LMFDB - Embedded newform 162.3.d.b.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, 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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.3.d.b.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 + 2.12132i) q^{5} +(2.00000 + 3.46410i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 + 2.12132i) q^{5} +(2.00000 + 3.46410i) q^{7} -2.82843i q^{8} +6.00000 q^{10} +(14.6969 - 8.48528i) q^{11} +(-4.00000 + 6.92820i) q^{13} +(4.89898 + 2.82843i) q^{14} +(-2.00000 - 3.46410i) q^{16} -12.7279i q^{17} -16.0000 q^{19} +(7.34847 - 4.24264i) q^{20} +(12.0000 - 20.7846i) q^{22} +(14.6969 + 8.48528i) q^{23} +(-3.50000 - 6.06218i) q^{25} +11.3137i q^{26} +8.00000 q^{28} +(3.67423 - 2.12132i) q^{29} +(-22.0000 + 38.1051i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-9.00000 - 15.5885i) q^{34} +16.9706i q^{35} -34.0000 q^{37} +(-19.5959 + 11.3137i) q^{38} +(6.00000 - 10.3923i) q^{40} +(-40.4166 - 23.3345i) q^{41} +(20.0000 + 34.6410i) q^{43} -33.9411i q^{44} +24.0000 q^{46} +(-73.4847 + 42.4264i) q^{47} +(16.5000 - 28.5788i) q^{49} +(-8.57321 - 4.94975i) q^{50} +(8.00000 + 13.8564i) q^{52} +38.1838i q^{53} +72.0000 q^{55} +(9.79796 - 5.65685i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-29.3939 - 16.9706i) q^{59} +(-25.0000 - 43.3013i) q^{61} +62.2254i q^{62} -8.00000 q^{64} +(-29.3939 + 16.9706i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-22.0454 - 12.7279i) q^{68} +(12.0000 + 20.7846i) q^{70} -50.9117i q^{71} -16.0000 q^{73} +(-41.6413 + 24.0416i) q^{74} +(-16.0000 + 27.7128i) q^{76} +(58.7878 + 33.9411i) q^{77} +(38.0000 + 65.8179i) q^{79} -16.9706i q^{80} -66.0000 q^{82} +(102.879 - 59.3970i) q^{83} +(27.0000 - 46.7654i) q^{85} +(48.9898 + 28.2843i) q^{86} +(-24.0000 - 41.5692i) q^{88} +12.7279i q^{89} -32.0000 q^{91} +(29.3939 - 16.9706i) q^{92} +(-60.0000 + 103.923i) q^{94} +(-58.7878 - 33.9411i) q^{95} +(-88.0000 - 152.420i) q^{97} -46.6690i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 8 q^{7}+O(q^{10}) $ 4 * q + 4 * q^4 + 8 * q^7	$ 4 q + 4 q^{4} + 8 q^{7} + 24 q^{10} - 16 q^{13} - 8 q^{16} - 64 q^{19} + 48 q^{22} - 14 q^{25} + 32 q^{28} - 88 q^{31} - 36 q^{34} - 136 q^{37} + 24 q^{40} + 80 q^{43} + 96 q^{46} + 66 q^{49} + 32 q^{52} + 288 q^{55} + 12 q^{58} - 100 q^{61} - 32 q^{64} - 16 q^{67} + 48 q^{70} - 64 q^{73} - 64 q^{76} + 152 q^{79} - 264 q^{82} + 108 q^{85} - 96 q^{88} - 128 q^{91} - 240 q^{94} - 352 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 + 8 * q^7 + 24 * q^10 - 16 * q^13 - 8 * q^16 - 64 * q^19 + 48 * q^22 - 14 * q^25 + 32 * q^28 - 88 * q^31 - 36 * q^34 - 136 * q^37 + 24 * q^40 + 80 * q^43 + 96 * q^46 + 66 * q^49 + 32 * q^52 + 288 * q^55 + 12 * q^58 - 100 * q^61 - 32 * q^64 - 16 * q^67 + 48 * q^70 - 64 * q^73 - 64 * q^76 + 152 * q^79 - 264 * q^82 + 108 * q^85 - 96 * q^88 - 128 * q^91 - 240 * q^94 - 352 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	3.67423	+	2.12132i	0.734847	+	0.424264i	0.820193	−	0.572087i	$-0.193866\pi$
$5$	3.67423	+	2.12132i	0.734847	+	0.424264i	−0.0853458	+	0.996351i	$0.527199\pi$
$6$		0			0
$7$	2.00000	+	3.46410i	0.285714	+	0.494872i	0.972782	−	0.231722i	$-0.0744358\pi$
$7$	2.00000	+	3.46410i	0.285714	+	0.494872i	−0.687068	+	0.726593i	$0.741103\pi$
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	6.00000			0.600000
$11$	14.6969	−	8.48528i	1.33609	−	0.771389i	0.349861	−	0.936802i	$-0.386229\pi$
$11$	14.6969	−	8.48528i	1.33609	−	0.771389i	0.986224	+	0.165412i	$0.0528955\pi$
$12$		0			0
$13$	−4.00000	+	6.92820i	−0.307692	+	0.532939i	−0.977857	−	0.209274i	$-0.932890\pi$
$13$	−4.00000	+	6.92820i	−0.307692	+	0.532939i	0.670165	+	0.742212i	$0.266223\pi$
$14$	4.89898	+	2.82843i	0.349927	+	0.202031i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	12.7279i		−	0.748701i	−0.927287	−	0.374351i	$-0.877866\pi$
$17$		−	12.7279i		−	0.748701i	0.927287	−	0.374351i	$-0.122134\pi$
$18$		0			0
$19$	−16.0000			−0.842105			−0.421053	−	0.907036i	$-0.638339\pi$
$19$	−16.0000			−0.842105			−0.421053	+	0.907036i	$0.638339\pi$
$20$	7.34847	−	4.24264i	0.367423	−	0.212132i
$21$		0			0
$22$	12.0000	−	20.7846i	0.545455	−	0.944755i
$23$	14.6969	+	8.48528i	0.638997	+	0.368925i	0.784228	−	0.620473i	$-0.213059\pi$
$23$	14.6969	+	8.48528i	0.638997	+	0.368925i	−0.145231	+	0.989398i	$0.546392\pi$
$24$		0			0
$25$	−3.50000	−	6.06218i	−0.140000	−	0.242487i
$26$			11.3137i			0.435143i
$27$		0			0
$28$	8.00000			0.285714
$29$	3.67423	−	2.12132i	0.126698	−	0.0731490i	−0.435312	−	0.900280i	$-0.643362\pi$
$29$	3.67423	−	2.12132i	0.126698	−	0.0731490i	0.562009	+	0.827131i	$0.310028\pi$
$30$		0			0
$31$	−22.0000	+	38.1051i	−0.709677	+	1.22920i	0.255299	+	0.966862i	$0.417826\pi$
$31$	−22.0000	+	38.1051i	−0.709677	+	1.22920i	−0.964977	+	0.262335i	$0.915507\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−9.00000	−	15.5885i	−0.264706	−	0.458484i
$35$			16.9706i			0.484873i
$36$		0			0
$37$	−34.0000			−0.918919			−0.459459	−	0.888199i	$-0.651957\pi$
$37$	−34.0000			−0.918919			−0.459459	+	0.888199i	$0.651957\pi$
$38$	−19.5959	+	11.3137i	−0.515682	+	0.297729i
$39$		0			0
$40$	6.00000	−	10.3923i	0.150000	−	0.259808i
$41$	−40.4166	−	23.3345i	−0.985770	−	0.569135i	−0.0817630	−	0.996652i	$-0.526055\pi$
$41$	−40.4166	−	23.3345i	−0.985770	−	0.569135i	−0.904007	+	0.427517i	$0.859388\pi$
$42$		0			0
$43$	20.0000	+	34.6410i	0.465116	+	0.805605i	0.999207	−	0.0398223i	$-0.0126792\pi$
$43$	20.0000	+	34.6410i	0.465116	+	0.805605i	−0.534090	+	0.845427i	$0.679346\pi$
$44$		−	33.9411i		−	0.771389i
$45$		0			0
$46$	24.0000			0.521739
$47$	−73.4847	+	42.4264i	−1.56350	+	0.902690i	−0.566606	+	0.823989i	$0.691744\pi$
$47$	−73.4847	+	42.4264i	−1.56350	+	0.902690i	−0.996898	+	0.0787005i	$0.974923\pi$
$48$		0			0
$49$	16.5000	−	28.5788i	0.336735	−	0.583242i
$50$	−8.57321	−	4.94975i	−0.171464	−	0.0989949i
$51$		0			0
$52$	8.00000	+	13.8564i	0.153846	+	0.266469i
$53$			38.1838i			0.720448i	0.932866	+	0.360224i	$0.117300\pi$
$53$			38.1838i			0.720448i	−0.932866	+	0.360224i	$0.882700\pi$
$54$		0			0
$55$	72.0000			1.30909
$56$	9.79796	−	5.65685i	0.174964	−	0.101015i
$57$		0			0
$58$	3.00000	−	5.19615i	0.0517241	−	0.0895888i
$59$	−29.3939	−	16.9706i	−0.498201	−	0.287637i	0.229769	−	0.973245i	$-0.426203\pi$
$59$	−29.3939	−	16.9706i	−0.498201	−	0.287637i	−0.727970	+	0.685609i	$0.759536\pi$
$60$		0			0
$61$	−25.0000	−	43.3013i	−0.409836	−	0.709857i	0.585035	−	0.811008i	$-0.301081\pi$
$61$	−25.0000	−	43.3013i	−0.409836	−	0.709857i	−0.994871	+	0.101151i	$0.967747\pi$
$62$			62.2254i			1.00364i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−29.3939	+	16.9706i	−0.452213	+	0.261086i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.0597015	+	0.103406i	−0.894331	−	0.447405i	$-0.852348\pi$
$67$	−4.00000	+	6.92820i	−0.0597015	+	0.103406i	0.834630	+	0.550811i	$0.185682\pi$
$68$	−22.0454	−	12.7279i	−0.324197	−	0.187175i
$69$		0			0
$70$	12.0000	+	20.7846i	0.171429	+	0.296923i
$71$		−	50.9117i		−	0.717066i	−0.933517	−	0.358533i	$-0.883277\pi$
$71$		−	50.9117i		−	0.717066i	0.933517	−	0.358533i	$-0.116723\pi$
$72$		0			0
$73$	−16.0000			−0.219178			−0.109589	−	0.993977i	$-0.534953\pi$
$73$	−16.0000			−0.219178			−0.109589	+	0.993977i	$0.534953\pi$
$74$	−41.6413	+	24.0416i	−0.562721	+	0.324887i
$75$		0			0
$76$	−16.0000	+	27.7128i	−0.210526	+	0.364642i
$77$	58.7878	+	33.9411i	0.763477	+	0.440794i
$78$		0			0
$79$	38.0000	+	65.8179i	0.481013	+	0.833138i	0.999763	−	0.0217876i	$-0.00693577\pi$
$79$	38.0000	+	65.8179i	0.481013	+	0.833138i	−0.518750	+	0.854926i	$0.673602\pi$
$80$		−	16.9706i		−	0.212132i
$81$		0			0
$82$	−66.0000			−0.804878
$83$	102.879	−	59.3970i	1.23950	−	0.715626i	0.270509	−	0.962718i	$-0.412808\pi$
$83$	102.879	−	59.3970i	1.23950	−	0.715626i	0.968992	+	0.247091i	$0.0794748\pi$
$84$		0			0
$85$	27.0000	−	46.7654i	0.317647	−	0.550181i
$86$	48.9898	+	28.2843i	0.569649	+	0.328887i
$87$		0			0
$88$	−24.0000	−	41.5692i	−0.272727	−	0.472377i
$89$			12.7279i			0.143010i	0.997440	+	0.0715052i	$0.0227802\pi$
$89$			12.7279i			0.143010i	−0.997440	+	0.0715052i	$0.977220\pi$
$90$		0			0
$91$	−32.0000			−0.351648
$92$	29.3939	−	16.9706i	0.319499	−	0.184463i
$93$		0			0
$94$	−60.0000	+	103.923i	−0.638298	+	1.10556i
$95$	−58.7878	−	33.9411i	−0.618818	−	0.357275i
$96$		0			0
$97$	−88.0000	−	152.420i	−0.907216	−	1.57135i	−0.817914	−	0.575341i	$-0.804870\pi$
$97$	−88.0000	−	152.420i	−0.907216	−	1.57135i	−0.0893025	−	0.996005i	$-0.528464\pi$
$98$		−	46.6690i		−	0.476215i
$99$		0			0
$100$	−14.0000			−0.140000
$101$	25.7196	−	14.8492i	0.254650	−	0.147022i	−0.367242	−	0.930126i	$-0.619698\pi$
$101$	25.7196	−	14.8492i	0.254650	−	0.147022i	0.621892	+	0.783103i	$0.286364\pi$
$102$		0			0
$103$	14.0000	−	24.2487i	0.135922	−	0.235424i	−0.790027	−	0.613072i	$-0.789934\pi$
$103$	14.0000	−	24.2487i	0.135922	−	0.235424i	0.925949	+	0.377648i	$0.123267\pi$
$104$	19.5959	+	11.3137i	0.188422	+	0.108786i
$105$		0			0
$106$	27.0000	+	46.7654i	0.254717	+	0.441183i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	56.0000			0.513761			0.256881	−	0.966443i	$-0.417305\pi$
$109$	56.0000			0.513761			0.256881	+	0.966443i	$0.417305\pi$
$110$	88.1816	−	50.9117i	0.801651	−	0.462834i
$111$		0			0
$112$	8.00000	−	13.8564i	0.0714286	−	0.123718i
$113$	135.947	+	78.4889i	1.20307	+	0.694592i	0.961236	−	0.275727i	$-0.0889184\pi$
$113$	135.947	+	78.4889i	1.20307	+	0.694592i	0.241832	+	0.970318i	$0.422252\pi$
$114$		0			0
$115$	36.0000	+	62.3538i	0.313043	+	0.542207i
$116$		−	8.48528i		−	0.0731490i
$117$		0			0
$118$	−48.0000			−0.406780
$119$	44.0908	−	25.4558i	0.370511	−	0.213915i
$120$		0			0
$121$	83.5000	−	144.626i	0.690083	−	1.19526i
$122$	−61.2372	−	35.3553i	−0.501945	−	0.289798i
$123$		0			0
$124$	44.0000	+	76.2102i	0.354839	+	0.614599i
$125$		−	135.765i		−	1.08612i
$126$		0			0
$127$	92.0000			0.724409			0.362205	−	0.932099i	$-0.382024\pi$
$127$	92.0000			0.724409			0.362205	+	0.932099i	$0.382024\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−24.0000	+	41.5692i	−0.184615	+	0.319763i
$131$	146.969	+	84.8528i	1.12190	+	0.647731i	0.941886	−	0.335932i	$-0.109051\pi$
$131$	146.969	+	84.8528i	1.12190	+	0.647731i	0.180017	+	0.983663i	$0.442385\pi$
$132$		0			0
$133$	−32.0000	−	55.4256i	−0.240602	−	0.416734i
$134$			11.3137i			0.0844307i
$135$		0			0
$136$	−36.0000			−0.264706
$137$	135.947	−	78.4889i	0.992312	−	0.572911i	0.0863471	−	0.996265i	$-0.472481\pi$
$137$	135.947	−	78.4889i	0.992312	−	0.572911i	0.905964	+	0.423354i	$0.139147\pi$
$138$		0			0
$139$	−76.0000	+	131.636i	−0.546763	+	0.947021i	0.451731	+	0.892154i	$0.350807\pi$
$139$	−76.0000	+	131.636i	−0.546763	+	0.947021i	−0.998494	+	0.0548664i	$0.982527\pi$
$140$	29.3939	+	16.9706i	0.209956	+	0.121218i
$141$		0			0
$142$	−36.0000	−	62.3538i	−0.253521	−	0.439111i
$143$			135.765i			0.949402i
$144$		0			0
$145$	18.0000			0.124138
$146$	−19.5959	+	11.3137i	−0.134219	+	0.0774912i
$147$		0			0
$148$	−34.0000	+	58.8897i	−0.229730	+	0.397904i
$149$	−238.825	−	137.886i	−1.60285	−	0.925408i	−0.990913	−	0.134505i	$-0.957056\pi$
$149$	−238.825	−	137.886i	−1.60285	−	0.925408i	−0.611941	−	0.790903i	$-0.709611\pi$
$150$		0			0
$151$	74.0000	+	128.172i	0.490066	+	0.848820i	0.999935	−	0.0114328i	$-0.00363925\pi$
$151$	74.0000	+	128.172i	0.490066	+	0.848820i	−0.509868	+	0.860252i	$0.670306\pi$
$152$			45.2548i			0.297729i
$153$		0			0
$154$	96.0000			0.623377
$155$	−161.666	+	93.3381i	−1.04301	+	0.602181i
$156$		0			0
$157$	41.0000	−	71.0141i	0.261146	−	0.452319i	−0.705400	−	0.708809i	$-0.749233\pi$
$157$	41.0000	−	71.0141i	0.261146	−	0.452319i	0.966547	+	0.256490i	$0.0825661\pi$
$158$	93.0806	+	53.7401i	0.589118	+	0.340127i
$159$		0			0
$160$	−12.0000	−	20.7846i	−0.0750000	−	0.129904i
$161$			67.8823i			0.421629i
$162$		0			0
$163$	56.0000			0.343558			0.171779	−	0.985135i	$-0.445048\pi$
$163$	56.0000			0.343558			0.171779	+	0.985135i	$0.445048\pi$
$164$	−80.8332	+	46.6690i	−0.492885	+	0.284567i
$165$		0			0
$166$	84.0000	−	145.492i	0.506024	−	0.876459i
$167$	−29.3939	−	16.9706i	−0.176011	−	0.101620i	0.409406	−	0.912352i	$-0.365736\pi$
$167$	−29.3939	−	16.9706i	−0.176011	−	0.101620i	−0.585417	+	0.810732i	$0.699069\pi$
$168$		0			0
$169$	52.5000	+	90.9327i	0.310651	+	0.538063i
$170$		−	76.3675i		−	0.449221i
$171$		0			0
$172$	80.0000			0.465116
$173$	−150.644	+	86.9741i	−0.870772	+	0.502741i	−0.867605	−	0.497254i	$-0.834342\pi$
$173$	−150.644	+	86.9741i	−0.870772	+	0.502741i	−0.00316754	+	0.999995i	$0.501008\pi$
$174$		0			0
$175$	14.0000	−	24.2487i	0.0800000	−	0.138564i
$176$	−58.7878	−	33.9411i	−0.334021	−	0.192847i
$177$		0			0
$178$	9.00000	+	15.5885i	0.0505618	+	0.0875756i
$179$		−	203.647i		−	1.13769i	−0.822444	−	0.568846i	$-0.807390\pi$
$179$		−	203.647i		−	1.13769i	0.822444	−	0.568846i	$-0.192610\pi$
$180$		0			0
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$	−39.1918	+	22.6274i	−0.215340	+	0.124326i
$183$		0			0
$184$	24.0000	−	41.5692i	0.130435	−	0.225920i
$185$	−124.924	−	72.1249i	−0.675265	−	0.389864i
$186$		0			0
$187$	−108.000	−	187.061i	−0.577540	−	1.00033i
$188$			169.706i			0.902690i
$189$		0			0
$190$	−96.0000			−0.505263
$191$	−29.3939	+	16.9706i	−0.153895	+	0.0888511i	−0.574970	−	0.818175i	$-0.694986\pi$
$191$	−29.3939	+	16.9706i	−0.153895	+	0.0888511i	0.421075	+	0.907026i	$0.361653\pi$
$192$		0			0
$193$	−103.000	+	178.401i	−0.533679	+	0.924359i	0.465547	+	0.885023i	$0.345858\pi$
$193$	−103.000	+	178.401i	−0.533679	+	0.924359i	−0.999226	+	0.0393357i	$0.987476\pi$
$194$	−215.555	−	124.451i	−1.11111	−	0.641499i
$195$		0			0
$196$	−33.0000	−	57.1577i	−0.168367	−	0.291621i
$197$			165.463i			0.839914i	0.907544	+	0.419957i	$0.137955\pi$
$197$			165.463i			0.839914i	−0.907544	+	0.419957i	$0.862045\pi$
$198$		0			0
$199$	20.0000			0.100503			0.0502513	−	0.998737i	$-0.483998\pi$
$199$	20.0000			0.100503			0.0502513	+	0.998737i	$0.483998\pi$
$200$	−17.1464	+	9.89949i	−0.0857321	+	0.0494975i
$201$		0			0
$202$	21.0000	−	36.3731i	0.103960	−	0.180065i
$203$	14.6969	+	8.48528i	0.0723987	+	0.0417994i
$204$		0			0
$205$	−99.0000	−	171.473i	−0.482927	−	0.836454i
$206$		−	39.5980i		−	0.192223i
$207$		0			0
$208$	32.0000			0.153846
$209$	−235.151	+	135.765i	−1.12512	+	0.649591i
$210$		0			0
$211$	−148.000	+	256.344i	−0.701422	+	1.21490i	0.266546	+	0.963822i	$0.414118\pi$
$211$	−148.000	+	256.344i	−0.701422	+	1.21490i	−0.967967	+	0.251076i	$0.919216\pi$
$212$	66.1362	+	38.1838i	0.311963	+	0.180112i
$213$		0			0
$214$		0			0
$215$			169.706i			0.789328i
$216$		0			0
$217$	−176.000			−0.811060
$218$	68.5857	−	39.5980i	0.314613	−	0.181642i
$219$		0			0
$220$	72.0000	−	124.708i	0.327273	−	0.566853i
$221$	88.1816	+	50.9117i	0.399012	+	0.230370i
$222$		0			0
$223$	218.000	+	377.587i	0.977578	+	1.69322i	0.671149	+	0.741322i	$0.265801\pi$
$223$	218.000	+	377.587i	0.977578	+	1.69322i	0.306429	+	0.951894i	$0.400866\pi$
$224$		−	22.6274i		−	0.101015i
$225$		0			0
$226$	222.000			0.982301
$227$	14.6969	−	8.48528i	0.0647442	−	0.0373801i	−0.467278	−	0.884110i	$-0.654765\pi$
$227$	14.6969	−	8.48528i	0.0647442	−	0.0373801i	0.532023	+	0.846730i	$0.321432\pi$
$228$		0			0
$229$	−4.00000	+	6.92820i	−0.0174672	+	0.0302542i	−0.874627	−	0.484797i	$-0.838894\pi$
$229$	−4.00000	+	6.92820i	−0.0174672	+	0.0302542i	0.857160	+	0.515051i	$0.172227\pi$
$230$	88.1816	+	50.9117i	0.383398	+	0.221355i
$231$		0			0
$232$	−6.00000	−	10.3923i	−0.0258621	−	0.0447944i
$233$		−	12.7279i		−	0.0546263i	−0.999627	−	0.0273131i	$-0.991305\pi$
$233$		−	12.7279i		−	0.0546263i	0.999627	−	0.0273131i	$-0.00869512\pi$
$234$		0			0
$235$	−360.000			−1.53191
$236$	−58.7878	+	33.9411i	−0.249101	+	0.143818i
$237$		0			0
$238$	36.0000	−	62.3538i	0.151261	−	0.261991i
$239$	−117.576	−	67.8823i	−0.491948	−	0.284026i	0.233434	−	0.972373i	$-0.425004\pi$
$239$	−117.576	−	67.8823i	−0.491948	−	0.284026i	−0.725382	+	0.688346i	$0.758337\pi$
$240$		0			0
$241$	−16.0000	−	27.7128i	−0.0663900	−	0.114991i	0.830920	−	0.556392i	$-0.187815\pi$
$241$	−16.0000	−	27.7128i	−0.0663900	−	0.114991i	−0.897310	+	0.441401i	$0.854481\pi$
$242$		−	236.174i		−	0.975924i
$243$		0			0
$244$	−100.000			−0.409836
$245$	121.250	−	70.0036i	0.494897	−	0.285729i
$246$		0			0
$247$	64.0000	−	110.851i	0.259109	−	0.448790i
$248$	107.778	+	62.2254i	0.434587	+	0.250909i
$249$		0			0
$250$	−96.0000	−	166.277i	−0.384000	−	0.665108i
$251$			50.9117i			0.202835i	0.994844	+	0.101418i	$0.0323379\pi$
$251$			50.9117i			0.202835i	−0.994844	+	0.101418i	$0.967662\pi$
$252$		0			0
$253$	288.000			1.13834
$254$	112.677	−	65.0538i	0.443608	−	0.256117i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	157.992	+	91.2168i	0.614755	+	0.354929i	0.774824	−	0.632177i	$-0.217838\pi$
$257$	157.992	+	91.2168i	0.614755	+	0.354929i	−0.160069	+	0.987106i	$0.551172\pi$
$258$		0			0
$259$	−68.0000	−	117.779i	−0.262548	−	0.454747i
$260$			67.8823i			0.261086i
$261$		0			0
$262$	240.000			0.916031
$263$	323.333	−	186.676i	1.22940	−	0.709795i	0.262497	−	0.964933i	$-0.415454\pi$
$263$	323.333	−	186.676i	1.22940	−	0.709795i	0.966905	+	0.255137i	$0.0821207\pi$
$264$		0			0
$265$	−81.0000	+	140.296i	−0.305660	+	0.529419i
$266$	−78.3837	−	45.2548i	−0.294675	−	0.170131i
$267$		0			0
$268$	8.00000	+	13.8564i	0.0298507	+	0.0517030i
$269$		−	343.654i		−	1.27752i	−0.769404	−	0.638762i	$-0.779447\pi$
$269$		−	343.654i		−	1.27752i	0.769404	−	0.638762i	$-0.220553\pi$
$270$		0			0
$271$	380.000			1.40221			0.701107	−	0.713056i	$-0.252690\pi$
$271$	380.000			1.40221			0.701107	+	0.713056i	$0.252690\pi$
$272$	−44.0908	+	25.4558i	−0.162099	+	0.0935877i
$273$		0			0
$274$	111.000	−	192.258i	0.405109	−	0.701670i
$275$	−102.879	−	59.3970i	−0.374104	−	0.215989i
$276$		0			0
$277$	164.000	+	284.056i	0.592058	+	1.02547i	0.993955	+	0.109789i	$0.0350176\pi$
$277$	164.000	+	284.056i	0.592058	+	1.02547i	−0.401897	+	0.915685i	$0.631649\pi$
$278$			214.960i			0.773239i
$279$		0			0
$280$	48.0000			0.171429
$281$	246.174	−	142.128i	0.876063	−	0.505795i	0.00670475	−	0.999978i	$-0.497866\pi$
$281$	246.174	−	142.128i	0.876063	−	0.505795i	0.869358	+	0.494182i	$0.164532\pi$
$282$		0			0
$283$	104.000	−	180.133i	0.367491	−	0.636513i	−0.621681	−	0.783270i	$-0.713550\pi$
$283$	104.000	−	180.133i	0.367491	−	0.636513i	0.989173	+	0.146757i	$0.0468835\pi$
$284$	−88.1816	−	50.9117i	−0.310499	−	0.179267i
$285$		0			0
$286$	96.0000	+	166.277i	0.335664	+	0.581388i
$287$		−	186.676i		−	0.650440i
$288$		0			0
$289$	127.000			0.439446
$290$	22.0454	−	12.7279i	0.0760186	−	0.0438894i
$291$		0			0
$292$	−16.0000	+	27.7128i	−0.0547945	+	0.0949069i
$293$	378.446	+	218.496i	1.29163	+	0.745720i	0.978942	−	0.204137i	$-0.0654389\pi$
$293$	378.446	+	218.496i	1.29163	+	0.745720i	0.312683	+	0.949858i	$0.398772\pi$
$294$		0			0
$295$	−72.0000	−	124.708i	−0.244068	−	0.422738i
$296$			96.1665i			0.324887i
$297$		0			0
$298$	−390.000			−1.30872
$299$	−117.576	+	67.8823i	−0.393229	+	0.227031i
$300$		0			0
$301$	−80.0000	+	138.564i	−0.265781	+	0.460346i
$302$	181.262	+	104.652i	0.600206	+	0.346529i
$303$		0			0
$304$	32.0000	+	55.4256i	0.105263	+	0.182321i
$305$		−	212.132i		−	0.695515i
$306$		0			0
$307$	−520.000			−1.69381			−0.846906	−	0.531743i	$-0.821537\pi$
$307$	−520.000			−1.69381			−0.846906	+	0.531743i	$0.821537\pi$
$308$	117.576	−	67.8823i	0.381739	−	0.220397i
$309$		0			0
$310$	−132.000	+	228.631i	−0.425806	+	0.737518i
$311$	323.333	+	186.676i	1.03965	+	0.600245i	0.919736	−	0.392539i	$-0.128403\pi$
$311$	323.333	+	186.676i	1.03965	+	0.600245i	0.119919	+	0.992784i	$0.461736\pi$
$312$		0			0
$313$	47.0000	+	81.4064i	0.150160	+	0.260084i	0.931286	−	0.364289i	$-0.118688\pi$
$313$	47.0000	+	81.4064i	0.150160	+	0.260084i	−0.781126	+	0.624373i	$0.785355\pi$
$314$		−	115.966i		−	0.369317i
$315$		0			0
$316$	152.000			0.481013
$317$	290.265	−	167.584i	0.915661	−	0.528657i	0.0334128	−	0.999442i	$-0.489362\pi$
$317$	290.265	−	167.584i	0.915661	−	0.528657i	0.882248	+	0.470785i	$0.156029\pi$
$318$		0			0
$319$	36.0000	−	62.3538i	0.112853	−	0.195467i
$320$	−29.3939	−	16.9706i	−0.0918559	−	0.0530330i
$321$		0			0
$322$	48.0000	+	83.1384i	0.149068	+	0.258194i
$323$			203.647i			0.630485i
$324$		0			0
$325$	56.0000			0.172308
$326$	68.5857	−	39.5980i	0.210386	−	0.121466i
$327$		0			0
$328$	−66.0000	+	114.315i	−0.201220	+	0.348522i
$329$	−293.939	−	169.706i	−0.893431	−	0.515823i
$330$		0			0
$331$	−268.000	−	464.190i	−0.809668	−	1.40239i	−0.913094	−	0.407748i	$-0.866314\pi$
$331$	−268.000	−	464.190i	−0.809668	−	1.40239i	0.103427	−	0.994637i	$-0.467019\pi$
$332$		−	237.588i		−	0.715626i
$333$		0			0
$334$	−48.0000			−0.143713
$335$	−29.3939	+	16.9706i	−0.0877429	+	0.0506584i
$336$		0			0
$337$	104.000	−	180.133i	0.308605	−	0.534520i	−0.669452	−	0.742855i	$-0.733471\pi$
$337$	104.000	−	180.133i	0.308605	−	0.534520i	0.978058	+	0.208335i	$0.0668044\pi$
$338$	128.598	+	74.2462i	0.380468	+	0.219663i
$339$		0			0
$340$	−54.0000	−	93.5307i	−0.158824	−	0.275090i
$341$			746.705i			2.18975i
$342$		0			0
$343$	328.000			0.956268
$344$	97.9796	−	56.5685i	0.284824	−	0.164443i
$345$		0			0
$346$	−123.000	+	213.042i	−0.355491	+	0.615729i
$347$	−249.848	−	144.250i	−0.720023	−	0.415705i	0.0947382	−	0.995502i	$-0.469799\pi$
$347$	−249.848	−	144.250i	−0.720023	−	0.415705i	−0.814761	+	0.579797i	$0.803132\pi$
$348$		0			0
$349$	119.000	+	206.114i	0.340974	+	0.590585i	0.984614	−	0.174744i	$-0.0559098\pi$
$349$	119.000	+	206.114i	0.340974	+	0.590585i	−0.643640	+	0.765329i	$0.722576\pi$
$350$		−	39.5980i		−	0.113137i
$351$		0			0
$352$	−96.0000			−0.272727
$353$	−194.734	+	112.430i	−0.551656	+	0.318499i	−0.749789	−	0.661676i	$-0.769845\pi$
$353$	−194.734	+	112.430i	−0.551656	+	0.318499i	0.198134	+	0.980175i	$0.436512\pi$
$354$		0			0
$355$	108.000	−	187.061i	0.304225	−	0.526934i
$356$	22.0454	+	12.7279i	0.0619253	+	0.0357526i
$357$		0			0
$358$	−144.000	−	249.415i	−0.402235	−	0.696691i
$359$		−	560.029i		−	1.55997i	−0.625799	−	0.779984i	$-0.715227\pi$
$359$		−	560.029i		−	1.55997i	0.625799	−	0.779984i	$-0.284773\pi$
$360$		0			0
$361$	−105.000			−0.290859
$362$	−284.141	+	164.049i	−0.784919	+	0.453173i
$363$		0			0
$364$	−32.0000	+	55.4256i	−0.0879121	+	0.152268i
$365$	−58.7878	−	33.9411i	−0.161062	−	0.0929894i
$366$		0			0
$367$	−142.000	−	245.951i	−0.386921	−	0.670167i	0.605113	−	0.796140i	$-0.293128\pi$
$367$	−142.000	−	245.951i	−0.386921	−	0.670167i	−0.992034	+	0.125973i	$0.959795\pi$
$368$		−	67.8823i		−	0.184463i
$369$		0			0
$370$	−204.000			−0.551351
$371$	−132.272	+	76.3675i	−0.356530	+	0.205842i
$372$		0			0
$373$	95.0000	−	164.545i	0.254692	−	0.441139i	−0.710120	−	0.704081i	$-0.751359\pi$
$373$	95.0000	−	164.545i	0.254692	−	0.441139i	0.964812	+	0.262942i	$0.0846927\pi$
$374$	−264.545	−	152.735i	−0.707339	−	0.408383i
$375$		0			0
$376$	120.000	+	207.846i	0.319149	+	0.552782i
$377$			33.9411i			0.0900295i
$378$		0			0
$379$	−160.000			−0.422164			−0.211082	−	0.977468i	$-0.567699\pi$
$379$	−160.000			−0.422164			−0.211082	+	0.977468i	$0.567699\pi$
$380$	−117.576	+	67.8823i	−0.309409	+	0.178638i
$381$		0			0
$382$	−24.0000	+	41.5692i	−0.0628272	+	0.108820i
$383$	235.151	+	135.765i	0.613971	+	0.354477i	0.774518	−	0.632552i	$-0.217992\pi$
$383$	235.151	+	135.765i	0.613971	+	0.354477i	−0.160547	+	0.987028i	$0.551326\pi$
$384$		0			0
$385$	144.000	+	249.415i	0.374026	+	0.647832i
$386$			291.328i			0.754736i
$387$		0			0
$388$	−352.000			−0.907216
$389$	−349.052	+	201.525i	−0.897307	+	0.518060i	−0.876325	−	0.481720i	$-0.840012\pi$
$389$	−349.052	+	201.525i	−0.897307	+	0.518060i	−0.0209813	+	0.999780i	$0.506679\pi$
$390$		0			0
$391$	108.000	−	187.061i	0.276215	−	0.478418i
$392$	−80.8332	−	46.6690i	−0.206207	−	0.119054i
$393$		0			0
$394$	117.000	+	202.650i	0.296954	+	0.514340i
$395$			322.441i			0.816306i
$396$		0			0
$397$	146.000			0.367758			0.183879	−	0.982949i	$-0.441135\pi$
$397$	146.000			0.367758			0.183879	+	0.982949i	$0.441135\pi$
$398$	24.4949	−	14.1421i	0.0615450	−	0.0355330i
$399$		0			0
$400$	−14.0000	+	24.2487i	−0.0350000	+	0.0606218i
$401$	−282.916	−	163.342i	−0.705526	−	0.407336i	0.103876	−	0.994590i	$-0.466875\pi$
$401$	−282.916	−	163.342i	−0.705526	−	0.407336i	−0.809402	+	0.587254i	$0.800209\pi$
$402$		0			0
$403$	−176.000	−	304.841i	−0.436725	−	0.756429i
$404$		−	59.3970i		−	0.147022i
$405$		0			0
$406$	24.0000			0.0591133
$407$	−499.696	+	288.500i	−1.22775	+	0.708844i
$408$		0			0
$409$	−184.000	+	318.697i	−0.449878	+	0.779211i	−0.998378	−	0.0569395i	$-0.981866\pi$
$409$	−184.000	+	318.697i	−0.449878	+	0.779211i	0.548500	+	0.836151i	$0.315199\pi$
$410$	−242.499	−	140.007i	−0.591462	−	0.341481i
$411$		0			0
$412$	−28.0000	−	48.4974i	−0.0679612	−	0.117712i
$413$		−	135.765i		−	0.328728i
$414$		0			0
$415$	504.000			1.21446
$416$	39.1918	−	22.6274i	0.0942111	−	0.0543928i
$417$		0			0
$418$	−192.000	+	332.554i	−0.459330	+	0.795583i
$419$	−338.030	−	195.161i	−0.806753	−	0.465779i	0.0390739	−	0.999236i	$-0.487559\pi$
$419$	−338.030	−	195.161i	−0.806753	−	0.465779i	−0.845827	+	0.533457i	$0.820893\pi$
$420$		0			0
$421$	20.0000	+	34.6410i	0.0475059	+	0.0822827i	0.888801	−	0.458294i	$-0.151539\pi$
$421$	20.0000	+	34.6410i	0.0475059	+	0.0822827i	−0.841295	+	0.540577i	$0.818206\pi$
$422$			418.607i			0.991960i
$423$		0			0
$424$	108.000			0.254717
$425$	−77.1589	+	44.5477i	−0.181550	+	0.104818i
$426$		0			0
$427$	100.000	−	173.205i	0.234192	−	0.405633i
$428$		0			0
$429$		0			0
$430$	120.000	+	207.846i	0.279070	+	0.483363i
$431$		−	152.735i		−	0.354374i	−0.984177	−	0.177187i	$-0.943300\pi$
$431$		−	152.735i		−	0.354374i	0.984177	−	0.177187i	$-0.0566997\pi$
$432$		0			0
$433$	542.000			1.25173			0.625866	−	0.779931i	$-0.284746\pi$
$433$	542.000			1.25173			0.625866	+	0.779931i	$0.284746\pi$
$434$	−215.555	+	124.451i	−0.496671	+	0.286753i
$435$		0			0
$436$	56.0000	−	96.9948i	0.128440	−	0.222465i
$437$	−235.151	−	135.765i	−0.538103	−	0.310674i
$438$		0			0
$439$	2.00000	+	3.46410i	0.00455581	+	0.00789089i	0.868294	−	0.496049i	$-0.165217\pi$
$439$	2.00000	+	3.46410i	0.00455581	+	0.00789089i	−0.863739	+	0.503940i	$0.831883\pi$
$440$		−	203.647i		−	0.462834i
$441$		0			0
$442$	144.000			0.325792
$443$	279.242	−	161.220i	0.630343	−	0.363929i	−0.150542	−	0.988604i	$-0.548102\pi$
$443$	279.242	−	161.220i	0.630343	−	0.363929i	0.780885	+	0.624675i	$0.214769\pi$
$444$		0			0
$445$	−27.0000	+	46.7654i	−0.0606742	+	0.105091i
$446$	533.989	+	308.299i	1.19728	+	0.691252i
$447$		0			0
$448$	−16.0000	−	27.7128i	−0.0357143	−	0.0618590i
$449$			216.375i			0.481904i	0.970537	+	0.240952i	$0.0774596\pi$
$449$			216.375i			0.481904i	−0.970537	+	0.240952i	$0.922540\pi$
$450$		0			0
$451$	−792.000			−1.75610
$452$	271.893	−	156.978i	0.601534	−	0.347296i
$453$		0			0
$454$	12.0000	−	20.7846i	0.0264317	−	0.0457811i
$455$	−117.576	−	67.8823i	−0.258408	−	0.149192i
$456$		0			0
$457$	200.000	+	346.410i	0.437637	+	0.758009i	0.997507	−	0.0705714i	$-0.0224823\pi$
$457$	200.000	+	346.410i	0.437637	+	0.758009i	−0.559870	+	0.828580i	$0.689149\pi$
$458$			11.3137i			0.0247024i
$459$		0			0
$460$	144.000			0.313043
$461$	−260.871	+	150.614i	−0.565880	+	0.326711i	−0.755502	−	0.655146i	$-0.772607\pi$
$461$	−260.871	+	150.614i	−0.565880	+	0.326711i	0.189622	+	0.981857i	$0.439274\pi$
$462$		0			0
$463$	302.000	−	523.079i	0.652268	−	1.12976i	−0.330303	−	0.943875i	$-0.607151\pi$
$463$	302.000	−	523.079i	0.652268	−	1.12976i	0.982571	−	0.185886i	$-0.0595156\pi$
$464$	−14.6969	−	8.48528i	−0.0316744	−	0.0182872i
$465$		0			0
$466$	−9.00000	−	15.5885i	−0.0193133	−	0.0334516i
$467$			356.382i			0.763130i	0.924342	+	0.381565i	$0.124615\pi$
$467$			356.382i			0.763130i	−0.924342	+	0.381565i	$0.875385\pi$
$468$		0			0
$469$	−32.0000			−0.0682303
$470$	−440.908	+	254.558i	−0.938102	+	0.541614i
$471$		0			0
$472$	−48.0000	+	83.1384i	−0.101695	+	0.176141i
$473$	587.878	+	339.411i	1.24287	+	0.717571i
$474$		0			0
$475$	56.0000	+	96.9948i	0.117895	+	0.204200i
$476$		−	101.823i		−	0.213915i
$477$		0			0
$478$	−192.000			−0.401674
$479$	455.605	−	263.044i	0.951159	−	0.549152i	0.0577181	−	0.998333i	$-0.481618\pi$
$479$	455.605	−	263.044i	0.951159	−	0.549152i	0.893441	+	0.449181i	$0.148284\pi$
$480$		0			0
$481$	136.000	−	235.559i	0.282744	−	0.489727i
$482$	−39.1918	−	22.6274i	−0.0813109	−	0.0469448i
$483$		0			0
$484$	−167.000	−	289.252i	−0.345041	−	0.597629i
$485$		−	746.705i		−	1.53960i
$486$		0			0
$487$	596.000			1.22382			0.611910	−	0.790928i	$-0.290402\pi$
$487$	596.000			1.22382			0.611910	+	0.790928i	$0.290402\pi$
$488$	−122.474	+	70.7107i	−0.250972	+	0.144899i
$489$		0			0
$490$	99.0000	−	171.473i	0.202041	−	0.349945i
$491$	235.151	+	135.765i	0.478923	+	0.276506i	0.719967	−	0.694008i	$-0.244157\pi$
$491$	235.151	+	135.765i	0.478923	+	0.276506i	−0.241045	+	0.970514i	$0.577490\pi$
$492$		0			0
$493$	−27.0000	−	46.7654i	−0.0547667	−	0.0948588i
$494$		−	181.019i		−	0.366436i
$495$		0			0
$496$	176.000			0.354839
$497$	176.363	−	101.823i	0.354856	−	0.204876i
$498$		0			0
$499$	−112.000	+	193.990i	−0.224449	+	0.388757i	−0.956154	−	0.292864i	$-0.905392\pi$
$499$	−112.000	+	193.990i	−0.224449	+	0.388757i	0.731705	+	0.681621i	$0.238725\pi$
$500$	−235.151	−	135.765i	−0.470302	−	0.271529i
$501$		0			0
$502$	36.0000	+	62.3538i	0.0717131	+	0.124211i
$503$			865.499i			1.72067i	0.509726	+	0.860337i	$0.329747\pi$
$503$			865.499i			1.72067i	−0.509726	+	0.860337i	$0.670253\pi$
$504$		0			0
$505$	126.000			0.249505
$506$	352.727	−	203.647i	0.697088	−	0.402464i
$507$		0			0
$508$	92.0000	−	159.349i	0.181102	−	0.313678i
$509$	−415.189	−	239.709i	−0.815695	−	0.470941i	0.0332350	−	0.999448i	$-0.489419\pi$
$509$	−415.189	−	239.709i	−0.815695	−	0.470941i	−0.848929	+	0.528506i	$0.822752\pi$
$510$		0			0
$511$	−32.0000	−	55.4256i	−0.0626223	−	0.108465i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	258.000			0.501946
$515$	102.879	−	59.3970i	0.199764	−	0.115334i
$516$		0			0
$517$	−720.000	+	1247.08i	−1.39265	+	2.41214i
$518$	−166.565	−	96.1665i	−0.321555	−	0.185650i
$519$		0			0
$520$	48.0000	+	83.1384i	0.0923077	+	0.159882i
$521$		−	521.845i		−	1.00162i	−0.865557	−	0.500811i	$-0.833035\pi$
$521$		−	521.845i		−	1.00162i	0.865557	−	0.500811i	$-0.166965\pi$
$522$		0			0
$523$	−736.000			−1.40727			−0.703633	−	0.710564i	$-0.748440\pi$
$523$	−736.000			−1.40727			−0.703633	+	0.710564i	$0.748440\pi$
$524$	293.939	−	169.706i	0.560952	−	0.323866i
$525$		0			0
$526$	264.000	−	457.261i	0.501901	−	0.869318i
$527$	484.999	+	280.014i	0.920302	+	0.531336i
$528$		0			0
$529$	−120.500	−	208.712i	−0.227788	−	0.394541i
$530$			229.103i			0.432269i
$531$		0			0
$532$	−128.000			−0.240602
$533$	323.333	−	186.676i	0.606628	−	0.350237i
$534$		0			0
$535$		0			0
$536$	19.5959	+	11.3137i	0.0365595	+	0.0211077i
$537$		0			0
$538$	−243.000	−	420.888i	−0.451673	−	0.782320i
$539$		−	560.029i		−	1.03901i
$540$		0			0
$541$	−808.000			−1.49353			−0.746765	−	0.665088i	$-0.768394\pi$
$541$	−808.000			−1.49353			−0.746765	+	0.665088i	$0.768394\pi$
$542$	465.403	−	268.701i	0.858677	−	0.495758i
$543$		0			0
$544$	−36.0000	+	62.3538i	−0.0661765	+	0.114621i
$545$	205.757	+	118.794i	0.377536	+	0.217971i
$546$		0			0
$547$	−268.000	−	464.190i	−0.489945	−	0.848610i	0.509988	−	0.860182i	$-0.329650\pi$
$547$	−268.000	−	464.190i	−0.489945	−	0.848610i	−0.999933	+	0.0115717i	$0.996317\pi$
$548$		−	313.955i		−	0.572911i
$549$		0			0
$550$	−168.000			−0.305455
$551$	−58.7878	+	33.9411i	−0.106693	+	0.0615991i
$552$		0			0
$553$	−152.000	+	263.272i	−0.274864	+	0.476079i
$554$	401.716	+	231.931i	0.725120	+	0.418648i
$555$		0			0
$556$	152.000	+	263.272i	0.273381	+	0.473510i
$557$		−	165.463i		−	0.297061i	−0.988908	−	0.148531i	$-0.952546\pi$
$557$		−	165.463i		−	0.297061i	0.988908	−	0.148531i	$-0.0474543\pi$
$558$		0			0
$559$	−320.000			−0.572451
$560$	58.7878	−	33.9411i	0.104978	−	0.0606092i
$561$		0			0
$562$	201.000	−	348.142i	0.357651	−	0.619470i
$563$	279.242	+	161.220i	0.495989	+	0.286359i	0.727056	−	0.686579i	$-0.240888\pi$
$563$	279.242	+	161.220i	0.495989	+	0.286359i	−0.231067	+	0.972938i	$0.574222\pi$
$564$		0			0
$565$	333.000	+	576.773i	0.589381	+	1.02084i
$566$		−	294.156i		−	0.519711i
$567$		0			0
$568$	−144.000			−0.253521
$569$	135.947	−	78.4889i	0.238922	−	0.137942i	−0.375759	−	0.926717i	$-0.622618\pi$
$569$	135.947	−	78.4889i	0.238922	−	0.137942i	0.614681	+	0.788776i	$0.289285\pi$
$570$		0			0
$571$	−184.000	+	318.697i	−0.322242	+	0.558139i	−0.980950	−	0.194259i	$-0.937770\pi$
$571$	−184.000	+	318.697i	−0.322242	+	0.558139i	0.658709	+	0.752398i	$0.271103\pi$
$572$	235.151	+	135.765i	0.411103	+	0.237351i
$573$		0			0
$574$	−132.000	−	228.631i	−0.229965	−	0.398311i
$575$		−	118.794i		−	0.206598i
$576$		0			0
$577$	−142.000			−0.246101			−0.123050	−	0.992400i	$-0.539268\pi$
$577$	−142.000			−0.246101			−0.123050	+	0.992400i	$0.539268\pi$
$578$	155.543	−	89.8026i	0.269105	−	0.155368i
$579$		0			0
$580$	18.0000	−	31.1769i	0.0310345	−	0.0537533i
$581$	411.514	+	237.588i	0.708286	+	0.408929i
$582$		0			0
$583$	324.000	+	561.184i	0.555746	+	0.962581i
$584$			45.2548i			0.0774912i
$585$		0			0
$586$	618.000			1.05461
$587$	323.333	−	186.676i	0.550822	−	0.318017i	−0.198631	−	0.980074i	$-0.563650\pi$
$587$	323.333	−	186.676i	0.550822	−	0.318017i	0.749454	+	0.662057i	$0.230316\pi$
$588$		0			0
$589$	352.000	−	609.682i	0.597623	−	1.03511i
$590$	−176.363	−	101.823i	−0.298921	−	0.172582i
$591$		0			0
$592$	68.0000	+	117.779i	0.114865	+	0.198952i
$593$			1107.33i			1.86733i	0.358142	+	0.933667i	$0.383410\pi$
$593$			1107.33i			1.86733i	−0.358142	+	0.933667i	$0.616590\pi$
$594$		0			0
$595$	216.000			0.363025
$596$	−477.650	+	275.772i	−0.801427	+	0.462704i
$597$		0			0
$598$	−96.0000	+	166.277i	−0.160535	+	0.278055i
$599$	−690.756	−	398.808i	−1.15318	−	0.665790i	−0.203521	−	0.979070i	$-0.565239\pi$
$599$	−690.756	−	398.808i	−1.15318	−	0.665790i	−0.949661	+	0.313280i	$0.898572\pi$
$600$		0			0
$601$	−79.0000	−	136.832i	−0.131448	−	0.227674i	0.792787	−	0.609499i	$-0.208629\pi$
$601$	−79.0000	−	136.832i	−0.131448	−	0.227674i	−0.924235	+	0.381825i	$0.875296\pi$
$602$			226.274i			0.375871i
$603$		0			0
$604$	296.000			0.490066
$605$	613.597	−	354.260i	1.01421	−	0.585555i
$606$		0			0
$607$	−166.000	+	287.520i	−0.273476	+	0.473675i	−0.969750	−	0.244102i	$-0.921507\pi$
$607$	−166.000	+	287.520i	−0.273476	+	0.473675i	0.696273	+	0.717777i	$0.254840\pi$
$608$	78.3837	+	45.2548i	0.128921	+	0.0744323i
$609$		0			0
$610$	−150.000	−	259.808i	−0.245902	−	0.425914i
$611$		−	678.823i		−	1.11100i
$612$		0			0
$613$	578.000			0.942904			0.471452	−	0.881892i	$-0.343730\pi$
$613$	578.000			0.942904			0.471452	+	0.881892i	$0.343730\pi$
$614$	−636.867	+	367.696i	−1.03724	+	0.598853i
$615$		0			0
$616$	96.0000	−	166.277i	0.155844	−	0.269930i
$617$	47.7650	+	27.5772i	0.0774150	+	0.0446956i	0.538208	−	0.842812i	$-0.319102\pi$
$617$	47.7650	+	27.5772i	0.0774150	+	0.0446956i	−0.460793	+	0.887508i	$0.652435\pi$
$618$		0			0
$619$	−448.000	−	775.959i	−0.723748	−	1.25357i	−0.959487	−	0.281752i	$-0.909084\pi$
$619$	−448.000	−	775.959i	−0.723748	−	1.25357i	0.235739	−	0.971816i	$-0.424249\pi$
$620$			373.352i			0.602181i
$621$		0			0
$622$	528.000			0.848875
$623$	−44.0908	+	25.4558i	−0.0707718	+	0.0408601i
$624$		0			0
$625$	200.500	−	347.276i	0.320800	−	0.555642i
$626$	115.126	+	66.4680i	0.183907	+	0.106179i
$627$		0			0
$628$	−82.0000	−	142.028i	−0.130573	−	0.226160i
$629$			432.749i			0.687996i
$630$		0			0
$631$	20.0000			0.0316957			0.0158479	−	0.999874i	$-0.494955\pi$
$631$	20.0000			0.0316957			0.0158479	+	0.999874i	$0.494955\pi$
$632$	186.161	−	107.480i	0.294559	−	0.170064i
$633$		0			0
$634$	237.000	−	410.496i	0.373817	−	0.647470i
$635$	338.030	+	195.161i	0.532330	+	0.307341i
$636$		0			0
$637$	132.000	+	228.631i	0.207221	+	0.358918i
$638$		−	101.823i		−	0.159598i
$639$		0			0
$640$	−48.0000			−0.0750000
$641$	224.128	−	129.401i	0.349654	−	0.201873i	−0.314879	−	0.949132i	$-0.601964\pi$
$641$	224.128	−	129.401i	0.349654	−	0.201873i	0.664533	+	0.747259i	$0.268631\pi$
$642$		0			0
$643$	−364.000	+	630.466i	−0.566096	+	0.980508i	0.430850	+	0.902423i	$0.358214\pi$
$643$	−364.000	+	630.466i	−0.566096	+	0.980508i	−0.996947	+	0.0780844i	$0.975120\pi$
$644$	117.576	+	67.8823i	0.182571	+	0.105407i
$645$		0			0
$646$	144.000	+	249.415i	0.222910	+	0.386092i
$647$		−	458.205i		−	0.708200i	−0.935208	−	0.354100i	$-0.884787\pi$
$647$		−	458.205i		−	0.708200i	0.935208	−	0.354100i	$-0.115213\pi$
$648$		0			0
$649$	−576.000			−0.887519
$650$	68.5857	−	39.5980i	0.105516	−	0.0609200i
$651$		0			0
$652$	56.0000	−	96.9948i	0.0858896	−	0.148765i
$653$	−260.871	−	150.614i	−0.399496	−	0.230649i	0.286771	−	0.957999i	$-0.407418\pi$
$653$	−260.871	−	150.614i	−0.399496	−	0.230649i	−0.686266	+	0.727350i	$0.740752\pi$
$654$		0			0
$655$	360.000	+	623.538i	0.549618	+	0.951967i
$656$			186.676i			0.284567i
$657$		0			0
$658$	−480.000			−0.729483
$659$	−911.210	+	526.087i	−1.38272	+	0.798312i	−0.992480	−	0.122403i	$-0.960940\pi$
$659$	−911.210	+	526.087i	−1.38272	+	0.798312i	−0.390236	+	0.920715i	$0.627607\pi$
$660$		0			0
$661$	−31.0000	+	53.6936i	−0.0468986	+	0.0812308i	−0.888522	−	0.458834i	$-0.848267\pi$
$661$	−31.0000	+	53.6936i	−0.0468986	+	0.0812308i	0.841623	+	0.540065i	$0.181600\pi$
$662$	−656.463	−	379.009i	−0.991636	−	0.572522i
$663$		0			0
$664$	−168.000	−	290.985i	−0.253012	−	0.438230i
$665$		−	271.529i		−	0.408314i
$666$		0			0
$667$	72.0000			0.107946
$668$	−58.7878	+	33.9411i	−0.0880056	+	0.0508101i
$669$		0			0
$670$	−24.0000	+	41.5692i	−0.0358209	+	0.0620436i
$671$	−734.847	−	424.264i	−1.09515	−	0.632286i
$672$		0			0
$673$	335.000	+	580.237i	0.497771	+	0.862165i	0.999997	−	0.00257172i	$-0.000818604\pi$
$673$	335.000	+	580.237i	0.497771	+	0.862165i	−0.502226	+	0.864737i	$0.667485\pi$
$674$		−	294.156i		−	0.436434i
$675$		0			0
$676$	210.000			0.310651
$677$	−1120.64	+	647.003i	−1.65531	+	0.955691i	−0.680466	+	0.732779i	$0.738223\pi$
$677$	−1120.64	+	647.003i	−1.65531	+	0.955691i	−0.974839	+	0.222912i	$0.928444\pi$
$678$		0			0
$679$	352.000	−	609.682i	0.518409	−	0.897911i
$680$	−132.272	−	76.3675i	−0.194518	−	0.112305i
$681$		0			0
$682$	528.000	+	914.523i	0.774194	+	1.34094i
$683$		−	560.029i		−	0.819954i	−0.912096	−	0.409977i	$-0.865537\pi$
$683$		−	560.029i		−	0.819954i	0.912096	−	0.409977i	$-0.134463\pi$
$684$		0			0
$685$	666.000			0.972263
$686$	401.716	−	231.931i	0.585592	−	0.338092i
$687$		0			0
$688$	80.0000	−	138.564i	0.116279	−	0.201401i
$689$	−264.545	−	152.735i	−0.383955	−	0.221676i
$690$		0			0
$691$	20.0000	+	34.6410i	0.0289436	+	0.0501317i	0.880134	−	0.474725i	$-0.157452\pi$
$691$	20.0000	+	34.6410i	0.0289436	+	0.0501317i	−0.851191	+	0.524856i	$0.824119\pi$
$692$			347.897i			0.502741i
$693$		0			0
$694$	−408.000			−0.587896
$695$	−558.484	+	322.441i	−0.803574	+	0.463943i
$696$		0			0
$697$	−297.000	+	514.419i	−0.426112	+	0.738047i
$698$	291.489	+	168.291i	0.417606	+	0.241105i
$699$		0			0
$700$	−28.0000	−	48.4974i	−0.0400000	−	0.0692820i
$701$			954.594i			1.36176i	0.732395	+	0.680880i	$0.238403\pi$
$701$			954.594i			1.36176i	−0.732395	+	0.680880i	$0.761597\pi$
$702$		0			0
$703$	544.000			0.773826
$704$	−117.576	+	67.8823i	−0.167011	+	0.0964237i
$705$		0			0
$706$	−159.000	+	275.396i	−0.225212	+	0.390079i
$707$	102.879	+	59.3970i	0.145514	+	0.0840127i
$708$		0			0
$709$	−484.000	−	838.313i	−0.682652	−	1.18239i	−0.974169	−	0.225822i	$-0.927493\pi$
$709$	−484.000	−	838.313i	−0.682652	−	1.18239i	0.291517	−	0.956566i	$-0.405840\pi$
$710$		−	305.470i		−	0.430240i
$711$		0			0
$712$	36.0000			0.0505618
$713$	−646.665	+	373.352i	−0.906964	+	0.523636i
$714$		0			0
$715$	−288.000	+	498.831i	−0.402797	+	0.697665i
$716$	−352.727	−	203.647i	−0.492635	−	0.284423i
$717$		0			0
$718$	−396.000	−	685.892i	−0.551532	−	0.955282i
$719$			1170.97i			1.62861i	0.580439	+	0.814304i	$0.302881\pi$
$719$			1170.97i			1.62861i	−0.580439	+	0.814304i	$0.697119\pi$
$720$		0			0
$721$	112.000			0.155340
$722$	−128.598	+	74.2462i	−0.178114	+	0.102834i
$723$		0			0
$724$	−232.000	+	401.836i	−0.320442	+	0.555022i
$725$	−25.7196	−	14.8492i	−0.0354754	−	0.0204817i
$726$		0			0
$727$	254.000	+	439.941i	0.349381	+	0.605146i	0.986140	−	0.165918i	$-0.0530586\pi$
$727$	254.000	+	439.941i	0.349381	+	0.605146i	−0.636759	+	0.771063i	$0.719725\pi$
$728$			90.5097i			0.124326i
$729$		0			0
$730$	−96.0000			−0.131507
$731$	440.908	−	254.558i	0.603158	−	0.348233i
$732$		0			0
$733$	572.000	−	990.733i	0.780355	−	1.35161i	−0.151380	−	0.988476i	$-0.548372\pi$
$733$	572.000	−	990.733i	0.780355	−	1.35161i	0.931735	−	0.363138i	$-0.118295\pi$
$734$	−347.828	−	200.818i	−0.473879	−	0.273594i
$735$		0			0
$736$	−48.0000	−	83.1384i	−0.0652174	−	0.112960i
$737$			135.765i			0.184212i
$738$		0			0
$739$	−304.000			−0.411367			−0.205683	−	0.978619i	$-0.565942\pi$
$739$	−304.000			−0.411367			−0.205683	+	0.978619i	$0.565942\pi$
$740$	−249.848	+	144.250i	−0.337632	+	0.194932i
$741$		0			0
$742$	−108.000	+	187.061i	−0.145553	+	0.252104i
$743$	−734.847	−	424.264i	−0.989027	−	0.571015i	−0.0840436	−	0.996462i	$-0.526783\pi$
$743$	−734.847	−	424.264i	−0.989027	−	0.571015i	−0.904983	+	0.425447i	$0.860117\pi$
$744$		0			0
$745$	−585.000	−	1013.25i	−0.785235	−	1.36007i
$746$		−	268.701i		−	0.360188i
$747$		0			0
$748$	−432.000			−0.577540
$749$		0			0
$750$		0			0
$751$	−94.0000	+	162.813i	−0.125166	+	0.216795i	−0.921798	−	0.387671i	$-0.873280\pi$
$751$	−94.0000	+	162.813i	−0.125166	+	0.216795i	0.796632	+	0.604465i	$0.206613\pi$
$752$	293.939	+	169.706i	0.390876	+	0.225672i
$753$		0			0
$754$	24.0000	+	41.5692i	0.0318302	+	0.0551316i
$755$			627.911i			0.831670i
$756$		0			0
$757$	−1240.00			−1.63804			−0.819022	−	0.573761i	$-0.805484\pi$
$757$	−1240.00			−1.63804			−0.819022	+	0.573761i	$0.805484\pi$
$758$	−195.959	+	113.137i	−0.258521	+	0.149257i
$759$		0			0
$760$	−96.0000	+	166.277i	−0.126316	+	0.218785i
$761$	135.947	+	78.4889i	0.178642	+	0.103139i	0.586655	−	0.809837i	$-0.300445\pi$
$761$	135.947	+	78.4889i	0.178642	+	0.103139i	−0.408012	+	0.912976i	$0.633778\pi$
$762$		0			0
$763$	112.000	+	193.990i	0.146789	+	0.254246i
$764$			67.8823i			0.0888511i
$765$		0			0
$766$	384.000			0.501305
$767$	235.151	−	135.765i	0.306585	−	0.177007i
$768$		0			0
$769$	455.000	−	788.083i	0.591678	−	1.02482i	−0.402329	−	0.915495i	$-0.631799\pi$
$769$	455.000	−	788.083i	0.591678	−	1.02482i	0.994007	−	0.109320i	$-0.0348674\pi$
$770$	352.727	+	203.647i	0.458086	+	0.264476i
$771$		0			0
$772$	206.000	+	356.802i	0.266839	+	0.462179i
$773$		−	1387.34i		−	1.79475i	−0.441266	−	0.897376i	$-0.645471\pi$
$773$		−	1387.34i		−	1.79475i	0.441266	−	0.897376i	$-0.354529\pi$
$774$		0			0
$775$	308.000			0.397419
$776$	−431.110	+	248.902i	−0.555554	+	0.320749i
$777$		0			0
$778$	−285.000	+	493.634i	−0.366324	+	0.634492i
$779$	646.665	+	373.352i	0.830122	+	0.479271i
$780$		0			0
$781$	−432.000	−	748.246i	−0.553137	−	0.958061i
$782$		−	305.470i		−	0.390627i
$783$		0			0
$784$	−132.000			−0.168367
$785$	301.287	−	173.948i	0.383805	−	0.221590i
$786$		0			0
$787$	680.000	−	1177.79i	0.864041	−	1.49656i	−0.00395593	−	0.999992i	$-0.501259\pi$
$787$	680.000	−	1177.79i	0.864041	−	1.49656i	0.867997	−	0.496570i	$-0.165407\pi$
$788$	286.590	+	165.463i	0.363693	+	0.209978i
$789$		0			0
$790$	228.000	+	394.908i	0.288608	+	0.499883i
$791$			627.911i			0.793819i
$792$		0			0
$793$	400.000			0.504414
$794$	178.813	−	103.238i	0.225205	−	0.130022i
$795$		0			0
$796$	20.0000	−	34.6410i	0.0251256	−	0.0435189i
$797$	91.8559	+	53.0330i	0.115252	+	0.0665408i	0.556518	−	0.830836i	$-0.312137\pi$
$797$	91.8559	+	53.0330i	0.115252	+	0.0665408i	−0.441266	+	0.897376i	$0.645470\pi$
$798$		0			0
$799$	540.000	+	935.307i	0.675845	+	1.17060i
$800$			39.5980i			0.0494975i
$801$		0			0
$802$	−462.000			−0.576060
$803$	−235.151	+	135.765i	−0.292841	+	0.169072i
$804$		0			0
$805$	−144.000	+	249.415i	−0.178882	+	0.309833i
$806$	−431.110	−	248.902i	−0.534876	−	0.308811i
$807$		0			0
$808$	−42.0000	−	72.7461i	−0.0519802	−	0.0900323i
$809$		−	1107.33i		−	1.36876i	−0.729124	−	0.684381i	$-0.760072\pi$
$809$		−	1107.33i		−	1.36876i	0.729124	−	0.684381i	$-0.239928\pi$
$810$		0			0
$811$	−160.000			−0.197287			−0.0986436	−	0.995123i	$-0.531450\pi$
$811$	−160.000			−0.197287			−0.0986436	+	0.995123i	$0.531450\pi$
$812$	29.3939	−	16.9706i	0.0361994	−	0.0208997i
$813$		0			0
$814$	−408.000	+	706.677i	−0.501229	+	0.868153i
$815$	205.757	+	118.794i	0.252463	+	0.145759i
$816$		0			0
$817$	−320.000	−	554.256i	−0.391677	−	0.678404i
$818$			520.431i			0.636223i
$819$		0			0
$820$	−396.000			−0.482927
$821$	378.446	−	218.496i	0.460958	−	0.266134i	−0.251489	−	0.967860i	$-0.580920\pi$
$821$	378.446	−	218.496i	0.460958	−	0.266134i	0.712447	+	0.701726i	$0.247587\pi$
$822$		0			0
$823$	−166.000	+	287.520i	−0.201701	+	0.349357i	−0.949077	−	0.315045i	$-0.897980\pi$
$823$	−166.000	+	287.520i	−0.201701	+	0.349357i	0.747376	+	0.664402i	$0.231314\pi$
$824$	−68.5857	−	39.5980i	−0.0832351	−	0.0480558i
$825$		0			0
$826$	−96.0000	−	166.277i	−0.116223	−	0.201304i
$827$			101.823i			0.123124i	0.998103	+	0.0615619i	$0.0196082\pi$
$827$			101.823i			0.123124i	−0.998103	+	0.0615619i	$0.980392\pi$
$828$		0			0
$829$	632.000			0.762364			0.381182	−	0.924500i	$-0.375517\pi$
$829$	632.000			0.762364			0.381182	+	0.924500i	$0.375517\pi$
$830$	617.271	−	356.382i	0.743701	−	0.429376i
$831$		0			0
$832$	32.0000	−	55.4256i	0.0384615	−	0.0666173i
$833$	−363.749	−	210.011i	−0.436674	−	0.252114i
$834$		0			0
$835$	−72.0000	−	124.708i	−0.0862275	−	0.149350i
$836$			543.058i			0.649591i
$837$		0			0
$838$	−552.000			−0.658711
$839$	631.968	−	364.867i	0.753240	−	0.434883i	−0.0736234	−	0.997286i	$-0.523456\pi$
$839$	631.968	−	364.867i	0.753240	−	0.434883i	0.826863	+	0.562403i	$0.190123\pi$
$840$		0			0
$841$	−411.500	+	712.739i	−0.489298	+	0.847490i
$842$	48.9898	+	28.2843i	0.0581827	+	0.0335918i
$843$		0			0
$844$	296.000	+	512.687i	0.350711	+	0.607449i
$845$			445.477i			0.527192i
$846$		0			0
$847$	668.000			0.788666
$848$	132.272	−	76.3675i	0.155982	−	0.0900561i
$849$		0			0
$850$	−63.0000	+	109.119i	−0.0741176	+	0.128376i
$851$	−499.696	−	288.500i	−0.587187	−	0.339012i
$852$		0			0
$853$	−223.000	−	386.247i	−0.261430	−	0.452810i	0.705192	−	0.709016i	$-0.250861\pi$
$853$	−223.000	−	386.247i	−0.261430	−	0.452810i	−0.966622	+	0.256206i	$0.917527\pi$
$854$		−	282.843i		−	0.331198i
$855$		0			0
$856$		0			0
$857$	−371.098	+	214.253i	−0.433019	+	0.250004i	−0.700632	−	0.713523i	$-0.747099\pi$
$857$	−371.098	+	214.253i	−0.433019	+	0.250004i	0.267613	+	0.963527i	$0.413765\pi$
$858$		0			0
$859$	−364.000	+	630.466i	−0.423749	+	0.733954i	−0.996303	−	0.0859129i	$-0.972619\pi$
$859$	−364.000	+	630.466i	−0.423749	+	0.733954i	0.572554	+	0.819867i	$0.305953\pi$
$860$	293.939	+	169.706i	0.341789	+	0.197332i
$861$		0			0
$862$	−108.000	−	187.061i	−0.125290	−	0.217009i
$863$		−	916.410i		−	1.06189i	−0.847407	−	0.530945i	$-0.821837\pi$
$863$		−	916.410i		−	1.06189i	0.847407	−	0.530945i	$-0.178163\pi$
$864$		0			0
$865$	−738.000			−0.853179
$866$	663.812	−	383.252i	0.766526	−	0.442554i
$867$		0			0
$868$	−176.000	+	304.841i	−0.202765	+	0.351199i
$869$	1116.97	+	644.881i	1.28535	+	0.742096i
$870$		0			0
$871$	−32.0000	−	55.4256i	−0.0367394	−	0.0636345i
$872$		−	158.392i		−	0.181642i
$873$		0			0
$874$	−384.000			−0.439359
$875$	470.302	−	271.529i	0.537488	−	0.310319i
$876$		0			0
$877$	455.000	−	788.083i	0.518814	−	0.898612i	−0.480947	−	0.876750i	$-0.659707\pi$
$877$	455.000	−	788.083i	0.518814	−	0.898612i	0.999761	−	0.0218627i	$-0.00695967\pi$
$878$	4.89898	+	2.82843i	0.00557970	+	0.00322144i
$879$		0			0
$880$	−144.000	−	249.415i	−0.163636	−	0.283426i
$881$		−	929.138i		−	1.05464i	−0.849667	−	0.527320i	$-0.823197\pi$
$881$		−	929.138i		−	1.05464i	0.849667	−	0.527320i	$-0.176803\pi$
$882$		0			0
$883$	1064.00			1.20498			0.602492	−	0.798125i	$-0.294175\pi$
$883$	1064.00			1.20498			0.602492	+	0.798125i	$0.294175\pi$
$884$	176.363	−	101.823i	0.199506	−	0.115185i
$885$		0			0
$886$	228.000	−	394.908i	0.257336	−	0.445720i
$887$	1205.15	+	695.793i	1.35868	+	0.784434i	0.989446	−	0.144902i	$-0.0462868\pi$
$887$	1205.15	+	695.793i	1.35868	+	0.784434i	0.369234	+	0.929337i	$0.379620\pi$
$888$		0			0
$889$	184.000	+	318.697i	0.206974	+	0.358490i
$890$			76.3675i			0.0858062i
$891$		0			0
$892$	872.000			0.977578
$893$	1175.76	−	678.823i	1.31664	−	0.760160i
$894$		0			0
$895$	432.000	−	748.246i	0.482682	−	0.836029i
$896$	−39.1918	−	22.6274i	−0.0437409	−	0.0252538i
$897$		0			0
$898$	153.000	+	265.004i	0.170379	+	0.295104i
$899$			186.676i			0.207649i
$900$		0			0
$901$	486.000			0.539401
$902$	−969.998	+	560.029i	−1.07539	+	0.620874i
$903$		0			0
$904$	222.000	−	384.515i	0.245575	−	0.425349i
$905$	−852.422	−	492.146i	−0.941903	−	0.543808i
$906$		0			0
$907$	884.000	+	1531.13i	0.974642	+	1.68813i	0.681112	+	0.732179i	$0.261496\pi$
$907$	884.000	+	1531.13i	0.974642	+	1.68813i	0.293529	+	0.955950i	$0.405170\pi$
$908$		−	33.9411i		−	0.0373801i
$909$		0			0
$910$	−192.000			−0.210989
$911$	−205.757	+	118.794i	−0.225859	+	0.130399i	−0.608660	−	0.793431i	$-0.708293\pi$
$911$	−205.757	+	118.794i	−0.225859	+	0.130399i	0.382801	+	0.923831i	$0.374959\pi$
$912$		0			0
$913$	1008.00	−	1745.91i	1.10405	−	1.91228i
$914$	489.898	+	282.843i	0.535993	+	0.309456i
$915$		0			0
$916$	8.00000	+	13.8564i	0.00873362	+	0.0151271i
$917$			678.823i			0.740264i
$918$		0			0
$919$	380.000			0.413493			0.206746	−	0.978395i	$-0.433712\pi$
$919$	380.000			0.413493			0.206746	+	0.978395i	$0.433712\pi$
$920$	176.363	−	101.823i	0.191699	−	0.110678i
$921$		0			0
$922$	−213.000	+	368.927i	−0.231020	+	0.400138i
$923$	352.727	+	203.647i	0.382152	+	0.220636i
$924$		0			0
$925$	119.000	+	206.114i	0.128649	+	0.222826i
$926$		−	854.185i		−	0.922446i
$927$		0			0
$928$	−24.0000			−0.0258621
$929$	576.855	−	333.047i	0.620942	−	0.358501i	−0.156294	−	0.987711i	$-0.549955\pi$
$929$	576.855	−	333.047i	0.620942	−	0.358501i	0.777236	+	0.629210i	$0.216621\pi$
$930$		0			0
$931$	−264.000	+	457.261i	−0.283566	+	0.491151i
$932$	−22.0454	−	12.7279i	−0.0236539	−	0.0136566i
$933$		0			0
$934$	252.000	+	436.477i	0.269807	+	0.467320i
$935$		−	916.410i		−	0.980118i
$936$		0			0
$937$	−178.000			−0.189968			−0.0949840	−	0.995479i	$-0.530280\pi$
$937$	−178.000			−0.189968			−0.0949840	+	0.995479i	$0.530280\pi$
$938$	−39.1918	+	22.6274i	−0.0417823	+	0.0241230i
$939$		0			0
$940$	−360.000	+	623.538i	−0.382979	+	0.663339i
$941$	378.446	+	218.496i	0.402174	+	0.232196i	0.687422	−	0.726258i	$-0.258742\pi$
$941$	378.446	+	218.496i	0.402174	+	0.232196i	−0.285247	+	0.958454i	$0.592076\pi$
$942$		0			0
$943$	−396.000	−	685.892i	−0.419936	−	0.727351i
$944$			135.765i			0.143818i
$945$		0			0
$946$	960.000			1.01480
$947$	1557.88	−	899.440i	1.64506	−	0.949778i	0.666070	−	0.745889i	$-0.267975\pi$
$947$	1557.88	−	899.440i	1.64506	−	0.949778i	0.978994	−	0.203889i	$-0.0653580\pi$
$948$		0			0
$949$	64.0000	−	110.851i	0.0674394	−	0.116808i
$950$	137.171	+	79.1960i	0.144391	+	0.0833642i
$951$		0			0
$952$	−72.0000	−	124.708i	−0.0756303	−	0.130995i
$953$			1310.98i			1.37563i	0.725886	+	0.687815i	$0.241430\pi$
$953$			1310.98i			1.37563i	−0.725886	+	0.687815i	$0.758570\pi$
$954$		0			0
$955$	−144.000			−0.150785
$956$	−235.151	+	135.765i	−0.245974	+	0.142013i
$957$		0			0
$958$	372.000	−	644.323i	0.388309	−	0.672571i
$959$	543.787	+	313.955i	0.567035	+	0.327378i
$960$		0			0
$961$	−487.500	−	844.375i	−0.507284	−	0.878642i
$962$		−	384.666i		−	0.399861i
$963$		0			0
$964$	−64.0000			−0.0663900
$965$	−756.892	+	436.992i	−0.784344	+	0.452841i
$966$		0			0
$967$	−850.000	+	1472.24i	−0.879007	+	1.52249i	−0.0265754	+	0.999647i	$0.508460\pi$
$967$	−850.000	+	1472.24i	−0.879007	+	1.52249i	−0.852432	+	0.522838i	$0.824873\pi$
$968$	−409.065	−	236.174i	−0.422588	−	0.243981i
$969$		0			0
$970$	−528.000	−	914.523i	−0.544330	−	0.942807i
$971$			458.205i			0.471890i	0.971766	+	0.235945i	$0.0758185\pi$
$971$			458.205i			0.471890i	−0.971766	+	0.235945i	$0.924181\pi$
$972$		0			0
$973$	−608.000			−0.624872
$974$	729.948	−	421.436i	0.749433	−	0.432685i
$975$		0			0
$976$	−100.000	+	173.205i	−0.102459	+	0.177464i
$977$	−657.688	−	379.716i	−0.673171	−	0.388655i	0.124106	−	0.992269i	$-0.460394\pi$
$977$	−657.688	−	379.716i	−0.673171	−	0.388655i	−0.797277	+	0.603614i	$0.793727\pi$
$978$		0			0
$979$	108.000	+	187.061i	0.110317	+	0.191074i
$980$		−	280.014i		−	0.285729i
$981$		0			0
$982$	384.000			0.391039
$983$	−911.210	+	526.087i	−0.926969	+	0.535186i	−0.885852	−	0.463969i	$-0.846425\pi$
$983$	−911.210	+	526.087i	−0.926969	+	0.535186i	−0.0411171	+	0.999154i	$0.513092\pi$
$984$		0			0
$985$	−351.000	+	607.950i	−0.356345	+	0.617208i
$986$	−66.1362	−	38.1838i	−0.0670753	−	0.0387259i
$987$		0			0
$988$	−128.000	−	221.703i	−0.129555	−	0.224395i
$989$			678.823i			0.686373i
$990$		0			0
$991$	−772.000			−0.779011			−0.389506	−	0.921024i	$-0.627354\pi$
$991$	−772.000			−0.779011			−0.389506	+	0.921024i	$0.627354\pi$
$992$	215.555	−	124.451i	0.217293	−	0.125454i
$993$		0			0
$994$	144.000	−	249.415i	0.144869	−	0.250921i
$995$	73.4847	+	42.4264i	0.0738540	+	0.0426396i
$996$		0			0
$997$	−97.0000	−	168.009i	−0.0972919	−	0.168514i	0.813271	−	0.581885i	$-0.197685\pi$
$997$	−97.0000	−	168.009i	−0.0972919	−	0.168514i	−0.910563	+	0.413371i	$0.864351\pi$
$998$			316.784i			0.317419i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.d.b.53.2		4
3.2	odd	2	inner	162.3.d.b.53.1		4
4.3	odd	2		1296.3.q.f.1025.2		4
9.2	odd	6	inner	162.3.d.b.107.2		4
9.4	even	3		18.3.b.a.17.2	yes	2
9.5	odd	6		18.3.b.a.17.1	✓	2
9.7	even	3	inner	162.3.d.b.107.1		4
12.11	even	2		1296.3.q.f.1025.1		4
36.7	odd	6		1296.3.q.f.593.1		4
36.11	even	6		1296.3.q.f.593.2		4
36.23	even	6		144.3.e.b.17.2		2
36.31	odd	6		144.3.e.b.17.1		2
45.4	even	6		450.3.d.f.251.1		2
45.13	odd	12		450.3.b.b.449.4		4
45.14	odd	6		450.3.d.f.251.2		2
45.22	odd	12		450.3.b.b.449.1		4
45.23	even	12		450.3.b.b.449.2		4
45.32	even	12		450.3.b.b.449.3		4
63.4	even	3		882.3.s.b.863.1		4
63.5	even	6		882.3.s.d.557.1		4
63.13	odd	6		882.3.b.a.197.2		2
63.23	odd	6		882.3.s.b.557.1		4
63.31	odd	6		882.3.s.d.863.1		4
63.32	odd	6		882.3.s.b.863.2		4
63.40	odd	6		882.3.s.d.557.2		4
63.41	even	6		882.3.b.a.197.1		2
63.58	even	3		882.3.s.b.557.2		4
63.59	even	6		882.3.s.d.863.2		4
72.5	odd	6		576.3.e.c.449.1		2
72.13	even	6		576.3.e.c.449.2		2
72.59	even	6		576.3.e.f.449.1		2
72.67	odd	6		576.3.e.f.449.2		2
99.32	even	6		2178.3.c.d.485.2		2
99.76	odd	6		2178.3.c.d.485.1		2
117.5	even	12		3042.3.d.a.3041.1		4
117.31	odd	12		3042.3.d.a.3041.3		4
117.77	odd	6		3042.3.c.e.1691.2		2
117.86	even	12		3042.3.d.a.3041.4		4
117.103	even	6		3042.3.c.e.1691.1		2
117.112	odd	12		3042.3.d.a.3041.2		4
144.5	odd	12		2304.3.h.f.2177.1		4
144.13	even	12		2304.3.h.f.2177.2		4
144.59	even	12		2304.3.h.c.2177.1		4
144.67	odd	12		2304.3.h.c.2177.2		4
144.77	odd	12		2304.3.h.f.2177.4		4
144.85	even	12		2304.3.h.f.2177.3		4
144.131	even	12		2304.3.h.c.2177.4		4
144.139	odd	12		2304.3.h.c.2177.3		4
180.23	odd	12		3600.3.c.b.449.2		4
180.59	even	6		3600.3.l.d.1601.2		2
180.67	even	12		3600.3.c.b.449.3		4
180.103	even	12		3600.3.c.b.449.1		4
180.139	odd	6		3600.3.l.d.1601.1		2
180.167	odd	12		3600.3.c.b.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.b.a.17.1	✓	2	9.5	odd	6
18.3.b.a.17.2	yes	2	9.4	even	3
144.3.e.b.17.1		2	36.31	odd	6
144.3.e.b.17.2		2	36.23	even	6
162.3.d.b.53.1		4	3.2	odd	2	inner
162.3.d.b.53.2		4	1.1	even	1	trivial
162.3.d.b.107.1		4	9.7	even	3	inner
162.3.d.b.107.2		4	9.2	odd	6	inner
450.3.b.b.449.1		4	45.22	odd	12
450.3.b.b.449.2		4	45.23	even	12
450.3.b.b.449.3		4	45.32	even	12
450.3.b.b.449.4		4	45.13	odd	12
450.3.d.f.251.1		2	45.4	even	6
450.3.d.f.251.2		2	45.14	odd	6
576.3.e.c.449.1		2	72.5	odd	6
576.3.e.c.449.2		2	72.13	even	6
576.3.e.f.449.1		2	72.59	even	6
576.3.e.f.449.2		2	72.67	odd	6
882.3.b.a.197.1		2	63.41	even	6
882.3.b.a.197.2		2	63.13	odd	6
882.3.s.b.557.1		4	63.23	odd	6
882.3.s.b.557.2		4	63.58	even	3
882.3.s.b.863.1		4	63.4	even	3
882.3.s.b.863.2		4	63.32	odd	6
882.3.s.d.557.1		4	63.5	even	6
882.3.s.d.557.2		4	63.40	odd	6
882.3.s.d.863.1		4	63.31	odd	6
882.3.s.d.863.2		4	63.59	even	6
1296.3.q.f.593.1		4	36.7	odd	6
1296.3.q.f.593.2		4	36.11	even	6
1296.3.q.f.1025.1		4	12.11	even	2
1296.3.q.f.1025.2		4	4.3	odd	2
2178.3.c.d.485.1		2	99.76	odd	6
2178.3.c.d.485.2		2	99.32	even	6
2304.3.h.c.2177.1		4	144.59	even	12
2304.3.h.c.2177.2		4	144.67	odd	12
2304.3.h.c.2177.3		4	144.139	odd	12
2304.3.h.c.2177.4		4	144.131	even	12
2304.3.h.f.2177.1		4	144.5	odd	12
2304.3.h.f.2177.2		4	144.13	even	12
2304.3.h.f.2177.3		4	144.85	even	12
2304.3.h.f.2177.4		4	144.77	odd	12
3042.3.c.e.1691.1		2	117.103	even	6
3042.3.c.e.1691.2		2	117.77	odd	6
3042.3.d.a.3041.1		4	117.5	even	12
3042.3.d.a.3041.2		4	117.112	odd	12
3042.3.d.a.3041.3		4	117.31	odd	12
3042.3.d.a.3041.4		4	117.86	even	12
3600.3.c.b.449.1		4	180.103	even	12
3600.3.c.b.449.2		4	180.23	odd	12
3600.3.c.b.449.3		4	180.67	even	12
3600.3.c.b.449.4		4	180.167	odd	12
3600.3.l.d.1601.1		2	180.139	odd	6
3600.3.l.d.1601.2		2	180.59	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 + 2.12132i) q^{5} +(2.00000 + 3.46410i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.67423 + 2.12132i) q^{5} +(2.00000 + 3.46410i) q^{7} -2.82843i q^{8} +6.00000 q^{10} +(14.6969 - 8.48528i) q^{11} +(-4.00000 + 6.92820i) q^{13} +(4.89898 + 2.82843i) q^{14} +(-2.00000 - 3.46410i) q^{16} -12.7279i q^{17} -16.0000 q^{19} +(7.34847 - 4.24264i) q^{20} +(12.0000 - 20.7846i) q^{22} +(14.6969 + 8.48528i) q^{23} +(-3.50000 - 6.06218i) q^{25} +11.3137i q^{26} +8.00000 q^{28} +(3.67423 - 2.12132i) q^{29} +(-22.0000 + 38.1051i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-9.00000 - 15.5885i) q^{34} +16.9706i q^{35} -34.0000 q^{37} +(-19.5959 + 11.3137i) q^{38} +(6.00000 - 10.3923i) q^{40} +(-40.4166 - 23.3345i) q^{41} +(20.0000 + 34.6410i) q^{43} -33.9411i q^{44} +24.0000 q^{46} +(-73.4847 + 42.4264i) q^{47} +(16.5000 - 28.5788i) q^{49} +(-8.57321 - 4.94975i) q^{50} +(8.00000 + 13.8564i) q^{52} +38.1838i q^{53} +72.0000 q^{55} +(9.79796 - 5.65685i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-29.3939 - 16.9706i) q^{59} +(-25.0000 - 43.3013i) q^{61} +62.2254i q^{62} -8.00000 q^{64} +(-29.3939 + 16.9706i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-22.0454 - 12.7279i) q^{68} +(12.0000 + 20.7846i) q^{70} -50.9117i q^{71} -16.0000 q^{73} +(-41.6413 + 24.0416i) q^{74} +(-16.0000 + 27.7128i) q^{76} +(58.7878 + 33.9411i) q^{77} +(38.0000 + 65.8179i) q^{79} -16.9706i q^{80} -66.0000 q^{82} +(102.879 - 59.3970i) q^{83} +(27.0000 - 46.7654i) q^{85} +(48.9898 + 28.2843i) q^{86} +(-24.0000 - 41.5692i) q^{88} +12.7279i q^{89} -32.0000 q^{91} +(29.3939 - 16.9706i) q^{92} +(-60.0000 + 103.923i) q^{94} +(-58.7878 - 33.9411i) q^{95} +(-88.0000 - 152.420i) q^{97} -46.6690i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 8 q^{7}+O(q^{10}) \) 4 * q + 4 * q^4 + 8 * q^7	\( 4 q + 4 q^{4} + 8 q^{7} + 24 q^{10} - 16 q^{13} - 8 q^{16} - 64 q^{19} + 48 q^{22} - 14 q^{25} + 32 q^{28} - 88 q^{31} - 36 q^{34} - 136 q^{37} + 24 q^{40} + 80 q^{43} + 96 q^{46} + 66 q^{49} + 32 q^{52} + 288 q^{55} + 12 q^{58} - 100 q^{61} - 32 q^{64} - 16 q^{67} + 48 q^{70} - 64 q^{73} - 64 q^{76} + 152 q^{79} - 264 q^{82} + 108 q^{85} - 96 q^{88} - 128 q^{91} - 240 q^{94} - 352 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 + 8 * q^7 + 24 * q^10 - 16 * q^13 - 8 * q^16 - 64 * q^19 + 48 * q^22 - 14 * q^25 + 32 * q^28 - 88 * q^31 - 36 * q^34 - 136 * q^37 + 24 * q^40 + 80 * q^43 + 96 * q^46 + 66 * q^49 + 32 * q^52 + 288 * q^55 + 12 * q^58 - 100 * q^61 - 32 * q^64 - 16 * q^67 + 48 * q^70 - 64 * q^73 - 64 * q^76 + 152 * q^79 - 264 * q^82 + 108 * q^85 - 96 * q^88 - 128 * q^91 - 240 * q^94 - 352 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more