LMFDB - Embedded newform 405.3.s.a.37.26

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			37.26
Character	$\chi$	$=$	405.37
Dual form			405.3.s.a.208.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.21433 + 0.193729i) q^{2} +(0.926495 + 0.163366i) q^{4} +(1.95462 + 4.60212i) q^{5} +(-4.75945 + 6.79720i) q^{7} +(-6.56828 - 1.75996i) q^{8} +(3.43660 + 10.5693i) q^{10} +(10.2854 + 3.74359i) q^{11} +(-8.91787 + 0.780213i) q^{13} +(-11.8558 + 14.1292i) q^{14} +(-17.7396 - 6.45668i) q^{16} +(2.30094 - 0.616536i) q^{17} +(-22.6505 + 13.0773i) q^{19} +(1.05911 + 4.58315i) q^{20} +(22.0501 + 10.2821i) q^{22} +(1.53390 + 2.19063i) q^{23} +(-17.3589 + 17.9907i) q^{25} -19.8983 q^{26} +(-5.52004 + 5.52004i) q^{28} +(18.9366 + 22.5678i) q^{29} +(-6.10711 + 34.6352i) q^{31} +(-13.3789 - 6.23870i) q^{32} +(5.21449 - 0.919455i) q^{34} +(-40.5844 - 8.61763i) q^{35} +(61.9402 - 16.5968i) q^{37} +(-52.6890 + 24.5693i) q^{38} +(-4.73890 - 33.6680i) q^{40} +(7.59358 + 6.37177i) q^{41} +(57.2506 - 26.6964i) q^{43} +(8.91781 + 5.14870i) q^{44} +(2.97217 + 5.14795i) q^{46} +(35.0118 - 50.0020i) q^{47} +(-6.79059 - 18.6570i) q^{49} +(-41.9238 + 36.4745i) q^{50} +(-8.38982 - 0.734014i) q^{52} +(-34.1539 + 34.1539i) q^{53} +(2.87563 + 54.6520i) q^{55} +(43.2242 - 36.2694i) q^{56} +(37.5599 + 53.6411i) q^{58} +(-20.8579 - 57.3066i) q^{59} +(-3.82205 - 21.6759i) q^{61} +(-20.2330 + 75.5106i) q^{62} +(36.9788 + 21.3497i) q^{64} +(-21.0216 - 39.5161i) q^{65} +(6.37962 + 72.9194i) q^{67} +(2.23253 - 0.195321i) q^{68} +(-88.1978 - 26.9446i) q^{70} +(-34.1068 + 59.0747i) q^{71} +(27.4196 + 7.34705i) q^{73} +(140.371 - 24.7513i) q^{74} +(-23.1219 + 8.41569i) q^{76} +(-74.3989 + 52.0946i) q^{77} +(-64.3561 - 76.6966i) q^{79} +(-4.95969 - 94.2600i) q^{80} +(15.5803 + 15.5803i) q^{82} +(9.53095 - 108.939i) q^{83} +(7.33483 + 9.38412i) q^{85} +(131.944 - 48.0236i) q^{86} +(-60.9689 - 42.6909i) q^{88} +(42.9194 - 24.7795i) q^{89} +(37.1409 - 64.3300i) q^{91} +(1.06327 + 2.28020i) q^{92} +(87.2144 - 103.938i) q^{94} +(-104.456 - 78.6791i) q^{95} +(-34.3548 - 73.6740i) q^{97} +(-11.4222 - 42.6283i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	2.21433	+	0.193729i	1.10716	+	0.0968644i	0.626042	−	0.779789i	$-0.284674\pi$
$2$	2.21433	+	0.193729i	1.10716	+	0.0968644i	0.481122	+	0.876653i	$0.340229\pi$
$3$		0			0
$3$		0			0
$4$	0.926495	+	0.163366i	0.231624	+	0.0408415i
$5$	1.95462	+	4.60212i	0.390923	+	0.920423i
$5$	1.95462	+	4.60212i	0.390923	+	0.920423i
$6$		0			0
$7$	−4.75945	+	6.79720i	−0.679922	+	0.971029i	0.319801	+	0.947485i	$0.396384\pi$
$7$	−4.75945	+	6.79720i	−0.679922	+	0.971029i	−0.999723	+	0.0235443i	$0.992505\pi$
$8$	−6.56828	−	1.75996i	−0.821035	−	0.219996i
$9$		0			0
$10$	3.43660	+	10.5693i	0.343660	+	1.05693i
$11$	10.2854	+	3.74359i	0.935038	+	0.340326i	0.764205	−	0.644974i	$-0.223132\pi$
$11$	10.2854	+	3.74359i	0.935038	+	0.340326i	0.170833	+	0.985300i	$0.445354\pi$
$12$		0			0
$13$	−8.91787	+	0.780213i	−0.685990	+	0.0600164i	−0.424822	−	0.905277i	$-0.639663\pi$
$13$	−8.91787	+	0.780213i	−0.685990	+	0.0600164i	−0.261168	+	0.965293i	$0.584108\pi$
$14$	−11.8558	+	14.1292i	−0.846844	+	1.00923i
$15$		0			0
$16$	−17.7396	−	6.45668i	−1.10872	−	0.403542i
$17$	2.30094	−	0.616536i	0.135350	−	0.0362668i	−0.190508	−	0.981686i	$-0.561014\pi$
$17$	2.30094	−	0.616536i	0.135350	−	0.0362668i	0.325858	+	0.945419i	$0.394347\pi$
$18$		0			0
$19$	−22.6505	+	13.0773i	−1.19213	+	0.688276i	−0.958789	−	0.284119i	$-0.908299\pi$
$19$	−22.6505	+	13.0773i	−1.19213	+	0.688276i	−0.233341	+	0.972395i	$0.574966\pi$
$20$	1.05911	+	4.58315i	0.0529556	+	0.229158i
$21$		0			0
$22$	22.0501	+	10.2821i	1.00228	+	0.467369i
$23$	1.53390	+	2.19063i	0.0666912	+	0.0952450i	0.851112	−	0.524984i	$-0.175929\pi$
$23$	1.53390	+	2.19063i	0.0666912	+	0.0952450i	−0.784421	+	0.620229i	$0.787040\pi$
$24$		0			0
$25$	−17.3589	+	17.9907i	−0.694358	+	0.719630i
$26$	−19.8983			−0.765318
$27$		0			0
$28$	−5.52004	+	5.52004i	−0.197144	+	0.197144i
$29$	18.9366	+	22.5678i	0.652987	+	0.778200i	0.986361	−	0.164595i	$-0.0526316\pi$
$29$	18.9366	+	22.5678i	0.652987	+	0.778200i	−0.333374	+	0.942795i	$0.608187\pi$
$30$		0			0
$31$	−6.10711	+	34.6352i	−0.197004	+	1.11726i	0.712533	+	0.701639i	$0.247548\pi$
$31$	−6.10711	+	34.6352i	−0.197004	+	1.11726i	−0.909536	+	0.415624i	$0.863563\pi$
$32$	−13.3789	−	6.23870i	−0.418092	−	0.194959i
$33$		0			0
$34$	5.21449	−	0.919455i	0.153367	−	0.0270428i
$35$	−40.5844	−	8.61763i	−1.15955	−	0.246218i
$36$		0			0
$37$	61.9402	−	16.5968i	1.67406	−	0.448563i	0.707859	−	0.706354i	$-0.249661\pi$
$37$	61.9402	−	16.5968i	1.67406	−	0.448563i	0.966201	+	0.257791i	$0.0829945\pi$
$38$	−52.6890	+	24.5693i	−1.38655	+	0.646561i
$39$		0			0
$40$	−4.73890	−	33.6680i	−0.118473	−	0.841701i
$41$	7.59358	+	6.37177i	0.185209	+	0.155409i	0.730678	−	0.682722i	$-0.239204\pi$
$41$	7.59358	+	6.37177i	0.185209	+	0.155409i	−0.545469	+	0.838131i	$0.683648\pi$
$42$		0			0
$43$	57.2506	−	26.6964i	1.33141	−	0.620847i	0.378924	−	0.925428i	$-0.376294\pi$
$43$	57.2506	−	26.6964i	1.33141	−	0.620847i	0.952486	+	0.304581i	$0.0985164\pi$
$44$	8.91781	+	5.14870i	0.202678	+	0.117016i
$45$		0			0
$46$	2.97217	+	5.14795i	0.0646124	+	0.111912i
$47$	35.0118	−	50.0020i	0.744931	−	1.06387i	−0.250474	−	0.968123i	$-0.580587\pi$
$47$	35.0118	−	50.0020i	0.744931	−	1.06387i	0.995406	−	0.0957488i	$-0.0305246\pi$
$48$		0			0
$49$	−6.79059	−	18.6570i	−0.138583	−	0.380755i
$50$	−41.9238	+	36.4745i	−0.838475	+	0.729490i
$51$		0			0
$52$	−8.38982	−	0.734014i	−0.161343	−	0.0141157i
$53$	−34.1539	+	34.1539i	−0.644414	+	0.644414i	−0.951637	−	0.307223i	$-0.900600\pi$
$53$	−34.1539	+	34.1539i	−0.644414	+	0.644414i	0.307223	+	0.951637i	$0.400600\pi$
$54$		0			0
$55$	2.87563	+	54.6520i	0.0522841	+	0.993672i
$56$	43.2242	−	36.2694i	0.771862	−	0.647669i
$57$		0			0
$58$	37.5599	+	53.6411i	0.647585	+	0.924847i
$59$	−20.8579	−	57.3066i	−0.353524	−	0.971299i	−0.981229	−	0.192847i	$-0.938228\pi$
$59$	−20.8579	−	57.3066i	−0.353524	−	0.971299i	0.627705	−	0.778451i	$-0.283994\pi$
$60$		0			0
$61$	−3.82205	−	21.6759i	−0.0626566	−	0.355343i	−0.999976	−	0.00687287i	$-0.997812\pi$
$61$	−3.82205	−	21.6759i	−0.0626566	−	0.355343i	0.937320	−	0.348470i	$-0.113299\pi$
$62$	−20.2330	+	75.5106i	−0.326339	+	1.21791i
$63$		0			0
$64$	36.9788	+	21.3497i	0.577794	+	0.333589i
$65$	−21.0216	−	39.5161i	−0.323410	−	0.607939i
$66$		0			0
$67$	6.37962	+	72.9194i	0.0952183	+	1.08835i	0.882042	+	0.471172i	$0.156169\pi$
$67$	6.37962	+	72.9194i	0.0952183	+	1.08835i	−0.786823	+	0.617178i	$0.788276\pi$
$68$	2.23253	−	0.195321i	0.0328314	−	0.00287237i
$69$		0			0
$70$	−88.1978	−	26.9446i	−1.25997	−	0.384924i
$71$	−34.1068	+	59.0747i	−0.480377	+	0.832038i	−0.999747	−	0.0225119i	$-0.992834\pi$
$71$	−34.1068	+	59.0747i	−0.480377	+	0.832038i	0.519369	+	0.854550i	$0.326167\pi$
$72$		0			0
$73$	27.4196	+	7.34705i	0.375610	+	0.100644i	0.441685	−	0.897170i	$-0.354381\pi$
$73$	27.4196	+	7.34705i	0.375610	+	0.100644i	−0.0660747	+	0.997815i	$0.521048\pi$
$74$	140.371	−	24.7513i	1.89691	−	0.334476i
$75$		0			0
$76$	−23.1219	+	8.41569i	−0.304236	+	0.110733i
$77$	−74.3989	+	52.0946i	−0.966219	+	0.676554i
$78$		0			0
$79$	−64.3561	−	76.6966i	−0.814634	−	0.970843i	0.185296	−	0.982683i	$-0.440676\pi$
$79$	−64.3561	−	76.6966i	−0.814634	−	0.970843i	−0.999930	+	0.0118396i	$0.996231\pi$
$80$	−4.95969	−	94.2600i	−0.0619961	−	1.17825i
$81$		0			0
$82$	15.5803	+	15.5803i	0.190004	+	0.190004i
$83$	9.53095	−	108.939i	0.114831	−	1.31252i	−0.692068	−	0.721832i	$-0.743300\pi$
$83$	9.53095	−	108.939i	0.114831	−	1.31252i	0.806899	−	0.590689i	$-0.201144\pi$
$84$		0			0
$85$	7.33483	+	9.38412i	0.0862921	+	0.110401i
$86$	131.944	−	48.0236i	1.53423	−	0.558414i
$87$		0			0
$88$	−60.9689	−	42.6909i	−0.692828	−	0.485124i
$89$	42.9194	−	24.7795i	0.482240	−	0.278421i	−0.239110	−	0.970993i	$-0.576856\pi$
$89$	42.9194	−	24.7795i	0.482240	−	0.278421i	0.721349	+	0.692571i	$0.243522\pi$
$90$		0			0
$91$	37.1409	−	64.3300i	0.408142	−	0.706923i
$92$	1.06327	+	2.28020i	0.0115573	+	0.0247848i
$93$		0			0
$94$	87.2144	−	103.938i	0.927813	−	1.10572i
$95$	−104.456	−	78.6791i	−1.09954	−	0.828201i
$96$		0			0
$97$	−34.3548	−	73.6740i	−0.354173	−	0.759526i	0.645819	−	0.763490i	$-0.276516\pi$
$97$	−34.3548	−	73.6740i	−0.354173	−	0.759526i	−0.999992	+	0.00396432i	$0.998738\pi$
$98$	−11.4222	−	42.6283i	−0.116553	−	0.434982i
$99$		0			0
$100$	−19.0221	+	13.8325i	−0.190221	+	0.138325i
$101$	1.90940	+	10.8287i	0.0189049	+	0.107215i	0.992800	−	0.119783i	$-0.0382199\pi$
$101$	1.90940	+	10.8287i	0.0189049	+	0.107215i	−0.973895	+	0.226998i	$0.927109\pi$
$102$		0			0
$103$	−3.71709	+	7.97133i	−0.0360883	+	0.0773915i	−0.923525	−	0.383537i	$-0.874706\pi$
$103$	−3.71709	+	7.97133i	−0.0360883	+	0.0773915i	0.887437	+	0.460929i	$0.152484\pi$
$104$	59.9482	+	10.5705i	0.576425	+	0.101639i
$105$		0			0
$106$	−82.2447	+	69.0115i	−0.775893	+	0.651052i
$107$	112.987	+	112.987i	1.05595	+	1.05595i	0.998339	+	0.0576110i	$0.0183483\pi$
$107$	112.987	+	112.987i	1.05595	+	1.05595i	0.0576110	+	0.998339i	$0.481652\pi$
$108$		0			0
$109$			16.9651i			0.155643i	0.996967	+	0.0778217i	$0.0247965\pi$
$109$			16.9651i			0.155643i	−0.996967	+	0.0778217i	$0.975204\pi$
$110$	−4.22007	+	121.575i	−0.0383642	+	1.10522i
$111$		0			0
$112$	128.318	−	89.8493i	1.14570	−	0.802226i
$113$	58.4147	−	125.271i	0.516944	−	1.10859i	−0.458571	−	0.888658i	$-0.651639\pi$
$113$	58.4147	−	125.271i	0.516944	−	1.10859i	0.975515	−	0.219932i	$-0.0705836\pi$
$114$		0			0
$115$	−7.08337	+	11.3410i	−0.0615945	+	0.0986176i
$116$	13.8579	+	24.0026i	0.119464	+	0.206919i
$117$		0			0
$118$	−35.0843	−	130.937i	−0.297325	−	1.10963i
$119$	−6.76051	+	18.5743i	−0.0568110	+	0.156087i
$120$		0			0
$121$	−0.916012	−	0.768626i	−0.00757035	−	0.00635228i
$122$	−4.26403	−	48.7381i	−0.0349511	−	0.399493i
$123$		0			0
$124$	−11.3164	+	31.0916i	−0.0912614	+	0.250739i
$125$	−116.726	−	44.7229i	−0.933805	−	0.357783i
$126$		0			0
$127$	−57.4505	+	214.408i	−0.452366	+	1.68825i	0.243353	+	0.969938i	$0.421753\pi$
$127$	−57.4505	+	214.408i	−0.452366	+	1.68825i	−0.695719	+	0.718314i	$0.744914\pi$
$128$	126.117	+	88.3078i	0.985285	+	0.689904i
$129$		0			0
$130$	−38.8935	−	91.5741i	−0.299180	−	0.704416i
$131$	−38.5218	+	218.468i	−0.294059	+	1.66769i	0.376942	+	0.926237i	$0.376976\pi$
$131$	−38.5218	+	218.468i	−0.294059	+	1.66769i	−0.671001	+	0.741456i	$0.734135\pi$
$132$		0			0
$133$	18.9151	−	216.200i	0.142219	−	1.62557i
$134$			162.704i			1.21421i
$135$		0			0
$136$	−16.1983			−0.119105
$137$	98.2291	+	8.59393i	0.717001	+	0.0627295i	0.439817	−	0.898087i	$-0.355043\pi$
$137$	98.2291	+	8.59393i	0.717001	+	0.0627295i	0.277184	+	0.960817i	$0.410599\pi$
$138$		0			0
$139$	−86.9760	−	15.3362i	−0.625727	−	0.110332i	−0.148211	−	0.988956i	$-0.547351\pi$
$139$	−86.9760	−	15.3362i	−0.625727	−	0.110332i	−0.477516	+	0.878623i	$0.658463\pi$
$140$	−36.1934	−	14.6143i	−0.258524	−	0.104388i
$141$		0			0
$142$	−86.9682	+	124.203i	−0.612452	+	0.874672i
$143$	−94.6448	−	25.3600i	−0.661852	−	0.177343i
$144$		0			0
$145$	−66.8458	+	131.260i	−0.461005	+	0.905241i
$146$	59.2926	+	21.5807i	0.406114	+	0.147813i
$147$		0			0
$148$	60.0986	−	5.25795i	0.406072	−	0.0355267i
$149$	123.868	−	147.621i	0.831331	−	0.990742i	−0.168656	−	0.985675i	$-0.553943\pi$
$149$	123.868	−	147.621i	0.831331	−	0.990742i	0.999987	−	0.00506714i	$-0.00161293\pi$
$150$		0			0
$151$	266.680	+	97.0637i	1.76610	+	0.642806i	1.00000		7.97203e-5i	$2.53758e-5\pi$
$151$	266.680	+	97.0637i	1.76610	+	0.642806i	0.766096	+	0.642727i	$0.222197\pi$
$152$	171.790	−	46.0310i	1.13020	−	0.302836i
$153$		0			0
$154$	−174.836	+	100.942i	−1.13530	+	0.655464i
$155$	−171.332	+	39.5928i	−1.10537	+	0.255438i
$156$		0			0
$157$	182.422	+	85.0646i	1.16192	+	0.541813i	0.905331	−	0.424707i	$-0.139623\pi$
$157$	182.422	+	85.0646i	1.16192	+	0.541813i	0.256591	+	0.966520i	$0.417401\pi$
$158$	−127.647	−	182.299i	−0.807894	−	1.15379i
$159$		0			0
$160$	2.56054	−	73.7657i	0.0160034	−	0.461036i
$161$	−22.1907			−0.137830
$162$		0			0
$163$	−74.5106	+	74.5106i	−0.457121	+	0.457121i	−0.897709	−	0.440589i	$-0.854770\pi$
$163$	−74.5106	+	74.5106i	−0.457121	+	0.457121i	0.440589	+	0.897709i	$0.354770\pi$
$164$	5.99448	+	7.14395i	0.0365517	+	0.0435606i
$165$		0			0
$166$	42.2093	−	239.381i	0.254273	−	1.44205i
$167$	27.1808	+	12.6746i	0.162759	+	0.0758960i	0.502291	−	0.864699i	$-0.332491\pi$
$167$	27.1808	+	12.6746i	0.162759	+	0.0758960i	−0.339531	+	0.940595i	$0.610268\pi$
$168$		0			0
$169$	−87.5128	+	15.4309i	−0.517827	+	0.0913069i
$170$	14.4238	+	22.2005i	0.0848456	+	0.130591i
$171$		0			0
$172$	57.4037	−	15.3813i	0.333743	−	0.0894260i
$173$	186.451	−	86.9434i	1.07775	−	0.502563i	0.199075	−	0.979984i	$-0.436206\pi$
$173$	186.451	−	86.9434i	1.07775	−	0.502563i	0.878674	+	0.477421i	$0.158428\pi$
$174$		0			0
$175$	−39.6676	−	203.618i	−0.226672	−	1.16353i
$176$	−158.288	−	132.819i	−0.899363	−	0.754655i
$177$		0			0
$178$	99.8381	−	46.5553i	0.560888	−	0.261546i
$179$	42.6513	+	24.6247i	0.238275	+	0.137568i	0.614384	−	0.789007i	$-0.289405\pi$
$179$	42.6513	+	24.6247i	0.238275	+	0.137568i	−0.376109	+	0.926576i	$0.622738\pi$
$180$		0			0
$181$	−33.4818	−	57.9921i	−0.184982	−	0.320398i	0.758588	−	0.651570i	$-0.225889\pi$
$181$	−33.4818	−	57.9921i	−0.184982	−	0.320398i	−0.943570	+	0.331172i	$0.892556\pi$
$182$	94.7048	−	135.253i	0.520356	−	0.743146i
$183$		0			0
$184$	−6.21963	−	17.0883i	−0.0338024	−	0.0928712i
$185$	197.450	+	252.616i	1.06730	+	1.36549i
$186$		0			0
$187$	25.9742	+	2.27245i	0.138900	+	0.0121521i
$188$	40.6068	−	40.6068i	0.215994	−	0.215994i
$189$		0			0
$190$	−216.058	−	194.458i	−1.13715	−	1.02346i
$191$	−277.961	+	233.237i	−1.45529	+	1.22113i	−0.526688	+	0.850058i	$0.676567\pi$
$191$	−277.961	+	233.237i	−1.45529	+	1.22113i	−0.928603	+	0.371076i	$0.878989\pi$
$192$		0			0
$193$	−1.11055	−	1.58604i	−0.00575416	−	0.00821780i	0.816265	−	0.577678i	$-0.196041\pi$
$193$	−1.11055	−	1.58604i	−0.00575416	−	0.00821780i	−0.822019	+	0.569460i	$0.807152\pi$
$194$	−61.8000	−	169.794i	−0.318557	−	0.875227i
$195$		0			0
$196$	−3.24353	−	18.3950i	−0.0165486	−	0.0938518i
$197$	−36.7752	+	137.247i	−0.186676	+	0.696685i	0.807589	+	0.589745i	$0.200772\pi$
$197$	−36.7752	+	137.247i	−0.186676	+	0.696685i	−0.994265	+	0.106940i	$0.965895\pi$
$198$		0			0
$199$	151.039	+	87.2026i	0.758992	+	0.438204i	0.828934	−	0.559347i	$-0.188948\pi$
$199$	151.039	+	87.2026i	0.758992	+	0.438204i	−0.0699420	+	0.997551i	$0.522281\pi$
$200$	145.681	−	87.6171i	0.728407	−	0.438085i
$201$		0			0
$202$	2.13020	+	24.3483i	0.0105455	+	0.120536i
$203$	−243.526	+	21.3058i	−1.19964	+	0.104954i
$204$		0			0
$205$	−14.4811	+	47.4009i	−0.0706395	+	0.231224i
$206$	−9.77514	+	16.9310i	−0.0474521	+	0.0821895i
$207$		0			0
$208$	163.237	+	43.7392i	0.784793	+	0.210285i
$209$	−281.925	+	49.7110i	−1.34892	+	0.237852i
$210$		0			0
$211$	−235.974	+	85.8877i	−1.11836	+	0.407051i	−0.834054	−	0.551682i	$-0.813986\pi$
$211$	−235.974	+	85.8877i	−1.11836	+	0.407051i	−0.284308	+	0.958733i	$0.591764\pi$
$212$	−37.2230	+	26.0639i	−0.175580	+	0.122943i
$213$		0			0
$214$	228.301	+	272.079i	1.06683	+	1.27139i
$215$	234.763	+	211.293i	1.09192	+	0.982758i
$216$		0			0
$217$	−206.356	−	206.356i	−0.950948	−	0.950948i
$218$	−3.28663	+	37.5664i	−0.0150763	+	0.172323i
$219$		0			0
$220$	−6.26402	+	51.1045i	−0.0284728	+	0.232293i
$221$	−20.0385	+	7.29341i	−0.0906719	+	0.0330019i
$222$		0			0
$223$	260.413	+	182.343i	1.16777	+	0.817681i	0.986177	−	0.165693i	$-0.0529860\pi$
$223$	260.413	+	182.343i	1.16777	+	0.817681i	0.181592	+	0.983374i	$0.441875\pi$
$224$	106.082	−	61.2465i	0.473581	−	0.273422i
$225$		0			0
$226$	153.618	−	266.074i	0.679725	−	1.17732i
$227$	−188.950	−	405.205i	−0.832381	−	1.78505i	−0.573660	−	0.819094i	$-0.694477\pi$
$227$	−188.950	−	405.205i	−0.832381	−	1.78505i	−0.258721	−	0.965952i	$-0.583301\pi$
$228$		0			0
$229$	26.8340	−	31.9795i	0.117179	−	0.139648i	−0.704266	−	0.709936i	$-0.748724\pi$
$229$	26.8340	−	31.9795i	0.117179	−	0.139648i	0.821445	+	0.570288i	$0.193168\pi$
$230$	−17.8820	+	23.7405i	−0.0777478	+	0.103220i
$231$		0			0
$232$	−84.6625	−	181.559i	−0.364925	−	0.782584i
$233$	−25.5129	−	95.2155i	−0.109497	−	0.408650i	0.889319	−	0.457287i	$-0.151179\pi$
$233$	−25.5129	−	95.2155i	−0.109497	−	0.408650i	−0.998817	+	0.0486371i	$0.984512\pi$
$234$		0			0
$235$	298.550	+	63.3935i	1.27042	+	0.269760i
$236$	−9.96279	−	56.5018i	−0.0422152	−	0.239414i
$237$		0			0
$238$	−18.5684	+	39.8200i	−0.0780184	+	0.167311i
$239$	98.1358	+	17.3040i	0.410610	+	0.0724016i	0.375138	−	0.926969i	$-0.377595\pi$
$239$	98.1358	+	17.3040i	0.410610	+	0.0724016i	0.0354721	+	0.999371i	$0.488707\pi$
$240$		0			0
$241$	−118.754	+	99.6468i	−0.492757	+	0.413472i	−0.855013	−	0.518606i	$-0.826451\pi$
$241$	−118.754	+	99.6468i	−0.492757	+	0.413472i	0.362256	+	0.932079i	$0.382007\pi$
$242$	−1.87945	−	1.87945i	−0.00776632	−	0.00776632i
$243$		0			0
$244$		−	20.7070i		−	0.0848649i
$245$	72.5887	−	67.7184i	0.296280	−	0.276401i
$246$		0			0
$247$	191.791	−	134.293i	0.776481	−	0.543698i
$248$	101.070	−	216.745i	0.407540	−	0.873972i
$249$		0			0
$250$	−249.805	−	121.644i	−0.999219	−	0.486577i
$251$	8.98206	+	15.5574i	0.0357851	+	0.0619816i	0.883363	−	0.468689i	$-0.155273\pi$
$251$	8.98206	+	15.5574i	0.0357851	+	0.0619816i	−0.847578	+	0.530671i	$0.821940\pi$
$252$		0			0
$253$	7.57596	+	28.2739i	0.0299445	+	0.111754i
$254$	−168.751	+	463.640i	−0.664375	+	1.82536i
$255$		0			0
$256$	131.317	+	110.188i	0.512958	+	0.430423i
$257$	−0.883925	−	10.1033i	−0.00343939	−	0.0393125i	0.994281	−	0.106795i	$-0.0340589\pi$
$257$	−0.883925	−	10.1033i	−0.00343939	−	0.0393125i	−0.997720	+	0.0674825i	$0.978503\pi$
$258$		0			0
$259$	−181.990	+	500.012i	−0.702662	+	1.93055i
$260$	−13.0209	−	40.0457i	−0.0500802	−	0.154022i
$261$		0			0
$262$	−127.623	+	476.297i	−0.487112	+	1.81793i
$263$	−12.8003	−	8.96289i	−0.0486704	−	0.0340794i	0.548988	−	0.835830i	$-0.315013\pi$
$263$	−12.8003	−	8.96289i	−0.0486704	−	0.0340794i	−0.597658	+	0.801751i	$0.703902\pi$
$264$		0			0
$265$	−223.938	−	90.4226i	−0.845050	−	0.341217i
$266$	83.7685	−	475.075i	0.314919	−	1.78599i
$267$		0			0
$268$	−6.00187	+	68.6017i	−0.0223950	+	0.255976i
$269$		−	302.818i		−	1.12572i	−0.826553	−	0.562859i	$-0.809702\pi$
$269$		−	302.818i		−	1.12572i	0.826553	−	0.562859i	$-0.190298\pi$
$270$		0			0
$271$	−467.978			−1.72686			−0.863428	−	0.504471i	$-0.831687\pi$
$271$	−467.978			−1.72686			−0.863428	+	0.504471i	$0.831687\pi$
$272$	−44.7985	−	3.91936i	−0.164701	−	0.0144094i
$273$		0			0
$274$	215.847	+	38.0596i	0.787762	+	0.138904i
$275$	−245.894	+	120.058i	−0.894160	+	0.436573i
$276$		0			0
$277$	107.574	−	153.631i	0.388353	−	0.554626i	−0.576607	−	0.817022i	$-0.695624\pi$
$277$	107.574	−	153.631i	0.388353	−	0.554626i	0.964960	+	0.262396i	$0.0845126\pi$
$278$	−189.622	−	50.8092i	−0.682095	−	0.182767i
$279$		0			0
$280$	251.403	+	128.030i	0.897868	+	0.457251i
$281$	202.070	+	73.5475i	0.719110	+	0.261735i	0.675548	−	0.737316i	$-0.263907\pi$
$281$	202.070	+	73.5475i	0.719110	+	0.261735i	0.0435623	+	0.999051i	$0.486129\pi$
$282$		0			0
$283$	−121.219	+	10.6053i	−0.428335	+	0.0374745i	−0.299285	−	0.954164i	$-0.596748\pi$
$283$	−121.219	+	10.6053i	−0.428335	+	0.0374745i	−0.129050	+	0.991638i	$0.541193\pi$
$284$	−41.2506	+	49.1605i	−0.145248	+	0.173100i
$285$		0			0
$286$	−204.662	−	74.4908i	−0.715601	−	0.260457i
$287$	−79.4515	+	21.2890i	−0.276835	+	0.0741776i
$288$		0			0
$289$	−245.367	+	141.663i	−0.849021	+	0.490183i
$290$	−173.447	+	277.703i	−0.598095	+	0.957596i
$291$		0			0
$292$	24.2038	+	11.2864i	0.0828898	+	0.0386521i
$293$	101.496	+	144.952i	0.346404	+	0.494716i	0.954114	−	0.299443i	$-0.0968007\pi$
$293$	101.496	+	144.952i	0.346404	+	0.494716i	−0.607710	+	0.794159i	$0.707912\pi$
$294$		0			0
$295$	222.963	−	208.003i	0.755805	−	0.705095i
$296$	−436.050			−1.47314
$297$		0			0
$298$	302.884	−	302.884i	1.01639	−	1.01639i
$299$	−15.3883	−	18.3390i	−0.0514658	−	0.0613345i
$300$		0			0
$301$	−91.0208	+	516.205i	−0.302395	+	1.71497i
$302$	571.714	+	266.595i	1.89309	+	0.882764i
$303$		0			0
$304$	486.245	−	85.7382i	1.59949	−	0.282034i
$305$	92.2846	−	59.9577i	0.302572	−	0.196583i
$306$		0			0
$307$	106.733	−	28.5989i	0.347664	−	0.0931562i	−0.0807616	−	0.996733i	$-0.525735\pi$
$307$	106.733	−	28.5989i	0.347664	−	0.0931562i	0.428425	+	0.903577i	$0.359069\pi$
$308$	−77.4407	+	36.1112i	−0.251431	+	0.117244i
$309$		0			0
$310$	−387.056	+	54.4796i	−1.24857	+	0.175741i
$311$	67.0720	+	56.2801i	0.215665	+	0.180965i	0.744220	−	0.667934i	$-0.232821\pi$
$311$	67.0720	+	56.2801i	0.215665	+	0.180965i	−0.528555	+	0.848899i	$0.677266\pi$
$312$		0			0
$313$	54.1726	−	25.2611i	0.173075	−	0.0807063i	−0.334150	−	0.942520i	$-0.608449\pi$
$313$	54.1726	−	25.2611i	0.173075	−	0.0807063i	0.507225	+	0.861814i	$0.330671\pi$
$314$	387.462	+	223.701i	1.23396	+	0.712425i
$315$		0			0
$316$	−47.0960	−	81.5726i	−0.149038	−	0.258141i
$317$	105.485	−	150.648i	0.332760	−	0.475231i	−0.617552	−	0.786530i	$-0.711875\pi$
$317$	105.485	−	150.648i	0.332760	−	0.475231i	0.950312	+	0.311300i	$0.100764\pi$
$318$		0			0
$319$	110.287	+	303.010i	0.345726	+	0.949875i
$320$	−25.9745	+	211.911i	−0.0811704	+	0.662222i
$321$		0			0
$322$	−49.1375	−	4.29898i	−0.152601	−	0.0133509i
$323$	−44.0548	+	44.0548i	−0.136393	+	0.136393i
$324$		0			0
$325$	140.768	−	173.983i	0.433133	−	0.535332i
$326$	−179.426	+	150.556i	−0.550387	+	0.461829i
$327$		0			0
$328$	−38.6627	−	55.2160i	−0.117874	−	0.168341i
$329$	173.237	+	475.964i	0.526556	+	1.44670i
$330$		0			0
$331$	27.2809	+	154.718i	0.0824198	+	0.467426i	0.997884	+	0.0650254i	$0.0207129\pi$
$331$	27.2809	+	154.718i	0.0824198	+	0.467426i	−0.915464	+	0.402400i	$0.868176\pi$
$332$	26.6273	−	99.3746i	0.0802029	−	0.299321i
$333$		0			0
$334$	57.7319	+	33.3315i	0.172850	+	0.0997949i
$335$	−323.114	+	171.889i	−0.964519	+	0.513102i
$336$		0			0
$337$	34.5167	+	394.528i	0.102423	+	1.17070i	0.857293	+	0.514829i	$0.172145\pi$
$337$	34.5167	+	394.528i	0.102423	+	1.17070i	−0.754869	+	0.655875i	$0.772300\pi$
$338$	−196.772	+	17.2153i	−0.582165	+	0.0509328i
$339$		0			0
$340$	5.26264	+	9.89260i	0.0154783	+	0.0290959i
$341$	−192.474	+	333.375i	−0.564440	+	0.977638i
$342$		0			0
$343$	−233.606	−	62.5944i	−0.681066	−	0.182491i
$344$	−423.023	+	74.5904i	−1.22972	+	0.216832i
$345$		0			0
$346$	429.707	−	156.400i	1.24193	−	0.452024i
$347$	−276.053	+	193.294i	−0.795541	+	0.557044i	−0.899184	−	0.437571i	$-0.855839\pi$
$347$	−276.053	+	193.294i	−0.795541	+	0.557044i	0.103643	+	0.994615i	$0.466950\pi$
$348$		0			0
$349$	34.7252	+	41.3839i	0.0994991	+	0.118578i	0.813496	−	0.581570i	$-0.197561\pi$
$349$	34.7252	+	41.3839i	0.0994991	+	0.118578i	−0.713997	+	0.700149i	$0.753117\pi$
$350$	−48.3905	−	458.563i	−0.138259	−	1.31018i
$351$		0			0
$352$	−114.253	−	114.253i	−0.324582	−	0.324582i
$353$	22.2925	−	254.804i	0.0631514	−	0.721824i	−0.896943	−	0.442147i	$-0.854217\pi$
$353$	22.2925	−	254.804i	0.0631514	−	0.721824i	0.960094	−	0.279677i	$-0.0902275\pi$
$354$		0			0
$355$	−338.534	−	41.4951i	−0.953618	−	0.116888i
$356$	43.8127	−	15.9465i	0.123069	−	0.0447936i
$357$		0			0
$358$	89.6734	+	62.7900i	0.250484	+	0.175391i
$359$	−102.875	+	59.3949i	−0.286560	+	0.165445i	−0.636389	−	0.771368i	$-0.719573\pi$
$359$	−102.875	+	59.3949i	−0.286560	+	0.165445i	0.349830	+	0.936813i	$0.386240\pi$
$360$		0			0
$361$	161.529	−	279.777i	0.447449	−	0.775004i
$362$	−62.9049	−	134.900i	−0.173771	−	0.372652i
$363$		0			0
$364$	44.9202	−	53.5338i	0.123407	−	0.147071i
$365$	19.7827	+	140.549i	0.0541993	+	0.385065i
$366$		0			0
$367$	−166.553	−	357.174i	−0.453823	−	0.973226i	−0.991504	−	0.130077i	$-0.958477\pi$
$367$	−166.553	−	357.174i	−0.453823	−	0.973226i	0.537681	−	0.843148i	$-0.319300\pi$
$368$	−13.0665	−	48.7648i	−0.0355068	−	0.132513i
$369$		0			0
$370$	388.280	+	597.626i	1.04941	+	1.61521i
$371$	−69.5972	−	394.705i	−0.187594	−	1.06390i
$372$		0			0
$373$	23.6413	−	50.6990i	0.0633816	−	0.135922i	−0.872065	−	0.489389i	$-0.837220\pi$
$373$	23.6413	−	50.6990i	0.0633816	−	0.135922i	0.935447	+	0.353467i	$0.114997\pi$
$374$	57.0752	+	10.0639i	0.152608	+	0.0269088i
$375$		0			0
$376$	−317.969	+	266.807i	−0.845662	+	0.709594i
$377$	−186.482	−	186.482i	−0.494648	−	0.494648i
$378$		0			0
$379$		−	82.8766i		−	0.218672i	−0.994005	−	0.109336i	$-0.965128\pi$
$379$		−	82.8766i		−	0.218672i	0.994005	−	0.109336i	$-0.0348724\pi$
$380$	−83.9245	−	89.9603i	−0.220854	−	0.236738i
$381$		0			0
$382$	−660.681	+	462.614i	−1.72953	+	1.21103i
$383$	−130.902	+	280.720i	−0.341781	+	0.732952i	−0.999799	−	0.0200506i	$-0.993617\pi$
$383$	−130.902	+	280.720i	−0.341781	+	0.732952i	0.658018	+	0.753002i	$0.271395\pi$
$384$		0			0
$385$	−385.167	−	240.567i	−1.00043	−	0.624850i
$386$	−2.15187	−	3.72715i	−0.00557480	−	0.00965583i
$387$		0			0
$388$	−19.7937	−	73.8710i	−0.0510146	−	0.190389i
$389$	−97.2536	+	267.202i	−0.250009	+	0.686895i	0.749676	+	0.661805i	$0.230209\pi$
$389$	−97.2536	+	267.202i	−0.250009	+	0.686895i	−0.999685	+	0.0250898i	$0.992013\pi$
$390$		0			0
$391$	4.88002	+	4.09482i	0.0124809	+	0.0104727i
$392$	11.7668	+	134.496i	0.0300174	+	0.343101i
$393$		0			0
$394$	−108.021	+	296.786i	−0.274165	+	0.753263i
$395$	227.175	−	446.087i	0.575127	−	1.12933i
$396$		0			0
$397$	168.158	−	627.574i	0.423572	−	1.58079i	−0.343450	−	0.939171i	$-0.611596\pi$
$397$	168.158	−	627.574i	0.423572	−	1.58079i	0.767022	−	0.641621i	$-0.221738\pi$
$398$	317.557	+	222.356i	0.797882	+	0.558683i
$399$		0			0
$400$	424.101	−	207.067i	1.06025	−	0.517668i
$401$	48.8338	−	276.950i	0.121780	−	0.690649i	−0.861388	−	0.507947i	$-0.830405\pi$
$401$	48.8338	−	276.950i	0.121780	−	0.690649i	0.983168	−	0.182702i	$-0.0584844\pi$
$402$		0			0
$403$	27.4397	−	313.637i	0.0680885	−	0.778255i
$404$			10.3447i			0.0256057i
$405$		0			0
$406$	−543.374			−1.33836
$407$	699.213	+	61.1732i	1.71797	+	0.150303i
$408$		0			0
$409$	−696.105	−	122.742i	−1.70197	−	0.300103i	−0.763587	−	0.645705i	$-0.776564\pi$
$409$	−696.105	−	122.742i	−1.70197	−	0.300103i	−0.938381	+	0.345602i	$0.887675\pi$
$410$	−41.2488	+	102.156i	−0.100607	+	0.249161i
$411$		0			0
$412$	−4.74611	+	6.77815i	−0.0115197	+	0.0164518i
$413$	488.797	+	130.973i	1.18353	+	0.317125i
$414$		0			0
$415$	519.980	−	169.072i	1.25296	−	0.407402i
$416$	124.179	+	45.1975i	0.298508	+	0.108648i
$417$		0			0
$418$	−633.906	+	55.4596i	−1.51652	+	0.132678i
$419$	−139.446	+	166.185i	−0.332806	+	0.396623i	−0.906333	−	0.422564i	$-0.861130\pi$
$419$	−139.446	+	166.185i	−0.332806	+	0.396623i	0.573527	+	0.819186i	$0.305575\pi$
$420$		0			0
$421$	546.181	+	198.794i	1.29734	+	0.472194i	0.896130	−	0.443792i	$-0.146367\pi$
$421$	546.181	+	198.794i	1.29734	+	0.472194i	0.401211	+	0.915985i	$0.368589\pi$
$422$	−539.164	+	144.469i	−1.27764	+	0.342343i
$423$		0			0
$424$	284.442	−	164.223i	0.670855	−	0.387318i
$425$	−28.8500	+	52.0981i	−0.0678824	+	0.122584i
$426$		0			0
$427$	165.527	+	77.1864i	0.387650	+	0.180764i
$428$	86.2234	+	123.140i	0.201456	+	0.287710i
$429$		0			0
$430$	478.909	+	513.352i	1.11374	+	1.19384i
$431$	197.302			0.457777			0.228889	−	0.973453i	$-0.426491\pi$
$431$	197.302			0.457777			0.228889	+	0.973453i	$0.426491\pi$
$432$		0			0
$433$	−46.8682	+	46.8682i	−0.108241	+	0.108241i	−0.759153	−	0.650912i	$-0.774387\pi$
$433$	−46.8682	+	46.8682i	−0.108241	+	0.108241i	0.650912	+	0.759153i	$0.274387\pi$
$434$	−416.963	−	496.917i	−0.960743	−	1.14497i
$435$		0			0
$436$	−2.77152	+	15.7181i	−0.00635671	+	0.0360507i
$437$	−63.3910	−	29.5597i	−0.145059	−	0.0676423i
$438$		0			0
$439$	356.651	−	62.8872i	0.812417	−	0.143251i	0.248021	−	0.968755i	$-0.420220\pi$
$439$	356.651	−	62.8872i	0.812417	−	0.143251i	0.564397	+	0.825504i	$0.309109\pi$
$440$	77.2976	−	364.030i	0.175676	−	0.827341i
$441$		0			0
$442$	−45.7848	+	12.2680i	−0.103585	+	0.0277556i
$443$	497.142	−	231.821i	1.12222	−	0.523299i	0.229226	−	0.973373i	$-0.426380\pi$
$443$	497.142	−	231.821i	1.12222	−	0.523299i	0.892991	+	0.450075i	$0.148603\pi$
$444$		0			0
$445$	197.929	+	149.085i	0.444784	+	0.335023i
$446$	541.314	+	454.217i	1.21371	+	1.01842i
$447$		0			0
$448$	−321.117	+	149.739i	−0.716779	+	0.334240i
$449$	220.408	+	127.252i	0.490885	+	0.283413i	0.724942	−	0.688810i	$-0.241867\pi$
$449$	220.408	+	127.252i	0.490885	+	0.283413i	−0.234056	+	0.972223i	$0.575200\pi$
$450$		0			0
$451$	54.2499	+	93.9635i	0.120288	+	0.208345i
$452$	74.5858	−	106.520i	0.165013	−	0.235663i
$453$		0			0
$454$	−339.899	−	933.864i	−0.748675	−	2.05697i
$455$	368.650	+	45.1864i	0.810220	+	0.0993109i
$456$		0			0
$457$	70.2693	+	6.14777i	0.153762	+	0.0134525i	0.163777	−	0.986497i	$-0.447632\pi$
$457$	70.2693	+	6.14777i	0.153762	+	0.0134525i	−0.0100147	+	0.999950i	$0.503188\pi$
$458$	65.6146	−	65.6146i	0.143263	−	0.143263i
$459$		0			0
$460$	−8.41544	+	9.35022i	−0.0182944	+	0.0203266i
$461$	470.717	−	394.978i	1.02108	−	0.856786i	0.0313151	−	0.999510i	$-0.490030\pi$
$461$	470.717	−	394.978i	1.02108	−	0.856786i	0.989763	+	0.142724i	$0.0455860\pi$
$462$		0			0
$463$	68.7580	+	98.1967i	0.148506	+	0.212088i	0.886512	−	0.462706i	$-0.153121\pi$
$463$	68.7580	+	98.1967i	0.148506	+	0.212088i	−0.738006	+	0.674794i	$0.764233\pi$
$464$	−190.215	−	522.611i	−0.409946	−	1.12632i
$465$		0			0
$466$	−38.0480	−	215.781i	−0.0816481	−	0.463050i
$467$	132.100	−	493.003i	0.282869	−	1.05568i	−0.667514	−	0.744597i	$-0.732642\pi$
$467$	132.100	−	493.003i	0.282869	−	1.05568i	0.950383	−	0.311083i	$-0.100692\pi$
$468$		0			0
$469$	−526.012	−	303.693i	−1.12156	−	0.647533i
$470$	648.806	+	198.212i	1.38044	+	0.421727i
$471$		0			0
$472$	36.1429	+	413.115i	0.0765739	+	0.875244i
$473$	688.787	−	60.2611i	1.45621	−	0.127402i
$474$		0			0
$475$	157.919	−	634.506i	0.332461	−	1.33580i
$476$	−9.29799	+	16.1046i	−0.0195336	+	0.0338332i
$477$		0			0
$478$	213.953	+	57.3284i	0.447600	+	0.119934i
$479$	−31.7508	+	5.59852i	−0.0662856	+	0.0116879i	−0.206693	−	0.978406i	$-0.566270\pi$
$479$	−31.7508	+	5.59852i	−0.0662856	+	0.0116879i	0.140407	+	0.990094i	$0.455159\pi$
$480$		0			0
$481$	−539.426	+	196.335i	−1.12147	+	0.408181i
$482$	−282.266	+	197.645i	−0.585614	+	0.410051i
$483$		0			0
$484$	−0.723113	−	0.861773i	−0.00149404	−	0.00178052i
$485$	271.906	−	302.109i	0.560631	−	0.622905i
$486$		0			0
$487$	−508.915	−	508.915i	−1.04500	−	1.04500i	−0.998939	−	0.0460613i	$-0.985333\pi$
$487$	−508.915	−	508.915i	−1.04500	−	1.04500i	−0.0460613	−	0.998939i	$-0.514667\pi$
$488$	−13.0446	+	149.100i	−0.0267307	+	0.305533i
$489$		0			0
$490$	173.854	−	135.888i	0.354805	−	0.277323i
$491$	181.036	−	65.8918i	0.368709	−	0.134199i	−0.151019	−	0.988531i	$-0.548255\pi$
$491$	181.036	−	65.8918i	0.368709	−	0.134199i	0.519728	+	0.854332i	$0.326033\pi$
$492$		0			0
$493$	57.4860	+	40.2521i	0.116604	+	0.0816473i
$494$	450.705	−	260.215i	0.912358	−	0.526750i
$495$		0			0
$496$	331.966	−	574.982i	0.669286	−	1.15924i
$497$	−239.213	−	512.994i	−0.481314	−	1.03218i
$498$		0			0
$499$	137.298	−	163.626i	0.275147	−	0.327907i	−0.610720	−	0.791846i	$-0.709120\pi$
$499$	137.298	−	163.626i	0.275147	−	0.327907i	0.885867	+	0.463939i	$0.153564\pi$
$500$	−100.839	−	60.5045i	−0.201679	−	0.121009i
$501$		0			0
$502$	16.8753	+	36.1892i	0.0336162	+	0.0720901i
$503$	−95.0065	−	354.569i	−0.188880	−	0.704909i	−0.993767	−	0.111480i	$-0.964441\pi$
$503$	−95.0065	−	354.569i	−0.188880	−	0.704909i	0.804887	−	0.593428i	$-0.202226\pi$
$504$		0			0
$505$	−46.1029	+	29.9533i	−0.0912929	+	0.0593134i
$506$	11.2982	+	64.0753i	0.0223285	+	0.126631i
$507$		0			0
$508$	−88.2545	+	189.262i	−0.173729	+	0.372564i
$509$	−167.773	−	29.5829i	−0.329613	−	0.0581196i	0.00639300	−	0.999980i	$-0.497965\pi$
$509$	−167.773	−	29.5829i	−0.329613	−	0.0581196i	−0.336006	+	0.941860i	$0.609076\pi$
$510$		0			0
$511$	−180.441	+	151.408i	−0.353114	+	0.296298i
$512$	−166.031	−	166.031i	−0.324280	−	0.324280i
$513$		0			0
$514$		−	22.5433i		−	0.0438585i
$515$	−43.9505	−	1.52560i	−0.0853407	−	0.00296233i
$516$		0			0
$517$	547.297	−	383.222i	1.05860	−	0.741241i
$518$	−499.851	+	1071.93i	−0.964964	+	2.06937i
$519$		0			0
$520$	68.5291	+	296.550i	0.131787	+	0.570288i
$521$	−71.1832	−	123.293i	−0.136628	−	0.236647i	0.789590	−	0.613634i	$-0.210293\pi$
$521$	−71.1832	−	123.293i	−0.136628	−	0.236647i	−0.926218	+	0.376988i	$0.876960\pi$
$522$		0			0
$523$	−37.4797	−	139.876i	−0.0716629	−	0.267450i	0.920793	−	0.390052i	$-0.127543\pi$
$523$	−37.4797	−	139.876i	−0.0716629	−	0.267450i	−0.992456	+	0.122602i	$0.960876\pi$
$524$	−71.3804	+	196.116i	−0.136222	+	0.374267i
$525$		0			0
$526$	−26.6078	−	22.3266i	−0.0505851	−	0.0424460i
$527$	7.30170	+	83.4588i	0.0138552	+	0.158366i
$528$		0			0
$529$	178.483	−	490.377i	0.337396	−	0.926989i
$530$	−478.356	−	243.609i	−0.902558	−	0.459639i
$531$		0			0
$532$	52.8445	−	197.218i	0.0993318	−	0.370711i
$533$	−72.6899	−	50.8980i	−0.136379	−	0.0954935i
$534$		0			0
$535$	−299.132	+	740.823i	−0.559126	+	1.38472i
$536$	86.4325	−	490.183i	0.161255	−	0.914521i
$537$		0			0
$538$	58.6645	−	670.539i	0.109042	−	1.24635i
$539$		−	217.316i		−	0.403184i
$540$		0			0
$541$	697.034			1.28842			0.644208	−	0.764850i	$-0.277187\pi$
$541$	697.034			1.28842			0.644208	+	0.764850i	$0.277187\pi$
$542$	−1036.26	−	90.6608i	−1.91192	−	0.167271i
$543$		0			0
$544$	−34.6305	−	6.10630i	−0.0636591	−	0.0112248i
$545$	−78.0755	+	33.1603i	−0.143258	+	0.0608446i
$546$		0			0
$547$	76.0594	−	108.624i	0.139048	−	0.198582i	−0.743588	−	0.668638i	$-0.766878\pi$
$547$	76.0594	−	108.624i	0.139048	−	0.198582i	0.882636	+	0.470057i	$0.155766\pi$
$548$	89.6048	+	24.0095i	0.163512	+	0.0438130i
$549$		0			0
$550$	−567.749	+	218.210i	−1.03227	+	0.396746i
$551$	−724.048	−	263.532i	−1.31406	−	0.478280i
$552$		0			0
$553$	827.622	−	72.4076i	1.49660	−	0.130936i
$554$	267.967	−	319.350i	0.483694	−	0.576445i
$555$		0			0
$556$	−78.0774	−	28.4178i	−0.140427	−	0.0511112i
$557$	36.4649	−	9.77073i	0.0654665	−	0.0175417i	−0.225937	−	0.974142i	$-0.572544\pi$
$557$	36.4649	−	9.77073i	0.0654665	−	0.0175417i	0.291404	+	0.956600i	$0.405878\pi$
$558$		0			0
$559$	−489.725	+	282.743i	−0.876073	+	0.505801i
$560$	664.309	+	414.914i	1.18627	+	0.740917i
$561$		0			0
$562$	433.201	+	202.005i	0.770821	+	0.359440i
$563$	−548.647	−	783.549i	−0.974506	−	1.39174i	−0.919429	−	0.393257i	$-0.871348\pi$
$563$	−548.647	−	783.549i	−0.974506	−	1.39174i	−0.0550777	−	0.998482i	$-0.517541\pi$
$564$		0			0
$565$	690.688	+	23.9750i	1.22246	+	0.0424336i
$566$	−270.473			−0.477868
$567$		0			0
$568$	327.992	−	327.992i	0.577451	−	0.577451i
$569$	79.1792	+	94.3621i	0.139155	+	0.165838i	0.831121	−	0.556092i	$-0.187700\pi$
$569$	79.1792	+	94.3621i	0.139155	+	0.165838i	−0.691966	+	0.721930i	$0.743255\pi$
$570$		0			0
$571$	22.5624	−	127.958i	0.0395139	−	0.224095i	−0.958656	−	0.284568i	$-0.908150\pi$
$571$	22.5624	−	127.958i	0.0395139	−	0.224095i	0.998170	+	0.0604733i	$0.0192610\pi$
$572$	−83.5450	−	38.9577i	−0.146058	−	0.0681078i
$573$		0			0
$574$	−180.056	+	31.7488i	−0.313687	+	0.0553114i
$575$	−66.0380	−	10.4311i	−0.114849	−	0.0181411i
$576$		0			0
$577$	969.281	−	259.718i	1.67986	−	0.450118i	0.712120	−	0.702058i	$-0.247735\pi$
$577$	969.281	−	259.718i	1.67986	−	0.450118i	0.967743	+	0.251940i	$0.0810685\pi$
$578$	−570.768	+	266.153i	−0.987488	+	0.460473i
$579$		0			0
$580$	−83.3757	+	110.691i	−0.143751	+	0.190847i
$581$	695.120	+	583.275i	1.19642	+	1.00392i
$582$		0			0
$583$	−479.146	+	223.429i	−0.821862	+	0.383241i
$584$	−167.169	−	96.5149i	−0.286248	−	0.165265i
$585$		0			0
$586$	196.665	+	340.634i	0.335606	+	0.581287i
$587$	−351.488	+	501.977i	−0.598787	+	0.855156i	−0.998097	−	0.0616594i	$-0.980361\pi$
$587$	−351.488	+	501.977i	−0.598787	+	0.855156i	0.399310	+	0.916816i	$0.369250\pi$
$588$		0			0
$589$	−314.604	−	864.367i	−0.534132	−	1.46752i
$590$	534.009	−	417.393i	0.905100	−	0.707446i
$591$		0			0
$592$	−1205.95	−	105.507i	−2.03708	−	0.178222i
$593$	−387.205	+	387.205i	−0.652959	+	0.652959i	−0.953704	−	0.300746i	$-0.902764\pi$
$593$	−387.205	+	387.205i	−0.652959	+	0.652959i	0.300746	+	0.953704i	$0.402764\pi$
$594$		0			0
$595$	−98.6955	+	5.19307i	−0.165875	+	0.00872785i
$596$	138.880	−	116.534i	0.233019	−	0.195527i
$597$		0			0
$598$	−30.5219	−	43.5898i	−0.0510400	−	0.0728927i
$599$	−296.186	−	813.763i	−0.494467	−	1.35854i	−0.896554	−	0.442935i	$-0.853937\pi$
$599$	−296.186	−	813.763i	−0.494467	−	1.35854i	0.402087	−	0.915601i	$-0.368285\pi$
$600$		0			0
$601$	−82.6600	−	468.788i	−0.137537	−	0.780014i	−0.973059	−	0.230556i	$-0.925945\pi$
$601$	−82.6600	−	468.788i	−0.137537	−	0.780014i	0.835522	−	0.549458i	$-0.185166\pi$
$602$	−301.554	+	1125.41i	−0.500920	+	1.86946i
$603$		0			0
$604$	231.221	+	133.496i	0.382816	+	0.221019i
$605$	1.74685	−	5.71796i	0.00288736	−	0.00945118i
$606$		0			0
$607$	20.3033	+	232.067i	0.0334485	+	0.382318i	0.994406	+	0.105623i	$0.0336837\pi$
$607$	20.3033	+	232.067i	0.0334485	+	0.382318i	−0.960958	+	0.276695i	$0.910761\pi$
$608$	384.624	−	33.6503i	0.632606	−	0.0553458i
$609$		0			0
$610$	215.964	−	114.888i	0.354039	−	0.188341i
$611$	−273.218	+	473.228i	−0.447166	+	0.774514i
$612$		0			0
$613$	−160.912	−	43.1162i	−0.262499	−	0.0703364i	0.125169	−	0.992135i	$-0.460053\pi$
$613$	−160.912	−	43.1162i	−0.262499	−	0.0703364i	−0.387668	+	0.921799i	$0.626719\pi$
$614$	241.882	−	42.6503i	0.393944	−	0.0694630i
$615$		0			0
$616$	580.357	−	211.233i	0.942138	−	0.342910i
$617$	964.973	−	675.682i	1.56398	−	1.09511i	0.611183	−	0.791490i	$-0.290694\pi$
$617$	964.973	−	675.682i	1.56398	−	1.09511i	0.952794	−	0.303619i	$-0.0981948\pi$
$618$		0			0
$619$	537.579	+	640.661i	0.868463	+	1.03499i	0.999051	+	0.0435574i	$0.0138691\pi$
$619$	537.579	+	640.661i	0.868463	+	1.03499i	−0.130588	+	0.991437i	$0.541686\pi$
$620$	−165.206	+	8.69269i	−0.266462	+	0.0140205i
$621$		0			0
$622$	137.616	+	137.616i	0.221248	+	0.221248i
$623$	−35.8413	+	409.668i	−0.0575302	+	0.657574i
$624$		0			0
$625$	−22.3337	−	624.601i	−0.0357340	−	0.999361i
$626$	124.850	−	45.4416i	0.199440	−	0.0725904i
$627$		0			0
$628$	155.116	+	108.613i	0.247000	+	0.172951i
$629$	132.288	−	76.3767i	0.210315	−	0.121426i
$630$		0			0
$631$	−179.602	+	311.080i	−0.284631	+	0.492996i	−0.972520	−	0.232821i	$-0.925205\pi$
$631$	−179.602	+	311.080i	−0.284631	+	0.492996i	0.687888	+	0.725816i	$0.258538\pi$
$632$	287.725	+	617.029i	0.455262	+	0.976312i
$633$		0			0
$634$	262.763	−	313.149i	0.414453	−	0.493926i
$635$	−1099.02	+	154.692i	−1.73075	+	0.243609i
$636$		0			0
$637$	75.1140	+	161.083i	0.117918	+	0.252877i
$638$	185.509	+	692.330i	0.290767	+	1.08516i
$639$		0			0
$640$	−159.893	+	753.011i	−0.249833	+	1.17658i
$641$	−26.1194	−	148.130i	−0.0407479	−	0.231093i	0.957632	−	0.287995i	$-0.0929887\pi$
$641$	−26.1194	−	148.130i	−0.0407479	−	0.231093i	−0.998380	+	0.0569025i	$0.981878\pi$
$642$		0			0
$643$	−458.197	+	982.606i	−0.712592	+	1.52816i	0.131122	+	0.991366i	$0.458142\pi$
$643$	−458.197	+	982.606i	−0.712592	+	1.52816i	−0.843714	+	0.536793i	$0.819636\pi$
$644$	−20.5596	−	3.62521i	−0.0319248	−	0.00562920i
$645$		0			0
$646$	−106.087	+	89.0172i	−0.164221	+	0.137798i
$647$	479.015	+	479.015i	0.740364	+	0.740364i	0.972648	−	0.232284i	$-0.0746199\pi$
$647$	479.015	+	479.015i	0.740364	+	0.740364i	−0.232284	+	0.972648i	$0.574620\pi$
$648$		0			0
$649$		−	667.506i		−	1.02851i
$650$	345.413	−	357.984i	0.531404	−	0.550745i
$651$		0			0
$652$	−81.2062	+	56.8612i	−0.124549	+	0.0872105i
$653$	−471.486	+	1011.10i	−0.722031	+	1.54840i	0.110162	+	0.993914i	$0.464863\pi$
$653$	−471.486	+	1011.10i	−0.722031	+	1.54840i	−0.832193	+	0.554486i	$0.812915\pi$
$654$		0			0
$655$	−1080.71	+	249.739i	−1.64994	+	0.381281i
$656$	−93.5665	−	162.062i	−0.142632	−	0.247046i
$657$		0			0
$658$	291.395	+	1087.50i	0.442850	+	1.65274i
$659$	−33.9839	+	93.3700i	−0.0515689	+	0.141684i	−0.962803	−	0.270205i	$-0.912909\pi$
$659$	−33.9839	+	93.3700i	−0.0515689	+	0.141684i	0.911234	+	0.411889i	$0.135131\pi$
$660$		0			0
$661$	243.240	+	204.103i	0.367989	+	0.308779i	0.807965	−	0.589230i	$-0.200569\pi$
$661$	243.240	+	204.103i	0.367989	+	0.308779i	−0.439977	+	0.898009i	$0.645013\pi$
$662$	30.4357	+	347.882i	0.0459754	+	0.525501i
$663$		0			0
$664$	−254.331	+	698.769i	−0.383029	+	1.05236i
$665$	1031.95	−	335.539i	1.55181	−	0.504571i
$666$		0			0
$667$	−20.3909	+	76.1000i	−0.0305711	+	0.114093i
$668$	23.1123	+	16.1834i	0.0345992	+	0.0242266i
$669$		0			0
$670$	−748.781	+	318.023i	−1.11758	+	0.474661i
$671$	41.8343	−	237.254i	0.0623462	−	0.353583i
$672$		0			0
$673$	7.30411	−	83.4864i	0.0108531	−	0.124051i	−0.988835	−	0.149012i	$-0.952391\pi$
$673$	7.30411	−	83.4864i	0.0108531	−	0.124051i	0.999688	+	0.0249611i	$0.00794619\pi$
$674$			880.301i			1.30608i
$675$		0			0
$676$	−83.6010			−0.123670
$677$	−482.612	−	42.2231i	−0.712868	−	0.0623679i	−0.275048	−	0.961430i	$-0.588694\pi$
$677$	−482.612	−	42.2231i	−0.712868	−	0.0623679i	−0.437820	+	0.899063i	$0.644249\pi$
$678$		0			0
$679$	664.287	+	117.132i	0.978331	+	0.172506i
$680$	−31.6615	−	74.5465i	−0.0465610	−	0.109627i
$681$		0			0
$682$	−490.785	+	700.914i	−0.719626	+	1.02773i
$683$	−26.3109	−	7.04997i	−0.0385225	−	0.0103221i	0.239506	−	0.970895i	$-0.423014\pi$
$683$	−26.3109	−	7.04997i	−0.0385225	−	0.0103221i	−0.278029	+	0.960573i	$0.589681\pi$
$684$		0			0
$685$	152.450	+	468.860i	0.222555	+	0.684467i
$686$	−505.153	−	183.861i	−0.736375	−	0.268019i
$687$		0			0
$688$	−1187.97	+	103.934i	−1.72670	+	0.151067i
$689$	277.933	−	331.228i	0.403386	−	0.480737i
$690$		0			0
$691$	348.531	+	126.855i	0.504386	+	0.183581i	0.581666	−	0.813428i	$-0.302401\pi$
$691$	348.531	+	126.855i	0.504386	+	0.183581i	−0.0772797	+	0.997009i	$0.524623\pi$
$692$	186.949	−	50.0929i	0.270158	−	0.0723885i
$693$		0			0
$694$	−648.718	+	374.538i	−0.934753	+	0.539680i
$695$	−99.4257	−	430.250i	−0.143059	−	0.619065i
$696$		0			0
$697$	21.4008	+	9.97937i	0.0307042	+	0.0143176i
$698$	68.8758	+	98.3648i	0.0986759	+	0.140924i
$699$		0			0
$700$	−3.48753	−	195.132i	−0.00498219	−	0.278760i
$701$	1351.23			1.92758			0.963789	−	0.266664i	$-0.0859216\pi$
$701$	1351.23			1.92758			0.963789	+	0.266664i	$0.0859216\pi$
$702$		0			0
$703$	−1185.93	+	1185.93i	−1.68696	+	1.68696i
$704$	300.418	+	358.024i	0.426730	+	0.508557i
$705$		0			0
$706$	98.7257	−	559.901i	0.139838	−	0.793061i
$707$	−82.6928	−	38.5603i	−0.116963	−	0.0545407i
$708$		0			0
$709$	1062.88	−	187.415i	1.49913	−	0.264337i	0.636935	−	0.770917i	$-0.280202\pi$
$709$	1062.88	−	187.415i	1.49913	−	0.264337i	0.862193	+	0.506580i	$0.169091\pi$
$710$	−741.588	−	157.468i	−1.04449	−	0.221785i
$711$		0			0
$712$	−325.517	+	87.2221i	−0.457187	+	0.122503i
$713$	−85.2407	+	39.7484i	−0.119552	+	0.0557481i
$714$		0			0
$715$	−68.2846	−	485.136i	−0.0955030	−	0.678511i
$716$	35.4933	+	29.7824i	0.0495717	+	0.0415956i
$717$		0			0
$718$	−239.306	+	111.590i	−0.333295	+	0.155418i
$719$	133.672	+	77.1756i	0.185914	+	0.107337i	0.590068	−	0.807353i	$-0.299101\pi$
$719$	133.672	+	77.1756i	0.185914	+	0.107337i	−0.404154	+	0.914691i	$0.632434\pi$
$720$		0			0
$721$	−36.4914	−	63.2050i	−0.0506122	−	0.0876629i
$722$	411.879	−	588.225i	0.570470	−	0.814716i
$723$		0			0
$724$	−21.5467	−	59.1992i	−0.0297607	−	0.0817668i
$725$	−734.732	−	51.0692i	−1.01342	−	0.0704403i
$726$		0			0
$727$	453.346	+	39.6627i	0.623585	+	0.0545566i	0.394569	−	0.918866i	$-0.370894\pi$
$727$	453.346	+	39.6627i	0.623585	+	0.0545566i	0.229016	+	0.973423i	$0.426449\pi$
$728$	−357.170	+	357.170i	−0.490619	+	0.490619i
$729$		0			0
$730$	16.5772	+	315.054i	0.0227085	+	0.431580i
$731$	115.271	−	96.7240i	0.157690	−	0.132317i
$732$		0			0
$733$	29.7166	+	42.4397i	0.0405411	+	0.0578987i	0.838911	−	0.544269i	$-0.183193\pi$
$733$	29.7166	+	42.4397i	0.0405411	+	0.0578987i	−0.798370	+	0.602167i	$0.794304\pi$
$734$	−299.608	−	823.167i	−0.408186	−	1.12148i
$735$		0			0
$736$	−6.85522	−	38.8779i	−0.00931416	−	0.0528232i
$737$	−207.363	+	773.889i	−0.281361	+	1.05005i
$738$		0			0
$739$	−1051.21	−	606.914i	−1.42247	−	0.821264i	−0.425961	−	0.904742i	$-0.640064\pi$
$739$	−1051.21	−	606.914i	−1.42247	−	0.821264i	−0.996510	+	0.0834781i	$0.973397\pi$
$740$	141.667	+	266.304i	0.191443	+	0.359870i
$741$		0			0
$742$	−77.6454	−	887.491i	−0.104643	−	1.19608i
$743$	241.327	−	21.1134i	0.324801	−	0.0284164i	0.0764106	−	0.997076i	$-0.475654\pi$
$743$	241.327	−	21.1134i	0.324801	−	0.0284164i	0.248390	+	0.968660i	$0.420098\pi$
$744$		0			0
$745$	921.482	+	281.515i	1.23689	+	0.377873i
$746$	62.1715	−	107.684i	0.0833398	−	0.144349i
$747$		0			0
$748$	23.6937	+	6.34872i	0.0316761	+	0.00848759i
$749$	−1305.75	+	230.239i	−1.74332	+	0.307395i
$750$		0			0
$751$	932.424	−	339.375i	1.24158	−	0.451897i	0.364029	−	0.931387i	$-0.381401\pi$
$751$	932.424	−	339.375i	1.24158	−	0.451897i	0.877547	+	0.479491i	$0.159179\pi$
$752$	−943.941	+	660.955i	−1.25524	+	0.878929i
$753$		0			0
$754$	−376.806	−	449.060i	−0.499743	−	0.595570i
$755$	74.5593	+	1417.02i	0.0987541	+	1.87684i
$756$		0			0
$757$	159.288	+	159.288i	0.210420	+	0.210420i	0.804446	−	0.594026i	$-0.202462\pi$
$757$	159.288	+	159.288i	0.210420	+	0.210420i	−0.594026	+	0.804446i	$0.702462\pi$
$758$	16.0556	−	183.516i	0.0211815	−	0.242106i
$759$		0			0
$760$	547.624	+	700.625i	0.720558	+	0.921875i
$761$	−1023.53	+	372.536i	−1.34499	+	0.489535i	−0.911380	−	0.411567i	$-0.864982\pi$
$761$	−1023.53	+	372.536i	−1.34499	+	0.489535i	−0.433607	+	0.901102i	$0.642759\pi$
$762$		0			0
$763$	−115.315	−	80.7447i	−0.151134	−	0.105825i
$764$	−295.632	+	170.683i	−0.386953	+	0.223407i
$765$		0			0
$766$	−344.244	+	596.248i	−0.449405	+	0.778392i
$767$	230.720	+	494.780i	0.300808	+	0.645084i
$768$		0			0
$769$	698.674	−	832.648i	0.908549	−	1.08277i	−0.0876922	−	0.996148i	$-0.527949\pi$
$769$	698.674	−	832.648i	0.908549	−	1.08277i	0.996241	−	0.0866193i	$-0.0276064\pi$
$770$	−806.282	−	607.313i	−1.04712	−	0.788718i
$771$		0			0
$772$	−0.769818	−	1.65088i	−0.000997174	−	0.00213845i
$773$	−160.753	−	599.939i	−0.207960	−	0.776118i	−0.988527	−	0.151045i	$-0.951736\pi$
$773$	−160.753	−	599.939i	−0.207960	−	0.776118i	0.780567	−	0.625072i	$-0.214931\pi$
$774$		0			0
$775$	−517.099	−	711.102i	−0.667225	−	0.917550i
$776$	95.9879	+	544.375i	0.123696	+	0.701514i
$777$		0			0
$778$	−267.116	+	572.833i	−0.343337	+	0.736289i
$779$	−255.323	−	45.0204i	−0.327758	−	0.0577926i
$780$		0			0
$781$	−571.954	+	479.926i	−0.732335	+	0.614502i
$782$	10.0127	+	10.0127i	0.0128039	+	0.0128039i
$783$		0			0
$784$			374.812i			0.478076i
$785$	−34.9129	+	1005.79i	−0.0444750	+	1.28127i
$786$		0			0
$787$	−514.207	+	360.051i	−0.653376	+	0.457499i	−0.852676	−	0.522440i	$-0.825022\pi$
$787$	−514.207	+	360.051i	−0.653376	+	0.457499i	0.199301	+	0.979938i	$0.436133\pi$
$788$	−56.4936	+	121.151i	−0.0716923	+	0.153745i
$789$		0			0
$790$	589.461	−	943.773i	0.746153	−	1.19465i
$791$	573.468	+	993.276i	0.724991	+	1.25572i
$792$		0			0
$793$	50.9964	+	190.321i	0.0643082	+	0.240002i
$794$	493.936	−	1357.08i	0.622086	−	1.70917i
$795$		0			0
$796$	125.691	+	105.467i	0.157904	+	0.132497i
$797$	−110.300	−	1260.73i	−0.138394	−	1.58185i	−0.674874	−	0.737933i	$-0.735802\pi$
$797$	−110.300	−	1260.73i	−0.138394	−	1.58185i	0.536480	−	0.843913i	$-0.319754\pi$
$798$		0			0
$799$	49.7321	−	136.638i	0.0622429	−	0.171011i
$800$	344.483	−	132.400i	0.430604	−	0.165500i
$801$		0			0
$802$	161.787	−	603.799i	0.201730	−	0.752866i
$803$	254.517	+	178.215i	0.316958	+	0.221936i
$804$		0			0
$805$	−43.3743	−	102.124i	−0.0538811	−	0.126862i
$806$	121.521	−	689.180i	0.150770	−	0.855061i
$807$		0			0
$808$	6.51673	−	74.4866i	0.00806526	−	0.0921863i
$809$		−	817.617i		−	1.01065i	−0.862929	−	0.505326i	$-0.831372\pi$
$809$		−	817.617i		−	1.01065i	0.862929	−	0.505326i	$-0.168628\pi$
$810$		0			0
$811$	−3.09205			−0.00381264			−0.00190632	−	0.999998i	$-0.500607\pi$
$811$	−3.09205			−0.00381264			−0.00190632	+	0.999998i	$0.500607\pi$
$812$	−229.106	−	20.0442i	−0.282150	−	0.0246850i
$813$		0			0
$814$	1536.44	+	270.915i	1.88751	+	0.332820i
$815$	−488.546	−	197.267i	−0.599443	−	0.242045i
$816$		0			0
$817$	−947.638	+	1353.37i	−1.15990	+	1.65651i
$818$	−1517.63	−	406.647i	−1.85529	−	0.497124i
$819$		0			0
$820$	−21.1604	+	41.5510i	−0.0258053	+	0.0506719i
$821$	−447.576	−	162.904i	−0.545159	−	0.198422i	0.0547353	−	0.998501i	$-0.482569\pi$
$821$	−447.576	−	162.904i	−0.545159	−	0.198422i	−0.599894	+	0.800079i	$0.704791\pi$
$822$		0			0
$823$	461.104	−	40.3413i	0.560272	−	0.0490174i	0.196497	−	0.980504i	$-0.437043\pi$
$823$	461.104	−	40.3413i	0.560272	−	0.0490174i	0.363775	+	0.931487i	$0.381488\pi$
$824$	38.4441	−	45.8159i	0.0466555	−	0.0556019i
$825$		0			0
$826$	1056.98	+	384.711i	1.27964	+	0.465752i
$827$	−307.391	+	82.3651i	−0.371694	+	0.0995950i	−0.439830	−	0.898081i	$-0.644961\pi$
$827$	−307.391	+	82.3651i	−0.371694	+	0.0995950i	0.0681365	+	0.997676i	$0.478295\pi$
$828$		0			0
$829$	120.093	−	69.3356i	0.144865	−	0.0836377i	−0.425816	−	0.904810i	$-0.640013\pi$
$829$	120.093	−	69.3356i	0.144865	−	0.0836377i	0.570680	+	0.821172i	$0.306680\pi$
$830$	1184.16	−	273.646i	1.42670	−	0.329694i
$831$		0			0
$832$	−346.429	−	161.543i	−0.416381	−	0.194162i
$833$	−27.1275	−	38.7420i	−0.0325660	−	0.0465090i
$834$		0			0
$835$	−5.20202	+	149.863i	−0.00622996	+	0.179477i
$836$	−269.323			−0.322157
$837$		0			0
$838$	−340.973	+	340.973i	−0.406890	+	0.406890i
$839$	813.216	+	969.153i	0.969268	+	1.15513i	0.987867	+	0.155302i	$0.0496349\pi$
$839$	813.216	+	969.153i	0.969268	+	1.15513i	−0.0185992	+	0.999827i	$0.505921\pi$
$840$		0			0
$841$	−4.67146	+	26.4932i	−0.00555465	+	0.0315020i
$842$	1170.91	+	546.005i	1.39063	+	0.648462i
$843$		0			0
$844$	−232.660	+	41.0243i	−0.275664	+	0.0486070i
$845$	−242.069	−	372.583i	−0.286472	−	0.440926i
$846$		0			0
$847$	9.58422	−	2.56808i	0.0113155	−	0.00303198i
$848$	826.398	−	385.356i	0.974526	−	0.454429i
$849$		0			0
$850$	−73.9763	+	109.773i	−0.0870310	+	0.129145i
$851$	131.368	+	110.230i	0.154368	+	0.129531i
$852$		0			0
$853$	−1432.03	+	667.765i	−1.67881	+	0.782843i	−0.680046	+	0.733169i	$0.738040\pi$
$853$	−1432.03	+	667.765i	−1.67881	+	0.782843i	−0.998765	+	0.0496738i	$0.984182\pi$
$854$	351.577	+	202.983i	0.411683	+	0.237685i
$855$		0			0
$856$	−543.275	−	940.980i	−0.634667	−	1.09928i
$857$	106.121	−	151.557i	0.123829	−	0.176846i	−0.752451	−	0.658648i	$-0.771129\pi$
$857$	106.121	−	151.557i	0.123829	−	0.176846i	0.876280	+	0.481802i	$0.160018\pi$
$858$		0			0
$859$	224.945	+	618.032i	0.261869	+	0.719478i	0.999041	+	0.0437739i	$0.0139381\pi$
$859$	224.945	+	618.032i	0.261869	+	0.719478i	−0.737173	+	0.675704i	$0.763840\pi$
$860$	182.989	+	234.114i	0.212778	+	0.272226i
$861$		0			0
$862$	436.892	+	38.2231i	0.506835	+	0.0443423i
$863$	1010.20	−	1010.20i	1.17057	−	1.17057i	0.188492	−	0.982075i	$-0.439640\pi$
$863$	1010.20	−	1010.20i	1.17057	−	1.17057i	0.982075	−	0.188492i	$-0.0603600\pi$
$864$		0			0
$865$	764.563	+	688.127i	0.883888	+	0.795522i
$866$	−112.861	+	94.7020i	−0.130325	+	0.109356i
$867$		0			0
$868$	−157.476	−	224.899i	−0.181424	−	0.259100i
$869$	−374.809	−	1029.78i	−0.431311	−	1.18502i
$870$		0			0
$871$	−113.785	−	645.309i	−0.130638	−	0.740883i
$872$	29.8580	−	111.432i	0.0342408	−	0.127789i
$873$		0			0
$874$	−134.642	−	77.7356i	−0.154053	−	0.0889423i
$875$	859.541	−	580.551i	0.982332	−	0.663487i
$876$		0			0
$877$	−138.564	−	1583.79i	−0.157997	−	1.80592i	−0.499795	−	0.866144i	$-0.666591\pi$
$877$	−138.564	−	1583.79i	−0.157997	−	1.80592i	0.341797	−	0.939774i	$-0.388964\pi$
$878$	801.927	−	70.1595i	0.913356	−	0.0799083i
$879$		0			0
$880$	301.858	−	988.070i	0.343020	−	1.12281i
$881$	30.9598	−	53.6239i	0.0351416	−	0.0608671i	−0.847920	−	0.530125i	$-0.822145\pi$
$881$	30.9598	−	53.6239i	0.0351416	−	0.0608671i	0.883061	+	0.469258i	$0.155478\pi$
$882$		0			0
$883$	1221.46	+	327.290i	1.38331	+	0.370657i	0.872322	−	0.488931i	$-0.162613\pi$
$883$	1221.46	+	327.290i	1.38331	+	0.370657i	0.510988	+	0.859588i	$0.329280\pi$
$884$	−19.7570	+	3.48370i	−0.0223496	+	0.00394084i
$885$		0			0
$886$	1145.75	−	417.018i	1.29317	−	0.470675i
$887$	−250.884	+	175.671i	−0.282846	+	0.198051i	−0.706387	−	0.707826i	$-0.749676\pi$
$887$	−250.884	+	175.671i	−0.282846	+	0.198051i	0.423541	+	0.905877i	$0.360787\pi$
$888$		0			0
$889$	−1183.94	−	1410.97i	−1.33177	−	1.58714i
$890$	409.398	+	368.469i	0.459998	+	0.414010i
$891$		0			0
$892$	211.482	+	211.482i	0.237088	+	0.237088i
$893$	−139.144	+	1590.43i	−0.155817	+	1.78099i
$894$		0			0
$895$	−29.9590	+	244.418i	−0.0334737	+	0.273093i
$896$	−1200.49	+	436.943i	−1.33983	+	0.487660i
$897$		0			0
$898$	463.403	+	324.478i	0.516039	+	0.361334i
$899$	−897.288	+	518.049i	−0.998095	+	0.576251i
$900$		0			0
$901$	−57.5291	+	99.6434i	−0.0638503	+	0.110592i
$902$	101.924	+	218.576i	0.112997	+	0.242324i
$903$		0			0
$904$	−604.156	+	720.005i	−0.668314	+	0.796465i
$905$	201.442	−	267.439i	0.222588	−	0.295513i
$906$		0			0
$907$	−439.998	−	943.579i	−0.485114	−	1.04033i	−0.984731	−	0.174083i	$-0.944304\pi$
$907$	−439.998	−	943.579i	−0.485114	−	1.04033i	0.499617	−	0.866246i	$-0.333474\pi$
$908$	−108.865	−	406.289i	−0.119895	−	0.447455i
$909$		0			0
$910$	807.559	+	171.476i	0.887428	+	0.188435i
$911$	−65.8449	−	373.425i	−0.0722776	−	0.409907i	−0.999384	−	0.0351074i	$-0.988823\pi$
$911$	−65.8449	−	373.425i	−0.0722776	−	0.409907i	0.927106	−	0.374799i	$-0.122288\pi$
$912$		0			0
$913$	505.853	−	1084.81i	0.554056	−	1.18818i
$914$	154.409	+	27.2264i	0.168937	+	0.0297882i
$915$		0			0
$916$	30.0859	−	25.2451i	0.0328448	−	0.0275601i
$917$	−1301.63	−	1301.63i	−1.41944	−	1.41944i
$918$		0			0
$919$			1242.02i			1.35149i	0.737135	+	0.675745i	$0.236178\pi$
$919$			1242.02i			1.35149i	−0.737135	+	0.675745i	$0.763822\pi$
$920$	66.4854	−	62.0245i	0.0722667	−	0.0674180i
$921$		0			0
$922$	1118.84	−	783.421i	1.21349	−	0.849697i
$923$	258.069	−	553.431i	0.279598	−	0.599600i
$924$		0			0
$925$	−776.628	+	1402.45i	−0.839598	+	1.51617i
$926$	133.229	+	230.760i	0.143876	+	0.249201i
$927$		0			0
$928$	−112.558	−	420.073i	−0.121291	−	0.452665i
$929$	246.952	−	678.494i	0.265825	−	0.730349i	−0.732922	−	0.680312i	$-0.761844\pi$
$929$	246.952	−	678.494i	0.265825	−	0.730349i	0.998747	−	0.0500361i	$-0.0159337\pi$
$930$		0			0
$931$	397.792	+	333.787i	0.427274	+	0.358526i
$932$	−8.08260	−	92.3846i	−0.00867232	−	0.0991251i
$933$		0			0
$934$	388.021	−	1066.08i	0.415440	−	1.14141i
$935$	40.3115	+	123.978i	0.0431139	+	0.132597i
$936$		0			0
$937$	63.1470	−	235.668i	0.0673928	−	0.251513i	−0.924008	−	0.382373i	$-0.875107\pi$
$937$	63.1470	−	235.668i	0.0673928	−	0.251513i	0.991401	+	0.130859i	$0.0417737\pi$
$938$	−1105.93	−	774.380i	−1.17903	−	0.825565i
$939$		0			0
$940$	266.248	+	107.507i	0.283243	+	0.114369i
$941$	−135.021	+	765.742i	−0.143487	+	0.813754i	0.825083	+	0.565012i	$0.191128\pi$
$941$	−135.021	+	765.742i	−0.143487	+	0.813754i	−0.968570	+	0.248742i	$0.919983\pi$
$942$		0			0
$943$	−2.31044	+	26.4084i	−0.00245009	+	0.0280047i
$944$			1151.27i			1.21956i
$945$		0			0
$946$	1536.88			1.62460
$947$	765.633	+	66.9842i	0.808482	+	0.0707331i	0.483899	−	0.875124i	$-0.339220\pi$
$947$	765.633	+	66.9842i	0.808482	+	0.0707331i	0.324584	+	0.945857i	$0.394776\pi$
$948$		0			0
$949$	−250.256	−	44.1269i	−0.263705	−	0.0464984i
$950$	472.606	−	1374.41i	0.497480	−	1.44675i
$951$		0			0
$952$	77.0951	−	110.103i	0.0809823	−	0.115655i
$953$	1207.46	+	323.539i	1.26701	+	0.339496i	0.828886	−	0.559417i	$-0.188975\pi$
$953$	1207.46	+	323.539i	1.26701	+	0.339496i	0.438128	+	0.898913i	$0.355642\pi$
$954$		0			0
$955$	−1616.69	−	823.319i	−1.69287	−	0.862114i
$956$	88.0954	+	32.0641i	0.0921500	+	0.0335399i
$957$		0			0
$958$	−71.3913	+	6.24593i	−0.0745212	+	0.00651976i
$959$	−525.932	+	626.781i	−0.548417	+	0.653578i
$960$		0			0
$961$	−259.253	−	94.3605i	−0.269774	−	0.0981899i
$962$	−1232.50	+	330.248i	−1.28119	+	0.343293i
$963$		0			0
$964$	−126.304	+	72.9218i	−0.131021	+	0.0756450i
$965$	5.12841	−	8.21099i	0.00531442	−	0.00850880i
$966$		0			0
$967$	323.258	+	150.738i	0.334290	+	0.155882i	0.582514	−	0.812821i	$-0.302069\pi$
$967$	323.258	+	150.738i	0.334290	+	0.155882i	−0.248224	+	0.968703i	$0.579847\pi$
$968$	4.66387	+	6.66070i	0.00481805	+	0.00688089i
$969$		0			0
$970$	660.617	−	616.293i	0.681048	−	0.635354i
$971$	−1720.12			−1.77149			−0.885745	−	0.464172i	$-0.846352\pi$
$971$	−1720.12			−1.77149			−0.885745	+	0.464172i	$0.846352\pi$
$972$		0			0
$973$	518.202	−	518.202i	0.532581	−	0.532581i
$974$	−1028.31	−	1225.50i	−1.05576	−	1.25821i
$975$		0			0
$976$	−72.1530	+	409.200i	−0.0739272	+	0.419262i
$977$	1417.23	+	660.867i	1.45060	+	0.676425i	0.978713	−	0.205235i	$-0.0657958\pi$
$977$	1417.23	+	660.867i	1.45060	+	0.676425i	0.471886	+	0.881660i	$0.343574\pi$
$978$		0			0
$979$	534.208	−	94.1952i	0.545667	−	0.0962157i
$980$	78.3159	−	50.8822i	0.0799142	−	0.0519206i
$981$		0			0
$982$	413.639	−	110.834i	0.421221	−	0.112866i
$983$	736.233	−	343.311i	0.748966	−	0.349248i	−0.0103711	−	0.999946i	$-0.503301\pi$
$983$	736.233	−	343.311i	0.748966	−	0.349248i	0.759337	+	0.650698i	$0.225524\pi$
$984$		0			0
$985$	−703.508	+	99.0214i	−0.714222	+	0.100529i
$986$	119.495	+	100.268i	0.121192	+	0.101692i
$987$		0			0
$988$	199.632	−	93.0901i	0.202057	−	0.0942207i
$989$	146.299	+	84.4656i	0.147926	+	0.0854051i
$990$		0			0
$991$	216.645	+	375.241i	0.218613	+	0.378649i	0.954384	−	0.298582i	$-0.0965135\pi$
$991$	216.645	+	375.241i	0.218613	+	0.378649i	−0.735771	+	0.677230i	$0.763180\pi$
$992$	297.785	−	425.281i	0.300187	−	0.428711i
$993$		0			0
$994$	−430.315	−	1182.28i	−0.432912	−	1.18942i
$995$	−106.093	+	865.548i	−0.106626	+	0.869898i
$996$		0			0
$997$	549.144	+	48.0439i	0.550797	+	0.0481885i	0.359157	−	0.933277i	$-0.383064\pi$
$997$	549.144	+	48.0439i	0.550797	+	0.0481885i	0.191639	+	0.981465i	$0.438620\pi$
$998$	335.722	−	335.722i	0.336395	−	0.336395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.37.26		408
3.2	odd	2		135.3.r.a.22.9	✓	408
5.3	odd	4	inner	405.3.s.a.118.26		408
15.8	even	4		135.3.r.a.103.9	yes	408
27.11	odd	18		135.3.r.a.97.9	yes	408
27.16	even	9	inner	405.3.s.a.127.26		408
135.38	even	36		135.3.r.a.43.9	yes	408
135.43	odd	36	inner	405.3.s.a.208.26		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.9	✓	408	3.2	odd	2
135.3.r.a.43.9	yes	408	135.38	even	36
135.3.r.a.97.9	yes	408	27.11	odd	18
135.3.r.a.103.9	yes	408	15.8	even	4
405.3.s.a.37.26		408	1.1	even	1	trivial
405.3.s.a.118.26		408	5.3	odd	4	inner
405.3.s.a.127.26		408	27.16	even	9	inner
405.3.s.a.208.26		408	135.43	odd	36	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)

\(f(q)\)	\(=\)	\(q+(2.21433 + 0.193729i) q^{2} +(0.926495 + 0.163366i) q^{4} +(1.95462 + 4.60212i) q^{5} +(-4.75945 + 6.79720i) q^{7} +(-6.56828 - 1.75996i) q^{8} +(3.43660 + 10.5693i) q^{10} +(10.2854 + 3.74359i) q^{11} +(-8.91787 + 0.780213i) q^{13} +(-11.8558 + 14.1292i) q^{14} +(-17.7396 - 6.45668i) q^{16} +(2.30094 - 0.616536i) q^{17} +(-22.6505 + 13.0773i) q^{19} +(1.05911 + 4.58315i) q^{20} +(22.0501 + 10.2821i) q^{22} +(1.53390 + 2.19063i) q^{23} +(-17.3589 + 17.9907i) q^{25} -19.8983 q^{26} +(-5.52004 + 5.52004i) q^{28} +(18.9366 + 22.5678i) q^{29} +(-6.10711 + 34.6352i) q^{31} +(-13.3789 - 6.23870i) q^{32} +(5.21449 - 0.919455i) q^{34} +(-40.5844 - 8.61763i) q^{35} +(61.9402 - 16.5968i) q^{37} +(-52.6890 + 24.5693i) q^{38} +(-4.73890 - 33.6680i) q^{40} +(7.59358 + 6.37177i) q^{41} +(57.2506 - 26.6964i) q^{43} +(8.91781 + 5.14870i) q^{44} +(2.97217 + 5.14795i) q^{46} +(35.0118 - 50.0020i) q^{47} +(-6.79059 - 18.6570i) q^{49} +(-41.9238 + 36.4745i) q^{50} +(-8.38982 - 0.734014i) q^{52} +(-34.1539 + 34.1539i) q^{53} +(2.87563 + 54.6520i) q^{55} +(43.2242 - 36.2694i) q^{56} +(37.5599 + 53.6411i) q^{58} +(-20.8579 - 57.3066i) q^{59} +(-3.82205 - 21.6759i) q^{61} +(-20.2330 + 75.5106i) q^{62} +(36.9788 + 21.3497i) q^{64} +(-21.0216 - 39.5161i) q^{65} +(6.37962 + 72.9194i) q^{67} +(2.23253 - 0.195321i) q^{68} +(-88.1978 - 26.9446i) q^{70} +(-34.1068 + 59.0747i) q^{71} +(27.4196 + 7.34705i) q^{73} +(140.371 - 24.7513i) q^{74} +(-23.1219 + 8.41569i) q^{76} +(-74.3989 + 52.0946i) q^{77} +(-64.3561 - 76.6966i) q^{79} +(-4.95969 - 94.2600i) q^{80} +(15.5803 + 15.5803i) q^{82} +(9.53095 - 108.939i) q^{83} +(7.33483 + 9.38412i) q^{85} +(131.944 - 48.0236i) q^{86} +(-60.9689 - 42.6909i) q^{88} +(42.9194 - 24.7795i) q^{89} +(37.1409 - 64.3300i) q^{91} +(1.06327 + 2.28020i) q^{92} +(87.2144 - 103.938i) q^{94} +(-104.456 - 78.6791i) q^{95} +(-34.3548 - 73.6740i) q^{97} +(-11.4222 - 42.6283i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 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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