LMFDB - Embedded newform 405.3.s.a.118.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(37,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([28, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			118.27
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.217924 - 2.49089i) q^{2} +(-2.21779 - 0.391056i) q^{4} +(-4.81982 + 1.33016i) q^{5} +(1.23887 + 0.867466i) q^{7} +(1.13122 - 4.22177i) q^{8} +(2.26293 + 12.2955i) q^{10} +(-7.38848 - 2.68919i) q^{11} +(-1.63449 - 18.6824i) q^{13} +(2.43074 - 2.89684i) q^{14} +(-18.7342 - 6.81868i) q^{16} +(5.25283 + 19.6038i) q^{17} +(-26.7540 + 15.4465i) q^{19} +(11.2095 - 1.06520i) q^{20} +(-8.30859 + 17.8178i) q^{22} +(-31.0483 + 21.7403i) q^{23} +(21.4613 - 12.8223i) q^{25} -46.8918 q^{26} +(-2.40833 - 2.40833i) q^{28} +(6.52085 + 7.77124i) q^{29} +(-4.53255 + 25.7054i) q^{31} +(-13.6787 + 29.3340i) q^{32} +(49.9756 - 8.81204i) q^{34} +(-7.12500 - 2.53313i) q^{35} +(8.54330 + 31.8840i) q^{37} +(32.6450 + 70.0074i) q^{38} +(0.163367 + 21.8529i) q^{40} +(-31.8883 - 26.7575i) q^{41} +(-19.2652 - 41.3143i) q^{43} +(15.3345 + 8.85336i) q^{44} +(47.3864 + 82.0756i) q^{46} +(-36.3695 - 25.4662i) q^{47} +(-15.9767 - 43.8956i) q^{49} +(-27.2619 - 56.2520i) q^{50} +(-3.68088 + 42.0727i) q^{52} +(-10.0402 - 10.0402i) q^{53} +(39.1882 + 3.13351i) q^{55} +(5.06367 - 4.24893i) q^{56} +(20.7783 - 14.5491i) q^{58} +(-4.53496 - 12.4597i) q^{59} +(-5.74775 - 32.5971i) q^{61} +(63.0414 + 16.8919i) q^{62} +(1.02459 + 0.591547i) q^{64} +(32.7285 + 87.8714i) q^{65} +(92.0596 - 8.05417i) q^{67} +(-3.98347 - 45.5313i) q^{68} +(-7.86245 + 17.1955i) q^{70} +(22.0775 - 38.2394i) q^{71} +(-13.2076 + 49.2915i) q^{73} +(81.2813 - 14.3321i) q^{74} +(65.3753 - 23.7946i) q^{76} +(-6.82059 - 9.74081i) q^{77} +(-20.5814 - 24.5280i) q^{79} +(99.3653 + 7.94531i) q^{80} +(-73.5991 + 73.5991i) q^{82} +(45.4188 + 3.97363i) q^{83} +(-51.3940 - 87.4997i) q^{85} +(-107.108 + 38.9840i) q^{86} +(-19.7111 + 28.1504i) q^{88} +(26.4081 - 15.2467i) q^{89} +(14.1814 - 24.5629i) q^{91} +(77.3604 - 36.0737i) q^{92} +(-71.3592 + 85.0426i) q^{94} +(108.403 - 110.036i) q^{95} +(-109.882 + 51.2388i) q^{97} +(-112.821 + 30.2302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.217924	−	2.49089i	0.108962	−	1.24544i	−0.723093	−	0.690750i	$-0.757280\pi$
$2$	0.217924	−	2.49089i	0.108962	−	1.24544i	0.832055	−	0.554692i	$-0.187164\pi$
$3$		0			0
$3$		0			0
$4$	−2.21779	−	0.391056i	−0.554447	−	0.0977640i
$5$	−4.81982	+	1.33016i	−0.963964	+	0.266033i
$5$	−4.81982	+	1.33016i	−0.963964	+	0.266033i
$6$		0			0
$7$	1.23887	+	0.867466i	0.176981	+	0.123924i	0.658711	−	0.752396i	$-0.271102\pi$
$7$	1.23887	+	0.867466i	0.176981	+	0.123924i	−0.481729	+	0.876320i	$0.659991\pi$
$8$	1.13122	−	4.22177i	0.141402	−	0.527721i
$9$		0			0
$10$	2.26293	+	12.2955i	0.226293	+	1.22955i
$11$	−7.38848	−	2.68919i	−0.671680	−	0.244472i	−0.0164089	−	0.999865i	$-0.505223\pi$
$11$	−7.38848	−	2.68919i	−0.671680	−	0.244472i	−0.655271	+	0.755394i	$0.727446\pi$
$12$		0			0
$13$	−1.63449	−	18.6824i	−0.125730	−	1.43710i	−0.752856	−	0.658186i	$-0.771324\pi$
$13$	−1.63449	−	18.6824i	−0.125730	−	1.43710i	0.627125	−	0.778918i	$-0.284231\pi$
$14$	2.43074	−	2.89684i	0.173624	−	0.206917i
$15$		0			0
$16$	−18.7342	−	6.81868i	−1.17089	−	0.426168i
$17$	5.25283	+	19.6038i	0.308990	+	1.15317i	0.929456	+	0.368933i	$0.120277\pi$
$17$	5.25283	+	19.6038i	0.308990	+	1.15317i	−0.620466	+	0.784233i	$0.713057\pi$
$18$		0			0
$19$	−26.7540	+	15.4465i	−1.40811	+	0.812971i	−0.995206	−	0.0978043i	$-0.968818\pi$
$19$	−26.7540	+	15.4465i	−1.40811	+	0.812971i	−0.412902	+	0.910776i	$0.635485\pi$
$20$	11.2095	−	1.06520i	0.560476	−	0.0532601i
$21$		0			0
$22$	−8.30859	+	17.8178i	−0.377663	+	0.809901i
$23$	−31.0483	+	21.7403i	−1.34993	+	0.945230i	−0.349964	+	0.936763i	$0.613806\pi$
$23$	−31.0483	+	21.7403i	−1.34993	+	0.945230i	−0.999964	+	0.00846647i	$0.997305\pi$
$24$		0			0
$25$	21.4613	−	12.8223i	0.858453	−	0.512892i
$26$	−46.8918			−1.80353
$27$		0			0
$28$	−2.40833	−	2.40833i	−0.0860116	−	0.0860116i
$29$	6.52085	+	7.77124i	0.224857	+	0.267974i	0.866664	−	0.498892i	$-0.166260\pi$
$29$	6.52085	+	7.77124i	0.224857	+	0.267974i	−0.641807	+	0.766866i	$0.721815\pi$
$30$		0			0
$31$	−4.53255	+	25.7054i	−0.146211	+	0.829206i	0.820175	+	0.572113i	$0.193876\pi$
$31$	−4.53255	+	25.7054i	−0.146211	+	0.829206i	−0.966387	+	0.257094i	$0.917235\pi$
$32$	−13.6787	+	29.3340i	−0.427458	+	0.916686i
$33$		0			0
$34$	49.9756	−	8.81204i	1.46987	−	0.259178i
$35$	−7.12500	−	2.53313i	−0.203572	−	0.0723752i
$36$		0			0
$37$	8.54330	+	31.8840i	0.230900	+	0.861731i	0.979954	+	0.199222i	$0.0638415\pi$
$37$	8.54330	+	31.8840i	0.230900	+	0.861731i	−0.749054	+	0.662509i	$0.769492\pi$
$38$	32.6450	+	70.0074i	0.859079	+	1.84230i
$39$		0			0
$40$	0.163367	+	21.8529i	0.00408418	+	0.546321i
$41$	−31.8883	−	26.7575i	−0.777764	−	0.652622i	0.164920	−	0.986307i	$-0.447263\pi$
$41$	−31.8883	−	26.7575i	−0.777764	−	0.652622i	−0.942685	+	0.333685i	$0.891708\pi$
$42$		0			0
$43$	−19.2652	−	41.3143i	−0.448027	−	0.960798i	−0.992526	−	0.122036i	$-0.961058\pi$
$43$	−19.2652	−	41.3143i	−0.448027	−	0.960798i	0.544498	−	0.838762i	$-0.316720\pi$
$44$	15.3345	+	8.85336i	0.348511	+	0.201213i
$45$		0			0
$46$	47.3864	+	82.0756i	1.03014	+	1.78425i
$47$	−36.3695	−	25.4662i	−0.773819	−	0.541834i	0.118653	−	0.992936i	$-0.462142\pi$
$47$	−36.3695	−	25.4662i	−0.773819	−	0.541834i	−0.892473	+	0.451102i	$0.851031\pi$
$48$		0			0
$49$	−15.9767	−	43.8956i	−0.326055	−	0.895828i
$50$	−27.2619	−	56.2520i	−0.545239	−	1.12504i
$51$		0			0
$52$	−3.68088	+	42.0727i	−0.0707862	+	0.809090i
$53$	−10.0402	−	10.0402i	−0.189438	−	0.189438i	0.606015	−	0.795453i	$-0.292767\pi$
$53$	−10.0402	−	10.0402i	−0.189438	−	0.189438i	−0.795453	+	0.606015i	$0.792767\pi$
$54$		0			0
$55$	39.1882	+	3.13351i	0.712513	+	0.0569729i
$56$	5.06367	−	4.24893i	0.0904227	−	0.0758737i
$57$		0			0
$58$	20.7783	−	14.5491i	0.358247	−	0.250847i
$59$	−4.53496	−	12.4597i	−0.0768638	−	0.211181i	0.895309	−	0.445445i	$-0.146954\pi$
$59$	−4.53496	−	12.4597i	−0.0768638	−	0.211181i	−0.972173	+	0.234263i	$0.924732\pi$
$60$		0			0
$61$	−5.74775	−	32.5971i	−0.0942254	−	0.534379i	−0.994982	−	0.100054i	$-0.968098\pi$
$61$	−5.74775	−	32.5971i	−0.0942254	−	0.534379i	0.900757	−	0.434324i	$-0.143013\pi$
$62$	63.0414	+	16.8919i	1.01680	+	0.272450i
$63$		0			0
$64$	1.02459	+	0.591547i	0.0160092	+	0.00924292i
$65$	32.7285	+	87.8714i	0.503516	+	1.35187i
$66$		0			0
$67$	92.0596	−	8.05417i	1.37402	−	0.120212i	0.623898	−	0.781506i	$-0.285548\pi$
$67$	92.0596	−	8.05417i	1.37402	−	0.120212i	0.750126	+	0.661295i	$0.229993\pi$
$68$	−3.98347	−	45.5313i	−0.0585805	−	0.669578i
$69$		0			0
$70$	−7.86245	+	17.1955i	−0.112321	+	0.245651i
$71$	22.0775	−	38.2394i	0.310951	−	0.538583i	−0.667618	−	0.744504i	$-0.732686\pi$
$71$	22.0775	−	38.2394i	0.310951	−	0.538583i	0.978568	+	0.205922i	$0.0660192\pi$
$72$		0			0
$73$	−13.2076	+	49.2915i	−0.180926	+	0.675226i	0.814540	+	0.580108i	$0.196990\pi$
$73$	−13.2076	+	49.2915i	−0.180926	+	0.675226i	−0.995466	+	0.0951183i	$0.969677\pi$
$74$	81.2813	−	14.3321i	1.09840	−	0.193677i
$75$		0			0
$76$	65.3753	−	23.7946i	0.860201	−	0.313087i
$77$	−6.82059	−	9.74081i	−0.0885791	−	0.126504i
$78$		0			0
$79$	−20.5814	−	24.5280i	−0.260525	−	0.310481i	0.619887	−	0.784691i	$-0.287178\pi$
$79$	−20.5814	−	24.5280i	−0.260525	−	0.310481i	−0.880412	+	0.474210i	$0.842734\pi$
$80$	99.3653	+	7.94531i	1.24207	+	0.0993164i
$81$		0			0
$82$	−73.5991	+	73.5991i	−0.897550	+	0.897550i
$83$	45.4188	+	3.97363i	0.547214	+	0.0478750i	0.357411	−	0.933947i	$-0.383660\pi$
$83$	45.4188	+	3.97363i	0.547214	+	0.0478750i	0.189803	+	0.981822i	$0.439215\pi$
$84$		0			0
$85$	−51.3940	−	87.4997i	−0.604635	−	1.02941i
$86$	−107.108	+	38.9840i	−1.24544	+	0.453302i
$87$		0			0
$88$	−19.7111	+	28.1504i	−0.223990	+	0.319891i
$89$	26.4081	−	15.2467i	0.296720	−	0.171312i	−0.344248	−	0.938879i	$-0.611866\pi$
$89$	26.4081	−	15.2467i	0.296720	−	0.171312i	0.640969	+	0.767567i	$0.278533\pi$
$90$		0			0
$91$	14.1814	−	24.5629i	0.155839	−	0.269922i
$92$	77.3604	−	36.0737i	0.840873	−	0.392106i
$93$		0			0
$94$	−71.3592	+	85.0426i	−0.759140	+	0.904708i
$95$	108.403	−	110.036i	1.14109	−	1.15828i
$96$		0			0
$97$	−109.882	+	51.2388i	−1.13280	+	0.528235i	−0.896323	−	0.443402i	$-0.853771\pi$
$97$	−109.882	+	51.2388i	−1.13280	+	0.528235i	−0.236480	+	0.971636i	$0.575994\pi$
$98$	−112.821	+	30.2302i	−1.15123	+	0.308471i
$99$		0			0
$100$	−52.6110	+	20.0446i	−0.526110	+	0.200446i
$101$	2.01063	+	11.4029i	0.0199072	+	0.112900i	0.993142	−	0.116913i	$-0.0372998\pi$
$101$	2.01063	+	11.4029i	0.0199072	+	0.112900i	−0.973235	+	0.229812i	$0.926189\pi$
$102$		0			0
$103$	−21.2687	−	9.91776i	−0.206492	−	0.0962890i	0.316621	−	0.948552i	$-0.397452\pi$
$103$	−21.2687	−	9.91776i	−0.206492	−	0.0962890i	−0.523113	+	0.852263i	$0.675229\pi$
$104$	−80.7215	−	14.2334i	−0.776168	−	0.136859i
$105$		0			0
$106$	−27.1970	+	22.8210i	−0.256575	+	0.215292i
$107$	−71.3346	+	71.3346i	−0.666679	+	0.666679i	−0.956946	−	0.290267i	$-0.906256\pi$
$107$	−71.3346	+	71.3346i	−0.666679	+	0.666679i	0.290267	+	0.956946i	$0.406256\pi$
$108$		0			0
$109$		−	117.131i		−	1.07459i	−0.843393	−	0.537297i	$-0.819445\pi$
$109$		−	117.131i		−	1.07459i	0.843393	−	0.537297i	$-0.180555\pi$
$110$	16.3453	−	96.9305i	0.148593	−	0.881186i
$111$		0			0
$112$	−17.2942	−	24.6987i	−0.154413	−	0.220524i
$113$	116.476	+	54.3136i	1.03076	+	0.480651i	0.863014	−	0.505179i	$-0.168574\pi$
$113$	116.476	+	54.3136i	1.03076	+	0.480651i	0.167745	+	0.985830i	$0.446351\pi$
$114$		0			0
$115$	120.729	−	146.084i	1.04982	−	1.27029i
$116$	−11.4229	−	19.7850i	−0.0984731	−	0.170560i
$117$		0			0
$118$	−32.0240	+	8.58080i	−0.271390	+	0.0727187i
$119$	−10.4981	+	28.8432i	−0.0882192	+	0.242380i
$120$		0			0
$121$	−45.3335	−	38.0393i	−0.374657	−	0.314374i
$122$	−82.4482	+	7.21329i	−0.675805	+	0.0591253i
$123$		0			0
$124$	20.1045	−	55.2367i	0.162133	−	0.445457i
$125$	−86.3840	+	90.3482i	−0.691072	+	0.722786i
$126$		0			0
$127$	76.6121	+	20.5282i	0.603245	+	0.161639i	0.547499	−	0.836806i	$-0.315580\pi$
$127$	76.6121	+	20.5282i	0.603245	+	0.161639i	0.0557454	+	0.998445i	$0.482246\pi$
$128$	−72.5618	+	103.629i	−0.566889	+	0.809601i
$129$		0			0
$130$	226.010	−	62.3737i	1.73854	−	0.479798i
$131$	30.1965	−	171.253i	0.230508	−	1.30727i	−0.621364	−	0.783522i	$-0.713421\pi$
$131$	30.1965	−	171.253i	0.230508	−	1.30727i	0.851871	−	0.523751i	$-0.175468\pi$
$132$		0			0
$133$	−46.5441	−	4.07208i	−0.349955	−	0.0306171i
$134$		−	231.065i		−	1.72437i
$135$		0			0
$136$	88.7048			0.652241
$137$	6.79618	−	77.6807i	0.0496072	−	0.567012i	−0.930198	−	0.367058i	$-0.880365\pi$
$137$	6.79618	−	77.6807i	0.0496072	−	0.567012i	0.979805	−	0.199954i	$-0.0640794\pi$
$138$		0			0
$139$	45.5336	+	8.02880i	0.327580	+	0.0577611i	0.335020	−	0.942211i	$-0.391257\pi$
$139$	45.5336	+	8.02880i	0.327580	+	0.0577611i	−0.00743985	+	0.999972i	$0.502368\pi$
$140$	14.8112	+	8.40423i	0.105794	+	0.0600302i
$141$		0			0
$142$	−90.4387	−	63.3258i	−0.636892	−	0.445957i
$143$	−38.1639	+	142.430i	−0.266880	+	0.996011i
$144$		0			0
$145$	−41.7663	−	28.7822i	−0.288044	−	0.198498i
$146$	119.901	+	43.6405i	0.821242	+	0.298907i
$147$		0			0
$148$	−6.47880	−	74.0530i	−0.0437757	−	0.500358i
$149$	157.603	−	187.824i	1.05774	−	1.26056i	0.0934742	−	0.995622i	$-0.470203\pi$
$149$	157.603	−	187.824i	1.05774	−	1.26056i	0.964264	−	0.264942i	$-0.0853528\pi$
$150$		0			0
$151$	−159.561	−	58.0755i	−1.05670	−	0.384606i	−0.245511	−	0.969394i	$-0.578956\pi$
$151$	−159.561	−	58.0755i	−1.05670	−	0.384606i	−0.811186	+	0.584788i	$0.801178\pi$
$152$	34.9466	+	130.423i	0.229912	+	0.858044i
$153$		0			0
$154$	−25.7496	+	14.8665i	−0.167205	+	0.0965360i
$155$	−12.3463	−	129.924i	−0.0796534	−	0.838222i
$156$		0			0
$157$	−11.1496	+	23.9104i	−0.0710166	+	0.152296i	−0.938611	−	0.344976i	$-0.887887\pi$
$157$	−11.1496	+	23.9104i	−0.0710166	+	0.152296i	0.867595	+	0.497272i	$0.165665\pi$
$158$	−65.5817	+	45.9208i	−0.415074	+	0.290638i
$159$		0			0
$160$	26.9097	−	159.579i	0.168185	−	0.997370i
$161$	−57.3238			−0.356049
$162$		0			0
$163$	−145.013	−	145.013i	−0.889652	−	0.889652i	0.104837	−	0.994489i	$-0.466568\pi$
$163$	−145.013	−	145.013i	−0.889652	−	0.889652i	−0.994489	+	0.104837i	$0.966568\pi$
$164$	60.2579	+	71.8126i	0.367426	+	0.437882i
$165$		0			0
$166$	19.7957	−	112.267i	0.119251	−	0.676307i
$167$	−81.8374	+	175.501i	−0.490044	+	1.05090i	0.493419	+	0.869792i	$0.335747\pi$
$167$	−81.8374	+	175.501i	−0.490044	+	1.05090i	−0.983463	+	0.181111i	$0.942031\pi$
$168$		0			0
$169$	−179.926	+	31.7258i	−1.06465	+	0.187727i
$170$	−229.152	+	108.948i	−1.34795	+	0.640871i
$171$		0			0
$172$	26.5699	+	99.1602i	0.154476	+	0.576513i
$173$	−114.312	−	245.143i	−0.660762	−	1.41701i	−0.895549	−	0.444963i	$-0.853217\pi$
$173$	−114.312	−	245.143i	−0.660762	−	1.41701i	0.234787	−	0.972047i	$-0.424561\pi$
$174$		0			0
$175$	37.7107	+	2.73182i	0.215490	+	0.0156104i
$176$	120.080	+	100.759i	0.682275	+	0.572497i
$177$		0			0
$178$	−32.2229	−	69.1022i	−0.181027	−	0.388215i
$179$	−79.5086	−	45.9043i	−0.444182	−	0.256449i	0.261188	−	0.965288i	$-0.415886\pi$
$179$	−79.5086	−	45.9043i	−0.444182	−	0.256449i	−0.705370	+	0.708839i	$0.749219\pi$
$180$		0			0
$181$	4.51197	+	7.81497i	0.0249280	+	0.0431766i	0.878220	−	0.478256i	$-0.158731\pi$
$181$	4.51197	+	7.81497i	0.0249280	+	0.0431766i	−0.853292	+	0.521433i	$0.825398\pi$
$182$	−58.0929	−	40.6771i	−0.319192	−	0.223500i
$183$		0			0
$184$	56.6599	+	155.672i	0.307934	+	0.846043i
$185$	−83.5882	−	142.311i	−0.451828	−	0.769250i
$186$		0			0
$187$	13.9079	−	158.968i	0.0743739	−	0.850097i
$188$	70.7012	+	70.7012i	0.376070	+	0.376070i
$189$		0			0
$190$	−250.464	−	294.000i	−1.31823	−	1.54737i
$191$	84.8059	−	71.1606i	0.444010	−	0.372568i	−0.393198	−	0.919454i	$-0.628631\pi$
$191$	84.8059	−	71.1606i	0.444010	−	0.372568i	0.837207	+	0.546886i	$0.184187\pi$
$192$		0			0
$193$	163.890	−	114.757i	0.849172	−	0.594596i	−0.0659278	−	0.997824i	$-0.521001\pi$
$193$	163.890	−	114.757i	0.849172	−	0.594596i	0.915100	+	0.403228i	$0.132112\pi$
$194$	103.684	+	284.869i	0.534453	+	1.46840i
$195$		0			0
$196$	18.2673	+	103.599i	0.0932004	+	0.528566i
$197$	295.205	+	79.0998i	1.49850	+	0.401522i	0.912597	−	0.408859i	$-0.134073\pi$
$197$	295.205	+	79.0998i	1.49850	+	0.401522i	0.585903	+	0.810381i	$0.300740\pi$
$198$		0			0
$199$	239.148	+	138.072i	1.20175	+	0.693831i	0.960944	−	0.276742i	$-0.0892547\pi$
$199$	239.148	+	138.072i	1.20175	+	0.693831i	0.240807	+	0.970573i	$0.422588\pi$
$200$	−29.8553	−	105.110i	−0.149276	−	0.525548i
$201$		0			0
$202$	28.8414	−	2.52329i	0.142779	−	0.0124916i
$203$	1.33719	+	15.2842i	0.00658715	+	0.0752915i
$204$		0			0
$205$	189.288	+	86.5496i	0.923355	+	0.422193i
$206$	−29.3390	+	50.8166i	−0.142422	+	0.246683i
$207$		0			0
$208$	−96.7681	+	361.144i	−0.465231	+	1.73627i
$209$	239.210	−	42.1792i	1.14455	−	0.201814i
$210$		0			0
$211$	−84.2672	+	30.6708i	−0.399371	+	0.145359i	−0.533894	−	0.845551i	$-0.679272\pi$
$211$	−84.2672	+	30.6708i	−0.399371	+	0.145359i	0.134523	+	0.990910i	$0.457050\pi$
$212$	18.3408	+	26.1933i	0.0865130	+	0.123553i
$213$		0			0
$214$	162.141	+	193.232i	0.757668	+	0.902953i
$215$	147.809	+	173.502i	0.687486	+	0.806985i
$216$		0			0
$217$	−27.9138	+	27.9138i	−0.128635	+	0.128635i
$218$	−291.759	−	25.5256i	−1.33835	−	0.117090i
$219$		0			0
$220$	−85.6858	−	22.2743i	−0.389481	−	0.101247i
$221$	357.660	−	130.177i	1.61837	−	0.589038i
$222$		0			0
$223$	−218.591	+	312.181i	−0.980230	+	1.39991i	−0.0645906	+	0.997912i	$0.520574\pi$
$223$	−218.591	+	312.181i	−0.980230	+	1.39991i	−0.915639	+	0.402001i	$0.868315\pi$
$224$	−42.3923	+	24.4752i	−0.189251	+	0.109264i
$225$		0			0
$226$	160.672	−	278.292i	0.710937	−	1.23138i
$227$	9.95983	−	4.64435i	0.0438759	−	0.0204597i	−0.400556	−	0.916272i	$-0.631183\pi$
$227$	9.95983	−	4.64435i	0.0438759	−	0.0204597i	0.444432	+	0.895812i	$0.353405\pi$
$228$		0			0
$229$	−124.474	+	148.343i	−0.543556	+	0.647785i	−0.965981	−	0.258613i	$-0.916735\pi$
$229$	−124.474	+	148.343i	−0.543556	+	0.647785i	0.422425	+	0.906398i	$0.361179\pi$
$230$	−337.568	−	332.558i	−1.46769	−	1.44590i
$231$		0			0
$232$	40.1849	−	18.7385i	0.173211	−	0.0807695i
$233$	57.2817	−	15.3486i	0.245844	−	0.0658737i	−0.133793	−	0.991009i	$-0.542716\pi$
$233$	57.2817	−	15.3486i	0.245844	−	0.0658737i	0.379637	+	0.925136i	$0.376049\pi$
$234$		0			0
$235$	209.169	+	74.3651i	0.890079	+	0.316447i
$236$	5.18515	+	29.4064i	0.0219710	+	0.124604i
$237$		0			0
$238$	69.5574	+	32.4352i	0.292258	+	0.136282i
$239$	−146.929	−	25.9075i	−0.614766	−	0.108400i	−0.142410	−	0.989808i	$-0.545485\pi$
$239$	−146.929	−	25.9075i	−0.614766	−	0.108400i	−0.472356	+	0.881408i	$0.656596\pi$
$240$		0			0
$241$	−255.936	+	214.756i	−1.06197	+	0.891102i	−0.994301	−	0.106606i	$-0.966002\pi$
$241$	−255.936	+	214.756i	−1.06197	+	0.891102i	−0.0676725	+	0.997708i	$0.521557\pi$
$242$	−104.631	+	104.631i	−0.432359	+	0.432359i
$243$		0			0
$244$			74.5412i			0.305497i
$245$	135.393	+	190.317i	0.552625	+	0.776805i
$246$		0			0
$247$	332.305	+	474.581i	1.34537	+	1.92138i
$248$	103.395	+	48.2138i	0.416915	+	0.194411i
$249$		0			0
$250$	206.222	+	234.862i	0.824888	+	0.939447i
$251$	−115.237	−	199.597i	−0.459113	−	0.795207i	0.539801	−	0.841793i	$-0.318499\pi$
$251$	−115.237	−	199.597i	−0.459113	−	0.795207i	−0.998914	+	0.0465852i	$0.985166\pi$
$252$		0			0
$253$	287.864	−	77.1328i	1.13780	−	0.304873i
$254$	67.8289	−	186.358i	0.267043	−	0.733695i
$255$		0			0
$256$	245.940	+	206.368i	0.960703	+	0.806126i
$257$	359.446	−	31.4475i	1.39862	−	0.122364i	0.637240	−	0.770665i	$-0.280076\pi$
$257$	359.446	−	31.4475i	1.39862	−	0.122364i	0.761384	+	0.648301i	$0.224520\pi$
$258$		0			0
$259$	−17.0743	+	46.9112i	−0.0659239	+	0.181124i
$260$	−38.2224	−	207.679i	−0.147009	−	0.798765i
$261$		0			0
$262$	−419.991	−	112.536i	−1.60302	−	0.429527i
$263$	−234.720	+	335.214i	−0.892470	+	1.27458i	0.0684226	+	0.997656i	$0.478203\pi$
$263$	−234.720	+	335.214i	−0.892470	+	1.27458i	−0.960892	+	0.276922i	$0.910686\pi$
$264$		0			0
$265$	61.7470	+	35.0368i	0.233008	+	0.132214i
$266$	−20.2862	+	115.049i	−0.0762638	+	0.432513i
$267$		0			0
$268$	−207.318	−	18.1380i	−0.773576	−	0.0676792i
$269$			238.334i			0.886001i	0.896521	+	0.443001i	$0.146086\pi$
$269$			238.334i			0.886001i	−0.896521	+	0.443001i	$0.853914\pi$
$270$		0			0
$271$	160.306			0.591533			0.295767	−	0.955260i	$-0.404425\pi$
$271$	160.306			0.591533			0.295767	+	0.955260i	$0.404425\pi$
$272$	35.2648	−	403.079i	0.129650	−	1.48191i
$273$		0			0
$274$	−192.013	−	33.8570i	−0.700776	−	0.123566i
$275$	−193.048	+	37.0237i	−0.701993	+	0.134632i
$276$		0			0
$277$	−261.061	−	182.797i	−0.942457	−	0.659916i	−0.00206152	−	0.999998i	$-0.500656\pi$
$277$	−261.061	−	182.797i	−0.942457	−	0.659916i	−0.940396	+	0.340082i	$0.889545\pi$
$278$	29.9217	−	111.669i	0.107632	−	0.401688i
$279$		0			0
$280$	−18.7542	+	27.2146i	−0.0669794	+	0.0971949i
$281$	−357.089	−	129.970i	−1.27078	−	0.462526i	−0.383408	−	0.923579i	$-0.625250\pi$
$281$	−357.089	−	129.970i	−1.27078	−	0.462526i	−0.887373	+	0.461053i	$0.847472\pi$
$282$		0			0
$283$	−10.4723	−	119.699i	−0.0370046	−	0.422964i	−0.991990	−	0.126313i	$-0.959686\pi$
$283$	−10.4723	−	119.699i	−0.0370046	−	0.422964i	0.954986	−	0.296651i	$-0.0958699\pi$
$284$	−63.9170	+	76.1733i	−0.225060	+	0.268216i
$285$		0			0
$286$	346.459	+	126.101i	1.21140	+	0.440912i
$287$	−16.2943	−	60.8111i	−0.0567745	−	0.211885i
$288$		0			0
$289$	−106.436	+	61.4509i	−0.368291	+	0.212633i
$290$	−80.7951	+	97.7628i	−0.278604	+	0.337113i
$291$		0			0
$292$	48.5675	−	104.153i	0.166327	−	0.356689i
$293$	97.8177	−	68.4927i	0.333849	−	0.233763i	−0.394617	−	0.918846i	$-0.629123\pi$
$293$	97.8177	−	68.4927i	0.333849	−	0.233763i	0.728466	+	0.685082i	$0.240234\pi$
$294$		0			0
$295$	38.4312	+	54.0213i	0.130275	+	0.183123i
$296$	144.271			0.487403
$297$		0			0
$298$	−433.503	−	433.503i	−1.45471	−	1.45471i
$299$	456.908	+	544.522i	1.52812	+	1.82114i
$300$		0			0
$301$	11.9717	−	67.8950i	0.0397731	−	0.225565i
$302$	−179.432	+	384.793i	−0.594145	+	1.27415i
$303$		0			0
$304$	606.539	−	106.949i	1.99520	−	0.351807i
$305$	71.0626	+	149.467i	0.232992	+	0.490055i
$306$		0			0
$307$	76.4108	+	285.169i	0.248895	+	0.928889i	0.971386	+	0.237508i	$0.0763307\pi$
$307$	76.4108	+	285.169i	0.248895	+	0.928889i	−0.722490	+	0.691381i	$0.757003\pi$
$308$	11.3174	+	24.2703i	0.0367449	+	0.0787997i
$309$		0			0
$310$	−326.317	+	2.43948i	−1.05264	+	0.00786928i
$311$	178.496	+	149.776i	0.573942	+	0.481595i	0.882951	−	0.469464i	$-0.155553\pi$
$311$	178.496	+	149.776i	0.573942	+	0.481595i	−0.309009	+	0.951059i	$0.599997\pi$
$312$		0			0
$313$	8.40699	+	18.0288i	0.0268594	+	0.0576002i	0.919280	−	0.393605i	$-0.128772\pi$
$313$	8.40699	+	18.0288i	0.0268594	+	0.0576002i	−0.892420	+	0.451205i	$0.850994\pi$
$314$	57.1283	+	32.9831i	0.181937	+	0.105042i
$315$		0			0
$316$	36.0535	+	62.4465i	0.114093	+	0.197615i
$317$	−43.1234	−	30.1953i	−0.136036	−	0.0952533i	0.503578	−	0.863950i	$-0.332017\pi$
$317$	−43.1234	−	30.1953i	−0.136036	−	0.0952533i	−0.639614	+	0.768697i	$0.720906\pi$
$318$		0			0
$319$	−27.2808	−	74.9534i	−0.0855198	−	0.234964i
$320$	−5.72519	−	1.48828i	−0.0178912	−	0.00465087i
$321$		0			0
$322$	−12.4923	+	142.787i	−0.0387958	+	0.443438i
$323$	−443.344	−	443.344i	−1.37258	−	1.37258i
$324$		0			0
$325$	−274.629	−	379.990i	−0.845012	−	1.16920i
$326$	−392.813	+	329.610i	−1.20495	+	1.01107i
$327$		0			0
$328$	−149.037	+	104.356i	−0.454380	+	0.318160i
$329$	−22.9660	−	63.0986i	−0.0698056	−	0.191789i
$330$		0			0
$331$	−94.5778	−	536.377i	−0.285733	−	1.62048i	−0.702654	−	0.711532i	$-0.748002\pi$
$331$	−94.5778	−	536.377i	−0.285733	−	1.62048i	0.416920	−	0.908943i	$-0.363109\pi$
$332$	−99.1753	−	26.5740i	−0.298721	−	0.0800420i
$333$		0			0
$334$	419.318	+	242.093i	1.25544	+	0.724831i
$335$	−432.997	+	161.274i	−1.29253	+	0.481415i
$336$		0			0
$337$	560.582	−	49.0446i	1.66345	−	0.145533i	0.783754	−	0.621071i	$-0.213302\pi$
$337$	560.582	−	49.0446i	1.66345	−	0.145533i	0.879695	+	0.475538i	$0.157747\pi$
$338$	39.8152	+	455.089i	0.117796	+	1.34642i
$339$		0			0
$340$	79.7637	+	214.154i	0.234599	+	0.629865i
$341$	102.615	−	177.735i	0.300925	−	0.521217i
$342$		0			0
$343$	37.4651	−	139.822i	0.109228	−	0.407644i
$344$	−196.212	+	34.5976i	−0.570385	+	0.100574i
$345$		0			0
$346$	−635.534	+	231.315i	−1.83680	+	0.668541i
$347$	174.873	+	249.745i	0.503957	+	0.719726i	0.987851	−	0.155401i	$-0.0496669\pi$
$347$	174.873	+	249.745i	0.503957	+	0.719726i	−0.483894	+	0.875127i	$0.660778\pi$
$348$		0			0
$349$	135.744	+	161.774i	0.388952	+	0.463535i	0.924618	−	0.380895i	$-0.124384\pi$
$349$	135.744	+	161.774i	0.388952	+	0.463535i	−0.535666	+	0.844430i	$0.679939\pi$
$350$	15.0227	−	93.3378i	0.0429221	−	0.266679i
$351$		0			0
$352$	179.949	−	179.949i	0.511219	−	0.511219i
$353$	−398.519	−	34.8659i	−1.12895	−	0.0987703i	−0.492661	−	0.870221i	$-0.663976\pi$
$353$	−398.519	−	34.8659i	−1.12895	−	0.0987703i	−0.636289	+	0.771451i	$0.719531\pi$
$354$		0			0
$355$	−55.5450	+	213.674i	−0.156465	+	0.601897i
$356$	−64.5299	+	23.4870i	−0.181264	+	0.0659747i
$357$		0			0
$358$	−131.669	+	188.043i	−0.367791	+	0.525260i
$359$	9.76776	−	5.63942i	0.0272082	−	0.0157087i	−0.486334	−	0.873773i	$-0.661666\pi$
$359$	9.76776	−	5.63942i	0.0272082	−	0.0157087i	0.513542	+	0.858064i	$0.328333\pi$
$360$		0			0
$361$	296.686	−	513.875i	0.821844	−	1.42348i
$362$	20.4495	−	9.53574i	0.0564902	−	0.0263418i
$363$		0			0
$364$	−41.0568	+	48.9296i	−0.112793	+	0.134422i
$365$	−1.90741	−	255.145i	−0.00522577	−	0.699026i
$366$		0			0
$367$	−142.914	+	66.6419i	−0.389412	+	0.181586i	−0.607456	−	0.794353i	$-0.707810\pi$
$367$	−142.914	+	66.6419i	−0.389412	+	0.181586i	0.218044	+	0.975939i	$0.430032\pi$
$368$	729.905	−	195.578i	1.98344	−	0.531461i
$369$		0			0
$370$	−372.697	+	177.195i	−1.00729	+	0.478907i
$371$	−3.72897	−	21.1480i	−0.0100511	−	0.0570028i
$372$		0			0
$373$	−362.150	−	168.873i	−0.970911	−	0.452743i	−0.128577	−	0.991700i	$-0.541041\pi$
$373$	−362.150	−	168.873i	−0.970911	−	0.452743i	−0.842334	+	0.538956i	$0.818819\pi$
$374$	−392.941	−	69.2861i	−1.05064	−	0.185257i
$375$		0			0
$376$	−148.654	+	124.736i	−0.395357	+	0.331744i
$377$	134.527	−	134.527i	0.356835	−	0.356835i
$378$		0			0
$379$			366.291i			0.966468i	0.875491	+	0.483234i	$0.160538\pi$
$379$			366.291i			0.966468i	−0.875491	+	0.483234i	$0.839462\pi$
$380$	−283.446	+	201.646i	−0.745911	+	0.530647i
$381$		0			0
$382$	−158.772	−	226.749i	−0.415632	−	0.593585i
$383$	−581.532	−	271.173i	−1.51836	−	0.708023i	−0.528352	−	0.849025i	$-0.677190\pi$
$383$	−581.532	−	271.173i	−1.51836	−	0.708023i	−0.990009	+	0.141002i	$0.954968\pi$
$384$		0			0
$385$	45.8309	+	37.8765i	0.119041	+	0.0983804i
$386$	−250.131	−	433.240i	−0.648008	−	1.12238i
$387$		0			0
$388$	263.732	−	70.6668i	0.679722	−	0.182131i
$389$	−183.702	+	504.717i	−0.472241	+	1.29747i	0.443705	+	0.896173i	$0.353664\pi$
$389$	−183.702	+	504.717i	−0.472241	+	1.29747i	−0.915947	+	0.401300i	$0.868559\pi$
$390$		0			0
$391$	−589.284	−	494.468i	−1.50712	−	1.26462i
$392$	−203.390	+	17.7943i	−0.518852	+	0.0453937i
$393$		0			0
$394$	261.361	−	718.083i	0.663352	−	1.82255i
$395$	131.825	+	90.8439i	0.333735	+	0.229985i
$396$		0			0
$397$	52.9425	+	14.1859i	0.133356	+	0.0357327i	0.324880	−	0.945755i	$-0.394676\pi$
$397$	52.9425	+	14.1859i	0.133356	+	0.0357327i	−0.191523	+	0.981488i	$0.561343\pi$
$398$	396.039	−	565.602i	0.995072	−	1.42111i
$399$		0			0
$400$	−489.492	+	93.8771i	−1.22373	+	0.234693i
$401$	−103.149	+	584.989i	−0.257230	+	1.45883i	0.533052	+	0.846083i	$0.321045\pi$
$401$	−103.149	+	584.989i	−0.257230	+	1.45883i	−0.790282	+	0.612743i	$0.790066\pi$
$402$		0			0
$403$	487.646	+	42.6635i	1.21004	+	0.105865i
$404$		−	26.0754i		−	0.0645431i
$405$		0			0
$406$	38.3626			0.0944890
$407$	22.6201	−	258.549i	0.0555777	−	0.635256i
$408$		0			0
$409$	−329.194	−	58.0457i	−0.804875	−	0.141921i	−0.243950	−	0.969788i	$-0.578443\pi$
$409$	−329.194	−	58.0457i	−0.804875	−	0.141921i	−0.560925	+	0.827867i	$0.689554\pi$
$410$	256.835	−	452.633i	0.626428	−	1.10398i
$411$		0			0
$412$	43.2911	+	30.3128i	0.105076	+	0.0735747i
$413$	5.19015	−	19.3699i	0.0125669	−	0.0469005i
$414$		0			0
$415$	−224.196	+	41.2622i	−0.540231	+	0.0994270i
$416$	570.385	+	207.603i	1.37112	+	0.499046i
$417$		0			0
$418$	−52.9339	−	605.037i	−0.126636	−	1.44746i
$419$	−218.086	+	259.905i	−0.520491	+	0.620297i	−0.960697	−	0.277600i	$-0.910461\pi$
$419$	−218.086	+	259.905i	−0.520491	+	0.620297i	0.440206	+	0.897897i	$0.354906\pi$
$420$		0			0
$421$	604.194	+	219.909i	1.43514	+	0.522349i	0.938400	−	0.345550i	$-0.112308\pi$
$421$	604.194	+	219.909i	1.43514	+	0.522349i	0.496741	+	0.867899i	$0.334530\pi$
$422$	58.0335	+	216.584i	0.137520	+	0.513232i
$423$		0			0
$424$	−53.7450	+	31.0297i	−0.126757	+	0.0731833i
$425$	364.099	+	353.371i	0.856703	+	0.831460i
$426$		0			0
$427$	21.1562	−	45.3696i	0.0495461	−	0.106252i
$428$	186.101	−	130.309i	0.434816	−	0.304461i
$429$		0			0
$430$	464.384	−	330.366i	1.07996	−	0.768294i
$431$	−234.638			−0.544404			−0.272202	−	0.962240i	$-0.587752\pi$
$431$	−234.638			−0.544404			−0.272202	+	0.962240i	$0.587752\pi$
$432$		0			0
$433$	588.065	+	588.065i	1.35812	+	1.35812i	0.876236	+	0.481882i	$0.160046\pi$
$433$	588.065	+	588.065i	1.35812	+	1.35812i	0.481882	+	0.876236i	$0.339954\pi$
$434$	63.4470	+	75.6132i	0.146191	+	0.174224i
$435$		0			0
$436$	−45.8047	+	259.771i	−0.105057	+	0.595806i
$437$	494.858	−	1061.23i	1.13240	−	2.42844i
$438$		0			0
$439$	−255.257	+	45.0087i	−0.581451	+	0.102525i	−0.456635	−	0.889654i	$-0.650945\pi$
$439$	−255.257	+	45.0087i	−0.581451	+	0.102525i	−0.124816	+	0.992180i	$0.539834\pi$
$440$	57.5594	−	161.899i	0.130817	−	0.367952i
$441$		0			0
$442$	−246.314	−	919.258i	−0.557273	−	2.07977i
$443$	50.3545	+	107.986i	0.113667	+	0.243760i	0.954909	−	0.296899i	$-0.0959526\pi$
$443$	50.3545	+	107.986i	0.113667	+	0.243760i	−0.841242	+	0.540659i	$0.818175\pi$
$444$		0			0
$445$	−107.002	+	108.614i	−0.240453	+	0.244075i
$446$	729.970	+	612.517i	1.63670	+	1.37336i
$447$		0			0
$448$	0.756187	+	1.62165i	0.00168792	+	0.00361975i
$449$	−699.258	−	403.717i	−1.55737	−	0.899146i	−0.997508	−	0.0705578i	$-0.977522\pi$
$449$	−699.258	−	403.717i	−1.55737	−	0.899146i	−0.559859	−	0.828588i	$-0.689145\pi$
$450$		0			0
$451$	163.650	+	283.451i	0.362861	+	0.628494i
$452$	−237.079	−	166.005i	−0.524511	−	0.367267i
$453$		0			0
$454$	−9.39805	−	25.8209i	−0.0207005	−	0.0568743i
$455$	−35.6791	+	137.252i	−0.0784156	+	0.301653i
$456$		0			0
$457$	69.9584	−	799.628i	0.153082	−	1.74973i	−0.399918	−	0.916551i	$-0.630961\pi$
$457$	69.9584	−	799.628i	0.153082	−	1.74973i	0.552999	−	0.833182i	$-0.313483\pi$
$458$	342.379	+	342.379i	0.747552	+	0.747552i
$459$		0			0
$460$	−324.879	+	276.771i	−0.706259	+	0.601676i
$461$	424.380	−	356.097i	0.920564	−	0.772445i	−0.0535349	−	0.998566i	$-0.517049\pi$
$461$	424.380	−	356.097i	0.920564	−	0.772445i	0.974099	+	0.226121i	$0.0726044\pi$
$462$		0			0
$463$	−603.577	+	422.629i	−1.30362	+	0.912806i	−0.999210	−	0.0397349i	$-0.987349\pi$
$463$	−603.577	+	422.629i	−1.30362	+	0.912806i	−0.304411	+	0.952541i	$0.598460\pi$
$464$	−69.1731	−	190.051i	−0.149080	−	0.409594i
$465$		0			0
$466$	−25.7485	−	146.027i	−0.0552543	−	0.313362i
$467$	−197.181	−	52.8345i	−0.422229	−	0.113136i	0.0414471	−	0.999141i	$-0.486803\pi$
$467$	−197.181	−	52.8345i	−0.422229	−	0.113136i	−0.463676	+	0.886005i	$0.653470\pi$
$468$		0			0
$469$	121.037	+	69.8805i	0.258074	+	0.148999i
$470$	230.818	−	504.809i	0.491102	−	1.07406i
$471$		0			0
$472$	−57.7320	+	5.05090i	−0.122314	+	0.0107011i
$473$	31.2385	+	357.058i	0.0660433	+	0.754878i
$474$		0			0
$475$	−376.118	+	674.550i	−0.791828	+	1.42010i
$476$	34.5619	−	59.8629i	0.0726089	−	0.125762i
$477$		0			0
$478$	−96.5521	+	360.337i	−0.201992	+	0.753844i
$479$	83.7408	−	14.7658i	0.174824	−	0.0308262i	−0.0855507	−	0.996334i	$-0.527265\pi$
$479$	83.7408	−	14.7658i	0.174824	−	0.0308262i	0.260375	+	0.965508i	$0.416154\pi$
$480$		0			0
$481$	581.705	−	211.723i	1.20937	−	0.440173i
$482$	479.157	+	684.307i	0.994102	+	1.41972i
$483$		0			0
$484$	85.6646	+	102.091i	0.176993	+	0.210932i
$485$	461.455	−	393.122i	0.951453	−	0.810562i
$486$		0			0
$487$	−133.297	+	133.297i	−0.273711	+	0.273711i	−0.830592	−	0.556881i	$-0.811998\pi$
$487$	−133.297	+	133.297i	−0.273711	+	0.273711i	0.556881	+	0.830592i	$0.311998\pi$
$488$	−144.119	−	12.6088i	−0.295326	−	0.0258377i
$489$		0			0
$490$	503.564	−	295.774i	1.02768	−	0.603620i
$491$	−194.091	+	70.6434i	−0.395297	+	0.143877i	−0.532018	−	0.846733i	$-0.678566\pi$
$491$	−194.091	+	70.6434i	−0.395297	+	0.143877i	0.136720	+	0.990610i	$0.456344\pi$
$492$		0			0
$493$	−118.093	+	168.654i	−0.239540	+	0.342098i
$494$	1254.55	−	724.312i	2.53957	−	1.46622i
$495$		0			0
$496$	260.191	−	450.663i	0.524578	−	0.908595i
$497$	60.5225	−	28.2221i	0.121776	−	0.0567850i
$498$		0			0
$499$	−182.688	+	217.719i	−0.366108	+	0.436311i	−0.917379	−	0.398016i	$-0.869699\pi$
$499$	−182.688	+	217.719i	−0.366108	+	0.436311i	0.551270	+	0.834327i	$0.314143\pi$
$500$	226.913	−	166.592i	0.453826	−	0.333185i
$501$		0			0
$502$	−522.286	+	243.546i	−1.04041	+	0.485152i
$503$	439.500	−	117.764i	0.873757	−	0.234122i	0.206045	−	0.978543i	$-0.433941\pi$
$503$	439.500	−	117.764i	0.873757	−	0.234122i	0.667712	+	0.744420i	$0.267274\pi$
$504$		0			0
$505$	−24.8585	−	52.2853i	−0.0492248	−	0.103535i
$506$	−129.397	−	733.845i	−0.255725	−	1.45029i
$507$		0			0
$508$	−161.882	−	75.4867i	−0.318665	−	0.148596i
$509$	−258.517	−	45.5835i	−0.507892	−	0.0895550i	−0.0861703	−	0.996280i	$-0.527463\pi$
$509$	−258.517	−	45.5835i	−0.507892	−	0.0895550i	−0.421722	+	0.906725i	$0.638574\pi$
$510$		0			0
$511$	−59.1213	+	49.6086i	−0.115697	+	0.0970815i
$512$	209.819	−	209.819i	0.409802	−	0.409802i
$513$		0			0
$514$		−	902.193i		−	1.75524i
$515$	115.704	+	19.5110i	0.224667	+	0.0378854i
$516$		0			0
$517$	200.232	+	285.961i	0.387296	+	0.553116i
$518$	113.130	+	52.7532i	0.218397	+	0.101840i
$519$		0			0
$520$	407.996	−	38.7705i	0.784607	−	0.0745586i
$521$	−279.823	−	484.668i	−0.537089	−	0.930265i	−0.999059	−	0.0433694i	$-0.986191\pi$
$521$	−279.823	−	484.668i	−0.537089	−	0.930265i	0.461971	−	0.886895i	$-0.347143\pi$
$522$		0			0
$523$	249.257	−	66.7883i	0.476591	−	0.127702i	−0.0125237	−	0.999922i	$-0.503987\pi$
$523$	249.257	−	66.7883i	0.476591	−	0.127702i	0.489115	+	0.872219i	$0.337320\pi$
$524$	−133.939	+	367.994i	−0.255609	+	0.702279i
$525$		0			0
$526$	783.829	+	657.711i	1.49017	+	1.25040i
$527$	−527.733	+	46.1706i	−1.00139	+	0.0876103i
$528$		0			0
$529$	310.431	−	852.902i	0.586826	−	1.61229i
$530$	100.729	−	146.169i	0.190055	−	0.275791i
$531$		0			0
$532$	101.633	+	27.2324i	0.191039	+	0.0511886i
$533$	−447.771	+	639.484i	−0.840096	+	1.19978i
$534$		0			0
$535$	248.933	−	438.707i	0.465296	−	0.820013i
$536$	70.1367	−	397.765i	0.130852	−	0.742099i
$537$		0			0
$538$	593.664	+	51.9388i	1.10346	+	0.0965406i
$539$			367.286i			0.681421i
$540$		0			0
$541$	−424.251			−0.784198			−0.392099	−	0.919923i	$-0.628251\pi$
$541$	−424.251			−0.784198			−0.392099	+	0.919923i	$0.628251\pi$
$542$	34.9345	−	399.303i	0.0644547	−	0.736721i
$543$		0			0
$544$	−646.909	−	114.068i	−1.18917	−	0.209683i
$545$	155.803	+	564.549i	0.285877	+	1.03587i
$546$		0			0
$547$	524.455	+	367.227i	0.958785	+	0.671348i	0.944487	−	0.328550i	$-0.106560\pi$
$547$	524.455	+	367.227i	0.958785	+	0.671348i	0.0142979	+	0.999898i	$0.495449\pi$
$548$	−45.4500	+	169.622i	−0.0829380	+	0.309529i
$549$		0			0
$550$	50.1520	+	488.929i	0.0911855	+	0.888962i
$551$	−294.497	−	107.188i	−0.534478	−	0.194534i
$552$		0			0
$553$	−4.22052	−	48.2407i	−0.00763204	−	0.0872346i
$554$	−512.217	+	610.436i	−0.924579	+	1.10187i
$555$		0			0
$556$	−97.8442	−	35.6124i	−0.175979	−	0.0640510i
$557$	−94.1808	−	351.487i	−0.169086	−	0.631037i	−0.997484	−	0.0708966i	$-0.977414\pi$
$557$	−94.1808	−	351.487i	−0.169086	−	0.631037i	0.828398	−	0.560140i	$-0.189253\pi$
$558$		0			0
$559$	−740.360	+	427.447i	−1.32444	+	0.764663i
$560$	116.208	+	96.0393i	0.207515	+	0.171499i
$561$		0			0
$562$	−401.559	+	861.145i	−0.714517	+	1.53229i
$563$	621.291	−	435.033i	1.10354	−	0.772705i	0.127832	−	0.991796i	$-0.459198\pi$
$563$	621.291	−	435.033i	1.10354	−	0.772705i	0.975704	+	0.219091i	$0.0703092\pi$
$564$		0			0
$565$	−633.638	−	106.850i	−1.12148	−	0.189115i
$566$	−300.438			−0.530810
$567$		0			0
$568$	−136.463	−	136.463i	−0.240252	−	0.240252i
$569$	−333.693	−	397.680i	−0.586455	−	0.698910i	0.388465	−	0.921463i	$-0.373005\pi$
$569$	−333.693	−	397.680i	−0.586455	−	0.698910i	−0.974920	+	0.222553i	$0.928561\pi$
$570$		0			0
$571$	−51.8056	+	293.804i	−0.0907279	+	0.514543i	0.905245	+	0.424890i	$0.139687\pi$
$571$	−51.8056	+	293.804i	−0.0907279	+	0.514543i	−0.995973	+	0.0896537i	$0.971424\pi$
$572$	140.337	−	300.955i	0.245345	−	0.526145i
$573$		0			0
$574$	−155.024	+	27.3350i	−0.270077	+	0.0476219i
$575$	−387.578	+	864.686i	−0.674049	+	1.50380i
$576$		0			0
$577$	−23.8985	−	89.1903i	−0.0414185	−	0.154576i	0.942120	−	0.335277i	$-0.108830\pi$
$577$	−23.8985	−	89.1903i	−0.0414185	−	0.154576i	−0.983538	+	0.180701i	$0.942163\pi$
$578$	129.872	+	278.512i	0.224692	+	0.481854i
$579$		0			0
$580$	81.3735	+	80.1658i	0.140299	+	0.138217i
$581$	52.8210	+	44.3221i	0.0909139	+	0.0762858i
$582$		0			0
$583$	47.1818	+	101.182i	0.0809294	+	0.173554i
$584$	193.157	+	111.519i	0.330747	+	0.190957i
$585$		0			0
$586$	−149.291	−	258.579i	−0.254762	−	0.441261i
$587$	309.803	+	216.926i	0.527773	+	0.369551i	0.806886	−	0.590708i	$-0.201151\pi$
$587$	309.803	+	216.926i	0.527773	+	0.369551i	−0.279113	+	0.960258i	$0.590040\pi$
$588$		0			0
$589$	−275.793	−	757.735i	−0.468239	−	1.28648i
$590$	142.936	−	83.9551i	0.242264	−	0.142297i
$591$		0			0
$592$	57.3554	−	655.575i	0.0968841	−	1.10739i
$593$	450.055	+	450.055i	0.758945	+	0.758945i	0.976130	−	0.217185i	$-0.0696876\pi$
$593$	450.055	+	450.055i	0.758945	+	0.758945i	−0.217185	+	0.976130i	$0.569688\pi$
$594$		0			0
$595$	12.2326	−	152.983i	0.0205591	−	0.257115i
$596$	−422.980	+	354.922i	−0.709698	+	0.595507i
$597$		0			0
$598$	1455.91	−	1019.44i	2.43464	−	1.70475i
$599$	−291.283	−	800.294i	−0.486282	−	1.33605i	−0.904023	−	0.427483i	$-0.859400\pi$
$599$	−291.283	−	800.294i	−0.486282	−	1.33605i	0.417741	−	0.908566i	$-0.362822\pi$
$600$		0			0
$601$	40.3813	+	229.014i	0.0671902	+	0.381055i	0.999797	+	0.0201599i	$0.00641754\pi$
$601$	40.3813	+	229.014i	0.0671902	+	0.381055i	−0.932607	+	0.360895i	$0.882471\pi$
$602$	−166.510	−	44.6161i	−0.276594	−	0.0741132i
$603$		0			0
$604$	331.162	+	191.197i	0.548282	+	0.316551i
$605$	269.098	+	123.042i	0.444790	+	0.203375i
$606$		0			0
$607$	4.10796	−	0.359400i	0.00676764	−	0.000592092i	−0.0837714	−	0.996485i	$-0.526697\pi$
$607$	4.10796	−	0.359400i	0.00676764	−	0.000592092i	0.0905391	+	0.995893i	$0.471141\pi$
$608$	−87.1465	−	996.089i	−0.143333	−	1.63830i
$609$		0			0
$610$	387.791	−	144.436i	0.635723	−	0.236781i
$611$	−416.323	+	721.092i	−0.681379	+	1.18018i
$612$		0			0
$613$	57.3893	−	214.180i	0.0936203	−	0.349396i	−0.903186	−	0.429249i	$-0.858778\pi$
$613$	57.3893	−	214.180i	0.0936203	−	0.349396i	0.996807	+	0.0798529i	$0.0254451\pi$
$614$	726.975	−	128.185i	1.18400	−	0.208771i
$615$		0			0
$616$	−48.8390	+	17.7759i	−0.0792841	+	0.0288571i
$617$	95.5350	+	136.438i	0.154838	+	0.221131i	0.889075	−	0.457762i	$-0.151349\pi$
$617$	95.5350	+	136.438i	0.154838	+	0.221131i	−0.734237	+	0.678893i	$0.762460\pi$
$618$		0			0
$619$	−281.498	−	335.476i	−0.454762	−	0.541965i	0.489133	−	0.872209i	$-0.337313\pi$
$619$	−281.498	−	335.476i	−0.454762	−	0.541965i	−0.943895	+	0.330245i	$0.892869\pi$
$620$	−23.4263	+	292.973i	−0.0377843	+	0.472537i
$621$		0			0
$622$	411.973	−	411.973i	0.662337	−	0.662337i
$623$	45.9422	+	4.01943i	0.0737436	+	0.00645173i
$624$		0			0
$625$	296.177	−	550.367i	0.473884	−	0.880587i
$626$	46.7399	−	17.0119i	0.0746644	−	0.0271756i
$627$		0			0
$628$	34.0778	−	48.6681i	0.0542640	−	0.0774970i
$629$	−580.172	+	334.963i	−0.922373	+	0.532532i
$630$		0			0
$631$	−262.915	+	455.382i	−0.416664	+	0.721683i	−0.995602	−	0.0936889i	$-0.970134\pi$
$631$	−262.915	+	455.382i	−0.416664	+	0.721683i	0.578938	+	0.815372i	$0.303467\pi$
$632$	−126.834	+	59.1435i	−0.200686	+	0.0935815i
$633$		0			0
$634$	−84.6107	+	100.835i	−0.133455	+	0.159046i
$635$	−396.562	+	2.96461i	−0.624508	+	0.00466868i
$636$		0			0
$637$	−793.959	+	370.229i	−1.24640	+	0.581207i
$638$	−192.646	+	51.6192i	−0.301952	+	0.0809079i
$639$		0			0
$640$	211.891	−	595.992i	0.331080	−	0.931237i
$641$	42.8495	+	243.011i	0.0668478	+	0.379113i	0.999817	+	0.0191554i	$0.00609772\pi$
$641$	42.8495	+	243.011i	0.0668478	+	0.379113i	−0.932969	+	0.359958i	$0.882791\pi$
$642$		0			0
$643$	716.410	+	334.068i	1.11417	+	0.519545i	0.890437	−	0.455106i	$-0.150398\pi$
$643$	716.410	+	334.068i	1.11417	+	0.519545i	0.223731	+	0.974651i	$0.428176\pi$
$644$	127.132	+	22.4168i	0.197410	+	0.0348088i
$645$		0			0
$646$	−1200.93	+	1007.70i	−1.85903	+	1.55991i
$647$	−519.013	+	519.013i	−0.802184	+	0.802184i	−0.983437	−	0.181253i	$-0.941985\pi$
$647$	−519.013	+	519.013i	−0.802184	+	0.802184i	0.181253	+	0.983437i	$0.441985\pi$
$648$		0			0
$649$			104.254i			0.160637i
$650$	−1006.36	+	601.260i	−1.54825	+	0.925016i
$651$		0			0
$652$	264.901	+	378.317i	0.406289	+	0.580241i
$653$	315.296	+	147.025i	0.482843	+	0.225153i	0.648770	−	0.760985i	$-0.275284\pi$
$653$	315.296	+	147.025i	0.482843	+	0.225153i	−0.165927	+	0.986138i	$0.553062\pi$
$654$		0			0
$655$	82.2526	+	865.574i	0.125576	+	1.32149i
$656$	414.951	+	718.716i	0.632547	+	1.09560i
$657$		0			0
$658$	−162.176	+	43.4550i	−0.246469	+	0.0660411i
$659$	244.610	−	672.060i	0.371184	−	1.01982i	−0.603721	−	0.797196i	$-0.706316\pi$
$659$	244.610	−	672.060i	0.371184	−	1.01982i	0.974905	−	0.222623i	$-0.0714619\pi$
$660$		0			0
$661$	−374.311	−	314.084i	−0.566280	−	0.475165i	0.314129	−	0.949380i	$-0.398288\pi$
$661$	−374.311	−	314.084i	−0.566280	−	0.475165i	−0.880409	+	0.474215i	$0.842732\pi$
$662$	−1356.67	+	118.693i	−2.04934	+	0.179294i
$663$		0			0
$664$	68.1543	−	187.252i	0.102642	−	0.282007i
$665$	229.751	−	42.2845i	0.345490	−	0.0635858i
$666$		0			0
$667$	−371.411	−	99.5192i	−0.556837	−	0.149204i
$668$	250.129	−	357.221i	0.374444	−	0.534762i
$669$		0			0
$670$	307.354	+	1113.69i	0.458738	+	1.66223i
$671$	−45.1926	+	256.300i	−0.0673511	+	0.381967i
$672$		0			0
$673$	376.228	+	32.9157i	0.559031	+	0.0489089i	0.363170	−	0.931723i	$-0.381694\pi$
$673$	376.228	+	32.9157i	0.559031	+	0.0489089i	0.195861	+	0.980632i	$0.437250\pi$
$674$		−	1407.03i		−	2.08759i
$675$		0			0
$676$	411.445			0.608646
$677$	−62.5370	+	714.801i	−0.0923737	+	1.05584i	0.798625	+	0.601829i	$0.205561\pi$
$677$	−62.5370	+	714.801i	−0.0923737	+	1.05584i	−0.890998	+	0.454007i	$0.849994\pi$
$678$		0			0
$679$	−180.577	−	31.8406i	−0.265946	−	0.0468934i
$680$	−427.541	+	117.992i	−0.628737	+	0.173518i
$681$		0			0
$682$	−420.355	−	294.336i	−0.616356	−	0.431577i
$683$	−56.0992	+	209.365i	−0.0821365	+	0.306537i	−0.994757	−	0.102271i	$-0.967389\pi$
$683$	−56.0992	+	209.365i	−0.0821365	+	0.306537i	0.912620	+	0.408809i	$0.134056\pi$
$684$		0			0
$685$	70.5716	+	383.447i	0.103024	+	0.559777i
$686$	−340.115	−	123.792i	−0.495795	−	0.180455i
$687$		0			0
$688$	79.2081	+	905.353i	0.115128	+	1.31592i
$689$	−171.164	+	203.985i	−0.248424	+	0.296060i
$690$		0			0
$691$	−229.279	−	83.4506i	−0.331807	−	0.120768i	0.170744	−	0.985315i	$-0.445383\pi$
$691$	−229.279	−	83.4506i	−0.331807	−	0.120768i	−0.502551	+	0.864547i	$0.667605\pi$
$692$	157.655	+	588.377i	0.227825	+	0.850256i
$693$		0			0
$694$	660.195	−	381.164i	0.951289	−	0.549227i
$695$	−230.143	+	21.8697i	−0.331141	+	0.0314672i
$696$		0			0
$697$	357.045	−	765.685i	0.512260	−	1.09854i
$698$	432.542	−	302.869i	0.619688	−	0.433910i
$699$		0			0
$700$	−82.5661	−	20.8056i	−0.117952	−	0.0297223i
$701$	−287.312			−0.409861			−0.204930	−	0.978777i	$-0.565697\pi$
$701$	−287.312			−0.409861			−0.204930	+	0.978777i	$0.565697\pi$
$702$		0			0
$703$	−721.063	−	721.063i	−1.02569	−	1.02569i
$704$	−5.97938	−	7.12595i	−0.00849344	−	0.0101221i
$705$		0			0
$706$	−173.694	+	985.068i	−0.246026	+	1.39528i
$707$	−7.40068	+	15.8708i	−0.0104677	+	0.0224481i
$708$		0			0
$709$	−876.568	+	154.563i	−1.23634	+	0.218001i	−0.753348	−	0.657622i	$-0.771563\pi$
$709$	−876.568	+	154.563i	−1.23634	+	0.218001i	−0.482996	+	0.875623i	$0.660451\pi$
$710$	520.132	+	184.921i	0.732580	+	0.260452i
$711$		0			0
$712$	−34.4948	−	128.736i	−0.0484477	−	0.180809i
$713$	−418.114	−	896.649i	−0.586415	−	1.25757i
$714$		0			0
$715$	−5.51152	−	737.249i	−0.00770842	−	1.03112i
$716$	158.382	+	132.898i	0.221204	+	0.185612i
$717$		0			0
$718$	−11.9185	−	25.5593i	−0.0165996	−	0.0355980i
$719$	−746.732	−	431.126i	−1.03857	−	0.599619i	−0.119142	−	0.992877i	$-0.538014\pi$
$719$	−746.732	−	431.126i	−1.03857	−	0.599619i	−0.919428	+	0.393259i	$0.871348\pi$
$720$		0			0
$721$	−17.7459	−	30.7367i	−0.0246128	−	0.0426307i
$722$	−1215.35	−	850.996i	−1.68331	−	1.17867i
$723$		0			0
$724$	−6.95051	−	19.0964i	−0.00960016	−	0.0263762i
$725$	239.591	+	83.1690i	0.330471	+	0.114716i
$726$		0			0
$727$	−107.388	+	1227.45i	−0.147714	+	1.68837i	0.455058	+	0.890462i	$0.349618\pi$
$727$	−107.388	+	1227.45i	−0.147714	+	1.68837i	−0.602772	+	0.797913i	$0.705937\pi$
$728$	−87.6565	−	87.6565i	−0.120407	−	0.120407i
$729$		0			0
$730$	−635.952	−	50.8511i	−0.871166	−	0.0696590i
$731$	708.721	−	594.688i	0.969523	−	0.813526i
$732$		0			0
$733$	181.798	−	127.296i	0.248019	−	0.173664i	−0.442956	−	0.896543i	$-0.646070\pi$
$733$	181.798	−	127.296i	0.248019	−	0.173664i	0.690975	+	0.722879i	$0.257181\pi$
$734$	134.853	+	370.506i	0.183723	+	0.504776i
$735$		0			0
$736$	−213.029	−	1208.15i	−0.289442	−	1.64151i
$737$	−701.840	−	188.057i	−0.952293	−	0.255166i
$738$		0			0
$739$	862.244	+	497.817i	1.16677	+	0.673635i	0.952917	−	0.303230i	$-0.0980651\pi$
$739$	862.244	+	497.817i	1.16677	+	0.673635i	0.213854	+	0.976866i	$0.431398\pi$
$740$	129.729	+	348.304i	0.175310	+	0.470681i
$741$		0			0
$742$	−53.4900	+	4.67977i	−0.0720889	+	0.00630696i
$743$	−23.7038	−	270.935i	−0.0319028	−	0.364650i	−0.995319	−	0.0966417i	$-0.969190\pi$
$743$	−23.7038	−	270.935i	−0.0319028	−	0.364650i	0.963416	−	0.268009i	$-0.0863656\pi$
$744$		0			0
$745$	−509.782	+	1114.92i	−0.684271	+	1.49653i
$746$	−499.565	+	865.272i	−0.669658	+	1.15988i
$747$		0			0
$748$	−93.0103	+	347.119i	−0.124345	+	0.464063i
$749$	−150.255	+	26.4940i	−0.200607	+	0.0353725i
$750$		0			0
$751$	−67.0427	+	24.4015i	−0.0892712	+	0.0324921i	−0.386270	−	0.922386i	$-0.626237\pi$
$751$	−67.0427	+	24.4015i	−0.0892712	+	0.0324921i	0.296998	+	0.954878i	$0.404014\pi$
$752$	507.707	+	725.080i	0.675142	+	0.964203i
$753$		0			0
$754$	−305.774	−	364.408i	−0.405536	−	0.483299i
$755$	846.306	+	67.6711i	1.12094	+	0.0896307i
$756$		0			0
$757$	449.679	−	449.679i	0.594028	−	0.594028i	−0.344689	−	0.938717i	$-0.612016\pi$
$757$	449.679	−	449.679i	0.594028	−	0.594028i	0.938717	+	0.344689i	$0.112016\pi$
$758$	912.390	+	79.8238i	1.20368	+	0.105308i
$759$		0			0
$760$	−341.920	−	582.129i	−0.449895	−	0.765959i
$761$	−1091.88	+	397.413i	−1.43480	+	0.522224i	−0.938303	−	0.345814i	$-0.887603\pi$
$761$	−1091.88	+	397.413i	−1.43480	+	0.522224i	−0.496497	+	0.868039i	$0.665381\pi$
$762$		0			0
$763$	101.607	−	145.110i	0.133168	−	0.190183i
$764$	−215.909	+	124.655i	−0.282604	+	0.163161i
$765$		0			0
$766$	−802.191	+	1389.44i	−1.04725	+	1.81388i
$767$	−225.364	+	105.089i	−0.293826	+	0.137013i
$768$		0			0
$769$	129.235	−	154.017i	0.168056	−	0.200282i	−0.675443	−	0.737412i	$-0.736047\pi$
$769$	129.235	−	154.017i	0.168056	−	0.200282i	0.843499	+	0.537131i	$0.180492\pi$
$770$	104.334	−	105.905i	0.135498	−	0.137539i
$771$		0			0
$772$	−408.350	+	190.417i	−0.528951	+	0.246654i
$773$	−768.252	+	205.852i	−0.993858	+	0.266303i	−0.718870	−	0.695144i	$-0.755340\pi$
$773$	−768.252	+	205.852i	−0.993858	+	0.266303i	−0.274988	+	0.961448i	$0.588674\pi$
$774$		0			0
$775$	232.327	+	609.790i	0.299777	+	0.786825i
$776$	92.0176	+	521.858i	0.118579	+	0.672497i
$777$		0			0
$778$	1217.16	+	567.570i	1.56447	+	0.729525i
$779$	1266.45	+	223.309i	1.62574	+	0.286661i
$780$		0			0
$781$	−265.952	+	223.160i	−0.340528	+	0.285737i
$782$	−1360.08	+	1360.08i	−1.73924	+	1.73924i
$783$		0			0
$784$			931.288i			1.18787i
$785$	21.9343	−	130.075i	0.0279418	−	0.165700i
$786$		0			0
$787$	183.306	+	261.788i	0.232917	+	0.332640i	0.918548	−	0.395309i	$-0.129363\pi$
$787$	183.306	+	261.788i	0.232917	+	0.332640i	−0.685631	+	0.727949i	$0.740474\pi$
$788$	−623.769	−	290.868i	−0.791585	−	0.369122i
$789$		0			0
$790$	255.010	−	308.564i	0.322797	−	0.390588i
$791$	97.1832	+	168.326i	0.122861	+	0.212802i
$792$		0			0
$793$	−599.596	+	160.661i	−0.756111	+	0.202599i
$794$	46.8729	−	128.782i	0.0590339	−	0.162194i
$795$		0			0
$796$	−476.387	−	399.736i	−0.598476	−	0.502181i
$797$	606.547	−	53.0660i	0.761037	−	0.0665821i	0.299972	−	0.953948i	$-0.403023\pi$
$797$	606.547	−	53.0660i	0.761037	−	0.0665821i	0.461066	+	0.887366i	$0.347467\pi$
$798$		0			0
$799$	308.192	−	846.751i	0.385722	−	1.05976i
$800$	82.5667	+	804.938i	0.103208	+	1.00617i
$801$		0			0
$802$	1434.66	+	384.417i	1.78886	+	0.479322i
$803$	230.138	−	328.672i	0.286598	−	0.409305i
$804$		0			0
$805$	276.291	−	76.2501i	0.343218	−	0.0947206i
$806$	212.540	−	1205.37i	0.263697	−	1.49550i
$807$		0			0
$808$	50.4147	+	4.41071i	0.0623944	+	0.00545880i
$809$		−	610.430i		−	0.754549i	−0.926102	−	0.377274i	$-0.876861\pi$
$809$		−	610.430i		−	0.754549i	0.926102	−	0.377274i	$-0.123139\pi$
$810$		0			0
$811$	−1157.70			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$811$	−1157.70			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$812$	3.01136	−	34.4200i	0.00370857	−	0.0423892i
$813$		0			0
$814$	−639.087	−	112.688i	−0.785119	−	0.138438i
$815$	891.829	+	506.047i	1.09427	+	0.620916i
$816$		0			0
$817$	1153.58	+	807.746i	1.41197	+	0.988673i
$818$	−216.325	+	807.334i	−0.264456	+	0.986961i
$819$		0			0
$820$	−385.955	−	265.971i	−0.470677	−	0.324355i
$821$	431.833	+	157.175i	0.525985	+	0.191443i	0.591345	−	0.806419i	$-0.298597\pi$
$821$	431.833	+	157.175i	0.525985	+	0.191443i	−0.0653599	+	0.997862i	$0.520820\pi$
$822$		0			0
$823$	124.102	+	1418.50i	0.150793	+	1.72357i	0.575129	+	0.818062i	$0.304952\pi$
$823$	124.102	+	1418.50i	0.150793	+	1.72357i	−0.424337	+	0.905504i	$0.639493\pi$
$824$	−65.9300	+	78.5724i	−0.0800122	+	0.0953548i
$825$		0			0
$826$	−47.1171	−	17.1492i	−0.0570425	−	0.0207618i
$827$	−147.921	−	552.049i	−0.178865	−	0.667532i	−0.995861	−	0.0908891i	$-0.971029\pi$
$827$	−147.921	−	552.049i	−0.178865	−	0.667532i	0.816996	−	0.576643i	$-0.195638\pi$
$828$		0			0
$829$	265.795	−	153.457i	0.320621	−	0.185111i	−0.331048	−	0.943614i	$-0.607402\pi$
$829$	265.795	−	153.457i	0.320621	−	0.185111i	0.651669	+	0.758503i	$0.274069\pi$
$830$	53.9217	+	567.438i	0.0649659	+	0.683660i
$831$		0			0
$832$	9.37680	−	20.1086i	0.0112702	−	0.0241690i
$833$	776.598	−	543.780i	0.932291	−	0.652797i
$834$		0			0
$835$	160.997	−	954.739i	0.192810	−	1.14340i
$836$	−547.012			−0.654321
$837$		0			0
$838$	599.866	+	599.866i	0.715831	+	0.715831i
$839$	116.028	+	138.277i	0.138293	+	0.164811i	0.830746	−	0.556652i	$-0.187914\pi$
$839$	116.028	+	138.277i	0.138293	+	0.164811i	−0.692453	+	0.721463i	$0.743470\pi$
$840$		0			0
$841$	128.167	−	726.873i	0.152399	−	0.864296i
$842$	679.436	−	1457.06i	0.806931	−	1.73047i
$843$		0			0
$844$	198.881	−	35.0681i	0.235641	−	0.0415499i
$845$	825.011	−	392.244i	0.976345	−	0.464194i
$846$		0			0
$847$	−23.1645	−	86.4510i	−0.0273489	−	0.102067i
$848$	119.634	+	256.556i	0.141078	+	0.302542i
$849$		0			0
$850$	959.552	−	829.920i	1.12888	−	0.976376i
$851$	−958.423	−	804.213i	−1.12623	−	0.945021i
$852$		0			0
$853$	−85.4401	−	183.227i	−0.100164	−	0.214803i	0.849839	−	0.527042i	$-0.176699\pi$
$853$	−85.4401	−	183.227i	−0.100164	−	0.214803i	−0.950004	+	0.312239i	$0.898921\pi$
$854$	−108.400	−	62.5847i	−0.126932	−	0.0732842i
$855$		0			0
$856$	220.463	+	381.853i	0.257550	+	0.446090i
$857$	734.080	+	514.009i	0.856570	+	0.599777i	0.917219	−	0.398382i	$-0.130428\pi$
$857$	734.080	+	514.009i	0.856570	+	0.599777i	−0.0606495	+	0.998159i	$0.519317\pi$
$858$		0			0
$859$	168.173	+	462.051i	0.195777	+	0.537894i	0.998272	−	0.0587657i	$-0.0187165\pi$
$859$	168.173	+	462.051i	0.195777	+	0.537894i	−0.802494	+	0.596660i	$0.796494\pi$
$860$	−259.961	−	442.592i	−0.302281	−	0.514642i
$861$		0			0
$862$	−51.1334	+	584.457i	−0.0593194	+	0.678024i
$863$	−535.726	−	535.726i	−0.620771	−	0.620771i	0.324957	−	0.945729i	$-0.394650\pi$
$863$	−535.726	−	535.726i	−0.620771	−	0.620771i	−0.945729	+	0.324957i	$0.894650\pi$
$864$		0			0
$865$	877.043	+	1029.49i	1.01392	+	1.19016i
$866$	1592.96	−	1336.65i	1.83944	−	1.54347i
$867$		0			0
$868$	72.8228	−	50.9911i	0.0838973	−	0.0587455i
$869$	86.1052	+	236.572i	0.0990854	+	0.272235i
$870$		0			0
$871$	−300.942	−	1706.73i	−0.345513	−	1.95950i
$872$	−494.499	−	132.501i	−0.567086	−	0.151950i
$873$		0			0
$874$	−2535.55	−	1463.90i	−2.90109	−	1.67495i
$875$	−185.393	+	36.9945i	−0.211877	+	0.0422795i
$876$		0			0
$877$	−275.094	+	24.0676i	−0.313676	+	0.0274431i	−0.242907	−	0.970050i	$-0.578101\pi$
$877$	−275.094	+	24.0676i	−0.313676	+	0.0274431i	−0.0707694	+	0.997493i	$0.522545\pi$
$878$	56.4848	+	645.624i	0.0643335	+	0.735335i
$879$		0			0
$880$	−712.792	−	325.916i	−0.809991	−	0.370359i
$881$	300.344	−	520.212i	0.340913	−	0.590478i	−0.643690	−	0.765287i	$-0.722597\pi$
$881$	300.344	−	520.212i	0.340913	−	0.590478i	0.984603	+	0.174808i	$0.0559305\pi$
$882$		0			0
$883$	258.323	−	964.073i	0.292551	−	1.09182i	−0.650592	−	0.759428i	$-0.725479\pi$
$883$	258.323	−	964.073i	0.292551	−	1.09182i	0.943143	−	0.332388i	$-0.107854\pi$
$884$	−844.121	+	148.841i	−0.954887	+	0.168372i
$885$		0			0
$886$	279.953	−	101.895i	0.315974	−	0.115005i
$887$	126.896	+	181.226i	0.143061	+	0.204313i	0.884288	−	0.466942i	$-0.154644\pi$
$887$	126.896	+	181.226i	0.143061	+	0.204313i	−0.741226	+	0.671255i	$0.765756\pi$
$888$		0			0
$889$	77.1050	+	91.8901i	0.0867323	+	0.103363i
$890$	247.226	+	290.198i	0.277782	+	0.326066i
$891$		0			0
$892$	606.869	−	606.869i	0.680347	−	0.680347i
$893$	1366.39	+	119.544i	1.53012	+	0.133868i
$894$		0			0
$895$	444.277	+	115.491i	0.496399	+	0.129040i
$896$	−179.789	+	65.4379i	−0.200658	+	0.0730334i
$897$		0			0
$898$	−1158.00	+	1653.79i	−1.28953	+	1.84164i
$899$	−229.319	+	132.397i	−0.255082	+	0.147272i
$900$		0			0
$901$	144.087	−	249.566i	0.159919	−	0.276987i
$902$	741.707	−	345.864i	0.822291	−	0.383441i
$903$		0			0
$904$	361.059	−	430.293i	0.399401	−	0.475988i
$905$	−32.1421	−	31.6651i	−0.0355161	−	0.0349890i
$906$		0			0
$907$	1021.43	−	476.303i	1.12617	−	0.525141i	0.231930	−	0.972732i	$-0.425496\pi$
$907$	1021.43	−	476.303i	1.12617	−	0.525141i	0.894238	+	0.447591i	$0.147718\pi$
$908$	−23.9050	+	6.40533i	−0.0263271	+	0.00705433i
$909$		0			0
$910$	334.104	+	118.783i	0.367148	+	0.130531i
$911$	40.7800	+	231.275i	0.0447639	+	0.253869i	0.998975	−	0.0452652i	$-0.0144133\pi$
$911$	40.7800	+	231.275i	0.0447639	+	0.253869i	−0.954211	+	0.299134i	$0.903302\pi$
$912$		0			0
$913$	−324.890	−	151.499i	−0.355849	−	0.165935i
$914$	−1976.54	−	348.517i	−2.16251	−	0.381309i
$915$		0			0
$916$	334.068	−	280.316i	0.364703	−	0.306022i
$917$	185.966	−	185.966i	0.202798	−	0.202798i
$918$		0			0
$919$			1188.19i			1.29291i	0.762951	+	0.646456i	$0.223750\pi$
$919$			1188.19i			1.29291i	−0.762951	+	0.646456i	$0.776250\pi$
$920$	−480.160	−	674.943i	−0.521913	−	0.733634i
$921$		0			0
$922$	−794.515	−	1134.68i	−0.861730	−	1.23068i
$923$	−750.487	−	349.958i	−0.813095	−	0.379152i
$924$		0			0
$925$	592.177	+	574.729i	0.640192	+	0.621329i
$926$	921.187	+	1595.54i	0.994802	+	1.72305i
$927$		0			0
$928$	−317.158	+	84.9822i	−0.341765	+	0.0915756i
$929$	−67.6920	+	185.982i	−0.0728654	+	0.200196i	−0.970779	−	0.239976i	$-0.922860\pi$
$929$	−67.6920	+	185.982i	−0.0728654	+	0.200196i	0.897913	+	0.440172i	$0.145083\pi$
$930$		0			0
$931$	1105.47	+	927.601i	1.18740	+	0.996349i
$932$	−133.041	+	11.6396i	−0.142748	+	0.0124888i
$933$		0			0
$934$	−174.575	+	479.641i	−0.186911	+	0.513535i
$935$	144.420	+	784.698i	0.154460	+	0.839249i
$936$		0			0
$937$	305.720	+	81.9174i	0.326275	+	0.0874252i	0.418239	−	0.908337i	$-0.362648\pi$
$937$	305.720	+	81.9174i	0.326275	+	0.0874252i	−0.0919634	+	0.995762i	$0.529314\pi$
$938$	200.441	−	286.260i	0.213690	−	0.305181i
$939$		0			0
$940$	−434.811	−	246.723i	−0.462565	−	0.262471i
$941$	−66.2170	+	375.536i	−0.0703688	+	0.399081i	0.929196	+	0.369587i	$0.120501\pi$
$941$	−66.2170	+	375.536i	−0.0703688	+	0.399081i	−0.999565	+	0.0294943i	$0.990610\pi$
$942$		0			0
$943$	1571.79	+	137.514i	1.66680	+	0.145826i
$944$			264.345i			0.280026i
$945$		0			0
$946$	896.197			0.947354
$947$	18.7132	−	213.893i	0.0197605	−	0.225864i	−0.979893	−	0.199526i	$-0.936060\pi$
$947$	18.7132	−	213.893i	0.0197605	−	0.225864i	0.999653	−	0.0263379i	$-0.00838460\pi$
$948$		0			0
$949$	942.469	+	166.183i	0.993118	+	0.175114i
$950$	1598.26	+	1083.87i	1.68238	+	1.14091i
$951$		0			0
$952$	109.894	+	76.9485i	0.115435	+	0.0808282i
$953$	219.916	−	820.738i	0.230762	−	0.861215i	−0.749252	−	0.662285i	$-0.769587\pi$
$953$	219.916	−	820.738i	0.230762	−	0.861215i	0.980014	−	0.198930i	$-0.0637465\pi$
$954$		0			0
$955$	−314.094	+	455.787i	−0.328894	+	0.477264i
$956$	315.726	+	114.915i	0.330258	+	0.120204i
$957$		0			0
$958$	−18.5307	−	211.807i	−0.0193431	−	0.221093i
$959$	75.8050	−	90.3408i	0.0790459	−	0.0942032i
$960$		0			0
$961$	262.821	+	95.6592i	0.273487	+	0.0995413i
$962$	−400.611	−	1495.10i	−0.416435	−	1.55416i
$963$		0			0
$964$	651.593	−	376.197i	0.675926	−	0.390246i
$965$	−637.275	+	771.109i	−0.660389	+	0.799077i
$966$		0			0
$967$	592.483	−	1270.58i	0.612702	−	1.31394i	−0.317974	−	0.948100i	$-0.603002\pi$
$967$	592.483	−	1270.58i	0.612702	−	1.31394i	0.930676	−	0.365845i	$-0.119220\pi$
$968$	−211.875	+	148.357i	−0.218879	+	0.153261i
$969$		0			0
$970$	−878.661	−	1235.10i	−0.905836	−	1.27330i
$971$	1406.37			1.44838			0.724188	−	0.689603i	$-0.242215\pi$
$971$	1406.37			1.44838			0.724188	+	0.689603i	$0.242215\pi$
$972$		0			0
$973$	49.4455	+	49.4455i	0.0508176	+	0.0508176i
$974$	302.980	+	361.077i	0.311067	+	0.370716i
$975$		0			0
$976$	−114.590	+	649.872i	−0.117408	+	0.665852i
$977$	288.383	−	618.440i	0.295172	−	0.632999i	−0.701662	−	0.712510i	$-0.747558\pi$
$977$	288.383	−	618.440i	0.295172	−	0.632999i	0.996834	+	0.0795115i	$0.0253360\pi$
$978$		0			0
$979$	−236.117	+	41.6338i	−0.241182	+	0.0425269i
$980$	−225.849	−	475.030i	−0.230458	−	0.484724i
$981$		0			0
$982$	133.667	+	498.853i	0.136118	+	0.507997i
$983$	−91.7729	−	196.808i	−0.0933601	−	0.200211i	0.854082	−	0.520138i	$-0.174119\pi$
$983$	−91.7729	−	196.808i	−0.0933601	−	0.200211i	−0.947442	+	0.319927i	$0.896342\pi$
$984$		0			0
$985$	−1528.05	+	11.4234i	−1.55132	+	0.0115973i
$986$	394.364	+	330.910i	0.399963	+	0.335609i
$987$		0			0
$988$	−551.395	−	1182.47i	−0.558093	−	1.19683i
$989$	1496.34	+	863.910i	1.51298	+	0.873519i
$990$		0			0
$991$	−386.026	−	668.617i	−0.389532	−	0.674689i	0.602855	−	0.797851i	$-0.294030\pi$
$991$	−386.026	−	668.617i	−0.389532	−	0.674689i	−0.992387	+	0.123162i	$0.960697\pi$
$992$	−692.042	−	484.573i	−0.697623	−	0.488481i
$993$		0			0
$994$	−57.1087	−	156.905i	−0.0574535	−	0.157852i
$995$	−1336.31	−	347.378i	−1.34303	−	0.349123i
$996$		0			0
$997$	49.5772	−	566.670i	0.0497264	−	0.568375i	−0.929936	−	0.367722i	$-0.880138\pi$
$997$	49.5772	−	566.670i	0.0497264	−	0.568375i	0.979662	−	0.200654i	$-0.0643066\pi$
$998$	502.501	+	502.501i	0.503508	+	0.503508i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.27		408
3.2	odd	2		135.3.r.a.103.8	yes	408
5.2	odd	4	inner	405.3.s.a.37.27		408
15.2	even	4		135.3.r.a.22.8	✓	408
27.11	odd	18		135.3.r.a.43.8	yes	408
27.16	even	9	inner	405.3.s.a.208.27		408
135.92	even	36		135.3.r.a.97.8	yes	408
135.97	odd	36	inner	405.3.s.a.127.27		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.8	✓	408	15.2	even	4
135.3.r.a.43.8	yes	408	27.11	odd	18
135.3.r.a.97.8	yes	408	135.92	even	36
135.3.r.a.103.8	yes	408	3.2	odd	2
405.3.s.a.37.27		408	5.2	odd	4	inner
405.3.s.a.118.27		408	1.1	even	1	trivial
405.3.s.a.127.27		408	135.97	odd	36	inner
405.3.s.a.208.27		408	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.217924 - 2.49089i) q^{2} +(-2.21779 - 0.391056i) q^{4} +(-4.81982 + 1.33016i) q^{5} +(1.23887 + 0.867466i) q^{7} +(1.13122 - 4.22177i) q^{8} +(2.26293 + 12.2955i) q^{10} +(-7.38848 - 2.68919i) q^{11} +(-1.63449 - 18.6824i) q^{13} +(2.43074 - 2.89684i) q^{14} +(-18.7342 - 6.81868i) q^{16} +(5.25283 + 19.6038i) q^{17} +(-26.7540 + 15.4465i) q^{19} +(11.2095 - 1.06520i) q^{20} +(-8.30859 + 17.8178i) q^{22} +(-31.0483 + 21.7403i) q^{23} +(21.4613 - 12.8223i) q^{25} -46.8918 q^{26} +(-2.40833 - 2.40833i) q^{28} +(6.52085 + 7.77124i) q^{29} +(-4.53255 + 25.7054i) q^{31} +(-13.6787 + 29.3340i) q^{32} +(49.9756 - 8.81204i) q^{34} +(-7.12500 - 2.53313i) q^{35} +(8.54330 + 31.8840i) q^{37} +(32.6450 + 70.0074i) q^{38} +(0.163367 + 21.8529i) q^{40} +(-31.8883 - 26.7575i) q^{41} +(-19.2652 - 41.3143i) q^{43} +(15.3345 + 8.85336i) q^{44} +(47.3864 + 82.0756i) q^{46} +(-36.3695 - 25.4662i) q^{47} +(-15.9767 - 43.8956i) q^{49} +(-27.2619 - 56.2520i) q^{50} +(-3.68088 + 42.0727i) q^{52} +(-10.0402 - 10.0402i) q^{53} +(39.1882 + 3.13351i) q^{55} +(5.06367 - 4.24893i) q^{56} +(20.7783 - 14.5491i) q^{58} +(-4.53496 - 12.4597i) q^{59} +(-5.74775 - 32.5971i) q^{61} +(63.0414 + 16.8919i) q^{62} +(1.02459 + 0.591547i) q^{64} +(32.7285 + 87.8714i) q^{65} +(92.0596 - 8.05417i) q^{67} +(-3.98347 - 45.5313i) q^{68} +(-7.86245 + 17.1955i) q^{70} +(22.0775 - 38.2394i) q^{71} +(-13.2076 + 49.2915i) q^{73} +(81.2813 - 14.3321i) q^{74} +(65.3753 - 23.7946i) q^{76} +(-6.82059 - 9.74081i) q^{77} +(-20.5814 - 24.5280i) q^{79} +(99.3653 + 7.94531i) q^{80} +(-73.5991 + 73.5991i) q^{82} +(45.4188 + 3.97363i) q^{83} +(-51.3940 - 87.4997i) q^{85} +(-107.108 + 38.9840i) q^{86} +(-19.7111 + 28.1504i) q^{88} +(26.4081 - 15.2467i) q^{89} +(14.1814 - 24.5629i) q^{91} +(77.3604 - 36.0737i) q^{92} +(-71.3592 + 85.0426i) q^{94} +(108.403 - 110.036i) q^{95} +(-109.882 + 51.2388i) q^{97} +(-112.821 + 30.2302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Introduction

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