LMFDB - Embedded newform 288.2.v.d.109.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (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:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.7
Character	$\chi$	$=$	288.109
Dual form			288.2.v.d.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26685 + 0.628571i) q^{2} +(1.20980 + 1.59260i) q^{4} +(3.09318 - 1.28124i) q^{5} +(-1.73503 + 1.73503i) q^{7} +(0.531562 + 2.77803i) q^{8} +O(q^{10})$	\(q+(1.26685 + 0.628571i) q^{2} +(1.20980 + 1.59260i) q^{4} +(3.09318 - 1.28124i) q^{5} +(-1.73503 + 1.73503i) q^{7} +(0.531562 + 2.77803i) q^{8} +(4.72394 + 0.321153i) q^{10} +(-2.39923 - 5.79225i) q^{11} +(0.0173304 + 0.00717850i) q^{13} +(-3.28860 + 1.10742i) q^{14} +(-1.07278 + 3.85346i) q^{16} +5.57978i q^{17} +(-1.03052 - 0.426856i) q^{19} +(5.78263 + 3.37618i) q^{20} +(0.601386 - 8.84597i) q^{22} +(-2.01868 - 2.01868i) q^{23} +(4.39068 - 4.39068i) q^{25} +(0.0174428 + 0.0199875i) q^{26} +(-4.86224 - 0.664180i) q^{28} +(0.706079 - 1.70463i) q^{29} +1.38048 q^{31} +(-3.78122 + 4.20742i) q^{32} +(-3.50729 + 7.06872i) q^{34} +(-3.14377 + 7.58973i) q^{35} +(-2.87315 + 1.19010i) q^{37} +(-1.03720 - 1.18852i) q^{38} +(5.20354 + 7.91189i) q^{40} +(-6.97897 - 6.97897i) q^{41} +(1.67010 + 4.03197i) q^{43} +(6.32218 - 10.8285i) q^{44} +(-1.28847 - 3.82623i) q^{46} -1.15993i q^{47} +0.979375i q^{49} +(8.32217 - 2.80246i) q^{50} +(0.00953380 + 0.0362851i) q^{52} +(-2.56680 - 6.19681i) q^{53} +(-14.8425 - 14.8425i) q^{55} +(-5.74222 - 3.89767i) q^{56} +(1.96597 - 1.71568i) q^{58} +(0.735935 - 0.304834i) q^{59} +(4.82262 - 11.6428i) q^{61} +(1.74885 + 0.867729i) q^{62} +(-7.43488 + 2.95339i) q^{64} +0.0628036 q^{65} +(-2.05899 + 4.97085i) q^{67} +(-8.88638 + 6.75040i) q^{68} +(-8.75336 + 7.63894i) q^{70} +(1.78298 - 1.78298i) q^{71} +(1.67500 + 1.67500i) q^{73} +(-4.38789 - 0.298307i) q^{74} +(-0.566909 - 2.15762i) q^{76} +(14.2124 + 5.88697i) q^{77} -2.67236i q^{79} +(1.61890 + 13.2939i) q^{80} +(-4.45450 - 13.2281i) q^{82} +(6.91877 + 2.86585i) q^{83} +(7.14903 + 17.2593i) q^{85} +(-0.418623 + 6.15766i) q^{86} +(14.8157 - 9.74406i) q^{88} +(-6.73869 + 6.73869i) q^{89} +(-0.0425236 + 0.0176139i) q^{91} +(0.772764 - 5.65714i) q^{92} +(0.729098 - 1.46945i) q^{94} -3.73450 q^{95} -1.75001 q^{97} +(-0.615607 + 1.24072i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.26685	+	0.628571i	0.895795	+	0.444467i
$2$	1.26685	+	0.628571i	0.895795	+	0.444467i
$3$		0			0
$3$		0			0
$4$	1.20980	+	1.59260i	0.604899	+	0.796302i
$5$	3.09318	−	1.28124i	1.38331	−	0.572987i	0.437949	−	0.899000i	$-0.355705\pi$
$5$	3.09318	−	1.28124i	1.38331	−	0.572987i	0.945365	+	0.326013i	$0.105705\pi$
$6$		0			0
$7$	−1.73503	+	1.73503i	−0.655778	+	0.655778i	−0.954378	−	0.298600i	$-0.903480\pi$
$7$	−1.73503	+	1.73503i	−0.655778	+	0.655778i	0.298600	+	0.954378i	$0.403480\pi$
$8$	0.531562	+	2.77803i	0.187936	+	0.982181i
$9$		0			0
$10$	4.72394	+	0.321153i	1.49384	+	0.101557i
$11$	−2.39923	−	5.79225i	−0.723394	−	1.74643i	−0.663443	−	0.748227i	$-0.730905\pi$
$11$	−2.39923	−	5.79225i	−0.723394	−	1.74643i	−0.0599515	−	0.998201i	$-0.519095\pi$
$12$		0			0
$13$	0.0173304	+	0.00717850i	0.00480660	+	0.00199096i	0.385085	−	0.922881i	$-0.374172\pi$
$13$	0.0173304	+	0.00717850i	0.00480660	+	0.00199096i	−0.380279	+	0.924872i	$0.624172\pi$
$14$	−3.28860	+	1.10742i	−0.878914	+	0.295971i
$15$		0			0
$16$	−1.07278	+	3.85346i	−0.268195	+	0.963365i
$17$			5.57978i			1.35329i	0.736307	+	0.676647i	$0.236568\pi$
$17$			5.57978i			1.35329i	−0.736307	+	0.676647i	$0.763432\pi$
$18$		0			0
$19$	−1.03052	−	0.426856i	−0.236418	−	0.0979274i	0.261329	−	0.965250i	$-0.415839\pi$
$19$	−1.03052	−	0.426856i	−0.236418	−	0.0979274i	−0.497747	+	0.867322i	$0.665839\pi$
$20$	5.78263	+	3.37618i	1.29304	+	0.754937i
$21$		0			0
$22$	0.601386	−	8.84597i	0.128216	−	1.88597i
$23$	−2.01868	−	2.01868i	−0.420923	−	0.420923i	0.464598	−	0.885522i	$-0.346199\pi$
$23$	−2.01868	−	2.01868i	−0.420923	−	0.420923i	−0.885522	+	0.464598i	$0.846199\pi$
$24$		0			0
$25$	4.39068	−	4.39068i	0.878136	−	0.878136i
$26$	0.0174428	+	0.0199875i	0.00342081	+	0.00391986i
$27$		0			0
$28$	−4.86224	−	0.664180i	−0.918877	−	0.125518i
$29$	0.706079	−	1.70463i	0.131116	−	0.316541i	−0.844664	−	0.535297i	$-0.820200\pi$
$29$	0.706079	−	1.70463i	0.131116	−	0.316541i	0.975780	+	0.218756i	$0.0701998\pi$
$30$		0			0
$31$	1.38048			0.247941			0.123971	−	0.992286i	$-0.460437\pi$
$31$	1.38048			0.247941			0.123971	+	0.992286i	$0.460437\pi$
$32$	−3.78122	+	4.20742i	−0.668431	+	0.743774i
$33$		0			0
$34$	−3.50729	+	7.06872i	−0.601495	+	1.21228i
$35$	−3.14377	+	7.58973i	−0.531394	+	1.28290i
$36$		0			0
$37$	−2.87315	+	1.19010i	−0.472342	+	0.195651i	−0.606140	−	0.795358i	$-0.707283\pi$
$37$	−2.87315	+	1.19010i	−0.472342	+	0.195651i	0.133797	+	0.991009i	$0.457283\pi$
$38$	−1.03720	−	1.18852i	−0.168256	−	0.192803i
$39$		0			0
$40$	5.20354	+	7.91189i	0.822752	+	1.25098i
$41$	−6.97897	−	6.97897i	−1.08993	−	1.08993i	−0.995535	−	0.0943974i	$-0.969908\pi$
$41$	−6.97897	−	6.97897i	−1.08993	−	1.08993i	−0.0943974	−	0.995535i	$-0.530092\pi$
$42$		0			0
$43$	1.67010	+	4.03197i	0.254687	+	0.614869i	0.998571	−	0.0534396i	$-0.0170184\pi$
$43$	1.67010	+	4.03197i	0.254687	+	0.614869i	−0.743884	+	0.668309i	$0.767018\pi$
$44$	6.32218	−	10.8285i	0.953105	−	1.63245i
$45$		0			0
$46$	−1.28847	−	3.82623i	−0.189975	−	0.564147i
$47$		−	1.15993i		−	0.169193i	−0.996415	−	0.0845966i	$-0.973040\pi$
$47$		−	1.15993i		−	0.169193i	0.996415	−	0.0845966i	$-0.0269601\pi$
$48$		0			0
$49$			0.979375i			0.139911i
$50$	8.32217	−	2.80246i	1.17693	−	0.396328i
$51$		0			0
$52$	0.00953380	+	0.0362851i	0.00132210	+	0.00503183i
$53$	−2.56680	−	6.19681i	−0.352577	−	0.851197i	−0.996300	−	0.0859383i	$-0.972611\pi$
$53$	−2.56680	−	6.19681i	−0.352577	−	0.851197i	0.643723	−	0.765258i	$-0.277389\pi$
$54$		0			0
$55$	−14.8425	−	14.8425i	−2.00136	−	2.00136i
$56$	−5.74222	−	3.89767i	−0.767337	−	0.520849i
$57$		0			0
$58$	1.96597	−	1.71568i	0.258145	−	0.225280i
$59$	0.735935	−	0.304834i	0.0958106	−	0.0396860i	−0.334263	−	0.942480i	$-0.608487\pi$
$59$	0.735935	−	0.304834i	0.0958106	−	0.0396860i	0.430074	+	0.902794i	$0.358487\pi$
$60$		0			0
$61$	4.82262	−	11.6428i	0.617473	−	1.49071i	−0.237156	−	0.971472i	$-0.576215\pi$
$61$	4.82262	−	11.6428i	0.617473	−	1.49071i	0.854629	−	0.519240i	$-0.173785\pi$
$62$	1.74885	+	0.867729i	0.222105	+	0.110202i
$63$		0			0
$64$	−7.43488	+	2.95339i	−0.929360	+	0.369174i
$65$	0.0628036			0.00778983
$66$		0			0
$67$	−2.05899	+	4.97085i	−0.251546	+	0.607286i	−0.998329	−	0.0577816i	$-0.981597\pi$
$67$	−2.05899	+	4.97085i	−0.251546	+	0.607286i	0.746783	+	0.665068i	$0.231597\pi$
$68$	−8.88638	+	6.75040i	−1.07763	+	0.818606i
$69$		0			0
$70$	−8.75336	+	7.63894i	−1.04623	+	0.913028i
$71$	1.78298	−	1.78298i	0.211600	−	0.211600i	−0.593347	−	0.804947i	$-0.702194\pi$
$71$	1.78298	−	1.78298i	0.211600	−	0.211600i	0.804947	+	0.593347i	$0.202194\pi$
$72$		0			0
$73$	1.67500	+	1.67500i	0.196044	+	0.196044i	0.798302	−	0.602258i	$-0.205732\pi$
$73$	1.67500	+	1.67500i	0.196044	+	0.196044i	−0.602258	+	0.798302i	$0.705732\pi$
$74$	−4.38789	−	0.298307i	−0.510082	−	0.0346775i
$75$		0			0
$76$	−0.566909	−	2.15762i	−0.0650290	−	0.247496i
$77$	14.2124	+	5.88697i	1.61965	+	0.670883i
$78$		0			0
$79$		−	2.67236i		−	0.300664i	−0.988636	−	0.150332i	$-0.951966\pi$
$79$		−	2.67236i		−	0.300664i	0.988636	−	0.150332i	$-0.0480343\pi$
$80$	1.61890	+	13.2939i	0.180998	+	1.48631i
$81$		0			0
$82$	−4.45450	−	13.2281i	−0.491918	−	1.46079i
$83$	6.91877	+	2.86585i	0.759433	+	0.314568i	0.728584	−	0.684956i	$-0.240179\pi$
$83$	6.91877	+	2.86585i	0.759433	+	0.314568i	0.0308494	+	0.999524i	$0.490179\pi$
$84$		0			0
$85$	7.14903	+	17.2593i	0.775421	+	1.87203i
$86$	−0.418623	+	6.15766i	−0.0451413	+	0.663997i
$87$		0			0
$88$	14.8157	−	9.74406i	1.57936	−	1.03872i
$89$	−6.73869	+	6.73869i	−0.714300	+	0.714300i	−0.967432	−	0.253132i	$-0.918539\pi$
$89$	−6.73869	+	6.73869i	−0.714300	+	0.714300i	0.253132	+	0.967432i	$0.418539\pi$
$90$		0			0
$91$	−0.0425236	+	0.0176139i	−0.00445769	+	0.00184643i
$92$	0.772764	−	5.65714i	0.0805662	−	0.589798i
$93$		0			0
$94$	0.729098	−	1.46945i	0.0752007	−	0.151562i
$95$	−3.73450			−0.383151
$96$		0			0
$97$	−1.75001			−0.177686			−0.0888431	−	0.996046i	$-0.528317\pi$
$97$	−1.75001			−0.177686			−0.0888431	+	0.996046i	$0.528317\pi$
$98$	−0.615607	+	1.24072i	−0.0621857	+	0.125331i
$99$		0			0
$100$	12.3045	+	1.68078i	1.23045	+	0.168078i
$101$	7.71200	−	3.19442i	0.767373	−	0.317856i	0.0355651	−	0.999367i	$-0.488677\pi$
$101$	7.71200	−	3.19442i	0.767373	−	0.317856i	0.731808	+	0.681511i	$0.238677\pi$
$102$		0			0
$103$	−3.90293	+	3.90293i	−0.384567	+	0.384567i	−0.872744	−	0.488177i	$-0.837662\pi$
$103$	−3.90293	+	3.90293i	−0.384567	+	0.384567i	0.488177	+	0.872744i	$0.337662\pi$
$104$	−0.0107299	+	0.0519602i	−0.00105215	+	0.00509512i
$105$		0			0
$106$	0.643389	−	9.46381i	0.0624915	−	0.919207i
$107$	5.55747	+	13.4169i	0.537261	+	1.29706i	0.926628	+	0.375981i	$0.122694\pi$
$107$	5.55747	+	13.4169i	0.537261	+	1.29706i	−0.389366	+	0.921083i	$0.627306\pi$
$108$		0			0
$109$	14.8488	+	6.15056i	1.42225	+	0.589117i	0.955426	−	0.295231i	$-0.0953967\pi$
$109$	14.8488	+	6.15056i	1.42225	+	0.589117i	0.466828	+	0.884348i	$0.345397\pi$
$110$	−9.47360	−	28.1327i	−0.903273	−	2.68235i
$111$		0			0
$112$	−4.82455	−	8.54715i	−0.455877	−	0.807630i
$113$		−	2.72924i		−	0.256745i	−0.991726	−	0.128373i	$-0.959025\pi$
$113$		−	2.72924i		−	0.256745i	0.991726	−	0.128373i	$-0.0409753\pi$
$114$		0			0
$115$	−8.83055	−	3.65773i	−0.823453	−	0.341085i
$116$	3.56901	−	0.937747i	0.331374	−	0.0870677i
$117$		0			0
$118$	1.12393	+	0.0764092i	0.103466	+	0.00703403i
$119$	−9.68106	−	9.68106i	−0.887461	−	0.887461i
$120$		0			0
$121$	−20.0157	+	20.0157i	−1.81961	+	1.81961i
$122$	13.4279	−	11.7183i	1.21570	−	1.06093i
$123$		0			0
$124$	1.67010	+	2.19856i	0.149979	+	0.197436i
$125$	1.54948	−	3.74078i	0.138590	−	0.334585i
$126$		0			0
$127$	15.3336			1.36064			0.680319	−	0.732916i	$-0.261841\pi$
$127$	15.3336			1.36064			0.680319	+	0.732916i	$0.261841\pi$
$128$	−11.2753	−	0.931859i	−0.996602	−	0.0823655i
$129$		0			0
$130$	0.0795625	+	0.0394765i	0.00697809	+	0.00346232i
$131$	−5.70595	+	13.7754i	−0.498531	+	1.20356i	0.451744	+	0.892148i	$0.350802\pi$
$131$	−5.70595	+	13.7754i	−0.498531	+	1.20356i	−0.950275	+	0.311412i	$0.899198\pi$
$132$		0			0
$133$	2.52859	−	1.04737i	0.219256	−	0.0908189i
$134$	−5.73296	+	5.00308i	−0.495252	+	0.432200i
$135$		0			0
$136$	−15.5008	+	2.96600i	−1.32918	+	0.254332i
$137$	3.06155	+	3.06155i	0.261566	+	0.261566i	0.825690	−	0.564124i	$-0.190786\pi$
$137$	3.06155	+	3.06155i	0.261566	+	0.261566i	−0.564124	+	0.825690i	$0.690786\pi$
$138$		0			0
$139$	0.621401	+	1.50020i	0.0527066	+	0.127245i	0.948040	−	0.318152i	$-0.103062\pi$
$139$	0.621401	+	1.50020i	0.0527066	+	0.127245i	−0.895333	+	0.445397i	$0.853062\pi$
$140$	−15.8908	+	4.17526i	−1.34302	+	0.352874i
$141$		0			0
$142$	3.37948	−	1.13803i	0.283600	−	0.0955013i
$143$		−	0.117605i		−	0.00983462i
$144$		0			0
$145$		−	6.17738i		−	0.513003i
$146$	1.06911	+	3.17483i	0.0884804	+	0.262751i
$147$		0			0
$148$	−5.37128	−	3.13601i	−0.441516	−	0.257779i
$149$	8.53959	+	20.6164i	0.699591	+	1.68896i	0.724503	+	0.689272i	$0.242070\pi$
$149$	8.53959	+	20.6164i	0.699591	+	1.68896i	−0.0249118	+	0.999690i	$0.507930\pi$
$150$		0			0
$151$	9.42348	+	9.42348i	0.766872	+	0.766872i	0.977555	−	0.210683i	$-0.0675687\pi$
$151$	9.42348	+	9.42348i	0.766872	+	0.766872i	−0.210683	+	0.977555i	$0.567569\pi$
$152$	0.638031	−	3.08972i	0.0517512	−	0.250609i
$153$		0			0
$154$	14.3046	+	16.3914i	1.15269	+	1.32086i
$155$	4.27007	−	1.76872i	0.342981	−	0.142067i
$156$		0			0
$157$	7.53965	−	18.2023i	0.601729	−	1.45270i	−0.270070	−	0.962841i	$-0.587047\pi$
$157$	7.53965	−	18.2023i	0.601729	−	1.45270i	0.871800	−	0.489863i	$-0.162953\pi$
$158$	1.67977	−	3.38547i	0.133635	−	0.269334i
$159$		0			0
$160$	−6.30529	+	17.8590i	−0.498477	+	1.41188i
$161$	7.00491			0.552064
$162$		0			0
$163$	−6.01448	+	14.5202i	−0.471090	+	1.13731i	0.492592	+	0.870260i	$0.336050\pi$
$163$	−6.01448	+	14.5202i	−0.471090	+	1.13731i	−0.963682	+	0.267052i	$0.913950\pi$
$164$	2.67160	−	19.5579i	0.208617	−	1.52721i
$165$		0			0
$166$	6.96363	+	7.97952i	0.540482	+	0.619331i
$167$	11.8392	−	11.8392i	0.916142	−	0.916142i	−0.0806038	−	0.996746i	$-0.525685\pi$
$167$	11.8392	−	11.8392i	0.916142	−	0.916142i	0.996746	+	0.0806038i	$0.0256848\pi$
$168$		0			0
$169$	−9.19214	−	9.19214i	−0.707088	−	0.707088i
$170$	−1.79196	+	26.3585i	−0.137437	+	2.02161i
$171$		0			0
$172$	−4.40085	+	7.53767i	−0.335562	+	0.574742i
$173$	−21.0615	−	8.72397i	−1.60128	−	0.663271i	−0.609683	−	0.792645i	$-0.708703\pi$
$173$	−21.0615	−	8.72397i	−1.60128	−	0.663271i	−0.991596	+	0.129374i	$0.958703\pi$
$174$		0			0
$175$			15.2359i			1.15172i
$176$	24.8940	−	3.03152i	1.87646	−	0.228509i
$177$		0			0
$178$	−12.7726	+	4.30114i	−0.957349	+	0.322384i
$179$	4.75826	+	1.97094i	0.355649	+	0.147315i	0.553353	−	0.832947i	$-0.313348\pi$
$179$	4.75826	+	1.97094i	0.355649	+	0.147315i	−0.197703	+	0.980262i	$0.563348\pi$
$180$		0			0
$181$	−3.71100	−	8.95914i	−0.275836	−	0.665928i	0.723876	−	0.689931i	$-0.242359\pi$
$181$	−3.71100	−	8.95914i	−0.275836	−	0.665928i	−0.999712	+	0.0240027i	$0.992359\pi$
$182$	−0.0649424	−	0.00441506i	−0.00481385	−	0.000327266i
$183$		0			0
$184$	4.53489	−	6.68099i	0.334316	−	0.492529i
$185$	−7.36237	+	7.36237i	−0.541293	+	0.541293i
$186$		0			0
$187$	32.3195	−	13.3872i	2.36343	−	0.978966i
$188$	1.84731	−	1.40328i	0.134729	−	0.102345i
$189$		0			0
$190$	−4.73103	−	2.34739i	−0.343225	−	0.170298i
$191$	−11.4844			−0.830980			−0.415490	−	0.909598i	$-0.636390\pi$
$191$	−11.4844			−0.830980			−0.415490	+	0.909598i	$0.636390\pi$
$192$		0			0
$193$	19.2681			1.38695			0.693474	−	0.720482i	$-0.256079\pi$
$193$	19.2681			1.38695			0.693474	+	0.720482i	$0.256079\pi$
$194$	−2.21699	−	1.10000i	−0.159170	−	0.0789756i
$195$		0			0
$196$	−1.55976	+	1.18485i	−0.111411	+	0.0846319i
$197$	−6.48659	+	2.68683i	−0.462151	+	0.191429i	−0.601596	−	0.798801i	$-0.705468\pi$
$197$	−6.48659	+	2.68683i	−0.462151	+	0.191429i	0.139445	+	0.990230i	$0.455468\pi$
$198$		0			0
$199$	14.6525	−	14.6525i	1.03868	−	1.03868i	0.0394638	−	0.999221i	$-0.487435\pi$
$199$	14.6525	−	14.6525i	1.03868	−	1.03868i	0.999221	−	0.0394638i	$-0.0125650\pi$
$200$	14.5314	+	9.86352i	1.02752	+	0.697456i
$201$		0			0
$202$	11.7778	+	0.800706i	0.828686	+	0.0563375i
$203$	1.73250	+	4.18263i	0.121598	+	0.293563i
$204$		0			0
$205$	−30.5290	−	12.6455i	−2.13224	−	0.883201i
$206$	−7.39768	+	2.49114i	−0.515421	+	0.173566i
$207$		0			0
$208$	−0.0462538	+	0.0590811i	−0.00320712	+	0.00409654i
$209$			6.99316i			0.483727i
$210$		0			0
$211$	−2.80379	−	1.16137i	−0.193021	−	0.0799519i	0.284079	−	0.958801i	$-0.408312\pi$
$211$	−2.80379	−	1.16137i	−0.193021	−	0.0799519i	−0.477100	+	0.878849i	$0.658312\pi$
$212$	6.76375	−	11.5848i	0.464536	−	0.795646i
$213$		0			0
$214$	−1.39303	+	20.4905i	−0.0952253	+	1.40070i
$215$	10.3318	+	10.3318i	0.704625	+	0.704625i
$216$		0			0
$217$	−2.39517	+	2.39517i	−0.162594	+	0.162594i
$218$	14.9450	+	17.1253i	1.01221	+	1.15987i
$219$		0			0
$220$	5.68182	−	41.5947i	0.383068	−	2.80431i
$221$	−0.0400544	+	0.0966999i	−0.00269435	+	0.00650474i
$222$		0			0
$223$	−6.12103			−0.409894			−0.204947	−	0.978773i	$-0.565702\pi$
$223$	−6.12103			−0.409894			−0.204947	+	0.978773i	$0.565702\pi$
$224$	−0.739472	−	13.8605i	−0.0494080	−	0.926093i
$225$		0			0
$226$	1.71552	−	3.45752i	0.114115	−	0.229991i
$227$	6.52469	−	15.7520i	0.433059	−	1.04550i	−0.545237	−	0.838282i	$-0.683560\pi$
$227$	6.52469	−	15.7520i	0.433059	−	1.04550i	0.978296	−	0.207214i	$-0.0664397\pi$
$228$		0			0
$229$	−8.60895	+	3.56595i	−0.568896	+	0.235644i	−0.648542	−	0.761179i	$-0.724621\pi$
$229$	−8.60895	+	3.56595i	−0.568896	+	0.235644i	0.0796463	+	0.996823i	$0.474621\pi$
$230$	−8.88780	−	10.1844i	−0.586044	−	0.671540i
$231$		0			0
$232$	5.11083	+	1.05539i	0.335542	+	0.0692900i
$233$	−7.99720	−	7.99720i	−0.523914	−	0.523914i	0.394837	−	0.918751i	$-0.370801\pi$
$233$	−7.99720	−	7.99720i	−0.523914	−	0.523914i	−0.918751	+	0.394837i	$0.870801\pi$
$234$		0			0
$235$	−1.48615	−	3.58788i	−0.0969456	−	0.234047i
$236$	1.37581	+	0.803266i	0.0895578	+	0.0522881i
$237$		0			0
$238$	−6.17918	−	18.3496i	−0.400537	−	1.18943i
$239$		−	6.26707i		−	0.405383i	−0.979243	−	0.202692i	$-0.935031\pi$
$239$		−	6.26707i		−	0.405383i	0.979243	−	0.202692i	$-0.0649689\pi$
$240$		0			0
$241$			15.7602i			1.01520i	0.861592	+	0.507601i	$0.169468\pi$
$241$			15.7602i			1.01520i	−0.861592	+	0.507601i	$0.830532\pi$
$242$	−37.9380	+	12.7755i	−2.43875	+	0.821240i
$243$		0			0
$244$	24.3768	−	6.40494i	1.56057	−	0.410034i
$245$	1.25481	+	3.02939i	0.0801671	+	0.193541i
$246$		0			0
$247$	−0.0147952	−	0.0147952i	−0.000941395	−	0.000941395i
$248$	0.733811	+	3.83501i	0.0465970	+	0.243523i
$249$		0			0
$250$	4.31430	−	3.76503i	0.272860	−	0.238121i
$251$	19.0196	−	7.87816i	1.20050	−	0.497265i	0.309342	−	0.950951i	$-0.399891\pi$
$251$	19.0196	−	7.87816i	1.20050	−	0.497265i	0.891162	+	0.453686i	$0.149891\pi$
$252$		0			0
$253$	−6.84941	+	16.5359i	−0.430619	+	1.03961i
$254$	19.4253	+	9.63826i	1.21885	+	0.604758i
$255$		0			0
$256$	−13.6983	−	8.26783i	−0.856143	−	0.516739i
$257$	5.22771			0.326096			0.163048	−	0.986618i	$-0.447868\pi$
$257$	5.22771			0.326096			0.163048	+	0.986618i	$0.447868\pi$
$258$		0			0
$259$	2.92013	−	7.04983i	0.181448	−	0.438055i
$260$	0.0759796	+	0.100021i	0.00471206	+	0.00620306i
$261$		0			0
$262$	−15.8874	+	13.8647i	−0.981524	+	0.856563i
$263$	−5.59065	+	5.59065i	−0.344734	+	0.344734i	−0.858144	−	0.513410i	$-0.828382\pi$
$263$	−5.59065	+	5.59065i	−0.344734	+	0.344734i	0.513410	+	0.858144i	$0.328382\pi$
$264$		0			0
$265$	−15.8792	−	15.8792i	−0.975450	−	0.975450i
$266$	3.86168	+	0.262533i	0.236775	+	0.0160969i
$267$		0			0
$268$	−10.4076	+	2.73456i	−0.635743	+	0.167040i
$269$	−9.92617	−	4.11155i	−0.605209	−	0.250686i	0.0589693	−	0.998260i	$-0.481219\pi$
$269$	−9.92617	−	4.11155i	−0.605209	−	0.250686i	−0.664179	+	0.747574i	$0.731219\pi$
$270$		0			0
$271$			15.4368i			0.937717i	0.883273	+	0.468858i	$0.155335\pi$
$271$			15.4368i			0.937717i	−0.883273	+	0.468858i	$0.844665\pi$
$272$	−21.5014	−	5.98587i	−1.30372	−	0.362947i
$273$		0			0
$274$	1.95411	+	5.80292i	0.118052	+	0.350567i
$275$	−35.9662	−	14.8977i	−2.16884	−	0.898363i
$276$		0			0
$277$	1.79136	+	4.32473i	0.107633	+	0.259848i	0.968515	−	0.248956i	$-0.0800876\pi$
$277$	1.79136	+	4.32473i	0.107633	+	0.259848i	−0.860882	+	0.508804i	$0.830088\pi$
$278$	−0.155759	+	2.29111i	−0.00934182	+	0.137412i
$279$		0			0
$280$	−22.7556	−	4.69907i	−1.35991	−	0.280823i
$281$	3.70347	−	3.70347i	0.220931	−	0.220931i	−0.587960	−	0.808890i	$-0.700069\pi$
$281$	3.70347	−	3.70347i	0.220931	−	0.220931i	0.808890	+	0.587960i	$0.200069\pi$
$282$		0			0
$283$	−16.1605	+	6.69389i	−0.960641	+	0.397910i	−0.807220	−	0.590250i	$-0.799029\pi$
$283$	−16.1605	+	6.69389i	−0.960641	+	0.397910i	−0.153421	+	0.988161i	$0.549029\pi$
$284$	4.99662	+	0.682536i	0.296495	+	0.0405011i
$285$		0			0
$286$	0.0739231	−	0.148987i	0.00437116	−	0.00880981i
$287$	24.2174			1.42951
$288$		0			0
$289$	−14.1339			−0.831407
$290$	3.88292	−	7.82579i	0.228013	−	0.459546i
$291$		0			0
$292$	−0.641203	+	4.69403i	−0.0375236	+	0.274697i
$293$	−13.5656	+	5.61904i	−0.792509	+	0.328268i	−0.741952	−	0.670453i	$-0.766100\pi$
$293$	−13.5656	+	5.61904i	−0.792509	+	0.328268i	−0.0505573	+	0.998721i	$0.516100\pi$
$294$		0			0
$295$	1.88582	−	1.88582i	0.109796	−	0.109796i
$296$	−4.83338	−	7.34907i	−0.280934	−	0.427156i
$297$		0			0
$298$	−2.14052	+	31.4855i	−0.123997	+	1.82391i
$299$	−0.0204935	−	0.0494756i	−0.00118517	−	0.00286125i
$300$		0			0
$301$	−9.89322	−	4.09791i	−0.570236	−	0.236199i
$302$	6.01477	+	17.8614i	0.346111	+	1.02781i
$303$		0			0
$304$	2.75039	−	3.51315i	0.157746	−	0.201493i
$305$		−	42.1923i		−	2.41593i
$306$		0			0
$307$	15.6321	+	6.47504i	0.892173	+	0.369550i	0.781206	−	0.624274i	$-0.214605\pi$
$307$	15.6321	+	6.47504i	0.892173	+	0.369550i	0.110968	+	0.993824i	$0.464605\pi$
$308$	7.81852	+	29.7568i	0.445502	+	1.69555i
$309$		0			0
$310$	6.52129	+	0.443345i	0.370385	+	0.0251803i
$311$	−22.8167	−	22.8167i	−1.29381	−	1.29381i	−0.932408	−	0.361407i	$-0.882297\pi$
$311$	−22.8167	−	22.8167i	−1.29381	−	1.29381i	−0.361407	−	0.932408i	$-0.617703\pi$
$312$		0			0
$313$	7.52178	−	7.52178i	0.425156	−	0.425156i	−0.461819	−	0.886974i	$-0.652803\pi$
$313$	7.52178	−	7.52178i	0.425156	−	0.425156i	0.886974	+	0.461819i	$0.152803\pi$
$314$	20.9930	−	18.3203i	1.18470	−	1.03388i
$315$		0			0
$316$	4.25602	−	3.23302i	0.239420	−	0.181872i
$317$	9.98241	−	24.0997i	0.560668	−	1.35357i	−0.348565	−	0.937285i	$-0.613331\pi$
$317$	9.98241	−	24.0997i	0.560668	−	1.35357i	0.909233	−	0.416288i	$-0.136669\pi$
$318$		0			0
$319$	−11.5677			−0.647665
$320$	−19.2135	+	18.6612i	−1.07407	+	1.04320i
$321$		0			0
$322$	8.87414	+	4.40308i	0.494537	+	0.245374i
$323$	2.38176	−	5.75008i	0.132525	−	0.319943i
$324$		0			0
$325$	0.107611	−	0.0445739i	0.00596918	−	0.00247251i
$326$	−16.7464	+	14.6144i	−0.927498	+	0.809415i
$327$		0			0
$328$	15.6780	−	23.0975i	0.865674	−	1.27535i
$329$	2.01251	+	2.01251i	0.110953	+	0.110953i
$330$		0			0
$331$	−12.9034	−	31.1516i	−0.709235	−	1.71225i	−0.701903	−	0.712272i	$-0.747666\pi$
$331$	−12.9034	−	31.1516i	−0.709235	−	1.71225i	−0.00733222	−	0.999973i	$-0.502334\pi$
$332$	3.80615	+	14.4860i	0.208889	+	0.795020i
$333$		0			0
$334$	22.4402	−	7.55665i	1.22787	−	0.413481i
$335$			18.0138i			0.984200i
$336$		0			0
$337$		−	0.925243i		−	0.0504012i	−0.999682	−	0.0252006i	$-0.991978\pi$
$337$		−	0.925243i		−	0.0504012i	0.999682	−	0.0252006i	$-0.00802245\pi$
$338$	−5.86711	−	17.4229i	−0.319129	−	0.947683i
$339$		0			0
$340$	−18.8383	+	32.2658i	−1.02165	+	1.74986i
$341$	−3.31208	−	7.99607i	−0.179359	−	0.433012i
$342$		0			0
$343$	−13.8444	−	13.8444i	−0.747528	−	0.747528i
$344$	−10.3132	+	6.78282i	−0.556048	+	0.365705i
$345$		0			0
$346$	−21.1981	−	24.2906i	−1.13962	−	1.30587i
$347$	−8.68292	+	3.59658i	−0.466123	+	0.193075i	−0.603369	−	0.797462i	$-0.706175\pi$
$347$	−8.68292	+	3.59658i	−0.466123	+	0.193075i	0.137245	+	0.990537i	$0.456175\pi$
$348$		0			0
$349$	0.586633	−	1.41626i	0.0314017	−	0.0758105i	−0.907401	−	0.420266i	$-0.861937\pi$
$349$	0.586633	−	1.41626i	0.0314017	−	0.0758105i	0.938802	+	0.344456i	$0.111937\pi$
$350$	−9.57683	+	19.3015i	−0.511903	+	1.03171i
$351$		0			0
$352$	33.4424	+	11.8072i	1.78249	+	0.629326i
$353$	−10.8550			−0.577751			−0.288876	−	0.957367i	$-0.593281\pi$
$353$	−10.8550			−0.577751			−0.288876	+	0.957367i	$0.593281\pi$
$354$		0			0
$355$	3.23066	−	7.79949i	0.171465	−	0.413954i
$356$	−18.8845	−	2.57962i	−1.00088	−	0.136720i
$357$		0			0
$358$	4.78911	+	5.48778i	0.253113	+	0.290038i
$359$	−21.6767	+	21.6767i	−1.14406	+	1.14406i	−0.156354	+	0.987701i	$0.549974\pi$
$359$	−21.6767	+	21.6767i	−1.14406	+	1.14406i	−0.987701	+	0.156354i	$0.950026\pi$
$360$		0			0
$361$	−12.5553	−	12.5553i	−0.660803	−	0.660803i
$362$	0.930192	−	13.6825i	0.0488898	−	0.719135i
$363$		0			0
$364$	−0.0794969	−	0.0464141i	−0.00416677	−	0.00243276i
$365$	7.32717	+	3.03501i	0.383521	+	0.158860i
$366$		0			0
$367$		−	0.154514i		−	0.00806555i	−0.999992	−	0.00403277i	$-0.998716\pi$
$367$		−	0.154514i		−	0.00806555i	0.999992	−	0.00403277i	$-0.00128367\pi$
$368$	9.94448	−	5.61329i	0.518392	−	0.292613i
$369$		0			0
$370$	−13.9548	+	4.69922i	−0.725474	+	0.244301i
$371$	15.2051	+	6.29815i	0.789408	+	0.326984i
$372$		0			0
$373$	5.40842	+	13.0571i	0.280037	+	0.676070i	0.999836	−	0.0181131i	$-0.00576589\pi$
$373$	5.40842	+	13.0571i	0.280037	+	0.676070i	−0.719799	+	0.694183i	$0.755766\pi$
$374$	49.3585	+	3.35560i	2.55227	+	0.173514i
$375$		0			0
$376$	3.22232	−	0.616575i	0.166178	−	0.0317974i
$377$	0.0244733	−	0.0244733i	0.00126044	−	0.00126044i
$378$		0			0
$379$	17.4888	−	7.24410i	0.898340	−	0.372105i	0.114758	−	0.993393i	$-0.463391\pi$
$379$	17.4888	−	7.24410i	0.898340	−	0.372105i	0.783582	+	0.621289i	$0.213391\pi$
$380$	−4.51798	−	5.94758i	−0.231768	−	0.305104i
$381$		0			0
$382$	−14.5489	−	7.21874i	−0.744388	−	0.369343i
$383$	30.0898			1.53752			0.768759	−	0.639538i	$-0.220874\pi$
$383$	30.0898			1.53752			0.768759	+	0.639538i	$0.220874\pi$
$384$		0			0
$385$	51.5042			2.62490
$386$	24.4097	+	12.1114i	1.24242	+	0.616452i
$387$		0			0
$388$	−2.11715	−	2.78707i	−0.107482	−	0.141492i
$389$	−11.7666	+	4.87387i	−0.596589	+	0.247115i	−0.660482	−	0.750842i	$-0.729648\pi$
$389$	−11.7666	+	4.87387i	−0.596589	+	0.247115i	0.0638936	+	0.997957i	$0.479648\pi$
$390$		0			0
$391$	11.2638	−	11.2638i	0.569633	−	0.569633i
$392$	−2.72073	+	0.520599i	−0.137418	+	0.0262942i
$393$		0			0
$394$	−9.90638	−	0.673477i	−0.499076	−	0.0339293i
$395$	−3.42394	−	8.26611i	−0.172277	−	0.415913i
$396$		0			0
$397$	15.2331	+	6.30976i	0.764527	+	0.316678i	0.730653	−	0.682749i	$-0.239216\pi$
$397$	15.2331	+	6.30976i	0.764527	+	0.316678i	0.0338739	+	0.999426i	$0.489216\pi$
$398$	27.7725	−	9.35230i	1.39211	−	0.468788i
$399$		0			0
$400$	12.2091	+	21.6295i	0.610454	+	1.08148i
$401$			35.7766i			1.78660i	0.449463	+	0.893299i	$0.351615\pi$
$401$			35.7766i			1.78660i	−0.449463	+	0.893299i	$0.648385\pi$
$402$		0			0
$403$	0.0239243	+	0.00990976i	0.00119175	+	0.000493641i
$404$	14.4174	+	8.41757i	0.717293	+	0.418790i
$405$		0			0
$406$	−0.434266	+	6.38776i	−0.0215523	+	0.317019i
$407$	13.7867	+	13.7867i	0.683380	+	0.683380i
$408$		0			0
$409$	−4.31657	+	4.31657i	−0.213440	+	0.213440i	−0.805727	−	0.592287i	$-0.798225\pi$
$409$	−4.31657	+	4.31657i	−0.213440	+	0.213440i	0.592287	+	0.805727i	$0.298225\pi$
$410$	−30.7269	−	35.2095i	−1.51749	−	1.73887i
$411$		0			0
$412$	−10.9376	−	1.49407i	−0.538856	−	0.0736075i
$413$	−0.747970	+	1.80576i	−0.0368052	+	0.0888557i
$414$		0			0
$415$	25.0729			1.23078
$416$	−0.0957331	+	0.0457729i	−0.00469370	+	0.00224420i
$417$		0			0
$418$	−4.39569	+	8.85925i	−0.215000	+	0.433320i
$419$	7.37576	−	17.8067i	0.360330	−	0.869913i	−0.634922	−	0.772576i	$-0.718968\pi$
$419$	7.37576	−	17.8067i	0.360330	−	0.869913i	0.995252	−	0.0973364i	$-0.0310323\pi$
$420$		0			0
$421$	−5.03356	+	2.08497i	−0.245321	+	0.101615i	−0.501956	−	0.864893i	$-0.667386\pi$
$421$	−5.03356	+	2.08497i	−0.245321	+	0.101615i	0.256635	+	0.966508i	$0.417386\pi$
$422$	−2.82197	−	3.23365i	−0.137371	−	0.157412i
$423$		0			0
$424$	15.8505	−	10.4246i	0.769768	−	0.506265i
$425$	24.4990	+	24.4990i	1.18838	+	1.18838i
$426$		0			0
$427$	11.8332	+	28.5680i	0.572651	+	1.38250i
$428$	−14.6444	+	25.0826i	−0.707866	+	1.21241i
$429$		0			0
$430$	6.59455	+	19.5831i	0.318017	+	0.944382i
$431$			18.4128i			0.886914i	0.896296	+	0.443457i	$0.146248\pi$
$431$			18.4128i			0.886914i	−0.896296	+	0.443457i	$0.853752\pi$
$432$		0			0
$433$			0.227663i			0.0109408i	0.999985	+	0.00547038i	$0.00174129\pi$
$433$			0.227663i			0.0109408i	−0.999985	+	0.00547038i	$0.998259\pi$
$434$	−4.53984	+	1.52877i	−0.217919	+	0.0733835i
$435$		0			0
$436$	8.16859	+	31.0891i	0.391204	+	1.48890i
$437$	1.21860	+	2.94197i	0.0582938	+	0.140734i
$438$		0			0
$439$	−19.0619	−	19.0619i	−0.909774	−	0.909774i	0.0864799	−	0.996254i	$-0.472438\pi$
$439$	−19.0619	−	19.0619i	−0.909774	−	0.909774i	−0.996254	+	0.0864799i	$0.972438\pi$
$440$	33.3432	−	49.1226i	1.58957	−	2.34183i
$441$		0			0
$442$	−0.111526	+	0.0973269i	−0.00530473	+	0.00462937i
$443$	−28.0493	+	11.6184i	−1.33266	+	0.552008i	−0.931414	−	0.363961i	$-0.881424\pi$
$443$	−28.0493	+	11.6184i	−1.33266	+	0.552008i	−0.401250	+	0.915968i	$0.631424\pi$
$444$		0			0
$445$	−12.2101	+	29.4779i	−0.578816	+	1.39739i
$446$	−7.75440	−	3.84750i	−0.367182	−	0.182184i
$447$		0			0
$448$	7.77550	−	18.0239i	0.367358	−	0.851550i
$449$	−33.0005			−1.55739			−0.778696	−	0.627401i	$-0.784119\pi$
$449$	−33.0005			−1.55739			−0.778696	+	0.627401i	$0.784119\pi$
$450$		0			0
$451$	−23.6798	+	57.1681i	−1.11504	+	2.69194i
$452$	4.34660	−	3.30183i	0.204447	−	0.155305i
$453$		0			0
$454$	18.1670	−	15.8541i	0.852620	−	0.744070i
$455$	−0.108966	+	0.108966i	−0.00510839	+	0.00510839i
$456$		0			0
$457$	19.3344	+	19.3344i	0.904423	+	0.904423i	0.995815	−	0.0913920i	$-0.0291316\pi$
$457$	19.3344	+	19.3344i	0.904423	+	0.904423i	−0.0913920	+	0.995815i	$0.529132\pi$
$458$	−13.1477	−	0.893833i	−0.614350	−	0.0417661i
$459$		0			0
$460$	−4.85785	−	18.4887i	−0.226498	−	0.862039i
$461$	19.0532	+	7.89211i	0.887398	+	0.367572i	0.779361	−	0.626575i	$-0.215544\pi$
$461$	19.0532	+	7.89211i	0.887398	+	0.367572i	0.108037	+	0.994147i	$0.465544\pi$
$462$		0			0
$463$		−	18.6664i		−	0.867499i	−0.901034	−	0.433749i	$-0.857190\pi$
$463$		−	18.6664i		−	0.867499i	0.901034	−	0.433749i	$-0.142810\pi$
$464$	5.81124	+	4.54954i	0.269780	+	0.211207i
$465$		0			0
$466$	−5.10441	−	15.1580i	−0.236457	−	0.702182i
$467$	1.38748	+	0.574712i	0.0642048	+	0.0265945i	0.414555	−	0.910024i	$-0.363937\pi$
$467$	1.38748	+	0.574712i	0.0642048	+	0.0265945i	−0.350350	+	0.936619i	$0.613937\pi$
$468$		0			0
$469$	−5.05214	−	12.1970i	−0.233286	−	0.563203i
$470$	0.372515	−	5.47944i	0.0171828	−	0.252748i
$471$		0			0
$472$	1.23803	+	1.88241i	0.0569851	+	0.0866449i
$473$	19.3472	−	19.3472i	0.889586	−	0.889586i
$474$		0			0
$475$	−6.39888	+	2.65050i	−0.293601	+	0.121613i
$476$	3.70598	−	27.1302i	0.169863	−	1.24351i
$477$		0			0
$478$	3.93930	−	7.93942i	0.180179	−	0.363140i
$479$	20.1621			0.921229			0.460615	−	0.887600i	$-0.347629\pi$
$479$	20.1621			0.921229			0.460615	+	0.887600i	$0.347629\pi$
$480$		0			0
$481$	−0.0583360			−0.00265989
$482$	−9.90639	+	19.9657i	−0.451224	+	0.909414i
$483$		0			0
$484$	−56.0919	−	7.66214i	−2.54963	−	0.348279i
$485$	−5.41309	+	2.24218i	−0.245796	+	0.101812i
$486$		0			0
$487$	−14.3589	+	14.3589i	−0.650665	+	0.650665i	−0.953153	−	0.302488i	$-0.902183\pi$
$487$	−14.3589	+	14.3589i	−0.650665	+	0.650665i	0.302488	+	0.953153i	$0.402183\pi$
$488$	34.9076	+	7.20848i	1.58019	+	0.326313i
$489$		0			0
$490$	−0.314529	+	4.62651i	−0.0142090	+	0.209004i
$491$	−7.84066	−	18.9290i	−0.353844	−	0.854255i	−0.996138	−	0.0877968i	$-0.972017\pi$
$491$	−7.84066	−	18.9290i	−0.353844	−	0.854255i	0.642294	−	0.766458i	$-0.277983\pi$
$492$		0			0
$493$	9.51144	+	3.93977i	0.428374	+	0.177438i
$494$	−0.00944340	−	0.0280430i	−0.000424879	−	0.00126172i
$495$		0			0
$496$	−1.48095	+	5.31962i	−0.0664966	+	0.238858i
$497$			6.18702i			0.277526i
$498$		0			0
$499$	11.1249	+	4.60809i	0.498020	+	0.206286i	0.617531	−	0.786546i	$-0.288133\pi$
$499$	11.1249	+	4.60809i	0.498020	+	0.206286i	−0.119512	+	0.992833i	$0.538133\pi$
$500$	7.83214	−	2.05787i	0.350264	−	0.0920308i
$501$		0			0
$502$	29.0468	+	1.97472i	1.29642	+	0.0881363i
$503$	10.7388	+	10.7388i	0.478820	+	0.478820i	0.904754	−	0.425934i	$-0.140054\pi$
$503$	10.7388	+	10.7388i	0.478820	+	0.478820i	−0.425934	+	0.904754i	$0.640054\pi$
$504$		0			0
$505$	19.7618	−	19.7618i	0.879390	−	0.879390i
$506$	−19.0712	+	16.6431i	−0.847816	+	0.739878i
$507$		0			0
$508$	18.5506	+	24.4204i	0.823048	+	1.08348i
$509$	7.73386	−	18.6712i	0.342797	−	0.827586i	−0.654633	−	0.755947i	$-0.727177\pi$
$509$	7.73386	−	18.6712i	0.342797	−	0.827586i	0.997431	−	0.0716392i	$-0.0228230\pi$
$510$		0			0
$511$	−5.81234			−0.257123
$512$	−12.1567	−	19.0844i	−0.537256	−	0.843419i
$513$		0			0
$514$	6.62270	+	3.28599i	0.292115	+	0.144939i
$515$	−7.07189	+	17.0731i	−0.311625	+	0.752329i
$516$		0			0
$517$	−6.71860	+	2.78294i	−0.295484	+	0.122393i
$518$	8.13068	−	7.09554i	0.357241	−	0.311760i
$519$		0			0
$520$	0.0333840	+	0.174470i	0.00146399	+	0.00765102i
$521$	−13.6485	−	13.6485i	−0.597953	−	0.597953i	0.341815	−	0.939767i	$-0.388958\pi$
$521$	−13.6485	−	13.6485i	−0.597953	−	0.597953i	−0.939767	+	0.341815i	$0.888958\pi$
$522$		0			0
$523$	−6.91544	−	16.6954i	−0.302391	−	0.730037i	−0.999909	−	0.0134697i	$-0.995712\pi$
$523$	−6.91544	−	16.6954i	−0.302391	−	0.730037i	0.697518	−	0.716567i	$-0.254288\pi$
$524$	−28.8418	+	7.57809i	−1.25996	+	0.331051i
$525$		0			0
$526$	−10.5966	+	3.56837i	−0.462034	+	0.155588i
$527$			7.70276i			0.335538i
$528$		0			0
$529$		−	14.8499i		−	0.645647i
$530$	−10.1353	−	30.0977i	−0.440249	−	1.30736i
$531$		0			0
$532$	4.72713	+	2.75993i	0.204947	+	0.119658i
$533$	−0.0708500	−	0.171047i	−0.00306885	−	0.00740887i
$534$		0			0
$535$	34.3806	+	34.3806i	1.48640	+	1.48640i
$536$	−14.9036	−	3.07763i	−0.643740	−	0.132933i
$537$		0			0
$538$	−9.99053	−	11.4480i	−0.430722	−	0.493559i
$539$	5.67279	−	2.34974i	0.244344	−	0.101211i
$540$		0			0
$541$	9.51555	−	22.9726i	0.409106	−	0.987668i	−0.576268	−	0.817261i	$-0.695492\pi$
$541$	9.51555	−	22.9726i	0.409106	−	0.987668i	0.985374	−	0.170407i	$-0.0545084\pi$
$542$	−9.70310	+	19.5560i	−0.416784	+	0.840002i
$543$		0			0
$544$	−23.4765	−	21.0984i	−1.00655	−	0.904585i
$545$	53.8103			2.30498
$546$		0			0
$547$	11.3958	−	27.5119i	0.487250	−	1.17633i	−0.468848	−	0.883279i	$-0.655331\pi$
$547$	11.3958	−	27.5119i	0.487250	−	1.17633i	0.956098	−	0.293046i	$-0.0946690\pi$
$548$	−1.17198	+	8.57971i	−0.0500647	+	0.366507i
$549$		0			0
$550$	−36.1993	−	41.4803i	−1.54355	−	1.76873i
$551$	−1.45526	+	1.45526i	−0.0619961	+	0.0619961i
$552$		0			0
$553$	4.63662	+	4.63662i	0.197169	+	0.197169i
$554$	−0.449020	+	6.60477i	−0.0190770	+	0.280610i
$555$		0			0
$556$	−1.63745	+	2.80458i	−0.0694433	+	0.118941i
$557$	−1.70939	−	0.708053i	−0.0724292	−	0.0300012i	0.346175	−	0.938170i	$-0.387480\pi$
$557$	−1.70939	−	0.708053i	−0.0724292	−	0.0300012i	−0.418604	+	0.908169i	$0.637480\pi$
$558$		0			0
$559$			0.0818645i			0.00346250i
$560$	−25.8742	−	20.2565i	−1.09338	−	0.855994i
$561$		0			0
$562$	7.01962	−	2.36383i	0.296105	−	0.0997123i
$563$	−19.1605	−	7.93652i	−0.807517	−	0.334485i	−0.0595542	−	0.998225i	$-0.518968\pi$
$563$	−19.1605	−	7.93652i	−0.807517	−	0.334485i	−0.747963	+	0.663741i	$0.768968\pi$
$564$		0			0
$565$	−3.49681	−	8.44204i	−0.147112	−	0.355159i
$566$	−24.6804	−	1.67788i	−1.03740	−	0.0705265i
$567$		0			0
$568$	5.90092	+	4.00540i	0.247597	+	0.168063i
$569$	15.1289	−	15.1289i	0.634235	−	0.634235i	−0.314892	−	0.949127i	$-0.601968\pi$
$569$	15.1289	−	15.1289i	0.634235	−	0.634235i	0.949127	+	0.314892i	$0.101968\pi$
$570$		0			0
$571$	−12.1094	+	5.01587i	−0.506761	+	0.209907i	−0.621391	−	0.783501i	$-0.713432\pi$
$571$	−12.1094	+	5.01587i	−0.506761	+	0.209907i	0.114629	+	0.993408i	$0.463432\pi$
$572$	0.187298	−	0.142278i	0.00783133	−	0.00594895i
$573$		0			0
$574$	30.6797	+	15.2223i	1.28055	+	0.635368i
$575$	−17.7267			−0.739256
$576$		0			0
$577$	−35.7790			−1.48950			−0.744749	−	0.667344i	$-0.767431\pi$
$577$	−35.7790			−1.48950			−0.744749	+	0.667344i	$0.767431\pi$
$578$	−17.9055	−	8.88417i	−0.744771	−	0.369533i
$579$		0			0
$580$	9.83812	−	7.47338i	0.408506	−	0.310315i
$581$	−16.9766	+	7.03192i	−0.704306	+	0.291733i
$582$		0			0
$583$	−29.7351	+	29.7351i	−1.23150	+	1.23150i
$584$	−3.76283	+	5.54357i	−0.155707	+	0.229395i
$585$		0			0
$586$	−20.7175	−	1.40846i	−0.855830	−	0.0581829i
$587$	−10.9958	−	26.5462i	−0.453845	−	1.09568i	−0.970848	−	0.239696i	$-0.922952\pi$
$587$	−10.9958	−	26.5462i	−0.453845	−	1.09568i	0.517003	−	0.855984i	$-0.327048\pi$
$588$		0			0
$589$	−1.42261	−	0.589265i	−0.0586177	−	0.0242803i
$590$	3.57441	−	1.20367i	0.147156	−	0.0495543i
$591$		0			0
$592$	−1.50373	−	12.3483i	−0.0618031	−	0.507510i
$593$			13.4778i			0.553469i	0.960946	+	0.276734i	$0.0892522\pi$
$593$			13.4778i			0.553469i	−0.960946	+	0.276734i	$0.910748\pi$
$594$		0			0
$595$	−42.3490	−	17.5415i	−1.73614	−	0.719133i
$596$	−22.5026	+	38.5419i	−0.921743	+	1.57874i
$597$		0			0
$598$	0.00513685	−	0.0755596i	0.000210062	−	0.00308986i
$599$	11.7247	+	11.7247i	0.479059	+	0.479059i	0.904831	−	0.425771i	$-0.139997\pi$
$599$	11.7247	+	11.7247i	0.479059	+	0.479059i	−0.425771	+	0.904831i	$0.639997\pi$
$600$		0			0
$601$	−14.2752	+	14.2752i	−0.582299	+	0.582299i	−0.935535	−	0.353235i	$-0.885082\pi$
$601$	−14.2752	+	14.2752i	−0.582299	+	0.582299i	0.353235	+	0.935535i	$0.385082\pi$
$602$	−9.95737	−	11.4100i	−0.405832	−	0.465037i
$603$		0			0
$604$	−3.60738	+	26.4084i	−0.146782	+	1.07454i
$605$	−36.2673	+	87.5570i	−1.47447	+	3.55970i
$606$		0			0
$607$	−30.9234			−1.25514			−0.627571	−	0.778559i	$-0.715951\pi$
$607$	−30.9234			−1.25514			−0.627571	+	0.778559i	$0.715951\pi$
$608$	5.69259	−	2.72180i	0.230865	−	0.110384i
$609$		0			0
$610$	26.5209	−	53.4512i	1.07380	−	2.16418i
$611$	0.00832655	−	0.0201021i	0.000336856	−	0.000813243i
$612$		0			0
$613$	34.3535	−	14.2297i	1.38753	−	0.574732i	0.441043	−	0.897486i	$-0.354609\pi$
$613$	34.3535	−	14.2297i	1.38753	−	0.574732i	0.946483	+	0.322754i	$0.104609\pi$
$614$	15.7335	+	18.0288i	0.634952	+	0.727583i
$615$		0			0
$616$	−8.79940	+	42.6118i	−0.354538	+	1.71688i
$617$	10.2583	+	10.2583i	0.412985	+	0.412985i	0.882777	−	0.469792i	$-0.155671\pi$
$617$	10.2583	+	10.2583i	0.412985	+	0.412985i	−0.469792	+	0.882777i	$0.655671\pi$
$618$		0			0
$619$	−8.23548	−	19.8822i	−0.331012	−	0.799133i	−0.998512	−	0.0545238i	$-0.982636\pi$
$619$	−8.23548	−	19.8822i	−0.331012	−	0.799133i	0.667501	−	0.744609i	$-0.267364\pi$
$620$	7.98280	+	4.66074i	0.320597	+	0.187180i
$621$		0			0
$622$	−14.5633	−	43.2471i	−0.583936	−	1.73405i
$623$		−	23.3836i		−	0.936844i
$624$		0			0
$625$			17.4906i			0.699626i
$626$	14.2569	−	4.80096i	0.569820	−	0.191885i
$627$		0			0
$628$	38.1105	−	10.0134i	1.52078	−	0.399580i
$629$	−6.64047	−	16.0315i	−0.264773	−	0.639219i
$630$		0			0
$631$	10.2772	+	10.2772i	0.409128	+	0.409128i	0.881434	−	0.472307i	$-0.156579\pi$
$631$	10.2772	+	10.2772i	0.409128	+	0.409128i	−0.472307	+	0.881434i	$0.656579\pi$
$632$	7.42390	−	1.42053i	0.295307	−	0.0565056i
$633$		0			0
$634$	27.7945	−	24.2559i	1.10386	−	0.963326i
$635$	47.4297	−	19.6460i	1.88219	−	0.779629i
$636$		0			0
$637$	−0.00703045	+	0.0169730i	−0.000278556	+	0.000672495i
$638$	−14.6544	−	7.27109i	−0.580175	−	0.287865i
$639$		0			0
$640$	−36.0704	+	11.5639i	−1.42581	+	0.457103i
$641$	14.5702			0.575489			0.287745	−	0.957707i	$-0.407095\pi$
$641$	14.5702			0.575489			0.287745	+	0.957707i	$0.407095\pi$
$642$		0			0
$643$	7.72635	−	18.6531i	0.304698	−	0.735605i	−0.695162	−	0.718853i	$-0.744667\pi$
$643$	7.72635	−	18.6531i	0.304698	−	0.735605i	0.999860	−	0.0167519i	$-0.00533255\pi$
$644$	8.47452	+	11.1561i	0.333943	+	0.439610i
$645$		0			0
$646$	6.63166	−	5.78736i	0.260919	−	0.227701i
$647$	−5.45944	+	5.45944i	−0.214633	+	0.214633i	−0.806232	−	0.591599i	$-0.798497\pi$
$647$	−5.45944	+	5.45944i	−0.214633	+	0.214633i	0.591599	+	0.806232i	$0.298497\pi$
$648$		0			0
$649$	−3.53135	−	3.53135i	−0.138618	−	0.138618i
$650$	0.164344	+	0.0111728i	0.00644611	+	0.000438234i
$651$		0			0
$652$	−30.4013	+	7.98786i	−1.19061	+	0.312829i
$653$	8.05307	+	3.33569i	0.315141	+	0.130536i	0.534647	−	0.845075i	$-0.320445\pi$
$653$	8.05307	+	3.33569i	0.315141	+	0.130536i	−0.219506	+	0.975611i	$0.570445\pi$
$654$		0			0
$655$			49.9204i			1.95055i
$656$	34.3801	−	19.4063i	1.34232	−	0.757688i
$657$		0			0
$658$	1.28453	+	3.81454i	0.0500763	+	0.148706i
$659$	−11.5755	−	4.79474i	−0.450919	−	0.186777i	0.145654	−	0.989336i	$-0.453471\pi$
$659$	−11.5755	−	4.79474i	−0.450919	−	0.186777i	−0.596573	+	0.802559i	$0.703471\pi$
$660$		0			0
$661$	−4.73190	−	11.4238i	−0.184049	−	0.444335i	0.804745	−	0.593621i	$-0.202302\pi$
$661$	−4.73190	−	11.4238i	−0.184049	−	0.444335i	−0.988794	+	0.149287i	$0.952302\pi$
$662$	3.23434	−	47.5750i	0.125706	−	1.84905i
$663$		0			0
$664$	−4.28365	+	20.7439i	−0.166238	+	0.805020i
$665$	6.47944	−	6.47944i	0.251262	−	0.251262i
$666$		0			0
$667$	−4.86643	+	2.01574i	−0.188429	+	0.0780499i
$668$	33.1781	+	4.53212i	1.28370	+	0.175353i
$669$		0			0
$670$	−11.3230	+	22.8207i	−0.437444	+	0.881642i
$671$	−79.0087			−3.05010
$672$		0			0
$673$	11.7838			0.454233			0.227117	−	0.973868i	$-0.427070\pi$
$673$	11.7838			0.454233			0.227117	+	0.973868i	$0.427070\pi$
$674$	0.581581	−	1.17214i	0.0224017	−	0.0451492i
$675$		0			0
$676$	3.51882	−	25.7601i	0.135339	−	0.990772i
$677$	31.1449	−	12.9006i	1.19700	−	0.495812i	0.306969	−	0.951719i	$-0.400685\pi$
$677$	31.1449	−	12.9006i	1.19700	−	0.495812i	0.890027	+	0.455907i	$0.150685\pi$
$678$		0			0
$679$	3.03630	−	3.03630i	0.116523	−	0.116523i
$680$	−44.1466	+	29.0346i	−1.69295	+	1.11343i
$681$		0			0
$682$	0.830200	−	12.2117i	0.0317900	−	0.467609i
$683$	2.44866	+	5.91159i	0.0936954	+	0.226201i	0.963778	−	0.266705i	$-0.0859349\pi$
$683$	2.44866	+	5.91159i	0.0936954	+	0.226201i	−0.870083	+	0.492905i	$0.835935\pi$
$684$		0			0
$685$	13.3925	+	5.54737i	0.511702	+	0.211954i
$686$	−8.83655	−	26.2409i	−0.337381	−	1.00188i
$687$		0			0
$688$	−17.3287	+	2.11023i	−0.660649	+	0.0804518i
$689$		−	0.125819i		−	0.00479333i
$690$		0			0
$691$	6.81893	+	2.82449i	0.259404	+	0.107449i	0.508596	−	0.861005i	$-0.330165\pi$
$691$	6.81893	+	2.82449i	0.259404	+	0.107449i	−0.249191	+	0.968454i	$0.580165\pi$
$692$	−11.5864	−	44.0969i	−0.440447	−	1.67631i
$693$		0			0
$694$	−13.2606	−	0.901513i	−0.503367	−	0.0342210i
$695$	3.84422	+	3.84422i	0.145819	+	0.145819i
$696$		0			0
$697$	38.9411	−	38.9411i	1.47500	−	1.47500i
$698$	1.63339	−	1.42544i	0.0618248	−	0.0539537i
$699$		0			0
$700$	−24.2647	+	18.4323i	−0.917121	+	0.696677i
$701$	−2.75369	+	6.64799i	−0.104005	+	0.251091i	−0.967312	−	0.253588i	$-0.918389\pi$
$701$	−2.75369	+	6.64799i	−0.104005	+	0.251091i	0.863307	+	0.504679i	$0.168389\pi$
$702$		0			0
$703$	3.46884			0.130830
$704$	34.9447	+	35.9788i	1.31703	+	1.35600i
$705$		0			0
$706$	−13.7516	−	6.82311i	−0.517547	−	0.256791i
$707$	−7.83813	+	18.9229i	−0.294783	+	0.711669i
$708$		0			0
$709$	−46.0951	+	19.0932i	−1.73114	+	0.717061i	−0.731770	+	0.681552i	$0.761305\pi$
$709$	−46.0951	+	19.0932i	−1.73114	+	0.717061i	−0.999369	+	0.0355098i	$0.988695\pi$
$710$	8.99528	−	7.85006i	0.337587	−	0.294607i
$711$		0			0
$712$	−22.3023	−	15.1382i	−0.835814	−	0.567329i
$713$	−2.78674	−	2.78674i	−0.104364	−	0.104364i
$714$		0			0
$715$	−0.150680	−	0.363774i	−0.00563512	−	0.0136044i
$716$	2.61761	+	9.96247i	0.0978247	+	0.372315i
$717$		0			0
$718$	−41.0865	+	13.8357i	−1.53333	+	0.516345i
$719$		−	22.0801i		−	0.823447i	−0.911309	−	0.411724i	$-0.864927\pi$
$719$		−	22.0801i		−	0.823447i	0.911309	−	0.411724i	$-0.135073\pi$
$720$		0			0
$721$		−	13.5434i		−	0.504381i
$722$	−8.01371	−	23.7975i	−0.298239	−	0.885649i
$723$		0			0
$724$	9.77882	−	16.7489i	0.363427	−	0.622468i
$725$	−4.38430	−	10.5846i	−0.162829	−	0.393104i
$726$		0			0
$727$	12.2216	+	12.2216i	0.453274	+	0.453274i	0.896440	−	0.443166i	$-0.146145\pi$
$727$	12.2216	+	12.2216i	0.453274	+	0.453274i	−0.443166	+	0.896440i	$0.646145\pi$
$728$	−0.0715357	−	0.108769i	−0.00265129	−	0.00403124i
$729$		0			0
$730$	7.37467	+	8.45054i	0.272949	+	0.312768i
$731$	−22.4975	+	9.31876i	−0.832100	+	0.344667i
$732$		0			0
$733$	10.2112	−	24.6520i	0.377159	−	0.910541i	−0.615337	−	0.788264i	$-0.710980\pi$
$733$	10.2112	−	24.6520i	0.377159	−	0.910541i	0.992496	−	0.122278i	$-0.0390198\pi$
$734$	0.0971227	−	0.195745i	0.00358487	−	0.00722508i
$735$		0			0
$736$	16.1265	−	0.860365i	0.594430	−	0.0317135i
$737$	33.7324			1.24255
$738$		0			0
$739$	12.9929	−	31.3677i	0.477953	−	1.15388i	−0.482614	−	0.875833i	$-0.660313\pi$
$739$	12.9929	−	31.3677i	0.477953	−	1.15388i	0.960567	−	0.278048i	$-0.0896874\pi$
$740$	−20.6323	−	2.81837i	−0.758460	−	0.103605i
$741$		0			0
$742$	15.3037	+	17.5363i	0.561815	+	0.643776i
$743$	14.2568	−	14.2568i	0.523030	−	0.523030i	−0.395455	−	0.918485i	$-0.629413\pi$
$743$	14.2568	−	14.2568i	0.523030	−	0.523030i	0.918485	+	0.395455i	$0.129413\pi$
$744$		0			0
$745$	52.8291	+	52.8291i	1.93551	+	1.93551i
$746$	−1.35566	+	19.9409i	−0.0496344	+	0.730087i
$747$		0			0
$748$	60.4204	+	35.2764i	2.20919	+	1.28983i
$749$	−32.9211	−	13.6364i	−1.20291	−	0.498262i
$750$		0			0
$751$		−	37.4275i		−	1.36575i	−0.730536	−	0.682874i	$-0.760730\pi$
$751$		−	37.4275i		−	1.36575i	0.730536	−	0.682874i	$-0.239270\pi$
$752$	4.46974	+	1.24435i	0.162995	+	0.0453768i
$753$		0			0
$754$	0.0463871	−	0.0156207i	0.00168932	−	0.000568873i
$755$	41.2223	+	17.0748i	1.50023	+	0.621417i
$756$		0			0
$757$	14.2534	+	34.4107i	0.518048	+	1.25068i	0.939100	+	0.343643i	$0.111661\pi$
$757$	14.2534	+	34.4107i	0.518048	+	1.25068i	−0.421052	+	0.907036i	$0.638339\pi$
$758$	26.7091	+	1.81579i	0.970117	+	0.0659526i
$759$		0			0
$760$	−1.98512	−	10.3745i	−0.0720078	−	0.376324i
$761$	−4.71958	+	4.71958i	−0.171085	+	0.171085i	−0.787456	−	0.616371i	$-0.788602\pi$
$761$	−4.71958	+	4.71958i	−0.171085	+	0.171085i	0.616371	+	0.787456i	$0.288602\pi$
$762$		0			0
$763$	−36.4344	+	15.0916i	−1.31901	+	0.546353i
$764$	−13.8938	−	18.2901i	−0.502659	−	0.661711i
$765$		0			0
$766$	38.1192	+	18.9136i	1.37730	+	0.683376i
$767$	0.0149423			0.000539536
$768$		0			0
$769$	−0.848264			−0.0305892			−0.0152946	−	0.999883i	$-0.504869\pi$
$769$	−0.848264			−0.0305892			−0.0152946	+	0.999883i	$0.504869\pi$
$770$	65.2479	+	32.3741i	2.35137	+	1.16668i
$771$		0			0
$772$	23.3105	+	30.6864i	0.838963	+	1.10443i
$773$	7.34212	−	3.04121i	0.264078	−	0.109385i	−0.246716	−	0.969088i	$-0.579352\pi$
$773$	7.34212	−	3.04121i	0.264078	−	0.109385i	0.510794	+	0.859703i	$0.329352\pi$
$774$		0			0
$775$	6.06124	−	6.06124i	0.217726	−	0.217726i
$776$	−0.930237	−	4.86157i	−0.0333936	−	0.174520i
$777$		0			0
$778$	−17.9700	−	1.22168i	−0.644256	−	0.0437992i
$779$	4.21296	+	10.1710i	0.150945	+	0.364413i
$780$		0			0
$781$	−14.6052	−	6.04967i	−0.522615	−	0.216474i
$782$	21.3495	−	7.18938i	0.763458	−	0.257092i
$783$		0			0
$784$	−3.77398	−	1.05065i	−0.134785	−	0.0375234i
$785$		−	65.9632i		−	2.35433i
$786$		0			0
$787$	−19.1514	−	7.93278i	−0.682674	−	0.282773i	0.0142701	−	0.999898i	$-0.495458\pi$
$787$	−19.1514	−	7.93278i	−0.682674	−	0.282773i	−0.696944	+	0.717125i	$0.745458\pi$
$788$	−12.1265	−	7.08005i	−0.431990	−	0.252216i
$789$		0			0
$790$	0.858237	−	12.6241i	0.0305347	−	0.449145i
$791$	4.73530	+	4.73530i	0.168368	+	0.168368i
$792$		0			0
$793$	0.167156	−	0.167156i	0.00593589	−	0.00593589i
$794$	15.3319	+	17.5686i	0.544107	+	0.623485i
$795$		0			0
$796$	41.0621	+	5.60906i	1.45541	+	0.198808i
$797$	8.34929	−	20.1570i	0.295747	−	0.713997i	−0.704245	−	0.709957i	$-0.748714\pi$
$797$	8.34929	−	20.1570i	0.295747	−	0.713997i	0.999992	−	0.00403944i	$-0.00128580\pi$
$798$		0			0
$799$	6.47215			0.228968
$800$	1.87132	+	35.0756i	0.0661611	+	1.24011i
$801$		0			0
$802$	−22.4881	+	45.3234i	−0.794083	+	1.60043i
$803$	5.68331	−	13.7207i	0.200560	−	0.484194i
$804$		0			0
$805$	21.6675	−	8.97496i	0.763678	−	0.316326i
$806$	0.0240794	+	0.0275923i	0.000848161	+	0.000971896i
$807$		0			0
$808$	12.9736	+	19.7261i	0.456409	+	0.693963i
$809$	−2.49506	−	2.49506i	−0.0877217	−	0.0877217i	0.661884	−	0.749606i	$-0.269757\pi$
$809$	−2.49506	−	2.49506i	−0.0877217	−	0.0877217i	−0.749606	+	0.661884i	$0.769757\pi$
$810$		0			0
$811$	11.3640	+	27.4351i	0.399044	+	0.963378i	0.987893	+	0.155135i	$0.0495812\pi$
$811$	11.3640	+	27.4351i	0.399044	+	0.963378i	−0.588849	+	0.808243i	$0.700419\pi$
$812$	−4.56531	+	7.81934i	−0.160211	+	0.274405i
$813$		0			0
$814$	8.79969	+	26.1315i	0.308429	+	0.915908i
$815$			52.6197i			1.84319i
$816$		0			0
$817$		−	4.86792i		−	0.170307i
$818$	−8.18169	+	2.75516i	−0.286066	+	0.0963318i
$819$		0			0
$820$	−16.7946	−	63.9191i	−0.586492	−	2.23215i
$821$	11.7466	+	28.3588i	0.409959	+	0.989728i	0.985148	+	0.171708i	$0.0549285\pi$
$821$	11.7466	+	28.3588i	0.409959	+	0.989728i	−0.575189	+	0.818020i	$0.695072\pi$
$822$		0			0
$823$	−13.6697	−	13.6697i	−0.476496	−	0.476496i	0.427513	−	0.904009i	$-0.359390\pi$
$823$	−13.6697	−	13.6697i	−0.476496	−	0.476496i	−0.904009	+	0.427513i	$0.859390\pi$
$824$	−12.9171	−	8.76780i	−0.449988	−	0.305441i
$825$		0			0
$826$	−2.08261	+	1.81747i	−0.0724633	+	0.0632378i
$827$	−35.2612	+	14.6057i	−1.22615	+	0.507889i	−0.899361	−	0.437207i	$-0.855968\pi$
$827$	−35.2612	+	14.6057i	−1.22615	+	0.507889i	−0.326792	+	0.945096i	$0.605968\pi$
$828$		0			0
$829$	−16.0030	+	38.6346i	−0.555806	+	1.34184i	0.357253	+	0.934008i	$0.383714\pi$
$829$	−16.0030	+	38.6346i	−0.555806	+	1.34184i	−0.913059	+	0.407828i	$0.866286\pi$
$830$	31.7634	+	15.7601i	1.10253	+	0.547040i
$831$		0			0
$832$	−0.150051	−	0.00218777i	−0.00520207	−	7.58473e-5i
$833$	−5.46470			−0.189341
$834$		0			0
$835$	21.4519	−	51.7895i	0.742375	−	1.79225i
$836$	−11.1373	+	8.46030i	−0.385193	+	0.292606i
$837$		0			0
$838$	20.5367	−	17.9221i	0.709429	−	0.619109i
$839$	−14.1294	+	14.1294i	−0.487800	+	0.487800i	−0.907611	−	0.419811i	$-0.862096\pi$
$839$	−14.1294	+	14.1294i	−0.487800	+	0.487800i	0.419811	+	0.907611i	$0.362096\pi$
$840$		0			0
$841$	18.0989	+	18.0989i	0.624100	+	0.624100i
$842$	−7.68729	−	0.522614i	−0.264922	−	0.0180105i
$843$		0			0
$844$	−1.54242	−	5.87035i	−0.0530922	−	0.202066i
$845$	−40.2103	−	16.6557i	−1.38328	−	0.572972i
$846$		0			0
$847$		−	69.4554i		−	2.38651i
$848$	26.6327	−	3.24325i	0.914572	−	0.111374i
$849$		0			0
$850$	15.6371	+	46.4359i	0.536349	+	1.59274i
$851$	8.20237	+	3.39753i	0.281174	+	0.116466i
$852$		0			0
$853$	−19.9078	−	48.0618i	−0.681631	−	1.64560i	−0.760995	−	0.648758i	$-0.775289\pi$
$853$	−19.9078	−	48.0618i	−0.681631	−	1.64560i	0.0793634	−	0.996846i	$-0.474711\pi$
$854$	−2.96610	+	43.6292i	−0.101498	+	1.49296i
$855$		0			0
$856$	−34.3185	+	22.5708i	−1.17298	+	0.771453i
$857$	−34.0981	+	34.0981i	−1.16477	+	1.16477i	−0.181349	+	0.983419i	$0.558046\pi$
$857$	−34.0981	+	34.0981i	−1.16477	+	1.16477i	−0.983419	+	0.181349i	$0.941954\pi$
$858$		0			0
$859$	3.10766	−	1.28723i	0.106032	−	0.0439199i	−0.329037	−	0.944317i	$-0.606724\pi$
$859$	3.10766	−	1.28723i	0.106032	−	0.0439199i	0.435069	+	0.900397i	$0.356724\pi$
$860$	−3.95510	+	28.9539i	−0.134868	+	0.987321i
$861$		0			0
$862$	−11.5738	+	23.3262i	−0.394204	+	0.794493i
$863$	10.0110			0.340777			0.170389	−	0.985377i	$-0.445498\pi$
$863$	10.0110			0.340777			0.170389	+	0.985377i	$0.445498\pi$
$864$		0			0
$865$	−76.3247			−2.59512
$866$	−0.143102	+	0.288413i	−0.00486281	+	0.00980069i
$867$		0			0
$868$	−6.71222	−	0.916887i	−0.227827	−	0.0311212i
$869$	−15.4790	+	6.41161i	−0.525089	+	0.217499i
$870$		0			0
$871$	−0.0713665	+	0.0713665i	−0.00241816	+	0.00241816i
$872$	−9.19339	+	44.5197i	−0.311327	+	1.50763i
$873$		0			0
$874$	−0.305453	+	4.49301i	−0.0103321	+	0.151978i
$875$	3.80195	+	9.17873i	0.128529	+	0.310298i
$876$		0			0
$877$	22.1720	+	9.18393i	0.748694	+	0.310119i	0.724209	−	0.689581i	$-0.242205\pi$
$877$	22.1720	+	9.18393i	0.748694	+	0.310119i	0.0244855	+	0.999700i	$0.492205\pi$
$878$	−12.1667	−	36.1302i	−0.410607	−	1.21934i
$879$		0			0
$880$	73.1177	−	41.2722i	2.46480	−	1.39129i
$881$		−	16.0746i		−	0.541568i	−0.962640	−	0.270784i	$-0.912717\pi$
$881$		−	16.0746i		−	0.541568i	0.962640	−	0.270784i	$-0.0872829\pi$
$882$		0			0
$883$	−12.8293	−	5.31406i	−0.431740	−	0.178832i	0.156221	−	0.987722i	$-0.450069\pi$
$883$	−12.8293	−	5.31406i	−0.431740	−	0.178832i	−0.587960	+	0.808890i	$0.700069\pi$
$884$	−0.202463	+	0.0531965i	−0.00680955	+	0.00178919i
$885$		0			0
$886$	−42.8372	−	2.91225i	−1.43914	−	0.0978390i
$887$	−29.2489	−	29.2489i	−0.982081	−	0.982081i	0.0177612	−	0.999842i	$-0.494346\pi$
$887$	−29.2489	−	29.2489i	−0.982081	−	0.982081i	−0.999842	+	0.0177612i	$0.994346\pi$
$888$		0			0
$889$	−26.6042	+	26.6042i	−0.892276	+	0.892276i
$890$	−33.9973	+	29.6690i	−1.13959	+	0.994507i
$891$		0			0
$892$	−7.40521	−	9.74838i	−0.247945	−	0.326400i
$893$	−0.495123	+	1.19533i	−0.0165687	+	0.0400003i
$894$		0			0
$895$	17.2434			0.576384
$896$	21.1797	−	17.9461i	0.707563	−	0.599536i
$897$		0			0
$898$	−41.8066	−	20.7432i	−1.39510	−	0.692209i
$899$	0.974727	−	2.35320i	0.0325090	−	0.0784836i
$900$		0			0
$901$	34.5768	−	14.3222i	1.15192	−	0.477141i
$902$	−65.9328	+	57.5387i	−2.19532	+	1.91583i
$903$		0			0
$904$	7.58190	−	1.45076i	0.252170	−	0.0482516i
$905$	−22.9576	−	22.9576i	−0.763137	−	0.763137i
$906$		0			0
$907$	21.8942	+	52.8573i	0.726986	+	1.75510i	0.652387	+	0.757886i	$0.273768\pi$
$907$	21.8942	+	52.8573i	0.726986	+	1.75510i	0.0745987	+	0.997214i	$0.476232\pi$
$908$	32.9802	−	8.66547i	1.09449	−	0.287574i
$909$		0			0
$910$	−0.206536	+	0.0695502i	−0.00684659	+	0.00230557i
$911$		−	59.8222i		−	1.98200i	−0.133873	−	0.990999i	$-0.542741\pi$
$911$		−	59.8222i		−	1.98200i	0.133873	−	0.990999i	$-0.457259\pi$
$912$		0			0
$913$		−	46.9510i		−	1.55385i
$914$	12.3406	+	36.6467i	0.408192	+	1.21216i
$915$		0			0
$916$	−16.0942	−	9.39659i	−0.531768	−	0.310472i
$917$	−14.0007	−	33.8006i	−0.462342	−	1.11619i
$918$		0			0
$919$	17.5355	+	17.5355i	0.578444	+	0.578444i	0.934474	−	0.356030i	$-0.115870\pi$
$919$	17.5355	+	17.5355i	0.578444	+	0.578444i	−0.356030	+	0.934474i	$0.615870\pi$
$920$	5.46730	−	26.4758i	0.180251	−	0.872882i
$921$		0			0
$922$	19.1768	+	21.9744i	0.631553	+	0.723688i
$923$	0.0436988	−	0.0181006i	0.00143836	−	0.000595790i
$924$		0			0
$925$	−7.38974	+	17.8404i	−0.242973	+	0.586589i
$926$	11.7331	−	23.6474i	0.385574	−	0.777102i
$927$		0			0
$928$	4.50224	+	9.41634i	0.147793	+	0.309106i
$929$	−47.3964			−1.55502			−0.777512	−	0.628868i	$-0.783519\pi$
$929$	−47.3964			−1.55502			−0.777512	+	0.628868i	$0.783519\pi$
$930$		0			0
$931$	0.418052	−	1.00927i	0.0137011	−	0.0330774i
$932$	3.06139	−	22.4114i	0.100279	−	0.734109i
$933$		0			0
$934$	1.39647	+	1.60020i	0.0456940	+	0.0523601i
$935$	82.8179	−	82.8179i	2.70843	−	2.70843i
$936$		0			0
$937$	−3.12631	−	3.12631i	−0.102132	−	0.102132i	0.654194	−	0.756326i	$-0.273008\pi$
$937$	−3.12631	−	3.12631i	−0.102132	−	0.102132i	−0.756326	+	0.654194i	$0.773008\pi$
$938$	1.26636	−	18.6273i	0.0413482	−	0.608203i
$939$		0			0
$940$	3.91613	−	6.70745i	0.127730	−	0.218773i
$941$	−6.78357	−	2.80985i	−0.221138	−	0.0915984i	0.269364	−	0.963038i	$-0.413187\pi$
$941$	−6.78357	−	2.80985i	−0.221138	−	0.0915984i	−0.490502	+	0.871440i	$0.663187\pi$
$942$		0			0
$943$			28.1766i			0.917555i
$944$	0.385170	+	3.16291i	0.0125362	+	0.102944i
$945$		0			0
$946$	36.6710	−	12.3488i	1.19228	−	0.401496i
$947$	48.2859	+	20.0007i	1.56908	+	0.649935i	0.986637	−	0.162936i	$-0.0520965\pi$
$947$	48.2859	+	20.0007i	1.56908	+	0.649935i	0.582444	+	0.812871i	$0.302096\pi$
$948$		0			0
$949$	0.0170045	+	0.0410525i	0.000551990	+	0.00133262i
$950$	−9.77242	−	0.664370i	−0.317059	−	0.0215550i
$951$		0			0
$952$	21.7482	−	32.0403i	0.704862	−	1.03843i
$953$	12.2493	−	12.2493i	0.396794	−	0.396794i	−0.480307	−	0.877101i	$-0.659475\pi$
$953$	12.2493	−	12.2493i	0.396794	−	0.396794i	0.877101	+	0.480307i	$0.159475\pi$
$954$		0			0
$955$	−35.5233	+	14.7142i	−1.14951	+	0.476141i
$956$	9.98097	−	7.58189i	0.322808	−	0.245216i
$957$		0			0
$958$	25.5423	+	12.6733i	0.825233	+	0.409456i
$959$	−10.6237			−0.343059
$960$		0			0
$961$	−29.0943			−0.938525
$962$	−0.0739027	−	0.0366683i	−0.00238272	−	0.00118223i
$963$		0			0
$964$	−25.0997	+	19.0666i	−0.808408	+	0.614095i
$965$	59.5997	−	24.6870i	1.91858	−	0.794703i
$966$		0			0
$967$	−11.6821	+	11.6821i	−0.375671	+	0.375671i	−0.869538	−	0.493867i	$-0.835583\pi$
$967$	−11.6821	+	11.6821i	−0.375671	+	0.375671i	0.493867	+	0.869538i	$0.335583\pi$
$968$	−66.2437	−	44.9645i	−2.12915	−	1.44521i
$969$		0			0
$970$	−8.26692	−	0.562019i	−0.265435	−	0.0180454i
$971$	12.0421	+	29.0723i	0.386451	+	0.932975i	0.990686	+	0.136168i	$0.0434788\pi$
$971$	12.0421	+	29.0723i	0.386451	+	0.932975i	−0.604235	+	0.796806i	$0.706521\pi$
$972$		0			0
$973$	−3.68102	−	1.52473i	−0.118008	−	0.0488806i
$974$	−27.2161	+	9.16494i	−0.872061	+	0.293664i
$975$		0			0
$976$	39.6916	+	31.0740i	1.27050	+	0.994653i
$977$			46.2289i			1.47899i	0.673159	+	0.739497i	$0.264937\pi$
$977$			46.2289i			1.47899i	−0.673159	+	0.739497i	$0.735063\pi$
$978$		0			0
$979$	55.1998	+	22.8645i	1.76419	+	0.730753i
$980$	−3.30655	+	5.66337i	−0.105624	+	0.180910i
$981$		0			0
$982$	1.96532	−	28.9086i	0.0627160	−	0.922509i
$983$	36.8328	+	36.8328i	1.17478	+	1.17478i	0.981055	+	0.193729i	$0.0620583\pi$
$983$	36.8328	+	36.8328i	1.17478	+	1.17478i	0.193729	+	0.981055i	$0.437942\pi$
$984$		0			0
$985$	−16.6217	+	16.6217i	−0.529613	+	0.529613i
$986$	9.57310	+	10.9697i	0.304870	+	0.349346i
$987$		0			0
$988$	0.00566370	−	0.0414621i	0.000180186	−	0.00131908i
$989$	4.76786	−	11.5106i	0.151609	−	0.366016i
$990$		0			0
$991$	−0.0778010			−0.00247143			−0.00123571	−	0.999999i	$-0.500393\pi$
$991$	−0.0778010			−0.00247143			−0.00123571	+	0.999999i	$0.500393\pi$
$992$	−5.21989	+	5.80825i	−0.165732	+	0.184412i
$993$		0			0
$994$	−3.88898	+	7.83800i	−0.123351	+	0.248606i
$995$	26.5494	−	64.0960i	0.841674	−	2.03198i
$996$		0			0
$997$	−14.8961	+	6.17018i	−0.471765	+	0.195412i	−0.605883	−	0.795554i	$-0.707180\pi$
$997$	−14.8961	+	6.17018i	−0.471765	+	0.195412i	0.134118	+	0.990965i	$0.457180\pi$
$998$	11.1970	+	12.8305i	0.354436	+	0.406144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.109.7		32
3.2	odd	2		96.2.n.a.13.2	✓	32
4.3	odd	2		1152.2.v.c.145.8		32
12.11	even	2		384.2.n.a.145.5		32
24.5	odd	2		768.2.n.a.289.8		32
24.11	even	2		768.2.n.b.289.4		32
32.5	even	8	inner	288.2.v.d.37.7		32
32.27	odd	8		1152.2.v.c.1009.8		32
96.5	odd	8		96.2.n.a.37.2	yes	32
96.11	even	8		768.2.n.b.481.4		32
96.53	odd	8		768.2.n.a.481.8		32
96.59	even	8		384.2.n.a.241.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.2	✓	32	3.2	odd	2
96.2.n.a.37.2	yes	32	96.5	odd	8
288.2.v.d.37.7		32	32.5	even	8	inner
288.2.v.d.109.7		32	1.1	even	1	trivial
384.2.n.a.145.5		32	12.11	even	2
384.2.n.a.241.5		32	96.59	even	8
768.2.n.a.289.8		32	24.5	odd	2
768.2.n.a.481.8		32	96.53	odd	8
768.2.n.b.289.4		32	24.11	even	2
768.2.n.b.481.4		32	96.11	even	8
1152.2.v.c.145.8		32	4.3	odd	2
1152.2.v.c.1009.8		32	32.27	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26685 + 0.628571i) q^{2} +(1.20980 + 1.59260i) q^{4} +(3.09318 - 1.28124i) q^{5} +(-1.73503 + 1.73503i) q^{7} +(0.531562 + 2.77803i) q^{8} +O(q^{10})\)	\(q+(1.26685 + 0.628571i) q^{2} +(1.20980 + 1.59260i) q^{4} +(3.09318 - 1.28124i) q^{5} +(-1.73503 + 1.73503i) q^{7} +(0.531562 + 2.77803i) q^{8} +(4.72394 + 0.321153i) q^{10} +(-2.39923 - 5.79225i) q^{11} +(0.0173304 + 0.00717850i) q^{13} +(-3.28860 + 1.10742i) q^{14} +(-1.07278 + 3.85346i) q^{16} +5.57978i q^{17} +(-1.03052 - 0.426856i) q^{19} +(5.78263 + 3.37618i) q^{20} +(0.601386 - 8.84597i) q^{22} +(-2.01868 - 2.01868i) q^{23} +(4.39068 - 4.39068i) q^{25} +(0.0174428 + 0.0199875i) q^{26} +(-4.86224 - 0.664180i) q^{28} +(0.706079 - 1.70463i) q^{29} +1.38048 q^{31} +(-3.78122 + 4.20742i) q^{32} +(-3.50729 + 7.06872i) q^{34} +(-3.14377 + 7.58973i) q^{35} +(-2.87315 + 1.19010i) q^{37} +(-1.03720 - 1.18852i) q^{38} +(5.20354 + 7.91189i) q^{40} +(-6.97897 - 6.97897i) q^{41} +(1.67010 + 4.03197i) q^{43} +(6.32218 - 10.8285i) q^{44} +(-1.28847 - 3.82623i) q^{46} -1.15993i q^{47} +0.979375i q^{49} +(8.32217 - 2.80246i) q^{50} +(0.00953380 + 0.0362851i) q^{52} +(-2.56680 - 6.19681i) q^{53} +(-14.8425 - 14.8425i) q^{55} +(-5.74222 - 3.89767i) q^{56} +(1.96597 - 1.71568i) q^{58} +(0.735935 - 0.304834i) q^{59} +(4.82262 - 11.6428i) q^{61} +(1.74885 + 0.867729i) q^{62} +(-7.43488 + 2.95339i) q^{64} +0.0628036 q^{65} +(-2.05899 + 4.97085i) q^{67} +(-8.88638 + 6.75040i) q^{68} +(-8.75336 + 7.63894i) q^{70} +(1.78298 - 1.78298i) q^{71} +(1.67500 + 1.67500i) q^{73} +(-4.38789 - 0.298307i) q^{74} +(-0.566909 - 2.15762i) q^{76} +(14.2124 + 5.88697i) q^{77} -2.67236i q^{79} +(1.61890 + 13.2939i) q^{80} +(-4.45450 - 13.2281i) q^{82} +(6.91877 + 2.86585i) q^{83} +(7.14903 + 17.2593i) q^{85} +(-0.418623 + 6.15766i) q^{86} +(14.8157 - 9.74406i) q^{88} +(-6.73869 + 6.73869i) q^{89} +(-0.0425236 + 0.0176139i) q^{91} +(0.772764 - 5.65714i) q^{92} +(0.729098 - 1.46945i) q^{94} -3.73450 q^{95} -1.75001 q^{97} +(-0.615607 + 1.24072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Introduction

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