LMFDB - Embedded newform 216.2.q.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	216.25
Dual form			216.2.q.a.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.962247 - 1.44017i) q^{3} +(2.75433 - 2.31115i) q^{5} +(-1.28512 + 0.467744i) q^{7} +(-1.14816 + 2.77159i) q^{9} +O(q^{10})$	\(q+(-0.962247 - 1.44017i) q^{3} +(2.75433 - 2.31115i) q^{5} +(-1.28512 + 0.467744i) q^{7} +(-1.14816 + 2.77159i) q^{9} +(-0.884935 - 0.742548i) q^{11} +(-1.09441 - 6.20668i) q^{13} +(-5.97879 - 1.74279i) q^{15} +(0.526489 + 0.911906i) q^{17} +(1.05282 - 1.82353i) q^{19} +(1.91023 + 1.40070i) q^{21} +(6.16425 + 2.24360i) q^{23} +(1.37664 - 7.80731i) q^{25} +(5.09637 - 1.01341i) q^{27} +(-1.37595 + 7.80343i) q^{29} +(-5.95928 - 2.16900i) q^{31} +(-0.217868 + 1.98897i) q^{33} +(-2.45860 + 4.25842i) q^{35} +(4.41445 + 7.64606i) q^{37} +(-7.88557 + 7.54849i) q^{39} +(0.448188 + 2.54180i) q^{41} +(0.115307 + 0.0967537i) q^{43} +(3.24317 + 10.2874i) q^{45} +(9.75077 - 3.54899i) q^{47} +(-3.92957 + 3.29730i) q^{49} +(0.806685 - 1.63571i) q^{51} +2.09348 q^{53} -4.15354 q^{55} +(-3.63926 + 0.238457i) q^{57} +(3.16766 - 2.65798i) q^{59} +(8.44358 - 3.07321i) q^{61} +(0.179125 - 4.09886i) q^{63} +(-17.3589 - 14.5659i) q^{65} +(1.79209 + 10.1634i) q^{67} +(-2.70037 - 11.0364i) q^{69} +(8.05951 + 13.9595i) q^{71} +(1.63815 - 2.83736i) q^{73} +(-12.5685 + 5.52997i) q^{75} +(1.48457 + 0.540338i) q^{77} +(0.318057 - 1.80379i) q^{79} +(-6.36345 - 6.36447i) q^{81} +(1.68430 - 9.55214i) q^{83} +(3.55768 + 1.29489i) q^{85} +(12.5622 - 5.52722i) q^{87} +(-3.14496 + 5.44724i) q^{89} +(4.30957 + 7.46440i) q^{91} +(2.61058 + 10.6695i) q^{93} +(-1.31466 - 7.45583i) q^{95} +(-10.4149 - 8.73916i) q^{97} +(3.07409 - 1.60011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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			0
$2$		0			0
$3$	−0.962247	−	1.44017i	−0.555554	−	0.831481i
$3$	−0.962247	−	1.44017i	−0.555554	−	0.831481i
$4$		0			0
$5$	2.75433	−	2.31115i	1.23177	−	1.03358i	0.233650	−	0.972321i	$-0.424933\pi$
$5$	2.75433	−	2.31115i	1.23177	−	1.03358i	0.998122	−	0.0612589i	$-0.0195115\pi$
$6$		0			0
$7$	−1.28512	+	0.467744i	−0.485728	+	0.176791i	−0.573264	−	0.819371i	$-0.694323\pi$
$7$	−1.28512	+	0.467744i	−0.485728	+	0.176791i	0.0875358	+	0.996161i	$0.472101\pi$
$8$		0			0
$9$	−1.14816	+	2.77159i	−0.382720	+	0.923864i
$10$		0			0
$11$	−0.884935	−	0.742548i	−0.266818	−	0.223887i	0.499556	−	0.866282i	$-0.333497\pi$
$11$	−0.884935	−	0.742548i	−0.266818	−	0.223887i	−0.766374	+	0.642395i	$0.777941\pi$
$12$		0			0
$13$	−1.09441	−	6.20668i	−0.303533	−	1.72142i	−0.630329	−	0.776328i	$-0.717080\pi$
$13$	−1.09441	−	6.20668i	−0.303533	−	1.72142i	0.326795	−	0.945095i	$-0.394031\pi$
$14$		0			0
$15$	−5.97879	−	1.74279i	−1.54372	−	0.449986i
$16$		0			0
$17$	0.526489	+	0.911906i	0.127692	+	0.221170i	0.922782	−	0.385322i	$-0.125910\pi$
$17$	0.526489	+	0.911906i	0.127692	+	0.221170i	−0.795090	+	0.606492i	$0.792576\pi$
$18$		0			0
$19$	1.05282	−	1.82353i	0.241533	−	0.418347i	−0.719618	−	0.694370i	$-0.755683\pi$
$19$	1.05282	−	1.82353i	0.241533	−	0.418347i	0.961151	+	0.276023i	$0.0890165\pi$
$20$		0			0
$21$	1.91023	+	1.40070i	0.416846	+	0.305657i
$22$		0			0
$23$	6.16425	+	2.24360i	1.28533	+	0.467823i	0.892193	−	0.451655i	$-0.149166\pi$
$23$	6.16425	+	2.24360i	1.28533	+	0.467823i	0.393141	+	0.919478i	$0.371388\pi$
$24$		0			0
$25$	1.37664	−	7.80731i	0.275328	−	1.56146i
$26$		0			0
$27$	5.09637	−	1.01341i	0.980797	−	0.195031i
$28$		0			0
$29$	−1.37595	+	7.80343i	−0.255508	+	1.44906i	0.539256	+	0.842142i	$0.318706\pi$
$29$	−1.37595	+	7.80343i	−0.255508	+	1.44906i	−0.794764	+	0.606918i	$0.792406\pi$
$30$		0			0
$31$	−5.95928	−	2.16900i	−1.07032	−	0.389564i	−0.254023	−	0.967198i	$-0.581754\pi$
$31$	−5.95928	−	2.16900i	−1.07032	−	0.389564i	−0.816296	+	0.577634i	$0.803976\pi$
$32$		0			0
$33$	−0.217868	+	1.98897i	−0.0379259	+	0.346235i
$34$		0			0
$35$	−2.45860	+	4.25842i	−0.415579	+	0.719804i
$36$		0			0
$37$	4.41445	+	7.64606i	0.725732	+	1.25700i	0.958672	+	0.284513i	$0.0918319\pi$
$37$	4.41445	+	7.64606i	0.725732	+	1.25700i	−0.232940	+	0.972491i	$0.574835\pi$
$38$		0			0
$39$	−7.88557	+	7.54849i	−1.26270	+	1.20873i
$40$		0			0
$41$	0.448188	+	2.54180i	0.0699952	+	0.396963i	0.999597	+	0.0283964i	$0.00904007\pi$
$41$	0.448188	+	2.54180i	0.0699952	+	0.396963i	−0.929602	+	0.368566i	$0.879849\pi$
$42$		0			0
$43$	0.115307	+	0.0967537i	0.0175841	+	0.0147548i	0.651537	−	0.758617i	$-0.274124\pi$
$43$	0.115307	+	0.0967537i	0.0175841	+	0.0147548i	−0.633953	+	0.773371i	$0.718569\pi$
$44$		0			0
$45$	3.24317	+	10.2874i	0.483463	+	1.53356i
$46$		0			0
$47$	9.75077	−	3.54899i	1.42230	−	0.517673i	0.487583	−	0.873077i	$-0.337879\pi$
$47$	9.75077	−	3.54899i	1.42230	−	0.517673i	0.934713	+	0.355403i	$0.115657\pi$
$48$		0			0
$49$	−3.92957	+	3.29730i	−0.561368	+	0.471043i
$50$		0			0
$51$	0.806685	−	1.63571i	0.112958	−	0.229045i
$52$		0			0
$53$	2.09348			0.287562			0.143781	−	0.989610i	$-0.454074\pi$
$53$	2.09348			0.287562			0.143781	+	0.989610i	$0.454074\pi$
$54$		0			0
$55$	−4.15354			−0.560064
$56$		0			0
$57$	−3.63926	+	0.238457i	−0.482032	+	0.0315843i
$58$		0			0
$59$	3.16766	−	2.65798i	0.412394	−	0.346040i	−0.412867	−	0.910791i	$-0.635473\pi$
$59$	3.16766	−	2.65798i	0.412394	−	0.346040i	0.825261	+	0.564752i	$0.191028\pi$
$60$		0			0
$61$	8.44358	−	3.07321i	1.08109	−	0.393484i	0.260776	−	0.965399i	$-0.416021\pi$
$61$	8.44358	−	3.07321i	1.08109	−	0.393484i	0.820313	+	0.571915i	$0.193799\pi$
$62$		0			0
$63$	0.179125	−	4.09886i	0.0225676	−	0.516408i
$64$		0			0
$65$	−17.3589	−	14.5659i	−2.15311	−	1.80668i
$66$		0			0
$67$	1.79209	+	10.1634i	0.218938	+	1.24166i	0.873940	+	0.486033i	$0.161557\pi$
$67$	1.79209	+	10.1634i	0.218938	+	1.24166i	−0.655002	+	0.755627i	$0.727332\pi$
$68$		0			0
$69$	−2.70037	−	11.0364i	−0.325086	−	1.32863i
$70$		0			0
$71$	8.05951	+	13.9595i	0.956488	+	1.65669i	0.730925	+	0.682458i	$0.239089\pi$
$71$	8.05951	+	13.9595i	0.956488	+	1.65669i	0.225563	+	0.974228i	$0.427578\pi$
$72$		0			0
$73$	1.63815	−	2.83736i	0.191731	−	0.332088i	−0.754093	−	0.656768i	$-0.771923\pi$
$73$	1.63815	−	2.83736i	0.191731	−	0.332088i	0.945824	+	0.324680i	$0.105257\pi$
$74$		0			0
$75$	−12.5685	+	5.52997i	−1.45128	+	0.638546i
$76$		0			0
$77$	1.48457	+	0.540338i	0.169182	+	0.0615772i
$78$		0			0
$79$	0.318057	−	1.80379i	0.0357842	−	0.202942i	−0.961674	−	0.274195i	$-0.911589\pi$
$79$	0.318057	−	1.80379i	0.0357842	−	0.202942i	0.997458	+	0.0712528i	$0.0226997\pi$
$80$		0			0
$81$	−6.36345	−	6.36447i	−0.707050	−	0.707164i
$82$		0			0
$83$	1.68430	−	9.55214i	0.184876	−	1.04848i	−0.741239	−	0.671241i	$-0.765761\pi$
$83$	1.68430	−	9.55214i	0.184876	−	1.04848i	0.926115	−	0.377242i	$-0.123127\pi$
$84$		0			0
$85$	3.55768	+	1.29489i	0.385885	+	0.140450i
$86$		0			0
$87$	12.5622	−	5.52722i	1.34681	−	0.592580i
$88$		0			0
$89$	−3.14496	+	5.44724i	−0.333366	+	0.577406i	−0.983169	−	0.182696i	$-0.941518\pi$
$89$	−3.14496	+	5.44724i	−0.333366	+	0.577406i	0.649804	+	0.760102i	$0.274851\pi$
$90$		0			0
$91$	4.30957	+	7.46440i	0.451766	+	0.782482i
$92$		0			0
$93$	2.61058	+	10.6695i	0.270704	+	1.10637i
$94$		0			0
$95$	−1.31466	−	7.45583i	−0.134882	−	0.764952i
$96$		0			0
$97$	−10.4149	−	8.73916i	−1.05748	−	0.887328i	−0.0636160	−	0.997974i	$-0.520263\pi$
$97$	−10.4149	−	8.73916i	−1.05748	−	0.887328i	−0.993860	+	0.110647i	$0.964708\pi$
$98$		0			0
$99$	3.07409	−	1.60011i	0.308958	−	0.160817i
$100$		0			0
$101$	−5.41688	+	1.97158i	−0.538999	+	0.196180i	−0.597152	−	0.802128i	$-0.703701\pi$
$101$	−5.41688	+	1.97158i	−0.538999	+	0.196180i	0.0581529	+	0.998308i	$0.481479\pi$
$102$		0			0
$103$	−10.2693	+	8.61694i	−1.01186	+	0.849052i	−0.988583	−	0.150677i	$-0.951855\pi$
$103$	−10.2693	+	8.61694i	−1.01186	+	0.849052i	−0.0232779	+	0.999729i	$0.507410\pi$
$104$		0			0
$105$	8.49861	−	0.556857i	0.829380	−	0.0543437i
$106$		0			0
$107$	−3.97825			−0.384592			−0.192296	−	0.981337i	$-0.561593\pi$
$107$	−3.97825			−0.384592			−0.192296	+	0.981337i	$0.561593\pi$
$108$		0			0
$109$	−9.74366			−0.933273			−0.466637	−	0.884449i	$-0.654534\pi$
$109$	−9.74366			−0.933273			−0.466637	+	0.884449i	$0.654534\pi$
$110$		0			0
$111$	6.76380	−	13.7149i	0.641992	−	1.30176i
$112$		0			0
$113$	−0.800156	+	0.671411i	−0.0752724	+	0.0631610i	−0.679648	−	0.733539i	$-0.737867\pi$
$113$	−0.800156	+	0.671411i	−0.0752724	+	0.0631610i	0.604375	+	0.796700i	$0.293423\pi$
$114$		0			0
$115$	22.1637	−	8.06691i	2.06677	−	0.752243i
$116$		0			0
$117$	18.4589	+	4.09303i	1.70653	+	0.378400i
$118$		0			0
$119$	−1.10314	−	0.925643i	−0.101125	−	0.0848535i
$120$		0			0
$121$	−1.67840	−	9.51867i	−0.152582	−	0.865334i
$122$		0			0
$123$	3.22935	−	3.09131i	0.291181	−	0.278734i
$124$		0			0
$125$	−5.26338	−	9.11645i	−0.470771	−	0.815400i
$126$		0			0
$127$	1.39248	−	2.41185i	0.123563	−	0.214017i	−0.797607	−	0.603177i	$-0.793901\pi$
$127$	1.39248	−	2.41185i	0.123563	−	0.214017i	0.921170	+	0.389160i	$0.127235\pi$
$128$		0			0
$129$	0.0283881	−	0.259162i	0.00249943	−	0.0228179i
$130$		0			0
$131$	−12.2292	−	4.45105i	−1.06847	−	0.388890i	−0.252864	−	0.967502i	$-0.581373\pi$
$131$	−12.2292	−	4.45105i	−1.06847	−	0.388890i	−0.815603	+	0.578611i	$0.803595\pi$
$132$		0			0
$133$	−0.500046	+	2.83590i	−0.0433594	+	0.245904i
$134$		0			0
$135$	11.6949	−	14.5698i	1.00654	−	1.25397i
$136$		0			0
$137$	1.25063	−	7.09266i	0.106848	−	0.605967i	−0.883618	−	0.468209i	$-0.844899\pi$
$137$	1.25063	−	7.09266i	0.106848	−	0.605967i	0.990466	−	0.137758i	$-0.0439895\pi$
$138$		0			0
$139$	−17.4272	−	6.34299i	−1.47816	−	0.538005i	−0.527855	−	0.849334i	$-0.677004\pi$
$139$	−17.4272	−	6.34299i	−1.47816	−	0.538005i	−0.950302	+	0.311329i	$0.899226\pi$
$140$		0			0
$141$	−14.4938	−	10.6277i	−1.22060	−	0.895016i
$142$		0			0
$143$	−3.64028	+	6.30516i	−0.304416	+	0.527264i
$144$		0			0
$145$	14.2451	+	24.6732i	1.18299	+	2.04900i
$146$		0			0
$147$	8.52989	+	2.48642i	0.703533	+	0.205077i
$148$		0			0
$149$	0.00399184	+	0.0226389i	0.000327025	+	0.00185465i	0.984971	−	0.172721i	$-0.0552558\pi$
$149$	0.00399184	+	0.0226389i	0.000327025	+	0.00185465i	−0.984644	+	0.174575i	$0.944145\pi$
$150$		0			0
$151$	13.6742	+	11.4740i	1.11279	+	0.933744i	0.998218	−	0.0596701i	$-0.0190049\pi$
$151$	13.6742	+	11.4740i	1.11279	+	0.933744i	0.114575	+	0.993415i	$0.463449\pi$
$152$		0			0
$153$	−3.13193	+	0.412198i	−0.253201	+	0.0333243i
$154$		0			0
$155$	−21.4267	+	7.79868i	−1.72103	+	0.626405i
$156$		0			0
$157$	4.52658	−	3.79825i	0.361261	−	0.303134i	−0.444032	−	0.896011i	$-0.646452\pi$
$157$	4.52658	−	3.79825i	0.361261	−	0.303134i	0.805293	+	0.592877i	$0.202008\pi$
$158$		0			0
$159$	−2.01445	−	3.01496i	−0.159756	−	0.239102i
$160$		0			0
$161$	−8.97120			−0.707030
$162$		0			0
$163$	−7.58861			−0.594385			−0.297193	−	0.954818i	$-0.596050\pi$
$163$	−7.58861			−0.594385			−0.297193	+	0.954818i	$0.596050\pi$
$164$		0			0
$165$	3.99673	+	5.98179i	0.311145	+	0.465682i
$166$		0			0
$167$	4.71901	−	3.95972i	0.365168	−	0.306412i	−0.441679	−	0.897173i	$-0.645617\pi$
$167$	4.71901	−	3.95972i	0.365168	−	0.306412i	0.806847	+	0.590761i	$0.201172\pi$
$168$		0			0
$169$	−25.1092	+	9.13899i	−1.93147	+	0.702999i
$170$		0			0
$171$	3.84529	+	5.01169i	0.294056	+	0.383254i
$172$		0			0
$173$	1.67125	+	1.40235i	0.127063	+	0.106618i	0.704105	−	0.710096i	$-0.251349\pi$
$173$	1.67125	+	1.40235i	0.127063	+	0.106618i	−0.577042	+	0.816715i	$0.695793\pi$
$174$		0			0
$175$	1.88268	+	10.6772i	0.142317	+	0.807121i
$176$		0			0
$177$	−6.87601	−	2.00432i	−0.516832	−	0.150654i
$178$		0			0
$179$	−2.91718	−	5.05271i	−0.218040	−	0.377657i	0.736168	−	0.676798i	$-0.236633\pi$
$179$	−2.91718	−	5.05271i	−0.218040	−	0.377657i	−0.954209	+	0.299141i	$0.903300\pi$
$180$		0			0
$181$	−2.09298	+	3.62516i	−0.155570	+	0.269456i	−0.933267	−	0.359185i	$-0.883055\pi$
$181$	−2.09298	+	3.62516i	−0.155570	+	0.269456i	0.777696	+	0.628640i	$0.216388\pi$
$182$		0			0
$183$	−12.5507	−	9.20297i	−0.927778	−	0.680303i
$184$		0			0
$185$	29.8301	+	10.8573i	2.19315	+	0.798241i
$186$		0			0
$187$	0.211226	−	1.19792i	0.0154464	−	0.0876007i
$188$		0			0
$189$	−6.07541	+	3.68615i	−0.441921	+	0.268128i
$190$		0			0
$191$	0.318913	−	1.80865i	0.0230758	−	0.130869i	−0.971094	−	0.238699i	$-0.923279\pi$
$191$	0.318913	−	1.80865i	0.0230758	−	0.130869i	0.994169	+	0.107830i	$0.0343902\pi$
$192$		0			0
$193$	11.7434	+	4.27425i	0.845308	+	0.307667i	0.728126	−	0.685443i	$-0.240392\pi$
$193$	11.7434	+	4.27425i	0.845308	+	0.307667i	0.117182	+	0.993110i	$0.462614\pi$
$194$		0			0
$195$	−4.27371	+	39.0158i	−0.306047	+	2.79398i
$196$		0			0
$197$	4.59728	−	7.96272i	0.327542	−	0.567320i	−0.654481	−	0.756078i	$-0.727113\pi$
$197$	4.59728	−	7.96272i	0.327542	−	0.567320i	0.982024	+	0.188758i	$0.0604462\pi$
$198$		0			0
$199$	9.27622	+	16.0669i	0.657574	+	1.13895i	0.981242	+	0.192780i	$0.0617505\pi$
$199$	9.27622	+	16.0669i	0.657574	+	1.13895i	−0.323668	+	0.946171i	$0.604916\pi$
$200$		0			0
$201$	12.9126	−	12.3606i	0.910785	−	0.871852i
$202$		0			0
$203$	−1.88174	−	10.6719i	−0.132073	−	0.749021i
$204$		0			0
$205$	7.10895	+	5.96512i	0.496511	+	0.416622i
$206$		0			0
$207$	−13.2959	+	14.5088i	−0.924129	+	1.00843i
$208$		0			0
$209$	−2.28574	+	0.831940i	−0.158108	+	0.0575465i
$210$		0			0
$211$	7.60326	−	6.37989i	0.523430	−	0.439210i	−0.342396	−	0.939556i	$-0.611238\pi$
$211$	7.60326	−	6.37989i	0.523430	−	0.439210i	0.865826	+	0.500346i	$0.166794\pi$
$212$		0			0
$213$	12.3487	−	25.0395i	0.846122	−	1.71568i
$214$		0			0
$215$	0.541205			0.0369098
$216$		0			0
$217$	8.67290			0.588755
$218$		0			0
$219$	−5.66258	+	0.371031i	−0.382642	+	0.0250720i
$220$		0			0
$221$	5.08372	−	4.26575i	0.341968	−	0.286945i
$222$		0			0
$223$	−19.5545	+	7.11727i	−1.30947	+	0.476607i	−0.900069	−	0.435748i	$-0.856484\pi$
$223$	−19.5545	+	7.11727i	−1.30947	+	0.476607i	−0.409399	+	0.912355i	$0.634262\pi$
$224$		0			0
$225$	20.0581	+	12.7795i	1.33720	+	0.851969i
$226$		0			0
$227$	21.0896	+	17.6963i	1.39977	+	1.17454i	0.961203	+	0.275842i	$0.0889568\pi$
$227$	21.0896	+	17.6963i	1.39977	+	1.17454i	0.438563	+	0.898700i	$0.355488\pi$
$228$		0			0
$229$	1.87659	+	10.6427i	0.124009	+	0.703288i	0.981892	+	0.189443i	$0.0606683\pi$
$229$	1.87659	+	10.6427i	0.124009	+	0.703288i	−0.857883	+	0.513845i	$0.828221\pi$
$230$		0			0
$231$	−0.650342	−	2.65796i	−0.0427894	−	0.174881i
$232$		0			0
$233$	0.224797	+	0.389361i	0.0147270	+	0.0255079i	0.873295	−	0.487192i	$-0.161979\pi$
$233$	0.224797	+	0.389361i	0.0147270	+	0.0255079i	−0.858568	+	0.512700i	$0.828645\pi$
$234$		0			0
$235$	18.6545	−	32.3106i	1.21689	−	2.10771i
$236$		0			0
$237$	−2.90381	+	1.27764i	−0.188623	+	0.0829914i
$238$		0			0
$239$	−19.3110	−	7.02864i	−1.24913	−	0.454645i	−0.369021	−	0.929421i	$-0.620307\pi$
$239$	−19.3110	−	7.02864i	−1.24913	−	0.454645i	−0.880107	+	0.474776i	$0.842529\pi$
$240$		0			0
$241$	−1.88096	+	10.6675i	−0.121163	+	0.687151i	0.862350	+	0.506313i	$0.168992\pi$
$241$	−1.88096	+	10.6675i	−0.121163	+	0.687151i	−0.983513	+	0.180838i	$0.942119\pi$
$242$		0			0
$243$	−3.04269	+	15.2886i	−0.195189	+	0.980766i
$244$		0			0
$245$	−3.20275	+	18.1637i	−0.204616	+	1.16044i
$246$		0			0
$247$	−12.4703	−	4.53882i	−0.793466	−	0.288798i
$248$		0			0
$249$	−15.3774	+	6.76584i	−0.974502	+	0.428768i
$250$		0			0
$251$	−5.50004	+	9.52636i	−0.347160	+	0.601298i	−0.985744	−	0.168254i	$-0.946187\pi$
$251$	−5.50004	+	9.52636i	−0.347160	+	0.601298i	0.638584	+	0.769552i	$0.279520\pi$
$252$		0			0
$253$	−3.78897	−	6.56269i	−0.238211	−	0.412593i
$254$		0			0
$255$	−1.55851	−	6.36966i	−0.0975977	−	0.398883i
$256$		0			0
$257$	2.84563	+	16.1384i	0.177506	+	1.00668i	0.935212	+	0.354089i	$0.115209\pi$
$257$	2.84563	+	16.1384i	0.177506	+	1.00668i	−0.757706	+	0.652596i	$0.773680\pi$
$258$		0			0
$259$	−9.24948	−	7.76123i	−0.574735	−	0.482260i
$260$		0			0
$261$	−20.0481	−	12.7732i	−1.24095	−	0.790640i
$262$		0			0
$263$	−7.11938	+	2.59124i	−0.439000	+	0.159783i	−0.552058	−	0.833805i	$-0.686157\pi$
$263$	−7.11938	+	2.59124i	−0.439000	+	0.159783i	0.113059	+	0.993588i	$0.463935\pi$
$264$		0			0
$265$	5.76613	−	4.83836i	0.354211	−	0.297218i
$266$		0			0
$267$	10.8712	−	0.712315i	0.665304	−	0.0435930i
$268$		0			0
$269$	1.73753			0.105939			0.0529695	−	0.998596i	$-0.483131\pi$
$269$	1.73753			0.105939			0.0529695	+	0.998596i	$0.483131\pi$
$270$		0			0
$271$	−20.7783			−1.26219			−0.631095	−	0.775705i	$-0.717394\pi$
$271$	−20.7783			−1.26219			−0.631095	+	0.775705i	$0.717394\pi$
$272$		0			0
$273$	6.60311	−	13.3891i	0.399638	−	0.810345i
$274$		0			0
$275$	−7.01554	+	5.88674i	−0.423053	+	0.354984i
$276$		0			0
$277$	2.03552	−	0.740867i	0.122302	−	0.0445144i	−0.280144	−	0.959958i	$-0.590382\pi$
$277$	2.03552	−	0.740867i	0.122302	−	0.0445144i	0.402446	+	0.915444i	$0.368160\pi$
$278$		0			0
$279$	12.8538	−	14.0263i	0.769537	−	0.839735i
$280$		0			0
$281$	6.00308	+	5.03719i	0.358114	+	0.300493i	0.804038	−	0.594577i	$-0.202681\pi$
$281$	6.00308	+	5.03719i	0.358114	+	0.300493i	−0.445924	+	0.895071i	$0.647125\pi$
$282$		0			0
$283$	−4.11954	−	23.3630i	−0.244881	−	1.38879i	−0.820769	−	0.571260i	$-0.806455\pi$
$283$	−4.11954	−	23.3630i	−0.244881	−	1.38879i	0.575888	−	0.817529i	$-0.304656\pi$
$284$		0			0
$285$	−9.47261	+	9.06768i	−0.561109	+	0.537123i
$286$		0			0
$287$	−1.76488	−	3.05687i	−0.104178	−	0.180441i
$288$		0			0
$289$	7.94562	−	13.7622i	0.467389	−	0.809542i
$290$		0			0
$291$	−2.56412	+	23.4085i	−0.150311	+	1.37223i
$292$		0			0
$293$	−7.94941	−	2.89335i	−0.464409	−	0.169031i	0.0992089	−	0.995067i	$-0.468369\pi$
$293$	−7.94941	−	2.89335i	−0.464409	−	0.169031i	−0.563618	+	0.826036i	$0.690591\pi$
$294$		0			0
$295$	2.58176	−	14.6419i	0.150316	−	0.852484i
$296$		0			0
$297$	−5.26246	−	2.88750i	−0.305359	−	0.167550i
$298$		0			0
$299$	7.17914	−	40.7149i	0.415180	−	2.35460i
$300$		0			0
$301$	−0.193438	−	0.0704057i	−0.0111496	−	0.00405812i
$302$		0			0
$303$	8.05178	+	5.90406i	0.462563	+	0.339179i
$304$		0			0
$305$	16.1537	−	27.9790i	0.924958	−	1.60208i
$306$		0			0
$307$	−9.69418	−	16.7908i	−0.553276	−	0.958302i	−0.998035	−	0.0626523i	$-0.980044\pi$
$307$	−9.69418	−	16.7908i	−0.553276	−	0.958302i	0.444759	−	0.895650i	$-0.353289\pi$
$308$		0			0
$309$	22.2914	+	6.49784i	1.26811	+	0.369649i
$310$		0			0
$311$	3.47766	+	19.7228i	0.197200	+	1.11838i	0.909251	+	0.416248i	$0.136655\pi$
$311$	3.47766	+	19.7228i	0.197200	+	1.11838i	−0.712051	+	0.702127i	$0.752234\pi$
$312$		0			0
$313$	−8.22142	−	6.89859i	−0.464702	−	0.389931i	0.380156	−	0.924923i	$-0.375870\pi$
$313$	−8.22142	−	6.89859i	−0.464702	−	0.389931i	−0.844858	+	0.534991i	$0.820315\pi$
$314$		0			0
$315$	−8.97973	−	11.7036i	−0.505951	−	0.659422i
$316$		0			0
$317$	22.5676	−	8.21393i	1.26752	−	0.461340i	0.381236	−	0.924478i	$-0.375499\pi$
$317$	22.5676	−	8.21393i	1.26752	−	0.461340i	0.886286	+	0.463138i	$0.153276\pi$
$318$		0			0
$319$	7.01205	−	5.88381i	0.392600	−	0.329430i
$320$		0			0
$321$	3.82806	+	5.72935i	0.213662	+	0.319781i
$322$		0			0
$323$	2.21719			0.123368
$324$		0			0
$325$	−49.9641			−2.77151
$326$		0			0
$327$	9.37581	+	14.0325i	0.518483	+	0.775999i
$328$		0			0
$329$	−10.8708	+	9.12172i	−0.599329	+	0.502897i
$330$		0			0
$331$	19.1244	−	6.96070i	1.05117	−	0.382595i	0.242066	−	0.970260i	$-0.422175\pi$
$331$	19.1244	−	6.96070i	1.05117	−	0.382595i	0.809104	+	0.587665i	$0.199953\pi$
$332$		0			0
$333$	−26.2603	+	3.45616i	−1.43905	+	0.189396i
$334$		0			0
$335$	28.4252	+	23.8516i	1.55304	+	1.30315i
$336$		0			0
$337$	−1.51357	−	8.58388i	−0.0824494	−	0.467594i	−0.997878	−	0.0651132i	$-0.979259\pi$
$337$	−1.51357	−	8.58388i	−0.0824494	−	0.467594i	0.915428	−	0.402481i	$-0.131852\pi$
$338$		0			0
$339$	1.73689	+	0.506296i	0.0943350	+	0.0274982i
$340$		0			0
$341$	3.66299	+	6.34448i	0.198362	+	0.343573i
$342$		0			0
$343$	8.29423	−	14.3660i	0.447846	−	0.775693i
$344$		0			0
$345$	−32.9446	−	24.1570i	−1.77368	−	1.30057i
$346$		0			0
$347$	−2.80009	−	1.01915i	−0.150317	−	0.0547107i	0.265766	−	0.964038i	$-0.414375\pi$
$347$	−2.80009	−	1.01915i	−0.150317	−	0.0547107i	−0.416083	+	0.909327i	$0.636597\pi$
$348$		0			0
$349$	3.37235	−	19.1255i	0.180518	−	1.02377i	−0.751062	−	0.660231i	$-0.770458\pi$
$349$	3.37235	−	19.1255i	0.180518	−	1.02377i	0.931580	−	0.363536i	$-0.118431\pi$
$350$		0			0
$351$	−11.8674	−	30.5225i	−0.633436	−	1.62917i
$352$		0			0
$353$	−1.26208	+	7.15761i	−0.0671738	+	0.380961i	0.932624	+	0.360850i	$0.117513\pi$
$353$	−1.26208	+	7.15761i	−0.0671738	+	0.380961i	−0.999798	+	0.0201116i	$0.993598\pi$
$354$		0			0
$355$	54.4611	+	19.8222i	2.89049	+	1.05205i
$356$		0			0
$357$	−0.271589	+	2.47940i	−0.0143740	+	0.131224i
$358$		0			0
$359$	6.31207	−	10.9328i	0.333138	−	0.577012i	−0.649987	−	0.759945i	$-0.725226\pi$
$359$	6.31207	−	10.9328i	0.333138	−	0.577012i	0.983125	+	0.182933i	$0.0585591\pi$
$360$		0			0
$361$	7.28315	+	12.6148i	0.383324	+	0.663936i
$362$		0			0
$363$	−12.0934	+	11.5765i	−0.634741	+	0.607608i
$364$		0			0
$365$	−2.04558	−	11.6010i	−0.107070	−	0.607226i
$366$		0			0
$367$	10.1988	+	8.55779i	0.532372	+	0.446713i	0.868920	−	0.494953i	$-0.164815\pi$
$367$	10.1988	+	8.55779i	0.532372	+	0.446713i	−0.336547	+	0.941666i	$0.609259\pi$
$368$		0			0
$369$	−7.55943	−	1.67620i	−0.393528	−	0.0872596i
$370$		0			0
$371$	−2.69037	+	0.979213i	−0.139677	+	0.0508382i
$372$		0			0
$373$	−8.23624	+	6.91103i	−0.426456	+	0.357839i	−0.830613	−	0.556851i	$-0.812010\pi$
$373$	−8.23624	+	6.91103i	−0.426456	+	0.357839i	0.404156	+	0.914690i	$0.367565\pi$
$374$		0			0
$375$	−8.06453	+	16.3524i	−0.416451	+	0.844435i
$376$		0			0
$377$	49.9392			2.57200
$378$		0			0
$379$	−0.137196			−0.00704729			−0.00352364	−	0.999994i	$-0.501122\pi$
$379$	−0.137196			−0.00704729			−0.00352364	+	0.999994i	$0.501122\pi$
$380$		0			0
$381$	−4.81338	+	0.315389i	−0.246597	+	0.0161579i
$382$		0			0
$383$	−15.9605	+	13.3924i	−0.815542	+	0.684321i	−0.951924	−	0.306335i	$-0.900897\pi$
$383$	−15.9605	+	13.3924i	−0.815542	+	0.684321i	0.136381	+	0.990656i	$0.456453\pi$
$384$		0			0
$385$	5.33778	−	1.94279i	0.272039	−	0.0990139i
$386$		0			0
$387$	−0.400552	+	0.208494i	−0.0203612	+	0.0105983i
$388$		0			0
$389$	6.54997	+	5.49608i	0.332097	+	0.278662i	0.793554	−	0.608500i	$-0.208229\pi$
$389$	6.54997	+	5.49608i	0.332097	+	0.278662i	−0.461457	+	0.887163i	$0.652673\pi$
$390$		0			0
$391$	1.19946	+	6.80245i	0.0606591	+	0.344015i
$392$		0			0
$393$	5.35722	+	21.8951i	0.270236	+	1.10446i
$394$		0			0
$395$	−3.29281	−	5.70331i	−0.165679	−	0.286965i
$396$		0			0
$397$	8.06321	−	13.9659i	0.404681	−	0.700928i	−0.589603	−	0.807693i	$-0.700716\pi$
$397$	8.06321	−	13.9659i	0.404681	−	0.700928i	0.994284	+	0.106765i	$0.0340493\pi$
$398$		0			0
$399$	4.56534	−	2.00869i	0.228553	−	0.100560i
$400$		0			0
$401$	−22.8666	−	8.32277i	−1.14190	−	0.415619i	−0.299304	−	0.954158i	$-0.596754\pi$
$401$	−22.8666	−	8.32277i	−1.14190	−	0.415619i	−0.842601	+	0.538539i	$0.818977\pi$
$402$		0			0
$403$	−6.94043	+	39.3611i	−0.345727	+	1.96072i
$404$		0			0
$405$	−32.2363	−	2.82292i	−1.60183	−	0.140272i
$406$		0			0
$407$	1.77106	−	10.0442i	0.0877884	−	0.497873i
$408$		0			0
$409$	−14.7027	−	5.35134i	−0.727000	−	0.264607i	−0.0481058	−	0.998842i	$-0.515318\pi$
$409$	−14.7027	−	5.35134i	−0.727000	−	0.264607i	−0.678895	+	0.734236i	$0.737541\pi$
$410$		0			0
$411$	−11.4180	+	5.02378i	−0.563210	+	0.247805i
$412$		0			0
$413$	−2.82755	+	4.89747i	−0.139135	+	0.240989i
$414$		0			0
$415$	−17.4374	−	30.2024i	−0.855966	−	1.48258i
$416$		0			0
$417$	7.63433	+	31.2016i	0.373855	+	1.52795i
$418$		0			0
$419$	−0.650367	−	3.68842i	−0.0317725	−	0.180191i	0.964792	−	0.263015i	$-0.0847170\pi$
$419$	−0.650367	−	3.68842i	−0.0317725	−	0.180191i	−0.996564	+	0.0828245i	$0.973606\pi$
$420$		0			0
$421$	−7.32303	−	6.14475i	−0.356902	−	0.299477i	0.446652	−	0.894708i	$-0.352616\pi$
$421$	−7.32303	−	6.14475i	−0.356902	−	0.299477i	−0.803555	+	0.595231i	$0.797061\pi$
$422$		0			0
$423$	−1.35910	+	31.1000i	−0.0660819	+	1.51213i
$424$		0			0
$425$	7.84432	−	2.85510i	0.380505	−	0.138493i
$426$		0			0
$427$	−9.41350	+	7.89886i	−0.455551	+	0.382253i
$428$		0			0
$429$	12.5833	−	0.824502i	0.607529	−	0.0398073i
$430$		0			0
$431$	−2.34947			−0.113170			−0.0565850	−	0.998398i	$-0.518021\pi$
$431$	−2.34947			−0.113170			−0.0565850	+	0.998398i	$0.518021\pi$
$432$		0			0
$433$	−10.7070			−0.514546			−0.257273	−	0.966339i	$-0.582824\pi$
$433$	−10.7070			−0.514546			−0.257273	+	0.966339i	$0.582824\pi$
$434$		0			0
$435$	21.8263	−	44.2571i	1.04649	−	2.12196i
$436$		0			0
$437$	10.5811	−	8.87860i	0.506163	−	0.424721i
$438$		0			0
$439$	−10.8979	+	3.96651i	−0.520128	+	0.189311i	−0.588725	−	0.808333i	$-0.700370\pi$
$439$	−10.8979	+	3.96651i	−0.520128	+	0.189311i	0.0685970	+	0.997644i	$0.478148\pi$
$440$		0			0
$441$	−4.62700	−	14.6770i	−0.220333	−	0.698905i
$442$		0			0
$443$	−10.8382	−	9.09433i	−0.514938	−	0.432085i	0.347925	−	0.937523i	$-0.386887\pi$
$443$	−10.8382	−	9.09433i	−0.514938	−	0.432085i	−0.862863	+	0.505438i	$0.831331\pi$
$444$		0			0
$445$	3.92715	+	22.2720i	0.186165	+	1.05579i
$446$		0			0
$447$	0.0287626	−	0.0275331i	0.00136043	−	0.00130227i
$448$		0			0
$449$	3.34568	+	5.79489i	0.157893	+	0.273478i	0.934109	−	0.356989i	$-0.116197\pi$
$449$	3.34568	+	5.79489i	0.157893	+	0.273478i	−0.776216	+	0.630467i	$0.782863\pi$
$450$		0			0
$451$	1.49079	−	2.58213i	0.0701987	−	0.121588i
$452$		0			0
$453$	3.36655	−	30.7340i	0.158174	−	1.44401i
$454$		0			0
$455$	29.1214	+	10.5993i	1.36523	+	0.496903i
$456$		0			0
$457$	−6.15555	+	34.9099i	−0.287945	+	1.63301i	0.406629	+	0.913593i	$0.366704\pi$
$457$	−6.15555	+	34.9099i	−0.287945	+	1.63301i	−0.694574	+	0.719422i	$0.744407\pi$
$458$		0			0
$459$	3.60732	+	4.11386i	0.168375	+	0.192019i
$460$		0			0
$461$	−5.57477	+	31.6161i	−0.259643	+	1.47251i	0.524225	+	0.851580i	$0.324355\pi$
$461$	−5.57477	+	31.6161i	−0.259643	+	1.47251i	−0.783868	+	0.620928i	$0.786756\pi$
$462$		0			0
$463$	27.5952	+	10.0438i	1.28246	+	0.466776i	0.891244	−	0.453525i	$-0.149834\pi$
$463$	27.5952	+	10.0438i	1.28246	+	0.466776i	0.391212	+	0.920300i	$0.372056\pi$
$464$		0			0
$465$	31.8492	+	23.3538i	1.47697	+	1.08301i
$466$		0			0
$467$	−0.922653	+	1.59808i	−0.0426953	+	0.0739504i	−0.886583	−	0.462569i	$-0.846928\pi$
$467$	−0.922653	+	1.59808i	−0.0426953	+	0.0739504i	0.843888	+	0.536519i	$0.180261\pi$
$468$		0			0
$469$	−7.05692	−	12.2229i	−0.325858	−	0.564403i
$470$		0			0
$471$	−9.82581	−	2.86418i	−0.452749	−	0.131974i
$472$		0			0
$473$	−0.0301945	−	0.171241i	−0.00138834	−	0.00787369i
$474$		0			0
$475$	−12.7875	−	10.7300i	−0.586732	−	0.492327i
$476$		0			0
$477$	−2.40366	+	5.80228i	−0.110056	+	0.265668i
$478$		0			0
$479$	6.85289	−	2.49425i	0.313116	−	0.113965i	−0.180682	−	0.983542i	$-0.557830\pi$
$479$	6.85289	−	2.49425i	0.313116	−	0.113965i	0.493798	+	0.869577i	$0.335608\pi$
$480$		0			0
$481$	42.6254	−	35.7670i	1.94355	−	1.63083i
$482$		0			0
$483$	8.63251	+	12.9200i	0.392793	+	0.587881i
$484$		0			0
$485$	−48.8837			−2.21969
$486$		0			0
$487$	−13.6636			−0.619157			−0.309579	−	0.950874i	$-0.600188\pi$
$487$	−13.6636			−0.619157			−0.309579	+	0.950874i	$0.600188\pi$
$488$		0			0
$489$	7.30211	+	10.9289i	0.330213	+	0.494220i
$490$		0			0
$491$	−23.5527	+	19.7631i	−1.06292	+	0.891896i	−0.994392	−	0.105753i	$-0.966275\pi$
$491$	−23.5527	+	19.7631i	−1.06292	+	0.891896i	−0.0685276	+	0.997649i	$0.521830\pi$
$492$		0			0
$493$	−7.84042	+	2.85368i	−0.353115	+	0.128523i
$494$		0			0
$495$	4.76894	−	11.5119i	0.214348	−	0.517423i
$496$		0			0
$497$	−16.8869	−	14.1698i	−0.757480	−	0.635601i
$498$		0			0
$499$	−1.39459	−	7.90910i	−0.0624303	−	0.354060i	−0.999981	−	0.00621041i	$-0.998023\pi$
$499$	−1.39459	−	7.90910i	−0.0624303	−	0.354060i	0.937550	−	0.347849i	$-0.113088\pi$
$500$		0			0
$501$	−10.2435	−	2.98593i	−0.457646	−	0.133402i
$502$		0			0
$503$	1.93019	+	3.34319i	0.0860629	+	0.149065i	0.905844	−	0.423612i	$-0.139238\pi$
$503$	1.93019	+	3.34319i	0.0860629	+	0.149065i	−0.819781	+	0.572677i	$0.805905\pi$
$504$		0			0
$505$	−10.3632	+	17.9496i	−0.461157	+	0.798747i
$506$		0			0
$507$	37.3229	+	27.3674i	1.65757	+	1.21543i
$508$		0			0
$509$	−14.4450	−	5.25756i	−0.640264	−	0.233037i	0.00142837	−	0.999999i	$-0.499545\pi$
$509$	−14.4450	−	5.25756i	−0.640264	−	0.233037i	−0.641693	+	0.766962i	$0.721768\pi$
$510$		0			0
$511$	−0.778056	+	4.41257i	−0.0344192	+	0.195201i
$512$		0			0
$513$	3.51756	−	10.3603i	0.155304	−	0.457420i
$514$		0			0
$515$	−8.36984	+	47.4677i	−0.368819	+	2.09168i
$516$		0			0
$517$	−11.2641	−	4.09979i	−0.495394	−	0.180309i
$518$		0			0
$519$	0.411457	−	3.75629i	0.0180609	−	0.164883i
$520$		0			0
$521$	−3.15663	+	5.46745i	−0.138295	+	0.239533i	−0.926851	−	0.375429i	$-0.877495\pi$
$521$	−3.15663	+	5.46745i	−0.138295	+	0.239533i	0.788557	+	0.614962i	$0.210829\pi$
$522$		0			0
$523$	17.3108	+	29.9832i	0.756948	+	1.31107i	0.944400	+	0.328798i	$0.106644\pi$
$523$	17.3108	+	29.9832i	0.756948	+	1.31107i	−0.187452	+	0.982274i	$0.560023\pi$
$524$		0			0
$525$	13.5654	−	12.9855i	0.592041	−	0.566733i
$526$		0			0
$527$	−1.15957	−	6.57626i	−0.0505118	−	0.286467i
$528$		0			0
$529$	15.3452	+	12.8761i	0.667181	+	0.559831i
$530$		0			0
$531$	3.72986	+	11.8313i	0.161862	+	0.513433i
$532$		0			0
$533$	15.2856	−	5.56352i	0.662095	−	0.240983i
$534$		0			0
$535$	−10.9574	+	9.19435i	−0.473730	+	0.397507i
$536$		0			0
$537$	−4.46969	+	9.06318i	−0.192881	+	0.391105i
$538$		0			0
$539$	5.92582			0.255243
$540$		0			0
$541$	42.2320			1.81570			0.907849	−	0.419298i	$-0.137724\pi$
$541$	42.2320			1.81570			0.907849	+	0.419298i	$0.137724\pi$
$542$		0			0
$543$	7.23480	−	0.474048i	0.310475	−	0.0203433i
$544$		0			0
$545$	−26.8372	+	22.5191i	−1.14958	+	0.964612i
$546$		0			0
$547$	−20.4133	+	7.42984i	−0.872811	+	0.317677i	−0.739305	−	0.673371i	$-0.764846\pi$
$547$	−20.4133	+	7.42984i	−0.872811	+	0.317677i	−0.133506	+	0.991048i	$0.542624\pi$
$548$		0			0
$549$	−1.17690	+	26.9307i	−0.0502290	+	1.14937i
$550$		0			0
$551$	12.7812	+	10.7247i	0.544497	+	0.456887i
$552$		0			0
$553$	0.434972	+	2.46685i	0.0184969	+	0.104901i
$554$		0			0
$555$	−13.0676	−	53.4076i	−0.554690	−	2.26703i
$556$		0			0
$557$	−21.7606	−	37.6905i	−0.922026	−	1.59700i	−0.796276	−	0.604934i	$-0.793200\pi$
$557$	−21.7606	−	37.6905i	−0.922026	−	1.59700i	−0.125750	−	0.992062i	$-0.540134\pi$
$558$		0			0
$559$	0.474327	−	0.821559i	0.0200619	−	0.0347482i
$560$		0			0
$561$	−1.92846	+	0.848496i	−0.0814196	+	0.0358235i
$562$		0			0
$563$	2.00604	+	0.730139i	0.0845445	+	0.0307717i	0.383946	−	0.923355i	$-0.374565\pi$
$563$	2.00604	+	0.730139i	0.0845445	+	0.0307717i	−0.299402	+	0.954127i	$0.596787\pi$
$564$		0			0
$565$	−0.652158	+	3.69857i	−0.0274365	+	0.155600i
$566$		0			0
$567$	11.1547	+	5.20262i	0.468454	+	0.218489i
$568$		0			0
$569$	−4.73401	+	26.8479i	−0.198460	+	1.12552i	0.708945	+	0.705264i	$0.249172\pi$
$569$	−4.73401	+	26.8479i	−0.198460	+	1.12552i	−0.907405	+	0.420258i	$0.861940\pi$
$570$		0			0
$571$	−14.5274	−	5.28756i	−0.607955	−	0.221277i	0.0196535	−	0.999807i	$-0.493744\pi$
$571$	−14.5274	−	5.28756i	−0.607955	−	0.221277i	−0.627608	+	0.778529i	$0.715966\pi$
$572$		0			0
$573$	−2.91163	+	1.28108i	−0.121635	+	0.0535178i
$574$		0			0
$575$	26.0024	−	45.0375i	1.08438	−	1.87819i
$576$		0			0
$577$	4.70243	+	8.14485i	0.195765	+	0.339074i	0.947151	−	0.320788i	$-0.103948\pi$
$577$	4.70243	+	8.14485i	0.195765	+	0.339074i	−0.751386	+	0.659863i	$0.770614\pi$
$578$		0			0
$579$	−5.14442	−	21.0253i	−0.213795	−	0.873783i
$580$		0			0
$581$	2.30343	+	13.0634i	0.0955625	+	0.541962i
$582$		0			0
$583$	−1.85259	−	1.55451i	−0.0767266	−	0.0643813i
$584$		0			0
$585$	60.3016	−	31.3879i	2.49316	−	1.29773i
$586$		0			0
$587$	12.1937	−	4.43816i	0.503290	−	0.183182i	−0.0778833	−	0.996962i	$-0.524816\pi$
$587$	12.1937	−	4.43816i	0.503290	−	0.183182i	0.581173	+	0.813780i	$0.302594\pi$
$588$		0			0
$589$	−10.2293	+	8.58339i	−0.421490	+	0.353672i
$590$		0			0
$591$	−15.8914	+	1.04125i	−0.653683	+	0.0428315i
$592$		0			0
$593$	6.25307			0.256783			0.128391	−	0.991724i	$-0.459019\pi$
$593$	6.25307			0.256783			0.128391	+	0.991724i	$0.459019\pi$
$594$		0			0
$595$	−5.17771			−0.212265
$596$		0			0
$597$	14.2130	−	28.8196i	0.581698	−	1.17951i
$598$		0			0
$599$	35.9278	−	30.1470i	1.46797	−	1.23177i	0.549973	−	0.835183i	$-0.314638\pi$
$599$	35.9278	−	30.1470i	1.46797	−	1.23177i	0.917996	−	0.396590i	$-0.129806\pi$
$600$		0			0
$601$	−0.998722	+	0.363505i	−0.0407387	+	0.0148277i	−0.362309	−	0.932058i	$-0.618012\pi$
$601$	−0.998722	+	0.363505i	−0.0407387	+	0.0148277i	0.321570	+	0.946886i	$0.395789\pi$
$602$		0			0
$603$	−30.2265	−	6.70232i	−1.23092	−	0.272940i
$604$		0			0
$605$	−26.6220	−	22.3385i	−1.08234	−	0.908189i
$606$		0			0
$607$	−6.28614	−	35.6505i	−0.255146	−	1.44701i	−0.795697	−	0.605695i	$-0.792895\pi$
$607$	−6.28614	−	35.6505i	−0.255146	−	1.44701i	0.540550	−	0.841312i	$-0.318216\pi$
$608$		0			0
$609$	−13.5586	+	12.9790i	−0.549423	+	0.525937i
$610$		0			0
$611$	−32.6987	−	56.6359i	−1.32285	−	2.29124i
$612$		0			0
$613$	21.0552	−	36.4686i	0.850410	−	1.47295i	−0.0304291	−	0.999537i	$-0.509687\pi$
$613$	21.0552	−	36.4686i	0.850410	−	1.47295i	0.880839	−	0.473416i	$-0.156979\pi$
$614$		0			0
$615$	1.75020	−	15.9780i	0.0705748	−	0.644295i
$616$		0			0
$617$	−44.7894	−	16.3020i	−1.80315	−	0.656295i	−0.997999	−	0.0632309i	$-0.979860\pi$
$617$	−44.7894	−	16.3020i	−1.80315	−	0.656295i	−0.805156	−	0.593064i	$-0.797918\pi$
$618$		0			0
$619$	−2.56293	+	14.5351i	−0.103013	+	0.584215i	0.888983	+	0.457941i	$0.151413\pi$
$619$	−2.56293	+	14.5351i	−0.103013	+	0.584215i	−0.991995	+	0.126274i	$0.959698\pi$
$620$		0			0
$621$	33.6890	+	5.18730i	1.35189	+	0.208159i
$622$		0			0
$623$	1.49373	−	8.47137i	0.0598450	−	0.339398i
$624$		0			0
$625$	1.68164	+	0.612067i	0.0672656	+	0.0244827i
$626$		0			0
$627$	3.39757	+	2.49131i	0.135686	+	0.0994933i
$628$		0			0
$629$	−4.64833	+	8.05114i	−0.185341	+	0.321020i
$630$		0			0
$631$	18.6252	+	32.2599i	0.741459	+	1.28425i	0.951831	+	0.306624i	$0.0991993\pi$
$631$	18.6252	+	32.2599i	0.741459	+	1.28425i	−0.210371	+	0.977622i	$0.567467\pi$
$632$		0			0
$633$	−16.5043	−	4.81093i	−0.655988	−	0.191217i
$634$		0			0
$635$	−1.73881	−	9.86128i	−0.0690025	−	0.391333i
$636$		0			0
$637$	24.7659	+	20.7810i	0.981259	+	0.823374i
$638$		0			0
$639$	−47.9436	+	6.30994i	−1.89662	+	0.249617i
$640$		0			0
$641$	45.8575	−	16.6908i	1.81126	−	0.659246i	0.814383	−	0.580328i	$-0.197076\pi$
$641$	45.8575	−	16.6908i	1.81126	−	0.659246i	0.996881	−	0.0789177i	$-0.0251464\pi$
$642$		0			0
$643$	0.984817	−	0.826360i	0.0388374	−	0.0325885i	−0.623162	−	0.782093i	$-0.714152\pi$
$643$	0.984817	−	0.826360i	0.0388374	−	0.0325885i	0.662000	+	0.749504i	$0.269708\pi$
$644$		0			0
$645$	−0.520772	−	0.779425i	−0.0205054	−	0.0306898i
$646$		0			0
$647$	−24.4378			−0.960747			−0.480374	−	0.877064i	$-0.659499\pi$
$647$	−24.4378			−0.960747			−0.480374	+	0.877064i	$0.659499\pi$
$648$		0			0
$649$	−4.77685			−0.187508
$650$		0			0
$651$	−8.34548	−	12.4904i	−0.327085	−	0.489539i
$652$		0			0
$653$	25.2867	−	21.2180i	0.989544	−	0.830326i	0.00404267	−	0.999992i	$-0.498713\pi$
$653$	25.2867	−	21.2180i	0.989544	−	0.830326i	0.985502	+	0.169666i	$0.0542687\pi$
$654$		0			0
$655$	−43.9702	+	16.0038i	−1.71806	+	0.625322i
$656$		0			0
$657$	5.98315	+	7.79804i	0.233425	+	0.304230i
$658$		0			0
$659$	−3.49546	−	2.93304i	−0.136164	−	0.114255i	0.572162	−	0.820141i	$-0.306105\pi$
$659$	−3.49546	−	2.93304i	−0.136164	−	0.114255i	−0.708326	+	0.705886i	$0.750549\pi$
$660$		0			0
$661$	5.98676	+	33.9526i	0.232858	+	1.32060i	0.847078	+	0.531469i	$0.178360\pi$
$661$	5.98676	+	33.9526i	0.232858	+	1.32060i	−0.614220	+	0.789135i	$0.710529\pi$
$662$		0			0
$663$	−11.0352	−	3.21670i	−0.428571	−	0.124926i
$664$		0			0
$665$	5.17691	+	8.96667i	0.200752	+	0.347713i
$666$		0			0
$667$	−25.9895	+	45.0152i	−1.00632	+	1.74299i
$668$		0			0
$669$	29.0663	+	21.3132i	1.12377	+	0.824017i
$670$		0			0
$671$	−9.75402	−	3.55017i	−0.376550	−	0.137053i
$672$		0			0
$673$	1.90947	−	10.8291i	0.0736046	−	0.417432i	−0.925634	−	0.378420i	$-0.876468\pi$
$673$	1.90947	−	10.8291i	0.0736046	−	0.417432i	0.999239	−	0.0390127i	$-0.0124213\pi$
$674$		0			0
$675$	−0.896160	−	41.1840i	−0.0344932	−	1.58517i
$676$		0			0
$677$	0.632906	−	3.58939i	0.0243246	−	0.137951i	−0.970227	−	0.242197i	$-0.922132\pi$
$677$	0.632906	−	3.58939i	0.0243246	−	0.137951i	0.994552	+	0.104246i	$0.0332429\pi$
$678$		0			0
$679$	17.4721	+	6.35932i	0.670517	+	0.244048i
$680$		0			0
$681$	5.19219	−	47.4007i	0.198965	−	1.81640i
$682$		0			0
$683$	−16.1778	+	28.0208i	−0.619027	+	1.07219i	0.370637	+	0.928778i	$0.379139\pi$
$683$	−16.1778	+	28.0208i	−0.619027	+	1.07219i	−0.989664	+	0.143408i	$0.954194\pi$
$684$		0			0
$685$	−12.9476	−	22.4259i	−0.494702	−	0.856849i
$686$		0			0
$687$	13.5215	−	12.9435i	0.515877	−	0.493825i
$688$		0			0
$689$	−2.29112	−	12.9936i	−0.0872846	−	0.495016i
$690$		0			0
$691$	3.13390	+	2.62966i	0.119219	+	0.100037i	0.700448	−	0.713703i	$-0.252983\pi$
$691$	3.13390	+	2.62966i	0.119219	+	0.100037i	−0.581229	+	0.813740i	$0.697428\pi$
$692$		0			0
$693$	−3.20212	+	3.49422i	−0.121638	+	0.132734i
$694$		0			0
$695$	−62.6599	+	22.8063i	−2.37682	+	0.865093i
$696$		0			0
$697$	−2.08192	+	1.74694i	−0.0788583	+	0.0661699i
$698$		0			0
$699$	0.344434	−	0.698407i	0.0130277	−	0.0264162i
$700$		0			0
$701$	−38.5416			−1.45570			−0.727848	−	0.685738i	$-0.759479\pi$
$701$	−38.5416			−1.45570			−0.727848	+	0.685738i	$0.759479\pi$
$702$		0			0
$703$	18.5905			0.701152
$704$		0			0
$705$	−64.4829	+	4.22514i	−2.42857	+	0.159128i
$706$		0			0
$707$	6.03912	−	5.06742i	0.227124	−	0.190580i
$708$		0			0
$709$	16.7950	−	6.11287i	0.630748	−	0.229573i	−0.00680885	−	0.999977i	$-0.502167\pi$
$709$	16.7950	−	6.11287i	0.630748	−	0.229573i	0.637557	+	0.770403i	$0.279945\pi$
$710$		0			0
$711$	4.63419	+	2.95257i	0.173796	+	0.110730i
$712$		0			0
$713$	−31.8681	−	26.7405i	−1.19347	−	1.00144i
$714$		0			0
$715$	4.54566	+	25.7797i	0.169998	+	0.964107i
$716$		0			0
$717$	8.45957	+	34.5744i	0.315928	+	1.29121i
$718$		0			0
$719$	19.5493	+	33.8605i	0.729068	+	1.26278i	0.957278	+	0.289170i	$0.0933793\pi$
$719$	19.5493	+	33.8605i	0.729068	+	1.26278i	−0.228210	+	0.973612i	$0.573287\pi$
$720$		0			0
$721$	9.16668	−	15.8771i	0.341385	−	0.591296i
$722$		0			0
$723$	17.1729	−	7.55583i	0.638666	−	0.281004i
$724$		0			0
$725$	59.0296	+	21.4850i	2.19230	+	0.797933i
$726$		0			0
$727$	7.53322	−	42.7230i	0.279392	−	1.58451i	−0.445265	−	0.895399i	$-0.646891\pi$
$727$	7.53322	−	42.7230i	0.279392	−	1.58451i	0.724657	−	0.689110i	$-0.241998\pi$
$728$		0			0
$729$	24.9460	−	10.3295i	0.923926	−	0.382572i
$730$		0			0
$731$	−0.0275226	+	0.156089i	−0.00101796	+	0.00577314i
$732$		0			0
$733$	25.1160	+	9.14149i	0.927682	+	0.337649i	0.761291	−	0.648411i	$-0.224566\pi$
$733$	25.1160	+	9.14149i	0.927682	+	0.337649i	0.166392	+	0.986060i	$0.446788\pi$
$734$		0			0
$735$	29.2406	−	12.8655i	1.07856	−	0.474550i
$736$		0			0
$737$	5.96096	−	10.3247i	0.219575	−	0.380314i
$738$		0			0
$739$	−1.78346	−	3.08905i	−0.0656057	−	0.113632i	0.831357	−	0.555739i	$-0.187565\pi$
$739$	−1.78346	−	3.08905i	−0.0656057	−	0.113632i	−0.896963	+	0.442107i	$0.854231\pi$
$740$		0			0
$741$	5.46285	+	22.3268i	0.200683	+	0.820194i
$742$		0			0
$743$	1.46549	+	8.31121i	0.0537636	+	0.304909i	0.999818	−	0.0191006i	$-0.00608026\pi$
$743$	1.46549	+	8.31121i	0.0537636	+	0.304909i	−0.946054	+	0.324009i	$0.894969\pi$
$744$		0			0
$745$	0.0633168	+	0.0531291i	0.00231975	+	0.00194650i
$746$		0			0
$747$	24.5408	+	15.6356i	0.897900	+	0.572076i
$748$		0			0
$749$	5.11251	−	1.86080i	0.186807	−	0.0679922i
$750$		0			0
$751$	1.64825	−	1.38305i	0.0601456	−	0.0504682i	−0.612219	−	0.790688i	$-0.709723\pi$
$751$	1.64825	−	1.38305i	0.0601456	−	0.0504682i	0.672365	+	0.740220i	$0.265279\pi$
$752$		0			0
$753$	19.0119	−	1.24573i	0.692834	−	0.0453968i
$754$		0			0
$755$	64.1816			2.33581
$756$		0			0
$757$	−11.3432			−0.412274			−0.206137	−	0.978523i	$-0.566089\pi$
$757$	−11.3432			−0.412274			−0.206137	+	0.978523i	$0.566089\pi$
$758$		0			0
$759$	−5.80545	+	11.7717i	−0.210724	+	0.427285i
$760$		0			0
$761$	−31.4102	+	26.3563i	−1.13862	+	0.955414i	−0.999393	−	0.0348469i	$-0.988906\pi$
$761$	−31.4102	+	26.3563i	−1.13862	+	0.955414i	−0.139225	+	0.990261i	$0.544461\pi$
$762$		0			0
$763$	12.5217	−	4.55754i	0.453317	−	0.164994i
$764$		0			0
$765$	−7.67370	+	8.37370i	−0.277443	+	0.302752i
$766$		0			0
$767$	−19.9639	−	16.7517i	−0.720856	−	0.604870i
$768$		0			0
$769$	−3.89632	−	22.0971i	−0.140505	−	0.796843i	−0.970867	−	0.239619i	$-0.922978\pi$
$769$	−3.89632	−	22.0971i	−0.140505	−	0.796843i	0.830362	−	0.557224i	$-0.188134\pi$
$770$		0			0
$771$	20.5038	−	19.6273i	0.738425	−	0.706860i
$772$		0			0
$773$	20.4321	+	35.3895i	0.734893	+	1.27287i	0.954770	+	0.297344i	$0.0961008\pi$
$773$	20.4321	+	35.3895i	0.734893	+	1.27287i	−0.219878	+	0.975527i	$0.570566\pi$
$774$		0			0
$775$	−25.1378	+	43.5400i	−0.902978	+	1.56400i
$776$		0			0
$777$	−2.27719	+	20.7890i	−0.0816937	+	0.745802i
$778$		0			0
$779$	5.10692	+	1.85877i	0.182974	+	0.0665972i
$780$		0			0
$781$	3.23345	−	18.3378i	0.115702	−	0.656179i
$782$		0			0
$783$	0.895715	+	41.1636i	0.0320102	+	1.47107i
$784$		0			0
$785$	3.68933	−	20.9233i	0.131678	−	0.746783i
$786$		0			0
$787$	−45.4984	−	16.5601i	−1.62184	−	0.590302i	−0.638110	−	0.769945i	$-0.720283\pi$
$787$	−45.4984	−	16.5601i	−1.62184	−	0.590302i	−0.983732	+	0.179643i	$0.942506\pi$
$788$		0			0
$789$	10.5824	+	7.75968i	0.376744	+	0.276252i
$790$		0			0
$791$	0.714245	−	1.23711i	0.0253956	−	0.0439865i
$792$		0			0
$793$	−28.3151	−	49.0433i	−1.00550	−	1.74158i
$794$		0			0
$795$	−12.5165	−	3.64850i	−0.443914	−	0.129399i
$796$		0			0
$797$	−7.44962	−	42.2489i	−0.263879	−	1.49653i	−0.772208	−	0.635369i	$-0.780848\pi$
$797$	−7.44962	−	42.2489i	−0.263879	−	1.49653i	0.508329	−	0.861163i	$-0.330263\pi$
$798$		0			0
$799$	8.37002	+	7.02328i	0.296110	+	0.248466i
$800$		0			0
$801$	−11.4866	−	14.9709i	−0.405859	−	0.528970i
$802$		0			0
$803$	−3.55654	+	1.29447i	−0.125507	+	0.0456810i
$804$		0			0
$805$	−24.7096	+	20.7338i	−0.870899	+	0.730771i
$806$		0			0
$807$	−1.67193	−	2.50233i	−0.0588548	−	0.0880862i
$808$		0			0
$809$	4.16656			0.146488			0.0732441	−	0.997314i	$-0.476665\pi$
$809$	4.16656			0.146488			0.0732441	+	0.997314i	$0.476665\pi$
$810$		0			0
$811$	26.9727			0.947141			0.473570	−	0.880756i	$-0.342965\pi$
$811$	26.9727			0.947141			0.473570	+	0.880756i	$0.342965\pi$
$812$		0			0
$813$	19.9938	+	29.9242i	0.701214	+	1.04949i
$814$		0			0
$815$	−20.9015	+	17.5384i	−0.732147	+	0.614345i
$816$		0			0
$817$	0.297830	−	0.108401i	0.0104198	−	0.00379248i
$818$		0			0
$819$	−25.6364	+	3.37405i	−0.895807	+	0.117899i
$820$		0			0
$821$	31.7558	+	26.6463i	1.10829	+	0.929963i	0.997954	−	0.0639322i	$-0.0203641\pi$
$821$	31.7558	+	26.6463i	1.10829	+	0.929963i	0.110332	+	0.993895i	$0.464809\pi$
$822$		0			0
$823$	1.08223	+	6.13763i	0.0377241	+	0.213944i	0.997843	−	0.0656486i	$-0.0209116\pi$
$823$	1.08223	+	6.13763i	0.0377241	+	0.213944i	−0.960119	+	0.279593i	$0.909801\pi$
$824$		0			0
$825$	15.2286	+	4.43905i	0.530191	+	0.154548i
$826$		0			0
$827$	23.8942	+	41.3860i	0.830884	+	1.43913i	0.897338	+	0.441344i	$0.145498\pi$
$827$	23.8942	+	41.3860i	0.830884	+	1.43913i	−0.0664537	+	0.997790i	$0.521168\pi$
$828$		0			0
$829$	−4.50421	+	7.80152i	−0.156438	+	0.270958i	−0.933582	−	0.358365i	$-0.883334\pi$
$829$	−4.50421	+	7.80152i	−0.156438	+	0.270958i	0.777144	+	0.629323i	$0.216668\pi$
$830$		0			0
$831$	−3.02564	−	2.21859i	−0.104958	−	0.0769619i
$832$		0			0
$833$	−5.07571	−	1.84741i	−0.175863	−	0.0640089i
$834$		0			0
$835$	3.84617	−	21.8127i	0.133102	−	0.754860i
$836$		0			0
$837$	−32.5688	−	5.01483i	−1.12574	−	0.173338i
$838$		0			0
$839$	3.76622	−	21.3593i	0.130024	−	0.737404i	−0.848172	−	0.529721i	$-0.822297\pi$
$839$	3.76622	−	21.3593i	0.130024	−	0.737404i	0.978196	−	0.207683i	$-0.0665923\pi$
$840$		0			0
$841$	−31.7492	−	11.5557i	−1.09480	−	0.398474i
$842$		0			0
$843$	1.47794	−	13.4925i	0.0509029	−	0.464705i
$844$		0			0
$845$	−48.0372	+	83.2029i	−1.65253	+	2.86227i
$846$		0			0
$847$	6.60924	+	11.4475i	0.227096	+	0.393342i
$848$		0			0
$849$	−29.6827	+	28.4138i	−1.01871	+	0.975160i
$850$		0			0
$851$	10.0571	+	57.0365i	0.344752	+	1.95518i
$852$		0			0
$853$	−14.0169	−	11.7615i	−0.479928	−	0.402708i	0.370472	−	0.928844i	$-0.379196\pi$
$853$	−14.0169	−	11.7615i	−0.479928	−	0.402708i	−0.850400	+	0.526136i	$0.823640\pi$
$854$		0			0
$855$	22.1740	+	4.91678i	0.758334	+	0.168150i
$856$		0			0
$857$	0.173374	−	0.0631030i	0.00592235	−	0.00215556i	−0.339057	−	0.940766i	$-0.610108\pi$
$857$	0.173374	−	0.0631030i	0.00592235	−	0.00215556i	0.344980	+	0.938610i	$0.387886\pi$
$858$		0			0
$859$	8.14138	−	6.83143i	0.277780	−	0.233085i	−0.493244	−	0.869891i	$-0.664189\pi$
$859$	8.14138	−	6.83143i	0.277780	−	0.233085i	0.771024	+	0.636806i	$0.219745\pi$
$860$		0			0
$861$	−2.70415	+	5.48319i	−0.0921571	+	0.186867i
$862$		0			0
$863$	−17.7092			−0.602828			−0.301414	−	0.953493i	$-0.597459\pi$
$863$	−17.7092			−0.602828			−0.301414	+	0.953493i	$0.597459\pi$
$864$		0			0
$865$	7.84421			0.266711
$866$		0			0
$867$	−27.4655	+	1.79963i	−0.932778	+	0.0611187i
$868$		0			0
$869$	−1.62086	+	1.36006i	−0.0549840	+	0.0461370i
$870$		0			0
$871$	61.1199	−	22.2458i	2.07097	−	0.753771i
$872$		0			0
$873$	36.1794	−	18.8320i	1.22449	−	0.637366i
$874$		0			0
$875$	11.0282	+	9.25377i	0.372822	+	0.312835i
$876$		0			0
$877$	3.42889	+	19.4462i	0.115785	+	0.656652i	0.986358	+	0.164613i	$0.0526374\pi$
$877$	3.42889	+	19.4462i	0.115785	+	0.656652i	−0.870573	+	0.492040i	$0.836252\pi$
$878$		0			0
$879$	3.48239	+	14.2326i	0.117458	+	0.480053i
$880$		0			0
$881$	7.89848	+	13.6806i	0.266107	+	0.460910i	0.967853	−	0.251517i	$-0.0809294\pi$
$881$	7.89848	+	13.6806i	0.266107	+	0.460910i	−0.701746	+	0.712427i	$0.747596\pi$
$882$		0			0
$883$	−8.12127	+	14.0664i	−0.273302	+	0.473374i	−0.969705	−	0.244277i	$-0.921449\pi$
$883$	−8.12127	+	14.0664i	−0.273302	+	0.473374i	0.696403	+	0.717651i	$0.254783\pi$
$884$		0			0
$885$	−23.5711	+	10.3710i	−0.792333	+	0.348616i
$886$		0			0
$887$	−2.88222	−	1.04904i	−0.0967754	−	0.0352234i	0.293179	−	0.956058i	$-0.405287\pi$
$887$	−2.88222	−	1.04904i	−0.0967754	−	0.0352234i	−0.389954	+	0.920834i	$0.627509\pi$
$888$		0			0
$889$	−0.661373	+	3.75084i	−0.0221818	+	0.125799i
$890$		0			0
$891$	0.905310	+	10.3573i	0.0303290	+	0.346983i
$892$		0			0
$893$	3.79408	−	21.5173i	0.126964	−	0.720049i
$894$		0			0
$895$	−19.7125	−	7.17475i	−0.658915	−	0.239825i
$896$		0			0
$897$	−65.5444	+	28.8387i	−2.18846	+	0.962895i
$898$		0			0
$899$	25.1254	−	43.5184i	0.837977	−	1.45142i
$900$		0			0
$901$	1.10220	+	1.90906i	0.0367195	+	0.0636000i
$902$		0			0
$903$	0.0847393	+	0.346331i	0.00281995	+	0.0115252i
$904$		0			0
$905$	2.61353	+	14.8221i	0.0868767	+	0.492702i
$906$		0			0
$907$	−30.2392	−	25.3737i	−1.00408	−	0.842521i	−0.0165334	−	0.999863i	$-0.505263\pi$
$907$	−30.2392	−	25.3737i	−1.00408	−	0.842521i	−0.987544	+	0.157342i	$0.949707\pi$
$908$		0			0
$909$	0.755027	−	17.2771i	0.0250427	−	0.573044i
$910$		0			0
$911$	−22.1938	+	8.07787i	−0.735312	+	0.267632i	−0.682412	−	0.730968i	$-0.739069\pi$
$911$	−22.1938	+	8.07787i	−0.735312	+	0.267632i	−0.0529007	+	0.998600i	$0.516847\pi$
$912$		0			0
$913$	−8.58342	+	7.20234i	−0.284070	+	0.238363i
$914$		0			0
$915$	−55.8383	+	3.65871i	−1.84596	+	0.120953i
$916$		0			0
$917$	17.7978			0.587737
$918$		0			0
$919$	12.3646			0.407871			0.203935	−	0.978984i	$-0.434627\pi$
$919$	12.3646			0.407871			0.203935	+	0.978984i	$0.434627\pi$
$920$		0			0
$921$	−14.8534	+	30.1182i	−0.489435	+	0.992427i
$922$		0			0
$923$	77.8217	−	65.3002i	2.56153	−	2.14938i
$924$		0			0
$925$	65.7722	−	23.9391i	2.16258	−	0.787114i
$926$		0			0
$927$	−12.0919	−	38.3559i	−0.397149	−	1.25977i
$928$		0			0
$929$	−16.8757	−	14.1604i	−0.553674	−	0.464588i	0.322509	−	0.946566i	$-0.395474\pi$
$929$	−16.8757	−	14.1604i	−0.553674	−	0.464588i	−0.876183	+	0.481979i	$0.839918\pi$
$930$		0			0
$931$	1.87562	+	10.6372i	0.0614709	+	0.348619i
$932$		0			0
$933$	25.0577	−	23.9866i	0.820353	−	0.785285i
$934$		0			0
$935$	−2.18680	−	3.78764i	−0.0715159	−	0.123869i
$936$		0			0
$937$	−27.4005	+	47.4590i	−0.895135	+	1.55042i	−0.0614968	+	0.998107i	$0.519587\pi$
$937$	−27.4005	+	47.4590i	−0.895135	+	1.55042i	−0.833638	+	0.552311i	$0.813746\pi$
$938$		0			0
$939$	−2.02408	+	18.4784i	−0.0660535	+	0.603018i
$940$		0			0
$941$	−29.0707	−	10.5809i	−0.947679	−	0.344927i	−0.178485	−	0.983943i	$-0.557120\pi$
$941$	−29.0707	−	10.5809i	−0.947679	−	0.344927i	−0.769194	+	0.639016i	$0.779342\pi$
$942$		0			0
$943$	−2.94005	+	16.6738i	−0.0957411	+	0.542975i
$944$		0			0
$945$	−8.21440	+	24.1941i	−0.267214	+	0.787033i
$946$		0			0
$947$	2.21582	−	12.5665i	0.0720045	−	0.408358i	−0.927407	−	0.374054i	$-0.877967\pi$
$947$	2.21582	−	12.5665i	0.0720045	−	0.408358i	0.999411	−	0.0343039i	$-0.0109214\pi$
$948$		0			0
$949$	−19.4034	−	7.06226i	−0.629861	−	0.229251i
$950$		0			0
$951$	−33.5450	−	24.5973i	−1.08777	−	0.797621i
$952$		0			0
$953$	−7.95129	+	13.7720i	−0.257567	+	0.446120i	−0.965590	−	0.260070i	$-0.916254\pi$
$953$	−7.95129	+	13.7720i	−0.257567	+	0.446120i	0.708022	+	0.706190i	$0.249588\pi$
$954$		0			0
$955$	−3.30167	−	5.71866i	−0.106840	−	0.185052i
$956$		0			0
$957$	−15.2210	−	4.43685i	−0.492025	−	0.143423i
$958$		0			0
$959$	1.71035	+	9.69986i	0.0552300	+	0.313225i
$960$		0			0
$961$	7.06111	+	5.92497i	0.227778	+	0.191128i
$962$		0			0
$963$	4.56768	−	11.0261i	0.147191	−	0.355311i
$964$		0			0
$965$	42.2236	−	15.3681i	1.35923	−	0.494718i
$966$		0			0
$967$	26.9884	−	22.6460i	0.867889	−	0.728245i	−0.0957634	−	0.995404i	$-0.530529\pi$
$967$	26.9884	−	22.6460i	0.867889	−	0.728245i	0.963653	+	0.267159i	$0.0860848\pi$
$968$		0			0
$969$	−2.13348	−	3.19312i	−0.0685373	−	0.102578i
$970$		0			0
$971$	30.4217			0.976277			0.488139	−	0.872766i	$-0.337676\pi$
$971$	30.4217			0.976277			0.488139	+	0.872766i	$0.337676\pi$
$972$		0			0
$973$	25.3629			0.813097
$974$		0			0
$975$	48.0778	+	71.9566i	1.53972	+	2.30446i
$976$		0			0
$977$	17.7324	−	14.8792i	0.567309	−	0.476029i	−0.313443	−	0.949607i	$-0.601482\pi$
$977$	17.7324	−	14.8792i	0.567309	−	0.476029i	0.880752	+	0.473578i	$0.157038\pi$
$978$		0			0
$979$	6.82793	−	2.48516i	0.218221	−	0.0794261i
$980$		0			0
$981$	11.1873	−	27.0055i	0.357183	−	0.862218i
$982$		0			0
$983$	5.17653	+	4.34362i	0.165106	+	0.138540i	0.721597	−	0.692313i	$-0.243408\pi$
$983$	5.17653	+	4.34362i	0.165106	+	0.138540i	−0.556492	+	0.830853i	$0.687853\pi$
$984$		0			0
$985$	−5.74067	−	32.5569i	−0.182913	−	1.03735i
$986$		0			0
$987$	23.5972	+	6.87848i	0.751108	+	0.218945i
$988$		0			0
$989$	0.493701	+	0.855116i	0.0156988	+	0.0271911i
$990$		0			0
$991$	13.1604	−	22.7945i	0.418055	−	0.724093i	−0.577689	−	0.816257i	$-0.696045\pi$
$991$	13.1604	−	22.7945i	0.418055	−	0.724093i	0.995744	+	0.0921645i	$0.0293786\pi$
$992$		0			0
$993$	−28.4269	−	20.8444i	−0.902101	−	0.661476i
$994$		0			0
$995$	62.6828	+	22.8147i	1.98718	+	0.723273i
$996$		0			0
$997$	4.06362	−	23.0459i	0.128696	−	0.729872i	−0.850348	−	0.526221i	$-0.823608\pi$
$997$	4.06362	−	23.0459i	0.128696	−	0.729872i	0.979044	−	0.203650i	$-0.0652806\pi$
$998$		0			0
$999$	30.2463	+	34.4935i	0.956951	+	1.09133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.25.2	✓	24
3.2	odd	2		648.2.q.a.73.1		24
4.3	odd	2		432.2.u.e.241.3		24
27.11	odd	18		5832.2.a.i.1.1		12
27.13	even	9	inner	216.2.q.a.121.2	yes	24
27.14	odd	18		648.2.q.a.577.1		24
27.16	even	9		5832.2.a.h.1.12		12
108.67	odd	18		432.2.u.e.337.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.25.2	✓	24	1.1	even	1	trivial
216.2.q.a.121.2	yes	24	27.13	even	9	inner
432.2.u.e.241.3		24	4.3	odd	2
432.2.u.e.337.3		24	108.67	odd	18
648.2.q.a.73.1		24	3.2	odd	2
648.2.q.a.577.1		24	27.14	odd	18
5832.2.a.h.1.12		12	27.16	even	9
5832.2.a.i.1.1		12	27.11	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.962247 - 1.44017i) q^{3} +(2.75433 - 2.31115i) q^{5} +(-1.28512 + 0.467744i) q^{7} +(-1.14816 + 2.77159i) q^{9} +O(q^{10})\)	\(q+(-0.962247 - 1.44017i) q^{3} +(2.75433 - 2.31115i) q^{5} +(-1.28512 + 0.467744i) q^{7} +(-1.14816 + 2.77159i) q^{9} +(-0.884935 - 0.742548i) q^{11} +(-1.09441 - 6.20668i) q^{13} +(-5.97879 - 1.74279i) q^{15} +(0.526489 + 0.911906i) q^{17} +(1.05282 - 1.82353i) q^{19} +(1.91023 + 1.40070i) q^{21} +(6.16425 + 2.24360i) q^{23} +(1.37664 - 7.80731i) q^{25} +(5.09637 - 1.01341i) q^{27} +(-1.37595 + 7.80343i) q^{29} +(-5.95928 - 2.16900i) q^{31} +(-0.217868 + 1.98897i) q^{33} +(-2.45860 + 4.25842i) q^{35} +(4.41445 + 7.64606i) q^{37} +(-7.88557 + 7.54849i) q^{39} +(0.448188 + 2.54180i) q^{41} +(0.115307 + 0.0967537i) q^{43} +(3.24317 + 10.2874i) q^{45} +(9.75077 - 3.54899i) q^{47} +(-3.92957 + 3.29730i) q^{49} +(0.806685 - 1.63571i) q^{51} +2.09348 q^{53} -4.15354 q^{55} +(-3.63926 + 0.238457i) q^{57} +(3.16766 - 2.65798i) q^{59} +(8.44358 - 3.07321i) q^{61} +(0.179125 - 4.09886i) q^{63} +(-17.3589 - 14.5659i) q^{65} +(1.79209 + 10.1634i) q^{67} +(-2.70037 - 11.0364i) q^{69} +(8.05951 + 13.9595i) q^{71} +(1.63815 - 2.83736i) q^{73} +(-12.5685 + 5.52997i) q^{75} +(1.48457 + 0.540338i) q^{77} +(0.318057 - 1.80379i) q^{79} +(-6.36345 - 6.36447i) q^{81} +(1.68430 - 9.55214i) q^{83} +(3.55768 + 1.29489i) q^{85} +(12.5622 - 5.52722i) q^{87} +(-3.14496 + 5.44724i) q^{89} +(4.30957 + 7.46440i) q^{91} +(2.61058 + 10.6695i) q^{93} +(-1.31466 - 7.45583i) q^{95} +(-10.4149 - 8.73916i) q^{97} +(3.07409 - 1.60011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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