LMFDB - Embedded newform 546.2.bg.a.311.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.4
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.a.467.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.34147 + 1.09565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.44950 + 1.41422i) q^{5} +(1.61960 + 0.613923i) q^{6} +(-2.60728 + 0.449563i) q^{7} +1.00000 q^{8} +(0.599095 - 2.93957i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.34147 + 1.09565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.44950 + 1.41422i) q^{5} +(1.61960 + 0.613923i) q^{6} +(-2.60728 + 0.449563i) q^{7} +1.00000 q^{8} +(0.599095 - 2.93957i) q^{9} +(2.44950 + 1.41422i) q^{10} +(-2.97657 + 5.15557i) q^{11} +(-0.278126 - 1.70957i) q^{12} +(3.07921 - 1.87576i) q^{13} +(1.69297 + 2.03319i) q^{14} +(1.73644 - 4.58093i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.83737 - 4.91448i) q^{17} +(-2.84529 + 0.950954i) q^{18} +(-0.972964 - 1.68522i) q^{19} -2.82844i q^{20} +(3.00503 - 3.45974i) q^{21} +5.95314 q^{22} +(-2.43857 + 1.40791i) q^{23} +(-1.34147 + 1.09565i) q^{24} +(1.50002 - 2.59812i) q^{25} +(-3.16406 - 1.72880i) q^{26} +(2.41708 + 4.59975i) q^{27} +(0.914306 - 2.48275i) q^{28} -0.0658578i q^{29} +(-4.83542 + 0.786662i) q^{30} +(4.39516 - 7.61265i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.65572 - 10.1773i) q^{33} -5.67475 q^{34} +(5.75074 - 4.78846i) q^{35} +(2.24620 + 1.98862i) q^{36} +(0.160796 - 0.0928358i) q^{37} +(-0.972964 + 1.68522i) q^{38} +(-2.07550 + 5.89002i) q^{39} +(-2.44950 + 1.41422i) q^{40} -4.04876i q^{41} +(-4.49874 - 0.872557i) q^{42} +3.48177 q^{43} +(-2.97657 - 5.15557i) q^{44} +(2.68971 + 8.04773i) q^{45} +(2.43857 + 1.40791i) q^{46} +(6.77981 - 3.91432i) q^{47} +(1.61960 + 0.613923i) q^{48} +(6.59579 - 2.34427i) q^{49} -3.00005 q^{50} +(1.57830 + 9.70141i) q^{51} +(0.0848486 + 3.60455i) q^{52} +(-3.77930 - 2.18198i) q^{53} +(2.77497 - 4.39313i) q^{54} -16.8381i q^{55} +(-2.60728 + 0.449563i) q^{56} +(3.15162 + 1.19465i) q^{57} +(-0.0570345 + 0.0329289i) q^{58} +(-11.6234 - 6.71079i) q^{59} +(3.09898 + 3.79427i) q^{60} +(-12.8084 + 7.39493i) q^{61} -8.79033 q^{62} +(-0.240485 + 7.93361i) q^{63} +1.00000 q^{64} +(-4.88979 + 8.94934i) q^{65} +(-7.98598 + 6.52257i) q^{66} +(0.912896 + 0.527061i) q^{67} +(2.83737 + 4.91448i) q^{68} +(1.72869 - 4.56049i) q^{69} +(-7.02230 - 2.58606i) q^{70} -6.16979 q^{71} +(0.599095 - 2.93957i) q^{72} +(-0.140240 + 0.242904i) q^{73} +(-0.160796 - 0.0928358i) q^{74} +(0.834392 + 5.12881i) q^{75} +1.94593 q^{76} +(5.44299 - 14.7802i) q^{77} +(6.13865 - 1.14757i) q^{78} +(4.18074 + 7.24125i) q^{79} +(2.44950 + 1.41422i) q^{80} +(-8.28217 - 3.52217i) q^{81} +(-3.50633 + 2.02438i) q^{82} +0.940520i q^{83} +(1.49371 + 4.33230i) q^{84} +16.0507i q^{85} +(-1.74089 - 3.01530i) q^{86} +(0.0721572 + 0.0883464i) q^{87} +(-2.97657 + 5.15557i) q^{88} +(4.61927 - 2.66694i) q^{89} +(5.62468 - 6.35322i) q^{90} +(-7.18508 + 6.27492i) q^{91} -2.81581i q^{92} +(2.44482 + 15.0277i) q^{93} +(-6.77981 - 3.91432i) q^{94} +(4.76654 + 2.75197i) q^{95} +(-0.278126 - 1.70957i) q^{96} +9.60289 q^{97} +(-5.32809 - 4.53998i) q^{98} +(13.3719 + 11.8385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.34147	+	1.09565i	−0.774499	+	0.632575i
$3$	−1.34147	+	1.09565i	−0.774499	+	0.632575i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.44950	+	1.41422i	−1.09545	+	0.632458i	−0.935022	−	0.354590i	$-0.884620\pi$
$5$	−2.44950	+	1.41422i	−1.09545	+	0.632458i	−0.160427	+	0.987048i	$0.551287\pi$
$6$	1.61960	+	0.613923i	0.661198	+	0.250633i
$7$	−2.60728	+	0.449563i	−0.985458	+	0.169919i
$7$	−2.60728	+	0.449563i	−0.985458	+	0.169919i
$8$	1.00000			0.353553
$9$	0.599095	−	2.93957i	0.199698	−	0.979857i
$10$	2.44950	+	1.41422i	0.774599	+	0.447215i
$11$	−2.97657	+	5.15557i	−0.897470	+	1.55446i	−0.0667525	+	0.997770i	$0.521264\pi$
$11$	−2.97657	+	5.15557i	−0.897470	+	1.55446i	−0.830718	+	0.556694i	$0.812070\pi$
$12$	−0.278126	−	1.70957i	−0.0802881	−	0.493512i
$13$	3.07921	−	1.87576i	0.854019	−	0.520241i
$13$	3.07921	−	1.87576i	0.854019	−	0.520241i
$14$	1.69297	+	2.03319i	0.452466	+	0.543392i
$15$	1.73644	−	4.58093i	0.448348	−	1.18279i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.83737	−	4.91448i	0.688164	−	1.19194i	−0.284267	−	0.958745i	$-0.591750\pi$
$17$	2.83737	−	4.91448i	0.688164	−	1.19194i	0.972431	−	0.233190i	$-0.0749165\pi$
$18$	−2.84529	+	0.950954i	−0.670642	+	0.224142i
$19$	−0.972964	−	1.68522i	−0.223213	−	0.386617i	0.732569	−	0.680693i	$-0.238321\pi$
$19$	−0.972964	−	1.68522i	−0.223213	−	0.386617i	−0.955782	+	0.294077i	$0.904988\pi$
$20$		−	2.82844i		−	0.632458i
$21$	3.00503	−	3.45974i	0.655750	−	0.754978i
$22$	5.95314			1.26921
$23$	−2.43857	+	1.40791i	−0.508476	+	0.293569i	−0.732207	−	0.681082i	$-0.761510\pi$
$23$	−2.43857	+	1.40791i	−0.508476	+	0.293569i	0.223731	+	0.974651i	$0.428176\pi$
$24$	−1.34147	+	1.09565i	−0.273827	+	0.223649i
$25$	1.50002	−	2.59812i	0.300005	−	0.519624i
$26$	−3.16406	−	1.72880i	−0.620523	−	0.339045i
$27$	2.41708	+	4.59975i	0.465167	+	0.885223i
$28$	0.914306	−	2.48275i	0.172788	−	0.469196i
$29$		−	0.0658578i		−	0.0122295i	−0.999981	−	0.00611474i	$-0.998054\pi$
$29$		−	0.0658578i		−	0.0122295i	0.999981	−	0.00611474i	$-0.00194640\pi$
$30$	−4.83542	+	0.786662i	−0.882823	+	0.143624i
$31$	4.39516	−	7.61265i	0.789395	−	1.36727i	−0.136944	−	0.990579i	$-0.543728\pi$
$31$	4.39516	−	7.61265i	0.789395	−	1.36727i	0.926338	−	0.376693i	$-0.122939\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.65572	−	10.1773i	−0.288225	−	1.77165i
$34$	−5.67475			−0.973211
$35$	5.75074	−	4.78846i	0.972052	−	0.809398i
$36$	2.24620	+	1.98862i	0.374366	+	0.331436i
$37$	0.160796	−	0.0928358i	0.0264348	−	0.0152621i	−0.486724	−	0.873556i	$-0.661808\pi$
$37$	0.160796	−	0.0928358i	0.0264348	−	0.0152621i	0.513159	+	0.858293i	$0.328475\pi$
$38$	−0.972964	+	1.68522i	−0.157836	+	0.273379i
$39$	−2.07550	+	5.89002i	−0.332346	+	0.943158i
$40$	−2.44950	+	1.41422i	−0.387300	+	0.223607i
$41$		−	4.04876i		−	0.632310i	−0.948707	−	0.316155i	$-0.897608\pi$
$41$		−	4.04876i		−	0.632310i	0.948707	−	0.316155i	$-0.102392\pi$
$42$	−4.49874	−	0.872557i	−0.694170	−	0.134638i
$43$	3.48177			0.530965			0.265483	−	0.964116i	$-0.414469\pi$
$43$	3.48177			0.530965			0.265483	+	0.964116i	$0.414469\pi$
$44$	−2.97657	−	5.15557i	−0.448735	−	0.777232i
$45$	2.68971	+	8.04773i	0.400959	+	1.19968i
$46$	2.43857	+	1.40791i	0.359547	+	0.207585i
$47$	6.77981	−	3.91432i	0.988937	−	0.570963i	0.0839804	−	0.996467i	$-0.473237\pi$
$47$	6.77981	−	3.91432i	0.988937	−	0.570963i	0.904956	+	0.425505i	$0.139903\pi$
$48$	1.61960	+	0.613923i	0.233769	+	0.0886122i
$49$	6.59579	−	2.34427i	0.942255	−	0.334896i
$50$	−3.00005			−0.424271
$51$	1.57830	+	9.70141i	0.221006	+	1.35847i
$52$	0.0848486	+	3.60455i	0.0117664	+	0.499862i
$53$	−3.77930	−	2.18198i	−0.519127	−	0.299718i	0.217450	−	0.976071i	$-0.430226\pi$
$53$	−3.77930	−	2.18198i	−0.519127	−	0.299718i	−0.736578	+	0.676353i	$0.763559\pi$
$54$	2.77497	−	4.39313i	0.377625	−	0.597829i
$55$		−	16.8381i		−	2.27045i
$56$	−2.60728	+	0.449563i	−0.348412	+	0.0600753i
$57$	3.15162	+	1.19465i	0.417442	+	0.158235i
$58$	−0.0570345	+	0.0329289i	−0.00748900	+	0.00432378i
$59$	−11.6234	−	6.71079i	−1.51324	−	0.873670i	−0.999880	−	0.0154976i	$-0.995067\pi$
$59$	−11.6234	−	6.71079i	−1.51324	−	0.873670i	−0.513361	−	0.858173i	$-0.671600\pi$
$60$	3.09898	+	3.79427i	0.400077	+	0.489838i
$61$	−12.8084	+	7.39493i	−1.63995	+	0.946823i	−0.659096	+	0.752059i	$0.729061\pi$
$61$	−12.8084	+	7.39493i	−1.63995	+	0.946823i	−0.980850	+	0.194765i	$0.937606\pi$
$62$	−8.79033			−1.11637
$63$	−0.240485	+	7.93361i	−0.0302983	+	0.999541i
$64$	1.00000			0.125000
$65$	−4.88979	+	8.94934i	−0.606503	+	1.11003i
$66$	−7.98598	+	6.52257i	−0.983006	+	0.802873i
$67$	0.912896	+	0.527061i	0.111528	+	0.0643907i	0.554726	−	0.832033i	$-0.312823\pi$
$67$	0.912896	+	0.527061i	0.111528	+	0.0643907i	−0.443198	+	0.896424i	$0.646156\pi$
$68$	2.83737	+	4.91448i	0.344082	+	0.595968i
$69$	1.72869	−	4.56049i	0.208110	−	0.549018i
$70$	−7.02230	−	2.58606i	−0.839325	−	0.309093i
$71$	−6.16979			−0.732220			−0.366110	−	0.930572i	$-0.619311\pi$
$71$	−6.16979			−0.732220			−0.366110	+	0.930572i	$0.619311\pi$
$72$	0.599095	−	2.93957i	0.0706040	−	0.346432i
$73$	−0.140240	+	0.242904i	−0.0164139	+	0.0284297i	−0.874116	−	0.485718i	$-0.838558\pi$
$73$	−0.140240	+	0.242904i	−0.0164139	+	0.0284297i	0.857702	+	0.514147i	$0.171892\pi$
$74$	−0.160796	−	0.0928358i	−0.0186922	−	0.0107919i
$75$	0.834392	+	5.12881i	0.0963473	+	0.592224i
$76$	1.94593			0.223213
$77$	5.44299	−	14.7802i	0.620287	−	1.68436i
$78$	6.13865	−	1.14757i	0.695066	−	0.129937i
$79$	4.18074	+	7.24125i	0.470370	+	0.814704i	0.999426	−	0.0338825i	$-0.0107872\pi$
$79$	4.18074	+	7.24125i	0.470370	+	0.814704i	−0.529056	+	0.848587i	$0.677454\pi$
$80$	2.44950	+	1.41422i	0.273862	+	0.158114i
$81$	−8.28217	−	3.52217i	−0.920241	−	0.391352i
$82$	−3.50633	+	2.02438i	−0.387209	+	0.223556i
$83$			0.940520i			0.103235i	0.998667	+	0.0516177i	$0.0164377\pi$
$83$			0.940520i			0.103235i	−0.998667	+	0.0516177i	$0.983562\pi$
$84$	1.49371	+	4.33230i	0.162977	+	0.472693i
$85$			16.0507i			1.74094i
$86$	−1.74089	−	3.01530i	−0.187725	−	0.325149i
$87$	0.0721572	+	0.0883464i	0.00773606	+	0.00947173i
$88$	−2.97657	+	5.15557i	−0.317304	+	0.549586i
$89$	4.61927	−	2.66694i	0.489642	−	0.282695i	−0.234784	−	0.972048i	$-0.575438\pi$
$89$	4.61927	−	2.66694i	0.489642	−	0.282695i	0.724426	+	0.689353i	$0.242105\pi$
$90$	5.62468	−	6.35322i	0.592893	−	0.669689i
$91$	−7.18508	+	6.27492i	−0.753201	+	0.657790i
$92$		−	2.81581i		−	0.293569i
$93$	2.44482	+	15.0277i	0.253516	+	1.55830i
$94$	−6.77981	−	3.91432i	−0.699284	−	0.403732i
$95$	4.76654	+	2.75197i	0.489037	+	0.282346i
$96$	−0.278126	−	1.70957i	−0.0283861	−	0.174483i
$97$	9.60289			0.975026			0.487513	−	0.873116i	$-0.337904\pi$
$97$	9.60289			0.975026			0.487513	+	0.873116i	$0.337904\pi$
$98$	−5.32809	−	4.53998i	−0.538218	−	0.458608i
$99$	13.3719	+	11.8385i	1.34393	+	1.18982i
$100$	1.50002	+	2.59812i	0.150002	+	0.259812i
$101$	3.31762	−	5.74628i	0.330115	−	0.571777i	−0.652419	−	0.757859i	$-0.726246\pi$
$101$	3.31762	−	5.74628i	0.330115	−	0.571777i	0.982534	+	0.186082i	$0.0595790\pi$
$102$	7.61252	−	6.21755i	0.753752	−	0.615629i
$103$	−6.33025	+	3.65477i	−0.623738	+	0.360115i	−0.778323	−	0.627864i	$-0.783929\pi$
$103$	−6.33025	+	3.65477i	−0.623738	+	0.360115i	0.154585	+	0.987980i	$0.450596\pi$
$104$	3.07921	−	1.87576i	0.301941	−	0.183933i
$105$	−2.46797	+	12.7244i	−0.240849	+	1.24177i
$106$			4.36396i			0.423866i
$107$	14.1105	−	8.14672i	1.36412	−	0.787573i	0.373947	−	0.927450i	$-0.378004\pi$
$107$	14.1105	−	8.14672i	1.36412	−	0.787573i	0.990169	+	0.139877i	$0.0446707\pi$
$108$	−5.19204	−	0.206627i	−0.499605	−	0.0198826i
$109$	1.45673	+	0.841043i	0.139529	+	0.0805573i	0.568140	−	0.822932i	$-0.307663\pi$
$109$	1.45673	+	0.841043i	0.139529	+	0.0805573i	−0.428610	+	0.903489i	$0.640997\pi$
$110$	−14.5822	+	8.41904i	−1.39036	+	0.802724i
$111$	−0.113988	+	0.300714i	−0.0108193	+	0.0285425i
$112$	1.69297	+	2.03319i	0.159971	+	0.192118i
$113$		−	8.45921i		−	0.795775i	−0.917434	−	0.397888i	$-0.869743\pi$
$113$		−	8.45921i		−	0.795775i	0.917434	−	0.397888i	$-0.130257\pi$
$114$	−0.541213	−	3.32671i	−0.0506893	−	0.311575i
$115$	3.98217	−	6.89733i	0.371340	−	0.643179i
$116$	0.0570345	+	0.0329289i	0.00529552	+	0.00305737i
$117$	−3.66918	−	10.1753i	−0.339216	−	0.940708i
$118$			13.4216i			1.23556i
$119$	−5.18846	+	14.0890i	−0.475625	+	1.29153i
$120$	1.73644	−	4.58093i	0.158515	−	0.418180i
$121$	−12.2200	−	21.1656i	−1.11091	−	1.92414i
$122$	12.8084	+	7.39493i	1.15962	+	0.669505i
$123$	4.43603	+	5.43130i	0.399984	+	0.489724i
$124$	4.39516	+	7.61265i	0.394697	+	0.683636i
$125$		−	5.65673i		−	0.505953i
$126$	6.99095	−	3.75854i	0.622803	−	0.334837i
$127$	0.564130			0.0500584			0.0250292	−	0.999687i	$-0.492032\pi$
$127$	0.564130			0.0500584			0.0250292	+	0.999687i	$0.492032\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.67070	+	3.81481i	−0.411232	+	0.335875i
$130$	10.1952	−	0.239989i	0.894182	−	0.0210484i
$131$	8.86611	+	15.3566i	0.774636	+	1.34171i	0.934999	+	0.354651i	$0.115400\pi$
$131$	8.86611	+	15.3566i	0.774636	+	1.34171i	−0.160363	+	0.987058i	$0.551267\pi$
$132$	9.64170	+	3.65477i	0.839202	+	0.318107i
$133$	3.29440	+	3.95643i	0.285661	+	0.343066i
$134$		−	1.05412i		−	0.0910622i
$135$	−12.4257	−	7.84881i	−1.06943	−	0.675518i
$136$	2.83737	−	4.91448i	0.243303	−	0.421413i
$137$	−2.86927	+	4.96972i	−0.245138	+	0.424592i	−0.962170	−	0.272448i	$-0.912167\pi$
$137$	−2.86927	+	4.96972i	−0.245138	+	0.424592i	0.717032	+	0.697040i	$0.245500\pi$
$138$	−4.81384	+	0.783151i	−0.409782	+	0.0666662i
$139$		−	8.16905i		−	0.692890i	−0.938070	−	0.346445i	$-0.887389\pi$
$139$		−	8.16905i		−	0.692890i	0.938070	−	0.346445i	$-0.112611\pi$
$140$	1.27156	+	7.37452i	0.107466	+	0.623260i
$141$	−4.80619	+	12.6793i	−0.404754	+	1.06779i
$142$	3.08490	+	5.34320i	0.258879	+	0.448391i
$143$	0.505116	+	21.4584i	0.0422399	+	1.79444i
$144$	−2.84529	+	0.950954i	−0.237108	+	0.0792462i
$145$	0.0931373	+	0.161318i	0.00773463	+	0.0133968i
$146$	0.280481			0.0232128
$147$	−6.27956	+	10.3715i	−0.517930	+	0.855423i
$148$			0.185672i			0.0152621i
$149$	−7.77314	−	13.4635i	−0.636801	−	1.10297i	−0.986131	−	0.165971i	$-0.946924\pi$
$149$	−7.77314	−	13.4635i	−0.636801	−	1.10297i	0.349330	−	0.937000i	$-0.386409\pi$
$150$	4.02448	−	3.28701i	0.328598	−	0.268383i
$151$	−18.1605	−	10.4850i	−1.47788	−	0.853256i	−0.478196	−	0.878253i	$-0.658709\pi$
$151$	−18.1605	−	10.4850i	−1.47788	−	0.853256i	−0.999688	+	0.0249970i	$0.992042\pi$
$152$	−0.972964	−	1.68522i	−0.0789178	−	0.136690i
$153$	−12.7466	−	11.2849i	−1.03050	−	0.912331i
$154$	−15.5215	+	2.67631i	−1.25076	+	0.215663i
$155$			24.8629i			1.99703i
$156$	−4.06316	−	4.74244i	−0.325313	−	0.379699i
$157$	12.5843	+	7.26555i	1.00434	+	0.579854i	0.909528	−	0.415642i	$-0.136443\pi$
$157$	12.5843	+	7.26555i	1.00434	+	0.579854i	0.0948076	+	0.995496i	$0.469776\pi$
$158$	4.18074	−	7.24125i	0.332602	−	0.576083i
$159$	7.46052	−	1.21373i	0.591658	−	0.0962552i
$160$		−	2.82844i		−	0.223607i
$161$	5.72508	−	4.76709i	0.451199	−	0.375699i
$162$	1.09080	+	8.93365i	0.0857012	+	0.701894i
$163$	−1.09419	+	0.631733i	−0.0857039	+	0.0494812i	−0.542239	−	0.840224i	$-0.682423\pi$
$163$	−1.09419	+	0.631733i	−0.0857039	+	0.0494812i	0.456536	+	0.889705i	$0.349090\pi$
$164$	3.50633	+	2.02438i	0.273798	+	0.158078i
$165$	18.4487	+	22.5878i	1.43623	+	1.75846i
$166$	0.814514	−	0.470260i	0.0632185	−	0.0364992i
$167$		−	14.8995i		−	1.15296i	−0.817111	−	0.576480i	$-0.804426\pi$
$167$		−	14.8995i		−	1.15296i	0.817111	−	0.576480i	$-0.195574\pi$
$168$	3.00503	−	3.45974i	0.231843	−	0.266925i
$169$	5.96307	−	11.5517i	0.458698	−	0.888592i
$170$	13.9003	−	8.02533i	1.06610	−	0.615515i
$171$	−5.53673	+	1.85049i	−0.423404	+	0.141510i
$172$	−1.74089	+	3.01530i	−0.132741	+	0.229915i
$173$	−5.85736	−	10.1453i	−0.445327	−	0.771329i	0.552748	−	0.833349i	$-0.313579\pi$
$173$	−5.85736	−	10.1453i	−0.445327	−	0.771329i	−0.998075	+	0.0620193i	$0.980246\pi$
$174$	0.0404316	−	0.106663i	0.00306511	−	0.00808611i
$175$	−2.74296	+	7.44837i	−0.207349	+	0.563044i
$176$	5.95314			0.448735
$177$	22.9452	−	3.73289i	1.72467	−	0.280581i
$178$	−4.61927	−	2.66694i	−0.346229	−	0.199895i
$179$	−4.54314	−	2.62298i	−0.339570	−	0.196051i	0.320512	−	0.947245i	$-0.396145\pi$
$179$	−4.54314	−	2.62298i	−0.339570	−	0.196051i	−0.660082	+	0.751194i	$0.729478\pi$
$180$	−8.31439	−	1.69450i	−0.619718	−	0.126301i
$181$			3.34763i			0.248827i	0.992230	+	0.124414i	$0.0397049\pi$
$181$			3.34763i			0.248827i	−0.992230	+	0.124414i	$0.960295\pi$
$182$	9.02678	+	3.08501i	0.669109	+	0.228676i
$183$	9.07983	−	23.9536i	0.671201	−	1.77070i
$184$	−2.43857	+	1.40791i	−0.179773	+	0.103792i
$185$	−0.262580	+	0.454802i	−0.0193053	+	0.0334377i
$186$	11.7920	−	9.63114i	0.864630	−	0.706189i
$187$	16.8913	+	29.2566i	1.23521	+	2.13945i
$188$			7.82865i			0.570963i
$189$	−8.36987	−	10.9062i	−0.608818	−	0.793310i
$190$		−	5.50393i		−	0.399297i
$191$	−12.5958	+	7.27218i	−0.911399	+	0.526196i	−0.880881	−	0.473338i	$-0.843049\pi$
$191$	−12.5958	+	7.27218i	−0.911399	+	0.526196i	−0.0305177	+	0.999534i	$0.509716\pi$
$192$	−1.34147	+	1.09565i	−0.0968124	+	0.0790718i
$193$	−3.56744	−	2.05966i	−0.256790	−	0.148258i	0.366079	−	0.930584i	$-0.380700\pi$
$193$	−3.56744	−	2.05966i	−0.256790	−	0.148258i	−0.622869	+	0.782326i	$0.714033\pi$
$194$	−4.80144	−	8.31634i	−0.344724	−	0.597079i
$195$	−3.24584	−	17.3628i	−0.232440	−	1.24338i
$196$	−1.26770	+	6.88425i	−0.0905498	+	0.491732i
$197$	−4.31746			−0.307606			−0.153803	−	0.988102i	$-0.549152\pi$
$197$	−4.31746			−0.307606			−0.153803	+	0.988102i	$0.549152\pi$
$198$	3.56650	−	17.4997i	0.253460	−	1.24365i
$199$	−17.9961	−	10.3900i	−1.27571	−	0.736530i	−0.299651	−	0.954049i	$-0.596870\pi$
$199$	−17.9961	−	10.3900i	−1.27571	−	0.736530i	−0.976056	+	0.217519i	$0.930204\pi$
$200$	1.50002	−	2.59812i	0.106068	−	0.183715i
$201$	−1.80210	+	0.293179i	−0.127110	+	0.0206792i
$202$	−6.63524			−0.466854
$203$	0.0296072	+	0.171710i	0.00207802	+	0.0120516i
$204$	−9.19081	−	3.48386i	−0.643486	−	0.243919i
$205$	5.72583	+	9.91743i	0.399909	+	0.692664i
$206$	6.33025	+	3.65477i	0.441050	+	0.254640i
$207$	2.67771	+	8.01181i	0.186114	+	0.556859i
$208$	−3.16406	−	1.72880i	−0.219388	−	0.119870i
$209$	11.5844			0.801309
$210$	12.2536	−	4.22487i	0.845581	−	0.291544i
$211$	7.95214			0.547448			0.273724	−	0.961808i	$-0.411745\pi$
$211$	7.95214			0.547448			0.273724	+	0.961808i	$0.411745\pi$
$212$	3.77930	−	2.18198i	0.259564	−	0.149859i
$213$	8.27661	−	6.75994i	0.567104	−	0.463184i
$214$	−14.1105	−	8.14672i	−0.964576	−	0.556898i
$215$	−8.52859	+	4.92399i	−0.581645	+	0.335813i
$216$	2.41708	+	4.59975i	0.164461	+	0.312974i
$217$	−8.03705	+	21.8242i	−0.545590	+	1.48152i
$218$		−	1.68209i		−	0.113925i
$219$	−0.0780090	−	0.479503i	−0.00527136	−	0.0324018i
$220$	14.5822	+	8.41904i	0.983132	+	0.567612i
$221$	−0.481494	−	20.4549i	−0.0323888	−	1.37595i
$222$	0.317420	−	0.0516401i	0.0213038	−	0.00346586i
$223$	7.45226			0.499040			0.249520	−	0.968370i	$-0.419727\pi$
$223$	7.45226			0.499040			0.249520	+	0.968370i	$0.419727\pi$
$224$	0.914306	−	2.48275i	0.0610896	−	0.165886i
$225$	−6.73870	−	5.96595i	−0.449247	−	0.397730i
$226$	−7.32589	+	4.22960i	−0.487311	+	0.281349i
$227$	2.98035	+	1.72071i	0.197813	+	0.114207i	0.595635	−	0.803255i	$-0.296901\pi$
$227$	2.98035	+	1.72071i	0.197813	+	0.114207i	−0.397822	+	0.917463i	$0.630234\pi$
$228$	−2.61041	+	2.13206i	−0.172878	+	0.141199i
$229$	−11.6436	−	20.1673i	−0.769429	−	1.33269i	−0.937873	−	0.346979i	$-0.887208\pi$
$229$	−11.6436	−	20.1673i	−0.769429	−	1.33269i	0.168444	−	0.985711i	$-0.446126\pi$
$230$	−7.96435			−0.525154
$231$	8.89228	+	25.7908i	0.585069	+	1.69691i
$232$		−	0.0658578i		−	0.00432378i
$233$	−11.5261	+	6.65459i	−0.755099	+	0.435957i	−0.827533	−	0.561417i	$-0.810257\pi$
$233$	−11.5261	+	6.65459i	−0.755099	+	0.435957i	0.0724345	+	0.997373i	$0.476923\pi$
$234$	−6.97749	+	8.26527i	−0.456133	+	0.540317i
$235$	−11.0714	+	19.1763i	−0.722219	+	1.25092i
$236$	11.6234	−	6.71079i	0.756621	−	0.436835i
$237$	−13.5422	−	5.13330i	−0.879663	−	0.333444i
$238$	14.7956	−	2.55116i	0.959059	−	0.165367i
$239$	0.340722			0.0220395			0.0110197	−	0.999939i	$-0.496492\pi$
$239$	0.340722			0.0220395			0.0110197	+	0.999939i	$0.496492\pi$
$240$	−4.83542	+	0.786662i	−0.312125	+	0.0507788i
$241$	−2.07800	+	3.59921i	−0.133856	+	0.231845i	−0.925160	−	0.379578i	$-0.876069\pi$
$241$	−2.07800	+	3.59921i	−0.133856	+	0.231845i	0.791304	+	0.611423i	$0.209403\pi$
$242$	−12.2200	+	21.1656i	−0.785528	+	1.36058i
$243$	14.9694	−	4.34948i	0.960285	−	0.279019i
$244$		−	14.7899i		−	0.946823i
$245$	−12.8411	+	15.0702i	−0.820385	+	0.962797i
$246$	2.48563	−	6.55737i	0.158478	−	0.418083i
$247$	−6.15703	−	3.36411i	−0.391762	−	0.214053i
$248$	4.39516	−	7.61265i	0.279093	−	0.483404i
$249$	−1.03048	−	1.26168i	−0.0653041	−	0.0799558i
$250$	−4.89887	+	2.82837i	−0.309832	+	0.178882i
$251$	−24.1872			−1.52668			−0.763341	−	0.645995i	$-0.776443\pi$
$251$	−24.1872			−1.52668			−0.763341	+	0.645995i	$0.776443\pi$
$252$	−6.75047	−	4.17507i	−0.425239	−	0.263005i
$253$		−	16.7629i		−	1.05388i
$254$	−0.282065	−	0.488551i	−0.0176983	−	0.0306544i
$255$	−17.5859	−	21.5315i	−1.10127	−	1.34836i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.25640	+	9.10435i	0.327885	+	0.567914i	0.982092	−	0.188402i	$-0.0603308\pi$
$257$	5.25640	+	9.10435i	0.327885	+	0.567914i	−0.654207	+	0.756316i	$0.726997\pi$
$258$	5.63907	+	2.13754i	0.351073	+	0.133077i
$259$	−0.377505	+	0.314337i	−0.0234570	+	0.0195319i
$260$	−5.30546	−	8.70935i	−0.329031	−	0.540131i
$261$	−0.193594	−	0.0394551i	−0.0119832	−	0.00244221i
$262$	8.86611	−	15.3566i	0.547750	−	0.948731i
$263$	−25.1348	−	14.5116i	−1.54988	−	0.894822i	−0.998150	−	0.0607961i	$-0.980636\pi$
$263$	−25.1348	−	14.5116i	−1.54988	−	0.894822i	−0.551726	−	0.834025i	$-0.686031\pi$
$264$	−1.65572	−	10.1773i	−0.101903	−	0.626372i
$265$	12.3432			0.758236
$266$	1.77917	−	4.83125i	0.109088	−	0.296223i
$267$	−3.27459	+	8.63873i	−0.200402	+	0.528682i
$268$	−0.912896	+	0.527061i	−0.0557640	+	0.0321953i
$269$	11.3788	−	19.7086i	0.693777	−	1.20166i	−0.276815	−	0.960923i	$-0.589279\pi$
$269$	11.3788	−	19.7086i	0.693777	−	1.20166i	0.970591	−	0.240733i	$-0.0773878\pi$
$270$	−0.584430	+	14.6854i	−0.0355673	+	0.893723i
$271$	−7.71867	−	13.3691i	−0.468876	−	0.812116i	0.530491	−	0.847690i	$-0.322007\pi$
$271$	−7.71867	−	13.3691i	−0.468876	−	0.812116i	−0.999367	+	0.0355739i	$0.988674\pi$
$272$	−5.67475			−0.344082
$273$	2.76347	−	16.2900i	0.167253	−	0.985914i
$274$	5.73854			0.346678
$275$	8.92986	+	15.4670i	0.538491	+	0.932694i
$276$	3.08515	+	3.77734i	0.185704	+	0.227369i
$277$	11.7800	−	20.4035i	0.707791	−	1.22593i	−0.257884	−	0.966176i	$-0.583025\pi$
$277$	11.7800	−	20.4035i	0.707791	−	1.22593i	0.965675	−	0.259754i	$-0.0836416\pi$
$278$	−7.07460	+	4.08452i	−0.424307	+	0.244974i
$279$	−19.7448	−	17.4806i	−1.18209	−	1.04654i
$280$	5.75074	−	4.78846i	0.343672	−	0.286165i
$281$	2.59314			0.154694			0.0773469	−	0.997004i	$-0.475355\pi$
$281$	2.59314			0.154694			0.0773469	+	0.997004i	$0.475355\pi$
$282$	13.3837	−	2.17735i	0.796985	−	0.129659i
$283$	−18.2700	−	10.5482i	−1.08604	−	0.627024i	−0.153519	−	0.988146i	$-0.549061\pi$
$283$	−18.2700	−	10.5482i	−1.08604	−	0.627024i	−0.932519	+	0.361121i	$0.882394\pi$
$284$	3.08490	−	5.34320i	0.183055	−	0.317060i
$285$	−9.40938	+	1.53079i	−0.557364	+	0.0906760i
$286$	18.3310	−	11.1667i	1.08393	−	0.660298i
$287$	1.82017	+	10.5562i	0.107441	+	0.623115i
$288$	2.24620	+	1.98862i	0.132358	+	0.117180i
$289$	−7.60139	−	13.1660i	−0.447140	−	0.774470i
$290$	0.0931373	−	0.161318i	0.00546921	−	0.00947295i
$291$	−12.8820	+	10.5214i	−0.755157	+	0.616777i
$292$	−0.140240	−	0.242904i	−0.00820695	−	0.0142149i
$293$			13.6747i			0.798886i	0.916758	+	0.399443i	$0.130796\pi$
$293$			13.6747i			0.798886i	−0.916758	+	0.399443i	$0.869204\pi$
$294$	12.1217	+	0.252533i	0.706953	+	0.0147280i
$295$	37.9621			2.21024
$296$	0.160796	−	0.0928358i	0.00934610	−	0.00539597i
$297$	−30.9090	−	1.23008i	−1.79352	−	0.0713763i
$298$	−7.77314	+	13.4635i	−0.450286	+	0.779918i
$299$	−4.86797	+	8.90940i	−0.281522	+	0.515244i
$300$	−4.85888	−	1.84180i	−0.280527	−	0.106336i
$301$	−9.07795	+	1.56528i	−0.523244	+	0.0902210i
$302$			20.9700i			1.20669i
$303$	1.84543	+	11.3434i	0.106017	+	0.651663i
$304$	−0.972964	+	1.68522i	−0.0558033	+	0.0966542i
$305$	20.9161	−	36.2277i	1.19765	−	2.07439i
$306$	−3.39971	+	16.6813i	−0.194349	+	0.953608i
$307$	12.9292			0.737908			0.368954	−	0.929448i	$-0.379716\pi$
$307$	12.9292			0.737908			0.368954	+	0.929448i	$0.379716\pi$
$308$	10.0785	+	12.1039i	0.574276	+	0.689681i
$309$	4.48750	−	11.8385i	0.255285	−	0.673470i
$310$	21.5319	−	12.4314i	1.22293	−	0.706058i
$311$	7.53321	−	13.0479i	0.427169	−	0.739878i	−0.569451	−	0.822025i	$-0.692844\pi$
$311$	7.53321	−	13.0479i	0.427169	−	0.739878i	0.996620	+	0.0821467i	$0.0261776\pi$
$312$	−2.07550	+	5.89002i	−0.117502	+	0.333457i
$313$	10.6006	−	6.12027i	0.599183	−	0.345938i	−0.169537	−	0.985524i	$-0.554227\pi$
$313$	10.6006	−	6.12027i	0.599183	−	0.345938i	0.768720	+	0.639585i	$0.220894\pi$
$314$		−	14.5311i		−	0.820037i
$315$	−10.6308	−	19.7735i	−0.598977	−	1.11411i
$316$	−8.36148			−0.470370
$317$	7.30130	+	12.6462i	0.410082	+	0.710283i	0.994898	−	0.100883i	$-0.0321667\pi$
$317$	7.30130	+	12.6462i	0.410082	+	0.710283i	−0.584816	+	0.811166i	$0.698833\pi$
$318$	−4.78138	−	5.85414i	−0.268127	−	0.328284i
$319$	0.339535	+	0.196030i	0.0190103	+	0.0109756i
$320$	−2.44950	+	1.41422i	−0.136931	+	0.0790572i
$321$	−10.0029	+	26.3888i	−0.558308	+	1.47288i
$322$	−6.99096	−	2.57451i	−0.389591	−	0.143472i
$323$	−11.0427			−0.614429
$324$	7.19137	−	5.41149i	0.399521	−	0.300638i
$325$	−0.254550	−	10.8138i	−0.0141199	−	0.599844i
$326$	1.09419	+	0.631733i	0.0606018	+	0.0349885i
$327$	−2.87565	+	0.467832i	−0.159024	+	0.0258712i
$328$		−	4.04876i		−	0.223556i
$329$	−15.9171	+	13.2537i	−0.877538	+	0.730699i
$330$	10.3373	−	27.2709i	0.569049	−	1.50122i
$331$	30.8306	−	17.8001i	1.69461	−	0.978381i	0.743897	−	0.668294i	$-0.232975\pi$
$331$	30.8306	−	17.8001i	1.69461	−	0.978381i	0.950708	−	0.310087i	$-0.100358\pi$
$332$	−0.814514	−	0.470260i	−0.0447023	−	0.0258089i
$333$	−0.176565	−	0.528290i	−0.00967572	−	0.0289501i
$334$	−12.9034	+	7.44977i	−0.706041	+	0.407633i
$335$	−2.98151			−0.162898
$336$	−4.49874	−	0.872557i	−0.245426	−	0.0476019i
$337$	−2.05641			−0.112020			−0.0560098	−	0.998430i	$-0.517838\pi$
$337$	−2.05641			−0.112020			−0.0560098	+	0.998430i	$0.517838\pi$
$338$	−12.9856	+	0.611682i	−0.706324	+	0.0332711i
$339$	9.26834	+	11.3478i	0.503387	+	0.616327i
$340$	−13.9003	−	8.02533i	−0.753849	−	0.435235i
$341$	26.1650	+	45.3192i	1.41692	+	2.45417i
$342$	4.37094	+	3.86971i	0.236353	+	0.209250i
$343$	−16.1431	+	9.07738i	−0.871648	+	0.490132i
$344$	3.48177			0.187725
$345$	2.21509	+	13.6156i	0.119257	+	0.733042i
$346$	−5.85736	+	10.1453i	−0.314894	+	0.545412i
$347$	10.6785	+	6.16526i	0.573254	+	0.330968i	0.758448	−	0.651734i	$-0.225958\pi$
$347$	10.6785	+	6.16526i	0.573254	+	0.330968i	−0.185194	+	0.982702i	$0.559291\pi$
$348$	−0.112589	+	0.0183168i	−0.00603539	+	0.000981882i
$349$	−31.2915			−1.67500			−0.837498	−	0.546441i	$-0.815982\pi$
$349$	−31.2915			−1.67500			−0.837498	+	0.546441i	$0.815982\pi$
$350$	7.82196	−	1.34871i	0.418101	−	0.0720916i
$351$	16.0707	+	9.62976i	0.857791	+	0.513998i
$352$	−2.97657	−	5.15557i	−0.158652	−	0.274793i
$353$	−3.55499	−	2.05247i	−0.189213	−	0.109242i	0.402401	−	0.915463i	$-0.368176\pi$
$353$	−3.55499	−	2.05247i	−0.189213	−	0.109242i	−0.591614	+	0.806221i	$0.701509\pi$
$354$	−14.7054	−	18.0047i	−0.781582	−	0.956937i
$355$	15.1129	−	8.72543i	0.802109	−	0.463098i
$356$			5.33387i			0.282695i
$357$	−8.47644	−	24.5847i	−0.448621	−	1.30116i
$358$			5.24597i			0.277258i
$359$	12.8433	+	22.2452i	0.677842	+	1.17406i	0.975630	+	0.219424i	$0.0704178\pi$
$359$	12.8433	+	22.2452i	0.677842	+	1.17406i	−0.297788	+	0.954632i	$0.596249\pi$
$360$	2.68971	+	8.04773i	0.141760	+	0.424152i
$361$	7.60668	−	13.1752i	0.400352	−	0.693430i
$362$	2.89913	−	1.67381i	0.152375	−	0.0879736i
$363$	39.5828	+	15.0042i	2.07756	+	0.787518i
$364$	−1.84170	−	9.35992i	−0.0965311	−	0.490593i
$365$		−	0.793322i		−	0.0415244i
$366$	−25.2844	+	4.11344i	−1.32163	+	0.215013i
$367$	−13.3337	−	7.69823i	−0.696015	−	0.401844i	0.109847	−	0.993949i	$-0.464964\pi$
$367$	−13.3337	−	7.69823i	−0.696015	−	0.401844i	−0.805861	+	0.592104i	$0.798297\pi$
$368$	2.43857	+	1.40791i	0.127119	+	0.0733922i
$369$	−11.9016	−	2.42559i	−0.619574	−	0.126271i
$370$	0.525161			0.0273018
$371$	10.8346	+	3.99000i	0.562506	+	0.207150i
$372$	−14.2368	−	5.39659i	−0.738144	−	0.279800i
$373$	14.7842	+	25.6070i	0.765498	+	1.32588i	0.939983	+	0.341221i	$0.110841\pi$
$373$	14.7842	+	25.6070i	0.765498	+	1.32588i	−0.174485	+	0.984660i	$0.555826\pi$
$374$	16.8913	−	29.2566i	0.873428	−	1.51282i
$375$	6.19781	+	7.58835i	0.320053	+	0.391861i
$376$	6.77981	−	3.91432i	0.349642	−	0.201866i
$377$	−0.123533	−	0.202790i	−0.00636229	−	0.0104442i
$378$	−5.26012	+	12.7016i	−0.270551	+	0.653301i
$379$		−	14.2729i		−	0.733151i	−0.930388	−	0.366576i	$-0.880530\pi$
$379$		−	14.2729i		−	0.733151i	0.930388	−	0.366576i	$-0.119470\pi$
$380$	−4.76654	+	2.75197i	−0.244519	+	0.141173i
$381$	−0.756764	+	0.618090i	−0.0387702	+	0.0316657i
$382$	12.5958	+	7.27218i	0.644456	+	0.372077i
$383$	23.7432	−	13.7081i	1.21322	−	0.700453i	0.249761	−	0.968308i	$-0.419648\pi$
$383$	23.7432	−	13.7081i	1.21322	−	0.700453i	0.963459	+	0.267855i	$0.0863148\pi$
$384$	1.61960	+	0.613923i	0.0826498	+	0.0313291i
$385$	7.56977	+	43.9015i	0.385791	+	2.23743i
$386$			4.11932i			0.209668i
$387$	2.08591	−	10.2349i	0.106033	−	0.520270i
$388$	−4.80144	+	8.31634i	−0.243756	+	0.422198i
$389$	−28.0439	−	16.1912i	−1.42188	−	0.820925i	−0.425424	−	0.904994i	$-0.639875\pi$
$389$	−28.0439	−	16.1912i	−1.42188	−	0.820925i	−0.996460	+	0.0840687i	$0.973208\pi$
$390$	−13.4137	+	11.4924i	−0.679229	+	0.581939i
$391$			15.9790i			0.808095i
$392$	6.59579	−	2.34427i	0.333138	−	0.118403i
$393$	−28.7191	−	10.8862i	−1.44869	−	0.549137i
$394$	2.15873	+	3.73903i	0.108755	+	0.188370i
$395$	−20.4814	−	11.8250i	−1.03053	−	0.594978i
$396$	−16.9384	+	5.66117i	−0.851188	+	0.284484i
$397$	−3.64884	−	6.31997i	−0.183130	−	0.317190i	0.759815	−	0.650139i	$-0.225290\pi$
$397$	−3.64884	−	6.31997i	−0.183130	−	0.317190i	−0.942945	+	0.332949i	$0.891956\pi$
$398$			20.7801i			1.04161i
$399$	−8.75422	−	1.69793i	−0.438259	−	0.0850029i
$400$	−3.00005			−0.150002
$401$	10.5538	+	18.2797i	0.527030	+	0.912842i	0.999504	+	0.0314978i	$0.0100277\pi$
$401$	10.5538	+	18.2797i	0.527030	+	0.912842i	−0.472474	+	0.881345i	$0.656639\pi$
$402$	1.15495	+	1.41407i	0.0576036	+	0.0705276i
$403$	−0.745847	−	31.6852i	−0.0371533	−	1.57835i
$404$	3.31762	+	5.74628i	0.165058	+	0.285888i
$405$	25.2683	−	3.08525i	1.25559	−	0.153308i
$406$	0.133901	−	0.111495i	0.00664540	−	0.00553342i
$407$			1.10533i			0.0547892i
$408$	1.57830	+	9.70141i	0.0781373	+	0.480291i
$409$	−17.8308	+	30.8839i	−0.881677	+	1.52711i	−0.0322023	+	0.999481i	$0.510252\pi$
$409$	−17.8308	+	30.8839i	−0.881677	+	1.52711i	−0.849475	+	0.527629i	$0.823081\pi$
$410$	5.72583	−	9.91743i	0.282779	−	0.489787i
$411$	−1.59604	−	9.81046i	−0.0787266	−	0.483914i
$412$		−	7.30954i		−	0.360115i
$413$	33.3224	+	12.2714i	1.63969	+	0.603837i
$414$	5.59958	−	6.32487i	0.275204	−	0.310850i
$415$	−1.33010	−	2.30380i	−0.0652920	−	0.113089i
$416$	0.0848486	+	3.60455i	0.00416004	+	0.176728i
$417$	8.95043	+	10.9586i	0.438305	+	0.536643i
$418$	−5.79219	−	10.0324i	−0.283305	−	0.490699i
$419$	26.4452			1.29193			0.645966	−	0.763367i	$-0.276455\pi$
$419$	26.4452			1.29193			0.645966	+	0.763367i	$0.276455\pi$
$420$	−9.78566	−	8.49952i	−0.477491	−	0.414734i
$421$			14.7368i			0.718230i	0.933293	+	0.359115i	$0.116921\pi$
$421$			14.7368i			0.718230i	−0.933293	+	0.359115i	$0.883079\pi$
$422$	−3.97607	−	6.88675i	−0.193552	−	0.335242i
$423$	−7.44469	−	22.2748i	−0.361973	−	1.08304i
$424$	−3.77930	−	2.18198i	−0.183539	−	0.105966i
$425$	−8.51226	−	14.7437i	−0.412905	−	0.715173i
$426$	−9.99259	−	3.78778i	−0.484142	−	0.183518i
$427$	30.0705	−	25.0388i	1.45522	−	1.21171i
$428$			16.2934i			0.787573i
$429$	−24.1885	−	28.2324i	−1.16783	−	1.36308i
$430$	8.52859	+	4.92399i	0.411285	+	0.237456i
$431$	−0.156980	+	0.271898i	−0.00756147	+	0.0130968i	−0.869781	−	0.493437i	$-0.835740\pi$
$431$	−0.156980	+	0.271898i	−0.00756147	+	0.0130968i	0.862220	+	0.506534i	$0.169074\pi$
$432$	2.77497	−	4.39313i	0.133511	−	0.211364i
$433$		−	7.25461i		−	0.348634i	−0.984690	−	0.174317i	$-0.944228\pi$
$433$		−	7.25461i		−	0.348634i	0.984690	−	0.174317i	$-0.0557718\pi$
$434$	22.9188	−	3.95180i	1.10014	−	0.189693i
$435$	−0.301690	−	0.114358i	−0.0144649	−	0.00548306i
$436$	−1.45673	+	0.841043i	−0.0697647	+	0.0402787i
$437$	4.74527	+	2.73968i	0.226997	+	0.131057i
$438$	−0.376257	+	0.307309i	−0.0179783	+	0.0146838i
$439$	−14.6535	+	8.46021i	−0.699374	+	0.403784i	−0.807114	−	0.590395i	$-0.798972\pi$
$439$	−14.6535	+	8.46021i	−0.699374	+	0.403784i	0.107740	+	0.994179i	$0.465639\pi$
$440$		−	16.8381i		−	0.802724i
$441$	−2.93964	−	20.7932i	−0.139983	−	0.990154i
$442$	−17.4737	+	10.6445i	−0.831141	+	0.506305i
$443$	15.1134	−	8.72575i	0.718061	−	0.414573i	−0.0959775	−	0.995384i	$-0.530598\pi$
$443$	15.1134	−	8.72575i	0.718061	−	0.414573i	0.814039	+	0.580811i	$0.197264\pi$
$444$	−0.203431	−	0.249073i	−0.00965443	−	0.0118205i
$445$	−7.54326	+	13.0653i	−0.357585	+	0.619355i
$446$	−3.72613	−	6.45385i	−0.176437	−	0.305598i
$447$	25.1787	+	9.54423i	1.19091	+	0.451426i
$448$	−2.60728	+	0.449563i	−0.123182	+	0.0212398i
$449$	17.9838			0.848710			0.424355	−	0.905496i	$-0.360501\pi$
$449$	17.9838			0.848710			0.424355	+	0.905496i	$0.360501\pi$
$450$	−1.79732	+	8.81886i	−0.0847263	+	0.415725i
$451$	20.8737	+	12.0514i	0.982904	+	0.567480i
$452$	7.32589	+	4.22960i	0.344581	+	0.198944i
$453$	35.8497	−	5.83230i	1.68437	−	0.274025i
$454$		−	3.44142i		−	0.161514i
$455$	8.72574	−	25.5317i	0.409069	−	1.19694i
$456$	3.15162	+	1.19465i	0.147588	+	0.0559446i
$457$	11.6122	−	6.70430i	0.543195	−	0.313614i	−0.203178	−	0.979142i	$-0.565127\pi$
$457$	11.6122	−	6.70430i	0.543195	−	0.313614i	0.746373	+	0.665528i	$0.231794\pi$
$458$	−11.6436	+	20.1673i	−0.544068	+	0.942354i
$459$	29.4635	+	1.17255i	1.37524	+	0.0547301i
$460$	3.98217	+	6.89733i	0.185670	+	0.321590i
$461$			26.0507i			1.21330i	0.794968	+	0.606652i	$0.207488\pi$
$461$			26.0507i			1.21330i	−0.794968	+	0.606652i	$0.792512\pi$
$462$	17.8893	−	20.5963i	0.832288	−	0.958229i
$463$		−	2.25851i		−	0.104962i	−0.998622	−	0.0524809i	$-0.983287\pi$
$463$		−	2.25851i		−	0.104962i	0.998622	−	0.0524809i	$-0.0167129\pi$
$464$	−0.0570345	+	0.0329289i	−0.00264776	+	0.00152869i
$465$	−27.2411	−	33.3529i	−1.26327	−	1.54670i
$466$	11.5261	+	6.65459i	0.533935	+	0.308268i
$467$	−3.10488	−	5.37781i	−0.143677	−	0.248856i	0.785202	−	0.619240i	$-0.212559\pi$
$467$	−3.10488	−	5.37781i	−0.143677	−	0.248856i	−0.928879	+	0.370385i	$0.879226\pi$
$468$	10.6467	+	1.91005i	0.492143	+	0.0882922i
$469$	−2.61712	−	0.963789i	−0.120847	−	0.0445036i
$470$	22.1428			1.02137
$471$	−24.8420	+	4.04147i	−1.14466	+	0.186221i
$472$	−11.6234	−	6.71079i	−0.535012	−	0.308889i
$473$	−10.3637	+	17.9505i	−0.476526	+	0.825366i
$474$	2.32554	+	14.2946i	0.106816	+	0.656571i
$475$	−5.83788			−0.267860
$476$	−9.60719	−	11.5378i	−0.440345	−	0.528835i
$477$	−8.67826	+	9.80232i	−0.397350	+	0.448818i
$478$	−0.170361	−	0.295074i	−0.00779212	−	0.0134964i
$479$	−4.98664	−	2.87904i	−0.227845	−	0.131547i	0.381732	−	0.924273i	$-0.375328\pi$
$479$	−4.98664	−	2.87904i	−0.227845	−	0.131547i	−0.609578	+	0.792726i	$0.708661\pi$
$480$	3.09898	+	3.79427i	0.141448	+	0.173184i
$481$	0.320988	−	0.587476i	0.0146358	−	0.0267866i
$482$	4.15601			0.189301
$483$	−2.45696	+	12.6676i	−0.111795	+	0.576396i
$484$	24.4399			1.11091
$485$	−23.5222	+	13.5806i	−1.06809	+	0.616662i
$486$	−11.2514	−	10.7891i	−0.510376	−	0.489404i
$487$	26.9169	+	15.5405i	1.21972	+	0.704207i	0.964858	−	0.262770i	$-0.0846361\pi$
$487$	26.9169	+	15.5405i	1.21972	+	0.704207i	0.254864	+	0.966977i	$0.417969\pi$
$488$	−12.8084	+	7.39493i	−0.579809	+	0.334753i
$489$	0.775672	−	2.04631i	0.0350771	−	0.0925373i
$490$	19.4717	+	3.58560i	0.879640	+	0.161981i
$491$			7.69142i			0.347109i	0.984824	+	0.173554i	$0.0555253\pi$
$491$			7.69142i			0.347109i	−0.984824	+	0.173554i	$0.944475\pi$
$492$	−6.92166	+	1.12607i	−0.312053	+	0.0507670i
$493$	−0.323657	−	0.186863i	−0.0145768	−	0.00841590i
$494$	0.165109	+	7.01420i	0.00742861	+	0.315584i
$495$	−49.4968	−	10.0876i	−2.22471	−	0.453405i
$496$	−8.79033			−0.394697
$497$	16.0864	−	2.77371i	0.721572	−	0.124418i
$498$	−0.577407	+	1.52326i	−0.0258742	+	0.0682591i
$499$	4.05046	−	2.33853i	0.181323	−	0.104687i	−0.406591	−	0.913610i	$-0.633283\pi$
$499$	4.05046	−	2.33853i	0.181323	−	0.104687i	0.587914	+	0.808923i	$0.299949\pi$
$500$	4.89887	+	2.82837i	0.219084	+	0.126488i
$501$	16.3247	+	19.9873i	0.729334	+	0.892967i
$502$	12.0936	+	20.9467i	0.539764	+	0.934898i
$503$	−24.1876			−1.07847			−0.539236	−	0.842155i	$-0.681287\pi$
$503$	−24.1876			−1.07847			−0.539236	+	0.842155i	$0.681287\pi$
$504$	−0.240485	+	7.93361i	−0.0107121	+	0.353391i
$505$			18.7673i			0.835136i
$506$	−14.5171	+	8.38147i	−0.645365	+	0.372602i
$507$	4.65735	+	22.0297i	0.206840	+	0.978375i
$508$	−0.282065	+	0.488551i	−0.0125146	+	0.0216759i
$509$	−24.6547	+	14.2344i	−1.09280	+	0.630929i	−0.934321	−	0.356434i	$-0.883993\pi$
$509$	−24.6547	+	14.2344i	−1.09280	+	0.630929i	−0.158480	+	0.987362i	$0.550659\pi$
$510$	−9.85387	+	25.9956i	−0.436337	+	1.15111i
$511$	0.256445	−	0.696364i	0.0113445	−	0.0308053i
$512$	1.00000			0.0441942
$513$	5.39988	−	8.54871i	0.238411	−	0.377435i
$514$	5.25640	−	9.10435i	0.231850	−	0.401576i
$515$	10.3373	−	17.9047i	0.455515	−	0.788976i
$516$	−0.968372	−	5.95235i	−0.0426302	−	0.262038i
$517$			46.6051i			2.04969i
$518$	0.460976	+	0.169761i	0.0202541	+	0.00745886i
$519$	18.9732	+	7.19194i	0.832829	+	0.315691i
$520$	−4.88979	+	8.94934i	−0.214431	+	0.392454i
$521$	1.14358	−	1.98074i	0.0501012	−	0.0867779i	−0.839887	−	0.542761i	$-0.817379\pi$
$521$	1.14358	−	1.98074i	0.0501012	−	0.0867779i	0.889988	+	0.455983i	$0.150712\pi$
$522$	0.0626278	+	0.187385i	0.00274114	+	0.00820160i
$523$	2.06219	−	1.19060i	0.0901732	−	0.0520615i	−0.454235	−	0.890882i	$-0.650087\pi$
$523$	2.06219	−	1.19060i	0.0901732	−	0.0520615i	0.544409	+	0.838820i	$0.316754\pi$
$524$	−17.7322			−0.774636
$525$	−4.48121	−	12.9971i	−0.195576	−	0.567241i
$526$			29.0231i			1.26547i
$527$	−24.9414	−	43.1999i	−1.08647	−	1.88182i
$528$	−7.98598	+	6.52257i	−0.347545	+	0.283858i
$529$	−7.53560	+	13.0520i	−0.327635	+	0.567480i
$530$	−6.17160	−	10.6895i	−0.268077	−	0.464323i
$531$	−26.6904	+	30.1475i	−1.15826	+	1.30829i
$532$	−5.07357	+	0.874816i	−0.219967	+	0.0379281i
$533$	−7.59450	−	12.4670i	−0.328954	−	0.540005i
$534$	9.11865	−	1.48349i	0.394603	−	0.0641968i
$535$	−23.0425	+	39.9107i	−0.996213	+	1.72549i
$536$	0.912896	+	0.527061i	0.0394311	+	0.0227655i
$537$	8.96838	−	1.45904i	0.387014	−	0.0629622i
$538$	−22.7576			−0.981148
$539$	−7.54678	+	40.9829i	−0.325063	+	1.76526i
$540$	13.0101	−	6.83655i	0.559866	−	0.294198i
$541$	−9.26863	+	5.35124i	−0.398489	+	0.230068i	−0.685832	−	0.727760i	$-0.740562\pi$
$541$	−9.26863	+	5.35124i	−0.398489	+	0.230068i	0.287343	+	0.957828i	$0.407228\pi$
$542$	−7.71867	+	13.3691i	−0.331545	+	0.574253i
$543$	−3.66783	−	4.49075i	−0.157402	−	0.192716i
$544$	2.83737	+	4.91448i	0.121651	+	0.210706i
$545$	−4.75767			−0.203796
$546$	−15.4893	+	5.75176i	−0.662879	+	0.246152i
$547$	−37.8140			−1.61681			−0.808406	−	0.588626i	$-0.799669\pi$
$547$	−37.8140			−1.61681			−0.808406	+	0.588626i	$0.799669\pi$
$548$	−2.86927	−	4.96972i	−0.122569	−	0.212296i
$549$	14.0645	+	42.0815i	0.600257	+	1.79599i
$550$	8.92986	−	15.4670i	0.380771	−	0.659514i
$551$	−0.110985	+	0.0640772i	−0.00472812	+	0.00272978i
$552$	1.72869	−	4.56049i	0.0735781	−	0.194107i
$553$	−14.1557	−	17.0004i	−0.601963	−	0.722932i
$554$	−23.5600			−1.00097
$555$	−0.146061	−	0.897801i	−0.00619994	−	0.0381095i
$556$	7.07460	+	4.08452i	0.300030	+	0.173222i
$557$	14.7923	−	25.6210i	0.626769	−	1.08560i	−0.361427	−	0.932400i	$-0.617710\pi$
$557$	14.7923	−	25.6210i	0.626769	−	1.08560i	0.988196	−	0.153195i	$-0.0489563\pi$
$558$	−5.26624	+	25.8398i	−0.222938	+	1.09389i
$559$	10.7211	−	6.53096i	0.453455	−	0.276230i
$560$	−7.02230	−	2.58606i	−0.296746	−	0.109281i
$561$	−54.7142	−	20.7399i	−2.31004	−	0.875640i
$562$	−1.29657	−	2.24573i	−0.0546925	−	0.0947303i
$563$	17.0347	−	29.5050i	0.717928	−	1.24349i	−0.243891	−	0.969803i	$-0.578424\pi$
$563$	17.0347	−	29.5050i	0.717928	−	1.24349i	0.961819	−	0.273686i	$-0.0882428\pi$
$564$	−8.57747	−	10.5019i	−0.361177	−	0.442210i
$565$	11.9632	+	20.7208i	0.503294	+	0.871731i
$566$			21.0964i			0.886746i
$567$	23.1773	+	5.45991i	0.973357	+	0.229295i
$568$	−6.16979			−0.258879
$569$	−31.3283	+	18.0874i	−1.31335	+	0.758263i	−0.982649	−	0.185473i	$-0.940618\pi$
$569$	−31.3283	+	18.0874i	−1.31335	+	0.758263i	−0.330700	+	0.943736i	$0.607285\pi$
$570$	6.03039	+	7.38337i	0.252585	+	0.309255i
$571$	−9.51154	+	16.4745i	−0.398046	+	0.689435i	−0.993485	−	0.113965i	$-0.963645\pi$
$571$	−9.51154	+	16.4745i	−0.398046	+	0.689435i	0.595439	+	0.803400i	$0.296978\pi$
$572$	−18.8361	−	10.2918i	−0.787577	−	0.430320i
$573$	8.92911	−	23.5560i	0.373019	−	0.984066i
$574$	8.23189	−	6.85444i	0.343592	−	0.286099i
$575$			8.44758i			0.352289i
$576$	0.599095	−	2.93957i	0.0249623	−	0.122482i
$577$	11.4956	−	19.9110i	0.478569	−	0.828906i	−0.521129	−	0.853478i	$-0.674489\pi$
$577$	11.4956	−	19.9110i	0.478569	−	0.828906i	0.999698	+	0.0245722i	$0.00782238\pi$
$578$	−7.60139	+	13.1660i	−0.316176	+	0.547633i
$579$	7.04229	−	1.14569i	0.292668	−	0.0476133i
$580$	−0.186275			−0.00773463
$581$	−0.422823	−	2.45220i	−0.0175416	−	0.101734i
$582$	15.5528	+	5.89544i	0.644685	+	0.244374i
$583$	22.4987	−	12.9897i	0.931803	−	0.537976i
$584$	−0.140240	+	0.242904i	−0.00580319	+	0.0100514i
$585$	23.3778	+	19.7354i	0.966552	+	0.815958i
$586$	11.8427	−	6.83736i	0.489215	−	0.282449i
$587$			19.0243i			0.785216i	0.919706	+	0.392608i	$0.128427\pi$
$587$			19.0243i			0.785216i	−0.919706	+	0.392608i	$0.871573\pi$
$588$	−5.84216	−	10.6240i	−0.240927	−	0.438126i
$589$	−17.1053			−0.704813
$590$	−18.9810	−	32.8761i	−0.781437	−	1.35349i
$591$	5.79175	−	4.73043i	0.238241	−	0.194584i
$592$	−0.160796	−	0.0928358i	−0.00660869	−	0.00381553i
$593$	39.8303	−	22.9960i	1.63563	−	0.944333i	0.653322	−	0.757080i	$-0.273375\pi$
$593$	39.8303	−	22.9960i	1.63563	−	0.944333i	0.982312	−	0.187253i	$-0.0599584\pi$
$594$	14.3892	+	27.3830i	0.590396	+	1.12354i
$595$	−7.21578	−	41.8485i	−0.295818	−	1.71562i
$596$	15.5463			0.636801
$597$	35.5251	−	5.77948i	1.45394	−	0.236538i
$598$	10.1497	−	0.238918i	0.415054	−	0.00977007i
$599$	35.1898	+	20.3169i	1.43782	+	0.830124i	0.997698	−	0.0678154i	$-0.0216029\pi$
$599$	35.1898	+	20.3169i	1.43782	+	0.830124i	0.440119	+	0.897939i	$0.354936\pi$
$600$	0.834392	+	5.12881i	0.0340639	+	0.209383i
$601$		−	14.9537i		−	0.609973i	−0.952357	−	0.304986i	$-0.901348\pi$
$601$		−	14.9537i		−	0.609973i	0.952357	−	0.304986i	$-0.0986519\pi$
$602$	5.89454	+	7.07909i	0.240244	+	0.288522i
$603$	2.09624	−	2.36776i	0.0853657	−	0.0964228i
$604$	18.1605	−	10.4850i	0.738942	−	0.426628i
$605$	59.8655	+	34.5634i	2.43388	+	1.40520i
$606$	8.90099	−	7.26991i	0.361578	−	0.295320i
$607$	−38.9035	+	22.4609i	−1.57904	+	0.911661i	−0.584050	+	0.811718i	$0.698533\pi$
$607$	−38.9035	+	22.4609i	−1.57904	+	0.911661i	−0.994993	+	0.0999432i	$0.968134\pi$
$608$	1.94593			0.0789178
$609$	−0.227851	−	0.197904i	−0.00923299	−	0.00801949i
$610$	−41.8322			−1.69373
$611$	13.5341	−	24.7703i	0.547532	−	1.00210i
$612$	16.1463	−	5.39643i	0.652676	−	0.218138i
$613$	21.2198	+	12.2513i	0.857062	+	0.494825i	0.863027	−	0.505157i	$-0.168566\pi$
$613$	21.2198	+	12.2513i	0.857062	+	0.494825i	−0.00596561	+	0.999982i	$0.501899\pi$
$614$	−6.46460	−	11.1970i	−0.260890	−	0.451875i
$615$	−18.5471	−	7.03044i	−0.747891	−	0.283495i
$616$	5.44299	−	14.7802i	0.219304	−	0.595510i
$617$	−5.16102			−0.207775			−0.103887	−	0.994589i	$-0.533128\pi$
$617$	−5.16102			−0.207775			−0.103887	+	0.994589i	$0.533128\pi$
$618$	−12.4962	+	2.03297i	−0.502671	+	0.0817782i
$619$	−23.5913	+	40.8613i	−0.948214	+	1.64235i	−0.199028	+	0.979994i	$0.563779\pi$
$619$	−23.5913	+	40.8613i	−0.948214	+	1.64235i	−0.749185	+	0.662360i	$0.769555\pi$
$620$	−21.5319	−	12.4314i	−0.864741	−	0.499259i
$621$	−12.3702	−	7.81378i	−0.496400	−	0.313556i
$622$	−15.0664			−0.604108
$623$	−10.8448	+	9.03009i	−0.434486	+	0.361783i
$624$	6.13865	−	1.14757i	0.245743	−	0.0459398i
$625$	15.5000	+	26.8467i	0.619999	+	1.07387i
$626$	−10.6006	−	6.12027i	−0.423686	−	0.244615i
$627$	−15.5401	+	12.6925i	−0.620613	+	0.506888i
$628$	−12.5843	+	7.26555i	−0.502168	+	0.289927i
$629$		−	1.05364i		−	0.0420114i
$630$	−11.8089	+	19.0933i	−0.470479	+	0.760694i
$631$			6.15939i			0.245201i	0.992456	+	0.122601i	$0.0391234\pi$
$631$			6.15939i			0.245201i	−0.992456	+	0.122601i	$0.960877\pi$
$632$	4.18074	+	7.24125i	0.166301	+	0.288042i
$633$	−10.6676	+	8.71277i	−0.423998	+	0.346302i
$634$	7.30130	−	12.6462i	0.289972	−	0.502246i
$635$	−1.38183	+	0.797803i	−0.0548364	+	0.0316598i
$636$	−2.67914	+	7.06787i	−0.106235	+	0.280259i
$637$	15.9125	−	19.5906i	0.630478	−	0.776208i
$638$		−	0.392061i		−	0.0155218i
$639$	−3.69629	+	18.1366i	−0.146223	+	0.717471i
$640$	2.44950	+	1.41422i	0.0968249	+	0.0559019i
$641$	22.4818	+	12.9799i	0.887978	+	0.512674i	0.873281	−	0.487218i	$-0.161988\pi$
$641$	22.4818	+	12.9799i	0.887978	+	0.512674i	0.0146975	+	0.999892i	$0.495321\pi$
$642$	27.8548	−	4.53163i	1.09934	−	0.178849i
$643$	−38.3382			−1.51191			−0.755956	−	0.654622i	$-0.772828\pi$
$643$	−38.3382			−1.51191			−0.755956	+	0.654622i	$0.772828\pi$
$644$	1.26588	+	7.34161i	0.0498828	+	0.289300i
$645$	6.04590	−	15.9498i	0.238057	−	0.628021i
$646$	5.52133	+	9.56322i	0.217234	+	0.376260i
$647$	16.4037	−	28.4120i	0.644896	−	1.11699i	−0.339430	−	0.940631i	$-0.610234\pi$
$647$	16.4037	−	28.4120i	0.644896	−	1.11699i	0.984326	−	0.176361i	$-0.0564326\pi$
$648$	−8.28217	−	3.52217i	−0.325354	−	0.138364i
$649$	69.1959	−	39.9503i	2.71618	−	1.56819i
$650$	−9.23778	+	5.62737i	−0.362336	+	0.220723i
$651$	−13.1302	−	38.0823i	−0.514614	−	1.49256i
$652$		−	1.26347i		−	0.0494812i
$653$	−2.21204	+	1.27712i	−0.0865637	+	0.0499776i	−0.542657	−	0.839954i	$-0.682582\pi$
$653$	−2.21204	+	1.27712i	−0.0865637	+	0.0499776i	0.456093	+	0.889932i	$0.349248\pi$
$654$	1.84298	+	2.25647i	0.0720662	+	0.0882350i
$655$	−43.4350	−	25.0772i	−1.69715	−	0.979849i
$656$	−3.50633	+	2.02438i	−0.136899	+	0.0790388i
$657$	0.630015	+	0.557769i	0.0245792	+	0.0217606i
$658$	19.4366	+	7.15778i	0.757716	+	0.279039i
$659$			12.5915i			0.490495i	0.969460	+	0.245248i	$0.0788693\pi$
$659$			12.5915i			0.490495i	−0.969460	+	0.245248i	$0.921131\pi$
$660$	−28.7860	+	4.68311i	−1.12049	+	0.182290i
$661$	3.19978	−	5.54218i	0.124457	−	0.215566i	−0.797064	−	0.603895i	$-0.793614\pi$
$661$	3.19978	−	5.54218i	0.124457	−	0.215566i	0.921521	+	0.388330i	$0.126948\pi$
$662$	−30.8306	−	17.8001i	−1.19827	−	0.691820i
$663$	23.0574	+	26.9122i	0.895475	+	1.04518i
$664$			0.940520i			0.0364992i
$665$	−13.6649	−	5.03228i	−0.529901	−	0.195143i
$666$	−0.369230	+	0.417055i	−0.0143074	+	0.0161606i
$667$	0.0927216	+	0.160599i	0.00359020	+	0.00621840i
$668$	12.9034	+	7.44977i	0.499247	+	0.288240i
$669$	−9.99700	+	8.16508i	−0.386506	+	0.315680i
$670$	1.49076	+	2.58207i	0.0575930	+	0.0997540i
$671$		−	88.0461i		−	3.39898i
$672$	1.49371	+	4.33230i	0.0576212	+	0.167122i
$673$	−16.4797			−0.635248			−0.317624	−	0.948217i	$-0.602885\pi$
$673$	−16.4797			−0.635248			−0.317624	+	0.948217i	$0.602885\pi$
$674$	1.02820	+	1.78090i	0.0396049	+	0.0685977i
$675$	15.5764	+	0.619890i	0.599535	+	0.0238596i
$676$	7.02253	+	10.9400i	0.270097	+	0.420770i
$677$	−9.07040	−	15.7104i	−0.348604	−	0.603800i	0.637398	−	0.770535i	$-0.280011\pi$
$677$	−9.07040	−	15.7104i	−0.348604	−	0.603800i	−0.986002	+	0.166735i	$0.946677\pi$
$678$	5.19330	−	13.7005i	0.199448	−	0.526165i
$679$	−25.0374	+	4.31710i	−0.960847	+	0.165675i
$680$			16.0507i			0.615515i
$681$	−5.88336	+	0.957147i	−0.225451	+	0.0366780i
$682$	26.1650	−	45.3192i	1.00191	−	1.73536i
$683$	8.00820	−	13.8706i	0.306425	−	0.530744i	−0.671152	−	0.741319i	$-0.734200\pi$
$683$	8.00820	−	13.8706i	0.306425	−	0.530744i	0.977578	+	0.210575i	$0.0675337\pi$
$684$	1.16580	−	5.72019i	0.0445753	−	0.218717i
$685$		−	16.2311i		−	0.620158i
$686$	15.9328	+	9.44169i	0.608318	+	0.360485i
$687$	37.7158	+	14.2965i	1.43895	+	0.545446i
$688$	−1.74089	−	3.01530i	−0.0663707	−	0.114957i
$689$	−15.7301	+	0.370276i	−0.599271	+	0.0141064i
$690$	10.6840	−	8.72615i	0.406731	−	0.332199i
$691$	−7.72531	−	13.3806i	−0.293885	−	0.509023i	0.680840	−	0.732432i	$-0.261615\pi$
$691$	−7.72531	−	13.3806i	−0.293885	−	0.509023i	−0.974725	+	0.223409i	$0.928282\pi$
$692$	11.7147			0.445327
$693$	−40.1865	−	24.8548i	−1.52656	−	0.944156i
$694$		−	12.3305i		−	0.468060i
$695$	11.5528	+	20.0101i	0.438223	+	0.759025i
$696$	0.0721572	+	0.0883464i	0.00273511	+	0.00334876i
$697$	−19.8975	−	11.4879i	−0.753673	−	0.435133i
$698$	15.6457	+	27.0992i	0.592200	+	1.02572i
$699$	8.17081	−	21.5555i	0.309048	−	0.815304i
$700$	−5.07900	−	6.09966i	−0.191968	−	0.230546i
$701$		−	12.6204i		−	0.476664i	−0.971184	−	0.238332i	$-0.923399\pi$
$701$		−	12.6204i		−	0.476664i	0.971184	−	0.238332i	$-0.0766007\pi$
$702$	0.304259	−	18.7325i	0.0114835	−	0.707014i
$703$	−0.312898	−	0.180652i	−0.0118012	−	0.00681341i
$704$	−2.97657	+	5.15557i	−0.112184	+	0.194308i
$705$	−6.15850	−	37.8548i	−0.231942	−	1.42570i
$706$			4.10495i			0.154492i
$707$	−6.06664	+	16.4736i	−0.228159	+	0.619555i
$708$	−8.23982	+	21.7376i	−0.309671	+	0.816948i
$709$	−26.7736	+	15.4578i	−1.00550	+	0.580528i	−0.909872	−	0.414888i	$-0.863821\pi$
$709$	−26.7736	+	15.4578i	−1.00550	+	0.580528i	−0.0956324	+	0.995417i	$0.530487\pi$
$710$	−15.1129	−	8.72543i	−0.567177	−	0.327460i
$711$	23.7908	−	7.95138i	0.892226	−	0.298200i
$712$	4.61927	−	2.66694i	0.173114	−	0.0999477i
$713$			24.7519i			0.926967i
$714$	−17.0528	+	19.6332i	−0.638184	+	0.734753i
$715$	−31.5842	−	51.8480i	−1.18118	−	1.93901i
$716$	4.54314	−	2.62298i	0.169785	−	0.0980255i
$717$	−0.457069	+	0.373312i	−0.0170695	+	0.0139416i
$718$	12.8433	−	22.2452i	0.479306	−	0.830183i
$719$	−7.90278	−	13.6880i	−0.294724	−	0.510477i	0.680197	−	0.733030i	$-0.261894\pi$
$719$	−7.90278	−	13.6880i	−0.294724	−	0.510477i	−0.974921	+	0.222553i	$0.928561\pi$
$720$	5.62468	−	6.35322i	0.209619	−	0.236771i
$721$	14.8617	−	12.3748i	0.553478	−	0.460863i
$722$	−15.2134			−0.566183
$723$	−1.15589	−	7.10501i	−0.0429882	−	0.264238i
$724$	−2.89913	−	1.67381i	−0.107745	−	0.0622068i
$725$	−0.171106	−	0.0987883i	−0.00635473	−	0.00366891i
$726$	−6.79738	−	41.7819i	−0.252274	−	1.55067i
$727$			40.5576i			1.50420i	0.659050	+	0.752099i	$0.270959\pi$
$727$			40.5576i			1.50420i	−0.659050	+	0.752099i	$0.729041\pi$
$728$	−7.18508	+	6.27492i	−0.266297	+	0.232564i
$729$	−15.3155	+	22.2359i	−0.567240	+	0.823553i
$730$	−0.687037	+	0.396661i	−0.0254284	+	0.0146811i
$731$	9.87909	−	17.1111i	0.365391	−	0.632877i
$732$	16.2045	+	19.8402i	0.598937	+	0.733314i
$733$	−8.36320	−	14.4855i	−0.308902	−	0.535033i	0.669221	−	0.743064i	$-0.266628\pi$
$733$	−8.36320	−	14.4855i	−0.308902	−	0.535033i	−0.978122	+	0.208030i	$0.933295\pi$
$734$			15.3965i			0.568294i
$735$	0.714273	−	34.2855i	0.0263463	−	1.26464i
$736$		−	2.81581i		−	0.103792i
$737$	−5.43460	+	3.13767i	−0.200186	+	0.115577i
$738$	3.85019	+	11.5199i	0.141727	+	0.424054i
$739$	13.4521	+	7.76657i	0.494843	+	0.285698i	0.726582	−	0.687080i	$-0.241108\pi$
$739$	13.4521	+	7.76657i	0.494843	+	0.285698i	−0.231738	+	0.972778i	$0.574441\pi$
$740$	−0.262580	−	0.454802i	−0.00965264	−	0.0167189i
$741$	11.9454	−	2.23310i	0.438824	−	0.0820349i
$742$	−1.96188	−	11.3781i	−0.0720227	−	0.417702i
$743$	−10.6415			−0.390398			−0.195199	−	0.980764i	$-0.562535\pi$
$743$	−10.6415			−0.390398			−0.195199	+	0.980764i	$0.562535\pi$
$744$	2.44482	+	15.0277i	0.0896314	+	0.550943i
$745$	38.0806	+	21.9858i	1.39516	+	0.805499i
$746$	14.7842	−	25.6070i	0.541289	−	0.937540i
$747$	2.76473	+	0.563461i	0.101156	+	0.0206160i
$748$	−33.7826			−1.23521
$749$	−33.1276	+	27.5843i	−1.21046	+	1.00791i
$750$	3.47280	−	9.16163i	0.126809	−	0.334535i
$751$	−0.864522	−	1.49740i	−0.0315468	−	0.0546407i	0.849821	−	0.527072i	$-0.176710\pi$
$751$	−0.864522	−	1.49740i	−0.0315468	−	0.0546407i	−0.881368	+	0.472431i	$0.843377\pi$
$752$	−6.77981	−	3.91432i	−0.247234	−	0.142741i
$753$	32.4465	−	26.5007i	1.18241	−	0.965741i
$754$	−0.113855	+	0.208378i	−0.00414634	+	0.00758868i
$755$	59.3122			2.15859
$756$	13.6300	−	1.79542i	0.495718	−	0.0652986i
$757$	19.1023			0.694286			0.347143	−	0.937812i	$-0.387152\pi$
$757$	19.1023			0.694286			0.347143	+	0.937812i	$0.387152\pi$
$758$	−12.3607	+	7.13646i	−0.448962	+	0.259208i
$759$	18.3663	+	22.4870i	0.666656	+	0.816227i
$760$	4.76654	+	2.75197i	0.172901	+	0.0998243i
$761$	−9.00493	+	5.19900i	−0.326429	+	0.188464i	−0.654254	−	0.756275i	$-0.727017\pi$
$761$	−9.00493	+	5.19900i	−0.326429	+	0.188464i	0.327826	+	0.944738i	$0.393684\pi$
$762$	0.913664	+	0.346332i	0.0330985	+	0.0125463i
$763$	−4.17620	−	1.53794i	−0.151189	−	0.0556772i
$764$		−	14.5444i		−	0.526196i
$765$	47.1821	+	9.61587i	1.70587	+	0.347663i
$766$	−23.7432	−	13.7081i	−0.857876	−	0.495295i
$767$	−48.3788	+	1.13880i	−1.74686	+	0.0411197i
$768$	−0.278126	−	1.70957i	−0.0100360	−	0.0616890i
$769$	20.6870			0.745993			0.372997	−	0.927833i	$-0.378330\pi$
$769$	20.6870			0.745993			0.372997	+	0.927833i	$0.378330\pi$
$770$	34.2350	−	28.5064i	1.23374	−	1.02730i
$771$	−17.0265	−	6.45405i	−0.613194	−	0.232437i
$772$	3.56744	−	2.05966i	0.128395	−	0.0741289i
$773$	−6.95733	−	4.01681i	−0.250238	−	0.144475i	0.369635	−	0.929177i	$-0.379483\pi$
$773$	−6.95733	−	4.01681i	−0.250238	−	0.144475i	−0.619873	+	0.784702i	$0.712816\pi$
$774$	−9.90666	+	3.31101i	−0.356088	+	0.119012i
$775$	−13.1857	−	22.8383i	−0.473645	−	0.820377i
$776$	9.60289			0.344724
$777$	0.162009	−	0.835288i	0.00581204	−	0.0299658i
$778$			32.3824i			1.16096i
$779$	−6.82307	+	3.93930i	−0.244462	+	0.141140i
$780$	16.6595	+	5.87041i	0.596507	+	0.210195i
$781$	18.3648	−	31.8088i	0.657145	−	1.13821i
$782$	13.8382	−	7.98952i	0.494855	−	0.285705i
$783$	0.302930	−	0.159183i	0.0108258	−	0.00568875i
$784$	−5.32809	−	4.53998i	−0.190289	−	0.162142i
$785$	−41.1003			−1.46693
$786$	4.93179	+	30.3146i	0.175911	+	1.08128i
$787$	10.2024	−	17.6710i	0.363675	−	0.629904i	−0.624887	−	0.780715i	$-0.714855\pi$
$787$	10.2024	−	17.6710i	0.363675	−	0.629904i	0.988563	+	0.150811i	$0.0481884\pi$
$788$	2.15873	−	3.73903i	0.0769015	−	0.133197i
$789$	49.6172	−	8.07209i	1.76642	−	0.287374i
$790$			23.6499i			0.841426i
$791$	3.80294	+	22.0555i	0.135217	+	0.784203i
$792$	13.3719	+	11.8385i	0.475151	+	0.420664i
$793$	−25.5686	+	46.7960i	−0.907969	+	1.66177i
$794$	−3.64884	+	6.31997i	−0.129492	+	0.224287i
$795$	−16.5581	+	13.5238i	−0.587254	+	0.479641i
$796$	17.9961	−	10.3900i	0.637854	−	0.368265i
$797$	−3.19379			−0.113130			−0.0565649	−	0.998399i	$-0.518015\pi$
$797$	−3.19379			−0.113130			−0.0565649	+	0.998399i	$0.518015\pi$
$798$	2.90666	+	8.43034i	0.102895	+	0.298431i
$799$		−	44.4256i		−	1.57167i
$800$	1.50002	+	2.59812i	0.0530339	+	0.0918574i
$801$	−5.07227	−	15.1764i	−0.179220	−	0.536233i
$802$	10.5538	−	18.2797i	0.372666	−	0.645477i
$803$	−0.834871	−	1.44604i	−0.0294620	−	0.0510296i
$804$	0.647149	−	1.70725i	0.0228232	−	0.0602102i
$805$	−7.28185	+	19.7735i	−0.256651	+	0.696924i
$806$	−27.0673	+	16.4885i	−0.953404	+	0.580783i
$807$	6.32947	+	38.9058i	0.222808	+	1.36955i
$808$	3.31762	−	5.74628i	0.116713	−	0.202154i
$809$	15.7183	+	9.07497i	0.552626	+	0.319059i	0.750181	−	0.661233i	$-0.229967\pi$
$809$	15.7183	+	9.07497i	0.552626	+	0.319059i	−0.197554	+	0.980292i	$0.563300\pi$
$810$	−15.3060	−	20.3403i	−0.537799	−	0.714686i
$811$	−23.7993			−0.835708			−0.417854	−	0.908514i	$-0.637218\pi$
$811$	−23.7993			−0.835708			−0.417854	+	0.908514i	$0.637218\pi$
$812$	−0.163508	−	0.0602142i	−0.00573802	−	0.00211310i
$813$	25.0023	+	9.47734i	0.876868	+	0.332385i
$814$	0.957244	−	0.552665i	0.0335514	−	0.0193709i
$815$	1.78682	−	3.09486i	0.0625895	−	0.108408i
$816$	7.61252	−	6.21755i	0.266491	−	0.217658i
$817$	−3.38764	−	5.86756i	−0.118518	−	0.205280i
$818$	35.6616			1.24688
$819$	14.1410	+	24.8803i	0.494127	+	0.869390i
$820$	−11.4517			−0.399909
$821$	−14.0903	−	24.4051i	−0.491755	−	0.851744i	0.508200	−	0.861239i	$-0.330311\pi$
$821$	−14.0903	−	24.4051i	−0.491755	−	0.851744i	−0.999955	+	0.00949494i	$0.996978\pi$
$822$	−7.69809	+	6.28744i	−0.268502	+	0.219299i
$823$	−17.6636	+	30.5942i	−0.615714	+	1.06645i	0.374545	+	0.927209i	$0.377799\pi$
$823$	−17.6636	+	30.5942i	−0.615714	+	1.06645i	−0.990259	+	0.139239i	$0.955534\pi$
$824$	−6.33025	+	3.65477i	−0.220525	+	0.127320i
$825$	−28.9256	−	10.9645i	−1.00706	−	0.381735i
$826$	−6.03384	−	34.9938i	−0.209944	−	1.21759i
$827$	−31.7151			−1.10284			−0.551421	−	0.834227i	$-0.685914\pi$
$827$	−31.7151			−1.10284			−0.551421	+	0.834227i	$0.685914\pi$
$828$	−8.27729	−	1.68694i	−0.287656	−	0.0586252i
$829$	19.0489	+	10.9979i	0.661597	+	0.381973i	0.792885	−	0.609371i	$-0.208578\pi$
$829$	19.0489	+	10.9979i	0.661597	+	0.381973i	−0.131288	+	0.991344i	$0.541911\pi$
$830$	−1.33010	+	2.30380i	−0.0461684	+	0.0799661i
$831$	6.55265	+	40.2776i	0.227309	+	1.39721i
$832$	3.07921	−	1.87576i	0.106752	−	0.0650302i
$833$	7.19386	−	39.0664i	0.249253	−	1.35357i
$834$	5.01517	−	13.2306i	0.173661	−	0.458137i
$835$	21.0712	+	36.4964i	0.729199	+	1.26301i
$836$	−5.79219	+	10.0324i	−0.200327	+	0.346977i
$837$	45.6398	+	1.81631i	1.57754	+	0.0627810i
$838$	−13.2226	−	22.9022i	−0.456767	−	0.791143i
$839$		−	14.3301i		−	0.494731i	−0.968922	−	0.247366i	$-0.920435\pi$
$839$		−	14.3301i		−	0.494731i	0.968922	−	0.247366i	$-0.0795649\pi$
$840$	−2.46797	+	12.7244i	−0.0851531	+	0.439033i
$841$	28.9957			0.999850
$842$	12.7625	−	7.36842i	0.439824	−	0.253933i
$843$	−3.47863	+	2.84118i	−0.119810	+	0.0978554i
$844$	−3.97607	+	6.88675i	−0.136862	+	0.237052i
$845$	1.73010	+	36.7289i	0.0595174	+	1.26351i
$846$	−15.5682	+	17.5847i	−0.535245	+	0.604574i
$847$	41.3761	+	49.6909i	1.42170	+	1.70740i
$848$			4.36396i			0.149859i
$849$	36.0658	−	5.86745i	1.23778	−	0.201370i
$850$	−8.51226	+	14.7437i	−0.291968	+	0.505704i
$851$	−0.261408	+	0.452773i	−0.00896097	+	0.0155208i
$852$	1.71598	+	10.5477i	0.0587885	+	0.361359i
$853$	33.9556			1.16262			0.581309	−	0.813683i	$-0.302541\pi$
$853$	33.9556			1.16262			0.581309	+	0.813683i	$0.302541\pi$
$854$	−36.7195	−	13.5224i	−1.25652	−	0.462729i
$855$	10.9452	−	12.3629i	0.374319	−	0.422803i
$856$	14.1105	−	8.14672i	0.482288	−	0.278449i
$857$	−3.99034	+	6.91148i	−0.136307	+	0.236092i	−0.926096	−	0.377288i	$-0.876857\pi$
$857$	−3.99034	+	6.91148i	−0.136307	+	0.236092i	0.789789	+	0.613379i	$0.210190\pi$
$858$	−12.3557	+	35.0641i	−0.421818	+	1.19707i
$859$	13.2780	−	7.66606i	0.453039	−	0.261562i	−0.256074	−	0.966657i	$-0.582429\pi$
$859$	13.2780	−	7.66606i	0.453039	−	0.261562i	0.709113	+	0.705095i	$0.249096\pi$
$860$		−	9.84797i		−	0.335813i
$861$	−14.0077	−	12.1666i	−0.477380	−	0.414638i
$862$	0.313960			0.0106935
$863$	−11.2232	−	19.4391i	−0.382041	−	0.661714i	0.609313	−	0.792930i	$-0.291445\pi$
$863$	−11.2232	−	19.4391i	−0.382041	−	0.661714i	−0.991354	+	0.131216i	$0.958112\pi$
$864$	−5.19204	−	0.206627i	−0.176637	−	0.00702958i
$865$	28.6952	+	16.5672i	0.975666	+	0.563301i
$866$	−6.28267	+	3.62730i	−0.213494	+	0.123261i
$867$	24.6224	+	9.33333i	0.836220	+	0.316977i
$868$	−14.8818	−	17.8724i	−0.505120	−	0.606628i
$869$	−49.7771			−1.68857
$870$	0.0518078	+	0.318450i	0.00175645	+	0.0107965i
$871$	3.79964	−	0.0894407i	0.128746	−	0.00303058i
$872$	1.45673	+	0.841043i	0.0493311	+	0.0284813i
$873$	5.75304	−	28.2284i	0.194711	−	0.955386i
$874$		−	5.47937i		−	0.185342i
$875$	2.54306	+	14.7487i	0.0859710	+	0.498596i
$876$	0.454266	+	0.172194i	0.0153482	+	0.00581789i
$877$	−38.0125	+	21.9465i	−1.28359	+	0.741082i	−0.977503	−	0.210921i	$-0.932354\pi$
$877$	−38.0125	+	21.9465i	−1.28359	+	0.741082i	−0.306088	+	0.952003i	$0.599020\pi$
$878$	14.6535	+	8.46021i	0.494532	+	0.285518i
$879$	−14.9827	−	18.3443i	−0.505355	−	0.618736i
$880$	−14.5822	+	8.41904i	−0.491566	+	0.283806i
$881$	22.2301			0.748951			0.374475	−	0.927237i	$-0.377823\pi$
$881$	22.2301			0.748951			0.374475	+	0.927237i	$0.377823\pi$
$882$	−16.5376	+	12.9424i	−0.556851	+	0.435794i
$883$	5.75781			0.193766			0.0968828	−	0.995296i	$-0.469113\pi$
$883$	5.75781			0.193766			0.0968828	+	0.995296i	$0.469113\pi$
$884$	17.9552	+	9.81048i	0.603900	+	0.329962i
$885$	−50.9251	+	41.5932i	−1.71183	+	1.39814i
$886$	−15.1134	−	8.72575i	−0.507746	−	0.293147i
$887$	−17.5629	−	30.4199i	−0.589705	−	1.02140i	−0.994271	−	0.106890i	$-0.965911\pi$
$887$	−17.5629	−	30.4199i	−0.589705	−	1.02140i	0.404566	−	0.914509i	$-0.367423\pi$
$888$	−0.113988	+	0.300714i	−0.00382519	+	0.0100913i
$889$	−1.47084	+	0.253612i	−0.0493305	+	0.00850586i
$890$	15.0865			0.505701
$891$	42.8113	−	32.2153i	1.43423	−	1.07925i
$892$	−3.72613	+	6.45385i	−0.124760	+	0.216091i
$893$	−13.1930	−	7.61699i	−0.441487	−	0.254893i
$894$	−4.32383	−	26.5775i	−0.144610	−	0.888886i
$895$	14.8379			0.495976
$896$	1.69297	+	2.03319i	0.0565582	+	0.0679240i
$897$	−3.23136	−	17.2853i	−0.107892	−	0.577140i
$898$	−8.99192	−	15.5745i	−0.300064	−	0.519727i
$899$	−0.501352	−	0.289456i	−0.0167210	−	0.00965389i
$900$	8.53602	−	2.85291i	0.284534	−	0.0950970i
$901$	−21.4466	+	12.3822i	−0.714490	+	0.412511i
$902$		−	24.1029i		−	0.802537i
$903$	10.4628	−	12.0460i	0.348181	−	0.400867i
$904$		−	8.45921i		−	0.281349i
$905$	−4.73427	−	8.20000i	−0.157373	−	0.272577i
$906$	−22.9758	−	28.1306i	−0.763319	−	0.934578i
$907$	19.1076	−	33.0953i	0.634456	−	1.09891i	−0.352174	−	0.935934i	$-0.614558\pi$
$907$	19.1076	−	33.0953i	0.634456	−	1.09891i	0.986630	−	0.162975i	$-0.0521091\pi$
$908$	−2.98035	+	1.72071i	−0.0989065	+	0.0571037i
$909$	−14.9040	−	13.1950i	−0.494336	−	0.437649i
$910$	−26.4739	+	5.20912i	−0.877603	+	0.172681i
$911$			24.2986i			0.805050i	0.915409	+	0.402525i	$0.131867\pi$
$911$			24.2986i			0.805050i	−0.915409	+	0.402525i	$0.868133\pi$
$912$	−0.541213	−	3.32671i	−0.0179214	−	0.110158i
$913$	−4.84892	−	2.79952i	−0.160476	−	0.0926507i
$914$	−11.6122	−	6.70430i	−0.384097	−	0.221759i
$915$	11.6346	+	71.5152i	0.384628	+	2.36422i
$916$	23.2871			0.769429
$917$	−30.0201	−	36.0529i	−0.991353	−	1.19057i
$918$	−13.7163	−	26.1024i	−0.452706	−	0.861509i
$919$	−19.8864	−	34.4442i	−0.655990	−	1.13621i	−0.981645	−	0.190719i	$-0.938918\pi$
$919$	−19.8864	−	34.4442i	−0.655990	−	1.13621i	0.325654	−	0.945489i	$-0.394415\pi$
$920$	3.98217	−	6.89733i	0.131288	−	0.227398i
$921$	−17.3442	+	14.1659i	−0.571509	+	0.466782i
$922$	22.5606	−	13.0254i	0.742994	−	0.428968i
$923$	−18.9981	+	11.5730i	−0.625330	+	0.380931i
$924$	−26.7816	−	5.19446i	−0.881051	−	0.170885i
$925$		−	0.557024i		−	0.0183148i
$926$	−1.95593	+	1.12925i	−0.0642757	+	0.0371096i
$927$	6.95104	+	20.7978i	0.228302	+	0.683089i
$928$	0.0570345	+	0.0329289i	0.00187225	+	0.00108094i
$929$	22.9223	−	13.2342i	0.752058	−	0.434201i	−0.0743792	−	0.997230i	$-0.523698\pi$
$929$	22.9223	−	13.2342i	0.752058	−	0.434201i	0.826437	+	0.563029i	$0.190364\pi$
$930$	−15.2639	+	40.2679i	−0.500523	+	1.32044i
$931$	−10.3681	−	8.83448i	−0.339800	−	0.289538i
$932$		−	13.3092i		−	0.435957i
$933$	4.19036	+	25.7572i	0.137186	+	0.843252i
$934$	−3.10488	+	5.37781i	−0.101595	+	0.175967i
$935$	−82.7504	−	47.7759i	−2.70623	−	1.56244i
$936$	−3.66918	−	10.1753i	−0.119931	−	0.332591i
$937$			31.6644i			1.03443i	0.855856	+	0.517215i	$0.173031\pi$
$937$			31.6644i			1.03443i	−0.855856	+	0.517215i	$0.826969\pi$
$938$	0.473894	+	2.74839i	0.0154732	+	0.0897380i
$939$	−7.51475	+	19.8248i	−0.245235	+	0.646957i
$940$	−11.0714	−	19.1763i	−0.361110	−	0.625460i
$941$	17.3083	+	9.99297i	0.564236	+	0.325762i	0.754844	−	0.655905i	$-0.227713\pi$
$941$	17.3083	+	9.99297i	0.564236	+	0.325762i	−0.190608	+	0.981666i	$0.561046\pi$
$942$	15.9210	+	19.4931i	0.518735	+	0.635118i
$943$	5.70028	+	9.87317i	0.185627	+	0.321515i
$944$			13.4216i			0.436835i
$945$	35.9257	+	14.8779i	1.16866	+	0.483978i
$946$	20.7275			0.673909
$947$	3.07700	+	5.32952i	0.0999891	+	0.173186i	0.911680	−	0.410901i	$-0.134786\pi$
$947$	3.07700	+	5.32952i	0.0999891	+	0.173186i	−0.811691	+	0.584087i	$0.801453\pi$
$948$	11.2167	−	9.16127i	0.364301	−	0.297544i
$949$	0.0237984	+	1.01101i	0.000772529	+	0.0328187i
$950$	2.91894	+	5.05575i	0.0947029	+	0.164030i
$951$	−23.6504	−	8.96488i	−0.766915	−	0.290706i
$952$	−5.18846	+	14.0890i	−0.168159	+	0.456626i
$953$		−	25.6981i		−	0.832443i	−0.909263	−	0.416222i	$-0.863354\pi$
$953$		−	25.6981i		−	0.832443i	0.909263	−	0.416222i	$-0.136646\pi$
$954$	12.8282	+	2.61443i	0.415328	+	0.0846453i
$955$	20.5689	−	35.6264i	0.665593	−	1.15284i
$956$	−0.170361	+	0.295074i	−0.00550986	+	0.00954336i
$957$	−0.670257	+	0.109042i	−0.0216663	+	0.00352484i
$958$			5.75808i			0.186035i
$959$	5.24678	−	14.2473i	0.169427	−	0.460071i
$960$	1.73644	−	4.58093i	0.0560434	−	0.147849i
$961$	−23.1349	−	40.0709i	−0.746288	−	1.29261i
$962$	−0.669263	+	0.0157540i	−0.0215779	+	0.000507929i
$963$	−15.4943	−	46.3596i	−0.499297	−	1.49392i
$964$	−2.07800	−	3.59921i	−0.0669280	−	0.115923i
$965$	11.6512			0.375067
$966$	12.1989	−	4.20602i	0.392495	−	0.135326i
$967$		−	51.5125i		−	1.65653i	−0.560336	−	0.828265i	$-0.689328\pi$
$967$		−	51.5125i		−	1.65653i	0.560336	−	0.828265i	$-0.310672\pi$
$968$	−12.2200	−	21.1656i	−0.392764	−	0.680288i
$969$	14.8134	−	12.0989i	0.475875	−	0.388673i
$970$	23.5222	+	13.5806i	0.755254	+	0.436046i
$971$	−16.4408	−	28.4764i	−0.527612	−	0.913851i	−0.999482	−	0.0321826i	$-0.989754\pi$
$971$	−16.4408	−	28.4764i	−0.527612	−	0.913851i	0.471870	−	0.881668i	$-0.343579\pi$
$972$	−3.71792	+	15.1386i	−0.119252	+	0.485571i
$973$	3.67250	+	21.2990i	0.117735	+	0.682814i
$974$		−	31.0810i		−	0.995899i
$975$	12.1897	+	14.2276i	0.390382	+	0.455647i
$976$	12.8084	+	7.39493i	0.409987	+	0.236706i
$977$	−10.4578	+	18.1135i	−0.334575	+	0.579501i	−0.983403	−	0.181434i	$-0.941926\pi$
$977$	−10.4578	+	18.1135i	−0.334575	+	0.579501i	0.648828	+	0.760935i	$0.275259\pi$
$978$	−2.15999	+	0.351403i	−0.0690689	+	0.0112366i
$979$			31.7533i			1.01484i
$980$	−6.63061	−	18.6558i	−0.211807	−	0.595936i
$981$	3.34503	−	3.77830i	0.106798	−	0.120632i
$982$	6.66097	−	3.84571i	0.212560	−	0.122722i
$983$	16.9327	+	9.77611i	0.540070	+	0.311810i	0.745107	−	0.666945i	$-0.232398\pi$
$983$	16.9327	+	9.77611i	0.540070	+	0.311810i	−0.205037	+	0.978754i	$0.565732\pi$
$984$	4.43603	+	5.43130i	0.141416	+	0.173144i
$985$	10.5756	−	6.10583i	0.336967	−	0.194548i
$986$			0.373726i			0.0119019i
$987$	6.83094	−	35.2190i	0.217431	−	1.12103i
$988$	5.99192	−	3.65009i	0.190628	−	0.116125i
$989$	−8.49053	+	4.90201i	−0.269983	+	0.155875i
$990$	16.0123	+	47.9093i	0.508903	+	1.52266i
$991$	−8.09235	+	14.0164i	−0.257062	+	0.445244i	−0.965454	−	0.260575i	$-0.916088\pi$
$991$	−8.09235	+	14.0164i	−0.257062	+	0.445244i	0.708392	+	0.705820i	$0.249421\pi$
$992$	4.39516	+	7.61265i	0.139547	+	0.241702i
$993$	−21.8558	+	57.6580i	−0.693572	+	1.82972i
$994$	−10.4453	−	12.5443i	−0.331304	−	0.397882i
$995$	58.7751			1.86330
$996$	1.60789	−	0.261583i	0.0509479	−	0.00828857i
$997$	−12.2227	−	7.05681i	−0.387098	−	0.223491i	0.293804	−	0.955866i	$-0.405079\pi$
$997$	−12.2227	−	7.05681i	−0.387098	−	0.223491i	−0.680902	+	0.732374i	$0.738412\pi$
$998$	−4.05046	−	2.33853i	−0.128215	−	0.0740249i
$999$	0.815679	+	0.515232i	0.0258070	+	0.0163012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.a.311.4	✓	36
3.2	odd	2		546.2.bg.b.311.10	yes	36
7.5	odd	6	inner	546.2.bg.a.467.10	yes	36
13.12	even	2		546.2.bg.b.311.4	yes	36
21.5	even	6		546.2.bg.b.467.4	yes	36
39.38	odd	2	inner	546.2.bg.a.311.10	yes	36
91.12	odd	6		546.2.bg.b.467.10	yes	36
273.194	even	6	inner	546.2.bg.a.467.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.4	✓	36	1.1	even	1	trivial
546.2.bg.a.311.10	yes	36	39.38	odd	2	inner
546.2.bg.a.467.4	yes	36	273.194	even	6	inner
546.2.bg.a.467.10	yes	36	7.5	odd	6	inner
546.2.bg.b.311.4	yes	36	13.12	even	2
546.2.bg.b.311.10	yes	36	3.2	odd	2
546.2.bg.b.467.4	yes	36	21.5	even	6
546.2.bg.b.467.10	yes	36	91.12	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.34147 + 1.09565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.44950 + 1.41422i) q^{5} +(1.61960 + 0.613923i) q^{6} +(-2.60728 + 0.449563i) q^{7} +1.00000 q^{8} +(0.599095 - 2.93957i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.34147 + 1.09565i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.44950 + 1.41422i) q^{5} +(1.61960 + 0.613923i) q^{6} +(-2.60728 + 0.449563i) q^{7} +1.00000 q^{8} +(0.599095 - 2.93957i) q^{9} +(2.44950 + 1.41422i) q^{10} +(-2.97657 + 5.15557i) q^{11} +(-0.278126 - 1.70957i) q^{12} +(3.07921 - 1.87576i) q^{13} +(1.69297 + 2.03319i) q^{14} +(1.73644 - 4.58093i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.83737 - 4.91448i) q^{17} +(-2.84529 + 0.950954i) q^{18} +(-0.972964 - 1.68522i) q^{19} -2.82844i q^{20} +(3.00503 - 3.45974i) q^{21} +5.95314 q^{22} +(-2.43857 + 1.40791i) q^{23} +(-1.34147 + 1.09565i) q^{24} +(1.50002 - 2.59812i) q^{25} +(-3.16406 - 1.72880i) q^{26} +(2.41708 + 4.59975i) q^{27} +(0.914306 - 2.48275i) q^{28} -0.0658578i q^{29} +(-4.83542 + 0.786662i) q^{30} +(4.39516 - 7.61265i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.65572 - 10.1773i) q^{33} -5.67475 q^{34} +(5.75074 - 4.78846i) q^{35} +(2.24620 + 1.98862i) q^{36} +(0.160796 - 0.0928358i) q^{37} +(-0.972964 + 1.68522i) q^{38} +(-2.07550 + 5.89002i) q^{39} +(-2.44950 + 1.41422i) q^{40} -4.04876i q^{41} +(-4.49874 - 0.872557i) q^{42} +3.48177 q^{43} +(-2.97657 - 5.15557i) q^{44} +(2.68971 + 8.04773i) q^{45} +(2.43857 + 1.40791i) q^{46} +(6.77981 - 3.91432i) q^{47} +(1.61960 + 0.613923i) q^{48} +(6.59579 - 2.34427i) q^{49} -3.00005 q^{50} +(1.57830 + 9.70141i) q^{51} +(0.0848486 + 3.60455i) q^{52} +(-3.77930 - 2.18198i) q^{53} +(2.77497 - 4.39313i) q^{54} -16.8381i q^{55} +(-2.60728 + 0.449563i) q^{56} +(3.15162 + 1.19465i) q^{57} +(-0.0570345 + 0.0329289i) q^{58} +(-11.6234 - 6.71079i) q^{59} +(3.09898 + 3.79427i) q^{60} +(-12.8084 + 7.39493i) q^{61} -8.79033 q^{62} +(-0.240485 + 7.93361i) q^{63} +1.00000 q^{64} +(-4.88979 + 8.94934i) q^{65} +(-7.98598 + 6.52257i) q^{66} +(0.912896 + 0.527061i) q^{67} +(2.83737 + 4.91448i) q^{68} +(1.72869 - 4.56049i) q^{69} +(-7.02230 - 2.58606i) q^{70} -6.16979 q^{71} +(0.599095 - 2.93957i) q^{72} +(-0.140240 + 0.242904i) q^{73} +(-0.160796 - 0.0928358i) q^{74} +(0.834392 + 5.12881i) q^{75} +1.94593 q^{76} +(5.44299 - 14.7802i) q^{77} +(6.13865 - 1.14757i) q^{78} +(4.18074 + 7.24125i) q^{79} +(2.44950 + 1.41422i) q^{80} +(-8.28217 - 3.52217i) q^{81} +(-3.50633 + 2.02438i) q^{82} +0.940520i q^{83} +(1.49371 + 4.33230i) q^{84} +16.0507i q^{85} +(-1.74089 - 3.01530i) q^{86} +(0.0721572 + 0.0883464i) q^{87} +(-2.97657 + 5.15557i) q^{88} +(4.61927 - 2.66694i) q^{89} +(5.62468 - 6.35322i) q^{90} +(-7.18508 + 6.27492i) q^{91} -2.81581i q^{92} +(2.44482 + 15.0277i) q^{93} +(-6.77981 - 3.91432i) q^{94} +(4.76654 + 2.75197i) q^{95} +(-0.278126 - 1.70957i) q^{96} +9.60289 q^{97} +(-5.32809 - 4.53998i) q^{98} +(13.3719 + 11.8385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Introduction

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