LMFDB - Embedded newform 567.2.e.e.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.4
Root			$-0.335166 + 0.580525i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.e.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(0.712469 - 1.23403i) q^{5} +(0.145107 - 2.64177i) q^{7} +2.38012 q^{8} +(-0.477591 - 0.827212i) q^{10} +(-2.46539 - 4.27018i) q^{11} +2.75460 q^{13} +(-1.48498 - 0.969670i) q^{14} +(-0.752918 + 1.30409i) q^{16} +(-0.559839 - 0.969670i) q^{17} +(-2.00752 + 3.47713i) q^{19} +2.20958 q^{20} -3.30526 q^{22} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(0.923251 - 1.59912i) q^{26} +(3.66015 - 1.85337i) q^{28} +6.81109 q^{29} +(-1.25292 - 2.17012i) q^{31} +(2.88483 + 4.99666i) q^{32} -0.750557 q^{34} +(-3.15664 - 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} +(1.34571 + 2.33083i) q^{38} +(1.69576 - 2.93714i) q^{40} +0.248768 q^{41} +0.996627 q^{43} +(3.82296 - 6.62156i) q^{44} +(-1.82217 - 3.15609i) q^{46} +(-4.73790 + 8.20628i) q^{47} +(-6.95789 - 0.766676i) q^{49} +1.99059 q^{50} +(2.13572 + 3.69917i) q^{52} +(0.410229 + 0.710537i) q^{53} -7.02604 q^{55} +(0.345371 - 6.28773i) q^{56} +(2.28285 - 3.95401i) q^{58} +(-3.29204 - 5.70197i) q^{59} +(-0.0376322 + 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(1.96257 - 3.39927i) q^{65} +(6.29385 + 10.9013i) q^{67} +(0.868117 - 1.50362i) q^{68} +(-2.25460 + 1.14165i) q^{70} -0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +(-0.475793 - 0.824098i) q^{74} -6.22595 q^{76} +(-11.6386 + 5.89335i) q^{77} +(0.922457 - 1.59774i) q^{79} +(1.07286 + 1.85825i) q^{80} +(0.0833788 - 0.144416i) q^{82} -14.4717 q^{83} -1.59547 q^{85} +(0.334036 - 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(-6.76292 + 11.7137i) q^{89} +(0.399711 - 7.27703i) q^{91} +8.43030 q^{92} +(3.17597 + 5.50094i) q^{94} +(2.86059 + 4.95469i) q^{95} -5.40319 q^{97} +(-2.77712 + 3.78226i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 + 16 * q^13 - 4 * q^14 + 2 * q^16 - 12 * q^17 + q^19 + 10 * q^20 + 2 * q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 + 14 * q^29 - 3 * q^31 + 2 * q^32 - 6 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 + 10 * q^41 + 14 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 - 17 * q^49 + 38 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 27 * q^56 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 - 11 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 - 10 * q^76 - 20 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 + 18 * q^83 + 12 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 + 54 * q^92 - 3 * q^94 + 14 * q^95 + 24 * q^97 - 59 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.335166	−	0.580525i	0.236998	−	0.410493i	−0.722853	−	0.691002i	$-0.757170\pi$
$2$	0.335166	−	0.580525i	0.236998	−	0.410493i	0.959852	+	0.280508i	$0.0905031\pi$
$3$		0			0
$3$		0			0
$4$	0.775327	+	1.34291i	0.387664	+	0.671453i
$5$	0.712469	−	1.23403i	0.318626	−	0.551876i	−0.661576	−	0.749878i	$-0.730112\pi$
$5$	0.712469	−	1.23403i	0.318626	−	0.551876i	0.980202	+	0.198002i	$0.0634454\pi$
$6$		0			0
$7$	0.145107	−	2.64177i	0.0548451	−	0.998495i
$7$	0.145107	−	2.64177i	0.0548451	−	0.998495i
$8$	2.38012			0.841499
$9$		0			0
$10$	−0.477591	−	0.827212i	−0.151028	−	0.261587i
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	−0.950965	−	0.309297i	$-0.899906\pi$
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	0.207623	−	0.978209i	$-0.433427\pi$
$12$		0			0
$13$	2.75460			0.763990			0.381995	−	0.924164i	$-0.375237\pi$
$13$	2.75460			0.763990			0.381995	+	0.924164i	$0.375237\pi$
$14$	−1.48498	−	0.969670i	−0.396877	−	0.259155i
$15$		0			0
$16$	−0.752918	+	1.30409i	−0.188230	+	0.326023i
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	0.790115	−	0.612959i	$-0.210021\pi$
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	−0.925896	+	0.377780i	$0.876688\pi$
$18$		0			0
$19$	−2.00752	+	3.47713i	−0.460557	+	0.797709i	−0.998989	−	0.0449606i	$-0.985684\pi$
$19$	−2.00752	+	3.47713i	−0.460557	+	0.797709i	0.538431	+	0.842669i	$0.319017\pi$
$20$	2.20958			0.494078
$21$		0			0
$22$	−3.30526			−0.704684
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	−0.430073	−	0.902794i	$-0.641512\pi$
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	0.996879	−	0.0789424i	$-0.0251543\pi$
$24$		0			0
$25$	1.48478	+	2.57171i	0.296955	+	0.514342i
$26$	0.923251	−	1.59912i	0.181064	−	0.313613i
$27$		0			0
$28$	3.66015	−	1.85337i	0.691704	−	0.350254i
$29$	6.81109			1.26479			0.632394	−	0.774647i	$-0.282072\pi$
$29$	6.81109			1.26479			0.632394	+	0.774647i	$0.282072\pi$
$30$		0			0
$31$	−1.25292	−	2.17012i	−0.225031	−	0.389765i	0.731298	−	0.682058i	$-0.238915\pi$
$31$	−1.25292	−	2.17012i	−0.225031	−	0.389765i	−0.956329	+	0.292294i	$0.905582\pi$
$32$	2.88483	+	4.99666i	0.509970	+	0.883294i
$33$		0			0
$34$	−0.750557			−0.128719
$35$	−3.15664	−	2.06124i	−0.533570	−	0.348414i
$36$		0			0
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	−0.801765	−	0.597639i	$-0.796106\pi$
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	0.918453	+	0.395529i	$0.129439\pi$
$38$	1.34571	+	2.33083i	0.218303	+	0.378111i
$39$		0			0
$40$	1.69576	−	2.93714i	0.268123	−	0.464403i
$41$	0.248768			0.0388511			0.0194256	−	0.999811i	$-0.493816\pi$
$41$	0.248768			0.0388511			0.0194256	+	0.999811i	$0.493816\pi$
$42$		0			0
$43$	0.996627			0.151984			0.0759921	−	0.997108i	$-0.475788\pi$
$43$	0.996627			0.151984			0.0759921	+	0.997108i	$0.475788\pi$
$44$	3.82296	−	6.62156i	0.576333	−	0.998238i
$45$		0			0
$46$	−1.82217	−	3.15609i	−0.268664	−	0.465340i
$47$	−4.73790	+	8.20628i	−0.691093	+	1.19701i	0.280387	+	0.959887i	$0.409537\pi$
$47$	−4.73790	+	8.20628i	−0.691093	+	1.19701i	−0.971480	+	0.237122i	$0.923796\pi$
$48$		0			0
$49$	−6.95789	−	0.766676i	−0.993984	−	0.109525i
$50$	1.99059			0.281512
$51$		0			0
$52$	2.13572	+	3.69917i	0.296171	+	0.512983i
$53$	0.410229	+	0.710537i	0.0563493	+	0.0975998i	0.892824	−	0.450406i	$-0.148721\pi$
$53$	0.410229	+	0.710537i	0.0563493	+	0.0975998i	−0.836475	+	0.548005i	$0.815387\pi$
$54$		0			0
$55$	−7.02604			−0.947392
$56$	0.345371	−	6.28773i	0.0461521	−	0.840233i
$57$		0			0
$58$	2.28285	−	3.95401i	0.299753	−	0.519187i
$59$	−3.29204	−	5.70197i	−0.428586	−	0.742334i	0.568161	−	0.822917i	$-0.307655\pi$
$59$	−3.29204	−	5.70197i	−0.428586	−	0.742334i	−0.996748	+	0.0805836i	$0.974322\pi$
$60$		0			0
$61$	−0.0376322	+	0.0651809i	−0.00481831	+	0.00834556i	−0.868425	−	0.495821i	$-0.834867\pi$
$61$	−0.0376322	+	0.0651809i	−0.00481831	+	0.00834556i	0.863606	+	0.504167i	$0.168200\pi$
$62$	−1.67974			−0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	1.96257	−	3.39927i	0.243427	−	0.421628i
$66$		0			0
$67$	6.29385	+	10.9013i	0.768916	+	1.33180i	0.938151	+	0.346226i	$0.112537\pi$
$67$	6.29385	+	10.9013i	0.768916	+	1.33180i	−0.169235	+	0.985576i	$0.554130\pi$
$68$	0.868117	−	1.50362i	0.105275	−	0.182341i
$69$		0			0
$70$	−2.25460	+	1.14165i	−0.269477	+	0.136453i
$71$	−0.0804951			−0.00955301			−0.00477651	−	0.999989i	$-0.501520\pi$
$71$	−0.0804951			−0.00955301			−0.00477651	+	0.999989i	$0.501520\pi$
$72$		0			0
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	0.988416	+	0.151769i	$0.0484971\pi$
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	−0.362772	+	0.931878i	$0.618170\pi$
$74$	−0.475793	−	0.824098i	−0.0553098	−	0.0957995i
$75$		0			0
$76$	−6.22595			−0.714165
$77$	−11.6386	+	5.89335i	−1.32634	+	0.671610i
$78$		0			0
$79$	0.922457	−	1.59774i	0.103785	−	0.179760i	−0.809456	−	0.587180i	$-0.800238\pi$
$79$	0.922457	−	1.59774i	0.103785	−	0.179760i	0.913241	+	0.407420i	$0.133571\pi$
$80$	1.07286	+	1.85825i	0.119950	+	0.207759i
$81$		0			0
$82$	0.0833788	−	0.144416i	0.00920765	−	0.0159481i
$83$	−14.4717			−1.58847			−0.794236	−	0.607610i	$-0.792128\pi$
$83$	−14.4717			−1.58847			−0.794236	+	0.607610i	$0.792128\pi$
$84$		0			0
$85$	−1.59547			−0.173053
$86$	0.334036	−	0.578567i	0.0360200	−	0.0623885i
$87$		0			0
$88$	−5.86792	−	10.1635i	−0.625522	−	1.08344i
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	0.245366	+	0.969430i	$0.421092\pi$
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	−0.962235	+	0.272222i	$0.912242\pi$
$90$		0			0
$91$	0.399711	−	7.27703i	0.0419011	−	0.762840i
$92$	8.43030			0.878920
$93$		0			0
$94$	3.17597	+	5.50094i	0.327576	+	0.567378i
$95$	2.86059	+	4.95469i	0.293491	+	0.508341i
$96$		0			0
$97$	−5.40319			−0.548611			−0.274306	−	0.961643i	$-0.588448\pi$
$97$	−5.40319			−0.548611			−0.274306	+	0.961643i	$0.588448\pi$
$98$	−2.77712	+	3.78226i	−0.280532	+	0.382066i
$99$		0			0
$100$	−2.30238	+	3.98783i	−0.230238	+	0.398783i
$101$	−2.56770	−	4.44739i	−0.255496	−	0.442531i	0.709534	−	0.704671i	$-0.248905\pi$
$101$	−2.56770	−	4.44739i	−0.255496	−	0.442531i	−0.965030	+	0.262139i	$0.915572\pi$
$102$		0			0
$103$	7.10561	−	12.3073i	0.700137	−	1.21267i	−0.268282	−	0.963341i	$-0.586456\pi$
$103$	7.10561	−	12.3073i	0.700137	−	1.21267i	0.968418	−	0.249332i	$-0.0802109\pi$
$104$	6.55629			0.642897
$105$		0			0
$106$	0.549980			0.0534188
$107$	−3.83015	+	6.63401i	−0.370274	+	0.641334i	−0.989608	−	0.143794i	$-0.954070\pi$
$107$	−3.83015	+	6.63401i	−0.370274	+	0.641334i	0.619333	+	0.785128i	$0.287403\pi$
$108$		0			0
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	0.822476	−	0.568800i	$-0.192592\pi$
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	−0.903833	+	0.427885i	$0.859259\pi$
$110$	−2.35489	+	4.07880i	−0.224530	+	0.388898i
$111$		0			0
$112$	3.33586	+	2.17827i	0.315209	+	0.205827i
$113$	−0.600703			−0.0565093			−0.0282547	−	0.999601i	$-0.508995\pi$
$113$	−0.600703			−0.0565093			−0.0282547	+	0.999601i	$0.508995\pi$
$114$		0			0
$115$	−3.87341	−	6.70895i	−0.361198	−	0.625613i
$116$	5.28083	+	9.14666i	0.490312	+	0.849246i
$117$		0			0
$118$	−4.41352			−0.406297
$119$	−2.64288	+	1.33826i	−0.242273	+	0.122678i
$120$		0			0
$121$	−6.65626	+	11.5290i	−0.605115	+	1.04809i
$122$	0.0252261	+	0.0436929i	0.00228386	+	0.00395577i
$123$		0			0
$124$	1.94284	−	3.36510i	0.174472	−	0.302195i
$125$	11.3561			1.01572
$126$		0			0
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	−5.48278	+	9.49645i	−0.484614	+	0.839375i
$129$		0			0
$130$	−1.31557	−	2.27864i	−0.115384	−	0.199850i
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.0578326	+	0.998326i	$0.518419\pi$
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.835660	+	0.549248i	$0.814914\pi$
$132$		0			0
$133$	8.89447	+	5.80797i	0.771249	+	0.503615i
$134$	8.43794			0.728927
$135$		0			0
$136$	−1.33248	−	2.30793i	−0.114260	−	0.197903i
$137$	6.10581	+	10.5756i	0.521655	+	0.903532i	0.999683	+	0.0251879i	$0.00801840\pi$
$137$	6.10581	+	10.5756i	0.521655	+	0.903532i	−0.478028	+	0.878345i	$0.658648\pi$
$138$		0			0
$139$	2.48183			0.210506			0.105253	−	0.994445i	$-0.466435\pi$
$139$	2.48183			0.210506			0.105253	+	0.994445i	$0.466435\pi$
$140$	0.320625	−	5.83721i	0.0270978	−	0.493335i
$141$		0			0
$142$	−0.0269793	+	0.0467294i	−0.00226405	+	0.00392145i
$143$	−6.79117	−	11.7626i	−0.567906	−	0.983642i
$144$		0			0
$145$	4.85269	−	8.40511i	0.402994	−	0.698006i
$146$	7.16654			0.593107
$147$		0			0
$148$	2.20127			0.180943
$149$	−4.27797	+	7.40966i	−0.350465	+	0.607023i	−0.986331	−	0.164777i	$-0.947310\pi$
$149$	−4.27797	+	7.40966i	−0.350465	+	0.607023i	0.635866	+	0.771799i	$0.280643\pi$
$150$		0			0
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	0.961577	+	0.274537i	$0.0885244\pi$
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	−0.243033	+	0.970018i	$0.578142\pi$
$152$	−4.77814	+	8.27599i	−0.387559	+	0.671271i
$153$		0			0
$154$	−0.479615	+	8.73173i	−0.0386485	+	0.703623i
$155$	−3.57066			−0.286802
$156$		0			0
$157$	−3.16074	−	5.47457i	−0.252255	−	0.436918i	0.711891	−	0.702289i	$-0.247839\pi$
$157$	−3.16074	−	5.47457i	−0.252255	−	0.436918i	−0.964146	+	0.265371i	$0.914505\pi$
$158$	−0.618353	−	1.07102i	−0.0491936	−	0.0852057i
$159$		0			0
$160$	8.22139			0.649958
$161$	−12.0436	−	7.86433i	−0.949172	−	0.619796i
$162$		0			0
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	−0.979265	−	0.202581i	$-0.935067\pi$
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	0.665073	+	0.746778i	$0.268400\pi$
$164$	0.192877	+	0.334073i	0.0150612	+	0.0260867i
$165$		0			0
$166$	−4.85041	+	8.40116i	−0.376465	+	0.652057i
$167$	2.12076			0.164109			0.0820545	−	0.996628i	$-0.473852\pi$
$167$	2.12076			0.164109			0.0820545	+	0.996628i	$0.473852\pi$
$168$		0			0
$169$	−5.41215			−0.416319
$170$	−0.534749	+	0.926212i	−0.0410133	+	0.0710372i
$171$		0			0
$172$	0.772712	+	1.33838i	0.0589187	+	0.102050i
$173$	−9.14404	+	15.8379i	−0.695208	+	1.20414i	0.274902	+	0.961472i	$0.411354\pi$
$173$	−9.14404	+	15.8379i	−0.695208	+	1.20414i	−0.970110	+	0.242664i	$0.921979\pi$
$174$		0			0
$175$	7.00931	−	3.54927i	0.529854	−	0.268299i
$176$	7.42494			0.559676
$177$		0			0
$178$	4.53341	+	7.85209i	0.339793	+	0.588539i
$179$	−3.81276	−	6.60389i	−0.284979	−	0.493598i	0.687625	−	0.726066i	$-0.258653\pi$
$179$	−3.81276	−	6.60389i	−0.284979	−	0.493598i	−0.972604	+	0.232468i	$0.925320\pi$
$180$		0			0
$181$	15.5305			1.15438			0.577188	−	0.816611i	$-0.304150\pi$
$181$	15.5305			1.15438			0.577188	+	0.816611i	$0.304150\pi$
$182$	−4.09053	−	2.67106i	−0.303210	−	0.197992i
$183$		0			0
$184$	6.46989	−	11.2062i	0.476967	−	0.826130i
$185$	−1.01140	−	1.75180i	−0.0743597	−	0.128795i
$186$		0			0
$187$	−2.76044	+	4.78122i	−0.201863	+	0.349638i
$188$	−14.6937			−1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	7.41624	−	12.8453i	0.536620	−	0.929454i	−0.462463	−	0.886639i	$-0.653034\pi$
$191$	7.41624	−	12.8453i	0.536620	−	0.929454i	0.999083	−	0.0428150i	$-0.0136326\pi$
$192$		0			0
$193$	−8.28387	−	14.3481i	−0.596286	−	1.03280i	−0.993364	−	0.115013i	$-0.963309\pi$
$193$	−8.28387	−	14.3481i	−0.596286	−	1.03280i	0.397078	−	0.917785i	$-0.370024\pi$
$194$	−1.81097	+	3.13669i	−0.130020	+	0.225201i
$195$		0			0
$196$	−4.36506	−	9.93821i	−0.311790	−	0.709872i
$197$	4.03740			0.287653			0.143826	−	0.989603i	$-0.454059\pi$
$197$	4.03740			0.287653			0.143826	+	0.989603i	$0.454059\pi$
$198$		0			0
$199$	−12.6407	−	21.8943i	−0.896076	−	1.55205i	−0.832468	−	0.554074i	$-0.813073\pi$
$199$	−12.6407	−	21.8943i	−0.896076	−	1.55205i	−0.0636081	−	0.997975i	$-0.520261\pi$
$200$	3.53395	+	6.12097i	0.249888	+	0.432818i
$201$		0			0
$202$	−3.44243			−0.242208
$203$	0.988335	−	17.9933i	0.0693675	−	1.26288i
$204$		0			0
$205$	0.177240	−	0.306988i	0.0123790	−	0.0214410i
$206$	−4.76312	−	8.24997i	−0.331862	−	0.574803i
$207$		0			0
$208$	−2.07399	+	3.59226i	−0.143805	+	0.249078i
$209$	19.7973			1.36941
$210$		0			0
$211$	7.52493			0.518037			0.259019	−	0.965872i	$-0.416601\pi$
$211$	7.52493			0.518037			0.259019	+	0.965872i	$0.416601\pi$
$212$	−0.636123	+	1.10180i	−0.0436891	+	0.0756718i
$213$		0			0
$214$	2.56747	+	4.44699i	0.175509	+	0.303990i
$215$	0.710065	−	1.22987i	0.0484261	−	0.0838764i
$216$		0			0
$217$	−5.91476	+	2.99502i	−0.401520	+	0.203315i
$218$	−1.13875			−0.0771261
$219$		0			0
$220$	−5.44748	−	9.43531i	−0.367269	−	0.636129i
$221$	−1.54214	−	2.67106i	−0.103735	−	0.179675i
$222$		0			0
$223$	−12.9846			−0.869513			−0.434757	−	0.900548i	$-0.643166\pi$
$223$	−12.9846			−0.869513			−0.434757	+	0.900548i	$0.643166\pi$
$224$	13.6186	−	6.89599i	0.909934	−	0.460758i
$225$		0			0
$226$	−0.201335	+	0.348723i	−0.0133926	+	0.0231967i
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.719277	−	0.694723i	$-0.755527\pi$
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.242009	−	0.970274i	$-0.577806\pi$
$228$		0			0
$229$	−7.71790	+	13.3678i	−0.510013	+	0.883369i	0.489919	+	0.871768i	$0.337026\pi$
$229$	−7.71790	+	13.3678i	−0.510013	+	0.883369i	−0.999933	+	0.0116012i	$0.996307\pi$
$230$	−5.19295			−0.342413
$231$		0			0
$232$	16.2112			1.06432
$233$	2.47324	−	4.28378i	0.162027	−	0.280640i	−0.773568	−	0.633713i	$-0.781530\pi$
$233$	2.47324	−	4.28378i	0.162027	−	0.280640i	0.935596	+	0.353073i	$0.114863\pi$
$234$		0			0
$235$	6.75121	+	11.6934i	0.440400	+	0.762795i
$236$	5.10481	−	8.84179i	0.332295	−	0.575551i
$237$		0			0
$238$	−0.108911	+	1.98280i	−0.00705964	+	0.128526i
$239$	13.0346			0.843141			0.421571	−	0.906796i	$-0.361479\pi$
$239$	13.0346			0.843141			0.421571	+	0.906796i	$0.361479\pi$
$240$		0			0
$241$	−7.29123	−	12.6288i	−0.469670	−	0.813492i	0.529729	−	0.848167i	$-0.322294\pi$
$241$	−7.29123	−	12.6288i	−0.469670	−	0.813492i	−0.999399	+	0.0346754i	$0.988960\pi$
$242$	4.46191	+	7.72826i	0.286823	+	0.496791i
$243$		0			0
$244$	−0.116709			−0.00747154
$245$	−5.90338	+	8.04002i	−0.377153	+	0.513658i
$246$		0			0
$247$	−5.52993	+	9.57812i	−0.351861	+	0.609441i
$248$	−2.98209	−	5.16514i	−0.189363	−	0.327987i
$249$		0			0
$250$	3.80619	−	6.59251i	0.240724	−	0.416947i
$251$	14.0715			0.888187			0.444094	−	0.895980i	$-0.353526\pi$
$251$	14.0715			0.888187			0.444094	+	0.895980i	$0.353526\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$	2.43323	−	4.21448i	0.152674	−	0.264440i
$255$		0			0
$256$	4.53120	+	7.84826i	0.283200	+	0.490517i
$257$	−4.18108	+	7.24184i	−0.260808	+	0.451733i	−0.966457	−	0.256829i	$-0.917322\pi$
$257$	−4.18108	+	7.24184i	−0.260808	+	0.451733i	0.705649	+	0.708562i	$0.250656\pi$
$258$		0			0
$259$	−3.14476	−	2.05349i	−0.195406	−	0.127597i
$260$	6.08653			0.377471
$261$		0			0
$262$	6.85515	+	11.8735i	0.423512	+	0.733545i
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	0.912030	−	0.410122i	$-0.134514\pi$
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	−0.811192	+	0.584780i	$0.801181\pi$
$264$		0			0
$265$	1.16910			0.0718173
$266$	6.35280	−	3.21683i	0.389515	−	0.197237i
$267$		0			0
$268$	−9.75958	+	16.9041i	−0.596161	+	1.03258i
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	0.999375	−	0.0353420i	$-0.0112521\pi$
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	−0.530295	+	0.847813i	$0.677919\pi$
$270$		0			0
$271$	4.06308	−	7.03747i	0.246815	−	0.427496i	−0.715825	−	0.698279i	$-0.753949\pi$
$271$	4.06308	−	7.03747i	0.246815	−	0.427496i	0.962640	+	0.270783i	$0.0872827\pi$
$272$	1.68605			0.102232
$273$		0			0
$274$	8.18585			0.494525
$275$	7.32110	−	12.6805i	0.441479	−	0.764664i
$276$		0			0
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	0.605982	−	0.795478i	$-0.292780\pi$
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	−0.991895	+	0.127057i	$0.959447\pi$
$278$	0.831826	−	1.44077i	0.0498896	−	0.0864114i
$279$		0			0
$280$	−7.51319	−	4.90601i	−0.448999	−	0.293190i
$281$	−1.44816			−0.0863901			−0.0431951	−	0.999067i	$-0.513754\pi$
$281$	−1.44816			−0.0863901			−0.0431951	+	0.999067i	$0.513754\pi$
$282$		0			0
$283$	8.71926	+	15.1022i	0.518306	+	0.897732i	0.999774	+	0.0212686i	$0.00677053\pi$
$283$	8.71926	+	15.1022i	0.518306	+	0.897732i	−0.481468	+	0.876464i	$0.659896\pi$
$284$	−0.0624100	−	0.108097i	−0.00370335	−	0.00641440i
$285$		0			0
$286$	−9.10468			−0.538371
$287$	0.0360979	−	0.657189i	0.00213079	−	0.0387926i
$288$		0			0
$289$	7.87316	−	13.6367i	0.463127	−	0.802160i
$290$	−3.25292	−	5.63422i	−0.191018	−	0.330853i
$291$		0			0
$292$	−8.28903	+	14.3570i	−0.485079	+	0.840181i
$293$	−1.80010			−0.105163			−0.0525814	−	0.998617i	$-0.516745\pi$
$293$	−1.80010			−0.105163			−0.0525814	+	0.998617i	$0.516745\pi$
$294$		0			0
$295$	−9.38189			−0.546235
$296$	1.68938	−	2.92609i	0.0981931	−	0.170075i
$297$		0			0
$298$	2.86766	+	4.96693i	0.166119	+	0.287727i
$299$	7.48786	−	12.9693i	0.433034	−	0.750037i
$300$		0			0
$301$	0.144617	−	2.63286i	0.00833559	−	0.151755i
$302$	11.8376			0.681175
$303$		0			0
$304$	−3.02300	−	5.23599i	−0.173381	−	0.300305i
$305$	0.0536236	+	0.0928787i	0.00307048	+	0.00531822i
$306$		0			0
$307$	1.06478			0.0607699			0.0303850	−	0.999538i	$-0.490327\pi$
$307$	1.06478			0.0607699			0.0303850	+	0.999538i	$0.490327\pi$
$308$	−16.9379	−	11.0602i	−0.965127	−	0.630214i
$309$		0			0
$310$	−1.19676	+	2.07286i	−0.0679717	+	0.117730i
$311$	−8.46463	−	14.6612i	−0.479985	−	0.831359i	0.519751	−	0.854318i	$-0.326025\pi$
$311$	−8.46463	−	14.6612i	−0.479985	−	0.831359i	−0.999736	+	0.0229591i	$0.992691\pi$
$312$		0			0
$313$	4.13928	−	7.16944i	0.233966	−	0.405241i	−0.725006	−	0.688743i	$-0.758163\pi$
$313$	4.13928	−	7.16944i	0.233966	−	0.405241i	0.958972	+	0.283502i	$0.0914963\pi$
$314$	−4.23750			−0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	3.27371	−	5.67023i	0.183870	−	0.318472i	−0.759325	−	0.650711i	$-0.774471\pi$
$317$	3.27371	−	5.67023i	0.183870	−	0.318472i	0.943195	+	0.332239i	$0.107804\pi$
$318$		0			0
$319$	−16.7920	−	29.0846i	−0.940171	−	1.62842i
$320$	0.609811	−	1.05622i	0.0340895	−	0.0590447i
$321$		0			0
$322$	−8.60207	+	4.35578i	−0.479374	+	0.242738i
$323$	4.49556			0.250140
$324$		0			0
$325$	4.08997	+	7.08404i	0.226871	+	0.392952i
$326$	2.68893	+	4.65736i	0.148926	+	0.257947i
$327$		0			0
$328$	0.592099			0.0326932
$329$	20.9916	+	13.7072i	1.15730	+	0.755703i
$330$		0			0
$331$	13.3629	−	23.1453i	0.734493	−	1.27218i	−0.220453	−	0.975398i	$-0.570754\pi$
$331$	13.3629	−	23.1453i	0.734493	−	1.27218i	0.954946	−	0.296781i	$-0.0959131\pi$
$332$	−11.2203	−	19.4341i	−0.615792	−	1.06658i
$333$		0			0
$334$	0.710806	−	1.23115i	0.0388936	−	0.0673657i
$335$	17.9367			0.979985
$336$		0			0
$337$	9.52328			0.518766			0.259383	−	0.965775i	$-0.416481\pi$
$337$	9.52328			0.518766			0.259383	+	0.965775i	$0.416481\pi$
$338$	−1.81397	+	3.14189i	−0.0986670	+	0.170896i
$339$		0			0
$340$	−1.23701	−	2.14257i	−0.0670864	−	0.116197i
$341$	−6.17786	+	10.7004i	−0.334550	+	0.579457i
$342$		0			0
$343$	−3.03502	+	18.2699i	−0.163876	+	0.986481i
$344$	2.37209			0.127895
$345$		0			0
$346$	6.12955	+	10.6167i	0.329526	+	0.570757i
$347$	−9.35156	−	16.1974i	−0.502018	−	0.869521i	−0.999997	−	0.00233189i	$-0.999258\pi$
$347$	−9.35156	−	16.1974i	−0.502018	−	0.869521i	0.497979	−	0.867189i	$-0.334076\pi$
$348$		0			0
$349$	30.1084			1.61167			0.805834	−	0.592142i	$-0.201718\pi$
$349$	30.1084			1.61167			0.805834	+	0.592142i	$0.201718\pi$
$350$	0.288848	−	5.25868i	0.0154396	−	0.281088i
$351$		0			0
$352$	14.2244	−	24.6374i	0.758164	−	1.31318i
$353$	3.12966	+	5.42074i	0.166575	+	0.288517i	0.937214	−	0.348756i	$-0.113396\pi$
$353$	3.12966	+	5.42074i	0.166575	+	0.288517i	−0.770638	+	0.637273i	$0.780062\pi$
$354$		0			0
$355$	−0.0573502	+	0.0993335i	−0.00304383	+	0.00527208i
$356$	−20.9739			−1.11161
$357$		0			0
$358$	−5.11163			−0.270158
$359$	5.09755	−	8.82921i	0.269038	−	0.465988i	−0.699575	−	0.714559i	$-0.746628\pi$
$359$	5.09755	−	8.82921i	0.269038	−	0.465988i	0.968614	+	0.248571i	$0.0799608\pi$
$360$		0			0
$361$	1.43970	+	2.49364i	0.0757739	+	0.131244i
$362$	5.20532	−	9.01587i	0.273585	−	0.473864i
$363$		0			0
$364$	10.0823	−	5.10530i	0.528455	−	0.267591i
$365$	15.2340			0.797385
$366$		0			0
$367$	14.3278	+	24.8165i	0.747906	+	1.29541i	0.948824	+	0.315804i	$0.102274\pi$
$367$	14.3278	+	24.8165i	0.747906	+	1.29541i	−0.200918	+	0.979608i	$0.564392\pi$
$368$	4.09332	+	7.08984i	0.213379	+	0.369584i
$369$		0			0
$370$	−1.35595			−0.0704926
$371$	1.93660	−	0.980627i	0.100543	−	0.0509116i
$372$		0			0
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	−0.579421	−	0.815028i	$-0.696721\pi$
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	0.995546	+	0.0942796i	$0.0300548\pi$
$374$	1.85041	+	3.20501i	0.0956826	+	0.165727i
$375$		0			0
$376$	−11.2768	+	19.5319i	−0.581555	+	1.00728i
$377$	18.7619			0.966286
$378$		0			0
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	−4.43579	+	7.68302i	−0.227551	+	0.394130i
$381$		0			0
$382$	−4.97135	−	8.61063i	−0.254356	−	0.440558i
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	−0.975222	−	0.221228i	$-0.928994\pi$
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	0.679200	+	0.733953i	$0.262327\pi$
$384$		0			0
$385$	−1.01953	+	18.5612i	−0.0519598	+	0.945966i
$386$	−11.1059			−0.565275
$387$		0			0
$388$	−4.18924	−	7.25598i	−0.212677	−	0.368367i
$389$	8.90675	+	15.4270i	0.451590	+	0.782178i	0.998485	−	0.0550239i	$-0.0175235\pi$
$389$	8.90675	+	15.4270i	0.451590	+	0.782178i	−0.546895	+	0.837201i	$0.684190\pi$
$390$		0			0
$391$	−6.08726			−0.307846
$392$	−16.5606	−	1.82478i	−0.836437	−	0.0921654i
$393$		0			0
$394$	1.35320	−	2.34381i	0.0681732	−	0.118079i
$395$	−1.31444	−	2.27668i	−0.0661369	−	0.114552i
$396$		0			0
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	−0.982184	−	0.187921i	$-0.939825\pi$
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	0.653836	+	0.756636i	$0.273159\pi$
$398$	−16.9470			−0.849474
$399$		0			0
$400$	−4.47166			−0.223583
$401$	7.05165	−	12.2138i	0.352143	−	0.609929i	−0.634482	−	0.772938i	$-0.718787\pi$
$401$	7.05165	−	12.2138i	0.352143	−	0.609929i	0.986625	+	0.163009i	$0.0521199\pi$
$402$		0			0
$403$	−3.45129	−	5.97782i	−0.171921	−	0.297776i
$404$	3.98161	−	6.89636i	0.198093	−	0.343107i
$405$		0			0
$406$	−10.1143	−	6.60452i	−0.501966	−	0.327777i
$407$	−6.99960			−0.346957
$408$		0			0
$409$	1.32300	+	2.29150i	0.0654179	+	0.113307i	0.896879	−	0.442275i	$-0.145829\pi$
$409$	1.32300	+	2.29150i	0.0654179	+	0.113307i	−0.831461	+	0.555583i	$0.812495\pi$
$410$	−0.118810	−	0.205784i	−0.00586759	−	0.0101630i
$411$		0			0
$412$	22.0367			1.08567
$413$	−15.5410	+	7.86940i	−0.764722	+	0.387228i
$414$		0			0
$415$	−10.3106	+	17.8585i	−0.506128	+	0.876639i
$416$	7.94655	+	13.7638i	0.389612	+	0.674827i
$417$		0			0
$418$	6.63538	−	11.4928i	0.324547	−	0.562132i
$419$	33.5134			1.63724			0.818619	−	0.574337i	$-0.194740\pi$
$419$	33.5134			1.63724			0.818619	+	0.574337i	$0.194740\pi$
$420$		0			0
$421$	4.83901			0.235839			0.117919	−	0.993023i	$-0.462378\pi$
$421$	4.83901			0.235839			0.117919	+	0.993023i	$0.462378\pi$
$422$	2.52210	−	4.36841i	0.122774	−	0.212651i
$423$		0			0
$424$	0.976394	+	1.69116i	0.0474179	+	0.0821302i
$425$	1.66247	−	2.87949i	0.0806418	−	0.139676i
$426$		0			0
$427$	0.166732	+	0.108874i	0.00806874	+	0.00526877i
$428$	−11.8785			−0.574167
$429$		0			0
$430$	−0.475980	−	0.824422i	−0.0229538	−	0.0397571i
$431$	−17.6643	−	30.5954i	−0.850858	−	1.47373i	−0.880435	−	0.474166i	$-0.842749\pi$
$431$	−17.6643	−	30.5954i	−0.850858	−	1.47373i	0.0295774	−	0.999562i	$-0.490584\pi$
$432$		0			0
$433$	5.47404			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$433$	5.47404			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$434$	−0.243742	+	4.43750i	−0.0117000	+	0.213007i
$435$		0			0
$436$	1.31712	−	2.28131i	0.0630785	−	0.109255i
$437$	10.9141	+	18.9038i	0.522093	+	0.904292i
$438$		0			0
$439$	−3.19906	+	5.54093i	−0.152683	+	0.264454i	−0.932213	−	0.361911i	$-0.882125\pi$
$439$	−3.19906	+	5.54093i	−0.152683	+	0.264454i	0.779530	+	0.626365i	$0.215458\pi$
$440$	−16.7228			−0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	−3.19341	+	5.53115i	−0.151723	+	0.262793i	−0.931861	−	0.362815i	$-0.881816\pi$
$443$	−3.19341	+	5.53115i	−0.151723	+	0.262793i	0.780138	+	0.625608i	$0.215149\pi$
$444$		0			0
$445$	9.63674	+	16.6913i	0.456825	+	0.791245i
$446$	−4.35200	+	7.53789i	−0.206073	+	0.356929i
$447$		0			0
$448$	0.124199	−	2.26112i	0.00586783	−	0.106828i
$449$	11.7460			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$449$	11.7460			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$450$		0			0
$451$	−0.613311	−	1.06229i	−0.0288797	−	0.0500210i
$452$	−0.465741	−	0.806687i	−0.0219066	−	0.0379434i
$453$		0			0
$454$	−19.4172			−0.911293
$455$	−8.69531	−	5.67791i	−0.407642	−	0.266185i
$456$		0			0
$457$	−5.26120	+	9.11266i	−0.246108	+	0.426272i	−0.962443	−	0.271485i	$-0.912485\pi$
$457$	−5.26120	+	9.11266i	−0.246108	+	0.426272i	0.716334	+	0.697757i	$0.245819\pi$
$458$	5.17356	+	8.96087i	0.241745	+	0.418714i
$459$		0			0
$460$	6.00633	−	10.4033i	0.280046	−	0.485055i
$461$	−7.08555			−0.330007			−0.165004	−	0.986293i	$-0.552764\pi$
$461$	−7.08555			−0.330007			−0.165004	+	0.986293i	$0.552764\pi$
$462$		0			0
$463$	−32.7521			−1.52212			−0.761059	−	0.648683i	$-0.775320\pi$
$463$	−32.7521			−1.52212			−0.761059	+	0.648683i	$0.775320\pi$
$464$	−5.12820	+	8.88230i	−0.238071	+	0.412350i
$465$		0			0
$466$	−1.65789	−	2.87156i	−0.0768004	−	0.133022i
$467$	−1.96216	+	3.39856i	−0.0907978	+	0.157266i	−0.907847	−	0.419301i	$-0.862275\pi$
$467$	−1.96216	+	3.39856i	−0.0907978	+	0.157266i	0.817049	+	0.576568i	$0.195608\pi$
$468$		0			0
$469$	29.7119	−	15.0450i	1.37197	−	0.694716i
$470$	9.05111			0.417497
$471$		0			0
$472$	−7.83544	−	13.5714i	−0.360655	−	0.624673i
$473$	−2.45707	−	4.25577i	−0.112976	−	0.195681i
$474$		0			0
$475$	−11.9229			−0.547060
$476$	−3.84626	−	2.51155i	−0.176293	−	0.115117i
$477$		0			0
$478$	4.36878	−	7.56694i	0.199823	−	0.346104i
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	0.989175	−	0.146742i	$-0.0468787\pi$
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	−0.621670	+	0.783279i	$0.713545\pi$
$480$		0			0
$481$	1.95518	−	3.38647i	0.0891486	−	0.154410i
$482$	−9.77510			−0.445244
$483$		0			0
$484$	−20.6431			−0.938324
$485$	−3.84961	+	6.66771i	−0.174802	+	0.302765i
$486$		0			0
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	0.823604	−	0.567166i	$-0.191960\pi$
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	−0.902982	+	0.429679i	$0.858627\pi$
$488$	−0.0895692	+	0.155138i	−0.00405461	+	0.00702279i
$489$		0			0
$490$	2.68882	+	6.12181i	0.121469	+	0.276555i
$491$	−41.1093			−1.85524			−0.927618	−	0.373531i	$-0.878147\pi$
$491$	−41.1093			−1.85524			−0.927618	+	0.373531i	$0.878147\pi$
$492$		0			0
$493$	−3.81312	−	6.60452i	−0.171734	−	0.297452i
$494$	3.70689	+	6.42053i	0.166781	+	0.288873i
$495$		0			0
$496$	3.77338			0.169430
$497$	−0.0116804	+	0.212649i	−0.000523936	+	0.00953863i
$498$		0			0
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	−0.967507	−	0.252843i	$-0.918634\pi$
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	0.702722	+	0.711465i	$0.251968\pi$
$500$	8.80470	+	15.2502i	0.393758	+	0.682009i
$501$		0			0
$502$	4.71631	−	8.16888i	0.210499	−	0.364595i
$503$	−21.8595			−0.974665			−0.487332	−	0.873217i	$-0.662030\pi$
$503$	−21.8595			−0.974665			−0.487332	+	0.873217i	$0.662030\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$	−8.98470	+	15.5620i	−0.399419	+	0.691813i
$507$		0			0
$508$	5.62869	+	9.74918i	0.249733	+	0.432550i
$509$	8.44831	−	14.6329i	0.374465	−	0.648592i	−0.615782	−	0.787917i	$-0.711160\pi$
$509$	8.44831	−	14.6329i	0.374465	−	0.648592i	0.990247	+	0.139324i	$0.0444931\pi$
$510$		0			0
$511$	25.2350	−	12.7781i	1.11633	−	0.565270i
$512$	−15.8563			−0.700756
$513$		0			0
$514$	2.80271	+	4.85444i	0.123622	+	0.214120i
$515$	−10.1250	−	17.5371i	−0.446163	−	0.772777i
$516$		0			0
$517$	46.7230			2.05487
$518$	−2.24612	+	1.13735i	−0.0986888	+	0.0499725i
$519$		0			0
$520$	4.67115	−	8.09067i	0.204843	−	0.354799i
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	0.945082	+	0.326834i	$0.105982\pi$
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	−0.189495	+	0.981882i	$0.560685\pi$
$522$		0			0
$523$	0.995615	−	1.72445i	0.0435352	−	0.0754051i	−0.843437	−	0.537229i	$-0.819471\pi$
$523$	0.995615	−	1.72445i	0.0435352	−	0.0754051i	0.886972	+	0.461823i	$0.152805\pi$
$524$	−31.7155			−1.38550
$525$		0			0
$526$	2.19243			0.0955945
$527$	−1.40287	+	2.42983i	−0.0611098	+	0.105845i
$528$		0			0
$529$	−3.27836	−	5.67829i	−0.142538	−	0.246882i
$530$	0.391843	−	0.678693i	0.0170206	−	0.0294805i
$531$		0			0
$532$	−0.903426	+	16.4475i	−0.0391685	+	0.713090i
$533$	0.685259			0.0296819
$534$		0			0
$535$	5.45772	+	9.45305i	0.235958	+	0.408691i
$536$	14.9801	+	25.9463i	0.647042	+	1.12071i
$537$		0			0
$538$	10.3144			0.444685
$539$	13.8800	+	31.6016i	0.597856	+	1.36118i
$540$		0			0
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	0.335810	+	0.941930i	$0.390990\pi$
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	−0.983640	+	0.180145i	$0.942343\pi$
$542$	−2.72362	−	4.71745i	−0.116989	−	0.202632i
$543$		0			0
$544$	3.23008	−	5.59466i	0.138488	−	0.239869i
$545$	−2.42067			−0.103690
$546$		0			0
$547$	−15.3614			−0.656806			−0.328403	−	0.944538i	$-0.606510\pi$
$547$	−15.3614			−0.656806			−0.328403	+	0.944538i	$0.606510\pi$
$548$	−9.46800	+	16.3991i	−0.404453	+	0.700533i
$549$		0			0
$550$	−4.90757	−	8.50016i	−0.209260	−	0.362448i
$551$	−13.6734	+	23.6831i	−0.582508	+	1.00893i
$552$		0			0
$553$	−4.08701	−	2.66876i	−0.173797	−	0.113487i
$554$	−8.61092			−0.365843
$555$		0			0
$556$	1.92423	+	3.33287i	0.0816056	+	0.141345i
$557$	11.6412	+	20.1631i	0.493252	+	0.854338i	0.999970	−	0.00777438i	$-0.00247469\pi$
$557$	11.6412	+	20.1631i	0.493252	+	0.854338i	−0.506718	+	0.862112i	$0.669141\pi$
$558$		0			0
$559$	2.74531			0.116114
$560$	5.06475	−	2.56461i	0.214025	−	0.108374i
$561$		0			0
$562$	−0.485375	+	0.840695i	−0.0204743	+	0.0354626i
$563$	2.27942	+	3.94808i	0.0960663	+	0.166392i	0.910053	−	0.414492i	$-0.136041\pi$
$563$	2.27942	+	3.94808i	0.0960663	+	0.166392i	−0.813987	+	0.580883i	$0.802707\pi$
$564$		0			0
$565$	−0.427982	+	0.741286i	−0.0180053	+	0.0311861i
$566$	11.6896			0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	9.09976	−	15.7612i	0.381482	−	0.660746i	−0.609793	−	0.792561i	$-0.708747\pi$
$569$	9.09976	−	15.7612i	0.381482	−	0.660746i	0.991274	+	0.131815i	$0.0420806\pi$
$570$		0			0
$571$	8.52275	+	14.7618i	0.356666	+	0.617763i	0.987402	−	0.158234i	$-0.0505801\pi$
$571$	8.52275	+	14.7618i	0.356666	+	0.617763i	−0.630736	+	0.775998i	$0.717247\pi$
$572$	10.5307	−	18.2398i	0.440313	−	0.762644i
$573$		0			0
$574$	−0.369416	−	0.241223i	−0.0154191	−	0.0100685i
$575$	16.1443			0.673264
$576$		0			0
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	0.722503	−	0.691368i	$-0.242992\pi$
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	−0.959994	+	0.280022i	$0.909658\pi$
$578$	−5.27764	−	9.14113i	−0.219521	−	0.380221i
$579$		0			0
$580$	15.0497			0.624904
$581$	−2.09993	+	38.2308i	−0.0871199	+	1.58608i
$582$		0			0
$583$	2.02275	−	3.50350i	0.0837736	−	0.145100i
$584$	12.7229	+	22.0368i	0.526479	+	0.911889i
$585$		0			0
$586$	−0.603332	+	1.04500i	−0.0249234	+	0.0431686i
$587$	5.05089			0.208473			0.104236	−	0.994553i	$-0.466760\pi$
$587$	5.05089			0.208473			0.104236	+	0.994553i	$0.466760\pi$
$588$		0			0
$589$	10.0610			0.414558
$590$	−3.14449	+	5.44642i	−0.129457	+	0.224226i
$591$		0			0
$592$	1.06882	+	1.85126i	0.0439283	+	0.0760861i
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	−0.584715	−	0.811239i	$-0.698794\pi$
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	0.994911	+	0.100759i	$0.0321271\pi$
$594$		0			0
$595$	−0.231513	+	4.21487i	−0.00949113	+	0.172793i
$596$	−13.2673			−0.543449
$597$		0			0
$598$	−5.01935	−	8.69378i	−0.205257	−	0.355515i
$599$	2.19660	+	3.80463i	0.0897508	+	0.155453i	0.907406	−	0.420256i	$-0.138060\pi$
$599$	2.19660	+	3.80463i	0.0897508	+	0.155453i	−0.817655	+	0.575709i	$0.804726\pi$
$600$		0			0
$601$	−24.3556			−0.993487			−0.496743	−	0.867897i	$-0.665471\pi$
$601$	−24.3556			−0.993487			−0.496743	+	0.867897i	$0.665471\pi$
$602$	−1.47997	−	0.966399i	−0.0603191	−	0.0393875i
$603$		0			0
$604$	−13.6917	+	23.7147i	−0.557107	+	0.964937i
$605$	9.48476	+	16.4281i	0.385610	+	0.667897i
$606$		0			0
$607$	−6.56281	+	11.3671i	−0.266376	+	0.461377i	−0.967923	−	0.251246i	$-0.919160\pi$
$607$	−6.56281	+	11.3671i	−0.266376	+	0.461377i	0.701547	+	0.712623i	$0.252493\pi$
$608$	−23.1654			−0.939481
$609$		0			0
$610$	0.0718913			0.00291079
$611$	−13.0510	+	22.6051i	−0.527988	+	0.914502i
$612$		0			0
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.767960	−	0.640497i	$-0.778728\pi$
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.170707	−	0.985322i	$-0.554605\pi$
$614$	0.356877	−	0.618129i	0.0144024	−	0.0249456i
$615$		0			0
$616$	−27.7012	+	14.0269i	−1.11611	+	0.565159i
$617$	28.3897			1.14293			0.571463	−	0.820628i	$-0.306376\pi$
$617$	28.3897			1.14293			0.571463	+	0.820628i	$0.306376\pi$
$618$		0			0
$619$	−15.9606	−	27.6446i	−0.641511	−	1.11113i	−0.985096	−	0.172008i	$-0.944975\pi$
$619$	−15.9606	−	27.6446i	−0.641511	−	1.11113i	0.343585	−	0.939122i	$-0.388359\pi$
$620$	−2.76843	−	4.79506i	−0.111183	−	0.192574i
$621$		0			0
$622$	−11.3482			−0.455023
$623$	29.9636	+	19.5658i	1.20047	+	0.783888i
$624$		0			0
$625$	0.666993	−	1.15527i	0.0266797	−	0.0462106i
$626$	−2.77469	−	4.80591i	−0.110899	−	0.192083i
$627$		0			0
$628$	4.90122	−	8.48916i	0.195580	−	0.338754i
$629$	−1.58947			−0.0633762
$630$		0			0
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	2.19556	−	3.80282i	0.0873346	−	0.151268i
$633$		0			0
$634$	−2.19447	−	3.80094i	−0.0871537	−	0.150955i
$635$	5.17236	−	8.95878i	0.205259	−	0.355519i
$636$		0			0
$637$	−19.1662	−	2.11189i	−0.759394	−	0.0836761i
$638$	−22.5124			−0.891276
$639$		0			0
$640$	7.81261	+	13.5318i	0.308821	+	0.534893i
$641$	−20.2001	−	34.9875i	−0.797854	−	1.38192i	−0.921011	−	0.389537i	$-0.872635\pi$
$641$	−20.2001	−	34.9875i	−0.797854	−	1.38192i	0.123157	−	0.992387i	$-0.460698\pi$
$642$		0			0
$643$	−12.5471			−0.494809			−0.247405	−	0.968912i	$-0.579578\pi$
$643$	−12.5471			−0.494809			−0.247405	+	0.968912i	$0.579578\pi$
$644$	1.22329	−	22.2709i	0.0482045	−	0.877597i
$645$		0			0
$646$	1.50676	−	2.60979i	0.0592827	−	0.102681i
$647$	−17.2774	−	29.9253i	−0.679245	−	1.17649i	−0.975209	−	0.221287i	$-0.928974\pi$
$647$	−17.2774	−	29.9253i	−0.679245	−	1.17649i	0.295964	−	0.955199i	$-0.404359\pi$
$648$		0			0
$649$	−16.2323	+	28.1151i	−0.637173	+	1.10362i
$650$	5.48329			0.215072
$651$		0			0
$652$	−12.4404			−0.487203
$653$	−11.1472	+	19.3075i	−0.436223	+	0.755560i	−0.997395	−	0.0721392i	$-0.977017\pi$
$653$	−11.1472	+	19.3075i	−0.436223	+	0.755560i	0.561172	+	0.827699i	$0.310351\pi$
$654$		0			0
$655$	14.5721	+	25.2396i	0.569379	+	0.986194i
$656$	−0.187302	+	0.324417i	−0.00731293	+	0.0126664i
$657$		0			0
$658$	14.9931	−	7.59195i	0.584490	−	0.295965i
$659$	7.14986			0.278519			0.139259	−	0.990256i	$-0.455528\pi$
$659$	7.14986			0.278519			0.139259	+	0.990256i	$0.455528\pi$
$660$		0			0
$661$	−21.4530	−	37.1577i	−0.834425	−	1.44527i	−0.894498	−	0.447072i	$-0.852467\pi$
$661$	−21.4530	−	37.1577i	−0.834425	−	1.44527i	0.0600736	−	0.998194i	$-0.480866\pi$
$662$	−8.95760	−	15.5150i	−0.348147	−	0.603008i
$663$		0			0
$664$	−34.4443			−1.33670
$665$	13.5043	−	6.83807i	0.523672	−	0.265169i
$666$		0			0
$667$	18.5146	−	32.0683i	0.716889	−	1.24169i
$668$	1.64428	+	2.84798i	0.0636191	+	0.110192i
$669$		0			0
$670$	6.01177	−	10.4127i	0.232255	−	0.402277i
$671$	0.371112			0.0143266
$672$		0			0
$673$	37.6541			1.45146			0.725729	−	0.687980i	$-0.241503\pi$
$673$	37.6541			1.45146			0.725729	+	0.687980i	$0.241503\pi$
$674$	3.19188	−	5.52850i	0.122947	−	0.212950i
$675$		0			0
$676$	−4.19619	−	7.26801i	−0.161392	−	0.279539i
$677$	−13.1808	+	22.8298i	−0.506580	+	0.877422i	0.493391	+	0.869808i	$0.335757\pi$
$677$	−13.1808	+	22.8298i	−0.506580	+	0.877422i	−0.999971	+	0.00761453i	$0.997576\pi$
$678$		0			0
$679$	−0.784039	+	14.2740i	−0.0300887	+	0.547785i
$680$	−3.79741			−0.145624
$681$		0			0
$682$	4.14122	+	7.17280i	0.158575	+	0.274661i
$683$	−1.96588	−	3.40500i	−0.0752222	−	0.130289i	0.825961	−	0.563728i	$-0.190633\pi$
$683$	−1.96588	−	3.40500i	−0.0752222	−	0.130289i	−0.901183	+	0.433439i	$0.857300\pi$
$684$		0			0
$685$	17.4008			0.664850
$686$	9.58889	+	7.88535i	0.366106	+	0.301064i
$687$		0			0
$688$	−0.750378	+	1.29969i	−0.0286079	+	0.0495503i
$689$	1.13002	+	1.95725i	0.0430503	+	0.0745653i
$690$		0			0
$691$	−9.95052	+	17.2348i	−0.378536	+	0.655643i	−0.990849	−	0.134972i	$-0.956906\pi$
$691$	−9.95052	+	17.2348i	−0.378536	+	0.655643i	0.612314	+	0.790615i	$0.290239\pi$
$692$	−28.3585			−1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	1.76823	−	3.06266i	0.0670727	−	0.116173i
$696$		0			0
$697$	−0.139270	−	0.241223i	−0.00527524	−	0.00913699i
$698$	10.0913	−	17.4787i	0.381963	−	0.661579i
$699$		0			0
$700$	10.2008	+	6.66100i	0.385555	+	0.251762i
$701$	−43.7908			−1.65396			−0.826979	−	0.562234i	$-0.809942\pi$
$701$	−43.7908			−1.65396			−0.826979	+	0.562234i	$0.809942\pi$
$702$		0			0
$703$	2.84983	+	4.93604i	0.107483	+	0.186166i
$704$	−2.11016	−	3.65490i	−0.0795295	−	0.137749i
$705$		0			0
$706$	4.19583			0.157912
$707$	−12.1216	+	6.13792i	−0.455878	+	0.230840i
$708$		0			0
$709$	−22.3172	+	38.6545i	−0.838139	+	1.45170i	0.0533097	+	0.998578i	$0.483023\pi$
$709$	−22.3172	+	38.6545i	−0.838139	+	1.45170i	−0.891449	+	0.453121i	$0.850310\pi$
$710$	0.0384437	+	0.0665865i	0.00144277	+	0.00249895i
$711$		0			0
$712$	−16.0966	+	27.8801i	−0.603244	+	1.04485i
$713$	−13.6233			−0.510195
$714$		0			0
$715$	−19.3540			−0.723798
$716$	5.91227	−	10.2403i	0.220952	−	0.382700i
$717$		0			0
$718$	−3.41705	−	5.91851i	−0.127523	−	0.220877i
$719$	19.5096	−	33.7917i	0.727586	−	1.26022i	−0.230315	−	0.973116i	$-0.573976\pi$
$719$	19.5096	−	33.7917i	0.727586	−	1.26022i	0.957901	−	0.287100i	$-0.0926912\pi$
$720$		0			0
$721$	−31.4819	−	20.5572i	−1.17245	−	0.765592i
$722$	1.93016			0.0718332
$723$		0			0
$724$	12.0413	+	20.8561i	0.447510	+	0.775109i
$725$	10.1130	+	17.5162i	0.375586	+	0.650534i
$726$		0			0
$727$	22.5107			0.834877			0.417439	−	0.908705i	$-0.362928\pi$
$727$	22.5107			0.834877			0.417439	+	0.908705i	$0.362928\pi$
$728$	0.951361	−	17.3202i	0.0352598	−	0.641929i
$729$		0			0
$730$	5.10593	−	8.84373i	0.188979	−	0.327321i
$731$	−0.557951	−	0.966399i	−0.0206366	−	0.0357436i
$732$		0			0
$733$	0.448519	−	0.776858i	0.0165664	−	0.0286939i	−0.857623	−	0.514278i	$-0.828060\pi$
$733$	0.448519	−	0.776858i	0.0165664	−	0.0286939i	0.874190	+	0.485584i	$0.161393\pi$
$734$	19.2088			0.709011
$735$		0			0
$736$	31.3673			1.15622
$737$	31.0335	−	53.7517i	1.14314	−	1.97997i
$738$		0			0
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	0.897074	−	0.441880i	$-0.145688\pi$
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	−0.831216	+	0.555949i	$0.812355\pi$
$740$	1.56833	−	2.71643i	0.0576531	−	0.0998581i
$741$		0			0
$742$	0.0798057	−	1.45292i	0.00292976	−	0.0533384i
$743$	−49.5928			−1.81938			−0.909691	−	0.415286i	$-0.863682\pi$
$743$	−49.5928			−1.81938			−0.909691	+	0.415286i	$0.863682\pi$
$744$		0			0
$745$	6.09583	+	10.5583i	0.223334	+	0.386826i
$746$	−5.38726	−	9.33101i	−0.197242	−	0.341633i
$747$		0			0
$748$	−8.56098			−0.313020
$749$	16.9697	+	11.0810i	0.620061	+	0.404891i
$750$		0			0
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	−0.147543	−	0.989056i	$-0.547136\pi$
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	0.930319	−	0.366752i	$-0.119530\pi$
$752$	−7.13450	−	12.3573i	−0.260168	−	0.450625i
$753$		0			0
$754$	6.28835	−	10.8917i	0.229008	−	0.396654i
$755$	25.1633			0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	−0.341510	+	0.591513i	−0.0124042	+	0.0214847i
$759$		0			0
$760$	6.80856	+	11.7928i	0.246972	+	0.427769i
$761$	20.3599	−	35.2643i	0.738044	−	1.27833i	−0.215330	−	0.976541i	$-0.569083\pi$
$761$	20.3599	−	35.2643i	0.738044	−	1.27833i	0.953375	−	0.301789i	$-0.0975839\pi$
$762$		0			0
$763$	−4.00981	+	2.03042i	−0.145165	+	0.0735063i
$764$	23.0001			0.832113
$765$		0			0
$766$	3.88342	+	6.72627i	0.140313	+	0.243030i
$767$	−9.06826	−	15.7067i	−0.327436	−	0.567135i
$768$		0			0
$769$	−11.1476			−0.401994			−0.200997	−	0.979592i	$-0.564418\pi$
$769$	−11.1476			−0.401994			−0.200997	+	0.979592i	$0.564418\pi$
$770$	10.4335	+	6.81294i	0.375998	+	0.245521i
$771$		0			0
$772$	12.8454	−	22.2489i	0.462317	−	0.800756i
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	0.874229	−	0.485514i	$-0.161368\pi$
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	−0.857582	+	0.514347i	$0.828034\pi$
$774$		0			0
$775$	3.72061	−	6.44428i	0.133648	−	0.231485i
$776$	−12.8602			−0.461656
$777$		0			0
$778$	11.9410			0.428105
$779$	−0.499408	+	0.865001i	−0.0178932	+	0.0309919i
$780$		0			0
$781$	0.198452	+	0.343728i	0.00710116	+	0.0122996i
$782$	−2.04024	+	3.53381i	−0.0729590	+	0.126369i
$783$		0			0
$784$	6.23854	−	8.49648i	0.222805	−	0.303446i
$785$	−9.00772			−0.321499
$786$		0			0
$787$	−11.5120	−	19.9393i	−0.410358	−	0.710761i	0.584571	−	0.811343i	$-0.301263\pi$
$787$	−11.5120	−	19.9393i	−0.410358	−	0.710761i	−0.994929	+	0.100582i	$0.967930\pi$
$788$	3.13030	+	5.42184i	0.111512	+	0.193145i
$789$		0			0
$790$	−1.76223			−0.0626973
$791$	−0.0871659	+	1.58692i	−0.00309926	+	0.0564243i
$792$		0			0
$793$	−0.103662	+	0.179548i	−0.00368114	+	0.00637593i
$794$	4.38551	+	7.59592i	0.155636	+	0.269569i
$795$		0			0
$796$	19.6014	−	33.9505i	0.694752	−	1.20335i
$797$	22.7851			0.807089			0.403544	−	0.914960i	$-0.367778\pi$
$797$	22.7851			0.807089			0.403544	+	0.914960i	$0.367778\pi$
$798$		0			0
$799$	10.6098			0.375349
$800$	−8.56664	+	14.8379i	−0.302877	+	0.524598i
$801$		0			0
$802$	−4.72695	−	8.18732i	−0.166914	−	0.289104i
$803$	26.3575	−	45.6525i	0.930135	−	1.61104i
$804$		0			0
$805$	−18.2856	+	9.25915i	−0.644481	+	0.326342i
$806$	−4.62703			−0.162980
$807$		0			0
$808$	−6.11143	−	10.5853i	−0.214999	−	0.372390i
$809$	−6.73753	−	11.6697i	−0.236879	−	0.410286i	0.722938	−	0.690913i	$-0.242791\pi$
$809$	−6.73753	−	11.6697i	−0.236879	−	0.410286i	−0.959817	+	0.280627i	$0.909458\pi$
$810$		0			0
$811$	−30.7348			−1.07924			−0.539622	−	0.841907i	$-0.681433\pi$
$811$	−30.7348			−1.07924			−0.539622	+	0.841907i	$0.681433\pi$
$812$	24.9296	−	12.6235i	0.874859	−	0.442997i
$813$		0			0
$814$	−2.34603	+	4.06344i	−0.0822283	+	0.142424i
$815$	5.71590	+	9.90023i	0.200219	+	0.346790i
$816$		0			0
$817$	−2.00075	+	3.46540i	−0.0699974	+	0.121239i
$818$	1.77369			0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	−8.49319	+	14.7106i	−0.296414	+	0.513405i	−0.975313	−	0.220827i	$-0.929124\pi$
$821$	−8.49319	+	14.7106i	−0.296414	+	0.513405i	0.678899	+	0.734232i	$0.262458\pi$
$822$		0			0
$823$	9.29157	+	16.0935i	0.323884	+	0.560983i	0.981286	−	0.192557i	$-0.0616780\pi$
$823$	9.29157	+	16.0935i	0.323884	+	0.560983i	−0.657402	+	0.753540i	$0.728345\pi$
$824$	16.9122	−	29.2928i	0.589164	−	1.02046i
$825$		0			0
$826$	−0.640430	+	11.6595i	−0.0222834	+	0.405686i
$827$	−14.5419			−0.505670			−0.252835	−	0.967509i	$-0.581363\pi$
$827$	−14.5419			−0.505670			−0.252835	+	0.967509i	$0.581363\pi$
$828$		0			0
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	0.937104	−	0.349051i	$-0.113496\pi$
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	−0.770839	+	0.637030i	$0.780163\pi$
$830$	6.91154	+	11.9711i	0.239903	+	0.415524i
$831$		0			0
$832$	2.35770			0.0817386
$833$	3.15188	+	7.17607i	0.109206	+	0.248636i
$834$		0			0
$835$	1.51097	−	2.61708i	0.0522894	−	0.0905678i
$836$	15.3494	+	26.5859i	0.530869	+	0.919492i
$837$		0			0
$838$	11.2326	−	19.4554i	0.388023	−	0.672075i
$839$	42.4606			1.46590			0.732952	−	0.680281i	$-0.238142\pi$
$839$	42.4606			1.46590			0.732952	+	0.680281i	$0.238142\pi$
$840$		0			0
$841$	17.3910			0.599690
$842$	1.62187	−	2.80917i	0.0558934	−	0.0968103i
$843$		0			0
$844$	5.83428	+	10.1053i	0.200824	+	0.347838i
$845$	−3.85599	+	6.67877i	−0.132650	+	0.229757i
$846$		0			0
$847$	29.4911	+	19.2572i	1.01332	+	0.661687i
$848$	−1.23548			−0.0424264
$849$		0			0
$850$	−1.11441	−	1.93021i	−0.0382239	−	0.0662058i
$851$	−3.85883	−	6.68370i	−0.132279	−	0.229114i
$852$		0			0
$853$	−14.2808			−0.488965			−0.244482	−	0.969654i	$-0.578618\pi$
$853$	−14.2808			−0.488965			−0.244482	+	0.969654i	$0.578618\pi$
$854$	0.119087	−	0.0603014i	0.00407507	−	0.00206347i
$855$		0			0
$856$	−9.11621	+	15.7897i	−0.311586	+	0.539682i
$857$	17.3895	+	30.1195i	0.594013	+	1.02886i	0.993685	+	0.112203i	$0.0357907\pi$
$857$	17.3895	+	30.1195i	0.594013	+	1.02886i	−0.399672	+	0.916658i	$0.630876\pi$
$858$		0			0
$859$	6.32429	−	10.9540i	0.215782	−	0.373745i	−0.737732	−	0.675093i	$-0.764103\pi$
$859$	6.32429	−	10.9540i	0.215782	−	0.373745i	0.953514	+	0.301348i	$0.0974366\pi$
$860$	2.20213			0.0750921
$861$		0			0
$862$	−23.6819			−0.806608
$863$	−13.2398	+	22.9321i	−0.450690	+	0.780617i	−0.998429	−	0.0560318i	$-0.982155\pi$
$863$	−13.2398	+	22.9321i	−0.450690	+	0.780617i	0.547739	+	0.836649i	$0.315489\pi$
$864$		0			0
$865$	13.0297	+	22.5681i	0.443022	+	0.767337i
$866$	1.83471	−	3.17782i	0.0623461	−	0.107987i
$867$		0			0
$868$	−8.60790	−	5.62084i	−0.292171	−	0.190784i
$869$	−9.09686			−0.308590
$870$		0			0
$871$	17.3371	+	30.0287i	0.587444	+	1.01748i
$872$	−2.02166	−	3.50162i	−0.0684621	−	0.118580i
$873$		0			0
$874$	14.6322			0.494941
$875$	1.64785	−	30.0002i	0.0557074	−	1.01419i
$876$		0			0
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	−0.999747	−	0.0224835i	$-0.992843\pi$
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	0.519345	+	0.854565i	$0.326176\pi$
$878$	2.14443	+	3.71427i	0.0723711	+	0.125350i
$879$		0			0
$880$	5.29004	−	9.16261i	0.178327	−	0.308872i
$881$	20.3637			0.686071			0.343036	−	0.939322i	$-0.388545\pi$
$881$	20.3637			0.686071			0.343036	+	0.939322i	$0.388545\pi$
$882$		0			0
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	2.39132	−	4.14189i	0.0804288	−	0.139307i
$885$		0			0
$886$	2.14065	+	3.70771i	0.0719164	+	0.124563i
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	−0.899250	−	0.437435i	$-0.855887\pi$
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	0.828455	+	0.560056i	$0.189220\pi$
$888$		0			0
$889$	1.05344	−	19.1786i	0.0353312	−	0.643231i
$890$	12.9196			0.433067
$891$		0			0
$892$	−10.0673	−	17.4371i	−0.337078	−	0.583837i
$893$	−19.0229	−	32.9486i	−0.636576	−	1.10258i
$894$		0			0
$895$	−10.8659			−0.363206
$896$	24.2918	+	15.8622i	0.811533	+	0.529920i
$897$		0			0
$898$	3.93685	−	6.81883i	0.131375	−	0.227547i
$899$	−8.53374	−	14.7809i	−0.284616	−	0.492970i
$900$		0			0
$901$	0.459325	−	0.795574i	0.0153023	−	0.0265044i
$902$	−0.822244			−0.0273777
$903$		0			0
$904$	−1.42974			−0.0475526
$905$	11.0650	−	19.1652i	0.367814	−	0.637072i
$906$		0			0
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	−0.921780	−	0.387713i	$-0.873265\pi$
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	0.125121	−	0.992142i	$-0.460068\pi$
$908$	22.4585	−	38.8993i	0.745311	−	1.29092i
$909$		0			0
$910$	−6.21054	+	3.14480i	−0.205878	+	0.104249i
$911$	−25.7335			−0.852587			−0.426294	−	0.904585i	$-0.640181\pi$
$911$	−25.7335			−0.852587			−0.426294	+	0.904585i	$0.640181\pi$
$912$		0			0
$913$	35.6782	+	61.7965i	1.18078	+	2.04517i
$914$	3.52675	+	6.10852i	0.116655	+	0.202052i
$915$		0			0
$916$	−23.9356			−0.790854
$917$	45.3092	+	29.5863i	1.49624	+	0.977024i
$918$		0			0
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	−0.846702	−	0.532068i	$-0.821415\pi$
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	0.884135	+	0.467232i	$0.154749\pi$
$920$	−9.21919	−	15.9681i	−0.303948	−	0.526453i
$921$		0			0
$922$	−2.37484	+	4.11334i	−0.0782111	+	0.135466i
$923$	−0.221732			−0.00729840
$924$		0			0
$925$	4.21550			0.138605
$926$	−10.9774	+	19.0134i	−0.360740	+	0.624819i
$927$		0			0
$928$	19.6488	+	34.0328i	0.645004	+	1.11718i
$929$	22.9248	−	39.7069i	0.752138	−	1.30274i	−0.194647	−	0.980873i	$-0.562356\pi$
$929$	22.9248	−	39.7069i	0.752138	−	1.30274i	0.946785	−	0.321868i	$-0.104311\pi$
$930$		0			0
$931$	16.6340	−	22.6544i	0.545156	−	0.742467i
$932$	7.67028			0.251248
$933$		0			0
$934$	1.31530	+	2.27816i	0.0430379	+	0.0745438i
$935$	3.93346	+	6.81294i	0.128638	+	0.222807i
$936$		0			0
$937$	−56.2075			−1.83622			−0.918110	−	0.396325i	$-0.870285\pi$
$937$	−56.2075			−1.83622			−0.918110	+	0.396325i	$0.870285\pi$
$938$	1.22440	−	22.2911i	0.0399781	−	0.727830i
$939$		0			0
$940$	−10.4688	+	18.1325i	−0.341454	+	0.591416i
$941$	−17.6402	−	30.5536i	−0.575053	−	0.996020i	−0.996036	−	0.0889519i	$-0.971648\pi$
$941$	−17.6402	−	30.5536i	−0.575053	−	0.996020i	0.420983	−	0.907068i	$-0.361685\pi$
$942$		0			0
$943$	0.676229	−	1.17126i	0.0220210	−	0.0381415i
$944$	9.91453			0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	−25.3565	+	43.9188i	−0.823976	+	1.42717i	0.0787236	+	0.996896i	$0.474916\pi$
$947$	−25.3565	+	43.9188i	−0.823976	+	1.42717i	−0.902699	+	0.430272i	$0.858418\pi$
$948$		0			0
$949$	14.7248	+	25.5040i	0.477986	+	0.827896i
$950$	−3.99615	+	6.92154i	−0.129652	+	0.224564i
$951$		0			0
$952$	−6.29037	+	3.18522i	−0.203872	+	0.103234i
$953$	−25.9988			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$953$	−25.9988			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$954$		0			0
$955$	−10.5677	−	18.3038i	−0.341962	−	0.592296i
$956$	10.1061	+	17.5043i	0.326855	+	0.566130i
$957$		0			0
$958$	10.7833			0.348392
$959$	28.8242	−	14.5956i	0.930783	−	0.471315i
$960$		0			0
$961$	12.3604	−	21.4088i	0.398722	−	0.690607i
$962$	−1.31062	−	2.27006i	−0.0422562	−	0.0731898i
$963$		0			0
$964$	11.3062	−	19.5829i	0.364148	−	0.630722i
$965$	−23.6080			−0.759968
$966$		0			0
$967$	25.9621			0.834885			0.417442	−	0.908703i	$-0.362927\pi$
$967$	25.9621			0.834885			0.417442	+	0.908703i	$0.362927\pi$
$968$	−15.8427	+	27.4404i	−0.509204	+	0.881967i
$969$		0			0
$970$	2.58052	+	4.46959i	0.0828554	+	0.143510i
$971$	3.97206	−	6.87981i	0.127469	−	0.220783i	−0.795226	−	0.606313i	$-0.792648\pi$
$971$	3.97206	−	6.87981i	0.127469	−	0.220783i	0.922696	+	0.385530i	$0.125981\pi$
$972$		0			0
$973$	0.360130	−	6.55643i	0.0115452	−	0.210189i
$974$	−2.34847			−0.0752499
$975$		0			0
$976$	−0.0566680	−	0.0981518i	−0.00181390	−	0.00314176i
$977$	−26.1274	−	45.2540i	−0.835889	−	1.44780i	−0.893304	−	0.449452i	$-0.851619\pi$
$977$	−26.1274	−	45.2540i	−0.835889	−	1.44780i	0.0574149	−	0.998350i	$-0.481714\pi$
$978$		0			0
$979$	66.6929			2.13151
$980$	−15.3740	−	1.69404i	−0.491106	−	0.0541140i
$981$		0			0
$982$	−13.7784	+	23.8650i	−0.439688	+	0.761562i
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	−0.989601	−	0.143839i	$-0.954055\pi$
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	0.370232	−	0.928939i	$-0.379278\pi$
$984$		0			0
$985$	2.87652	−	4.98228i	0.0916535	−	0.158749i
$986$	−5.11212			−0.162803
$987$		0			0
$988$	−17.1500			−0.545615
$989$	2.70914	−	4.69236i	0.0861455	−	0.149208i
$990$		0			0
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	0.508565	−	0.861023i	$-0.330176\pi$
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	−0.999951	+	0.00991892i	$0.996843\pi$
$992$	7.22890	−	12.5208i	0.229518	−	0.397536i
$993$		0			0
$994$	0.119534	+	0.0780537i	0.00379137	+	0.00247571i
$995$	−36.0244			−1.14205
$996$		0			0
$997$	−23.5335	−	40.7612i	−0.745313	−	1.29092i	−0.950048	−	0.312103i	$-0.898967\pi$
$997$	−23.5335	−	40.7612i	−0.745313	−	1.29092i	0.204735	−	0.978817i	$-0.434367\pi$
$998$	3.96492	+	6.86745i	0.125507	+	0.217385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.e.163.4		10
3.2	odd	2		567.2.e.f.163.2		10
7.2	even	3		3969.2.a.bc.1.2		5
7.4	even	3	inner	567.2.e.e.487.4		10
7.5	odd	6		3969.2.a.bb.1.2		5
9.2	odd	6		63.2.h.b.58.4	yes	10
9.4	even	3		189.2.g.b.100.4		10
9.5	odd	6		63.2.g.b.16.2	yes	10
9.7	even	3		189.2.h.b.37.2		10
21.2	odd	6		3969.2.a.z.1.4		5
21.5	even	6		3969.2.a.ba.1.4		5
21.11	odd	6		567.2.e.f.487.2		10
36.7	odd	6		3024.2.q.i.2305.5		10
36.11	even	6		1008.2.q.i.625.1		10
36.23	even	6		1008.2.t.i.961.4		10
36.31	odd	6		3024.2.t.i.289.1		10
63.2	odd	6		441.2.f.e.148.2		10
63.4	even	3		189.2.h.b.46.2		10
63.5	even	6		441.2.f.f.295.2		10
63.11	odd	6		63.2.g.b.4.2	✓	10
63.13	odd	6		1323.2.g.f.667.4		10
63.16	even	3		1323.2.f.e.442.4		10
63.20	even	6		441.2.h.f.373.4		10
63.23	odd	6		441.2.f.e.295.2		10
63.25	even	3		189.2.g.b.172.4		10
63.31	odd	6		1323.2.h.f.802.2		10
63.32	odd	6		63.2.h.b.25.4	yes	10
63.34	odd	6		1323.2.h.f.226.2		10
63.38	even	6		441.2.g.f.67.2		10
63.40	odd	6		1323.2.f.f.883.4		10
63.41	even	6		441.2.g.f.79.2		10
63.47	even	6		441.2.f.f.148.2		10
63.52	odd	6		1323.2.g.f.361.4		10
63.58	even	3		1323.2.f.e.883.4		10
63.59	even	6		441.2.h.f.214.4		10
63.61	odd	6		1323.2.f.f.442.4		10
252.11	even	6		1008.2.t.i.193.4		10
252.67	odd	6		3024.2.q.i.2881.5		10
252.95	even	6		1008.2.q.i.529.1		10
252.151	odd	6		3024.2.t.i.1873.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	63.11	odd	6
63.2.g.b.16.2	yes	10	9.5	odd	6
63.2.h.b.25.4	yes	10	63.32	odd	6
63.2.h.b.58.4	yes	10	9.2	odd	6
189.2.g.b.100.4		10	9.4	even	3
189.2.g.b.172.4		10	63.25	even	3
189.2.h.b.37.2		10	9.7	even	3
189.2.h.b.46.2		10	63.4	even	3
441.2.f.e.148.2		10	63.2	odd	6
441.2.f.e.295.2		10	63.23	odd	6
441.2.f.f.148.2		10	63.47	even	6
441.2.f.f.295.2		10	63.5	even	6
441.2.g.f.67.2		10	63.38	even	6
441.2.g.f.79.2		10	63.41	even	6
441.2.h.f.214.4		10	63.59	even	6
441.2.h.f.373.4		10	63.20	even	6
567.2.e.e.163.4		10	1.1	even	1	trivial
567.2.e.e.487.4		10	7.4	even	3	inner
567.2.e.f.163.2		10	3.2	odd	2
567.2.e.f.487.2		10	21.11	odd	6
1008.2.q.i.529.1		10	252.95	even	6
1008.2.q.i.625.1		10	36.11	even	6
1008.2.t.i.193.4		10	252.11	even	6
1008.2.t.i.961.4		10	36.23	even	6
1323.2.f.e.442.4		10	63.16	even	3
1323.2.f.e.883.4		10	63.58	even	3
1323.2.f.f.442.4		10	63.61	odd	6
1323.2.f.f.883.4		10	63.40	odd	6
1323.2.g.f.361.4		10	63.52	odd	6
1323.2.g.f.667.4		10	63.13	odd	6
1323.2.h.f.226.2		10	63.34	odd	6
1323.2.h.f.802.2		10	63.31	odd	6
3024.2.q.i.2305.5		10	36.7	odd	6
3024.2.q.i.2881.5		10	252.67	odd	6
3024.2.t.i.289.1		10	36.31	odd	6
3024.2.t.i.1873.1		10	252.151	odd	6
3969.2.a.z.1.4		5	21.2	odd	6
3969.2.a.ba.1.4		5	21.5	even	6
3969.2.a.bb.1.2		5	7.5	odd	6
3969.2.a.bc.1.2		5	7.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(0.712469 - 1.23403i) q^{5} +(0.145107 - 2.64177i) q^{7} +2.38012 q^{8} +(-0.477591 - 0.827212i) q^{10} +(-2.46539 - 4.27018i) q^{11} +2.75460 q^{13} +(-1.48498 - 0.969670i) q^{14} +(-0.752918 + 1.30409i) q^{16} +(-0.559839 - 0.969670i) q^{17} +(-2.00752 + 3.47713i) q^{19} +2.20958 q^{20} -3.30526 q^{22} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(0.923251 - 1.59912i) q^{26} +(3.66015 - 1.85337i) q^{28} +6.81109 q^{29} +(-1.25292 - 2.17012i) q^{31} +(2.88483 + 4.99666i) q^{32} -0.750557 q^{34} +(-3.15664 - 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} +(1.34571 + 2.33083i) q^{38} +(1.69576 - 2.93714i) q^{40} +0.248768 q^{41} +0.996627 q^{43} +(3.82296 - 6.62156i) q^{44} +(-1.82217 - 3.15609i) q^{46} +(-4.73790 + 8.20628i) q^{47} +(-6.95789 - 0.766676i) q^{49} +1.99059 q^{50} +(2.13572 + 3.69917i) q^{52} +(0.410229 + 0.710537i) q^{53} -7.02604 q^{55} +(0.345371 - 6.28773i) q^{56} +(2.28285 - 3.95401i) q^{58} +(-3.29204 - 5.70197i) q^{59} +(-0.0376322 + 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(1.96257 - 3.39927i) q^{65} +(6.29385 + 10.9013i) q^{67} +(0.868117 - 1.50362i) q^{68} +(-2.25460 + 1.14165i) q^{70} -0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +(-0.475793 - 0.824098i) q^{74} -6.22595 q^{76} +(-11.6386 + 5.89335i) q^{77} +(0.922457 - 1.59774i) q^{79} +(1.07286 + 1.85825i) q^{80} +(0.0833788 - 0.144416i) q^{82} -14.4717 q^{83} -1.59547 q^{85} +(0.334036 - 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(-6.76292 + 11.7137i) q^{89} +(0.399711 - 7.27703i) q^{91} +8.43030 q^{92} +(3.17597 + 5.50094i) q^{94} +(2.86059 + 4.95469i) q^{95} -5.40319 q^{97} +(-2.77712 + 3.78226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 + 16 * q^13 - 4 * q^14 + 2 * q^16 - 12 * q^17 + q^19 + 10 * q^20 + 2 * q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 + 14 * q^29 - 3 * q^31 + 2 * q^32 - 6 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 + 10 * q^41 + 14 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 - 17 * q^49 + 38 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 27 * q^56 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 - 11 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 - 10 * q^76 - 20 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 + 18 * q^83 + 12 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 + 54 * q^92 - 3 * q^94 + 14 * q^95 + 24 * q^97 - 59 * q^98

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