LMFDB - Embedded newform 288.2.w.a.179.1

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			179.1
Character	$\chi$	$=$	288.179
Dual form			288.2.w.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40684 + 0.144194i) q^{2} +(1.95842 - 0.405715i) q^{4} +(0.366958 + 0.885915i) q^{5} +(1.21471 + 1.21471i) q^{7} +(-2.69668 + 0.853169i) q^{8} +O(q^{10})$	\(q+(-1.40684 + 0.144194i) q^{2} +(1.95842 - 0.405715i) q^{4} +(0.366958 + 0.885915i) q^{5} +(1.21471 + 1.21471i) q^{7} +(-2.69668 + 0.853169i) q^{8} +(-0.643996 - 1.19343i) q^{10} +(0.545272 + 1.31640i) q^{11} +(0.0270492 + 0.0112041i) q^{13} +(-1.88406 - 1.53375i) q^{14} +(3.67079 - 1.58912i) q^{16} +1.32687 q^{17} +(-1.73653 + 4.19236i) q^{19} +(1.07809 + 1.58611i) q^{20} +(-0.956929 - 1.77335i) q^{22} +(0.934512 + 0.934512i) q^{23} +(2.88535 - 2.88535i) q^{25} +(-0.0396695 - 0.0118622i) q^{26} +(2.87173 + 1.88608i) q^{28} +(9.35195 + 3.87371i) q^{29} +9.74390i q^{31} +(-4.93509 + 2.76495i) q^{32} +(-1.86670 + 0.191327i) q^{34} +(-0.630382 + 1.52188i) q^{35} +(-6.28278 + 2.60241i) q^{37} +(1.83852 - 6.14839i) q^{38} +(-1.74541 - 2.07596i) q^{40} +(3.42377 - 3.42377i) q^{41} +(0.997463 - 0.413163i) q^{43} +(1.60195 + 2.35684i) q^{44} +(-1.44946 - 1.17996i) q^{46} -6.21143i q^{47} -4.04896i q^{49} +(-3.64318 + 4.47528i) q^{50} +(0.0575193 + 0.0109681i) q^{52} +(2.94741 - 1.22086i) q^{53} +(-0.966130 + 0.966130i) q^{55} +(-4.31204 - 2.23933i) q^{56} +(-13.7153 - 4.10121i) q^{58} +(-10.4533 + 4.32990i) q^{59} +(2.76809 - 6.68277i) q^{61} +(-1.40501 - 13.7081i) q^{62} +(6.54421 - 4.60145i) q^{64} +0.0280747i q^{65} +(-10.1069 - 4.18640i) q^{67} +(2.59857 - 0.538333i) q^{68} +(0.667404 - 2.23194i) q^{70} +(7.38725 - 7.38725i) q^{71} +(-8.30156 - 8.30156i) q^{73} +(8.46364 - 4.56712i) q^{74} +(-1.69995 + 8.91492i) q^{76} +(-0.936700 + 2.26139i) q^{77} +5.54363 q^{79} +(2.75485 + 2.66887i) q^{80} +(-4.32302 + 5.31039i) q^{82} +(-11.4571 - 4.74570i) q^{83} +(0.486907 + 1.17550i) q^{85} +(-1.34370 + 0.725083i) q^{86} +(-2.59354 - 3.08471i) q^{88} +(-7.93127 - 7.93127i) q^{89} +(0.0192471 + 0.0464667i) q^{91} +(2.20931 + 1.45102i) q^{92} +(0.895648 + 8.73851i) q^{94} -4.35131 q^{95} +12.5582 q^{97} +(0.583834 + 5.69626i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.40684	+	0.144194i	−0.994788	+	0.101960i
$2$	−1.40684	+	0.144194i	−0.994788	+	0.101960i
$3$		0			0
$3$		0			0
$4$	1.95842	−	0.405715i	0.979208	−	0.202858i
$5$	0.366958	+	0.885915i	0.164109	+	0.396193i	0.984446	−	0.175686i	$-0.0562144\pi$
$5$	0.366958	+	0.885915i	0.164109	+	0.396193i	−0.820338	+	0.571880i	$0.806214\pi$
$6$		0			0
$7$	1.21471	+	1.21471i	0.459117	+	0.459117i	0.898366	−	0.439249i	$-0.144755\pi$
$7$	1.21471	+	1.21471i	0.459117	+	0.459117i	−0.439249	+	0.898366i	$0.644755\pi$
$8$	−2.69668	+	0.853169i	−0.953422	+	0.301641i
$9$		0			0
$10$	−0.643996	−	1.19343i	−0.203649	−	0.377396i
$11$	0.545272	+	1.31640i	0.164406	+	0.396910i	0.984516	−	0.175295i	$-0.0560879\pi$
$11$	0.545272	+	1.31640i	0.164406	+	0.396910i	−0.820110	+	0.572206i	$0.806088\pi$
$12$		0			0
$13$	0.0270492	+	0.0112041i	0.00750210	+	0.00310747i	0.386431	−	0.922318i	$-0.373708\pi$
$13$	0.0270492	+	0.0112041i	0.00750210	+	0.00310747i	−0.378929	+	0.925426i	$0.623708\pi$
$14$	−1.88406	−	1.53375i	−0.503536	−	0.409913i
$15$		0			0
$16$	3.67079	−	1.58912i	0.917698	−	0.397280i
$17$	1.32687			0.321814			0.160907	−	0.986970i	$-0.448558\pi$
$17$	1.32687			0.321814			0.160907	+	0.986970i	$0.448558\pi$
$18$		0			0
$19$	−1.73653	+	4.19236i	−0.398388	+	0.961793i	0.589661	+	0.807651i	$0.299261\pi$
$19$	−1.73653	+	4.19236i	−0.398388	+	0.961793i	−0.988049	+	0.154142i	$0.950739\pi$
$20$	1.07809	+	1.58611i	0.241067	+	0.354665i
$21$		0			0
$22$	−0.956929	−	1.77335i	−0.204018	−	0.378079i
$23$	0.934512	+	0.934512i	0.194859	+	0.194859i	0.797792	−	0.602933i	$-0.206001\pi$
$23$	0.934512	+	0.934512i	0.194859	+	0.194859i	−0.602933	+	0.797792i	$0.706001\pi$
$24$		0			0
$25$	2.88535	−	2.88535i	0.577069	−	0.577069i
$26$	−0.0396695	−	0.0118622i	−0.00777984	−	0.00232636i
$27$		0			0
$28$	2.87173	+	1.88608i	0.542706	+	0.356436i
$29$	9.35195	+	3.87371i	1.73661	+	0.719329i	0.999028	+	0.0440761i	$0.0140344\pi$
$29$	9.35195	+	3.87371i	1.73661	+	0.719329i	0.737586	+	0.675253i	$0.235966\pi$
$30$		0			0
$31$			9.74390i			1.75006i	0.484072	+	0.875028i	$0.339157\pi$
$31$			9.74390i			1.75006i	−0.484072	+	0.875028i	$0.660843\pi$
$32$	−4.93509	+	2.76495i	−0.872408	+	0.488778i
$33$		0			0
$34$	−1.86670	+	0.191327i	−0.320137	+	0.0328122i
$35$	−0.630382	+	1.52188i	−0.106554	+	0.257244i
$36$		0			0
$37$	−6.28278	+	2.60241i	−1.03288	+	0.427834i	−0.833752	−	0.552139i	$-0.813812\pi$
$37$	−6.28278	+	2.60241i	−1.03288	+	0.427834i	−0.199131	+	0.979973i	$0.563812\pi$
$38$	1.83852	−	6.14839i	0.298247	−	0.997400i
$39$		0			0
$40$	−1.74541	−	2.07596i	−0.275973	−	0.328237i
$41$	3.42377	−	3.42377i	0.534703	−	0.534703i	−0.387266	−	0.921968i	$-0.626580\pi$
$41$	3.42377	−	3.42377i	0.534703	−	0.534703i	0.921968	+	0.387266i	$0.126580\pi$
$42$		0			0
$43$	0.997463	−	0.413163i	0.152112	−	0.0630067i	−0.305329	−	0.952247i	$-0.598766\pi$
$43$	0.997463	−	0.413163i	0.152112	−	0.0630067i	0.457440	+	0.889240i	$0.348766\pi$
$44$	1.60195	+	2.35684i	0.241504	+	0.355307i
$45$		0			0
$46$	−1.44946	−	1.17996i	−0.213712	−	0.173976i
$47$		−	6.21143i		−	0.906031i	−0.891503	−	0.453015i	$-0.850348\pi$
$47$		−	6.21143i		−	0.906031i	0.891503	−	0.453015i	$-0.149652\pi$
$48$		0			0
$49$		−	4.04896i		−	0.578423i
$50$	−3.64318	+	4.47528i	−0.515224	+	0.632900i
$51$		0			0
$52$	0.0575193	+	0.0109681i	0.00797649	+	0.00152100i
$53$	2.94741	−	1.22086i	0.404858	−	0.167698i	−0.170955	−	0.985279i	$-0.554685\pi$
$53$	2.94741	−	1.22086i	0.404858	−	0.167698i	0.575814	+	0.817581i	$0.304685\pi$
$54$		0			0
$55$	−0.966130	+	0.966130i	−0.130273	+	0.130273i
$56$	−4.31204	−	2.23933i	−0.576220	−	0.299244i
$57$		0			0
$58$	−13.7153	−	4.10121i	−1.80091	−	0.538515i
$59$	−10.4533	+	4.32990i	−1.36090	+	0.563704i	−0.939306	−	0.343079i	$-0.888530\pi$
$59$	−10.4533	+	4.32990i	−1.36090	+	0.563704i	−0.421596	+	0.906784i	$0.638530\pi$
$60$		0			0
$61$	2.76809	−	6.68277i	0.354418	−	0.855641i	−0.641646	−	0.767001i	$-0.721748\pi$
$61$	2.76809	−	6.68277i	0.354418	−	0.855641i	0.996064	−	0.0886397i	$-0.0282520\pi$
$62$	−1.40501	−	13.7081i	−0.178436	−	1.74094i
$63$		0			0
$64$	6.54421	−	4.60145i	0.818026	−	0.575182i
$65$			0.0280747i			0.00348224i
$66$		0			0
$67$	−10.1069	−	4.18640i	−1.23475	−	0.511450i	−0.332680	−	0.943040i	$-0.607953\pi$
$67$	−10.1069	−	4.18640i	−1.23475	−	0.511450i	−0.902070	+	0.431590i	$0.857953\pi$
$68$	2.59857	−	0.538333i	0.315123	−	0.0652825i
$69$		0			0
$70$	0.667404	−	2.23194i	0.0797700	−	0.266768i
$71$	7.38725	−	7.38725i	0.876705	−	0.876705i	−0.116487	−	0.993192i	$-0.537163\pi$
$71$	7.38725	−	7.38725i	0.876705	−	0.876705i	0.993192	+	0.116487i	$0.0371633\pi$
$72$		0			0
$73$	−8.30156	−	8.30156i	−0.971625	−	0.971625i	0.0279838	−	0.999608i	$-0.491091\pi$
$73$	−8.30156	−	8.30156i	−0.971625	−	0.971625i	−0.999608	+	0.0279838i	$0.991091\pi$
$74$	8.46364	−	4.56712i	0.983878	−	0.530917i
$75$		0			0
$76$	−1.69995	+	8.91492i	−0.194997	+	1.02261i
$77$	−0.936700	+	2.26139i	−0.106747	+	0.257710i
$78$		0			0
$79$	5.54363			0.623707			0.311853	−	0.950130i	$-0.399050\pi$
$79$	5.54363			0.623707			0.311853	+	0.950130i	$0.399050\pi$
$80$	2.75485	+	2.66887i	0.308002	+	0.298389i
$81$		0			0
$82$	−4.32302	+	5.31039i	−0.477398	+	0.586434i
$83$	−11.4571	−	4.74570i	−1.25758	−	0.520909i	−0.348417	−	0.937340i	$-0.613281\pi$
$83$	−11.4571	−	4.74570i	−1.25758	−	0.520909i	−0.909167	+	0.416431i	$0.863281\pi$
$84$		0			0
$85$	0.486907	+	1.17550i	0.0528125	+	0.127501i
$86$	−1.34370	+	0.725083i	−0.144895	+	0.0781877i
$87$		0			0
$88$	−2.59354	−	3.08471i	−0.276472	−	0.328832i
$89$	−7.93127	−	7.93127i	−0.840713	−	0.840713i	0.148238	−	0.988952i	$-0.452640\pi$
$89$	−7.93127	−	7.93127i	−0.840713	−	0.840713i	−0.988952	+	0.148238i	$0.952640\pi$
$90$		0			0
$91$	0.0192471	+	0.0464667i	0.00201765	+	0.00487103i
$92$	2.20931	+	1.45102i	0.230337	+	0.151279i
$93$		0			0
$94$	0.895648	+	8.73851i	0.0923791	+	0.901309i
$95$	−4.35131			−0.446435
$96$		0			0
$97$	12.5582			1.27509			0.637545	−	0.770413i	$-0.279950\pi$
$97$	12.5582			1.27509			0.637545	+	0.770413i	$0.279950\pi$
$98$	0.583834	+	5.69626i	0.0589762	+	0.575409i
$99$		0			0
$100$	4.48008	−	6.82134i	0.448008	−	0.682134i
$101$	1.67080	+	4.03367i	0.166251	+	0.401365i	0.984946	−	0.172864i	$-0.0553020\pi$
$101$	1.67080	+	4.03367i	0.166251	+	0.401365i	−0.818695	+	0.574229i	$0.805302\pi$
$102$		0			0
$103$	−2.18742	−	2.18742i	−0.215533	−	0.215533i	0.591080	−	0.806613i	$-0.298702\pi$
$103$	−2.18742	−	2.18742i	−0.215533	−	0.215533i	−0.806613	+	0.591080i	$0.798702\pi$
$104$	−0.0825021	−	0.00713650i	−0.00809000	−	0.000699791i
$105$		0			0
$106$	−3.97051	+	2.14256i	−0.385650	+	0.208103i
$107$	3.09671	+	7.47611i	0.299370	+	0.722743i	0.999958	+	0.00917704i	$0.00292118\pi$
$107$	3.09671	+	7.47611i	0.299370	+	0.722743i	−0.700588	+	0.713566i	$0.747079\pi$
$108$		0			0
$109$	−0.499988	−	0.207102i	−0.0478902	−	0.0198368i	0.358610	−	0.933488i	$-0.383251\pi$
$109$	−0.499988	−	0.207102i	−0.0478902	−	0.0198368i	−0.406500	+	0.913651i	$0.633251\pi$
$110$	1.21988	−	1.49850i	0.116311	−	0.142877i
$111$		0			0
$112$	6.38926	+	2.52862i	0.603728	+	0.238933i
$113$	−19.7112			−1.85427			−0.927137	−	0.374722i	$-0.877738\pi$
$113$	−19.7112			−1.85427			−0.927137	+	0.374722i	$0.877738\pi$
$114$		0			0
$115$	−0.484972	+	1.17083i	−0.0452239	+	0.109180i
$116$	19.8866	+	3.79210i	1.84643	+	0.352088i
$117$		0			0
$118$	14.0818	−	7.59878i	1.29633	−	0.699524i
$119$	1.61177	+	1.61177i	0.147750	+	0.147750i
$120$		0			0
$121$	6.34258	−	6.34258i	0.576598	−	0.576598i
$122$	−2.93066	+	9.80075i	−0.265330	+	0.887318i
$123$		0			0
$124$	3.95325	+	19.0826i	0.355012	+	1.71367i
$125$	8.04455	+	3.33216i	0.719526	+	0.298038i
$126$		0			0
$127$			12.1620i			1.07920i	0.841920	+	0.539602i	$0.181425\pi$
$127$			12.1620i			1.07920i	−0.841920	+	0.539602i	$0.818575\pi$
$128$	−8.54317	+	7.41716i	−0.755117	+	0.655590i
$129$		0			0
$130$	−0.00404820	−	0.0394968i	−0.000355050	−	0.00346410i
$131$	−1.68416	+	4.06591i	−0.147145	+	0.355240i	−0.980217	−	0.197924i	$-0.936580\pi$
$131$	−1.68416	+	4.06591i	−0.147145	+	0.355240i	0.833072	+	0.553165i	$0.186580\pi$
$132$		0			0
$133$	−7.20188	+	2.98312i	−0.624482	+	0.258669i
$134$	14.8224	+	4.43226i	1.28046	+	0.382889i
$135$		0			0
$136$	−3.57816	+	1.13205i	−0.306825	+	0.0970723i
$137$	7.05217	−	7.05217i	0.602508	−	0.602508i	−0.338470	−	0.940977i	$-0.609909\pi$
$137$	7.05217	−	7.05217i	0.602508	−	0.602508i	0.940977	+	0.338470i	$0.109909\pi$
$138$		0			0
$139$	13.5567	−	5.61536i	1.14986	−	0.476288i	0.275374	−	0.961337i	$-0.411198\pi$
$139$	13.5567	−	5.61536i	1.14986	−	0.476288i	0.874487	+	0.485049i	$0.161198\pi$
$140$	−0.617102	+	3.23622i	−0.0521546	+	0.273511i
$141$		0			0
$142$	−9.32751	+	11.4579i	−0.782747	+	0.961525i
$143$			0.0417169i			0.00348855i
$144$		0			0
$145$			9.70653i			0.806083i
$146$	12.8760	+	10.4820i	1.06563	+	0.867494i
$147$		0			0
$148$	−11.2485	+	7.64563i	−0.924618	+	0.628467i
$149$	−8.14803	+	3.37503i	−0.667513	+	0.276493i	−0.690596	−	0.723241i	$-0.742652\pi$
$149$	−8.14803	+	3.37503i	−0.667513	+	0.276493i	0.0230832	+	0.999734i	$0.492652\pi$
$150$		0			0
$151$	13.4470	−	13.4470i	1.09430	−	1.09430i	0.0992395	−	0.995064i	$-0.468359\pi$
$151$	13.4470	−	13.4470i	1.09430	−	1.09430i	0.995064	−	0.0992395i	$-0.0316410\pi$
$152$	1.10609	−	12.7870i	0.0897155	−	1.03716i
$153$		0			0
$154$	0.991712	−	3.31649i	0.0799144	−	0.267251i
$155$	−8.63227	+	3.57560i	−0.693361	+	0.287199i
$156$		0			0
$157$	1.17205	−	2.82959i	0.0935400	−	0.225826i	−0.870184	−	0.492727i	$-0.836000\pi$
$157$	1.17205	−	2.82959i	0.0935400	−	0.225826i	0.963724	+	0.266902i	$0.0860000\pi$
$158$	−7.79901	+	0.799355i	−0.620456	+	0.0635933i
$159$		0			0
$160$	−4.26048	−	3.35745i	−0.336820	−	0.265430i
$161$			2.27032i			0.178926i
$162$		0			0
$163$	−14.7015	−	6.08955i	−1.15151	−	0.476970i	−0.276469	−	0.961023i	$-0.589164\pi$
$163$	−14.7015	−	6.08955i	−1.15151	−	0.476970i	−0.875039	+	0.484052i	$0.839164\pi$
$164$	5.31609	−	8.09424i	0.415117	−	0.632054i
$165$		0			0
$166$	16.8027	+	5.02441i	1.30414	+	0.389970i
$167$	8.30270	−	8.30270i	0.642482	−	0.642482i	−0.308683	−	0.951165i	$-0.599888\pi$
$167$	8.30270	−	8.30270i	0.642482	−	0.642482i	0.951165	+	0.308683i	$0.0998882\pi$
$168$		0			0
$169$	−9.19178	−	9.19178i	−0.707060	−	0.707060i
$170$	−0.854501	−	1.58353i	−0.0655373	−	0.121451i
$171$		0			0
$172$	1.78582	−	1.21383i	0.136168	−	0.0925538i
$173$	−5.16308	+	12.4648i	−0.392542	+	0.947680i	0.596843	+	0.802358i	$0.296422\pi$
$173$	−5.16308	+	12.4648i	−0.392542	+	0.947680i	−0.989384	+	0.145322i	$0.953578\pi$
$174$		0			0
$175$	7.00971			0.529885
$176$	4.09350	+	3.96574i	0.308559	+	0.298929i
$177$		0			0
$178$	12.3017	+	10.0144i	0.922051	+	0.750613i
$179$	1.43728	+	0.595340i	0.107427	+	0.0444978i	0.435750	−	0.900068i	$-0.356483\pi$
$179$	1.43728	+	0.595340i	0.107427	+	0.0444978i	−0.328323	+	0.944566i	$0.606483\pi$
$180$		0			0
$181$	5.57818	+	13.4669i	0.414623	+	1.00099i	0.983880	+	0.178828i	$0.0572307\pi$
$181$	5.57818	+	13.4669i	0.414623	+	1.00099i	−0.569258	+	0.822159i	$0.692769\pi$
$182$	−0.0337779	−	0.0625960i	−0.00250378	−	0.00463993i
$183$		0			0
$184$	−3.31738	−	1.72279i	−0.244561	−	0.127006i
$185$	−4.61104	−	4.61104i	−0.339010	−	0.339010i
$186$		0			0
$187$	0.723507	+	1.74670i	0.0529081	+	0.127731i
$188$	−2.52007	−	12.1646i	−0.183795	−	0.887193i
$189$		0			0
$190$	6.12161	−	0.627430i	0.444108	−	0.0455186i
$191$	−7.01680			−0.507718			−0.253859	−	0.967241i	$-0.581700\pi$
$191$	−7.01680			−0.507718			−0.253859	+	0.967241i	$0.581700\pi$
$192$		0			0
$193$	21.3761			1.53868			0.769342	−	0.638837i	$-0.220584\pi$
$193$	21.3761			1.53868			0.769342	+	0.638837i	$0.220584\pi$
$194$	−17.6674	+	1.81081i	−1.26844	+	0.130008i
$195$		0			0
$196$	−1.64273	−	7.92956i	−0.117338	−	0.566397i
$197$	−4.34168	−	10.4817i	−0.309332	−	0.746793i	−0.999727	−	0.0233605i	$-0.992563\pi$
$197$	−4.34168	−	10.4817i	−0.309332	−	0.746793i	0.690395	−	0.723432i	$-0.257437\pi$
$198$		0			0
$199$	−9.04307	−	9.04307i	−0.641047	−	0.641047i	0.309766	−	0.950813i	$-0.399749\pi$
$199$	−9.04307	−	9.04307i	−0.641047	−	0.641047i	−0.950813	+	0.309766i	$0.899749\pi$
$200$	−5.31918	+	10.2426i	−0.376123	+	0.724258i
$201$		0			0
$202$	−2.93219	−	5.43383i	−0.206308	−	0.382323i
$203$	6.65448	+	16.0653i	0.467053	+	1.12757i
$204$		0			0
$205$	4.28955	+	1.77679i	0.299595	+	0.124096i
$206$	3.39277	+	2.76195i	0.236386	+	0.192434i
$207$		0			0
$208$	0.117097	−	0.00185634i	0.00811919	−	0.000128714i
$209$	−6.46572			−0.447243
$210$		0			0
$211$	5.73872	−	13.8545i	0.395070	−	0.953783i	−0.593747	−	0.804652i	$-0.702352\pi$
$211$	5.73872	−	13.8545i	0.395070	−	0.953783i	0.988817	−	0.149132i	$-0.0476479\pi$
$212$	5.27694	−	3.58676i	0.362422	−	0.246340i
$213$		0			0
$214$	−5.43459	−	10.0712i	−0.371501	−	0.688453i
$215$	0.732055	+	0.732055i	0.0499257	+	0.0499257i
$216$		0			0
$217$	−11.8360	+	11.8360i	−0.803480	+	0.803480i
$218$	0.733268	+	0.219265i	0.0496632	+	0.0148505i
$219$		0			0
$220$	−1.50011	+	2.28406i	−0.101137	+	0.153991i
$221$	0.0358909	+	0.0148665i	0.00241428	+	0.00100003i
$222$		0			0
$223$		−	0.0857822i		−	0.00574440i	−0.999996	−	0.00287220i	$-0.999086\pi$
$223$		−	0.0857822i		−	0.00574440i	0.999996	−	0.00287220i	$-0.000914251\pi$
$224$	−9.35330	−	2.63609i	−0.624944	−	0.176131i
$225$		0			0
$226$	27.7306	−	2.84223i	1.84461	−	0.189062i
$227$	9.62555	−	23.2381i	0.638870	−	1.54237i	−0.189317	−	0.981916i	$-0.560627\pi$
$227$	9.62555	−	23.2381i	0.638870	−	1.54237i	0.828187	−	0.560452i	$-0.189373\pi$
$228$		0			0
$229$	−24.5201	+	10.1566i	−1.62034	+	0.671165i	−0.994100	−	0.108468i	$-0.965406\pi$
$229$	−24.5201	+	10.1566i	−1.62034	+	0.671165i	−0.626237	+	0.779633i	$0.715406\pi$
$230$	0.513454	−	1.71710i	0.0338562	−	0.113222i
$231$		0			0
$232$	−28.5242	−	2.46736i	−1.87270	−	0.161990i
$233$	−2.44973	+	2.44973i	−0.160487	+	0.160487i	−0.782782	−	0.622295i	$-0.786200\pi$
$233$	−2.44973	+	2.44973i	−0.160487	+	0.160487i	0.622295	+	0.782782i	$0.286200\pi$
$234$		0			0
$235$	5.50280	−	2.27934i	0.358963	−	0.148687i
$236$	−18.7152	+	12.7208i	−1.21826	+	0.828053i
$237$		0			0
$238$	−2.49991	−	2.03510i	−0.162045	−	0.131916i
$239$			11.3256i			0.732589i	0.930499	+	0.366295i	$0.119374\pi$
$239$			11.3256i			0.732589i	−0.930499	+	0.366295i	$0.880626\pi$
$240$		0			0
$241$			13.4166i			0.864239i	0.901816	+	0.432119i	$0.142234\pi$
$241$			13.4166i			0.864239i	−0.901816	+	0.432119i	$0.857766\pi$
$242$	−8.00846	+	9.83757i	−0.514803	+	0.632383i
$243$		0			0
$244$	2.70978	−	14.2107i	0.173476	−	0.909747i
$245$	3.58704	−	1.48580i	0.229167	−	0.0949243i
$246$		0			0
$247$	−0.0939436	+	0.0939436i	−0.00597749	+	0.00597749i
$248$	−8.31319	−	26.2762i	−0.527888	−	1.66854i
$249$		0			0
$250$	−11.7979	−	3.52786i	−0.746165	−	0.223121i
$251$	15.2970	−	6.33621i	0.965535	−	0.399938i	0.156487	−	0.987680i	$-0.449983\pi$
$251$	15.2970	−	6.33621i	0.965535	−	0.399938i	0.809048	+	0.587742i	$0.199983\pi$
$252$		0			0
$253$	−0.720632	+	1.73976i	−0.0453057	+	0.109378i
$254$	−1.75368	−	17.1100i	−0.110036	−	1.07358i
$255$		0			0
$256$	10.9494	−	11.6666i	0.684337	−	0.729165i
$257$		−	2.43408i		−	0.151833i	−0.997114	−	0.0759167i	$-0.975812\pi$
$257$		−	2.43408i		−	0.151833i	0.997114	−	0.0759167i	$-0.0241883\pi$
$258$		0			0
$259$	−10.7929	−	4.47058i	−0.670640	−	0.277788i
$260$	0.0113904	+	0.0549820i	0.000706400	+	0.00340984i
$261$		0			0
$262$	1.78307	−	5.96295i	0.110158	−	0.368392i
$263$	15.2250	−	15.2250i	0.938816	−	0.938816i	−0.0594176	−	0.998233i	$-0.518924\pi$
$263$	15.2250	−	15.2250i	0.938816	−	0.938816i	0.998233	+	0.0594176i	$0.0189244\pi$
$264$		0			0
$265$	2.16316	+	2.16316i	0.132882	+	0.132882i
$266$	9.70177	−	5.23524i	0.594854	−	0.320993i
$267$		0			0
$268$	−21.4919	−	4.09820i	−1.31283	−	0.250338i
$269$	2.29849	−	5.54904i	0.140141	−	0.338331i	−0.838190	−	0.545379i	$-0.816386\pi$
$269$	2.29849	−	5.54904i	0.140141	−	0.338331i	0.978331	+	0.207048i	$0.0663857\pi$
$270$		0			0
$271$	−10.5866			−0.643088			−0.321544	−	0.946895i	$-0.604202\pi$
$271$	−10.5866			−0.643088			−0.321544	+	0.946895i	$0.604202\pi$
$272$	4.87068	−	2.10856i	0.295328	−	0.127850i
$273$		0			0
$274$	−8.90442	+	10.9382i	−0.537936	+	0.660800i
$275$	5.37158	+	2.22498i	0.323918	+	0.134171i
$276$		0			0
$277$	5.91980	+	14.2917i	0.355686	+	0.858702i	0.995896	+	0.0905024i	$0.0288473\pi$
$277$	5.91980	+	14.2917i	0.355686	+	0.858702i	−0.640210	+	0.768200i	$0.721153\pi$
$278$	−18.2624	+	9.85471i	−1.09531	+	0.591046i
$279$		0			0
$280$	0.401523	−	4.64184i	0.0239956	−	0.277403i
$281$	12.0206	+	12.0206i	0.717087	+	0.717087i	0.968008	−	0.250921i	$-0.0807334\pi$
$281$	12.0206	+	12.0206i	0.717087	+	0.717087i	−0.250921	+	0.968008i	$0.580733\pi$
$282$		0			0
$283$	−5.86696	−	14.1641i	−0.348754	−	0.841968i	−0.996768	−	0.0803386i	$-0.974400\pi$
$283$	−5.86696	−	14.1641i	−0.348754	−	0.841968i	0.648013	−	0.761629i	$-0.275600\pi$
$284$	11.4702	−	17.4644i	0.680631	−	1.03632i
$285$		0			0
$286$	−0.00601531	−	0.0586892i	−0.000355693	−	0.00347037i
$287$	8.31776			0.490982
$288$		0			0
$289$	−15.2394			−0.896436
$290$	−1.39962	−	13.6556i	−0.0821884	−	0.801882i
$291$		0			0
$292$	−19.6260	−	12.8898i	−1.14852	−	0.754321i
$293$	−6.02149	−	14.5372i	−0.351779	−	0.849270i	−0.996401	−	0.0847682i	$-0.972985\pi$
$293$	−6.02149	−	14.5372i	−0.351779	−	0.849270i	0.644622	−	0.764502i	$-0.277015\pi$
$294$		0			0
$295$	−7.67184	−	7.67184i	−0.446672	−	0.446672i
$296$	14.7224	−	12.3782i	0.855721	−	0.719466i
$297$		0			0
$298$	10.9764	−	5.92303i	0.635843	−	0.343112i
$299$	0.0148074	+	0.0357482i	0.000856334	+	0.00206737i
$300$		0			0
$301$	1.71350	+	0.709755i	0.0987645	+	0.0409096i
$302$	−16.9789	+	20.8568i	−0.977025	+	1.20018i
$303$		0			0
$304$	0.287714	+	18.1488i	0.0165015	+	1.04091i
$305$	6.93614			0.397162
$306$		0			0
$307$	−10.0677	+	24.3055i	−0.574592	+	1.38719i	0.323016	+	0.946394i	$0.395303\pi$
$307$	−10.0677	+	24.3055i	−0.574592	+	1.38719i	−0.897608	+	0.440795i	$0.854697\pi$
$308$	−0.916967	+	4.80878i	−0.0522490	+	0.274006i
$309$		0			0
$310$	11.6287	−	6.27503i	0.660464	−	0.356398i
$311$	22.5777	+	22.5777i	1.28027	+	1.28027i	0.940516	+	0.339751i	$0.110343\pi$
$311$	22.5777	+	22.5777i	1.28027	+	1.28027i	0.339751	+	0.940516i	$0.389657\pi$
$312$		0			0
$313$	−9.91862	+	9.91862i	−0.560633	+	0.560633i	−0.929487	−	0.368854i	$-0.879750\pi$
$313$	−9.91862	+	9.91862i	−0.560633	+	0.560633i	0.368854	+	0.929487i	$0.379750\pi$
$314$	−1.24089	+	4.14979i	−0.0700273	+	0.234186i
$315$		0			0
$316$	10.8567	−	2.24913i	0.610739	−	0.126524i
$317$	10.4152	+	4.31414i	0.584979	+	0.242306i	0.655489	−	0.755205i	$-0.272463\pi$
$317$	10.4152	+	4.31414i	0.584979	+	0.242306i	−0.0705101	+	0.997511i	$0.522463\pi$
$318$		0			0
$319$			14.4232i			0.807542i
$320$	6.47795	+	4.10907i	0.362128	+	0.229704i
$321$		0			0
$322$	−0.327366	−	3.19399i	−0.0182434	−	0.177994i
$323$	−2.30416	+	5.56273i	−0.128207	+	0.309519i
$324$		0			0
$325$	0.110374	−	0.0457185i	0.00612245	−	0.00253600i
$326$	21.5607	+	6.44719i	1.19414	+	0.357077i
$327$		0			0
$328$	−6.31177	+	12.1539i	−0.348509	+	0.671085i
$329$	7.54509	−	7.54509i	0.415974	−	0.415974i
$330$		0			0
$331$	13.0127	−	5.39006i	0.715245	−	0.296264i	0.00477208	−	0.999989i	$-0.498481\pi$
$331$	13.0127	−	5.39006i	0.715245	−	0.296264i	0.710473	+	0.703724i	$0.248481\pi$
$332$	−24.3633	−	4.64572i	−1.33711	−	0.254967i
$333$		0			0
$334$	−10.4834	+	12.8778i	−0.573626	+	0.704642i
$335$		−	10.4901i		−	0.573133i
$336$		0			0
$337$			16.7271i			0.911182i	0.890189	+	0.455591i	$0.150572\pi$
$337$			16.7271i			0.911182i	−0.890189	+	0.455591i	$0.849428\pi$
$338$	14.2568	+	11.6060i	0.775467	+	0.631283i
$339$		0			0
$340$	1.43048	+	2.10457i	0.0775789	+	0.114136i
$341$	−12.8269	+	5.31308i	−0.694616	+	0.287719i
$342$		0			0
$343$	13.4213	−	13.4213i	0.724681	−	0.724681i
$344$	−2.33735	+	1.96517i	−0.126021	+	0.105955i
$345$		0			0
$346$	5.46631	−	18.2805i	0.293871	−	0.982765i
$347$	17.4060	−	7.20981i	0.934404	−	0.387043i	0.137056	−	0.990563i	$-0.456236\pi$
$347$	17.4060	−	7.20981i	0.934404	−	0.387043i	0.797347	+	0.603521i	$0.206236\pi$
$348$		0			0
$349$	8.01279	−	19.3446i	0.428915	−	1.03549i	−0.550718	−	0.834692i	$-0.685646\pi$
$349$	8.01279	−	19.3446i	0.428915	−	1.03549i	0.979632	−	0.200800i	$-0.0643541\pi$
$350$	−9.86157	+	1.01076i	−0.527123	+	0.0540271i
$351$		0			0
$352$	−6.33075	−	4.98891i	−0.337430	−	0.265910i
$353$			29.2201i			1.55523i	0.628743	+	0.777613i	$0.283570\pi$
$353$			29.2201i			1.55523i	−0.628743	+	0.777613i	$0.716430\pi$
$354$		0			0
$355$	9.25529	+	3.83367i	0.491220	+	0.203470i
$356$	−18.7506	−	12.3149i	−0.993778	−	0.652688i
$357$		0			0
$358$	−2.10787	−	0.630304i	−0.111404	−	0.0333126i
$359$	−23.8752	+	23.8752i	−1.26008	+	1.26008i	−0.309032	+	0.951052i	$0.600005\pi$
$359$	−23.8752	+	23.8752i	−1.26008	+	1.26008i	−0.951052	+	0.309032i	$0.899995\pi$
$360$		0			0
$361$	−1.12530	−	1.12530i	−0.0592262	−	0.0592262i
$362$	−9.78946	−	18.1415i	−0.514523	−	0.953496i
$363$		0			0
$364$	0.0565461	+	0.0831923i	0.00296382	+	0.00436046i
$365$	4.30816	−	10.4008i	0.225499	−	0.544403i
$366$		0			0
$367$	−7.91904			−0.413370			−0.206685	−	0.978408i	$-0.566268\pi$
$367$	−7.91904			−0.413370			−0.206685	+	0.978408i	$0.566268\pi$
$368$	4.91545	+	1.94535i	0.256236	+	0.101408i
$369$		0			0
$370$	7.15189	+	5.82212i	0.371809	+	0.302678i
$371$	5.06324	+	2.09726i	0.262870	+	0.108884i
$372$		0			0
$373$	−0.910870	−	2.19904i	−0.0471631	−	0.113862i	0.898542	−	0.438887i	$-0.144627\pi$
$373$	−0.910870	−	2.19904i	−0.0471631	−	0.113862i	−0.945705	+	0.325025i	$0.894627\pi$
$374$	−1.26972	−	2.35301i	−0.0656559	−	0.121671i
$375$		0			0
$376$	5.29940	+	16.7503i	0.273296	+	0.863829i
$377$	0.209561	+	0.209561i	0.0107930	+	0.0107930i
$378$		0			0
$379$	8.94487	+	21.5948i	0.459467	+	1.10925i	0.968613	+	0.248572i	$0.0799613\pi$
$379$	8.94487	+	21.5948i	0.459467	+	1.10925i	−0.509146	+	0.860680i	$0.670039\pi$
$380$	−8.52167	+	1.76539i	−0.437153	+	0.0905627i
$381$		0			0
$382$	9.87154	−	1.01178i	0.505072	−	0.0517670i
$383$	−8.41070			−0.429767			−0.214883	−	0.976640i	$-0.568937\pi$
$383$	−8.41070			−0.429767			−0.214883	+	0.976640i	$0.568937\pi$
$384$		0			0
$385$	−2.34713			−0.119621
$386$	−30.0728	+	3.08229i	−1.53067	+	0.156885i
$387$		0			0
$388$	24.5941	−	5.09505i	1.24858	−	0.258662i
$389$	−4.66887	−	11.2717i	−0.236721	−	0.571496i	0.760219	−	0.649667i	$-0.225092\pi$
$389$	−4.66887	−	11.2717i	−0.236721	−	0.571496i	−0.996940	+	0.0781715i	$0.975092\pi$
$390$		0			0
$391$	1.23998	+	1.23998i	0.0627085	+	0.0627085i
$392$	3.45445	+	10.9188i	0.174476	+	0.551481i
$393$		0			0
$394$	7.61946	+	14.1201i	0.383863	+	0.711361i
$395$	2.03428	+	4.91118i	0.102356	+	0.247108i
$396$		0			0
$397$	13.1886	+	5.46289i	0.661916	+	0.274175i	0.688245	−	0.725479i	$-0.258382\pi$
$397$	13.1886	+	5.46289i	0.661916	+	0.274175i	−0.0263285	+	0.999653i	$0.508382\pi$
$398$	14.0261	+	11.4182i	0.703067	+	0.572344i
$399$		0			0
$400$	6.00634	−	15.1767i	0.300317	−	0.758833i
$401$	3.87685			0.193601			0.0968004	−	0.995304i	$-0.469139\pi$
$401$	3.87685			0.193601			0.0968004	+	0.995304i	$0.469139\pi$
$402$		0			0
$403$	−0.109172	+	0.263565i	−0.00543825	+	0.0131291i
$404$	4.90865	+	7.22174i	0.244214	+	0.359295i
$405$		0			0
$406$	−11.6783	−	21.6419i	−0.579586	−	1.07407i
$407$	−6.85165	−	6.85165i	−0.339624	−	0.339624i
$408$		0			0
$409$	6.61246	−	6.61246i	0.326965	−	0.326965i	−0.524466	−	0.851431i	$-0.675735\pi$
$409$	6.61246	−	6.61246i	0.326965	−	0.326965i	0.851431	+	0.524466i	$0.175735\pi$
$410$	−6.29092	−	1.88114i	−0.310686	−	0.0929028i
$411$		0			0
$412$	−5.17135	−	3.39641i	−0.254774	−	0.167329i
$413$	−17.9573	−	7.43815i	−0.883620	−	0.366007i
$414$		0			0
$415$		−	11.8915i		−	0.583732i
$416$	−0.164469	+	0.0194962i	−0.00806375	+	0.000955878i
$417$		0			0
$418$	9.09625	−	0.932314i	0.444912	−	0.0456010i
$419$	7.69097	−	18.5676i	0.375729	−	0.907089i	−0.617028	−	0.786942i	$-0.711663\pi$
$419$	7.69097	−	18.5676i	0.375729	−	0.907089i	0.992756	−	0.120147i	$-0.0383367\pi$
$420$		0			0
$421$	15.8875	−	6.58080i	0.774307	−	0.320729i	0.0396916	−	0.999212i	$-0.487362\pi$
$421$	15.8875	−	6.58080i	0.774307	−	0.320729i	0.734616	+	0.678483i	$0.237362\pi$
$422$	−6.07576	+	20.3186i	−0.295763	+	0.989094i
$423$		0			0
$424$	−6.90664	+	5.80691i	−0.335416	+	0.282009i
$425$	3.82849	−	3.82849i	0.185709	−	0.185709i
$426$		0			0
$427$	11.4800	−	4.75519i	0.555558	−	0.230120i
$428$	9.09782	+	13.3850i	0.439760	+	0.646987i
$429$		0			0
$430$	−1.13544	−	0.924329i	−0.0547559	−	0.0445751i
$431$			12.7583i			0.614548i	0.951621	+	0.307274i	$0.0994168\pi$
$431$			12.7583i			0.614548i	−0.951621	+	0.307274i	$0.900583\pi$
$432$		0			0
$433$			1.18066i			0.0567390i	0.999598	+	0.0283695i	$0.00903150\pi$
$433$			1.18066i			0.0567390i	−0.999598	+	0.0283695i	$0.990968\pi$
$434$	14.9447	−	18.3581i	0.717370	−	0.881216i
$435$		0			0
$436$	−1.06321	−	0.202739i	−0.0509185	−	0.00970943i
$437$	−5.54062	+	2.29500i	−0.265044	+	0.109785i
$438$		0			0
$439$	−8.88783	+	8.88783i	−0.424193	+	0.424193i	−0.886644	−	0.462452i	$-0.846970\pi$
$439$	−8.88783	+	8.88783i	−0.424193	+	0.424193i	0.462452	+	0.886644i	$0.346970\pi$
$440$	1.78107	−	3.42962i	0.0849094	−	0.163501i
$441$		0			0
$442$	−0.0526365	−	0.0157396i	−0.00250366	−	0.000748656i
$443$	−12.1498	+	5.03262i	−0.577255	+	0.239107i	−0.652157	−	0.758084i	$-0.726136\pi$
$443$	−12.1498	+	5.03262i	−0.577255	+	0.239107i	0.0749018	+	0.997191i	$0.476136\pi$
$444$		0			0
$445$	4.11599	−	9.93688i	0.195117	−	0.471053i
$446$	0.0123692	+	0.120682i	0.000585700	+	0.00571446i
$447$		0			0
$448$	13.5387	+	2.35988i	0.639645	+	0.111494i
$449$		−	0.529631i		−	0.0249948i	−0.999922	−	0.0124974i	$-0.996022\pi$
$449$		−	0.529631i		−	0.0249948i	0.999922	−	0.0124974i	$-0.00397815\pi$
$450$		0			0
$451$	6.37394	+	2.64017i	0.300137	+	0.124321i
$452$	−38.6028	+	7.99714i	−1.81572	+	0.376154i
$453$		0			0
$454$	−10.1908	+	34.0803i	−0.478280	+	1.59947i
$455$	−0.0341027	+	0.0341027i	−0.00159876	+	0.00159876i
$456$		0			0
$457$	−5.43494	−	5.43494i	−0.254236	−	0.254236i	0.568469	−	0.822705i	$-0.307536\pi$
$457$	−5.43494	−	5.43494i	−0.254236	−	0.254236i	−0.822705	+	0.568469i	$0.807536\pi$
$458$	33.0315	−	17.8244i	1.54346	−	0.832877i
$459$		0			0
$460$	−0.474755	+	2.48973i	−0.0221356	+	0.116084i
$461$	−7.55433	+	18.2378i	−0.351840	+	0.849418i	0.644553	+	0.764560i	$0.277044\pi$
$461$	−7.55433	+	18.2378i	−0.351840	+	0.849418i	−0.996393	+	0.0848579i	$0.972956\pi$
$462$		0			0
$463$	4.63562			0.215436			0.107718	−	0.994182i	$-0.465646\pi$
$463$	4.63562			0.215436			0.107718	+	0.994182i	$0.465646\pi$
$464$	40.4848	−	0.641808i	1.87946	−	0.0297952i
$465$		0			0
$466$	3.09315	−	3.79962i	0.143287	−	0.176014i
$467$	−18.9494	−	7.84910i	−0.876874	−	0.363213i	−0.101590	−	0.994826i	$-0.532393\pi$
$467$	−18.9494	−	7.84910i	−0.876874	−	0.363213i	−0.775284	+	0.631613i	$0.782393\pi$
$468$		0			0
$469$	−7.19164	−	17.3622i	−0.332079	−	0.801710i
$470$	−7.41292	+	4.00014i	−0.341932	+	0.184513i
$471$		0			0
$472$	24.4951	−	20.5948i	1.12748	−	0.947952i
$473$	1.08778	+	1.08778i	0.0500161	+	0.0500161i
$474$		0			0
$475$	7.08591	+	17.1069i	0.325124	+	0.784918i
$476$	3.81043	+	2.50259i	0.174651	+	0.114706i
$477$		0			0
$478$	−1.63307	−	15.9333i	−0.0746949	−	0.728771i
$479$	−41.5437			−1.89818			−0.949089	−	0.315008i	$-0.897993\pi$
$479$	−41.5437			−1.89818			−0.949089	+	0.315008i	$0.897993\pi$
$480$		0			0
$481$	−0.199102			−0.00907827
$482$	−1.93459	−	18.8750i	−0.0881180	−	0.859735i
$483$		0			0
$484$	9.84813	−	14.9947i	0.447642	−	0.681577i
$485$	4.60833	+	11.1255i	0.209253	+	0.505182i
$486$		0			0
$487$	−18.8137	−	18.8137i	−0.852529	−	0.852529i	0.137915	−	0.990444i	$-0.455960\pi$
$487$	−18.8137	−	18.8137i	−0.852529	−	0.852529i	−0.990444	+	0.137915i	$0.955960\pi$
$488$	−1.76314	+	20.3830i	−0.0798137	+	0.922693i
$489$		0			0
$490$	−4.83216	+	2.60752i	−0.218295	+	0.117796i
$491$	−7.29239	−	17.6054i	−0.329101	−	0.794520i	−0.998660	−	0.0517607i	$-0.983517\pi$
$491$	−7.29239	−	17.6054i	−0.329101	−	0.794520i	0.669559	−	0.742759i	$-0.266483\pi$
$492$		0			0
$493$	12.4089	+	5.13992i	0.558867	+	0.231490i
$494$	0.118618	−	0.145710i	0.00533687	−	0.00655580i
$495$		0			0
$496$	15.4842	+	35.7678i	0.695262	+	1.60602i
$497$	17.9467			0.805020
$498$		0			0
$499$	−2.21640	+	5.35086i	−0.0992197	+	0.239537i	−0.965693	−	0.259685i	$-0.916381\pi$
$499$	−2.21640	+	5.35086i	−0.0992197	+	0.239537i	0.866474	+	0.499223i	$0.166381\pi$
$500$	17.1065	+	3.26196i	0.765025	+	0.145879i
$501$		0			0
$502$	−20.6068	+	11.1198i	−0.919726	+	0.496300i
$503$	−13.1494	−	13.1494i	−0.586303	−	0.586303i	0.350325	−	0.936628i	$-0.386071\pi$
$503$	−13.1494	−	13.1494i	−0.586303	−	0.586303i	−0.936628	+	0.350325i	$0.886071\pi$
$504$		0			0
$505$	−2.96038	+	2.96038i	−0.131735	+	0.131735i
$506$	0.762954	−	2.55148i	0.0339174	−	0.113427i
$507$		0			0
$508$	4.93431	+	23.8183i	0.218925	+	1.05677i
$509$	−11.1362	−	4.61276i	−0.493603	−	0.204457i	0.121975	−	0.992533i	$-0.461077\pi$
$509$	−11.1362	−	4.61276i	−0.493603	−	0.204457i	−0.615578	+	0.788076i	$0.711077\pi$
$510$		0			0
$511$		−	20.1680i		−	0.892179i
$512$	−13.7218	+	17.9920i	−0.606425	+	0.795141i
$513$		0			0
$514$	0.350978	+	3.42436i	0.0154810	+	0.151042i
$515$	1.13518	−	2.74056i	0.0500219	−	0.120764i
$516$		0			0
$517$	8.17675	−	3.38692i	0.359613	−	0.148957i
$518$	15.8286	+	4.73313i	0.695468	+	0.207962i
$519$		0			0
$520$	−0.0239525	−	0.0757087i	−0.00105039	−	0.00332005i
$521$	−12.8812	+	12.8812i	−0.564338	+	0.564338i	−0.930537	−	0.366199i	$-0.880659\pi$
$521$	−12.8812	+	12.8812i	−0.564338	+	0.564338i	0.366199	+	0.930537i	$0.380659\pi$
$522$		0			0
$523$	−14.3454	+	5.94206i	−0.627280	+	0.259828i	−0.673597	−	0.739099i	$-0.735252\pi$
$523$	−14.3454	+	5.94206i	−0.627280	+	0.259828i	0.0463167	+	0.998927i	$0.485252\pi$
$524$	−1.64868	+	8.64604i	−0.0720227	+	0.377704i
$525$		0			0
$526$	−19.2239	+	23.6146i	−0.838201	+	1.02964i
$527$			12.9289i			0.563193i
$528$		0			0
$529$		−	21.2534i		−	0.924060i
$530$	−3.35513	−	2.73131i	−0.145738	−	0.118640i
$531$		0			0
$532$	−12.8940	+	8.76409i	−0.559025	+	0.379972i
$533$	0.130971	−	0.0542498i	0.00567296	−	0.00234982i
$534$		0			0
$535$	−5.48684	+	5.48684i	−0.237217	+	0.237217i
$536$	30.8267	+	2.66653i	1.33151	+	0.115177i
$537$		0			0
$538$	−2.43348	+	8.13805i	−0.104915	+	0.350856i
$539$	5.33007	−	2.20779i	0.229582	−	0.0950961i
$540$		0			0
$541$	5.53641	−	13.3661i	0.238029	−	0.574653i	−0.759050	−	0.651033i	$-0.774336\pi$
$541$	5.53641	−	13.3661i	0.238029	−	0.574653i	0.997079	+	0.0763798i	$0.0243361\pi$
$542$	14.8936	−	1.52651i	0.639737	−	0.0655694i
$543$		0			0
$544$	−6.54824	+	3.66873i	−0.280753	+	0.157296i
$545$		−	0.518945i		−	0.0222292i
$546$		0			0
$547$	34.8390	+	14.4308i	1.48961	+	0.617016i	0.971232	−	0.238137i	$-0.0765367\pi$
$547$	34.8390	+	14.4308i	1.48961	+	0.617016i	0.518376	+	0.855153i	$0.326537\pi$
$548$	10.9499	−	16.6723i	0.467757	−	0.712204i
$549$		0			0
$550$	−7.87780	−	2.35565i	−0.335910	−	0.100445i
$551$	−32.4799	+	32.4799i	−1.38369	+	1.38369i
$552$		0			0
$553$	6.73389	+	6.73389i	0.286354	+	0.286354i
$554$	−10.3890	−	19.2525i	−0.441386	−	0.817961i
$555$		0			0
$556$	24.2714	−	16.4974i	1.02934	−	0.699644i
$557$	12.6874	−	30.6300i	0.537581	−	1.29784i	−0.388826	−	0.921311i	$-0.627119\pi$
$557$	12.6874	−	30.6300i	0.537581	−	1.29784i	0.926407	−	0.376524i	$-0.122881\pi$
$558$		0			0
$559$	0.0316097			0.00133695
$560$	0.104444	+	6.58824i	0.00441355	+	0.278404i
$561$		0			0
$562$	−18.6443	−	15.1778i	−0.786464	−	0.640235i
$563$	35.8986	+	14.8697i	1.51294	+	0.626682i	0.976163	−	0.217040i	$-0.0696401\pi$
$563$	35.8986	+	14.8697i	1.51294	+	0.626682i	0.536781	+	0.843722i	$0.319640\pi$
$564$		0			0
$565$	−7.23319	−	17.4625i	−0.304302	−	0.734651i
$566$	10.2963	+	19.0807i	0.432784	+	0.802021i
$567$		0			0
$568$	−13.6185	+	26.2236i	−0.571420	+	1.10032i
$569$	19.9044	+	19.9044i	0.834436	+	0.834436i	0.988120	−	0.153684i	$-0.0491137\pi$
$569$	19.9044	+	19.9044i	0.834436	+	0.834436i	−0.153684	+	0.988120i	$0.549114\pi$
$570$		0			0
$571$	−2.51768	−	6.07821i	−0.105361	−	0.254365i	0.862403	−	0.506223i	$-0.168959\pi$
$571$	−2.51768	−	6.07821i	−0.105361	−	0.254365i	−0.967764	+	0.251857i	$0.918959\pi$
$572$	0.0169252	+	0.0816992i	0.000707678	+	0.00341601i
$573$		0			0
$574$	−11.7018	+	1.19937i	−0.488423	+	0.0500606i
$575$	5.39278			0.224895
$576$		0			0
$577$	−18.7117			−0.778980			−0.389490	−	0.921031i	$-0.627349\pi$
$577$	−18.7117			−0.778980			−0.389490	+	0.921031i	$0.627349\pi$
$578$	21.4395	−	2.19742i	0.891764	−	0.0914008i
$579$		0			0
$580$	3.93809	+	19.0094i	0.163520	+	0.789323i
$581$	−8.15244	−	19.6817i	−0.338220	−	0.816536i
$582$		0			0
$583$	3.21428	+	3.21428i	0.133122	+	0.133122i
$584$	29.4693	+	15.3041i	1.21945	+	0.633286i
$585$		0			0
$586$	10.5675	+	19.5833i	0.436538	+	0.808977i
$587$	−12.8204	−	30.9512i	−0.529155	−	1.27749i	−0.932077	−	0.362260i	$-0.882005\pi$
$587$	−12.8204	−	30.9512i	−0.529155	−	1.27749i	0.402922	−	0.915234i	$-0.367995\pi$
$588$		0			0
$589$	−40.8499	−	16.9206i	−1.68319	−	0.697201i
$590$	11.8993	+	9.68685i	0.489887	+	0.398801i
$591$		0			0
$592$	−18.9272	+	19.5370i	−0.777904	+	0.802966i
$593$	14.7730			0.606654			0.303327	−	0.952887i	$-0.401903\pi$
$593$	14.7730			0.606654			0.303327	+	0.952887i	$0.401903\pi$
$594$		0			0
$595$	−0.836437	+	2.01934i	−0.0342906	+	0.0827848i
$596$	−14.5879	+	9.91549i	−0.597545	+	0.406154i
$597$		0			0
$598$	−0.0259864	−	0.0481570i	−0.00106266	−	0.00196929i
$599$	−17.9159	−	17.9159i	−0.732022	−	0.732022i	0.238998	−	0.971020i	$-0.423181\pi$
$599$	−17.9159	−	17.9159i	−0.732022	−	0.732022i	−0.971020	+	0.238998i	$0.923181\pi$
$600$		0			0
$601$	4.12098	−	4.12098i	0.168098	−	0.168098i	−0.618045	−	0.786143i	$-0.712075\pi$
$601$	4.12098	−	4.12098i	0.168098	−	0.168098i	0.786143	+	0.618045i	$0.212075\pi$
$602$	−2.51297	−	0.751439i	−0.102421	−	0.0306264i
$603$		0			0
$604$	20.8792	−	31.7905i	0.849563	−	1.29354i
$605$	7.94645	+	3.29153i	0.323069	+	0.133820i
$606$		0			0
$607$			25.4859i			1.03444i	0.855852	+	0.517220i	$0.173033\pi$
$607$			25.4859i			1.03444i	−0.855852	+	0.517220i	$0.826967\pi$
$608$	−3.02171	−	25.4911i	−0.122547	−	1.03380i
$609$		0			0
$610$	−9.75806	+	1.00015i	−0.395092	+	0.0404947i
$611$	0.0695938	−	0.168014i	0.00281546	−	0.00679713i
$612$		0			0
$613$	35.2820	−	14.6143i	1.42503	−	0.590265i	0.468908	−	0.883247i	$-0.344648\pi$
$613$	35.2820	−	14.6143i	1.42503	−	0.590265i	0.956118	+	0.292982i	$0.0946476\pi$
$614$	10.6589	−	35.6457i	0.430160	−	1.43854i
$615$		0			0
$616$	0.596633	−	6.89743i	0.0240390	−	0.277905i
$617$	13.7171	−	13.7171i	0.552229	−	0.552229i	−0.374855	−	0.927084i	$-0.622307\pi$
$617$	13.7171	−	13.7171i	0.552229	−	0.552229i	0.927084	+	0.374855i	$0.122307\pi$
$618$		0			0
$619$	−21.5287	+	8.91748i	−0.865311	+	0.358424i	−0.770782	−	0.637099i	$-0.780134\pi$
$619$	−21.5287	+	8.91748i	−0.865311	+	0.358424i	−0.0945288	+	0.995522i	$0.530134\pi$
$620$	−15.4549	+	10.5048i	−0.620684	+	0.421881i
$621$		0			0
$622$	−35.0189	−	28.5078i	−1.40413	−	1.14306i
$623$		−	19.2684i		−	0.771971i
$624$		0			0
$625$		−	12.0529i		−	0.482117i
$626$	12.5237	−	15.3841i	0.500549	−	0.614874i
$627$		0			0
$628$	1.14736	−	6.01703i	0.0457847	−	0.240106i
$629$	−8.33646	+	3.45307i	−0.332396	+	0.137683i
$630$		0			0
$631$	−16.8025	+	16.8025i	−0.668896	+	0.668896i	−0.957460	−	0.288565i	$-0.906822\pi$
$631$	−16.8025	+	16.8025i	−0.668896	+	0.668896i	0.288565	+	0.957460i	$0.406822\pi$
$632$	−14.9494	+	4.72965i	−0.594655	+	0.188135i
$633$		0			0
$634$	−15.2747	−	4.56750i	−0.606636	−	0.181399i
$635$	−10.7745	+	4.46295i	−0.427573	+	0.177107i
$636$		0			0
$637$	0.0453652	−	0.109521i	0.00179743	−	0.00433939i
$638$	−2.07973	−	20.2911i	−0.0823372	−	0.803334i
$639$		0			0
$640$	−9.70596	−	4.84674i	−0.383662	−	0.191584i
$641$			10.7233i			0.423546i	0.977319	+	0.211773i	$0.0679238\pi$
$641$			10.7233i			0.423546i	−0.977319	+	0.211773i	$0.932076\pi$
$642$		0			0
$643$	−30.3018	−	12.5514i	−1.19499	−	0.494980i	−0.305612	−	0.952156i	$-0.598861\pi$
$643$	−30.3018	−	12.5514i	−1.19499	−	0.494980i	−0.889376	+	0.457176i	$0.848861\pi$
$644$	0.921104	+	4.44624i	0.0362966	+	0.175206i
$645$		0			0
$646$	2.43948	−	8.15814i	0.0959801	−	0.320978i
$647$	4.94231	−	4.94231i	0.194302	−	0.194302i	−0.603250	−	0.797552i	$-0.706128\pi$
$647$	4.94231	−	4.94231i	0.194302	−	0.194302i	0.797552	+	0.603250i	$0.206128\pi$
$648$		0			0
$649$	−11.3998	−	11.3998i	−0.447480	−	0.447480i
$650$	−0.148687	+	0.0802339i	−0.00583198	+	0.00314703i
$651$		0			0
$652$	−31.2622	−	5.96126i	−1.22432	−	0.233461i
$653$	5.01854	−	12.1158i	0.196391	−	0.474129i	−0.794751	−	0.606935i	$-0.792399\pi$
$653$	5.01854	−	12.1158i	0.196391	−	0.474129i	0.991142	+	0.132806i	$0.0423988\pi$
$654$		0			0
$655$	−4.22007			−0.164892
$656$	7.12716	−	18.0087i	0.278269	−	0.703122i
$657$		0			0
$658$	−9.52680	+	11.7027i	−0.371393	+	0.456219i
$659$	−29.1760	−	12.0851i	−1.13653	−	0.470768i	−0.266537	−	0.963825i	$-0.585879\pi$
$659$	−29.1760	−	12.0851i	−1.13653	−	0.470768i	−0.869997	+	0.493057i	$0.835879\pi$
$660$		0			0
$661$	−15.3024	−	36.9433i	−0.595196	−	1.43693i	−0.878426	−	0.477877i	$-0.841406\pi$
$661$	−15.3024	−	36.9433i	−0.595196	−	1.43693i	0.283231	−	0.959052i	$-0.408594\pi$
$662$	−17.5297	+	9.45932i	−0.681310	+	0.367647i
$663$		0			0
$664$	34.9452	+	3.02278i	1.35614	+	0.117307i
$665$	−5.28557	−	5.28557i	−0.204966	−	0.204966i
$666$		0			0
$667$	5.11949	+	12.3595i	0.198227	+	0.478563i
$668$	12.8916	−	19.6287i	0.498791	−	0.759456i
$669$		0			0
$670$	1.51260	+	14.7579i	0.0584367	+	0.570146i
$671$	10.3066			0.397881
$672$		0			0
$673$	−6.49552			−0.250384			−0.125192	−	0.992133i	$-0.539955\pi$
$673$	−6.49552			−0.250384			−0.125192	+	0.992133i	$0.539955\pi$
$674$	−2.41194	−	23.5324i	−0.0929043	−	0.906434i
$675$		0			0
$676$	−21.7306	−	14.2721i	−0.835792	−	0.548927i
$677$	−2.62635	−	6.34057i	−0.100939	−	0.243688i	0.865340	−	0.501185i	$-0.167102\pi$
$677$	−2.62635	−	6.34057i	−0.100939	−	0.243688i	−0.966279	+	0.257497i	$0.917102\pi$
$678$		0			0
$679$	15.2545	+	15.2545i	0.585415	+	0.585415i
$680$	−2.31593	−	2.75453i	−0.0888120	−	0.105631i
$681$		0			0
$682$	17.2793	−	9.32422i	0.661660	−	0.357043i
$683$	−4.22340	−	10.1962i	−0.161604	−	0.390146i	0.822248	−	0.569129i	$-0.192719\pi$
$683$	−4.22340	−	10.1962i	−0.161604	−	0.390146i	−0.983852	+	0.178982i	$0.942719\pi$
$684$		0			0
$685$	8.83548	+	3.65978i	0.337586	+	0.139833i
$686$	−16.9464	+	20.8169i	−0.647016	+	0.794793i
$687$		0			0
$688$	3.00491	−	3.10172i	0.114561	−	0.118252i
$689$	0.0934039			0.00355840
$690$		0			0
$691$	−2.10014	+	5.07018i	−0.0798931	+	0.192879i	−0.958779	−	0.284153i	$-0.908288\pi$
$691$	−2.10014	+	5.07018i	−0.0798931	+	0.192879i	0.878886	+	0.477032i	$0.158288\pi$
$692$	−5.05431	+	26.5060i	−0.192136	+	1.00761i
$693$		0			0
$694$	−23.4479	+	12.6529i	−0.890071	+	0.480298i
$695$	9.94946	+	9.94946i	0.377404	+	0.377404i
$696$		0			0
$697$	4.54291	−	4.54291i	0.172075	−	0.172075i
$698$	−8.48337	+	28.3702i	−0.321100	+	1.07383i
$699$		0			0
$700$	13.7279	−	2.84395i	0.518867	−	0.107491i
$701$	−39.8651	−	16.5127i	−1.50568	−	0.623675i	−0.531022	−	0.847358i	$-0.678192\pi$
$701$	−39.8651	−	16.5127i	−1.50568	−	0.623675i	−0.974662	+	0.223683i	$0.928192\pi$
$702$		0			0
$703$		−	30.8588i		−	1.16386i
$704$	9.62574	+	6.10577i	0.362784	+	0.230120i
$705$		0			0
$706$	−4.21334	−	41.1080i	−0.158571	−	1.54712i
$707$	−2.87020	+	6.92928i	−0.107945	+	0.260602i
$708$		0			0
$709$	13.6775	−	5.66541i	0.513670	−	0.212769i	−0.110764	−	0.993847i	$-0.535330\pi$
$709$	13.6775	−	5.66541i	0.513670	−	0.212769i	0.624434	+	0.781078i	$0.285330\pi$
$710$	−13.5735	−	4.05881i	−0.509405	−	0.152325i
$711$		0			0
$712$	28.1548	+	14.6214i	1.05515	+	0.547961i
$713$	−9.10580	+	9.10580i	−0.341015	+	0.341015i
$714$		0			0
$715$	−0.0369577	+	0.0153084i	−0.00138214	+	0.000572501i
$716$	3.05633	+	0.582798i	0.114220	+	0.0217802i
$717$		0			0
$718$	30.1460	−	37.0313i	1.12504	−	1.38199i
$719$			38.0055i			1.41736i	0.705528	+	0.708682i	$0.250710\pi$
$719$			38.0055i			1.41736i	−0.705528	+	0.708682i	$0.749290\pi$
$720$		0			0
$721$		−	5.31416i		−	0.197910i
$722$	1.74538	+	1.42086i	0.0649563	+	0.0528788i
$723$		0			0
$724$	16.3881	+	24.1107i	0.609060	+	0.896066i
$725$	38.1606	−	15.8066i	1.41725	−	0.587044i
$726$		0			0
$727$	−3.50408	+	3.50408i	−0.129959	+	0.129959i	−0.769094	−	0.639135i	$-0.779292\pi$
$727$	−3.50408	+	3.50408i	−0.129959	+	0.129959i	0.639135	+	0.769094i	$0.279292\pi$
$728$	−0.0915473	−	0.108885i	−0.00339297	−	0.00403554i
$729$		0			0
$730$	−4.56117	+	15.2535i	−0.168817	+	0.564558i
$731$	1.32351	−	0.548215i	0.0489517	−	0.0202765i
$732$		0			0
$733$	−18.0521	+	43.5817i	−0.666771	+	1.60973i	0.120210	+	0.992749i	$0.461643\pi$
$733$	−18.0521	+	43.5817i	−0.666771	+	1.60973i	−0.786980	+	0.616978i	$0.788357\pi$
$734$	11.1408	−	1.14187i	0.411216	−	0.0421473i
$735$		0			0
$736$	−7.19578	−	2.02802i	−0.265240	−	0.0747539i
$737$		−	15.5874i		−	0.574170i
$738$		0			0
$739$	39.4444	+	16.3384i	1.45098	+	0.601018i	0.962433	−	0.271518i	$-0.0875255\pi$
$739$	39.4444	+	16.3384i	1.45098	+	0.601018i	0.488551	+	0.872535i	$0.337526\pi$
$740$	−10.9011	−	7.15956i	−0.400732	−	0.263191i
$741$		0			0
$742$	−7.42560	−	2.22043i	−0.272602	−	0.0815147i
$743$	−10.7638	+	10.7638i	−0.394884	+	0.394884i	−0.876424	−	0.481540i	$-0.840078\pi$
$743$	−10.7638	+	10.7638i	−0.394884	+	0.394884i	0.481540	+	0.876424i	$0.340078\pi$
$744$		0			0
$745$	−5.97997	−	5.97997i	−0.219089	−	0.219089i
$746$	1.59854	+	2.96236i	0.0585266	+	0.108460i
$747$		0			0
$748$	2.12559	+	3.12723i	0.0777193	+	0.114343i
$749$	−5.31970	+	12.8429i	−0.194378	+	0.469269i
$750$		0			0
$751$	−20.8234			−0.759856			−0.379928	−	0.925016i	$-0.624051\pi$
$751$	−20.8234			−0.759856			−0.379928	+	0.925016i	$0.624051\pi$
$752$	−9.87071	−	22.8009i	−0.359948	−	0.831462i
$753$		0			0
$754$	−0.325037	−	0.264602i	−0.0118372	−	0.00963625i
$755$	16.8474	+	6.97843i	0.613140	+	0.253971i
$756$		0			0
$757$	4.51339	+	10.8963i	0.164042	+	0.396032i	0.984431	−	0.175774i	$-0.0562428\pi$
$757$	4.51339	+	10.8963i	0.164042	+	0.396032i	−0.820389	+	0.571806i	$0.806243\pi$
$758$	−15.6979	−	29.0908i	−0.570172	−	1.05662i
$759$		0			0
$760$	11.7341	−	3.71240i	0.425641	−	0.134663i
$761$	13.8159	+	13.8159i	0.500826	+	0.500826i	0.911695	−	0.410868i	$-0.134774\pi$
$761$	13.8159	+	13.8159i	0.500826	+	0.500826i	−0.410868	+	0.911695i	$0.634774\pi$
$762$		0			0
$763$	−0.355772	−	0.858909i	−0.0128798	−	0.0310946i
$764$	−13.7418	+	2.84682i	−0.497162	+	0.102994i
$765$		0			0
$766$	11.8325	−	1.21277i	0.427527	−	0.0438191i
$767$	−0.331266			−0.0119613
$768$		0			0
$769$	10.2754			0.370539			0.185270	−	0.982688i	$-0.440684\pi$
$769$	10.2754			0.370539			0.185270	+	0.982688i	$0.440684\pi$
$770$	3.30205	−	0.338441i	0.118998	−	0.0121966i
$771$		0			0
$772$	41.8633	−	8.67260i	1.50669	−	0.312134i
$773$	20.3918	+	49.2302i	0.733442	+	1.77069i	0.630769	+	0.775971i	$0.282740\pi$
$773$	20.3918	+	49.2302i	0.733442	+	1.77069i	0.102674	+	0.994715i	$0.467260\pi$
$774$		0			0
$775$	28.1145	+	28.1145i	1.00990	+	1.00990i
$776$	−33.8654	+	10.7142i	−1.21570	+	0.384619i
$777$		0			0
$778$	8.19368	+	15.1842i	0.293758	+	0.544381i
$779$	8.40818	+	20.2991i	0.301254	+	0.727292i
$780$		0			0
$781$	13.7527	+	5.69654i	0.492109	+	0.203838i
$782$	−1.92326	−	1.56566i	−0.0687755	−	0.0559879i
$783$		0			0
$784$	−6.43429	−	14.8629i	−0.229796	−	0.530818i
$785$	2.93687			0.104821
$786$		0			0
$787$	12.3657	−	29.8534i	0.440789	−	1.06416i	−0.534883	−	0.844926i	$-0.679644\pi$
$787$	12.3657	−	29.8534i	0.440789	−	1.06416i	0.975672	−	0.219233i	$-0.0703556\pi$
$788$	−12.7554	−	18.7661i	−0.454393	−	0.668515i
$789$		0			0
$790$	−3.57007	−	6.61593i	−0.127017	−	0.235384i
$791$	−23.9434	−	23.9434i	−0.851329	−	0.851329i
$792$		0			0
$793$	0.149749	−	0.149749i	0.00531776	−	0.00531776i
$794$	−19.3420	−	5.78372i	−0.686421	−	0.205257i
$795$		0			0
$796$	−21.3790	−	14.0412i	−0.757759	−	0.497677i
$797$	−3.74523	−	1.55133i	−0.132663	−	0.0549508i	0.315364	−	0.948971i	$-0.397873\pi$
$797$	−3.74523	−	1.55133i	−0.132663	−	0.0549508i	−0.448027	+	0.894020i	$0.647873\pi$
$798$		0			0
$799$		−	8.24179i		−	0.291574i
$800$	−6.26161	+	22.2173i	−0.221381	+	0.785499i
$801$		0			0
$802$	−5.45412	+	0.559017i	−0.192592	+	0.0197396i
$803$	6.40159	−	15.4548i	0.225907	−	0.545389i
$804$		0			0
$805$	−2.01131	+	0.833113i	−0.0708895	+	0.0293634i
$806$	0.115584	−	0.386536i	0.00407126	−	0.0136152i
$807$		0			0
$808$	−7.94703	−	9.45206i	−0.279575	−	0.332522i
$809$	−20.1580	+	20.1580i	−0.708716	+	0.708716i	−0.966265	−	0.257549i	$-0.917085\pi$
$809$	−20.1580	+	20.1580i	−0.708716	+	0.708716i	0.257549	+	0.966265i	$0.417085\pi$
$810$		0			0
$811$	−24.3626	+	10.0913i	−0.855487	+	0.354354i	−0.766941	−	0.641718i	$-0.778222\pi$
$811$	−24.3626	+	10.0913i	−0.855487	+	0.354354i	−0.0885462	+	0.996072i	$0.528222\pi$
$812$	19.5502	+	28.7628i	0.686077	+	1.00938i
$813$		0			0
$814$	10.6272	+	8.65124i	0.372482	+	0.303226i
$815$		−	15.2589i		−	0.534495i
$816$		0			0
$817$			4.89919i			0.171401i
$818$	−8.34922	+	10.2562i	−0.291924	+	0.358598i
$819$		0			0
$820$	9.12159	+	1.73936i	0.318540	+	0.0607410i
$821$	13.0897	−	5.42194i	0.456834	−	0.189227i	−0.142386	−	0.989811i	$-0.545477\pi$
$821$	13.0897	−	5.42194i	0.456834	−	0.189227i	0.599220	+	0.800584i	$0.295477\pi$
$822$		0			0
$823$	−25.7815	+	25.7815i	−0.898685	+	0.898685i	−0.995320	−	0.0966346i	$-0.969192\pi$
$823$	−25.7815	+	25.7815i	−0.898685	+	0.898685i	0.0966346	+	0.995320i	$0.469192\pi$
$824$	7.76502	+	4.03254i	0.270507	+	0.140480i
$825$		0			0
$826$	26.3356	+	7.87498i	0.916333	+	0.274006i
$827$	38.7610	−	16.0553i	1.34785	−	0.558299i	0.412159	−	0.911112i	$-0.364775\pi$
$827$	38.7610	−	16.0553i	1.34785	−	0.558299i	0.935694	+	0.352813i	$0.114775\pi$
$828$		0			0
$829$	0.355576	−	0.858437i	0.0123497	−	0.0298148i	−0.917584	−	0.397541i	$-0.869864\pi$
$829$	0.355576	−	0.858437i	0.0123497	−	0.0298148i	0.929934	+	0.367726i	$0.119864\pi$
$830$	1.71468	+	16.7295i	0.0595175	+	0.580690i
$831$		0			0
$832$	0.228571	−	0.0511434i	0.00792427	−	0.00177308i
$833$		−	5.37246i		−	0.186145i
$834$		0			0
$835$	10.4022	+	4.30875i	0.359984	+	0.149110i
$836$	−12.6626	+	2.62324i	−0.437944	+	0.0907267i
$837$		0			0
$838$	−8.14266	+	27.2308i	−0.281283	+	0.940671i
$839$	17.1750	−	17.1750i	0.592947	−	0.592947i	−0.345479	−	0.938426i	$-0.612284\pi$
$839$	17.1750	−	17.1750i	0.592947	−	0.592947i	0.938426	+	0.345479i	$0.112284\pi$
$840$		0			0
$841$	51.9474	+	51.9474i	1.79129	+	1.79129i
$842$	−21.4023	+	11.5490i	−0.737570	+	0.398006i
$843$		0			0
$844$	5.61783	−	29.4612i	0.193374	−	1.01410i
$845$	4.77014	−	11.5161i	0.164098	−	0.396167i
$846$		0			0
$847$	15.4088			0.529452
$848$	8.87925	−	9.16531i	0.304915	−	0.314738i
$849$		0			0
$850$	−4.83404	+	5.93813i	−0.165806	+	0.203676i
$851$	−8.30333	−	3.43935i	−0.284634	−	0.117899i
$852$		0			0
$853$	16.4371	+	39.6827i	0.562797	+	1.35871i	0.907521	+	0.420007i	$0.137972\pi$
$853$	16.4371	+	39.6827i	0.562797	+	1.35871i	−0.344724	+	0.938704i	$0.612028\pi$
$854$	−15.4650	+	8.34516i	−0.529200	+	0.285565i
$855$		0			0
$856$	−14.7292	−	17.5187i	−0.503435	−	0.598777i
$857$	18.0099	+	18.0099i	0.615208	+	0.615208i	0.944298	−	0.329090i	$-0.106742\pi$
$857$	18.0099	+	18.0099i	0.615208	+	0.615208i	−0.329090	+	0.944298i	$0.606742\pi$
$858$		0			0
$859$	−7.09982	−	17.1405i	−0.242243	−	0.584826i	0.755262	−	0.655423i	$-0.227510\pi$
$859$	−7.09982	−	17.1405i	−0.242243	−	0.584826i	−0.997505	+	0.0705969i	$0.977510\pi$
$860$	1.73067	+	1.13666i	0.0590155	+	0.0387598i
$861$		0			0
$862$	−1.83967	−	17.9490i	−0.0626594	−	0.611345i
$863$	56.4875			1.92286			0.961429	−	0.275052i	$-0.0886952\pi$
$863$	56.4875			1.92286			0.961429	+	0.275052i	$0.0886952\pi$
$864$		0			0
$865$	−12.9374			−0.439884
$866$	−0.170244	−	1.66101i	−0.00578512	−	0.0564433i
$867$		0			0
$868$	−18.3778	+	27.9819i	−0.623782	+	0.949767i
$869$	3.02278	+	7.29765i	0.102541	+	0.247556i
$870$		0			0
$871$	−0.226477	−	0.226477i	−0.00767389	−	0.00767389i
$872$	1.52500	+	0.131914i	0.0516431	+	0.00446717i
$873$		0			0
$874$	7.46386	−	4.02763i	0.252469	−	0.136237i
$875$	5.72418	+	13.8194i	0.193513	+	0.467181i
$876$		0			0
$877$	−31.8952	−	13.2114i	−1.07702	−	0.446118i	−0.227560	−	0.973764i	$-0.573075\pi$
$877$	−31.8952	−	13.2114i	−1.07702	−	0.446118i	−0.849464	+	0.527646i	$0.823075\pi$
$878$	11.2222	−	13.7853i	0.378731	−	0.465233i
$879$		0			0
$880$	−2.01116	+	5.08175i	−0.0677963	+	0.171306i
$881$	38.8053			1.30739			0.653693	−	0.756760i	$-0.273219\pi$
$881$	38.8053			1.30739			0.653693	+	0.756760i	$0.273219\pi$
$882$		0			0
$883$	0.251252	−	0.606576i	0.00845531	−	0.0204129i	−0.919595	−	0.392867i	$-0.871483\pi$
$883$	0.251252	−	0.606576i	0.00845531	−	0.0204129i	0.928051	+	0.372454i	$0.121483\pi$
$884$	0.0763208	+	0.0145533i	0.00256695	+	0.000489480i
$885$		0			0
$886$	16.3672	−	8.83203i	0.549867	−	0.296718i
$887$	35.1536	+	35.1536i	1.18034	+	1.18034i	0.979655	+	0.200687i	$0.0643173\pi$
$887$	35.1536	+	35.1536i	1.18034	+	1.18034i	0.200687	+	0.979655i	$0.435683\pi$
$888$		0			0
$889$	−14.7733	+	14.7733i	−0.495481	+	0.495481i
$890$	−4.35772	+	14.5731i	−0.146071	+	0.488493i
$891$		0			0
$892$	−0.0348032	−	0.167997i	−0.00116530	−	0.00562497i
$893$	26.0406	+	10.7864i	0.871414	+	0.360952i
$894$		0			0
$895$			1.49177i			0.0498644i
$896$	−19.3872	−	1.36778i	−0.647680	−	0.0456944i
$897$		0			0
$898$	0.0763693	+	0.745107i	0.00254848	+	0.0248646i
$899$	−37.7450	+	91.1245i	−1.25887	+	3.03917i
$900$		0			0
$901$	3.91085	−	1.61993i	0.130289	−	0.0539676i
$902$	−9.34783	−	2.79523i	−0.311249	−	0.0930710i
$903$		0			0
$904$	53.1549	−	16.8170i	1.76791	−	0.559325i
$905$	−9.88358	+	9.88358i	−0.328541	+	0.328541i
$906$		0			0
$907$	−24.2246	+	10.0341i	−0.804363	+	0.333178i	−0.746703	−	0.665158i	$-0.768364\pi$
$907$	−24.2246	+	10.0341i	−0.804363	+	0.333178i	−0.0576607	+	0.998336i	$0.518364\pi$
$908$	9.42276	−	49.4152i	0.312705	−	1.63990i
$909$		0			0
$910$	0.0430597	−	0.0528945i	0.00142742	−	0.00175343i
$911$		−	21.9666i		−	0.727787i	−0.931441	−	0.363894i	$-0.881447\pi$
$911$		−	21.9666i		−	0.727787i	0.931441	−	0.363894i	$-0.118553\pi$
$912$		0			0
$913$		−	17.6699i		−	0.584789i
$914$	8.42979	+	6.86242i	0.278833	+	0.226989i
$915$		0			0
$916$	−43.9000	+	29.8390i	−1.45050	+	0.985908i
$917$	−6.98466	+	2.89314i	−0.230654	+	0.0955399i
$918$		0			0
$919$	29.5302	−	29.5302i	0.974110	−	0.974110i	−0.0255634	−	0.999673i	$-0.508138\pi$
$919$	29.5302	−	29.5302i	0.974110	−	0.974110i	0.999673	+	0.0255634i	$0.00813797\pi$
$920$	0.308904	−	3.57111i	0.0101843	−	0.117736i
$921$		0			0
$922$	7.99799	−	26.7470i	0.263400	−	0.880865i
$923$	0.282587	−	0.117051i	0.00930146	−	0.00385279i
$924$		0			0
$925$	−10.6191	+	25.6369i	−0.349155	+	0.842935i
$926$	−6.52159	+	0.668426i	−0.214313	+	0.0219659i
$927$		0			0
$928$	−56.8633	+	6.74058i	−1.86663	+	0.221270i
$929$		−	39.0425i		−	1.28094i	−0.767983	−	0.640471i	$-0.778739\pi$
$929$		−	39.0425i		−	1.28094i	0.767983	−	0.640471i	$-0.221261\pi$
$930$		0			0
$931$	16.9747	+	7.03115i	0.556323	+	0.230437i
$932$	−3.80369	+	5.79148i	−0.124594	+	0.189706i
$933$		0			0
$934$	27.7906	+	8.31007i	0.909337	+	0.271914i
$935$	−1.28193	+	1.28193i	−0.0419237	+	0.0419237i
$936$		0			0
$937$	32.3364	+	32.3364i	1.05638	+	1.05638i	0.998312	+	0.0580711i	$0.0184950\pi$
$937$	32.3364	+	32.3364i	1.05638	+	1.05638i	0.0580711	+	0.998312i	$0.481505\pi$
$938$	12.6210	+	23.3888i	0.412091	+	0.763673i
$939$		0			0
$940$	9.85202	−	6.69646i	0.321337	−	0.218414i
$941$	−15.7360	+	37.9900i	−0.512979	+	1.23844i	0.429164	+	0.903227i	$0.358808\pi$
$941$	−15.7360	+	37.9900i	−0.512979	+	1.23844i	−0.942142	+	0.335213i	$0.891192\pi$
$942$		0			0
$943$	6.39911			0.208384
$944$	−31.4911	+	32.5057i	−1.02495	+	1.05797i
$945$		0			0
$946$	−1.68718	−	1.37348i	−0.0548551	−	0.0446558i
$947$	38.4816	+	15.9396i	1.25048	+	0.517967i	0.906976	−	0.421182i	$-0.138385\pi$
$947$	38.4816	+	15.9396i	1.25048	+	0.517967i	0.343508	+	0.939150i	$0.388385\pi$
$948$		0			0
$949$	−0.131539	−	0.317563i	−0.00426993	−	0.0103085i
$950$	−12.4355	−	23.0450i	−0.403460	−	0.747678i
$951$		0			0
$952$	−5.72153	−	2.97131i	−0.185436	−	0.0963009i
$953$	−41.7980	−	41.7980i	−1.35397	−	1.35397i	−0.881170	−	0.472800i	$-0.843243\pi$
$953$	−41.7980	−	41.7980i	−1.35397	−	1.35397i	−0.472800	−	0.881170i	$-0.656757\pi$
$954$		0			0
$955$	−2.57487	−	6.21629i	−0.0833209	−	0.201154i
$956$	4.59495	+	22.1802i	0.148611	+	0.717357i
$957$		0			0
$958$	58.4454	−	5.99033i	1.88829	−	0.193539i
$959$	17.1327			0.553243
$960$		0			0
$961$	−63.9436			−2.06270
$962$	0.280105	−	0.0287092i	0.00903096	−	0.000925622i
$963$		0			0
$964$	5.44332	+	26.2753i	0.175317	+	0.846270i
$965$	7.84413	+	18.9374i	0.252511	+	0.609616i
$966$		0			0
$967$	31.3866	+	31.3866i	1.00933	+	1.00933i	0.999956	+	0.00937024i	$0.00298268\pi$
$967$	31.3866	+	31.3866i	1.00933	+	1.00933i	0.00937024	+	0.999956i	$0.497017\pi$
$968$	−11.6926	+	22.5152i	−0.375816	+	0.723667i
$969$		0			0
$970$	−8.08741	−	14.9873i	−0.259671	−	0.481214i
$971$	−20.4873	−	49.4608i	−0.657469	−	1.58727i	−0.801700	−	0.597727i	$-0.796071\pi$
$971$	−20.4873	−	49.4608i	−0.657469	−	1.58727i	0.144230	−	0.989544i	$-0.453929\pi$
$972$		0			0
$973$	23.2884	+	9.64638i	0.746593	+	0.309249i
$974$	29.1807	+	23.7551i	0.935010	+	0.761162i
$975$		0			0
$976$	−0.458627	−	28.9299i	−0.0146803	−	0.926023i
$977$	−15.6979			−0.502221			−0.251110	−	0.967958i	$-0.580796\pi$
$977$	−15.6979			−0.502221			−0.251110	+	0.967958i	$0.580796\pi$
$978$		0			0
$979$	6.11605	−	14.7655i	0.195470	−	0.471906i
$980$	6.42210	−	4.36513i	0.205147	−	0.139439i
$981$		0			0
$982$	12.7978	+	23.7165i	0.408395	+	0.756824i
$983$	−17.7012	−	17.7012i	−0.564581	−	0.564581i	0.366024	−	0.930605i	$-0.380719\pi$
$983$	−17.7012	−	17.7012i	−0.564581	−	0.564581i	−0.930605	+	0.366024i	$0.880719\pi$
$984$		0			0
$985$	7.69271	−	7.69271i	0.245110	−	0.245110i
$986$	−18.1985	−	5.44178i	−0.579557	−	0.173302i
$987$		0			0
$988$	−0.145866	+	0.222095i	−0.00464062	+	0.00706578i
$989$	1.31825	+	0.546036i	0.0419178	+	0.0173629i
$990$		0			0
$991$		−	58.1793i		−	1.84813i	−0.382240	−	0.924063i	$-0.624847\pi$
$991$		−	58.1793i		−	1.84813i	0.382240	−	0.924063i	$-0.375153\pi$
$992$	−26.9414	−	48.0870i	−0.855389	−	1.52676i
$993$		0			0
$994$	−25.2482	+	2.58780i	−0.800825	+	0.0820800i
$995$	4.69297	−	11.3298i	0.148777	−	0.359180i
$996$		0			0
$997$	−9.72099	+	4.02656i	−0.307867	+	0.127523i	−0.531268	−	0.847204i	$-0.678284\pi$
$997$	−9.72099	+	4.02656i	−0.307867	+	0.127523i	0.223401	+	0.974727i	$0.428284\pi$
$998$	2.34657	−	7.84741i	0.0742793	−	0.248406i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.179.1	✓	32
3.2	odd	2		288.2.w.b.179.8	yes	32
4.3	odd	2		1152.2.w.b.1007.6		32
12.11	even	2		1152.2.w.a.1007.3		32
32.5	even	8		1152.2.w.a.143.3		32
32.27	odd	8		288.2.w.b.251.8	yes	32
96.5	odd	8		1152.2.w.b.143.6		32
96.59	even	8	inner	288.2.w.a.251.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.1	✓	32	1.1	even	1	trivial
288.2.w.a.251.1	yes	32	96.59	even	8	inner
288.2.w.b.179.8	yes	32	3.2	odd	2
288.2.w.b.251.8	yes	32	32.27	odd	8
1152.2.w.a.143.3		32	32.5	even	8
1152.2.w.a.1007.3		32	12.11	even	2
1152.2.w.b.143.6		32	96.5	odd	8
1152.2.w.b.1007.6		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)

\(f(q)\)	\(=\)	\(q+(-1.40684 + 0.144194i) q^{2} +(1.95842 - 0.405715i) q^{4} +(0.366958 + 0.885915i) q^{5} +(1.21471 + 1.21471i) q^{7} +(-2.69668 + 0.853169i) q^{8} +O(q^{10})\)	\(q+(-1.40684 + 0.144194i) q^{2} +(1.95842 - 0.405715i) q^{4} +(0.366958 + 0.885915i) q^{5} +(1.21471 + 1.21471i) q^{7} +(-2.69668 + 0.853169i) q^{8} +(-0.643996 - 1.19343i) q^{10} +(0.545272 + 1.31640i) q^{11} +(0.0270492 + 0.0112041i) q^{13} +(-1.88406 - 1.53375i) q^{14} +(3.67079 - 1.58912i) q^{16} +1.32687 q^{17} +(-1.73653 + 4.19236i) q^{19} +(1.07809 + 1.58611i) q^{20} +(-0.956929 - 1.77335i) q^{22} +(0.934512 + 0.934512i) q^{23} +(2.88535 - 2.88535i) q^{25} +(-0.0396695 - 0.0118622i) q^{26} +(2.87173 + 1.88608i) q^{28} +(9.35195 + 3.87371i) q^{29} +9.74390i q^{31} +(-4.93509 + 2.76495i) q^{32} +(-1.86670 + 0.191327i) q^{34} +(-0.630382 + 1.52188i) q^{35} +(-6.28278 + 2.60241i) q^{37} +(1.83852 - 6.14839i) q^{38} +(-1.74541 - 2.07596i) q^{40} +(3.42377 - 3.42377i) q^{41} +(0.997463 - 0.413163i) q^{43} +(1.60195 + 2.35684i) q^{44} +(-1.44946 - 1.17996i) q^{46} -6.21143i q^{47} -4.04896i q^{49} +(-3.64318 + 4.47528i) q^{50} +(0.0575193 + 0.0109681i) q^{52} +(2.94741 - 1.22086i) q^{53} +(-0.966130 + 0.966130i) q^{55} +(-4.31204 - 2.23933i) q^{56} +(-13.7153 - 4.10121i) q^{58} +(-10.4533 + 4.32990i) q^{59} +(2.76809 - 6.68277i) q^{61} +(-1.40501 - 13.7081i) q^{62} +(6.54421 - 4.60145i) q^{64} +0.0280747i q^{65} +(-10.1069 - 4.18640i) q^{67} +(2.59857 - 0.538333i) q^{68} +(0.667404 - 2.23194i) q^{70} +(7.38725 - 7.38725i) q^{71} +(-8.30156 - 8.30156i) q^{73} +(8.46364 - 4.56712i) q^{74} +(-1.69995 + 8.91492i) q^{76} +(-0.936700 + 2.26139i) q^{77} +5.54363 q^{79} +(2.75485 + 2.66887i) q^{80} +(-4.32302 + 5.31039i) q^{82} +(-11.4571 - 4.74570i) q^{83} +(0.486907 + 1.17550i) q^{85} +(-1.34370 + 0.725083i) q^{86} +(-2.59354 - 3.08471i) q^{88} +(-7.93127 - 7.93127i) q^{89} +(0.0192471 + 0.0464667i) q^{91} +(2.20931 + 1.45102i) q^{92} +(0.895648 + 8.73851i) q^{94} -4.35131 q^{95} +12.5582 q^{97} +(0.583834 + 5.69626i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 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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