LMFDB - Embedded newform 231.2.s.a.8.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, degree $4$, 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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.15
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.487641 - 0.354292i) q^{2} +(1.64708 - 0.535846i) q^{3} +(-0.505763 + 1.55658i) q^{4} +(-2.33078 + 3.20804i) q^{5} +(0.613338 - 0.844848i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.677377 + 2.08475i) q^{8} +(2.42574 - 1.76516i) q^{9} +O(q^{10})$	\(q+(0.487641 - 0.354292i) q^{2} +(1.64708 - 0.535846i) q^{3} +(-0.505763 + 1.55658i) q^{4} +(-2.33078 + 3.20804i) q^{5} +(0.613338 - 0.844848i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.677377 + 2.08475i) q^{8} +(2.42574 - 1.76516i) q^{9} +2.39015i q^{10} +(0.00642177 - 3.31662i) q^{11} +(0.00105446 + 2.83482i) q^{12} +(2.46740 + 3.39608i) q^{13} +(0.573257 - 0.186262i) q^{14} +(-2.11996 + 6.53284i) q^{15} +(-1.57928 - 1.14741i) q^{16} +(-2.81824 - 2.04757i) q^{17} +(0.557508 - 1.72019i) q^{18} +(4.00875 - 1.30252i) q^{19} +(-3.81475 - 5.25055i) q^{20} +(1.73205 - 0.000644264i) q^{21} +(-1.17192 - 1.61960i) q^{22} -5.57936i q^{23} +(2.23280 + 3.07078i) q^{24} +(-3.31392 - 10.1992i) q^{25} +(2.40641 + 0.781890i) q^{26} +(3.04953 - 4.20718i) q^{27} +(-0.962018 + 1.32410i) q^{28} +(-1.53470 + 4.72333i) q^{29} +(1.28075 + 3.93677i) q^{30} +(2.78958 - 2.02675i) q^{31} -5.56072 q^{32} +(-1.76662 - 5.46617i) q^{33} -2.09973 q^{34} +(-3.20804 + 2.33078i) q^{35} +(1.52076 + 4.66860i) q^{36} +(-0.987188 + 3.03825i) q^{37} +(1.49336 - 2.05543i) q^{38} +(5.88377 + 4.27147i) q^{39} +(-8.26679 - 2.68604i) q^{40} +(1.29105 + 3.97343i) q^{41} +(0.844391 - 0.613966i) q^{42} -5.65055i q^{43} +(5.15933 + 1.68742i) q^{44} +(0.00884987 + 11.8961i) q^{45} +(-1.97672 - 2.72073i) q^{46} +(4.06215 - 1.31987i) q^{47} +(-3.21603 - 1.04363i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-5.22950 - 3.79945i) q^{50} +(-5.73905 - 1.86237i) q^{51} +(-6.53418 + 2.12308i) q^{52} +(0.890316 + 1.22542i) q^{53} +(-0.00349501 - 3.13202i) q^{54} +(10.6249 + 7.75091i) q^{55} +2.19204i q^{56} +(5.90478 - 4.29343i) q^{57} +(0.925055 + 2.84703i) q^{58} +(-3.48487 - 1.13230i) q^{59} +(-9.09667 - 6.60395i) q^{60} +(-3.27372 + 4.50588i) q^{61} +(0.642253 - 1.97665i) q^{62} +(2.85248 - 0.929173i) q^{63} +(0.446921 - 0.324707i) q^{64} -16.6457 q^{65} +(-2.79810 - 2.03963i) q^{66} -6.20942 q^{67} +(4.61257 - 3.35123i) q^{68} +(-2.98968 - 9.18964i) q^{69} +(-0.738597 + 2.27317i) q^{70} +(3.41346 - 4.69822i) q^{71} +(5.32307 + 3.86139i) q^{72} +(5.39761 + 1.75379i) q^{73} +(0.595035 + 1.83133i) q^{74} +(-10.9235 - 15.0231i) q^{75} +6.89871i q^{76} +(1.03100 - 3.15231i) q^{77} +(4.38252 - 0.00163015i) q^{78} +(-8.74306 - 12.0338i) q^{79} +(7.36190 - 2.39203i) q^{80} +(2.76841 - 8.56364i) q^{81} +(2.03732 + 1.48020i) q^{82} +(2.98348 + 2.16763i) q^{83} +(-0.875004 + 2.69640i) q^{84} +(13.1374 - 4.26860i) q^{85} +(-2.00195 - 2.75544i) q^{86} +(0.00319968 + 8.60207i) q^{87} +(6.91868 - 2.23321i) q^{88} +3.29930i q^{89} +(4.21900 + 5.79788i) q^{90} +(1.29719 + 3.99233i) q^{91} +(8.68471 + 2.82183i) q^{92} +(3.50863 - 4.83300i) q^{93} +(1.51325 - 2.08281i) q^{94} +(-5.16497 + 15.8961i) q^{95} +(-9.15895 + 2.97969i) q^{96} +(-15.6905 + 11.3998i) q^{97} +0.602758 q^{98} +(-5.83879 - 8.05658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.487641	−	0.354292i	0.344815	−	0.250522i	−0.401876	−	0.915694i	$-0.631642\pi$
$2$	0.487641	−	0.354292i	0.344815	−	0.250522i	0.746690	+	0.665172i	$0.231642\pi$
$3$	1.64708	−	0.535846i	0.950942	−	0.309371i
$3$	1.64708	−	0.535846i	0.950942	−	0.309371i
$4$	−0.505763	+	1.55658i	−0.252881	+	0.778289i
$5$	−2.33078	+	3.20804i	−1.04236	+	1.43468i	−0.147104	+	0.989121i	$0.546995\pi$
$5$	−2.33078	+	3.20804i	−1.04236	+	1.43468i	−0.895253	+	0.445559i	$0.853005\pi$
$6$	0.613338	−	0.844848i	0.250394	−	0.344908i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.677377	+	2.08475i	0.239489	+	0.737072i
$9$	2.42574	−	1.76516i	0.808579	−	0.588387i
$10$			2.39015i			0.755832i
$11$	0.00642177	−	3.31662i	0.00193624	−	0.999998i
$11$	0.00642177	−	3.31662i	0.00193624	−	0.999998i
$12$	0.00105446	+	2.83482i	0.000304395	+	0.818341i
$13$	2.46740	+	3.39608i	0.684333	+	0.941903i	0.999976	−	0.00697476i	$-0.00222015\pi$
$13$	2.46740	+	3.39608i	0.684333	+	0.941903i	−0.315643	+	0.948878i	$0.602220\pi$
$14$	0.573257	−	0.186262i	0.153209	−	0.0497807i
$15$	−2.11996	+	6.53284i	−0.547372	+	1.68677i
$16$	−1.57928	−	1.14741i	−0.394820	−	0.286853i
$17$	−2.81824	−	2.04757i	−0.683525	−	0.496610i	0.191001	−	0.981590i	$-0.438827\pi$
$17$	−2.81824	−	2.04757i	−0.683525	−	0.496610i	−0.874525	+	0.484980i	$0.838827\pi$
$18$	0.557508	−	1.72019i	0.131406	−	0.405452i
$19$	4.00875	−	1.30252i	0.919671	−	0.298819i	0.189339	−	0.981912i	$-0.439365\pi$
$19$	4.00875	−	1.30252i	0.919671	−	0.298819i	0.730332	+	0.683092i	$0.239365\pi$
$20$	−3.81475	−	5.25055i	−0.853003	−	1.17406i
$21$	1.73205		0.000644264i	0.377964		0.000140590i
$22$	−1.17192	−	1.61960i	−0.249854	−	0.345299i
$23$		−	5.57936i		−	1.16338i	−0.813412	−	0.581688i	$-0.802392\pi$
$23$		−	5.57936i		−	1.16338i	0.813412	−	0.581688i	$-0.197608\pi$
$24$	2.23280	+	3.07078i	0.455768	+	0.626821i
$25$	−3.31392	−	10.1992i	−0.662784	−	2.03984i
$26$	2.40641	+	0.781890i	0.471936	+	0.153341i
$27$	3.04953	−	4.20718i	0.586882	−	0.809672i
$28$	−0.962018	+	1.32410i	−0.181804	+	0.250232i
$29$	−1.53470	+	4.72333i	−0.284987	+	0.877101i	0.701415	+	0.712753i	$0.252552\pi$
$29$	−1.53470	+	4.72333i	−0.284987	+	0.877101i	−0.986402	+	0.164348i	$0.947448\pi$
$30$	1.28075	+	3.93677i	0.233832	+	0.718752i
$31$	2.78958	−	2.02675i	0.501023	−	0.364015i	−0.308384	−	0.951262i	$-0.599788\pi$
$31$	2.78958	−	2.02675i	0.501023	−	0.364015i	0.809408	+	0.587247i	$0.199788\pi$
$32$	−5.56072			−0.983006
$33$	−1.76662	−	5.46617i	−0.307529	−	0.951539i
$34$	−2.09973			−0.360101
$35$	−3.20804	+	2.33078i	−0.542258	+	0.393974i
$36$	1.52076	+	4.66860i	0.253460	+	0.778101i
$37$	−0.987188	+	3.03825i	−0.162293	+	0.499486i	−0.998827	−	0.0484296i	$-0.984578\pi$
$37$	−0.987188	+	3.03825i	−0.162293	+	0.499486i	0.836534	+	0.547915i	$0.184578\pi$
$38$	1.49336	−	2.05543i	0.242255	−	0.333436i
$39$	5.88377	+	4.27147i	0.942158	+	0.683982i
$40$	−8.26679	−	2.68604i	−1.30709	−	0.424701i
$41$	1.29105	+	3.97343i	0.201627	+	0.620545i	0.999835	+	0.0181629i	$0.00578175\pi$
$41$	1.29105	+	3.97343i	0.201627	+	0.620545i	−0.798208	+	0.602382i	$0.794218\pi$
$42$	0.844391	−	0.613966i	0.130292	−	0.0947370i
$43$		−	5.65055i		−	0.861701i	−0.902423	−	0.430850i	$-0.858214\pi$
$43$		−	5.65055i		−	0.861701i	0.902423	−	0.430850i	$-0.141786\pi$
$44$	5.15933	+	1.68742i	0.777798	+	0.254388i
$45$	0.00884987	+	11.8961i	0.00131926	+	1.77336i
$46$	−1.97672	−	2.72073i	−0.291452	−	0.401149i
$47$	4.06215	−	1.31987i	0.592526	−	0.192523i	0.00262177	−	0.999997i	$-0.499165\pi$
$47$	4.06215	−	1.31987i	0.592526	−	0.192523i	0.589904	+	0.807473i	$0.299165\pi$
$48$	−3.21603	−	1.04363i	−0.464195	−	0.150635i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−5.22950	−	3.79945i	−0.739563	−	0.537324i
$51$	−5.73905	−	1.86237i	−0.803628	−	0.260784i
$52$	−6.53418	+	2.12308i	−0.906128	+	0.294419i
$53$	0.890316	+	1.22542i	0.122294	+	0.168324i	0.865775	−	0.500434i	$-0.166826\pi$
$53$	0.890316	+	1.22542i	0.122294	+	0.168324i	−0.743480	+	0.668758i	$0.766826\pi$
$54$	−0.00349501	−	3.13202i	−0.000475611	−	0.426214i
$55$	10.6249	+	7.75091i	1.43266	+	1.04513i
$56$			2.19204i			0.292924i
$57$	5.90478	−	4.29343i	0.782108	−	0.568679i
$58$	0.925055	+	2.84703i	0.121466	+	0.373833i
$59$	−3.48487	−	1.13230i	−0.453692	−	0.147413i	0.0732520	−	0.997313i	$-0.476662\pi$
$59$	−3.48487	−	1.13230i	−0.453692	−	0.147413i	−0.526944	+	0.849900i	$0.676662\pi$
$60$	−9.09667	−	6.60395i	−1.17438	−	0.852566i
$61$	−3.27372	+	4.50588i	−0.419156	+	0.576919i	−0.965422	−	0.260693i	$-0.916049\pi$
$61$	−3.27372	+	4.50588i	−0.419156	+	0.576919i	0.546265	+	0.837612i	$0.316049\pi$
$62$	0.642253	−	1.97665i	0.0815663	−	0.251035i
$63$	2.85248	−	0.929173i	0.359379	−	0.117065i
$64$	0.446921	−	0.324707i	0.0558652	−	0.0405884i
$65$	−16.6457			−2.06465
$66$	−2.79810	−	2.03963i	−0.344422	−	0.251062i
$67$	−6.20942			−0.758602			−0.379301	−	0.925273i	$-0.623836\pi$
$67$	−6.20942			−0.758602			−0.379301	+	0.925273i	$0.623836\pi$
$68$	4.61257	−	3.35123i	0.559357	−	0.406396i
$69$	−2.98968	−	9.18964i	−0.359915	−	1.10630i
$70$	−0.738597	+	2.27317i	−0.0882793	+	0.271696i
$71$	3.41346	−	4.69822i	0.405103	−	0.557577i	−0.556912	−	0.830571i	$-0.688014\pi$
$71$	3.41346	−	4.69822i	0.405103	−	0.557577i	0.962016	+	0.272995i	$0.0880141\pi$
$72$	5.32307	+	3.86139i	0.627329	+	0.455069i
$73$	5.39761	+	1.75379i	0.631743	+	0.205266i	0.607347	−	0.794437i	$-0.292234\pi$
$73$	5.39761	+	1.75379i	0.631743	+	0.205266i	0.0243960	+	0.999702i	$0.492234\pi$
$74$	0.595035	+	1.83133i	0.0691715	+	0.212888i
$75$	−10.9235	−	15.0231i	−1.26134	−	1.73472i
$76$			6.89871i			0.791336i
$77$	1.03100	−	3.15231i	0.117493	−	0.359239i
$78$	4.38252	−	0.00163015i	0.496223	−	0.000184578i
$79$	−8.74306	−	12.0338i	−0.983671	−	1.35391i	−0.934828	−	0.355101i	$-0.884447\pi$
$79$	−8.74306	−	12.0338i	−0.983671	−	1.35391i	−0.0488429	−	0.998806i	$-0.515553\pi$
$80$	7.36190	−	2.39203i	0.823086	−	0.267437i
$81$	2.76841	−	8.56364i	0.307602	−	0.951515i
$82$	2.03732	+	1.48020i	0.224985	+	0.163461i
$83$	2.98348	+	2.16763i	0.327480	+	0.237928i	0.739360	−	0.673310i	$-0.235128\pi$
$83$	2.98348	+	2.16763i	0.327480	+	0.237928i	−0.411881	+	0.911238i	$0.635128\pi$
$84$	−0.875004	+	2.69640i	−0.0954708	+	0.294201i
$85$	13.1374	−	4.26860i	1.42495	−	0.462995i
$86$	−2.00195	−	2.75544i	−0.215875	−	0.297127i
$87$	0.00319968	+	8.60207i	0.000343041	+	0.922239i
$88$	6.91868	−	2.23321i	0.737534	−	0.238061i
$89$			3.29930i			0.349725i	0.984593	+	0.174863i	$0.0559481\pi$
$89$			3.29930i			0.349725i	−0.984593	+	0.174863i	$0.944052\pi$
$90$	4.21900	+	5.79788i	0.444722	+	0.611150i
$91$	1.29719	+	3.99233i	0.135982	+	0.418510i
$92$	8.68471	+	2.82183i	0.905443	+	0.294196i
$93$	3.50863	−	4.83300i	0.363828	−	0.501159i
$94$	1.51325	−	2.08281i	0.156080	−	0.214826i
$95$	−5.16497	+	15.8961i	−0.529915	+	1.63091i
$96$	−9.15895	+	2.97969i	−0.934781	+	0.304113i
$97$	−15.6905	+	11.3998i	−1.59312	+	1.15747i	−0.693821	+	0.720147i	$0.744074\pi$
$97$	−15.6905	+	11.3998i	−1.59312	+	1.15747i	−0.899303	+	0.437325i	$0.855926\pi$
$98$	0.602758			0.0608877
$99$	−5.83879	−	8.05658i	−0.586820	−	0.809717i
$100$	17.5519			1.75519
$101$	−5.17799	+	3.76203i	−0.515229	+	0.374336i	−0.814804	−	0.579737i	$-0.803155\pi$
$101$	−5.17799	+	3.76203i	−0.515229	+	0.374336i	0.299575	+	0.954073i	$0.403155\pi$
$102$	−3.45842	+	1.12513i	−0.342435	+	0.111405i
$103$	2.31898	−	7.13708i	0.228496	−	0.703237i	−0.769422	−	0.638740i	$-0.779456\pi$
$103$	2.31898	−	7.13708i	0.228496	−	0.703237i	0.997918	−	0.0644968i	$-0.0205442\pi$
$104$	−5.40863	+	7.44434i	−0.530360	+	0.729978i
$105$	−4.03496	+	5.55799i	−0.393772	+	0.542405i
$106$	0.868310	+	0.282131i	0.0843377	+	0.0274030i
$107$	2.25551	+	6.94175i	0.218049	+	0.671084i	0.998923	+	0.0463966i	$0.0147738\pi$
$107$	2.25551	+	6.94175i	0.218049	+	0.671084i	−0.780875	+	0.624688i	$0.785226\pi$
$108$	5.00647	+	6.87467i	0.481748	+	0.661515i
$109$		−	9.18295i		−	0.879567i	−0.898104	−	0.439784i	$-0.855055\pi$
$109$		−	9.18295i		−	0.879567i	0.898104	−	0.439784i	$-0.144945\pi$
$110$	7.92722	+	0.0153490i	0.755831	+	0.00146347i
$111$	0.00205817	+	5.53322i	0.000195353	+	0.525190i
$112$	−1.14741	−	1.57928i	−0.108420	−	0.149228i
$113$	6.62813	−	2.15361i	0.623522	−	0.202595i	0.0198188	−	0.999804i	$-0.493691\pi$
$113$	6.62813	−	2.15361i	0.623522	−	0.202595i	0.603704	+	0.797209i	$0.293691\pi$
$114$	1.35829	−	4.18567i	0.127215	−	0.392024i
$115$	17.8988	+	13.0043i	1.66907	+	1.21265i
$116$	−6.57604	−	4.77777i	−0.610570	−	0.443605i
$117$	11.9799	+	3.88265i	1.10754	+	0.358951i
$118$	−2.10054	+	0.682505i	−0.193370	+	0.0628297i
$119$	−2.04757	−	2.81824i	−0.187701	−	0.258348i
$120$	−15.0554	+	0.00560008i	−1.37436	+	0.000511215i
$121$	−10.9999	−	0.0425971i	−0.999993	−	0.00387247i
$122$			3.35711i			0.303938i
$123$	4.25560	+	5.85275i	0.383714	+	0.527725i
$124$	1.74393	+	5.36725i	0.156609	+	0.481994i
$125$	21.5871	+	7.01406i	1.93081	+	0.627357i
$126$	1.06179	−	1.46371i	0.0945916	−	0.130398i
$127$	−12.5921	+	17.3315i	−1.11737	+	1.53792i	−0.307274	+	0.951621i	$0.599417\pi$
$127$	−12.5921	+	17.3315i	−1.11737	+	1.53792i	−0.810092	+	0.586302i	$0.800583\pi$
$128$	3.53961	−	10.8938i	0.312860	−	0.962885i
$129$	−3.02782	−	9.30690i	−0.266585	−	0.819427i
$130$	−8.11715	+	5.89745i	−0.711921	+	0.517241i
$131$	−3.18567			−0.278334			−0.139167	−	0.990269i	$-0.544442\pi$
$131$	−3.18567			−0.278334			−0.139167	+	0.990269i	$0.544442\pi$
$132$	9.40202	+	0.0147073i	0.818340	+	0.00128011i
$133$	4.21505			0.365492
$134$	−3.02797	+	2.19995i	−0.261577	+	0.190047i
$135$	6.38904	+	19.5890i	0.549881	+	1.68596i
$136$	2.35967	−	7.26232i	0.202340	−	0.622739i
$137$	11.4927	−	15.8183i	0.981886	−	1.35145i	0.0460784	−	0.998938i	$-0.485328\pi$
$137$	11.4927	−	15.8183i	0.981886	−	1.35145i	0.935807	−	0.352512i	$-0.114672\pi$
$138$	−4.71371	−	3.42203i	−0.401258	−	0.291303i
$139$	16.1532	+	5.24850i	1.37010	+	0.445172i	0.899402	−	0.437123i	$-0.144002\pi$
$139$	16.1532	+	5.24850i	1.37010	+	0.445172i	0.470697	+	0.882295i	$0.344002\pi$
$140$	−2.00553	−	6.17239i	−0.169498	−	0.521662i
$141$	5.98344	−	4.35062i	0.503897	−	0.366389i
$142$		−	3.50041i		−	0.293748i
$143$	11.2793	−	8.16161i	0.943227	−	0.682508i
$144$	−5.85629	+	0.00435668i	−0.488024	+	0.000363057i
$145$	−11.5756	−	15.9324i	−0.961301	−	1.32312i
$146$	3.25345	−	1.05711i	0.269258	−	0.0874872i
$147$	1.64748	+	0.534620i	0.135882	+	0.0440947i
$148$	−4.22999	−	3.07327i	−0.347703	−	0.252621i
$149$	−8.91163	−	6.47468i	−0.730069	−	0.530426i	0.159516	−	0.987195i	$-0.449007\pi$
$149$	−8.91163	−	6.47468i	−0.730069	−	0.530426i	−0.889585	+	0.456769i	$0.849007\pi$
$150$	−10.6493	−	3.45579i	−0.869513	−	0.282164i
$151$	−5.10585	+	1.65899i	−0.415508	+	0.135007i	−0.509308	−	0.860584i	$-0.670099\pi$
$151$	−5.10585	+	1.65899i	−0.415508	+	0.135007i	0.0937998	+	0.995591i	$0.470099\pi$
$152$	5.43088	+	7.47496i	0.440503	+	0.606300i
$153$	−10.4506	+	0.00777455i	−0.844883	+	0.000628535i
$154$	−0.614080	−	1.90247i	−0.0494840	−	0.153305i
$155$			13.6730i			1.09824i
$156$	−9.62467	+	6.99820i	−0.770590	+	0.560305i
$157$	−1.81214	−	5.57720i	−0.144625	−	0.445109i	0.852338	−	0.522992i	$-0.175184\pi$
$157$	−1.81214	−	5.57720i	−0.144625	−	0.445109i	−0.996963	+	0.0778825i	$0.975184\pi$
$158$	−8.52696	−	2.77058i	−0.678368	−	0.220415i
$159$	2.12306	+	1.54128i	0.168369	+	0.122232i
$160$	12.9608	−	17.8390i	1.02464	−	1.41030i
$161$	1.72412	−	5.30628i	0.135879	−	0.418194i
$162$	−1.68404	−	5.15681i	−0.132310	−	0.405157i
$163$	−3.88441	+	2.82219i	−0.304251	+	0.221051i	−0.729426	−	0.684060i	$-0.760213\pi$
$163$	−3.88441	+	2.82219i	−0.304251	+	0.221051i	0.425175	+	0.905111i	$0.360213\pi$
$164$	−6.83791			−0.533951
$165$	21.6533	+	7.07306i	1.68571	+	0.550637i
$166$	2.22284			0.172526
$167$	−14.1750	+	10.2987i	−1.09689	+	0.796938i	−0.980550	−	0.196271i	$-0.937117\pi$
$167$	−14.1750	+	10.2987i	−1.09689	+	0.796938i	−0.116341	+	0.993209i	$0.537117\pi$
$168$	1.17460	+	3.61046i	0.0906220	+	0.278553i
$169$	−1.42809	+	4.39522i	−0.109853	+	0.338094i
$170$	4.89401	−	6.73603i	0.375354	−	0.516630i
$171$	7.42503	−	10.2357i	0.567806	−	0.782742i
$172$	8.79552	+	2.85784i	0.670652	+	0.217908i
$173$	4.20392	+	12.9383i	0.319618	+	0.983684i	0.973812	+	0.227356i	$0.0730082\pi$
$173$	4.20392	+	12.9383i	0.319618	+	0.983684i	−0.654193	+	0.756327i	$0.726992\pi$
$174$	3.04921	+	4.19359i	0.231160	+	0.317915i
$175$		−	10.7241i		−	0.810663i
$176$	−3.81568	+	5.23050i	−0.287617	+	0.394264i
$177$	−6.34660	+	0.00236072i	−0.477040	+	0.000177443i
$178$	1.16892	+	1.60888i	0.0876140	+	0.120590i
$179$	−4.64298	+	1.50859i	−0.347032	+	0.112758i	−0.477347	−	0.878715i	$-0.658401\pi$
$179$	−4.64298	+	1.50859i	−0.347032	+	0.112758i	0.130314	+	0.991473i	$0.458401\pi$
$180$	−18.5216	−	6.00282i	−1.38052	−	0.447423i
$181$	−6.05937	−	4.40239i	−0.450389	−	0.327227i	0.339360	−	0.940656i	$-0.389789\pi$
$181$	−6.05937	−	4.40239i	−0.450389	−	0.327227i	−0.789749	+	0.613430i	$0.789789\pi$
$182$	2.04701	+	1.48724i	0.151735	+	0.110242i
$183$	−2.97761	+	9.17575i	−0.220111	+	0.678291i
$184$	11.6316	−	3.77933i	0.857492	−	0.278616i
$185$	−7.44592	−	10.2484i	−0.547435	−	0.753480i
$186$	−0.00133902	−	3.59985i	−9.81819e−5	−	0.263954i
$187$	−6.80912	+	9.33389i	−0.497932	+	0.682562i
$188$			6.99060i			0.509842i
$189$	4.20036	−	3.05891i	0.305532	−	0.222503i
$190$	3.11323	+	9.58153i	0.225857	+	0.695117i
$191$	22.0662	+	7.16975i	1.59666	+	0.518785i	0.966278	−	0.257503i	$-0.0828996\pi$
$191$	22.0662	+	7.16975i	1.59666	+	0.518785i	0.630379	+	0.776288i	$0.282900\pi$
$192$	0.562122	−	0.774300i	0.0405676	−	0.0558803i
$193$	3.29338	−	4.53295i	0.237063	−	0.326289i	−0.673865	−	0.738854i	$-0.735367\pi$
$193$	3.29338	−	4.53295i	0.237063	−	0.326289i	0.910928	+	0.412565i	$0.135367\pi$
$194$	−3.61246	+	11.1180i	−0.259360	+	0.798227i
$195$	−27.4168	+	8.91954i	−1.96336	+	0.638742i
$196$	−1.32410	+	0.962018i	−0.0945789	+	0.0687156i
$197$	9.79855			0.698118			0.349059	−	0.937101i	$-0.386501\pi$
$197$	9.79855			0.698118			0.349059	+	0.937101i	$0.386501\pi$
$198$	−5.70162	−	1.86009i	−0.405196	−	0.132191i
$199$	−23.6476			−1.67634			−0.838168	−	0.545413i	$-0.816373\pi$
$199$	−23.6476			−1.67634			−0.838168	+	0.545413i	$0.816373\pi$
$200$	19.0180	−	13.8174i	1.34478	−	0.977038i
$201$	−10.2274	+	3.32729i	−0.721386	+	0.234689i
$202$	−1.19214	+	3.66904i	−0.0838790	+	0.258153i
$203$	−2.91918	+	4.01791i	−0.204886	+	0.282002i
$204$	5.80153	−	7.99137i	0.406188	−	0.559508i
$205$	−15.7561	−	5.11946i	−1.10045	−	0.357558i
$206$	−1.39778	−	4.30193i	−0.0973881	−	0.299730i
$207$	−9.84846	−	13.5341i	−0.684516	−	0.940682i
$208$		−	8.19449i		−	0.568185i
$209$	−4.29423	−	13.3039i	−0.297038	−	0.920248i
$210$	0.00153989	+	4.13986i	0.000106262	+	0.285678i
$211$	7.29790	+	10.0447i	0.502408	+	0.691505i	0.982616	−	0.185649i	$-0.0594389\pi$
$211$	7.29790	+	10.0447i	0.502408	+	0.691505i	−0.480208	+	0.877155i	$0.659439\pi$
$212$	−2.35774	+	0.766077i	−0.161930	+	0.0526144i
$213$	3.10471	−	9.56743i	0.212731	−	0.655550i
$214$	3.55929	+	2.58598i	0.243308	+	0.176774i
$215$	18.1272	+	13.1702i	1.23627	+	0.898199i
$216$	10.8366	+	3.50767i	0.737338	+	0.238666i
$217$	3.27935	−	1.06552i	0.222617	−	0.0723325i
$218$	−3.25345	−	4.47799i	−0.220351	−	0.303288i
$219$	9.83006	−	0.00365645i	0.664254	−	0.000247080i
$220$	−17.4386	+	12.6183i	−1.17571	+	0.850728i
$221$		−	14.6232i		−	0.983660i
$222$	1.96138	+	2.69750i	0.131639	+	0.181044i
$223$	−7.10712	−	21.8735i	−0.475928	−	1.46476i	−0.844702	−	0.535237i	$-0.820222\pi$
$223$	−7.10712	−	21.8735i	−0.475928	−	1.46476i	0.368774	−	0.929519i	$-0.379778\pi$
$224$	−5.28856	−	1.71836i	−0.353357	−	0.114813i
$225$	−26.0419	−	18.8910i	−1.73613	−	1.25940i
$226$	2.46914	−	3.39849i	0.164245	−	0.226064i
$227$	−2.96160	+	9.11486i	−0.196568	+	0.604975i	0.803386	+	0.595458i	$0.203029\pi$
$227$	−2.96160	+	9.11486i	−0.196568	+	0.604975i	−0.999955	+	0.00951684i	$0.996971\pi$
$228$	3.69664	+	11.3627i	0.244816	+	0.752514i
$229$	14.6493	−	10.6433i	0.968053	−	0.703331i	0.0130458	−	0.999915i	$-0.495847\pi$
$229$	14.6493	−	10.6433i	0.968053	−	0.703331i	0.955007	+	0.296583i	$0.0958473\pi$
$230$	13.3355			0.879317
$231$	0.00898606	−	5.74456i	0.000591239	−	0.377964i
$232$	−10.8866			−0.714738
$233$	−7.15962	+	5.20177i	−0.469042	+	0.340779i	−0.797068	−	0.603890i	$-0.793617\pi$
$233$	−7.15962	+	5.20177i	−0.469042	+	0.340779i	0.328026	+	0.944669i	$0.393617\pi$
$234$	7.21748	−	2.35104i	0.471822	−	0.153692i
$235$	−5.23377	+	16.1079i	−0.341414	+	1.05076i
$236$	3.52504	−	4.85180i	0.229461	−	0.315825i
$237$	−20.8488	−	15.1357i	−1.35427	−	0.983167i
$238$	−1.99696	−	0.648853i	−0.129444	−	0.0420589i
$239$	3.75525	+	11.5575i	0.242907	+	0.747591i	0.995974	+	0.0896466i	$0.0285738\pi$
$239$	3.75525	+	11.5575i	0.242907	+	0.747591i	−0.753067	+	0.657944i	$0.771426\pi$
$240$	10.8439	−	7.88470i	0.699969	−	0.508955i
$241$			14.8675i			0.957702i	0.877896	+	0.478851i	$0.158947\pi$
$241$			14.8675i			0.957702i	−0.877896	+	0.478851i	$0.841053\pi$
$242$	−5.37911	+	3.87641i	−0.345782	+	0.249185i
$243$	−0.0289918	−	15.5884i	−0.00185983	−	0.999998i
$244$	−5.35803	−	7.37470i	−0.343013	−	0.472117i
$245$	−3.77128	+	1.22536i	−0.240938	+	0.0782856i
$246$	4.14879	+	1.34632i	0.264517	+	0.0858381i
$247$	14.3147	+	10.4002i	0.910820	+	0.661750i
$248$	6.11487	+	4.44271i	0.388295	+	0.282113i
$249$	6.07554	+	1.97157i	0.385022	+	0.124943i
$250$	13.0118	−	4.22778i	0.822937	−	0.267388i
$251$	−7.68447	−	10.5768i	−0.485040	−	0.667600i	0.494424	−	0.869221i	$-0.335379\pi$
$251$	−7.68447	−	10.5768i	−0.485040	−	0.667600i	−0.979464	+	0.201621i	$0.935379\pi$
$252$	0.00365274	+	4.91005i	0.000230101	+	0.309304i
$253$	−18.5046	−	0.0358294i	−1.16337	−	0.00225257i
$254$			12.9128i			0.810224i
$255$	19.3510	−	14.0704i	1.21181	−	0.881120i
$256$	−1.79211	−	5.51555i	−0.112007	−	0.344722i
$257$	−13.9332	−	4.52718i	−0.869131	−	0.282398i	−0.159694	−	0.987167i	$-0.551051\pi$
$257$	−13.9332	−	4.52718i	−0.869131	−	0.282398i	−0.709437	+	0.704769i	$0.751051\pi$
$258$	−4.77386	−	3.46570i	−0.297207	−	0.215765i
$259$	−1.87774	+	2.58449i	−0.116677	+	0.160592i
$260$	8.41879	−	25.9104i	0.522111	−	1.60689i
$261$	4.61465	+	14.1666i	0.285640	+	0.876889i
$262$	−1.55347	+	1.12866i	−0.0959735	+	0.0697288i
$263$	−26.2067			−1.61597			−0.807986	−	0.589202i	$-0.799442\pi$
$263$	−26.2067			−1.61597			−0.807986	+	0.589202i	$0.799442\pi$
$264$	10.1990	−	7.38563i	0.627702	−	0.454554i
$265$	−6.00632			−0.368965
$266$	2.05543	−	1.49336i	0.126027	−	0.0915638i
$267$	1.76792	+	5.43421i	0.108195	+	0.332568i
$268$	3.14050	−	9.66545i	0.191836	−	0.590412i
$269$	−6.94387	+	9.55742i	−0.423375	+	0.582726i	−0.966417	−	0.256980i	$-0.917273\pi$
$269$	−6.94387	+	9.55742i	−0.423375	+	0.582726i	0.543042	+	0.839706i	$0.317273\pi$
$270$	10.0558	+	7.28883i	0.611976	+	0.443584i
$271$	−6.03514	−	1.96093i	−0.366608	−	0.119118i	0.119919	−	0.992784i	$-0.461737\pi$
$271$	−6.03514	−	1.96093i	−0.366608	−	0.119118i	−0.486527	+	0.873665i	$0.661737\pi$
$272$	2.10138	+	6.46738i	0.127415	+	0.392143i
$273$	4.27584	+	5.88059i	0.258786	+	0.355910i
$274$		−	11.7854i		−	0.711984i
$275$	−33.8481	+	10.9255i	−2.04112	+	0.658833i
$276$	15.8165	−	0.00588318i	0.952039	−	0.000354126i
$277$	18.3553	+	25.2639i	1.10286	+	1.51796i	0.831534	+	0.555474i	$0.187463\pi$
$277$	18.3553	+	25.2639i	1.10286	+	1.51796i	0.271329	+	0.962487i	$0.412537\pi$
$278$	9.73649	−	3.16358i	0.583956	−	0.189739i
$279$	3.18925	−	9.84042i	0.190936	−	0.589131i
$280$	−7.03216	−	5.10916i	−0.420252	−	0.305331i
$281$	11.8423	+	8.60393i	0.706452	+	0.513268i	0.882027	−	0.471198i	$-0.156178\pi$
$281$	11.8423	+	8.60393i	0.706452	+	0.513268i	−0.175575	+	0.984466i	$0.556178\pi$
$282$	1.37638	−	4.24143i	0.0819623	−	0.252574i
$283$	1.57963	−	0.513252i	0.0938991	−	0.0305097i	−0.261691	−	0.965152i	$-0.584280\pi$
$283$	1.57963	−	0.513252i	0.0938991	−	0.0305097i	0.355590	+	0.934642i	$0.384280\pi$
$284$	5.58675	+	7.68950i	0.331513	+	0.456288i
$285$	0.0107684	+	28.9498i	0.000637862	+	1.71484i
$286$	2.60868	−	7.97612i	0.154255	−	0.471638i
$287$			4.17791i			0.246614i
$288$	−13.4889	+	9.81557i	−0.794838	+	0.578388i
$289$	−1.50335	−	4.62683i	−0.0884323	−	0.272167i
$290$	−11.2895	−	3.66818i	−0.662941	−	0.215403i
$291$	−19.7349	+	27.1840i	−1.15688	+	1.59355i
$292$	−5.45983	+	7.51481i	−0.319512	+	0.439771i
$293$	6.13264	−	18.8743i	0.358273	−	1.10265i	−0.595815	−	0.803122i	$-0.703171\pi$
$293$	6.13264	−	18.8743i	0.358273	−	1.10265i	0.954087	−	0.299528i	$-0.0968293\pi$
$294$	0.992790	−	0.322985i	0.0579007	−	0.0188369i
$295$	11.7550	−	8.54047i	0.684400	−	0.497246i
$296$	−7.00271			−0.407024
$297$	−13.9340	−	10.1411i	−0.808535	−	0.588449i
$298$	−6.63961			−0.384622
$299$	18.9479	−	13.7665i	1.09579	−	0.796137i
$300$	28.9094	−	9.40511i	1.66908	−	0.543004i
$301$	1.74612	−	5.37399i	0.100644	−	0.309752i
$302$	−1.90206	+	2.61796i	−0.109451	+	0.150646i
$303$	−6.51269	+	8.97096i	−0.374144	+	0.515368i
$304$	−7.82548	−	2.54265i	−0.448822	−	0.145831i
$305$	−6.82476	−	21.0044i	−0.390784	−	1.20271i
$306$	−5.09340	+	3.70636i	−0.291170	+	0.211879i
$307$		−	9.93123i		−	0.566805i	−0.959001	−	0.283403i	$-0.908537\pi$
$307$		−	9.93123i		−	0.566805i	0.959001	−	0.283403i	$-0.0914633\pi$
$308$	4.38537	+	3.19915i	0.249880	+	0.182288i
$309$	−0.00483479	−	12.9979i	−0.000275042	−	0.739427i
$310$	4.84424	+	6.66752i	0.275134	+	0.378690i
$311$	−23.5982	+	7.66751i	−1.33813	+	0.434785i	−0.888683	−	0.458522i	$-0.848379\pi$
$311$	−23.5982	+	7.66751i	−1.33813	+	0.434785i	−0.449447	+	0.893307i	$0.648379\pi$
$312$	−4.91942	+	15.1596i	−0.278508	+	0.858244i
$313$	12.6908	+	9.22040i	0.717326	+	0.521168i	0.885529	−	0.464584i	$-0.153796\pi$
$313$	12.6908	+	9.22040i	0.717326	+	0.521168i	−0.168203	+	0.985752i	$0.553796\pi$
$314$	−2.85964	−	2.07765i	−0.161379	−	0.117248i
$315$	−3.66767	+	11.3166i	−0.206650	+	0.637617i
$316$	23.1534	−	7.52301i	1.30248	−	0.423202i
$317$	2.54970	+	3.50936i	0.143205	+	0.197105i	0.874595	−	0.484855i	$-0.161128\pi$
$317$	2.54970	+	3.50936i	0.143205	+	0.197105i	−0.731389	+	0.681960i	$0.761128\pi$
$318$	1.58135		0.000588210i	0.0886779		3.29852e-5i
$319$	15.6556	+	5.12036i	0.876548	+	0.286685i
$320$			2.19056i			0.122456i
$321$	7.43471	+	10.2250i	0.414965	+	0.570704i
$322$	−1.03922	−	3.19840i	−0.0579137	−	0.178240i
$323$	−13.9647	−	4.53739i	−0.777015	−	0.252467i
$324$	11.9298	+	8.64042i	0.662767	+	0.480023i
$325$	26.4605	−	36.4198i	1.46777	−	2.02021i
$326$	−0.894321	+	2.75244i	−0.0495318	+	0.152443i
$327$	−4.92065	−	15.1250i	−0.272112	−	0.836417i
$328$	−7.40909	+	5.38302i	−0.409099	+	0.297228i
$329$	4.27120			0.235479
$330$	13.0650	−	4.22249i	0.719204	−	0.232440i
$331$	−13.7629			−0.756476			−0.378238	−	0.925708i	$-0.623470\pi$
$331$	−13.7629			−0.756476			−0.378238	+	0.925708i	$0.623470\pi$
$332$	−4.88301	+	3.54772i	−0.267990	+	0.194706i
$333$	2.96834	+	9.11255i	0.162664	+	0.499365i
$334$	−3.26354	+	10.0442i	−0.178573	+	0.549592i
$335$	14.4728	−	19.9201i	0.790733	−	1.08835i
$336$	−2.73613	−	1.98636i	−0.149268	−	0.108365i
$337$	−2.83380	−	0.920759i	−0.154367	−	0.0501569i	0.230814	−	0.972998i	$-0.425861\pi$
$337$	−2.83380	−	0.920759i	−0.154367	−	0.0501569i	−0.385181	+	0.922841i	$0.625861\pi$
$338$	0.860795	+	2.64926i	0.0468211	+	0.144101i
$339$	9.76306	−	7.09882i	0.530256	−	0.385555i
$340$			22.6083i			1.22611i
$341$	−6.70404	−	9.26499i	−0.363044	−	0.501727i
$342$	−0.00567023	−	7.62197i	−0.000306611	−	0.412149i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	11.7800	−	3.82756i	0.635135	−	0.206368i
$345$	36.4490	+	11.8280i	1.96235	+	0.636799i
$346$	6.63396	+	4.81985i	0.356644	+	0.259117i
$347$	9.48940	+	6.89445i	0.509418	+	0.370114i	0.812603	−	0.582818i	$-0.198050\pi$
$347$	9.48940	+	6.89445i	0.509418	+	0.370114i	−0.303185	+	0.952932i	$0.598050\pi$
$348$	−13.3914	−	4.34563i	−0.717855	−	0.232950i
$349$	7.78025	−	2.52796i	0.416467	−	0.135318i	−0.0932854	−	0.995639i	$-0.529737\pi$
$349$	7.78025	−	2.52796i	0.416467	−	0.135318i	0.509753	+	0.860321i	$0.329737\pi$
$350$	−3.79945	−	5.22950i	−0.203089	−	0.279528i
$351$	21.8123	−	0.0243403i	1.16426	−	0.00129919i
$352$	−0.0357097	+	18.4428i	−0.00190333	+	0.983004i
$353$			2.11407i			0.112521i	0.998416	+	0.0562603i	$0.0179177\pi$
$353$			2.11407i			0.112521i	−0.998416	+	0.0562603i	$0.982082\pi$
$354$	−3.09403	+	2.24970i	−0.164446	+	0.119570i
$355$	7.11608	+	21.9010i	0.377682	+	1.16239i
$356$	−5.13562	−	1.66866i	−0.272187	−	0.0884390i
$357$	−4.88266	−	3.54469i	−0.258418	−	0.187605i
$358$	−1.72962	+	2.38062i	−0.0914135	+	0.125820i
$359$	5.48029	−	16.8666i	0.289239	−	0.890186i	−0.695857	−	0.718180i	$-0.744975\pi$
$359$	5.48029	−	16.8666i	0.289239	−	0.890186i	0.985096	−	0.172005i	$-0.0550246\pi$
$360$	−24.7944	+	8.07658i	−1.30678	+	0.425673i
$361$	−0.997777	+	0.724927i	−0.0525146	+	0.0381541i
$362$	−4.51453			−0.237278
$363$	−18.1406	+	5.82410i	−0.952132	+	0.305686i
$364$	−6.87045			−0.360109
$365$	−18.2069	+	13.2281i	−0.952992	+	0.692389i
$366$	1.79889	+	5.52942i	0.0940296	+	0.289027i
$367$	−3.91324	+	12.0437i	−0.204269	+	0.628676i	0.795473	+	0.605989i	$0.207222\pi$
$367$	−3.91324	+	12.0437i	−0.204269	+	0.628676i	−0.999743	+	0.0226876i	$0.992778\pi$
$368$	−6.40183	+	8.81136i	−0.333719	+	0.459324i
$369$	10.1455	+	7.35960i	0.528153	+	0.383125i
$370$	−7.26188	−	2.35953i	−0.377527	−	0.122666i
$371$	0.468067	+	1.44056i	0.0243008	+	0.0747903i
$372$	5.74840	+	7.90581i	0.298041	+	0.409897i
$373$			29.3636i			1.52039i	0.649695	+	0.760195i	$0.274897\pi$
$373$			29.3636i			1.52039i	−0.649695	+	0.760195i	$0.725103\pi$
$374$	−0.0134840	+	6.96401i	−0.000697241	+	0.360100i
$375$	39.3140	−	0.0146235i	2.03017	−	0.000755153i
$376$	5.50322	+	7.57454i	0.283807	+	0.390627i
$377$	−19.8275	+	6.44236i	−1.02117	+	0.331798i
$378$	0.964523	−	2.97981i	0.0496097	−	0.153265i
$379$	0.855852	+	0.621813i	0.0439621	+	0.0319404i	0.609549	−	0.792748i	$-0.291350\pi$
$379$	0.855852	+	0.621813i	0.0439621	+	0.0319404i	−0.565587	+	0.824689i	$0.691350\pi$
$380$	−22.1313	−	16.0794i	−1.13531	−	0.824854i
$381$	−11.4531	+	35.2938i	−0.586762	+	1.80816i
$382$	13.3006	−	4.32163i	0.680518	−	0.221114i
$383$	18.1537	+	24.9865i	0.927613	+	1.27675i	0.960783	+	0.277300i	$0.0894396\pi$
$383$	18.1537	+	24.9865i	0.927613	+	1.27675i	−0.0331704	+	0.999450i	$0.510560\pi$
$384$	−0.00737967	−	19.8396i	−0.000376592	−	1.01244i
$385$	7.70970	+	10.6548i	0.392923	+	0.543020i
$386$		−	3.37727i		−	0.171899i
$387$	−9.97413	−	13.7068i	−0.507014	−	0.696754i
$388$	−9.80900	−	30.1890i	−0.497977	−	1.53261i
$389$	−14.2343	−	4.62499i	−0.721705	−	0.234496i	−0.0749428	−	0.997188i	$-0.523877\pi$
$389$	−14.2343	−	4.62499i	−0.721705	−	0.234496i	−0.646762	+	0.762692i	$0.723877\pi$
$390$	−10.2095	+	14.0631i	−0.516976	+	0.712113i
$391$	−11.4241	+	15.7240i	−0.577744	+	0.795196i
$392$	−0.677377	+	2.08475i	−0.0342127	+	0.105296i
$393$	−5.24706	+	1.70703i	−0.264679	+	0.0861083i
$394$	4.77818	−	3.47155i	0.240721	−	0.174894i
$395$	58.9830			2.96776
$396$	15.4937	−	5.01381i	0.778590	−	0.251953i
$397$	25.2222			1.26587			0.632933	−	0.774207i	$-0.281851\pi$
$397$	25.2222			1.26587			0.632933	+	0.774207i	$0.281851\pi$
$398$	−11.5316	+	8.37817i	−0.578025	+	0.419960i
$399$	6.94253	−	2.25862i	0.347561	−	0.113072i
$400$	−6.46909	+	19.9098i	−0.323455	+	0.995491i
$401$	−0.182407	+	0.251062i	−0.00910899	+	0.0125375i	−0.813547	−	0.581499i	$-0.802466\pi$
$401$	−0.182407	+	0.251062i	−0.00910899	+	0.0125375i	0.804438	+	0.594036i	$0.202466\pi$
$402$	−3.80848	+	5.24602i	−0.189949	+	0.261648i
$403$	13.7660	+	4.47285i	0.685733	+	0.222808i
$404$	−3.23706	−	9.96264i	−0.161050	−	0.495660i
$405$	21.0199	+	28.8411i	1.04449	+	1.43313i
$406$			2.99354i			0.148567i
$407$	10.0704	+	3.29364i	0.499170	+	0.163260i
$408$	−0.00491964	−	13.2260i	−0.000243558	−	0.654787i
$409$	−16.5574	−	22.7894i	−0.818713	−	1.12686i	−0.989920	−	0.141626i	$-0.954767\pi$
$409$	−16.5574	−	22.7894i	−0.818713	−	1.12686i	0.171207	−	0.985235i	$-0.445233\pi$
$410$	−9.49709	+	3.08579i	−0.469028	+	0.152396i
$411$	10.4532	−	32.2123i	0.515617	−	1.58892i
$412$	9.93657	+	7.21934i	0.489539	+	0.355671i
$413$	−2.96441	−	2.15377i	−0.145869	−	0.105980i
$414$	−9.59753	−	3.11054i	−0.471693	−	0.152874i
$415$	−13.9077	+	4.51888i	−0.682701	+	0.221823i
$416$	−13.7205	−	18.8847i	−0.672703	−	0.925896i
$417$	29.4180	−	0.0109425i	1.44061	−	0.000535857i
$418$	−6.80750	−	4.96611i	−0.332966	−	0.242900i
$419$		−	11.5059i		−	0.562099i	−0.959693	−	0.281049i	$-0.909318\pi$
$419$		−	11.5059i		−	0.562099i	0.959693	−	0.281049i	$-0.0906825\pi$
$420$	−6.61072	−	9.09176i	−0.322570	−	0.443632i
$421$	−11.4999	−	35.3931i	−0.560472	−	1.72495i	−0.681037	−	0.732249i	$-0.738471\pi$
$421$	−11.4999	−	35.3931i	−0.560472	−	1.72495i	0.120566	−	0.992705i	$-0.461529\pi$
$422$	7.11751	+	2.31262i	0.346475	+	0.112577i
$423$	7.52393	−	10.3720i	0.365826	−	0.504305i
$424$	−1.95161	+	2.68616i	−0.0947785	+	0.130451i
$425$	−11.5442	+	35.5293i	−0.559975	+	1.72342i
$426$	−1.87568	−	5.76545i	−0.0908770	−	0.279337i
$427$	−4.50588	+	3.27372i	−0.218055	+	0.158426i
$428$	−11.9461			−0.577438
$429$	14.2046	−	19.4868i	0.685805	−	0.940832i
$430$	13.5057			0.651301
$431$	26.1241	−	18.9803i	1.25835	−	0.914247i	0.259678	−	0.965695i	$-0.416384\pi$
$431$	26.1241	−	18.9803i	1.25835	−	0.914247i	0.998676	+	0.0514481i	$0.0163837\pi$
$432$	−9.64344	+	3.14524i	−0.463970	+	0.151326i
$433$	−3.62879	+	11.1683i	−0.174389	+	0.536713i	−0.999605	−	0.0281038i	$-0.991053\pi$
$433$	−3.62879	+	11.1683i	−0.174389	+	0.536713i	0.825216	+	0.564817i	$0.191053\pi$
$434$	1.22164	−	1.68144i	0.0586405	−	0.0807118i
$435$	−27.6033	−	20.0393i	−1.32348	−	0.960809i
$436$	14.2940	+	4.64440i	0.684557	+	0.222426i
$437$	−7.26724	−	22.3663i	−0.347639	−	1.06992i
$438$	4.79225	−	3.48450i	0.228982	−	0.166496i
$439$		−	5.65329i		−	0.269817i	−0.990858	−	0.134909i	$-0.956926\pi$
$439$		−	5.65329i		−	0.269817i	0.990858	−	0.134909i	$-0.0430741\pi$
$440$	−8.96167	+	27.4006i	−0.427231	+	1.30627i
$441$	3.00000	−	0.00223179i	0.142857	−	0.000106276i
$442$	−5.18087	−	7.13086i	−0.246429	−	0.339180i
$443$	11.3424	−	3.68536i	0.538892	−	0.175097i	−0.0269099	−	0.999638i	$-0.508567\pi$
$443$	11.3424	−	3.68536i	0.538892	−	0.175097i	0.565802	+	0.824541i	$0.308567\pi$
$444$	−8.61393	−	2.79529i	−0.408799	−	0.132659i
$445$	−10.5843	−	7.68994i	−0.501744	−	0.364538i
$446$	−11.2153	−	8.14841i	−0.531061	−	0.385839i
$447$	−18.1476	−	5.88904i	−0.858351	−	0.278542i
$448$	0.525388	−	0.170709i	0.0248222	−	0.00806523i
$449$	−6.94958	−	9.56528i	−0.327971	−	0.451413i	0.612909	−	0.790154i	$-0.289999\pi$
$449$	−6.94958	−	9.56528i	−0.327971	−	0.451413i	−0.940880	+	0.338740i	$0.889999\pi$
$450$	−19.3920	+	0.0144264i	−0.914150	+	0.000680065i
$451$	13.1866	−	4.25639i	0.620935	−	0.200425i
$452$			11.4064i			0.536513i
$453$	−7.52078	+	5.46844i	−0.353357	+	0.256930i
$454$	1.78513	+	5.49406i	0.0837802	+	0.257849i
$455$	−15.8310	−	5.14381i	−0.742170	−	0.241146i
$456$	12.9505	+	9.40174i	0.606464	+	0.440277i
$457$	−4.34195	+	5.97618i	−0.203108	+	0.279554i	−0.898405	−	0.439169i	$-0.855273\pi$
$457$	−4.34195	+	5.97618i	−0.203108	+	0.279554i	0.695297	+	0.718723i	$0.255273\pi$
$458$	3.37275	−	10.3803i	0.157598	−	0.485038i
$459$	−17.2088	+	5.61273i	−0.803240	+	0.261980i
$460$	−29.2947	+	21.2838i	−1.36587	+	0.992364i
$461$	2.87688			0.133990			0.0669949	−	0.997753i	$-0.478659\pi$
$461$	2.87688			0.133990			0.0669949	+	0.997753i	$0.478659\pi$
$462$	−2.03087	−	2.80447i	−0.0944846	−	0.130476i
$463$	11.2020			0.520603			0.260301	−	0.965527i	$-0.416178\pi$
$463$	11.2020			0.520603			0.260301	+	0.965527i	$0.416178\pi$
$464$	7.84334	−	5.69852i	0.364118	−	0.264547i
$465$	7.32662	+	22.5205i	0.339764	+	1.04436i
$466$	−1.64838	+	5.07320i	−0.0763598	+	0.235011i
$467$	1.26359	−	1.73918i	0.0584719	−	0.0804796i	−0.778780	−	0.627298i	$-0.784161\pi$
$467$	1.26359	−	1.73918i	0.0584719	−	0.0804796i	0.837252	+	0.546818i	$0.184161\pi$
$468$	−12.1026	+	16.6839i	−0.559444	+	0.771215i
$469$	−5.90551	−	1.91882i	−0.272691	−	0.0886028i
$470$	3.15470	+	9.70916i	0.145515	+	0.447850i
$471$	−5.97326	−	8.21506i	−0.275233	−	0.378530i
$472$		−	8.03210i		−	0.369707i
$473$	−18.7407	−	0.0362866i	−0.861699	−	0.00166846i
$474$	−15.5292	+	0.00577632i	−0.713278	+	0.000265315i
$475$	−26.5694	−	36.5696i	−1.21909	−	1.67793i
$476$	5.42240	−	1.76185i	0.248535	−	0.0807541i
$477$	4.32273	+	1.40099i	0.197924	+	0.0641467i
$478$	5.92594	+	4.30545i	0.271046	+	0.196927i
$479$	1.56224	+	1.13504i	0.0713807	+	0.0518611i	0.622903	−	0.782299i	$-0.285953\pi$
$479$	1.56224	+	1.13504i	0.0713807	+	0.0518611i	−0.551523	+	0.834160i	$0.685953\pi$
$480$	11.7885	−	36.3273i	0.538070	−	1.65811i
$481$	−12.7539	+	4.14400i	−0.581529	+	0.188950i
$482$	5.26745	+	7.25003i	0.239926	+	0.330230i
$483$	−0.00359458	−	9.66373i	−0.000163559	−	0.439715i
$484$	5.62966	−	17.1007i	0.255893	−	0.777304i
$485$		−	76.9060i		−	3.49212i
$486$	−5.53700	−	7.59129i	−0.251163	−	0.344348i
$487$	3.08998	+	9.50998i	0.140020	+	0.430938i	0.996337	−	0.0855126i	$-0.0272528\pi$
$487$	3.08998	+	9.50998i	0.140020	+	0.430938i	−0.856317	+	0.516451i	$0.827253\pi$
$488$	−11.6112	−	3.77271i	−0.525614	−	0.170782i
$489$	−4.88568	+	6.72982i	−0.220938	+	0.304333i
$490$	−1.40490	+	1.93367i	−0.0634667	+	0.0873544i
$491$	10.2834	−	31.6491i	0.464084	−	1.42830i	−0.396047	−	0.918230i	$-0.629618\pi$
$491$	10.2834	−	31.6491i	0.464084	−	1.42830i	0.860131	−	0.510073i	$-0.170382\pi$
$492$	−11.2626	+	3.66407i	−0.507757	+	0.165189i
$493$	13.9965	−	10.1691i	0.630373	−	0.457993i
$494$	10.6651			0.479847
$495$	39.4548	+	0.0470422i	1.77336	+	0.00211439i
$496$	−6.73105			−0.302233
$497$	4.69822	−	3.41346i	0.210744	−	0.153115i
$498$	3.66120	−	1.19110i	0.164062	−	0.0533745i
$499$	7.54652	−	23.2258i	0.337829	−	1.03973i	−0.627483	−	0.778630i	$-0.715915\pi$
$499$	7.54652	−	23.2258i	0.337829	−	1.03973i	0.965312	−	0.261100i	$-0.0840852\pi$
$500$	−21.8359	+	30.0545i	−0.976530	+	1.34408i
$501$	−17.8288	+	24.5584i	−0.796530	+	1.09719i
$502$	−7.49453	−	2.43512i	−0.334497	−	0.108685i
$503$	4.68422	+	14.4165i	0.208859	+	0.642802i	0.999533	+	0.0305644i	$0.00973045\pi$
$503$	4.68422	+	14.4165i	0.208859	+	0.642802i	−0.790674	+	0.612238i	$0.790270\pi$
$504$	3.86930	+	5.31731i	0.172352	+	0.236852i
$505$		−	25.3797i		−	1.12938i
$506$	−9.03630	+	6.53856i	−0.401713	+	0.290675i
$507$	0.00297741	+	8.00452i	0.000132231	+	0.355493i
$508$	−20.6092	−	28.3662i	−0.914387	−	1.25855i
$509$	−5.94207	+	1.93070i	−0.263378	+	0.0855766i	−0.437729	−	0.899107i	$-0.644217\pi$
$509$	−5.94207	+	1.93070i	−0.263378	+	0.0855766i	0.174351	+	0.984683i	$0.444217\pi$
$510$	4.45135	−	13.7172i	0.197109	−	0.607408i
$511$	4.59149	+	3.33591i	0.203115	+	0.147572i
$512$	15.7056	+	11.4108i	0.694097	+	0.504291i
$513$	6.74486	−	20.8376i	0.297793	−	0.920004i
$514$	−8.39836	+	2.72879i	−0.370436	+	0.120362i
$515$	17.4910	+	24.0743i	0.770747	+	1.06084i
$516$	16.0183	−	0.00595825i	0.705166	−	0.000262297i
$517$	−4.35143	−	13.4811i	−0.191376	−	0.592898i
$518$			1.92557i			0.0846049i
$519$	13.8571	+	19.0578i	0.608261	+	0.836545i
$520$	−11.2754	−	34.7022i	−0.494461	−	1.52179i
$521$	−0.511768	−	0.166284i	−0.0224210	−	0.00728501i	0.297785	−	0.954633i	$-0.403752\pi$
$521$	−0.511768	−	0.166284i	−0.0224210	−	0.00728501i	−0.320206	+	0.947348i	$0.603752\pi$
$522$	7.26940	+	5.27327i	0.318173	+	0.230805i
$523$	4.39362	−	6.04730i	0.192120	−	0.264430i	−0.702080	−	0.712098i	$-0.747745\pi$
$523$	4.39362	−	6.04730i	0.192120	−	0.264430i	0.894200	+	0.447668i	$0.147745\pi$
$524$	1.61120	−	4.95875i	0.0703854	−	0.216624i
$525$	−5.74645	−	17.6634i	−0.250795	−	0.770893i
$526$	−12.7794	+	9.28481i	−0.557210	+	0.404837i
$527$	−12.0116			−0.523235
$528$	−3.48198	+	10.6597i	−0.151534	+	0.463902i
$529$	−8.12923			−0.353445
$530$	−2.92893	+	2.12799i	−0.127225	+	0.0924340i
$531$	−10.4521	+	3.40469i	−0.453582	+	0.147751i
$532$	−2.13182	+	6.56106i	−0.0924260	+	0.284458i
$533$	−10.3086	+	14.1885i	−0.446513	+	0.614573i
$534$	2.78741	+	2.02359i	0.120623	+	0.0875692i
$535$	−27.5265	−	8.94391i	−1.19008	−	0.386679i
$536$	−4.20612	−	12.9451i	−0.181677	−	0.559144i
$537$	−6.83898	+	4.97270i	−0.295124	+	0.214588i
$538$			7.12075i			0.306997i
$539$	1.95465	−	2.67943i	0.0841929	−	0.115411i
$540$	−33.7232	+	0.0376316i	−1.45121	+	0.00161941i
$541$	16.2326	+	22.3423i	0.697895	+	0.960570i	0.999973	+	0.00728677i	$0.00231947\pi$
$541$	16.2326	+	22.3423i	0.697895	+	0.960570i	−0.302079	+	0.953283i	$0.597681\pi$
$542$	−3.63773	+	1.18197i	−0.156254	+	0.0507699i
$543$	−12.3393	−	4.00419i	−0.529528	−	0.171836i
$544$	15.6715	+	11.3860i	0.671909	+	0.488170i
$545$	29.4593	+	21.4034i	1.26190	+	0.916822i
$546$	4.16853	+	1.35272i	0.178397	+	0.0578912i
$547$	−18.3343	+	5.95716i	−0.783916	+	0.254710i	−0.673511	−	0.739177i	$-0.735215\pi$
$547$	−18.3343	+	5.95716i	−0.783916	+	0.254710i	−0.110405	+	0.993887i	$0.535215\pi$
$548$	18.8099	+	25.8896i	0.803518	+	1.10595i
$549$	0.0124302	+	16.7087i	0.000530506	+	0.713111i
$550$	−12.6349	+	17.3199i	−0.538755	+	0.738521i
$551$			20.9337i			0.891805i
$552$	17.1330	−	12.4576i	0.729229	−	0.530230i
$553$	−4.59650	−	14.1466i	−0.195463	−	0.601573i
$554$	17.9016	+	5.81658i	0.760566	+	0.247123i
$555$	−17.7556	−	12.8901i	−0.753684	−	0.547155i
$556$	−16.3394	+	22.4893i	−0.692945	+	0.953757i
$557$	−12.5122	+	38.5085i	−0.530158	+	1.63166i	0.223727	+	0.974652i	$0.428178\pi$
$557$	−12.5122	+	38.5085i	−0.530158	+	1.63166i	−0.753885	+	0.657006i	$0.771822\pi$
$558$	−1.93117	−	5.92852i	−0.0817530	−	0.250974i
$559$	19.1897	−	13.9422i	0.811639	−	0.589690i
$560$	7.74076			0.327107
$561$	−6.21363	+	19.0223i	−0.262340	+	0.803122i
$562$	8.82310			0.372180
$563$	−3.21142	+	2.33323i	−0.135345	+	0.0983341i	−0.653398	−	0.757015i	$-0.726657\pi$
$563$	−3.21142	+	2.33323i	−0.135345	+	0.0983341i	0.518053	+	0.855349i	$0.326657\pi$
$564$	3.74589	+	11.5141i	0.157730	+	0.484830i
$565$	−8.53984	+	26.2829i	−0.359274	+	1.10573i
$566$	0.588451	−	0.809933i	0.0247344	−	0.0340440i
$567$	5.27923	−	7.28902i	0.221707	−	0.306110i
$568$	12.1068	+	3.93375i	0.507992	+	0.165056i
$569$	10.9286	+	33.6349i	0.458152	+	1.41005i	0.867395	+	0.497621i	$0.165793\pi$
$569$	10.9286	+	33.6349i	0.458152	+	1.41005i	−0.409243	+	0.912426i	$0.634207\pi$
$570$	10.2620	+	14.1133i	0.429826	+	0.591142i
$571$		−	27.6721i		−	1.15804i	−0.815312	−	0.579021i	$-0.803435\pi$
$571$		−	27.6721i		−	1.15804i	0.815312	−	0.579021i	$-0.196565\pi$
$572$	6.99950	+	21.6850i	0.292664	+	0.906696i
$573$	40.1867	−	0.0149481i	1.67882	−	0.000624465i
$574$	1.48020	+	2.03732i	0.0617824	+	0.0850362i
$575$	−56.9050	+	18.4895i	−2.37310	+	0.771067i
$576$	0.510954	−	1.57654i	0.0212897	−	0.0656893i
$577$	−11.5579	−	8.39734i	−0.481163	−	0.349586i	0.320613	−	0.947210i	$-0.396111\pi$
$577$	−11.5579	−	8.39734i	−0.481163	−	0.349586i	−0.801776	+	0.597625i	$0.796111\pi$
$578$	−2.37235	−	1.72361i	−0.0986766	−	0.0716927i
$579$	2.99550	−	9.23088i	0.124489	−	0.383622i
$580$	30.6546	−	9.96028i	1.27286	−	0.413578i
$581$	2.16763	+	2.98348i	0.0899283	+	0.123776i
$582$	0.00753155	+	20.2480i	0.000312193	+	0.839305i
$583$	4.06995	−	2.94497i	0.168560	−	0.121968i
$584$			12.4407i			0.514799i
$585$	−40.3782	+	29.3824i	−1.66943	+	1.21481i
$586$	−3.69650	−	11.3767i	−0.152701	−	0.469965i
$587$	26.7406	+	8.68854i	1.10370	+	0.358615i	0.803526	−	0.595269i	$-0.202955\pi$
$587$	26.7406	+	8.68854i	1.10370	+	0.358615i	0.300176	+	0.953884i	$0.402955\pi$
$588$	−1.66541	+	2.29404i	−0.0686804	+	0.0946044i
$589$	8.54285	−	11.7582i	0.352002	−	0.484489i
$590$	2.70638	−	8.32938i	0.111420	−	0.342915i
$591$	16.1390	−	5.25051i	0.663869	−	0.215977i
$592$	5.04518	−	3.66554i	0.207356	−	0.150653i
$593$	38.8077			1.59364			0.796821	−	0.604216i	$-0.206513\pi$
$593$	38.8077			1.59364			0.796821	+	0.604216i	$0.206513\pi$
$594$	−10.3877	−	0.00852149i	−0.426214	−	0.000349641i
$595$	13.8135			0.566298
$596$	14.5855	−	10.5970i	0.597446	−	0.434070i
$597$	−38.9495	+	12.6715i	−1.59410	+	0.518609i
$598$	4.36244	−	13.4262i	0.178394	−	0.549039i
$599$	9.32449	−	12.8341i	0.380988	−	0.524386i	−0.574858	−	0.818253i	$-0.694943\pi$
$599$	9.32449	−	12.8341i	0.380988	−	0.524386i	0.955846	+	0.293868i	$0.0949425\pi$
$600$	23.9202	−	32.9491i	0.976538	−	1.34514i
$601$	−8.94685	−	2.90701i	−0.364950	−	0.118579i	0.120801	−	0.992677i	$-0.461454\pi$
$601$	−8.94685	−	2.90701i	−0.364950	−	0.118579i	−0.485751	+	0.874097i	$0.661454\pi$
$602$	−1.05249	−	3.23922i	−0.0428961	−	0.132021i
$603$	−15.0624	+	10.9606i	−0.613390	+	0.446351i
$604$		−	8.78671i		−	0.357526i
$605$	25.7750	−	35.1889i	1.04790	−	1.43063i
$606$	0.00248548	+	6.68201i	0.000100966	+	0.271438i
$607$	−10.4830	−	14.4285i	−0.425490	−	0.585637i	0.541421	−	0.840752i	$-0.317887\pi$
$607$	−10.4830	−	14.4285i	−0.425490	−	0.585637i	−0.966911	+	0.255115i	$0.917887\pi$
$608$	−22.2916	+	7.24297i	−0.904042	+	0.293741i
$609$	−2.65514	+	8.18204i	−0.107592	+	0.331553i
$610$	−10.7697	−	7.82468i	−0.436054	−	0.316812i
$611$	14.5053	+	10.5387i	0.586823	+	0.426352i
$612$	5.27343	−	16.2711i	0.213166	−	0.657722i
$613$	41.1687	−	13.3765i	1.66279	−	0.540273i	0.681335	−	0.731972i	$-0.261400\pi$
$613$	41.1687	−	13.3765i	1.66279	−	0.540273i	0.981454	+	0.191699i	$0.0613999\pi$
$614$	−3.51856	−	4.84288i	−0.141997	−	0.195443i
$615$	−28.6947	+	0.0106735i	−1.15708	+	0.000430395i
$616$	7.27016	+	0.0140768i	0.292923	+	0.000567170i
$617$		−	32.2071i		−	1.29661i	−0.761381	−	0.648304i	$-0.775479\pi$
$617$		−	32.2071i		−	1.29661i	0.761381	−	0.648304i	$-0.224521\pi$
$618$	−4.60743	−	6.33662i	−0.185338	−	0.254896i
$619$	12.6519	+	38.9384i	0.508521	+	1.56507i	0.794769	+	0.606912i	$0.207592\pi$
$619$	12.6519	+	38.9384i	0.508521	+	1.56507i	−0.286248	+	0.958156i	$0.592408\pi$
$620$	−21.2831	−	6.91529i	−0.854749	−	0.277725i
$621$	−23.4734	−	17.0144i	−0.941954	−	0.682765i
$622$	−8.79091	+	12.0996i	−0.352483	+	0.485152i
$623$	−1.01954	+	3.13782i	−0.0408470	+	0.125714i
$624$	−4.39098	−	13.4970i	−0.175780	−	0.540311i
$625$	−29.4363	+	21.3867i	−1.17745	+	0.855469i
$626$	9.45528			0.377909
$627$	−14.2018	−	19.6115i	−0.567164	−	0.783207i
$628$	9.59786			0.382996
$629$	9.00318	−	6.54120i	0.358980	−	0.260815i
$630$	2.22086	+	6.81786i	0.0884814	+	0.271630i
$631$	−4.46868	+	13.7532i	−0.177895	+	0.547505i	−0.999754	−	0.0221862i	$-0.992937\pi$
$631$	−4.46868	+	13.7532i	−0.177895	+	0.547505i	0.821859	+	0.569692i	$0.192937\pi$
$632$	19.1651	−	26.3785i	0.762348	−	1.04928i
$633$	17.4026	+	12.6339i	0.691692	+	0.502151i
$634$	2.48668	+	0.807971i	0.0987586	+	0.0320886i
$635$	−26.2509	−	80.7919i	−1.04173	−	3.20613i
$636$	−3.47289	+	2.52518i	−0.137709	+	0.100130i
$637$			4.19779i			0.166322i
$638$	9.44844	−	3.04977i	0.374067	−	0.120742i
$639$	−0.0129608	−	17.4220i	−0.000512719	−	0.689202i
$640$	26.6977	+	36.7463i	1.05532	+	1.45252i
$641$	26.4033	−	8.57894i	1.04287	−	0.338848i	0.263001	−	0.964796i	$-0.415288\pi$
$641$	26.4033	−	8.57894i	1.04287	−	0.338848i	0.779865	+	0.625948i	$0.215288\pi$
$642$	7.24811	+	2.35207i	0.286060	+	0.0928290i
$643$	2.01761	+	1.46588i	0.0795669	+	0.0578088i	0.626858	−	0.779134i	$-0.284341\pi$
$643$	2.01761	+	1.46588i	0.0795669	+	0.0578088i	−0.547291	+	0.836943i	$0.684341\pi$
$644$	7.38765	+	5.36744i	0.291114	+	0.211507i
$645$	36.9141	+	11.9789i	1.45349	+	0.471671i
$646$	−8.41731	+	2.73495i	−0.331175	+	0.107605i
$647$	13.8739	+	19.0958i	0.545441	+	0.750735i	0.989385	−	0.145319i	$-0.0464210\pi$
$647$	13.8739	+	19.0958i	0.545441	+	0.750735i	−0.443944	+	0.896055i	$0.646421\pi$
$648$	19.7283	−	0.0293531i	0.775002	−	0.00115310i
$649$	−3.77780	+	11.5507i	−0.148292	+	0.453406i
$650$		−	27.1346i		−	1.06431i
$651$	4.83039	−	3.51223i	0.189318	−	0.137655i
$652$	−2.42837	−	7.47375i	−0.0951023	−	0.292695i
$653$	21.1773	+	6.88092i	0.828731	+	0.269271i	0.692511	−	0.721408i	$-0.256505\pi$
$653$	21.1773	+	6.88092i	0.828731	+	0.269271i	0.136220	+	0.990679i	$0.456505\pi$
$654$	−7.75820	−	5.63225i	−0.303370	−	0.220238i
$655$	7.42510	−	10.2198i	0.290123	−	0.399320i
$656$	2.52025	−	7.75652i	0.0983990	−	0.302841i
$657$	16.1889	−	5.27342i	0.631590	−	0.205736i
$658$	2.08281	−	1.51325i	0.0811966	−	0.0589928i
$659$	2.16490			0.0843324			0.0421662	−	0.999111i	$-0.486574\pi$
$659$	2.16490			0.0843324			0.0421662	+	0.999111i	$0.486574\pi$
$660$	−21.9612	+	30.1278i	−0.854839	+	1.17272i
$661$	−22.3517			−0.869382			−0.434691	−	0.900580i	$-0.643142\pi$
$661$	−22.3517			−0.869382			−0.434691	+	0.900580i	$0.643142\pi$
$662$	−6.71135	+	4.87608i	−0.260844	+	0.189514i
$663$	−7.83576	−	24.0855i	−0.304316	−	0.935403i
$664$	−2.49802	+	7.68813i	−0.0969421	+	0.298357i
$665$	−9.82436	+	13.5221i	−0.380972	+	0.524363i
$666$	4.67599	+	3.39200i	0.181191	+	0.131437i
$667$	26.3532	+	8.56266i	1.02040	+	0.331548i
$668$	−8.86158	−	27.2731i	−0.342865	−	1.05523i
$669$	−23.4268	−	32.2190i	−0.905732	−	1.24566i
$670$		−	14.8415i		−	0.573376i
$671$	14.9233	+	10.8866i	0.576107	+	0.420273i
$672$	−9.63145	+	0.00358257i	−0.371541	+	0.000138201i
$673$	20.8500	+	28.6975i	0.803707	+	1.10621i	0.992264	+	0.124145i	$0.0396189\pi$
$673$	20.8500	+	28.6975i	0.803707	+	1.10621i	−0.188557	+	0.982062i	$0.560381\pi$
$674$	−1.70810	+	0.554995i	−0.0657935	+	0.0213776i
$675$	−53.0157	−	17.1605i	−2.04058	−	0.660507i
$676$	−6.11923	−	4.44588i	−0.235355	−	0.170995i
$677$	−31.6848	−	23.0204i	−1.21775	−	0.884745i	−0.221835	−	0.975084i	$-0.571205\pi$
$677$	−31.6848	−	23.0204i	−1.21775	−	0.884745i	−0.995911	+	0.0903395i	$0.971205\pi$
$678$	2.24581	−	6.92066i	0.0862499	−	0.265786i
$679$	−18.4452	+	5.99322i	−0.707863	+	0.229999i
$680$	17.7980	+	24.4968i	0.682521	+	0.939410i
$681$	0.00617458	+	16.5999i	0.000236610	+	0.636108i
$682$	−6.55168	−	2.14280i	−0.250877	−	0.0820522i
$683$			28.5288i			1.09162i	0.837908	+	0.545812i	$0.183779\pi$
$683$			28.5288i			1.09162i	−0.837908	+	0.545812i	$0.816221\pi$
$684$	12.1773	+	16.7345i	0.465612	+	0.639858i
$685$	23.9589	+	73.7380i	0.915424	+	2.81738i
$686$	0.573257	+	0.186262i	0.0218870	+	0.00711153i
$687$	18.4254	−	25.3802i	0.702971	−	0.968314i
$688$	−6.48352	+	8.92380i	−0.247182	+	0.340217i
$689$	−1.96485	+	6.04717i	−0.0748546	+	0.230379i
$690$	21.9646	−	7.14578i	0.836179	−	0.272035i
$691$	13.2741	−	9.64422i	0.504972	−	0.366883i	−0.305941	−	0.952050i	$-0.598971\pi$
$691$	13.2741	−	9.64422i	0.504972	−	0.366883i	0.810913	+	0.585167i	$0.198971\pi$
$692$	−22.2657			−0.846416
$693$	−3.06340	−	9.46655i	−0.116369	−	0.359605i
$694$	7.07007			0.268376
$695$	−54.4870	+	39.5871i	−2.06681	+	1.50163i
$696$	−17.9310	+	5.83352i	−0.679674	+	0.221119i
$697$	4.49741	−	13.8416i	0.170352	−	0.524288i
$698$	2.89834	−	3.98922i	0.109704	−	0.150994i
$699$	−9.00512	+	12.4042i	−0.340605	+	0.469169i
$700$	16.6928	+	5.42383i	0.630930	+	0.205002i
$701$	−4.21794	−	12.9815i	−0.159309	−	0.490304i	0.839263	−	0.543726i	$-0.182987\pi$
$701$	−4.21794	−	12.9815i	−0.159309	−	0.490304i	−0.998572	+	0.0534225i	$0.982987\pi$
$702$	10.6280	−	7.73981i	0.401127	−	0.292120i
$703$			13.4654i			0.507859i
$704$	−1.07406	−	1.48435i	−0.0404802	−	0.0559437i
$705$	0.0109118	+	29.3355i	0.000410962	+	1.10484i
$706$	0.748999	+	1.03091i	0.0281890	+	0.0387988i
$707$	−6.08709	+	1.97782i	−0.228929	+	0.0743834i
$708$	3.20620	−	9.88018i	0.120496	−	0.371320i
$709$	11.2593	+	8.18038i	0.422853	+	0.307221i	0.778785	−	0.627291i	$-0.215836\pi$
$709$	11.2593	+	8.18038i	0.422853	+	0.307221i	−0.355932	+	0.934512i	$0.615836\pi$
$710$	11.2295	+	8.15868i	0.421434	+	0.306190i
$711$	−42.4499	−	13.7579i	−1.59200	−	0.515962i
$712$	−6.87823	+	2.23487i	−0.257773	+	0.0837554i
$713$	−11.3080	−	15.5641i	−0.423486	−	0.582879i
$714$	−3.63684	+	0.00135278i	−0.136105	+	5.06266e-5i
$715$	−0.106895	+	55.2075i	−0.00399765	+	2.06464i
$716$		−	7.99015i		−	0.298606i
$717$	12.3782	+	17.0238i	0.462273	+	0.635767i
$718$	−3.30329	−	10.1665i	−0.123278	−	0.379410i
$719$	−8.33965	−	2.70972i	−0.311016	−	0.101055i	0.149350	−	0.988784i	$-0.452282\pi$
$719$	−8.33965	−	2.70972i	−0.311016	−	0.101055i	−0.460366	+	0.887729i	$0.652282\pi$
$720$	13.6357	−	18.7974i	0.508174	−	0.700537i
$721$	4.41096	−	6.07116i	0.164273	−	0.226102i
$722$	−0.229721	+	0.707009i	−0.00854934	+	0.0263121i
$723$	7.96671	+	24.4880i	0.296285	+	0.910719i
$724$	9.91726	−	7.20531i	0.368572	−	0.267783i
$725$	53.2601			1.97803
$726$	−6.78265	+	9.26713i	−0.251728	+	0.343935i
$727$	−20.6194			−0.764733			−0.382366	−	0.924011i	$-0.624891\pi$
$727$	−20.6194			−0.764733			−0.382366	+	0.924011i	$0.624891\pi$
$728$	−7.44434	+	5.40863i	−0.275906	+	0.200457i
$729$	−8.40075	−	25.6598i	−0.311139	−	0.950364i
$730$	−4.19183	+	12.9011i	−0.155146	+	0.477492i
$731$	−11.5699	+	15.9246i	−0.427929	+	0.588994i
$732$	−12.7768	−	9.27564i	−0.472245	−	0.342837i
$733$	42.6422	+	13.8553i	1.57502	+	0.511756i	0.960769	−	0.277351i	$-0.0894565\pi$
$733$	42.6422	+	13.8553i	1.57502	+	0.511756i	0.614255	+	0.789107i	$0.289457\pi$
$734$	2.35873	+	7.25944i	0.0870625	+	0.267951i
$735$	−5.55499	+	4.03909i	−0.204899	+	0.148984i
$736$			31.0252i			1.14361i
$737$	−0.0398755	+	20.5943i	−0.00146883	+	0.758601i
$738$	7.55480	−	0.00562026i	0.278096	−	0.000206885i
$739$	−2.27163	−	3.12663i	−0.0835633	−	0.115015i	0.765189	−	0.643806i	$-0.222646\pi$
$739$	−2.27163	−	3.12663i	−0.0835633	−	0.115015i	−0.848752	+	0.528791i	$0.822646\pi$
$740$	19.7184	−	6.40688i	0.724861	−	0.235522i
$741$	29.1503	+	9.45952i	1.07086	+	0.347504i
$742$	0.738629	+	0.536645i	0.0271159	+	0.0197009i
$743$	−2.87687	−	2.09017i	−0.105542	−	0.0766810i	0.533762	−	0.845635i	$-0.320778\pi$
$743$	−2.87687	−	2.09017i	−0.105542	−	0.0766810i	−0.639305	+	0.768954i	$0.720778\pi$
$744$	12.4523	+	4.04087i	0.456523	+	0.148146i
$745$	41.5421	−	13.4978i	1.52198	−	0.494522i
$746$	10.4033	+	14.3189i	0.380892	+	0.524253i
$747$	11.0634	−	0.00823038i	0.404787	−	0.000301134i
$748$	−11.0851	−	15.3197i	−0.405312	−	0.560142i
$749$			7.29899i			0.266699i
$750$	19.1660	−	13.9358i	0.699842	−	0.508863i
$751$	−6.87650	−	21.1637i	−0.250927	−	0.772274i	−0.994605	−	0.103736i	$-0.966920\pi$
$751$	−6.87650	−	21.1637i	−0.250927	−	0.772274i	0.743678	−	0.668538i	$-0.233080\pi$
$752$	−7.92972	−	2.57652i	−0.289167	−	0.0939561i
$753$	−18.3245	−	13.3031i	−0.667780	−	0.484791i
$754$	−7.38625	+	10.1663i	−0.268992	+	0.370235i
$755$	6.57850	−	20.2465i	0.239416	−	0.736847i
$756$	2.63704	+	8.08528i	0.0959084	+	0.294059i
$757$	15.5043	−	11.2646i	0.563515	−	0.409417i	−0.269229	−	0.963076i	$-0.586769\pi$
$757$	15.5043	−	11.2646i	0.563515	−	0.409417i	0.832744	+	0.553659i	$0.186769\pi$
$758$	0.637652			0.0231606
$759$	−30.4977	+	9.85660i	−1.10700	+	0.357772i
$760$	−36.6382			−1.32901
$761$	21.8967	−	15.9089i	0.793755	−	0.576697i	−0.115320	−	0.993328i	$-0.536789\pi$
$761$	21.8967	−	15.9089i	0.793755	−	0.576697i	0.909075	+	0.416632i	$0.136789\pi$
$762$	6.91929	+	21.2685i	0.250660	+	0.770475i
$763$	2.83769	−	8.73351i	0.102731	−	0.316174i
$764$	−22.3206	+	30.7216i	−0.807529	+	1.11147i
$765$	24.3331	−	33.5442i	0.879767	−	1.21279i
$766$	17.7050	+	5.75271i	0.639709	+	0.207854i
$767$	−4.75317	−	14.6288i	−0.171627	−	0.528214i
$768$	−5.90723	−	8.12425i	−0.213159	−	0.293159i
$769$		−	2.32657i		−	0.0838982i	−0.999120	−	0.0419491i	$-0.986643\pi$
$769$		−	2.32657i		−	0.0838982i	0.999120	−	0.0419491i	$-0.0133567\pi$
$770$	7.53449	+	2.46424i	0.271524	+	0.0888052i
$771$	−25.3750	+	0.00943863i	−0.913858	+	0.000339924i
$772$	5.39022	+	7.41901i	0.193998	+	0.267016i
$773$	38.7688	−	12.5967i	1.39442	−	0.453073i	0.487035	−	0.873383i	$-0.338079\pi$
$773$	38.7688	−	12.5967i	1.39442	−	0.453073i	0.907381	+	0.420310i	$0.138079\pi$
$774$	−9.72000	−	3.15023i	−0.349378	−	0.113233i
$775$	−29.9156	−	21.7350i	−1.07460	−	0.780744i
$776$	−34.3941	−	24.9888i	−1.23468	−	0.897045i
$777$	−1.70790	+	5.26304i	−0.0612706	+	0.188811i
$778$	−8.57981	+	2.78775i	−0.307601	+	0.0999456i
$779$	10.3510	+	14.2469i	0.370862	+	0.510448i
$780$	−0.0175522	−	47.1876i	−0.000628469	−	1.68959i
$781$	−15.5603	−	11.3513i	−0.556791	−	0.406182i
$782$			11.7152i			0.418933i
$783$	15.1918	+	20.8607i	0.542911	+	0.745501i
$784$	−0.603231	−	1.85655i	−0.0215440	−	0.0663055i
$785$	22.1156	+	7.18580i	0.789340	+	0.256472i
$786$	−1.95389	+	2.69141i	−0.0696931	+	0.0959994i
$787$	4.51841	−	6.21905i	0.161064	−	0.221685i	−0.720856	−	0.693085i	$-0.756251\pi$
$787$	4.51841	−	6.21905i	0.161064	−	0.221685i	0.881920	+	0.471400i	$0.156251\pi$
$788$	−4.95574	+	15.2522i	−0.176541	+	0.543337i
$789$	−43.1644	+	14.0427i	−1.53669	+	0.499934i
$790$	28.7626	−	20.8972i	1.02333	−	0.743490i
$791$	6.96923			0.247797
$792$	12.8409	−	17.6298i	0.456283	−	0.626447i
$793$	−23.3799			−0.830245
$794$	12.2994	−	8.93603i	0.436489	−	0.317128i
$795$	−9.89288	+	3.21846i	−0.350864	+	0.114147i
$796$	11.9601	−	36.8094i	0.423914	−	1.30467i
$797$	−23.6855	+	32.6003i	−0.838983	+	1.15476i	0.147201	+	0.989107i	$0.452974\pi$
$797$	−23.6855	+	32.6003i	−0.838983	+	1.15476i	−0.986184	+	0.165654i	$0.947026\pi$
$798$	2.58525	−	3.56108i	0.0915169	−	0.126061i
$799$	−14.1507	−	4.59784i	−0.500615	−	0.162660i
$800$	18.4278	+	56.7149i	0.651520	+	2.00517i
$801$	5.82380	+	8.00324i	0.205774	+	0.282781i
$802$			0.187054i			0.00660510i
$803$	5.85132	−	17.8906i	0.206489	−	0.631344i
$804$	−0.00654756	−	17.6026i	−0.000230915	−	0.620795i
$805$	13.0043	+	17.8988i	0.458340	+	0.630850i
$806$	8.29757	−	2.69604i	0.292269	−	0.0949641i
$807$	−6.31580	+	19.4627i	−0.222327	+	0.685118i
$808$	−11.3504	−	8.24651i	−0.399304	−	0.290111i
$809$	−25.7435	−	18.7038i	−0.905094	−	0.657589i	0.0346752	−	0.999399i	$-0.488960\pi$
$809$	−25.7435	−	18.7038i	−0.905094	−	0.657589i	−0.939769	+	0.341809i	$0.888960\pi$
$810$	20.4684	+	6.61693i	0.719186	+	0.232495i
$811$	46.0702	−	14.9691i	1.61774	−	0.525637i	0.646336	−	0.763053i	$-0.276301\pi$
$811$	46.0702	−	14.9691i	1.61774	−	0.525637i	0.971408	+	0.237416i	$0.0763005\pi$
$812$	−4.77777	−	6.57604i	−0.167667	−	0.230774i
$813$	−10.9911	+	0.00408831i	−0.385475	+	0.000143383i
$814$	6.07765	−	1.96174i	0.213021	−	0.0687591i
$815$		−	19.0393i		−	0.666917i
$816$	6.92666	+	9.52628i	0.242482	+	0.333486i
$817$	−7.35997	−	22.6517i	−0.257493	−	0.792482i
$818$	−16.1482	−	5.24686i	−0.564608	−	0.183452i
$819$	10.1937	+	7.39461i	0.356198	+	0.258389i
$820$	15.9377	−	21.9363i	0.556567	−	0.766049i
$821$	4.10135	−	12.6227i	0.143138	−	0.440534i	−0.853629	−	0.520882i	$-0.825603\pi$
$821$	4.10135	−	12.6227i	0.143138	−	0.440534i	0.996767	+	0.0803481i	$0.0256032\pi$
$822$	−6.31517	−	19.4115i	−0.220267	−	0.677055i
$823$	−8.55048	+	6.21229i	−0.298051	+	0.216547i	−0.726752	−	0.686900i	$-0.758971\pi$
$823$	−8.55048	+	6.21229i	−0.298051	+	0.216547i	0.428701	+	0.903446i	$0.358971\pi$
$824$	16.4499			0.573058
$825$	−49.8961	+	36.1325i	−1.73716	+	1.25797i
$826$	−2.20863			−0.0768482
$827$	−3.50004	+	2.54293i	−0.121708	+	0.0884262i	−0.646974	−	0.762512i	$-0.723966\pi$
$827$	−3.50004	+	2.54293i	−0.121708	+	0.0884262i	0.525266	+	0.850938i	$0.323966\pi$
$828$	26.0478	−	8.48488i	0.905224	−	0.294870i
$829$	−12.8056	+	39.4115i	−0.444756	+	1.36882i	0.437996	+	0.898977i	$0.355689\pi$
$829$	−12.8056	+	39.4115i	−0.444756	+	1.36882i	−0.882751	+	0.469840i	$0.844311\pi$
$830$	−5.18096	+	7.13097i	−0.179834	+	0.247520i
$831$	43.7702	+	31.7760i	1.51837	+	1.10230i
$832$	2.20546	+	0.716599i	0.0764607	+	0.0248436i
$833$	−1.07647	−	3.31304i	−0.0372976	−	0.114790i
$834$	14.3416	−	10.4279i	0.496608	−	0.361089i
$835$		−	69.4779i		−	2.40438i
$836$	22.8804	+	0.0443019i	0.791334	+	0.00153221i
$837$	−0.0199934	−	17.9169i	−0.000691074	−	0.619299i
$838$	−4.07644	−	5.61074i	−0.140818	−	0.193820i
$839$	18.2812	−	5.93991i	0.631136	−	0.205068i	0.0240577	−	0.999711i	$-0.492341\pi$
$839$	18.2812	−	5.93991i	0.631136	−	0.205068i	0.607078	+	0.794642i	$0.292341\pi$
$840$	−14.3202	−	4.64704i	−0.494095	−	0.160338i
$841$	3.50693	+	2.54793i	0.120928	+	0.0878597i
$842$	−18.1473	−	13.1848i	−0.625398	−	0.454379i
$843$	24.1156	+	7.82571i	0.830585	+	0.269532i
$844$	−19.3264	+	6.27951i	−0.665241	+	0.216150i
$845$	−10.7715	−	14.8257i	−0.370551	−	0.510019i
$846$	−0.00574576	−	7.72350i	−0.000197543	−	0.265539i
$847$	−10.4484	−	3.43967i	−0.359011	−	0.118189i
$848$		−	2.95683i		−	0.101538i
$849$	2.32675	−	1.69180i	0.0798538	−	0.0580626i
$850$	6.95834	+	21.4156i	0.238669	+	0.734548i
$851$	16.9515	+	5.50787i	0.581090	+	0.188808i
$852$	13.3222	+	9.67158i	0.456411	+	0.331343i
$853$	−25.8069	+	35.5202i	−0.883612	+	1.21619i	0.0917955	+	0.995778i	$0.470739\pi$
$853$	−25.8069	+	35.5202i	−0.883612	+	1.21619i	−0.975407	+	0.220410i	$0.929261\pi$
$854$	−1.03740	+	3.19280i	−0.0354992	+	0.109255i
$855$	15.5304	+	47.6769i	0.531128	+	1.63052i
$856$	−12.9440	+	9.40437i	−0.442417	+	0.321435i
$857$	−27.6584			−0.944794			−0.472397	−	0.881386i	$-0.656611\pi$
$857$	−27.6584			−0.944794			−0.472397	+	0.881386i	$0.656611\pi$
$858$	0.0227370	−	14.5352i	0.000776227	−	0.496222i
$859$	−36.5824			−1.24818			−0.624088	−	0.781354i	$-0.714529\pi$
$859$	−36.5824			−1.24818			−0.624088	+	0.781354i	$0.714529\pi$
$860$	−29.6685	+	21.5554i	−1.01169	+	0.735034i
$861$	2.23872	+	6.88135i	0.0762952	+	0.234516i
$862$	6.01463	−	18.5111i	0.204859	−	0.630491i
$863$	−3.28941	+	4.52748i	−0.111973	+	0.154117i	−0.861325	−	0.508054i	$-0.830365\pi$
$863$	−3.28941	+	4.52748i	−0.111973	+	0.154117i	0.749352	+	0.662171i	$0.230365\pi$
$864$	−16.9576	+	23.3950i	−0.576909	+	0.795913i
$865$	−51.3051	−	16.6701i	−1.74443	−	0.566799i
$866$	2.18728	+	6.73176i	0.0743269	+	0.228755i
$867$	−4.95540	−	6.81520i	−0.168294	−	0.231456i
$868$			5.64346i			0.191552i
$869$	−39.9676	+	28.9201i	−1.35581	+	0.981048i
$870$	−20.5602	+	0.00764771i	−0.697058	+	0.000259282i
$871$	−15.3211	−	21.0877i	−0.519136	−	0.714530i
$872$	19.1442	−	6.22032i	0.648304	−	0.210647i
$873$	−17.9385	+	55.3491i	−0.607126	+	1.87328i
$874$	−11.4680	−	8.33199i	−0.387911	−	0.281834i
$875$	18.3630	+	13.3415i	0.620784	+	0.451026i
$876$	−4.96599	+	15.3031i	−0.167785	+	0.517044i
$877$	−30.3029	+	9.84601i	−1.02326	+	0.332476i	−0.772121	−	0.635476i	$-0.780804\pi$
$877$	−30.3029	+	9.84601i	−1.02326	+	0.332476i	−0.251135	+	0.967952i	$0.580804\pi$
$878$	−2.00292	−	2.75678i	−0.0675952	−	0.0930368i
$879$	−0.0127858	−	34.3737i	−0.000431255	−	1.15940i
$880$	−7.88617	−	24.4320i	−0.265843	−	0.823602i
$881$		−	48.3051i		−	1.62744i	−0.581256	−	0.813721i	$-0.697439\pi$
$881$		−	48.3051i		−	1.62744i	0.581256	−	0.813721i	$-0.302561\pi$
$882$	1.46213	−	1.06396i	0.0492326	−	0.0358256i
$883$	5.50208	+	16.9337i	0.185160	+	0.569863i	0.999951	−	0.00989123i	$-0.00314853\pi$
$883$	5.50208	+	16.9337i	0.185160	+	0.569863i	−0.814791	+	0.579754i	$0.803149\pi$
$884$	22.7621	+	7.39585i	0.765572	+	0.248749i
$885$	14.7850	−	20.3657i	0.496991	−	0.684585i
$886$	4.22531	−	5.81564i	0.141952	−	0.195380i
$887$	−7.64629	+	23.5329i	−0.256737	+	0.790156i	0.736745	+	0.676171i	$0.236362\pi$
$887$	−7.64629	+	23.5329i	−0.256737	+	0.790156i	−0.993482	+	0.113986i	$0.963638\pi$
$888$	−11.5340	+	3.75237i	−0.387056	+	0.125921i
$889$	−17.3315	+	12.5921i	−0.581280	+	0.422325i
$890$	−7.88583			−0.264334
$891$	−28.3845	−	9.23677i	−0.950918	−	0.309443i
$892$	37.6423			1.26036
$893$	14.5650	−	10.5821i	0.487400	−	0.354116i
$894$	−10.9360	+	3.55780i	−0.365753	+	0.118991i
$895$	5.98212	−	18.4111i	0.199960	−	0.615414i
$896$	6.73274	−	9.26682i	0.224925	−	0.309583i
$897$	23.8321	−	32.8277i	0.795729	−	1.09608i
$898$	−6.77781	−	2.20224i	−0.226178	−	0.0734898i
$899$	5.29183	+	16.2866i	0.176492	+	0.543188i
$900$	42.5763	−	30.9819i	1.41921	−	1.03273i
$901$		−	5.27651i		−	0.175786i
$902$	4.92235	−	6.74751i	0.163896	−	0.224668i
$903$	−0.00364044	−	9.78704i	−0.000121146	−	0.325692i
$904$	8.97950	+	12.3592i	0.298654	+	0.411061i
$905$	28.2461	−	9.17771i	0.938932	−	0.305077i
$906$	−1.73002	+	5.33119i	−0.0574760	+	0.177117i
$907$	1.08594	+	0.788982i	0.0360581	+	0.0261977i	0.605668	−	0.795717i	$-0.292906\pi$
$907$	1.08594	+	0.788982i	0.0360581	+	0.0261977i	−0.569610	+	0.821915i	$0.692906\pi$
$908$	−12.6901	−	9.21992i	−0.421137	−	0.305974i
$909$	−5.91986	+	18.2657i	−0.196349	+	0.605834i
$910$	−9.54228	+	3.10047i	−0.316323	+	0.102780i
$911$	−17.9256	−	24.6725i	−0.593901	−	0.817435i	0.401232	−	0.915977i	$-0.368582\pi$
$911$	−17.9256	−	24.6725i	−0.593901	−	0.817435i	−0.995133	+	0.0985417i	$0.968582\pi$
$912$	−14.2516	+	0.00530113i	−0.471919	+	0.000175538i
$913$	7.20835	−	9.88115i	0.238562	−	0.327018i
$914$			4.45255i			0.147277i
$915$	−22.4961	−	30.9390i	−0.743697	−	1.02281i
$916$	9.15811	+	28.1858i	0.302593	+	0.931284i
$917$	−3.02976	−	0.984427i	−0.100051	−	0.0325087i
$918$	−6.40319	+	8.83395i	−0.211337	+	0.291564i
$919$	34.0186	−	46.8226i	1.12217	−	1.54453i	0.320021	−	0.947410i	$-0.396310\pi$
$919$	34.0186	−	46.8226i	1.12217	−	1.54453i	0.802149	−	0.597124i	$-0.203690\pi$
$920$	−14.9864	+	46.1234i	−0.494087	+	1.52064i
$921$	−5.32161	−	16.3575i	−0.175353	−	0.538999i
$922$	1.40289	−	1.01926i	0.0462016	−	0.0335674i
$923$	24.3779			0.802408
$924$	8.93730	+	2.91937i	0.294016	+	0.0960402i
$925$	34.2592			1.12644
$926$	5.46258	−	3.96879i	0.179511	−	0.130423i
$927$	−6.97286	−	21.4061i	−0.229019	−	0.703067i
$928$	8.53406	−	26.2651i	0.280144	−	0.862195i
$929$	−33.5903	+	46.2331i	−1.10206	+	1.51686i	−0.269443	+	0.963016i	$0.586840\pi$
$929$	−33.5903	+	46.2331i	−1.10206	+	1.51686i	−0.832620	+	0.553844i	$0.813160\pi$
$930$	11.5516	+	8.38617i	0.378792	+	0.274993i
$931$	4.00875	+	1.30252i	0.131382	+	0.0426885i
$932$	−4.47589	−	13.7754i	−0.146613	−	0.451227i
$933$	−34.7595	+	25.2740i	−1.13797	+	0.827433i
$934$		−	1.29578i		−	0.0423991i
$935$	−14.0730	−	43.5992i	−0.460235	−	1.42585i
$936$	0.0205363	+	27.6051i	0.000671251	+	0.902302i
$937$	−23.6424	−	32.5410i	−0.772365	−	1.06307i	−0.996084	−	0.0884156i	$-0.971820\pi$
$937$	−23.6424	−	32.5410i	−0.772365	−	1.06307i	0.223719	−	0.974654i	$-0.428180\pi$
$938$	−3.55960	+	1.15658i	−0.116225	+	0.0377638i
$939$	25.8435	+	8.38642i	0.843370	+	0.273681i
$940$	−22.4261	−	16.2936i	−0.731460	−	0.531437i
$941$	−27.3466	−	19.8685i	−0.891473	−	0.647693i	0.0447883	−	0.998996i	$-0.485739\pi$
$941$	−27.3466	−	19.8685i	−0.891473	−	0.647693i	−0.936262	+	0.351303i	$0.885739\pi$
$942$	−5.82334	−	1.88972i	−0.189735	−	0.0615706i
$943$	22.1692	−	7.20320i	0.721928	−	0.234569i
$944$	4.20437	+	5.78682i	0.136841	+	0.188345i
$945$	0.0229926	+	20.6046i	0.000747950	+	0.670267i
$946$	−9.15161	+	6.62200i	−0.297544	+	0.215300i
$947$			39.1998i			1.27382i	0.770937	+	0.636912i	$0.219788\pi$
$947$			39.1998i			1.27382i	−0.770937	+	0.636912i	$0.780212\pi$
$948$	34.1044	−	24.7977i	1.10766	−	0.805391i
$949$	7.36204	+	22.6580i	0.238982	+	0.735511i
$950$	−25.9127	−	8.41953i	−0.840718	−	0.273166i
$951$	6.08003	+	4.41395i	0.197159	+	0.143132i
$952$	4.48836	−	6.17770i	0.145469	−	0.200220i
$953$	−13.4117	+	41.2771i	−0.434448	+	1.33709i	0.459202	+	0.888332i	$0.348135\pi$
$953$	−13.4117	+	41.2771i	−0.434448	+	1.33709i	−0.893651	+	0.448763i	$0.851865\pi$
$954$	2.60430	−	0.848331i	0.0843173	−	0.0274657i
$955$	−74.4324	+	54.0783i	−2.40858	+	1.74993i
$956$	−19.8894			−0.643268
$957$	28.5298	+	0.0446284i	0.922238	+	0.00144263i
$958$	1.16395			0.0376055
$959$	15.8183	−	11.4927i	0.510800	−	0.371118i
$960$	1.17380	+	3.60803i	0.0378844	+	0.116449i
$961$	−5.90548	+	18.1752i	−0.190499	+	0.586297i
$962$	−4.75116	+	6.53941i	−0.153183	+	0.210839i
$963$	17.7246	+	12.8575i	0.571167	+	0.414328i
$964$	−23.1425	−	7.51945i	−0.745369	−	0.242185i
$965$	6.86575	+	21.1306i	0.221016	+	0.680219i
$966$	−3.42554	−	4.71116i	−0.110215	−	0.151579i
$967$			15.6224i			0.502383i	0.967937	+	0.251191i	$0.0808223\pi$
$967$			15.6224i			0.502383i	−0.967937	+	0.251191i	$0.919178\pi$
$968$	−7.36229	−	22.9610i	−0.236633	−	0.737994i
$969$	−25.4322	+	0.00945993i	−0.817001	+	0.000303897i
$970$	−27.2472	−	37.5026i	−0.874855	−	1.20413i
$971$	−43.8678	+	14.2535i	−1.40779	+	0.457417i	−0.911700	−	0.410857i	$-0.865230\pi$
$971$	−43.8678	+	14.2535i	−1.40779	+	0.457417i	−0.496085	+	0.868274i	$0.665230\pi$
$972$	24.2793	+	7.83892i	0.778758	+	0.251433i
$973$	13.7408	+	9.98324i	0.440508	+	0.320048i
$974$	4.87612	+	3.54271i	0.156241	+	0.113516i
$975$	24.0672	−	74.1650i	0.770767	−	2.37518i
$976$	10.3402	−	3.35974i	0.330983	−	0.107543i
$977$	2.28144	+	3.14013i	0.0729896	+	0.100462i	0.843951	−	0.536420i	$-0.180224\pi$
$977$	2.28144	+	3.14013i	0.0729896	+	0.100462i	−0.770961	+	0.636882i	$0.780224\pi$
$978$	0.00186455	+	5.01270i	5.96218e−5	+	0.160288i
$979$	10.9425	+	0.0211874i	0.349725	+	0.000677151i
$980$		−	6.49003i		−	0.207317i
$981$	−16.2094	−	22.2754i	−0.517526	−	0.711200i
$982$	−6.19841	−	19.0767i	−0.197799	−	0.608763i
$983$	−50.8176	−	16.5116i	−1.62083	−	0.526640i	−0.648693	−	0.761050i	$-0.724684\pi$
$983$	−50.8176	−	16.5116i	−1.62083	−	0.526640i	−0.972138	+	0.234410i	$0.924684\pi$
$984$	−9.31889	+	12.8364i	−0.297075	+	0.409209i
$985$	−22.8383	+	31.4342i	−0.727687	+	1.00158i
$986$	3.22247	−	9.91774i	0.102624	−	0.315845i
$987$	7.03501	−	2.28871i	0.223927	−	0.0728503i
$988$	−23.4286	+	17.0218i	−0.745362	+	0.541537i
$989$	−31.5264			−1.00248
$990$	19.2565	−	13.9556i	0.612010	−	0.443538i
$991$	31.5396			1.00189			0.500944	−	0.865479i	$-0.332986\pi$
$991$	31.5396			1.00189			0.500944	+	0.865479i	$0.332986\pi$
$992$	−15.5121	+	11.2702i	−0.492509	+	0.357829i
$993$	−22.6685	+	7.37478i	−0.719364	+	0.234032i
$994$	1.08169	−	3.32909i	0.0343090	−	0.105592i
$995$	55.1174	−	75.8626i	1.74734	−	2.40500i
$996$	−6.14168	+	8.45991i	−0.194607	+	0.268063i
$997$	23.5982	+	7.66751i	0.747361	+	0.242832i	0.657845	−	0.753153i	$-0.271468\pi$
$997$	23.5982	+	7.66751i	0.747361	+	0.242832i	0.0895160	+	0.995985i	$0.471468\pi$
$998$	−4.54873	−	13.9995i	−0.143987	−	0.443148i
$999$	9.77202	+	13.4185i	0.309173	+	0.424543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.15	yes	96
3.2	odd	2	inner	231.2.s.a.8.10	✓	96
11.7	odd	10	inner	231.2.s.a.29.10	yes	96
33.29	even	10	inner	231.2.s.a.29.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.10	✓	96	3.2	odd	2	inner
231.2.s.a.8.15	yes	96	1.1	even	1	trivial
231.2.s.a.29.10	yes	96	11.7	odd	10	inner
231.2.s.a.29.15	yes	96	33.29	even	10	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.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.487641 - 0.354292i) q^{2} +(1.64708 - 0.535846i) q^{3} +(-0.505763 + 1.55658i) q^{4} +(-2.33078 + 3.20804i) q^{5} +(0.613338 - 0.844848i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.677377 + 2.08475i) q^{8} +(2.42574 - 1.76516i) q^{9} +O(q^{10})\)	\(q+(0.487641 - 0.354292i) q^{2} +(1.64708 - 0.535846i) q^{3} +(-0.505763 + 1.55658i) q^{4} +(-2.33078 + 3.20804i) q^{5} +(0.613338 - 0.844848i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.677377 + 2.08475i) q^{8} +(2.42574 - 1.76516i) q^{9} +2.39015i q^{10} +(0.00642177 - 3.31662i) q^{11} +(0.00105446 + 2.83482i) q^{12} +(2.46740 + 3.39608i) q^{13} +(0.573257 - 0.186262i) q^{14} +(-2.11996 + 6.53284i) q^{15} +(-1.57928 - 1.14741i) q^{16} +(-2.81824 - 2.04757i) q^{17} +(0.557508 - 1.72019i) q^{18} +(4.00875 - 1.30252i) q^{19} +(-3.81475 - 5.25055i) q^{20} +(1.73205 - 0.000644264i) q^{21} +(-1.17192 - 1.61960i) q^{22} -5.57936i q^{23} +(2.23280 + 3.07078i) q^{24} +(-3.31392 - 10.1992i) q^{25} +(2.40641 + 0.781890i) q^{26} +(3.04953 - 4.20718i) q^{27} +(-0.962018 + 1.32410i) q^{28} +(-1.53470 + 4.72333i) q^{29} +(1.28075 + 3.93677i) q^{30} +(2.78958 - 2.02675i) q^{31} -5.56072 q^{32} +(-1.76662 - 5.46617i) q^{33} -2.09973 q^{34} +(-3.20804 + 2.33078i) q^{35} +(1.52076 + 4.66860i) q^{36} +(-0.987188 + 3.03825i) q^{37} +(1.49336 - 2.05543i) q^{38} +(5.88377 + 4.27147i) q^{39} +(-8.26679 - 2.68604i) q^{40} +(1.29105 + 3.97343i) q^{41} +(0.844391 - 0.613966i) q^{42} -5.65055i q^{43} +(5.15933 + 1.68742i) q^{44} +(0.00884987 + 11.8961i) q^{45} +(-1.97672 - 2.72073i) q^{46} +(4.06215 - 1.31987i) q^{47} +(-3.21603 - 1.04363i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-5.22950 - 3.79945i) q^{50} +(-5.73905 - 1.86237i) q^{51} +(-6.53418 + 2.12308i) q^{52} +(0.890316 + 1.22542i) q^{53} +(-0.00349501 - 3.13202i) q^{54} +(10.6249 + 7.75091i) q^{55} +2.19204i q^{56} +(5.90478 - 4.29343i) q^{57} +(0.925055 + 2.84703i) q^{58} +(-3.48487 - 1.13230i) q^{59} +(-9.09667 - 6.60395i) q^{60} +(-3.27372 + 4.50588i) q^{61} +(0.642253 - 1.97665i) q^{62} +(2.85248 - 0.929173i) q^{63} +(0.446921 - 0.324707i) q^{64} -16.6457 q^{65} +(-2.79810 - 2.03963i) q^{66} -6.20942 q^{67} +(4.61257 - 3.35123i) q^{68} +(-2.98968 - 9.18964i) q^{69} +(-0.738597 + 2.27317i) q^{70} +(3.41346 - 4.69822i) q^{71} +(5.32307 + 3.86139i) q^{72} +(5.39761 + 1.75379i) q^{73} +(0.595035 + 1.83133i) q^{74} +(-10.9235 - 15.0231i) q^{75} +6.89871i q^{76} +(1.03100 - 3.15231i) q^{77} +(4.38252 - 0.00163015i) q^{78} +(-8.74306 - 12.0338i) q^{79} +(7.36190 - 2.39203i) q^{80} +(2.76841 - 8.56364i) q^{81} +(2.03732 + 1.48020i) q^{82} +(2.98348 + 2.16763i) q^{83} +(-0.875004 + 2.69640i) q^{84} +(13.1374 - 4.26860i) q^{85} +(-2.00195 - 2.75544i) q^{86} +(0.00319968 + 8.60207i) q^{87} +(6.91868 - 2.23321i) q^{88} +3.29930i q^{89} +(4.21900 + 5.79788i) q^{90} +(1.29719 + 3.99233i) q^{91} +(8.68471 + 2.82183i) q^{92} +(3.50863 - 4.83300i) q^{93} +(1.51325 - 2.08281i) q^{94} +(-5.16497 + 15.8961i) q^{95} +(-9.15895 + 2.97969i) q^{96} +(-15.6905 + 11.3998i) q^{97} +0.602758 q^{98} +(-5.83879 - 8.05658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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