LMFDB - Embedded newform 1600.2.l.h.1201.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (of order $4$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1201.5
Root			$-1.32661 - 0.490008i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.h.401.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.183790 - 0.183790i) q^{3} -3.84853i q^{7} +2.93244i q^{9} +O(q^{10})$	$q+(0.183790 - 0.183790i) q^{3} -3.84853i q^{7} +2.93244i q^{9} +(-1.60020 - 1.60020i) q^{11} +(-1.80775 + 1.80775i) q^{13} -4.93886 q^{17} +(-4.77162 + 4.77162i) q^{19} +(-0.707323 - 0.707323i) q^{21} +0.134544i q^{23} +(1.09033 + 1.09033i) q^{27} +(-2.17142 + 2.17142i) q^{29} -2.26371 q^{31} -0.588201 q^{33} +(4.35066 + 4.35066i) q^{37} +0.664493i q^{39} +3.34709i q^{41} +(-2.70896 - 2.70896i) q^{43} +7.03343 q^{47} -7.81119 q^{49} +(-0.907714 + 0.907714i) q^{51} +(3.40020 + 3.40020i) q^{53} +1.75396i q^{57} +(-0.107127 - 0.107127i) q^{59} +(-3.46410 + 3.46410i) q^{61} +11.2856 q^{63} +(-1.91078 + 1.91078i) q^{67} +(0.0247279 + 0.0247279i) q^{69} +9.32899i q^{71} -9.82769i q^{73} +(-6.15840 + 6.15840i) q^{77} -11.0073 q^{79} -8.39654 q^{81} +(-8.80967 + 8.80967i) q^{83} +0.798174i q^{87} -1.12125i q^{89} +(6.95717 + 6.95717i) q^{91} +(-0.416048 + 0.416048i) q^{93} +6.10461 q^{97} +(4.69248 - 4.69248i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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			0
$2$		0			0
$3$	0.183790	−	0.183790i	0.106111	−	0.106111i	−0.652058	−	0.758169i	$-0.726094\pi$
$3$	0.183790	−	0.183790i	0.106111	−	0.106111i	0.758169	+	0.652058i	$0.226094\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	3.84853i		−	1.45461i	−0.686315	−	0.727304i	$-0.740773\pi$
$7$		−	3.84853i		−	1.45461i	0.686315	−	0.727304i	$-0.259227\pi$
$8$		0			0
$9$			2.93244i			0.977481i
$10$		0			0
$11$	−1.60020	−	1.60020i	−0.482477	−	0.482477i	0.423445	−	0.905922i	$-0.360821\pi$
$11$	−1.60020	−	1.60020i	−0.482477	−	0.482477i	−0.905922	+	0.423445i	$0.860821\pi$
$12$		0			0
$13$	−1.80775	+	1.80775i	−0.501379	+	0.501379i	−0.911866	−	0.410487i	$-0.865359\pi$
$13$	−1.80775	+	1.80775i	−0.501379	+	0.501379i	0.410487	+	0.911866i	$0.365359\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.93886			−1.19785			−0.598924	−	0.800806i	$-0.704405\pi$
$17$	−4.93886			−1.19785			−0.598924	+	0.800806i	$0.704405\pi$
$18$		0			0
$19$	−4.77162	+	4.77162i	−1.09468	+	1.09468i	−0.0996636	+	0.995021i	$0.531777\pi$
$19$	−4.77162	+	4.77162i	−1.09468	+	1.09468i	−0.995021	+	0.0996636i	$0.968223\pi$
$20$		0			0
$21$	−0.707323	−	0.707323i	−0.154351	−	0.154351i
$22$		0			0
$23$			0.134544i			0.0280543i	0.999902	+	0.0140272i	$0.00446513\pi$
$23$			0.134544i			0.0280543i	−0.999902	+	0.0140272i	$0.995535\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.09033	+	1.09033i	0.209833	+	0.209833i
$28$		0			0
$29$	−2.17142	+	2.17142i	−0.403223	+	0.403223i	−0.879367	−	0.476144i	$-0.842034\pi$
$29$	−2.17142	+	2.17142i	−0.403223	+	0.403223i	0.476144	+	0.879367i	$0.342034\pi$
$30$		0			0
$31$	−2.26371			−0.406574			−0.203287	−	0.979119i	$-0.565163\pi$
$31$	−2.26371			−0.406574			−0.203287	+	0.979119i	$0.565163\pi$
$32$		0			0
$33$	−0.588201			−0.102393
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.35066	+	4.35066i	0.715243	+	0.715243i	0.967627	−	0.252384i	$-0.0812146\pi$
$37$	4.35066	+	4.35066i	0.715243	+	0.715243i	−0.252384	+	0.967627i	$0.581215\pi$
$38$		0			0
$39$			0.664493i			0.106404i
$40$		0			0
$41$			3.34709i			0.522727i	0.965240	+	0.261364i	$0.0841722\pi$
$41$			3.34709i			0.522727i	−0.965240	+	0.261364i	$0.915828\pi$
$42$		0			0
$43$	−2.70896	−	2.70896i	−0.413112	−	0.413112i	0.469709	−	0.882821i	$-0.344359\pi$
$43$	−2.70896	−	2.70896i	−0.413112	−	0.413112i	−0.882821	+	0.469709i	$0.844359\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.03343			1.02593			0.512966	−	0.858409i	$-0.328547\pi$
$47$	7.03343			1.02593			0.512966	+	0.858409i	$0.328547\pi$
$48$		0			0
$49$	−7.81119			−1.11588
$50$		0			0
$51$	−0.907714	+	0.907714i	−0.127105	+	0.127105i
$52$		0			0
$53$	3.40020	+	3.40020i	0.467053	+	0.467053i	0.900958	−	0.433905i	$-0.142865\pi$
$53$	3.40020	+	3.40020i	0.467053	+	0.467053i	−0.433905	+	0.900958i	$0.642865\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.75396i			0.232317i
$58$		0			0
$59$	−0.107127	−	0.107127i	−0.0139468	−	0.0139468i	0.700099	−	0.714046i	$-0.253139\pi$
$59$	−0.107127	−	0.107127i	−0.0139468	−	0.0139468i	−0.714046	+	0.700099i	$0.753139\pi$
$60$		0			0
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	−0.893197	−	0.449665i	$-0.851543\pi$
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	0.449665	+	0.893197i	$0.351543\pi$
$62$		0			0
$63$	11.2856			1.42185
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.91078	+	1.91078i	−0.233440	+	0.233440i	−0.814127	−	0.580687i	$-0.802784\pi$
$67$	−1.91078	+	1.91078i	−0.233440	+	0.233440i	0.580687	+	0.814127i	$0.302784\pi$
$68$		0			0
$69$	0.0247279	+	0.0247279i	0.00297689	+	0.00297689i
$70$		0			0
$71$			9.32899i			1.10715i	0.832800	+	0.553573i	$0.186736\pi$
$71$			9.32899i			1.10715i	−0.832800	+	0.553573i	$0.813264\pi$
$72$		0			0
$73$		−	9.82769i		−	1.15024i	−0.818068	−	0.575122i	$-0.804955\pi$
$73$		−	9.82769i		−	1.15024i	0.818068	−	0.575122i	$-0.195045\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.15840	+	6.15840i	−0.701815	+	0.701815i
$78$		0			0
$79$	−11.0073			−1.23842			−0.619211	−	0.785224i	$-0.712548\pi$
$79$	−11.0073			−1.23842			−0.619211	+	0.785224i	$0.712548\pi$
$80$		0			0
$81$	−8.39654			−0.932949
$82$		0			0
$83$	−8.80967	+	8.80967i	−0.966987	+	0.966987i	−0.999472	−	0.0324850i	$-0.989658\pi$
$83$	−8.80967	+	8.80967i	−0.966987	+	0.966987i	0.0324850	+	0.999472i	$0.489658\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			0.798174i			0.0855732i
$88$		0			0
$89$		−	1.12125i		−	0.118853i	−0.998233	−	0.0594263i	$-0.981073\pi$
$89$		−	1.12125i		−	0.118853i	0.998233	−	0.0594263i	$-0.0189271\pi$
$90$		0			0
$91$	6.95717	+	6.95717i	0.729310	+	0.729310i
$92$		0			0
$93$	−0.416048	+	0.416048i	−0.0431422	+	0.0431422i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.10461			0.619829			0.309915	−	0.950764i	$-0.399700\pi$
$97$	6.10461			0.619829			0.309915	+	0.950764i	$0.399700\pi$
$98$		0			0
$99$	4.69248	−	4.69248i	0.471612	−	0.471612i
$100$		0			0
$101$	2.17142	+	2.17142i	0.216065	+	0.216065i	0.806838	−	0.590773i	$-0.201177\pi$
$101$	2.17142	+	2.17142i	0.216065	+	0.216065i	−0.590773	+	0.806838i	$0.701177\pi$
$102$		0			0
$103$		−	15.3778i		−	1.51522i	−0.652707	−	0.757610i	$-0.726367\pi$
$103$		−	15.3778i		−	1.51522i	0.652707	−	0.757610i	$-0.273633\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.98419	−	6.98419i	−0.675187	−	0.675187i	0.283720	−	0.958907i	$-0.408431\pi$
$107$	−6.98419	−	6.98419i	−0.675187	−	0.675187i	−0.958907	+	0.283720i	$0.908431\pi$
$108$		0			0
$109$	−8.59694	+	8.59694i	−0.823437	+	0.823437i	−0.986599	−	0.163162i	$-0.947831\pi$
$109$	−8.59694	+	8.59694i	−0.823437	+	0.823437i	0.163162	+	0.986599i	$0.447831\pi$
$110$		0			0
$111$	1.59922			0.151791
$112$		0			0
$113$	−14.5329			−1.36714			−0.683572	−	0.729883i	$-0.739574\pi$
$113$	−14.5329			−1.36714			−0.683572	+	0.729883i	$0.739574\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.30111	−	5.30111i	−0.490088	−	0.490088i
$118$		0			0
$119$			19.0073i			1.74240i
$120$		0			0
$121$		−	5.87875i		−	0.534432i
$122$		0			0
$123$	0.615163	+	0.615163i	0.0554673	+	0.0554673i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.96617			−0.529412			−0.264706	−	0.964329i	$-0.585275\pi$
$127$	−5.96617			−0.529412			−0.264706	+	0.964329i	$0.585275\pi$
$128$		0			0
$129$	−0.995761			−0.0876719
$130$		0			0
$131$	−2.37084	+	2.37084i	−0.207141	+	0.207141i	−0.803051	−	0.595910i	$-0.796791\pi$
$131$	−2.37084	+	2.37084i	−0.207141	+	0.207141i	0.595910	+	0.803051i	$0.296791\pi$
$132$		0			0
$133$	18.3637	+	18.3637i	1.59234	+	1.59234i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	18.2745i		−	1.56129i	−0.624973	−	0.780646i	$-0.714890\pi$
$137$		−	18.2745i		−	1.56129i	0.624973	−	0.780646i	$-0.285110\pi$
$138$		0			0
$139$	−0.136094	−	0.136094i	−0.0115433	−	0.0115433i	0.701312	−	0.712855i	$-0.252598\pi$
$139$	−0.136094	−	0.136094i	−0.0115433	−	0.0115433i	−0.712855	+	0.701312i	$0.752598\pi$
$140$		0			0
$141$	1.29268	−	1.29268i	0.108863	−	0.108863i
$142$		0			0
$143$	5.78550			0.483808
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.43562	+	1.43562i	−0.118408	+	0.118408i
$148$		0			0
$149$	2.40078	+	2.40078i	0.196680	+	0.196680i	0.798575	−	0.601895i	$-0.205588\pi$
$149$	2.40078	+	2.40078i	0.196680	+	0.196680i	−0.601895	+	0.798575i	$0.705588\pi$
$150$		0			0
$151$		−	17.9935i		−	1.46429i	−0.681150	−	0.732144i	$-0.738520\pi$
$151$		−	17.9935i		−	1.46429i	0.681150	−	0.732144i	$-0.261480\pi$
$152$		0			0
$153$		−	14.4829i		−	1.17087i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.6359	−	12.6359i	1.00846	−	1.00846i	0.00849213	−	0.999964i	$-0.497297\pi$
$157$	12.6359	−	12.6359i	1.00846	−	1.00846i	0.999964	−	0.00849213i	$-0.00270316\pi$
$158$		0			0
$159$	1.24985			0.0991193
$160$		0			0
$161$	0.517796			0.0408081
$162$		0			0
$163$	−15.8470	+	15.8470i	−1.24123	+	1.24123i	−0.281743	+	0.959490i	$0.590913\pi$
$163$	−15.8470	+	15.8470i	−1.24123	+	1.24123i	−0.959490	+	0.281743i	$0.909087\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			12.7559i			0.987083i	0.869722	+	0.493541i	$0.164298\pi$
$167$			12.7559i			0.987083i	−0.869722	+	0.493541i	$0.835702\pi$
$168$		0			0
$169$			6.46410i			0.497239i
$170$		0			0
$171$	−13.9925	−	13.9925i	−1.07003	−	1.07003i
$172$		0			0
$173$	2.64673	−	2.64673i	0.201227	−	0.201227i	−0.599299	−	0.800525i	$-0.704554\pi$
$173$	2.64673	−	2.64673i	0.201227	−	0.201227i	0.800525	+	0.599299i	$0.204554\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.0393779			−0.00295983
$178$		0			0
$179$	−11.6497	+	11.6497i	−0.870736	+	0.870736i	−0.992553	−	0.121817i	$-0.961128\pi$
$179$	−11.6497	+	11.6497i	−0.870736	+	0.870736i	0.121817	+	0.992553i	$0.461128\pi$
$180$		0			0
$181$	1.24322	+	1.24322i	0.0924079	+	0.0924079i	0.751800	−	0.659392i	$-0.229186\pi$
$181$	1.24322	+	1.24322i	0.0924079	+	0.0924079i	−0.659392	+	0.751800i	$0.729186\pi$
$182$		0			0
$183$			1.27334i			0.0941278i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	7.90314	+	7.90314i	0.577935	+	0.577935i
$188$		0			0
$189$	4.19615	−	4.19615i	0.305225	−	0.305225i
$190$		0			0
$191$	−5.07180			−0.366982			−0.183491	−	0.983021i	$-0.558740\pi$
$191$	−5.07180			−0.366982			−0.183491	+	0.983021i	$0.558740\pi$
$192$		0			0
$193$	−2.30278			−0.165758			−0.0828788	−	0.996560i	$-0.526411\pi$
$193$	−2.30278			−0.165758			−0.0828788	+	0.996560i	$0.526411\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.06997	+	8.06997i	0.574961	+	0.574961i	0.933511	−	0.358549i	$-0.116729\pi$
$197$	8.06997	+	8.06997i	0.574961	+	0.574961i	−0.358549	+	0.933511i	$0.616729\pi$
$198$		0			0
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$		0			0
$201$			0.702368i			0.0495412i
$202$		0			0
$203$	8.35679	+	8.35679i	0.586532	+	0.586532i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.394542			−0.0274226
$208$		0			0
$209$	15.2711			1.05632
$210$		0			0
$211$	−0.478227	+	0.478227i	−0.0329225	+	0.0329225i	−0.723376	−	0.690454i	$-0.757411\pi$
$211$	−0.478227	+	0.478227i	−0.0329225	+	0.0329225i	0.690454	+	0.723376i	$0.257411\pi$
$212$		0			0
$213$	1.71458	+	1.71458i	0.117481	+	0.117481i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			8.71196i			0.591406i
$218$		0			0
$219$	−1.80623	−	1.80623i	−0.122054	−	0.122054i
$220$		0			0
$221$	8.92820	−	8.92820i	0.600576	−	0.600576i
$222$		0			0
$223$	7.50859			0.502813			0.251406	−	0.967882i	$-0.419107\pi$
$223$	7.50859			0.502813			0.251406	+	0.967882i	$0.419107\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.8788	+	12.8788i	−0.854798	+	0.854798i	−0.990720	−	0.135922i	$-0.956600\pi$
$227$	−12.8788	+	12.8788i	−0.854798	+	0.854798i	0.135922	+	0.990720i	$0.456600\pi$
$228$		0			0
$229$	−8.62166	−	8.62166i	−0.569736	−	0.569736i	0.362319	−	0.932054i	$-0.381985\pi$
$229$	−8.62166	−	8.62166i	−0.569736	−	0.569736i	−0.932054	+	0.362319i	$0.881985\pi$
$230$		0			0
$231$			2.26371i			0.148941i
$232$		0			0
$233$		−	4.63429i		−	0.303602i	−0.988411	−	0.151801i	$-0.951493\pi$
$233$		−	4.63429i		−	0.303602i	0.988411	−	0.151801i	$-0.0485073\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.02304	+	2.02304i	−0.131411	+	0.131411i
$238$		0			0
$239$	18.4220			1.19162			0.595810	−	0.803126i	$-0.296831\pi$
$239$	18.4220			1.19162			0.595810	+	0.803126i	$0.296831\pi$
$240$		0			0
$241$	18.3247			1.18040			0.590200	−	0.807257i	$-0.299049\pi$
$241$	18.3247			1.18040			0.590200	+	0.807257i	$0.299049\pi$
$242$		0			0
$243$	−4.81418	+	4.81418i	−0.308830	+	0.308830i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	17.2518i		−	1.09770i
$248$		0			0
$249$			3.23827i			0.205217i
$250$		0			0
$251$	16.0222	+	16.0222i	1.01131	+	1.01131i	0.999935	+	0.0113760i	$0.00362116\pi$
$251$	16.0222	+	16.0222i	1.01131	+	1.01131i	0.0113760	+	0.999935i	$0.496379\pi$
$252$		0			0
$253$	0.215297	−	0.215297i	0.0135356	−	0.0135356i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.82098			0.363103			0.181551	−	0.983381i	$-0.441888\pi$
$257$	5.82098			0.363103			0.181551	+	0.983381i	$0.441888\pi$
$258$		0			0
$259$	16.7436	−	16.7436i	1.04040	−	1.04040i
$260$		0			0
$261$	−6.36758	−	6.36758i	−0.394143	−	0.394143i
$262$		0			0
$263$		−	0.806693i		−	0.0497428i	−0.999691	−	0.0248714i	$-0.992082\pi$
$263$		−	0.806693i		−	0.0497428i	0.999691	−	0.0248714i	$-0.00791763\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.206075	−	0.206075i	−0.0126116	−	0.0126116i
$268$		0			0
$269$	15.1939	−	15.1939i	0.926387	−	0.926387i	−0.0710837	−	0.997470i	$-0.522646\pi$
$269$	15.1939	−	15.1939i	0.926387	−	0.926387i	0.997470	+	0.0710837i	$0.0226458\pi$
$270$		0			0
$271$	10.8491			0.659034			0.329517	−	0.944150i	$-0.393114\pi$
$271$	10.8491			0.659034			0.329517	+	0.944150i	$0.393114\pi$
$272$		0			0
$273$	2.55732			0.154776
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.27334	+	1.27334i	0.0765074	+	0.0765074i	0.744325	−	0.667818i	$-0.232771\pi$
$277$	1.27334	+	1.27334i	0.0765074	+	0.0765074i	−0.667818	+	0.744325i	$0.732771\pi$
$278$		0			0
$279$		−	6.63820i		−	0.397419i
$280$		0			0
$281$			20.2174i			1.20607i	0.797716	+	0.603033i	$0.206041\pi$
$281$			20.2174i			1.20607i	−0.797716	+	0.603033i	$0.793959\pi$
$282$		0			0
$283$	−21.3741	−	21.3741i	−1.27056	−	1.27056i	−0.945797	−	0.324759i	$-0.894717\pi$
$283$	−21.3741	−	21.3741i	−1.27056	−	1.27056i	−0.324759	−	0.945797i	$-0.605283\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.8814			0.760363
$288$		0			0
$289$	7.39230			0.434841
$290$		0			0
$291$	1.12197	−	1.12197i	0.0657710	−	0.0657710i
$292$		0			0
$293$	−11.1656	−	11.1656i	−0.652301	−	0.652301i	0.301246	−	0.953547i	$-0.402598\pi$
$293$	−11.1656	−	11.1656i	−0.652301	−	0.652301i	−0.953547	+	0.301246i	$0.902598\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	3.48947i		−	0.202480i
$298$		0			0
$299$	−0.243221	−	0.243221i	−0.0140659	−	0.0140659i
$300$		0			0
$301$	−10.4255	+	10.4255i	−0.600916	+	0.600916i
$302$		0			0
$303$	0.798174			0.0458539
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.18143	−	2.18143i	0.124501	−	0.124501i	−0.642111	−	0.766612i	$-0.721941\pi$
$307$	2.18143	−	2.18143i	0.124501	−	0.124501i	0.766612	+	0.642111i	$0.221941\pi$
$308$		0			0
$309$	−2.82629	−	2.82629i	−0.160782	−	0.160782i
$310$		0			0
$311$			11.5517i			0.655038i	0.944845	+	0.327519i	$0.106213\pi$
$311$			11.5517i			0.655038i	−0.944845	+	0.327519i	$0.893787\pi$
$312$		0			0
$313$			10.4265i			0.589343i	0.955599	+	0.294671i	$0.0952102\pi$
$313$			10.4265i			0.589343i	−0.955599	+	0.294671i	$0.904790\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.0785	+	10.0785i	−0.566063	+	0.566063i	−0.931023	−	0.364960i	$-0.881083\pi$
$317$	−10.0785	+	10.0785i	−0.566063	+	0.566063i	0.364960	+	0.931023i	$0.381083\pi$
$318$		0			0
$319$	6.94941			0.389092
$320$		0			0
$321$	−2.56725			−0.143290
$322$		0			0
$323$	23.5663	−	23.5663i	1.31127	−	1.31127i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			3.16007i			0.174752i
$328$		0			0
$329$		−	27.0684i		−	1.49233i
$330$		0			0
$331$	−8.77162	−	8.77162i	−0.482132	−	0.482132i	0.423680	−	0.905812i	$-0.360738\pi$
$331$	−8.77162	−	8.77162i	−0.482132	−	0.482132i	−0.905812	+	0.423680i	$0.860738\pi$
$332$		0			0
$333$	−12.7580	+	12.7580i	−0.699137	+	0.699137i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−33.0226			−1.79885			−0.899427	−	0.437072i	$-0.856016\pi$
$337$	−33.0226			−1.79885			−0.899427	+	0.437072i	$0.856016\pi$
$338$		0			0
$339$	−2.67101	+	2.67101i	−0.145070	+	0.145070i
$340$		0			0
$341$	3.62238	+	3.62238i	0.196163	+	0.196163i
$342$		0			0
$343$			3.12189i			0.168566i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.1412	−	11.1412i	−0.598090	−	0.598090i	0.341714	−	0.939804i	$-0.388993\pi$
$347$	−11.1412	−	11.1412i	−0.598090	−	0.598090i	−0.939804	+	0.341714i	$0.888993\pi$
$348$		0			0
$349$	10.8656	−	10.8656i	0.581622	−	0.581622i	−0.353727	−	0.935349i	$-0.615086\pi$
$349$	10.8656	−	10.8656i	0.581622	−	0.581622i	0.935349	+	0.353727i	$0.115086\pi$
$350$		0			0
$351$	−3.94207			−0.210412
$352$		0			0
$353$	11.3480			0.603995			0.301998	−	0.953309i	$-0.402347\pi$
$353$	11.3480			0.603995			0.301998	+	0.953309i	$0.402347\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.49337	+	3.49337i	0.184889	+	0.184889i
$358$		0			0
$359$		−	26.5788i		−	1.40278i	−0.712779	−	0.701389i	$-0.752564\pi$
$359$		−	26.5788i		−	1.40278i	0.712779	−	0.701389i	$-0.247436\pi$
$360$		0			0
$361$		−	26.5367i		−	1.39667i
$362$		0			0
$363$	−1.08046	−	1.08046i	−0.0567093	−	0.0567093i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.90729			−0.151760			−0.0758798	−	0.997117i	$-0.524177\pi$
$367$	−2.90729			−0.151760			−0.0758798	+	0.997117i	$0.524177\pi$
$368$		0			0
$369$	−9.81514			−0.510956
$370$		0			0
$371$	13.0858	−	13.0858i	0.679379	−	0.679379i
$372$		0			0
$373$	−4.65522	−	4.65522i	−0.241038	−	0.241038i	0.576241	−	0.817280i	$-0.304519\pi$
$373$	−4.65522	−	4.65522i	−0.241038	−	0.241038i	−0.817280	+	0.576241i	$0.804519\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	7.85077i		−	0.404335i
$378$		0			0
$379$	9.52106	+	9.52106i	0.489064	+	0.489064i	0.908011	−	0.418947i	$-0.137601\pi$
$379$	9.52106	+	9.52106i	0.489064	+	0.489064i	−0.418947	+	0.908011i	$0.637601\pi$
$380$		0			0
$381$	−1.09652	+	1.09652i	−0.0561767	+	0.0561767i
$382$		0			0
$383$	−6.92429			−0.353815			−0.176907	−	0.984228i	$-0.556609\pi$
$383$	−6.92429			−0.353815			−0.176907	+	0.984228i	$0.556609\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.94386	−	7.94386i	0.403809	−	0.403809i
$388$		0			0
$389$	20.0232	+	20.0232i	1.01521	+	1.01521i	0.999882	+	0.0153322i	$0.00488057\pi$
$389$	20.0232	+	20.0232i	1.01521	+	1.01521i	0.0153322	+	0.999882i	$0.495119\pi$
$390$		0			0
$391$		−	0.664493i		−	0.0336049i
$392$		0			0
$393$			0.871474i			0.0439601i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3.81625	−	3.81625i	0.191532	−	0.191532i	−0.604826	−	0.796358i	$-0.706757\pi$
$397$	3.81625	−	3.81625i	0.191532	−	0.191532i	0.796358	+	0.604826i	$0.206757\pi$
$398$		0			0
$399$	6.75015			0.337930
$400$		0			0
$401$	1.68031			0.0839108			0.0419554	−	0.999119i	$-0.486641\pi$
$401$	1.68031			0.0839108			0.0419554	+	0.999119i	$0.486641\pi$
$402$		0			0
$403$	4.09222	−	4.09222i	0.203848	−	0.203848i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	13.9238i		−	0.690177i
$408$		0			0
$409$		−	20.1317i		−	0.995448i	−0.867335	−	0.497724i	$-0.834169\pi$
$409$		−	20.1317i		−	0.995448i	0.867335	−	0.497724i	$-0.165831\pi$
$410$		0			0
$411$	−3.35867	−	3.35867i	−0.165671	−	0.165671i
$412$		0			0
$413$	−0.412282	+	0.412282i	−0.0202871	+	0.0202871i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0500256			−0.00244976
$418$		0			0
$419$	22.6570	−	22.6570i	1.10687	−	1.10687i	0.113306	−	0.993560i	$-0.463856\pi$
$419$	22.6570	−	22.6570i	1.10687	−	1.10687i	0.993560	−	0.113306i	$-0.0361442\pi$
$420$		0			0
$421$	−10.1583	−	10.1583i	−0.495084	−	0.495084i	0.414820	−	0.909904i	$-0.363845\pi$
$421$	−10.1583	−	10.1583i	−0.495084	−	0.495084i	−0.909904	+	0.414820i	$0.863845\pi$
$422$		0			0
$423$			20.6251i			1.00283i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	13.3317	+	13.3317i	0.645166	+	0.645166i
$428$		0			0
$429$	1.06332	−	1.06332i	0.0513375	−	0.0513375i
$430$		0			0
$431$	26.1518			1.25969			0.629843	−	0.776723i	$-0.283119\pi$
$431$	26.1518			1.25969			0.629843	+	0.776723i	$0.283119\pi$
$432$		0			0
$433$	9.30795			0.447312			0.223656	−	0.974668i	$-0.428201\pi$
$433$	9.30795			0.447312			0.223656	+	0.974668i	$0.428201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.641992	−	0.641992i	−0.0307107	−	0.0307107i
$438$		0			0
$439$			30.4799i			1.45473i	0.686252	+	0.727364i	$0.259255\pi$
$439$			30.4799i			1.45473i	−0.686252	+	0.727364i	$0.740745\pi$
$440$		0			0
$441$		−	22.9059i		−	1.09076i
$442$		0			0
$443$	16.7437	+	16.7437i	0.795516	+	0.795516i	0.982385	−	0.186869i	$-0.0598340\pi$
$443$	16.7437	+	16.7437i	0.795516	+	0.795516i	−0.186869	+	0.982385i	$0.559834\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.882482			0.0417399
$448$		0			0
$449$	−5.40502			−0.255079			−0.127539	−	0.991834i	$-0.540708\pi$
$449$	−5.40502			−0.255079			−0.127539	+	0.991834i	$0.540708\pi$
$450$		0			0
$451$	5.35600	−	5.35600i	0.252204	−	0.252204i
$452$		0			0
$453$	−3.30703	−	3.30703i	−0.155378	−	0.155378i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			34.5929i			1.61819i	0.587678	+	0.809095i	$0.300042\pi$
$457$			34.5929i			1.61819i	−0.587678	+	0.809095i	$0.699958\pi$
$458$		0			0
$459$	−5.38496	−	5.38496i	−0.251349	−	0.251349i
$460$		0			0
$461$	14.3876	−	14.3876i	0.670099	−	0.670099i	−0.287640	−	0.957739i	$-0.592871\pi$
$461$	14.3876	−	14.3876i	0.670099	−	0.670099i	0.957739	+	0.287640i	$0.0928706\pi$
$462$		0			0
$463$	−20.6591			−0.960108			−0.480054	−	0.877239i	$-0.659383\pi$
$463$	−20.6591			−0.960108			−0.480054	+	0.877239i	$0.659383\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.3222	−	16.3222i	0.755300	−	0.755300i	−0.220163	−	0.975463i	$-0.570659\pi$
$467$	16.3222	−	16.3222i	0.755300	−	0.755300i	0.975463	+	0.220163i	$0.0706590\pi$
$468$		0			0
$469$	7.35371	+	7.35371i	0.339563	+	0.339563i
$470$		0			0
$471$		−	4.64472i		−	0.214017i
$472$		0			0
$473$			8.66973i			0.398635i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−9.97088	+	9.97088i	−0.456535	+	0.456535i
$478$		0			0
$479$	−19.5136			−0.891597			−0.445799	−	0.895133i	$-0.647080\pi$
$479$	−19.5136			−0.891597			−0.445799	+	0.895133i	$0.647080\pi$
$480$		0			0
$481$	−15.7298			−0.717216
$482$		0			0
$483$	0.0951660	−	0.0951660i	0.00433020	−	0.00433020i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	15.6638i		−	0.709794i	−0.934905	−	0.354897i	$-0.884516\pi$
$487$		−	15.6638i		−	0.709794i	0.934905	−	0.354897i	$-0.115484\pi$
$488$		0			0
$489$			5.82505i			0.263418i
$490$		0			0
$491$	17.9076	+	17.9076i	0.808157	+	0.808157i	0.984355	−	0.176198i	$-0.0563799\pi$
$491$	17.9076	+	17.9076i	0.808157	+	0.808157i	−0.176198	+	0.984355i	$0.556380\pi$
$492$		0			0
$493$	10.7244	−	10.7244i	0.483001	−	0.483001i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	35.9029			1.61046
$498$		0			0
$499$	−2.32067	+	2.32067i	−0.103887	+	0.103887i	−0.757140	−	0.653253i	$-0.773404\pi$
$499$	−2.32067	+	2.32067i	−0.103887	+	0.103887i	0.653253	+	0.757140i	$0.273404\pi$
$500$		0			0
$501$	2.34441	+	2.34441i	0.104741	+	0.104741i
$502$		0			0
$503$		−	6.18913i		−	0.275960i	−0.990435	−	0.137980i	$-0.955939\pi$
$503$		−	6.18913i		−	0.275960i	0.990435	−	0.137980i	$-0.0440609\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.18804	+	1.18804i	0.0527627	+	0.0527627i
$508$		0			0
$509$	−18.6217	+	18.6217i	−0.825391	+	0.825391i	−0.986875	−	0.161485i	$-0.948372\pi$
$509$	−18.6217	+	18.6217i	−0.825391	+	0.825391i	0.161485	+	0.986875i	$0.448372\pi$
$510$		0			0
$511$	−37.8222			−1.67315
$512$		0			0
$513$	−10.4052			−0.459403
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−11.2549	−	11.2549i	−0.494988	−	0.494988i
$518$		0			0
$519$		−	0.972885i		−	0.0427049i
$520$		0			0
$521$			24.0232i			1.05247i	0.850338	+	0.526237i	$0.176397\pi$
$521$			24.0232i			1.05247i	−0.850338	+	0.526237i	$0.823603\pi$
$522$		0			0
$523$	16.1791	+	16.1791i	0.707463	+	0.707463i	0.966001	−	0.258538i	$-0.0832408\pi$
$523$	16.1791	+	16.1791i	0.707463	+	0.707463i	−0.258538	+	0.966001i	$0.583241\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.1801			0.487015
$528$		0			0
$529$	22.9819			0.999213
$530$		0			0
$531$	0.314144	−	0.314144i	0.0136327	−	0.0136327i
$532$		0			0
$533$	−6.05069	−	6.05069i	−0.262084	−	0.262084i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			4.28219i			0.184790i
$538$		0			0
$539$	12.4994	+	12.4994i	0.538389	+	0.538389i
$540$		0			0
$541$	6.76526	−	6.76526i	0.290861	−	0.290861i	−0.546559	−	0.837420i	$-0.684063\pi$
$541$	6.76526	−	6.76526i	0.290861	−	0.290861i	0.837420	+	0.546559i	$0.184063\pi$
$542$		0			0
$543$	0.456984			0.0196111
$544$		0			0
$545$		0			0
$546$		0			0
$547$	4.38359	−	4.38359i	0.187429	−	0.187429i	−0.607155	−	0.794584i	$-0.707689\pi$
$547$	4.38359	−	4.38359i	0.187429	−	0.187429i	0.794584	+	0.607155i	$0.207689\pi$
$548$		0			0
$549$	−10.1583	−	10.1583i	−0.433545	−	0.433545i
$550$		0			0
$551$		−	20.7224i		−	0.882805i
$552$		0			0
$553$			42.3621i			1.80142i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	−0.619071	−	0.785335i	$-0.712491\pi$
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	0.785335	+	0.619071i	$0.212491\pi$
$558$		0			0
$559$	9.79422			0.414252
$560$		0			0
$561$	2.90504			0.122651
$562$		0			0
$563$	6.61660	−	6.61660i	0.278857	−	0.278857i	−0.553796	−	0.832652i	$-0.686821\pi$
$563$	6.61660	−	6.61660i	0.278857	−	0.278857i	0.832652	+	0.553796i	$0.186821\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			32.3144i			1.35708i
$568$		0			0
$569$			40.2900i			1.68904i	0.535521	+	0.844522i	$0.320115\pi$
$569$			40.2900i			1.68904i	−0.535521	+	0.844522i	$0.679885\pi$
$570$		0			0
$571$	−22.6010	−	22.6010i	−0.945823	−	0.945823i	0.0527829	−	0.998606i	$-0.483191\pi$
$571$	−22.6010	−	22.6010i	−0.945823	−	0.945823i	−0.998606	+	0.0527829i	$0.983191\pi$
$572$		0			0
$573$	−0.932147	+	0.932147i	−0.0389410	+	0.0389410i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−18.8020			−0.782737			−0.391368	−	0.920234i	$-0.627998\pi$
$577$	−18.8020			−0.782737			−0.391368	+	0.920234i	$0.627998\pi$
$578$		0			0
$579$	−0.423229	+	0.423229i	−0.0175888	+	0.0175888i
$580$		0			0
$581$	33.9043	+	33.9043i	1.40659	+	1.40659i
$582$		0			0
$583$		−	10.8820i		−	0.450685i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.71961	−	2.71961i	−0.112250	−	0.112250i	0.648751	−	0.761001i	$-0.275292\pi$
$587$	−2.71961	−	2.71961i	−0.112250	−	0.112250i	−0.761001	+	0.648751i	$0.775292\pi$
$588$		0			0
$589$	10.8016	−	10.8016i	0.445071	−	0.445071i
$590$		0			0
$591$	2.96636			0.122020
$592$		0			0
$593$	4.04894			0.166270			0.0831350	−	0.996538i	$-0.473507\pi$
$593$	4.04894			0.166270			0.0831350	+	0.996538i	$0.473507\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.01700	−	4.01700i	−0.164405	−	0.164405i
$598$		0			0
$599$			19.0455i			0.778178i	0.921200	+	0.389089i	$0.127210\pi$
$599$			19.0455i			0.778178i	−0.921200	+	0.389089i	$0.872790\pi$
$600$		0			0
$601$			14.4406i			0.589045i	0.955645	+	0.294522i	$0.0951606\pi$
$601$			14.4406i			0.589045i	−0.955645	+	0.294522i	$0.904839\pi$
$602$		0			0
$603$	−5.60327	−	5.60327i	−0.228183	−	0.228183i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−46.3473			−1.88118			−0.940589	−	0.339546i	$-0.889727\pi$
$607$	−46.3473			−1.88118			−0.940589	+	0.339546i	$0.889727\pi$
$608$		0			0
$609$	3.07180			0.124475
$610$		0			0
$611$	−12.7147	+	12.7147i	−0.514380	+	0.514380i
$612$		0			0
$613$	−0.961106	−	0.961106i	−0.0388187	−	0.0388187i	0.687431	−	0.726250i	$-0.258738\pi$
$613$	−0.961106	−	0.961106i	−0.0388187	−	0.0388187i	−0.726250	+	0.687431i	$0.758738\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			3.44724i			0.138781i	0.997590	+	0.0693903i	$0.0221054\pi$
$617$			3.44724i			0.138781i	−0.997590	+	0.0693903i	$0.977895\pi$
$618$		0			0
$619$	−24.5574	−	24.5574i	−0.987044	−	0.987044i	0.0128733	−	0.999917i	$-0.495902\pi$
$619$	−24.5574	−	24.5574i	−0.987044	−	0.987044i	−0.999917	+	0.0128733i	$0.995902\pi$
$620$		0			0
$621$	−0.146697	+	0.146697i	−0.00588673	+	0.00588673i
$622$		0			0
$623$	−4.31517			−0.172884
$624$		0			0
$625$		0			0
$626$		0			0
$627$	2.80667	−	2.80667i	0.112088	−	0.112088i
$628$		0			0
$629$	−21.4873	−	21.4873i	−0.856753	−	0.856753i
$630$		0			0
$631$			22.7950i			0.907456i	0.891140	+	0.453728i	$0.149906\pi$
$631$			22.7950i			0.907456i	−0.891140	+	0.453728i	$0.850094\pi$
$632$		0			0
$633$			0.175787i			0.00698691i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	14.1207	−	14.1207i	0.559481	−	0.559481i
$638$		0			0
$639$	−27.3567			−1.08221
$640$		0			0
$641$	30.4468			1.20258			0.601289	−	0.799032i	$-0.294654\pi$
$641$	30.4468			1.20258			0.601289	+	0.799032i	$0.294654\pi$
$642$		0			0
$643$	20.4452	−	20.4452i	0.806282	−	0.806282i	−0.177787	−	0.984069i	$-0.556894\pi$
$643$	20.4452	−	20.4452i	0.806282	−	0.806282i	0.984069	+	0.177787i	$0.0568939\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			29.5876i			1.16321i	0.813472	+	0.581604i	$0.197575\pi$
$647$			29.5876i			1.16321i	−0.813472	+	0.581604i	$0.802425\pi$
$648$		0			0
$649$			0.342849i			0.0134580i
$650$		0			0
$651$	1.60117	+	1.60117i	0.0627550	+	0.0627550i
$652$		0			0
$653$	21.2334	−	21.2334i	0.830928	−	0.830928i	−0.156716	−	0.987644i	$-0.550091\pi$
$653$	21.2334	−	21.2334i	0.830928	−	0.830928i	0.987644	+	0.156716i	$0.0500908\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	28.8191			1.12434
$658$		0			0
$659$	−20.0222	+	20.0222i	−0.779954	+	0.779954i	−0.979823	−	0.199869i	$-0.935948\pi$
$659$	−20.0222	+	20.0222i	−0.779954	+	0.779954i	0.199869	+	0.979823i	$0.435948\pi$
$660$		0			0
$661$	−19.9536	−	19.9536i	−0.776107	−	0.776107i	0.203059	−	0.979166i	$-0.434912\pi$
$661$	−19.9536	−	19.9536i	−0.776107	−	0.776107i	−0.979166	+	0.203059i	$0.934912\pi$
$662$		0			0
$663$		−	3.28184i		−	0.127456i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.292152	−	0.292152i	−0.0113122	−	0.0113122i
$668$		0			0
$669$	1.38001	−	1.38001i	0.0533542	−	0.0533542i
$670$		0			0
$671$	11.0865			0.427989
$672$		0			0
$673$	2.91192			0.112246			0.0561231	−	0.998424i	$-0.482126\pi$
$673$	2.91192			0.112246			0.0561231	+	0.998424i	$0.482126\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−34.6045	−	34.6045i	−1.32996	−	1.32996i	−0.905401	−	0.424558i	$-0.860430\pi$
$677$	−34.6045	−	34.6045i	−1.32996	−	1.32996i	−0.424558	−	0.905401i	$-0.639570\pi$
$678$		0			0
$679$		−	23.4938i		−	0.901609i
$680$		0			0
$681$			4.73401i			0.181408i
$682$		0			0
$683$	−24.7435	−	24.7435i	−0.946785	−	0.946785i	0.0518690	−	0.998654i	$-0.483482\pi$
$683$	−24.7435	−	24.7435i	−0.946785	−	0.946785i	−0.998654	+	0.0518690i	$0.983482\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.16916			−0.120911
$688$		0			0
$689$	−12.2934			−0.468341
$690$		0			0
$691$	−25.3782	+	25.3782i	−0.965431	+	0.965431i	−0.999422	−	0.0339907i	$-0.989178\pi$
$691$	−25.3782	+	25.3782i	−0.965431	+	0.965431i	0.0339907	+	0.999422i	$0.489178\pi$
$692$		0			0
$693$	−18.0592	−	18.0592i	−0.686011	−	0.686011i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	16.5308i		−	0.626148i
$698$		0			0
$699$	−0.851738	−	0.851738i	−0.0322157	−	0.0322157i
$700$		0			0
$701$	−32.3544	+	32.3544i	−1.22201	+	1.22201i	−0.255094	+	0.966916i	$0.582106\pi$
$701$	−32.3544	+	32.3544i	−1.22201	+	1.22201i	−0.966916	+	0.255094i	$0.917894\pi$
$702$		0			0
$703$	−41.5194			−1.56593
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.35679	−	8.35679i	0.314290	−	0.314290i
$708$		0			0
$709$	−6.64939	−	6.64939i	−0.249723	−	0.249723i	0.571134	−	0.820857i	$-0.306504\pi$
$709$	−6.64939	−	6.64939i	−0.249723	−	0.249723i	−0.820857	+	0.571134i	$0.806504\pi$
$710$		0			0
$711$		−	32.2784i		−	1.21053i
$712$		0			0
$713$		−	0.304568i		−	0.0114062i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.38578	−	3.38578i	0.126444	−	0.126444i
$718$		0			0
$719$	45.0785			1.68115			0.840573	−	0.541699i	$-0.182219\pi$
$719$	45.0785			1.68115			0.840573	+	0.541699i	$0.182219\pi$
$720$		0			0
$721$	−59.1820			−2.20405
$722$		0			0
$723$	3.36791	−	3.36791i	0.125254	−	0.125254i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			18.6075i			0.690116i	0.938581	+	0.345058i	$0.112141\pi$
$727$			18.6075i			0.690116i	−0.938581	+	0.345058i	$0.887859\pi$
$728$		0			0
$729$		−	23.4200i		−	0.867409i
$730$		0			0
$731$	13.3792	+	13.3792i	0.494846	+	0.494846i
$732$		0			0
$733$	7.95550	−	7.95550i	0.293843	−	0.293843i	−0.544753	−	0.838596i	$-0.683377\pi$
$733$	7.95550	−	7.95550i	0.293843	−	0.293843i	0.838596	+	0.544753i	$0.183377\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.11526			0.225258
$738$		0			0
$739$	−15.2636	+	15.2636i	−0.561479	+	0.561479i	−0.929727	−	0.368249i	$-0.879958\pi$
$739$	−15.2636	+	15.2636i	−0.561479	+	0.561479i	0.368249	+	0.929727i	$0.379958\pi$
$740$		0			0
$741$	−3.17071	−	3.17071i	−0.116479	−	0.116479i
$742$		0			0
$743$			33.3017i			1.22172i	0.791738	+	0.610861i	$0.209177\pi$
$743$			33.3017i			1.22172i	−0.791738	+	0.610861i	$0.790823\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−25.8339	−	25.8339i	−0.945211	−	0.945211i
$748$		0			0
$749$	−26.8789	+	26.8789i	−0.982132	+	0.982132i
$750$		0			0
$751$	−1.17214			−0.0427720			−0.0213860	−	0.999771i	$-0.506808\pi$
$751$	−1.17214			−0.0427720			−0.0213860	+	0.999771i	$0.506808\pi$
$752$		0			0
$753$	5.88945			0.214623
$754$		0			0
$755$		0			0
$756$		0			0
$757$	17.9408	+	17.9408i	0.652069	+	0.652069i	0.953491	−	0.301422i	$-0.0974612\pi$
$757$	17.9408	+	17.9408i	0.652069	+	0.652069i	−0.301422	+	0.953491i	$0.597461\pi$
$758$		0			0
$759$		−	0.0791389i		−	0.00287256i
$760$		0			0
$761$		−	15.4641i		−	0.560573i	−0.959916	−	0.280287i	$-0.909570\pi$
$761$		−	15.4641i		−	0.560573i	0.959916	−	0.280287i	$-0.0904295\pi$
$762$		0			0
$763$	33.0856	+	33.0856i	1.19778	+	1.19778i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.387318			0.0139852
$768$		0			0
$769$	−14.9777			−0.540108			−0.270054	−	0.962845i	$-0.587042\pi$
$769$	−14.9777			−0.540108			−0.270054	+	0.962845i	$0.587042\pi$
$770$		0			0
$771$	1.06984	−	1.06984i	0.0385293	−	0.0385293i
$772$		0			0
$773$	−33.0120	−	33.0120i	−1.18736	−	1.18736i	−0.977794	−	0.209566i	$-0.932795\pi$
$773$	−33.0120	−	33.0120i	−1.18736	−	1.18736i	−0.209566	−	0.977794i	$-0.567205\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	6.15464i		−	0.220796i
$778$		0			0
$779$	−15.9710	−	15.9710i	−0.572222	−	0.572222i
$780$		0			0
$781$	14.9282	−	14.9282i	0.534173	−	0.534173i
$782$		0			0
$783$	−4.73512			−0.169219
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−28.8326	+	28.8326i	−1.02777	+	1.02777i	−0.0281690	+	0.999603i	$0.508968\pi$
$787$	−28.8326	+	28.8326i	−1.02777	+	1.02777i	−0.999603	+	0.0281690i	$0.991032\pi$
$788$		0			0
$789$	−0.148262	−	0.148262i	−0.00527828	−	0.00527828i
$790$		0			0
$791$			55.9305i			1.98866i
$792$		0			0
$793$		−	12.5244i		−	0.444756i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.1556	+	23.1556i	−0.820214	+	0.820214i	−0.986139	−	0.165924i	$-0.946939\pi$
$797$	−23.1556	+	23.1556i	−0.820214	+	0.820214i	0.165924	+	0.986139i	$0.446939\pi$
$798$		0			0
$799$	−34.7371			−1.22891
$800$		0			0
$801$	3.28801			0.116176
$802$		0			0
$803$	−15.7262	+	15.7262i	−0.554966	+	0.554966i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	5.58497i		−	0.196600i
$808$		0			0
$809$			36.2210i			1.27346i	0.771086	+	0.636731i	$0.219714\pi$
$809$			36.2210i			1.27346i	−0.771086	+	0.636731i	$0.780286\pi$
$810$		0			0
$811$	−9.17312	−	9.17312i	−0.322112	−	0.322112i	0.527465	−	0.849577i	$-0.323143\pi$
$811$	−9.17312	−	9.17312i	−0.322112	−	0.322112i	−0.849577	+	0.527465i	$0.823143\pi$
$812$		0			0
$813$	1.99395	−	1.99395i	0.0699310	−	0.0699310i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	25.8522			0.904456
$818$		0			0
$819$	−20.4015	+	20.4015i	−0.712886	+	0.712886i
$820$		0			0
$821$	7.26795	+	7.26795i	0.253653	+	0.253653i	0.822467	−	0.568813i	$-0.192597\pi$
$821$	7.26795	+	7.26795i	0.253653	+	0.253653i	−0.568813	+	0.822467i	$0.692597\pi$
$822$		0			0
$823$			28.2974i			0.986384i	0.869920	+	0.493192i	$0.164170\pi$
$823$			28.2974i			0.986384i	−0.869920	+	0.493192i	$0.835830\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.1661	+	18.1661i	0.631697	+	0.631697i	0.948494	−	0.316797i	$-0.102607\pi$
$827$	18.1661	+	18.1661i	0.631697	+	0.631697i	−0.316797	+	0.948494i	$0.602607\pi$
$828$		0			0
$829$	−11.0865	+	11.0865i	−0.385049	+	0.385049i	−0.872917	−	0.487868i	$-0.837775\pi$
$829$	−11.0865	+	11.0865i	−0.385049	+	0.385049i	0.487868	+	0.872917i	$0.337775\pi$
$830$		0			0
$831$	0.468054			0.0162366
$832$		0			0
$833$	38.5783			1.33666
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.46818	−	2.46818i	−0.0853128	−	0.0853128i
$838$		0			0
$839$			11.9093i			0.411153i	0.978641	+	0.205577i	$0.0659069\pi$
$839$			11.9093i			0.411153i	−0.978641	+	0.205577i	$0.934093\pi$
$840$		0			0
$841$			19.5698i			0.674822i
$842$		0			0
$843$	3.71576	+	3.71576i	0.127977	+	0.127977i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−22.6245			−0.777388
$848$		0			0
$849$	−7.85669			−0.269641
$850$		0			0
$851$	−0.585354	+	0.585354i	−0.0200657	+	0.0200657i
$852$		0			0
$853$	−2.44597	−	2.44597i	−0.0837485	−	0.0837485i	0.663992	−	0.747740i	$-0.268861\pi$
$853$	−2.44597	−	2.44597i	−0.0837485	−	0.0837485i	−0.747740	+	0.663992i	$0.768861\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			2.57862i			0.0880839i	0.999030	+	0.0440419i	$0.0140235\pi$
$857$			2.57862i			0.0880839i	−0.999030	+	0.0440419i	$0.985976\pi$
$858$		0			0
$859$	33.0076	+	33.0076i	1.12620	+	1.12620i	0.990789	+	0.135416i	$0.0432371\pi$
$859$	33.0076	+	33.0076i	1.12620	+	1.12620i	0.135416	+	0.990789i	$0.456763\pi$
$860$		0			0
$861$	2.36747	−	2.36747i	0.0806832	−	0.0806832i
$862$		0			0
$863$	−23.5500			−0.801652			−0.400826	−	0.916154i	$-0.631277\pi$
$863$	−23.5500			−0.801652			−0.400826	+	0.916154i	$0.631277\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.35863	−	1.35863i	0.0461416	−	0.0461416i
$868$		0			0
$869$	17.6139	+	17.6139i	0.597511	+	0.597511i
$870$		0			0
$871$		−	6.90843i		−	0.234083i
$872$		0			0
$873$			17.9014i			0.605871i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	34.2135	−	34.2135i	1.15531	−	1.15531i	0.169836	−	0.985472i	$-0.445676\pi$
$877$	34.2135	−	34.2135i	1.15531	−	1.15531i	0.985472	−	0.169836i	$-0.0543237\pi$
$878$		0			0
$879$	−4.10426			−0.138433
$880$		0			0
$881$	40.6823			1.37062			0.685310	−	0.728251i	$-0.259667\pi$
$881$	40.6823			1.37062			0.685310	+	0.728251i	$0.259667\pi$
$882$		0			0
$883$	35.8531	−	35.8531i	1.20655	−	1.20655i	0.234415	−	0.972137i	$-0.424682\pi$
$883$	35.8531	−	35.8531i	1.20655	−	1.20655i	0.972137	−	0.234415i	$-0.0753176\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			9.33231i			0.313348i	0.987650	+	0.156674i	$0.0500773\pi$
$887$			9.33231i			0.313348i	−0.987650	+	0.156674i	$0.949923\pi$
$888$		0			0
$889$			22.9610i			0.770087i
$890$		0			0
$891$	13.4361	+	13.4361i	0.450127	+	0.450127i
$892$		0			0
$893$	−33.5609	+	33.5609i	−1.12307	+	1.12307i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.0894035			−0.00298510
$898$		0			0
$899$	4.91548	−	4.91548i	0.163940	−	0.163940i
$900$		0			0
$901$	−16.7931	−	16.7931i	−0.559459	−	0.559459i
$902$		0			0
$903$			3.83222i			0.127528i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	33.2170	+	33.2170i	1.10295	+	1.10295i	0.994053	+	0.108899i	$0.0347327\pi$
$907$	33.2170	+	33.2170i	1.10295	+	1.10295i	0.108899	+	0.994053i	$0.465267\pi$
$908$		0			0
$909$	−6.36758	+	6.36758i	−0.211199	+	0.211199i
$910$		0			0
$911$	−5.77870			−0.191457			−0.0957284	−	0.995407i	$-0.530518\pi$
$911$	−5.77870			−0.191457			−0.0957284	+	0.995407i	$0.530518\pi$
$912$		0			0
$913$	28.1944			0.933098
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.12424	+	9.12424i	0.301309	+	0.301309i
$918$		0			0
$919$			50.8572i			1.67763i	0.544420	+	0.838813i	$0.316750\pi$
$919$			50.8572i			1.67763i	−0.544420	+	0.838813i	$0.683250\pi$
$920$		0			0
$921$		−	0.801852i		−	0.0264219i
$922$		0			0
$923$	−16.8644	−	16.8644i	−0.555100	−	0.555100i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	45.0945			1.48110
$928$		0			0
$929$	−21.6815			−0.711346			−0.355673	−	0.934611i	$-0.615748\pi$
$929$	−21.6815			−0.711346			−0.355673	+	0.934611i	$0.615748\pi$
$930$		0			0
$931$	37.2720	−	37.2720i	1.22154	−	1.22154i
$932$		0			0
$933$	2.12309	+	2.12309i	0.0695070	+	0.0695070i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			19.7948i			0.646668i	0.946285	+	0.323334i	$0.104804\pi$
$937$			19.7948i			0.646668i	−0.946285	+	0.323334i	$0.895196\pi$
$938$		0			0
$939$	1.91630	+	1.91630i	0.0625360	+	0.0625360i
$940$		0			0
$941$	−29.4510	+	29.4510i	−0.960074	+	0.960074i	−0.999233	−	0.0391593i	$-0.987532\pi$
$941$	−29.4510	+	29.4510i	−0.960074	+	0.960074i	0.0391593	+	0.999233i	$0.487532\pi$
$942$		0			0
$943$	−0.450330			−0.0146648
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.11783	+	4.11783i	−0.133811	+	0.133811i	−0.770840	−	0.637029i	$-0.780163\pi$
$947$	−4.11783	+	4.11783i	−0.133811	+	0.133811i	0.637029	+	0.770840i	$0.280163\pi$
$948$		0			0
$949$	17.7660	+	17.7660i	0.576708	+	0.576708i
$950$		0			0
$951$			3.70465i			0.120131i
$952$		0			0
$953$			40.3245i			1.30624i	0.757255	+	0.653119i	$0.226540\pi$
$953$			40.3245i			1.30624i	−0.757255	+	0.653119i	$0.773460\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.27723	−	1.27723i	0.0412871	−	0.0412871i
$958$		0			0
$959$	−70.3298			−2.27107
$960$		0			0
$961$	−25.8756			−0.834697
$962$		0			0
$963$	20.4807	−	20.4807i	0.659982	−	0.659982i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	58.1740i		−	1.87075i	−0.353656	−	0.935375i	$-0.615062\pi$
$967$		−	58.1740i		−	1.87075i	0.353656	−	0.935375i	$-0.384938\pi$
$968$		0			0
$969$		−	8.66254i		−	0.278281i
$970$		0			0
$971$	1.70830	+	1.70830i	0.0548220	+	0.0548220i	0.733986	−	0.679164i	$-0.237658\pi$
$971$	1.70830	+	1.70830i	0.0548220	+	0.0548220i	−0.679164	+	0.733986i	$0.737658\pi$
$972$		0			0
$973$	−0.523762	+	0.523762i	−0.0167910	+	0.0167910i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−35.1811			−1.12554			−0.562772	−	0.826612i	$-0.690265\pi$
$977$	−35.1811			−1.12554			−0.562772	+	0.826612i	$0.690265\pi$
$978$		0			0
$979$	−1.79422	+	1.79422i	−0.0573436	+	0.0573436i
$980$		0			0
$981$	−25.2100	−	25.2100i	−0.804894	−	0.804894i
$982$		0			0
$983$			27.7257i			0.884312i	0.896938	+	0.442156i	$0.145786\pi$
$983$			27.7257i			0.884312i	−0.896938	+	0.442156i	$0.854214\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.97491	−	4.97491i	−0.158353	−	0.158353i
$988$		0			0
$989$	0.364474	−	0.364474i	0.0115896	−	0.0115896i
$990$		0			0
$991$	7.02711			0.223224			0.111612	−	0.993752i	$-0.464399\pi$
$991$	7.02711			0.223224			0.111612	+	0.993752i	$0.464399\pi$
$992$		0			0
$993$	−3.22428			−0.102319
$994$		0			0
$995$		0			0
$996$		0			0
$997$	14.2467	+	14.2467i	0.451197	+	0.451197i	0.895752	−	0.444555i	$-0.146638\pi$
$997$	14.2467	+	14.2467i	0.451197	+	0.451197i	−0.444555	+	0.895752i	$0.646638\pi$
$998$		0			0
$999$			9.48726i			0.300164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.h.1201.5		16
4.3	odd	2		400.2.l.i.101.5		16
5.2	odd	4		320.2.q.c.49.4		16
5.3	odd	4		320.2.q.c.49.5		16
5.4	even	2	inner	1600.2.l.h.1201.4		16
16.3	odd	4		400.2.l.i.301.5		16
16.13	even	4	inner	1600.2.l.h.401.5		16
20.3	even	4		80.2.q.c.69.1	yes	16
20.7	even	4		80.2.q.c.69.8	yes	16
20.19	odd	2		400.2.l.i.101.4		16
40.3	even	4		640.2.q.e.609.5		16
40.13	odd	4		640.2.q.f.609.4		16
40.27	even	4		640.2.q.e.609.4		16
40.37	odd	4		640.2.q.f.609.5		16
60.23	odd	4		720.2.bm.f.469.8		16
60.47	odd	4		720.2.bm.f.469.1		16
80.3	even	4		80.2.q.c.29.8	yes	16
80.13	odd	4		320.2.q.c.209.4		16
80.19	odd	4		400.2.l.i.301.4		16
80.27	even	4		640.2.q.e.289.5		16
80.29	even	4	inner	1600.2.l.h.401.4		16
80.37	odd	4		640.2.q.f.289.4		16
80.43	even	4		640.2.q.e.289.4		16
80.53	odd	4		640.2.q.f.289.5		16
80.67	even	4		80.2.q.c.29.1	✓	16
80.77	odd	4		320.2.q.c.209.5		16
240.83	odd	4		720.2.bm.f.109.1		16
240.227	odd	4		720.2.bm.f.109.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.1	✓	16	80.67	even	4
80.2.q.c.29.8	yes	16	80.3	even	4
80.2.q.c.69.1	yes	16	20.3	even	4
80.2.q.c.69.8	yes	16	20.7	even	4
320.2.q.c.49.4		16	5.2	odd	4
320.2.q.c.49.5		16	5.3	odd	4
320.2.q.c.209.4		16	80.13	odd	4
320.2.q.c.209.5		16	80.77	odd	4
400.2.l.i.101.4		16	20.19	odd	2
400.2.l.i.101.5		16	4.3	odd	2
400.2.l.i.301.4		16	80.19	odd	4
400.2.l.i.301.5		16	16.3	odd	4
640.2.q.e.289.4		16	80.43	even	4
640.2.q.e.289.5		16	80.27	even	4
640.2.q.e.609.4		16	40.27	even	4
640.2.q.e.609.5		16	40.3	even	4
640.2.q.f.289.4		16	80.37	odd	4
640.2.q.f.289.5		16	80.53	odd	4
640.2.q.f.609.4		16	40.13	odd	4
640.2.q.f.609.5		16	40.37	odd	4
720.2.bm.f.109.1		16	240.83	odd	4
720.2.bm.f.109.8		16	240.227	odd	4
720.2.bm.f.469.1		16	60.47	odd	4
720.2.bm.f.469.8		16	60.23	odd	4
1600.2.l.h.401.4		16	80.29	even	4	inner
1600.2.l.h.401.5		16	16.13	even	4	inner
1600.2.l.h.1201.4		16	5.4	even	2	inner
1600.2.l.h.1201.5		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.183790 - 0.183790i) q^{3} -3.84853i q^{7} +2.93244i q^{9} +O(q^{10})\)	\(q+(0.183790 - 0.183790i) q^{3} -3.84853i q^{7} +2.93244i q^{9} +(-1.60020 - 1.60020i) q^{11} +(-1.80775 + 1.80775i) q^{13} -4.93886 q^{17} +(-4.77162 + 4.77162i) q^{19} +(-0.707323 - 0.707323i) q^{21} +0.134544i q^{23} +(1.09033 + 1.09033i) q^{27} +(-2.17142 + 2.17142i) q^{29} -2.26371 q^{31} -0.588201 q^{33} +(4.35066 + 4.35066i) q^{37} +0.664493i q^{39} +3.34709i q^{41} +(-2.70896 - 2.70896i) q^{43} +7.03343 q^{47} -7.81119 q^{49} +(-0.907714 + 0.907714i) q^{51} +(3.40020 + 3.40020i) q^{53} +1.75396i q^{57} +(-0.107127 - 0.107127i) q^{59} +(-3.46410 + 3.46410i) q^{61} +11.2856 q^{63} +(-1.91078 + 1.91078i) q^{67} +(0.0247279 + 0.0247279i) q^{69} +9.32899i q^{71} -9.82769i q^{73} +(-6.15840 + 6.15840i) q^{77} -11.0073 q^{79} -8.39654 q^{81} +(-8.80967 + 8.80967i) q^{83} +0.798174i q^{87} -1.12125i q^{89} +(6.95717 + 6.95717i) q^{91} +(-0.416048 + 0.416048i) q^{93} +6.10461 q^{97} +(4.69248 - 4.69248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

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