LMFDB - Embedded newform 729.2.c.e.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:	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} + \cdots + 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			487.3
Root			$0.500000 + 0.258654i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.e.244.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207733 - 0.359804i) q^{2} +(0.913694 + 1.58256i) q^{4} +(-1.10759 - 1.91841i) q^{5} +(0.659815 - 1.14283i) q^{7} +1.59015 q^{8} +O(q^{10})$	\(q+(0.207733 - 0.359804i) q^{2} +(0.913694 + 1.58256i) q^{4} +(-1.10759 - 1.91841i) q^{5} +(0.659815 - 1.14283i) q^{7} +1.59015 q^{8} -0.920335 q^{10} +(2.60759 - 4.51648i) q^{11} +(0.00902926 + 0.0156391i) q^{13} +(-0.274131 - 0.474808i) q^{14} +(-1.49706 + 2.59299i) q^{16} -3.13280 q^{17} +0.417352 q^{19} +(2.02400 - 3.50568i) q^{20} +(-1.08337 - 1.87645i) q^{22} +(0.517193 + 0.895805i) q^{23} +(0.0464738 - 0.0804949i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(3.90361 - 6.76125i) q^{29} +(-1.86483 - 3.22998i) q^{31} +(2.21213 + 3.83152i) q^{32} +(-0.650785 + 1.12719i) q^{34} -2.92322 q^{35} +4.42476 q^{37} +(0.0866979 - 0.150165i) q^{38} +(-1.76124 - 3.05056i) q^{40} +(1.83747 + 3.18259i) q^{41} +(4.15394 - 7.19483i) q^{43} +9.53017 q^{44} +0.429753 q^{46} +(3.54895 - 6.14697i) q^{47} +(2.62929 + 4.55406i) q^{49} +(-0.0193083 - 0.0334429i) q^{50} +(-0.0165000 + 0.0285788i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(1.04920 - 1.81728i) q^{56} +(-1.62182 - 2.80907i) q^{58} +(1.85091 + 3.20586i) q^{59} +(-3.45712 + 5.98791i) q^{61} -1.54955 q^{62} -4.15011 q^{64} +(0.0200015 - 0.0346436i) q^{65} +(5.51340 + 9.54949i) q^{67} +(-2.86242 - 4.95785i) q^{68} +(-0.607251 + 1.05179i) q^{70} -6.08428 q^{71} -0.546973 q^{73} +(0.919169 - 1.59205i) q^{74} +(0.381332 + 0.660487i) q^{76} +(-3.44106 - 5.96008i) q^{77} +(-0.244572 + 0.423611i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(-2.30684 + 3.99556i) q^{83} +(3.46986 + 6.00998i) q^{85} +(-1.72582 - 2.98921i) q^{86} +(4.14647 - 7.18189i) q^{88} -3.37307 q^{89} +0.0238305 q^{91} +(-0.945113 + 1.63698i) q^{92} +(-1.47447 - 2.55386i) q^{94} +(-0.462257 - 0.800652i) q^{95} +(-4.97068 + 8.60947i) q^{97} +2.18476 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.207733	−	0.359804i	0.146889	−	0.254420i	−0.783187	−	0.621786i	$-0.786407\pi$
$2$	0.207733	−	0.359804i	0.146889	−	0.254420i	0.930076	+	0.367366i	$0.119740\pi$
$3$		0			0
$3$		0			0
$4$	0.913694	+	1.58256i	0.456847	+	0.791282i
$5$	−1.10759	−	1.91841i	−0.495331	−	0.857938i	0.504655	−	0.863321i	$-0.331620\pi$
$5$	−1.10759	−	1.91841i	−0.495331	−	0.857938i	−0.999986	+	0.00538314i	$0.998286\pi$
$6$		0			0
$7$	0.659815	−	1.14283i	0.249386	−	0.431950i	−0.713969	−	0.700177i	$-0.753104\pi$
$7$	0.659815	−	1.14283i	0.249386	−	0.431950i	0.963356	+	0.268227i	$0.0864377\pi$
$8$	1.59015			0.562203
$9$		0			0
$10$	−0.920335			−0.291036
$11$	2.60759	−	4.51648i	0.786219	−	1.36177i	−0.142049	−	0.989860i	$-0.545369\pi$
$11$	2.60759	−	4.51648i	0.786219	−	1.36177i	0.928268	−	0.371912i	$-0.121298\pi$
$12$		0			0
$13$	0.00902926	+	0.0156391i	0.00250427	+	0.00433752i	0.867275	−	0.497830i	$-0.165870\pi$
$13$	0.00902926	+	0.0156391i	0.00250427	+	0.00433752i	−0.864771	+	0.502167i	$0.832536\pi$
$14$	−0.274131	−	0.474808i	−0.0732645	−	0.126898i
$15$		0			0
$16$	−1.49706	+	2.59299i	−0.374265	+	0.648246i
$17$	−3.13280			−0.759814			−0.379907	−	0.925025i	$-0.624044\pi$
$17$	−3.13280			−0.759814			−0.379907	+	0.925025i	$0.624044\pi$
$18$		0			0
$19$	0.417352			0.0957472			0.0478736	−	0.998853i	$-0.484756\pi$
$19$	0.417352			0.0957472			0.0478736	+	0.998853i	$0.484756\pi$
$20$	2.02400	−	3.50568i	0.452581	−	0.783893i
$21$		0			0
$22$	−1.08337	−	1.87645i	−0.230975	−	0.400060i
$23$	0.517193	+	0.895805i	0.107842	+	0.186788i	0.914896	−	0.403690i	$-0.132273\pi$
$23$	0.517193	+	0.895805i	0.107842	+	0.186788i	−0.807054	+	0.590478i	$0.798939\pi$
$24$		0			0
$25$	0.0464738	−	0.0804949i	0.00929475	−	0.0160990i
$26$	0.00750270			0.00147140
$27$		0			0
$28$	2.41147			0.455726
$29$	3.90361	−	6.76125i	0.724882	−	1.25553i	−0.234140	−	0.972203i	$-0.575227\pi$
$29$	3.90361	−	6.76125i	0.724882	−	1.25553i	0.959022	−	0.283330i	$-0.0914393\pi$
$30$		0			0
$31$	−1.86483	−	3.22998i	−0.334934	−	0.580122i	0.648538	−	0.761182i	$-0.275381\pi$
$31$	−1.86483	−	3.22998i	−0.334934	−	0.580122i	−0.983472	+	0.181060i	$0.942047\pi$
$32$	2.21213	+	3.83152i	0.391053	+	0.677323i
$33$		0			0
$34$	−0.650785	+	1.12719i	−0.111609	+	0.193312i
$35$	−2.92322			−0.494115
$36$		0			0
$37$	4.42476			0.727426			0.363713	−	0.931511i	$-0.381509\pi$
$37$	4.42476			0.727426			0.363713	+	0.931511i	$0.381509\pi$
$38$	0.0866979	−	0.150165i	0.0140643	−	0.0243600i
$39$		0			0
$40$	−1.76124	−	3.05056i	−0.278477	−	0.482335i
$41$	1.83747	+	3.18259i	0.286965	+	0.497037i	0.973084	−	0.230452i	$-0.0740205\pi$
$41$	1.83747	+	3.18259i	0.286965	+	0.497037i	−0.686119	+	0.727489i	$0.740687\pi$
$42$		0			0
$43$	4.15394	−	7.19483i	0.633469	−	1.09720i	−0.353368	−	0.935484i	$-0.614964\pi$
$43$	4.15394	−	7.19483i	0.633469	−	1.09720i	0.986837	−	0.161717i	$-0.0517031\pi$
$44$	9.53017			1.43673
$45$		0			0
$46$	0.429753			0.0633636
$47$	3.54895	−	6.14697i	0.517668	−	0.896628i	−0.482121	−	0.876105i	$-0.660133\pi$
$47$	3.54895	−	6.14697i	0.517668	−	0.896628i	0.999789	−	0.0205231i	$-0.00653317\pi$
$48$		0			0
$49$	2.62929	+	4.55406i	0.375613	+	0.650580i
$50$	−0.0193083	−	0.0334429i	−0.00273060	−	0.00472954i
$51$		0			0
$52$	−0.0165000	+	0.0285788i	−0.00228813	+	0.00396316i
$53$	−1.30057			−0.178648			−0.0893238	−	0.996003i	$-0.528471\pi$
$53$	−1.30057			−0.178648			−0.0893238	+	0.996003i	$0.528471\pi$
$54$		0			0
$55$	−11.5526			−1.55775
$56$	1.04920	−	1.81728i	0.140206	−	0.242844i
$57$		0			0
$58$	−1.62182	−	2.80907i	−0.212955	−	0.368849i
$59$	1.85091	+	3.20586i	0.240967	+	0.417368i	0.960990	−	0.276583i	$-0.0892020\pi$
$59$	1.85091	+	3.20586i	0.240967	+	0.417368i	−0.720023	+	0.693950i	$0.755869\pi$
$60$		0			0
$61$	−3.45712	+	5.98791i	−0.442639	+	0.766673i	−0.997884	−	0.0650137i	$-0.979291\pi$
$61$	−3.45712	+	5.98791i	−0.442639	+	0.766673i	0.555246	+	0.831686i	$0.312624\pi$
$62$	−1.54955			−0.196793
$63$		0			0
$64$	−4.15011			−0.518764
$65$	0.0200015	−	0.0346436i	0.00248088	−	0.00429701i
$66$		0			0
$67$	5.51340	+	9.54949i	0.673569	+	1.16666i	0.976885	+	0.213765i	$0.0685728\pi$
$67$	5.51340	+	9.54949i	0.673569	+	1.16666i	−0.303316	+	0.952890i	$0.598094\pi$
$68$	−2.86242	−	4.95785i	−0.347119	−	0.601228i
$69$		0			0
$70$	−0.607251	+	1.05179i	−0.0725803	+	0.125713i
$71$	−6.08428			−0.722071			−0.361035	−	0.932552i	$-0.617577\pi$
$71$	−6.08428			−0.722071			−0.361035	+	0.932552i	$0.617577\pi$
$72$		0			0
$73$	−0.546973			−0.0640183			−0.0320092	−	0.999488i	$-0.510191\pi$
$73$	−0.546973			−0.0640183			−0.0320092	+	0.999488i	$0.510191\pi$
$74$	0.919169	−	1.59205i	0.106851	−	0.185072i
$75$		0			0
$76$	0.381332	+	0.660487i	0.0437418	+	0.0757630i
$77$	−3.44106	−	5.96008i	−0.392145	−	0.679215i
$78$		0			0
$79$	−0.244572	+	0.423611i	−0.0275165	+	0.0476600i	−0.879456	−	0.475981i	$-0.842093\pi$
$79$	−0.244572	+	0.423611i	−0.0275165	+	0.0476600i	0.851939	+	0.523641i	$0.175427\pi$
$80$	6.63254			0.741540
$81$		0			0
$82$	1.52681			0.168608
$83$	−2.30684	+	3.99556i	−0.253208	+	0.438569i	−0.964407	−	0.264421i	$-0.914819\pi$
$83$	−2.30684	+	3.99556i	−0.253208	+	0.438569i	0.711199	+	0.702991i	$0.248152\pi$
$84$		0			0
$85$	3.46986	+	6.00998i	0.376360	+	0.651874i
$86$	−1.72582	−	2.98921i	−0.186100	−	0.322335i
$87$		0			0
$88$	4.14647	−	7.18189i	0.442015	−	0.765592i
$89$	−3.37307			−0.357544			−0.178772	−	0.983891i	$-0.557212\pi$
$89$	−3.37307			−0.357544			−0.178772	+	0.983891i	$0.557212\pi$
$90$		0			0
$91$	0.0238305			0.00249812
$92$	−0.945113	+	1.63698i	−0.0985348	+	0.170667i
$93$		0			0
$94$	−1.47447	−	2.55386i	−0.152080	−	0.263410i
$95$	−0.462257	−	0.800652i	−0.0474265	−	0.0821452i
$96$		0			0
$97$	−4.97068	+	8.60947i	−0.504696	+	0.874159i	0.495289	+	0.868728i	$0.335062\pi$
$97$	−4.97068	+	8.60947i	−0.504696	+	0.874159i	−0.999985	+	0.00543103i	$0.998271\pi$
$98$	2.18476			0.220694
$99$		0			0
$100$	0.169851			0.0169851
$101$	−6.89974	+	11.9507i	−0.686550	+	1.18914i	0.286397	+	0.958111i	$0.407542\pi$
$101$	−6.89974	+	11.9507i	−0.686550	+	1.18914i	−0.972947	+	0.231029i	$0.925791\pi$
$102$		0			0
$103$	−2.28256	−	3.95351i	−0.224907	−	0.389551i	0.731384	−	0.681966i	$-0.238875\pi$
$103$	−2.28256	−	3.95351i	−0.224907	−	0.389551i	−0.956292	+	0.292415i	$0.905541\pi$
$104$	0.0143579	+	0.0248686i	0.00140791	+	0.00243856i
$105$		0			0
$106$	−0.270172	+	0.467952i	−0.0262415	+	0.0454515i
$107$	−11.2965			−1.09207			−0.546035	−	0.837762i	$-0.683864\pi$
$107$	−11.2965			−1.09207			−0.546035	+	0.837762i	$0.683864\pi$
$108$		0			0
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$	−2.39986	+	4.15668i	−0.228818	+	0.396324i
$111$		0			0
$112$	1.97557	+	3.42178i	0.186673	+	0.323328i
$113$	−6.27921	−	10.8759i	−0.590699	−	1.02312i	−0.994139	−	0.108114i	$-0.965519\pi$
$113$	−6.27921	−	10.8759i	−0.590699	−	1.02312i	0.403440	−	0.915006i	$-0.367814\pi$
$114$		0			0
$115$	1.14568	−	1.98438i	0.106835	−	0.185044i
$116$	14.2668			1.32464
$117$		0			0
$118$	1.53798			0.141582
$119$	−2.06706	+	3.58026i	−0.189487	+	0.328202i
$120$		0			0
$121$	−8.09909	−	14.0280i	−0.736281	−	1.27528i
$122$	1.43632	+	2.48777i	0.130038	+	0.225232i
$123$		0			0
$124$	3.40777	−	5.90243i	0.306027	−	0.530054i
$125$	−11.2818			−1.00908
$126$		0			0
$127$	−8.39499			−0.744935			−0.372467	−	0.928045i	$-0.621488\pi$
$127$	−8.39499			−0.744935			−0.372467	+	0.928045i	$0.621488\pi$
$128$	−5.28637	+	9.15627i	−0.467254	+	0.809307i
$129$		0			0
$130$	−0.00830995	−	0.0143932i	−0.000728831	−	0.00126237i
$131$	7.76745	+	13.4536i	0.678645	+	1.17545i	0.975389	+	0.220491i	$0.0707659\pi$
$131$	7.76745	+	13.4536i	0.678645	+	1.17545i	−0.296744	+	0.954957i	$0.595901\pi$
$132$		0			0
$133$	0.275375	−	0.476964i	0.0238781	−	0.0413580i
$134$	4.58126			0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	−6.00370	+	10.3987i	−0.512930	+	0.888421i	0.486957	+	0.873426i	$0.338107\pi$
$137$	−6.00370	+	10.3987i	−0.512930	+	0.888421i	−0.999888	+	0.0149956i	$0.995227\pi$
$138$		0			0
$139$	−3.07256	−	5.32183i	−0.260611	−	0.451392i	0.705793	−	0.708418i	$-0.250591\pi$
$139$	−3.07256	−	5.32183i	−0.260611	−	0.451392i	−0.966404	+	0.257026i	$0.917257\pi$
$140$	−2.67093	−	4.62619i	−0.225735	−	0.390985i
$141$		0			0
$142$	−1.26391	+	2.18915i	−0.106065	+	0.183709i
$143$	0.0941785			0.00787561
$144$		0			0
$145$	−17.2945			−1.43623
$146$	−0.113624	+	0.196803i	−0.00940362	+	0.0162876i
$147$		0			0
$148$	4.04287	+	7.00246i	0.332322	+	0.575599i
$149$	−0.441410	−	0.764545i	−0.0361617	−	0.0626340i	0.847378	−	0.530990i	$-0.178180\pi$
$149$	−0.441410	−	0.764545i	−0.0361617	−	0.0626340i	−0.883540	+	0.468356i	$0.844846\pi$
$150$		0			0
$151$	−4.11274	+	7.12347i	−0.334690	+	0.579700i	−0.983425	−	0.181314i	$-0.941965\pi$
$151$	−4.11274	+	7.12347i	−0.334690	+	0.579700i	0.648735	+	0.761014i	$0.275298\pi$
$152$	0.663653			0.0538294
$153$		0			0
$154$	−2.85929			−0.230408
$155$	−4.13095	+	7.15502i	−0.331806	+	0.574705i
$156$		0			0
$157$	−6.27991	−	10.8771i	−0.501192	−	0.868089i	−0.999999	−	0.00137640i	$-0.999562\pi$
$157$	−6.27991	−	10.8771i	−0.501192	−	0.868089i	0.498808	−	0.866713i	$-0.333771\pi$
$158$	0.101611	+	0.175996i	0.00808377	+	0.0140015i
$159$		0			0
$160$	4.90028	−	8.48753i	0.387401	−	0.670998i
$161$	1.36501			0.107578
$162$		0			0
$163$	3.31466			0.259624			0.129812	−	0.991539i	$-0.458563\pi$
$163$	3.31466			0.259624			0.129812	+	0.991539i	$0.458563\pi$
$164$	−3.35777	+	5.81583i	−0.262198	+	0.454140i
$165$		0			0
$166$	0.958412	+	1.66002i	0.0743872	+	0.128842i
$167$	10.2815	+	17.8081i	0.795606	+	1.37803i	0.922454	+	0.386107i	$0.126180\pi$
$167$	10.2815	+	17.8081i	0.795606	+	1.37803i	−0.126848	+	0.991922i	$0.540486\pi$
$168$		0			0
$169$	6.49984	−	11.2580i	0.499987	−	0.866004i
$170$	2.88322			0.221133
$171$		0			0
$172$	15.1817			1.15759
$173$	−7.01663	+	12.1532i	−0.533465	+	0.923988i	0.465771	+	0.884905i	$0.345777\pi$
$173$	−7.01663	+	12.1532i	−0.533465	+	0.923988i	−0.999236	+	0.0390830i	$0.987556\pi$
$174$		0			0
$175$	−0.0613281	−	0.106223i	−0.00463597	−	0.00802974i
$176$	7.80745	+	13.5229i	0.588509	+	1.01933i
$177$		0			0
$178$	−0.700697	+	1.21364i	−0.0525195	+	0.0909664i
$179$	10.1900			0.761636			0.380818	−	0.924650i	$-0.375642\pi$
$179$	10.1900			0.761636			0.380818	+	0.924650i	$0.375642\pi$
$180$		0			0
$181$	24.0547			1.78797			0.893987	−	0.448093i	$-0.147897\pi$
$181$	24.0547			1.78797			0.893987	+	0.448093i	$0.147897\pi$
$182$	0.00495039	−	0.00857433i	0.000366948	−	0.000635572i
$183$		0			0
$184$	0.822415	+	1.42446i	0.0606292	+	0.105013i
$185$	−4.90083	−	8.48849i	−0.360316	−	0.624086i
$186$		0			0
$187$	−8.16906	+	14.1492i	−0.597381	+	1.03469i
$188$	12.9706			0.945981
$189$		0			0
$190$	−0.384104			−0.0278658
$191$	−5.47318	+	9.47983i	−0.396026	+	0.685937i	−0.993232	−	0.116151i	$-0.962944\pi$
$191$	−5.47318	+	9.47983i	−0.396026	+	0.685937i	0.597206	+	0.802088i	$0.296278\pi$
$192$		0			0
$193$	5.40298	+	9.35824i	0.388915	+	0.673621i	0.992304	−	0.123826i	$-0.0395166\pi$
$193$	5.40298	+	9.35824i	0.388915	+	0.673621i	−0.603389	+	0.797447i	$0.706183\pi$
$194$	2.06515	+	3.57694i	0.148269	+	0.256810i
$195$		0			0
$196$	−4.80473	+	8.32204i	−0.343195	+	0.594431i
$197$	−22.0734			−1.57266			−0.786331	−	0.617806i	$-0.788022\pi$
$197$	−22.0734			−1.57266			−0.786331	+	0.617806i	$0.788022\pi$
$198$		0			0
$199$	12.8868			0.913518			0.456759	−	0.889590i	$-0.349010\pi$
$199$	12.8868			0.913518			0.456759	+	0.889590i	$0.349010\pi$
$200$	0.0739003	−	0.127999i	0.00522554	−	0.00905090i
$201$		0			0
$202$	2.86661	+	4.96512i	0.201694	+	0.349344i
$203$	−5.15132	−	8.92235i	−0.361552	−	0.626226i
$204$		0			0
$205$	4.07034	−	7.05003i	0.284285	−	0.492396i
$206$	−1.89665			−0.132146
$207$		0			0
$208$	−0.0540694			−0.00374904
$209$	1.08829	−	1.88497i	0.0752783	−	0.130386i
$210$		0			0
$211$	11.9978	+	20.7808i	0.825964	+	1.43061i	0.901181	+	0.433444i	$0.142702\pi$
$211$	11.9978	+	20.7808i	0.825964	+	1.43061i	−0.0752168	+	0.997167i	$0.523965\pi$
$212$	−1.18833	−	2.05824i	−0.0816146	−	0.141361i
$213$		0			0
$214$	−2.34665	+	4.06452i	−0.160414	+	0.277845i
$215$	−18.4035			−1.25511
$216$		0			0
$217$	−4.92177			−0.334112
$218$	3.01279	−	5.21831i	0.204052	−	0.353428i
$219$		0			0
$220$	−10.5556	−	18.2828i	−0.711655	−	1.23262i
$221$	−0.0282868	−	0.0489942i	−0.00190278	−	0.00329571i
$222$		0			0
$223$	−10.8311	+	18.7600i	−0.725303	+	1.25626i	0.233546	+	0.972346i	$0.424967\pi$
$223$	−10.8311	+	18.7600i	−0.725303	+	1.25626i	−0.958849	+	0.283916i	$0.908366\pi$
$224$	5.83838			0.390093
$225$		0			0
$226$	−5.21760			−0.347070
$227$	−10.8209	+	18.7424i	−0.718211	+	1.24398i	0.243497	+	0.969902i	$0.421705\pi$
$227$	−10.8209	+	18.7424i	−0.718211	+	1.24398i	−0.961708	+	0.274076i	$0.911628\pi$
$228$		0			0
$229$	5.40268	+	9.35772i	0.357019	+	0.618375i	0.987461	−	0.157861i	$-0.0504598\pi$
$229$	5.40268	+	9.35772i	0.357019	+	0.618375i	−0.630442	+	0.776236i	$0.717126\pi$
$230$	−0.475991	−	0.824441i	−0.0313859	−	0.0543620i
$231$		0			0
$232$	6.20733	−	10.7514i	0.407531	−	0.705865i
$233$	7.63900			0.500447			0.250224	−	0.968188i	$-0.419496\pi$
$233$	7.63900			0.500447			0.250224	+	0.968188i	$0.419496\pi$
$234$		0			0
$235$	−15.7232			−1.02567
$236$	−3.38232	+	5.85835i	−0.220170	+	0.381346i
$237$		0			0
$238$	0.858795	+	1.48748i	0.0556674	+	0.0964188i
$239$	1.61575	+	2.79855i	0.104514	+	0.181023i	0.913540	−	0.406750i	$-0.133338\pi$
$239$	1.61575	+	2.79855i	0.104514	+	0.181023i	−0.809026	+	0.587773i	$0.800005\pi$
$240$		0			0
$241$	13.2725	−	22.9886i	0.854955	−	1.48083i	−0.0217316	−	0.999764i	$-0.506918\pi$
$241$	13.2725	−	22.9886i	0.854955	−	1.48083i	0.876687	−	0.481062i	$-0.159749\pi$
$242$	−6.72979			−0.432608
$243$		0			0
$244$	−12.6350			−0.808873
$245$	5.82437	−	10.0881i	0.372105	−	0.644505i
$246$		0			0
$247$	0.00376838	+	0.00652703i	0.000239776	+	0.000415305i
$248$	−2.96536	−	5.13616i	−0.188301	−	0.326147i
$249$		0			0
$250$	−2.34361	+	4.05925i	−0.148223	+	0.256730i
$251$	−4.49930			−0.283993			−0.141997	−	0.989867i	$-0.545352\pi$
$251$	−4.49930			−0.283993			−0.141997	+	0.989867i	$0.545352\pi$
$252$		0			0
$253$	5.39452			0.339150
$254$	−1.74392	+	3.02055i	−0.109423	+	0.189526i
$255$		0			0
$256$	−1.95380	−	3.38409i	−0.122113	−	0.211506i
$257$	−6.86771	−	11.8952i	−0.428396	−	0.742003i	0.568335	−	0.822797i	$-0.307588\pi$
$257$	−6.86771	−	11.8952i	−0.428396	−	0.742003i	−0.996731	+	0.0807940i	$0.974254\pi$
$258$		0			0
$259$	2.91952	−	5.05676i	0.181410	−	0.314211i
$260$	0.0731010			0.00453353
$261$		0			0
$262$	6.45423			0.398743
$263$	12.1013	−	20.9600i	0.746197	−	1.29245i	−0.203437	−	0.979088i	$-0.565211\pi$
$263$	12.1013	−	20.9600i	0.746197	−	1.29245i	0.949634	−	0.313363i	$-0.101456\pi$
$264$		0			0
$265$	1.44051	+	2.49503i	0.0884897	+	0.153269i
$266$	−0.114409	−	0.198162i	−0.00701487	−	0.0121501i
$267$		0			0
$268$	−10.0751	+	17.4506i	−0.615436	+	1.06597i
$269$	12.0062			0.732032			0.366016	−	0.930609i	$-0.380722\pi$
$269$	12.0062			0.732032			0.366016	+	0.930609i	$0.380722\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	4.68999	−	8.12329i	0.284372	−	0.492547i
$273$		0			0
$274$	2.49433	+	4.32031i	0.150688	+	0.261000i
$275$	−0.242369	−	0.419796i	−0.0146154	−	0.0253146i
$276$		0			0
$277$	11.7416	−	20.3370i	0.705482	−	1.22193i	−0.261035	−	0.965329i	$-0.584064\pi$
$277$	11.7416	−	20.3370i	0.705482	−	1.22193i	0.966517	−	0.256601i	$-0.0826027\pi$
$278$	−2.55309			−0.153124
$279$		0			0
$280$	−4.64837			−0.277793
$281$	10.1859	−	17.6424i	0.607638	−	1.05246i	−0.383991	−	0.923337i	$-0.625451\pi$
$281$	10.1859	−	17.6424i	0.607638	−	1.05246i	0.991629	−	0.129123i	$-0.0412162\pi$
$282$		0			0
$283$	−5.79997	−	10.0458i	−0.344772	−	0.597163i	0.640540	−	0.767925i	$-0.278711\pi$
$283$	−5.79997	−	10.0458i	−0.344772	−	0.597163i	−0.985312	+	0.170761i	$0.945377\pi$
$284$	−5.55917	−	9.62876i	−0.329876	−	0.571362i
$285$		0			0
$286$	0.0195640	−	0.0338858i	0.00115684	−	0.00200371i
$287$	4.84956			0.286260
$288$		0			0
$289$	−7.18559			−0.422682
$290$	−3.59263	+	6.22262i	−0.210967	+	0.365405i
$291$		0			0
$292$	−0.499766	−	0.865620i	−0.0292466	−	0.0506566i
$293$	−15.7871	−	27.3440i	−0.922291	−	1.59745i	−0.795861	−	0.605479i	$-0.792981\pi$
$293$	−15.7871	−	27.3440i	−0.922291	−	1.59745i	−0.126430	−	0.991976i	$-0.540352\pi$
$294$		0			0
$295$	4.10010	−	7.10158i	0.238717	−	0.413470i
$296$	7.03603			0.408961
$297$		0			0
$298$	−0.366782			−0.0212471
$299$	−0.00933974	+	0.0161769i	−0.000540131	+	0.000935535i
$300$		0			0
$301$	−5.48166	−	9.49451i	−0.315957	−	0.547254i
$302$	1.70870	+	2.95956i	0.0983248	+	0.170304i
$303$		0			0
$304$	−0.624802	+	1.08219i	−0.0358348	+	0.0620678i
$305$	15.3163			0.877010
$306$		0			0
$307$	−8.12054			−0.463464			−0.231732	−	0.972780i	$-0.574439\pi$
$307$	−8.12054			−0.463464			−0.231732	+	0.972780i	$0.574439\pi$
$308$	6.28814	−	10.8914i	0.358300	−	0.620594i
$309$		0			0
$310$	1.71627	+	2.97267i	0.0974776	+	0.168836i
$311$	11.9243	+	20.6535i	0.676164	+	1.17115i	0.976127	+	0.217199i	$0.0696922\pi$
$311$	11.9243	+	20.6535i	0.676164	+	1.17115i	−0.299963	+	0.953951i	$0.596974\pi$
$312$		0			0
$313$	−13.4552	+	23.3051i	−0.760535	+	1.31728i	0.182040	+	0.983291i	$0.441730\pi$
$313$	−13.4552	+	23.3051i	−0.760535	+	1.31728i	−0.942575	+	0.333994i	$0.891604\pi$
$314$	−5.21818			−0.294479
$315$		0			0
$316$	−0.893856			−0.0502833
$317$	4.16617	−	7.21601i	0.233995	−	0.405292i	−0.724985	−	0.688765i	$-0.758153\pi$
$317$	4.16617	−	7.21601i	0.233995	−	0.405292i	0.958980	+	0.283473i	$0.0914867\pi$
$318$		0			0
$319$	−20.3581	−	35.2612i	−1.13983	−	1.97425i
$320$	4.59664	+	7.96161i	0.256960	+	0.445068i
$321$		0			0
$322$	0.283557	−	0.491135i	0.0158020	−	0.0273699i
$323$	−1.30748			−0.0727501
$324$		0			0
$325$	0.00167849			9.31061e−5
$326$	0.688565	−	1.19263i	0.0381361	−	0.0660536i
$327$		0			0
$328$	2.92185	+	5.06080i	0.161332	+	0.279436i
$329$	−4.68330	−	8.11172i	−0.258199	−	0.447214i
$330$		0			0
$331$	3.21013	−	5.56011i	0.176445	−	0.305611i	−0.764216	−	0.644961i	$-0.776874\pi$
$331$	3.21013	−	5.56011i	0.176445	−	0.305611i	0.940660	+	0.339350i	$0.110207\pi$
$332$	−8.43096			−0.462709
$333$		0			0
$334$	8.54322			0.467464
$335$	12.2132	−	21.1539i	0.667279	−	1.15576i
$336$		0			0
$337$	−3.73745	−	6.47345i	−0.203592	−	0.352631i	0.746091	−	0.665844i	$-0.231928\pi$
$337$	−3.73745	−	6.47345i	−0.203592	−	0.352631i	−0.949683	+	0.313212i	$0.898595\pi$
$338$	−2.70046	−	4.67734i	−0.146886	−	0.254414i
$339$		0			0
$340$	−6.34079	+	10.9826i	−0.343877	+	0.595613i
$341$	−19.4509			−1.05333
$342$		0			0
$343$	16.1768			0.873464
$344$	6.60538	−	11.4409i	0.356138	−	0.616850i
$345$		0			0
$346$	2.91517	+	5.04923i	0.156721	+	0.271448i
$347$	15.7272	+	27.2404i	0.844283	+	1.46234i	0.886243	+	0.463222i	$0.153307\pi$
$347$	15.7272	+	27.2404i	0.844283	+	1.46234i	−0.0419596	+	0.999119i	$0.513360\pi$
$348$		0			0
$349$	−5.92647	+	10.2650i	−0.317237	+	0.549470i	−0.979910	−	0.199438i	$-0.936088\pi$
$349$	−5.92647	+	10.2650i	−0.317237	+	0.549470i	0.662674	+	0.748908i	$0.269422\pi$
$350$	−0.0509595			−0.00272390
$351$		0			0
$352$	23.0733			1.22981
$353$	4.10354	−	7.10754i	0.218409	−	0.378296i	−0.735912	−	0.677077i	$-0.763246\pi$
$353$	4.10354	−	7.10754i	0.218409	−	0.378296i	0.954322	+	0.298780i	$0.0965798\pi$
$354$		0			0
$355$	6.73891	+	11.6721i	0.357664	+	0.619492i
$356$	−3.08195	−	5.33809i	−0.163343	−	0.282918i
$357$		0			0
$358$	2.11680	−	3.66640i	0.111876	−	0.193775i
$359$	17.7273			0.935611			0.467806	−	0.883831i	$-0.345045\pi$
$359$	17.7273			0.935611			0.467806	+	0.883831i	$0.345045\pi$
$360$		0			0
$361$	−18.8258			−0.990832
$362$	4.99696	−	8.65499i	0.262635	−	0.454896i
$363$		0			0
$364$	0.0217738	+	0.0377134i	0.00114126	+	0.00197672i
$365$	0.605824	+	1.04932i	0.0317103	+	0.0549238i
$366$		0			0
$367$	10.1598	−	17.5972i	0.530335	−	0.918568i	−0.469038	−	0.883178i	$-0.655399\pi$
$367$	10.1598	−	17.5972i	0.530335	−	0.918568i	0.999374	−	0.0353899i	$-0.0112673\pi$
$368$	−3.09708			−0.161446
$369$		0			0
$370$	−4.07226			−0.211707
$371$	−0.858138	+	1.48634i	−0.0445523	+	0.0771668i
$372$		0			0
$373$	4.84072	+	8.38437i	0.250643	+	0.434126i	0.963703	−	0.266977i	$-0.0860247\pi$
$373$	4.84072	+	8.38437i	0.250643	+	0.434126i	−0.713060	+	0.701103i	$0.752691\pi$
$374$	3.39397	+	5.87852i	0.175498	+	0.303971i
$375$		0			0
$376$	5.64337	−	9.77461i	0.291035	−	0.504087i
$377$	0.140987			0.00726119
$378$		0			0
$379$	−4.12905			−0.212095			−0.106048	−	0.994361i	$-0.533820\pi$
$379$	−4.12905			−0.212095			−0.106048	+	0.994361i	$0.533820\pi$
$380$	0.844722	−	1.46310i	0.0433333	−	0.0750555i
$381$		0			0
$382$	2.27392	+	3.93855i	0.116344	+	0.201514i
$383$	−2.37509	−	4.11378i	−0.121362	−	0.210204i	0.798943	−	0.601406i	$-0.205393\pi$
$383$	−2.37509	−	4.11378i	−0.121362	−	0.210204i	−0.920305	+	0.391202i	$0.872059\pi$
$384$		0			0
$385$	−7.62258	+	13.2027i	−0.388483	+	0.672872i
$386$	4.48951			0.228510
$387$		0			0
$388$	−18.1667			−0.922275
$389$	10.9067	−	18.8909i	0.552990	−	0.957806i	−0.445067	−	0.895497i	$-0.646820\pi$
$389$	10.9067	−	18.8909i	0.552990	−	0.957806i	0.998057	−	0.0623089i	$-0.0198464\pi$
$390$		0			0
$391$	−1.62026	−	2.80637i	−0.0819401	−	0.141924i
$392$	4.18097	+	7.24165i	0.211171	+	0.365758i
$393$		0			0
$394$	−4.58537	+	7.94209i	−0.231007	+	0.400117i
$395$	1.08355			0.0545191
$396$		0			0
$397$	−34.8490			−1.74902			−0.874512	−	0.485005i	$-0.838818\pi$
$397$	−34.8490			−1.74902			−0.874512	+	0.485005i	$0.838818\pi$
$398$	2.67701	−	4.63671i	0.134186	−	0.232417i
$399$		0			0
$400$	0.139148	+	0.241012i	0.00695740	+	0.0120506i
$401$	9.41304	+	16.3039i	0.470065	+	0.814176i	0.999414	−	0.0342279i	$-0.0108972\pi$
$401$	9.41304	+	16.3039i	0.470065	+	0.814176i	−0.529349	+	0.848404i	$0.677564\pi$
$402$		0			0
$403$	0.0336761	−	0.0583287i	0.00167753	−	0.00290556i
$404$	−25.2170			−1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	11.5380	−	19.9843i	0.571916	−	0.990587i
$408$		0			0
$409$	3.17998	+	5.50788i	0.157240	+	0.272347i	0.933872	−	0.357607i	$-0.116407\pi$
$409$	3.17998	+	5.50788i	0.157240	+	0.272347i	−0.776633	+	0.629954i	$0.783074\pi$
$410$	−1.69109	−	2.92905i	−0.0835169	−	0.144656i
$411$		0			0
$412$	4.17112	−	7.22459i	0.205496	−	0.355930i
$413$	4.88502			0.240376
$414$		0			0
$415$	10.2201			0.501687
$416$	−0.0399478	+	0.0691916i	−0.00195860	+	0.00339240i
$417$		0			0
$418$	−0.452146	−	0.783139i	−0.0221152	−	0.0383046i
$419$	12.1590	+	21.0600i	0.594005	+	1.02885i	0.993686	+	0.112193i	$0.0357875\pi$
$419$	12.1590	+	21.0600i	0.594005	+	1.02885i	−0.399681	+	0.916654i	$0.630879\pi$
$420$		0			0
$421$	3.99502	−	6.91957i	0.194705	−	0.337239i	−0.752099	−	0.659051i	$-0.770958\pi$
$421$	3.99502	−	6.91957i	0.194705	−	0.337239i	0.946804	+	0.321811i	$0.104292\pi$
$422$	9.96937			0.485302
$423$		0			0
$424$	−2.06811			−0.100436
$425$	−0.145593	+	0.252174i	−0.00706229	+	0.0122322i
$426$		0			0
$427$	4.56211	+	7.90181i	0.220776	+	0.382396i
$428$	−10.3215	−	17.8774i	−0.498909	−	0.864136i
$429$		0			0
$430$	−3.82301	+	6.62166i	−0.184362	+	0.319325i
$431$	9.87124			0.475481			0.237740	−	0.971329i	$-0.423593\pi$
$431$	9.87124			0.475481			0.237740	+	0.971329i	$0.423593\pi$
$432$		0			0
$433$	−6.10369			−0.293325			−0.146662	−	0.989187i	$-0.546853\pi$
$433$	−6.10369			−0.293325			−0.146662	+	0.989187i	$0.546853\pi$
$434$	−1.02242	+	1.77088i	−0.0490775	+	0.0850047i
$435$		0			0
$436$	13.2515	+	22.9522i	0.634630	+	1.09921i
$437$	0.215852	+	0.373866i	0.0103256	+	0.0178844i
$438$		0			0
$439$	7.56701	−	13.1064i	0.361154	−	0.625537i	−0.626997	−	0.779021i	$-0.715716\pi$
$439$	7.56701	−	13.1064i	0.361154	−	0.625537i	0.988151	+	0.153485i	$0.0490496\pi$
$440$	−18.3704			−0.875774
$441$		0			0
$442$	−0.0235044			−0.00111799
$443$	0.361397	−	0.625957i	0.0171705	−	0.0297401i	−0.857312	−	0.514796i	$-0.827868\pi$
$443$	0.361397	−	0.625957i	0.0171705	−	0.0297401i	0.874483	+	0.485056i	$0.161201\pi$
$444$		0			0
$445$	3.73598	+	6.47092i	0.177103	+	0.306751i
$446$	4.49995	+	7.79414i	0.213079	+	0.369063i
$447$		0			0
$448$	−2.73831	+	4.74288i	−0.129373	+	0.224080i
$449$	1.66845			0.0787389			0.0393695	−	0.999225i	$-0.487465\pi$
$449$	1.66845			0.0787389			0.0393695	+	0.999225i	$0.487465\pi$
$450$		0			0
$451$	19.1655			0.902468
$452$	11.4746	−	19.8745i	0.539718	−	0.934819i
$453$		0			0
$454$	4.49573	+	7.78684i	0.210995	+	0.365455i
$455$	−0.0263946	−	0.0457167i	−0.00123740	−	0.00214323i
$456$		0			0
$457$	−5.54172	+	9.59855i	−0.259231	+	0.449001i	−0.966036	−	0.258407i	$-0.916802\pi$
$457$	−5.54172	+	9.59855i	−0.259231	+	0.449001i	0.706805	+	0.707408i	$0.250136\pi$
$458$	4.48926			0.209769
$459$		0			0
$460$	4.18720			0.195229
$461$	10.9422	−	18.9524i	0.509629	−	0.882703i	−0.490309	−	0.871549i	$-0.663116\pi$
$461$	10.9422	−	18.9524i	0.509629	−	0.882703i	0.999938	−	0.0111543i	$-0.00355060\pi$
$462$		0			0
$463$	−12.4259	−	21.5222i	−0.577479	−	1.00022i	−0.995767	−	0.0919086i	$-0.970703\pi$
$463$	−12.4259	−	21.5222i	−0.577479	−	1.00022i	0.418289	−	0.908314i	$-0.362630\pi$
$464$	11.6879	+	20.2440i	0.542597	+	0.939805i
$465$		0			0
$466$	1.58687	−	2.74854i	0.0735105	−	0.127324i
$467$	−11.8355			−0.547683			−0.273842	−	0.961775i	$-0.588294\pi$
$467$	−11.8355			−0.547683			−0.273842	+	0.961775i	$0.588294\pi$
$468$		0			0
$469$	14.5513			0.671916
$470$	−3.26623	+	5.65727i	−0.150660	+	0.260951i
$471$		0			0
$472$	2.94322	+	5.09780i	0.135473	+	0.234645i
$473$	−21.6636	−	37.5224i	−0.996091	−	1.72528i
$474$		0			0
$475$	0.0193959	−	0.0335947i	0.000889946	−	0.00154143i
$476$	−7.55465			−0.346267
$477$		0			0
$478$	1.34258			0.0614080
$479$	−1.44368	+	2.50052i	−0.0659632	+	0.114252i	−0.897121	−	0.441785i	$-0.854345\pi$
$479$	−1.44368	+	2.50052i	−0.0659632	+	0.114252i	0.831158	+	0.556037i	$0.187679\pi$
$480$		0			0
$481$	0.0399523	+	0.0691994i	0.00182167	+	0.00315522i
$482$	−5.51426	−	9.55099i	−0.251168	−	0.435035i
$483$		0			0
$484$	14.8002	−	25.6347i	0.672735	−	1.16521i
$485$	22.0220			0.999966
$486$		0			0
$487$	8.75903			0.396910			0.198455	−	0.980110i	$-0.436408\pi$
$487$	8.75903			0.396910			0.198455	+	0.980110i	$0.436408\pi$
$488$	−5.49734	+	9.52167i	−0.248853	+	0.431026i
$489$		0			0
$490$	−2.41983	−	4.19127i	−0.109317	−	0.189342i
$491$	11.2865	+	19.5488i	0.509354	+	0.882226i	0.999941	+	0.0108346i	$0.00344882\pi$
$491$	11.2865	+	19.5488i	0.509354	+	0.882226i	−0.490588	+	0.871392i	$0.663218\pi$
$492$		0			0
$493$	−12.2292	+	21.1816i	−0.550776	+	0.953972i
$494$	0.00313127			0.000140883
$495$		0			0
$496$	11.1671			0.501416
$497$	−4.01449	+	6.95331i	−0.180075	+	0.311899i
$498$		0			0
$499$	12.6664	+	21.9389i	0.567026	+	0.982118i	0.996858	+	0.0792092i	$0.0252395\pi$
$499$	12.6664	+	21.9389i	0.567026	+	0.982118i	−0.429832	+	0.902909i	$0.641427\pi$
$500$	−10.3081	−	17.8542i	−0.460994	−	0.798465i
$501$		0			0
$502$	−0.934653	+	1.61887i	−0.0417156	+	0.0722536i
$503$	3.74414			0.166943			0.0834714	−	0.996510i	$-0.473399\pi$
$503$	3.74414			0.166943			0.0834714	+	0.996510i	$0.473399\pi$
$504$		0			0
$505$	30.5684			1.36028
$506$	1.12062	−	1.94097i	0.0498176	−	0.0862867i
$507$		0			0
$508$	−7.67045	−	13.2856i	−0.340321	−	0.589454i
$509$	−12.1749	−	21.0876i	−0.539645	−	0.934692i	−0.998923	−	0.0463997i	$-0.985225\pi$
$509$	−12.1749	−	21.0876i	−0.539645	−	0.934692i	0.459278	−	0.888292i	$-0.348108\pi$
$510$		0			0
$511$	−0.360901	+	0.625098i	−0.0159653	+	0.0276527i
$512$	−22.7690			−1.00626
$513$		0			0
$514$	−5.70660			−0.251707
$515$	−5.05630	+	8.75776i	−0.222807	+	0.385913i
$516$		0			0
$517$	−18.5085	−	32.0576i	−0.814001	−	1.40989i
$518$	−1.21296	−	2.10091i	−0.0532945	−	0.0923087i
$519$		0			0
$520$	0.0318054	−	0.0550885i	0.00139476	−	0.00241579i
$521$	19.6209			0.859608			0.429804	−	0.902922i	$-0.358583\pi$
$521$	19.6209			0.859608			0.429804	+	0.902922i	$0.358583\pi$
$522$		0			0
$523$	20.8154			0.910194			0.455097	−	0.890442i	$-0.349605\pi$
$523$	20.8154			0.910194			0.455097	+	0.890442i	$0.349605\pi$
$524$	−14.1941	+	24.5850i	−0.620074	+	1.07400i
$525$		0			0
$526$	−5.02767	−	8.70819i	−0.219217	−	0.379695i
$527$	5.84214	+	10.1189i	0.254488	+	0.440785i
$528$		0			0
$529$	10.9650	−	18.9920i	0.476740	−	0.825738i
$530$	1.19696			0.0519928
$531$		0			0
$532$	1.00643			0.0436345
$533$	−0.0331820	+	0.0574729i	−0.00143727	+	0.00248943i
$534$		0			0
$535$	12.5119	+	21.6712i	0.540936	+	0.936929i
$536$	8.76713	+	15.1851i	0.378682	+	0.655897i
$537$		0			0
$538$	2.49409	−	4.31989i	0.107528	−	0.186244i
$539$	27.4245			1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$	0.772305	−	1.33767i	0.0331733	−	0.0574579i
$543$		0			0
$544$	−6.93015	−	12.0034i	−0.297128	−	0.514640i
$545$	−16.0636	−	27.8230i	−0.688090	−	1.19181i
$546$		0			0
$547$	−11.3238	+	19.6135i	−0.484172	+	0.838611i	−0.999835	−	0.0181808i	$-0.994213\pi$
$547$	−11.3238	+	19.6135i	−0.484172	+	0.838611i	0.515662	+	0.856792i	$0.327546\pi$
$548$	−21.9422			−0.937323
$549$		0			0
$550$	−0.201393			−0.00858741
$551$	1.62918	−	2.82182i	0.0694055	−	0.120214i
$552$		0			0
$553$	0.322744	+	0.559010i	0.0137245	+	0.0237715i
$554$	−4.87822	−	8.44933i	−0.207256	−	0.358978i
$555$		0			0
$556$	5.61476	−	9.72504i	0.238119	−	0.412434i
$557$	36.4518			1.54451			0.772256	−	0.635311i	$-0.219128\pi$
$557$	36.4518			1.54451			0.772256	+	0.635311i	$0.219128\pi$
$558$		0			0
$559$	0.150028			0.00634550
$560$	4.37625	−	7.57988i	0.184930	−	0.320308i
$561$		0			0
$562$	−4.23188	−	7.32984i	−0.178511	−	0.309191i
$563$	−13.2581	−	22.9637i	−0.558763	−	0.967806i	−0.997600	−	0.0692393i	$-0.977943\pi$
$563$	−13.2581	−	22.9637i	−0.558763	−	0.967806i	0.438837	−	0.898567i	$-0.355391\pi$
$564$		0			0
$565$	−13.9096	+	24.0922i	−0.585183	+	1.01357i
$566$	−4.81938			−0.202574
$567$		0			0
$568$	−9.67492			−0.405950
$569$	−11.4837	+	19.8904i	−0.481422	+	0.833847i	−0.999773	−	0.0213210i	$-0.993213\pi$
$569$	−11.4837	+	19.8904i	−0.481422	+	0.833847i	0.518351	+	0.855168i	$0.326546\pi$
$570$		0			0
$571$	2.39900	+	4.15519i	0.100395	+	0.173889i	0.911848	−	0.410529i	$-0.134656\pi$
$571$	2.39900	+	4.15519i	0.100395	+	0.173889i	−0.811452	+	0.584419i	$0.801323\pi$
$572$	0.0860504	+	0.149044i	0.00359795	+	0.00623183i
$573$		0			0
$574$	1.00741	−	1.74489i	0.0420486	−	0.0728304i
$575$	0.0961436			0.00400947
$576$		0			0
$577$	−4.31333			−0.179566			−0.0897831	−	0.995961i	$-0.528617\pi$
$577$	−4.31333			−0.179566			−0.0897831	+	0.995961i	$0.528617\pi$
$578$	−1.49269	+	2.58541i	−0.0620876	+	0.107539i
$579$		0			0
$580$	−15.8018	−	27.3696i	−0.656136	−	1.13646i
$581$	3.04417	+	5.27265i	0.126293	+	0.218746i
$582$		0			0
$583$	−3.39137	+	5.87402i	−0.140456	+	0.243277i
$584$	−0.869769			−0.0359913
$585$		0			0
$586$	−13.1180			−0.541899
$587$	−20.9111	+	36.2191i	−0.863094	+	1.49492i	0.00583407	+	0.999983i	$0.498143\pi$
$587$	−20.9111	+	36.2191i	−0.863094	+	1.49492i	−0.868928	+	0.494939i	$0.835190\pi$
$588$		0			0
$589$	−0.778292	−	1.34804i	−0.0320690	−	0.0555451i
$590$	−1.70345	−	2.95047i	−0.0701301	−	0.121469i
$591$		0			0
$592$	−6.62413	+	11.4733i	−0.272250	+	0.471551i
$593$	−31.5370			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$593$	−31.5370			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$594$		0			0
$595$	9.15786			0.375436
$596$	0.806628	−	1.39712i	0.0330408	−	0.0572283i
$597$		0			0
$598$	0.00388035	+	0.00672096i	0.000158679	+	0.000274840i
$599$	6.31515	+	10.9382i	0.258030	+	0.446921i	0.965714	−	0.259608i	$-0.0835933\pi$
$599$	6.31515	+	10.9382i	0.258030	+	0.446921i	−0.707684	+	0.706529i	$0.750260\pi$
$600$		0			0
$601$	−10.2715	+	17.7907i	−0.418983	+	0.725699i	−0.995837	−	0.0911474i	$-0.970947\pi$
$601$	−10.2715	+	17.7907i	−0.418983	+	0.725699i	0.576855	+	0.816847i	$0.304280\pi$
$602$	−4.55489			−0.185643
$603$		0			0
$604$	−15.0311			−0.611608
$605$	−17.9410	+	31.0747i	−0.729405	+	1.26337i
$606$		0			0
$607$	−6.45628	−	11.1826i	−0.262052	−	0.453888i	0.704735	−	0.709471i	$-0.251066\pi$
$607$	−6.45628	−	11.1826i	−0.262052	−	0.453888i	−0.966787	+	0.255583i	$0.917733\pi$
$608$	0.923237	+	1.59909i	0.0374422	+	0.0648518i
$609$		0			0
$610$	3.18171	−	5.51088i	0.128824	−	0.223129i
$611$	0.128178			0.00518552
$612$		0			0
$613$	−31.1598			−1.25853			−0.629265	−	0.777191i	$-0.716644\pi$
$613$	−31.1598			−1.25853			−0.629265	+	0.777191i	$0.716644\pi$
$614$	−1.68690	+	2.92180i	−0.0680779	+	0.117914i
$615$		0			0
$616$	−5.47180	−	9.47743i	−0.220465	−	0.381857i
$617$	3.57039	+	6.18410i	0.143739	+	0.248962i	0.928902	−	0.370327i	$-0.120754\pi$
$617$	3.57039	+	6.18410i	0.143739	+	0.248962i	−0.785163	+	0.619289i	$0.787421\pi$
$618$		0			0
$619$	5.01545	−	8.68702i	0.201588	−	0.349161i	−0.747452	−	0.664316i	$-0.768723\pi$
$619$	5.01545	−	8.68702i	0.201588	−	0.349161i	0.949040	+	0.315155i	$0.102056\pi$
$620$	−15.0977			−0.606338
$621$		0			0
$622$	9.90827			0.397285
$623$	−2.22560	+	3.85485i	−0.0891667	+	0.154441i
$624$		0			0
$625$	12.2633	+	21.2407i	0.490532	+	0.849627i
$626$	5.59020	+	9.68250i	0.223429	+	0.386991i
$627$		0			0
$628$	11.4758	−	19.8767i	0.457936	−	0.793168i
$629$	−13.8619			−0.552708
$630$		0			0
$631$	−7.07560			−0.281675			−0.140838	−	0.990033i	$-0.544980\pi$
$631$	−7.07560			−0.281675			−0.140838	+	0.990033i	$0.544980\pi$
$632$	−0.388906	+	0.673606i	−0.0154699	+	0.0267946i
$633$		0			0
$634$	−1.73090	−	2.99801i	−0.0687429	−	0.119066i
$635$	9.29823	+	16.1050i	0.368989	+	0.639108i
$636$		0			0
$637$	−0.0474811	+	0.0822396i	−0.00188127	+	0.00325845i
$638$	−16.9162			−0.669718
$639$		0			0
$640$	23.4206			0.925781
$641$	2.50561	−	4.33984i	0.0989655	−	0.171413i	−0.812291	−	0.583252i	$-0.801780\pi$
$641$	2.50561	−	4.33984i	0.0989655	−	0.171413i	0.911257	+	0.411839i	$0.135113\pi$
$642$		0			0
$643$	−0.819202	−	1.41890i	−0.0323062	−	0.0559559i	0.849420	−	0.527717i	$-0.176952\pi$
$643$	−0.819202	−	1.41890i	−0.0323062	−	0.0559559i	−0.881726	+	0.471761i	$0.843618\pi$
$644$	1.24720	+	2.16021i	0.0491465	+	0.0851242i
$645$		0			0
$646$	−0.271607	+	0.470437i	−0.0106862	+	0.0185091i
$647$	34.4927			1.35605			0.678024	−	0.735040i	$-0.262836\pi$
$647$	34.4927			1.35605			0.678024	+	0.735040i	$0.262836\pi$
$648$		0			0
$649$	19.3056			0.757813
$650$	0.000348679	0	0.000603929i	1.36763e−5	0	2.36881e-5i
$651$		0			0
$652$	3.02858	+	5.24566i	0.118609	+	0.205436i
$653$	−19.3803	−	33.5677i	−0.758410	−	1.31360i	−0.943661	−	0.330913i	$-0.892643\pi$
$653$	−19.3803	−	33.5677i	−0.758410	−	1.31360i	0.185252	−	0.982691i	$-0.440690\pi$
$654$		0			0
$655$	17.2064	−	29.8023i	0.672308	−	1.16447i
$656$	−11.0032			−0.429604
$657$		0			0
$658$	−3.89151			−0.151707
$659$	−4.69596	+	8.13364i	−0.182929	+	0.316842i	−0.942877	−	0.333142i	$-0.891891\pi$
$659$	−4.69596	+	8.13364i	−0.182929	+	0.316842i	0.759948	+	0.649984i	$0.225224\pi$
$660$		0			0
$661$	12.0737	+	20.9123i	0.469613	+	0.813394i	0.999396	−	0.0347394i	$-0.0110601\pi$
$661$	12.0737	+	20.9123i	0.469613	+	0.813394i	−0.529783	+	0.848133i	$0.677727\pi$
$662$	−1.33370	−	2.31004i	−0.0518357	−	0.0897821i
$663$		0			0
$664$	−3.66821	+	6.35353i	−0.142354	+	0.246565i
$665$	−1.22001			−0.0473101
$666$		0			0
$667$	8.07569			0.312692
$668$	−18.7883	+	32.5422i	−0.726940	+	1.25910i
$669$		0			0
$670$	−5.07417	−	8.78873i	−0.196032	−	0.339538i
$671$	18.0295	+	31.2280i	0.696022	+	1.20555i
$672$		0			0
$673$	13.2331	−	22.9203i	0.510097	−	0.883514i	−0.489834	−	0.871816i	$-0.662943\pi$
$673$	13.2331	−	22.9203i	0.510097	−	0.883514i	0.999932	−	0.0116988i	$-0.00372393\pi$
$674$	−3.10557			−0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	−15.5334	+	26.9047i	−0.596998	+	1.03403i	0.396264	+	0.918137i	$0.370307\pi$
$677$	−15.5334	+	26.9047i	−0.596998	+	1.03403i	−0.993262	+	0.115894i	$0.963027\pi$
$678$		0			0
$679$	6.55945	+	11.3613i	0.251729	+	0.436007i
$680$	5.51760	+	9.55677i	0.211590	+	0.366485i
$681$		0			0
$682$	−4.04060	+	6.99852i	−0.154722	+	0.267987i
$683$	38.1361			1.45924			0.729619	−	0.683854i	$-0.239697\pi$
$683$	38.1361			1.45924			0.729619	+	0.683854i	$0.239697\pi$
$684$		0			0
$685$	26.5986			1.01628
$686$	3.36045	−	5.82047i	0.128303	−	0.222227i
$687$		0			0
$688$	12.4374	+	21.5422i	0.474171	+	0.821288i
$689$	−0.0117432	−	0.0203399i	−0.000447381	−	0.000774887i
$690$		0			0
$691$	−16.4648	+	28.5178i	−0.626349	+	1.08487i	0.361929	+	0.932206i	$0.382118\pi$
$691$	−16.4648	+	28.5178i	−0.626349	+	1.08487i	−0.988278	+	0.152663i	$0.951215\pi$
$692$	−25.6442			−0.974847
$693$		0			0
$694$	13.0683			0.496065
$695$	−6.80629	+	11.7888i	−0.258177	+	0.447176i
$696$		0			0
$697$	−5.75642	−	9.97041i	−0.218040	−	0.377656i
$698$	2.46225	+	4.26474i	0.0931975	+	0.161423i
$699$		0			0
$700$	0.112070	−	0.194111i	0.00423586	−	0.00733672i
$701$	−2.30710			−0.0871381			−0.0435690	−	0.999050i	$-0.513873\pi$
$701$	−2.30710			−0.0871381			−0.0435690	+	0.999050i	$0.513873\pi$
$702$		0			0
$703$	1.84668			0.0696490
$704$	−10.8218	+	18.7439i	−0.407862	+	0.706438i
$705$		0			0
$706$	−1.70488	−	2.95294i	−0.0641641	−	0.111136i
$707$	9.10510	+	15.7705i	0.342433	+	0.593111i
$708$		0			0
$709$	5.57603	−	9.65797i	0.209412	−	0.362713i	−0.742117	−	0.670270i	$-0.766178\pi$
$709$	5.57603	−	9.65797i	0.209412	−	0.362713i	0.951530	+	0.307557i	$0.0995116\pi$
$710$	5.59958			0.210148
$711$		0			0
$712$	−5.36368			−0.201012
$713$	1.92896	−	3.34105i	0.0722400	−	0.125123i
$714$		0			0
$715$	−0.104312	−	0.180673i	−0.00390103	−	0.00675678i
$716$	9.31053	+	16.1263i	0.347951	+	0.602669i
$717$		0			0
$718$	3.68255	−	6.37836i	0.137431	−	0.238038i
$719$	−32.1700			−1.19974			−0.599869	−	0.800098i	$-0.704781\pi$
$719$	−32.1700			−1.19974			−0.599869	+	0.800098i	$0.704781\pi$
$720$		0			0
$721$	−6.02426			−0.224355
$722$	−3.91075	+	6.77361i	−0.145543	+	0.252088i
$723$		0			0
$724$	21.9787	+	38.0681i	0.816830	+	1.41479i
$725$	−0.362831	−	0.628442i	−0.0134752	−	0.0233397i
$726$		0			0
$727$	2.68275	−	4.64667i	0.0994979	−	0.172335i	−0.811979	−	0.583687i	$-0.801610\pi$
$727$	2.68275	−	4.64667i	0.0994979	−	0.172335i	0.911477	+	0.411351i	$0.134943\pi$
$728$	0.0378942			0.00140445
$729$		0			0
$730$	0.503399			0.0186316
$731$	−13.0134	+	22.5399i	−0.481319	+	0.833669i
$732$		0			0
$733$	7.29818	+	12.6408i	0.269564	+	0.466899i	0.968749	−	0.248042i	$-0.0797870\pi$
$733$	7.29818	+	12.6408i	0.269564	+	0.466899i	−0.699185	+	0.714941i	$0.746454\pi$
$734$	−4.22104	−	7.31105i	−0.155801	−	0.269856i
$735$		0			0
$736$	−2.28820	+	3.96327i	−0.0843440	+	0.146088i
$737$	57.5068			2.11829
$738$		0			0
$739$	−43.2165			−1.58975			−0.794873	−	0.606776i	$-0.792463\pi$
$739$	−43.2165			−1.58975			−0.794873	+	0.606776i	$0.792463\pi$
$740$	8.95572	−	15.5118i	0.329219	−	0.570224i
$741$		0			0
$742$	0.356527	+	0.617523i	0.0130885	+	0.0226700i
$743$	−4.05610	−	7.02538i	−0.148804	−	0.257736i	0.781982	−	0.623301i	$-0.214209\pi$
$743$	−4.05610	−	7.02538i	−0.148804	−	0.257736i	−0.930786	+	0.365565i	$0.880876\pi$
$744$		0			0
$745$	−0.977806	+	1.69361i	−0.0358240	+	0.0620491i
$746$	4.02231			0.147267
$747$		0			0
$748$	−29.8561			−1.09165
$749$	−7.45357	+	12.9100i	−0.272348	+	0.471720i
$750$		0			0
$751$	−4.37773	−	7.58245i	−0.159746	−	0.276687i	0.775031	−	0.631923i	$-0.217734\pi$
$751$	−4.37773	−	7.58245i	−0.159746	−	0.276687i	−0.934777	+	0.355235i	$0.884401\pi$
$752$	10.6260	+	18.4048i	0.387490	+	0.671153i
$753$		0			0
$754$	0.0292876	−	0.0507277i	0.00106659	−	0.00184739i
$755$	18.2210			0.663129
$756$		0			0
$757$	−32.1511			−1.16855			−0.584276	−	0.811555i	$-0.698622\pi$
$757$	−32.1511			−1.16855			−0.584276	+	0.811555i	$0.698622\pi$
$758$	−0.857741	+	1.48565i	−0.0311546	+	0.0539613i
$759$		0			0
$760$	−0.735058	−	1.27316i	−0.0266633	−	0.0461823i
$761$	12.2730	+	21.2574i	0.444894	+	0.770580i	0.998045	−	0.0625018i	$-0.0199079\pi$
$761$	12.2730	+	21.2574i	0.444894	+	0.770580i	−0.553151	+	0.833081i	$0.686575\pi$
$762$		0			0
$763$	9.56941	−	16.5747i	0.346436	−	0.600045i
$764$	−20.0033			−0.723693
$765$		0			0
$766$	−1.97354			−0.0713069
$767$	−0.0334246	+	0.0578931i	−0.00120689	+	0.00209040i
$768$		0			0
$769$	−15.7072	−	27.2057i	−0.566416	−	0.981061i	−0.996916	−	0.0784710i	$-0.974996\pi$
$769$	−15.7072	−	27.2057i	−0.566416	−	0.981061i	0.430500	−	0.902590i	$-0.358337\pi$
$770$	3.16693	+	5.48528i	0.114128	+	0.197676i
$771$		0			0
$772$	−9.87335	+	17.1011i	−0.355349	+	0.615483i
$773$	28.7145			1.03279			0.516395	−	0.856351i	$-0.327274\pi$
$773$	28.7145			1.03279			0.516395	+	0.856351i	$0.327274\pi$
$774$		0			0
$775$	−0.346663			−0.0124525
$776$	−7.90413	+	13.6904i	−0.283742	+	0.491455i
$777$		0			0
$778$	−4.53135	−	7.84853i	−0.162457	−	0.281383i
$779$	0.766872	+	1.32826i	0.0274761	+	0.0475899i
$780$		0			0
$781$	−15.8653	+	27.4795i	−0.567706	+	0.983295i
$782$	−1.34633			−0.0481446
$783$		0			0
$784$	−15.7448			−0.562315
$785$	−13.9112	+	24.0949i

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)

\(f(q)\)	\(=\)	\(q+(0.207733 - 0.359804i) q^{2} +(0.913694 + 1.58256i) q^{4} +(-1.10759 - 1.91841i) q^{5} +(0.659815 - 1.14283i) q^{7} +1.59015 q^{8} +O(q^{10})\)	\(q+(0.207733 - 0.359804i) q^{2} +(0.913694 + 1.58256i) q^{4} +(-1.10759 - 1.91841i) q^{5} +(0.659815 - 1.14283i) q^{7} +1.59015 q^{8} -0.920335 q^{10} +(2.60759 - 4.51648i) q^{11} +(0.00902926 + 0.0156391i) q^{13} +(-0.274131 - 0.474808i) q^{14} +(-1.49706 + 2.59299i) q^{16} -3.13280 q^{17} +0.417352 q^{19} +(2.02400 - 3.50568i) q^{20} +(-1.08337 - 1.87645i) q^{22} +(0.517193 + 0.895805i) q^{23} +(0.0464738 - 0.0804949i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(3.90361 - 6.76125i) q^{29} +(-1.86483 - 3.22998i) q^{31} +(2.21213 + 3.83152i) q^{32} +(-0.650785 + 1.12719i) q^{34} -2.92322 q^{35} +4.42476 q^{37} +(0.0866979 - 0.150165i) q^{38} +(-1.76124 - 3.05056i) q^{40} +(1.83747 + 3.18259i) q^{41} +(4.15394 - 7.19483i) q^{43} +9.53017 q^{44} +0.429753 q^{46} +(3.54895 - 6.14697i) q^{47} +(2.62929 + 4.55406i) q^{49} +(-0.0193083 - 0.0334429i) q^{50} +(-0.0165000 + 0.0285788i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(1.04920 - 1.81728i) q^{56} +(-1.62182 - 2.80907i) q^{58} +(1.85091 + 3.20586i) q^{59} +(-3.45712 + 5.98791i) q^{61} -1.54955 q^{62} -4.15011 q^{64} +(0.0200015 - 0.0346436i) q^{65} +(5.51340 + 9.54949i) q^{67} +(-2.86242 - 4.95785i) q^{68} +(-0.607251 + 1.05179i) q^{70} -6.08428 q^{71} -0.546973 q^{73} +(0.919169 - 1.59205i) q^{74} +(0.381332 + 0.660487i) q^{76} +(-3.44106 - 5.96008i) q^{77} +(-0.244572 + 0.423611i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(-2.30684 + 3.99556i) q^{83} +(3.46986 + 6.00998i) q^{85} +(-1.72582 - 2.98921i) q^{86} +(4.14647 - 7.18189i) q^{88} -3.37307 q^{89} +0.0238305 q^{91} +(-0.945113 + 1.63698i) q^{92} +(-1.47447 - 2.55386i) q^{94} +(-0.462257 - 0.800652i) q^{95} +(-4.97068 + 8.60947i) q^{97} +2.18476 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 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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