LMFDB - Embedded newform 729.2.c.e.244.1

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:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.1
Root			$0.500000 - 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.e.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.840456 - 1.45571i) q^{2} +(-0.412733 + 0.714874i) q^{4} +(0.564772 - 0.978214i) q^{5} +(1.95446 + 3.38523i) q^{7} -1.97429 q^{8} +O(q^{10})$	\(q+(-0.840456 - 1.45571i) q^{2} +(-0.412733 + 0.714874i) q^{4} +(0.564772 - 0.978214i) q^{5} +(1.95446 + 3.38523i) q^{7} -1.97429 q^{8} -1.89866 q^{10} +(0.935228 + 1.61986i) q^{11} +(0.366299 - 0.634448i) q^{13} +(3.28528 - 5.69027i) q^{14} +(2.48477 + 4.30375i) q^{16} +1.88964 q^{17} +2.74286 q^{19} +(0.466200 + 0.807482i) q^{20} +(1.57204 - 2.72285i) q^{22} +(2.91385 - 5.04694i) q^{23} +(1.86207 + 3.22519i) q^{25} -1.23143 q^{26} -3.22668 q^{28} +(2.65997 + 4.60720i) q^{29} +(-0.670300 + 1.16099i) q^{31} +(2.20239 - 3.81465i) q^{32} +(-1.58816 - 2.75078i) q^{34} +4.41530 q^{35} +3.39611 q^{37} +(-2.30525 - 3.99281i) q^{38} +(-1.11502 + 1.93128i) q^{40} +(-0.898166 + 1.55567i) q^{41} +(-2.51508 - 4.35624i) q^{43} -1.54400 q^{44} -9.79585 q^{46} +(-0.854339 - 1.47976i) q^{47} +(-4.13984 + 7.17041i) q^{49} +(3.12997 - 5.42126i) q^{50} +(0.302367 + 0.523715i) q^{52} +2.84494 q^{53} +2.11276 q^{55} +(-3.85867 - 6.68342i) q^{56} +(4.47117 - 7.74430i) q^{58} +(5.63002 - 9.75149i) q^{59} +(-2.61545 - 4.53009i) q^{61} +2.25343 q^{62} +2.53503 q^{64} +(-0.413751 - 0.716637i) q^{65} +(0.944514 - 1.63595i) q^{67} +(-0.779918 + 1.35086i) q^{68} +(-3.71087 - 6.42741i) q^{70} -12.1839 q^{71} +9.88768 q^{73} +(-2.85428 - 4.94376i) q^{74} +(-1.13207 + 1.96080i) q^{76} +(-3.65573 + 6.33192i) q^{77} +(-6.17644 - 10.6979i) q^{79} +5.61331 q^{80} +3.01948 q^{82} +(5.84158 + 10.1179i) q^{83} +(1.06722 - 1.84848i) q^{85} +(-4.22762 + 7.32246i) q^{86} +(-1.84641 - 3.19808i) q^{88} -5.72873 q^{89} +2.86367 q^{91} +(2.40528 + 4.16607i) q^{92} +(-1.43607 + 2.48734i) q^{94} +(1.54909 - 2.68310i) q^{95} +(0.171689 + 0.297374i) q^{97} +13.9174 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * 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 $

$2$	−0.840456	−	1.45571i	−0.594292	−	1.02934i	−0.993646	−	0.112548i	$-0.964099\pi$
$2$	−0.840456	−	1.45571i	−0.594292	−	1.02934i	0.399354	−	0.916797i	$-0.369234\pi$
$3$		0			0
$3$		0			0
$4$	−0.412733	+	0.714874i	−0.206366	+	0.357437i
$5$	0.564772	−	0.978214i	0.252574	−	0.437471i	−0.711660	−	0.702524i	$-0.752056\pi$
$5$	0.564772	−	0.978214i	0.252574	−	0.437471i	0.964234	+	0.265054i	$0.0853896\pi$
$6$		0			0
$7$	1.95446	+	3.38523i	0.738717	+	1.27950i	0.953073	+	0.302740i	$0.0979013\pi$
$7$	1.95446	+	3.38523i	0.738717	+	1.27950i	−0.214356	+	0.976756i	$0.568765\pi$
$8$	−1.97429			−0.698017
$9$		0			0
$10$	−1.89866			−0.600410
$11$	0.935228	+	1.61986i	0.281982	+	0.488407i	0.971873	−	0.235506i	$-0.0756749\pi$
$11$	0.935228	+	1.61986i	0.281982	+	0.488407i	−0.689891	+	0.723913i	$0.742342\pi$
$12$		0			0
$13$	0.366299	−	0.634448i	0.101593	−	0.175964i	−0.810748	−	0.585395i	$-0.800939\pi$
$13$	0.366299	−	0.634448i	0.101593	−	0.175964i	0.912341	+	0.409431i	$0.134273\pi$
$14$	3.28528	−	5.69027i	0.878027	−	1.52079i
$15$		0			0
$16$	2.48477	+	4.30375i	0.621192	+	1.07594i
$17$	1.88964			0.458306			0.229153	−	0.973390i	$-0.426404\pi$
$17$	1.88964			0.458306			0.229153	+	0.973390i	$0.426404\pi$
$18$		0			0
$19$	2.74286			0.629254			0.314627	−	0.949215i	$-0.398121\pi$
$19$	2.74286			0.629254			0.314627	+	0.949215i	$0.398121\pi$
$20$	0.466200	+	0.807482i	0.104245	+	0.180558i
$21$		0			0
$22$	1.57204	−	2.72285i	0.335159	−	0.580513i
$23$	2.91385	−	5.04694i	0.607580	−	1.05236i	−0.384058	−	0.923309i	$-0.625474\pi$
$23$	2.91385	−	5.04694i	0.607580	−	1.05236i	0.991638	−	0.129050i	$-0.0411928\pi$
$24$		0			0
$25$	1.86207	+	3.22519i	0.372413	+	0.645038i
$26$	−1.23143			−0.241504
$27$		0			0
$28$	−3.22668			−0.609786
$29$	2.65997	+	4.60720i	0.493944	+	0.855535i	0.999976	−	0.00697928i	$-0.00222159\pi$
$29$	2.65997	+	4.60720i	0.493944	+	0.855535i	−0.506032	+	0.862515i	$0.668888\pi$
$30$		0			0
$31$	−0.670300	+	1.16099i	−0.120390	+	0.208521i	−0.919921	−	0.392103i	$-0.871748\pi$
$31$	−0.670300	+	1.16099i	−0.120390	+	0.208521i	0.799532	+	0.600624i	$0.205081\pi$
$32$	2.20239	−	3.81465i	0.389331	−	0.674341i
$33$		0			0
$34$	−1.58816	−	2.75078i	−0.272368	−	0.471755i
$35$	4.41530			0.746322
$36$		0			0
$37$	3.39611			0.558318			0.279159	−	0.960245i	$-0.409944\pi$
$37$	3.39611			0.558318			0.279159	+	0.960245i	$0.409944\pi$
$38$	−2.30525	−	3.99281i	−0.373961	−	0.647719i
$39$		0			0
$40$	−1.11502	+	1.93128i	−0.176301	+	0.305362i
$41$	−0.898166	+	1.55567i	−0.140270	+	0.242955i	−0.927598	−	0.373579i	$-0.878130\pi$
$41$	−0.898166	+	1.55567i	−0.140270	+	0.242955i	0.787328	+	0.616534i	$0.211464\pi$
$42$		0			0
$43$	−2.51508	−	4.35624i	−0.383546	−	0.664320i	0.608021	−	0.793921i	$-0.291964\pi$
$43$	−2.51508	−	4.35624i	−0.383546	−	0.664320i	−0.991566	+	0.129601i	$0.958630\pi$
$44$	−1.54400			−0.232766
$45$		0			0
$46$	−9.79585			−1.44432
$47$	−0.854339	−	1.47976i	−0.124618	−	0.215845i	0.796965	−	0.604025i	$-0.206437\pi$
$47$	−0.854339	−	1.47976i	−0.124618	−	0.215845i	−0.921584	+	0.388180i	$0.873104\pi$
$48$		0			0
$49$	−4.13984	+	7.17041i	−0.591405	+	1.02434i
$50$	3.12997	−	5.42126i	0.442644	−	0.766682i
$51$		0			0
$52$	0.302367	+	0.523715i	0.0419308	+	0.0726263i
$53$	2.84494			0.390783			0.195391	−	0.980725i	$-0.437402\pi$
$53$	2.84494			0.390783			0.195391	+	0.980725i	$0.437402\pi$
$54$		0			0
$55$	2.11276			0.284885
$56$	−3.85867	−	6.68342i	−0.515637	−	0.893109i
$57$		0			0
$58$	4.47117	−	7.74430i	0.587094	−	1.01688i
$59$	5.63002	−	9.75149i	0.732967	−	1.26954i	−0.222643	−	0.974900i	$-0.571469\pi$
$59$	5.63002	−	9.75149i	0.732967	−	1.26954i	0.955610	−	0.294635i	$-0.0951982\pi$
$60$		0			0
$61$	−2.61545	−	4.53009i	−0.334874	−	0.580018i	0.648587	−	0.761141i	$-0.275360\pi$
$61$	−2.61545	−	4.53009i	−0.334874	−	0.580018i	−0.983461	+	0.181122i	$0.942027\pi$
$62$	2.25343			0.286186
$63$		0			0
$64$	2.53503			0.316879
$65$	−0.413751	−	0.716637i	−0.0513195	−	0.0888879i
$66$		0			0
$67$	0.944514	−	1.63595i	0.115391	−	0.199863i	−0.802545	−	0.596591i	$-0.796521\pi$
$67$	0.944514	−	1.63595i	0.115391	−	0.199863i	0.917936	+	0.396729i	$0.129855\pi$
$68$	−0.779918	+	1.35086i	−0.0945789	+	0.163816i
$69$		0			0
$70$	−3.71087	−	6.42741i	−0.443533	−	0.768222i
$71$	−12.1839			−1.44596			−0.722980	−	0.690869i	$-0.757228\pi$
$71$	−12.1839			−1.44596			−0.722980	+	0.690869i	$0.757228\pi$
$72$		0			0
$73$	9.88768			1.15727			0.578633	−	0.815588i	$-0.303587\pi$
$73$	9.88768			1.15727			0.578633	+	0.815588i	$0.303587\pi$
$74$	−2.85428	−	4.94376i	−0.331804	−	0.574701i
$75$		0			0
$76$	−1.13207	+	1.96080i	−0.129857	+	0.224919i
$77$	−3.65573	+	6.33192i	−0.416610	+	0.721589i
$78$		0			0
$79$	−6.17644	−	10.6979i	−0.694904	−	1.20361i	−0.970213	−	0.242253i	$-0.922114\pi$
$79$	−6.17644	−	10.6979i	−0.694904	−	1.20361i	0.275310	−	0.961356i	$-0.411220\pi$
$80$	5.61331			0.627587
$81$		0			0
$82$	3.01948			0.333445
$83$	5.84158	+	10.1179i	0.641197	+	1.11059i	0.985166	+	0.171605i	$0.0548952\pi$
$83$	5.84158	+	10.1179i	0.641197	+	1.11059i	−0.343969	+	0.938981i	$0.611772\pi$
$84$		0			0
$85$	1.06722	−	1.84848i	0.115756	−	0.200495i
$86$	−4.22762	+	7.32246i	−0.455876	+	0.789601i
$87$		0			0
$88$	−1.84641	−	3.19808i	−0.196828	−	0.340916i
$89$	−5.72873			−0.607244			−0.303622	−	0.952793i	$-0.598196\pi$
$89$	−5.72873			−0.607244			−0.303622	+	0.952793i	$0.598196\pi$
$90$		0			0
$91$	2.86367			0.300194
$92$	2.40528	+	4.16607i	0.250768	+	0.434343i
$93$		0			0
$94$	−1.43607	+	2.48734i	−0.148119	+	0.256550i
$95$	1.54909	−	2.68310i	0.158933	−	0.275280i
$96$		0			0
$97$	0.171689	+	0.297374i	0.0174324	+	0.0301938i	0.874610	−	0.484827i	$-0.161117\pi$
$97$	0.171689	+	0.297374i	0.0174324	+	0.0301938i	−0.857178	+	0.515021i	$0.827784\pi$
$98$	13.9174			1.40587
$99$		0			0
$100$	−3.07414			−0.307414
$101$	8.70113	+	15.0708i	0.865794	+	1.49960i	0.866256	+	0.499600i	$0.166520\pi$
$101$	8.70113	+	15.0708i	0.865794	+	1.49960i	−0.000461665		1.00000i	$0.500147\pi$
$102$		0			0
$103$	7.90650	−	13.6945i	0.779051	−	1.34936i	−0.153439	−	0.988158i	$-0.549035\pi$
$103$	7.90650	−	13.6945i	0.779051	−	1.34936i	0.932489	−	0.361197i	$-0.117632\pi$
$104$	−0.723180	+	1.25258i	−0.0709136	+	0.122826i
$105$		0			0
$106$	−2.39105	−	4.14142i	−0.232239	−	0.402250i
$107$	−16.5298			−1.59800			−0.798999	−	0.601332i	$-0.794637\pi$
$107$	−16.5298			−1.59800			−0.798999	+	0.601332i	$0.794637\pi$
$108$		0			0
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$	−1.77568	−	3.07557i	−0.169305	−	0.293245i
$111$		0			0
$112$	−9.71277	+	16.8230i	−0.917770	+	1.58963i
$113$	−9.97241	+	17.2727i	−0.938125	+	1.62488i	−0.169161	+	0.985588i	$0.554106\pi$
$113$	−9.97241	+	17.2727i	−0.938125	+	1.62488i	−0.768964	+	0.639292i	$0.779228\pi$
$114$		0			0
$115$	−3.29132	−	5.70074i	−0.306917	−	0.531596i
$116$	−4.39142			−0.407733
$117$		0			0
$118$	−18.9271			−1.74239
$119$	3.69324	+	6.39687i	0.338558	+	0.586400i
$120$		0			0
$121$	3.75070	−	6.49640i	0.340972	−	0.590582i
$122$	−4.39634	+	7.61468i	−0.398026	+	0.689401i
$123$		0			0
$124$	−0.553310	−	0.958361i	−0.0496887	−	0.0860634i
$125$	9.85429			0.881394
$126$		0			0
$127$	1.06946			0.0948989			0.0474495	−	0.998874i	$-0.484891\pi$
$127$	1.06946			0.0948989			0.0474495	+	0.998874i	$0.484891\pi$
$128$	−6.53536	−	11.3196i	−0.577650	−	1.00052i
$129$		0			0
$130$	−0.695479	+	1.20460i	−0.0609975	+	0.105651i
$131$	−3.82015	+	6.61669i	−0.333768	+	0.578103i	−0.983247	−	0.182276i	$-0.941654\pi$
$131$	−3.82015	+	6.61669i	−0.333768	+	0.578103i	0.649479	+	0.760379i	$0.274987\pi$
$132$		0			0
$133$	5.36081	+	9.28519i	0.464841	+	0.805128i
$134$	−3.17529			−0.274303
$135$		0			0
$136$	−3.73070			−0.319905
$137$	−7.82525	−	13.5537i	−0.668556	−	1.15797i	−0.978308	−	0.207156i	$-0.933579\pi$
$137$	−7.82525	−	13.5537i	−0.668556	−	1.15797i	0.309752	−	0.950818i	$-0.399754\pi$
$138$		0			0
$139$	−4.32847	+	7.49712i	−0.367136	+	0.635898i	−0.989116	−	0.147135i	$-0.952995\pi$
$139$	−4.32847	+	7.49712i	−0.367136	+	0.635898i	0.621981	+	0.783033i	$0.286328\pi$
$140$	−1.82234	+	3.15638i	−0.154016	+	0.266763i
$141$		0			0
$142$	10.2400	+	17.7362i	0.859322	+	1.48839i
$143$	1.37029			0.114590
$144$		0			0
$145$	6.00910			0.499029
$146$	−8.31016	−	14.3936i	−0.687754	−	1.19122i
$147$		0			0
$148$	−1.40169	+	2.42779i	−0.115218	+	0.199563i
$149$	1.23191	−	2.13373i	0.100922	−	0.174802i	−0.811143	−	0.584848i	$-0.801154\pi$
$149$	1.23191	−	2.13373i	0.100922	−	0.174802i	0.912065	+	0.410046i	$0.134487\pi$
$150$		0			0
$151$	5.25670	+	9.10488i	0.427785	+	0.740945i	0.996676	−	0.0814681i	$-0.0259609\pi$
$151$	5.25670	+	9.10488i	0.427785	+	0.740945i	−0.568891	+	0.822413i	$0.692628\pi$
$152$	−5.41519			−0.439230
$153$		0			0
$154$	12.2899			0.990351
$155$	0.757134	+	1.31139i	0.0608145	+	0.105334i
$156$		0			0
$157$	−0.179974	+	0.311725i	−0.0143635	+	0.0248783i	−0.873118	−	0.487509i	$-0.837906\pi$
$157$	−0.179974	+	0.311725i	−0.0143635	+	0.0248783i	0.858754	+	0.512388i	$0.171239\pi$
$158$	−10.3820	+	17.9822i	−0.825951	+	1.43059i
$159$		0			0
$160$	−2.48770	−	4.30882i	−0.196670	−	0.340642i
$161$	22.7800			1.79532
$162$		0			0
$163$	14.6186			1.14502			0.572508	−	0.819899i	$-0.305971\pi$
$163$	14.6186			1.14502			0.572508	+	0.819899i	$0.305971\pi$
$164$	−0.741405	−	1.28415i	−0.0578940	−	0.100275i
$165$		0			0
$166$	9.81919	−	17.0073i	0.762117	−	1.32002i
$167$	−1.08792	+	1.88434i	−0.0841861	+	0.145815i	−0.905044	−	0.425318i	$-0.860162\pi$
$167$	−1.08792	+	1.88434i	−0.0841861	+	0.145815i	0.820858	+	0.571132i	$0.193496\pi$
$168$		0			0
$169$	6.23165	+	10.7935i	0.479358	+	0.830272i
$170$	−3.58780			−0.275172
$171$		0			0
$172$	4.15222			0.316604
$173$	8.78351	+	15.2135i	0.667798	+	1.15666i	0.978519	+	0.206159i	$0.0660963\pi$
$173$	8.78351	+	15.2135i	0.667798	+	1.15666i	−0.310721	+	0.950501i	$0.600570\pi$
$174$		0			0
$175$	−7.27867	+	12.6070i	−0.550216	+	0.953001i
$176$	−4.64765	+	8.04997i	−0.350330	+	0.606789i
$177$		0			0
$178$	4.81475	+	8.33939i	0.360881	+	0.625064i
$179$	1.00447			0.0750777			0.0375388	−	0.999295i	$-0.488048\pi$
$179$	1.00447			0.0750777			0.0375388	+	0.999295i	$0.488048\pi$
$180$		0			0
$181$	−21.1732			−1.57380			−0.786898	−	0.617084i	$-0.788314\pi$
$181$	−21.1732			−1.57380			−0.786898	+	0.617084i	$0.788314\pi$
$182$	−2.40679	−	4.16868i	−0.178403	−	0.309003i
$183$		0			0
$184$	−5.75278	+	9.96411i	−0.424101	+	0.734564i
$185$	1.91803	−	3.32212i	0.141016	−	0.244247i
$186$		0			0
$187$	1.76725	+	3.06096i	0.129234	+	0.223840i
$188$	1.41045			0.102868
$189$		0			0
$190$	−5.20776			−0.377811
$191$	4.91419	+	8.51163i	0.355578	+	0.615880i	0.987217	−	0.159383i	$-0.0509506\pi$
$191$	4.91419	+	8.51163i	0.355578	+	0.615880i	−0.631638	+	0.775263i	$0.717617\pi$
$192$		0			0
$193$	5.57804	−	9.66145i	0.401516	−	0.695447i	−0.592393	−	0.805649i	$-0.701817\pi$
$193$	5.57804	−	9.66145i	0.401516	−	0.695447i	0.993909	+	0.110203i	$0.0351500\pi$
$194$	0.288594	−	0.499860i	0.0207199	−	0.0358879i
$195$		0			0
$196$	−3.41729	−	5.91893i	−0.244092	−	0.422781i
$197$	9.08994			0.647631			0.323816	−	0.946120i	$-0.395034\pi$
$197$	9.08994			0.647631			0.323816	+	0.946120i	$0.395034\pi$
$198$		0			0
$199$	−14.6939			−1.04162			−0.520811	−	0.853672i	$-0.674370\pi$
$199$	−14.6939			−1.04162			−0.520811	+	0.853672i	$0.674370\pi$
$200$	−3.67625	−	6.36746i	−0.259950	−	0.450247i
$201$		0			0
$202$	14.6258	−	25.3327i	1.02907	−	1.78240i
$203$	−10.3976	+	18.0092i	−0.729769	+	1.26400i
$204$		0			0
$205$	1.01452	+	1.75720i	0.0708570	+	0.122728i
$206$	−26.5803			−1.85194
$207$		0			0
$208$	3.64067			0.252435
$209$	2.56520	+	4.44305i	0.177438	+	0.307332i
$210$		0			0
$211$	−3.92915	+	6.80549i	−0.270494	+	0.468509i	−0.968988	−	0.247106i	$-0.920520\pi$
$211$	−3.92915	+	6.80549i	−0.270494	+	0.468509i	0.698495	+	0.715615i	$0.253854\pi$
$212$	−1.17420	+	2.03378i	−0.0806445	+	0.139680i
$213$		0			0
$214$	13.8926	+	24.0627i	0.949678	+	1.64489i
$215$	−5.68178			−0.387494
$216$		0			0
$217$	−5.24030			−0.355735
$218$	3.96564	+	6.86869i	0.268587	+	0.465207i
$219$		0			0
$220$	−0.872006	+	1.51036i	−0.0587907	+	0.101828i
$221$	0.692174	−	1.19888i	0.0465607	−	0.0806455i
$222$		0			0
$223$	4.37044	+	7.56983i	0.292666	+	0.506913i	0.974439	−	0.224651i	$-0.0721241\pi$
$223$	4.37044	+	7.56983i	0.292666	+	0.506913i	−0.681773	+	0.731564i	$0.738791\pi$
$224$	17.2179			1.15042
$225$		0			0
$226$	33.5255			2.23008
$227$	−2.03421	−	3.52335i	−0.135015	−	0.233853i	0.790588	−	0.612348i	$-0.209775\pi$
$227$	−2.03421	−	3.52335i	−0.135015	−	0.233853i	−0.925603	+	0.378495i	$0.876442\pi$
$228$		0			0
$229$	−8.07794	+	13.9914i	−0.533805	+	0.924577i	0.465415	+	0.885093i	$0.345905\pi$
$229$	−8.07794	+	13.9914i	−0.533805	+	0.924577i	−0.999220	+	0.0394849i	$0.987428\pi$
$230$	−5.53242	+	9.58244i	−0.364797	+	0.631847i
$231$		0			0
$232$	−5.25154	−	9.09594i	−0.344781	−	0.597178i
$233$	17.2132			1.12767			0.563836	−	0.825887i	$-0.309325\pi$
$233$	17.2132			1.12767			0.563836	+	0.825887i	$0.309325\pi$
$234$		0			0
$235$	−1.93003			−0.125901
$236$	4.64739	+	8.04952i	0.302519	+	0.523979i
$237$		0			0
$238$	6.20800	−	10.7526i	0.402405	−	0.696986i
$239$	0.767720	−	1.32973i	0.0496597	−	0.0860131i	−0.840127	−	0.542390i	$-0.817520\pi$
$239$	0.767720	−	1.32973i	0.0496597	−	0.0860131i	0.889787	+	0.456377i	$0.150853\pi$
$240$		0			0
$241$	2.76084	+	4.78191i	0.177841	+	0.308030i	0.941141	−	0.338015i	$-0.109755\pi$
$241$	2.76084	+	4.78191i	0.177841	+	0.308030i	−0.763300	+	0.646045i	$0.776422\pi$
$242$	−12.6092			−0.810549
$243$		0			0
$244$	4.31792			0.276427
$245$	4.67613	+	8.09929i	0.298747	+	0.517445i
$246$		0			0
$247$	1.00471	−	1.74020i	0.0639279	−	0.110726i
$248$	1.32337	−	2.29214i	0.0840339	−	0.145551i
$249$		0			0
$250$	−8.28210	−	14.3450i	−0.523806	−	0.907258i
$251$	−21.4409			−1.35334			−0.676668	−	0.736288i	$-0.736577\pi$
$251$	−21.4409			−1.35334			−0.676668	+	0.736288i	$0.736577\pi$
$252$		0			0
$253$	10.9005			0.685306
$254$	−0.898831	−	1.55682i	−0.0563977	−	0.0976837i
$255$		0			0
$256$	−8.45034	+	14.6364i	−0.528146	+	0.914776i
$257$	7.39324	−	12.8055i	0.461177	−	0.798783i	−0.537843	−	0.843045i	$-0.680761\pi$
$257$	7.39324	−	12.8055i	0.461177	−	0.798783i	0.999020	+	0.0442626i	$0.0140938\pi$
$258$		0			0
$259$	6.63757	+	11.4966i	0.412439	+	0.714365i
$260$	0.683074			0.0423625
$261$		0			0
$262$	12.8427			0.793423
$263$	−1.40138	−	2.42726i	−0.0864127	−	0.149671i	0.819580	−	0.572965i	$-0.194207\pi$
$263$	−1.40138	−	2.42726i	−0.0864127	−	0.149671i	−0.905992	+	0.423294i	$0.860874\pi$
$264$		0			0
$265$	1.60674	−	2.78296i	0.0987015	−	0.170956i
$266$	9.01104	−	15.6076i	0.552503	−	0.956963i
$267$		0			0
$268$	0.779664	+	1.35042i	0.0476256	+	0.0824899i
$269$	−0.356528			−0.0217379			−0.0108689	−	0.999941i	$-0.503460\pi$
$269$	−0.356528			−0.0217379			−0.0108689	+	0.999941i	$0.503460\pi$
$270$		0			0
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	4.69533	+	8.13255i	0.284696	+	0.493108i
$273$		0			0
$274$	−13.1536	+	22.7826i	−0.794636	+	1.37635i
$275$	−3.48291	+	6.03258i	−0.210027	+	0.363778i
$276$		0			0
$277$	−12.4950	−	21.6419i	−0.750751	−	1.30034i	−0.947459	−	0.319876i	$-0.896359\pi$
$277$	−12.4950	−	21.6419i	−0.750751	−	1.30034i	0.196709	−	0.980462i	$-0.436975\pi$
$278$	14.5515			0.872744
$279$		0			0
$280$	−8.71708			−0.520945
$281$	−3.66143	−	6.34179i	−0.218423	−	0.378319i	0.735903	−	0.677087i	$-0.236758\pi$
$281$	−3.66143	−	6.34179i	−0.218423	−	0.378319i	−0.954326	+	0.298767i	$0.903425\pi$
$282$		0			0
$283$	7.19404	−	12.4604i	0.427641	−	0.740697i	−0.569022	−	0.822323i	$-0.692678\pi$
$283$	7.19404	−	12.4604i	0.427641	−	0.740697i	0.996663	+	0.0816258i	$0.0260112\pi$
$284$	5.02868	−	8.70993i	0.298397	−	0.516839i
$285$		0			0
$286$	−1.15167	−	1.99475i	−0.0680997	−	0.117952i
$287$	−7.02172			−0.414479
$288$		0			0
$289$	−13.4292			−0.789956
$290$	−5.05039	−	8.74752i	−0.296569	−	0.513672i
$291$		0			0
$292$	−4.08097	+	7.06845i	−0.238821	+	0.413650i
$293$	7.20776	−	12.4842i	0.421082	−	0.729335i	−0.574964	−	0.818179i	$-0.694984\pi$
$293$	7.20776	−	12.4842i	0.421082	−	0.729335i	0.996046	+	0.0888441i	$0.0283173\pi$
$294$		0			0
$295$	−6.35936	−	11.0147i	−0.370256	−	0.641303i
$296$	−6.70491			−0.389715
$297$		0			0
$298$	−4.14147			−0.239909
$299$	−2.13468	−	3.69737i	−0.123452	−	0.213825i
$300$		0			0
$301$	9.83124	−	17.0282i	0.566663	−	0.981489i
$302$	8.83606	−	15.3045i	0.508458	−	0.880675i
$303$		0			0
$304$	6.81536	+	11.8046i	0.390888	+	0.677038i
$305$	−5.90853			−0.338321
$306$		0			0
$307$	−30.4326			−1.73688			−0.868440	−	0.495795i	$-0.834877\pi$
$307$	−30.4326			−1.73688			−0.868440	+	0.495795i	$0.834877\pi$
$308$	−3.01768	−	5.22678i	−0.171948	−	0.297823i
$309$		0			0
$310$	1.27268	−	2.20434i	0.0722831	−	0.125198i
$311$	6.99780	−	12.1206i	0.396809	−	0.687293i	−0.596521	−	0.802597i	$-0.703451\pi$
$311$	6.99780	−	12.1206i	0.396809	−	0.687293i	0.993330	+	0.115304i	$0.0367842\pi$
$312$		0			0
$313$	−11.0438	−	19.1284i	−0.624231	−	1.08120i	−0.988689	−	0.149981i	$-0.952079\pi$
$313$	−11.0438	−	19.1284i	−0.624231	−	1.08120i	0.364457	−	0.931220i	$-0.381254\pi$
$314$	0.605042			0.0341445
$315$		0			0
$316$	10.1969			0.573619
$317$	−8.69436	−	15.0591i	−0.488324	−	0.845802i	0.511586	−	0.859232i	$-0.329058\pi$
$317$	−8.69436	−	15.0591i	−0.488324	−	0.845802i	−0.999910	+	0.0134302i	$0.995725\pi$
$318$		0			0
$319$	−4.97535	+	8.61756i	−0.278566	+	0.482491i
$320$	1.43171	−	2.47980i	0.0800352	−	0.138625i
$321$		0			0
$322$	−19.1456	−	33.1612i	−1.06694	−	1.84800i
$323$	5.18302			0.288391
$324$		0			0
$325$	2.72829			0.151338
$326$	−12.2863	−	21.2804i	−0.680474	−	1.17861i
$327$		0			0
$328$	1.77324	−	3.07134i	0.0979108	−	0.169586i
$329$	3.33954	−	5.78426i	0.184115	−	0.318897i
$330$		0			0
$331$	−0.432074	−	0.748374i	−0.0237489	−	0.0411343i	0.853907	−	0.520426i	$-0.174227\pi$
$331$	−0.432074	−	0.748374i	−0.0237489	−	0.0411343i	−0.877656	+	0.479292i	$0.840894\pi$
$332$	−9.64405			−0.529286
$333$		0			0
$334$	3.65741			0.200124
$335$	−1.06687	−	1.84787i	−0.0582893	−	0.100960i
$336$		0			0
$337$	−0.209264	+	0.362457i	−0.0113994	+	0.0197443i	−0.871669	−	0.490095i	$-0.836962\pi$
$337$	−0.209264	+	0.362457i	−0.0113994	+	0.0197443i	0.860269	+	0.509840i	$0.170295\pi$
$338$	10.4749	−	18.1430i	0.569757	−	0.986848i
$339$		0			0
$340$	0.880952	+	1.52585i	0.0477763	+	0.0827510i
$341$	−2.50753			−0.135791
$342$		0			0
$343$	−5.00216			−0.270091
$344$	4.96549	+	8.60048i	0.267721	+	0.463707i
$345$		0			0
$346$	14.7643	−	25.5725i	0.793734	−	1.37479i
$347$	−11.7049	+	20.2734i	−0.628351	+	1.08834i	0.359532	+	0.933133i	$0.382936\pi$
$347$	−11.7049	+	20.2734i	−0.628351	+	1.08834i	−0.987883	+	0.155202i	$0.950397\pi$
$348$		0			0
$349$	−10.5882	−	18.3393i	−0.566773	−	0.981680i	−0.996882	−	0.0789033i	$-0.974858\pi$
$349$	−10.5882	−	18.3393i	−0.566773	−	0.981680i	0.430109	−	0.902777i	$-0.358475\pi$
$350$	24.4696			1.30796
$351$		0			0
$352$	8.23894			0.439137
$353$	−11.7722	−	20.3901i	−0.626573	−	1.08526i	−0.988235	−	0.152946i	$-0.951124\pi$
$353$	−11.7722	−	20.3901i	−0.626573	−	1.08526i	0.361662	−	0.932309i	$-0.382209\pi$
$354$		0			0
$355$	−6.88111	+	11.9184i	−0.365211	+	0.632565i
$356$	2.36444	−	4.09532i	0.125315	−	0.217052i
$357$		0			0
$358$	−0.844214	−	1.46222i	−0.0446181	−	0.0772808i
$359$	−10.4609			−0.552107			−0.276053	−	0.961142i	$-0.589027\pi$
$359$	−10.4609			−0.552107			−0.276053	+	0.961142i	$0.589027\pi$
$360$		0			0
$361$	−11.4767			−0.604039
$362$	17.7952	+	30.8222i	0.935294	+	1.61998i
$363$		0			0
$364$	−1.18193	+	2.04716i	−0.0619500	+	0.107301i
$365$	5.58428	−	9.67227i	0.292295	−	0.506269i
$366$		0			0
$367$	−10.6291	−	18.4102i	−0.554836	−	0.961005i	−0.997916	−	0.0645226i	$-0.979448\pi$
$367$	−10.6291	−	18.4102i	−0.554836	−	0.961005i	0.443080	−	0.896482i	$-0.353886\pi$
$368$	28.9610			1.50970
$369$		0			0
$370$	−6.44808			−0.335220
$371$	5.56033	+	9.63077i	0.288678	+	0.500005i
$372$		0			0
$373$	−1.15504	+	2.00059i	−0.0598059	+	0.103587i	−0.894378	−	0.447312i	$-0.852381\pi$
$373$	−1.15504	+	2.00059i	−0.0598059	+	0.103587i	0.834572	+	0.550898i	$0.185715\pi$
$374$	2.97059	−	5.14521i	0.153605	−	0.266052i
$375$		0			0
$376$	1.68671	+	2.92147i	0.0869855	+	0.150663i
$377$	3.89737			0.200725
$378$		0			0
$379$	12.5539			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$379$	12.5539			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$380$	1.27872	+	2.21481i	0.0655969	+	0.113617i
$381$		0			0
$382$	8.26032	−	14.3073i	0.422635	−	0.732025i
$383$	9.82727	−	17.0213i	0.502150	−	0.869749i	−0.497847	−	0.867265i	$-0.665876\pi$
$383$	9.82727	−	17.0213i	0.502150	−	0.869749i	0.999997	−	0.00248418i	$-0.000790741\pi$
$384$		0			0
$385$	4.12931	+	7.15218i	0.210449	+	0.364509i
$386$	−18.7524			−0.954472
$387$		0			0
$388$	−0.283447			−0.0143898
$389$	9.42129	+	16.3182i	0.477679	+	0.827364i	0.999673	−	0.0255856i	$-0.00814502\pi$
$389$	9.42129	+	16.3182i	0.477679	+	0.827364i	−0.521994	+	0.852949i	$0.674812\pi$
$390$		0			0
$391$	5.50614	−	9.53691i	0.278457	−	0.482302i
$392$	8.17324	−	14.1565i	0.412811	−	0.715009i
$393$		0			0
$394$	−7.63969	−	13.2323i	−0.384882	−	0.666636i
$395$	−13.9531			−0.702058
$396$		0			0
$397$	20.1178			1.00968			0.504841	−	0.863212i	$-0.331551\pi$
$397$	20.1178			1.00968			0.504841	+	0.863212i	$0.331551\pi$
$398$	12.3496	+	21.3901i	0.619028	+	1.07219i
$399$		0			0
$400$	−9.25360	+	16.0277i	−0.462680	+	0.801385i
$401$	15.4028	−	26.6785i	0.769181	−	1.33226i	−0.168826	−	0.985646i	$-0.553998\pi$
$401$	15.4028	−	26.6785i	0.769181	−	1.33226i	0.938007	−	0.346615i	$-0.112669\pi$
$402$		0			0
$403$	0.491061	+	0.850542i	0.0244615	+	0.0423685i
$404$	−14.3650			−0.714684
$405$		0			0
$406$	34.9549			1.73478
$407$	3.17614	+	5.50124i	0.157435	+	0.272686i
$408$		0			0
$409$	−19.8460	+	34.3743i	−0.981323	+	1.69970i	−0.324067	+	0.946034i	$0.605050\pi$
$409$	−19.8460	+	34.3743i	−0.981323	+	1.69970i	−0.657256	+	0.753667i	$0.728283\pi$
$410$	1.70532	−	2.95369i	0.0842196	−	0.145873i
$411$		0			0
$412$	6.52655	+	11.3043i	0.321540	+	0.556923i
$413$	44.0146			2.16582
$414$		0			0
$415$	13.1966			0.647798
$416$	−1.61347	−	2.79460i	−0.0791067	−	0.137017i
$417$		0			0
$418$	4.31187	−	7.46838i	0.210900	−	0.365290i
$419$	−7.72057	+	13.3724i	−0.377174	+	0.653285i	−0.990650	−	0.136429i	$-0.956438\pi$
$419$	−7.72057	+	13.3724i	−0.377174	+	0.653285i	0.613476	+	0.789714i	$0.289771\pi$
$420$		0			0
$421$	9.04682	+	15.6696i	0.440915	+	0.763687i	0.997758	−	0.0669307i	$-0.0213206\pi$
$421$	9.04682	+	15.6696i	0.440915	+	0.763687i	−0.556843	+	0.830618i	$0.687987\pi$
$422$	13.2091			0.643009
$423$		0			0
$424$	−5.61674			−0.272773
$425$	3.51864	+	6.09446i	0.170679	+	0.295625i
$426$		0			0
$427$	10.2236	−	17.7078i	0.494754	−	0.856939i
$428$	6.82240	−	11.8167i	0.329773	−	0.571184i
$429$		0			0
$430$	4.77529	+	8.27104i	0.230285	+	0.398865i
$431$	−28.9683			−1.39535			−0.697677	−	0.716412i	$-0.745783\pi$
$431$	−28.9683			−1.39535			−0.697677	+	0.716412i	$0.745783\pi$
$432$		0			0
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$	4.40425	+	7.62838i	0.211411	+	0.366174i
$435$		0			0
$436$	1.94746	−	3.37309i	0.0932662	−	0.161542i
$437$	7.99227	−	13.8430i	0.382322	−	0.662201i
$438$		0			0
$439$	−5.13177	−	8.88848i	−0.244926	−	0.424224i	0.717185	−	0.696883i	$-0.245430\pi$
$439$	−5.13177	−	8.88848i	−0.244926	−	0.424224i	−0.962111	+	0.272659i	$0.912097\pi$
$440$	−4.17120			−0.198854
$441$		0			0
$442$	−2.32697			−0.110683
$443$	−10.9543	−	18.9733i	−0.520452	−	0.901450i	−0.999717	−	0.0237794i	$-0.992430\pi$
$443$	−10.9543	−	18.9733i	−0.520452	−	0.901450i	0.479265	−	0.877670i	$-0.340903\pi$
$444$		0			0
$445$	−3.23543	+	5.60393i	−0.153374	+	0.265652i
$446$	7.34633	−	12.7242i	0.347859	−	0.602509i
$447$		0			0
$448$	4.95462	+	8.58165i	0.234084	+	0.405445i
$449$	9.97130			0.470575			0.235287	−	0.971926i	$-0.424397\pi$
$449$	9.97130			0.470575			0.235287	+	0.971926i	$0.424397\pi$
$450$		0			0
$451$	−3.35996			−0.158214
$452$	−8.23188	−	14.2580i	−0.387195	−	0.670642i
$453$		0			0
$454$	−3.41932	+	5.92244i	−0.160477	+	0.277954i
$455$	1.61732	−	2.80128i	0.0758211	−	0.131326i
$456$		0			0
$457$	3.80905	+	6.59747i	0.178180	+	0.308617i	0.941257	−	0.337691i	$-0.109646\pi$
$457$	3.80905	+	6.59747i	0.178180	+	0.308617i	−0.763077	+	0.646307i	$0.776312\pi$
$458$	27.1566			1.26894
$459$		0			0
$460$	5.43375			0.253350
$461$	11.4003	+	19.7458i	0.530963	+	0.919656i	0.999347	+	0.0361304i	$0.0115032\pi$
$461$	11.4003	+	19.7458i	0.530963	+	0.919656i	−0.468384	+	0.883525i	$0.655164\pi$
$462$		0			0
$463$	4.39787	−	7.61733i	0.204386	−	0.354007i	−0.745551	−	0.666449i	$-0.767813\pi$
$463$	4.39787	−	7.61733i	0.204386	−	0.354007i	0.949937	+	0.312442i	$0.101147\pi$
$464$	−13.2188	+	22.8956i	−0.613668	+	1.06290i
$465$		0			0
$466$	−14.4669	−	25.0574i	−0.670166	−	1.16076i
$467$	−10.9976			−0.508906			−0.254453	−	0.967085i	$-0.581895\pi$
$467$	−10.9976			−0.508906			−0.254453	+	0.967085i	$0.581895\pi$
$468$		0			0
$469$	7.38406			0.340964
$470$	1.62210	+	2.80956i	0.0748220	+	0.129596i
$471$		0			0
$472$	−11.1153	+	19.2523i	−0.511623	+	0.886157i
$473$	4.70434	−	8.14816i	0.216306	−	0.374653i
$474$		0			0
$475$	5.10738	+	8.84624i	0.234343	+	0.405893i
$476$	−6.09728			−0.279468
$477$		0			0
$478$	−2.58094			−0.118049
$479$	−12.8463	−	22.2504i	−0.586961	−	1.01665i	−0.994628	−	0.103515i	$-0.966991\pi$
$479$	−12.8463	−	22.2504i	−0.586961	−	1.01665i	0.407667	−	0.913131i	$-0.366342\pi$
$480$		0			0
$481$	1.24399	−	2.15466i	0.0567212	−	0.0982440i
$482$	4.64072	−	8.03797i	0.211379	−	0.366119i
$483$		0			0
$484$	3.09607	+	5.36255i	0.140731	+	0.243752i
$485$	0.387861			0.0176119
$486$		0			0
$487$	−30.3800			−1.37665			−0.688325	−	0.725402i	$-0.741654\pi$
$487$	−30.3800			−1.37665			−0.688325	+	0.725402i	$0.741654\pi$
$488$	5.16365	+	8.94370i	0.233747	+	0.404862i
$489$		0			0
$490$	7.86016	−	13.6142i	0.355086	−	0.615027i
$491$	−4.35414	+	7.54159i	−0.196499	+	0.340347i	−0.947391	−	0.320078i	$-0.896291\pi$
$491$	−4.35414	+	7.54159i	−0.196499	+	0.340347i	0.750892	+	0.660425i	$0.229624\pi$
$492$		0			0
$493$	5.02639	+	8.70596i	0.226377	+	0.392097i
$494$	−3.37764			−0.151967
$495$		0			0
$496$	−6.66217			−0.299140
$497$	−23.8129	−	41.2451i	−1.06815	−	1.85010i
$498$		0			0
$499$	−5.81774	+	10.0766i	−0.260438	+	0.451091i	−0.966358	−	0.257200i	$-0.917200\pi$
$499$	−5.81774	+	10.0766i	−0.260438	+	0.451091i	0.705921	+	0.708291i	$0.250534\pi$
$500$	−4.06719	+	7.04458i	−0.181890	+	0.315043i
$501$		0			0
$502$	18.0201	+	31.2118i	0.804277	+	1.39305i
$503$	−37.7991			−1.68538			−0.842689	−	0.538400i	$-0.819029\pi$
$503$	−37.7991			−1.68538			−0.842689	+	0.538400i	$0.819029\pi$
$504$		0			0
$505$	19.6566			0.874708
$506$	−9.16135	−	15.8679i	−0.407272	−	0.705416i
$507$		0			0
$508$	−0.441400	+	0.764527i	−0.0195840	+	0.0339204i
$509$	−11.7868	+	20.4154i	−0.522442	+	0.904896i	0.477217	+	0.878785i	$0.341645\pi$
$509$	−11.7868	+	20.4154i	−0.522442	+	0.904896i	−0.999659	+	0.0261103i	$0.991688\pi$
$510$		0			0
$511$	19.3251	+	33.4720i	0.854891	+	1.48072i
$512$	2.26711			0.100193
$513$		0			0
$514$	−24.8548			−1.09630
$515$	−8.93074	−	15.4685i	−0.393536	−	0.681623i
$516$		0			0
$517$	1.59800	−	2.76782i	0.0702801	−	0.121729i
$518$	11.1572	−	19.3248i	0.490218	−	0.849083i
$519$		0			0
$520$	0.816864	+	1.41485i	0.0358218	+	0.0620453i
$521$	7.86948			0.344768			0.172384	−	0.985030i	$-0.444853\pi$
$521$	7.86948			0.344768			0.172384	+	0.985030i	$0.444853\pi$
$522$		0			0
$523$	33.2935			1.45582			0.727911	−	0.685672i	$-0.240491\pi$
$523$	33.2935			1.45582			0.727911	+	0.685672i	$0.240491\pi$
$524$	−3.15340	−	5.46185i	−0.137757	−	0.238602i
$525$		0			0
$526$	−2.35559	+	4.08001i	−0.102709	+	0.177897i
$527$	−1.26663	+	2.19387i	−0.0551752	+	0.0955663i
$528$		0			0
$529$	−5.48104	−	9.49344i	−0.238306	−	0.412758i
$530$	−5.40159			−0.234630
$531$		0			0
$532$	−8.85032			−0.383710
$533$	0.657995	+	1.13968i	0.0285009	+	0.0493650i
$534$		0			0
$535$	−9.33558	+	16.1697i	−0.403612	+	0.699077i
$536$	−1.86474	+	3.22983i	−0.0805447	+	0.139507i
$537$		0			0
$538$	0.299646	+	0.519002i	0.0129186	+	0.0223758i
$539$	−15.4868			−0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	10.2087	+	17.6820i	0.438503	+	0.759509i
$543$		0			0
$544$	4.16173	−	7.20833i	0.178433	−	0.309055i
$545$	−2.66484	+	4.61564i	−0.114149	+	0.197712i
$546$		0			0
$547$	10.4456	+	18.0923i	0.446621	+	0.773570i	0.998164	−	0.0605770i	$-0.0192941\pi$
$547$	10.4456	+	18.0923i	0.446621	+	0.773570i	−0.551543	+	0.834146i	$0.685961\pi$
$548$	12.9190			0.551870
$549$		0			0
$550$	11.7089			0.499271
$551$	7.29591	+	12.6369i	0.310816	+	0.538349i
$552$		0			0
$553$	24.1432	−	41.8173i	1.02667	−	1.77825i
$554$	−21.0030	+	36.3782i	−0.892330	+	1.54556i
$555$		0			0
$556$	−3.57300	−	6.18862i	−0.151529	−	0.262456i
$557$	8.57840			0.363478			0.181739	−	0.983347i	$-0.441827\pi$
$557$	8.57840			0.363478			0.181739	+	0.983347i	$0.441827\pi$
$558$		0			0
$559$	−3.68508			−0.155862
$560$	10.9710	+	19.0023i	0.463609	+	0.802995i
$561$		0			0
$562$	−6.15455	+	10.6600i	−0.259614	+	0.449665i
$563$	7.85744	−	13.6095i	0.331152	−	0.573571i	−0.651586	−	0.758574i	$-0.725896\pi$
$563$	7.85744	−	13.6095i	0.331152	−	0.573571i	0.982738	+	0.185003i	$0.0592295\pi$
$564$		0			0
$565$	11.2643	+	19.5103i	0.473892	+	0.820804i
$566$	−24.1851			−1.01658
$567$		0			0
$568$	24.0545			1.00930
$569$	−6.33639	−	10.9750i	−0.265635	−	0.460094i	0.702094	−	0.712084i	$-0.252248\pi$
$569$	−6.33639	−	10.9750i	−0.265635	−	0.460094i	−0.967730	+	0.251990i	$0.918915\pi$
$570$		0			0
$571$	13.1613	−	22.7961i	0.550785	−	0.953988i	−0.447433	−	0.894317i	$-0.647662\pi$
$571$	13.1613	−	22.7961i	0.550785	−	0.953988i	0.998218	−	0.0596704i	$-0.0190050\pi$
$572$	−0.565565	+	0.979587i	−0.0236474	+	0.0409586i
$573$		0			0
$574$	5.90145	+	10.2216i	0.246322	+	0.426642i
$575$	21.7031			0.905082
$576$		0			0
$577$	−22.1154			−0.920676			−0.460338	−	0.887744i	$-0.652272\pi$
$577$	−22.1154			−0.920676			−0.460338	+	0.887744i	$0.652272\pi$
$578$	11.2867	+	19.5491i	0.469465	+	0.813136i
$579$		0			0
$580$	−2.48015	+	4.29575i	−0.102983	+	0.178371i
$581$	−22.8343	+	39.5502i	−0.947326	+	1.64082i
$582$		0			0
$583$	2.66067	+	4.60842i	0.110194	+	0.190861i
$584$	−19.5211			−0.807790
$585$		0			0
$586$	−24.2312			−1.00098
$587$	−7.15157	−	12.3869i	−0.295177	−	0.511261i	0.679849	−	0.733352i	$-0.262045\pi$
$587$	−7.15157	−	12.3869i	−0.295177	−	0.511261i	−0.975026	+	0.222091i	$0.928712\pi$
$588$		0			0
$589$	−1.83854	+	3.18444i	−0.0757556	+	0.131213i
$590$	−10.6895	+	18.5148i	−0.440081	+	0.762242i
$591$		0			0
$592$	8.43856	+	14.6160i	0.346823	+	0.600714i
$593$	47.7300			1.96004			0.980018	−	0.198908i	$-0.0637397\pi$
$593$	47.7300			1.96004			0.980018	+	0.198908i	$0.0637397\pi$
$594$		0			0
$595$	8.34334			0.342044
$596$	1.01690	+	1.76132i	0.0416539	+	0.0721466i
$597$		0			0
$598$	−3.58821	+	6.21496i	−0.146733	+	0.254149i
$599$	0.249785	−	0.432640i	0.0102059	−	0.0176772i	−0.860877	−	0.508813i	$-0.830085\pi$
$599$	0.249785	−	0.432640i	0.0102059	−	0.0176772i	0.871083	+	0.491135i	$0.163418\pi$
$600$		0			0
$601$	8.46354	+	14.6593i	0.345235	+	0.597965i	0.985396	−	0.170276i	$-0.0544659\pi$
$601$	8.46354	+	14.6593i	0.345235	+	0.597965i	−0.640161	+	0.768240i	$0.721133\pi$
$602$	−33.0509			−1.34705
$603$		0			0
$604$	−8.67846			−0.353121
$605$	−4.23658	−	7.33797i	−0.172241	−	0.298331i
$606$		0			0
$607$	−0.347316	+	0.601569i	−0.0140971	+	0.0244170i	−0.872988	−	0.487742i	$-0.837821\pi$
$607$	−0.347316	+	0.601569i	−0.0140971	+	0.0244170i	0.858891	+	0.512159i	$0.171154\pi$
$608$	6.04084	−	10.4630i	0.244988	−	0.424332i
$609$		0			0
$610$	4.96586	+	8.60112i	0.201062	+	0.348249i
$611$	−1.25177			−0.0506413
$612$		0			0
$613$	−32.6633			−1.31926			−0.659630	−	0.751590i	$-0.729287\pi$
$613$	−32.6633			−1.31926			−0.659630	+	0.751590i	$0.729287\pi$
$614$	25.5772	+	44.3011i	1.03221	+	1.78785i
$615$		0			0
$616$	7.21747	−	12.5010i	0.290800	−	0.503681i
$617$	−11.4422	+	19.8185i	−0.460646	+	0.797863i	−0.998993	−	0.0448606i	$-0.985716\pi$
$617$	−11.4422	+	19.8185i	−0.460646	+	0.797863i	0.538347	+	0.842723i	$0.319049\pi$
$618$		0			0
$619$	−4.24287	−	7.34886i	−0.170535	−	0.295376i	0.768072	−	0.640364i	$-0.221216\pi$
$619$	−4.24287	−	7.34886i	−0.170535	−	0.295376i	−0.938607	+	0.344988i	$0.887883\pi$
$620$	−1.24998			−0.0502002
$621$		0			0
$622$	−23.5254			−0.943282
$623$	−11.1966	−	19.3931i	−0.448582	−	0.776966i
$624$		0			0
$625$	−3.74490	+	6.48635i	−0.149796	+	0.259454i
$626$	−18.5636	+	32.1531i	−0.741952	+	1.28510i
$627$		0			0
$628$	−0.148563	−	0.257318i	−0.00592829	−	0.0102681i
$629$	6.41744			0.255880
$630$		0			0
$631$	1.59173			0.0633657			0.0316829	−	0.999498i	$-0.489913\pi$
$631$	1.59173			0.0633657			0.0316829	+	0.999498i	$0.489913\pi$
$632$	12.1941	+	21.1208i	0.485054	+	0.840138i
$633$		0			0
$634$	−14.6145	+	25.3130i	−0.580414	+	1.00531i
$635$	0.603999	−	1.04616i	0.0239690	−	0.0415155i
$636$		0			0
$637$	3.03284	+	5.25303i	0.120165	+	0.208133i
$638$	16.7263			0.662199
$639$		0			0
$640$	−14.7640			−0.583597
$641$	−10.8373	−	18.7708i	−0.428049	−	0.741402i	0.568651	−	0.822579i	$-0.307466\pi$
$641$	−10.8373	−	18.7708i	−0.428049	−	0.741402i	−0.996700	+	0.0811767i	$0.974132\pi$
$642$		0			0
$643$	3.45103	−	5.97736i	0.136095	−	0.235724i	−0.789920	−	0.613210i	$-0.789878\pi$
$643$	3.45103	−	5.97736i	0.136095	−	0.235724i	0.926015	+	0.377486i	$0.123211\pi$
$644$	−9.40207	+	16.2849i	−0.370493	+	0.641713i
$645$		0			0
$646$	−4.35610	−	7.54499i	−0.171388	−	0.296854i
$647$	−6.18972			−0.243343			−0.121671	−	0.992570i	$-0.538825\pi$
$647$	−6.18972			−0.243343			−0.121671	+	0.992570i	$0.538825\pi$
$648$		0			0
$649$	21.0614			0.826733
$650$	−2.29301	−	3.97161i	−0.0899392	−	0.155779i
$651$		0			0
$652$	−6.03357	+	10.4504i	−0.236293	+	0.409271i
$653$	13.6072	−	23.5684i	0.532492	−	0.922304i	−0.466788	−	0.884369i	$-0.654589\pi$
$653$	13.6072	−	23.5684i	0.532492	−	0.922304i	0.999280	−	0.0379345i	$-0.0120778\pi$
$654$		0			0
$655$	4.31503	+	7.47385i	0.168602	+	0.292027i
$656$	−8.92694			−0.348539
$657$		0			0
$658$	−11.2270			−0.437672
$659$	−2.64100	−	4.57434i	−0.102879	−	0.178191i	0.809991	−	0.586443i	$-0.199472\pi$
$659$	−2.64100	−	4.57434i	−0.102879	−	0.178191i	−0.912870	+	0.408251i	$0.866139\pi$
$660$		0			0
$661$	−5.83252	+	10.1022i	−0.226859	+	0.392931i	−0.956875	−	0.290498i	$-0.906179\pi$
$661$	−5.83252	+	10.1022i	−0.226859	+	0.392931i	0.730017	+	0.683429i	$0.239512\pi$
$662$	−0.726278	+	1.25795i	−0.0282276	+	0.0488916i
$663$		0			0
$664$	−11.5330	−	19.9757i	−0.447566	−	0.775207i
$665$	12.1105			0.469626
$666$		0			0
$667$	31.0030			1.20044
$668$	−0.898044	−	1.55546i	−0.0347464	−	0.0601824i
$669$		0			0
$670$	−1.79332	+	3.10611i	−0.0692818	+	0.120000i
$671$	4.89208	−	8.47333i	0.188857	−	0.327109i
$672$		0			0
$673$	−24.5512	−	42.5239i	−0.946380	−	1.63918i	−0.752965	−	0.658061i	$-0.771377\pi$
$673$	−24.5512	−	42.5239i	−0.946380	−	1.63918i	−0.193415	−	0.981117i	$-0.561956\pi$
$674$	0.703510			0.0270982
$675$		0			0
$676$	−10.2880			−0.395693
$677$	11.3095	+	19.5887i	0.434660	+	0.752854i	0.997268	−	0.0738704i	$-0.0235351\pi$
$677$	11.3095	+	19.5887i	0.434660	+	0.752854i	−0.562608	+	0.826724i	$0.690202\pi$
$678$		0			0
$679$	−0.671120	+	1.16241i	−0.0257552	+	0.0446093i
$680$	−2.10700	+	3.64942i	−0.0807996	+	0.139949i
$681$		0			0
$682$	2.10747	+	3.65025i	0.0806993	+	0.139775i
$683$	−17.1386			−0.655791			−0.327896	−	0.944714i	$-0.606339\pi$
$683$	−17.1386			−0.655791			−0.327896	+	0.944714i	$0.606339\pi$
$684$		0			0
$685$	−17.6779			−0.675439
$686$	4.20409	+	7.28170i	0.160513	+	0.278017i
$687$		0			0
$688$	12.4988	−	21.6485i	0.476511	−	0.825341i
$689$	1.04210	−	1.80497i	0.0397008	−	0.0687639i
$690$		0			0
$691$	−9.12796	−	15.8101i	−0.347244	−	0.601444i	0.638515	−	0.769609i	$-0.279549\pi$
$691$	−9.12796	−	15.8101i	−0.347244	−	0.601444i	−0.985759	+	0.168165i	$0.946216\pi$
$692$	−14.5010			−0.551244
$693$		0			0
$694$	39.3497			1.49370
$695$	4.88919	+	8.46833i	0.185458	+	0.321222i
$696$		0			0
$697$	−1.69721	+	2.93966i	−0.0642866	+	0.111348i
$698$	−17.7978	+	30.8268i	−0.673658	+	1.16681i
$699$		0			0
$700$	−6.00829	−	10.4067i	−0.227092	−	0.393335i
$701$	−2.92075			−0.110315			−0.0551575	−	0.998478i	$-0.517566\pi$
$701$	−2.92075			−0.110315			−0.0551575	+	0.998478i	$0.517566\pi$
$702$		0			0
$703$	9.31505			0.351324
$704$	2.37083	+	4.10640i	0.0893540	+	0.154766i
$705$		0			0
$706$	−19.7881	+	34.2740i	−0.744734	+	1.28992i
$707$	−34.0120	+	58.9106i	−1.27915	+	2.21556i
$708$		0			0
$709$	−15.0137	−	26.0044i	−0.563850	−	0.976617i	−0.997156	−	0.0753698i	$-0.975986\pi$
$709$	−15.0137	−	26.0044i	−0.563850	−	0.976617i	0.433306	−	0.901247i	$-0.357347\pi$
$710$	23.1331			0.868169
$711$		0			0
$712$	11.3102			0.423867
$713$	3.90631	+	6.76593i	0.146292	+	0.253386i
$714$		0			0
$715$	0.773903	−	1.34044i	0.0289423	−	0.0501296i
$716$	−0.414578	+	0.718071i	−0.0154935	+	0.0268356i
$717$		0			0
$718$	8.79195	+	15.2281i	0.328113	+	0.568308i
$719$	40.0569			1.49387			0.746936	−	0.664896i	$-0.231524\pi$
$719$	40.0569			1.49387			0.746936	+	0.664896i	$0.231524\pi$
$720$		0			0
$721$	61.8118			2.30199
$722$	9.64570	+	16.7068i	0.358976	+	0.621764i
$723$		0			0
$724$	8.73890	−	15.1362i	0.324779	−	0.562533i
$725$	−9.90607	+	17.1578i	−0.367902	+	0.637225i
$726$		0			0
$727$	0.769390	+	1.33262i	0.0285351	+	0.0494243i	0.879940	−	0.475084i	$-0.157582\pi$
$727$	0.769390	+	1.33262i	0.0285351	+	0.0494243i	−0.851405	+	0.524509i	$0.824249\pi$
$728$	−5.65371			−0.209540
$729$		0			0
$730$	−18.7734			−0.694834
$731$	−4.75260	−	8.23174i	−0.175781	−	0.304462i
$732$		0			0
$733$	0.755947	−	1.30934i	0.0279215	−	0.0483615i	−0.851727	−	0.523986i	$-0.824444\pi$
$733$	0.755947	−	1.30934i	0.0279215	−	0.0483615i	0.879649	+	0.475624i	$0.157778\pi$
$734$	−17.8666	+	30.9459i	−0.659470	+	1.14224i
$735$		0			0
$736$	−12.8349	−	22.2306i	−0.473099	−	0.819432i
$737$	3.53334			0.130152
$738$		0			0
$739$	21.3558			0.785584			0.392792	−	0.919627i	$-0.371509\pi$
$739$	21.3558			0.785584			0.392792	+	0.919627i	$0.371509\pi$
$740$	1.58327	+	2.74230i	0.0582021	+	0.100809i
$741$		0			0
$742$	9.34643	−	16.1885i	0.343118	−	0.594298i
$743$	10.1644	−	17.6052i	0.372895	−	0.645872i	−0.617115	−	0.786873i	$-0.711699\pi$
$743$	10.1644	−	17.6052i	0.372895	−	0.645872i	0.990009	+	0.141001i	$0.0450320\pi$
$744$		0			0
$745$	−1.39150	−	2.41015i	−0.0509806	−	0.0883009i
$746$	3.88305			0.142169
$747$		0			0
$748$	−2.91760			−0.106678
$749$	−32.3069	−	55.9572i	−1.18047	−	2.04463i
$750$		0			0
$751$	−2.13158	+	3.69200i	−0.0777824	+	0.134723i	−0.902293	−	0.431124i	$-0.858117\pi$
$751$	−2.13158	+	3.69200i	−0.0777824	+	0.134723i	0.824510	+	0.565847i	$0.191451\pi$
$752$	4.24567	−	7.35371i	0.154824	−	0.268162i
$753$		0			0
$754$	−3.27557	−	5.67346i	−0.119289	−	0.206615i
$755$	11.8754			0.432189
$756$		0			0
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$	−10.5510	−	18.2748i	−0.383229	−	0.663772i
$759$		0			0
$760$	−3.05835	+	5.29721i	−0.110938	+	0.192150i
$761$	−9.08056	+	15.7280i	−0.329170	+	0.570139i	−0.982347	−	0.187066i	$-0.940102\pi$
$761$	−9.08056	+	15.7280i	−0.329170	+	0.570139i	0.653177	+	0.757205i	$0.273436\pi$
$762$		0			0
$763$	−9.22201	−	15.9730i	−0.333859	−	0.578261i
$764$	−8.11299			−0.293518
$765$		0			0
$766$	−33.0375			−1.19369
$767$	−4.12454	−	7.14392i	−0.148929	−	0.257952i
$768$		0			0
$769$	−12.4274	+	21.5248i	−0.448142	+	0.776205i	−0.998265	−	0.0588785i	$-0.981248\pi$
$769$	−12.4274	+	21.5248i	−0.448142	+	0.776205i	0.550123	+	0.835084i	$0.314581\pi$
$770$	6.94101	−	12.0222i	0.250137	−	0.433249i
$771$		0			0
$772$	4.60448	+	7.97520i	0.165719	+	0.287034i
$773$	38.4832			1.38414			0.692071	−	0.721829i	$-0.256698\pi$
$773$	38.4832			1.38414			0.692071	+	0.721829i	$0.256698\pi$
$774$		0			0
$775$	−4.99257			−0.179338
$776$	−0.338964	−	0.587103i	−0.0121681	−	0.0210758i
$777$		0			0
$778$	15.8364	−	27.4294i	0.567761	−	0.983391i
$779$	−2.46354	+	4.26698i	−0.0882655	+	0.152880i
$780$		0			0
$781$	−11.3947	−	19.7362i	−0.407734	−	0.706216i
$782$	−18.5107			−0.661940
$783$		0			0
$784$	−41.1462			−1.46951
$785$	0.203289	+	0.352107i	0.00725569	+	0.0125672i
$786$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.840456 - 1.45571i) q^{2} +(-0.412733 + 0.714874i) q^{4} +(0.564772 - 0.978214i) q^{5} +(1.95446 + 3.38523i) q^{7} -1.97429 q^{8} +O(q^{10})\)	\(q+(-0.840456 - 1.45571i) q^{2} +(-0.412733 + 0.714874i) q^{4} +(0.564772 - 0.978214i) q^{5} +(1.95446 + 3.38523i) q^{7} -1.97429 q^{8} -1.89866 q^{10} +(0.935228 + 1.61986i) q^{11} +(0.366299 - 0.634448i) q^{13} +(3.28528 - 5.69027i) q^{14} +(2.48477 + 4.30375i) q^{16} +1.88964 q^{17} +2.74286 q^{19} +(0.466200 + 0.807482i) q^{20} +(1.57204 - 2.72285i) q^{22} +(2.91385 - 5.04694i) q^{23} +(1.86207 + 3.22519i) q^{25} -1.23143 q^{26} -3.22668 q^{28} +(2.65997 + 4.60720i) q^{29} +(-0.670300 + 1.16099i) q^{31} +(2.20239 - 3.81465i) q^{32} +(-1.58816 - 2.75078i) q^{34} +4.41530 q^{35} +3.39611 q^{37} +(-2.30525 - 3.99281i) q^{38} +(-1.11502 + 1.93128i) q^{40} +(-0.898166 + 1.55567i) q^{41} +(-2.51508 - 4.35624i) q^{43} -1.54400 q^{44} -9.79585 q^{46} +(-0.854339 - 1.47976i) q^{47} +(-4.13984 + 7.17041i) q^{49} +(3.12997 - 5.42126i) q^{50} +(0.302367 + 0.523715i) q^{52} +2.84494 q^{53} +2.11276 q^{55} +(-3.85867 - 6.68342i) q^{56} +(4.47117 - 7.74430i) q^{58} +(5.63002 - 9.75149i) q^{59} +(-2.61545 - 4.53009i) q^{61} +2.25343 q^{62} +2.53503 q^{64} +(-0.413751 - 0.716637i) q^{65} +(0.944514 - 1.63595i) q^{67} +(-0.779918 + 1.35086i) q^{68} +(-3.71087 - 6.42741i) q^{70} -12.1839 q^{71} +9.88768 q^{73} +(-2.85428 - 4.94376i) q^{74} +(-1.13207 + 1.96080i) q^{76} +(-3.65573 + 6.33192i) q^{77} +(-6.17644 - 10.6979i) q^{79} +5.61331 q^{80} +3.01948 q^{82} +(5.84158 + 10.1179i) q^{83} +(1.06722 - 1.84848i) q^{85} +(-4.22762 + 7.32246i) q^{86} +(-1.84641 - 3.19808i) q^{88} -5.72873 q^{89} +2.86367 q^{91} +(2.40528 + 4.16607i) q^{92} +(-1.43607 + 2.48734i) q^{94} +(1.54909 - 2.68310i) q^{95} +(0.171689 + 0.297374i) q^{97} +13.9174 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * q^98

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