LMFDB - Embedded newform 585.2.bt.b.376.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 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("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.15
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22618 - 0.707937i) q^{2} +(1.65800 - 0.501035i) q^{3} +(0.00235097 + 0.00407201i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-2.38771 - 0.559399i) q^{6} +(-0.00992873 - 0.00573236i) q^{7} +2.82509i q^{8} +(2.49793 - 1.66143i) q^{9} +O(q^{10})$	\(q+(-1.22618 - 0.707937i) q^{2} +(1.65800 - 0.501035i) q^{3} +(0.00235097 + 0.00407201i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-2.38771 - 0.559399i) q^{6} +(-0.00992873 - 0.00573236i) q^{7} +2.82509i q^{8} +(2.49793 - 1.66143i) q^{9} -1.41587 q^{10} +(-3.20924 - 1.85286i) q^{11} +(0.00593813 + 0.00557347i) q^{12} +(-3.01269 - 1.98083i) q^{13} +(0.00811630 + 0.0140578i) q^{14} +(1.18535 - 1.26291i) q^{15} +(2.00469 - 3.47223i) q^{16} +4.64895 q^{17} +(-4.23911 + 0.268844i) q^{18} -6.04019i q^{19} +(0.00407201 + 0.00235097i) q^{20} +(-0.0193339 - 0.00452960i) q^{21} +(2.62341 + 4.54388i) q^{22} +(-2.42067 - 4.19273i) q^{23} +(1.41547 + 4.68400i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.29181 + 4.56166i) q^{26} +(3.30913 - 4.00620i) q^{27} -5.39065e-5i q^{28} +(-4.46472 + 7.73312i) q^{29} +(-2.34752 + 0.709403i) q^{30} +(5.72460 - 3.30510i) q^{31} +(-0.0230347 + 0.0132991i) q^{32} +(-6.24926 - 1.46409i) q^{33} +(-5.70047 - 3.29117i) q^{34} -0.0114647 q^{35} +(0.0126379 + 0.00626559i) q^{36} -4.52388i q^{37} +(-4.27608 + 7.40639i) q^{38} +(-5.98751 - 1.77475i) q^{39} +(1.41255 + 2.44660i) q^{40} +(-3.46246 + 1.99905i) q^{41} +(0.0205003 + 0.0192414i) q^{42} +(-0.571044 + 0.989078i) q^{43} -0.0174241i q^{44} +(1.33255 - 2.68781i) q^{45} +6.85474i q^{46} +(8.97044 + 5.17908i) q^{47} +(1.58407 - 6.76137i) q^{48} +(-3.49993 - 6.06206i) q^{49} +(-1.22618 + 0.707937i) q^{50} +(7.70796 - 2.32929i) q^{51} +(0.000983196 - 0.0169246i) q^{52} +2.37762 q^{53} +(-6.89374 + 2.56968i) q^{54} -3.70571 q^{55} +(0.0161944 - 0.0280496i) q^{56} +(-3.02635 - 10.0146i) q^{57} +(10.9491 - 6.32148i) q^{58} +(-1.19273 + 0.688625i) q^{59} +(0.00792930 + 0.00185770i) q^{60} +(-4.33838 + 7.51430i) q^{61} -9.35922 q^{62} +(-0.0343252 + 0.00217690i) q^{63} -7.98110 q^{64} +(-3.59948 - 0.209104i) q^{65} +(6.62626 + 6.21933i) q^{66} +(8.37253 - 4.83388i) q^{67} +(0.0109296 + 0.0189305i) q^{68} +(-6.11418 - 5.73870i) q^{69} +(0.0140578 + 0.00811630i) q^{70} +5.79546i q^{71} +(4.69370 + 7.05688i) q^{72} -1.97265i q^{73} +(-3.20262 + 5.54710i) q^{74} +(0.395091 - 1.68639i) q^{75} +(0.0245957 - 0.0142003i) q^{76} +(0.0212424 + 0.0367930i) q^{77} +(6.08537 + 6.41496i) q^{78} +(-0.376913 + 0.652832i) q^{79} -4.00938i q^{80} +(3.47929 - 8.30027i) q^{81} +5.66082 q^{82} +(-7.33925 - 4.23732i) q^{83} +(-2.70090e-5 - 8.93769e-5i) q^{84} +(4.02611 - 2.32447i) q^{85} +(1.40041 - 0.808527i) q^{86} +(-3.52794 + 15.0585i) q^{87} +(5.23449 - 9.06640i) q^{88} +3.56933i q^{89} +(-3.53675 + 2.35238i) q^{90} +(0.0185574 + 0.0369370i) q^{91} +(0.0113819 - 0.0197140i) q^{92} +(7.83542 - 8.34808i) q^{93} +(-7.33293 - 12.7010i) q^{94} +(-3.02010 - 5.23096i) q^{95} +(-0.0315282 + 0.0335911i) q^{96} +(-0.00405446 - 0.00234084i) q^{97} +9.91094i q^{98} +(-11.0948 + 0.703634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−1.22618	−	0.707937i	−0.867043	−	0.500587i	−0.000678402	−	1.00000i	$-0.500216\pi$
$2$	−1.22618	−	0.707937i	−0.867043	−	0.500587i	−0.866364	+	0.499412i	$0.833549\pi$
$3$	1.65800	−	0.501035i	0.957247	−	0.289273i
$3$	1.65800	−	0.501035i	0.957247	−	0.289273i
$4$	0.00235097	+	0.00407201i	0.00117549	+	0.00203600i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−2.38771	−	0.559399i	−0.974780	−	0.228374i
$7$	−0.00992873	−	0.00573236i	−0.00375271	−	0.00216663i	0.498122	−	0.867107i	$-0.334023\pi$
$7$	−0.00992873	−	0.00573236i	−0.00375271	−	0.00216663i	−0.501875	+	0.864940i	$0.667356\pi$
$8$			2.82509i			0.998821i
$9$	2.49793	−	1.66143i	0.832643	−	0.553811i
$10$	−1.41587			−0.447739
$11$	−3.20924	−	1.85286i	−0.967622	−	0.558657i	−0.0691115	−	0.997609i	$-0.522016\pi$
$11$	−3.20924	−	1.85286i	−0.967622	−	0.558657i	−0.898510	+	0.438952i	$0.855350\pi$
$12$	0.00593813	+	0.00557347i	0.00171419	+	0.00160892i
$13$	−3.01269	−	1.98083i	−0.835570	−	0.549384i
$13$	−3.01269	−	1.98083i	−0.835570	−	0.549384i
$14$	0.00811630	+	0.0140578i	0.00216917	+	0.00375712i
$15$	1.18535	−	1.26291i	0.306057	−	0.326082i
$16$	2.00469	−	3.47223i	0.501173	−	0.868057i
$17$	4.64895			1.12754			0.563768	−	0.825933i	$-0.309351\pi$
$17$	4.64895			1.12754			0.563768	+	0.825933i	$0.309351\pi$
$18$	−4.23911	+	0.268844i	−0.999167	+	0.0633671i
$19$		−	6.04019i		−	1.38572i	−0.721074	−	0.692858i	$-0.756351\pi$
$19$		−	6.04019i		−	1.38572i	0.721074	−	0.692858i	$-0.243649\pi$
$20$	0.00407201	+	0.00235097i	0.000910528	+	0.000525694i
$21$	−0.0193339	−	0.00452960i	−0.00421901	−	0.000988441i
$22$	2.62341	+	4.54388i	0.559313	+	0.968759i
$23$	−2.42067	−	4.19273i	−0.504745	−	0.874245i	−0.999985	−	0.00548811i	$-0.998253\pi$
$23$	−2.42067	−	4.19273i	−0.504745	−	0.874245i	0.495240	−	0.868756i	$-0.335080\pi$
$24$	1.41547	+	4.68400i	0.288932	+	0.956118i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.29181	+	4.56166i	0.449461	+	0.894615i
$27$	3.30913	−	4.00620i	0.636842	−	0.770994i
$28$		0	5.39065e-5i		0	1.01874e-5i
$29$	−4.46472	+	7.73312i	−0.829077	+	1.43600i	0.0696859	+	0.997569i	$0.477800\pi$
$29$	−4.46472	+	7.73312i	−0.829077	+	1.43600i	−0.898763	+	0.438435i	$0.855533\pi$
$30$	−2.34752	+	0.709403i	−0.428597	+	0.129519i
$31$	5.72460	−	3.30510i	1.02817	−	0.593614i	0.111709	−	0.993741i	$-0.464367\pi$
$31$	5.72460	−	3.30510i	1.02817	−	0.593614i	0.916460	+	0.400127i	$0.131034\pi$
$32$	−0.0230347	+	0.0132991i	−0.00407200	+	0.00235097i
$33$	−6.24926	−	1.46409i	−1.08786	−	0.254866i
$34$	−5.70047	−	3.29117i	−0.977622	−	0.564430i
$35$	−0.0114647			−0.00193789
$36$	0.0126379	+	0.00626559i	0.00210632	+	0.00104427i
$37$		−	4.52388i		−	0.743721i	−0.928289	−	0.371860i	$-0.878720\pi$
$37$		−	4.52388i		−	0.743721i	0.928289	−	0.371860i	$-0.121280\pi$
$38$	−4.27608	+	7.40639i	−0.693672	+	1.20147i
$39$	−5.98751	−	1.77475i	−0.958769	−	0.284188i
$40$	1.41255	+	2.44660i	0.223343	+	0.386842i
$41$	−3.46246	+	1.99905i	−0.540746	+	0.312200i	−0.745381	−	0.666639i	$-0.767732\pi$
$41$	−3.46246	+	1.99905i	−0.540746	+	0.312200i	0.204635	+	0.978838i	$0.434399\pi$
$42$	0.0205003	+	0.0192414i	0.00316326	+	0.00296901i
$43$	−0.571044	+	0.989078i	−0.0870834	+	0.150833i	−0.906277	−	0.422684i	$-0.861088\pi$
$43$	−0.571044	+	0.989078i	−0.0870834	+	0.150833i	0.819194	+	0.573517i	$0.194421\pi$
$44$		−	0.0174241i		−	0.00262677i
$45$	1.33255	−	2.68781i	0.198645	−	0.400674i
$46$			6.85474i			1.01068i
$47$	8.97044	+	5.17908i	1.30847	+	0.755447i	0.981841	−	0.189705i	$-0.0607531\pi$
$47$	8.97044	+	5.17908i	1.30847	+	0.755447i	0.326631	+	0.945152i	$0.394086\pi$
$48$	1.58407	−	6.76137i	0.228641	−	0.975920i
$49$	−3.49993	−	6.06206i	−0.499991	−	0.866009i
$50$	−1.22618	+	0.707937i	−0.173409	+	0.100117i
$51$	7.70796	−	2.32929i	1.07933	−	0.326165i
$52$	0.000983196	−	0.0169246i	0.000136345	−	0.00234702i
$53$	2.37762			0.326591			0.163295	−	0.986577i	$-0.447788\pi$
$53$	2.37762			0.326591			0.163295	+	0.986577i	$0.447788\pi$
$54$	−6.89374	+	2.56968i	−0.938119	+	0.349690i
$55$	−3.70571			−0.499678
$56$	0.0161944	−	0.0280496i	0.00216407	−	0.00374828i
$57$	−3.02635	−	10.0146i	−0.400850	−	1.32647i
$58$	10.9491	−	6.32148i	1.43769	−	0.830051i
$59$	−1.19273	+	0.688625i	−0.155281	+	0.0896513i	−0.575627	−	0.817712i	$-0.695242\pi$
$59$	−1.19273	+	0.688625i	−0.155281	+	0.0896513i	0.420346	+	0.907364i	$0.361909\pi$
$60$	0.00792930	+	0.00185770i	0.00102367	+	0.000239828i
$61$	−4.33838	+	7.51430i	−0.555473	+	0.962108i	0.442393	+	0.896821i	$0.354130\pi$
$61$	−4.33838	+	7.51430i	−0.555473	+	0.962108i	−0.997867	+	0.0652867i	$0.979204\pi$
$62$	−9.35922			−1.18862
$63$	−0.0343252	+	0.00217690i	−0.00432457	+	0.000274264i
$64$	−7.98110			−0.997638
$65$	−3.59948	−	0.209104i	−0.446461	−	0.0259362i
$66$	6.62626	+	6.21933i	0.815636	+	0.765547i
$67$	8.37253	−	4.83388i	1.02287	−	0.590553i	0.107934	−	0.994158i	$-0.465576\pi$
$67$	8.37253	−	4.83388i	1.02287	−	0.590553i	0.914933	+	0.403605i	$0.132243\pi$
$68$	0.0109296	+	0.0189305i	0.00132540	+	0.00229567i
$69$	−6.11418	−	5.73870i	−0.736061	−	0.690859i
$70$	0.0140578	+	0.00811630i	0.00168023	+	0.000970083i
$71$			5.79546i			0.687794i	0.939007	+	0.343897i	$0.111747\pi$
$71$			5.79546i			0.687794i	−0.939007	+	0.343897i	$0.888253\pi$
$72$	4.69370	+	7.05688i	0.553158	+	0.831661i
$73$		−	1.97265i		−	0.230882i	−0.993314	−	0.115441i	$-0.963172\pi$
$73$		−	1.97265i		−	0.230882i	0.993314	−	0.115441i	$-0.0368280\pi$
$74$	−3.20262	+	5.54710i	−0.372297	+	0.644838i
$75$	0.395091	−	1.68639i	0.0456212	−	0.194727i
$76$	0.0245957	−	0.0142003i	0.00282132	−	0.00162889i
$77$	0.0212424	+	0.0367930i	0.00242080	+	0.00419295i
$78$	6.08537	+	6.41496i	0.689032	+	0.726351i
$79$	−0.376913	+	0.652832i	−0.0424060	+	0.0734494i	−0.886449	−	0.462826i	$-0.846836\pi$
$79$	−0.376913	+	0.652832i	−0.0424060	+	0.0734494i	0.844043	+	0.536275i	$0.180169\pi$
$80$		−	4.00938i		−	0.448263i
$81$	3.47929	−	8.30027i	0.386588	−	0.922253i
$82$	5.66082			0.625133
$83$	−7.33925	−	4.23732i	−0.805587	−	0.465106i	0.0398338	−	0.999206i	$-0.487317\pi$
$83$	−7.33925	−	4.23732i	−0.805587	−	0.465106i	−0.845421	+	0.534100i	$0.820650\pi$
$84$	−2.70090e−5	0	8.93769e-5i	−2.94693e−6	0	9.75182e-6i
$85$	4.02611	−	2.32447i	0.436693	−	0.252125i
$86$	1.40041	−	0.808527i	0.151010	−	0.0871858i
$87$	−3.52794	+	15.0585i	−0.378235	+	1.61444i
$88$	5.23449	−	9.06640i	0.557998	−	0.966481i
$89$			3.56933i			0.378348i	0.981944	+	0.189174i	$0.0605811\pi$
$89$			3.56933i			0.378348i	−0.981944	+	0.189174i	$0.939419\pi$
$90$	−3.53675	+	2.35238i	−0.372807	+	0.247963i
$91$	0.0185574	+	0.0369370i	0.00194534	+	0.00387205i
$92$	0.0113819	−	0.0197140i	0.00118664	−	0.00205533i
$93$	7.83542	−	8.34808i	0.812495	−	0.865656i
$94$	−7.33293	−	12.7010i	−0.756334	−	1.31001i
$95$	−3.02010	−	5.23096i	−0.309855	−	0.536685i
$96$	−0.0315282	+	0.0335911i	−0.00321783	+	0.00342837i
$97$	−0.00405446	−	0.00234084i	−0.000411668	−	0.000237676i	0.499794	−	0.866144i	$-0.333409\pi$
$97$	−0.00405446	−	0.00234084i	−0.000411668	−	0.000237676i	−0.500206	+	0.865907i	$0.666742\pi$
$98$			9.91094i			1.00116i
$99$	−11.0948	+	0.703634i	−1.11507	+	0.0707179i
$100$	0.00470195			0.000470195
$101$	−1.00162	+	1.73486i	−0.0996649	+	0.172625i	−0.911546	−	0.411198i	$-0.865110\pi$
$101$	−1.00162	+	1.73486i	−0.0996649	+	0.172625i	0.811881	+	0.583823i	$0.198444\pi$
$102$	−11.1004	−	2.60062i	−1.09910	−	0.257500i
$103$	8.12311	+	14.0696i	0.800394	+	1.38632i	0.919357	+	0.393424i	$0.128710\pi$
$103$	8.12311	+	14.0696i	0.800394	+	1.38632i	−0.118963	+	0.992899i	$0.537957\pi$
$104$	5.59603	−	8.51113i	0.548736	−	0.834585i
$105$	−0.0190085	+	0.00574422i	−0.00185504	+	0.000560579i
$106$	−2.91540	−	1.68320i	−0.283168	−	0.163487i
$107$	−2.25946			−0.218430			−0.109215	−	0.994018i	$-0.534834\pi$
$107$	−2.25946			−0.218430			−0.109215	+	0.994018i	$0.534834\pi$
$108$	0.0240930	+	0.00405631i	0.00231835	+	0.000390319i
$109$		−	8.34833i		−	0.799625i	−0.916597	−	0.399812i	$-0.869075\pi$
$109$		−	8.34833i		−	0.799625i	0.916597	−	0.399812i	$-0.130925\pi$
$110$	4.54388	+	2.62341i	0.433242	+	0.250132i
$111$	−2.26662	−	7.50059i	−0.215138	−	0.711924i
$112$	−0.0398081	+	0.0229832i	−0.00376151	+	0.00217171i
$113$	4.45996	+	7.72487i	0.419558	+	0.726695i	0.995895	−	0.0905169i	$-0.0288519\pi$
$113$	4.45996	+	7.72487i	0.419558	+	0.726695i	−0.576337	+	0.817212i	$0.695519\pi$
$114$	−3.37888	+	14.4223i	−0.316461	+	1.35077i
$115$	−4.19273	−	2.42067i	−0.390974	−	0.225729i
$116$	−0.0419857			−0.00389828
$117$	−10.8165	+	0.0574092i	−0.999986	+	0.00530749i
$118$	1.95001			0.179513
$119$	−0.0461582	−	0.0266494i	−0.00423131	−	0.00244295i
$120$	3.56783	+	3.34873i	0.325697	+	0.305696i
$121$	1.36614	+	2.36623i	0.124195	+	0.215112i
$122$	10.6393	−	6.14261i	0.963238	−	0.556126i
$123$	−4.73917	+	5.04924i	−0.427316	+	0.455275i
$124$	0.0269168	+	0.0155404i	0.00241720	+	0.00139557i
$125$		−	1.00000i		−	0.0894427i
$126$	0.0436301	+	0.0216308i	0.00388688	+	0.00192702i
$127$	18.7915			1.66748			0.833739	−	0.552159i	$-0.186196\pi$
$127$	18.7915			1.66748			0.833739	+	0.552159i	$0.186196\pi$
$128$	9.83237	+	5.67672i	0.869067	+	0.501756i
$129$	−0.451229	+	1.92600i	−0.0397285	+	0.169575i
$130$	4.26559	+	2.80461i	0.374117	+	0.245980i
$131$	−1.48159	−	2.56619i	−0.129447	−	0.224209i	0.794015	−	0.607898i	$-0.207987\pi$
$131$	−1.48159	−	2.56619i	−0.129447	−	0.224209i	−0.923463	+	0.383688i	$0.874654\pi$
$132$	−0.00873006	−	0.0288891i	−0.000759854	−	0.00251447i
$133$	−0.0346245	+	0.0599715i	−0.00300233	+	0.00520019i
$134$	−13.6884			−1.18249
$135$	0.862688	−	5.12404i	0.0742484	−	0.441007i
$136$			13.1337i			1.12621i
$137$	17.0849	+	9.86395i	1.45966	+	0.842734i	0.998994	−	0.0448403i	$-0.0142779\pi$
$137$	17.0849	+	9.86395i	1.45966	+	0.842734i	0.460664	+	0.887574i	$0.347611\pi$
$138$	3.43447	+	11.3652i	0.292361	+	0.967467i
$139$	9.05260	+	15.6796i	0.767831	+	1.32992i	0.938737	+	0.344635i	$0.111997\pi$
$139$	9.05260	+	15.6796i	0.767831	+	1.32992i	−0.170906	+	0.985287i	$0.554669\pi$
$140$	−2.69532e−5	0	4.66844e-5i	−2.27796e−6	0	3.94555e-6i
$141$	17.4679	+	4.09242i	1.47106	+	0.344644i
$142$	4.10282	−	7.10630i	0.344301	−	0.596347i
$143$	5.99825	+	11.9390i	0.501599	+	0.998393i
$144$	−0.761294	−	12.0040i	−0.0634412	−	1.00034i
$145$			8.92943i			0.741549i
$146$	−1.39651	+	2.41883i	−0.115576	+	0.200184i
$147$	−8.84020	−	8.29731i	−0.729127	−	0.684351i
$148$	0.0184213	−	0.0106355i	0.00151422	−	0.000874234i
$149$	−10.4375	+	6.02608i	−0.855071	+	0.493676i	−0.862359	−	0.506298i	$-0.831014\pi$
$149$	−10.4375	+	6.02608i	−0.855071	+	0.493676i	0.00728749	+	0.999973i	$0.497680\pi$
$150$	−1.67831	+	1.78812i	−0.137034	+	0.145999i
$151$	16.7981	+	9.69837i	1.36701	+	0.789242i	0.990545	−	0.137190i	$-0.0438069\pi$
$151$	16.7981	+	9.69837i	1.36701	+	0.789242i	0.376463	+	0.926432i	$0.377140\pi$
$152$	17.0641			1.38408
$153$	11.6127	−	7.72391i	0.938834	−	0.624441i
$154$		−	0.0601533i		−	0.00484729i
$155$	3.30510	−	5.72460i	0.265472	−	0.459811i
$156$	−0.00684967	−	0.0285536i	−0.000548412	−	0.00228611i
$157$	8.35313	+	14.4680i	0.666652	+	1.15468i	0.978834	+	0.204653i	$0.0656068\pi$
$157$	8.35313	+	14.4680i	0.666652	+	1.15468i	−0.312182	+	0.950022i	$0.601060\pi$
$158$	0.924329	−	0.533661i	0.0735356	−	0.0424558i
$159$	3.94209	−	1.19127i	0.312628	−	0.0944738i
$160$	−0.0132991	+	0.0230347i	−0.00105139	+	0.00182105i
$161$			0.0555046i			0.00437438i
$162$	−10.1423	+	7.71454i	−0.796856	+	0.606112i
$163$			7.00872i			0.548965i	0.961592	+	0.274483i	$0.0885065\pi$
$163$			7.00872i			0.548965i	−0.961592	+	0.274483i	$0.911493\pi$
$164$	−0.0162803	−	0.00939944i	−0.00127128	−	0.000733973i
$165$	−6.14407	+	1.85669i	−0.478315	+	0.144543i
$166$	5.99951	+	10.3915i	0.465652	+	0.806534i
$167$	15.4948	−	8.94595i	1.19903	−	0.692259i	0.238689	−	0.971096i	$-0.423282\pi$
$167$	15.4948	−	8.94595i	1.19903	−	0.692259i	0.960338	+	0.278838i	$0.0899491\pi$
$168$	0.0127966	−	0.0546202i	0.000987275	−	0.00421404i
$169$	5.15262	+	11.9353i	0.396355	+	0.918097i
$170$	−6.58233			−0.504842
$171$	−10.0354	−	15.0880i	−0.767424	−	1.15381i
$172$	−0.00537004			−0.000409462
$173$	12.9562	−	22.4409i	0.985045	−	1.70615i	0.343308	−	0.939223i	$-0.388452\pi$
$173$	12.9562	−	22.4409i	0.985045	−	1.70615i	0.641737	−	0.766925i	$-0.278214\pi$
$174$	14.9864	−	15.9669i	1.13611	−	1.21045i
$175$	−0.00992873	+	0.00573236i	−0.000750542	+	0.000433325i
$176$	−12.8671	+	7.42880i	−0.969892	+	0.559967i
$177$	−1.63253	+	1.73934i	−0.122708	+	0.130737i
$178$	2.52686	−	4.37665i	0.189396	−	0.328044i
$179$	3.63380			0.271603			0.135801	−	0.990736i	$-0.456639\pi$
$179$	3.63380			0.271603			0.135801	+	0.990736i	$0.456639\pi$
$180$	0.0140776		0.000892797i	0.00104928		6.65452e-5i
$181$	−9.03354			−0.671458			−0.335729	−	0.941959i	$-0.608983\pi$
$181$	−9.03354			−0.671458			−0.335729	+	0.941959i	$0.608983\pi$
$182$	0.00339430	−	0.0584290i	0.000251602	−	0.00433104i
$183$	−3.42811	+	14.6324i	−0.253413	+	1.08166i
$184$	11.8448	−	6.83863i	0.873214	−	0.504150i
$185$	−2.26194	−	3.91779i	−0.166301	−	0.288042i
$186$	−15.5176	+	4.68930i	−1.13780	+	0.343836i
$187$	−14.9196	−	8.61383i	−1.09103	−	0.629905i
$188$			0.0487035i			0.00355207i
$189$	−0.0558204	+	0.0208074i	−0.00406034	+	0.00151352i
$190$			8.55216i			0.620439i
$191$	10.5689	−	18.3058i	0.764737	−	1.32456i	−0.175648	−	0.984453i	$-0.556202\pi$
$191$	10.5689	−	18.3058i	0.764737	−	1.32456i	0.940385	−	0.340111i	$-0.110465\pi$
$192$	−13.2327	+	3.99881i	−0.954986	+	0.288589i
$193$	−0.210790	+	0.121700i	−0.0151730	+	0.00876015i	−0.507567	−	0.861612i	$-0.669455\pi$
$193$	−0.210790	+	0.121700i	−0.0151730	+	0.00876015i	0.492394	+	0.870372i	$0.336122\pi$
$194$	0.00331434	+	0.00574060i	0.000237956	+	0.000412151i
$195$	−6.07271	+	1.45677i	−0.434876	+	0.104322i
$196$	0.0164565	−	0.0285035i	0.00117546	−	0.00203596i
$197$			18.3729i			1.30901i	0.756057	+	0.654506i	$0.227123\pi$
$197$			18.3729i			1.30901i	−0.756057	+	0.654506i	$0.772877\pi$
$198$	14.1024	+	6.99167i	1.00222	+	0.496876i
$199$	−13.3674			−0.947587			−0.473793	−	0.880636i	$-0.657116\pi$
$199$	−13.3674			−0.947587			−0.473793	+	0.880636i	$0.657116\pi$
$200$	2.44660	+	1.41255i	0.173001	+	0.0998821i
$201$	11.4597	−	12.2095i	0.808306	−	0.861192i
$202$	2.45634	−	1.41817i	0.172828	−	0.0997820i
$203$	0.0886580	−	0.0511867i	0.00622257	−	0.00359260i
$204$	0.0276061	+	0.0259108i	0.00193281	+	0.00181412i
$205$	−1.99905	+	3.46246i	−0.139620	+	0.241829i
$206$		−	23.0026i		−	1.60267i
$207$	−13.0126	−	6.45135i	−0.904438	−	0.448400i
$208$	−12.9174	+	6.48979i	−0.895661	+	0.449986i
$209$	−11.1916	+	19.3844i	−0.774139	+	1.34085i
$210$	0.0273745	+	0.00641335i	0.00188902	+	0.000442563i
$211$	−8.07314	−	13.9831i	−0.555778	−	0.962635i	−0.997843	−	0.0656523i	$-0.979087\pi$
$211$	−8.07314	−	13.9831i	−0.555778	−	0.962635i	0.442065	−	0.896983i	$-0.354246\pi$
$212$	0.00558972	+	0.00968167i	0.000383903	+	0.000664940i
$213$	2.90373	+	9.60887i	0.198960	+	0.658389i
$214$	2.77051	+	1.59956i	0.189388	+	0.109343i
$215$			1.14209i			0.0778898i
$216$	11.3179	+	9.34860i	0.770085	+	0.636091i
$217$	−0.0757841			−0.00514456
$218$	−5.91010	+	10.2366i	−0.400282	+	0.693309i
$219$	−0.988368	−	3.27066i	−0.0667877	−	0.221011i
$220$	−0.00871203	−	0.0150897i	−0.000587365	−	0.00101735i
$221$	−14.0058	−	9.20878i	−0.942135	−	0.619450i
$222$	−2.53065	+	10.8017i	−0.169846	+	0.724964i
$223$	−19.0098	−	10.9753i	−1.27299	−	0.734959i	−0.297438	−	0.954741i	$-0.596132\pi$
$223$	−19.0098	−	10.9753i	−1.27299	−	0.734959i	−0.975549	+	0.219782i	$0.929465\pi$
$224$	0.000304940	0		2.03747e−5	0
$225$	−0.189878	−	2.99399i	−0.0126586	−	0.199599i
$226$		−	12.6295i		−	0.840101i
$227$	0.780807	+	0.450799i	0.0518240	+	0.0299206i	0.525688	−	0.850677i	$-0.323808\pi$
$227$	0.780807	+	0.450799i	0.0518240	+	0.0299206i	−0.473864	+	0.880598i	$0.657141\pi$
$228$	0.0336648	−	0.0358675i	0.00222951	−	0.00237538i
$229$	−1.49691	+	0.864240i	−0.0989184	+	0.0571106i	−0.548643	−	0.836057i	$-0.684855\pi$
$229$	−1.49691	+	0.864240i	−0.0989184	+	0.0571106i	0.449725	+	0.893167i	$0.351522\pi$
$230$	3.42737	+	5.93638i	0.225994	+	0.391433i
$231$	0.0536546	+	0.0503596i	0.00353021	+	0.00331342i
$232$	−21.8468	−	12.6132i	−1.43431	−	0.828100i
$233$	18.1858			1.19139			0.595696	−	0.803210i	$-0.296876\pi$
$233$	18.1858			1.19139			0.595696	+	0.803210i	$0.296876\pi$
$234$	13.3037	+	7.58701i	0.869687	+	0.495979i
$235$	10.3582			0.675692
$236$	−0.00560817	−	0.00323788i	−0.000365061	−	0.000210768i
$237$	−0.297830	+	1.27124i	−0.0193461	+	0.0825761i
$238$	0.0377323	+	0.0653542i	0.00244582	+	0.00423628i
$239$	12.8933	−	7.44396i	0.833999	−	0.481510i	−0.0212209	−	0.999775i	$-0.506755\pi$
$239$	12.8933	−	7.44396i	0.833999	−	0.481510i	0.855220	+	0.518265i	$0.173422\pi$
$240$	−2.00884	−	6.64755i	−0.129670	−	0.429098i
$241$	−8.04501	−	4.64479i	−0.518225	−	0.299197i	0.217983	−	0.975952i	$-0.430052\pi$
$241$	−8.04501	−	4.64479i	−0.518225	−	0.299197i	−0.736208	+	0.676755i	$0.763385\pi$
$242$		−	3.86858i		−	0.248682i
$243$	1.60993	−	15.5051i	0.103277	−	0.994653i
$244$	−0.0407977			−0.00261181
$245$	−6.06206	−	3.49993i	−0.387291	−	0.223603i
$246$	9.38564	−	2.83627i	0.598406	−	0.180834i
$247$	−11.9646	+	18.1972i	−0.761289	+	1.15786i
$248$	9.33722	+	16.1725i	0.592914	+	1.02696i
$249$	−14.2915	−	3.34825i	−0.905688	−	0.212187i
$250$	−0.707937	+	1.22618i	−0.0447739	+	0.0775507i
$251$	−3.40713			−0.215056			−0.107528	−	0.994202i	$-0.534294\pi$
$251$	−3.40713			−0.215056			−0.107528	+	0.994202i	$0.534294\pi$
$252$	−8.95619e−5	0	0.000134654i	−5.64187e−6	0	8.48243e-6i
$253$			17.9406i			1.12792i
$254$	−23.0419	−	13.3032i	−1.44577	−	0.834718i
$255$	5.51064	−	5.87120i	0.345090	−	0.367669i
$256$	−0.0564231	−	0.0977276i	−0.00352644	−	0.00610797i
$257$	−15.0941	−	26.1437i	−0.941543	−	1.63080i	−0.762530	−	0.646953i	$-0.776043\pi$
$257$	−15.0941	−	26.1437i	−0.941543	−	1.63080i	−0.179013	−	0.983847i	$-0.557290\pi$
$258$	1.91678	−	2.04219i	0.119334	−	0.127141i
$259$	−0.0259325	+	0.0449164i	−0.00161137	+	0.00279097i
$260$	−0.00761082	−	0.0151487i	−0.000472003	−	0.000939483i
$261$	1.69551	+	26.7346i	0.104949	+	1.65483i
$262$			4.19550i			0.259199i
$263$	−9.48439	+	16.4275i	−0.584833	+	1.01296i	0.410064	+	0.912057i	$0.365507\pi$
$263$	−9.48439	+	16.4275i	−0.584833	+	1.01296i	−0.994896	+	0.100903i	$0.967827\pi$
$264$	4.13620	−	17.6547i	0.254565	−	1.08657i
$265$	2.05908	−	1.18881i	0.126488	−	0.0730279i
$266$	0.0849121	−	0.0490240i	0.00520630	−	0.00300586i
$267$	1.78836	+	5.91795i	0.109446	+	0.362173i
$268$	0.0393672	+	0.0227287i	0.00240473	+	0.00138837i
$269$	3.45377			0.210580			0.105290	−	0.994442i	$-0.466423\pi$
$269$	3.45377			0.210580			0.105290	+	0.994442i	$0.466423\pi$
$270$	−4.68531	+	5.67228i	−0.285139	+	0.345204i
$271$			13.5998i			0.826131i	0.910701	+	0.413065i	$0.135542\pi$
$271$			13.5998i			0.826131i	−0.910701	+	0.413065i	$0.864458\pi$
$272$	9.31971	−	16.1422i	0.565090	−	0.978765i
$273$	0.0492748	+	0.0519436i	0.00298225	+	0.00314377i
$274$	−13.9661	−	24.1900i	−0.843724	−	1.46137i
$275$	−3.20924	+	1.85286i	−0.193524	+	0.111731i
$276$	0.00899376	−	0.0383885i	0.000541360	−	0.00231072i
$277$	−3.82426	+	6.62382i	−0.229778	+	0.397987i	−0.957742	−	0.287628i	$-0.907133\pi$
$277$	−3.82426	+	6.62382i	−0.229778	+	0.397987i	0.727964	+	0.685615i	$0.240467\pi$
$278$		−	25.6347i		−	1.53747i
$279$	8.80845	−	17.7669i	0.527348	−	1.06368i
$280$		−	0.0323889i		−	0.00193561i
$281$	−19.5232	−	11.2717i	−1.16466	−	0.672414i	−0.212240	−	0.977218i	$-0.568076\pi$
$281$	−19.5232	−	11.2717i	−1.16466	−	0.672414i	−0.952415	+	0.304803i	$0.901409\pi$
$282$	−18.5217	−	17.3842i	−1.10295	−	1.03522i
$283$	0.221480	+	0.383614i	0.0131656	+	0.0228035i	0.872533	−	0.488555i	$-0.162476\pi$
$283$	0.221480	+	0.383614i	0.0131656	+	0.0228035i	−0.859368	+	0.511358i	$0.829142\pi$
$284$	−0.0235991	+	0.0136250i	−0.00140035	+	0.000808493i
$285$	−7.62822	−	7.15976i	−0.451857	−	0.424108i
$286$	1.09713	−	18.8858i	0.0648747	−	1.11674i
$287$	0.0458371			0.00270568
$288$	−0.0354435	+	0.0714907i	−0.00208853	+	0.00421263i
$289$	4.61272			0.271337
$290$	6.32148	−	10.9491i	0.371210	−	0.642955i
$291$	−0.00789513	−	0.00184969i	−0.000462821	−	0.000108431i
$292$	0.00803265	−	0.00463765i	0.000470075	−	0.000271398i
$293$	−0.131806	+	0.0760981i	−0.00770018	+	0.00444570i	−0.503845	−	0.863794i	$-0.668082\pi$
$293$	−0.131806	+	0.0760981i	−0.00770018	+	0.00444570i	0.496145	+	0.868240i	$0.334748\pi$
$294$	4.96573	+	16.4323i	0.289607	+	0.958353i
$295$	−0.688625	+	1.19273i	−0.0400933	+	0.0694436i
$296$	12.7804			0.742844
$297$	−18.0427	+	6.72553i	−1.04694	+	0.390255i
$298$	17.0643			0.988511
$299$	−1.01235	+	17.4263i	−0.0585454	+	1.00779i
$300$	0.00779583	−	0.00235584i	0.000450092	−	0.000136014i
$301$	0.0113395	−	0.00654686i	0.000653597	−	0.000377355i
$302$	−13.7317	−	23.7840i	−0.790169	−	1.36861i
$303$	−0.791462	+	3.37824i	−0.0454683	+	0.194075i
$304$	−20.9729	−	12.1087i	−1.20288	−	0.694483i
$305$			8.67677i			0.496830i
$306$	−19.7074	+	1.24984i	−1.12660	+	0.0714487i
$307$			12.2212i			0.697503i	0.937215	+	0.348751i	$0.113394\pi$
$307$			12.2212i			0.697503i	−0.937215	+	0.348751i	$0.886606\pi$
$308$	−9.98809e−5	0	0.000172999i	−5.69124e−6	0	9.85752e-6i
$309$	20.5175	+	19.2575i	1.16720	+	1.09552i
$310$	−8.10532	+	4.67961i	−0.460351	+	0.265784i
$311$	14.5035	+	25.1209i	0.822421	+	1.42447i	0.903875	+	0.427797i	$0.140710\pi$
$311$	14.5035	+	25.1209i	0.822421	+	1.42447i	−0.0814542	+	0.996677i	$0.525956\pi$
$312$	5.01384	−	16.9153i	0.283853	−	0.957638i
$313$	13.4272	−	23.2565i	0.758949	−	1.31454i	−0.184439	−	0.982844i	$-0.559047\pi$
$313$	13.4272	−	23.2565i	0.758949	−	1.31454i	0.943387	−	0.331693i	$-0.107620\pi$
$314$		−	23.6540i		−	1.33487i
$315$	−0.0286380	+	0.0190478i	−0.00161357	+	0.00107322i
$316$	−0.00354445			−0.000199391
$317$	−26.8476	−	15.5005i	−1.50791	−	0.870595i	−0.999958	−	0.00921179i	$-0.997068\pi$
$317$	−26.8476	−	15.5005i	−1.50791	−	0.870595i	−0.507956	−	0.861383i	$-0.669599\pi$
$318$	−5.67707	−	1.33004i	−0.318354	−	0.0745848i
$319$	28.6567	−	16.5449i	1.60447	−	0.926339i
$320$	−6.91184	+	3.99055i	−0.386384	+	0.223079i
$321$	−3.74619	+	1.13207i	−0.209092	+	0.0631859i
$322$	0.0392938	−	0.0680589i	0.00218976	−	0.00379277i
$323$		−	28.0806i		−	1.56244i
$324$	0.0419785	−	0.00534604i	0.00233214	−	0.000297002i
$325$	−3.22180	+	1.61865i	−0.178713	+	0.0897867i
$326$	4.96173	−	8.59397i	0.274805	−	0.475976i
$327$	−4.18280	−	13.8415i	−0.231310	−	0.765438i
$328$	−5.64751	−	9.78177i	−0.311832	−	0.540108i
$329$	−0.0593767	−	0.102843i	−0.00327354	−	0.00566994i
$330$	8.84818	+	2.07297i	0.487076	+	0.114113i
$331$	25.1339	+	14.5110i	1.38148	+	0.797599i	0.992335	−	0.123576i	$-0.0394363\pi$
$331$	25.1339	+	14.5110i	1.38148	+	0.797599i	0.389147	+	0.921175i	$0.372770\pi$
$332$		−	0.0398473i		−	0.00218690i
$333$	−7.51611	−	11.3003i	−0.411880	−	0.619254i
$334$	−25.3327			−1.38614
$335$	4.83388	−	8.37253i	0.264103	−	0.457440i
$336$	−0.0544864	+	0.0580514i	−0.00297248	+	0.00316696i
$337$	8.04981	+	13.9427i	0.438501	+	0.759506i	0.997574	−	0.0696121i	$-0.0221761\pi$
$337$	8.04981	+	13.9427i	0.438501	+	0.759506i	−0.559073	+	0.829119i	$0.688843\pi$
$338$	2.13136	−	18.2826i	0.115931	−	0.994440i
$339$	11.2650	+	10.5732i	0.611833	+	0.574260i
$340$	0.0189305	+	0.0109296i	0.00102665	+	0.000592738i
$341$	−24.4955			−1.32651
$342$	1.62387	+	25.6050i	0.0878088	+	1.38456i
$343$			0.160504i			0.00866643i
$344$	−2.79424	−	1.61325i	−0.150655	−	0.0869808i
$345$	−8.16439	−	1.91277i	−0.439556	−	0.102980i
$346$	−31.7735	+	18.3444i	−1.70815	+	0.986202i
$347$	−6.18075	−	10.7054i	−0.331800	−	0.574694i	0.651065	−	0.759022i	$-0.274323\pi$
$347$	−6.18075	−	10.7054i	−0.331800	−	0.574694i	−0.982865	+	0.184328i	$0.940989\pi$
$348$	−0.0696123	+	0.0210363i	−0.00373161	+	0.00112766i
$349$	0.966423	+	0.557965i	0.0517314	+	0.0298672i	0.525643	−	0.850705i	$-0.323825\pi$
$349$	0.966423	+	0.557965i	0.0517314	+	0.0298672i	−0.473911	+	0.880573i	$0.657158\pi$
$350$	0.0162326			0.000867669
$351$	−17.9050	+	5.51463i	−0.955698	+	0.294349i
$352$	0.0985651			0.00525354
$353$	−13.4303	−	7.75398i	−0.714822	−	0.412703i	0.0980218	−	0.995184i	$-0.468749\pi$
$353$	−13.4303	−	7.75398i	−0.714822	−	0.412703i	−0.812844	+	0.582481i	$0.802082\pi$
$354$	3.23312	−	0.977025i	0.171839	−	0.0519283i
$355$	2.89773	+	5.01901i	0.153796	+	0.266382i
$356$	−0.0145343	+	0.00839140i	−0.000770318	+	0.000444743i
$357$	−0.0898825	−	0.0210579i	−0.00475709	−	0.00111450i
$358$	−4.45570	−	2.57250i	−0.235491	−	0.135961i
$359$			25.6452i			1.35350i	0.736213	+	0.676750i	$0.236612\pi$
$359$			25.6452i			1.35350i	−0.736213	+	0.676750i	$0.763388\pi$
$360$	7.59330	+	3.76459i	0.400202	+	0.198411i
$361$	−17.4839			−0.920208
$362$	11.0768	+	6.39518i	0.582183	+	0.336123i
$363$	3.45063	+	3.23872i	0.181111	+	0.169989i
$364$	−0.000106780	0	0.000162404i	−5.59677e−6	0	8.51226e-6i
$365$	−0.986326	−	1.70837i	−0.0516267	−	0.0894200i
$366$	14.5623	−	15.5151i	0.761185	−	0.810988i
$367$	9.19797	−	15.9314i	0.480130	−	0.831610i	−0.519610	−	0.854404i	$-0.673923\pi$
$367$	9.19797	−	15.9314i	0.480130	−	0.831610i	0.999740	+	0.0227937i	$0.00725608\pi$
$368$	−19.4108			−1.01186
$369$	−5.32769	+	10.7461i	−0.277348	+	0.559421i
$370$			6.40524i			0.332993i
$371$	−0.0236067	−	0.0136293i	−0.00122560	−	0.000707601i
$372$	0.0524143	+	0.0122798i	0.00271756	+	0.000636675i
$373$	−7.49714	−	12.9854i	−0.388187	−	0.672360i	0.604018	−	0.796970i	$-0.293565\pi$
$373$	−7.49714	−	12.9854i	−0.388187	−	0.672360i	−0.992206	+	0.124610i	$0.960232\pi$
$374$	12.1961	+	21.1243i	0.630646	+	1.09231i
$375$	−0.501035	−	1.65800i	−0.0258733	−	0.0856188i
$376$	−14.6314	+	25.3423i	−0.754556	+	1.30693i
$377$	28.7688	−	14.4536i	1.48167	−	0.744401i
$378$	0.0831765	+	0.0140037i	0.00427814	+	0.000720271i
$379$		−	31.4375i		−	1.61483i	−0.589981	−	0.807417i	$-0.700865\pi$
$379$		−	31.4375i		−	1.61483i	0.589981	−	0.807417i	$-0.299135\pi$
$380$	0.0142003	−	0.0245957i	0.000728462	−	0.00126173i
$381$	31.1563	−	9.41521i	1.59619	−	0.482356i
$382$	−25.9188	+	14.9642i	−1.32612	+	0.765636i
$383$	−23.3236	+	13.4659i	−1.19178	+	0.688074i	−0.958710	−	0.284386i	$-0.908210\pi$
$383$	−23.3236	+	13.4659i	−1.19178	+	0.688074i	−0.233069	+	0.972460i	$0.574877\pi$
$384$	19.1463	+	4.48564i	0.977056	+	0.228907i
$385$	0.0367930	+	0.0212424i	0.00187515	+	0.00108262i
$386$	0.344624			0.0175409
$387$	0.216858	+	3.41940i	0.0110235	+	0.173818i
$388$		0	2.20130e-5i		0	1.11754e-6i
$389$	9.70578	−	16.8109i	0.492103	−	0.852347i	−0.507856	−	0.861442i	$-0.669562\pi$
$389$	9.70578	−	16.8109i	0.492103	−	0.852347i	0.999959	+	0.00909505i	$0.00289508\pi$
$390$	8.47756	+	2.51283i	0.429278	+	0.127242i
$391$	−11.2536	−	19.4918i	−0.569118	−	0.985742i
$392$	17.1259	−	9.88764i	0.864988	−	0.499401i
$393$	−3.74223	−	3.51242i	−0.188771	−	0.177178i
$394$	13.0068	−	22.5285i	0.655275	−	1.13497i
$395$			0.753826i			0.0379291i
$396$	−0.0289489	−	0.0435240i	−0.00145474	−	0.00218716i
$397$			16.7410i			0.840208i	0.907476	+	0.420104i	$0.138006\pi$
$397$			16.7410i			0.840208i	−0.907476	+	0.420104i	$0.861994\pi$
$398$	16.3908	+	9.46325i	0.821598	+	0.474350i
$399$	−0.0273597	+	0.116781i	−0.00136970	+	0.00584635i
$400$	−2.00469	−	3.47223i	−0.100235	−	0.173611i
$401$	−5.03467	+	2.90677i	−0.251420	+	0.145157i	−0.620414	−	0.784274i	$-0.713035\pi$
$401$	−5.03467	+	2.90677i	−0.251420	+	0.145157i	0.368995	+	0.929432i	$0.379702\pi$
$402$	−22.6953	+	6.85834i	−1.13194	+	0.342063i
$403$	−23.7933	−	1.38222i	−1.18523	−	0.0688533i
$404$	−0.00941913			−0.000468619
$405$	−1.13699	−	8.92789i	−0.0564973	−	0.443631i
$406$	−0.144948			−0.00719364
$407$	−8.38209	+	14.5182i	−0.415485	+	0.719641i
$408$	6.58045	+	21.7757i	0.325781	+	1.07806i
$409$	−14.1966	+	8.19644i	−0.701979	+	0.405288i	−0.808084	−	0.589067i	$-0.799495\pi$
$409$	−14.1966	+	8.19644i	−0.701979	+	0.405288i	0.106105	+	0.994355i	$0.466162\pi$
$410$	4.90241	−	2.83041i	0.242113	−	0.139784i
$411$	33.2689	+	7.79432i	1.64103	+	0.384465i
$412$	−0.0381944	+	0.0661547i	−0.00188171	+	0.00325921i
$413$	0.0157898			0.000776964
$414$	11.3887	+	17.1227i	0.559723	+	0.841532i
$415$	−8.47464			−0.416004
$416$	0.0957397	+	0.00556178i	0.00469402	+	0.000272689i
$417$	22.8652	+	21.4610i	1.11971	+	1.05095i
$418$	27.4459	−	15.8459i	1.34242	−	0.775049i
$419$	12.1069	+	20.9698i	0.591462	+	1.02444i	0.994036	+	0.109055i	$0.0347823\pi$
$419$	12.1069	+	20.9698i	0.591462	+	1.02444i	−0.402574	+	0.915388i	$0.631884\pi$
$420$	−6.80790e−5	0	6.38982e-5i	−3.32191e−6	0	3.11791e-6i
$421$	27.4941	+	15.8737i	1.33998	+	0.773638i	0.986804	−	0.161919i	$-0.0517684\pi$
$421$	27.4941	+	15.8737i	1.33998	+	0.773638i	0.353176	+	0.935557i	$0.385102\pi$
$422$			22.8611i			1.11286i
$423$	31.0122	−	1.96679i	1.50786	−	0.0956286i
$424$			6.71699i			0.326206i
$425$	2.32447	−	4.02611i	0.112754	−	0.195295i
$426$	3.24198	−	13.8379i	0.157074	−	0.670448i
$427$	0.0861493	−	0.0497383i	0.00416906	−	0.00240701i
$428$	−0.00531193	−	0.00920054i	−0.000256762	−	0.000444725i
$429$	15.9270	+	16.7896i	0.768962	+	0.810609i
$430$	0.808527	−	1.40041i	0.0389907	−	0.0675338i
$431$		−	17.8910i		−	0.861777i	−0.902405	−	0.430888i	$-0.858200\pi$
$431$		−	17.8910i		−	0.861777i	0.902405	−	0.430888i	$-0.141800\pi$
$432$	−7.27666	−	19.5212i	−0.350099	−	0.939216i
$433$	−25.4679			−1.22391			−0.611955	−	0.790892i	$-0.709617\pi$
$433$	−25.4679			−1.22391			−0.611955	+	0.790892i	$0.709617\pi$
$434$	0.0929252	+	0.0536504i	0.00446055	+	0.00257530i
$435$	4.47396	+	14.8050i	0.214510	+	0.709846i
$436$	0.0339944	−	0.0196267i	0.00162804	−	0.000939949i
$437$	−25.3249	+	14.6213i	−1.21145	+	0.699433i
$438$	−1.10350	+	4.71013i	−0.0527273	+	0.225059i
$439$	3.31068	−	5.73426i	0.158010	−	0.273681i	−0.776141	−	0.630559i	$-0.782825\pi$
$439$	3.31068	−	5.73426i	0.158010	−	0.273681i	0.934151	+	0.356878i	$0.116159\pi$
$440$		−	10.4690i		−	0.499089i
$441$	−18.8143	−	9.32770i	−0.895919	−	0.444176i
$442$	10.6545	+	21.2069i	0.506783	+	1.00871i
$443$	−8.33283	+	14.4329i	−0.395905	+	0.685727i	−0.993216	−	0.116282i	$-0.962902\pi$
$443$	−8.33283	+	14.4329i	−0.395905	+	0.685727i	0.597312	+	0.802009i	$0.296236\pi$
$444$	0.0252137	−	0.0268634i	0.00119659	−	0.00127488i
$445$	1.78466	+	3.09113i	0.0846012	+	0.146534i
$446$	15.5396	+	26.9154i	0.735823	+	1.27448i
$447$	−14.2861	+	15.2208i	−0.675707	+	0.719918i
$448$	0.0792422	+	0.0457505i	0.00374384	+	0.00216151i
$449$		−	5.30273i		−	0.250251i	−0.992141	−	0.125126i	$-0.960067\pi$
$449$		−	5.30273i		−	0.250251i	0.992141	−	0.125126i	$-0.0399334\pi$
$450$	−1.88673	+	3.80560i	−0.0889412	+	0.179398i
$451$	14.8158			0.697650
$452$	−0.0209705	+	0.0363219i	−0.000986369	+	0.00170844i
$453$	32.7104	+	7.66348i	1.53687	+	0.360062i
$454$	−0.638275	−	1.10553i	−0.0299557	−	0.0518849i
$455$	0.0345396	+	0.0227097i	0.00161924	+	0.00106464i
$456$	28.2923	−	8.54971i	1.32491	−	0.400377i
$457$	29.4541	+	17.0053i	1.37780	+	0.795476i	0.991895	−	0.127061i	$-0.0405544\pi$
$457$	29.4541	+	17.0053i	1.37780	+	0.795476i	0.385909	+	0.922537i	$0.373888\pi$
$458$	2.44731			0.114355
$459$	15.3840	−	18.6246i	0.718062	−	0.869323i
$460$		−	0.0227638i		−	0.00106137i
$461$	−2.59939	−	1.50076i	−0.121066	−	0.0698972i	0.438244	−	0.898856i	$-0.355600\pi$
$461$	−2.59939	−	1.50076i	−0.121066	−	0.0698972i	−0.559310	+	0.828959i	$0.688934\pi$
$462$	−0.0301389	−	0.0997342i	−0.00140219	−	0.00464005i
$463$	25.6151	−	14.7889i	1.19044	−	0.687298i	0.232030	−	0.972709i	$-0.425463\pi$
$463$	25.6151	−	14.7889i	1.19044	−	0.687298i	0.958405	+	0.285411i	$0.0921300\pi$
$464$	17.9008	+	31.0050i	0.831022	+	1.43937i
$465$	2.61163	−	11.1474i	0.121112	−	0.516947i
$466$	−22.2991	−	12.8744i	−1.03299	−	0.596396i
$467$	9.39049			0.434540			0.217270	−	0.976112i	$-0.430285\pi$
$467$	9.39049			0.434540			0.217270	+	0.976112i	$0.430285\pi$
$468$	−0.0256631	−	0.0439099i	−0.00118628	−	0.00202974i
$469$	−0.110838			−0.00511803
$470$	−12.7010	−	7.33293i	−0.585854	−	0.338243i
$471$	21.0985	+	19.8028i	0.972167	+	0.912465i
$472$	−1.94543	−	3.36958i	−0.0895456	−	0.155098i
$473$	3.66524	−	2.11612i	0.168528	−	0.0972995i
$474$	1.26515	−	1.34793i	0.0581104	−	0.0619125i
$475$	−5.23096	−	3.02010i	−0.240013	−	0.138572i
$476$		0	0.000250608i		0	1.14866e-5i
$477$	5.93912	−	3.95025i	0.271933	−	0.180869i
$478$	−21.0794			−0.964151
$479$	−4.16324	−	2.40365i	−0.190223	−	0.109825i	0.401864	−	0.915699i	$-0.368363\pi$
$479$	−4.16324	−	2.40365i	−0.190223	−	0.109825i	−0.592087	+	0.805874i	$0.701696\pi$
$480$	−0.0105087	+	0.0448548i	−0.000479654	+	0.00204733i
$481$	−8.96103	+	13.6290i	−0.408588	+	0.621431i
$482$	6.57644	+	11.3907i	0.299549	+	0.518833i
$483$	0.0278098	+	0.0920267i	0.00126539	+	0.00418736i
$484$	−0.00642354	+	0.0111259i	−0.000291979	+	0.000505722i
$485$	−0.00468168			−0.000212584
$486$	−12.9507	+	17.8724i	−0.587456	+	0.810707i
$487$			3.65883i			0.165797i	0.996558	+	0.0828987i	$0.0264178\pi$
$487$			3.65883i			0.165797i	−0.996558	+	0.0828987i	$0.973582\pi$
$488$	−21.2286	−	12.2563i	−0.960974	−	0.554818i
$489$	3.51161	+	11.6205i	0.158801	+	0.525495i
$490$	4.95547	+	8.58312i	0.223865	+	0.387746i
$491$	−1.64741	−	2.85340i	−0.0743467	−	0.128772i	0.826455	−	0.563002i	$-0.190354\pi$
$491$	−1.64741	−	2.85340i	−0.0743467	−	0.128772i	−0.900802	+	0.434230i	$0.857020\pi$
$492$	−0.0317022	−	0.00742727i	−0.00142925	−	0.000334847i
$493$	−20.7562	+	35.9509i	−0.934814	+	1.61915i
$494$	27.5533	−	13.8430i	1.23968	−	0.622825i
$495$	−9.25660	+	6.15679i	−0.416053	+	0.276727i
$496$		−	26.5028i		−	1.19001i
$497$	0.0332216	−	0.0575416i	0.00149019	−	0.00258109i
$498$	15.1537	+	14.2231i	0.679053	+	0.637351i
$499$	−12.0212	+	6.94041i	−0.538141	+	0.310696i	−0.744325	−	0.667818i	$-0.767229\pi$
$499$	−12.0212	+	6.94041i	−0.538141	+	0.310696i	0.206184	+	0.978513i	$0.433895\pi$
$500$	0.00407201	−	0.00235097i	0.000182106	−	0.000105139i
$501$	21.2082	−	22.5958i	0.947513	−	1.00951i
$502$	4.17776	+	2.41203i	0.186463	+	0.107654i
$503$	−14.3269			−0.638806			−0.319403	−	0.947619i	$-0.603482\pi$
$503$	−14.3269			−0.638806			−0.319403	+	0.947619i	$0.603482\pi$
$504$	−0.00614994	−	0.0969718i	−0.000273940	−	0.00431947i
$505$			2.00324i			0.0891430i
$506$	12.7008	−	21.9985i	0.564621	−	0.977953i
$507$	14.5230	+	17.2070i	0.644990	+	0.764191i
$508$	0.0441784	+	0.0765192i	0.00196010	+	0.00339499i
$509$	−20.2696	+	11.7027i	−0.898434	+	0.518711i	−0.876692	−	0.481052i	$-0.840255\pi$
$509$	−20.2696	+	11.7027i	−0.898434	+	0.518711i	−0.0217423	+	0.999764i	$0.506921\pi$
$510$	−10.9135	+	3.29798i	−0.483258	+	0.146037i
$511$	−0.0113079	+	0.0195859i	−0.000500234	+	0.000866431i
$512$		−	22.5471i		−	0.996451i
$513$	−24.1982	−	19.9878i	−1.06838	−	0.882482i
$514$			42.7426i			1.88530i
$515$	14.0696	+	8.12311i	0.619983	+	0.357947i
$516$	−0.00890353	+	0.00269058i	−0.000391956	+	0.000118446i
$517$	−19.1922	−	33.2418i	−0.844071	−	1.46197i
$518$	0.0635960	−	0.0367171i	0.00279425	−	0.00161326i
$519$	10.2378	−	43.6985i	0.449389	−	1.91815i
$520$	0.590738	−	10.1689i	0.0259056	−	0.445935i
$521$	−40.3139			−1.76619			−0.883093	−	0.469198i	$-0.844543\pi$
$521$	−40.3139			−1.76619			−0.883093	+	0.469198i	$0.844543\pi$
$522$	16.8474	−	33.9818i	0.737391	−	1.48734i
$523$	−20.3832			−0.891297			−0.445648	−	0.895208i	$-0.647027\pi$
$523$	−20.3832			−0.891297			−0.445648	+	0.895208i	$0.647027\pi$
$524$	0.00696637	−	0.0120661i	0.000304327	−	0.000527110i
$525$	−0.0135897	+	0.0144789i	−0.000593104	+	0.000631910i
$526$	23.2592	−	13.4287i	1.01415	−	0.585520i
$527$	26.6134	−	15.3652i	1.15930	−	0.669321i
$528$	−17.6115	+	18.7638i	−0.766442	+	0.816590i
$529$	−0.219320	+	0.379874i	−0.00953567	+	0.0165163i
$530$	−3.36641			−0.146227
$531$	−1.83526	+	3.70178i	−0.0796434	+	0.160644i
$532$	−0.000325606	0		−1.41168e−5	0
$533$	14.3911	+	0.836020i	0.623348	+	0.0362120i
$534$	1.99668	−	8.52254i	0.0864048	−	0.368806i
$535$	−1.95675	+	1.12973i	−0.0845977	+	0.0488425i
$536$	13.6562	+	23.6532i	0.589857	+	1.02166i
$537$	6.02483	−	1.82066i	0.259991	−	0.0785672i
$538$	−4.23496	−	2.44505i	−0.182582	−	0.105414i
$539$			25.9395i			1.11729i
$540$	0.0228933	−	0.00853361i	0.000985169	−	0.000367228i
$541$			12.9137i			0.555204i	0.960696	+	0.277602i	$0.0895396\pi$
$541$			12.9137i			0.555204i	−0.960696	+	0.277602i	$0.910460\pi$
$542$	9.62783	−	16.6759i	0.413551	−	0.716291i
$543$	−14.9776	+	4.52612i	−0.642751	+	0.194234i
$544$	−0.107087	+	0.0618268i	−0.00459132	+	0.00265080i
$545$	−4.17416	−	7.22987i	−0.178802	−	0.309693i
$546$	−0.0236472	−	0.0985759i	−0.00101201	−	0.00421866i
$547$	−3.77468	+	6.53794i	−0.161394	+	0.279542i	−0.935369	−	0.353674i	$-0.884932\pi$
$547$	−3.77468	+	6.53794i	−0.161394	+	0.279542i	0.773975	+	0.633216i	$0.218266\pi$
$548$			0.0927595i			0.00396249i
$549$	1.64753	+	25.9781i	0.0703149	+	1.10872i
$550$	5.24682			0.223725
$551$	46.7095	+	26.9678i	1.98989	+	1.14887i
$552$	16.2124	−	17.2731i	0.690044	−	0.735193i
$553$	0.00748453	−	0.00432120i	0.000318275	−	0.000183756i
$554$	9.37850	−	5.41468i	0.398454	−	0.230048i
$555$	−5.71325	−	5.36239i	−0.242514	−	0.227621i
$556$	−0.0425648	+	0.0737244i	−0.00180515	+	0.00312661i
$557$			19.3602i			0.820318i	0.912014	+	0.410159i	$0.134527\pi$
$557$			19.3602i			0.820318i	−0.912014	+	0.410159i	$0.865473\pi$
$558$	−23.3787	+	15.5497i	−0.989697	+	0.658272i
$559$	3.67958	−	1.84864i	0.155629	−	0.0781893i
$560$	−0.0229832	+	0.0398081i	−0.000971218	+	0.00168220i
$561$	−29.0525	−	6.80649i	−1.22660	−	0.287370i
$562$	15.9593	+	27.6424i	0.673204	+	1.16602i
$563$	15.2746	+	26.4563i	0.643746	+	1.11500i	0.984590	+	0.174880i	$0.0559539\pi$
$563$	15.2746	+	26.4563i	0.643746	+	1.11500i	−0.340844	+	0.940120i	$0.610713\pi$
$564$	0.0244022	+	0.0807505i	0.00102752	+	0.00340021i
$565$	7.72487	+	4.45996i	0.324988	+	0.187632i
$566$		−	0.627175i		−	0.0263621i
$567$	−0.0821250	+	0.0624667i	−0.00344893	+	0.00262335i
$568$	−16.3727			−0.686984
$569$	−23.1980	+	40.1802i	−0.972512	+	1.68444i	−0.284601	+	0.958646i	$0.591861\pi$
$569$	−23.1980	+	40.1802i	−0.972512	+	1.68444i	−0.687911	+	0.725795i	$0.741472\pi$
$570$	4.28493	+	14.1795i	0.179476	+	0.593913i
$571$	−3.72019	−	6.44356i	−0.155685	−	0.269655i	0.777623	−	0.628731i	$-0.216425\pi$
$571$	−3.72019	−	6.44356i	−0.155685	−	0.269655i	−0.933308	+	0.359076i	$0.883092\pi$
$572$	−0.0345141	+	0.0524933i	−0.00144311	+	0.00219485i
$573$	8.35134	−	35.6465i	0.348882	−	1.48915i
$574$	−0.0562047	−	0.0324498i	−0.00234594	−	0.00135443i
$575$	−4.84135			−0.201898
$576$	−19.9362	+	13.2601i	−0.830676	+	0.552503i
$577$		−	18.5451i		−	0.772042i	−0.922490	−	0.386021i	$-0.873849\pi$
$577$		−	18.5451i		−	0.772042i	0.922490	−	0.386021i	$-0.126151\pi$
$578$	−5.65605	−	3.26552i	−0.235261	−	0.135828i
$579$	−0.288515	+	0.307392i	−0.0119903	+	0.0127748i
$580$	−0.0363607	+	0.0209929i	−0.00150980	+	0.000871681i
$581$	0.0485796	+	0.0841424i	0.00201542	+	0.00349081i
$582$	0.00837141	+	0.00785732i	0.000347006	+	0.000325696i
$583$	−7.63034	−	4.40538i	−0.316017	−	0.182452i
$584$	5.57293			0.230609
$585$	−9.33866	+	5.45797i	−0.386106	+	0.225659i
$586$	0.215491			0.00890185
$587$	−13.2268	−	7.63650i	−0.545929	−	0.315192i	0.201550	−	0.979478i	$-0.435402\pi$
$587$	−13.2268	−	7.63650i	−0.545929	−	0.315192i	−0.747478	+	0.664286i	$0.768736\pi$
$588$	0.0130036	−	0.0555041i	0.000536261	−	0.00228895i
$589$	−19.9635	−	34.5777i	−0.822580	−	1.42475i
$590$	1.68876	−	0.975007i	0.0695252	−	0.0401404i
$591$	9.20545	+	30.4622i	0.378661	+	1.25305i
$592$	−15.7079	−	9.06898i	−0.645592	−	0.372733i
$593$			15.5028i			0.636624i	0.947986	+	0.318312i	$0.103116\pi$
$593$			15.5028i			0.636624i	−0.947986	+	0.318312i	$0.896884\pi$
$594$	26.8849	+	4.52637i	1.10310	+	0.185719i
$595$	−0.0532989			−0.00218504
$596$	−0.0490764	−	0.0283343i	−0.00201025	−	0.00116062i
$597$	−22.1631	+	6.69751i	−0.907074	+	0.274111i
$598$	13.5781	−	20.6512i	0.555249	−	0.844491i
$599$	−23.4811	−	40.6704i	−0.959410	−	1.66175i	−0.723936	−	0.689867i	$-0.757669\pi$
$599$	−23.4811	−	40.6704i	−0.959410	−	1.66175i	−0.235474	−	0.971881i	$-0.575664\pi$
$600$	4.76420	+	1.11617i	0.194498	+	0.0455674i
$601$	9.90852	−	17.1621i	0.404177	−	0.700055i	−0.590048	−	0.807368i	$-0.700891\pi$
$601$	9.90852	−	17.1621i	0.404177	−	0.700055i	0.994225	+	0.107313i	$0.0342247\pi$
$602$	−0.0185391			−0.000755596
$603$	12.8828	−	25.9851i	0.524629	−	1.05819i
$604$			0.0912024i			0.00371097i
$605$	2.36623	+	1.36614i	0.0962009	+	0.0555416i
$606$	3.36206	−	3.58204i	0.136574	−	0.145510i
$607$	9.73052	+	16.8538i	0.394950	+	0.684073i	0.993095	−	0.117315i	$-0.0374287\pi$
$607$	9.73052	+	16.8538i	0.394950	+	0.684073i	−0.598145	+	0.801388i	$0.704095\pi$
$608$	0.0803291	+	0.139134i	0.00325777	+	0.00564263i
$609$	0.121349	−	0.129288i	0.00491729	−	0.00523903i
$610$	6.14261	−	10.6393i	0.248707	−	0.430773i
$611$	−16.7663	−	33.3719i	−0.678291	−	1.35008i
$612$	0.0587530	+	0.0291284i	0.00237495	+	0.00117745i
$613$			35.8156i			1.44658i	0.690546	+	0.723288i	$0.257370\pi$
$613$			35.8156i			1.44658i	−0.690546	+	0.723288i	$0.742630\pi$
$614$	8.65187	−	14.9855i	0.349161	−	0.604765i
$615$	−1.57962	+	6.74236i	−0.0636963	+	0.271878i
$616$	−0.103944	+	0.0600119i	−0.00418801	+	0.00241795i
$617$	−7.87734	+	4.54798i	−0.317130	+	0.183095i	−0.650112	−	0.759838i	$-0.725278\pi$
$617$	−7.87734	+	4.54798i	−0.317130	+	0.183095i	0.332983	+	0.942933i	$0.391945\pi$
$618$	−11.5251	−	38.1383i	−0.463608	−	1.53415i
$619$	−4.43877	−	2.56273i	−0.178409	−	0.103005i	0.408136	−	0.912921i	$-0.366179\pi$
$619$	−4.43877	−	2.56273i	−0.178409	−	0.103005i	−0.586545	+	0.809917i	$0.699512\pi$
$620$	0.0310808			0.00124824
$621$	−24.8072	−	4.17657i	−0.995481	−	0.167600i
$622$		−	41.0704i		−	1.64677i
$623$	0.0204607	−	0.0354389i	0.000819739	−	0.00141983i
$624$	−18.1654	+	17.2322i	−0.727200	+	0.689838i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−32.9284	+	19.0112i	−1.31608	+	0.759840i
$627$	−8.84340	+	37.7468i	−0.353172	+	1.50746i
$628$	−0.0392760	+	0.0680280i	−0.00156728	+	0.00271461i
$629$		−	21.0313i		−	0.838572i
$630$	0.0486002	−	0.00308222i	0.00193628	−	0.000122798i
$631$		−	44.9471i		−	1.78931i	−0.446753	−	0.894657i	$-0.647420\pi$
$631$		−	44.9471i		−	1.78931i	0.446753	−	0.894657i	$-0.352580\pi$
$632$	−1.84431	−	1.06481i	−0.0733628	−	0.0423560i
$633$	−20.3913	−	19.1390i	−0.810481	−	0.760708i
$634$	21.9468	+	38.0129i	0.871617	+	1.50969i
$635$	16.2739	−	9.39576i	0.645811	−	0.372859i
$636$	0.0141186	+	0.0132516i	0.000559839	+	0.000525459i
$637$	−1.46370	+	25.1959i	−0.0579939	+	0.998298i
$638$	−46.8512			−1.85485
$639$	9.62876	+	14.4766i	0.380908	+	0.572687i
$640$	11.3534			0.448784
$641$	8.58775	−	14.8744i	0.339196	−	0.587504i	−0.645086	−	0.764110i	$-0.723178\pi$
$641$	8.58775	−	14.8744i	0.339196	−	0.587504i	0.984282	+	0.176606i	$0.0565118\pi$
$642$	5.39495	+	1.26394i	0.212922	+	0.0498838i
$643$	22.8056	−	13.1668i	0.899366	−	0.519249i	0.0223716	−	0.999750i	$-0.492878\pi$
$643$	22.8056	−	13.1668i	0.899366	−	0.519249i	0.876994	+	0.480500i	$0.159545\pi$
$644$	−0.000226015	0	0.000130490i	−8.90625e−6	0	5.14202e-6i
$645$	0.572226	+	1.89358i	0.0225314	+	0.0745598i
$646$	−19.8793	+	34.4319i	−0.782140	+	1.35471i
$647$	8.35488			0.328464			0.164232	−	0.986422i	$-0.447485\pi$
$647$	8.35488			0.328464			0.164232	+	0.986422i	$0.447485\pi$
$648$	23.4490	+	9.82931i	0.921165	+	0.386132i
$649$	5.10369			0.200337
$650$	5.09642	+	0.296065i	0.199898	+	0.0116126i
$651$	−0.125650	+	0.0379705i	−0.00492461	+	0.00148818i
$652$	−0.0285395	+	0.0164773i	−0.00111769	+	0.000645301i
$653$	−9.65746	−	16.7272i	−0.377926	−	0.654587i	0.612835	−	0.790211i	$-0.290029\pi$
$653$	−9.65746	−	16.7272i	−0.377926	−	0.654587i	−0.990760	+	0.135625i	$0.956696\pi$
$654$	−4.67005	+	19.9334i	−0.182613	+	0.779459i
$655$	−2.56619	−	1.48159i	−0.100269	−	0.0578906i
$656$			16.0299i			0.625864i
$657$	−3.27743	−	4.92754i	−0.127865	−	0.192242i
$658$			0.168140i			0.00655478i
$659$	4.11302	−	7.12397i	0.160221	−	0.277510i	−0.774727	−	0.632296i	$-0.782113\pi$
$659$	4.11302	−	7.12397i	0.160221	−	0.277510i	0.934948	+	0.354785i	$0.115446\pi$
$660$	−0.0220050	−	0.0206536i	−0.000856543	−	0.000803942i
$661$	−15.8360	+	9.14292i	−0.615949	+	0.355618i	−0.775290	−	0.631605i	$-0.782396\pi$
$661$	−15.8360	+	9.14292i	−0.615949	+	0.355618i	0.159341	+	0.987224i	$0.449063\pi$
$662$	−20.5458	−	35.5864i	−0.798536	−	1.38311i
$663$	−27.8356	−	8.25074i	−1.08105	−	0.320432i
$664$	11.9708	−	20.7341i	0.464558	−	0.804638i
$665$			0.0692491i			0.00268536i
$666$	1.21622	+	19.1772i	0.0471274	+	0.743102i
$667$	43.2305			1.67389
$668$	0.0728559	+	0.0420634i	0.00281888	+	0.00162748i
$669$	−37.0172	−	8.67247i	−1.43117	−	0.335297i
$670$	−11.8545	+	6.84418i	−0.457978	+	0.264414i
$671$	27.8458	−	16.0768i	1.07498	−	0.620638i
$672$	0.000505591	0	0.000152786i	1.95036e−5	0	5.89384e-6i
$673$	6.31801	−	10.9431i	0.243542	−	0.421826i	−0.718179	−	0.695858i	$-0.755024\pi$
$673$	6.31801	−	10.9431i	0.243542	−	0.421826i	0.961721	+	0.274032i	$0.0883574\pi$
$674$		−	22.7951i		−	0.878033i
$675$	−1.81491	−	4.86889i	−0.0698559	−	0.187404i
$676$	−0.0364868	+	0.0490410i	−0.00140334	+	0.00188619i
$677$	1.00014	−	1.73230i	0.0384386	−	0.0665775i	−0.846166	−	0.532919i	$-0.821095\pi$
$677$	1.00014	−	1.73230i	0.0384386	−	0.0665775i	0.884605	+	0.466342i	$0.154428\pi$
$678$	−6.32781	−	20.9397i	−0.243018	−	0.804184i
$679$	2.68371e−5	0	4.64832e-5i	1.02991e−6	0	1.78386e-6i
$680$	6.56686	+	11.3741i	0.251827	+	0.436178i
$681$	1.52044	+	0.356213i	0.0582636	+	0.0136501i
$682$	30.0360	+	17.3413i	1.15014	+	0.664032i
$683$			11.3285i			0.433475i	0.976230	+	0.216737i	$0.0695415\pi$
$683$			11.3285i			0.433475i	−0.976230	+	0.216737i	$0.930458\pi$
$684$	0.0378454	−	0.0763355i	0.00144706	−	0.00291876i
$685$	19.7279			0.753764
$686$	0.113627	−	0.196808i	0.00433830	−	0.00751416i
$687$	−2.04886	+	2.18291i	−0.0781688	+	0.0832833i
$688$	2.28953	+	3.96559i	0.0872877	+	0.151187i
$689$	−7.16303	−	4.70966i	−0.272890	−	0.179424i
$690$	8.65692	+	8.12529i	0.329563	+	0.309324i
$691$	15.1112	+	8.72447i	0.574858	+	0.331895i	0.759087	−	0.650989i	$-0.225646\pi$
$691$	15.1112	+	8.72447i	0.574858	+	0.331895i	−0.184229	+	0.982883i	$0.558979\pi$
$692$	0.121839			0.00463163
$693$	0.114191	+	0.0566134i	0.00433776	+	0.00215056i
$694$			17.5023i			0.664379i
$695$	15.6796	+	9.05260i	0.594759	+	0.343385i
$696$	−42.5416	−	9.96675i	−1.61254	−	0.377789i
$697$	−16.0968	+	9.29349i	−0.609710	+	0.352016i
$698$	−0.790008	−	1.36833i	−0.0299022	−	0.0517922i
$699$	30.1521	−	9.11172i	1.14046	−	0.344637i
$700$	−4.66844e−5	0	2.69532e-5i	−1.76450e−6	0	1.01874e-6i
$701$	−14.9281			−0.563828			−0.281914	−	0.959440i	$-0.590969\pi$
$701$	−14.9281			−0.563828			−0.281914	+	0.959440i	$0.590969\pi$
$702$	25.8588	+	5.91367i	0.975979	+	0.223197i
$703$	−27.3251			−1.03059
$704$	25.6133	+	14.7878i	0.965336	+	0.557337i
$705$	17.1738	−	5.18980i	0.646804	−	0.195459i
$706$	10.9787	+	19.0156i	0.413188	+	0.715662i
$707$	0.0198896	−	0.0114833i	0.000748027	−	0.000431873i
$708$	−0.0109206	−	0.00255851i	−0.000410423	−	9.61548e-5i
$709$	28.4274	+	16.4125i	1.06761	+	0.616386i	0.927528	−	0.373753i	$-0.121929\pi$
$709$	28.4274	+	16.4125i	1.06761	+	0.616386i	0.140084	+	0.990140i	$0.455263\pi$
$710$		−	8.20565i		−	0.307952i
$711$	0.143135	+	2.25694i	0.00536799	+	0.0846420i
$712$	−10.0837			−0.377902
$713$	−27.7148	−	16.0011i	−1.03793	−	0.599247i
$714$	0.0953048	+	0.0894521i	0.00356669	+	0.00334766i
$715$	11.1642	+	7.34038i	0.417516	+	0.274515i
$716$	0.00854296	+	0.0147968i	0.000319265	+	0.000552984i
$717$	17.6474	−	18.8021i	0.659055	−	0.702177i
$718$	18.1552	−	31.4457i	0.677545	−	1.17354i
$719$	26.2659			0.979554			0.489777	−	0.871848i	$-0.337078\pi$
$719$	26.2659			0.979554			0.489777	+	0.871848i	$0.337078\pi$
$720$	−6.66131	−	10.0151i	−0.248253	−	0.373242i
$721$		−	0.186258i		−	0.00693662i
$722$	21.4385	+	12.3775i	0.797860	+	0.460644i
$723$	−15.6658	−	3.67023i	−0.582618	−	0.136497i
$724$	−0.0212376	−	0.0367846i	−0.000789290	−	0.00136709i
$725$	4.46472	+	7.73312i	0.165815	+	0.287201i
$726$	−1.93829	−	6.41410i	−0.0719368	−	0.238050i
$727$	−14.8130	+	25.6568i	−0.549382	+	0.951558i	0.448935	+	0.893565i	$0.351804\pi$
$727$	−14.8130	+	25.6568i	−0.549382	+	0.951558i	−0.998317	+	0.0579934i	$0.981530\pi$
$728$	−0.104350	+	0.0524263i	−0.00386748	+	0.00194305i
$729$	−5.09933	−	26.5141i	−0.188864	−	0.982003i
$730$			2.79303i			0.103375i
$731$	−2.65476	+	4.59817i	−0.0981897	+	0.170070i
$732$	−0.0676426	+	0.0204411i	−0.00250014	+	0.000755524i
$733$	−40.5515	+	23.4124i	−1.49780	+	0.864758i	−0.999997	−	0.00253007i	$-0.999195\pi$
$733$	−40.5515	+	23.4124i	−1.49780	+	0.864758i	−0.497807	+	0.867288i	$0.665861\pi$
$734$	−22.5568	+	13.0232i	−0.832587	+	0.480694i
$735$	−11.8045	−	2.76559i	−0.435415	−	0.102010i
$736$	0.111519	+	0.0643855i	0.00411064	+	0.00237328i
$737$	−35.8259			−1.31967
$738$	14.1403	−	9.40506i	0.520512	−	0.346205i
$739$			9.80336i			0.360622i	0.983610	+	0.180311i	$0.0577105\pi$
$739$			9.80336i			0.360622i	−0.983610	+	0.180311i	$0.942290\pi$
$740$	0.0106355	−	0.0184213i	0.000390969	−	0.000677179i
$741$	−10.7199	+	36.1657i	−0.393804	+	1.32858i
$742$	0.0192975	+	0.0334242i	0.000708432	+	0.00122704i
$743$	3.08670	−	1.78211i	0.113240	−	0.0653792i	−0.442310	−	0.896862i	$-0.645841\pi$
$743$	3.08670	−	1.78211i	0.113240	−	0.0653792i	0.555550	+	0.831483i	$0.312508\pi$
$744$	23.5841	+	22.1358i	0.864635	+	0.811537i
$745$	−6.02608	+	10.4375i	−0.220778	+	0.382399i
$746$			21.2300i			0.777287i
$747$	−25.3729	+	1.60915i	−0.928347	+	0.0588757i
$748$		−	0.0810035i		−	0.00296178i
$749$	0.0224336	+	0.0129520i	0.000819705	+	0.000473257i
$750$	−0.559399	+	2.38771i	−0.0204264	+	0.0871870i
$751$	−7.98664	−	13.8333i	−0.291437	−	0.504783i	0.682713	−	0.730687i	$-0.260800\pi$
$751$	−7.98664	−	13.8333i	−0.291437	−	0.504783i	−0.974150	+	0.225904i	$0.927467\pi$
$752$	35.9659	−	20.7649i	1.31154	−	0.757219i
$753$	−5.64901	+	1.70709i	−0.205862	+	0.0622098i
$754$	−45.5081	−	2.64369i	−1.65731	−	0.0962777i
$755$	19.3967			0.705920
$756$	−0.000215960	0	0.000178383i	−7.85440e−6	0	6.48774e-6i
$757$	−5.47878			−0.199130			−0.0995648	−	0.995031i	$-0.531745\pi$
$757$	−5.47878			−0.199130			−0.0995648	+	0.995031i	$0.531745\pi$
$758$	−22.2558	+	38.5481i	−0.808366	+	1.40013i
$759$	8.98888	+	29.7456i	0.326276	+	1.07970i
$760$	14.7780	−	8.53205i	0.536053	−	0.309490i
$761$	−24.3314	+	14.0478i	−0.882013	+	0.509231i	−0.871322	−	0.490712i	$-0.836737\pi$
$761$	−24.3314	+	14.0478i	−0.882013	+	0.509231i	−0.0106917	+	0.999943i	$0.503403\pi$
$762$	−44.8688	−	10.5120i	−1.62542	−	0.380808i
$763$	−0.0478556	+	0.0828883i	−0.00173249	+	0.00300076i
$764$	0.0993886			0.00359575
$765$	6.19497	−	12.4955i	0.223980	−	0.451775i
$766$	38.1320			1.37776
$767$	4.95739	+	0.287988i	0.179001	+	0.0103987i
$768$	−0.142514	−	0.133762i	−0.00514254	−	0.00482674i
$769$	6.60502	−	3.81341i	0.238183	−	0.137515i	−0.376158	−	0.926555i	$-0.622755\pi$
$769$	6.60502	−	3.81341i	0.238183	−	0.137515i	0.614341	+	0.789040i	$0.289422\pi$
$770$	−0.0300767	−	0.0520943i	−0.00108389	−	0.00187735i
$771$	−38.1249	−	35.7836i	−1.37303	−	1.28872i
$772$	−0.000991126	0	0.000572227i	−3.56714e−5	0	2.05949e-5i
$773$			40.5127i			1.45714i	0.684971	+	0.728570i	$0.259815\pi$
$773$			40.5127i			1.45714i	−0.684971	+	0.728570i	$0.740185\pi$
$774$	2.15481	−	4.34633i	0.0774531	−	0.156226i
$775$		−	6.61020i		−	0.237445i
$776$	0.00661309	−	0.0114542i	0.000237396	−	0.000411182i
$777$	−0.0204914	+	0.0874644i	−0.000735124	+	0.00313777i
$778$	−23.8021	+	13.7422i	−0.853348	+	0.492681i
$779$	12.0747	+	20.9139i	0.432620	+	0.749320i
$780$	−0.0202088	−	0.0213033i	−0.000723590	−	0.000762780i
$781$	10.7381	−	18.5990i	0.384241	−	0.665525i
$782$			31.8673i			1.13957i
$783$	16.2061	+	43.4764i	0.579159	+	1.55372i
$784$	−28.0651			−1.00233
$785$	14.4680	+	8.35313i	0.516387	+	0.298136i
$786$	2.10209	+	6.95614i	0.0749791	+	0.248117i
$787$	35.7232	−	20.6248i	1.27340	−	0.735196i	0.297771	−	0.954637i	$-0.403757\pi$
$787$	35.7232	−	20.6248i	1.27340	−	0.735196i	0.975626	+	0.219442i	$0.0704236\pi$
$788$	−0.0748144	+	0.0431941i	−0.00266515	+	0.00153873i
$789$	−7.49440	+	31.9887i	−0.266808	+	1.13883i
$790$	0.533661	−	0.924329i	0.0189868	−	0.0328861i
$791$		−	0.102264i		−	0.00363610i
$792$	−1.98783	−	31.3440i	−0.0706345	−	1.11376i
$793$	27.9548	−	14.0447i	0.992703	−	0.498741i
$794$	11.8516	−	20.5276i	0.420597	−	0.728496i
$795$	2.81832	−	3.00271i	0.0999553	−	0.106495i
$796$	−0.0314263	−	0.0544319i	−0.00111388	−	0.00192929i
$797$	8.17615	+	14.1615i	0.289614	+	0.501626i	0.973718	−	0.227759i	$-0.0731397\pi$
$797$	8.17615	+	14.1615i	0.289614	+	0.501626i	−0.684104	+	0.729385i	$0.739806\pi$
$798$	0.116222	−	0.123826i	0.00411420	−	0.00438338i
$799$	41.7031	+	24.0773i	1.47535	+	0.851793i
$800$			0.0265982i			0.000940387i
$801$	5.93020	+	8.91593i	0.209533	+	0.315029i
$802$	8.23124			0.290655
$803$	−3.65504	+	6.33071i	−0.128984	+	0.223406i
$804$	0.0766587	+	0.0179598i	0.00270354	+	0.000633393i
$805$	0.0277523	+	0.0480684i	0.000978141	+	0.00169419i
$806$	28.1964	+	18.5390i	0.993177	+	0.653009i
$807$	5.72635	−	1.73046i	0.201577	−	0.0609150i
$808$	−4.90113	−	2.82967i	−0.172421	−	0.0995474i
$809$	−27.3316			−0.960927			−0.480463	−	0.877015i	$-0.659532\pi$
$809$	−27.3316			−0.960927			−0.480463	+	0.877015i	$0.659532\pi$
$810$	−4.92624	+	11.7522i	−0.173090	+	0.412928i
$811$		−	55.6820i		−	1.95526i	−0.210336	−	0.977629i	$-0.567456\pi$
$811$		−	55.6820i		−	1.95526i	0.210336	−	0.977629i	$-0.432544\pi$
$812$	0.000416865	0	0.000240677i	1.46291e−5	0	8.44611e-6i
$813$	6.81399	+	22.5485i	0.238977	+	0.790811i
$814$	20.5560	−	11.8680i	0.720486	−	0.415973i
$815$	3.50436	+	6.06973i	0.122752	+	0.212613i
$816$	7.36426	−	31.4333i	0.257801	−	1.10038i
$817$	5.97422	+	3.44922i	0.209012	+	0.120673i
$818$	23.2103			0.811528
$819$	0.107723	+	0.0614340i	0.00376415	+	0.00214668i
$820$	−0.0187989			−0.000656485
$821$	1.33908	+	0.773119i	0.0467343	+	0.0269820i	0.523185	−	0.852219i	$-0.324744\pi$
$821$	1.33908	+	0.773119i	0.0467343	+	0.0269820i	−0.476451	+	0.879201i	$0.658077\pi$
$822$	−35.2759	−	33.1096i	−1.23039	−	1.15483i
$823$	15.9113	+	27.5591i	0.554631	+	0.960650i	0.997932	+	0.0642768i	$0.0204741\pi$
$823$	15.9113	+	27.5591i	0.554631	+	0.960650i	−0.443301	+	0.896373i	$0.646193\pi$
$824$	−39.7480	+	22.9485i	−1.38469	+	0.799450i
$825$	−4.39257	+	4.67997i	−0.152930	+	0.162936i
$826$	−0.0193612	−	0.0111782i	−0.000673661	−	0.000388938i
$827$		−	22.7332i		−	0.790510i	−0.918571	−	0.395255i	$-0.870656\pi$
$827$		−	22.7332i		−	0.790510i	0.918571	−	0.395255i	$-0.129344\pi$
$828$	−0.00432234	−	0.0681543i	−0.000150212	−	0.00236853i
$829$	36.3527			1.26258			0.631291	−	0.775546i	$-0.282526\pi$
$829$	36.3527			1.26258			0.631291	+	0.775546i	$0.282526\pi$
$830$	10.3915	+	5.99951i	0.360693	+	0.208246i
$831$	−3.02186	+	12.8984i	−0.104827	+	0.447440i
$832$	24.0446	+	15.8092i	0.833597	+	0.548086i
$833$	−16.2710	−	28.1822i	−0.563757	−	0.976456i
$834$	−12.8439	−	42.5023i	−0.444747	−	1.47173i
$835$	8.94595	−	15.4948i	0.309587	−	0.536221i
$836$	−0.105245			−0.00363996
$837$	5.70254	−	33.8709i	0.197109	−	1.17075i
$838$		−	34.2838i		−	1.18431i
$839$	8.60189	+	4.96630i	0.296970	+	0.171456i	0.641081	−	0.767473i	$-0.278486\pi$
$839$	8.60189	+	4.96630i	0.296970	+	0.171456i	−0.344111	+	0.938929i	$0.611820\pi$
$840$	−0.0162280	−	0.0537008i	−0.000559918	−	0.00185285i
$841$	−25.3674	−	43.9376i	−0.874738	−	1.51509i
$842$	−22.4752	−	38.9282i	−0.774547	−	1.34155i
$843$	−38.0170	−	8.90671i	−1.30937	−	0.306763i
$844$	0.0379595	−	0.0657477i	0.00130662	−	0.00226313i
$845$	10.4299	+	7.75993i	0.358801	+	0.266950i
$846$	−39.4190	−	19.5430i	−1.35525	−	0.671904i
$847$		−	0.0313249i		−	0.00107634i
$848$	4.76639	−	8.25563i	0.163678	−	0.283499i
$849$	0.559418	+	0.525063i	0.0191992	+	0.0180201i
$850$	−5.70047	+	3.29117i	−0.195524	+	0.112886i
$851$	−18.9674	+	10.9508i	−0.650194	+	0.375390i
$852$	−0.0323008	+	0.0344142i	−0.00110661	+	0.00117901i
$853$	−8.72420	−	5.03692i	−0.298711	−	0.172461i	0.343153	−	0.939280i	$-0.388505\pi$
$853$	−8.72420	−	5.03692i	−0.298711	−	0.172461i	−0.641864	+	0.766819i	$0.721839\pi$
$854$	−0.140847			−0.00481967
$855$	−16.2349	−	8.04888i	−0.555221	−	0.275266i
$856$		−	6.38319i		−	0.218173i
$857$	9.28122	−	16.0755i	0.317040	−	0.549130i	−0.662829	−	0.748771i	$-0.730644\pi$
$857$	9.28122	−	16.0755i	0.317040	−	0.549130i	0.979869	+	0.199641i	$0.0639776\pi$
$858$	−7.64342	−	31.8624i	−0.260942	−	1.08777i
$859$	−20.4160	−	35.3616i	−0.696586	−	1.20652i	−0.969643	−	0.244524i	$-0.921368\pi$
$859$	−20.4160	−	35.3616i	−0.696586	−	1.20652i	0.273058	−	0.961998i	$-0.411965\pi$
$860$	−0.00465059	+	0.00268502i	−0.000158584	+	9.15584e-5i
$861$	0.0759980	−	0.0229660i	0.00259000	−	0.000782679i
$862$	−12.6657	+	21.9376i	−0.431395	+	0.747197i
$863$		−	24.6388i		−	0.838714i	−0.907821	−	0.419357i	$-0.862256\pi$
$863$		−	24.6388i		−	0.838714i	0.907821	−	0.419357i	$-0.137744\pi$
$864$	−0.0229459	+	0.136290i	−0.000780636	+	0.00463668i
$865$		−	25.9125i		−	0.881051i
$866$	31.2284	+	18.0297i	1.06118	+	0.612674i
$867$	7.64790	−	2.31114i	0.259736	−	0.0784903i
$868$	−0.000178166	0	0.000308593i	−6.04736e−6	0	1.04743e-5i
$869$	2.41921	−	1.39673i	0.0820660	−	0.0473808i
$870$	4.99512	−	21.3209i	0.169350	−	0.722847i
$871$	−34.7990	−	2.02157i	−1.17912	−	0.0684982i
$872$	23.5848			0.798682
$873$	−0.0140169		0.000888949i	−0.000474400		3.00864e-5i
$874$	41.4040			1.40051
$875$	−0.00573236	+	0.00992873i	−0.000193789	+	0.000335652i
$876$	0.0109945	−	0.0117139i	0.000371470	−	0.000395775i
$877$	−41.5931	+	24.0138i	−1.40450	+	0.810889i	−0.994850	−	0.101354i	$-0.967683\pi$
$877$	−41.5931	+	24.0138i	−1.40450	+	0.810889i	−0.409650	+	0.912243i	$0.634349\pi$
$878$	−8.11900	+	4.68751i	−0.274003	+	0.158196i
$879$	−0.180406	+	0.192210i	−0.00608495	+	0.00648308i
$880$	−7.42880	+	12.8671i	−0.250425	+	0.433749i
$881$	16.2470			0.547374			0.273687	−	0.961819i	$-0.411757\pi$
$881$	16.2470			0.547374			0.273687	+	0.961819i	$0.411757\pi$
$882$	16.4663	+	24.7568i	0.554451	+	0.833605i
$883$	−13.1468			−0.442426			−0.221213	−	0.975225i	$-0.571002\pi$
$883$	−13.1468			−0.442426			−0.221213	+	0.975225i	$0.571002\pi$
$884$	0.00457083	−	0.0786815i	0.000153734	−	0.00264634i
$885$	−0.544139	+	2.32258i	−0.0182910	+	0.0780726i
$886$	20.4352	−	11.7982i	0.686533	−	0.396370i
$887$	7.81958	+	13.5439i	0.262556	+	0.454760i	0.966920	−	0.255078i	$-0.0821013\pi$
$887$	7.81958	+	13.5439i	0.262556	+	0.454760i	−0.704365	+	0.709838i	$0.748768\pi$
$888$	21.1899	−	6.40341i	0.711085	−	0.214884i
$889$	−0.186576	−	0.107720i	−0.00625756	−	0.00361280i
$890$		−	5.05372i		−	0.169401i
$891$	−26.5451	+	20.1909i	−0.889293	+	0.676422i
$892$		−	0.103210i		−	0.00345574i
$893$	31.2827	−	54.1832i	1.04683	−	1.81317i
$894$	28.2927	−	8.54983i	0.946249	−	0.285949i
$895$	3.14696	−	1.81690i	0.105191	−	0.0607322i
$896$	−0.0650820	−	0.112725i	−0.00217424	−	0.00376589i
$897$	7.05274	+	29.4001i	0.235484	+	0.981641i
$898$	−3.75400	+	6.50213i	−0.125273	+	0.216979i
$899$			59.0254i			1.96861i
$900$	0.0117451	−	0.00781196i	0.000391504	−	0.000260399i
$901$	11.0534			0.368243
$902$	−18.1669	−	10.4887i	−0.604892	−	0.349235i
$903$	0.0155207	−	0.0165362i	0.000516496	−	0.000550289i
$904$	−21.8235	+	12.5998i	−0.725838	+	0.419063i
$905$	−7.82328	+	4.51677i	−0.260055	+	0.150143i
$906$	−34.6837	−	32.5538i	−1.15229	−	1.08153i
$907$	12.4039	−	21.4842i	0.411864	−	0.713370i	−0.583229	−	0.812307i	$-0.698211\pi$
$907$	12.4039	−	21.4842i	0.411864	−	0.713370i	0.995094	+	0.0989378i	$0.0315445\pi$
$908$			0.00423927i			0.000140685i
$909$	0.380372	+	5.99767i	0.0126161	+	0.198930i
$910$	−0.0262749	−	0.0522981i	−0.000871005	−	0.00173367i
$911$	−9.44811	+	16.3646i	−0.313030	+	0.542183i	−0.979017	−	0.203780i	$-0.934677\pi$
$911$	−9.44811	+	16.3646i	−0.313030	+	0.542183i	0.665987	+	0.745963i	$0.268011\pi$
$912$	−40.8400	−	9.56809i	−1.35235	−	0.316831i
$913$	15.7023	+	27.1971i	0.519669	+	0.900094i
$914$	−24.0774	−	41.7033i	−0.796410	−	1.37942i
$915$	4.34736	+	14.3861i	0.143719	+	0.475589i
$916$	−0.00703838	−	0.00406361i	−0.000232555	−	0.000134265i
$917$			0.0339721i			0.00112186i
$918$	−32.0487	+	11.9463i	−1.05776	+	0.394288i
$919$	16.2588			0.536328			0.268164	−	0.963373i	$-0.413583\pi$
$919$	16.2588			0.536328			0.268164	+	0.963373i	$0.413583\pi$
$920$	6.83863	−	11.8448i	0.225463	−	0.390513i
$921$	6.12327	+	20.2628i	0.201768	+	0.667682i
$922$	2.12488	+	3.68041i	0.0699793	+	0.121208i
$923$	11.4798	−	17.4599i	0.377863	−	0.574701i
$924$	−7.89241e−5	0	0.000336876i	−2.59641e−6	0	1.10824e-5i
$925$	−3.91779	−	2.26194i	−0.128816	−	0.0743721i
$926$	−41.8784			−1.37621
$927$	43.6667	+	21.6490i	1.43420	+	0.711045i
$928$		−	0.237507i		−	0.00779654i
$929$	−50.0587	−	28.9014i	−1.64237	−	0.948224i	−0.979987	−	0.199062i	$-0.936211\pi$
$929$	−50.0587	−	28.9014i	−1.64237	−	0.948224i	−0.662386	−	0.749163i	$-0.730456\pi$
$930$	−11.0940	+	11.8198i	−0.363786	+	0.387588i
$931$	−36.6160	+	21.1403i	−1.20004	+	0.692845i
$932$	0.0427543	+	0.0740527i	0.00140046	+	0.00242568i
$933$	36.6333	+	34.3836i	1.19932	+	1.12567i
$934$	−11.5145	−	6.64788i	−0.376765	−	0.217525i
$935$	−17.2277			−0.563405
$936$	−0.162186	−	30.5576i	−0.00530123	−	0.998807i
$937$	25.0975			0.819898			0.409949	−	0.912108i	$-0.365546\pi$
$937$	25.0975			0.819898			0.409949	+	0.912108i	$0.365546\pi$
$938$	0.135908	+	0.0784665i	0.00443755	+	0.00256202i
$939$	10.6099	−	45.2868i	0.346241	−	1.47788i
$940$	0.0243518	+	0.0421785i	0.000794267	+	0.00137571i
$941$	46.5349	−	26.8670i	1.51700	−	0.875838i	0.517195	−	0.855867i	$-0.326976\pi$
$941$	46.5349	−	26.8670i	1.51700	−	0.875838i	0.999801	−	0.0199705i	$-0.00635724\pi$
$942$	−11.8515	−	39.2183i	−0.386142	−	1.27780i
$943$	16.7630	+	9.67811i	0.545878	+	0.315163i
$944$			5.52192i			0.179723i
$945$	−0.0379382	+	0.0459300i	−0.00123413	+	0.00149410i
$946$	−5.99234			−0.194828
$947$	0.109296	+	0.0631019i	0.00355163	+	0.00205054i	0.501775	−	0.864998i	$-0.332681\pi$
$947$	0.109296	+	0.0631019i	0.00355163	+	0.00205054i	−0.498223	+	0.867049i	$0.666014\pi$
$948$	−0.00587669	+	0.00177589i	−0.000190866	+	5.76783e-5i
$949$	−3.90749	+	5.94299i	−0.126843	+	0.192918i
$950$	4.27608	+	7.40639i	0.138734	+	0.240295i
$951$	−52.2797	−	12.2482i	−1.69528	−	0.397176i
$952$	0.0752871	−	0.130401i	0.00244007	−	0.00422632i
$953$	9.74893			0.315799			0.157899	−	0.987455i	$-0.449528\pi$
$953$	9.74893			0.315799			0.157899	+	0.987455i	$0.449528\pi$
$954$	−10.0790	+	0.639208i	−0.326319	+	0.0206951i
$955$		−	21.1378i		−	0.684002i
$956$	0.0606237	+	0.0350011i	0.00196071	+	0.00113202i
$957$	39.2232	−	41.7895i	1.26791	−	1.35086i
$958$	3.40326	+	5.89462i	0.109954	+	0.190447i
$959$	−0.113087	−	0.195873i	−0.00365178	−	0.00632507i
$960$	−9.46042	+	10.0794i	−0.305334	+	0.325311i
$961$	6.34739	−	10.9940i	0.204754	−	0.354645i
$962$	20.6364	−	10.3679i	0.665344	−	0.334273i
$963$	−5.64397	+	3.75394i	−0.181874	+	0.120969i
$964$		−	0.0436791i		−	0.00140681i
$965$	−0.121700	+	0.210790i	−0.00391766	+	0.00678559i
$966$	0.0310493	−	0.132529i	0.000998994	−	0.00426406i
$967$	−16.8821	+	9.74690i	−0.542893	+	0.313439i	−0.746250	−	0.665665i	$-0.768148\pi$
$967$	−16.8821	+	9.74690i	−0.542893	+	0.313439i	0.203358	+	0.979104i	$0.434815\pi$
$968$	−6.68482	+	3.85948i	−0.214858	+	0.124048i
$969$	−14.0693	−	46.5576i	−0.451972	−	1.49564i
$970$	0.00574060	+	0.00331434i	0.000184320	+	0.000106417i
$971$	−9.64346			−0.309473			−0.154737	−	0.987956i	$-0.549453\pi$
$971$	−9.64346			−0.309473			−0.154737	+	0.987956i	$0.549453\pi$
$972$	0.0669218	−	0.0298964i	0.00214652	−	0.000958928i
$973$		−	0.207571i		−	0.00665441i
$974$	2.59022	−	4.48640i	0.0829960	−	0.143753i
$975$	−4.53074	+	4.29796i	−0.145100	+	0.137645i
$976$	17.3942	+	30.1277i	0.556776	+	0.964364i
$977$	−31.9311	+	18.4354i	−1.02157	+	0.589801i	−0.914557	−	0.404457i	$-0.867461\pi$
$977$	−31.9311	+	18.4354i	−1.02157	+	0.589801i	−0.107009	+	0.994258i	$0.534127\pi$
$978$	3.92067	−	16.7348i	0.125369	−	0.535120i
$979$	6.61345	−	11.4548i	0.211367	−	0.366098i
$980$		−	0.0329130i		−	0.00105137i
$981$	−13.8702	−	20.8535i	−0.442841	−	0.665802i
$982$			4.66506i			0.148868i
$983$	−4.06226	−	2.34535i	−0.129566	−	0.0748050i	0.433816	−	0.901001i	$-0.357167\pi$
$983$	−4.06226	−	2.34535i	−0.129566	−	0.0748050i	−0.563382	+	0.826196i	$0.690500\pi$
$984$	−14.2646	−	13.3886i	−0.454738	−	0.426812i
$985$	9.18643	+	15.9114i	0.292704	+	0.506978i
$986$	50.9019	−	29.3882i	1.62105	−	0.935912i
$987$	−0.149975	−	0.140765i	−0.00477375	−	0.00448059i
$988$	−0.102228	−	0.00593869i	−0.00325230	−	0.000188935i
$989$	5.52925			0.175820
$990$	15.7089	−	0.996257i	0.499262	−	0.0316631i
$991$	31.0206			0.985402			0.492701	−	0.870199i	$-0.336010\pi$
$991$	31.0206			0.985402			0.492701	+	0.870199i	$0.336010\pi$
$992$	−0.0879097	+	0.152264i	−0.00279113	+	0.00483439i
$993$	48.9425	+	11.4664i	1.55314	+	0.363874i
$994$	−0.0814717	+	0.0470377i	−0.00258412	+	0.00149194i
$995$	−11.5765	+	6.68368i	−0.366999	+	0.211887i
$996$	−0.0199649	−	0.0660668i	−0.000632612	−	0.00209341i
$997$	0.519357	−	0.899552i	0.0164482	−	0.0284891i	−0.857684	−	0.514177i	$-0.828097\pi$
$997$	0.519357	−	0.899552i	0.0164482	−	0.0284891i	0.874132	+	0.485688i	$0.161431\pi$
$998$	19.6535			0.622121
$999$	−18.1236	−	14.9701i	−0.573404	−	0.473633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.15	✓	108
9.4	even	3	inner	585.2.bt.b.571.40	yes	108
13.12	even	2	inner	585.2.bt.b.376.40	yes	108
117.103	even	6	inner	585.2.bt.b.571.15	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.15	✓	108	1.1	even	1	trivial
585.2.bt.b.376.40	yes	108	13.12	even	2	inner
585.2.bt.b.571.15	yes	108	117.103	even	6	inner
585.2.bt.b.571.40	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22618 - 0.707937i) q^{2} +(1.65800 - 0.501035i) q^{3} +(0.00235097 + 0.00407201i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-2.38771 - 0.559399i) q^{6} +(-0.00992873 - 0.00573236i) q^{7} +2.82509i q^{8} +(2.49793 - 1.66143i) q^{9} +O(q^{10})\)	\(q+(-1.22618 - 0.707937i) q^{2} +(1.65800 - 0.501035i) q^{3} +(0.00235097 + 0.00407201i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-2.38771 - 0.559399i) q^{6} +(-0.00992873 - 0.00573236i) q^{7} +2.82509i q^{8} +(2.49793 - 1.66143i) q^{9} -1.41587 q^{10} +(-3.20924 - 1.85286i) q^{11} +(0.00593813 + 0.00557347i) q^{12} +(-3.01269 - 1.98083i) q^{13} +(0.00811630 + 0.0140578i) q^{14} +(1.18535 - 1.26291i) q^{15} +(2.00469 - 3.47223i) q^{16} +4.64895 q^{17} +(-4.23911 + 0.268844i) q^{18} -6.04019i q^{19} +(0.00407201 + 0.00235097i) q^{20} +(-0.0193339 - 0.00452960i) q^{21} +(2.62341 + 4.54388i) q^{22} +(-2.42067 - 4.19273i) q^{23} +(1.41547 + 4.68400i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.29181 + 4.56166i) q^{26} +(3.30913 - 4.00620i) q^{27} -5.39065e-5i q^{28} +(-4.46472 + 7.73312i) q^{29} +(-2.34752 + 0.709403i) q^{30} +(5.72460 - 3.30510i) q^{31} +(-0.0230347 + 0.0132991i) q^{32} +(-6.24926 - 1.46409i) q^{33} +(-5.70047 - 3.29117i) q^{34} -0.0114647 q^{35} +(0.0126379 + 0.00626559i) q^{36} -4.52388i q^{37} +(-4.27608 + 7.40639i) q^{38} +(-5.98751 - 1.77475i) q^{39} +(1.41255 + 2.44660i) q^{40} +(-3.46246 + 1.99905i) q^{41} +(0.0205003 + 0.0192414i) q^{42} +(-0.571044 + 0.989078i) q^{43} -0.0174241i q^{44} +(1.33255 - 2.68781i) q^{45} +6.85474i q^{46} +(8.97044 + 5.17908i) q^{47} +(1.58407 - 6.76137i) q^{48} +(-3.49993 - 6.06206i) q^{49} +(-1.22618 + 0.707937i) q^{50} +(7.70796 - 2.32929i) q^{51} +(0.000983196 - 0.0169246i) q^{52} +2.37762 q^{53} +(-6.89374 + 2.56968i) q^{54} -3.70571 q^{55} +(0.0161944 - 0.0280496i) q^{56} +(-3.02635 - 10.0146i) q^{57} +(10.9491 - 6.32148i) q^{58} +(-1.19273 + 0.688625i) q^{59} +(0.00792930 + 0.00185770i) q^{60} +(-4.33838 + 7.51430i) q^{61} -9.35922 q^{62} +(-0.0343252 + 0.00217690i) q^{63} -7.98110 q^{64} +(-3.59948 - 0.209104i) q^{65} +(6.62626 + 6.21933i) q^{66} +(8.37253 - 4.83388i) q^{67} +(0.0109296 + 0.0189305i) q^{68} +(-6.11418 - 5.73870i) q^{69} +(0.0140578 + 0.00811630i) q^{70} +5.79546i q^{71} +(4.69370 + 7.05688i) q^{72} -1.97265i q^{73} +(-3.20262 + 5.54710i) q^{74} +(0.395091 - 1.68639i) q^{75} +(0.0245957 - 0.0142003i) q^{76} +(0.0212424 + 0.0367930i) q^{77} +(6.08537 + 6.41496i) q^{78} +(-0.376913 + 0.652832i) q^{79} -4.00938i q^{80} +(3.47929 - 8.30027i) q^{81} +5.66082 q^{82} +(-7.33925 - 4.23732i) q^{83} +(-2.70090e-5 - 8.93769e-5i) q^{84} +(4.02611 - 2.32447i) q^{85} +(1.40041 - 0.808527i) q^{86} +(-3.52794 + 15.0585i) q^{87} +(5.23449 - 9.06640i) q^{88} +3.56933i q^{89} +(-3.53675 + 2.35238i) q^{90} +(0.0185574 + 0.0369370i) q^{91} +(0.0113819 - 0.0197140i) q^{92} +(7.83542 - 8.34808i) q^{93} +(-7.33293 - 12.7010i) q^{94} +(-3.02010 - 5.23096i) q^{95} +(-0.0315282 + 0.0335911i) q^{96} +(-0.00405446 - 0.00234084i) q^{97} +9.91094i q^{98} +(-11.0948 + 0.703634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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