LMFDB - Embedded newform 432.3.x.a.125.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(125,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.31
Character	$\chi$	$=$	432.125
Dual form			432.3.x.a.197.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03470 - 1.71155i) q^{2} +(-1.85881 - 3.54187i) q^{4} +(7.78777 - 2.08673i) q^{5} +(2.60739 - 1.50538i) q^{7} +(-7.98539 - 0.483303i) q^{8} +O(q^{10})$	\(q+(1.03470 - 1.71155i) q^{2} +(-1.85881 - 3.54187i) q^{4} +(7.78777 - 2.08673i) q^{5} +(2.60739 - 1.50538i) q^{7} +(-7.98539 - 0.483303i) q^{8} +(4.48643 - 15.4883i) q^{10} +(1.54872 - 5.77989i) q^{11} +(14.7171 - 3.94343i) q^{13} +(0.121324 - 6.02028i) q^{14} +(-9.08964 + 13.1673i) q^{16} +23.3509i q^{17} +(-8.30523 - 8.30523i) q^{19} +(-21.8669 - 23.7044i) q^{20} +(-8.29013 - 8.63114i) q^{22} +(2.08290 - 3.60768i) q^{23} +(34.6443 - 20.0019i) q^{25} +(8.47832 - 29.2693i) q^{26} +(-10.1785 - 6.43681i) q^{28} +(-24.6026 - 6.59225i) q^{29} +(11.4094 - 19.7616i) q^{31} +(13.1315 + 29.1815i) q^{32} +(39.9662 + 24.1610i) q^{34} +(17.1644 - 17.1644i) q^{35} +(27.8343 - 27.8343i) q^{37} +(-22.8082 + 5.62144i) q^{38} +(-63.1969 + 12.8995i) q^{40} +(-36.7431 + 63.6409i) q^{41} +(-70.9710 - 19.0166i) q^{43} +(-23.3504 + 5.25838i) q^{44} +(-4.01957 - 7.29783i) q^{46} +(39.5925 - 22.8588i) q^{47} +(-19.9677 + 34.5851i) q^{49} +(1.61203 - 79.9912i) q^{50} +(-41.3234 - 44.7959i) q^{52} +(21.0485 + 21.0485i) q^{53} -48.2442i q^{55} +(-21.5485 + 10.7608i) q^{56} +(-36.7392 + 35.2876i) q^{58} +(-77.1219 + 20.6648i) q^{59} +(13.6831 - 51.0660i) q^{61} +(-22.0177 - 39.9749i) q^{62} +(63.5328 + 7.71872i) q^{64} +(106.384 - 61.4211i) q^{65} +(44.8100 - 12.0068i) q^{67} +(82.7056 - 43.4048i) q^{68} +(-11.6178 - 47.1377i) q^{70} -82.1279 q^{71} +25.3786i q^{73} +(-18.8398 - 76.4397i) q^{74} +(-13.9782 + 44.8539i) q^{76} +(-4.66280 - 17.4018i) q^{77} +(45.7098 + 79.1717i) q^{79} +(-43.3114 + 121.512i) q^{80} +(70.9068 + 128.737i) q^{82} +(45.3324 + 12.1468i) q^{83} +(48.7268 + 181.851i) q^{85} +(-105.981 + 101.794i) q^{86} +(-15.1605 + 45.4062i) q^{88} +79.4644 q^{89} +(32.4368 - 32.4368i) q^{91} +(-16.6496 - 0.671340i) q^{92} +(1.84228 - 91.4165i) q^{94} +(-82.0099 - 47.3485i) q^{95} +(-57.7693 - 100.059i) q^{97} +(38.5336 + 69.9607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.03470	−	1.71155i	0.517348	−	0.855775i
$2$	1.03470	−	1.71155i	0.517348	−	0.855775i
$3$		0			0
$3$		0			0
$4$	−1.85881	−	3.54187i	−0.464703	−	0.885467i
$5$	7.78777	−	2.08673i	1.55755	−	0.417345i	0.625665	−	0.780091i	$-0.284828\pi$
$5$	7.78777	−	2.08673i	1.55755	−	0.417345i	0.931888	+	0.362746i	$0.118161\pi$
$6$		0			0
$7$	2.60739	−	1.50538i	0.372484	−	0.215054i	−0.302059	−	0.953289i	$-0.597674\pi$
$7$	2.60739	−	1.50538i	0.372484	−	0.215054i	0.674543	+	0.738236i	$0.264341\pi$
$8$	−7.98539	−	0.483303i	−0.998173	−	0.0604128i
$9$		0			0
$10$	4.48643	−	15.4883i	0.448643	−	1.54883i
$11$	1.54872	−	5.77989i	0.140793	−	0.525445i	−0.859114	−	0.511784i	$-0.828985\pi$
$11$	1.54872	−	5.77989i	0.140793	−	0.525445i	0.999907	−	0.0136608i	$-0.00434851\pi$
$12$		0			0
$13$	14.7171	−	3.94343i	1.13208	−	0.303341i	0.356320	−	0.934364i	$-0.384031\pi$
$13$	14.7171	−	3.94343i	1.13208	−	0.303341i	0.775764	+	0.631023i	$0.217365\pi$
$14$	0.121324	−	6.02028i	0.00866602	−	0.430020i
$15$		0			0
$16$	−9.08964	+	13.1673i	−0.568103	+	0.822958i
$17$			23.3509i			1.37358i	0.726856	+	0.686790i	$0.240981\pi$
$17$			23.3509i			1.37358i	−0.726856	+	0.686790i	$0.759019\pi$
$18$		0			0
$19$	−8.30523	−	8.30523i	−0.437117	−	0.437117i	0.453923	−	0.891041i	$-0.350024\pi$
$19$	−8.30523	−	8.30523i	−0.437117	−	0.437117i	−0.891041	+	0.453923i	$0.850024\pi$
$20$	−21.8669	−	23.7044i	−1.09334	−	1.18522i
$21$		0			0
$22$	−8.29013	−	8.63114i	−0.376824	−	0.392324i
$23$	2.08290	−	3.60768i	0.0905607	−	0.156856i	−0.817187	−	0.576373i	$-0.804467\pi$
$23$	2.08290	−	3.60768i	0.0905607	−	0.156856i	0.907747	+	0.419518i	$0.137801\pi$
$24$		0			0
$25$	34.6443	−	20.0019i	1.38577	−	0.800075i
$26$	8.47832	−	29.2693i	0.326089	−	1.12574i
$27$		0			0
$28$	−10.1785	−	6.43681i	−0.363517	−	0.229886i
$29$	−24.6026	−	6.59225i	−0.848365	−	0.227319i	−0.191656	−	0.981462i	$-0.561386\pi$
$29$	−24.6026	−	6.59225i	−0.848365	−	0.227319i	−0.656710	+	0.754143i	$0.728052\pi$
$30$		0			0
$31$	11.4094	−	19.7616i	0.368044	−	0.637470i	−0.621216	−	0.783639i	$-0.713361\pi$
$31$	11.4094	−	19.7616i	0.368044	−	0.637470i	0.989260	+	0.146169i	$0.0466943\pi$
$32$	13.1315	+	29.1815i	0.410361	+	0.911923i
$33$		0			0
$34$	39.9662	+	24.1610i	1.17548	+	0.710618i
$35$	17.1644	−	17.1644i	0.490412	−	0.490412i
$36$		0			0
$37$	27.8343	−	27.8343i	0.752277	−	0.752277i	−0.222626	−	0.974904i	$-0.571463\pi$
$37$	27.8343	−	27.8343i	0.752277	−	0.752277i	0.974904	+	0.222626i	$0.0714630\pi$
$38$	−22.8082	+	5.62144i	−0.600216	+	0.147933i
$39$		0			0
$40$	−63.1969	+	12.8995i	−1.57992	+	0.322487i
$41$	−36.7431	+	63.6409i	−0.896173	+	1.55222i	−0.0638280	+	0.997961i	$0.520331\pi$
$41$	−36.7431	+	63.6409i	−0.896173	+	1.55222i	−0.832346	+	0.554257i	$0.813002\pi$
$42$		0			0
$43$	−70.9710	−	19.0166i	−1.65049	−	0.442247i	−0.690738	−	0.723105i	$-0.742714\pi$
$43$	−70.9710	−	19.0166i	−1.65049	−	0.442247i	−0.959749	+	0.280858i	$0.909381\pi$
$44$	−23.3504	+	5.25838i	−0.530691	+	0.119509i
$45$		0			0
$46$	−4.01957	−	7.29783i	−0.0873819	−	0.158648i
$47$	39.5925	−	22.8588i	0.842395	−	0.486357i	−0.0156829	−	0.999877i	$-0.504992\pi$
$47$	39.5925	−	22.8588i	0.842395	−	0.486357i	0.858077	+	0.513520i	$0.171659\pi$
$48$		0			0
$49$	−19.9677	+	34.5851i	−0.407504	+	0.705817i
$50$	1.61203	−	79.9912i	0.0322407	−	1.59982i
$51$		0			0
$52$	−41.3234	−	44.7959i	−0.794681	−	0.861459i
$53$	21.0485	+	21.0485i	0.397142	+	0.397142i	0.877224	−	0.480082i	$-0.159393\pi$
$53$	21.0485	+	21.0485i	0.397142	+	0.397142i	−0.480082	+	0.877224i	$0.659393\pi$
$54$		0			0
$55$		−	48.2442i		−	0.877167i
$56$	−21.5485	+	10.7608i	−0.384795	+	0.192158i
$57$		0			0
$58$	−36.7392	+	35.2876i	−0.633434	+	0.608407i
$59$	−77.1219	+	20.6648i	−1.30715	+	0.350250i	−0.844150	−	0.536108i	$-0.819894\pi$
$59$	−77.1219	+	20.6648i	−1.30715	+	0.350250i	−0.463001	+	0.886358i	$0.653227\pi$
$60$		0			0
$61$	13.6831	−	51.0660i	0.224313	−	0.837147i	−0.758366	−	0.651829i	$-0.774002\pi$
$61$	13.6831	−	51.0660i	0.224313	−	0.837147i	0.982679	−	0.185318i	$-0.0593315\pi$
$62$	−22.0177	−	39.9749i	−0.355125	−	0.644757i
$63$		0			0
$64$	63.5328	+	7.71872i	0.992701	+	0.120605i
$65$	106.384	−	61.4211i	1.63668	−	0.944939i
$66$		0			0
$67$	44.8100	−	12.0068i	0.668806	−	0.179206i	0.0915891	−	0.995797i	$-0.470805\pi$
$67$	44.8100	−	12.0068i	0.668806	−	0.179206i	0.577217	+	0.816591i	$0.304139\pi$
$68$	82.7056	−	43.4048i	1.21626	−	0.638307i
$69$		0			0
$70$	−11.6178	−	47.1377i	−0.165969	−	0.673396i
$71$	−82.1279			−1.15673			−0.578366	−	0.815778i	$-0.696309\pi$
$71$	−82.1279			−1.15673			−0.578366	+	0.815778i	$0.696309\pi$
$72$		0			0
$73$			25.3786i			0.347652i	0.984776	+	0.173826i	$0.0556130\pi$
$73$			25.3786i			0.347652i	−0.984776	+	0.173826i	$0.944387\pi$
$74$	−18.8398	−	76.4397i	−0.254592	−	1.03297i
$75$		0			0
$76$	−13.9782	+	44.8539i	−0.183923	+	0.590183i
$77$	−4.66280	−	17.4018i	−0.0605559	−	0.225998i
$78$		0			0
$79$	45.7098	+	79.1717i	0.578605	+	1.00217i	0.995640	+	0.0932826i	$0.0297360\pi$
$79$	45.7098	+	79.1717i	0.578605	+	1.00217i	−0.417035	+	0.908891i	$0.636931\pi$
$80$	−43.3114	+	121.512i	−0.541393	+	1.51890i
$81$		0			0
$82$	70.9068	+	128.737i	0.864717	+	1.56996i
$83$	45.3324	+	12.1468i	0.546173	+	0.146347i	0.521346	−	0.853345i	$-0.325430\pi$
$83$	45.3324	+	12.1468i	0.546173	+	0.146347i	0.0248266	+	0.999692i	$0.492097\pi$
$84$		0			0
$85$	48.7268	+	181.851i	0.573257	+	2.13942i
$86$	−105.981	+	101.794i	−1.23234	+	1.18365i
$87$		0			0
$88$	−15.1605	+	45.4062i	−0.172279	+	0.515979i
$89$	79.4644			0.892858			0.446429	−	0.894819i	$-0.352695\pi$
$89$	79.4644			0.892858			0.446429	+	0.894819i	$0.352695\pi$
$90$		0			0
$91$	32.4368	−	32.4368i	0.356448	−	0.356448i
$92$	−16.6496	−	0.671340i	−0.180974	−	0.00729717i
$93$		0			0
$94$	1.84228	−	91.4165i	0.0195987	−	0.972516i
$95$	−82.0099	−	47.3485i	−0.863263	−	0.498405i
$96$		0			0
$97$	−57.7693	−	100.059i	−0.595560	−	1.03154i	−0.993468	−	0.114114i	$-0.963597\pi$
$97$	−57.7693	−	100.059i	−0.595560	−	1.03154i	0.397908	−	0.917425i	$-0.369736\pi$
$98$	38.5336	+	69.9607i	0.393200	+	0.713885i
$99$		0			0
$100$	−135.241	−	85.5256i	−1.35241	−	0.855256i
$101$	−19.6289	+	73.2561i	−0.194346	+	0.725308i	0.798090	+	0.602539i	$0.205844\pi$
$101$	−19.6289	+	73.2561i	−0.194346	+	0.725308i	−0.992435	+	0.122769i	$0.960823\pi$
$102$		0			0
$103$	47.2845	+	27.2997i	0.459072	+	0.265046i	0.711654	−	0.702530i	$-0.247946\pi$
$103$	47.2845	+	27.2997i	0.459072	+	0.265046i	−0.252582	+	0.967576i	$0.581280\pi$
$104$	−119.428	+	24.3770i	−1.14834	+	0.234394i
$105$		0			0
$106$	57.8044	−	14.2468i	0.545325	−	0.134404i
$107$	137.095	+	137.095i	1.28126	+	1.28126i	0.939952	+	0.341307i	$0.110869\pi$
$107$	137.095	+	137.095i	1.28126	+	1.28126i	0.341307	+	0.939952i	$0.389131\pi$
$108$		0			0
$109$	113.630	+	113.630i	1.04247	+	1.04247i	0.999057	+	0.0434170i	$0.0138244\pi$
$109$	113.630	+	113.630i	1.04247	+	1.04247i	0.0434170	+	0.999057i	$0.486176\pi$
$110$	−82.5724	−	49.9181i	−0.750658	−	0.453800i
$111$		0			0
$112$	−3.87844	+	48.0156i	−0.0346289	+	0.428711i
$113$	11.3738	+	6.56666i	0.100653	+	0.0581121i	0.549482	−	0.835506i	$-0.314825\pi$
$113$	11.3738	+	6.56666i	0.100653	+	0.0581121i	−0.448829	+	0.893618i	$0.648159\pi$
$114$		0			0
$115$	8.69286	−	32.4422i	0.0755901	−	0.282106i
$116$	22.3827	+	99.3929i	0.192955	+	0.856835i
$117$		0			0
$118$	−44.4289	+	153.380i	−0.376516	+	1.29983i
$119$	35.1518	+	60.8847i	0.295393	+	0.511636i
$120$		0			0
$121$	73.7804	+	42.5972i	0.609756	+	0.352043i
$122$	−73.2442	−	76.2570i	−0.600362	−	0.625058i
$123$		0			0
$124$	−91.2007	−	3.67736i	−0.735490	−	0.0296561i
$125$	85.5369	−	85.5369i	0.684296	−	0.684296i
$126$		0			0
$127$	90.5005			0.712602			0.356301	−	0.934371i	$-0.384038\pi$
$127$	90.5005			0.712602			0.356301	+	0.934371i	$0.384038\pi$
$128$	78.9481	−	100.753i	0.616782	−	0.787134i
$129$		0			0
$130$	4.95017	−	245.634i	0.0380783	−	1.88949i
$131$	16.4238	+	61.2946i	0.125373	+	0.467897i	0.999853	−	0.0171642i	$-0.00546381\pi$
$131$	16.4238	+	61.2946i	0.125373	+	0.467897i	−0.874480	+	0.485062i	$0.838797\pi$
$132$		0			0
$133$	−34.1574	−	9.15246i	−0.256823	−	0.0688155i
$134$	25.8144	−	89.1180i	0.192645	−	0.665060i
$135$		0			0
$136$	11.2855	−	186.466i	0.0829819	−	1.37107i
$137$	73.8486	+	127.909i	0.539041	+	0.933646i	0.998956	+	0.0456831i	$0.0145465\pi$
$137$	73.8486	+	127.909i	0.539041	+	0.933646i	−0.459915	+	0.887963i	$0.652120\pi$
$138$		0			0
$139$	−22.9822	−	85.7706i	−0.165339	−	0.617055i	−0.997997	−	0.0632661i	$-0.979848\pi$
$139$	−22.9822	−	85.7706i	−0.165339	−	0.617055i	0.832657	−	0.553788i	$-0.186818\pi$
$140$	−92.6995	−	28.8887i	−0.662139	−	0.206348i
$141$		0			0
$142$	−84.9774	+	140.566i	−0.598432	+	0.989902i
$143$		−	91.1704i		−	0.637556i
$144$		0			0
$145$	−205.356			−1.41624
$146$	43.4368	+	26.2591i	0.297512	+	0.179857i
$147$		0			0
$148$	−150.324	−	46.8466i	−1.01570	−	0.316531i
$149$	241.049	−	64.5889i	1.61778	−	0.433482i	0.667431	−	0.744672i	$-0.267394\pi$
$149$	241.049	−	64.5889i	1.61778	−	0.433482i	0.950348	+	0.311190i	$0.100727\pi$
$150$		0			0
$151$	−199.871	+	115.396i	−1.32365	+	0.764210i	−0.984309	−	0.176453i	$-0.943538\pi$
$151$	−199.871	+	115.396i	−1.32365	+	0.764210i	−0.339342	+	0.940663i	$0.610204\pi$
$152$	62.3065	+	70.3344i	0.409911	+	0.462726i
$153$		0			0
$154$	−34.6087	−	10.0250i	−0.224732	−	0.0650971i
$155$	47.6164	−	177.707i	0.307203	−	1.14650i
$156$		0			0
$157$	5.93179	−	1.58942i	0.0377821	−	0.0101237i	−0.239878	−	0.970803i	$-0.577108\pi$
$157$	5.93179	−	1.58942i	0.0377821	−	0.0101237i	0.277661	+	0.960679i	$0.410441\pi$
$158$	182.802	+	3.68394i	1.15697	+	0.0233161i
$159$		0			0
$160$	163.159	+	199.857i	1.01975	+	1.24911i
$161$		−	12.5422i		−	0.0779016i
$162$		0			0
$163$	−129.554	−	129.554i	−0.794811	−	0.794811i	0.187461	−	0.982272i	$-0.439974\pi$
$163$	−129.554	−	129.554i	−0.794811	−	0.794811i	−0.982272	+	0.187461i	$0.939974\pi$
$164$	293.706	+	11.8427i	1.79089	+	0.0722116i
$165$		0			0
$166$	67.6950	−	65.0204i	0.407801	−	0.391689i
$167$	−141.391	+	244.897i	−0.846653	+	1.46645i	0.0375246	+	0.999296i	$0.488053\pi$
$167$	−141.391	+	244.897i	−0.846653	+	1.46645i	−0.884178	+	0.467151i	$0.845281\pi$
$168$		0			0
$169$	54.6837	−	31.5717i	0.323572	−	0.186815i
$170$	361.665	+	104.762i	2.12744	+	0.616247i
$171$		0			0
$172$	64.5673	+	286.718i	0.375391	+	1.66697i
$173$	−218.009	−	58.4155i	−1.26017	−	0.337662i	−0.433913	−	0.900955i	$-0.642868\pi$
$173$	−218.009	−	58.4155i	−1.26017	−	0.337662i	−0.826257	+	0.563293i	$0.809534\pi$
$174$		0			0
$175$	60.2206	−	104.305i	0.344118	−	0.596030i
$176$	62.0284	+	72.9296i	0.352434	+	0.414373i
$177$		0			0
$178$	82.2214	−	136.007i	0.461918	−	0.764086i
$179$	38.3604	−	38.3604i	0.214304	−	0.214304i	−0.591789	−	0.806093i	$-0.701578\pi$
$179$	38.3604	−	38.3604i	0.214304	−	0.214304i	0.806093	+	0.591789i	$0.201578\pi$
$180$		0			0
$181$	20.4423	−	20.4423i	0.112941	−	0.112941i	−0.648378	−	0.761319i	$-0.724552\pi$
$181$	20.4423	−	20.4423i	0.112941	−	0.112941i	0.761319	+	0.648378i	$0.224552\pi$
$182$	−21.9550	−	89.0794i	−0.120632	−	0.489447i
$183$		0			0
$184$	−18.3763	+	27.8021i	−0.0998713	+	0.151098i
$185$	158.684	−	274.849i	0.857753	−	1.48567i
$186$		0			0
$187$	134.965	+	36.1639i	0.721740	+	0.193390i
$188$	−154.558	−	97.7414i	−0.822116	−	0.519901i
$189$		0			0
$190$	−165.895	+	91.3729i	−0.873129	+	0.480910i
$191$	−68.3229	+	39.4463i	−0.357712	+	0.206525i	−0.668077	−	0.744093i	$-0.732882\pi$
$191$	−68.3229	+	39.4463i	−0.357712	+	0.206525i	0.310365	+	0.950618i	$0.399549\pi$
$192$		0			0
$193$	25.8209	−	44.7231i	0.133787	−	0.231726i	−0.791346	−	0.611368i	$-0.790620\pi$
$193$	25.8209	−	44.7231i	0.133787	−	0.231726i	0.925133	+	0.379642i	$0.123953\pi$
$194$	−231.030	−	4.65586i	−1.19088	−	0.0239993i
$195$		0			0
$196$	159.612	+	6.43580i	0.814346	+	0.0328357i
$197$	121.764	+	121.764i	0.618089	+	0.618089i	0.945041	−	0.326952i	$-0.106021\pi$
$197$	121.764	+	121.764i	0.618089	+	0.618089i	−0.326952	+	0.945041i	$0.606021\pi$
$198$		0			0
$199$		−	14.7523i		−	0.0741321i	−0.999313	−	0.0370661i	$-0.988199\pi$
$199$		−	14.7523i		−	0.0741321i	0.999313	−	0.0370661i	$-0.0118012\pi$
$200$	−286.315	+	142.979i	−1.43157	+	0.714895i
$201$		0			0
$202$	105.072	+	109.394i	0.520156	+	0.541552i
$203$	−74.0723	+	19.8476i	−0.364888	+	0.0977715i
$204$		0			0
$205$	−153.346	+	572.294i	−0.748027	+	2.79168i
$206$	95.6498	−	52.6829i	0.464319	−	0.255742i
$207$		0			0
$208$	−81.8486	+	229.629i	−0.393503	+	1.10399i
$209$	−60.8658	+	35.1409i	−0.291224	+	0.168138i
$210$		0			0
$211$	8.76223	−	2.34783i	0.0415272	−	0.0111272i	−0.237996	−	0.971266i	$-0.576490\pi$
$211$	8.76223	−	2.34783i	0.0415272	−	0.0111272i	0.279523	+	0.960139i	$0.409824\pi$
$212$	35.4258	−	113.676i	0.167103	−	0.536209i
$213$		0			0
$214$	376.496	−	92.7933i	1.75933	−	0.433613i
$215$	−592.388			−2.75529
$216$		0			0
$217$		−	68.7014i		−	0.316597i
$218$	312.055	−	76.9109i	1.43145	−	0.352802i
$219$		0			0
$220$	−170.875	+	89.6769i	−0.776702	+	0.407622i
$221$	92.0825	+	343.657i	0.416663	+	1.55501i
$222$		0			0
$223$	−204.189	−	353.666i	−0.915646	−	1.58594i	−0.805953	−	0.591979i	$-0.798347\pi$
$223$	−204.189	−	353.666i	−0.915646	−	1.58594i	−0.109692	−	0.993966i	$-0.534987\pi$
$224$	78.1682	+	56.3197i	0.348965	+	0.251427i
$225$		0			0
$226$	23.0076	−	12.6723i	0.101803	−	0.0560723i
$227$	−39.8196	−	10.6696i	−0.175417	−	0.0470028i	0.170042	−	0.985437i	$-0.445610\pi$
$227$	−39.8196	−	10.6696i	−0.175417	−	0.0470028i	−0.345458	+	0.938434i	$0.612276\pi$
$228$		0			0
$229$	5.66706	+	21.1498i	0.0247470	+	0.0923570i	0.977195	−	0.212345i	$-0.0681099\pi$
$229$	5.66706	+	21.1498i	0.0247470	+	0.0923570i	−0.952448	+	0.304702i	$0.901443\pi$
$230$	−46.5320	−	48.4461i	−0.202313	−	0.210635i
$231$		0			0
$232$	193.275	+	64.5322i	0.833083	+	0.278156i
$233$	39.8502			0.171031			0.0855155	−	0.996337i	$-0.472746\pi$
$233$	39.8502			0.171031			0.0855155	+	0.996337i	$0.472746\pi$
$234$		0			0
$235$	260.638	−	260.638i	1.10910	−	1.10910i
$236$	216.547	+	234.744i	0.917571	+	0.994676i
$237$		0			0
$238$	140.579	+	2.83303i	0.590667	+	0.0119035i
$239$	−191.059	−	110.308i	−0.799409	−	0.461539i	0.0438555	−	0.999038i	$-0.486036\pi$
$239$	−191.059	−	110.308i	−0.799409	−	0.461539i	−0.843264	+	0.537499i	$0.819369\pi$
$240$		0			0
$241$	−4.52961	−	7.84552i	−0.0187951	−	0.0325540i	0.856475	−	0.516189i	$-0.172650\pi$
$241$	−4.52961	−	7.84552i	−0.0187951	−	0.0325540i	−0.875270	+	0.483635i	$0.839316\pi$
$242$	149.247	−	82.2039i	0.616725	−	0.339685i
$243$		0			0
$244$	−206.303	+	46.4583i	−0.845505	+	0.190403i
$245$	−83.3342	+	311.007i	−0.340140	+	1.26942i
$246$		0			0
$247$	−154.980	−	89.4777i	−0.627449	−	0.362258i
$248$	−100.659	+	152.290i	−0.405883	+	0.614072i
$249$		0			0
$250$	−57.8961	−	234.905i	−0.231585	−	0.939622i
$251$	−14.8880	−	14.8880i	−0.0593147	−	0.0593147i	0.676827	−	0.736142i	$-0.263354\pi$
$251$	−14.8880	−	14.8880i	−0.0593147	−	0.0593147i	−0.736142	+	0.676827i	$0.763354\pi$
$252$		0			0
$253$	−17.6262	−	17.6262i	−0.0696687	−	0.0696687i
$254$	93.6405	−	154.896i	0.368663	−	0.609828i
$255$		0			0
$256$	−90.7569	−	239.372i	−0.354519	−	0.935049i
$257$	−159.082	−	91.8461i	−0.618997	−	0.357378i	0.157481	−	0.987522i	$-0.449663\pi$
$257$	−159.082	−	91.8461i	−0.618997	−	0.357378i	−0.776478	+	0.630144i	$0.782996\pi$
$258$		0			0
$259$	30.6737	−	114.476i	0.118431	−	0.441991i
$260$	−415.294	−	262.629i	−1.59728	−	1.01011i
$261$		0			0
$262$	121.902	+	35.3110i	0.465276	+	0.134775i
$263$	−136.494	−	236.415i	−0.518989	−	0.898915i	−0.999756	−	0.0220670i	$-0.992975\pi$
$263$	−136.494	−	236.415i	−0.518989	−	0.898915i	0.480768	−	0.876848i	$-0.340358\pi$
$264$		0			0
$265$	207.843	+	119.998i	0.784315	+	0.452825i
$266$	−51.0074	+	48.9922i	−0.191757	+	0.184181i
$267$		0			0
$268$	−125.820	−	136.393i	−0.469477	−	0.508928i
$269$	−183.737	+	183.737i	−0.683036	+	0.683036i	−0.960683	−	0.277647i	$-0.910445\pi$
$269$	−183.737	+	183.737i	−0.683036	+	0.683036i	0.277647	+	0.960683i	$0.410445\pi$
$270$		0			0
$271$	−274.391			−1.01251			−0.506256	−	0.862383i	$-0.668971\pi$
$271$	−274.391			−1.01251			−0.506256	+	0.862383i	$0.668971\pi$
$272$	−307.468	−	212.251i	−1.13040	−	0.780334i
$273$		0			0
$274$	295.334	+	5.95176i	1.07786	+	0.0217217i
$275$	−61.9545	−	231.217i	−0.225289	−	0.840790i
$276$		0			0
$277$	157.909	+	42.3116i	0.570068	+	0.152749i	0.532328	−	0.846538i	$-0.321317\pi$
$277$	157.909	+	42.3116i	0.570068	+	0.152749i	0.0377403	+	0.999288i	$0.487984\pi$
$278$	−170.580	−	49.4113i	−0.613598	−	0.177738i
$279$		0			0
$280$	−145.360	+	128.769i	−0.519143	+	0.459889i
$281$	−265.130	−	459.219i	−0.943524	−	1.63423i	−0.758681	−	0.651463i	$-0.774156\pi$
$281$	−265.130	−	459.219i	−0.943524	−	1.63423i	−0.184843	−	0.982768i	$-0.559178\pi$
$282$		0			0
$283$	59.9128	+	223.598i	0.211706	+	0.790098i	0.987300	+	0.158866i	$0.0507838\pi$
$283$	59.9128	+	223.598i	0.211706	+	0.790098i	−0.775594	+	0.631232i	$0.782550\pi$
$284$	152.660	+	290.886i	0.537536	+	1.02425i
$285$		0			0
$286$	−156.043	−	94.3336i	−0.545604	−	0.329838i
$287$			221.249i			0.770901i
$288$		0			0
$289$	−256.263			−0.886722
$290$	−212.480	+	351.476i	−0.732691	+	1.21199i
$291$		0			0
$292$	89.8876	−	47.1740i	0.307834	−	0.161555i
$293$	216.522	−	58.0169i	0.738983	−	0.198010i	0.130357	−	0.991467i	$-0.458388\pi$
$293$	216.522	−	58.0169i	0.738983	−	0.198010i	0.608626	+	0.793457i	$0.291721\pi$
$294$		0			0
$295$	−557.486	+	321.865i	−1.88978	+	1.09107i
$296$	−235.720	+	208.815i	−0.796351	+	0.705456i
$297$		0			0
$298$	138.865	−	479.397i	0.465990	−	1.60872i
$299$	16.4275	−	61.3083i	0.0549415	−	0.205044i
$300$		0			0
$301$	−213.676	+	57.2543i	−0.709887	+	0.190214i
$302$	−9.30021	+	461.489i	−0.0307954	+	1.52811i
$303$		0			0
$304$	184.849	−	33.8661i	0.608057	−	0.111402i
$305$		−	426.243i		−	1.39752i
$306$		0			0
$307$	57.4022	+	57.4022i	0.186978	+	0.186978i	0.794388	−	0.607410i	$-0.207792\pi$
$307$	57.4022	+	57.4022i	0.186978	+	0.186978i	−0.607410	+	0.794388i	$0.707792\pi$
$308$	−52.9676	+	48.8617i	−0.171973	+	0.158642i
$309$		0			0
$310$	−254.886	−	265.370i	−0.822212	−	0.856033i
$311$	188.714	−	326.862i	0.606797	−	1.05100i	−0.384968	−	0.922930i	$-0.625787\pi$
$311$	188.714	−	326.862i	0.606797	−	1.05100i	0.991765	−	0.128073i	$-0.0408792\pi$
$312$		0			0
$313$	−224.605	+	129.676i	−0.717588	+	0.414300i	−0.813864	−	0.581055i	$-0.802640\pi$
$313$	−224.605	+	129.676i	−0.717588	+	0.414300i	0.0962760	+	0.995355i	$0.469307\pi$
$314$	3.41723	−	11.7971i	0.0108829	−	0.0375705i
$315$		0			0
$316$	195.450	−	309.063i	0.618512	−	0.978048i
$317$	−141.196	−	37.8333i	−0.445413	−	0.119348i	0.0291393	−	0.999575i	$-0.490723\pi$
$317$	−141.196	−	37.8333i	−0.445413	−	0.119348i	−0.474552	+	0.880227i	$0.657390\pi$
$318$		0			0
$319$	−76.2050	+	131.991i	−0.238887	+	0.413764i
$320$	510.886	−	72.4640i	1.59652	−	0.226450i
$321$		0			0
$322$	−21.4665	−	12.9773i	−0.0666663	−	0.0403022i
$323$	193.934	−	193.934i	0.600416	−	0.600416i
$324$		0			0
$325$	430.987	−	430.987i	1.32611	−	1.32611i
$326$	−355.788	+	87.6895i	−1.09137	+	0.268986i
$327$		0			0
$328$	324.166	−	490.440i	0.988311	−	1.49524i
$329$	68.8220	−	119.203i	0.209186	−	0.362320i
$330$		0			0
$331$	361.013	+	96.7332i	1.09067	+	0.292245i	0.758962	−	0.651135i	$-0.225707\pi$
$331$	361.013	+	96.7332i	1.09067	+	0.292245i	0.331712	+	0.943381i	$0.392374\pi$
$332$	−41.2421	−	183.140i	−0.124223	−	0.551626i
$333$		0			0
$334$	272.856	+	495.391i	0.816935	+	1.48321i
$335$	323.915	−	187.012i	0.966910	−	0.558246i
$336$		0			0
$337$	19.0170	−	32.9383i	0.0564301	−	0.0977399i	−0.836430	−	0.548073i	$-0.815362\pi$
$337$	19.0170	−	32.9383i	0.0564301	−	0.0977399i	0.892861	+	0.450333i	$0.148695\pi$
$338$	2.54449	−	126.261i	0.00752807	−	0.373553i
$339$		0			0
$340$	553.518	−	510.611i	1.62799	−	1.50180i
$341$	−96.5500	−	96.5500i	−0.283138	−	0.283138i
$342$		0			0
$343$			267.762i			0.780648i
$344$	557.540	+	186.156i	1.62076	+	0.541150i
$345$		0			0
$346$	−325.554	+	312.692i	−0.940909	+	0.903734i
$347$	−152.120	+	40.7606i	−0.438388	+	0.117466i	−0.471261	−	0.881994i	$-0.656201\pi$
$347$	−152.120	+	40.7606i	−0.438388	+	0.117466i	0.0328732	+	0.999460i	$0.489534\pi$
$348$		0			0
$349$	54.1182	−	201.972i	0.155067	−	0.578716i	−0.844033	−	0.536291i	$-0.819825\pi$
$349$	54.1182	−	201.972i	0.155067	−	0.578716i	0.999100	−	0.0424253i	$-0.0135084\pi$
$350$	−116.214	−	210.995i	−0.332039	−	0.602842i
$351$		0			0
$352$	189.003	−	30.7049i	0.536941	−	0.0872298i
$353$	99.4507	−	57.4179i	0.281730	−	0.162657i	−0.352476	−	0.935821i	$-0.614660\pi$
$353$	99.4507	−	57.4179i	0.281730	−	0.162657i	0.634206	+	0.773164i	$0.281327\pi$
$354$		0			0
$355$	−639.593	+	171.378i	−1.80167	+	0.482756i
$356$	−147.709	−	281.452i	−0.414914	−	0.790596i
$357$		0			0
$358$	−25.9645	−	105.347i	−0.0725264	−	0.294266i
$359$	202.626			0.564419			0.282209	−	0.959353i	$-0.408933\pi$
$359$	202.626			0.564419			0.282209	+	0.959353i	$0.408933\pi$
$360$		0			0
$361$		−	223.046i		−	0.617857i
$362$	−13.8365	−	56.1395i	−0.0382223	−	0.155081i
$363$		0			0
$364$	−175.181	−	54.5929i	−0.481266	−	0.149981i
$365$	52.9582	+	197.643i	0.145091	+	0.541487i
$366$		0			0
$367$	198.330	+	343.518i	0.540409	+	0.936016i	0.998880	+	0.0473067i	$0.0150638\pi$
$367$	198.330	+	343.518i	0.540409	+	0.936016i	−0.458471	+	0.888709i	$0.651603\pi$
$368$	28.5707	+	60.2187i	0.0776379	+	0.163638i
$369$		0			0
$370$	−306.229	−	555.981i	−0.827645	−	1.50265i
$371$	86.5676	+	23.1957i	0.233336	+	0.0625221i
$372$		0			0
$373$	94.3996	+	352.304i	0.253082	+	0.944515i	0.969147	+	0.246482i	$0.0792745\pi$
$373$	94.3996	+	352.304i	0.253082	+	0.944515i	−0.716065	+	0.698033i	$0.754059\pi$
$374$	201.544	−	193.582i	0.538889	−	0.517598i
$375$		0			0
$376$	−327.210	+	163.401i	−0.870238	+	0.434577i
$377$	−388.075			−1.02938
$378$		0			0
$379$	291.312	−	291.312i	0.768633	−	0.768633i	−0.209232	−	0.977866i	$-0.567097\pi$
$379$	291.312	−	291.312i	0.768633	−	0.768633i	0.977866	+	0.209232i	$0.0670965\pi$
$380$	−15.2609	+	378.480i	−0.0401603	+	0.996000i
$381$		0			0
$382$	−3.17914	+	157.753i	−0.00832235	+	0.412966i
$383$	16.9453	+	9.78336i	0.0442435	+	0.0255440i	0.521959	−	0.852971i	$-0.325202\pi$
$383$	16.9453	+	9.78336i	0.0442435	+	0.0255440i	−0.477715	+	0.878515i	$0.658535\pi$
$384$		0			0
$385$	−72.6256	−	125.791i	−0.188638	−	0.326731i
$386$	−49.8291	−	90.4686i	−0.129091	−	0.234375i
$387$		0			0
$388$	−247.015	+	390.603i	−0.636636	+	1.00671i
$389$	38.2977	−	142.929i	0.0984518	−	0.367427i	−0.899068	−	0.437808i	$-0.855755\pi$
$389$	38.2977	−	142.929i	0.0984518	−	0.367427i	0.997520	+	0.0703812i	$0.0224216\pi$
$390$		0			0
$391$	84.2424	+	48.6374i	0.215454	+	0.124392i
$392$	176.165	−	266.525i	0.449400	−	0.679910i
$393$		0			0
$394$	334.393	−	82.4164i	0.848713	−	0.209179i
$395$	521.187	+	521.187i	1.31946	+	1.31946i
$396$		0			0
$397$	−91.7365	−	91.7365i	−0.231074	−	0.231074i	0.582067	−	0.813141i	$-0.302244\pi$
$397$	−91.7365	−	91.7365i	−0.231074	−	0.231074i	−0.813141	+	0.582067i	$0.802244\pi$
$398$	−25.2493	−	15.2641i	−0.0634404	−	0.0383521i
$399$		0			0
$400$	−51.5327	+	637.982i	−0.128832	+	1.59495i
$401$	−213.356	−	123.181i	−0.532060	−	0.307185i	0.209795	−	0.977745i	$-0.432720\pi$
$401$	−213.356	−	123.181i	−0.532060	−	0.307185i	−0.741855	+	0.670560i	$0.766054\pi$
$402$		0			0
$403$	89.9840	−	335.825i	0.223285	−	0.833313i
$404$	295.950	−	66.6462i	0.732549	−	0.164966i
$405$		0			0
$406$	−42.6721	+	147.315i	−0.105104	+	0.362844i
$407$	−117.772	−	203.986i	−0.289365	−	0.501195i
$408$		0			0
$409$	−551.068	−	318.159i	−1.34735	−	0.777896i	−0.359480	−	0.933153i	$-0.617046\pi$
$409$	−551.068	−	318.159i	−1.34735	−	0.777896i	−0.987874	+	0.155257i	$0.950379\pi$
$410$	820.844	+	854.608i	2.00206	+	2.08441i
$411$		0			0
$412$	8.79899	−	218.220i	0.0213568	−	0.529661i
$413$	−169.978	+	169.978i	−0.411570	+	0.411570i
$414$		0			0
$415$	378.385			0.911771
$416$	308.333	+	377.684i	0.741186	+	0.907894i
$417$		0			0
$418$	−2.83215	+	140.535i	−0.00677547	+	0.336208i
$419$	−16.3087	−	60.8647i	−0.0389228	−	0.145262i	0.943730	−	0.330717i	$-0.107291\pi$
$419$	−16.3087	−	60.8647i	−0.0389228	−	0.145262i	−0.982653	+	0.185455i	$0.940624\pi$
$420$		0			0
$421$	−421.729	−	113.002i	−1.00173	−	0.268413i	−0.279561	−	0.960128i	$-0.590189\pi$
$421$	−421.729	−	113.002i	−1.00173	−	0.268413i	−0.722171	+	0.691715i	$0.756856\pi$
$422$	5.04781	−	17.4263i	0.0119616	−	0.0412946i
$423$		0			0
$424$	−157.908	−	178.253i	−0.372424	−	0.420409i
$425$	467.061	+	808.973i	1.09897	+	1.90347i
$426$		0			0
$427$	−41.1964	−	153.747i	−0.0964786	−	0.360063i
$428$	230.738	−	740.404i	0.539107	−	1.72992i
$429$		0			0
$430$	−612.941	+	1013.90i	−1.42544	+	2.35791i
$431$			513.207i			1.19074i	0.803453	+	0.595368i	$0.202994\pi$
$431$			513.207i			1.19074i	−0.803453	+	0.595368i	$0.797006\pi$
$432$		0			0
$433$	−292.020			−0.674411			−0.337205	−	0.941431i	$-0.609482\pi$
$433$	−292.020			−0.674411			−0.337205	+	0.941431i	$0.609482\pi$
$434$	−117.586	−	71.0851i	−0.270936	−	0.163790i
$435$		0			0
$436$	191.245	−	613.677i	0.438635	−	1.40752i
$437$	−47.2615	+	12.6637i	−0.108150	+	0.0289787i
$438$		0			0
$439$	−121.141	+	69.9406i	−0.275947	+	0.159318i	−0.631587	−	0.775305i	$-0.717596\pi$
$439$	−121.141	+	69.9406i	−0.275947	+	0.159318i	0.355640	+	0.934623i	$0.384263\pi$
$440$	−23.3166	+	385.249i	−0.0529922	+	0.875565i
$441$		0			0
$442$	683.463	+	197.976i	1.54630	+	0.447909i
$443$	−135.706	+	506.463i	−0.306335	+	1.14326i	0.625456	+	0.780260i	$0.284913\pi$
$443$	−135.706	+	506.463i	−0.306335	+	1.14326i	−0.931790	+	0.362997i	$0.881754\pi$
$444$		0			0
$445$	618.850	−	165.820i	1.39067	−	0.372630i
$446$	−816.590	−	16.4564i	−1.83092	−	0.0368978i
$447$		0			0
$448$	177.274	−	75.5151i	0.395701	−	0.168560i
$449$		−	843.172i		−	1.87789i	−0.344069	−	0.938944i	$-0.611805\pi$
$449$		−	843.172i		−	1.87789i	0.344069	−	0.938944i	$-0.388195\pi$
$450$		0			0
$451$	310.933	+	310.933i	0.689430	+	0.689430i
$452$	2.11651	−	52.4907i	0.00468254	−	0.116130i
$453$		0			0
$454$	−59.4627	+	57.1134i	−0.130975	+	0.125800i
$455$	184.923	−	320.297i	0.406425	−	0.703949i
$456$		0			0
$457$	−142.799	+	82.4450i	−0.312470	+	0.180405i	−0.648031	−	0.761614i	$-0.724407\pi$
$457$	−142.799	+	82.4450i	−0.312470	+	0.180405i	0.335561	+	0.942018i	$0.391074\pi$
$458$	42.0626	+	12.1841i	0.0918396	+	0.0266028i
$459$		0			0
$460$	−131.064	+	29.5150i	−0.284923	+	0.0641630i
$461$	−440.470	−	118.024i	−0.955467	−	0.256017i	−0.252786	−	0.967522i	$-0.581347\pi$
$461$	−440.470	−	118.024i	−0.955467	−	0.256017i	−0.702680	+	0.711506i	$0.748014\pi$
$462$		0			0
$463$	−110.082	+	190.668i	−0.237759	+	0.411810i	−0.960071	−	0.279757i	$-0.909746\pi$
$463$	−110.082	+	190.668i	−0.237759	+	0.411810i	0.722312	+	0.691567i	$0.243079\pi$
$464$	310.431	−	264.029i	0.669032	−	0.569029i
$465$		0			0
$466$	41.2328	−	68.2056i	0.0884824	−	0.146364i
$467$	−281.438	+	281.438i	−0.602651	+	0.602651i	−0.941015	−	0.338364i	$-0.890126\pi$
$467$	−281.438	+	281.438i	−0.602651	+	0.602651i	0.338364	+	0.941015i	$0.390126\pi$
$468$		0			0
$469$	98.7623	−	98.7623i	0.210581	−	0.210581i
$470$	−176.414	−	715.775i	−0.375349	−	1.52292i
$471$		0			0
$472$	625.836	−	127.743i	1.32592	−	0.270642i
$473$	−219.828	+	380.753i	−0.464753	+	0.804975i
$474$		0			0
$475$	−453.849	−	121.608i	−0.955471	−	0.256018i
$476$	150.305	−	237.676i	0.315767	−	0.499320i
$477$		0			0
$478$	−386.485	+	212.872i	−0.808546	+	0.445338i
$479$	321.243	−	185.470i	0.670653	−	0.387202i	−0.125671	−	0.992072i	$-0.540108\pi$
$479$	321.243	−	185.470i	0.670653	−	0.387202i	0.796324	+	0.604870i	$0.206775\pi$
$480$		0			0
$481$	299.877	−	519.402i	0.623444	−	1.07984i
$482$	−18.1148	−	0.365060i	−0.0375825	−	0.000757386i
$483$		0			0
$484$	13.7295	−	340.501i	0.0283668	−	0.703514i
$485$	−658.690	−	658.690i	−1.35812	−	1.35812i
$486$		0			0
$487$			144.495i			0.296705i	0.988935	+	0.148352i	$0.0473970\pi$
$487$			144.495i			0.296705i	−0.988935	+	0.148352i	$0.952603\pi$
$488$	−133.945	+	401.169i	−0.274478	+	0.822067i
$489$		0			0
$490$	446.080	+	464.429i	0.910366	+	0.947814i
$491$	−28.7374	+	7.70017i	−0.0585284	+	0.0156826i	−0.287964	−	0.957641i	$-0.592978\pi$
$491$	−28.7374	+	7.70017i	−0.0585284	+	0.0156826i	0.229436	+	0.973324i	$0.426312\pi$
$492$		0			0
$493$	153.935	−	574.492i	0.312241	−	1.16530i
$494$	−313.503	+	172.674i	−0.634621	+	0.349542i
$495$		0			0
$496$	156.500	+	329.856i	0.315525	+	0.665033i
$497$	−214.139	+	123.633i	−0.430864	+	0.248759i
$498$		0			0
$499$	436.369	−	116.925i	0.874487	−	0.234318i	0.206460	−	0.978455i	$-0.433806\pi$
$499$	436.369	−	116.925i	0.874487	−	0.234318i	0.668027	+	0.744137i	$0.267139\pi$
$500$	−461.958	−	143.963i	−0.923915	−	0.287927i
$501$		0			0
$502$	−40.8861	+	10.0770i	−0.0814464	+	0.0200737i
$503$	94.4911			0.187855			0.0939275	−	0.995579i	$-0.470058\pi$
$503$	94.4911			0.187855			0.0939275	+	0.995579i	$0.470058\pi$
$504$		0			0
$505$			611.461i			1.21081i
$506$	−48.4058	+	11.9304i	−0.0956637	+	0.0235778i
$507$		0			0
$508$	−168.223	−	320.541i	−0.331148	−	0.630986i
$509$	84.3073	+	314.639i	0.165633	+	0.618152i	0.997959	+	0.0638642i	$0.0203425\pi$
$509$	84.3073	+	314.639i	0.165633	+	0.618152i	−0.832325	+	0.554287i	$0.812991\pi$
$510$		0			0
$511$	38.2043	+	66.1718i	0.0747638	+	0.129495i
$512$	−503.604	−	92.3426i	−0.983601	−	0.180357i
$513$		0			0
$514$	−321.801	+	177.244i	−0.626072	+	0.344834i
$515$	425.207	+	113.934i	0.825645	+	0.221231i
$516$		0			0
$517$	−70.8035	−	264.242i	−0.136951	−	0.511107i
$518$	−164.193	−	170.947i	−0.316975	−	0.330014i
$519$		0			0
$520$	−879.206	+	439.055i	−1.69078	+	0.844337i
$521$	325.511			0.624781			0.312391	−	0.949954i	$-0.398870\pi$
$521$	325.511			0.624781			0.312391	+	0.949954i	$0.398870\pi$
$522$		0			0
$523$	−539.325	+	539.325i	−1.03121	+	1.03121i	−0.0317170	+	0.999497i	$0.510098\pi$
$523$	−539.325	+	539.325i	−1.03121	+	1.03121i	−0.999497	+	0.0317170i	$0.989902\pi$
$524$	186.568	−	172.106i	0.356047	−	0.328447i
$525$		0			0
$526$	−545.865	−	11.0006i	−1.03777	−	0.0209137i
$527$	461.450	+	266.418i	0.875617	+	0.505538i
$528$		0			0
$529$	255.823	+	443.099i	0.483598	+	0.837616i
$530$	420.438	−	231.573i	0.793280	−	0.436930i
$531$		0			0
$532$	31.0754	+	137.994i	0.0584125	+	0.259387i
$533$	−289.788	+	1081.50i	−0.543692	+	2.02909i
$534$		0			0
$535$	1353.74	+	781.582i	2.53036	+	1.46090i
$536$	−363.628	+	74.2222i	−0.678411	+	0.138474i
$537$		0			0
$538$	124.363	+	504.586i	0.231158	+	0.937892i
$539$	168.974	+	168.974i	0.313495	+	0.313495i
$540$		0			0
$541$	−114.321	−	114.321i	−0.211315	−	0.211315i	0.593511	−	0.804826i	$-0.297741\pi$
$541$	−114.321	−	114.321i	−0.211315	−	0.211315i	−0.804826	+	0.593511i	$0.797741\pi$
$542$	−283.911	+	469.634i	−0.523821	+	0.866483i
$543$		0			0
$544$	−681.414	+	306.633i	−1.25260	+	0.563663i
$545$	1122.04	+	647.807i	2.05878	+	1.18864i
$546$		0			0
$547$	201.904	−	753.518i	0.369112	−	1.37755i	−0.492647	−	0.870229i	$-0.663971\pi$
$547$	201.904	−	753.518i	0.369112	−	1.37755i	0.861760	−	0.507317i	$-0.169363\pi$
$548$	315.768	−	499.321i	0.576219	−	0.911171i
$549$		0			0
$550$	−459.844	−	133.201i	−0.836080	−	0.242184i
$551$	149.580	+	259.080i	0.271470	+	0.470200i
$552$		0			0
$553$	238.366	+	137.621i	0.431042	+	0.248862i
$554$	235.806	−	226.489i	0.425642	−	0.408826i
$555$		0			0
$556$	−261.068	+	240.831i	−0.469548	+	0.433149i
$557$	102.575	−	102.575i	0.184157	−	0.184157i	−0.609008	−	0.793164i	$-0.708432\pi$
$557$	102.575	−	102.575i	0.184157	−	0.184157i	0.793164	+	0.609008i	$0.208432\pi$
$558$		0			0
$559$	−1119.48			−2.00264
$560$	69.9911	+	382.028i	0.124984	+	0.682192i
$561$		0			0
$562$	−1060.31	−	21.3679i	−1.88666	−	0.0380212i
$563$	−155.383	−	579.897i	−0.275991	−	1.03001i	−0.955174	−	0.296044i	$-0.904332\pi$
$563$	−155.383	−	579.897i	−0.275991	−	1.03001i	0.679183	−	0.733969i	$-0.262334\pi$
$564$		0			0
$565$	102.279	+	27.4057i	0.181025	+	0.0485056i
$566$	444.690	+	128.812i	0.785672	+	0.227582i
$567$		0			0
$568$	655.823	+	39.6927i	1.15462	+	0.0698814i
$569$	−138.669	−	240.182i	−0.243707	−	0.422113i	0.718060	−	0.695981i	$-0.245030\pi$
$569$	−138.669	−	240.182i	−0.243707	−	0.422113i	−0.961767	+	0.273868i	$0.911697\pi$
$570$		0			0
$571$	198.136	+	739.455i	0.346999	+	1.29502i	0.890259	+	0.455454i	$0.150523\pi$
$571$	198.136	+	739.455i	0.346999	+	1.29502i	−0.543260	+	0.839564i	$0.682810\pi$
$572$	−322.914	+	169.469i	−0.564534	+	0.296274i
$573$		0			0
$574$	378.678	+	228.925i	0.659718	+	0.398824i
$575$		−	166.647i		−	0.289821i
$576$		0			0
$577$	283.334			0.491048			0.245524	−	0.969391i	$-0.421040\pi$
$577$	283.334			0.491048			0.245524	+	0.969391i	$0.421040\pi$
$578$	−265.154	+	438.606i	−0.458743	+	0.758835i
$579$		0			0
$580$	381.717	+	727.342i	0.658133	+	1.25404i
$581$	136.484	−	36.5709i	0.234913	−	0.0629447i
$582$		0			0
$583$	154.256	−	89.0600i	0.264591	−	0.152762i
$584$	12.2655	−	202.658i	0.0210026	−	0.347017i
$585$		0			0
$586$	124.735	−	430.618i	0.212859	−	0.734843i
$587$	−192.982	+	720.218i	−0.328759	+	1.22695i	0.581719	+	0.813390i	$0.302380\pi$
$587$	−192.982	+	720.218i	−0.328759	+	1.22695i	−0.910478	+	0.413557i	$0.864286\pi$
$588$		0			0
$589$	−258.882	+	69.3672i	−0.439528	+	0.117771i
$590$	−25.9404	+	1287.20i	−0.0439667	+	2.18169i
$591$		0			0
$592$	113.499	+	619.506i	0.191722	+	1.04646i
$593$		−	496.014i		−	0.836449i	−0.908344	−	0.418224i	$-0.862653\pi$
$593$		−	496.014i		−	0.836449i	0.908344	−	0.418224i	$-0.137347\pi$
$594$		0			0
$595$	400.804	+	400.804i	0.673620	+	0.673620i
$596$	−676.830	−	733.705i	−1.13562	−	1.23105i
$597$		0			0
$598$	−87.9348	−	91.5519i	−0.147048	−	0.153097i
$599$	−485.209	+	840.406i	−0.810032	+	1.40302i	0.102810	+	0.994701i	$0.467217\pi$
$599$	−485.209	+	840.406i	−0.810032	+	1.40302i	−0.912841	+	0.408315i	$0.866117\pi$
$600$		0			0
$601$	313.781	−	181.162i	0.522099	−	0.301434i	−0.215694	−	0.976461i	$-0.569201\pi$
$601$	313.781	−	181.162i	0.522099	−	0.301434i	0.737793	+	0.675027i	$0.235868\pi$
$602$	−123.096	+	424.958i	−0.204478	+	0.705910i
$603$		0			0
$604$	780.239	+	493.418i	1.29179	+	0.816918i
$605$	663.474	+	177.777i	1.09665	+	0.293847i
$606$		0			0
$607$	252.276	−	436.954i	0.415611	−	0.719859i	−0.579882	−	0.814701i	$-0.696901\pi$
$607$	252.276	−	436.954i	0.415611	−	0.719859i	0.995492	+	0.0948420i	$0.0302346\pi$
$608$	133.299	−	351.420i	0.219242	−	0.577993i
$609$		0			0
$610$	−729.536	−	441.031i	−1.19596	−	0.723002i
$611$	492.545	−	492.545i	0.806129	−	0.806129i
$612$		0			0
$613$	423.437	−	423.437i	0.690762	−	0.690762i	−0.271637	−	0.962400i	$-0.587565\pi$
$613$	423.437	−	423.437i	0.690762	−	0.690762i	0.962400	+	0.271637i	$0.0875651\pi$
$614$	157.640	−	38.8530i	0.256743	−	0.0632784i
$615$		0			0
$616$	28.8239	+	141.214i	0.0467921	+	0.229243i
$617$	−209.043	+	362.074i	−0.338806	+	0.586829i	−0.984208	−	0.177013i	$-0.943356\pi$
$617$	−209.043	+	362.074i	−0.338806	+	0.586829i	0.645402	+	0.763843i	$0.276690\pi$
$618$		0			0
$619$	741.141	+	198.588i	1.19732	+	0.320821i	0.801775	−	0.597626i	$-0.203889\pi$
$619$	741.141	+	198.588i	1.19732	+	0.320821i	0.395544	+	0.918447i	$0.370556\pi$
$620$	−717.924	+	161.673i	−1.15794	+	0.260762i
$621$		0			0
$622$	−364.180	−	661.196i	−0.585498	−	1.06302i
$623$	207.194	−	119.624i	0.332575	−	0.192012i
$624$		0			0
$625$	−12.3971	+	21.4724i	−0.0198354	+	0.0343559i
$626$	−10.4511	+	518.598i	−0.0166951	+	0.828432i
$627$		0			0
$628$	−16.6556	−	18.0552i	−0.0265217	−	0.0287503i
$629$	649.954	+	649.954i	1.03331	+	1.03331i
$630$		0			0
$631$		−	371.144i		−	0.588184i	−0.955777	−	0.294092i	$-0.904983\pi$
$631$		−	371.144i		−	0.588184i	0.955777	−	0.294092i	$-0.0950172\pi$
$632$	−326.746	−	654.308i	−0.517004	−	1.03530i
$633$		0			0
$634$	−210.848	+	202.518i	−0.332568	+	0.319429i
$635$	704.797	−	188.850i	1.10992	−	0.297401i
$636$		0			0
$637$	−157.482	+	587.732i	−0.247225	+	0.922657i
$638$	147.060	+	266.999i	0.230502	+	0.418494i
$639$		0			0
$640$	404.585	−	949.385i	0.632164	−	1.48341i
$641$	−816.691	+	471.517i	−1.27409	+	0.735596i	−0.975755	−	0.218866i	$-0.929764\pi$
$641$	−816.691	+	471.517i	−1.27409	+	0.735596i	−0.298334	+	0.954462i	$0.596431\pi$
$642$		0			0
$643$	−603.124	+	161.607i	−0.937984	+	0.251332i	−0.695256	−	0.718762i	$-0.744709\pi$
$643$	−603.124	+	161.607i	−0.937984	+	0.251332i	−0.242728	+	0.970094i	$0.578042\pi$
$644$	−44.4226	+	23.3135i	−0.0689793	+	0.0362011i
$645$		0			0
$646$	−131.265	−	532.591i	−0.203197	−	0.824445i
$647$	842.116			1.30157			0.650785	−	0.759262i	$-0.274440\pi$
$647$	842.116			1.30157			0.650785	+	0.759262i	$0.274440\pi$
$648$		0			0
$649$			477.760i			0.736148i
$650$	−291.716	−	1183.59i	−0.448793	−	1.82092i
$651$		0			0
$652$	−218.047	+	699.680i	−0.334428	+	1.07313i
$653$	−261.752	−	976.873i	−0.400846	−	1.49598i	−0.811591	−	0.584226i	$-0.801398\pi$
$653$	−261.752	−	976.873i	−0.400846	−	1.49598i	0.410745	−	0.911750i	$-0.365269\pi$
$654$		0			0
$655$	255.810	+	443.076i	0.390549	+	0.676452i
$656$	−503.999	−	1062.28i	−0.768292	−	1.61933i
$657$		0			0
$658$	−132.813	−	241.131i	−0.201843	−	0.366461i
$659$	812.320	+	217.660i	1.23266	+	0.330289i	0.815613	−	0.578598i	$-0.196400\pi$
$659$	812.320	+	217.660i	1.23266	+	0.330289i	0.417042	+	0.908887i	$0.363067\pi$
$660$		0			0
$661$	26.4383	+	98.6689i	0.0399974	+	0.149272i	0.983037	−	0.183409i	$-0.0587133\pi$
$661$	26.4383	+	98.6689i	0.0399974	+	0.149272i	−0.943039	+	0.332681i	$0.892047\pi$
$662$	539.102	−	517.803i	0.814354	−	0.782180i
$663$		0			0
$664$	−356.126	−	118.906i	−0.536334	−	0.179075i
$665$	−285.109			−0.428735
$666$		0			0
$667$	−75.0273	+	75.0273i	−0.112485	+	0.112485i
$668$	1130.21	+	45.5719i	1.69193	+	0.0682214i
$669$		0			0
$670$	15.0721	−	747.898i	0.0224957	−	1.11627i
$671$	−273.965	−	158.174i	−0.408293	−	0.235728i
$672$		0			0
$673$	−345.603	−	598.603i	−0.513527	−	0.889454i	−0.999877	−	0.0156903i	$-0.995005\pi$
$673$	−345.603	−	598.603i	−0.513527	−	0.889454i	0.486350	−	0.873764i	$-0.338328\pi$
$674$	−36.6989	−	66.6296i	−0.0544494	−	0.0988570i
$675$		0			0
$676$	−213.469	−	134.997i	−0.315783	−	0.199699i
$677$	211.396	−	788.942i	0.312255	−	1.16535i	−0.614264	−	0.789101i	$-0.710547\pi$
$677$	211.396	−	788.942i	0.312255	−	1.16535i	0.926518	−	0.376250i	$-0.122787\pi$
$678$		0			0
$679$	−301.254	−	173.929i	−0.443673	−	0.256155i
$680$	−301.214	−	1475.70i	−0.442961	−	2.17015i
$681$		0			0
$682$	−265.150	+	65.3504i	−0.388783	+	0.0958217i
$683$	−722.723	−	722.723i	−1.05816	−	1.05816i	−0.998201	−	0.0599580i	$-0.980903\pi$
$683$	−722.723	−	722.723i	−1.05816	−	1.05816i	−0.0599580	−	0.998201i	$-0.519097\pi$
$684$		0			0
$685$	842.028	+	842.028i	1.22924	+	1.22924i
$686$	458.289	+	277.052i	0.668059	+	0.403866i
$687$		0			0
$688$	895.498	−	761.644i	1.30160	−	1.10704i
$689$	392.776	+	226.770i	0.570067	+	0.329128i
$690$		0			0
$691$	276.067	−	1030.30i	0.399518	−	1.49102i	−0.414429	−	0.910082i	$-0.636019\pi$
$691$	276.067	−	1030.30i	0.399518	−	1.49102i	0.813947	−	0.580939i	$-0.197315\pi$
$692$	198.339	+	880.744i	0.286617	+	1.27275i
$693$		0			0
$694$	−87.6346	+	302.537i	−0.126275	+	0.435932i
$695$	−357.959	−	620.004i	−0.515049	−	0.892092i
$696$		0			0
$697$	−1486.07	−	857.983i	−2.13210	−	1.23097i
$698$	−289.689	−	301.606i	−0.415028	−	0.432100i
$699$		0			0
$700$	−481.374	−	19.4098i	−0.687677	−	0.0277282i
$701$	55.9778	−	55.9778i	0.0798542	−	0.0798542i	−0.666052	−	0.745906i	$-0.732017\pi$
$701$	55.9778	−	55.9778i	0.0798542	−	0.0798542i	0.745906	+	0.666052i	$0.232017\pi$
$702$		0			0
$703$	−462.340			−0.657667
$704$	143.008	−	355.259i	0.203136	−	0.504629i
$705$		0			0
$706$	4.62754	−	229.625i	0.00655459	−	0.325248i
$707$	59.0977	+	220.556i	0.0835894	+	0.311960i
$708$		0			0
$709$	−569.856	−	152.692i	−0.803746	−	0.215363i	−0.166518	−	0.986038i	$-0.553252\pi$
$709$	−569.856	−	152.692i	−0.803746	−	0.215363i	−0.637228	+	0.770675i	$0.719919\pi$
$710$	−368.461	+	1272.02i	−0.518959	+	1.79158i
$711$		0			0
$712$	−634.554	−	38.4054i	−0.891227	−	0.0539401i
$713$	−47.5290	−	82.3226i	−0.0666606	−	0.115459i
$714$		0			0
$715$	−190.248	−	710.014i	−0.266081	−	0.993027i
$716$	−207.172	−	64.5627i	−0.289347	−	0.0901714i
$717$		0			0
$718$	209.656	−	346.805i	0.292001	−	0.483016i
$719$		−	43.5371i		−	0.0605523i	−0.999542	−	0.0302762i	$-0.990361\pi$
$719$		−	43.5371i		−	0.0605523i	0.999542	−	0.0302762i	$-0.00963868\pi$
$720$		0			0
$721$	164.385			0.227996
$722$	−381.755	−	230.785i	−0.528747	−	0.319647i
$723$		0			0
$724$	−110.402	−	34.4055i	−0.152489	−	0.0475214i
$725$	−984.196	+	263.715i	−1.35751	+	0.363744i
$726$		0			0
$727$	182.291	−	105.246i	0.250745	−	0.144768i	−0.369360	−	0.929286i	$-0.620423\pi$
$727$	182.291	−	105.246i	0.250745	−	0.144768i	0.620105	+	0.784519i	$0.287090\pi$
$728$	−274.697	+	243.344i	−0.377331	+	0.334263i
$729$		0			0
$730$	393.071	+	113.859i	0.538453	+	0.155972i
$731$	444.054	−	1657.23i	0.607461	−	2.26708i
$732$		0			0
$733$	−800.550	+	214.507i	−1.09216	+	0.292642i	−0.759567	−	0.650429i	$-0.774589\pi$
$733$	−800.550	+	214.507i	−1.09216	+	0.292642i	−0.332589	+	0.943072i	$0.607922\pi$
$734$	793.159	+	15.9842i	1.08060	+	0.0217769i
$735$		0			0
$736$	132.629	+	13.4077i	0.180203	+	0.0182170i
$737$		−	277.592i		−	0.376652i
$738$		0			0
$739$	−423.799	−	423.799i	−0.573476	−	0.573476i	0.359622	−	0.933098i	$-0.382906\pi$
$739$	−423.799	−	423.799i	−0.573476	−	0.573476i	−0.933098	+	0.359622i	$0.882906\pi$
$740$	−1268.44	−	51.1457i	−1.71411	−	0.0691158i
$741$		0			0
$742$	129.272	−	124.164i	0.174221	−	0.167337i
$743$	−270.936	+	469.275i	−0.364652	+	0.631596i	−0.988720	−	0.149774i	$-0.952145\pi$
$743$	−270.936	+	469.275i	−0.364652	+	0.631596i	0.624068	+	0.781370i	$0.285479\pi$
$744$		0			0
$745$	1742.45	−	1006.01i	2.33886	−	1.35034i
$746$	700.661	+	202.958i	0.939224	+	0.272061i
$747$		0			0
$748$	−122.788	−	545.251i	−0.164155	−	0.728946i
$749$	563.838	+	151.080i	0.752787	+	0.201709i
$750$		0			0
$751$	615.386	−	1065.88i	0.819422	−	1.41928i	−0.0866868	−	0.996236i	$-0.527628\pi$
$751$	615.386	−	1065.88i	0.819422	−	1.41928i	0.906109	−	0.423045i	$-0.139039\pi$
$752$	−58.8932	+	729.106i	−0.0783154	+	0.969556i
$753$		0			0
$754$	−401.539	+	664.209i	−0.532545	+	0.880914i
$755$	−1315.75	+	1315.75i	−1.74272	+	1.74272i
$756$		0			0
$757$	−41.7353	+	41.7353i	−0.0551326	+	0.0551326i	−0.734136	−	0.679003i	$-0.762412\pi$
$757$	−41.7353	+	41.7353i	−0.0551326	+	0.0551326i	0.679003	+	0.734136i	$0.262412\pi$
$758$	−197.176	−	800.015i	−0.260127	−	1.05543i
$759$		0			0
$760$	631.998	+	417.731i	0.831576	+	0.549647i
$761$	56.7643	−	98.3187i	0.0745917	−	0.129197i	−0.826317	−	0.563205i	$-0.809568\pi$
$761$	56.7643	−	98.3187i	0.0745917	−	0.129197i	0.900909	+	0.434009i	$0.142901\pi$
$762$		0			0
$763$	467.332	+	125.221i	0.612492	+	0.164117i
$764$	266.713	+	168.668i	0.349101	+	0.220769i
$765$		0			0
$766$	34.2779	−	18.8799i	0.0447492	−	0.0246474i
$767$	−1053.52	+	608.250i	−1.37356	+	0.793025i
$768$		0			0
$769$	348.676	−	603.925i	0.453415	−	0.785338i	−0.545180	−	0.838319i	$-0.683539\pi$
$769$	348.676	−	603.925i	0.453415	−	0.785338i	0.998596	+	0.0529807i	$0.0168722\pi$
$770$	−290.444	−	5.85320i	−0.377199	−	0.00760155i
$771$		0			0
$772$	−206.399	−	8.32236i	−0.267357	−	0.0107803i
$773$	−380.830	−	380.830i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$773$	−380.830	−	380.830i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$774$		0			0
$775$		−	912.834i		−	1.17785i
$776$	412.951	+	826.933i	0.532154	+	1.06564i
$777$		0			0
$778$	−205.004	−	213.437i	−0.263501	−	0.274340i
$779$	833.713	−	223.393i	1.07023	−	0.286768i
$780$		0			0
$781$	−127.193	+	474.691i	−0.162859	+	0.607799i
$782$	170.411	−	93.8603i	0.217916	−	0.120026i
$783$		0			0
$784$	−273.894	−	577.287i	−0.349354	−	0.736335i
$785$	42.8788	−	24.7561i	0.0546226	−	0.0315364i
$786$		0			0
$787$	−151.011	+	40.4632i	−0.191882	+	0.0514145i	−0.353480	−	0.935442i	$-0.615002\pi$
$787$	−151.011	+	40.4632i	−0.191882	+	0.0514145i	0.161598	+	0.986857i	$0.448335\pi$
$788$	204.935	−	657.606i	0.260070	−	0.834526i
$789$		0			0
$790$	1431.31	−	352.768i	1.81178	−	0.446542i
$791$	39.5412			0.0499888
$792$		0			0
$793$		−	805.501i		−	1.01576i
$794$	−251.931	+	62.0923i	−0.317293	+	0.0782019i
$795$		0			0
$796$	−52.2506	+	27.4217i	−0.0656415	+	0.0344494i
$797$	−10.9138	−	40.7309i	−0.0136936	−	0.0511052i	0.958741	−	0.284281i	$-0.0917549\pi$
$797$	−10.9138	−	40.7309i	−0.0136936	−	0.0511052i	−0.972435	+	0.233176i	$0.925088\pi$
$798$		0			0
$799$	533.772	+	924.520i	0.668050	+	1.15710i
$800$	1038.62	+	748.318i	1.29827	+	0.935397i
$801$		0			0
$802$	−431.589	+	237.715i	−0.538141	+	0.296402i
$803$	146.686	+	39.3043i	0.182672	+	0.0489468i
$804$		0			0
$805$	−26.1720	−	97.6754i	−0.0325118	−	0.121336i
$806$	−481.675	−	501.489i	−0.597612	−	0.622194i
$807$		0			0
$808$	192.149	−	575.491i	0.237808	−	0.712242i
$809$	−478.319			−0.591248			−0.295624	−	0.955304i	$-0.595528\pi$
$809$	−478.319			−0.591248			−0.295624	+	0.955304i	$0.595528\pi$
$810$		0			0
$811$	−677.084	+	677.084i	−0.834876	+	0.834876i	−0.988179	−	0.153304i	$-0.951009\pi$
$811$	−677.084	+	677.084i	−0.834876	+	0.834876i	0.153304	+	0.988179i	$0.451009\pi$
$812$	207.984	+	225.461i	0.256138	+	0.277662i
$813$		0			0
$814$	−470.991	−	9.49170i	−0.578613	−	0.0116606i
$815$	−1279.28	−	738.594i	−1.56967	−	0.906250i
$816$		0			0
$817$	431.493	+	747.368i	0.528143	+	0.914771i
$818$	−1114.73	+	613.983i	−1.36275	+	0.750590i
$819$		0			0
$820$	2312.03	−	520.656i	2.81955	−	0.634947i
$821$	283.124	−	1056.63i	0.344852	−	1.28701i	−0.547932	−	0.836523i	$-0.684585\pi$
$821$	283.124	−	1056.63i	0.344852	−	1.28701i	0.892784	−	0.450484i	$-0.148749\pi$
$822$		0			0
$823$	242.222	+	139.847i	0.294316	+	0.169924i	0.639887	−	0.768469i	$-0.278981\pi$
$823$	242.222	+	139.847i	0.294316	+	0.169924i	−0.345571	+	0.938393i	$0.612315\pi$
$824$	−364.391	−	240.851i	−0.442222	−	0.292295i
$825$		0			0
$826$	115.051	+	466.802i	0.139287	+	0.565136i
$827$	569.091	+	569.091i	0.688139	+	0.688139i	0.961820	−	0.273681i	$-0.0882414\pi$
$827$	569.091	+	569.091i	0.688139	+	0.688139i	−0.273681	+	0.961820i	$0.588241\pi$
$828$		0			0
$829$	−80.7363	−	80.7363i	−0.0973900	−	0.0973900i	0.656733	−	0.754123i	$-0.271938\pi$
$829$	−80.7363	−	80.7363i	−0.0973900	−	0.0973900i	−0.754123	+	0.656733i	$0.771938\pi$
$830$	391.513	−	647.625i	0.471702	−	0.780271i
$831$		0			0
$832$	965.457	−	136.940i	1.16040	−	0.164592i
$833$	−807.591	−	466.263i	−0.969497	−	0.559739i
$834$		0			0
$835$	−590.089	+	2202.24i	−0.706693	+	2.63741i
$836$	237.602	+	150.258i	0.284213	+	0.179735i
$837$		0			0
$838$	−121.048	−	35.0634i	−0.144448	−	0.0418417i
$839$	289.410	+	501.274i	0.344947	+	0.597465i	0.985344	−	0.170578i	$-0.0545636\pi$
$839$	289.410	+	501.274i	0.344947	+	0.597465i	−0.640397	+	0.768044i	$0.721230\pi$
$840$		0			0
$841$	−166.497	−	96.1272i	−0.197975	−	0.114301i
$842$	−629.770	+	604.888i	−0.747945	+	0.718395i
$843$		0			0
$844$	−24.6031	−	26.6705i	−0.0291505	−	0.0316001i
$845$	359.983	−	359.983i	0.426015	−	0.426015i
$846$		0			0
$847$	256.499			0.302832
$848$	−468.476	+	85.8292i	−0.552448	+	0.101214i
$849$		0			0
$850$	1867.86	+	37.6423i	2.19749	+	0.0442851i
$851$	−42.4413	−	158.393i	−0.0498722	−	0.186126i
$852$		0			0
$853$	−1018.79	−	272.983i	−1.19436	−	0.320027i	−0.393750	−	0.919218i	$-0.628822\pi$
$853$	−1018.79	−	272.983i	−1.19436	−	0.320027i	−0.800606	+	0.599191i	$0.795489\pi$
$854$	−305.771	−	88.5715i	−0.358046	−	0.103714i
$855$		0			0
$856$	−1028.50	−	1161.01i	−1.20151	−	1.35632i
$857$	−217.412	−	376.568i	−0.253689	−	0.439403i	0.710849	−	0.703344i	$-0.248311\pi$
$857$	−217.412	−	376.568i	−0.253689	−	0.439403i	−0.964539	+	0.263942i	$0.914977\pi$
$858$		0			0
$859$	132.535	+	494.627i	0.154290	+	0.575817i	0.999165	+	0.0408540i	$0.0130079\pi$
$859$	132.535	+	494.627i	0.154290	+	0.575817i	−0.844875	+	0.534963i	$0.820325\pi$
$860$	1101.14	+	2098.16i	1.28039	+	2.43972i
$861$		0			0
$862$	878.380	+	531.013i	1.01900	+	0.616024i
$863$			793.043i			0.918938i	0.888194	+	0.459469i	$0.151960\pi$
$863$			793.043i			0.918938i	−0.888194	+	0.459469i	$0.848040\pi$
$864$		0			0
$865$	−1819.70			−2.10370
$866$	−302.152	+	499.807i	−0.348905	+	0.577144i
$867$		0			0
$868$	−243.331	+	127.703i	−0.280336	+	0.147123i
$869$	528.395	−	141.583i	0.608050	−	0.162926i
$870$		0			0
$871$	612.125	−	353.410i	0.702784	−	0.405752i
$872$	−852.459	−	962.295i	−0.977591	−	1.10355i
$873$		0			0
$874$	−27.2267	+	93.9936i	−0.0311519	+	0.107544i
$875$	94.2627	−	351.793i	0.107729	−	0.402049i
$876$		0			0
$877$	−508.981	+	136.381i	−0.580366	+	0.155509i	−0.537046	−	0.843553i	$-0.680460\pi$
$877$	−508.981	+	136.381i	−0.580366	+	0.155509i	−0.0433195	+	0.999061i	$0.513793\pi$
$878$	−5.63680	+	279.706i	−0.00642004	+	0.318571i
$879$		0			0
$880$	635.247	+	438.522i	0.721872	+	0.498321i
$881$			526.136i			0.597204i	0.954378	+	0.298602i	$0.0965202\pi$
$881$			526.136i			0.597204i	−0.954378	+	0.298602i	$0.903480\pi$
$882$		0			0
$883$	525.594	+	525.594i	0.595237	+	0.595237i	0.939041	−	0.343804i	$-0.111716\pi$
$883$	525.594	+	525.594i	0.595237	+	0.595237i	−0.343804	+	0.939041i	$0.611716\pi$
$884$	1046.02	−	964.937i	1.18328	−	1.09156i
$885$		0			0
$886$	726.422	+	756.303i	0.819889	+	0.853615i
$887$	−103.642	+	179.513i	−0.116846	+	0.202383i	−0.918516	−	0.395384i	$-0.870612\pi$
$887$	−103.642	+	179.513i	−0.116846	+	0.202383i	0.801670	+	0.597766i	$0.203945\pi$
$888$		0			0
$889$	235.970	−	136.237i	0.265433	−	0.153248i
$890$	356.511	−	1230.77i	0.400574	−	1.38288i
$891$		0			0
$892$	−873.088	+	1380.61i	−0.978798	+	1.54777i
$893$	−518.672	−	138.978i	−0.580820	−	0.155630i
$894$		0			0
$895$	218.694	−	378.790i	0.244351	−	0.423229i
$896$	54.1769	−	381.549i	0.0604653	−	0.425836i
$897$		0			0
$898$	−1443.13	−	872.426i	−1.60705	−	0.971521i
$899$	−410.973	+	410.973i	−0.457145	+	0.457145i
$900$		0			0
$901$	−491.501	+	491.501i	−0.545506	+	0.545506i
$902$	853.899	−	210.457i	0.946673	−	0.233322i
$903$		0			0
$904$	−87.6505	−	57.9343i	−0.0969585	−	0.0640867i
$905$	116.542	−	201.857i	0.128776	−	0.223046i
$906$		0			0
$907$	−251.324	−	67.3421i	−0.277094	−	0.0742470i	0.117596	−	0.993062i	$-0.462481\pi$
$907$	−251.324	−	67.3421i	−0.277094	−	0.0742470i	−0.394690	+	0.918814i	$0.629148\pi$
$908$	36.2267	+	160.868i	0.0398973	+	0.177168i
$909$		0			0
$910$	−356.865	−	647.915i	−0.392159	−	0.711995i
$911$	713.768	−	412.094i	0.783500	−	0.452354i	−0.0541694	−	0.998532i	$-0.517251\pi$
$911$	713.768	−	412.094i	0.783500	−	0.452354i	0.837669	+	0.546178i	$0.183918\pi$
$912$		0			0
$913$	140.414	−	243.204i	0.153794	−	0.266379i
$914$	−6.64458	+	329.713i	−0.00726978	+	0.360736i
$915$		0			0
$916$	64.3756	−	59.3854i	0.0702791	−	0.0648312i
$917$	135.095	+	135.095i	0.147322	+	0.147322i
$918$		0			0
$919$		−	443.203i		−	0.482267i	−0.970492	−	0.241133i	$-0.922481\pi$
$919$		−	443.203i		−	0.482267i	0.970492	−	0.241133i	$-0.0775191\pi$
$920$	−85.0953	+	254.862i	−0.0924949	+	0.277024i
$921$		0			0
$922$	−657.756	+	631.768i	−0.713401	+	0.685215i
$923$	−1208.68	+	323.866i	−1.30952	+	0.350884i
$924$		0			0
$925$	407.560	−	1521.03i	0.440605	−	1.64436i
$926$	212.436	+	385.695i	0.229413	+	0.416517i
$927$		0			0
$928$	−130.698	−	804.508i	−0.140838	−	0.866927i
$929$	−45.8533	+	26.4734i	−0.0493577	+	0.0284967i	−0.524476	−	0.851425i	$-0.675739\pi$
$929$	−45.8533	+	26.4734i	−0.0493577	+	0.0284967i	0.475118	+	0.879922i	$0.342405\pi$
$930$		0			0
$931$	453.073	−	121.401i	0.486652	−	0.130398i
$932$	−74.0740	−	141.144i	−0.0794786	−	0.151442i
$933$		0			0
$934$	190.493	+	772.898i	0.203954	+	0.827513i
$935$	1126.54			1.20486
$936$		0			0
$937$			1456.88i			1.55484i	0.628983	+	0.777419i	$0.283471\pi$
$937$			1456.88i			1.55484i	−0.628983	+	0.777419i	$0.716529\pi$
$938$	−66.8478	−	271.225i	−0.0712663	−	0.289153i
$939$		0			0
$940$	−1407.62	−	438.667i	−1.49747	−	0.466667i
$941$	−12.5017	−	46.6568i	−0.0132855	−	0.0495822i	0.958965	−	0.283525i	$-0.0915038\pi$
$941$	−12.5017	−	46.6568i	−0.0132855	−	0.0495822i	−0.972250	+	0.233943i	$0.924837\pi$
$942$		0			0
$943$	153.064	+	265.115i	0.162316	+	0.281140i
$944$	428.911	−	1203.32i	0.454355	−	1.27471i
$945$		0			0
$946$	424.223	+	770.210i	0.448439	+	0.814176i
$947$	−1671.21	−	447.800i	−1.76474	−	0.472861i	−0.777073	−	0.629411i	$-0.783296\pi$
$947$	−1671.21	−	447.800i	−1.76474	−	0.472861i	−0.987670	+	0.156549i	$0.949963\pi$
$948$		0			0
$949$	100.079	+	373.499i	0.105457	+	0.393571i
$950$	−677.734	+	650.957i	−0.713404	+	0.685218i
$951$		0			0
$952$	−251.275	−	503.177i	−0.263944	−	0.528547i
$953$	314.313			0.329814			0.164907	−	0.986309i	$-0.447268\pi$
$953$	314.313			0.329814			0.164907	+	0.986309i	$0.447268\pi$
$954$		0			0
$955$	−449.770	+	449.770i	−0.470963	+	0.470963i
$956$	−35.5534	+	881.746i	−0.0371898	+	0.922328i
$957$		0			0
$958$	14.9477	−	741.728i	0.0156031	−	0.774246i
$959$	385.104	+	222.340i	0.401568	+	0.231845i
$960$		0			0
$961$	220.153	+	381.316i	0.229088	+	0.396791i
$962$	−578.701	−	1050.68i	−0.601561	−	1.09218i
$963$		0			0
$964$	−19.3681	+	30.6266i	−0.0200914	+	0.0317704i
$965$	107.762	−	402.174i	0.111671	−	0.416761i
$966$		0			0
$967$	−1491.50	−	861.116i	−1.54240	−	0.890503i	−0.998687	−	0.0512290i	$-0.983686\pi$
$967$	−1491.50	−	861.116i	−1.54240	−	0.890503i	−0.543709	−	0.839274i	$-0.682981\pi$
$968$	−568.578	−	375.813i	−0.587374	−	0.388237i
$969$		0			0
$970$	−1808.93	+	445.838i	−1.86487	+	0.459627i
$971$	695.679	+	695.679i	0.716456	+	0.716456i	0.967878	−	0.251422i	$-0.0808981\pi$
$971$	695.679	+	695.679i	0.716456	+	0.716456i	−0.251422	+	0.967878i	$0.580898\pi$
$972$		0			0
$973$	−189.040	−	189.040i	−0.194286	−	0.194286i
$974$	247.311	+	149.508i	0.253913	+	0.153499i
$975$		0			0
$976$	548.028	+	644.341i	0.561504	+	0.660185i
$977$	360.870	+	208.348i	0.369365	+	0.213253i	0.673181	−	0.739478i	$-0.264927\pi$
$977$	360.870	+	208.348i	0.369365	+	0.213253i	−0.303816	+	0.952731i	$0.598261\pi$
$978$		0			0
$979$	123.068	−	459.296i	0.125708	−	0.469148i
$980$	1256.45	−	282.946i	1.28209	−	0.288720i
$981$		0			0
$982$	−16.5552	+	57.1529i	−0.0168587	+	0.0582005i
$983$	−205.834	−	356.515i	−0.209394	−	0.362680i	0.742130	−	0.670256i	$-0.233816\pi$
$983$	−205.834	−	356.515i	−0.209394	−	0.362680i	−0.951524	+	0.307576i	$0.900482\pi$
$984$		0			0
$985$	1202.35	+	694.179i	1.22066	+	0.704751i
$986$	−823.996	−	857.891i	−0.835696	−	0.870072i
$987$		0			0
$988$	−28.8396	+	715.240i	−0.0291899	+	0.723927i
$989$	−216.431	+	216.431i	−0.218838	+	0.218838i
$990$		0			0
$991$	556.918			0.561976			0.280988	−	0.959711i	$-0.409338\pi$
$991$	556.918			0.561976			0.280988	+	0.959711i	$0.409338\pi$
$992$	726.496	+	73.4427i	0.732355	+	0.0740350i
$993$		0			0
$994$	−9.96412	+	494.433i	−0.0100243	+	0.497418i
$995$	−30.7840	−	114.887i	−0.0309387	−	0.115465i
$996$		0			0
$997$	617.519	+	165.464i	0.619377	+	0.165962i	0.554845	−	0.831954i	$-0.312778\pi$
$997$	617.519	+	165.464i	0.619377	+	0.165962i	0.0645326	+	0.997916i	$0.479444\pi$
$998$	251.386	−	867.849i	0.251890	−	0.869589i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.125.31		184
3.2	odd	2		144.3.w.a.77.16	yes	184
9.2	odd	6	inner	432.3.x.a.413.46		184
9.7	even	3		144.3.w.a.29.1	yes	184
16.5	even	4	inner	432.3.x.a.341.46		184
48.5	odd	4		144.3.w.a.5.1	✓	184
144.101	odd	12	inner	432.3.x.a.197.31		184
144.133	even	12		144.3.w.a.101.16	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.1	✓	184	48.5	odd	4
144.3.w.a.29.1	yes	184	9.7	even	3
144.3.w.a.77.16	yes	184	3.2	odd	2
144.3.w.a.101.16	yes	184	144.133	even	12
432.3.x.a.125.31		184	1.1	even	1	trivial
432.3.x.a.197.31		184	144.101	odd	12	inner
432.3.x.a.341.46		184	16.5	even	4	inner
432.3.x.a.413.46		184	9.2	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03470 - 1.71155i) q^{2} +(-1.85881 - 3.54187i) q^{4} +(7.78777 - 2.08673i) q^{5} +(2.60739 - 1.50538i) q^{7} +(-7.98539 - 0.483303i) q^{8} +O(q^{10})\)	\(q+(1.03470 - 1.71155i) q^{2} +(-1.85881 - 3.54187i) q^{4} +(7.78777 - 2.08673i) q^{5} +(2.60739 - 1.50538i) q^{7} +(-7.98539 - 0.483303i) q^{8} +(4.48643 - 15.4883i) q^{10} +(1.54872 - 5.77989i) q^{11} +(14.7171 - 3.94343i) q^{13} +(0.121324 - 6.02028i) q^{14} +(-9.08964 + 13.1673i) q^{16} +23.3509i q^{17} +(-8.30523 - 8.30523i) q^{19} +(-21.8669 - 23.7044i) q^{20} +(-8.29013 - 8.63114i) q^{22} +(2.08290 - 3.60768i) q^{23} +(34.6443 - 20.0019i) q^{25} +(8.47832 - 29.2693i) q^{26} +(-10.1785 - 6.43681i) q^{28} +(-24.6026 - 6.59225i) q^{29} +(11.4094 - 19.7616i) q^{31} +(13.1315 + 29.1815i) q^{32} +(39.9662 + 24.1610i) q^{34} +(17.1644 - 17.1644i) q^{35} +(27.8343 - 27.8343i) q^{37} +(-22.8082 + 5.62144i) q^{38} +(-63.1969 + 12.8995i) q^{40} +(-36.7431 + 63.6409i) q^{41} +(-70.9710 - 19.0166i) q^{43} +(-23.3504 + 5.25838i) q^{44} +(-4.01957 - 7.29783i) q^{46} +(39.5925 - 22.8588i) q^{47} +(-19.9677 + 34.5851i) q^{49} +(1.61203 - 79.9912i) q^{50} +(-41.3234 - 44.7959i) q^{52} +(21.0485 + 21.0485i) q^{53} -48.2442i q^{55} +(-21.5485 + 10.7608i) q^{56} +(-36.7392 + 35.2876i) q^{58} +(-77.1219 + 20.6648i) q^{59} +(13.6831 - 51.0660i) q^{61} +(-22.0177 - 39.9749i) q^{62} +(63.5328 + 7.71872i) q^{64} +(106.384 - 61.4211i) q^{65} +(44.8100 - 12.0068i) q^{67} +(82.7056 - 43.4048i) q^{68} +(-11.6178 - 47.1377i) q^{70} -82.1279 q^{71} +25.3786i q^{73} +(-18.8398 - 76.4397i) q^{74} +(-13.9782 + 44.8539i) q^{76} +(-4.66280 - 17.4018i) q^{77} +(45.7098 + 79.1717i) q^{79} +(-43.3114 + 121.512i) q^{80} +(70.9068 + 128.737i) q^{82} +(45.3324 + 12.1468i) q^{83} +(48.7268 + 181.851i) q^{85} +(-105.981 + 101.794i) q^{86} +(-15.1605 + 45.4062i) q^{88} +79.4644 q^{89} +(32.4368 - 32.4368i) q^{91} +(-16.6496 - 0.671340i) q^{92} +(1.84228 - 91.4165i) q^{94} +(-82.0099 - 47.3485i) q^{95} +(-57.7693 - 100.059i) q^{97} +(38.5336 + 69.9607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

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