LMFDB - Embedded newform 378.2.h.c.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(289,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("378.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.h (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	378.361
Dual form			378.2.h.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(-0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(-0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(0.296790 - 0.514055i) q^{10} +0.593579 q^{11} +(-1.25729 + 2.17770i) q^{13} +(-2.25729 - 1.38008i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.46050 + 2.52967i) q^{17} +(2.69076 + 4.66053i) q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} -4.46050 q^{23} -4.64766 q^{25} +(-1.25729 - 2.17770i) q^{26} +(2.32383 - 1.26483i) q^{28} +(3.09718 + 5.36447i) q^{29} +(3.93346 + 6.81296i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.46050 - 2.52967i) q^{34} +(0.0394951 - 1.56997i) q^{35} +(0.500000 + 0.866025i) q^{37} -5.38151 q^{38} -0.593579 q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(-0.296790 - 0.514055i) q^{44} +(2.23025 - 3.86291i) q^{46} +(6.08113 - 10.5328i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(2.32383 - 4.02499i) q^{50} +2.51459 q^{52} +(-4.02704 + 6.97504i) q^{53} -0.352336 q^{55} +(-0.0665372 + 2.64491i) q^{56} -6.19436 q^{58} +(4.32383 + 7.48910i) q^{59} +(3.32383 - 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(0.746304 - 1.29264i) q^{65} +(0.956906 + 1.65741i) q^{67} +2.92101 q^{68} +(1.33988 + 0.819187i) q^{70} +14.4107 q^{71} +(3.95691 - 6.85356i) q^{73} -1.00000 q^{74} +(2.69076 - 4.66053i) q^{76} +(-0.0394951 + 1.56997i) q^{77} +(4.62422 - 8.00938i) q^{79} +(0.296790 - 0.514055i) q^{80} +(0.136673 + 0.236725i) q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +11.1623 q^{86} +0.593579 q^{88} +(6.21780 + 10.7695i) q^{89} +(-5.67617 - 3.47033i) q^{91} +(2.23025 + 3.86291i) q^{92} +(6.08113 + 10.5328i) q^{94} +(-1.59718 - 2.76639i) q^{95} +(5.86693 + 10.1618i) q^{97} +(3.80039 - 5.87852i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 2 * q^5 - 4 * q^7 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8} - q^{10} - 2 q^{11} + 8 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} - q^{20} + q^{22} - 14 q^{23} - 4 q^{25} + 8 q^{26} + 2 q^{28} + 5 q^{29} + 20 q^{31} - 3 q^{32} + 4 q^{34} + 13 q^{35} + 3 q^{37} + 6 q^{38} + 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 9 q^{47} - 12 q^{49} + 2 q^{50} - 16 q^{52} - 15 q^{53} - 26 q^{55} - 4 q^{56} - 10 q^{58} + 14 q^{59} + 8 q^{61} - 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} - 8 q^{68} + 10 q^{70} - 14 q^{71} + 19 q^{73} - 6 q^{74} - 3 q^{76} - 13 q^{77} + 5 q^{79} - q^{80} - 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} + 9 q^{89} - 46 q^{91} + 7 q^{92} + 9 q^{94} + 4 q^{95} + 28 q^{97} + 12 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 2 * q^5 - 4 * q^7 + 6 * q^8 - q^10 - 2 * q^11 + 8 * q^13 + 2 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 - q^20 + q^22 - 14 * q^23 - 4 * q^25 + 8 * q^26 + 2 * q^28 + 5 * q^29 + 20 * q^31 - 3 * q^32 + 4 * q^34 + 13 * q^35 + 3 * q^37 + 6 * q^38 + 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 + 9 * q^47 - 12 * q^49 + 2 * q^50 - 16 * q^52 - 15 * q^53 - 26 * q^55 - 4 * q^56 - 10 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 - 8 * q^68 + 10 * q^70 - 14 * q^71 + 19 * q^73 - 6 * q^74 - 3 * q^76 - 13 * q^77 + 5 * q^79 - q^80 - 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 + 9 * q^89 - 46 * q^91 + 7 * q^92 + 9 * q^94 + 4 * q^95 + 28 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.593579			−0.265457			−0.132728	−	0.991152i	$-0.542374\pi$
$5$	−0.593579			−0.265457			−0.132728	+	0.991152i	$0.542374\pi$
$6$		0			0
$7$	−0.0665372	+	2.64491i	−0.0251487	+	0.999684i
$7$	−0.0665372	+	2.64491i	−0.0251487	+	0.999684i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.296790	−	0.514055i	0.0938531	−	0.162558i
$11$	0.593579			0.178971			0.0894855	−	0.995988i	$-0.471478\pi$
$11$	0.593579			0.178971			0.0894855	+	0.995988i	$0.471478\pi$
$12$		0			0
$13$	−1.25729	+	2.17770i	−0.348711	+	0.603985i	−0.986021	−	0.166623i	$-0.946714\pi$
$13$	−1.25729	+	2.17770i	−0.348711	+	0.603985i	0.637310	+	0.770608i	$0.280047\pi$
$14$	−2.25729	−	1.38008i	−0.603287	−	0.368842i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.46050	+	2.52967i	−0.354224	+	0.613535i	−0.986985	−	0.160813i	$-0.948588\pi$
$17$	−1.46050	+	2.52967i	−0.354224	+	0.613535i	0.632760	+	0.774348i	$0.281922\pi$
$18$		0			0
$19$	2.69076	+	4.66053i	0.617302	+	1.06920i	0.989976	+	0.141236i	$0.0451077\pi$
$19$	2.69076	+	4.66053i	0.617302	+	1.06920i	−0.372674	+	0.927962i	$0.621559\pi$
$20$	0.296790	+	0.514055i	0.0663642	+	0.114946i
$21$		0			0
$22$	−0.296790	+	0.514055i	−0.0632758	+	0.109597i
$23$	−4.46050			−0.930080			−0.465040	−	0.885290i	$-0.653960\pi$
$23$	−4.46050			−0.930080			−0.465040	+	0.885290i	$0.653960\pi$
$24$		0			0
$25$	−4.64766			−0.929533
$26$	−1.25729	−	2.17770i	−0.246576	−	0.427082i
$27$		0			0
$28$	2.32383	−	1.26483i	0.439163	−	0.239031i
$29$	3.09718	+	5.36447i	0.575132	+	0.996157i	0.996027	+	0.0890480i	$0.0283825\pi$
$29$	3.09718	+	5.36447i	0.575132	+	0.996157i	−0.420896	+	0.907109i	$0.638284\pi$
$30$		0			0
$31$	3.93346	+	6.81296i	0.706471	+	1.22364i	0.966158	+	0.257951i	$0.0830472\pi$
$31$	3.93346	+	6.81296i	0.706471	+	1.22364i	−0.259687	+	0.965693i	$0.583620\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−1.46050	−	2.52967i	−0.250475	−	0.433835i
$35$	0.0394951	−	1.56997i	0.00667590	−	0.265373i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−5.38151			−0.872997
$39$		0			0
$40$	−0.593579			−0.0938531
$41$	0.136673	−	0.236725i	0.0213448	−	0.0369702i	−0.855156	−	0.518371i	$-0.826539\pi$
$41$	0.136673	−	0.236725i	0.0213448	−	0.0369702i	0.876500	+	0.481401i	$0.159872\pi$
$42$		0			0
$43$	−5.58113	−	9.66679i	−0.851114	−	1.47417i	−0.880204	−	0.474596i	$-0.842594\pi$
$43$	−5.58113	−	9.66679i	−0.851114	−	1.47417i	0.0290902	−	0.999577i	$-0.490739\pi$
$44$	−0.296790	−	0.514055i	−0.0447427	−	0.0774967i
$45$		0			0
$46$	2.23025	−	3.86291i	0.328833	−	0.569555i
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.0436467	−	0.999047i	$-0.486102\pi$
$47$	6.08113	−	10.5328i	0.887023	−	1.53637i	0.843377	−	0.537323i	$-0.180564\pi$
$48$		0			0
$49$	−6.99115	−	0.351971i	−0.998735	−	0.0502815i
$50$	2.32383	−	4.02499i	0.328639	−	0.569220i
$51$		0			0
$52$	2.51459			0.348711
$53$	−4.02704	+	6.97504i	−0.553157	+	0.958096i	0.444888	+	0.895586i	$0.353244\pi$
$53$	−4.02704	+	6.97504i	−0.553157	+	0.958096i	−0.998044	+	0.0625092i	$0.980090\pi$
$54$		0			0
$55$	−0.352336			−0.0475090
$56$	−0.0665372	+	2.64491i	−0.00889141	+	0.353442i
$57$		0			0
$58$	−6.19436			−0.813359
$59$	4.32383	+	7.48910i	0.562915	+	0.974997i	0.997240	+	0.0742412i	$0.0236535\pi$
$59$	4.32383	+	7.48910i	0.562915	+	0.974997i	−0.434325	+	0.900756i	$0.643013\pi$
$60$		0			0
$61$	3.32383	−	5.75705i	0.425573	−	0.737114i	−0.570901	−	0.821019i	$-0.693406\pi$
$61$	3.32383	−	5.75705i	0.425573	−	0.737114i	0.996474	+	0.0839050i	$0.0267392\pi$
$62$	−7.86693			−0.999101
$63$		0			0
$64$	1.00000			0.125000
$65$	0.746304	−	1.29264i	0.0925676	−	0.160332i
$66$		0			0
$67$	0.956906	+	1.65741i	0.116905	+	0.202485i	0.918540	−	0.395329i	$-0.129369\pi$
$67$	0.956906	+	1.65741i	0.116905	+	0.202485i	−0.801635	+	0.597814i	$0.796036\pi$
$68$	2.92101			0.354224
$69$		0			0
$70$	1.33988	+	0.819187i	0.160147	+	0.0979116i
$71$	14.4107			1.71023			0.855117	−	0.518435i	$-0.173485\pi$
$71$	14.4107			1.71023			0.855117	+	0.518435i	$0.173485\pi$
$72$		0			0
$73$	3.95691	−	6.85356i	0.463121	−	0.802149i	−0.535994	−	0.844222i	$-0.680063\pi$
$73$	3.95691	−	6.85356i	0.463121	−	0.802149i	0.999115	+	0.0420732i	$0.0133963\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	2.69076	−	4.66053i	0.308651	−	0.534599i
$77$	−0.0394951	+	1.56997i	−0.00450089	+	0.178914i
$78$		0			0
$79$	4.62422	−	8.00938i	0.520265	−	0.901126i	−0.479457	−	0.877565i	$-0.659166\pi$
$79$	4.62422	−	8.00938i	0.520265	−	0.901126i	0.999722	−	0.0235607i	$-0.00750031\pi$
$80$	0.296790	−	0.514055i	0.0331821	−	0.0574731i
$81$		0			0
$82$	0.136673	+	0.236725i	0.0150930	+	0.0261419i
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	0.573513	−	0.819196i	$-0.305580\pi$
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	−0.996201	+	0.0870787i	$0.972247\pi$
$84$		0			0
$85$	0.866926	−	1.50156i	0.0940313	−	0.162867i
$86$	11.1623			1.20366
$87$		0			0
$88$	0.593579			0.0632758
$89$	6.21780	+	10.7695i	0.659085	+	1.14157i	0.980853	+	0.194751i	$0.0623898\pi$
$89$	6.21780	+	10.7695i	0.659085	+	1.14157i	−0.321767	+	0.946819i	$0.604277\pi$
$90$		0			0
$91$	−5.67617	−	3.47033i	−0.595024	−	0.363790i
$92$	2.23025	+	3.86291i	0.232520	+	0.402736i
$93$		0			0
$94$	6.08113	+	10.5328i	0.627220	+	1.08638i
$95$	−1.59718	−	2.76639i	−0.163867	−	0.283826i
$96$		0			0
$97$	5.86693	+	10.1618i	0.595696	+	1.03178i	0.993448	+	0.114283i	$0.0364570\pi$
$97$	5.86693	+	10.1618i	0.595696	+	1.03178i	−0.397752	+	0.917493i	$0.630210\pi$
$98$	3.80039	−	5.87852i	0.383897	−	0.593821i
$99$		0			0
$100$	2.32383	+	4.02499i	0.232383	+	0.402499i
$101$	1.62276			0.161470			0.0807352	−	0.996736i	$-0.474273\pi$
$101$	1.62276			0.161470			0.0807352	+	0.996736i	$0.474273\pi$
$102$		0			0
$103$	6.38151			0.628789			0.314395	−	0.949292i	$-0.398198\pi$
$103$	6.38151			0.628789			0.314395	+	0.949292i	$0.398198\pi$
$104$	−1.25729	+	2.17770i	−0.123288	+	0.213541i
$105$		0			0
$106$	−4.02704	−	6.97504i	−0.391141	−	0.677476i
$107$	−9.35447	−	16.2024i	−0.904331	−	1.56635i	−0.821813	−	0.569758i	$-0.807037\pi$
$107$	−9.35447	−	16.2024i	−0.904331	−	1.56635i	−0.0825182	−	0.996590i	$-0.526296\pi$
$108$		0			0
$109$	−1.43346	+	2.48283i	−0.137301	+	0.237812i	−0.926474	−	0.376359i	$-0.877176\pi$
$109$	−1.43346	+	2.48283i	−0.137301	+	0.237812i	0.789173	+	0.614171i	$0.210509\pi$
$110$	0.176168	−	0.305132i	0.0167970	−	0.0290932i
$111$		0			0
$112$	−2.25729	−	1.38008i	−0.213294	−	0.130405i
$113$	6.16012	−	10.6696i	0.579495	−	1.00371i	−0.416042	−	0.909345i	$-0.636583\pi$
$113$	6.16012	−	10.6696i	0.579495	−	1.00371i	0.995537	−	0.0943695i	$-0.0300835\pi$
$114$		0			0
$115$	2.64766			0.246896
$116$	3.09718	−	5.36447i	0.287566	−	0.498078i
$117$		0			0
$118$	−8.64766			−0.796082
$119$	−6.59358	−	4.03123i	−0.604432	−	0.369542i
$120$		0			0
$121$	−10.6477			−0.967969
$122$	3.32383	+	5.75705i	0.300926	+	0.521218i
$123$		0			0
$124$	3.93346	−	6.81296i	0.353235	−	0.611822i
$125$	5.72665			0.512207
$126$		0			0
$127$	12.3346			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$127$	12.3346			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	0.746304	+	1.29264i	0.0654552	+	0.113372i
$131$	1.18716			0.103723			0.0518613	−	0.998654i	$-0.483485\pi$
$131$	1.18716			0.103723			0.0518613	+	0.998654i	$0.483485\pi$
$132$		0			0
$133$	−12.5057	+	6.80672i	−1.08438	+	0.590218i
$134$	−1.91381			−0.165328
$135$		0			0
$136$	−1.46050	+	2.52967i	−0.125237	+	0.216917i
$137$	−2.52179			−0.215451			−0.107725	−	0.994181i	$-0.534357\pi$
$137$	−2.52179			−0.215451			−0.107725	+	0.994181i	$0.534357\pi$
$138$		0			0
$139$	2.45691	−	4.25549i	0.208392	−	0.360946i	−0.742816	−	0.669496i	$-0.766510\pi$
$139$	2.45691	−	4.25549i	0.208392	−	0.360946i	0.951208	+	0.308550i	$0.0998437\pi$
$140$	−1.37938	+	0.750780i	−0.116579	+	0.0634525i
$141$		0			0
$142$	−7.20535	+	12.4800i	−0.604659	+	1.04730i
$143$	−0.746304	+	1.29264i	−0.0624091	+	0.108096i
$144$		0			0
$145$	−1.83842	−	3.18424i	−0.152673	−	0.264437i
$146$	3.95691	+	6.85356i	0.327476	+	0.567205i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−18.0512			−1.47881			−0.739404	−	0.673262i	$-0.764893\pi$
$149$	−18.0512			−1.47881			−0.739404	+	0.673262i	$0.764893\pi$
$150$		0			0
$151$	1.64766			0.134085			0.0670425	−	0.997750i	$-0.478644\pi$
$151$	1.64766			0.134085			0.0670425	+	0.997750i	$0.478644\pi$
$152$	2.69076	+	4.66053i	0.218249	+	0.378019i
$153$		0			0
$154$	−1.33988	−	0.819187i	−0.107971	−	0.0660120i
$155$	−2.33482	−	4.04403i	−0.187537	−	0.324824i
$156$		0			0
$157$	3.30039	+	5.71644i	0.263400	+	0.456222i	0.967143	−	0.254233i	$-0.0818229\pi$
$157$	3.30039	+	5.71644i	0.263400	+	0.456222i	−0.703743	+	0.710454i	$0.748490\pi$
$158$	4.62422	+	8.00938i	0.367883	+	0.637192i
$159$		0			0
$160$	0.296790	+	0.514055i	0.0234633	+	0.0406396i
$161$	0.296790	−	11.7977i	0.0233903	−	0.929785i
$162$		0			0
$163$	−2.99115	−	5.18082i	−0.234285	−	0.405793i	0.724780	−	0.688980i	$-0.241941\pi$
$163$	−2.99115	−	5.18082i	−0.234285	−	0.405793i	−0.959065	+	0.283188i	$0.908608\pi$
$164$	−0.273346			−0.0213448
$165$		0			0
$166$	7.70175			0.597772
$167$	−3.73025	+	6.46099i	−0.288656	+	0.499966i	−0.973489	−	0.228733i	$-0.926542\pi$
$167$	−3.73025	+	6.46099i	−0.288656	+	0.499966i	0.684833	+	0.728700i	$0.259875\pi$
$168$		0			0
$169$	3.33842	+	5.78231i	0.256802	+	0.444793i
$170$	0.866926	+	1.50156i	0.0664902	+	0.115164i
$171$		0			0
$172$	−5.58113	+	9.66679i	−0.425557	+	0.737086i
$173$	−12.8296	+	22.2215i	−0.975414	+	1.68947i	−0.296851	+	0.954924i	$0.595937\pi$
$173$	−12.8296	+	22.2215i	−0.975414	+	1.68947i	−0.678562	+	0.734543i	$0.737397\pi$
$174$		0			0
$175$	0.309243	−	12.2927i	0.0233766	−	0.929239i
$176$	−0.296790	+	0.514055i	−0.0223714	+	0.0387483i
$177$		0			0
$178$	−12.4356			−0.932088
$179$	−7.51819	+	13.0219i	−0.561936	+	0.973301i	0.435392	+	0.900241i	$0.356610\pi$
$179$	−7.51819	+	13.0219i	−0.561936	+	0.973301i	−0.997328	+	0.0730602i	$0.976723\pi$
$180$		0			0
$181$	−0.0861875			−0.00640627			−0.00320313	−	0.999995i	$-0.501020\pi$
$181$	−0.0861875			−0.00640627			−0.00320313	+	0.999995i	$0.501020\pi$
$182$	5.84348	−	3.18054i	0.433148	−	0.235757i
$183$		0			0
$184$	−4.46050			−0.328833
$185$	−0.296790	−	0.514055i	−0.0218204	−	0.0377941i
$186$		0			0
$187$	−0.866926	+	1.50156i	−0.0633959	+	0.109805i
$188$	−12.1623			−0.887023
$189$		0			0
$190$	3.19436			0.231743
$191$	1.99115	−	3.44877i	0.144074	−	0.249544i	−0.784953	−	0.619555i	$-0.787313\pi$
$191$	1.99115	−	3.44877i	0.144074	−	0.249544i	0.929027	+	0.370011i	$0.120646\pi$
$192$		0			0
$193$	−3.39037	−	5.87229i	−0.244044	−	0.422697i	0.717818	−	0.696230i	$-0.245141\pi$
$193$	−3.39037	−	5.87229i	−0.244044	−	0.422697i	−0.961862	+	0.273534i	$0.911808\pi$
$194$	−11.7339			−0.842441
$195$		0			0
$196$	3.19076	+	6.23049i	0.227911	+	0.445035i
$197$	−11.0584			−0.787875			−0.393938	−	0.919137i	$-0.628887\pi$
$197$	−11.0584			−0.787875			−0.393938	+	0.919137i	$0.628887\pi$
$198$		0			0
$199$	2.80924	−	4.86575i	0.199142	−	0.344924i	−0.749109	−	0.662447i	$-0.769518\pi$
$199$	2.80924	−	4.86575i	0.199142	−	0.344924i	0.948250	+	0.317523i	$0.102851\pi$
$200$	−4.64766			−0.328639
$201$		0			0
$202$	−0.811379	+	1.40535i	−0.0570884	+	0.0988800i
$203$	−14.3946	+	7.83483i	−1.01031	+	0.549898i
$204$		0			0
$205$	−0.0811263	+	0.140515i	−0.00566611	+	0.00981399i
$206$	−3.19076	+	5.52655i	−0.222311	+	0.385053i
$207$		0			0
$208$	−1.25729	−	2.17770i	−0.0871777	−	0.150996i
$209$	1.59718	+	2.76639i	0.110479	+	0.191355i
$210$		0			0
$211$	9.66225	−	16.7355i	0.665177	−	1.15212i	−0.314060	−	0.949403i	$-0.601689\pi$
$211$	9.66225	−	16.7355i	0.665177	−	1.15212i	0.979237	−	0.202717i	$-0.0649772\pi$
$212$	8.05408			0.553157
$213$		0			0
$214$	18.7089			1.27892
$215$	3.31284	+	5.73801i	0.225934	+	0.391329i
$216$		0			0
$217$	−18.2814	+	9.95036i	−1.24102	+	0.675474i
$218$	−1.43346	−	2.48283i	−0.0970863	−	0.168158i
$219$		0			0
$220$	0.176168	+	0.305132i	0.0118773	+	0.0205720i
$221$	−3.67257	−	6.36108i	−0.247044	−	0.427892i
$222$		0			0
$223$	12.6623	+	21.9317i	0.847927	+	1.46865i	0.883055	+	0.469270i	$0.155483\pi$
$223$	12.6623	+	21.9317i	0.847927	+	1.46865i	−0.0351275	+	0.999383i	$0.511184\pi$
$224$	2.32383	−	1.26483i	0.155268	−	0.0845103i
$225$		0			0
$226$	6.16012	+	10.6696i	0.409765	+	0.709734i
$227$	−4.81711			−0.319723			−0.159862	−	0.987139i	$-0.551105\pi$
$227$	−4.81711			−0.319723			−0.159862	+	0.987139i	$0.551105\pi$
$228$		0			0
$229$	−9.29533			−0.614253			−0.307126	−	0.951669i	$-0.599367\pi$
$229$	−9.29533			−0.614253			−0.307126	+	0.951669i	$0.599367\pi$
$230$	−1.32383	+	2.29294i	−0.0872909	+	0.151192i
$231$		0			0
$232$	3.09718	+	5.36447i	0.203340	+	0.352195i
$233$	−0.0971780	−	0.168317i	−0.00636634	−	0.0110268i	0.862825	−	0.505503i	$-0.168693\pi$
$233$	−0.0971780	−	0.168317i	−0.00636634	−	0.0110268i	−0.869191	+	0.494476i	$0.835360\pi$
$234$		0			0
$235$	−3.60963	+	6.25206i	−0.235466	+	0.407840i
$236$	4.32383	−	7.48910i	0.281457	−	0.487499i
$237$		0			0
$238$	6.78794	−	3.69459i	0.439996	−	0.239485i
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	−0.556181	−	0.831061i	$-0.687734\pi$
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	0.997811	+	0.0661361i	$0.0210672\pi$
$240$		0			0
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$	5.32383	−	9.22115i	0.342229	−	0.592758i
$243$		0			0
$244$	−6.64766			−0.425573
$245$	4.14980	+	0.208922i	0.265121	+	0.0133476i
$246$		0			0
$247$	−13.5323			−0.861039
$248$	3.93346	+	6.81296i	0.249775	+	0.432623i
$249$		0			0
$250$	−2.86333	+	4.95943i	−0.181093	+	0.313662i
$251$	19.5438			1.23359			0.616796	−	0.787123i	$-0.288430\pi$
$251$	19.5438			1.23359			0.616796	+	0.787123i	$0.288430\pi$
$252$		0			0
$253$	−2.64766			−0.166457
$254$	−6.16731	+	10.6821i	−0.386972	+	0.670255i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.32743			−0.519451			−0.259725	−	0.965683i	$-0.583632\pi$
$257$	−8.32743			−0.519451			−0.259725	+	0.965683i	$0.583632\pi$
$258$		0			0
$259$	−2.32383	+	1.26483i	−0.144396	+	0.0785930i
$260$	−1.49261			−0.0925676
$261$		0			0
$262$	−0.593579	+	1.02811i	−0.0366715	+	0.0635168i
$263$	17.0905			1.05384			0.526921	−	0.849914i	$-0.323346\pi$
$263$	17.0905			1.05384			0.526921	+	0.849914i	$0.323346\pi$
$264$		0			0
$265$	2.39037	−	4.14024i	0.146839	−	0.254333i
$266$	0.358071	−	14.2336i	0.0219547	−	0.872721i
$267$		0			0
$268$	0.956906	−	1.65741i	0.0584524	−	0.101242i
$269$	5.00720	−	8.67272i	0.305294	−	0.528785i	−0.672033	−	0.740522i	$-0.734579\pi$
$269$	5.00720	−	8.67272i	0.305294	−	0.528785i	0.977327	+	0.211737i	$0.0679119\pi$
$270$		0			0
$271$	5.10457	+	8.84137i	0.310081	+	0.537075i	0.978380	−	0.206818i	$-0.0663106\pi$
$271$	5.10457	+	8.84137i	0.310081	+	0.537075i	−0.668299	+	0.743893i	$0.732977\pi$
$272$	−1.46050	−	2.52967i	−0.0885561	−	0.153384i
$273$		0			0
$274$	1.26089	−	2.18393i	0.0761733	−	0.131936i
$275$	−2.75876			−0.166359
$276$		0			0
$277$	19.3422			1.16216			0.581081	−	0.813846i	$-0.302630\pi$
$277$	19.3422			1.16216			0.581081	+	0.813846i	$0.302630\pi$
$278$	2.45691	+	4.25549i	0.147355	+	0.255227i
$279$		0			0
$280$	0.0394951	−	1.56997i	0.00236029	−	0.0938235i
$281$	6.40136	+	11.0875i	0.381873	+	0.661424i	0.991330	−	0.131396i	$-0.0419458\pi$
$281$	6.40136	+	11.0875i	0.381873	+	0.661424i	−0.609457	+	0.792819i	$0.708612\pi$
$282$		0			0
$283$	8.17617	+	14.1615i	0.486023	+	0.841816i	0.999871	−	0.0160650i	$-0.00511388\pi$
$283$	8.17617	+	14.1615i	0.486023	+	0.841816i	−0.513848	+	0.857881i	$0.671781\pi$
$284$	−7.20535	−	12.4800i	−0.427559	−	0.740553i
$285$		0			0
$286$	−0.746304	−	1.29264i	−0.0441299	−	0.0764352i
$287$	0.617023	+	0.377240i	0.0364217	+	0.0222678i
$288$		0			0
$289$	4.23385	+	7.33325i	0.249050	+	0.431367i
$290$	3.67684			0.215912
$291$		0			0
$292$	−7.91381			−0.463121
$293$	10.3889	−	17.9941i	0.606926	−	1.05123i	−0.384817	−	0.922993i	$-0.625736\pi$
$293$	10.3889	−	17.9941i	0.606926	−	1.05123i	0.991744	−	0.128235i	$-0.0409311\pi$
$294$		0			0
$295$	−2.56654	−	4.44537i	−0.149430	−	0.258820i
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$	9.02558	−	15.6328i	0.522838	−	0.905582i
$299$	5.60817	−	9.71363i	0.324329	−	0.561754i
$300$		0			0
$301$	25.9392	−	14.1184i	1.49511	−	0.813771i
$302$	−0.823832	+	1.42692i	−0.0474062	+	0.0821099i
$303$		0			0
$304$	−5.38151			−0.308651
$305$	−1.97296	+	3.41726i	−0.112971	+	0.195672i
$306$		0			0
$307$	−22.6768			−1.29424			−0.647118	−	0.762390i	$-0.724026\pi$
$307$	−22.6768			−1.29424			−0.647118	+	0.762390i	$0.724026\pi$
$308$	1.37938	−	0.750780i	0.0785974	−	0.0427796i
$309$		0			0
$310$	4.66964			0.265218
$311$	−3.25729	−	5.64180i	−0.184704	−	0.319917i	0.758773	−	0.651356i	$-0.225799\pi$
$311$	−3.25729	−	5.64180i	−0.184704	−	0.319917i	−0.943477	+	0.331439i	$0.892466\pi$
$312$		0			0
$313$	−0.133074	+	0.230492i	−0.00752181	+	0.0130282i	−0.869762	−	0.493472i	$-0.835728\pi$
$313$	−0.133074	+	0.230492i	−0.00752181	+	0.0130282i	0.862240	+	0.506500i	$0.169061\pi$
$314$	−6.60078			−0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	7.86186	−	13.6171i	0.441566	−	0.764815i	−0.556240	−	0.831022i	$-0.687756\pi$
$317$	7.86186	−	13.6171i	0.441566	−	0.764815i	0.997806	+	0.0662067i	$0.0210897\pi$
$318$		0			0
$319$	1.83842	+	3.18424i	0.102932	+	0.178283i
$320$	−0.593579			−0.0331821
$321$		0			0
$322$	10.0687	+	6.15585i	0.561105	+	0.343052i
$323$	−15.7195			−0.874654
$324$		0			0
$325$	5.84348	−	10.1212i	0.324138	−	0.561424i
$326$	5.98229			0.331328
$327$		0			0
$328$	0.136673	−	0.236725i	0.00754651	−	0.0130709i
$329$	27.4538	+	16.7849i	1.51358	+	0.925381i
$330$		0			0
$331$	12.5811	−	21.7912i	0.691521	−	1.19775i	−0.279818	−	0.960053i	$-0.590274\pi$
$331$	12.5811	−	21.7912i	0.691521	−	1.19775i	0.971339	−	0.237697i	$-0.0763925\pi$
$332$	−3.85087	+	6.66991i	−0.211344	+	0.366059i
$333$		0			0
$334$	−3.73025	−	6.46099i	−0.204110	−	0.353529i
$335$	−0.568000	−	0.983804i	−0.0310331	−	0.0537510i
$336$		0			0
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	0.489681	+	0.871902i	$0.337113\pi$
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	−0.999929	+	0.0118752i	$0.996220\pi$
$338$	−6.67684			−0.363172
$339$		0			0
$340$	−1.73385			−0.0940313
$341$	2.33482	+	4.04403i	0.126438	+	0.218997i
$342$		0			0
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$	−5.58113	−	9.66679i	−0.300914	−	0.521199i
$345$		0			0
$346$	−12.8296	−	22.2215i	−0.689722	−	1.19463i
$347$	11.2719	+	19.5235i	0.605106	+	1.04808i	0.992035	+	0.125965i	$0.0402028\pi$
$347$	11.2719	+	19.5235i	0.605106	+	1.04808i	−0.386928	+	0.922110i	$0.626464\pi$
$348$		0			0
$349$	1.89543	+	3.28298i	0.101460	+	0.175734i	0.912286	−	0.409553i	$-0.134315\pi$
$349$	1.89543	+	3.28298i	0.101460	+	0.175734i	−0.810826	+	0.585287i	$0.800982\pi$
$350$	10.4911	+	6.41415i	0.560775	+	0.342851i
$351$		0			0
$352$	−0.296790	−	0.514055i	−0.0158189	−	0.0273992i
$353$	−6.83482			−0.363781			−0.181890	−	0.983319i	$-0.558222\pi$
$353$	−6.83482			−0.363781			−0.181890	+	0.983319i	$0.558222\pi$
$354$		0			0
$355$	−8.55389			−0.453993
$356$	6.21780	−	10.7695i	0.329543	−	0.570785i
$357$		0			0
$358$	−7.51819	−	13.0219i	−0.397349	−	0.688228i
$359$	6.32237	+	10.9507i	0.333682	+	0.577954i	0.983231	−	0.182366i	$-0.0583755\pi$
$359$	6.32237	+	10.9507i	0.333682	+	0.577954i	−0.649549	+	0.760320i	$0.725042\pi$
$360$		0			0
$361$	−4.98035	+	8.62622i	−0.262124	+	0.454012i
$362$	0.0430937	−	0.0746406i	0.00226496	−	0.00392302i
$363$		0			0
$364$	−0.167314	+	6.65087i	−0.00876963	+	0.348600i
$365$	−2.34874	+	4.06813i	−0.122939	+	0.212936i
$366$		0			0
$367$	6.54377			0.341582			0.170791	−	0.985307i	$-0.445368\pi$
$367$	6.54377			0.341582			0.170791	+	0.985307i	$0.445368\pi$
$368$	2.23025	−	3.86291i	0.116260	−	0.201368i
$369$		0			0
$370$	0.593579			0.0308587
$371$	−18.1804	−	11.1153i	−0.943881	−	0.577077i
$372$		0			0
$373$	9.42840			0.488184			0.244092	−	0.969752i	$-0.421510\pi$
$373$	9.42840			0.488184			0.244092	+	0.969752i	$0.421510\pi$
$374$	−0.866926	−	1.50156i	−0.0448277	−	0.0776438i
$375$		0			0
$376$	6.08113	−	10.5328i	0.313610	−	0.543189i
$377$	−15.5763			−0.802218
$378$		0			0
$379$	−7.27762			−0.373826			−0.186913	−	0.982376i	$-0.559848\pi$
$379$	−7.27762			−0.373826			−0.186913	+	0.982376i	$0.559848\pi$
$380$	−1.59718	+	2.76639i	−0.0819335	+	0.141913i
$381$		0			0
$382$	1.99115	+	3.44877i	0.101876	+	0.176454i
$383$	24.0833			1.23060			0.615299	−	0.788294i	$-0.289035\pi$
$383$	24.0833			1.23060			0.615299	+	0.788294i	$0.289035\pi$
$384$		0			0
$385$	0.0234435	−	0.931900i	0.00119479	−	0.0474940i
$386$	6.78074			0.345130
$387$		0			0
$388$	5.86693	−	10.1618i	0.297848	−	0.515888i
$389$	16.2983			0.826354			0.413177	−	0.910651i	$-0.364419\pi$
$389$	16.2983			0.826354			0.413177	+	0.910651i	$0.364419\pi$
$390$		0			0
$391$	6.51459	−	11.2836i	0.329457	−	0.570636i
$392$	−6.99115	−	0.351971i	−0.353106	−	0.0177772i
$393$		0			0
$394$	5.52918	−	9.57682i	0.278556	−	0.482473i
$395$	−2.74484	+	4.75420i	−0.138108	+	0.239210i
$396$		0			0
$397$	−6.08619	−	10.5416i	−0.305457	−	0.529067i	0.671906	−	0.740636i	$-0.265476\pi$
$397$	−6.08619	−	10.5416i	−0.305457	−	0.529067i	−0.977363	+	0.211569i	$0.932143\pi$
$398$	2.80924	+	4.86575i	0.140815	+	0.243898i
$399$		0			0
$400$	2.32383	−	4.02499i	0.116192	−	0.201250i
$401$	33.3609			1.66596			0.832981	−	0.553301i	$-0.186632\pi$
$401$	33.3609			1.66596			0.832981	+	0.553301i	$0.186632\pi$
$402$		0			0
$403$	−19.7821			−0.985416
$404$	−0.811379	−	1.40535i	−0.0403676	−	0.0699187i
$405$		0			0
$406$	0.412155	−	16.3835i	0.0204549	−	0.813102i
$407$	0.296790	+	0.514055i	0.0147113	+	0.0254808i
$408$		0			0
$409$	2.89037	+	5.00627i	0.142920	+	0.247544i	0.928595	−	0.371095i	$-0.121018\pi$
$409$	2.89037	+	5.00627i	0.142920	+	0.247544i	−0.785675	+	0.618639i	$0.787684\pi$
$410$	−0.0811263	−	0.140515i	−0.00400654	−	0.00693954i
$411$		0			0
$412$	−3.19076	−	5.52655i	−0.157197	−	0.272274i
$413$	−20.0957	+	10.9379i	−0.988846	+	0.538217i
$414$		0			0
$415$	2.28580	+	3.95912i	0.112205	+	0.194346i
$416$	2.51459			0.123288
$417$		0			0
$418$	−3.19436			−0.156241
$419$	−15.4356	+	26.7352i	−0.754078	+	1.30610i	0.191753	+	0.981443i	$0.438583\pi$
$419$	−15.4356	+	26.7352i	−0.754078	+	1.30610i	−0.945831	+	0.324659i	$0.894751\pi$
$420$		0			0
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	0.816939	−	0.576724i	$-0.195669\pi$
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	−0.907927	+	0.419128i	$0.862336\pi$
$422$	9.66225	+	16.7355i	0.470351	+	0.814672i
$423$		0			0
$424$	−4.02704	+	6.97504i	−0.195570	+	0.338738i
$425$	6.78794	−	11.7570i	0.329263	−	0.570301i
$426$		0			0
$427$	15.0057	+	9.17431i	0.726178	+	0.443976i
$428$	−9.35447	+	16.2024i	−0.452165	+	0.783174i
$429$		0			0
$430$	−6.62568			−0.319519
$431$	14.0979	−	24.4182i	0.679070	−	1.17618i	−0.296192	−	0.955128i	$-0.595717\pi$
$431$	14.0979	−	24.4182i	0.679070	−	1.17618i	0.975261	−	0.221055i	$-0.0709499\pi$
$432$		0			0
$433$	12.5438			0.602815			0.301407	−	0.953495i	$-0.402544\pi$
$433$	12.5438			0.602815			0.301407	+	0.953495i	$0.402544\pi$
$434$	0.523443	−	20.8073i	0.0251261	−	0.998785i
$435$		0			0
$436$	2.86693			0.137301
$437$	−12.0021	−	20.7883i	−0.574140	−	0.994440i
$438$		0			0
$439$	−13.0203	+	22.5519i	−0.621426	+	1.07634i	0.367794	+	0.929907i	$0.380113\pi$
$439$	−13.0203	+	22.5519i	−0.621426	+	1.07634i	−0.989220	+	0.146434i	$0.953220\pi$
$440$	−0.352336			−0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	−11.7865	+	20.4148i	−0.559992	+	0.969935i	0.437504	+	0.899216i	$0.355863\pi$
$443$	−11.7865	+	20.4148i	−0.559992	+	0.969935i	−0.997496	+	0.0707186i	$0.977471\pi$
$444$		0			0
$445$	−3.69076	−	6.39258i	−0.174959	−	0.303037i
$446$	−25.3245			−1.19915
$447$		0			0
$448$	−0.0665372	+	2.64491i	−0.00314359	+	0.124960i
$449$	−13.6870			−0.645928			−0.322964	−	0.946411i	$-0.604679\pi$
$449$	−13.6870			−0.645928			−0.322964	+	0.946411i	$0.604679\pi$
$450$		0			0
$451$	0.0811263	−	0.140515i	0.00382009	−	0.00661659i
$452$	−12.3202			−0.579495
$453$		0			0
$454$	2.40856	−	4.17174i	0.113039	−	0.195790i
$455$	3.36926	+	2.05992i	0.157953	+	0.0965705i
$456$		0			0
$457$	11.1762	−	19.3577i	0.522799	−	0.905515i	−0.476849	−	0.878985i	$-0.658221\pi$
$457$	11.1762	−	19.3577i	0.522799	−	0.905515i	0.999648	−	0.0265293i	$-0.00844554\pi$
$458$	4.64766	−	8.04999i	0.217171	−	0.376151i
$459$		0			0
$460$	−1.32383	−	2.29294i	−0.0617240	−	0.106909i
$461$	3.98755	+	6.90663i	0.185719	+	0.321674i	0.943818	−	0.330464i	$-0.107205\pi$
$461$	3.98755	+	6.90663i	0.185719	+	0.321674i	−0.758100	+	0.652138i	$0.773872\pi$
$462$		0			0
$463$	−14.3676	+	24.8854i	−0.667719	+	1.15652i	0.310821	+	0.950468i	$0.399396\pi$
$463$	−14.3676	+	24.8854i	−0.667719	+	1.15652i	−0.978540	+	0.206055i	$0.933937\pi$
$464$	−6.19436			−0.287566
$465$		0			0
$466$	0.194356			0.00900336
$467$	−16.7829	−	29.0688i	−0.776619	−	1.34514i	−0.933880	−	0.357586i	$-0.883600\pi$
$467$	−16.7829	−	29.0688i	−0.776619	−	1.34514i	0.157261	−	0.987557i	$-0.449733\pi$
$468$		0			0
$469$	−4.44738	+	2.42066i	−0.205361	+	0.111775i
$470$	−3.60963	−	6.25206i	−0.166500	−	0.288386i
$471$		0			0
$472$	4.32383	+	7.48910i	0.199020	+	0.344714i
$473$	−3.31284	−	5.73801i	−0.152325	−	0.263834i
$474$		0			0
$475$	−12.5057	−	21.6606i	−0.573802	−	0.993855i
$476$	−0.194356	+	7.72582i	−0.00890829	+	0.354112i
$477$		0			0
$478$	6.82743	+	11.8255i	0.312279	+	0.540884i
$479$	−0.367120			−0.0167741			−0.00838707	−	0.999965i	$-0.502670\pi$
$479$	−0.367120			−0.0167741			−0.00838707	+	0.999965i	$0.502670\pi$
$480$		0			0
$481$	−2.51459			−0.114655
$482$	6.50000	−	11.2583i	0.296067	−	0.512803i
$483$		0			0
$484$	5.32383	+	9.22115i	0.241992	+	0.419143i
$485$	−3.48249	−	6.03184i	−0.158132	−	0.273892i
$486$		0			0
$487$	−14.9538	+	25.9007i	−0.677621	+	1.17367i	0.298075	+	0.954543i	$0.403656\pi$
$487$	−14.9538	+	25.9007i	−0.677621	+	1.17367i	−0.975695	+	0.219131i	$0.929678\pi$
$488$	3.32383	−	5.75705i	0.150463	−	0.260609i
$489$		0			0
$490$	−2.25583	+	3.48937i	−0.101908	+	0.157634i
$491$	0.255158	−	0.441947i	0.0115151	−	0.0199448i	−0.860210	−	0.509939i	$-0.829668\pi$
$491$	0.255158	−	0.441947i	0.0115151	−	0.0199448i	0.871726	+	0.489994i	$0.163001\pi$
$492$		0			0
$493$	−18.0938			−0.814903
$494$	6.76615	−	11.7193i	0.304423	−	0.527277i
$495$		0			0
$496$	−7.86693			−0.353235
$497$	−0.958848	+	38.1151i	−0.0430102	+	1.70969i
$498$		0			0
$499$	−19.0191			−0.851410			−0.425705	−	0.904862i	$-0.639974\pi$
$499$	−19.0191			−0.851410			−0.425705	+	0.904862i	$0.639974\pi$
$500$	−2.86333	−	4.95943i	−0.128052	−	0.221792i
$501$		0			0
$502$	−9.77188	+	16.9254i	−0.436141	+	0.755418i
$503$	37.7807			1.68456			0.842280	−	0.539040i	$-0.181213\pi$
$503$	37.7807			1.68456			0.842280	+	0.539040i	$0.181213\pi$
$504$		0			0
$505$	−0.963235			−0.0428634
$506$	1.32383	−	2.29294i	0.0588515	−	0.101934i
$507$		0			0
$508$	−6.16731	−	10.6821i	−0.273630	−	0.473942i
$509$	11.2163			0.497155			0.248578	−	0.968612i	$-0.420037\pi$
$509$	11.2163			0.497155			0.248578	+	0.968612i	$0.420037\pi$
$510$		0			0
$511$	17.8638	+	10.9217i	0.790248	+	0.483147i
$512$	1.00000			0.0441942
$513$		0			0
$514$	4.16372	−	7.21177i	0.183654	−	0.318097i
$515$	−3.78794			−0.166916
$516$		0			0
$517$	3.60963	−	6.25206i	0.158751	−	0.274965i
$518$	0.0665372	−	2.64491i	0.00292348	−	0.116211i
$519$		0			0
$520$	0.746304	−	1.29264i	0.0327276	−	0.0566859i
$521$	13.7360	−	23.7914i	0.601785	−	1.04232i	−0.390766	−	0.920490i	$-0.627790\pi$
$521$	13.7360	−	23.7914i	0.601785	−	1.04232i	0.992551	−	0.121831i	$-0.0388767\pi$
$522$		0			0
$523$	11.0919	+	19.2118i	0.485016	+	0.840072i	0.999852	−	0.0172166i	$-0.00548048\pi$
$523$	11.0919	+	19.2118i	0.485016	+	0.840072i	−0.514836	+	0.857289i	$0.672147\pi$
$524$	−0.593579	−	1.02811i	−0.0259306	−	0.0449132i
$525$		0			0
$526$	−8.54523	+	14.8008i	−0.372590	+	0.645344i
$527$	−22.9794			−1.00100
$528$		0			0
$529$	−3.10390			−0.134952
$530$	2.39037	+	4.14024i	0.103831	+	0.179841i
$531$		0			0
$532$	12.1477	+	7.42692i	0.526668	+	0.321998i
$533$	0.343677	+	0.595265i	0.0148863	+	0.0257838i
$534$		0			0
$535$	5.55262	+	9.61742i	0.240061	+	0.415797i
$536$	0.956906	+	1.65741i	0.0413321	+	0.0715892i
$537$		0			0
$538$	5.00720	+	8.67272i	0.215876	+	0.373908i
$539$	−4.14980	−	0.208922i	−0.178745	−	0.00899893i
$540$		0			0
$541$	14.9246	+	25.8502i	0.641659	+	1.11139i	0.985062	+	0.172198i	$0.0550869\pi$
$541$	14.9246	+	25.8502i	0.641659	+	1.11139i	−0.343403	+	0.939188i	$0.611580\pi$
$542$	−10.2091			−0.438520
$543$		0			0
$544$	2.92101			0.125237
$545$	0.850874	−	1.47376i	0.0364474	−	0.0631288i
$546$		0			0
$547$	8.84348	+	15.3174i	0.378120	+	0.654923i	0.990789	−	0.135417i	$-0.0432373\pi$
$547$	8.84348	+	15.3174i	0.378120	+	0.654923i	−0.612669	+	0.790340i	$0.709904\pi$
$548$	1.26089	+	2.18393i	0.0538627	+	0.0932929i
$549$		0			0
$550$	1.37938	−	2.38915i	0.0588169	−	0.101874i
$551$	−16.6675	+	28.8690i	−0.710060	+	1.22986i
$552$		0			0
$553$	20.8765	+	12.7636i	0.887757	+	0.542763i
$554$	−9.67111	+	16.7508i	−0.410886	+	0.711675i
$555$		0			0
$556$	−4.91381			−0.208392
$557$	−15.0651	+	26.0935i	−0.638328	+	1.10562i	0.347472	+	0.937690i	$0.387040\pi$
$557$	−15.0651	+	26.0935i	−0.638328	+	1.10562i	−0.985800	+	0.167926i	$0.946293\pi$
$558$		0			0
$559$	28.0685			1.18717
$560$	1.33988	+	0.819187i	0.0566204	+	0.0346170i
$561$		0			0
$562$	−12.8027			−0.540050
$563$	2.04883	+	3.54867i	0.0863478	+	0.149559i	0.905965	−	0.423353i	$-0.139147\pi$
$563$	2.04883	+	3.54867i	0.0863478	+	0.149559i	−0.819617	+	0.572912i	$0.805814\pi$
$564$		0			0
$565$	−3.65652	+	6.33327i	−0.153831	+	0.266443i
$566$	−16.3523			−0.687340
$567$		0			0
$568$	14.4107			0.604659
$569$	3.11849	−	5.40138i	0.130734	−	0.226437i	−0.793226	−	0.608927i	$-0.791600\pi$
$569$	3.11849	−	5.40138i	0.130734	−	0.226437i	0.923960	+	0.382490i	$0.124933\pi$
$570$		0			0
$571$	−17.8011	−	30.8323i	−0.744951	−	1.29029i	−0.950218	−	0.311587i	$-0.899139\pi$
$571$	−17.8011	−	30.8323i	−0.744951	−	1.29029i	0.205266	−	0.978706i	$-0.434194\pi$
$572$	1.49261			0.0624091
$573$		0			0
$574$	−0.635211	+	0.345738i	−0.0265132	+	0.0144308i
$575$	20.7309			0.864539
$576$		0			0
$577$	23.1388	−	40.0776i	0.963281	−	1.66845i	0.249118	−	0.968473i	$-0.419859\pi$
$577$	23.1388	−	40.0776i	0.963281	−	1.66845i	0.714164	−	0.699979i	$-0.246807\pi$
$578$	−8.46770			−0.352210
$579$		0			0
$580$	−1.83842	+	3.18424i	−0.0763363	+	0.132218i
$581$	17.8976	−	9.74143i	0.742516	−	0.404143i
$582$		0			0
$583$	−2.39037	+	4.14024i	−0.0989990	+	0.171471i
$584$	3.95691	−	6.85356i	0.163738	−	0.283602i
$585$		0			0
$586$	10.3889	+	17.9941i	0.429162	+	0.743330i
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	0.841727	−	0.539903i	$-0.181539\pi$
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	−0.888434	+	0.459005i	$0.848206\pi$
$588$		0			0
$589$	−21.1680	+	36.6640i	−0.872212	+	1.51072i
$590$	5.13307			0.211325
$591$		0			0
$592$	−1.00000			−0.0410997
$593$	−23.0979	−	40.0067i	−0.948515	−	1.64288i	−0.748555	−	0.663072i	$-0.769252\pi$
$593$	−23.0979	−	40.0067i	−0.948515	−	1.64288i	−0.199960	−	0.979804i	$-0.564081\pi$
$594$		0			0
$595$	3.91381	+	2.39285i	0.160451	+	0.0980974i
$596$	9.02558	+	15.6328i	0.369702	+	0.640343i
$597$		0			0
$598$	5.60817	+	9.71363i	0.229335	+	0.397220i
$599$	−8.39037	−	14.5325i	−0.342821	−	0.593784i	0.642134	−	0.766592i	$-0.278049\pi$
$599$	−8.39037	−	14.5325i	−0.342821	−	0.593784i	−0.984955	+	0.172808i	$0.944716\pi$
$600$		0			0
$601$	−5.69961	−	9.87202i	−0.232492	−	0.402688i	0.726049	−	0.687643i	$-0.241355\pi$
$601$	−5.69961	−	9.87202i	−0.232492	−	0.402688i	−0.958541	+	0.284955i	$0.908021\pi$
$602$	−0.742705	+	29.5232i	−0.0302704	+	1.20328i
$603$		0			0
$604$	−0.823832	−	1.42692i	−0.0335212	−	0.0580605i
$605$	6.32023			0.256954
$606$		0			0
$607$	−14.4284			−0.585631			−0.292815	−	0.956169i	$-0.594592\pi$
$607$	−14.4284			−0.585631			−0.292815	+	0.956169i	$0.594592\pi$
$608$	2.69076	−	4.66053i	0.109125	−	0.189009i
$609$		0			0
$610$	−1.97296	−	3.41726i	−0.0798827	−	0.138361i
$611$	15.2915	+	26.4857i	0.618629	+	1.07150i
$612$		0			0
$613$	12.2053	−	21.1403i	0.492969	−	0.853848i	−0.506998	−	0.861947i	$-0.669245\pi$
$613$	12.2053	−	21.1403i	0.492969	−	0.853848i	0.999967	+	0.00809942i	$0.00257815\pi$
$614$	11.3384	−	19.6387i	0.457581	−	0.792554i
$615$		0			0
$616$	−0.0394951	+	1.56997i	−0.00159130	+	0.0632558i
$617$	−24.4698	+	42.3830i	−0.985119	+	1.70628i	−0.343710	+	0.939076i	$0.611684\pi$
$617$	−24.4698	+	42.3830i	−0.985119	+	1.70628i	−0.641408	+	0.767200i	$0.721650\pi$
$618$		0			0
$619$	−44.6591			−1.79500			−0.897501	−	0.441012i	$-0.854620\pi$
$619$	−44.6591			−1.79500			−0.897501	+	0.441012i	$0.854620\pi$
$620$	−2.33482	+	4.04403i	−0.0937687	+	0.162412i
$621$		0			0
$622$	6.51459			0.261211
$623$	−28.8982	+	15.7290i	−1.15778	+	0.630168i
$624$		0			0
$625$	19.8391			0.793564
$626$	−0.133074	−	0.230492i	−0.00531873	−	0.00921230i
$627$		0			0
$628$	3.30039	−	5.71644i	0.131700	−	0.228111i
$629$	−2.92101			−0.116468
$630$		0			0
$631$	33.2852			1.32506			0.662532	−	0.749034i	$-0.269482\pi$
$631$	33.2852			1.32506			0.662532	+	0.749034i	$0.269482\pi$
$632$	4.62422	−	8.00938i	0.183942	−	0.318596i
$633$		0			0
$634$	7.86186	+	13.6171i	0.312235	+	0.540806i
$635$	−7.32158			−0.290548
$636$		0			0
$637$	9.55641	−	14.7821i	0.378639	−	0.585687i
$638$	−3.67684			−0.145568
$639$		0			0
$640$	0.296790	−	0.514055i	0.0117316	−	0.0203198i
$641$	−30.7879			−1.21605			−0.608025	−	0.793918i	$-0.708038\pi$
$641$	−30.7879			−1.21605			−0.608025	+	0.793918i	$0.708038\pi$
$642$		0			0
$643$	−13.7345	+	23.7889i	−0.541637	+	0.938142i	0.457174	+	0.889378i	$0.348862\pi$
$643$	−13.7345	+	23.7889i	−0.541637	+	0.938142i	−0.998810	+	0.0487649i	$0.984471\pi$
$644$	−10.3655	+	5.64180i	−0.408456	+	0.222318i
$645$		0			0
$646$	7.85973	−	13.6134i	0.309237	−	0.535614i
$647$	6.63521	−	11.4925i	0.260857	−	0.451818i	−0.705613	−	0.708598i	$-0.749328\pi$
$647$	6.63521	−	11.4925i	0.260857	−	0.451818i	0.966470	+	0.256780i	$0.0826615\pi$
$648$		0			0
$649$	2.56654	+	4.44537i	0.100745	+	0.174496i
$650$	5.84348	+	10.1212i	0.229200	+	0.396986i
$651$		0			0
$652$	−2.99115	+	5.18082i	−0.117142	+	0.202896i
$653$	17.1416			0.670803			0.335402	−	0.942075i	$-0.391128\pi$
$653$	17.1416			0.670803			0.335402	+	0.942075i	$0.391128\pi$
$654$		0			0
$655$	−0.704673			−0.0275338
$656$	0.136673	+	0.236725i	0.00533619	+	0.00924255i
$657$		0			0
$658$	−28.2630	+	15.3832i	−1.10181	+	0.599701i
$659$	−4.26089	−	7.38008i	−0.165981	−	0.287487i	0.771022	−	0.636808i	$-0.219746\pi$
$659$	−4.26089	−	7.38008i	−0.165981	−	0.287487i	−0.937003	+	0.349321i	$0.886412\pi$
$660$		0			0
$661$	−17.1680	−	29.7358i	−0.667757	−	1.15659i	−0.978530	−	0.206105i	$-0.933921\pi$
$661$	−17.1680	−	29.7358i	−0.667757	−	1.15659i	0.310773	−	0.950484i	$-0.399412\pi$
$662$	12.5811	+	21.7912i	0.488979	+	0.846937i
$663$		0			0
$664$	−3.85087	−	6.66991i	−0.149443	−	0.258843i
$665$	7.42315	−	4.04033i	0.287857	−	0.156677i
$666$		0			0
$667$	−13.8150	−	23.9282i	−0.534918	−	0.926505i
$668$	7.46050			0.288656
$669$		0			0
$670$	1.13600			0.0438875
$671$	1.97296	−	3.41726i	0.0761652	−	0.131922i
$672$		0			0
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	0.678546	−	0.734558i	$-0.262610\pi$
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	−0.975419	+	0.220359i	$0.929277\pi$
$674$	−9.36693	−	16.2240i	−0.360800	−	0.624925i
$675$		0			0
$676$	3.33842	−	5.78231i	0.128401	−	0.222397i
$677$	−3.69076	+	6.39258i	−0.141847	+	0.245687i	−0.928192	−	0.372101i	$-0.878638\pi$
$677$	−3.69076	+	6.39258i	−0.141847	+	0.245687i	0.786345	+	0.617788i	$0.211971\pi$
$678$		0			0
$679$	−27.2675	+	14.8414i	−1.04643	+	0.569560i
$680$	0.866926	−	1.50156i	0.0332451	−	0.0575822i
$681$		0			0
$682$	−4.66964			−0.178810
$683$	−4.79893	+	8.31198i	−0.183626	+	0.318049i	−0.943113	−	0.332474i	$-0.892117\pi$
$683$	−4.79893	+	8.31198i	−0.183626	+	0.318049i	0.759487	+	0.650523i	$0.225450\pi$
$684$		0			0
$685$	1.49688			0.0571929
$686$	15.2953	+	10.4428i	0.583978	+	0.398710i
$687$		0			0
$688$	11.1623			0.425557
$689$	−10.1264	−	17.5394i	−0.385783	−	0.668197i
$690$		0			0
$691$	7.07227	−	12.2495i	0.269042	−	0.465994i	−0.699573	−	0.714561i	$-0.746626\pi$
$691$	7.07227	−	12.2495i	0.269042	−	0.465994i	0.968615	+	0.248567i	$0.0799597\pi$
$692$	25.6591			0.975414
$693$		0			0
$694$	−22.5438			−0.855750
$695$	−1.45837	+	2.52597i	−0.0553191	+	0.0958155i
$696$		0			0
$697$	0.399223	+	0.691475i	0.0151217	+	0.0261915i
$698$	−3.79086			−0.143486
$699$		0			0
$700$	−10.8004	+	5.87852i	−0.408216	+	0.222187i
$701$	−37.3753			−1.41164			−0.705822	−	0.708389i	$-0.749422\pi$
$701$	−37.3753			−1.41164			−0.705822	+	0.708389i	$0.749422\pi$
$702$		0			0
$703$	−2.69076	+	4.66053i	−0.101484	+	0.175775i
$704$	0.593579			0.0223714
$705$		0			0
$706$	3.41741	−	5.91913i	0.128616	−	0.222769i
$707$	−0.107974	+	4.29205i	−0.00406077	+	0.161419i
$708$		0			0
$709$	5.24338	−	9.08180i	0.196919	−	0.341074i	−0.750609	−	0.660747i	$-0.770240\pi$
$709$	5.24338	−	9.08180i	0.196919	−	0.341074i	0.947528	+	0.319673i	$0.103573\pi$
$710$	4.27694	−	7.40789i	0.160511	−	0.278013i
$711$		0			0
$712$	6.21780	+	10.7695i	0.233022	+	0.403606i
$713$	−17.5452	−	30.3892i	−0.657074	−	1.13809i
$714$		0			0
$715$	0.442991	−	0.767282i	0.0165669	−	0.0286947i
$716$	15.0364			0.561936
$717$		0			0
$718$	−12.6447			−0.471897
$719$	−1.11995	−	1.93981i	−0.0417670	−	0.0723426i	0.844386	−	0.535735i	$-0.179965\pi$
$719$	−1.11995	−	1.93981i	−0.0417670	−	0.0723426i	−0.886153	+	0.463392i	$0.846632\pi$
$720$		0			0
$721$	−0.424608	+	16.8786i	−0.0158132	+	0.628590i
$722$	−4.98035	−	8.62622i	−0.185349	−	0.321035i
$723$		0			0
$724$	0.0430937	+	0.0746406i	0.00160157	+	0.00277399i
$725$	−14.3946	−	24.9322i	−0.534604	−	0.925961i
$726$		0			0
$727$	0.185023	+	0.320469i	0.00686211	+	0.0118855i	0.869436	−	0.494045i	$-0.164482\pi$
$727$	0.185023	+	0.320469i	0.00686211	+	0.0118855i	−0.862574	+	0.505931i	$0.831149\pi$
$728$	−5.67617	−	3.47033i	−0.210373	−	0.128619i
$729$		0			0
$730$	−2.34874	−	4.06813i	−0.0869307	−	0.150568i
$731$	32.6050			1.20594
$732$		0			0
$733$	14.0191			0.517806			0.258903	−	0.965903i	$-0.416639\pi$
$733$	14.0191			0.517806			0.258903	+	0.965903i	$0.416639\pi$
$734$	−3.27188	+	5.66707i	−0.120767	+	0.209175i
$735$		0			0
$736$	2.23025	+	3.86291i	0.0822082	+	0.142389i
$737$	0.568000	+	0.983804i	0.0209225	+	0.0362389i
$738$		0			0
$739$	13.3872	−	23.1874i	0.492458	−	0.852962i	−0.507504	−	0.861649i	$-0.669432\pi$
$739$	13.3872	−	23.1874i	0.492458	−	0.852962i	0.999962	+	0.00868705i	$0.00276521\pi$
$740$	−0.296790	+	0.514055i	−0.0109102	+	0.0188970i
$741$		0			0
$742$	18.7163	−	10.1871i	0.687098	−	0.373980i
$743$	5.04669	−	8.74113i	0.185145	−	0.320681i	−0.758480	−	0.651696i	$-0.774058\pi$
$743$	5.04669	−	8.74113i	0.185145	−	0.320681i	0.943625	+	0.331015i	$0.107391\pi$
$744$		0			0
$745$	10.7148			0.392560
$746$	−4.71420	+	8.16524i	−0.172599	+	0.298951i
$747$		0			0
$748$	1.73385			0.0633959
$749$	43.4764	−	23.6637i	1.58859	−	0.864653i
$750$		0			0
$751$	11.5146			0.420173			0.210087	−	0.977683i	$-0.432625\pi$
$751$	11.5146			0.420173			0.210087	+	0.977683i	$0.432625\pi$
$752$	6.08113	+	10.5328i	0.221756	+	0.384092i
$753$		0			0
$754$	7.78813	−	13.4894i	0.283627	−	0.491256i
$755$	−0.978019			−0.0355938
$756$		0			0
$757$	−15.2484			−0.554214			−0.277107	−	0.960839i	$-0.589376\pi$
$757$	−15.2484			−0.554214			−0.277107	+	0.960839i	$0.589376\pi$
$758$	3.63881	−	6.30260i	0.132168	−	0.228921i
$759$		0			0
$760$	−1.59718	−	2.76639i	−0.0579357	−	0.100348i
$761$	1.70175			0.0616883			0.0308442	−	0.999524i	$-0.490180\pi$
$761$	1.70175			0.0616883			0.0308442	+	0.999524i	$0.490180\pi$
$762$		0			0
$763$	−6.47150	−	3.95659i	−0.234284	−	0.143238i
$764$	−3.98229			−0.144074
$765$		0			0
$766$	−12.0416	+	20.8567i	−0.435082	+	0.753584i
$767$	−21.7453			−0.785178
$768$		0			0
$769$	24.1211	−	41.7790i	0.869829	−	1.50659i	0.00765823	−	0.999971i	$-0.497562\pi$
$769$	24.1211	−	41.7790i	0.869829	−	1.50659i	0.862171	−	0.506618i	$-0.169104\pi$
$770$	0.795327	+	0.486253i	0.0286616	+	0.0175233i
$771$		0			0
$772$	−3.39037	+	5.87229i	−0.122022	+	0.211348i
$773$	−3.10243	+	5.37357i	−0.111587	+	0.193274i	−0.916410	−	0.400240i	$-0.868927\pi$
$773$	−3.10243	+	5.37357i	−0.111587	+	0.193274i	0.804823	+	0.593514i	$0.202260\pi$
$774$		0			0
$775$	−18.2814	−	31.6643i	−0.656688	−	1.13742i
$776$	5.86693	+	10.1618i	0.210610	+	0.364788i
$777$		0			0
$778$	−8.14913	+	14.1147i	−0.292160	+	0.506037i
$779$	1.47102			0.0527046
$780$		0			0
$781$	8.55389			0.306082
$782$	6.51459	+	11.2836i	0.232961	+	0.403501i
$783$		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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(-0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(-0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(0.296790 - 0.514055i) q^{10} +0.593579 q^{11} +(-1.25729 + 2.17770i) q^{13} +(-2.25729 - 1.38008i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.46050 + 2.52967i) q^{17} +(2.69076 + 4.66053i) q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} -4.46050 q^{23} -4.64766 q^{25} +(-1.25729 - 2.17770i) q^{26} +(2.32383 - 1.26483i) q^{28} +(3.09718 + 5.36447i) q^{29} +(3.93346 + 6.81296i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.46050 - 2.52967i) q^{34} +(0.0394951 - 1.56997i) q^{35} +(0.500000 + 0.866025i) q^{37} -5.38151 q^{38} -0.593579 q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(-0.296790 - 0.514055i) q^{44} +(2.23025 - 3.86291i) q^{46} +(6.08113 - 10.5328i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(2.32383 - 4.02499i) q^{50} +2.51459 q^{52} +(-4.02704 + 6.97504i) q^{53} -0.352336 q^{55} +(-0.0665372 + 2.64491i) q^{56} -6.19436 q^{58} +(4.32383 + 7.48910i) q^{59} +(3.32383 - 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(0.746304 - 1.29264i) q^{65} +(0.956906 + 1.65741i) q^{67} +2.92101 q^{68} +(1.33988 + 0.819187i) q^{70} +14.4107 q^{71} +(3.95691 - 6.85356i) q^{73} -1.00000 q^{74} +(2.69076 - 4.66053i) q^{76} +(-0.0394951 + 1.56997i) q^{77} +(4.62422 - 8.00938i) q^{79} +(0.296790 - 0.514055i) q^{80} +(0.136673 + 0.236725i) q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +11.1623 q^{86} +0.593579 q^{88} +(6.21780 + 10.7695i) q^{89} +(-5.67617 - 3.47033i) q^{91} +(2.23025 + 3.86291i) q^{92} +(6.08113 + 10.5328i) q^{94} +(-1.59718 - 2.76639i) q^{95} +(5.86693 + 10.1618i) q^{97} +(3.80039 - 5.87852i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 2 * q^5 - 4 * q^7 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8} - q^{10} - 2 q^{11} + 8 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} - q^{20} + q^{22} - 14 q^{23} - 4 q^{25} + 8 q^{26} + 2 q^{28} + 5 q^{29} + 20 q^{31} - 3 q^{32} + 4 q^{34} + 13 q^{35} + 3 q^{37} + 6 q^{38} + 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 9 q^{47} - 12 q^{49} + 2 q^{50} - 16 q^{52} - 15 q^{53} - 26 q^{55} - 4 q^{56} - 10 q^{58} + 14 q^{59} + 8 q^{61} - 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} - 8 q^{68} + 10 q^{70} - 14 q^{71} + 19 q^{73} - 6 q^{74} - 3 q^{76} - 13 q^{77} + 5 q^{79} - q^{80} - 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} + 9 q^{89} - 46 q^{91} + 7 q^{92} + 9 q^{94} + 4 q^{95} + 28 q^{97} + 12 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 2 * q^5 - 4 * q^7 + 6 * q^8 - q^10 - 2 * q^11 + 8 * q^13 + 2 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 - q^20 + q^22 - 14 * q^23 - 4 * q^25 + 8 * q^26 + 2 * q^28 + 5 * q^29 + 20 * q^31 - 3 * q^32 + 4 * q^34 + 13 * q^35 + 3 * q^37 + 6 * q^38 + 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 + 9 * q^47 - 12 * q^49 + 2 * q^50 - 16 * q^52 - 15 * q^53 - 26 * q^55 - 4 * q^56 - 10 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 - 8 * q^68 + 10 * q^70 - 14 * q^71 + 19 * q^73 - 6 * q^74 - 3 * q^76 - 13 * q^77 + 5 * q^79 - q^80 - 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 + 9 * q^89 - 46 * q^91 + 7 * q^92 + 9 * q^94 + 4 * q^95 + 28 * q^97 + 12 * q^98

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