LMFDB - Embedded newform 1638.2.bj.f.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$1.72124 - 0.193255i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.f.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.52798 + 2.64654i) q^{10} +(2.98127 - 1.72124i) q^{11} +(3.25253 - 1.55596i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.41449 - 2.44997i) q^{17} +(1.49425 + 0.862708i) q^{19} +(-2.64654 - 1.52798i) q^{20} +(-1.72124 + 2.98127i) q^{22} +(-1.53130 - 2.65229i) q^{23} -4.33891 q^{25} +(-2.03880 + 2.97377i) q^{26} +(0.866025 - 0.500000i) q^{28} +(1.92531 + 3.33473i) q^{29} +0.978370i q^{31} +(0.866025 + 0.500000i) q^{32} +2.82898i q^{34} +(1.52798 - 2.64654i) q^{35} +(4.58394 - 2.64654i) q^{37} -1.72542 q^{38} +3.05596 q^{40} +(-8.62781 + 4.98127i) q^{41} +(-1.51082 + 2.61681i) q^{43} -3.44247i q^{44} +(2.65229 + 1.53130i) q^{46} +8.04447i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.75760 - 2.16945i) q^{50} +(0.278764 - 3.59476i) q^{52} +8.33405 q^{53} +(-5.26003 - 9.11064i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.33473 - 1.92531i) q^{58} +(-8.64080 - 4.98877i) q^{59} +(5.77260 - 9.99843i) q^{61} +(-0.489185 - 0.847293i) q^{62} -1.00000 q^{64} +(-4.75496 - 9.93962i) q^{65} +(4.11410 - 2.37527i) q^{67} +(-1.41449 - 2.44997i) q^{68} +3.05596i q^{70} +(3.17784 + 1.83473i) q^{71} -10.1119i q^{73} +(-2.64654 + 4.58394i) q^{74} +(1.49425 - 0.862708i) q^{76} +3.44247 q^{77} -4.49843 q^{79} +(-2.64654 + 1.52798i) q^{80} +(4.98127 - 8.62781i) q^{82} +7.15869i q^{83} +(-7.48701 - 4.32263i) q^{85} -3.02163i q^{86} +(1.72124 + 2.98127i) q^{88} +(6.84426 - 3.95154i) q^{89} +(3.59476 + 0.278764i) q^{91} -3.06260 q^{92} +(-4.02224 - 6.96672i) q^{94} +(2.63640 - 4.56638i) q^{95} +(-7.88016 - 4.54961i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.05596i		−	1.36667i	−0.730106	−	0.683334i	$-0.760529\pi$
$5$		−	3.05596i		−	1.36667i	0.730106	−	0.683334i	$-0.239471\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.52798	+	2.64654i	0.483190	+	0.836910i
$11$	2.98127	−	1.72124i	0.898886	−	0.518972i	0.0220475	−	0.999757i	$-0.492982\pi$
$11$	2.98127	−	1.72124i	0.898886	−	0.518972i	0.876839	+	0.480785i	$0.159648\pi$
$12$		0			0
$13$	3.25253	−	1.55596i	0.902091	−	0.431546i
$13$	3.25253	−	1.55596i	0.902091	−	0.431546i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.41449	−	2.44997i	0.343064	−	0.594205i	−0.641936	−	0.766758i	$-0.721868\pi$
$17$	1.41449	−	2.44997i	0.343064	−	0.594205i	0.985000	+	0.172554i	$0.0552018\pi$
$18$		0			0
$19$	1.49425	+	0.862708i	0.342805	+	0.197919i	0.661512	−	0.749935i	$-0.269915\pi$
$19$	1.49425	+	0.862708i	0.342805	+	0.197919i	−0.318707	+	0.947853i	$0.603248\pi$
$20$	−2.64654	−	1.52798i	−0.591785	−	0.341667i
$21$		0			0
$22$	−1.72124	+	2.98127i	−0.366969	+	0.635608i
$23$	−1.53130	−	2.65229i	−0.319298	−	0.553040i	0.661044	−	0.750347i	$-0.270114\pi$
$23$	−1.53130	−	2.65229i	−0.319298	−	0.553040i	−0.980342	+	0.197307i	$0.936780\pi$
$24$		0			0
$25$	−4.33891			−0.867781
$26$	−2.03880	+	2.97377i	−0.399841	+	0.583204i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	1.92531	+	3.33473i	0.357520	+	0.619243i	0.987546	−	0.157331i	$-0.0502890\pi$
$29$	1.92531	+	3.33473i	0.357520	+	0.619243i	−0.630026	+	0.776574i	$0.716956\pi$
$30$		0			0
$31$			0.978370i			0.175720i	0.996133	+	0.0878602i	$0.0280029\pi$
$31$			0.978370i			0.175720i	−0.996133	+	0.0878602i	$0.971997\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			2.82898i			0.485166i
$35$	1.52798	−	2.64654i	0.258276	−	0.447347i
$36$		0			0
$37$	4.58394	−	2.64654i	0.753596	−	0.435089i	−0.0733959	−	0.997303i	$-0.523384\pi$
$37$	4.58394	−	2.64654i	0.753596	−	0.435089i	0.826992	+	0.562214i	$0.190050\pi$
$38$	−1.72542			−0.279899
$39$		0			0
$40$	3.05596			0.483190
$41$	−8.62781	+	4.98127i	−1.34744	+	0.777943i	−0.987886	−	0.155182i	$-0.950404\pi$
$41$	−8.62781	+	4.98127i	−1.34744	+	0.777943i	−0.359551	+	0.933125i	$0.617070\pi$
$42$		0			0
$43$	−1.51082	+	2.61681i	−0.230397	+	0.399060i	−0.957925	−	0.287019i	$-0.907336\pi$
$43$	−1.51082	+	2.61681i	−0.230397	+	0.399060i	0.727528	+	0.686078i	$0.240669\pi$
$44$		−	3.44247i		−	0.518972i
$45$		0			0
$46$	2.65229	+	1.53130i	0.391058	+	0.225778i
$47$			8.04447i			1.17341i	0.809802	+	0.586703i	$0.199575\pi$
$47$			8.04447i			1.17341i	−0.809802	+	0.586703i	$0.800425\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.75760	−	2.16945i	0.531405	−	0.306807i
$51$		0			0
$52$	0.278764	−	3.59476i	0.0386576	−	0.498503i
$53$	8.33405			1.14477			0.572385	−	0.819985i	$-0.306018\pi$
$53$	8.33405			1.14477			0.572385	+	0.819985i	$0.306018\pi$
$54$		0			0
$55$	−5.26003	−	9.11064i	−0.709263	−	1.22848i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−3.33473	−	1.92531i	−0.437871	−	0.252805i
$59$	−8.64080	−	4.98877i	−1.12494	−	0.649482i	−0.182279	−	0.983247i	$-0.558348\pi$
$59$	−8.64080	−	4.98877i	−1.12494	−	0.649482i	−0.942656	+	0.333765i	$0.891681\pi$
$60$		0			0
$61$	5.77260	−	9.99843i	0.739106	−	1.28017i	−0.213793	−	0.976879i	$-0.568582\pi$
$61$	5.77260	−	9.99843i	0.739106	−	1.28017i	0.952899	−	0.303289i	$-0.0980849\pi$
$62$	−0.489185	−	0.847293i	−0.0621266	−	0.107606i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.75496	−	9.93962i	−0.589781	−	1.23286i
$66$		0			0
$67$	4.11410	−	2.37527i	0.502617	−	0.290186i	−0.227177	−	0.973854i	$-0.572950\pi$
$67$	4.11410	−	2.37527i	0.502617	−	0.290186i	0.729794	+	0.683668i	$0.239616\pi$
$68$	−1.41449	−	2.44997i	−0.171532	−	0.297102i
$69$		0			0
$70$			3.05596i			0.365257i
$71$	3.17784	+	1.83473i	0.377140	+	0.217742i	0.676573	−	0.736375i	$-0.263464\pi$
$71$	3.17784	+	1.83473i	0.377140	+	0.217742i	−0.299433	+	0.954117i	$0.596798\pi$
$72$		0			0
$73$		−	10.1119i		−	1.18351i	−0.806117	−	0.591756i	$-0.798435\pi$
$73$		−	10.1119i		−	1.18351i	0.806117	−	0.591756i	$-0.201565\pi$
$74$	−2.64654	+	4.58394i	−0.307654	+	0.532873i
$75$		0			0
$76$	1.49425	−	0.862708i	0.171403	−	0.0989594i
$77$	3.44247			0.392306
$78$		0			0
$79$	−4.49843			−0.506113			−0.253057	−	0.967451i	$-0.581436\pi$
$79$	−4.49843			−0.506113			−0.253057	+	0.967451i	$0.581436\pi$
$80$	−2.64654	+	1.52798i	−0.295892	+	0.170833i
$81$		0			0
$82$	4.98127	−	8.62781i	0.550089	−	0.952782i
$83$			7.15869i			0.785768i	0.919588	+	0.392884i	$0.128523\pi$
$83$			7.15869i			0.785768i	−0.919588	+	0.392884i	$0.871477\pi$
$84$		0			0
$85$	−7.48701	−	4.32263i	−0.812081	−	0.468855i
$86$		−	3.02163i		−	0.325831i
$87$		0			0
$88$	1.72124	+	2.98127i	0.183484	+	0.317804i
$89$	6.84426	−	3.95154i	0.725490	−	0.418862i	−0.0912800	−	0.995825i	$-0.529096\pi$
$89$	6.84426	−	3.95154i	0.725490	−	0.418862i	0.816770	+	0.576963i	$0.195762\pi$
$90$		0			0
$91$	3.59476	+	0.278764i	0.376833	+	0.0292224i
$92$	−3.06260			−0.319298
$93$		0			0
$94$	−4.02224	−	6.96672i	−0.414862	−	0.718562i
$95$	2.63640	−	4.56638i	0.270489	−	0.468501i
$96$		0			0
$97$	−7.88016	−	4.54961i	−0.800109	−	0.461943i	0.0434004	−	0.999058i	$-0.486181\pi$
$97$	−7.88016	−	4.54961i	−0.800109	−	0.461943i	−0.843509	+	0.537115i	$0.819514\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	−2.16945	+	3.75760i	−0.216945	+	0.375760i
$101$	−9.42664	−	16.3274i	−0.937985	−	1.62464i	−0.769222	−	0.638982i	$-0.779356\pi$
$101$	−9.42664	−	16.3274i	−0.937985	−	1.62464i	−0.168764	−	0.985657i	$-0.553977\pi$
$102$		0			0
$103$	−13.7079			−1.35068			−0.675338	−	0.737509i	$-0.736002\pi$
$103$	−13.7079			−1.35068			−0.675338	+	0.737509i	$0.736002\pi$
$104$	1.55596	+	3.25253i	0.152575	+	0.318937i
$105$		0			0
$106$	−7.21750	+	4.16702i	−0.701025	+	0.404737i
$107$	−1.65736	−	2.87063i	−0.160223	−	0.277514i	0.774726	−	0.632297i	$-0.217888\pi$
$107$	−1.65736	−	2.87063i	−0.160223	−	0.277514i	−0.934948	+	0.354784i	$0.884555\pi$
$108$		0			0
$109$		−	8.67525i		−	0.830938i	−0.909607	−	0.415469i	$-0.863617\pi$
$109$		−	8.67525i		−	0.830938i	0.909607	−	0.415469i	$-0.136383\pi$
$110$	9.11064	+	5.26003i	0.868666	+	0.501524i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	−5.60557	+	9.70914i	−0.527328	+	0.913359i	0.472165	+	0.881510i	$0.343473\pi$
$113$	−5.60557	+	9.70914i	−0.527328	+	0.913359i	−0.999493	+	0.0318486i	$0.989861\pi$
$114$		0			0
$115$	−8.10529	+	4.67959i	−0.755822	+	0.436374i
$116$	3.85061			0.357520
$117$		0			0
$118$	9.97753			0.918506
$119$	2.44997	−	1.41449i	0.224588	−	0.129666i
$120$		0			0
$121$	0.425305	−	0.736650i	0.0386641	−	0.0669682i
$122$			11.5452i			1.04525i
$123$		0			0
$124$	0.847293	+	0.489185i	0.0760892	+	0.0439301i
$125$		−	2.02028i		−	0.180699i
$126$		0			0
$127$	2.55753	+	4.42977i	0.226944	+	0.393078i	0.956901	−	0.290415i	$-0.0937932\pi$
$127$	2.55753	+	4.42977i	0.226944	+	0.393078i	−0.729957	+	0.683493i	$0.760460\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	9.08773	+	6.23048i	0.797047	+	0.546450i
$131$	18.7757			1.64044			0.820219	−	0.572049i	$-0.193851\pi$
$131$	18.7757			1.64044			0.820219	+	0.572049i	$0.193851\pi$
$132$		0			0
$133$	0.862708	+	1.49425i	0.0748063	+	0.129568i
$134$	−2.37527	+	4.11410i	−0.205192	+	0.355404i
$135$		0			0
$136$	2.44997	+	1.41449i	0.210083	+	0.121292i
$137$	−2.30457	−	1.33055i	−0.196893	−	0.113676i	0.398312	−	0.917250i	$-0.369596\pi$
$137$	−2.30457	−	1.33055i	−0.196893	−	0.113676i	−0.595205	+	0.803574i	$0.702929\pi$
$138$		0			0
$139$	8.35322	−	14.4682i	0.708511	−	1.22718i	−0.256898	−	0.966439i	$-0.582700\pi$
$139$	8.35322	−	14.4682i	0.708511	−	1.22718i	0.965409	−	0.260739i	$-0.0839662\pi$
$140$	−1.52798	−	2.64654i	−0.129138	−	0.223674i
$141$		0			0
$142$	−3.66945			−0.307934
$143$	7.01850	−	10.2371i	0.586916	−	0.856071i
$144$		0			0
$145$	10.1908	−	5.88366i	0.846300	−	0.488611i
$146$	5.05596	+	8.75718i	0.418434	+	0.724750i
$147$		0			0
$148$		−	5.29308i		−	0.435089i
$149$	−2.16642	−	1.25078i	−0.177480	−	0.102468i	0.408628	−	0.912701i	$-0.366007\pi$
$149$	−2.16642	−	1.25078i	−0.177480	−	0.102468i	−0.586108	+	0.810233i	$0.699341\pi$
$150$		0			0
$151$			12.6465i			1.02916i	0.857444	+	0.514578i	$0.172051\pi$
$151$			12.6465i			1.02916i	−0.857444	+	0.514578i	$0.827949\pi$
$152$	−0.862708	+	1.49425i	−0.0699749	+	0.121200i
$153$		0			0
$154$	−2.98127	+	1.72124i	−0.240237	+	0.138701i
$155$	2.98986			0.240151
$156$		0			0
$157$	17.8131			1.42164			0.710822	−	0.703372i	$-0.248323\pi$
$157$	17.8131			1.42164			0.710822	+	0.703372i	$0.248323\pi$
$158$	3.89576	−	2.24922i	0.309930	−	0.178938i
$159$		0			0
$160$	1.52798	−	2.64654i	0.120798	−	0.209227i
$161$		−	3.06260i		−	0.241366i
$162$		0			0
$163$	−7.68884	−	4.43915i	−0.602236	−	0.347701i	0.167684	−	0.985841i	$-0.446371\pi$
$163$	−7.68884	−	4.43915i	−0.602236	−	0.347701i	−0.769921	+	0.638139i	$0.779704\pi$
$164$			9.96254i			0.777943i
$165$		0			0
$166$	−3.57934	−	6.19961i	−0.277811	−	0.481183i
$167$	8.46097	−	4.88494i	0.654730	−	0.378008i	−0.135536	−	0.990772i	$-0.543276\pi$
$167$	8.46097	−	4.88494i	0.654730	−	0.378008i	0.790266	+	0.612764i	$0.209942\pi$
$168$		0			0
$169$	8.15796	−	10.1216i	0.627535	−	0.778588i
$170$	8.64526			0.663061
$171$		0			0
$172$	1.51082	+	2.61681i	0.115199	+	0.199530i
$173$	−4.33762	+	7.51299i	−0.329783	+	0.571202i	−0.982469	−	0.186427i	$-0.940309\pi$
$173$	−4.33762	+	7.51299i	−0.329783	+	0.571202i	0.652685	+	0.757629i	$0.273642\pi$
$174$		0			0
$175$	−3.75760	−	2.16945i	−0.284048	−	0.163995i
$176$	−2.98127	−	1.72124i	−0.224722	−	0.129743i
$177$		0			0
$178$	−3.95154	+	6.84426i	−0.296180	+	0.512999i
$179$	11.7139	+	20.2891i	0.875540	+	1.51648i	0.856187	+	0.516667i	$0.172827\pi$
$179$	11.7139	+	20.2891i	0.875540	+	1.51648i	0.0193531	+	0.999813i	$0.493839\pi$
$180$		0			0
$181$	7.66632			0.569833			0.284917	−	0.958552i	$-0.408034\pi$
$181$	7.66632			0.569833			0.284917	+	0.958552i	$0.408034\pi$
$182$	−3.25253	+	1.55596i	−0.241094	+	0.115336i
$183$		0			0
$184$	2.65229	−	1.53130i	0.195529	−	0.112889i
$185$	−8.08773	−	14.0084i	−0.594622	−	1.02992i
$186$		0			0
$187$		−	9.73869i		−	0.712163i
$188$	6.96672	+	4.02224i	0.508100	+	0.293352i
$189$		0			0
$190$			5.27281i			0.382530i
$191$	12.7472	−	22.0789i	0.922357	−	1.59757i	0.126600	−	0.991954i	$-0.459593\pi$
$191$	12.7472	−	22.0789i	0.922357	−	1.59757i	0.795757	−	0.605616i	$-0.207073\pi$
$192$		0			0
$193$	−7.38361	+	4.26293i	−0.531484	+	0.306852i	−0.741621	−	0.670820i	$-0.765942\pi$
$193$	−7.38361	+	4.26293i	−0.531484	+	0.306852i	0.210137	+	0.977672i	$0.432609\pi$
$194$	9.09922			0.653286
$195$		0			0
$196$	1.00000			0.0714286
$197$	−20.5094	+	11.8411i	−1.46124	+	0.843645i	−0.999069	−	0.0431470i	$-0.986262\pi$
$197$	−20.5094	+	11.8411i	−1.46124	+	0.843645i	−0.462168	+	0.886792i	$0.652928\pi$
$198$		0			0
$199$	−12.4233	+	21.5178i	−0.880666	+	1.52536i	−0.0300637	+	0.999548i	$0.509571\pi$
$199$	−12.4233	+	21.5178i	−0.880666	+	1.52536i	−0.850602	+	0.525810i	$0.823762\pi$
$200$		−	4.33891i		−	0.306807i
$201$		0			0
$202$	16.3274	+	9.42664i	1.14879	+	0.663256i
$203$			3.85061i			0.270260i
$204$		0			0
$205$	15.2226	+	26.3663i	1.06319	+	1.84150i
$206$	11.8714	−	6.85393i	0.827116	−	0.477536i
$207$		0			0
$208$	−2.97377	−	2.03880i	−0.206194	−	0.141365i
$209$	5.93970			0.410857
$210$		0			0
$211$	−0.386509	−	0.669453i	−0.0266084	−	0.0460871i	0.852415	−	0.522867i	$-0.175137\pi$
$211$	−0.386509	−	0.669453i	−0.0266084	−	0.0460871i	−0.879023	+	0.476779i	$0.841804\pi$
$212$	4.16702	−	7.21750i	0.286192	−	0.495700i
$213$		0			0
$214$	2.87063	+	1.65736i	0.196232	+	0.113295i
$215$	7.99687	+	4.61699i	0.545382	+	0.314876i
$216$		0			0
$217$	−0.489185	+	0.847293i	−0.0332080	+	0.0575180i
$218$	4.33762	+	7.51299i	0.293781	+	0.508844i
$219$		0			0
$220$	−10.5201			−0.709263
$221$	0.788619	−	10.1695i	0.0530482	−	0.684075i
$222$		0			0
$223$	−18.6502	+	10.7677i	−1.24891	+	0.721060i	−0.970892	−	0.239516i	$-0.923011\pi$
$223$	−18.6502	+	10.7677i	−1.24891	+	0.721060i	−0.278019	+	0.960575i	$0.589678\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$		−	11.2111i		−	0.745754i
$227$	−15.1939	−	8.77218i	−1.00845	−	0.582230i	−0.0977139	−	0.995215i	$-0.531153\pi$
$227$	−15.1939	−	8.77218i	−1.00845	−	0.582230i	−0.910738	+	0.412985i	$0.864486\pi$
$228$		0			0
$229$		−	10.3222i		−	0.682109i	−0.940043	−	0.341055i	$-0.889216\pi$
$229$		−	10.3222i		−	0.682109i	0.940043	−	0.341055i	$-0.110784\pi$
$230$	4.67959	−	8.10529i	0.308563	−	0.534447i
$231$		0			0
$232$	−3.33473	+	1.92531i	−0.218936	+	0.126402i
$233$	17.8290			1.16802			0.584008	−	0.811748i	$-0.301484\pi$
$233$	17.8290			1.16802			0.584008	+	0.811748i	$0.301484\pi$
$234$		0			0
$235$	24.5836			1.60366
$236$	−8.64080	+	4.98877i	−0.562468	+	0.324741i
$237$		0			0
$238$	−1.41449	+	2.44997i	−0.0916878	+	0.158808i
$239$			5.71271i			0.369525i	0.982783	+	0.184762i	$0.0591515\pi$
$239$			5.71271i			0.369525i	−0.982783	+	0.184762i	$0.940848\pi$
$240$		0			0
$241$	0.868738	+	0.501566i	0.0559603	+	0.0323087i	0.527719	−	0.849419i	$-0.323047\pi$
$241$	0.868738	+	0.501566i	0.0559603	+	0.0323087i	−0.471759	+	0.881728i	$0.656381\pi$
$242$			0.850611i			0.0546793i
$243$		0			0
$244$	−5.77260	−	9.99843i	−0.369553	−	0.640084i
$245$	2.64654	−	1.52798i	0.169081	−	0.0976191i
$246$		0			0
$247$	6.20245	+	0.480984i	0.394653	+	0.0306043i
$248$	−0.978370			−0.0621266
$249$		0			0
$250$	1.01014	+	1.74961i	0.0638867	+	0.110655i
$251$	0.336293	−	0.582476i	0.0212266	−	0.0367656i	−0.855217	−	0.518270i	$-0.826576\pi$
$251$	0.336293	−	0.582476i	0.0212266	−	0.0367656i	0.876444	+	0.481505i	$0.159910\pi$
$252$		0			0
$253$	−9.13042	−	5.27145i	−0.574025	−	0.331413i
$254$	−4.42977	−	2.55753i	−0.277948	−	0.160474i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.1717	−	21.0820i	−0.759248	−	1.31506i	−0.943234	−	0.332128i	$-0.892234\pi$
$257$	−12.1717	−	21.0820i	−0.759248	−	1.31506i	0.183986	−	0.982929i	$-0.441100\pi$
$258$		0			0
$259$	5.29308			0.328896
$260$	−10.9854	−	0.851893i	−0.681289	−	0.0528322i
$261$		0			0
$262$	−16.2602	+	9.38784i	−1.00456	+	0.579983i
$263$	−8.54648	−	14.8029i	−0.526999	−	0.912788i	−0.999505	−	0.0314610i	$-0.989984\pi$
$263$	−8.54648	−	14.8029i	−0.526999	−	0.912788i	0.472506	−	0.881327i	$-0.343349\pi$
$264$		0			0
$265$		−	25.4685i		−	1.56452i
$266$	−1.49425	−	0.862708i	−0.0916186	−	0.0528960i
$267$		0			0
$268$		−	4.75055i		−	0.290186i
$269$	−13.3297	+	23.0877i	−0.812727	+	1.40768i	0.0982223	+	0.995165i	$0.468684\pi$
$269$	−13.3297	+	23.0877i	−0.812727	+	1.40768i	−0.910949	+	0.412519i	$0.864649\pi$
$270$		0			0
$271$	21.1739	−	12.2247i	1.28622	−	0.742600i	0.308243	−	0.951308i	$-0.400259\pi$
$271$	21.1739	−	12.2247i	1.28622	−	0.742600i	0.977978	+	0.208708i	$0.0669257\pi$
$272$	−2.82898			−0.171532
$273$		0			0
$274$	2.66109			0.160763
$275$	−12.9354	+	7.46828i	−0.780037	+	0.450354i
$276$		0			0
$277$	−14.2406	+	24.6655i	−0.855636	+	1.48201i	0.0204175	+	0.999792i	$0.493500\pi$
$277$	−14.2406	+	24.6655i	−0.855636	+	1.48201i	−0.876054	+	0.482214i	$0.839833\pi$
$278$			16.7064i			1.00199i
$279$		0			0
$280$	2.64654	+	1.52798i	0.158161	+	0.0913143i
$281$			9.76032i			0.582252i	0.956685	+	0.291126i	$0.0940298\pi$
$281$			9.76032i			0.582252i	−0.956685	+	0.291126i	$0.905970\pi$
$282$		0			0
$283$	5.83562	+	10.1076i	0.346891	+	0.600833i	0.985696	−	0.168536i	$-0.0539039\pi$
$283$	5.83562	+	10.1076i	0.346891	+	0.600833i	−0.638804	+	0.769369i	$0.720571\pi$
$284$	3.17784	−	1.83473i	0.188570	−	0.108871i
$285$		0			0
$286$	−0.959638	+	12.3749i	−0.0567446	+	0.731741i
$287$	−9.96254			−0.588070
$288$		0			0
$289$	4.49843	+	7.79152i	0.264614	+	0.458324i
$290$	−5.88366	+	10.1908i	−0.345500	+	0.598424i
$291$		0			0
$292$	−8.75718	−	5.05596i	−0.512475	−	0.295878i
$293$	−18.8968	−	10.9101i	−1.10396	−	0.637373i	−0.166704	−	0.986007i	$-0.553312\pi$
$293$	−18.8968	−	10.9101i	−1.10396	−	0.637373i	−0.937259	+	0.348634i	$0.886646\pi$
$294$		0			0
$295$	−15.2455	+	26.4059i	−0.887626	+	1.53741i
$296$	2.64654	+	4.58394i	0.153827	+	0.266436i
$297$		0			0
$298$	2.50157			0.144912
$299$	−9.10746	−	6.24401i	−0.526698	−	0.361101i
$300$		0			0
$301$	−2.61681	+	1.51082i	−0.150830	+	0.0870819i
$302$	−6.32323	−	10.9522i	−0.363861	−	0.630226i
$303$		0			0
$304$		−	1.72542i		−	0.0989594i
$305$	−30.5548	−	17.6408i	−1.74957	−	1.01011i
$306$		0			0
$307$			4.87046i			0.277972i	0.990294	+	0.138986i	$0.0443843\pi$
$307$			4.87046i			0.277972i	−0.990294	+	0.138986i	$0.955616\pi$
$308$	1.72124	−	2.98127i	0.0980765	−	0.169874i
$309$		0			0
$310$	−2.58930	+	1.49493i	−0.147062	+	0.0849064i
$311$	3.90344			0.221344			0.110672	−	0.993857i	$-0.464700\pi$
$311$	3.90344			0.221344			0.110672	+	0.993857i	$0.464700\pi$
$312$		0			0
$313$	26.0528			1.47259			0.736297	−	0.676659i	$-0.236573\pi$
$313$	26.0528			1.47259			0.736297	+	0.676659i	$0.236573\pi$
$314$	−15.4266	+	8.90657i	−0.870576	+	0.502627i
$315$		0			0
$316$	−2.24922	+	3.89576i	−0.126528	+	0.219154i
$317$			11.1107i			0.624040i	0.950076	+	0.312020i	$0.101006\pi$
$317$			11.1107i			0.624040i	−0.950076	+	0.312020i	$0.898994\pi$
$318$		0			0
$319$	11.4797	+	6.62781i	0.642740	+	0.371086i
$320$			3.05596i			0.170833i
$321$		0			0
$322$	1.53130	+	2.65229i	0.0853359	+	0.147806i
$323$	4.22722	−	2.44058i	0.235209	−	0.135798i
$324$		0			0
$325$	−14.1124	+	6.75118i	−0.782818	+	0.374488i
$326$	8.87831			0.491724
$327$		0			0
$328$	−4.98127	−	8.62781i	−0.275045	−	0.476391i
$329$	−4.02224	+	6.96672i	−0.221753	+	0.384087i
$330$		0			0
$331$	12.6854	+	7.32391i	0.697252	+	0.402559i	0.806323	−	0.591475i	$-0.201454\pi$
$331$	12.6854	+	7.32391i	0.697252	+	0.402559i	−0.109071	+	0.994034i	$0.534788\pi$
$332$	6.19961	+	3.57934i	0.340248	+	0.196442i
$333$		0			0
$334$	−4.88494	+	8.46097i	−0.267292	+	0.462964i
$335$	−7.25875	−	12.5725i	−0.396588	−	0.686910i
$336$		0			0
$337$	−27.5456			−1.50050			−0.750251	−	0.661153i	$-0.770068\pi$
$337$	−27.5456			−1.50050			−0.750251	+	0.661153i	$0.770068\pi$
$338$	−2.00418	+	12.8446i	−0.109013	+	0.698653i
$339$		0			0
$340$	−7.48701	+	4.32263i	−0.406040	+	0.234427i
$341$	1.68401	+	2.91678i	0.0911940	+	0.157953i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−2.61681	−	1.51082i	−0.141089	−	0.0814577i
$345$		0			0
$346$		−	8.67525i		−	0.466384i
$347$	2.62073	−	4.53924i	0.140688	−	0.243679i	−0.787068	−	0.616867i	$-0.788402\pi$
$347$	2.62073	−	4.53924i	0.140688	−	0.243679i	0.927756	+	0.373187i	$0.121735\pi$
$348$		0			0
$349$	−4.52901	+	2.61482i	−0.242432	+	0.139968i	−0.616294	−	0.787516i	$-0.711367\pi$
$349$	−4.52901	+	2.61482i	−0.242432	+	0.139968i	0.373862	+	0.927484i	$0.378033\pi$
$350$	4.33891			0.231924
$351$		0			0
$352$	3.44247			0.183484
$353$	−3.26227	+	1.88348i	−0.173633	+	0.100247i	−0.584298	−	0.811539i	$-0.698630\pi$
$353$	−3.26227	+	1.88348i	−0.173633	+	0.100247i	0.410665	+	0.911786i	$0.365297\pi$
$354$		0			0
$355$	5.60686	−	9.71136i	0.297581	−	0.515425i
$356$		−	7.90307i		−	0.418862i
$357$		0			0
$358$	−20.2891	−	11.7139i	−1.07231	−	0.619100i
$359$			20.6003i			1.08724i	0.839330	+	0.543622i	$0.182947\pi$
$359$			20.6003i			1.08724i	−0.839330	+	0.543622i	$0.817053\pi$
$360$		0			0
$361$	−8.01147	−	13.8763i	−0.421656	−	0.730330i
$362$	−6.63923	+	3.83316i	−0.348950	+	0.201466i
$363$		0			0
$364$	2.03880	−	2.97377i	0.106862	−	0.155868i
$365$	−30.9017			−1.61747
$366$		0			0
$367$	13.9579	+	24.1759i	0.728598	+	1.26197i	0.957476	+	0.288514i	$0.0931612\pi$
$367$	13.9579	+	24.1759i	0.728598	+	1.26197i	−0.228877	+	0.973455i	$0.573505\pi$
$368$	−1.53130	+	2.65229i	−0.0798245	+	0.138260i
$369$		0			0
$370$	14.0084	+	8.08773i	0.728260	+	0.420461i
$371$	7.21750	+	4.16702i	0.374714	+	0.216341i
$372$		0			0
$373$	−15.7091	+	27.2090i	−0.813388	+	1.40883i	0.0970910	+	0.995276i	$0.469046\pi$
$373$	−15.7091	+	27.2090i	−0.813388	+	1.40883i	−0.910479	+	0.413554i	$0.864287\pi$
$374$	4.86934	+	8.43395i	0.251788	+	0.436109i
$375$		0			0
$376$	−8.04447			−0.414862
$377$	11.4508	+	7.85061i	0.589748	+	0.404327i
$378$		0			0
$379$	−27.5747	+	15.9203i	−1.41642	+	0.817770i	−0.995982	−	0.0895514i	$-0.971457\pi$
$379$	−27.5747	+	15.9203i	−1.41642	+	0.817770i	−0.420437	+	0.907322i	$0.638123\pi$
$380$	−2.63640	−	4.56638i	−0.135245	−	0.234251i
$381$		0			0
$382$			25.4945i			1.30441i
$383$	4.08962	+	2.36114i	0.208970	+	0.120649i	0.600832	−	0.799375i	$-0.294836\pi$
$383$	4.08962	+	2.36114i	0.208970	+	0.120649i	−0.391863	+	0.920024i	$0.628169\pi$
$384$		0			0
$385$		−	10.5201i		−	0.536152i
$386$	4.26293	−	7.38361i	0.216977	−	0.375816i
$387$		0			0
$388$	−7.88016	+	4.54961i	−0.400054	+	0.230972i
$389$	30.5902			1.55099			0.775493	−	0.631356i	$-0.217501\pi$
$389$	30.5902			1.55099			0.775493	+	0.631356i	$0.217501\pi$
$390$		0			0
$391$	−8.66403			−0.438159
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	11.8411	−	20.5094i	0.596547	−	1.03325i
$395$			13.7470i			0.691689i
$396$		0			0
$397$	10.1133	+	5.83891i	0.507571	+	0.293046i	0.731835	−	0.681482i	$-0.238664\pi$
$397$	10.1133	+	5.83891i	0.507571	+	0.293046i	−0.224264	+	0.974529i	$0.571998\pi$
$398$		−	24.8466i		−	1.24545i
$399$		0			0
$400$	2.16945	+	3.75760i	0.108473	+	0.187880i
$401$	−8.01677	+	4.62849i	−0.400339	+	0.231136i	−0.686630	−	0.727007i	$-0.740911\pi$
$401$	−8.01677	+	4.62849i	−0.400339	+	0.231136i	0.286292	+	0.958143i	$0.407577\pi$
$402$		0			0
$403$	1.52231	+	3.18218i	0.0758315	+	0.158516i
$404$	−18.8533			−0.937985
$405$		0			0
$406$	−1.92531	−	3.33473i	−0.0955513	−	0.165500i
$407$	9.11064	−	15.7801i	0.451598	−	0.782190i
$408$		0			0
$409$	−22.1693	−	12.7994i	−1.09620	−	0.632891i	−0.160980	−	0.986958i	$-0.551465\pi$
$409$	−22.1693	−	12.7994i	−1.09620	−	0.632891i	−0.935220	+	0.354066i	$0.884799\pi$
$410$	−26.3663	−	15.2226i	−1.30214	−	0.751789i
$411$		0			0
$412$	−6.85393	+	11.8714i	−0.337669	+	0.584860i
$413$	−4.98877	−	8.64080i	−0.245481	−	0.425186i
$414$		0			0
$415$	21.8767			1.07388
$416$	3.59476	+	0.278764i	0.176248	+	0.0136675i
$417$		0			0
$418$	−5.14393	+	2.96985i	−0.251598	+	0.145260i
$419$	14.1018	+	24.4251i	0.688920	+	1.19324i	0.972188	+	0.234203i	$0.0752481\pi$
$419$	14.1018	+	24.4251i	0.688920	+	1.19324i	−0.283268	+	0.959041i	$0.591419\pi$
$420$		0			0
$421$		−	5.07012i		−	0.247102i	−0.992338	−	0.123551i	$-0.960572\pi$
$421$		−	5.07012i		−	0.247102i	0.992338	−	0.123551i	$-0.0394283\pi$
$422$	0.669453	+	0.386509i	0.0325885	+	0.0188150i
$423$		0			0
$424$			8.33405i			0.404737i
$425$	−6.13734	+	10.6302i	−0.297705	+	0.515640i
$426$		0			0
$427$	9.99843	−	5.77260i	0.483858	−	0.279356i
$428$	−3.31471			−0.160223
$429$		0			0
$430$	−9.23399			−0.445302
$431$	13.9808	−	8.07185i	0.673434	−	0.388807i	−0.123943	−	0.992289i	$-0.539554\pi$
$431$	13.9808	−	8.07185i	0.673434	−	0.388807i	0.797376	+	0.603482i	$0.206221\pi$
$432$		0			0
$433$	−11.3014	+	19.5747i	−0.543113	+	0.940699i	0.455610	+	0.890179i	$0.349421\pi$
$433$	−11.3014	+	19.5747i	−0.543113	+	0.940699i	−0.998723	+	0.0505195i	$0.983912\pi$
$434$		−	0.978370i		−	0.0469633i
$435$		0			0
$436$	−7.51299	−	4.33762i	−0.359807	−	0.207735i
$437$		−	5.28425i		−	0.252780i
$438$		0			0
$439$	14.1486	+	24.5060i	0.675273	+	1.16961i	0.976389	+	0.216020i	$0.0693077\pi$
$439$	14.1486	+	24.5060i	0.675273	+	1.16961i	−0.301115	+	0.953588i	$0.597359\pi$
$440$	9.11064	−	5.26003i	0.434333	−	0.250762i
$441$		0			0
$442$	4.40179	+	9.20136i	0.209372	+	0.437664i
$443$	1.38096			0.0656112			0.0328056	−	0.999462i	$-0.489556\pi$
$443$	1.38096			0.0656112			0.0328056	+	0.999462i	$0.489556\pi$
$444$		0			0
$445$	−12.0757	−	20.9158i	−0.572445	−	0.991504i
$446$	10.7677	−	18.6502i	0.509866	−	0.883114i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	32.0480	+	18.5029i	1.51244	+	0.873208i	0.999894	+	0.0145487i	$0.00463115\pi$
$449$	32.0480	+	18.5029i	1.51244	+	0.873208i	0.512547	+	0.858659i	$0.328702\pi$
$450$		0			0
$451$	−17.1479	+	29.7010i	−0.807462	+	1.39856i
$452$	5.60557	+	9.70914i	0.263664	+	0.456679i
$453$		0			0
$454$	17.5444			0.823398
$455$	0.851893	−	10.9854i	0.0399374	−	0.515006i
$456$		0			0
$457$	12.0530	−	6.95878i	0.563813	−	0.325518i	−0.190861	−	0.981617i	$-0.561128\pi$
$457$	12.0530	−	6.95878i	0.563813	−	0.325518i	0.754675	+	0.656099i	$0.227795\pi$
$458$	5.16109	+	8.93928i	0.241162	+	0.417705i
$459$		0			0
$460$			9.35918i			0.436374i
$461$	−4.19845	−	2.42397i	−0.195541	−	0.112896i	0.399033	−	0.916937i	$-0.369346\pi$
$461$	−4.19845	−	2.42397i	−0.195541	−	0.112896i	−0.594574	+	0.804041i	$0.702679\pi$
$462$		0			0
$463$		−	24.4377i		−	1.13571i	−0.823127	−	0.567857i	$-0.807773\pi$
$463$		−	24.4377i		−	1.13571i	0.823127	−	0.567857i	$-0.192227\pi$
$464$	1.92531	−	3.33473i	0.0893801	−	0.154811i
$465$		0			0
$466$	−15.4404	+	8.91449i	−0.715260	+	0.412956i
$467$	36.0027			1.66600			0.833002	−	0.553270i	$-0.186620\pi$
$467$	36.0027			1.66600			0.833002	+	0.553270i	$0.186620\pi$
$468$		0			0
$469$	4.75055			0.219360
$470$	−21.2900	+	12.2918i	−0.982035	+	0.566978i
$471$		0			0
$472$	4.98877	−	8.64080i	0.229627	−	0.397725i
$473$			10.4019i			0.478279i
$474$		0			0
$475$	−6.48343	−	3.74321i	−0.297480	−	0.171750i
$476$		−	2.82898i		−	0.129666i
$477$		0			0
$478$	−2.85636	−	4.94735i	−0.130647	−	0.226287i
$479$	8.22108	−	4.74644i	0.375631	−	0.216870i	−0.300285	−	0.953850i	$-0.597082\pi$
$479$	8.22108	−	4.74644i	0.375631	−	0.216870i	0.675915	+	0.736979i	$0.263748\pi$
$480$		0			0
$481$	10.7915	−	15.7404i	0.492051	−	0.717701i
$482$	−1.00313			−0.0456914
$483$		0			0
$484$	−0.425305	−	0.736650i	−0.0193321	−	0.0334841i
$485$	−13.9034	+	24.0815i	−0.631323	+	1.09348i
$486$		0			0
$487$	−35.4383	−	20.4603i	−1.60586	−	0.927144i	−0.990283	−	0.139069i	$-0.955589\pi$
$487$	−35.4383	−	20.4603i	−1.60586	−	0.927144i	−0.615578	−	0.788076i	$-0.711078\pi$
$488$	9.99843	+	5.77260i	0.452608	+	0.261313i
$489$		0			0
$490$	−1.52798	+	2.64654i	−0.0690272	+	0.119559i
$491$	2.55753	+	4.42977i	0.115420	+	0.199913i	0.917947	−	0.396702i	$-0.129845\pi$
$491$	2.55753	+	4.42977i	0.115420	+	0.199913i	−0.802528	+	0.596615i	$0.796512\pi$
$492$		0			0
$493$	10.8933			0.490610
$494$	−5.61197	+	2.68468i	−0.252495	+	0.120790i
$495$		0			0
$496$	0.847293	−	0.489185i	0.0380446	−	0.0219651i
$497$	1.83473	+	3.17784i	0.0822987	+	0.142546i
$498$		0			0
$499$		−	19.5827i		−	0.876640i	−0.898819	−	0.438320i	$-0.855574\pi$
$499$		−	19.5827i		−	0.876640i	0.898819	−	0.438320i	$-0.144426\pi$
$500$	−1.74961	−	1.01014i	−0.0782450	−	0.0451747i
$501$		0			0
$502$			0.672585i			0.0300189i
$503$	−14.5429	+	25.1890i	−0.648436	+	1.12312i	0.335060	+	0.942197i	$0.391243\pi$
$503$	−14.5429	+	25.1890i	−0.648436	+	1.12312i	−0.983496	+	0.180928i	$0.942090\pi$
$504$		0			0
$505$	−49.8960	+	28.8075i	−2.22034	+	1.28191i
$506$	10.5429			0.468689
$507$		0			0
$508$	5.11506			0.226944
$509$	4.52051	−	2.60992i	0.200368	−	0.115682i	−0.396459	−	0.918052i	$-0.629761\pi$
$509$	4.52051	−	2.60992i	0.200368	−	0.115682i	0.596827	+	0.802370i	$0.296428\pi$
$510$		0			0
$511$	5.05596	−	8.75718i	0.223663	−	0.387395i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.0820	+	12.1717i	0.929885	+	0.536870i
$515$			41.8907i			1.84592i
$516$		0			0
$517$	13.8464	+	23.9827i	0.608965	+	1.05476i
$518$	−4.58394	+	2.64654i	−0.201407	+	0.116282i
$519$		0			0
$520$	9.93962	−	4.75496i	0.435881	−	0.208519i
$521$	14.5259			0.636389			0.318195	−	0.948025i	$-0.396923\pi$
$521$	14.5259			0.636389			0.318195	+	0.948025i	$0.396923\pi$
$522$		0			0
$523$	−13.9367	−	24.1391i	−0.609410	−	1.05553i	−0.991338	−	0.131337i	$-0.958073\pi$
$523$	−13.9367	−	24.1391i	−0.609410	−	1.05553i	0.381927	−	0.924192i	$-0.375260\pi$
$524$	9.38784	−	16.2602i	0.410110	−	0.710331i
$525$		0			0
$526$	14.8029	+	8.54648i	0.645439	+	0.372644i
$527$	2.39698	+	1.38389i	0.104414	+	0.0602834i
$528$		0			0
$529$	6.81025	−	11.7957i	0.296098	−	0.512856i
$530$	12.7343	+	22.0564i	0.553141	+	0.958069i
$531$		0			0
$532$	1.72542			0.0748063
$533$	−20.3116	+	29.6263i	−0.879792	+	1.28326i
$534$		0			0
$535$	−8.77252	+	5.06482i	−0.379269	+	0.218971i
$536$	2.37527	+	4.11410i	0.102596	+	0.177702i
$537$		0			0
$538$		−	26.6594i		−	1.14937i
$539$	2.98127	+	1.72124i	0.128412	+	0.0741389i
$540$		0			0
$541$			1.42341i			0.0611970i	0.999532	+	0.0305985i	$0.00974133\pi$
$541$			1.42341i			0.0611970i	−0.999532	+	0.0305985i	$0.990259\pi$
$542$	−12.2247	+	21.1739i	−0.525097	+	0.909496i
$543$		0			0
$544$	2.44997	−	1.41449i	0.105042	−	0.0606458i
$545$	−26.5112			−1.13562
$546$		0			0
$547$	−9.33008			−0.398925			−0.199463	−	0.979905i	$-0.563920\pi$
$547$	−9.33008			−0.398925			−0.199463	+	0.979905i	$0.563920\pi$
$548$	−2.30457	+	1.33055i	−0.0984465	+	0.0568381i
$549$		0			0
$550$	7.46828	−	12.9354i	0.318449	−	0.551569i
$551$			6.64390i			0.283040i
$552$		0			0
$553$	−3.89576	−	2.24922i	−0.165664	−	0.0956464i
$554$		−	28.4812i		−	1.21005i
$555$		0			0
$556$	−8.35322	−	14.4682i	−0.354256	−	0.613589i
$557$	−9.34071	+	5.39286i	−0.395779	+	0.228503i	−0.684661	−	0.728862i	$-0.740050\pi$
$557$	−9.34071	+	5.39286i	−0.395779	+	0.228503i	0.288882	+	0.957365i	$0.406716\pi$
$558$		0			0
$559$	−0.842322	+	10.8620i	−0.0356264	+	0.459415i
$560$	−3.05596			−0.129138
$561$		0			0
$562$	−4.88016	−	8.45268i	−0.205857	−	0.356555i
$563$	−12.7541	+	22.0908i	−0.537522	+	0.931016i	0.461514	+	0.887133i	$0.347306\pi$
$563$	−12.7541	+	22.0908i	−0.537522	+	0.931016i	−0.999037	+	0.0438831i	$0.986027\pi$
$564$		0			0
$565$	29.6708	+	17.1304i	1.24826	+	0.720682i
$566$	−10.1076	−	5.83562i	−0.424853	−	0.245289i
$567$		0			0
$568$	−1.83473	+	3.17784i	−0.0769834	+	0.133339i
$569$	4.10835	+	7.11587i	0.172231	+	0.298313i	0.939200	−	0.343372i	$-0.111569\pi$
$569$	4.10835	+	7.11587i	0.172231	+	0.298313i	−0.766969	+	0.641685i	$0.778236\pi$
$570$		0			0
$571$	2.70500			0.113201			0.0566003	−	0.998397i	$-0.481974\pi$
$571$	2.70500			0.113201			0.0566003	+	0.998397i	$0.481974\pi$
$572$	−5.35636	−	11.1968i	−0.223961	−	0.468160i
$573$		0			0
$574$	8.62781	−	4.98127i	0.360118	−	0.207914i
$575$	6.64416	+	11.5080i	0.277081	+	0.479918i
$576$		0			0
$577$		−	21.4253i		−	0.891946i	−0.895046	−	0.445973i	$-0.852858\pi$
$577$		−	21.4253i		−	0.891946i	0.895046	−	0.445973i	$-0.147142\pi$
$578$	−7.79152	−	4.49843i	−0.324084	−	0.187110i
$579$		0			0
$580$		−	11.7673i		−	0.488611i
$581$	−3.57934	+	6.19961i	−0.148496	+	0.257203i
$582$		0			0
$583$	24.8460	−	14.3449i	1.02902	−	0.594104i
$584$	10.1119			0.418434
$585$		0			0
$586$	21.8202			0.901382
$587$	4.96515	−	2.86663i	0.204934	−	0.118319i	−0.394021	−	0.919101i	$-0.628916\pi$
$587$	4.96515	−	2.86663i	0.204934	−	0.118319i	0.598955	+	0.800783i	$0.295583\pi$
$588$		0			0
$589$	−0.844048	+	1.46193i	−0.0347784	+	0.0602379i
$590$		−	30.4910i		−	1.25529i
$591$		0			0
$592$	−4.58394	−	2.64654i	−0.188399	−	0.108772i
$593$		−	17.3442i		−	0.712240i	−0.934440	−	0.356120i	$-0.884099\pi$
$593$		−	17.3442i		−	0.712240i	0.934440	−	0.356120i	$-0.115901\pi$
$594$		0			0
$595$	−4.32263	−	7.48701i	−0.177211	−	0.306938i
$596$	−2.16642	+	1.25078i	−0.0887400	+	0.0512341i
$597$		0			0
$598$	11.0093	+	0.853743i	0.450204	+	0.0349121i
$599$	31.5835			1.29047			0.645234	−	0.763985i	$-0.276760\pi$
$599$	31.5835			1.29047			0.645234	+	0.763985i	$0.276760\pi$
$600$		0			0
$601$	−12.4478	−	21.5603i	−0.507757	−	0.879462i	−0.999960	−	0.00898069i	$-0.997141\pi$
$601$	−12.4478	−	21.5603i	−0.507757	−	0.879462i	0.492202	−	0.870481i	$-0.336192\pi$
$602$	1.51082	−	2.61681i	0.0615762	−	0.106653i
$603$		0			0
$604$	10.9522	+	6.32323i	0.445637	+	0.257289i
$605$	−2.25118	−	1.29972i	−0.0915233	−	0.0528410i
$606$		0			0
$607$	−7.62951	+	13.2147i	−0.309672	+	0.536368i	−0.978291	−	0.207238i	$-0.933553\pi$
$607$	−7.62951	+	13.2147i	−0.309672	+	0.536368i	0.668618	+	0.743606i	$0.266886\pi$
$608$	0.862708	+	1.49425i	0.0349874	+	0.0606000i
$609$		0			0
$610$	35.2817			1.42851
$611$	12.5169	+	26.1649i	0.506379	+	1.05852i
$612$		0			0
$613$	−39.6220	+	22.8757i	−1.60032	+	0.923943i	−0.608892	+	0.793253i	$0.708386\pi$
$613$	−39.6220	+	22.8757i	−1.60032	+	0.923943i	−0.991423	+	0.130690i	$0.958281\pi$
$614$	−2.43523	−	4.21794i	−0.0982779	−	0.170222i
$615$		0			0
$616$			3.44247i			0.138701i
$617$	−36.6167	−	21.1406i	−1.47413	−	0.851090i	−0.474555	−	0.880226i	$-0.657391\pi$
$617$	−36.6167	−	21.1406i	−1.47413	−	0.851090i	−0.999575	+	0.0291358i	$0.990724\pi$
$618$		0			0
$619$		−	22.0261i		−	0.885303i	−0.896694	−	0.442651i	$-0.854038\pi$
$619$		−	22.0261i		−	0.885303i	0.896694	−	0.442651i	$-0.145962\pi$
$620$	1.49493	−	2.58930i	0.0600379	−	0.103989i
$621$		0			0
$622$	−3.38048	+	1.95172i	−0.135545	+	0.0782569i
$623$	7.90307			0.316630
$624$		0			0
$625$	−27.8684			−1.11474
$626$	−22.5624	+	13.0264i	−0.901775	+	0.520640i
$627$		0			0
$628$	8.90657	−	15.4266i	0.355411	−	0.615590i
$629$		−	14.9740i		−	0.597054i
$630$		0			0
$631$	18.0721	+	10.4339i	0.719440	+	0.415369i	0.814547	−	0.580098i	$-0.196986\pi$
$631$	18.0721	+	10.4339i	0.719440	+	0.415369i	−0.0951064	+	0.995467i	$0.530319\pi$
$632$		−	4.49843i		−	0.178938i
$633$		0			0
$634$	−5.55536	−	9.62216i	−0.220631	−	0.382145i
$635$	13.5372	−	7.81571i	0.537208	−	0.310157i
$636$		0			0
$637$	2.97377	+	2.03880i	0.117825	+	0.0807800i
$638$	−13.2556			−0.524795
$639$		0			0
$640$	−1.52798	−	2.64654i	−0.0603988	−	0.104614i
$641$	10.4526	−	18.1045i	0.412853	−	0.715083i	−0.582347	−	0.812940i	$-0.697866\pi$
$641$	10.4526	−	18.1045i	0.412853	−	0.715083i	0.995200	+	0.0978574i	$0.0311989\pi$
$642$		0			0
$643$	33.8703	+	19.5550i	1.33571	+	0.771174i	0.986168	−	0.165746i	$-0.0530032\pi$
$643$	33.8703	+	19.5550i	1.33571	+	0.771174i	0.349544	+	0.936920i	$0.386337\pi$
$644$	−2.65229	−	1.53130i	−0.104515	−	0.0603416i
$645$		0			0
$646$	−2.44058	+	4.22722i	−0.0960235	+	0.166318i
$647$	3.96755	+	6.87201i	0.155981	+	0.270166i	0.933416	−	0.358797i	$-0.116813\pi$
$647$	3.96755	+	6.87201i	0.155981	+	0.270166i	−0.777435	+	0.628963i	$0.783480\pi$
$648$		0			0
$649$	−34.3474			−1.34825
$650$	8.84615	−	12.9029i	0.346974	−	0.506094i
$651$		0			0
$652$	−7.68884	+	4.43915i	−0.301118	+	0.173851i
$653$	21.3998	+	37.0655i	0.837439	+	1.45049i	0.892029	+	0.451978i	$0.149281\pi$
$653$	21.3998	+	37.0655i	0.837439	+	1.45049i	−0.0545901	+	0.998509i	$0.517385\pi$
$654$		0			0
$655$		−	57.3778i		−	2.24194i
$656$	8.62781	+	4.98127i	0.336859	+	0.194486i
$657$		0			0
$658$		−	8.04447i		−	0.313606i
$659$	0.364274	−	0.630941i	0.0141901	−	0.0245780i	−0.858843	−	0.512239i	$-0.828816\pi$
$659$	0.364274	−	0.630941i	0.0141901	−	0.0245780i	0.873033	+	0.487661i	$0.162150\pi$
$660$		0			0
$661$	−2.04352	+	1.17983i	−0.0794836	+	0.0458899i	−0.539215	−	0.842168i	$-0.681279\pi$
$661$	−2.04352	+	1.17983i	−0.0794836	+	0.0458899i	0.459731	+	0.888058i	$0.347946\pi$
$662$	−14.6478			−0.569304
$663$		0			0
$664$	−7.15869			−0.277811
$665$	4.56638	−	2.63640i	0.177077	−	0.102235i
$666$		0			0
$667$	5.89644	−	10.2129i	0.228311	−	0.395446i
$668$		−	9.76989i		−	0.378008i
$669$		0			0
$670$	12.5725	+	7.25875i	0.485719	+	0.280430i
$671$		−	39.7440i		−	1.53430i
$672$		0			0
$673$	15.6279	+	27.0682i	0.602410	+	1.04340i	0.992455	+	0.122609i	$0.0391260\pi$
$673$	15.6279	+	27.0682i	0.602410	+	1.04340i	−0.390045	+	0.920796i	$0.627541\pi$
$674$	23.8552	−	13.7728i	0.918867	−	0.530508i
$675$		0			0
$676$	−4.68662	−	12.1258i	−0.180255	−	0.466378i
$677$	41.7294			1.60379			0.801895	−	0.597464i	$-0.203825\pi$
$677$	41.7294			1.60379			0.801895	+	0.597464i	$0.203825\pi$
$678$		0			0
$679$	−4.54961	−	7.88016i	−0.174598	−	0.302413i
$680$	4.32263	−	7.48701i	0.165765	−	0.287114i
$681$		0			0
$682$	−2.91678	−	1.68401i	−0.111689	−	0.0644839i
$683$	7.98473	+	4.60999i	0.305527	+	0.176396i	0.644923	−	0.764247i	$-0.276889\pi$
$683$	7.98473	+	4.60999i	0.305527	+	0.176396i	−0.339396	+	0.940644i	$0.610223\pi$
$684$		0			0
$685$	−4.06610	+	7.04269i	−0.155358	+	0.269087i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	3.02163			0.115199
$689$	27.1068	−	12.9675i	1.03269	−	0.494021i
$690$		0			0
$691$	−7.97487	+	4.60429i	−0.303378	+	0.175156i	−0.643960	−	0.765060i	$-0.722709\pi$
$691$	−7.97487	+	4.60429i	−0.303378	+	0.175156i	0.340581	+	0.940215i	$0.389376\pi$
$692$	4.33762	+	7.51299i	0.164892	+	0.285601i
$693$		0			0
$694$			5.24146i			0.198963i
$695$	−44.2143	−	25.5271i	−1.67714	−	0.968300i
$696$		0			0
$697$			28.1838i			1.06754i
$698$	2.61482	−	4.52901i	0.0989725	−	0.171425i
$699$		0			0
$700$	−3.75760	+	2.16945i	−0.142024	+	0.0819976i
$701$	−20.8683			−0.788184			−0.394092	−	0.919071i	$-0.628941\pi$
$701$	−20.8683			−0.788184			−0.394092	+	0.919071i	$0.628941\pi$
$702$		0			0
$703$	9.13277			0.344449
$704$	−2.98127	+	1.72124i	−0.112361	+	0.0648715i
$705$		0			0
$706$	1.88348	−	3.26227i	0.0708855	−	0.122777i
$707$		−	18.8533i		−	0.709050i
$708$		0			0
$709$	−12.8731	−	7.43226i	−0.483458	−	0.279124i	0.238399	−	0.971167i	$-0.423378\pi$
$709$	−12.8731	−	7.43226i	−0.483458	−	0.279124i	−0.721856	+	0.692043i	$0.756711\pi$
$710$			11.2137i			0.420843i
$711$		0			0
$712$	3.95154	+	6.84426i	0.148090	+	0.256499i
$713$	2.59492	−	1.49818i	0.0971804	−	0.0561072i
$714$		0			0
$715$	−31.2843	−	21.4483i	−1.16996	−	0.802120i
$716$	23.4278			0.875540
$717$		0			0
$718$	−10.3002	−	17.8404i	−0.384399	−	0.665798i
$719$	12.8265	−	22.2162i	0.478349	−	0.828524i	−0.521343	−	0.853347i	$-0.674569\pi$
$719$	12.8265	−	22.2162i	0.478349	−	0.828524i	0.999692	+	0.0248229i	$0.00790218\pi$
$720$		0			0
$721$	−11.8714	−	6.85393i	−0.442112	−	0.255254i
$722$	13.8763	+	8.01147i	0.516421	+	0.298156i
$723$		0			0
$724$	3.83316	−	6.63923i	0.142458	−	0.246745i
$725$	−8.35372	−	14.4691i	−0.310249	−	0.537368i
$726$		0			0
$727$	41.6568			1.54497			0.772483	−	0.635036i	$-0.219015\pi$
$727$	41.6568			1.54497			0.772483	+	0.635036i	$0.219015\pi$
$728$	−0.278764	+	3.59476i	−0.0103317	+	0.133231i
$729$		0			0
$730$	26.7616	−	15.4508i	0.990492	−	0.571861i
$731$	4.27407	+	7.40290i	0.158082	+	0.273806i
$732$		0			0
$733$			26.4965i			0.978671i	0.872096	+	0.489336i	$0.162761\pi$
$733$			26.4965i			0.978671i	−0.872096	+	0.489336i	$0.837239\pi$
$734$	−24.1759	−	13.9579i	−0.892347	−	0.515197i
$735$		0			0
$736$		−	3.06260i		−	0.112889i
$737$	8.17682	−	14.1627i	0.301197	−	0.521688i
$738$		0			0
$739$	18.1009	−	10.4506i	0.665853	−	0.384431i	−0.128650	−	0.991690i	$-0.541064\pi$
$739$	18.1009	−	10.4506i	0.665853	−	0.384431i	0.794504	+	0.607259i	$0.207731\pi$
$740$	−16.1755			−0.594622
$741$		0			0
$742$	−8.33405			−0.305953
$743$	−4.88999	+	2.82323i	−0.179396	+	0.103574i	−0.587009	−	0.809580i	$-0.699695\pi$
$743$	−4.88999	+	2.82323i	−0.179396	+	0.103574i	0.407613	+	0.913155i	$0.366361\pi$
$744$		0			0
$745$	−3.82235	+	6.62050i	−0.140040	+	0.242556i
$746$		−	31.4183i		−	1.15030i
$747$		0			0
$748$	−8.43395	−	4.86934i	−0.308376	−	0.178041i
$749$		−	3.31471i		−	0.121117i
$750$		0			0
$751$	7.70439	+	13.3444i	0.281137	+	0.486944i	0.971665	−	0.236362i	$-0.0759551\pi$
$751$	7.70439	+	13.3444i	0.281137	+	0.486944i	−0.690528	+	0.723306i	$0.742622\pi$
$752$	6.96672	−	4.02224i	0.254050	−	0.146676i
$753$		0			0
$754$	−13.8420	−	1.07341i	−0.504097	−	0.0390914i
$755$	38.6471			1.40651
$756$		0			0
$757$	17.7686	+	30.7761i	0.645811	+	1.11858i	0.984114	+	0.177540i	$0.0568139\pi$
$757$	17.7686	+	30.7761i	0.645811	+	1.11858i	−0.338303	+	0.941037i	$0.609853\pi$
$758$	15.9203	−	27.5747i	0.578251	−	1.00156i
$759$		0			0
$760$	4.56638	+	2.63640i	0.165640	+	0.0956324i
$761$	−36.2213	−	20.9124i	−1.31302	−	0.758073i	−0.330425	−	0.943832i	$-0.607192\pi$
$761$	−36.2213	−	20.9124i	−1.31302	−	0.758073i	−0.982595	+	0.185759i	$0.940526\pi$
$762$		0			0
$763$	4.33762	−	7.51299i	0.157033	−	0.271988i
$764$	−12.7472	−	22.0789i	−0.461179	−	0.798785i
$765$		0			0
$766$	−4.72228			−0.170623
$767$	−35.8668	−	2.78138i	−1.29508	−	0.100430i
$768$		0			0
$769$	15.4609	−	8.92635i	0.557534	−	0.321893i	−0.194621	−	0.980879i	$-0.562348\pi$
$769$	15.4609	−	8.92635i	0.557534	−	0.321893i	0.752155	+	0.658986i	$0.229014\pi$
$770$	5.26003	+	9.11064i	0.189558	+	0.328325i
$771$		0			0
$772$			8.52586i			0.306852i
$773$	−10.4892	−	6.05596i	−0.377272	−	0.217818i	0.299359	−	0.954141i	$-0.403227\pi$
$773$	−10.4892	−	6.05596i	−0.377272	−	0.217818i	−0.676630	+	0.736323i	$0.736561\pi$
$774$		0			0
$775$		−	4.24506i		−	0.152487i
$776$	4.54961	−	7.88016i	0.163322	−	0.282881i
$777$		0			0
$778$	−26.4919	+	15.2951i	−0.949781	+	0.548357i
$779$	−17.1895			−0.615878
$780$		0			0
$781$	12.6320			0.452008
$782$	7.50327	−	4.33201i	0.268316	−	0.154913i
$783$		0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.52798 + 2.64654i) q^{10} +(2.98127 - 1.72124i) q^{11} +(3.25253 - 1.55596i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.41449 - 2.44997i) q^{17} +(1.49425 + 0.862708i) q^{19} +(-2.64654 - 1.52798i) q^{20} +(-1.72124 + 2.98127i) q^{22} +(-1.53130 - 2.65229i) q^{23} -4.33891 q^{25} +(-2.03880 + 2.97377i) q^{26} +(0.866025 - 0.500000i) q^{28} +(1.92531 + 3.33473i) q^{29} +0.978370i q^{31} +(0.866025 + 0.500000i) q^{32} +2.82898i q^{34} +(1.52798 - 2.64654i) q^{35} +(4.58394 - 2.64654i) q^{37} -1.72542 q^{38} +3.05596 q^{40} +(-8.62781 + 4.98127i) q^{41} +(-1.51082 + 2.61681i) q^{43} -3.44247i q^{44} +(2.65229 + 1.53130i) q^{46} +8.04447i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.75760 - 2.16945i) q^{50} +(0.278764 - 3.59476i) q^{52} +8.33405 q^{53} +(-5.26003 - 9.11064i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.33473 - 1.92531i) q^{58} +(-8.64080 - 4.98877i) q^{59} +(5.77260 - 9.99843i) q^{61} +(-0.489185 - 0.847293i) q^{62} -1.00000 q^{64} +(-4.75496 - 9.93962i) q^{65} +(4.11410 - 2.37527i) q^{67} +(-1.41449 - 2.44997i) q^{68} +3.05596i q^{70} +(3.17784 + 1.83473i) q^{71} -10.1119i q^{73} +(-2.64654 + 4.58394i) q^{74} +(1.49425 - 0.862708i) q^{76} +3.44247 q^{77} -4.49843 q^{79} +(-2.64654 + 1.52798i) q^{80} +(4.98127 - 8.62781i) q^{82} +7.15869i q^{83} +(-7.48701 - 4.32263i) q^{85} -3.02163i q^{86} +(1.72124 + 2.98127i) q^{88} +(6.84426 - 3.95154i) q^{89} +(3.59476 + 0.278764i) q^{91} -3.06260 q^{92} +(-4.02224 - 6.96672i) q^{94} +(2.63640 - 4.56638i) q^{95} +(-7.88016 - 4.54961i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

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