LMFDB - Embedded newform 288.2.w.a.107.1

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			107.1
Character	$\chi$	$=$	288.107
Dual form			288.2.w.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39224 + 0.248345i) q^{2} +(1.87665 - 0.691511i) q^{4} +(4.01952 + 1.66494i) q^{5} +(2.72280 - 2.72280i) q^{7} +(-2.44101 + 1.42881i) q^{8} +O(q^{10})$	\(q+(-1.39224 + 0.248345i) q^{2} +(1.87665 - 0.691511i) q^{4} +(4.01952 + 1.66494i) q^{5} +(2.72280 - 2.72280i) q^{7} +(-2.44101 + 1.42881i) q^{8} +(-6.00960 - 1.31976i) q^{10} +(-2.48139 - 1.02782i) q^{11} +(-0.146124 - 0.352776i) q^{13} +(-3.11459 + 4.46698i) q^{14} +(3.04362 - 2.59545i) q^{16} -1.69470 q^{17} +(-3.86698 + 1.60175i) q^{19} +(8.69455 + 0.344964i) q^{20} +(3.70993 + 0.814734i) q^{22} +(3.96620 - 3.96620i) q^{23} +(9.84898 + 9.84898i) q^{25} +(0.291050 + 0.454858i) q^{26} +(3.22690 - 6.99259i) q^{28} +(-0.582357 - 1.40593i) q^{29} -0.247051i q^{31} +(-3.59288 + 4.36935i) q^{32} +(2.35943 - 0.420871i) q^{34} +(15.4777 - 6.41106i) q^{35} +(-2.88111 + 6.95561i) q^{37} +(4.98596 - 3.19037i) q^{38} +(-12.1905 + 1.67898i) q^{40} +(-4.26947 - 4.26947i) q^{41} +(-1.21117 + 2.92402i) q^{43} +(-5.36744 - 0.212958i) q^{44} +(-4.53690 + 6.50688i) q^{46} +8.76291i q^{47} -7.82731i q^{49} +(-16.1581 - 11.2662i) q^{50} +(-0.518173 - 0.560989i) q^{52} +(-3.22418 + 7.78387i) q^{53} +(-8.26271 - 8.26271i) q^{55} +(-2.75603 + 10.5367i) q^{56} +(1.15994 + 1.81277i) q^{58} +(1.77515 - 4.28559i) q^{59} +(6.31262 - 2.61477i) q^{61} +(0.0613541 + 0.343954i) q^{62} +(3.91703 - 6.97545i) q^{64} -1.66128i q^{65} +(0.346872 + 0.837424i) q^{67} +(-3.18036 + 1.17191i) q^{68} +(-19.9564 + 12.7695i) q^{70} +(-9.14205 - 9.14205i) q^{71} +(0.0835551 - 0.0835551i) q^{73} +(2.28379 - 10.3994i) q^{74} +(-6.14933 + 5.67999i) q^{76} +(-9.55488 + 3.95776i) q^{77} -9.01313 q^{79} +(16.5552 - 5.36501i) q^{80} +(7.00441 + 4.88381i) q^{82} +(2.10417 + 5.07993i) q^{83} +(-6.81189 - 2.82158i) q^{85} +(0.960066 - 4.37171i) q^{86} +(7.52564 - 1.03649i) q^{88} +(3.77409 - 3.77409i) q^{89} +(-1.35841 - 0.562670i) q^{91} +(4.70049 - 10.1858i) q^{92} +(-2.17623 - 12.2000i) q^{94} -18.2102 q^{95} -2.20840 q^{97} +(1.94388 + 10.8975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.39224	+	0.248345i	−0.984460	+	0.175607i
$2$	−1.39224	+	0.248345i	−0.984460	+	0.175607i
$3$		0			0
$3$		0			0
$4$	1.87665	−	0.691511i	0.938325	−	0.345756i
$5$	4.01952	+	1.66494i	1.79758	+	0.744583i	0.987366	+	0.158453i	$0.0506508\pi$
$5$	4.01952	+	1.66494i	1.79758	+	0.744583i	0.810217	+	0.586130i	$0.199349\pi$
$6$		0			0
$7$	2.72280	−	2.72280i	1.02912	−	1.02912i	0.0295596	−	0.999563i	$-0.490590\pi$
$7$	2.72280	−	2.72280i	1.02912	−	1.02912i	0.999563	−	0.0295596i	$-0.00941050\pi$
$8$	−2.44101	+	1.42881i	−0.863026	+	0.505159i
$9$		0			0
$10$	−6.00960	−	1.31976i	−1.90040	−	0.417345i
$11$	−2.48139	−	1.02782i	−0.748166	−	0.309900i	−0.0241729	−	0.999708i	$-0.507695\pi$
$11$	−2.48139	−	1.02782i	−0.748166	−	0.309900i	−0.723993	+	0.689807i	$0.757695\pi$
$12$		0			0
$13$	−0.146124	−	0.352776i	−0.0405276	−	0.0978423i	0.902320	−	0.431068i	$-0.141863\pi$
$13$	−0.146124	−	0.352776i	−0.0405276	−	0.0978423i	−0.942847	+	0.333225i	$0.891863\pi$
$14$	−3.11459	+	4.46698i	−0.832410	+	1.19385i
$15$		0			0
$16$	3.04362	−	2.59545i	0.760906	−	0.648862i
$17$	−1.69470			−0.411026			−0.205513	−	0.978654i	$-0.565886\pi$
$17$	−1.69470			−0.411026			−0.205513	+	0.978654i	$0.565886\pi$
$18$		0			0
$19$	−3.86698	+	1.60175i	−0.887145	+	0.367468i	−0.779264	−	0.626696i	$-0.784407\pi$
$19$	−3.86698	+	1.60175i	−0.887145	+	0.367468i	−0.107881	+	0.994164i	$0.534407\pi$
$20$	8.69455	+	0.344964i	1.94416	+	0.0771362i
$21$		0			0
$22$	3.70993	+	0.814734i	0.790960	+	0.173702i
$23$	3.96620	−	3.96620i	0.827010	−	0.827010i	−0.160092	−	0.987102i	$-0.551179\pi$
$23$	3.96620	−	3.96620i	0.827010	−	0.827010i	0.987102	+	0.160092i	$0.0511792\pi$
$24$		0			0
$25$	9.84898	+	9.84898i	1.96980	+	1.96980i
$26$	0.291050	+	0.454858i	0.0570796	+	0.0892050i
$27$		0			0
$28$	3.22690	−	6.99259i	0.609826	−	1.32148i
$29$	−0.582357	−	1.40593i	−0.108141	−	0.261075i	0.860541	−	0.509382i	$-0.170126\pi$
$29$	−0.582357	−	1.40593i	−0.108141	−	0.261075i	−0.968681	+	0.248307i	$0.920126\pi$
$30$		0			0
$31$		−	0.247051i		−	0.0443717i	−0.999754	−	0.0221859i	$-0.992937\pi$
$31$		−	0.247051i		−	0.0443717i	0.999754	−	0.0221859i	$-0.00706256\pi$
$32$	−3.59288	+	4.36935i	−0.635137	+	0.772399i
$33$		0			0
$34$	2.35943	−	0.420871i	0.404638	−	0.0721789i
$35$	15.4777	−	6.41106i	2.61620	−	1.08367i
$36$		0			0
$37$	−2.88111	+	6.95561i	−0.473651	+	1.14350i	0.488886	+	0.872347i	$0.337403\pi$
$37$	−2.88111	+	6.95561i	−0.473651	+	1.14350i	−0.962538	+	0.271148i	$0.912597\pi$
$38$	4.98596	−	3.19037i	0.808829	−	0.517546i
$39$		0			0
$40$	−12.1905	+	1.67898i	−1.92749	+	0.265470i
$41$	−4.26947	−	4.26947i	−0.666779	−	0.666779i	0.290190	−	0.956969i	$-0.406281\pi$
$41$	−4.26947	−	4.26947i	−0.666779	−	0.666779i	−0.956969	+	0.290190i	$0.906281\pi$
$42$		0			0
$43$	−1.21117	+	2.92402i	−0.184701	+	0.445908i	−0.988925	−	0.148419i	$-0.952582\pi$
$43$	−1.21117	+	2.92402i	−0.184701	+	0.445908i	0.804223	+	0.594327i	$0.202582\pi$
$44$	−5.36744	−	0.212958i	−0.809172	−	0.0321046i
$45$		0			0
$46$	−4.53690	+	6.50688i	−0.668930	+	0.959387i
$47$			8.76291i			1.27820i	0.769123	+	0.639101i	$0.220693\pi$
$47$			8.76291i			1.27820i	−0.769123	+	0.639101i	$0.779307\pi$
$48$		0			0
$49$		−	7.82731i		−	1.11819i
$50$	−16.1581	−	11.2662i	−2.28509	−	1.59328i
$51$		0			0
$52$	−0.518173	−	0.560989i	−0.0718576	−	0.0777952i
$53$	−3.22418	+	7.78387i	−0.442876	+	1.06920i	0.532059	+	0.846707i	$0.321418\pi$
$53$	−3.22418	+	7.78387i	−0.442876	+	1.06920i	−0.974935	+	0.222489i	$0.928582\pi$
$54$		0			0
$55$	−8.26271	−	8.26271i	−1.11414	−	1.11414i
$56$	−2.75603	+	10.5367i	−0.368289	+	1.40803i
$57$		0			0
$58$	1.15994	+	1.81277i	0.152307	+	0.238028i
$59$	1.77515	−	4.28559i	0.231105	−	0.557936i	−0.765203	−	0.643789i	$-0.777361\pi$
$59$	1.77515	−	4.28559i	0.231105	−	0.557936i	0.996308	+	0.0858528i	$0.0273615\pi$
$60$		0			0
$61$	6.31262	−	2.61477i	0.808249	−	0.334788i	0.0599937	−	0.998199i	$-0.480892\pi$
$61$	6.31262	−	2.61477i	0.808249	−	0.334788i	0.748255	+	0.663411i	$0.230892\pi$
$62$	0.0613541	+	0.343954i	0.00779197	+	0.0436822i
$63$		0			0
$64$	3.91703	−	6.97545i	0.489629	−	0.871931i
$65$		−	1.66128i		−	0.206056i
$66$		0			0
$67$	0.346872	+	0.837424i	0.0423772	+	0.102308i	0.943651	−	0.330943i	$-0.107367\pi$
$67$	0.346872	+	0.837424i	0.0423772	+	0.102308i	−0.901274	+	0.433250i	$0.857367\pi$
$68$	−3.18036	+	1.17191i	−0.385675	+	0.142114i
$69$		0			0
$70$	−19.9564	+	12.7695i	−2.38525	+	1.52625i
$71$	−9.14205	−	9.14205i	−1.08496	−	1.08496i	−0.996039	−	0.0889229i	$-0.971658\pi$
$71$	−9.14205	−	9.14205i	−1.08496	−	1.08496i	−0.0889229	−	0.996039i	$-0.528342\pi$
$72$		0			0
$73$	0.0835551	−	0.0835551i	0.00977939	−	0.00977939i	−0.702200	−	0.711980i	$-0.747799\pi$
$73$	0.0835551	−	0.0835551i	0.00977939	−	0.00977939i	0.711980	+	0.702200i	$0.247799\pi$
$74$	2.28379	−	10.3994i	0.265485	−	1.20890i
$75$		0			0
$76$	−6.14933	+	5.67999i	−0.705376	+	0.651539i
$77$	−9.55488	+	3.95776i	−1.08888	+	0.451029i
$78$		0			0
$79$	−9.01313			−1.01406			−0.507028	−	0.861930i	$-0.669256\pi$
$79$	−9.01313			−1.01406			−0.507028	+	0.861930i	$0.669256\pi$
$80$	16.5552	−	5.36501i	1.85092	−	0.599826i
$81$		0			0
$82$	7.00441	+	4.88381i	0.773508	+	0.539326i
$83$	2.10417	+	5.07993i	0.230963	+	0.557594i	0.996291	−	0.0860461i	$-0.0274232\pi$
$83$	2.10417	+	5.07993i	0.230963	+	0.557594i	−0.765328	+	0.643640i	$0.777423\pi$
$84$		0			0
$85$	−6.81189	−	2.82158i	−0.738853	−	0.306043i
$86$	0.960066	−	4.37171i	0.103527	−	0.471414i
$87$		0			0
$88$	7.52564	−	1.03649i	0.802236	−	0.110490i
$89$	3.77409	−	3.77409i	0.400053	−	0.400053i	−0.478199	−	0.878252i	$-0.658710\pi$
$89$	3.77409	−	3.77409i	0.400053	−	0.400053i	0.878252	+	0.478199i	$0.158710\pi$
$90$		0			0
$91$	−1.35841	−	0.562670i	−0.142400	−	0.0589839i
$92$	4.70049	−	10.1858i	0.490060	−	1.06195i
$93$		0			0
$94$	−2.17623	−	12.2000i	−0.224461	−	1.25834i
$95$	−18.2102			−1.86833
$96$		0			0
$97$	−2.20840			−0.224229			−0.112114	−	0.993695i	$-0.535762\pi$
$97$	−2.20840			−0.224229			−0.112114	+	0.993695i	$0.535762\pi$
$98$	1.94388	+	10.8975i	0.196361	+	1.10081i
$99$		0			0
$100$	25.2937	+	11.6724i	2.52937	+	1.16724i
$101$	−6.00246	−	2.48630i	−0.597267	−	0.247396i	0.0635063	−	0.997981i	$-0.479772\pi$
$101$	−6.00246	−	2.48630i	−0.597267	−	0.247396i	−0.660774	+	0.750585i	$0.729772\pi$
$102$		0			0
$103$	−6.28711	+	6.28711i	−0.619487	+	0.619487i	−0.945400	−	0.325913i	$-0.894328\pi$
$103$	−6.28711	+	6.28711i	−0.619487	+	0.619487i	0.325913	+	0.945400i	$0.394328\pi$
$104$	0.860738	+	0.652344i	0.0844023	+	0.0639676i
$105$		0			0
$106$	2.55574	−	11.6377i	0.248235	−	1.13035i
$107$	4.52481	+	1.87424i	0.437430	+	0.181189i	0.590520	−	0.807023i	$-0.298923\pi$
$107$	4.52481	+	1.87424i	0.437430	+	0.181189i	−0.153091	+	0.988212i	$0.548923\pi$
$108$		0			0
$109$	3.45233	+	8.33466i	0.330673	+	0.798316i	0.998539	+	0.0540343i	$0.0172080\pi$
$109$	3.45233	+	8.33466i	0.330673	+	0.798316i	−0.667866	+	0.744282i	$0.732792\pi$
$110$	13.5557	+	9.45165i	1.29248	+	0.901179i
$111$		0			0
$112$	1.22029	−	15.3541i	0.115307	−	1.45082i
$113$	4.91698			0.462550			0.231275	−	0.972888i	$-0.425710\pi$
$113$	4.91698			0.462550			0.231275	+	0.972888i	$0.425710\pi$
$114$		0			0
$115$	22.5457	−	9.33873i	2.10240	−	0.870841i
$116$	−2.06510	−	2.23574i	−0.191740	−	0.207583i
$117$		0			0
$118$	−1.40712	+	6.40741i	−0.129536	+	0.589850i
$119$	−4.61434	+	4.61434i	−0.422996	+	0.422996i
$120$		0			0
$121$	−2.67732	−	2.67732i	−0.243393	−	0.243393i
$122$	−8.13930	+	5.20810i	−0.736898	+	0.471519i
$123$		0			0
$124$	−0.170839	−	0.463629i	−0.0153418	−	0.0416351i
$125$	14.8655	+	35.8885i	1.32961	+	3.20996i
$126$		0			0
$127$		−	14.1288i		−	1.25373i	−0.779128	−	0.626865i	$-0.784338\pi$
$127$		−	14.1288i		−	1.25373i	0.779128	−	0.626865i	$-0.215662\pi$
$128$	−3.72112	+	10.6843i	−0.328903	+	0.944364i
$129$		0			0
$130$	0.412570	+	2.31289i	0.0361848	+	0.202854i
$131$	−5.24402	+	2.17214i	−0.458172	+	0.189781i	−0.599818	−	0.800136i	$-0.704760\pi$
$131$	−5.24402	+	2.17214i	−0.458172	+	0.189781i	0.141646	+	0.989917i	$0.454760\pi$
$132$		0			0
$133$	−6.16775	+	14.8903i	−0.534812	+	1.29115i
$134$	−0.690899	−	1.07975i	−0.0596846	−	0.0932761i
$135$		0			0
$136$	4.13678	−	2.42140i	0.354726	−	0.207633i
$137$	−4.12927	−	4.12927i	−0.352787	−	0.352787i	0.508358	−	0.861146i	$-0.330253\pi$
$137$	−4.12927	−	4.12927i	−0.352787	−	0.352787i	−0.861146	+	0.508358i	$0.830253\pi$
$138$		0			0
$139$	−6.65987	+	16.0783i	−0.564883	+	1.36375i	0.340938	+	0.940086i	$0.389256\pi$
$139$	−6.65987	+	16.0783i	−0.564883	+	1.36375i	−0.905820	+	0.423662i	$0.860744\pi$
$140$	24.6128	−	22.7343i	2.08016	−	1.92140i
$141$		0			0
$142$	14.9983	+	10.4575i	1.25863	+	0.877575i
$143$			1.02556i			0.0857618i
$144$		0			0
$145$		−	6.62077i		−	0.549825i
$146$	−0.0955780	+	0.137079i	−0.00791010	+	0.0113447i
$147$		0			0
$148$	−0.596945	+	15.0456i	−0.0490686	+	1.23674i
$149$	2.01676	−	4.86889i	0.165219	−	0.398875i	−0.819487	−	0.573098i	$-0.805741\pi$
$149$	2.01676	−	4.86889i	0.165219	−	0.398875i	0.984706	+	0.174223i	$0.0557414\pi$
$150$		0			0
$151$	−11.9010	−	11.9010i	−0.968489	−	0.968489i	0.0310293	−	0.999518i	$-0.490121\pi$
$151$	−11.9010	−	11.9010i	−0.968489	−	0.968489i	−0.999518	+	0.0310293i	$0.990121\pi$
$152$	7.15072	−	9.43505i	0.580000	−	0.765283i
$153$		0			0
$154$	12.3198	−	7.88306i	0.992756	−	0.635235i
$155$	0.411325	−	0.993027i	0.0330385	−	0.0797619i
$156$		0			0
$157$	7.63032	−	3.16058i	0.608966	−	0.252242i	−0.0568202	−	0.998384i	$-0.518096\pi$
$157$	7.63032	−	3.16058i	0.608966	−	0.252242i	0.665786	+	0.746142i	$0.268096\pi$
$158$	12.5484	−	2.23837i	0.998298	−	0.178075i
$159$		0			0
$160$	−21.7163	+	11.5808i	−1.71683	+	0.915540i
$161$		−	21.5984i		−	1.70219i
$162$		0			0
$163$	−7.59947	−	18.3468i	−0.595237	−	1.43703i	−0.878386	−	0.477953i	$-0.841379\pi$
$163$	−7.59947	−	18.3468i	−0.595237	−	1.43703i	0.283149	−	0.959076i	$-0.408621\pi$
$164$	−10.9647	−	5.05991i	−0.856197	−	0.395112i
$165$		0			0
$166$	−4.19109	−	6.54990i	−0.325291	−	0.508371i
$167$	0.106628	+	0.106628i	0.00825110	+	0.00825110i	0.711220	−	0.702969i	$-0.248143\pi$
$167$	0.106628	+	0.106628i	0.00825110	+	0.00825110i	−0.702969	+	0.711220i	$0.748143\pi$
$168$		0			0
$169$	9.08929	−	9.08929i	0.699176	−	0.699176i
$170$	10.1845	+	2.23660i	0.781115	+	0.171540i
$171$		0			0
$172$	−0.250945	+	6.32489i	−0.0191344	+	0.482268i
$173$	13.5633	−	5.61809i	1.03120	−	0.427135i	0.198052	−	0.980192i	$-0.436539\pi$
$173$	13.5633	−	5.61809i	1.03120	−	0.427135i	0.833144	+	0.553056i	$0.186539\pi$
$174$		0			0
$175$	53.6336			4.05432
$176$	−10.2201	+	3.31200i	−0.770367	+	0.249651i
$177$		0			0
$178$	−4.31716	+	6.19171i	−0.323585	+	0.464089i
$179$	7.90273	+	19.0789i	0.590678	+	1.42602i	0.882849	+	0.469657i	$0.155622\pi$
$179$	7.90273	+	19.0789i	0.590678	+	1.42602i	−0.292171	+	0.956366i	$0.594378\pi$
$180$		0			0
$181$	−22.9664	−	9.51301i	−1.70708	−	0.707097i	−0.707082	−	0.707132i	$-0.749989\pi$
$181$	−22.9664	−	9.51301i	−1.70708	−	0.707097i	−1.00000		3.50523e-5i	$0.999989\pi$
$182$	2.03096	+	0.446017i	0.150545	+	0.0330609i
$183$		0			0
$184$	−4.01459	+	15.3484i	−0.295960	+	1.13150i
$185$	−23.1613	+	23.1613i	−1.70286	+	1.70286i
$186$		0			0
$187$	4.20521	+	1.74185i	0.307515	+	0.127377i
$188$	6.05965	+	16.4449i	0.441945	+	1.19937i
$189$		0			0
$190$	25.3529	−	4.52242i	1.83929	−	0.328091i
$191$	13.5743			0.982202			0.491101	−	0.871103i	$-0.336595\pi$
$191$	13.5743			0.982202			0.491101	+	0.871103i	$0.336595\pi$
$192$		0			0
$193$	12.6233			0.908648			0.454324	−	0.890837i	$-0.349881\pi$
$193$	12.6233			0.908648			0.454324	+	0.890837i	$0.349881\pi$
$194$	3.07461	−	0.548446i	0.220744	−	0.0393761i
$195$		0			0
$196$	−5.41267	−	14.6891i	−0.386620	−	1.04922i
$197$	−16.4327	−	6.80666i	−1.17078	−	0.484954i	−0.289332	−	0.957229i	$-0.593433\pi$
$197$	−16.4327	−	6.80666i	−1.17078	−	0.484954i	−0.881452	+	0.472275i	$0.843433\pi$
$198$		0			0
$199$	−9.74888	+	9.74888i	−0.691080	+	0.691080i	−0.962470	−	0.271390i	$-0.912517\pi$
$199$	−9.74888	+	9.74888i	−0.691080	+	0.691080i	0.271390	+	0.962470i	$0.412517\pi$
$200$	−38.1137	−	9.96915i	−2.69504	−	0.704926i
$201$		0			0
$202$	8.97432	+	1.97084i	0.631431	+	0.138668i
$203$	−5.41372	−	2.24244i	−0.379969	−	0.157388i
$204$		0			0
$205$	−10.0528	−	24.2696i	−0.702118	−	1.69506i
$206$	7.19177	−	10.3145i	0.501074	−	0.718646i
$207$		0			0
$208$	−1.36036	−	0.694458i	−0.0943239	−	0.0481520i
$209$	11.2418			0.777610
$210$		0			0
$211$	−9.94055	+	4.11751i	−0.684336	+	0.283461i	−0.697638	−	0.716450i	$-0.745766\pi$
$211$	−9.94055	+	4.11751i	−0.684336	+	0.283461i	0.0133022	+	0.999912i	$0.495766\pi$
$212$	−0.668028	+	16.8371i	−0.0458803	+	1.15638i
$213$		0			0
$214$	−6.76506	−	1.48567i	−0.462450	−	0.101558i
$215$	−9.73662	+	9.73662i	−0.664032	+	0.664032i
$216$		0			0
$217$	−0.672672	−	0.672672i	−0.0456640	−	0.0456640i
$218$	−6.87634	−	10.7465i	−0.465725	−	0.727842i
$219$		0			0
$220$	−21.2200	−	9.79245i	−1.43065	−	0.660207i
$221$	0.247637	+	0.597849i	0.0166579	+	0.0402157i
$222$		0			0
$223$			25.9205i			1.73576i	0.496770	+	0.867882i	$0.334519\pi$
$223$			25.9205i			1.73576i	−0.496770	+	0.867882i	$0.665481\pi$
$224$	2.11418	+	21.6796i	0.141259	+	1.44853i
$225$		0			0
$226$	−6.84560	+	1.22111i	−0.455363	+	0.0812270i
$227$	−5.86548	+	2.42956i	−0.389306	+	0.161256i	−0.568746	−	0.822513i	$-0.692571\pi$
$227$	−5.86548	+	2.42956i	−0.389306	+	0.161256i	0.179440	+	0.983769i	$0.442571\pi$
$228$		0			0
$229$	5.60080	−	13.5215i	0.370111	−	0.893527i	−0.623620	−	0.781728i	$-0.714339\pi$
$229$	5.60080	−	13.5215i	0.370111	−	0.893527i	0.993731	−	0.111799i	$-0.0356614\pi$
$230$	−29.0697	+	18.6008i	−1.91680	+	1.22650i
$231$		0			0
$232$	3.43034	+	2.59982i	0.225213	+	0.170687i
$233$	−9.51909	−	9.51909i	−0.623616	−	0.623616i	0.322838	−	0.946454i	$-0.395363\pi$
$233$	−9.51909	−	9.51909i	−0.623616	−	0.623616i	−0.946454	+	0.322838i	$0.895363\pi$
$234$		0			0
$235$	−14.5897	+	35.2227i	−0.951727	+	2.29767i
$236$	0.367798	−	9.27008i	0.0239416	−	0.603431i
$237$		0			0
$238$	5.27830	−	7.57020i	0.342142	−	0.490703i
$239$			3.25912i			0.210815i	0.994429	+	0.105407i	$0.0336147\pi$
$239$			3.25912i			0.210815i	−0.994429	+	0.105407i	$0.966385\pi$
$240$		0			0
$241$		−	6.61960i		−	0.426406i	−0.977008	−	0.213203i	$-0.931610\pi$
$241$		−	6.61960i		−	0.426406i	0.977008	−	0.213203i	$-0.0683896\pi$
$242$	4.39237	+	3.06257i	0.282352	+	0.196869i
$243$		0			0
$244$	10.0384	−	9.27227i	0.642645	−	0.593596i
$245$	13.0320	−	31.4620i	0.832583	−	2.01003i
$246$		0			0
$247$	1.13012	+	1.13012i	0.0719078	+	0.0719078i
$248$	0.352988	+	0.603054i	0.0224148	+	0.0382940i
$249$		0			0
$250$	−29.6090	−	46.2735i	−1.87264	−	2.92659i
$251$	5.13077	−	12.3868i	0.323852	−	0.781847i	−0.675172	−	0.737661i	$-0.735930\pi$
$251$	5.13077	−	12.3868i	0.323852	−	0.781847i	0.999023	−	0.0441864i	$-0.0140695\pi$
$252$		0			0
$253$	−13.9182	+	5.76512i	−0.875031	+	0.362450i
$254$	3.50882	+	19.6707i	0.220163	+	1.23425i
$255$		0			0
$256$	2.52729	−	15.7991i	0.157956	−	0.987446i
$257$		−	12.3745i		−	0.771901i	−0.922520	−	0.385950i	$-0.873874\pi$
$257$		−	12.3745i		−	0.771901i	0.922520	−	0.385950i	$-0.126126\pi$
$258$		0			0
$259$	11.0941	+	26.7834i	0.689352	+	1.66424i
$260$	−1.14879	−	3.11763i	−0.0712450	−	0.193347i
$261$		0			0
$262$	6.76148	−	4.32647i	0.417726	−	0.267290i
$263$	18.1214	+	18.1214i	1.11741	+	1.11741i	0.992120	+	0.125291i	$0.0399866\pi$
$263$	18.1214	+	18.1214i	1.11741	+	1.11741i	0.125291	+	0.992120i	$0.460013\pi$
$264$		0			0
$265$	−25.9193	+	25.9193i	−1.59221	+	1.59221i
$266$	4.88904	−	22.2625i	0.299767	−	1.36500i
$267$		0			0
$268$	1.23005	+	1.33168i	0.0751370	+	0.0813456i
$269$	11.0992	−	4.59744i	0.676731	−	0.280311i	−0.0177286	−	0.999843i	$-0.505643\pi$
$269$	11.0992	−	4.59744i	0.676731	−	0.280311i	0.694460	+	0.719532i	$0.255643\pi$
$270$		0			0
$271$	−6.01956			−0.365662			−0.182831	−	0.983144i	$-0.558526\pi$
$271$	−6.01956			−0.365662			−0.182831	+	0.983144i	$0.558526\pi$
$272$	−5.15804	+	4.39851i	−0.312752	+	0.266699i
$273$		0			0
$274$	6.77441	+	4.72344i	0.409257	+	0.285353i
$275$	−14.3161	−	34.5621i	−0.863293	−	2.08417i
$276$		0			0
$277$	−1.76130	−	0.729552i	−0.105826	−	0.0438346i	0.329142	−	0.944280i	$-0.393240\pi$
$277$	−1.76130	−	0.729552i	−0.105826	−	0.0438346i	−0.434968	+	0.900446i	$0.643240\pi$
$278$	5.27914	−	24.0388i	0.316622	−	1.44175i
$279$		0			0
$280$	−28.6209	+	37.7640i	−1.71043	+	2.25683i
$281$	5.91271	−	5.91271i	0.352722	−	0.352722i	−0.508399	−	0.861122i	$-0.669763\pi$
$281$	5.91271	−	5.91271i	0.352722	−	0.352722i	0.861122	+	0.508399i	$0.169763\pi$
$282$		0			0
$283$	10.6146	+	4.39669i	0.630970	+	0.261356i	0.675165	−	0.737667i	$-0.264072\pi$
$283$	10.6146	+	4.39669i	0.630970	+	0.261356i	−0.0441953	+	0.999023i	$0.514072\pi$
$284$	−23.4782	−	10.8346i	−1.39318	−	0.642914i
$285$		0			0
$286$	−0.254694	−	1.42783i	−0.0150604	−	0.0844291i
$287$	−23.2498			−1.37239
$288$		0			0
$289$	−14.1280			−0.831058
$290$	1.64424	+	9.21768i	0.0965529	+	0.541281i
$291$		0			0
$292$	0.0990243	−	0.214583i	0.00579496	−	0.0125575i
$293$	6.96499	+	2.88499i	0.406899	+	0.168543i	0.576739	−	0.816929i	$-0.304325\pi$
$293$	6.96499	+	2.88499i	0.406899	+	0.168543i	−0.169840	+	0.985472i	$0.554325\pi$
$294$		0			0
$295$	14.2705	−	14.2705i	0.830860	−	0.830860i
$296$	−2.90541	−	21.0952i	−0.168873	−	1.22614i
$297$		0			0
$298$	−1.59864	+	7.27950i	−0.0926069	+	0.421690i
$299$	−1.97874	−	0.819619i	−0.114433	−	0.0473998i
$300$		0			0
$301$	4.66375	+	11.2593i	0.268814	+	0.648974i
$302$	19.5246	+	13.6135i	1.12351	+	0.783366i
$303$		0			0
$304$	−7.61235	+	14.9117i	−0.436598	+	0.855243i
$305$	29.7272			1.70217
$306$		0			0
$307$	17.4648	−	7.23418i	0.996771	−	0.412876i	0.176159	−	0.984362i	$-0.443633\pi$
$307$	17.4648	−	7.23418i	0.996771	−	0.412876i	0.820612	+	0.571485i	$0.193633\pi$
$308$	−15.1943	+	14.0346i	−0.865777	+	0.799698i
$309$		0			0
$310$	−0.326049	+	1.48468i	−0.0185183	+	0.0843242i
$311$	20.0044	−	20.0044i	1.13435	−	1.13435i	0.144901	−	0.989446i	$-0.453714\pi$
$311$	20.0044	−	20.0044i	1.13435	−	1.13435i	0.989446	−	0.144901i	$-0.0462865\pi$
$312$		0			0
$313$	16.1777	+	16.1777i	0.914417	+	0.914417i	0.996616	−	0.0821987i	$-0.0261942\pi$
$313$	16.1777	+	16.1777i	0.914417	+	0.914417i	−0.0821987	+	0.996616i	$0.526194\pi$
$314$	−9.83831	+	6.29524i	−0.555208	+	0.355261i
$315$		0			0
$316$	−16.9145	+	6.23268i	−0.951514	+	0.350616i
$317$	−6.71779	−	16.2182i	−0.377309	−	0.910904i	−0.992468	−	0.122501i	$-0.960908\pi$
$317$	−6.71779	−	16.2182i	−0.377309	−	0.910904i	0.615160	−	0.788403i	$-0.289092\pi$
$318$		0			0
$319$			4.08722i			0.228841i
$320$	27.3583	−	21.5163i	1.52937	−	1.20280i
$321$		0			0
$322$	5.36385	+	30.0700i	0.298916	+	1.67574i
$323$	6.55337	−	2.71450i	0.364639	−	0.151039i
$324$		0			0
$325$	2.03530	−	4.91365i	0.112898	−	0.272560i
$326$	15.1366	+	23.6557i	0.838339	+	1.31017i
$327$		0			0
$328$	16.5220	+	4.32156i	0.912277	+	0.238618i
$329$	23.8597	+	23.8597i	1.31543	+	1.31543i
$330$		0			0
$331$	5.15446	−	12.4440i	0.283315	−	0.683982i	−0.716594	−	0.697490i	$-0.754300\pi$
$331$	5.15446	−	12.4440i	0.283315	−	0.683982i	0.999909	+	0.0135083i	$0.00429997\pi$
$332$	7.46162	+	8.07818i	0.409510	+	0.443348i
$333$		0			0
$334$	−0.174932	−	0.121971i	−0.00957183	−	0.00667393i
$335$			3.94356i			0.215460i
$336$		0			0
$337$		−	4.35461i		−	0.237211i	−0.992941	−	0.118605i	$-0.962158\pi$
$337$		−	4.35461i		−	0.237211i	0.992941	−	0.118605i	$-0.0378423\pi$
$338$	−10.3972	+	14.9117i	−0.565531	+	0.811091i
$339$		0			0
$340$	−14.7347	−	0.584610i	−0.799100	−	0.0317049i
$341$	−0.253925	+	0.613030i	−0.0137508	+	0.0331974i
$342$		0			0
$343$	−2.25260	−	2.25260i	−0.121629	−	0.121629i
$344$	−1.22138	−	8.86806i	−0.0658525	−	0.478134i
$345$		0			0
$346$	−17.4881	+	11.1901i	−0.940163	+	0.601583i
$347$	−10.8641	+	26.2282i	−0.583215	+	1.40800i	0.306669	+	0.951816i	$0.400786\pi$
$347$	−10.8641	+	26.2282i	−0.583215	+	1.40800i	−0.889883	+	0.456188i	$0.849214\pi$
$348$		0			0
$349$	23.9337	−	9.91367i	1.28114	−	0.530667i	0.364809	−	0.931082i	$-0.381134\pi$
$349$	23.9337	−	9.91367i	1.28114	−	0.530667i	0.916334	+	0.400416i	$0.131134\pi$
$350$	−74.6707	+	13.3197i	−3.99132	+	0.711966i
$351$		0			0
$352$	13.4062	−	7.14920i	0.714555	−	0.381054i
$353$			15.8830i			0.845369i	0.906277	+	0.422685i	$0.138912\pi$
$353$			15.8830i			0.845369i	−0.906277	+	0.422685i	$0.861088\pi$
$354$		0			0
$355$	−21.5257	−	51.9676i	−1.14246	−	2.75815i
$356$	4.47282	−	9.69248i	0.237059	−	0.513700i
$357$		0			0
$358$	−15.7406	−	24.5997i	−0.831918	−	1.30014i
$359$	−14.9900	−	14.9900i	−0.791139	−	0.791139i	0.190540	−	0.981679i	$-0.438976\pi$
$359$	−14.9900	−	14.9900i	−0.791139	−	0.791139i	−0.981679	+	0.190540i	$0.938976\pi$
$360$		0			0
$361$	−1.04714	+	1.04714i	−0.0551128	+	0.0551128i
$362$	34.3372	+	7.54076i	1.80473	+	0.396333i
$363$		0			0
$364$	−2.93834	−	0.116581i	−0.154011	−	0.00611052i
$365$	0.474966	−	0.196737i	0.0248608	−	0.0102977i
$366$		0			0
$367$	5.97060			0.311663			0.155831	−	0.987784i	$-0.450194\pi$
$367$	5.97060			0.311663			0.155831	+	0.987784i	$0.450194\pi$
$368$	1.77755	−	22.3657i	0.0926613	−	1.16589i
$369$		0			0
$370$	26.4941	−	37.9981i	1.37736	−	1.97543i
$371$	12.4151	+	29.9727i	0.644561	+	1.55611i
$372$		0			0
$373$	18.6887	+	7.74110i	0.967662	+	0.400819i	0.809841	−	0.586649i	$-0.199553\pi$
$373$	18.6887	+	7.74110i	0.967662	+	0.400819i	0.157821	+	0.987468i	$0.449553\pi$
$374$	−6.28723	−	1.38073i	−0.325105	−	0.0713959i
$375$		0			0
$376$	−12.5205	−	21.3903i	−0.645695	−	1.10312i
$377$	−0.410882	+	0.410882i	−0.0211615	+	0.0211615i
$378$		0			0
$379$	26.5608	+	11.0018i	1.36434	+	0.565127i	0.940247	−	0.340493i	$-0.110594\pi$
$379$	26.5608	+	11.0018i	1.36434	+	0.565127i	0.424090	+	0.905620i	$0.360594\pi$
$380$	−34.1742	+	12.5926i	−1.75310	+	0.645985i
$381$		0			0
$382$	−18.8987	+	3.37112i	−0.966939	+	0.172481i
$383$	23.9456			1.22356			0.611782	−	0.791027i	$-0.290453\pi$
$383$	23.9456			1.22356			0.611782	+	0.791027i	$0.290453\pi$
$384$		0			0
$385$	−44.9955			−2.29318
$386$	−17.5747	+	3.13495i	−0.894528	+	0.159565i
$387$		0			0
$388$	−4.14439	+	1.52713i	−0.210399	+	0.0775284i
$389$	0.507585	+	0.210249i	0.0257356	+	0.0106600i	0.395514	−	0.918460i	$-0.370566\pi$
$389$	0.507585	+	0.210249i	0.0257356	+	0.0106600i	−0.369779	+	0.929120i	$0.620566\pi$
$390$		0			0
$391$	−6.72153	+	6.72153i	−0.339922	+	0.339922i
$392$	11.1837	+	19.1065i	0.564862	+	0.965025i
$393$		0			0
$394$	24.5687	+	5.39549i	1.23775	+	0.271821i
$395$	−36.2284	−	15.0063i	−1.82285	−	0.755049i
$396$		0			0
$397$	3.58568	+	8.65661i	0.179960	+	0.434463i	0.987958	−	0.154723i	$-0.0494486\pi$
$397$	3.58568	+	8.65661i	0.179960	+	0.434463i	−0.807998	+	0.589186i	$0.799449\pi$
$398$	11.1517	−	15.9938i	0.558982	−	0.801699i
$399$		0			0
$400$	55.5391	+	4.41407i	2.77695	+	0.220703i
$401$	5.26389			0.262866			0.131433	−	0.991325i	$-0.458042\pi$
$401$	5.26389			0.262866			0.131433	+	0.991325i	$0.458042\pi$
$402$		0			0
$403$	−0.0871537	+	0.0361002i	−0.00434143	+	0.00179828i
$404$	−12.9838	−	0.515144i	−0.645969	−	0.0256294i
$405$		0			0
$406$	8.09408	+	1.77753i	0.401703	+	0.0882174i
$407$	14.2983	−	14.2983i	0.708739	−	0.708739i
$408$		0			0
$409$	10.2522	+	10.2522i	0.506940	+	0.506940i	0.913586	−	0.406646i	$-0.133302\pi$
$409$	10.2522	+	10.2522i	0.506940	+	0.506940i	−0.406646	+	0.913586i	$0.633302\pi$
$410$	20.0231	+	31.2925i	0.988872	+	1.54543i
$411$		0			0
$412$	−7.45109	+	16.1463i	−0.367089	+	0.795471i
$413$	−6.83543	−	16.5022i	−0.336350	−	0.812020i
$414$		0			0
$415$			23.9222i			1.17429i
$416$	2.06641	+	0.629011i	0.101314	+	0.0308398i
$417$		0			0
$418$	−15.6512	+	2.79184i	−0.765526	+	0.136554i
$419$	21.9319	−	9.08450i	1.07145	−	0.443807i	0.223945	−	0.974602i	$-0.428107\pi$
$419$	21.9319	−	9.08450i	1.07145	−	0.443807i	0.847500	+	0.530795i	$0.178107\pi$
$420$		0			0
$421$	−13.0403	+	31.4820i	−0.635544	+	1.53434i	0.197013	+	0.980401i	$0.436876\pi$
$421$	−13.0403	+	31.4820i	−0.635544	+	1.53434i	−0.832557	+	0.553939i	$0.813124\pi$
$422$	12.8170	−	8.20124i	0.623924	−	0.399230i
$423$		0			0
$424$	−3.25137	−	23.6072i	−0.157901	−	1.14647i
$425$	−16.6911	−	16.6911i	−0.809636	−	0.809636i
$426$		0			0
$427$	10.0685	−	24.3075i	0.487250	−	1.17632i
$428$	9.78753	+	0.388328i	0.473098	+	0.0187706i
$429$		0			0
$430$	11.1376	−	15.9737i	0.537104	−	0.770321i
$431$			15.1928i			0.731811i	0.930652	+	0.365906i	$0.119241\pi$
$431$			15.1928i			0.731811i	−0.930652	+	0.365906i	$0.880759\pi$
$432$		0			0
$433$		−	36.6873i		−	1.76308i	−0.472109	−	0.881540i	$-0.656507\pi$
$433$		−	36.6873i		−	1.76308i	0.472109	−	0.881540i	$-0.343493\pi$
$434$	1.10357	+	0.769464i	0.0529732	+	0.0369355i
$435$		0			0
$436$	12.2423	+	13.2539i	0.586301	+	0.634747i
$437$	−8.98432	+	21.6901i	−0.429778	+	1.03758i
$438$		0			0
$439$	12.7407	+	12.7407i	0.608081	+	0.608081i	0.942444	−	0.334363i	$-0.108521\pi$
$439$	12.7407	+	12.7407i	0.608081	+	0.608081i	−0.334363	+	0.942444i	$0.608521\pi$
$440$	31.9751	+	8.36353i	1.52436	+	0.398716i
$441$		0			0
$442$	−0.493243	−	0.770849i	−0.0234612	−	0.0366655i
$443$	−7.30243	+	17.6296i	−0.346949	+	0.837609i	0.650028	+	0.759910i	$0.274757\pi$
$443$	−7.30243	+	17.6296i	−0.346949	+	0.837609i	−0.996977	+	0.0776987i	$0.975243\pi$
$444$		0			0
$445$	21.4537	−	8.88641i	1.01700	−	0.421256i
$446$	−6.43723	−	36.0875i	−0.304812	−	1.70879i
$447$		0			0
$448$	−8.32746	−	29.6581i	−0.393436	−	1.40121i
$449$			32.1128i			1.51550i	0.652546	+	0.757749i	$0.273701\pi$
$449$			32.1128i			1.51550i	−0.652546	+	0.757749i	$0.726299\pi$
$450$		0			0
$451$	6.20594	+	14.9825i	0.292226	+	0.705496i
$452$	9.22744	−	3.40015i	0.434022	−	0.159929i
$453$		0			0
$454$	7.56277	−	4.83919i	0.354938	−	0.227114i
$455$	−4.52333	−	4.52333i	−0.212057	−	0.212057i
$456$		0			0
$457$	22.7090	−	22.7090i	1.06228	−	1.06228i	0.0643566	−	0.997927i	$-0.479500\pi$
$457$	22.7090	−	22.7090i	1.06228	−	1.06228i	0.997927	−	0.0643566i	$-0.0204995\pi$
$458$	−4.43963	+	20.2161i	−0.207450	+	0.944636i
$459$		0			0
$460$	35.8525	−	33.1161i	1.67163	−	1.54405i
$461$	−28.4173	+	11.7708i	−1.32352	+	0.548222i	−0.928801	−	0.370579i	$-0.879159\pi$
$461$	−28.4173	+	11.7708i	−1.32352	+	0.548222i	−0.394723	+	0.918800i	$0.629159\pi$
$462$		0			0
$463$	−41.0327			−1.90695			−0.953475	−	0.301471i	$-0.902522\pi$
$463$	−41.0327			−1.90695			−0.953475	+	0.301471i	$0.902522\pi$
$464$	−5.42150	−	2.76766i	−0.251687	−	0.128485i
$465$		0			0
$466$	15.6168	+	10.8888i	0.723437	+	0.504414i
$467$	1.75394	+	4.23439i	0.0811628	+	0.195944i	0.959252	−	0.282553i	$-0.0911815\pi$
$467$	1.75394	+	4.23439i	0.0811628	+	0.195944i	−0.878089	+	0.478498i	$0.841181\pi$
$468$		0			0
$469$	3.22461	+	1.33568i	0.148898	+	0.0616758i
$470$	11.5649	−	52.6616i	0.533451	−	2.42910i
$471$		0			0
$472$	1.79012	+	12.9975i	0.0823970	+	0.598258i
$473$	6.01074	−	6.01074i	0.276374	−	0.276374i
$474$		0			0
$475$	−53.8614	−	22.3101i	−2.47133	−	1.02366i
$476$	−5.46863	+	11.8504i	−0.250654	+	0.543161i
$477$		0			0
$478$	−0.809387	−	4.53746i	−0.0370205	−	0.207539i
$479$	−17.2694			−0.789060			−0.394530	−	0.918883i	$-0.629093\pi$
$479$	−17.2694			−0.789060			−0.394530	+	0.918883i	$0.629093\pi$
$480$		0			0
$481$	2.87477			0.131078
$482$	1.64395	+	9.21605i	0.0748797	+	0.419780i
$483$		0			0
$484$	−6.87579	−	3.17299i	−0.312536	−	0.144227i
$485$	−8.87670	−	3.67685i	−0.403070	−	0.166957i
$486$		0			0
$487$	−13.9346	+	13.9346i	−0.631435	+	0.631435i	−0.948428	−	0.316993i	$-0.897327\pi$
$487$	−13.9346	+	13.9346i	−0.631435	+	0.631435i	0.316993	+	0.948428i	$0.397327\pi$
$488$	−11.6732	+	15.4022i	−0.528419	+	0.697225i
$489$		0			0
$490$	−10.3302	+	47.0390i	−0.466670	+	2.12501i
$491$	8.73949	+	3.62001i	0.394408	+	0.163369i	0.571068	−	0.820903i	$-0.306529\pi$
$491$	8.73949	+	3.62001i	0.394408	+	0.163369i	−0.176660	+	0.984272i	$0.556529\pi$
$492$		0			0
$493$	0.986921	+	2.38264i	0.0444487	+	0.107309i
$494$	−1.85405	−	1.29273i	−0.0834178	−	0.0581629i
$495$		0			0
$496$	−0.641209	−	0.751931i	−0.0287911	−	0.0337627i
$497$	−49.7840			−2.23312
$498$		0			0
$499$	−0.0879672	+	0.0364372i	−0.00393795	+	0.00163115i	−0.384652	−	0.923062i	$-0.625678\pi$
$499$	−0.0879672	+	0.0364372i	−0.00393795	+	0.00163115i	0.380714	+	0.924693i	$0.375678\pi$
$500$	52.7146	+	57.0704i	2.35747	+	2.55227i
$501$		0			0
$502$	−4.06705	+	18.5195i	−0.181522	+	0.826568i
$503$	23.2085	−	23.2085i	1.03482	−	1.03482i	0.0354464	−	0.999372i	$-0.488715\pi$
$503$	23.2085	−	23.2085i	1.03482	−	1.03482i	0.999372	−	0.0354464i	$-0.0112853\pi$
$504$		0			0
$505$	−19.9875	−	19.9875i	−0.889431	−	0.889431i
$506$	17.9457	−	11.4829i	0.797785	−	0.510479i
$507$		0			0
$508$	−9.77023	−	26.5148i	−0.433484	−	1.17640i
$509$	−6.36787	−	15.3734i	−0.282251	−	0.681414i	0.717637	−	0.696418i	$-0.245224\pi$
$509$	−6.36787	−	15.3734i	−0.282251	−	0.681414i	−0.999887	+	0.0150040i	$0.995224\pi$
$510$		0			0
$511$		−	0.455008i		−	0.0201284i
$512$	0.405052	+	22.6238i	0.0179010	+	0.999840i
$513$		0			0
$514$	3.07315	+	17.2283i	0.135551	+	0.759906i
$515$	−35.7388	+	14.8035i	−1.57484	+	0.652320i
$516$		0			0
$517$	9.00672	−	21.7441i	0.396115	−	0.956307i
$518$	−22.0971	−	34.5337i	−0.970892	−	1.51733i
$519$		0			0
$520$	2.37364	+	4.05519i	0.104091	+	0.177832i
$521$	12.2835	+	12.2835i	0.538151	+	0.538151i	0.922986	−	0.384835i	$-0.125742\pi$
$521$	12.2835	+	12.2835i	0.538151	+	0.538151i	−0.384835	+	0.922986i	$0.625742\pi$
$522$		0			0
$523$	17.3222	−	41.8195i	0.757448	−	1.82864i	0.246165	−	0.969228i	$-0.420829\pi$
$523$	17.3222	−	41.8195i	0.757448	−	1.82864i	0.511282	−	0.859413i	$-0.329171\pi$
$524$	−8.33912	+	7.70265i	−0.364296	+	0.336492i
$525$		0			0
$526$	−29.7296	−	20.7289i	−1.29627	−	0.903822i
$527$			0.418678i			0.0182379i
$528$		0			0
$529$		−	8.46147i		−	0.367890i
$530$	29.6489	−	42.5228i	1.28787	−	1.84707i
$531$		0			0
$532$	−1.27791	+	32.2089i	−0.0554046	+	1.39643i
$533$	−0.882290	+	2.13004i	−0.0382162	+	0.0922621i
$534$		0			0
$535$	15.0671	+	15.0671i	0.651406	+	0.651406i
$536$	−2.04323	−	1.54854i	−0.0882543	−	0.0668870i
$537$		0			0
$538$	−14.3110	+	9.15717i	−0.616990	+	0.394794i
$539$	−8.04509	+	19.4226i	−0.346527	+	0.836589i
$540$		0			0
$541$	12.7841	−	5.29536i	0.549633	−	0.227665i	−0.0905446	−	0.995892i	$-0.528861\pi$
$541$	12.7841	−	5.29536i	0.549633	−	0.227665i	0.640178	+	0.768227i	$0.278861\pi$
$542$	8.38065	−	1.49493i	0.359980	−	0.0642127i
$543$		0			0
$544$	6.08886	−	7.40475i	0.261058	−	0.317476i
$545$			39.2493i			1.68125i
$546$		0			0
$547$	6.74549	+	16.2851i	0.288416	+	0.696299i	0.999980	−	0.00632291i	$-0.00201266\pi$
$547$	6.74549	+	16.2851i	0.288416	+	0.696299i	−0.711564	+	0.702622i	$0.752013\pi$
$548$	−10.6046	−	4.89375i	−0.453007	−	0.209051i
$549$		0			0
$550$	28.5147	+	44.5633i	1.21587	+	1.90019i
$551$	4.50392	+	4.50392i	0.191873	+	0.191873i
$552$		0			0
$553$	−24.5410	+	24.5410i	−1.04359	+	1.04359i
$554$	2.63332	+	0.578300i	0.111879	+	0.0245696i
$555$		0			0
$556$	−1.37988	+	34.7788i	−0.0585198	+	1.47495i
$557$	−5.47610	+	2.26827i	−0.232030	+	0.0961099i	−0.495669	−	0.868511i	$-0.665077\pi$
$557$	−5.47610	+	2.26827i	−0.232030	+	0.0961099i	0.263639	+	0.964621i	$0.415077\pi$
$558$		0			0
$559$	1.20850			0.0511142
$560$	30.4686	−	59.6843i	1.28753	−	2.52212i
$561$		0			0
$562$	−6.76350	+	9.70028i	−0.285301	+	0.409182i
$563$	1.36413	+	3.29330i	0.0574912	+	0.138796i	0.950015	−	0.312204i	$-0.101067\pi$
$563$	1.36413	+	3.29330i	0.0574912	+	0.138796i	−0.892524	+	0.451000i	$0.851067\pi$
$564$		0			0
$565$	19.7639	+	8.18647i	0.831473	+	0.344407i
$566$	−15.8699	−	3.48516i	−0.667061	−	0.146492i
$567$		0			0
$568$	35.3780	+	9.25360i	1.48443	+	0.388272i
$569$	14.7396	−	14.7396i	0.617917	−	0.617917i	−0.327080	−	0.944997i	$-0.606065\pi$
$569$	14.7396	−	14.7396i	0.617917	−	0.617917i	0.944997	+	0.327080i	$0.106065\pi$
$570$		0			0
$571$	−35.0355	−	14.5122i	−1.46619	−	0.607315i	−0.500202	−	0.865909i	$-0.666741\pi$
$571$	−35.0355	−	14.5122i	−1.46619	−	0.607315i	−0.965986	+	0.258593i	$0.916741\pi$
$572$	0.709188	+	1.92462i	0.0296526	+	0.0804724i
$573$		0			0
$574$	32.3693	−	5.77399i	1.35107	−	0.241002i
$575$	78.1260			3.25808
$576$		0			0
$577$	30.4146			1.26618			0.633089	−	0.774079i	$-0.281787\pi$
$577$	30.4146			1.26618			0.633089	+	0.774079i	$0.281787\pi$
$578$	19.6695	−	3.50862i	0.818144	−	0.145939i
$579$		0			0
$580$	−4.57833	−	12.4249i	−0.190105	−	0.515914i
$581$	19.5609	+	8.10238i	0.811522	+	0.336144i
$582$		0			0
$583$	16.0009	−	16.0009i	0.662689	−	0.662689i
$584$	−0.0845747	+	0.323343i	−0.00349973	+	0.0133800i
$585$		0			0
$586$	−10.4134	−	2.28687i	−0.430173	−	0.0944698i
$587$	−16.7256	−	6.92795i	−0.690338	−	0.285947i	0.00980329	−	0.999952i	$-0.496879\pi$
$587$	−16.7256	−	6.92795i	−0.690338	−	0.285947i	−0.700141	+	0.714005i	$0.746879\pi$
$588$		0			0
$589$	0.395715	+	0.955341i	0.0163052	+	0.0393642i
$590$	−16.3239	+	23.4119i	−0.672044	+	0.963853i
$591$		0			0
$592$	9.28392	+	28.6480i	0.381567	+	1.17743i
$593$	−30.1105			−1.23649			−0.618244	−	0.785986i	$-0.712156\pi$
$593$	−30.1105			−1.23649			−0.618244	+	0.785986i	$0.712156\pi$
$594$		0			0
$595$	−26.2300	+	10.8648i	−1.07533	+	0.445415i
$596$	0.417858	−	10.5318i	0.0171161	−	0.431400i
$597$		0			0
$598$	2.95842	+	0.649695i	0.120979	+	0.0265680i
$599$	3.58332	−	3.58332i	0.146410	−	0.146410i	−0.630102	−	0.776512i	$-0.716987\pi$
$599$	3.58332	−	3.58332i	0.146410	−	0.146410i	0.776512	+	0.630102i	$0.216987\pi$
$600$		0			0
$601$	−6.50070	−	6.50070i	−0.265169	−	0.265169i	0.561981	−	0.827150i	$-0.310039\pi$
$601$	−6.50070	−	6.50070i	−0.265169	−	0.265169i	−0.827150	+	0.561981i	$0.810039\pi$
$602$	−9.28924	−	14.5174i	−0.378601	−	0.591684i
$603$		0			0
$604$	−30.5637	−	14.1043i	−1.24362	−	0.573897i
$605$	−6.30397	−	15.2191i	−0.256293	−	0.618745i
$606$		0			0
$607$		−	35.4863i		−	1.44035i	−0.693795	−	0.720173i	$-0.744062\pi$
$607$		−	35.4863i		−	1.44035i	0.693795	−	0.720173i	$-0.255938\pi$
$608$	6.89495	−	22.6511i	0.279627	−	0.918623i
$609$		0			0
$610$	−41.3873	+	7.38260i	−1.67572	+	0.298913i
$611$	3.09134	−	1.28047i	0.125062	−	0.0518025i
$612$		0			0
$613$	−6.45635	+	15.5870i	−0.260770	+	0.629553i	−0.998987	−	0.0450099i	$-0.985668\pi$
$613$	−6.45635	+	15.5870i	−0.260770	+	0.629553i	0.738217	+	0.674563i	$0.235668\pi$
$614$	−22.5186	+	14.4090i	−0.908778	+	0.581500i
$615$		0			0
$616$	17.6687	−	23.3130i	0.711891	−	0.939307i
$617$	19.8183	+	19.8183i	0.797856	+	0.797856i	0.982757	−	0.184901i	$-0.0591964\pi$
$617$	19.8183	+	19.8183i	0.797856	+	0.797856i	−0.184901	+	0.982757i	$0.559196\pi$
$618$		0			0
$619$	−3.86437	+	9.32942i	−0.155322	+	0.374981i	−0.982316	−	0.187230i	$-0.940049\pi$
$619$	−3.86437	+	9.32942i	−0.155322	+	0.374981i	0.826994	+	0.562211i	$0.190049\pi$
$620$	0.0852237	−	2.14800i	0.00342267	−	0.0862658i
$621$		0			0
$622$	−22.8829	+	32.8189i	−0.917521	+	1.31592i
$623$		−	20.5522i		−	0.823408i
$624$		0			0
$625$			99.3619i			3.97447i
$626$	−26.5408	−	18.5055i	−1.06079	−	0.739630i
$627$		0			0
$628$	12.1339	−	11.2078i	0.484194	−	0.447238i
$629$	4.88262	−	11.7877i	0.194683	−	0.470006i
$630$		0			0
$631$	−21.6037	−	21.6037i	−0.860029	−	0.860029i	0.131312	−	0.991341i	$-0.458081\pi$
$631$	−21.6037	−	21.6037i	−0.860029	−	0.860029i	−0.991341	+	0.131312i	$0.958081\pi$
$632$	22.0011	−	12.8780i	0.875157	−	0.512260i
$633$		0			0
$634$	13.3805	+	20.9112i	0.531406	+	0.830491i
$635$	23.5236	−	56.7910i	0.933506	−	2.25368i
$636$		0			0
$637$	−2.76128	+	1.14376i	−0.109406	+	0.0453175i
$638$	−1.01504	−	5.69038i	−0.0401859	−	0.225284i
$639$		0			0
$640$	−32.7457	+	36.7501i	−1.29439	+	1.45268i
$641$		−	8.42611i		−	0.332811i	−0.986057	−	0.166406i	$-0.946784\pi$
$641$		−	8.42611i		−	0.332811i	0.986057	−	0.166406i	$-0.0532161\pi$
$642$		0			0
$643$	−11.7410	−	28.3452i	−0.463019	−	1.11783i	−0.967152	−	0.254201i	$-0.918188\pi$
$643$	−11.7410	−	28.3452i	−0.463019	−	1.11783i	0.504132	−	0.863626i	$-0.331812\pi$
$644$	−14.9355	−	40.5325i	−0.588541	−	1.59721i
$645$		0			0
$646$	−8.44972	+	5.40672i	−0.332450	+	0.212725i
$647$	−17.0638	−	17.0638i	−0.670846	−	0.670846i	0.287065	−	0.957911i	$-0.407320\pi$
$647$	−17.0638	−	17.0638i	−0.670846	−	0.670846i	−0.957911	+	0.287065i	$0.907320\pi$
$648$		0			0
$649$	−8.80966	+	8.80966i	−0.345809	+	0.345809i
$650$	−1.61334	+	7.34643i	−0.0632804	+	0.288151i
$651$		0			0
$652$	−26.9485	−	29.1753i	−1.05539	−	1.14259i
$653$	−6.30700	+	2.61244i	−0.246812	+	0.102233i	−0.502660	−	0.864484i	$-0.667645\pi$
$653$	−6.30700	+	2.61244i	−0.246812	+	0.102233i	0.255848	+	0.966717i	$0.417645\pi$
$654$		0			0
$655$	−24.6949			−0.964911
$656$	−24.0758	−	1.91347i	−0.940003	−	0.0747084i
$657$		0			0
$658$	−39.1437	−	27.2929i	−1.52598	−	1.06399i
$659$	−4.86215	−	11.7383i	−0.189403	−	0.457258i	0.800442	−	0.599410i	$-0.204598\pi$
$659$	−4.86215	−	11.7383i	−0.189403	−	0.457258i	−0.989845	+	0.142151i	$0.954598\pi$
$660$		0			0
$661$	−20.5534	−	8.51349i	−0.799434	−	0.331137i	−0.0547045	−	0.998503i	$-0.517422\pi$
$661$	−20.5534	−	8.51349i	−0.799434	−	0.331137i	−0.744730	+	0.667366i	$0.767422\pi$
$662$	−4.08583	+	18.6050i	−0.158800	+	0.723105i
$663$		0			0
$664$	−12.3945	−	9.39368i	−0.481001	−	0.364545i
$665$	−49.5828	+	49.5828i	−1.92274	+	1.92274i
$666$		0			0
$667$	−7.88596	−	3.26647i	−0.305345	−	0.126478i
$668$	0.273837	+	0.126369i	0.0105951	+	0.00488934i
$669$		0			0
$670$	−0.979366	−	5.49038i	−0.0378362	−	0.212112i
$671$	−18.3516			−0.708455
$672$		0			0
$673$	6.21343			0.239510			0.119755	−	0.992803i	$-0.461789\pi$
$673$	6.21343			0.239510			0.119755	+	0.992803i	$0.461789\pi$
$674$	1.08145	+	6.06265i	0.0416558	+	0.233525i
$675$		0			0
$676$	10.7721	−	23.3428i	0.414310	−	0.897798i
$677$	−7.24712	−	3.00186i	−0.278529	−	0.115371i	0.239046	−	0.971008i	$-0.423165\pi$
$677$	−7.24712	−	3.00186i	−0.278529	−	0.115371i	−0.517575	+	0.855638i	$0.673165\pi$
$678$		0			0
$679$	−6.01303	+	6.01303i	−0.230759	+	0.230759i
$680$	20.6593	−	2.84537i	0.792250	−	0.109115i
$681$		0			0
$682$	0.201281	−	0.916544i	0.00770745	−	0.0350963i
$683$	−20.8146	−	8.62168i	−0.796448	−	0.329899i	−0.0529151	−	0.998599i	$-0.516851\pi$
$683$	−20.8146	−	8.62168i	−0.796448	−	0.329899i	−0.743533	+	0.668700i	$0.766851\pi$
$684$		0			0
$685$	−9.72269	−	23.4727i	−0.371485	−	0.896844i
$686$	3.69557	+	2.57673i	0.141098	+	0.0983799i
$687$		0			0
$688$	3.90280	+	12.0431i	0.148793	+	0.459140i
$689$	3.21709			0.122561
$690$		0			0
$691$	−3.70220	+	1.53350i	−0.140839	+	0.0583372i	−0.451989	−	0.892023i	$-0.649286\pi$
$691$	−3.70220	+	1.53350i	−0.140839	+	0.0583372i	0.311151	+	0.950361i	$0.399286\pi$
$692$	21.5685	−	19.9223i	0.819912	−	0.757333i
$693$		0			0
$694$	8.61173	−	39.2139i	0.326897	−	1.48854i
$695$	−53.5389	+	53.5389i	−2.03085	+	2.03085i
$696$		0			0
$697$	7.23547	+	7.23547i	0.274063	+	0.274063i
$698$	−30.8594	+	19.7460i	−1.16805	+	0.747398i
$699$		0			0
$700$	100.652	−	37.0883i	3.80427	−	1.40180i
$701$	−0.0211624	−	0.0510906i	−0.000799293	−	0.00192966i	0.923479	−	0.383648i	$-0.125332\pi$
$701$	−0.0211624	−	0.0510906i	−0.000799293	−	0.00192966i	−0.924279	+	0.381718i	$0.875332\pi$
$702$		0			0
$703$		−	31.5120i		−	1.18850i
$704$	−16.8892	+	13.2828i	−0.636535	+	0.500613i
$705$		0			0
$706$	−3.94448	−	22.1130i	−0.148453	−	0.832233i
$707$	−23.1132	+	9.57382i	−0.869263	+	0.360060i
$708$		0			0
$709$	−3.05325	+	7.37121i	−0.114667	+	0.276831i	−0.970786	−	0.239948i	$-0.922869\pi$
$709$	−3.05325	+	7.37121i	−0.114667	+	0.276831i	0.856118	+	0.516780i	$0.172869\pi$
$710$	42.8748	+	67.0054i	1.60906	+	2.51467i
$711$		0			0
$712$	−3.82015	+	14.6050i	−0.143166	+	0.547347i
$713$	−0.979855	−	0.979855i	−0.0366958	−	0.0366958i
$714$		0			0
$715$	−1.70750	+	4.12227i	−0.0638568	+	0.154164i
$716$	28.0239	+	30.3395i	1.04730	+	1.13384i
$717$		0			0
$718$	24.5923	+	17.1469i	0.917775	+	0.639916i
$719$			18.5820i			0.692993i	0.938051	+	0.346496i	$0.112629\pi$
$719$			18.5820i			0.692993i	−0.938051	+	0.346496i	$0.887371\pi$
$720$		0			0
$721$			34.2371i			1.27506i
$722$	1.19782	−	1.71792i	0.0445782	−	0.0639345i
$723$		0			0
$724$	−49.6783	−	1.97103i	−1.84628	−	0.0732527i
$725$	8.11139	−	19.5826i	0.301249	−	0.727280i
$726$		0			0
$727$	6.06048	+	6.06048i	0.224771	+	0.224771i	0.810504	−	0.585733i	$-0.199193\pi$
$727$	6.06048	+	6.06048i	0.224771	+	0.224771i	−0.585733	+	0.810504i	$0.699193\pi$
$728$	4.11983	−	0.567416i	0.152691	−	0.0210298i
$729$		0			0
$730$	−0.612406	+	0.391860i	−0.0226662	+	0.0145034i
$731$	2.05257	−	4.95533i	0.0759169	−	0.183280i
$732$		0			0
$733$	−4.62261	+	1.91475i	−0.170740	+	0.0707229i	−0.466416	−	0.884565i	$-0.654455\pi$
$733$	−4.62261	+	1.91475i	−0.170740	+	0.0707229i	0.295676	+	0.955288i	$0.404455\pi$
$734$	−8.31249	+	1.48277i	−0.306820	+	0.0547301i
$735$		0			0
$736$	3.07964	+	31.5798i	0.113517	+	1.16405i
$737$		−	2.43450i		−	0.0896758i
$738$		0			0
$739$	9.64164	+	23.2770i	0.354674	+	0.856258i	0.996030	+	0.0890150i	$0.0283719\pi$
$739$	9.64164	+	23.2770i	0.354674	+	0.856258i	−0.641357	+	0.767243i	$0.721628\pi$
$740$	−27.4494	+	59.4820i	−1.00906	+	2.18660i
$741$		0			0
$742$	−24.7284	−	38.6459i	−0.907808	−	1.41874i
$743$	34.5314	+	34.5314i	1.26684	+	1.26684i	0.947714	+	0.319122i	$0.103388\pi$
$743$	34.5314	+	34.5314i	1.26684	+	1.26684i	0.319122	+	0.947714i	$0.396612\pi$
$744$		0			0
$745$	16.2128	−	16.2128i	0.593992	−	0.593992i
$746$	−27.9415	−	6.13620i	−1.02301	−	0.224662i
$747$		0			0
$748$	9.09621	+	0.360900i	0.332591	+	0.0131958i
$749$	17.4233	−	7.21698i	0.636635	−	0.263703i
$750$		0			0
$751$	41.8141			1.52582			0.762910	−	0.646505i	$-0.223770\pi$
$751$	41.8141			1.52582			0.762910	+	0.646505i	$0.223770\pi$
$752$	22.7437	+	26.6710i	0.829376	+	0.972591i
$753$		0			0
$754$	0.470005	−	0.674087i	0.0171166	−	0.0245488i
$755$	−28.0218	−	67.6507i	−1.01982	−	2.46206i
$756$		0			0
$757$	10.9506	+	4.53588i	0.398005	+	0.164859i	0.572703	−	0.819763i	$-0.305895\pi$
$757$	10.9506	+	4.53588i	0.398005	+	0.164859i	−0.174698	+	0.984622i	$0.555895\pi$
$758$	−39.7112	−	8.72093i	−1.44238	−	0.316758i
$759$		0			0
$760$	44.4512	−	26.0188i	1.61242	−	0.943802i
$761$	24.3672	−	24.3672i	0.883311	−	0.883311i	−0.110559	−	0.993870i	$-0.535264\pi$
$761$	24.3672	−	24.3672i	0.883311	−	0.883311i	0.993870	+	0.110559i	$0.0352641\pi$
$762$		0			0
$763$	32.0937	+	13.2936i	1.16187	+	0.481262i
$764$	25.4742	−	9.38679i	0.921624	−	0.339602i
$765$		0			0
$766$	−33.3380	+	5.94678i	−1.20455	+	0.214866i
$767$	−1.77124			−0.0639559
$768$		0			0
$769$	−13.3474			−0.481321			−0.240660	−	0.970609i	$-0.577364\pi$
$769$	−13.3474			−0.481321			−0.240660	+	0.970609i	$0.577364\pi$
$770$	62.6444	−	11.1744i	2.25755	−	0.402698i
$771$		0			0
$772$	23.6896	−	8.72918i	0.852606	−	0.314170i
$773$	−39.8083	−	16.4891i	−1.43180	−	0.593072i	−0.474007	−	0.880521i	$-0.657193\pi$
$773$	−39.8083	−	16.4891i	−1.43180	−	0.593072i	−0.957796	+	0.287449i	$0.907193\pi$
$774$		0			0
$775$	2.43320	−	2.43320i	0.0874032	−	0.0874032i
$776$	5.39072	−	3.15537i	0.193515	−	0.113271i
$777$		0			0
$778$	−0.758893	−	0.166660i	−0.0272076	−	0.00597504i
$779$	23.3486	+	9.67129i	0.836549	+	0.346510i
$780$		0			0
$781$	13.2885	+	32.0814i	0.475501	+	1.14796i
$782$	7.68870	−	11.0272i	0.274947	−	0.394333i
$783$		0			0
$784$	−20.3154	−	23.8234i	−0.725549	−	0.850835i
$785$	35.9324			1.28248
$786$		0			0
$787$	−18.6805	+	7.73773i	−0.665889	+	0.275820i	−0.689914	−	0.723891i	$-0.742352\pi$
$787$	−18.6805	+	7.73773i	−0.665889	+	0.275820i	0.0240253	+	0.999711i	$0.492352\pi$
$788$	−35.5453	−	1.41029i	−1.26625	−	0.0502395i
$789$		0			0
$790$	54.1653	+	11.8952i	1.92712	+	0.423212i
$791$	13.3880	−	13.3880i	0.476021	−	0.476021i
$792$		0			0
$793$	−1.84486	−	1.84486i	−0.0655128	−	0.0655128i
$794$	−7.14195	−	11.1616i	−0.253458	−	0.396109i
$795$		0			0
$796$	−11.5538	+	25.0367i	−0.409512	+	0.887402i
$797$	14.4902	+	34.9825i	0.513270	+	1.23914i	0.941970	+	0.335697i	$0.108972\pi$
$797$	14.4902	+	34.9825i	0.513270	+	1.23914i	−0.428700	+	0.903447i	$0.641028\pi$
$798$		0			0
$799$		−	14.8505i		−	0.525373i
$800$	−78.4198	+	7.64745i	−2.77256	+	0.270378i
$801$		0			0
$802$	−7.32858	+	1.30726i	−0.258781	+	0.0461610i
$803$	−0.293212	+	0.121453i	−0.0103472	+	0.00428597i
$804$		0			0
$805$	35.9599	−	86.8150i	1.26742	−	3.05983i
$806$	0.112373	−	0.0719043i	0.00395818	−	0.00253272i
$807$		0			0
$808$	18.2045	−	2.50727i	0.640432	−	0.0882055i
$809$	36.6401	+	36.6401i	1.28820	+	1.28820i	0.935881	+	0.352317i	$0.114606\pi$
$809$	36.6401	+	36.6401i	1.28820	+	1.28820i	0.352317	+	0.935881i	$0.385394\pi$
$810$		0			0
$811$	−2.81717	+	6.80125i	−0.0989242	+	0.238824i	−0.965592	−	0.260061i	$-0.916257\pi$
$811$	−2.81717	+	6.80125i	−0.0989242	+	0.238824i	0.866668	+	0.498886i	$0.166257\pi$
$812$	−11.7103	−	0.464617i	−0.410952	−	0.0163049i
$813$		0			0
$814$	−16.3557	+	23.4575i	−0.573267	+	0.822185i
$815$		−	86.3978i		−	3.02638i
$816$		0			0
$817$		−	13.2471i		−	0.463457i
$818$	−16.8196	−	11.7274i	−0.588085	−	0.410040i
$819$		0			0
$820$	−35.6483	−	38.5939i	−1.24489	−	1.34776i
$821$	−4.71525	+	11.3836i	−0.164564	+	0.397291i	−0.984553	−	0.175087i	$-0.943979\pi$
$821$	−4.71525	+	11.3836i	−0.164564	+	0.397291i	0.819989	+	0.572379i	$0.193979\pi$
$822$		0			0
$823$	31.3892	+	31.3892i	1.09416	+	1.09416i	0.995080	+	0.0990779i	$0.0315893\pi$
$823$	31.3892	+	31.3892i	1.09416	+	1.09416i	0.0990779	+	0.995080i	$0.468411\pi$
$824$	6.36382	−	24.3299i	0.221694	−	0.847573i
$825$		0			0
$826$	13.6148	+	21.2774i	0.473719	+	0.740336i
$827$	−1.55224	+	3.74744i	−0.0539767	+	0.130311i	−0.948567	−	0.316575i	$-0.897467\pi$
$827$	−1.55224	+	3.74744i	−0.0539767	+	0.130311i	0.894591	+	0.446886i	$0.147467\pi$
$828$		0			0
$829$	−38.2591	+	15.8474i	−1.32879	+	0.550405i	−0.930311	−	0.366771i	$-0.880463\pi$
$829$	−38.2591	+	15.8474i	−1.32879	+	0.550405i	−0.398483	+	0.917176i	$0.630463\pi$
$830$	−5.94096	−	33.3053i	−0.206214	−	1.15605i
$831$		0			0
$832$	−3.03314	−	0.362550i	−0.105155	−	0.0125692i
$833$			13.2650i			0.459603i
$834$		0			0
$835$	0.251063	+	0.606121i	0.00868841	+	0.0209757i
$836$	21.0969	−	7.77382i	0.729651	−	0.268863i
$837$		0			0
$838$	−28.2784	+	18.0945i	−0.976860	+	0.625063i
$839$	25.6778	+	25.6778i	0.886496	+	0.886496i	0.994185	−	0.107689i	$-0.0343449\pi$
$839$	25.6778	+	25.6778i	0.886496	+	0.886496i	−0.107689	+	0.994185i	$0.534345\pi$
$840$		0			0
$841$	18.8686	−	18.8686i	0.650641	−	0.650641i
$842$	10.3367	−	47.0689i	0.356228	−	1.62210i
$843$		0			0
$844$	−15.8076	+	14.6011i	−0.544121	+	0.502592i
$845$	51.6677	−	21.4015i	1.77742	−	0.736232i
$846$		0			0
$847$	−14.5796			−0.500962
$848$	10.3894	+	32.0594i	0.356774	+	1.10092i
$849$		0			0
$850$	27.3831	+	19.0928i	0.939232	+	0.654877i
$851$	16.1603	+	39.0144i	0.553967	+	1.33740i
$852$		0			0
$853$	52.0914	+	21.5770i	1.78358	+	0.738782i	0.991773	+	0.128005i	$0.0408575\pi$
$853$	52.0914	+	21.5770i	1.78358	+	0.738782i	0.791803	+	0.610776i	$0.209143\pi$
$854$	−7.98109	+	36.3423i	−0.273107	+	1.24361i
$855$		0			0
$856$	−13.7230	+	1.89004i	−0.469043	+	0.0646004i
$857$	30.1094	−	30.1094i	1.02852	−	1.02852i	0.0289357	−	0.999581i	$-0.490788\pi$
$857$	30.1094	−	30.1094i	1.02852	−	1.02852i	0.999581	−	0.0289357i	$-0.00921179\pi$
$858$		0			0
$859$	5.58448	+	2.31317i	0.190540	+	0.0789243i	0.475913	−	0.879492i	$-0.342118\pi$
$859$	5.58448	+	2.31317i	0.190540	+	0.0789243i	−0.285373	+	0.958416i	$0.592118\pi$
$860$	−11.5392	+	25.0052i	−0.393484	+	0.852670i
$861$		0			0
$862$	−3.77306	−	21.1520i	−0.128511	−	0.720439i
$863$	10.1934			0.346987			0.173494	−	0.984835i	$-0.444494\pi$
$863$	10.1934			0.346987			0.173494	+	0.984835i	$0.444494\pi$
$864$		0			0
$865$	63.8716			2.17170
$866$	9.11113	+	51.0775i	0.309609	+	1.73568i
$867$		0			0
$868$	−1.72753	−	0.797209i	−0.0586362	−	0.0270590i
$869$	22.3650	+	9.26391i	0.758682	+	0.314257i
$870$		0			0
$871$	0.244736	−	0.244736i	0.00829257	−	0.00829257i
$872$	−20.3358	−	15.4123i	−0.688656	−	0.521925i
$873$		0			0
$874$	7.12168	−	32.4289i	0.240894	−	1.09693i
$875$	138.193	+	57.2415i	4.67178	+	1.93511i
$876$		0			0
$877$	−6.80087	−	16.4188i	−0.229649	−	0.554422i	0.766486	−	0.642262i	$-0.222004\pi$
$877$	−6.80087	−	16.4188i	−0.229649	−	0.554422i	−0.996135	+	0.0878397i	$0.972004\pi$
$878$	−20.9022	−	14.5740i	−0.705415	−	0.491849i
$879$		0			0
$880$	−46.5940	−	3.70314i	−1.57068	−	0.124833i
$881$	5.21177			0.175589			0.0877945	−	0.996139i	$-0.472018\pi$
$881$	5.21177			0.175589			0.0877945	+	0.996139i	$0.472018\pi$
$882$		0			0
$883$	24.3949	−	10.1047i	0.820955	−	0.340051i	0.0676391	−	0.997710i	$-0.478453\pi$
$883$	24.3949	−	10.1047i	0.820955	−	0.340051i	0.753315	+	0.657659i	$0.228453\pi$
$884$	0.878148	+	0.950710i	0.0295353	+	0.0319758i
$885$		0			0
$886$	5.78848	−	26.3582i	0.194468	−	0.885520i
$887$	−19.5814	+	19.5814i	−0.657479	+	0.657479i	−0.954783	−	0.297304i	$-0.903913\pi$
$887$	−19.5814	+	19.5814i	−0.657479	+	0.657479i	0.297304	+	0.954783i	$0.403913\pi$
$888$		0			0
$889$	−38.4700	−	38.4700i	−1.29024	−	1.29024i
$890$	−27.6617	+	17.6999i	−0.927223	+	0.593302i
$891$		0			0
$892$	17.9243	+	48.6437i	0.600150	+	1.62871i
$893$	−14.0360	−	33.8859i	−0.469697	−	1.13395i
$894$		0			0
$895$			89.8455i			3.00320i
$896$	18.9592	+	39.2230i	0.633384	+	1.31035i
$897$		0			0
$898$	−7.97508	−	44.7087i	−0.266132	−	1.49195i
$899$	−0.347338	+	0.143872i	−0.0115844	+	0.00479840i
$900$		0			0
$901$	5.46403	−	13.1913i	0.182033	−	0.439467i
$902$	−12.3610	−	19.3179i	−0.411575	−	0.643216i
$903$		0			0
$904$	−12.0024	+	7.02541i	−0.399193	+	0.233661i
$905$	−76.4755	−	76.4755i	−2.54213	−	2.54213i
$906$		0			0
$907$	10.2086	−	24.6458i	0.338971	−	0.818349i	−0.658844	−	0.752280i	$-0.728954\pi$
$907$	10.2086	−	24.6458i	0.338971	−	0.818349i	0.997815	−	0.0660694i	$-0.0210459\pi$
$908$	−9.32738	+	8.61548i	−0.309540	+	0.285915i
$909$		0			0
$910$	7.42089	+	5.17420i	0.246000	+	0.171523i
$911$		−	3.31050i		−	0.109682i	−0.998495	−	0.0548409i	$-0.982535\pi$
$911$		−	3.31050i		−	0.109682i	0.998495	−	0.0548409i	$-0.0174652\pi$
$912$		0			0
$913$		−	14.7680i		−	0.488749i
$914$	−25.9767	+	37.2560i	−0.859232	+	1.23232i
$915$		0			0
$916$	1.16045	−	29.2482i	0.0383422	−	0.966386i
$917$	−8.36411	+	20.1928i	−0.276207	+	0.666823i
$918$		0			0
$919$	14.5101	+	14.5101i	0.478643	+	0.478643i	0.904698	−	0.426054i	$-0.140097\pi$
$919$	14.5101	+	14.5101i	0.478643	+	0.478643i	−0.426054	+	0.904698i	$0.640097\pi$
$920$	−41.6910	+	55.0093i	−1.37451	+	1.81360i
$921$		0			0
$922$	36.6403	−	23.4451i	1.20669	−	0.772122i
$923$	−1.88921	+	4.56097i	−0.0621843	+	0.150126i
$924$		0			0
$925$	−96.8816	+	40.1297i	−3.18545	+	1.31946i
$926$	57.1272	−	10.1903i	1.87732	−	0.334873i
$927$		0			0
$928$	8.23535	+	2.50683i	0.270339	+	0.0822907i
$929$		−	53.8129i		−	1.76554i	−0.469803	−	0.882771i	$-0.655675\pi$
$929$		−	53.8129i		−	1.76554i	0.469803	−	0.882771i	$-0.344325\pi$
$930$		0			0
$931$	12.5374	+	30.2680i	0.410897	+	0.991994i
$932$	−24.4465	−	11.2814i	−0.800773	−	0.369535i
$933$		0			0
$934$	−3.49350	−	5.45970i	−0.114311	−	0.178647i
$935$	14.0028	+	14.0028i	0.457942	+	0.457942i
$936$		0			0
$937$	21.2984	−	21.2984i	0.695790	−	0.695790i	−0.267710	−	0.963500i	$-0.586267\pi$
$937$	21.2984	−	21.2984i	0.695790	−	0.695790i	0.963500	+	0.267710i	$0.0862668\pi$
$938$	−4.82112	−	1.05876i	−0.157415	−	0.0345698i
$939$		0			0
$940$	−3.02288	+	76.1895i	−0.0985956	+	2.48503i
$941$	−32.2242	+	13.3477i	−1.05048	+	0.435122i	−0.840062	−	0.542490i	$-0.817482\pi$
$941$	−32.2242	+	13.3477i	−1.05048	+	0.435122i	−0.210415	+	0.977612i	$0.567482\pi$
$942$		0			0
$943$	−33.8671			−1.10286
$944$	−5.72014	−	17.6510i	−0.186175	−	0.574492i
$945$		0			0
$946$	−6.87564	+	9.86112i	−0.223546	+	0.320613i
$947$	−3.53793	−	8.54132i	−0.114967	−	0.277556i	0.855913	−	0.517119i	$-0.172996\pi$
$947$	−3.53793	−	8.54132i	−0.114967	−	0.277556i	−0.970881	+	0.239564i	$0.922996\pi$
$948$		0			0
$949$	−0.0416857	−	0.0172668i	−0.00135317	−	0.000560503i
$950$	80.5284	+	17.6847i	2.61269	+	0.573769i
$951$		0			0
$952$	4.67064	−	17.8566i	0.151376	−	0.578737i
$953$	−29.5436	+	29.5436i	−0.957010	+	0.957010i	−0.999113	−	0.0421028i	$-0.986594\pi$
$953$	−29.5436	+	29.5436i	−0.957010	+	0.957010i	0.0421028	+	0.999113i	$0.486594\pi$
$954$		0			0
$955$	54.5622	+	22.6004i	1.76559	+	0.731331i
$956$	2.25372	+	6.11622i	0.0728904	+	0.197813i
$957$		0			0
$958$	24.0431	−	4.28878i	0.776799	−	0.138564i
$959$	−22.4864			−0.726123
$960$		0			0
$961$	30.9390			0.998031
$962$	−4.00236	+	0.713936i	−0.129041	+	0.0230182i
$963$		0			0
$964$	−4.57753	−	12.4227i	−0.147432	−	0.400107i
$965$	50.7397	+	21.0171i	1.63337	+	0.676564i
$966$		0			0
$967$	11.9235	−	11.9235i	0.383432	−	0.383432i	−0.488905	−	0.872337i	$-0.662603\pi$
$967$	11.9235	−	11.9235i	0.383432	−	0.383432i	0.872337	+	0.488905i	$0.162603\pi$
$968$	10.3607	+	2.70999i	0.333006	+	0.0871024i
$969$		0			0
$970$	13.2716	+	2.91456i	0.426125	+	0.0935808i
$971$	1.10035	+	0.455781i	0.0353120	+	0.0146267i	0.400270	−	0.916397i	$-0.368917\pi$
$971$	1.10035	+	0.455781i	0.0353120	+	0.0146267i	−0.364958	+	0.931024i	$0.618917\pi$
$972$		0			0
$973$	25.6447	+	61.9117i	0.822130	+	1.98480i
$974$	15.9396	−	22.8608i	0.510738	−	0.732507i
$975$		0			0
$976$	12.4267	−	24.3425i	0.397770	−	0.779184i
$977$	−14.9871			−0.479479			−0.239739	−	0.970837i	$-0.577062\pi$
$977$	−14.9871			−0.479479			−0.239739	+	0.970837i	$0.577062\pi$
$978$		0			0
$979$	−13.2441	+	5.48588i	−0.423283	+	0.175330i
$980$	2.70014	−	68.0549i	0.0862527	−	2.17394i
$981$		0			0
$982$	−13.0665	−	2.86951i	−0.416967	−	0.0915697i
$983$	−6.59049	+	6.59049i	−0.210204	+	0.210204i	−0.804354	−	0.594150i	$-0.797489\pi$
$983$	−6.59049	+	6.59049i	−0.210204	+	0.210204i	0.594150	+	0.804354i	$0.297489\pi$
$984$		0			0
$985$	−54.7190	−	54.7190i	−1.74349	−	1.74349i
$986$	−1.96575	−	3.07210i	−0.0626021	−	0.0978356i
$987$		0			0
$988$	2.90233	+	1.33935i	0.0923353	+	0.0426103i
$989$	6.79350	+	16.4010i	0.216021	+	0.521520i
$990$		0			0
$991$		−	37.2049i		−	1.18185i	−0.806726	−	0.590926i	$-0.798762\pi$
$991$		−	37.2049i		−	1.18185i	0.806726	−	0.590926i	$-0.201238\pi$
$992$	1.07945	+	0.887625i	0.0342727	+	0.0281821i
$993$		0			0
$994$	69.3111	−	12.3636i	2.19842	−	0.392150i
$995$	−55.4171	+	22.9545i	−1.75684	+	0.727707i
$996$		0			0
$997$	1.77382	−	4.28237i	0.0561773	−	0.135624i	−0.893299	−	0.449463i	$-0.851615\pi$
$997$	1.77382	−	4.28237i	0.0561773	−	0.135624i	0.949476	+	0.313839i	$0.101615\pi$
$998$	0.113422	−	0.0725754i	0.00359032	−	0.00229734i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.107.1	yes	32
3.2	odd	2		288.2.w.b.107.8	yes	32
4.3	odd	2		1152.2.w.b.719.8		32
12.11	even	2		1152.2.w.a.719.1		32
32.3	odd	8		288.2.w.b.35.8	yes	32
32.29	even	8		1152.2.w.a.431.1		32
96.29	odd	8		1152.2.w.b.431.8		32
96.35	even	8	inner	288.2.w.a.35.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.1	✓	32	96.35	even	8	inner
288.2.w.a.107.1	yes	32	1.1	even	1	trivial
288.2.w.b.35.8	yes	32	32.3	odd	8
288.2.w.b.107.8	yes	32	3.2	odd	2
1152.2.w.a.431.1		32	32.29	even	8
1152.2.w.a.719.1		32	12.11	even	2
1152.2.w.b.431.8		32	96.29	odd	8
1152.2.w.b.719.8		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)

\(f(q)\)	\(=\)	\(q+(-1.39224 + 0.248345i) q^{2} +(1.87665 - 0.691511i) q^{4} +(4.01952 + 1.66494i) q^{5} +(2.72280 - 2.72280i) q^{7} +(-2.44101 + 1.42881i) q^{8} +O(q^{10})\)	\(q+(-1.39224 + 0.248345i) q^{2} +(1.87665 - 0.691511i) q^{4} +(4.01952 + 1.66494i) q^{5} +(2.72280 - 2.72280i) q^{7} +(-2.44101 + 1.42881i) q^{8} +(-6.00960 - 1.31976i) q^{10} +(-2.48139 - 1.02782i) q^{11} +(-0.146124 - 0.352776i) q^{13} +(-3.11459 + 4.46698i) q^{14} +(3.04362 - 2.59545i) q^{16} -1.69470 q^{17} +(-3.86698 + 1.60175i) q^{19} +(8.69455 + 0.344964i) q^{20} +(3.70993 + 0.814734i) q^{22} +(3.96620 - 3.96620i) q^{23} +(9.84898 + 9.84898i) q^{25} +(0.291050 + 0.454858i) q^{26} +(3.22690 - 6.99259i) q^{28} +(-0.582357 - 1.40593i) q^{29} -0.247051i q^{31} +(-3.59288 + 4.36935i) q^{32} +(2.35943 - 0.420871i) q^{34} +(15.4777 - 6.41106i) q^{35} +(-2.88111 + 6.95561i) q^{37} +(4.98596 - 3.19037i) q^{38} +(-12.1905 + 1.67898i) q^{40} +(-4.26947 - 4.26947i) q^{41} +(-1.21117 + 2.92402i) q^{43} +(-5.36744 - 0.212958i) q^{44} +(-4.53690 + 6.50688i) q^{46} +8.76291i q^{47} -7.82731i q^{49} +(-16.1581 - 11.2662i) q^{50} +(-0.518173 - 0.560989i) q^{52} +(-3.22418 + 7.78387i) q^{53} +(-8.26271 - 8.26271i) q^{55} +(-2.75603 + 10.5367i) q^{56} +(1.15994 + 1.81277i) q^{58} +(1.77515 - 4.28559i) q^{59} +(6.31262 - 2.61477i) q^{61} +(0.0613541 + 0.343954i) q^{62} +(3.91703 - 6.97545i) q^{64} -1.66128i q^{65} +(0.346872 + 0.837424i) q^{67} +(-3.18036 + 1.17191i) q^{68} +(-19.9564 + 12.7695i) q^{70} +(-9.14205 - 9.14205i) q^{71} +(0.0835551 - 0.0835551i) q^{73} +(2.28379 - 10.3994i) q^{74} +(-6.14933 + 5.67999i) q^{76} +(-9.55488 + 3.95776i) q^{77} -9.01313 q^{79} +(16.5552 - 5.36501i) q^{80} +(7.00441 + 4.88381i) q^{82} +(2.10417 + 5.07993i) q^{83} +(-6.81189 - 2.82158i) q^{85} +(0.960066 - 4.37171i) q^{86} +(7.52564 - 1.03649i) q^{88} +(3.77409 - 3.77409i) q^{89} +(-1.35841 - 0.562670i) q^{91} +(4.70049 - 10.1858i) q^{92} +(-2.17623 - 12.2000i) q^{94} -18.2102 q^{95} -2.20840 q^{97} +(1.94388 + 10.8975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 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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