LMFDB - Embedded newform 288.2.w.b.107.8

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			107.8
Character	$\chi$	$=$	288.107
Dual form			288.2.w.b.35.8

$q$-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	$-0.949349\pi$
$5$	−4.01952	−	1.66494i	−1.79758	−	0.744583i	−0.810217	−	0.586130i	$-0.800651\pi$
$6$		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	0.723993	−	0.689807i	$-0.242305\pi$
$11$	2.48139	+	1.02782i	0.748166	+	0.309900i	0.0241729	+	0.999708i	$0.492305\pi$
$12$		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	$-0.434114\pi$
$17$	1.69470			0.411026			0.205513	+	0.978654i	$0.434114\pi$
$18$		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	−0.987102	−	0.160092i	$-0.948821\pi$
$23$	−3.96620	+	3.96620i	−0.827010	+	0.827010i	0.160092	+	0.987102i	$0.448821\pi$
$24$		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	$-0.0798741\pi$
$29$	0.582357	+	1.40593i	0.108141	+	0.261075i	−0.860541	+	0.509382i	$0.829874\pi$
$30$		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	0.956969	−	0.290190i	$-0.0937186\pi$
$41$	4.26947	+	4.26947i	0.666779	+	0.666779i	−0.290190	+	0.956969i	$0.593719\pi$
$42$		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	$-0.779307\pi$
$47$		−	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	−0.532059	−	0.846707i	$-0.678582\pi$
$53$	3.22418	−	7.78387i	0.442876	−	1.06920i	0.974935	−	0.222489i	$-0.0714183\pi$
$54$		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	$-0.972639\pi$
$59$	−1.77515	+	4.28559i	−0.231105	+	0.557936i	0.765203	+	0.643789i	$0.222639\pi$
$60$		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	$0.0283425\pi$
$71$	9.14205	+	9.14205i	1.08496	+	1.08496i	0.0889229	+	0.996039i	$0.471658\pi$
$72$		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	0.765328	−	0.643640i	$-0.222577\pi$
$83$	−2.10417	−	5.07993i	−0.230963	−	0.557594i	−0.996291	+	0.0860461i	$0.972577\pi$
$84$		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	$-0.841290\pi$
$89$	−3.77409	+	3.77409i	−0.400053	+	0.400053i	0.478199	+	0.878252i	$0.341290\pi$
$90$		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	$-0.270228\pi$
$101$	6.00246	+	2.48630i	0.597267	+	0.247396i	−0.0635063	+	0.997981i	$0.520228\pi$
$102$		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	0.153091	−	0.988212i	$-0.451077\pi$
$107$	−4.52481	−	1.87424i	−0.437430	−	0.181189i	−0.590520	+	0.807023i	$0.701077\pi$
$108$		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	$-0.574290\pi$
$113$	−4.91698			−0.462550			−0.231275	+	0.972888i	$0.574290\pi$
$114$		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	−0.141646	−	0.989917i	$-0.545240\pi$
$131$	5.24402	−	2.17214i	0.458172	−	0.189781i	0.599818	+	0.800136i	$0.295240\pi$
$132$		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	$-0.169747\pi$
$137$	4.12927	+	4.12927i	0.352787	+	0.352787i	−0.508358	+	0.861146i	$0.669747\pi$
$138$		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	−0.984706	−	0.174223i	$-0.944259\pi$
$149$	−2.01676	+	4.86889i	−0.165219	+	0.398875i	0.819487	+	0.573098i	$0.194259\pi$
$150$		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	0.702969	−	0.711220i	$-0.251857\pi$
$167$	−0.106628	−	0.106628i	−0.00825110	−	0.00825110i	−0.711220	+	0.702969i	$0.751857\pi$
$168$		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	$-0.813461\pi$
$173$	−13.5633	+	5.61809i	−1.03120	+	0.427135i	−0.198052	+	0.980192i	$0.563461\pi$
$174$		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	$-0.844378\pi$
$179$	−7.90273	−	19.0789i	−0.590678	−	1.42602i	0.292171	−	0.956366i	$-0.405622\pi$
$180$		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	$-0.663405\pi$
$191$	−13.5743			−0.982202			−0.491101	+	0.871103i	$0.663405\pi$
$192$		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	$-0.156567\pi$
$197$	16.4327	+	6.80666i	1.17078	+	0.484954i	0.289332	+	0.957229i	$0.406567\pi$
$198$		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	−0.179440	−	0.983769i	$-0.557429\pi$
$227$	5.86548	−	2.42956i	0.389306	−	0.161256i	0.568746	+	0.822513i	$0.307429\pi$
$228$		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	0.946454	−	0.322838i	$-0.104637\pi$
$233$	9.51909	+	9.51909i	0.623616	+	0.623616i	−0.322838	+	0.946454i	$0.604637\pi$
$234$		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	$-0.931610\pi$
$241$		−	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	$0.264070\pi$
$251$	−5.13077	+	12.3868i	−0.323852	+	0.781847i	−0.999023	+	0.0441864i	$0.985930\pi$
$252$		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	−0.992120	−	0.125291i	$-0.960013\pi$
$263$	−18.1214	−	18.1214i	−1.11741	−	1.11741i	−0.125291	−	0.992120i	$-0.539987\pi$
$264$		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	$-0.744357\pi$
$269$	−11.0992	+	4.59744i	−0.676731	+	0.280311i	0.0177286	+	0.999843i	$0.494357\pi$
$270$		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	−0.861122	−	0.508399i	$-0.830237\pi$
$281$	−5.91271	+	5.91271i	−0.352722	+	0.352722i	0.508399	+	0.861122i	$0.330237\pi$
$282$		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	0.169840	−	0.985472i	$-0.445675\pi$
$293$	−6.96499	−	2.88499i	−0.406899	−	0.168543i	−0.576739	+	0.816929i	$0.695675\pi$
$294$		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	$0.546286\pi$
$311$	−20.0044	+	20.0044i	−1.13435	+	1.13435i	−0.989446	+	0.144901i	$0.953714\pi$
$312$		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	$0.0390915\pi$
$317$	6.71779	+	16.2182i	0.377309	+	0.910904i	−0.615160	+	0.788403i	$0.710908\pi$
$318$		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	$-0.599214\pi$
$347$	10.8641	−	26.2282i	0.583215	−	1.40800i	0.889883	−	0.456188i	$-0.150786\pi$
$348$		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	$-0.861088\pi$
$353$		−	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	$-0.0610239\pi$
$359$	14.9900	+	14.9900i	0.791139	+	0.791139i	−0.190540	+	0.981679i	$0.561024\pi$
$360$		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	$-0.709547\pi$
$383$	−23.9456			−1.22356			−0.611782	+	0.791027i	$0.709547\pi$
$384$		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	$-0.379434\pi$
$389$	−0.507585	−	0.210249i	−0.0257356	−	0.0106600i	−0.395514	+	0.918460i	$0.629434\pi$
$390$		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	$-0.541958\pi$
$401$	−5.26389			−0.262866			−0.131433	+	0.991325i	$0.541958\pi$
$402$		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	−0.847500	−	0.530795i	$-0.821893\pi$
$419$	−21.9319	+	9.08450i	−1.07145	+	0.443807i	−0.223945	+	0.974602i	$0.571893\pi$
$420$		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	$-0.880759\pi$
$431$		−	15.1928i		−	0.731811i	0.930652	−	0.365906i	$-0.119241\pi$
$432$		0			0
$433$		−	36.6873i		−	1.76308i	−0.472109	−	0.881540i	$-0.656507\pi$
$433$		−	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	$-0.725243\pi$
$443$	7.30243	−	17.6296i	0.346949	−	0.837609i	0.996977	−	0.0776987i	$-0.0247572\pi$
$444$		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	0.0643566	−	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	0.394723	−	0.918800i	$-0.370841\pi$
$461$	28.4173	−	11.7708i	1.32352	−	0.548222i	0.928801	+	0.370579i	$0.120841\pi$
$462$		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	$-0.158819\pi$
$467$	−1.75394	−	4.23439i	−0.0811628	−	0.195944i	−0.959252	+	0.282553i	$0.908819\pi$
$468$		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	$-0.370907\pi$
$479$	17.2694			0.789060			0.394530	+	0.918883i	$0.370907\pi$
$480$		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	0.176660	−	0.984272i	$-0.443471\pi$
$491$	−8.73949	−	3.62001i	−0.394408	−	0.163369i	−0.571068	+	0.820903i	$0.693471\pi$
$492$		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	$0.511285\pi$
$503$	−23.2085	+	23.2085i	−1.03482	+	1.03482i	−0.999372	+	0.0354464i	$0.988715\pi$
$504$		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	$-0.00477611\pi$
$509$	6.36787	+	15.3734i	0.282251	+	0.681414i	−0.717637	+	0.696418i	$0.754776\pi$
$510$		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	$-0.374258\pi$
$521$	−12.2835	−	12.2835i	−0.538151	−	0.538151i	−0.922986	+	0.384835i	$0.874258\pi$
$522$		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	−0.263639	−	0.964621i	$-0.584923\pi$
$557$	5.47610	−	2.26827i	0.232030	−	0.0961099i	0.495669	+	0.868511i	$0.334923\pi$
$558$		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	$-0.148933\pi$
$563$	−1.36413	−	3.29330i	−0.0574912	−	0.138796i	−0.950015	+	0.312204i	$0.898933\pi$
$564$		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	$-0.893935\pi$
$569$	−14.7396	+	14.7396i	−0.617917	+	0.617917i	0.327080	+	0.944997i	$0.393935\pi$
$570$		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	0.700141	−	0.714005i	$-0.253121\pi$
$587$	16.7256	+	6.92795i	0.690338	+	0.285947i	−0.00980329	+	0.999952i	$0.503121\pi$
$588$		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	$-0.287844\pi$
$593$	30.1105			1.23649			0.618244	+	0.785986i	$0.287844\pi$
$594$		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	$-0.783013\pi$
$599$	−3.58332	+	3.58332i	−0.146410	+	0.146410i	0.630102	+	0.776512i	$0.283013\pi$
$600$		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	0.184901	−	0.982757i	$-0.440804\pi$
$617$	−19.8183	−	19.8183i	−0.797856	−	0.797856i	−0.982757	+	0.184901i	$0.940804\pi$
$618$		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	$0.0532161\pi$
$641$			8.42611i			0.332811i	−0.986057	+	0.166406i	$0.946784\pi$
$642$		0			0
$643$	−11.7410	−	28.3452i	−0.463019	−	1.11783i	−0.967152	−	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	0.957911	−	0.287065i	$-0.0926796\pi$
$647$	17.0638	+	17.0638i	0.670846	+	0.670846i	−0.287065	+	0.957911i	$0.592680\pi$
$648$		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	$-0.582355\pi$
$653$	6.30700	−	2.61244i	0.246812	−	0.102233i	0.502660	+	0.864484i	$0.332355\pi$
$654$		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	$-0.0454020\pi$
$659$	4.86215	+	11.7383i	0.189403	+	0.457258i	−0.800442	+	0.599410i	$0.795402\pi$
$660$		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	0.517575	−	0.855638i	$-0.326835\pi$
$677$	7.24712	+	3.00186i	0.278529	+	0.115371i	−0.239046	+	0.971008i	$0.576835\pi$
$678$		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	$-0.233149\pi$
$683$	20.8146	+	8.62168i	0.796448	+	0.329899i	0.0529151	+	0.998599i	$0.483149\pi$
$684$		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	0.924279	−	0.381718i	$-0.124668\pi$
$701$	0.0211624	+	0.0510906i	0.000799293	+	0.00192966i	−0.923479	+	0.383648i	$0.874668\pi$
$702$		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	$-0.887371\pi$
$719$		−	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	0.810504	−	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	$-0.896612\pi$
$743$	−34.5314	−	34.5314i	−1.26684	−	1.26684i	−0.319122	−	0.947714i	$-0.603388\pi$
$744$		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	−0.993870	−	0.110559i	$-0.964736\pi$
$761$	−24.3672	+	24.3672i	−0.883311	+	0.883311i	0.110559	+	0.993870i	$0.464736\pi$
$762$		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	$-0.0928070\pi$
$773$	39.8083	+	16.4891i	1.43180	+	0.593072i	0.474007	+	0.880521i	$0.342807\pi$
$774$		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	$-0.891028\pi$
$797$	−14.4902	−	34.9825i	−0.513270	−	1.23914i	0.428700	−	0.903447i	$-0.358972\pi$
$798$		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	$-0.885394\pi$
$809$	−36.6401	−	36.6401i	−1.28820	−	1.28820i	−0.352317	−	0.935881i	$-0.614606\pi$
$810$		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	−0.819989	−	0.572379i	$-0.806021\pi$
$821$	4.71525	−	11.3836i	0.164564	−	0.397291i	0.984553	+	0.175087i	$0.0560207\pi$
$822$		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	−0.894591	−	0.446886i	$-0.852533\pi$
$827$	1.55224	−	3.74744i	0.0539767	−	0.130311i	0.948567	+	0.316575i	$0.102533\pi$
$828$		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	0.107689	−	0.994185i	$-0.465655\pi$
$839$	−25.6778	−	25.6778i	−0.886496	−	0.886496i	−0.994185	+	0.107689i	$0.965655\pi$
$840$		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	$0.509212\pi$
$857$	−30.1094	+	30.1094i	−1.02852	+	1.02852i	−0.999581	+	0.0289357i	$0.990788\pi$
$858$		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	$-0.555506\pi$
$863$	−10.1934			−0.346987			−0.173494	+	0.984835i	$0.555506\pi$
$864$		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	$-0.527982\pi$
$881$	−5.21177			−0.175589			−0.0877945	+	0.996139i	$0.527982\pi$
$882$		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	−0.297304	−	0.954783i	$-0.596087\pi$
$887$	19.5814	−	19.5814i	0.657479	−	0.657479i	0.954783	+	0.297304i	$0.0960873\pi$
$888$		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	$0.0174652\pi$
$911$			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	0.904698	−	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	$0.344325\pi$
$929$			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	−0.267710	−	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	0.210415	−	0.977612i	$-0.432518\pi$
$941$	32.2242	−	13.3477i	1.05048	−	0.435122i	0.840062	+	0.542490i	$0.182518\pi$
$942$		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	$-0.0770043\pi$
$947$	3.53793	+	8.54132i	0.114967	+	0.277556i	−0.855913	+	0.517119i	$0.827004\pi$
$948$		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	$-0.513406\pi$
$953$	29.5436	−	29.5436i	0.957010	−	0.957010i	0.999113	+	0.0421028i	$0.0134057\pi$
$954$		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	0.364958	−	0.931024i	$-0.381083\pi$
$971$	−1.10035	−	0.455781i	−0.0353120	−	0.0146267i	−0.400270	+	0.916397i	$0.631083\pi$
$972$		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	$-0.422938\pi$
$977$	14.9871			0.479479			0.239739	+	0.970837i	$0.422938\pi$
$978$		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	$-0.702511\pi$
$983$	6.59049	−	6.59049i	0.210204	−	0.210204i	0.804354	+	0.594150i	$0.202511\pi$
$984$		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.b.107.8	yes	32
3.2	odd	2		288.2.w.a.107.1	yes	32
4.3	odd	2		1152.2.w.a.719.1		32
12.11	even	2		1152.2.w.b.719.8		32
32.3	odd	8		288.2.w.a.35.1	✓	32
32.29	even	8		1152.2.w.b.431.8		32
96.29	odd	8		1152.2.w.a.431.1		32
96.35	even	8	inner	288.2.w.b.35.8	yes	32

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