LMFDB - Embedded newform 231.2.n.a.89.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(89,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("231.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.6
Character	$\chi$	$=$	231.89
Dual form			231.2.n.a.122.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36585 - 0.788573i) q^{2} +(1.68141 + 0.415762i) q^{3} +(0.243696 + 0.422094i) q^{4} +(-1.12576 + 1.94987i) q^{5} +(-1.96869 - 1.89378i) q^{6} +(-1.68560 + 2.03930i) q^{7} +2.38560i q^{8} +(2.65428 + 1.39813i) q^{9} +O(q^{10})$	\(q+(-1.36585 - 0.788573i) q^{2} +(1.68141 + 0.415762i) q^{3} +(0.243696 + 0.422094i) q^{4} +(-1.12576 + 1.94987i) q^{5} +(-1.96869 - 1.89378i) q^{6} +(-1.68560 + 2.03930i) q^{7} +2.38560i q^{8} +(2.65428 + 1.39813i) q^{9} +(3.07523 - 1.77549i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.234263 + 0.811032i) q^{12} +5.33562i q^{13} +(3.91041 - 1.45616i) q^{14} +(-2.70354 + 2.81049i) q^{15} +(2.36862 - 4.10256i) q^{16} +(-3.21297 - 5.56503i) q^{17} +(-2.52282 - 4.00274i) q^{18} +(1.65298 + 0.954348i) q^{19} -1.09737 q^{20} +(-3.68205 + 2.72810i) q^{21} +1.57715 q^{22} +(1.30084 + 0.751040i) q^{23} +(-0.991843 + 4.01118i) q^{24} +(-0.0346657 - 0.0600428i) q^{25} +(4.20753 - 7.28765i) q^{26} +(3.88165 + 3.45439i) q^{27} +(-1.27155 - 0.214511i) q^{28} +2.27822i q^{29} +(5.90891 - 1.70676i) q^{30} +(7.36933 - 4.25469i) q^{31} +(-2.33836 + 1.35005i) q^{32} +(-1.66403 + 0.480645i) q^{33} +10.1347i q^{34} +(-2.07880 - 5.58246i) q^{35} +(0.0566953 + 1.46108i) q^{36} +(-1.78478 + 3.09134i) q^{37} +(-1.50515 - 2.60699i) q^{38} +(-2.21835 + 8.97137i) q^{39} +(-4.65162 - 2.68562i) q^{40} +7.61738 q^{41} +(7.18043 - 0.822608i) q^{42} -9.59170 q^{43} +(-0.422094 - 0.243696i) q^{44} +(-5.71426 + 3.60155i) q^{45} +(-1.18450 - 2.05161i) q^{46} +(2.06490 - 3.57651i) q^{47} +(5.68831 - 5.91332i) q^{48} +(-1.31752 - 6.87489i) q^{49} +0.109346i q^{50} +(-3.08860 - 10.6929i) q^{51} +(-2.25213 + 1.30027i) q^{52} +(-1.23010 + 0.710197i) q^{53} +(-2.57772 - 7.77914i) q^{54} -2.25152i q^{55} +(-4.86497 - 4.02117i) q^{56} +(2.38256 + 2.29190i) q^{57} +(1.79655 - 3.11171i) q^{58} +(2.68086 + 4.64338i) q^{59} +(-1.84513 - 0.456245i) q^{60} +(-6.77000 - 3.90866i) q^{61} -13.4205 q^{62} +(-7.32527 + 3.05620i) q^{63} -5.21601 q^{64} +(-10.4038 - 6.00662i) q^{65} +(2.65183 + 0.655717i) q^{66} +(-4.48013 - 7.75982i) q^{67} +(1.56598 - 2.71235i) q^{68} +(1.87499 + 1.80365i) q^{69} +(-1.56285 + 9.26409i) q^{70} +6.27800i q^{71} +(-3.33539 + 6.33207i) q^{72} +(7.42669 - 4.28780i) q^{73} +(4.87549 - 2.81487i) q^{74} +(-0.0333238 - 0.115369i) q^{75} +0.930283i q^{76} +(0.440119 - 2.60889i) q^{77} +(10.1045 - 10.5042i) q^{78} +(0.795814 - 1.37839i) q^{79} +(5.33298 + 9.23700i) q^{80} +(5.09045 + 7.42208i) q^{81} +(-10.4042 - 6.00687i) q^{82} +2.78609 q^{83} +(-2.04881 - 0.889343i) q^{84} +14.4681 q^{85} +(13.1008 + 7.56376i) q^{86} +(-0.947199 + 3.83063i) q^{87} +(-1.19280 - 2.06599i) q^{88} +(4.28107 - 7.41503i) q^{89} +(10.6449 - 0.413063i) q^{90} +(-10.8810 - 8.99371i) q^{91} +0.732101i q^{92} +(14.1598 - 4.08999i) q^{93} +(-5.64069 + 3.25665i) q^{94} +(-3.72171 + 2.14873i) q^{95} +(-4.49304 + 1.29779i) q^{96} +8.81814i q^{97} +(-3.62183 + 10.4290i) q^{98} +(-2.99774 + 0.116324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.36585	−	0.788573i	−0.965801	−	0.557606i	−0.0678476	−	0.997696i	$-0.521613\pi$
$2$	−1.36585	−	0.788573i	−0.965801	−	0.557606i	−0.897954	+	0.440090i	$0.854946\pi$
$3$	1.68141	+	0.415762i	0.970763	+	0.240040i
$3$	1.68141	+	0.415762i	0.970763	+	0.240040i
$4$	0.243696	+	0.422094i	0.121848	+	0.211047i
$5$	−1.12576	+	1.94987i	−0.503455	+	0.872009i	0.496537	+	0.868015i	$0.334605\pi$
$5$	−1.12576	+	1.94987i	−0.503455	+	0.872009i	−0.999992	+	0.00399368i	$0.998729\pi$
$6$	−1.96869	−	1.89378i	−0.803716	−	0.773134i
$7$	−1.68560	+	2.03930i	−0.637096	+	0.770784i
$7$	−1.68560	+	2.03930i	−0.637096	+	0.770784i
$8$			2.38560i			0.843439i
$9$	2.65428	+	1.39813i	0.884761	+	0.466044i
$10$	3.07523	−	1.77549i	0.972474	−	0.561458i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	0.234263	+	0.811032i	0.0676258	+	0.234125i
$13$			5.33562i			1.47984i	0.672697	+	0.739918i	$0.265136\pi$
$13$			5.33562i			1.47984i	−0.672697	+	0.739918i	$0.734864\pi$
$14$	3.91041	−	1.45616i	1.04510	−	0.389176i
$15$	−2.70354	+	2.81049i	−0.698052	+	0.725665i
$16$	2.36862	−	4.10256i	0.592154	−	1.02564i
$17$	−3.21297	−	5.56503i	−0.779261	−	1.34972i	−0.932368	−	0.361509i	$-0.882262\pi$
$17$	−3.21297	−	5.56503i	−0.779261	−	1.34972i	0.153108	−	0.988209i	$-0.451072\pi$
$18$	−2.52282	−	4.00274i	−0.594635	−	0.943454i
$19$	1.65298	+	0.954348i	0.379219	+	0.218942i	0.677479	−	0.735542i	$-0.263073\pi$
$19$	1.65298	+	0.954348i	0.379219	+	0.218942i	−0.298259	+	0.954485i	$0.596406\pi$
$20$	−1.09737			−0.245380
$21$	−3.68205	+	2.72810i	−0.803489	+	0.595320i
$22$	1.57715			0.336249
$23$	1.30084	+	0.751040i	0.271244	+	0.156603i	0.629453	−	0.777039i	$-0.283279\pi$
$23$	1.30084	+	0.751040i	0.271244	+	0.156603i	−0.358209	+	0.933641i	$0.616612\pi$
$24$	−0.991843	+	4.01118i	−0.202459	+	0.818779i
$25$	−0.0346657	−	0.0600428i	−0.00693315	−	0.0120086i
$26$	4.20753	−	7.28765i	0.825164	−	1.42923i
$27$	3.88165	+	3.45439i	0.747024	+	0.664797i
$28$	−1.27155	−	0.214511i	−0.240301	−	0.0405387i
$29$			2.27822i			0.423056i	0.977372	+	0.211528i	$0.0678439\pi$
$29$			2.27822i			0.423056i	−0.977372	+	0.211528i	$0.932156\pi$
$30$	5.90891	−	1.70676i	1.07881	−	0.311610i
$31$	7.36933	−	4.25469i	1.32357	−	0.764164i	0.339275	−	0.940687i	$-0.389818\pi$
$31$	7.36933	−	4.25469i	1.32357	−	0.764164i	0.984296	+	0.176523i	$0.0564851\pi$
$32$	−2.33836	+	1.35005i	−0.413367	+	0.238658i
$33$	−1.66403	+	0.480645i	−0.289670	+	0.0836696i
$34$			10.1347i			1.73808i
$35$	−2.07880	−	5.58246i	−0.351382	−	0.943609i
$36$	0.0566953	+	1.46108i	0.00944921	+	0.243513i
$37$	−1.78478	+	3.09134i	−0.293417	+	0.508213i	−0.974615	−	0.223886i	$-0.928126\pi$
$37$	−1.78478	+	3.09134i	−0.293417	+	0.508213i	0.681199	+	0.732099i	$0.261459\pi$
$38$	−1.50515	−	2.60699i	−0.244167	−	0.422910i
$39$	−2.21835	+	8.97137i	−0.355220	+	1.43657i
$40$	−4.65162	−	2.68562i	−0.735486	−	0.424633i
$41$	7.61738			1.18964			0.594818	−	0.803861i	$-0.297224\pi$
$41$	7.61738			1.18964			0.594818	+	0.803861i	$0.297224\pi$
$42$	7.18043	−	0.822608i	1.10796	−	0.126931i
$43$	−9.59170			−1.46272			−0.731360	−	0.681992i	$-0.761114\pi$
$43$	−9.59170			−1.46272			−0.731360	+	0.681992i	$0.761114\pi$
$44$	−0.422094	−	0.243696i	−0.0636330	−	0.0367385i
$45$	−5.71426	+	3.60155i	−0.851832	+	0.536888i
$46$	−1.18450	−	2.05161i	−0.174645	−	0.302494i
$47$	2.06490	−	3.57651i	0.301197	−	0.521688i	−0.675211	−	0.737625i	$-0.735947\pi$
$47$	2.06490	−	3.57651i	0.301197	−	0.521688i	0.976407	+	0.215937i	$0.0692806\pi$
$48$	5.68831	−	5.91332i	0.821036	−	0.853514i
$49$	−1.31752	−	6.87489i	−0.188217	−	0.982128i
$50$			0.109346i			0.0154638i
$51$	−3.08860	−	10.6929i	−0.432491	−	1.49731i
$52$	−2.25213	+	1.30027i	−0.312315	+	0.180315i
$53$	−1.23010	+	0.710197i	−0.168967	+	0.0975530i	−0.582099	−	0.813118i	$-0.697768\pi$
$53$	−1.23010	+	0.710197i	−0.168967	+	0.0975530i	0.413132	+	0.910671i	$0.364435\pi$
$54$	−2.57772	−	7.77914i	−0.350783	−	1.05861i
$55$		−	2.25152i		−	0.303595i
$56$	−4.86497	−	4.02117i	−0.650109	−	0.537352i
$57$	2.38256	+	2.29190i	0.315577	+	0.303569i
$58$	1.79655	−	3.11171i	0.235898	−	0.408588i
$59$	2.68086	+	4.64338i	0.349018	+	0.604517i	0.986075	−	0.166300i	$-0.0531819\pi$
$59$	2.68086	+	4.64338i	0.349018	+	0.604517i	−0.637057	+	0.770816i	$0.719849\pi$
$60$	−1.84513	−	0.456245i	−0.238206	−	0.0589010i
$61$	−6.77000	−	3.90866i	−0.866809	−	0.500453i	−0.000522619	−	1.00000i	$-0.500166\pi$
$61$	−6.77000	−	3.90866i	−0.866809	−	0.500453i	−0.866287	+	0.499547i	$0.833500\pi$
$62$	−13.4205			−1.70441
$63$	−7.32527	+	3.05620i	−0.922898	+	0.385045i
$64$	−5.21601			−0.652001
$65$	−10.4038	−	6.00662i	−1.29043	−	0.745030i
$66$	2.65183	+	0.655717i	0.326418	+	0.0807132i
$67$	−4.48013	−	7.75982i	−0.547335	−	0.948013i	−0.998456	−	0.0555497i	$-0.982309\pi$
$67$	−4.48013	−	7.75982i	−0.547335	−	0.948013i	0.451121	−	0.892463i	$-0.351024\pi$
$68$	1.56598	−	2.71235i	0.189903	−	0.328921i
$69$	1.87499	+	1.80365i	0.225722	+	0.217133i
$70$	−1.56285	+	9.26409i	−0.186797	+	1.10727i
$71$			6.27800i			0.745061i	0.928020	+	0.372531i	$0.121510\pi$
$71$			6.27800i			0.745061i	−0.928020	+	0.372531i	$0.878490\pi$
$72$	−3.33539	+	6.33207i	−0.393080	+	0.746242i
$73$	7.42669	−	4.28780i	0.869228	−	0.501849i	0.00213642	−	0.999998i	$-0.499320\pi$
$73$	7.42669	−	4.28780i	0.869228	−	0.501849i	0.867092	+	0.498149i	$0.165987\pi$
$74$	4.87549	−	2.81487i	0.566764	−	0.327222i
$75$	−0.0333238	−	0.115369i	−0.00384791	−	0.0133217i
$76$			0.930283i			0.106711i
$77$	0.440119	−	2.60889i	0.0501562	−	0.297310i
$78$	10.1045	−	10.5042i	1.14411	−	1.18937i
$79$	0.795814	−	1.37839i	0.0895360	−	0.155081i	−0.817779	−	0.575532i	$-0.804795\pi$
$79$	0.795814	−	1.37839i	0.0895360	−	0.155081i	0.907315	+	0.420451i	$0.138128\pi$
$80$	5.33298	+	9.23700i	0.596245	+	1.03273i
$81$	5.09045	+	7.42208i	0.565606	+	0.824676i
$82$	−10.4042	−	6.00687i	−1.14895	−	0.663347i
$83$	2.78609			0.305813			0.152907	−	0.988241i	$-0.451137\pi$
$83$	2.78609			0.305813			0.152907	+	0.988241i	$0.451137\pi$
$84$	−2.04881	−	0.889343i	−0.223544	−	0.0970352i
$85$	14.4681			1.56929
$86$	13.1008	+	7.56376i	1.41270	+	0.815621i
$87$	−0.947199	+	3.83063i	−0.101550	+	0.410687i
$88$	−1.19280	−	2.06599i	−0.127153	−	0.220236i
$89$	4.28107	−	7.41503i	0.453792	−	0.785991i	−0.544826	−	0.838549i	$-0.683404\pi$
$89$	4.28107	−	7.41503i	0.453792	−	0.785991i	0.998618	+	0.0525582i	$0.0167375\pi$
$90$	10.6449	−	0.413063i	1.12207	−	0.0435406i
$91$	−10.8810	−	8.99371i	−1.14063	−	0.942798i
$92$			0.732101i			0.0763269i
$93$	14.1598	−	4.08999i	1.46830	−	0.424112i
$94$	−5.64069	+	3.25665i	−0.581792	+	0.335898i
$95$	−3.72171	+	2.14873i	−0.381840	+	0.220455i
$96$	−4.49304	+	1.29779i	−0.458569	+	0.132455i
$97$			8.81814i			0.895347i	0.894197	+	0.447673i	$0.147747\pi$
$97$			8.81814i			0.895347i	−0.894197	+	0.447673i	$0.852253\pi$
$98$	−3.62183	+	10.4290i	−0.365860	+	1.05349i
$99$	−2.99774	+	0.116324i	−0.301285	+	0.0116910i
$100$	0.0168958	−	0.0292644i	0.00168958	−	0.00292644i
$101$	−6.62510	−	11.4750i	−0.659222	−	1.14181i	−0.980817	−	0.194929i	$-0.937552\pi$
$101$	−6.62510	−	11.4750i	−0.659222	−	1.14181i	0.321595	−	0.946877i	$-0.395781\pi$
$102$	−4.21361	+	17.0405i	−0.417209	+	1.68726i
$103$	14.3188	+	8.26694i	1.41087	+	0.814565i	0.995470	−	0.0950741i	$-0.0303088\pi$
$103$	14.3188	+	8.26694i	1.41087	+	0.814565i	0.415399	+	0.909640i	$0.363642\pi$
$104$	−12.7287			−1.24815
$105$	−1.17435	−	10.2507i	−0.114604	−	1.00037i
$106$	2.24017			0.217584
$107$	14.7571	+	8.52002i	1.42662	+	0.823662i	0.996853	−	0.0792765i	$-0.0252610\pi$
$107$	14.7571	+	8.52002i	1.42662	+	0.823662i	0.429771	+	0.902938i	$0.358594\pi$
$108$	−0.512132	+	2.48024i	−0.0492799	+	0.238661i
$109$	8.11286	+	14.0519i	0.777071	+	1.34593i	0.933623	+	0.358256i	$0.116629\pi$
$109$	8.11286	+	14.0519i	0.777071	+	1.34593i	−0.156553	+	0.987670i	$0.550038\pi$
$110$	−1.77549	+	3.07523i	−0.169286	+	0.293212i
$111$	−4.28621	+	4.45576i	−0.406829	+	0.422922i
$112$	4.37384	+	11.7456i	0.413289	+	1.10986i
$113$		−	5.09818i		−	0.479596i	−0.970823	−	0.239798i	$-0.922919\pi$
$113$		−	5.09818i		−	0.479596i	0.970823	−	0.239798i	$-0.0770813\pi$
$114$	−1.44688	−	5.00920i	−0.135513	−	0.469155i
$115$	−2.92886	+	1.69098i	−0.273118	+	0.157685i
$116$	−0.961624	+	0.555194i	−0.0892846	+	0.0515485i
$117$	−7.45991	+	14.1623i	−0.689669	+	1.30930i
$118$		−	8.45621i		−	0.778457i
$119$	16.7646	+	2.82818i	1.53681	+	0.259259i
$120$	−6.70471	−	6.44959i	−0.612054	−	0.588764i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	6.16453	+	10.6773i	0.558110	+	0.966675i
$123$	12.8080	+	3.16702i	1.15485	+	0.285560i
$124$	3.59175	+	2.07370i	0.322549	+	0.186224i
$125$	−11.1015			−0.992947
$126$	12.4153	+	1.60221i	1.10604	+	0.142736i
$127$	12.4384			1.10373			0.551867	−	0.833932i	$-0.313916\pi$
$127$	12.4384			1.10373			0.551867	+	0.833932i	$0.313916\pi$
$128$	11.8010	+	6.81331i	1.04307	+	0.602217i
$129$	−16.1276	−	3.98786i	−1.41995	−	0.351112i
$130$	9.47333	+	16.4083i	0.830866	+	1.43910i
$131$	3.93926	−	6.82300i	0.344175	−	0.596129i	−0.641029	−	0.767517i	$-0.721492\pi$
$131$	3.93926	−	6.82300i	0.344175	−	0.596129i	0.985204	+	0.171389i	$0.0548253\pi$
$132$	−0.608394	−	0.585243i	−0.0529539	−	0.0509389i
$133$	−4.73246	+	1.76228i	−0.410357	+	0.152809i
$134$			14.1317i			1.22079i
$135$	−11.1054	+	3.67992i	−0.955802	+	0.316717i
$136$	13.2760	−	7.66489i	1.13841	−	0.657259i
$137$	−13.2037	+	7.62318i	−1.12807	+	0.651292i	−0.943449	−	0.331518i	$-0.892439\pi$
$137$	−13.2037	+	7.62318i	−1.12807	+	0.651292i	−0.184622	+	0.982810i	$0.559106\pi$
$138$	−1.13865	−	3.94208i	−0.0969282	−	0.335572i
$139$		−	18.8641i		−	1.60003i	−0.599977	−	0.800017i	$-0.704824\pi$
$139$		−	18.8641i		−	1.60003i	0.599977	−	0.800017i	$-0.295176\pi$
$140$	1.84973	−	2.23787i	0.156331	−	0.189135i
$141$	4.95892	−	5.15508i	0.417617	−	0.434136i
$142$	4.95066	−	8.57480i	0.415450	−	0.719581i
$143$	−2.66781	−	4.62078i	−0.223094	−	0.386409i
$144$	12.0229	−	7.57773i	1.00191	−	0.631478i
$145$	−4.44224	−	2.56473i	−0.368908	−	0.212989i
$146$	−13.5250			−1.11934
$147$	0.643030	−	12.1073i	0.0530363	−	0.998593i
$148$	−1.73978			−0.143009
$149$	6.46956	+	3.73520i	0.530007	+	0.306000i	0.741019	−	0.671484i	$-0.234343\pi$
$149$	6.46956	+	3.73520i	0.530007	+	0.306000i	−0.211012	+	0.977483i	$0.567676\pi$
$150$	−0.0454619	+	0.183855i	−0.00371194	+	0.0150117i
$151$	−1.46936	−	2.54500i	−0.119575	−	0.207109i	0.800025	−	0.599967i	$-0.204820\pi$
$151$	−1.46936	−	2.54500i	−0.119575	−	0.207109i	−0.919599	+	0.392858i	$0.871486\pi$
$152$	−2.27670	+	3.94336i	−0.184665	+	0.319848i
$153$	−0.747490	−	19.2633i	−0.0604310	−	1.55735i
$154$	−2.65844	+	3.21628i	−0.214223	+	0.259175i
$155$			19.1590i			1.53889i
$156$	−4.32736	+	1.24994i	−0.346466	+	0.100075i
$157$	−4.21215	+	2.43188i	−0.336166	+	0.194086i	−0.658575	−	0.752515i	$-0.728841\pi$
$157$	−4.21215	+	2.43188i	−0.336166	+	0.194086i	0.322409	+	0.946600i	$0.395507\pi$
$158$	−2.17392	+	1.25512i	−0.172948	+	0.0998516i
$159$	−2.36357	+	0.682705i	−0.187443	+	0.0541420i
$160$		−	6.07933i		−	0.480613i
$161$	−3.72429	+	1.38685i	−0.293515	+	0.109299i
$162$	−1.09993	−	14.1516i	−0.0864187	−	1.11186i
$163$	−0.603957	+	1.04609i	−0.0473056	+	0.0819357i	−0.888709	−	0.458472i	$-0.848397\pi$
$163$	−0.603957	+	1.04609i	−0.0473056	+	0.0819357i	0.841403	+	0.540408i	$0.181730\pi$
$164$	1.85633	+	3.21525i	0.144955	+	0.251069i
$165$	0.936095	−	3.78573i	0.0728749	−	0.294718i
$166$	−3.80538	−	2.19704i	−0.295355	−	0.170523i
$167$	11.6396			0.900700			0.450350	−	0.892852i	$-0.351299\pi$
$167$	11.6396			0.900700			0.450350	+	0.892852i	$0.351299\pi$
$168$	−6.50817	−	8.78391i	−0.502116	−	0.677693i
$169$	−15.4689			−1.18991
$170$	−19.7613	−	11.4092i	−1.51562	−	0.875045i
$171$	3.05317	+	4.84419i	0.233482	+	0.370445i
$172$	−2.33746	−	4.04860i	−0.178229	−	0.308703i
$173$	−3.56805	+	6.18004i	−0.271273	+	0.469859i	−0.969188	−	0.246321i	$-0.920778\pi$
$173$	−3.56805	+	6.18004i	−0.271273	+	0.469859i	0.697915	+	0.716181i	$0.254111\pi$
$174$	4.31446	−	4.48513i	0.327079	−	0.340017i
$175$	0.180878	+	0.0305141i	0.0136731	+	0.00230665i
$176$			4.73723i			0.357082i
$177$	2.57708	+	8.92203i	0.193705	+	0.670621i
$178$	−11.6946	+	6.75187i	−0.876546	+	0.506074i
$179$	8.00280	−	4.62042i	0.598157	−	0.345346i	−0.170159	−	0.985417i	$-0.554428\pi$
$179$	8.00280	−	4.62042i	0.598157	−	0.345346i	0.768316	+	0.640070i	$0.221095\pi$
$180$	−2.91274	−	1.53427i	−0.217103	−	0.114358i
$181$		−	0.302668i		−	0.0224972i	−0.999937	−	0.0112486i	$-0.996419\pi$
$181$		−	0.302668i		−	0.0224972i	0.999937	−	0.0112486i	$-0.00358061\pi$
$182$	7.76953	+	20.8645i	0.575916	+	1.54658i
$183$	−9.75807	−	9.38677i	−0.721338	−	0.693890i
$184$	−1.79168	+	3.10329i	−0.132085	+	0.228777i
$185$	−4.01847	−	6.96020i	−0.295444	−	0.511724i
$186$	−22.5654	−	5.57974i	−1.65458	−	0.409127i
$187$	5.56503	+	3.21297i	0.406956	+	0.234956i
$188$	2.01283			0.146801
$189$	−13.5874	+	2.09316i	−0.988341	+	0.152255i
$190$	6.77773			0.491708
$191$	1.04928	+	0.605800i	0.0759229	+	0.0438341i	0.537481	−	0.843276i	$-0.319376\pi$
$191$	1.04928	+	0.605800i	0.0759229	+	0.0438341i	−0.461558	+	0.887110i	$0.652709\pi$
$192$	−8.77025	−	2.16862i	−0.632939	−	0.156506i
$193$	−5.45616	−	9.45034i	−0.392743	−	0.680250i	0.600068	−	0.799949i	$-0.295140\pi$
$193$	−5.45616	−	9.45034i	−0.392743	−	0.680250i	−0.992810	+	0.119699i	$0.961807\pi$
$194$	6.95375	−	12.0443i	0.499250	−	0.864727i
$195$	−14.9957	−	14.4251i	−1.07386	−	1.03300i
$196$	2.58078	−	2.23150i	0.184341	−	0.159393i
$197$			6.52668i			0.465007i	0.972596	+	0.232503i	$0.0746917\pi$
$197$			6.52668i			0.465007i	−0.972596	+	0.232503i	$0.925308\pi$
$198$	4.18620	+	2.20506i	0.297500	+	0.156707i
$199$	12.0323	−	6.94682i	0.852944	−	0.492447i	−0.00869919	−	0.999962i	$-0.502769\pi$
$199$	12.0323	−	6.94682i	0.852944	−	0.492447i	0.861643	+	0.507515i	$0.169436\pi$
$200$	0.143238	−	0.0826988i	0.0101285	−	0.00584769i
$201$	−4.30671	−	14.9101i	−0.303772	−	1.05168i
$202$			20.8975i			1.47034i
$203$	−4.64599	−	3.84017i	−0.326085	−	0.269527i
$204$	3.76074	−	3.90951i	0.263305	−	0.273720i
$205$	−8.57534	+	14.8529i	−0.598928	+	1.03737i
$206$	−13.0382	−	22.5828i	−0.908412	−	1.57342i
$207$	2.40274	+	3.81222i	0.167002	+	0.264968i
$208$	21.8897	+	12.6380i	1.51778	+	0.876291i
$209$	−1.90870			−0.132027
$210$	−6.47945	+	14.9270i	−0.447125	+	1.03006i
$211$	14.2926			0.983945			0.491972	−	0.870611i	$-0.336276\pi$
$211$	14.2926			0.983945			0.491972	+	0.870611i	$0.336276\pi$
$212$	−0.599539	−	0.346144i	−0.0411765	−	0.0237733i
$213$	−2.61015	+	10.5559i	−0.178845	+	0.723278i
$214$	−13.4373	−	23.2741i	−0.918557	−	1.59099i
$215$	10.7979	−	18.7026i	0.736413	−	1.27551i
$216$	−8.24080	+	9.26009i	−0.560715	+	0.630069i
$217$	−3.74514	+	22.2000i	−0.254237	+	1.50703i
$218$		−	25.5903i		−	1.73320i
$219$	14.2700	−	4.12182i	0.964278	−	0.278527i
$220$	0.950352	−	0.548686i	0.0640727	−	0.0369924i
$221$	29.6929	−	17.1432i	1.99736	−	1.15318i
$222$	9.36802	−	2.70590i	0.628740	−	0.181608i
$223$			0.328284i			0.0219835i	0.999940	+	0.0109918i	$0.00349886\pi$
$223$			0.328284i			0.0219835i	−0.999940	+	0.0109918i	$0.996501\pi$
$224$	1.18837	−	7.04426i	0.0794011	−	0.470665i
$225$	−0.00806490	−	0.207838i	−0.000537660	−	0.0138559i
$226$	−4.02029	+	6.96334i	−0.267426	+	0.463195i
$227$	8.75369	+	15.1618i	0.581003	+	1.00633i	0.995361	+	0.0962127i	$0.0306729\pi$
$227$	8.75369	+	15.1618i	0.581003	+	1.00633i	−0.414358	+	0.910114i	$0.635994\pi$
$228$	−0.386776	+	1.56419i	−0.0256149	+	0.103591i
$229$	−6.14624	−	3.54854i	−0.406155	−	0.234494i	0.282981	−	0.959125i	$-0.408677\pi$
$229$	−6.14624	−	3.54854i	−0.406155	−	0.234494i	−0.689136	+	0.724632i	$0.742010\pi$
$230$	5.33385			0.351703
$231$	1.82470	−	4.20363i	0.120056	−	0.276578i
$232$	−5.43494			−0.356821
$233$	−11.0322	−	6.36943i	−0.722742	−	0.417275i	0.0930189	−	0.995664i	$-0.470348\pi$
$233$	−11.0322	−	6.36943i	−0.722742	−	0.417275i	−0.815761	+	0.578389i	$0.803682\pi$
$234$	21.3571	−	13.4608i	1.39616	−	0.879962i
$235$	4.64916	+	8.05258i	0.303278	+	0.525293i
$236$	−1.30663	+	2.26315i	−0.0850542	+	0.147318i
$237$	1.91117	−	1.98677i	0.124144	−	0.129055i
$238$	−20.6677	−	17.0830i	−1.33968	−	1.10732i
$239$			14.0593i			0.909422i	0.890639	+	0.454711i	$0.150257\pi$
$239$			14.0593i			0.909422i	−0.890639	+	0.454711i	$0.849743\pi$
$240$	5.12654	+	17.7484i	0.330917	+	1.14566i
$241$	−4.26069	+	2.45991i	−0.274455	+	0.158457i	−0.630911	−	0.775856i	$-0.717319\pi$
$241$	−4.26069	+	2.45991i	−0.274455	+	0.158457i	0.356455	+	0.934312i	$0.383985\pi$
$242$	−1.36585	+	0.788573i	−0.0878001	+	0.0506914i
$243$	5.47332	+	14.5960i	0.351114	+	0.936333i
$244$		−	3.81010i		−	0.243917i
$245$	14.8884	+	5.17048i	0.951183	+	0.330330i
$246$	−14.9963	−	14.4257i	−0.956129	−	0.919748i
$247$	−5.09204	+	8.81967i	−0.323999	+	0.561182i
$248$	10.1500	+	17.5803i	0.644526	+	1.11635i
$249$	4.68456	+	1.15835i	0.296872	+	0.0734075i
$250$	15.1630	+	8.75434i	0.958990	+	0.553673i
$251$	−4.76384			−0.300691			−0.150345	−	0.988634i	$-0.548039\pi$
$251$	−4.76384			−0.300691			−0.150345	+	0.988634i	$0.548039\pi$
$252$	−3.07514	−	2.34717i	−0.193716	−	0.147858i
$253$	−1.50208			−0.0944349
$254$	−16.9890	−	9.80863i	−1.06599	−	0.615448i
$255$	24.3269	+	6.01530i	1.52341	+	0.376693i
$256$	−5.52958	−	9.57751i	−0.345599	−	0.598594i
$257$	−2.01144	+	3.48392i	−0.125470	+	0.217321i	−0.921917	−	0.387388i	$-0.873377\pi$
$257$	−2.01144	+	3.48392i	−0.125470	+	0.217321i	0.796446	+	0.604709i	$0.206711\pi$
$258$	18.8831	+	18.1646i	1.17561	+	1.13088i
$259$	−3.29574	−	8.85047i	−0.204788	−	0.549941i
$260$		−	5.85516i		−	0.363122i
$261$	−3.18526	+	6.04705i	−0.197163	+	0.374303i
$262$	−10.7609	+	6.21280i	−0.664809	+	0.383828i
$263$	16.6198	−	9.59546i	1.02482	−	0.591681i	0.109325	−	0.994006i	$-0.465131\pi$
$263$	16.6198	−	9.59546i	1.02482	−	0.591681i	0.915497	+	0.402325i	$0.131798\pi$
$264$	−1.14663	−	3.96971i	−0.0705702	−	0.244319i
$265$		−	3.19804i		−	0.196454i
$266$	7.85352	+	1.32489i	0.481530	+	0.0812341i
$267$	10.2811	−	10.6878i	0.629194	−	0.654083i
$268$	2.18358	−	3.78207i	0.133383	−	0.231027i
$269$	−7.77810	−	13.4721i	−0.474239	−	0.821406i	0.525326	−	0.850901i	$-0.323943\pi$
$269$	−7.77810	−	13.4721i	−0.474239	−	0.821406i	−0.999565	+	0.0294948i	$0.990610\pi$
$270$	18.0702	+	3.73122i	1.09972	+	0.227075i
$271$	6.39054	+	3.68958i	0.388198	+	0.224126i	0.681379	−	0.731931i	$-0.261381\pi$
$271$	6.39054	+	3.68958i	0.388198	+	0.224126i	−0.293181	+	0.956057i	$0.594714\pi$
$272$	−30.4412			−1.84577
$273$	−14.5561	−	19.6460i	−0.880976	−	1.18903i
$274$	24.0457			1.45266
$275$	0.0600428	+	0.0346657i	0.00362072	+	0.00209042i
$276$	−0.304380	+	1.23096i	−0.0183215	+	0.0740953i
$277$	−10.3420	−	17.9129i	−0.621391	−	1.07628i	−0.989227	−	0.146390i	$-0.953234\pi$
$277$	−10.3420	−	17.9129i	−0.621391	−	1.07628i	0.367836	−	0.929891i	$-0.380099\pi$
$278$	−14.8758	+	25.7656i	−0.892188	+	1.54532i
$279$	25.5089	−	0.989842i	1.52718	−	0.0592603i
$280$	13.3176	−	4.95920i	0.795876	−	0.296369i
$281$		−	4.90073i		−	0.292353i	−0.989259	−	0.146177i	$-0.953303\pi$
$281$		−	4.90073i		−	0.292353i	0.989259	−	0.146177i	$-0.0466968\pi$
$282$	−10.8383	+	3.13059i	−0.645411	+	0.186424i
$283$	−21.8290	+	12.6030i	−1.29760	+	0.749168i	−0.979988	−	0.199054i	$-0.936213\pi$
$283$	−21.8290	+	12.6030i	−1.29760	+	0.749168i	−0.317608	+	0.948222i	$0.602880\pi$
$284$	−2.64990	+	1.52992i	−0.157243	+	0.0907842i
$285$	−7.15109	+	2.06555i	−0.423594	+	0.122353i
$286$			8.41506i			0.497593i
$287$	−12.8398	+	15.5342i	−0.757912	+	0.916952i
$288$	−8.09421	+	0.314086i	−0.476956	+	0.0185077i
$289$	−12.1464	+	21.0382i	−0.714494	+	1.23754i
$290$	4.04496	+	7.00607i	0.237528	+	0.411411i
$291$	−3.66625	+	14.8269i	−0.214919	+	0.869169i
$292$	3.61971	+	2.08984i	0.211827	+	0.122299i
$293$	1.37733			0.0804644			0.0402322	−	0.999190i	$-0.487190\pi$
$293$	1.37733			0.0804644			0.0402322	+	0.999190i	$0.487190\pi$
$294$	−10.4258	+	16.0297i	−0.608043	+	0.934869i
$295$	−12.0720			−0.702859
$296$	−7.37471	−	4.25779i	−0.428646	−	0.247479i
$297$	−5.08880	−	1.05076i	−0.295282	−	0.0609712i
$298$	−5.89096	−	10.2034i	−0.341254	−	0.591070i
$299$	−4.00726	+	6.94079i	−0.231746	+	0.401396i
$300$	0.0405758	−	0.0421808i	0.00234264	−	0.00243531i
$301$	16.1677	−	19.5604i	0.931894	−	1.12744i
$302$			4.63478i			0.266702i
$303$	−6.36865	−	22.0487i	−0.365869	−	1.26666i
$304$	7.83055	−	4.52097i	0.449113	−	0.259295i
$305$	15.2428	−	8.80042i	0.872798	−	0.503910i
$306$	−14.1696	+	26.9003i	−0.810022	+	1.53779i
$307$		−	12.8569i		−	0.733781i	−0.930264	−	0.366891i	$-0.880422\pi$
$307$		−	12.8569i		−	0.733781i	0.930264	−	0.366891i	$-0.119578\pi$
$308$	1.20845	−	0.450004i	0.0688579	−	0.0256413i
$309$	20.6386	+	19.8533i	1.17409	+	1.12942i
$310$	15.1083	−	26.1683i	0.858093	−	1.48626i
$311$	−1.23937	−	2.14665i	−0.0702782	−	0.121725i	0.828745	−	0.559626i	$-0.189055\pi$
$311$	−1.23937	−	2.14665i	−0.0702782	−	0.121725i	−0.899023	+	0.437901i	$0.855722\pi$
$312$	−21.4021	−	5.29210i	−1.21166	−	0.299606i
$313$	−13.4869	−	7.78668i	−0.762326	−	0.440129i	0.0678045	−	0.997699i	$-0.478401\pi$
$313$	−13.4869	−	7.78668i	−0.762326	−	0.440129i	−0.830130	+	0.557570i	$0.811734\pi$
$314$	7.67088			0.432893
$315$	2.28729	−	17.7239i	0.128874	−	0.998628i
$316$	0.775746			0.0436391
$317$	−28.3339	−	16.3586i	−1.59139	−	0.918790i	−0.993069	−	0.117535i	$-0.962501\pi$
$317$	−28.3339	−	16.3586i	−1.59139	−	0.918790i	−0.598322	−	0.801256i	$-0.704166\pi$
$318$	3.76664	+	0.931376i	0.211223	+	0.0522290i
$319$	−1.13911	−	1.97300i	−0.0637780	−	0.110467i
$320$	5.87197	−	10.1705i	0.328253	−	0.568551i
$321$	21.2705	+	20.4611i	1.18720	+	1.14203i
$322$	6.18046	+	1.04264i	0.344423	+	0.0581042i
$323$		−	12.2652i		−	0.682453i
$324$	−1.89229	+	3.95738i	−0.105127	+	0.219854i
$325$	0.320366	−	0.184963i	0.0177707	−	0.0102599i
$326$	1.64983	−	0.952530i	0.0913756	−	0.0527557i
$327$	7.79881	+	27.0000i	0.431275	+	1.49310i
$328$			18.1721i			1.00338i
$329$	3.81300	+	10.2395i	0.210218	+	0.564523i
$330$	−4.26389	+	4.43255i	−0.234719	+	0.244004i
$331$	2.57192	−	4.45470i	0.141366	−	0.244852i	−0.786646	−	0.617405i	$-0.788184\pi$
$331$	2.57192	−	4.45470i	0.141366	−	0.244852i	0.928011	+	0.372553i	$0.121517\pi$
$332$	0.678959	+	1.17599i	0.0372627	+	0.0645409i
$333$	−9.05942	+	5.70992i	−0.496453	+	0.312902i
$334$	−15.8979	−	9.17868i	−0.869897	−	0.502235i
$335$	20.1742			1.10223
$336$	2.47084	+	21.5677i	0.134796	+	1.17661i
$337$	16.3793			0.892235			0.446117	−	0.894974i	$-0.352806\pi$
$337$	16.3793			0.892235			0.446117	+	0.894974i	$0.352806\pi$
$338$	21.1281	+	12.1983i	1.14922	+	0.663502i
$339$	2.11963	−	8.57213i	0.115122	−	0.465574i
$340$	3.52583	+	6.10691i	0.191215	+	0.331194i
$341$	−4.25469	+	7.36933i	−0.230404	+	0.399072i
$342$	−0.350169	−	9.02409i	−0.0189350	−	0.487967i
$343$	16.2408	+	8.90149i	0.876921	+	0.480635i
$344$		−	22.8820i		−	1.23371i
$345$	−5.62767	+	1.62552i	−0.302983	+	0.0875152i
$346$	9.74682	−	5.62733i	0.523993	−	0.302527i
$347$	−20.1799	+	11.6509i	−1.08332	+	0.625452i	−0.931789	−	0.363001i	$-0.881752\pi$
$347$	−20.1799	+	11.6509i	−1.08332	+	0.625452i	−0.151526	+	0.988453i	$0.548419\pi$
$348$	−1.84771	+	0.533703i	−0.0990479	+	0.0286095i
$349$		−	11.3304i		−	0.606504i	−0.952910	−	0.303252i	$-0.901928\pi$
$349$		−	11.3304i		−	0.606504i	0.952910	−	0.303252i	$-0.0980724\pi$
$350$	−0.222990	−	0.184313i	−0.0119193	−	0.00985196i
$351$	−18.4313	+	20.7110i	−0.983790	+	1.10547i
$352$	1.35005	−	2.33836i	0.0719580	−	0.124635i
$353$	−13.4857	−	23.3580i	−0.717773	−	1.24322i	−0.961880	−	0.273470i	$-0.911828\pi$
$353$	−13.4857	−	23.3580i	−0.717773	−	1.24322i	0.244108	−	0.969748i	$-0.421505\pi$
$354$	3.51577	−	14.2184i	0.186861	−	0.755697i
$355$	−12.2413	−	7.06751i	−0.649700	−	0.375104i
$356$	4.17312			0.221175
$357$	27.0123	+	11.7254i	1.42964	+	0.620574i
$358$	−14.5742			−0.770268
$359$	−14.2547	−	8.22995i	−0.752334	−	0.434360i	0.0742028	−	0.997243i	$-0.476359\pi$
$359$	−14.2547	−	8.22995i	−0.752334	−	0.434360i	−0.826537	+	0.562883i	$0.809692\pi$
$360$	−8.59188	−	13.6320i	−0.452832	−	0.718468i
$361$	−7.67844	−	13.2994i	−0.404128	−	0.699971i
$362$	−0.238676	+	0.413399i	−0.0125445	+	0.0217278i
$363$	1.20077	−	1.24826i	0.0630239	−	0.0655168i
$364$	1.14455	−	6.78451i	0.0599906	−	0.355605i
$365$			19.3081i			1.01063i
$366$	5.92590	+	20.5159i	0.309752	+	1.07238i
$367$	30.6589	−	17.7009i	1.60038	−	0.923981i	0.608971	−	0.793192i	$-0.291583\pi$
$367$	30.6589	−	17.7009i	1.60038	−	0.923981i	0.991410	−	0.130788i	$-0.0417508\pi$
$368$	6.16238	−	3.55785i	0.321236	−	0.185466i
$369$	20.2187	+	10.6501i	1.05254	+	0.554423i
$370$			12.6754i			0.658965i
$371$	0.625142	−	3.70565i	0.0324558	−	0.192388i
$372$	5.17705	+	4.98005i	0.268417	+	0.258204i
$373$	−10.6841	+	18.5054i	−0.553201	+	0.958173i	0.444840	+	0.895610i	$0.353261\pi$
$373$	−10.6841	+	18.5054i	−0.553201	+	0.958173i	−0.998041	+	0.0625628i	$0.980073\pi$
$374$	−5.06733	−	8.77688i	−0.262025	−	0.453841i
$375$	−18.6662	−	4.61557i	−0.963916	−	0.238347i
$376$	8.53215	+	4.92604i	0.440012	+	0.254041i
$377$	−12.1557			−0.626053
$378$	20.2090	+	7.85576i	1.03944	+	0.404056i
$379$	−31.0103			−1.59289			−0.796445	−	0.604710i	$-0.793289\pi$
$379$	−31.0103			−1.59289			−0.796445	+	0.604710i	$0.793289\pi$
$380$	−1.81393	−	1.04727i	−0.0930528	−	0.0537240i
$381$	20.9141	+	5.17143i	1.07146	+	0.264940i
$382$	−0.955435	−	1.65486i	−0.0488843	−	0.0846701i
$383$	1.36422	−	2.36290i	0.0697084	−	0.120738i	−0.829065	−	0.559153i	$-0.811126\pi$
$383$	1.36422	−	2.36290i	0.0697084	−	0.120738i	0.898773	+	0.438415i	$0.144460\pi$
$384$	17.0096	+	16.3624i	0.868018	+	0.834989i
$385$	4.59153	+	3.79515i	0.234006	+	0.193419i
$386$			17.2103i			0.875982i
$387$	−25.4591	−	13.4105i	−1.29416	−	0.681692i
$388$	−3.72208	+	2.14895i	−0.188960	+	0.109096i
$389$	−27.9050	+	16.1110i	−1.41484	+	0.816858i	−0.995839	−	0.0911278i	$-0.970953\pi$
$389$	−27.9050	+	16.1110i	−1.41484	+	0.816858i	−0.419001	+	0.907986i	$0.637619\pi$
$390$	9.10662	+	31.5277i	0.461131	+	1.59647i
$391$		−	9.65229i		−	0.488137i
$392$	16.4008	−	3.14307i	0.828364	−	0.158749i
$393$	9.46026	−	9.83448i	0.477207	−	0.496084i
$394$	5.14677	−	8.91446i	0.259290	−	0.449104i
$395$	1.79179	+	3.10347i	0.0901547	+	0.156152i
$396$	−0.779638	−	1.23698i	−0.0391783	−	0.0621607i
$397$	15.1809	+	8.76472i	0.761910	+	0.439889i	0.829981	−	0.557792i	$-0.188351\pi$
$397$	15.1809	+	8.76472i	0.761910	+	0.439889i	−0.0680713	+	0.997680i	$0.521685\pi$
$398$	−21.9123			−1.09837
$399$	−8.68990	+	0.995537i	−0.435039	+	0.0498392i
$400$	−0.328439			−0.0164220
$401$	6.74195	+	3.89247i	0.336677	+	0.194380i	0.658802	−	0.752317i	$-0.271064\pi$
$401$	6.74195	+	3.89247i	0.336677	+	0.194380i	−0.322125	+	0.946697i	$0.604397\pi$
$402$	−5.87540	+	23.7611i	−0.293038	+	1.18510i
$403$	22.7014	+	39.3200i	1.13084	+	1.95867i
$404$	3.22902	−	5.59283i	0.160650	−	0.278254i
$405$	−20.2027	+	1.57025i	−1.00388	+	0.0780263i
$406$	3.31747	+	8.90880i	0.164643	+	0.442136i
$407$		−	3.56957i		−	0.176937i
$408$	25.5091	−	7.36818i	1.26289	−	0.364779i
$409$	−1.27262	+	0.734750i	−0.0629272	+	0.0363311i	−0.531134	−	0.847288i	$-0.678234\pi$
$409$	−1.27262	+	0.734750i	−0.0629272	+	0.0363311i	0.468206	+	0.883619i	$0.344900\pi$
$410$	23.4252	−	13.5246i	1.15689	−	0.667931i
$411$	−25.3703	+	7.32808i	−1.25143	+	0.361468i
$412$			8.05848i			0.397013i
$413$	−13.9881	−	2.35979i	−0.688310	−	0.116118i
$414$	−0.275571	−	7.10166i	−0.0135436	−	0.349027i
$415$	−3.13647	+	5.43252i	−0.153963	+	0.266672i
$416$	−7.20336	−	12.4766i	−0.353174	−	0.611715i
$417$	7.84299	−	31.7184i	0.384073	−	1.55325i
$418$	2.60699	+	1.50515i	0.127512	+	0.0736191i
$419$	12.3697			0.604301			0.302150	−	0.953260i	$-0.402296\pi$
$419$	12.3697			0.604301			0.302150	+	0.953260i	$0.402296\pi$
$420$	4.04057	−	2.99374i	0.197160	−	0.146079i
$421$	−11.1527			−0.543551			−0.271775	−	0.962361i	$-0.587611\pi$
$421$	−11.1527			−0.543551			−0.271775	+	0.962361i	$0.587611\pi$
$422$	−19.5216	−	11.2708i	−0.950295	−	0.548653i
$423$	10.4813	−	6.60608i	0.509617	−	0.321198i
$424$	−1.69425	−	2.93452i	−0.0822800	−	0.142513i
$425$	−0.222760	+	0.385832i	−0.0108055	+	0.0187156i
$426$	11.8892	−	12.3595i	0.576032	−	0.598818i
$427$	19.3824	−	7.21765i	0.937982	−	0.349286i
$428$			8.30518i			0.401446i
$429$	−2.56454	−	8.87861i	−0.123817	−	0.428663i
$430$	−29.4967	+	17.0299i	−1.42246	+	0.821256i
$431$	−13.9275	+	8.04107i	−0.670866	+	0.387325i	−0.796405	−	0.604764i	$-0.793267\pi$
$431$	−13.9275	+	8.04107i	−0.670866	+	0.387325i	0.125539	+	0.992089i	$0.459934\pi$
$432$	23.3660	−	7.74261i	1.12420	−	0.372517i
$433$			22.8903i			1.10004i	0.835153	+	0.550018i	$0.185379\pi$
$433$			22.8903i			1.10004i	−0.835153	+	0.550018i	$0.814621\pi$
$434$	22.6216	−	27.3685i	1.08587	−	1.31373i
$435$	−6.40292	−	6.15928i	−0.306997	−	0.295315i
$436$	−3.95414	+	6.84877i	−0.189369	+	0.327997i
$437$	1.43351	+	2.48291i	0.0685739	+	0.118774i
$438$	−22.7410	−	5.62317i	−1.08661	−	0.268685i
$439$	−6.83286	−	3.94495i	−0.326114	−	0.188282i	0.328000	−	0.944678i	$-0.393625\pi$
$439$	−6.83286	−	3.94495i	−0.326114	−	0.188282i	−0.654115	+	0.756395i	$0.726959\pi$
$440$	5.37123			0.256063
$441$	6.11495	−	20.0900i	0.291188	−	0.956666i
$442$	−54.0747			−2.57207
$443$	23.2172	+	13.4044i	1.10308	+	0.636864i	0.937029	−	0.349252i	$-0.113564\pi$
$443$	23.2172	+	13.4044i	1.10308	+	0.636864i	0.166053	+	0.986117i	$0.446898\pi$
$444$	−2.92528	−	0.723333i	−0.138828	−	0.0343279i
$445$	9.63890	+	16.6951i	0.456928	+	0.791422i
$446$	0.258876	−	0.448386i	0.0122581	−	0.0212317i
$447$	9.32503	+	8.97020i	0.441059	+	0.424276i
$448$	8.79210	−	10.6370i	0.415387	−	0.502552i
$449$			25.3182i			1.19484i	0.801929	+	0.597419i	$0.203807\pi$
$449$			25.3182i			1.19484i	−0.801929	+	0.597419i	$0.796193\pi$
$450$	−0.152880	+	0.290235i	−0.00720684	+	0.0136818i
$451$	−6.59685	+	3.80869i	−0.310633	+	0.179344i
$452$	2.15191	−	1.24241i	0.101217	−	0.0584379i
$453$	−1.41248	−	4.89009i	−0.0663640	−	0.229757i
$454$		−	27.6117i		−	1.29588i
$455$	29.7859	−	11.0917i	1.39639	−	0.519987i
$456$	−5.46756	+	5.68384i	−0.256042	+	0.266170i
$457$	2.88869	−	5.00336i	0.135127	−	0.234047i	−0.790519	−	0.612438i	$-0.790189\pi$
$457$	2.88869	−	5.00336i	0.135127	−	0.234047i	0.925646	+	0.378390i	$0.123522\pi$
$458$	5.59656	+	9.69353i	0.261510	+	0.452949i
$459$	6.75212	−	32.7004i	0.315162	−	1.52632i
$460$	−1.42750	−	0.824170i	−0.0665577	−	0.0384271i
$461$	23.2550			1.08309			0.541546	−	0.840671i	$-0.317839\pi$
$461$	23.2550			1.08309			0.541546	+	0.840671i	$0.317839\pi$
$462$	−5.80713	+	4.30261i	−0.270172	+	0.200176i
$463$	−8.55715			−0.397684			−0.198842	−	0.980032i	$-0.563718\pi$
$463$	−8.55715			−0.397684			−0.198842	+	0.980032i	$0.563718\pi$
$464$	9.34656	+	5.39624i	0.433903	+	0.250514i
$465$	−7.96558	+	32.2142i	−0.369395	+	1.49390i
$466$	10.0455	+	17.3994i	0.465350	+	0.806010i
$467$	5.65000	−	9.78609i	0.261451	−	0.452846i	−0.705177	−	0.709032i	$-0.749132\pi$
$467$	5.65000	−	9.78609i	0.261451	−	0.452846i	0.966628	+	0.256185i	$0.0824657\pi$
$468$	−7.79575	+	0.302505i	−0.360359	+	0.0139833i
$469$	23.3763	+	3.94359i	1.07942	+	0.182098i
$470$		−	14.6648i		−	0.676438i
$471$	−8.09344	+	2.33775i	−0.372926	+	0.107718i
$472$	−11.0773	+	6.39546i	−0.509873	+	0.294375i
$473$	8.30665	−	4.79585i	0.381940	−	0.220513i
$474$	−4.17709	+	1.20653i	−0.191860	+	0.0554178i
$475$		−	0.132333i		−	0.00607184i
$476$	2.89170	+	7.76544i	0.132541	+	0.355928i
$477$	−4.25798	+	0.165226i	−0.194959	+	0.00756516i
$478$	11.0868	−	19.2029i	0.507099	−	0.878321i
$479$	−16.3519	−	28.3223i	−0.747137	−	1.29408i	−0.949190	−	0.314705i	$-0.898095\pi$
$479$	−16.3519	−	28.3223i	−0.747137	−	1.29408i	0.202053	−	0.979375i	$-0.435239\pi$
$480$	2.52755	−	10.2218i	0.115366	−	0.466561i
$481$	−16.4942	−	9.52293i	−0.752071	−	0.434208i
$482$	7.75928			0.353425
$483$	−6.83866	+	0.783454i	−0.311170	+	0.0356484i
$484$	0.487392			0.0221542
$485$	−17.1942	−	9.92710i	−0.780750	−	0.450766i
$486$	4.03428	−	24.2520i	0.182998	−	1.10009i
$487$	9.00793	+	15.6022i	0.408188	+	0.707003i	0.994687	−	0.102948i	$-0.0328274\pi$
$487$	9.00793	+	15.6022i	0.408188	+	0.707003i	−0.586499	+	0.809950i	$0.699494\pi$
$488$	9.32452	−	16.1505i	0.422101	−	0.731100i
$489$	−1.45042	+	1.50780i	−0.0655904	+	0.0681849i
$490$	−16.2580	−	18.8027i	−0.734459	−	0.849418i
$491$		−	36.5472i		−	1.64935i	−0.565605	−	0.824676i	$-0.691357\pi$
$491$		−	36.5472i		−	1.64935i	0.565605	−	0.824676i	$-0.308643\pi$
$492$	1.78447	+	6.17795i	0.0804500	+	0.278523i
$493$	12.6784	−	7.31987i	0.571006	−	0.329671i
$494$	13.9099	−	8.03089i	0.625837	−	0.361327i
$495$	3.14792	−	5.97617i	0.141488	−	0.268609i
$496$		−	40.3109i		−	1.81001i
$497$	−12.8027	−	10.5822i	−0.574281	−	0.474676i
$498$	−5.48496	−	5.27625i	−0.245787	−	0.236435i
$499$	−14.9604	+	25.9121i	−0.669717	+	1.15998i	0.308266	+	0.951300i	$0.400251\pi$
$499$	−14.9604	+	25.9121i	−0.669717	+	1.15998i	−0.977983	+	0.208684i	$0.933082\pi$
$500$	−2.70539	−	4.68587i	−0.120989	−	0.209558i
$501$	19.5710	+	4.83930i	0.874366	+	0.216204i
$502$	6.50669	+	3.75664i	0.290408	+	0.167667i
$503$	−12.0126			−0.535614			−0.267807	−	0.963473i	$-0.586299\pi$
$503$	−12.0126			−0.535614			−0.267807	+	0.963473i	$0.586299\pi$
$504$	−7.29089	−	17.4752i	−0.324762	−	0.778408i
$505$	29.8331			1.32755
$506$	2.05161	+	1.18450i	0.0912054	+	0.0526574i
$507$	−26.0095	−	6.43136i	−1.15512	−	0.285627i
$508$	3.03120	+	5.25019i	0.134488	+	0.232940i
$509$	−13.7021	+	23.7328i	−0.607336	+	1.05194i	0.384341	+	0.923191i	$0.374429\pi$
$509$	−13.7021	+	23.7328i	−0.607336	+	1.05194i	−0.991678	+	0.128746i	$0.958905\pi$
$510$	−28.4833	−	27.3995i	−1.26126	−	1.21327i
$511$	−3.77429	+	22.3728i	−0.166965	+	0.989713i
$512$		−	9.81132i		−	0.433603i
$513$	3.11960	+	9.41447i	0.137734	+	0.415659i
$514$	5.49466	−	3.17234i	0.242359	−	0.139926i
$515$	−32.2389	+	18.6132i	−1.42062	+	0.820193i
$516$	−2.24698	−	7.77918i	−0.0989176	−	0.342459i
$517$			4.12980i			0.181628i
$518$	−2.47775	+	14.6873i	−0.108866	+	0.645325i
$519$	−8.56877	+	8.90772i	−0.376127	+	0.391006i
$520$	14.3294	−	24.8193i	0.628387	−	1.08840i
$521$	14.3055	+	24.7779i	0.626736	+	1.08554i	0.988202	+	0.153153i	$0.0489428\pi$
$521$	14.3055	+	24.7779i	0.626736	+	1.08554i	−0.361467	+	0.932385i	$0.617724\pi$
$522$	9.11913	−	5.74755i	0.399134	−	0.251564i
$523$	4.73881	+	2.73595i	0.207214	+	0.119635i	0.600016	−	0.799988i	$-0.295161\pi$
$523$	4.73881	+	2.73595i	0.207214	+	0.119635i	−0.392802	+	0.919623i	$0.628494\pi$
$524$	3.83993			0.167748
$525$	0.291444	+	0.126509i	0.0127196	+	0.00552130i
$526$	−30.2669			−1.31970
$527$	−47.3549	−	27.3404i	−2.06281	−	1.19097i
$528$	−1.96956	+	7.96523i	−0.0857141	+	0.346642i
$529$	−10.3719	−	17.9646i	−0.450951	−	0.781070i
$530$	−2.52189	+	4.36804i	−0.109544	+	0.189736i
$531$	0.623695	+	16.0730i	0.0270660	+	0.697511i
$532$	−1.89713	−	1.56808i	−0.0822510	−	0.0679850i
$533$			40.6435i			1.76046i
$534$	−22.4706	+	6.49051i	−0.972397	+	0.280872i
$535$	−33.2259	+	19.1830i	−1.43648	+	0.829352i
$536$	18.5119	−	10.6878i	0.799591	−	0.461644i
$537$	15.3770	−	4.44156i	0.663566	−	0.191668i
$538$			24.5344i			1.05775i
$539$	4.57845	+	5.29507i	0.197208	+	0.228075i
$540$	−4.25961	−	3.79074i	−0.183305	−	0.163128i
$541$	5.03036	−	8.71284i	0.216272	−	0.374594i	−0.737393	−	0.675464i	$-0.763944\pi$
$541$	5.03036	−	8.71284i	0.216272	−	0.374594i	0.953665	+	0.300869i	$0.0972769\pi$
$542$	−5.81901	−	10.0788i	−0.249948	−	0.432922i
$543$	0.125838	−	0.508910i	0.00540022	−	0.0218394i
$544$	15.0262	+	8.67536i	0.644241	+	0.371953i
$545$	−36.5325			−1.56488
$546$	4.38912	+	38.3120i	0.187837	+	1.63960i
$547$	45.7373			1.95559			0.977793	−	0.209571i	$-0.0672067\pi$
$547$	45.7373			1.95559			0.977793	+	0.209571i	$0.0672067\pi$
$548$	−6.43539	−	3.71547i	−0.274906	−	0.158717i
$549$	−12.5047	−	19.8400i	−0.533686	−	0.846753i
$550$	−0.0546730	−	0.0946963i	−0.00233126	−	0.00403787i
$551$	−2.17422	+	3.76586i	−0.0926248	+	0.160431i
$552$	−4.30279	+	4.47299i	−0.183139	+	0.190383i
$553$	1.46953	+	3.94632i	0.0624909	+	0.167814i
$554$			32.6217i			1.38597i
$555$	−3.86292	−	13.3737i	−0.163972	−	0.567681i
$556$	7.96243	−	4.59711i	0.337682	−	0.194961i
$557$	−20.5631	+	11.8721i	−0.871287	+	0.503038i	−0.867776	−	0.496956i	$-0.834451\pi$
$557$	−20.5631	+	11.8721i	−0.871287	+	0.503038i	−0.00351124	+	0.999994i	$0.501118\pi$
$558$	−35.6219	−	18.7637i	−1.50800	−	0.794330i
$559$		−	51.1777i		−	2.16458i
$560$	−27.8263	−	4.69430i	−1.17588	−	0.198370i
$561$	8.02128	+	7.71606i	0.338659	+	0.325772i
$562$	−3.86459	+	6.69366i	−0.163018	+	0.282355i
$563$	−9.22090	−	15.9711i	−0.388615	−	0.673101i	0.603649	−	0.797250i	$-0.293713\pi$
$563$	−9.22090	−	15.9711i	−0.388615	−	0.673101i	−0.992263	+	0.124150i	$0.960380\pi$
$564$	3.38440	+	0.836859i	0.142509	+	0.0352381i
$565$	9.94080	+	5.73932i	0.418212	+	0.241455i
$566$	39.7534			1.67096
$567$	−23.7163	−	2.12968i	−0.995992	−	0.0894380i
$568$	−14.9768			−0.628413
$569$	37.1149	+	21.4283i	1.55594	+	0.898320i	0.997639	+	0.0686796i	$0.0218786\pi$
$569$	37.1149	+	21.4283i	1.55594	+	0.898320i	0.558298	+	0.829641i	$0.311455\pi$
$570$	11.3961	+	2.81792i	0.477332	+	0.118030i
$571$	7.28459	+	12.6173i	0.304850	+	0.528017i	0.977228	−	0.212192i	$-0.0680602\pi$
$571$	7.28459	+	12.6173i	0.304850	+	0.528017i	−0.672378	+	0.740208i	$0.734727\pi$
$572$	1.30027	−	2.25213i	0.0543670	−	0.0941664i
$573$	1.51240	+	1.45485i	0.0631812	+	0.0607771i
$574$	29.7871	−	11.0922i	1.24329	−	0.462978i
$575$		−	0.104141i		−	0.00434300i
$576$	−13.8448	−	7.29267i	−0.576865	−	0.303861i
$577$	−10.9234	+	6.30664i	−0.454748	+	0.262549i	−0.709833	−	0.704370i	$-0.751230\pi$
$577$	−10.9234	+	6.30664i	−0.454748	+	0.262549i	0.255085	+	0.966919i	$0.417896\pi$
$578$	33.1803	−	19.1567i	1.38012	−	0.796812i
$579$	−5.24495	−	18.1584i	−0.217973	−	0.754636i
$580$		−	2.50006i		−	0.103809i
$581$	−4.69623	+	5.68169i	−0.194832	+	0.235716i
$582$	16.6997	−	17.3602i	0.692223	−	0.719605i
$583$	0.710197	−	1.23010i	0.0294133	−	0.0509454i
$584$	10.2290	+	17.7171i	0.423279	+	0.733141i
$585$	−19.2165	−	30.4891i	−0.794506	−	1.26057i
$586$	−1.88122	−	1.08612i	−0.0777126	−	0.0448674i
$587$	6.33605			0.261517			0.130758	−	0.991414i	$-0.458259\pi$
$587$	6.33605			0.261517			0.130758	+	0.991414i	$0.458259\pi$
$588$	5.26712	−	2.67908i	0.217212	−	0.110483i
$589$	16.2418			0.669232
$590$	16.4885	+	9.51965i	0.678822	+	0.391918i
$591$	−2.71354	+	10.9740i	−0.111620	+	0.451411i
$592$	8.45494	+	14.6444i	0.347496	+	0.601880i
$593$	15.8082	−	27.3806i	0.649165	−	1.12439i	−0.334157	−	0.942517i	$-0.608452\pi$
$593$	15.8082	−	27.3806i	0.649165	−	1.12439i	0.983323	−	0.181870i	$-0.0582149\pi$
$594$	6.12194	+	5.44807i	0.251186	+	0.223537i
$595$	−24.3875	+	29.5049i	−0.999788	+	1.20958i
$596$			3.64101i			0.149142i
$597$	23.1194	−	6.67792i	0.946213	−	0.273309i
$598$	10.9466	−	6.32004i	0.447641	−	0.258446i
$599$	8.13661	−	4.69767i	0.332453	−	0.191942i	−0.324477	−	0.945894i	$-0.605188\pi$
$599$	8.13661	−	4.69767i	0.332453	−	0.191942i	0.656930	+	0.753952i	$0.271855\pi$
$600$	0.275226	−	0.0794975i	0.0112360	−	0.00324547i
$601$		−	23.7292i		−	0.967935i	−0.875086	−	0.483968i	$-0.839195\pi$
$601$		−	23.7292i		−	0.967935i	0.875086	−	0.483968i	$-0.160805\pi$
$602$	−37.5075	+	13.9671i	−1.52869	+	0.569255i
$603$	−1.04229	−	26.8606i	−0.0424454	−	1.09385i
$604$	0.716153	−	1.24041i	0.0291398	−	0.0504717i
$605$	1.12576	+	1.94987i	0.0457686	+	0.0792735i
$606$	−8.68839	+	35.1373i	−0.352942	+	1.42736i
$607$	−27.3857	−	15.8111i	−1.11155	−	0.641755i	−0.172321	−	0.985041i	$-0.555127\pi$
$607$	−27.3857	−	15.8111i	−1.11155	−	0.641755i	−0.939231	+	0.343286i	$0.888460\pi$
$608$	−5.15367			−0.209009
$609$	−6.21522	−	8.38853i	−0.251854	−	0.339920i
$610$	−27.7591			−1.12393
$611$	19.0829	+	11.0175i	0.772012	+	0.445722i
$612$	7.94878	−	5.00991i	0.321310	−	0.202514i
$613$	−2.25660	−	3.90855i	−0.0911433	−	0.157865i	0.816849	−	0.576851i	$-0.195719\pi$
$613$	−2.25660	−	3.90855i	−0.0911433	−	0.157865i	−0.907992	+	0.418987i	$0.862385\pi$
$614$	−10.1386	+	17.5606i	−0.409161	+	0.708687i
$615$	−20.5939	+	21.4086i	−0.830428	+	0.863277i
$616$	6.22378	+	1.04995i	0.250763	+	0.0423037i
$617$		−	38.1089i		−	1.53420i	−0.641525	−	0.767102i	$-0.721698\pi$
$617$		−	38.1089i		−	1.53420i	0.641525	−	0.767102i	$-0.278302\pi$
$618$	−12.5335	−	43.3917i	−0.504170	−	1.74547i
$619$	21.3664	−	12.3359i	0.858790	−	0.495822i	−0.00481713	−	0.999988i	$-0.501533\pi$
$619$	21.3664	−	12.3359i	0.858790	−	0.495822i	0.863607	+	0.504166i	$0.168200\pi$
$620$	−8.08690	+	4.66897i	−0.324778	+	0.187510i
$621$	2.45502	+	7.40887i	0.0985167	+	0.297308i
$622$			3.90934i			0.156750i
$623$	7.90533	+	21.2291i	0.316720	+	0.850528i
$624$	31.5512	+	30.3507i	1.26306	+	1.21500i
$625$	12.6709	−	21.9467i	0.506837	−	0.877867i
$626$	12.2807	+	21.2708i	0.490837	+	0.850154i
$627$	−3.20930	−	0.793563i	−0.128167	−	0.0316918i
$628$	−2.05297	−	1.18528i	−0.0819223	−	0.0472979i
$629$	22.9379			0.914592
$630$	−17.1007	+	22.4045i	−0.681307	+	0.892615i
$631$	−5.05337			−0.201172			−0.100586	−	0.994928i	$-0.532072\pi$
$631$	−5.05337			−0.201172			−0.100586	+	0.994928i	$0.532072\pi$
$632$	3.28829	+	1.89850i	0.130801	+	0.0755182i
$633$	24.0318	+	5.94233i	0.955177	+	0.236186i
$634$	25.7999	+	44.6867i	1.02464	+	1.77474i
$635$	−14.0027	+	24.2534i	−0.555680	+	0.962466i
$636$	−0.864158	−	0.831276i	−0.0342661	−	0.0329622i
$637$	36.6818	−	7.02977i	1.45339	−	0.278530i
$638$			3.59309i			0.142252i
$639$	−8.77747	+	16.6636i	−0.347231	+	0.659201i
$640$	−26.5701	+	15.3403i	−1.05028	+	0.606378i
$641$	−20.9499	+	12.0954i	−0.827471	+	0.477740i	−0.852986	−	0.521934i	$-0.825211\pi$
$641$	−20.9499	+	12.0954i	−0.827471	+	0.477740i	0.0255153	+	0.999674i	$0.491877\pi$
$642$	−12.9172	−	44.7201i	−0.509800	−	1.76496i
$643$			26.7505i			1.05493i	0.849575	+	0.527467i	$0.176858\pi$
$643$			26.7505i			1.05493i	−0.849575	+	0.527467i	$0.823142\pi$
$644$	−1.49298	−	1.23403i	−0.0588315	−	0.0486276i
$645$	25.9316	−	26.9573i	1.02106	−	1.06144i
$646$	−9.67199	+	16.7524i	−0.380540	+	0.659114i
$647$	17.2678	+	29.9087i	0.678867	+	1.17583i	0.975323	+	0.220785i	$0.0708619\pi$
$647$	17.2678	+	29.9087i	0.678867	+	1.17583i	−0.296456	+	0.955047i	$0.595805\pi$
$648$	−17.7062	+	12.1438i	−0.695564	+	0.477054i
$649$	−4.64338	−	2.68086i	−0.182269	−	0.105233i
$650$	−0.583428			−0.0228839
$651$	−15.5270	+	35.7702i	−0.608552	+	1.40195i
$652$	−0.588728			−0.0230564
$653$	−6.60827	−	3.81529i	−0.258602	−	0.149304i	0.365095	−	0.930970i	$-0.381037\pi$
$653$	−6.60827	−	3.81529i	−0.258602	−	0.149304i	−0.623696	+	0.781667i	$0.714370\pi$
$654$	10.6395	−	43.0279i	0.416037	−	1.68252i
$655$	8.86932	+	15.3621i	0.346553	+	0.600247i
$656$	18.0427	−	31.2508i	0.704448	−	1.22014i
$657$	25.7075	−	0.997546i	1.00294	−	0.0389180i
$658$	2.86663	−	16.9925i	0.111753	−	0.662436i
$659$			3.95418i			0.154033i	0.997030	+	0.0770165i	$0.0245394\pi$
$659$			3.95418i			0.154033i	−0.997030	+	0.0770165i	$0.975461\pi$
$660$	1.82605	−	0.527446i	0.0710791	−	0.0205308i
$661$	−10.7635	+	6.21431i	−0.418652	+	0.241709i	−0.694500	−	0.719492i	$-0.744374\pi$
$661$	−10.7635	+	6.21431i	−0.418652	+	0.241709i	0.275849	+	0.961201i	$0.411041\pi$
$662$	−7.02571	+	4.05630i	−0.273062	+	0.157652i
$663$	57.0535	−	16.4796i	2.21577	−	0.640015i
$664$			6.64651i			0.257935i
$665$	1.89140	−	11.2116i	0.0733452	−	0.434767i
$666$	16.8765	−	0.654872i	0.653951	−	0.0253758i
$667$	−1.71104	+	2.96360i	−0.0662516	+	0.114751i
$668$	2.83652	+	4.91300i	0.109748	+	0.190090i
$669$	−0.136488	+	0.551980i	−0.00527693	+	0.0213408i
$670$	−27.5549	−	15.9088i	−1.06454	−	0.614612i
$671$	7.81732			0.301784
$672$	4.92687	−	11.3502i	0.190058	−	0.437844i
$673$	−18.0578			−0.696077			−0.348038	−	0.937480i	$-0.613152\pi$
$673$	−18.0578			−0.696077			−0.348038	+	0.937480i	$0.613152\pi$
$674$	−22.3716	−	12.9162i	−0.861721	−	0.497515i
$675$	0.0728507	−	0.352814i	0.00280402	−	0.0135798i
$676$	−3.76970	−	6.52931i	−0.144988	−	0.251127i
$677$	−13.4708	+	23.3322i	−0.517727	+	0.896729i	0.482061	+	0.876137i	$0.339888\pi$
$677$	−13.4708	+	23.3322i	−0.517727	+	0.896729i	−0.999788	+	0.0205913i	$0.993445\pi$
$678$	−9.65485	+	10.0368i	−0.370792	+	0.385459i
$679$	−17.9829	−	14.8638i	−0.690119	−	0.570422i
$680$			34.5153i			1.32360i
$681$	8.41484	+	29.1327i	0.322457	+	1.11637i
$682$	11.6225	−	6.71026i	0.445049	−	0.256949i
$683$	−24.1636	+	13.9509i	−0.924596	+	0.533816i	−0.885098	−	0.465404i	$-0.845909\pi$
$683$	−24.1636	+	13.9509i	−0.924596	+	0.533816i	−0.0394973	+	0.999220i	$0.512576\pi$
$684$	−1.30066	+	2.46924i	−0.0497319	+	0.0944136i
$685$		−	34.3274i		−	1.31158i
$686$	−15.1630	−	24.9652i	−0.578926	−	0.953174i
$687$	−8.85901	−	8.52192i	−0.337992	−	0.325131i
$688$	−22.7191	+	39.3506i	−0.866156	+	1.50023i
$689$	−3.78934	−	6.56333i	−0.144362	−	0.250043i
$690$	8.96838	+	2.21761i	0.341421	+	0.0844229i
$691$	−3.00681	−	1.73598i	−0.114384	−	0.0660399i	0.441716	−	0.897155i	$-0.354370\pi$
$691$	−3.00681	−	1.73598i	−0.114384	−	0.0660399i	−0.556101	+	0.831115i	$0.687703\pi$
$692$	−3.47807			−0.132217
$693$	4.81577	−	6.30938i	0.182936	−	0.239674i
$694$	36.7503			1.39502
$695$	36.7826	+	21.2365i	1.39524	+	0.805545i
$696$	−9.13837	−	2.25964i	−0.346389	−	0.0856515i
$697$	−24.4745	−	42.3910i	−0.927036	−	1.60567i
$698$	−8.93487	+	15.4757i	−0.338190	+	0.585762i
$699$	−15.9015	−	15.2964i	−0.601449	−	0.578563i
$700$	0.0311994	+	0.0837837i	0.00117923	+	0.00316672i
$701$		−	35.2401i		−	1.33100i	−0.746398	−	0.665500i	$-0.768218\pi$
$701$		−	35.2401i		−	1.33100i	0.746398	−	0.665500i	$-0.231782\pi$
$702$	41.5065	−	13.7537i	1.56656	−	0.519100i
$703$	−5.90042	+	3.40661i	−0.222539	+	0.128483i
$704$	4.51720	−	2.60800i	0.170248	−	0.0982929i
$705$	4.46919	+	15.4726i	0.168320	+	0.582733i
$706$			42.5379i			1.60094i
$707$	34.5683	+	5.83167i	1.30007	+	0.219322i
$708$	−3.13791	+	3.26203i	−0.117930	+	0.122595i
$709$	16.8974	−	29.2672i	0.634595	−	1.09915i	−0.352006	−	0.935998i	$-0.614500\pi$
$709$	16.8974	−	29.2672i	0.634595	−	1.09915i	0.986601	−	0.163153i	$-0.0521665\pi$
$710$	11.1465	+	19.3063i	0.418321	+	0.724553i
$711$	4.03949	−	2.54599i	0.151493	−	0.0954819i
$712$	17.6893	+	10.2129i	0.662935	+	0.382746i
$713$	12.7818			0.478680
$714$	−27.6484	−	37.3163i	−1.03471	−	1.39653i
$715$	12.0132			0.449270
$716$	3.90050	+	2.25195i	0.145768	+	0.0841595i
$717$	−5.84533	+	23.6395i	−0.218298	+	0.882833i
$718$	12.9798	+	22.4817i	0.484403	+	0.839011i
$719$	−6.13510	+	10.6263i	−0.228800	+	0.396294i	−0.957453	−	0.288590i	$-0.906814\pi$
$719$	−6.13510	+	10.6263i	−0.228800	+	0.396294i	0.728652	+	0.684884i	$0.240147\pi$
$720$	1.24071	+	31.9738i	0.0462383	+	1.19159i
$721$	−40.9945	+	15.2655i	−1.52671	+	0.568519i
$722$			24.2201i			0.901377i
$723$	−8.18671	+	2.36469i	−0.304467	+	0.0879437i
$724$	0.127754	−	0.0737590i	0.00474795	−	0.00274123i
$725$	0.136791	−	0.0789763i	0.00508029	−	0.00293311i
$726$	−2.62441	+	0.758048i	−0.0974011	+	0.0281338i
$727$		−	30.1257i		−	1.11730i	−0.829403	−	0.558651i	$-0.811319\pi$
$727$		−	30.1257i		−	1.11730i	0.829403	−	0.558651i	$-0.188681\pi$
$728$	21.4555	−	25.9577i	0.795192	−	0.962055i
$729$	3.13445	+	26.8174i	0.116091	+	0.993239i
$730$	15.2259	−	26.3720i	0.563535	−	0.976071i
$731$	30.8179	+	53.3781i	1.13984	+	1.97426i
$732$	1.58409	−	6.40634i	0.0585498	−	0.236785i
$733$	2.15093	+	1.24184i	0.0794464	+	0.0458684i	0.539197	−	0.842180i	$-0.318728\pi$
$733$	2.15093	+	1.24184i	0.0794464	+	0.0458684i	−0.459751	+	0.888048i	$0.652061\pi$
$734$	−55.8339			−2.06087
$735$	22.8838	+	14.8837i	0.844080	+	0.548994i
$736$	−4.05577			−0.149498
$737$	7.75982	+	4.48013i	0.285837	+	0.165028i
$738$	−19.2173	−	30.4904i	−0.707399	−	1.12237i
$739$	9.48006	+	16.4199i	0.348730	+	0.604017i	0.986024	−	0.166603i	$-0.0532798\pi$
$739$	9.48006	+	16.4199i	0.348730	+	0.604017i	−0.637294	+	0.770620i	$0.719947\pi$
$740$	1.95857	−	3.39234i	0.0719985	−	0.124705i
$741$	−12.2287	+	12.7124i	−0.449232	+	0.467002i
$742$	−3.77602	+	4.56838i	−0.138622	+	0.167711i
$743$		−	18.6276i		−	0.683380i	−0.939813	−	0.341690i	$-0.889001\pi$
$743$		−	18.6276i		−	0.683380i	0.939813	−	0.341690i	$-0.110999\pi$
$744$	9.75710	+	33.7797i	0.357713	+	1.23842i
$745$	−14.5663	+	8.40987i	−0.533669	+	0.308114i
$746$	29.1857	−	16.8504i	1.06857	−	0.616936i
$747$	7.39508	+	3.89533i	0.270572	+	0.142523i
$748$			3.13195i			0.114516i
$749$	−42.2495	+	15.7329i	−1.54376	+	0.574867i
$750$	21.8554	+	21.0238i	0.798048	+	0.767681i
$751$	−12.0372	+	20.8490i	−0.439243	+	0.760790i	−0.997631	−	0.0687891i	$-0.978086\pi$
$751$	−12.0372	+	20.8490i	−0.439243	+	0.760790i	0.558389	+	0.829579i	$0.311420\pi$
$752$	−9.78192	−	16.9428i	−0.356710	−	0.617839i
$753$	−8.00997	−	1.98062i	−0.291900	−	0.0721779i
$754$	16.6029	+	9.58570i	0.604642	+	0.349090i
$755$	6.61657			0.240802
$756$	−4.19472	−	5.22508i	−0.152560	−	0.190034i
$757$	53.8553			1.95741			0.978703	−	0.205283i	$-0.0658114\pi$
$757$	53.8553			1.95741			0.978703	+	0.205283i	$0.0658114\pi$
$758$	42.3554	+	24.4539i	1.53842	+	0.888205i
$759$	−2.52561	−	0.624507i	−0.0916739	−	0.0226682i
$760$	−5.12602	−	8.87853i	−0.185940	−	0.322058i
$761$	−10.0994	+	17.4928i	−0.366105	+	0.634112i	−0.988953	−	0.148231i	$-0.952642\pi$
$761$	−10.0994	+	17.4928i	−0.366105	+	0.634112i	0.622848	+	0.782343i	$0.285975\pi$
$762$	−24.4875	−	23.5557i	−0.887089	−	0.853334i
$763$	−42.3311	−	7.14125i	−1.53249	−	0.258531i
$764$			0.590524i			0.0213644i
$765$	38.4025	+	20.2284i	1.38845	+	0.731358i
$766$	−3.72664	+	2.15157i	−0.134649	+	0.0777395i
$767$	−24.7753	+	14.3040i	−0.894585	+	0.516489i
$768$	−5.31553	−	18.4027i	−0.191808	−	0.664051i
$769$			36.7978i			1.32696i	0.748193	+	0.663482i	$0.230922\pi$
$769$			36.7978i			1.32696i	−0.748193	+	0.663482i	$0.769078\pi$
$770$	−3.27858	−	8.80436i	−0.118152	−	0.317287i
$771$	−4.83054	+	5.02162i	−0.173968	+	0.180849i
$772$	2.65929	−	4.60602i	0.0957098	−	0.165774i
$773$	−4.55071	−	7.88205i	−0.163677	−	0.283498i	0.772507	−	0.635006i	$-0.219002\pi$
$773$	−4.55071	−	7.88205i	−0.163677	−	0.283498i	−0.936185	+	0.351508i	$0.885669\pi$
$774$	24.1981	+	38.3930i	0.869784	+	1.38001i
$775$	−0.510927	−	0.294984i	−0.0183530	−	0.0105961i
$776$	−21.0366			−0.755170
$777$	−1.86181	−	16.2515i	−0.0667922	−	0.583020i
$778$	50.8187			1.82194
$779$	12.5914	+	7.26964i	0.451133	+	0.260462i
$780$	2.43435	−	9.84493i	0.0871638	−	0.352505i
$781$	−3.13900	−	5.43690i	−0.112322	−	0.194548i
$782$	−7.61154	+	13.1836i	−0.272188	+	0.471443i
$783$	−7.86986	+	8.84327i	−0.281246	+	0.316033i
$784$	−31.3254	−	10.8788i	−1.11876	−	0.388528i
$785$		−	10.9509i		−	0.390853i
$786$	−20.6765	+	5.97230i	−0.737506	+	0.213025i
$787$	16.7217	−	9.65425i	0.596063	−	0.344137i	−0.171428	−	0.985197i	$-0.554838\pi$
$787$	16.7217	−	9.65425i	0.596063	−	0.344137i	0.767491	+	0.641060i	$0.221505\pi$
$788$	−2.75487	+	1.59053i	−0.0981382	+	0.0566601i
$789$	31.9342	−	9.22402i	1.13689	−	0.328384i
$790$		−	5.65183i		−	0.201083i
$791$	10.3967	+	8.59348i	0.369665	+	0.305549i
$792$	−0.277503	−	7.15143i	−0.00986062	−	0.254115i
$793$	20.8551	−	36.1221i	0.740587	−	1.28273i
$794$	−13.8233	−	23.9426i	−0.490569	−	0.849690i
$795$	1.32962	−	5.37722i	0.0471569	−	0.190710i
$796$	5.86442	+	3.38583i	0.207859	+	0.120007i
$797$	34.2821			1.21433			0.607167	−	0.794574i	$-0.292306\pi$
$797$	34.2821			1.21433			0.607167	+	0.794574i	$0.292306\pi$
$798$	12.6542	+	5.49287i	0.447952	+	0.194446i
$799$	−26.5379			−0.938843
$800$	0.162122	+	0.0936010i	0.00573187	+	0.00330930i
$801$	21.7304	−	13.6961i	0.767804	−	0.483927i
$802$	−6.13899	−	10.6330i	−0.216775	−	0.375466i
$803$	−4.28780	+	7.42669i	−0.151313	+	0.262082i
$804$	5.24394	−	5.45137i	0.184939	−	0.192255i
$805$	1.48847	−	8.82315i	0.0524615	−	0.310975i
$806$		−	71.6069i		−	2.52224i
$807$	−7.47701	−	25.8859i	−0.263203	−	0.911227i
$808$	27.3748	−	15.8049i	0.963044	−	0.556014i
$809$	7.32244	−	4.22761i	0.257443	−	0.148635i	−0.365724	−	0.930723i	$-0.619179\pi$
$809$	7.32244	−	4.22761i	0.257443	−	0.148635i	0.623168	+	0.782088i	$0.285845\pi$
$810$	28.8321	+	13.7866i	1.01306	+	0.484412i
$811$			10.8470i			0.380890i	0.981698	+	0.190445i	$0.0609931\pi$
$811$			10.8470i			0.380890i	−0.981698	+	0.190445i	$0.939007\pi$
$812$	0.488703	−	2.89688i	0.0171501	−	0.101660i
$813$	9.21114	+	8.86064i	0.323049	+	0.310756i
$814$	−2.81487	+	4.87549i	−0.0986610	+	0.170886i
$815$	−1.35982	−	2.35528i	−0.0476324	−	0.0825018i
$816$	−51.1842	−	12.6563i	−1.79180	−	0.443059i
$817$	−15.8549	−	9.15382i	−0.554692	−	0.320252i
$818$	2.31762			0.0810336
$819$	−16.3067	−	39.0849i	−0.569803	−	1.36574i
$820$	−8.35910			−0.291912
$821$	21.4692	+	12.3953i	0.749281	+	0.432597i	0.825434	−	0.564499i	$-0.190931\pi$
$821$	21.4692	+	12.3953i	0.749281	+	0.432597i	−0.0761533	+	0.997096i	$0.524264\pi$
$822$	40.4308	+	9.99730i	1.41018	+	0.348696i
$823$	−18.1046	−	31.3580i	−0.631086	−	1.09307i	−0.987330	−	0.158679i	$-0.949276\pi$
$823$	−18.1046	−	31.3580i	−0.631086	−	1.09307i	0.356245	−	0.934393i	$-0.384057\pi$
$824$	−19.7216	+	34.1589i	−0.687036	+	1.18998i
$825$	0.0865440	+	0.0832509i	0.00301307	+	0.00289842i
$826$	17.2448	+	14.2538i	0.600022	+	0.495952i
$827$		−	37.7276i		−	1.31192i	−0.754797	−	0.655958i	$-0.772265\pi$
$827$		−	37.7276i		−	1.31192i	0.754797	−	0.655958i	$-0.227735\pi$
$828$	−1.02357	+	1.94321i	−0.0355717	+	0.0675311i
$829$	−17.1681	+	9.91199i	−0.596272	+	0.344258i	−0.767573	−	0.640961i	$-0.778536\pi$
$829$	−17.1681	+	9.91199i	−0.596272	+	0.344258i	0.171302	+	0.985219i	$0.445203\pi$
$830$	8.56788	−	4.94667i	0.297396	−	0.171701i
$831$	−9.94168	−	34.4187i	−0.344873	−	1.19397i
$832$		−	27.8307i		−	0.964854i
$833$	−34.0259	+	29.4209i	−1.17893	+	1.01937i
$834$	−35.7246	+	37.1377i	−1.23704	+	1.28597i
$835$	−13.1034	+	22.6957i	−0.453461	+	0.785418i
$836$	−0.465141	−	0.805649i	−0.0160873	−	0.0278639i
$837$	43.3025	+	8.94130i	1.49675	+	0.309057i
$838$	−16.8952	−	9.75444i	−0.583634	−	0.336961i
$839$	−38.6892			−1.33570			−0.667850	−	0.744296i	$-0.732785\pi$
$839$	−38.6892			−1.33570			−0.667850	+	0.744296i	$0.732785\pi$
$840$	24.4541	−	2.80153i	0.843747	−	0.0966618i
$841$	23.8097			0.821024
$842$	15.2329	+	8.79475i	0.524962	+	0.303087i
$843$	2.03754	−	8.24015i	0.0701765	−	0.283806i
$844$	3.48306	+	6.03283i	0.119892	+	0.207659i
$845$	17.4142	−	30.1623i	0.599067	−	1.03761i
$846$	−19.5252	+	0.757652i	−0.671291	+	0.0260486i
$847$	0.923289	+	2.47942i	0.0317246	+	0.0851940i
$848$			6.72873i			0.231066i
$849$	−41.9433	+	12.1151i	−1.43949	+	0.415789i
$850$	0.608514	−	0.351326i	0.0208718	−	0.0120504i
$851$	−4.64343	+	2.68089i	−0.159175	+	0.0918996i
$852$	−5.09166	+	1.47070i	−0.174437	+	0.0503853i
$853$			6.35051i			0.217437i	0.994073	+	0.108719i	$0.0346748\pi$
$853$			6.35051i			0.217437i	−0.994073	+	0.108719i	$0.965325\pi$
$854$	−32.1651	−	5.42626i	−1.10067	−	0.185683i
$855$	−12.8827	+	0.499897i	−0.440579	+	0.0170961i
$856$	−20.3254	+	35.2046i	−0.694708	+	1.20327i
$857$	−13.5421	−	23.4557i	−0.462591	−	0.801231i	0.536499	−	0.843901i	$-0.319747\pi$
$857$	−13.5421	−	23.4557i	−0.462591	−	0.801231i	−0.999089	+	0.0426707i	$0.986413\pi$
$858$	−3.49866	+	14.1492i	−0.119442	+	0.483045i
$859$	−39.4259	−	22.7626i	−1.34520	−	0.776649i	−0.357631	−	0.933863i	$-0.616415\pi$
$859$	−39.4259	−	22.7626i	−1.34520	−	0.776649i	−0.987565	+	0.157214i	$0.949749\pi$
$860$	10.5257			0.358922
$861$	−28.0476	+	20.7810i	−0.955859	+	0.708214i
$862$	25.3639			0.863897
$863$	−22.9262	−	13.2365i	−0.780418	−	0.450575i	0.0561601	−	0.998422i	$-0.482114\pi$
$863$	−22.9262	−	13.2365i	−0.780418	−	0.450575i	−0.836579	+	0.547847i	$0.815448\pi$
$864$	−13.7403	−	2.83716i	−0.467454	−	0.0965220i
$865$	−8.03352	−	13.9145i	−0.273148	−	0.473106i
$866$	18.0507	−	31.2647i	0.613386	−	1.06242i
$867$	−29.1700	+	30.3238i	−0.990664	+	1.02985i
$868$	−10.2832	+	3.82925i	−0.349033	+	0.129973i
$869$			1.59163i			0.0539923i
$870$	3.88838	+	13.4618i	0.131828	+	0.456399i
$871$	41.4035	−	23.9043i	1.40290	−	0.809966i
$872$	−33.5222	+	19.3541i	−1.13521	+	0.655412i
$873$	−12.3289	+	23.4059i	−0.417271	+	0.792168i
$874$		−	4.52170i		−	0.152949i
$875$	18.7126	−	22.6393i	0.632603	−	0.765348i
$876$	5.21734	+	5.01881i	0.176278	+	0.169570i
$877$	11.4106	−	19.7638i	0.385310	−	0.667376i	−0.606502	−	0.795082i	$-0.707428\pi$
$877$	11.4106	−	19.7638i	0.385310	−	0.667376i	0.991812	+	0.127706i	$0.0407612\pi$
$878$	6.22177	+	10.7764i	0.209974	+	0.363686i
$879$	2.31585	+	0.572640i	0.0781118	+	0.0193147i
$880$	−9.23700	−	5.33298i	−0.311379	−	0.179775i
$881$	−15.8271			−0.533229			−0.266615	−	0.963803i	$-0.585905\pi$
$881$	−15.8271			−0.533229			−0.266615	+	0.963803i	$0.585905\pi$
$882$	−24.1945	+	22.6178i	−0.814672	+	0.761581i
$883$	−21.8582			−0.735587			−0.367793	−	0.929908i	$-0.619887\pi$
$883$	−21.8582			−0.735587			−0.367793	+	0.929908i	$0.619887\pi$
$884$	14.4721	+	8.35546i	0.486749	+	0.281025i
$885$	−20.2980	−	5.01907i	−0.682309	−	0.168714i
$886$	−21.1408	−	36.6169i	−0.710238	−	1.23017i
$887$	20.1465	−	34.8947i	0.676452	−	1.17165i	−0.299590	−	0.954068i	$-0.596850\pi$
$887$	20.1465	−	34.8947i	0.676452	−	1.17165i	0.976042	−	0.217582i	$-0.0698169\pi$
$888$	−10.6297	−	10.2252i	−0.356709	−	0.343136i
$889$	−20.9662	+	25.3658i	−0.703185	+	0.850741i
$890$		−	30.4039i		−	1.01914i
$891$	−8.11950	−	3.88249i	−0.272014	−	0.130068i
$892$	−0.138567	+	0.0800015i	−0.00463955	+	0.00267865i
$893$	6.82648	−	3.94127i	0.228439	−	0.131889i
$894$	−5.66292	−	19.6054i	−0.189396	−	0.655703i
$895$			20.8059i			0.695465i
$896$	−33.7861	+	12.5813i	−1.12872	+	0.420312i
$897$	−9.62357	+	10.0042i	−0.321322	+	0.334032i
$898$	19.9652	−	34.5808i	0.666248	−	1.15398i
$899$	9.69313	+	16.7890i	0.323284	+	0.559944i
$900$	0.0857618	−	0.0540534i	0.00285873	−	0.00180178i
$901$	7.90454	+	4.56369i	0.263338	+	0.152038i
$902$	12.0137			0.400014
$903$	35.3171	−	26.1671i	1.17528	−	0.870787i
$904$	12.1622			0.404510
$905$	0.590164	+	0.340731i	0.0196177	+	0.0113263i
$906$	−1.92697	+	7.79297i	−0.0640192	+	0.258904i
$907$	−13.7174	−	23.7592i	−0.455479	−	0.788913i	0.543237	−	0.839580i	$-0.317199\pi$
$907$	−13.7174	−	23.7592i	−0.455479	−	0.788913i	−0.998716	+	0.0506669i	$0.983865\pi$
$908$	−4.26648	+	7.38976i	−0.141588	+	0.245238i
$909$	−1.54131	−	39.7207i	−0.0511221	−	1.31745i
$910$	−49.4297	−	8.33879i	−1.63858	−	0.276428i
$911$		−	29.7719i		−	0.986386i	−0.869920	−	0.493193i	$-0.835830\pi$
$911$		−	29.7719i		−	0.986386i	0.869920	−	0.493193i	$-0.164170\pi$
$912$	15.0460	−	4.34596i	0.498223	−	0.143909i
$913$	−2.41283	+	1.39305i	−0.0798529	+	0.0461031i
$914$	−7.89103	+	4.55589i	−0.261012	+	0.150695i
$915$	29.2882	−	8.45975i	0.968239	−	0.279671i
$916$		−	3.45905i		−	0.114290i
$917$	7.27416	+	19.5342i	0.240214	+	0.645076i
$918$	−35.0090	+	39.3392i	−1.15547	+	1.29839i
$919$	4.11943	−	7.13507i	0.135888	−	0.235364i	−0.790049	−	0.613044i	$-0.789945\pi$
$919$	4.11943	−	7.13507i	0.135888	−	0.235364i	0.925936	+	0.377680i	$0.123278\pi$
$920$	−4.03401	−	6.98711i	−0.132997	−	0.230358i
$921$	5.34540	−	21.6177i	0.176137	−	0.712328i
$922$	−31.7628	−	18.3383i	−1.04605	−	0.603938i
$923$	−33.4970			−1.10257
$924$	2.21900	−	0.254214i	0.0729996	−	0.00836302i
$925$	0.247483			0.00813720
$926$	11.6878	+	6.74794i	0.384084	+	0.221751i
$927$	26.4478	+	41.9623i	0.868659	+	1.37822i
$928$	−3.07572	−	5.32730i	−0.100965	−	0.174877i
$929$	29.6612	−	51.3747i	0.973152	−	1.68555i	0.287248	−	0.957856i	$-0.407260\pi$
$929$	29.6612	−	51.3747i	0.973152	−	1.68555i	0.685904	−	0.727692i	$-0.259407\pi$
$930$	36.2830	−	37.7182i	1.18977	−	1.23683i
$931$	4.38321	−	12.6214i	0.143654	−	0.413650i
$932$		−	6.20882i		−	0.203377i
$933$	−1.19139	−	4.12468i	−0.0390045	−	0.135036i
$934$	−15.4341	+	8.91088i	−0.505019	+	0.291573i
$935$	−12.5298	+	7.23407i	−0.409767	+	0.236579i
$936$	−33.7856	−	17.7964i	−1.10432	−	0.581693i
$937$		−	28.3294i		−	0.925482i	−0.886494	−	0.462741i	$-0.846866\pi$
$937$		−	28.3294i		−	0.925482i	0.886494	−	0.462741i	$-0.153134\pi$
$938$	−28.8187	−	23.8203i	−0.940965	−	0.777760i
$939$	−19.4396	−	18.6999i	−0.634389	−	0.610250i
$940$	−2.26596	+	3.92476i	−0.0739076	+	0.128012i
$941$	−4.16239	−	7.20947i	−0.135690	−	0.235022i	0.790171	−	0.612887i	$-0.209992\pi$
$941$	−4.16239	−	7.20947i	−0.135690	−	0.235022i	−0.925861	+	0.377865i	$0.876658\pi$
$942$	12.8979	+	3.18926i	0.420236	+	0.103912i
$943$	9.90899	+	5.72096i	0.322681	+	0.186300i
$944$	25.3997			0.826689
$945$	11.2148	−	28.8502i	0.364817	−	0.938496i
$946$	−15.1275			−0.491838
$947$	34.7815	+	20.0811i	1.13025	+	0.652549i	0.943997	−	0.329953i	$-0.107033\pi$
$947$	34.7815	+	20.0811i	1.13025	+	0.652549i	0.186251	+	0.982502i	$0.440366\pi$
$948$	1.30435	+	0.322526i	0.0423633	+	0.0104751i
$949$	22.8781	+	39.6260i	0.742654	+	1.28631i
$950$	−0.104354	+	0.180747i	−0.00338569	+	0.00586419i
$951$	−40.8397	−	39.2857i	−1.32432	−	1.27393i
$952$	−6.74693	+	39.9937i	−0.218669	+	1.29620i
$953$			7.48216i			0.242371i	0.992630	+	0.121185i	$0.0386696\pi$
$953$			7.48216i			0.242371i	−0.992630	+	0.121185i	$0.961330\pi$
$954$	5.94604	+	3.13205i	0.192510	+	0.101404i
$955$	−2.36246	+	1.36397i	−0.0764475	+	0.0441370i
$956$	−5.93435	+	3.42620i	−0.191931	+	0.110811i
$957$	−1.09502	−	3.79102i	−0.0353969	−	0.122546i
$958$			51.5787i			1.66643i
$959$	6.71021	−	39.7760i	0.216684	−	1.28443i
$960$	14.1017	−	14.6595i	0.455131	−	0.473134i
$961$	20.7047	−	35.8616i	0.667894	−	1.15683i
$962$	15.0191	+	26.0138i	0.484234	+	0.838718i
$963$	27.2574	+	43.2470i	0.878359	+	1.39361i
$964$	−2.07663	−	1.19894i	−0.0668836	−	0.0386153i
$965$	24.5693			0.790913
$966$	9.95839	+	4.32271i	0.320406	+	0.139081i
$967$	−20.6305			−0.663433			−0.331716	−	0.943379i	$-0.607628\pi$
$967$	−20.6305			−0.663433			−0.331716	+	0.943379i	$0.607628\pi$
$968$	2.06599	+	1.19280i	0.0664036	+	0.0383381i
$969$	5.09939	−	20.6228i	0.163816	−	0.662500i
$970$	15.6565	+	27.1178i	0.502700	+	0.870701i
$971$	16.2629	−	28.1682i	0.521902	−	0.903961i	−0.477773	−	0.878483i	$-0.658556\pi$
$971$	16.2629	−	28.1682i	0.521902	−	0.903961i	0.999675	−	0.0254778i	$-0.00811073\pi$
$972$	−4.82705	+	5.86724i	−0.154828	+	0.188192i
$973$	38.4697	+	31.7974i	1.23328	+	1.01938i
$974$		−	28.4136i		−	0.910432i
$975$	0.615567	−	0.177803i	0.0197139	−	0.00569427i
$976$	−32.0710	+	18.5162i	−1.02657	+	0.592690i
$977$	4.26031	−	2.45969i	0.136299	−	0.0786925i	−0.430300	−	0.902686i	$-0.641592\pi$
$977$	4.26031	−	2.45969i	0.136299	−	0.0786925i	0.566599	+	0.823994i	$0.308259\pi$
$978$	3.17007	−	0.915657i	0.101368	−	0.0292795i
$979$			8.56213i			0.273647i
$980$	1.44581	+	7.54431i	0.0461846	+	0.240994i
$981$	1.88744	+	48.6405i	0.0602612	+	1.55297i
$982$	−28.8202	+	49.9180i	−0.919688	+	1.59295i
$983$	−20.1146	−	34.8396i	−0.641558	−	1.11121i	−0.985085	−	0.172068i	$-0.944955\pi$
$983$	−20.1146	−	34.8396i	−0.641558	−	1.11121i	0.343528	−	0.939143i	$-0.388378\pi$
$984$	−7.55525	+	30.5547i	−0.240853	+	0.974049i
$985$	−12.7262	−	7.34747i	−0.405490	−	0.234110i
$986$	−23.0890			−0.735305
$987$	2.15402	+	18.8021i	0.0685632	+	0.598479i
$988$	−4.96364			−0.157914
$989$	−12.4773	−	7.20375i	−0.396754	−	0.229066i
$990$	−9.01223	+	5.68018i	−0.286428	+	0.180528i
$991$	22.3667	+	38.7402i	0.710501	+	1.23062i	0.964669	+	0.263463i	$0.0848648\pi$
$991$	22.3667	+	38.7402i	0.710501	+	1.23062i	−0.254169	+	0.967160i	$0.581802\pi$
$992$	−11.4881	+	19.8979i	−0.364747	+	0.631760i
$993$	6.17655	−	6.42087i	0.196007	−	0.203760i
$994$	9.14179	+	24.5496i	0.289960	+	0.778665i
$995$			31.2818i			0.991700i
$996$	0.652677	+	2.25961i	0.0206809	+	0.0715985i
$997$	−17.4764	+	10.0900i	−0.553484	+	0.319554i	−0.750526	−	0.660841i	$-0.770200\pi$
$997$	−17.4764	+	10.0900i	−0.553484	+	0.319554i	0.197042	+	0.980395i	$0.436866\pi$
$998$	40.8672	−	23.5947i	1.29363	−	0.746876i
$999$	−17.6066	+	5.83416i	−0.557047	+	0.184585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.n.a.89.6	✓	52
3.2	odd	2	inner	231.2.n.a.89.21	yes	52
7.3	odd	6	inner	231.2.n.a.122.21	yes	52
21.17	even	6	inner	231.2.n.a.122.6	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.n.a.89.6	✓	52	1.1	even	1	trivial
231.2.n.a.89.21	yes	52	3.2	odd	2	inner
231.2.n.a.122.6	yes	52	21.17	even	6	inner
231.2.n.a.122.21	yes	52	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36585 - 0.788573i) q^{2} +(1.68141 + 0.415762i) q^{3} +(0.243696 + 0.422094i) q^{4} +(-1.12576 + 1.94987i) q^{5} +(-1.96869 - 1.89378i) q^{6} +(-1.68560 + 2.03930i) q^{7} +2.38560i q^{8} +(2.65428 + 1.39813i) q^{9} +O(q^{10})\)	\(q+(-1.36585 - 0.788573i) q^{2} +(1.68141 + 0.415762i) q^{3} +(0.243696 + 0.422094i) q^{4} +(-1.12576 + 1.94987i) q^{5} +(-1.96869 - 1.89378i) q^{6} +(-1.68560 + 2.03930i) q^{7} +2.38560i q^{8} +(2.65428 + 1.39813i) q^{9} +(3.07523 - 1.77549i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.234263 + 0.811032i) q^{12} +5.33562i q^{13} +(3.91041 - 1.45616i) q^{14} +(-2.70354 + 2.81049i) q^{15} +(2.36862 - 4.10256i) q^{16} +(-3.21297 - 5.56503i) q^{17} +(-2.52282 - 4.00274i) q^{18} +(1.65298 + 0.954348i) q^{19} -1.09737 q^{20} +(-3.68205 + 2.72810i) q^{21} +1.57715 q^{22} +(1.30084 + 0.751040i) q^{23} +(-0.991843 + 4.01118i) q^{24} +(-0.0346657 - 0.0600428i) q^{25} +(4.20753 - 7.28765i) q^{26} +(3.88165 + 3.45439i) q^{27} +(-1.27155 - 0.214511i) q^{28} +2.27822i q^{29} +(5.90891 - 1.70676i) q^{30} +(7.36933 - 4.25469i) q^{31} +(-2.33836 + 1.35005i) q^{32} +(-1.66403 + 0.480645i) q^{33} +10.1347i q^{34} +(-2.07880 - 5.58246i) q^{35} +(0.0566953 + 1.46108i) q^{36} +(-1.78478 + 3.09134i) q^{37} +(-1.50515 - 2.60699i) q^{38} +(-2.21835 + 8.97137i) q^{39} +(-4.65162 - 2.68562i) q^{40} +7.61738 q^{41} +(7.18043 - 0.822608i) q^{42} -9.59170 q^{43} +(-0.422094 - 0.243696i) q^{44} +(-5.71426 + 3.60155i) q^{45} +(-1.18450 - 2.05161i) q^{46} +(2.06490 - 3.57651i) q^{47} +(5.68831 - 5.91332i) q^{48} +(-1.31752 - 6.87489i) q^{49} +0.109346i q^{50} +(-3.08860 - 10.6929i) q^{51} +(-2.25213 + 1.30027i) q^{52} +(-1.23010 + 0.710197i) q^{53} +(-2.57772 - 7.77914i) q^{54} -2.25152i q^{55} +(-4.86497 - 4.02117i) q^{56} +(2.38256 + 2.29190i) q^{57} +(1.79655 - 3.11171i) q^{58} +(2.68086 + 4.64338i) q^{59} +(-1.84513 - 0.456245i) q^{60} +(-6.77000 - 3.90866i) q^{61} -13.4205 q^{62} +(-7.32527 + 3.05620i) q^{63} -5.21601 q^{64} +(-10.4038 - 6.00662i) q^{65} +(2.65183 + 0.655717i) q^{66} +(-4.48013 - 7.75982i) q^{67} +(1.56598 - 2.71235i) q^{68} +(1.87499 + 1.80365i) q^{69} +(-1.56285 + 9.26409i) q^{70} +6.27800i q^{71} +(-3.33539 + 6.33207i) q^{72} +(7.42669 - 4.28780i) q^{73} +(4.87549 - 2.81487i) q^{74} +(-0.0333238 - 0.115369i) q^{75} +0.930283i q^{76} +(0.440119 - 2.60889i) q^{77} +(10.1045 - 10.5042i) q^{78} +(0.795814 - 1.37839i) q^{79} +(5.33298 + 9.23700i) q^{80} +(5.09045 + 7.42208i) q^{81} +(-10.4042 - 6.00687i) q^{82} +2.78609 q^{83} +(-2.04881 - 0.889343i) q^{84} +14.4681 q^{85} +(13.1008 + 7.56376i) q^{86} +(-0.947199 + 3.83063i) q^{87} +(-1.19280 - 2.06599i) q^{88} +(4.28107 - 7.41503i) q^{89} +(10.6449 - 0.413063i) q^{90} +(-10.8810 - 8.99371i) q^{91} +0.732101i q^{92} +(14.1598 - 4.08999i) q^{93} +(-5.64069 + 3.25665i) q^{94} +(-3.72171 + 2.14873i) q^{95} +(-4.49304 + 1.29779i) q^{96} +8.81814i q^{97} +(-3.62183 + 10.4290i) q^{98} +(-2.99774 + 0.116324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

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