LMFDB - Embedded newform 567.2.g.j.541.1

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			541.1
Root			$-1.54162 + 1.88572i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.j.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$-0.881558\pi$
$2$	−1.10400	−	1.91218i	−0.780644	−	1.35212i	0.150922	−	0.988546i	$-0.451776\pi$
$3$		0			0
$3$		0			0
$4$	−1.43762	+	2.49004i	−0.718812	+	1.24502i
$5$	−3.80779			−1.70289			−0.851447	−	0.524441i	$-0.824274\pi$
$5$	−3.80779			−1.70289			−0.851447	+	0.524441i	$0.824274\pi$
$6$		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	$-0.273965\pi$
$11$	4.32433			1.30384			0.651918	+	0.758290i	$0.273965\pi$
$12$		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	0.511690	−	0.859170i	$-0.329020\pi$
$17$	−2.01297	−	3.48657i	−0.488218	−	0.845618i	−0.999908	+	0.0135517i	$0.995686\pi$
$18$		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	$-0.589698\pi$
$23$	−2.66725			−0.556160			−0.278080	+	0.960558i	$0.589698\pi$
$24$		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	−0.898761	−	0.438439i	$-0.855532\pi$
$29$	−0.375246	+	0.649945i	−0.0696815	+	0.120692i	0.829080	+	0.559131i	$0.188865\pi$
$30$		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	$0.133926\pi$
$41$	5.18724	+	8.98456i	0.810111	+	1.40315i	−0.102675	+	0.994715i	$0.532740\pi$
$42$		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	$0.0297106\pi$
$47$	3.96627	+	6.86978i	0.578540	+	1.00206i	−0.417107	+	0.908857i	$0.636956\pi$
$48$		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	$0.113503\pi$
$53$	5.61189	+	9.72008i	0.770852	+	1.33516i	−0.166244	+	0.986085i	$0.553164\pi$
$54$		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	−0.842582	−	0.538569i	$-0.818965\pi$
$59$	0.346599	−	0.600327i	0.0451234	−	0.0781560i	0.887705	+	0.460413i	$0.152299\pi$
$60$		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	$-0.431010\pi$
$71$	3.62399			0.430088			0.215044	+	0.976604i	$0.431010\pi$
$72$		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	−0.986856	−	0.161601i	$-0.948334\pi$
$83$	−3.22034	+	5.57779i	−0.353478	+	0.612241i	0.633378	+	0.773842i	$0.281668\pi$
$84$		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	−0.872752	−	0.488163i	$-0.837667\pi$
$89$	−0.128437	+	0.222459i	−0.0136143	+	0.0235806i	0.859138	+	0.511744i	$0.171000\pi$
$90$		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	$-0.521647\pi$
$101$	−1.36585			−0.135907			−0.0679534	+	0.997688i	$0.521647\pi$
$102$		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	−0.992533	−	0.121974i	$-0.961077\pi$
$107$	−4.04075	+	6.99878i	−0.390634	+	0.676597i	0.601900	+	0.798572i	$0.294411\pi$
$108$		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	0.793612	−	0.608424i	$-0.208198\pi$
$113$	−1.38303	−	2.39547i	−0.130104	−	0.225347i	−0.923717	+	0.383077i	$0.874865\pi$
$114$		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	$-0.220524\pi$
$131$	17.6138			1.53893			0.769463	+	0.638691i	$0.220524\pi$
$132$		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	$-0.379273\pi$
$137$	8.66725			0.740493			0.370247	+	0.928934i	$0.379273\pi$
$138$		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	$-0.439513\pi$
$149$	4.61122			0.377766			0.188883	+	0.982000i	$0.439513\pi$
$150$		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	0.547988	−	0.836486i	$-0.315394\pi$
$167$	−5.82076	−	10.0819i	−0.450424	−	0.780157i	−0.998412	+	0.0563288i	$0.982060\pi$
$168$		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	$-0.905233\pi$
$173$	−9.62855	−	16.6771i	−0.732045	−	1.26794i	0.223963	−	0.974598i	$-0.428101\pi$
$174$		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	0.796799	−	0.604244i	$-0.206525\pi$
$179$	−1.67093	−	2.89414i	−0.124891	−	0.216318i	−0.921690	+	0.387926i	$0.873192\pi$
$180$		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	0.780568	−	0.625070i	$-0.214930\pi$
$191$	−2.08745	−	3.61557i	−0.151043	−	0.261613i	−0.931611	+	0.363457i	$0.881596\pi$
$192$		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	$-0.414083\pi$
$197$	7.48520			0.533299			0.266649	+	0.963794i	$0.414083\pi$
$198$		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	$-0.454534\pi$
$227$	4.28949			0.284703			0.142352	+	0.989816i	$0.454534\pi$
$228$		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	−0.921186	−	0.389123i	$-0.872778\pi$
$233$	−1.88671	+	3.26788i	−0.123603	+	0.214086i	0.797583	+	0.603209i	$0.206111\pi$
$234$		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	0.953699	−	0.300761i	$-0.0972407\pi$
$239$	3.34520	+	5.79405i	0.216383	+	0.374786i	−0.737317	+	0.675547i	$0.763907\pi$
$240$		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	$-0.318803\pi$
$251$	17.0787			1.07800			0.538999	+	0.842307i	$0.318803\pi$
$252$		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	$-0.586152\pi$
$257$	−8.57231			−0.534726			−0.267363	+	0.963596i	$0.586152\pi$
$258$		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	$-0.443800\pi$
$263$	5.69685			0.351283			0.175641	+	0.984454i	$0.443800\pi$
$264$		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	0.999610	−	0.0279249i	$-0.00888992\pi$
$269$	7.80077	+	13.5113i	0.475621	+	0.823800i	−0.523989	+	0.851725i	$0.675557\pi$
$270$		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	$-0.660068\pi$
$281$	8.68065	−	15.0353i	0.517844	−	0.896932i	0.999785	−	0.0207285i	$-0.00659857\pi$
$282$		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	0.666407	−	0.745588i	$-0.267831\pi$
$293$	−5.34906	−	9.26484i	−0.312495	−	0.541258i	−0.978902	+	0.204331i	$0.934498\pi$
$294$		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	−0.608964	−	0.793198i	$-0.708415\pi$
$311$	6.74453	−	11.6819i	0.382447	−	0.662418i	0.991411	+	0.130779i	$0.0417480\pi$
$312$		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	0.996984	−	0.0776033i	$-0.0247268\pi$
$317$	7.67882	+	13.3001i	0.431286	+	0.747009i	−0.565699	+	0.824612i	$0.691393\pi$
$318$		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	−0.801774	−	0.597628i	$-0.796110\pi$
$347$	2.17339	−	3.76442i	0.116674	−	0.202085i	0.918448	+	0.395543i	$0.129443\pi$
$348$		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	$-0.267201\pi$
$353$	25.0967			1.33576			0.667881	+	0.744268i	$0.267201\pi$
$354$		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	$0.486609\pi$
$359$	−15.9959	+	27.7057i	−0.844231	+	1.46225i	−0.886287	+	0.463136i	$0.846724\pi$
$360$		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	$-0.361685\pi$
$383$	16.4776			0.841968			0.420984	+	0.907068i	$0.361685\pi$
$384$		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	$-0.800887\pi$
$389$	−31.9771			−1.62130			−0.810651	+	0.585529i	$0.800887\pi$
$390$		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	$-0.741883\pi$
$401$	−27.5883			−1.37769			−0.688847	+	0.724907i	$0.741883\pi$
$402$		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	0.953384	−	0.301759i	$-0.0975737\pi$
$419$	4.40834	+	7.63547i	0.215362	+	0.373017i	−0.738023	+	0.674776i	$0.764240\pi$
$420$		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	0.593493	−	0.804839i	$-0.297749\pi$
$431$	−8.30972	−	14.3929i	−0.400265	−	0.693279i	−0.993758	+	0.111560i	$0.964415\pi$
$432$		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	$0.114781\pi$
$443$	16.2783	+	28.1948i	0.773404	+	1.33957i	−0.162284	+	0.986744i	$0.551886\pi$
$444$		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	$-0.498709\pi$
$449$	0.171881			0.00811158			0.00405579	+	0.999992i	$0.498709\pi$
$450$		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	−0.954693	−	0.297592i	$-0.903817\pi$
$461$	−4.71554	+	8.16755i	−0.219624	+	0.380401i	0.735069	+	0.677993i	$0.237150\pi$
$462$		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	−0.941272	−	0.337649i	$-0.890368\pi$
$467$	−3.85144	+	6.67089i	−0.178223	+	0.308692i	0.763049	+	0.646341i	$0.223702\pi$
$468$		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	$-0.210054\pi$
$479$	34.5822			1.58010			0.790051	+	0.613041i	$0.210054\pi$
$480$		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	0.828248	−	0.560361i	$-0.189338\pi$
$491$	−1.57686	−	2.73120i	−0.0711627	−	0.123257i	−0.899411	+	0.437104i	$0.856004\pi$
$492$		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	$-0.341092\pi$
$503$	21.4742			0.957487			0.478744	+	0.877955i	$0.341092\pi$
$504$		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	$-0.437346\pi$
$509$	8.82435			0.391133			0.195566	+	0.980690i	$0.437346\pi$
$510$		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	$-0.941461\pi$
$521$	−14.8351	−	25.6952i	−0.649939	−	1.12573i	0.333198	−	0.942857i	$-0.391872\pi$
$522$		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	0.961562	−	0.274587i	$-0.0885411\pi$
$557$	5.73458	+	9.93258i	0.242982	+	0.420857i	−0.718580	+	0.695444i	$0.755208\pi$
$558$		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	$-0.653700\pi$
$563$	12.6908	−	21.9811i	0.534854	−	0.926394i	0.999170	−	0.0407249i	$-0.0129667\pi$
$564$		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	$-0.225000\pi$
$569$	−4.34702	−	7.52926i	−0.182237	−	0.315643i	−0.942642	+	0.333806i	$0.891667\pi$
$570$		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	$0.385244\pi$
$587$	−15.3600	+	26.6043i	−0.633975	+	1.09808i	−0.986731	+	0.162362i	$0.948089\pi$
$588$		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	$-0.473278\pi$
$593$	22.0358	−	38.1671i	0.904901	−	1.56733i	0.821050	−	0.570856i	$-0.193388\pi$
$594$		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	$-0.644489\pi$
$599$	13.6831	−	23.6999i	0.559078	−	0.968351i	0.997574	−	0.0696182i	$-0.0221781\pi$
$600$		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	0.998237	−	0.0593607i	$-0.0189062\pi$
$617$	11.1209	+	19.2620i	0.447710	+	0.775457i	−0.550526	+	0.834818i	$0.685573\pi$
$618$		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	$-0.554688\pi$
$641$	−8.65682			−0.341924			−0.170962	+	0.985278i	$0.554688\pi$
$642$		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	0.960108	−	0.279631i	$-0.0902121\pi$
$647$	6.05092	+	10.4805i	0.237886	+	0.412031i	−0.722221	+	0.691662i	$0.756879\pi$
$648$		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	$-0.750665\pi$
$653$	−36.2140			−1.41717			−0.708583	+	0.705628i	$0.750665\pi$
$654$		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	$0.444552\pi$
$659$	−19.6707	+	34.0706i	−0.766261	+	1.32720i	−0.939577	+	0.342337i	$0.888781\pi$
$660$		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	$0.188317\pi$
$677$	23.3654	+	40.4701i	0.898006	+	1.55539i	0.0679653	+	0.997688i	$0.478349\pi$
$678$		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	0.994278	−	0.106820i	$-0.0340669\pi$
$683$	10.5747	+	18.3159i	0.404630	+	0.700840i	−0.589648	+	0.807660i	$0.700734\pi$
$684$		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	$-0.792971\pi$
$701$	−42.1420			−1.59168			−0.795841	+	0.605505i	$0.792971\pi$
$702$		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	$-0.621974\pi$
$719$	16.5249	−	28.6220i	0.616275	−	1.06742i	0.990159	−	0.139944i	$-0.0446922\pi$
$720$		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	0.882176	−	0.470920i	$-0.156078\pi$
$743$	0.906592	+	1.57026i	0.0332596	+	0.0576073i	−0.848916	+	0.528527i	$0.822745\pi$
$744$		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	$-0.574898\pi$
$761$	−12.8626			−0.466270			−0.233135	+	0.972444i	$0.574898\pi$
$762$		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	0.944788	−	0.327681i	$-0.106267\pi$
$773$	5.24400	+	9.08288i	0.188614	+	0.326688i	−0.756175	+	0.654370i	$0.772934\pi$
$774$		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	$0.0270372\pi$
$797$	16.1389	+	27.9534i	0.571669	+	0.990160i	−0.424726	+	0.905322i	$0.639629\pi$
$798$		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	$0.00991818\pi$
$809$	14.9820	+	25.9495i	0.526737	+	0.912336i	−0.472777	+	0.881182i	$0.656748\pi$
$810$		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	0.787352	−	0.616503i	$-0.211451\pi$
$821$	−4.01806	−	6.95948i	−0.140231	−	0.242888i	−0.927584	+	0.373616i	$0.878118\pi$
$822$		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	$-0.206583\pi$
$827$	45.8218			1.59338			0.796690	+	0.604389i	$0.206583\pi$
$828$		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	$0.377299\pi$
$839$	−17.7986	+	30.8281i	−0.614476	+	1.06430i	−0.990476	+	0.137684i	$0.956034\pi$
$840$		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	$-0.354657\pi$
$857$	25.8147			0.881814			0.440907	+	0.897553i	$0.354657\pi$
$858$		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	−0.623039	−	0.782191i	$-0.714102\pi$
$863$	10.7483	−	18.6166i	0.365877	−	0.633718i	0.988917	+	0.148473i	$0.0474357\pi$
$864$		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	$-0.718378\pi$
$881$	−37.6060			−1.26698			−0.633490	+	0.773751i	$0.718378\pi$
$882$		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	$-0.353691\pi$
$887$	26.4248			0.887259			0.443630	+	0.896210i	$0.353691\pi$
$888$		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	−0.902644	−	0.430389i	$-0.858377\pi$
$911$	−2.37220	+	4.10877i	−0.0785944	+	0.136129i	0.824049	+	0.566518i	$0.191710\pi$
$912$		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	$-0.901709\pi$
$929$	−22.5409	−	39.0419i	−0.739541	−	1.28092i	0.213160	−	0.977017i	$-0.431624\pi$
$930$		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	−0.939127	−	0.343569i	$-0.888364\pi$
$941$	−5.27697	+	9.13997i	−0.172024	+	0.297955i	0.767103	+	0.641524i	$0.221697\pi$
$942$		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	$-0.883914\pi$
$947$	−23.8800	−	41.3614i	−0.775996	−	1.34407i	0.158236	−	0.987401i	$-0.449419\pi$
$948$		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	$-0.163121\pi$
$953$	53.8101			1.74308			0.871540	+	0.490324i	$0.163121\pi$
$954$		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	−0.609462	−	0.792815i	$-0.708615\pi$
$971$	11.8993	−	20.6102i	0.381867	−	0.661413i	0.991329	+	0.131402i	$0.0419479\pi$
$972$		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	$-0.612391\pi$
$977$	19.9951	−	34.6326i	0.639701	−	1.10799i	0.985498	−	0.169685i	$-0.0542752\pi$
$978$		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	$-0.763867\pi$
$983$	−46.2286			−1.47446			−0.737231	+	0.675641i	$0.763867\pi$
$984$		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.j.541.1		8
3.2	odd	2		567.2.g.k.541.4		8
7.4	even	3		567.2.h.k.298.4		8
9.2	odd	6		567.2.e.d.163.4	yes	8
9.4	even	3		567.2.h.k.352.4		8
9.5	odd	6		567.2.h.j.352.1		8
9.7	even	3		567.2.e.c.163.1	✓	8
21.11	odd	6		567.2.h.j.298.1		8
63.2	odd	6		3969.2.a.s.1.1		4
63.4	even	3	inner	567.2.g.j.109.1		8
63.11	odd	6		567.2.e.d.487.4	yes	8
63.16	even	3		3969.2.a.x.1.4		4
63.25	even	3		567.2.e.c.487.1	yes	8
63.32	odd	6		567.2.g.k.109.4		8
63.47	even	6		3969.2.a.t.1.1		4
63.61	odd	6		3969.2.a.w.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.1	✓	8	9.7	even	3
567.2.e.c.487.1	yes	8	63.25	even	3
567.2.e.d.163.4	yes	8	9.2	odd	6
567.2.e.d.487.4	yes	8	63.11	odd	6
567.2.g.j.109.1		8	63.4	even	3	inner
567.2.g.j.541.1		8	1.1	even	1	trivial
567.2.g.k.109.4		8	63.32	odd	6
567.2.g.k.541.4		8	3.2	odd	2
567.2.h.j.298.1		8	21.11	odd	6
567.2.h.j.352.1		8	9.5	odd	6
567.2.h.k.298.4		8	7.4	even	3
567.2.h.k.352.4		8	9.4	even	3
3969.2.a.s.1.1		4	63.2	odd	6
3969.2.a.t.1.1		4	63.47	even	6
3969.2.a.w.1.4		4	63.61	odd	6
3969.2.a.x.1.4		4	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.g (of order \(3\), degree \(2\), not minimal)

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