LMFDB - Embedded newform 432.2.u.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.2
Root			$0.500000 + 2.22827i$ of defining polynomial
Character	$\chi$	$=$	432.49
Dual form			432.2.u.c.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.986166 - 1.42389i) q^{3} +(2.52129 - 0.917674i) q^{5} +(-0.168844 - 0.957561i) q^{7} +(-1.05495 - 2.80839i) q^{9} +O(q^{10})$	\(q+(0.986166 - 1.42389i) q^{3} +(2.52129 - 0.917674i) q^{5} +(-0.168844 - 0.957561i) q^{7} +(-1.05495 - 2.80839i) q^{9} +(-0.297791 - 0.108387i) q^{11} +(-1.15981 - 0.973200i) q^{13} +(1.17974 - 4.49503i) q^{15} +(-0.587342 + 1.01731i) q^{17} +(3.11040 + 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(-0.375556 + 2.12988i) q^{23} +(1.68454 - 1.41350i) q^{25} +(-5.03922 - 1.26740i) q^{27} +(-3.37436 + 2.83142i) q^{29} +(1.50609 - 8.54146i) q^{31} +(-0.448003 + 0.317135i) q^{33} +(-1.30443 - 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(-2.52950 + 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(5.25381 + 1.91223i) q^{43} +(-5.23703 - 6.11267i) q^{45} +(0.429965 + 2.43845i) q^{47} +(5.68943 - 2.07078i) q^{49} +(0.869320 + 1.83955i) q^{51} -10.8920 q^{53} -0.850279 q^{55} +(10.7384 + 0.883963i) q^{57} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(-2.51109 + 1.48436i) q^{63} +(-3.81731 - 1.38939i) q^{65} +(-0.656156 - 0.550580i) q^{67} +(2.66237 + 2.63517i) q^{69} +(-4.79788 + 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(-0.351434 - 3.79256i) q^{75} +(-0.0535070 + 0.303453i) q^{77} +(8.59024 - 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +(-3.58886 + 3.01141i) q^{83} +(-0.547303 + 3.10391i) q^{85} +(0.703969 + 7.59698i) q^{87} +(7.74976 + 13.4230i) q^{89} +(-0.736071 + 1.27491i) q^{91} +(-10.6769 - 10.5678i) q^{93} +(12.7861 + 10.7288i) q^{95} +(5.21481 + 1.89804i) q^{97} +(0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.986166	−	1.42389i	0.569363	−	0.822086i
$3$	0.986166	−	1.42389i	0.569363	−	0.822086i
$4$		0			0
$5$	2.52129	−	0.917674i	1.12755	−	0.410396i	0.290150	−	0.956981i	$-0.406295\pi$
$5$	2.52129	−	0.917674i	1.12755	−	0.410396i	0.837404	+	0.546585i	$0.184072\pi$
$6$		0			0
$7$	−0.168844	−	0.957561i	−0.0638170	−	0.361924i	−0.999947	−	0.0102706i	$-0.996731\pi$
$7$	−0.168844	−	0.957561i	−0.0638170	−	0.361924i	0.936130	−	0.351653i	$-0.114380\pi$
$8$		0			0
$9$	−1.05495	−	2.80839i	−0.351651	−	0.936131i
$10$		0			0
$11$	−0.297791	−	0.108387i	−0.0897872	−	0.0326799i	0.296736	−	0.954960i	$-0.404102\pi$
$11$	−0.297791	−	0.108387i	−0.0897872	−	0.0326799i	−0.386523	+	0.922280i	$0.626324\pi$
$12$		0			0
$13$	−1.15981	−	0.973200i	−0.321675	−	0.269917i	0.467623	−	0.883928i	$-0.345111\pi$
$13$	−1.15981	−	0.973200i	−0.321675	−	0.269917i	−0.789297	+	0.614011i	$0.789555\pi$
$14$		0			0
$15$	1.17974	−	4.49503i	0.304607	−	1.16061i
$16$		0			0
$17$	−0.587342	+	1.01731i	−0.142451	+	0.246733i	−0.928419	−	0.371534i	$-0.878832\pi$
$17$	−0.587342	+	1.01731i	−0.142451	+	0.246733i	0.785968	+	0.618267i	$0.212165\pi$
$18$		0			0
$19$	3.11040	+	5.38737i	0.713575	+	1.23595i	0.963507	+	0.267685i	$0.0862586\pi$
$19$	3.11040	+	5.38737i	0.713575	+	1.23595i	−0.249931	+	0.968264i	$0.580408\pi$
$20$		0			0
$21$	−1.52997	−	0.703898i	−0.333868	−	0.153603i
$22$		0			0
$23$	−0.375556	+	2.12988i	−0.0783089	+	0.444112i	0.920292	+	0.391232i	$0.127951\pi$
$23$	−0.375556	+	2.12988i	−0.0783089	+	0.444112i	−0.998601	+	0.0528796i	$0.983160\pi$
$24$		0			0
$25$	1.68454	−	1.41350i	0.336909	−	0.282700i
$26$		0			0
$27$	−5.03922	−	1.26740i	−0.969797	−	0.243912i
$28$		0			0
$29$	−3.37436	+	2.83142i	−0.626602	+	0.525782i	−0.899871	−	0.436156i	$-0.856340\pi$
$29$	−3.37436	+	2.83142i	−0.626602	+	0.525782i	0.273269	+	0.961938i	$0.411895\pi$
$30$		0			0
$31$	1.50609	−	8.54146i	0.270502	−	1.53409i	−0.482395	−	0.875954i	$-0.660233\pi$
$31$	1.50609	−	8.54146i	0.270502	−	1.53409i	0.752897	−	0.658138i	$-0.228656\pi$
$32$		0			0
$33$	−0.448003	+	0.317135i	−0.0779872	+	0.0552061i
$34$		0			0
$35$	−1.30443	−	2.25934i	−0.220489	−	0.381899i
$36$		0			0
$37$	2.23332	−	3.86823i	0.367156	−	0.635933i	−0.621964	−	0.783046i	$-0.713665\pi$
$37$	2.23332	−	3.86823i	0.367156	−	0.635933i	0.989120	+	0.147113i	$0.0469982\pi$
$38$		0			0
$39$	−2.52950	+	0.691717i	−0.405045	+	0.110763i
$40$		0			0
$41$	4.47767	+	3.75721i	0.699295	+	0.586778i	0.921573	−	0.388205i	$-0.126905\pi$
$41$	4.47767	+	3.75721i	0.699295	+	0.586778i	−0.222278	+	0.974983i	$0.571349\pi$
$42$		0			0
$43$	5.25381	+	1.91223i	0.801199	+	0.291613i	0.709983	−	0.704219i	$-0.248702\pi$
$43$	5.25381	+	1.91223i	0.801199	+	0.291613i	0.0912158	+	0.995831i	$0.470925\pi$
$44$		0			0
$45$	−5.23703	−	6.11267i	−0.780690	−	0.911223i
$46$		0			0
$47$	0.429965	+	2.43845i	0.0627168	+	0.355685i	0.999975	+	0.00704911i	$0.00224382\pi$
$47$	0.429965	+	2.43845i	0.0627168	+	0.355685i	−0.937258	+	0.348636i	$0.886645\pi$
$48$		0			0
$49$	5.68943	−	2.07078i	0.812776	−	0.295826i
$50$		0			0
$51$	0.869320	+	1.83955i	0.121729	+	0.257588i
$52$		0			0
$53$	−10.8920			−1.49613			−0.748063	−	0.663628i	$-0.769016\pi$
$53$	−10.8920			−1.49613			−0.748063	+	0.663628i	$0.769016\pi$
$54$		0			0
$55$	−0.850279			−0.114652
$56$		0			0
$57$	10.7384	+	0.883963i	1.42234	+	0.117084i
$58$		0			0
$59$	−1.62023	+	0.589715i	−0.210936	+	0.0767743i	−0.445327	−	0.895368i	$-0.646913\pi$
$59$	−1.62023	+	0.589715i	−0.210936	+	0.0767743i	0.234391	+	0.972142i	$0.424690\pi$
$60$		0			0
$61$	0.176214	+	0.999361i	0.0225619	+	0.127955i	0.994008	−	0.109304i	$-0.0348621\pi$
$61$	0.176214	+	0.999361i	0.0225619	+	0.127955i	−0.971446	+	0.237259i	$0.923751\pi$
$62$		0			0
$63$	−2.51109	+	1.48436i	−0.316367	+	0.187012i
$64$		0			0
$65$	−3.81731	−	1.38939i	−0.473478	−	0.172332i
$66$		0			0
$67$	−0.656156	−	0.550580i	−0.0801622	−	0.0672641i	0.601826	−	0.798627i	$-0.294440\pi$
$67$	−0.656156	−	0.550580i	−0.0801622	−	0.0672641i	−0.681988	+	0.731363i	$0.738884\pi$
$68$		0			0
$69$	2.66237	+	2.63517i	0.320512	+	0.317238i
$70$		0			0
$71$	−4.79788	+	8.31018i	−0.569404	+	0.986237i	0.427221	+	0.904147i	$0.359493\pi$
$71$	−4.79788	+	8.31018i	−0.569404	+	0.986237i	−0.996625	+	0.0820894i	$0.973841\pi$
$72$		0			0
$73$	7.62091	+	13.1998i	0.891960	+	1.54492i	0.837522	+	0.546404i	$0.184004\pi$
$73$	7.62091	+	13.1998i	0.891960	+	1.54492i	0.0544385	+	0.998517i	$0.482663\pi$
$74$		0			0
$75$	−0.351434	−	3.79256i	−0.0405802	−	0.437927i
$76$		0			0
$77$	−0.0535070	+	0.303453i	−0.00609768	+	0.0345817i
$78$		0			0
$79$	8.59024	−	7.20807i	0.966478	−	0.810971i	−0.0155168	−	0.999880i	$-0.504939\pi$
$79$	8.59024	−	7.20807i	0.966478	−	0.810971i	0.981995	+	0.188908i	$0.0604949\pi$
$80$		0			0
$81$	−6.77415	+	5.92544i	−0.752684	+	0.658382i
$82$		0			0
$83$	−3.58886	+	3.01141i	−0.393929	+	0.330546i	−0.818141	−	0.575017i	$-0.804995\pi$
$83$	−3.58886	+	3.01141i	−0.393929	+	0.330546i	0.424212	+	0.905563i	$0.360551\pi$
$84$		0			0
$85$	−0.547303	+	3.10391i	−0.0593633	+	0.336666i
$86$		0			0
$87$	0.703969	+	7.59698i	0.0754734	+	0.814482i
$88$		0			0
$89$	7.74976	+	13.4230i	0.821473	+	1.42283i	0.904586	+	0.426292i	$0.140180\pi$
$89$	7.74976	+	13.4230i	0.821473	+	1.42283i	−0.0831130	+	0.996540i	$0.526486\pi$
$90$		0			0
$91$	−0.736071	+	1.27491i	−0.0771612	+	0.133647i
$92$		0			0
$93$	−10.6769	−	10.5678i	−1.10714	−	1.09583i
$94$		0			0
$95$	12.7861	+	10.7288i	1.31182	+	1.10075i
$96$		0			0
$97$	5.21481	+	1.89804i	0.529484	+	0.192716i	0.592908	−	0.805270i	$-0.297980\pi$
$97$	5.21481	+	1.89804i	0.529484	+	0.192716i	−0.0634241	+	0.997987i	$0.520202\pi$
$98$		0			0
$99$	0.00976156	+	0.950656i	0.000981074	+	0.0955445i
$100$		0			0
$101$	−1.76063	−	9.98501i	−0.175189	−	0.993546i	−0.937926	−	0.346836i	$-0.887256\pi$
$101$	−1.76063	−	9.98501i	−0.175189	−	0.993546i	0.762737	−	0.646709i	$-0.223855\pi$
$102$		0			0
$103$	−9.25906	+	3.37002i	−0.912323	+	0.332058i	−0.755180	−	0.655518i	$-0.772451\pi$
$103$	−9.25906	+	3.37002i	−0.912323	+	0.332058i	−0.157143	+	0.987576i	$0.550228\pi$
$104$		0			0
$105$	−4.50345	−	0.370714i	−0.439492	−	0.0361780i
$106$		0			0
$107$	−5.17080			−0.499880			−0.249940	−	0.968261i	$-0.580411\pi$
$107$	−5.17080			−0.499880			−0.249940	+	0.968261i	$0.580411\pi$
$108$		0			0
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$		0			0
$111$	−3.30552	−	6.99473i	−0.313746	−	0.663911i
$112$		0			0
$113$	−9.74991	+	3.54868i	−0.917195	+	0.333832i	−0.757122	−	0.653274i	$-0.773395\pi$
$113$	−9.74991	+	3.54868i	−0.917195	+	0.333832i	−0.160073	+	0.987105i	$0.551173\pi$
$114$		0			0
$115$	1.00765	+	5.71469i	0.0939642	+	0.532898i
$116$		0			0
$117$	−1.50958	+	4.28390i	−0.139561	+	0.396046i
$118$		0			0
$119$	1.07330	+	0.390650i	0.0983894	+	0.0358108i
$120$		0			0
$121$	−8.34956	−	7.00611i	−0.759051	−	0.636919i
$122$		0			0
$123$	9.76560	−	2.67050i	0.880535	−	0.240790i
$124$		0			0
$125$	−3.75766	+	6.50846i	−0.336095	+	0.582134i
$126$		0			0
$127$	2.61372	+	4.52709i	0.231930	+	0.401714i	0.958376	−	0.285509i	$-0.0921627\pi$
$127$	2.61372	+	4.52709i	0.231930	+	0.401714i	−0.726446	+	0.687223i	$0.758829\pi$
$128$		0			0
$129$	7.90395	−	5.59510i	0.695904	−	0.492621i
$130$		0			0
$131$	1.25622	−	7.12440i	0.109757	−	0.622461i	−0.879457	−	0.475979i	$-0.842094\pi$
$131$	1.25622	−	7.12440i	0.109757	−	0.622461i	0.989213	−	0.146482i	$-0.0467951\pi$
$132$		0			0
$133$	4.63357	−	3.88802i	0.401781	−	0.337134i
$134$		0			0
$135$	−13.8684	+	1.42887i	−1.19360	+	0.122977i
$136$		0			0
$137$	8.61748	−	7.23092i	0.736241	−	0.617779i	−0.195584	−	0.980687i	$-0.562660\pi$
$137$	8.61748	−	7.23092i	0.736241	−	0.617779i	0.931825	+	0.362907i	$0.118216\pi$
$138$		0			0
$139$	−1.62885	+	9.23766i	−0.138157	+	0.783528i	0.834452	+	0.551081i	$0.185784\pi$
$139$	−1.62885	+	9.23766i	−0.138157	+	0.783528i	−0.972609	+	0.232447i	$0.925327\pi$
$140$		0			0
$141$	3.89612	+	1.79249i	0.328112	+	0.150955i
$142$		0			0
$143$	0.239900	+	0.415518i	0.0200614	+	0.0347474i
$144$		0			0
$145$	−5.90940	+	10.2354i	−0.490749	+	0.850003i
$146$		0			0
$147$	2.66215	−	10.1433i	0.219570	−	0.836605i
$148$		0			0
$149$	14.5941	+	12.2459i	1.19560	+	1.00322i	0.999745	+	0.0225899i	$0.00719121\pi$
$149$	14.5941	+	12.2459i	1.19560	+	1.00322i	0.195851	+	0.980634i	$0.437253\pi$
$150$		0			0
$151$	3.77193	+	1.37287i	0.306955	+	0.111723i	0.490905	−	0.871213i	$-0.336666\pi$
$151$	3.77193	+	1.37287i	0.306955	+	0.111723i	−0.183950	+	0.982936i	$0.558888\pi$
$152$		0			0
$153$	3.47661	+	0.576279i	0.281068	+	0.0465894i
$154$		0			0
$155$	−4.04099	−	22.9176i	−0.324580	−	1.84078i
$156$		0			0
$157$	−6.83713	+	2.48851i	−0.545662	+	0.198605i	−0.600118	−	0.799911i	$-0.704880\pi$
$157$	−6.83713	+	2.48851i	−0.545662	+	0.198605i	0.0544560	+	0.998516i	$0.482658\pi$
$158$		0			0
$159$	−10.7413	+	15.5090i	−0.851839	+	1.22994i
$160$		0			0
$161$	2.10290			0.165732
$162$		0			0
$163$	−12.4492			−0.975094			−0.487547	−	0.873097i	$-0.662108\pi$
$163$	−12.4492			−0.975094			−0.487547	+	0.873097i	$0.662108\pi$
$164$		0			0
$165$	−0.838517	+	1.21071i	−0.0652785	+	0.0942535i
$166$		0			0
$167$	−2.19126	+	0.797553i	−0.169565	+	0.0617165i	−0.425408	−	0.905002i	$-0.639869\pi$
$167$	−2.19126	+	0.797553i	−0.169565	+	0.0617165i	0.255843	+	0.966718i	$0.417647\pi$
$168$		0			0
$169$	−1.85937	−	10.5450i	−0.143029	−	0.811157i
$170$		0			0
$171$	11.8485	−	14.4187i	0.906081	−	1.10262i
$172$		0			0
$173$	3.36623	+	1.22521i	0.255930	+	0.0931509i	0.466799	−	0.884363i	$-0.345407\pi$
$173$	3.36623	+	1.22521i	0.255930	+	0.0931509i	−0.210869	+	0.977514i	$0.567629\pi$
$174$		0			0
$175$	−1.63794	−	1.37439i	−0.123816	−	0.103894i
$176$		0			0
$177$	−0.758123	+	2.88859i	−0.0569840	+	0.217120i
$178$		0			0
$179$	−9.99785	+	17.3168i	−0.747275	+	1.29432i	0.201850	+	0.979416i	$0.435305\pi$
$179$	−9.99785	+	17.3168i	−0.747275	+	1.29432i	−0.949124	+	0.314901i	$0.898029\pi$
$180$		0			0
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	0.626542	−	0.779388i	$-0.284470\pi$
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	−0.988241	+	0.152907i	$0.951136\pi$
$182$		0			0
$183$	1.59676	+	0.734626i	0.118036	+	0.0543051i
$184$		0			0
$185$	2.08108	−	11.8024i	0.153004	−	0.867728i
$186$		0			0
$187$	0.285168	−	0.239284i	0.0208535	−	0.0174982i
$188$		0			0
$189$	−0.362776	+	5.03935i	−0.0263881	+	0.366559i
$190$		0			0
$191$	13.6023	−	11.4137i	0.984227	−	0.825864i	−0.000494763	−	1.00000i	$-0.500157\pi$
$191$	13.6023	−	11.4137i	0.984227	−	0.825864i	0.984722	+	0.174135i	$0.0557130\pi$
$192$		0			0
$193$	1.83795	−	10.4235i	0.132299	−	0.750303i	−0.844404	−	0.535706i	$-0.820045\pi$
$193$	1.83795	−	10.4235i	0.132299	−	0.750303i	0.976703	−	0.214596i	$-0.0688435\pi$
$194$		0			0
$195$	−5.74284	+	4.06528i	−0.411253	+	0.291120i
$196$		0			0
$197$	−7.07945	−	12.2620i	−0.504390	−	0.873628i	−0.999987	−	0.00507615i	$-0.998384\pi$
$197$	−7.07945	−	12.2620i	−0.504390	−	0.873628i	0.495597	−	0.868552i	$-0.334949\pi$
$198$		0			0
$199$	3.77010	−	6.53000i	0.267255	−	0.462899i	−0.700897	−	0.713263i	$-0.747217\pi$
$199$	3.77010	−	6.53000i	0.267255	−	0.462899i	0.968152	+	0.250363i	$0.0805501\pi$
$200$		0			0
$201$	−1.43105	+	0.391333i	−0.100938	+	0.0276025i
$202$		0			0
$203$	3.28100	+	2.75308i	0.230281	+	0.193229i
$204$		0			0
$205$	14.7374	+	5.36397i	1.02930	+	0.374636i
$206$		0			0
$207$	6.37775	−	1.19222i	0.443284	−	0.0828648i
$208$		0			0
$209$	−0.342328	−	1.94144i	−0.0236793	−	0.134292i
$210$		0			0
$211$	4.89922	−	1.78317i	0.337276	−	0.122758i	−0.167829	−	0.985816i	$-0.553676\pi$
$211$	4.89922	−	1.78317i	0.337276	−	0.122758i	0.505106	+	0.863058i	$0.331454\pi$
$212$		0			0
$213$	7.10131	+	15.0269i	0.486573	+	1.02963i
$214$		0			0
$215$	15.0012			1.02307
$216$		0			0
$217$	−8.43326			−0.572487
$218$		0			0
$219$	26.3106	+	2.16583i	1.77791	+	0.146353i
$220$		0			0
$221$	1.67125	−	0.608285i	0.112420	−	0.0409177i
$222$		0			0
$223$	−3.07250	−	17.4250i	−0.205750	−	1.16686i	−0.896256	−	0.443537i	$-0.853723\pi$
$223$	−3.07250	−	17.4250i	−0.205750	−	1.16686i	0.690506	−	0.723326i	$-0.257388\pi$
$224$		0			0
$225$	−5.74677	−	3.23969i	−0.383118	−	0.215979i
$226$		0			0
$227$	−14.8208	−	5.39434i	−0.983692	−	0.358035i	−0.200418	−	0.979711i	$-0.564230\pi$
$227$	−14.8208	−	5.39434i	−0.983692	−	0.358035i	−0.783275	+	0.621676i	$0.786452\pi$
$228$		0			0
$229$	−1.35350	−	1.13572i	−0.0894415	−	0.0750504i	0.596971	−	0.802263i	$-0.296371\pi$
$229$	−1.35350	−	1.13572i	−0.0894415	−	0.0750504i	−0.686412	+	0.727213i	$0.740815\pi$
$230$		0			0
$231$	0.379318	+	0.375443i	0.0249573	+	0.0247024i
$232$		0			0
$233$	6.94920	−	12.0364i	0.455257	−	0.788529i	−0.543446	−	0.839444i	$-0.682881\pi$
$233$	6.94920	−	12.0364i	0.455257	−	0.788529i	0.998703	+	0.0509157i	$0.0162140\pi$
$234$		0			0
$235$	3.32177	+	5.75347i	0.216688	+	0.375315i
$236$		0			0
$237$	−1.79212	−	19.3400i	−0.116411	−	1.25627i
$238$		0			0
$239$	3.44391	−	19.5314i	0.222768	−	1.26338i	−0.644138	−	0.764909i	$-0.722784\pi$
$239$	3.44391	−	19.5314i	0.222768	−	1.26338i	0.866906	−	0.498471i	$-0.166105\pi$
$240$		0			0
$241$	14.8419	−	12.4538i	0.956050	−	0.802221i	−0.0242563	−	0.999706i	$-0.507722\pi$
$241$	14.8419	−	12.4538i	0.956050	−	0.802221i	0.980306	+	0.197485i	$0.0632773\pi$
$242$		0			0
$243$	1.75676	+	15.4892i	0.112696	+	0.993629i
$244$		0			0
$245$	12.4444	−	10.4421i	0.795043	−	0.667120i
$246$		0			0
$247$	1.63550	−	9.27540i	0.104065	−	0.590179i
$248$		0			0
$249$	0.748720	+	8.07992i	0.0474482	+	0.512044i
$250$		0			0
$251$	−2.73786	−	4.74212i	−0.172812	−	0.299320i	0.766590	−	0.642137i	$-0.221952\pi$
$251$	−2.73786	−	4.74212i	−0.172812	−	0.299320i	−0.939402	+	0.342818i	$0.888619\pi$
$252$		0			0
$253$	0.342689	−	0.593554i	0.0215447	−	0.0373164i
$254$		0			0
$255$	3.87991	+	3.84027i	0.242969	+	0.240487i
$256$		0			0
$257$	−8.85943	−	7.43395i	−0.552636	−	0.463717i	0.323196	−	0.946332i	$-0.395243\pi$
$257$	−8.85943	−	7.43395i	−0.552636	−	0.463717i	−0.875833	+	0.482615i	$0.839687\pi$
$258$		0			0
$259$	−4.08115	−	1.48542i	−0.253590	−	0.0922993i
$260$		0			0
$261$	11.5115	+	6.48951i	0.712546	+	0.401691i
$262$		0			0
$263$	−1.12488	−	6.37952i	−0.0693632	−	0.393378i	−0.999648	−	0.0265395i	$-0.991551\pi$
$263$	−1.12488	−	6.37952i	−0.0693632	−	0.393378i	0.930285	−	0.366839i	$-0.119560\pi$
$264$		0			0
$265$	−27.4618	+	9.99526i	−1.68696	+	0.614004i
$266$		0			0
$267$	26.7554	+	2.20245i	1.63741	+	0.134788i
$268$		0			0
$269$	−13.8387			−0.843758			−0.421879	−	0.906652i	$-0.638629\pi$
$269$	−13.8387			−0.843758			−0.421879	+	0.906652i	$0.638629\pi$
$270$		0			0
$271$	−1.94536			−0.118172			−0.0590860	−	0.998253i	$-0.518819\pi$
$271$	−1.94536			−0.118172			−0.0590860	+	0.998253i	$0.518819\pi$
$272$		0			0
$273$	1.08945	+	2.30536i	0.0659366	+	0.139527i
$274$		0			0
$275$	−0.654846	+	0.238344i	−0.0394887	+	0.0143727i
$276$		0			0
$277$	2.16586	+	12.2832i	0.130134	+	0.738026i	0.978125	+	0.208016i	$0.0667007\pi$
$277$	2.16586	+	12.2832i	0.130134	+	0.738026i	−0.847991	+	0.530010i	$0.822188\pi$
$278$		0			0
$279$	−25.5766	+	4.78114i	−1.53123	+	0.286239i
$280$		0			0
$281$	−9.16752	−	3.33670i	−0.546888	−	0.199051i	0.0537751	−	0.998553i	$-0.482875\pi$
$281$	−9.16752	−	3.33670i	−0.546888	−	0.199051i	−0.600663	+	0.799502i	$0.705097\pi$
$282$		0			0
$283$	−20.3547	−	17.0797i	−1.20996	−	1.01528i	−0.999288	−	0.0377246i	$-0.987989\pi$
$283$	−20.3547	−	17.0797i	−1.20996	−	1.01528i	−0.210676	−	0.977556i	$-0.567567\pi$
$284$		0			0
$285$	27.8858	−	7.62565i	1.65181	−	0.451704i
$286$		0			0
$287$	2.84173	−	4.92202i	0.167742	−	0.290538i
$288$		0			0
$289$	7.81006	+	13.5274i	0.459415	+	0.795730i
$290$		0			0
$291$	7.84527	−	5.55356i	0.459898	−	0.325556i
$292$		0			0
$293$	2.12849	−	12.0712i	0.124347	−	0.705210i	−0.857346	−	0.514741i	$-0.827888\pi$
$293$	2.12849	−	12.0712i	0.124347	−	0.705210i	0.981693	−	0.190469i	$-0.0610008\pi$
$294$		0			0
$295$	−3.54389	+	2.97368i	−0.206334	+	0.173134i
$296$		0			0
$297$	1.36326	+	0.923606i	0.0791044	+	0.0535930i
$298$		0			0
$299$	2.50838	−	2.10478i	0.145063	−	0.121723i
$300$		0			0
$301$	0.944004	−	5.35371i	0.0544115	−	0.308583i
$302$		0			0
$303$	−15.9539	−	7.33993i	−0.916526	−	0.421668i
$304$		0			0
$305$	1.36137	+	2.35797i	0.0779521	+	0.135017i
$306$		0			0
$307$	−13.2370	+	22.9271i	−0.755475	+	1.30852i	0.189663	+	0.981849i	$0.439260\pi$
$307$	−13.2370	+	22.9271i	−0.755475	+	1.30852i	−0.945138	+	0.326671i	$0.894073\pi$
$308$		0			0
$309$	−4.33242	+	16.5073i	−0.246463	+	0.939070i
$310$		0			0
$311$	13.5280	+	11.3513i	0.767100	+	0.643673i	0.939964	−	0.341272i	$-0.110858\pi$
$311$	13.5280	+	11.3513i	0.767100	+	0.643673i	−0.172865	+	0.984946i	$0.555302\pi$
$312$		0			0
$313$	−9.06541	−	3.29954i	−0.512407	−	0.186501i	0.0728589	−	0.997342i	$-0.476788\pi$
$313$	−9.06541	−	3.29954i	−0.512407	−	0.186501i	−0.585266	+	0.810841i	$0.699010\pi$
$314$		0			0
$315$	−4.96901	+	6.04686i	−0.279972	+	0.340702i
$316$		0			0
$317$	−0.644320	−	3.65412i	−0.0361886	−	0.205236i	0.961352	−	0.275321i	$-0.0887841\pi$
$317$	−0.644320	−	3.65412i	−0.0361886	−	0.205236i	−0.997541	+	0.0700850i	$0.977673\pi$
$318$		0			0
$319$	1.31174	−	0.477435i	0.0734434	−	0.0267312i
$320$		0			0
$321$	−5.09927	+	7.36268i	−0.284614	+	0.410945i
$322$		0			0
$323$	−7.30748			−0.406599
$324$		0			0
$325$	−3.32937			−0.184680
$326$		0			0
$327$	−7.20952	+	10.4096i	−0.398687	+	0.575652i
$328$		0			0
$329$	2.26237	−	0.823435i	0.124728	−	0.0453974i
$330$		0			0
$331$	0.245329	+	1.39133i	0.0134845	+	0.0764745i	0.990807	−	0.135280i	$-0.0431934\pi$
$331$	0.245329	+	1.39133i	0.0134845	+	0.0764745i	−0.977323	+	0.211755i	$0.932082\pi$
$332$		0			0
$333$	−13.2196	−	2.19126i	−0.724427	−	0.120080i
$334$		0			0
$335$	−2.15961	−	0.786034i	−0.117992	−	0.0429456i
$336$		0			0
$337$	−9.95097	−	8.34986i	−0.542064	−	0.454846i	0.330179	−	0.943918i	$-0.392891\pi$
$337$	−9.95097	−	8.34986i	−0.542064	−	0.454846i	−0.872243	+	0.489073i	$0.837335\pi$
$338$		0			0
$339$	−4.56209	+	17.3824i	−0.247779	+	0.944084i
$340$		0			0
$341$	−1.37428	+	2.38033i	−0.0744215	+	0.128902i
$342$		0			0
$343$	−6.34669	−	10.9928i	−0.342689	−	0.593555i
$344$		0			0
$345$	9.13083	+	4.20084i	0.491587	+	0.226166i
$346$		0			0
$347$	0.833591	−	4.72753i	0.0447495	−	0.253787i	−0.954224	−	0.299094i	$-0.903316\pi$
$347$	0.833591	−	4.72753i	0.0447495	−	0.253787i	0.998973	+	0.0453070i	$0.0144266\pi$
$348$		0			0
$349$	−17.2954	+	14.5126i	−0.925803	+	0.776841i	−0.975059	−	0.221946i	$-0.928759\pi$
$349$	−17.2954	+	14.5126i	−0.925803	+	0.776841i	0.0492565	+	0.998786i	$0.484315\pi$
$350$		0			0
$351$	4.61112	+	6.37412i	0.246123	+	0.340225i
$352$		0			0
$353$	−22.7565	+	19.0950i	−1.21121	+	1.01632i	−0.211972	+	0.977276i	$0.567988\pi$
$353$	−22.7565	+	19.0950i	−1.21121	+	1.01632i	−0.999237	+	0.0390490i	$0.987567\pi$
$354$		0			0
$355$	−4.47081	+	25.3552i	−0.237286	+	1.34572i
$356$		0			0
$357$	1.61470	−	1.14302i	0.0854589	−	0.0604952i
$358$		0			0
$359$	6.70991	+	11.6219i	0.354136	+	0.613381i	0.986970	−	0.160906i	$-0.0514418\pi$
$359$	6.70991	+	11.6219i	0.354136	+	0.613381i	−0.632834	+	0.774288i	$0.718108\pi$
$360$		0			0
$361$	−9.84920	+	17.0593i	−0.518379	+	0.897858i
$362$		0			0
$363$	−18.2100	+	4.97970i	−0.955778	+	0.261366i
$364$		0			0
$365$	31.3276	+	26.2870i	1.63976	+	1.37592i
$366$		0			0
$367$	−7.47054	−	2.71905i	−0.389959	−	0.141933i	0.139597	−	0.990208i	$-0.455419\pi$
$367$	−7.47054	−	2.71905i	−0.389959	−	0.141933i	−0.529556	+	0.848275i	$0.677641\pi$
$368$		0			0
$369$	5.82801	−	16.5387i	0.303394	−	0.860973i
$370$		0			0
$371$	1.83904	+	10.4297i	0.0954782	+	0.541484i
$372$		0			0
$373$	10.7318	−	3.90604i	0.555670	−	0.202247i	−0.0488939	−	0.998804i	$-0.515570\pi$
$373$	10.7318	−	3.90604i	0.555670	−	0.202247i	0.604564	+	0.796557i	$0.293347\pi$
$374$		0			0
$375$	5.56168	+	11.7689i	0.287204	+	0.607745i
$376$		0			0
$377$	6.66917			0.343480
$378$		0			0
$379$	24.1705			1.24155			0.620777	−	0.783987i	$-0.286817\pi$
$379$	24.1705			1.24155			0.620777	+	0.783987i	$0.286817\pi$
$380$		0			0
$381$	9.02366	+	0.742807i	0.462296	+	0.0380551i
$382$		0			0
$383$	8.87378	−	3.22979i	0.453429	−	0.165035i	−0.105202	−	0.994451i	$-0.533549\pi$
$383$	8.87378	−	3.22979i	0.453429	−	0.165035i	0.558631	+	0.829416i	$0.311327\pi$
$384$		0			0
$385$	0.143564	+	0.814194i	0.00731672	+	0.0414952i
$386$		0			0
$387$	−0.172220	−	16.7721i	−0.00875442	−	0.852573i
$388$		0			0
$389$	2.39406	+	0.871367i	0.121384	+	0.0441801i	0.401998	−	0.915641i	$-0.368316\pi$
$389$	2.39406	+	0.871367i	0.121384	+	0.0441801i	−0.280614	+	0.959821i	$0.590538\pi$
$390$		0			0
$391$	−1.94617	−	1.63303i	−0.0984218	−	0.0825857i
$392$		0			0
$393$	−8.90554	−	8.81457i	−0.449225	−	0.444636i
$394$		0			0
$395$	15.0438	−	26.0567i	0.756937	−	1.31105i
$396$		0			0
$397$	−1.83759	−	3.18279i	−0.0922258	−	0.159740i	0.816222	−	0.577739i	$-0.196065\pi$
$397$	−1.83759	−	3.18279i	−0.0922258	−	0.159740i	−0.908447	+	0.417999i	$0.862731\pi$
$398$		0			0
$399$	−0.966669	−	10.4319i	−0.0483940	−	0.522251i
$400$		0			0
$401$	2.80420	−	15.9034i	0.140035	−	0.794177i	−0.831186	−	0.555995i	$-0.812337\pi$
$401$	2.80420	−	15.9034i	0.140035	−	0.794177i	0.971220	−	0.238182i	$-0.0765516\pi$
$402$		0			0
$403$	−10.0593	+	8.44078i	−0.501091	+	0.420465i
$404$		0			0
$405$	−11.6420	+	21.1562i	−0.578494	+	1.05126i
$406$		0			0
$407$	−1.08433	+	0.909859i	−0.0537481	+	0.0451000i
$408$		0			0
$409$	1.59443	−	9.04248i	0.0788396	−	0.447122i	−0.919677	−	0.392676i	$-0.871550\pi$
$409$	1.59443	−	9.04248i	0.0788396	−	0.447122i	0.998517	−	0.0544462i	$-0.0173393\pi$
$410$		0			0
$411$	−1.79780	−	19.4013i	−0.0886792	−	0.956994i
$412$		0			0
$413$	0.838253	+	1.45190i	0.0412477	+	0.0714432i
$414$		0			0
$415$	−6.28506	+	10.8860i	−0.308522	+	0.534375i
$416$		0			0
$417$	11.5471	+	11.4292i	0.565466	+	0.559689i
$418$		0			0
$419$	5.34613	+	4.48594i	0.261176	+	0.219152i	0.763967	−	0.645256i	$-0.223249\pi$
$419$	5.34613	+	4.48594i	0.261176	+	0.219152i	−0.502791	+	0.864408i	$0.667694\pi$
$420$		0			0
$421$	−28.9525	−	10.5379i	−1.41106	−	0.513584i	−0.479619	−	0.877477i	$-0.659225\pi$
$421$	−28.9525	−	10.5379i	−1.41106	−	0.513584i	−0.931441	+	0.363894i	$0.881447\pi$
$422$		0			0
$423$	6.39454	−	3.77996i	0.310913	−	0.183788i
$424$		0			0
$425$	0.448559	+	2.54390i	0.0217583	+	0.123397i
$426$		0			0
$427$	0.927196	−	0.337472i	0.0448702	−	0.0163314i
$428$		0			0
$429$	0.828236	+	0.0681784i	0.0399876	+	0.00329169i
$430$		0			0
$431$	−27.8971			−1.34376			−0.671879	−	0.740661i	$-0.734513\pi$
$431$	−27.8971			−1.34376			−0.671879	+	0.740661i	$0.734513\pi$
$432$		0			0
$433$	19.1706			0.921278			0.460639	−	0.887588i	$-0.347620\pi$
$433$	19.1706			0.921278			0.460639	+	0.887588i	$0.347620\pi$
$434$		0			0
$435$	8.74646	+	18.5082i	0.419361	+	0.887398i
$436$		0			0
$437$	−12.6426	+	4.60154i	−0.604778	+	0.220121i
$438$		0			0
$439$	4.12397	+	23.3882i	0.196826	+	1.11626i	0.909794	+	0.415060i	$0.136239\pi$
$439$	4.12397	+	23.3882i	0.196826	+	1.11626i	−0.712968	+	0.701197i	$0.752649\pi$
$440$		0			0
$441$	−11.8177	−	13.7936i	−0.562746	−	0.656838i
$442$		0			0
$443$	21.9496	+	7.98900i	1.04286	+	0.379569i	0.805962	−	0.591967i	$-0.201648\pi$
$443$	21.9496	+	7.98900i	1.04286	+	0.379569i	0.236894	+	0.971536i	$0.423871\pi$
$444$		0			0
$445$	31.8573	+	26.7314i	1.51018	+	1.26719i
$446$		0			0
$447$	31.8291	−	8.70396i	1.50546	−	0.411683i
$448$		0			0
$449$	−2.40953	+	4.17343i	−0.113713	+	0.196956i	−0.917264	−	0.398279i	$-0.869608\pi$
$449$	−2.40953	+	4.17343i	−0.113713	+	0.196956i	0.803552	+	0.595235i	$0.202941\pi$
$450$		0			0
$451$	−0.926176	−	1.60418i	−0.0436119	−	0.0755380i
$452$		0			0
$453$	5.67457	−	4.01695i	0.266615	−	0.188733i
$454$		0			0
$455$	−0.685893	+	3.88989i	−0.0321552	+	0.182361i
$456$		0			0
$457$	−3.74872	+	3.14555i	−0.175358	+	0.147142i	−0.726242	−	0.687439i	$-0.758735\pi$
$457$	−3.74872	+	3.14555i	−0.175358	+	0.147142i	0.550885	+	0.834581i	$0.314290\pi$
$458$		0			0
$459$	4.24908	−	4.38203i	0.198330	−	0.204535i
$460$		0			0
$461$	21.4419	−	17.9919i	0.998650	−	0.837967i	0.0118535	−	0.999930i	$-0.496227\pi$
$461$	21.4419	−	17.9919i	0.998650	−	0.837967i	0.986797	+	0.161963i	$0.0517824\pi$
$462$		0			0
$463$	4.77104	−	27.0579i	0.221729	−	1.25749i	−0.647111	−	0.762396i	$-0.724023\pi$
$463$	4.77104	−	27.0579i	0.221729	−	1.25749i	0.868840	−	0.495093i	$-0.164866\pi$
$464$		0			0
$465$	−36.6173	−	16.8466i	−1.69809	−	0.781243i
$466$		0			0
$467$	−10.6232	−	18.4000i	−0.491585	−	0.851450i	0.508368	−	0.861140i	$-0.330249\pi$
$467$	−10.6232	−	18.4000i	−0.491585	−	0.851450i	−0.999953	+	0.00968963i	$0.996916\pi$
$468$		0			0
$469$	−0.416426	+	0.721272i	−0.0192288	+	0.0333052i
$470$		0			0
$471$	−3.19917	+	12.1894i	−0.147410	+	0.561659i
$472$		0			0
$473$	−1.35728	−	1.13889i	−0.0624076	−	0.0523662i
$474$		0			0
$475$	12.8547	+	4.67871i	0.589812	+	0.214674i
$476$		0			0
$477$	11.4905	+	30.5889i	0.526113	+	1.40057i
$478$		0			0
$479$	7.23745	+	41.0456i	0.330688	+	1.87542i	0.466248	+	0.884654i	$0.345606\pi$
$479$	7.23745	+	41.0456i	0.330688	+	1.87542i	−0.135560	+	0.990769i	$0.543283\pi$
$480$		0			0
$481$	−6.35480	+	2.31296i	−0.289754	+	0.105462i
$482$		0			0
$483$	2.07381	−	2.99431i	0.0943618	−	0.136246i
$484$		0			0
$485$	14.8898			0.676112
$486$		0			0
$487$	−4.02801			−0.182527			−0.0912634	−	0.995827i	$-0.529091\pi$
$487$	−4.02801			−0.182527			−0.0912634	+	0.995827i	$0.529091\pi$
$488$		0			0
$489$	−12.2769	+	17.7263i	−0.555183	+	0.801611i
$490$		0			0
$491$	−36.2922	+	13.2093i	−1.63784	+	0.596126i	−0.986660	−	0.162793i	$-0.947950\pi$
$491$	−36.2922	+	13.2093i	−1.63784	+	0.596126i	−0.651184	+	0.758920i	$0.725727\pi$
$492$		0			0
$493$	−0.898521	−	5.09577i	−0.0404674	−	0.229502i
$494$		0			0
$495$	0.897004	+	2.38792i	0.0403173	+	0.107329i
$496$		0			0
$497$	8.76759	+	3.19114i	0.393280	+	0.143142i
$498$		0			0
$499$	3.11922	+	2.61734i	0.139636	+	0.117168i	0.709930	−	0.704272i	$-0.248726\pi$
$499$	3.11922	+	2.61734i	0.139636	+	0.117168i	−0.570295	+	0.821440i	$0.693171\pi$
$500$		0			0
$501$	−1.02531	+	3.90664i	−0.0458076	+	0.174536i
$502$		0			0
$503$	−1.71297	+	2.96695i	−0.0763775	+	0.132290i	−0.901684	−	0.432395i	$-0.857669\pi$
$503$	−1.71297	+	2.96695i	−0.0763775	+	0.132290i	0.825307	+	0.564684i	$0.191002\pi$
$504$		0			0
$505$	−13.6020	−	23.5594i	−0.605282	−	1.04838i
$506$		0			0
$507$	−16.8487	−	7.75161i	−0.748276	−	0.344261i
$508$		0			0
$509$	−2.12952	+	12.0771i	−0.0943893	+	0.535308i	0.900543	+	0.434766i	$0.143169\pi$
$509$	−2.12952	+	12.0771i	−0.0943893	+	0.535308i	−0.994933	+	0.100542i	$0.967942\pi$
$510$		0			0
$511$	11.3529	−	9.52619i	0.502222	−	0.421414i
$512$		0			0
$513$	−8.84601	−	31.0903i	−0.390561	−	1.37267i
$514$		0			0
$515$	−20.2522	+	16.9936i	−0.892418	+	0.748827i
$516$		0			0
$517$	0.136257	−	0.772750i	0.00599257	−	0.0339855i
$518$		0			0
$519$	5.06423	−	3.58490i	0.222295	−	0.157360i
$520$		0			0
$521$	−7.04117	−	12.1957i	−0.308479	−	0.534302i	0.669551	−	0.742766i	$-0.266487\pi$
$521$	−7.04117	−	12.1957i	−0.308479	−	0.534302i	−0.978030	+	0.208465i	$0.933153\pi$
$522$		0			0
$523$	4.88956	−	8.46897i	0.213806	−	0.370322i	−0.739097	−	0.673599i	$-0.764747\pi$
$523$	4.88956	−	8.46897i	0.213806	−	0.370322i	0.952902	+	0.303277i	$0.0980808\pi$
$524$		0			0
$525$	−3.57227	+	0.976870i	−0.155906	+	0.0426341i
$526$		0			0
$527$	7.80469	+	6.54892i	0.339978	+	0.285275i
$528$		0			0
$529$	17.2176	+	6.26668i	0.748590	+	0.272464i
$530$		0			0
$531$	3.36541	+	3.92812i	0.146047	+	0.170466i
$532$		0			0
$533$	−1.53675	−	8.71534i	−0.0665640	−	0.377503i
$534$		0			0
$535$	−13.0371	+	4.74511i	−0.563642	+	0.205149i
$536$		0			0
$537$	14.7977	+	31.3131i	0.638569	+	1.35126i
$538$		0			0
$539$	−1.91871			−0.0826445
$540$		0			0
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$		0			0
$543$	−16.8001	−	1.38294i	−0.720959	−	0.0593477i
$544$		0			0
$545$	−18.4323	+	6.70879i	−0.789551	+	0.287373i
$546$		0			0
$547$	−0.192798	−	1.09341i	−0.00824343	−	0.0467508i	0.980409	−	0.196975i	$-0.0631117\pi$
$547$	−0.192798	−	1.09341i	−0.00824343	−	0.0467508i	−0.988652	+	0.150224i	$0.952001\pi$
$548$		0			0
$549$	2.62070	−	1.54916i	0.111849	−	0.0661164i
$550$		0			0
$551$	−25.7495	−	9.37206i	−1.09697	−	0.399263i
$552$		0			0
$553$	−8.35257	−	7.00864i	−0.355188	−	0.298038i
$554$		0			0
$555$	−14.7531	−	14.6023i	−0.626232	−	0.619835i
$556$		0			0
$557$	−17.5201	+	30.3458i	−0.742352	+	1.28579i	0.209070	+	0.977901i	$0.432956\pi$
$557$	−17.5201	+	30.3458i	−0.742352	+	1.28579i	−0.951422	+	0.307890i	$0.900377\pi$
$558$		0			0
$559$	−4.23247	−	7.33084i	−0.179014	−	0.310062i
$560$		0			0
$561$	−0.0594925	−	0.642022i	−0.00251178	−	0.0271062i
$562$		0			0
$563$	6.73255	−	38.1822i	0.283743	−	1.60919i	−0.425998	−	0.904724i	$-0.640077\pi$
$563$	6.73255	−	38.1822i	0.283743	−	1.60919i	0.709741	−	0.704463i	$-0.248812\pi$
$564$		0			0
$565$	−21.3258	+	17.8945i	−0.897183	+	0.752826i
$566$		0			0
$567$	6.81774	+	5.48619i	0.286318	+	0.230398i
$568$		0			0
$569$	−26.0213	+	21.8344i	−1.09087	+	0.915347i	−0.996777	−	0.0802169i	$-0.974439\pi$
$569$	−26.0213	+	21.8344i	−1.09087	+	0.915347i	−0.0940904	+	0.995564i	$0.529994\pi$
$570$		0			0
$571$	−1.75191	+	9.93559i	−0.0733153	+	0.415792i	0.925956	+	0.377631i	$0.123261\pi$
$571$	−1.75191	+	9.93559i	−0.0733153	+	0.415792i	−0.999272	+	0.0381610i	$0.987850\pi$
$572$		0			0
$573$	−2.83775	−	30.6240i	−0.118549	−	1.27934i
$574$		0			0
$575$	2.37795	+	4.11873i	0.0991674	+	0.171763i
$576$		0			0
$577$	6.06615	−	10.5069i	0.252537	−	0.437407i	−0.711687	−	0.702497i	$-0.752068\pi$
$577$	6.06615	−	10.5069i	0.252537	−	0.437407i	0.964224	+	0.265090i	$0.0854017\pi$
$578$		0			0
$579$	−13.0295	−	12.8964i	−0.541487	−	0.535956i
$580$		0			0
$581$	3.48957	+	2.92810i	0.144772	+	0.121478i
$582$		0			0
$583$	3.24352	+	1.18055i	0.134333	+	0.0488932i
$584$		0			0
$585$	0.125131	+	12.1862i	0.00517353	+	0.503839i
$586$		0			0
$587$	−5.51319	−	31.2669i	−0.227554	−	1.29052i	−0.857743	−	0.514079i	$-0.828134\pi$
$587$	−5.51319	−	31.2669i	−0.227554	−	1.29052i	0.630189	−	0.776442i	$-0.282977\pi$
$588$		0			0
$589$	50.7006	−	18.4535i	2.08908	−	0.760363i
$590$		0			0
$591$	−24.4412	−	2.01195i	−1.00538	−	0.0827605i
$592$		0			0
$593$	13.4906			0.553993			0.276996	−	0.960871i	$-0.410661\pi$
$593$	13.4906			0.553993			0.276996	+	0.960871i	$0.410661\pi$
$594$		0			0
$595$	3.06459			0.125636
$596$		0			0
$597$	−5.58009	−	11.8079i	−0.228378	−	0.483265i
$598$		0			0
$599$	−39.8715	+	14.5120i	−1.62911	+	0.592946i	−0.985086	−	0.172063i	$-0.944957\pi$
$599$	−39.8715	+	14.5120i	−1.62911	+	0.592946i	−0.644020	+	0.765009i	$0.722735\pi$
$600$		0			0
$601$	−3.43906	−	19.5039i	−0.140282	−	0.795579i	−0.971035	−	0.238938i	$-0.923201\pi$
$601$	−3.43906	−	19.5039i	−0.140282	−	0.795579i	0.830753	−	0.556641i	$-0.187910\pi$
$602$		0			0
$603$	−0.854034	+	2.42358i	−0.0347789	+	0.0986958i
$604$		0			0
$605$	−27.4810	−	10.0022i	−1.11726	−	0.406649i
$606$		0			0
$607$	27.5769	+	23.1397i	1.11931	+	0.939213i	0.998569	−	0.0534715i	$-0.0170286\pi$
$607$	27.5769	+	23.1397i	1.11931	+	0.939213i	0.120741	+	0.992684i	$0.461473\pi$
$608$		0			0
$609$	7.15571	−	1.95680i	0.289964	−	0.0792934i
$610$		0			0
$611$	1.87442	−	3.24659i	0.0758310	−	0.131343i
$612$		0			0
$613$	−13.2314	−	22.9175i	−0.534411	−	0.925627i	−0.999192	−	0.0402013i	$-0.987200\pi$
$613$	−13.2314	−	22.9175i	−0.534411	−	0.925627i	0.464780	−	0.885426i	$-0.346133\pi$
$614$		0			0
$615$	22.1712	−	15.6947i	0.894031	−	0.632872i
$616$		0			0
$617$	8.52903	−	48.3705i	0.343366	−	1.94732i	0.0239406	−	0.999713i	$-0.492379\pi$
$617$	8.52903	−	48.3705i	0.343366	−	1.94732i	0.319425	−	0.947611i	$-0.396510\pi$
$618$		0			0
$619$	18.5430	−	15.5595i	0.745307	−	0.625387i	−0.188950	−	0.981987i	$-0.560508\pi$
$619$	18.5430	−	15.5595i	0.745307	−	0.625387i	0.934257	+	0.356600i	$0.116064\pi$
$620$		0			0
$621$	4.59193	−	10.2570i	0.184268	−	0.411598i
$622$		0			0
$623$	11.5448	−	9.68725i	0.462533	−	0.388111i
$624$		0			0
$625$	−5.41077	+	30.6860i	−0.216431	+	1.22744i
$626$		0			0
$627$	−3.10199	−	1.42714i	−0.123882	−	0.0569945i
$628$		0			0
$629$	2.62345	+	4.54395i	0.104604	+	0.181179i
$630$		0			0
$631$	8.84842	−	15.3259i	0.352250	−	0.610115i	−0.634393	−	0.773010i	$-0.718750\pi$
$631$	8.84842	−	15.3259i	0.352250	−	0.610115i	0.986643	+	0.162895i	$0.0520833\pi$
$632$		0			0
$633$	2.29240	−	8.73447i	0.0911147	−	0.347164i
$634$		0			0
$635$	10.7443	+	9.01555i	0.426375	+	0.357771i
$636$		0			0
$637$	−8.61398	−	3.13523i	−0.341298	−	0.124222i
$638$		0			0
$639$	28.3998	+	4.70751i	1.12348	+	0.186226i
$640$		0			0
$641$	6.60738	+	37.4723i	0.260976	+	1.48007i	0.780254	+	0.625463i	$0.215090\pi$
$641$	6.60738	+	37.4723i	0.260976	+	1.48007i	−0.519278	+	0.854605i	$0.673799\pi$
$642$		0			0
$643$	44.1115	−	16.0553i	1.73959	−	0.633158i	0.740352	−	0.672220i	$-0.234659\pi$
$643$	44.1115	−	16.0553i	1.73959	−	0.633158i	0.999237	+	0.0390615i	$0.0124368\pi$
$644$		0			0
$645$	14.7937	−	21.3601i	0.582500	−	0.841053i
$646$		0			0
$647$	28.2333			1.10997			0.554983	−	0.831862i	$-0.312725\pi$
$647$	28.2333			1.10997			0.554983	+	0.831862i	$0.312725\pi$
$648$		0			0
$649$	0.546406			0.0214483
$650$		0			0
$651$	−8.31660	+	12.0081i	−0.325953	+	0.470634i
$652$		0			0
$653$	−33.1779	+	12.0758i	−1.29835	+	0.472562i	−0.896460	−	0.443125i	$-0.853870\pi$
$653$	−33.1779	+	12.0758i	−1.29835	+	0.472562i	−0.401893	+	0.915687i	$0.631647\pi$
$654$		0			0
$655$	−3.37057	−	19.1155i	−0.131699	−	0.746902i
$656$		0			0
$657$	29.0306	−	35.3277i	1.13259	−	1.37826i
$658$		0			0
$659$	39.1793	+	14.2601i	1.52621	+	0.555494i	0.962689	−	0.270609i	$-0.0872250\pi$
$659$	39.1793	+	14.2601i	1.52621	+	0.555494i	0.563519	+	0.826103i	$0.309447\pi$
$660$		0			0
$661$	0.975874	+	0.818856i	0.0379571	+	0.0318498i	0.661569	−	0.749884i	$-0.269891\pi$
$661$	0.975874	+	0.818856i	0.0379571	+	0.0318498i	−0.623612	+	0.781734i	$0.714335\pi$
$662$		0			0
$663$	0.781997	−	2.97956i	0.0303702	−	0.115716i
$664$		0			0
$665$	8.11461	−	14.0549i	0.314671	−	0.545027i
$666$		0			0
$667$	−4.76334	−	8.25035i	−0.184437	−	0.319455i
$668$		0			0
$669$	−27.8413	−	12.8090i	−1.07641	−	0.495226i
$670$		0			0
$671$	0.0558427	−	0.316700i	0.00215578	−	0.0122261i
$672$		0			0
$673$	27.2963	−	22.9043i	1.05219	−	0.882896i	0.0588715	−	0.998266i	$-0.481250\pi$
$673$	27.2963	−	22.9043i	1.05219	−	0.882896i	0.993323	+	0.115370i	$0.0368053\pi$
$674$		0			0
$675$	−10.2802	+	4.98793i	−0.395687	+	0.191986i
$676$		0			0
$677$	13.7902	−	11.5714i	0.530002	−	0.444725i	−0.338100	−	0.941110i	$-0.609784\pi$
$677$	13.7902	−	11.5714i	0.530002	−	0.444725i	0.868102	+	0.496386i	$0.165340\pi$
$678$		0			0
$679$	0.936996	−	5.31397i	0.0359586	−	0.203931i
$680$		0			0
$681$	−22.2968	+	15.7836i	−0.854414	+	0.604828i
$682$		0			0
$683$	19.8807	+	34.4344i	0.760715	+	1.31760i	0.942483	+	0.334255i	$0.108485\pi$
$683$	19.8807	+	34.4344i	0.760715	+	1.31760i	−0.181768	+	0.983341i	$0.558182\pi$
$684$		0			0
$685$	15.0915	−	26.1393i	0.576617	−	0.998730i
$686$		0			0
$687$	−2.95192	+	0.807229i	−0.112623	+	0.0307977i
$688$		0			0
$689$	12.6327	+	10.6001i	0.481266	+	0.403830i
$690$		0			0
$691$	−15.8251	−	5.75986i	−0.602015	−	0.219115i	0.0229909	−	0.999736i	$-0.492681\pi$
$691$	−15.8251	−	5.75986i	−0.602015	−	0.219115i	−0.625006	+	0.780620i	$0.714903\pi$
$692$		0			0
$693$	0.908663	−	0.169860i	0.0345173	−	0.00645244i
$694$		0			0
$695$	4.37036	+	24.7855i	0.165777	+	0.940169i
$696$		0			0
$697$	−6.45216	+	2.34839i	−0.244393	+	0.0889518i
$698$		0			0
$699$	−10.2854	−	21.7648i	−0.389031	−	0.823220i
$700$		0			0
$701$	−8.96921			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$701$	−8.96921			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$702$		0			0
$703$	27.7861			1.04797
$704$		0			0
$705$	11.4682	+	0.944032i	0.431916	+	0.0355543i
$706$		0			0
$707$	−9.26398	+	3.37181i	−0.348408	+	0.126810i
$708$		0			0
$709$	3.15026	+	17.8660i	0.118311	+	0.670973i	0.985058	+	0.172225i	$0.0550955\pi$
$709$	3.15026	+	17.8660i	0.118311	+	0.670973i	−0.866747	+	0.498748i	$0.833793\pi$
$710$		0			0
$711$	−29.3054	−	16.5206i	−1.09904	−	0.619572i
$712$		0			0
$713$	17.6267	+	6.41560i	0.660125	+	0.240266i
$714$		0			0
$715$	0.986166	+	0.827492i	0.0368805	+	0.0309464i
$716$		0			0
$717$	−24.4144	−	24.1650i	−0.911771	−	0.902457i
$718$		0			0
$719$	15.7860	−	27.3421i	0.588718	−	1.01969i	−0.405683	−	0.914014i	$-0.632966\pi$
$719$	15.7860	−	27.3421i	0.588718	−	1.01969i	0.994401	−	0.105675i	$-0.0337004\pi$
$720$		0			0
$721$	4.79034	+	8.29711i	0.178402	+	0.309001i
$722$		0			0
$723$	−3.09636	−	33.4148i	−0.115155	−	1.24271i
$724$		0			0
$725$	−1.68204	+	9.53930i	−0.0624693	+	0.354281i
$726$		0			0
$727$	−29.4232	+	24.6890i	−1.09125	+	0.915664i	−0.996806	−	0.0798662i	$-0.974551\pi$
$727$	−29.4232	+	24.6890i	−1.09125	+	0.915664i	−0.0944407	+	0.995530i	$0.530106\pi$
$728$		0			0
$729$	23.7874	+	12.7734i	0.881014	+	0.473090i
$730$		0			0
$731$	−5.03111	+	4.22160i	−0.186082	+	0.156142i
$732$		0			0
$733$	−5.26680	+	29.8695i	−0.194534	+	1.10326i	0.718547	+	0.695478i	$0.244807\pi$
$733$	−5.26680	+	29.8695i	−0.194534	+	1.10326i	−0.913081	+	0.407778i	$0.866304\pi$
$734$		0			0
$735$	−2.59619	−	28.0171i	−0.0957618	−	1.03343i
$736$		0			0
$737$	0.135721	+	0.235076i	0.00499936	+	0.00865915i
$738$		0			0
$739$	5.00127	−	8.66245i	0.183975	−	0.318653i	−0.759256	−	0.650792i	$-0.774437\pi$
$739$	5.00127	−	8.66245i	0.183975	−	0.318653i	0.943230	+	0.332139i	$0.107770\pi$
$740$		0			0
$741$	−11.5943	−	11.4759i	−0.425928	−	0.421577i
$742$		0			0
$743$	−27.7873	−	23.3163i	−1.01942	−	0.855394i	−0.0298642	−	0.999554i	$-0.509507\pi$
$743$	−27.7873	−	23.3163i	−1.01942	−	0.855394i	−0.989554	+	0.144160i	$0.953952\pi$
$744$		0			0
$745$	48.0337	+	17.4828i	1.75982	+	0.640521i
$746$		0			0
$747$	12.2433	+	6.90205i	0.447960	+	0.252533i
$748$		0			0
$749$	0.873058	+	4.95136i	0.0319008	+	0.180919i
$750$		0			0
$751$	−13.6766	+	4.97788i	−0.499067	+	0.181646i	−0.579274	−	0.815133i	$-0.696664\pi$
$751$	−13.6766	+	4.97788i	−0.499067	+	0.181646i	0.0802073	+	0.996778i	$0.474442\pi$
$752$		0			0
$753$	−9.45226	−	0.778089i	−0.344460	−	0.0283551i
$754$		0			0
$755$	10.7700			0.391959
$756$		0			0
$757$	−45.5754			−1.65646			−0.828232	−	0.560385i	$-0.810653\pi$
$757$	−45.5754			−1.65646			−0.828232	+	0.560385i	$0.810653\pi$
$758$		0			0
$759$	−0.507211	−	1.07330i	−0.0184106	−	0.0389582i
$760$		0			0
$761$	−20.9040	+	7.60843i	−0.757769	+	0.275805i	−0.691871	−	0.722021i	$-0.743213\pi$
$761$	−20.9040	+	7.60843i	−0.757769	+	0.275805i	−0.0658978	+	0.997826i	$0.520991\pi$
$762$		0			0
$763$	1.23436	+	7.00040i	0.0446868	+	0.253431i
$764$		0			0
$765$	9.29438	−	1.73743i	0.336039	−	0.0628170i
$766$		0			0
$767$	2.45307	+	0.892846i	0.0885754	+	0.0322388i
$768$		0			0
$769$	10.4679	+	8.78365i	0.377484	+	0.316747i	0.811714	−	0.584056i	$-0.198535\pi$
$769$	10.4679	+	8.78365i	0.377484	+	0.316747i	−0.434230	+	0.900802i	$0.642979\pi$
$770$		0			0
$771$	−19.3220	+	5.28379i	−0.695866	+	0.190291i
$772$		0			0
$773$	10.3270	−	17.8869i	0.371436	−	0.643345i	−0.618351	−	0.785902i	$-0.712199\pi$
$773$	10.3270	−	17.8869i	0.371436	−	0.643345i	0.989787	+	0.142557i	$0.0455323\pi$
$774$		0			0
$775$	−9.53628	−	16.5173i	−0.342553	−	0.593319i
$776$		0			0
$777$	−6.13977	+	4.34626i	−0.220263	+	0.155921i
$778$		0			0
$779$	−6.31415	+	35.8093i	−0.226228	+	1.28300i
$780$		0			0
$781$	2.32948	−	1.95466i	0.0833553	−	0.0699434i
$782$		0			0
$783$	20.5927	−	9.99147i	0.735922	−	0.357066i
$784$		0			0
$785$	−14.9547	+	12.5485i	−0.533757	+	0.447875i
$786$		0			0
$787$	4.28970	−	24.3281i	0.152911	−	0.867202i	−0.807759	−	0.589512i	$-0.799320\pi$
$787$	4.28970	−	24.3281i	0.152911	−	0.867202i	0.960671	−	0.277690i	$-0.0895689\pi$
$788$		0			0

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.986166 - 1.42389i) q^{3} +(2.52129 - 0.917674i) q^{5} +(-0.168844 - 0.957561i) q^{7} +(-1.05495 - 2.80839i) q^{9} +O(q^{10})\)	\(q+(0.986166 - 1.42389i) q^{3} +(2.52129 - 0.917674i) q^{5} +(-0.168844 - 0.957561i) q^{7} +(-1.05495 - 2.80839i) q^{9} +(-0.297791 - 0.108387i) q^{11} +(-1.15981 - 0.973200i) q^{13} +(1.17974 - 4.49503i) q^{15} +(-0.587342 + 1.01731i) q^{17} +(3.11040 + 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(-0.375556 + 2.12988i) q^{23} +(1.68454 - 1.41350i) q^{25} +(-5.03922 - 1.26740i) q^{27} +(-3.37436 + 2.83142i) q^{29} +(1.50609 - 8.54146i) q^{31} +(-0.448003 + 0.317135i) q^{33} +(-1.30443 - 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(-2.52950 + 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(5.25381 + 1.91223i) q^{43} +(-5.23703 - 6.11267i) q^{45} +(0.429965 + 2.43845i) q^{47} +(5.68943 - 2.07078i) q^{49} +(0.869320 + 1.83955i) q^{51} -10.8920 q^{53} -0.850279 q^{55} +(10.7384 + 0.883963i) q^{57} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(-2.51109 + 1.48436i) q^{63} +(-3.81731 - 1.38939i) q^{65} +(-0.656156 - 0.550580i) q^{67} +(2.66237 + 2.63517i) q^{69} +(-4.79788 + 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(-0.351434 - 3.79256i) q^{75} +(-0.0535070 + 0.303453i) q^{77} +(8.59024 - 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +(-3.58886 + 3.01141i) q^{83} +(-0.547303 + 3.10391i) q^{85} +(0.703969 + 7.59698i) q^{87} +(7.74976 + 13.4230i) q^{89} +(-0.736071 + 1.27491i) q^{91} +(-10.6769 - 10.5678i) q^{93} +(12.7861 + 10.7288i) q^{95} +(5.21481 + 1.89804i) q^{97} +(0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

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