LMFDB - Embedded newform 288.2.w.a.35.1

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			35.1
Character	$\chi$	$=$	288.35
Dual form			288.2.w.a.107.1

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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	0.810217	−	0.586130i	$-0.199349\pi$
$5$	4.01952	−	1.66494i	1.79758	−	0.744583i	0.987366	−	0.158453i	$-0.0506508\pi$
$6$		0			0
$7$	2.72280	+	2.72280i	1.02912	+	1.02912i	0.999563	+	0.0295596i	$0.00941050\pi$
$7$	2.72280	+	2.72280i	1.02912	+	1.02912i	0.0295596	+	0.999563i	$0.490590\pi$
$8$	−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	−0.723993	−	0.689807i	$-0.757695\pi$
$11$	−2.48139	+	1.02782i	−0.748166	+	0.309900i	−0.0241729	+	0.999708i	$0.507695\pi$
$12$		0			0
$13$	−0.146124	+	0.352776i	−0.0405276	+	0.0978423i	−0.942847	−	0.333225i	$-0.891863\pi$
$13$	−0.146124	+	0.352776i	−0.0405276	+	0.0978423i	0.902320	+	0.431068i	$0.141863\pi$
$14$	−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	−0.107881	−	0.994164i	$-0.534407\pi$
$19$	−3.86698	−	1.60175i	−0.887145	−	0.367468i	−0.779264	+	0.626696i	$0.784407\pi$
$20$	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	0.987102	−	0.160092i	$-0.0511792\pi$
$23$	3.96620	+	3.96620i	0.827010	+	0.827010i	−0.160092	+	0.987102i	$0.551179\pi$
$24$		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	−0.968681	−	0.248307i	$-0.920126\pi$
$29$	−0.582357	+	1.40593i	−0.108141	+	0.261075i	0.860541	+	0.509382i	$0.170126\pi$
$30$		0			0
$31$			0.247051i			0.0443717i	0.999754	+	0.0221859i	$0.00706256\pi$
$31$			0.247051i			0.0443717i	−0.999754	+	0.0221859i	$0.992937\pi$
$32$	−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	−0.962538	−	0.271148i	$-0.912597\pi$
$37$	−2.88111	−	6.95561i	−0.473651	−	1.14350i	0.488886	−	0.872347i	$-0.337403\pi$
$38$	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	−0.956969	−	0.290190i	$-0.906281\pi$
$41$	−4.26947	+	4.26947i	−0.666779	+	0.666779i	0.290190	+	0.956969i	$0.406281\pi$
$42$		0			0
$43$	−1.21117	−	2.92402i	−0.184701	−	0.445908i	0.804223	−	0.594327i	$-0.202582\pi$
$43$	−1.21117	−	2.92402i	−0.184701	−	0.445908i	−0.988925	+	0.148419i	$0.952582\pi$
$44$	−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	$-0.779307\pi$
$47$		−	8.76291i		−	1.27820i	0.769123	−	0.639101i	$-0.220693\pi$
$48$		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	−0.974935	−	0.222489i	$-0.928582\pi$
$53$	−3.22418	−	7.78387i	−0.442876	−	1.06920i	0.532059	−	0.846707i	$-0.321418\pi$
$54$		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	0.996308	−	0.0858528i	$-0.0273615\pi$
$59$	1.77515	+	4.28559i	0.231105	+	0.557936i	−0.765203	+	0.643789i	$0.777361\pi$
$60$		0			0
$61$	6.31262	+	2.61477i	0.808249	+	0.334788i	0.748255	−	0.663411i	$-0.230892\pi$
$61$	6.31262	+	2.61477i	0.808249	+	0.334788i	0.0599937	+	0.998199i	$0.480892\pi$
$62$	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	−0.901274	−	0.433250i	$-0.857367\pi$
$67$	0.346872	−	0.837424i	0.0423772	−	0.102308i	0.943651	+	0.330943i	$0.107367\pi$
$68$	−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	−0.0889229	+	0.996039i	$0.528342\pi$
$71$	−9.14205	+	9.14205i	−1.08496	+	1.08496i	−0.996039	+	0.0889229i	$0.971658\pi$
$72$		0			0
$73$	0.0835551	+	0.0835551i	0.00977939	+	0.00977939i	0.711980	−	0.702200i	$-0.247799\pi$
$73$	0.0835551	+	0.0835551i	0.00977939	+	0.00977939i	−0.702200	+	0.711980i	$0.747799\pi$
$74$	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	−0.765328	−	0.643640i	$-0.777423\pi$
$83$	2.10417	−	5.07993i	0.230963	−	0.557594i	0.996291	+	0.0860461i	$0.0274232\pi$
$84$		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	0.878252	−	0.478199i	$-0.158710\pi$
$89$	3.77409	+	3.77409i	0.400053	+	0.400053i	−0.478199	+	0.878252i	$0.658710\pi$
$90$		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	−0.660774	−	0.750585i	$-0.729772\pi$
$101$	−6.00246	+	2.48630i	−0.597267	+	0.247396i	0.0635063	+	0.997981i	$0.479772\pi$
$102$		0			0
$103$	−6.28711	−	6.28711i	−0.619487	−	0.619487i	0.325913	−	0.945400i	$-0.394328\pi$
$103$	−6.28711	−	6.28711i	−0.619487	−	0.619487i	−0.945400	+	0.325913i	$0.894328\pi$
$104$	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	−0.153091	−	0.988212i	$-0.548923\pi$
$107$	4.52481	−	1.87424i	0.437430	−	0.181189i	0.590520	+	0.807023i	$0.298923\pi$
$108$		0			0
$109$	3.45233	−	8.33466i	0.330673	−	0.798316i	−0.667866	−	0.744282i	$-0.732792\pi$
$109$	3.45233	−	8.33466i	0.330673	−	0.798316i	0.998539	−	0.0540343i	$-0.0172080\pi$
$110$	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	$0.215662\pi$
$127$			14.1288i			1.25373i	−0.779128	+	0.626865i	$0.784338\pi$
$128$	−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	0.141646	−	0.989917i	$-0.454760\pi$
$131$	−5.24402	−	2.17214i	−0.458172	−	0.189781i	−0.599818	+	0.800136i	$0.704760\pi$
$132$		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	−0.861146	−	0.508358i	$-0.830253\pi$
$137$	−4.12927	+	4.12927i	−0.352787	+	0.352787i	0.508358	+	0.861146i	$0.330253\pi$
$138$		0			0
$139$	−6.65987	−	16.0783i	−0.564883	−	1.36375i	−0.905820	−	0.423662i	$-0.860744\pi$
$139$	−6.65987	−	16.0783i	−0.564883	−	1.36375i	0.340938	−	0.940086i	$-0.389256\pi$
$140$	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	0.984706	−	0.174223i	$-0.0557414\pi$
$149$	2.01676	+	4.86889i	0.165219	+	0.398875i	−0.819487	+	0.573098i	$0.805741\pi$
$150$		0			0
$151$	−11.9010	+	11.9010i	−0.968489	+	0.968489i	−0.999518	−	0.0310293i	$-0.990121\pi$
$151$	−11.9010	+	11.9010i	−0.968489	+	0.968489i	0.0310293	+	0.999518i	$0.490121\pi$
$152$	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	0.665786	−	0.746142i	$-0.268096\pi$
$157$	7.63032	+	3.16058i	0.608966	+	0.252242i	−0.0568202	+	0.998384i	$0.518096\pi$
$158$	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	0.283149	+	0.959076i	$0.408621\pi$
$163$	−7.59947	+	18.3468i	−0.595237	+	1.43703i	−0.878386	+	0.477953i	$0.841379\pi$
$164$	−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	−0.702969	−	0.711220i	$-0.748143\pi$
$167$	0.106628	−	0.106628i	0.00825110	−	0.00825110i	0.711220	+	0.702969i	$0.248143\pi$
$168$		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	0.833144	−	0.553056i	$-0.186539\pi$
$173$	13.5633	+	5.61809i	1.03120	+	0.427135i	0.198052	+	0.980192i	$0.436539\pi$
$174$		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	−0.292171	−	0.956366i	$-0.594378\pi$
$179$	7.90273	−	19.0789i	0.590678	−	1.42602i	0.882849	−	0.469657i	$-0.155622\pi$
$180$		0			0
$181$	−22.9664	+	9.51301i	−1.70708	+	0.707097i	−1.00000		3.50523e-5i	$-0.999989\pi$
$181$	−22.9664	+	9.51301i	−1.70708	+	0.707097i	−0.707082	+	0.707132i	$0.749989\pi$
$182$	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	−0.881452	−	0.472275i	$-0.843433\pi$
$197$	−16.4327	+	6.80666i	−1.17078	+	0.484954i	−0.289332	+	0.957229i	$0.593433\pi$
$198$		0			0
$199$	−9.74888	−	9.74888i	−0.691080	−	0.691080i	0.271390	−	0.962470i	$-0.412517\pi$
$199$	−9.74888	−	9.74888i	−0.691080	−	0.691080i	−0.962470	+	0.271390i	$0.912517\pi$
$200$	−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	0.0133022	−	0.999912i	$-0.495766\pi$
$211$	−9.94055	−	4.11751i	−0.684336	−	0.283461i	−0.697638	+	0.716450i	$0.745766\pi$
$212$	−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	$-0.665481\pi$
$223$		−	25.9205i		−	1.73576i	0.496770	−	0.867882i	$-0.334519\pi$
$224$	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	0.179440	−	0.983769i	$-0.442571\pi$
$227$	−5.86548	−	2.42956i	−0.389306	−	0.161256i	−0.568746	+	0.822513i	$0.692571\pi$
$228$		0			0
$229$	5.60080	+	13.5215i	0.370111	+	0.893527i	0.993731	+	0.111799i	$0.0356614\pi$
$229$	5.60080	+	13.5215i	0.370111	+	0.893527i	−0.623620	+	0.781728i	$0.714339\pi$
$230$	−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	−0.946454	−	0.322838i	$-0.895363\pi$
$233$	−9.51909	+	9.51909i	−0.623616	+	0.623616i	0.322838	+	0.946454i	$0.395363\pi$
$234$		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	$-0.966385\pi$
$239$		−	3.25912i		−	0.210815i	0.994429	−	0.105407i	$-0.0336147\pi$
$240$		0			0
$241$			6.61960i			0.426406i	0.977008	+	0.213203i	$0.0683896\pi$
$241$			6.61960i			0.426406i	−0.977008	+	0.213203i	$0.931610\pi$
$242$	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	0.999023	+	0.0441864i	$0.0140695\pi$
$251$	5.13077	+	12.3868i	0.323852	+	0.781847i	−0.675172	+	0.737661i	$0.735930\pi$
$252$		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	$0.126126\pi$
$257$			12.3745i			0.771901i	−0.922520	+	0.385950i	$0.873874\pi$
$258$		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	0.125291	−	0.992120i	$-0.460013\pi$
$263$	18.1214	−	18.1214i	1.11741	−	1.11741i	0.992120	−	0.125291i	$-0.0399866\pi$
$264$		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	0.694460	−	0.719532i	$-0.255643\pi$
$269$	11.0992	+	4.59744i	0.676731	+	0.280311i	−0.0177286	+	0.999843i	$0.505643\pi$
$270$		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	−0.434968	−	0.900446i	$-0.643240\pi$
$277$	−1.76130	+	0.729552i	−0.105826	+	0.0438346i	0.329142	+	0.944280i	$0.393240\pi$
$278$	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	0.861122	−	0.508399i	$-0.169763\pi$
$281$	5.91271	+	5.91271i	0.352722	+	0.352722i	−0.508399	+	0.861122i	$0.669763\pi$
$282$		0			0
$283$	10.6146	−	4.39669i	0.630970	−	0.261356i	−0.0441953	−	0.999023i	$-0.514072\pi$
$283$	10.6146	−	4.39669i	0.630970	−	0.261356i	0.675165	+	0.737667i	$0.264072\pi$
$284$	−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	−0.169840	−	0.985472i	$-0.554325\pi$
$293$	6.96499	−	2.88499i	0.406899	−	0.168543i	0.576739	+	0.816929i	$0.304325\pi$
$294$		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	0.820612	−	0.571485i	$-0.193633\pi$
$307$	17.4648	+	7.23418i	0.996771	+	0.412876i	0.176159	+	0.984362i	$0.443633\pi$
$308$	−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	0.989446	+	0.144901i	$0.0462865\pi$
$311$	20.0044	+	20.0044i	1.13435	+	1.13435i	0.144901	+	0.989446i	$0.453714\pi$
$312$		0			0
$313$	16.1777	−	16.1777i	0.914417	−	0.914417i	−0.0821987	−	0.996616i	$-0.526194\pi$
$313$	16.1777	−	16.1777i	0.914417	−	0.914417i	0.996616	+	0.0821987i	$0.0261942\pi$
$314$	−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	0.615160	+	0.788403i	$0.289092\pi$
$317$	−6.71779	+	16.2182i	−0.377309	+	0.910904i	−0.992468	+	0.122501i	$0.960908\pi$
$318$		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	0.999909	−	0.0135083i	$-0.00429997\pi$
$331$	5.15446	+	12.4440i	0.283315	+	0.683982i	−0.716594	+	0.697490i	$0.754300\pi$
$332$	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	$0.0378423\pi$
$337$			4.35461i			0.237211i	−0.992941	+	0.118605i	$0.962158\pi$
$338$	−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	−0.889883	−	0.456188i	$-0.849214\pi$
$347$	−10.8641	−	26.2282i	−0.583215	−	1.40800i	0.306669	−	0.951816i	$-0.400786\pi$
$348$		0			0
$349$	23.9337	+	9.91367i	1.28114	+	0.530667i	0.916334	−	0.400416i	$-0.131134\pi$
$349$	23.9337	+	9.91367i	1.28114	+	0.530667i	0.364809	+	0.931082i	$0.381134\pi$
$350$	−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	$-0.861088\pi$
$353$		−	15.8830i		−	0.845369i	0.906277	−	0.422685i	$-0.138912\pi$
$354$		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	−0.981679	−	0.190540i	$-0.938976\pi$
$359$	−14.9900	+	14.9900i	−0.791139	+	0.791139i	0.190540	+	0.981679i	$0.438976\pi$
$360$		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	0.157821	−	0.987468i	$-0.449553\pi$
$373$	18.6887	−	7.74110i	0.967662	−	0.400819i	0.809841	+	0.586649i	$0.199553\pi$
$374$	−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	0.424090	−	0.905620i	$-0.360594\pi$
$379$	26.5608	−	11.0018i	1.36434	−	0.565127i	0.940247	+	0.340493i	$0.110594\pi$
$380$	−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	−0.369779	−	0.929120i	$-0.620566\pi$
$389$	0.507585	−	0.210249i	0.0257356	−	0.0106600i	0.395514	+	0.918460i	$0.370566\pi$
$390$		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	−0.807998	−	0.589186i	$-0.799449\pi$
$397$	3.58568	−	8.65661i	0.179960	−	0.434463i	0.987958	+	0.154723i	$0.0494486\pi$
$398$	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	−0.406646	−	0.913586i	$-0.633302\pi$
$409$	10.2522	−	10.2522i	0.506940	−	0.506940i	0.913586	+	0.406646i	$0.133302\pi$
$410$	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	0.847500	−	0.530795i	$-0.178107\pi$
$419$	21.9319	+	9.08450i	1.07145	+	0.443807i	0.223945	+	0.974602i	$0.428107\pi$
$420$		0			0
$421$	−13.0403	−	31.4820i	−0.635544	−	1.53434i	−0.832557	−	0.553939i	$-0.813124\pi$
$421$	−13.0403	−	31.4820i	−0.635544	−	1.53434i	0.197013	−	0.980401i	$-0.436876\pi$
$422$	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	$-0.880759\pi$
$431$		−	15.1928i		−	0.731811i	0.930652	−	0.365906i	$-0.119241\pi$
$432$		0			0
$433$			36.6873i			1.76308i	0.472109	+	0.881540i	$0.343493\pi$
$433$			36.6873i			1.76308i	−0.472109	+	0.881540i	$0.656507\pi$
$434$	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	−0.334363	−	0.942444i	$-0.608521\pi$
$439$	12.7407	−	12.7407i	0.608081	−	0.608081i	0.942444	+	0.334363i	$0.108521\pi$
$440$	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	−0.996977	−	0.0776987i	$-0.975243\pi$
$443$	−7.30243	−	17.6296i	−0.346949	−	0.837609i	0.650028	−	0.759910i	$-0.274757\pi$
$444$		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	$-0.726299\pi$
$449$		−	32.1128i		−	1.51550i	0.652546	−	0.757749i	$-0.273701\pi$
$450$		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	0.997927	+	0.0643566i	$0.0204995\pi$
$457$	22.7090	+	22.7090i	1.06228	+	1.06228i	0.0643566	+	0.997927i	$0.479500\pi$
$458$	−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	−0.394723	−	0.918800i	$-0.629159\pi$
$461$	−28.4173	−	11.7708i	−1.32352	−	0.548222i	−0.928801	+	0.370579i	$0.879159\pi$
$462$		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	−0.878089	−	0.478498i	$-0.841181\pi$
$467$	1.75394	−	4.23439i	0.0811628	−	0.195944i	0.959252	+	0.282553i	$0.0911815\pi$
$468$		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	0.316993	−	0.948428i	$-0.397327\pi$
$487$	−13.9346	−	13.9346i	−0.631435	−	0.631435i	−0.948428	+	0.316993i	$0.897327\pi$
$488$	−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	−0.176660	−	0.984272i	$-0.556529\pi$
$491$	8.73949	−	3.62001i	0.394408	−	0.163369i	0.571068	+	0.820903i	$0.306529\pi$
$492$		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	0.380714	−	0.924693i	$-0.375678\pi$
$499$	−0.0879672	−	0.0364372i	−0.00393795	−	0.00163115i	−0.384652	+	0.923062i	$0.625678\pi$
$500$	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	0.999372	+	0.0354464i	$0.0112853\pi$
$503$	23.2085	+	23.2085i	1.03482	+	1.03482i	0.0354464	+	0.999372i	$0.488715\pi$
$504$		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	−0.999887	−	0.0150040i	$-0.995224\pi$
$509$	−6.36787	+	15.3734i	−0.282251	+	0.681414i	0.717637	+	0.696418i	$0.245224\pi$
$510$		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	−0.384835	−	0.922986i	$-0.625742\pi$
$521$	12.2835	−	12.2835i	0.538151	−	0.538151i	0.922986	+	0.384835i	$0.125742\pi$
$522$		0			0
$523$	17.3222	+	41.8195i	0.757448	+	1.82864i	0.511282	+	0.859413i	$0.329171\pi$
$523$	17.3222	+	41.8195i	0.757448	+	1.82864i	0.246165	+	0.969228i	$0.420829\pi$
$524$	−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	0.640178	−	0.768227i	$-0.278861\pi$
$541$	12.7841	+	5.29536i	0.549633	+	0.227665i	−0.0905446	+	0.995892i	$0.528861\pi$
$542$	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	−0.711564	−	0.702622i	$-0.752013\pi$
$547$	6.74549	−	16.2851i	0.288416	−	0.696299i	0.999980	+	0.00632291i	$0.00201266\pi$
$548$	−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	0.263639	−	0.964621i	$-0.415077\pi$
$557$	−5.47610	−	2.26827i	−0.232030	−	0.0961099i	−0.495669	+	0.868511i	$0.665077\pi$
$558$		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	−0.892524	−	0.451000i	$-0.851067\pi$
$563$	1.36413	−	3.29330i	0.0574912	−	0.138796i	0.950015	+	0.312204i	$0.101067\pi$
$564$		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	0.944997	−	0.327080i	$-0.106065\pi$
$569$	14.7396	+	14.7396i	0.617917	+	0.617917i	−0.327080	+	0.944997i	$0.606065\pi$
$570$		0			0
$571$	−35.0355	+	14.5122i	−1.46619	+	0.607315i	−0.965986	−	0.258593i	$-0.916741\pi$
$571$	−35.0355	+	14.5122i	−1.46619	+	0.607315i	−0.500202	+	0.865909i	$0.666741\pi$
$572$	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	−0.700141	−	0.714005i	$-0.746879\pi$
$587$	−16.7256	+	6.92795i	−0.690338	+	0.285947i	0.00980329	+	0.999952i	$0.496879\pi$
$588$		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	0.776512	−	0.630102i	$-0.216987\pi$
$599$	3.58332	+	3.58332i	0.146410	+	0.146410i	−0.630102	+	0.776512i	$0.716987\pi$
$600$		0			0
$601$	−6.50070	+	6.50070i	−0.265169	+	0.265169i	−0.827150	−	0.561981i	$-0.810039\pi$
$601$	−6.50070	+	6.50070i	−0.265169	+	0.265169i	0.561981	+	0.827150i	$0.310039\pi$
$602$	−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	$0.255938\pi$
$607$			35.4863i			1.44035i	−0.693795	+	0.720173i	$0.744062\pi$
$608$	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	0.738217	−	0.674563i	$-0.235668\pi$
$613$	−6.45635	−	15.5870i	−0.260770	−	0.629553i	−0.998987	+	0.0450099i	$0.985668\pi$
$614$	−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	−0.184901	−	0.982757i	$-0.559196\pi$
$617$	19.8183	−	19.8183i	0.797856	−	0.797856i	0.982757	+	0.184901i	$0.0591964\pi$
$618$		0			0
$619$	−3.86437	−	9.32942i	−0.155322	−	0.374981i	0.826994	−	0.562211i	$-0.190049\pi$
$619$	−3.86437	−	9.32942i	−0.155322	−	0.374981i	−0.982316	+	0.187230i	$0.940049\pi$
$620$	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	−0.991341	−	0.131312i	$-0.958081\pi$
$631$	−21.6037	+	21.6037i	−0.860029	+	0.860029i	0.131312	+	0.991341i	$0.458081\pi$
$632$	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	$0.0532161\pi$
$641$			8.42611i			0.332811i	−0.986057	+	0.166406i	$0.946784\pi$
$642$		0			0
$643$	−11.7410	+	28.3452i	−0.463019	+	1.11783i	0.504132	+	0.863626i	$0.331812\pi$
$643$	−11.7410	+	28.3452i	−0.463019	+	1.11783i	−0.967152	+	0.254201i	$0.918188\pi$
$644$	−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	−0.957911	−	0.287065i	$-0.907320\pi$
$647$	−17.0638	+	17.0638i	−0.670846	+	0.670846i	0.287065	+	0.957911i	$0.407320\pi$
$648$		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	0.255848	−	0.966717i	$-0.417645\pi$
$653$	−6.30700	−	2.61244i	−0.246812	−	0.102233i	−0.502660	+	0.864484i	$0.667645\pi$
$654$		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	−0.989845	−	0.142151i	$-0.954598\pi$
$659$	−4.86215	+	11.7383i	−0.189403	+	0.457258i	0.800442	+	0.599410i	$0.204598\pi$
$660$		0			0
$661$	−20.5534	+	8.51349i	−0.799434	+	0.331137i	−0.744730	−	0.667366i	$-0.767422\pi$
$661$	−20.5534	+	8.51349i	−0.799434	+	0.331137i	−0.0547045	+	0.998503i	$0.517422\pi$
$662$	−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	−0.517575	−	0.855638i	$-0.673165\pi$
$677$	−7.24712	+	3.00186i	−0.278529	+	0.115371i	0.239046	+	0.971008i	$0.423165\pi$
$678$		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	−0.743533	−	0.668700i	$-0.766851\pi$
$683$	−20.8146	+	8.62168i	−0.796448	+	0.329899i	−0.0529151	+	0.998599i	$0.516851\pi$
$684$		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	0.311151	−	0.950361i	$-0.399286\pi$
$691$	−3.70220	−	1.53350i	−0.140839	−	0.0583372i	−0.451989	+	0.892023i	$0.649286\pi$
$692$	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	−0.924279	−	0.381718i	$-0.875332\pi$
$701$	−0.0211624	+	0.0510906i	−0.000799293	+	0.00192966i	0.923479	+	0.383648i	$0.125332\pi$
$702$		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	0.856118	−	0.516780i	$-0.172869\pi$
$709$	−3.05325	−	7.37121i	−0.114667	−	0.276831i	−0.970786	+	0.239948i	$0.922869\pi$
$710$	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	$-0.887371\pi$
$719$		−	18.5820i		−	0.692993i	0.938051	−	0.346496i	$-0.112629\pi$
$720$		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	−0.585733	−	0.810504i	$-0.699193\pi$
$727$	6.06048	−	6.06048i	0.224771	−	0.224771i	0.810504	+	0.585733i	$0.199193\pi$
$728$	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	0.295676	−	0.955288i	$-0.404455\pi$
$733$	−4.62261	−	1.91475i	−0.170740	−	0.0707229i	−0.466416	+	0.884565i	$0.654455\pi$
$734$	−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	−0.641357	−	0.767243i	$-0.721628\pi$
$739$	9.64164	−	23.2770i	0.354674	−	0.856258i	0.996030	−	0.0890150i	$-0.0283719\pi$
$740$	−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	0.319122	−	0.947714i	$-0.396612\pi$
$743$	34.5314	−	34.5314i	1.26684	−	1.26684i	0.947714	−	0.319122i	$-0.103388\pi$
$744$		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	−0.174698	−	0.984622i	$-0.555895\pi$
$757$	10.9506	−	4.53588i	0.398005	−	0.164859i	0.572703	+	0.819763i	$0.305895\pi$
$758$	−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	0.993870	−	0.110559i	$-0.0352641\pi$
$761$	24.3672	+	24.3672i	0.883311	+	0.883311i	−0.110559	+	0.993870i	$0.535264\pi$
$762$		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	−0.957796	−	0.287449i	$-0.907193\pi$
$773$	−39.8083	+	16.4891i	−1.43180	+	0.593072i	−0.474007	+	0.880521i	$0.657193\pi$
$774$		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	0.0240253	−	0.999711i	$-0.492352\pi$
$787$	−18.6805	−	7.73773i	−0.665889	−	0.275820i	−0.689914	+	0.723891i	$0.742352\pi$
$788$	−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	−0.428700	−	0.903447i	$-0.641028\pi$
$797$	14.4902	−	34.9825i	0.513270	−	1.23914i	0.941970	−	0.335697i	$-0.108972\pi$
$798$		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	0.352317	−	0.935881i	$-0.385394\pi$
$809$	36.6401	−	36.6401i	1.28820	−	1.28820i	0.935881	−	0.352317i	$-0.114606\pi$
$810$		0			0
$811$	−2.81717	−	6.80125i	−0.0989242	−	0.238824i	0.866668	−	0.498886i	$-0.166257\pi$
$811$	−2.81717	−	6.80125i	−0.0989242	−	0.238824i	−0.965592	+	0.260061i	$0.916257\pi$
$812$	−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	0.819989	−	0.572379i	$-0.193979\pi$
$821$	−4.71525	−	11.3836i	−0.164564	−	0.397291i	−0.984553	+	0.175087i	$0.943979\pi$
$822$		0			0
$823$	31.3892	−	31.3892i	1.09416	−	1.09416i	0.0990779	−	0.995080i	$-0.468411\pi$
$823$	31.3892	−	31.3892i	1.09416	−	1.09416i	0.995080	−	0.0990779i	$-0.0315893\pi$
$824$	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	0.894591	−	0.446886i	$-0.147467\pi$
$827$	−1.55224	−	3.74744i	−0.0539767	−	0.130311i	−0.948567	+	0.316575i	$0.897467\pi$
$828$		0			0
$829$	−38.2591	−	15.8474i	−1.32879	−	0.550405i	−0.398483	−	0.917176i	$-0.630463\pi$
$829$	−38.2591	−	15.8474i	−1.32879	−	0.550405i	−0.930311	+	0.366771i	$0.880463\pi$
$830$	−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	−0.107689	−	0.994185i	$-0.534345\pi$
$839$	25.6778	−	25.6778i	0.886496	−	0.886496i	0.994185	+	0.107689i	$0.0343449\pi$
$840$		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	0.791803	−	0.610776i	$-0.209143\pi$
$853$	52.0914	−	21.5770i	1.78358	−	0.738782i	0.991773	−	0.128005i	$-0.0408575\pi$
$854$	−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	0.999581	+	0.0289357i	$0.00921179\pi$
$857$	30.1094	+	30.1094i	1.02852	+	1.02852i	0.0289357	+	0.999581i	$0.490788\pi$
$858$		0			0
$859$	5.58448	−	2.31317i	0.190540	−	0.0789243i	−0.285373	−	0.958416i	$-0.592118\pi$
$859$	5.58448	−	2.31317i	0.190540	−	0.0789243i	0.475913	+	0.879492i	$0.342118\pi$
$860$	−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	−0.996135	−	0.0878397i	$-0.972004\pi$
$877$	−6.80087	+	16.4188i	−0.229649	+	0.554422i	0.766486	+	0.642262i	$0.222004\pi$
$878$	−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	0.753315	−	0.657659i	$-0.228453\pi$
$883$	24.3949	+	10.1047i	0.820955	+	0.340051i	0.0676391	+	0.997710i	$0.478453\pi$
$884$	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	0.297304	−	0.954783i	$-0.403913\pi$
$887$	−19.5814	−	19.5814i	−0.657479	−	0.657479i	−0.954783	+	0.297304i	$0.903913\pi$
$888$		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	0.997815	+	0.0660694i	$0.0210459\pi$
$907$	10.2086	+	24.6458i	0.338971	+	0.818349i	−0.658844	+	0.752280i	$0.728954\pi$
$908$	−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	$0.0174652\pi$
$911$			3.31050i			0.109682i	−0.998495	+	0.0548409i	$0.982535\pi$
$912$		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	−0.426054	−	0.904698i	$-0.640097\pi$
$919$	14.5101	−	14.5101i	0.478643	−	0.478643i	0.904698	+	0.426054i	$0.140097\pi$
$920$	−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	$0.344325\pi$
$929$			53.8129i			1.76554i	−0.469803	+	0.882771i	$0.655675\pi$
$930$		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	0.963500	−	0.267710i	$-0.0862668\pi$
$937$	21.2984	+	21.2984i	0.695790	+	0.695790i	−0.267710	+	0.963500i	$0.586267\pi$
$938$	−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	−0.210415	−	0.977612i	$-0.567482\pi$
$941$	−32.2242	−	13.3477i	−1.05048	−	0.435122i	−0.840062	+	0.542490i	$0.817482\pi$
$942$		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	−0.970881	−	0.239564i	$-0.922996\pi$
$947$	−3.53793	+	8.54132i	−0.114967	+	0.277556i	0.855913	+	0.517119i	$0.172996\pi$
$948$		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	0.0421028	−	0.999113i	$-0.486594\pi$
$953$	−29.5436	−	29.5436i	−0.957010	−	0.957010i	−0.999113	+	0.0421028i	$0.986594\pi$
$954$		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	0.872337	−	0.488905i	$-0.162603\pi$
$967$	11.9235	+	11.9235i	0.383432	+	0.383432i	−0.488905	+	0.872337i	$0.662603\pi$
$968$	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	−0.364958	−	0.931024i	$-0.618917\pi$
$971$	1.10035	−	0.455781i	0.0353120	−	0.0146267i	0.400270	+	0.916397i	$0.368917\pi$
$972$		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	0.594150	−	0.804354i	$-0.297489\pi$
$983$	−6.59049	−	6.59049i	−0.210204	−	0.210204i	−0.804354	+	0.594150i	$0.797489\pi$
$984$		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	$0.201238\pi$
$991$			37.2049i			1.18185i	−0.806726	+	0.590926i	$0.798762\pi$
$992$	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	0.949476	−	0.313839i	$-0.101615\pi$
$997$	1.77382	+	4.28237i	0.0561773	+	0.135624i	−0.893299	+	0.449463i	$0.851615\pi$
$998$	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.35.1	✓	32
3.2	odd	2		288.2.w.b.35.8	yes	32
4.3	odd	2		1152.2.w.b.431.8		32
12.11	even	2		1152.2.w.a.431.1		32
32.11	odd	8		288.2.w.b.107.8	yes	32
32.21	even	8		1152.2.w.a.719.1		32
96.11	even	8	inner	288.2.w.a.107.1	yes	32
96.53	odd	8		1152.2.w.b.719.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.1	✓	32	1.1	even	1	trivial
288.2.w.a.107.1	yes	32	96.11	even	8	inner
288.2.w.b.35.8	yes	32	3.2	odd	2
288.2.w.b.107.8	yes	32	32.11	odd	8
1152.2.w.a.431.1		32	12.11	even	2
1152.2.w.a.719.1		32	32.21	even	8
1152.2.w.b.431.8		32	4.3	odd	2
1152.2.w.b.719.8		32	96.53	odd	8

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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