LMFDB - Embedded newform 729.2.c.d.487.3

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			487.3
Root			$-1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.d.244.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0864880 + 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(1.86828 + 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} -0.686728 q^{8} +O(q^{10})$	\(q+(-0.0864880 + 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(1.86828 + 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} -0.686728 q^{8} -0.646335 q^{10} +(1.24585 - 2.15787i) q^{11} +(0.382569 + 0.662630i) q^{13} +(-0.262188 - 0.454123i) q^{14} +(-1.91069 + 3.30940i) q^{16} +4.62278 q^{17} -0.611844 q^{19} +(-3.68066 + 6.37509i) q^{20} +(0.215502 + 0.373260i) q^{22} +(-3.26219 - 5.65028i) q^{23} +(-4.48095 + 7.76123i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(3.27545 - 5.67324i) q^{29} +(-3.27521 - 5.67283i) q^{31} +(-1.01723 - 1.76190i) q^{32} +(-0.399815 + 0.692500i) q^{34} -11.3274 q^{35} +4.95969 q^{37} +(0.0529171 - 0.0916552i) q^{38} +(-1.28300 - 2.22222i) q^{40} +(-2.63012 - 4.55550i) q^{41} +(-2.78529 + 4.82426i) q^{43} +4.90884 q^{44} +1.12856 q^{46} +(-0.553808 + 0.959223i) q^{47} +(-1.09499 - 1.89658i) q^{49} +(-0.775096 - 1.34251i) q^{50} +(-0.753692 + 1.30543i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(1.04091 - 1.80290i) q^{56} +(0.566573 + 0.981334i) q^{58} +(5.92588 + 10.2639i) q^{59} +(-4.09350 + 7.09015i) q^{61} +1.13307 q^{62} -7.29083 q^{64} +(-1.42949 + 2.47596i) q^{65} +(0.606169 + 1.04992i) q^{67} +(4.55362 + 7.88711i) q^{68} +(0.979682 - 1.69686i) q^{70} -4.91946 q^{71} +4.29945 q^{73} +(-0.428953 + 0.742969i) q^{74} +(-0.602691 - 1.04389i) q^{76} +(3.77679 + 6.54158i) q^{77} +(5.89730 - 10.2144i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(-4.50804 + 7.80815i) q^{83} +(8.63666 + 14.9591i) q^{85} +(-0.481788 - 0.834481i) q^{86} +(-0.855559 + 1.48187i) q^{88} +7.53885 q^{89} -2.31952 q^{91} +(6.42677 - 11.1315i) q^{92} +(-0.0957954 - 0.165923i) q^{94} +(-1.14310 - 1.97990i) q^{95} +(0.474177 - 0.821299i) q^{97} +0.378814 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0864880	+	0.149802i	−0.0611562	+	0.105926i	−0.894982	−	0.446101i	$-0.852812\pi$
$2$	−0.0864880	+	0.149802i	−0.0611562	+	0.105926i	0.833826	+	0.552027i	$0.186145\pi$
$3$		0			0
$3$		0			0
$4$	0.985040	+	1.70614i	0.492520	+	0.853069i
$5$	1.86828	+	3.23596i	0.835521	+	1.44716i	0.893606	+	0.448853i	$0.148167\pi$
$5$	1.86828	+	3.23596i	0.835521	+	1.44716i	−0.0580849	+	0.998312i	$0.518499\pi$
$6$		0			0
$7$	−1.51575	+	2.62535i	−0.572899	+	0.992291i	0.423367	+	0.905958i	$0.360848\pi$
$7$	−1.51575	+	2.62535i	−0.572899	+	0.992291i	−0.996266	+	0.0863324i	$0.972485\pi$
$8$	−0.686728			−0.242795
$9$		0			0
$10$	−0.646335			−0.204389
$11$	1.24585	−	2.15787i	0.375637	−	0.650623i	−0.614785	−	0.788695i	$-0.710757\pi$
$11$	1.24585	−	2.15787i	0.375637	−	0.650623i	0.990422	+	0.138072i	$0.0440905\pi$
$12$		0			0
$13$	0.382569	+	0.662630i	0.106106	+	0.183780i	0.914189	−	0.405287i	$-0.132828\pi$
$13$	0.382569	+	0.662630i	0.106106	+	0.183780i	−0.808084	+	0.589068i	$0.799495\pi$
$14$	−0.262188	−	0.454123i	−0.0700727	−	0.121369i
$15$		0			0
$16$	−1.91069	+	3.30940i	−0.477671	+	0.827351i
$17$	4.62278			1.12119			0.560595	−	0.828090i	$-0.310573\pi$
$17$	4.62278			1.12119			0.560595	+	0.828090i	$0.310573\pi$
$18$		0			0
$19$	−0.611844			−0.140367			−0.0701833	−	0.997534i	$-0.522358\pi$
$19$	−0.611844			−0.140367			−0.0701833	+	0.997534i	$0.522358\pi$
$20$	−3.68066	+	6.37509i	−0.823021	+	1.42551i
$21$		0			0
$22$	0.215502	+	0.373260i	0.0459451	+	0.0795793i
$23$	−3.26219	−	5.65028i	−0.680213	−	1.17816i	−0.974916	−	0.222575i	$-0.928554\pi$
$23$	−3.26219	−	5.65028i	−0.680213	−	1.17816i	0.294702	−	0.955589i	$-0.404779\pi$
$24$		0			0
$25$	−4.48095	+	7.76123i	−0.896190	+	1.55225i
$26$	−0.132351			−0.0259561
$27$		0			0
$28$	−5.97229			−1.12866
$29$	3.27545	−	5.67324i	0.608235	−	1.05349i	−0.383296	−	0.923626i	$-0.625211\pi$
$29$	3.27545	−	5.67324i	0.608235	−	1.05349i	0.991531	−	0.129869i	$-0.0414555\pi$
$30$		0			0
$31$	−3.27521	−	5.67283i	−0.588246	−	1.01887i	−0.994462	−	0.105094i	$-0.966486\pi$
$31$	−3.27521	−	5.67283i	−0.588246	−	1.01887i	0.406217	−	0.913777i	$-0.366848\pi$
$32$	−1.01723	−	1.76190i	−0.179823	−	0.311462i
$33$		0			0
$34$	−0.399815	+	0.692500i	−0.0685677	+	0.118763i
$35$	−11.3274			−1.91468
$36$		0			0
$37$	4.95969			0.815368			0.407684	−	0.913123i	$-0.366337\pi$
$37$	4.95969			0.815368			0.407684	+	0.913123i	$0.366337\pi$
$38$	0.0529171	−	0.0916552i	0.00858429	−	0.0148684i
$39$		0			0
$40$	−1.28300	−	2.22222i	−0.202860	−	0.351364i
$41$	−2.63012	−	4.55550i	−0.410756	−	0.711450i	0.584217	−	0.811598i	$-0.301402\pi$
$41$	−2.63012	−	4.55550i	−0.410756	−	0.711450i	−0.994973	+	0.100148i	$0.968068\pi$
$42$		0			0
$43$	−2.78529	+	4.82426i	−0.424752	+	0.735692i	−0.996397	−	0.0848086i	$-0.972972\pi$
$43$	−2.78529	+	4.82426i	−0.424752	+	0.735692i	0.571645	+	0.820501i	$0.306305\pi$
$44$	4.90884			0.740035
$45$		0			0
$46$	1.12856			0.166397
$47$	−0.553808	+	0.959223i	−0.0807812	+	0.139917i	−0.903586	−	0.428407i	$-0.859075\pi$
$47$	−0.553808	+	0.959223i	−0.0807812	+	0.139917i	0.822805	+	0.568324i	$0.192408\pi$
$48$		0			0
$49$	−1.09499	−	1.89658i	−0.156427	−	0.270940i
$50$	−0.775096	−	1.34251i	−0.109615	−	0.189859i
$51$		0			0
$52$	−0.753692	+	1.30543i	−0.104518	+	0.181031i
$53$	8.84310			1.21469			0.607346	−	0.794437i	$-0.292234\pi$
$53$	8.84310			1.21469			0.607346	+	0.794437i	$0.292234\pi$
$54$		0			0
$55$	9.31038			1.25541
$56$	1.04091	−	1.80290i	0.139097	−	0.240923i
$57$		0			0
$58$	0.566573	+	0.981334i	0.0743947	+	0.128855i
$59$	5.92588	+	10.2639i	0.771484	+	1.33625i	0.936750	+	0.350000i	$0.113818\pi$
$59$	5.92588	+	10.2639i	0.771484	+	1.33625i	−0.165266	+	0.986249i	$0.552848\pi$
$60$		0			0
$61$	−4.09350	+	7.09015i	−0.524119	+	0.907801i	0.475486	+	0.879723i	$0.342272\pi$
$61$	−4.09350	+	7.09015i	−0.524119	+	0.907801i	−0.999606	+	0.0280781i	$0.991061\pi$
$62$	1.13307			0.143900
$63$		0			0
$64$	−7.29083			−0.911354
$65$	−1.42949	+	2.47596i	−0.177307	+	0.307105i
$66$		0			0
$67$	0.606169	+	1.04992i	0.0740553	+	0.128268i	0.900675	−	0.434493i	$-0.143073\pi$
$67$	0.606169	+	1.04992i	0.0740553	+	0.128268i	−0.826620	+	0.562761i	$0.809739\pi$
$68$	4.55362	+	7.88711i	0.552208	+	0.956452i
$69$		0			0
$70$	0.979682	−	1.69686i	0.117094	−	0.202813i
$71$	−4.91946			−0.583833			−0.291916	−	0.956444i	$-0.594293\pi$
$71$	−4.91946			−0.583833			−0.291916	+	0.956444i	$0.594293\pi$
$72$		0			0
$73$	4.29945			0.503213			0.251606	−	0.967830i	$-0.419041\pi$
$73$	4.29945			0.503213			0.251606	+	0.967830i	$0.419041\pi$
$74$	−0.428953	+	0.742969i	−0.0498648	+	0.0863684i
$75$		0			0
$76$	−0.602691	−	1.04389i	−0.0691333	−	0.119742i
$77$	3.77679	+	6.54158i	0.430405	+	0.745483i
$78$		0			0
$79$	5.89730	−	10.2144i	0.663498	−	1.14921i	−0.316192	−	0.948695i	$-0.602404\pi$
$79$	5.89730	−	10.2144i	0.663498	−	1.14921i	0.979690	−	0.200518i	$-0.0642624\pi$
$80$	−14.2788			−1.59642
$81$		0			0
$82$	0.909895			0.100481
$83$	−4.50804	+	7.80815i	−0.494821	+	0.857056i	−0.999982	−	0.00596962i	$-0.998100\pi$
$83$	−4.50804	+	7.80815i	−0.494821	+	0.857056i	0.505161	+	0.863025i	$0.331433\pi$
$84$		0			0
$85$	8.63666	+	14.9591i	0.936777	+	1.62255i
$86$	−0.481788	−	0.834481i	−0.0519525	−	0.0899844i
$87$		0			0
$88$	−0.855559	+	1.48187i	−0.0912029	+	0.157968i
$89$	7.53885			0.799117			0.399558	−	0.916708i	$-0.369163\pi$
$89$	7.53885			0.799117			0.399558	+	0.916708i	$0.369163\pi$
$90$		0			0
$91$	−2.31952			−0.243151
$92$	6.42677	−	11.1315i	0.670037	−	1.16054i
$93$		0			0
$94$	−0.0957954	−	0.165923i	−0.00988055	−	0.0171136i
$95$	−1.14310	−	1.97990i	−0.117279	−	0.203134i
$96$		0			0
$97$	0.474177	−	0.821299i	0.0481454	−	0.0833903i	−0.840948	−	0.541115i	$-0.818002\pi$
$97$	0.474177	−	0.821299i	0.0481454	−	0.0833903i	0.889094	+	0.457725i	$0.151336\pi$
$98$	0.378814			0.0382659
$99$		0			0
$100$	−17.6557			−1.76557
$101$	2.80408	−	4.85680i	0.279016	−	0.483270i	−0.692124	−	0.721778i	$-0.743325\pi$
$101$	2.80408	−	4.85680i	0.279016	−	0.483270i	0.971140	+	0.238508i	$0.0766584\pi$
$102$		0			0
$103$	4.71251	+	8.16231i	0.464337	+	0.804256i	0.999171	−	0.0407012i	$-0.0129592\pi$
$103$	4.71251	+	8.16231i	0.464337	+	0.804256i	−0.534834	+	0.844957i	$0.679626\pi$
$104$	−0.262721	−	0.455046i	−0.0257619	−	0.0446210i
$105$		0			0
$106$	−0.764821	+	1.32471i	−0.0742860	+	0.128667i
$107$	−1.27825			−0.123573			−0.0617864	−	0.998089i	$-0.519680\pi$
$107$	−1.27825			−0.123573			−0.0617864	+	0.998089i	$0.519680\pi$
$108$		0			0
$109$	−7.40689			−0.709451			−0.354726	−	0.934970i	$-0.615426\pi$
$109$	−7.40689			−0.709451			−0.354726	+	0.934970i	$0.615426\pi$
$110$	−0.805236	+	1.39471i	−0.0767762	+	0.132980i
$111$		0			0
$112$	−5.79224	−	10.0325i	−0.547315	−	0.947978i
$113$	−4.67598	−	8.09904i	−0.439879	−	0.761893i	0.557800	−	0.829975i	$-0.311645\pi$
$113$	−4.67598	−	8.09904i	−0.439879	−	0.761893i	−0.997680	+	0.0680818i	$0.978312\pi$
$114$		0			0
$115$	12.1894	−	21.1126i	1.13666	−	1.96876i
$116$	12.9058			1.19827
$117$		0			0
$118$	−2.05007			−0.188724
$119$	−7.00698	+	12.1364i	−0.642329	+	1.11255i
$120$		0			0
$121$	2.39573	+	4.14952i	0.217793	+	0.377229i
$122$	−0.708077	−	1.22643i	−0.0641063	−	0.111035i
$123$		0			0
$124$	6.45243	−	11.1759i	0.579445	−	1.00363i
$125$	−14.8039			−1.32410
$126$		0			0
$127$	20.7968			1.84542			0.922710	−	0.385496i	$-0.125970\pi$
$127$	20.7968			1.84542			0.922710	+	0.385496i	$0.125970\pi$
$128$	2.66503	−	4.61597i	0.235558	−	0.407998i
$129$		0			0
$130$	−0.247268	−	0.428281i	−0.0216868	−	0.0375627i
$131$	0.327915	+	0.567965i	0.0286501	+	0.0496233i	0.879995	−	0.474983i	$-0.157546\pi$
$131$	0.327915	+	0.567965i	0.0286501	+	0.0496233i	−0.851345	+	0.524606i	$0.824212\pi$
$132$		0			0
$133$	0.927402	−	1.60631i	0.0804159	−	0.139284i
$134$	−0.209705			−0.0181158
$135$		0			0
$136$	−3.17460			−0.272219
$137$	−4.29380	+	7.43708i	−0.366844	+	0.635393i	−0.989070	−	0.147445i	$-0.952895\pi$
$137$	−4.29380	+	7.43708i	−0.366844	+	0.635393i	0.622226	+	0.782838i	$0.286228\pi$
$138$		0			0
$139$	−6.72307	−	11.6447i	−0.570243	−	0.987691i	−0.996541	−	0.0831074i	$-0.973516\pi$
$139$	−6.72307	−	11.6447i	−0.570243	−	0.987691i	0.426297	−	0.904583i	$-0.359818\pi$
$140$	−11.1579	−	19.3261i	−0.943016	−	1.63335i
$141$		0			0
$142$	0.425474	−	0.736943i	0.0357050	−	0.0618429i
$143$	1.90649			0.159429
$144$		0			0
$145$	24.4778			2.03277
$146$	−0.371851	+	0.644064i	−0.0307746	+	0.0533031i
$147$		0			0
$148$	4.88549	+	8.46192i	0.401585	+	0.695565i
$149$	−4.81103	−	8.33295i	−0.394135	−	0.682662i	0.598855	−	0.800857i	$-0.295623\pi$
$149$	−4.81103	−	8.33295i	−0.394135	−	0.682662i	−0.992990	+	0.118195i	$0.962289\pi$
$150$		0			0
$151$	3.56410	−	6.17320i	0.290042	−	0.502368i	−0.683777	−	0.729691i	$-0.739664\pi$
$151$	3.56410	−	6.17320i	0.290042	−	0.502368i	0.973819	+	0.227323i	$0.0729972\pi$
$152$	0.420170			0.0340803
$153$		0			0
$154$	−1.30659			−0.105288
$155$	12.2380	−	21.1969i	0.982983	−	1.70258i
$156$		0			0
$157$	−3.84288	−	6.65607i	−0.306696	−	0.531212i	0.670942	−	0.741510i	$-0.265890\pi$
$157$	−3.84288	−	6.65607i	−0.306696	−	0.531212i	−0.977637	+	0.210298i	$0.932557\pi$
$158$	1.02009	+	1.76685i	0.0811541	+	0.140563i
$159$		0			0
$160$	3.80095	−	6.58343i	0.300491	−	0.520466i
$161$	19.7786			1.55877
$162$		0			0
$163$	1.04750			0.0820465			0.0410232	−	0.999158i	$-0.486938\pi$
$163$	1.04750			0.0820465			0.0410232	+	0.999158i	$0.486938\pi$
$164$	5.18154	−	8.97470i	0.404611	−	0.700806i
$165$		0			0
$166$	−0.779782	−	1.35062i	−0.0605228	−	0.104829i
$167$	−4.17704	−	7.23484i	−0.323229	−	0.559849i	0.657923	−	0.753085i	$-0.271435\pi$
$167$	−4.17704	−	7.23484i	−0.323229	−	0.559849i	−0.981152	+	0.193236i	$0.938102\pi$
$168$		0			0
$169$	6.20728	−	10.7513i	0.477483	−	0.827025i
$170$	−2.98787			−0.229159
$171$		0			0
$172$	−10.9745			−0.836796
$173$	−10.9229	+	18.9190i	−0.830452	+	1.43839i	0.0672277	+	0.997738i	$0.478585\pi$
$173$	−10.9229	+	18.9190i	−0.830452	+	1.43839i	−0.897680	+	0.440648i	$0.854749\pi$
$174$		0			0
$175$	−13.5840	−	23.5282i	−1.02685	−	1.77856i
$176$	4.76085	+	8.24603i	0.358862	+	0.621568i
$177$		0			0
$178$	−0.652020	+	1.12933i	−0.0488710	+	0.0846470i
$179$	−9.08866			−0.679319			−0.339659	−	0.940549i	$-0.610312\pi$
$179$	−9.08866			−0.679319			−0.339659	+	0.940549i	$0.610312\pi$
$180$		0			0
$181$	−7.13077			−0.530026			−0.265013	−	0.964245i	$-0.585376\pi$
$181$	−7.13077			−0.530026			−0.265013	+	0.964245i	$0.585376\pi$
$182$	0.200610	−	0.347467i	0.0148702	−	0.0257560i
$183$		0			0
$184$	2.24024	+	3.88020i	0.165152	+	0.286052i
$185$	9.26609	+	16.0493i	0.681257	+	1.17997i
$186$		0			0
$187$	5.75929	−	9.97537i	0.421161	−	0.729472i
$188$	−2.18209			−0.159145
$189$		0			0
$190$	0.395456			0.0286894
$191$	−5.97781	+	10.3539i	−0.432539	+	0.749180i	−0.997091	−	0.0762174i	$-0.975716\pi$
$191$	−5.97781	+	10.3539i	−0.432539	+	0.749180i	0.564552	+	0.825398i	$0.309049\pi$
$192$		0			0
$193$	4.43682	+	7.68479i	0.319369	+	0.553164i	0.980357	−	0.197233i	$-0.0631957\pi$
$193$	4.43682	+	7.68479i	0.319369	+	0.553164i	−0.660987	+	0.750397i	$0.729862\pi$
$194$	0.0820212	+	0.142065i	0.00588878	+	0.0101997i
$195$		0			0
$196$	2.15722	−	3.73641i	0.154087	−	0.266886i
$197$	7.39790			0.527079			0.263539	−	0.964649i	$-0.415110\pi$
$197$	7.39790			0.527079			0.263539	+	0.964649i	$0.415110\pi$
$198$		0			0
$199$	−10.3837			−0.736084			−0.368042	−	0.929809i	$-0.619972\pi$
$199$	−10.3837			−0.736084			−0.368042	+	0.929809i	$0.619972\pi$
$200$	3.07719	−	5.32986i	0.217591	−	0.376878i
$201$		0			0
$202$	0.485038	+	0.840110i	0.0341271	+	0.0591099i
$203$	9.92951	+	17.1984i	0.696915	+	1.20709i
$204$		0			0
$205$	9.82761	−	17.0219i	0.686390	−	1.18886i
$206$	−1.63030			−0.113588
$207$		0			0
$208$	−2.92388			−0.202735
$209$	−0.762265	+	1.32028i	−0.0527269	+	0.0913257i
$210$		0			0
$211$	−10.4306	−	18.0663i	−0.718070	−	1.24373i	−0.961763	−	0.273882i	$-0.911692\pi$
$211$	−10.4306	−	18.0663i	−0.718070	−	1.24373i	0.243693	−	0.969852i	$-0.421641\pi$
$212$	8.71080	+	15.0875i	0.598260	+	1.03622i
$213$		0			0
$214$	0.110553	−	0.191483i	0.00755724	−	0.0130895i
$215$	−20.8148			−1.41956
$216$		0			0
$217$	19.8576			1.34802
$218$	0.640607	−	1.10956i	0.0433874	−	0.0751491i
$219$		0			0
$220$	9.17109	+	15.8848i	0.618315	+	1.07095i
$221$	1.76854	+	3.06319i	0.118965	+	0.206053i
$222$		0			0
$223$	−11.7892	+	20.4196i	−0.789466	+	1.36740i	0.136828	+	0.990595i	$0.456309\pi$
$223$	−11.7892	+	20.4196i	−0.789466	+	1.36740i	−0.926294	+	0.376801i	$0.877024\pi$
$224$	6.16747			0.412081
$225$		0			0
$226$	1.61766			0.107605
$227$	5.24207	−	9.07952i	0.347928	−	0.602629i	−0.637953	−	0.770075i	$-0.720219\pi$
$227$	5.24207	−	9.07952i	0.347928	−	0.602629i	0.985881	+	0.167446i	$0.0535520\pi$
$228$		0			0
$229$	6.94121	+	12.0225i	0.458688	+	0.794471i	0.998892	−	0.0470633i	$-0.0149862\pi$
$229$	6.94121	+	12.0225i	0.458688	+	0.794471i	−0.540204	+	0.841534i	$0.681653\pi$
$230$	2.10847	+	3.65197i	0.139028	+	0.240804i
$231$		0			0
$232$	−2.24934	+	3.89597i	−0.147676	+	0.255783i
$233$	7.59964			0.497869			0.248935	−	0.968520i	$-0.419920\pi$
$233$	7.59964			0.497869			0.248935	+	0.968520i	$0.419920\pi$
$234$		0			0
$235$	−4.13868			−0.269977
$236$	−11.6745	+	20.2207i	−0.759942	+	1.31626i
$237$		0			0
$238$	−1.21204	−	2.09931i	−0.0785648	−	0.136078i
$239$	−8.27934	−	14.3402i	−0.535546	−	0.927593i	−0.999137	−	0.0415436i	$-0.986772\pi$
$239$	−8.27934	−	14.3402i	−0.535546	−	0.927593i	0.463591	−	0.886050i	$-0.346561\pi$
$240$		0			0
$241$	7.25924	−	12.5734i	0.467609	−	0.809923i	−0.531706	−	0.846929i	$-0.678449\pi$
$241$	7.25924	−	12.5734i	0.467609	−	0.809923i	0.999315	+	0.0370064i	$0.0117822\pi$
$242$	−0.828806			−0.0532776
$243$		0			0
$244$	−16.1290			−1.03256
$245$	4.09150	−	7.08668i	0.261396	−	0.452751i
$246$		0			0
$247$	−0.234073	−	0.405426i	−0.0148937	−	0.0257966i
$248$	2.24918	+	3.89570i	0.142823	+	0.247377i
$249$		0			0
$250$	1.28036	−	2.21765i	0.0809769	−	0.140256i
$251$	9.05181			0.571345			0.285673	−	0.958327i	$-0.407783\pi$
$251$	9.05181			0.571345			0.285673	+	0.958327i	$0.407783\pi$
$252$		0			0
$253$	−16.2568			−1.02205
$254$	−1.79867	+	3.11540i	−0.112859	+	0.195477i
$255$		0			0
$256$	−6.82984	−	11.8296i	−0.426865	−	0.739352i
$257$	−4.84994	−	8.40034i	−0.302531	−	0.523999i	0.674178	−	0.738569i	$-0.264498\pi$
$257$	−4.84994	−	8.40034i	−0.302531	−	0.523999i	−0.976709	+	0.214570i	$0.931165\pi$
$258$		0			0
$259$	−7.51764	+	13.0209i	−0.467124	+	0.809082i
$260$	−5.63243			−0.349309
$261$		0			0
$262$	−0.113443			−0.00700852
$263$	13.4276	−	23.2573i	0.827983	−	1.43411i	−0.0716358	−	0.997431i	$-0.522822\pi$
$263$	13.4276	−	23.2573i	0.827983	−	1.43411i	0.899618	−	0.436677i	$-0.143845\pi$
$264$		0			0
$265$	16.5214	+	28.6159i	1.01490	+	1.75786i
$266$	0.160418	+	0.277852i	0.00983587	+	0.0170362i
$267$		0			0
$268$	−1.19420	+	2.06842i	−0.0729474	+	0.126349i
$269$	11.7388			0.715729			0.357865	−	0.933774i	$-0.383505\pi$
$269$	11.7388			0.715729			0.357865	+	0.933774i	$0.383505\pi$
$270$		0			0
$271$	0.144576			0.00878238			0.00439119	−	0.999990i	$-0.498602\pi$
$271$	0.144576			0.00878238			0.00439119	+	0.999990i	$0.498602\pi$
$272$	−8.83268	+	15.2987i	−0.535560	+	0.927617i
$273$		0			0
$274$	−0.742724	−	1.28644i	−0.0448696	−	0.0777165i
$275$	11.1652	+	19.3386i	0.673285	+	1.16616i
$276$		0			0
$277$	0.507212	−	0.878518i	0.0304754	−	0.0527850i	−0.850385	−	0.526160i	$-0.823631\pi$
$277$	0.507212	−	0.878518i	0.0304754	−	0.0527850i	0.880861	+	0.473375i	$0.156965\pi$
$278$	2.32586			0.139496
$279$		0			0
$280$	7.77883			0.464874
$281$	13.7647	−	23.8412i	0.821135	−	1.42225i	−0.0837029	−	0.996491i	$-0.526675\pi$
$281$	13.7647	−	23.8412i	0.821135	−	1.42225i	0.904838	−	0.425756i	$-0.139992\pi$
$282$		0			0
$283$	13.4014	+	23.2120i	0.796633	+	1.37981i	0.921797	+	0.387673i	$0.126721\pi$
$283$	13.4014	+	23.2120i	0.796633	+	1.37981i	−0.125164	+	0.992136i	$0.539946\pi$
$284$	−4.84587	−	8.39329i	−0.287549	−	0.498050i
$285$		0			0
$286$	−0.164889	+	0.285596i	−0.00975007	+	0.0168876i
$287$	15.9464			0.941286
$288$		0			0
$289$	4.37012			0.257066
$290$	−2.11704	+	3.66682i	−0.124317	+	0.215323i
$291$		0			0
$292$	4.23513	+	7.33546i	0.247842	+	0.429275i
$293$	−9.32863	−	16.1577i	−0.544984	−	0.943941i	−0.998608	−	0.0527472i	$-0.983202\pi$
$293$	−9.32863	−	16.1577i	−0.544984	−	0.943941i	0.453624	−	0.891193i	$-0.350131\pi$
$294$		0			0
$295$	−22.1424	+	38.3518i	−1.28918	+	2.23293i
$296$	−3.40596			−0.197967
$297$		0			0
$298$	1.66439			0.0964153
$299$	2.49603	−	4.32324i	0.144349	−	0.250020i
$300$		0			0
$301$	−8.44359	−	14.6247i	−0.486680	−	0.842955i
$302$	0.616504	+	1.06782i	0.0354758	+	0.0614459i
$303$		0			0
$304$	1.16904	−	2.02484i	0.0670491	−	0.116132i
$305$	−30.5913			−1.75165
$306$		0			0
$307$	33.7893			1.92845			0.964227	−	0.265077i	$-0.0853973\pi$
$307$	33.7893			1.92845			0.964227	+	0.265077i	$0.0853973\pi$
$308$	−7.44057	+	12.8874i	−0.423966	+	0.734330i
$309$		0			0
$310$	2.11689	+	3.66655i	0.120231	+	0.208246i
$311$	−17.3433	−	30.0395i	−0.983448	−	1.70338i	−0.648642	−	0.761094i	$-0.724663\pi$
$311$	−17.3433	−	30.0395i	−0.983448	−	1.70338i	−0.334806	−	0.942287i	$-0.608671\pi$
$312$		0			0
$313$	−1.67019	+	2.89285i	−0.0944047	+	0.163514i	−0.909360	−	0.416010i	$-0.863428\pi$
$313$	−1.67019	+	2.89285i	−0.0944047	+	0.163514i	0.814955	+	0.579524i	$0.196761\pi$
$314$	1.32945			0.0750254
$315$		0			0
$316$	23.2363			1.30714
$317$	−15.5164	+	26.8752i	−0.871488	+	1.50946i	−0.0110301	+	0.999939i	$0.503511\pi$
$317$	−15.5164	+	26.8752i	−0.871488	+	1.50946i	−0.860458	+	0.509522i	$0.829822\pi$
$318$		0			0
$319$	−8.16142	−	14.1360i	−0.456952	−	0.791463i
$320$	−13.6213	−	23.5928i	−0.761455	−	1.31888i
$321$		0			0
$322$	−1.71061	+	2.96287i	−0.0953288	+	0.165114i
$323$	−2.82842			−0.157378
$324$		0			0
$325$	−6.85710			−0.380363
$326$	−0.0905961	+	0.156917i	−0.00501765	+	0.00869083i
$327$		0			0
$328$	1.80618	+	3.12839i	0.0997295	+	0.172736i
$329$	−1.67887	−	2.90788i	−0.0925590	−	0.160317i
$330$		0			0
$331$	−1.63584	+	2.83336i	−0.0899138	+	0.155735i	−0.907475	−	0.420107i	$-0.861992\pi$
$331$	−1.63584	+	2.83336i	−0.0899138	+	0.155735i	0.817561	+	0.575842i	$0.195326\pi$
$332$	−17.7624			−0.974837
$333$		0			0
$334$	1.44505			0.0790699
$335$	−2.26499	+	3.92308i	−0.123750	+	0.214341i
$336$		0			0
$337$	−3.18290	−	5.51295i	−0.173384	−	0.300310i	0.766217	−	0.642582i	$-0.222137\pi$
$337$	−3.18290	−	5.51295i	−0.173384	−	0.300310i	−0.939601	+	0.342272i	$0.888803\pi$
$338$	1.07371	+	1.85972i	0.0584021	+	0.101155i
$339$		0			0
$340$	−17.0149	+	29.4707i	−0.922763	+	1.59827i
$341$	−16.3217			−0.883868
$342$		0			0
$343$	−14.5816			−0.787331
$344$	1.91273	−	3.31295i	0.103128	−	0.178623i
$345$		0			0
$346$	−1.88940	−	3.27253i	−0.101575	−	0.175932i
$347$	−4.39620	−	7.61445i	−0.236001	−	0.408765i	0.723562	−	0.690259i	$-0.242503\pi$
$347$	−4.39620	−	7.61445i	−0.236001	−	0.408765i	−0.959563	+	0.281494i	$0.909170\pi$
$348$		0			0
$349$	−7.20011	+	12.4710i	−0.385413	+	0.667555i	−0.991826	−	0.127595i	$-0.959274\pi$
$349$	−7.20011	+	12.4710i	−0.385413	+	0.667555i	0.606413	+	0.795150i	$0.292608\pi$
$350$	4.69941			0.251194
$351$		0			0
$352$	−5.06926			−0.270192
$353$	16.6002	−	28.7525i	0.883542	−	1.53034i	0.0361653	−	0.999346i	$-0.488486\pi$
$353$	16.6002	−	28.7525i	0.883542	−	1.53034i	0.847376	−	0.530993i	$-0.178181\pi$
$354$		0			0
$355$	−9.19094	−	15.9192i	−0.487804	−	0.844902i
$356$	7.42607	+	12.8623i	0.393581	+	0.681702i
$357$		0			0
$358$	0.786060	−	1.36150i	0.0415446	−	0.0719573i
$359$	−4.94514			−0.260995			−0.130497	−	0.991449i	$-0.541657\pi$
$359$	−4.94514			−0.260995			−0.130497	+	0.991449i	$0.541657\pi$
$360$		0			0
$361$	−18.6256			−0.980297
$362$	0.616726	−	1.06820i	0.0324144	−	0.0561434i
$363$		0			0
$364$	−2.28482	−	3.95742i	−0.119757	−	0.207425i
$365$	8.03258	+	13.9128i	0.420445	+	0.728231i
$366$		0			0
$367$	1.24623	−	2.15853i	0.0650525	−	0.112674i	−0.831665	−	0.555278i	$-0.812612\pi$
$367$	1.24623	−	2.15853i	0.0650525	−	0.112674i	0.896717	+	0.442604i	$0.145945\pi$
$368$	24.9321			1.29967
$369$		0			0
$370$	−3.20562			−0.166652
$371$	−13.4039	+	23.2163i	−0.695896	+	1.20533i
$372$		0			0
$373$	14.0238	+	24.2899i	0.726124	+	1.25768i	0.958510	+	0.285060i	$0.0920136\pi$
$373$	14.0238	+	24.2899i	0.726124	+	1.25768i	−0.232385	+	0.972624i	$0.574653\pi$
$374$	0.996218	+	1.72550i	0.0515132	+	0.0892235i
$375$		0			0
$376$	0.380316	−	0.658726i	0.0196133	−	0.0339712i
$377$	5.01234			0.258149
$378$		0			0
$379$	5.13991			0.264019			0.132010	−	0.991248i	$-0.457857\pi$
$379$	5.13991			0.264019			0.132010	+	0.991248i	$0.457857\pi$
$380$	2.25199	−	3.90056i	0.115525	−	0.200095i
$381$		0			0
$382$	−1.03402	−	1.79097i	−0.0529050	−	0.0916341i
$383$	−0.0223364	−	0.0386879i	−0.00114134	−	0.00197686i	0.865454	−	0.500988i	$-0.167030\pi$
$383$	−0.0223364	−	0.0386879i	−0.00114134	−	0.00197686i	−0.866596	+	0.499011i	$0.833697\pi$
$384$		0			0
$385$	−14.1122	+	24.4430i	−0.719224	+	1.24573i
$386$	−1.53493			−0.0781256
$387$		0			0
$388$	1.86833			0.0948502
$389$	10.4911	−	18.1712i	0.531921	−	0.921315i	−0.467384	−	0.884054i	$-0.654803\pi$
$389$	10.4911	−	18.1712i	0.531921	−	0.921315i	0.999306	−	0.0372607i	$-0.0118632\pi$
$390$		0			0
$391$	−15.0804	−	26.1200i	−0.762648	−	1.32095i
$392$	0.751960	+	1.30243i	0.0379797	+	0.0657828i
$393$		0			0
$394$	−0.639830	+	1.10822i	−0.0322341	+	0.0558312i
$395$	44.0713			2.21747
$396$		0			0
$397$	−0.00245641			−0.000123284			−6.16419e−5	−	1.00000i	$-0.500020\pi$
$397$	−0.00245641			−0.000123284			−6.16419e−5		1.00000i	$0.500020\pi$
$398$	0.898069	−	1.55550i	0.0450161	−	0.0779703i
$399$		0			0
$400$	−17.1234	−	29.6586i	−0.856169	−	1.48293i
$401$	12.6282	+	21.8726i	0.630620	+	1.09227i	0.987425	+	0.158088i	$0.0505328\pi$
$401$	12.6282	+	21.8726i	0.630620	+	1.09227i	−0.356805	+	0.934179i	$0.616134\pi$
$402$		0			0
$403$	2.50599	−	4.34051i	0.124832	−	0.216216i
$404$	11.0485			0.549684
$405$		0			0
$406$	−3.43513			−0.170483
$407$	6.17902	−	10.7024i	0.306283	−	0.530497i
$408$		0			0
$409$	11.6443	+	20.1685i	0.575772	+	0.997267i	0.995957	+	0.0898282i	$0.0286318\pi$
$409$	11.6443	+	20.1685i	0.575772	+	0.997267i	−0.420185	+	0.907438i	$0.638035\pi$
$410$	1.69994	+	2.94438i	0.0839540	+	0.145413i
$411$		0			0
$412$	−9.28402	+	16.0804i	−0.457391	+	0.792224i
$413$	−35.9286			−1.76793
$414$		0			0
$415$	−33.6891			−1.65373
$416$	0.778323	−	1.34809i	0.0381604	−	0.0660958i
$417$		0			0
$418$	−0.131853	−	0.228377i	−0.00644916	−	0.0111703i
$419$	15.6442	+	27.0965i	0.764268	+	1.32375i	0.940633	+	0.339427i	$0.110233\pi$
$419$	15.6442	+	27.0965i	0.764268	+	1.32375i	−0.176364	+	0.984325i	$0.556434\pi$
$420$		0			0
$421$	−15.2648	+	26.4394i	−0.743960	+	1.28858i	0.206719	+	0.978400i	$0.433722\pi$
$421$	−15.2648	+	26.4394i	−0.743960	+	1.28858i	−0.950679	+	0.310177i	$0.899612\pi$
$422$	3.60848			0.175658
$423$		0			0
$424$	−6.07280			−0.294921
$425$	−20.7145	+	35.8785i	−1.00480	+	1.74036i
$426$		0			0
$427$	−12.4094	−	21.4938i	−0.600535	−	1.04016i
$428$	−1.25912	−	2.18087i	−0.0608620	−	0.105416i
$429$		0			0
$430$	1.80023	−	3.11809i	0.0868148	−	0.150368i
$431$	−12.4246			−0.598474			−0.299237	−	0.954179i	$-0.596732\pi$
$431$	−12.4246			−0.598474			−0.299237	+	0.954179i	$0.596732\pi$
$432$		0			0
$433$	−0.760649			−0.0365545			−0.0182772	−	0.999833i	$-0.505818\pi$
$433$	−0.760649			−0.0365545			−0.0182772	+	0.999833i	$0.505818\pi$
$434$	−1.71744	+	2.97470i	−0.0824399	+	0.142790i
$435$		0			0
$436$	−7.29608	−	12.6372i	−0.349419	−	0.605211i
$437$	1.99595	+	3.45709i	0.0954792	+	0.165375i
$438$		0			0
$439$	−15.0547	+	26.0755i	−0.718521	+	1.24451i	0.243065	+	0.970010i	$0.421847\pi$
$439$	−15.0547	+	26.0755i	−0.718521	+	1.24451i	−0.961586	+	0.274504i	$0.911486\pi$
$440$	−6.39370			−0.304808
$441$		0			0
$442$	−0.611828			−0.0291017
$443$	−6.83079	+	11.8313i	−0.324541	+	0.562121i	−0.981419	−	0.191875i	$-0.938543\pi$
$443$	−6.83079	+	11.8313i	−0.324541	+	0.562121i	0.656879	+	0.753996i	$0.271876\pi$
$444$		0			0
$445$	14.0847	+	24.3954i	0.667679	+	1.15645i
$446$	−2.03926	−	3.53209i	−0.0965616	−	0.167250i
$447$		0			0
$448$	11.0511	−	19.1410i	0.522114	−	0.904328i
$449$	−21.9989			−1.03819			−0.519097	−	0.854715i	$-0.673732\pi$
$449$	−21.9989			−1.03819			−0.519097	+	0.854715i	$0.673732\pi$
$450$		0			0
$451$	−13.1069			−0.617181
$452$	9.21205	−	15.9557i	0.433299	−	0.750495i
$453$		0			0
$454$	0.906751	+	1.57054i	0.0425559	+	0.0737091i
$455$	−4.33351	−	7.50586i	−0.203158	−	0.351880i
$456$		0			0
$457$	0.744414	−	1.28936i	0.0348222	−	0.0603138i	−0.848089	−	0.529854i	$-0.822247\pi$
$457$	0.744414	−	1.28936i	0.0348222	−	0.0603138i	0.882911	+	0.469540i	$0.155580\pi$
$458$	−2.40132			−0.112206
$459$		0			0
$460$	48.0281			2.23932
$461$	3.55667	−	6.16033i	0.165651	−	0.286915i	−0.771236	−	0.636550i	$-0.780361\pi$
$461$	3.55667	−	6.16033i	0.165651	−	0.286915i	0.936886	+	0.349635i	$0.113694\pi$
$462$		0			0
$463$	13.2704	+	22.9849i	0.616726	+	1.06820i	0.990079	+	0.140512i	$0.0448748\pi$
$463$	13.2704	+	22.9849i	0.616726	+	1.06820i	−0.373353	+	0.927689i	$0.621792\pi$
$464$	12.5167	+	21.6796i	0.581073	+	1.00645i
$465$		0			0
$466$	−0.657278	+	1.13844i	−0.0304478	+	0.0527371i
$467$	26.1519			1.21017			0.605084	−	0.796162i	$-0.293140\pi$
$467$	26.1519			1.21017			0.605084	+	0.796162i	$0.293140\pi$
$468$		0			0
$469$	−3.67520			−0.169705
$470$	0.357946	−	0.619980i	0.0165108	−	0.0285975i
$471$		0			0
$472$	−4.06947	−	7.04852i	−0.187312	−	0.324435i
$473$	6.94009	+	12.0206i	0.319106	+	0.552707i
$474$		0			0
$475$	2.74164	−	4.74866i	0.125795	−	0.217884i
$476$	−27.6086			−1.26544
$477$		0			0
$478$	2.86425			0.131008
$479$	5.20327	−	9.01234i	0.237744	−	0.411784i	−0.722323	−	0.691556i	$-0.756926\pi$
$479$	5.20327	−	9.01234i	0.237744	−	0.411784i	0.960067	+	0.279772i	$0.0902588\pi$
$480$		0			0
$481$	1.89742	+	3.28644i	0.0865151	+	0.149849i
$482$	1.25567	+	2.17489i	0.0571944	+	0.0990636i
$483$		0			0
$484$	−4.71977	+	8.17488i	−0.214535	+	0.371585i
$485$	3.54358			0.160906
$486$		0			0
$487$	−18.4664			−0.836791			−0.418396	−	0.908265i	$-0.637407\pi$
$487$	−18.4664			−0.836791			−0.418396	+	0.908265i	$0.637407\pi$
$488$	2.81112	−	4.86901i	0.127254	−	0.220410i
$489$		0			0
$490$	0.707730	+	1.22582i	0.0319720	+	0.0553771i
$491$	8.48695	+	14.6998i	0.383011	+	0.663394i	0.991491	−	0.130175i	$-0.0415540\pi$
$491$	8.48695	+	14.6998i	0.383011	+	0.663394i	−0.608480	+	0.793569i	$0.708221\pi$
$492$		0			0
$493$	15.1417	−	26.2262i	0.681947	−	1.18117i
$494$	0.0809779			0.00364337
$495$		0			0
$496$	25.0316			1.12395
$497$	7.45667	−	12.9153i	0.334477	−	0.579332i
$498$		0			0
$499$	−12.3231	−	21.3442i	−0.551657	−	0.955498i	−0.998155	−	0.0607136i	$-0.980662\pi$
$499$	−12.3231	−	21.3442i	−0.551657	−	0.955498i	0.446498	−	0.894785i	$-0.352671\pi$
$500$	−14.5824	−	25.2575i	−0.652145	−	1.12955i
$501$		0			0
$502$	−0.782873	+	1.35598i	−0.0349413	+	0.0605201i
$503$	40.1137			1.78858			0.894291	−	0.447485i	$-0.147680\pi$
$503$	40.1137			1.78858			0.894291	+	0.447485i	$0.147680\pi$
$504$		0			0
$505$	20.9552			0.932495
$506$	1.40601	−	2.43529i	0.0625050	−	0.108262i
$507$		0			0
$508$	20.4857	+	35.4823i	0.908905	+	1.57427i
$509$	−2.47426	−	4.28554i	−0.109670	−	0.189953i	0.805967	−	0.591961i	$-0.201646\pi$
$509$	−2.47426	−	4.28554i	−0.109670	−	0.189953i	−0.915636	+	0.402007i	$0.868313\pi$
$510$		0			0
$511$	−6.51689	+	11.2876i	−0.288290	+	0.499333i
$512$	13.0229			0.575537
$513$		0			0
$514$	1.67785			0.0740066
$515$	−17.6086	+	30.4990i	−0.775927	+	1.34395i
$516$		0			0
$517$	1.37992	+	2.39009i	0.0606889	+	0.105116i
$518$	−1.30037	−	2.25231i	−0.0571350	−	0.0989608i
$519$		0			0
$520$	0.981674	−	1.70031i	0.0430493	−	0.0745635i
$521$	7.73958			0.339077			0.169539	−	0.985524i	$-0.445772\pi$
$521$	7.73958			0.339077			0.169539	+	0.985524i	$0.445772\pi$
$522$		0			0
$523$	36.0140			1.57478			0.787391	−	0.616453i	$-0.211431\pi$
$523$	36.0140			1.57478			0.787391	+	0.616453i	$0.211431\pi$
$524$	−0.646018	+	1.11894i	−0.0282214	+	0.0488810i
$525$		0			0
$526$	2.32266	+	4.02296i	0.101273	+	0.175409i
$527$	−15.1406	−	26.2243i	−0.659535	−	1.14235i
$528$		0			0
$529$	−9.78374	+	16.9459i	−0.425380	+	0.736780i
$530$	−5.71561			−0.248270
$531$		0			0
$532$	3.65411			0.158426
$533$	2.01241	−	3.48559i	0.0871670	−	0.150978i
$534$		0			0
$535$	−2.38812	−	4.13635i	−0.103248	−	0.178830i
$536$	−0.416273	−	0.721007i	−0.0179803	−	0.0311427i
$537$		0			0
$538$	−1.01527	+	1.75849i	−0.0437713	+	0.0758141i
$539$	−5.45676			−0.235039
$540$		0			0
$541$	−24.4147			−1.04967			−0.524834	−	0.851204i	$-0.675873\pi$
$541$	−24.4147			−1.04967			−0.524834	+	0.851204i	$0.675873\pi$
$542$	−0.0125041	+	0.0216577i	−0.000537097	+	0.000930280i
$543$		0			0
$544$	−4.70244	−	8.14486i	−0.201615	−	0.349208i
$545$	−13.8381	−	23.9684i	−0.592761	−	1.02669i
$546$		0			0
$547$	14.1809	−	24.5620i	0.606331	−	1.05020i	−0.385509	−	0.922704i	$-0.625974\pi$
$547$	14.1809	−	24.5620i	0.606331	−	1.05020i	0.991840	−	0.127492i	$-0.0406927\pi$
$548$	−16.9183			−0.722712
$549$		0			0
$550$	−3.86261			−0.164702
$551$	−2.00406	+	3.47114i	−0.0853759	+	0.147875i
$552$		0			0
$553$	17.8777	+	30.9650i	0.760235	+	1.31677i
$554$	0.0877355	+	0.151962i	0.00372753	+	0.00645626i
$555$		0			0
$556$	13.2450	−	22.9410i	0.561712	−	0.972914i
$557$	−36.9373			−1.56508			−0.782542	−	0.622598i	$-0.786077\pi$
$557$	−36.9373			−1.56508			−0.782542	+	0.622598i	$0.786077\pi$
$558$		0			0
$559$	−4.26226			−0.180274
$560$	21.6431	−	37.4869i	0.914586	−	1.58411i
$561$		0			0
$562$	2.38097	+	4.12396i	0.100435	+	0.173959i
$563$	−11.3877	−	19.7241i	−0.479935	−	0.831271i	0.519800	−	0.854288i	$-0.326006\pi$
$563$	−11.3877	−	19.7241i	−0.479935	−	0.831271i	−0.999735	+	0.0230164i	$0.992673\pi$
$564$		0			0
$565$	17.4721	−	30.2626i	0.735057	−	1.27316i
$566$	−4.63625			−0.194876
$567$		0			0
$568$	3.37833			0.141752
$569$	−15.4344	+	26.7331i	−0.647043	+	1.12071i	0.336783	+	0.941582i	$0.390661\pi$
$569$	−15.4344	+	26.7331i	−0.647043	+	1.12071i	−0.983826	+	0.179129i	$0.942672\pi$
$570$		0			0
$571$	−6.41025	−	11.1029i	−0.268260	−	0.464641i	0.700152	−	0.713994i	$-0.253115\pi$
$571$	−6.41025	−	11.1029i	−0.268260	−	0.464641i	−0.968413	+	0.249353i	$0.919782\pi$
$572$	1.87797	+	3.25274i	0.0785219	+	0.136004i
$573$		0			0
$574$	−1.37917	+	2.38880i	−0.0575655	+	0.0997064i
$575$	58.4708			2.43840
$576$		0			0
$577$	−23.5264			−0.979417			−0.489708	−	0.871886i	$-0.662897\pi$
$577$	−23.5264			−0.979417			−0.489708	+	0.871886i	$0.662897\pi$
$578$	−0.377963	+	0.654651i	−0.0157212	+	0.0272299i
$579$		0			0
$580$	24.1116	+	41.7626i	1.00118	+	1.73410i
$581$	−13.6661	−	23.6704i	−0.566965	−	0.982013i
$582$		0			0
$583$	11.0172	−	19.0823i	0.456284	−	0.790307i
$584$	−2.95255			−0.122178
$585$		0			0
$586$	3.22726			0.133317
$587$	−5.69372	+	9.86181i	−0.235005	+	0.407041i	−0.959274	−	0.282477i	$-0.908844\pi$
$587$	−5.69372	+	9.86181i	−0.235005	+	0.407041i	0.724269	+	0.689517i	$0.242177\pi$
$588$		0			0
$589$	2.00392	+	3.47089i	0.0825700	+	0.143016i
$590$	−3.83011	−	6.63394i	−0.157683	−	0.273115i
$591$		0			0
$592$	−9.47640	+	16.4136i	−0.389478	+	0.674595i
$593$	−37.7324			−1.54948			−0.774742	−	0.632277i	$-0.782120\pi$
$593$	−37.7324			−1.54948			−0.774742	+	0.632277i	$0.782120\pi$
$594$		0			0
$595$	−52.3640			−2.14672
$596$	9.47812	−	16.4166i	0.388239	−	0.672449i
$597$		0			0
$598$	0.431753	+	0.747817i	0.0176557	+	0.0305805i
$599$	−23.6791	−	41.0134i	−0.967502	−	1.67576i	−0.702738	−	0.711449i	$-0.748039\pi$
$599$	−23.6791	−	41.0134i	−0.967502	−	1.67576i	−0.264764	−	0.964313i	$-0.585294\pi$
$600$		0			0
$601$	15.5537	−	26.9398i	0.634449	−	1.09890i	−0.352182	−	0.935932i	$-0.614560\pi$
$601$	15.5537	−	26.9398i	0.634449	−	1.09890i	0.986631	−	0.162967i	$-0.0521065\pi$
$602$	2.92108			0.119054
$603$		0			0
$604$	14.0431			0.571407
$605$	−8.95178	+	15.5049i	−0.363942	+	0.630365i
$606$		0			0
$607$	−14.7432	−	25.5360i	−0.598409	−	1.03647i	−0.993056	−	0.117642i	$-0.962467\pi$
$607$	−14.7432	−	25.5360i	−0.598409	−	1.03647i	0.394647	−	0.918833i	$-0.370867\pi$
$608$	0.622386	+	1.07801i	0.0252411	+	0.0437189i
$609$		0			0
$610$	2.64578	−	4.58262i	0.107124	−	0.185545i
$611$	−0.847480			−0.0342854
$612$		0			0
$613$	−6.10428			−0.246550			−0.123275	−	0.992373i	$-0.539340\pi$
$613$	−6.10428			−0.246550			−0.123275	+	0.992373i	$0.539340\pi$
$614$	−2.92236	+	5.06168i	−0.117937	+	0.204273i
$615$		0			0
$616$	−2.59363	−	4.49229i	−0.104500	−	0.181000i
$617$	9.56005	+	16.5585i	0.384873	+	0.666620i	0.991752	−	0.128175i	$-0.0409118\pi$
$617$	9.56005	+	16.5585i	0.384873	+	0.666620i	−0.606878	+	0.794795i	$0.707578\pi$
$618$		0			0
$619$	3.37693	−	5.84901i	0.135730	−	0.235092i	−0.790146	−	0.612919i	$-0.789995\pi$
$619$	3.37693	−	5.84901i	0.135730	−	0.235092i	0.925876	+	0.377827i	$0.123329\pi$
$620$	48.2198			1.93655
$621$		0			0
$622$	5.99994			0.240576
$623$	−11.4270	+	19.7922i	−0.457813	+	0.792956i
$624$		0			0
$625$	−5.25307	−	9.09859i	−0.210123	−	0.363944i
$626$	−0.288903	−	0.500394i	−0.0115469	−	0.0199998i
$627$		0			0
$628$	7.57079	−	13.1130i	0.302107	−	0.523265i
$629$	22.9276			0.914182
$630$		0			0
$631$	−0.456907			−0.0181892			−0.00909458	−	0.999959i	$-0.502895\pi$
$631$	−0.456907			−0.0181892			−0.00909458	+	0.999959i	$0.502895\pi$
$632$	−4.04984	+	7.01454i	−0.161094	+	0.279023i
$633$		0			0
$634$	−2.68396	−	4.64876i	−0.106594	−	0.184626i
$635$	38.8543	+	67.2976i	1.54189	+	2.67062i
$636$		0			0
$637$	0.837819	−	1.45114i	0.0331956	−	0.0574964i
$638$	2.82346			0.111782
$639$		0			0
$640$	19.9161			0.787253
$641$	−1.43552	+	2.48639i	−0.0566994	+	0.0982063i	−0.892982	−	0.450092i	$-0.851391\pi$
$641$	−1.43552	+	2.48639i	−0.0566994	+	0.0982063i	0.836282	+	0.548299i	$0.184724\pi$
$642$		0			0
$643$	0.851422	+	1.47471i	0.0335768	+	0.0581567i	0.882325	−	0.470640i	$-0.155977\pi$
$643$	0.851422	+	1.47471i	0.0335768	+	0.0581567i	−0.848749	+	0.528796i	$0.822643\pi$
$644$	19.4827	+	33.7451i	0.767727	+	1.32974i
$645$		0			0
$646$	0.244624	−	0.423702i	0.00962462	−	0.0166703i
$647$	−36.1004			−1.41925			−0.709626	−	0.704579i	$-0.751136\pi$
$647$	−36.1004			−1.41925			−0.709626	+	0.704579i	$0.751136\pi$
$648$		0			0
$649$	29.5310			1.15919
$650$	0.593056	−	1.02720i	0.0232616	−	0.0402902i
$651$		0			0
$652$	1.03183	+	1.78718i	0.0404095	+	0.0699914i
$653$	−21.7840	−	37.7310i	−0.852473	−	1.47653i	−0.878969	−	0.476878i	$-0.841768\pi$
$653$	−21.7840	−	37.7310i	−0.852473	−	1.47653i	0.0264960	−	0.999649i	$-0.491565\pi$
$654$		0			0
$655$	−1.22527	+	2.12224i	−0.0478754	+	0.0829227i
$656$	20.1013			0.784825
$657$		0			0
$658$	0.580807			0.0226422
$659$	12.7405	−	22.0672i	0.496299	−	0.859615i	−0.503692	−	0.863883i	$-0.668025\pi$
$659$	12.7405	−	22.0672i	0.496299	−	0.859615i	0.999991	+	0.00426823i	$0.00135862\pi$
$660$		0			0
$661$	−17.0836	−	29.5897i	−0.664475	−	1.15090i	−0.979427	−	0.201797i	$-0.935322\pi$
$661$	−17.0836	−	29.5897i	−0.664475	−	1.15090i	0.314952	−	0.949107i	$-0.398011\pi$
$662$	−0.282961	−	0.490102i	−0.0109976	−	0.0190484i
$663$		0			0
$664$	3.09580	−	5.36207i	0.120140	−	0.208089i
$665$	6.93059			0.268757
$666$		0			0
$667$	−42.7405			−1.65492
$668$	8.22910	−	14.2532i	0.318393	−	0.551473i
$669$		0			0
$670$	−0.391789	−	0.678598i	−0.0151361	−	0.0262165i
$671$	10.1998	+	17.6665i	0.393757	+	0.682008i
$672$		0			0
$673$	14.7719	−	25.5856i	0.569413	−	0.986253i	−0.427211	−	0.904152i	$-0.640504\pi$
$673$	14.7719	−	25.5856i	0.569413	−	0.986253i	0.996624	−	0.0821009i	$-0.0261630\pi$
$674$	1.10113			0.0424140
$675$		0			0
$676$	24.4577			0.940680
$677$	20.3901	−	35.3167i	0.783656	−	1.35733i	−0.146143	−	0.989264i	$-0.546686\pi$
$677$	20.3901	−	35.3167i	0.783656	−	1.35733i	0.929799	−	0.368068i	$-0.119981\pi$
$678$		0			0
$679$	1.43747	+	2.48977i	0.0551649	+	0.0955484i
$680$	−5.93104	−	10.2729i	−0.227445	−	0.393946i
$681$		0			0
$682$	1.41163	−	2.44501i	0.0540540	−	0.0936243i
$683$	−31.6426			−1.21077			−0.605384	−	0.795933i	$-0.706981\pi$
$683$	−31.6426			−1.21077			−0.605384	+	0.795933i	$0.706981\pi$
$684$		0			0
$685$	−32.0881			−1.22602
$686$	1.26113	−	2.18434i	0.0481502	−	0.0833986i
$687$		0			0
$688$	−10.6436	−	18.4353i	−0.405784	−	0.702839i
$689$	3.38310	+	5.85970i	0.128886	+	0.223237i
$690$		0			0
$691$	14.2924	−	24.7551i	0.543708	−	0.941729i	−0.454979	−	0.890502i	$-0.650353\pi$
$691$	14.2924	−	24.7551i	0.543708	−	0.941729i	0.998687	−	0.0512273i	$-0.0163133\pi$
$692$	−43.0379			−1.63606
$693$		0			0
$694$	1.52088			0.0577316
$695$	25.1212	−	43.5112i	0.952900	−	1.65047i
$696$		0			0
$697$	−12.1585	−	21.0591i	−0.460535	−	0.797670i
$698$	−1.24545	−	2.15718i	−0.0471408	−	0.0816503i
$699$		0			0
$700$	26.7615	−	46.3523i	1.01149	−	1.75195i
$701$	7.52982			0.284397			0.142199	−	0.989838i	$-0.454583\pi$
$701$	7.52982			0.284397			0.142199	+	0.989838i	$0.454583\pi$
$702$		0			0
$703$	−3.03455			−0.114450
$704$	−9.08327	+	15.7327i	−0.342338	+	0.592948i
$705$		0			0
$706$	2.87144	+	4.97348i	0.108068	+	0.187180i
$707$	8.50055	+	14.7234i	0.319696	+	0.553730i
$708$		0			0
$709$	−4.00699	+	6.94032i	−0.150486	+	0.260649i	−0.931406	−	0.363982i	$-0.881417\pi$
$709$	−4.00699	+	6.94032i	−0.150486	+	0.260649i	0.780920	+	0.624631i	$0.214750\pi$
$710$	3.17962			0.119329
$711$		0			0
$712$	−5.17714			−0.194022
$713$	−21.3687	+	37.0117i	−0.800265	+	1.38610i
$714$		0			0
$715$	3.56187	+	6.16933i	0.133206	+	0.230720i
$716$	−8.95269	−	15.5065i	−0.334578	−	0.579506i
$717$		0			0
$718$	0.427695	−	0.740790i	0.0159615	−	0.0276460i
$719$	−26.9826			−1.00628			−0.503140	−	0.864205i	$-0.667822\pi$
$719$	−26.9826			−1.00628			−0.503140	+	0.864205i	$0.667822\pi$
$720$		0			0
$721$	−28.5719			−1.06407
$722$	1.61089	−	2.79015i	0.0599513	−	0.103839i
$723$		0			0
$724$	−7.02409	−	12.1661i	−0.261048	−	0.452149i
$725$	29.3542	+	50.8430i	1.09019	+	1.88826i
$726$		0			0
$727$	7.34717	−	12.7257i	0.272491	−	0.471969i	−0.697008	−	0.717064i	$-0.745486\pi$
$727$	7.34717	−	12.7257i	0.272491	−	0.471969i	0.969499	+	0.245095i	$0.0788190\pi$
$728$	1.59288			0.0590360
$729$		0			0
$730$	−2.77889			−0.102851
$731$	−12.8758	+	22.3015i	−0.476228	+	0.824851i
$732$		0			0
$733$	15.6719	+	27.1445i	0.578854	+	1.00261i	0.995611	+	0.0935872i	$0.0298334\pi$
$733$	15.6719	+	27.1445i	0.578854	+	1.00261i	−0.416757	+	0.909018i	$0.636833\pi$
$734$	0.215567	+	0.373373i	0.00795673	+	0.0137815i
$735$		0			0
$736$	−6.63680	+	11.4953i	−0.244636	+	0.423721i
$737$	3.02078			0.111272
$738$		0			0
$739$	0.482909			0.0177641			0.00888205	−	0.999961i	$-0.497173\pi$
$739$	0.482909			0.0177641			0.00888205	+	0.999961i	$0.497173\pi$
$740$	−18.2549	+	31.6185i	−0.671065	+	1.16232i
$741$		0			0
$742$	−2.31855	−	4.01585i	−0.0851168	−	0.147427i
$743$	21.5254	+	37.2830i	0.789689	+	1.36778i	0.926157	+	0.377137i	$0.123092\pi$
$743$	21.5254	+	37.2830i	0.789689	+	1.36778i	−0.136468	+	0.990644i	$0.543575\pi$
$744$		0			0
$745$	17.9767	−	31.1366i	0.658616	−	1.14076i
$746$	−4.85156			−0.177628
$747$		0			0
$748$	22.6925			0.829720
$749$	1.93750	−	3.35585i	0.0707947	−	0.122620i
$750$		0			0
$751$	−21.9608	−	38.0372i	−0.801361	−	1.38800i	−0.918720	−	0.394909i	$-0.870776\pi$
$751$	−21.9608	−	38.0372i	−0.801361	−	1.38800i	0.117359	−	0.993090i	$-0.462557\pi$
$752$	−2.11631	−	3.66555i	−0.0771737	−	0.133669i
$753$		0			0
$754$	−0.433507	+	0.750857i	−0.0157874	+	0.0273446i
$755$	26.6350			0.969346
$756$		0			0
$757$	22.4143			0.814661			0.407331	−	0.913281i	$-0.366460\pi$
$757$	22.4143			0.814661			0.407331	+	0.913281i	$0.366460\pi$
$758$	−0.444540	+	0.769966i	−0.0161464	+	0.0279664i
$759$		0			0
$760$	0.784997	+	1.35965i	0.0284748	+	0.0493198i
$761$	−4.99837	−	8.65743i	−0.181191	−	0.313832i	0.761096	−	0.648640i	$-0.224662\pi$
$761$	−4.99837	−	8.65743i	−0.181191	−	0.313832i	−0.942286	+	0.334808i	$0.891328\pi$
$762$		0			0
$763$	11.2270	−	19.4457i	0.406444	−	0.703982i
$764$	−23.5535			−0.852137
$765$		0			0
$766$	0.00772733			0.000279200
$767$	−4.53412	+	7.85332i	−0.163718	+	0.283567i
$768$		0			0
$769$	3.74810	+	6.49189i	0.135160	+	0.234104i	0.925658	−	0.378360i	$-0.123512\pi$
$769$	3.74810	+	6.49189i	0.135160	+	0.234104i	−0.790499	+	0.612464i	$0.790179\pi$
$770$	−2.44107	−	4.22806i	−0.0879701	−	0.152369i
$771$		0			0
$772$	−8.74088	+	15.1397i	−0.314591	+	0.544888i
$773$	19.8391			0.713562			0.356781	−	0.934188i	$-0.383874\pi$
$773$	19.8391			0.713562			0.356781	+	0.934188i	$0.383874\pi$
$774$		0			0
$775$	58.7043			2.10872
$776$	−0.325631	+	0.564009i	−0.0116895	+	0.0202467i
$777$		0			0
$778$	1.81471	+	3.14318i	0.0650606	+	0.112688i
$779$	1.60922	+	2.78726i	0.0576564	+	0.0998638i
$780$		0			0
$781$	−6.12890	+	10.6156i	−0.219309	+	0.379855i
$782$	5.21709			0.186563
$783$		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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0864880 + 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(1.86828 + 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} -0.686728 q^{8} +O(q^{10})\)	\(q+(-0.0864880 + 0.149802i) q^{2} +(0.985040 + 1.70614i) q^{4} +(1.86828 + 3.23596i) q^{5} +(-1.51575 + 2.62535i) q^{7} -0.686728 q^{8} -0.646335 q^{10} +(1.24585 - 2.15787i) q^{11} +(0.382569 + 0.662630i) q^{13} +(-0.262188 - 0.454123i) q^{14} +(-1.91069 + 3.30940i) q^{16} +4.62278 q^{17} -0.611844 q^{19} +(-3.68066 + 6.37509i) q^{20} +(0.215502 + 0.373260i) q^{22} +(-3.26219 - 5.65028i) q^{23} +(-4.48095 + 7.76123i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(3.27545 - 5.67324i) q^{29} +(-3.27521 - 5.67283i) q^{31} +(-1.01723 - 1.76190i) q^{32} +(-0.399815 + 0.692500i) q^{34} -11.3274 q^{35} +4.95969 q^{37} +(0.0529171 - 0.0916552i) q^{38} +(-1.28300 - 2.22222i) q^{40} +(-2.63012 - 4.55550i) q^{41} +(-2.78529 + 4.82426i) q^{43} +4.90884 q^{44} +1.12856 q^{46} +(-0.553808 + 0.959223i) q^{47} +(-1.09499 - 1.89658i) q^{49} +(-0.775096 - 1.34251i) q^{50} +(-0.753692 + 1.30543i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(1.04091 - 1.80290i) q^{56} +(0.566573 + 0.981334i) q^{58} +(5.92588 + 10.2639i) q^{59} +(-4.09350 + 7.09015i) q^{61} +1.13307 q^{62} -7.29083 q^{64} +(-1.42949 + 2.47596i) q^{65} +(0.606169 + 1.04992i) q^{67} +(4.55362 + 7.88711i) q^{68} +(0.979682 - 1.69686i) q^{70} -4.91946 q^{71} +4.29945 q^{73} +(-0.428953 + 0.742969i) q^{74} +(-0.602691 - 1.04389i) q^{76} +(3.77679 + 6.54158i) q^{77} +(5.89730 - 10.2144i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(-4.50804 + 7.80815i) q^{83} +(8.63666 + 14.9591i) q^{85} +(-0.481788 - 0.834481i) q^{86} +(-0.855559 + 1.48187i) q^{88} +7.53885 q^{89} -2.31952 q^{91} +(6.42677 - 11.1315i) q^{92} +(-0.0957954 - 0.165923i) q^{94} +(-1.14310 - 1.97990i) q^{95} +(0.474177 - 0.821299i) q^{97} +0.378814 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) 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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