	0.0311488i
$965$	−3.52064	−	8.49958i	−0.113334	−	0.273611i
$966$		0			0
$967$	13.4056	+	13.4056i	0.431097	+	0.431097i	0.889001	−	0.457905i	$-0.151400\pi$
$967$	13.4056	+	13.4056i	0.431097	+	0.431097i	−0.457905	+	0.889001i	$0.651400\pi$
$968$	14.2142	−	75.4938i	0.456860	−	2.42646i
$969$		0			0
$970$	−3.37389	+	0.232711i	−0.108329	+	0.00747191i
$971$	7.93498	+	19.1567i	0.254645	+	0.614769i	0.998568	−	0.0534973i	$-0.0170369\pi$
$971$	7.93498	+	19.1567i	0.254645	+	0.614769i	−0.743923	+	0.668266i	$0.767037\pi$
$972$		0			0
$973$	−1.68200	−	0.696707i	−0.0539224	−	0.0223354i
$974$	2.97949	−	1.48199i	0.0954690	−	0.0474861i
$975$		0			0
$976$	27.8193	+	3.27652i	0.890473	+	0.104879i
$977$	−5.52723			−0.176832			−0.0884159	−	0.996084i	$-0.528180\pi$
$977$	−5.52723			−0.176832			−0.0884159	+	0.996084i	$0.528180\pi$
$978$		0			0
$979$	16.6320	−	40.1533i	0.531562	−	1.28330i
$980$	25.0823	+	6.53748i	0.801224	+	0.208832i
$981$		0			0
$982$	45.2396	−	3.12036i	1.44365	−	0.0995747i
$983$	28.1493	+	28.1493i	0.897822	+	0.897822i	0.995243	−	0.0974212i	$-0.0310594\pi$
$983$	28.1493	+	28.1493i	0.897822	+	0.897822i	−0.0974212	+	0.995243i	$0.531059\pi$
$984$		0			0
$985$	−11.4435	+	11.4435i	−0.364622	+	0.364622i
$986$	3.73629	−	4.28989i	0.118988	−	0.136618i
$987$		0			0
$988$	−16.4718	+	2.28312i	−0.524039	+	0.0726358i
$989$	−8.18744	−	3.39135i	−0.260345	−	0.107839i
$990$		0			0
$991$		−	24.7160i		−	0.785131i	−0.919724	−	0.392565i	$-0.871588\pi$
$991$		−	24.7160i		−	0.785131i	0.919724	−	0.392565i	$-0.128412\pi$
$992$	−0.932049	+	19.2526i	−0.0295926	+	0.611272i
$993$		0			0
$994$	−2.20985	+	6.58381i	−0.0700923	+	0.208826i
$995$	16.6442	−	40.1825i	0.527655	−	1.27387i
$996$		0			0
$997$	−26.8087	+	11.1045i	−0.849039	+	0.351684i	−0.764411	−	0.644729i	$-0.776970\pi$
$997$	−26.8087	+	11.1045i	−0.849039	+	0.351684i	−0.0846280	+	0.996413i	$0.526970\pi$
$998$	38.1880	+	33.2599i	1.20882	+	1.05282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.179.6	✓	32
3.2	odd	2		288.2.w.b.179.3	yes	32
4.3	odd	2		1152.2.w.b.1007.3		32
12.11	even	2		1152.2.w.a.1007.6		32
32.5	even	8		1152.2.w.a.143.6		32
32.27	odd	8		288.2.w.b.251.3	yes	32
96.5	odd	8		1152.2.w.b.143.3		32
96.59	even	8	inner	288.2.w.a.251.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.6	✓	32	1.1	even	1	trivial
288.2.w.a.251.6	yes	32	96.59	even	8	inner
288.2.w.b.179.3	yes	32	3.2	odd	2
288.2.w.b.251.3	yes	32	32.27	odd	8
1152.2.w.a.143.6		32	32.5	even	8
1152.2.w.a.1007.6		32	12.11	even	2
1152.2.w.b.143.3		32	96.5	odd	8
1152.2.w.b.1007.3		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.450008 - 1.34071i) q^{2} +(-1.59499 - 1.20666i) q^{4} +(-0.739921 - 1.78633i) q^{5} +(0.385417 + 0.385417i) q^{7} +(-2.33553 + 1.59540i) q^{8} +O(q^{10})\)	\(q+(0.450008 - 1.34071i) q^{2} +(-1.59499 - 1.20666i) q^{4} +(-0.739921 - 1.78633i) q^{5} +(0.385417 + 0.385417i) q^{7} +(-2.33553 + 1.59540i) q^{8} +(-2.72791 + 0.188155i) q^{10} +(-2.36398 - 5.70716i) q^{11} +(-2.30916 - 0.956485i) q^{13} +(0.690171 - 0.343290i) q^{14} +(1.08796 + 3.84920i) q^{16} +5.05518 q^{17} +(-1.27305 + 3.07341i) q^{19} +(-0.975320 + 3.74200i) q^{20} +(-8.71543 + 0.601139i) q^{22} +(-2.28291 - 2.28291i) q^{23} +(0.892052 - 0.892052i) q^{25} +(-2.32151 + 2.66548i) q^{26} +(-0.149669 - 1.07980i) q^{28} +(0.735171 + 0.304518i) q^{29} +3.40740i q^{31} +(5.65024 + 0.273536i) q^{32} +(2.27487 - 6.77751i) q^{34} +(0.403302 - 0.973658i) q^{35} +(9.56094 - 3.96027i) q^{37} +(3.54766 + 3.08984i) q^{38} +(4.57802 + 2.99155i) q^{40} +(5.27801 - 5.27801i) q^{41} +(2.53597 - 1.05043i) q^{43} +(-3.11606 + 11.9553i) q^{44} +(-4.08804 + 2.03338i) q^{46} +6.85609i q^{47} -6.70291i q^{49} +(-0.794549 - 1.59741i) q^{50} +(2.52893 + 4.31194i) q^{52} +(-7.45793 + 3.08917i) q^{53} +(-8.44569 + 8.44569i) q^{55} +(-1.51505 - 0.285257i) q^{56} +(0.739101 - 0.848613i) q^{58} +(6.14066 - 2.54355i) q^{59} +(2.67989 - 6.46983i) q^{61} +(4.56833 + 1.53336i) q^{62} +(2.90938 - 7.45221i) q^{64} +4.83264i q^{65} +(10.2890 + 4.26184i) q^{67} +(-8.06294 - 6.09987i) q^{68} +(-1.12390 - 0.978864i) q^{70} +(-6.37064 + 6.37064i) q^{71} +(9.03739 + 9.03739i) q^{73} +(-1.00706 - 14.6006i) q^{74} +(5.73905 - 3.36592i) q^{76} +(1.28852 - 3.11075i) q^{77} +1.22095 q^{79} +(6.07093 - 4.79156i) q^{80} +(-4.70112 - 9.45141i) q^{82} +(-14.8416 - 6.14761i) q^{83} +(-3.74043 - 9.03021i) q^{85} +(-0.267116 - 3.87270i) q^{86} +(14.6264 + 9.55772i) q^{88} +(4.97492 + 4.97492i) q^{89} +(-0.521343 - 1.25863i) q^{91} +(0.886520 + 6.39590i) q^{92} +(9.19200 + 3.08529i) q^{94} +6.43208 q^{95} +1.23680 q^{97} +(-8.98663 - 3.01636i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 - 4 * q^8	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

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