LMFDB - Embedded newform 384.2.v.a.109.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			109.29
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38550 - 0.283508i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.83925 - 0.785602i) q^{4} +(-0.311554 + 0.379630i) q^{5} +(-1.35555 - 0.403091i) q^{6} +(2.05811 + 1.37518i) q^{7} +(2.32556 - 1.60990i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(1.38550 - 0.283508i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.83925 - 0.785602i) q^{4} +(-0.311554 + 0.379630i) q^{5} +(-1.35555 - 0.403091i) q^{6} +(2.05811 + 1.37518i) q^{7} +(2.32556 - 1.60990i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.324032 + 0.614307i) q^{10} +(0.708920 + 0.215049i) q^{11} +(-1.99240 - 0.174176i) q^{12} +(1.87893 - 1.54200i) q^{13} +(3.24140 + 1.32184i) q^{14} +(0.453723 - 0.187938i) q^{15} +(2.76566 - 2.88983i) q^{16} +(0.338982 + 0.140411i) q^{17} +(1.00547 + 0.994497i) q^{18} +(0.634562 - 6.44281i) q^{19} +(-0.274787 + 0.942991i) q^{20} +(-1.16683 - 2.18299i) q^{21} +(1.04318 + 0.0969667i) q^{22} +(-7.28620 - 1.44931i) q^{23} +(-2.80986 + 0.323539i) q^{24} +(0.928399 + 4.66738i) q^{25} +(2.16610 - 2.66914i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(4.86572 + 0.912450i) q^{28} +(0.561081 + 1.84964i) q^{29} +(0.575353 - 0.389023i) q^{30} +(-5.57748 + 5.57748i) q^{31} +(3.01254 - 4.78796i) q^{32} +(-0.523839 - 0.523839i) q^{33} +(0.509468 + 0.0984360i) q^{34} +(-1.16327 + 0.352875i) q^{35} +(1.67504 + 1.09282i) q^{36} +(6.92412 - 0.681966i) q^{37} +(-0.947398 - 9.10645i) q^{38} +(-2.38396 + 0.474200i) q^{39} +(-0.113374 + 1.38442i) q^{40} +(-0.989289 + 4.97349i) q^{41} +(-2.23555 - 2.69374i) q^{42} +(-5.69893 + 3.04614i) q^{43} +(1.47282 - 0.161402i) q^{44} +(-0.488741 - 0.0481368i) q^{45} +(-10.5060 + 0.0576591i) q^{46} +(-1.01282 + 2.44515i) q^{47} +(-3.80135 + 1.24488i) q^{48} +(-0.334102 - 0.806595i) q^{49} +(2.60954 + 6.20346i) q^{50} +(-0.232766 - 0.283626i) q^{51} +(2.24442 - 4.31221i) q^{52} +(-2.92011 + 9.62630i) q^{53} +(-0.417946 - 1.35104i) q^{54} +(-0.302506 + 0.202128i) q^{55} +(7.00016 - 0.115265i) q^{56} +(-3.59675 + 5.38292i) q^{57} +(1.30177 + 2.40361i) q^{58} +(-8.85770 - 7.26933i) q^{59} +(0.686863 - 0.702110i) q^{60} +(0.238013 - 0.445291i) q^{61} +(-6.14637 + 9.30888i) q^{62} +2.47527i q^{63} +(2.81647 - 7.48782i) q^{64} +1.19372i q^{65} +(-0.874293 - 0.577269i) q^{66} +(1.29140 - 2.41603i) q^{67} +(0.733778 - 0.00805453i) q^{68} +(5.74265 + 4.71287i) q^{69} +(-1.51168 + 0.818707i) q^{70} +(0.719325 - 1.07655i) q^{71} +(2.63059 + 1.03922i) q^{72} +(-0.675000 + 0.451021i) q^{73} +(9.40006 - 2.90791i) q^{74} +(1.38141 - 4.55390i) q^{75} +(-3.89437 - 12.3484i) q^{76} +(1.16330 + 1.41749i) q^{77} +(-3.16855 + 1.33288i) q^{78} +(3.41873 + 8.25355i) q^{79} +(0.235414 + 1.95027i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(0.0393575 + 7.17127i) q^{82} +(-11.2884 - 1.11181i) q^{83} +(-3.86106 - 3.09839i) q^{84} +(-0.158915 + 0.0849420i) q^{85} +(-7.03230 + 5.83614i) q^{86} +(0.377083 - 1.89573i) q^{87} +(1.99484 - 0.641179i) q^{88} +(-9.94691 + 1.97856i) q^{89} +(-0.690800 + 0.0718680i) q^{90} +(5.98758 - 0.589726i) q^{91} +(-14.5397 + 3.05840i) q^{92} +(7.54810 - 2.28969i) q^{93} +(-0.710042 + 3.67491i) q^{94} +(2.24818 + 2.24818i) q^{95} +(-4.91386 + 2.80250i) q^{96} +(1.02015 - 1.02015i) q^{97} +(-0.691576 - 1.02282i) q^{98} +(0.215049 + 0.708920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$	1.38550	−	0.283508i	0.979700	−	0.200470i
$2$	1.38550	−	0.283508i	0.979700	−	0.200470i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$4$	1.83925	−	0.785602i	0.919623	−	0.392801i
$5$	−0.311554	+	0.379630i	−0.139331	+	0.169776i	−0.838001	−	0.545669i	$-0.816276\pi$
$5$	−0.311554	+	0.379630i	−0.139331	+	0.169776i	0.698670	+	0.715444i	$0.253776\pi$
$6$	−1.35555	−	0.403091i	−0.553401	−	0.164561i
$7$	2.05811	+	1.37518i	0.777892	+	0.519771i	0.879984	−	0.475004i	$-0.157553\pi$
$7$	2.05811	+	1.37518i	0.777892	+	0.519771i	−0.102091	+	0.994775i	$0.532553\pi$
$8$	2.32556	−	1.60990i	0.822210	−	0.569184i
$9$	0.555570	+	0.831470i	0.185190	+	0.277157i
$10$	−0.324032	+	0.614307i	−0.102468	+	0.194261i
$11$	0.708920	+	0.215049i	0.213748	+	0.0648396i	0.395342	−	0.918534i	$-0.370626\pi$
$11$	0.708920	+	0.215049i	0.213748	+	0.0648396i	−0.181595	+	0.983373i	$0.558126\pi$
$12$	−1.99240	−	0.174176i	−0.575157	−	0.0502803i
$13$	1.87893	−	1.54200i	0.521122	−	0.427674i	−0.336707	−	0.941610i	$-0.609313\pi$
$13$	1.87893	−	1.54200i	0.521122	−	0.427674i	0.857829	+	0.513936i	$0.171813\pi$
$14$	3.24140	+	1.32184i	0.866299	+	0.353275i
$15$	0.453723	−	0.187938i	0.117151	−	0.0485254i
$16$	2.76566	−	2.88983i	0.691415	−	0.722458i
$17$	0.338982	+	0.140411i	0.0822151	+	0.0340546i	0.423412	−	0.905937i	$-0.360832\pi$
$17$	0.338982	+	0.140411i	0.0822151	+	0.0340546i	−0.341197	+	0.939992i	$0.610832\pi$
$18$	1.00547	+	0.994497i	0.236992	+	0.234405i
$19$	0.634562	−	6.44281i	0.145578	−	1.47808i	−0.593702	−	0.804685i	$-0.702334\pi$
$19$	0.634562	−	6.44281i	0.145578	−	1.47808i	0.739280	−	0.673398i	$-0.235166\pi$
$20$	−0.274787	+	0.942991i	−0.0614443	+	0.210859i
$21$	−1.16683	−	2.18299i	−0.254624	−	0.476368i
$22$	1.04318	+	0.0969667i	0.222407	+	0.0206734i
$23$	−7.28620	−	1.44931i	−1.51928	−	0.302203i	−0.636234	−	0.771496i	$-0.719509\pi$
$23$	−7.28620	−	1.44931i	−1.51928	−	0.302203i	−0.883043	+	0.469293i	$0.844509\pi$
$24$	−2.80986	+	0.323539i	−0.573561	+	0.0660421i
$25$	0.928399	+	4.66738i	0.185680	+	0.933475i
$26$	2.16610	−	2.66914i	0.424807	−	0.523461i
$27$	−0.0980171	−	0.995185i	−0.0188634	−	0.191523i
$28$	4.86572	+	0.912450i	0.919535	+	0.172437i
$29$	0.561081	+	1.84964i	0.104190	+	0.343469i	0.993499	−	0.113837i	$-0.0363143\pi$
$29$	0.561081	+	1.84964i	0.104190	+	0.343469i	−0.889309	+	0.457306i	$0.848814\pi$
$30$	0.575353	−	0.389023i	0.105045	−	0.0710255i
$31$	−5.57748	+	5.57748i	−1.00174	+	1.00174i	−0.00174611	+	0.999998i	$0.500556\pi$
$31$	−5.57748	+	5.57748i	−1.00174	+	1.00174i	−0.999998	+	0.00174611i	$0.999444\pi$
$32$	3.01254	−	4.78796i	0.532548	−	0.846400i
$33$	−0.523839	−	0.523839i	−0.0911886	−	0.0911886i
$34$	0.509468	+	0.0984360i	0.0873731	+	0.0168816i
$35$	−1.16327	+	0.352875i	−0.196629	+	0.0596468i
$36$	1.67504	+	1.09282i	0.279173	+	0.182137i
$37$	6.92412	−	0.681966i	1.13832	−	0.112115i	0.488754	−	0.872422i	$-0.337452\pi$
$37$	6.92412	−	0.681966i	1.13832	−	0.112115i	0.649564	+	0.760307i	$0.274952\pi$
$38$	−0.947398	−	9.10645i	−0.153688	−	1.47726i
$39$	−2.38396	+	0.474200i	−0.381740	+	0.0759328i
$40$	−0.113374	+	1.38442i	−0.0179260	+	0.218896i
$41$	−0.989289	+	4.97349i	−0.154501	+	0.776729i	0.823368	+	0.567508i	$0.192093\pi$
$41$	−0.989289	+	4.97349i	−0.154501	+	0.776729i	−0.977869	+	0.209220i	$0.932907\pi$
$42$	−2.23555	−	2.69374i	−0.344952	−	0.415653i
$43$	−5.69893	+	3.04614i	−0.869079	+	0.464533i	−0.844744	−	0.535171i	$-0.820247\pi$
$43$	−5.69893	+	3.04614i	−0.869079	+	0.464533i	−0.0243358	+	0.999704i	$0.507747\pi$
$44$	1.47282	−	0.161402i	0.222036	−	0.0243322i
$45$	−0.488741	−	0.0481368i	−0.0728572	−	0.00717581i
$46$	−10.5060	+	0.0576591i	−1.54902	+	0.00850136i
$47$	−1.01282	+	2.44515i	−0.147734	+	0.356662i	−0.980372	−	0.197155i	$-0.936830\pi$
$47$	−1.01282	+	2.44515i	−0.147734	+	0.356662i	0.832638	+	0.553818i	$0.186830\pi$
$48$	−3.80135	+	1.24488i	−0.548678	+	0.179683i
$49$	−0.334102	−	0.806595i	−0.0477289	−	0.115228i
$50$	2.60954	+	6.20346i	0.369044	+	0.877302i
$51$	−0.232766	−	0.283626i	−0.0325938	−	0.0397156i
$52$	2.24442	−	4.31221i	0.311245	−	0.597996i
$53$	−2.92011	+	9.62630i	−0.401107	+	1.32227i	0.491279	+	0.871002i	$0.336529\pi$
$53$	−2.92011	+	9.62630i	−0.401107	+	1.32227i	−0.892387	+	0.451272i	$0.850971\pi$
$54$	−0.417946	−	1.35104i	−0.0568752	−	0.183854i
$55$	−0.302506	+	0.202128i	−0.0407899	+	0.0272549i
$56$	7.00016	−	0.115265i	0.935436	−	0.0154029i
$57$	−3.59675	+	5.38292i	−0.476402	+	0.712986i
$58$	1.30177	+	2.40361i	0.170930	+	0.315610i
$59$	−8.85770	−	7.26933i	−1.15317	−	0.946386i	−0.154044	−	0.988064i	$-0.549230\pi$
$59$	−8.85770	−	7.26933i	−1.15317	−	0.946386i	−0.999131	+	0.0416778i	$0.986730\pi$
$60$	0.686863	−	0.702110i	0.0886737	−	0.0906420i
$61$	0.238013	−	0.445291i	0.0304745	−	0.0570137i	−0.866223	−	0.499657i	$-0.833459\pi$
$61$	0.238013	−	0.445291i	0.0304745	−	0.0570137i	0.896698	+	0.442644i	$0.145959\pi$
$62$	−6.14637	+	9.30888i	−0.780589	+	1.18223i
$63$			2.47527i			0.311854i
$64$	2.81647	−	7.48782i	0.352059	−	0.935978i
$65$			1.19372i			0.148062i
$66$	−0.874293	−	0.577269i	−0.107618	−	0.0710569i
$67$	1.29140	−	2.41603i	0.157769	−	0.295165i	−0.790601	−	0.612332i	$-0.790232\pi$
$67$	1.29140	−	2.41603i	0.157769	−	0.295165i	0.948370	+	0.317167i	$0.102732\pi$
$68$	0.733778	−	0.00805453i	0.0889837	−	0.000976755i
$69$	5.74265	+	4.71287i	0.691334	+	0.567363i
$70$	−1.51168	+	0.818707i	−0.180680	+	0.0978543i
$71$	0.719325	−	1.07655i	0.0853682	−	0.127762i	−0.786328	−	0.617809i	$-0.788020\pi$
$71$	0.719325	−	1.07655i	0.0853682	−	0.127762i	0.871696	+	0.490047i	$0.163020\pi$
$72$	2.63059	+	1.03922i	0.310018	+	0.122474i
$73$	−0.675000	+	0.451021i	−0.0790028	+	0.0527880i	−0.594444	−	0.804137i	$-0.702628\pi$
$73$	−0.675000	+	0.451021i	−0.0790028	+	0.0527880i	0.515442	+	0.856925i	$0.327628\pi$
$74$	9.40006	−	2.90791i	1.09273	−	0.338037i
$75$	1.38141	−	4.55390i	0.159512	−	0.525839i
$76$	−3.89437	−	12.3484i	−0.446715	−	1.41646i
$77$	1.16330	+	1.41749i	0.132571	+	0.161538i
$78$	−3.16855	+	1.33288i	−0.358768	+	0.150919i
$79$	3.41873	+	8.25355i	0.384637	+	0.928597i	0.991055	+	0.133451i	$0.0426058\pi$
$79$	3.41873	+	8.25355i	0.384637	+	0.928597i	−0.606418	+	0.795146i	$0.707394\pi$
$80$	0.235414	+	1.95027i	0.0263201	+	0.218046i
$81$	−0.382683	+	0.923880i	−0.0425204	+	0.102653i
$82$	0.0393575	+	7.17127i	0.00434631	+	0.791934i
$83$	−11.2884	−	1.11181i	−1.23906	−	0.122037i	−0.542824	−	0.839847i	$-0.682645\pi$
$83$	−11.2884	−	1.11181i	−1.23906	−	0.122037i	−0.696239	+	0.717810i	$0.745145\pi$
$84$	−3.86106	−	3.09839i	−0.421276	−	0.338062i
$85$	−0.158915	+	0.0849420i	−0.0172368	+	0.00921326i
$86$	−7.03230	+	5.83614i	−0.758312	+	0.629327i
$87$	0.377083	−	1.89573i	0.0404276	−	0.203243i
$88$	1.99484	−	0.641179i	0.212651	−	0.0683499i
$89$	−9.94691	+	1.97856i	−1.05437	+	0.209727i	−0.691696	−	0.722189i	$-0.743136\pi$
$89$	−9.94691	+	1.97856i	−1.05437	+	0.209727i	−0.362674	+	0.931916i	$0.618136\pi$
$90$	−0.690800	+	0.0718680i	−0.0728167	+	0.00757555i
$91$	5.98758	−	0.589726i	0.627669	−	0.0618200i
$92$	−14.5397	+	3.05840i	−1.51587	+	0.318861i
$93$	7.54810	−	2.28969i	0.782702	−	0.237430i
$94$	−0.710042	+	3.67491i	−0.0732352	+	0.379038i
$95$	2.24818	+	2.24818i	0.230659	+	0.230659i
$96$	−4.91386	+	2.80250i	−0.501518	+	0.286029i
$97$	1.02015	−	1.02015i	0.103581	−	0.103581i	−0.653417	−	0.756998i	$-0.726665\pi$
$97$	1.02015	−	1.02015i	0.103581	−	0.103581i	0.756998	+	0.653417i	$0.226665\pi$
$98$	−0.691576	−	1.02282i	−0.0698597	−	0.103320i
$99$	0.215049	+	0.708920i	0.0216132	+	0.0712492i
$100$	5.37425	+	7.85510i	0.537425	+	0.785510i
$101$	−1.15179	−	11.6943i	−0.114607	−	1.16363i	−0.864697	−	0.502293i	$-0.832490\pi$
$101$	−1.15179	−	11.6943i	−0.114607	−	1.16363i	0.750090	−	0.661336i	$-0.230010\pi$
$102$	−0.402909	−	0.326975i	−0.0398939	−	0.0323753i
$103$	−1.68498	−	8.47094i	−0.166026	−	0.834667i	−0.970578	−	0.240786i	$-0.922595\pi$
$103$	−1.68498	−	8.47094i	−0.166026	−	0.834667i	0.804553	−	0.593881i	$-0.202405\pi$
$104$	1.88711	−	6.61090i	0.185047	−	0.648252i
$105$	1.19226	+	0.237155i	0.116353	+	0.0231440i
$106$	−1.31669	+	14.1652i	−0.127888	+	1.37584i
$107$	0.0725158	+	0.135668i	0.00701037	+	0.0131155i	0.885402	−	0.464826i	$-0.153883\pi$
$107$	0.0725158	+	0.135668i	0.00701037	+	0.0131155i	−0.878392	+	0.477941i	$0.841383\pi$
$108$	−0.962097	−	1.75339i	−0.0925778	−	0.168720i
$109$	−0.228073	+	2.31567i	−0.0218455	+	0.221801i	0.978063	+	0.208307i	$0.0667953\pi$
$109$	−0.228073	+	2.31567i	−0.0218455	+	0.221801i	−0.999909	+	0.0134938i	$0.995705\pi$
$110$	−0.361819	+	0.365812i	−0.0344981	+	0.0348788i
$111$	−6.42800	−	2.66257i	−0.610119	−	0.252720i
$112$	9.66608	−	2.14430i	0.913359	−	0.202617i
$113$	4.53955	−	1.88034i	0.427045	−	0.176888i	−0.158801	−	0.987311i	$-0.550763\pi$
$113$	4.53955	−	1.88034i	0.427045	−	0.176888i	0.585845	+	0.810423i	$0.300763\pi$
$114$	−3.45722	+	8.47777i	−0.323798	+	0.794016i
$115$	2.82025	−	2.31452i	0.262990	−	0.215830i
$116$	2.48505	+	2.96115i	0.230731	+	0.274936i
$117$	2.32600	+	0.705586i	0.215039	+	0.0652314i
$118$	−14.3333	−	7.56047i	−1.31949	−	0.695997i
$119$	0.504571	+	0.755143i	0.0462539	+	0.0692239i
$120$	0.752599	−	1.16751i	0.0687026	−	0.106578i
$121$	−8.68984	−	5.80637i	−0.789986	−	0.527852i
$122$	0.203525	−	0.684432i	0.0184263	−	0.0619655i
$123$	3.21696	−	3.91988i	0.290064	−	0.353444i
$124$	−5.87668	+	14.6400i	−0.527742	+	1.31471i
$125$	−4.22671	−	2.25922i	−0.378048	−	0.202071i
$126$	0.701757	+	3.42949i	0.0625175	+	0.305524i
$127$	17.8119			1.58055			0.790274	−	0.612753i	$-0.209938\pi$
$127$	17.8119			1.58055			0.790274	+	0.612753i	$0.209938\pi$
$128$	1.77938	−	11.1729i	0.157277	−	0.987555i
$129$	6.46195			0.568943
$130$	0.338427	+	1.65390i	0.0296820	+	0.145057i
$131$	−8.63086	−	4.61329i	−0.754082	−	0.403065i	0.0491041	−	0.998794i	$-0.484363\pi$
$131$	−8.63086	−	4.61329i	−0.754082	−	0.403065i	−0.803186	+	0.595729i	$0.796863\pi$
$132$	−1.37500	−	0.551940i	−0.119678	−	0.0480402i
$133$	10.1661	−	12.3874i	0.881509	−	1.07412i
$134$	1.10427	−	3.71354i	0.0953945	−	0.320801i
$135$	0.408340	+	0.272844i	0.0351443	+	0.0234827i
$136$	1.01437	−	0.219191i	0.0869815	−	0.0187955i
$137$	0.690622	+	1.03359i	0.0590038	+	0.0883055i	0.859798	−	0.510634i	$-0.170589\pi$
$137$	0.690622	+	1.03359i	0.0590038	+	0.0883055i	−0.800795	+	0.598939i	$0.795589\pi$
$138$	9.29260	+	4.90162i	0.791039	+	0.417254i
$139$	20.2956	+	6.15660i	1.72145	+	0.522196i	0.987583	−	0.157098i	$-0.0502139\pi$
$139$	20.2956	+	6.15660i	1.72145	+	0.522196i	0.733866	+	0.679294i	$0.237714\pi$
$140$	−1.86233	+	1.56290i	−0.157396	+	0.132089i
$141$	2.04586	−	1.67900i	0.172293	−	0.141397i
$142$	0.691419	−	1.69549i	0.0580226	−	0.142283i
$143$	1.66362	−	0.689093i	0.139119	−	0.0576249i
$144$	3.93933	+	0.694057i	0.328277	+	0.0578381i
$145$	−0.876985	−	0.363259i	−0.0728296	−	0.0301670i
$146$	−0.807348	+	0.816259i	−0.0668166	+	0.0675541i
$147$	−0.0855740	+	0.868848i	−0.00705803	+	0.0716614i
$148$	12.1994	−	6.69390i	1.00279	−	0.550236i
$149$	10.1289	+	18.9498i	0.829790	+	1.55243i	0.833556	+	0.552435i	$0.186301\pi$
$149$	10.1289	+	18.9498i	0.829790	+	1.55243i	−0.00376611	+	0.999993i	$0.501199\pi$
$150$	0.622886	−	6.70109i	0.0508585	−	0.547142i
$151$	4.88254	+	0.971198i	0.397336	+	0.0790350i	0.389714	−	0.920936i	$-0.372574\pi$
$151$	4.88254	+	0.971198i	0.397336	+	0.0790350i	0.00762170	+	0.999971i	$0.497574\pi$
$152$	−8.89654	−	16.0047i	−0.721605	−	1.29816i
$153$	0.0715808	+	0.359861i	0.00578697	+	0.0290930i
$154$	2.01363	+	1.63413i	0.162263	+	0.131682i
$155$	−0.379691	−	3.85506i	−0.0304975	−	0.309646i
$156$	−4.01217	+	2.74502i	−0.321230	+	0.219777i
$157$	−1.77342	−	5.84617i	−0.141534	−	0.466576i	0.857302	−	0.514814i	$-0.172139\pi$
$157$	−1.77342	−	5.84617i	−0.141534	−	0.466576i	−0.998836	+	0.0482388i	$0.984639\pi$
$158$	7.07661	+	10.4661i	0.562985	+	0.832638i
$159$	7.11311	−	7.11311i	0.564106	−	0.564106i
$160$	0.879082	+	2.63536i	0.0694976	+	0.208344i
$161$	−13.0027	−	13.0027i	−1.02476	−	1.02476i
$162$	−0.268283	+	1.38853i	−0.0210783	+	0.109093i
$163$	−7.14497	+	2.16740i	−0.559637	+	0.169764i	−0.557416	−	0.830233i	$-0.688207\pi$
$163$	−7.14497	+	2.16740i	−0.559637	+	0.169764i	−0.00222143	+	0.999998i	$0.500707\pi$
$164$	2.08764	+	9.92466i	0.163017	+	0.774986i
$165$	0.362069	−	0.0356607i	0.0281870	−	0.00277618i
$166$	−15.9553	+	1.65993i	−1.23837	+	0.128835i
$167$	4.89712	−	0.974098i	0.378951	−	0.0753779i	−0.00193992	−	0.999998i	$-0.500617\pi$
$167$	4.89712	−	0.974098i	0.378951	−	0.0753779i	0.380890	+	0.924620i	$0.375617\pi$
$168$	−6.22793	−	3.19820i	−0.480495	−	0.246746i
$169$	−1.38355	+	6.95558i	−0.106427	+	0.535045i
$170$	−0.196096	+	0.162741i	−0.0150399	+	0.0124817i
$171$	5.70955	−	3.05182i	0.436620	−	0.233378i
$172$	−8.08869	+	10.0797i	−0.616757	+	0.768570i
$173$	−0.154378	−	0.0152050i	−0.0117372	−	0.00115601i	0.0921468	−	0.995745i	$-0.470627\pi$
$173$	−0.154378	−	0.0152050i	−0.0117372	−	0.00115601i	−0.103884	+	0.994589i	$0.533127\pi$
$174$	−0.0150018	−	2.73344i	−0.00113728	−	0.207222i
$175$	−4.50776	+	10.8827i	−0.340754	+	0.822654i
$176$	2.58209	−	1.45391i	0.194632	−	0.109593i
$177$	4.38506	+	10.5865i	0.329601	+	0.795728i
$178$	−13.2206	+	5.56133i	−0.990923	+	0.416840i
$179$	−15.3595	−	18.7156i	−1.14802	−	1.39887i	−0.903157	−	0.429310i	$-0.858757\pi$
$179$	−15.3595	−	18.7156i	−1.14802	−	1.39887i	−0.244864	−	0.969557i	$-0.578743\pi$
$180$	−0.936732	+	0.295420i	−0.0698199	+	0.0220193i
$181$	5.40417	−	17.8152i	0.401689	−	1.32419i	−0.490072	−	0.871682i	$-0.663029\pi$
$181$	5.40417	−	17.8152i	0.401689	−	1.32419i	0.891760	−	0.452508i	$-0.149471\pi$
$182$	8.12863	−	2.51459i	0.602534	−	0.186394i
$183$	−0.419818	+	0.280513i	−0.0310338	+	0.0207361i
$184$	−19.2777	+	8.35955i	−1.42117	+	0.616274i
$185$	−1.89834	+	2.84107i	−0.139569	+	0.208880i
$186$	9.80879	−	5.31232i	0.719215	−	0.389518i
$187$	0.210116	+	0.172438i	0.0153652	+	0.0126099i
$188$	0.0580992	+	5.29291i	0.00423732	+	0.386025i
$189$	1.16683	−	2.18299i	0.0848746	−	0.158789i
$190$	3.75225	+	2.47749i	0.272217	+	0.179736i
$191$		−	0.756233i		−	0.0547191i	−0.999626	−	0.0273596i	$-0.991290\pi$
$191$		−	0.756233i		−	0.0547191i	0.999626	−	0.0273596i	$-0.00870990\pi$
$192$	−6.01364	+	5.27599i	−0.433997	+	0.380762i
$193$		−	11.5295i		−	0.829911i	−0.909842	−	0.414956i	$-0.863797\pi$
$193$		−	11.5295i		−	0.829911i	0.909842	−	0.414956i	$-0.136203\pi$
$194$	1.12420	−	1.70264i	0.0807130	−	0.122243i
$195$	0.562714	−	1.05276i	0.0402968	−	0.0753899i
$196$	−1.24816	−	1.22106i	−0.0891542	−	0.0872182i
$197$	18.2143	+	14.9481i	1.29771	+	1.06501i	0.993669	+	0.112347i	$0.0358369\pi$
$197$	18.2143	+	14.9481i	1.29771	+	1.06501i	0.304044	+	0.952658i	$0.401663\pi$
$198$	0.498935	+	0.921245i	0.0354578	+	0.0654700i
$199$	−6.73463	+	10.0791i	−0.477405	+	0.714488i	−0.989515	−	0.144433i	$-0.953864\pi$
$199$	−6.73463	+	10.0791i	−0.477405	+	0.714488i	0.512109	+	0.858920i	$0.328864\pi$
$200$	9.67304	+	9.35964i	0.683987	+	0.661827i
$201$	−2.27782	+	1.52199i	−0.160665	+	0.107353i
$202$	−4.91124	−	15.8760i	−0.345554	−	1.11703i
$203$	−1.38883	+	4.57835i	−0.0974765	+	0.321337i
$204$	−0.650931	−	0.338797i	−0.0455743	−	0.0237205i
$205$	−1.57987	−	1.92508i	−0.110343	−	0.134453i
$206$	−4.73612	−	11.2588i	−0.329981	−	0.784440i
$207$	−2.84293	−	6.86345i	−0.197598	−	0.477043i
$208$	0.740365	−	9.69445i	0.0513351	−	0.672189i
$209$	1.83537	−	4.43098i	0.126955	−	0.306497i
$210$	1.71912	−	0.00943491i	0.118630	−	0.000651071i
$211$	−11.3205	−	1.11497i	−0.779333	−	0.0767576i	−0.299475	−	0.954104i	$-0.596812\pi$
$211$	−11.3205	−	1.11497i	−0.779333	−	0.0767576i	−0.479857	+	0.877346i	$0.659312\pi$
$212$	2.19164	+	19.9992i	0.150523	+	1.37355i
$213$	−1.14187	+	0.610341i	−0.0782395	+	0.0418199i
$214$	0.138934	+	0.167409i	0.00949732	+	0.0114439i
$215$	0.619120	−	3.11253i	0.0422236	−	0.212272i
$216$	−1.83009	−	2.15657i	−0.124522	−	0.146736i
$217$	−19.1491	+	3.80900i	−1.29993	+	0.258572i
$218$	0.340513	+	3.27303i	0.0230624	+	0.221678i
$219$	0.807906	−	0.0795718i	0.0545933	−	0.00537697i
$220$	−0.397591	+	0.609413i	−0.0268056	+	0.0410866i
$221$	0.853437	−	0.258887i	0.0574084	−	0.0174146i
$222$	−9.66089	−	1.86661i	−0.648396	−	0.125279i
$223$	14.3472	+	14.3472i	0.960760	+	0.960760i	0.999259	−	0.0384989i	$-0.0122576\pi$
$223$	14.3472	+	14.3472i	0.960760	+	0.960760i	−0.0384989	+	0.999259i	$0.512258\pi$
$224$	12.7845	−	5.71134i	0.854199	−	0.381605i
$225$	−3.36499	+	3.36499i	−0.224333	+	0.224333i
$226$	5.75647	−	3.89222i	0.382915	−	0.258906i
$227$	2.08908	+	6.88677i	0.138657	+	0.457091i	0.998576	−	0.0533389i	$-0.0169864\pi$
$227$	2.08908	+	6.88677i	0.138657	+	0.457091i	−0.859919	+	0.510430i	$0.829486\pi$
$228$	−2.38648	+	12.7261i	−0.158049	+	0.842809i
$229$	−1.03919	−	10.5511i	−0.0686715	−	0.697233i	−0.966462	−	0.256810i	$-0.917328\pi$
$229$	−1.03919	−	10.5511i	−0.0686715	−	0.697233i	0.897790	−	0.440423i	$-0.145172\pi$
$230$	3.25128	−	4.00634i	0.214383	−	0.264170i
$231$	−0.357742	−	1.79849i	−0.0235377	−	0.118332i
$232$	4.28255	+	3.39816i	0.281163	+	0.223100i
$233$	8.68924	+	1.72840i	0.569251	+	0.113231i	0.471320	−	0.881962i	$-0.343778\pi$
$233$	8.68924	+	1.72840i	0.569251	+	0.113231i	0.0979307	+	0.995193i	$0.468778\pi$
$234$	3.42273	+	0.318153i	0.223751	+	0.0207983i
$235$	−0.612707	−	1.14629i	−0.0399686	−	0.0747759i
$236$	−22.0023	−	6.41146i	−1.43223	−	0.417351i
$237$	0.875644	−	8.89056i	0.0568792	−	0.577504i
$238$	0.913174	+	0.903205i	0.0591923	+	0.0585461i
$239$	21.4321	+	8.87748i	1.38633	+	0.574236i	0.946166	−	0.323682i	$-0.104921\pi$
$239$	21.4321	+	8.87748i	1.38633	+	0.574236i	0.440163	+	0.897918i	$0.354921\pi$
$240$	0.711733	−	1.83095i	0.0459421	−	0.118188i
$241$	19.0558	−	7.89317i	1.22749	−	0.508444i	0.327708	−	0.944779i	$-0.393724\pi$
$241$	19.0558	−	7.89317i	1.22749	−	0.508444i	0.899784	+	0.436335i	$0.143724\pi$
$242$	−13.6860	−	5.58111i	−0.879767	−	0.358768i
$243$	0.773010	−	0.634393i	0.0495886	−	0.0406963i
$244$	0.0879433	−	1.00598i	0.00562999	−	0.0644016i
$245$	0.410299	+	0.124463i	0.0262130	+	0.00795163i
$246$	3.34580	−	6.34304i	0.213320	−	0.404418i
$247$	−8.74252	−	13.0841i	−0.556273	−	0.832522i
$248$	−3.99161	+	21.9499i	−0.253467	+	1.39382i
$249$	9.43138	+	6.30184i	0.597689	+	0.399363i
$250$	−6.49663	−	1.93186i	−0.410883	−	0.122181i
$251$	15.2723	−	18.6094i	0.963980	−	1.17461i	−0.0206196	−	0.999787i	$-0.506564\pi$
$251$	15.2723	−	18.6094i	0.963980	−	1.17461i	0.984599	−	0.174825i	$-0.0559361\pi$
$252$	1.94457	+	4.55263i	0.122497	+	0.286789i
$253$	−4.85366	−	2.59434i	−0.305147	−	0.163104i
$254$	24.6784	−	5.04980i	1.54846	−	0.316853i
$255$	0.180192			0.0112841
$256$	−0.702260	−	15.9846i	−0.0438913	−	0.999036i
$257$	9.65253			0.602109			0.301054	−	0.953607i	$-0.402661\pi$
$257$	9.65253			0.602109			0.301054	+	0.953607i	$0.402661\pi$
$258$	8.95307	−	1.83201i	0.557394	−	0.114056i
$259$	15.1884	+	8.11838i	0.943763	+	0.504452i
$260$	0.937785	+	2.19554i	0.0581590	+	0.136161i
$261$	−1.22620	+	1.49413i	−0.0758997	+	0.0924841i
$262$	−13.2660	−	3.94482i	−0.819576	−	0.243712i
$263$	19.4975	+	13.0278i	1.20227	+	0.803331i	0.984962	−	0.172772i	$-0.0552723\pi$
$263$	19.4975	+	13.0278i	1.20227	+	0.803331i	0.217308	+	0.976103i	$0.430272\pi$
$264$	−2.06154	−	0.374893i	−0.126879	−	0.0230731i
$265$	−2.74466	−	4.10767i	−0.168603	−	0.252332i
$266$	10.5732	−	20.0449i	0.648285	−	1.22903i
$267$	9.70508	+	2.94400i	0.593941	+	0.180170i
$268$	0.477156	−	5.45820i	0.0291470	−	0.333413i
$269$	0.943970	−	0.774696i	0.0575549	−	0.0472341i	−0.605176	−	0.796092i	$-0.706897\pi$
$269$	0.943970	−	0.774696i	0.0575549	−	0.0472341i	0.662731	+	0.748858i	$0.269397\pi$
$270$	0.643110	+	0.262259i	0.0391384	+	0.0159606i
$271$	−27.3744	+	11.3388i	−1.66288	+	0.688786i	−0.998292	−	0.0584268i	$-0.981392\pi$
$271$	−27.3744	+	11.3388i	−1.66288	+	0.688786i	−0.664585	+	0.747213i	$0.731392\pi$
$272$	1.34327	−	0.591272i	0.0814478	−	0.0358511i
$273$	−5.55857	−	2.30244i	−0.336420	−	0.139350i
$274$	1.24989	+	1.23625i	0.0755087	+	0.0746844i
$275$	−0.345552	+	3.50845i	−0.0208376	+	0.211567i
$276$	14.2646	+	4.15670i	0.858628	+	0.250204i
$277$	3.31322	+	6.19860i	0.199072	+	0.372438i	0.961573	−	0.274550i	$-0.0885287\pi$
$277$	3.31322	+	6.19860i	0.199072	+	0.372438i	−0.762501	+	0.646987i	$0.776029\pi$
$278$	29.8651	+	2.77605i	1.79119	+	0.166496i
$279$	−7.73618	−	1.53882i	−0.463153	−	0.0921269i
$280$	−2.13717	+	2.69338i	−0.127721	+	0.160960i
$281$	−4.82980	−	24.2811i	−0.288122	−	1.44849i	−0.805432	−	0.592688i	$-0.798067\pi$
$281$	−4.82980	−	24.2811i	−0.288122	−	1.44849i	0.517310	−	0.855798i	$-0.326933\pi$
$282$	2.35854	−	2.90627i	0.140449	−	0.173066i
$283$	−1.93573	−	19.6538i	−0.115067	−	1.16830i	−0.863241	−	0.504793i	$-0.831569\pi$
$283$	−1.93573	−	19.6538i	−0.115067	−	1.16830i	0.748174	−	0.663503i	$-0.230931\pi$
$284$	0.477280	−	2.54514i	0.0283213	−	0.151026i
$285$	−0.922935	−	3.04251i	−0.0546699	−	0.180223i
$286$	2.10959	−	1.42639i	0.124743	−	0.0843442i
$287$	−8.87553	+	8.87553i	−0.523906	+	0.523906i
$288$	5.65472	−	0.155209i	0.333208	−	0.00914581i
$289$	−11.9256	−	11.9256i	−0.701507	−	0.701507i
$290$	−1.31805	−	0.254665i	−0.0773988	−	0.0149545i
$291$	−1.38059	+	0.418797i	−0.0809315	+	0.0245503i
$292$	−0.887169	+	1.35982i	−0.0519176	+	0.0795774i
$293$	−0.296358	+	0.0291888i	−0.0173134	+	0.00170522i	−0.106670	−	0.994294i	$-0.534019\pi$
$293$	−0.296358	+	0.0291888i	−0.0173134	+	0.00170522i	0.0893567	+	0.996000i	$0.471519\pi$
$294$	0.127762	+	1.22805i	0.00745121	+	0.0716215i
$295$	5.51931	−	1.09786i	0.321347	−	0.0639198i
$296$	15.0046	−	12.7331i	0.872123	−	0.740094i
$297$	0.144527	−	0.726585i	0.00838629	−	0.0421607i
$298$	19.4060	+	23.3834i	1.12416	+	1.35457i
$299$	−15.9251	+	8.51215i	−0.920973	+	0.492270i
$300$	−1.03680	−	9.46099i	−0.0598596	−	0.546231i
$301$	−15.9180	−	1.56779i	−0.917501	−	0.0903659i
$302$	7.04013	−	0.0386378i	0.405114	−	0.00222336i
$303$	−4.49688	+	10.8564i	−0.258339	+	0.623685i
$304$	−16.8637	−	19.6524i	−0.967198	−	1.12714i
$305$	0.0948919	+	0.229089i	0.00543350	+	0.0131176i
$306$	0.201199	+	0.478296i	0.0115018	+	0.0273423i
$307$	10.2266	+	12.4612i	0.583663	+	0.711196i	0.978195	−	0.207687i	$-0.0665934\pi$
$307$	10.2266	+	12.4612i	0.583663	+	0.711196i	−0.394532	+	0.918882i	$0.629093\pi$
$308$	3.25319	+	1.69322i	0.185368	+	0.0964802i
$309$	−2.50716	+	8.26500i	−0.142627	+	0.470179i
$310$	−1.61900	−	5.23357i	−0.0919532	−	0.297247i
$311$	7.75890	−	5.18433i	0.439967	−	0.293977i	−0.315790	−	0.948829i	$-0.602269\pi$
$311$	7.75890	−	5.18433i	0.439967	−	0.293977i	0.755757	+	0.654853i	$0.227269\pi$
$312$	−4.78064	+	4.94071i	−0.270651	+	0.279713i
$313$	−14.8489	+	22.2229i	−0.839309	+	1.25611i	0.125218	+	0.992129i	$0.460037\pi$
$313$	−14.8489	+	22.2229i	−0.839309	+	1.25611i	−0.964527	+	0.263985i	$0.914963\pi$
$314$	−4.11451	−	7.59713i	−0.232195	−	0.428731i
$315$	−0.939686	−	0.771180i	−0.0529453	−	0.0434511i
$316$	12.7719	+	12.4946i	0.718475	+	0.702874i
$317$	−0.598309	+	1.11936i	−0.0336044	+	0.0628693i	−0.898163	−	0.439663i	$-0.855098\pi$
$317$	−0.598309	+	1.11936i	−0.0336044	+	0.0628693i	0.864559	+	0.502532i	$0.167598\pi$
$318$	7.83863	−	11.8719i	0.439568	−	0.665741i
$319$			1.43191i			0.0801713i
$320$	1.96512	+	3.40208i	0.109853	+	0.190182i
$321$		−	0.153832i		−	0.00858605i
$322$	−21.7017	−	14.3290i	−1.20939	−	0.798522i
$323$	1.11975	−	2.09490i	0.0623043	−	0.116563i
$324$	0.0219523	+	1.99988i	0.00121957	+	0.111104i
$325$	8.94149	+	7.33809i	0.495985	+	0.407044i
$326$	−9.28492	+	5.02860i	−0.514244	+	0.278508i
$327$	1.29274	−	1.93472i	0.0714888	−	0.106990i
$328$	5.70615	+	13.1588i	0.315069	+	0.726574i
$329$	−5.44703	+	3.63959i	−0.300304	+	0.200657i
$330$	0.491538	−	0.152057i	0.0270583	−	0.00837048i
$331$	−6.48114	+	21.3655i	−0.356236	+	1.17435i	0.577500	+	0.816390i	$0.304028\pi$
$331$	−6.48114	+	21.3655i	−0.356236	+	1.17435i	−0.933736	+	0.357962i	$0.883472\pi$
$332$	−21.6356	+	6.82330i	−1.18741	+	0.374477i
$333$	4.41387	+	5.37831i	0.241878	+	0.294730i
$334$	6.50882	−	2.73799i	0.356147	−	0.149816i
$335$	0.514858	+	1.24298i	0.0281297	+	0.0679111i
$336$	−9.53554	−	2.66546i	−0.520206	−	0.145413i
$337$	−6.97957	+	16.8502i	−0.380201	+	0.917887i	0.611725	+	0.791071i	$0.290476\pi$
$337$	−6.97957	+	16.8502i	−0.380201	+	0.917887i	−0.991926	+	0.126817i	$0.959524\pi$
$338$	0.0550427	+	10.0292i	0.00299393	+	0.545519i
$339$	−4.88991	−	0.481614i	−0.265583	−	0.0261577i
$340$	−0.225554	+	0.281074i	−0.0122324	+	0.0152434i
$341$	−5.15342	+	2.75456i	−0.279073	+	0.149168i
$342$	7.04539	−	5.84701i	0.380971	−	0.316170i
$343$	3.80190	−	19.1135i	0.205283	−	1.03203i
$344$	−8.34925	+	16.2587i	−0.450161	+	0.876610i
$345$	−3.57829	+	0.711767i	−0.192649	+	0.0383202i
$346$	−0.218203	+	0.0227009i	−0.0117307	+	0.00122041i
$347$	30.7824	−	3.03180i	1.65248	−	0.162755i	0.771607	−	0.636100i	$-0.219453\pi$
$347$	30.7824	−	3.03180i	1.65248	−	0.162755i	0.880877	+	0.473344i	$0.156953\pi$
$348$	−0.795737	−	3.78295i	−0.0426560	−	0.202787i
$349$	−29.5463	+	8.96279i	−1.58158	+	0.479767i	−0.954256	−	0.298992i	$-0.903350\pi$
$349$	−29.5463	+	8.96279i	−1.58158	+	0.479767i	−0.627324	+	0.778759i	$0.715850\pi$
$350$	−3.16020	+	16.3560i	−0.168920	+	0.874265i
$351$	−1.71874	−	1.71874i	−0.0917397	−	0.0917397i
$352$	3.16530	−	2.74644i	0.168711	−	0.146386i
$353$	−1.61361	+	1.61361i	−0.0858839	+	0.0858839i	−0.748744	−	0.662860i	$-0.769343\pi$
$353$	−1.61361	+	1.61361i	−0.0858839	+	0.0858839i	0.662860	+	0.748744i	$0.269343\pi$
$354$	9.07686	+	13.4244i	0.482430	+	0.713499i
$355$	0.184580	+	0.608480i	0.00979651	+	0.0322948i
$356$	−16.7405	+	11.4534i	−0.887243	+	0.607028i
$357$	−0.0890195	−	0.903830i	−0.00471141	−	0.0478358i
$358$	−26.5866	−	21.5760i	−1.40515	−	1.14033i
$359$	−1.19192	−	5.99220i	−0.0629073	−	0.316256i	0.936500	−	0.350666i	$-0.114045\pi$
$359$	−1.19192	−	5.99220i	−0.0629073	−	0.316256i	−0.999408	+	0.0344099i	$0.989045\pi$
$360$	−1.21409	+	0.674877i	−0.0639883	+	0.0355691i
$361$	−22.4722	−	4.47001i	−1.18275	−	0.235264i
$362$	2.43677	−	26.2151i	0.128074	−	1.37784i
$363$	4.92665	+	9.21712i	0.258582	+	0.483774i
$364$	10.5494	−	5.78851i	0.552936	−	0.303400i
$365$	0.0390782	−	0.396768i	0.00204545	−	0.0207678i
$366$	−0.502132	+	0.507674i	−0.0262469	+	0.0265365i
$367$	−11.6008	−	4.80520i	−0.605555	−	0.250829i	0.0587715	−	0.998271i	$-0.481282\pi$
$367$	−11.6008	−	4.80520i	−0.605555	−	0.250829i	−0.664327	+	0.747442i	$0.731282\pi$
$368$	−24.3394	+	17.0476i	−1.26878	+	0.888666i
$369$	−4.68493	+	1.94056i	−0.243887	+	0.101022i
$370$	−1.82470	+	4.47451i	−0.0948616	+	0.232619i
$371$	−19.2478	+	15.7963i	−0.999298	+	0.820102i
$372$	12.0840	−	10.1411i	0.626528	−	0.525792i
$373$	−13.9131	−	4.22048i	−0.720391	−	0.218528i	−0.0912596	−	0.995827i	$-0.529089\pi$
$373$	−13.9131	−	4.22048i	−0.720391	−	0.218528i	−0.629131	+	0.777299i	$0.716589\pi$
$374$	0.340004	+	0.179344i	0.0175812	+	0.00927365i
$375$	2.66263	+	3.98491i	0.137498	+	0.205780i
$376$	1.58108	+	7.31688i	0.0815378	+	0.377340i
$377$	3.90637	+	2.61016i	0.201189	+	0.134430i
$378$	0.997758	−	3.35535i	0.0513192	−	0.172581i
$379$	−18.5506	+	22.6040i	−0.952880	+	1.16109i	0.0339662	+	0.999423i	$0.489186\pi$
$379$	−18.5506	+	22.6040i	−0.952880	+	1.16109i	−0.986846	+	0.161664i	$0.948314\pi$
$380$	5.90114	+	2.36879i	0.302722	+	0.121516i
$381$	−15.7087	−	8.39646i	−0.804780	−	0.430164i
$382$	−0.214398	−	1.04776i	−0.0109695	−	0.0536083i
$383$	22.5543			1.15247			0.576234	−	0.817284i	$-0.304522\pi$
$383$	22.5543			1.15247			0.576234	+	0.817284i	$0.304522\pi$
$384$	−6.83615	+	9.01483i	−0.348856	+	0.460036i
$385$	−0.900554			−0.0458965
$386$	−3.26870	−	15.9742i	−0.166372	−	0.813064i
$387$	−5.69893	−	3.04614i	−0.289693	−	0.154844i
$388$	1.07488	−	2.67774i	0.0545686	−	0.135942i
$389$	1.17511	−	1.43188i	0.0595804	−	0.0725990i	−0.742367	−	0.669993i	$-0.766297\pi$
$389$	1.17511	−	1.43188i	0.0595804	−	0.0725990i	0.801948	+	0.597394i	$0.203797\pi$
$390$	0.481176	−	1.61814i	0.0243653	−	0.0819378i
$391$	−2.26639	−	1.51435i	−0.114616	−	0.0765841i
$392$	−2.07551	−	1.33792i	−0.104829	−	0.0675749i
$393$	5.43705	+	8.13712i	0.274263	+	0.410463i
$394$	29.4738	+	15.5467i	1.48487	+	0.783233i
$395$	−4.19841	−	1.27358i	−0.211245	−	0.0640805i
$396$	0.952457	+	1.13494i	0.0478628	+	0.0570327i
$397$	9.65882	−	7.92679i	0.484762	−	0.397834i	−0.360020	−	0.932945i	$-0.617230\pi$
$397$	9.65882	−	7.92679i	0.484762	−	0.397834i	0.844782	+	0.535111i	$0.179730\pi$
$398$	−6.47337	+	15.8739i	−0.324481	+	0.795689i
$399$	−14.8050	+	6.13244i	−0.741179	+	0.307006i
$400$	16.0556	+	10.2255i	0.802778	+	0.511273i
$401$	−16.5526	−	6.85629i	−0.826595	−	0.342387i	−0.0710413	−	0.997473i	$-0.522632\pi$
$401$	−16.5526	−	6.85629i	−0.826595	−	0.342387i	−0.755554	+	0.655086i	$0.772632\pi$
$402$	−2.72443	+	2.75450i	−0.135882	+	0.137382i
$403$	−1.87923	+	19.0802i	−0.0936113	+	0.950451i
$404$	−11.3055	−	20.6039i	−0.562470	−	1.02508i
$405$	−0.231506	−	0.433117i	−0.0115036	−	0.0215217i
$406$	−0.626230	+	6.73706i	−0.0310793	+	0.334355i
$407$	5.05530	+	1.00556i	0.250582	+	0.0498439i
$408$	−0.997920	−	0.284861i	−0.0494044	−	0.0141027i
$409$	−4.76127	−	23.9365i	−0.235430	−	1.18358i	−0.899841	−	0.436218i	$-0.856318\pi$
$409$	−4.76127	−	23.9365i	−0.235430	−	1.18358i	0.664412	−	0.747367i	$-0.268682\pi$
$410$	−2.73469	−	2.21930i	−0.135057	−	0.109603i
$411$	−0.121844	−	1.23710i	−0.00601011	−	0.0610217i
$412$	−9.75388	−	14.2564i	−0.480539	−	0.702364i
$413$	−8.23345	−	27.1421i	−0.405142	−	1.33557i
$414$	−5.88474	−	8.70335i	−0.289219	−	0.427746i
$415$	3.93903	−	3.93903i	0.193359	−	0.193359i
$416$	−1.72267	−	13.6416i	−0.0844608	−	0.668834i
$417$	−14.9969	−	14.9969i	−0.734402	−	0.734402i
$418$	1.28670	−	6.65949i	0.0629346	−	0.325726i
$419$	−1.54642	+	0.469103i	−0.0755478	+	0.0229172i	−0.327832	−	0.944736i	$-0.606318\pi$
$419$	−1.54642	+	0.469103i	−0.0755478	+	0.0229172i	0.252285	+	0.967653i	$0.418818\pi$
$420$	2.37917	−	0.500455i	0.116092	−	0.0244197i
$421$	−13.9875	+	1.37765i	−0.681709	+	0.0671424i	−0.432943	−	0.901421i	$-0.642525\pi$
$421$	−13.9875	+	1.37765i	−0.681709	+	0.0671424i	−0.248766	+	0.968564i	$0.580025\pi$
$422$	−16.0007	+	1.66464i	−0.778900	+	0.0810335i
$423$	−2.59576	+	0.516329i	−0.126210	+	0.0251048i
$424$	8.70645	+	27.0876i	0.422823	+	1.31549i
$425$	−0.340640	+	1.71251i	−0.0165235	+	0.0830691i
$426$	−1.40903	+	1.16936i	−0.0682676	+	0.0566556i
$427$	1.10222	−	0.589146i	0.0533399	−	0.0285108i
$428$	0.239955	+	0.192558i	0.0115987	+	0.00930762i
$429$	−1.79202	−	0.176498i	−0.0865194	−	0.00852142i
$430$	−0.0246309	−	4.48794i	−0.00118781	−	0.216428i
$431$	−1.96723	+	4.74932i	−0.0947584	+	0.228767i	−0.964151	−	0.265356i	$-0.914511\pi$
$431$	−1.96723	+	4.74932i	−0.0947584	+	0.228767i	0.869392	+	0.494123i	$0.164511\pi$
$432$	−3.14700	−	2.46909i	−0.151410	−	0.118794i
$433$	9.80140	+	23.6627i	0.471025	+	1.13716i	0.963711	+	0.266948i	$0.0860152\pi$
$433$	9.80140	+	23.6627i	0.471025	+	1.13716i	−0.492686	+	0.870207i	$0.663985\pi$
$434$	−25.4513	+	10.7063i	−1.22170	+	0.513919i
$435$	0.602193	+	0.733774i	0.0288729	+	0.0351818i
$436$	1.39971	+	4.43826i	0.0670340	+	0.212554i
$437$	−13.9612	+	46.0239i	−0.667855	+	2.20162i
$438$	1.09680	−	0.339295i	0.0524071	−	0.0162121i
$439$	−13.3181	+	8.89884i	−0.635636	+	0.424719i	−0.831201	−	0.555972i	$-0.812346\pi$
$439$	−13.3181	+	8.89884i	−0.635636	+	0.424719i	0.195565	+	0.980691i	$0.437346\pi$
$440$	−0.378091	+	0.957064i	−0.0180248	+	0.0456263i
$441$	0.485042	−	0.725916i	0.0230972	−	0.0345674i
$442$	1.10904	−	0.600646i	0.0527519	−	0.0285698i
$443$	12.8752	+	10.5664i	0.611718	+	0.502024i	0.888480	−	0.458915i	$-0.151762\pi$
$443$	12.8752	+	10.5664i	0.611718	+	0.502024i	−0.276763	+	0.960938i	$0.589262\pi$
$444$	−13.9144	+	0.152735i	−0.660348	+	0.00724850i
$445$	2.34788	−	4.39258i	0.111300	−	0.208228i
$446$	23.9457	+	15.8106i	1.13386	+	0.748653i
$447$		−	21.4869i		−	1.01630i
$448$	16.0937	−	11.5376i	0.760358	−	0.545100i
$449$		−	23.9091i		−	1.12834i	−0.825659	−	0.564170i	$-0.809196\pi$
$449$		−	23.9091i		−	1.12834i	0.825659	−	0.564170i	$-0.190804\pi$
$450$	−3.70821	+	5.61621i	−0.174807	+	0.264751i
$451$	−1.77087	+	3.31306i	−0.0833870	+	0.156006i
$452$	6.87215	−	7.02469i	0.323239	−	0.330414i
$453$	−3.84820	−	3.15813i	−0.180804	−	0.148382i
$454$	4.84688	+	8.94938i	0.227475	+	0.420015i
$455$	−1.64158	+	2.45680i	−0.0769584	+	0.115176i
$456$	0.301471	+	18.3087i	0.0141177	+	0.857384i
$457$	27.0954	−	18.1046i	1.26747	−	0.846896i	0.274082	−	0.961706i	$-0.411626\pi$
$457$	27.0954	−	18.1046i	1.26747	−	0.846896i	0.993387	+	0.114810i	$0.0366259\pi$
$458$	−4.43110	−	14.3239i	−0.207052	−	0.669313i
$459$	0.106509	−	0.351112i	0.00497140	−	0.0163885i
$460$	3.36884	−	6.47256i	0.157073	−	0.301785i
$461$	14.9424	+	18.2074i	0.695937	+	0.848002i	0.994319	−	0.106445i	$-0.0339468\pi$
$461$	14.9424	+	18.2074i	0.695937	+	0.848002i	−0.298382	+	0.954447i	$0.596447\pi$
$462$	−1.00554	−	2.39040i	−0.0467820	−	0.111211i
$463$	9.70182	+	23.4223i	0.450882	+	1.08852i	0.971988	+	0.235032i	$0.0755196\pi$
$463$	9.70182	+	23.4223i	0.450882	+	1.08852i	−0.521106	+	0.853492i	$0.674480\pi$
$464$	6.89690	+	3.49404i	0.320181	+	0.162207i
$465$	−1.48241	+	3.57885i	−0.0687450	+	0.165965i
$466$	12.5290	−	0.0687620i	0.580394	−	0.00318534i
$467$	−34.8104	−	3.42852i	−1.61083	−	0.158653i	−0.747843	−	0.663875i	$-0.768911\pi$
$467$	−34.8104	−	3.42852i	−1.61083	−	0.158653i	−0.862989	+	0.505222i	$0.831411\pi$
$468$	4.83241	−	0.529567i	0.223378	−	0.0244793i
$469$	5.98032	−	3.19655i	0.276146	−	0.147603i
$470$	−1.17389	−	1.41449i	−0.0541475	−	0.0652455i
$471$	−1.19185	+	5.99185i	−0.0549177	+	0.276090i
$472$	−32.3020	−	2.64529i	−1.48682	−	0.121760i
$473$	−4.69516	+	0.933925i	−0.215884	+	0.0429419i
$474$	−1.30733	−	12.5662i	−0.0600477	−	0.577183i
$475$	30.6602	−	3.01976i	1.40678	−	0.138556i
$476$	1.52127	+	0.992504i	0.0697274	+	0.0454913i
$477$	−9.62630	+	2.92011i	−0.440758	+	0.133702i
$478$	32.2111	+	6.22362i	1.47330	+	0.284662i
$479$	11.1129	+	11.1129i	0.507759	+	0.507759i	0.913838	−	0.406079i	$-0.133104\pi$
$479$	11.1129	+	11.1129i	0.507759	+	0.507759i	−0.406079	+	0.913838i	$0.633104\pi$
$480$	0.467019	−	2.73858i	0.0213164	−	0.124998i
$481$	11.9584	−	11.9584i	0.545254	−	0.545254i
$482$	24.1641	−	16.3385i	1.10065	−	0.744198i
$483$	5.33793	+	17.5968i	0.242884	+	0.800683i
$484$	−20.5443	−	3.85259i	−0.933830	−	0.175118i
$485$	0.0694474	+	0.705112i	0.00315345	+	0.0320175i
$486$	0.891154	−	1.09811i	0.0404236	−	0.0498112i
$487$	−3.76330	−	18.9194i	−0.170531	−	0.857318i	−0.967417	−	0.253188i	$-0.918521\pi$
$487$	−3.76330	−	18.9194i	−0.170531	−	0.857318i	0.796886	−	0.604130i	$-0.206479\pi$
$488$	−0.163358	−	1.41873i	−0.00739488	−	0.0642228i
$489$	7.32301	+	1.45664i	0.331158	+	0.0658714i
$490$	0.603757	+	0.0561210i	0.0272749	+	0.00253529i
$491$	−11.1184	−	20.8011i	−0.501766	−	0.938739i	−0.997527	−	0.0702798i	$-0.977611\pi$
$491$	−11.1184	−	20.8011i	−0.501766	−	0.938739i	0.495761	−	0.868459i	$-0.334889\pi$
$492$	2.83732	−	9.73688i	0.127916	−	0.438972i
$493$	−0.0695128	+	0.705775i	−0.00313070	+	0.0317865i
$494$	−15.8222	−	15.6495i	−0.711876	−	0.704105i
$495$	−0.336127	−	0.139228i	−0.0151078	−	0.00625784i
$496$	0.692573	+	31.5434i	0.0310975	+	1.41634i
$497$	2.96090	−	1.22644i	0.132814	−	0.0550136i
$498$	14.8538	+	6.05737i	0.665616	+	0.271437i
$499$	17.5280	−	14.3849i	0.784663	−	0.643956i	−0.154281	−	0.988027i	$-0.549306\pi$
$499$	17.5280	−	14.3849i	0.784663	−	0.643956i	0.938944	+	0.344071i	$0.111806\pi$
$500$	−9.54880	−	0.834757i	−0.427036	−	0.0373315i
$501$	−4.77806	−	1.44941i	−0.213468	−	0.0647548i
$502$	15.8840	−	30.1132i	0.708936	−	1.34402i
$503$	−2.72838	−	4.08331i	−0.121653	−	0.182066i	0.765645	−	0.643263i	$-0.222420\pi$
$503$	−2.72838	−	4.08331i	−0.121653	−	0.182066i	−0.887298	+	0.461197i	$0.847420\pi$
$504$	3.98492	+	5.75639i	0.177503	+	0.256410i
$505$	4.79836	+	3.20616i	0.213524	+	0.142672i
$506$	−7.46028	−	2.21842i	−0.331650	−	0.0986206i
$507$	4.49902	−	5.48207i	0.199809	−	0.243467i
$508$	32.7604	−	13.9930i	1.45351	−	0.620841i
$509$	−5.21574	−	2.78787i	−0.231184	−	0.123570i	0.351738	−	0.936098i	$-0.385591\pi$
$509$	−5.21574	−	2.78787i	−0.231184	−	0.123570i	−0.582922	+	0.812528i	$0.698091\pi$
$510$	0.249657	−	0.0510858i	0.0110550	−	0.00226212i
$511$	−2.00946			−0.0888933
$512$	−5.50473	−	21.9476i	−0.243277	−	0.969957i
$513$	−6.47399			−0.285834
$514$	13.3736	−	2.73657i	0.589886	−	0.120705i
$515$	3.74079	+	1.99949i	0.164839	+	0.0881081i
$516$	11.8851	−	5.07652i	0.523214	−	0.223482i
$517$	−1.24383	+	1.51561i	−0.0547037	+	0.0666567i
$518$	23.3453	+	6.94202i	1.02573	+	0.305015i
$519$	0.128982	+	0.0861831i	0.00566169	+	0.00378302i
$520$	1.92176	+	2.77606i	0.0842746	+	0.121738i
$521$	19.6734	+	29.4434i	0.861909	+	1.28994i	0.955699	+	0.294345i	$0.0951016\pi$
$521$	19.6734	+	29.4434i	0.861909	+	1.28994i	−0.0937906	+	0.995592i	$0.529898\pi$
$522$	−1.27531	+	2.41775i	−0.0558186	+	0.105822i
$523$	2.74840	+	0.833718i	0.120179	+	0.0364560i	0.349801	−	0.936824i	$-0.386249\pi$
$523$	2.74840	+	0.833718i	0.120179	+	0.0364560i	−0.229622	+	0.973280i	$0.573749\pi$
$524$	−19.4985	−	1.70456i	−0.851796	−	0.0744641i
$525$	9.10555	−	7.47273i	0.397399	−	0.326137i
$526$	30.7074	+	12.5224i	1.33891	+	0.546004i
$527$	−2.67380	+	1.10752i	−0.116473	+	0.0482445i
$528$	−2.96257	+	0.0650467i	−0.128929	+	0.00283080i
$529$	29.7389	+	12.3183i	1.29300	+	0.535577i
$530$	−4.96729	−	4.91307i	−0.215765	−	0.213410i
$531$	1.12315	−	11.4035i	0.0487406	−	0.494871i
$532$	8.96634	−	30.7699i	0.388740	−	1.33405i
$533$	5.81032	+	10.8703i	0.251673	+	0.470846i
$534$	14.2811	+	1.32747i	0.618003	+	0.0574452i
$535$	−0.0740961	−	0.0147386i	−0.00320345	−	0.000637206i
$536$	−0.886338	−	7.69764i	−0.0382840	−	0.332487i
$537$	4.72339	+	23.7461i	0.203829	+	1.02472i
$538$	1.08824	−	1.34097i	0.0469175	−	0.0578132i
$539$	−0.0633949	−	0.643660i	−0.00273061	−	0.0277244i
$540$	0.965384	+	0.181035i	0.0415435	+	0.00779049i
$541$	−11.7557	−	38.7535i	−0.505419	−	1.66614i	−0.723588	−	0.690232i	$-0.757508\pi$
$541$	−11.7557	−	38.7535i	−0.505419	−	1.66614i	0.218169	−	0.975911i	$-0.429992\pi$
$542$	−34.7127	+	23.4709i	−1.49104	+	1.00816i
$543$	−13.1641	+	13.1641i	−0.564924	+	0.564924i
$544$	1.69348	−	1.20004i	0.0726073	−	0.0514512i
$545$	−0.808040	−	0.808040i	−0.0346126	−	0.0346126i
$546$	−8.35419	−	1.61414i	−0.357526	−	0.0690788i
$547$	27.6135	−	8.37647i	1.18067	−	0.358152i	0.361868	−	0.932229i	$-0.382139\pi$
$547$	27.6135	−	8.37647i	1.18067	−	0.358152i	0.818801	+	0.574077i	$0.194639\pi$
$548$	2.08221	+	1.35847i	0.0889478	+	0.0580310i
$549$	0.502479	−	0.0494899i	0.0214453	−	0.00211218i
$550$	0.515908	+	4.95894i	0.0219984	+	0.211450i
$551$	12.2729	−	2.44123i	0.522844	−	0.104000i
$552$	20.9421	+	1.71500i	0.891356	+	0.0729954i
$553$	−4.31403	+	21.6881i	−0.183451	+	0.922272i
$554$	6.34783	+	7.64886i	0.269693	+	0.324969i
$555$	3.01346	−	1.61073i	0.127914	−	0.0683716i
$556$	42.1652	−	4.62075i	1.78820	−	0.195963i
$557$	−39.1922	−	3.86009i	−1.66063	−	0.163557i	−0.776280	−	0.630389i	$-0.782895\pi$
$557$	−39.1922	−	3.86009i	−1.66063	−	0.163557i	−0.884346	+	0.466832i	$0.845395\pi$
$558$	−11.1548	+	0.0612200i	−0.472220	+	0.00259165i
$559$	−6.01076	+	14.5113i	−0.254228	+	0.613761i
$560$	−2.19747	+	4.33760i	−0.0928600	+	0.183297i
$561$	−0.104019	−	0.251124i	−0.00439169	−	0.0106025i
$562$	−13.5756	−	32.2722i	−0.572651	−	1.36132i
$563$	24.3271	+	29.6426i	1.02526	+	1.24929i	0.968006	+	0.250929i	$0.0807359\pi$
$563$	24.3271	+	29.6426i	1.02526	+	1.24929i	0.0572586	+	0.998359i	$0.481764\pi$
$564$	2.44382	−	4.69532i	0.102904	−	0.197709i
$565$	−0.700481	+	2.30918i	−0.0294694	+	0.0971478i
$566$	−8.25395	−	26.6816i	−0.346939	−	1.12151i
$567$	−2.05811	+	1.37518i	−0.0864325	+	0.0577523i
$568$	−0.0602921	−	3.66161i	−0.00252980	−	0.153638i
$569$	16.7260	−	25.0322i	0.701188	−	1.04940i	−0.294410	−	0.955679i	$-0.595123\pi$
$569$	16.7260	−	25.0322i	0.701188	−	1.04940i	0.995598	−	0.0937233i	$-0.0298769\pi$
$570$	−2.14130	−	3.95375i	−0.0896894	−	0.165604i
$571$	−22.3838	−	18.3699i	−0.936734	−	0.768758i	0.0363185	−	0.999340i	$-0.488437\pi$
$571$	−22.3838	−	18.3699i	−0.936734	−	0.768758i	−0.973053	+	0.230582i	$0.925937\pi$
$572$	2.51845	−	2.57435i	0.105302	−	0.107639i
$573$	−0.356486	+	0.666938i	−0.0148924	+	0.0278617i
$574$	−9.78081	+	14.8134i	−0.408243	+	0.618298i
$575$		−	35.3530i		−	1.47432i
$576$	7.79064	−	1.81820i	0.324610	−	0.0757583i
$577$			0.995066i			0.0414251i	0.999785	+	0.0207126i	$0.00659349\pi$
$577$			0.995066i			0.0414251i	−0.999785	+	0.0207126i	$0.993407\pi$
$578$	−19.9040	−	13.1420i	−0.827898	−	0.546635i
$579$	−5.43497	+	10.1681i	−0.225869	+	0.422572i
$580$	−1.89837	+	0.0208380i	−0.0788255	+	0.000865251i
$581$	−21.7038	−	17.8119i	−0.900426	−	0.738961i
$582$	−1.79408	+	0.971652i	−0.0743669	+	0.0402763i
$583$	−4.14024	+	6.19631i	−0.171471	+	0.256625i
$584$	−0.843658	+	2.13556i	−0.0349108	+	0.0883699i
$585$	−0.992538	+	0.663193i	−0.0410364	+	0.0274197i
$586$	−0.402331	+	0.124461i	−0.0166201	+	0.00514144i
$587$	−0.436117	+	1.43769i	−0.0180005	+	0.0593397i	−0.965481	−	0.260475i	$-0.916121\pi$
$587$	−0.436117	+	1.43769i	−0.0180005	+	0.0593397i	0.947480	+	0.319815i	$0.103621\pi$
$588$	0.525177	+	1.66525i	0.0216579	+	0.0686739i
$589$	32.3954	+	39.4739i	1.33483	+	1.62649i
$590$	7.33578	−	3.08586i	0.302009	−	0.127043i
$591$	−9.01708	−	21.7692i	−0.370913	−	0.895463i
$592$	17.1790	−	21.8956i	0.706052	−	0.899905i
$593$	18.0032	−	43.4635i	0.739302	−	1.78483i	0.130599	−	0.991435i	$-0.458310\pi$
$593$	18.0032	−	43.4635i	0.739302	−	1.78483i	0.608703	−	0.793398i	$-0.291690\pi$
$594$	−0.00574981	−	1.04766i	−0.000235917	−	0.0429861i
$595$	−0.443876	−	0.0437180i	−0.0181972	−	0.00179226i
$596$	33.5165	+	26.8961i	1.37289	+	1.10171i
$597$	10.6907	−	5.71428i	0.437540	−	0.233870i
$598$	−19.6511	+	16.3085i	−0.803592	+	0.666905i
$599$	8.43163	−	42.3886i	0.344507	−	1.73195i	−0.288208	−	0.957568i	$-0.593059\pi$
$599$	8.43163	−	42.3886i	0.344507	−	1.73195i	0.632715	−	0.774385i	$-0.281941\pi$
$600$	−4.11875	−	12.8143i	−0.168147	−	0.523142i
$601$	−15.9170	+	3.16609i	−0.649268	+	0.129147i	−0.508728	−	0.860928i	$-0.669884\pi$
$601$	−15.9170	+	3.16609i	−0.649268	+	0.129147i	−0.140540	+	0.990075i	$0.544884\pi$
$602$	−22.4990	+	2.34070i	−0.916991	+	0.0954000i
$603$	2.72632	−	0.268519i	0.111024	−	0.0109349i
$604$	9.74317	−	2.04946i	0.396444	−	0.0833914i
$605$	4.91163	−	1.48993i	0.199686	−	0.0605741i
$606$	−3.15257	+	16.3165i	−0.128064	+	0.662814i
$607$	6.88231	+	6.88231i	0.279344	+	0.279344i	0.832847	−	0.553503i	$-0.186709\pi$
$607$	6.88231	+	6.88231i	0.279344	+	0.279344i	−0.553503	+	0.832847i	$0.686709\pi$
$608$	−28.9363	−	22.4475i	−1.17352	−	0.910367i
$609$	3.38305	−	3.38305i	0.137088	−	0.137088i
$610$	0.196422	+	0.290502i	0.00795288	+	0.0117621i
$611$	1.86741	+	6.15604i	0.0755475	+	0.249047i
$612$	0.414362	+	0.605639i	0.0167496	+	0.0244815i
$613$	−2.79093	−	28.3368i	−0.112725	−	1.14451i	−0.870559	−	0.492065i	$-0.836242\pi$
$613$	−2.79093	−	28.3368i	−0.112725	−	1.14451i	0.757834	−	0.652447i	$-0.226258\pi$
$614$	17.7018	+	14.3657i	0.714388	+	0.579751i
$615$	0.485845	+	2.44251i	0.0195912	+	0.0984915i
$616$	4.98735	+	1.42366i	0.200946	+	0.0573610i
$617$	32.9808	+	6.56030i	1.32776	+	0.264108i	0.807483	−	0.589891i	$-0.200829\pi$
$617$	32.9808	+	6.56030i	1.32776	+	0.264108i	0.520276	+	0.853998i	$0.325829\pi$
$618$	−1.13049	+	12.1620i	−0.0454751	+	0.489227i
$619$	10.2936	+	19.2580i	0.413735	+	0.774043i	0.999331	−	0.0365593i	$-0.0116398\pi$
$619$	10.2936	+	19.2580i	0.413735	+	0.774043i	−0.585597	+	0.810603i	$0.699140\pi$
$620$	−3.72689	−	6.79213i	−0.149676	−	0.272779i
$621$	−0.728164	+	7.39317i	−0.0292202	+	0.296678i
$622$	9.28020	−	9.38262i	0.372102	−	0.376209i
$623$	−23.1927	−	9.60674i	−0.929197	−	0.384886i
$624$	−5.22287	+	8.20073i	−0.209082	+	0.328292i
$625$	−19.8083	+	8.20488i	−0.792334	+	0.328195i
$626$	−14.2728	+	34.9998i	−0.570457	+	1.39887i
$627$	−3.70740	+	3.04259i	−0.148059	+	0.121509i
$628$	−7.85452	−	9.35936i	−0.313429	−	0.373479i
$629$	2.44290	+	0.741047i	0.0974050	+	0.0295475i
$630$	−1.52057	−	0.802066i	−0.0605811	−	0.0319551i
$631$	−20.2363	−	30.2857i	−0.805594	−	1.20566i	−0.975457	−	0.220189i	$-0.929333\pi$
$631$	−20.2363	−	30.2857i	−0.805594	−	1.20566i	0.169863	−	0.985468i	$-0.445667\pi$
$632$	21.2378	+	13.6903i	0.844795	+	0.544572i
$633$	9.45816	+	6.31974i	0.375928	+	0.251187i
$634$	−0.511613	+	1.72050i	−0.0203188	+	0.0683297i
$635$	−5.54937	+	6.76192i	−0.220220	+	0.268339i
$636$	7.49469	−	18.6708i	0.297184	−	0.740347i
$637$	−1.87152	−	1.00035i	−0.0741525	−	0.0396353i
$638$	0.405956	+	1.98391i	0.0160719	+	0.0785438i
$639$	1.29475			0.0512195
$640$	3.68720	+	4.15647i	0.145749	+	0.164299i
$641$	14.5334			0.574033			0.287017	−	0.957926i	$-0.407336\pi$
$641$	14.5334			0.574033			0.287017	+	0.957926i	$0.407336\pi$
$642$	−0.0436125	−	0.213135i	−0.00172125	−	0.00841176i
$643$	22.2473	+	11.8914i	0.877348	+	0.468952i	0.847619	−	0.530606i	$-0.178035\pi$
$643$	22.2473	+	11.8914i	0.877348	+	0.468952i	0.0297292	+	0.999558i	$0.490535\pi$
$644$	−34.1302	−	13.7002i	−1.34492	−	0.539865i
$645$	−2.01325	+	2.45315i	−0.0792716	+	0.0965927i
$646$	0.957494	−	3.21995i	0.0376721	−	0.126687i
$647$	30.5640	+	20.4222i	1.20160	+	0.802880i	0.984860	−	0.173350i	$-0.0554593\pi$
$647$	30.5640	+	20.4222i	1.20160	+	0.802880i	0.216735	+	0.976230i	$0.430459\pi$
$648$	0.597396	+	2.76462i	0.0234679	+	0.108604i
$649$	−4.71615	−	7.05821i	−0.185125	−	0.277059i
$650$	14.4689	+	7.63198i	0.567516	+	0.299351i
$651$	18.6836	+	5.66760i	0.732267	+	0.222131i
$652$	−11.4387	+	9.59949i	−0.447972	+	0.375945i
$653$	−8.82768	+	7.24469i	−0.345454	+	0.283507i	−0.791080	−	0.611712i	$-0.790481\pi$
$653$	−8.82768	+	7.24469i	−0.345454	+	0.283507i	0.445626	+	0.895219i	$0.352981\pi$
$654$	1.24259	−	3.04707i	0.0485891	−	0.119150i
$655$	4.44032	−	1.83924i	0.173498	−	0.0718652i
$656$	11.6365	+	16.6139i	0.454330	+	0.648662i
$657$	−0.750020	−	0.310668i	−0.0292611	−	0.0121203i
$658$	−6.51503	+	6.58694i	−0.253982	+	0.256786i
$659$	0.266457	−	2.70538i	0.0103797	−	0.105387i	−0.988599	−	0.150573i	$-0.951888\pi$
$659$	0.266457	−	2.70538i	0.0103797	−	0.105387i	0.998979	+	0.0451863i	$0.0143881\pi$
$660$	0.637919	−	0.350031i	0.0248310	−	0.0136249i
$661$	4.47772	+	8.37722i	0.174163	+	0.325836i	0.953824	−	0.300366i	$-0.0971087\pi$
$661$	4.47772	+	8.37722i	0.174163	+	0.325836i	−0.779661	+	0.626202i	$0.784609\pi$
$662$	−2.92239	+	31.4394i	−0.113582	+	1.22193i
$663$	−0.874703	−	0.173989i	−0.0339707	−	0.00675718i
$664$	−28.0418	+	15.5876i	−1.08823	+	0.604915i
$665$	1.53534	+	7.71868i	0.0595380	+	0.299318i
$666$	7.64023	+	6.20031i	0.296053	+	0.240257i
$667$	−1.40744	−	14.2900i	−0.0544964	−	0.553311i
$668$	8.24176	−	5.63879i	0.318883	−	0.218171i
$669$	−5.88988	−	19.4163i	−0.227716	−	0.750679i
$670$	1.06573	+	1.57618i	0.0411728	+	0.0608933i
$671$	0.264492	−	0.264492i	0.0102106	−	0.0102106i
$672$	−13.9672	−	0.989606i	−0.538797	−	0.0381749i
$673$	29.4051	+	29.4051i	1.13348	+	1.13348i	0.989594	+	0.143889i	$0.0459609\pi$
$673$	29.4051	+	29.4051i	1.13348	+	1.13348i	0.143889	+	0.989594i	$0.454039\pi$
$674$	−4.89308	+	25.3247i	−0.188474	+	0.975473i
$675$	4.55390	−	1.38141i	0.175280	−	0.0531705i
$676$	2.91963	+	13.8800i	0.112293	+	0.533844i
$677$	13.8641	−	1.36550i	0.532842	−	0.0524803i	0.171981	−	0.985100i	$-0.444983\pi$
$677$	13.8641	−	1.36550i	0.532842	−	0.0524803i	0.360860	+	0.932620i	$0.382483\pi$
$678$	−6.91153	+	0.719047i	−0.265436	+	0.0276148i
$679$	3.50248	−	0.696686i	0.134413	−	0.0267363i
$680$	−0.232820	+	0.453375i	−0.00892823	+	0.0173861i
$681$	1.40400	−	7.05837i	0.0538013	−	0.270477i
$682$	−6.35915	+	5.27749i	−0.243504	+	0.202085i
$683$	−9.89117	+	5.28694i	−0.378475	+	0.202299i	−0.649654	−	0.760230i	$-0.725086\pi$
$683$	−9.89117	+	5.28694i	−0.378475	+	0.202299i	0.271179	+	0.962529i	$0.412586\pi$
$684$	8.10375	−	10.0985i	0.309855	−	0.386125i
$685$	−0.607548	−	0.0598382i	−0.0232132	−	0.00228630i
$686$	−0.151254	−	27.5596i	−0.00577489	−	1.05223i
$687$	−4.05725	+	9.79507i	−0.154794	+	0.373705i
$688$	−6.95847	+	24.8936i	−0.265289	+	0.949058i
$689$	9.35707	+	22.5900i	0.356476	+	0.860609i
$690$	−4.75595	+	2.00063i	−0.181056	+	0.0761627i
$691$	−16.0668	−	19.5774i	−0.611208	−	0.744760i	0.371802	−	0.928312i	$-0.378740\pi$
$691$	−16.0668	−	19.5774i	−0.611208	−	0.744760i	−0.983010	+	0.183553i	$0.941240\pi$
$692$	−0.295885	+	0.0933144i	−0.0112479	+	0.00354728i
$693$	−0.532303	+	1.75477i	−0.0202205	+	0.0666581i
$694$	41.7896	−	12.9276i	1.58631	−	0.490725i
$695$	−8.66041	+	5.78670i	−0.328508	+	0.219502i
$696$	−2.17499	−	5.01569i	−0.0824428	−	0.190119i
$697$	−1.03368	+	1.54702i	−0.0391535	+	0.0585974i
$698$	−38.3956	+	20.7946i	−1.45329	+	0.787087i
$699$	−6.84846	−	5.62039i	−0.259033	−	0.212583i
$700$	0.258583	+	23.5573i	0.00977352	+	0.890381i
$701$	−12.4828	+	23.3536i	−0.471468	+	0.882054i	0.527994	+	0.849248i	$0.322944\pi$
$701$	−12.4828	+	23.3536i	−0.471468	+	0.882054i	−0.999462	+	0.0328060i	$0.989556\pi$
$702$	−2.86860	−	1.89405i	−0.108268	−	0.0714863i
$703$		−	45.0435i		−	1.69885i
$704$	3.60690	−	4.70259i	0.135940	−	0.177236i
$705$			1.29977i			0.0489521i
$706$	−1.77820	+	2.69314i	−0.0669233	+	0.101358i
$707$	13.7114	−	25.6521i	0.515668	−	0.964748i
$708$	16.3820	+	16.0262i	0.615672	+	0.602302i
$709$	27.1986	+	22.3213i	1.02147	+	0.838295i	0.986937	−	0.161108i	$-0.0515069\pi$
$709$	27.1986	+	22.3213i	1.02147	+	0.838295i	0.0345291	+	0.999404i	$0.489007\pi$
$710$	0.428245	+	0.790722i	0.0160718	+	0.0296753i
$711$	−4.96323	+	7.42800i	−0.186136	+	0.278572i
$712$	−19.9469	+	20.6148i	−0.747541	+	0.772571i
$713$	48.7221	−	32.5551i	1.82466	−	1.21920i
$714$	−0.379580	−	1.22702i	−0.0142054	−	0.0459202i
$715$	−0.256707	+	0.846249i	−0.00960029	+	0.0316479i
$716$	−42.9529	−	22.3561i	−1.60522	−	0.835488i
$717$	−14.7166	−	17.9323i	−0.549603	−	0.669693i
$718$	−3.35025	−	7.96431i	−0.125030	−	0.297225i
$719$	−15.8309	−	38.2191i	−0.590391	−	1.42533i	−0.883125	−	0.469137i	$-0.844565\pi$
$719$	−15.8309	−	38.2191i	−0.590391	−	1.42533i	0.292734	−	0.956194i	$-0.405435\pi$
$720$	−1.49080	+	1.27925i	−0.0555588	+	0.0476748i
$721$	8.18125	−	19.7513i	0.304686	−	0.735576i
$722$	−32.4027	+	0.177833i	−1.20590	+	0.00661827i
$723$	−20.5265	−	2.02169i	−0.763390	−	0.0751873i
$724$	−4.05602	−	37.0120i	−0.150741	−	1.37554i
$725$	−8.11205	+	4.33598i	−0.301274	+	0.161034i
$726$	9.43903	+	11.3736i	0.350315	+	0.422115i
$727$	6.93358	−	34.8574i	0.257152	−	1.29279i	−0.609064	−	0.793121i	$-0.708455\pi$
$727$	6.93358	−	34.8574i	0.257152	−	1.29279i	0.866216	−	0.499670i	$-0.166545\pi$
$728$	12.9751	−	11.0108i	0.480889	−	0.408088i
$729$	−0.980785	+	0.195090i	−0.0363254	+	0.00722557i
$730$	−0.0583436	−	0.560802i	−0.00215939	−	0.0207562i
$731$	−2.35955	+	0.232395i	−0.0872710	+	0.00859544i
$732$	−0.551777	+	0.845743i	−0.0203943	+	0.0312596i
$733$	−15.0990	+	4.58023i	−0.557694	+	0.169175i	−0.556534	−	0.830825i	$-0.687869\pi$
$733$	−15.0990	+	4.58023i	−0.557694	+	0.169175i	−0.00115966	+	0.999999i	$0.500369\pi$
$734$	−17.4352	−	3.36872i	−0.643546	−	0.124342i
$735$	−0.303180	−	0.303180i	−0.0111830	−	0.0111830i
$736$	−28.8893	+	30.5199i	−1.06487	+	1.12498i
$737$	1.43506	−	1.43506i	0.0528611	−	0.0528611i
$738$	−5.94082	+	4.01687i	−0.218685	+	0.147863i
$739$	0.216045	+	0.712206i	0.00794735	+	0.0261989i	0.960824	−	0.277158i	$-0.0893926\pi$
$739$	0.216045	+	0.712206i	0.00794735	+	0.0261989i	−0.952877	+	0.303357i	$0.901893\pi$
$740$	−1.25957	+	6.71678i	−0.0463027	+	0.246914i
$741$	1.54241	+	15.6603i	0.0566618	+	0.575297i
$742$	−22.1896	+	27.3427i	−0.814606	+	1.00378i
$743$	3.16656	+	15.9194i	0.116170	+	0.584025i	0.994391	+	0.105770i	$0.0337306\pi$
$743$	3.16656	+	15.9194i	0.116170	+	0.584025i	−0.878221	+	0.478255i	$0.841269\pi$
$744$	13.8674	−	17.4765i	0.508404	−	0.640719i
$745$	−10.3496	−	2.05866i	−0.379180	−	0.0754236i
$746$	−20.4732	−	1.90304i	−0.749575	−	0.0696752i
$747$	−5.34706	−	10.0037i	−0.195639	−	0.366014i
$748$	0.521922	+	0.152088i	0.0190834	+	0.00556089i
$749$	−0.0373225	+	0.378941i	−0.00136373	+	0.0138462i
$750$	4.81884	+	4.76624i	0.175959	+	0.174038i
$751$	24.9381	+	10.3297i	0.910004	+	0.376936i	0.788058	−	0.615601i	$-0.211087\pi$
$751$	24.9381	+	10.3297i	0.910004	+	0.376936i	0.121946	+	0.992537i	$0.461087\pi$
$752$	4.26498	+	9.68933i	0.155528	+	0.353334i
$753$	−22.2414	+	9.21268i	−0.810521	+	0.335729i
$754$	6.15230	+	2.50890i	0.224054	+	0.0913687i
$755$	−1.88987	+	1.55098i	−0.0687795	+	0.0564459i
$756$	0.431132	−	4.93173i	0.0156801	−	0.179365i
$757$	−23.1385	−	7.01899i	−0.840984	−	0.255110i	−0.159733	−	0.987160i	$-0.551063\pi$
$757$	−23.1385	−	7.01899i	−0.840984	−	0.255110i	−0.681250	+	0.732051i	$0.738563\pi$
$758$	−19.2935	+	36.5771i	−0.700773	+	1.32854i
$759$	3.05758	+	4.57600i	0.110983	+	0.166098i
$760$	8.84763	+	1.60895i	0.320937	+	0.0583627i
$761$	2.15070	+	1.43705i	0.0779628	+	0.0520931i	0.593941	−	0.804509i	$-0.297571\pi$
$761$	2.15070	+	1.43705i	0.0779628	+	0.0520931i	−0.515978	+	0.856602i	$0.672571\pi$
$762$	−24.1449	−	7.17981i	−0.874677	−	0.260097i
$763$	−3.65387	+	4.45226i	−0.132279	+	0.161182i
$764$	−0.594098	−	1.39090i	−0.0214937	−	0.0503210i
$765$	−0.158915	−	0.0849420i	−0.00574560	−	0.00307109i
$766$	31.2490	−	6.39430i	1.12907	−	0.231036i
$767$	−27.8523			−1.00569
$768$	−6.91574	+	14.4282i	−0.249550	+	0.520632i
$769$	53.4795			1.92852			0.964261	−	0.264956i	$-0.0853573\pi$
$769$	53.4795			1.92852			0.964261	+	0.264956i	$0.0853573\pi$
$770$	−1.24772	+	0.255314i	−0.0449648	+	0.00920087i
$771$	−8.51278	−	4.55017i	−0.306580	−	0.163870i
$772$	−9.05759	−	21.2056i	−0.325990	−	0.763206i
$773$	22.4262	−	27.3264i	0.806615	−	0.982863i	−0.193384	−	0.981123i	$-0.561946\pi$
$773$	22.4262	−	27.3264i	0.806615	−	0.982863i	0.999998	−	0.00173946i	$-0.000553689\pi$
$774$	−8.75951	−	2.60476i	−0.314854	−	0.0936260i
$775$	−31.2103	−	20.8541i	−1.12111	−	0.749100i
$776$	0.730087	−	4.01476i	0.0262086	−	0.144121i
$777$	−9.56801	−	14.3195i	−0.343251	−	0.513711i
$778$	1.22217	−	2.31702i	0.0438170	−	0.0830693i
$779$	31.4155	+	9.52979i	1.12558	+	0.341440i
$780$	0.207917	−	2.37836i	0.00744461	−	0.0851590i
$781$	0.741454	−	0.608495i	0.0265313	−	0.0217737i
$782$	−3.56942	−	1.45560i	−0.127642	−	0.0520523i
$783$	1.78574	−	0.739676i	0.0638170	−	0.0264339i
$784$	−3.25494	−	1.26527i	−0.116248	−	0.0451881i
$785$	2.77190	+	1.14816i	0.0989333	+	0.0409795i
$786$	9.83999	+	9.73257i	0.350981	+	0.347149i
$787$	1.96776	−	19.9790i	0.0701429	−	0.712173i	−0.894227	−	0.447614i	$-0.852274\pi$
$787$	1.96776	−	19.9790i	0.0701429	−	0.712173i	0.964370	−	0.264559i	$-0.0852262\pi$
$788$	45.2438	+	13.1840i	1.61174	+	0.469661i
$789$	−11.0540	−	20.6806i	−0.393533	−	0.736249i
$790$	−6.17799	−	0.574262i	−0.219803	−	0.0204313i
$791$	11.9287	+	2.37277i	0.424136	+	0.0843658i
$792$	1.64140	+	1.30243i	0.0583245	+	0.0462799i
$793$	−0.239429	−	1.20369i	−0.00850236	−	0.0427442i
$794$	11.1350	−	13.7210i	0.395168	−	0.486938i
$795$	0.484230	+	4.91647i	0.0171739	+	0.174369i
$796$	−4.46850	+	23.8287i	−0.158382	+	0.844585i
$797$	7.23028	+	23.8350i	0.256110	+	0.844280i	0.986852	+	0.161627i	$0.0516741\pi$
$797$	7.23028	+	23.8350i	0.256110	+	0.844280i	−0.730742	+	0.682653i	$0.760826\pi$
$798$	−18.7738	+	12.6939i	−0.664587	+	0.449358i
$799$	−0.686652	+	0.686652i	−0.0242920	+	0.0242920i
$800$	25.1441	+	9.61554i	0.888977	+	0.339961i
$801$	−7.17132	−	7.17132i	−0.253386	−	0.253386i
$802$	−24.8775	−	4.80665i	−0.878454	−	0.169729i
$803$	−0.575513	+	0.174580i	−0.0203094	+	0.00616079i
$804$	−2.99379	+	4.58877i	−0.105583	+	0.161834i
$805$	8.98727	−	0.885169i	0.316760	−	0.0311981i
$806$	2.80569	+	26.9684i	0.0988261	+	0.949923i
$807$	−1.19770	+	0.238237i	−0.0421609	+	0.00838633i
$808$	−21.5052	−	25.3416i	−0.756551	−	0.891515i
$809$	9.87484	−	49.6442i	0.347181	−	1.74540i	−0.274000	−	0.961730i	$-0.588347\pi$
$809$	9.87484	−	49.6442i	0.347181	−	1.74540i	0.621181	−	0.783667i	$-0.286653\pi$
$810$	−0.443544	−	0.534452i	−0.0155845	−	0.0187787i
$811$	−30.7057	+	16.4126i	−1.07822	+	0.576323i	−0.912178	−	0.409795i	$-0.865600\pi$
$811$	−30.7057	+	16.4126i	−1.07822	+	0.576323i	−0.166046	+	0.986118i	$0.553100\pi$
$812$	1.04236	+	9.51178i	0.0365798	+	0.333798i
$813$	29.4872	+	2.90423i	1.03416	+	0.101856i
$814$	7.28923	−	0.0400050i	0.255487	−	0.00140217i
$815$	1.40323	−	3.38771i	0.0491532	−	0.118666i
$816$	−1.46338	−	0.111759i	−0.0512287	−	0.00391234i
$817$	16.0094	+	38.6501i	0.560098	+	1.35220i
$818$	−13.3829	−	31.8143i	−0.467924	−	1.11236i
$819$	3.81686	+	4.65086i	0.133372	+	0.162514i
$820$	−4.41811	−	2.29954i	−0.154287	−	0.0803035i
$821$	−8.68213	+	28.6212i	−0.303009	+	0.998885i	0.664763	+	0.747054i	$0.268533\pi$
$821$	−8.68213	+	28.6212i	−0.303009	+	0.998885i	−0.967771	+	0.251831i	$0.918967\pi$
$822$	−0.519543	−	1.67947i	−0.0181211	−	0.0585781i
$823$	−31.9315	+	21.3359i	−1.11306	+	0.743724i	−0.969298	−	0.245888i	$-0.920921\pi$
$823$	−31.9315	+	21.3359i	−1.11306	+	0.743724i	−0.143764	+	0.989612i	$0.545921\pi$
$824$	−17.5558	−	16.9871i	−0.611587	−	0.591772i
$825$	1.95862	−	2.93128i	0.0681904	−	0.102054i
$826$	−19.1025	−	35.2712i	−0.664660	−	1.22724i
$827$	12.5611	+	10.3086i	0.436791	+	0.358465i	0.826943	−	0.562285i	$-0.190078\pi$
$827$	12.5611	+	10.3086i	0.436791	+	0.358465i	−0.390152	+	0.920750i	$0.627578\pi$
$828$	−10.6208	−	10.3902i	−0.369098	−	0.361083i
$829$	−22.0978	+	41.3420i	−0.767487	+	1.43587i	0.128464	+	0.991714i	$0.458995\pi$
$829$	−22.0978	+	41.3420i	−0.767487	+	1.43587i	−0.895951	+	0.444153i	$0.853505\pi$
$830$	4.34080	−	6.57428i	0.150671	−	0.228197i
$831$		−	7.02852i		−	0.243817i
$832$	−6.25426	−	18.4121i	−0.216827	−	0.638325i
$833$		−	0.320332i		−	0.0110989i
$834$	−25.0300	−	16.5266i	−0.866719	−	0.572268i
$835$	−1.15592	+	2.16258i	−0.0400023	+	0.0748391i
$836$	−0.105284	−	9.59154i	−0.00364133	−	0.331730i
$837$	6.09731	+	5.00393i	0.210754	+	0.172961i
$838$	−2.00958	+	1.08837i	−0.0694200	+	0.0375970i
$839$	−29.0292	+	43.4453i	−1.00220	+	1.49990i	−0.142047	+	0.989860i	$0.545368\pi$
$839$	−29.0292	+	43.4453i	−1.00220	+	1.49990i	−0.860152	+	0.510037i	$0.829632\pi$
$840$	3.15447	−	1.36790i	0.108840	−	0.0471969i
$841$	21.0063	−	14.0359i	0.724354	−	0.483998i
$842$	−18.9892	+	5.87430i	−0.654410	+	0.202442i
$843$	−7.18651	+	23.6907i	−0.247516	+	0.815952i
$844$	−21.6970	+	6.84268i	−0.746843	+	0.235535i
$845$	−2.20950	−	2.69228i	−0.0760090	−	0.0926172i
$846$	−3.45006	+	1.45129i	−0.118615	+	0.0498965i
$847$	−9.89982	−	23.9003i	−0.340162	−	0.821223i
$848$	19.7424	+	35.0617i	0.677956	+	1.20402i
$849$	−7.55757	+	18.2456i	−0.259375	+	0.626187i
$850$	0.0135519	+	2.46927i	0.000464827	+	0.0846952i
$851$	−51.4389	−	5.06629i	−1.76330	−	0.173670i
$852$	−1.62069	+	2.01962i	−0.0555240	+	0.0691911i
$853$	22.3872	−	11.9662i	0.766524	−	0.409715i	−0.0412947	−	0.999147i	$-0.513148\pi$
$853$	22.3872	−	11.9662i	0.766524	−	0.409715i	0.807818	+	0.589432i	$0.200648\pi$
$854$	1.36010	−	1.12875i	0.0465416	−	0.0386251i
$855$	−0.620273	+	3.11832i	−0.0212129	+	0.106644i
$856$	0.387051	+	0.198760i	0.0132291	+	0.00679349i
$857$	−49.7326	+	9.89244i	−1.69883	+	0.337919i	−0.946951	−	0.321377i	$-0.895854\pi$
$857$	−49.7326	+	9.89244i	−1.69883	+	0.337919i	−0.751883	+	0.659296i	$0.770854\pi$
$858$	−2.53289	+	0.263511i	−0.0864713	+	0.00899612i
$859$	−27.9598	+	2.75380i	−0.953976	+	0.0939584i	−0.563013	−	0.826448i	$-0.690358\pi$
$859$	−27.9598	+	2.75380i	−0.953976	+	0.0939584i	−0.390963	+	0.920406i	$0.627858\pi$
$860$	−1.30649	−	6.21108i	−0.0445510	−	0.211796i
$861$	12.0114	−	3.64362i	0.409348	−	0.124174i
$862$	−1.37914	+	7.13794i	−0.0469738	+	0.243119i
$863$	−15.5198	−	15.5198i	−0.528301	−	0.528301i	0.391764	−	0.920066i	$-0.371865\pi$
$863$	−15.5198	−	15.5198i	−0.528301	−	0.528301i	−0.920066	+	0.391764i	$0.871865\pi$
$864$	−5.06019	−	2.52874i	−0.172151	−	0.0860294i
$865$	0.0538695	−	0.0538695i	0.00183162	−	0.00183162i
$866$	20.2884	+	30.0060i	0.689429	+	1.01964i
$867$	4.89576	+	16.1392i	0.166269	+	0.548115i
$868$	−32.2276	+	22.0493i	−1.09388	+	0.748401i
$869$	0.648694	+	6.58630i	0.0220054	+	0.223425i
$870$	1.04237	+	0.845921i	0.0353397	+	0.0286794i
$871$	−1.29907	−	6.53089i	−0.0440175	−	0.221291i
$872$	3.19759	+	5.75240i	0.108284	+	0.194801i
$873$	1.41499	+	0.281459i	0.0478901	+	0.00952594i
$874$	−6.29519	+	67.7245i	−0.212938	+	2.29081i
$875$	−5.59218	−	10.4622i	−0.189050	−	0.353688i
$876$	1.42343	−	0.781045i	0.0480932	−	0.0263891i
$877$	−1.01819	+	10.3378i	−0.0343817	+	0.349084i	0.962568	+	0.271040i	$0.0873675\pi$
$877$	−1.01819	+	10.3378i	−0.0343817	+	0.349084i	−0.996950	+	0.0780440i	$0.975133\pi$
$878$	−15.9293	+	16.1052i	−0.537589	+	0.543523i
$879$	0.275124	+	0.113960i	0.00927971	+	0.00384378i
$880$	−0.252512	+	1.43321i	−0.00851219	+	0.0483135i
$881$	11.9493	−	4.94958i	0.402583	−	0.166756i	−0.172198	−	0.985062i	$-0.555087\pi$
$881$	11.9493	−	4.94958i	0.402583	−	0.166756i	0.574782	+	0.818307i	$0.305087\pi$
$882$	0.466225	−	1.14327i	0.0156986	−	0.0384960i
$883$	15.7021	−	12.8863i	0.528416	−	0.433660i	−0.331980	−	0.943287i	$-0.607716\pi$
$883$	15.7021	−	12.8863i	0.528416	−	0.433660i	0.860396	+	0.509627i	$0.170216\pi$
$884$	1.36630	−	1.14662i	0.0459536	−	0.0385650i
$885$	−5.38512	−	1.63356i	−0.181019	−	0.0549115i
$886$	20.8343	+	10.9896i	0.699940	+	0.369201i
$887$	−14.3131	−	21.4211i	−0.480587	−	0.719249i	0.509381	−	0.860541i	$-0.329874\pi$
$887$	−14.3131	−	21.4211i	−0.480587	−	0.719249i	−0.989968	+	0.141292i	$0.954874\pi$
$888$	−19.2352	+	4.15645i	−0.645490	+	0.139481i
$889$	36.6588	+	24.4946i	1.22950	+	0.821523i
$890$	2.00767	−	6.75158i	0.0672973	−	0.226313i
$891$	−0.469971	+	0.572661i	−0.0157446	+	0.0191849i
$892$	37.6592	+	15.1169i	1.26092	+	0.506150i
$893$	15.1110	+	8.07699i	0.505670	+	0.270286i
$894$	−6.09171	−	29.7703i	−0.203737	−	0.995667i
$895$	11.8903			0.397449
$896$	19.0270	−	20.5481i	0.635647	−	0.686463i
$897$	18.0573			0.602916
$898$	−6.77840	−	33.1262i	−0.226198	−	1.10543i
$899$	−13.4457	−	7.18689i	−0.448440	−	0.239696i
$900$	−3.54551	+	8.83259i	−0.118184	+	0.294420i
$901$	−2.34150	+	2.85312i	−0.0780066	+	0.0950514i
$902$	−1.51427	+	5.09232i	−0.0504197	+	0.169556i
$903$	13.2994	+	8.88638i	0.442577	+	0.295720i
$904$	7.52984	−	11.6810i	0.250439	−	0.388506i
$905$	5.07947	+	7.60197i	0.168847	+	0.252698i
$906$	−6.22705	−	3.28462i	−0.206880	−	0.109124i
$907$	−35.9968	−	10.9195i	−1.19526	−	0.362577i	−0.370912	−	0.928668i	$-0.620955\pi$
$907$	−35.9968	−	10.9195i	−1.19526	−	0.362577i	−0.824343	+	0.566091i	$0.808455\pi$
$908$	9.25259	+	11.0253i	0.307058	+	0.365887i
$909$	9.08358	−	7.45470i	0.301283	−	0.247257i
$910$	−1.57790	+	3.86930i	−0.0523067	+	0.128266i
$911$	10.9276	−	4.52635i	0.362047	−	0.149965i	−0.194242	−	0.980954i	$-0.562225\pi$
$911$	10.9276	−	4.52635i	0.362047	−	0.149965i	0.556289	+	0.830989i	$0.312225\pi$
$912$	5.60835	+	25.2813i	0.185711	+	0.837149i
$913$	−7.76348	−	3.21574i	−0.256934	−	0.106425i
$914$	32.4080	−	32.7657i	1.07196	−	1.08379i
$915$	0.0243048	−	0.246771i	0.000803491	−	0.00815798i
$916$	−10.2003	−	18.5896i	−0.337026	−	0.614218i
$917$	−11.4191	−	21.3637i	−0.377093	−	0.705491i
$918$	0.0480254	−	0.516664i	0.00158507	−	0.0170524i
$919$	−15.6184	−	3.10669i	−0.515203	−	0.102480i	−0.0693607	−	0.997592i	$-0.522096\pi$
$919$	−15.6184	−	3.10669i	−0.515203	−	0.102480i	−0.445843	+	0.895111i	$0.647096\pi$
$920$	2.83253	−	9.92286i	0.0933857	−	0.327147i
$921$	−3.14491	−	15.8105i	−0.103628	−	0.520975i
$922$	25.8647	+	20.9901i	0.851808	+	0.691273i
$923$	−0.308471	−	3.13196i	−0.0101534	−	0.103090i
$924$	−2.07088	−	3.02683i	−0.0681268	−	0.0995754i
$925$	9.61133	+	31.6843i	0.316019	+	1.04177i
$926$	20.0823	+	29.7011i	0.659945	+	0.976039i
$927$	6.10721	−	6.10721i	0.200587	−	0.200587i
$928$	10.5463	+	2.88568i	0.346198	+	0.0947271i
$929$	−29.8430	−	29.8430i	−0.979118	−	0.979118i	0.0206687	−	0.999786i	$-0.493420\pi$
$929$	−29.8430	−	29.8430i	−0.979118	−	0.979118i	−0.999786	+	0.0206687i	$0.993420\pi$
$930$	−1.03925	+	5.37879i	−0.0340784	+	0.176377i
$931$	−5.40875	+	1.64073i	−0.177265	+	0.0537726i
$932$	17.3395	−	3.64733i	0.567974	−	0.119472i
$933$	−9.28662	+	0.914652i	−0.304030	+	0.0299444i
$934$	−49.2020	+	5.11877i	−1.60994	+	0.167491i
$935$	−0.130925	+	0.0260426i	−0.00428171	+	0.000851684i
$936$	6.54519	−	2.10374i	0.213936	−	0.0687630i
$937$	−5.03060	+	25.2905i	−0.164342	+	0.826205i	0.807371	+	0.590044i	$0.200889\pi$
$937$	−5.03060	+	25.2905i	−0.164342	+	0.826205i	−0.971714	+	0.236162i	$0.924111\pi$
$938$	7.37952	−	6.12430i	0.240950	−	0.199965i
$939$	23.5714	−	12.5992i	0.769223	−	0.411158i
$940$	−2.02745	−	1.62697i	−0.0661281	−	0.0530660i
$941$	33.4427	+	3.29382i	1.09020	+	0.107376i	0.627107	−	0.778933i	$-0.284239\pi$
$941$	33.4427	+	3.29382i	1.09020	+	0.107376i	0.463095	+	0.886309i	$0.346739\pi$
$942$	0.0474163	+	8.63963i	0.00154491	+	0.281495i
$943$	14.4163	−	34.8040i	0.469459	−	1.13338i
$944$	−45.5045	+	5.49279i	−1.48105	+	0.178775i
$945$	0.465197	+	1.12308i	0.0151329	+	0.0365340i
$946$	−6.24039	+	2.62507i	−0.202893	+	0.0853484i
$947$	26.7392	+	32.5818i	0.868906	+	1.05876i	0.997746	+	0.0670995i	$0.0213745\pi$
$947$	26.7392	+	32.5818i	0.868906	+	1.05876i	−0.128840	+	0.991665i	$0.541125\pi$
$948$	−5.37392	−	17.0398i	−0.174537	−	0.553428i
$949$	−0.572806	+	1.88829i	−0.0185941	+	0.0612964i
$950$	41.6237	−	12.8763i	1.35045	−	0.417762i
$951$	1.05532	−	0.705144i	0.0342212	−	0.0228658i
$952$	2.38911	+	0.943826i	0.0774316	+	0.0305896i
$953$	−25.9677	+	38.8634i	−0.841176	+	1.25891i	0.122670	+	0.992448i	$0.460854\pi$
$953$	−25.9677	+	38.8634i	−0.841176	+	1.25891i	−0.963846	+	0.266461i	$0.914146\pi$
$954$	−12.5094	+	6.77495i	−0.405007	+	0.219347i
$955$	0.287089	+	0.235608i	0.00928997	+	0.00762408i
$956$	46.3931	−	0.509248i	1.50046	−	0.0164702i
$957$	0.674996	−	1.26283i	0.0218195	−	0.0408214i
$958$	18.5475	+	12.2463i	0.599242	+	0.395661i
$959$			3.07697i			0.0993607i
$960$	−0.129350	−	3.92672i	−0.00417475	−	0.126734i
$961$		−	31.2165i		−	1.00698i
$962$	13.1781	−	19.9586i	0.424878	−	0.643493i
$963$	−0.0725158	+	0.135668i	−0.00233679	+	0.00437183i
$964$	28.8474	−	29.4878i	0.929113	−	0.949737i
$965$	4.37694	+	3.59206i	0.140899	+	0.115633i
$966$	12.3846	+	22.8671i	0.398467	+	0.735737i
$967$	6.23801	−	9.33584i	0.200601	−	0.300220i	−0.717507	−	0.696552i	$-0.754717\pi$
$967$	6.23801	−	9.33584i	0.200601	−	0.300220i	0.918108	+	0.396331i	$0.129717\pi$
$968$	−29.5564	+	0.486676i	−0.949979	+	0.0156424i
$969$	−1.97505	+	1.31969i	−0.0634479	+	0.0423945i
$970$	0.296124	+	0.957247i	0.00950797	+	0.0307353i
$971$	−12.5189	+	41.2692i	−0.401750	+	1.32439i	0.489945	+	0.871753i	$0.337017\pi$
$971$	−12.5189	+	41.2692i	−0.401750	+	1.32439i	−0.891694	+	0.452638i	$0.850483\pi$
$972$	0.923377	−	1.77408i	0.0296173	−	0.0569038i
$973$	33.3041	+	40.5811i	1.06768	+	1.30097i
$974$	−10.5778	−	25.1460i	−0.338936	−	0.805728i
$975$	−4.42654	−	10.6866i	−0.141763	−	0.342245i
$976$	−0.628554	−	1.91934i	−0.0201195	−	0.0614367i
$977$	−6.72611	+	16.2383i	−0.215187	+	0.519508i	−0.994206	−	0.107493i	$-0.965718\pi$
$977$	−6.72611	+	16.2383i	−0.215187	+	0.519508i	0.779019	+	0.627001i	$0.215718\pi$
$978$	10.5590	−	0.0579504i	0.337641	−	0.00185305i
$979$	−7.47706	−	0.736426i	−0.238968	−	0.0235363i
$980$	0.852419	−	0.0934137i	0.0272295	−	0.00298399i
$981$	−2.05212	+	1.09688i	−0.0655191	+	0.0350207i
$982$	−21.3019	−	25.6678i	−0.679769	−	0.819093i
$983$	3.04884	−	15.3275i	0.0972428	−	0.488873i	−0.901216	−	0.433371i	$-0.857324\pi$
$983$	3.04884	−	15.3275i	0.0972428	−	0.488873i	0.998459	−	0.0555019i	$-0.0176759\pi$
$984$	1.17065	−	14.2949i	0.0373188	−	0.455705i
$985$	−11.3495	+	2.25755i	−0.361624	+	0.0719315i
$986$	0.103782	+	0.997562i	0.00330510	+	0.0317689i
$987$	6.51954	−	0.642118i	0.207519	−	0.0204389i
$988$	−26.3585	−	17.1968i	−0.838577	−	0.547102i
$989$	45.9384	−	13.9353i	1.46076	−	0.443115i
$990$	−0.505177	−	0.0976070i	−0.0160556	−	0.00310215i
$991$	−8.98226	−	8.98226i	−0.285331	−	0.285331i	0.549900	−	0.835231i	$-0.314666\pi$
$991$	−8.98226	−	8.98226i	−0.285331	−	0.285331i	−0.835231	+	0.549900i	$0.814666\pi$
$992$	9.90235	+	43.5071i	0.314400	+	1.38135i
$993$	15.7875	−	15.7875i	0.501000	−	0.501000i
$994$	3.75463	−	2.53868i	0.119090	−	0.0805221i
$995$	−1.72812	−	5.69685i	−0.0547851	−	0.180602i
$996$	22.2974	+	4.18134i	0.706519	+	0.132491i
$997$	−3.02699	−	30.7336i	−0.0958658	−	0.973341i	−0.916002	−	0.401173i	$-0.868603\pi$
$997$	−3.02699	−	30.7336i	−0.0958658	−	0.973341i	0.820136	−	0.572168i	$-0.193897\pi$
$998$	20.2070	−	24.8997i	0.639640	−	0.788185i
$999$	−1.35736	−	6.82393i	−0.0429451	−	0.215900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.109.29	✓	512
128.101	even	32	inner	384.2.v.a.229.29	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.29	✓	512	1.1	even	1	trivial
384.2.v.a.229.29	yes	512	128.101	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38550 - 0.283508i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.83925 - 0.785602i) q^{4} +(-0.311554 + 0.379630i) q^{5} +(-1.35555 - 0.403091i) q^{6} +(2.05811 + 1.37518i) q^{7} +(2.32556 - 1.60990i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.38550 - 0.283508i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.83925 - 0.785602i) q^{4} +(-0.311554 + 0.379630i) q^{5} +(-1.35555 - 0.403091i) q^{6} +(2.05811 + 1.37518i) q^{7} +(2.32556 - 1.60990i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.324032 + 0.614307i) q^{10} +(0.708920 + 0.215049i) q^{11} +(-1.99240 - 0.174176i) q^{12} +(1.87893 - 1.54200i) q^{13} +(3.24140 + 1.32184i) q^{14} +(0.453723 - 0.187938i) q^{15} +(2.76566 - 2.88983i) q^{16} +(0.338982 + 0.140411i) q^{17} +(1.00547 + 0.994497i) q^{18} +(0.634562 - 6.44281i) q^{19} +(-0.274787 + 0.942991i) q^{20} +(-1.16683 - 2.18299i) q^{21} +(1.04318 + 0.0969667i) q^{22} +(-7.28620 - 1.44931i) q^{23} +(-2.80986 + 0.323539i) q^{24} +(0.928399 + 4.66738i) q^{25} +(2.16610 - 2.66914i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(4.86572 + 0.912450i) q^{28} +(0.561081 + 1.84964i) q^{29} +(0.575353 - 0.389023i) q^{30} +(-5.57748 + 5.57748i) q^{31} +(3.01254 - 4.78796i) q^{32} +(-0.523839 - 0.523839i) q^{33} +(0.509468 + 0.0984360i) q^{34} +(-1.16327 + 0.352875i) q^{35} +(1.67504 + 1.09282i) q^{36} +(6.92412 - 0.681966i) q^{37} +(-0.947398 - 9.10645i) q^{38} +(-2.38396 + 0.474200i) q^{39} +(-0.113374 + 1.38442i) q^{40} +(-0.989289 + 4.97349i) q^{41} +(-2.23555 - 2.69374i) q^{42} +(-5.69893 + 3.04614i) q^{43} +(1.47282 - 0.161402i) q^{44} +(-0.488741 - 0.0481368i) q^{45} +(-10.5060 + 0.0576591i) q^{46} +(-1.01282 + 2.44515i) q^{47} +(-3.80135 + 1.24488i) q^{48} +(-0.334102 - 0.806595i) q^{49} +(2.60954 + 6.20346i) q^{50} +(-0.232766 - 0.283626i) q^{51} +(2.24442 - 4.31221i) q^{52} +(-2.92011 + 9.62630i) q^{53} +(-0.417946 - 1.35104i) q^{54} +(-0.302506 + 0.202128i) q^{55} +(7.00016 - 0.115265i) q^{56} +(-3.59675 + 5.38292i) q^{57} +(1.30177 + 2.40361i) q^{58} +(-8.85770 - 7.26933i) q^{59} +(0.686863 - 0.702110i) q^{60} +(0.238013 - 0.445291i) q^{61} +(-6.14637 + 9.30888i) q^{62} +2.47527i q^{63} +(2.81647 - 7.48782i) q^{64} +1.19372i q^{65} +(-0.874293 - 0.577269i) q^{66} +(1.29140 - 2.41603i) q^{67} +(0.733778 - 0.00805453i) q^{68} +(5.74265 + 4.71287i) q^{69} +(-1.51168 + 0.818707i) q^{70} +(0.719325 - 1.07655i) q^{71} +(2.63059 + 1.03922i) q^{72} +(-0.675000 + 0.451021i) q^{73} +(9.40006 - 2.90791i) q^{74} +(1.38141 - 4.55390i) q^{75} +(-3.89437 - 12.3484i) q^{76} +(1.16330 + 1.41749i) q^{77} +(-3.16855 + 1.33288i) q^{78} +(3.41873 + 8.25355i) q^{79} +(0.235414 + 1.95027i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(0.0393575 + 7.17127i) q^{82} +(-11.2884 - 1.11181i) q^{83} +(-3.86106 - 3.09839i) q^{84} +(-0.158915 + 0.0849420i) q^{85} +(-7.03230 + 5.83614i) q^{86} +(0.377083 - 1.89573i) q^{87} +(1.99484 - 0.641179i) q^{88} +(-9.94691 + 1.97856i) q^{89} +(-0.690800 + 0.0718680i) q^{90} +(5.98758 - 0.589726i) q^{91} +(-14.5397 + 3.05840i) q^{92} +(7.54810 - 2.28969i) q^{93} +(-0.710042 + 3.67491i) q^{94} +(2.24818 + 2.24818i) q^{95} +(-4.91386 + 2.80250i) q^{96} +(1.02015 - 1.02015i) q^{97} +(-0.691576 - 1.02282i) q^{98} +(0.215049 + 0.708920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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