LMFDB - Embedded newform 400.2.s.c.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.s (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			107.5
Root			$-1.35949 + 0.389597i$ of defining polynomial
Character	$\chi$	$=$	400.107
Dual form			400.2.s.c.243.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.389597 - 1.35949i) q^{2} -0.207468 q^{3} +(-1.69643 - 1.05931i) q^{4} +(-0.0808289 + 0.282051i) q^{6} +(-1.32185 - 1.32185i) q^{7} +(-2.10104 + 1.89357i) q^{8} -2.95696 q^{9} +(-2.39286 + 2.39286i) q^{11} +(0.351954 + 0.219772i) q^{12} -4.20208i q^{13} +(-2.31203 + 1.28205i) q^{14} +(1.75574 + 3.59408i) q^{16} +(-3.29071 - 3.29071i) q^{17} +(-1.15202 + 4.01995i) q^{18} +(-0.838342 + 0.838342i) q^{19} +(0.274241 + 0.274241i) q^{21} +(2.32081 + 4.18531i) q^{22} +(2.67277 - 2.67277i) q^{23} +(0.435899 - 0.392856i) q^{24} +(-5.71269 - 1.63712i) q^{26} +1.23588 q^{27} +(0.842176 + 3.64266i) q^{28} +(-2.55451 - 2.55451i) q^{29} +6.23723i q^{31} +(5.57014 - 0.986662i) q^{32} +(0.496441 - 0.496441i) q^{33} +(-5.75574 + 3.19163i) q^{34} +(5.01626 + 3.13233i) q^{36} +4.29451i q^{37} +(0.813102 + 1.46633i) q^{38} +0.871798i q^{39} -7.06598i q^{41} +(0.479671 - 0.265984i) q^{42} -9.43258i q^{43} +(6.59408 - 1.52454i) q^{44} +(-2.59230 - 4.67491i) q^{46} +(-8.31820 + 8.31820i) q^{47} +(-0.364259 - 0.745656i) q^{48} -3.50544i q^{49} +(0.682716 + 0.682716i) q^{51} +(-4.45130 + 7.12853i) q^{52} +7.66672 q^{53} +(0.481494 - 1.68016i) q^{54} +(5.28027 + 0.274241i) q^{56} +(0.173929 - 0.173929i) q^{57} +(-4.46807 + 2.47761i) q^{58} +(7.07557 + 7.07557i) q^{59} +(8.74267 - 8.74267i) q^{61} +(8.47945 + 2.43001i) q^{62} +(3.90865 + 3.90865i) q^{63} +(0.828755 - 7.95696i) q^{64} +(-0.481494 - 0.868318i) q^{66} -12.5494i q^{67} +(2.09658 + 9.06832i) q^{68} +(-0.554514 + 0.554514i) q^{69} -10.4624 q^{71} +(6.21269 - 5.59922i) q^{72} +(-4.79095 - 4.79095i) q^{73} +(5.83834 + 1.67313i) q^{74} +(2.31025 - 0.534125i) q^{76} +6.32598 q^{77} +(1.18520 + 0.339650i) q^{78} +8.69963 q^{79} +8.61447 q^{81} +(-9.60614 - 2.75289i) q^{82} -4.14519 q^{83} +(-0.174724 - 0.755735i) q^{84} +(-12.8235 - 3.67491i) q^{86} +(0.529980 + 0.529980i) q^{87} +(0.496441 - 9.55854i) q^{88} +0.548482 q^{89} +(-5.55451 + 5.55451i) q^{91} +(-7.36544 + 1.70288i) q^{92} -1.29403i q^{93} +(8.06776 + 14.5493i) q^{94} +(-1.15563 + 0.204701i) q^{96} +(-12.2022 - 12.2022i) q^{97} +(-4.76561 - 1.36571i) 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.389597	−	1.35949i	0.275487	−	0.961305i
$2$	0.389597	−	1.35949i	0.275487	−	0.961305i
$3$	−0.207468			−0.119782			−0.0598908	−	0.998205i	$-0.519075\pi$
$3$	−0.207468			−0.119782			−0.0598908	+	0.998205i	$0.519075\pi$
$4$	−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	0.411706	−	0.911317i	$-0.364933\pi$
$7$	−1.32185	−	1.32185i	−0.499611	−	0.499611i	−0.911317	+	0.411706i	$0.864933\pi$
$8$	−2.10104	+	1.89357i	−0.742831	+	0.669480i
$9$	−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	$0.420413\pi$
$12$	0.351954	+	0.219772i	0.101600	+	0.0634428i
$13$		−	4.20208i		−	1.16545i	−0.812670	−	0.582724i	$-0.801987\pi$
$13$		−	4.20208i		−	1.16545i	0.812670	−	0.582724i	$-0.198013\pi$
$14$	−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	0.184684	−	0.982798i	$-0.440874\pi$
$17$	−3.29071	−	3.29071i	−0.798114	−	0.798114i	−0.982798	+	0.184684i	$0.940874\pi$
$18$	−1.15202	+	4.01995i	−0.271534	+	0.947512i
$19$	−0.838342	+	0.838342i	−0.192329	+	0.192329i	−0.796702	−	0.604373i	$-0.793424\pi$
$19$	−0.838342	+	0.838342i	−0.192329	+	0.192329i	0.604373	+	0.796702i	$0.293424\pi$
$20$		0			0
$21$	0.274241	+	0.274241i	0.0598443	+	0.0598443i
$22$	2.32081	+	4.18531i	0.494799	+	0.892312i
$23$	2.67277	−	2.67277i	0.557311	−	0.557311i	−0.371230	−	0.928541i	$-0.621064\pi$
$23$	2.67277	−	2.67277i	0.557311	−	0.557311i	0.928541	+	0.371230i	$0.121064\pi$
$24$	0.435899	−	0.392856i	0.0889775	−	0.0801914i
$25$		0			0
$26$	−5.71269	−	1.63712i	−1.12035	−	0.321066i
$27$	1.23588			0.237845
$28$	0.842176	+	3.64266i	0.159156	+	0.688398i
$29$	−2.55451	−	2.55451i	−0.474361	−	0.474361i	0.428961	−	0.903323i	$-0.358880\pi$
$29$	−2.55451	−	2.55451i	−0.474361	−	0.474361i	−0.903323	+	0.428961i	$0.858880\pi$
$30$		0			0
$31$			6.23723i			1.12024i	0.828412	+	0.560120i	$0.189245\pi$
$31$			6.23723i			1.12024i	−0.828412	+	0.560120i	$0.810755\pi$
$32$	5.57014	−	0.986662i	0.984672	−	0.174419i
$33$	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
$37$			4.29451i			0.706013i	0.935621	+	0.353006i	$0.114841\pi$
$37$			4.29451i			0.706013i	−0.935621	+	0.353006i	$0.885159\pi$
$38$	0.813102	+	1.46633i	0.131903	+	0.237871i
$39$			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	$-0.186044\pi$
$42$	0.479671	−	0.265984i	0.0740149	−	0.0410423i
$43$		−	9.43258i		−	1.43845i	−0.694775	−	0.719227i	$-0.744496\pi$
$43$		−	9.43258i		−	1.43845i	0.694775	−	0.719227i	$-0.255504\pi$
$44$	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	−0.243410	+	0.969923i	$0.578266\pi$
$47$	−8.31820	+	8.31820i	−1.21333	+	1.21333i	−0.969923	+	0.243410i	$0.921734\pi$
$48$	−0.364259	−	0.745656i	−0.0525762	−	0.107626i
$49$		−	3.50544i		−	0.500777i
$50$		0			0
$51$	0.682716	+	0.682716i	0.0955994	+	0.0955994i
$52$	−4.45130	+	7.12853i	−0.617284	+	0.988550i
$53$	7.66672			1.05311			0.526553	−	0.850143i	$-0.323484\pi$
$53$	7.66672			1.05311			0.526553	+	0.850143i	$0.323484\pi$
$54$	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
$58$	−4.46807	+	2.47761i	−0.586686	+	0.325325i
$59$	7.07557	+	7.07557i	0.921161	+	0.921161i	0.997112	−	0.0759506i	$-0.0241991\pi$
$59$	7.07557	+	7.07557i	0.921161	+	0.921161i	−0.0759506	+	0.997112i	$0.524199\pi$
$60$		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	$-0.0407120\pi$
$62$	8.47945	+	2.43001i	1.07689	+	0.308611i
$63$	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
$67$		−	12.5494i		−	1.53315i	−0.642156	−	0.766574i	$-0.721960\pi$
$67$		−	12.5494i		−	1.53315i	0.642156	−	0.766574i	$-0.278040\pi$
$68$	2.09658	+	9.06832i	0.254247	+	1.09970i
$69$	−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	$0.713204\pi$
$72$	6.21269	−	5.59922i	0.732173	−	0.659874i
$73$	−4.79095	−	4.79095i	−0.560738	−	0.560738i	0.368779	−	0.929517i	$-0.379776\pi$
$73$	−4.79095	−	4.79095i	−0.560738	−	0.560738i	−0.929517	+	0.368779i	$0.879776\pi$
$74$	5.83834	+	1.67313i	0.678693	+	0.194497i
$75$		0			0
$76$	2.31025	−	0.534125i	0.265004	−	0.0612683i
$77$	6.32598			0.720912
$78$	1.18520	+	0.339650i	0.134198	+	0.0384578i
$79$	8.69963			0.978784			0.489392	−	0.872064i	$-0.337219\pi$
$79$	8.69963			0.978784			0.489392	+	0.872064i	$0.337219\pi$
$80$		0			0
$81$	8.61447			0.957163
$82$	−9.60614	−	2.75289i	−1.06082	−	0.304006i
$83$	−4.14519			−0.454993			−0.227497	−	0.973779i	$-0.573054\pi$
$83$	−4.14519			−0.454993			−0.227497	+	0.973779i	$0.573054\pi$
$84$	−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
$88$	0.496441	−	9.55854i	0.0529208	−	1.01894i
$89$	0.548482			0.0581390			0.0290695	−	0.999577i	$-0.490746\pi$
$89$	0.548482			0.0581390			0.0290695	+	0.999577i	$0.490746\pi$
$90$		0			0
$91$	−5.55451	+	5.55451i	−0.582271	+	0.582271i
$92$	−7.36544	+	1.70288i	−0.767901	+	0.177537i
$93$		−	1.29403i		−	0.134184i
$94$	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	−0.960431	−	0.278518i	$-0.910157\pi$
$97$	−12.2022	−	12.2022i	−1.23895	−	1.23895i	−0.278518	−	0.960431i	$-0.589843\pi$
$98$	−4.76561	−	1.36571i	−0.481399	−	0.137957i
$99$	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	$0.900403\pi$
$102$	1.19413	−	0.662162i	0.118237	−	0.0655638i
$103$	−6.55234	+	6.55234i	−0.645621	+	0.645621i	−0.951932	−	0.306310i	$-0.900905\pi$
$103$	−6.55234	+	6.55234i	−0.645621	+	0.645621i	0.306310	+	0.951932i	$0.400905\pi$
$104$	7.95696	+	8.82875i	0.780244	+	0.865731i
$105$		0			0
$106$	2.98693	−	10.4228i	0.290117	−	1.01235i
$107$	16.3708			1.58262			0.791312	−	0.611413i	$-0.209399\pi$
$107$	16.3708			1.58262			0.791312	+	0.611413i	$0.209399\pi$
$108$	−2.09658	−	1.30917i	−0.201743	−	0.125975i
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	0.604807	−	0.796372i	$-0.293250\pi$
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	−0.796372	+	0.604807i	$0.793250\pi$
$110$		0			0
$111$		−	0.890973i		−	0.0845674i
$112$	2.43001	−	7.07164i	0.229614	−	0.668207i
$113$	−11.8688	+	11.8688i	−1.11652	+	1.11652i	−0.124275	+	0.992248i	$0.539661\pi$
$113$	−11.8688	+	11.8688i	−1.11652	+	1.11652i	−0.992248	+	0.124275i	$0.960339\pi$
$114$	−0.168693	−	0.304217i	−0.0157995	−	0.0284926i
$115$		0			0
$116$	1.62753	+	7.03956i	0.151113	+	0.653607i
$117$			12.4254i			1.14873i
$118$	12.3758	−	6.86255i	1.13928	−	0.631749i
$119$			8.69963i			0.797493i
$120$		0			0
$121$		−	0.451518i		−	0.0410471i
$122$	−8.47945	−	15.2917i	−0.767694	−	1.38444i
$123$			1.46597i			0.132182i
$124$	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	$-0.863421\pi$
$127$	−5.55946	+	5.55946i	−0.493322	+	0.493322i	0.416029	+	0.909351i	$0.363421\pi$
$128$	−10.4945	−	4.22669i	−0.927594	−	0.373590i
$129$			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	$0.687423\pi$
$132$	−1.36806	+	0.316293i	−0.119074	+	0.0275297i
$133$	2.21632			0.192179
$134$	−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	$-0.740242\pi$
$137$	0.507360	−	0.507360i	0.0433467	−	0.0433467i	0.728448	+	0.685101i	$0.240242\pi$
$138$	0.537819	+	0.969893i	0.0457822	+	0.0825628i
$139$	−5.52106	−	5.52106i	−0.468290	−	0.468290i	0.433070	−	0.901360i	$-0.357430\pi$
$139$	−5.52106	−	5.52106i	−0.468290	−	0.468290i	−0.901360	+	0.433070i	$0.857430\pi$
$140$		0			0
$141$	1.72576	−	1.72576i	0.145335	−	0.145335i
$142$	−4.07612	+	14.2235i	−0.342060	+	1.19361i
$143$	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
$147$			0.727266i			0.0599839i
$148$	4.54920	−	7.28532i	0.373942	−	0.598850i
$149$	2.82875	−	2.82875i	0.231741	−	0.231741i	−0.581678	−	0.813419i	$-0.697604\pi$
$149$	2.82875	−	2.82875i	0.231741	−	0.231741i	0.813419	+	0.581678i	$0.197604\pi$
$150$		0			0
$151$	7.12820			0.580085			0.290042	−	0.957014i	$-0.406331\pi$
$151$	7.12820			0.580085			0.290042	+	0.957014i	$0.406331\pi$
$152$	0.173929	−	3.34885i	0.0141075	−	0.271628i
$153$	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
$157$	20.7371			1.65500			0.827501	−	0.561464i	$-0.189762\pi$
$157$	20.7371			1.65500			0.827501	+	0.561464i	$0.189762\pi$
$158$	3.38935	−	11.8271i	0.269642	−	0.940910i
$159$	−1.59060			−0.126143
$160$		0			0
$161$	−7.06598			−0.556878
$162$	3.35617	−	11.7113i	0.263686	−	0.920125i
$163$	−10.8985			−0.853640			−0.426820	−	0.904337i	$-0.640366\pi$
$163$	−10.8985			−0.853640			−0.426820	+	0.904337i	$0.640366\pi$
$164$	−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	0.658871	−	0.752256i	$-0.271034\pi$
$167$	−1.20680	−	1.20680i	−0.0933853	−	0.0933853i	−0.752256	+	0.658871i	$0.771034\pi$
$168$	−1.09549	−	0.0568962i	−0.0845187	−	0.00438964i
$169$	−4.65751			−0.358270
$170$		0			0
$171$	2.47894	−	2.47894i	0.189569	−	0.189569i
$172$	−9.99200	+	16.0017i	−0.761883	+	1.22012i
$173$		−	5.12438i		−	0.389599i	−0.980843	−	0.194800i	$-0.937594\pi$
$173$		−	5.12438i		−	0.389599i	0.980843	−	0.194800i	$-0.0624057\pi$
$174$	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
$178$	0.213687	−	0.745656i	0.0160165	−	0.0558893i
$179$	−12.6301	+	12.6301i	−0.944017	+	0.944017i	−0.998514	−	0.0544970i	$-0.982644\pi$
$179$	−12.6301	+	12.6301i	−0.944017	+	0.944017i	0.0544970	+	0.998514i	$0.482644\pi$
$180$		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	$0.603171\pi$
$182$	5.38728	+	9.71533i	0.399332	+	0.720148i
$183$	−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
$187$	15.7484			1.15164
$188$	22.9228	−	5.29969i	1.67181	−	0.386520i
$189$	−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	$0.865267\pi$
$192$	−0.171940	+	1.65081i	−0.0124087	+	0.119137i
$193$	−11.0245	+	11.0245i	−0.793561	+	0.793561i	−0.982071	−	0.188510i	$-0.939634\pi$
$193$	−11.0245	+	11.0245i	−0.793561	+	0.793561i	0.188510	+	0.982071i	$0.439634\pi$
$194$	−21.3428	+	11.8349i	−1.53232	+	0.849694i
$195$		0			0
$196$	−3.71334	+	5.94672i	−0.265238	+	0.424766i
$197$			21.1953i			1.51010i	0.655667	+	0.755050i	$0.272388\pi$
$197$			21.1953i			1.51010i	−0.655667	+	0.755050i	$0.727612\pi$
$198$	−6.86255	−	12.3758i	−0.487700	−	0.879509i
$199$		−	8.68045i		−	0.615341i	−0.951493	−	0.307670i	$-0.900451\pi$
$199$		−	8.68045i		−	0.615341i	0.951493	−	0.307670i	$-0.0995494\pi$
$200$		0			0
$201$			2.60359i			0.183643i
$202$	−11.3138	+	6.27368i	−0.796039	+	0.441415i
$203$			6.75335i			0.473993i
$204$	−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
$208$	15.1026	−	7.37775i	1.04718	−	0.511555i
$209$		−	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	$0.849053\pi$
$212$	−13.0060	−	8.12141i	−0.893258	−	0.557781i
$213$	2.17061			0.148728
$214$	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
$218$	−3.49818	+	1.93979i	−0.236926	+	0.131379i
$219$	0.993968	+	0.993968i	0.0671661	+	0.0671661i
$220$		0			0
$221$	−13.8278	+	13.8278i	−0.930160	+	0.930160i
$222$	−1.21127	−	0.347120i	−0.0812950	−	0.0232972i
$223$	3.50264	+	3.50264i	0.234554	+	0.234554i	0.814591	−	0.580036i	$-0.196962\pi$
$223$	3.50264	+	3.50264i	0.234554	+	0.234554i	−0.580036	+	0.814591i	$0.696962\pi$
$224$	−8.66710	−	6.05866i	−0.579095	−	0.404811i
$225$		0			0
$226$	11.5115	+	20.7596i	0.765732	+	1.38091i
$227$		−	0.622404i		−	0.0413104i	−0.999787	−	0.0206552i	$-0.993425\pi$
$227$		−	0.622404i		−	0.0413104i	0.999787	−	0.0206552i	$-0.00657522\pi$
$228$	−0.479303	+	0.110814i	−0.0317426	+	0.00733882i
$229$	−9.35940	+	9.35940i	−0.618487	+	0.618487i	−0.945143	−	0.326657i	$-0.894078\pi$
$229$	−9.35940	+	9.35940i	−0.618487	+	0.618487i	0.326657	+	0.945143i	$0.394078\pi$
$230$		0			0
$231$	−1.31244			−0.0863521
$232$	10.2043	+	0.529980i	0.669945	+	0.0347949i
$233$	1.79047	+	1.79047i	0.117297	+	0.117297i	0.763319	−	0.646022i	$-0.223568\pi$
$233$	1.79047	+	1.79047i	0.117297	+	0.117297i	−0.646022	+	0.763319i	$0.723568\pi$
$234$	16.8922	+	4.84089i	1.10428	+	0.316459i
$235$		0			0
$236$	−4.50799	−	19.4984i	−0.293445	−	1.26924i
$237$	−1.80489			−0.117240
$238$	11.8271	+	3.38935i	0.766634	+	0.219699i
$239$	−20.9056			−1.35227			−0.676136	−	0.736777i	$-0.736347\pi$
$239$	−20.9056			−1.35227			−0.676136	+	0.736777i	$0.736347\pi$
$240$		0			0
$241$	−3.70055			−0.238374			−0.119187	−	0.992872i	$-0.538029\pi$
$241$	−3.70055			−0.238374			−0.119187	+	0.992872i	$0.538029\pi$
$242$	−0.613835	−	0.175910i	−0.0394588	−	0.0113079i
$243$	−5.49486			−0.352495
$244$	−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
$248$	−11.8107	−	13.1047i	−0.749977	−	0.832148i
$249$	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	$0.241047\pi$
$252$	−2.49028	−	10.7712i	−0.156873	−	0.678521i
$253$			12.7911i			0.804170i
$254$	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	0.584980	−	0.811048i	$-0.301102\pi$
$257$	−3.62414	−	3.62414i	−0.226068	−	0.226068i	−0.811048	+	0.584980i	$0.801102\pi$
$258$	2.66046	+	0.762425i	0.165633	+	0.0474665i
$259$	5.67668	−	5.67668i	0.352732	−	0.352732i
$260$		0			0
$261$	7.55359	+	7.55359i	0.467555	+	0.467555i
$262$	5.53002	−	3.06647i	0.341646	−	0.189447i
$263$	5.25957	−	5.25957i	0.324319	−	0.324319i	−0.526102	−	0.850421i	$-0.676347\pi$
$263$	5.25957	−	5.25957i	0.324319	−	0.324319i	0.850421	+	0.526102i	$0.176347\pi$
$264$	−0.102996	+	1.98309i	−0.00633894	+	0.122051i
$265$		0			0
$266$	0.863473	−	3.01307i	0.0529429	−	0.184743i
$267$	−0.113792			−0.00696398
$268$	−13.2936	+	21.2891i	−0.812037	+	1.30044i
$269$	8.82875	+	8.82875i	0.538299	+	0.538299i	0.923029	−	0.384730i	$-0.125706\pi$
$269$	8.82875	+	8.82875i	0.538299	+	0.538299i	−0.384730	+	0.923029i	$0.625706\pi$
$270$		0			0
$271$		−	30.9177i		−	1.87812i	−0.343760	−	0.939058i	$-0.611701\pi$
$271$		−	30.9177i		−	1.87812i	0.343760	−	0.939058i	$-0.388299\pi$
$272$	6.04945	−	17.6047i	0.366802	−	1.06744i
$273$	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
$277$		−	18.9322i		−	1.13753i	−0.822501	−	0.568764i	$-0.807422\pi$
$277$		−	18.9322i		−	1.13753i	0.822501	−	0.568764i	$-0.192578\pi$
$278$	−9.65681	+	5.35484i	−0.579177	+	0.321162i
$279$		−	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	$0.937724\pi$
$282$	−1.67380	−	3.01850i	−0.0996734	−	0.179749i
$283$		−	16.0721i		−	0.955390i	−0.878526	−	0.477695i	$-0.841472\pi$
$283$		−	16.0721i		−	0.955390i	0.878526	−	0.477695i	$-0.158528\pi$
$284$	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
$288$	−16.4707	+	2.91752i	−0.970544	+	0.171916i
$289$			4.65751i			0.273971i
$290$		0			0
$291$	2.53157	+	2.53157i	0.148403	+	0.148403i
$292$	3.05241	+	13.2026i	0.178629	+	0.772623i
$293$	0.829872			0.0484816			0.0242408	−	0.999706i	$-0.492283\pi$
$293$	0.829872			0.0484816			0.0242408	+	0.999706i	$0.492283\pi$
$294$	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
$298$	−2.74359	−	4.94774i	−0.158932	−	0.286615i
$299$	−11.2312	−	11.2312i	−0.649517	−	0.649517i
$300$		0			0
$301$	−12.4684	+	12.4684i	−0.718668	+	0.718668i
$302$	2.77713	−	9.69072i	0.159806	−	0.557638i
$303$	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
$307$		−	28.4115i		−	1.62153i	−0.585371	−	0.810766i	$-0.699051\pi$
$307$		−	28.4115i		−	1.62153i	0.585371	−	0.810766i	$-0.300949\pi$
$308$	−10.7316	−	6.70116i	−0.611488	−	0.381834i
$309$	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	$0.142208\pi$
$312$	−1.65081	−	1.83168i	−0.0934589	−	0.103699i
$313$	−18.7727	−	18.7727i	−1.06110	−	1.06110i	−0.998008	−	0.0630896i	$-0.979905\pi$
$313$	−18.7727	−	18.7727i	−1.06110	−	1.06110i	−0.0630896	−	0.998008i	$-0.520095\pi$
$314$	8.07913	−	28.1919i	0.455932	−	1.59096i
$315$		0			0
$316$	−14.7583	−	9.21558i	−0.830219	−	0.518417i
$317$	−10.6205			−0.596506			−0.298253	−	0.954487i	$-0.596404\pi$
$317$	−10.6205			−0.596506			−0.298253	+	0.954487i	$0.596404\pi$
$318$	−0.619693	+	2.16240i	−0.0347506	+	0.121262i
$319$	12.2252			0.684478
$320$		0			0
$321$	−3.39641			−0.189569
$322$	−2.75289	+	9.60614i	−0.153412	+	0.535329i
$323$	5.51748			0.307001
$324$	−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
$328$	13.3800	+	14.8459i	0.738785	+	0.819729i
$329$	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	$-0.0865153\pi$
$332$	7.03201	+	4.39103i	0.385932	+	0.240989i
$333$		−	12.6987i		−	0.695883i
$334$	−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	0.621958	−	0.783051i	$-0.286338\pi$
$337$	−2.95728	−	2.95728i	−0.161093	−	0.161093i	−0.783051	+	0.621958i	$0.786338\pi$
$338$	−1.81455	+	6.33184i	−0.0986987	+	0.344407i
$339$	2.46240	−	2.46240i	0.133739	−	0.133739i
$340$		0			0
$341$	−14.9248	−	14.9248i	−0.808223	−	0.808223i
$342$	−2.40431	−	4.33589i	−0.130010	−	0.234458i
$343$	−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
$347$	−13.8901			−0.745659			−0.372830	−	0.927900i	$-0.621612\pi$
$347$	−13.8901			−0.745659			−0.372830	+	0.927900i	$0.621612\pi$
$348$	−0.337661	−	1.46048i	−0.0181005	−	0.0782901i
$349$	13.4914	+	13.4914i	0.722176	+	0.722176i	0.969048	−	0.246872i	$-0.0794026\pi$
$349$	13.4914	+	13.4914i	0.722176	+	0.722176i	−0.246872	+	0.969048i	$0.579403\pi$
$350$		0			0
$351$		−	5.19326i		−	0.277196i
$352$	−10.9676	+	15.6895i	−0.584576	+	0.836253i
$353$	15.9785	−	15.9785i	0.850448	−	0.850448i	−0.139740	−	0.990188i	$-0.544627\pi$
$353$	15.9785	−	15.9785i	0.850448	−	0.850448i	0.990188	+	0.139740i	$0.0446268\pi$
$354$	−2.56758	+	1.42376i	−0.136465	+	0.0756719i
$355$		0			0
$356$	−0.930460	−	0.581011i	−0.0493143	−	0.0307935i
$357$		−	1.80489i		−	0.0955251i
$358$	12.2498	+	22.0911i	0.647424	+	1.16755i
$359$			28.2831i			1.49273i	0.665539	+	0.746363i	$0.268202\pi$
$359$			28.2831i			1.49273i	−0.665539	+	0.746363i	$0.731798\pi$
$360$		0			0
$361$			17.5944i			0.926019i
$362$	14.8120	−	8.21347i	0.778503	−	0.431690i
$363$			0.0936755i			0.00491669i
$364$	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	$-0.536666\pi$
$367$	16.8285	−	16.8285i	0.878439	−	0.878439i	0.993373	+	0.114934i	$0.0366656\pi$
$368$	14.2988	+	4.91346i	0.745377	+	0.256132i
$369$			20.8938i			1.08769i
$370$		0			0
$371$	−10.1342	−	10.1342i	−0.526143	−	0.526143i
$372$	−1.37077	+	2.19522i	−0.0710711	+	0.113817i
$373$	8.03845			0.416215			0.208108	−	0.978106i	$-0.433270\pi$
$373$	8.03845			0.416215			0.208108	+	0.978106i	$0.433270\pi$
$374$	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
$378$	−2.85738	+	1.58446i	−0.146968	+	0.0814957i
$379$	−2.30677	−	2.30677i	−0.118491	−	0.118491i	0.645375	−	0.763866i	$-0.276701\pi$
$379$	−2.30677	−	2.30677i	−0.118491	−	0.118491i	−0.763866	+	0.645375i	$0.776701\pi$
$380$		0			0
$381$	1.15341	−	1.15341i	0.0590910	−	0.0590910i
$382$	15.4348	+	4.42324i	0.789713	+	0.226313i
$383$	−7.85530	−	7.85530i	−0.401387	−	0.401387i	0.477335	−	0.878722i	$-0.341603\pi$
$383$	−7.85530	−	7.85530i	−0.401387	−	0.401387i	−0.878722	+	0.477335i	$0.841603\pi$
$384$	2.17728	+	0.876903i	0.111109	+	0.0447493i
$385$		0			0
$386$	10.6926	+	19.2828i	0.544239	+	0.981470i
$387$			27.8917i			1.41782i
$388$	7.77429	+	33.6261i	0.394680	+	1.70711i
$389$	27.2171	−	27.2171i	1.37996	−	1.37996i	0.535303	−	0.844660i	$-0.320197\pi$
$389$	27.2171	−	27.2171i	1.37996	−	1.37996i	0.844660	−	0.535303i	$-0.179803\pi$
$390$		0			0
$391$	−17.5906			−0.889595
$392$	6.63781	+	7.36507i	0.335260	+	0.371992i
$393$	−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
$397$	4.38693			0.220174			0.110087	−	0.993922i	$-0.464887\pi$
$397$	4.38693			0.220174			0.110087	+	0.993922i	$0.464887\pi$
$398$	−11.8010	−	3.38188i	−0.591530	−	0.169518i
$399$	−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	$0.710478\pi$
$402$	3.53955	+	1.01435i	0.176537	+	0.0505912i
$403$	26.2094			1.30558
$404$	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
$408$	−2.72719	−	0.141642i	−0.135016	−	0.00701231i
$409$	7.06598			0.349390			0.174695	−	0.984623i	$-0.444106\pi$
$409$	7.06598			0.349390			0.174695	+	0.984623i	$0.444106\pi$
$410$		0			0
$411$	−0.105261	+	0.105261i	−0.00519214	+	0.00519214i
$412$	18.0565	−	4.17463i	0.889581	−	0.205669i
$413$		−	18.7057i		−	0.920445i
$414$	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
$418$	−5.45436	−	1.56309i	−0.266782	−	0.0764532i
$419$	−4.54400	+	4.54400i	−0.221989	+	0.221989i	−0.809336	−	0.587347i	$-0.800173\pi$
$419$	−4.54400	+	4.54400i	−0.221989	+	0.221989i	0.587347	+	0.809336i	$0.300173\pi$
$420$		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	$0.689574\pi$
$422$	−11.0015	+	6.10049i	−0.535545	+	0.296967i
$423$	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
$427$	−23.1129			−1.11851
$428$	−27.7718	−	17.3417i	−1.34240	−	0.838242i
$429$	−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	$-0.0986716\pi$
$432$	2.16987	+	4.44184i	0.104398	+	0.213708i
$433$	11.0499	−	11.0499i	0.531022	−	0.531022i	−0.389854	−	0.920876i	$-0.627475\pi$
$433$	11.0499	−	11.0499i	0.531022	−	0.531022i	0.920876	+	0.389854i	$0.127475\pi$
$434$	−7.99644	−	14.4206i	−0.383842	−	0.692213i
$435$		0			0
$436$	1.27424	+	5.51147i	0.0610251	+	0.263952i
$437$			4.48139i			0.214374i
$438$	1.73854	−	0.964043i	0.0830705	−	0.0460637i
$439$		−	20.4936i		−	0.978108i	−0.872254	−	0.489054i	$-0.837342\pi$
$439$		−	20.4936i		−	0.978108i	0.872254	−	0.489054i	$-0.162658\pi$
$440$		0			0
$441$			10.3654i			0.493592i
$442$	13.4115	+	24.1861i	0.637921	+	1.15041i
$443$		−	11.0123i		−	0.523212i	−0.965175	−	0.261606i	$-0.915748\pi$
$443$		−	11.0123i		−	0.523212i	0.965175	−	0.261606i	$-0.0842521\pi$
$444$	−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
$448$	−11.6134	+	9.42240i	−0.548680	+	0.445166i
$449$		−	15.4423i		−	0.728767i	−0.931249	−	0.364383i	$-0.881280\pi$
$449$		−	15.4423i		−	0.728767i	0.931249	−	0.364383i	$-0.118720\pi$
$450$		0			0
$451$	16.9079	+	16.9079i	0.796161	+	0.796161i
$452$	32.7073	−	7.56186i	1.53842	−	0.355680i
$453$	−1.47887			−0.0694835
$454$	−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	$-0.783143\pi$
$457$	−3.14212	+	3.14212i	−0.146982	+	0.146982i	0.629786	+	0.776769i	$0.283143\pi$
$458$	9.07762	+	16.3704i	0.424169	+	0.764939i
$459$	−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	$0.160164\pi$
$462$	−0.511322	+	1.78425i	−0.0237889	+	0.0830107i
$463$	−21.5859	−	21.5859i	−1.00318	−	1.00318i	−0.999995	−	0.00318643i	$-0.998986\pi$
$463$	−21.5859	−	21.5859i	−1.00318	−	1.00318i	−0.00318643	−	0.999995i	$-0.501014\pi$
$464$	4.69607	−	13.6662i	0.218010	−	0.634436i
$465$		0			0
$466$	3.13168	−	1.73656i	0.145072	−	0.0804446i
$467$			22.4880i			1.04062i	0.853977	+	0.520311i	$0.174184\pi$
$467$			22.4880i			1.04062i	−0.853977	+	0.520311i	$0.825816\pi$
$468$	13.1623	−	21.0788i	0.608428	−	0.974366i
$469$	−16.5883	+	16.5883i	−0.765978	+	0.765978i
$470$		0			0
$471$	−4.30229			−0.198239
$472$	−28.2642	−	1.46795i	−1.30096	−	0.0675681i
$473$	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
$477$	−22.6702			−1.03800
$478$	−8.14477	+	28.4210i	−0.372533	+	1.29995i
$479$	−0.852623			−0.0389573			−0.0194787	−	0.999810i	$-0.506201\pi$
$479$	−0.852623			−0.0389573			−0.0194787	+	0.999810i	$0.506201\pi$
$480$		0			0
$481$	18.0459			0.822821
$482$	−1.44173	+	5.03086i	−0.0656688	+	0.229150i
$483$	1.46597			0.0667037
$484$	−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	0.761469	−	0.648202i	$-0.224479\pi$
$487$	2.49958	+	2.49958i	0.113267	+	0.113267i	−0.648202	+	0.761469i	$0.724479\pi$
$488$	−1.81382	+	34.9236i	−0.0821079	+	1.58092i
$489$	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	$0.000586006\pi$
$492$	1.55291	−	2.48690i	0.0700105	−	0.112118i
$493$			16.8123i			0.757189i
$494$	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
$498$	0.335051	−	1.16915i	0.0150140	−	0.0523910i
$499$	7.73911	−	7.73911i	0.346450	−	0.346450i	−0.512335	−	0.858786i	$-0.671219\pi$
$499$	7.73911	−	7.73911i	0.346450	−	0.346450i	0.858786	+	0.512335i	$0.171219\pi$
$500$		0			0
$501$	0.250373	+	0.250373i	0.0111858	+	0.0111858i
$502$	−0.611116	−	1.10208i	−0.0272754	−	0.0491880i
$503$	13.9144	−	13.9144i	0.620413	−	0.620413i	−0.325224	−	0.945637i	$-0.605440\pi$
$503$	13.9144	−	13.9144i	0.620413	−	0.620413i	0.945637	+	0.325224i	$0.105440\pi$
$504$	−15.6135	−	0.810919i	−0.695482	−	0.0361212i
$505$		0			0
$506$	17.3894	+	4.98338i	0.773052	+	0.221538i
$507$	0.966284			0.0429142
$508$	15.3204	−	3.54205i	0.679733	−	0.157153i
$509$	−4.48049	−	4.48049i	−0.198594	−	0.198594i	0.600803	−	0.799397i	$-0.294848\pi$
$509$	−4.48049	−	4.48049i	−0.198594	−	0.198594i	−0.799397	+	0.600803i	$0.794848\pi$
$510$		0			0
$511$			12.6658i			0.560302i
$512$	13.3258	+	18.2872i	0.588924	+	0.808188i
$513$	−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
$517$		−	39.8085i		−	1.75078i
$518$	−5.50578	−	9.92902i	−0.241910	−	0.436256i
$519$			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	$0.977199\pi$
$522$	13.2119	−	7.32617i	0.578269	−	0.320658i
$523$			10.1372i			0.443270i	0.975130	+	0.221635i	$0.0711393\pi$
$523$			10.1372i			0.443270i	−0.975130	+	0.221635i	$0.928861\pi$
$524$	−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
$528$	2.65587	+	0.912628i	0.115582	+	0.0397170i
$529$			8.71262i			0.378809i
$530$		0			0
$531$	−20.9222	−	20.9222i	−0.907945	−	0.907945i
$532$	−3.75983	−	2.34777i	−0.163009	−	0.101789i
$533$	−29.6919			−1.28610
$534$	−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
$538$	15.4423	−	8.56295i	0.665763	−	0.369175i
$539$	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	$0.438753\pi$
$542$	−42.0323	−	12.0454i	−1.80544	−	0.517396i
$543$	−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
$547$		−	3.60503i		−	0.154140i	−0.997026	−	0.0770699i	$-0.975444\pi$
$547$		−	3.60503i		−	0.154140i	0.997026	−	0.0770699i	$-0.0245565\pi$
$548$	−1.39815	+	0.323249i	−0.0597260	+	0.0138085i
$549$	−25.8517	+	25.8517i	−1.10332	+	1.10332i
$550$		0			0
$551$	4.28311			0.182467
$552$	0.115044	−	2.21507i	0.00489659	−	0.0942796i
$553$	−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
$557$	−21.5670			−0.913823			−0.456911	−	0.889512i	$-0.651044\pi$
$557$	−21.5670			−0.913823			−0.456911	+	0.889512i	$0.651044\pi$
$558$	−25.0734	−	7.18543i	−1.06144	−	0.304183i
$559$	−39.6365			−1.67644
$560$		0			0
$561$	−3.26728			−0.137945
$562$	8.86048	+	2.53920i	0.373757	+	0.107110i
$563$	−26.5306			−1.11813			−0.559066	−	0.829123i	$-0.688840\pi$
$563$	−26.5306			−1.11813			−0.559066	+	0.829123i	$0.688840\pi$
$564$	−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
$568$	21.9819	−	19.8113i	0.922341	−	0.831265i
$569$	−9.23630			−0.387206			−0.193603	−	0.981080i	$-0.562017\pi$
$569$	−9.23630			−0.387206			−0.193603	+	0.981080i	$0.562017\pi$
$570$		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	$0.863900\pi$
$572$	−6.40623	−	27.7089i	−0.267858	−	1.15857i
$573$		−	2.35546i		−	0.0984007i
$574$	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	0.999976	−	0.00692502i	$-0.00220432\pi$
$577$	23.8539	+	23.8539i	0.993051	+	0.993051i	−0.00692502	+	0.999976i	$0.502204\pi$
$578$	6.33184	+	1.81455i	0.263370	+	0.0754755i
$579$	2.28723	−	2.28723i	0.0950541	−	0.0950541i
$580$		0			0
$581$	5.47931	+	5.47931i	0.227320	+	0.227320i
$582$	4.42794	−	2.45535i	0.183544	−	0.101778i
$583$	−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
$587$	−24.2348			−1.00028			−0.500138	−	0.865946i	$-0.666718\pi$
$587$	−24.2348			−1.00028			−0.500138	+	0.865946i	$0.666718\pi$
$588$	0.770398	−	1.23375i	0.0317707	−	0.0508792i
$589$	−5.22893	−	5.22893i	−0.215454	−	0.215454i
$590$		0			0
$591$		−	4.39734i		−	0.180882i
$592$	−15.4348	+	7.54002i	−0.634366	+	0.309893i
$593$	15.4929	−	15.4929i	0.636219	−	0.636219i	−0.313402	−	0.949621i	$-0.601469\pi$
$593$	15.4929	−	15.4929i	0.636219	−	0.636219i	0.949621	+	0.313402i	$0.101469\pi$
$594$	2.86824	+	5.17254i	0.117685	+	0.212232i
$595$		0			0
$596$	−7.79530	+	1.80226i	−0.319308	+	0.0738233i
$597$			1.80091i			0.0737065i
$598$	−19.6443	+	10.8931i	−0.803317	+	0.445450i
$599$		−	19.1812i		−	0.783722i	−0.920024	−	0.391861i	$-0.871831\pi$
$599$		−	19.1812i		−	0.783722i	0.920024	−	0.391861i	$-0.128169\pi$
$600$		0			0
$601$		−	21.7464i		−	0.887056i	−0.896261	−	0.443528i	$-0.853727\pi$
$601$		−	21.7464i		−	0.887056i	0.896261	−	0.443528i	$-0.146273\pi$
$602$	12.0930	+	21.8084i	0.492876	+	0.888843i
$603$			37.1079i			1.51115i
$604$	−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	$-0.552543\pi$
$607$	20.2541	−	20.2541i	0.822088	−	0.822088i	0.986407	+	0.164319i	$0.0525428\pi$
$608$	−3.84253	+	5.49685i	−0.155835	+	0.222927i
$609$		−	1.40110i		−	0.0567756i
$610$		0			0
$611$	34.9538	+	34.9538i	1.41408	+	1.41408i
$612$	−6.19949	−	26.8146i	−0.250599	−	1.08392i
$613$	−6.00698			−0.242620			−0.121310	−	0.992615i	$-0.538709\pi$
$613$	−6.00698			−0.242620			−0.121310	+	0.992615i	$0.538709\pi$
$614$	−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	$-0.546841\pi$
$617$	20.9289	−	20.9289i	0.842566	−	0.842566i	0.989192	+	0.146626i	$0.0468413\pi$
$618$	−1.31847	−	2.37771i	−0.0530368	−	0.0956455i
$619$	3.30074	+	3.30074i	0.132668	+	0.132668i	0.770322	−	0.637655i	$-0.220095\pi$
$619$	3.30074	+	3.30074i	0.132668	+	0.132668i	−0.637655	+	0.770322i	$0.720095\pi$
$620$		0			0
$621$	3.30321	−	3.30321i	0.132553	−	0.132553i
$622$	12.3926	−	43.2436i	0.496897	−	1.73391i
$623$	−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
$627$			0.832374i			0.0332418i
$628$	−35.1790	−	21.9670i	−1.40380	−	0.876578i
$629$	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	$0.472103\pi$
$632$	−18.2783	+	16.4734i	−0.727071	+	0.655276i
$633$	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
$637$	−14.7301			−0.583630
$638$	4.76289	−	16.6200i	0.188565	−	0.657992i
$639$	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	$0.444719\pi$
$642$	−1.32323	+	4.61739i	−0.0522238	+	0.182234i
$643$	26.4968			1.04493			0.522466	−	0.852660i	$-0.325012\pi$
$643$	26.4968			1.04493			0.522466	+	0.852660i	$0.325012\pi$
$644$	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	0.946173	−	0.323661i	$-0.104914\pi$
$647$	15.8343	+	15.8343i	0.622512	+	0.622512i	−0.323661	+	0.946173i	$0.604914\pi$
$648$	−18.0994	+	16.3121i	−0.711010	+	0.640801i
$649$	−33.8616			−1.32919
$650$		0			0
$651$	−1.71050	+	1.71050i	−0.0670399	+	0.0670399i
$652$	18.4886	+	11.5449i	0.724069	+	0.452133i
$653$			26.4608i			1.03549i	0.855534	+	0.517746i	$0.173229\pi$
$653$			26.4608i			1.03549i	−0.855534	+	0.517746i	$0.826771\pi$
$654$	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
$658$	8.56755	−	29.8962i	0.333998	−	1.16548i
$659$	−30.5128	+	30.5128i	−1.18861	+	1.18861i	−0.211156	+	0.977452i	$0.567723\pi$
$659$	−30.5128	+	30.5128i	−1.18861	+	1.18861i	−0.977452	+	0.211156i	$0.932277\pi$
$660$		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	$0.792295\pi$
$662$	−21.7351	−	39.1966i	−0.844758	−	1.52342i
$663$	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
$667$	−13.6552			−0.528733
$668$	0.768879	+	3.32563i	0.0297488	+	0.128673i
$669$	−0.726685	−	0.726685i	−0.0280953	−	0.0280953i
$670$		0			0
$671$			41.8399i			1.61521i
$672$	1.79814	+	1.25698i	0.0693649	+	0.0484890i
$673$	2.80519	−	2.80519i	0.108132	−	0.108132i	−0.650971	−	0.759103i	$-0.725638\pi$
$673$	2.80519	−	2.80519i	0.108132	−	0.108132i	0.759103	+	0.650971i	$0.225638\pi$
$674$	−5.17254	+	2.86824i	−0.199239	+	0.110481i
$675$		0			0
$676$	7.90113	+	4.93373i	0.303890	+	0.189759i
$677$		−	17.5498i		−	0.674492i	−0.941417	−	0.337246i	$-0.890505\pi$
$677$		−	17.5498i		−	0.674492i	0.941417	−	0.337246i	$-0.109495\pi$
$678$	−2.38826	−	4.30695i	−0.0917206	−	0.165407i
$679$			32.2590i			1.23799i
$680$		0			0
$681$			0.129129i			0.00494823i
$682$	−26.1048	+	14.4755i	−0.999603	+	0.554294i
$683$			21.7834i			0.833518i	0.909017	+	0.416759i	$0.136834\pi$
$683$			21.7834i			0.833518i	−0.909017	+	0.416759i	$0.863166\pi$
$684$	−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
$688$	33.9014	−	16.5611i	1.29248	−	0.631386i
$689$		−	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	$-0.567247\pi$
$692$	−5.42829	+	8.69314i	−0.206353	+	0.330464i
$693$	−18.7057			−0.710569
$694$	−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
$698$	23.5976	−	13.0852i	0.893182	−	0.495282i
$699$	−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	$0.0612468\pi$
$702$	−7.06019	−	2.02328i	−0.266470	−	0.0763638i
$703$	−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
$707$			17.1005i			0.643132i
$708$	0.935264	+	4.04529i	0.0351494	+	0.152031i
$709$	26.3703	−	26.3703i	0.990357	−	0.990357i	−0.00959736	−	0.999954i	$-0.503055\pi$
$709$	26.3703	−	26.3703i	0.990357	−	0.990357i	0.999954	+	0.00959736i	$0.00305498\pi$
$710$		0			0
$711$	−25.7244			−0.964741
$712$	−1.15238	+	1.03859i	−0.0431874	+	0.0389228i
$713$	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
$717$	4.33724			0.161977
$718$	38.4506	+	11.0190i	1.43496	+	0.411226i
$719$	−2.65374			−0.0989679			−0.0494840	−	0.998775i	$-0.515758\pi$
$719$	−2.65374			−0.0989679			−0.0494840	+	0.998775i	$0.515758\pi$
$720$		0			0
$721$	17.3224			0.645119
$722$	23.9194	+	6.85472i	0.890187	+	0.255106i
$723$	0.767746			0.0285528
$724$	−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	0.987329	+	0.158685i	$0.0507255\pi$
$727$	30.8999	+	30.8999i	1.14601	+	1.14601i	0.158685	+	0.987329i	$0.449275\pi$
$728$	1.15238	−	22.1881i	0.0427102	−	0.822348i
$729$	−24.7034			−0.914940
$730$		0			0
$731$	−31.0399	+	31.0399i	−1.14805	+	1.14805i
$732$	4.99842	−	1.15562i	0.184747	−	0.0427131i
$733$			46.2726i			1.70912i	0.519354	+	0.854559i	$0.326172\pi$
$733$			46.2726i			1.70912i	−0.519354	+	0.854559i	$0.673828\pi$
$734$	−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
$738$	28.4049	+	8.14017i	1.04560	+	0.299644i
$739$	12.0504	−	12.0504i	0.443280	−	0.443280i	−0.449833	−	0.893113i	$-0.648516\pi$
$739$	12.0504	−	12.0504i	0.443280	−	0.443280i	0.893113	+	0.449833i	$0.148516\pi$
$740$		0			0
$741$	−0.730865	−	0.730865i	−0.0268490	−	0.0268490i
$742$	−17.7257	+	9.82912i	−0.650730	+	0.360838i
$743$	−21.4100	+	21.4100i	−0.785456	+	0.785456i	−0.980746	−	0.195290i	$-0.937435\pi$
$743$	−21.4100	+	21.4100i	−0.785456	+	0.785456i	0.195290	+	0.980746i	$0.437435\pi$
$744$	2.45033	+	2.71880i	0.0898335	+	0.0996761i
$745$		0			0
$746$	3.13176	−	10.9282i	0.114662	−	0.400110i
$747$	12.2571			0.448465
$748$	−26.7160	−	16.6824i	−0.976833	−	0.609968i
$749$	−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	$0.950386\pi$
$752$	−44.5008	−	15.2917i	−1.62278	−	0.557631i
$753$	−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
$757$		−	29.2794i		−	1.06418i	−0.846688	−	0.532089i	$-0.821407\pi$
$757$		−	29.2794i		−	1.06418i	0.846688	−	0.532089i	$-0.178593\pi$
$758$	−4.03474	+	2.23732i	−0.146548	+	0.0812631i
$759$		−	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	$-0.252460\pi$
$762$	−1.11868	−	2.01741i	−0.0405256	−	0.0730832i
$763$			5.28739i			0.191416i
$764$	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
$768$	2.04040	−	2.61835i	0.0736267	−	0.0944815i
$769$			26.4222i			0.952809i	0.879226	+	0.476404i	$0.158060\pi$
$769$			26.4222i			0.952809i	−0.879226	+	0.476404i	$0.841940\pi$
$770$		0			0
$771$	0.751892	+	0.751892i	0.0270787	+	0.0270787i
$772$	30.3806	−	7.02394i	1.09342	−	0.252797i
$773$	−8.08416			−0.290767			−0.145383	−	0.989375i	$-0.546442\pi$
$773$	−8.08416			−0.290767			−0.145383	+	0.989375i	$0.546442\pi$
$774$	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
$778$	−26.3977	−	47.6051i	−0.946404	−	1.70673i
$779$	5.92371	+	5.92371i	0.212239	+	0.212239i
$780$		0			0
$781$	25.0350	−	25.0350i	0.895823	−	0.895823i
$782$	−6.85325	+	23.9142i	−0.245072	+	0.855172i
$783$	−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
$787$			40.5596i			1.44579i	0.690955	+	0.722897i	$0.257190\pi$
$787$			40.5596i			1.44579i	−0.690955	+	0.722897i	$0.742810\pi$
$788$	22.4523	−	35.9562i	0.799830	−	1.28089i
$789$	−1.09119	+	1.09119i	−0.0388474	+	0.0388474i
$790$		0			0
$791$	31.3775			1.11566
$792$	−1.46795	+	28.2642i	−0.0521615	+	1.00432i
$793$	−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
$797$	−1.85060			−0.0655517			−0.0327759	−	0.999463i	$-0.510435\pi$
$797$	−1.85060			−0.0655517			−0.0327759	+	0.999463i	$0.510435\pi$
$798$	−0.179143	+	0.625115i	−0.00634159	+	0.0221288i
$799$	54.7455			1.93676
$800$		0			0
$801$	−1.62184			−0.0573048
$802$	−9.58190	+	33.4358i	−0.338349	+	1.18066i
$803$	22.9281			0.809115
$804$	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
$808$	25.8389	+	1.34199i	0.909009	+	0.0472111i
$809$	26.5823			0.934584			0.467292	−	0.884103i	$-0.345230\pi$
$809$	26.5823			0.934584			0.467292	+	0.884103i	$0.345230\pi$
$810$		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	$0.198416\pi$
$812$	7.15388	−	11.4566i	0.251052	−	0.402047i
$813$			6.41443i			0.224964i
$814$	−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
$818$	2.75289	−	9.60614i	0.0962525	−	0.335871i
$819$	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	$0.702694\pi$
$822$	0.102092	+	0.184111i	0.00356086	+	0.00642159i
$823$	−15.1106	+	15.1106i	−0.526722	+	0.526722i	−0.919593	−	0.392871i	$-0.871482\pi$
$823$	−15.1106	+	15.1106i	−0.526722	+	0.526722i	0.392871	+	0.919593i	$0.371482\pi$
$824$	1.35940	−	26.1741i	0.0473570	−	0.911817i
$825$		0			0
$826$	−25.4302	−	7.28767i	−0.884828	−	0.253571i
$827$	−13.3792			−0.465241			−0.232621	−	0.972568i	$-0.574730\pi$
$827$	−13.3792			−0.465241			−0.232621	+	0.972568i	$0.574730\pi$
$828$	21.7793	−	5.03533i	0.756883	−	0.174990i
$829$	5.81788	+	5.81788i	0.202063	+	0.202063i	0.800883	−	0.598820i	$-0.204364\pi$
$829$	5.81788	+	5.81788i	0.202063	+	0.202063i	−0.598820	+	0.800883i	$0.704364\pi$
$830$		0			0
$831$			3.92783i			0.136255i
$832$	−33.4358	−	3.48250i	−1.15918	−	0.120734i
$833$	−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
$837$			7.70845i			0.266443i
$838$	4.40719	+	7.94785i	0.152244	+	0.274554i
$839$			27.4305i			0.947006i	0.880792	+	0.473503i	$0.157011\pi$
$839$			27.4305i			0.947006i	−0.880792	+	0.473503i	$0.842989\pi$
$840$		0			0
$841$		−	15.9489i		−	0.549963i
$842$	9.57693	−	5.31054i	0.330043	−	0.183013i
$843$		−	1.35217i		−	0.0465713i
$844$	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
$848$	13.4607	+	27.5548i	0.462243	+	0.946235i
$849$			3.33445i			0.114438i
$850$		0			0
$851$	11.4782	+	11.4782i	0.393469	+	0.393469i
$852$	−3.68229	−	2.29934i	−0.126153	−	0.0787743i
$853$	16.6692			0.570742			0.285371	−	0.958417i	$-0.407883\pi$
$853$	16.6692			0.570742			0.285371	+	0.958417i	$0.407883\pi$
$854$	−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	$-0.713528\pi$
$857$	4.73331	−	4.73331i	0.161687	−	0.161687i	0.783314	+	0.621627i	$0.213528\pi$
$858$	−3.64875	+	2.02328i	−0.124566	+	0.0690736i
$859$	26.3237	+	26.3237i	0.898152	+	0.898152i	0.995273	−	0.0971203i	$-0.0309632\pi$
$859$	26.3237	+	26.3237i	0.898152	+	0.898152i	−0.0971203	+	0.995273i	$0.530963\pi$
$860$		0			0
$861$	1.93778	−	1.93778i	0.0660394	−	0.0660394i
$862$	−17.2190	−	4.93456i	−0.586483	−	0.168072i
$863$	−8.71130	−	8.71130i	−0.296536	−	0.296536i	0.543119	−	0.839655i	$-0.317243\pi$
$863$	−8.71130	−	8.71130i	−0.296536	−	0.296536i	−0.839655	+	0.543119i	$0.817243\pi$
$864$	6.88401	−	1.21939i	0.234199	−	0.0414846i
$865$		0			0
$866$	−10.7172	−	19.3272i	−0.364184	−	0.656764i
$867$		−	0.966284i		−	0.0328167i
$868$	−22.7201	+	5.25285i	−0.771171	+	0.178293i
$869$	−20.8170	+	20.8170i	−0.706167	+	0.706167i
$870$		0			0
$871$	−52.7334			−1.78680
$872$	7.98923	+	0.414936i	0.270550	+	0.0140515i
$873$	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
$877$	33.6674			1.13687			0.568433	−	0.822730i	$-0.307550\pi$
$877$	33.6674			1.13687			0.568433	+	0.822730i	$0.307550\pi$
$878$	−27.8609	−	7.98426i	−0.940260	−	0.269456i
$879$	−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	$0.347857\pi$
$882$	14.0917	+	4.03834i	0.474492	+	0.135978i
$883$	27.9628			0.941023			0.470511	−	0.882394i	$-0.344070\pi$
$883$	27.9628			0.941023			0.470511	+	0.882394i	$0.344070\pi$
$884$	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	0.466501	−	0.884521i	$-0.345514\pi$
$887$	−12.4497	−	12.4497i	−0.418020	−	0.418020i	−0.884521	+	0.466501i	$0.845514\pi$
$888$	1.68712	+	1.87197i	0.0566161	+	0.0628192i
$889$	14.6975			0.492939
$890$		0			0
$891$	−20.6132	+	20.6132i	−0.690567	+	0.690567i
$892$	−2.23160	−	9.65235i	−0.0747196	−	0.323185i
$893$		−	13.9470i		−	0.466718i
$894$	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
$898$	−20.9937	−	6.01628i	−0.700567	−	0.200766i
$899$	15.9331	−	15.9331i	0.531398	−	0.531398i
$900$		0			0
$901$	−25.2289	−	25.2289i	−0.840498	−	0.840498i
$902$	29.5734	−	16.3988i	0.984685	−	0.546022i
$903$	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
$907$	−38.3527			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$907$	−38.3527			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$908$	−0.659317	+	1.05586i	−0.0218802	+	0.0350400i
$909$	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	$-0.130259\pi$
$912$	0.930488	+	0.319741i	0.0308115	+	0.0105877i
$913$	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
$917$		−	8.35846i		−	0.276021i
$918$	−7.11338	+	3.94447i	−0.234777	+	0.130187i
$919$		−	25.1211i		−	0.828668i	−0.910125	−	0.414334i	$-0.864014\pi$
$919$		−	25.1211i		−	0.828668i	0.910125	−	0.414334i	$-0.135986\pi$
$920$		0			0
$921$			5.89448i			0.194230i
$922$	−8.20177	−	14.7909i	−0.270111	−	0.487113i
$923$			43.9639i			1.44709i
$924$	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
$928$	−16.7495	−	11.7086i	−0.549828	−	0.384352i
$929$		−	39.8307i		−	1.30680i	−0.757012	−	0.653401i	$-0.773342\pi$
$929$		−	39.8307i		−	1.30680i	0.757012	−	0.653401i	$-0.226658\pi$
$930$		0			0
$931$	2.93876	+	2.93876i	0.0963139	+	0.0963139i
$932$	−1.14074	−	4.93405i	−0.0373663	−	0.161620i
$933$	−6.59927			−0.216051
$934$	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	$-0.888737\pi$
$937$	−18.2763	+	18.2763i	−0.597060	+	0.597060i	0.342469	+	0.939529i	$0.388737\pi$
$938$	16.0889	+	29.0144i	0.525321	+	0.947355i
$939$	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	$0.267240\pi$
$942$	−1.67616	+	5.84892i	−0.0546122	+	0.190568i
$943$	−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
$947$			18.7829i			0.610363i	0.952294	+	0.305181i	$0.0987171\pi$
$947$			18.7829i			0.610363i	−0.952294	+	0.305181i	$0.901283\pi$
$948$	3.06187	+	1.91194i	0.0994450	+	0.0620968i
$949$	−20.1320	+	20.1320i	−0.653511	+	0.653511i
$950$		0			0
$951$	2.20341			0.0714505
$952$	−16.4734	−	18.2783i	−0.533905	−	0.592402i
$953$	9.07454	+	9.07454i	0.293953	+	0.293953i	0.838640	−	0.544687i	$-0.183351\pi$
$953$	9.07454	+	9.07454i	0.293953	+	0.293953i	−0.544687	+	0.838640i	$0.683351\pi$
$954$	−8.83223	+	30.8199i	−0.285954	+	0.997830i
$955$		0			0
$956$	35.4649	+	22.1455i	1.14702	+	0.716236i
$957$	−2.53633			−0.0819879
$958$	−0.332179	+	1.15913i	−0.0107322	+	0.0374499i
$959$	−1.34130			−0.0433130
$960$		0			0
$961$	−7.90304			−0.254937
$962$	7.03063	−	24.5332i	0.226677	−	0.790982i
$963$	−48.4077			−1.55992
$964$	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	0.460024	−	0.887906i	$-0.347841\pi$
$967$	−13.3057	−	13.3057i	−0.427882	−	0.427882i	−0.887906	+	0.460024i	$0.847841\pi$
$968$	0.854983	+	0.948659i	0.0274802	+	0.0304910i
$969$	−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	$0.111024\pi$
$972$	9.32163	+	5.82074i	0.298991	+	0.186700i
$973$			14.5960i			0.467926i
$974$	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	0.580921	−	0.813960i	$-0.302692\pi$
$977$	−7.28407	−	7.28407i	−0.233038	−	0.233038i	−0.813960	+	0.580921i	$0.802692\pi$
$978$	0.880918	−	3.07394i	0.0281686	−	0.0982938i
$979$	−1.31244	+	1.31244i	−0.0419457	+	0.0419457i
$980$		0			0
$981$	5.91391	+	5.91391i	0.188817	+	0.188817i
$982$	−21.4518	−	38.6858i	−0.684554	−	1.23451i
$983$	31.0322	−	31.0322i	0.989772	−	0.989772i	−0.0101761	−	0.999948i	$-0.503239\pi$
$983$	31.0322	−	31.0322i	0.989772	−	0.989772i	0.999948	+	0.0101761i	$0.00323922\pi$
$984$	−2.77591	−	3.08005i	−0.0884929	−	0.0981885i
$985$		0			0
$986$	22.8562	+	6.55003i	0.727889	+	0.208596i
$987$	−4.56238			−0.145222
$988$	−2.24444	−	9.70786i	−0.0714051	−	0.308848i
$989$	−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	$0.780173\pi$
$992$	6.15404	+	34.7423i	0.195391	+	1.10307i
$993$	−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
$997$		−	2.58204i		−	0.0817740i	−0.999164	−	0.0408870i	$-0.986982\pi$
$997$		−	2.58204i		−	0.0817740i	0.999164	−	0.0408870i	$-0.0130184\pi$
$998$	−7.50611	−	13.5364i	−0.237602	−	0.428487i
$999$			5.30749i			0.167921i

Twists

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

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

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