LMFDB - Embedded newform 288.2.v.d.253.8

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			253.8
Character	$\chi$	$=$	288.253
Dual form			288.2.v.d.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36002 + 0.387756i) q^{2} +(1.69929 + 1.05471i) q^{4} +(-0.705805 - 1.70396i) q^{5} +(3.24150 - 3.24150i) q^{7} +(1.90209 + 2.09333i) q^{8} +O(q^{10})$	\(q+(1.36002 + 0.387756i) q^{2} +(1.69929 + 1.05471i) q^{4} +(-0.705805 - 1.70396i) q^{5} +(3.24150 - 3.24150i) q^{7} +(1.90209 + 2.09333i) q^{8} +(-0.299183 - 2.59110i) q^{10} +(-3.38931 + 1.40390i) q^{11} +(-0.503962 + 1.21667i) q^{13} +(5.66540 - 3.15158i) q^{14} +(1.77517 + 3.58452i) q^{16} -0.622706i q^{17} +(-2.14250 + 5.17245i) q^{19} +(0.597821 - 3.63995i) q^{20} +(-5.15388 + 0.595097i) q^{22} +(2.47578 + 2.47578i) q^{23} +(1.13020 - 1.13020i) q^{25} +(-1.15717 + 1.45928i) q^{26} +(8.92709 - 2.08940i) q^{28} +(2.16691 + 0.897562i) q^{29} -10.4506 q^{31} +(1.02434 + 5.56334i) q^{32} +(0.241458 - 0.846890i) q^{34} +(-7.81126 - 3.23553i) q^{35} +(-0.0714604 - 0.172521i) q^{37} +(-4.91948 + 6.20385i) q^{38} +(2.22446 - 4.71858i) q^{40} +(-8.50664 - 8.50664i) q^{41} +(-3.62132 + 1.50000i) q^{43} +(-7.24012 - 1.18911i) q^{44} +(2.40710 + 4.32711i) q^{46} +5.02899i q^{47} -14.0146i q^{49} +(1.97533 - 1.09885i) q^{50} +(-2.13961 + 1.53594i) q^{52} +(7.15914 - 2.96541i) q^{53} +(4.78438 + 4.78438i) q^{55} +(12.9512 + 0.619913i) q^{56} +(2.59899 + 2.06093i) q^{58} +(1.52516 + 3.68206i) q^{59} +(-3.07333 - 1.27302i) q^{61} +(-14.2131 - 4.05231i) q^{62} +(-0.764096 + 7.96343i) q^{64} +2.42886 q^{65} +(-2.17574 - 0.901222i) q^{67} +(0.656774 - 1.05816i) q^{68} +(-9.36885 - 7.42925i) q^{70} +(1.11161 - 1.11161i) q^{71} +(3.71598 + 3.71598i) q^{73} +(-0.0302913 - 0.262340i) q^{74} +(-9.09616 + 6.52977i) q^{76} +(-6.43570 + 15.5372i) q^{77} +10.2251i q^{79} +(4.85496 - 5.55480i) q^{80} +(-8.27067 - 14.8677i) q^{82} +(4.69181 - 11.3270i) q^{83} +(-1.06107 + 0.439509i) q^{85} +(-5.50670 + 0.635835i) q^{86} +(-9.38560 - 4.42461i) q^{88} +(3.54033 - 3.54033i) q^{89} +(2.31025 + 5.57743i) q^{91} +(1.59584 + 6.81830i) q^{92} +(-1.95003 + 6.83952i) q^{94} +10.3259 q^{95} +0.139594 q^{97} +(5.43426 - 19.0601i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.36002	+	0.387756i	0.961677	+	0.274185i
$2$	1.36002	+	0.387756i	0.961677	+	0.274185i
$3$		0			0
$3$		0			0
$4$	1.69929	+	1.05471i	0.849645	+	0.527355i
$5$	−0.705805	−	1.70396i	−0.315646	−	0.762036i	−0.999475	−	0.0323942i	$-0.989687\pi$
$5$	−0.705805	−	1.70396i	−0.315646	−	0.762036i	0.683829	−	0.729642i	$-0.260313\pi$
$6$		0			0
$7$	3.24150	−	3.24150i	1.22517	−	1.22517i	0.259402	−	0.965769i	$-0.416475\pi$
$7$	3.24150	−	3.24150i	1.22517	−	1.22517i	0.965769	−	0.259402i	$-0.0835254\pi$
$8$	1.90209	+	2.09333i	0.672491	+	0.740105i
$9$		0			0
$10$	−0.299183	−	2.59110i	−0.0946101	−	0.819378i
$11$	−3.38931	+	1.40390i	−1.02191	+	0.423291i	−0.829788	−	0.558079i	$-0.811538\pi$
$11$	−3.38931	+	1.40390i	−1.02191	+	0.423291i	−0.192127	+	0.981370i	$0.561538\pi$
$12$		0			0
$13$	−0.503962	+	1.21667i	−0.139774	+	0.337444i	−0.978230	−	0.207526i	$-0.933459\pi$
$13$	−0.503962	+	1.21667i	−0.139774	+	0.337444i	0.838456	+	0.544970i	$0.183459\pi$
$14$	5.66540	−	3.15158i	1.51414	−	0.842295i
$15$		0			0
$16$	1.77517	+	3.58452i	0.443793	+	0.896129i
$17$		−	0.622706i		−	0.151028i	−0.997145	−	0.0755142i	$-0.975940\pi$
$17$		−	0.622706i		−	0.151028i	0.997145	−	0.0755142i	$-0.0240598\pi$
$18$		0			0
$19$	−2.14250	+	5.17245i	−0.491523	+	1.18664i	0.462422	+	0.886660i	$0.346980\pi$
$19$	−2.14250	+	5.17245i	−0.491523	+	1.18664i	−0.953945	+	0.299981i	$0.903020\pi$
$20$	0.597821	−	3.63995i	0.133677	−	0.813917i
$21$		0			0
$22$	−5.15388	+	0.595097i	−1.09881	+	0.126875i
$23$	2.47578	+	2.47578i	0.516236	+	0.516236i	0.916430	−	0.400194i	$-0.131057\pi$
$23$	2.47578	+	2.47578i	0.516236	+	0.516236i	−0.400194	+	0.916430i	$0.631057\pi$
$24$		0			0
$25$	1.13020	−	1.13020i	0.226040	−	0.226040i
$26$	−1.15717	+	1.45928i	−0.226939	+	0.286188i
$27$		0			0
$28$	8.92709	−	2.08940i	1.68706	−	0.394860i
$29$	2.16691	+	0.897562i	0.402384	+	0.166673i	0.574691	−	0.818370i	$-0.305122\pi$
$29$	2.16691	+	0.897562i	0.402384	+	0.166673i	−0.172307	+	0.985043i	$0.555122\pi$
$30$		0			0
$31$	−10.4506			−1.87699			−0.938496	−	0.345290i	$-0.887780\pi$
$31$	−10.4506			−1.87699			−0.938496	+	0.345290i	$0.887780\pi$
$32$	1.02434	+	5.56334i	0.181080	+	0.983468i
$33$		0			0
$34$	0.241458	−	0.846890i	0.0414097	−	0.145240i
$35$	−7.81126	−	3.23553i	−1.32034	−	0.546905i
$36$		0			0
$37$	−0.0714604	−	0.172521i	−0.0117480	−	0.0283622i	0.917897	−	0.396819i	$-0.129886\pi$
$37$	−0.0714604	−	0.172521i	−0.0117480	−	0.0283622i	−0.929645	+	0.368457i	$0.879886\pi$
$38$	−4.91948	+	6.20385i	−0.798045	+	1.00640i
$39$		0			0
$40$	2.22446	−	4.71858i	0.351718	−	0.746073i
$41$	−8.50664	−	8.50664i	−1.32851	−	1.32851i	−0.906667	−	0.421847i	$-0.861382\pi$
$41$	−8.50664	−	8.50664i	−1.32851	−	1.32851i	−0.421847	−	0.906667i	$-0.638618\pi$
$42$		0			0
$43$	−3.62132	+	1.50000i	−0.552247	+	0.228748i	−0.641315	−	0.767277i	$-0.721611\pi$
$43$	−3.62132	+	1.50000i	−0.552247	+	0.228748i	0.0890686	+	0.996025i	$0.471611\pi$
$44$	−7.24012	−	1.18911i	−1.09149	−	0.179265i
$45$		0			0
$46$	2.40710	+	4.32711i	0.354908	+	0.637997i
$47$			5.02899i			0.733554i	0.930309	+	0.366777i	$0.119539\pi$
$47$			5.02899i			0.733554i	−0.930309	+	0.366777i	$0.880461\pi$
$48$		0			0
$49$		−	14.0146i		−	2.00209i
$50$	1.97533	−	1.09885i	0.279354	−	0.155401i
$51$		0			0
$52$	−2.13961	+	1.53594i	−0.296711	+	0.212997i
$53$	7.15914	−	2.96541i	0.983383	−	0.407331i	0.167706	−	0.985837i	$-0.446364\pi$
$53$	7.15914	−	2.96541i	0.983383	−	0.407331i	0.815678	+	0.578506i	$0.196364\pi$
$54$		0			0
$55$	4.78438	+	4.78438i	0.645126	+	0.645126i
$56$	12.9512	+	0.619913i	1.73067	+	0.0828394i
$57$		0			0
$58$	2.59899	+	2.06093i	0.341264	+	0.270614i
$59$	1.52516	+	3.68206i	0.198559	+	0.479363i	0.991527	−	0.129900i	$-0.0414655\pi$
$59$	1.52516	+	3.68206i	0.198559	+	0.479363i	−0.792968	+	0.609263i	$0.791465\pi$
$60$		0			0
$61$	−3.07333	−	1.27302i	−0.393500	−	0.162993i	0.177155	−	0.984183i	$-0.443311\pi$
$61$	−3.07333	−	1.27302i	−0.393500	−	0.162993i	−0.570655	+	0.821190i	$0.693311\pi$
$62$	−14.2131	−	4.05231i	−1.80506	−	0.514643i
$63$		0			0
$64$	−0.764096	+	7.96343i	−0.0955120	+	0.995428i
$65$	2.42886			0.301264
$66$		0			0
$67$	−2.17574	−	0.901222i	−0.265809	−	0.110102i	0.245798	−	0.969321i	$-0.420950\pi$
$67$	−2.17574	−	0.901222i	−0.265809	−	0.110102i	−0.511608	+	0.859219i	$0.670950\pi$
$68$	0.656774	−	1.05816i	0.0796456	−	0.128320i
$69$		0			0
$70$	−9.36885	−	7.42925i	−1.11979	−	0.887965i
$71$	1.11161	−	1.11161i	0.131924	−	0.131924i	−0.638061	−	0.769986i	$-0.720263\pi$
$71$	1.11161	−	1.11161i	0.131924	−	0.131924i	0.769986	+	0.638061i	$0.220263\pi$
$72$		0			0
$73$	3.71598	+	3.71598i	0.434923	+	0.434923i	0.890299	−	0.455376i	$-0.150495\pi$
$73$	3.71598	+	3.71598i	0.434923	+	0.434923i	−0.455376	+	0.890299i	$0.650495\pi$
$74$	−0.0302913	−	0.262340i	−0.00352130	−	0.0304964i
$75$		0			0
$76$	−9.09616	+	6.52977i	−1.04340	+	0.749016i
$77$	−6.43570	+	15.5372i	−0.733416	+	1.77062i
$78$		0			0
$79$			10.2251i			1.15041i	0.818008	+	0.575207i	$0.195079\pi$
$79$			10.2251i			1.15041i	−0.818008	+	0.575207i	$0.804921\pi$
$80$	4.85496	−	5.55480i	0.542802	−	0.621046i
$81$		0			0
$82$	−8.27067	−	14.8677i	−0.913342	−	1.64186i
$83$	4.69181	−	11.3270i	0.514993	−	1.24330i	−0.425953	−	0.904745i	$-0.640061\pi$
$83$	4.69181	−	11.3270i	0.514993	−	1.24330i	0.940946	−	0.338558i	$-0.109939\pi$
$84$		0			0
$85$	−1.06107	+	0.439509i	−0.115089	+	0.0476714i
$86$	−5.50670	+	0.635835i	−0.593802	+	0.0685639i
$87$		0			0
$88$	−9.38560	−	4.42461i	−1.00051	−	0.471665i
$89$	3.54033	−	3.54033i	0.375274	−	0.375274i	−0.494120	−	0.869394i	$-0.664510\pi$
$89$	3.54033	−	3.54033i	0.375274	−	0.375274i	0.869394	+	0.494120i	$0.164510\pi$
$90$		0			0
$91$	2.31025	+	5.57743i	0.242180	+	0.584674i
$92$	1.59584	+	6.81830i	0.166378	+	0.710857i
$93$		0			0
$94$	−1.95003	+	6.83952i	−0.201130	+	0.705442i
$95$	10.3259			1.05941
$96$		0			0
$97$	0.139594			0.0141737			0.00708683	−	0.999975i	$-0.497744\pi$
$97$	0.139594			0.0141737			0.00708683	+	0.999975i	$0.497744\pi$
$98$	5.43426	−	19.0601i	0.548943	−	1.92536i
$99$		0			0
$100$	3.11257	−	0.728504i	0.311257	−	0.0728504i
$101$	4.89005	+	11.8056i	0.486578	+	1.17470i	0.956431	+	0.291958i	$0.0943068\pi$
$101$	4.89005	+	11.8056i	0.486578	+	1.17470i	−0.469853	+	0.882744i	$0.655693\pi$
$102$		0			0
$103$	3.64510	−	3.64510i	0.359162	−	0.359162i	−0.504342	−	0.863504i	$-0.668265\pi$
$103$	3.64510	−	3.64510i	0.359162	−	0.359162i	0.863504	+	0.504342i	$0.168265\pi$
$104$	−3.50548	+	1.25926i	−0.343741	+	0.123481i
$105$		0			0
$106$	10.8864	−	1.25701i	1.05738	−	0.122091i
$107$	−6.93872	+	2.87411i	−0.670792	+	0.277851i	−0.691972	−	0.721925i	$-0.743258\pi$
$107$	−6.93872	+	2.87411i	−0.670792	+	0.277851i	0.0211799	+	0.999776i	$0.493258\pi$
$108$		0			0
$109$	5.91722	−	14.2854i	0.566767	−	1.36830i	−0.337498	−	0.941326i	$-0.609581\pi$
$109$	5.91722	−	14.2854i	0.566767	−	1.36830i	0.904266	−	0.426971i	$-0.140419\pi$
$110$	4.65166	+	8.36201i	0.443519	+	0.797286i
$111$		0			0
$112$	17.3734	+	5.86499i	1.64163	+	0.554189i
$113$		−	9.04489i		−	0.850872i	−0.904989	−	0.425436i	$-0.860121\pi$
$113$		−	9.04489i		−	0.850872i	0.904989	−	0.425436i	$-0.139879\pi$
$114$		0			0
$115$	2.47122	−	5.96606i	0.230443	−	0.556338i
$116$	2.73553	+	3.81068i	0.253988	+	0.353812i
$117$		0			0
$118$	0.646499	+	5.59905i	0.0595150	+	0.515434i
$119$	−2.01850	−	2.01850i	−0.185036	−	0.185036i
$120$		0			0
$121$	1.73830	−	1.73830i	0.158027	−	0.158027i
$122$	−3.68616	−	2.92303i	−0.333730	−	0.264639i
$123$		0			0
$124$	−17.7587	−	11.0224i	−1.59478	−	0.989841i
$125$	−11.2433	−	4.65715i	−1.00564	−	0.416548i
$126$		0			0
$127$	5.82989			0.517319			0.258659	−	0.965969i	$-0.416719\pi$
$127$	5.82989			0.517319			0.258659	+	0.965969i	$0.416719\pi$
$128$	−4.12705	+	10.5341i	−0.364783	+	0.931092i
$129$		0			0
$130$	3.30330	+	0.941808i	0.289718	+	0.0826020i
$131$	−6.80141	−	2.81723i	−0.594242	−	0.246143i	0.0652326	−	0.997870i	$-0.479221\pi$
$131$	−6.80141	−	2.81723i	−0.594242	−	0.246143i	−0.659474	+	0.751727i	$0.729221\pi$
$132$		0			0
$133$	9.82158	+	23.7114i	0.851639	+	2.05604i
$134$	−2.60959	−	2.06934i	−0.225434	−	0.178763i
$135$		0			0
$136$	1.30353	−	1.18444i	0.111777	−	0.101565i
$137$	13.7370	+	13.7370i	1.17363	+	1.17363i	0.981337	+	0.192295i	$0.0615930\pi$
$137$	13.7370	+	13.7370i	1.17363	+	1.17363i	0.192295	+	0.981337i	$0.438407\pi$
$138$		0			0
$139$	2.14254	−	0.887468i	0.181728	−	0.0752740i	−0.289964	−	0.957037i	$-0.593643\pi$
$139$	2.14254	−	0.887468i	0.181728	−	0.0752740i	0.471692	+	0.881763i	$0.343643\pi$
$140$	−9.86105	−	13.7367i	−0.833411	−	1.16097i
$141$		0			0
$142$	1.94285	−	1.08078i	0.163040	−	0.0906968i
$143$		−	4.83118i		−	0.404004i
$144$		0			0
$145$		−	4.32584i		−	0.359241i
$146$	3.61290	+	6.49469i	0.299006	+	0.537504i
$147$		0			0
$148$	0.0605274	−	0.368533i	0.00497533	−	0.0302932i
$149$	−0.926481	+	0.383761i	−0.0759003	+	0.0314389i	−0.420311	−	0.907380i	$-0.638079\pi$
$149$	−0.926481	+	0.383761i	−0.0759003	+	0.0314389i	0.344410	+	0.938819i	$0.388079\pi$
$150$		0			0
$151$	7.02526	+	7.02526i	0.571707	+	0.571707i	0.932605	−	0.360898i	$-0.117530\pi$
$151$	7.02526	+	7.02526i	0.571707	+	0.571707i	−0.360898	+	0.932605i	$0.617530\pi$
$152$	−14.9029	+	5.35350i	−1.20878	+	0.434227i
$153$		0			0
$154$	−14.7773	+	18.6353i	−1.19079	+	1.50168i
$155$	7.37612	+	17.8075i	0.592464	+	1.43034i
$156$		0			0
$157$	−5.63224	−	2.33295i	−0.449502	−	0.186190i	0.146436	−	0.989220i	$-0.453220\pi$
$157$	−5.63224	−	2.33295i	−0.449502	−	0.186190i	−0.595938	+	0.803030i	$0.703220\pi$
$158$	−3.96485	+	13.9063i	−0.315427	+	1.10633i
$159$		0			0
$160$	8.75674	−	5.67208i	0.692281	−	0.448417i
$161$	16.0505			1.26496
$162$		0			0
$163$	−20.2647	−	8.39392i	−1.58726	−	0.657463i	−0.597714	−	0.801709i	$-0.703924\pi$
$163$	−20.2647	−	8.39392i	−1.58726	−	0.657463i	−0.989542	+	0.144246i	$0.953924\pi$
$164$	−5.48321	−	23.4273i	−0.428166	−	1.82936i
$165$		0			0
$166$	10.7731	−	13.5857i	0.836152	−	1.05445i
$167$	9.26966	−	9.26966i	0.717308	−	0.717308i	−0.250745	−	0.968053i	$-0.580676\pi$
$167$	9.26966	−	9.26966i	0.717308	−	0.717308i	0.968053	+	0.250745i	$0.0806756\pi$
$168$		0			0
$169$	7.96608	+	7.96608i	0.612775	+	0.612775i
$170$	−1.61349	+	0.186303i	−0.123749	+	0.0142888i
$171$		0			0
$172$	−7.73575	−	1.27051i	−0.589845	−	0.0968756i
$173$	5.07428	−	12.2504i	0.385790	−	0.931380i	−0.605031	−	0.796202i	$-0.706839\pi$
$173$	5.07428	−	12.2504i	0.385790	−	0.931380i	0.990821	−	0.135178i	$-0.0431607\pi$
$174$		0			0
$175$		−	7.32708i		−	0.553875i
$176$	−11.0489	−	9.65687i	−0.832842	−	0.727914i
$177$		0			0
$178$	6.18769	−	3.44212i	0.463787	−	0.257998i
$179$	−7.17721	+	17.3273i	−0.536449	+	1.29510i	0.390737	+	0.920503i	$0.372220\pi$
$179$	−7.17721	+	17.3273i	−0.536449	+	1.29510i	−0.927186	+	0.374601i	$0.877780\pi$
$180$		0			0
$181$	13.7526	−	5.69651i	1.02222	−	0.423418i	0.192322	−	0.981332i	$-0.438398\pi$
$181$	13.7526	−	5.69651i	1.02222	−	0.423418i	0.829899	+	0.557914i	$0.188398\pi$
$182$	0.979290	+	8.48121i	0.0725898	+	0.628669i
$183$		0			0
$184$	−0.473475	+	9.89180i	−0.0349051	+	0.729233i
$185$	−0.243532	+	0.243532i	−0.0179048	+	0.0179048i
$186$		0			0
$187$	0.874215	+	2.11054i	0.0639289	+	0.154338i
$188$	−5.30413	+	8.54572i	−0.386844	+	0.623261i
$189$		0			0
$190$	14.0433	+	4.00392i	1.01881	+	0.290475i
$191$	10.2073			0.738576			0.369288	−	0.929315i	$-0.379602\pi$
$191$	10.2073			0.738576			0.369288	+	0.929315i	$0.379602\pi$
$192$		0			0
$193$	−10.7026			−0.770391			−0.385196	−	0.922835i	$-0.625866\pi$
$193$	−10.7026			−0.770391			−0.385196	+	0.922835i	$0.625866\pi$
$194$	0.189851	+	0.0541286i	0.0136305	+	0.00388621i
$195$		0			0
$196$	14.7814	−	23.8149i	1.05581	−	1.70106i
$197$	1.95833	+	4.72783i	0.139525	+	0.336844i	0.978161	−	0.207849i	$-0.0666462\pi$
$197$	1.95833	+	4.72783i	0.139525	+	0.336844i	−0.838636	+	0.544693i	$0.816646\pi$
$198$		0			0
$199$	9.72068	−	9.72068i	0.689081	−	0.689081i	−0.272948	−	0.962029i	$-0.587999\pi$
$199$	9.72068	−	9.72068i	0.689081	−	0.689081i	0.962029	+	0.272948i	$0.0879987\pi$
$200$	4.51563	+	0.216143i	0.319303	+	0.0152836i
$201$		0			0
$202$	2.07284	+	17.9520i	0.145844	+	1.26310i
$203$	9.93347	−	4.11458i	0.697193	−	0.288787i
$204$		0			0
$205$	−8.49098	+	20.4990i	−0.593036	+	1.43172i
$206$	6.37080	−	3.54398i	0.443875	−	0.246921i
$207$		0			0
$208$	−5.25580	+	0.353341i	−0.364424	+	0.0244998i
$209$		−	20.5389i		−	1.42070i
$210$		0			0
$211$	9.52388	−	22.9927i	0.655651	−	1.58288i	−0.148804	−	0.988867i	$-0.547542\pi$
$211$	9.52388	−	22.9927i	0.655651	−	1.58288i	0.804455	−	0.594014i	$-0.202458\pi$
$212$	15.2931	+	2.51172i	1.05033	+	0.172506i
$213$		0			0
$214$	−10.5512	+	1.21831i	−0.721268	+	0.0832817i
$215$	5.11190	+	5.11190i	0.348629	+	0.348629i
$216$		0			0
$217$	−33.8758	+	33.8758i	−2.29964	+	2.29964i
$218$	13.5868	−	17.1340i	0.920214	−	1.16046i
$219$		0			0
$220$	3.08391	+	13.1762i	0.207917	+	0.888338i
$221$	0.757629	+	0.313820i	0.0509636	+	0.0211098i
$222$		0			0
$223$	−0.519173			−0.0347664			−0.0173832	−	0.999849i	$-0.505534\pi$
$223$	−0.519173			−0.0347664			−0.0173832	+	0.999849i	$0.505534\pi$
$224$	21.3540	+	14.7131i	1.42677	+	0.983063i
$225$		0			0
$226$	3.50722	−	12.3012i	0.233296	−	0.818264i
$227$	4.61839	+	1.91300i	0.306533	+	0.126970i	0.530647	−	0.847593i	$-0.321949\pi$
$227$	4.61839	+	1.91300i	0.306533	+	0.126970i	−0.224114	+	0.974563i	$0.571949\pi$
$228$		0			0
$229$	−2.20642	−	5.32677i	−0.145804	−	0.352003i	0.834058	−	0.551677i	$-0.186012\pi$
$229$	−2.20642	−	5.32677i	−0.145804	−	0.352003i	−0.979862	+	0.199674i	$0.936012\pi$
$230$	5.67429	−	7.15571i	0.374151	−	0.471834i
$231$		0			0
$232$	2.24276	+	6.24330i	0.147244	+	0.409893i
$233$	−11.4133	−	11.4133i	−0.747713	−	0.747713i	0.226336	−	0.974049i	$-0.427325\pi$
$233$	−11.4133	−	11.4133i	−0.747713	−	0.747713i	−0.974049	+	0.226336i	$0.927325\pi$
$234$		0			0
$235$	8.56923	−	3.54949i	0.558995	−	0.231543i
$236$	−1.29182	+	7.86548i	−0.0840902	+	0.511999i
$237$		0			0
$238$	−1.96251	−	3.52788i	−0.127210	−	0.228678i
$239$		−	4.75090i		−	0.307310i	−0.988125	−	0.153655i	$-0.950896\pi$
$239$		−	4.75090i		−	0.307310i	0.988125	−	0.153655i	$-0.0491044\pi$
$240$		0			0
$241$		−	5.92434i		−	0.381620i	−0.981627	−	0.190810i	$-0.938888\pi$
$241$		−	5.92434i		−	0.381620i	0.981627	−	0.190810i	$-0.0611115\pi$
$242$	3.03815	−	1.69008i	0.195300	−	0.108642i
$243$		0			0
$244$	−3.87982	−	5.40470i	−0.248380	−	0.346001i
$245$	−23.8804	+	9.89159i	−1.52566	+	0.631951i
$246$		0			0
$247$	−5.21343	−	5.21343i	−0.331723	−	0.331723i
$248$	−19.8781	−	21.8767i	−1.26226	−	1.38917i
$249$		0			0
$250$	−13.4853	−	10.6935i	−0.852885	−	0.676315i
$251$	−10.2886	−	24.8389i	−0.649411	−	1.56782i	−0.813624	−	0.581392i	$-0.802508\pi$
$251$	−10.2886	−	24.8389i	−0.649411	−	1.56782i	0.164212	−	0.986425i	$-0.447492\pi$
$252$		0			0
$253$	−11.8669	−	4.91544i	−0.746067	−	0.309031i
$254$	7.92874	+	2.26058i	0.497494	+	0.141841i
$255$		0			0
$256$	−9.69753	+	12.7263i	−0.606096	+	0.795392i
$257$	−21.7192			−1.35480			−0.677402	−	0.735613i	$-0.736894\pi$
$257$	−21.7192			−1.35480			−0.677402	+	0.735613i	$0.736894\pi$
$258$		0			0
$259$	−0.790865	−	0.327587i	−0.0491419	−	0.0203553i
$260$	4.12734	+	2.56175i	0.255967	+	0.158873i
$261$		0			0
$262$	−8.15762	−	6.46878i	−0.503980	−	0.399642i
$263$	1.86567	−	1.86567i	0.115042	−	0.115042i	−0.647242	−	0.762284i	$-0.724078\pi$
$263$	1.86567	−	1.86567i	0.115042	−	0.115042i	0.762284	+	0.647242i	$0.224078\pi$
$264$		0			0
$265$	−10.1059	−	10.1059i	−0.620801	−	0.620801i
$266$	4.16326	+	36.0563i	0.255266	+	2.21075i
$267$		0			0
$268$	−2.74669	−	3.82622i	−0.167781	−	0.233723i
$269$	−2.52305	+	6.09118i	−0.153833	+	0.371386i	−0.981942	−	0.189181i	$-0.939417\pi$
$269$	−2.52305	+	6.09118i	−0.153833	+	0.371386i	0.828109	+	0.560567i	$0.189417\pi$
$270$		0			0
$271$			0.286319i			0.0173926i	0.999962	+	0.00869632i	$0.00276816\pi$
$271$			0.286319i			0.0173926i	−0.999962	+	0.00869632i	$0.997232\pi$
$272$	2.23210	−	1.10541i	0.135341	−	0.0670253i
$273$		0			0
$274$	13.3559	+	24.0092i	0.806862	+	1.45045i
$275$	−2.24391	+	5.41728i	−0.135313	+	0.326674i
$276$		0			0
$277$	−0.181363	+	0.0751232i	−0.0108971	+	0.00451371i	−0.388125	−	0.921607i	$-0.626877\pi$
$277$	−0.181363	+	0.0751232i	−0.0108971	+	0.00451371i	0.377228	+	0.926120i	$0.376877\pi$
$278$	3.25801	−	0.376188i	0.195402	−	0.0225623i
$279$		0			0
$280$	−8.08469	−	22.5059i	−0.483153	−	1.34498i
$281$	−20.3637	+	20.3637i	−1.21480	+	1.21480i	−0.245365	+	0.969431i	$0.578908\pi$
$281$	−20.3637	+	20.3637i	−1.21480	+	1.21480i	−0.969431	+	0.245365i	$0.921092\pi$
$282$		0			0
$283$	5.49343	+	13.2623i	0.326550	+	0.788362i	0.998844	+	0.0480775i	$0.0153094\pi$
$283$	5.49343	+	13.2623i	0.326550	+	0.788362i	−0.672293	+	0.740285i	$0.734691\pi$
$284$	3.06138	−	0.716523i	0.181660	−	0.0425178i
$285$		0			0
$286$	1.87332	−	6.57049i	0.110772	−	0.388521i
$287$	−55.1485			−3.25531
$288$		0			0
$289$	16.6122			0.977190
$290$	1.67737	−	5.88321i	0.0984986	−	0.345474i
$291$		0			0
$292$	2.39524	+	10.2338i	0.140171	+	0.598888i
$293$	3.82263	+	9.22865i	0.223321	+	0.539143i	0.995337	−	0.0964591i	$-0.0307517\pi$
$293$	3.82263	+	9.22865i	0.223321	+	0.539143i	−0.772016	+	0.635603i	$0.780752\pi$
$294$		0			0
$295$	5.19763	−	5.19763i	0.302618	−	0.302618i
$296$	0.225219	−	0.477741i	0.0130906	−	0.0277681i
$297$		0			0
$298$	−1.40884	+	0.162672i	−0.0816117	+	0.00942336i
$299$	−4.25991	+	1.76451i	−0.246357	+	0.102044i
$300$		0			0
$301$	−6.87626	+	16.6008i	−0.396341	+	0.956853i
$302$	6.83038	+	12.2786i	0.393044	+	0.706551i
$303$		0			0
$304$	−22.3440	+	1.50216i	−1.28152	+	0.0861549i
$305$			6.13535i			0.351309i
$306$		0			0
$307$	−2.37991	+	5.74561i	−0.135829	+	0.327919i	−0.977129	−	0.212649i	$-0.931791\pi$
$307$	−2.37991	+	5.74561i	−0.135829	+	0.327919i	0.841300	+	0.540568i	$0.181791\pi$
$308$	−27.3233	+	19.6143i	−1.55689	+	1.11763i
$309$		0			0
$310$	3.12666	+	27.0787i	0.177582	+	1.53797i
$311$	−0.675375	−	0.675375i	−0.0382970	−	0.0382970i	0.687699	−	0.725996i	$-0.258621\pi$
$311$	−0.675375	−	0.675375i	−0.0382970	−	0.0382970i	−0.725996	+	0.687699i	$0.758621\pi$
$312$		0			0
$313$	11.3106	−	11.3106i	0.639315	−	0.639315i	−0.311072	−	0.950386i	$-0.600688\pi$
$313$	11.3106	−	11.3106i	0.639315	−	0.639315i	0.950386	+	0.311072i	$0.100688\pi$
$314$	−6.75532	−	5.35679i	−0.381225	−	0.302301i
$315$		0			0
$316$	−10.7845	+	17.3754i	−0.606677	+	0.977444i
$317$	−10.5105	−	4.35358i	−0.590327	−	0.244522i	0.0674641	−	0.997722i	$-0.478509\pi$
$317$	−10.5105	−	4.35358i	−0.590327	−	0.244522i	−0.657791	+	0.753200i	$0.728509\pi$
$318$		0			0
$319$	−8.60439			−0.481754
$320$	14.1087	−	4.31864i	0.788700	−	0.241419i
$321$		0			0
$322$	21.8289	+	6.22368i	1.21648	+	0.346832i
$323$	3.22091	+	1.33415i	0.179216	+	0.0742339i
$324$		0			0
$325$	0.805505	+	1.94466i	0.0446814	+	0.107870i
$326$	−24.3056	−	19.2737i	−1.34616	−	1.06747i
$327$		0			0
$328$	1.62683	−	33.9877i	0.0898268	−	1.87665i
$329$	16.3015	+	16.3015i	0.898730	+	0.898730i
$330$		0			0
$331$	−4.12595	+	1.70902i	−0.226783	+	0.0939365i	−0.493182	−	0.869926i	$-0.664166\pi$
$331$	−4.12595	+	1.70902i	−0.226783	+	0.0939365i	0.266399	+	0.963863i	$0.414166\pi$
$332$	19.9195	−	14.2994i	1.09322	−	0.784782i
$333$		0			0
$334$	16.2013	−	9.01252i	0.886494	−	0.493143i
$335$			4.34348i			0.237309i
$336$		0			0
$337$			4.39557i			0.239442i	0.992808	+	0.119721i	$0.0382000\pi$
$337$			4.39557i			0.239442i	−0.992808	+	0.119721i	$0.961800\pi$
$338$	7.74510	+	13.9229i	0.421278	+	0.757305i
$339$		0			0
$340$	−2.26662	−	0.372267i	−0.122925	−	0.0201890i
$341$	35.4204	−	14.6716i	1.91812	−	0.794513i
$342$		0			0
$343$	−22.7379	−	22.7379i	−1.22773	−	1.22773i
$344$	−10.0281	−	4.72750i	−0.540679	−	0.254890i
$345$		0			0
$346$	11.6513	−	14.6931i	0.626376	−	0.789909i
$347$	−8.23821	−	19.8888i	−0.442250	−	1.06769i	−0.975158	−	0.221513i	$-0.928901\pi$
$347$	−8.23821	−	19.8888i	−0.442250	−	1.06769i	0.532907	−	0.846174i	$-0.321099\pi$
$348$		0			0
$349$	−17.5916	−	7.28668i	−0.941657	−	0.390047i	−0.141568	−	0.989928i	$-0.545215\pi$
$349$	−17.5916	−	7.28668i	−0.941657	−	0.390047i	−0.800089	+	0.599881i	$0.795215\pi$
$350$	2.84112	−	9.96495i	0.151864	−	0.532649i
$351$		0			0
$352$	−11.2822	−	17.4178i	−0.601341	−	0.928371i
$353$	−15.0586			−0.801490			−0.400745	−	0.916190i	$-0.631249\pi$
$353$	−15.0586			−0.801490			−0.400745	+	0.916190i	$0.631249\pi$
$354$		0			0
$355$	−2.67873	−	1.10957i	−0.142172	−	0.0588897i
$356$	9.75007	−	2.28202i	0.516753	−	0.120947i
$357$		0			0
$358$	−16.4799	+	20.7824i	−0.870989	+	1.09838i
$359$	1.78051	−	1.78051i	0.0939719	−	0.0939719i	−0.658558	−	0.752530i	$-0.728833\pi$
$359$	1.78051	−	1.78051i	0.0939719	−	0.0939719i	0.752530	+	0.658558i	$0.228833\pi$
$360$		0			0
$361$	−8.72889	−	8.72889i	−0.459415	−	0.459415i
$362$	20.9126	−	2.41469i	1.09914	−	0.126913i
$363$		0			0
$364$	−1.95679	+	11.9143i	−0.102564	+	0.624480i
$365$	3.70914	−	8.95466i	0.194145	−	0.468708i
$366$		0			0
$367$			19.5858i			1.02237i	0.859470	+	0.511186i	$0.170794\pi$
$367$			19.5858i			1.02237i	−0.859470	+	0.511186i	$0.829206\pi$
$368$	−4.47955	+	13.2694i	−0.233512	+	0.691717i
$369$		0			0
$370$	−0.425639	+	0.236777i	−0.0221279	+	0.0123094i
$371$	13.5940	−	32.8187i	0.705763	−	1.70386i
$372$		0			0
$373$	27.0247	−	11.1940i	1.39928	−	0.579603i	0.449719	−	0.893170i	$-0.351524\pi$
$373$	27.0247	−	11.1940i	1.39928	−	0.579603i	0.949566	+	0.313568i	$0.101524\pi$
$374$	0.370571	+	3.20935i	0.0191617	+	0.165952i
$375$		0			0
$376$	−10.5274	+	9.56561i	−0.542907	+	0.493309i
$377$	−2.18408	+	2.18408i	−0.112486	+	0.112486i
$378$		0			0
$379$	5.77531	+	13.9428i	0.296658	+	0.716195i	0.999986	+	0.00532948i	$0.00169643\pi$
$379$	5.77531	+	13.9428i	0.296658	+	0.716195i	−0.703328	+	0.710865i	$0.748304\pi$
$380$	17.5466	+	10.8908i	0.900123	+	0.558685i
$381$		0			0
$382$	13.8821	+	3.95796i	0.710272	+	0.202507i
$383$	10.9987			0.562008			0.281004	−	0.959707i	$-0.409333\pi$
$383$	10.9987			0.562008			0.281004	+	0.959707i	$0.409333\pi$
$384$		0			0
$385$	31.0171			1.58078
$386$	−14.5557	−	4.15001i	−0.740867	−	0.211230i
$387$		0			0
$388$	0.237211	+	0.147232i	0.0120426	+	0.00747455i
$389$	−7.85456	−	18.9626i	−0.398242	−	0.961441i	−0.988083	−	0.153922i	$-0.950810\pi$
$389$	−7.85456	−	18.9626i	−0.398242	−	0.961441i	0.589841	−	0.807519i	$-0.299190\pi$
$390$		0			0
$391$	1.54168	−	1.54168i	0.0779663	−	0.0779663i
$392$	29.3373	−	26.6571i	1.48176	−	1.34639i
$393$		0			0
$394$	0.830117	+	7.18929i	0.0418207	+	0.362191i
$395$	17.4232	−	7.21694i	0.876658	−	0.363123i
$396$		0			0
$397$	−1.90361	+	4.59572i	−0.0955395	+	0.230653i	−0.964423	−	0.264364i	$-0.914838\pi$
$397$	−1.90361	+	4.59572i	−0.0955395	+	0.230653i	0.868884	+	0.495017i	$0.164838\pi$
$398$	16.9895	−	9.45103i	0.851609	−	0.473737i
$399$		0			0
$400$	6.05752	+	2.04492i	0.302876	+	0.102246i
$401$			33.4589i			1.67086i	0.549599	+	0.835429i	$0.314780\pi$
$401$			33.4589i			1.67086i	−0.549599	+	0.835429i	$0.685220\pi$
$402$		0			0
$403$	5.26673	−	12.7150i	0.262354	−	0.633380i
$404$	−4.14190	+	25.2187i	−0.206067	+	1.25468i
$405$		0			0
$406$	15.1051	−	1.74413i	0.749655	−	0.0865596i
$407$	0.484403	+	0.484403i	0.0240109	+	0.0240109i
$408$		0			0
$409$	−2.46531	+	2.46531i	−0.121902	+	0.121902i	−0.765426	−	0.643524i	$-0.777472\pi$
$409$	−2.46531	+	2.46531i	−0.121902	+	0.121902i	0.643524	+	0.765426i	$0.277472\pi$
$410$	−19.4965	+	24.5866i	−0.962864	+	1.21425i
$411$		0			0
$412$	10.0386	−	2.34955i	0.494566	−	0.115754i
$413$	16.8792	+	6.99159i	0.830570	+	0.344034i
$414$		0			0
$415$	−22.6124			−1.11000
$416$	−7.28498	−	1.55742i	−0.357176	−	0.0763588i
$417$		0			0
$418$	7.96407	−	27.9332i	0.389536	−	1.36626i
$419$	14.6327	+	6.06106i	0.714854	+	0.296102i	0.710312	−	0.703887i	$-0.248554\pi$
$419$	14.6327	+	6.06106i	0.714854	+	0.296102i	0.00454254	+	0.999990i	$0.498554\pi$
$420$		0			0
$421$	−10.0070	−	24.1590i	−0.487711	−	1.17744i	−0.955869	−	0.293793i	$-0.905082\pi$
$421$	−10.0070	−	24.1590i	−0.487711	−	1.17744i	0.468158	−	0.883645i	$-0.344918\pi$
$422$	21.8682	−	27.5775i	1.06453	−	1.34245i
$423$		0			0
$424$	19.8249	+	9.34599i	0.962784	+	0.453881i
$425$	−0.703782	−	0.703782i	−0.0341384	−	0.0341384i
$426$		0			0
$427$	−14.0887	+	5.83573i	−0.681799	+	0.282411i
$428$	−14.8223	−	2.43439i	−0.716461	−	0.117671i
$429$		0			0
$430$	4.97010	+	8.93444i	0.239679	+	0.430857i
$431$			23.7227i			1.14268i	0.820713	+	0.571341i	$0.193577\pi$
$431$			23.7227i			1.14268i	−0.820713	+	0.571341i	$0.806423\pi$
$432$		0			0
$433$			23.6074i			1.13450i	0.823546	+	0.567249i	$0.191992\pi$
$433$			23.6074i			1.13450i	−0.823546	+	0.567249i	$0.808008\pi$
$434$	−59.2071	+	32.9360i	−2.84203	+	1.58098i
$435$		0			0
$436$	25.1221	−	18.0341i	1.20313	−	0.863679i
$437$	−18.1102	+	7.50150i	−0.866329	+	0.358845i
$438$		0			0
$439$	17.9050	+	17.9050i	0.854557	+	0.854557i	0.990690	−	0.136134i	$-0.0434676\pi$
$439$	17.9050	+	17.9050i	0.854557	+	0.854557i	−0.136134	+	0.990690i	$0.543468\pi$
$440$	−0.914978	+	19.1156i	−0.0436199	+	0.911302i
$441$		0			0
$442$	0.908702	+	0.720576i	0.0432225	+	0.0342743i
$443$	6.84608	+	16.5279i	0.325267	+	0.785265i	0.998931	+	0.0462266i	$0.0147196\pi$
$443$	6.84608	+	16.5279i	0.325267	+	0.785265i	−0.673664	+	0.739038i	$0.735280\pi$
$444$		0			0
$445$	−8.53138	−	3.53381i	−0.404426	−	0.167519i
$446$	−0.706084	−	0.201313i	−0.0334340	−	0.00953243i
$447$		0			0
$448$	23.3366	+	28.2903i	1.10255	+	1.33659i
$449$	20.0312			0.945332			0.472666	−	0.881242i	$-0.343292\pi$
$449$	20.0312			0.945332			0.472666	+	0.881242i	$0.343292\pi$
$450$		0			0
$451$	40.7741	+	16.8892i	1.91998	+	0.795280i
$452$	9.53974	−	15.3699i	0.448712	−	0.722939i
$453$		0			0
$454$	5.53931	+	4.39252i	0.259973	+	0.206151i
$455$	7.87316	−	7.87316i	0.369099	−	0.369099i
$456$		0			0
$457$	−1.43011	−	1.43011i	−0.0668975	−	0.0668975i	0.672866	−	0.739764i	$-0.265063\pi$
$457$	−1.43011	−	1.43011i	−0.0668975	−	0.0668975i	−0.739764	+	0.672866i	$0.765063\pi$
$458$	−0.935279	−	8.10005i	−0.0437027	−	0.378491i
$459$		0			0
$460$	10.4918	−	7.53165i	0.489183	−	0.351165i
$461$	11.8633	−	28.6405i	0.552528	−	1.33392i	−0.363046	−	0.931771i	$-0.618263\pi$
$461$	11.8633	−	28.6405i	0.552528	−	1.33392i	0.915574	−	0.402150i	$-0.131737\pi$
$462$		0			0
$463$		−	23.3331i		−	1.08438i	−0.840255	−	0.542191i	$-0.817595\pi$
$463$		−	23.3331i		−	1.08438i	0.840255	−	0.542191i	$-0.182405\pi$
$464$	0.629305	+	9.36064i	0.0292147	+	0.434557i
$465$		0			0
$466$	−11.0967	−	19.9479i	−0.514046	−	0.924070i
$467$	−1.25228	+	3.02327i	−0.0579485	+	0.139900i	−0.950202	−	0.311635i	$-0.899123\pi$
$467$	−1.25228	+	3.02327i	−0.0579485	+	0.139900i	0.892253	+	0.451535i	$0.149123\pi$
$468$		0			0
$469$	−9.97398	+	4.13136i	−0.460556	+	0.190768i
$470$	13.0306	−	1.50459i	0.601058	−	0.0694017i
$471$		0			0
$472$	−4.80679	+	10.1963i	−0.221250	+	0.469322i
$473$	10.1679	−	10.1679i	0.467522	−	0.467522i
$474$		0			0
$475$	3.42445	+	8.26735i	0.157124	+	0.379332i
$476$	−1.30108	−	5.55895i	−0.0596351	−	0.254794i
$477$		0			0
$478$	1.84219	−	6.46130i	0.0842598	−	0.295533i
$479$	−20.4084			−0.932486			−0.466243	−	0.884657i	$-0.654393\pi$
$479$	−20.4084			−0.932486			−0.466243	+	0.884657i	$0.654393\pi$
$480$		0			0
$481$	0.245914			0.0112127
$482$	2.29720	−	8.05720i	0.104635	−	0.366996i
$483$		0			0
$484$	4.78727	−	1.12047i	0.217603	−	0.0509305i
$485$	−0.0985264	−	0.237864i	−0.00447385	−	0.0108008i
$486$		0			0
$487$	−14.1551	+	14.1551i	−0.641430	+	0.641430i	−0.950907	−	0.309477i	$-0.899846\pi$
$487$	−14.1551	+	14.1551i	−0.641430	+	0.641430i	0.309477	+	0.950907i	$0.399846\pi$
$488$	−3.18091	−	8.85491i	−0.143993	−	0.400843i
$489$		0			0
$490$	−36.3133	+	4.19294i	−1.64047	+	0.189418i
$491$	9.93954	−	4.11709i	0.448565	−	0.185802i	−0.146953	−	0.989143i	$-0.546947\pi$
$491$	9.93954	−	4.11709i	0.448565	−	0.185802i	0.595518	+	0.803342i	$0.296947\pi$
$492$		0			0
$493$	0.558917	−	1.34935i	0.0251724	−	0.0607715i
$494$	−5.06881	−	9.11190i	−0.228057	−	0.409964i
$495$		0			0
$496$	−18.5517	−	37.4605i	−0.832996	−	1.68203i
$497$		−	7.20658i		−	0.323259i
$498$		0			0
$499$	−2.81268	+	6.79042i	−0.125913	+	0.303981i	−0.974248	−	0.225479i	$-0.927605\pi$
$499$	−2.81268	+	6.79042i	−0.125913	+	0.303981i	0.848335	+	0.529460i	$0.177605\pi$
$500$	−14.1938	−	19.7723i	−0.634764	−	0.884245i
$501$		0			0
$502$	−4.36123	−	37.7708i	−0.194651	−	1.68579i
$503$	8.42826	+	8.42826i	0.375798	+	0.375798i	0.869584	−	0.493786i	$-0.164387\pi$
$503$	8.42826	+	8.42826i	0.375798	+	0.375798i	−0.493786	+	0.869584i	$0.664387\pi$
$504$		0			0
$505$	16.6649	−	16.6649i	0.741580	−	0.741580i
$506$	−14.2332	−	11.2866i	−0.632744	−	0.501749i
$507$		0			0
$508$	9.90667	+	6.14884i	0.439537	+	0.272811i
$509$	−2.80732	−	1.16283i	−0.124432	−	0.0515415i	0.319599	−	0.947553i	$-0.396452\pi$
$509$	−2.80732	−	1.16283i	−0.124432	−	0.0515415i	−0.444031	+	0.896011i	$0.646452\pi$
$510$		0			0
$511$	24.0907			1.06571
$512$	−18.1235	+	13.5477i	−0.800953	+	0.598727i
$513$		0			0
$514$	−29.5384	−	8.42175i	−1.30288	−	0.371467i
$515$	−8.78384	−	3.63839i	−0.387062	−	0.160326i
$516$		0			0
$517$	−7.06019	−	17.0448i	−0.310507	−	0.749630i
$518$	−0.948565	−	0.752186i	−0.0416776	−	0.0330492i
$519$		0			0
$520$	4.61992	+	5.08442i	0.202597	+	0.222967i
$521$	23.5959	+	23.5959i	1.03376	+	1.03376i	0.999410	+	0.0343468i	$0.0109351\pi$
$521$	23.5959	+	23.5959i	1.03376	+	1.03376i	0.0343468	+	0.999410i	$0.489065\pi$
$522$		0			0
$523$	30.1407	−	12.4847i	1.31796	−	0.545916i	0.390762	−	0.920492i	$-0.372211\pi$
$523$	30.1407	−	12.4847i	1.31796	−	0.545916i	0.927196	+	0.374575i	$0.122211\pi$
$524$	−8.58619	−	11.9608i	−0.375090	−	0.522511i
$525$		0			0
$526$	3.26076	−	1.81391i	0.142176	−	0.0790903i
$527$			6.50768i			0.283479i
$528$		0			0
$529$		−	10.7410i		−	0.467000i
$530$	−9.82558	−	17.6628i	−0.426796	−	0.767225i
$531$		0			0
$532$	−8.31894	+	50.6514i	−0.360672	+	2.19602i
$533$	14.6368	−	6.06277i	0.633991	−	0.262608i
$534$		0			0
$535$	9.79478	+	9.79478i	0.423465	+	0.423465i
$536$	−2.25190	−	6.26876i	−0.0972674	−	0.270769i
$537$		0			0
$538$	−5.79328	+	7.30577i	−0.249766	+	0.314974i
$539$	19.6751	+	47.4999i	0.847466	+	2.04596i
$540$		0			0
$541$	27.9752	+	11.5877i	1.20275	+	0.498194i	0.891885	−	0.452261i	$-0.149383\pi$
$541$	27.9752	+	11.5877i	1.20275	+	0.498194i	0.310861	+	0.950455i	$0.399383\pi$
$542$	−0.111022	+	0.389398i	−0.00476880	+	0.0167261i
$543$		0			0
$544$	3.46432	−	0.637865i	0.148532	−	0.0273482i
$545$	−28.5183			−1.22159
$546$		0			0
$547$	−29.3726	−	12.1665i	−1.25588	−	0.520204i	−0.347240	−	0.937776i	$-0.612881\pi$
$547$	−29.3726	−	12.1665i	−1.25588	−	0.520204i	−0.908644	+	0.417573i	$0.862881\pi$
$548$	8.85459	+	37.8317i	0.378250	+	1.61609i
$549$		0			0
$550$	−5.15234	+	6.49750i	−0.219696	+	0.277054i
$551$	−9.28519	+	9.28519i	−0.395562	+	0.395562i
$552$		0			0
$553$	33.1447	+	33.1447i	1.40946	+	1.40946i
$554$	−0.275787	+	0.0318439i	−0.0117171	+	0.00135292i
$555$		0			0
$556$	4.57681	+	0.751691i	0.194100	+	0.0318788i
$557$	7.20303	−	17.3897i	0.305202	−	0.736824i	−0.694645	−	0.719353i	$-0.744439\pi$
$557$	7.20303	−	17.3897i	0.305202	−	0.736824i	0.999847	−	0.0174710i	$-0.00556147\pi$
$558$		0			0
$559$		−	5.16191i		−	0.218325i
$560$	−2.26852	−	33.7432i	−0.0958624	−	1.42591i
$561$		0			0
$562$	−35.5911	+	19.7988i	−1.50132	+	0.835162i
$563$	−10.5977	+	25.5852i	−0.446641	+	1.07829i	0.526931	+	0.849908i	$0.323343\pi$
$563$	−10.5977	+	25.5852i	−0.446641	+	1.07829i	−0.973572	+	0.228379i	$0.926657\pi$
$564$		0			0
$565$	−15.4122	+	6.38393i	−0.648395	+	0.268574i
$566$	2.32861	+	20.1671i	0.0978787	+	0.847685i
$567$		0			0
$568$	4.44137	+	0.212588i	0.186356	+	0.00891999i
$569$	−10.6978	+	10.6978i	−0.448475	+	0.448475i	−0.894847	−	0.446372i	$-0.852716\pi$
$569$	−10.6978	+	10.6978i	−0.448475	+	0.448475i	0.446372	+	0.894847i	$0.352716\pi$
$570$		0			0
$571$	−1.08014	−	2.60770i	−0.0452026	−	0.109129i	0.899666	−	0.436580i	$-0.143810\pi$
$571$	−1.08014	−	2.60770i	−0.0452026	−	0.109129i	−0.944868	+	0.327451i	$0.893810\pi$
$572$	5.09550	−	8.20958i	0.213054	−	0.343260i
$573$		0			0
$574$	−75.0029	−	21.3842i	−3.13056	−	0.892559i
$575$	5.59626			0.233380
$576$		0			0
$577$	−21.4373			−0.892445			−0.446223	−	0.894922i	$-0.647231\pi$
$577$	−21.4373			−0.892445			−0.446223	+	0.894922i	$0.647231\pi$
$578$	22.5929	+	6.44150i	0.939741	+	0.267931i
$579$		0			0
$580$	4.56250	−	7.35085i	0.189448	−	0.305227i
$581$	−21.5081	−	51.9250i	−0.892305	−	2.15421i
$582$		0			0
$583$	−20.1014	+	20.1014i	−0.832514	+	0.832514i
$584$	−0.710654	+	14.8469i	−0.0294071	+	0.614370i
$585$		0			0
$586$	1.62037	+	14.0334i	0.0669370	+	0.579713i
$587$	−1.40199	+	0.580725i	−0.0578665	+	0.0239691i	−0.411429	−	0.911442i	$-0.634970\pi$
$587$	−1.40199	+	0.580725i	−0.0578665	+	0.0239691i	0.353562	+	0.935411i	$0.384970\pi$
$588$		0			0
$589$	22.3905	−	54.0554i	0.922584	−	2.22732i
$590$	9.08428	−	5.05345i	0.373994	−	0.208047i
$591$		0			0
$592$	0.491549	−	0.562405i	0.0202025	−	0.0231147i
$593$		−	2.08256i		−	0.0855207i	−0.999085	−	0.0427603i	$-0.986385\pi$
$593$		−	2.08256i		−	0.0855207i	0.999085	−	0.0427603i	$-0.0136152\pi$
$594$		0			0
$595$	−2.01478	+	4.86412i	−0.0825981	+	0.199409i
$596$	−1.97912	−	0.325048i	−0.0810678	−	0.0133145i
$597$		0			0
$598$	−6.47775	+	0.747959i	−0.264895	+	0.0305863i
$599$	−13.5781	−	13.5781i	−0.554786	−	0.554786i	0.373033	−	0.927818i	$-0.378318\pi$
$599$	−13.5781	−	13.5781i	−0.554786	−	0.554786i	−0.927818	+	0.373033i	$0.878318\pi$
$600$		0			0
$601$	5.03476	−	5.03476i	0.205372	−	0.205372i	−0.596925	−	0.802297i	$-0.703611\pi$
$601$	5.03476	−	5.03476i	0.205372	−	0.205372i	0.802297	+	0.596925i	$0.203611\pi$
$602$	−15.7889	+	19.9110i	−0.643507	+	0.811512i
$603$		0			0
$604$	4.52834	+	19.3476i	0.184255	+	0.787241i
$605$	−4.18890	−	1.73510i	−0.170303	−	0.0705418i
$606$		0			0
$607$	−8.30054			−0.336909			−0.168454	−	0.985709i	$-0.553878\pi$
$607$	−8.30054			−0.336909			−0.168454	+	0.985709i	$0.553878\pi$
$608$	−30.9707	−	6.62108i	−1.25603	−	0.268520i
$609$		0			0
$610$	−2.37902	+	8.34418i	−0.0963238	+	0.337846i
$611$	−6.11864	−	2.53442i	−0.247533	−	0.102532i
$612$		0			0
$613$	10.3825	+	25.0655i	0.419344	+	1.01239i	0.982538	+	0.186062i	$0.0595725\pi$
$613$	10.3825	+	25.0655i	0.419344	+	1.01239i	−0.563194	+	0.826325i	$0.690428\pi$
$614$	−5.46461	+	6.89129i	−0.220534	+	0.278110i
$615$		0			0
$616$	−44.7658	+	16.0810i	−1.80366	+	0.647923i
$617$	−4.65911	−	4.65911i	−0.187569	−	0.187569i	0.607076	−	0.794644i	$-0.292343\pi$
$617$	−4.65911	−	4.65911i	−0.187569	−	0.187569i	−0.794644	+	0.607076i	$0.792343\pi$
$618$		0			0
$619$	−14.6048	+	6.04953i	−0.587018	+	0.243151i	−0.656367	−	0.754441i	$-0.727908\pi$
$619$	−14.6048	+	6.04953i	−0.587018	+	0.243151i	0.0693489	+	0.997592i	$0.477908\pi$
$620$	−6.24762	+	38.0398i	−0.250911	+	1.52772i
$621$		0			0
$622$	−0.656640	−	1.18040i	−0.0263289	−	0.0473298i
$623$		−	22.9519i		−	0.919550i
$624$		0			0
$625$			14.4536i			0.578143i
$626$	19.7684	−	10.9969i	0.790105	−	0.439523i
$627$		0			0
$628$	−7.11022	−	9.90474i	−0.283729	−	0.395242i
$629$	−0.107430	+	0.0444988i	−0.00428350	+	0.00177428i
$630$		0			0
$631$	−34.7967	−	34.7967i	−1.38524	−	1.38524i	−0.835028	−	0.550208i	$-0.814549\pi$
$631$	−34.7967	−	34.7967i	−1.38524	−	1.38524i	−0.550208	−	0.835028i	$-0.685451\pi$
$632$	−21.4046	+	19.4491i	−0.851428	+	0.773643i
$633$		0			0
$634$	−12.6063	−	9.99645i	−0.500660	−	0.397010i
$635$	−4.11477	−	9.93392i	−0.163289	−	0.394216i
$636$		0			0
$637$	17.0512	+	7.06284i	0.675593	+	0.279840i
$638$	−11.7021	−	3.33641i	−0.463291	−	0.132090i
$639$		0			0
$640$	20.8626	−	0.402676i	0.824668	−	0.0159172i
$641$	34.7091			1.37093			0.685464	−	0.728107i	$-0.259599\pi$
$641$	34.7091			1.37093			0.685464	+	0.728107i	$0.259599\pi$
$642$		0			0
$643$	−18.3692	−	7.60876i	−0.724409	−	0.300060i	−0.0101569	−	0.999948i	$-0.503233\pi$
$643$	−18.3692	−	7.60876i	−0.724409	−	0.300060i	−0.714252	+	0.699888i	$0.753233\pi$
$644$	27.2744	+	16.9286i	1.07476	+	0.667081i
$645$		0			0
$646$	3.86317	+	3.06339i	0.151994	+	0.120527i
$647$	−31.4202	+	31.4202i	−1.23526	+	1.23526i	−0.273339	+	0.961918i	$0.588128\pi$
$647$	−31.4202	+	31.4202i	−1.23526	+	1.23526i	−0.961918	+	0.273339i	$0.911872\pi$
$648$		0			0
$649$	−10.3385	−	10.3385i	−0.405820	−	0.405820i
$650$	0.341445	+	2.95711i	0.0133926	+	0.115987i
$651$		0			0
$652$	−25.5825	−	35.6371i	−1.00189	−	1.39566i
$653$	−7.10749	+	17.1590i	−0.278138	+	0.671484i	−0.999784	−	0.0207782i	$-0.993386\pi$
$653$	−7.10749	+	17.1590i	−0.278138	+	0.671484i	0.721647	+	0.692262i	$0.243386\pi$
$654$		0			0
$655$			13.5778i			0.530528i
$656$	15.3915	−	45.5930i	0.600935	−	1.78011i
$657$		0			0
$658$	15.8493	+	28.4913i	0.617869	+	1.11071i
$659$	2.78866	−	6.73242i	0.108631	−	0.262258i	−0.860211	−	0.509938i	$-0.829668\pi$
$659$	2.78866	−	6.73242i	0.108631	−	0.262258i	0.968842	+	0.247680i	$0.0796683\pi$
$660$		0			0
$661$	−24.8628	+	10.2985i	−0.967049	+	0.400565i	−0.809613	−	0.586964i	$-0.800323\pi$
$661$	−24.8628	+	10.2985i	−0.967049	+	0.400565i	−0.157436	+	0.987529i	$0.550323\pi$
$662$	−6.27405	+	0.724438i	−0.243848	+	0.0281561i
$663$		0			0
$664$	32.6355	−	11.7235i	1.26650	−	0.454961i
$665$	33.4712	−	33.4712i	1.29796	−	1.29796i
$666$		0			0
$667$	3.14262	+	7.58696i	0.121683	+	0.293768i
$668$	25.5287	−	5.97503i	0.987733	−	0.231181i
$669$		0			0
$670$	−1.68421	+	5.90720i	−0.0650668	+	0.228215i
$671$	12.2037			0.471117
$672$		0			0
$673$	−30.7959			−1.18710			−0.593548	−	0.804799i	$-0.702273\pi$
$673$	−30.7959			−1.18710			−0.593548	+	0.804799i	$0.702273\pi$
$674$	−1.70441	+	5.97805i	−0.0656515	+	0.230266i
$675$		0			0
$676$	5.13477	+	21.9386i	0.197491	+	0.843791i
$677$	13.2209	+	31.9181i	0.508121	+	1.22671i	0.944964	+	0.327175i	$0.106097\pi$
$677$	13.2209	+	31.9181i	0.508121	+	1.22671i	−0.436842	+	0.899538i	$0.643903\pi$
$678$		0			0
$679$	0.452495	−	0.452495i	0.0173652	−	0.0173652i
$680$	−2.93829	−	1.38518i	−0.112678	−	0.0531194i
$681$		0			0
$682$	53.8614	−	6.21915i	2.06246	−	0.238144i
$683$	−30.6208	+	12.6835i	−1.17167	+	0.485322i	−0.881745	−	0.471726i	$-0.843631\pi$
$683$	−30.6208	+	12.6835i	−1.17167	+	0.485322i	−0.289927	+	0.957049i	$0.593631\pi$
$684$		0			0
$685$	13.7117	−	33.1030i	0.523898	−	1.26480i
$686$	−22.1071	−	39.7407i	−0.844055	−	1.51731i
$687$		0			0
$688$	−11.8053	−	10.3179i	−0.450071	−	0.393368i
$689$			10.2048i			0.388771i
$690$		0			0
$691$	−5.49715	+	13.2713i	−0.209121	+	0.504864i	−0.993285	−	0.115690i	$-0.963092\pi$
$691$	−5.49715	+	13.2713i	−0.209121	+	0.504864i	0.784164	+	0.620554i	$0.213092\pi$
$692$	21.5433	−	15.4651i	0.818953	−	0.587894i
$693$		0			0
$694$	−3.49209	−	30.2435i	−0.132558	−	1.14803i
$695$	−3.02443	−	3.02443i	−0.114723	−	0.114723i
$696$		0			0
$697$	−5.29714	+	5.29714i	−0.200643	+	0.200643i
$698$	−21.0994	−	16.7313i	−0.798625	−	0.633288i
$699$		0			0
$700$	7.72795	−	12.4508i	0.292089	−	0.470597i
$701$	20.5608	+	8.51658i	0.776572	+	0.321667i	0.735531	−	0.677491i	$-0.236933\pi$
$701$	20.5608	+	8.51658i	0.776572	+	0.321667i	0.0410410	+	0.999157i	$0.486933\pi$
$702$		0			0
$703$	1.04546			0.0394302
$704$	−8.59007	−	28.0632i	−0.323751	−	1.05767i
$705$		0			0
$706$	−20.4800	−	5.83908i	−0.770775	−	0.219757i
$707$	54.1190	+	22.4168i	2.03535	+	0.843071i
$708$		0			0
$709$	6.40422	+	15.4612i	0.240516	+	0.580656i	0.997334	−	0.0729689i	$-0.0232474\pi$
$709$	6.40422	+	15.4612i	0.240516	+	0.580656i	−0.756819	+	0.653625i	$0.773247\pi$
$710$	−3.21288	−	2.54772i	−0.120577	−	0.0956144i
$711$		0			0
$712$	14.1451	+	0.677062i	0.530111	+	0.0253740i
$713$	−25.8735	−	25.8735i	−0.968971	−	0.968971i
$714$		0			0
$715$	−8.23216	+	3.40987i	−0.307866	+	0.127522i
$716$	−30.4714	+	21.8742i	−1.13877	+	0.817479i
$717$		0			0
$718$	3.11193	−	1.73112i	0.116136	−	0.0646049i
$719$		−	43.9490i		−	1.63902i	−0.573063	−	0.819511i	$-0.694245\pi$
$719$		−	43.9490i		−	1.63902i	0.573063	−	0.819511i	$-0.305755\pi$
$720$		0			0
$721$		−	23.6311i		−	0.880070i
$722$	−8.48675	−	15.2561i	−0.315844	−	0.567774i
$723$		0			0
$724$	29.3778	+	4.82498i	1.09182	+	0.179319i
$725$	3.46346	−	1.43461i	0.128630	−	0.0532802i
$726$		0			0
$727$	21.5021	+	21.5021i	0.797468	+	0.797468i	0.982696	−	0.185228i	$-0.0593022\pi$
$727$	21.5021	+	21.5021i	0.797468	+	0.797468i	−0.185228	+	0.982696i	$0.559302\pi$
$728$	−7.28112	+	15.4449i	−0.269856	+	0.572426i
$729$		0			0
$730$	8.51672	−	10.7402i	0.315218	−	0.397514i
$731$	0.934060	+	2.25502i	0.0345475	+	0.0834049i
$732$		0			0
$733$	26.7967	+	11.0995i	0.989758	+	0.409971i	0.818031	−	0.575174i	$-0.195066\pi$
$733$	26.7967	+	11.0995i	0.989758	+	0.409971i	0.171726	+	0.985145i	$0.445066\pi$
$734$	−7.59453	+	26.6370i	−0.280319	+	0.983191i
$735$		0			0
$736$	−11.2376	+	16.3097i	−0.414222	+	0.601182i
$737$	8.63948			0.318239
$738$		0			0
$739$	49.0126	+	20.3017i	1.80296	+	0.746810i	0.985237	+	0.171195i	$0.0547628\pi$
$739$	49.0126	+	20.3017i	1.80296	+	0.746810i	0.817721	+	0.575615i	$0.195237\pi$
$740$	−0.670687	+	0.156976i	−0.0246550	+	0.00577054i
$741$		0			0
$742$	31.2137	−	39.3629i	1.14589	−	1.44506i
$743$	−23.7552	+	23.7552i	−0.871494	+	0.871494i	−0.992635	−	0.121141i	$-0.961345\pi$
$743$	−23.7552	+	23.7552i	−0.871494	+	0.871494i	0.121141	+	0.992635i	$0.461345\pi$
$744$		0			0
$745$	1.30783	+	1.30783i	0.0479152	+	0.0479152i
$746$	41.0945	−	4.74501i	1.50458	−	0.173727i
$747$		0			0
$748$	−0.740465	+	4.50846i	−0.0270741	+	0.164846i
$749$	−13.1754	+	31.8083i	−0.481420	+	1.16225i
$750$		0			0
$751$			25.2687i			0.922066i	0.887383	+	0.461033i	$0.152521\pi$
$751$			25.2687i			0.922066i	−0.887383	+	0.461033i	$0.847479\pi$
$752$	−18.0265	+	8.92733i	−0.657359	+	0.325546i
$753$		0			0
$754$	−3.81727	+	2.12349i	−0.139017	+	0.0773330i
$755$	7.01233	−	16.9293i	0.255205	−	0.616119i
$756$		0			0
$757$	39.9969	−	16.5672i	1.45371	−	0.602147i	0.490632	−	0.871367i	$-0.336766\pi$
$757$	39.9969	−	16.5672i	1.45371	−	0.602147i	0.963079	+	0.269220i	$0.0867659\pi$
$758$	2.44809	+	21.2019i	0.0889187	+	0.770087i
$759$		0			0
$760$	19.6407	+	21.6155i	0.712444	+	0.784075i
$761$	−14.0902	+	14.0902i	−0.510769	+	0.510769i	−0.914762	−	0.403993i	$-0.867622\pi$
$761$	−14.0902	+	14.0902i	−0.510769	+	0.510769i	0.403993	+	0.914762i	$0.367622\pi$
$762$		0			0
$763$	−27.1256	−	65.4869i	−0.982011	−	2.37078i
$764$	17.3452	+	10.7658i	0.627527	+	0.389492i
$765$		0			0
$766$	14.9584	+	4.26482i	0.540470	+	0.154094i
$767$	−5.24848			−0.189512
$768$		0			0
$769$	−36.5306			−1.31733			−0.658663	−	0.752438i	$-0.728878\pi$
$769$	−36.5306			−1.31733			−0.658663	+	0.752438i	$0.728878\pi$
$770$	42.1838	+	12.0271i	1.52020	+	0.433426i
$771$		0			0
$772$	−18.1868	−	11.2882i	−0.654559	−	0.406270i
$773$	7.29955	+	17.6227i	0.262546	+	0.633843i	0.999095	−	0.0425418i	$-0.0135456\pi$
$773$	7.29955	+	17.6227i	0.262546	+	0.633843i	−0.736548	+	0.676385i	$0.763546\pi$
$774$		0			0
$775$	−11.8113	+	11.8113i	−0.424275	+	0.424275i
$776$	0.265521	+	0.292218i	0.00953166	+	0.0104900i
$777$		0			0
$778$	−3.32947	−	28.8351i	−0.119367	−	1.03379i
$779$	62.2256	−	25.7747i	2.22946	−	0.923474i
$780$		0			0
$781$	−2.20701	+	5.32819i	−0.0789729	+	0.190658i
$782$	2.69451	−	1.49892i	0.0963556	−	0.0536012i
$783$		0			0
$784$	50.2357	−	24.8784i	1.79413	−	0.888513i
$785$			11.2437i			0.401306i
$786$		0			0
$787$	−11.4660	+	27.6814i	−0.408719	+	0.986735i	0.576756	+	0.816916i	$0.304318\pi$
$787$	−11.4660	+	27.6814i	−0.408719	+	0.986735i	−0.985475	+	0.169819i	$0.945682\pi$
$788$	−1.65872	+	10.0994i	−0.0590894	+	0.359777i
$789$		0			0
$790$	26.4943	−	3.05918i	0.942624	−	0.108841i
$791$	−29.3190	−	29.3190i	−1.04246	−	1.04246i
$792$		0			0
$793$	3.09769	−	3.09769i	0.110002	−	0.110002i
$794$	−4.37096	+	5.51212i	−0.155120	+	0.195618i
$795$		0			0
$796$	26.7708	−	6.26575i	0.948864	−	0.222084i
$797$	−19.1294	−	7.92366i	−0.677599	−	0.280671i	0.0172239	−	0.999852i	$-0.494517\pi$
$797$	−19.1294	−	7.92366i	−0.677599	−	0.280671i	−0.694823	+	0.719181i	$0.744517\pi$
$798$		0			0
$799$	3.13158			0.110787
$800$	7.44540	+	5.12997i	0.263235	+	0.181372i
$801$		0			0
$802$	−12.9739	+	45.5046i	−0.458124	+	1.60682i
$803$	−17.8114	−	7.37774i	−0.628552	−	0.260355i
$804$		0			0
$805$	−11.3285	−	27.3495i	−0.399278	−	0.963942i
$806$	12.0932	−	15.2504i	0.425964	−	0.537173i
$807$		0			0
$808$	−15.4118	+	32.6919i	−0.542185	+	1.15010i
$809$	−9.08298	−	9.08298i	−0.319341	−	0.319341i	0.529173	−	0.848514i	$-0.322502\pi$
$809$	−9.08298	−	9.08298i	−0.319341	−	0.319341i	−0.848514	+	0.529173i	$0.822502\pi$
$810$		0			0
$811$	−2.93057	+	1.21388i	−0.102906	+	0.0426251i	−0.433543	−	0.901133i	$-0.642737\pi$
$811$	−2.93057	+	1.21388i	−0.102906	+	0.0426251i	0.330636	+	0.943758i	$0.392737\pi$
$812$	21.2195	+	3.48507i	0.744660	+	0.122302i
$813$		0			0
$814$	0.470965	+	0.846626i	0.0165073	+	0.0296742i
$815$			40.4549i			1.41707i
$816$		0			0
$817$		−	21.9449i		−	0.767754i
$818$	−4.30880	+	2.39692i	−0.150654	+	0.0838064i
$819$		0			0
$820$	−36.0492	+	25.8783i	−1.25889	+	0.903709i
$821$	−5.06148	+	2.09653i	−0.176647	+	0.0731696i	−0.469254	−	0.883063i	$-0.655477\pi$
$821$	−5.06148	+	2.09653i	−0.176647	+	0.0731696i	0.292607	+	0.956233i	$0.405477\pi$
$822$		0			0
$823$	18.7772	+	18.7772i	0.654534	+	0.654534i	0.954081	−	0.299548i	$-0.0968357\pi$
$823$	18.7772	+	18.7772i	0.654534	+	0.654534i	−0.299548	+	0.954081i	$0.596836\pi$
$824$	14.5637	+	0.697098i	0.507351	+	0.0242846i
$825$		0			0
$826$	20.2449	+	16.0537i	0.704411	+	0.558579i
$827$	−7.97891	−	19.2628i	−0.277454	−	0.669833i	0.722310	−	0.691569i	$-0.243080\pi$
$827$	−7.97891	−	19.2628i	−0.277454	−	0.669833i	−0.999764	+	0.0217368i	$0.993080\pi$
$828$		0			0
$829$	−6.18715	−	2.56280i	−0.214889	−	0.0890098i	0.272642	−	0.962115i	$-0.412102\pi$
$829$	−6.18715	−	2.56280i	−0.214889	−	0.0890098i	−0.487531	+	0.873106i	$0.662102\pi$
$830$	−30.7532	−	8.76809i	−1.06746	−	0.304345i
$831$		0			0
$832$	−9.30380	−	4.94292i	−0.322551	−	0.171365i
$833$	−8.72699			−0.302372
$834$		0			0
$835$	−22.3378	−	9.25260i	−0.773030	−	0.320199i
$836$	21.6625	−	34.9015i	0.749215	−	1.20709i
$837$		0			0
$838$	17.5505	+	13.9171i	0.606272	+	0.480757i
$839$	17.9608	−	17.9608i	0.620075	−	0.620075i	−0.325476	−	0.945550i	$-0.605524\pi$
$839$	17.9608	−	17.9608i	0.620075	−	0.620075i	0.945550	+	0.325476i	$0.105524\pi$
$840$		0			0
$841$	−16.6162	−	16.6162i	−0.572973	−	0.572973i
$842$	−4.24186	−	36.7369i	−0.146184	−	1.26604i
$843$		0			0
$844$	40.4344	−	29.0263i	1.39181	−	0.999126i
$845$	7.95141	−	19.1964i	0.273537	−	0.660377i
$846$		0			0
$847$		−	11.2694i		−	0.387220i
$848$	23.3383	+	20.3979i	0.801440	+	0.700468i
$849$		0			0
$850$	−0.684259	−	1.23005i	−0.0234699	−	0.0421904i
$851$	0.250203	−	0.604044i	0.00857686	−	0.0207064i
$852$		0			0
$853$	−31.8461	+	13.1911i	−1.09039	+	0.451655i	−0.854143	−	0.520038i	$-0.825918\pi$
$853$	−31.8461	+	13.1911i	−1.09039	+	0.451655i	−0.236248	+	0.971693i	$0.575918\pi$
$854$	−21.4237	+	2.47370i	−0.733104	+	0.0846484i
$855$		0			0
$856$	−19.2146	−	9.05824i	−0.656740	−	0.309604i
$857$	6.69068	−	6.69068i	0.228549	−	0.228549i	−0.583537	−	0.812086i	$-0.698332\pi$
$857$	6.69068	−	6.69068i	0.228549	−	0.228549i	0.812086	+	0.583537i	$0.198332\pi$
$858$		0			0
$859$	−12.1865	−	29.4209i	−0.415799	−	1.00383i	−0.983551	−	0.180628i	$-0.942187\pi$
$859$	−12.1865	−	29.4209i	−0.415799	−	1.00383i	0.567752	−	0.823199i	$-0.307813\pi$
$860$	3.29503	+	14.0782i	0.112359	+	0.480062i
$861$		0			0
$862$	−9.19863	+	32.2633i	−0.313307	+	1.09889i
$863$	41.6835			1.41892			0.709461	−	0.704744i	$-0.248938\pi$
$863$	41.6835			1.41892			0.709461	+	0.704744i	$0.248938\pi$
$864$		0			0
$865$	−24.4557			−0.831518
$866$	−9.15392	+	32.1064i	−0.311063	+	1.09102i
$867$		0			0
$868$	−93.2939	+	21.8356i	−3.16660	+	0.741149i
$869$	−14.3550	−	34.6560i	−0.486960	−	1.17563i
$870$		0			0
$871$	2.19298	−	2.19298i	0.0743064	−	0.0743064i
$872$	41.1593	−	14.7855i	1.39383	−	0.500700i
$873$		0			0
$874$	−27.5389	+	3.17981i	−0.931519	+	0.107559i
$875$	−51.5414	+	21.3492i	−1.74242	+	0.721733i
$876$		0			0
$877$	−13.1498	+	31.7463i	−0.444036	+	1.07200i	0.530484	+	0.847695i	$0.322010\pi$
$877$	−13.1498	+	31.7463i	−0.444036	+	1.07200i	−0.974520	+	0.224303i	$0.927990\pi$
$878$	17.4083	+	31.2938i	0.587501	+	1.05611i
$879$		0			0
$880$	−8.65660	+	25.6428i	−0.291814	+	0.864418i
$881$			23.2168i			0.782193i	0.920350	+	0.391097i	$0.127904\pi$
$881$			23.2168i			0.782193i	−0.920350	+	0.391097i	$0.872096\pi$
$882$		0			0
$883$	−7.49214	+	18.0876i	−0.252131	+	0.608697i	−0.998376	−	0.0569741i	$-0.981855\pi$
$883$	−7.49214	+	18.0876i	−0.252131	+	0.608697i	0.746245	+	0.665671i	$0.231855\pi$
$884$	0.956441	+	1.33235i	0.0321686	+	0.0448118i
$885$		0			0
$886$	2.90198	+	25.1328i	0.0974940	+	0.844354i
$887$	−27.3487	−	27.3487i	−0.918281	−	0.918281i	0.0786233	−	0.996904i	$-0.474948\pi$
$887$	−27.3487	−	27.3487i	−0.918281	−	0.918281i	−0.996904	+	0.0786233i	$0.974948\pi$
$888$		0			0
$889$	18.8976	−	18.8976i	0.633804	−	0.633804i
$890$	−10.2326	−	8.11414i	−0.342996	−	0.271987i
$891$		0			0
$892$	−0.882225	−	0.547577i	−0.0295391	−	0.0183342i
$893$	−26.0122	−	10.7746i	−0.870465	−	0.360559i
$894$		0			0
$895$	34.5908			1.15624
$896$	20.7685	+	47.5241i	0.693825	+	1.58767i
$897$		0			0
$898$	27.2428	+	7.76724i	0.909104	+	0.259196i
$899$	−22.6456	−	9.38010i	−0.755272	−	0.312844i
$900$		0			0
$901$	−1.84658	−	4.45804i	−0.0615185	−	0.148519i
$902$	48.9045	+	38.7800i	1.62834	+	1.29123i
$903$		0			0
$904$	18.9340	−	17.2042i	0.629735	−	0.572204i
$905$	−19.4133	−	19.4133i	−0.645319	−	0.645319i
$906$		0			0
$907$	25.0936	−	10.3941i	0.833219	−	0.345131i	0.0750427	−	0.997180i	$-0.476091\pi$
$907$	25.0936	−	10.3941i	0.833219	−	0.345131i	0.758176	+	0.652050i	$0.226091\pi$
$908$	5.83032	+	8.12180i	0.193486	+	0.269532i
$909$		0			0
$910$	13.7605	−	7.65476i	0.456156	−	0.253753i
$911$		−	42.9196i		−	1.42199i	−0.703197	−	0.710995i	$-0.748245\pi$
$911$		−	42.9196i		−	1.42199i	0.703197	−	0.710995i	$-0.251755\pi$
$912$		0			0
$913$			44.9776i			1.48854i
$914$	−1.39043	−	2.49950i	−0.0459915	−	0.0826761i
$915$		0			0
$916$	1.86885	−	11.3789i	0.0617486	−	0.375968i
$917$	−31.1788	+	12.9147i	−1.02962	+	0.426481i
$918$		0			0
$919$	4.48091	+	4.48091i	0.147812	+	0.147812i	0.777140	−	0.629328i	$-0.216670\pi$
$919$	4.48091	+	4.48091i	0.147812	+	0.147812i	−0.629328	+	0.777140i	$0.716670\pi$
$920$	17.1895	−	6.17490i	0.566720	−	0.203580i
$921$		0			0
$922$	27.2398	−	34.3515i	0.897095	−	1.13131i
$923$	0.792257	+	1.91268i	0.0260775	+	0.0629566i
$924$		0			0
$925$	−0.275748	−	0.114218i	−0.00906652	−	0.00375548i
$926$	9.04757	−	31.7334i	0.297322	−	1.04283i
$927$		0			0
$928$	−2.77378	+	12.9746i	−0.0910539	+	0.425914i
$929$	41.1385			1.34971			0.674855	−	0.737950i	$-0.264206\pi$
$929$	41.1385			1.34971			0.674855	+	0.737950i	$0.264206\pi$
$930$		0			0
$931$	72.4899	+	30.0263i	2.37576	+	0.984072i
$932$	−7.35680	−	31.4323i	−0.240980	−	1.02960i
$933$		0			0
$934$	−2.87541	+	3.62611i	−0.0940863	+	0.118650i
$935$	2.97926	−	2.97926i	0.0974323	−	0.0974323i
$936$		0			0
$937$	9.98625	+	9.98625i	0.326237	+	0.326237i	0.851153	−	0.524917i	$-0.175904\pi$
$937$	9.98625	+	9.98625i	0.326237	+	0.326237i	−0.524917	+	0.851153i	$0.675904\pi$
$938$	−15.1667	+	1.75124i	−0.495212	+	0.0571800i
$939$		0			0
$940$	18.3053	+	3.00644i	0.597053	+	0.0980593i
$941$	−20.7835	+	50.1758i	−0.677522	+	1.63568i	0.0909934	+	0.995851i	$0.470996\pi$
$941$	−20.7835	+	50.1758i	−0.677522	+	1.63568i	−0.768515	+	0.639831i	$0.779004\pi$
$942$		0			0
$943$		−	42.1212i		−	1.37165i
$944$	−10.4910	+	12.0032i	−0.341452	+	0.390672i
$945$		0			0
$946$	17.7712	−	9.88587i	0.577793	−	0.321417i
$947$	−8.98007	+	21.6798i	−0.291813	+	0.704499i	−0.999999	−	0.00152707i	$-0.999514\pi$
$947$	−8.98007	+	21.6798i	−0.291813	+	0.704499i	0.708186	+	0.706026i	$0.249514\pi$
$948$		0			0
$949$	−6.39384	+	2.64842i	−0.207553	+	0.0859712i
$950$	1.45159	+	12.5716i	0.0470957	+	0.407876i
$951$		0			0
$952$	0.386023	−	8.06477i	0.0125111	−	0.261381i
$953$	−33.7694	+	33.7694i	−1.09390	+	1.09390i	−0.0987882	+	0.995108i	$0.531497\pi$
$953$	−33.7694	+	33.7694i	−1.09390	+	1.09390i	−0.995108	+	0.0987882i	$0.968503\pi$
$954$		0			0
$955$	−7.20438	−	17.3929i	−0.233128	−	0.562822i
$956$	5.01082	−	8.07315i	0.162061	−	0.261104i
$957$		0			0
$958$	−27.7558	−	7.91351i	−0.896750	−	0.255674i
$959$	89.0570			2.87580
$960$		0			0
$961$	78.2161			2.52310
$962$	0.334448	+	0.0953549i	0.0107830	+	0.00307437i
$963$		0			0
$964$	6.24847	−	10.0672i	0.201250	−	0.324242i
$965$	7.55396	+	18.2369i	0.243171	+	0.587066i
$966$		0			0
$967$	−0.543237	+	0.543237i	−0.0174693	+	0.0174693i	−0.715787	−	0.698318i	$-0.753932\pi$
$967$	−0.543237	+	0.543237i	−0.0174693	+	0.0174693i	0.698318	+	0.715787i	$0.253932\pi$
$968$	6.94524	+	0.332437i	0.223228	+	0.0106849i
$969$		0			0
$970$	−0.0417643	−	0.361703i	−0.00134097	−	0.0116136i
$971$	−47.8546	+	19.8220i	−1.53573	+	0.636119i	−0.980666	−	0.195690i	$-0.937305\pi$
$971$	−47.8546	+	19.8220i	−1.53573	+	0.636119i	−0.555062	+	0.831809i	$0.687305\pi$
$972$		0			0
$973$	4.06830	−	9.82176i	0.130424	−	0.314871i
$974$	−24.7400	+	13.7625i	−0.792719	+	0.440978i
$975$		0			0
$976$	−0.892546	−	13.2762i	−0.0285697	−	0.424962i
$977$		−	0.231742i		−	0.00741408i	−0.999993	−	0.00370704i	$-0.998820\pi$
$977$		−	0.231742i		−	0.00741408i	0.999993	−	0.00370704i	$-0.00117999\pi$
$978$		0			0
$979$	−7.02901	+	16.9695i	−0.224648	+	0.542348i
$980$	−51.0125	−	8.37824i	−1.62954	−	0.267633i
$981$		0			0
$982$	15.1144	−	1.74519i	0.482319	−	0.0556913i
$983$	31.7418	+	31.7418i	1.01241	+	1.01241i	0.999922	+	0.0124854i	$0.00397434\pi$
$983$	31.7418	+	31.7418i	1.01241	+	1.01241i	0.0124854	+	0.999922i	$0.496026\pi$
$984$		0			0
$985$	6.67386	−	6.67386i	0.212647	−	0.212647i
$986$	1.28335	−	1.61841i	0.0408703	−	0.0515406i
$987$		0			0
$988$	−3.36047	−	14.3578i	−0.106911	−	0.456782i
$989$	−12.6793	−	5.25193i	−0.403178	−	0.167002i
$990$		0			0
$991$	−33.3427			−1.05917			−0.529583	−	0.848258i	$-0.677652\pi$
$991$	−33.3427			−1.05917			−0.529583	+	0.848258i	$0.677652\pi$
$992$	−10.7051	−	58.1405i	−0.339886	−	1.84596i
$993$		0			0
$994$	2.79440	−	9.80107i	0.0886330	−	0.310871i
$995$	−23.4246	−	9.70279i	−0.742610	−	0.307599i
$996$		0			0
$997$	−18.9709	−	45.7997i	−0.600813	−	1.45049i	−0.872746	−	0.488175i	$-0.837663\pi$
$997$	−18.9709	−	45.7997i	−0.600813	−	1.45049i	0.271933	−	0.962316i	$-0.412337\pi$
$998$	−6.45833	+	8.14445i	−0.204435	+	0.257808i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.253.8		32
3.2	odd	2		96.2.n.a.61.1	✓	32
4.3	odd	2		1152.2.v.c.721.3		32
12.11	even	2		384.2.n.a.337.7		32
24.5	odd	2		768.2.n.a.673.6		32
24.11	even	2		768.2.n.b.673.2		32
32.11	odd	8		1152.2.v.c.433.3		32
32.21	even	8	inner	288.2.v.d.181.8		32
96.5	odd	8		768.2.n.a.97.6		32
96.11	even	8		384.2.n.a.49.7		32
96.53	odd	8		96.2.n.a.85.1	yes	32
96.59	even	8		768.2.n.b.97.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.1	✓	32	3.2	odd	2
96.2.n.a.85.1	yes	32	96.53	odd	8
288.2.v.d.181.8		32	32.21	even	8	inner
288.2.v.d.253.8		32	1.1	even	1	trivial
384.2.n.a.49.7		32	96.11	even	8
384.2.n.a.337.7		32	12.11	even	2
768.2.n.a.97.6		32	96.5	odd	8
768.2.n.a.673.6		32	24.5	odd	2
768.2.n.b.97.2		32	96.59	even	8
768.2.n.b.673.2		32	24.11	even	2
1152.2.v.c.433.3		32	32.11	odd	8
1152.2.v.c.721.3		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36002 + 0.387756i) q^{2} +(1.69929 + 1.05471i) q^{4} +(-0.705805 - 1.70396i) q^{5} +(3.24150 - 3.24150i) q^{7} +(1.90209 + 2.09333i) q^{8} +O(q^{10})\)	\(q+(1.36002 + 0.387756i) q^{2} +(1.69929 + 1.05471i) q^{4} +(-0.705805 - 1.70396i) q^{5} +(3.24150 - 3.24150i) q^{7} +(1.90209 + 2.09333i) q^{8} +(-0.299183 - 2.59110i) q^{10} +(-3.38931 + 1.40390i) q^{11} +(-0.503962 + 1.21667i) q^{13} +(5.66540 - 3.15158i) q^{14} +(1.77517 + 3.58452i) q^{16} -0.622706i q^{17} +(-2.14250 + 5.17245i) q^{19} +(0.597821 - 3.63995i) q^{20} +(-5.15388 + 0.595097i) q^{22} +(2.47578 + 2.47578i) q^{23} +(1.13020 - 1.13020i) q^{25} +(-1.15717 + 1.45928i) q^{26} +(8.92709 - 2.08940i) q^{28} +(2.16691 + 0.897562i) q^{29} -10.4506 q^{31} +(1.02434 + 5.56334i) q^{32} +(0.241458 - 0.846890i) q^{34} +(-7.81126 - 3.23553i) q^{35} +(-0.0714604 - 0.172521i) q^{37} +(-4.91948 + 6.20385i) q^{38} +(2.22446 - 4.71858i) q^{40} +(-8.50664 - 8.50664i) q^{41} +(-3.62132 + 1.50000i) q^{43} +(-7.24012 - 1.18911i) q^{44} +(2.40710 + 4.32711i) q^{46} +5.02899i q^{47} -14.0146i q^{49} +(1.97533 - 1.09885i) q^{50} +(-2.13961 + 1.53594i) q^{52} +(7.15914 - 2.96541i) q^{53} +(4.78438 + 4.78438i) q^{55} +(12.9512 + 0.619913i) q^{56} +(2.59899 + 2.06093i) q^{58} +(1.52516 + 3.68206i) q^{59} +(-3.07333 - 1.27302i) q^{61} +(-14.2131 - 4.05231i) q^{62} +(-0.764096 + 7.96343i) q^{64} +2.42886 q^{65} +(-2.17574 - 0.901222i) q^{67} +(0.656774 - 1.05816i) q^{68} +(-9.36885 - 7.42925i) q^{70} +(1.11161 - 1.11161i) q^{71} +(3.71598 + 3.71598i) q^{73} +(-0.0302913 - 0.262340i) q^{74} +(-9.09616 + 6.52977i) q^{76} +(-6.43570 + 15.5372i) q^{77} +10.2251i q^{79} +(4.85496 - 5.55480i) q^{80} +(-8.27067 - 14.8677i) q^{82} +(4.69181 - 11.3270i) q^{83} +(-1.06107 + 0.439509i) q^{85} +(-5.50670 + 0.635835i) q^{86} +(-9.38560 - 4.42461i) q^{88} +(3.54033 - 3.54033i) q^{89} +(2.31025 + 5.57743i) q^{91} +(1.59584 + 6.81830i) q^{92} +(-1.95003 + 6.83952i) q^{94} +10.3259 q^{95} +0.139594 q^{97} +(5.43426 - 19.0601i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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