LMFDB - Embedded newform 405.3.s.a.118.26

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			118.26
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.193729 - 2.21433i) q^{2} +(-0.926495 - 0.163366i) q^{4} +(-1.46086 - 4.78183i) q^{5} +(6.79720 + 4.75945i) q^{7} +(1.75996 - 6.56828i) q^{8} +(-10.8716 + 2.30845i) q^{10} +(10.2854 + 3.74359i) q^{11} +(-0.780213 - 8.91787i) q^{13} +(11.8558 - 14.1292i) q^{14} +(-17.7396 - 6.45668i) q^{16} +(-0.616536 - 2.30094i) q^{17} +(22.6505 - 13.0773i) q^{19} +(0.572291 + 4.66899i) q^{20} +(10.2821 - 22.0501i) q^{22} +(-2.19063 + 1.53390i) q^{23} +(-20.7318 + 13.9712i) q^{25} -19.8983 q^{26} +(-5.52004 - 5.52004i) q^{28} +(-18.9366 - 22.5678i) q^{29} +(-6.10711 + 34.6352i) q^{31} +(-6.23870 + 13.3789i) q^{32} +(-5.21449 + 0.919455i) q^{34} +(12.8291 - 39.4560i) q^{35} +(-16.5968 - 61.9402i) q^{37} +(-24.5693 - 52.6890i) q^{38} +(-33.9794 + 1.17949i) q^{40} +(7.59358 + 6.37177i) q^{41} +(26.6964 + 57.2506i) q^{43} +(-8.91781 - 5.14870i) q^{44} +(2.97217 + 5.14795i) q^{46} +(-50.0020 - 35.0118i) q^{47} +(6.79059 + 18.6570i) q^{49} +(26.9204 + 48.6136i) q^{50} +(-0.734014 + 8.38982i) q^{52} +(-34.1539 - 34.1539i) q^{53} +(2.87563 - 54.6520i) q^{55} +(43.2242 - 36.2694i) q^{56} +(-53.6411 + 37.5599i) q^{58} +(20.8579 + 57.3066i) q^{59} +(-3.82205 - 21.6759i) q^{61} +(75.5106 + 20.2330i) q^{62} +(-36.9788 - 21.3497i) q^{64} +(-41.5040 + 16.7586i) q^{65} +(72.9194 - 6.37962i) q^{67} +(0.195321 + 2.23253i) q^{68} +(-84.8831 - 36.0517i) q^{70} +(-34.1068 + 59.0747i) q^{71} +(-7.34705 + 27.4196i) q^{73} +(-140.371 + 24.7513i) q^{74} +(-23.1219 + 8.41569i) q^{76} +(52.0946 + 74.3989i) q^{77} +(64.3561 + 76.6966i) q^{79} +(-4.95969 + 94.2600i) q^{80} +(15.5803 - 15.5803i) q^{82} +(108.939 + 9.53095i) q^{83} +(-10.1020 + 6.30952i) q^{85} +(131.944 - 48.0236i) q^{86} +(42.6909 - 60.9689i) q^{88} +(-42.9194 + 24.7795i) q^{89} +(37.1409 - 64.3300i) q^{91} +(2.28020 - 1.06327i) q^{92} +(-87.2144 + 103.938i) q^{94} +(-95.6224 - 89.2066i) q^{95} +(-73.6740 + 34.3548i) q^{97} +(42.6283 - 11.4222i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.193729	−	2.21433i	0.0968644	−	1.10716i	−0.779789	−	0.626042i	$-0.784674\pi$
$2$	0.193729	−	2.21433i	0.0968644	−	1.10716i	0.876653	−	0.481122i	$-0.159771\pi$
$3$		0			0
$3$		0			0
$4$	−0.926495	−	0.163366i	−0.231624	−	0.0408415i
$5$	−1.46086	−	4.78183i	−0.292172	−	0.956366i
$5$	−1.46086	−	4.78183i	−0.292172	−	0.956366i
$6$		0			0
$7$	6.79720	+	4.75945i	0.971029	+	0.679922i	0.947485	−	0.319801i	$-0.103616\pi$
$7$	6.79720	+	4.75945i	0.971029	+	0.679922i	0.0235443	+	0.999723i	$0.492505\pi$
$8$	1.75996	−	6.56828i	0.219996	−	0.821035i
$9$		0			0
$10$	−10.8716	+	2.30845i	−1.08716	+	0.230845i
$11$	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
$13$	−0.780213	−	8.91787i	−0.0600164	−	0.685990i	−0.965293	−	0.261168i	$-0.915892\pi$
$13$	−0.780213	−	8.91787i	−0.0600164	−	0.685990i	0.905277	−	0.424822i	$-0.139663\pi$
$14$	11.8558	−	14.1292i	0.846844	−	1.00923i
$15$		0			0
$16$	−17.7396	−	6.45668i	−1.10872	−	0.403542i
$17$	−0.616536	−	2.30094i	−0.0362668	−	0.135350i	0.945419	−	0.325858i	$-0.105653\pi$
$17$	−0.616536	−	2.30094i	−0.0362668	−	0.135350i	−0.981686	+	0.190508i	$0.938986\pi$
$18$		0			0
$19$	22.6505	−	13.0773i	1.19213	−	0.688276i	0.233341	−	0.972395i	$-0.425034\pi$
$19$	22.6505	−	13.0773i	1.19213	−	0.688276i	0.958789	+	0.284119i	$0.0917009\pi$
$20$	0.572291	+	4.66899i	0.0286146	+	0.233450i
$21$		0			0
$22$	10.2821	−	22.0501i	0.467369	−	1.00228i
$23$	−2.19063	+	1.53390i	−0.0952450	+	0.0666912i	−0.620229	−	0.784421i	$-0.712960\pi$
$23$	−2.19063	+	1.53390i	−0.0952450	+	0.0666912i	0.524984	+	0.851112i	$0.324071\pi$
$24$		0			0
$25$	−20.7318	+	13.9712i	−0.829271	+	0.558847i
$26$	−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	0.333374	−	0.942795i	$-0.391813\pi$
$29$	−18.9366	−	22.5678i	−0.652987	−	0.778200i	−0.986361	+	0.164595i	$0.947368\pi$
$30$		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	$0.863563\pi$
$32$	−6.23870	+	13.3789i	−0.194959	+	0.418092i
$33$		0			0
$34$	−5.21449	+	0.919455i	−0.153367	+	0.0270428i
$35$	12.8291	−	39.4560i	0.366546	−	1.12731i
$36$		0			0
$37$	−16.5968	−	61.9402i	−0.448563	−	1.67406i	−0.706354	−	0.707859i	$-0.749661\pi$
$37$	−16.5968	−	61.9402i	−0.448563	−	1.67406i	0.257791	−	0.966201i	$-0.417006\pi$
$38$	−24.5693	−	52.6890i	−0.646561	−	1.38655i
$39$		0			0
$40$	−33.9794	+	1.17949i	−0.849486	+	0.0294872i
$41$	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
$43$	26.6964	+	57.2506i	0.620847	+	1.33141i	0.925428	+	0.378924i	$0.123706\pi$
$43$	26.6964	+	57.2506i	0.620847	+	1.33141i	−0.304581	+	0.952486i	$0.598516\pi$
$44$	−8.91781	−	5.14870i	−0.202678	−	0.117016i
$45$		0			0
$46$	2.97217	+	5.14795i	0.0646124	+	0.111912i
$47$	−50.0020	−	35.0118i	−1.06387	−	0.744931i	−0.0957488	−	0.995406i	$-0.530525\pi$
$47$	−50.0020	−	35.0118i	−1.06387	−	0.744931i	−0.968123	+	0.250474i	$0.919413\pi$
$48$		0			0
$49$	6.79059	+	18.6570i	0.138583	+	0.380755i
$50$	26.9204	+	48.6136i	0.538409	+	0.972272i
$51$		0			0
$52$	−0.734014	+	8.38982i	−0.0141157	+	0.161343i
$53$	−34.1539	−	34.1539i	−0.644414	−	0.644414i	0.307223	−	0.951637i	$-0.400600\pi$
$53$	−34.1539	−	34.1539i	−0.644414	−	0.644414i	−0.951637	+	0.307223i	$0.900600\pi$
$54$		0			0
$55$	2.87563	−	54.6520i	0.0522841	−	0.993672i
$56$	43.2242	−	36.2694i	0.771862	−	0.647669i
$57$		0			0
$58$	−53.6411	+	37.5599i	−0.924847	+	0.647585i
$59$	20.8579	+	57.3066i	0.353524	+	0.971299i	0.981229	+	0.192847i	$0.0617723\pi$
$59$	20.8579	+	57.3066i	0.353524	+	0.971299i	−0.627705	+	0.778451i	$0.716006\pi$
$60$		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	$-0.113299\pi$
$62$	75.5106	+	20.2330i	1.21791	+	0.326339i
$63$		0			0
$64$	−36.9788	−	21.3497i	−0.577794	−	0.333589i
$65$	−41.5040	+	16.7586i	−0.638522	+	0.257825i
$66$		0			0
$67$	72.9194	−	6.37962i	1.08835	−	0.0952183i	0.471172	−	0.882042i	$-0.343831\pi$
$67$	72.9194	−	6.37962i	1.08835	−	0.0952183i	0.617178	+	0.786823i	$0.288276\pi$
$68$	0.195321	+	2.23253i	0.00287237	+	0.0328314i
$69$		0			0
$70$	−84.8831	−	36.0517i	−1.21262	−	0.515024i
$71$	−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
$73$	−7.34705	+	27.4196i	−0.100644	+	0.375610i	−0.997815	−	0.0660747i	$-0.978952\pi$
$73$	−7.34705	+	27.4196i	−0.100644	+	0.375610i	0.897170	+	0.441685i	$0.145619\pi$
$74$	−140.371	+	24.7513i	−1.89691	+	0.334476i
$75$		0			0
$76$	−23.1219	+	8.41569i	−0.304236	+	0.110733i
$77$	52.0946	+	74.3989i	0.676554	+	0.966219i
$78$		0			0
$79$	64.3561	+	76.6966i	0.814634	+	0.970843i	0.999930	−	0.0118396i	$-0.00376873\pi$
$79$	64.3561	+	76.6966i	0.814634	+	0.970843i	−0.185296	+	0.982683i	$0.559324\pi$
$80$	−4.95969	+	94.2600i	−0.0619961	+	1.17825i
$81$		0			0
$82$	15.5803	−	15.5803i	0.190004	−	0.190004i
$83$	108.939	+	9.53095i	1.31252	+	0.114831i	0.721832	−	0.692068i	$-0.243300\pi$
$83$	108.939	+	9.53095i	1.31252	+	0.114831i	0.590689	+	0.806899i	$0.298856\pi$
$84$		0			0
$85$	−10.1020	+	6.30952i	−0.118848	+	0.0742297i
$86$	131.944	−	48.0236i	1.53423	−	0.558414i
$87$		0			0
$88$	42.6909	−	60.9689i	0.485124	−	0.692828i
$89$	−42.9194	+	24.7795i	−0.482240	+	0.278421i	−0.721349	−	0.692571i	$-0.756478\pi$
$89$	−42.9194	+	24.7795i	−0.482240	+	0.278421i	0.239110	+	0.970993i	$0.423144\pi$
$90$		0			0
$91$	37.1409	−	64.3300i	0.408142	−	0.706923i
$92$	2.28020	−	1.06327i	0.0247848	−	0.0115573i
$93$		0			0
$94$	−87.2144	+	103.938i	−0.927813	+	1.10572i
$95$	−95.6224	−	89.2066i	−1.00655	−	0.939017i
$96$		0			0
$97$	−73.6740	+	34.3548i	−0.759526	+	0.354173i	−0.763490	−	0.645819i	$-0.776516\pi$
$97$	−73.6740	+	34.3548i	−0.759526	+	0.354173i	0.00396432	+	0.999992i	$0.498738\pi$
$98$	42.6283	−	11.4222i	0.434982	−	0.116553i
$99$		0			0
$100$	21.4903	−	9.55735i	0.214903	−	0.0955735i
$101$	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
$103$	−7.97133	−	3.71709i	−0.0773915	−	0.0360883i	0.383537	−	0.923525i	$-0.374706\pi$
$103$	−7.97133	−	3.71709i	−0.0773915	−	0.0360883i	−0.460929	+	0.887437i	$0.652484\pi$
$104$	−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	0.0576110	−	0.998339i	$-0.481652\pi$
$107$	112.987	−	112.987i	1.05595	−	1.05595i	0.998339	−	0.0576110i	$-0.0183483\pi$
$108$		0			0
$109$		−	16.9651i		−	0.155643i	−0.996967	−	0.0778217i	$-0.975204\pi$
$109$		−	16.9651i		−	0.155643i	0.996967	−	0.0778217i	$-0.0247965\pi$
$110$	−120.460	−	16.9552i	−1.09509	−	0.154139i
$111$		0			0
$112$	−89.8493	−	128.318i	−0.802226	−	1.14570i
$113$	125.271	+	58.4147i	1.10859	+	0.516944i	0.888658	−	0.458571i	$-0.151639\pi$
$113$	125.271	+	58.4147i	1.10859	+	0.516944i	0.219932	+	0.975515i	$0.429416\pi$
$114$		0			0
$115$	10.5351	+	8.23443i	0.0916091	+	0.0716037i
$116$	13.8579	+	24.0026i	0.119464	+	0.206919i
$117$		0			0
$118$	130.937	−	35.0843i	1.10963	−	0.297325i
$119$	6.76051	−	18.5743i	0.0568110	−	0.156087i
$120$		0			0
$121$	−0.916012	−	0.768626i	−0.00757035	−	0.00635228i
$122$	−48.7381	+	4.26403i	−0.399493	+	0.0349511i
$123$		0			0
$124$	11.3164	−	31.0916i	0.0912614	−	0.250739i
$125$	97.0940	+	78.7259i	0.776752	+	0.629807i
$126$		0			0
$127$	214.408	+	57.4505i	1.68825	+	0.452366i	0.969938	−	0.243353i	$-0.0782474\pi$
$127$	214.408	+	57.4505i	1.68825	+	0.452366i	0.718314	+	0.695719i	$0.244914\pi$
$128$	−88.3078	+	126.117i	−0.689904	+	0.985285i
$129$		0			0
$130$	29.0686	+	95.1501i	0.223604	+	0.731924i
$131$	−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
$133$	216.200	+	18.9151i	1.62557	+	0.142219i
$134$		−	162.704i		−	1.21421i
$135$		0			0
$136$	−16.1983			−0.119105
$137$	8.59393	−	98.2291i	0.0627295	−	0.717001i	−0.898087	−	0.439817i	$-0.855043\pi$
$137$	8.59393	−	98.2291i	0.0627295	−	0.717001i	0.960817	−	0.277184i	$-0.0894011\pi$
$138$		0			0
$139$	86.9760	+	15.3362i	0.625727	+	0.110332i	0.477516	−	0.878623i	$-0.341537\pi$
$139$	86.9760	+	15.3362i	0.625727	+	0.110332i	0.148211	+	0.988956i	$0.452649\pi$
$140$	−18.3319	+	34.4599i	−0.130942	+	0.246142i
$141$		0			0
$142$	124.203	+	86.9682i	0.874672	+	0.612452i
$143$	25.3600	−	94.6448i	0.177343	−	0.661852i
$144$		0			0
$145$	−80.2516	+	123.520i	−0.553459	+	0.851863i
$146$	59.2926	+	21.5807i	0.406114	+	0.147813i
$147$		0			0
$148$	5.25795	+	60.0986i	0.0355267	+	0.406072i
$149$	−123.868	+	147.621i	−0.831331	+	0.990742i	0.168656	+	0.985675i	$0.446057\pi$
$149$	−123.868	+	147.621i	−0.831331	+	0.990742i	−0.999987	+	0.00506714i	$0.998387\pi$
$150$		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	$0.222197\pi$
$152$	−46.0310	−	171.790i	−0.302836	−	1.13020i
$153$		0			0
$154$	174.836	−	100.942i	1.13530	−	0.655464i
$155$	174.541	−	21.3940i	1.12607	−	0.138026i
$156$		0			0
$157$	85.0646	−	182.422i	0.541813	−	1.16192i	−0.424707	−	0.905331i	$-0.639623\pi$
$157$	85.0646	−	182.422i	0.541813	−	1.16192i	0.966520	−	0.256591i	$-0.0825993\pi$
$158$	182.299	−	127.647i	1.15379	−	0.807894i
$159$		0			0
$160$	73.0896	+	10.2876i	0.456810	+	0.0642977i
$161$	−22.1907			−0.137830
$162$		0			0
$163$	−74.5106	−	74.5106i	−0.457121	−	0.457121i	0.440589	−	0.897709i	$-0.354770\pi$
$163$	−74.5106	−	74.5106i	−0.457121	−	0.457121i	−0.897709	+	0.440589i	$0.854770\pi$
$164$	−5.99448	−	7.14395i	−0.0365517	−	0.0435606i
$165$		0			0
$166$	42.2093	−	239.381i	0.254273	−	1.44205i
$167$	12.6746	−	27.1808i	0.0758960	−	0.162759i	−0.864699	−	0.502291i	$-0.832491\pi$
$167$	12.6746	−	27.1808i	0.0758960	−	0.162759i	0.940595	+	0.339531i	$0.110268\pi$
$168$		0			0
$169$	87.5128	−	15.4309i	0.517827	−	0.0913069i
$170$	12.0143	+	23.5916i	0.0706724	+	0.138774i
$171$		0			0
$172$	−15.3813	−	57.4037i	−0.0894260	−	0.333743i
$173$	86.9434	+	186.451i	0.502563	+	1.07775i	0.979984	+	0.199075i	$0.0637937\pi$
$173$	86.9434	+	186.451i	0.502563	+	1.07775i	−0.477421	+	0.878674i	$0.658428\pi$
$174$		0			0
$175$	−207.413	−	3.70703i	−1.18522	−	0.0211831i
$176$	−158.288	−	132.819i	−0.899363	−	0.754655i
$177$		0			0
$178$	46.5553	+	99.8381i	0.261546	+	0.560888i
$179$	−42.6513	−	24.6247i	−0.238275	−	0.137568i	0.376109	−	0.926576i	$-0.377262\pi$
$179$	−42.6513	−	24.6247i	−0.238275	−	0.137568i	−0.614384	+	0.789007i	$0.710595\pi$
$180$		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	$0.892556\pi$
$182$	−135.253	−	94.7048i	−0.743146	−	0.520356i
$183$		0			0
$184$	6.21963	+	17.0883i	0.0338024	+	0.0928712i
$185$	−271.942	+	169.849i	−1.46996	+	0.918104i
$186$		0			0
$187$	2.27245	−	25.9742i	0.0121521	−	0.138900i
$188$	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
$193$	1.58604	−	1.11055i	0.00821780	−	0.00575416i	−0.569460	−	0.822019i	$-0.692848\pi$
$193$	1.58604	−	1.11055i	0.00821780	−	0.00575416i	0.577678	+	0.816265i	$0.303959\pi$
$194$	61.8000	+	169.794i	0.318557	+	0.875227i
$195$		0			0
$196$	−3.24353	−	18.3950i	−0.0165486	−	0.0938518i
$197$	137.247	+	36.7752i	0.696685	+	0.186676i	0.589745	−	0.807589i	$-0.299228\pi$
$197$	137.247	+	36.7752i	0.696685	+	0.186676i	0.106940	+	0.994265i	$0.465895\pi$
$198$		0			0
$199$	−151.039	−	87.2026i	−0.758992	−	0.438204i	0.0699420	−	0.997551i	$-0.477719\pi$
$199$	−151.039	−	87.2026i	−0.758992	−	0.438204i	−0.828934	+	0.559347i	$0.811052\pi$
$200$	55.2793	+	160.761i	0.276397	+	0.803804i
$201$		0			0
$202$	24.3483	−	2.13020i	0.120536	−	0.0105455i
$203$	−21.3058	−	243.526i	−0.104954	−	1.19964i
$204$		0			0
$205$	19.3756	−	45.6195i	0.0945149	−	0.222534i
$206$	−9.77514	+	16.9310i	−0.0474521	+	0.0821895i
$207$		0			0
$208$	−43.7392	+	163.237i	−0.210285	+	0.784793i
$209$	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	$0.591764\pi$
$212$	26.0639	+	37.2230i	0.122943	+	0.175580i
$213$		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
$218$	−37.5664	−	3.28663i	−0.172323	−	0.0150763i
$219$		0			0
$220$	−11.5925	+	50.1650i	−0.0526933	+	0.228023i
$221$	−20.0385	+	7.29341i	−0.0906719	+	0.0330019i
$222$		0			0
$223$	−182.343	+	260.413i	−0.817681	+	1.16777i	0.165693	+	0.986177i	$0.447014\pi$
$223$	−182.343	+	260.413i	−0.817681	+	1.16777i	−0.983374	+	0.181592i	$0.941875\pi$
$224$	−106.082	+	61.2465i	−0.473581	+	0.273422i
$225$		0			0
$226$	153.618	−	266.074i	0.679725	−	1.17732i
$227$	−405.205	+	188.950i	−1.78505	+	0.832381i	−0.819094	+	0.573660i	$0.805523\pi$
$227$	−405.205	+	188.950i	−1.78505	+	0.832381i	−0.965952	+	0.258721i	$0.916699\pi$
$228$		0			0
$229$	−26.8340	+	31.9795i	−0.117179	+	0.139648i	−0.821445	−	0.570288i	$-0.806832\pi$
$229$	−26.8340	+	31.9795i	−0.117179	+	0.139648i	0.704266	+	0.709936i	$0.251276\pi$
$230$	20.2747	−	21.7328i	0.0881508	−	0.0944906i
$231$		0			0
$232$	−181.559	+	84.6625i	−0.782584	+	0.364925i
$233$	95.2155	−	25.5129i	0.408650	−	0.109497i	−0.0486371	−	0.998817i	$-0.515488\pi$
$233$	95.2155	−	25.5129i	0.408650	−	0.109497i	0.457287	+	0.889319i	$0.348821\pi$
$234$		0			0
$235$	−94.3744	+	290.248i	−0.401593	+	1.23510i
$236$	−9.96279	−	56.5018i	−0.0422152	−	0.239414i
$237$		0			0
$238$	−39.8200	−	18.5684i	−0.167311	−	0.0780184i
$239$	−98.1358	−	17.3040i	−0.410610	−	0.0724016i	−0.0354721	−	0.999371i	$-0.511293\pi$
$239$	−98.1358	−	17.3040i	−0.410610	−	0.0724016i	−0.375138	+	0.926969i	$0.622405\pi$
$240$		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
$245$	79.2945	−	59.7267i	0.323651	−	0.243782i
$246$		0			0
$247$	−134.293	−	191.791i	−0.543698	−	0.776481i
$248$	216.745	+	101.070i	0.873972	+	0.407540i
$249$		0			0
$250$	193.135	−	199.747i	0.772540	−	0.798986i
$251$	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
$253$	−28.2739	+	7.57596i	−0.111754	+	0.0299445i
$254$	168.751	−	463.640i	0.664375	−	1.82536i
$255$		0			0
$256$	131.317	+	110.188i	0.512958	+	0.430423i
$257$	−10.1033	+	0.883925i	−0.0393125	+	0.00343939i	−0.106795	−	0.994281i	$-0.534059\pi$
$257$	−10.1033	+	0.883925i	−0.0393125	+	0.00343939i	0.0674825	+	0.997720i	$0.478503\pi$
$258$		0			0
$259$	181.990	−	500.012i	0.702662	−	1.93055i
$260$	41.1910	−	8.74643i	0.158427	−	0.0336401i
$261$		0			0
$262$	476.297	+	127.623i	1.81793	+	0.487112i
$263$	8.96289	−	12.8003i	0.0340794	−	0.0486704i	−0.801751	−	0.597658i	$-0.796098\pi$
$263$	8.96289	−	12.8003i	0.0340794	−	0.0486704i	0.835830	+	0.548988i	$0.184987\pi$
$264$		0			0
$265$	−113.424	+	213.212i	−0.428016	+	0.804575i
$266$	83.7685	−	475.075i	0.314919	−	1.78599i
$267$		0			0
$268$	−68.6017	−	6.00187i	−0.255976	−	0.0223950i
$269$			302.818i			1.12572i	0.826553	+	0.562859i	$0.190298\pi$
$269$			302.818i			1.12572i	−0.826553	+	0.562859i	$0.809702\pi$
$270$		0			0
$271$	−467.978			−1.72686			−0.863428	−	0.504471i	$-0.831687\pi$
$271$	−467.978			−1.72686			−0.863428	+	0.504471i	$0.831687\pi$
$272$	−3.91936	+	44.7985i	−0.0144094	+	0.164701i
$273$		0			0
$274$	−215.847	−	38.0596i	−0.787762	−	0.138904i
$275$	−265.537	+	66.0881i	−0.965590	+	0.240320i
$276$		0			0
$277$	−153.631	−	107.574i	−0.554626	−	0.388353i	0.262396	−	0.964960i	$-0.415487\pi$
$277$	−153.631	−	107.574i	−0.554626	−	0.388353i	−0.817022	+	0.576607i	$0.804376\pi$
$278$	50.8092	−	189.622i	0.182767	−	0.682095i
$279$		0			0
$280$	−236.579	−	153.706i	−0.844925	−	0.548951i
$281$	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
$283$	−10.6053	−	121.219i	−0.0374745	−	0.428335i	−0.991638	−	0.129050i	$-0.958807\pi$
$283$	−10.6053	−	121.219i	−0.0374745	−	0.428335i	0.954164	−	0.299285i	$-0.0967483\pi$
$284$	41.2506	−	49.1605i	0.145248	−	0.173100i
$285$		0			0
$286$	−204.662	−	74.4908i	−0.715601	−	0.260457i
$287$	21.2890	+	79.4515i	0.0741776	+	0.276835i
$288$		0			0
$289$	245.367	−	141.663i	0.849021	−	0.490183i
$290$	257.967	+	201.633i	0.889543	+	0.695286i
$291$		0			0
$292$	11.2864	−	24.2038i	0.0386521	−	0.0828898i
$293$	−144.952	+	101.496i	−0.494716	+	0.346404i	−0.794159	−	0.607710i	$-0.792088\pi$
$293$	−144.952	+	101.496i	−0.494716	+	0.346404i	0.299443	+	0.954114i	$0.403199\pi$
$294$		0			0
$295$	243.560	−	183.456i	0.825627	−	0.621885i
$296$	−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
$302$	266.595	−	571.714i	0.882764	−	1.89309i
$303$		0			0
$304$	−486.245	+	85.7382i	−1.59949	+	0.282034i
$305$	−98.0672	+	49.9419i	−0.321532	+	0.163744i
$306$		0			0
$307$	−28.5989	−	106.733i	−0.0931562	−	0.347664i	0.903577	−	0.428425i	$-0.140931\pi$
$307$	−28.5989	−	106.733i	−0.0931562	−	0.347664i	−0.996733	+	0.0807616i	$0.974265\pi$
$308$	−36.1112	−	77.4407i	−0.117244	−	0.251431i
$309$		0			0
$310$	−13.5597	−	390.636i	−0.0437409	−	1.26012i
$311$	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
$313$	25.2611	+	54.1726i	0.0807063	+	0.173075i	0.942520	−	0.334150i	$-0.108449\pi$
$313$	25.2611	+	54.1726i	0.0807063	+	0.173075i	−0.861814	+	0.507225i	$0.830671\pi$
$314$	−387.462	−	223.701i	−1.23396	−	0.712425i
$315$		0			0
$316$	−47.0960	−	81.5726i	−0.149038	−	0.258141i
$317$	−150.648	−	105.485i	−0.475231	−	0.332760i	0.311300	−	0.950312i	$-0.399236\pi$
$317$	−150.648	−	105.485i	−0.475231	−	0.332760i	−0.786530	+	0.617552i	$0.788125\pi$
$318$		0			0
$319$	−110.287	−	303.010i	−0.345726	−	0.949875i
$320$	−48.0698	+	208.015i	−0.150218	+	0.650047i
$321$		0			0
$322$	−4.29898	+	49.1375i	−0.0133509	+	0.152601i
$323$	−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
$328$	55.2160	−	38.6627i	0.168341	−	0.117874i
$329$	−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	$0.868176\pi$
$332$	−99.3746	−	26.6273i	−0.299321	−	0.0802029i
$333$		0			0
$334$	−57.7319	−	33.3315i	−0.172850	−	0.0997949i
$335$	−137.031	−	339.369i	−0.409049	−	1.01304i
$336$		0			0
$337$	394.528	−	34.5167i	1.17070	−	0.102423i	0.514829	−	0.857293i	$-0.327855\pi$
$337$	394.528	−	34.5167i	1.17070	−	0.102423i	0.655875	+	0.754869i	$0.272300\pi$
$338$	−17.2153	−	196.772i	−0.0509328	−	0.582165i
$339$		0			0
$340$	10.3903	−	4.19541i	0.0305596	−	0.0123394i
$341$	−192.474	+	333.375i	−0.564440	+	0.977638i
$342$		0			0
$343$	62.5944	−	233.606i	0.182491	−	0.681066i
$344$	423.023	−	74.5904i	1.22972	−	0.216832i
$345$		0			0
$346$	429.707	−	156.400i	1.24193	−	0.452024i
$347$	193.294	+	276.053i	0.557044	+	0.795541i	0.994615	−	0.103643i	$-0.0330499\pi$
$347$	193.294	+	276.053i	0.557044	+	0.795541i	−0.437571	+	0.899184i	$0.644161\pi$
$348$		0			0
$349$	−34.7252	−	41.3839i	−0.0994991	−	0.118578i	0.713997	−	0.700149i	$-0.246883\pi$
$349$	−34.7252	−	41.3839i	−0.0994991	−	0.118578i	−0.813496	+	0.581570i	$0.802439\pi$
$350$	−48.3905	+	458.563i	−0.138259	+	1.31018i
$351$		0			0
$352$	−114.253	+	114.253i	−0.324582	+	0.324582i
$353$	254.804	+	22.2925i	0.721824	+	0.0631514i	0.442147	−	0.896943i	$-0.354217\pi$
$353$	254.804	+	22.2925i	0.721824	+	0.0631514i	0.279677	+	0.960094i	$0.409773\pi$
$354$		0			0
$355$	332.310	+	76.7930i	0.936086	+	0.216318i
$356$	43.8127	−	15.9465i	0.123069	−	0.0447936i
$357$		0			0
$358$	−62.7900	+	89.6734i	−0.175391	+	0.250484i
$359$	102.875	−	59.3949i	0.286560	−	0.165445i	−0.349830	−	0.936813i	$-0.613760\pi$
$359$	102.875	−	59.3949i	0.286560	−	0.165445i	0.636389	+	0.771368i	$0.280427\pi$
$360$		0			0
$361$	161.529	−	279.777i	0.447449	−	0.775004i
$362$	−134.900	+	62.9049i	−0.372652	+	0.173771i
$363$		0			0
$364$	−44.9202	+	53.5338i	−0.123407	+	0.147071i
$365$	141.849	−	4.92382i	0.388626	−	0.0134899i
$366$		0			0
$367$	−357.174	+	166.553i	−0.973226	+	0.453823i	−0.843148	−	0.537681i	$-0.819300\pi$
$367$	−357.174	+	166.553i	−0.973226	+	0.453823i	−0.130077	+	0.991504i	$0.541523\pi$
$368$	48.7648	−	13.0665i	0.132513	−	0.0355068i
$369$		0			0
$370$	323.419	+	635.074i	0.874106	+	1.71642i
$371$	−69.5972	−	394.705i	−0.187594	−	1.06390i
$372$		0			0
$373$	50.6990	+	23.6413i	0.135922	+	0.0633816i	0.489389	−	0.872065i	$-0.337220\pi$
$373$	50.6990	+	23.6413i	0.135922	+	0.0633816i	−0.353467	+	0.935447i	$0.614997\pi$
$374$	−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	$0.0348724\pi$
$379$			82.8766i			0.218672i	−0.994005	+	0.109336i	$0.965128\pi$
$380$	74.0203	+	98.2709i	0.194790	+	0.258608i
$381$		0			0
$382$	462.614	+	660.681i	1.21103	+	1.72953i
$383$	−280.720	−	130.902i	−0.732952	−	0.341781i	0.0200506	−	0.999799i	$-0.493617\pi$
$383$	−280.720	−	130.902i	−0.732952	−	0.341781i	−0.753002	+	0.658018i	$0.771395\pi$
$384$		0			0
$385$	279.660	−	357.794i	0.726389	−	0.929335i
$386$	−2.15187	−	3.72715i	−0.00557480	−	0.00965583i
$387$		0			0
$388$	73.8710	−	19.7937i	0.190389	−	0.0510146i
$389$	97.2536	−	267.202i	0.250009	−	0.686895i	−0.749676	−	0.661805i	$-0.769791\pi$
$389$	97.2536	−	267.202i	0.250009	−	0.686895i	0.999685	−	0.0250898i	$-0.00798716\pi$
$390$		0			0
$391$	4.88002	+	4.09482i	0.0124809	+	0.0104727i
$392$	134.496	−	11.7668i	0.343101	−	0.0300174i
$393$		0			0
$394$	108.021	−	296.786i	0.274165	−	0.753263i
$395$	272.735	−	419.783i	0.690468	−	1.06274i
$396$		0			0
$397$	−627.574	−	168.158i	−1.58079	−	0.423572i	−0.641621	−	0.767022i	$-0.721738\pi$
$397$	−627.574	−	168.158i	−1.58079	−	0.423572i	−0.939171	+	0.343450i	$0.888404\pi$
$398$	−222.356	+	317.557i	−0.558683	+	0.797882i
$399$		0			0
$400$	457.980	−	113.984i	1.14495	−	0.284961i
$401$	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
$403$	313.637	+	27.4397i	0.778255	+	0.0680885i
$404$		−	10.3447i		−	0.0256057i
$405$		0			0
$406$	−543.374			−1.33836
$407$	61.1732	−	699.213i	0.150303	−	1.71797i
$408$		0			0
$409$	696.105	+	122.742i	1.70197	+	0.300103i	0.938381	−	0.345602i	$-0.112325\pi$
$409$	696.105	+	122.742i	1.70197	+	0.300103i	0.763587	+	0.645705i	$0.223436\pi$
$410$	−97.2629	−	51.7417i	−0.237227	−	0.126199i
$411$		0			0
$412$	6.77815	+	4.74611i	0.0164518	+	0.0115197i
$413$	−130.973	+	488.797i	−0.317125	+	1.18353i
$414$		0			0
$415$	−113.570	−	534.852i	−0.273662	−	1.28880i
$416$	124.179	+	45.1975i	0.298508	+	0.108648i
$417$		0			0
$418$	−55.4596	−	633.906i	−0.132678	−	1.51652i
$419$	139.446	−	166.185i	0.332806	−	0.396623i	−0.573527	−	0.819186i	$-0.694425\pi$
$419$	139.446	−	166.185i	0.332806	−	0.396623i	0.906333	+	0.422564i	$0.138870\pi$
$420$		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	$0.368589\pi$
$422$	144.469	+	539.164i	0.342343	+	1.27764i
$423$		0			0
$424$	−284.442	+	164.223i	−0.670855	+	0.387318i
$425$	44.9287	+	39.0889i	0.105715	+	0.0919739i
$426$		0			0
$427$	77.1864	−	165.527i	0.180764	−	0.387650i
$428$	−123.140	+	86.2234i	−0.287710	+	0.201456i
$429$		0			0
$430$	−422.392	−	560.776i	−0.982306	−	1.30413i
$431$	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	0.650912	−	0.759153i	$-0.274387\pi$
$433$	−46.8682	−	46.8682i	−0.108241	−	0.108241i	−0.759153	+	0.650912i	$0.774387\pi$
$434$	416.963	+	496.917i	0.960743	+	1.14497i
$435$		0			0
$436$	−2.77152	+	15.7181i	−0.00635671	+	0.0360507i
$437$	−29.5597	+	63.3910i	−0.0676423	+	0.145059i
$438$		0			0
$439$	−356.651	+	62.8872i	−0.812417	+	0.143251i	−0.564397	−	0.825504i	$-0.690891\pi$
$439$	−356.651	+	62.8872i	−0.812417	+	0.143251i	−0.248021	+	0.968755i	$0.579780\pi$
$440$	−353.908	−	115.073i	−0.804337	−	0.261531i
$441$		0			0
$442$	12.2680	+	45.7848i	0.0277556	+	0.103585i
$443$	231.821	+	497.142i	0.523299	+	1.12222i	0.973373	+	0.229226i	$0.0736196\pi$
$443$	231.821	+	497.142i	0.523299	+	1.12222i	−0.450075	+	0.892991i	$0.648603\pi$
$444$		0			0
$445$	181.191	+	169.034i	0.407170	+	0.379851i
$446$	541.314	+	454.217i	1.21371	+	1.01842i
$447$		0			0
$448$	−149.739	−	321.117i	−0.334240	−	0.716779i
$449$	−220.408	−	127.252i	−0.490885	−	0.283413i	0.234056	−	0.972223i	$-0.424800\pi$
$449$	−220.408	−	127.252i	−0.490885	−	0.283413i	−0.724942	+	0.688810i	$0.758133\pi$
$450$		0			0
$451$	54.2499	+	93.9635i	0.120288	+	0.208345i
$452$	−106.520	−	74.5858i	−0.235663	−	0.165013i
$453$		0			0
$454$	339.899	+	933.864i	0.748675	+	2.05697i
$455$	−361.873	−	83.6244i	−0.795324	−	0.183790i
$456$		0			0
$457$	6.14777	−	70.2693i	0.0134525	−	0.153762i	−0.986497	−	0.163777i	$-0.947632\pi$
$457$	6.14777	−	70.2693i	0.0134525	−	0.153762i	0.999950	+	0.0100147i	$0.00318783\pi$
$458$	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
$463$	−98.1967	+	68.7580i	−0.212088	+	0.148506i	−0.674794	−	0.738006i	$-0.735767\pi$
$463$	−98.1967	+	68.7580i	−0.212088	+	0.148506i	0.462706	+	0.886512i	$0.346879\pi$
$464$	190.215	+	522.611i	0.409946	+	1.12632i
$465$		0			0
$466$	−38.0480	−	215.781i	−0.0816481	−	0.463050i
$467$	−493.003	−	132.100i	−1.05568	−	0.282869i	−0.311083	−	0.950383i	$-0.600692\pi$
$467$	−493.003	−	132.100i	−1.05568	−	0.282869i	−0.744597	+	0.667514i	$0.767358\pi$
$468$		0			0
$469$	526.012	+	303.693i	1.12156	+	0.647533i
$470$	624.422	+	265.205i	1.32856	+	0.564267i
$471$		0			0
$472$	413.115	−	36.1429i	0.875244	−	0.0765739i
$473$	60.2611	+	688.787i	0.127402	+	1.45621i
$474$		0			0
$475$	−286.880	+	587.568i	−0.603958	+	1.23699i
$476$	−9.29799	+	16.1046i	−0.0195336	+	0.0338332i
$477$		0			0
$478$	−57.3284	+	213.953i	−0.119934	+	0.447600i
$479$	31.7508	−	5.59852i	0.0662856	−	0.0116879i	−0.140407	−	0.990094i	$-0.544841\pi$
$479$	31.7508	−	5.59852i	0.0662856	−	0.0116879i	0.206693	+	0.978406i	$0.433730\pi$
$480$		0			0
$481$	−539.426	+	196.335i	−1.12147	+	0.408181i
$482$	197.645	+	282.266i	0.410051	+	0.585614i
$483$		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	−0.0460613	+	0.998939i	$0.514667\pi$
$487$	−508.915	+	508.915i	−1.04500	+	1.04500i	−0.998939	+	0.0460613i	$0.985333\pi$
$488$	−149.100	−	13.0446i	−0.305533	−	0.0267307i
$489$		0			0
$490$	−116.893	−	187.155i	−0.238557	−	0.381949i
$491$	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
$493$	−40.2521	+	57.4860i	−0.0816473	+	0.116604i
$494$	−450.705	+	260.215i	−0.912358	+	0.526750i
$495$		0			0
$496$	331.966	−	574.982i	0.669286	−	1.15924i
$497$	−512.994	+	239.213i	−1.03218	+	0.481314i
$498$		0			0
$499$	−137.298	+	163.626i	−0.275147	+	0.327907i	−0.885867	−	0.463939i	$-0.846436\pi$
$499$	−137.298	+	163.626i	−0.275147	+	0.327907i	0.610720	+	0.791846i	$0.290880\pi$
$500$	−77.0959	−	88.8010i	−0.154192	−	0.177602i
$501$		0			0
$502$	36.1892	−	16.8753i	0.0720901	−	0.0336162i
$503$	354.569	−	95.0065i	0.704909	−	0.188880i	0.111480	−	0.993767i	$-0.464441\pi$
$503$	354.569	−	95.0065i	0.704909	−	0.188880i	0.593428	+	0.804887i	$0.297774\pi$
$504$		0			0
$505$	48.9918	−	24.9497i	0.0970134	−	0.0494053i
$506$	11.2982	+	64.0753i	0.0223285	+	0.126631i
$507$		0			0
$508$	−189.262	−	88.2545i	−0.372564	−	0.173729i
$509$	167.773	+	29.5829i	0.329613	+	0.0581196i	0.336006	−	0.941860i	$-0.390924\pi$
$509$	167.773	+	29.5829i	0.329613	+	0.0581196i	−0.00639300	+	0.999980i	$0.502035\pi$
$510$		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
$515$	−6.12950	+	43.5477i	−0.0119019	+	0.0845586i
$516$		0			0
$517$	−383.222	−	547.297i	−0.741241	−	1.05860i
$518$	−1071.93	−	499.851i	−2.06937	−	0.964964i
$519$		0			0
$520$	37.0297	+	302.104i	0.0712110	+	0.580969i
$521$	−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
$523$	139.876	−	37.4797i	0.267450	−	0.0716629i	−0.122602	−	0.992456i	$-0.539124\pi$
$523$	139.876	−	37.4797i	0.267450	−	0.0716629i	0.390052	+	0.920793i	$0.372457\pi$
$524$	71.3804	−	196.116i	0.136222	−	0.374267i
$525$		0			0
$526$	−26.6078	−	22.3266i	−0.0505851	−	0.0424460i
$527$	83.4588	−	7.30170i	0.158366	−	0.0138552i
$528$		0			0
$529$	−178.483	+	490.377i	−0.337396	+	0.926989i
$530$	450.149	+	292.464i	0.849338	+	0.551819i
$531$		0			0
$532$	−197.218	−	52.8445i	−0.370711	−	0.0993318i
$533$	50.8980	−	72.6899i	0.0954935	−	0.136379i
$534$		0			0
$535$	−705.341	−	375.225i	−1.31839	−	0.701355i
$536$	86.4325	−	490.183i	0.161255	−	0.914521i
$537$		0			0
$538$	670.539	+	58.6645i	1.24635	+	0.109042i
$539$			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	$0.277187\pi$
$542$	−90.6608	+	1036.26i	−0.167271	+	1.91192i
$543$		0			0
$544$	34.6305	+	6.10630i	0.0636591	+	0.0112248i
$545$	−81.1243	+	24.7837i	−0.148852	+	0.0454746i
$546$		0			0
$547$	−108.624	−	76.0594i	−0.198582	−	0.139048i	0.470057	−	0.882636i	$-0.344234\pi$
$547$	−108.624	−	76.0594i	−0.198582	−	0.139048i	−0.668638	+	0.743588i	$0.733122\pi$
$548$	−24.0095	+	89.6048i	−0.0438130	+	0.163512i
$549$		0			0
$550$	94.8987	+	600.790i	0.172543	+	1.09235i
$551$	−724.048	−	263.532i	−1.31406	−	0.478280i
$552$		0			0
$553$	72.4076	+	827.622i	0.130936	+	1.49660i
$554$	−267.967	+	319.350i	−0.483694	+	0.576445i
$555$		0			0
$556$	−78.0774	−	28.4178i	−0.140427	−	0.0511112i
$557$	−9.77073	−	36.4649i	−0.0175417	−	0.0654665i	0.956600	−	0.291404i	$-0.0941223\pi$
$557$	−9.77073	−	36.4649i	−0.0175417	−	0.0654665i	−0.974142	+	0.225937i	$0.927456\pi$
$558$		0			0
$559$	489.725	−	282.743i	0.876073	−	0.505801i
$560$	−482.338	+	617.099i	−0.861317	+	1.10196i
$561$		0			0
$562$	202.005	−	433.201i	0.359440	−	0.770821i
$563$	783.549	−	548.647i	1.39174	−	0.974506i	0.393257	−	0.919429i	$-0.371348\pi$
$563$	783.549	−	548.647i	1.39174	−	0.974506i	0.998482	−	0.0550777i	$-0.0175407\pi$
$564$		0			0
$565$	96.3260	−	684.358i	0.170488	−	1.21125i
$566$	−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	0.691966	−	0.721930i	$-0.256745\pi$
$569$	−79.1792	−	94.3621i	−0.139155	−	0.165838i	−0.831121	+	0.556092i	$0.812300\pi$
$570$		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	$0.0192610\pi$
$572$	−38.9577	+	83.5450i	−0.0681078	+	0.146058i
$573$		0			0
$574$	180.056	−	31.7488i	0.313687	−	0.0553114i
$575$	23.9854	−	62.4062i	0.0417137	−	0.108532i
$576$		0			0
$577$	−259.718	−	969.281i	−0.450118	−	1.67986i	−0.702058	−	0.712120i	$-0.747735\pi$
$577$	−259.718	−	969.281i	−0.450118	−	1.67986i	0.251940	−	0.967743i	$-0.418932\pi$
$578$	−266.153	−	570.768i	−0.460473	−	0.987488i
$579$		0			0
$580$	94.5317	−	101.330i	0.162986	−	0.174708i
$581$	695.120	+	583.275i	1.19642	+	1.00392i
$582$		0			0
$583$	−223.429	−	479.146i	−0.383241	−	0.821862i
$584$	167.169	+	96.5149i	0.286248	+	0.165265i
$585$		0			0
$586$	196.665	+	340.634i	0.335606	+	0.581287i
$587$	501.977	+	351.488i	0.855156	+	0.598787i	0.916816	−	0.399310i	$-0.130750\pi$
$587$	501.977	+	351.488i	0.855156	+	0.598787i	−0.0616594	+	0.998097i	$0.519639\pi$
$588$		0			0
$589$	314.604	+	864.367i	0.534132	+	1.46752i
$590$	−359.047	−	574.863i	−0.608555	−	0.974344i
$591$		0			0
$592$	−105.507	+	1205.95i	−0.178222	+	2.03708i
$593$	−387.205	−	387.205i	−0.652959	−	0.652959i	0.300746	−	0.953704i	$-0.402764\pi$
$593$	−387.205	−	387.205i	−0.652959	−	0.652959i	−0.953704	+	0.300746i	$0.902764\pi$
$594$		0			0
$595$	−98.6955	−	5.19307i	−0.165875	−	0.00872785i
$596$	138.880	−	116.534i	0.233019	−	0.195527i
$597$		0			0
$598$	43.5898	−	30.5219i	0.0728927	−	0.0510400i
$599$	296.186	+	813.763i	0.494467	+	1.35854i	0.896554	+	0.442935i	$0.146063\pi$
$599$	296.186	+	813.763i	0.494467	+	1.35854i	−0.402087	+	0.915601i	$0.631715\pi$
$600$		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	$-0.185166\pi$
$602$	1125.41	+	301.554i	1.86946	+	0.500920i
$603$		0			0
$604$	−231.221	−	133.496i	−0.382816	−	0.221019i
$605$	−2.33727	+	5.50307i	−0.00386326	+	0.00909598i
$606$		0			0
$607$	232.067	−	20.3033i	0.382318	−	0.0334485i	0.105623	−	0.994406i	$-0.466316\pi$
$607$	232.067	−	20.3033i	0.382318	−	0.0334485i	0.276695	+	0.960958i	$0.410761\pi$
$608$	33.6503	+	384.624i	0.0553458	+	0.632606i
$609$		0			0
$610$	91.5895	+	226.828i	0.150147	+	0.371850i
$611$	−273.218	+	473.228i	−0.447166	+	0.774514i
$612$		0			0
$613$	43.1162	−	160.912i	0.0703364	−	0.262499i	−0.921799	−	0.387668i	$-0.873281\pi$
$613$	43.1162	−	160.912i	0.0703364	−	0.262499i	0.992135	+	0.125169i	$0.0399474\pi$
$614$	−241.882	+	42.6503i	−0.393944	+	0.0694630i
$615$		0			0
$616$	580.357	−	211.233i	0.942138	−	0.342910i
$617$	−675.682	−	964.973i	−1.09511	−	1.56398i	−0.791490	−	0.611183i	$-0.790694\pi$
$617$	−675.682	−	964.973i	−1.09511	−	1.56398i	−0.303619	−	0.952794i	$-0.598195\pi$
$618$		0			0
$619$	−537.579	−	640.661i	−0.868463	−	1.03499i	−0.999051	−	0.0435574i	$-0.986131\pi$
$619$	−537.579	−	640.661i	−0.868463	−	1.03499i	0.130588	−	0.991437i	$-0.458314\pi$
$620$	−165.206	−	8.69269i	−0.266462	−	0.0140205i
$621$		0			0
$622$	137.616	−	137.616i	0.221248	−	0.221248i
$623$	−409.668	−	35.8413i	−0.657574	−	0.0575302i
$624$		0			0
$625$	234.613	−	579.294i	0.375381	−	0.926871i
$626$	124.850	−	45.4416i	0.199440	−	0.0725904i
$627$		0			0
$628$	−108.613	+	155.116i	−0.172951	+	0.247000i
$629$	−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	$0.258538\pi$
$632$	617.029	−	287.725i	0.976312	−	0.455262i
$633$		0			0
$634$	−262.763	+	313.149i	−0.414453	+	0.493926i
$635$	−38.5019	−	1109.19i	−0.0606329	−	1.74676i
$636$		0			0
$637$	161.083	−	75.1140i	0.252877	−	0.117918i
$638$	−692.330	+	185.509i	−1.08516	+	0.290767i
$639$		0			0
$640$	732.073	+	238.034i	1.14386	+	0.371928i
$641$	−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
$643$	−982.606	−	458.197i	−1.52816	−	0.712592i	−0.536793	−	0.843714i	$-0.680364\pi$
$643$	−982.606	−	458.197i	−1.52816	−	0.712592i	−0.991366	+	0.131122i	$0.958142\pi$
$644$	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	−0.232284	−	0.972648i	$-0.574620\pi$
$647$	479.015	−	479.015i	0.740364	−	0.740364i	0.972648	+	0.232284i	$0.0746199\pi$
$648$		0			0
$649$			667.506i			1.02851i
$650$	412.526	−	278.002i	0.634656	−	0.427695i
$651$		0			0
$652$	56.8612	+	81.2062i	0.0872105	+	0.124549i
$653$	−1011.10	−	471.486i	−1.54840	−	0.722031i	−0.554486	−	0.832193i	$-0.687085\pi$
$653$	−1011.10	−	471.486i	−1.54840	−	0.722031i	−0.993914	+	0.110162i	$0.964863\pi$
$654$		0			0
$655$	1100.95	−	134.946i	1.68084	−	0.206025i
$656$	−93.5665	−	162.062i	−0.142632	−	0.247046i
$657$		0			0
$658$	−1087.50	+	291.395i	−1.65274	+	0.442850i
$659$	33.9839	−	93.3700i	0.0515689	−	0.141684i	−0.911234	−	0.411889i	$-0.864869\pi$
$659$	33.9839	−	93.3700i	0.0515689	−	0.141684i	0.962803	+	0.270205i	$0.0870914\pi$
$660$		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	$0.645013\pi$
$662$	347.882	−	30.4357i	0.525501	−	0.0459754i
$663$		0			0
$664$	254.331	−	698.769i	0.383029	−	1.05236i
$665$	−225.390	−	1061.47i	−0.338932	−	1.59619i
$666$		0			0
$667$	76.1000	+	20.3909i	0.114093	+	0.0305711i
$668$	−16.1834	+	23.1123i	−0.0242266	+	0.0345992i
$669$		0			0
$670$	−778.021	+	237.687i	−1.16123	+	0.354757i
$671$	41.8343	−	237.254i	0.0623462	−	0.353583i
$672$		0			0
$673$	83.4864	+	7.30411i	0.124051	+	0.0108531i	0.149012	−	0.988835i	$-0.452391\pi$
$673$	83.4864	+	7.30411i	0.124051	+	0.0108531i	−0.0249611	+	0.999688i	$0.507946\pi$
$674$		−	880.301i		−	1.30608i
$675$		0			0
$676$	−83.6010			−0.123670
$677$	−42.2231	+	482.612i	−0.0623679	+	0.712868i	0.899063	+	0.437820i	$0.144249\pi$
$677$	−42.2231	+	482.612i	−0.0623679	+	0.712868i	−0.961430	+	0.275048i	$0.911306\pi$
$678$		0			0
$679$	−664.287	−	117.132i	−0.978331	−	0.172506i
$680$	23.6635	+	77.4576i	0.0347992	+	0.113908i
$681$		0			0
$682$	700.914	+	490.785i	1.02773	+	0.719626i
$683$	7.04997	−	26.3109i	0.0103221	−	0.0385225i	−0.960573	−	0.278029i	$-0.910319\pi$
$683$	7.04997	−	26.3109i	0.0103221	−	0.0385225i	0.970895	+	0.239506i	$0.0769856\pi$
$684$		0			0
$685$	−482.269	+	102.404i	−0.704043	+	0.149495i
$686$	−505.153	−	183.861i	−0.736375	−	0.268019i
$687$		0			0
$688$	−103.934	−	1187.97i	−0.151067	−	1.72670i
$689$	−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	$0.524623\pi$
$692$	−50.0929	−	186.949i	−0.0723885	−	0.270158i
$693$		0			0
$694$	648.718	−	374.538i	0.934753	−	0.539680i
$695$	−53.7246	−	438.308i	−0.0773016	−	0.630660i
$696$		0			0
$697$	9.97937	−	21.4008i	0.0143176	−	0.0307042i
$698$	−98.3648	+	68.8758i	−0.140924	+	0.0986759i
$699$		0			0
$700$	191.562	+	37.3188i	0.273659	+	0.0533126i
$701$	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
$707$	−38.5603	+	82.6928i	−0.0545407	+	0.116963i
$708$		0			0
$709$	−1062.88	+	187.415i	−1.49913	+	0.264337i	−0.862193	−	0.506580i	$-0.830909\pi$
$709$	−1062.88	+	187.415i	−1.49913	+	0.264337i	−0.636935	+	0.770917i	$0.719798\pi$
$710$	234.423	−	720.968i	0.330173	−	1.01545i
$711$		0			0
$712$	87.2221	+	325.517i	0.122503	+	0.457187i
$713$	−39.7484	−	85.2407i	−0.0557481	−	0.119552i
$714$		0			0
$715$	−489.623	+	16.9957i	−0.684787	+	0.0237702i
$716$	35.4933	+	29.7824i	0.0495717	+	0.0415956i
$717$		0			0
$718$	−111.590	−	239.306i	−0.155418	−	0.333295i
$719$	−133.672	−	77.1756i	−0.185914	−	0.107337i	0.404154	−	0.914691i	$-0.367566\pi$
$719$	−133.672	−	77.1756i	−0.185914	−	0.107337i	−0.590068	+	0.807353i	$0.700899\pi$
$720$		0			0
$721$	−36.4914	−	63.2050i	−0.0506122	−	0.0876629i
$722$	−588.225	−	411.879i	−0.814716	−	0.570470i
$723$		0			0
$724$	21.5467	+	59.1992i	0.0297607	+	0.0817668i
$725$	707.889	+	203.304i	0.976398	+	0.280419i
$726$		0			0
$727$	39.6627	−	453.346i	0.0545566	−	0.623585i	−0.918866	−	0.394569i	$-0.870894\pi$
$727$	39.6627	−	453.346i	0.0545566	−	0.623585i	0.973423	−	0.229016i	$-0.0735507\pi$
$728$	−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
$733$	−42.4397	+	29.7166i	−0.0578987	+	0.0405411i	−0.602167	−	0.798370i	$-0.705696\pi$
$733$	−42.4397	+	29.7166i	−0.0578987	+	0.0405411i	0.544269	+	0.838911i	$0.316807\pi$
$734$	299.608	+	823.167i	0.408186	+	1.12148i
$735$		0			0
$736$	−6.85522	−	38.8779i	−0.00931416	−	0.0528232i
$737$	773.889	+	207.363i	1.05005	+	0.281361i
$738$		0			0
$739$	1051.21	+	606.914i	1.42247	+	0.821264i	0.996510	−	0.0834781i	$-0.0266029\pi$
$739$	1051.21	+	606.914i	1.42247	+	0.821264i	0.425961	+	0.904742i	$0.359936\pi$
$740$	279.700	−	112.938i	0.377973	−	0.152619i
$741$		0			0
$742$	−887.491	+	77.6454i	−1.19608	+	0.104643i
$743$	21.1134	+	241.327i	0.0284164	+	0.324801i	0.997076	+	0.0764106i	$0.0243460\pi$
$743$	21.1134	+	241.327i	0.0284164	+	0.324801i	−0.968660	+	0.248390i	$0.920098\pi$
$744$		0			0
$745$	886.851	+	376.664i	1.19040	+	0.505590i
$746$	62.1715	−	107.684i	0.0833398	−	0.144349i
$747$		0			0
$748$	−6.34872	+	23.6937i	−0.00848759	+	0.0316761i
$749$	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	$0.159179\pi$
$752$	660.955	+	943.941i	0.878929	+	1.25524i
$753$		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	−0.594026	−	0.804446i	$-0.702462\pi$
$757$	159.288	−	159.288i	0.210420	−	0.210420i	0.804446	+	0.594026i	$0.202462\pi$
$758$	183.516	+	16.0556i	0.242106	+	0.0211815i
$759$		0			0
$760$	−754.226	+	471.074i	−0.992402	+	0.619834i
$761$	−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
$763$	80.7447	−	115.315i	0.105825	−	0.151134i
$764$	295.632	−	170.683i	0.386953	−	0.223407i
$765$		0			0
$766$	−344.244	+	596.248i	−0.449405	+	0.778392i
$767$	494.780	−	230.720i	0.645084	−	0.300808i
$768$		0			0
$769$	−698.674	+	832.648i	−0.908549	+	1.08277i	0.0876922	+	0.996148i	$0.472051\pi$
$769$	−698.674	+	832.648i	−0.908549	+	1.08277i	−0.996241	+	0.0866193i	$0.972394\pi$
$770$	−738.096	−	688.574i	−0.958566	−	0.894252i
$771$		0			0
$772$	−1.65088	+	0.769818i	−0.00213845	+	0.000997174i
$773$	599.939	−	160.753i	0.776118	−	0.207960i	0.151045	−	0.988527i	$-0.451736\pi$
$773$	599.939	−	160.753i	0.776118	−	0.207960i	0.625072	+	0.780567i	$0.285069\pi$
$774$		0			0
$775$	−357.282	−	803.372i	−0.461010	−	1.03661i
$776$	95.9879	+	544.375i	0.123696	+	0.701514i
$777$		0			0
$778$	−572.833	−	267.116i	−0.736289	−	0.343337i
$779$	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
$785$	−996.577	−	140.272i	−1.26952	−	0.178690i
$786$		0			0
$787$	360.051	+	514.207i	0.457499	+	0.653376i	0.979938	−	0.199301i	$-0.0638670\pi$
$787$	360.051	+	514.207i	0.457499	+	0.653376i	−0.522440	+	0.852676i	$0.674978\pi$
$788$	−121.151	−	56.4936i	−0.153745	−	0.0716923i
$789$		0			0
$790$	−876.701	−	685.249i	−1.10975	−	0.867404i
$791$	573.468	+	993.276i	0.724991	+	1.25572i
$792$		0			0
$793$	−190.321	+	50.9964i	−0.240002	+	0.0643082i
$794$	−493.936	+	1357.08i	−0.622086	+	1.70917i
$795$		0			0
$796$	125.691	+	105.467i	0.157904	+	0.132497i
$797$	−1260.73	+	110.300i	−1.58185	+	0.138394i	−0.843913	−	0.536480i	$-0.819754\pi$
$797$	−1260.73	+	110.300i	−1.58185	+	0.138394i	−0.737933	+	0.674874i	$0.764198\pi$
$798$		0			0
$799$	−49.7321	+	136.638i	−0.0622429	+	0.171011i
$800$	−57.5800	−	364.531i	−0.0719750	−	0.455664i
$801$		0			0
$802$	−603.799	−	161.787i	−0.752866	−	0.201730i
$803$	−178.215	+	254.517i	−0.221936	+	0.316958i
$804$		0			0
$805$	32.4175	+	106.112i	0.0402702	+	0.131816i
$806$	121.521	−	689.180i	0.150770	−	0.855061i
$807$		0			0
$808$	74.4866	+	6.51673i	0.0921863	+	0.00806526i
$809$			817.617i			1.01065i	0.862929	+	0.505326i	$0.168628\pi$
$809$			817.617i			1.01065i	−0.862929	+	0.505326i	$0.831372\pi$
$810$		0			0
$811$	−3.09205			−0.00381264			−0.00190632	−	0.999998i	$-0.500607\pi$
$811$	−3.09205			−0.00381264			−0.00190632	+	0.999998i	$0.500607\pi$
$812$	−20.0442	+	229.106i	−0.0246850	+	0.282150i
$813$		0			0
$814$	−1536.44	−	270.915i	−1.88751	−	0.332820i
$815$	−247.448	+	465.147i	−0.303617	+	0.570732i
$816$		0			0
$817$	1353.37	+	947.638i	1.65651	+	1.15990i
$818$	406.647	−	1517.63i	0.497124	−	1.85529i
$819$		0			0
$820$	−25.4040	+	39.1009i	−0.0309805	+	0.0476840i
$821$	−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
$823$	40.3413	+	461.104i	0.0490174	+	0.560272i	0.980504	+	0.196497i	$0.0629566\pi$
$823$	40.3413	+	461.104i	0.0490174	+	0.560272i	−0.931487	+	0.363775i	$0.881488\pi$
$824$	−38.4441	+	45.8159i	−0.0466555	+	0.0556019i
$825$		0			0
$826$	1056.98	+	384.711i	1.27964	+	0.465752i
$827$	82.3651	+	307.391i	0.0995950	+	0.371694i	0.997676	−	0.0681365i	$-0.0217053\pi$
$827$	82.3651	+	307.391i	0.0995950	+	0.371694i	−0.898081	+	0.439830i	$0.855039\pi$
$828$		0			0
$829$	−120.093	+	69.3356i	−0.144865	+	0.0836377i	−0.570680	−	0.821172i	$-0.693320\pi$
$829$	−120.093	+	69.3356i	−0.144865	+	0.0836377i	0.425816	+	0.904810i	$0.359987\pi$
$830$	−1206.34	+	147.864i	−1.45342	+	0.178150i
$831$		0			0
$832$	−161.543	+	346.429i	−0.194162	+	0.416381i
$833$	38.7420	−	27.1275i	0.0465090	−	0.0325660i
$834$		0			0
$835$	−148.490	−	20.9005i	−0.177832	−	0.0250305i
$836$	−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	$-0.950365\pi$
$839$	−813.216	−	969.153i	−0.969268	−	1.15513i	0.0185992	−	0.999827i	$-0.494079\pi$
$840$		0			0
$841$	−4.67146	+	26.4932i	−0.00555465	+	0.0315020i
$842$	546.005	−	1170.91i	0.648462	−	1.39063i
$843$		0			0
$844$	232.660	−	41.0243i	0.275664	−	0.0486070i
$845$	−201.632	−	395.929i	−0.238617	−	0.468555i
$846$		0			0
$847$	−2.56808	−	9.58422i	−0.00303198	−	0.0113155i
$848$	385.356	+	826.398i	0.454429	+	0.974526i
$849$		0			0
$850$	95.2597	−	91.9144i	0.112070	−	0.108135i
$851$	131.368	+	110.230i	0.154368	+	0.129531i
$852$		0			0
$853$	−667.765	−	1432.03i	−0.782843	−	1.67881i	−0.733169	−	0.680046i	$-0.761960\pi$
$853$	−667.765	−	1432.03i	−0.782843	−	1.67881i	−0.0496738	−	0.998765i	$-0.515818\pi$
$854$	−351.577	−	202.983i	−0.411683	−	0.237685i
$855$		0			0
$856$	−543.275	−	940.980i	−0.634667	−	1.09928i
$857$	−151.557	−	106.121i	−0.176846	−	0.123829i	0.481802	−	0.876280i	$-0.339982\pi$
$857$	−151.557	−	106.121i	−0.176846	−	0.123829i	−0.658648	+	0.752451i	$0.728871\pi$
$858$		0			0
$859$	−224.945	−	618.032i	−0.261869	−	0.719478i	−0.999041	−	0.0437739i	$-0.986062\pi$
$859$	−224.945	−	618.032i	−0.261869	−	0.719478i	0.737173	−	0.675704i	$-0.236160\pi$
$860$	−252.025	+	157.409i	−0.293052	+	0.183034i
$861$		0			0
$862$	38.2231	−	436.892i	0.0443423	−	0.506835i
$863$	1010.20	+	1010.20i	1.17057	+	1.17057i	0.982075	+	0.188492i	$0.0603600\pi$
$863$	1010.20	+	1010.20i	1.17057	+	1.17057i	0.188492	+	0.982075i	$0.439640\pi$
$864$		0			0
$865$	764.563	−	688.127i	0.883888	−	0.795522i
$866$	−112.861	+	94.7020i	−0.130325	+	0.109356i
$867$		0			0
$868$	224.899	−	157.476i	0.259100	−	0.181424i
$869$	374.809	+	1029.78i	0.431311	+	1.18502i
$870$		0			0
$871$	−113.785	−	645.309i	−0.130638	−	0.740883i
$872$	−111.432	−	29.8580i	−0.127789	−	0.0342408i
$873$		0			0
$874$	134.642	+	77.7356i	0.154053	+	0.0889423i
$875$	285.275	+	997.230i	0.326029	+	1.13969i
$876$		0			0
$877$	−1583.79	+	138.564i	−1.80592	+	0.157997i	−0.939774	−	0.341797i	$-0.888964\pi$
$877$	−1583.79	+	138.564i	−1.80592	+	0.157997i	−0.866144	+	0.499795i	$0.833409\pi$
$878$	70.1595	+	801.927i	0.0799083	+	0.913356i
$879$		0			0
$880$	−403.883	+	950.936i	−0.458958	+	1.08061i
$881$	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
$883$	−327.290	+	1221.46i	−0.370657	+	1.38331i	0.488931	+	0.872322i	$0.337387\pi$
$883$	−327.290	+	1221.46i	−0.370657	+	1.38331i	−0.859588	+	0.510988i	$0.829280\pi$
$884$	19.7570	−	3.48370i	0.0223496	−	0.00394084i
$885$		0			0
$886$	1145.75	−	417.018i	1.29317	−	0.470675i
$887$	175.671	+	250.884i	0.198051	+	0.282846i	0.905877	−	0.423541i	$-0.139213\pi$
$887$	175.671	+	250.884i	0.198051	+	0.282846i	−0.707826	+	0.706387i	$0.750324\pi$
$888$		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
$893$	−1590.43	−	139.144i	−1.78099	−	0.155817i
$894$		0			0
$895$	−55.4436	+	239.924i	−0.0619482	+	0.268072i
$896$	−1200.49	+	436.943i	−1.33983	+	0.487660i
$897$		0			0
$898$	−324.478	+	463.403i	−0.361334	+	0.516039i
$899$	897.288	−	518.049i	0.998095	−	0.576251i
$900$		0			0
$901$	−57.5291	+	99.6434i	−0.0638503	+	0.110592i
$902$	218.576	−	101.924i	0.242324	−	0.112997i
$903$		0			0
$904$	604.156	−	720.005i	0.668314	−	0.796465i
$905$	−228.396	+	244.822i	−0.252371	+	0.270522i
$906$		0			0
$907$	−943.579	+	439.998i	−1.04033	+	0.485114i	−0.866246	−	0.499617i	$-0.833474\pi$
$907$	−943.579	+	439.998i	−1.04033	+	0.485114i	−0.174083	+	0.984731i	$0.555696\pi$
$908$	406.289	−	108.865i	0.447455	−	0.119895i
$909$		0			0
$910$	−255.277	+	785.105i	−0.280524	+	0.862753i
$911$	−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
$913$	1084.81	+	505.853i	1.18818	+	0.554056i
$914$	−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	$-0.763822\pi$
$919$		−	1242.02i		−	1.35149i	0.737135	−	0.675745i	$-0.236178\pi$
$920$	72.6273	−	54.7048i	0.0789427	−	0.0594618i
$921$		0			0
$922$	−783.421	−	1118.84i	−0.849697	−	1.21349i
$923$	553.431	+	258.069i	0.599600	+	0.279598i
$924$		0			0
$925$	1209.46	+	1052.25i	1.30752	+	1.13757i
$926$	133.229	+	230.760i	0.143876	+	0.249201i
$927$		0			0
$928$	420.073	−	112.558i	0.452665	−	0.121291i
$929$	−246.952	+	678.494i	−0.265825	+	0.730349i	0.732922	+	0.680312i	$0.238156\pi$
$929$	−246.952	+	678.494i	−0.265825	+	0.730349i	−0.998747	+	0.0500361i	$0.984066\pi$
$930$		0			0
$931$	397.792	+	333.787i	0.427274	+	0.358526i
$932$	−92.3846	+	8.08260i	−0.0991251	+	0.00867232i
$933$		0			0
$934$	−388.021	+	1066.08i	−0.415440	+	1.14141i
$935$	−127.524	+	27.0782i	−0.136389	+	0.0289607i
$936$		0			0
$937$	−235.668	−	63.1470i	−0.251513	−	0.0673928i	0.130859	−	0.991401i	$-0.458226\pi$
$937$	−235.668	−	63.1470i	−0.251513	−	0.0673928i	−0.382373	+	0.924008i	$0.624893\pi$
$938$	774.380	−	1105.93i	0.825565	−	1.17903i
$939$		0			0
$940$	134.854	−	253.496i	0.143462	−	0.269677i
$941$	−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
$943$	−26.4084	−	2.31044i	−0.0280047	−	0.00245009i
$944$		−	1151.27i		−	1.21956i
$945$		0			0
$946$	1536.88			1.62460
$947$	66.9842	−	765.633i	0.0707331	−	0.808482i	−0.875124	−	0.483899i	$-0.839220\pi$
$947$	66.9842	−	765.633i	0.0707331	−	0.808482i	0.945857	−	0.324584i	$-0.105224\pi$
$948$		0			0
$949$	250.256	+	44.1269i	0.263705	+	0.0464984i
$950$	1245.49	+	749.075i	1.31105	+	0.788500i
$951$		0			0
$952$	−110.103	−	77.0951i	−0.115655	−	0.0809823i
$953$	−323.539	+	1207.46i	−0.339496	+	1.26701i	0.559417	+	0.828886i	$0.311025\pi$
$953$	−323.539	+	1207.46i	−0.339496	+	1.26701i	−0.898913	+	0.438128i	$0.855642\pi$
$954$		0			0
$955$	1521.36	+	988.434i	1.59305	+	1.03501i
$956$	88.0954	+	32.0641i	0.0921500	+	0.0335399i
$957$		0			0
$958$	−6.24593	−	71.3913i	−0.00651976	−	0.0745212i
$959$	525.932	−	626.781i	0.548417	−	0.653578i
$960$		0			0
$961$	−259.253	−	94.3605i	−0.269774	−	0.0981899i
$962$	330.248	+	1232.50i	0.343293	+	1.28119i
$963$		0			0
$964$	126.304	−	72.9218i	0.131021	−	0.0756450i
$965$	−7.62745	−	5.96178i	−0.00790410	−	0.00617802i
$966$		0			0
$967$	150.738	−	323.258i	0.155882	−	0.334290i	−0.812821	−	0.582514i	$-0.802069\pi$
$967$	150.738	−	323.258i	0.155882	−	0.334290i	0.968703	+	0.248224i	$0.0798469\pi$
$968$	−6.66070	+	4.66387i	−0.00688089	+	0.00481805i
$969$		0			0
$970$	721.645	−	543.562i	0.743964	−	0.560374i
$971$	−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
$977$	660.867	−	1417.23i	0.676425	−	1.45060i	−0.205235	−	0.978713i	$-0.565796\pi$
$977$	660.867	−	1417.23i	0.676425	−	1.45060i	0.881660	−	0.471886i	$-0.156426\pi$
$978$		0			0
$979$	−534.208	+	94.1952i	−0.545667	+	0.0962157i
$980$	−83.2232	+	42.3825i	−0.0849216	+	0.0432474i
$981$		0			0
$982$	−110.834	−	413.639i	−0.112866	−	0.421221i
$983$	343.311	+	736.233i	0.349248	+	0.748966i	0.999946	−	0.0103711i	$-0.00330128\pi$
$983$	343.311	+	736.233i	0.349248	+	0.748966i	−0.650698	+	0.759337i	$0.725524\pi$
$984$		0			0
$985$	−24.6459	−	710.015i	−0.0250212	−	0.720828i
$986$	119.495	+	100.268i	0.121192	+	0.101692i
$987$		0			0
$988$	93.0901	+	199.632i	0.0942207	+	0.202057i
$989$	−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	$0.763180\pi$
$992$	−425.281	−	297.785i	−0.428711	−	0.300187i
$993$		0			0
$994$	430.315	+	1182.28i	0.432912	+	1.18942i
$995$	−196.341	+	849.635i	−0.197327	+	0.853904i
$996$		0			0
$997$	48.0439	−	549.144i	0.0481885	−	0.550797i	−0.933277	−	0.359157i	$-0.883064\pi$
$997$	48.0439	−	549.144i	0.0481885	−	0.550797i	0.981465	−	0.191639i	$-0.0613803\pi$
$998$	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.118.26		408
3.2	odd	2		135.3.r.a.103.9	yes	408
5.2	odd	4	inner	405.3.s.a.37.26		408
15.2	even	4		135.3.r.a.22.9	✓	408
27.11	odd	18		135.3.r.a.43.9	yes	408
27.16	even	9	inner	405.3.s.a.208.26		408
135.92	even	36		135.3.r.a.97.9	yes	408
135.97	odd	36	inner	405.3.s.a.127.26		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.9	✓	408	15.2	even	4
135.3.r.a.43.9	yes	408	27.11	odd	18
135.3.r.a.97.9	yes	408	135.92	even	36
135.3.r.a.103.9	yes	408	3.2	odd	2
405.3.s.a.37.26		408	5.2	odd	4	inner
405.3.s.a.118.26		408	1.1	even	1	trivial
405.3.s.a.127.26		408	135.97	odd	36	inner
405.3.s.a.208.26		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)

\(f(q)\)	\(=\)	\(q+(0.193729 - 2.21433i) q^{2} +(-0.926495 - 0.163366i) q^{4} +(-1.46086 - 4.78183i) q^{5} +(6.79720 + 4.75945i) q^{7} +(1.75996 - 6.56828i) q^{8} +(-10.8716 + 2.30845i) q^{10} +(10.2854 + 3.74359i) q^{11} +(-0.780213 - 8.91787i) q^{13} +(11.8558 - 14.1292i) q^{14} +(-17.7396 - 6.45668i) q^{16} +(-0.616536 - 2.30094i) q^{17} +(22.6505 - 13.0773i) q^{19} +(0.572291 + 4.66899i) q^{20} +(10.2821 - 22.0501i) q^{22} +(-2.19063 + 1.53390i) q^{23} +(-20.7318 + 13.9712i) q^{25} -19.8983 q^{26} +(-5.52004 - 5.52004i) q^{28} +(-18.9366 - 22.5678i) q^{29} +(-6.10711 + 34.6352i) q^{31} +(-6.23870 + 13.3789i) q^{32} +(-5.21449 + 0.919455i) q^{34} +(12.8291 - 39.4560i) q^{35} +(-16.5968 - 61.9402i) q^{37} +(-24.5693 - 52.6890i) q^{38} +(-33.9794 + 1.17949i) q^{40} +(7.59358 + 6.37177i) q^{41} +(26.6964 + 57.2506i) q^{43} +(-8.91781 - 5.14870i) q^{44} +(2.97217 + 5.14795i) q^{46} +(-50.0020 - 35.0118i) q^{47} +(6.79059 + 18.6570i) q^{49} +(26.9204 + 48.6136i) q^{50} +(-0.734014 + 8.38982i) q^{52} +(-34.1539 - 34.1539i) q^{53} +(2.87563 - 54.6520i) q^{55} +(43.2242 - 36.2694i) q^{56} +(-53.6411 + 37.5599i) q^{58} +(20.8579 + 57.3066i) q^{59} +(-3.82205 - 21.6759i) q^{61} +(75.5106 + 20.2330i) q^{62} +(-36.9788 - 21.3497i) q^{64} +(-41.5040 + 16.7586i) q^{65} +(72.9194 - 6.37962i) q^{67} +(0.195321 + 2.23253i) q^{68} +(-84.8831 - 36.0517i) q^{70} +(-34.1068 + 59.0747i) q^{71} +(-7.34705 + 27.4196i) q^{73} +(-140.371 + 24.7513i) q^{74} +(-23.1219 + 8.41569i) q^{76} +(52.0946 + 74.3989i) q^{77} +(64.3561 + 76.6966i) q^{79} +(-4.95969 + 94.2600i) q^{80} +(15.5803 - 15.5803i) q^{82} +(108.939 + 9.53095i) q^{83} +(-10.1020 + 6.30952i) q^{85} +(131.944 - 48.0236i) q^{86} +(42.6909 - 60.9689i) q^{88} +(-42.9194 + 24.7795i) q^{89} +(37.1409 - 64.3300i) q^{91} +(2.28020 - 1.06327i) q^{92} +(-87.2144 + 103.938i) q^{94} +(-95.6224 - 89.2066i) q^{95} +(-73.6740 + 34.3548i) q^{97} +(42.6283 - 11.4222i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 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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