LMFDB - Embedded newform 729.2.c.a.244.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.6
Root			$1.22778i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.a.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22889 + 2.12851i) q^{2} +(-2.02036 + 3.49937i) q^{4} +(1.54013 - 2.66759i) q^{5} +(1.32933 + 2.30247i) q^{7} -5.01568 q^{8} +O(q^{10})$	\(q+(1.22889 + 2.12851i) q^{2} +(-2.02036 + 3.49937i) q^{4} +(1.54013 - 2.66759i) q^{5} +(1.32933 + 2.30247i) q^{7} -5.01568 q^{8} +7.57064 q^{10} +(1.71717 + 2.97423i) q^{11} +(1.67198 - 2.89595i) q^{13} +(-3.26722 + 5.65899i) q^{14} +(-2.12302 - 3.67717i) q^{16} +2.57282 q^{17} -2.09676 q^{19} +(6.22325 + 10.7790i) q^{20} +(-4.22044 + 7.31002i) q^{22} +(-0.267222 + 0.462842i) q^{23} +(-2.24401 - 3.88674i) q^{25} +8.21874 q^{26} -10.7430 q^{28} +(-1.26545 - 2.19182i) q^{29} +(-3.85735 + 6.68113i) q^{31} +(0.202245 - 0.350299i) q^{32} +(3.16172 + 5.47626i) q^{34} +8.18939 q^{35} -10.2957 q^{37} +(-2.57670 - 4.46298i) q^{38} +(-7.72481 + 13.3798i) q^{40} +(2.44250 - 4.23054i) q^{41} +(-1.37075 - 2.37420i) q^{43} -13.8772 q^{44} -1.31355 q^{46} +(2.82900 + 4.89997i) q^{47} +(-0.0342555 + 0.0593322i) q^{49} +(5.51530 - 9.55279i) q^{50} +(6.75601 + 11.7018i) q^{52} +6.42657 q^{53} +10.5787 q^{55} +(-6.66751 - 11.5485i) q^{56} +(3.11020 - 5.38703i) q^{58} +(-0.827475 + 1.43323i) q^{59} +(-7.18610 - 12.4467i) q^{61} -18.9611 q^{62} -7.49791 q^{64} +(-5.15013 - 8.92029i) q^{65} +(2.93949 - 5.09135i) q^{67} +(-5.19803 + 9.00325i) q^{68} +(10.0639 + 17.4312i) q^{70} +14.8163 q^{71} +1.88140 q^{73} +(-12.6523 - 21.9144i) q^{74} +(4.23623 - 7.33736i) q^{76} +(-4.56538 + 7.90748i) q^{77} +(-8.59674 - 14.8900i) q^{79} -13.0789 q^{80} +12.0063 q^{82} +(-1.98439 - 3.43707i) q^{83} +(3.96248 - 6.86321i) q^{85} +(3.36900 - 5.83528i) q^{86} +(-8.61278 - 14.9178i) q^{88} +5.09880 q^{89} +8.89047 q^{91} +(-1.07977 - 1.87022i) q^{92} +(-6.95308 + 12.0431i) q^{94} +(-3.22929 + 5.59330i) q^{95} +(5.31594 + 9.20748i) q^{97} -0.168385 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.22889	+	2.12851i	0.868960	+	1.50508i	0.863061	+	0.505100i	$0.168544\pi$
$2$	1.22889	+	2.12851i	0.868960	+	1.50508i	0.00589892	+	0.999983i	$0.498122\pi$
$3$		0			0
$3$		0			0
$4$	−2.02036	+	3.49937i	−1.01018	+	1.74969i
$5$	1.54013	−	2.66759i	0.688768	−	1.19298i	−0.283469	−	0.958981i	$-0.591485\pi$
$5$	1.54013	−	2.66759i	0.688768	−	1.19298i	0.972237	−	0.233999i	$-0.0751813\pi$
$6$		0			0
$7$	1.32933	+	2.30247i	0.502441	+	0.870253i	0.999996	+	0.00282076i	$0.000897877\pi$
$7$	1.32933	+	2.30247i	0.502441	+	0.870253i	−0.497555	+	0.867432i	$0.665769\pi$
$8$	−5.01568			−1.77331
$9$		0			0
$10$	7.57064			2.39405
$11$	1.71717	+	2.97423i	0.517746	+	0.896763i	0.999788	+	0.0206144i	$0.00656223\pi$
$11$	1.71717	+	2.97423i	0.517746	+	0.896763i	−0.482041	+	0.876149i	$0.660104\pi$
$12$		0			0
$13$	1.67198	−	2.89595i	0.463723	−	0.803192i	−0.535420	−	0.844586i	$-0.679847\pi$
$13$	1.67198	−	2.89595i	0.463723	−	0.803192i	0.999143	+	0.0413939i	$0.0131799\pi$
$14$	−3.26722	+	5.65899i	−0.873202	+	1.51243i
$15$		0			0
$16$	−2.12302	−	3.67717i	−0.530754	−	0.919293i
$17$	2.57282			0.624000			0.312000	−	0.950082i	$-0.399001\pi$
$17$	2.57282			0.624000			0.312000	+	0.950082i	$0.399001\pi$
$18$		0			0
$19$	−2.09676			−0.481030			−0.240515	−	0.970645i	$-0.577316\pi$
$19$	−2.09676			−0.481030			−0.240515	+	0.970645i	$0.577316\pi$
$20$	6.22325	+	10.7790i	1.39156	+	2.41026i
$21$		0			0
$22$	−4.22044	+	7.31002i	−0.899802	+	1.55850i
$23$	−0.267222	+	0.462842i	−0.0557196	+	0.0965093i	−0.892540	−	0.450969i	$-0.851079\pi$
$23$	−0.267222	+	0.462842i	−0.0557196	+	0.0965093i	0.836820	+	0.547478i	$0.184412\pi$
$24$		0			0
$25$	−2.24401	−	3.88674i	−0.448802	−	0.777348i
$26$	8.21874			1.61183
$27$		0			0
$28$	−10.7430			−2.03023
$29$	−1.26545	−	2.19182i	−0.234988	−	0.407010i	0.724281	−	0.689504i	$-0.242172\pi$
$29$	−1.26545	−	2.19182i	−0.234988	−	0.407010i	−0.959269	+	0.282494i	$0.908838\pi$
$30$		0			0
$31$	−3.85735	+	6.68113i	−0.692801	+	1.19997i	0.278116	+	0.960548i	$0.410290\pi$
$31$	−3.85735	+	6.68113i	−0.692801	+	1.19997i	−0.970917	+	0.239418i	$0.923043\pi$
$32$	0.202245	−	0.350299i	0.0357522	−	0.0619247i
$33$		0			0
$34$	3.16172	+	5.47626i	0.542231	+	0.939171i
$35$	8.18939			1.38426
$36$		0			0
$37$	−10.2957			−1.69260			−0.846298	−	0.532709i	$-0.821174\pi$
$37$	−10.2957			−1.69260			−0.846298	+	0.532709i	$0.821174\pi$
$38$	−2.57670	−	4.46298i	−0.417996	−	0.723991i
$39$		0			0
$40$	−7.72481	+	13.3798i	−1.22140	+	2.11553i
$41$	2.44250	−	4.23054i	0.381455	−	0.660699i	−0.609816	−	0.792543i	$-0.708756\pi$
$41$	2.44250	−	4.23054i	0.381455	−	0.660699i	0.991270	+	0.131844i	$0.0420898\pi$
$42$		0			0
$43$	−1.37075	−	2.37420i	−0.209037	−	0.362062i	0.742375	−	0.669985i	$-0.233699\pi$
$43$	−1.37075	−	2.37420i	−0.209037	−	0.362062i	−0.951411	+	0.307923i	$0.900366\pi$
$44$	−13.8772			−2.09207
$45$		0			0
$46$	−1.31355			−0.193673
$47$	2.82900	+	4.89997i	0.412652	+	0.714734i	0.995179	−	0.0980775i	$-0.0312693\pi$
$47$	2.82900	+	4.89997i	0.412652	+	0.714734i	−0.582527	+	0.812811i	$0.697936\pi$
$48$		0			0
$49$	−0.0342555	+	0.0593322i	−0.00489364	+	0.00847603i
$50$	5.51530	−	9.55279i	0.779982	−	1.35097i
$51$		0			0
$52$	6.75601	+	11.7018i	0.936890	+	1.62274i
$53$	6.42657			0.882758			0.441379	−	0.897321i	$-0.354489\pi$
$53$	6.42657			0.882758			0.441379	+	0.897321i	$0.354489\pi$
$54$		0			0
$55$	10.5787			1.42643
$56$	−6.66751	−	11.5485i	−0.890984	−	1.54323i
$57$		0			0
$58$	3.11020	−	5.38703i	0.408390	−	0.707351i
$59$	−0.827475	+	1.43323i	−0.107728	+	0.186590i	−0.914850	−	0.403795i	$-0.867691\pi$
$59$	−0.827475	+	1.43323i	−0.107728	+	0.186590i	0.807121	+	0.590385i	$0.201024\pi$
$60$		0			0
$61$	−7.18610	−	12.4467i	−0.920086	−	1.59364i	−0.799279	−	0.600960i	$-0.794785\pi$
$61$	−7.18610	−	12.4467i	−0.920086	−	1.59364i	−0.120808	−	0.992676i	$-0.538548\pi$
$62$	−18.9611			−2.40806
$63$		0			0
$64$	−7.49791			−0.937239
$65$	−5.15013	−	8.92029i	−0.638795	−	1.10643i
$66$		0			0
$67$	2.93949	−	5.09135i	0.359116	−	0.622007i	−0.628697	−	0.777650i	$-0.716412\pi$
$67$	2.93949	−	5.09135i	0.359116	−	0.622007i	0.987813	+	0.155643i	$0.0497449\pi$
$68$	−5.19803	+	9.00325i	−0.630354	+	1.09180i
$69$		0			0
$70$	10.0639	+	17.4312i	1.20287	+	2.08343i
$71$	14.8163			1.75837			0.879184	−	0.476483i	$-0.158089\pi$
$71$	14.8163			1.75837			0.879184	+	0.476483i	$0.158089\pi$
$72$		0			0
$73$	1.88140			0.220201			0.110101	−	0.993920i	$-0.464883\pi$
$73$	1.88140			0.220201			0.110101	+	0.993920i	$0.464883\pi$
$74$	−12.6523	−	21.9144i	−1.47080	−	2.54750i
$75$		0			0
$76$	4.23623	−	7.33736i	0.485928	−	0.841653i
$77$	−4.56538	+	7.90748i	−0.520274	+	0.901141i
$78$		0			0
$79$	−8.59674	−	14.8900i	−0.967209	−	1.67526i	−0.703558	−	0.710637i	$-0.748407\pi$
$79$	−8.59674	−	14.8900i	−0.967209	−	1.67526i	−0.263651	−	0.964618i	$-0.584927\pi$
$80$	−13.0789			−1.46227
$81$		0			0
$82$	12.0063			1.32588
$83$	−1.98439	−	3.43707i	−0.217815	−	0.377267i	0.736324	−	0.676629i	$-0.236560\pi$
$83$	−1.98439	−	3.43707i	−0.217815	−	0.377267i	−0.954140	+	0.299361i	$0.903226\pi$
$84$		0			0
$85$	3.96248	−	6.86321i	0.429791	−	0.744420i
$86$	3.36900	−	5.83528i	0.363289	−	0.629235i
$87$		0			0
$88$	−8.61278	−	14.9178i	−0.918126	−	1.59024i
$89$	5.09880			0.540471			0.270236	−	0.962794i	$-0.412898\pi$
$89$	5.09880			0.540471			0.270236	+	0.962794i	$0.412898\pi$
$90$		0			0
$91$	8.89047			0.931974
$92$	−1.07977	−	1.87022i	−0.112574	−	0.194984i
$93$		0			0
$94$	−6.95308	+	12.0431i	−0.717156	+	1.24215i
$95$	−3.22929	+	5.59330i	−0.331318	+	0.573860i
$96$		0			0
$97$	5.31594	+	9.20748i	0.539752	+	0.934878i	0.998917	+	0.0465267i	$0.0148153\pi$
$97$	5.31594	+	9.20748i	0.539752	+	0.934878i	−0.459165	+	0.888351i	$0.651851\pi$
$98$	−0.168385			−0.0170095
$99$		0			0
$100$	18.1349			1.81349
$101$	−2.82904	−	4.90005i	−0.281500	−	0.487573i	0.690254	−	0.723567i	$-0.257499\pi$
$101$	−2.82904	−	4.90005i	−0.281500	−	0.487573i	−0.971755	+	0.235994i	$0.924165\pi$
$102$		0			0
$103$	−5.18527	+	8.98115i	−0.510920	+	0.884939i	0.489000	+	0.872284i	$0.337362\pi$
$103$	−5.18527	+	8.98115i	−0.510920	+	0.884939i	−0.999920	+	0.0126554i	$0.995972\pi$
$104$	−8.38611	+	14.5252i	−0.822326	+	1.42431i
$105$		0			0
$106$	7.89758	+	13.6790i	0.767081	+	1.32862i
$107$	−14.2457			−1.37719			−0.688594	−	0.725147i	$-0.741772\pi$
$107$	−14.2457			−1.37719			−0.688594	+	0.725147i	$0.741772\pi$
$108$		0			0
$109$	5.76064			0.551769			0.275884	−	0.961191i	$-0.411029\pi$
$109$	5.76064			0.551769			0.275884	+	0.961191i	$0.411029\pi$
$110$	13.0001	+	22.5168i	1.23951	+	2.14689i
$111$		0			0
$112$	5.64439	−	9.77638i	0.533345	−	0.923781i
$113$	5.70835	−	9.88715i	0.536996	−	0.930104i	−0.462068	−	0.886845i	$-0.652892\pi$
$113$	5.70835	−	9.88715i	0.536996	−	0.930104i	0.999064	−	0.0432598i	$-0.0137743\pi$
$114$		0			0
$115$	0.823114	+	1.42568i	0.0767558	+	0.132945i
$116$	10.2267			0.949521
$117$		0			0
$118$	−4.06752			−0.374445
$119$	3.42013	+	5.92384i	0.313523	+	0.543038i
$120$		0			0
$121$	−0.397348	+	0.688227i	−0.0361225	+	0.0625661i
$122$	17.6619	−	30.5914i	1.59904	−	2.76961i
$123$		0			0
$124$	−15.5865	−	26.9966i	−1.39971	−	2.42437i
$125$	1.57703			0.141054
$126$		0			0
$127$	2.59019			0.229843			0.114921	−	0.993375i	$-0.463338\pi$
$127$	2.59019			0.229843			0.114921	+	0.993375i	$0.463338\pi$
$128$	−9.61864	−	16.6600i	−0.850175	−	1.47255i
$129$		0			0
$130$	12.6579	−	21.9242i	1.11017	−	1.92288i
$131$	2.20549	−	3.82003i	0.192695	−	0.333757i	−0.753448	−	0.657508i	$-0.771611\pi$
$131$	2.20549	−	3.82003i	0.192695	−	0.333757i	0.946142	+	0.323751i	$0.104944\pi$
$132$		0			0
$133$	−2.78730	−	4.82774i	−0.241689	−	0.418618i
$134$	14.4493			1.24823
$135$		0			0
$136$	−12.9044			−1.10655
$137$	−9.08384	−	15.7337i	−0.776085	−	1.34422i	−0.934183	−	0.356795i	$-0.883869\pi$
$137$	−9.08384	−	15.7337i	−0.776085	−	1.34422i	0.158098	−	0.987423i	$-0.449464\pi$
$138$		0			0
$139$	−0.978972	+	1.69563i	−0.0830353	+	0.143821i	−0.904552	−	0.426363i	$-0.859795\pi$
$139$	−0.978972	+	1.69563i	−0.0830353	+	0.143821i	0.821517	+	0.570184i	$0.193128\pi$
$140$	−16.5456	+	28.6578i	−1.39836	+	2.42202i
$141$		0			0
$142$	18.2076	+	31.5365i	1.52795	+	2.64649i
$143$	11.4843			0.960364
$144$		0			0
$145$	−7.79582			−0.647407
$146$	2.31204	+	4.00457i	0.191346	+	0.331421i
$147$		0			0
$148$	20.8010	−	36.0284i	1.70983	−	2.96151i
$149$	−3.65759	+	6.33514i	−0.299642	+	0.518995i	−0.976054	−	0.217528i	$-0.930201\pi$
$149$	−3.65759	+	6.33514i	−0.299642	+	0.518995i	0.676412	+	0.736523i	$0.263534\pi$
$150$		0			0
$151$	−2.42549	−	4.20108i	−0.197384	−	0.341879i	0.750296	−	0.661103i	$-0.229911\pi$
$151$	−2.42549	−	4.20108i	−0.197384	−	0.341879i	−0.947679	+	0.319224i	$0.896578\pi$
$152$	10.5167			0.853017
$153$		0			0
$154$	−22.4415			−1.80839
$155$	11.8817	+	20.5796i	0.954357	+	1.65300i
$156$		0			0
$157$	−0.738351	+	1.27886i	−0.0589269	+	0.102064i	−0.893984	−	0.448099i	$-0.852101\pi$
$157$	−0.738351	+	1.27886i	−0.0589269	+	0.102064i	0.835057	+	0.550163i	$0.185435\pi$
$158$	21.1290	−	36.5965i	1.68093	−	2.91146i
$159$		0			0
$160$	−0.622969	−	1.07901i	−0.0492500	−	0.0853035i
$161$	−1.42091			−0.111983
$162$		0			0
$163$	−17.2536			−1.35141			−0.675703	−	0.737174i	$-0.736160\pi$
$163$	−17.2536			−1.35141			−0.675703	+	0.737174i	$0.736160\pi$
$164$	9.86949	+	17.0945i	0.770678	+	1.33485i
$165$		0			0
$166$	4.87722	−	8.44759i	0.378546	−	0.655660i
$167$	−3.42018	+	5.92393i	−0.264662	+	0.458407i	−0.967475	−	0.252967i	$-0.918594\pi$
$167$	−3.42018	+	5.92393i	−0.264662	+	0.458407i	0.702813	+	0.711374i	$0.251927\pi$
$168$		0			0
$169$	0.908979	+	1.57440i	0.0699214	+	0.121107i
$170$	19.4779			1.49388
$171$		0			0
$172$	11.0776			0.844661
$173$	11.9837	+	20.7564i	0.911103	+	1.57808i	0.812509	+	0.582949i	$0.198101\pi$
$173$	11.9837	+	20.7564i	0.911103	+	1.57808i	0.0985945	+	0.995128i	$0.468565\pi$
$174$		0			0
$175$	5.96608	−	10.3335i	0.450993	−	0.781143i
$176$	7.29116	−	12.6287i	0.549592	−	0.951921i
$177$		0			0
$178$	6.26588	+	10.8528i	0.469648	+	0.813454i
$179$	−20.5722			−1.53764			−0.768820	−	0.639466i	$-0.779156\pi$
$179$	−20.5722			−1.53764			−0.768820	+	0.639466i	$0.779156\pi$
$180$		0			0
$181$	−15.4701			−1.14989			−0.574943	−	0.818194i	$-0.694976\pi$
$181$	−15.4701			−1.14989			−0.574943	+	0.818194i	$0.694976\pi$
$182$	10.9254	+	18.9234i	0.809848	+	1.40270i
$183$		0			0
$184$	1.34030	−	2.32147i	0.0988083	−	0.171141i
$185$	−15.8567	+	27.4646i	−1.16581	+	2.01924i
$186$		0			0
$187$	4.41797	+	7.65214i	0.323074	+	0.559580i
$188$	−22.8624			−1.66741
$189$		0			0
$190$	−15.8738			−1.15161
$191$	5.47542	+	9.48371i	0.396188	+	0.686217i	0.993252	−	0.115976i	$-0.0369996\pi$
$191$	5.47542	+	9.48371i	0.396188	+	0.686217i	−0.597064	+	0.802193i	$0.703666\pi$
$192$		0			0
$193$	−0.572426	+	0.991470i	−0.0412041	+	0.0713676i	−0.885892	−	0.463892i	$-0.846453\pi$
$193$	−0.572426	+	0.991470i	−0.0412041	+	0.0713676i	0.844688	+	0.535259i	$0.179786\pi$
$194$	−13.0655	+	22.6300i	−0.938045	+	1.62474i
$195$		0			0
$196$	−0.138417	−	0.239745i	−0.00988693	−	0.0171247i
$197$	−5.04195			−0.359224			−0.179612	−	0.983738i	$-0.557484\pi$
$197$	−5.04195			−0.359224			−0.179612	+	0.983738i	$0.557484\pi$
$198$		0			0
$199$	13.7258			0.972997			0.486499	−	0.873681i	$-0.338274\pi$
$199$	13.7258			0.972997			0.486499	+	0.873681i	$0.338274\pi$
$200$	11.2552	+	19.4946i	0.795866	+	1.37848i
$201$		0			0
$202$	6.95320	−	12.0433i	0.489225	−	0.847363i
$203$	3.36440	−	5.82732i	0.236135	−	0.408997i
$204$		0			0
$205$	−7.52355	−	13.0312i	−0.525468	−	0.910137i
$206$	−25.4886			−1.77588
$207$		0			0
$208$	−14.1985			−0.984492
$209$	−3.60050	−	6.23625i	−0.249052	−	0.431370i
$210$		0			0
$211$	2.91757	−	5.05337i	0.200854	−	0.347888i	−0.747950	−	0.663755i	$-0.768962\pi$
$211$	2.91757	−	5.05337i	0.200854	−	0.347888i	0.948804	+	0.315866i	$0.102295\pi$
$212$	−12.9840	+	22.4890i	−0.891746	+	1.54455i
$213$		0			0
$214$	−17.5065	−	30.3222i	−1.19672	−	2.07278i
$215$	−8.44451			−0.575911
$216$		0			0
$217$	−20.5108			−1.39237
$218$	7.07922	+	12.2616i	0.479465	+	0.830458i
$219$		0			0
$220$	−21.3728	+	37.0187i	−1.44095	+	2.49580i
$221$	4.30170	−	7.45075i	0.289363	−	0.501192i
$222$		0			0
$223$	−4.36434	−	7.55926i	−0.292258	−	0.506205i	0.682085	−	0.731272i	$-0.261073\pi$
$223$	−4.36434	−	7.55926i	−0.292258	−	0.506205i	−0.974343	+	0.225067i	$0.927740\pi$
$224$	1.07541			0.0718536
$225$		0			0
$226$	28.0598			1.86651
$227$	−12.1413	−	21.0293i	−0.805844	−	1.39576i	−0.915720	−	0.401817i	$-0.868379\pi$
$227$	−12.1413	−	21.0293i	−0.805844	−	1.39576i	0.109876	−	0.993945i	$-0.464955\pi$
$228$		0			0
$229$	−9.07571	+	15.7196i	−0.599740	+	1.03878i	0.393119	+	0.919488i	$0.371396\pi$
$229$	−9.07571	+	15.7196i	−0.599740	+	1.03878i	−0.992859	+	0.119293i	$0.961937\pi$
$230$	−2.02304	+	3.50401i	−0.133395	+	0.231048i
$231$		0			0
$232$	6.34708	+	10.9935i	0.416706	+	0.721756i
$233$	10.5380			0.690367			0.345183	−	0.938535i	$-0.387817\pi$
$233$	10.5380			0.690367			0.345183	+	0.938535i	$0.387817\pi$
$234$		0			0
$235$	17.4281			1.13688
$236$	−3.34360	−	5.79129i	−0.217650	−	0.376981i
$237$		0			0
$238$	−8.40597	+	14.5596i	−0.544878	+	0.943756i
$239$	4.76830	−	8.25894i	0.308436	−	0.534226i	−0.669585	−	0.742736i	$-0.733528\pi$
$239$	4.76830	−	8.25894i	0.308436	−	0.534226i	0.978020	+	0.208509i	$0.0668612\pi$
$240$		0			0
$241$	3.51864	+	6.09446i	0.226656	+	0.392579i	0.956815	−	0.290698i	$-0.0938875\pi$
$241$	3.51864	+	6.09446i	0.226656	+	0.392579i	−0.730159	+	0.683277i	$0.760554\pi$
$242$	−1.95320			−0.125556
$243$		0			0
$244$	58.0742			3.71782
$245$	0.105516	+	0.182759i	0.00674116	+	0.0116760i
$246$		0			0
$247$	−3.50574	+	6.07212i	−0.223065	+	0.386360i
$248$	19.3472	−	33.5104i	1.22855	−	2.12791i
$249$		0			0
$250$	1.93801	+	3.35673i	0.122570	+	0.212298i
$251$	−15.5870			−0.983843			−0.491921	−	0.870640i	$-0.663705\pi$
$251$	−15.5870			−0.983843			−0.491921	+	0.870640i	$0.663705\pi$
$252$		0			0
$253$	−1.83546			−0.115395
$254$	3.18308	+	5.51325i	0.199724	+	0.345932i
$255$		0			0
$256$	16.1427	−	27.9599i	1.00892	−	1.74750i
$257$	6.09489	−	10.5567i	0.380189	−	0.658506i	−0.610900	−	0.791708i	$-0.709192\pi$
$257$	6.09489	−	10.5567i	0.380189	−	0.658506i	0.991089	+	0.133201i	$0.0425257\pi$
$258$		0			0
$259$	−13.6864	−	23.7055i	−0.850430	−	1.47299i
$260$	41.6206			2.58120
$261$		0			0
$262$	10.8413			0.669776
$263$	−3.44482	−	5.96660i	−0.212417	−	0.367916i	0.740054	−	0.672548i	$-0.234800\pi$
$263$	−3.44482	−	5.96660i	−0.212417	−	0.367916i	−0.952470	+	0.304632i	$0.901467\pi$
$264$		0			0
$265$	9.89777	−	17.1434i	0.608015	−	1.05311i
$266$	6.85059	−	11.8656i	0.420037	−	0.727525i
$267$		0			0
$268$	11.8777	+	20.5728i	0.725545	+	1.25668i
$269$	−7.05875			−0.430380			−0.215190	−	0.976572i	$-0.569037\pi$
$269$	−7.05875			−0.430380			−0.215190	+	0.976572i	$0.569037\pi$
$270$		0			0
$271$	23.7575			1.44316			0.721581	−	0.692330i	$-0.243416\pi$
$271$	23.7575			1.44316			0.721581	+	0.692330i	$0.243416\pi$
$272$	−5.46213	−	9.46070i	−0.331191	−	0.573639i
$273$		0			0
$274$	22.3262	−	38.6701i	1.34877	−	2.33614i
$275$	7.70669	−	13.3484i	0.464731	−	0.804938i
$276$		0			0
$277$	0.0522319	+	0.0904682i	0.00313831	+	0.00543571i	0.867590	−	0.497280i	$-0.165668\pi$
$277$	0.0522319	+	0.0904682i	0.00313831	+	0.00543571i	−0.864452	+	0.502715i	$0.832334\pi$
$278$	−4.81221			−0.288617
$279$		0			0
$280$	−41.0754			−2.45472
$281$	4.07610	+	7.06001i	0.243160	+	0.421165i	0.961613	−	0.274411i	$-0.0884828\pi$
$281$	4.07610	+	7.06001i	0.243160	+	0.421165i	−0.718453	+	0.695576i	$0.755149\pi$
$282$		0			0
$283$	−11.8080	+	20.4520i	−0.701912	+	1.21575i	0.265882	+	0.964006i	$0.414337\pi$
$283$	−11.8080	+	20.4520i	−0.701912	+	1.21575i	−0.967794	+	0.251742i	$0.918996\pi$
$284$	−29.9343	+	51.8477i	−1.77627	+	3.07659i
$285$		0			0
$286$	14.1130	+	24.4444i	0.834518	+	1.44543i
$287$	12.9876			0.766634
$288$		0			0
$289$	−10.3806			−0.610624
$290$	−9.58024	−	16.5935i	−0.562571	−	0.974402i
$291$		0			0
$292$	−3.80111	+	6.58372i	−0.222443	+	0.385283i
$293$	10.8129	−	18.7285i	0.631695	−	1.09413i	−0.355510	−	0.934672i	$-0.615693\pi$
$293$	10.8129	−	18.7285i	0.631695	−	1.09413i	0.987205	−	0.159455i	$-0.0509738\pi$
$294$		0			0
$295$	2.54884	+	4.41472i	0.148399	+	0.257035i
$296$	51.6398			3.00150
$297$		0			0
$298$	−17.9792			−1.04151
$299$	0.893579	+	1.54772i	0.0516770	+	0.0895072i
$300$		0			0
$301$	3.64435	−	6.31221i	0.210057	−	0.363830i
$302$	5.96135	−	10.3254i	0.343037	−	0.594158i
$303$		0			0
$304$	4.45146	+	7.71016i	0.255309	+	0.442208i
$305$	−44.2702			−2.53490
$306$		0			0
$307$	16.3599			0.933711			0.466855	−	0.884334i	$-0.345387\pi$
$307$	16.3599			0.933711			0.466855	+	0.884334i	$0.345387\pi$
$308$	−18.4475	−	31.9520i	−1.05114	−	1.82063i
$309$		0			0
$310$	−29.2026	+	50.5804i	−1.65860	+	2.87277i
$311$	3.87743	−	6.71591i	0.219869	−	0.380824i	−0.734899	−	0.678177i	$-0.762770\pi$
$311$	3.87743	−	6.71591i	0.219869	−	0.380824i	0.954768	+	0.297353i	$0.0961037\pi$
$312$		0			0
$313$	−7.70903	−	13.3524i	−0.435740	−	0.754724i	0.561616	−	0.827398i	$-0.310180\pi$
$313$	−7.70903	−	13.3524i	−0.435740	−	0.754724i	−0.997356	+	0.0726744i	$0.976847\pi$
$314$	−3.62942			−0.204820
$315$		0			0
$316$	69.4742			3.90823
$317$	−4.31810	−	7.47917i	−0.242529	−	0.420072i	0.718905	−	0.695108i	$-0.244644\pi$
$317$	−4.31810	−	7.47917i	−0.242529	−	0.420072i	−0.961434	+	0.275036i	$0.911310\pi$
$318$		0			0
$319$	4.34598	−	7.52745i	0.243328	−	0.421456i
$320$	−11.5478	+	20.0013i	−0.645540	+	1.11811i
$321$		0			0
$322$	−1.74615	−	3.02442i	−0.0973090	−	0.168544i
$323$	−5.39459			−0.300163
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−21.2029	−	36.7244i	−1.17432	−	2.03398i
$327$		0			0
$328$	−12.2508	+	21.2190i	−0.676438	+	1.17163i
$329$	−7.52136	+	13.0274i	−0.414666	+	0.718223i
$330$		0			0
$331$	−10.2723	−	17.7921i	−0.564614	−	0.977941i	−0.997085	−	0.0762930i	$-0.975692\pi$
$331$	−10.2723	−	17.7921i	−0.564614	−	0.977941i	0.432471	−	0.901648i	$-0.357642\pi$
$332$	16.0368			0.880133
$333$		0			0
$334$	−16.8122			−0.919921
$335$	−9.05441	−	15.6827i	−0.494695	−	0.856837i
$336$		0			0
$337$	−7.98910	+	13.8375i	−0.435194	+	0.753778i	−0.997311	−	0.0732792i	$-0.976654\pi$
$337$	−7.98910	+	13.8375i	−0.435194	+	0.753778i	0.562117	+	0.827057i	$0.309987\pi$
$338$	−2.23408	+	3.86954i	−0.121518	+	0.210475i
$339$		0			0
$340$	16.0113	+	27.7324i	0.868335	+	1.50400i
$341$	−26.4949			−1.43478
$342$		0			0
$343$	18.4285			0.995047
$344$	6.87522	+	11.9082i	0.370687	+	0.642049i
$345$		0			0
$346$	−29.4534	+	51.0148i	−1.58342	+	2.74257i
$347$	4.90214	−	8.49075i	0.263161	−	0.455807i	−0.703920	−	0.710280i	$-0.748568\pi$
$347$	4.90214	−	8.49075i	0.263161	−	0.455807i	0.967080	+	0.254472i	$0.0819018\pi$
$348$		0			0
$349$	4.71749	+	8.17093i	0.252521	+	0.437380i	0.964219	−	0.265106i	$-0.0854069\pi$
$349$	4.71749	+	8.17093i	0.252521	+	0.437380i	−0.711698	+	0.702486i	$0.752074\pi$
$350$	29.3267			1.56758
$351$		0			0
$352$	1.38916			0.0740424
$353$	1.69258	+	2.93164i	0.0900870	+	0.156035i	0.907548	−	0.419949i	$-0.137952\pi$
$353$	1.69258	+	2.93164i	0.0900870	+	0.156035i	−0.817461	+	0.575985i	$0.804619\pi$
$354$		0			0
$355$	22.8190	−	39.5237i	1.21111	−	2.09770i
$356$	−10.3014	+	17.8426i	−0.545975	+	0.945656i
$357$		0			0
$358$	−25.2811	−	43.7881i	−1.33615	−	2.31427i
$359$	35.2273			1.85923			0.929614	−	0.368535i	$-0.120141\pi$
$359$	35.2273			1.85923			0.929614	+	0.368535i	$0.120141\pi$
$360$		0			0
$361$	−14.6036			−0.768610
$362$	−19.0112	−	32.9283i	−0.999205	−	1.73067i
$363$		0			0
$364$	−17.9620	+	31.1111i	−0.941464	+	1.63066i
$365$	2.89760	−	5.01879i	0.151667	−	0.262696i
$366$		0			0
$367$	15.7727	+	27.3191i	0.823329	+	1.42605i	0.903190	+	0.429242i	$0.141219\pi$
$367$	15.7727	+	27.3191i	0.823329	+	1.42605i	−0.0798606	+	0.996806i	$0.525448\pi$
$368$	2.26927			0.118294
$369$		0			0
$370$	−77.9447			−4.05215
$371$	8.54306	+	14.7970i	0.443534	+	0.768223i
$372$		0			0
$373$	−7.22116	+	12.5074i	−0.373897	+	0.647609i	−0.990161	−	0.139931i	$-0.955312\pi$
$373$	−7.22116	+	12.5074i	−0.373897	+	0.647609i	0.616264	+	0.787540i	$0.288645\pi$
$374$	−10.8584	+	18.8074i	−0.561476	+	0.972505i
$375$		0			0
$376$	−14.1894	−	24.5767i	−0.731760	−	1.26745i
$377$	−8.46320			−0.435877
$378$		0			0
$379$	1.00099			0.0514176			0.0257088	−	0.999669i	$-0.491816\pi$
$379$	1.00099			0.0514176			0.0257088	+	0.999669i	$0.491816\pi$
$380$	−13.0487	−	22.6010i	−0.669384	−	1.15941i
$381$		0			0
$382$	−13.4574	+	23.3090i	−0.688543	+	1.19259i
$383$	−2.05867	+	3.56572i	−0.105193	+	0.182200i	−0.913817	−	0.406126i	$-0.866879\pi$
$383$	−2.05867	+	3.56572i	−0.105193	+	0.182200i	0.808624	+	0.588326i	$0.200213\pi$
$384$		0			0
$385$	14.0626	+	24.3571i	0.716696	+	1.24135i
$386$	−2.81380			−0.143219
$387$		0			0
$388$	−42.9605			−2.18099
$389$	7.75996	+	13.4406i	0.393445	+	0.681468i	0.992901	−	0.118940i	$-0.0379497\pi$
$389$	7.75996	+	13.4406i	0.393445	+	0.681468i	−0.599456	+	0.800408i	$0.704616\pi$
$390$		0			0
$391$	−0.687514	+	1.19081i	−0.0347691	+	0.0602218i
$392$	0.171815	−	0.297591i	0.00867794	−	0.0150306i
$393$		0			0
$394$	−6.19602	−	10.7318i	−0.312151	−	0.540662i
$395$	−52.9605			−2.66473
$396$		0			0
$397$	−1.54893			−0.0777384			−0.0388692	−	0.999244i	$-0.512376\pi$
$397$	−1.54893			−0.0777384			−0.0388692	+	0.999244i	$0.512376\pi$
$398$	16.8676	+	29.2155i	0.845495	+	1.46444i
$399$		0			0
$400$	−9.52814	+	16.5032i	−0.476407	+	0.825161i
$401$	−3.97369	+	6.88263i	−0.198437	+	0.343702i	−0.948022	−	0.318206i	$-0.896920\pi$
$401$	−3.97369	+	6.88263i	−0.198437	+	0.343702i	0.749585	+	0.661908i	$0.230253\pi$
$402$		0			0
$403$	12.8988	+	22.3414i	0.642536	+	1.11290i
$404$	22.8628			1.13747
$405$		0			0
$406$	16.5380			0.820766
$407$	−17.6794	−	30.6216i	−0.876336	−	1.51786i
$408$		0			0
$409$	−13.2277	+	22.9110i	−0.654068	+	1.13288i	0.328059	+	0.944657i	$0.393606\pi$
$409$	−13.2277	+	22.9110i	−0.654068	+	1.13288i	−0.982127	+	0.188221i	$0.939728\pi$
$410$	18.4913	−	32.0279i	0.913221	−	1.58174i
$411$		0			0
$412$	−20.9523	−	36.2904i	−1.03224	−	1.78790i
$413$	−4.39996			−0.216508
$414$		0			0
$415$	−12.2249			−0.600097
$416$	−0.676299	−	1.17138i	−0.0331583	−	0.0574319i
$417$		0			0
$418$	8.84927	−	15.3274i	0.432832	−	0.749687i
$419$	−19.1700	+	33.2034i	−0.936516	+	1.62209i	−0.164607	+	0.986359i	$0.552636\pi$
$419$	−19.1700	+	33.2034i	−0.936516	+	1.62209i	−0.771909	+	0.635733i	$0.780698\pi$
$420$		0			0
$421$	−3.67225	−	6.36052i	−0.178974	−	0.309993i	0.762555	−	0.646923i	$-0.223945\pi$
$421$	−3.67225	−	6.36052i	−0.178974	−	0.309993i	−0.941530	+	0.336930i	$0.890611\pi$
$422$	14.3415			0.698134
$423$		0			0
$424$	−32.2337			−1.56540
$425$	−5.77343	−	9.99987i	−0.280052	−	0.485065i
$426$		0			0
$427$	19.1055	−	33.0916i	0.924578	−	1.60142i
$428$	28.7816	−	49.8512i	1.39121	−	2.40965i
$429$		0			0
$430$	−10.3774	−	17.9742i	−0.500443	−	0.866793i
$431$	−15.8463			−0.763289			−0.381644	−	0.924309i	$-0.624642\pi$
$431$	−15.8463			−0.763289			−0.381644	+	0.924309i	$0.624642\pi$
$432$		0			0
$433$	−23.8507			−1.14619			−0.573097	−	0.819488i	$-0.694258\pi$
$433$	−23.8507			−1.14619			−0.573097	+	0.819488i	$0.694258\pi$
$434$	−25.2056	−	43.6575i	−1.20991	−	2.09562i
$435$		0			0
$436$	−11.6386	+	20.1586i	−0.557387	+	0.965423i
$437$	0.560301	−	0.970470i	0.0268028	−	0.0464239i
$438$		0			0
$439$	10.7350	+	18.5935i	0.512352	+	0.887420i	0.999897	+	0.0143222i	$0.00455904\pi$
$439$	10.7350	+	18.5935i	0.512352	+	0.887420i	−0.487545	+	0.873098i	$0.662108\pi$
$440$	−53.0593			−2.52950
$441$		0			0
$442$	21.1453			1.00578
$443$	−15.7740	−	27.3213i	−0.749443	−	1.29807i	−0.948090	−	0.318003i	$-0.896988\pi$
$443$	−15.7740	−	27.3213i	−0.749443	−	1.29807i	0.198646	−	0.980071i	$-0.436345\pi$
$444$		0			0
$445$	7.85282	−	13.6015i	0.372259	−	0.644772i
$446$	10.7266	−	18.5791i	0.507921	−	0.879744i
$447$		0			0
$448$	−9.96723	−	17.2637i	−0.470907	−	0.815635i
$449$	20.7898			0.981130			0.490565	−	0.871405i	$-0.336790\pi$
$449$	20.7898			0.981130			0.490565	+	0.871405i	$0.336790\pi$
$450$		0			0
$451$	16.7768			0.789988
$452$	23.0659	+	39.9513i	1.08493	+	1.87915i
$453$		0			0
$454$	29.8407	−	51.6855i	1.40049	−	2.42572i
$455$	13.6925	−	23.7161i	0.641914	−	1.11183i
$456$		0			0
$457$	8.71387	+	15.0929i	0.407618	+	0.706014i	0.994622	−	0.103569i	$-0.0330263\pi$
$457$	8.71387	+	15.0929i	0.407618	+	0.706014i	−0.587005	+	0.809584i	$0.699693\pi$
$458$	−44.6124			−2.08460
$459$		0			0
$460$	−6.65196			−0.310149
$461$	15.5022	+	26.8507i	0.722011	+	1.25056i	0.960193	+	0.279339i	$0.0901154\pi$
$461$	15.5022	+	26.8507i	0.722011	+	1.25056i	−0.238181	+	0.971221i	$0.576551\pi$
$462$		0			0
$463$	−3.24398	+	5.61873i	−0.150760	+	0.261125i	−0.931507	−	0.363723i	$-0.881506\pi$
$463$	−3.24398	+	5.61873i	−0.150760	+	0.261125i	0.780747	+	0.624847i	$0.214839\pi$
$464$	−5.37313	+	9.30653i	−0.249441	+	0.432045i
$465$		0			0
$466$	12.9501	+	22.4302i	0.599901	+	1.03906i
$467$	1.94390			0.0899530			0.0449765	−	0.998988i	$-0.485679\pi$
$467$	1.94390			0.0899530			0.0449765	+	0.998988i	$0.485679\pi$
$468$		0			0
$469$	15.6303			0.721738
$470$	21.4173	+	37.0959i	0.987907	+	1.71111i
$471$		0			0
$472$	4.15035	−	7.18862i	0.191035	−	0.330883i
$473$	4.70761	−	8.15381i	0.216456	−	0.374913i
$474$		0			0
$475$	4.70516	+	8.14957i	0.215887	+	0.373928i
$476$	−27.6397			−1.26686
$477$		0			0
$478$	23.4390			1.07207
$479$	−0.664695	−	1.15129i	−0.0303707	−	0.0526036i	0.850441	−	0.526071i	$-0.176335\pi$
$479$	−0.664695	−	1.15129i	−0.0303707	−	0.0526036i	−0.880811	+	0.473468i	$0.843002\pi$
$480$		0			0
$481$	−17.2141	+	29.8157i	−0.784896	+	1.35948i
$482$	−8.64808	+	14.9789i	−0.393909	+	0.682271i
$483$		0			0
$484$	−1.60558	−	2.78094i	−0.0729807	−	0.126406i
$485$	32.7490			1.48705
$486$		0			0
$487$	21.2040			0.960844			0.480422	−	0.877037i	$-0.340484\pi$
$487$	21.2040			0.960844			0.480422	+	0.877037i	$0.340484\pi$
$488$	36.0432	+	62.4287i	1.63160	+	2.82601i
$489$		0			0
$490$	−0.259336	+	0.449183i	−0.0117156	+	0.0202920i
$491$	−13.5051	+	23.3915i	−0.609475	+	1.05564i	0.381852	+	0.924224i	$0.375287\pi$
$491$	−13.5051	+	23.3915i	−0.609475	+	1.05564i	−0.991327	+	0.131419i	$0.958047\pi$
$492$		0			0
$493$	−3.25576	−	5.63915i	−0.146632	−	0.253975i
$494$	−17.2328			−0.775338
$495$		0			0
$496$	32.7569			1.47083
$497$	19.6958	+	34.1141i	0.883476	+	1.53022i
$498$		0			0
$499$	−7.51946	+	13.0241i	−0.336617	+	0.583038i	−0.983794	−	0.179302i	$-0.942616\pi$
$499$	−7.51946	+	13.0241i	−0.336617	+	0.583038i	0.647177	+	0.762340i	$0.275949\pi$
$500$	−3.18618	+	5.51863i	−0.142490	+	0.246801i
$501$		0			0
$502$	−19.1548	−	33.1771i	−0.854920	−	1.48076i
$503$	4.60650			0.205394			0.102697	−	0.994713i	$-0.467253\pi$
$503$	4.60650			0.205394			0.102697	+	0.994713i	$0.467253\pi$
$504$		0			0
$505$	−17.4284			−0.775554
$506$	−2.25559	−	3.90680i	−0.100273	−	0.173678i
$507$		0			0
$508$	−5.23314	+	9.06406i	−0.232183	+	0.402153i
$509$	−14.8983	+	25.8047i	−0.660357	+	1.14377i	0.320165	+	0.947362i	$0.396262\pi$
$509$	−14.8983	+	25.8047i	−0.660357	+	1.14377i	−0.980522	+	0.196410i	$0.937072\pi$
$510$		0			0
$511$	2.50101	+	4.33187i	0.110638	+	0.191631i
$512$	40.8760			1.80648
$513$		0			0
$514$	29.9599			1.32147
$515$	15.9720	+	27.6643i	0.703810	+	1.21904i
$516$		0			0
$517$	−9.71574	+	16.8282i	−0.427298	+	0.740102i
$518$	33.6382	−	58.2631i	1.47798	−	2.55993i
$519$		0			0
$520$	25.8314	+	44.7413i	1.13278	+	1.96204i
$521$	−11.7621			−0.515306			−0.257653	−	0.966237i	$-0.582949\pi$
$521$	−11.7621			−0.515306			−0.257653	+	0.966237i	$0.582949\pi$
$522$		0			0
$523$	29.3853			1.28493			0.642464	−	0.766316i	$-0.277912\pi$
$523$	29.3853			1.28493			0.642464	+	0.766316i	$0.277912\pi$
$524$	8.91180	+	15.4357i	0.389314	+	0.674311i
$525$		0			0
$526$	8.46663	−	14.6646i	0.369163	−	0.639409i
$527$	−9.92426	+	17.1893i	−0.432308	+	0.748779i
$528$		0			0
$529$	11.3572	+	19.6712i	0.493791	+	0.855270i
$530$	48.6533			2.11336
$531$		0			0
$532$	22.5254			0.976601
$533$	−8.16762	−	14.1467i	−0.353779	−	0.612763i
$534$		0			0
$535$	−21.9403	+	38.0017i	−0.948562	+	1.64296i
$536$	−14.7436	+	25.5366i	−0.636825	+	1.10301i
$537$		0			0
$538$	−8.67446	−	15.0246i	−0.373983	−	0.647757i
$539$	−0.235290			−0.0101347
$540$		0			0
$541$	−22.9116			−0.985046			−0.492523	−	0.870300i	$-0.663925\pi$
$541$	−22.9116			−0.985046			−0.492523	+	0.870300i	$0.663925\pi$
$542$	29.1954	+	50.5679i	1.25405	+	2.17208i
$543$		0			0
$544$	0.520340	−	0.901256i	0.0223094	−	0.0386410i
$545$	8.87214	−	15.3670i	0.380041	−	0.658250i
$546$		0			0
$547$	6.87885	+	11.9145i	0.294118	+	0.509428i	0.974779	−	0.223171i	$-0.0716407\pi$
$547$	6.87885	+	11.9145i	0.294118	+	0.509428i	−0.680661	+	0.732598i	$0.738307\pi$
$548$	73.4107			3.13595
$549$		0			0
$550$	37.8829			1.61533
$551$	2.65334	+	4.59572i	0.113036	+	0.195784i
$552$		0			0
$553$	22.8559	−	39.5875i	0.971931	−	1.68343i
$554$	−0.128375	+	0.222352i	−0.00545413	+	0.00944682i
$555$		0			0
$556$	−3.95576	−	6.85158i	−0.167762	−	0.290572i
$557$	21.9041			0.928105			0.464053	−	0.885808i	$-0.346395\pi$
$557$	21.9041			0.928105			0.464053	+	0.885808i	$0.346395\pi$
$558$		0			0
$559$	−9.16742			−0.387741
$560$	−17.3862	−	30.1138i	−0.734702	−	1.27254i
$561$		0			0
$562$	−10.0182	+	17.3520i	−0.422592	+	0.731951i
$563$	−7.28421	+	12.6166i	−0.306993	+	0.531727i	−0.977703	−	0.209992i	$-0.932656\pi$
$563$	−7.28421	+	12.6166i	−0.306993	+	0.531727i	0.670710	+	0.741720i	$0.265989\pi$
$564$		0			0
$565$	−17.5832	−	30.4550i	−0.739731	−	1.28125i
$566$	−58.0431			−2.43973
$567$		0			0
$568$	−74.3137			−3.11813
$569$	11.1785	+	19.3618i	0.468628	+	0.811687i	0.999357	−	0.0358544i	$-0.0114153\pi$
$569$	11.1785	+	19.3618i	0.468628	+	0.811687i	−0.530729	+	0.847541i	$0.678082\pi$
$570$		0			0
$571$	7.71307	−	13.3594i	0.322782	−	0.559075i	−0.658279	−	0.752774i	$-0.728715\pi$
$571$	7.71307	−	13.3594i	0.322782	−	0.559075i	0.981061	+	0.193699i	$0.0620486\pi$
$572$	−23.2024	+	40.1878i	−0.970143	+	1.68034i
$573$		0			0
$574$	15.9604	+	27.6442i	0.666174	+	1.15385i
$575$	2.39860			0.100028
$576$		0			0
$577$	32.8081			1.36582			0.682909	−	0.730503i	$-0.260714\pi$
$577$	32.8081			1.36582			0.682909	+	0.730503i	$0.260714\pi$
$578$	−12.7567	−	22.0952i	−0.530608	−	0.919040i
$579$		0			0
$580$	15.7504	−	27.2805i	0.654000	−	1.13276i
$581$	5.27584	−	9.13802i	0.218879	−	0.379109i
$582$		0			0
$583$	11.0355	+	19.1141i	0.457045	+	0.791625i
$584$	−9.43650			−0.390485
$585$		0			0
$586$	53.1515			2.19567
$587$	−15.1171	−	26.1836i	−0.623951	−	1.08071i	−0.988743	−	0.149625i	$-0.952193\pi$
$587$	−15.1171	−	26.1836i	−0.623951	−	1.08071i	0.364792	−	0.931089i	$-0.381140\pi$
$588$		0			0
$589$	8.08795	−	14.0087i	0.333258	−	0.577220i
$590$	−6.26451	+	10.8505i	−0.257906	+	0.446706i
$591$		0			0
$592$	21.8579	+	37.8589i	0.898353	+	1.55599i
$593$	41.1023			1.68787			0.843935	−	0.536446i	$-0.180234\pi$
$593$	41.1023			1.68787			0.843935	+	0.536446i	$0.180234\pi$
$594$		0			0
$595$	21.0698			0.863778
$596$	−14.7793	−	25.5986i	−0.605386	−	1.04856i
$597$		0			0
$598$	−2.19623	+	3.80398i	−0.0898105	+	0.155556i
$599$	−18.2753	+	31.6537i	−0.746707	+	1.29333i	0.202686	+	0.979244i	$0.435033\pi$
$599$	−18.2753	+	31.6537i	−0.746707	+	1.29333i	−0.949393	+	0.314091i	$0.898300\pi$
$600$		0			0
$601$	−1.97290	−	3.41717i	−0.0804764	−	0.139389i	0.822978	−	0.568073i	$-0.192311\pi$
$601$	−1.97290	−	3.41717i	−0.0804764	−	0.139389i	−0.903455	+	0.428684i	$0.858977\pi$
$602$	17.9141			0.730125
$603$		0			0
$604$	19.6015			0.797575
$605$	1.22394	+	2.11992i	0.0497601	+	0.0861870i
$606$		0			0
$607$	−5.00576	+	8.67023i	−0.203178	+	0.351914i	−0.949551	−	0.313614i	$-0.898460\pi$
$607$	−5.00576	+	8.67023i	−0.203178	+	0.351914i	0.746373	+	0.665528i	$0.231794\pi$
$608$	−0.424060	+	0.734494i	−0.0171979	+	0.0297877i
$609$		0			0
$610$	−54.4034	−	94.2294i	−2.20273	−	3.81524i
$611$	18.9201			0.765425
$612$		0			0
$613$	−18.7568			−0.757578			−0.378789	−	0.925483i	$-0.623659\pi$
$613$	−18.7568			−0.757578			−0.378789	+	0.925483i	$0.623659\pi$
$614$	20.1046	+	34.8223i	0.811357	+	1.40531i
$615$		0			0
$616$	22.8985	−	39.6614i	0.922608	−	1.59800i
$617$	11.5050	−	19.9273i	0.463175	−	0.802243i	−0.535942	−	0.844255i	$-0.680043\pi$
$617$	11.5050	−	19.9273i	0.463175	−	0.802243i	0.999117	+	0.0420119i	$0.0133767\pi$
$618$		0			0
$619$	−3.70701	−	6.42073i	−0.148997	−	0.258071i	0.781860	−	0.623454i	$-0.214271\pi$
$619$	−3.70701	−	6.42073i	−0.148997	−	0.258071i	−0.930857	+	0.365383i	$0.880938\pi$
$620$	−96.0211			−3.85630
$621$		0			0
$622$	19.0598			0.764229
$623$	6.77800	+	11.7398i	0.271555	+	0.470347i
$624$		0			0
$625$	13.6489	−	23.6406i	0.545956	−	0.945623i
$626$	18.9472	−	32.8175i	0.757281	−	1.31165i
$627$		0			0
$628$	−2.98348	−	5.16754i	−0.119054	−	0.206207i
$629$	−26.4889			−1.05618
$630$		0			0
$631$	−30.9924			−1.23379			−0.616894	−	0.787046i	$-0.711609\pi$
$631$	−30.9924			−1.23379			−0.616894	+	0.787046i	$0.711609\pi$
$632$	43.1185	+	74.6835i	1.71516	+	2.97075i
$633$		0			0
$634$	10.6130	−	18.3822i	0.421496	−	0.730052i
$635$	3.98924	−	6.90957i	0.158308	−	0.274198i
$636$		0			0
$637$	0.114549	+	0.198404i	0.00453859	+	0.00786106i
$638$	21.3630			0.845769
$639$		0			0
$640$	−59.2559			−2.34229
$641$	17.6731	+	30.6106i	0.698044	+	1.20905i	0.969144	+	0.246496i	$0.0792794\pi$
$641$	17.6731	+	30.6106i	0.698044	+	1.20905i	−0.271100	+	0.962551i	$0.587387\pi$
$642$		0			0
$643$	9.85047	−	17.0615i	0.388465	−	0.672840i	−0.603779	−	0.797152i	$-0.706339\pi$
$643$	9.85047	−	17.0615i	0.388465	−	0.672840i	0.992243	+	0.124312i	$0.0396723\pi$
$644$	2.87075	−	4.97229i	0.113124	−	0.195936i
$645$		0			0
$646$	−6.62938	−	11.4824i	−0.260830	−	0.451770i
$647$	46.8317			1.84114			0.920572	−	0.390572i	$-0.127723\pi$
$647$	46.8317			1.84114			0.920572	+	0.390572i	$0.127723\pi$
$648$		0			0
$649$	−5.68366			−0.223103
$650$	−18.4429	−	31.9441i	−0.723391	−	1.25295i
$651$		0			0
$652$	34.8586	−	60.3768i	1.36517	−	2.36454i
$653$	−8.66336	+	15.0054i	−0.339023	+	0.587206i	−0.984249	−	0.176786i	$-0.943430\pi$
$653$	−8.66336	+	15.0054i	−0.339023	+	0.587206i	0.645226	+	0.763992i	$0.276763\pi$
$654$		0			0
$655$	−6.79350	−	11.7667i	−0.265444	−	0.459762i
$656$	−20.7419			−0.809835
$657$		0			0
$658$	−36.9719			−1.44131
$659$	−21.8671	−	37.8749i	−0.851821	−	1.47540i	−0.879563	−	0.475782i	$-0.842165\pi$
$659$	−21.8671	−	37.8749i	−0.851821	−	1.47540i	0.0277419	−	0.999615i	$-0.491168\pi$
$660$		0			0
$661$	4.54343	−	7.86945i	0.176719	−	0.306086i	−0.764036	−	0.645174i	$-0.776785\pi$
$661$	4.54343	−	7.86945i	0.176719	−	0.306086i	0.940755	+	0.339088i	$0.110118\pi$
$662$	25.2470	−	43.7292i	0.981254	−	1.69958i
$663$		0			0
$664$	9.95308	+	17.2392i	0.386254	+	0.669012i
$665$	−17.1712			−0.665871
$666$		0			0
$667$	1.35262			0.0523737
$668$	−13.8200	−	23.9370i	−0.534713	−	0.926150i
$669$		0			0
$670$	22.2538	−	38.5448i	0.859740	−	1.48911i
$671$	24.6795	−	42.7462i	0.952743	−	1.65020i
$672$		0			0
$673$	−3.74834	−	6.49232i	−0.144488	−	0.250261i	0.784694	−	0.619884i	$-0.212820\pi$
$673$	−3.74834	−	6.49232i	−0.144488	−	0.250261i	−0.929182	+	0.369623i	$0.879487\pi$
$674$	−39.2711			−1.51266
$675$		0			0
$676$	−7.34587			−0.282534
$677$	−7.68128	−	13.3044i	−0.295215	−	0.511328i	0.679820	−	0.733379i	$-0.262058\pi$
$677$	−7.68128	−	13.3044i	−0.295215	−	0.511328i	−0.975035	+	0.222051i	$0.928725\pi$
$678$		0			0
$679$	−14.1333	+	24.4796i	−0.542387	+	0.939441i
$680$	−19.8745	+	34.4237i	−0.762153	+	1.32009i
$681$		0			0
$682$	−32.5595	−	56.3946i	−1.24677	−	2.15946i
$683$	6.62157			0.253367			0.126684	−	0.991943i	$-0.459567\pi$
$683$	6.62157			0.253367			0.126684	+	0.991943i	$0.459567\pi$
$684$		0			0
$685$	−55.9612			−2.13817
$686$	22.6467	+	39.2253i	0.864656	+	1.49763i
$687$		0			0
$688$	−5.82023	+	10.0809i	−0.221894	+	0.384332i
$689$	10.7451	−	18.6110i	0.409355	−	0.709024i
$690$		0			0
$691$	9.32843	+	16.1573i	0.354870	+	0.614653i	0.987096	−	0.160131i	$-0.0511918\pi$
$691$	9.32843	+	16.1573i	0.354870	+	0.614653i	−0.632226	+	0.774784i	$0.717858\pi$
$692$	−96.8457			−3.68152
$693$		0			0
$694$	24.0968			0.914704
$695$	3.01549	+	5.22298i	0.114384	+	0.198119i
$696$		0			0
$697$	6.28412	−	10.8844i	0.238028	−	0.412276i
$698$	−11.5946	+	20.0824i	−0.438862	+	0.760131i
$699$		0			0
$700$	24.1073	+	41.7551i	0.911170	+	1.57819i
$701$	24.8903			0.940092			0.470046	−	0.882642i	$-0.344237\pi$
$701$	24.8903			0.940092			0.470046	+	0.882642i	$0.344237\pi$
$702$		0			0
$703$	21.5876			0.814190
$704$	−12.8752	−	22.3005i	−0.485252	−	0.840481i
$705$		0			0
$706$	−4.16001	+	7.20535i	−0.156564	+	0.271177i
$707$	7.52149	−	13.0276i	0.282875	−	0.489953i
$708$		0			0
$709$	13.0894	+	22.6715i	0.491582	+	0.851445i	0.999953	−	0.00969346i	$-0.00308557\pi$
$709$	13.0894	+	22.6715i	0.491582	+	0.851445i	−0.508371	+	0.861138i	$0.669752\pi$
$710$	112.169			4.20961
$711$		0			0
$712$	−25.5739			−0.958424
$713$	−2.06154	−	3.57069i	−0.0772052	−	0.133723i
$714$		0			0
$715$	17.6873	−	30.6353i	0.661468	−	1.14570i
$716$	41.5634	−	71.9899i	1.55330	−	2.69039i
$717$		0			0
$718$	43.2907	+	74.9817i	1.61559	+	2.79829i
$719$	21.0290			0.784251			0.392125	−	0.919912i	$-0.371740\pi$
$719$	21.0290			0.784251			0.392125	+	0.919912i	$0.371740\pi$
$720$		0			0
$721$	−27.5718			−1.02683
$722$	−17.9463	−	31.0838i	−0.667891	−	1.15682i
$723$		0			0
$724$	31.2553	−	54.1358i	1.16159	−	2.01194i
$725$	−5.67935	+	9.83692i	−0.210926	+	0.365334i
$726$		0			0
$727$	−20.6978	−	35.8497i	−0.767640	−	1.32959i	−0.938839	−	0.344356i	$-0.888097\pi$
$727$	−20.6978	−	35.8497i	−0.767640	−	1.32959i	0.171199	−	0.985236i	$-0.445236\pi$
$728$	−44.5918			−1.65268
$729$		0			0
$730$	14.2434			0.527171
$731$	−3.52668	−	6.10838i	−0.130439	−	0.225927i
$732$		0			0
$733$	−16.8134	+	29.1216i	−0.621016	+	1.07563i	0.368281	+	0.929714i	$0.379946\pi$
$733$	−16.8134	+	29.1216i	−0.621016	+	1.07563i	−0.989297	+	0.145916i	$0.953387\pi$
$734$	−38.7660	+	67.1447i	−1.43088	+	2.47836i
$735$		0			0
$736$	0.108089	+	0.187215i	0.00398421	+	0.00690085i
$737$	20.1904			0.743724
$738$		0			0
$739$	−12.9454			−0.476202			−0.238101	−	0.971240i	$-0.576525\pi$
$739$	−12.9454			−0.476202			−0.238101	+	0.971240i	$0.576525\pi$
$740$	−64.0725	−	110.977i	−2.35535	−	4.07959i
$741$		0			0
$742$	−20.9970	+	36.3679i	−0.770826	+	1.33511i
$743$	0.0439646	−	0.0761489i	0.00161290	−	0.00279363i	−0.865218	−	0.501396i	$-0.832820\pi$
$743$	0.0439646	−	0.0761489i	0.00161290	−	0.00279363i	0.866831	+	0.498603i	$0.166153\pi$
$744$		0			0
$745$	11.2664	+	19.5139i	0.412767	+	0.714934i
$746$	−35.4962			−1.29961
$747$		0			0
$748$	−35.7036			−1.30545
$749$	−18.9373	−	32.8004i	−0.691955	−	1.19850i
$750$		0			0
$751$	−24.9480	+	43.2112i	−0.910366	+	1.57680i	−0.0968179	+	0.995302i	$0.530866\pi$
$751$	−24.9480	+	43.2112i	−0.910366	+	1.57680i	−0.813548	+	0.581498i	$0.802467\pi$
$752$	12.0120	−	20.8054i	0.438033	−	0.758696i
$753$		0			0
$754$	−10.4004	−	18.0140i	−0.378759	−	0.656031i
$755$	−14.9423			−0.543806
$756$		0			0
$757$	−11.8679			−0.431348			−0.215674	−	0.976465i	$-0.569195\pi$
$757$	−11.8679			−0.431348			−0.215674	+	0.976465i	$0.569195\pi$
$758$	1.23011	+	2.13062i	0.0446798	+	0.0773877i
$759$		0			0
$760$	16.1971	−	28.0542i	0.587530	−	1.01763i
$761$	−1.89515	+	3.28250i	−0.0686992	+	0.118990i	−0.898329	−	0.439323i	$-0.855218\pi$
$761$	−1.89515	+	3.28250i	−0.0686992	+	0.118990i	0.829630	+	0.558314i	$0.188552\pi$
$762$		0			0
$763$	7.65781	+	13.2637i	0.277231	+	0.480179i
$764$	−44.2494			−1.60089
$765$		0			0
$766$	−10.1196			−0.365634
$767$	2.76704	+	4.79265i	0.0999120	+	0.173053i
$768$		0			0
$769$	−3.13475	+	5.42955i	−0.113042	+	0.195795i	−0.916995	−	0.398898i	$-0.869393\pi$
$769$	−3.13475	+	5.42955i	−0.113042	+	0.195795i	0.803953	+	0.594692i	$0.202726\pi$
$770$	−34.5629	+	59.8646i	−1.24556	+	2.15737i
$771$		0			0
$772$	−2.31302	−	4.00626i	−0.0832473	−	0.144189i
$773$	−1.29536			−0.0465907			−0.0232954	−	0.999729i	$-0.507416\pi$
$773$	−1.29536			−0.0465907			−0.0232954	+	0.999729i	$0.507416\pi$
$774$		0			0
$775$	34.6237			1.24372
$776$	−26.6631	−	46.1818i	−0.957148	−	1.65783i
$777$		0			0
$778$	−19.0723	+	33.0343i	−0.683777	+	1.18434i
$779$	−5.12135	+	8.87044i	−0.183491	+	0.317816i
$780$		0			0
$781$	25.4421	+	44.0669i	0.910388	+	1.57684i
$782$	−3.37953			−0.120852
$783$		0			0
$784$	0.290900			0.0103893
$785$	2.27432	+	3.93923i	0.0811738

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22889 + 2.12851i) q^{2} +(-2.02036 + 3.49937i) q^{4} +(1.54013 - 2.66759i) q^{5} +(1.32933 + 2.30247i) q^{7} -5.01568 q^{8} +O(q^{10})\)	\(q+(1.22889 + 2.12851i) q^{2} +(-2.02036 + 3.49937i) q^{4} +(1.54013 - 2.66759i) q^{5} +(1.32933 + 2.30247i) q^{7} -5.01568 q^{8} +7.57064 q^{10} +(1.71717 + 2.97423i) q^{11} +(1.67198 - 2.89595i) q^{13} +(-3.26722 + 5.65899i) q^{14} +(-2.12302 - 3.67717i) q^{16} +2.57282 q^{17} -2.09676 q^{19} +(6.22325 + 10.7790i) q^{20} +(-4.22044 + 7.31002i) q^{22} +(-0.267222 + 0.462842i) q^{23} +(-2.24401 - 3.88674i) q^{25} +8.21874 q^{26} -10.7430 q^{28} +(-1.26545 - 2.19182i) q^{29} +(-3.85735 + 6.68113i) q^{31} +(0.202245 - 0.350299i) q^{32} +(3.16172 + 5.47626i) q^{34} +8.18939 q^{35} -10.2957 q^{37} +(-2.57670 - 4.46298i) q^{38} +(-7.72481 + 13.3798i) q^{40} +(2.44250 - 4.23054i) q^{41} +(-1.37075 - 2.37420i) q^{43} -13.8772 q^{44} -1.31355 q^{46} +(2.82900 + 4.89997i) q^{47} +(-0.0342555 + 0.0593322i) q^{49} +(5.51530 - 9.55279i) q^{50} +(6.75601 + 11.7018i) q^{52} +6.42657 q^{53} +10.5787 q^{55} +(-6.66751 - 11.5485i) q^{56} +(3.11020 - 5.38703i) q^{58} +(-0.827475 + 1.43323i) q^{59} +(-7.18610 - 12.4467i) q^{61} -18.9611 q^{62} -7.49791 q^{64} +(-5.15013 - 8.92029i) q^{65} +(2.93949 - 5.09135i) q^{67} +(-5.19803 + 9.00325i) q^{68} +(10.0639 + 17.4312i) q^{70} +14.8163 q^{71} +1.88140 q^{73} +(-12.6523 - 21.9144i) q^{74} +(4.23623 - 7.33736i) q^{76} +(-4.56538 + 7.90748i) q^{77} +(-8.59674 - 14.8900i) q^{79} -13.0789 q^{80} +12.0063 q^{82} +(-1.98439 - 3.43707i) q^{83} +(3.96248 - 6.86321i) q^{85} +(3.36900 - 5.83528i) q^{86} +(-8.61278 - 14.9178i) q^{88} +5.09880 q^{89} +8.89047 q^{91} +(-1.07977 - 1.87022i) q^{92} +(-6.95308 + 12.0431i) q^{94} +(-3.22929 + 5.59330i) q^{95} +(5.31594 + 9.20748i) q^{97} -0.168385 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

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