LMFDB - Embedded newform 567.2.e.d.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.4
Root			$-1.54162 - 1.88572i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.d.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10400 - 1.91218i) q^{2} +(-1.43762 - 2.49004i) q^{4} +(-1.90389 + 3.29764i) q^{5} +(1.82854 + 1.91218i) q^{7} -1.93254 q^{8} +O(q^{10})$	\(q+(1.10400 - 1.91218i) q^{2} +(-1.43762 - 2.49004i) q^{4} +(-1.90389 + 3.29764i) q^{5} +(1.82854 + 1.91218i) q^{7} -1.93254 q^{8} +(4.20379 + 7.28117i) q^{10} +(2.16217 + 3.74498i) q^{11} -2.87525 q^{13} +(5.67514 - 1.38546i) q^{14} +(0.741726 - 1.28471i) q^{16} +(2.01297 + 3.48657i) q^{17} +(0.804103 - 1.39275i) q^{19} +10.9483 q^{20} +9.54811 q^{22} +(-1.33363 + 2.30991i) q^{23} +(-4.74962 - 8.22658i) q^{25} +(-3.17427 + 5.49799i) q^{26} +(2.13264 - 7.30213i) q^{28} -0.750492 q^{29} +(-0.0702679 - 0.121708i) q^{31} +(-3.57027 - 6.18389i) q^{32} +8.88928 q^{34} +(-9.78703 + 2.38928i) q^{35} +(4.14141 - 7.17313i) q^{37} +(-1.77546 - 3.07518i) q^{38} +(3.67935 - 6.37282i) q^{40} +10.3745 q^{41} +0.267040 q^{43} +(6.21676 - 10.7677i) q^{44} +(2.94464 + 5.10026i) q^{46} +(-3.96627 + 6.86978i) q^{47} +(-0.312869 + 6.99300i) q^{49} -20.9743 q^{50} +(4.13352 + 7.15947i) q^{52} +(-5.61189 - 9.72008i) q^{53} -16.4661 q^{55} +(-3.53373 - 3.69537i) q^{56} +(-0.828542 + 1.43508i) q^{58} +(-0.346599 - 0.600327i) q^{59} +(-1.05372 + 1.82510i) q^{61} -0.310302 q^{62} -12.7994 q^{64} +(5.47416 - 9.48152i) q^{65} +(5.38314 + 9.32387i) q^{67} +(5.78780 - 10.0248i) q^{68} +(-6.23612 + 21.3523i) q^{70} -3.62399 q^{71} +(1.78756 + 3.09614i) q^{73} +(-9.14422 - 15.8383i) q^{74} -4.62399 q^{76} +(-3.20747 + 10.9823i) q^{77} +(7.71168 - 13.3570i) q^{79} +(2.82433 + 4.89189i) q^{80} +(11.4534 - 19.8379i) q^{82} -6.44067 q^{83} -15.3299 q^{85} +(0.294812 - 0.510629i) q^{86} +(-4.17847 - 7.23733i) q^{88} +(0.128437 - 0.222459i) q^{89} +(-5.25751 - 5.49799i) q^{91} +7.66900 q^{92} +(8.75751 + 15.1684i) q^{94} +(3.06185 + 5.30328i) q^{95} +1.05856 q^{97} +(13.0265 + 8.31853i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q + q^2 - 5 * q^4 + 2 * q^5 + q^7 + 6 * q^8	$ 8 q + q^{2} - 5 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} - 10 q^{13} + 23 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} + 16 q^{20} - 14 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} + 20 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} + 10 q^{41} - 14 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 17 q^{49} - 76 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} - 39 q^{56} + 7 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} + 51 q^{68} + 17 q^{70} + 18 q^{71} + 6 q^{73} + 10 q^{76} + 37 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} - 18 q^{83} - 18 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} + 72 q^{92} + 15 q^{94} - 16 q^{95} - 18 q^{97} - 11 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 - 10 * q^13 + 23 * q^14 + q^16 + 6 * q^17 + 8 * q^19 + 16 * q^20 - 14 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 + 20 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 + 10 * q^41 - 14 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 17 * q^49 - 76 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 - 39 * q^56 + 7 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 + 51 * q^68 + 17 * q^70 + 18 * q^71 + 6 * q^73 + 10 * q^76 + 37 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 - 18 * q^83 - 18 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 + 72 * q^92 + 15 * q^94 - 16 * q^95 - 18 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.10400	−	1.91218i	0.780644	−	1.35212i	−0.150922	−	0.988546i	$-0.548224\pi$
$2$	1.10400	−	1.91218i	0.780644	−	1.35212i	0.931567	−	0.363570i	$-0.118442\pi$
$3$		0			0
$3$		0			0
$4$	−1.43762	−	2.49004i	−0.718812	−	1.24502i
$5$	−1.90389	+	3.29764i	−0.851447	+	1.47475i	0.0284558	+	0.999595i	$0.490941\pi$
$5$	−1.90389	+	3.29764i	−0.851447	+	1.47475i	−0.879903	+	0.475154i	$0.842392\pi$
$6$		0			0
$7$	1.82854	+	1.91218i	0.691124	+	0.722736i
$7$	1.82854	+	1.91218i	0.691124	+	0.722736i
$8$	−1.93254			−0.683256
$9$		0			0
$10$	4.20379	+	7.28117i	1.32935	+	2.30251i
$11$	2.16217	+	3.74498i	0.651918	+	1.12915i	0.982657	+	0.185433i	$0.0593687\pi$
$11$	2.16217	+	3.74498i	0.651918	+	1.12915i	−0.330739	+	0.943722i	$0.607298\pi$
$12$		0			0
$13$	−2.87525			−0.797450			−0.398725	−	0.917071i	$-0.630547\pi$
$13$	−2.87525			−0.797450			−0.398725	+	0.917071i	$0.630547\pi$
$14$	5.67514	−	1.38546i	1.51675	−	0.370279i
$15$		0			0
$16$	0.741726	−	1.28471i	0.185432	−	0.321177i
$17$	2.01297	+	3.48657i	0.488218	+	0.845618i	0.999908	−	0.0135517i	$-0.00431378\pi$
$17$	2.01297	+	3.48657i	0.488218	+	0.845618i	−0.511690	+	0.859170i	$0.670980\pi$
$18$		0			0
$19$	0.804103	−	1.39275i	0.184474	−	0.319518i	−0.758925	−	0.651178i	$-0.774275\pi$
$19$	0.804103	−	1.39275i	0.184474	−	0.319518i	0.943399	+	0.331660i	$0.107609\pi$
$20$	10.9483			2.44812
$21$		0			0
$22$	9.54811			2.03566
$23$	−1.33363	+	2.30991i	−0.278080	+	0.481649i	−0.970908	−	0.239455i	$-0.923031\pi$
$23$	−1.33363	+	2.30991i	−0.278080	+	0.481649i	0.692828	+	0.721103i	$0.256365\pi$
$24$		0			0
$25$	−4.74962	−	8.22658i	−0.949923	−	1.64532i
$26$	−3.17427	+	5.49799i	−0.622525	+	1.07824i
$27$		0			0
$28$	2.13264	−	7.30213i	0.403032	−	1.37997i
$29$	−0.750492			−0.139363			−0.0696815	−	0.997569i	$-0.522198\pi$
$29$	−0.750492			−0.139363			−0.0696815	+	0.997569i	$0.522198\pi$
$30$		0			0
$31$	−0.0702679	−	0.121708i	−0.0126205	−	0.0218593i	0.859646	−	0.510890i	$-0.170684\pi$
$31$	−0.0702679	−	0.121708i	−0.0126205	−	0.0218593i	−0.872267	+	0.489031i	$0.837351\pi$
$32$	−3.57027	−	6.18389i	−0.631140	−	1.09317i
$33$		0			0
$34$	8.88928			1.52450
$35$	−9.78703	+	2.38928i	−1.65431	+	0.403863i
$36$		0			0
$37$	4.14141	−	7.17313i	0.680844	−	1.17926i	−0.293880	−	0.955842i	$-0.594947\pi$
$37$	4.14141	−	7.17313i	0.680844	−	1.17926i	0.974724	−	0.223414i	$-0.0717201\pi$
$38$	−1.77546	−	3.07518i	−0.288017	−	0.498860i
$39$		0			0
$40$	3.67935	−	6.37282i	0.581756	−	1.00763i
$41$	10.3745			1.62022			0.810111	−	0.586277i	$-0.199407\pi$
$41$	10.3745			1.62022			0.810111	+	0.586277i	$0.199407\pi$
$42$		0			0
$43$	0.267040			0.0407232			0.0203616	−	0.999793i	$-0.493518\pi$
$43$	0.267040			0.0407232			0.0203616	+	0.999793i	$0.493518\pi$
$44$	6.21676	−	10.7677i	0.937212	−	1.62330i
$45$		0			0
$46$	2.94464	+	5.10026i	0.434163	+	0.751993i
$47$	−3.96627	+	6.86978i	−0.578540	+	1.00206i	0.417107	+	0.908857i	$0.363044\pi$
$47$	−3.96627	+	6.86978i	−0.578540	+	1.00206i	−0.995647	+	0.0932032i	$0.970289\pi$
$48$		0			0
$49$	−0.312869	+	6.99300i	−0.0446956	+	0.999001i
$50$	−20.9743			−2.96621
$51$		0			0
$52$	4.13352	+	7.15947i	0.573216	+	0.992839i
$53$	−5.61189	−	9.72008i	−0.770852	−	1.33516i	−0.937096	−	0.349071i	$-0.886497\pi$
$53$	−5.61189	−	9.72008i	−0.770852	−	1.33516i	0.166244	−	0.986085i	$-0.446836\pi$
$54$		0			0
$55$	−16.4661			−2.22029
$56$	−3.53373	−	3.69537i	−0.472215	−	0.493814i
$57$		0			0
$58$	−0.828542	+	1.43508i	−0.108793	+	0.188435i
$59$	−0.346599	−	0.600327i	−0.0451234	−	0.0781560i	0.842582	−	0.538569i	$-0.181035\pi$
$59$	−0.346599	−	0.600327i	−0.0451234	−	0.0781560i	−0.887705	+	0.460413i	$0.847701\pi$
$60$		0			0
$61$	−1.05372	+	1.82510i	−0.134915	+	0.233680i	−0.925565	−	0.378589i	$-0.876409\pi$
$61$	−1.05372	+	1.82510i	−0.134915	+	0.233680i	0.790650	+	0.612268i	$0.209743\pi$
$62$	−0.310302			−0.0394085
$63$		0			0
$64$	−12.7994			−1.59992
$65$	5.47416	−	9.48152i	0.678986	−	1.17604i
$66$		0			0
$67$	5.38314	+	9.32387i	0.657655	+	1.13909i	0.981221	+	0.192886i	$0.0617848\pi$
$67$	5.38314	+	9.32387i	0.657655	+	1.13909i	−0.323566	+	0.946206i	$0.604882\pi$
$68$	5.78780	−	10.0248i	0.701873	−	1.21568i
$69$		0			0
$70$	−6.23612	+	21.3523i	−0.745359	+	2.55209i
$71$	−3.62399			−0.430088			−0.215044	−	0.976604i	$-0.568990\pi$
$71$	−3.62399			−0.430088			−0.215044	+	0.976604i	$0.568990\pi$
$72$		0			0
$73$	1.78756	+	3.09614i	0.209217	+	0.362375i	0.951468	−	0.307747i	$-0.0995750\pi$
$73$	1.78756	+	3.09614i	0.209217	+	0.362375i	−0.742251	+	0.670122i	$0.766242\pi$
$74$	−9.14422	−	15.8383i	−1.06299	−	1.84116i
$75$		0			0
$76$	−4.62399			−0.530408
$77$	−3.20747	+	10.9823i	−0.365525	+	1.25155i
$78$		0			0
$79$	7.71168	−	13.3570i	0.867632	−	1.50278i	0.00322152	−	0.999995i	$-0.498975\pi$
$79$	7.71168	−	13.3570i	0.867632	−	1.50278i	0.864410	−	0.502787i	$-0.167692\pi$
$80$	2.82433	+	4.89189i	0.315770	+	0.546930i
$81$		0			0
$82$	11.4534	−	19.8379i	1.26482	−	2.19073i
$83$	−6.44067			−0.706956			−0.353478	−	0.935443i	$-0.615001\pi$
$83$	−6.44067			−0.706956			−0.353478	+	0.935443i	$0.615001\pi$
$84$		0			0
$85$	−15.3299			−1.66277
$86$	0.294812	−	0.510629i	0.0317904	−	0.0550625i
$87$		0			0
$88$	−4.17847	−	7.23733i	−0.445427	−	0.771502i
$89$	0.128437	−	0.222459i	0.0136143	−	0.0235806i	−0.859138	−	0.511744i	$-0.829000\pi$
$89$	0.128437	−	0.222459i	0.0136143	−	0.0235806i	0.872752	+	0.488163i	$0.162333\pi$
$90$		0			0
$91$	−5.25751	−	5.49799i	−0.551137	−	0.576346i
$92$	7.66900			0.799549
$93$		0			0
$94$	8.75751	+	15.1684i	0.903268	+	1.56451i
$95$	3.06185	+	5.30328i	0.314139	+	0.544105i
$96$		0			0
$97$	1.05856			0.107481			0.0537403	−	0.998555i	$-0.482886\pi$
$97$	1.05856			0.107481			0.0537403	+	0.998555i	$0.482886\pi$
$98$	13.0265	+	8.31853i	1.31587	+	0.840298i
$99$		0			0
$100$	−13.6563	+	23.6534i	−1.36563	+	2.36534i
$101$	−0.682923	−	1.18286i	−0.0679534	−	0.117699i	0.830047	−	0.557694i	$-0.188314\pi$
$101$	−0.682923	−	1.18286i	−0.0679534	−	0.117699i	−0.898000	+	0.439995i	$0.854980\pi$
$102$		0			0
$103$	7.48563	−	12.9655i	0.737581	−	1.27753i	−0.216001	−	0.976393i	$-0.569302\pi$
$103$	7.48563	−	12.9655i	0.737581	−	1.27753i	0.953582	−	0.301134i	$-0.0973651\pi$
$104$	5.55653			0.544862
$105$		0			0
$106$	−24.7821			−2.40705
$107$	4.04075	−	6.99878i	0.390634	−	0.676597i	−0.601900	−	0.798572i	$-0.705589\pi$
$107$	4.04075	−	6.99878i	0.390634	−	0.676597i	0.992533	+	0.121974i	$0.0389226\pi$
$108$		0			0
$109$	4.55460	+	7.88879i	0.436251	+	0.755609i	0.997397	−	0.0721080i	$-0.0229726\pi$
$109$	4.55460	+	7.88879i	0.436251	+	0.755609i	−0.561146	+	0.827717i	$0.689639\pi$
$110$	−18.1786	+	31.4862i	−1.73326	+	3.00209i
$111$		0			0
$112$	3.81287	−	0.930827i	0.360282	−	0.0879549i
$113$	−2.76606			−0.260209			−0.130104	−	0.991500i	$-0.541531\pi$
$113$	−2.76606			−0.260209			−0.130104	+	0.991500i	$0.541531\pi$
$114$		0			0
$115$	−5.07816	−	8.79563i	−0.473541	−	0.820197i
$116$	1.07892	+	1.86875i	0.100176	+	0.173509i
$117$		0			0
$118$	−1.53058			−0.140901
$119$	−2.98615	+	10.2245i	−0.273740	+	0.937280i
$120$		0			0
$121$	−3.84993	+	6.66828i	−0.349994	+	0.606207i
$122$	2.32661	+	4.02981i	0.210641	+	0.364841i
$123$		0			0
$124$	−0.202038	+	0.349939i	−0.0181435	+	0.0314255i
$125$	17.1321			1.53234
$126$		0			0
$127$	13.6573			1.21189			0.605945	−	0.795507i	$-0.292795\pi$
$127$	13.6573			1.21189			0.605945	+	0.795507i	$0.292795\pi$
$128$	−6.98994	+	12.1069i	−0.617829	+	1.07011i
$129$		0			0
$130$	−12.0869	−	20.9352i	−1.06009	−	1.83614i
$131$	8.80691	−	15.2540i	0.769463	−	1.33275i	−0.168391	−	0.985720i	$-0.553857\pi$
$131$	8.80691	−	15.2540i	0.769463	−	1.33275i	0.937854	−	0.347029i	$-0.112810\pi$
$132$		0			0
$133$	4.13352	−	1.00911i	0.358422	−	0.0875006i
$134$	23.7719			2.05358
$135$		0			0
$136$	−3.89015	−	6.73794i	−0.333578	−	0.577774i
$137$	4.33363	+	7.50606i	0.370247	+	0.641286i	0.989603	−	0.143824i	$-0.0459399\pi$
$137$	4.33363	+	7.50606i	0.370247	+	0.641286i	−0.619357	+	0.785110i	$0.712607\pi$
$138$		0			0
$139$	−3.76606			−0.319433			−0.159716	−	0.987163i	$-0.551058\pi$
$139$	−3.76606			−0.319433			−0.159716	+	0.987163i	$0.551058\pi$
$140$	20.0195	+	20.9352i	1.69195	+	1.76934i
$141$		0			0
$142$	−4.00088	+	6.92972i	−0.335746	+	0.581529i
$143$	−6.21676	−	10.7677i	−0.519872	−	0.900444i
$144$		0			0
$145$	1.42886	−	2.47485i	0.118660	−	0.205525i
$146$	7.89383			0.653298
$147$		0			0
$148$	−23.8152			−1.95759
$149$	2.30561	−	3.99344i	0.188883	−	0.327155i	−0.755995	−	0.654577i	$-0.772847\pi$
$149$	2.30561	−	3.99344i	0.188883	−	0.327155i	0.944878	+	0.327422i	$0.106180\pi$
$150$		0			0
$151$	−3.89881	−	6.75294i	−0.317281	−	0.549546i	0.662639	−	0.748939i	$-0.269436\pi$
$151$	−3.89881	−	6.75294i	−0.317281	−	0.549546i	−0.979920	+	0.199393i	$0.936103\pi$
$152$	−1.55396	+	2.69154i	−0.126043	+	0.218313i
$153$		0			0
$154$	17.4591	+	18.2577i	1.40690	+	1.47125i
$155$	0.535130			0.0429827
$156$		0			0
$157$	−11.6328	−	20.1485i	−0.928395	−	1.60803i	−0.786008	−	0.618216i	$-0.787856\pi$
$157$	−11.6328	−	20.1485i	−0.928395	−	1.60803i	−0.142387	−	0.989811i	$-0.545478\pi$
$158$	−17.0274	−	29.4922i	−1.35462	−	2.34628i
$159$		0			0
$160$	27.1896			2.14953
$161$	−6.85555	+	1.67363i	−0.540293	+	0.131900i
$162$		0			0
$163$	−3.05547	+	5.29223i	−0.239323	+	0.414519i	−0.960520	−	0.278210i	$-0.910259\pi$
$163$	−3.05547	+	5.29223i	−0.239323	+	0.414519i	0.721197	+	0.692730i	$0.243592\pi$
$164$	−14.9146	−	25.8328i	−1.16463	−	2.01721i
$165$		0			0
$166$	−7.11049	+	12.3157i	−0.551881	+	0.955886i
$167$	−11.6415			−0.900848			−0.450424	−	0.892815i	$-0.648727\pi$
$167$	−11.6415			−0.900848			−0.450424	+	0.892815i	$0.648727\pi$
$168$		0			0
$169$	−4.73296			−0.364074
$170$	−16.9242	+	29.3136i	−1.29803	+	2.24825i
$171$		0			0
$172$	−0.383903	−	0.664940i	−0.0292723	−	0.0507012i
$173$	9.62855	−	16.6771i	0.732045	−	1.26794i	−0.223963	−	0.974598i	$-0.571899\pi$
$173$	9.62855	−	16.6771i	0.732045	−	1.26794i	0.956008	−	0.293341i	$-0.0947672\pi$
$174$		0			0
$175$	7.04583	−	24.1248i	0.532615	−	1.82366i
$176$	6.41494			0.483544
$177$		0			0
$178$	−0.283588	−	0.491189i	−0.0212558	−	0.0368162i
$179$	1.67093	+	2.89414i	0.124891	+	0.216318i	0.921690	−	0.387926i	$-0.126808\pi$
$179$	1.67093	+	2.89414i	0.124891	+	0.216318i	−0.796799	+	0.604244i	$0.793475\pi$
$180$		0			0
$181$	−19.7358			−1.46695			−0.733474	−	0.679717i	$-0.762103\pi$
$181$	−19.7358			−1.46695			−0.733474	+	0.679717i	$0.762103\pi$
$182$	−16.3174	+	3.98354i	−1.20953	+	0.295279i
$183$		0			0
$184$	2.57728	−	4.46399i	0.190000	−	0.329089i
$185$	15.7696	+	27.3138i	1.15940	+	2.00815i
$186$		0			0
$187$	−8.70477	+	15.0771i	−0.636556	+	1.10255i
$188$	22.8080			1.66344
$189$		0			0
$190$	13.5211			0.980925
$191$	2.08745	−	3.61557i	0.151043	−	0.261613i	−0.780568	−	0.625070i	$-0.785070\pi$
$191$	2.08745	−	3.61557i	0.151043	−	0.261613i	0.931611	+	0.363457i	$0.118404\pi$
$192$		0			0
$193$	6.93686	+	12.0150i	0.499326	+	0.864858i	1.00000		0.000778217i	$-0.000247714\pi$
$193$	6.93686	+	12.0150i	0.499326	+	0.864858i	−0.500674	+	0.865636i	$0.666914\pi$
$194$	1.16865	−	2.02416i	0.0839042	−	0.145326i
$195$		0			0
$196$	17.8626	−	9.27425i	1.27590	−	0.662446i
$197$	−7.48520			−0.533299			−0.266649	−	0.963794i	$-0.585917\pi$
$197$	−7.48520			−0.533299			−0.266649	+	0.963794i	$0.585917\pi$
$198$		0			0
$199$	6.32767	+	10.9598i	0.448556	+	0.776922i	0.998292	−	0.0584160i	$-0.0186050\pi$
$199$	6.32767	+	10.9598i	0.448556	+	0.776922i	−0.549736	+	0.835338i	$0.685272\pi$
$200$	9.17882	+	15.8982i	0.649041	+	1.12417i
$201$		0			0
$202$	−3.01578			−0.212190
$203$	−1.37231	−	1.43508i	−0.0963170	−	0.100723i
$204$		0			0
$205$	−19.7519	+	34.2113i	−1.37953	+	2.38942i
$206$	−16.5282	−	28.6277i	−1.15158	−	1.99459i
$207$		0			0
$208$	−2.13264	+	3.69385i	−0.147872	+	0.256122i
$209$	6.95442			0.481047
$210$		0			0
$211$	−5.15197			−0.354676			−0.177338	−	0.984150i	$-0.556749\pi$
$211$	−5.15197			−0.354676			−0.177338	+	0.984150i	$0.556749\pi$
$212$	−16.1356	+	27.9476i	−1.10819	+	1.91945i
$213$		0			0
$214$	−8.92195	−	15.4533i	−0.609892	−	1.05636i
$215$	−0.508416	+	0.880602i	−0.0346737	+	0.0600566i
$216$		0			0
$217$	0.104239	−	0.356912i	0.00707621	−	0.0242288i
$218$	20.1131			1.36223
$219$		0			0
$220$	23.6721	+	41.0013i	1.59597	+	2.76431i
$221$	−5.78780	−	10.0248i	−0.389329	−	0.674338i
$222$		0			0
$223$	−15.2166			−1.01898			−0.509490	−	0.860476i	$-0.670166\pi$
$223$	−15.2166			−1.01898			−0.509490	+	0.860476i	$0.670166\pi$
$224$	5.29632	−	18.1345i	0.353875	−	1.21166i
$225$		0			0
$226$	−3.05372	+	5.28920i	−0.203130	+	0.351832i
$227$	2.14474	+	3.71481i	0.142352	+	0.246560i	0.928382	−	0.371628i	$-0.121200\pi$
$227$	2.14474	+	3.71481i	0.142352	+	0.246560i	−0.786030	+	0.618188i	$0.787867\pi$
$228$		0			0
$229$	−0.485626	+	0.841128i	−0.0320910	+	0.0555833i	−0.881625	−	0.471951i	$-0.843550\pi$
$229$	−0.485626	+	0.841128i	−0.0320910	+	0.0555833i	0.849534	+	0.527534i	$0.176883\pi$
$230$	−22.4251			−1.47867
$231$		0			0
$232$	1.45036			0.0952205
$233$	1.88671	−	3.26788i	0.123603	−	0.214086i	−0.797583	−	0.603209i	$-0.793889\pi$
$233$	1.88671	−	3.26788i	0.123603	−	0.214086i	0.921186	+	0.389123i	$0.127222\pi$
$234$		0			0
$235$	−15.1027	−	26.1587i	−0.985192	−	1.70640i
$236$	−0.996558	+	1.72609i	−0.0648704	+	0.112359i
$237$		0			0
$238$	16.2544	+	16.9979i	1.05362	+	1.10181i
$239$	6.69040			0.432766			0.216383	−	0.976309i	$-0.430574\pi$
$239$	6.69040			0.432766			0.216383	+	0.976309i	$0.430574\pi$
$240$		0			0
$241$	7.48563	+	12.9655i	0.482192	+	0.835180i	0.999791	−	0.0204428i	$-0.00650760\pi$
$241$	7.48563	+	12.9655i	0.482192	+	0.835180i	−0.517599	+	0.855623i	$0.673174\pi$
$242$	8.50063	+	14.7235i	0.546441	+	0.946464i
$243$		0			0
$244$	6.05941			0.387914
$245$	−22.4647	−	14.3457i	−1.43522	−	0.916511i
$246$		0			0
$247$	−2.31199	+	4.00449i	−0.147109	+	0.254800i
$248$	0.135796	+	0.235205i	0.00862302	+	0.0149355i
$249$		0			0
$250$	18.9138	−	32.7597i	1.19622	−	2.07191i
$251$	−17.0787			−1.07800			−0.538999	−	0.842307i	$-0.681197\pi$
$251$	−17.0787			−1.07800			−0.538999	+	0.842307i	$0.681197\pi$
$252$		0			0
$253$	−11.5341			−0.725141
$254$	15.0776	−	26.1152i	0.946055	−	1.63862i
$255$		0			0
$256$	2.63440	+	4.56291i	0.164650	+	0.285182i
$257$	−4.28615	+	7.42384i	−0.267363	+	0.463086i	−0.968180	−	0.250255i	$-0.919486\pi$
$257$	−4.28615	+	7.42384i	−0.267363	+	0.463086i	0.700817	+	0.713341i	$0.252819\pi$
$258$		0			0
$259$	21.2891	−	5.19725i	1.32284	−	0.322941i
$260$	−31.4791			−1.95225
$261$		0			0
$262$	−19.4456	−	33.6808i	−1.20135	−	2.08081i
$263$	2.84842	+	4.93361i	0.175641	+	0.304220i	0.940383	−	0.340117i	$-0.110467\pi$
$263$	2.84842	+	4.93361i	0.175641	+	0.304220i	−0.764742	+	0.644337i	$0.777133\pi$
$264$		0			0
$265$	42.7377			2.62536
$266$	2.63380	−	9.01809i	0.161489	−	0.552934i
$267$		0			0
$268$	15.4778	−	26.8084i	0.945460	−	1.63758i
$269$	−7.80077	−	13.5113i	−0.475621	−	0.823800i	0.523989	−	0.851725i	$-0.324443\pi$
$269$	−7.80077	−	13.5113i	−0.475621	−	0.823800i	−0.999610	+	0.0279249i	$0.991110\pi$
$270$		0			0
$271$	15.3688	−	26.6195i	0.933586	−	1.61702i	0.156449	−	0.987686i	$-0.449995\pi$
$271$	15.3688	−	26.6195i	0.933586	−	1.61702i	0.777136	−	0.629332i	$-0.216671\pi$
$272$	5.97230			0.362124
$273$		0			0
$274$	19.1373			1.15612
$275$	20.5389	−	35.5745i	1.23854	−	2.14522i
$276$		0			0
$277$	13.2963	+	23.0299i	0.798899	+	1.38373i	0.920334	+	0.391133i	$0.127917\pi$
$277$	13.2963	+	23.0299i	0.798899	+	1.38373i	−0.121435	+	0.992599i	$0.538750\pi$
$278$	−4.15772	+	7.20138i	−0.249363	+	0.431910i
$279$		0			0
$280$	18.9138	−	4.61739i	1.13032	−	0.275942i
$281$	17.3613			1.03569			0.517844	−	0.855475i	$-0.326735\pi$
$281$	17.3613			1.03569			0.517844	+	0.855475i	$0.326735\pi$
$282$		0			0
$283$	−9.17771	−	15.8963i	−0.545558	−	0.944934i	−0.998572	−	0.0534307i	$-0.982984\pi$
$283$	−9.17771	−	15.8963i	−0.545558	−	0.944934i	0.453013	−	0.891504i	$-0.350349\pi$
$284$	5.20993	+	9.02386i	0.309152	+	0.535468i
$285$		0			0
$286$	−27.4532			−1.62334
$287$	18.9702	+	19.8379i	1.11977	+	1.17099i
$288$		0			0
$289$	0.395870	−	0.685667i	0.0232865	−	0.0403334i
$290$	−3.15491	−	5.46446i	−0.185263	−	0.320884i
$291$		0			0
$292$	5.13966	−	8.90215i	0.300776	−	0.520959i
$293$	−10.6981			−0.624990			−0.312495	−	0.949919i	$-0.601165\pi$
$293$	−10.6981			−0.624990			−0.312495	+	0.949919i	$0.601165\pi$
$294$		0			0
$295$	2.63955			0.153681
$296$	−8.00344	+	13.8624i	−0.465191	+	0.805734i
$297$		0			0
$298$	−5.09078	−	8.81749i	−0.294901	−	0.510784i
$299$	3.83450	−	6.64155i	0.221755	−	0.384091i
$300$		0			0
$301$	0.488294	+	0.510629i	0.0281448	+	0.0294322i
$302$	−17.2171			−0.990733
$303$		0			0
$304$	−1.19285	−	2.06607i	−0.0684145	−	0.118497i
$305$	−4.01234	−	6.94958i	−0.229746	−	0.397932i
$306$		0			0
$307$	31.3948			1.79180			0.895899	−	0.444258i	$-0.146533\pi$
$307$	31.3948			1.79180			0.895899	+	0.444258i	$0.146533\pi$
$308$	31.9575	−	7.80171i	1.82095	−	0.444543i
$309$		0			0
$310$	0.590783	−	1.02327i	0.0335542	−	0.0581176i
$311$	−6.74453	−	11.6819i	−0.382447	−	0.662418i	0.608964	−	0.793198i	$-0.291585\pi$
$311$	−6.74453	−	11.6819i	−0.382447	−	0.662418i	−0.991411	+	0.130779i	$0.958252\pi$
$312$		0			0
$313$	9.67069	−	16.7501i	0.546620	−	0.946773i	−0.451883	−	0.892077i	$-0.649248\pi$
$313$	9.67069	−	16.7501i	0.546620	−	0.946773i	0.998503	−	0.0546962i	$-0.0174190\pi$
$314$	−51.3701			−2.89899
$315$		0			0
$316$	−44.3459			−2.49465
$317$	−7.67882	+	13.3001i	−0.431286	+	0.747009i	−0.996984	−	0.0776033i	$-0.975273\pi$
$317$	−7.67882	+	13.3001i	−0.431286	+	0.747009i	0.565699	+	0.824612i	$0.308607\pi$
$318$		0			0
$319$	−1.62269	−	2.81058i	−0.0908532	−	0.157362i
$320$	24.3686	−	42.2077i	1.36225	−	2.35948i
$321$		0			0
$322$	−4.36823	+	14.9567i	−0.243432	+	0.833506i
$323$	6.47455			0.360254
$324$		0			0
$325$	13.6563	+	23.6534i	0.757516	+	1.31206i
$326$	6.74647	+	11.6852i	0.373652	+	0.647185i
$327$		0			0
$328$	−20.0491			−1.10703
$329$	−20.3888	+	4.97746i	−1.12407	+	0.274416i
$330$		0			0
$331$	0.619146	−	1.07239i	0.0340313	−	0.0589440i	−0.848508	−	0.529182i	$-0.822499\pi$
$331$	0.619146	−	1.07239i	0.0340313	−	0.0589440i	0.882539	+	0.470238i	$0.155832\pi$
$332$	9.25926	+	16.0375i	0.508168	+	0.880172i
$333$		0			0
$334$	−12.8522	+	22.2607i	−0.703242	+	1.21805i
$335$	−40.9957			−2.23983
$336$		0			0
$337$	11.9086			0.648701			0.324350	−	0.945937i	$-0.394854\pi$
$337$	11.9086			0.648701			0.324350	+	0.945937i	$0.394854\pi$
$338$	−5.22518	+	9.05027i	−0.284212	+	0.492270i
$339$		0			0
$340$	22.0387	+	38.1721i	1.19522	+	2.07017i
$341$	0.303862	−	0.526304i	0.0164550	−	0.0285010i
$342$		0			0
$343$	−13.9440	+	12.1887i	−0.752904	+	0.658130i
$344$	−0.516066			−0.0278244
$345$		0			0
$346$	−21.2598	−	36.8230i	−1.14293	−	1.97962i
$347$	−2.17339	−	3.76442i	−0.116674	−	0.202085i	0.801774	−	0.597628i	$-0.203890\pi$
$347$	−2.17339	−	3.76442i	−0.116674	−	0.202085i	−0.918448	+	0.395543i	$0.870557\pi$
$348$		0			0
$349$	7.17560			0.384101			0.192051	−	0.981385i	$-0.438486\pi$
$349$	7.17560			0.384101			0.192051	+	0.981385i	$0.438486\pi$
$350$	−38.3523	−	40.1066i	−2.05002	−	2.14379i
$351$		0			0
$352$	15.4390	−	26.7412i	0.822903	−	1.42531i
$353$	12.5484	+	21.7344i	0.667881	+	1.15680i	0.978495	+	0.206268i	$0.0661320\pi$
$353$	12.5484	+	21.7344i	0.667881	+	1.15680i	−0.310614	+	0.950536i	$0.600535\pi$
$354$		0			0
$355$	6.89969	−	11.9506i	0.366197	−	0.634272i
$356$	−0.738575			−0.0391444
$357$		0			0
$358$	7.37883			0.389983
$359$	15.9959	−	27.7057i	0.844231	−	1.46225i	−0.0420557	−	0.999115i	$-0.513391\pi$
$359$	15.9959	−	27.7057i	0.844231	−	1.46225i	0.886287	−	0.463136i	$-0.153276\pi$
$360$		0			0
$361$	8.20684	+	14.2147i	0.431939	+	0.748140i
$362$	−21.7883	+	37.7384i	−1.14517	+	1.98348i
$363$		0			0
$364$	−6.13188	+	20.9954i	−0.321398	+	1.10046i
$365$	−13.6133			−0.712550
$366$		0			0
$367$	5.56238	+	9.63432i	0.290354	+	0.502907i	0.973893	−	0.227006i	$-0.0728937\pi$
$367$	5.56238	+	9.63432i	0.290354	+	0.502907i	−0.683540	+	0.729913i	$0.739560\pi$
$368$	1.97837	+	3.42664i	0.103130	+	0.178626i
$369$		0			0
$370$	69.6385			3.62033
$371$	8.32497	−	28.5045i	0.432211	−	1.47988i
$372$		0			0
$373$	−8.07728	+	13.9903i	−0.418226	+	0.724388i	−0.995761	−	0.0919773i	$-0.970681\pi$
$373$	−8.07728	+	13.9903i	−0.418226	+	0.724388i	0.577535	+	0.816366i	$0.304015\pi$
$374$	19.2201	+	33.2902i	0.993848	+	1.72139i
$375$		0			0
$376$	7.66497	−	13.2761i	0.395291	−	0.684664i
$377$	2.15785			0.111135
$378$		0			0
$379$	3.18485			0.163595			0.0817973	−	0.996649i	$-0.473934\pi$
$379$	3.18485			0.163595			0.0817973	+	0.996649i	$0.473934\pi$
$380$	8.80358	−	15.2482i	0.451614	−	0.782218i
$381$		0			0
$382$	−4.60908	−	7.98316i	−0.235821	−	0.408454i
$383$	8.23882	−	14.2700i	0.420984	−	0.729165i	−0.575052	−	0.818117i	$-0.695018\pi$
$383$	8.23882	−	14.2700i	0.420984	−	0.729165i	0.996036	+	0.0889514i	$0.0283516\pi$
$384$		0			0
$385$	−30.1090	−	31.4862i	−1.53450	−	1.60469i
$386$	30.6331			1.55918
$387$		0			0
$388$	−1.52181	−	2.63586i	−0.0772584	−	0.133815i
$389$	−15.9885	−	27.6930i	−0.810651	−	1.40409i	−0.912409	−	0.409280i	$-0.865780\pi$
$389$	−15.9885	−	27.6930i	−0.810651	−	1.40409i	0.101758	−	0.994809i	$-0.467553\pi$
$390$		0			0
$391$	−10.7382			−0.543055
$392$	0.604632	−	13.5143i	0.0305385	−	0.682573i
$393$		0			0
$394$	−8.26365	+	14.3131i	−0.416317	+	0.721081i
$395$	29.3644	+	50.8607i	1.47748	+	2.55908i
$396$		0			0
$397$	−13.9059	+	24.0858i	−0.697919	+	1.20883i	0.271268	+	0.962504i	$0.412557\pi$
$397$	−13.9059	+	24.0858i	−0.697919	+	1.20883i	−0.969187	+	0.246327i	$0.920776\pi$
$398$	27.9429			1.40065
$399$		0			0
$400$	−14.0917			−0.704583
$401$	−13.7942	+	23.8922i	−0.688847	+	1.19312i	0.283364	+	0.959012i	$0.408550\pi$
$401$	−13.7942	+	23.8922i	−0.688847	+	1.19312i	−0.972211	+	0.234106i	$0.924784\pi$
$402$		0			0
$403$	0.202038	+	0.349939i	0.0100642	+	0.0174317i
$404$	−1.96357	+	3.40101i	−0.0976913	+	0.169206i
$405$		0			0
$406$	−4.25915	+	1.03978i	−0.211378	+	0.0516032i
$407$	35.8177			1.77542
$408$		0			0
$409$	5.91231	+	10.2404i	0.292345	+	0.506356i	0.974364	−	0.224978i	$-0.0722312\pi$
$409$	5.91231	+	10.2404i	0.292345	+	0.506356i	−0.682019	+	0.731335i	$0.738898\pi$
$410$	43.6121	+	75.5384i	2.15385	+	3.73058i
$411$		0			0
$412$	−43.0460			−2.12073
$413$	0.514163	−	1.76048i	0.0253003	−	0.0866278i
$414$		0			0
$415$	12.2624	−	21.2390i	0.601935	−	1.04258i
$416$	10.2654	+	17.7802i	0.503303	+	0.871746i
$417$		0			0
$418$	7.67767	−	13.2981i	0.375527	−	0.650432i
$419$	8.81668			0.430723			0.215362	−	0.976534i	$-0.430907\pi$
$419$	8.81668			0.430723			0.215362	+	0.976534i	$0.430907\pi$
$420$		0			0
$421$	18.7001			0.911386			0.455693	−	0.890137i	$-0.349391\pi$
$421$	18.7001			0.911386			0.455693	+	0.890137i	$0.349391\pi$
$422$	−5.68776	+	9.85150i	−0.276876	+	0.479563i
$423$		0			0
$424$	10.8452	+	18.7844i	0.526689	+	0.912253i
$425$	19.1217	−	33.1198i	0.927539	−	1.60655i
$426$		0			0
$427$	−5.41669	+	1.32236i	−0.262132	+	0.0639936i
$428$	−23.2363			−1.12317
$429$		0			0
$430$	1.12258	+	1.94437i	0.0541356	+	0.0937657i
$431$	8.30972	+	14.3929i	0.400265	+	0.693279i	0.993758	−	0.111560i	$-0.0355847\pi$
$431$	8.30972	+	14.3929i	0.400265	+	0.693279i	−0.593493	+	0.804839i	$0.702251\pi$
$432$		0			0
$433$	−25.3004			−1.21586			−0.607929	−	0.793992i	$-0.707999\pi$
$433$	−25.3004			−1.21586			−0.607929	+	0.793992i	$0.707999\pi$
$434$	−0.567401	−	0.593354i	−0.0272361	−	0.0284819i
$435$		0			0
$436$	13.0956	−	22.6822i	0.627165	−	1.08628i
$437$	2.14474	+	3.71481i	0.102597	+	0.177703i
$438$		0			0
$439$	14.7262	−	25.5065i	0.702841	−	1.21736i	−0.264624	−	0.964352i	$-0.585248\pi$
$439$	14.7262	−	25.5065i	0.702841	−	1.21736i	0.967465	−	0.253005i	$-0.0814190\pi$
$440$	31.8215			1.51703
$441$		0			0
$442$	−25.5589			−1.21571
$443$	−16.2783	+	28.1948i	−0.773404	+	1.33957i	0.162284	+	0.986744i	$0.448114\pi$
$443$	−16.2783	+	28.1948i	−0.773404	+	1.33957i	−0.935687	+	0.352830i	$0.885219\pi$
$444$		0			0
$445$	0.489060	+	0.847077i	0.0231837	+	0.0401553i
$446$	−16.7991	+	29.0969i	−0.795462	+	1.37778i
$447$		0			0
$448$	−23.4042	−	24.4747i	−1.10574	−	1.15632i
$449$	−0.171881			−0.00811158			−0.00405579	−	0.999992i	$-0.501291\pi$
$449$	−0.171881			−0.00811158			−0.00405579	+	0.999992i	$0.501291\pi$
$450$		0			0
$451$	22.4314	+	38.8523i	1.05625	+	1.82948i
$452$	3.97655	+	6.88758i	0.187041	+	0.323964i
$453$		0			0
$454$	9.47117			0.444504
$455$	28.1401	−	6.86978i	1.31923	−	0.322060i
$456$		0			0
$457$	−12.2510	+	21.2194i	−0.573079	+	0.992602i	0.423169	+	0.906051i	$0.360918\pi$
$457$	−12.2510	+	21.2194i	−0.573079	+	0.992602i	−0.996247	+	0.0865506i	$0.972416\pi$
$458$	1.07226	+	1.85721i	0.0501034	+	0.0867816i
$459$		0			0
$460$	−14.6010	+	25.2896i	−0.680773	+	1.17913i
$461$	−9.43107			−0.439249			−0.219624	−	0.975584i	$-0.570483\pi$
$461$	−9.43107			−0.439249			−0.219624	+	0.975584i	$0.570483\pi$
$462$		0			0
$463$	2.86121			0.132972			0.0664860	−	0.997787i	$-0.478821\pi$
$463$	2.86121			0.132972			0.0664860	+	0.997787i	$0.478821\pi$
$464$	−0.556660	+	0.964163i	−0.0258423	+	0.0447601i
$465$		0			0
$466$	−4.16585	−	7.21546i	−0.192979	−	0.334250i
$467$	3.85144	−	6.67089i	0.178223	−	0.308692i	−0.763049	−	0.646341i	$-0.776298\pi$
$467$	3.85144	−	6.67089i	0.178223	−	0.308692i	0.941272	+	0.337649i	$0.109632\pi$
$468$		0			0
$469$	−7.98563	+	27.3426i	−0.368742	+	1.26256i
$470$	−66.6934			−3.07634
$471$		0			0
$472$	0.669817	+	1.16016i	0.0308308	+	0.0534005i
$473$	0.577385	+	1.00006i	0.0265482	+	0.0459829i
$474$		0			0
$475$	−15.2767			−0.700944
$476$	29.7524	−	7.26338i	1.36370	−	0.332916i
$477$		0			0
$478$	7.38619	−	12.7932i	0.337836	−	0.585150i
$479$	17.2911	+	29.9491i	0.790051	+	1.36841i	0.925935	+	0.377683i	$0.123279\pi$
$479$	17.2911	+	29.9491i	0.790051	+	1.36841i	−0.135884	+	0.990725i	$0.543387\pi$
$480$		0			0
$481$	−11.9076	+	20.6245i	−0.542939	+	0.940397i
$482$	33.0565			1.50568
$483$		0			0
$484$	22.1390			1.00632
$485$	−2.01539	+	3.49076i	−0.0915141	+	0.158507i
$486$		0			0
$487$	−9.21782	−	15.9657i	−0.417699	−	0.723476i	0.578008	−	0.816031i	$-0.303830\pi$
$487$	−9.21782	−	15.9657i	−0.417699	−	0.723476i	−0.995708	+	0.0925545i	$0.970497\pi$
$488$	2.03636	−	3.52707i	0.0921815	−	0.159663i
$489$		0			0
$490$	−52.2325	+	27.1191i	−2.35962	+	1.22511i
$491$	−3.15372			−0.142325			−0.0711627	−	0.997465i	$-0.522671\pi$
$491$	−3.15372			−0.142325			−0.0711627	+	0.997465i	$0.522671\pi$
$492$		0			0
$493$	−1.51072	−	2.61665i	−0.0680395	−	0.117848i
$494$	5.10487	+	8.84190i	0.229679	+	0.397816i
$495$		0			0
$496$	−0.208478			−0.00936094
$497$	−6.62661	−	6.92972i	−0.297244	−	0.310840i
$498$		0			0
$499$	−14.4399	+	25.0107i	−0.646419	+	1.11963i	0.337553	+	0.941307i	$0.390401\pi$
$499$	−14.4399	+	25.0107i	−0.646419	+	1.11963i	−0.983972	+	0.178324i	$0.942933\pi$
$500$	−24.6295	−	42.6596i	−1.10147	−	1.90780i
$501$		0			0
$502$	−18.8548	+	32.6575i	−0.841533	+	1.45758i
$503$	−21.4742			−0.957487			−0.478744	−	0.877955i	$-0.658908\pi$
$503$	−21.4742			−0.957487			−0.478744	+	0.877955i	$0.658908\pi$
$504$		0			0
$505$	5.20085			0.231435
$506$	−12.7336	+	22.0552i	−0.566078	+	0.980475i
$507$		0			0
$508$	−19.6341	−	34.0072i	−0.871120	−	1.50882i
$509$	4.41218	−	7.64211i	0.195566	−	0.338731i	−0.751520	−	0.659711i	$-0.770679\pi$
$509$	4.41218	−	7.64211i	0.195566	−	0.338731i	0.947086	+	0.320980i	$0.104012\pi$
$510$		0			0
$511$	−2.65175	+	9.07954i	−0.117307	+	0.401655i
$512$	−16.3263			−0.721527
$513$		0			0
$514$	9.46381	+	16.3918i	0.417431	+	0.723011i
$515$	28.5037	+	49.3698i	1.25602	+	2.17549i
$516$		0			0
$517$	−34.3030			−1.50864
$518$	13.5650	−	46.4463i	0.596012	−	2.04073i
$519$		0			0
$520$	−10.5790	+	18.3234i	−0.463921	+	0.803535i
$521$	14.8351	+	25.6952i	0.649939	+	1.12573i	0.983137	+	0.182871i	$0.0585391\pi$
$521$	14.8351	+	25.6952i	0.649939	+	1.12573i	−0.333198	+	0.942857i	$0.608128\pi$
$522$		0			0
$523$	3.46995	−	6.01013i	0.151730	−	0.262805i	−0.780133	−	0.625613i	$-0.784849\pi$
$523$	3.46995	−	6.01013i	0.151730	−	0.262805i	0.931864	+	0.362809i	$0.118182\pi$
$524$	−50.6441			−2.21240
$525$		0			0
$526$	12.5786			0.548454
$527$	0.282895	−	0.489988i	0.0123231	−	0.0213442i
$528$		0			0
$529$	7.94289	+	13.7575i	0.345343	+	0.598152i
$530$	47.1824	−	81.7223i	2.04947	−	3.54979i
$531$		0			0
$532$	−8.45516	−	8.84190i	−0.366577	−	0.383345i
$533$	−29.8292			−1.29205
$534$		0			0
$535$	15.3863	+	26.6498i	0.665208	+	1.15217i
$536$	−10.4031	−	18.0187i	−0.449347	−	0.778291i
$537$		0			0
$538$	−34.4481			−1.48516
$539$	−26.8652	+	13.9484i	−1.15716	+	0.600798i
$540$		0			0
$541$	8.34520	−	14.4543i	0.358788	−	0.621439i	−0.628971	−	0.777429i	$-0.716523\pi$
$541$	8.34520	−	14.4543i	0.358788	−	0.621439i	0.987759	+	0.155990i	$0.0498567\pi$
$542$	−33.9342	−	58.7757i	−1.45760	−	2.52463i
$543$		0			0
$544$	14.3737	−	24.8960i	0.616268	−	1.06741i
$545$	−34.6858			−1.48578
$546$		0			0
$547$	3.77924			0.161589			0.0807943	−	0.996731i	$-0.474254\pi$
$547$	3.77924			0.161589			0.0807943	+	0.996731i	$0.474254\pi$
$548$	12.4602	−	21.5818i	0.532275	−	0.921927i
$549$		0			0
$550$	−45.3499	−	78.5483i	−1.93373	−	3.34931i
$551$	−0.603473	+	1.04525i	−0.0257088	+	0.0445290i
$552$		0			0
$553$	39.6422	−	9.67775i	1.68576	−	0.411540i
$554$	58.7164			2.49462
$555$		0			0
$556$	5.41417	+	9.37762i	0.229612	+	0.397699i
$557$	−5.73458	−	9.93258i	−0.242982	−	0.420857i	0.718580	−	0.695444i	$-0.244792\pi$
$557$	−5.73458	−	9.93258i	−0.242982	−	0.420857i	−0.961562	+	0.274587i	$0.911459\pi$
$558$		0			0
$559$	−0.767806			−0.0324747
$560$	−4.18976	+	14.3457i	−0.177050	+	0.606215i
$561$		0			0
$562$	19.1668	−	33.1979i	0.808504	−	1.40037i
$563$	−12.6908	−	21.9811i	−0.534854	−	0.926394i	−0.999170	−	0.0407249i	$-0.987033\pi$
$563$	−12.6908	−	21.9811i	−0.534854	−	0.926394i	0.464316	−	0.885669i	$-0.346300\pi$
$564$		0			0
$565$	5.26627	−	9.12145i	0.221554	−	0.383742i
$566$	−40.5287			−1.70355
$567$		0			0
$568$	7.00350			0.293860
$569$	4.34702	−	7.52926i	0.182237	−	0.315643i	−0.760405	−	0.649449i	$-0.775000\pi$
$569$	4.34702	−	7.52926i	0.182237	−	0.315643i	0.942642	+	0.333806i	$0.108333\pi$
$570$		0			0
$571$	−4.06378	−	7.03868i	−0.170064	−	0.294560i	0.768378	−	0.639996i	$-0.221064\pi$
$571$	−4.06378	−	7.03868i	−0.170064	−	0.294560i	−0.938442	+	0.345437i	$0.887731\pi$
$572$	−17.8747	+	30.9599i	−0.747380	+	1.29450i
$573$		0			0
$574$	58.8766	−	14.3734i	2.45746	−	0.599935i
$575$	25.3368			1.05662
$576$		0			0
$577$	−11.0420	−	19.1253i	−0.459683	−	0.796195i	0.539261	−	0.842139i	$-0.318704\pi$
$577$	−11.0420	−	19.1253i	−0.459683	−	0.796195i	−0.998944	+	0.0459441i	$0.985370\pi$
$578$	−0.874080	−	1.51395i	−0.0363569	−	0.0629720i
$579$		0			0
$580$	−8.21663			−0.341177
$581$	−11.7770	−	12.3157i	−0.488594	−	0.510942i
$582$		0			0
$583$	24.2677	−	42.0329i	1.00506	−	1.74082i
$584$	−3.45452	−	5.98341i	−0.142949	−	0.247595i
$585$		0			0
$586$	−11.8107	+	20.4567i	−0.487895	+	0.845060i
$587$	−30.7200			−1.26795			−0.633975	−	0.773354i	$-0.718578\pi$
$587$	−30.7200			−1.26795			−0.633975	+	0.773354i	$0.718578\pi$
$588$		0			0
$589$	−0.226011			−0.00931260
$590$	2.91406	−	5.04730i	0.119970	−	0.207794i
$591$		0			0
$592$	−6.14358	−	10.6410i	−0.252500	−	0.437342i
$593$	−22.0358	+	38.1671i	−0.904901	+	1.56733i	−0.0838502	+	0.996478i	$0.526722\pi$
$593$	−22.0358	+	38.1671i	−0.904901	+	1.56733i	−0.821050	+	0.570856i	$0.806612\pi$
$594$		0			0
$595$	−28.0315	−	29.3136i	−1.14918	−	1.20174i
$596$	−13.2584			−0.543085
$597$		0			0
$598$	−8.46656	−	14.6645i	−0.346223	−	0.599677i
$599$	−13.6831	−	23.6999i	−0.559078	−	0.968351i	−0.997574	−	0.0696182i	$-0.977822\pi$
$599$	−13.6831	−	23.6999i	−0.559078	−	0.968351i	0.438496	−	0.898733i	$-0.355511\pi$
$600$		0			0
$601$	−7.21816			−0.294435			−0.147217	−	0.989104i	$-0.547032\pi$
$601$	−7.21816			−0.294435			−0.147217	+	0.989104i	$0.547032\pi$
$602$	1.51549	−	0.369973i	0.0617668	−	0.0150790i
$603$		0			0
$604$	−11.2100	+	19.4164i	−0.456130	+	0.790040i
$605$	−14.6597	−	25.3914i	−0.596002	−	1.03231i
$606$		0			0
$607$	−18.5024	+	32.0471i	−0.750989	+	1.30075i	0.196355	+	0.980533i	$0.437090\pi$
$607$	−18.5024	+	32.0471i	−0.750989	+	1.30075i	−0.947344	+	0.320218i	$0.896244\pi$
$608$	−11.4835			−0.465715
$609$		0			0
$610$	−17.7185			−0.717400
$611$	11.4040	−	19.7523i	0.461357	−	0.799093i
$612$		0			0
$613$	−0.830292	−	1.43811i	−0.0335352	−	0.0580847i	0.848771	−	0.528761i	$-0.177343\pi$
$613$	−0.830292	−	1.43811i	−0.0335352	−	0.0580847i	−0.882306	+	0.470676i	$0.844010\pi$
$614$	34.6598	−	60.0326i	1.39876	−	2.42272i
$615$		0			0
$616$	6.19857	−	21.2238i	0.249747	−	0.855129i
$617$	22.2418			0.895421			0.447710	−	0.894179i	$-0.352240\pi$
$617$	22.2418			0.895421			0.447710	+	0.894179i	$0.352240\pi$
$618$		0			0
$619$	−9.89026	−	17.1304i	−0.397523	−	0.688530i	0.595896	−	0.803061i	$-0.296797\pi$
$619$	−9.89026	−	17.1304i	−0.397523	−	0.688530i	−0.993420	+	0.114531i	$0.963464\pi$
$620$	−0.769316	−	1.33249i	−0.0308965	−	0.0535142i
$621$		0			0
$622$	−29.7838			−1.19422
$623$	0.660234	−	0.161181i	0.0264517	−	0.00645760i
$624$		0			0
$625$	−8.86964	+	15.3627i	−0.354786	+	0.614507i
$626$	−21.3528	−	36.9842i	−0.853431	−	1.47819i
$627$		0			0
$628$	−33.4470	+	57.9320i	−1.33468	+	2.31174i
$629$	33.3462			1.32960
$630$		0			0
$631$	49.2569			1.96089			0.980443	−	0.196804i	$-0.0630562\pi$
$631$	49.2569			1.96089			0.980443	+	0.196804i	$0.0630562\pi$
$632$	−14.9031	+	25.8130i	−0.592815	+	1.02678i
$633$		0			0
$634$	16.9548	+	29.3666i	0.673362	+	1.16630i
$635$	−26.0020	+	45.0369i	−1.03186	+	1.78723i
$636$		0			0
$637$	0.899576	−	20.1066i	0.0356425	−	0.796653i
$638$	−7.16578			−0.283696
$639$		0			0
$640$	−26.6162	−	46.1006i	−1.05210	−	1.82229i
$641$	−4.32841	−	7.49703i	−0.170962	−	0.296115i	0.767795	−	0.640696i	$-0.221354\pi$
$641$	−4.32841	−	7.49703i	−0.170962	−	0.296115i	−0.938756	+	0.344581i	$0.888021\pi$
$642$		0			0
$643$	17.7156			0.698637			0.349318	−	0.937004i	$-0.386413\pi$
$643$	17.7156			0.698637			0.349318	+	0.937004i	$0.386413\pi$
$644$	14.0231	+	14.6645i	0.552587	+	0.577863i
$645$		0			0
$646$	7.14789	−	12.3805i	0.281230	−	0.487105i
$647$	−6.05092	−	10.4805i	−0.237886	−	0.412031i	0.722221	−	0.691662i	$-0.243121\pi$
$647$	−6.05092	−	10.4805i	−0.237886	−	0.412031i	−0.960108	+	0.279631i	$0.909788\pi$
$648$		0			0
$649$	1.49881	−	2.59602i	0.0588335	−	0.101903i
$650$	60.3062			2.36540
$651$		0			0
$652$	17.5705			0.688112
$653$	−18.1070	+	31.3623i	−0.708583	+	1.22730i	0.256800	+	0.966464i	$0.417332\pi$
$653$	−18.1070	+	31.3623i	−0.708583	+	1.22730i	−0.965383	+	0.260837i	$0.916002\pi$
$654$		0			0
$655$	33.5348	+	58.0840i	1.31031	+	2.26953i
$656$	7.69502	−	13.3282i	0.300440	−	0.520378i
$657$		0			0
$658$	−12.9913	+	44.4821i	−0.506455	+	1.73409i
$659$	−39.3414			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$659$	−39.3414			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$660$		0			0
$661$	0.830402	+	1.43830i	0.0322989	+	0.0559433i	0.881723	−	0.471767i	$-0.156384\pi$
$661$	0.830402	+	1.43830i	0.0322989	+	0.0559433i	−0.849424	+	0.527711i	$0.823050\pi$
$662$	−1.36707	−	2.36784i	−0.0531327	−	0.0920286i
$663$		0			0
$664$	12.4469			0.483032
$665$	−4.54211	+	15.5521i	−0.176135	+	0.603084i
$666$		0			0
$667$	1.00088	−	1.73357i	0.0387540	−	0.0671240i
$668$	16.7361	+	28.9878i	0.647540	+	1.12157i
$669$		0			0
$670$	−45.2591	+	78.3911i	−1.74851	+	3.02851i
$671$	−9.11327			−0.351814
$672$		0			0
$673$	20.8307			0.802965			0.401483	−	0.915867i	$-0.368495\pi$
$673$	20.8307			0.802965			0.401483	+	0.915867i	$0.368495\pi$
$674$	13.1470	−	22.7713i	0.506405	−	0.877118i
$675$		0			0
$676$	6.80421	+	11.7852i	0.261700	+	0.453279i
$677$	−23.3654	+	40.4701i	−0.898006	+	1.55539i	−0.0679653	+	0.997688i	$0.521651\pi$
$677$	−23.3654	+	40.4701i	−0.898006	+	1.55539i	−0.830040	+	0.557704i	$0.811683\pi$
$678$		0			0
$679$	1.93563	+	2.02416i	0.0742825	+	0.0776802i
$680$	29.6257			1.13610
$681$		0			0
$682$	−0.670926	−	1.16208i	−0.0256911	−	0.0444982i
$683$	−10.5747	−	18.3159i	−0.404630	−	0.700840i	0.589648	−	0.807660i	$-0.299266\pi$
$683$	−10.5747	−	18.3159i	−0.404630	−	0.700840i	−0.994278	+	0.106820i	$0.965933\pi$
$684$		0			0
$685$	−33.0030			−1.26098
$686$	7.91294	+	40.1198i	0.302118	+	1.53178i
$687$		0			0
$688$	0.198071	−	0.343068i	0.00755137	−	0.0130794i
$689$	16.1356	+	27.9476i	0.614716	+	1.06472i
$690$		0			0
$691$	11.7985	−	20.4356i	0.448836	−	0.777407i	−0.549475	−	0.835510i	$-0.685172\pi$
$691$	11.7985	−	20.4356i	0.448836	−	0.777407i	0.998311	+	0.0581038i	$0.0185054\pi$
$692$	−55.3689			−2.10481
$693$		0			0
$694$	−9.59768			−0.364323
$695$	7.17017	−	12.4191i	0.271980	−	0.471083i
$696$		0			0
$697$	20.8836	+	36.1714i	0.791021	+	1.37009i
$698$	7.92185	−	13.7210i	0.299846	−	0.519349i
$699$		0			0
$700$	−70.2008	+	17.1380i	−2.65334	+	0.647754i
$701$	42.1420			1.59168			0.795841	−	0.605505i	$-0.207029\pi$
$701$	42.1420			1.59168			0.795841	+	0.605505i	$0.207029\pi$
$702$		0			0
$703$	−6.66024	−	11.5359i	−0.251196	−	0.435084i
$704$	−27.6744	−	47.9334i	−1.04302	−	1.80656i
$705$		0			0
$706$	55.4134			2.08551
$707$	1.01308	−	3.46878i	0.0381009	−	0.130457i
$708$		0			0
$709$	−22.9919	+	39.8231i	−0.863478	+	1.49559i	0.00507252	+	0.999987i	$0.498385\pi$
$709$	−22.9919	+	39.8231i	−0.863478	+	1.49559i	−0.868551	+	0.495601i	$0.834948\pi$
$710$	−15.2345	−	26.3869i	−0.571740	−	0.990282i
$711$		0			0
$712$	−0.248209	+	0.429911i	−0.00930204	+	0.0161116i
$713$	0.374844			0.0140380
$714$		0			0
$715$	47.3442			1.77057
$716$	4.80434	−	8.32137i	0.179547	−	0.310984i
$717$		0			0
$718$	−35.3189	−	61.1741i	−1.31809	−	2.28300i
$719$	−16.5249	+	28.6220i	−0.616275	+	1.06742i	0.373885	+	0.927475i	$0.378026\pi$
$719$	−16.5249	+	28.6220i	−0.616275	+	1.06742i	−0.990159	+	0.139944i	$0.955308\pi$
$720$		0			0
$721$	38.4801	−	9.39406i	1.43307	−	0.349853i
$722$	36.2413			1.34876
$723$		0			0
$724$	28.3726	+	49.1428i	1.05446	+	1.82638i
$725$	3.56455	+	6.17398i	0.132384	+	0.229296i
$726$		0			0
$727$	−25.0550			−0.929238			−0.464619	−	0.885511i	$-0.653809\pi$
$727$	−25.0550			−0.929238			−0.464619	+	0.885511i	$0.653809\pi$
$728$	10.1603	+	10.6251i	0.376567	+	0.393792i
$729$		0			0
$730$	−15.0290	+	26.0310i	−0.556248	+	0.963451i
$731$	0.537545	+	0.931055i	0.0198818	+	0.0344363i
$732$		0			0
$733$	−7.00625	+	12.1352i	−0.258782	+	0.448223i	−0.965916	−	0.258856i	$-0.916654\pi$
$733$	−7.00625	+	12.1352i	−0.258782	+	0.448223i	0.707134	+	0.707079i	$0.249988\pi$
$734$	24.5634			0.906652
$735$		0			0
$736$	19.0456			0.702030
$737$	−23.2785	+	40.3195i	−0.857474	+	1.48519i
$738$		0			0
$739$	19.3007	+	33.4297i	0.709987	+	1.22973i	0.964862	+	0.262759i	$0.0846323\pi$
$739$	19.3007	+	33.4297i	0.709987	+	1.22973i	−0.254875	+	0.966974i	$0.582034\pi$
$740$	45.3415	−	78.5338i	1.66679	−	2.88696i
$741$		0			0
$742$	−45.3150	−	47.3878i	−1.66357	−	1.73966i
$743$	1.81318			0.0665192			0.0332596	−	0.999447i	$-0.489411\pi$
$743$	1.81318			0.0665192			0.0332596	+	0.999447i	$0.489411\pi$
$744$		0			0
$745$	8.77928	+	15.2062i	0.321648	+	0.557110i
$746$	17.8346	+	30.8904i	0.652971	+	1.13098i
$747$		0			0
$748$	50.0567			1.83026
$749$	20.7716	−	5.07092i	0.758978	−	0.185287i
$750$		0			0
$751$	14.7131	−	25.4838i	0.536888	−	0.929918i	−0.462181	−	0.886785i	$-0.652933\pi$
$751$	14.7131	−	25.4838i	0.536888	−	0.929918i	0.999069	−	0.0431321i	$-0.0137336\pi$
$752$	5.88377	+	10.1910i	0.214559	+	0.371627i
$753$		0			0
$754$	2.38226	−	4.12620i	0.0867569	−	0.150267i
$755$	29.6917			1.08059
$756$		0			0
$757$	22.5455			0.819431			0.409715	−	0.912213i	$-0.365628\pi$
$757$	22.5455			0.819431			0.409715	+	0.912213i	$0.365628\pi$
$758$	3.51607	−	6.09000i	0.127709	−	0.221199i
$759$		0			0
$760$	−5.91715	−	10.2488i	−0.214638	−	0.371763i
$761$	−6.43131	+	11.1394i	−0.233135	+	0.403802i	−0.958729	−	0.284321i	$-0.908232\pi$
$761$	−6.43131	+	11.1394i	−0.233135	+	0.403802i	0.725594	+	0.688123i	$0.241565\pi$
$762$		0			0
$763$	−6.75652	+	23.1342i	−0.244603	+	0.837514i
$764$	−12.0039			−0.434285
$765$		0			0
$766$	−18.1913	−	31.5082i	−0.657277	−	1.13844i
$767$	0.996558	+	1.72609i	0.0359836	+	0.0623255i
$768$		0			0
$769$	−44.7222			−1.61272			−0.806362	−	0.591423i	$-0.798566\pi$
$769$	−44.7222			−1.61272			−0.806362	+	0.591423i	$0.798566\pi$
$770$	−93.4477	+	22.8132i	−3.36762	+	0.822129i
$771$		0			0
$772$	19.9452	−	34.5460i	0.717842	−	1.24334i
$773$	−5.24400	−	9.08288i	−0.188614	−	0.326688i	0.756175	−	0.654370i	$-0.227066\pi$
$773$	−5.24400	−	9.08288i	−0.188614	−	0.326688i	−0.944788	+	0.327681i	$0.893733\pi$
$774$		0			0
$775$	−0.667491	+	1.15613i	−0.0239770	+	0.0415294i
$776$	−2.04571			−0.0734368
$777$		0			0
$778$	−70.6053			−2.53132
$779$	8.34215	−	14.4490i	0.298889	−	0.517690i
$780$		0			0
$781$	−7.83567	−	13.5718i	−0.280382	−	0.485636i
$782$	−11.8550	+	20.5334i	−0.423933	+	0.734273i
$783$		0			0
$784$	8.75190	+	5.58884i	0.312568	+	0.199601i
$785$	88.5901			3.16192
$786$		0			0
$787$	−16.1037	−	27.8924i	−0.574035	−	0.994257i	−0.996146	−	0.0877130i	$-0.972044\pi$
$787$	−16.1037	−	27.8924i	−0.574035	−	0.994257i	0.422111	−	0.906544i	$-0.361289\pi$
$788$	10.7609	+	18.6384i	0.383341	+	0.663966i
$789$		0			0
$790$	129.673			4.61356
$791$	−5.05785	−	5.28920i	−0.179836	−	0.188062i
$792$		0			0
$793$	3.02970	−	5.24760i	0.107588	−	0.186348i
$794$	30.7042	+	53.1813i	1.08965	+	1.88733i
$795$		0			0
$796$	18.1936	−	31.5122i	0.644855	−	1.11692i
$797$	32.2778			1.14334			0.571669	−	0.820484i	$-0.306296\pi$
$797$	32.2778			1.14334			0.571669	+	0.820484i	$0.306296\pi$
$798$		0			0
$799$	−31.9360			−1.12981
$800$	−33.9148	+	58.7422i	−1.19907	+	2.07685i
$801$		0			0
$802$	30.4574	+	52.7538i	1.07549	+	1.86280i
$803$	−7.72998	+	13.3887i	−0.272785	+	0.472478i
$804$		0			0
$805$	7.53321	−	25.7935i	0.265511	−	0.909103i
$806$	0.892196			0.0314263
$807$		0			0
$808$	1.31978	+	2.28592i	0.0464295	+	0.0804183i
$809$	−14.9820	−	25.9495i	−0.526737	−	0.912336i	−0.999515	−	0.0311538i	$-0.990082\pi$
$809$	−14.9820	−	25.9495i	−0.526737	−	0.912336i	0.472777	−	0.881182i	$-0.343252\pi$
$810$		0			0
$811$	−13.1971			−0.463414			−0.231707	−	0.972786i	$-0.574431\pi$
$811$	−13.1971			−0.463414			−0.231707	+	0.972786i	$0.574431\pi$
$812$	−1.60053	+	5.48019i	−0.0561677	+	0.192317i
$813$		0			0
$814$	39.5427	−	68.4899i	1.38597	−	2.40057i
$815$	−11.6346	−	20.1517i	−0.407541	−	0.705883i
$816$		0			0
$817$	0.214728	−	0.371919i	0.00751237	−	0.0130118i
$818$	26.1087			0.912870
$819$		0			0
$820$	113.583			3.96650
$821$	4.01806	−	6.95948i	0.140231	−	0.242888i	−0.787352	−	0.616503i	$-0.788549\pi$
$821$	4.01806	−	6.95948i	0.140231	−	0.242888i	0.927584	+	0.373616i	$0.121882\pi$
$822$		0			0
$823$	−9.78282	−	16.9443i	−0.341008	−	0.590643i	0.643612	−	0.765352i	$-0.277435\pi$
$823$	−9.78282	−	16.9443i	−0.341008	−	0.590643i	−0.984620	+	0.174709i	$0.944102\pi$
$824$	−14.4663	+	25.0563i	−0.503956	+	0.872878i
$825$		0			0
$826$	−2.79873	−	2.92674i	−0.0973802	−	0.101834i
$827$	−45.8218			−1.59338			−0.796690	−	0.604389i	$-0.793417\pi$
$827$	−45.8218			−1.59338			−0.796690	+	0.604389i	$0.793417\pi$
$828$		0			0
$829$	−17.0773	−	29.5787i	−0.593119	−	1.02731i	−0.993809	−	0.111098i	$-0.964563\pi$
$829$	−17.0773	−	29.5787i	−0.593119	−	1.02731i	0.400691	−	0.916213i	$-0.368770\pi$
$830$	−27.0752	−	46.8957i	−0.939795	−	1.62777i
$831$		0			0
$832$	36.8013			1.27586
$833$	−25.0114	+	12.9859i	−0.866594	+	0.449935i
$834$		0			0
$835$	22.1642	−	38.3895i	0.767024	−	1.32852i
$836$	−9.99783	−	17.3168i	−0.345782	−	0.598913i
$837$		0			0
$838$	9.73360	−	16.8591i	0.336242	−	0.582388i
$839$	−35.5972			−1.22895			−0.614476	−	0.788935i	$-0.710633\pi$
$839$	−35.5972			−1.22895			−0.614476	+	0.788935i	$0.710633\pi$
$840$		0			0
$841$	−28.4368			−0.980578
$842$	20.6449	−	35.7579i	0.711469	−	1.23230i
$843$		0			0
$844$	7.40659	+	12.8286i	0.254945	+	0.441578i
$845$	9.01105	−	15.6076i	0.309990	−	0.536918i
$846$		0			0
$847$	−19.7907	+	4.83146i	−0.680017	+	0.166011i
$848$	−16.6499			−0.571761
$849$		0			0
$850$	−42.2207	−	73.1283i	−1.44816	−	2.50828i
$851$	11.0462	+	19.1325i	0.378658	+	0.655855i
$852$		0			0
$853$	33.3946			1.14341			0.571705	−	0.820459i	$-0.306282\pi$
$853$	33.3946			1.14341			0.571705	+	0.820459i	$0.306282\pi$
$854$	−3.45141	+	11.8176i	−0.118105	+	0.404389i
$855$		0			0
$856$	−7.80890	+	13.5254i	−0.266903	+	0.462289i
$857$	12.9074	+	22.3562i	0.440907	+	0.763674i	0.997757	−	0.0669395i	$-0.0213235\pi$
$857$	12.9074	+	22.3562i	0.440907	+	0.763674i	−0.556850	+	0.830613i	$0.687990\pi$
$858$		0			0
$859$	21.5003	−	37.2397i	0.733582	−	1.27060i	−0.221761	−	0.975101i	$-0.571181\pi$
$859$	21.5003	−	37.2397i	0.733582	−	1.27060i	0.955343	−	0.295500i	$-0.0954862\pi$
$860$	2.92364			0.0996954
$861$		0			0
$862$	36.6956			1.24986
$863$	−10.7483	+	18.6166i	−0.365877	+	0.633718i	−0.988917	−	0.148473i	$-0.952564\pi$
$863$	−10.7483	+	18.6166i	−0.365877	+	0.633718i	0.623039	+	0.782191i	$0.285898\pi$
$864$		0			0
$865$	36.6634	+	63.5029i	1.24659	+	2.15916i
$866$	−27.9315	+	48.3788i	−0.949152	+	1.64398i
$867$		0			0
$868$	−1.03858	+	0.253546i	−0.0352517	+	0.00860592i
$869$	66.6957			2.26250
$870$		0			0
$871$	−15.4778	−	26.8084i	−0.524447	−	0.908368i
$872$	−8.80194	−	15.2454i	−0.298071	−	0.516274i
$873$		0			0
$874$	9.47117			0.320367
$875$	31.3268	+	32.7597i	1.05904	+	1.10748i
$876$		0			0
$877$	−7.34204	+	12.7168i	−0.247923	+	0.429415i	−0.962949	−	0.269682i	$-0.913081\pi$
$877$	−7.34204	+	12.7168i	−0.247923	+	0.429415i	0.715026	+	0.699098i	$0.246415\pi$
$878$	−32.5153	−	56.3182i	−1.09734	−	1.90065i
$879$		0			0
$880$	−12.2134	+	21.1542i	−0.411712	+	0.713107i
$881$	37.6060			1.26698			0.633490	−	0.773751i	$-0.281622\pi$
$881$	37.6060			1.26698			0.633490	+	0.773751i	$0.281622\pi$
$882$		0			0
$883$	−46.9989			−1.58164			−0.790820	−	0.612049i	$-0.790345\pi$
$883$	−46.9989			−1.58164			−0.790820	+	0.612049i	$0.790345\pi$
$884$	−16.6413	+	28.8236i	−0.559709	+	0.969444i
$885$		0			0
$886$	35.9423	+	62.2540i	1.20751	+	2.09146i
$887$	13.2124	−	22.8846i	0.443630	−	0.768389i	−0.554326	−	0.832300i	$-0.687024\pi$
$887$	13.2124	−	22.8846i	0.443630	−	0.768389i	0.997956	+	0.0639105i	$0.0203572\pi$
$888$		0			0
$889$	24.9729	+	26.1152i	0.837566	+	0.875877i
$890$	2.15969			0.0723928
$891$		0			0
$892$	21.8758	+	37.8900i	0.732455	+	1.26865i
$893$	6.37858	+	11.0480i	0.213451	+	0.369708i
$894$		0			0
$895$	−12.7251			−0.425354
$896$	−35.9321	+	8.77201i	−1.20041	+	0.293052i
$897$		0			0
$898$	−0.189757	+	0.328668i	−0.00633226	+	0.0109678i
$899$	0.0527355	+	0.0913406i	0.00175883	+	0.00304638i
$900$		0			0
$901$	22.5932	−	39.1325i	0.752688	−	1.30369i
$902$	99.0567			3.29823
$903$		0			0
$904$	5.34551			0.177789
$905$	37.5748	−	65.0815i	1.24903	−	2.16338i
$906$		0			0
$907$	0.225026	+	0.389757i	0.00747187	+	0.0129417i	0.869737	−	0.493515i	$-0.164288\pi$
$907$	0.225026	+	0.389757i	0.00747187	+	0.0129417i	−0.862265	+	0.506457i	$0.830955\pi$
$908$	6.16667	−	10.6810i	0.204648	−	0.354461i
$909$		0			0
$910$	17.9304	−	61.3932i	0.594386	−	2.03517i
$911$	−4.74439			−0.157189			−0.0785944	−	0.996907i	$-0.525043\pi$
$911$	−4.74439			−0.157189			−0.0785944	+	0.996907i	$0.525043\pi$
$912$		0			0
$913$	−13.9258	−	24.1202i	−0.460877	−	0.798262i
$914$	27.0502	+	46.8523i	0.894742	+	1.54974i
$915$		0			0
$916$	2.79259			0.0922697
$917$	45.2722	−	11.0522i	1.49502	−	0.364976i
$918$		0			0
$919$	−21.2103	+	36.7372i	−0.699662	+	1.21185i	0.268922	+	0.963162i	$0.413333\pi$
$919$	−21.2103	+	36.7372i	−0.699662	+	1.21185i	−0.968584	+	0.248688i	$0.920001\pi$
$920$	9.81374	+	16.9979i	0.323550	+	0.560404i
$921$		0			0
$922$	−10.4119	+	18.0339i	−0.342897	+	0.593915i
$923$	10.4199			0.342974
$924$		0			0
$925$	−78.6805			−2.58700
$926$	3.15878	−	5.47116i	0.103804	−	0.179793i
$927$		0			0
$928$	2.67946	+	4.64096i	0.0879575	+	0.152347i
$929$	22.5409	−	39.0419i	0.739541	−	1.28092i	−0.213160	−	0.977017i	$-0.568376\pi$
$929$	22.5409	−	39.0419i	0.739541	−	1.28092i	0.952702	−	0.303906i	$-0.0982909\pi$
$930$		0			0
$931$	9.48791	+	6.05884i	0.310954	+	0.198571i
$932$	−10.8495			−0.355388
$933$		0			0
$934$	−8.50397	−	14.7293i	−0.278258	−	0.481958i
$935$	−33.1459	−	57.4104i	−1.08399	−	1.87752i
$936$		0			0
$937$	19.3045			0.630650			0.315325	−	0.948984i	$-0.397886\pi$
$937$	19.3045			0.630650			0.315325	+	0.948984i	$0.397886\pi$
$938$	43.4679	+	45.4561i	1.41928	+	1.48420i
$939$		0			0
$940$	−43.4240	+	75.2126i	−1.41633	+	2.45316i
$941$	5.27697	+	9.13997i	0.172024	+	0.297955i	0.939127	−	0.343569i	$-0.111636\pi$
$941$	5.27697	+	9.13997i	0.172024	+	0.297955i	−0.767103	+	0.641524i	$0.778303\pi$
$942$		0			0
$943$	−13.8357	+	23.9641i	−0.450551	+	0.780378i
$944$	−1.02833			−0.0334692
$945$		0			0
$946$	2.54973			0.0828989
$947$	23.8800	−	41.3614i	0.775996	−	1.34407i	−0.158236	−	0.987401i	$-0.550581\pi$
$947$	23.8800	−	41.3614i	0.775996	−	1.34407i	0.934233	−	0.356664i	$-0.116086\pi$
$948$		0			0
$949$	−5.13966	−	8.90215i	−0.166840	−	0.288976i
$950$	−16.8655	+	29.2119i	−0.547188	+	0.947758i
$951$		0			0
$952$	5.77086	−	19.7593i	0.187034	−	0.640402i
$953$	−53.8101			−1.74308			−0.871540	−	0.490324i	$-0.836879\pi$
$953$	−53.8101			−1.74308			−0.871540	+	0.490324i	$0.836879\pi$
$954$		0			0
$955$	7.94856	+	13.7673i	0.257209	+	0.445500i
$956$	−9.61827	−	16.6593i	−0.311077	−	0.538801i
$957$		0			0
$958$	76.3574			2.46700
$959$	−6.42872	+	22.0118i	−0.207594	+	0.710799i
$960$		0			0
$961$	15.4901	−	26.8297i	0.499681	−	0.865474i
$962$	26.2919	+	45.5389i	0.847684	+	1.46823i
$963$		0			0
$964$	21.5230	−	37.2790i	0.693210	−	1.20067i
$965$	−52.8281			−1.70060
$966$		0			0
$967$	−9.81775			−0.315718			−0.157859	−	0.987462i	$-0.550459\pi$
$967$	−9.81775			−0.315718			−0.157859	+	0.987462i	$0.550459\pi$
$968$	7.44015	−	12.8867i	0.239135	−	0.414195i
$969$		0			0
$970$	4.44997	+	7.70757i	0.142880	+	0.247475i
$971$	−11.8993	+	20.6102i	−0.381867	+	0.661413i	−0.991329	−	0.131402i	$-0.958052\pi$
$971$	−11.8993	+	20.6102i	−0.381867	+	0.661413i	0.609462	+	0.792815i	$0.291385\pi$
$972$		0			0
$973$	−6.88639	−	7.20138i	−0.220768	−	0.230866i
$974$	−40.7058			−1.30430
$975$		0			0
$976$	1.56314	+	2.70744i	0.0500350	+	0.0866631i
$977$	−19.9951	−	34.6326i	−0.639701	−	1.10799i	−0.985498	−	0.169685i	$-0.945725\pi$
$977$	−19.9951	−	34.6326i	−0.639701	−	1.10799i	0.345797	−	0.938309i	$-0.387609\pi$
$978$		0			0
$979$	1.11081			0.0355016
$980$	−3.42539	+	76.5617i	−0.109420	+	2.44567i
$981$		0			0
$982$	−3.48170	+	6.03048i	−0.111106	+	0.192440i
$983$	−23.1143	−	40.0351i	−0.737231	−	1.27692i	−0.953738	−	0.300640i	$-0.902800\pi$
$983$	−23.1143	−	40.0351i	−0.737231	−	1.27692i	0.216506	−	0.976281i	$-0.430534\pi$
$984$		0			0
$985$	14.2510	−	24.6835i	0.454075	−	0.786482i
$986$	−6.67133			−0.212459
$987$		0			0
$988$	13.2951			0.422974
$989$	−0.356131	+	0.616838i	−0.0113243	+	0.0196143i
$990$		0			0
$991$	−7.19818	−	12.4676i	−0.228658	−	0.396047i	0.728753	−	0.684777i	$-0.240100\pi$
$991$	−7.19818	−	12.4676i	−0.228658	−	0.396047i	−0.957411	+	0.288730i	$0.906767\pi$
$992$	−0.501750	+	0.869057i	−0.0159306	+	0.0275926i
$993$		0			0
$994$	−20.5666	+	5.02089i	−0.652334	+	0.159253i
$995$	−48.1888			−1.52769
$996$		0			0
$997$	−21.9273	−	37.9792i	−0.694444	−	1.20281i	−0.970368	−	0.241633i	$-0.922317\pi$
$997$	−21.9273	−	37.9792i	−0.694444	−	1.20281i	0.275924	−	0.961180i	$-0.411016\pi$
$998$	31.8833	+	55.2234i	1.00925	+	1.74807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.d.163.4	yes	8
3.2	odd	2		567.2.e.c.163.1	✓	8
7.2	even	3		3969.2.a.s.1.1		4
7.4	even	3	inner	567.2.e.d.487.4	yes	8
7.5	odd	6		3969.2.a.t.1.1		4
9.2	odd	6		567.2.h.k.352.4		8
9.4	even	3		567.2.g.k.541.4		8
9.5	odd	6		567.2.g.j.541.1		8
9.7	even	3		567.2.h.j.352.1		8
21.2	odd	6		3969.2.a.x.1.4		4
21.5	even	6		3969.2.a.w.1.4		4
21.11	odd	6		567.2.e.c.487.1	yes	8
63.4	even	3		567.2.h.j.298.1		8
63.11	odd	6		567.2.g.j.109.1		8
63.25	even	3		567.2.g.k.109.4		8
63.32	odd	6		567.2.h.k.298.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.1	✓	8	3.2	odd	2
567.2.e.c.487.1	yes	8	21.11	odd	6
567.2.e.d.163.4	yes	8	1.1	even	1	trivial
567.2.e.d.487.4	yes	8	7.4	even	3	inner
567.2.g.j.109.1		8	63.11	odd	6
567.2.g.j.541.1		8	9.5	odd	6
567.2.g.k.109.4		8	63.25	even	3
567.2.g.k.541.4		8	9.4	even	3
567.2.h.j.298.1		8	63.4	even	3
567.2.h.j.352.1		8	9.7	even	3
567.2.h.k.298.4		8	63.32	odd	6
567.2.h.k.352.4		8	9.2	odd	6
3969.2.a.s.1.1		4	7.2	even	3
3969.2.a.t.1.1		4	7.5	odd	6
3969.2.a.w.1.4		4	21.5	even	6
3969.2.a.x.1.4		4	21.2	odd	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10400 - 1.91218i) q^{2} +(-1.43762 - 2.49004i) q^{4} +(-1.90389 + 3.29764i) q^{5} +(1.82854 + 1.91218i) q^{7} -1.93254 q^{8} +O(q^{10})\)	\(q+(1.10400 - 1.91218i) q^{2} +(-1.43762 - 2.49004i) q^{4} +(-1.90389 + 3.29764i) q^{5} +(1.82854 + 1.91218i) q^{7} -1.93254 q^{8} +(4.20379 + 7.28117i) q^{10} +(2.16217 + 3.74498i) q^{11} -2.87525 q^{13} +(5.67514 - 1.38546i) q^{14} +(0.741726 - 1.28471i) q^{16} +(2.01297 + 3.48657i) q^{17} +(0.804103 - 1.39275i) q^{19} +10.9483 q^{20} +9.54811 q^{22} +(-1.33363 + 2.30991i) q^{23} +(-4.74962 - 8.22658i) q^{25} +(-3.17427 + 5.49799i) q^{26} +(2.13264 - 7.30213i) q^{28} -0.750492 q^{29} +(-0.0702679 - 0.121708i) q^{31} +(-3.57027 - 6.18389i) q^{32} +8.88928 q^{34} +(-9.78703 + 2.38928i) q^{35} +(4.14141 - 7.17313i) q^{37} +(-1.77546 - 3.07518i) q^{38} +(3.67935 - 6.37282i) q^{40} +10.3745 q^{41} +0.267040 q^{43} +(6.21676 - 10.7677i) q^{44} +(2.94464 + 5.10026i) q^{46} +(-3.96627 + 6.86978i) q^{47} +(-0.312869 + 6.99300i) q^{49} -20.9743 q^{50} +(4.13352 + 7.15947i) q^{52} +(-5.61189 - 9.72008i) q^{53} -16.4661 q^{55} +(-3.53373 - 3.69537i) q^{56} +(-0.828542 + 1.43508i) q^{58} +(-0.346599 - 0.600327i) q^{59} +(-1.05372 + 1.82510i) q^{61} -0.310302 q^{62} -12.7994 q^{64} +(5.47416 - 9.48152i) q^{65} +(5.38314 + 9.32387i) q^{67} +(5.78780 - 10.0248i) q^{68} +(-6.23612 + 21.3523i) q^{70} -3.62399 q^{71} +(1.78756 + 3.09614i) q^{73} +(-9.14422 - 15.8383i) q^{74} -4.62399 q^{76} +(-3.20747 + 10.9823i) q^{77} +(7.71168 - 13.3570i) q^{79} +(2.82433 + 4.89189i) q^{80} +(11.4534 - 19.8379i) q^{82} -6.44067 q^{83} -15.3299 q^{85} +(0.294812 - 0.510629i) q^{86} +(-4.17847 - 7.23733i) q^{88} +(0.128437 - 0.222459i) q^{89} +(-5.25751 - 5.49799i) q^{91} +7.66900 q^{92} +(8.75751 + 15.1684i) q^{94} +(3.06185 + 5.30328i) q^{95} +1.05856 q^{97} +(13.0265 + 8.31853i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{4} + 2 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q + q^2 - 5 * q^4 + 2 * q^5 + q^7 + 6 * q^8	\( 8 q + q^{2} - 5 q^{4} + 2 q^{5} + q^{7} + 6 q^{8} + 7 q^{10} + 5 q^{11} - 10 q^{13} + 23 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} + 16 q^{20} - 14 q^{22} - 12 q^{23} - 8 q^{25} + q^{26} + 5 q^{28} + 20 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} - 20 q^{38} + 18 q^{40} + 10 q^{41} - 14 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 17 q^{49} - 76 q^{50} + 25 q^{52} - 12 q^{53} - 52 q^{55} - 39 q^{56} + 7 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} + 51 q^{68} + 17 q^{70} + 18 q^{71} + 6 q^{73} + 10 q^{76} + 37 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} - 18 q^{83} - 18 q^{85} - 22 q^{86} - 18 q^{88} - 22 q^{89} + 13 q^{91} + 72 q^{92} + 15 q^{94} - 16 q^{95} - 18 q^{97} - 11 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^4 + 2 * q^5 + q^7 + 6 * q^8 + 7 * q^10 + 5 * q^11 - 10 * q^13 + 23 * q^14 + q^16 + 6 * q^17 + 8 * q^19 + 16 * q^20 - 14 * q^22 - 12 * q^23 - 8 * q^25 + q^26 + 5 * q^28 + 20 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 - 20 * q^38 + 18 * q^40 + 10 * q^41 - 14 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 17 * q^49 - 76 * q^50 + 25 * q^52 - 12 * q^53 - 52 * q^55 - 39 * q^56 + 7 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 + 51 * q^68 + 17 * q^70 + 18 * q^71 + 6 * q^73 + 10 * q^76 + 37 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 - 18 * q^83 - 18 * q^85 - 22 * q^86 - 18 * q^88 - 22 * q^89 + 13 * q^91 + 72 * q^92 + 15 * q^94 - 16 * q^95 - 18 * q^97 - 11 * q^98

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