LMFDB - Embedded newform 432.6.i.d.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,6,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	432.i (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:	$69.2858101592$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 $ x^10 + 175x^8 + 8800x^6 + 124623x^4 + 498609x^2 + 442368
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.3
Root			$7.64342i$ of defining polynomial
Character	$\chi$	$=$	432.145
Dual form			432.6.i.d.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.88422 + 8.45972i) q^{5} +(68.3340 + 118.358i) q^{7} +O(q^{10})$	$q+(-4.88422 + 8.45972i) q^{5} +(68.3340 + 118.358i) q^{7} +(-326.660 - 565.792i) q^{11} +(-125.247 + 216.934i) q^{13} -249.768 q^{17} +1754.03 q^{19} +(827.440 - 1433.17i) q^{23} +(1514.79 + 2623.69i) q^{25} +(2123.96 + 3678.81i) q^{29} +(4493.72 - 7783.34i) q^{31} -1335.03 q^{35} -6000.33 q^{37} +(-5372.59 + 9305.61i) q^{41} +(5023.30 + 8700.62i) q^{43} +(-11743.3 - 20340.0i) q^{47} +(-935.582 + 1620.48i) q^{49} -9411.34 q^{53} +6381.93 q^{55} +(-22083.4 + 38249.5i) q^{59} +(11202.4 + 19403.2i) q^{61} +(-1223.47 - 2119.11i) q^{65} +(-18001.5 + 31179.5i) q^{67} +78538.5 q^{71} +61305.5 q^{73} +(44644.1 - 77325.8i) q^{77} +(13745.0 + 23807.1i) q^{79} +(32403.2 + 56124.0i) q^{83} +(1219.92 - 2112.97i) q^{85} +34652.4 q^{89} -34234.5 q^{91} +(-8567.06 + 14838.6i) q^{95} +(-8056.14 - 13953.6i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 21 q^{5} - 29 q^{7}+O(q^{10}) $ 10 * q + 21 * q^5 - 29 * q^7	$ 10 q + 21 q^{5} - 29 q^{7} + 177 q^{11} - 181 q^{13} - 2280 q^{17} + 832 q^{19} + 399 q^{23} - 4778 q^{25} + 6033 q^{29} - 2759 q^{31} + 37146 q^{35} - 15172 q^{37} + 18435 q^{41} - 1469 q^{43} - 25155 q^{47} - 4056 q^{49} - 116844 q^{53} - 14778 q^{55} - 90537 q^{59} + 1403 q^{61} + 148407 q^{65} - 13907 q^{67} + 229368 q^{71} + 15200 q^{73} + 211983 q^{77} - 29993 q^{79} - 228951 q^{83} - 49662 q^{85} - 598332 q^{89} - 124930 q^{91} - 394764 q^{95} + 40541 q^{97}+O(q^{100}) $ 10 * q + 21 * q^5 - 29 * q^7 + 177 * q^11 - 181 * q^13 - 2280 * q^17 + 832 * q^19 + 399 * q^23 - 4778 * q^25 + 6033 * q^29 - 2759 * q^31 + 37146 * q^35 - 15172 * q^37 + 18435 * q^41 - 1469 * q^43 - 25155 * q^47 - 4056 * q^49 - 116844 * q^53 - 14778 * q^55 - 90537 * q^59 + 1403 * q^61 + 148407 * q^65 - 13907 * q^67 + 229368 * q^71 + 15200 * q^73 + 211983 * q^77 - 29993 * q^79 - 228951 * q^83 - 49662 * q^85 - 598332 * q^89 - 124930 * q^91 - 394764 * q^95 + 40541 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−4.88422	+	8.45972i	−0.0873716	+	0.151332i	−0.906399	−	0.422422i	$-0.861180\pi$
$5$	−4.88422	+	8.45972i	−0.0873716	+	0.151332i	0.819028	+	0.573754i	$0.194513\pi$
$6$		0			0
$7$	68.3340	+	118.358i	0.527099	+	0.912962i	0.999501	+	0.0315789i	$0.0100535\pi$
$7$	68.3340	+	118.358i	0.527099	+	0.912962i	−0.472403	+	0.881383i	$0.656613\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−326.660	−	565.792i	−0.813982	−	1.40986i	−0.910057	−	0.414484i	$-0.863962\pi$
$11$	−326.660	−	565.792i	−0.813982	−	1.40986i	0.0960745	−	0.995374i	$-0.469371\pi$
$12$		0			0
$13$	−125.247	+	216.934i	−0.205546	+	0.356016i	−0.950307	−	0.311316i	$-0.899230\pi$
$13$	−125.247	+	216.934i	−0.205546	+	0.356016i	0.744761	+	0.667332i	$0.232564\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−249.768			−0.209611			−0.104806	−	0.994493i	$-0.533422\pi$
$17$	−249.768			−0.209611			−0.104806	+	0.994493i	$0.533422\pi$
$18$		0			0
$19$	1754.03			1.11469			0.557343	−	0.830282i	$-0.311821\pi$
$19$	1754.03			1.11469			0.557343	+	0.830282i	$0.311821\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	827.440	−	1433.17i	0.326150	−	0.564908i	−0.655595	−	0.755113i	$-0.727582\pi$
$23$	827.440	−	1433.17i	0.326150	−	0.564908i	0.981744	+	0.190205i	$0.0609153\pi$
$24$		0			0
$25$	1514.79	+	2623.69i	0.484732	+	0.839581i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2123.96	+	3678.81i	0.468977	+	0.812292i	0.999371	−	0.0354595i	$-0.0112895\pi$
$29$	2123.96	+	3678.81i	0.468977	+	0.812292i	−0.530394	+	0.847751i	$0.677956\pi$
$30$		0			0
$31$	4493.72	−	7783.34i	0.839849	−	1.45466i	−0.0501712	−	0.998741i	$-0.515977\pi$
$31$	4493.72	−	7783.34i	0.839849	−	1.45466i	0.890020	−	0.455921i	$-0.150690\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1335.03			−0.184214
$36$		0			0
$37$	−6000.33			−0.720561			−0.360280	−	0.932844i	$-0.617319\pi$
$37$	−6000.33			−0.720561			−0.360280	+	0.932844i	$0.617319\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5372.59	+	9305.61i	−0.499142	+	0.864540i	−1.00000		0.000990010i	$-0.999685\pi$
$41$	−5372.59	+	9305.61i	−0.499142	+	0.864540i	0.500857	+	0.865530i	$0.333018\pi$
$42$		0			0
$43$	5023.30	+	8700.62i	0.414303	+	0.717594i	0.995355	−	0.0962724i	$-0.0306920\pi$
$43$	5023.30	+	8700.62i	0.414303	+	0.717594i	−0.581052	+	0.813867i	$0.697359\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11743.3	−	20340.0i	−0.775435	−	1.34309i	−0.934550	−	0.355833i	$-0.884197\pi$
$47$	−11743.3	−	20340.0i	−0.775435	−	1.34309i	0.159114	−	0.987260i	$-0.449136\pi$
$48$		0			0
$49$	−935.582	+	1620.48i	−0.0556662	+	0.0964167i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9411.34			−0.460216			−0.230108	−	0.973165i	$-0.573908\pi$
$53$	−9411.34			−0.460216			−0.230108	+	0.973165i	$0.573908\pi$
$54$		0			0
$55$	6381.93			0.284476
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−22083.4	+	38249.5i	−0.825915	+	1.43053i	0.0753026	+	0.997161i	$0.476008\pi$
$59$	−22083.4	+	38249.5i	−0.825915	+	1.43053i	−0.901218	+	0.433366i	$0.857326\pi$
$60$		0			0
$61$	11202.4	+	19403.2i	0.385467	+	0.667649i	0.991834	−	0.127536i	$-0.0407069\pi$
$61$	11202.4	+	19403.2i	0.385467	+	0.667649i	−0.606366	+	0.795185i	$0.707374\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1223.47	−	2119.11i	−0.0359177	−	0.0622113i
$66$		0			0
$67$	−18001.5	+	31179.5i	−0.489916	+	0.848560i	−0.999933	−	0.0116049i	$-0.996306\pi$
$67$	−18001.5	+	31179.5i	−0.489916	+	0.848560i	0.510016	+	0.860165i	$0.329639\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	78538.5			1.84900			0.924499	−	0.381184i	$-0.124483\pi$
$71$	78538.5			1.84900			0.924499	+	0.381184i	$0.124483\pi$
$72$		0			0
$73$	61305.5			1.34646			0.673229	−	0.739434i	$-0.264907\pi$
$73$	61305.5			1.34646			0.673229	+	0.739434i	$0.264907\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	44644.1	−	77325.8i	0.858098	−	1.48627i
$78$		0			0
$79$	13745.0	+	23807.1i	0.247787	+	0.429180i	0.962911	−	0.269817i	$-0.0869634\pi$
$79$	13745.0	+	23807.1i	0.247787	+	0.429180i	−0.715125	+	0.698997i	$0.753630\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	32403.2	+	56124.0i	0.516289	+	0.894238i	0.999821	+	0.0189117i	$0.00602013\pi$
$83$	32403.2	+	56124.0i	0.516289	+	0.894238i	−0.483533	+	0.875326i	$0.660647\pi$
$84$		0			0
$85$	1219.92	−	2112.97i	0.0183141	−	0.0317209i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	34652.4			0.463722			0.231861	−	0.972749i	$-0.425518\pi$
$89$	34652.4			0.463722			0.231861	+	0.972749i	$0.425518\pi$
$90$		0			0
$91$	−34234.5			−0.433372
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8567.06	+	14838.6i	−0.0973919	+	0.168688i
$96$		0			0
$97$	−8056.14	−	13953.6i	−0.0869356	−	0.150577i	0.819279	−	0.573395i	$-0.194374\pi$
$97$	−8056.14	−	13953.6i	−0.0869356	−	0.150577i	−0.906214	+	0.422819i	$0.861041\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	93469.6	+	161894.i	0.911731	+	1.57916i	0.811618	+	0.584189i	$0.198587\pi$
$101$	93469.6	+	161894.i	0.911731	+	1.57916i	0.100113	+	0.994976i	$0.468079\pi$
$102$		0			0
$103$	−84293.8	+	146001.i	−0.782893	+	1.35601i	0.147357	+	0.989083i	$0.452923\pi$
$103$	−84293.8	+	146001.i	−0.782893	+	1.35601i	−0.930250	+	0.366927i	$0.880410\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	155131.			1.30991			0.654953	−	0.755669i	$-0.272688\pi$
$107$	155131.			1.30991			0.654953	+	0.755669i	$0.272688\pi$
$108$		0			0
$109$	−115289.			−0.929439			−0.464720	−	0.885458i	$-0.653845\pi$
$109$	−115289.			−0.929439			−0.464720	+	0.885458i	$0.653845\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	62693.8	−	108589.i	0.461880	−	0.799999i	−0.537175	−	0.843471i	$-0.680509\pi$
$113$	62693.8	−	108589.i	0.461880	−	0.799999i	0.999055	+	0.0434719i	$0.0138419\pi$
$114$		0			0
$115$	8082.80	+	13999.8i	0.0569924	+	0.0987138i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17067.7	−	29562.1i	−0.110486	−	0.191367i
$120$		0			0
$121$	−132889.	+	230170.i	−0.825134	+	1.42917i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−60120.6			−0.344151
$126$		0			0
$127$	−17459.4			−0.0960548			−0.0480274	−	0.998846i	$-0.515293\pi$
$127$	−17459.4			−0.0960548			−0.0480274	+	0.998846i	$0.515293\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	14464.0	−	25052.4i	0.0736395	−	0.127547i	−0.826854	−	0.562416i	$-0.809872\pi$
$131$	14464.0	−	25052.4i	0.0736395	−	0.127547i	0.900494	+	0.434869i	$0.143205\pi$
$132$		0			0
$133$	119860.	+	207603.i	0.587549	+	1.01767i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	204277.	+	353818.i	0.929862	+	1.61057i	0.783550	+	0.621329i	$0.213407\pi$
$137$	204277.	+	353818.i	0.929862	+	1.61057i	0.146312	+	0.989239i	$0.453260\pi$
$138$		0			0
$139$	144577.	−	250415.i	0.634693	−	1.09932i	−0.351888	−	0.936042i	$-0.614460\pi$
$139$	144577.	−	250415.i	0.634693	−	1.09932i	0.986580	−	0.163278i	$-0.0522066\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	163653.			0.669243
$144$		0			0
$145$	−41495.6			−0.163901
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−169.673	+	293.882i	−0.000626104	+	0.00108444i	−0.866338	−	0.499458i	$-0.833533\pi$
$149$	−169.673	+	293.882i	−0.000626104	+	0.00108444i	0.865712	+	0.500542i	$0.166866\pi$
$150$		0			0
$151$	178737.	+	309581.i	0.637928	+	1.10492i	0.985887	+	0.167414i	$0.0535417\pi$
$151$	178737.	+	309581.i	0.637928	+	1.10492i	−0.347958	+	0.937510i	$0.613125\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	43896.6	+	76031.1i	0.146758	+	0.254192i
$156$		0			0
$157$	376.310	−	651.789i	0.00121842	−	0.00211037i	−0.865416	−	0.501055i	$-0.832945\pi$
$157$	376.310	−	651.789i	0.00121842	−	0.00211037i	0.866634	+	0.498944i	$0.166279\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	226169.			0.687653
$162$		0			0
$163$	358488.			1.05683			0.528416	−	0.848986i	$-0.322786\pi$
$163$	358488.			1.05683			0.528416	+	0.848986i	$0.322786\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	246875.	−	427601.i	0.684994	−	1.18644i	−0.288445	−	0.957496i	$-0.593138\pi$
$167$	246875.	−	427601.i	0.684994	−	1.18644i	0.973439	−	0.228948i	$-0.0735284\pi$
$168$		0			0
$169$	154273.	+	267209.i	0.415502	+	0.719670i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	83924.6	+	145362.i	0.213193	+	0.369262i	0.952712	−	0.303874i	$-0.0982802\pi$
$173$	83924.6	+	145362.i	0.213193	+	0.369262i	−0.739519	+	0.673136i	$0.764947\pi$
$174$		0			0
$175$	−207023.	+	358575.i	−0.511004	+	0.885084i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−483862.			−1.12873			−0.564364	−	0.825526i	$-0.690878\pi$
$179$	−483862.			−1.12873			−0.564364	+	0.825526i	$0.690878\pi$
$180$		0			0
$181$	74732.3			0.169555			0.0847777	−	0.996400i	$-0.472982\pi$
$181$	74732.3			0.169555			0.0847777	+	0.996400i	$0.472982\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	29306.9	−	50761.1i	0.0629565	−	0.109044i
$186$		0			0
$187$	81589.4	+	141317.i	0.170620	+	0.295522i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	297130.	+	514645.i	0.589337	+	1.02076i	0.994319	+	0.106437i	$0.0339441\pi$
$191$	297130.	+	514645.i	0.589337	+	1.02076i	−0.404983	+	0.914324i	$0.632723\pi$
$192$		0			0
$193$	44949.8	−	77855.4i	0.0868630	−	0.150451i	−0.819321	−	0.573336i	$-0.805649\pi$
$193$	44949.8	−	77855.4i	0.0868630	−	0.150451i	0.906184	+	0.422885i	$0.138982\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−425161.			−0.780527			−0.390263	−	0.920703i	$-0.627616\pi$
$197$	−425161.			−0.780527			−0.390263	+	0.920703i	$0.627616\pi$
$198$		0			0
$199$	−374339.			−0.670089			−0.335044	−	0.942202i	$-0.608751\pi$
$199$	−374339.			−0.670089			−0.335044	+	0.942202i	$0.608751\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−290278.	+	502775.i	−0.494394	+	0.856316i
$204$		0			0
$205$	−52481.9	−	90901.3i	−0.0872217	−	0.151072i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−572971.	−	992416.i	−0.907334	−	1.57155i
$210$		0			0
$211$	−82302.7	+	142552.i	−0.127265	+	0.220429i	−0.922616	−	0.385720i	$-0.873953\pi$
$211$	−82302.7	+	142552.i	−0.127265	+	0.220429i	0.795351	+	0.606149i	$0.207286\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−98139.7			−0.144793
$216$		0			0
$217$	1.22829e6			1.77073
$218$		0			0
$219$		0			0
$220$		0			0
$221$	31282.7	−	54183.2i	0.0430848	−	0.0746250i
$222$		0			0
$223$	−162339.	−	281179.i	−0.218605	−	0.378635i	0.735777	−	0.677224i	$-0.236817\pi$
$223$	−162339.	−	281179.i	−0.218605	−	0.378635i	−0.954382	+	0.298589i	$0.903484\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	354884.	+	614677.i	0.457111	+	0.791739i	0.998807	−	0.0488351i	$-0.0155509\pi$
$227$	354884.	+	614677.i	0.457111	+	0.791739i	−0.541696	+	0.840575i	$0.682218\pi$
$228$		0			0
$229$	126953.	−	219889.i	0.159976	−	0.277086i	−0.774884	−	0.632104i	$-0.782192\pi$
$229$	126953.	−	219889.i	0.159976	−	0.277086i	0.934860	+	0.355017i	$0.115525\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	557666.			0.672952			0.336476	−	0.941692i	$-0.390765\pi$
$233$	557666.			0.672952			0.336476	+	0.941692i	$0.390765\pi$
$234$		0			0
$235$	229427.			0.271004
$236$		0			0
$237$		0			0
$238$		0			0
$239$	266147.	−	460981.i	0.301389	−	0.522021i	−0.675062	−	0.737761i	$-0.735883\pi$
$239$	266147.	−	460981.i	0.301389	−	0.522021i	0.976451	+	0.215740i	$0.0692164\pi$
$240$		0			0
$241$	−332544.	−	575984.i	−0.368814	−	0.638804i	0.620567	−	0.784154i	$-0.286903\pi$
$241$	−332544.	−	575984.i	−0.368814	−	0.638804i	−0.989380	+	0.145350i	$0.953569\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9139.17	−	15829.5i	−0.00972729	−	0.0168482i
$246$		0			0
$247$	−219687.	+	380508.i	−0.229119	+	0.396846i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−906446.			−0.908150			−0.454075	−	0.890963i	$-0.650030\pi$
$251$	−906446.			−0.908150			−0.454075	+	0.890963i	$0.650030\pi$
$252$		0			0
$253$	−1.08117e6			−1.06192
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−362420.	+	627731.i	−0.342279	+	0.592844i	−0.984855	−	0.173377i	$-0.944532\pi$
$257$	−362420.	+	627731.i	−0.342279	+	0.592844i	0.642577	+	0.766221i	$0.277865\pi$
$258$		0			0
$259$	−410027.	−	710187.i	−0.379807	−	0.657844i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−126262.	−	218692.i	−0.112560	−	0.194959i	0.804242	−	0.594302i	$-0.202572\pi$
$263$	−126262.	−	218692.i	−0.112560	−	0.194959i	−0.916802	+	0.399343i	$0.869238\pi$
$264$		0			0
$265$	45967.1	−	79617.3i	0.0402098	−	0.0696455i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	191107.			0.161026			0.0805131	−	0.996754i	$-0.474344\pi$
$269$	191107.			0.161026			0.0805131	+	0.996754i	$0.474344\pi$
$270$		0			0
$271$	−86694.8			−0.0717084			−0.0358542	−	0.999357i	$-0.511415\pi$
$271$	−86694.8			−0.0717084			−0.0358542	+	0.999357i	$0.511415\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	989643.	−	1.71411e6i	0.789127	−	1.36681i
$276$		0			0
$277$	−635239.	−	1.10027e6i	−0.497437	−	0.861586i	0.502559	−	0.864543i	$-0.332392\pi$
$277$	−635239.	−	1.10027e6i	−0.497437	−	0.861586i	−0.999996	+	0.00295734i	$0.999059\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−28414.8	−	49215.9i	−0.0214674	−	0.0371826i	0.855092	−	0.518476i	$-0.173500\pi$
$281$	−28414.8	−	49215.9i	−0.0214674	−	0.0371826i	−0.876560	+	0.481293i	$0.840167\pi$
$282$		0			0
$283$	676798.	−	1.17225e6i	0.502335	−	0.870069i	−0.497662	−	0.867371i	$-0.665808\pi$
$283$	676798.	−	1.17225e6i	0.502335	−	0.870069i	0.999996	−	0.00269796i	$-0.000858787\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.46852e6			−1.05239
$288$		0			0
$289$	−1.35747e6			−0.956063
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−263851.	+	457003.i	−0.179552	+	0.310993i	−0.941727	−	0.336378i	$-0.890798\pi$
$293$	−263851.	+	457003.i	−0.179552	+	0.310993i	0.762175	+	0.647371i	$0.224131\pi$
$294$		0			0
$295$	−215720.	−	373638.i	−0.144323	−	0.249975i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	207269.	+	359000.i	0.134077	+	0.232229i
$300$		0			0
$301$	−686525.	+	1.18910e6i	−0.436757	+	0.756486i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−218861.			−0.134716
$306$		0			0
$307$	−1.15348e6			−0.698497			−0.349249	−	0.937030i	$-0.613563\pi$
$307$	−1.15348e6			−0.698497			−0.349249	+	0.937030i	$0.613563\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	758833.	−	1.31434e6i	0.444883	−	0.770559i	−0.553161	−	0.833074i	$-0.686579\pi$
$311$	758833.	−	1.31434e6i	0.444883	−	0.770559i	0.998044	+	0.0625148i	$0.0199121\pi$
$312$		0			0
$313$	979958.	+	1.69734e6i	0.565388	+	0.979281i	0.997013	+	0.0772280i	$0.0246069\pi$
$313$	979958.	+	1.69734e6i	0.565388	+	0.979281i	−0.431625	+	0.902053i	$0.642060\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	916140.	+	1.58680e6i	0.512052	+	0.886899i	0.999902	+	0.0139724i	$0.00444770\pi$
$317$	916140.	+	1.58680e6i	0.512052	+	0.886899i	−0.487851	+	0.872927i	$0.662219\pi$
$318$		0			0
$319$	1.38763e6	−	2.40344e6i	0.763477	−	1.32238i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−438100.			−0.233651
$324$		0			0
$325$	−758891.			−0.398539
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.60493e6	−	2.77983e6i	0.817462	−	1.41589i
$330$		0			0
$331$	−360056.	−	623635.i	−0.180634	−	0.312868i	0.761462	−	0.648209i	$-0.224482\pi$
$331$	−360056.	−	623635.i	−0.180634	−	0.312868i	−0.942097	+	0.335341i	$0.891148\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−175847.	−	304575.i	−0.0856095	−	0.148280i
$336$		0			0
$337$	1.55433e6	−	2.69218e6i	0.745537	−	1.29131i	−0.204406	−	0.978886i	$-0.565526\pi$
$337$	1.55433e6	−	2.69218e6i	0.745537	−	1.29131i	0.949943	−	0.312422i	$-0.101140\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.87168e6			−2.73449
$342$		0			0
$343$	2.04125e6			0.936831
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−136034.	+	235618.i	−0.0606490	+	0.105047i	−0.894756	−	0.446556i	$-0.852650\pi$
$347$	−136034.	+	235618.i	−0.0606490	+	0.105047i	0.834107	+	0.551603i	$0.185984\pi$
$348$		0			0
$349$	−1.51024e6	−	2.61582e6i	−0.663718	−	1.14959i	−0.979631	−	0.200805i	$-0.935644\pi$
$349$	−1.51024e6	−	2.61582e6i	−0.663718	−	1.14959i	0.315913	−	0.948788i	$-0.397689\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	526944.	+	912695.i	0.225075	+	0.389842i	0.956342	−	0.292250i	$-0.0944038\pi$
$353$	526944.	+	912695.i	0.225075	+	0.389842i	−0.731267	+	0.682092i	$0.761070\pi$
$354$		0			0
$355$	−383599.	+	664413.i	−0.161550	+	0.279813i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.26085e6			−1.74486			−0.872430	−	0.488739i	$-0.837457\pi$
$359$	−4.26085e6			−1.74486			−0.872430	+	0.488739i	$0.837457\pi$
$360$		0			0
$361$	600514.			0.242524
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−299430.	+	518628.i	−0.117642	+	0.203762i
$366$		0			0
$367$	−155650.	−	269594.i	−0.0603231	−	0.104483i	0.834287	−	0.551331i	$-0.185880\pi$
$367$	−155650.	−	269594.i	−0.0603231	−	0.104483i	−0.894610	+	0.446848i	$0.852546\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−643115.	−	1.11391e6i	−0.242579	−	0.420160i
$372$		0			0
$373$	1.13768e6	−	1.97052e6i	0.423397	−	0.733345i	−0.572872	−	0.819645i	$-0.694171\pi$
$373$	1.13768e6	−	1.97052e6i	0.423397	−	0.733345i	0.996269	+	0.0862997i	$0.0275043\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.06408e6			−0.385585
$378$		0			0
$379$	−3.28710e6			−1.17548			−0.587739	−	0.809050i	$-0.699982\pi$
$379$	−3.28710e6			−1.17548			−0.587739	+	0.809050i	$0.699982\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.12336e6	+	1.94572e6i	−0.391311	+	0.677770i	−0.992623	−	0.121244i	$-0.961312\pi$
$383$	−1.12336e6	+	1.94572e6i	−0.391311	+	0.677770i	0.601312	+	0.799014i	$0.294645\pi$
$384$		0			0
$385$	436103.	+	755352.i	0.149947	+	0.259715i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−683723.	−	1.18424e6i	−0.229090	−	0.396796i	0.728449	−	0.685100i	$-0.240242\pi$
$389$	−683723.	−	1.18424e6i	−0.229090	−	0.396796i	−0.957539	+	0.288305i	$0.906908\pi$
$390$		0			0
$391$	−206668.	+	357960.i	−0.0683647	+	0.118411i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−268535.			−0.0865982
$396$		0			0
$397$	1.52652e6			0.486099			0.243050	−	0.970014i	$-0.421852\pi$
$397$	1.52652e6			0.486099			0.243050	+	0.970014i	$0.421852\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.36998e6	−	4.10493e6i	0.736011	−	1.27481i	−0.218267	−	0.975889i	$-0.570040\pi$
$401$	2.36998e6	−	4.10493e6i	0.736011	−	1.27481i	0.954278	−	0.298920i	$-0.0966263\pi$
$402$		0			0
$403$	1.12565e6	+	1.94968e6i	0.345255	+	0.597999i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.96007e6	+	3.39494e6i	0.586523	+	1.01589i
$408$		0			0
$409$	−478468.	+	828731.i	−0.141431	+	0.244966i	−0.928036	−	0.372491i	$-0.878504\pi$
$409$	−478468.	+	828731.i	−0.141431	+	0.244966i	0.786605	+	0.617457i	$0.211837\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.03619e6			−1.74136
$414$		0			0
$415$	−633057.			−0.180436
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−885418.	+	1.53359e6i	−0.246384	+	0.426750i	−0.962520	−	0.271211i	$-0.912576\pi$
$419$	−885418.	+	1.53359e6i	−0.246384	+	0.426750i	0.716135	+	0.697961i	$0.245909\pi$
$420$		0			0
$421$	−1.54265e6	−	2.67194e6i	−0.424190	−	0.734719i	0.572154	−	0.820146i	$-0.306108\pi$
$421$	−1.54265e6	−	2.67194e6i	−0.424190	−	0.734719i	−0.996344	+	0.0854269i	$0.972775\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−378346.	−	655315.i	−0.101605	−	0.175986i
$426$		0			0
$427$	−1.53101e6	+	2.65180e6i	−0.406359	+	0.703834i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.16873e6			0.562356			0.281178	−	0.959656i	$-0.409275\pi$
$431$	2.16873e6			0.562356			0.281178	+	0.959656i	$0.409275\pi$
$432$		0			0
$433$	6.69677e6			1.71651			0.858253	−	0.513226i	$-0.171550\pi$
$433$	6.69677e6			1.71651			0.858253	+	0.513226i	$0.171550\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.45135e6	−	2.51382e6i	0.363554	−	0.629695i
$438$		0			0
$439$	−3.23130e6	−	5.59677e6i	−0.800231	−	1.38604i	−0.919464	−	0.393175i	$-0.871377\pi$
$439$	−3.23130e6	−	5.59677e6i	−0.800231	−	1.38604i	0.119232	−	0.992866i	$-0.461957\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−877362.	−	1.51964e6i	−0.212407	−	0.367900i	0.740060	−	0.672541i	$-0.234797\pi$
$443$	−877362.	−	1.51964e6i	−0.212407	−	0.367900i	−0.952467	+	0.304640i	$0.901464\pi$
$444$		0			0
$445$	−169250.	+	293149.i	−0.0405162	+	0.0701761i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	515131.			0.120587			0.0602937	−	0.998181i	$-0.480796\pi$
$449$	515131.			0.120587			0.0602937	+	0.998181i	$0.480796\pi$
$450$		0			0
$451$	7.02006e6			1.62517
$452$		0			0
$453$		0			0
$454$		0			0
$455$	167209.	−	289614.i	0.0378644	−	0.0655830i
$456$		0			0
$457$	2.46694e6	+	4.27287e6i	0.552546	+	0.957038i	0.998090	+	0.0617782i	$0.0196771\pi$
$457$	2.46694e6	+	4.27287e6i	0.552546	+	0.957038i	−0.445543	+	0.895260i	$0.646990\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.12932e6	+	7.15219e6i	0.904953	+	1.56742i	0.820981	+	0.570956i	$0.193427\pi$
$461$	4.12932e6	+	7.15219e6i	0.904953	+	1.56742i	0.0839718	+	0.996468i	$0.473239\pi$
$462$		0			0
$463$	1.09543e6	−	1.89734e6i	0.237482	−	0.411331i	−0.722509	−	0.691362i	$-0.757011\pi$
$463$	1.09543e6	−	1.89734e6i	0.237482	−	0.411331i	0.959991	+	0.280030i	$0.0903445\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.29374e6			0.486691			0.243345	−	0.969940i	$-0.421755\pi$
$467$	2.29374e6			0.486691			0.243345	+	0.969940i	$0.421755\pi$
$468$		0			0
$469$	−4.92046e6			−1.03294
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.28183e6	−	5.68429e6i	0.674471	−	1.16822i
$474$		0			0
$475$	2.65698e6	+	4.60203e6i	0.540324	+	0.935869i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−46443.2	−	80442.0i	−0.00924876	−	0.0160193i	0.861364	−	0.507988i	$-0.169611\pi$
$479$	−46443.2	−	80442.0i	−0.00924876	−	0.0160193i	−0.870613	+	0.491969i	$0.836277\pi$
$480$		0			0
$481$	751522.	−	1.30168e6i	0.148108	−	0.256531i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	157392.			0.0303828
$486$		0			0
$487$	1.13899e6			0.217620			0.108810	−	0.994063i	$-0.465296\pi$
$487$	1.13899e6			0.217620			0.108810	+	0.994063i	$0.465296\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.36473e6	−	7.55993e6i	0.817060	−	1.41519i	−0.0907800	−	0.995871i	$-0.528936\pi$
$491$	4.36473e6	−	7.55993e6i	0.817060	−	1.41519i	0.907840	−	0.419318i	$-0.137731\pi$
$492$		0			0
$493$	−530498.	−	918849.i	−0.0983029	−	0.170266i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.36685e6	+	9.29566e6i	0.974605	+	1.68807i
$498$		0			0
$499$	−738810.	+	1.27966e6i	−0.132825	+	0.230061i	−0.924765	−	0.380539i	$-0.875738\pi$
$499$	−738810.	+	1.27966e6i	−0.132825	+	0.230061i	0.791939	+	0.610600i	$0.209072\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−743514.			−0.131029			−0.0655147	−	0.997852i	$-0.520869\pi$
$503$	−743514.			−0.131029			−0.0655147	+	0.997852i	$0.520869\pi$
$504$		0			0
$505$	−1.82610e6			−0.318638
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.43560e6	+	7.68269e6i	−0.758854	+	1.31437i	0.184582	+	0.982817i	$0.440907\pi$
$509$	−4.43560e6	+	7.68269e6i	−0.758854	+	1.31437i	−0.943435	+	0.331556i	$0.892426\pi$
$510$		0			0
$511$	4.18926e6	+	7.25600e6i	0.709716	+	1.22926i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−823419.	−	1.42620e6i	−0.136805	−	0.236954i
$516$		0			0
$517$	−7.67214e6	+	1.32885e7i	−1.26238	+	2.18651i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.00935e6			0.324311			0.162155	−	0.986765i	$-0.448155\pi$
$521$	2.00935e6			0.324311			0.162155	+	0.986765i	$0.448155\pi$
$522$		0			0
$523$	−6.39895e6			−1.02295			−0.511475	−	0.859298i	$-0.670901\pi$
$523$	−6.39895e6			−1.02295			−0.511475	+	0.859298i	$0.670901\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.12239e6	+	1.94403e6i	−0.176042	+	0.304914i
$528$		0			0
$529$	1.84886e6	+	3.20231e6i	0.287253	+	0.497536i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.34580e6	−	2.33100e6i	−0.205193	−	0.355405i
$534$		0			0
$535$	−757696.	+	1.31237e6i	−0.114449	+	0.198231i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.22247e6			0.181245
$540$		0			0
$541$	−1.26335e7			−1.85580			−0.927899	−	0.372832i	$-0.878387\pi$
$541$	−1.26335e7			−1.85580			−0.927899	+	0.372832i	$0.878387\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	563096.	−	975311.i	0.0812066	−	0.140654i
$546$		0			0
$547$	−5.51776e6	−	9.55704e6i	−0.788487	−	1.36570i	−0.926894	−	0.375323i	$-0.877532\pi$
$547$	−5.51776e6	−	9.55704e6i	−0.788487	−	1.36570i	0.138407	−	0.990375i	$-0.455802\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.72548e6	+	6.45273e6i	0.522762	+	0.905450i
$552$		0			0
$553$	−1.87851e6	+	3.25367e6i	−0.261216	+	0.452440i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.08374e7			1.48009			0.740046	−	0.672557i	$-0.234804\pi$
$557$	1.08374e7			1.48009			0.740046	+	0.672557i	$0.234804\pi$
$558$		0			0
$559$	−2.51661e6			−0.340633
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.65688e6	−	2.86981e6i	0.220303	−	0.381577i	−0.734597	−	0.678504i	$-0.762629\pi$
$563$	1.65688e6	−	2.86981e6i	0.220303	−	0.381577i	0.954900	+	0.296927i	$0.0959619\pi$
$564$		0			0
$565$	612421.	+	1.06074e6i	0.0807103	+	0.139794i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−774757.	−	1.34192e6i	−0.100319	−	0.173758i	0.811497	−	0.584357i	$-0.198653\pi$
$569$	−774757.	−	1.34192e6i	−0.100319	−	0.173758i	−0.911816	+	0.410599i	$0.865320\pi$
$570$		0			0
$571$	1.59557e6	−	2.76361e6i	0.204798	−	0.354720i	−0.745271	−	0.666762i	$-0.767680\pi$
$571$	1.59557e6	−	2.76361e6i	0.204798	−	0.354720i	0.950068	+	0.312042i	$0.101013\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	5.01359e6			0.632381
$576$		0			0
$577$	9.55234e6			1.19446			0.597228	−	0.802072i	$-0.296269\pi$
$577$	9.55234e6			1.19446			0.597228	+	0.802072i	$0.296269\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.42848e6	+	7.67035e6i	−0.544270	+	0.942704i
$582$		0			0
$583$	3.07431e6	+	5.32487e6i	0.374608	+	0.648840i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.64410e6	+	9.77587e6i	0.676083	+	1.17101i	0.976151	+	0.217092i	$0.0696571\pi$
$587$	5.64410e6	+	9.77587e6i	0.676083	+	1.17101i	−0.300069	+	0.953918i	$0.597010\pi$
$588$		0			0
$589$	7.88210e6	−	1.36522e7i	0.936168	−	1.62149i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.91815e6			0.924671			0.462336	−	0.886705i	$-0.347012\pi$
$593$	7.91815e6			0.924671			0.462336	+	0.886705i	$0.347012\pi$
$594$		0			0
$595$	333449.			0.0386133
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.60914e6	−	2.78711e6i	0.183242	−	0.317385i	−0.759740	−	0.650227i	$-0.774674\pi$
$599$	1.60914e6	−	2.78711e6i	0.183242	−	0.317385i	0.942983	+	0.332841i	$0.108007\pi$
$600$		0			0
$601$	3.74304e6	+	6.48314e6i	0.422706	+	0.732149i	0.996203	−	0.0870589i	$-0.0277468\pi$
$601$	3.74304e6	+	6.48314e6i	0.422706	+	0.732149i	−0.573497	+	0.819208i	$0.694414\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.29811e6	−	2.24840e6i	−0.144186	−	0.249738i
$606$		0			0
$607$	−5.06061e6	+	8.76524e6i	−0.557483	+	0.965588i	0.440223	+	0.897888i	$0.354899\pi$
$607$	−5.06061e6	+	8.76524e6i	−0.557483	+	0.965588i	−0.997706	+	0.0676999i	$0.978434\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.88325e6			0.637550
$612$		0			0
$613$	−4.34715e6			−0.467254			−0.233627	−	0.972326i	$-0.575059\pi$
$613$	−4.34715e6			−0.467254			−0.233627	+	0.972326i	$0.575059\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.29590e6	−	1.61010e7i	0.983056	−	1.70270i	0.332781	−	0.943004i	$-0.392013\pi$
$617$	9.29590e6	−	1.61010e7i	0.983056	−	1.70270i	0.650275	−	0.759699i	$-0.274654\pi$
$618$		0			0
$619$	6.83014e6	+	1.18301e7i	0.716478	+	1.24098i	0.962387	+	0.271683i	$0.0875802\pi$
$619$	6.83014e6	+	1.18301e7i	0.716478	+	1.24098i	−0.245909	+	0.969293i	$0.579086\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.36794e6	+	4.10139e6i	0.244428	+	0.423361i
$624$		0			0
$625$	−4.44007e6	+	7.69043e6i	−0.454663	+	0.787500i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.49869e6			0.151038
$630$		0			0
$631$	3.33121e6			0.333065			0.166532	−	0.986036i	$-0.446743\pi$
$631$	3.33121e6			0.333065			0.166532	+	0.986036i	$0.446743\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	85275.4	−	147701.i	0.00839246	−	0.0145362i
$636$		0			0
$637$	−234358.	−	405919.i	−0.0228839	−	0.0396361i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.14477e6	+	1.98280e6i	0.110046	+	0.190604i	0.915788	−	0.401661i	$-0.131567\pi$
$641$	1.14477e6	+	1.98280e6i	0.110046	+	0.190604i	−0.805743	+	0.592266i	$0.798234\pi$
$642$		0			0
$643$	−3.40519e6	+	5.89797e6i	−0.324799	+	0.562568i	−0.981472	−	0.191608i	$-0.938630\pi$
$643$	−3.40519e6	+	5.89797e6i	−0.324799	+	0.562568i	0.656673	+	0.754176i	$0.271963\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.48250e7			−1.39231			−0.696153	−	0.717894i	$-0.745106\pi$
$647$	−1.48250e7			−1.39231			−0.696153	+	0.717894i	$0.745106\pi$
$648$		0			0
$649$	2.88551e7			2.68912
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.06356e6	+	7.03829e6i	−0.372927	+	0.645928i	−0.990014	−	0.140966i	$-0.954979\pi$
$653$	−4.06356e6	+	7.03829e6i	−0.372927	+	0.645928i	0.617088	+	0.786894i	$0.288312\pi$
$654$		0			0
$655$	141291.	+	244723.i	0.0128680	+	0.0222880i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.07616e6	+	7.06011e6i	0.365626	+	0.633283i	0.988876	−	0.148739i	$-0.0475215\pi$
$659$	4.07616e6	+	7.06011e6i	0.365626	+	0.633283i	−0.623250	+	0.782023i	$0.714188\pi$
$660$		0			0
$661$	4.37958e6	−	7.58565e6i	0.389878	−	0.675288i	−0.602555	−	0.798077i	$-0.705851\pi$
$661$	4.37958e6	−	7.58565e6i	0.389878	−	0.675288i	0.992433	+	0.122789i	$0.0391839\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.34169e6			−0.205341
$666$		0			0
$667$	7.02980e6			0.611827
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.31878e6	−	1.26765e7i	0.627527	−	1.08691i
$672$		0			0
$673$	−4.26745e6	−	7.39143e6i	−0.363187	−	0.629058i	0.625296	−	0.780387i	$-0.284978\pi$
$673$	−4.26745e6	−	7.39143e6i	−0.363187	−	0.629058i	−0.988483	+	0.151329i	$0.951645\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.58162e6	−	1.31317e7i	−0.635755	−	1.10116i	−0.986355	−	0.164635i	$-0.947355\pi$
$677$	−7.58162e6	−	1.31317e7i	−0.635755	−	1.10116i	0.350599	−	0.936526i	$-0.385978\pi$
$678$		0			0
$679$	1.10102e6	−	1.90702e6i	0.0916473	−	0.158738i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.33221e7			−1.09275			−0.546376	−	0.837540i	$-0.683993\pi$
$683$	−1.33221e7			−1.09275			−0.546376	+	0.837540i	$0.683993\pi$
$684$		0			0
$685$	−3.99094e6			−0.324974
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.17874e6	−	2.04164e6i	0.0945956	−	0.163844i
$690$		0			0
$691$	−981739.	−	1.70042e6i	−0.0782169	−	0.135476i	0.824264	−	0.566206i	$-0.191589\pi$
$691$	−981739.	−	1.70042e6i	−0.0782169	−	0.135476i	−0.902481	+	0.430730i	$0.858256\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.41230e6	+	2.44617e6i	0.110908	+	0.192099i
$696$		0			0
$697$	1.34190e6	−	2.32425e6i	0.104626	−	0.181217i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.36605e7			−1.81856			−0.909282	−	0.416180i	$-0.863369\pi$
$701$	−2.36605e7			−1.81856			−0.909282	+	0.416180i	$0.863369\pi$
$702$		0			0
$703$	−1.05247e7			−0.803199
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.27743e7	+	2.21257e7i	−0.961145	+	1.66475i
$708$		0			0
$709$	8.39194e6	+	1.45353e7i	0.626970	+	1.08594i	0.988156	+	0.153451i	$0.0490386\pi$
$709$	8.39194e6	+	1.45353e7i	0.626970	+	1.08594i	−0.361186	+	0.932494i	$0.617628\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.43656e6	−	1.28805e7i	−0.547833	−	0.948875i
$714$		0			0
$715$	−799317.	+	1.38446e6i	−0.0584728	+	0.101278i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.89621e6			−0.425355			−0.212677	−	0.977123i	$-0.568218\pi$
$719$	−5.89621e6			−0.425355			−0.212677	+	0.977123i	$0.568218\pi$
$720$		0			0
$721$	−2.30405e7			−1.65065
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.43470e6	+	1.11452e7i	−0.454656	+	0.787488i
$726$		0			0
$727$	−5.15459e6	−	8.92800e6i	−0.361708	−	0.626496i	0.626534	−	0.779394i	$-0.284473\pi$
$727$	−5.15459e6	−	8.92800e6i	−0.361708	−	0.626496i	−0.988242	+	0.152898i	$0.951139\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.25466e6	−	2.17314e6i	−0.0868427	−	0.150416i
$732$		0			0
$733$	−7.66868e6	+	1.32825e7i	−0.527182	+	0.913106i	0.472316	+	0.881429i	$0.343418\pi$
$733$	−7.66868e6	+	1.32825e7i	−0.527182	+	0.913106i	−0.999498	+	0.0316768i	$0.989915\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.35215e7			1.59513
$738$		0			0
$739$	1.97929e6			0.133321			0.0666606	−	0.997776i	$-0.478766\pi$
$739$	1.97929e6			0.133321			0.0666606	+	0.997776i	$0.478766\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.44874e7	−	2.50929e7i	0.962758	−	1.66755i	0.247238	−	0.968955i	$-0.420477\pi$
$743$	1.44874e7	−	2.50929e7i	0.962758	−	1.66755i	0.715520	−	0.698592i	$-0.246190\pi$
$744$		0			0
$745$	−1657.44	−	2870.77i	−0.000109407	−	0.000189499i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.06008e7	+	1.83611e7i	0.690450	+	1.19589i
$750$		0			0
$751$	5.21827e6	−	9.03831e6i	0.337619	−	0.584773i	−0.646366	−	0.763028i	$-0.723712\pi$
$751$	5.21827e6	−	9.03831e6i	0.337619	−	0.584773i	0.983984	+	0.178255i	$0.0570452\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.49196e6			−0.222947
$756$		0			0
$757$	1.51464e7			0.960661			0.480331	−	0.877087i	$-0.340517\pi$
$757$	1.51464e7			0.960661			0.480331	+	0.877087i	$0.340517\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.10900e7	+	1.92084e7i	−0.694176	+	1.20235i	0.276282	+	0.961077i	$0.410898\pi$
$761$	−1.10900e7	+	1.92084e7i	−0.694176	+	1.20235i	−0.970458	+	0.241271i	$0.922436\pi$
$762$		0			0
$763$	−7.87815e6	−	1.36454e7i	−0.489906	−	0.848542i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.53175e6	−	9.58127e6i	−0.339527	−	0.588078i
$768$		0			0
$769$	3.21191e6	−	5.56319e6i	0.195861	−	0.339241i	−0.751322	−	0.659936i	$-0.770583\pi$
$769$	3.21191e6	−	5.56319e6i	0.195861	−	0.339241i	0.947182	+	0.320695i	$0.103917\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.34346e6			−0.141062			−0.0705308	−	0.997510i	$-0.522469\pi$
$773$	−2.34346e6			−0.141062			−0.0705308	+	0.997510i	$0.522469\pi$
$774$		0			0
$775$	2.72281e7			1.62841
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.42368e6	+	1.63223e7i	−0.556387	+	0.963690i
$780$		0			0
$781$	−2.56554e7	−	4.44365e7i	−1.50505	−	2.60683i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3675.97	+	6366.96i	0.000212911	+	0.000368772i
$786$		0			0
$787$	1.42540e7	−	2.46887e7i	0.820354	−	1.42089i	−0.0850650	−	0.996375i	$-0.527110\pi$
$787$	1.42540e7	−	2.46887e7i	0.820354	−	1.42089i	0.905419	−	0.424519i	$-0.139557\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.71365e7			0.973824
$792$		0			0
$793$	−5.61228e6			−0.316925
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.77498e6	−	6.53845e6i	0.210508	−	0.364611i	−0.741366	−	0.671101i	$-0.765822\pi$
$797$	3.77498e6	−	6.53845e6i	0.210508	−	0.364611i	0.951874	+	0.306491i	$0.0991549\pi$
$798$		0			0
$799$	2.93310e6	+	5.08028e6i	0.162540	+	0.281528i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.00261e7	−	3.46862e7i	−1.09599	−	1.89831i
$804$		0			0
$805$	−1.10466e6	+	1.91333e6i	−0.0600813	+	0.104064i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.98225e6			−0.321361			−0.160680	−	0.987006i	$-0.551369\pi$
$809$	−5.98225e6			−0.321361			−0.160680	+	0.987006i	$0.551369\pi$
$810$		0			0
$811$	−9.22339e6			−0.492423			−0.246212	−	0.969216i	$-0.579186\pi$
$811$	−9.22339e6			−0.492423			−0.246212	+	0.969216i	$0.579186\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.75093e6	+	3.03271e6i	−0.0923370	+	0.159932i
$816$		0			0
$817$	8.81101e6	+	1.52611e7i	0.461818	+	0.799892i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.48011e6	+	1.12239e7i	0.335525	+	0.581146i	0.983585	−	0.180443i	$-0.0577531\pi$
$821$	6.48011e6	+	1.12239e7i	0.335525	+	0.581146i	−0.648061	+	0.761589i	$0.724420\pi$
$822$		0			0
$823$	−3.76675e6	+	6.52421e6i	−0.193851	+	0.335759i	−0.946523	−	0.322636i	$-0.895431\pi$
$823$	−3.76675e6	+	6.52421e6i	−0.193851	+	0.335759i	0.752672	+	0.658395i	$0.228764\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.59694e7			0.811942			0.405971	−	0.913886i	$-0.366933\pi$
$827$	1.59694e7			0.811942			0.405971	+	0.913886i	$0.366933\pi$
$828$		0			0
$829$	−2.71049e7			−1.36981			−0.684907	−	0.728631i	$-0.740157\pi$
$829$	−2.71049e7			−1.36981			−0.684907	+	0.728631i	$0.740157\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	233679.	−	404743.i	0.0116683	−	0.0202100i
$834$		0			0
$835$	2.41159e6	+	4.17699e6i	0.119698	+	0.207323i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.38138e7	−	2.39261e7i	−0.677497	−	1.17346i	−0.975732	−	0.218967i	$-0.929731\pi$
$839$	−1.38138e7	−	2.39261e7i	−0.677497	−	1.17346i	0.298236	−	0.954492i	$-0.403602\pi$
$840$		0			0
$841$	1.23316e6	−	2.13590e6i	0.0601216	−	0.104134i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.01401e6			−0.145212
$846$		0			0
$847$	−3.63233e7			−1.73971
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.96491e6	+	8.59948e6i	−0.235011	+	0.407050i
$852$		0			0
$853$	9.66982e6	+	1.67486e7i	0.455036	+	0.788145i	0.998690	−	0.0511638i	$-0.0162931\pi$
$853$	9.66982e6	+	1.67486e7i	0.455036	+	0.788145i	−0.543654	+	0.839309i	$0.682960\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.37449e7	−	2.38068e7i	−0.639277	−	1.10726i	−0.985592	−	0.169142i	$-0.945900\pi$
$857$	−1.37449e7	−	2.38068e7i	−0.639277	−	1.10726i	0.346315	−	0.938118i	$-0.387433\pi$
$858$		0			0
$859$	2.33195e6	−	4.03905e6i	0.107829	−	0.186765i	−0.807061	−	0.590467i	$-0.798943\pi$
$859$	2.33195e6	−	4.03905e6i	0.107829	−	0.186765i	0.914891	+	0.403702i	$0.132277\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.10059e6			−0.141716			−0.0708578	−	0.997486i	$-0.522574\pi$
$863$	−3.10059e6			−0.141716			−0.0708578	+	0.997486i	$0.522574\pi$
$864$		0			0
$865$	−1.63962e6			−0.0745082
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.97993e6	−	1.55537e7i	0.403388	−	0.698689i
$870$		0			0
$871$	−4.50927e6	−	7.81028e6i	−0.201400	−	0.348836i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.10829e6	−	7.11576e6i	−0.181401	−	0.314196i
$876$		0			0
$877$	8.22715e6	−	1.42498e7i	0.361202	−	0.625621i	−0.626957	−	0.779054i	$-0.715700\pi$
$877$	8.22715e6	−	1.42498e7i	0.361202	−	0.625621i	0.988159	+	0.153433i	$0.0490330\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.06332e6			−0.0895626			−0.0447813	−	0.998997i	$-0.514259\pi$
$881$	−2.06332e6			−0.0895626			−0.0447813	+	0.998997i	$0.514259\pi$
$882$		0			0
$883$	2.00336e7			0.864683			0.432342	−	0.901710i	$-0.357687\pi$
$883$	2.00336e7			0.864683			0.432342	+	0.901710i	$0.357687\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.41621e7	+	2.45295e7i	−0.604393	+	1.04684i	0.387754	+	0.921763i	$0.373251\pi$
$887$	−1.41621e7	+	2.45295e7i	−0.604393	+	1.04684i	−0.992147	+	0.125077i	$0.960082\pi$
$888$		0			0
$889$	−1.19307e6	−	2.06646e6i	−0.0506304	−	0.0876944i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.05981e7	−	3.56769e7i	−0.864366	−	1.49713i
$894$		0			0
$895$	2.36329e6	−	4.09334e6i	0.0986187	−	0.170813i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.81779e7			1.57548
$900$		0			0
$901$	2.35066e6			0.0964666
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−365009.	+	632214.i	−0.0148143	+	0.0256592i
$906$		0			0
$907$	−1.40375e7	−	2.43137e7i	−0.566593	−	0.981369i	−0.996899	−	0.0786856i	$-0.974928\pi$
$907$	−1.40375e7	−	2.43137e7i	−0.566593	−	0.981369i	0.430306	−	0.902683i	$-0.358406\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.35864e7	+	2.35324e7i	0.542387	+	0.939443i	0.998766	+	0.0496571i	$0.0158129\pi$
$911$	1.35864e7	+	2.35324e7i	0.542387	+	0.939443i	−0.456379	+	0.889786i	$0.650854\pi$
$912$		0			0
$913$	2.11697e7	−	3.66670e7i	0.840499	−	1.45579i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.95354e6			0.155261
$918$		0			0
$919$	−4.48360e7			−1.75121			−0.875604	−	0.483029i	$-0.839536\pi$
$919$	−4.48360e7			−1.75121			−0.875604	+	0.483029i	$0.839536\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.83670e6	+	1.70377e7i	−0.380054	+	0.658273i
$924$		0			0
$925$	−9.08923e6	−	1.57430e7i	−0.349279	−	0.604969i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−786592.	−	1.36242e6i	−0.0299027	−	0.0517930i	0.850687	−	0.525673i	$-0.176186\pi$
$929$	−786592.	−	1.36242e6i	−0.0299027	−	0.0517930i	−0.880589	+	0.473880i	$0.842853\pi$
$930$		0			0
$931$	−1.64104e6	+	2.84236e6i	−0.0620503	+	0.107474i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.59400e6			−0.0596293
$936$		0			0
$937$	2.08278e6			0.0774986			0.0387493	−	0.999249i	$-0.487663\pi$
$937$	2.08278e6			0.0774986			0.0387493	+	0.999249i	$0.487663\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.15451e6	+	7.19583e6i	−0.152949	+	0.264915i	−0.932310	−	0.361659i	$-0.882210\pi$
$941$	−4.15451e6	+	7.19583e6i	−0.152949	+	0.264915i	0.779361	+	0.626575i	$0.215544\pi$
$942$		0			0
$943$	8.89100e6	+	1.53997e7i	0.325590	+	0.563939i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.34570e7	−	4.06287e7i	−0.849958	−	1.47217i	−0.881245	−	0.472659i	$-0.843294\pi$
$947$	−2.34570e7	−	4.06287e7i	−0.849958	−	1.47217i	0.0312875	−	0.999510i	$-0.490039\pi$
$948$		0			0
$949$	−7.67833e6	+	1.32993e7i	−0.276759	+	0.479360i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.19875e7			−0.427559			−0.213779	−	0.976882i	$-0.568577\pi$
$953$	−1.19875e7			−0.427559			−0.213779	+	0.976882i	$0.568577\pi$
$954$		0			0
$955$	−5.80500e6			−0.205965
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.79182e7	+	4.83557e7i	−0.980258	+	1.69786i
$960$		0			0
$961$	−2.60724e7	−	4.51587e7i	−0.910693	−	1.57737i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	439090.	+	760525.i	0.0151787	+	0.0262903i
$966$		0			0
$967$	−1.44190e7	+	2.49745e7i	−0.495872	+	0.858876i	−0.999989	−	0.00475965i	$-0.998485\pi$
$967$	−1.44190e7	+	2.49745e7i	−0.495872	+	0.858876i	0.504116	+	0.863636i	$0.331818\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.30199e7			0.443158			0.221579	−	0.975142i	$-0.428879\pi$
$971$	1.30199e7			0.443158			0.221579	+	0.975142i	$0.428879\pi$
$972$		0			0
$973$	3.95182e7			1.33818
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.14539e6	+	1.58403e7i	−0.306525	+	0.530917i	−0.977600	−	0.210473i	$-0.932500\pi$
$977$	−9.14539e6	+	1.58403e7i	−0.306525	+	0.530917i	0.671075	+	0.741390i	$0.265833\pi$
$978$		0			0
$979$	−1.13196e7	−	1.96061e7i	−0.377462	−	0.653783i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−484901.	−	839872.i	−0.0160055	−	0.0277223i	0.857912	−	0.513797i	$-0.171762\pi$
$983$	−484901.	−	839872.i	−0.0160055	−	0.0277223i	−0.873917	+	0.486075i	$0.838428\pi$
$984$		0			0
$985$	2.07658e6	−	3.59674e6i	0.0681959	−	0.118119i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.66259e7			0.540500
$990$		0			0
$991$	5.04589e7			1.63213			0.816063	−	0.577962i	$-0.196152\pi$
$991$	5.04589e7			1.63213			0.816063	+	0.577962i	$0.196152\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.82835e6	−	3.16680e6i	0.0585467	−	0.101406i
$996$		0			0
$997$	−8.90625e6	−	1.54261e7i	−0.283764	−	0.491493i	0.688545	−	0.725194i	$-0.258250\pi$
$997$	−8.90625e6	−	1.54261e7i	−0.283764	−	0.491493i	−0.972309	+	0.233700i	$0.924917\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.6.i.d.145.3		10
3.2	odd	2		144.6.i.d.49.4		10
4.3	odd	2		108.6.e.a.37.3		10
9.2	odd	6		144.6.i.d.97.4		10
9.7	even	3	inner	432.6.i.d.289.3		10
12.11	even	2		36.6.e.a.13.2	✓	10
36.7	odd	6		108.6.e.a.73.3		10
36.11	even	6		36.6.e.a.25.2	yes	10
36.23	even	6		324.6.a.e.1.3		5
36.31	odd	6		324.6.a.d.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.e.a.13.2	✓	10	12.11	even	2
36.6.e.a.25.2	yes	10	36.11	even	6
108.6.e.a.37.3		10	4.3	odd	2
108.6.e.a.73.3		10	36.7	odd	6
144.6.i.d.49.4		10	3.2	odd	2
144.6.i.d.97.4		10	9.2	odd	6
324.6.a.d.1.3		5	36.31	odd	6
324.6.a.e.1.3		5	36.23	even	6
432.6.i.d.145.3		10	1.1	even	1	trivial
432.6.i.d.289.3		10	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.88422 + 8.45972i) q^{5} +(68.3340 + 118.358i) q^{7} +O(q^{10})\)	\(q+(-4.88422 + 8.45972i) q^{5} +(68.3340 + 118.358i) q^{7} +(-326.660 - 565.792i) q^{11} +(-125.247 + 216.934i) q^{13} -249.768 q^{17} +1754.03 q^{19} +(827.440 - 1433.17i) q^{23} +(1514.79 + 2623.69i) q^{25} +(2123.96 + 3678.81i) q^{29} +(4493.72 - 7783.34i) q^{31} -1335.03 q^{35} -6000.33 q^{37} +(-5372.59 + 9305.61i) q^{41} +(5023.30 + 8700.62i) q^{43} +(-11743.3 - 20340.0i) q^{47} +(-935.582 + 1620.48i) q^{49} -9411.34 q^{53} +6381.93 q^{55} +(-22083.4 + 38249.5i) q^{59} +(11202.4 + 19403.2i) q^{61} +(-1223.47 - 2119.11i) q^{65} +(-18001.5 + 31179.5i) q^{67} +78538.5 q^{71} +61305.5 q^{73} +(44644.1 - 77325.8i) q^{77} +(13745.0 + 23807.1i) q^{79} +(32403.2 + 56124.0i) q^{83} +(1219.92 - 2112.97i) q^{85} +34652.4 q^{89} -34234.5 q^{91} +(-8567.06 + 14838.6i) q^{95} +(-8056.14 - 13953.6i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 21 q^{5} - 29 q^{7}+O(q^{10}) \) 10 * q + 21 * q^5 - 29 * q^7	\( 10 q + 21 q^{5} - 29 q^{7} + 177 q^{11} - 181 q^{13} - 2280 q^{17} + 832 q^{19} + 399 q^{23} - 4778 q^{25} + 6033 q^{29} - 2759 q^{31} + 37146 q^{35} - 15172 q^{37} + 18435 q^{41} - 1469 q^{43} - 25155 q^{47} - 4056 q^{49} - 116844 q^{53} - 14778 q^{55} - 90537 q^{59} + 1403 q^{61} + 148407 q^{65} - 13907 q^{67} + 229368 q^{71} + 15200 q^{73} + 211983 q^{77} - 29993 q^{79} - 228951 q^{83} - 49662 q^{85} - 598332 q^{89} - 124930 q^{91} - 394764 q^{95} + 40541 q^{97}+O(q^{100}) \) 10 * q + 21 * q^5 - 29 * q^7 + 177 * q^11 - 181 * q^13 - 2280 * q^17 + 832 * q^19 + 399 * q^23 - 4778 * q^25 + 6033 * q^29 - 2759 * q^31 + 37146 * q^35 - 15172 * q^37 + 18435 * q^41 - 1469 * q^43 - 25155 * q^47 - 4056 * q^49 - 116844 * q^53 - 14778 * q^55 - 90537 * q^59 + 1403 * q^61 + 148407 * q^65 - 13907 * q^67 + 229368 * q^71 + 15200 * q^73 + 211983 * q^77 - 29993 * q^79 - 228951 * q^83 - 49662 * q^85 - 598332 * q^89 - 124930 * q^91 - 394764 * q^95 + 40541 * q^97

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