LMFDB - Embedded newform 567.2.g.k.541.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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([2, 4]))

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

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

chi := DirichletCharacter("567.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.g (of order $3$, 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:	$4.52751779461$
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			541.4
Root			$-1.54162 + 1.88572i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.k.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10400 + 1.91218i) q^{2} +(-1.43762 + 2.49004i) q^{4} +3.80779 q^{5} +(-2.57027 + 0.627473i) q^{7} -1.93254 q^{8} +O(q^{10})$	\(q+(1.10400 + 1.91218i) q^{2} +(-1.43762 + 2.49004i) q^{4} +3.80779 q^{5} +(-2.57027 + 0.627473i) q^{7} -1.93254 q^{8} +(4.20379 + 7.28117i) q^{10} -4.32433 q^{11} +(1.43762 + 2.49004i) q^{13} +(-4.03741 - 4.22209i) q^{14} +(0.741726 + 1.28471i) q^{16} +(2.01297 + 3.48657i) q^{17} +(0.804103 - 1.39275i) q^{19} +(-5.47416 + 9.48152i) q^{20} +(-4.77406 - 8.26891i) q^{22} +2.66725 q^{23} +9.49923 q^{25} +(-3.17427 + 5.49799i) q^{26} +(2.13264 - 7.30213i) q^{28} +(0.375246 - 0.649945i) q^{29} +(-0.0702679 + 0.121708i) q^{31} +(-3.57027 + 6.18389i) q^{32} +(-4.44464 + 7.69834i) q^{34} +(-9.78703 + 2.38928i) q^{35} +(4.14141 - 7.17313i) q^{37} +3.55091 q^{38} -7.35870 q^{40} +(-5.18724 - 8.98456i) q^{41} +(-0.133520 + 0.231264i) q^{43} +(6.21676 - 10.7677i) q^{44} +(2.94464 + 5.10026i) q^{46} +(-3.96627 - 6.86978i) q^{47} +(6.21255 - 3.22555i) q^{49} +(10.4871 + 18.1643i) q^{50} -8.26704 q^{52} +(-5.61189 - 9.72008i) q^{53} -16.4661 q^{55} +(4.96715 - 1.21262i) q^{56} +1.65708 q^{58} +(-0.346599 + 0.600327i) q^{59} +(-1.05372 - 1.82510i) q^{61} -0.310302 q^{62} -12.7994 q^{64} +(5.47416 + 9.48152i) q^{65} +(5.38314 - 9.32387i) q^{67} -11.5756 q^{68} +(-15.3736 - 16.0768i) q^{70} -3.62399 q^{71} +(1.78756 + 3.09614i) q^{73} +18.2884 q^{74} +(2.31199 + 4.00449i) q^{76} +(11.1147 - 2.71340i) q^{77} +(7.71168 + 13.3570i) q^{79} +(2.82433 + 4.89189i) q^{80} +(11.4534 - 19.8379i) q^{82} +(3.22034 - 5.57779i) q^{83} +(7.66497 + 13.2761i) q^{85} -0.589624 q^{86} +8.35695 q^{88} +(0.128437 - 0.222459i) q^{89} +(-5.25751 - 5.49799i) q^{91} +(-3.83450 + 6.64155i) q^{92} +(8.75751 - 15.1684i) q^{94} +(3.06185 - 5.30328i) q^{95} +(-0.529281 + 0.916742i) q^{97} +(13.0265 + 8.31853i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8	$ 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8} + 7 q^{10} - 10 q^{11} + 5 q^{13} - 7 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} + 24 q^{23} + 16 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} + 40 q^{38} - 36 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 2 q^{49} + 38 q^{50} - 50 q^{52} - 12 q^{53} - 52 q^{55} + 33 q^{56} - 14 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} - 102 q^{68} - 46 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} + 16 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} + 44 q^{86} + 36 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} + 15 q^{94} - 16 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8 + 7 * q^10 - 10 * q^11 + 5 * q^13 - 7 * q^14 + q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 + 24 * q^23 + 16 * q^25 + q^26 + 5 * q^28 - 10 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 + 40 * q^38 - 36 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 2 * q^49 + 38 * q^50 - 50 * q^52 - 12 * q^53 - 52 * q^55 + 33 * q^56 - 14 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 - 102 * q^68 - 46 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 + 16 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 + 44 * q^86 + 36 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 + 15 * q^94 - 16 * q^95 + 9 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.10400	+	1.91218i	0.780644	+	1.35212i	0.931567	+	0.363570i	$0.118442\pi$
$2$	1.10400	+	1.91218i	0.780644	+	1.35212i	−0.150922	+	0.988546i	$0.548224\pi$
$3$		0			0
$3$		0			0
$4$	−1.43762	+	2.49004i	−0.718812	+	1.24502i
$5$	3.80779			1.70289			0.851447	−	0.524441i	$-0.175726\pi$
$5$	3.80779			1.70289			0.851447	+	0.524441i	$0.175726\pi$
$6$		0			0
$7$	−2.57027	+	0.627473i	−0.971470	+	0.237163i
$7$	−2.57027	+	0.627473i	−0.971470	+	0.237163i
$8$	−1.93254			−0.683256
$9$		0			0
$10$	4.20379	+	7.28117i	1.32935	+	2.30251i
$11$	−4.32433			−1.30384			−0.651918	−	0.758290i	$-0.726035\pi$
$11$	−4.32433			−1.30384			−0.651918	+	0.758290i	$0.726035\pi$
$12$		0			0
$13$	1.43762	+	2.49004i	0.398725	+	0.690612i	0.993569	−	0.113229i	$-0.0361195\pi$
$13$	1.43762	+	2.49004i	0.398725	+	0.690612i	−0.594844	+	0.803841i	$0.702786\pi$
$14$	−4.03741	−	4.22209i	−1.07904	−	1.12840i
$15$		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	$0.107609\pi$
$20$	−5.47416	+	9.48152i	−1.22406	+	2.12013i
$21$		0			0
$22$	−4.77406	−	8.26891i	−1.01783	−	1.76294i
$23$	2.66725			0.556160			0.278080	−	0.960558i	$-0.410302\pi$
$23$	2.66725			0.556160			0.278080	+	0.960558i	$0.410302\pi$
$24$		0			0
$25$	9.49923			1.89985
$26$	−3.17427	+	5.49799i	−0.622525	+	1.07824i
$27$		0			0
$28$	2.13264	−	7.30213i	0.403032	−	1.37997i
$29$	0.375246	−	0.649945i	0.0696815	−	0.120692i	−0.829080	−	0.559131i	$-0.811135\pi$
$29$	0.375246	−	0.649945i	0.0696815	−	0.120692i	0.898761	+	0.438439i	$0.144468\pi$
$30$		0			0
$31$	−0.0702679	+	0.121708i	−0.0126205	+	0.0218593i	−0.872267	−	0.489031i	$-0.837351\pi$
$31$	−0.0702679	+	0.121708i	−0.0126205	+	0.0218593i	0.859646	+	0.510890i	$0.170684\pi$
$32$	−3.57027	+	6.18389i	−0.631140	+	1.09317i
$33$		0			0
$34$	−4.44464	+	7.69834i	−0.762249	+	1.32025i
$35$	−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	$-0.0717201\pi$
$38$	3.55091			0.576034
$39$		0			0
$40$	−7.35870			−1.16351
$41$	−5.18724	−	8.98456i	−0.810111	−	1.40315i	−0.912786	−	0.408438i	$-0.866074\pi$
$41$	−5.18724	−	8.98456i	−0.810111	−	1.40315i	0.102675	−	0.994715i	$-0.467260\pi$
$42$		0			0
$43$	−0.133520	+	0.231264i	−0.0203616	+	0.0352674i	−0.876027	−	0.482263i	$-0.839815\pi$
$43$	−0.133520	+	0.231264i	−0.0203616	+	0.0352674i	0.855665	+	0.517530i	$0.173148\pi$
$44$	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	−0.995647	−	0.0932032i	$-0.970289\pi$
$47$	−3.96627	−	6.86978i	−0.578540	−	1.00206i	0.417107	−	0.908857i	$-0.363044\pi$
$48$		0			0
$49$	6.21255	−	3.22555i	0.887508	−	0.460793i
$50$	10.4871	+	18.1643i	1.48310	+	2.56881i
$51$		0			0
$52$	−8.26704			−1.14643
$53$	−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
$56$	4.96715	−	1.21262i	0.663763	−	0.162043i
$57$		0			0
$58$	1.65708			0.217586
$59$	−0.346599	+	0.600327i	−0.0451234	+	0.0781560i	−0.887705	−	0.460413i	$-0.847701\pi$
$59$	−0.346599	+	0.600327i	−0.0451234	+	0.0781560i	0.842582	+	0.538569i	$0.181035\pi$
$60$		0			0
$61$	−1.05372	−	1.82510i	−0.134915	−	0.233680i	0.790650	−	0.612268i	$-0.209743\pi$
$61$	−1.05372	−	1.82510i	−0.134915	−	0.233680i	−0.925565	+	0.378589i	$0.876409\pi$
$62$	−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	−0.323566	−	0.946206i	$-0.604882\pi$
$67$	5.38314	−	9.32387i	0.657655	−	1.13909i	0.981221	−	0.192886i	$-0.0617848\pi$
$68$	−11.5756			−1.40375
$69$		0			0
$70$	−15.3736	−	16.0768i	−1.83750	−	1.92155i
$71$	−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	$0.766242\pi$
$74$	18.2884			2.12599
$75$		0			0
$76$	2.31199	+	4.00449i	0.265204	+	0.459347i
$77$	11.1147	−	2.71340i	1.26664	−	0.309221i
$78$		0			0
$79$	7.71168	+	13.3570i	0.867632	+	1.50278i	0.864410	+	0.502787i	$0.167692\pi$
$79$	7.71168	+	13.3570i	0.867632	+	1.50278i	0.00322152	+	0.999995i	$0.498975\pi$
$80$	2.82433	+	4.89189i	0.315770	+	0.546930i
$81$		0			0
$82$	11.4534	−	19.8379i	1.26482	−	2.19073i
$83$	3.22034	−	5.57779i	0.353478	−	0.612241i	−0.633378	−	0.773842i	$-0.718332\pi$
$83$	3.22034	−	5.57779i	0.353478	−	0.612241i	0.986856	+	0.161601i	$0.0516657\pi$
$84$		0			0
$85$	7.66497	+	13.2761i	0.831383	+	1.44000i
$86$	−0.589624			−0.0635808
$87$		0			0
$88$	8.35695			0.890854
$89$	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
$92$	−3.83450	+	6.64155i	−0.399774	+	0.692429i
$93$		0			0
$94$	8.75751	−	15.1684i	0.903268	−	1.56451i
$95$	3.06185	−	5.30328i	0.314139	−	0.544105i
$96$		0			0
$97$	−0.529281	+	0.916742i	−0.0537403	+	0.0930810i	−0.891644	−	0.452737i	$-0.850448\pi$
$97$	−0.529281	+	0.916742i	−0.0537403	+	0.0930810i	0.837904	+	0.545818i	$0.183781\pi$
$98$	13.0265	+	8.31853i	1.31587	+	0.840298i
$99$		0			0
$100$	−13.6563	+	23.6534i	−1.36563	+	2.36534i
$101$	1.36585			0.135907			0.0679534	−	0.997688i	$-0.478353\pi$
$101$	1.36585			0.135907			0.0679534	+	0.997688i	$0.478353\pi$
$102$		0			0
$103$	−14.9713			−1.47516			−0.737581	−	0.675259i	$-0.764032\pi$
$103$	−14.9713			−1.47516			−0.737581	+	0.675259i	$0.764032\pi$
$104$	−2.77826	−	4.81209i	−0.272431	−	0.471865i
$105$		0			0
$106$	12.3910	−	21.4619i	1.20352	−	2.08456i
$107$	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
$112$	−2.71255	−	2.83663i	−0.256312	−	0.268036i
$113$	1.38303	+	2.39547i	0.130104	+	0.225347i	0.923717	−	0.383077i	$-0.125135\pi$
$113$	1.38303	+	2.39547i	0.130104	+	0.225347i	−0.793612	+	0.608424i	$0.791802\pi$
$114$		0			0
$115$	10.1563			0.947082
$116$	1.07892	+	1.86875i	0.100176	+	0.173509i
$117$		0			0
$118$	−1.53058			−0.140901
$119$	−7.36162	−	7.69834i	−0.674838	−	0.705706i
$120$		0			0
$121$	7.69986			0.699988
$122$	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
$131$	−17.6138			−1.53893			−0.769463	−	0.638691i	$-0.779476\pi$
$131$	−17.6138			−1.53893			−0.769463	+	0.638691i	$0.779476\pi$
$132$		0			0
$133$	−1.19285	+	4.08429i	−0.103433	+	0.354153i
$134$	23.7719			2.05358
$135$		0			0
$136$	−3.89015	−	6.73794i	−0.333578	−	0.577774i
$137$	−8.66725			−0.740493			−0.370247	−	0.928934i	$-0.620727\pi$
$137$	−8.66725			−0.740493			−0.370247	+	0.928934i	$0.620727\pi$
$138$		0			0
$139$	1.88303	+	3.26150i	0.159716	+	0.276637i	0.934766	−	0.355263i	$-0.115609\pi$
$139$	1.88303	+	3.26150i	0.159716	+	0.276637i	−0.775050	+	0.631900i	$0.782275\pi$
$140$	8.12066	−	27.8049i	0.686321	−	2.34995i
$141$		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
$146$	−3.94691	+	6.83626i	−0.326649	+	0.565773i
$147$		0			0
$148$	11.9076	+	20.6245i	0.978797	+	1.69533i
$149$	−4.61122			−0.377766			−0.188883	−	0.982000i	$-0.560487\pi$
$149$	−4.61122			−0.377766			−0.188883	+	0.982000i	$0.560487\pi$
$150$		0			0
$151$	7.79762			0.634561			0.317281	−	0.948332i	$-0.397230\pi$
$151$	7.79762			0.634561			0.317281	+	0.948332i	$0.397230\pi$
$152$	−1.55396	+	2.69154i	−0.126043	+	0.218313i
$153$		0			0
$154$	17.4591	+	18.2577i	1.40690	+	1.47125i
$155$	−0.267565	+	0.463436i	−0.0214913	+	0.0372241i
$156$		0			0
$157$	−11.6328	+	20.1485i	−0.928395	+	1.60803i	−0.142387	+	0.989811i	$0.545478\pi$
$157$	−11.6328	+	20.1485i	−0.928395	+	1.60803i	−0.786008	+	0.618216i	$0.787856\pi$
$158$	−17.0274	+	29.4922i	−1.35462	+	2.34628i
$159$		0			0
$160$	−13.5948	+	23.5469i	−1.07476	+	1.86155i
$161$	−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	$0.243592\pi$
$164$	29.8292			2.32927
$165$		0			0
$166$	14.2210			1.10376
$167$	5.82076	+	10.0819i	0.450424	+	0.780157i	0.998412	−	0.0563288i	$-0.0179395\pi$
$167$	5.82076	+	10.0819i	0.450424	+	0.780157i	−0.547988	+	0.836486i	$0.684606\pi$
$168$		0			0
$169$	2.36648	−	4.09886i	0.182037	−	0.315297i
$170$	−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	0.956008	+	0.293341i	$0.0947672\pi$
$173$	9.62855	+	16.6771i	0.732045	+	1.26794i	−0.223963	+	0.974598i	$0.571899\pi$
$174$		0			0
$175$	−24.4156	+	5.96052i	−1.84564	+	0.450573i
$176$	−3.20747	−	5.55550i	−0.241772	−	0.418762i
$177$		0			0
$178$	0.567176			0.0425117
$179$	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	$0.762103\pi$
$182$	4.70887	−	16.1231i	0.349045	−	1.19512i
$183$		0			0
$184$	−5.15457			−0.380000
$185$	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	0.931611	−	0.363457i	$-0.118404\pi$
$191$	2.08745	+	3.61557i	0.151043	+	0.261613i	−0.780568	+	0.625070i	$0.785070\pi$
$192$		0			0
$193$	6.93686	−	12.0150i	0.499326	−	0.864858i	−0.500674	−	0.865636i	$-0.666914\pi$
$193$	6.93686	−	12.0150i	0.499326	−	0.864858i	1.00000		0.000778217i	$0.000247714\pi$
$194$	−2.33730			−0.167808
$195$		0			0
$196$	−0.899576	+	20.1066i	−0.0642554	+	1.43619i
$197$	−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	$0.685272\pi$
$200$	−18.3576			−1.29808
$201$		0			0
$202$	1.50789	+	2.61174i	0.106095	+	0.183762i
$203$	−0.556660	+	1.90599i	−0.0390698	+	0.133774i
$204$		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
$209$	−3.47721	+	6.02270i	−0.240524	+	0.416599i
$210$		0			0
$211$	2.57599	+	4.46174i	0.177338	+	0.307159i	0.940968	−	0.338496i	$-0.109918\pi$
$211$	2.57599	+	4.46174i	0.177338	+	0.307159i	−0.763630	+	0.645654i	$0.776585\pi$
$212$	32.2711			2.21639
$213$		0			0
$214$	17.8439			1.21978
$215$	−0.508416	+	0.880602i	−0.0346737	+	0.0600566i
$216$		0			0
$217$	0.104239	−	0.356912i	0.00707621	−	0.0242288i
$218$	−10.0565	+	17.4184i	−0.681114	+	1.17972i
$219$		0			0
$220$	23.6721	−	41.0013i	1.59597	−	2.76431i
$221$	−5.78780	+	10.0248i	−0.389329	+	0.674338i
$222$		0			0
$223$	7.60832	−	13.1780i	0.509490	−	0.882463i	−0.490449	−	0.871470i	$-0.663167\pi$
$223$	7.60832	−	13.1780i	0.509490	−	0.882463i	0.999940	−	0.0109935i	$-0.00349942\pi$
$224$	5.29632	−	18.1345i	0.353875	−	1.21166i
$225$		0			0
$226$	−3.05372	+	5.28920i	−0.203130	+	0.351832i
$227$	−4.28949			−0.284703			−0.142352	−	0.989816i	$-0.545466\pi$
$227$	−4.28949			−0.284703			−0.142352	+	0.989816i	$0.545466\pi$
$228$		0			0
$229$	0.971251			0.0641821			0.0320910	−	0.999485i	$-0.489783\pi$
$229$	0.971251			0.0641821			0.0320910	+	0.999485i	$0.489783\pi$
$230$	11.2126	+	19.4207i	0.739334	+	1.28056i
$231$		0			0
$232$	−0.725178	+	1.25605i	−0.0476103	+	0.0824634i
$233$	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
$238$	6.59341	−	22.5757i	0.427387	−	1.46336i
$239$	−3.34520	−	5.79405i	−0.216383	−	0.374786i	0.737317	−	0.675547i	$-0.236093\pi$
$239$	−3.34520	−	5.79405i	−0.216383	−	0.374786i	−0.953699	+	0.300761i	$0.902759\pi$
$240$		0			0
$241$	−14.9713			−0.964383			−0.482192	−	0.876066i	$-0.660159\pi$
$241$	−14.9713			−0.964383			−0.482192	+	0.876066i	$0.660159\pi$
$242$	8.50063	+	14.7235i	0.546441	+	0.946464i
$243$		0			0
$244$	6.05941			0.387914
$245$	23.6561	−	12.2822i	1.51133	−	0.784681i
$246$		0			0
$247$	4.62399			0.294217
$248$	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
$257$	8.57231			0.534726			0.267363	−	0.963596i	$-0.413848\pi$
$257$	8.57231			0.534726			0.267363	+	0.963596i	$0.413848\pi$
$258$		0			0
$259$	−6.14358	+	21.0355i	−0.381744	+	1.30708i
$260$	−31.4791			−1.95225
$261$		0			0
$262$	−19.4456	−	33.6808i	−1.20135	−	2.08081i
$263$	−5.69685			−0.351283			−0.175641	−	0.984454i	$-0.556200\pi$
$263$	−5.69685			−0.351283			−0.175641	+	0.984454i	$0.556200\pi$
$264$		0			0
$265$	−21.3689	−	37.0120i	−1.31268	−	2.27363i
$266$	−9.12680	+	2.22810i	−0.559600	+	0.136614i
$267$		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	$-0.216671\pi$
$272$	−2.98615	+	5.17216i	−0.181062	+	0.313609i
$273$		0			0
$274$	−9.56863	−	16.5733i	−0.578062	−	1.00123i
$275$	−41.0779			−2.47709
$276$		0			0
$277$	−26.5926			−1.59780			−0.798899	−	0.601466i	$-0.794584\pi$
$277$	−26.5926			−1.59780			−0.798899	+	0.601466i	$0.794584\pi$
$278$	−4.15772	+	7.20138i	−0.249363	+	0.431910i
$279$		0			0
$280$	18.9138	−	4.61739i	1.13032	−	0.275942i
$281$	−8.68065	+	15.0353i	−0.517844	+	0.896932i	0.481941	+	0.876204i	$0.339932\pi$
$281$	−8.68065	+	15.0353i	−0.517844	+	0.896932i	−0.999785	+	0.0207285i	$0.993401\pi$
$282$		0			0
$283$	−9.17771	+	15.8963i	−0.545558	+	0.944934i	0.453013	+	0.891504i	$0.350349\pi$
$283$	−9.17771	+	15.8963i	−0.545558	+	0.944934i	−0.998572	+	0.0534307i	$0.982984\pi$
$284$	5.20993	−	9.02386i	0.309152	−	0.535468i
$285$		0			0
$286$	13.7266	−	23.7751i	0.811670	−	1.40585i
$287$	18.9702	+	19.8379i	1.11977	+	1.17099i
$288$		0			0
$289$	0.395870	−	0.685667i	0.0232865	−	0.0403334i
$290$	6.30982			0.370525
$291$		0			0
$292$	−10.2793			−0.601552
$293$	5.34906	+	9.26484i	0.312495	+	0.541258i	0.978902	−	0.204331i	$-0.0655018\pi$
$293$	5.34906	+	9.26484i	0.312495	+	0.541258i	−0.666407	+	0.745588i	$0.732169\pi$
$294$		0			0
$295$	−1.31978	+	2.28592i	−0.0768403	+	0.133091i
$296$	−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
$301$	0.198071	−	0.678190i	0.0114166	−	0.0390902i
$302$	8.60856	+	14.9105i	0.495367	+	0.858000i
$303$		0			0
$304$	2.38570			0.136829
$305$	−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	$0.146533\pi$
$308$	−9.22227	+	31.5768i	−0.525488	+	1.79926i
$309$		0			0
$310$	−1.18157			−0.0671084
$311$	−6.74453	+	11.6819i	−0.382447	+	0.662418i	−0.991411	−	0.130779i	$-0.958252\pi$
$311$	−6.74453	+	11.6819i	−0.382447	+	0.662418i	0.608964	+	0.793198i	$0.291585\pi$
$312$		0			0
$313$	9.67069	+	16.7501i	0.546620	+	0.946773i	0.998503	+	0.0546962i	$0.0174190\pi$
$313$	9.67069	+	16.7501i	0.546620	+	0.946773i	−0.451883	+	0.892077i	$0.649248\pi$
$314$	−51.3701			−2.89899
$315$		0			0
$316$	−44.3459			−2.49465
$317$	−7.67882	−	13.3001i	−0.431286	−	0.747009i	0.565699	−	0.824612i	$-0.308607\pi$
$317$	−7.67882	−	13.3001i	−0.431286	−	0.747009i	−0.996984	+	0.0776033i	$0.975273\pi$
$318$		0			0
$319$	−1.62269	+	2.81058i	−0.0908532	+	0.157362i
$320$	−48.7373			−2.72450
$321$		0			0
$322$	−10.7688	−	11.2614i	−0.600121	−	0.627571i
$323$	6.47455			0.360254
$324$		0			0
$325$	13.6563	+	23.6534i	0.757516	+	1.31206i
$326$	−13.4929			−0.747304
$327$		0			0
$328$	10.0245	+	17.3630i	0.553513	+	0.958713i
$329$	14.5050	+	15.1684i	0.799686	+	0.836264i
$330$		0			0
$331$	0.619146	+	1.07239i	0.0340313	+	0.0589440i	0.882539	−	0.470238i	$-0.155832\pi$
$331$	0.619146	+	1.07239i	0.0340313	+	0.0589440i	−0.848508	+	0.529182i	$0.822499\pi$
$332$	9.25926	+	16.0375i	0.508168	+	0.880172i
$333$		0			0
$334$	−12.8522	+	22.2607i	−0.703242	+	1.21805i
$335$	20.4978	−	35.5033i	1.11992	−	1.93975i
$336$		0			0
$337$	−5.95428	−	10.3131i	−0.324350	−	0.561791i	0.657030	−	0.753864i	$-0.271812\pi$
$337$	−5.95428	−	10.3131i	−0.324350	−	0.561791i	−0.981381	+	0.192073i	$0.938479\pi$
$338$	10.4504			0.568424
$339$		0			0
$340$	−44.0774			−2.39043
$341$	0.303862	−	0.526304i	0.0164550	−	0.0285010i
$342$		0			0
$343$	−13.9440	+	12.1887i	−0.752904	+	0.658130i
$344$	0.258033	−	0.446926i	0.0139122	−	0.0240966i
$345$		0			0
$346$	−21.2598	+	36.8230i	−1.14293	+	1.97962i
$347$	−2.17339	+	3.76442i	−0.116674	+	0.202085i	−0.918448	−	0.395543i	$-0.870557\pi$
$347$	−2.17339	+	3.76442i	−0.116674	+	0.202085i	0.801774	+	0.597628i	$0.203890\pi$
$348$		0			0
$349$	−3.58780	+	6.21425i	−0.192051	+	0.332641i	−0.945930	−	0.324372i	$-0.894847\pi$
$349$	−3.58780	+	6.21425i	−0.192051	+	0.332641i	0.753879	+	0.657013i	$0.228180\pi$
$350$	−38.3523	−	40.1066i	−2.05002	−	2.14379i
$351$		0			0
$352$	15.4390	−	26.7412i	0.822903	−	1.42531i
$353$	−25.0967			−1.33576			−0.667881	−	0.744268i	$-0.732799\pi$
$353$	−25.0967			−1.33576			−0.667881	+	0.744268i	$0.732799\pi$
$354$		0			0
$355$	−13.7994			−0.732395
$356$	0.369288	+	0.639625i	0.0195722	+	0.0339001i
$357$		0			0
$358$	−3.68941	+	6.39025i	−0.194992	+	0.337735i
$359$	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
$364$	21.2485	−	5.18735i	1.11372	−	0.271891i
$365$	6.80663	+	11.7894i	0.356275	+	0.617087i
$366$		0			0
$367$	−11.1248			−0.580707			−0.290354	−	0.956919i	$-0.593773\pi$
$367$	−11.1248			−0.580707			−0.290354	+	0.956919i	$0.593773\pi$
$368$	1.97837	+	3.42664i	0.103130	+	0.178626i
$369$		0			0
$370$	69.6385			3.62033
$371$	20.5231	+	21.4619i	1.06551	+	1.11425i
$372$		0			0
$373$	16.1546			0.836452			0.418226	−	0.908343i	$-0.362652\pi$
$373$	16.1546			0.836452			0.418226	+	0.908343i	$0.362652\pi$
$374$	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
$383$	−16.4776			−0.841968			−0.420984	−	0.907068i	$-0.638315\pi$
$383$	−16.4776			−0.841968			−0.420984	+	0.907068i	$0.638315\pi$
$384$		0			0
$385$	42.3224	−	10.3321i	2.15695	−	0.526571i
$386$	30.6331			1.55918
$387$		0			0
$388$	−1.52181	−	2.63586i	−0.0772584	−	0.133815i
$389$	31.9771			1.62130			0.810651	−	0.585529i	$-0.199113\pi$
$389$	31.9771			1.62130			0.810651	+	0.585529i	$0.199113\pi$
$390$		0			0
$391$	5.36911	+	9.29956i	0.271527	+	0.470299i
$392$	−12.0060	+	6.23350i	−0.606395	+	0.314839i
$393$		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	$0.920776\pi$
$398$	−13.9715	+	24.1993i	−0.700326	+	1.21300i
$399$		0			0
$400$	7.04583	+	12.2037i	0.352291	+	0.610187i
$401$	27.5883			1.37769			0.688847	−	0.724907i	$-0.258117\pi$
$401$	27.5883			1.37769			0.688847	+	0.724907i	$0.258117\pi$
$402$		0			0
$403$	−0.404075			−0.0201284
$404$	−1.96357	+	3.40101i	−0.0976913	+	0.169206i
$405$		0			0
$406$	−4.25915	+	1.03978i	−0.211378	+	0.0516032i
$407$	−17.9088	+	31.0190i	−0.887708	+	1.53756i
$408$		0			0
$409$	5.91231	−	10.2404i	0.292345	−	0.506356i	−0.682019	−	0.731335i	$-0.738898\pi$
$409$	5.91231	−	10.2404i	0.292345	−	0.506356i	0.974364	+	0.224978i	$0.0722312\pi$
$410$	43.6121	−	75.5384i	2.15385	−	3.73058i
$411$		0			0
$412$	21.5230	−	37.2790i	1.06036	−	1.83660i
$413$	0.514163	−	1.76048i	0.0253003	−	0.0866278i
$414$		0			0
$415$	12.2624	−	21.2390i	0.601935	−	1.04258i
$416$	−20.5308			−1.00661
$417$		0			0
$418$	−15.3553			−0.751054
$419$	−4.40834	−	7.63547i	−0.215362	−	0.373017i	0.738023	−	0.674776i	$-0.235760\pi$
$419$	−4.40834	−	7.63547i	−0.215362	−	0.373017i	−0.953384	+	0.301759i	$0.902426\pi$
$420$		0			0
$421$	−9.35004	+	16.1947i	−0.455693	+	0.789284i	−0.998728	−	0.0504267i	$-0.983942\pi$
$421$	−9.35004	+	16.1947i	−0.455693	+	0.789284i	0.543035	+	0.839710i	$0.317275\pi$
$422$	−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
$427$	3.85354	+	4.02981i	0.186486	+	0.195016i
$428$	11.6181	+	20.1232i	0.561584	+	0.972692i
$429$		0			0
$430$	−2.24516			−0.108271
$431$	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	$0.707999\pi$
$434$	0.797561	−	0.194707i	0.0382841	−	0.00934621i
$435$		0			0
$436$	−26.1912			−1.25433
$437$	2.14474	−	3.71481i	0.102597	−	0.177703i
$438$		0			0
$439$	14.7262	+	25.5065i	0.702841	+	1.21736i	0.967465	+	0.253005i	$0.0814190\pi$
$439$	14.7262	+	25.5065i	0.702841	+	1.21736i	−0.264624	+	0.964352i	$0.585248\pi$
$440$	31.8215			1.51703
$441$		0			0
$442$	−25.5589			−1.21571
$443$	−16.2783	−	28.1948i	−0.773404	−	1.33957i	−0.935687	−	0.352830i	$-0.885219\pi$
$443$	−16.2783	−	28.1948i	−0.773404	−	1.33957i	0.162284	−	0.986744i	$-0.448114\pi$
$444$		0			0
$445$	0.489060	−	0.847077i	0.0231837	−	0.0401553i
$446$	33.5983			1.59092
$447$		0			0
$448$	32.8978	−	8.03126i	1.55428	−	0.379442i
$449$	−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
$452$	−7.95309			−0.374082
$453$		0			0
$454$	−4.73559	−	8.20227i	−0.222252	−	0.384952i
$455$	−20.0195	−	20.9352i	−0.938527	−	0.981456i
$456$		0			0
$457$	−12.2510	−	21.2194i	−0.573079	−	0.992602i	−0.996247	−	0.0865506i	$-0.972416\pi$
$457$	−12.2510	−	21.2194i	−0.573079	−	0.992602i	0.423169	−	0.906051i	$-0.360918\pi$
$458$	1.07226	+	1.85721i	0.0501034	+	0.0867816i
$459$		0			0
$460$	−14.6010	+	25.2896i	−0.680773	+	1.17913i
$461$	4.71554	−	8.16755i	0.219624	−	0.380401i	−0.735069	−	0.677993i	$-0.762850\pi$
$461$	4.71554	−	8.16755i	0.219624	−	0.380401i	0.954693	+	0.297592i	$0.0961835\pi$
$462$		0			0
$463$	−1.43061	−	2.47788i	−0.0664860	−	0.115157i	0.830866	−	0.556472i	$-0.187845\pi$
$463$	−1.43061	−	2.47788i	−0.0664860	−	0.115157i	−0.897352	+	0.441315i	$0.854512\pi$
$464$	1.11332			0.0516845
$465$		0			0
$466$	8.33170			0.385959
$467$	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
$470$	33.3467	−	57.7582i	1.53817	−	2.66419i
$471$		0			0
$472$	0.669817	−	1.16016i	0.0308308	−	0.0534005i
$473$	0.577385	−	1.00006i	0.0265482	−	0.0459829i
$474$		0			0
$475$	7.63836	−	13.2300i	0.350472	−	0.607035i
$476$	29.7524	−	7.26338i	1.36370	−	0.332916i
$477$		0			0
$478$	7.38619	−	12.7932i	0.337836	−	0.585150i
$479$	−34.5822			−1.58010			−0.790051	−	0.613041i	$-0.789946\pi$
$479$	−34.5822			−1.58010			−0.790051	+	0.613041i	$0.789946\pi$
$480$		0			0
$481$	23.8152			1.08588
$482$	−16.5282	−	28.6277i	−0.752840	−	1.30396i
$483$		0			0
$484$	−11.0695	+	19.1729i	−0.503159	+	0.871497i
$485$	−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
$490$	49.6021	+	31.6752i	2.24079	+	1.43094i
$491$	1.57686	+	2.73120i	0.0711627	+	0.123257i	0.899411	−	0.437104i	$-0.143996\pi$
$491$	1.57686	+	2.73120i	0.0711627	+	0.123257i	−0.828248	+	0.560361i	$0.810662\pi$
$492$		0			0
$493$	3.02144			0.136079
$494$	5.10487	+	8.84190i	0.229679	+	0.397816i
$495$		0			0
$496$	−0.208478			−0.00936094
$497$	9.31462	−	2.27396i	0.417818	−	0.102001i
$498$		0			0
$499$	28.8798			1.29284			0.646419	−	0.762983i	$-0.276266\pi$
$499$	28.8798			1.29284			0.646419	+	0.762983i	$0.276266\pi$
$500$	−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
$509$	−8.82435			−0.391133			−0.195566	−	0.980690i	$-0.562654\pi$
$509$	−8.82435			−0.391133			−0.195566	+	0.980690i	$0.562654\pi$
$510$		0			0
$511$	−6.53724	−	6.83626i	−0.289190	−	0.302418i
$512$	−16.3263			−0.721527
$513$		0			0
$514$	9.46381	+	16.3918i	0.417431	+	0.723011i
$515$	−57.0073			−2.51204
$516$		0			0
$517$	17.1515	+	29.7072i	0.754321	+	1.30652i
$518$	−47.0062	+	11.4755i	−2.06533	+	0.504205i
$519$		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	$0.118182\pi$
$524$	25.3220	−	43.8591i	1.10620	−	1.91599i
$525$		0			0
$526$	−6.28931	−	10.8934i	−0.274227	−	0.474975i
$527$	−0.565790			−0.0246462
$528$		0			0
$529$	−15.8858			−0.690686
$530$	47.1824	−	81.7223i	2.04947	−	3.54979i
$531$		0			0
$532$	−8.45516	−	8.84190i	−0.366577	−	0.383345i
$533$	14.9146	−	25.8328i	0.646023	−	1.11894i
$534$		0			0
$535$	15.3863	−	26.6498i	0.665208	−	1.15217i
$536$	−10.4031	+	18.0187i	−0.449347	+	0.778291i
$537$		0			0
$538$	17.2241	−	29.8330i	0.742582	−	1.28619i
$539$	−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	$0.0498567\pi$
$542$	67.8683			2.91519
$543$		0			0
$544$	−28.7474			−1.23254
$545$	17.3429	+	30.0388i	0.742889	+	1.28672i
$546$		0			0
$547$	−1.88962	+	3.27292i	−0.0807943	+	0.139940i	−0.903591	−	0.428395i	$-0.859079\pi$
$547$	−1.88962	+	3.27292i	−0.0807943	+	0.139940i	0.822797	+	0.568335i	$0.192412\pi$
$548$	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
$553$	−28.2023	−	29.4922i	−1.19928	−	1.25414i
$554$	−29.3582	−	50.8499i	−1.24731	−	2.16041i
$555$		0			0
$556$	−10.8283			−0.459224
$557$	−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
$560$	−10.3288	−	10.8013i	−0.436473	−	0.456437i
$561$		0			0
$562$	−38.3337			−1.61701
$563$	−12.6908	+	21.9811i	−0.534854	+	0.926394i	0.464316	+	0.885669i	$0.346300\pi$
$563$	−12.6908	+	21.9811i	−0.534854	+	0.926394i	−0.999170	+	0.0407249i	$0.987033\pi$
$564$		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	0.942642	−	0.333806i	$-0.108333\pi$
$569$	4.34702	+	7.52926i	0.182237	+	0.315643i	−0.760405	+	0.649449i	$0.775000\pi$
$570$		0			0
$571$	−4.06378	+	7.03868i	−0.170064	+	0.294560i	−0.938442	−	0.345437i	$-0.887731\pi$
$571$	−4.06378	+	7.03868i	−0.170064	+	0.294560i	0.768378	+	0.639996i	$0.221064\pi$
$572$	35.7494			1.49476
$573$		0			0
$574$	−16.9906	+	58.1754i	−0.709173	+	2.42819i
$575$	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	$0.985370\pi$
$578$	1.74816			0.0727138
$579$		0			0
$580$	4.10832	+	7.11581i	0.170589	+	0.295468i
$581$	−4.77721	+	16.3571i	−0.198192	+	0.678606i
$582$		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
$587$	15.3600	−	26.6043i	0.633975	−	1.09808i	−0.352756	−	0.935715i	$-0.614756\pi$
$587$	15.3600	−	26.6043i	0.633975	−	1.09808i	0.986731	−	0.162362i	$-0.0519111\pi$
$588$		0			0
$589$	0.113005	+	0.195731i	0.00465630	+	0.00806495i
$590$	−5.82812			−0.239940
$591$		0			0
$592$	12.2872			0.505000
$593$	−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
$596$	6.62920	−	11.4821i	0.271543	−	0.470326i
$597$		0			0
$598$	−8.46656	+	14.6645i	−0.346223	+	0.599677i
$599$	−13.6831	+	23.6999i	−0.559078	+	0.968351i	0.438496	+	0.898733i	$0.355511\pi$
$599$	−13.6831	+	23.6999i	−0.559078	+	0.968351i	−0.997574	+	0.0696182i	$0.977822\pi$
$600$		0			0
$601$	3.60908	−	6.25111i	0.147217	−	0.254988i	−0.782981	−	0.622046i	$-0.786302\pi$
$601$	3.60908	−	6.25111i	0.147217	−	0.254988i	0.930198	+	0.367058i	$0.119635\pi$
$602$	1.51549	−	0.369973i	0.0617668	−	0.0150790i
$603$		0			0
$604$	−11.2100	+	19.4164i	−0.456130	+	0.790040i
$605$	29.3194			1.19200
$606$		0			0
$607$	37.0048			1.50198			0.750989	−	0.660315i	$-0.229577\pi$
$607$	37.0048			1.50198			0.750989	+	0.660315i	$0.229577\pi$
$608$	5.74173	+	9.94496i	0.232858	+	0.403321i
$609$		0			0
$610$	8.85923	−	15.3446i	0.358700	−	0.621286i
$611$	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
$616$	−21.4796	+	5.24376i	−0.865438	+	0.211277i
$617$	−11.1209	−	19.2620i	−0.447710	−	0.775457i	0.550526	−	0.834818i	$-0.314427\pi$
$617$	−11.1209	−	19.2620i	−0.447710	−	0.775457i	−0.998237	+	0.0593607i	$0.981094\pi$
$618$		0			0
$619$	19.7805			0.795046			0.397523	−	0.917592i	$-0.369870\pi$
$619$	19.7805			0.795046			0.397523	+	0.917592i	$0.369870\pi$
$620$	−0.769316	−	1.33249i	−0.0308965	−	0.0535142i
$621$		0			0
$622$	−29.7838			−1.19422
$623$	−0.190530	+	0.652371i	−0.00763342	+	0.0261367i
$624$		0			0
$625$	17.7393			0.709571
$626$	−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
$635$	52.0041			2.06372
$636$		0			0
$637$	16.9630	+	10.8324i	0.672100	+	0.429194i
$638$	−7.16578			−0.283696
$639$		0			0
$640$	−26.6162	−	46.1006i	−1.05210	−	1.82229i
$641$	8.65682			0.341924			0.170962	−	0.985278i	$-0.445312\pi$
$641$	8.65682			0.341924			0.170962	+	0.985278i	$0.445312\pi$
$642$		0			0
$643$	−8.85782	−	15.3422i	−0.349318	−	0.605037i	0.636810	−	0.771021i	$-0.280254\pi$
$643$	−8.85782	−	15.3422i	−0.349318	−	0.605037i	−0.986129	+	0.165983i	$0.946920\pi$
$644$	5.68830	−	19.4766i	0.224150	−	0.767486i
$645$		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
$650$	−30.1531	+	52.2267i	−1.18270	+	2.04850i
$651$		0			0
$652$	−8.78523	−	15.2165i	−0.344056	−	0.595923i
$653$	36.2140			1.41717			0.708583	−	0.705628i	$-0.249335\pi$
$653$	36.2140			1.41717			0.708583	+	0.705628i	$0.249335\pi$
$654$		0			0
$655$	−67.0697			−2.62063
$656$	7.69502	−	13.3282i	0.300440	−	0.520378i
$657$		0			0
$658$	−12.9913	+	44.4821i	−0.506455	+	1.73409i
$659$	19.6707	−	34.0706i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$659$	19.6707	−	34.0706i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111219\pi$
$660$		0			0
$661$	0.830402	−	1.43830i	0.0322989	−	0.0559433i	−0.849424	−	0.527711i	$-0.823050\pi$
$661$	0.830402	−	1.43830i	0.0322989	−	0.0559433i	0.881723	+	0.471767i	$0.156384\pi$
$662$	−1.36707	+	2.36784i	−0.0531327	+	0.0920286i
$663$		0			0
$664$	−6.22343	+	10.7793i	−0.241516	+	0.418318i
$665$	−4.54211	+	15.5521i	−0.176135	+	0.603084i
$666$		0			0
$667$	1.00088	−	1.73357i	0.0387540	−	0.0671240i
$668$	−33.4722			−1.29508
$669$		0			0
$670$	90.5183			3.49703
$671$	4.55664	+	7.89233i	0.175907	+	0.304680i
$672$		0			0
$673$	−10.4154	+	18.0399i	−0.401483	+	0.695388i	−0.993905	−	0.110239i	$-0.964838\pi$
$673$	−10.4154	+	18.0399i	−0.401483	+	0.695388i	0.592423	+	0.805627i	$0.298172\pi$
$674$	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	−0.830040	−	0.557704i	$-0.811683\pi$
$677$	−23.3654	−	40.4701i	−0.898006	−	1.55539i	−0.0679653	−	0.997688i	$-0.521651\pi$
$678$		0			0
$679$	0.785163	−	2.68838i	0.0301318	−	0.103171i
$680$	−14.8129	−	25.6566i	−0.568048	−	0.983887i
$681$		0			0
$682$	1.34185			0.0513822
$683$	−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
$686$	−38.7012	−	13.2071i	−1.47762	−	0.504248i
$687$		0			0
$688$	−0.396141			−0.0151027
$689$	16.1356	−	27.9476i	0.614716	−	1.06472i
$690$		0			0
$691$	11.7985	+	20.4356i	0.448836	+	0.777407i	0.998311	−	0.0581038i	$-0.0185054\pi$
$691$	11.7985	+	20.4356i	0.448836	+	0.777407i	−0.549475	+	0.835510i	$0.685172\pi$
$692$	−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
$698$	−15.8437			−0.599693
$699$		0			0
$700$	20.2585	−	69.3646i	0.765699	−	2.62174i
$701$	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
$704$	55.3488			2.08603
$705$		0			0
$706$	−27.7067	−	47.9894i	−1.04276	−	1.80611i
$707$	−3.51059	+	0.857032i	−0.132029	+	0.0322320i
$708$		0			0
$709$	−22.9919	−	39.8231i	−0.863478	−	1.49559i	−0.868551	−	0.495601i	$-0.834948\pi$
$709$	−22.9919	−	39.8231i	−0.863478	−	1.49559i	0.00507252	−	0.999987i	$-0.498385\pi$
$710$	−15.2345	−	26.3869i	−0.571740	−	0.990282i
$711$		0			0
$712$	−0.248209	+	0.429911i	−0.00930204	+	0.0161116i
$713$	−0.187422	+	0.324625i	−0.00701901	+	0.0121573i
$714$		0			0
$715$	−23.6721	−	41.0013i	−0.885286	−	1.53336i
$716$	−9.60869			−0.359094
$717$		0			0
$718$	70.6378			2.63618
$719$	−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
$722$	−18.1207	+	31.3859i	−0.674381	+	1.16806i
$723$		0			0
$724$	28.3726	−	49.1428i	1.05446	−	1.82638i
$725$	3.56455	−	6.17398i	0.132384	−	0.229296i
$726$		0			0
$727$	12.5275	−	21.6982i	0.464619	−	0.804743i	−0.534565	−	0.845127i	$-0.679525\pi$
$727$	12.5275	−	21.6982i	0.464619	−	0.804743i	0.999184	+	0.0403837i	$0.0128580\pi$
$728$	10.1603	+	10.6251i	0.376567	+	0.393792i
$729$		0			0
$730$	−15.0290	+	26.0310i	−0.556248	+	0.963451i
$731$	−1.07509			−0.0397636
$732$		0			0
$733$	14.0125			0.517563			0.258782	−	0.965936i	$-0.416679\pi$
$733$	14.0125			0.517563			0.258782	+	0.965936i	$0.416679\pi$
$734$	−12.2817	−	21.2725i	−0.453326	−	0.785184i
$735$		0			0
$736$	−9.52280	+	16.4940i	−0.351015	+	0.607976i
$737$	−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
$742$	−18.3815	+	62.9378i	−0.674806	+	2.31052i
$743$	−0.906592	−	1.57026i	−0.0332596	−	0.0576073i	0.848916	−	0.528527i	$-0.177255\pi$
$743$	−0.906592	−	1.57026i	−0.0332596	−	0.0576073i	−0.882176	+	0.470920i	$0.843922\pi$
$744$		0			0
$745$	−17.5586			−0.643296
$746$	17.8346	+	30.8904i	0.652971	+	1.13098i
$747$		0			0
$748$	50.0567			1.83026
$749$	−5.99425	+	20.5242i	−0.219025	+	0.749938i
$750$		0			0
$751$	−29.4262			−1.07378			−0.536888	−	0.843653i	$-0.680400\pi$
$751$	−29.4262			−1.07378			−0.536888	+	0.843653i	$0.680400\pi$
$752$	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
$761$	12.8626			0.466270			0.233135	−	0.972444i	$-0.425102\pi$
$761$	12.8626			0.466270			0.233135	+	0.972444i	$0.425102\pi$
$762$		0			0
$763$	−16.6565	−	17.4184i	−0.603007	−	0.630589i
$764$	−12.0039			−0.434285
$765$		0			0
$766$	−18.1913	−	31.5082i	−0.657277	−	1.13844i
$767$	−1.99312			−0.0719673
$768$		0			0
$769$	22.3611	+	38.7305i	0.806362	+	1.39666i	0.915368	+	0.402618i	$0.131900\pi$
$769$	22.3611	+	38.7305i	0.806362	+	1.39666i	−0.109007	+	0.994041i	$0.534767\pi$
$770$	66.4806	+	69.5215i	2.39579	+	2.50538i
$771$		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
$776$	1.02286	−	1.77164i	0.0367184	−	0.0635982i
$777$		0			0
$778$	35.3026	+	61.1460i	1.26566	+	2.19219i
$779$	−16.6843			−0.597777
$780$		0			0
$781$	15.6713			0.560764
$782$	−11.8550	+	20.5334i	−0.423933	+	0.734273i
$783$		0			0
$784$	8.75190	+	5.58884i	0.312568	+	0.199601i
$785$	−44.2950	+	76.7213i	−1.58096	+	2.73830i
$786$		0			0
$787$	−16.1037	+	27.8924i	−0.574035	+	0.994257i	0.422111	+	0.906544i	$0.361289\pi$
$787$	−16.1037	+	27.8924i	−0.574035	+	0.994257i	−0.996146	+	0.0877130i	$0.972044\pi$
$788$	10.7609	−	18.6384i	0.383341	−	0.663966i
$789$		0			0
$790$	−64.8365	+	112.300i	−2.30678	+	3.99546i
$791$	−5.05785	−	5.28920i	−0.179836	−	0.188062i
$792$		0			0
$793$	3.02970	−	5.24760i	0.107588	−	0.186348i
$794$	−61.4085			−2.17931
$795$		0			0
$796$	−36.3872			−1.28971
$797$	−16.1389	−	27.9534i	−0.571669	−	0.990160i	−0.996395	−	0.0848377i	$-0.972963\pi$
$797$	−16.1389	−	27.9534i	−0.571669	−	0.990160i	0.424726	−	0.905322i	$-0.360371\pi$
$798$		0			0
$799$	15.9680	−	27.6574i	0.564907	−	0.978448i
$800$	−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
$805$	−26.1045	+	6.37282i	−0.920061	+	0.224612i
$806$	−0.446098	−	0.772664i	−0.0157131	−	0.0272159i
$807$		0			0
$808$	−2.63955			−0.0928591
$809$	−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	$0.574431\pi$
$812$	−3.94572	−	4.12620i	−0.138468	−	0.144801i
$813$		0			0
$814$	−79.0853			−2.77194
$815$	−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	0.927584	−	0.373616i	$-0.121882\pi$
$821$	4.01806	+	6.95948i	0.140231	+	0.242888i	−0.787352	+	0.616503i	$0.788549\pi$
$822$		0			0
$823$	−9.78282	+	16.9443i	−0.341008	+	0.590643i	−0.984620	−	0.174709i	$-0.944102\pi$
$823$	−9.78282	+	16.9443i	−0.341008	+	0.590643i	0.643612	+	0.765352i	$0.277435\pi$
$824$	28.9325			1.00791
$825$		0			0
$826$	3.93400	−	0.960398i	0.136881	−	0.0334165i
$827$	−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	$-0.368770\pi$
$830$	54.1504			1.87959
$831$		0			0
$832$	−18.4007	−	31.8709i	−0.637928	−	1.10492i
$833$	23.7518	+	15.1676i	0.822952	+	0.525525i
$834$		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
$839$	17.7986	−	30.8281i	0.614476	−	1.06430i	−0.376000	−	0.926620i	$-0.622701\pi$
$839$	17.7986	−	30.8281i	0.614476	−	1.06430i	0.990476	−	0.137684i	$-0.0439659\pi$
$840$		0			0
$841$	14.2184	+	24.6270i	0.490289	+	0.849205i
$842$	−41.2897			−1.42294
$843$		0			0
$844$	−14.8132			−0.509891
$845$	9.01105	−	15.6076i	0.309990	−	0.536918i
$846$		0			0
$847$	−19.7907	+	4.83146i	−0.680017	+	0.166011i
$848$	8.32497	−	14.4193i	0.285881	−	0.495160i
$849$		0			0
$850$	−42.2207	+	73.1283i	−1.44816	+	2.50828i
$851$	11.0462	−	19.1325i	0.378658	−	0.655855i
$852$		0			0
$853$	−16.6973	+	28.9206i	−0.571705	+	0.990222i	0.424686	+	0.905341i	$0.360384\pi$
$853$	−16.6973	+	28.9206i	−0.571705	+	0.990222i	−0.996391	+	0.0848812i	$0.972949\pi$
$854$	−3.45141	+	11.8176i	−0.118105	+	0.404389i
$855$		0			0
$856$	−7.80890	+	13.5254i	−0.266903	+	0.462289i
$857$	−25.8147			−0.881814			−0.440907	−	0.897553i	$-0.645343\pi$
$857$	−25.8147			−0.881814			−0.440907	+	0.897553i	$0.645343\pi$
$858$		0			0
$859$	−43.0007			−1.46716			−0.733582	−	0.679601i	$-0.762153\pi$
$859$	−43.0007			−1.46716			−0.733582	+	0.679601i	$0.762153\pi$
$860$	−1.46182	−	2.53195i	−0.0498477	−	0.0863387i
$861$		0			0
$862$	−18.3478	+	31.7794i	−0.624929	+	1.08241i
$863$	−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
$868$	0.738868	+	0.772664i	0.0250788	+	0.0262259i
$869$	−33.3479	−	57.7602i	−1.13125	−	1.95938i
$870$		0			0
$871$	30.9557			1.04889
$872$	−8.80194	−	15.2454i	−0.298071	−	0.516274i
$873$		0			0
$874$	9.47117			0.320367
$875$	−44.0341	+	10.7500i	−1.48863	+	0.363415i
$876$		0			0
$877$	14.6841			0.495846			0.247923	−	0.968780i	$-0.420252\pi$
$877$	14.6841			0.495846			0.247923	+	0.968780i	$0.420252\pi$
$878$	−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
$887$	−26.4248			−0.887259			−0.443630	−	0.896210i	$-0.646309\pi$
$887$	−26.4248			−0.887259			−0.443630	+	0.896210i	$0.646309\pi$
$888$		0			0
$889$	−35.1029	+	8.56959i	−1.17731	+	0.287415i
$890$	2.15969			0.0723928
$891$		0			0
$892$	21.8758	+	37.8900i	0.732455	+	1.26865i
$893$	−12.7572			−0.426902
$894$		0			0
$895$	6.36256	+	11.0203i	0.212677	+	0.368367i
$896$	25.5628	+	26.7321i	0.853993	+	0.893056i
$897$		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
$902$	−49.5283	+	85.7856i	−1.64911	+	2.85635i
$903$		0			0
$904$	−2.67276	−	4.62935i	−0.0888946	−	0.153970i
$905$	−75.1496			−2.49806
$906$		0			0
$907$	−0.450052			−0.0149437			−0.00747187	−	0.999972i	$-0.502378\pi$
$907$	−0.450052			−0.0149437			−0.00747187	+	0.999972i	$0.502378\pi$
$908$	6.16667	−	10.6810i	0.204648	−	0.354461i
$909$		0			0
$910$	17.9304	−	61.3932i	0.594386	−	2.03517i
$911$	2.37220	−	4.10877i	0.0785944	−	0.136129i	−0.824049	−	0.566518i	$-0.808290\pi$
$911$	2.37220	−	4.10877i	0.0785944	−	0.136129i	0.902644	+	0.430389i	$0.141623\pi$
$912$		0			0
$913$	−13.9258	+	24.1202i	−0.460877	+	0.798262i
$914$	27.0502	−	46.8523i	0.894742	−	1.54974i
$915$		0			0
$916$	−1.39629	+	2.41845i	−0.0461348	+	0.0799079i
$917$	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	$0.920001\pi$
$920$	−19.6275			−0.647099
$921$		0			0
$922$	20.8238			0.685794
$923$	−5.20993	−	9.02386i	−0.171487	−	0.297024i
$924$		0			0
$925$	39.3402	−	68.1393i	1.29350	−	2.24041i
$926$	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	0.952702	+	0.303906i	$0.0982909\pi$
$929$	22.5409	+	39.0419i	0.739541	+	1.28092i	−0.213160	+	0.977017i	$0.568376\pi$
$930$		0			0
$931$	0.503158	−	11.2462i	0.0164903	−	0.368579i
$932$	5.42476	+	9.39596i	0.177694	+	0.307775i
$933$		0			0
$934$	17.0079			0.556517
$935$	−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	$0.397886\pi$
$938$	−61.1001	+	14.9162i	−1.99499	+	0.487032i
$939$		0			0
$940$	86.8480			2.83267
$941$	5.27697	−	9.13997i	0.172024	−	0.297955i	−0.767103	−	0.641524i	$-0.778303\pi$
$941$	5.27697	−	9.13997i	0.172024	−	0.297955i	0.939127	+	0.343569i	$0.111636\pi$
$942$		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	0.934233	+	0.356664i	$0.116086\pi$
$947$	23.8800	+	41.3614i	0.775996	+	1.34407i	−0.158236	+	0.987401i	$0.550581\pi$
$948$		0			0
$949$	−5.13966	+	8.90215i	−0.166840	+	0.288976i
$950$	33.7309			1.09438
$951$		0			0
$952$	14.2266	+	14.8773i	0.461087	+	0.482178i
$953$	−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
$956$	19.2365			0.622154
$957$		0			0
$958$	−38.1787	−	66.1274i	−1.23350	−	2.13648i
$959$	22.2772	−	5.43847i	0.719367	−	0.175617i
$960$		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
$965$	26.4141	−	45.7505i	0.850299	−	1.47276i
$966$		0			0
$967$	4.90887	+	8.50242i	0.157859	+	0.273419i	0.934096	−	0.357021i	$-0.116208\pi$
$967$	4.90887	+	8.50242i	0.157859	+	0.273419i	−0.776238	+	0.630441i	$0.782874\pi$
$968$	−14.8803			−0.478271
$969$		0			0
$970$	−8.89994			−0.285760
$971$	−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
$974$	20.3529	−	35.2523i	0.652149	−	1.12956i
$975$		0			0
$976$	1.56314	−	2.70744i	0.0500350	−	0.0866631i
$977$	−19.9951	+	34.6326i	−0.639701	+	1.10799i	0.345797	+	0.938309i	$0.387609\pi$
$977$	−19.9951	+	34.6326i	−0.639701	+	1.10799i	−0.985498	+	0.169685i	$0.945725\pi$
$978$		0			0
$979$	−0.555404	+	0.961988i	−0.0177508	+	0.0307453i
$980$	−3.42539	+	76.5617i	−0.109420	+	2.44567i
$981$		0			0
$982$	−3.48170	+	6.03048i	−0.111106	+	0.192440i
$983$	46.2286			1.47446			0.737231	−	0.675641i	$-0.236133\pi$
$983$	46.2286			1.47446			0.737231	+	0.675641i	$0.236133\pi$
$984$		0			0
$985$	−28.5020			−0.908151
$986$	3.33567	+	5.77754i	0.106229	+	0.183994i
$987$		0			0
$988$	−6.64755	+	11.5139i	−0.211487	+	0.366306i
$989$	−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
$994$	14.6315	+	15.3008i	0.464084	+	0.485312i
$995$	24.0944	+	41.7327i	0.763844	+	1.32302i
$996$		0			0
$997$	43.8546			1.38889			0.694444	−	0.719547i	$-0.255650\pi$
$997$	43.8546			1.38889			0.694444	+	0.719547i	$0.255650\pi$
$998$	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.g.k.541.4		8
3.2	odd	2		567.2.g.j.541.1		8
7.4	even	3		567.2.h.j.298.1		8
9.2	odd	6		567.2.e.c.163.1	✓	8
9.4	even	3		567.2.h.j.352.1		8
9.5	odd	6		567.2.h.k.352.4		8
9.7	even	3		567.2.e.d.163.4	yes	8
21.11	odd	6		567.2.h.k.298.4		8
63.2	odd	6		3969.2.a.x.1.4		4
63.4	even	3	inner	567.2.g.k.109.4		8
63.11	odd	6		567.2.e.c.487.1	yes	8
63.16	even	3		3969.2.a.s.1.1		4
63.25	even	3		567.2.e.d.487.4	yes	8
63.32	odd	6		567.2.g.j.109.1		8
63.47	even	6		3969.2.a.w.1.4		4
63.61	odd	6		3969.2.a.t.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.1	✓	8	9.2	odd	6
567.2.e.c.487.1	yes	8	63.11	odd	6
567.2.e.d.163.4	yes	8	9.7	even	3
567.2.e.d.487.4	yes	8	63.25	even	3
567.2.g.j.109.1		8	63.32	odd	6
567.2.g.j.541.1		8	3.2	odd	2
567.2.g.k.109.4		8	63.4	even	3	inner
567.2.g.k.541.4		8	1.1	even	1	trivial
567.2.h.j.298.1		8	7.4	even	3
567.2.h.j.352.1		8	9.4	even	3
567.2.h.k.298.4		8	21.11	odd	6
567.2.h.k.352.4		8	9.5	odd	6
3969.2.a.s.1.1		4	63.16	even	3
3969.2.a.t.1.1		4	63.61	odd	6
3969.2.a.w.1.4		4	63.47	even	6
3969.2.a.x.1.4		4	63.2	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10400 + 1.91218i) q^{2} +(-1.43762 + 2.49004i) q^{4} +3.80779 q^{5} +(-2.57027 + 0.627473i) q^{7} -1.93254 q^{8} +O(q^{10})\)	\(q+(1.10400 + 1.91218i) q^{2} +(-1.43762 + 2.49004i) q^{4} +3.80779 q^{5} +(-2.57027 + 0.627473i) q^{7} -1.93254 q^{8} +(4.20379 + 7.28117i) q^{10} -4.32433 q^{11} +(1.43762 + 2.49004i) q^{13} +(-4.03741 - 4.22209i) q^{14} +(0.741726 + 1.28471i) q^{16} +(2.01297 + 3.48657i) q^{17} +(0.804103 - 1.39275i) q^{19} +(-5.47416 + 9.48152i) q^{20} +(-4.77406 - 8.26891i) q^{22} +2.66725 q^{23} +9.49923 q^{25} +(-3.17427 + 5.49799i) q^{26} +(2.13264 - 7.30213i) q^{28} +(0.375246 - 0.649945i) q^{29} +(-0.0702679 + 0.121708i) q^{31} +(-3.57027 + 6.18389i) q^{32} +(-4.44464 + 7.69834i) q^{34} +(-9.78703 + 2.38928i) q^{35} +(4.14141 - 7.17313i) q^{37} +3.55091 q^{38} -7.35870 q^{40} +(-5.18724 - 8.98456i) q^{41} +(-0.133520 + 0.231264i) q^{43} +(6.21676 - 10.7677i) q^{44} +(2.94464 + 5.10026i) q^{46} +(-3.96627 - 6.86978i) q^{47} +(6.21255 - 3.22555i) q^{49} +(10.4871 + 18.1643i) q^{50} -8.26704 q^{52} +(-5.61189 - 9.72008i) q^{53} -16.4661 q^{55} +(4.96715 - 1.21262i) q^{56} +1.65708 q^{58} +(-0.346599 + 0.600327i) q^{59} +(-1.05372 - 1.82510i) q^{61} -0.310302 q^{62} -12.7994 q^{64} +(5.47416 + 9.48152i) q^{65} +(5.38314 - 9.32387i) q^{67} -11.5756 q^{68} +(-15.3736 - 16.0768i) q^{70} -3.62399 q^{71} +(1.78756 + 3.09614i) q^{73} +18.2884 q^{74} +(2.31199 + 4.00449i) q^{76} +(11.1147 - 2.71340i) q^{77} +(7.71168 + 13.3570i) q^{79} +(2.82433 + 4.89189i) q^{80} +(11.4534 - 19.8379i) q^{82} +(3.22034 - 5.57779i) q^{83} +(7.66497 + 13.2761i) q^{85} -0.589624 q^{86} +8.35695 q^{88} +(0.128437 - 0.222459i) q^{89} +(-5.25751 - 5.49799i) q^{91} +(-3.83450 + 6.64155i) q^{92} +(8.75751 - 15.1684i) q^{94} +(3.06185 - 5.30328i) q^{95} +(-0.529281 + 0.916742i) q^{97} +(13.0265 + 8.31853i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8	\( 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8} + 7 q^{10} - 10 q^{11} + 5 q^{13} - 7 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} + 24 q^{23} + 16 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} + 40 q^{38} - 36 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 2 q^{49} + 38 q^{50} - 50 q^{52} - 12 q^{53} - 52 q^{55} + 33 q^{56} - 14 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} - 102 q^{68} - 46 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} + 16 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} + 44 q^{86} + 36 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} + 15 q^{94} - 16 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^4 - 4 * q^5 - 2 * q^7 + 6 * q^8 + 7 * q^10 - 10 * q^11 + 5 * q^13 - 7 * q^14 + q^16 + 6 * q^17 + 8 * q^19 - 8 * q^20 + 7 * q^22 + 24 * q^23 + 16 * q^25 + q^26 + 5 * q^28 - 10 * q^29 + 18 * q^31 - 10 * q^32 - 23 * q^35 + 40 * q^38 - 36 * q^40 - 5 * q^41 + 7 * q^43 + 13 * q^44 - 12 * q^46 - 21 * q^47 + 2 * q^49 + 38 * q^50 - 50 * q^52 - 12 * q^53 - 52 * q^55 + 33 * q^56 - 14 * q^58 + 6 * q^59 + 20 * q^61 - 36 * q^62 - 46 * q^64 + 8 * q^65 + 5 * q^67 - 102 * q^68 - 46 * q^70 + 18 * q^71 + 6 * q^73 - 5 * q^76 + 16 * q^77 + 10 * q^79 - 2 * q^80 + 35 * q^82 + 9 * q^83 + 9 * q^85 + 44 * q^86 + 36 * q^88 - 22 * q^89 + 13 * q^91 - 36 * q^92 + 15 * q^94 - 16 * q^95 + 9 * q^97 - 11 * q^98

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