LMFDB - Embedded newform 405.3.s.a.118.34

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			118.34
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.328387 - 3.75348i) q^{2} +(-10.0415 - 1.77059i) q^{4} +(1.58573 - 4.74188i) q^{5} +(-2.49919 - 1.74995i) q^{7} +(-6.04267 + 22.5515i) q^{8} +(-17.2778 - 7.50920i) q^{10} +(-8.21269 - 2.98918i) q^{11} +(-1.30944 - 14.9670i) q^{13} +(-7.38912 + 8.80601i) q^{14} +(44.3363 + 16.1371i) q^{16} +(6.46879 + 24.1418i) q^{17} +(-23.0066 + 13.2829i) q^{19} +(-24.3192 + 44.8081i) q^{20} +(-13.9168 + 29.8446i) q^{22} +(23.7975 - 16.6632i) q^{23} +(-19.9709 - 15.0387i) q^{25} -56.6083 q^{26} +(21.9973 + 21.9973i) q^{28} +(3.19342 + 3.80577i) q^{29} +(-2.35330 + 13.3462i) q^{31} +(35.6622 - 76.4778i) q^{32} +(92.7402 - 16.3526i) q^{34} +(-12.2611 + 9.07591i) q^{35} +(-5.80622 - 21.6691i) q^{37} +(42.3020 + 90.7169i) q^{38} +(97.3547 + 64.4144i) q^{40} +(10.7753 + 9.04151i) q^{41} +(10.1179 + 21.6979i) q^{43} +(77.1755 + 44.5573i) q^{44} +(-54.7302 - 94.7954i) q^{46} +(19.7104 + 13.8013i) q^{47} +(-13.5754 - 37.2980i) q^{49} +(-63.0058 + 70.0218i) q^{50} +(-13.3517 + 152.610i) q^{52} +(-35.7379 - 35.7379i) q^{53} +(-27.1975 + 34.2036i) q^{55} +(54.5659 - 45.7863i) q^{56} +(15.3335 - 10.7367i) q^{58} +(-7.15372 - 19.6547i) q^{59} +(-13.4180 - 76.0970i) q^{61} +(49.3221 + 13.2158i) q^{62} +(-111.904 - 64.6080i) q^{64} +(-73.0482 - 17.5245i) q^{65} +(-102.407 + 8.95949i) q^{67} +(-22.2112 - 253.875i) q^{68} +(30.0399 + 49.0023i) q^{70} +(12.6791 - 21.9608i) q^{71} +(-23.2289 + 86.6915i) q^{73} +(-83.2413 + 14.6777i) q^{74} +(254.541 - 92.6453i) q^{76} +(15.2942 + 21.8424i) q^{77} +(6.63920 + 7.91230i) q^{79} +(146.826 - 184.649i) q^{80} +(37.4756 - 37.4756i) q^{82} +(-69.0024 - 6.03693i) q^{83} +(124.736 + 7.60834i) q^{85} +(84.7654 - 30.8521i) q^{86} +(117.037 - 167.146i) q^{88} +(61.3185 - 35.4023i) q^{89} +(-22.9190 + 39.6969i) q^{91} +(-268.467 + 125.188i) q^{92} +(58.2757 - 69.4503i) q^{94} +(26.5035 + 130.158i) q^{95} +(-69.9225 + 32.6054i) q^{97} +(-144.455 + 38.7067i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.328387	−	3.75348i	0.164193	−	1.87674i	−0.252367	−	0.967632i	$-0.581209\pi$
$2$	0.328387	−	3.75348i	0.164193	−	1.87674i	0.416560	−	0.909108i	$-0.363236\pi$
$3$		0			0
$3$		0			0
$4$	−10.0415	−	1.77059i	−2.51039	−	0.442649i
$5$	1.58573	−	4.74188i	0.317147	−	0.948376i
$5$	1.58573	−	4.74188i	0.317147	−	0.948376i
$6$		0			0
$7$	−2.49919	−	1.74995i	−0.357027	−	0.249993i	0.381277	−	0.924461i	$-0.375484\pi$
$7$	−2.49919	−	1.74995i	−0.357027	−	0.249993i	−0.738305	+	0.674467i	$0.764373\pi$
$8$	−6.04267	+	22.5515i	−0.755334	+	2.81894i
$9$		0			0
$10$	−17.2778	−	7.50920i	−1.72778	−	0.750920i
$11$	−8.21269	−	2.98918i	−0.746608	−	0.271743i	−0.0594306	−	0.998232i	$-0.518928\pi$
$11$	−8.21269	−	2.98918i	−0.746608	−	0.271743i	−0.687178	+	0.726489i	$0.741151\pi$
$12$		0			0
$13$	−1.30944	−	14.9670i	−0.100726	−	1.15131i	−0.863399	−	0.504522i	$-0.831669\pi$
$13$	−1.30944	−	14.9670i	−0.100726	−	1.15131i	0.762672	−	0.646785i	$-0.223887\pi$
$14$	−7.38912	+	8.80601i	−0.527794	+	0.629000i
$15$		0			0
$16$	44.3363	+	16.1371i	2.77102	+	1.00857i
$17$	6.46879	+	24.1418i	0.380517	+	1.42011i	0.845114	+	0.534586i	$0.179533\pi$
$17$	6.46879	+	24.1418i	0.380517	+	1.42011i	−0.464597	+	0.885522i	$0.653801\pi$
$18$		0			0
$19$	−23.0066	+	13.2829i	−1.21088	+	0.699100i	−0.962950	−	0.269679i	$-0.913082\pi$
$19$	−23.0066	+	13.2829i	−1.21088	+	0.699100i	−0.247926	+	0.968779i	$0.579749\pi$
$20$	−24.3192	+	44.8081i	−1.21596	+	2.24041i
$21$		0			0
$22$	−13.9168	+	29.8446i	−0.632580	+	1.35657i
$23$	23.7975	−	16.6632i	1.03467	−	0.724487i	0.0726240	−	0.997359i	$-0.476863\pi$
$23$	23.7975	−	16.6632i	1.03467	−	0.724487i	0.962050	+	0.272873i	$0.0879738\pi$
$24$		0			0
$25$	−19.9709	−	15.0387i	−0.798836	−	0.601549i
$26$	−56.6083			−2.17724
$27$		0			0
$28$	21.9973	+	21.9973i	0.785617	+	0.785617i
$29$	3.19342	+	3.80577i	0.110118	+	0.131233i	0.818288	−	0.574809i	$-0.194923\pi$
$29$	3.19342	+	3.80577i	0.110118	+	0.131233i	−0.708170	+	0.706042i	$0.750479\pi$
$30$		0			0
$31$	−2.35330	+	13.3462i	−0.0759130	+	0.430524i	0.923037	+	0.384711i	$0.125699\pi$
$31$	−2.35330	+	13.3462i	−0.0759130	+	0.430524i	−0.998950	+	0.0458129i	$0.985412\pi$
$32$	35.6622	−	76.4778i	1.11444	−	2.38993i
$33$		0			0
$34$	92.7402	−	16.3526i	2.72765	−	0.480959i
$35$	−12.2611	+	9.07591i	−0.350318	+	0.259312i
$36$		0			0
$37$	−5.80622	−	21.6691i	−0.156925	−	0.585652i	−0.998933	−	0.0461868i	$-0.985293\pi$
$37$	−5.80622	−	21.6691i	−0.156925	−	0.585652i	0.842008	−	0.539465i	$-0.181374\pi$
$38$	42.3020	+	90.7169i	1.11321	+	2.38729i
$39$		0			0
$40$	97.3547	+	64.4144i	2.43387	+	1.61036i
$41$	10.7753	+	9.04151i	0.262811	+	0.220525i	0.764665	−	0.644427i	$-0.222904\pi$
$41$	10.7753	+	9.04151i	0.262811	+	0.220525i	−0.501854	+	0.864952i	$0.667349\pi$
$42$		0			0
$43$	10.1179	+	21.6979i	0.235300	+	0.504603i	0.988131	−	0.153610i	$-0.0490901\pi$
$43$	10.1179	+	21.6979i	0.235300	+	0.504603i	−0.752831	+	0.658214i	$0.771312\pi$
$44$	77.1755	+	44.5573i	1.75399	+	1.01267i
$45$		0			0
$46$	−54.7302	−	94.7954i	−1.18979	−	2.06077i
$47$	19.7104	+	13.8013i	0.419369	+	0.293646i	0.764151	−	0.645037i	$-0.223158\pi$
$47$	19.7104	+	13.8013i	0.419369	+	0.293646i	−0.344782	+	0.938683i	$0.612047\pi$
$48$		0			0
$49$	−13.5754	−	37.2980i	−0.277048	−	0.761184i
$50$	−63.0058	+	70.0218i	−1.26012	+	1.40044i
$51$		0			0
$52$	−13.3517	+	152.610i	−0.256763	+	2.93481i
$53$	−35.7379	−	35.7379i	−0.674300	−	0.674300i	0.284404	−	0.958704i	$-0.408204\pi$
$53$	−35.7379	−	35.7379i	−0.674300	−	0.674300i	−0.958704	+	0.284404i	$0.908204\pi$
$54$		0			0
$55$	−27.1975	+	34.2036i	−0.494500	+	0.621883i
$56$	54.5659	−	45.7863i	0.974392	−	0.817612i
$57$		0			0
$58$	15.3335	−	10.7367i	0.264371	−	0.185115i
$59$	−7.15372	−	19.6547i	−0.121250	−	0.333130i	0.864188	−	0.503169i	$-0.167833\pi$
$59$	−7.15372	−	19.6547i	−0.121250	−	0.333130i	−0.985437	+	0.170039i	$0.945611\pi$
$60$		0			0
$61$	−13.4180	−	76.0970i	−0.219966	−	1.24749i	−0.872077	−	0.489368i	$-0.837227\pi$
$61$	−13.4180	−	76.0970i	−0.219966	−	1.24749i	0.652111	−	0.758124i	$-0.273884\pi$
$62$	49.3221	+	13.2158i	0.795517	+	0.213158i
$63$		0			0
$64$	−111.904	−	64.6080i	−1.74851	−	1.00950i
$65$	−73.0482	−	17.5245i	−1.12382	−	0.269607i
$66$		0			0
$67$	−102.407	+	8.95949i	−1.52847	+	0.133724i	−0.820142	−	0.572160i	$-0.806106\pi$
$67$	−102.407	+	8.95949i	−1.52847	+	0.133724i	−0.708328	+	0.705884i	$0.750550\pi$
$68$	−22.2112	−	253.875i	−0.326635	−	3.73345i
$69$		0			0
$70$	30.0399	+	49.0023i	0.429141	+	0.700033i
$71$	12.6791	−	21.9608i	0.178579	−	0.309308i	−0.762815	−	0.646617i	$-0.776183\pi$
$71$	12.6791	−	21.9608i	0.178579	−	0.309308i	0.941394	+	0.337309i	$0.109517\pi$
$72$		0			0
$73$	−23.2289	+	86.6915i	−0.318204	+	1.18755i	0.602765	+	0.797919i	$0.294066\pi$
$73$	−23.2289	+	86.6915i	−0.318204	+	1.18755i	−0.920969	+	0.389635i	$0.872601\pi$
$74$	−83.2413	+	14.6777i	−1.12488	+	0.198347i
$75$		0			0
$76$	254.541	−	92.6453i	3.34922	−	1.21902i
$77$	15.2942	+	21.8424i	0.198626	+	0.283667i
$78$		0			0
$79$	6.63920	+	7.91230i	0.0840406	+	0.100156i	0.806426	−	0.591335i	$-0.201399\pi$
$79$	6.63920	+	7.91230i	0.0840406	+	0.100156i	−0.722386	+	0.691490i	$0.756954\pi$
$80$	146.826	−	184.649i	1.83532	−	2.30811i
$81$		0			0
$82$	37.4756	−	37.4756i	0.457019	−	0.457019i
$83$	−69.0024	−	6.03693i	−0.831354	−	0.0727341i	−0.336471	−	0.941694i	$-0.609234\pi$
$83$	−69.0024	−	6.03693i	−0.831354	−	0.0727341i	−0.494883	+	0.868960i	$0.664789\pi$
$84$		0			0
$85$	124.736	+	7.60834i	1.46748	+	0.0895099i
$86$	84.7654	−	30.8521i	0.985644	−	0.358745i
$87$		0			0
$88$	117.037	−	167.146i	1.32997	−	1.89939i
$89$	61.3185	−	35.4023i	0.688972	−	0.397778i	−0.114255	−	0.993452i	$-0.536448\pi$
$89$	61.3185	−	35.4023i	0.688972	−	0.397778i	0.803227	+	0.595673i	$0.203115\pi$
$90$		0			0
$91$	−22.9190	+	39.6969i	−0.251857	+	0.436229i
$92$	−268.467	+	125.188i	−2.91812	+	1.36074i
$93$		0			0
$94$	58.2757	−	69.4503i	0.619954	−	0.738833i
$95$	26.5035	+	130.158i	0.278984	+	1.37008i
$96$		0			0
$97$	−69.9225	+	32.6054i	−0.720850	+	0.336138i	−0.748187	−	0.663488i	$-0.769075\pi$
$97$	−69.9225	+	32.6054i	−0.720850	+	0.336138i	0.0273363	+	0.999626i	$0.491298\pi$
$98$	−144.455	+	38.7067i	−1.47403	+	0.394966i
$99$		0			0
$100$	173.911	+	186.372i	1.73911	+	1.86372i
$101$	−31.7898	−	180.289i	−0.314750	−	1.78504i	−0.573617	−	0.819124i	$-0.694460\pi$
$101$	−31.7898	−	180.289i	−0.314750	−	1.78504i	0.258867	−	0.965913i	$-0.416651\pi$
$102$		0			0
$103$	−165.779	−	77.3039i	−1.60950	−	0.750523i	−0.610368	−	0.792118i	$-0.708978\pi$
$103$	−165.779	−	77.3039i	−1.60950	−	0.750523i	−0.999135	+	0.0415948i	$0.986756\pi$
$104$	345.441	+	60.9106i	3.32155	+	0.585679i
$105$		0			0
$106$	−145.877	+	122.406i	−1.37620	+	1.15477i
$107$	5.45487	−	5.45487i	0.0509801	−	0.0509801i	−0.681157	−	0.732137i	$-0.738523\pi$
$107$	5.45487	−	5.45487i	0.0509801	−	0.0509801i	0.732137	+	0.681157i	$0.238523\pi$
$108$		0			0
$109$		−	30.3525i		−	0.278463i	−0.990260	−	0.139231i	$-0.955537\pi$
$109$		−	30.3525i		−	0.278463i	0.990260	−	0.139231i	$-0.0444632\pi$
$110$	119.451	+	113.317i	1.08592	+	1.03016i
$111$		0			0
$112$	−82.5659	−	117.916i	−0.737195	−	1.05282i
$113$	18.5274	+	8.63948i	0.163959	+	0.0764556i	0.502865	−	0.864365i	$-0.332279\pi$
$113$	18.5274	+	8.63948i	0.163959	+	0.0764556i	−0.338906	+	0.940820i	$0.610057\pi$
$114$		0			0
$115$	−41.2784	−	139.268i	−0.358942	−	1.21103i
$116$	−25.3284	−	43.8700i	−0.218348	−	0.378190i
$117$		0			0
$118$	−76.1227	+	20.3970i	−0.645107	+	0.172856i
$119$	26.0804	−	71.6552i	0.219163	−	0.602144i
$120$		0			0
$121$	−34.1782	−	28.6789i	−0.282465	−	0.237016i
$122$	−290.035	+	25.3748i	−2.37733	+	0.207990i
$123$		0			0
$124$	47.2616	−	129.850i	0.381142	−	1.04718i
$125$	−102.980	+	70.8522i	−0.823844	+	0.566817i
$126$		0			0
$127$	48.5567	+	13.0107i	0.382336	+	0.102447i	0.444868	−	0.895596i	$-0.353251\pi$
$127$	48.5567	+	13.0107i	0.382336	+	0.102447i	−0.0625315	+	0.998043i	$0.519917\pi$
$128$	−85.6504	+	122.321i	−0.669144	+	0.955637i
$129$		0			0
$130$	−89.7658	+	268.430i	−0.690506	+	2.06485i
$131$	−35.4480	+	201.036i	−0.270596	+	1.53462i	0.482018	+	0.876161i	$0.339904\pi$
$131$	−35.4480	+	201.036i	−0.270596	+	1.53462i	−0.752614	+	0.658462i	$0.771207\pi$
$132$		0			0
$133$	80.7425	+	7.06405i	0.607086	+	0.0531132i
$134$			387.327i			2.89050i
$135$		0			0
$136$	−583.525			−4.29062
$137$	−3.24744	+	37.1184i	−0.0237039	+	0.270937i	0.975089	+	0.221815i	$0.0711980\pi$
$137$	−3.24744	+	37.1184i	−0.0237039	+	0.270937i	−0.998793	+	0.0491224i	$0.984358\pi$
$138$		0			0
$139$	−182.916	−	32.2530i	−1.31594	−	0.232036i	−0.528766	−	0.848768i	$-0.677345\pi$
$139$	−182.916	−	32.2530i	−1.31594	−	0.232036i	−0.787173	+	0.616732i	$0.788456\pi$
$140$	139.190	−	69.4267i	0.994217	−	0.495905i
$141$		0			0
$142$	−78.2659	−	54.8024i	−0.551169	−	0.385932i
$143$	−33.9849	+	126.833i	−0.237657	+	0.886947i
$144$		0			0
$145$	23.1104	−	9.10787i	0.159382	−	0.0628129i
$146$	317.767	+	115.658i	2.17648	+	0.792175i
$147$		0			0
$148$	19.9362	+	227.872i	0.134704	+	1.53967i
$149$	25.6513	−	30.5701i	0.172157	−	0.205168i	−0.673066	−	0.739582i	$-0.735023\pi$
$149$	25.6513	−	30.5701i	0.172157	−	0.205168i	0.845223	+	0.534414i	$0.179468\pi$
$150$		0			0
$151$	143.221	+	52.1282i	0.948484	+	0.345220i	0.769511	−	0.638634i	$-0.220500\pi$
$151$	143.221	+	52.1282i	0.948484	+	0.345220i	0.178973	+	0.983854i	$0.442722\pi$
$152$	−160.528	−	599.100i	−1.05611	−	3.94145i
$153$		0			0
$154$	87.0072	−	50.2337i	0.564982	−	0.326193i
$155$	59.5546	+	32.3227i	0.384223	+	0.208534i
$156$		0			0
$157$	51.8286	−	111.147i	0.330119	−	0.707942i	−0.669266	−	0.743023i	$-0.733391\pi$
$157$	51.8286	−	111.147i	0.330119	−	0.707942i	0.999384	+	0.0350814i	$0.0111690\pi$
$158$	31.8789	−	22.3218i	0.201765	−	0.141277i
$159$		0			0
$160$	−306.098	−	290.379i	−1.91311	−	1.81487i
$161$	−88.6343			−0.550524
$162$		0			0
$163$	20.2656	+	20.2656i	0.124329	+	0.124329i	0.766533	−	0.642205i	$-0.221980\pi$
$163$	20.2656	+	20.2656i	0.124329	+	0.124329i	−0.642205	+	0.766533i	$0.721980\pi$
$164$	−92.1913	−	109.869i	−0.562142	−	0.669935i
$165$		0			0
$166$	−45.3190	+	257.017i	−0.273006	+	1.54829i
$167$	56.2102	−	120.543i	0.336588	−	0.721815i	−0.663054	−	0.748571i	$-0.730740\pi$
$167$	56.2102	−	120.543i	0.336588	−	0.721815i	0.999642	+	0.0267565i	$0.00851789\pi$
$168$		0			0
$169$	−55.8638	+	9.85029i	−0.330555	+	0.0582858i
$170$	69.5193	−	465.694i	0.408937	−	2.73938i
$171$		0			0
$172$	−63.1812	−	235.795i	−0.367333	−	1.37090i
$173$	9.20275	+	19.7354i	0.0531951	+	0.114077i	0.931109	−	0.364742i	$-0.118843\pi$
$173$	9.20275	+	19.7354i	0.0531951	+	0.114077i	−0.877914	+	0.478819i	$0.841065\pi$
$174$		0			0
$175$	23.5940	+	72.5328i	0.134823	+	0.414473i
$176$	−315.884	−	265.058i	−1.79480	−	1.50601i
$177$		0			0
$178$	−112.746	−	241.784i	−0.633402	−	1.35833i
$179$	−186.793	−	107.845i	−1.04354	−	0.602487i	−0.122704	−	0.992443i	$-0.539157\pi$
$179$	−186.793	−	107.845i	−1.04354	−	0.602487i	−0.920833	+	0.389957i	$0.872490\pi$
$180$		0			0
$181$	12.7646	+	22.1089i	0.0705224	+	0.122148i	0.899130	−	0.437681i	$-0.144200\pi$
$181$	12.7646	+	22.1089i	0.0705224	+	0.122148i	−0.828608	+	0.559829i	$0.810867\pi$
$182$	141.475	+	99.0619i	0.777335	+	0.544296i
$183$		0			0
$184$	231.980	+	637.361i	1.26076	+	3.46392i
$185$	−111.960	−	6.82906i	−0.605187	−	0.0369138i
$186$		0			0
$187$	19.0380	−	217.606i	0.101808	−	1.16367i
$188$	−173.486	−	173.486i	−0.922797	−	0.922797i
$189$		0			0
$190$	497.249	−	56.7381i	2.61710	−	0.298621i
$191$	241.803	−	202.897i	1.26599	−	1.06229i	0.270969	−	0.962588i	$-0.412656\pi$
$191$	241.803	−	202.897i	1.26599	−	1.06229i	0.995017	−	0.0997005i	$-0.0317885\pi$
$192$		0			0
$193$	−77.5331	+	54.2892i	−0.401726	+	0.281291i	−0.756928	−	0.653498i	$-0.773301\pi$
$193$	−77.5331	+	54.2892i	−0.401726	+	0.281291i	0.355203	+	0.934789i	$0.384412\pi$
$194$	99.4221	+	273.160i	0.512485	+	1.40804i
$195$		0			0
$196$	70.2779	+	398.566i	0.358561	+	2.03350i
$197$	−97.5085	−	26.1273i	−0.494967	−	0.132626i	0.00269614	−	0.999996i	$-0.499142\pi$
$197$	−97.5085	−	26.1273i	−0.494967	−	0.132626i	−0.497663	+	0.867370i	$0.665808\pi$
$198$		0			0
$199$	10.4704	+	6.04508i	0.0526150	+	0.0303773i	0.526077	−	0.850437i	$-0.323662\pi$
$199$	10.4704	+	6.04508i	0.0526150	+	0.0303773i	−0.473462	+	0.880814i	$0.656996\pi$
$200$	459.824	−	359.500i	2.29912	−	1.79750i
$201$		0			0
$202$	−687.149	+	60.1178i	−3.40173	+	0.297613i
$203$	−1.32105	−	15.0997i	−0.00650764	−	0.0743826i
$204$		0			0
$205$	59.9605	−	36.7576i	0.292490	−	0.179305i
$206$	−344.598	+	596.862i	−1.67281	+	2.89739i
$207$		0			0
$208$	183.468	−	684.712i	0.882058	−	3.29189i
$209$	228.651	−	40.3174i	1.09403	−	0.192906i
$210$		0			0
$211$	−43.6801	+	15.8982i	−0.207015	+	0.0753471i	−0.443446	−	0.896301i	$-0.646244\pi$
$211$	−43.6801	+	15.8982i	−0.207015	+	0.0753471i	0.236432	+	0.971648i	$0.424022\pi$
$212$	295.586	+	422.141i	1.39428	+	1.99123i
$213$		0			0
$214$	−18.6834	−	22.2661i	−0.0873058	−	0.104047i
$215$	118.933	−	13.5708i	0.553179	−	0.0631199i
$216$		0			0
$217$	29.2367	−	29.2367i	0.134731	−	0.134731i
$218$	−113.927	−	9.96735i	−0.522603	−	0.0457218i
$219$		0			0
$220$	333.665	−	295.301i	1.51666	−	1.34228i
$221$	352.860	−	128.431i	1.59665	−	0.581134i
$222$		0			0
$223$	59.9342	−	85.5949i	0.268763	−	0.383834i	−0.661971	−	0.749529i	$-0.730280\pi$
$223$	59.9342	−	85.5949i	0.268763	−	0.383834i	0.930735	+	0.365696i	$0.119169\pi$
$224$	−222.959	+	128.726i	−0.995353	+	0.574667i
$225$		0			0
$226$	38.5123	−	66.7052i	0.170408	−	0.295156i
$227$	−99.0566	+	46.1908i	−0.436373	+	0.203484i	−0.628375	−	0.777911i	$-0.716280\pi$
$227$	−99.0566	+	46.1908i	−0.436373	+	0.203484i	0.192002	+	0.981394i	$0.438502\pi$
$228$		0			0
$229$	186.679	−	222.475i	0.815192	−	0.971508i	−0.184744	−	0.982787i	$-0.559146\pi$
$229$	186.679	−	222.475i	0.815192	−	0.971508i	0.999936	+	0.0112785i	$0.00359014\pi$
$230$	−536.296	+	109.204i	−2.33172	+	0.474798i
$231$		0			0
$232$	−105.123	+	49.0195i	−0.453115	+	0.211291i
$233$	289.894	−	77.6767i	1.24418	−	0.333377i	0.424093	−	0.905618i	$-0.360593\pi$
$233$	289.894	−	77.6767i	1.24418	−	0.333377i	0.820085	+	0.572242i	$0.193926\pi$
$234$		0			0
$235$	96.6998	−	71.5789i	0.411488	−	0.304591i
$236$	37.0339	+	210.030i	0.156923	+	0.889956i
$237$		0			0
$238$	−260.392	−	121.423i	−1.09408	−	0.510179i
$239$	−59.1436	−	10.4286i	−0.247463	−	0.0436344i	0.0485408	−	0.998821i	$-0.484543\pi$
$239$	−59.1436	−	10.4286i	−0.247463	−	0.0436344i	−0.296004	+	0.955187i	$0.595654\pi$
$240$		0			0
$241$	352.232	−	295.558i	1.46154	−	1.22638i	0.537967	−	0.842966i	$-0.319193\pi$
$241$	352.232	−	295.558i	1.46154	−	1.22638i	0.923577	−	0.383414i	$-0.125252\pi$
$242$	−118.869	+	118.869i	−0.491196	+	0.491196i
$243$		0			0
$244$			787.889i			3.22905i
$245$	−198.390	+	5.22802i	−0.809754	+	0.0213389i
$246$		0			0
$247$	228.931	+	326.947i	0.926846	+	1.32367i
$248$	−286.758	−	133.718i	−1.15628	−	0.539184i
$249$		0			0
$250$	232.125	+	409.802i	0.928499	+	1.63921i
$251$	43.4873	+	75.3221i	0.173256	+	0.300088i	0.939556	−	0.342394i	$-0.111238\pi$
$251$	43.4873	+	75.3221i	0.173256	+	0.300088i	−0.766300	+	0.642483i	$0.777905\pi$
$252$		0			0
$253$	−245.251	+	65.7148i	−0.969371	+	0.259742i
$254$	64.7809	−	177.984i	0.255043	−	0.700724i
$255$		0			0
$256$	35.0638	+	29.4220i	0.136968	+	0.114930i
$257$	183.946	−	16.0932i	0.715743	−	0.0626194i	0.276534	−	0.961004i	$-0.410814\pi$
$257$	183.946	−	16.0932i	0.715743	−	0.0626194i	0.439209	+	0.898385i	$0.355259\pi$
$258$		0			0
$259$	−23.4091	+	64.3159i	−0.0903826	+	0.248324i
$260$	702.487	+	305.311i	2.70187	+	1.17427i
$261$		0			0
$262$	742.943	+	199.071i	2.83566	+	0.759813i
$263$	202.269	−	288.870i	0.769083	−	1.09836i	−0.223248	−	0.974762i	$-0.571666\pi$
$263$	202.269	−	288.870i	0.769083	−	1.09836i	0.992332	−	0.123603i	$-0.0394450\pi$
$264$		0			0
$265$	−226.136	+	112.794i	−0.853343	+	0.425638i
$266$	53.0295	−	300.746i	0.199359	−	1.13062i
$267$		0			0
$268$	1044.19	+	91.3550i	3.89624	+	0.340877i
$269$		−	359.275i		−	1.33560i	−0.744342	−	0.667798i	$-0.767237\pi$
$269$		−	359.275i		−	1.33560i	0.744342	−	0.667798i	$-0.232763\pi$
$270$		0			0
$271$	350.436			1.29312			0.646562	−	0.762862i	$-0.276206\pi$
$271$	350.436			1.29312			0.646562	+	0.762862i	$0.276206\pi$
$272$	−102.777	+	1174.75i	−0.377857	+	4.31893i
$273$		0			0
$274$	138.257	+	24.3784i	0.504586	+	0.0889722i
$275$	119.061	+	183.205i	0.432950	+	0.666200i
$276$		0			0
$277$	110.517	+	77.3848i	0.398978	+	0.279368i	0.755797	−	0.654806i	$-0.227250\pi$
$277$	110.517	+	77.3848i	0.398978	+	0.279368i	−0.356819	+	0.934174i	$0.616139\pi$
$278$	−181.128	+	675.978i	−0.651539	+	2.43158i
$279$		0			0
$280$	−130.586	−	331.350i	−0.466378	−	1.18339i
$281$	11.3445	+	4.12907i	0.0403720	+	0.0146942i	0.362127	−	0.932129i	$-0.382051\pi$
$281$	11.3445	+	4.12907i	0.0403720	+	0.0146942i	−0.321755	+	0.946823i	$0.604273\pi$
$282$		0			0
$283$	21.7412	+	248.503i	0.0768240	+	0.878102i	0.932637	+	0.360817i	$0.117502\pi$
$283$	21.7412	+	248.503i	0.0768240	+	0.878102i	−0.855813	+	0.517286i	$0.826942\pi$
$284$	−166.201	+	198.071i	−0.585216	+	0.697434i
$285$		0			0
$286$	464.907	+	169.212i	1.62555	+	0.591651i
$287$	−11.1072	−	41.4527i	−0.0387011	−	0.144434i
$288$		0			0
$289$	−290.702	+	167.837i	−1.00589	+	0.580751i
$290$	−26.5970	−	89.7353i	−0.0917140	−	0.309432i
$291$		0			0
$292$	386.749	−	829.387i	1.32448	−	2.84037i
$293$	−14.9763	+	10.4865i	−0.0511136	+	0.0357901i	−0.598854	−	0.800858i	$-0.704377\pi$
$293$	−14.9763	+	10.4865i	−0.0511136	+	0.0357901i	0.547740	+	0.836648i	$0.315488\pi$
$294$		0			0
$295$	−104.544	+	2.75498i	−0.354387	+	0.00933890i
$296$	523.757			1.76945
$297$		0			0
$298$	−106.321	−	106.321i	−0.356781	−	0.356781i
$299$	−280.559	−	334.358i	−0.938326	−	1.11825i
$300$		0			0
$301$	12.6838	−	71.9332i	0.0421388	−	0.238981i
$302$	242.694	−	520.459i	0.803623	−	1.72338i
$303$		0			0
$304$	−1234.38	+	217.654i	−4.06045	+	0.715968i
$305$	−382.120	−	57.0433i	−1.25285	−	0.187027i
$306$		0			0
$307$	126.810	+	473.261i	0.413062	+	1.54157i	0.788687	+	0.614796i	$0.210761\pi$
$307$	126.810	+	473.261i	0.413062	+	1.54157i	−0.375625	+	0.926772i	$0.622572\pi$
$308$	−114.903	−	246.411i	−0.373062	−	0.800035i
$309$		0			0
$310$	140.880	−	212.923i	0.454450	−	0.686847i
$311$	157.780	+	132.394i	0.507333	+	0.425703i	0.860189	−	0.509975i	$-0.170345\pi$
$311$	157.780	+	132.394i	0.507333	+	0.425703i	−0.352857	+	0.935677i	$0.614790\pi$
$312$		0			0
$313$	−216.999	−	465.356i	−0.693288	−	1.48676i	−0.865084	−	0.501628i	$-0.832735\pi$
$313$	−216.999	−	465.356i	−0.693288	−	1.48676i	0.171796	−	0.985133i	$-0.445043\pi$
$314$	−400.168	−	231.037i	−1.27442	−	0.735786i
$315$		0			0
$316$	−52.6584	−	91.2070i	−0.166640	−	0.288630i
$317$	−376.101	−	263.349i	−1.18644	−	0.830753i	−0.197679	−	0.980267i	$-0.563340\pi$
$317$	−376.101	−	263.349i	−1.18644	−	0.830753i	−0.988760	+	0.149514i	$0.952229\pi$
$318$		0			0
$319$	−14.8504	−	40.8013i	−0.0465531	−	0.127904i
$320$	−483.814	+	428.186i	−1.51192	+	1.33808i
$321$		0			0
$322$	−29.1064	+	332.687i	−0.0903924	+	1.03319i
$323$	−469.499	−	469.499i	−1.45356	−	1.45356i
$324$		0			0
$325$	−198.934	+	318.597i	−0.612104	+	0.980297i
$326$	82.7215	−	69.4116i	0.253747	−	0.212919i
$327$		0			0
$328$	−269.011	+	188.364i	−0.820157	+	0.574280i
$329$	−25.1083	−	68.9844i	−0.0763170	−	0.209679i
$330$		0			0
$331$	−47.9543	−	271.962i	−0.144877	−	0.821638i	−0.967466	−	0.253001i	$-0.918582\pi$
$331$	−47.9543	−	271.962i	−0.144877	−	0.821638i	0.822589	−	0.568636i	$-0.192529\pi$
$332$	682.202	+	182.795i	2.05482	+	0.550588i
$333$		0			0
$334$	−433.997	−	250.568i	−1.29939	−	0.750205i
$335$	−119.906	+	499.812i	−0.357929	+	1.49198i
$336$		0			0
$337$	320.162	−	28.0105i	0.950036	−	0.0831173i	0.398408	−	0.917208i	$-0.369563\pi$
$337$	320.162	−	28.0105i	0.950036	−	0.0831173i	0.551627	+	0.834091i	$0.314007\pi$
$338$	18.6279	+	212.918i	0.0551122	+	0.629936i
$339$		0			0
$340$	−1239.07	−	297.256i	−3.64431	−	0.874281i
$341$	59.2212	−	102.574i	0.173669	−	0.300804i
$342$		0			0
$343$	−70.0349	+	261.374i	−0.204183	+	0.762022i
$344$	−550.461	+	97.0612i	−1.60018	+	0.282155i
$345$		0			0
$346$	77.0984	−	28.0615i	0.222828	−	0.0811026i
$347$	252.105	+	360.044i	0.726528	+	1.03759i	0.997190	+	0.0749155i	$0.0238687\pi$
$347$	252.105	+	360.044i	0.726528	+	1.03759i	−0.270661	+	0.962675i	$0.587242\pi$
$348$		0			0
$349$	−129.078	−	153.829i	−0.369851	−	0.440771i	0.548733	−	0.835998i	$-0.315110\pi$
$349$	−129.078	−	153.829i	−0.369851	−	0.440771i	−0.918584	+	0.395227i	$0.870666\pi$
$350$	279.998	−	64.7408i	0.799995	−	0.184974i
$351$		0			0
$352$	−521.488	+	521.488i	−1.48150	+	1.48150i
$353$	284.218	+	24.8659i	0.805150	+	0.0704415i	0.482297	−	0.876008i	$-0.339802\pi$
$353$	284.218	+	24.8659i	0.805150	+	0.0704415i	0.322853	+	0.946449i	$0.395358\pi$
$354$		0			0
$355$	−84.0300	−	94.9469i	−0.236704	−	0.267456i
$356$	−678.416	+	246.923i	−1.90566	+	0.693604i
$357$		0			0
$358$	−466.135	+	665.710i	−1.30205	+	1.85952i
$359$	163.907	−	94.6319i	0.456566	−	0.263599i	−0.254033	−	0.967196i	$-0.581757\pi$
$359$	163.907	−	94.6319i	0.456566	−	0.263599i	0.710599	+	0.703597i	$0.248424\pi$
$360$		0			0
$361$	172.371	−	298.555i	0.477481	−	0.827021i
$362$	87.1768	−	40.6512i	0.240820	−	0.112296i
$363$		0			0
$364$	300.429	−	358.037i	0.825354	−	0.983619i
$365$	374.246	+	247.618i	1.02533	+	0.678407i
$366$		0			0
$367$	−398.763	+	185.946i	−1.08655	+	0.506666i	−0.881547	−	0.472096i	$-0.843498\pi$
$367$	−398.763	+	185.946i	−1.08655	+	0.506666i	−0.205001	+	0.978762i	$0.565720\pi$
$368$	1323.99	−	354.762i	3.59780	−	0.964027i
$369$		0			0
$370$	−62.3988	+	417.995i	−0.168645	+	1.12972i
$371$	26.7762	+	151.856i	0.0721732	+	0.409314i
$372$		0			0
$373$	247.160	+	115.252i	0.662626	+	0.308988i	0.724680	−	0.689085i	$-0.241987\pi$
$373$	247.160	+	115.252i	0.662626	+	0.308988i	−0.0620543	+	0.998073i	$0.519765\pi$
$374$	−810.527	−	142.918i	−2.16719	−	0.382133i
$375$		0			0
$376$	−430.345	+	361.102i	−1.14453	+	0.960378i
$377$	52.7793	−	52.7793i	0.139998	−	0.139998i
$378$		0			0
$379$		−	373.089i		−	0.984403i	−0.870481	−	0.492202i	$-0.836192\pi$
$379$		−	373.089i		−	0.984403i	0.870481	−	0.492202i	$-0.163808\pi$
$380$	−35.6787	−	1353.91i	−0.0938913	−	3.56293i
$381$		0			0
$382$	−682.165	−	974.233i	−1.78577	−	2.55035i
$383$	−329.969	−	153.867i	−0.861538	−	0.401742i	−0.0589394	−	0.998262i	$-0.518772\pi$
$383$	−329.969	−	153.867i	−0.861538	−	0.401742i	−0.802598	+	0.596520i	$0.796550\pi$
$384$		0			0
$385$	127.826	−	37.8870i	0.332017	−	0.0984078i
$386$	178.313	+	308.847i	0.461950	+	0.800121i
$387$		0			0
$388$	759.860	−	203.604i	1.95840	−	0.524753i
$389$	−186.117	+	511.351i	−0.478449	+	1.31453i	0.432361	+	0.901701i	$0.357681\pi$
$389$	−186.117	+	511.351i	−0.478449	+	1.31453i	−0.910810	+	0.412827i	$0.864542\pi$
$390$		0			0
$391$	556.221	+	466.725i	1.42256	+	1.19367i
$392$	923.159	−	80.7660i	2.35500	−	0.206036i
$393$		0			0
$394$	−130.089	+	357.416i	−0.330175	+	0.907148i
$395$	48.0472	−	18.9355i	0.121638	−	0.0479380i
$396$		0			0
$397$	114.505	+	30.6816i	0.288427	+	0.0772837i	0.400132	−	0.916458i	$-0.368964\pi$
$397$	114.505	+	30.6816i	0.288427	+	0.0772837i	−0.111705	+	0.993741i	$0.535631\pi$
$398$	26.1284	−	37.3153i	0.0656493	−	0.0937570i
$399$		0			0
$400$	−642.754	−	989.035i	−1.60689	−	2.47259i
$401$	28.2142	−	160.011i	0.0703596	−	0.399029i	−0.929206	−	0.369562i	$-0.879508\pi$
$401$	28.2142	−	160.011i	0.0703596	−	0.399029i	0.999566	−	0.0294672i	$-0.00938106\pi$
$402$		0			0
$403$	202.835	+	17.7457i	0.503312	+	0.0440341i
$404$			1866.66i			4.62045i
$405$		0			0
$406$	−57.1101			−0.140665
$407$	−17.0881	+	195.318i	−0.0419855	+	0.479896i
$408$		0			0
$409$	−241.096	−	42.5117i	−0.589476	−	0.103941i	−0.129049	−	0.991638i	$-0.541193\pi$
$409$	−241.096	−	42.5117i	−0.589476	−	0.103941i	−0.460427	+	0.887698i	$0.652304\pi$
$410$	−118.278	−	237.131i	−0.288484	−	0.578369i
$411$		0			0
$412$	1527.80	+	1069.78i	3.70825	+	2.59655i
$413$	−16.5163	+	61.6395i	−0.0399909	+	0.149248i
$414$		0			0
$415$	−138.046	+	317.628i	−0.332641	+	0.765369i
$416$	−1191.34	−	433.612i	−2.86380	−	1.04234i
$417$		0			0
$418$	−76.2445	−	871.478i	−0.182403	−	2.08488i
$419$	−39.9401	+	47.5987i	−0.0953223	+	0.113601i	−0.811597	−	0.584218i	$-0.801401\pi$
$419$	−39.9401	+	47.5987i	−0.0953223	+	0.113601i	0.716275	+	0.697819i	$0.245846\pi$
$420$		0			0
$421$	20.0465	+	7.29634i	0.0476165	+	0.0173310i	0.365719	−	0.930725i	$-0.380823\pi$
$421$	20.0465	+	7.29634i	0.0476165	+	0.0173310i	−0.318102	+	0.948056i	$0.603045\pi$
$422$	45.3298	+	169.173i	0.107417	+	0.400884i
$423$		0			0
$424$	1021.90	−	589.993i	2.41014	−	1.39149i
$425$	233.875	−	579.417i	0.550295	−	1.36333i
$426$		0			0
$427$	−99.6322	+	213.662i	−0.233331	+	0.500379i
$428$	−64.4337	+	45.1169i	−0.150546	+	0.105413i
$429$		0			0
$430$	−11.8815	−	450.871i	−0.0276313	−	1.04854i
$431$	486.219			1.12812			0.564059	−	0.825734i	$-0.309239\pi$
$431$	486.219			1.12812			0.564059	+	0.825734i	$0.309239\pi$
$432$		0			0
$433$	−120.602	−	120.602i	−0.278526	−	0.278526i	0.553995	−	0.832520i	$-0.313103\pi$
$433$	−120.602	−	120.602i	−0.278526	−	0.278526i	−0.832520	+	0.553995i	$0.813103\pi$
$434$	−100.138	−	119.340i	−0.230733	−	0.274977i
$435$		0			0
$436$	−53.7419	+	304.785i	−0.123261	+	0.699049i
$437$	−326.165	+	699.464i	−0.746374	+	1.60060i
$438$		0			0
$439$	−427.090	+	75.3075i	−0.972870	+	0.171543i	−0.637421	−	0.770515i	$-0.719999\pi$
$439$	−427.090	+	75.3075i	−0.972870	+	0.171543i	−0.335448	+	0.942059i	$0.608888\pi$
$440$	−606.998	−	820.026i	−1.37954	−	1.86370i
$441$		0			0
$442$	−366.187	−	1366.63i	−0.828478	−	3.09192i
$443$	126.504	+	271.289i	0.285563	+	0.612392i	0.995798	−	0.0915725i	$-0.0291893\pi$
$443$	126.504	+	271.289i	0.285563	+	0.612392i	−0.710236	+	0.703964i	$0.751412\pi$
$444$		0			0
$445$	−70.6385	−	346.904i	−0.158738	−	0.779559i
$446$	−301.597	−	253.070i	−0.676227	−	0.567421i
$447$		0			0
$448$	166.610	+	357.295i	0.371896	+	0.797534i
$449$	624.818	+	360.739i	1.39158	+	0.803428i	0.993490	−	0.113920i	$-0.0363407\pi$
$449$	624.818	+	360.739i	1.39158	+	0.803428i	0.398087	+	0.917347i	$0.369674\pi$
$450$		0			0
$451$	−61.4672	−	106.464i	−0.136291	−	0.236063i
$452$	−170.747	−	119.558i	−0.377758	−	0.264509i
$453$		0			0
$454$	140.847	+	386.975i	0.310237	+	0.852368i
$455$	151.894	+	171.628i	0.333834	+	0.377204i
$456$		0			0
$457$	−63.5274	+	726.121i	−0.139010	+	1.58889i	0.531547	+	0.847029i	$0.321611\pi$
$457$	−63.5274	+	726.121i	−0.139010	+	1.58889i	−0.670557	+	0.741858i	$0.733945\pi$
$458$	−773.754	−	773.754i	−1.68942	−	1.68942i
$459$		0			0
$460$	167.910	+	1471.56i	0.365023	+	3.19904i
$461$	−684.108	+	574.034i	−1.48396	+	1.24519i	−0.582142	+	0.813087i	$0.697785\pi$
$461$	−684.108	+	574.034i	−1.48396	+	1.24519i	−0.901822	+	0.432107i	$0.857770\pi$
$462$		0			0
$463$	485.944	−	340.262i	1.04956	−	0.734907i	0.0843598	−	0.996435i	$-0.473115\pi$
$463$	485.944	−	340.262i	1.04956	−	0.734907i	0.965196	+	0.261529i	$0.0842266\pi$
$464$	80.1704	+	220.266i	0.172781	+	0.474712i
$465$		0			0
$466$	−196.361	−	1113.62i	−0.421375	−	2.38974i
$467$	120.396	+	32.2601i	0.257808	+	0.0690794i	0.385408	−	0.922746i	$-0.374061\pi$
$467$	120.396	+	32.2601i	0.257808	+	0.0690794i	−0.127600	+	0.991826i	$0.540727\pi$
$468$		0			0
$469$	271.615	+	156.817i	0.579136	+	0.334364i
$470$	−236.915	−	386.466i	−0.504075	−	0.822269i
$471$		0			0
$472$	486.471	−	42.5607i	1.03066	−	0.0901710i
$473$	−18.2364	−	208.443i	−0.0385547	−	0.440682i
$474$		0			0
$475$	659.221	+	80.7197i	1.38783	+	0.169936i
$476$	−388.759	+	673.351i	−0.816721	+	1.41460i
$477$		0			0
$478$	−58.5656	+	218.570i	−0.122522	+	0.457259i
$479$	291.942	−	51.4772i	0.609482	−	0.107468i	0.139616	−	0.990206i	$-0.455413\pi$
$479$	291.942	−	51.4772i	0.609482	−	0.107468i	0.469866	+	0.882738i	$0.344302\pi$
$480$		0			0
$481$	−316.719	+	115.276i	−0.658459	+	0.239659i
$482$	−993.701	−	1419.15i	−2.06162	−	2.94430i
$483$		0			0
$484$	292.423	+	348.496i	0.604180	+	0.720034i
$485$	43.7324	+	383.268i	0.0901699	+	0.790243i
$486$		0			0
$487$	−187.665	+	187.665i	−0.385349	+	0.385349i	−0.873025	−	0.487676i	$-0.837845\pi$
$487$	−187.665	+	187.665i	−0.385349	+	0.385349i	0.487676	+	0.873025i	$0.337845\pi$
$488$	1797.19	+	157.233i	3.68276	+	0.322200i
$489$		0			0
$490$	−45.5253	+	746.368i	−0.0929088	+	1.52320i
$491$	223.725	−	81.4291i	0.455651	−	0.165843i	−0.103990	−	0.994578i	$-0.533161\pi$
$491$	223.725	−	81.4291i	0.455651	−	0.165843i	0.559641	+	0.828735i	$0.310939\pi$
$492$		0			0
$493$	−71.2207	+	101.714i	−0.144464	+	0.206316i
$494$	1302.37	−	751.922i	2.63637	−	1.52211i
$495$		0			0
$496$	−319.707	+	553.748i	−0.644570	+	1.11643i
$497$	−70.1180	+	32.6965i	−0.141082	+	0.0657878i
$498$		0			0
$499$	−206.163	+	245.695i	−0.413152	+	0.492375i	−0.931983	−	0.362501i	$-0.881923\pi$
$499$	−206.163	+	245.695i	−0.413152	+	0.492375i	0.518831	+	0.854877i	$0.326367\pi$
$500$	1159.53	−	529.128i	2.31907	−	1.05826i
$501$		0			0
$502$	297.001	−	138.494i	0.591635	−	0.275884i
$503$	−780.441	+	209.119i	−1.55157	+	0.415743i	−0.929984	−	0.367601i	$-0.880179\pi$
$503$	−780.441	+	209.119i	−1.55157	+	0.415743i	−0.621589	+	0.783344i	$0.713513\pi$
$504$		0			0
$505$	−905.318	−	135.147i	−1.79271	−	0.267617i
$506$	166.122	+	942.124i	0.328304	+	1.86190i
$507$		0			0
$508$	−464.547	−	216.622i	−0.914463	−	0.426421i
$509$	14.3637	+	2.53271i	0.0282195	+	0.00497586i	0.187740	−	0.982219i	$-0.439884\pi$
$509$	14.3637	+	2.53271i	0.0282195	+	0.00497586i	−0.159521	+	0.987195i	$0.550995\pi$
$510$		0			0
$511$	209.760	−	176.009i	0.410488	−	0.344441i
$512$	−300.411	+	300.411i	−0.586740	+	0.586740i
$513$		0			0
$514$		−	695.722i		−	1.35355i
$515$	−629.447	+	663.520i	−1.22223	+	1.28839i
$516$		0			0
$517$	−120.621	−	172.264i	−0.233309	−	0.333199i
$518$	233.721	+	108.986i	0.451199	+	0.210398i
$519$		0			0
$520$	836.610	−	1541.45i	1.60886	−	2.96434i
$521$	−193.021	−	334.321i	−0.370481	−	0.641692i	0.619159	−	0.785266i	$-0.287474\pi$
$521$	−193.021	−	334.321i	−0.370481	−	0.641692i	−0.989640	+	0.143574i	$0.954140\pi$
$522$		0			0
$523$	−147.655	+	39.5642i	−0.282324	+	0.0756485i	−0.397202	−	0.917731i	$-0.630019\pi$
$523$	−147.655	+	39.5642i	−0.282324	+	0.0756485i	0.114878	+	0.993380i	$0.463352\pi$
$524$	711.905	−	1955.94i	1.35860	−	3.73272i
$525$		0			0
$526$	−1017.85	−	854.073i	−1.93507	−	1.62371i
$527$	−337.426	+	29.5210i	−0.640277	+	0.0560170i
$528$		0			0
$529$	107.731	−	295.987i	0.203650	−	0.559523i
$530$	349.110	+	885.836i	0.658699	+	1.67139i
$531$		0			0
$532$	−798.271	−	213.896i	−1.50051	−	0.402060i
$533$	121.215	−	173.113i	0.227420	−	0.324789i
$534$		0			0
$535$	−17.2164	−	34.5163i	−0.0321801	−	0.0645165i
$536$	416.764	−	2363.59i	0.777545	−	4.40968i
$537$		0			0
$538$	−1348.53	−	117.981i	−2.50657	−	0.219296i
$539$			346.896i			0.643592i
$540$		0			0
$541$	−596.238			−1.10210			−0.551051	−	0.834471i	$-0.685773\pi$
$541$	−596.238			−1.10210			−0.551051	+	0.834471i	$0.685773\pi$
$542$	115.079	−	1315.36i	0.212322	−	2.42686i
$543$		0			0
$544$	2077.01	+	366.232i	3.81802	+	0.673221i
$545$	−143.928	−	48.1310i	−0.264088	−	0.0883137i
$546$		0			0
$547$	−34.6251	−	24.2447i	−0.0632999	−	0.0443231i	0.541498	−	0.840702i	$-0.317857\pi$
$547$	−34.6251	−	24.2447i	−0.0632999	−	0.0443231i	−0.604798	+	0.796379i	$0.706746\pi$
$548$	98.3309	−	366.976i	0.179436	−	0.669664i
$549$		0			0
$550$	726.754	−	386.732i	1.32137	−	0.703150i
$551$	−124.021	−	45.1401i	−0.225084	−	0.0819240i
$552$		0			0
$553$	−2.74650	−	31.3926i	−0.00496655	−	0.0567679i
$554$	326.755	−	389.411i	0.589810	−	0.702908i
$555$		0			0
$556$	1779.65	+	647.739i	3.20080	+	1.16500i
$557$	−99.0213	−	369.552i	−0.177776	−	0.663469i	−0.996062	−	0.0886581i	$-0.971742\pi$
$557$	−99.0213	−	369.552i	−0.177776	−	0.663469i	0.818286	−	0.574811i	$-0.194925\pi$
$558$		0			0
$559$	311.504	−	179.847i	0.557252	−	0.321730i
$560$	−690.073	+	204.534i	−1.23227	+	0.365239i
$561$		0			0
$562$	19.2238	−	41.2256i	0.0342060	−	0.0733551i
$563$	206.487	−	144.583i	0.366761	−	0.256809i	−0.375638	−	0.926766i	$-0.622577\pi$
$563$	206.487	−	144.583i	0.366761	−	0.256809i	0.742400	+	0.669957i	$0.233688\pi$
$564$		0			0
$565$	70.3470	−	74.1549i	0.124508	−	0.131248i
$566$	939.890			1.66058
$567$		0			0
$568$	418.635	+	418.635i	0.737034	+	0.737034i
$569$	−457.282	−	544.967i	−0.803658	−	0.957763i	0.196081	−	0.980588i	$-0.437178\pi$
$569$	−457.282	−	544.967i	−0.803658	−	0.957763i	−0.999739	+	0.0228251i	$0.992734\pi$
$570$		0			0
$571$	9.87196	−	55.9867i	0.0172889	−	0.0980502i	−0.974942	−	0.222458i	$-0.928592\pi$
$571$	9.87196	−	55.9867i	0.0172889	−	0.0980502i	0.992231	+	0.124408i	$0.0397031\pi$
$572$	565.832	−	1213.43i	0.989216	−	2.12138i
$573$		0			0
$574$	−159.239	+	28.0782i	−0.277420	+	0.0489167i
$575$	−725.851	−	25.1056i	−1.26235	−	0.0436620i
$576$		0			0
$577$	115.339	+	430.452i	0.199895	+	0.746017i	0.990945	+	0.134266i	$0.0428677\pi$
$577$	115.339	+	430.452i	0.199895	+	0.746017i	−0.791051	+	0.611751i	$0.790466\pi$
$578$	534.510	+	1146.26i	0.924757	+	1.98315i
$579$		0			0
$580$	−248.190	+	50.5379i	−0.427914	+	0.0871343i
$581$	161.886	+	135.838i	0.278633	+	0.233801i
$582$		0			0
$583$	186.678	+	400.331i	0.320202	+	0.686675i
$584$	−1814.66	−	1047.70i	−3.10730	−	1.79400i
$585$		0			0
$586$	34.4429	+	59.6568i	0.0587763	+	0.101803i
$587$	734.395	+	514.229i	1.25110	+	0.876028i	0.995865	−	0.0908509i	$-0.0289587\pi$
$587$	734.395	+	514.229i	1.25110	+	0.876028i	0.255234	+	0.966879i	$0.417848\pi$
$588$		0			0
$589$	−123.135	−	338.311i	−0.209058	−	0.574382i
$590$	−23.9902	+	393.309i	−0.0406613	+	0.666625i
$591$		0			0
$592$	92.2503	−	1054.43i	0.155828	−	1.78112i
$593$	536.873	+	536.873i	0.905351	+	0.905351i	0.995893	−	0.0905416i	$-0.0288598\pi$
$593$	536.873	+	536.873i	0.905351	+	0.905351i	−0.0905416	+	0.995893i	$0.528860\pi$
$594$		0			0
$595$	−298.424	−	237.296i	−0.501553	−	0.398817i
$596$	−311.706	+	261.553i	−0.522997	+	0.438847i
$597$		0			0
$598$	−1347.14	+	943.275i	−2.25274	+	1.57738i
$599$	72.2154	+	198.410i	0.120560	+	0.331236i	0.985263	−	0.171048i	$-0.0547154\pi$
$599$	72.2154	+	198.410i	0.120560	+	0.331236i	−0.864703	+	0.502284i	$0.832493\pi$
$600$		0			0
$601$	−167.417	−	949.470i	−0.278564	−	1.57982i	−0.727407	−	0.686206i	$-0.759275\pi$
$601$	−167.417	−	949.470i	−0.278564	−	1.57982i	0.448843	−	0.893611i	$-0.351836\pi$
$602$	−265.835	−	71.2302i	−0.441586	−	0.118323i
$603$		0			0
$604$	−1345.86	−	777.034i	−2.22825	−	1.28648i
$605$	−190.190	+	116.592i	−0.314363	+	0.192714i
$606$		0			0
$607$	−36.3991	+	3.18451i	−0.0599656	+	0.00524631i	−0.117099	−	0.993120i	$-0.537359\pi$
$607$	−36.3991	+	3.18451i	−0.0599656	+	0.00524631i	0.0571335	+	0.998367i	$0.481804\pi$
$608$	195.379	+	2233.19i	0.321347	+	3.67302i
$609$		0			0
$610$	−339.594	+	1415.55i	−0.556712	+	2.32057i
$611$	180.755	−	313.077i	0.295835	−	0.512401i
$612$		0			0
$613$	298.135	−	1112.65i	0.486353	−	1.81510i	−0.0875346	−	0.996161i	$-0.527899\pi$
$613$	298.135	−	1112.65i	0.486353	−	1.81510i	0.573888	−	0.818934i	$-0.305434\pi$
$614$	1818.02	−	320.566i	2.96094	−	0.522094i
$615$		0			0
$616$	−584.997	+	212.921i	−0.949670	+	0.345652i
$617$	−198.434	−	283.392i	−0.321610	−	0.459307i	0.625496	−	0.780227i	$-0.284897\pi$
$617$	−198.434	−	283.392i	−0.321610	−	0.459307i	−0.947106	+	0.320920i	$0.896008\pi$
$618$		0			0
$619$	426.792	+	508.631i	0.689487	+	0.821698i	0.991294	−	0.131671i	$-0.0420342\pi$
$619$	426.792	+	508.631i	0.689487	+	0.821698i	−0.301807	+	0.953369i	$0.597590\pi$
$620$	−540.790	−	430.017i	−0.872241	−	0.693575i
$621$		0			0
$622$	548.749	−	548.749i	0.882234	−	0.882234i
$623$	−215.199	−	18.8275i	−0.345424	−	0.0302207i
$624$		0			0
$625$	172.673	+	600.674i	0.276277	+	0.961078i
$626$	−1817.96	+	661.685i	−2.90410	+	1.05700i
$627$		0			0
$628$	−717.235	+	1024.32i	−1.14209	+	1.63108i
$629$	485.573	−	280.346i	0.771977	−	0.445701i
$630$		0			0
$631$	285.716	−	494.875i	0.452799	−	0.784270i	−0.545760	−	0.837942i	$-0.683759\pi$
$631$	285.716	−	494.875i	0.452799	−	0.784270i	0.998559	+	0.0536712i	$0.0170923\pi$
$632$	−218.553	+	101.913i	−0.345812	+	0.161255i
$633$		0			0
$634$	−1111.98	+	1325.21i	−1.75391	+	2.09023i
$635$	138.693	−	209.619i	0.218415	−	0.330108i
$636$		0			0
$637$	−540.463	+	252.022i	−0.848450	+	0.395639i
$638$	−158.023	+	42.3422i	−0.247686	+	0.0663672i
$639$		0			0
$640$	444.215	+	600.114i	0.694086	+	0.937678i
$641$	−84.2379	−	477.737i	−0.131416	−	0.745299i	−0.977288	−	0.211913i	$-0.932031\pi$
$641$	−84.2379	−	477.737i	−0.131416	−	0.745299i	0.845872	−	0.533386i	$-0.179081\pi$
$642$		0			0
$643$	456.186	+	212.723i	0.709465	+	0.330829i	0.743634	−	0.668587i	$-0.233101\pi$
$643$	456.186	+	212.723i	0.709465	+	0.330829i	−0.0341686	+	0.999416i	$0.510878\pi$
$644$	890.025	+	156.935i	1.38203	+	0.243689i
$645$		0			0
$646$	−1916.43	+	1608.08i	−2.96661	+	2.48928i
$647$	−802.350	+	802.350i	−1.24011	+	1.24011i	−0.280153	+	0.959955i	$0.590385\pi$
$647$	−802.350	+	802.350i	−1.24011	+	1.24011i	−0.959955	+	0.280153i	$0.909615\pi$
$648$		0			0
$649$			182.802i			0.281667i
$650$	1130.52	+	851.317i	1.73926	+	1.30972i
$651$		0			0
$652$	−167.616	−	239.380i	−0.257079	−	0.367147i
$653$	−722.752	−	337.025i	−1.10682	−	0.516118i	−0.218727	−	0.975786i	$-0.570191\pi$
$653$	−722.752	−	337.025i	−1.10682	−	0.516118i	−0.888091	+	0.459668i	$0.847968\pi$
$654$		0			0
$655$	897.076	+	486.880i	1.36958	+	0.743328i
$656$	331.832	+	574.749i	0.505841	+	0.876142i
$657$		0			0
$658$	−267.177	+	71.5898i	−0.406044	+	0.108799i
$659$	−254.736	+	699.880i	−0.386549	+	1.06203i	0.581996	+	0.813192i	$0.302272\pi$
$659$	−254.736	+	699.880i	−0.386549	+	1.06203i	−0.968544	+	0.248842i	$0.919950\pi$
$660$		0			0
$661$	415.794	+	348.892i	0.629037	+	0.527825i	0.900630	−	0.434587i	$-0.143106\pi$
$661$	415.794	+	348.892i	0.629037	+	0.527825i	−0.271592	+	0.962412i	$0.587550\pi$
$662$	−1036.55	+	90.6865i	−1.56579	+	0.136989i
$663$		0			0
$664$	553.101	−	1519.63i	0.832983	−	2.28860i
$665$	161.533	−	371.670i	0.242907	−	0.558902i
$666$		0			0
$667$	139.412	+	37.3552i	0.209013	+	0.0560048i
$668$	−777.870	+	1110.91i	−1.16448	+	1.66304i
$669$		0			0
$670$	1836.66	+	614.197i	2.74128	+	0.916713i
$671$	−117.270	+	665.070i	−0.174769	+	0.991162i
$672$		0			0
$673$	−1267.15	−	110.861i	−1.88284	−	0.164727i	−0.912918	−	0.408144i	$-0.866176\pi$
$673$	−1267.15	−	110.861i	−1.88284	−	0.164727i	−0.969922	+	0.243417i	$0.921732\pi$
$674$		−	1210.92i		−	1.79662i
$675$		0			0
$676$	578.399			0.855620
$677$	52.1727	−	596.336i	0.0770645	−	0.880851i	−0.855016	−	0.518601i	$-0.826453\pi$
$677$	52.1727	−	596.336i	0.0770645	−	0.880851i	0.932081	−	0.362250i	$-0.117991\pi$
$678$		0			0
$679$	231.808	+	40.8739i	0.341396	+	0.0601973i
$680$	−925.316	+	2767.01i	−1.36076	+	4.06913i
$681$		0			0
$682$	−365.563	−	255.970i	−0.536016	−	0.375322i
$683$	−200.381	+	747.832i	−0.293384	+	1.09492i	0.649109	+	0.760696i	$0.275142\pi$
$683$	−200.381	+	747.832i	−0.293384	+	1.09492i	−0.942493	+	0.334227i	$0.891525\pi$
$684$		0			0
$685$	170.861	+	74.2589i	0.249433	+	0.108407i
$686$	958.062	+	348.706i	1.39659	+	0.508318i
$687$		0			0
$688$	98.4493	+	1125.28i	0.143095	+	1.63558i
$689$	−488.092	+	581.686i	−0.708407	+	0.844247i
$690$		0			0
$691$	−79.8263	−	29.0544i	−0.115523	−	0.0420469i	0.283612	−	0.958939i	$-0.408467\pi$
$691$	−79.8263	−	29.0544i	−0.115523	−	0.0420469i	−0.399135	+	0.916892i	$0.630689\pi$
$692$	−57.4665	−	214.468i	−0.0830440	−	0.309925i
$693$		0			0
$694$	1434.21	−	828.039i	2.06658	−	1.19314i
$695$	−442.995	+	816.219i	−0.637403	+	1.17442i
$696$		0			0
$697$	−148.576	+	318.622i	−0.213165	+	0.457134i
$698$	−619.782	+	433.976i	−0.887940	+	0.621742i
$699$		0			0
$700$	−108.494	−	770.117i	−0.154991	−	1.10017i
$701$	430.049			0.613479			0.306740	−	0.951793i	$-0.400762\pi$
$701$	430.049			0.613479			0.306740	+	0.951793i	$0.400762\pi$
$702$		0			0
$703$	421.411	+	421.411i	0.599446	+	0.599446i
$704$	725.912	+	865.108i	1.03112	+	1.22885i
$705$		0			0
$706$	186.667	−	1058.64i	0.264401	−	1.49949i
$707$	−236.048	+	506.207i	−0.333873	+	0.715993i
$708$		0			0
$709$	−316.132	+	55.7426i	−0.445885	+	0.0786215i	−0.392082	−	0.919930i	$-0.628245\pi$
$709$	−316.132	+	55.7426i	−0.445885	+	0.0786215i	−0.0538023	+	0.998552i	$0.517134\pi$
$710$	−383.976	+	284.226i	−0.540811	+	0.400318i
$711$		0			0
$712$	427.849	+	1596.75i	0.600911	+	2.24263i
$713$	166.388	+	356.821i	0.233364	+	0.500450i
$714$		0			0
$715$	547.538	+	362.277i	0.765788	+	0.506681i
$716$	1684.74	+	1413.67i	2.35299	+	1.97439i
$717$		0			0
$718$	−301.374	−	646.298i	−0.419741	−	0.900137i
$719$	−483.899	−	279.379i	−0.673016	−	0.388566i	0.124202	−	0.992257i	$-0.460363\pi$
$719$	−483.899	−	279.379i	−0.673016	−	0.388566i	−0.797219	+	0.603691i	$0.793696\pi$
$720$		0			0
$721$	279.035	+	483.302i	0.387011	+	0.670322i
$722$	−1064.01	−	745.031i	−1.47370	−	1.03190i
$723$		0			0
$724$	−89.0300	−	244.608i	−0.122970	−	0.337856i
$725$	−6.54146	−	124.029i	−0.00902271	−	0.171075i
$726$		0			0
$727$	68.5713	−	783.774i	0.0943210	−	1.07809i	−0.790594	−	0.612341i	$-0.790228\pi$
$727$	68.5713	−	783.774i	0.0943210	−	1.07809i	0.884915	−	0.465753i	$-0.154216\pi$
$728$	−756.734	−	756.734i	−1.03947	−	1.03947i
$729$		0			0
$730$	1052.33	−	1323.41i	1.44155	−	1.81289i
$731$	−458.378	+	384.625i	−0.627056	+	0.526162i
$732$		0			0
$733$	1027.75	−	719.641i	1.40212	−	0.981774i	0.404378	−	0.914592i	$-0.367488\pi$
$733$	1027.75	−	719.641i	1.40212	−	0.981774i	0.997741	−	0.0671824i	$-0.0214010\pi$
$734$	566.997	+	1557.81i	0.772476	+	2.12236i
$735$		0			0
$736$	−425.693	−	2414.23i	−0.578387	−	3.28020i
$737$	867.823	+	232.532i	1.17751	+	0.315512i
$738$		0			0
$739$	236.827	+	136.732i	0.320469	+	0.185023i	0.651602	−	0.758561i	$-0.274097\pi$
$739$	236.827	+	136.732i	0.320469	+	0.185023i	−0.331132	+	0.943584i	$0.607431\pi$
$740$	1112.16	+	266.809i	1.50291	+	0.360553i
$741$		0			0
$742$	578.780	−	50.6367i	0.780027	−	0.0682435i
$743$	−96.6026	−	1104.17i	−0.130017	−	1.48610i	−0.728544	−	0.684999i	$-0.759803\pi$
$743$	−96.6026	−	1104.17i	−0.130017	−	1.48610i	0.598527	−	0.801103i	$-0.295753\pi$
$744$		0			0
$745$	−104.284	−	170.112i	−0.139978	−	0.228338i
$746$	513.761	−	889.861i	0.688688	−	1.19284i
$747$		0			0
$748$	−576.463	+	2151.39i	−0.770673	+	2.87619i
$749$	−23.1785	+	4.08700i	−0.0309460	+	0.00545661i
$750$		0			0
$751$	−165.200	+	60.1277i	−0.219973	+	0.0800636i	−0.449656	−	0.893202i	$-0.648453\pi$
$751$	−165.200	+	60.1277i	−0.219973	+	0.0800636i	0.229683	+	0.973266i	$0.426231\pi$
$752$	651.172	+	929.969i	0.865920	+	1.23666i
$753$		0			0
$754$	−180.774	−	215.438i	−0.239753	−	0.285727i
$755$	474.297	−	596.476i	0.628207	−	0.790035i
$756$		0			0
$757$	−712.642	+	712.642i	−0.941402	+	0.941402i	−0.998376	−	0.0569733i	$-0.981855\pi$
$757$	−712.642	+	712.642i	−0.941402	+	0.941402i	0.0569733	+	0.998376i	$0.481855\pi$
$758$	−1400.38	−	122.517i	−1.84747	−	0.161633i
$759$		0			0
$760$	−3095.42	−	188.807i	−4.07291	−	0.248430i
$761$	435.097	−	158.362i	0.571744	−	0.208098i	−0.0399372	−	0.999202i	$-0.512716\pi$
$761$	435.097	−	158.362i	0.571744	−	0.208098i	0.611681	+	0.791104i	$0.290494\pi$
$762$		0			0
$763$	−53.1154	+	75.8566i	−0.0696139	+	0.0994189i
$764$	−2787.33	+	1609.26i	−3.64833	+	2.10637i
$765$		0			0
$766$	−685.894	+	1188.00i	−0.895423	+	1.55092i
$767$	−284.804	+	132.806i	−0.371322	+	0.173150i
$768$		0			0
$769$	284.787	−	339.396i	0.370334	−	0.441347i	−0.548405	−	0.836213i	$-0.684765\pi$
$769$	284.787	−	339.396i	0.370334	−	0.441347i	0.918739	+	0.394866i	$0.129209\pi$
$770$	−100.232	−	492.235i	−0.130171	−	0.639267i
$771$		0			0
$772$	874.676	−	407.868i	1.13300	−	0.528326i
$773$	1113.18	−	298.276i	1.44008	−	0.385868i	0.547517	−	0.836795i	$-0.315573\pi$
$773$	1113.18	−	298.276i	1.44008	−	0.385868i	0.892561	+	0.450927i	$0.148906\pi$
$774$		0			0
$775$	247.708	−	231.146i	0.319624	−	0.298252i
$776$	−312.784	−	1773.88i	−0.403072	−	2.28593i
$777$		0			0
$778$	1858.23	+	866.506i	2.38847	+	1.11376i
$779$	−368.000	−	64.8883i	−0.472401	−	0.0832970i
$780$		0			0
$781$	−169.774	+	142.458i	−0.217381	+	0.182404i
$782$	1934.50	−	1934.50i	2.47378	−	2.47378i
$783$		0			0
$784$		−	1872.72i		−	2.38868i
$785$	−444.859	−	422.015i	−0.566699	−	0.537598i
$786$		0			0
$787$	−532.237	−	760.113i	−0.676286	−	0.965837i	−0.999808	−	0.0196158i	$-0.993756\pi$
$787$	−532.237	−	760.113i	−0.676286	−	0.965837i	0.323522	−	0.946221i	$-0.395133\pi$
$788$	932.875	+	435.007i	1.18385	+	0.552039i
$789$		0			0
$790$	−55.2960	−	186.562i	−0.0699950	−	0.236155i
$791$	−31.1849	−	54.0138i	−0.0394247	−	0.0682855i
$792$		0			0
$793$	−1121.37	+	300.471i	−1.41409	+	0.378904i
$794$	152.765	−	419.718i	0.192399	−	0.528612i
$795$		0			0
$796$	−94.4355	−	79.2408i	−0.118638	−	0.0995487i
$797$	310.684	−	27.1813i	0.389817	−	0.0341045i	0.109437	−	0.993994i	$-0.465095\pi$
$797$	310.684	−	27.1813i	0.389817	−	0.0341045i	0.280380	+	0.959889i	$0.409540\pi$
$798$		0			0
$799$	−205.688	+	565.123i	−0.257432	+	0.707287i
$800$	−1862.33	+	991.015i	−2.32792	+	1.23877i
$801$		0			0
$802$	−591.331	−	158.447i	−0.737321	−	0.197565i
$803$	449.908	−	642.535i	0.560284	−	0.800168i
$804$		0			0
$805$	−140.551	+	420.294i	−0.174597	+	0.522104i
$806$	133.217	−	755.508i	0.165281	−	0.937355i
$807$		0			0
$808$	4257.89	+	372.517i	5.26966	+	0.461035i
$809$		−	458.912i		−	0.567258i	−0.958934	−	0.283629i	$-0.908462\pi$
$809$		−	458.912i		−	0.567258i	0.958934	−	0.283629i	$-0.0915385\pi$
$810$		0			0
$811$	−581.518			−0.717039			−0.358519	−	0.933522i	$-0.616718\pi$
$811$	−581.518			−0.717039			−0.358519	+	0.933522i	$0.616718\pi$
$812$	−13.4700	+	153.963i	−0.0165887	+	0.189610i
$813$		0			0
$814$	727.510	+	128.280i	0.893746	+	0.157592i
$815$	128.233	−	63.9612i	0.157341	−	0.0784800i
$816$		0			0
$817$	−520.991	−	364.802i	−0.637688	−	0.446514i
$818$	−238.740	+	890.988i	−0.291858	+	1.08923i
$819$		0			0
$820$	−667.178	+	262.937i	−0.813632	+	0.320655i
$821$	−334.376	−	121.703i	−0.407279	−	0.148238i	0.130253	−	0.991481i	$-0.458421\pi$
$821$	−334.376	−	121.703i	−0.407279	−	0.148238i	−0.537532	+	0.843243i	$0.680643\pi$
$822$		0			0
$823$	59.6061	+	681.301i	0.0724254	+	0.827826i	0.942347	+	0.334636i	$0.108613\pi$
$823$	59.6061	+	681.301i	0.0724254	+	0.827826i	−0.869922	+	0.493189i	$0.835831\pi$
$824$	2745.07	−	3271.45i	3.33139	−	3.97020i
$825$		0			0
$826$	225.939	+	82.2351i	0.273534	+	0.0995582i
$827$	−61.5862	−	229.843i	−0.0744695	−	0.277924i	0.918643	−	0.395089i	$-0.129286\pi$
$827$	−61.5862	−	229.843i	−0.0744695	−	0.277924i	−0.993112	+	0.117165i	$0.962619\pi$
$828$		0			0
$829$	289.902	−	167.375i	0.349701	−	0.201900i	−0.314853	−	0.949140i	$-0.601955\pi$
$829$	289.902	−	167.375i	0.349701	−	0.201900i	0.664553	+	0.747241i	$0.268622\pi$
$830$	1146.88	+	622.458i	1.38178	+	0.749949i
$831$		0			0
$832$	−820.456	+	1759.47i	−0.986125	+	2.11475i
$833$	812.626	−	569.007i	0.975542	−	0.683082i
$834$		0			0
$835$	−482.467	−	457.691i	−0.577804	−	0.548133i
$836$	−2367.40			−2.83182
$837$		0			0
$838$	165.545	+	165.545i	0.197548	+	0.197548i
$839$	126.171	+	150.364i	0.150382	+	0.179218i	0.835976	−	0.548765i	$-0.184902\pi$
$839$	126.171	+	150.364i	0.150382	+	0.179218i	−0.685594	+	0.727984i	$0.740458\pi$
$840$		0			0
$841$	141.752	−	803.917i	0.168552	−	0.955906i
$842$	33.9697	−	72.8482i	0.0403440	−	0.0865181i
$843$		0			0
$844$	466.764	−	82.3032i	0.553038	−	0.0975156i
$845$	−41.8762	+	280.519i	−0.0495577	+	0.331976i
$846$		0			0
$847$	35.2312	+	131.484i	0.0415952	+	0.155236i
$848$	−1007.78	−	2161.20i	−1.18842	−	2.54858i
$849$		0			0
$850$	−2098.03	−	1068.12i	−2.46827	−	1.25661i
$851$	−499.250	−	418.921i	−0.586663	−	0.492269i
$852$		0			0
$853$	−143.161	−	307.011i	−0.167833	−	0.359919i	0.804345	−	0.594163i	$-0.202516\pi$
$853$	−143.161	−	307.011i	−0.167833	−	0.359919i	−0.972178	+	0.234244i	$0.924739\pi$
$854$	769.258	+	444.131i	0.900770	+	0.520060i
$855$		0			0
$856$	90.0538	+	155.978i	0.105203	+	0.182217i
$857$	1306.14	+	914.569i	1.52408	+	1.06717i	0.972457	+	0.233084i	$0.0748816\pi$
$857$	1306.14	+	914.569i	1.52408	+	1.06717i	0.551627	+	0.834091i	$0.314007\pi$
$858$		0			0
$859$	−399.816	−	1098.49i	−0.465444	−	1.27880i	−0.921338	−	0.388762i	$-0.872903\pi$
$859$	−399.816	−	1098.49i	−0.465444	−	1.27880i	0.455894	−	0.890034i	$-0.349320\pi$
$860$	−1218.30	−	74.3113i	−1.41663	−	0.0864085i
$861$		0			0
$862$	159.668	−	1825.01i	0.185230	−	2.11719i
$863$	373.723	+	373.723i	0.433051	+	0.433051i	0.889665	−	0.456614i	$-0.150938\pi$
$863$	373.723	+	373.723i	0.433051	+	0.433051i	−0.456614	+	0.889665i	$0.650938\pi$
$864$		0			0
$865$	108.176	−	12.3433i	0.125059	−	0.0142697i
$866$	−492.280	+	413.072i	−0.568452	+	0.476988i
$867$		0			0
$868$	−345.347	+	241.815i	−0.397866	+	0.278589i
$869$	−30.8745	−	84.8270i	−0.0355288	−	0.0976145i
$870$		0			0
$871$	268.193	+	1521.00i	0.307914	+	1.74627i
$872$	684.495	+	183.410i	0.784971	+	0.210332i
$873$		0			0
$874$	2518.32	+	1453.95i	2.88137	+	1.66356i
$875$	381.356	+	3.13783i	0.435835	+	0.00358609i
$876$		0			0
$877$	−50.7319	+	4.43847i	−0.0578471	+	0.00506097i	−0.116043	−	0.993244i	$-0.537021\pi$
$877$	−50.7319	+	4.43847i	−0.0578471	+	0.00506097i	0.0581955	+	0.998305i	$0.481465\pi$
$878$	142.414	+	1627.80i	0.162203	+	1.85399i
$879$		0			0
$880$	−1757.78	+	1077.57i	−1.99748	+	1.22451i
$881$	174.009	−	301.392i	0.197513	−	0.342102i	−0.750209	−	0.661201i	$-0.770047\pi$
$881$	174.009	−	301.392i	0.197513	−	0.342102i	0.947721	+	0.319099i	$0.103380\pi$
$882$		0			0
$883$	−172.713	+	644.574i	−0.195598	+	0.729982i	0.796513	+	0.604621i	$0.206676\pi$
$883$	−172.713	+	644.574i	−0.195598	+	0.729982i	−0.992111	+	0.125361i	$0.959991\pi$
$884$	−3770.66	+	664.869i	−4.26545	+	0.752114i
$885$		0			0
$886$	1059.82	−	385.744i	1.19619	−	0.435377i
$887$	295.192	+	421.577i	0.332798	+	0.475284i	0.950323	−	0.311267i	$-0.100753\pi$
$887$	295.192	+	421.577i	0.332798	+	0.475284i	−0.617525	+	0.786551i	$0.711864\pi$
$888$		0			0
$889$	−98.5843	−	117.488i	−0.110894	−	0.132158i
$890$	−1325.29	+	151.221i	−1.48909	+	0.169912i
$891$		0			0
$892$	−753.385	+	753.385i	−0.844602	+	0.844602i
$893$	−636.791	−	55.7120i	−0.713092	−	0.0623875i
$894$		0			0
$895$	−807.593	+	714.738i	−0.902339	+	0.798590i
$896$	428.114	−	155.821i	0.477806	−	0.173907i
$897$		0			0
$898$	1559.21	−	2226.78i	1.73631	−	2.47971i
$899$	−58.3078	+	33.6640i	−0.0648585	+	0.0374461i
$900$		0			0
$901$	631.598	−	1093.96i	0.700997	−	1.21416i
$902$	−419.797	+	195.754i	−0.465407	+	0.217023i
$903$		0			0
$904$	−306.789	+	365.616i	−0.339368	+	0.404443i
$905$	125.079	−	25.4692i	0.138209	−	0.0281428i
$906$		0			0
$907$	657.700	−	306.690i	0.725138	−	0.338137i	−0.0247580	−	0.999693i	$-0.507882\pi$
$907$	657.700	−	306.690i	0.725138	−	0.338137i	0.749895	+	0.661556i	$0.230104\pi$
$908$	1076.47	−	288.438i	1.18554	−	0.317663i
$909$		0			0
$910$	694.082	−	513.772i	0.762727	−	0.564585i
$911$	−118.300	−	670.913i	−0.129857	−	0.736458i	−0.978304	−	0.207176i	$-0.933573\pi$
$911$	−118.300	−	670.913i	−0.129857	−	0.736458i	0.848446	−	0.529282i	$-0.177539\pi$
$912$		0			0
$913$	548.650	+	255.840i	0.600931	+	0.280219i
$914$	2704.62	+	476.898i	2.95910	+	0.521770i
$915$		0			0
$916$	−2268.46	+	1903.46i	−2.47648	+	2.07802i
$917$	440.394	−	440.394i	0.480256	−	0.480256i
$918$		0			0
$919$		−	1623.73i		−	1.76685i	−0.468574	−	0.883424i	$-0.655232\pi$
$919$		−	1623.73i		−	1.76685i	0.468574	−	0.883424i	$-0.344768\pi$
$920$	3390.15	−	89.3382i	3.68494	−	0.0971067i
$921$		0			0
$922$	1929.97	+	2756.29i	2.09325	+	2.98947i
$923$	−345.290	−	161.012i	−0.374096	−	0.174444i
$924$		0			0
$925$	−209.921	+	520.070i	−0.226941	+	0.562238i
$926$	−1117.59	−	1935.72i	−1.20690	−	2.09041i
$927$		0			0
$928$	404.941	−	108.504i	0.436358	−	0.116922i
$929$	−14.1415	+	38.8534i	−0.0152223	+	0.0418228i	−0.947071	−	0.321024i	$-0.895973\pi$
$929$	−14.1415	+	38.8534i	−0.0152223	+	0.0418228i	0.931849	+	0.362847i	$0.118195\pi$
$930$		0			0
$931$	807.749	+	677.782i	0.867614	+	0.728015i
$932$	−3048.51	+	266.710i	−3.27094	+	0.286170i
$933$		0			0
$934$	160.624	−	441.311i	0.171974	−	0.472496i
$935$	−1001.67	−	435.341i	−1.07131	−	0.465606i
$936$		0			0
$937$	308.687	+	82.7125i	0.329442	+	0.0882737i	0.419749	−	0.907640i	$-0.362118\pi$
$937$	308.687	+	82.7125i	0.329442	+	0.0882737i	−0.0903068	+	0.995914i	$0.528785\pi$
$938$	677.803	−	968.004i	0.722605	−	1.03199i
$939$		0			0
$940$	−1097.75	+	547.547i	−1.16782	+	0.582497i
$941$	194.531	−	1103.24i	0.206728	−	1.17241i	−0.687969	−	0.725740i	$-0.741497\pi$
$941$	194.531	−	1103.24i	0.206728	−	1.17241i	0.894697	−	0.446674i	$-0.147392\pi$
$942$		0			0
$943$	407.085	+	35.6153i	0.431691	+	0.0377681i
$944$		−	986.857i		−	1.04540i
$945$		0			0
$946$	−788.374			−0.833376
$947$	55.3916	−	633.129i	0.0584916	−	0.668563i	−0.909189	−	0.416384i	$-0.863297\pi$
$947$	55.3916	−	633.129i	0.0584916	−	0.668563i	0.967681	−	0.252179i	$-0.0811471\pi$
$948$		0			0
$949$	1327.93	+	234.149i	1.39929	+	0.246733i
$950$	519.459	−	2447.87i	0.546799	−	2.57670i
$951$		0			0
$952$	1458.34	+	1021.14i	1.53187	+	1.07263i
$953$	391.386	−	1460.67i	0.410688	−	1.53271i	−0.382631	−	0.923901i	$-0.624982\pi$
$953$	391.386	−	1460.67i	0.410688	−	1.53271i	0.793319	−	0.608807i	$-0.208352\pi$
$954$		0			0
$955$	−578.678	−	1468.34i	−0.605946	−	1.53753i
$956$	575.428	+	209.439i	0.601912	+	0.219078i
$957$		0			0
$958$	−97.3488	−	1112.70i	−0.101617	−	1.16148i
$959$	73.0714	−	87.0831i	0.0761954	−	0.0908061i
$960$		0			0
$961$	730.460	+	265.866i	0.760104	+	0.276655i
$962$	328.681	+	1226.65i	0.341664	+	1.27511i
$963$		0			0
$964$	−4060.26	+	2344.19i	−4.21189	+	2.43174i
$965$	134.486	+	453.741i	0.139364	+	0.470198i
$966$		0			0
$967$	370.976	−	795.561i	0.383636	−	0.822710i	−0.615759	−	0.787934i	$-0.711151\pi$
$967$	370.976	−	795.561i	0.383636	−	0.822710i	0.999395	−	0.0347756i	$-0.0110717\pi$
$968$	853.282	−	597.475i	0.881490	−	0.617226i
$969$		0			0
$970$	1452.95	−	38.2885i	1.49789	−	0.0394727i
$971$	195.094			0.200920			0.100460	−	0.994941i	$-0.467968\pi$
$971$	195.094			0.200920			0.100460	+	0.994941i	$0.467968\pi$
$972$		0			0
$973$	400.700	+	400.700i	0.411819	+	0.411819i
$974$	642.770	+	766.023i	0.659928	+	0.786471i
$975$		0			0
$976$	633.083	−	3590.39i	0.648650	−	3.67868i
$977$	−241.973	+	518.912i	−0.247669	+	0.531128i	−0.990362	−	0.138504i	$-0.955771\pi$
$977$	−241.973	+	518.912i	−0.247669	+	0.531128i	0.742693	+	0.669632i	$0.233548\pi$
$978$		0			0
$979$	−609.414	+	107.456i	−0.622486	+	0.109761i
$980$	2001.39	+	298.770i	2.04224	+	0.304868i
$981$		0			0
$982$	−232.174	−	866.486i	−0.236430	−	0.882369i
$983$	629.058	+	1349.02i	0.639937	+	1.37235i	0.912048	+	0.410083i	$0.134500\pi$
$983$	629.058	+	1349.02i	0.639937	+	1.37235i	−0.272111	+	0.962266i	$0.587722\pi$
$984$		0			0
$985$	−278.515	+	420.943i	−0.282757	+	0.427353i
$986$	358.392	+	300.727i	0.363481	+	0.304997i
$987$		0			0
$988$	−1719.93	−	3688.40i	−1.74082	−	3.73320i
$989$	602.338	+	347.760i	0.609037	+	0.351628i
$990$		0			0
$991$	−758.343	−	1313.49i	−0.765230	−	1.32542i	−0.940125	−	0.340830i	$-0.889292\pi$
$991$	−758.343	−	1313.49i	−0.765230	−	1.32542i	0.174895	−	0.984587i	$-0.444042\pi$
$992$	936.767	+	655.931i	0.944322	+	0.661221i
$993$		0			0
$994$	99.7000	+	273.923i	0.100302	+	0.275577i
$995$	45.2683	−	40.0635i	0.0454958	−	0.0402648i
$996$		0			0
$997$	−119.437	+	1365.17i	−0.119796	+	1.36928i	0.663754	+	0.747951i	$0.268962\pi$
$997$	−119.437	+	1365.17i	−0.119796	+	1.36928i	−0.783551	+	0.621328i	$0.786594\pi$
$998$	854.511	+	854.511i	0.856223	+	0.856223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.34		408
3.2	odd	2		135.3.r.a.103.1	yes	408
5.2	odd	4	inner	405.3.s.a.37.34		408
15.2	even	4		135.3.r.a.22.1	✓	408
27.11	odd	18		135.3.r.a.43.1	yes	408
27.16	even	9	inner	405.3.s.a.208.34		408
135.92	even	36		135.3.r.a.97.1	yes	408
135.97	odd	36	inner	405.3.s.a.127.34		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.1	✓	408	15.2	even	4
135.3.r.a.43.1	yes	408	27.11	odd	18
135.3.r.a.97.1	yes	408	135.92	even	36
135.3.r.a.103.1	yes	408	3.2	odd	2
405.3.s.a.37.34		408	5.2	odd	4	inner
405.3.s.a.118.34		408	1.1	even	1	trivial
405.3.s.a.127.34		408	135.97	odd	36	inner
405.3.s.a.208.34		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)

\(f(q)\)	\(=\)	\(q+(0.328387 - 3.75348i) q^{2} +(-10.0415 - 1.77059i) q^{4} +(1.58573 - 4.74188i) q^{5} +(-2.49919 - 1.74995i) q^{7} +(-6.04267 + 22.5515i) q^{8} +(-17.2778 - 7.50920i) q^{10} +(-8.21269 - 2.98918i) q^{11} +(-1.30944 - 14.9670i) q^{13} +(-7.38912 + 8.80601i) q^{14} +(44.3363 + 16.1371i) q^{16} +(6.46879 + 24.1418i) q^{17} +(-23.0066 + 13.2829i) q^{19} +(-24.3192 + 44.8081i) q^{20} +(-13.9168 + 29.8446i) q^{22} +(23.7975 - 16.6632i) q^{23} +(-19.9709 - 15.0387i) q^{25} -56.6083 q^{26} +(21.9973 + 21.9973i) q^{28} +(3.19342 + 3.80577i) q^{29} +(-2.35330 + 13.3462i) q^{31} +(35.6622 - 76.4778i) q^{32} +(92.7402 - 16.3526i) q^{34} +(-12.2611 + 9.07591i) q^{35} +(-5.80622 - 21.6691i) q^{37} +(42.3020 + 90.7169i) q^{38} +(97.3547 + 64.4144i) q^{40} +(10.7753 + 9.04151i) q^{41} +(10.1179 + 21.6979i) q^{43} +(77.1755 + 44.5573i) q^{44} +(-54.7302 - 94.7954i) q^{46} +(19.7104 + 13.8013i) q^{47} +(-13.5754 - 37.2980i) q^{49} +(-63.0058 + 70.0218i) q^{50} +(-13.3517 + 152.610i) q^{52} +(-35.7379 - 35.7379i) q^{53} +(-27.1975 + 34.2036i) q^{55} +(54.5659 - 45.7863i) q^{56} +(15.3335 - 10.7367i) q^{58} +(-7.15372 - 19.6547i) q^{59} +(-13.4180 - 76.0970i) q^{61} +(49.3221 + 13.2158i) q^{62} +(-111.904 - 64.6080i) q^{64} +(-73.0482 - 17.5245i) q^{65} +(-102.407 + 8.95949i) q^{67} +(-22.2112 - 253.875i) q^{68} +(30.0399 + 49.0023i) q^{70} +(12.6791 - 21.9608i) q^{71} +(-23.2289 + 86.6915i) q^{73} +(-83.2413 + 14.6777i) q^{74} +(254.541 - 92.6453i) q^{76} +(15.2942 + 21.8424i) q^{77} +(6.63920 + 7.91230i) q^{79} +(146.826 - 184.649i) q^{80} +(37.4756 - 37.4756i) q^{82} +(-69.0024 - 6.03693i) q^{83} +(124.736 + 7.60834i) q^{85} +(84.7654 - 30.8521i) q^{86} +(117.037 - 167.146i) q^{88} +(61.3185 - 35.4023i) q^{89} +(-22.9190 + 39.6969i) q^{91} +(-268.467 + 125.188i) q^{92} +(58.2757 - 69.4503i) q^{94} +(26.5035 + 130.158i) q^{95} +(-69.9225 + 32.6054i) q^{97} +(-144.455 + 38.7067i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 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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