LMFDB - Embedded newform 567.2.e.f.487.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(163,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [10,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			487.5
Root			$1.19343 + 2.06709i$ of defining polynomial
Character	$\chi$	$=$	567.487
Dual form			567.2.e.f.163.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19343 + 2.06709i) q^{2} +(-1.84857 + 3.20182i) q^{4} +(1.46043 + 2.52954i) q^{5} +(-2.21886 + 1.44106i) q^{7} -4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +(0.676857 - 1.17235i) q^{11} +1.46600 q^{13} +(-5.62686 - 2.86678i) q^{14} +(-1.13729 - 1.96984i) q^{16} +(1.65514 - 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} -10.7989 q^{20} +3.23114 q^{22} +(-1.31415 - 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +(1.74958 + 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} -1.04344 q^{29} +(-1.63729 + 2.83587i) q^{31} +(-1.33629 + 2.31453i) q^{32} +7.90119 q^{34} +(-6.88572 - 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(2.63342 - 4.56121i) q^{38} +(-5.91601 - 10.2468i) q^{40} +1.80858 q^{41} +4.34257 q^{43} +(2.50244 + 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} +(-1.98957 - 3.44604i) q^{47} +(2.84671 - 6.39502i) q^{49} -8.42913 q^{50} +(-2.71001 + 4.69388i) q^{52} +(-3.22743 + 5.59008i) q^{53} +3.95402 q^{55} +(8.98830 - 5.83752i) q^{56} +(-1.24528 - 2.15688i) q^{58} +(6.10700 - 10.5776i) q^{59} +(-0.279867 - 0.484744i) q^{61} -7.81600 q^{62} -10.9283 q^{64} +(2.14100 + 3.70832i) q^{65} +(-6.40588 + 11.0953i) q^{67} +(6.11928 + 10.5989i) q^{68} +(-0.966003 - 18.4201i) q^{70} +12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-12.9791 + 22.4805i) q^{74} +8.15807 q^{76} +(0.187571 + 3.57668i) q^{77} +(-0.383838 - 0.664827i) q^{79} +(3.32187 - 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +1.96741 q^{83} +9.66887 q^{85} +(5.18258 + 8.97649i) q^{86} +(-2.74185 + 4.74903i) q^{88} +(3.20356 + 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +9.71719 q^{92} +(4.74884 - 8.22524i) q^{94} +(3.22257 - 5.58166i) q^{95} +8.28285 q^{97} +(16.6164 - 1.74763i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.19343	+	2.06709i	0.843886	+	1.46165i	0.886585	+	0.462565i	$0.153071\pi$
$2$	1.19343	+	2.06709i	0.843886	+	1.46165i	−0.0426999	+	0.999088i	$0.513596\pi$
$3$		0			0
$3$		0			0
$4$	−1.84857	+	3.20182i	−0.924286	+	1.60091i
$5$	1.46043	+	2.52954i	0.653125	+	1.13125i	0.982360	+	0.186998i	$0.0598759\pi$
$5$	1.46043	+	2.52954i	0.653125	+	1.13125i	−0.329235	+	0.944248i	$0.606791\pi$
$6$		0			0
$7$	−2.21886	+	1.44106i	−0.838652	+	0.544668i
$7$	−2.21886	+	1.44106i	−0.838652	+	0.544668i
$8$	−4.05086			−1.43219
$9$		0			0
$10$	−3.48586	+	6.03769i	−1.10233	+	1.90929i
$11$	0.676857	−	1.17235i	0.204080	−	0.353477i	−0.745759	−	0.666216i	$-0.767913\pi$
$11$	0.676857	−	1.17235i	0.204080	−	0.353477i	0.949839	+	0.312738i	$0.101246\pi$
$12$		0			0
$13$	1.46600			0.406596			0.203298	−	0.979117i	$-0.434834\pi$
$13$	1.46600			0.406596			0.203298	+	0.979117i	$0.434834\pi$
$14$	−5.62686	−	2.86678i	−1.50384	−	0.766180i
$15$		0			0
$16$	−1.13729	−	1.96984i	−0.284323	−	0.492461i
$17$	1.65514	−	2.86678i	0.401430	−	0.695297i	−0.592469	−	0.805593i	$-0.701847\pi$
$17$	1.65514	−	2.86678i	0.401430	−	0.695297i	0.993899	+	0.110297i	$0.0351801\pi$
$18$		0			0
$19$	−1.10329	−	1.91096i	−0.253113	−	0.438404i	0.711268	−	0.702921i	$-0.248121\pi$
$19$	−1.10329	−	1.91096i	−0.253113	−	0.438404i	−0.964381	+	0.264516i	$0.914788\pi$
$20$	−10.7989			−2.41470
$21$		0			0
$22$	3.23114			0.688881
$23$	−1.31415	−	2.27617i	−0.274019	−	0.474614i	0.695868	−	0.718169i	$-0.255020\pi$
$23$	−1.31415	−	2.27617i	−0.274019	−	0.474614i	−0.969887	+	0.243555i	$0.921686\pi$
$24$		0			0
$25$	−1.76573	+	3.05833i	−0.353146	+	0.611666i
$26$	1.74958	+	3.03036i	0.343121	+	0.594302i
$27$		0			0
$28$	−0.512277	−	9.76830i	−0.0968112	−	1.84603i
$29$	−1.04344			−0.193762			−0.0968810	−	0.995296i	$-0.530887\pi$
$29$	−1.04344			−0.193762			−0.0968810	+	0.995296i	$0.530887\pi$
$30$		0			0
$31$	−1.63729	+	2.83587i	−0.294066	+	0.509337i	−0.974767	−	0.223224i	$-0.928342\pi$
$31$	−1.63729	+	2.83587i	−0.294066	+	0.509337i	0.680701	+	0.732561i	$0.261675\pi$
$32$	−1.33629	+	2.31453i	−0.236226	+	0.409155i
$33$		0			0
$34$	7.90119			1.35504
$35$	−6.88572	−	3.50815i	−1.16390	−	0.592985i
$36$		0			0
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$	2.63342	−	4.56121i	0.427197	−	0.739926i
$39$		0			0
$40$	−5.91601	−	10.2468i	−0.935403	−	1.62017i
$41$	1.80858			0.282452			0.141226	−	0.989977i	$-0.454896\pi$
$41$	1.80858			0.282452			0.141226	+	0.989977i	$0.454896\pi$
$42$		0			0
$43$	4.34257			0.662236			0.331118	−	0.943589i	$-0.392574\pi$
$43$	4.34257			0.662236			0.331118	+	0.943589i	$0.392574\pi$
$44$	2.50244	+	4.33435i	0.377257	+	0.653428i
$45$		0			0
$46$	3.13670	−	5.43292i	0.462481	−	0.801041i
$47$	−1.98957	−	3.44604i	−0.290209	−	0.502656i	0.683650	−	0.729810i	$-0.260391\pi$
$47$	−1.98957	−	3.44604i	−0.290209	−	0.502656i	−0.973859	+	0.227154i	$0.927058\pi$
$48$		0			0
$49$	2.84671	−	6.39502i	0.406673	−	0.913574i
$50$	−8.42913			−1.19206
$51$		0			0
$52$	−2.71001	+	4.69388i	−0.375811	+	0.650924i
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	−0.997934	−	0.0642533i	$-0.979533\pi$
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	0.554612	+	0.832109i	$0.312867\pi$
$54$		0			0
$55$	3.95402			0.533160
$56$	8.98830	−	5.83752i	1.20111	−	0.780071i
$57$		0			0
$58$	−1.24528	−	2.15688i	−0.163513	−	0.283213i
$59$	6.10700	−	10.5776i	0.795064	−	1.37709i	−0.127735	−	0.991808i	$-0.540771\pi$
$59$	6.10700	−	10.5776i	0.795064	−	1.37709i	0.922799	−	0.385283i	$-0.125896\pi$
$60$		0			0
$61$	−0.279867	−	0.484744i	−0.0358333	−	0.0620651i	0.847553	−	0.530711i	$-0.178075\pi$
$61$	−0.279867	−	0.484744i	−0.0358333	−	0.0620651i	−0.883386	+	0.468646i	$0.844742\pi$
$62$	−7.81600			−0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	2.14100	+	3.70832i	0.265558	+	0.459960i
$66$		0			0
$67$	−6.40588	+	11.0953i	−0.782603	+	1.35551i	0.147817	+	0.989015i	$0.452775\pi$
$67$	−6.40588	+	11.0953i	−0.782603	+	1.35551i	−0.930420	+	0.366494i	$0.880558\pi$
$68$	6.11928	+	10.5989i	0.742072	+	1.28531i
$69$		0			0
$70$	−0.966003	−	18.4201i	−0.115459	−	2.20163i
$71$	12.9177			1.53305			0.766525	−	0.642214i	$-0.221984\pi$
$71$	12.9177			1.53305			0.766525	+	0.642214i	$0.221984\pi$
$72$		0			0
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	−0.379069	−	0.925368i	$-0.623756\pi$
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	0.990927	−	0.134401i	$-0.0429109\pi$
$74$	−12.9791	+	22.4805i	−1.50879	+	2.61331i
$75$		0			0
$76$	8.15807			0.935794
$77$	0.187571	+	3.57668i	0.0213757	+	0.407600i
$78$		0			0
$79$	−0.383838	−	0.664827i	−0.0431852	−	0.0747989i	0.843625	−	0.536933i	$-0.180417\pi$
$79$	−0.383838	−	0.664827i	−0.0431852	−	0.0747989i	−0.886810	+	0.462134i	$0.847084\pi$
$80$	3.32187	−	5.75365i	0.371397	−	0.643278i
$81$		0			0
$82$	2.15842	+	3.73849i	0.238358	+	0.412847i
$83$	1.96741			0.215952			0.107976	−	0.994154i	$-0.465563\pi$
$83$	1.96741			0.215952			0.107976	+	0.994154i	$0.465563\pi$
$84$		0			0
$85$	9.66887			1.04874
$86$	5.18258	+	8.97649i	0.558852	+	0.967960i
$87$		0			0
$88$	−2.74185	+	4.74903i	−0.292283	+	0.506248i
$89$	3.20356	+	5.54872i	0.339576	+	0.588163i	0.984353	−	0.176208i	$-0.0563830\pi$
$89$	3.20356	+	5.54872i	0.339576	+	0.588163i	−0.644777	+	0.764371i	$0.723050\pi$
$90$		0			0
$91$	−3.25286	+	2.11259i	−0.340992	+	0.221460i
$92$	9.71719			1.01309
$93$		0			0
$94$	4.74884	−	8.22524i	0.489806	−	0.848369i
$95$	3.22257	−	5.58166i	0.330629	−	0.572666i
$96$		0			0
$97$	8.28285			0.840996			0.420498	−	0.907293i	$-0.361855\pi$
$97$	8.28285			0.840996			0.420498	+	0.907293i	$0.361855\pi$
$98$	16.6164	−	1.74763i	1.67851	−	0.176537i
$99$		0			0
$100$	−6.52815	−	11.3071i	−0.652815	−	1.13071i
$101$	8.11331	−	14.0527i	0.807305	−	1.39829i	−0.107419	−	0.994214i	$-0.534259\pi$
$101$	8.11331	−	14.0527i	0.807305	−	1.39829i	0.914724	−	0.404079i	$-0.132408\pi$
$102$		0			0
$103$	1.11342	+	1.92849i	0.109708	+	0.190020i	0.915652	−	0.401972i	$-0.131675\pi$
$103$	1.11342	+	1.92849i	0.109708	+	0.190020i	−0.805944	+	0.591992i	$0.798342\pi$
$104$	−5.93857			−0.582325
$105$		0			0
$106$	−15.4069			−1.49645
$107$	−8.75403	−	15.1624i	−0.846284	−	1.46581i	−0.884501	−	0.466537i	$-0.845501\pi$
$107$	−8.75403	−	15.1624i	−0.846284	−	1.46581i	0.0382175	−	0.999269i	$-0.487832\pi$
$108$		0			0
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$	4.71886	+	8.17331i	0.449926	+	0.779295i
$111$		0			0
$112$	5.36215	+	2.73192i	0.506676	+	0.258142i
$113$	1.68911			0.158898			0.0794491	−	0.996839i	$-0.474684\pi$
$113$	1.68911			0.158898			0.0794491	+	0.996839i	$0.474684\pi$
$114$		0			0
$115$	3.83845	−	6.64839i	0.357937	−	0.619966i
$116$	1.92887	−	3.34091i	0.179092	−	0.310196i
$117$		0			0
$118$	29.1532			2.68377
$119$	0.458672	+	8.74614i	0.0420464	+	0.801758i
$120$		0			0
$121$	4.58373	+	7.93925i	0.416703	+	0.721750i
$122$	0.668005	−	1.15702i	0.0604784	−	0.104752i
$123$		0			0
$124$	−6.05330	−	10.4846i	−0.543602	−	0.941546i
$125$	4.28942			0.383657
$126$		0			0
$127$	−3.96918			−0.352208			−0.176104	−	0.984372i	$-0.556350\pi$
$127$	−3.96918			−0.352208			−0.176104	+	0.984372i	$0.556350\pi$
$128$	−10.3696	−	17.9607i	−0.916552	−	1.58751i
$129$		0			0
$130$	−5.11028	+	8.85127i	−0.448202	+	0.776308i
$131$	−2.66432	−	4.61473i	−0.232782	−	0.403191i	0.725844	−	0.687860i	$-0.241450\pi$
$131$	−2.66432	−	4.61473i	−0.232782	−	0.403191i	−0.958626	+	0.284669i	$0.908116\pi$
$132$		0			0
$133$	5.20186	+	2.65025i	0.451058	+	0.229806i
$134$	−30.5800			−2.64171
$135$		0			0
$136$	−6.70473	+	11.6129i	−0.574925	+	0.995800i
$137$	3.74772	−	6.49124i	0.320189	−	0.554584i	−0.660338	−	0.750969i	$-0.729587\pi$
$137$	3.74772	−	6.49124i	0.320189	−	0.554584i	0.980527	+	0.196385i	$0.0629202\pi$
$138$		0			0
$139$	−14.0657			−1.19304			−0.596518	−	0.802600i	$-0.703450\pi$
$139$	−14.0657			−1.19304			−0.596518	+	0.802600i	$0.703450\pi$
$140$	23.9612	−	15.5618i	2.02509	−	1.31521i
$141$		0			0
$142$	15.4164	+	26.7021i	1.29372	+	2.24079i
$143$	0.992275	−	1.71867i	0.0829782	−	0.143722i
$144$		0			0
$145$	−1.52388	−	2.63943i	−0.126551	−	0.219193i
$146$	24.9557			2.06535
$147$		0			0
$148$	−40.2081			−3.30509
$149$	−1.08986	−	1.88769i	−0.0892846	−	0.154645i	0.817924	−	0.575326i	$-0.195125\pi$
$149$	−1.08986	−	1.88769i	−0.0892846	−	0.154645i	−0.907209	+	0.420680i	$0.861791\pi$
$150$		0			0
$151$	−7.01387	+	12.1484i	−0.570781	+	0.988621i	0.425705	+	0.904862i	$0.360026\pi$
$151$	−7.01387	+	12.1484i	−0.570781	+	0.988621i	−0.996486	+	0.0837595i	$0.973307\pi$
$152$	4.46929	+	7.74103i	0.362507	+	0.627880i
$153$		0			0
$154$	−7.16946	+	4.65626i	−0.577731	+	0.375212i
$155$	−9.56461			−0.768248
$156$		0			0
$157$	−1.48312	+	2.56883i	−0.118365	+	0.205015i	−0.919120	−	0.393978i	$-0.871099\pi$
$157$	−1.48312	+	2.56883i	−0.118365	+	0.205015i	0.800755	+	0.598993i	$0.204432\pi$
$158$	0.916172	−	1.58686i	0.0728867	−	0.126243i
$159$		0			0
$160$	−7.80628			−0.617140
$161$	6.19601	+	3.15675i	0.488314	+	0.248787i
$162$		0			0
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	0.858317	−	0.513120i	$-0.171511\pi$
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	−0.873534	+	0.486764i	$0.838177\pi$
$164$	−3.34329	+	5.79074i	−0.261067	+	0.452181i
$165$		0			0
$166$	2.34798	+	4.06682i	0.182239	+	0.315646i
$167$	−7.29778			−0.564719			−0.282360	−	0.959309i	$-0.591117\pi$
$167$	−7.29778			−0.564719			−0.282360	+	0.959309i	$0.591117\pi$
$168$		0			0
$169$	−10.8508			−0.834680
$170$	11.5392	+	19.9864i	0.885013	+	1.53289i
$171$		0			0
$172$	−8.02756	+	13.9041i	−0.612096	+	1.06018i
$173$	2.02754	+	3.51181i	0.154151	+	0.266998i	0.932750	−	0.360525i	$-0.117402\pi$
$173$	2.02754	+	3.51181i	0.154151	+	0.266998i	−0.778598	+	0.627522i	$0.784069\pi$
$174$		0			0
$175$	−0.489319	−	9.33054i	−0.0369891	−	0.705322i
$176$	−3.07913			−0.232098
$177$		0			0
$178$	−7.64647	+	13.2441i	−0.573127	+	0.992685i
$179$	5.29243	−	9.16675i	0.395575	−	0.685155i	−0.597600	−	0.801795i	$-0.703879\pi$
$179$	5.29243	−	9.16675i	0.395575	−	0.685155i	0.993174	+	0.116639i	$0.0372121\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$	−8.24900	−	4.20271i	−0.611456	−	0.311526i
$183$		0			0
$184$	5.32343	+	9.22045i	0.392448	+	0.679740i
$185$	−15.8829	+	27.5099i	−1.16773	+	2.02257i
$186$		0			0
$187$	−2.24058	−	3.88081i	−0.163848	−	0.283793i
$188$	14.7115			1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	−4.14357	−	7.17688i	−0.299818	−	0.519301i	0.676276	−	0.736648i	$-0.263593\pi$
$191$	−4.14357	−	7.17688i	−0.299818	−	0.519301i	−0.976094	+	0.217348i	$0.930259\pi$
$192$		0			0
$193$	9.39242	−	16.2682i	0.676082	−	1.17101i	−0.300070	−	0.953917i	$-0.597010\pi$
$193$	9.39242	−	16.2682i	0.676082	−	1.17101i	0.976152	−	0.217090i	$-0.0696566\pi$
$194$	9.88504	+	17.1214i	0.709705	+	1.22924i
$195$		0			0
$196$	15.2133	+	20.9363i	1.08667	+	1.49545i
$197$	5.99634			0.427222			0.213611	−	0.976919i	$-0.431478\pi$
$197$	5.99634			0.427222			0.213611	+	0.976919i	$0.431478\pi$
$198$		0			0
$199$	7.20434	−	12.4783i	0.510702	−	0.884562i	−0.489221	−	0.872160i	$-0.662719\pi$
$199$	7.20434	−	12.4783i	0.510702	−	0.884562i	0.999923	−	0.0124022i	$-0.00394785\pi$
$200$	7.15272	−	12.3889i	0.505773	−	0.876025i
$201$		0			0
$202$	38.7308			2.72509
$203$	2.31525	−	1.50366i	0.162499	−	0.105536i
$204$		0			0
$205$	2.64131	+	4.57488i	0.184477	+	0.319523i
$206$	−2.65758	+	4.60306i	−0.185162	+	0.320710i
$207$		0			0
$208$	−1.66727	−	2.88780i	−0.115604	−	0.200233i
$209$	−2.98709			−0.206621
$210$		0			0
$211$	13.8484			0.953360			0.476680	−	0.879077i	$-0.341840\pi$
$211$	13.8484			0.953360			0.476680	+	0.879077i	$0.341840\pi$
$212$	−11.9323	−	20.6673i	−0.819512	−	1.41944i
$213$		0			0
$214$	20.8947	−	36.1907i	1.42833	−	2.47395i
$215$	6.34204	+	10.9847i	0.432523	+	0.749153i
$216$		0			0
$217$	−0.453726	−	8.65184i	−0.0308010	−	0.587325i
$218$	−37.2312			−2.52161
$219$		0			0
$220$	−7.30929	+	12.6601i	−0.492792	+	0.853541i
$221$	2.42644	−	4.20271i	0.163220	−	0.282705i
$222$		0			0
$223$	−4.67513			−0.313070			−0.156535	−	0.987672i	$-0.550032\pi$
$223$	−4.67513			−0.313070			−0.156535	+	0.987672i	$0.550032\pi$
$224$	−0.370314	−	7.06130i	−0.0247427	−	0.471803i
$225$		0			0
$226$	2.01584	+	3.49154i	0.134092	+	0.232254i
$227$	−9.85631	+	17.0716i	−0.654187	+	1.13308i	0.327910	+	0.944709i	$0.393656\pi$
$227$	−9.85631	+	17.0716i	−0.654187	+	1.13308i	−0.982097	+	0.188376i	$0.939678\pi$
$228$		0			0
$229$	−14.0364	−	24.3118i	−0.927552	−	1.60657i	−0.787404	−	0.616437i	$-0.788575\pi$
$229$	−14.0364	−	24.3118i	−0.927552	−	1.60657i	−0.140148	−	0.990131i	$-0.544758\pi$
$230$	18.3238			1.20823
$231$		0			0
$232$	4.22683			0.277505
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	0.546409	−	0.837518i	$-0.315994\pi$
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	−0.998517	+	0.0544448i	$0.982661\pi$
$234$		0			0
$235$	5.81127	−	10.0654i	0.379085	−	0.656595i
$236$	22.5785	+	39.1070i	1.46973	+	2.54565i
$237$		0			0
$238$	−17.5317	+	11.3861i	−1.13641	+	0.738049i
$239$	−11.0614			−0.715501			−0.357751	−	0.933817i	$-0.616456\pi$
$239$	−11.0614			−0.715501			−0.357751	+	0.933817i	$0.616456\pi$
$240$		0			0
$241$	11.5849	−	20.0656i	0.746247	−	1.29254i	−0.203362	−	0.979104i	$-0.565187\pi$
$241$	11.5849	−	20.0656i	0.746247	−	1.29254i	0.949610	−	0.313435i	$-0.101480\pi$
$242$	−10.9408	+	18.9499i	−0.703299	+	1.21815i
$243$		0			0
$244$	2.06942			0.132481
$245$	20.3339	−	2.13861i	1.29909	−	0.136631i
$246$		0			0
$247$	−1.61743	−	2.80147i	−0.102915	−	0.178253i
$248$	6.63243	−	11.4877i	0.421160	−	0.729470i
$249$		0			0
$250$	5.11914	+	8.86660i	0.323763	+	0.560773i
$251$	−7.78402			−0.491323			−0.245662	−	0.969356i	$-0.579005\pi$
$251$	−7.78402			−0.491323			−0.245662	+	0.969356i	$0.579005\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$	−4.73696	−	8.20466i	−0.297223	−	0.514806i
$255$		0			0
$256$	13.8226	−	23.9414i	0.863912	−	1.49634i
$257$	−5.18798	−	8.98585i	−0.323618	−	0.560522i	0.657614	−	0.753355i	$-0.271566\pi$
$257$	−5.18798	−	8.98585i	−0.323618	−	0.560522i	−0.981232	+	0.192833i	$0.938232\pi$
$258$		0			0
$259$	−25.6381	−	13.0621i	−1.59307	−	0.811640i
$260$	−15.8312			−0.981807
$261$		0			0
$262$	6.35937	−	11.0148i	0.392883	−	0.680494i
$263$	9.56654	−	16.5697i	0.589898	−	1.02173i	−0.404347	−	0.914605i	$-0.632501\pi$
$263$	9.56654	−	16.5697i	0.589898	−	1.02173i	0.994245	−	0.107128i	$-0.0341653\pi$
$264$		0			0
$265$	−18.8538			−1.15818
$266$	0.729773	+	13.9156i	0.0447453	+	0.853221i
$267$		0			0
$268$	−23.6835	−	41.0210i	−1.44670	−	2.50576i
$269$	−4.41840	+	7.65290i	−0.269395	+	0.466605i	−0.968706	−	0.248212i	$-0.920157\pi$
$269$	−4.41840	+	7.65290i	−0.269395	+	0.466605i	0.699311	+	0.714818i	$0.253490\pi$
$270$		0			0
$271$	−9.16955	−	15.8821i	−0.557010	−	0.964770i	−0.997744	−	0.0671321i	$-0.978615\pi$
$271$	−9.16955	−	15.8821i	−0.557010	−	0.964770i	0.440734	−	0.897638i	$-0.354718\pi$
$272$	−7.52949			−0.456542
$273$		0			0
$274$	17.8906			1.08081
$275$	2.39029	+	4.14011i	0.144140	+	0.249658i
$276$		0			0
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	−0.932460	−	0.361272i	$-0.882343\pi$
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	0.779101	+	0.626899i	$0.215676\pi$
$278$	−16.7865	−	29.0750i	−1.00679	−	1.74381i
$279$		0			0
$280$	27.8931	+	14.2110i	1.66693	+	0.849270i
$281$	1.70636			0.101793			0.0508964	−	0.998704i	$-0.483792\pi$
$281$	1.70636			0.101793			0.0508964	+	0.998704i	$0.483792\pi$
$282$		0			0
$283$	6.24415	−	10.8152i	0.371176	−	0.642896i	−0.618571	−	0.785729i	$-0.712288\pi$
$283$	6.24415	−	10.8152i	0.371176	−	0.642896i	0.989747	+	0.142833i	$0.0456213\pi$
$284$	−23.8793	+	41.3602i	−1.41698	+	2.45428i
$285$		0			0
$286$	4.73686			0.280096
$287$	−4.01299	+	2.60626i	−0.236879	+	0.153843i
$288$		0			0
$289$	3.02104	+	5.23260i	0.177708	+	0.307800i
$290$	3.63729	−	6.29997i	0.213589	−	0.369947i
$291$		0			0
$292$	19.3276	+	33.4764i	1.13106	+	1.95906i
$293$	5.20405			0.304024			0.152012	−	0.988379i	$-0.451425\pi$
$293$	5.20405			0.304024			0.152012	+	0.988379i	$0.451425\pi$
$294$		0			0
$295$	35.6755			2.07711
$296$	−22.0275	−	38.1527i	−1.28032	−	2.21758i
$297$		0			0
$298$	2.60135	−	4.50566i	0.150692	−	0.261006i
$299$	−1.92654	−	3.33687i	−0.111415	−	0.192976i
$300$		0			0
$301$	−9.63558	+	6.25790i	−0.555386	+	0.360699i
$302$	−33.4824			−1.92669
$303$		0			0
$304$	−2.50953	+	4.34663i	−0.143931	+	0.249297i
$305$	0.817453	−	1.41587i	0.0468072	−	0.0810725i
$306$		0			0
$307$	5.00136			0.285442			0.142721	−	0.989763i	$-0.454415\pi$
$307$	5.00136			0.285442			0.142721	+	0.989763i	$0.454415\pi$
$308$	−11.7986	−	6.01118i	−0.672289	−	0.342519i
$309$		0			0
$310$	−11.4147	−	19.7709i	−0.648313	−	1.12291i
$311$	16.1984	−	28.0565i	0.918528	−	1.59094i	0.116876	−	0.993146i	$-0.462712\pi$
$311$	16.1984	−	28.0565i	0.918528	−	1.59094i	0.801652	−	0.597791i	$-0.203955\pi$
$312$		0			0
$313$	−0.759535	−	1.31555i	−0.0429315	−	0.0743595i	0.843761	−	0.536719i	$-0.180336\pi$
$313$	−0.759535	−	1.31555i	−0.0429315	−	0.0743595i	−0.886693	+	0.462359i	$0.847003\pi$
$314$	−7.08000			−0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	10.7544	+	18.6272i	0.604029	+	1.04621i	0.992204	+	0.124623i	$0.0397723\pi$
$317$	10.7544	+	18.6272i	0.604029	+	1.04621i	−0.388175	+	0.921586i	$0.626894\pi$
$318$		0			0
$319$	−0.706261	+	1.22328i	−0.0395430	+	0.0684905i
$320$	−15.9600	−	27.6436i	−0.892193	−	1.54532i
$321$		0			0
$322$	0.869243	+	16.5751i	0.0484410	+	0.923693i
$323$	−7.30441			−0.406428
$324$		0			0
$325$	−2.58856	+	4.48352i	−0.143588	+	0.248701i
$326$	0.463715	−	0.803178i	0.0256828	−	0.0444839i
$327$		0			0
$328$	−7.32629			−0.404527
$329$	9.38052	+	4.77920i	0.517165	+	0.263486i
$330$		0			0
$331$	−9.73902	−	16.8685i	−0.535305	−	0.927175i	−0.999149	−	0.0412580i	$-0.986863\pi$
$331$	−9.73902	−	16.8685i	−0.535305	−	0.927175i	0.463844	−	0.885917i	$-0.346470\pi$
$332$	−3.63691	+	6.29931i	−0.199601	+	0.345719i
$333$		0			0
$334$	−8.70942	−	15.0852i	−0.476558	−	0.825423i
$335$	−37.4215			−2.04455
$336$		0			0
$337$	−9.69484			−0.528112			−0.264056	−	0.964507i	$-0.585060\pi$
$337$	−9.69484			−0.528112			−0.264056	+	0.964507i	$0.585060\pi$
$338$	−12.9498	−	22.4296i	−0.704374	−	1.22001i
$339$		0			0
$340$	−17.8736	+	30.9580i	−0.969332	+	1.67893i
$341$	2.21642	+	3.83896i	0.120026	+	0.207891i
$342$		0			0
$343$	2.89912	+	18.2919i	0.156538	+	0.987672i
$344$	−17.5912			−0.948451
$345$		0			0
$346$	−4.83948	+	8.38222i	−0.260172	+	0.450631i
$347$	−1.01302	+	1.75460i	−0.0543817	+	0.0941919i	−0.891935	−	0.452164i	$-0.850652\pi$
$347$	−1.01302	+	1.75460i	−0.0543817	+	0.0941919i	0.837553	+	0.546356i	$0.183985\pi$
$348$		0			0
$349$	−16.2915			−0.872066			−0.436033	−	0.899931i	$-0.643617\pi$
$349$	−16.2915			−0.872066			−0.436033	+	0.899931i	$0.643617\pi$
$350$	18.7031	−	12.1469i	0.999722	−	0.649276i
$351$		0			0
$352$	1.80896	+	3.13321i	0.0964180	+	0.167001i
$353$	−8.53072	+	14.7756i	−0.454045	+	0.786428i	−0.998633	−	0.0522753i	$-0.983353\pi$
$353$	−8.53072	+	14.7756i	−0.454045	+	0.786428i	0.544588	+	0.838704i	$0.316686\pi$
$354$		0			0
$355$	18.8655	+	32.6759i	1.00127	+	1.73426i
$356$	−23.6880			−1.25546
$357$		0			0
$358$	25.2647			1.33528
$359$	1.48363	+	2.56972i	0.0783030	+	0.135625i	0.902518	−	0.430652i	$-0.141717\pi$
$359$	1.48363	+	2.56972i	0.0783030	+	0.135625i	−0.824215	+	0.566277i	$0.808383\pi$
$360$		0			0
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$	−23.4285	−	40.5794i	−1.23137	−	2.13280i
$363$		0			0
$364$	−0.750999	−	14.3204i	−0.0393630	−	0.750590i
$365$	30.5389			1.59848
$366$		0			0
$367$	5.07874	−	8.79664i	0.265108	−	0.459181i	−0.702484	−	0.711700i	$-0.747926\pi$
$367$	5.07874	−	8.79664i	0.265108	−	0.459181i	0.967592	+	0.252519i	$0.0812590\pi$
$368$	−2.98914	+	5.17733i	−0.155819	+	0.269887i
$369$		0			0
$370$	−75.8207			−3.94173
$371$	−0.894387	−	17.0545i	−0.0464342	−	0.885427i
$372$		0			0
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	0.980675	+	0.195645i	$0.0626799\pi$
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	−0.320904	+	0.947112i	$0.603987\pi$
$374$	5.34798	−	9.26297i	0.276537	−	0.478977i
$375$		0			0
$376$	8.05947	+	13.9594i	0.415635	+	0.719902i
$377$	−1.52969			−0.0787829
$378$		0			0
$379$	9.85497			0.506216			0.253108	−	0.967438i	$-0.418547\pi$
$379$	9.85497			0.506216			0.253108	+	0.967438i	$0.418547\pi$
$380$	11.9143	+	20.6362i	0.611191	+	1.05861i
$381$		0			0
$382$	9.89016	−	17.1303i	0.506025	−	0.876460i
$383$	13.6563	+	23.6535i	0.697806	+	1.20864i	0.969225	+	0.246175i	$0.0791737\pi$
$383$	13.6563	+	23.6535i	0.697806	+	1.20864i	−0.271419	+	0.962461i	$0.587493\pi$
$384$		0			0
$385$	−8.77343	+	5.69797i	−0.447135	+	0.290395i
$386$	44.8370			2.28214
$387$		0			0
$388$	−15.3114	+	26.5202i	−0.777321	+	1.34636i
$389$	−2.09223	+	3.62385i	−0.106080	+	0.183736i	−0.914179	−	0.405311i	$-0.867163\pi$
$389$	−2.09223	+	3.62385i	−0.106080	+	0.183736i	0.808099	+	0.589047i	$0.200497\pi$
$390$		0			0
$391$	−8.70038			−0.439997
$392$	−11.5316	+	25.9053i	−0.582435	+	1.30842i
$393$		0			0
$394$	7.15624	+	12.3950i	0.360526	+	0.624450i
$395$	1.12114	−	1.94187i	0.0564107	−	0.0977062i
$396$		0			0
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	0.937745	+	0.347323i	$0.112909\pi$
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	−0.168082	+	0.985773i	$0.553757\pi$
$398$	34.3916			1.72390
$399$		0			0
$400$	8.03259			0.401629
$401$	3.42402	+	5.93057i	0.170987	+	0.296158i	0.938765	−	0.344557i	$-0.111971\pi$
$401$	3.42402	+	5.93057i	0.170987	+	0.296158i	−0.767778	+	0.640716i	$0.778638\pi$
$402$		0			0
$403$	−2.40027	+	4.15739i	−0.119566	+	0.207095i
$404$	29.9961	+	51.9547i	1.49236	+	2.58485i
$405$		0			0
$406$	5.87130	+	2.99132i	0.291388	+	0.148457i
$407$	14.7223			0.729756
$408$		0			0
$409$	9.13490	−	15.8221i	0.451692	−	0.782353i	−0.546799	−	0.837264i	$-0.684154\pi$
$409$	9.13490	−	15.8221i	0.451692	−	0.782353i	0.998491	+	0.0549104i	$0.0174873\pi$
$410$	−6.30445	+	10.9196i	−0.311355	+	0.539282i
$411$		0			0
$412$	−8.23291			−0.405606
$413$	1.69237	+	32.2709i	0.0832763	+	1.58795i
$414$		0			0
$415$	2.87328	+	4.97666i	0.141044	+	0.244295i
$416$	−1.95901	+	3.39311i	−0.0960485	+	0.166361i
$417$		0			0
$418$	−3.56490	−	6.17458i	−0.174365	−	0.302009i
$419$	−22.4619			−1.09734			−0.548669	−	0.836040i	$-0.684865\pi$
$419$	−22.4619			−1.09734			−0.548669	+	0.836040i	$0.684865\pi$
$420$		0			0
$421$	−20.8354			−1.01546			−0.507728	−	0.861517i	$-0.669515\pi$
$421$	−20.8354			−1.01546			−0.507728	+	0.861517i	$0.669515\pi$
$422$	16.5271	+	28.6258i	0.804527	+	1.39348i
$423$		0			0
$424$	13.0739	−	22.6446i	0.634923	−	1.09972i
$425$	5.84505	+	10.1239i	0.283526	+	0.491082i
$426$		0			0
$427$	1.31953	+	0.672276i	0.0638565	+	0.0325337i
$428$	64.7298			3.12883
$429$		0			0
$430$	−15.1376	+	26.2191i	−0.730001	+	1.26440i
$431$	−10.1213	+	17.5307i	−0.487527	+	0.844422i	−0.999897	−	0.0143427i	$-0.995434\pi$
$431$	−10.1213	+	17.5307i	−0.487527	+	0.844422i	0.512370	+	0.858765i	$0.328768\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$	17.3426	−	11.2633i	0.832473	−	0.540655i
$435$		0			0
$436$	−28.8346	−	49.9431i	−1.38093	−	2.39184i
$437$	−2.89978	+	5.02257i	−0.138715	+	0.240262i
$438$		0			0
$439$	17.7390	+	30.7249i	0.846639	+	1.46642i	0.884191	+	0.467126i	$0.154711\pi$
$439$	17.7390	+	30.7249i	0.846639	+	1.46642i	−0.0375520	+	0.999295i	$0.511956\pi$
$440$	−16.0172			−0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	9.60313	+	16.6331i	0.456258	+	0.790263i	0.998760	−	0.0497923i	$-0.0158559\pi$
$443$	9.60313	+	16.6331i	0.456258	+	0.790263i	−0.542501	+	0.840055i	$0.682523\pi$
$444$		0			0
$445$	−9.35716	+	16.2071i	−0.443572	+	0.768289i
$446$	−5.57946	−	9.66391i	−0.264195	−	0.457599i
$447$		0			0
$448$	24.2484	−	15.7483i	1.14563	−	0.744036i
$449$	−29.6082			−1.39730			−0.698648	−	0.715465i	$-0.746215\pi$
$449$	−29.6082			−1.39730			−0.698648	+	0.715465i	$0.746215\pi$
$450$		0			0
$451$	1.22415	−	2.12029i	0.0576429	−	0.0998405i
$452$	−3.12244	+	5.40823i	−0.146867	+	0.254382i
$453$		0			0
$454$	−47.0515			−2.20823
$455$	−10.0945	−	5.14295i	−0.473237	−	0.241105i
$456$		0			0
$457$	4.78098	+	8.28090i	0.223645	+	0.387364i	0.955912	−	0.293653i	$-0.0948711\pi$
$457$	4.78098	+	8.28090i	0.223645	+	0.387364i	−0.732267	+	0.681017i	$0.761538\pi$
$458$	33.5031	−	58.0290i	1.56550	−	2.71152i
$459$		0			0
$460$	14.1913	+	24.5800i	0.661673	+	1.14605i
$461$	−21.8374			−1.01707			−0.508536	−	0.861041i	$-0.669813\pi$
$461$	−21.8374			−1.01707			−0.508536	+	0.861041i	$0.669813\pi$
$462$		0			0
$463$	−26.1489			−1.21524			−0.607621	−	0.794227i	$-0.707876\pi$
$463$	−26.1489			−1.21524			−0.607621	+	0.794227i	$0.707876\pi$
$464$	1.18670	+	2.05542i	0.0550909	+	0.0954203i
$465$		0			0
$466$	16.4721	−	28.5305i	0.763054	−	1.32165i
$467$	−17.4764	−	30.2699i	−0.808709	−	1.40073i	−0.913758	−	0.406258i	$-0.866833\pi$
$467$	−17.4764	−	30.2699i	−0.808709	−	1.40073i	0.105049	−	0.994467i	$-0.466500\pi$
$468$		0			0
$469$	−1.77520	−	33.8502i	−0.0819711	−	1.56306i
$470$	27.7415			1.27962
$471$		0			0
$472$	−24.7386	+	42.8485i	−1.13869	+	1.97226i
$473$	2.93930	−	5.09102i	0.135149	−	0.234086i
$474$		0			0
$475$	7.79247			0.357543
$476$	−28.8515	−	14.6993i	−1.32240	−	0.673741i
$477$		0			0
$478$	−13.2010	−	22.8649i	−0.603801	−	1.04581i
$479$	14.9054	−	25.8170i	0.681047	−	1.17961i	−0.293615	−	0.955924i	$-0.594858\pi$
$479$	14.9054	−	25.8170i	0.681047	−	1.17961i	0.974662	−	0.223684i	$-0.0718083\pi$
$480$		0			0
$481$	7.97172	+	13.8074i	0.363479	+	0.629565i
$482$	55.3031			2.51899
$483$		0			0
$484$	−33.8934			−1.54061
$485$	12.0965	+	20.9518i	0.549276	+	0.951374i
$486$		0			0
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	0.491283	+	0.871000i	$0.336528\pi$
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	−0.999950	+	0.0100365i	$0.996805\pi$
$488$	1.13370	+	1.96363i	0.0513202	+	0.0888892i
$489$		0			0
$490$	28.6879	+	39.4797i	1.29599	+	1.78351i
$491$	−35.0444			−1.58153			−0.790767	−	0.612118i	$-0.790318\pi$
$491$	−35.0444			−1.58153			−0.790767	+	0.612118i	$0.790318\pi$
$492$		0			0
$493$	−1.72704	+	2.99132i	−0.0777819	+	0.134722i
$494$	3.86060	−	6.68675i	0.173696	−	0.300851i
$495$		0			0
$496$	7.44830			0.334438
$497$	−28.6626	+	18.6152i	−1.28570	+	0.835004i
$498$		0			0
$499$	4.46760	+	7.73811i	0.199997	+	0.346405i	0.948527	−	0.316696i	$-0.102573\pi$
$499$	4.46760	+	7.73811i	0.199997	+	0.346405i	−0.748530	+	0.663101i	$0.769240\pi$
$500$	−7.92929	+	13.7339i	−0.354609	+	0.614200i
$501$		0			0
$502$	−9.28972	−	16.0903i	−0.414621	−	0.718144i
$503$	−12.6403			−0.563603			−0.281802	−	0.959473i	$-0.590932\pi$
$503$	−12.6403			−0.563603			−0.281802	+	0.959473i	$0.590932\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$	−4.24620	−	7.35463i	−0.188766	−	0.326953i
$507$		0			0
$508$	7.33732	−	12.7086i	0.325541	−	0.563854i
$509$	14.0555	+	24.3449i	0.623000	+	1.07907i	0.988924	+	0.148423i	$0.0474196\pi$
$509$	14.0555	+	24.3449i	0.623000	+	1.07907i	−0.365924	+	0.930645i	$0.619247\pi$
$510$		0			0
$511$	1.44871	+	27.6245i	0.0640870	+	1.22204i
$512$	24.5070			1.08307
$513$		0			0
$514$	12.3830	−	21.4480i	0.546192	−	0.946033i
$515$	−3.25214	+	5.63287i	−0.143306	+	0.248214i
$516$		0			0
$517$	−5.38662			−0.236903
$518$	−3.59678	−	68.5849i	−0.158034	−	3.01345i
$519$		0			0
$520$	−8.67288	−	15.0219i	−0.380331	−	0.658753i
$521$	4.23768	−	7.33988i	0.185656	−	0.321566i	−0.758141	−	0.652090i	$-0.773892\pi$
$521$	4.23768	−	7.33988i	0.185656	−	0.321566i	0.943797	+	0.330524i	$0.107226\pi$
$522$		0			0
$523$	16.7236	+	28.9662i	0.731273	+	1.26660i	0.956339	+	0.292259i	$0.0944069\pi$
$523$	16.7236	+	28.9662i	0.731273	+	1.26660i	−0.225066	+	0.974344i	$0.572260\pi$
$524$	19.7007			0.860630
$525$		0			0
$526$	45.6681			1.99123
$527$	5.41988	+	9.38751i	0.236094	+	0.408926i
$528$		0			0
$529$	8.04603	−	13.9361i	0.349827	−	0.605919i
$530$	−22.5008	−	38.9725i	−0.977371	−	1.69286i
$531$		0			0
$532$	−18.1016	+	11.7562i	−0.784806	+	0.509698i
$533$	2.65138			0.114844
$534$		0			0
$535$	25.5693	−	44.2874i	1.10546	−	1.91471i
$536$	25.9493	−	44.9456i	1.12084	−	1.94135i
$537$		0			0
$538$	−21.0923			−0.909354
$539$	−5.57039	−	7.66586i	−0.239934	−	0.330192i
$540$		0			0
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$	21.8865	−	37.9085i	0.940106	−	1.62831i
$543$		0			0
$544$	4.42350	+	7.66173i	0.189656	+	0.328494i
$545$	−45.5606			−1.95160
$546$		0			0
$547$	5.77199			0.246792			0.123396	−	0.992357i	$-0.460621\pi$
$547$	5.77199			0.246792			0.123396	+	0.992357i	$0.460621\pi$
$548$	13.8558	+	23.9990i	0.591892	+	1.02519i
$549$		0			0
$550$	−5.70532	+	9.88190i	−0.243276	+	0.421366i
$551$	1.15122	+	1.99397i	0.0490437	+	0.0849461i
$552$		0			0
$553$	1.80974	+	0.922028i	0.0769579	+	0.0392086i
$554$	−12.1845			−0.517672
$555$		0			0
$556$	26.0014	−	45.0358i	1.10271	−	1.90994i
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	−0.258661	−	0.965968i	$-0.583281\pi$
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	0.965883	−	0.258977i	$-0.0833855\pi$
$558$		0			0
$559$	6.36623			0.269263
$560$	0.920558	+	17.5536i	0.0389007	+	0.741774i
$561$		0			0
$562$	2.03643	+	3.52720i	0.0859015	+	0.148786i
$563$	−1.09566	+	1.89773i	−0.0461764	+	0.0799799i	−0.888190	−	0.459477i	$-0.848037\pi$
$563$	−1.09566	+	1.89773i	−0.0461764	+	0.0799799i	0.842013	+	0.539457i	$0.181370\pi$
$564$		0			0
$565$	2.46683	+	4.27268i	0.103780	+	0.179753i
$566$	29.8079			1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	−9.49302	−	16.4424i	−0.397968	−	0.689301i	0.595507	−	0.803350i	$-0.296951\pi$
$569$	−9.49302	−	16.4424i	−0.397968	−	0.689301i	−0.993475	+	0.114049i	$0.963618\pi$
$570$		0			0
$571$	10.8690	−	18.8257i	0.454854	−	0.787831i	−0.543825	−	0.839198i	$-0.683025\pi$
$571$	10.8690	−	18.8257i	0.454854	−	0.787831i	0.998680	+	0.0513674i	$0.0163580\pi$
$572$	3.66858	+	6.35417i	0.153391	+	0.265681i
$573$		0			0
$574$	−10.1766	−	5.18480i	−0.424764	−	0.216409i
$575$	9.28172			0.387074
$576$		0			0
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	0.341443	+	0.939903i	$0.389084\pi$
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	−0.984701	+	0.174253i	$0.944249\pi$
$578$	−7.21083	+	12.4895i	−0.299931	+	0.519496i
$579$		0			0
$580$	11.2680			0.467877
$581$	−4.36542	+	2.83516i	−0.181108	+	0.117622i
$582$		0			0
$583$	4.36902	+	7.56737i	0.180946	+	0.313408i
$584$	−21.1767	+	36.6792i	−0.876299	+	1.51780i
$585$		0			0
$586$	6.21069	+	10.7572i	0.256561	+	0.444377i
$587$	18.3666			0.758072			0.379036	−	0.925382i	$-0.376256\pi$
$587$	18.3666			0.758072			0.379036	+	0.925382i	$0.376256\pi$
$588$		0			0
$589$	7.22565			0.297728
$590$	42.5763	+	73.7444i	1.75284	+	3.03601i
$591$		0			0
$592$	12.3685	−	21.4230i	0.508344	−	0.880478i
$593$	13.8775	+	24.0365i	0.569880	+	0.987061i	0.996577	+	0.0826662i	$0.0263435\pi$
$593$	13.8775	+	24.0365i	0.569880	+	0.987061i	−0.426698	+	0.904394i	$0.640323\pi$
$594$		0			0
$595$	−21.4539	+	13.9334i	−0.879524	+	0.571213i
$596$	8.05871			0.330098
$597$		0			0
$598$	4.59841	−	7.96468i	0.188043	−	0.325700i
$599$	−0.201412	+	0.348855i	−0.00822945	+	0.0142538i	−0.870111	−	0.492856i	$-0.835953\pi$
$599$	−0.201412	+	0.348855i	−0.00822945	+	0.0142538i	0.861881	+	0.507110i	$0.169286\pi$
$600$		0			0
$601$	−24.7466			−1.00943			−0.504717	−	0.863285i	$-0.668403\pi$
$601$	−24.7466			−1.00943			−0.504717	+	0.863285i	$0.668403\pi$
$602$	−24.4351	−	12.4492i	−0.995899	−	0.507392i
$603$		0			0
$604$	−25.9313	−	44.9143i	−1.05513	−	1.82754i
$605$	−13.3885	+	23.1895i	−0.544318	+	0.942787i
$606$		0			0
$607$	−12.0348	−	20.8449i	−0.488479	−	0.846070i	0.511434	−	0.859323i	$-0.329115\pi$
$607$	−12.0348	−	20.8449i	−0.488479	−	0.846070i	−0.999912	+	0.0132531i	$0.995781\pi$
$608$	5.89730			0.239167
$609$		0			0
$610$	3.90231			0.158000
$611$	−2.91672	−	5.05190i	−0.117998	−	0.204378i
$612$		0			0
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$	5.96879	+	10.3382i	0.240881	+	0.417218i
$615$		0			0
$616$	−0.759823	−	14.4886i	−0.0306141	−	0.583763i
$617$	41.8629			1.68534			0.842669	−	0.538431i	$-0.180983\pi$
$617$	41.8629			1.68534			0.842669	+	0.538431i	$0.180983\pi$
$618$		0			0
$619$	−7.41095	+	12.8361i	−0.297871	+	0.515928i	−0.975649	−	0.219339i	$-0.929610\pi$
$619$	−7.41095	+	12.8361i	−0.297871	+	0.515928i	0.677777	+	0.735267i	$0.262943\pi$
$620$	17.6809	−	30.6242i	0.710081	−	1.22990i
$621$		0			0
$622$	77.3270			3.10053
$623$	−15.1043	−	7.69535i	−0.605140	−	0.308308i
$624$		0			0
$625$	15.0930	+	26.1419i	0.603722	+	1.04568i
$626$	1.81291	−	3.14005i	0.0724585	−	0.125502i
$627$		0			0
$628$	−5.48329	−	9.49734i	−0.218807	−	0.378985i
$629$	36.0007			1.43544
$630$		0			0
$631$	−21.0294			−0.837169			−0.418585	−	0.908178i	$-0.637474\pi$
$631$	−21.0294			−0.837169			−0.418585	+	0.908178i	$0.637474\pi$
$632$	1.55487	+	2.69312i	0.0618496	+	0.107127i
$633$		0			0
$634$	−25.6694	+	44.4607i	−1.01946	+	1.76576i
$635$	−5.79673	−	10.0402i	−0.230036	−	0.398434i
$636$		0			0
$637$	4.17329	−	9.37511i	0.165352	−	0.371456i
$638$	−3.37150			−0.133479
$639$		0			0
$640$	30.2882	−	52.4607i	1.19725	−	2.07369i
$641$	−5.96592	+	10.3333i	−0.235640	+	0.408140i	−0.959458	−	0.281850i	$-0.909052\pi$
$641$	−5.96592	+	10.3333i	−0.235640	+	0.408140i	0.723819	+	0.689990i	$0.242385\pi$
$642$		0			0
$643$	39.9355			1.57490			0.787452	−	0.616377i	$-0.211400\pi$
$643$	39.9355			1.57490			0.787452	+	0.616377i	$0.211400\pi$
$644$	−21.5611	+	14.0030i	−0.849627	+	0.551796i
$645$		0			0
$646$	−8.71733	−	15.0989i	−0.342979	−	0.594057i
$647$	0.494477	−	0.856459i	0.0194399	−	0.0336709i	−0.856142	−	0.516741i	$-0.827145\pi$
$647$	0.494477	−	0.856459i	0.0194399	−	0.0336709i	0.875582	+	0.483070i	$0.160478\pi$
$648$		0			0
$649$	−8.26714	−	14.3191i	−0.324514	−	0.562074i
$650$	−12.3571			−0.484686
$651$		0			0
$652$	1.43654			0.0562594
$653$	−11.3573	−	19.6715i	−0.444447	−	0.769804i	0.553567	−	0.832805i	$-0.313266\pi$
$653$	−11.3573	−	19.6715i	−0.444447	−	0.769804i	−0.998014	+	0.0630004i	$0.979933\pi$
$654$		0			0
$655$	7.78211	−	13.4790i	0.304072	−	0.526668i
$656$	−2.05688	−	3.56262i	−0.0803076	−	0.139097i
$657$		0			0
$658$	1.31600	+	25.0940i	0.0513031	+	0.978267i
$659$	38.3885			1.49540			0.747702	−	0.664035i	$-0.231157\pi$
$659$	38.3885			1.49540			0.747702	+	0.664035i	$0.231157\pi$
$660$		0			0
$661$	−16.9629	+	29.3806i	−0.659780	+	1.14277i	0.320892	+	0.947116i	$0.396017\pi$
$661$	−16.9629	+	29.3806i	−0.659780	+	1.14277i	−0.980672	+	0.195657i	$0.937316\pi$
$662$	23.2458	−	40.2628i	0.903472	−	1.56486i
$663$		0			0
$664$	−7.96972			−0.309285
$665$	0.893040	+	17.0288i	0.0346306	+	0.660350i
$666$		0			0
$667$	1.37124	+	2.37505i	0.0530944	+	0.0919623i
$668$	13.4905	−	23.3662i	0.521962	−	0.904064i
$669$		0			0
$670$	−44.6601	−	77.3535i	−1.72537	−	2.98843i
$671$	−0.757720			−0.0292514
$672$		0			0
$673$	32.2060			1.24145			0.620725	−	0.784028i	$-0.286838\pi$
$673$	32.2060			1.24145			0.620725	+	0.784028i	$0.286838\pi$
$674$	−11.5702	−	20.0401i	−0.445666	−	0.771916i
$675$		0			0
$676$	20.0585	−	34.7424i	0.771483	−	1.33625i
$677$	18.9842	+	32.8816i	0.729622	+	1.26374i	0.957043	+	0.289946i	$0.0936375\pi$
$677$	18.9842	+	32.8816i	0.729622	+	1.26374i	−0.227421	+	0.973797i	$0.573029\pi$
$678$		0			0
$679$	−18.3785	+	11.9361i	−0.705303	+	0.458064i
$680$	−39.1672			−1.50199
$681$		0			0
$682$	−5.29031	+	9.16309i	−0.202577	+	0.350873i
$683$	7.59357	−	13.1525i	0.290560	−	0.503265i	−0.683382	−	0.730061i	$-0.739492\pi$
$683$	7.59357	−	13.1525i	0.290560	−	0.503265i	0.973942	+	0.226796i	$0.0728251\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$	−34.3512	+	27.8230i	−1.31153	+	1.06229i
$687$		0			0
$688$	−4.93877	−	8.55420i	−0.188289	−	0.326126i
$689$	−4.73142	+	8.19507i	−0.180253	+	0.312207i
$690$		0			0
$691$	−1.34574	−	2.33089i	−0.0511943	−	0.0886711i	0.839293	−	0.543680i	$-0.182969\pi$
$691$	−1.34574	−	2.33089i	−0.0511943	−	0.0886711i	−0.890487	+	0.455009i	$0.849636\pi$
$692$	−14.9922			−0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	−20.5420	−	35.5798i	−0.779203	−	1.34962i
$696$		0			0
$697$	2.99344	−	5.18480i	0.113385	−	0.196388i
$698$	−19.4429	−	33.6761i	−0.735924	−	1.27466i
$699$		0			0
$700$	30.7792	+	15.6815i	1.16335	+	0.592703i
$701$	−11.8515			−0.447625			−0.223813	−	0.974632i	$-0.571850\pi$
$701$	−11.8515			−0.447625			−0.223813	+	0.974632i	$0.571850\pi$
$702$		0			0
$703$	11.9988	−	20.7826i	0.452544	−	0.783829i
$704$	−7.39689	+	12.8118i	−0.278781	+	0.482862i
$705$		0			0
$706$	−40.7234			−1.53265
$707$	2.24836	+	42.8727i	0.0845584	+	1.61239i
$708$		0			0
$709$	20.5167	+	35.5359i	0.770520	+	1.33458i	0.937278	+	0.348582i	$0.113337\pi$
$709$	20.5167	+	35.5359i	0.770520	+	1.33458i	−0.166759	+	0.985998i	$0.553330\pi$
$710$	−45.0294	+	77.9931i	−1.68992	+	2.92703i
$711$		0			0
$712$	−12.9772	−	22.4771i	−0.486339	−	0.842364i
$713$	8.60657			0.322318
$714$		0			0
$715$	5.79660			0.216781
$716$	19.5669	+	33.8908i	0.731248	+	1.26656i
$717$		0			0
$718$	−3.54123	+	6.13359i	−0.132158	+	0.228904i
$719$	10.4555	+	18.1094i	0.389923	+	0.675366i	0.992439	−	0.122741i	$-0.0391685\pi$
$719$	10.4555	+	18.1094i	0.389923	+	0.675366i	−0.602516	+	0.798107i	$0.705835\pi$
$720$		0			0
$721$	−5.24958	−	2.67457i	−0.195505	−	0.0996060i
$722$	33.7288			1.25526
$723$		0			0
$724$	36.2896	−	62.8554i	1.34869	−	2.33600i
$725$	1.84243	−	3.19119i	0.0684263	−	0.118518i
$726$		0			0
$727$	−2.64330			−0.0980347			−0.0490173	−	0.998798i	$-0.515609\pi$
$727$	−2.64330			−0.0980347			−0.0490173	+	0.998798i	$0.515609\pi$
$728$	13.1769	−	8.55782i	0.488368	−	0.317174i
$729$		0			0
$730$	36.4462	+	63.1267i	1.34893	+	2.33642i
$731$	7.18756	−	12.4492i	0.265841	−	0.460451i
$732$		0			0
$733$	−7.07446	−	12.2533i	−0.261301	−	0.452587i	0.705287	−	0.708922i	$-0.250818\pi$
$733$	−7.07446	−	12.2533i	−0.261301	−	0.452587i	−0.966588	+	0.256335i	$0.917485\pi$
$734$	24.2446			0.894884
$735$		0			0
$736$	7.02436			0.258921
$737$	8.67174	+	15.0199i	0.319428	+	0.553265i
$738$		0			0
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	−0.973595	−	0.228282i	$-0.926689\pi$
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	0.684495	+	0.729017i	$0.260023\pi$
$740$	−58.7212	−	101.708i	−2.15864	−	3.73887i
$741$		0			0
$742$	34.1858	−	22.2022i	1.25500	−	0.815070i
$743$	−21.0991			−0.774051			−0.387026	−	0.922069i	$-0.626497\pi$
$743$	−21.0991			−0.774051			−0.387026	+	0.922069i	$0.626497\pi$
$744$		0			0
$745$	3.18333	−	5.51368i	0.116628	−	0.202006i
$746$	−30.4142	+	52.6789i	−1.11354	+	1.92871i
$747$		0			0
$748$	16.5675			0.605768
$749$	41.2739	+	21.0283i	1.50812	+	0.768357i
$750$		0			0
$751$	−6.51848	−	11.2903i	−0.237863	−	0.411990i	0.722238	−	0.691644i	$-0.243113\pi$
$751$	−6.51848	−	11.2903i	−0.237863	−	0.411990i	−0.960101	+	0.279654i	$0.909780\pi$
$752$	−4.52544	+	7.83829i	−0.165026	+	0.285833i
$753$		0			0
$754$	−1.82558	−	3.16200i	−0.0664838	−	0.115153i
$755$	−40.9732			−1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$	11.7613	+	20.3711i	0.427188	+	0.739912i
$759$		0			0
$760$	−13.0542	+	22.6105i	−0.473525	+	0.820169i
$761$	3.02038	+	5.23146i	0.109489	+	0.189640i	0.915563	−	0.402174i	$-0.131745\pi$
$761$	3.02038	+	5.23146i	0.109489	+	0.189640i	−0.806074	+	0.591814i	$0.798412\pi$
$762$		0			0
$763$	−2.16131	−	41.2127i	−0.0782446	−	1.49200i
$764$	30.6388			1.10847
$765$		0			0
$766$	−32.5959	+	56.4577i	−1.17774	+	2.03990i
$767$	8.95288	−	15.5068i	0.323270	−	0.559920i
$768$		0			0
$769$	−0.216258			−0.00779848			−0.00389924	−	0.999992i	$-0.501241\pi$
$769$	−0.216258			−0.00779848			−0.00389924	+	0.999992i	$0.501241\pi$
$770$	−22.2487	−	11.3353i	−0.801788	−	0.408496i
$771$		0			0
$772$	34.7251	+	60.1457i	1.24979	+	2.16469i
$773$	18.8132	−	32.5854i	0.676663	−	1.17202i	−0.299316	−	0.954154i	$-0.596759\pi$
$773$	18.8132	−	32.5854i	0.676663	−	1.17202i	0.975980	−	0.217861i	$-0.0699081\pi$
$774$		0			0
$775$	−5.78202	−	10.0148i	−0.207696	−	0.359741i
$776$	−33.5527			−1.20447
$777$		0			0
$778$	−9.98776			−0.358078
$779$	−1.99539	−	3.45612i	−0.0714923	−	0.123828i
$780$		0			0
$781$	8.74345	−	15.1441i	0.312865	−	0.541898i
$782$	−10.3833	−	17.9845i	−0.371307	−	0.643123i
$783$		0			0
$784$	−15.8347	+	1.66541i	−0.565526	+	0.0594791i
$785$	−8.66396			−0.309230
$786$		0			0
$787$	−15.4067	+	26.6853i	−0.549191	+	0.951226i	0.449139	+	0.893462i	$0.351731\pi$
$787$	−15.4067	+	26.6853i	−0.549191	+	0.951226i	−0.998330	+	0.0577648i	$0.981603\pi$
$788$	−11.0847	+	19.1992i	−0.394875	+	0.683943i
$789$		0			0
$790$	5.35203			0.190417
$791$	−3.74791	+	2.43410i	−0.133260	+	0.0865468i
$792$		0			0
$793$	−0.410286	−	0.710636i	−0.0145697	−	0.0252354i
$794$	−36.6037	+	63.3994i	−1.29902	+	2.24996i
$795$		0			0
$796$	26.6355	+	46.1340i	0.944070	+	1.63518i
$797$	35.9583			1.27371			0.636855	−	0.770984i	$-0.280235\pi$
$797$	35.9583			1.27371			0.636855	+	0.770984i	$0.280235\pi$
$798$		0			0
$799$	−13.1720			−0.465994
$800$	−4.71907	−	8.17367i	−0.166844	−	0.288983i
$801$		0			0
$802$	−8.17268	+	14.1555i	−0.288587	+	0.499848i
$803$	−7.07684	−	12.2574i	−0.249736	−	0.432556i
$804$		0			0
$805$	1.06371	+	20.2833i	0.0374909	+	0.714892i
$806$	−11.4583			−0.403600
$807$		0			0
$808$	−32.8659	+	56.9254i	−1.15622	+	2.00263i
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	0.288511	+	0.957477i	$0.406840\pi$
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	−0.973455	+	0.228880i	$0.926494\pi$
$810$		0			0
$811$	−28.2811			−0.993082			−0.496541	−	0.868013i	$-0.665397\pi$
$811$	−28.2811			−0.993082			−0.496541	+	0.868013i	$0.665397\pi$
$812$	0.534530	+	10.1926i	0.0187583	+	0.357692i
$813$		0			0
$814$	17.5701	+	30.4322i	0.615830	+	1.06665i
$815$	0.567459	−	0.982867i	0.0198772	−	0.0344283i
$816$		0			0
$817$	−4.79113	−	8.29849i	−0.167621	−	0.290327i
$818$	43.6076			1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	−20.7917	−	36.0123i	−0.725635	−	1.25684i	−0.958712	−	0.284378i	$-0.908213\pi$
$821$	−20.7917	−	36.0123i	−0.725635	−	1.25684i	0.233077	−	0.972458i	$-0.425121\pi$
$822$		0			0
$823$	−4.22999	+	7.32656i	−0.147448	+	0.255388i	−0.930284	−	0.366841i	$-0.880439\pi$
$823$	−4.22999	+	7.32656i	−0.147448	+	0.255388i	0.782835	+	0.622229i	$0.213773\pi$
$824$	−4.51029	−	7.81205i	−0.157123	−	0.272146i
$825$		0			0
$826$	−64.6870	+	42.0115i	−2.25075	+	1.46177i
$827$	44.2823			1.53985			0.769923	−	0.638137i	$-0.220294\pi$
$827$	44.2823			1.53985			0.769923	+	0.638137i	$0.220294\pi$
$828$		0			0
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	−0.973533	−	0.228547i	$-0.926603\pi$
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	0.684694	+	0.728831i	$0.259936\pi$
$830$	−6.85813	+	11.8786i	−0.238049	+	0.412314i
$831$		0			0
$832$	−16.0209			−0.555425
$833$	−13.6214	−	18.7455i	−0.471954	−	0.649494i
$834$		0			0
$835$	−10.6579	−	18.4601i	−0.368832	−	0.638836i
$836$	5.52185	−	9.56412i	0.190977	−	0.330782i
$837$		0			0
$838$	−26.8068	−	46.4308i	−0.926027	−	1.60393i
$839$	−29.6012			−1.02195			−0.510974	−	0.859596i	$-0.670715\pi$
$839$	−29.6012			−1.02195			−0.510974	+	0.859596i	$0.670715\pi$
$840$		0			0
$841$	−27.9112			−0.962456
$842$	−24.8657	−	43.0687i	−0.856929	−	1.48424i
$843$		0			0
$844$	−25.5997	+	44.3400i	−0.881178	+	1.52624i
$845$	−15.8469	−	27.4477i	−0.545151	−	0.944228i
$846$		0			0
$847$	−21.6116	−	11.0107i	−0.742583	−	0.378332i
$848$	14.6821			0.504186
$849$		0			0
$850$	−13.9514	+	24.1645i	−0.478528	+	0.828834i
$851$	14.2920	−	24.7544i	0.489922	−	0.848570i
$852$		0			0
$853$	30.1238			1.03142			0.515710	−	0.856763i	$-0.327528\pi$
$853$	30.1238			1.03142			0.515710	+	0.856763i	$0.327528\pi$
$854$	0.185118	+	3.52990i	0.00633460	+	0.120791i
$855$		0			0
$856$	35.4613	+	61.4208i	1.21204	+	2.09932i
$857$	−18.5447	+	32.1204i	−0.633475	+	1.09721i	0.353361	+	0.935487i	$0.385039\pi$
$857$	−18.5447	+	32.1204i	−0.633475	+	1.09721i	−0.986836	+	0.161724i	$0.948295\pi$
$858$		0			0
$859$	1.89166	+	3.27646i	0.0645427	+	0.111791i	0.896491	−	0.443062i	$-0.146108\pi$
$859$	1.89166	+	3.27646i	0.0645427	+	0.111791i	−0.831948	+	0.554853i	$0.812774\pi$
$860$	−46.8949			−1.59910
$861$		0			0
$862$	−48.3166			−1.64567
$863$	0.213559	+	0.369895i	0.00726963	+	0.0125914i	0.869637	−	0.493691i	$-0.164353\pi$
$863$	0.213559	+	0.369895i	0.00726963	+	0.0125914i	−0.862368	+	0.506282i	$0.831019\pi$
$864$		0			0
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$	−25.8694	−	44.8071i	−0.879077	−	1.52261i
$867$		0			0
$868$	28.5404	+	14.5408i	0.968723	+	0.493547i
$869$	−1.03922			−0.0352530
$870$		0			0
$871$	−9.39105	+	16.2658i	−0.318203	+	0.551145i
$872$	31.5933	−	54.7212i	1.06988	−	1.85309i
$873$		0			0
$874$	−13.8428			−0.468240
$875$	−9.51763	+	6.18129i	−0.321755	+	0.208966i
$876$		0			0
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	0.755167	−	0.655532i	$-0.227556\pi$
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	−0.945291	+	0.326228i	$0.894222\pi$
$878$	−42.3408	+	73.3364i	−1.42893	+	2.47498i
$879$		0			0
$880$	−4.49687	−	7.78881i	−0.151589	−	0.262561i
$881$	−35.4810			−1.19538			−0.597692	−	0.801726i	$-0.703916\pi$
$881$	−35.4810			−1.19538			−0.597692	+	0.801726i	$0.703916\pi$
$882$		0			0
$883$	−5.30092			−0.178390			−0.0891952	−	0.996014i	$-0.528429\pi$
$883$	−5.30092			−0.178390			−0.0891952	+	0.996014i	$0.528429\pi$
$884$	8.97088	+	15.5380i	0.301723	+	0.522600i
$885$		0			0
$886$	−22.9214	+	39.7010i	−0.770060	+	1.33378i
$887$	−28.7832	−	49.8540i	−0.966446	−	1.67393i	−0.705679	−	0.708532i	$-0.749358\pi$
$887$	−28.7832	−	49.8540i	−0.966446	−	1.67393i	−0.260767	−	0.965402i	$-0.583975\pi$
$888$		0			0
$889$	8.80708	−	5.71982i	0.295380	−	0.191837i
$890$	−44.6686			−1.49730
$891$		0			0
$892$	8.64231	−	14.9689i	0.289366	−	0.501197i
$893$	−4.39016	+	7.60398i	−0.146911	+	0.254458i
$894$		0			0
$895$	30.9169			1.03344
$896$	48.8911	+	24.9091i	1.63334	+	0.832155i
$897$		0			0
$898$	−35.3354	−	61.2027i	−1.17916	−	2.04236i
$899$	1.70842	−	2.95906i	0.0569788	−	0.0986903i
$900$		0			0
$901$	10.6837	+	18.5047i	0.355925	+	0.616480i
$902$	5.84377			0.194576
$903$		0			0
$904$	−6.84235			−0.227573
$905$	−28.6700	−	49.6579i	−0.953023	−	1.65068i
$906$		0			0
$907$	−10.4486	+	18.0975i	−0.346939	+	0.600917i	−0.985704	−	0.168485i	$-0.946112\pi$
$907$	−10.4486	+	18.0975i	−0.346939	+	0.600917i	0.638765	+	0.769402i	$0.279446\pi$
$908$	−36.4402	−	63.1163i	−1.20931	−	2.09459i
$909$		0			0
$910$	−1.41616	−	27.0040i	−0.0469454	−	0.895173i
$911$	−22.7639			−0.754201			−0.377101	−	0.926172i	$-0.623079\pi$
$911$	−22.7639			−0.754201			−0.377101	+	0.926172i	$0.623079\pi$
$912$		0			0
$913$	1.33166	−	2.30650i	0.0440715	−	0.0763340i
$914$	−11.4116	+	19.7654i	−0.377461	+	0.653782i
$915$		0			0
$916$	103.789			3.42929
$917$	12.5618	+	6.40002i	0.414828	+	0.211347i
$918$		0			0
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	0.990339	+	0.138664i	$0.0442809\pi$
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	−0.375083	+	0.926991i	$0.622386\pi$
$920$	−15.5490	+	26.9317i	−0.512636	+	0.887911i
$921$		0			0
$922$	−26.0616	−	45.1399i	−0.858292	−	1.48660i
$923$	18.9374			0.623332
$924$		0			0
$925$	−38.4062			−1.26279
$926$	−31.2070	−	54.0521i	−1.02553	−	1.77626i
$927$		0			0
$928$	1.39434	−	2.41508i	0.0457716	−	0.0792787i
$929$	−2.83363	−	4.90799i	−0.0929683	−	0.161026i	0.815791	−	0.578347i	$-0.196302\pi$
$929$	−2.83363	−	4.90799i	−0.0929683	−	0.161026i	−0.908759	+	0.417322i	$0.862969\pi$
$930$		0			0
$931$	−15.3614	+	1.61563i	−0.503449	+	0.0529501i
$932$	51.0289			1.67151
$933$		0			0
$934$	41.7138	−	72.2503i	1.36492	−	2.36410i
$935$	6.54444	−	11.3353i	0.214026	−	0.370704i
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$	67.8529	−	44.0675i	2.21547	−	1.43886i
$939$		0			0
$940$	21.4851	+	37.2133i	0.700766	+	1.21376i
$941$	−10.2276	+	17.7147i	−0.333410	+	0.577483i	−0.983178	−	0.182650i	$-0.941533\pi$
$941$	−10.2276	+	17.7147i	−0.333410	+	0.577483i	0.649768	+	0.760132i	$0.274866\pi$
$942$		0			0
$943$	−2.37674	−	4.11663i	−0.0773973	−	0.134056i
$944$	−27.7817			−0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	2.38343	+	4.12823i	0.0774512	+	0.134149i	0.902150	−	0.431423i	$-0.141988\pi$
$947$	2.38343	+	4.12823i	0.0774512	+	0.134149i	−0.824698	+	0.565573i	$0.808655\pi$
$948$		0			0
$949$	7.66385	−	13.2742i	0.248779	−	0.430898i
$950$	9.29980	+	16.1077i	0.301725	+	0.522604i
$951$		0			0
$952$	−1.85802	−	35.4294i	−0.0602186	−	1.14827i
$953$	−48.9412			−1.58536			−0.792680	−	0.609638i	$-0.791315\pi$
$953$	−48.9412			−1.58536			−0.792680	+	0.609638i	$0.791315\pi$
$954$		0			0
$955$	12.1028	−	20.9627i	0.391638	−	0.678337i
$956$	20.4478	−	35.4166i	0.661328	−	1.14545i
$957$		0			0
$958$	71.1546			2.29890
$959$	1.03857	+	19.8038i	0.0335371	+	0.639499i
$960$		0			0
$961$	10.1386	+	17.5605i	0.327050	+	0.566468i
$962$	−19.0275	+	32.9565i	−0.613470	+	1.06256i
$963$		0			0
$964$	42.8309	+	74.1854i	1.37949	+	2.38935i
$965$	54.8680			1.76626
$966$		0			0
$967$	5.91712			0.190282			0.0951409	−	0.995464i	$-0.469670\pi$
$967$	5.91712			0.190282			0.0951409	+	0.995464i	$0.469670\pi$
$968$	−18.5680	−	32.1608i	−0.596799	−	1.03369i
$969$		0			0
$970$	−28.8729	+	50.0093i	−0.927052	+	1.60570i
$971$	14.4888	+	25.0953i	0.464966	+	0.805345i	0.999200	−	0.0399914i	$-0.0127331\pi$
$971$	14.4888	+	25.0953i	0.464966	+	0.805345i	−0.534234	+	0.845337i	$0.679400\pi$
$972$		0			0
$973$	31.2099	−	20.2695i	1.00054	−	0.649809i
$974$	−53.5866			−1.71703
$975$		0			0
$976$	−0.636580	+	1.10259i	−0.0203764	+	0.0352930i
$977$	−11.4228	+	19.7848i	−0.365447	+	0.632972i	−0.988848	−	0.148930i	$-0.952417\pi$
$977$	−11.4228	+	19.7848i	−0.365447	+	0.632972i	0.623401	+	0.781902i	$0.285750\pi$
$978$		0			0
$979$	8.67340			0.277203
$980$	−30.7412	+	69.0589i	−0.981992	+	2.20601i
$981$		0			0
$982$	−41.8232	−	72.4400i	−1.33463	−	2.31165i
$983$	15.6351	−	27.0809i	0.498684	−	0.863745i	−0.501315	−	0.865265i	$-0.667150\pi$
$983$	15.6351	−	27.0809i	0.498684	−	0.863745i	0.999999	+	0.00151933i	$0.000483619\pi$
$984$		0			0
$985$	8.75726	+	15.1680i	0.279029	+	0.483293i
$986$	−8.24442			−0.262556
$987$		0			0
$988$	11.9598			0.380490
$989$	−5.70679	−	9.88444i	−0.181465	−	0.314307i
$990$		0			0
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	−0.804927	−	0.593374i	$-0.797796\pi$
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	0.916340	+	0.400400i	$0.131129\pi$
$992$	−4.37581	−	7.57912i	−0.138932	−	0.240637i
$993$		0			0
$994$	−72.6862	−	37.0323i	−2.30547	−	1.17459i
$995$	42.0858			1.33421
$996$		0			0
$997$	10.6439	−	18.4358i	0.337095	−	0.583866i	−0.646790	−	0.762668i	$-0.723889\pi$
$997$	10.6439	−	18.4358i	0.337095	−	0.583866i	0.983885	+	0.178802i	$0.0572222\pi$
$998$	−10.6636	+	18.4698i	−0.337549	+	0.584653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.f.487.5		10
3.2	odd	2		567.2.e.e.487.1		10
7.2	even	3	inner	567.2.e.f.163.5		10
7.3	odd	6		3969.2.a.ba.1.1		5
7.4	even	3		3969.2.a.z.1.1		5
9.2	odd	6		189.2.g.b.172.1		10
9.4	even	3		63.2.h.b.25.1	yes	10
9.5	odd	6		189.2.h.b.46.5		10
9.7	even	3		63.2.g.b.4.5	✓	10
21.2	odd	6		567.2.e.e.163.1		10
21.11	odd	6		3969.2.a.bc.1.5		5
21.17	even	6		3969.2.a.bb.1.5		5
36.7	odd	6		1008.2.t.i.193.3		10
36.11	even	6		3024.2.t.i.1873.4		10
36.23	even	6		3024.2.q.i.2881.2		10
36.31	odd	6		1008.2.q.i.529.4		10
63.2	odd	6		189.2.h.b.37.5		10
63.4	even	3		441.2.f.e.295.5		10
63.5	even	6		1323.2.g.f.667.1		10
63.11	odd	6		1323.2.f.e.442.1		10
63.13	odd	6		441.2.h.f.214.1		10
63.16	even	3		63.2.h.b.58.1	yes	10
63.20	even	6		1323.2.g.f.361.1		10
63.23	odd	6		189.2.g.b.100.1		10
63.25	even	3		441.2.f.e.148.5		10
63.31	odd	6		441.2.f.f.295.5		10
63.32	odd	6		1323.2.f.e.883.1		10
63.34	odd	6		441.2.g.f.67.5		10
63.38	even	6		1323.2.f.f.442.1		10
63.40	odd	6		441.2.g.f.79.5		10
63.41	even	6		1323.2.h.f.802.5		10
63.47	even	6		1323.2.h.f.226.5		10
63.52	odd	6		441.2.f.f.148.5		10
63.58	even	3		63.2.g.b.16.5	yes	10
63.59	even	6		1323.2.f.f.883.1		10
63.61	odd	6		441.2.h.f.373.1		10
252.23	even	6		3024.2.t.i.289.4		10
252.79	odd	6		1008.2.q.i.625.4		10
252.191	even	6		3024.2.q.i.2305.2		10
252.247	odd	6		1008.2.t.i.961.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	9.7	even	3
63.2.g.b.16.5	yes	10	63.58	even	3
63.2.h.b.25.1	yes	10	9.4	even	3
63.2.h.b.58.1	yes	10	63.16	even	3
189.2.g.b.100.1		10	63.23	odd	6
189.2.g.b.172.1		10	9.2	odd	6
189.2.h.b.37.5		10	63.2	odd	6
189.2.h.b.46.5		10	9.5	odd	6
441.2.f.e.148.5		10	63.25	even	3
441.2.f.e.295.5		10	63.4	even	3
441.2.f.f.148.5		10	63.52	odd	6
441.2.f.f.295.5		10	63.31	odd	6
441.2.g.f.67.5		10	63.34	odd	6
441.2.g.f.79.5		10	63.40	odd	6
441.2.h.f.214.1		10	63.13	odd	6
441.2.h.f.373.1		10	63.61	odd	6
567.2.e.e.163.1		10	21.2	odd	6
567.2.e.e.487.1		10	3.2	odd	2
567.2.e.f.163.5		10	7.2	even	3	inner
567.2.e.f.487.5		10	1.1	even	1	trivial
1008.2.q.i.529.4		10	36.31	odd	6
1008.2.q.i.625.4		10	252.79	odd	6
1008.2.t.i.193.3		10	36.7	odd	6
1008.2.t.i.961.3		10	252.247	odd	6
1323.2.f.e.442.1		10	63.11	odd	6
1323.2.f.e.883.1		10	63.32	odd	6
1323.2.f.f.442.1		10	63.38	even	6
1323.2.f.f.883.1		10	63.59	even	6
1323.2.g.f.361.1		10	63.20	even	6
1323.2.g.f.667.1		10	63.5	even	6
1323.2.h.f.226.5		10	63.47	even	6
1323.2.h.f.802.5		10	63.41	even	6
3024.2.q.i.2305.2		10	252.191	even	6
3024.2.q.i.2881.2		10	36.23	even	6
3024.2.t.i.289.4		10	252.23	even	6
3024.2.t.i.1873.4		10	36.11	even	6
3969.2.a.z.1.1		5	7.4	even	3
3969.2.a.ba.1.1		5	7.3	odd	6
3969.2.a.bb.1.5		5	21.17	even	6
3969.2.a.bc.1.5		5	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.19343 + 2.06709i) q^{2} +(-1.84857 + 3.20182i) q^{4} +(1.46043 + 2.52954i) q^{5} +(-2.21886 + 1.44106i) q^{7} -4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +(0.676857 - 1.17235i) q^{11} +1.46600 q^{13} +(-5.62686 - 2.86678i) q^{14} +(-1.13729 - 1.96984i) q^{16} +(1.65514 - 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} -10.7989 q^{20} +3.23114 q^{22} +(-1.31415 - 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +(1.74958 + 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} -1.04344 q^{29} +(-1.63729 + 2.83587i) q^{31} +(-1.33629 + 2.31453i) q^{32} +7.90119 q^{34} +(-6.88572 - 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(2.63342 - 4.56121i) q^{38} +(-5.91601 - 10.2468i) q^{40} +1.80858 q^{41} +4.34257 q^{43} +(2.50244 + 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} +(-1.98957 - 3.44604i) q^{47} +(2.84671 - 6.39502i) q^{49} -8.42913 q^{50} +(-2.71001 + 4.69388i) q^{52} +(-3.22743 + 5.59008i) q^{53} +3.95402 q^{55} +(8.98830 - 5.83752i) q^{56} +(-1.24528 - 2.15688i) q^{58} +(6.10700 - 10.5776i) q^{59} +(-0.279867 - 0.484744i) q^{61} -7.81600 q^{62} -10.9283 q^{64} +(2.14100 + 3.70832i) q^{65} +(-6.40588 + 11.0953i) q^{67} +(6.11928 + 10.5989i) q^{68} +(-0.966003 - 18.4201i) q^{70} +12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-12.9791 + 22.4805i) q^{74} +8.15807 q^{76} +(0.187571 + 3.57668i) q^{77} +(-0.383838 - 0.664827i) q^{79} +(3.32187 - 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +1.96741 q^{83} +9.66887 q^{85} +(5.18258 + 8.97649i) q^{86} +(-2.74185 + 4.74903i) q^{88} +(3.20356 + 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +9.71719 q^{92} +(4.74884 - 8.22524i) q^{94} +(3.22257 - 5.58166i) q^{95} +8.28285 q^{97} +(16.6164 - 1.74763i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29}+ \cdots + 59 q^{98}+O(q^{100}) \) 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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