LMFDB - Embedded newform 400.2.j.c.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(43,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 + 6x^12 - 12x^10 + 36x^8 - 48x^6 + 96x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$1.35949 - 0.389597i$ of defining polynomial
Character	$\chi$	$=$	400.43
Dual form			400.2.j.c.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35949 - 0.389597i) q^{2} -0.207468i q^{3} +(1.69643 + 1.05931i) q^{4} +(-0.0808289 + 0.282051i) q^{6} +(-1.32185 + 1.32185i) q^{7} +(-1.89357 - 2.10104i) q^{8} +2.95696 q^{9} +(-2.39286 + 2.39286i) q^{11} +(0.219772 - 0.351954i) q^{12} +4.20208 q^{13} +(2.31203 - 1.28205i) q^{14} +(1.75574 + 3.59408i) q^{16} +(-3.29071 + 3.29071i) q^{17} +(-4.01995 - 1.15202i) q^{18} +(0.838342 - 0.838342i) q^{19} +(0.274241 + 0.274241i) q^{21} +(4.18531 - 2.32081i) q^{22} +(2.67277 + 2.67277i) q^{23} +(-0.435899 + 0.392856i) q^{24} +(-5.71269 - 1.63712i) q^{26} -1.23588i q^{27} +(-3.64266 + 0.842176i) q^{28} +(2.55451 + 2.55451i) q^{29} +6.23723i q^{31} +(-0.986662 - 5.57014i) q^{32} +(0.496441 + 0.496441i) q^{33} +(5.75574 - 3.19163i) q^{34} +(5.01626 + 3.13233i) q^{36} +4.29451 q^{37} +(-1.46633 + 0.813102i) q^{38} -0.871798i q^{39} -7.06598i q^{41} +(-0.265984 - 0.479671i) q^{42} +9.43258 q^{43} +(-6.59408 + 1.52454i) q^{44} +(-2.59230 - 4.67491i) q^{46} +(8.31820 + 8.31820i) q^{47} +(0.745656 - 0.364259i) q^{48} +3.50544i q^{49} +(0.682716 + 0.682716i) q^{51} +(7.12853 + 4.45130i) q^{52} +7.66672i q^{53} +(-0.481494 + 1.68016i) q^{54} +(5.28027 + 0.274241i) q^{56} +(-0.173929 - 0.173929i) q^{57} +(-2.47761 - 4.46807i) q^{58} +(-7.07557 - 7.07557i) q^{59} +(8.74267 - 8.74267i) q^{61} +(2.43001 - 8.47945i) q^{62} +(-3.90865 + 3.90865i) q^{63} +(-0.828755 + 7.95696i) q^{64} +(-0.481494 - 0.868318i) q^{66} -12.5494 q^{67} +(-9.06832 + 2.09658i) q^{68} +(0.554514 - 0.554514i) q^{69} -10.4624 q^{71} +(-5.59922 - 6.21269i) q^{72} +(4.79095 - 4.79095i) q^{73} +(-5.83834 - 1.67313i) q^{74} +(2.31025 - 0.534125i) q^{76} -6.32598i q^{77} +(-0.339650 + 1.18520i) q^{78} -8.69963 q^{79} +8.61447 q^{81} +(-2.75289 + 9.60614i) q^{82} -4.14519i q^{83} +(0.174724 + 0.755735i) q^{84} +(-12.8235 - 3.67491i) q^{86} +(0.529980 - 0.529980i) q^{87} +(9.55854 + 0.496441i) q^{88} -0.548482 q^{89} +(-5.55451 + 5.55451i) q^{91} +(1.70288 + 7.36544i) q^{92} +1.29403 q^{93} +(-8.06776 - 14.5493i) q^{94} +(-1.15563 + 0.204701i) q^{96} +(-12.2022 + 12.2022i) q^{97} +(1.36571 - 4.76561i) q^{98} +(-7.07557 + 7.07557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 12 q^{6} - 16 q^{9} + 8 q^{11} - 20 q^{14} - 16 q^{16} - 8 q^{19} - 24 q^{24} + 16 q^{26} + 16 q^{29} + 48 q^{34} - 4 q^{36} - 40 q^{44} + 36 q^{46} - 48 q^{51} + 32 q^{54} + 64 q^{56}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 12 * q^6 - 16 * q^9 + 8 * q^11 - 20 * q^14 - 16 * q^16 - 8 * q^19 - 24 * q^24 + 16 * q^26 + 16 * q^29 + 48 * q^34 - 4 * q^36 - 40 * q^44 + 36 * q^46 - 48 * q^51 + 32 * q^54 + 64 * q^56 - 8 * q^59 - 16 * q^61 + 16 * q^64 + 32 * q^66 - 16 * q^69 - 32 * q^71 - 72 * q^74 - 32 * q^76 + 80 * q^79 + 16 * q^81 + 136 * q^84 - 60 * q^86 - 64 * q^91 - 28 * q^94 - 56 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.35949	−	0.389597i	−0.961305	−	0.275487i
$2$	−1.35949	−	0.389597i	−0.961305	−	0.275487i
$3$		−	0.207468i		−	0.119782i	−0.998205	−	0.0598908i	$-0.980925\pi$
$3$		−	0.207468i		−	0.119782i	0.998205	−	0.0598908i	$-0.0190753\pi$
$4$	1.69643	+	1.05931i	0.848214	+	0.529654i
$5$		0			0
$5$		0			0
$6$	−0.0808289	+	0.282051i	−0.0329983	+	0.115147i
$7$	−1.32185	+	1.32185i	−0.499611	+	0.499611i	−0.911317	−	0.411706i	$-0.864933\pi$
$7$	−1.32185	+	1.32185i	−0.499611	+	0.499611i	0.411706	+	0.911317i	$0.364933\pi$
$8$	−1.89357	−	2.10104i	−0.669480	−	0.742831i
$9$	2.95696			0.985652
$10$		0			0
$11$	−2.39286	+	2.39286i	−0.721473	+	0.721473i	−0.968905	−	0.247432i	$-0.920413\pi$
$11$	−2.39286	+	2.39286i	−0.721473	+	0.721473i	0.247432	+	0.968905i	$0.420413\pi$
$12$	0.219772	−	0.351954i	0.0634428	−	0.101600i
$13$	4.20208			1.16545			0.582724	−	0.812670i	$-0.301987\pi$
$13$	4.20208			1.16545			0.582724	+	0.812670i	$0.301987\pi$
$14$	2.31203	−	1.28205i	0.617915	−	0.342642i
$15$		0			0
$16$	1.75574	+	3.59408i	0.438934	+	0.898519i
$17$	−3.29071	+	3.29071i	−0.798114	+	0.798114i	−0.982798	−	0.184684i	$-0.940874\pi$
$17$	−3.29071	+	3.29071i	−0.798114	+	0.798114i	0.184684	+	0.982798i	$0.440874\pi$
$18$	−4.01995	−	1.15202i	−0.947512	−	0.271534i
$19$	0.838342	−	0.838342i	0.192329	−	0.192329i	−0.604373	−	0.796702i	$-0.706576\pi$
$19$	0.838342	−	0.838342i	0.192329	−	0.192329i	0.796702	+	0.604373i	$0.206576\pi$
$20$		0			0
$21$	0.274241	+	0.274241i	0.0598443	+	0.0598443i
$22$	4.18531	−	2.32081i	0.892312	−	0.494799i
$23$	2.67277	+	2.67277i	0.557311	+	0.557311i	0.928541	−	0.371230i	$-0.121064\pi$
$23$	2.67277	+	2.67277i	0.557311	+	0.557311i	−0.371230	+	0.928541i	$0.621064\pi$
$24$	−0.435899	+	0.392856i	−0.0889775	+	0.0801914i
$25$		0			0
$26$	−5.71269	−	1.63712i	−1.12035	−	0.321066i
$27$		−	1.23588i		−	0.237845i
$28$	−3.64266	+	0.842176i	−0.688398	+	0.159156i
$29$	2.55451	+	2.55451i	0.474361	+	0.474361i	0.903323	−	0.428961i	$-0.141120\pi$
$29$	2.55451	+	2.55451i	0.474361	+	0.474361i	−0.428961	+	0.903323i	$0.641120\pi$
$30$		0			0
$31$			6.23723i			1.12024i	0.828412	+	0.560120i	$0.189245\pi$
$31$			6.23723i			1.12024i	−0.828412	+	0.560120i	$0.810755\pi$
$32$	−0.986662	−	5.57014i	−0.174419	−	0.984672i
$33$	0.496441	+	0.496441i	0.0864192	+	0.0864192i
$34$	5.75574	−	3.19163i	0.987100	−	0.547361i
$35$		0			0
$36$	5.01626	+	3.13233i	0.836044	+	0.522054i
$37$	4.29451			0.706013			0.353006	−	0.935621i	$-0.385159\pi$
$37$	4.29451			0.706013			0.353006	+	0.935621i	$0.385159\pi$
$38$	−1.46633	+	0.813102i	−0.237871	+	0.131903i
$39$		−	0.871798i		−	0.139599i
$40$		0			0
$41$		−	7.06598i		−	1.10352i	−0.834002	−	0.551761i	$-0.813956\pi$
$41$		−	7.06598i		−	1.10352i	0.834002	−	0.551761i	$-0.186044\pi$
$42$	−0.265984	−	0.479671i	−0.0410423	−	0.0740149i
$43$	9.43258			1.43845			0.719227	−	0.694775i	$-0.244496\pi$
$43$	9.43258			1.43845			0.719227	+	0.694775i	$0.244496\pi$
$44$	−6.59408	+	1.52454i	−0.994095	+	0.229833i
$45$		0			0
$46$	−2.59230	−	4.67491i	−0.382214	−	0.689277i
$47$	8.31820	+	8.31820i	1.21333	+	1.21333i	0.969923	+	0.243410i	$0.0782662\pi$
$47$	8.31820	+	8.31820i	1.21333	+	1.21333i	0.243410	+	0.969923i	$0.421734\pi$
$48$	0.745656	−	0.364259i	0.107626	−	0.0525762i
$49$			3.50544i			0.500777i
$50$		0			0
$51$	0.682716	+	0.682716i	0.0955994	+	0.0955994i
$52$	7.12853	+	4.45130i	0.988550	+	0.617284i
$53$			7.66672i			1.05311i	0.850143	+	0.526553i	$0.176516\pi$
$53$			7.66672i			1.05311i	−0.850143	+	0.526553i	$0.823484\pi$
$54$	−0.481494	+	1.68016i	−0.0655231	+	0.228641i
$55$		0			0
$56$	5.28027	+	0.274241i	0.705606	+	0.0366470i
$57$	−0.173929	−	0.173929i	−0.0230375	−	0.0230375i
$58$	−2.47761	−	4.46807i	−0.325325	−	0.586686i
$59$	−7.07557	−	7.07557i	−0.921161	−	0.921161i	0.0759506	−	0.997112i	$-0.475801\pi$
$59$	−7.07557	−	7.07557i	−0.921161	−	0.921161i	−0.997112	+	0.0759506i	$0.975801\pi$
$60$		0			0
$61$	8.74267	−	8.74267i	1.11938	−	1.11938i	0.127552	−	0.991832i	$-0.459288\pi$
$61$	8.74267	−	8.74267i	1.11938	−	1.11938i	0.991832	−	0.127552i	$-0.0407120\pi$
$62$	2.43001	−	8.47945i	0.308611	−	1.07689i
$63$	−3.90865	+	3.90865i	−0.492443	+	0.492443i
$64$	−0.828755	+	7.95696i	−0.103594	+	0.994620i
$65$		0			0
$66$	−0.481494	−	0.868318i	−0.0592679	−	0.106883i
$67$	−12.5494			−1.53315			−0.766574	−	0.642156i	$-0.778040\pi$
$67$	−12.5494			−1.53315			−0.766574	+	0.642156i	$0.778040\pi$
$68$	−9.06832	+	2.09658i	−1.09970	+	0.254247i
$69$	0.554514	−	0.554514i	0.0667556	−	0.0667556i
$70$		0			0
$71$	−10.4624			−1.24166			−0.620829	−	0.783946i	$-0.713204\pi$
$71$	−10.4624			−1.24166			−0.620829	+	0.783946i	$0.713204\pi$
$72$	−5.59922	−	6.21269i	−0.659874	−	0.732173i
$73$	4.79095	−	4.79095i	0.560738	−	0.560738i	−0.368779	−	0.929517i	$-0.620224\pi$
$73$	4.79095	−	4.79095i	0.560738	−	0.560738i	0.929517	+	0.368779i	$0.120224\pi$
$74$	−5.83834	−	1.67313i	−0.678693	−	0.194497i
$75$		0			0
$76$	2.31025	−	0.534125i	0.265004	−	0.0612683i
$77$		−	6.32598i		−	0.720912i
$78$	−0.339650	+	1.18520i	−0.0384578	+	0.134198i
$79$	−8.69963			−0.978784			−0.489392	−	0.872064i	$-0.662781\pi$
$79$	−8.69963			−0.978784			−0.489392	+	0.872064i	$0.662781\pi$
$80$		0			0
$81$	8.61447			0.957163
$82$	−2.75289	+	9.60614i	−0.304006	+	1.06082i
$83$		−	4.14519i		−	0.454993i	−0.973779	−	0.227497i	$-0.926946\pi$
$83$		−	4.14519i		−	0.454993i	0.973779	−	0.227497i	$-0.0730541\pi$
$84$	0.174724	+	0.755735i	0.0190640	+	0.0824575i
$85$		0			0
$86$	−12.8235	−	3.67491i	−1.38279	−	0.396275i
$87$	0.529980	−	0.529980i	0.0568198	−	0.0568198i
$88$	9.55854	+	0.496441i	1.01894	+	0.0529208i
$89$	−0.548482			−0.0581390			−0.0290695	−	0.999577i	$-0.509254\pi$
$89$	−0.548482			−0.0581390			−0.0290695	+	0.999577i	$0.509254\pi$
$90$		0			0
$91$	−5.55451	+	5.55451i	−0.582271	+	0.582271i
$92$	1.70288	+	7.36544i	0.177537	+	0.767901i
$93$	1.29403			0.134184
$94$	−8.06776	−	14.5493i	−0.832126	−	1.50064i
$95$		0			0
$96$	−1.15563	+	0.204701i	−0.117946	+	0.0208922i
$97$	−12.2022	+	12.2022i	−1.23895	+	1.23895i	−0.278518	+	0.960431i	$0.589843\pi$
$97$	−12.2022	+	12.2022i	−1.23895	+	1.23895i	−0.960431	+	0.278518i	$0.910157\pi$
$98$	1.36571	−	4.76561i	0.137957	−	0.481399i
$99$	−7.07557	+	7.07557i	−0.711122	+	0.711122i
$100$		0			0
$101$	−6.46843	−	6.46843i	−0.643633	−	0.643633i	0.307814	−	0.951447i	$-0.400403\pi$
$101$	−6.46843	−	6.46843i	−0.643633	−	0.643633i	−0.951447	+	0.307814i	$0.900403\pi$
$102$	−0.662162	−	1.19413i	−0.0655638	−	0.118237i
$103$	−6.55234	−	6.55234i	−0.645621	−	0.645621i	0.306310	−	0.951932i	$-0.400905\pi$
$103$	−6.55234	−	6.55234i	−0.645621	−	0.645621i	−0.951932	+	0.306310i	$0.900905\pi$
$104$	−7.95696	−	8.82875i	−0.780244	−	0.865731i
$105$		0			0
$106$	2.98693	−	10.4228i	0.290117	−	1.01235i
$107$		−	16.3708i		−	1.58262i	−0.611413	−	0.791312i	$-0.709399\pi$
$107$		−	16.3708i		−	1.58262i	0.611413	−	0.791312i	$-0.290601\pi$
$108$	1.30917	−	2.09658i	0.125975	−	0.201743i
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	0.796372	−	0.604807i	$-0.206750\pi$
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	−0.604807	+	0.796372i	$0.706750\pi$
$110$		0			0
$111$		−	0.890973i		−	0.0845674i
$112$	−7.07164	−	2.43001i	−0.668207	−	0.229614i
$113$	−11.8688	−	11.8688i	−1.11652	−	1.11652i	−0.992248	−	0.124275i	$-0.960339\pi$
$113$	−11.8688	−	11.8688i	−1.11652	−	1.11652i	−0.124275	−	0.992248i	$-0.539661\pi$
$114$	0.168693	+	0.304217i	0.0157995	+	0.0284926i
$115$		0			0
$116$	1.62753	+	7.03956i	0.151113	+	0.653607i
$117$	12.4254			1.14873
$118$	6.86255	+	12.3758i	0.631749	+	1.13928i
$119$		−	8.69963i		−	0.797493i
$120$		0			0
$121$		−	0.451518i		−	0.0410471i
$122$	−15.2917	+	8.47945i	−1.38444	+	0.767694i
$123$	−1.46597			−0.132182
$124$	−6.60714	+	10.5810i	−0.593339	+	0.950203i
$125$		0			0
$126$	6.83656	−	3.79097i	0.609050	−	0.337726i
$127$	5.55946	+	5.55946i	0.493322	+	0.493322i	0.909351	−	0.416029i	$-0.136579\pi$
$127$	5.55946	+	5.55946i	0.493322	+	0.493322i	−0.416029	+	0.909351i	$0.636579\pi$
$128$	4.22669	−	10.4945i	0.373590	−	0.927594i
$129$		−	1.95696i		−	0.172300i
$130$		0			0
$131$	3.16166	+	3.16166i	0.276235	+	0.276235i	0.831604	−	0.555369i	$-0.187423\pi$
$131$	3.16166	+	3.16166i	0.276235	+	0.276235i	−0.555369	+	0.831604i	$0.687423\pi$
$132$	0.316293	+	1.36806i	0.0275297	+	0.119074i
$133$			2.21632i			0.192179i
$134$	17.0607	+	4.88919i	1.47382	+	0.422362i
$135$		0			0
$136$	13.1451	+	0.682716i	1.12718	+	0.0585424i
$137$	−0.507360	−	0.507360i	−0.0433467	−	0.0433467i	0.685101	−	0.728448i	$-0.259758\pi$
$137$	−0.507360	−	0.507360i	−0.0433467	−	0.0433467i	−0.728448	+	0.685101i	$0.759758\pi$
$138$	−0.969893	+	0.537819i	−0.0825628	+	0.0457822i
$139$	5.52106	+	5.52106i	0.468290	+	0.468290i	0.901360	−	0.433070i	$-0.142570\pi$
$139$	5.52106	+	5.52106i	0.468290	+	0.468290i	−0.433070	+	0.901360i	$0.642570\pi$
$140$		0			0
$141$	1.72576	−	1.72576i	0.145335	−	0.145335i
$142$	14.2235	+	4.07612i	1.19361	+	0.342060i
$143$	−10.0550	+	10.0550i	−0.840840	+	0.840840i
$144$	5.19163	+	10.6275i	0.432636	+	0.885628i
$145$		0			0
$146$	−8.37979	+	4.64671i	−0.693516	+	0.384564i
$147$	0.727266			0.0599839
$148$	7.28532	+	4.54920i	0.598850	+	0.373942i
$149$	−2.82875	+	2.82875i	−0.231741	+	0.231741i	−0.813419	−	0.581678i	$-0.802396\pi$
$149$	−2.82875	+	2.82875i	−0.231741	+	0.231741i	0.581678	+	0.813419i	$0.302396\pi$
$150$		0			0
$151$	7.12820			0.580085			0.290042	−	0.957014i	$-0.406331\pi$
$151$	7.12820			0.580085			0.290042	+	0.957014i	$0.406331\pi$
$152$	−3.34885	−	0.173929i	−0.271628	−	0.0141075i
$153$	−9.73048	+	9.73048i	−0.786663	+	0.786663i
$154$	−2.46458	+	8.60011i	−0.198602	+	0.693017i
$155$		0			0
$156$	0.923502	−	1.47894i	0.0739393	−	0.118410i
$157$		−	20.7371i		−	1.65500i	−0.561464	−	0.827501i	$-0.689762\pi$
$157$		−	20.7371i		−	1.65500i	0.561464	−	0.827501i	$-0.310238\pi$
$158$	11.8271	+	3.38935i	0.940910	+	0.269642i
$159$	1.59060			0.126143
$160$		0			0
$161$	−7.06598			−0.556878
$162$	−11.7113	−	3.35617i	−0.920125	−	0.263686i
$163$		−	10.8985i		−	0.853640i	−0.904337	−	0.426820i	$-0.859634\pi$
$163$		−	10.8985i		−	0.853640i	0.904337	−	0.426820i	$-0.140366\pi$
$164$	7.48505	−	11.9869i	0.584484	−	0.936022i
$165$		0			0
$166$	−1.61495	+	5.63534i	−0.125345	+	0.437387i
$167$	−1.20680	+	1.20680i	−0.0933853	+	0.0933853i	−0.752256	−	0.658871i	$-0.771034\pi$
$167$	−1.20680	+	1.20680i	−0.0933853	+	0.0933853i	0.658871	+	0.752256i	$0.271034\pi$
$168$	0.0568962	−	1.09549i	0.00438964	−	0.0845187i
$169$	4.65751			0.358270
$170$		0			0
$171$	2.47894	−	2.47894i	0.189569	−	0.189569i
$172$	16.0017	+	9.99200i	1.22012	+	0.761883i
$173$	5.12438			0.389599			0.194800	−	0.980843i	$-0.437594\pi$
$173$	5.12438			0.389599			0.194800	+	0.980843i	$0.437594\pi$
$174$	−0.926981	+	0.514024i	−0.0702742	+	0.0389680i
$175$		0			0
$176$	−12.8013	−	4.39889i	−0.964937	−	0.331579i
$177$	−1.46795	+	1.46795i	−0.110338	+	0.110338i
$178$	0.745656	+	0.213687i	0.0558893	+	0.0160165i
$179$	12.6301	−	12.6301i	0.944017	−	0.944017i	−0.0544970	−	0.998514i	$-0.517356\pi$
$179$	12.6301	−	12.6301i	0.944017	−	0.944017i	0.998514	+	0.0544970i	$0.0173555\pi$
$180$		0			0
$181$	8.46843	+	8.46843i	0.629453	+	0.629453i	0.947931	−	0.318477i	$-0.103171\pi$
$181$	8.46843	+	8.46843i	0.629453	+	0.629453i	−0.318477	+	0.947931i	$0.603171\pi$
$182$	9.71533	−	5.38728i	0.720148	−	0.399332i
$183$	−1.81382	−	1.81382i	−0.134082	−	0.134082i
$184$	0.554514	−	10.6767i	0.0408793	−	0.787096i
$185$		0			0
$186$	−1.75921	−	0.504149i	−0.128992	−	0.0369660i
$187$		−	15.7484i		−	1.15164i
$188$	5.29969	+	22.9228i	0.386520	+	1.67181i
$189$	1.63364	+	1.63364i	0.118830	+	0.118830i
$190$		0			0
$191$			11.3534i			0.821501i	0.911748	+	0.410750i	$0.134733\pi$
$191$			11.3534i			0.821501i	−0.911748	+	0.410750i	$0.865267\pi$
$192$	1.65081	+	0.171940i	0.119137	+	0.0124087i
$193$	−11.0245	−	11.0245i	−0.793561	−	0.793561i	0.188510	−	0.982071i	$-0.439634\pi$
$193$	−11.0245	−	11.0245i	−0.793561	−	0.793561i	−0.982071	+	0.188510i	$0.939634\pi$
$194$	21.3428	−	11.8349i	1.53232	−	0.849694i
$195$		0			0
$196$	−3.71334	+	5.94672i	−0.265238	+	0.424766i
$197$	21.1953			1.51010			0.755050	−	0.655667i	$-0.227612\pi$
$197$	21.1953			1.51010			0.755050	+	0.655667i	$0.227612\pi$
$198$	12.3758	−	6.86255i	0.879509	−	0.487700i
$199$			8.68045i			0.615341i	0.951493	+	0.307670i	$0.0995494\pi$
$199$			8.68045i			0.615341i	−0.951493	+	0.307670i	$0.900451\pi$
$200$		0			0
$201$			2.60359i			0.183643i
$202$	6.27368	+	11.3138i	0.441415	+	0.796039i
$203$	−6.75335			−0.473993
$204$	0.434972	+	1.88139i	0.0304542	+	0.131723i
$205$		0			0
$206$	6.35507	+	11.4606i	0.442779	+	0.798499i
$207$	7.90326	+	7.90326i	0.549315	+	0.549315i
$208$	7.37775	+	15.1026i	0.511555	+	1.04718i
$209$			4.01206i			0.277520i
$210$		0			0
$211$	−6.28986	−	6.28986i	−0.433012	−	0.433012i	0.456640	−	0.889652i	$-0.349053\pi$
$211$	−6.28986	−	6.28986i	−0.433012	−	0.433012i	−0.889652	+	0.456640i	$0.849053\pi$
$212$	−8.12141	+	13.0060i	−0.557781	+	0.893258i
$213$			2.17061i			0.148728i
$214$	−6.37801	+	22.2559i	−0.435992	+	1.52138i
$215$		0			0
$216$	−2.59663	+	2.34023i	−0.176678	+	0.159232i
$217$	−8.24467	−	8.24467i	−0.559684	−	0.559684i
$218$	−1.93979	−	3.49818i	−0.131379	−	0.236926i
$219$	−0.993968	−	0.993968i	−0.0671661	−	0.0671661i
$220$		0			0
$221$	−13.8278	+	13.8278i	−0.930160	+	0.930160i
$222$	−0.347120	+	1.21127i	−0.0232972	+	0.0812950i
$223$	−3.50264	+	3.50264i	−0.234554	+	0.234554i	−0.814591	−	0.580036i	$-0.803038\pi$
$223$	−3.50264	+	3.50264i	−0.234554	+	0.234554i	0.580036	+	0.814591i	$0.303038\pi$
$224$	8.66710	+	6.05866i	0.579095	+	0.404811i
$225$		0			0
$226$	11.5115	+	20.7596i	0.765732	+	1.38091i
$227$	−0.622404			−0.0413104			−0.0206552	−	0.999787i	$-0.506575\pi$
$227$	−0.622404			−0.0413104			−0.0206552	+	0.999787i	$0.506575\pi$
$228$	−0.110814	−	0.479303i	−0.00733882	−	0.0317426i
$229$	9.35940	−	9.35940i	0.618487	−	0.618487i	−0.326657	−	0.945143i	$-0.605922\pi$
$229$	9.35940	−	9.35940i	0.618487	−	0.618487i	0.945143	+	0.326657i	$0.105922\pi$
$230$		0			0
$231$	−1.31244			−0.0863521
$232$	0.529980	−	10.2043i	0.0347949	−	0.669945i
$233$	−1.79047	+	1.79047i	−0.117297	+	0.117297i	−0.763319	−	0.646022i	$-0.776432\pi$
$233$	−1.79047	+	1.79047i	−0.117297	+	0.117297i	0.646022	+	0.763319i	$0.276432\pi$
$234$	−16.8922	−	4.84089i	−1.10428	−	0.316459i
$235$		0			0
$236$	−4.50799	−	19.4984i	−0.293445	−	1.26924i
$237$			1.80489i			0.117240i
$238$	−3.38935	+	11.8271i	−0.219699	+	0.766634i
$239$	20.9056			1.35227			0.676136	−	0.736777i	$-0.263653\pi$
$239$	20.9056			1.35227			0.676136	+	0.736777i	$0.263653\pi$
$240$		0			0
$241$	−3.70055			−0.238374			−0.119187	−	0.992872i	$-0.538029\pi$
$241$	−3.70055			−0.238374			−0.119187	+	0.992872i	$0.538029\pi$
$242$	−0.175910	+	0.613835i	−0.0113079	+	0.0394588i
$243$		−	5.49486i		−	0.352495i
$244$	24.0925	−	5.57013i	1.54236	−	0.356591i
$245$		0			0
$246$	1.99297	+	0.571136i	0.127067	+	0.0364143i
$247$	3.52278	−	3.52278i	0.224149	−	0.224149i
$248$	13.1047	−	11.8107i	0.832148	−	0.749977i
$249$	−0.859993			−0.0544999
$250$		0			0
$251$	0.630086	−	0.630086i	0.0397707	−	0.0397707i	−0.686942	−	0.726712i	$-0.741047\pi$
$251$	0.630086	−	0.630086i	0.0397707	−	0.0397707i	0.726712	+	0.686942i	$0.241047\pi$
$252$	−10.7712	+	2.49028i	−0.678521	+	0.156873i
$253$	−12.7911			−0.804170
$254$	−5.39208	−	9.72398i	−0.338329	−	0.610137i
$255$		0			0
$256$	−9.83479	+	12.6205i	−0.614674	+	0.788781i
$257$	−3.62414	+	3.62414i	−0.226068	+	0.226068i	−0.811048	−	0.584980i	$-0.801102\pi$
$257$	−3.62414	+	3.62414i	−0.226068	+	0.226068i	0.584980	+	0.811048i	$0.301102\pi$
$258$	−0.762425	+	2.66046i	−0.0474665	+	0.165633i
$259$	−5.67668	+	5.67668i	−0.352732	+	0.352732i
$260$		0			0
$261$	7.55359	+	7.55359i	0.467555	+	0.467555i
$262$	−3.06647	−	5.53002i	−0.189447	−	0.341646i
$263$	5.25957	+	5.25957i	0.324319	+	0.324319i	0.850421	−	0.526102i	$-0.176347\pi$
$263$	5.25957	+	5.25957i	0.324319	+	0.324319i	−0.526102	+	0.850421i	$0.676347\pi$
$264$	0.102996	−	1.98309i	0.00633894	−	0.122051i
$265$		0			0
$266$	0.863473	−	3.01307i	0.0529429	−	0.184743i
$267$			0.113792i			0.00696398i
$268$	−21.2891	−	13.2936i	−1.30044	−	0.812037i
$269$	−8.82875	−	8.82875i	−0.538299	−	0.538299i	0.384730	−	0.923029i	$-0.374294\pi$
$269$	−8.82875	−	8.82875i	−0.538299	−	0.538299i	−0.923029	+	0.384730i	$0.874294\pi$
$270$		0			0
$271$		−	30.9177i		−	1.87812i	−0.343760	−	0.939058i	$-0.611701\pi$
$271$		−	30.9177i		−	1.87812i	0.343760	−	0.939058i	$-0.388299\pi$
$272$	−17.6047	−	6.04945i	−1.06744	−	0.366802i
$273$	1.15238	+	1.15238i	0.0697454	+	0.0697454i
$274$	0.492085	+	0.887417i	0.0297279	+	0.0536108i
$275$		0			0
$276$	1.52809	−	0.353292i	0.0919804	−	0.0212657i
$277$	−18.9322			−1.13753			−0.568764	−	0.822501i	$-0.692578\pi$
$277$	−18.9322			−1.13753			−0.568764	+	0.822501i	$0.692578\pi$
$278$	−5.35484	−	9.65681i	−0.321162	−	0.579177i
$279$			18.4432i			1.10417i
$280$		0			0
$281$			6.51750i			0.388802i	0.980922	+	0.194401i	$0.0622762\pi$
$281$			6.51750i			0.388802i	−0.980922	+	0.194401i	$0.937724\pi$
$282$	−3.01850	+	1.67380i	−0.179749	+	0.0996734i
$283$	16.0721			0.955390			0.477695	−	0.878526i	$-0.341472\pi$
$283$	16.0721			0.955390			0.477695	+	0.878526i	$0.341472\pi$
$284$	−17.7487	−	11.0829i	−1.05319	−	0.657649i
$285$		0			0
$286$	17.5870	−	9.75226i	1.03994	−	0.576663i
$287$	9.34015	+	9.34015i	0.551332	+	0.551332i
$288$	−2.91752	−	16.4707i	−0.171916	−	0.970544i
$289$		−	4.65751i		−	0.273971i
$290$		0			0
$291$	2.53157	+	2.53157i	0.148403	+	0.148403i
$292$	13.2026	−	3.05241i	0.772623	−	0.178629i
$293$			0.829872i			0.0484816i	0.999706	+	0.0242408i	$0.00771685\pi$
$293$			0.829872i			0.0484816i	−0.999706	+	0.0242408i	$0.992283\pi$
$294$	−0.988711	−	0.283341i	−0.0576628	−	0.0165248i
$295$		0			0
$296$	−8.13197	−	9.02294i	−0.472661	−	0.524448i
$297$	2.95728	+	2.95728i	0.171599	+	0.171599i
$298$	4.94774	−	2.74359i	0.286615	−	0.158932i
$299$	11.2312	+	11.2312i	0.649517	+	0.649517i
$300$		0			0
$301$	−12.4684	+	12.4684i	−0.718668	+	0.718668i
$302$	−9.69072	−	2.77713i	−0.557638	−	0.159806i
$303$	−1.34199	+	1.34199i	−0.0770954	+	0.0770954i
$304$	4.48497	+	1.54116i	0.257231	+	0.0883916i
$305$		0			0
$306$	17.0195	−	9.43753i	0.972938	−	0.539507i
$307$	−28.4115			−1.62153			−0.810766	−	0.585371i	$-0.800949\pi$
$307$	−28.4115			−1.62153			−0.810766	+	0.585371i	$0.800949\pi$
$308$	6.70116	−	10.7316i	0.381834	−	0.611488i
$309$	−1.35940	+	1.35940i	−0.0773336	+	0.0773336i
$310$		0			0
$311$	31.8087			1.80370			0.901852	−	0.432046i	$-0.142208\pi$
$311$	31.8087			1.80370			0.901852	+	0.432046i	$0.142208\pi$
$312$	−1.83168	+	1.65081i	−0.103699	+	0.0934589i
$313$	18.7727	−	18.7727i	1.06110	−	1.06110i	0.0630896	−	0.998008i	$-0.479905\pi$
$313$	18.7727	−	18.7727i	1.06110	−	1.06110i	0.998008	−	0.0630896i	$-0.0200954\pi$
$314$	−8.07913	+	28.1919i	−0.455932	+	1.59096i
$315$		0			0
$316$	−14.7583	−	9.21558i	−0.830219	−	0.518417i
$317$			10.6205i			0.596506i	0.954487	+	0.298253i	$0.0964039\pi$
$317$			10.6205i			0.596506i	−0.954487	+	0.298253i	$0.903596\pi$
$318$	−2.16240	−	0.619693i	−0.121262	−	0.0347506i
$319$	−12.2252			−0.684478
$320$		0			0
$321$	−3.39641			−0.189569
$322$	9.60614	+	2.75289i	0.535329	+	0.153412i
$323$			5.51748i			0.307001i
$324$	14.6138	+	9.12537i	0.811879	+	0.506965i
$325$		0			0
$326$	−4.24604	+	14.8165i	−0.235167	+	0.820608i
$327$	0.414936	−	0.414936i	0.0229460	−	0.0229460i
$328$	−14.8459	+	13.3800i	−0.819729	+	0.738785i
$329$	−21.9908			−1.21239
$330$		0			0
$331$	22.4098	−	22.4098i	1.23175	−	1.23175i	0.268462	−	0.963290i	$-0.413485\pi$
$331$	22.4098	−	22.4098i	1.23175	−	1.23175i	0.963290	−	0.268462i	$-0.0865153\pi$
$332$	4.39103	−	7.03201i	0.240989	−	0.385932i
$333$	12.6987			0.695883
$334$	2.11081	−	1.17047i	0.115498	−	0.0640453i
$335$		0			0
$336$	−0.504149	+	1.46714i	−0.0275036	+	0.0800389i
$337$	−2.95728	+	2.95728i	−0.161093	+	0.161093i	−0.783051	−	0.621958i	$-0.786338\pi$
$337$	−2.95728	+	2.95728i	−0.161093	+	0.161093i	0.621958	+	0.783051i	$0.286338\pi$
$338$	−6.33184	−	1.81455i	−0.344407	−	0.0986987i
$339$	−2.46240	+	2.46240i	−0.133739	+	0.133739i
$340$		0			0
$341$	−14.9248	−	14.9248i	−0.808223	−	0.808223i
$342$	−4.33589	+	2.40431i	−0.234458	+	0.130010i
$343$	−13.8866	−	13.8866i	−0.749805	−	0.749805i
$344$	−17.8613	−	19.8182i	−0.963016	−	1.06853i
$345$		0			0
$346$	−6.96654	−	1.99644i	−0.374524	−	0.107330i
$347$			13.8901i			0.745659i	0.927900	+	0.372830i	$0.121612\pi$
$347$			13.8901i			0.745659i	−0.927900	+	0.372830i	$0.878388\pi$
$348$	1.46048	−	0.337661i	0.0782901	−	0.0181005i
$349$	−13.4914	−	13.4914i	−0.722176	−	0.722176i	0.246872	−	0.969048i	$-0.420597\pi$
$349$	−13.4914	−	13.4914i	−0.722176	−	0.722176i	−0.969048	+	0.246872i	$0.920597\pi$
$350$		0			0
$351$		−	5.19326i		−	0.277196i
$352$	15.6895	+	10.9676i	0.836253	+	0.584576i
$353$	15.9785	+	15.9785i	0.850448	+	0.850448i	0.990188	−	0.139740i	$-0.0446268\pi$
$353$	15.9785	+	15.9785i	0.850448	+	0.850448i	−0.139740	+	0.990188i	$0.544627\pi$
$354$	2.56758	−	1.42376i	0.136465	−	0.0756719i
$355$		0			0
$356$	−0.930460	−	0.581011i	−0.0493143	−	0.0307935i
$357$	−1.80489			−0.0955251
$358$	−22.0911	+	12.2498i	−1.16755	+	0.647424i
$359$		−	28.2831i		−	1.49273i	−0.665539	−	0.746363i	$-0.731798\pi$
$359$		−	28.2831i		−	1.49273i	0.665539	−	0.746363i	$-0.268202\pi$
$360$		0			0
$361$			17.5944i			0.926019i
$362$	−8.21347	−	14.8120i	−0.431690	−	0.778503i
$363$	−0.0936755			−0.00491669
$364$	−15.3068	+	3.53889i	−0.802293	+	0.185488i
$365$		0			0
$366$	1.75921	+	3.17254i	0.0919556	+	0.165831i
$367$	−16.8285	−	16.8285i	−0.878439	−	0.878439i	0.114934	−	0.993373i	$-0.463334\pi$
$367$	−16.8285	−	16.8285i	−0.878439	−	0.878439i	−0.993373	+	0.114934i	$0.963334\pi$
$368$	−4.91346	+	14.2988i	−0.256132	+	0.745377i
$369$		−	20.8938i		−	1.08769i
$370$		0			0
$371$	−10.1342	−	10.1342i	−0.526143	−	0.526143i
$372$	2.19522	+	1.37077i	0.113817	+	0.0710711i
$373$			8.03845i			0.416215i	0.978106	+	0.208108i	$0.0667304\pi$
$373$			8.03845i			0.416215i	−0.978106	+	0.208108i	$0.933270\pi$
$374$	−6.13552	+	21.4098i	−0.317260	+	1.10707i
$375$		0			0
$376$	1.72576	−	33.2280i	0.0889992	−	1.71360i
$377$	10.7343	+	10.7343i	0.552844	+	0.552844i
$378$	−1.58446	−	2.85738i	−0.0814957	−	0.146968i
$379$	2.30677	+	2.30677i	0.118491	+	0.118491i	0.763866	−	0.645375i	$-0.223299\pi$
$379$	2.30677	+	2.30677i	0.118491	+	0.118491i	−0.645375	+	0.763866i	$0.723299\pi$
$380$		0			0
$381$	1.15341	−	1.15341i	0.0590910	−	0.0590910i
$382$	4.42324	−	15.4348i	0.226313	−	0.789713i
$383$	7.85530	−	7.85530i	0.401387	−	0.401387i	−0.477335	−	0.878722i	$-0.658397\pi$
$383$	7.85530	−	7.85530i	0.401387	−	0.401387i	0.878722	+	0.477335i	$0.158397\pi$
$384$	−2.17728	−	0.876903i	−0.111109	−	0.0447493i
$385$		0			0
$386$	10.6926	+	19.2828i	0.544239	+	0.981470i
$387$	27.8917			1.41782
$388$	−33.6261	+	7.77429i	−1.70711	+	0.394680i
$389$	−27.2171	+	27.2171i	−1.37996	+	1.37996i	−0.535303	+	0.844660i	$0.679803\pi$
$389$	−27.2171	+	27.2171i	−1.37996	+	1.37996i	−0.844660	+	0.535303i	$0.820197\pi$
$390$		0			0
$391$	−17.5906			−0.889595
$392$	7.36507	−	6.63781i	0.371992	−	0.335260i
$393$	0.655943	−	0.655943i	0.0330879	−	0.0330879i
$394$	−28.8148	−	8.25762i	−1.45167	−	0.416013i
$395$		0			0
$396$	−19.4984	+	4.50799i	−0.979832	+	0.226535i
$397$		−	4.38693i		−	0.220174i	−0.993922	−	0.110087i	$-0.964887\pi$
$397$		−	4.38693i		−	0.220174i	0.993922	−	0.110087i	$-0.0351129\pi$
$398$	3.38188	−	11.8010i	0.169518	−	0.591530i
$399$	0.459815			0.0230196
$400$		0			0
$401$	−24.5944			−1.22818			−0.614092	−	0.789234i	$-0.710478\pi$
$401$	−24.5944			−1.22818			−0.614092	+	0.789234i	$0.710478\pi$
$402$	1.01435	−	3.53955i	0.0505912	−	0.176537i
$403$			26.2094i			1.30558i
$404$	−4.12117	−	17.8253i	−0.205036	−	0.886841i
$405$		0			0
$406$	9.18112	+	2.63109i	0.455651	+	0.130579i
$407$	−10.2761	+	10.2761i	−0.509369	+	0.509369i
$408$	0.141642	−	2.72719i	0.00701231	−	0.135016i
$409$	−7.06598			−0.349390			−0.174695	−	0.984623i	$-0.555894\pi$
$409$	−7.06598			−0.349390			−0.174695	+	0.984623i	$0.555894\pi$
$410$		0			0
$411$	−0.105261	+	0.105261i	−0.00519214	+	0.00519214i
$412$	−4.17463	−	18.0565i	−0.205669	−	0.889581i
$413$	18.7057			0.920445
$414$	−7.66532	−	13.8235i	−0.376730	−	0.679388i
$415$		0			0
$416$	−4.14604	−	23.4062i	−0.203276	−	1.14758i
$417$	1.14544	−	1.14544i	0.0560926	−	0.0560926i
$418$	1.56309	−	5.45436i	0.0764532	−	0.266782i
$419$	4.54400	−	4.54400i	0.221989	−	0.221989i	−0.587347	−	0.809336i	$-0.699827\pi$
$419$	4.54400	−	4.54400i	0.221989	−	0.221989i	0.809336	+	0.587347i	$0.199827\pi$
$420$		0			0
$421$	5.47539	+	5.47539i	0.266854	+	0.266854i	0.827831	−	0.560977i	$-0.189574\pi$
$421$	5.47539	+	5.47539i	0.266854	+	0.266854i	−0.560977	+	0.827831i	$0.689574\pi$
$422$	6.10049	+	11.0015i	0.296967	+	0.535545i
$423$	24.5966	+	24.5966i	1.19593	+	1.19593i
$424$	16.1081	−	14.5175i	0.782279	−	0.705032i
$425$		0			0
$426$	0.845664	−	2.95093i	0.0409726	−	0.142973i
$427$			23.1129i			1.11851i
$428$	17.3417	−	27.7718i	0.838242	−	1.34240i
$429$	2.08609	+	2.08609i	0.100717	+	0.100717i
$430$		0			0
$431$		−	12.6658i		−	0.610090i	−0.952338	−	0.305045i	$-0.901328\pi$
$431$		−	12.6658i		−	0.610090i	0.952338	−	0.305045i	$-0.0986716\pi$
$432$	4.44184	−	2.16987i	0.213708	−	0.104398i
$433$	11.0499	+	11.0499i	0.531022	+	0.531022i	0.920876	−	0.389854i	$-0.127475\pi$
$433$	11.0499	+	11.0499i	0.531022	+	0.531022i	−0.389854	+	0.920876i	$0.627475\pi$
$434$	7.99644	+	14.4206i	0.383842	+	0.692213i
$435$		0			0
$436$	1.27424	+	5.51147i	0.0610251	+	0.263952i
$437$	4.48139			0.214374
$438$	0.964043	+	1.73854i	0.0460637	+	0.0830705i
$439$			20.4936i			0.978108i	0.872254	+	0.489054i	$0.162658\pi$
$439$			20.4936i			0.978108i	−0.872254	+	0.489054i	$0.837342\pi$
$440$		0			0
$441$			10.3654i			0.493592i
$442$	24.1861	−	13.4115i	1.15041	−	0.637921i
$443$	11.0123			0.523212			0.261606	−	0.965175i	$-0.415748\pi$
$443$	11.0123			0.523212			0.261606	+	0.965175i	$0.415748\pi$
$444$	0.943814	−	1.51147i	0.0447914	−	0.0717312i
$445$		0			0
$446$	6.12642	−	3.39719i	0.290095	−	0.160861i
$447$	0.586876	+	0.586876i	0.0277583	+	0.0277583i
$448$	−9.42240	−	11.6134i	−0.445166	−	0.548680i
$449$			15.4423i			0.728767i	0.931249	+	0.364383i	$0.118720\pi$
$449$			15.4423i			0.728767i	−0.931249	+	0.364383i	$0.881280\pi$
$450$		0			0
$451$	16.9079	+	16.9079i	0.796161	+	0.796161i
$452$	−7.56186	−	32.7073i	−0.355680	−	1.53842i
$453$		−	1.47887i		−	0.0694835i
$454$	0.846152	+	0.242487i	0.0397119	+	0.0113805i
$455$		0			0
$456$	−0.0360847	+	0.694780i	−0.00168982	+	0.0325361i
$457$	3.14212	+	3.14212i	0.146982	+	0.146982i	0.776769	−	0.629786i	$-0.216857\pi$
$457$	3.14212	+	3.14212i	0.146982	+	0.146982i	−0.629786	+	0.776769i	$0.716857\pi$
$458$	−16.3704	+	9.07762i	−0.764939	+	0.424169i
$459$	4.06691	+	4.06691i	0.189827	+	0.189827i
$460$		0			0
$461$	8.45636	−	8.45636i	0.393852	−	0.393852i	−0.482206	−	0.876058i	$-0.660164\pi$
$461$	8.45636	−	8.45636i	0.393852	−	0.393852i	0.876058	+	0.482206i	$0.160164\pi$
$462$	1.78425	+	0.511322i	0.0830107	+	0.0237889i
$463$	21.5859	−	21.5859i	1.00318	−	1.00318i	0.00318643	−	0.999995i	$-0.498986\pi$
$463$	21.5859	−	21.5859i	1.00318	−	1.00318i	0.999995	−	0.00318643i	$-0.00101428\pi$
$464$	−4.69607	+	13.6662i	−0.218010	+	0.634436i
$465$		0			0
$466$	3.13168	−	1.73656i	0.145072	−	0.0804446i
$467$	22.4880			1.04062			0.520311	−	0.853977i	$-0.325816\pi$
$467$	22.4880			1.04062			0.520311	+	0.853977i	$0.325816\pi$
$468$	21.0788	+	13.1623i	0.974366	+	0.608428i
$469$	16.5883	−	16.5883i	0.765978	−	0.765978i
$470$		0			0
$471$	−4.30229			−0.198239
$472$	−1.46795	+	28.2642i	−0.0675681	+	1.30096i
$473$	−22.5708	+	22.5708i	−1.03781	+	1.03781i
$474$	0.703181	−	2.45373i	0.0322982	−	0.112704i
$475$		0			0
$476$	9.21558	−	14.7583i	0.422395	−	0.676445i
$477$			22.6702i			1.03800i
$478$	−28.4210	−	8.14477i	−1.29995	−	0.372533i
$479$	0.852623			0.0389573			0.0194787	−	0.999810i	$-0.493799\pi$
$479$	0.852623			0.0389573			0.0194787	+	0.999810i	$0.493799\pi$
$480$		0			0
$481$	18.0459			0.822821
$482$	5.03086	+	1.44173i	0.229150	+	0.0656688i
$483$			1.46597i			0.0667037i
$484$	0.478297	−	0.765968i	0.0217408	−	0.0348167i
$485$		0			0
$486$	−2.14078	+	7.47021i	−0.0971078	+	0.338855i
$487$	2.49958	−	2.49958i	0.113267	−	0.113267i	−0.648202	−	0.761469i	$-0.724479\pi$
$487$	2.49958	−	2.49958i	0.113267	−	0.113267i	0.761469	+	0.648202i	$0.224479\pi$
$488$	−34.9236	−	1.81382i	−1.58092	−	0.0821079i
$489$	−2.26110			−0.102250
$490$		0			0
$491$	22.1177	−	22.1177i	0.998157	−	0.998157i	−0.00184099	−	0.999998i	$-0.500586\pi$
$491$	22.1177	−	22.1177i	0.998157	−	0.998157i	0.999998	+	0.00184099i	$0.000586006\pi$
$492$	−2.48690	−	1.55291i	−0.112118	−	0.0700105i
$493$	−16.8123			−0.757189
$494$	−6.16166	+	3.41672i	−0.277226	+	0.153726i
$495$		0			0
$496$	−22.4171	+	10.9509i	−1.00656	+	0.491711i
$497$	13.8297	−	13.8297i	0.620346	−	0.620346i
$498$	1.16915	+	0.335051i	0.0523910	+	0.0150140i
$499$	−7.73911	+	7.73911i	−0.346450	+	0.346450i	−0.858786	−	0.512335i	$-0.828781\pi$
$499$	−7.73911	+	7.73911i	−0.346450	+	0.346450i	0.512335	+	0.858786i	$0.328781\pi$
$500$		0			0
$501$	0.250373	+	0.250373i	0.0111858	+	0.0111858i
$502$	−1.10208	+	0.611116i	−0.0491880	+	0.0272754i
$503$	13.9144	+	13.9144i	0.620413	+	0.620413i	0.945637	−	0.325224i	$-0.105440\pi$
$503$	13.9144	+	13.9144i	0.620413	+	0.620413i	−0.325224	+	0.945637i	$0.605440\pi$
$504$	15.6135	+	0.810919i	0.695482	+	0.0361212i
$505$		0			0
$506$	17.3894	+	4.98338i	0.773052	+	0.221538i
$507$		−	0.966284i		−	0.0429142i
$508$	3.54205	+	15.3204i	0.157153	+	0.679733i
$509$	4.48049	+	4.48049i	0.198594	+	0.198594i	0.799397	−	0.600803i	$-0.205152\pi$
$509$	4.48049	+	4.48049i	0.198594	+	0.198594i	−0.600803	+	0.799397i	$0.705152\pi$
$510$		0			0
$511$			12.6658i			0.560302i
$512$	18.2872	−	13.3258i	0.808188	−	0.588924i
$513$	−1.03609	−	1.03609i	−0.0457444	−	0.0457444i
$514$	6.33894	−	3.51503i	0.279598	−	0.155041i
$515$		0			0
$516$	2.07302	−	3.31984i	0.0912596	−	0.146148i
$517$	−39.8085			−1.75078
$518$	9.92902	−	5.50578i	0.436256	−	0.241910i
$519$		−	1.06314i		−	0.0466669i
$520$		0			0
$521$			3.26728i			0.143142i	0.997435	+	0.0715711i	$0.0228013\pi$
$521$			3.26728i			0.143142i	−0.997435	+	0.0715711i	$0.977199\pi$
$522$	−7.32617	−	13.2119i	−0.320658	−	0.578269i
$523$	−10.1372			−0.443270			−0.221635	−	0.975130i	$-0.571139\pi$
$523$	−10.1372			−0.443270			−0.221635	+	0.975130i	$0.571139\pi$
$524$	2.01436	+	8.71269i	0.0879976	+	0.380616i
$525$		0			0
$526$	−5.10122	−	9.19944i	−0.222424	−	0.401115i
$527$	−20.5249	−	20.5249i	−0.894079	−	0.894079i
$528$	−0.912628	+	2.65587i	−0.0397170	+	0.115582i
$529$		−	8.71262i		−	0.378809i
$530$		0			0
$531$	−20.9222	−	20.9222i	−0.907945	−	0.907945i
$532$	−2.34777	+	3.75983i	−0.101789	+	0.163009i
$533$		−	29.6919i		−	1.28610i
$534$	0.0443332	−	0.154700i	0.00191849	−	0.00669451i
$535$		0			0
$536$	23.7631	+	26.3667i	1.02641	+	1.13887i
$537$	−2.62034	−	2.62034i	−0.113076	−	0.113076i
$538$	8.56295	+	15.4423i	0.369175	+	0.665763i
$539$	−8.38801	−	8.38801i	−0.361297	−	0.361297i
$540$		0			0
$541$	−18.3823	+	18.3823i	−0.790319	+	0.790319i	−0.981546	−	0.191227i	$-0.938753\pi$
$541$	−18.3823	+	18.3823i	−0.790319	+	0.790319i	0.191227	+	0.981546i	$0.438753\pi$
$542$	−12.0454	+	42.0323i	−0.517396	+	1.80544i
$543$	1.75693	−	1.75693i	0.0753970	−	0.0753970i
$544$	21.5765	+	15.0829i	0.925086	+	0.646674i
$545$		0			0
$546$	−1.11769	−	2.01562i	−0.0478327	−	0.0862605i
$547$	−3.60503			−0.154140			−0.0770699	−	0.997026i	$-0.524556\pi$
$547$	−3.60503			−0.154140			−0.0770699	+	0.997026i	$0.524556\pi$
$548$	−0.323249	−	1.39815i	−0.0138085	−	0.0597260i
$549$	25.8517	−	25.8517i	1.10332	−	1.10332i
$550$		0			0
$551$	4.28311			0.182467
$552$	−2.21507	−	0.115044i	−0.0942796	−	0.00489659i
$553$	11.4996	−	11.4996i	0.489012	−	0.489012i
$554$	25.7382	+	7.37595i	1.09351	+	0.313374i
$555$		0			0
$556$	3.51758	+	15.2146i	0.149179	+	0.645242i
$557$			21.5670i			0.913823i	0.889512	+	0.456911i	$0.151044\pi$
$557$			21.5670i			0.913823i	−0.889512	+	0.456911i	$0.848956\pi$
$558$	7.18543	−	25.0734i	0.304183	−	1.06144i
$559$	39.6365			1.67644
$560$		0			0
$561$	−3.26728			−0.137945
$562$	2.53920	−	8.86048i	0.107110	−	0.373757i
$563$		−	26.5306i		−	1.11813i	−0.829123	−	0.559066i	$-0.811160\pi$
$563$		−	26.5306i		−	1.11813i	0.829123	−	0.559066i	$-0.188840\pi$
$564$	4.75574	−	1.09952i	0.200253	−	0.0462980i
$565$		0			0
$566$	−21.8499	−	6.26166i	−0.918421	−	0.263197i
$567$	−11.3870	+	11.3870i	−0.478209	+	0.478209i
$568$	19.8113	+	21.9819i	0.831265	+	0.922341i
$569$	9.23630			0.387206			0.193603	−	0.981080i	$-0.437983\pi$
$569$	9.23630			0.387206			0.193603	+	0.981080i	$0.437983\pi$
$570$		0			0
$571$	−31.6530	+	31.6530i	−1.32464	+	1.32464i	−0.414663	+	0.909975i	$0.636100\pi$
$571$	−31.6530	+	31.6530i	−1.32464	+	1.32464i	−0.909975	+	0.414663i	$0.863900\pi$
$572$	−27.7089	+	6.40623i	−1.15857	+	0.267858i
$573$	2.35546			0.0984007
$574$	−9.05895	−	16.3367i	−0.378113	−	0.681883i
$575$		0			0
$576$	−2.45059	+	23.5284i	−0.102108	+	0.980349i
$577$	23.8539	−	23.8539i	0.993051	−	0.993051i	−0.00692502	−	0.999976i	$-0.502204\pi$
$577$	23.8539	−	23.8539i	0.993051	−	0.993051i	0.999976	+	0.00692502i	$0.00220432\pi$
$578$	−1.81455	+	6.33184i	−0.0754755	+	0.263370i
$579$	−2.28723	+	2.28723i	−0.0950541	+	0.0950541i
$580$		0			0
$581$	5.47931	+	5.47931i	0.227320	+	0.227320i
$582$	−2.45535	−	4.42794i	−0.101778	−	0.183544i
$583$	−18.3454	−	18.3454i	−0.759787	−	0.759787i
$584$	−19.1380	−	0.993968i	−0.791936	−	0.0411307i
$585$		0			0
$586$	0.323316	−	1.12820i	0.0133560	−	0.0466056i
$587$			24.2348i			1.00028i	0.865946	+	0.500138i	$0.166718\pi$
$587$			24.2348i			1.00028i	−0.865946	+	0.500138i	$0.833282\pi$
$588$	1.23375	+	0.770398i	0.0508792	+	0.0317707i
$589$	5.22893	+	5.22893i	0.215454	+	0.215454i
$590$		0			0
$591$		−	4.39734i		−	0.180882i
$592$	7.54002	+	15.4348i	0.309893	+	0.634366i
$593$	15.4929	+	15.4929i	0.636219	+	0.636219i	0.949621	−	0.313402i	$-0.101469\pi$
$593$	15.4929	+	15.4929i	0.636219	+	0.636219i	−0.313402	+	0.949621i	$0.601469\pi$
$594$	−2.86824	−	5.17254i	−0.117685	−	0.212232i
$595$		0			0
$596$	−7.79530	+	1.80226i	−0.319308	+	0.0738233i
$597$	1.80091			0.0737065
$598$	−10.8931	−	19.6443i	−0.445450	−	0.803317i
$599$			19.1812i			0.783722i	0.920024	+	0.391861i	$0.128169\pi$
$599$			19.1812i			0.783722i	−0.920024	+	0.391861i	$0.871831\pi$
$600$		0			0
$601$		−	21.7464i		−	0.887056i	−0.896261	−	0.443528i	$-0.853727\pi$
$601$		−	21.7464i		−	0.887056i	0.896261	−	0.443528i	$-0.146273\pi$
$602$	21.8084	−	12.0930i	0.888843	−	0.492876i
$603$	−37.1079			−1.51115
$604$	12.0925	+	7.55096i	0.492036	+	0.307244i
$605$		0			0
$606$	2.34726	−	1.30159i	0.0953509	−	0.0528734i
$607$	−20.2541	−	20.2541i	−0.822088	−	0.822088i	0.164319	−	0.986407i	$-0.447457\pi$
$607$	−20.2541	−	20.2541i	−0.822088	−	0.822088i	−0.986407	+	0.164319i	$0.947457\pi$
$608$	−5.49685	−	3.84253i	−0.222927	−	0.155835i
$609$			1.40110i			0.0567756i
$610$		0			0
$611$	34.9538	+	34.9538i	1.41408	+	1.41408i
$612$	−26.8146	+	6.19949i	−1.08392	+	0.250599i
$613$		−	6.00698i		−	0.242620i	−0.992615	−	0.121310i	$-0.961291\pi$
$613$		−	6.00698i		−	0.242620i	0.992615	−	0.121310i	$-0.0387094\pi$
$614$	38.6252	+	11.0691i	1.55879	+	0.446711i
$615$		0			0
$616$	−13.2912	+	11.9787i	−0.535516	+	0.482636i
$617$	−20.9289	−	20.9289i	−0.842566	−	0.842566i	0.146626	−	0.989192i	$-0.453159\pi$
$617$	−20.9289	−	20.9289i	−0.842566	−	0.842566i	−0.989192	+	0.146626i	$0.953159\pi$
$618$	2.37771	−	1.31847i	0.0956455	−	0.0530368i
$619$	−3.30074	−	3.30074i	−0.132668	−	0.132668i	0.637655	−	0.770322i	$-0.279905\pi$
$619$	−3.30074	−	3.30074i	−0.132668	−	0.132668i	−0.770322	+	0.637655i	$0.779905\pi$
$620$		0			0
$621$	3.30321	−	3.30321i	0.132553	−	0.132553i
$622$	−43.2436	−	12.3926i	−1.73391	−	0.496897i
$623$	0.725009	−	0.725009i	0.0290469	−	0.0290469i
$624$	3.13331	−	1.53065i	0.125433	−	0.0612749i
$625$		0			0
$626$	−32.8352	+	18.2075i	−1.31236	+	0.727720i
$627$	0.832374			0.0332418
$628$	21.9670	−	35.1790i	0.876578	−	1.40380i
$629$	−14.1320	+	14.1320i	−0.563479	+	0.563479i
$630$		0			0
$631$	4.39734			0.175055			0.0875276	−	0.996162i	$-0.472103\pi$
$631$	4.39734			0.175055			0.0875276	+	0.996162i	$0.472103\pi$
$632$	16.4734	+	18.2783i	0.655276	+	0.727071i
$633$	−1.30494	+	1.30494i	−0.0518669	+	0.0518669i
$634$	4.13771	−	14.4385i	0.164330	−	0.573424i
$635$		0			0
$636$	2.69834	+	1.68493i	0.106996	+	0.0668119i
$637$			14.7301i			0.583630i
$638$	16.6200	+	4.76289i	0.657992	+	0.188565i
$639$	−30.9369			−1.22384
$640$		0			0
$641$	8.74978			0.345596			0.172798	−	0.984957i	$-0.444719\pi$
$641$	8.74978			0.345596			0.172798	+	0.984957i	$0.444719\pi$
$642$	4.61739	+	1.32323i	0.182234	+	0.0522238i
$643$			26.4968i			1.04493i	0.852660	+	0.522466i	$0.174988\pi$
$643$			26.4968i			1.04493i	−0.852660	+	0.522466i	$0.825012\pi$
$644$	−11.9869	−	7.48505i	−0.472351	−	0.294952i
$645$		0			0
$646$	2.14959	−	7.50096i	0.0845746	−	0.295121i
$647$	15.8343	−	15.8343i	0.622512	−	0.622512i	−0.323661	−	0.946173i	$-0.604914\pi$
$647$	15.8343	−	15.8343i	0.622512	−	0.622512i	0.946173	+	0.323661i	$0.104914\pi$
$648$	−16.3121	−	18.0994i	−0.640801	−	0.711010i
$649$	33.8616			1.32919
$650$		0			0
$651$	−1.71050	+	1.71050i	−0.0670399	+	0.0670399i
$652$	11.5449	−	18.4886i	0.452133	−	0.724069i
$653$	−26.4608			−1.03549			−0.517746	−	0.855534i	$-0.673229\pi$
$653$	−26.4608			−1.03549			−0.517746	+	0.855534i	$0.673229\pi$
$654$	−0.725759	+	0.402443i	−0.0283794	+	0.0157368i
$655$		0			0
$656$	25.3957	−	12.4060i	0.991535	−	0.484373i
$657$	14.1666	−	14.1666i	0.552693	−	0.552693i
$658$	29.8962	+	8.56755i	1.16548	+	0.333998i
$659$	30.5128	−	30.5128i	1.18861	−	1.18861i	0.211156	−	0.977452i	$-0.432277\pi$
$659$	30.5128	−	30.5128i	1.18861	−	1.18861i	0.977452	−	0.211156i	$-0.0677228\pi$
$660$		0			0
$661$	−4.81695	−	4.81695i	−0.187358	−	0.187358i	0.607195	−	0.794553i	$-0.292295\pi$
$661$	−4.81695	−	4.81695i	−0.187358	−	0.187358i	−0.794553	+	0.607195i	$0.792295\pi$
$662$	−39.1966	+	21.7351i	−1.52342	+	0.844758i
$663$	2.86883	+	2.86883i	0.111416	+	0.111416i
$664$	−8.70921	+	7.84922i	−0.337983	+	0.304609i
$665$		0			0
$666$	−17.2637	−	4.94737i	−0.668956	−	0.191707i
$667$			13.6552i			0.528733i
$668$	−3.32563	+	0.768879i	−0.128673	+	0.0297488i
$669$	0.726685	+	0.726685i	0.0280953	+	0.0280953i
$670$		0			0
$671$			41.8399i			1.61521i
$672$	1.25698	−	1.79814i	0.0484890	−	0.0693649i
$673$	2.80519	+	2.80519i	0.108132	+	0.108132i	0.759103	−	0.650971i	$-0.225638\pi$
$673$	2.80519	+	2.80519i	0.108132	+	0.108132i	−0.650971	+	0.759103i	$0.725638\pi$
$674$	5.17254	−	2.86824i	0.199239	−	0.110481i
$675$		0			0
$676$	7.90113	+	4.93373i	0.303890	+	0.189759i
$677$	−17.5498			−0.674492			−0.337246	−	0.941417i	$-0.609495\pi$
$677$	−17.5498			−0.674492			−0.337246	+	0.941417i	$0.609495\pi$
$678$	4.30695	−	2.38826i	0.165407	−	0.0917206i
$679$		−	32.2590i		−	1.23799i
$680$		0			0
$681$			0.129129i			0.00494823i
$682$	14.4755	+	26.1048i	0.554294	+	0.999603i
$683$	−21.7834			−0.833518			−0.416759	−	0.909017i	$-0.636834\pi$
$683$	−21.7834			−0.833518			−0.416759	+	0.909017i	$0.636834\pi$
$684$	6.83131	−	1.57938i	0.261202	−	0.0603893i
$685$		0			0
$686$	13.4685	+	24.2889i	0.514230	+	0.927353i
$687$	−1.94178	−	1.94178i	−0.0740833	−	0.0740833i
$688$	16.5611	+	33.9014i	0.631386	+	1.29248i
$689$			32.2162i			1.22734i
$690$		0			0
$691$	−31.2147	−	31.2147i	−1.18746	−	1.18746i	−0.977767	−	0.209694i	$-0.932753\pi$
$691$	−31.2147	−	31.2147i	−1.18746	−	1.18746i	−0.209694	−	0.977767i	$-0.567247\pi$
$692$	8.69314	+	5.42829i	0.330464	+	0.206353i
$693$		−	18.7057i		−	0.710569i
$694$	5.41154	−	18.8835i	0.205419	−	0.716806i
$695$		0			0
$696$	−2.11707	−	0.109954i	−0.0802471	−	0.00416779i
$697$	23.2521	+	23.2521i	0.880736	+	0.880736i
$698$	13.0852	+	23.5976i	0.495282	+	0.893182i
$699$	0.371464	+	0.371464i	0.0140501	+	0.0140501i
$700$		0			0
$701$	20.9248	−	20.9248i	0.790318	−	0.790318i	−0.191227	−	0.981546i	$-0.561247\pi$
$701$	20.9248	−	20.9248i	0.790318	−	0.790318i	0.981546	+	0.191227i	$0.0612468\pi$
$702$	−2.02328	+	7.06019i	−0.0763638	+	0.266470i
$703$	3.60027	−	3.60027i	0.135787	−	0.135787i
$704$	−17.0568	−	21.0229i	−0.642851	−	0.792332i
$705$		0			0
$706$	−15.4974	−	27.9477i	−0.583252	−	1.05183i
$707$	17.1005			0.643132
$708$	−4.04529	+	0.935264i	−0.152031	+	0.0351494i
$709$	−26.3703	+	26.3703i	−0.990357	+	0.990357i	−0.999954	−	0.00959736i	$-0.996945\pi$
$709$	−26.3703	+	26.3703i	−0.990357	+	0.990357i	0.00959736	+	0.999954i	$0.496945\pi$
$710$		0			0
$711$	−25.7244			−0.964741
$712$	1.03859	+	1.15238i	0.0389228	+	0.0431874i
$713$	−16.6707	+	16.6707i	−0.624322	+	0.624322i
$714$	2.45373	+	0.703181i	0.0918287	+	0.0263159i
$715$		0			0
$716$	34.8052	−	8.04689i	1.30073	−	0.300726i
$717$		−	4.33724i		−	0.161977i
$718$	−11.0190	+	38.4506i	−0.411226	+	1.43496i
$719$	2.65374			0.0989679			0.0494840	−	0.998775i	$-0.484242\pi$
$719$	2.65374			0.0989679			0.0494840	+	0.998775i	$0.484242\pi$
$720$		0			0
$721$	17.3224			0.645119
$722$	6.85472	−	23.9194i	0.255106	−	0.890187i
$723$			0.767746i			0.0285528i
$724$	5.39541	+	23.3367i	0.200519	+	0.867303i
$725$		0			0
$726$	0.127351	+	0.0364957i	0.00472644	+	0.00135448i
$727$	30.8999	−	30.8999i	1.14601	−	1.14601i	0.158685	−	0.987329i	$-0.449275\pi$
$727$	30.8999	−	30.8999i	1.14601	−	1.14601i	0.987329	−	0.158685i	$-0.0507255\pi$
$728$	22.1881	+	1.15238i	0.822348	+	0.0427102i
$729$	24.7034			0.914940
$730$		0			0
$731$	−31.0399	+	31.0399i	−1.14805	+	1.14805i
$732$	−1.15562	−	4.99842i	−0.0427131	−	0.184747i
$733$	−46.2726			−1.70912			−0.854559	−	0.519354i	$-0.826172\pi$
$733$	−46.2726			−1.70912			−0.854559	+	0.519354i	$0.826172\pi$
$734$	16.3218	+	29.4345i	0.602450	+	1.08645i
$735$		0			0
$736$	12.2506	−	17.5248i	0.451563	−	0.645974i
$737$	30.0288	−	30.0288i	1.10613	−	1.10613i
$738$	−8.14017	+	28.4049i	−0.299644	+	1.04560i
$739$	−12.0504	+	12.0504i	−0.443280	+	0.443280i	−0.893113	−	0.449833i	$-0.851484\pi$
$739$	−12.0504	+	12.0504i	−0.443280	+	0.443280i	0.449833	+	0.893113i	$0.351484\pi$
$740$		0			0
$741$	−0.730865	−	0.730865i	−0.0268490	−	0.0268490i
$742$	9.82912	+	17.7257i	0.360838	+	0.650730i
$743$	−21.4100	−	21.4100i	−0.785456	−	0.785456i	0.195290	−	0.980746i	$-0.437435\pi$
$743$	−21.4100	−	21.4100i	−0.785456	−	0.785456i	−0.980746	+	0.195290i	$0.937435\pi$
$744$	−2.45033	−	2.71880i	−0.0898335	−	0.0996761i
$745$		0			0
$746$	3.13176	−	10.9282i	0.114662	−	0.400110i
$747$		−	12.2571i		−	0.448465i
$748$	16.6824	−	26.7160i	0.609968	−	0.976833i
$749$	21.6397	+	21.6397i	0.790696	+	0.790696i
$750$		0			0
$751$			8.50828i			0.310472i	0.987877	+	0.155236i	$0.0496137\pi$
$751$			8.50828i			0.310472i	−0.987877	+	0.155236i	$0.950386\pi$
$752$	−15.2917	+	44.5008i	−0.557631	+	1.62278i
$753$	−0.130723	−	0.130723i	−0.00476379	−	0.00476379i
$754$	−10.4111	−	18.7752i	−0.379150	−	0.683752i
$755$		0			0
$756$	1.04083	+	4.50188i	0.0378545	+	0.163732i
$757$	−29.2794			−1.06418			−0.532089	−	0.846688i	$-0.678593\pi$
$757$	−29.2794			−1.06418			−0.532089	+	0.846688i	$0.678593\pi$
$758$	−2.23732	−	4.03474i	−0.0812631	−	0.146548i
$759$			2.65374i			0.0963248i
$760$		0			0
$761$		−	39.3132i		−	1.42510i	−0.701621	−	0.712551i	$-0.747540\pi$
$761$		−	39.3132i		−	1.42510i	0.701621	−	0.712551i	$-0.252460\pi$
$762$	−2.01741	+	1.11868i	−0.0730832	+	0.0405256i
$763$	−5.28739			−0.191416
$764$	−12.0267	+	19.2602i	−0.435111	+	0.696809i
$765$		0			0
$766$	−13.7396	+	7.61880i	−0.496432	+	0.275278i
$767$	−29.7321	−	29.7321i	−1.07357	−	1.07357i
$768$	2.61835	+	2.04040i	0.0944815	+	0.0736267i
$769$		−	26.4222i		−	0.952809i	−0.879226	−	0.476404i	$-0.841940\pi$
$769$		−	26.4222i		−	0.952809i	0.879226	−	0.476404i	$-0.158060\pi$
$770$		0			0
$771$	0.751892	+	0.751892i	0.0270787	+	0.0270787i
$772$	−7.02394	−	30.3806i	−0.252797	−	1.09342i
$773$		−	8.08416i		−	0.290767i	−0.989375	−	0.145383i	$-0.953558\pi$
$773$		−	8.08416i		−	0.290767i	0.989375	−	0.145383i	$-0.0464416\pi$
$774$	−37.9185	−	10.8665i	−1.36295	−	0.390590i
$775$		0			0
$776$	48.7432	+	2.53157i	1.74978	+	0.0908781i
$777$	1.17773	+	1.17773i	0.0422508	+	0.0422508i
$778$	47.6051	−	26.3977i	1.70673	−	0.946404i
$779$	−5.92371	−	5.92371i	−0.212239	−	0.212239i
$780$		0			0
$781$	25.0350	−	25.0350i	0.895823	−	0.895823i
$782$	23.9142	+	6.85325i	0.855172	+	0.245072i
$783$	3.15707	−	3.15707i	0.112824	−	0.112824i
$784$	−12.5988	+	6.15462i	−0.449958	+	0.219808i
$785$		0			0
$786$	−1.14730	+	0.636194i	−0.0409229	+	0.0226923i
$787$	40.5596			1.44579			0.722897	−	0.690955i	$-0.242810\pi$
$787$	40.5596			1.44579			0.722897	+	0.690955i	$0.242810\pi$
$788$	35.9562	+	22.4523i	1.28089	+	0.799830i
$789$	1.09119	−	1.09119i	0.0388474	−	0.0388474i
$790$		0			0
$791$	31.3775			1.11566
$792$	28.2642	+	1.46795i	1.00432	+	0.0521615i
$793$	36.7374	−	36.7374i	1.30458	−	1.30458i
$794$	−1.70914	+	5.96399i	−0.0606550	+	0.211654i
$795$		0			0
$796$	−9.19527	+	14.7258i	−0.325918	+	0.521941i
$797$			1.85060i			0.0655517i	0.999463	+	0.0327759i	$0.0104347\pi$
$797$			1.85060i			0.0655517i	−0.999463	+	0.0327759i	$0.989565\pi$
$798$	−0.625115	−	0.179143i	−0.0221288	−	0.00634159i
$799$	−54.7455			−1.93676
$800$		0			0
$801$	−1.62184			−0.0573048
$802$	33.4358	+	9.58190i	1.18066	+	0.338349i
$803$			22.9281i			0.809115i
$804$	−2.75800	+	4.41680i	−0.0972672	+	0.155769i
$805$		0			0
$806$	10.2111	−	35.6314i	0.359671	−	1.25506i
$807$	−1.83168	+	1.83168i	−0.0644783	+	0.0644783i
$808$	−1.34199	+	25.8389i	−0.0472111	+	0.909009i
$809$	−26.5823			−0.934584			−0.467292	−	0.884103i	$-0.654770\pi$
$809$	−26.5823			−0.934584			−0.467292	+	0.884103i	$0.654770\pi$
$810$		0			0
$811$	6.49812	−	6.49812i	0.228180	−	0.228180i	−0.583752	−	0.811932i	$-0.698416\pi$
$811$	6.49812	−	6.49812i	0.228180	−	0.228180i	0.811932	+	0.583752i	$0.198416\pi$
$812$	−11.4566	−	7.15388i	−0.402047	−	0.251052i
$813$	−6.41443			−0.224964
$814$	17.9739	−	9.96676i	0.629984	−	0.349335i
$815$		0			0
$816$	−1.25507	+	3.65240i	−0.0439361	+	0.127860i
$817$	7.90773	−	7.90773i	0.276656	−	0.276656i
$818$	9.60614	+	2.75289i	0.335871	+	0.0962525i
$819$	−16.4245	+	16.4245i	−0.573917	+	0.573917i
$820$		0			0
$821$	6.00000	+	6.00000i	0.209401	+	0.209401i	0.804013	−	0.594612i	$-0.202694\pi$
$821$	6.00000	+	6.00000i	0.209401	+	0.209401i	−0.594612	+	0.804013i	$0.702694\pi$
$822$	0.184111	−	0.102092i	0.00642159	−	0.00356086i
$823$	−15.1106	−	15.1106i	−0.526722	−	0.526722i	0.392871	−	0.919593i	$-0.371482\pi$
$823$	−15.1106	−	15.1106i	−0.526722	−	0.526722i	−0.919593	+	0.392871i	$0.871482\pi$
$824$	−1.35940	+	26.1741i	−0.0473570	+	0.911817i
$825$		0			0
$826$	−25.4302	−	7.28767i	−0.884828	−	0.253571i
$827$			13.3792i			0.465241i	0.972568	+	0.232621i	$0.0747301\pi$
$827$			13.3792i			0.465241i	−0.972568	+	0.232621i	$0.925270\pi$
$828$	5.03533	+	21.7793i	0.174990	+	0.756883i
$829$	−5.81788	−	5.81788i	−0.202063	−	0.202063i	0.598820	−	0.800883i	$-0.295636\pi$
$829$	−5.81788	−	5.81788i	−0.202063	−	0.202063i	−0.800883	+	0.598820i	$0.795636\pi$
$830$		0			0
$831$			3.92783i			0.136255i
$832$	−3.48250	+	33.4358i	−0.120734	+	1.15918i
$833$	−11.5354	−	11.5354i	−0.399677	−	0.399677i
$834$	−2.00348	+	1.11096i	−0.0693748	+	0.0384693i
$835$		0			0
$836$	−4.25001	+	6.80618i	−0.146990	+	0.235397i
$837$	7.70845			0.266443
$838$	−7.94785	+	4.40719i	−0.274554	+	0.152244i
$839$		−	27.4305i		−	0.947006i	−0.880792	−	0.473503i	$-0.842989\pi$
$839$		−	27.4305i		−	0.947006i	0.880792	−	0.473503i	$-0.157011\pi$
$840$		0			0
$841$		−	15.9489i		−	0.549963i
$842$	−5.31054	−	9.57693i	−0.183013	−	0.330043i
$843$	1.35217			0.0465713
$844$	−4.00740	−	17.3332i	−0.137940	−	0.596633i
$845$		0			0
$846$	−23.8560	−	43.0215i	−0.820187	−	1.47911i
$847$	0.596838	+	0.596838i	0.0205076	+	0.0205076i
$848$	−27.5548	+	13.4607i	−0.946235	+	0.462243i
$849$		−	3.33445i		−	0.114438i
$850$		0			0
$851$	11.4782	+	11.4782i	0.393469	+	0.393469i
$852$	−2.29934	+	3.68229i	−0.0787743	+	0.126153i
$853$			16.6692i			0.570742i	0.958417	+	0.285371i	$0.0921169\pi$
$853$			16.6692i			0.570742i	−0.958417	+	0.285371i	$0.907883\pi$
$854$	9.00474	−	31.4218i	0.308136	−	1.07523i
$855$		0			0
$856$	−34.3957	+	30.9993i	−1.17562	+	1.05953i
$857$	−4.73331	−	4.73331i	−0.161687	−	0.161687i	0.621627	−	0.783314i	$-0.286472\pi$
$857$	−4.73331	−	4.73331i	−0.161687	−	0.161687i	−0.783314	+	0.621627i	$0.786472\pi$
$858$	−2.02328	−	3.64875i	−0.0690736	−	0.124566i
$859$	−26.3237	−	26.3237i	−0.898152	−	0.898152i	0.0971203	−	0.995273i	$-0.469037\pi$
$859$	−26.3237	−	26.3237i	−0.898152	−	0.898152i	−0.995273	+	0.0971203i	$0.969037\pi$
$860$		0			0
$861$	1.93778	−	1.93778i	0.0660394	−	0.0660394i
$862$	−4.93456	+	17.2190i	−0.168072	+	0.586483i
$863$	8.71130	−	8.71130i	0.296536	−	0.296536i	−0.543119	−	0.839655i	$-0.682757\pi$
$863$	8.71130	−	8.71130i	0.296536	−	0.296536i	0.839655	+	0.543119i	$0.182757\pi$
$864$	−6.88401	+	1.21939i	−0.234199	+	0.0414846i
$865$		0			0
$866$	−10.7172	−	19.3272i	−0.364184	−	0.656764i
$867$	−0.966284			−0.0328167
$868$	−5.25285	−	22.7201i	−0.178293	−	0.771171i
$869$	20.8170	−	20.8170i	0.706167	−	0.706167i
$870$		0			0
$871$	−52.7334			−1.78680
$872$	0.414936	−	7.98923i	0.0140515	−	0.270550i
$873$	−36.0815	+	36.0815i	−1.22117	+	1.22117i
$874$	−6.09241	−	1.74594i	−0.206079	−	0.0590572i
$875$		0			0
$876$	−0.633277	−	2.73911i	−0.0213965	−	0.0925461i
$877$		−	33.6674i		−	1.13687i	−0.822730	−	0.568433i	$-0.807550\pi$
$877$		−	33.6674i		−	1.13687i	0.822730	−	0.568433i	$-0.192450\pi$
$878$	7.98426	−	27.8609i	0.269456	−	0.940260i
$879$	0.172172			0.00580721
$880$		0			0
$881$	27.3058			0.919956			0.459978	−	0.887930i	$-0.347857\pi$
$881$	27.3058			0.919956			0.459978	+	0.887930i	$0.347857\pi$
$882$	4.03834	−	14.0917i	0.135978	−	0.474492i
$883$			27.9628i			0.941023i	0.882394	+	0.470511i	$0.155930\pi$
$883$			27.9628i			0.941023i	−0.882394	+	0.470511i	$0.844070\pi$
$884$	−38.1058	+	8.80999i	−1.28164	+	0.296312i
$885$		0			0
$886$	−14.9712	−	4.29038i	−0.502966	−	0.144138i
$887$	−12.4497	+	12.4497i	−0.418020	+	0.418020i	−0.884521	−	0.466501i	$-0.845514\pi$
$887$	−12.4497	+	12.4497i	−0.418020	+	0.418020i	0.466501	+	0.884521i	$0.345514\pi$
$888$	−1.87197	+	1.68712i	−0.0628192	+	0.0566161i
$889$	−14.6975			−0.492939
$890$		0			0
$891$	−20.6132	+	20.6132i	−0.690567	+	0.690567i
$892$	−9.65235	+	2.23160i	−0.323185	+	0.0747196i
$893$	13.9470			0.466718
$894$	−0.569207	−	1.02650i	−0.0190371	−	0.0343312i
$895$		0			0
$896$	8.28512	+	19.4592i	0.276786	+	0.650086i
$897$	2.33011	−	2.33011i	0.0778002	−	0.0778002i
$898$	6.01628	−	20.9937i	0.200766	−	0.700567i
$899$	−15.9331	+	15.9331i	−0.531398	+	0.531398i
$900$		0			0
$901$	−25.2289	−	25.2289i	−0.840498	−	0.840498i
$902$	−16.3988	−	29.5734i	−0.546022	−	0.984685i
$903$	2.58680	+	2.58680i	0.0860833	+	0.0860833i
$904$	−2.46240	+	47.4113i	−0.0818981	+	1.57688i
$905$		0			0
$906$	−0.576165	+	2.01051i	−0.0191418	+	0.0667948i
$907$			38.3527i			1.27348i	0.771078	+	0.636740i	$0.219718\pi$
$907$			38.3527i			1.27348i	−0.771078	+	0.636740i	$0.780282\pi$
$908$	−1.05586	−	0.659317i	−0.0350400	−	0.0218802i
$909$	−19.1269	−	19.1269i	−0.634398	−	0.634398i
$910$		0			0
$911$		−	24.0192i		−	0.795791i	−0.917431	−	0.397895i	$-0.869741\pi$
$911$		−	24.0192i		−	0.795791i	0.917431	−	0.397895i	$-0.130259\pi$
$912$	0.319741	−	0.930488i	0.0105877	−	0.0308115i
$913$	9.91884	+	9.91884i	0.328266	+	0.328266i
$914$	−3.04752	−	5.49585i	−0.100803	−	0.181787i
$915$		0			0
$916$	25.7920	−	5.96307i	0.852193	−	0.197025i
$917$	−8.35846			−0.276021
$918$	−3.94447	−	7.11338i	−0.130187	−	0.234777i
$919$			25.1211i			0.828668i	0.910125	+	0.414334i	$0.135986\pi$
$919$			25.1211i			0.828668i	−0.910125	+	0.414334i	$0.864014\pi$
$920$		0			0
$921$			5.89448i			0.194230i
$922$	−14.7909	+	8.20177i	−0.487113	+	0.270111i
$923$	−43.9639			−1.44709
$924$	−2.22646	−	1.39028i	−0.0732450	−	0.0457367i
$925$		0			0
$926$	−37.7556	+	20.9360i	−1.24073	+	0.688000i
$927$	−19.3750	−	19.3750i	−0.636358	−	0.636358i
$928$	11.7086	−	16.7495i	0.384352	−	0.549828i
$929$			39.8307i			1.30680i	0.757012	+	0.653401i	$0.226658\pi$
$929$			39.8307i			1.30680i	−0.757012	+	0.653401i	$0.773342\pi$
$930$		0			0
$931$	2.93876	+	2.93876i	0.0963139	+	0.0963139i
$932$	−4.93405	+	1.14074i	−0.161620	+	0.0373663i
$933$		−	6.59927i		−	0.216051i
$934$	−30.5723	−	8.76128i	−1.00036	−	0.286678i
$935$		0			0
$936$	−23.5284	−	26.1062i	−0.769049	−	0.853309i
$937$	18.2763	+	18.2763i	0.597060	+	0.597060i	0.939529	−	0.342469i	$-0.111263\pi$
$937$	18.2763	+	18.2763i	0.597060	+	0.597060i	−0.342469	+	0.939529i	$0.611263\pi$
$938$	−29.0144	+	16.0889i	−0.947355	+	0.525321i
$939$	−3.89474	−	3.89474i	−0.127100	−	0.127100i
$940$		0			0
$941$	−2.34852	+	2.34852i	−0.0765597	+	0.0765597i	−0.744350	−	0.667790i	$-0.767240\pi$
$941$	−2.34852	+	2.34852i	−0.0765597	+	0.0765597i	0.667790	+	0.744350i	$0.267240\pi$
$942$	5.84892	+	1.67616i	0.190568	+	0.0546122i
$943$	18.8857	−	18.8857i	0.615004	−	0.615004i
$944$	13.0073	−	37.8530i	0.423352	−	1.23201i
$945$		0			0
$946$	39.4783	−	21.8913i	1.28355	−	0.711746i
$947$	18.7829			0.610363			0.305181	−	0.952294i	$-0.401283\pi$
$947$	18.7829			0.610363			0.305181	+	0.952294i	$0.401283\pi$
$948$	−1.91194	+	3.06187i	−0.0620968	+	0.0994450i
$949$	20.1320	−	20.1320i	0.653511	−	0.653511i
$950$		0			0
$951$	2.20341			0.0714505
$952$	−18.2783	+	16.4734i	−0.592402	+	0.533905i
$953$	−9.07454	+	9.07454i	−0.293953	+	0.293953i	−0.838640	−	0.544687i	$-0.816649\pi$
$953$	−9.07454	+	9.07454i	−0.293953	+	0.293953i	0.544687	+	0.838640i	$0.316649\pi$
$954$	8.83223	−	30.8199i	0.285954	−	0.997830i
$955$		0			0
$956$	35.4649	+	22.1455i	1.14702	+	0.716236i
$957$			2.53633i			0.0819879i
$958$	−1.15913	−	0.332179i	−0.0374499	−	0.0107322i
$959$	1.34130			0.0433130
$960$		0			0
$961$	−7.90304			−0.254937
$962$	−24.5332	−	7.03063i	−0.790982	−	0.226677i
$963$		−	48.4077i		−	1.55992i
$964$	−6.27772	−	3.92002i	−0.202192	−	0.126255i
$965$		0			0
$966$	0.571136	−	1.99297i	0.0183760	−	0.0641226i
$967$	−13.3057	+	13.3057i	−0.427882	+	0.427882i	−0.887906	−	0.460024i	$-0.847841\pi$
$967$	−13.3057	+	13.3057i	−0.427882	+	0.427882i	0.460024	+	0.887906i	$0.347841\pi$
$968$	−0.948659	+	0.854983i	−0.0304910	+	0.0274802i
$969$	1.14470			0.0367730
$970$		0			0
$971$	18.6349	−	18.6349i	0.598023	−	0.598023i	−0.341763	−	0.939786i	$-0.611024\pi$
$971$	18.6349	−	18.6349i	0.598023	−	0.598023i	0.939786	+	0.341763i	$0.111024\pi$
$972$	5.82074	−	9.32163i	0.186700	−	0.298991i
$973$	−14.5960			−0.467926
$974$	−4.37198	+	2.42432i	−0.140087	+	0.0776803i
$975$		0			0
$976$	46.7716	+	16.0720i	1.49712	+	0.514453i
$977$	−7.28407	+	7.28407i	−0.233038	+	0.233038i	−0.813960	−	0.580921i	$-0.802692\pi$
$977$	−7.28407	+	7.28407i	−0.233038	+	0.233038i	0.580921	+	0.813960i	$0.302692\pi$
$978$	3.07394	+	0.880918i	0.0982938	+	0.0281686i
$979$	1.31244	−	1.31244i	0.0419457	−	0.0419457i
$980$		0			0
$981$	5.91391	+	5.91391i	0.188817	+	0.188817i
$982$	−38.6858	+	21.4518i	−1.23451	+	0.684554i
$983$	31.0322	+	31.0322i	0.989772	+	0.989772i	0.999948	−	0.0101761i	$-0.00323922\pi$
$983$	31.0322	+	31.0322i	0.989772	+	0.989772i	−0.0101761	+	0.999948i	$0.503239\pi$
$984$	2.77591	+	3.08005i	0.0884929	+	0.0981885i
$985$		0			0
$986$	22.8562	+	6.55003i	0.727889	+	0.208596i
$987$			4.56238i			0.145222i
$988$	9.70786	−	2.24444i	0.308848	−	0.0714051i
$989$	25.2111	+	25.2111i	0.801666	+	0.801666i
$990$		0			0
$991$			40.1060i			1.27401i	0.770860	+	0.637004i	$0.219827\pi$
$991$			40.1060i			1.27401i	−0.770860	+	0.637004i	$0.780173\pi$
$992$	34.7423	−	6.15404i	1.10307	−	0.195391i
$993$	−4.64931	−	4.64931i	−0.147541	−	0.147541i
$994$	−24.1893	+	13.4133i	−0.767239	+	0.425445i
$995$		0			0
$996$	−1.45892	−	0.910997i	−0.0462275	−	0.0288661i
$997$	−2.58204			−0.0817740			−0.0408870	−	0.999164i	$-0.513018\pi$
$997$	−2.58204			−0.0817740			−0.0408870	+	0.999164i	$0.513018\pi$
$998$	13.5364	−	7.50611i	0.428487	−	0.237602i
$999$		−	5.30749i		−	0.167921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.c.43.1	✓	16
4.3	odd	2		1600.2.j.c.143.5		16
5.2	odd	4		400.2.s.c.107.5	yes	16
5.3	odd	4		400.2.s.c.107.4	yes	16
5.4	even	2	inner	400.2.j.c.43.8	yes	16
16.3	odd	4		400.2.s.c.243.5	yes	16
16.13	even	4		1600.2.s.c.943.5		16
20.3	even	4		1600.2.s.c.207.4		16
20.7	even	4		1600.2.s.c.207.5		16
20.19	odd	2		1600.2.j.c.143.4		16
80.3	even	4	inner	400.2.j.c.307.8	yes	16
80.13	odd	4		1600.2.j.c.1007.5		16
80.19	odd	4		400.2.s.c.243.4	yes	16
80.29	even	4		1600.2.s.c.943.4		16
80.67	even	4	inner	400.2.j.c.307.1	yes	16
80.77	odd	4		1600.2.j.c.1007.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.1	✓	16	1.1	even	1	trivial
400.2.j.c.43.8	yes	16	5.4	even	2	inner
400.2.j.c.307.1	yes	16	80.67	even	4	inner
400.2.j.c.307.8	yes	16	80.3	even	4	inner
400.2.s.c.107.4	yes	16	5.3	odd	4
400.2.s.c.107.5	yes	16	5.2	odd	4
400.2.s.c.243.4	yes	16	80.19	odd	4
400.2.s.c.243.5	yes	16	16.3	odd	4
1600.2.j.c.143.4		16	20.19	odd	2
1600.2.j.c.143.5		16	4.3	odd	2
1600.2.j.c.1007.4		16	80.77	odd	4
1600.2.j.c.1007.5		16	80.13	odd	4
1600.2.s.c.207.4		16	20.3	even	4
1600.2.s.c.207.5		16	20.7	even	4
1600.2.s.c.943.4		16	80.29	even	4
1600.2.s.c.943.5		16	16.13	even	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35949 - 0.389597i) q^{2} -0.207468i q^{3} +(1.69643 + 1.05931i) q^{4} +(-0.0808289 + 0.282051i) q^{6} +(-1.32185 + 1.32185i) q^{7} +(-1.89357 - 2.10104i) q^{8} +2.95696 q^{9} +(-2.39286 + 2.39286i) q^{11} +(0.219772 - 0.351954i) q^{12} +4.20208 q^{13} +(2.31203 - 1.28205i) q^{14} +(1.75574 + 3.59408i) q^{16} +(-3.29071 + 3.29071i) q^{17} +(-4.01995 - 1.15202i) q^{18} +(0.838342 - 0.838342i) q^{19} +(0.274241 + 0.274241i) q^{21} +(4.18531 - 2.32081i) q^{22} +(2.67277 + 2.67277i) q^{23} +(-0.435899 + 0.392856i) q^{24} +(-5.71269 - 1.63712i) q^{26} -1.23588i q^{27} +(-3.64266 + 0.842176i) q^{28} +(2.55451 + 2.55451i) q^{29} +6.23723i q^{31} +(-0.986662 - 5.57014i) q^{32} +(0.496441 + 0.496441i) q^{33} +(5.75574 - 3.19163i) q^{34} +(5.01626 + 3.13233i) q^{36} +4.29451 q^{37} +(-1.46633 + 0.813102i) q^{38} -0.871798i q^{39} -7.06598i q^{41} +(-0.265984 - 0.479671i) q^{42} +9.43258 q^{43} +(-6.59408 + 1.52454i) q^{44} +(-2.59230 - 4.67491i) q^{46} +(8.31820 + 8.31820i) q^{47} +(0.745656 - 0.364259i) q^{48} +3.50544i q^{49} +(0.682716 + 0.682716i) q^{51} +(7.12853 + 4.45130i) q^{52} +7.66672i q^{53} +(-0.481494 + 1.68016i) q^{54} +(5.28027 + 0.274241i) q^{56} +(-0.173929 - 0.173929i) q^{57} +(-2.47761 - 4.46807i) q^{58} +(-7.07557 - 7.07557i) q^{59} +(8.74267 - 8.74267i) q^{61} +(2.43001 - 8.47945i) q^{62} +(-3.90865 + 3.90865i) q^{63} +(-0.828755 + 7.95696i) q^{64} +(-0.481494 - 0.868318i) q^{66} -12.5494 q^{67} +(-9.06832 + 2.09658i) q^{68} +(0.554514 - 0.554514i) q^{69} -10.4624 q^{71} +(-5.59922 - 6.21269i) q^{72} +(4.79095 - 4.79095i) q^{73} +(-5.83834 - 1.67313i) q^{74} +(2.31025 - 0.534125i) q^{76} -6.32598i q^{77} +(-0.339650 + 1.18520i) q^{78} -8.69963 q^{79} +8.61447 q^{81} +(-2.75289 + 9.60614i) q^{82} -4.14519i q^{83} +(0.174724 + 0.755735i) q^{84} +(-12.8235 - 3.67491i) q^{86} +(0.529980 - 0.529980i) q^{87} +(9.55854 + 0.496441i) q^{88} -0.548482 q^{89} +(-5.55451 + 5.55451i) q^{91} +(1.70288 + 7.36544i) q^{92} +1.29403 q^{93} +(-8.06776 - 14.5493i) q^{94} +(-1.15563 + 0.204701i) q^{96} +(-12.2022 + 12.2022i) q^{97} +(1.36571 - 4.76561i) q^{98} +(-7.07557 + 7.07557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 12 q^{6} - 16 q^{9} + 8 q^{11} - 20 q^{14} - 16 q^{16} - 8 q^{19} - 24 q^{24} + 16 q^{26} + 16 q^{29} + 48 q^{34} - 4 q^{36} - 40 q^{44} + 36 q^{46} - 48 q^{51} + 32 q^{54} + 64 q^{56}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 12 * q^6 - 16 * q^9 + 8 * q^11 - 20 * q^14 - 16 * q^16 - 8 * q^19 - 24 * q^24 + 16 * q^26 + 16 * q^29 + 48 * q^34 - 4 * q^36 - 40 * q^44 + 36 * q^46 - 48 * q^51 + 32 * q^54 + 64 * q^56 - 8 * q^59 - 16 * q^61 + 16 * q^64 + 32 * q^66 - 16 * q^69 - 32 * q^71 - 72 * q^74 - 32 * q^76 + 80 * q^79 + 16 * q^81 + 136 * q^84 - 60 * q^86 - 64 * q^91 - 28 * q^94 - 56 * q^96 - 8 * q^99

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