LMFDB - Embedded newform 567.2.g.h.541.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.h.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.380438 - 0.658939i) q^{2} +(0.710533 - 1.23068i) q^{4} +3.18194 q^{5} +(1.85185 - 1.88962i) q^{7} -2.60301 q^{8} +(-1.21053 - 2.09671i) q^{10} +2.23912 q^{11} +(-1.85185 - 3.20750i) q^{13} +(-1.94966 - 0.501371i) q^{14} +(-0.430782 - 0.746136i) q^{16} +(2.80150 + 4.85235i) q^{17} +(-2.21053 + 3.82876i) q^{19} +(2.26088 - 3.91595i) q^{20} +(-0.851848 - 1.47544i) q^{22} -0.942820 q^{23} +5.12476 q^{25} +(-1.40903 + 2.44051i) q^{26} +(-1.00972 - 3.62167i) q^{28} +(-5.06238 + 8.76830i) q^{29} +(2.85185 - 4.93955i) q^{31} +(-2.93078 + 5.07626i) q^{32} +(2.13160 - 3.69204i) q^{34} +(5.89248 - 6.01266i) q^{35} +(-1.56238 + 2.70612i) q^{37} +3.36389 q^{38} -8.28263 q^{40} +(-1.99316 - 3.45226i) q^{41} +(1.64132 - 2.84284i) q^{43} +(1.59097 - 2.75564i) q^{44} +(0.358685 + 0.621261i) q^{46} +(0.112725 + 0.195246i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(-1.94966 - 3.37690i) q^{50} -5.26320 q^{52} +(-5.33009 - 9.23200i) q^{53} +7.12476 q^{55} +(-4.82038 + 4.91870i) q^{56} +7.70370 q^{58} +(1.02859 - 1.78157i) q^{59} +(2.92107 + 5.05944i) q^{61} -4.33981 q^{62} +2.73680 q^{64} +(-5.89248 - 10.2061i) q^{65} +(-3.71053 + 6.42683i) q^{67} +7.96225 q^{68} +(-6.20370 - 1.59533i) q^{70} +7.26320 q^{71} +(-3.77975 - 6.54672i) q^{73} +2.37756 q^{74} +(3.14132 + 5.44092i) q^{76} +(4.14652 - 4.23109i) q^{77} +(3.41423 + 5.91362i) q^{79} +(-1.37072 - 2.37416i) q^{80} +(-1.51655 + 2.62674i) q^{82} +(4.05555 - 7.02441i) q^{83} +(8.91423 + 15.4399i) q^{85} -2.49768 q^{86} -5.82846 q^{88} +(-4.86389 + 8.42450i) q^{89} +(-9.49028 - 2.44051i) q^{91} +(-0.669905 + 1.16031i) q^{92} +(0.0857699 - 0.148558i) q^{94} +(-7.03379 + 12.1829i) q^{95} +(-0.421067 + 0.729309i) q^{97} +(-4.55787 + 2.75564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 2 q^{7} + 18 q^{8} + q^{10} + 14 q^{11} - 2 q^{13} - 4 q^{14} - 10 q^{16} - 5 q^{19} + 13 q^{20} + 4 q^{22} + 12 q^{23} - 4 q^{25} - 17 q^{26} - 30 q^{28} - 13 q^{29}+ \cdots + 49 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 2 * q^7 + 18 * q^8 + q^10 + 14 * q^11 - 2 * q^13 - 4 * q^14 - 10 * q^16 - 5 * q^19 + 13 * q^20 + 4 * q^22 + 12 * q^23 - 4 * q^25 - 17 * q^26 - 30 * q^28 - 13 * q^29 + 8 * q^31 - 25 * q^32 - 12 * q^34 + 10 * q^35 + 8 * q^37 - 14 * q^38 - 48 * q^40 - 2 * q^41 + 9 * q^43 + q^44 + 3 * q^46 - 9 * q^47 - 4 * q^50 + 18 * q^52 - 24 * q^53 + 8 * q^55 + 3 * q^56 + 28 * q^58 + 15 * q^59 + q^61 - 42 * q^62 + 66 * q^64 - 10 * q^65 - 14 * q^67 + 78 * q^68 - 19 * q^70 - 6 * q^71 - 7 * q^73 + 18 * q^76 - 11 * q^77 - 6 * q^79 + 16 * q^80 - 43 * q^82 - 3 * q^83 + 27 * q^85 - 64 * q^86 + 18 * q^88 + 5 * q^89 - 33 * q^91 - 12 * q^92 + 27 * q^94 - 16 * q^95 + 14 * q^97 + 49 * 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 $

$2$	−0.380438	−	0.658939i	−0.269011	−	0.465940i	0.699596	−	0.714539i	$-0.253363\pi$
$2$	−0.380438	−	0.658939i	−0.269011	−	0.465940i	−0.968607	+	0.248599i	$0.920030\pi$
$3$		0			0
$3$		0			0
$4$	0.710533	−	1.23068i	0.355267	−	0.615340i
$5$	3.18194			1.42301			0.711504	−	0.702682i	$-0.248014\pi$
$5$	3.18194			1.42301			0.711504	+	0.702682i	$0.248014\pi$
$6$		0			0
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$8$	−2.60301			−0.920303
$9$		0			0
$10$	−1.21053	−	2.09671i	−0.382804	−	0.663036i
$11$	2.23912			0.675121			0.337561	−	0.941304i	$-0.390398\pi$
$11$	2.23912			0.675121			0.337561	+	0.941304i	$0.390398\pi$
$12$		0			0
$13$	−1.85185	−	3.20750i	−0.513610	−	0.889599i	−0.999875	−	0.0157878i	$-0.994974\pi$
$13$	−1.85185	−	3.20750i	−0.513610	−	0.889599i	0.486265	−	0.873811i	$-0.338359\pi$
$14$	−1.94966	−	0.501371i	−0.521068	−	0.133997i
$15$		0			0
$16$	−0.430782	−	0.746136i	−0.107695	−	0.186534i
$17$	2.80150	+	4.85235i	0.679465	+	1.17687i	0.975142	+	0.221580i	$0.0711213\pi$
$17$	2.80150	+	4.85235i	0.679465	+	1.17687i	−0.295678	+	0.955288i	$0.595545\pi$
$18$		0			0
$19$	−2.21053	+	3.82876i	−0.507131	+	0.878377i	0.492835	+	0.870123i	$0.335961\pi$
$19$	−2.21053	+	3.82876i	−0.507131	+	0.878377i	−0.999966	+	0.00825398i	$0.997373\pi$
$20$	2.26088	−	3.91595i	0.505547	−	0.875634i
$21$		0			0
$22$	−0.851848	−	1.47544i	−0.181615	−	0.314566i
$23$	−0.942820			−0.196592			−0.0982958	−	0.995157i	$-0.531339\pi$
$23$	−0.942820			−0.196592			−0.0982958	+	0.995157i	$0.531339\pi$
$24$		0			0
$25$	5.12476			1.02495
$26$	−1.40903	+	2.44051i	−0.276333	+	0.478623i
$27$		0			0
$28$	−1.00972	−	3.62167i	−0.190818	−	0.684431i
$29$	−5.06238	+	8.76830i	−0.940061	+	1.62823i	−0.174709	+	0.984620i	$0.555899\pi$
$29$	−5.06238	+	8.76830i	−0.940061	+	1.62823i	−0.765351	+	0.643613i	$0.777435\pi$
$30$		0			0
$31$	2.85185	−	4.93955i	0.512207	−	0.887169i	−0.487693	−	0.873015i	$-0.662161\pi$
$31$	2.85185	−	4.93955i	0.512207	−	0.887169i	0.999900	−	0.0141534i	$-0.00450531\pi$
$32$	−2.93078	+	5.07626i	−0.518094	+	0.897365i
$33$		0			0
$34$	2.13160	−	3.69204i	0.365566	−	0.633180i
$35$	5.89248	−	6.01266i	0.996010	−	1.01632i
$36$		0			0
$37$	−1.56238	+	2.70612i	−0.256854	+	0.444884i	−0.965397	−	0.260783i	$-0.916019\pi$
$37$	−1.56238	+	2.70612i	−0.256854	+	0.444884i	0.708543	+	0.705667i	$0.249353\pi$
$38$	3.36389			0.545694
$39$		0			0
$40$	−8.28263			−1.30960
$41$	−1.99316	−	3.45226i	−0.311280	−	0.539152i	0.667360	−	0.744735i	$-0.267424\pi$
$41$	−1.99316	−	3.45226i	−0.311280	−	0.539152i	−0.978640	+	0.205583i	$0.934091\pi$
$42$		0			0
$43$	1.64132	−	2.84284i	0.250298	−	0.433529i	−0.713310	−	0.700849i	$-0.752805\pi$
$43$	1.64132	−	2.84284i	0.250298	−	0.433529i	0.963608	+	0.267320i	$0.0861380\pi$
$44$	1.59097	−	2.75564i	0.239848	−	0.415429i
$45$		0			0
$46$	0.358685	+	0.621261i	0.0528852	+	0.0915999i
$47$	0.112725	+	0.195246i	0.0164426	+	0.0284795i	0.874130	−	0.485693i	$-0.161433\pi$
$47$	0.112725	+	0.195246i	0.0164426	+	0.0284795i	−0.857687	+	0.514172i	$0.828099\pi$
$48$		0			0
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$	−1.94966	−	3.37690i	−0.275723	−	0.477566i
$51$		0			0
$52$	−5.26320			−0.729874
$53$	−5.33009	−	9.23200i	−0.732145	−	1.26811i	−0.955965	−	0.293482i	$-0.905186\pi$
$53$	−5.33009	−	9.23200i	−0.732145	−	1.26811i	0.223820	−	0.974631i	$-0.428147\pi$
$54$		0			0
$55$	7.12476			0.960703
$56$	−4.82038	+	4.91870i	−0.644150	+	0.657288i
$57$		0			0
$58$	7.70370			1.01154
$59$	1.02859	−	1.78157i	0.133911	−	0.231941i	−0.791270	−	0.611467i	$-0.790580\pi$
$59$	1.02859	−	1.78157i	0.133911	−	0.231941i	0.925181	+	0.379526i	$0.123913\pi$
$60$		0			0
$61$	2.92107	+	5.05944i	0.374004	+	0.647794i	0.990177	−	0.139816i	$-0.0446512\pi$
$61$	2.92107	+	5.05944i	0.374004	+	0.647794i	−0.616173	+	0.787611i	$0.711318\pi$
$62$	−4.33981			−0.551156
$63$		0			0
$64$	2.73680			0.342100
$65$	−5.89248	−	10.2061i	−0.730872	−	1.26591i
$66$		0			0
$67$	−3.71053	+	6.42683i	−0.453314	+	0.785163i	−0.998590	−	0.0530942i	$-0.983092\pi$
$67$	−3.71053	+	6.42683i	−0.453314	+	0.785163i	0.545276	+	0.838257i	$0.316425\pi$
$68$	7.96225			0.965565
$69$		0			0
$70$	−6.20370	−	1.59533i	−0.741484	−	0.190679i
$71$	7.26320			0.861983			0.430992	−	0.902356i	$-0.358164\pi$
$71$	7.26320			0.861983			0.430992	+	0.902356i	$0.358164\pi$
$72$		0			0
$73$	−3.77975	−	6.54672i	−0.442386	−	0.766236i	0.555480	−	0.831530i	$-0.312535\pi$
$73$	−3.77975	−	6.54672i	−0.442386	−	0.766236i	−0.997866	+	0.0652944i	$0.979201\pi$
$74$	2.37756			0.276386
$75$		0			0
$76$	3.14132	+	5.44092i	0.360334	+	0.624116i
$77$	4.14652	−	4.23109i	0.472539	−	0.482177i
$78$		0			0
$79$	3.41423	+	5.91362i	0.384131	+	0.665334i	0.991648	−	0.128972i	$-0.0411678\pi$
$79$	3.41423	+	5.91362i	0.384131	+	0.665334i	−0.607517	+	0.794306i	$0.707834\pi$
$80$	−1.37072	−	2.37416i	−0.153252	−	0.265439i
$81$		0			0
$82$	−1.51655	+	2.62674i	−0.167475	+	0.290075i
$83$	4.05555	−	7.02441i	0.445154	−	0.771029i	−0.552909	−	0.833242i	$-0.686482\pi$
$83$	4.05555	−	7.02441i	0.445154	−	0.771029i	0.998063	+	0.0622124i	$0.0198156\pi$
$84$		0			0
$85$	8.91423	+	15.4399i	0.966884	+	1.67469i
$86$	−2.49768			−0.269331
$87$		0			0
$88$	−5.82846			−0.621316
$89$	−4.86389	+	8.42450i	−0.515571	+	0.892995i	0.484266	+	0.874921i	$0.339087\pi$
$89$	−4.86389	+	8.42450i	−0.515571	+	0.892995i	−0.999837	+	0.0180741i	$0.994247\pi$
$90$		0			0
$91$	−9.49028	−	2.44051i	−0.994852	−	0.255835i
$92$	−0.669905	+	1.16031i	−0.0698424	+	0.120971i
$93$		0			0
$94$	0.0857699	−	0.148558i	0.00884649	−	0.0153226i
$95$	−7.03379	+	12.1829i	−0.721652	+	1.24994i
$96$		0			0
$97$	−0.421067	+	0.729309i	−0.0427528	+	0.0740501i	−0.886610	−	0.462518i	$-0.846946\pi$
$97$	−0.421067	+	0.729309i	−0.0427528	+	0.0740501i	0.843857	+	0.536568i	$0.180279\pi$
$98$	−4.55787	+	2.75564i	−0.460414	+	0.278362i
$99$		0			0
$100$	3.64132	−	6.30694i	0.364132	−	0.630694i
$101$	−7.74720			−0.770876			−0.385438	−	0.922734i	$-0.625950\pi$
$101$	−7.74720			−0.770876			−0.385438	+	0.922734i	$0.625950\pi$
$102$		0			0
$103$	−2.43474			−0.239902			−0.119951	−	0.992780i	$-0.538274\pi$
$103$	−2.43474			−0.239902			−0.119951	+	0.992780i	$0.538274\pi$
$104$	4.82038	+	8.34914i	0.472677	+	0.818701i
$105$		0			0
$106$	−4.05555	+	7.02441i	−0.393909	+	0.682271i
$107$	−5.73229	+	9.92861i	−0.554161	+	0.959835i	0.443807	+	0.896122i	$0.353628\pi$
$107$	−5.73229	+	9.92861i	−0.554161	+	0.959835i	−0.997968	+	0.0637128i	$0.979706\pi$
$108$		0			0
$109$	9.12476	+	15.8046i	0.873994	+	1.51380i	0.857831	+	0.513932i	$0.171812\pi$
$109$	9.12476	+	15.8046i	0.873994	+	1.51380i	0.0161631	+	0.999869i	$0.494855\pi$
$110$	−2.71053	−	4.69478i	−0.258439	−	0.447630i
$111$		0			0
$112$	−2.20765	−	0.567717i	−0.208604	−	0.0536443i
$113$	2.62476	+	4.54622i	0.246917	+	0.427673i	0.962669	−	0.270682i	$-0.0872492\pi$
$113$	2.62476	+	4.54622i	0.246917	+	0.427673i	−0.715752	+	0.698355i	$0.753916\pi$
$114$		0			0
$115$	−3.00000			−0.279751
$116$	7.19398	+	12.4603i	0.667944	+	1.15691i
$117$		0			0
$118$	−1.56526			−0.144094
$119$	14.3571	+	3.69204i	1.31611	+	0.338449i
$120$		0			0
$121$	−5.98633			−0.544212
$122$	2.22257	−	3.84961i	0.201222	−	0.348527i
$123$		0			0
$124$	−4.05267	−	7.01942i	−0.363940	−	0.630363i
$125$	0.396990			0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	4.82038	+	8.34914i	0.426065	+	0.737967i
$129$		0			0
$130$	−4.48345	+	7.76556i	−0.393224	+	0.681085i
$131$	−4.08126			−0.356581			−0.178291	−	0.983978i	$-0.557057\pi$
$131$	−4.08126			−0.356581			−0.178291	+	0.983978i	$0.557057\pi$
$132$		0			0
$133$	3.14132	+	11.2673i	0.272387	+	0.977002i
$134$	5.64652			0.487785
$135$		0			0
$136$	−7.29235	−	12.6307i	−0.625313	−	1.08307i
$137$	−1.88564			−0.161101			−0.0805506	−	0.996751i	$-0.525668\pi$
$137$	−1.88564			−0.161101			−0.0805506	+	0.996751i	$0.525668\pi$
$138$		0			0
$139$	6.39768	+	11.0811i	0.542644	+	0.939887i	0.998751	+	0.0499621i	$0.0159101\pi$
$139$	6.39768	+	11.0811i	0.542644	+	0.939887i	−0.456107	+	0.889925i	$0.650757\pi$
$140$	−3.21286	−	11.5239i	−0.271536	−	0.973951i
$141$		0			0
$142$	−2.76320	−	4.78600i	−0.231883	−	0.401632i
$143$	−4.14652	−	7.18198i	−0.346749	−	0.600587i
$144$		0			0
$145$	−16.1082	+	27.9002i	−1.33771	+	2.31699i
$146$	−2.87592	+	4.98125i	−0.238013	+	0.412251i
$147$		0			0
$148$	2.22025	+	3.84558i	0.182503	+	0.316105i
$149$	8.05718			0.660070			0.330035	−	0.943969i	$-0.392939\pi$
$149$	8.05718			0.660070			0.330035	+	0.943969i	$0.392939\pi$
$150$		0			0
$151$	−6.28263			−0.511273			−0.255637	−	0.966773i	$-0.582285\pi$
$151$	−6.28263			−0.511273			−0.255637	+	0.966773i	$0.582285\pi$
$152$	5.75404	−	9.96629i	0.466714	−	0.808373i
$153$		0			0
$154$	−4.36552	−	1.12263i	−0.351784	−	0.0904642i
$155$	9.07442	−	15.7174i	0.728875	−	1.26245i
$156$		0			0
$157$	−0.351848	+	0.609419i	−0.0280806	+	0.0486370i	−0.879724	−	0.475484i	$-0.842273\pi$
$157$	−0.351848	+	0.609419i	−0.0280806	+	0.0486370i	0.851644	+	0.524121i	$0.175606\pi$
$158$	2.59781	−	4.49954i	0.206671	−	0.357964i
$159$		0			0
$160$	−9.32558	+	16.1524i	−0.737252	+	1.27696i
$161$	−1.74596	+	1.78157i	−0.137601	+	0.140407i
$162$		0			0
$163$	9.61793	−	16.6587i	0.753334	−	1.30481i	−0.192864	−	0.981225i	$-0.561778\pi$
$163$	9.61793	−	16.6587i	0.753334	−	1.30481i	0.946198	−	0.323588i	$-0.104889\pi$
$164$	−5.66484			−0.442349
$165$		0			0
$166$	−6.17154			−0.479004
$167$	−11.6940	−	20.2546i	−0.904907	−	1.56735i	−0.821041	−	0.570869i	$-0.806607\pi$
$167$	−11.6940	−	20.2546i	−0.904907	−	1.56735i	−0.0838661	−	0.996477i	$-0.526727\pi$
$168$		0			0
$169$	−0.358685	+	0.621261i	−0.0275911	+	0.0477893i
$170$	6.78263	−	11.7479i	0.520204	−	0.901020i
$171$		0			0
$172$	−2.33242	−	4.03987i	−0.177845	−	0.308037i
$173$	4.11956	+	7.13529i	0.313204	+	0.542486i	0.979054	−	0.203600i	$-0.0652641\pi$
$173$	4.11956	+	7.13529i	0.313204	+	0.542486i	−0.665850	+	0.746086i	$0.731931\pi$
$174$		0			0
$175$	9.49028	−	9.68385i	0.717398	−	0.732030i
$176$	−0.964574	−	1.67069i	−0.0727075	−	0.125933i
$177$		0			0
$178$	7.40164			0.554776
$179$	−4.95486	−	8.58207i	−0.370344	−	0.641454i	0.619275	−	0.785174i	$-0.287427\pi$
$179$	−4.95486	−	8.58207i	−0.370344	−	0.641454i	−0.989618	+	0.143721i	$0.954093\pi$
$180$		0			0
$181$	−9.38796			−0.697802			−0.348901	−	0.937160i	$-0.613445\pi$
$181$	−9.38796			−0.697802			−0.348901	+	0.937160i	$0.613445\pi$
$182$	2.00232	+	7.18198i	0.148422	+	0.532364i
$183$		0			0
$184$	2.45417			0.180924
$185$	−4.97141	+	8.61073i	−0.365505	+	0.633074i
$186$		0			0
$187$	6.27292	+	10.8650i	0.458721	+	0.794528i
$188$	0.320380			0.0233661
$189$		0			0
$190$	10.7037			0.776528
$191$	12.3691	+	21.4239i	0.894996	+	1.55018i	0.833810	+	0.552052i	$0.186155\pi$
$191$	12.3691	+	21.4239i	0.894996	+	1.55018i	0.0611861	+	0.998126i	$0.480512\pi$
$192$		0			0
$193$	0.414230	−	0.717468i	0.0298169	−	0.0516444i	−0.850732	−	0.525600i	$-0.823841\pi$
$193$	0.414230	−	0.717468i	0.0298169	−	0.0516444i	0.880549	+	0.473955i	$0.157174\pi$
$194$	0.640760			0.0460039
$195$		0			0
$196$	−8.71341	−	4.79881i	−0.622387	−	0.342772i
$197$	5.86156			0.417619			0.208810	−	0.977956i	$-0.433041\pi$
$197$	5.86156			0.417619			0.208810	+	0.977956i	$0.433041\pi$
$198$		0			0
$199$	4.62476	+	8.01033i	0.327841	+	0.567837i	0.982083	−	0.188448i	$-0.0603457\pi$
$199$	4.62476	+	8.01033i	0.327841	+	0.567837i	−0.654242	+	0.756285i	$0.727012\pi$
$200$	−13.3398			−0.943267
$201$		0			0
$202$	2.94733	+	5.10493i	0.207374	+	0.359182i
$203$	7.19398	+	25.8035i	0.504919	+	1.81105i
$204$		0			0
$205$	−6.34213	−	10.9849i	−0.442954	−	0.767218i
$206$	0.926268	+	1.60434i	0.0645362	+	0.111780i
$207$		0			0
$208$	−1.59549	+	2.76346i	−0.110627	+	0.191612i
$209$	−4.94966	+	8.57306i	−0.342375	+	0.593011i
$210$		0			0
$211$	6.27975	+	10.8768i	0.432316	+	0.748793i	0.997072	−	0.0764645i	$-0.0243632\pi$
$211$	6.27975	+	10.8768i	0.432316	+	0.748793i	−0.564756	+	0.825258i	$0.691030\pi$
$212$	−15.1488			−1.04043
$213$		0			0
$214$	8.72313			0.596301
$215$	5.22257	−	9.04576i	0.356176	−	0.616916i
$216$		0			0
$217$	−4.05267	−	14.5362i	−0.275113	−	0.986781i
$218$	6.94282	−	12.0253i	0.470227	−	0.814457i
$219$		0			0
$220$	5.06238	−	8.76830i	0.341306	−	0.591159i
$221$	10.3759	−	17.9716i	0.697960	−	1.20890i
$222$		0			0
$223$	10.6940	−	18.5225i	0.716122	−	1.24036i	−0.246403	−	0.969167i	$-0.579249\pi$
$223$	10.6940	−	18.5225i	0.716122	−	1.24036i	0.962525	−	0.271192i	$-0.0874179\pi$
$224$	4.16484	+	14.9385i	0.278275	+	0.998122i
$225$		0			0
$226$	1.99712	−	3.45912i	0.132847	−	0.230097i
$227$	−12.6224			−0.837781			−0.418890	−	0.908037i	$-0.637581\pi$
$227$	−12.6224			−0.837781			−0.418890	+	0.908037i	$0.637581\pi$
$228$		0			0
$229$	−28.9201			−1.91110			−0.955548	−	0.294837i	$-0.904735\pi$
$229$	−28.9201			−1.91110			−0.955548	+	0.294837i	$0.904735\pi$
$230$	1.14132	+	1.97682i	0.0752561	+	0.130347i
$231$		0			0
$232$	13.1774	−	22.8240i	0.865141	−	1.49847i
$233$	−10.7255	+	18.5770i	−0.702648	+	1.21702i	0.264886	+	0.964280i	$0.414666\pi$
$233$	−10.7255	+	18.5770i	−0.702648	+	1.21702i	−0.967534	+	0.252742i	$0.918668\pi$
$234$		0			0
$235$	0.358685	+	0.621261i	0.0233980	+	0.0405266i
$236$	−1.46169	−	2.53173i	−0.0951482	−	0.164802i
$237$		0			0
$238$	−3.02915	−	10.8650i	−0.196350	−	0.704274i
$239$	3.86840	+	6.70027i	0.250226	+	0.433404i	0.963588	−	0.267392i	$-0.0861617\pi$
$239$	3.86840	+	6.70027i	0.250226	+	0.433404i	−0.713362	+	0.700796i	$0.752828\pi$
$240$		0			0
$241$	6.09166			0.392398			0.196199	−	0.980564i	$-0.437140\pi$
$241$	6.09166			0.392398			0.196199	+	0.980564i	$0.437140\pi$
$242$	2.27743	+	3.94462i	0.146399	+	0.253570i
$243$		0			0
$244$	8.30206			0.531485
$245$	−0.449657	−	22.2691i	−0.0287275	−	1.42272i
$246$		0			0
$247$	16.3743			1.04187
$248$	−7.42339	+	12.8577i	−0.471386	+	0.816464i
$249$		0			0
$250$	−0.151030	−	0.261592i	−0.00955199	−	0.0165445i
$251$	−1.40164			−0.0884705			−0.0442352	−	0.999021i	$-0.514085\pi$
$251$	−1.40164			−0.0884705			−0.0442352	+	0.999021i	$0.514085\pi$
$252$		0			0
$253$	−2.11109			−0.132723
$254$	−7.64884	−	13.2482i	−0.479931	−	0.831265i
$255$		0			0
$256$	6.40451	−	11.0929i	0.400282	−	0.693309i
$257$	−17.9565			−1.12010			−0.560048	−	0.828460i	$-0.689217\pi$
$257$	−17.9565			−1.12010			−0.560048	+	0.828460i	$0.689217\pi$
$258$		0			0
$259$	2.22025	+	7.96364i	0.137960	+	0.494836i
$260$	−16.7472			−1.03862
$261$		0			0
$262$	1.55267	+	2.68930i	0.0959241	+	0.166145i
$263$	−7.17619			−0.442503			−0.221251	−	0.975217i	$-0.571014\pi$
$263$	−7.17619			−0.442503			−0.221251	+	0.975217i	$0.571014\pi$
$264$		0			0
$265$	−16.9601	−	29.3757i	−1.04185	−	1.80453i
$266$	6.22941	−	6.35646i	0.381950	−	0.389740i
$267$		0			0
$268$	5.27292	+	9.13296i	0.322095	+	0.557884i
$269$	−1.69850	−	2.94188i	−0.103559	−	0.179370i	0.809590	−	0.586996i	$-0.199690\pi$
$269$	−1.69850	−	2.94188i	−0.103559	−	0.179370i	−0.913149	+	0.407627i	$0.866356\pi$
$270$		0			0
$271$	5.11793	−	8.86451i	0.310892	−	0.538481i	−0.667664	−	0.744463i	$-0.732706\pi$
$271$	5.11793	−	8.86451i	0.310892	−	0.538481i	0.978556	+	0.205982i	$0.0660389\pi$
$272$	2.41367	−	4.18061i	0.146351	−	0.253487i
$273$		0			0
$274$	0.717370	+	1.24252i	0.0433379	+	0.0750634i
$275$	11.4750			0.691967
$276$		0			0
$277$	−3.55950			−0.213870			−0.106935	−	0.994266i	$-0.534104\pi$
$277$	−3.55950			−0.213870			−0.106935	+	0.994266i	$0.534104\pi$
$278$	4.86784	−	8.43135i	0.291954	−	0.505679i
$279$		0			0
$280$	−15.3382	+	15.6510i	−0.916631	+	0.935327i
$281$	−3.49316	+	6.05034i	−0.208385	+	0.360933i	−0.951206	−	0.308557i	$-0.900154\pi$
$281$	−3.49316	+	6.05034i	−0.208385	+	0.360933i	0.742821	+	0.669490i	$0.233487\pi$
$282$		0			0
$283$	15.1082	−	26.1682i	0.898090	−	1.55554i	0.0681568	−	0.997675i	$-0.478288\pi$
$283$	15.1082	−	26.1682i	0.898090	−	1.55554i	0.829933	−	0.557863i	$-0.188378\pi$
$284$	5.16075	−	8.93867i	0.306234	−	0.530413i
$285$		0			0
$286$	−3.15499	+	5.46460i	−0.186558	+	0.323129i
$287$	−10.2145	−	2.62674i	−0.602942	−	0.155052i
$288$		0			0
$289$	−7.19686	+	12.4653i	−0.423345	+	0.733255i
$290$	24.5127			1.43944
$291$		0			0
$292$	−10.7426			−0.628661
$293$	7.61793	+	13.1946i	0.445044	+	0.770839i	0.998055	−	0.0623349i	$-0.0198547\pi$
$293$	7.61793	+	13.1946i	0.445044	+	0.770839i	−0.553011	+	0.833174i	$0.686521\pi$
$294$		0			0
$295$	3.27292	−	5.66886i	0.190556	−	0.330054i
$296$	4.06690	−	7.04407i	0.236383	−	0.409428i
$297$		0			0
$298$	−3.06526	−	5.30919i	−0.177566	−	0.307553i
$299$	1.74596	+	3.02409i	0.100971	+	0.174888i
$300$		0			0
$301$	−2.33242	−	8.36597i	−0.134438	−	0.482206i
$302$	2.39015	+	4.13987i	0.137538	+	0.238223i
$303$		0			0
$304$	3.80903			0.218463
$305$	9.29467	+	16.0988i	0.532211	+	0.921817i
$306$		0			0
$307$	−1.03310			−0.0589623			−0.0294812	−	0.999565i	$-0.509386\pi$
$307$	−1.03310			−0.0589623			−0.0294812	+	0.999565i	$0.509386\pi$
$308$	−2.26088	−	8.10936i	−0.128825	−	0.462074i
$309$		0			0
$310$	−13.8090			−0.784300
$311$	4.66019	−	8.07169i	0.264255	−	0.457703i	−0.703113	−	0.711078i	$-0.748207\pi$
$311$	4.66019	−	8.07169i	0.264255	−	0.457703i	0.967368	+	0.253375i	$0.0815406\pi$
$312$		0			0
$313$	−3.04583	−	5.27553i	−0.172160	−	0.298191i	0.767014	−	0.641630i	$-0.221741\pi$
$313$	−3.04583	−	5.27553i	−0.172160	−	0.298191i	−0.939175	+	0.343439i	$0.888408\pi$
$314$	0.535426			0.0302159
$315$		0			0
$316$	9.70370			0.545876
$317$	−11.6505	−	20.1792i	−0.654356	−	1.13338i	−0.982055	−	0.188595i	$-0.939607\pi$
$317$	−11.6505	−	20.1792i	−0.654356	−	1.13338i	0.327699	−	0.944782i	$-0.393727\pi$
$318$		0			0
$319$	−11.3353	+	19.6333i	−0.634655	+	1.09925i
$320$	8.70834			0.486811
$321$		0			0
$322$	1.83818	+	0.472703i	0.102438	+	0.0263427i
$323$	−24.7713			−1.37831
$324$		0			0
$325$	−9.49028	−	16.4377i	−0.526426	−	0.911797i
$326$	−14.6361			−0.810619
$327$		0			0
$328$	5.18822	+	8.98627i	0.286472	+	0.496184i
$329$	0.577690	+	0.148558i	0.0318491	+	0.00819026i
$330$		0			0
$331$	−7.33818	−	12.7101i	−0.403343	−	0.698610i	0.590784	−	0.806829i	$-0.298818\pi$
$331$	−7.33818	−	12.7101i	−0.403343	−	0.698610i	−0.994127	+	0.108220i	$0.965485\pi$
$332$	−5.76320	−	9.98215i	−0.316297	−	0.547842i
$333$		0			0
$334$	−8.89768	+	15.4112i	−0.486859	+	0.843265i
$335$	−11.8067	+	20.4498i	−0.645069	+	1.11729i
$336$		0			0
$337$	−12.8119	−	22.1909i	−0.697909	−	1.20881i	−0.969190	−	0.246314i	$-0.920781\pi$
$337$	−12.8119	−	22.1909i	−0.697909	−	1.20881i	0.271281	−	0.962500i	$-0.412553\pi$
$338$	0.545830			0.0296892
$339$		0			0
$340$	25.3354			1.37401
$341$	6.38564	−	11.0603i	0.345802	−	0.598946i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	−4.27236	+	7.39994i	−0.230350	+	0.398978i
$345$		0			0
$346$	3.13448	−	5.42908i	0.168511	−	0.291869i
$347$	5.64652	−	9.78005i	0.303121	−	0.525021i	−0.673720	−	0.738986i	$-0.735305\pi$
$347$	5.64652	−	9.78005i	0.303121	−	0.525021i	0.976841	+	0.213966i	$0.0686381\pi$
$348$		0			0
$349$	5.64815	−	9.78289i	0.302339	−	0.523666i	−0.674327	−	0.738433i	$-0.735566\pi$
$349$	5.64815	−	9.78289i	0.302339	−	0.523666i	0.976665	+	0.214767i	$0.0688993\pi$
$350$	−9.99153	−	2.56941i	−0.534070	−	0.137341i
$351$		0			0
$352$	−6.56238	+	11.3664i	−0.349776	+	0.605830i
$353$	18.5023			0.984779			0.492390	−	0.870375i	$-0.336124\pi$
$353$	18.5023			0.984779			0.492390	+	0.870375i	$0.336124\pi$
$354$		0			0
$355$	23.1111			1.22661
$356$	6.91191	+	11.9718i	0.366330	+	0.634503i
$357$		0			0
$358$	−3.77004	+	6.52989i	−0.199253	+	0.345116i
$359$	9.94802	−	17.2305i	0.525037	−	0.909390i	−0.474538	−	0.880235i	$-0.657385\pi$
$359$	9.94802	−	17.2305i	0.525037	−	0.909390i	0.999575	−	0.0291551i	$-0.00928167\pi$
$360$		0			0
$361$	−0.272915	−	0.472703i	−0.0143639	−	0.0248791i
$362$	3.57154	+	6.18609i	0.187716	+	0.325134i
$363$		0			0
$364$	−9.74665	+	9.94544i	−0.510863	+	0.521283i
$365$	−12.0270	−	20.8313i	−0.629520	−	1.09036i
$366$		0			0
$367$	5.75047			0.300172			0.150086	−	0.988673i	$-0.452045\pi$
$367$	5.75047			0.300172			0.150086	+	0.988673i	$0.452045\pi$
$368$	0.406150	+	0.703472i	0.0211720	+	0.0366710i
$369$		0			0
$370$	7.56526			0.393299
$371$	−27.3155	−	7.02441i	−1.41815	−	0.364689i
$372$		0			0
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$	4.77292	−	8.26693i	0.246802	−	0.427473i
$375$		0			0
$376$	−0.293425	−	0.508226i	−0.0151322	−	0.0262098i
$377$	37.4991			1.93130
$378$		0			0
$379$	8.95322			0.459896			0.229948	−	0.973203i	$-0.426144\pi$
$379$	8.95322			0.459896			0.229948	+	0.973203i	$0.426144\pi$
$380$	9.99549	+	17.3127i	0.512758	+	0.888122i
$381$		0			0
$382$	9.41135	−	16.3009i	0.481527	−	0.834029i
$383$	−20.1650			−1.03038			−0.515192	−	0.857075i	$-0.672279\pi$
$383$	−20.1650			−1.03038			−0.515192	+	0.857075i	$0.672279\pi$
$384$		0			0
$385$	13.1940	−	13.4631i	0.672428	−	0.686142i
$386$	−0.630356			−0.0320843
$387$		0			0
$388$	0.598364	+	1.03640i	0.0303773	+	0.0526151i
$389$	33.5997			1.70357			0.851787	−	0.523888i	$-0.175519\pi$
$389$	33.5997			1.70357			0.851787	+	0.523888i	$0.175519\pi$
$390$		0			0
$391$	−2.64132	−	4.57489i	−0.133577	−	0.231362i
$392$	0.367845	+	18.2174i	0.0185790	+	0.920115i
$393$		0			0
$394$	−2.22996	−	3.86241i	−0.112344	−	0.194585i
$395$	10.8639	+	18.8168i	0.546621	+	0.946776i
$396$		0			0
$397$	2.06922	−	3.58399i	0.103851	−	0.179875i	−0.809417	−	0.587234i	$-0.800217\pi$
$397$	2.06922	−	3.58399i	0.103851	−	0.179875i	0.913268	+	0.407359i	$0.133550\pi$
$398$	3.51887	−	6.09487i	0.176385	−	0.305508i
$399$		0			0
$400$	−2.20765	−	3.82377i	−0.110383	−	0.191189i
$401$	−15.4692			−0.772496			−0.386248	−	0.922395i	$-0.626229\pi$
$401$	−15.4692			−0.772496			−0.386248	+	0.922395i	$0.626229\pi$
$402$		0			0
$403$	−21.1248			−1.05230
$404$	−5.50465	+	9.53433i	−0.273866	+	0.474350i
$405$		0			0
$406$	14.2661	−	14.5570i	0.708014	−	0.722454i
$407$	−3.49837	+	6.05935i	−0.173408	+	0.300351i
$408$		0			0
$409$	−13.6969	+	23.7237i	−0.677266	+	1.17306i	0.298535	+	0.954399i	$0.403502\pi$
$409$	−13.6969	+	23.7237i	−0.677266	+	1.17306i	−0.975801	+	0.218661i	$0.929831\pi$
$410$	−4.82558	+	8.35815i	−0.238318	+	0.412780i
$411$		0			0
$412$	−1.72996	+	2.99638i	−0.0852292	+	0.147621i
$413$	−1.46169	−	5.24284i	−0.0719253	−	0.257983i
$414$		0			0
$415$	12.9045	−	22.3513i	0.633458	−	1.09718i
$416$	21.7095			1.06439
$417$		0			0
$418$	7.53216			0.368410
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	−0.999887	−	0.0150285i	$-0.995216\pi$
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	0.486928	−	0.873442i	$-0.338117\pi$
$420$		0			0
$421$	−9.97949	+	17.2850i	−0.486371	+	0.842419i	−0.999877	−	0.0156670i	$-0.995013\pi$
$421$	−9.97949	+	17.2850i	−0.486371	+	0.842419i	0.513507	+	0.858086i	$0.328346\pi$
$422$	4.77812	−	8.27594i	0.232595	−	0.402867i
$423$		0			0
$424$	13.8743	+	24.0310i	0.673795	+	1.16705i
$425$	14.3571	+	24.8671i	0.696419	+	1.20623i
$426$		0			0
$427$	14.9698	+	3.84961i	0.724438	+	0.186296i
$428$	8.14596	+	14.1092i	0.393750	+	0.681995i
$429$		0			0
$430$	−7.94747			−0.383261
$431$	10.0647	+	17.4326i	0.484800	+	0.839698i	0.999847	−	0.0174637i	$-0.00555914\pi$
$431$	10.0647	+	17.4326i	0.484800	+	0.839698i	−0.515048	+	0.857162i	$0.672226\pi$
$432$		0			0
$433$	11.8558			0.569754			0.284877	−	0.958564i	$-0.408047\pi$
$433$	11.8558			0.569754			0.284877	+	0.958564i	$0.408047\pi$
$434$	−8.03667	+	8.20058i	−0.385773	+	0.393641i
$435$		0			0
$436$	25.9338			1.24200
$437$	2.08414	−	3.60983i	0.0996977	−	0.172681i
$438$		0			0
$439$	1.07893	+	1.86877i	0.0514947	+	0.0891914i	0.890624	−	0.454741i	$-0.150268\pi$
$439$	1.07893	+	1.86877i	0.0514947	+	0.0891914i	−0.839129	+	0.543932i	$0.816935\pi$
$440$	−18.5458			−0.884138
$441$		0			0
$442$	−15.7896			−0.751035
$443$	0.981125	+	1.69936i	0.0466147	+	0.0807390i	0.888391	−	0.459087i	$-0.151823\pi$
$443$	0.981125	+	1.69936i	0.0466147	+	0.0807390i	−0.841777	+	0.539826i	$0.818490\pi$
$444$		0			0
$445$	−15.4766	+	26.8063i	−0.733662	+	1.27074i
$446$	−16.2736			−0.770577
$447$		0			0
$448$	5.06814	−	5.17151i	0.239447	−	0.244331i
$449$	2.15211			0.101564			0.0507822	−	0.998710i	$-0.483829\pi$
$449$	2.15211			0.101564			0.0507822	+	0.998710i	$0.483829\pi$
$450$		0			0
$451$	−4.46294	−	7.73004i	−0.210152	−	0.363993i
$452$	7.45993			0.350885
$453$		0			0
$454$	4.80206	+	8.31741i	0.225372	+	0.390356i
$455$	−30.1975	−	7.76556i	−1.41568	−	0.364055i
$456$		0			0
$457$	6.55267	+	11.3496i	0.306521	+	0.530910i	0.977599	−	0.210477i	$-0.0675018\pi$
$457$	6.55267	+	11.3496i	0.306521	+	0.530910i	−0.671078	+	0.741387i	$0.734168\pi$
$458$	11.0023	+	19.0566i	0.514105	+	0.890456i
$459$		0			0
$460$	−2.13160	+	3.69204i	−0.0993864	+	0.172142i
$461$	2.74364	−	4.75212i	0.127784	−	0.221328i	−0.795034	−	0.606565i	$-0.792547\pi$
$461$	2.74364	−	4.75212i	0.127784	−	0.221328i	0.922818	+	0.385237i	$0.125880\pi$
$462$		0			0
$463$	10.2495	+	17.7527i	0.476336	+	0.825038i	0.999632	−	0.0271127i	$-0.00863130\pi$
$463$	10.2495	+	17.7527i	0.476336	+	0.825038i	−0.523296	+	0.852151i	$0.675298\pi$
$464$	8.72313			0.404961
$465$		0			0
$466$	16.3215			0.756078
$467$	−19.6758	+	34.0795i	−0.910487	+	1.57701i	−0.0971099	+	0.995274i	$0.530960\pi$
$467$	−19.6758	+	34.0795i	−0.910487	+	1.57701i	−0.813377	+	0.581736i	$0.802374\pi$
$468$		0			0
$469$	5.27292	+	18.9130i	0.243481	+	0.873322i
$470$	0.272915	−	0.472703i	0.0125886	−	0.0218041i
$471$		0			0
$472$	−2.67743	+	4.63744i	−0.123239	+	0.213456i
$473$	3.67511	−	6.36547i	0.168982	−	0.292685i
$474$		0			0
$475$	−11.3285	+	19.6215i	−0.519785	+	0.900295i
$476$	14.7449	−	15.0456i	0.675830	−	0.689615i
$477$		0			0
$478$	2.94338	−	5.09808i	0.134627	−	0.233181i
$479$	−16.7472			−0.765199			−0.382600	−	0.923914i	$-0.624971\pi$
$479$	−16.7472			−0.765199			−0.382600	+	0.923914i	$0.624971\pi$
$480$		0			0
$481$	11.5732			0.527691
$482$	−2.31750	−	4.01403i	−0.105559	−	0.182834i
$483$		0			0
$484$	−4.25348	+	7.36725i	−0.193340	+	0.334875i
$485$	−1.33981	+	2.32062i	−0.0608376	+	0.105374i
$486$		0			0
$487$	−2.00288	−	3.46909i	−0.0907591	−	0.157199i	0.817072	−	0.576536i	$-0.195596\pi$
$487$	−2.00288	−	3.46909i	−0.0907591	−	0.157199i	−0.907831	+	0.419337i	$0.862263\pi$
$488$	−7.60357	−	13.1698i	−0.344197	−	0.596167i
$489$		0			0
$490$	−14.5029	+	8.76830i	−0.655173	+	0.396112i
$491$	12.3256	+	21.3485i	0.556246	+	0.963446i	0.997805	+	0.0662140i	$0.0210920\pi$
$491$	12.3256	+	21.3485i	0.556246	+	0.963446i	−0.441560	+	0.897232i	$0.645575\pi$
$492$		0			0
$493$	−56.7292			−2.55495
$494$	−6.22941	−	10.7897i	−0.280274	−	0.485449i
$495$		0			0
$496$	−4.91410			−0.220649
$497$	13.4503	−	13.7247i	0.603330	−	0.615636i
$498$		0			0
$499$	−24.5595			−1.09943			−0.549717	−	0.835351i	$-0.685265\pi$
$499$	−24.5595			−1.09943			−0.549717	+	0.835351i	$0.685265\pi$
$500$	0.282075	−	0.488568i	0.0126148	−	0.0218494i
$501$		0			0
$502$	0.533236	+	0.923592i	0.0237995	+	0.0412219i
$503$	12.3743			0.551742			0.275871	−	0.961195i	$-0.411034\pi$
$503$	12.3743			0.551742			0.275871	+	0.961195i	$0.411034\pi$
$504$		0			0
$505$	−24.6512			−1.09696
$506$	0.803140	+	1.39108i	0.0357039	+	0.0618410i
$507$		0			0
$508$	14.2855	−	24.7432i	0.633817	−	1.09780i
$509$	11.1956			0.496237			0.248118	−	0.968730i	$-0.420188\pi$
$509$	11.1956			0.496237			0.248118	+	0.968730i	$0.420188\pi$
$510$		0			0
$511$	−19.3703	−	4.98125i	−0.856893	−	0.220357i
$512$	9.53543			0.421410
$513$		0			0
$514$	6.83134	+	11.8322i	0.301317	+	0.521897i
$515$	−7.74720			−0.341383
$516$		0			0
$517$	0.252405	+	0.437179i	0.0111008	+	0.0192271i
$518$	4.40288	−	4.49268i	0.193451	−	0.197397i
$519$		0			0
$520$	15.3382	+	26.5665i	0.672623	+	1.16502i
$521$	−15.8096	−	27.3830i	−0.692631	−	1.19967i	−0.970973	−	0.239189i	$-0.923118\pi$
$521$	−15.8096	−	27.3830i	−0.692631	−	1.19967i	0.278342	−	0.960482i	$-0.410215\pi$
$522$		0			0
$523$	14.1179	−	24.4530i	0.617334	−	1.06925i	−0.372636	−	0.927977i	$-0.621546\pi$
$523$	14.1179	−	24.4530i	0.617334	−	1.06925i	0.989970	−	0.141276i	$-0.0451205\pi$
$524$	−2.89987	+	5.02272i	−0.126681	+	0.219419i
$525$		0			0
$526$	2.73010	+	4.72867i	0.119038	+	0.206180i
$527$	31.9579			1.39211
$528$		0			0
$529$	−22.1111			−0.961352
$530$	−12.9045	+	22.3513i	−0.560536	+	0.970877i
$531$		0			0
$532$	16.0985	+	4.13987i	0.697958	+	0.179486i
$533$	−7.38207	+	12.7861i	−0.319753	+	0.553829i
$534$		0			0
$535$	−18.2398	+	31.5923i	−0.788576	+	1.36585i
$536$	9.65856	−	16.7291i	0.417186	−	0.722587i
$537$		0			0
$538$	−1.29235	+	2.23841i	−0.0557170	+	0.0965046i
$539$	−0.316422	−	15.6707i	−0.0136293	−	0.674983i
$540$		0			0
$541$	−21.4045	+	37.0737i	−0.920252	+	1.59392i	−0.121227	+	0.992625i	$0.538683\pi$
$541$	−21.4045	+	37.0737i	−0.920252	+	1.59392i	−0.799025	+	0.601298i	$0.794650\pi$
$542$	−7.78822			−0.334533
$543$		0			0
$544$	−32.8424			−1.40811
$545$	29.0345	+	50.2892i	1.24370	+	2.15415i
$546$		0			0
$547$	−6.77579	+	11.7360i	−0.289712	+	0.501796i	−0.973741	−	0.227659i	$-0.926893\pi$
$547$	−6.77579	+	11.7360i	−0.289712	+	0.501796i	0.684029	+	0.729455i	$0.260226\pi$
$548$	−1.33981	+	2.32062i	−0.0572339	+	0.0991319i
$549$		0			0
$550$	−4.36552	−	7.56130i	−0.186146	−	0.322415i
$551$	−22.3811	−	38.7652i	−0.953468	−	1.65146i
$552$		0			0
$553$	17.4971	+	4.49954i	0.744053	+	0.191340i
$554$	1.35417	+	2.34549i	0.0575332	+	0.0996505i
$555$		0			0
$556$	18.1831			0.771133
$557$	−16.3925	−	28.3926i	−0.694572	−	1.20303i	−0.970325	−	0.241805i	$-0.922261\pi$
$557$	−16.3925	−	28.3926i	−0.694572	−	1.20303i	0.275753	−	0.961228i	$-0.411073\pi$
$558$		0			0
$559$	−12.1579			−0.514223
$560$	−7.02463	−	1.80644i	−0.296845	−	0.0763362i
$561$		0			0
$562$	5.31573			0.224231
$563$	8.57730	−	14.8563i	0.361490	−	0.626119i	−0.626716	−	0.779248i	$-0.715601\pi$
$563$	8.57730	−	14.8563i	0.361490	−	0.626119i	0.988206	+	0.153128i	$0.0489348\pi$
$564$		0			0
$565$	8.35185	+	14.4658i	0.351365	+	0.608582i
$566$	−22.9910			−0.966383
$567$		0			0
$568$	−18.9062			−0.793286
$569$	−6.44966	−	11.1711i	−0.270384	−	0.468318i	0.698576	−	0.715535i	$-0.253817\pi$
$569$	−6.44966	−	11.1711i	−0.270384	−	0.468318i	−0.968960	+	0.247217i	$0.920484\pi$
$570$		0			0
$571$	0.141315	−	0.244765i	0.00591385	−	0.0102431i	−0.863053	−	0.505113i	$-0.831451\pi$
$571$	0.141315	−	0.244765i	0.00591385	−	0.0102431i	0.868967	+	0.494870i	$0.164784\pi$
$572$	−11.7850			−0.492754
$573$		0			0
$574$	2.15512	+	7.73004i	0.0899530	+	0.322645i
$575$	−4.83173			−0.201497
$576$		0			0
$577$	1.08289	+	1.87562i	0.0450814	+	0.0780832i	0.887686	−	0.460450i	$-0.152312\pi$
$577$	1.08289	+	1.87562i	0.0450814	+	0.0780832i	−0.842604	+	0.538533i	$0.818979\pi$
$578$	10.9518			0.455537
$579$		0			0
$580$	22.8908	+	39.6481i	0.950490	+	1.64630i
$581$	−5.76320	−	20.6716i	−0.239098	−	0.857601i
$582$		0			0
$583$	−11.9347	−	20.6716i	−0.494286	−	0.856129i
$584$	9.83873	+	17.0412i	0.407130	+	0.705169i
$585$		0			0
$586$	5.79630	−	10.0395i	0.239443	−	0.414728i
$587$	8.38796	−	14.5284i	0.346208	−	0.599650i	−0.639364	−	0.768904i	$-0.720802\pi$
$587$	8.38796	−	14.5284i	0.346208	−	0.599650i	0.985573	+	0.169254i	$0.0541357\pi$
$588$		0			0
$589$	12.6082	+	21.8381i	0.519512	+	0.899822i
$590$	−4.98057			−0.205047
$591$		0			0
$592$	2.69218			0.110648
$593$	12.5933	−	21.8122i	0.517145	−	0.895721i	−0.482657	−	0.875809i	$-0.660328\pi$
$593$	12.5933	−	21.8122i	0.517145	−	0.895721i	0.999802	−	0.0199114i	$-0.00633841\pi$
$594$		0			0
$595$	45.6833	+	11.7479i	1.87283	+	0.481615i
$596$	5.72489	−	9.91581i	0.234501	−	0.406167i
$597$		0			0
$598$	1.32846	−	2.30096i	0.0543248	−	0.0940933i
$599$	−14.3662	+	24.8830i	−0.586987	+	1.01669i	0.407637	+	0.913144i	$0.366353\pi$
$599$	−14.3662	+	24.8830i	−0.586987	+	1.01669i	−0.994624	+	0.103548i	$0.966980\pi$
$600$		0			0
$601$	18.3977	−	31.8657i	0.750457	−	1.29983i	−0.197144	−	0.980374i	$-0.563167\pi$
$601$	18.3977	−	31.8657i	0.750457	−	1.29983i	0.947601	−	0.319455i	$-0.103500\pi$
$602$	−4.62532	+	4.71966i	−0.188514	+	0.192359i
$603$		0			0
$604$	−4.46402	+	7.73191i	−0.181638	+	0.314607i
$605$	−19.0482			−0.774418
$606$		0			0
$607$	37.9007			1.53834			0.769171	−	0.639043i	$-0.220670\pi$
$607$	37.9007			1.53834			0.769171	+	0.639043i	$0.220670\pi$
$608$	−12.9572	−	22.4425i	−0.525483	−	0.910163i
$609$		0			0
$610$	7.07210	−	12.2492i	0.286341	−	0.495957i
$611$	0.417500	−	0.723131i	0.0168902	−	0.0292547i
$612$		0			0
$613$	−19.0196	−	32.9428i	−0.768193	−	1.33055i	−0.938542	−	0.345165i	$-0.887823\pi$
$613$	−19.0196	−	32.9428i	−0.768193	−	1.33055i	0.170349	−	0.985384i	$-0.445511\pi$
$614$	0.393032	+	0.680752i	0.0158615	+	0.0274729i
$615$		0			0
$616$	−10.7934	+	11.0136i	−0.434879	+	0.443749i
$617$	−13.2632	−	22.9725i	−0.533956	−	0.924839i	−0.999213	−	0.0396637i	$-0.987371\pi$
$617$	−13.2632	−	22.9725i	−0.533956	−	0.924839i	0.465257	−	0.885176i	$-0.345962\pi$
$618$		0			0
$619$	12.7037			0.510605			0.255302	−	0.966861i	$-0.417825\pi$
$619$	12.7037			0.510605			0.255302	+	0.966861i	$0.417825\pi$
$620$	−12.8954	−	22.3354i	−0.517890	−	0.897012i
$621$		0			0
$622$	−7.09166			−0.284350
$623$	6.91191	+	24.7918i	0.276920	+	0.993262i
$624$		0			0
$625$	−24.3606			−0.974425
$626$	−2.31750	+	4.01403i	−0.0926260	+	0.160433i
$627$		0			0
$628$	0.500000	+	0.866025i	0.0199522	+	0.0345582i
$629$	−17.5081			−0.698093
$630$		0			0
$631$	20.6764			0.823113			0.411556	−	0.911384i	$-0.364985\pi$
$631$	20.6764			0.823113			0.411556	+	0.911384i	$0.364985\pi$
$632$	−8.88727	−	15.3932i	−0.353517	−	0.612309i
$633$		0			0
$634$	−8.86458	+	15.3539i	−0.352057	+	0.609781i
$635$	63.9740			2.53873
$636$		0			0
$637$	−22.1862	+	13.4136i	−0.879049	+	0.531465i
$638$	17.2495			0.682915
$639$		0			0
$640$	15.3382	+	26.5665i	0.606295	+	1.05013i
$641$	27.9740			1.10491			0.552454	−	0.833543i	$-0.313692\pi$
$641$	27.9740			1.10491			0.552454	+	0.833543i	$0.313692\pi$
$642$		0			0
$643$	−13.9903	−	24.2319i	−0.551723	−	0.955612i	−0.998150	−	0.0607924i	$-0.980637\pi$
$643$	−13.9903	−	24.2319i	−0.551723	−	0.955612i	0.446427	−	0.894820i	$-0.352696\pi$
$644$	0.951980	+	3.41458i	0.0375133	+	0.134553i
$645$		0			0
$646$	9.42395	+	16.3228i	0.370780	+	0.642210i
$647$	2.30834	+	3.99816i	0.0907503	+	0.157184i	0.907827	−	0.419345i	$-0.137740\pi$
$647$	2.30834	+	3.99816i	0.0907503	+	0.157184i	−0.817077	+	0.576529i	$0.804407\pi$
$648$		0			0
$649$	2.30314	−	3.98916i	0.0904061	−	0.156588i
$650$	−7.22094	+	12.5070i	−0.283228	+	0.490566i
$651$		0			0
$652$	−13.6677	−	23.6732i	−0.535269	−	0.927113i
$653$	−11.5803			−0.453173			−0.226586	−	0.973991i	$-0.572757\pi$
$653$	−11.5803			−0.453173			−0.226586	+	0.973991i	$0.572757\pi$
$654$		0			0
$655$	−12.9863			−0.507418
$656$	−1.71724	+	2.97434i	−0.0670468	+	0.116129i
$657$		0			0
$658$	−0.121885	−	0.437179i	−0.00475156	−	0.0170430i
$659$	2.36840	−	4.10219i	0.0922598	−	0.159799i	−0.816202	−	0.577767i	$-0.803924\pi$
$659$	2.36840	−	4.10219i	0.0922598	−	0.159799i	0.908462	+	0.417968i	$0.137258\pi$
$660$		0			0
$661$	6.91135	−	11.9708i	0.268820	−	0.465611i	−0.699737	−	0.714400i	$-0.746700\pi$
$661$	6.91135	−	11.9708i	0.268820	−	0.465611i	0.968557	+	0.248790i	$0.0800329\pi$
$662$	−5.58345	+	9.67081i	−0.217007	+	0.375867i
$663$		0			0
$664$	−10.5566	+	18.2846i	−0.409676	+	0.709580i
$665$	9.99549	+	35.8520i	0.387608	+	1.39028i
$666$		0			0
$667$	4.77292	−	8.26693i	0.184808	−	0.320097i
$668$	−33.2359			−1.28593
$669$		0			0
$670$	17.9669			0.694122
$671$	6.54063	+	11.3287i	0.252498	+	0.437340i
$672$		0			0
$673$	−3.01367	+	5.21983i	−0.116169	+	0.201210i	−0.918246	−	0.396010i	$-0.870395\pi$
$673$	−3.01367	+	5.21983i	−0.116169	+	0.201210i	0.802078	+	0.597220i	$0.203728\pi$
$674$	−9.74828	+	16.8845i	−0.375490	+	0.650367i
$675$		0			0
$676$	0.509715	+	0.882853i	0.0196044	+	0.0339559i
$677$	−11.4428	−	19.8195i	−0.439783	−	0.761727i	0.557889	−	0.829915i	$-0.311611\pi$
$677$	−11.4428	−	19.8195i	−0.439783	−	0.761727i	−0.997672	+	0.0681884i	$0.978278\pi$
$678$		0			0
$679$	0.598364	+	2.14622i	0.0229631	+	0.0823645i
$680$	−23.2038	−	40.1902i	−0.889826	−	1.54122i
$681$		0			0
$682$	−9.71737			−0.372097
$683$	5.14940	+	8.91901i	0.197036	+	0.341277i	0.947566	−	0.319560i	$-0.103535\pi$
$683$	5.14940	+	8.91901i	0.197036	+	0.341277i	−0.750530	+	0.660836i	$0.770202\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	−3.23337	+	13.7157i	−0.123450	+	0.523667i
$687$		0			0
$688$	−2.82819			−0.107824
$689$	−19.7411	+	34.1925i	−0.752074	+	1.30263i
$690$		0			0
$691$	−14.5361	−	25.1773i	−0.552980	−	0.957789i	−0.998058	−	0.0622973i	$-0.980157\pi$
$691$	−14.5361	−	25.1773i	−0.552980	−	0.957789i	0.445078	−	0.895492i	$-0.353176\pi$
$692$	11.7083			0.445084
$693$		0			0
$694$	−8.59261			−0.326171
$695$	20.3571	+	35.2594i	0.772187	+	1.33747i
$696$		0			0
$697$	11.1677	−	19.3430i	0.423007	−	0.732670i
$698$	−8.59509			−0.325329
$699$		0			0
$700$	−5.17455	−	18.5602i	−0.195580	−	0.701510i
$701$	27.4153			1.03546			0.517731	−	0.855543i	$-0.326777\pi$
$701$	27.4153			1.03546			0.517731	+	0.855543i	$0.326777\pi$
$702$		0			0
$703$	−6.90739	−	11.9640i	−0.260517	−	0.451229i
$704$	6.12803			0.230959
$705$		0			0
$706$	−7.03899	−	12.1919i	−0.264916	−	0.458848i
$707$	−14.3466	+	14.6393i	−0.539561	+	0.550566i
$708$		0			0
$709$	18.4834	+	32.0143i	0.694160	+	1.20232i	0.970463	+	0.241250i	$0.0775575\pi$
$709$	18.4834	+	32.0143i	0.694160	+	1.20232i	−0.276302	+	0.961071i	$0.589109\pi$
$710$	−8.79235	−	15.2288i	−0.329971	−	0.571526i
$711$		0			0
$712$	12.6607	−	21.9291i	0.474481	−	0.821826i
$713$	−2.68878	+	4.65710i	−0.100696	+	0.174410i
$714$		0			0
$715$	−13.1940	−	22.8526i	−0.493427	−	0.854641i
$716$	−14.0824			−0.526283
$717$		0			0
$718$	−15.1384			−0.564961
$719$	20.2599	−	35.0912i	0.755568	−	1.30868i	−0.189524	−	0.981876i	$-0.560694\pi$
$719$	20.2599	−	35.0912i	0.755568	−	1.30868i	0.945092	−	0.326806i	$-0.105972\pi$
$720$		0			0
$721$	−4.50877	+	4.60073i	−0.167915	+	0.171340i
$722$	−0.207655	+	0.359668i	−0.00772811	+	0.0133855i
$723$		0			0
$724$	−6.67046	+	11.5536i	−0.247906	+	0.429385i
$725$	−25.9435	+	44.9355i	−0.963518	+	1.66886i
$726$		0			0
$727$	7.62081	−	13.1996i	0.282640	−	0.489547i	−0.689394	−	0.724386i	$-0.742123\pi$
$727$	7.62081	−	13.1996i	0.282640	−	0.489547i	0.972034	+	0.234840i	$0.0754565\pi$
$728$	24.7033	+	6.35267i	0.915565	+	0.235446i
$729$		0			0
$730$	−9.15103	+	15.8500i	−0.338695	+	0.586637i
$731$	18.3926			0.680275
$732$		0			0
$733$	32.5789			1.20333			0.601665	−	0.798748i	$-0.294504\pi$
$733$	32.5789			1.20333			0.601665	+	0.798748i	$0.294504\pi$
$734$	−2.18770	−	3.78921i	−0.0807495	−	0.139862i
$735$		0			0
$736$	2.76320	−	4.78600i	0.101853	−	0.176414i
$737$	−8.30834	+	14.3905i	−0.306042	+	0.530080i
$738$		0			0
$739$	−3.50684	−	6.07402i	−0.129001	−	0.223436i	0.794289	−	0.607540i	$-0.207844\pi$
$739$	−3.50684	−	6.07402i	−0.129001	−	0.223436i	−0.923290	+	0.384104i	$0.874510\pi$
$740$	7.06470	+	12.2364i	0.259704	+	0.449820i
$741$		0			0
$742$	5.76320	+	20.6716i	0.211574	+	0.758877i
$743$	−17.5059	−	30.3211i	−0.642229	−	1.11237i	−0.984934	−	0.172930i	$-0.944677\pi$
$743$	−17.5059	−	30.3211i	−0.642229	−	1.11237i	0.342705	−	0.939443i	$-0.388657\pi$
$744$		0			0
$745$	25.6375			0.939285
$746$	−0.760877	−	1.31788i	−0.0278577	−	0.0482509i
$747$		0			0
$748$	17.8285			0.651873
$749$	8.14596	+	29.2181i	0.297647	+	1.06761i
$750$		0			0
$751$	−4.27687			−0.156065			−0.0780327	−	0.996951i	$-0.524864\pi$
$751$	−4.27687			−0.156065			−0.0780327	+	0.996951i	$0.524864\pi$
$752$	0.0971198	−	0.168217i	0.00354160	−	0.00613422i
$753$		0			0
$754$	−14.2661	−	24.7096i	−0.519540	−	0.899870i
$755$	−19.9910			−0.727546
$756$		0			0
$757$	−34.9611			−1.27068			−0.635342	−	0.772231i	$-0.719141\pi$
$757$	−34.9611			−1.27068			−0.635342	+	0.772231i	$0.719141\pi$
$758$	−3.40615	−	5.89962i	−0.123717	−	0.214284i
$759$		0			0
$760$	18.3090	−	31.7122i	0.664138	−	1.15032i
$761$	4.58358			0.166155			0.0830773	−	0.996543i	$-0.473525\pi$
$761$	4.58358			0.166155			0.0830773	+	0.996543i	$0.473525\pi$
$762$		0			0
$763$	46.7623	+	12.0253i	1.69291	+	0.435346i
$764$	35.1546			1.27185
$765$		0			0
$766$	7.67154	+	13.2875i	0.277184	+	0.480097i
$767$	−7.61917			−0.275112
$768$		0			0
$769$	−8.47949	−	14.6869i	−0.305778	−	0.529623i	0.671656	−	0.740863i	$-0.265583\pi$
$769$	−8.47949	−	14.6869i	−0.305778	−	0.529623i	−0.977434	+	0.211240i	$0.932250\pi$
$770$	−13.8908	−	3.57215i	−0.500591	−	0.128731i
$771$		0			0
$772$	−0.588649	−	1.01957i	−0.0211859	−	0.0366951i
$773$	−20.1420	−	34.8870i	−0.724458	−	1.25480i	−0.959197	−	0.282739i	$-0.908757\pi$
$773$	−20.1420	−	34.8870i	−0.724458	−	1.25480i	0.234739	−	0.972058i	$-0.424576\pi$
$774$		0			0
$775$	14.6150	−	25.3140i	0.524988	−	0.909306i
$776$	1.09604	−	1.89840i	0.0393456	−	0.0681485i
$777$		0			0
$778$	−12.7826	−	22.1402i	−0.458279	−	0.793763i
$779$	17.6238			0.631439
$780$		0			0
$781$	16.2632			0.581943
$782$	−2.00972	+	3.48093i	−0.0718673	+	0.124478i
$783$		0			0
$784$	−5.16101	+	3.12030i	−0.184322	+	0.111439i
$785$	−1.11956	+	1.93914i	−0.0399589	+	0.0692108i
$786$		0			0
$787$	−23.6053	+	40.8856i	−0.841439	+	1.45742i	0.0472387	+	0.998884i	$0.484958\pi$
$787$	−23.6053	+	40.8856i	−0.841439	+	1.45742i	−0.888678	+	0.458532i	$0.848375\pi$
$788$	4.16484	−	7.21371i	0.148366	−	0.256978i
$789$		0			0
$790$	8.26608	−	14.3173i	0.294094	−	0.509386i
$791$	13.4513	+	3.45912i	0.478273	+	0.122992i
$792$		0			0
$793$	10.8187	−	18.7386i	0.384185	−	0.665428i
$794$	−3.14884			−0.111748
$795$		0			0
$796$	13.1442			0.465884
$797$	2.01367	+	3.48778i	0.0713280	+	0.123544i	0.899484	−	0.436955i	$-0.143943\pi$
$797$	2.01367	+	3.48778i	0.0713280	+	0.123544i	−0.828156	+	0.560498i	$0.810610\pi$
$798$		0			0
$799$	−0.631600	+	1.09396i	−0.0223444	+	0.0387016i
$800$	−15.0196	+	26.0146i	−0.531022	+	0.919757i
$801$		0			0
$802$	5.88508	+	10.1933i	0.207810	+	0.359937i
$803$	−8.46333	−	14.6589i	−0.298664	−	0.517302i
$804$		0			0
$805$	−5.55555	+	5.66886i	−0.195807	+	0.199801i
$806$	8.03667	+	13.9199i	0.283080	+	0.490308i
$807$		0			0
$808$	20.1660			0.709439
$809$	−5.94119	−	10.2904i	−0.208881	−	0.361792i	0.742481	−	0.669867i	$-0.233649\pi$
$809$	−5.94119	−	10.2904i	−0.208881	−	0.361792i	−0.951362	+	0.308074i	$0.900315\pi$
$810$		0			0
$811$	−21.1111			−0.741311			−0.370655	−	0.928770i	$-0.620867\pi$
$811$	−21.1111			−0.741311			−0.370655	+	0.928770i	$0.620867\pi$
$812$	36.8675	+	9.48078i	1.29379	+	0.332710i
$813$		0			0
$814$	5.32365			0.186594
$815$	30.6037	−	53.0072i	1.07200	−	1.85676i
$816$		0			0
$817$	7.25636	+	12.5684i	0.253868	+	0.439712i
$818$	20.8432			0.728767
$819$		0			0
$820$	−18.0252			−0.629467
$821$	18.6460	+	32.2958i	0.650749	+	1.12713i	0.982942	+	0.183918i	$0.0588781\pi$
$821$	18.6460	+	32.2958i	0.650749	+	1.12713i	−0.332193	+	0.943211i	$0.607789\pi$
$822$		0			0
$823$	10.7261	−	18.5782i	0.373890	−	0.647596i	−0.616270	−	0.787535i	$-0.711357\pi$
$823$	10.7261	−	18.5782i	0.373890	−	0.647596i	0.990160	+	0.139939i	$0.0446905\pi$
$824$	6.33765			0.220783
$825$		0			0
$826$	−2.89862	+	2.95774i	−0.100856	+	0.102913i
$827$	−28.6375			−0.995823			−0.497912	−	0.867228i	$-0.665900\pi$
$827$	−28.6375			−0.995823			−0.497912	+	0.867228i	$0.665900\pi$
$828$		0			0
$829$	19.8646	+	34.4065i	0.689925	+	1.19499i	0.971862	+	0.235552i	$0.0756899\pi$
$829$	19.8646	+	34.4065i	0.689925	+	1.19499i	−0.281936	+	0.959433i	$0.590977\pi$
$830$	−19.6375			−0.681627
$831$		0			0
$832$	−5.06814	−	8.77827i	−0.175706	−	0.304332i
$833$	33.5636	−	20.2922i	1.16291	−	0.703085i
$834$		0			0
$835$	−37.2096	−	64.4489i	−1.28769	−	2.23035i
$836$	7.03379	+	12.1829i	0.243269	+	0.421354i
$837$		0			0
$838$	−7.98921	+	13.8377i	−0.275983	+	0.478016i
$839$	17.1803	−	29.7572i	0.593130	−	1.02733i	−0.400678	−	0.916219i	$-0.631225\pi$
$839$	17.1803	−	29.7572i	0.593130	−	1.02733i	0.993808	−	0.111112i	$-0.0354414\pi$
$840$		0			0
$841$	−36.7554	−	63.6622i	−1.26743	−	2.19525i
$842$	15.1863			0.523355
$843$		0			0
$844$	17.8479			0.614350
$845$	−1.14132	+	1.97682i	−0.0392624	+	0.0680045i
$846$		0			0
$847$	−11.0858	+	11.3119i	−0.380912	+	0.388681i
$848$	−4.59222	+	7.95395i	−0.157697	+	0.273140i
$849$		0			0
$850$	10.9239	−	18.9208i	0.374688	−	0.648979i
$851$	1.47304	−	2.55139i	0.0504953	−	0.0874605i
$852$		0			0
$853$	0.757310	−	1.31170i	0.0259298	−	0.0449117i	−0.852769	−	0.522288i	$-0.825079\pi$
$853$	0.757310	−	1.31170i	0.0259298	−	0.0449117i	0.878699	+	0.477376i	$0.158412\pi$
$854$	−3.15842	−	11.3287i	−0.108079	−	0.387660i
$855$		0			0
$856$	14.9212	−	25.8443i	0.509996	−	0.883339i
$857$	−4.50946			−0.154040			−0.0770201	−	0.997030i	$-0.524541\pi$
$857$	−4.50946			−0.154040			−0.0770201	+	0.997030i	$0.524541\pi$
$858$		0			0
$859$	12.6063			0.430121			0.215060	−	0.976601i	$-0.431005\pi$
$859$	12.6063			0.430121			0.215060	+	0.976601i	$0.431005\pi$
$860$	−7.42162	−	12.8546i	−0.253075	−	0.438339i
$861$		0			0
$862$	7.65800	−	13.2640i	0.260833	−	0.451775i
$863$	5.33009	−	9.23200i	0.181439	−	0.314261i	−0.760932	−	0.648832i	$-0.775258\pi$
$863$	5.33009	−	9.23200i	0.181439	−	0.314261i	0.942371	+	0.334571i	$0.108591\pi$
$864$		0			0
$865$	13.1082	+	22.7041i	0.445693	+	0.771962i
$866$	−4.51040	−	7.81225i	−0.153270	−	0.265471i
$867$		0			0
$868$	−20.7690	−	5.34092i	−0.704944	−	0.181283i
$869$	7.64488	+	13.2413i	0.259335	+	0.449181i
$870$		0			0
$871$	27.4854			0.931307
$872$	−23.7518	−	41.1394i	−0.804339	−	1.39316i
$873$		0			0
$874$	−3.17154			−0.107279
$875$	0.735165	−	0.750160i	0.0248531	−	0.0253600i
$876$		0			0
$877$	−32.2380			−1.08860			−0.544300	−	0.838891i	$-0.683205\pi$
$877$	−32.2380			−1.08860			−0.544300	+	0.838891i	$0.683205\pi$
$878$	0.820935	−	1.42190i	0.0277052	−	0.0479869i
$879$		0			0
$880$	−3.06922	−	5.31604i	−0.103463	−	0.179204i
$881$	−55.6375			−1.87447			−0.937237	−	0.348692i	$-0.886626\pi$
$881$	−55.6375			−1.87447			−0.937237	+	0.348692i	$0.886626\pi$
$882$		0			0
$883$	−42.4854			−1.42975			−0.714873	−	0.699254i	$-0.753516\pi$
$883$	−42.4854			−1.42975			−0.714873	+	0.699254i	$0.753516\pi$
$884$	−14.7449	−	25.5389i	−0.495924	−	0.858966i
$885$		0			0
$886$	0.746515	−	1.29300i	0.0250797	−	0.0434393i
$887$	−8.95649			−0.300730			−0.150365	−	0.988631i	$-0.548045\pi$
$887$	−8.95649			−0.300730			−0.150365	+	0.988631i	$0.548045\pi$
$888$		0			0
$889$	37.2320	−	37.9914i	1.24872	−	1.27419i
$890$	23.5516			0.789451
$891$		0			0
$892$	−15.1969	−	26.3217i	−0.508829	−	0.881317i
$893$	−0.996730			−0.0333543
$894$		0			0
$895$	−15.7661	−	27.3076i	−0.527002	−	0.912794i
$896$	24.7033	+	6.35267i	0.825280	+	0.212228i
$897$		0			0
$898$	−0.818745	−	1.41811i	−0.0273219	−	0.0473229i
$899$	28.8743	+	50.0117i	0.963011	+	1.66798i
$900$		0			0
$901$	29.8646	−	51.7270i	0.994933	−	1.72327i
$902$	−3.39575	+	5.88160i	−0.113066	+	0.195836i
$903$		0			0
$904$	−6.83229	−	11.8339i	−0.227238	−	0.393589i
$905$	−29.8720			−0.992978
$906$		0			0
$907$	10.7874			0.358191			0.179096	−	0.983832i	$-0.442683\pi$
$907$	10.7874			0.358191			0.179096	+	0.983832i	$0.442683\pi$
$908$	−8.96866	+	15.5342i	−0.297636	+	0.515520i
$909$		0			0
$910$	6.37128	+	22.8526i	0.211206	+	0.757558i
$911$	23.7427	−	41.1235i	0.786630	−	1.36248i	−0.141390	−	0.989954i	$-0.545157\pi$
$911$	23.7427	−	41.1235i	0.786630	−	1.36248i	0.928020	−	0.372530i	$-0.121510\pi$
$912$		0			0
$913$	9.08087	−	15.7285i	0.300533	−	0.520538i
$914$	4.98577	−	8.63561i	0.164915	−	0.285641i
$915$		0			0
$916$	−20.5487	+	35.5914i	−0.678948	+	1.17597i
$917$	−7.55787	+	7.71202i	−0.249583	+	0.254673i
$918$		0			0
$919$	−28.1375	+	48.7356i	−0.928170	+	1.60764i	−0.141788	+	0.989897i	$0.545285\pi$
$919$	−28.1375	+	48.7356i	−0.928170	+	1.60764i	−0.786382	+	0.617741i	$0.788048\pi$
$920$	7.80903			0.257456
$921$		0			0
$922$	−4.17514			−0.137501
$923$	−13.4503	−	23.2967i	−0.442723	−	0.766820i
$924$		0			0
$925$	−8.00684	+	13.8682i	−0.263263	+	0.455985i
$926$	7.79863	−	13.5076i	0.256279	−	0.443888i
$927$		0			0
$928$	−29.6735	−	51.3960i	−0.974079	−	1.68716i
$929$	−0.380438	−	0.658939i	−0.0124818	−	0.0216191i	0.859717	−	0.510771i	$-0.170640\pi$
$929$	−0.380438	−	0.658939i	−0.0124818	−	0.0216191i	−0.872199	+	0.489152i	$0.837307\pi$
$930$		0			0
$931$	27.1082	+	14.9295i	0.888436	+	0.489295i
$932$	15.2416	+	26.3992i	0.499255	+	0.864734i
$933$		0			0
$934$	29.9417			0.979723
$935$	19.9601	+	34.5718i	0.652764	+	1.13062i
$936$		0			0
$937$	−30.3218			−0.990569			−0.495284	−	0.868731i	$-0.664936\pi$
$937$	−30.3218			−0.990569			−0.495284	+	0.868731i	$0.664936\pi$
$938$	10.4565	−	10.6698i	0.341417	−	0.348380i
$939$		0			0
$940$	1.01943			0.0332502
$941$	−27.5406	+	47.7018i	−0.897799	+	1.55503i	−0.0674968	+	0.997719i	$0.521501\pi$
$941$	−27.5406	+	47.7018i	−0.897799	+	1.55503i	−0.830302	+	0.557314i	$0.811832\pi$
$942$		0			0
$943$	1.87919	+	3.25486i	0.0611950	+	0.105993i
$944$	−1.77239			−0.0576864
$945$		0			0
$946$	−5.59261			−0.181831
$947$	−15.3103	−	26.5182i	−0.497517	−	0.861725i	0.502479	−	0.864590i	$-0.332421\pi$
$947$	−15.3103	−	26.5182i	−0.497517	−	0.861725i	−0.999996	+	0.00286470i	$0.999088\pi$
$948$		0			0
$949$	−13.9991	+	24.2471i	−0.454429	+	0.787093i
$950$	17.2391			0.559311
$951$		0			0
$952$	−37.3715	−	9.61042i	−1.21122	−	0.311475i
$953$	7.83422			0.253775			0.126888	−	0.991917i	$-0.459501\pi$
$953$	7.83422			0.253775			0.126888	+	0.991917i	$0.459501\pi$
$954$		0			0
$955$	39.3577	+	68.1696i	1.27359	+	2.20592i
$956$	10.9945			0.355588
$957$		0			0
$958$	6.37128	+	11.0354i	0.205847	+	0.356537i
$959$	−3.49192	+	3.56314i	−0.112760	+	0.115060i
$960$		0			0
$961$	−0.766078	−	1.32689i	−0.0247122	−	0.0428028i
$962$	−4.40288	−	7.62601i	−0.141955	−	0.245872i
$963$		0			0
$964$	4.32833	−	7.49688i	0.139406	−	0.241458i
$965$	1.31806	−	2.28294i	0.0424297	−	0.0734905i
$966$		0			0
$967$	2.64815	+	4.58673i	0.0851588	+	0.147499i	0.905459	−	0.424434i	$-0.139527\pi$
$967$	2.64815	+	4.58673i	0.0851588	+	0.147499i	−0.820300	+	0.571933i	$0.806194\pi$
$968$	15.5825			0.500840
$969$		0			0
$970$	2.03886			0.0654639
$971$	−26.1202	+	45.2416i	−0.838239	+	1.45187i	0.0531273	+	0.998588i	$0.483081\pi$
$971$	−26.1202	+	45.2416i	−0.838239	+	1.45187i	−0.891366	+	0.453284i	$0.850252\pi$
$972$		0			0
$973$	32.7866	+	8.43135i	1.05109	+	0.270297i
$974$	−1.52394	+	2.63955i	−0.0488303	+	0.0845766i
$975$		0			0
$976$	2.51668	−	4.35903i	0.0805571	−	0.139529i
$977$	2.97304	−	5.14946i	0.0951161	−	0.164746i	−0.814541	−	0.580106i	$-0.803011\pi$
$977$	2.97304	−	5.14946i	0.0951161	−	0.164746i	0.909657	+	0.415360i	$0.136344\pi$
$978$		0			0
$979$	−10.8908	+	18.8635i	−0.348073	+	0.602880i
$980$	−27.7256	−	15.2695i	−0.885661	−	0.487767i
$981$		0			0
$982$	9.37825	−	16.2436i	0.299272	−	0.518354i
$983$	−18.5641			−0.592104			−0.296052	−	0.955172i	$-0.595670\pi$
$983$	−18.5641			−0.592104			−0.296052	+	0.955172i	$0.595670\pi$
$984$		0			0
$985$	18.6512			0.594275
$986$	21.5819	+	37.3810i	0.687309	+	1.19045i
$987$		0			0
$988$	11.6345	−	20.1515i	0.370142	−	0.641105i
$989$	−1.54746	+	2.68029i	−0.0492065	+	0.0852282i
$990$		0			0
$991$	−9.31875	−	16.1405i	−0.296020	−	0.512721i	0.679202	−	0.733951i	$-0.262326\pi$
$991$	−9.31875	−	16.1405i	−0.296020	−	0.512721i	−0.975222	+	0.221230i	$0.928993\pi$
$992$	16.7163	+	28.9535i	0.530743	+	0.919273i
$993$		0			0
$994$	−14.1607	−	3.64156i	−0.449152	−	0.115503i
$995$	14.7157	+	25.4884i	0.466520	+	0.808037i
$996$		0			0
$997$	−30.5595			−0.967829			−0.483915	−	0.875115i	$-0.660785\pi$
$997$	−30.5595			−0.967829			−0.483915	+	0.875115i	$0.660785\pi$
$998$	9.34338	+	16.1832i	0.295759	+	0.512270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.h.541.2		6
3.2	odd	2		567.2.g.i.541.2		6
7.4	even	3		567.2.h.i.298.2		6
9.2	odd	6		189.2.e.f.163.2	yes	6
9.4	even	3		567.2.h.i.352.2		6
9.5	odd	6		567.2.h.h.352.2		6
9.7	even	3		189.2.e.e.163.2	yes	6
21.11	odd	6		567.2.h.h.298.2		6
63.2	odd	6		1323.2.a.x.1.2		3
63.4	even	3	inner	567.2.g.h.109.2		6
63.11	odd	6		189.2.e.f.109.2	yes	6
63.16	even	3		1323.2.a.ba.1.2		3
63.25	even	3		189.2.e.e.109.2	✓	6
63.32	odd	6		567.2.g.i.109.2		6
63.47	even	6		1323.2.a.y.1.2		3
63.61	odd	6		1323.2.a.z.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.2	✓	6	63.25	even	3
189.2.e.e.163.2	yes	6	9.7	even	3
189.2.e.f.109.2	yes	6	63.11	odd	6
189.2.e.f.163.2	yes	6	9.2	odd	6
567.2.g.h.109.2		6	63.4	even	3	inner
567.2.g.h.541.2		6	1.1	even	1	trivial
567.2.g.i.109.2		6	63.32	odd	6
567.2.g.i.541.2		6	3.2	odd	2
567.2.h.h.298.2		6	21.11	odd	6
567.2.h.h.352.2		6	9.5	odd	6
567.2.h.i.298.2		6	7.4	even	3
567.2.h.i.352.2		6	9.4	even	3
1323.2.a.x.1.2		3	63.2	odd	6
1323.2.a.y.1.2		3	63.47	even	6
1323.2.a.z.1.2		3	63.61	odd	6
1323.2.a.ba.1.2		3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.380438 - 0.658939i) q^{2} +(0.710533 - 1.23068i) q^{4} +3.18194 q^{5} +(1.85185 - 1.88962i) q^{7} -2.60301 q^{8} +(-1.21053 - 2.09671i) q^{10} +2.23912 q^{11} +(-1.85185 - 3.20750i) q^{13} +(-1.94966 - 0.501371i) q^{14} +(-0.430782 - 0.746136i) q^{16} +(2.80150 + 4.85235i) q^{17} +(-2.21053 + 3.82876i) q^{19} +(2.26088 - 3.91595i) q^{20} +(-0.851848 - 1.47544i) q^{22} -0.942820 q^{23} +5.12476 q^{25} +(-1.40903 + 2.44051i) q^{26} +(-1.00972 - 3.62167i) q^{28} +(-5.06238 + 8.76830i) q^{29} +(2.85185 - 4.93955i) q^{31} +(-2.93078 + 5.07626i) q^{32} +(2.13160 - 3.69204i) q^{34} +(5.89248 - 6.01266i) q^{35} +(-1.56238 + 2.70612i) q^{37} +3.36389 q^{38} -8.28263 q^{40} +(-1.99316 - 3.45226i) q^{41} +(1.64132 - 2.84284i) q^{43} +(1.59097 - 2.75564i) q^{44} +(0.358685 + 0.621261i) q^{46} +(0.112725 + 0.195246i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(-1.94966 - 3.37690i) q^{50} -5.26320 q^{52} +(-5.33009 - 9.23200i) q^{53} +7.12476 q^{55} +(-4.82038 + 4.91870i) q^{56} +7.70370 q^{58} +(1.02859 - 1.78157i) q^{59} +(2.92107 + 5.05944i) q^{61} -4.33981 q^{62} +2.73680 q^{64} +(-5.89248 - 10.2061i) q^{65} +(-3.71053 + 6.42683i) q^{67} +7.96225 q^{68} +(-6.20370 - 1.59533i) q^{70} +7.26320 q^{71} +(-3.77975 - 6.54672i) q^{73} +2.37756 q^{74} +(3.14132 + 5.44092i) q^{76} +(4.14652 - 4.23109i) q^{77} +(3.41423 + 5.91362i) q^{79} +(-1.37072 - 2.37416i) q^{80} +(-1.51655 + 2.62674i) q^{82} +(4.05555 - 7.02441i) q^{83} +(8.91423 + 15.4399i) q^{85} -2.49768 q^{86} -5.82846 q^{88} +(-4.86389 + 8.42450i) q^{89} +(-9.49028 - 2.44051i) q^{91} +(-0.669905 + 1.16031i) q^{92} +(0.0857699 - 0.148558i) q^{94} +(-7.03379 + 12.1829i) q^{95} +(-0.421067 + 0.729309i) q^{97} +(-4.55787 + 2.75564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 2 q^{7} + 18 q^{8} + q^{10} + 14 q^{11} - 2 q^{13} - 4 q^{14} - 10 q^{16} - 5 q^{19} + 13 q^{20} + 4 q^{22} + 12 q^{23} - 4 q^{25} - 17 q^{26} - 30 q^{28} - 13 q^{29}+ \cdots + 49 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 2 * q^7 + 18 * q^8 + q^10 + 14 * q^11 - 2 * q^13 - 4 * q^14 - 10 * q^16 - 5 * q^19 + 13 * q^20 + 4 * q^22 + 12 * q^23 - 4 * q^25 - 17 * q^26 - 30 * q^28 - 13 * q^29 + 8 * q^31 - 25 * q^32 - 12 * q^34 + 10 * q^35 + 8 * q^37 - 14 * q^38 - 48 * q^40 - 2 * q^41 + 9 * q^43 + q^44 + 3 * q^46 - 9 * q^47 - 4 * q^50 + 18 * q^52 - 24 * q^53 + 8 * q^55 + 3 * q^56 + 28 * q^58 + 15 * q^59 + q^61 - 42 * q^62 + 66 * q^64 - 10 * q^65 - 14 * q^67 + 78 * q^68 - 19 * q^70 - 6 * q^71 - 7 * q^73 + 18 * q^76 - 11 * q^77 - 6 * q^79 + 16 * q^80 - 43 * q^82 - 3 * q^83 + 27 * q^85 - 64 * q^86 + 18 * q^88 + 5 * q^89 - 33 * q^91 - 12 * q^92 + 27 * q^94 - 16 * q^95 + 14 * q^97 + 49 * q^98

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