LMFDB - Embedded newform 546.2.bg.a.467.10

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			467.10
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.a.311.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.278126 + 1.70957i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.44950 - 1.41422i) q^{5} +(-1.61960 - 0.613923i) q^{6} +(2.60728 + 0.449563i) q^{7} +1.00000 q^{8} +(-2.84529 + 0.950954i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.278126 + 1.70957i) 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} +(-2.84529 + 0.950954i) q^{9} +(2.44950 - 1.41422i) q^{10} +(-2.97657 - 5.15557i) q^{11} +(1.34147 - 1.09565i) 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} +(0.599095 - 2.93957i) q^{18} +(0.972964 - 1.68522i) q^{19} +2.82844i q^{20} +(-0.0434094 + 4.58237i) q^{21} +5.95314 q^{22} +(2.43857 + 1.40791i) q^{23} +(0.278126 + 1.70957i) q^{24} +(1.50002 + 2.59812i) q^{25} +(-0.0848486 - 3.60455i) q^{26} +(-2.41708 - 4.59975i) q^{27} +(-0.914306 - 2.48275i) q^{28} -0.0658578i q^{29} +(3.09898 + 3.79427i) q^{30} +(-4.39516 - 7.61265i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(7.98598 - 6.52257i) 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} +(-4.06316 - 4.74244i) q^{39} +(-2.44950 - 1.41422i) q^{40} +4.04876i q^{41} +(-3.94674 - 2.32878i) q^{42} +3.48177 q^{43} +(-2.97657 + 5.15557i) q^{44} +(8.31439 + 1.69450i) 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} +(7.61252 - 6.21755i) q^{51} +(3.16406 + 1.72880i) q^{52} +(3.77930 - 2.18198i) q^{53} +(5.19204 + 0.206627i) 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} +(-4.83542 + 0.786662i) q^{60} +(-12.8084 - 7.39493i) q^{61} +8.79033 q^{62} +(-7.84598 + 1.20026i) q^{63} +1.00000 q^{64} +(10.1952 - 0.239989i) q^{65} +(1.65572 + 10.1773i) 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} +(-2.84529 + 0.950954i) q^{72} +(0.140240 + 0.242904i) q^{73} +(0.160796 - 0.0928358i) q^{74} +(-4.02448 + 3.28701i) 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} +(7.19137 - 5.41149i) q^{81} +(-3.50633 - 2.02438i) q^{82} -0.940520i q^{83} +(3.99015 - 2.25359i) q^{84} +16.0507i q^{85} +(-1.74089 + 3.01530i) q^{86} +(0.112589 - 0.0183168i) q^{87} +(-2.97657 - 5.15557i) q^{88} +(4.61927 + 2.66694i) q^{89} +(-5.62468 + 6.35322i) q^{90} +(-8.87162 + 3.50632i) q^{91} -2.81581i q^{92} +(11.7920 - 9.63114i) q^{93} +(-6.77981 + 3.91432i) q^{94} +(-4.76654 + 2.75197i) q^{95} +(1.34147 - 1.09565i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	0.278126	+	1.70957i	0.160576	+	0.987023i
$3$	0.278126	+	1.70957i	0.160576	+	0.987023i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.44950	−	1.41422i	−1.09545	−	0.632458i	−0.160427	−	0.987048i	$-0.551287\pi$
$5$	−2.44950	−	1.41422i	−1.09545	−	0.632458i	−0.935022	+	0.354590i	$0.884620\pi$
$6$	−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
$9$	−2.84529	+	0.950954i	−0.948431	+	0.316985i
$10$	2.44950	−	1.41422i	0.774599	−	0.447215i
$11$	−2.97657	−	5.15557i	−0.897470	−	1.55446i	−0.830718	−	0.556694i	$-0.812070\pi$
$11$	−2.97657	−	5.15557i	−0.897470	−	1.55446i	−0.0667525	−	0.997770i	$-0.521264\pi$
$12$	1.34147	−	1.09565i	0.387250	−	0.316287i
$13$	−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	−0.972431	−	0.233190i	$-0.925083\pi$
$17$	−2.83737	−	4.91448i	−0.688164	−	1.19194i	0.284267	−	0.958745i	$-0.408250\pi$
$18$	0.599095	−	2.93957i	0.141208	−	0.692864i
$19$	0.972964	−	1.68522i	0.223213	−	0.386617i	−0.732569	−	0.680693i	$-0.761679\pi$
$19$	0.972964	−	1.68522i	0.223213	−	0.386617i	0.955782	+	0.294077i	$0.0950121\pi$
$20$			2.82844i			0.632458i
$21$	−0.0434094	+	4.58237i	−0.00947272	+	0.999955i
$22$	5.95314			1.26921
$23$	2.43857	+	1.40791i	0.508476	+	0.293569i	0.732207	−	0.681082i	$-0.238490\pi$
$23$	2.43857	+	1.40791i	0.508476	+	0.293569i	−0.223731	+	0.974651i	$0.571824\pi$
$24$	0.278126	+	1.70957i	0.0567722	+	0.348965i
$25$	1.50002	+	2.59812i	0.300005	+	0.519624i
$26$	−0.0848486	−	3.60455i	−0.0166402	−	0.706911i
$27$	−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	$-0.00194640\pi$
$30$	3.09898	+	3.79427i	0.565794	+	0.692735i
$31$	−4.39516	−	7.61265i	−0.789395	−	1.36727i	−0.926338	−	0.376693i	$-0.877061\pi$
$31$	−4.39516	−	7.61265i	−0.789395	−	1.36727i	0.136944	−	0.990579i	$-0.456272\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	7.98598	−	6.52257i	1.39018	−	1.13543i
$34$	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	$-0.338192\pi$
$37$	−0.160796	−	0.0928358i	−0.0264348	−	0.0152621i	−0.513159	+	0.858293i	$0.671525\pi$
$38$	0.972964	+	1.68522i	0.157836	+	0.273379i
$39$	−4.06316	−	4.74244i	−0.650626	−	0.759399i
$40$	−2.44950	−	1.41422i	−0.387300	−	0.223607i
$41$			4.04876i			0.632310i	0.948707	+	0.316155i	$0.102392\pi$
$41$			4.04876i			0.632310i	−0.948707	+	0.316155i	$0.897608\pi$
$42$	−3.94674	−	2.32878i	−0.608996	−	0.359338i
$43$	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
$45$	8.31439	+	1.69450i	1.23944	+	0.252602i
$46$	−2.43857	+	1.40791i	−0.359547	+	0.207585i
$47$	6.77981	+	3.91432i	0.988937	+	0.570963i	0.904956	−	0.425505i	$-0.139903\pi$
$47$	6.77981	+	3.91432i	0.988937	+	0.570963i	0.0839804	+	0.996467i	$0.473237\pi$
$48$	−1.61960	−	0.613923i	−0.233769	−	0.0886122i
$49$	6.59579	+	2.34427i	0.942255	+	0.334896i
$50$	−3.00005			−0.424271
$51$	7.61252	−	6.21755i	1.06597	−	0.870631i
$52$	3.16406	+	1.72880i	0.438776	+	0.239741i
$53$	3.77930	−	2.18198i	0.519127	−	0.299718i	−0.217450	−	0.976071i	$-0.569774\pi$
$53$	3.77930	−	2.18198i	0.519127	−	0.299718i	0.736578	+	0.676353i	$0.236441\pi$
$54$	5.19204	+	0.206627i	0.706547	+	0.0281183i
$55$			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	−0.513361	+	0.858173i	$0.671600\pi$
$59$	−11.6234	+	6.71079i	−1.51324	+	0.873670i	−0.999880	+	0.0154976i	$0.995067\pi$
$60$	−4.83542	+	0.786662i	−0.624250	+	0.101558i
$61$	−12.8084	−	7.39493i	−1.63995	−	0.946823i	−0.980850	−	0.194765i	$-0.937606\pi$
$61$	−12.8084	−	7.39493i	−1.63995	−	0.946823i	−0.659096	−	0.752059i	$-0.729061\pi$
$62$	8.79033			1.11637
$63$	−7.84598	+	1.20026i	−0.988500	+	0.151219i
$64$	1.00000			0.125000
$65$	10.1952	−	0.239989i	1.26456	−	0.0297669i
$66$	1.65572	+	10.1773i	0.203806	+	1.25274i
$67$	−0.912896	+	0.527061i	−0.111528	+	0.0643907i	−0.554726	−	0.832033i	$-0.687177\pi$
$67$	−0.912896	+	0.527061i	−0.111528	+	0.0643907i	0.443198	+	0.896424i	$0.353844\pi$
$68$	−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	$0.619311\pi$
$72$	−2.84529	+	0.950954i	−0.335321	+	0.112071i
$73$	0.140240	+	0.242904i	0.0164139	+	0.0284297i	0.874116	−	0.485718i	$-0.161442\pi$
$73$	0.140240	+	0.242904i	0.0164139	+	0.0284297i	−0.857702	+	0.514147i	$0.828108\pi$
$74$	0.160796	−	0.0928358i	0.0186922	−	0.0107919i
$75$	−4.02448	+	3.28701i	−0.464707	+	0.379551i
$76$	−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	−0.529056	−	0.848587i	$-0.677454\pi$
$79$	4.18074	−	7.24125i	0.470370	−	0.814704i	0.999426	+	0.0338825i	$0.0107872\pi$
$80$	2.44950	−	1.41422i	0.273862	−	0.158114i
$81$	7.19137	−	5.41149i	0.799041	−	0.601276i
$82$	−3.50633	−	2.02438i	−0.387209	−	0.223556i
$83$		−	0.940520i		−	0.103235i	−0.998667	−	0.0516177i	$-0.983562\pi$
$83$		−	0.940520i		−	0.103235i	0.998667	−	0.0516177i	$-0.0164377\pi$
$84$	3.99015	−	2.25359i	0.435361	−	0.245887i
$85$			16.0507i			1.74094i
$86$	−1.74089	+	3.01530i	−0.187725	+	0.325149i
$87$	0.112589	−	0.0183168i	0.0120708	−	0.00196376i
$88$	−2.97657	−	5.15557i	−0.317304	−	0.549586i
$89$	4.61927	+	2.66694i	0.489642	+	0.282695i	0.724426	−	0.689353i	$-0.242105\pi$
$89$	4.61927	+	2.66694i	0.489642	+	0.282695i	−0.234784	+	0.972048i	$0.575438\pi$
$90$	−5.62468	+	6.35322i	−0.592893	+	0.669689i
$91$	−8.87162	+	3.50632i	−0.929999	+	0.367562i
$92$		−	2.81581i		−	0.293569i
$93$	11.7920	−	9.63114i	1.22277	−	0.998702i
$94$	−6.77981	+	3.91432i	−0.699284	+	0.403732i
$95$	−4.76654	+	2.75197i	−0.489037	+	0.282346i
$96$	1.34147	−	1.09565i	0.136913	−	0.111824i
$97$	−9.60289			−0.975026			−0.487513	−	0.873116i	$-0.662096\pi$
$97$	−9.60289			−0.975026			−0.487513	+	0.873116i	$0.662096\pi$
$98$	−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	$-0.273754\pi$
$101$	−3.31762	−	5.74628i	−0.330115	−	0.571777i	−0.982534	+	0.186082i	$0.940421\pi$
$102$	1.57830	+	9.70141i	0.156275	+	0.960582i
$103$	−6.33025	−	3.65477i	−0.623738	−	0.360115i	0.154585	−	0.987980i	$-0.450596\pi$
$103$	−6.33025	−	3.65477i	−0.623738	−	0.360115i	−0.778323	+	0.627864i	$0.783929\pi$
$104$	−3.07921	+	1.87576i	−0.301941	+	0.183933i
$105$	6.58680	−	11.1631i	0.642806	−	1.08941i
$106$			4.36396i			0.423866i
$107$	−14.1105	−	8.14672i	−1.36412	−	0.787573i	−0.373947	−	0.927450i	$-0.621996\pi$
$107$	−14.1105	−	8.14672i	−1.36412	−	0.787573i	−0.990169	+	0.139877i	$0.955329\pi$
$108$	−2.77497	+	4.39313i	−0.267021	+	0.422729i
$109$	−1.45673	+	0.841043i	−0.139529	+	0.0805573i	−0.568140	−	0.822932i	$-0.692337\pi$
$109$	−1.45673	+	0.841043i	−0.139529	+	0.0805573i	0.428610	+	0.903489i	$0.359003\pi$
$110$	−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	$-0.130257\pi$
$114$	−2.61041	+	2.13206i	−0.244487	+	0.199686i
$115$	−3.98217	−	6.89733i	−0.371340	−	0.643179i
$116$	−0.0570345	+	0.0329289i	−0.00529552	+	0.00305737i
$117$	6.97749	−	8.26527i	0.645069	−	0.764124i
$118$		−	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
$123$	−6.92166	+	1.12607i	−0.624105	+	0.101534i
$124$	−4.39516	+	7.61265i	−0.394697	+	0.683636i
$125$			5.65673i			0.505953i
$126$	2.88353	−	7.39495i	0.256885	−	0.658794i
$127$	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
$129$	0.968372	+	5.95235i	0.0852604	+	0.524075i
$130$	−4.88979	+	8.94934i	−0.428863	+	0.784909i
$131$	−8.86611	+	15.3566i	−0.774636	+	1.34171i	0.160363	+	0.987058i	$0.448733\pi$
$131$	−8.86611	+	15.3566i	−0.774636	+	1.34171i	−0.934999	+	0.354651i	$0.884600\pi$
$132$	−9.64170	−	3.65477i	−0.839202	−	0.318107i
$133$	3.29440	−	3.95643i	0.285661	−	0.343066i
$134$		−	1.05412i		−	0.0910622i
$135$	−0.584430	+	14.6854i	−0.0502997	+	1.26391i
$136$	−2.83737	−	4.91448i	−0.243303	−	0.421413i
$137$	−2.86927	−	4.96972i	−0.245138	−	0.424592i	0.717032	−	0.697040i	$-0.245500\pi$
$137$	−2.86927	−	4.96972i	−0.245138	−	0.424592i	−0.962170	+	0.272448i	$0.912167\pi$
$138$	−3.08515	−	3.77734i	−0.262625	−	0.321548i
$139$			8.16905i			0.692890i	0.938070	+	0.346445i	$0.112611\pi$
$139$			8.16905i			0.692890i	−0.938070	+	0.346445i	$0.887389\pi$
$140$	−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
$143$	18.8361	+	10.2918i	1.57515	+	0.860641i
$144$	0.599095	−	2.93957i	0.0499246	−	0.244964i
$145$	−0.0931373	+	0.161318i	−0.00773463	+	0.0133968i
$146$	−0.280481			−0.0232128
$147$	−2.17324	+	11.9280i	−0.179246	+	0.983804i
$148$			0.185672i			0.0152621i
$149$	−7.77314	+	13.4635i	−0.636801	+	1.10297i	0.349330	+	0.937000i	$0.386409\pi$
$149$	−7.77314	+	13.4635i	−0.636801	+	1.10297i	−0.986131	+	0.165971i	$0.946924\pi$
$150$	−0.834392	−	5.12881i	−0.0681278	−	0.418766i
$151$	18.1605	−	10.4850i	1.47788	−	0.853256i	0.478196	−	0.878253i	$-0.341291\pi$
$151$	18.1605	−	10.4850i	1.47788	−	0.853256i	0.999688	+	0.0249970i	$0.00795761\pi$
$152$	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
$156$	−2.07550	+	5.89002i	−0.166173	+	0.471579i
$157$	12.5843	−	7.26555i	1.00434	−	0.579854i	0.0948076	−	0.995496i	$-0.469776\pi$
$157$	12.5843	−	7.26555i	1.00434	−	0.579854i	0.909528	+	0.415642i	$0.136443\pi$
$158$	4.18074	+	7.24125i	0.332602	+	0.576083i
$159$	4.78138	+	5.85414i	0.379188	+	0.464263i
$160$			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	$-0.317577\pi$
$163$	1.09419	+	0.631733i	0.0857039	+	0.0494812i	−0.456536	+	0.889705i	$0.650910\pi$
$164$	3.50633	−	2.02438i	0.273798	−	0.158078i
$165$	−28.7860	+	4.68311i	−2.24098	+	0.364580i
$166$	0.814514	+	0.470260i	0.0632185	+	0.0364992i
$167$			14.8995i			1.15296i	0.817111	+	0.576480i	$0.195574\pi$
$167$			14.8995i			1.15296i	−0.817111	+	0.576480i	$0.804426\pi$
$168$	−0.0434094	+	4.58237i	−0.00334911	+	0.353538i
$169$	5.96307	−	11.5517i	0.458698	−	0.888592i
$170$	−13.9003	−	8.02533i	−1.06610	−	0.615515i
$171$	−1.16580	+	5.72019i	−0.0891506	+	0.437434i
$172$	−1.74089	−	3.01530i	−0.132741	−	0.229915i
$173$	5.85736	−	10.1453i	0.445327	−	0.771329i	−0.552748	−	0.833349i	$-0.686421\pi$
$173$	5.85736	−	10.1453i	0.445327	−	0.771329i	0.998075	+	0.0620193i	$0.0197540\pi$
$174$	−0.0404316	+	0.106663i	−0.00306511	+	0.00808611i
$175$	2.74296	+	7.44837i	0.207349	+	0.563044i
$176$	5.95314			0.448735
$177$	−14.7054	−	18.0047i	−1.10532	−	1.35331i
$178$	−4.61927	+	2.66694i	−0.346229	+	0.199895i
$179$	4.54314	−	2.62298i	0.339570	−	0.196051i	−0.320512	−	0.947245i	$-0.603855\pi$
$179$	4.54314	−	2.62298i	0.339570	−	0.196051i	0.660082	+	0.751194i	$0.270522\pi$
$180$	−2.68971	−	8.04773i	−0.200479	−	0.599842i
$181$		−	3.34763i		−	0.248827i	−0.992230	−	0.124414i	$-0.960295\pi$
$181$		−	3.34763i		−	0.248827i	0.992230	−	0.124414i	$-0.0397049\pi$
$182$	1.39925	−	9.43621i	0.103719	−	0.699459i
$183$	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
$186$	2.44482	+	15.0277i	0.179263	+	1.10189i
$187$	−16.8913	+	29.2566i	−1.23521	+	2.13945i
$188$		−	7.82865i		−	0.570963i
$189$	−4.23411	−	13.0795i	−0.307986	−	0.951391i
$190$		−	5.50393i		−	0.399297i
$191$	12.5958	+	7.27218i	0.911399	+	0.526196i	0.880881	−	0.473338i	$-0.156951\pi$
$191$	12.5958	+	7.27218i	0.911399	+	0.526196i	0.0305177	+	0.999534i	$0.490284\pi$
$192$	0.278126	+	1.70957i	0.0200720	+	0.123378i
$193$	3.56744	−	2.05966i	0.256790	−	0.148258i	−0.366079	−	0.930584i	$-0.619300\pi$
$193$	3.56744	−	2.05966i	0.256790	−	0.148258i	0.622869	+	0.782326i	$0.285967\pi$
$194$	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	$0.549152\pi$
$198$	−16.9384	+	5.66117i	−1.20376	+	0.402322i
$199$	−17.9961	+	10.3900i	−1.27571	+	0.736530i	−0.976056	−	0.217519i	$-0.930204\pi$
$199$	−17.9961	+	10.3900i	−1.27571	+	0.736530i	−0.299651	+	0.954049i	$0.596870\pi$
$200$	1.50002	+	2.59812i	0.106068	+	0.183715i
$201$	−1.15495	−	1.41407i	−0.0814639	−	0.0997411i
$202$	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
$207$	−8.27729	−	1.68694i	−0.575311	−	0.117250i
$208$	−0.0848486	−	3.60455i	−0.00588319	−	0.249931i
$209$	−11.5844			−0.801309
$210$	6.37414	+	11.2859i	0.439857	+	0.778801i
$211$	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
$213$	−1.71598	−	10.5477i	−0.117577	−	0.722718i
$214$	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
$219$	−0.376257	+	0.307309i	−0.0254251	+	0.0207660i
$220$	14.5822	−	8.41904i	0.983132	−	0.567612i
$221$	17.9552	+	9.81048i	1.20780	+	0.659924i
$222$	0.203431	+	0.249073i	0.0136534	+	0.0167167i
$223$	−7.45226			−0.499040			−0.249520	−	0.968370i	$-0.580273\pi$
$223$	−7.45226			−0.499040			−0.249520	+	0.968370i	$0.580273\pi$
$224$	−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	−0.397822	−	0.917463i	$-0.630234\pi$
$227$	2.98035	−	1.72071i	0.197813	−	0.114207i	0.595635	+	0.803255i	$0.296901\pi$
$228$	−0.541213	−	3.32671i	−0.0358427	−	0.220317i
$229$	11.6436	−	20.1673i	0.769429	−	1.33269i	−0.168444	−	0.985711i	$-0.553874\pi$
$229$	11.6436	−	20.1673i	0.769429	−	1.33269i	0.937873	−	0.346979i	$-0.112792\pi$
$230$	7.96435			0.525154
$231$	23.7540	−	13.4160i	1.56290	−	0.882705i
$232$		−	0.0658578i		−	0.00432378i
$233$	11.5261	+	6.65459i	0.755099	+	0.435957i	0.827533	−	0.561417i	$-0.189743\pi$
$233$	11.5261	+	6.65459i	0.755099	+	0.435957i	−0.0724345	+	0.997373i	$0.523077\pi$
$234$	3.66918	+	10.1753i	0.239862	+	0.665181i
$235$	−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	$0.496492\pi$
$240$	3.09898	+	3.79427i	0.200038	+	0.244919i
$241$	2.07800	+	3.59921i	0.133856	+	0.231845i	0.925160	−	0.379578i	$-0.123931\pi$
$241$	2.07800	+	3.59921i	0.133856	+	0.231845i	−0.791304	+	0.611423i	$0.790597\pi$
$242$	−12.2200	−	21.1656i	−0.785528	−	1.36058i
$243$	11.2514	+	10.7891i	0.721781	+	0.692122i
$244$			14.7899i			0.946823i
$245$	−12.8411	−	15.0702i	−0.820385	−	0.962797i
$246$	2.48563	−	6.55737i	0.158478	−	0.418083i
$247$	0.165109	+	7.01420i	0.0105056	+	0.446303i
$248$	−4.39516	−	7.61265i	−0.279093	−	0.483404i
$249$	1.60789	−	0.261583i	0.101896	−	0.0165771i
$250$	−4.89887	−	2.82837i	−0.309832	−	0.178882i
$251$	24.1872			1.52668			0.763341	−	0.645995i	$-0.223557\pi$
$251$	24.1872			1.52668			0.763341	+	0.645995i	$0.223557\pi$
$252$	4.96245	+	6.19468i	0.312605	+	0.390228i
$253$		−	16.7629i		−	1.05388i
$254$	−0.282065	+	0.488551i	−0.0176983	+	0.0306544i
$255$	−27.4398	+	4.46411i	−1.71835	+	0.279553i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.25640	+	9.10435i	−0.327885	+	0.567914i	−0.982092	−	0.188402i	$-0.939669\pi$
$257$	−5.25640	+	9.10435i	−0.327885	+	0.567914i	0.654207	+	0.756316i	$0.273003\pi$
$258$	−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
$261$	0.0626278	+	0.187385i	0.00387656	+	0.0115988i
$262$	−8.86611	−	15.3566i	−0.547750	−	0.948731i
$263$	25.1348	−	14.5116i	1.54988	−	0.894822i	0.551726	−	0.834025i	$-0.313969\pi$
$263$	25.1348	−	14.5116i	1.54988	−	0.894822i	0.998150	−	0.0607961i	$-0.0193640\pi$
$264$	7.98598	−	6.52257i	0.491503	−	0.401436i
$265$	−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	−0.970591	−	0.240733i	$-0.922612\pi$
$269$	−11.3788	−	19.7086i	−0.693777	−	1.20166i	0.276815	−	0.960923i	$-0.410721\pi$
$270$	−12.4257	−	7.84881i	−0.756203	−	0.477663i
$271$	7.71867	−	13.3691i	0.468876	−	0.812116i	−0.530491	−	0.847690i	$-0.677993\pi$
$271$	7.71867	−	13.3691i	0.468876	−	0.812116i	0.999367	+	0.0355739i	$0.0113259\pi$
$272$	5.67475			0.344082
$273$	−8.46175	−	14.1915i	−0.512128	−	0.858909i
$274$	5.73854			0.346678
$275$	8.92986	−	15.4670i	0.538491	−	0.932694i
$276$	4.81384	−	0.783151i	0.289759	−	0.0471402i
$277$	11.7800	+	20.4035i	0.707791	+	1.22593i	0.965675	+	0.259754i	$0.0836416\pi$
$277$	11.7800	+	20.4035i	0.707791	+	1.22593i	−0.257884	+	0.966176i	$0.583025\pi$
$278$	−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	$0.475355\pi$
$282$	−8.57747	−	10.5019i	−0.510781	−	0.625380i
$283$	−18.2700	+	10.5482i	−1.08604	+	0.627024i	−0.932519	−	0.361121i	$-0.882394\pi$
$283$	−18.2700	+	10.5482i	−1.08604	+	0.627024i	−0.153519	+	0.988146i	$0.549061\pi$
$284$	3.08490	+	5.34320i	0.183055	+	0.317060i
$285$	−6.03039	−	7.38337i	−0.357210	−	0.437353i
$286$	−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
$291$	−2.67081	−	16.4169i	−0.156566	−	0.962373i
$292$	0.140240	−	0.242904i	0.00820695	−	0.0142149i
$293$		−	13.6747i		−	0.798886i	−0.916758	−	0.399443i	$-0.869204\pi$
$293$		−	13.6747i		−	0.798886i	0.916758	−	0.399443i	$-0.130796\pi$
$294$	−9.24332	−	7.84608i	−0.539082	−	0.457593i
$295$	37.9621			2.21024
$296$	−0.160796	−	0.0928358i	−0.00934610	−	0.00539597i
$297$	−16.5198	+	26.1529i	−0.958574	+	1.51755i
$298$	−7.77314	−	13.4635i	−0.450286	−	0.779918i
$299$	−10.1497	+	0.238918i	−0.586975	+	0.0138170i
$300$	4.85888	+	1.84180i	0.280527	+	0.106336i
$301$	9.07795	+	1.56528i	0.523244	+	0.0902210i
$302$			20.9700i			1.20669i
$303$	8.90099	−	7.26991i	0.511348	−	0.417645i
$304$	0.972964	+	1.68522i	0.0558033	+	0.0966542i
$305$	20.9161	+	36.2277i	1.19765	+	2.07439i
$306$	−16.1463	+	5.39643i	−0.923023	+	0.308493i
$307$	−12.9292			−0.737908			−0.368954	−	0.929448i	$-0.620284\pi$
$307$	−12.9292			−0.737908			−0.368954	+	0.929448i	$0.620284\pi$
$308$	−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	$-0.307156\pi$
$311$	−7.53321	−	13.0479i	−0.427169	−	0.739878i	−0.996620	+	0.0821467i	$0.973822\pi$
$312$	−4.06316	−	4.74244i	−0.230031	−	0.268488i
$313$	10.6006	+	6.12027i	0.599183	+	0.345938i	0.768720	−	0.639585i	$-0.220894\pi$
$313$	10.6006	+	6.12027i	0.599183	+	0.345938i	−0.169537	+	0.985524i	$0.554227\pi$
$314$			14.5311i			0.820037i
$315$	20.9161	+	8.15588i	1.17849	+	0.459532i
$316$	−8.36148			−0.470370
$317$	7.30130	−	12.6462i	0.410082	−	0.710283i	−0.584816	−	0.811166i	$-0.698833\pi$
$317$	7.30130	−	12.6462i	0.410082	−	0.710283i	0.994898	+	0.100883i	$0.0321667\pi$
$318$	−7.46052	+	1.21373i	−0.418365	+	0.0680627i
$319$	−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
$324$	−8.28217	−	3.52217i	−0.460121	−	0.195676i
$325$	−9.49233	−	5.18647i	−0.526540	−	0.287694i
$326$	−1.09419	+	0.631733i	−0.0606018	+	0.0349885i
$327$	−1.84298	−	2.25647i	−0.101917	−	0.124783i
$328$			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	−0.950708	−	0.310087i	$-0.899642\pi$
$331$	−30.8306	−	17.8001i	−1.69461	−	0.978381i	−0.743897	−	0.668294i	$-0.767025\pi$
$332$	−0.814514	+	0.470260i	−0.0447023	+	0.0258089i
$333$	0.545795	+	0.111235i	0.0299094	+	0.00609564i
$334$	−12.9034	−	7.44977i	−0.706041	−	0.407633i
$335$	2.98151			0.162898
$336$	−3.94674	−	2.32878i	−0.215313	−	0.127045i
$337$	−2.05641			−0.112020			−0.0560098	−	0.998430i	$-0.517838\pi$
$337$	−2.05641			−0.112020			−0.0560098	+	0.998430i	$0.517838\pi$
$338$	7.02253	+	10.9400i	0.381975	+	0.595059i
$339$	14.4616	−	2.35273i	0.785449	−	0.127783i
$340$	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
$345$	10.6840	−	8.72615i	0.575205	−	0.469800i
$346$	5.85736	+	10.1453i	0.314894	+	0.545412i
$347$	−10.6785	+	6.16526i	−0.573254	+	0.330968i	−0.758448	−	0.651734i	$-0.774042\pi$
$347$	−10.6785	+	6.16526i	−0.573254	+	0.330968i	0.185194	+	0.982702i	$0.440709\pi$
$348$	−0.0721572	−	0.0883464i	−0.00386803	−	0.00473586i
$349$	31.2915			1.67500			0.837498	−	0.546441i	$-0.184018\pi$
$349$	31.2915			1.67500			0.837498	+	0.546441i	$0.184018\pi$
$350$	−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	−0.591614	−	0.806221i	$-0.701509\pi$
$353$	−3.55499	+	2.05247i	−0.189213	+	0.109242i	0.402401	+	0.915463i	$0.368176\pi$
$354$	22.9452	−	3.73289i	1.21952	−	0.198401i
$355$	15.1129	+	8.72543i	0.802109	+	0.463098i
$356$		−	5.33387i		−	0.282695i
$357$	22.6431	−	12.7886i	1.19840	−	0.676843i
$358$			5.24597i			0.277258i
$359$	12.8433	−	22.2452i	0.677842	−	1.17406i	−0.297788	−	0.954632i	$-0.596249\pi$
$359$	12.8433	−	22.2452i	0.677842	−	1.17406i	0.975630	−	0.219424i	$-0.0704178\pi$
$360$	8.31439	+	1.69450i	0.438207	+	0.0893081i
$361$	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
$364$	7.47238	+	5.92989i	0.391659	+	0.310811i
$365$		−	0.793322i		−	0.0415244i
$366$	16.2045	+	19.8402i	0.847024	+	1.03706i
$367$	−13.3337	+	7.69823i	−0.696015	+	0.401844i	−0.805861	−	0.592104i	$-0.798297\pi$
$367$	−13.3337	+	7.69823i	−0.696015	+	0.401844i	0.109847	+	0.993949i	$0.464964\pi$
$368$	−2.43857	+	1.40791i	−0.127119	+	0.0733922i
$369$	−3.85019	−	11.5199i	−0.200433	−	0.599703i
$370$	−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	−0.174485	−	0.984660i	$-0.555826\pi$
$373$	14.7842	−	25.6070i	0.765498	−	1.32588i	0.939983	−	0.341221i	$-0.110841\pi$
$374$	−16.8913	−	29.2566i	−0.873428	−	1.51282i
$375$	−9.67060	+	1.57328i	−0.499388	+	0.0812440i
$376$	6.77981	+	3.91432i	0.349642	+	0.201866i
$377$	0.123533	+	0.202790i	0.00636229	+	0.0104442i
$378$	13.4442	+	2.87288i	0.691495	+	0.147765i
$379$		−	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
$381$	0.156899	+	0.964422i	0.00803819	+	0.0494088i
$382$	−12.5958	+	7.27218i	−0.644456	+	0.372077i
$383$	23.7432	+	13.7081i	1.21322	+	0.700453i	0.963459	−	0.267855i	$-0.0863148\pi$
$383$	23.7432	+	13.7081i	1.21322	+	0.700453i	0.249761	+	0.968308i	$0.419648\pi$
$384$	−1.61960	−	0.613923i	−0.0826498	−	0.0313291i
$385$	−7.56977	+	43.9015i	−0.385791	+	2.23743i
$386$			4.11932i			0.209668i
$387$	−9.90666	+	3.31101i	−0.503584	+	0.168308i
$388$	4.80144	+	8.31634i	0.243756	+	0.422198i
$389$	28.0439	−	16.1912i	1.42188	−	0.820925i	0.425424	−	0.904994i	$-0.360125\pi$
$389$	28.0439	−	16.1912i	1.42188	−	0.820925i	0.996460	+	0.0840687i	$0.0267915\pi$
$390$	−16.6595	−	5.87041i	−0.843588	−	0.297260i
$391$		−	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
$396$	3.56650	−	17.4997i	0.179223	−	0.879393i
$397$	3.64884	−	6.31997i	0.183130	−	0.317190i	−0.759815	−	0.650139i	$-0.774710\pi$
$397$	3.64884	−	6.31997i	0.183130	−	0.317190i	0.942945	+	0.332949i	$0.108044\pi$
$398$		−	20.7801i		−	1.04161i
$399$	7.68008	+	4.53163i	0.384485	+	0.226866i
$400$	−3.00005			−0.150002
$401$	10.5538	−	18.2797i	0.527030	−	0.912842i	−0.472474	−	0.881345i	$-0.656639\pi$
$401$	10.5538	−	18.2797i	0.527030	−	0.912842i	0.999504	−	0.0314978i	$-0.0100277\pi$
$402$	1.80210	−	0.293179i	0.0898805	−	0.0146224i
$403$	27.8131	+	15.1967i	1.38547	+	0.757000i
$404$	−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
$408$	7.61252	−	6.21755i	0.376876	−	0.307814i
$409$	17.8308	+	30.8839i	0.881677	+	1.52711i	0.849475	+	0.527629i	$0.176919\pi$
$409$	17.8308	+	30.8839i	0.881677	+	1.52711i	0.0322023	+	0.999481i	$0.489748\pi$
$410$	5.72583	+	9.91743i	0.282779	+	0.489787i
$411$	7.69809	−	6.28744i	0.379719	−	0.310136i
$412$			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
$416$	3.16406	+	1.72880i	0.155131	+	0.0847612i
$417$	−13.9656	+	2.27203i	−0.683898	+	0.111262i
$418$	5.79219	−	10.0324i	0.283305	−	0.490699i
$419$	−26.4452			−1.29193			−0.645966	−	0.763367i	$-0.723545\pi$
$419$	−26.4452			−1.29193			−0.645966	+	0.763367i	$0.723545\pi$
$420$	−12.9609	−	0.122781i	−0.632429	−	0.00599109i
$421$			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
$423$	−23.0129	−	4.69011i	−1.11892	−	0.228041i
$424$	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
$429$	−12.3557	+	35.0641i	−0.596541	+	1.69291i
$430$	8.52859	−	4.92399i	0.411285	−	0.237456i
$431$	−0.156980	−	0.271898i	−0.00756147	−	0.0130968i	0.862220	−	0.506534i	$-0.169074\pi$
$431$	−0.156980	−	0.271898i	−0.00756147	−	0.0130968i	−0.869781	+	0.493437i	$0.835740\pi$
$432$	5.19204	+	0.206627i	0.249802	+	0.00994132i
$433$			7.25461i			0.348634i	0.984690	+	0.174317i	$0.0557718\pi$
$433$			7.25461i			0.348634i	−0.984690	+	0.174317i	$0.944228\pi$
$434$	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
$438$	−0.0780090	−	0.479503i	−0.00372742	−	0.0229115i
$439$	−14.6535	−	8.46021i	−0.699374	−	0.403784i	0.107740	−	0.994179i	$-0.465639\pi$
$439$	−14.6535	−	8.46021i	−0.699374	−	0.403784i	−0.807114	+	0.590395i	$0.798972\pi$
$440$			16.8381i			0.802724i
$441$	−20.9962	−	0.397836i	−0.999821	−	0.0189446i
$442$	−17.4737	+	10.6445i	−0.831141	+	0.506305i
$443$	−15.1134	−	8.72575i	−0.718061	−	0.414573i	0.0959775	−	0.995384i	$-0.469402\pi$
$443$	−15.1134	−	8.72575i	−0.718061	−	0.414573i	−0.814039	+	0.580811i	$0.802736\pi$
$444$	−0.317420	+	0.0516401i	−0.0150641	+	0.00245073i
$445$	−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	$0.360501\pi$
$450$	8.53602	−	2.85291i	0.402392	−	0.134488i
$451$	20.8737	−	12.0514i	0.982904	−	0.567480i
$452$	−7.32589	+	4.22960i	−0.344581	+	0.198944i
$453$	22.9758	+	28.1306i	1.07950	+	1.32169i
$454$			3.44142i			0.161514i
$455$	26.6897	+	3.95769i	1.25123	+	0.185539i
$456$	3.15162	+	1.19465i	0.147588	+	0.0559446i
$457$	−11.6122	−	6.70430i	−0.543195	−	0.313614i	0.203178	−	0.979142i	$-0.434873\pi$
$457$	−11.6122	−	6.70430i	−0.543195	−	0.313614i	−0.746373	+	0.665528i	$0.768206\pi$
$458$	11.6436	+	20.1673i	0.544068	+	0.942354i
$459$	−15.7472	+	24.9299i	−0.735018	+	1.16363i
$460$	−3.98217	+	6.89733i	−0.185670	+	0.321590i
$461$		−	26.0507i		−	1.21330i	−0.794968	−	0.606652i	$-0.792512\pi$
$461$		−	26.0507i		−	1.21330i	0.794968	−	0.606652i	$-0.207488\pi$
$462$	−0.258423	+	27.2795i	−0.0120229	+	1.26916i
$463$		−	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
$465$	−42.5049	+	6.91501i	−1.97112	+	0.320676i
$466$	−11.5261	+	6.65459i	−0.533935	+	0.308268i
$467$	3.10488	−	5.37781i	0.143677	−	0.248856i	−0.785202	−	0.619240i	$-0.787441\pi$
$467$	3.10488	−	5.37781i	0.143677	−	0.248856i	0.928879	+	0.370385i	$0.120774\pi$
$468$	−10.6467	−	1.91005i	−0.492143	−	0.0882922i
$469$	−2.61712	+	0.963789i	−0.120847	+	0.0445036i
$470$	22.1428			1.02137
$471$	15.9210	+	19.4931i	0.733602	+	0.898192i
$472$	−11.6234	+	6.71079i	−0.535012	+	0.308889i
$473$	−10.3637	−	17.9505i	−0.476526	−	0.825366i
$474$	−11.2167	+	9.16127i	−0.515200	+	0.420791i
$475$	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	−0.609578	−	0.792726i	$-0.708661\pi$
$479$	−4.98664	+	2.87904i	−0.227845	+	0.131547i	0.381732	+	0.924273i	$0.375328\pi$
$480$	−4.83542	+	0.786662i	−0.220706	+	0.0359060i
$481$	0.669263	−	0.0157540i	0.0305158	−	0.000718319i
$482$	−4.15601			−0.189301
$483$	−6.55741	+	11.1133i	−0.298372	+	0.505672i
$484$	24.4399			1.11091
$485$	23.5222	+	13.5806i	1.06809	+	0.616662i
$486$	−14.9694	+	4.34948i	−0.679024	+	0.197297i
$487$	−26.9169	+	15.5405i	−1.21972	+	0.704207i	−0.964858	−	0.262770i	$-0.915364\pi$
$487$	−26.9169	+	15.5405i	−1.21972	+	0.704207i	−0.254864	+	0.966977i	$0.582031\pi$
$488$	−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	$0.944475\pi$
$492$	4.43603	+	5.43130i	0.199992	+	0.244862i
$493$	−0.323657	+	0.186863i	−0.0145768	+	0.00841590i
$494$	−6.15703	−	3.36411i	−0.277018	−	0.151358i
$495$	−16.0123	−	47.9093i	−0.719697	−	2.15336i
$496$	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	$-0.366717\pi$
$499$	−4.05046	−	2.33853i	−0.181323	−	0.104687i	−0.587914	+	0.808923i	$0.700051\pi$
$500$	4.89887	−	2.82837i	0.219084	−	0.126488i
$501$	−25.4719	+	4.14395i	−1.13800	+	0.185138i
$502$	−12.0936	+	20.9467i	−0.539764	+	0.934898i
$503$	24.1876			1.07847			0.539236	−	0.842155i	$-0.318713\pi$
$503$	24.1876			1.07847			0.539236	+	0.842155i	$0.318713\pi$
$504$	−7.84598	+	1.20026i	−0.349488	+	0.0534640i
$505$			18.7673i			0.835136i
$506$	14.5171	+	8.38147i	0.645365	+	0.372602i
$507$	21.4070	+	6.98148i	0.950717	+	0.310059i
$508$	−0.282065	−	0.488551i	−0.0125146	−	0.0216759i
$509$	−24.6547	−	14.2344i	−1.09280	−	0.630929i	−0.158480	−	0.987362i	$-0.550659\pi$
$509$	−24.6547	−	14.2344i	−1.09280	−	0.630929i	−0.934321	+	0.356434i	$0.883993\pi$
$510$	9.85387	−	25.9956i	0.436337	−	1.15111i
$511$	0.256445	+	0.696364i	0.0113445	+	0.0308053i
$512$	1.00000			0.0441942
$513$	−10.1033	−	0.402080i	−0.446073	−	0.0177523i
$514$	−5.25640	−	9.10435i	−0.231850	−	0.401576i
$515$	10.3373	+	17.9047i	0.455515	+	0.788976i
$516$	4.67070	−	3.81481i	0.205616	−	0.167938i
$517$		−	46.6051i		−	2.04969i
$518$	0.460976	−	0.169761i	0.0202541	−	0.00745886i
$519$	18.9732	+	7.19194i	0.832829	+	0.315691i
$520$	10.1952	−	0.239989i	0.447091	−	0.0105242i
$521$	−1.14358	−	1.98074i	−0.0501012	−	0.0867779i	0.839887	−	0.542761i	$-0.182621\pi$
$521$	−1.14358	−	1.98074i	−0.0501012	−	0.0867779i	−0.889988	+	0.455983i	$0.849288\pi$
$522$	−0.193594	−	0.0394551i	−0.00847337	−	0.00172690i
$523$	2.06219	+	1.19060i	0.0901732	+	0.0520615i	0.544409	−	0.838820i	$-0.316754\pi$
$523$	2.06219	+	1.19060i	0.0901732	+	0.0520615i	−0.454235	+	0.890882i	$0.650087\pi$
$524$	17.7322			0.774636
$525$	−11.9707	+	6.76089i	−0.522442	+	0.295069i
$526$			29.0231i			1.26547i
$527$	−24.9414	+	43.1999i	−1.08647	+	1.88182i
$528$	1.65572	+	10.1773i	0.0720561	+	0.442912i
$529$	−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
$534$	−5.84407	−	7.15524i	−0.252897	−	0.309638i
$535$	23.0425	+	39.9107i	0.996213	+	1.72549i
$536$	−0.912896	+	0.527061i	−0.0394311	+	0.0227655i
$537$	5.74775	+	7.03732i	0.248034	+	0.303683i
$538$	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	$-0.259438\pi$
$541$	9.26863	+	5.35124i	0.398489	+	0.230068i	−0.287343	+	0.957828i	$0.592772\pi$
$542$	7.71867	+	13.3691i	0.331545	+	0.574253i
$543$	5.72302	−	0.931062i	0.245598	−	0.0399557i
$544$	−2.83737	+	4.91448i	−0.121651	+	0.210706i
$545$	4.75767			0.203796
$546$	16.5211	−	0.232336i	0.707037	−	0.00994306i
$547$	−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
$549$	43.4758	+	8.86053i	1.85550	+	0.378158i
$550$	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
$555$	−0.704488	+	0.575393i	−0.0299039	+	0.0244241i
$556$	7.07460	−	4.08452i	0.300030	−	0.173222i
$557$	14.7923	+	25.6210i	0.626769	+	1.08560i	0.988196	+	0.153195i	$0.0489563\pi$
$557$	14.7923	+	25.6210i	0.626769	+	1.08560i	−0.361427	+	0.932400i	$0.617710\pi$
$558$	−25.0110	+	8.35920i	−1.05880	+	0.353873i
$559$	−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	−0.961819	−	0.273686i	$-0.911757\pi$
$563$	−17.0347	−	29.5050i	−0.717928	−	1.24349i	0.243891	−	0.969803i	$-0.421576\pi$
$564$	13.3837	−	2.17735i	0.563554	−	0.0916830i
$565$	−11.9632	+	20.7208i	−0.503294	+	0.871731i
$566$		−	21.0964i		−	0.886746i
$567$	21.1827	−	10.8763i	0.889590	−	0.456760i
$568$	−6.16979			−0.258879
$569$	31.3283	+	18.0874i	1.31335	+	0.758263i	0.982649	−	0.185473i	$-0.0593819\pi$
$569$	31.3283	+	18.0874i	1.31335	+	0.758263i	0.330700	+	0.943736i	$0.392715\pi$
$570$	9.40938	−	1.53079i	0.394116	−	0.0641176i
$571$	−9.51154	−	16.4745i	−0.398046	−	0.689435i	0.595439	−	0.803400i	$-0.296978\pi$
$571$	−9.51154	−	16.4745i	−0.398046	−	0.689435i	−0.993485	+	0.113965i	$0.963645\pi$
$572$	−0.505116	−	21.4584i	−0.0211199	−	0.897222i
$573$	−8.92911	+	23.5560i	−0.373019	+	0.984066i
$574$	−8.23189	−	6.85444i	−0.343592	−	0.286099i
$575$			8.44758i			0.352289i
$576$	−2.84529	+	0.950954i	−0.118554	+	0.0396231i
$577$	−11.4956	−	19.9110i	−0.478569	−	0.828906i	0.521129	−	0.853478i	$-0.325511\pi$
$577$	−11.4956	−	19.9110i	−0.478569	−	0.828906i	−0.999698	+	0.0245722i	$0.992178\pi$
$578$	−7.60139	−	13.1660i	−0.316176	−	0.547633i
$579$	4.51334	+	5.52596i	0.187568	+	0.229651i
$580$	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
$585$	−28.7802	+	10.3781i	−1.18992	+	0.429080i
$586$	11.8427	+	6.83736i	0.489215	+	0.282449i
$587$		−	19.0243i		−	0.785216i	−0.919706	−	0.392608i	$-0.871573\pi$
$587$		−	19.0243i		−	0.785216i	0.919706	−	0.392608i	$-0.128427\pi$
$588$	11.4166	−	4.08191i	0.470811	−	0.168335i
$589$	−17.1053			−0.704813
$590$	−18.9810	+	32.8761i	−0.781437	+	1.35349i
$591$	−1.20080	−	7.38102i	−0.0493942	−	0.303614i
$592$	0.160796	−	0.0928358i	0.00660869	−	0.00381553i
$593$	39.8303	+	22.9960i	1.63563	+	0.944333i	0.982312	+	0.187253i	$0.0599584\pi$
$593$	39.8303	+	22.9960i	1.63563	+	0.944333i	0.653322	+	0.757080i	$0.273375\pi$
$594$	−14.3892	−	27.3830i	−0.590396	−	1.12354i
$595$	−7.21578	+	41.8485i	−0.295818	+	1.71562i
$596$	15.5463			0.636801
$597$	−22.7677	−	27.8759i	−0.931820	−	1.14088i
$598$	4.86797	−	8.90940i	0.199066	−	0.364332i
$599$	−35.1898	+	20.3169i	−1.43782	+	0.830124i	−0.997698	−	0.0678154i	$-0.978397\pi$
$599$	−35.1898	+	20.3169i	−1.43782	+	0.830124i	−0.440119	+	0.897939i	$0.645064\pi$
$600$	−4.02448	+	3.28701i	−0.164299	+	0.134192i
$601$			14.9537i			0.609973i	0.952357	+	0.304986i	$0.0986519\pi$
$601$			14.9537i			0.609973i	−0.952357	+	0.304986i	$0.901348\pi$
$602$	−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
$606$	1.84543	+	11.3434i	0.0749656	+	0.460796i
$607$	−38.9035	−	22.4609i	−1.57904	−	0.911661i	−0.994993	−	0.0999432i	$-0.968134\pi$
$607$	−38.9035	−	22.4609i	−1.57904	−	0.911661i	−0.584050	−	0.811718i	$-0.698533\pi$
$608$	−1.94593			−0.0789178
$609$	0.301785	+	0.00285885i	0.0122289	+	0.000115846i
$610$	−41.8322			−1.69373
$611$	−28.2188	+	0.664250i	−1.14161	+	0.0268727i
$612$	3.39971	−	16.6813i	0.137425	−	0.674303i
$613$	−21.2198	+	12.2513i	−0.857062	+	0.494825i	−0.863027	−	0.505157i	$-0.831434\pi$
$613$	−21.2198	+	12.2513i	−0.857062	+	0.494825i	0.00596561	+	0.999982i	$0.498101\pi$
$614$	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	$0.533128\pi$
$618$	8.00871	+	9.80555i	0.322158	+	0.394437i
$619$	23.5913	+	40.8613i	0.948214	+	1.64235i	0.749185	+	0.662360i	$0.230445\pi$
$619$	23.5913	+	40.8613i	0.948214	+	1.64235i	0.199028	+	0.979994i	$0.436221\pi$
$620$	21.5319	−	12.4314i	0.864741	−	0.499259i
$621$	0.581822	−	14.6198i	0.0233477	−	0.586673i
$622$	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
$627$	−3.22192	−	19.8044i	−0.128671	−	0.790910i
$628$	−12.5843	−	7.26555i	−0.502168	−	0.289927i
$629$			1.05364i			0.0420114i
$630$	−17.5213	+	14.0360i	−0.698064	+	0.559206i
$631$			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
$633$	2.21170	+	13.5948i	0.0879070	+	0.540344i
$634$	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
$637$	−24.7071	+	5.15360i	−0.978931	+	0.204193i
$638$		−	0.392061i		−	0.0155218i
$639$	17.5549	−	5.86719i	0.694460	−	0.232103i
$640$	2.44950	−	1.41422i	0.0968249	−	0.0559019i
$641$	−22.4818	+	12.9799i	−0.887978	+	0.512674i	−0.873281	−	0.487218i	$-0.838012\pi$
$641$	−22.4818	+	12.9799i	−0.887978	+	0.512674i	−0.0146975	+	0.999892i	$0.504679\pi$
$642$	17.8519	+	21.8572i	0.704559	+	0.862635i
$643$	38.3382			1.51191			0.755956	−	0.654622i	$-0.227172\pi$
$643$	38.3382			1.51191			0.755956	+	0.654622i	$0.227172\pi$
$644$	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	−0.984326	−	0.176361i	$-0.943567\pi$
$647$	−16.4037	−	28.4120i	−0.644896	−	1.11699i	0.339430	−	0.940631i	$-0.389766\pi$
$648$	7.19137	−	5.41149i	0.282504	−	0.212583i
$649$	69.1959	+	39.9503i	2.71618	+	1.56819i
$650$	9.23778	−	5.62737i	0.362336	−	0.220723i
$651$	35.0748	−	19.8098i	1.37469	−	0.776407i
$652$		−	1.26347i		−	0.0494812i
$653$	2.21204	+	1.27712i	0.0865637	+	0.0499776i	0.542657	−	0.839954i	$-0.317418\pi$
$653$	2.21204	+	1.27712i	0.0865637	+	0.0499776i	−0.456093	+	0.889932i	$0.650752\pi$
$654$	2.87565	−	0.467832i	0.112447	−	0.0182937i
$655$	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	$0.921131\pi$
$660$	18.4487	+	22.5878i	0.718114	+	0.879230i
$661$	−3.19978	−	5.54218i	−0.124457	−	0.215566i	0.797064	−	0.603895i	$-0.206386\pi$
$661$	−3.19978	−	5.54218i	−0.124457	−	0.215566i	−0.921521	+	0.388330i	$0.873052\pi$
$662$	30.8306	−	17.8001i	1.19827	−	0.691820i
$663$	−11.7779	+	33.4244i	−0.457417	+	1.29809i
$664$		−	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
$669$	−2.07267	−	12.7402i	−0.0801340	−	0.492564i
$670$	−1.49076	+	2.58207i	−0.0575930	+	0.0997540i
$671$			88.0461i			3.39898i
$672$	3.99015	−	2.25359i	0.153924	−	0.0869342i
$673$	−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
$675$	8.32503	−	13.1796i	0.320431	−	0.507283i
$676$	−12.9856	+	0.611682i	−0.499446	+	0.0235262i
$677$	9.07040	−	15.7104i	0.348604	−	0.603800i	−0.637398	−	0.770535i	$-0.719989\pi$
$677$	9.07040	−	15.7104i	0.348604	−	0.603800i	0.986002	+	0.166735i	$0.0533225\pi$
$678$	−5.19330	+	13.7005i	−0.199448	+	0.526165i
$679$	−25.0374	−	4.31710i	−0.960847	−	0.165675i
$680$			16.0507i			0.615515i
$681$	3.77059	+	4.61656i	0.144489	+	0.176907i
$682$	−26.1650	−	45.3192i	−1.00191	−	1.73536i
$683$	8.00820	+	13.8706i	0.306425	+	0.530744i	0.977578	−	0.210575i	$-0.0675337\pi$
$683$	8.00820	+	13.8706i	0.306425	+	0.530744i	−0.671152	+	0.741319i	$0.734200\pi$
$684$	5.53673	−	1.85049i	0.211702	−	0.0707552i
$685$			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
$689$	−7.54440	+	13.8078i	−0.287419	+	0.526037i
$690$	2.21509	+	13.6156i	0.0843271	+	0.518339i
$691$	7.72531	−	13.3806i	0.293885	−	0.509023i	−0.680840	−	0.732432i	$-0.738385\pi$
$691$	7.72531	−	13.3806i	0.293885	−	0.509023i	0.974725	+	0.223409i	$0.0717185\pi$
$692$	−11.7147			−0.445327
$693$	29.5422	+	36.8778i	1.12221	+	1.40087i
$694$		−	12.3305i		−	0.468060i
$695$	11.5528	−	20.0101i	0.438223	−	0.759025i
$696$	0.112589	−	0.0183168i	0.00426767	−	0.000694295i
$697$	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	$-0.0766007\pi$
$702$	−16.3750	+	9.10277i	−0.618033	+	0.343562i
$703$	−0.312898	+	0.180652i	−0.0118012	+	0.00681341i
$704$	−2.97657	−	5.15557i	−0.112184	−	0.194308i
$705$	29.7040	−	24.2608i	1.11872	−	0.913716i
$706$		−	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	$-0.136179\pi$
$709$	26.7736	+	15.4578i	1.00550	+	0.580528i	0.0956324	+	0.995417i	$0.469513\pi$
$710$	−15.1129	+	8.72543i	−0.567177	+	0.327460i
$711$	−5.00932	+	24.5792i	−0.187864	+	0.921791i
$712$	4.61927	+	2.66694i	0.173114	+	0.0999477i
$713$		−	24.7519i		−	0.926967i
$714$	−0.246338	+	26.0038i	−0.00921896	+	0.973168i
$715$	−31.5842	−	51.8480i	−1.18118	−	1.93901i
$716$	−4.54314	−	2.62298i	−0.169785	−	0.0980255i
$717$	0.0947636	+	0.582489i	0.00353901	+	0.0217535i
$718$	12.8433	+	22.2452i	0.479306	+	0.830183i
$719$	7.90278	−	13.6880i	0.294724	−	0.510477i	−0.680197	−	0.733030i	$-0.738106\pi$
$719$	7.90278	−	13.6880i	0.294724	−	0.510477i	0.974921	+	0.222553i	$0.0714390\pi$
$720$	−5.62468	+	6.35322i	−0.209619	+	0.236771i
$721$	−14.8617	−	12.3748i	−0.553478	−	0.460863i
$722$	−15.2134			−0.566183
$723$	−5.57517	+	4.55354i	−0.207343	+	0.169348i
$724$	−2.89913	+	1.67381i	−0.107745	+	0.0622068i
$725$	0.171106	−	0.0987883i	0.00635473	−	0.00366891i
$726$	32.7855	−	26.7776i	1.21678	−	0.993811i
$727$		−	40.5576i		−	1.50420i	−0.659050	−	0.752099i	$-0.729041\pi$
$727$		−	40.5576i		−	1.50420i	0.659050	−	0.752099i	$-0.270959\pi$
$728$	−8.87162	+	3.50632i	−0.328804	+	0.129953i
$729$	−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
$732$	−25.2844	+	4.11344i	−0.934537	+	0.152037i
$733$	8.36320	−	14.4855i	0.308902	−	0.535033i	−0.669221	−	0.743064i	$-0.733372\pi$
$733$	8.36320	−	14.4855i	0.308902	−	0.535033i	0.978122	+	0.208030i	$0.0667053\pi$
$734$		−	15.3965i		−	0.568294i
$735$	22.1921	−	26.1441i	0.818569	−	0.964341i
$736$		−	2.81581i		−	0.103792i
$737$	5.43460	+	3.13767i	0.200186	+	0.115577i
$738$	11.9016	+	2.42559i	0.438105	+	0.0892874i
$739$	−13.4521	+	7.76657i	−0.494843	+	0.285698i	−0.726582	−	0.687080i	$-0.758892\pi$
$739$	−13.4521	+	7.76657i	−0.494843	+	0.285698i	0.231738	+	0.972778i	$0.425559\pi$
$740$	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	$0.562535\pi$
$744$	11.7920	−	9.63114i	0.432315	−	0.353095i
$745$	38.0806	−	21.9858i	1.39516	−	0.805499i
$746$	14.7842	+	25.6070i	0.541289	+	0.937540i
$747$	0.894391	+	2.67605i	0.0327241	+	0.0979117i
$748$	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	−0.881368	−	0.472431i	$-0.843377\pi$
$751$	−0.864522	+	1.49740i	−0.0315468	+	0.0546407i	0.849821	+	0.527072i	$0.176710\pi$
$752$	−6.77981	+	3.91432i	−0.247234	+	0.142741i
$753$	6.72709	+	41.3498i	0.245149	+	1.50687i
$754$	−0.237388	+	0.00558794i	−0.00864516	+	0.000203501i
$755$	−59.3122			−2.15859
$756$	−9.21009	+	10.2066i	−0.334968	+	0.371210i
$757$	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
$759$	28.6575	−	4.66221i	1.04020	−	0.169228i
$760$	−4.76654	+	2.75197i	−0.172901	+	0.0998243i
$761$	−9.00493	−	5.19900i	−0.326429	−	0.188464i	0.327826	−	0.944738i	$-0.393684\pi$
$761$	−9.00493	−	5.19900i	−0.326429	−	0.188464i	−0.654254	+	0.756275i	$0.727017\pi$
$762$	−0.913664	−	0.346332i	−0.0330985	−	0.0125463i
$763$	−4.17620	+	1.53794i	−0.151189	+	0.0556772i
$764$		−	14.5444i		−	0.526196i
$765$	−15.2634	−	45.6688i	−0.551851	−	1.65116i
$766$	−23.7432	+	13.7081i	−0.857876	+	0.495295i
$767$	23.2032	−	42.4667i	0.837818	−	1.53338i
$768$	1.34147	−	1.09565i	0.0484062	−	0.0395359i
$769$	−20.6870			−0.745993			−0.372997	−	0.927833i	$-0.621670\pi$
$769$	−20.6870			−0.745993			−0.372997	+	0.927833i	$0.621670\pi$
$770$	−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	−0.619873	−	0.784702i	$-0.712816\pi$
$773$	−6.95733	+	4.01681i	−0.250238	+	0.144475i	0.369635	+	0.929177i	$0.379483\pi$
$774$	2.08591	−	10.2349i	0.0749766	−	0.367887i
$775$	13.1857	−	22.8383i	0.473645	−	0.820377i
$776$	−9.60289			−0.344724
$777$	0.432388	−	0.732799i	0.0155118	−	0.0262890i
$778$			32.3824i			1.16096i
$779$	6.82307	+	3.93930i	0.244462	+	0.141140i
$780$	13.4137	−	11.4924i	0.480287	−	0.411493i
$781$	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
$786$	23.7873	−	19.4283i	0.848464	−	0.692986i
$787$	−10.2024	−	17.6710i	−0.363675	−	0.629904i	0.624887	−	0.780715i	$-0.285145\pi$
$787$	−10.2024	−	17.6710i	−0.363675	−	0.629904i	−0.988563	+	0.150811i	$0.951812\pi$
$788$	2.15873	+	3.73903i	0.0769015	+	0.133197i
$789$	31.7992	+	38.9337i	1.13208	+	1.38608i
$790$		−	23.6499i		−	0.841426i
$791$	3.80294	−	22.0555i	0.135217	−	0.784203i
$792$	13.3719	+	11.8385i	0.475151	+	0.420664i
$793$	53.3108	−	1.25490i	1.89312	−	0.0445627i
$794$	3.64884	+	6.31997i	0.129492	+	0.224287i
$795$	−3.43296	−	21.1016i	−0.121755	−	0.748397i
$796$	17.9961	+	10.3900i	0.637854	+	0.368265i
$797$	3.19379			0.113130			0.0565649	−	0.998399i	$-0.481985\pi$
$797$	3.19379			0.113130			0.0565649	+	0.998399i	$0.481985\pi$
$798$	−7.76455	+	4.38533i	−0.274862	+	0.155239i
$799$		−	44.4256i		−	1.57167i
$800$	1.50002	−	2.59812i	0.0530339	−	0.0918574i
$801$	−15.6793	−	3.19550i	−0.554001	−	0.112907i
$802$	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
$807$	30.5286	−	24.9344i	1.07466	−	0.877731i
$808$	−3.31762	−	5.74628i	−0.116713	−	0.202154i
$809$	−15.7183	+	9.07497i	−0.552626	+	0.319059i	−0.750181	−	0.661233i	$-0.770033\pi$
$809$	−15.7183	+	9.07497i	−0.552626	+	0.319059i	0.197554	+	0.980292i	$0.436700\pi$
$810$	9.96222	−	23.4256i	0.350037	−	0.823091i
$811$	23.7993			0.835708			0.417854	−	0.908514i	$-0.362782\pi$
$811$	23.7993			0.835708			0.417854	+	0.908514i	$0.362782\pi$
$812$	−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
$816$	1.57830	+	9.70141i	0.0552514	+	0.339617i
$817$	3.38764	−	5.86756i	0.118518	−	0.205280i
$818$	−35.6616			−1.24688
$819$	21.9080	−	18.4130i	0.765528	−	0.643403i
$820$	−11.4517			−0.399909
$821$	−14.0903	+	24.4051i	−0.491755	+	0.851744i	−0.999955	−	0.00949494i	$-0.996978\pi$
$821$	−14.0903	+	24.4051i	−0.491755	+	0.851744i	0.508200	+	0.861239i	$0.330311\pi$
$822$	1.59604	+	9.81046i	0.0556681	+	0.342179i
$823$	−17.6636	−	30.5942i	−0.615714	−	1.06645i	−0.990259	−	0.139239i	$-0.955534\pi$
$823$	−17.6636	−	30.5942i	−0.615714	−	1.06645i	0.374545	−	0.927209i	$-0.377799\pi$
$824$	−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	$0.685914\pi$
$828$	2.67771	+	8.01181i	0.0930569	+	0.278430i
$829$	19.0489	−	10.9979i	0.661597	−	0.381973i	−0.131288	−	0.991344i	$-0.541911\pi$
$829$	19.0489	−	10.9979i	0.661597	−	0.381973i	0.792885	+	0.609371i	$0.208578\pi$
$830$	−1.33010	−	2.30380i	−0.0461684	−	0.0799661i
$831$	−31.6051	+	25.8135i	−1.09637	+	0.895462i
$832$	−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
$837$	−24.3929	+	38.6170i	−0.843140	+	1.33480i
$838$	13.2226	−	22.9022i	0.456767	−	0.791143i
$839$			14.3301i			0.494731i	0.968922	+	0.247366i	$0.0795649\pi$
$839$			14.3301i			0.494731i	−0.968922	+	0.247366i	$0.920435\pi$
$840$	6.58680	−	11.1631i	0.227266	−	0.385164i
$841$	28.9957			0.999850
$842$	−12.7625	−	7.36842i	−0.439824	−	0.253933i
$843$	0.721220	+	4.43317i	0.0248401	+	0.152686i
$844$	−3.97607	−	6.88675i	−0.136862	−	0.237052i
$845$	−30.9431	+	19.8628i	−1.06448	+	0.683301i
$846$	15.5682	−	17.5847i	0.535245	−	0.604574i
$847$	−41.3761	+	49.6909i	−1.42170	+	1.70740i
$848$			4.36396i			0.149859i
$849$	−23.1143	−	28.3002i	−0.793279	−	0.971260i
$850$	8.51226	+	14.7437i	0.291968	+	0.505704i
$851$	−0.261408	−	0.452773i	−0.00896097	−	0.0155208i
$852$	−8.27661	+	6.75994i	−0.283552	+	0.231592i
$853$	−33.9556			−1.16262			−0.581309	−	0.813683i	$-0.697459\pi$
$853$	−33.9556			−1.16262			−0.581309	+	0.813683i	$0.697459\pi$
$854$	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	$-0.123143\pi$
$857$	3.99034	+	6.91148i	0.136307	+	0.236092i	−0.789789	+	0.613379i	$0.789810\pi$
$858$	−24.1885	−	28.2324i	−0.825783	−	0.963840i
$859$	13.2780	+	7.66606i	0.453039	+	0.261562i	0.709113	−	0.705095i	$-0.249096\pi$
$859$	13.2780	+	7.66606i	0.453039	+	0.261562i	−0.256074	+	0.966657i	$0.582429\pi$
$860$			9.84797i			0.335813i
$861$	−18.5529	−	0.175755i	−0.632282	−	0.00598970i
$862$	0.313960			0.0106935
$863$	−11.2232	+	19.4391i	−0.382041	+	0.661714i	−0.991354	−	0.131216i	$-0.958112\pi$
$863$	−11.2232	+	19.4391i	−0.382041	+	0.661714i	0.609313	+	0.792930i	$0.291445\pi$
$864$	−2.77497	+	4.39313i	−0.0944062	+	0.149457i
$865$	−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
$870$	0.249882	−	0.204092i	0.00847180	−	0.00691937i
$871$	1.82236	−	3.33530i	0.0617483	−	0.113012i
$872$	−1.45673	+	0.841043i	−0.0493311	+	0.0284813i
$873$	27.3230	−	9.13191i	0.924744	−	0.309068i
$874$			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	$-0.0676464\pi$
$877$	38.0125	+	21.9465i	1.28359	+	0.741082i	0.306088	+	0.952003i	$0.400980\pi$
$878$	14.6535	−	8.46021i	0.494532	−	0.285518i
$879$	23.3780	−	3.80329i	0.788519	−	0.128282i
$880$	−14.5822	−	8.41904i	−0.491566	−	0.283806i
$881$	−22.2301			−0.748951			−0.374475	−	0.927237i	$-0.622177\pi$
$881$	−22.2301			−0.748951			−0.374475	+	0.927237i	$0.622177\pi$
$882$	10.8427	−	17.9844i	0.365091	−	0.605565i
$883$	5.75781			0.193766			0.0968828	−	0.995296i	$-0.469113\pi$
$883$	5.75781			0.193766			0.0968828	+	0.995296i	$0.469113\pi$
$884$	−0.481494	−	20.4549i	−0.0161944	−	0.687974i
$885$	10.5582	+	64.8990i	0.354911	+	2.18156i
$886$	15.1134	−	8.72575i	0.507746	−	0.293147i
$887$	17.5629	−	30.4199i	0.589705	−	1.02140i	−0.404566	−	0.914509i	$-0.632577\pi$
$887$	17.5629	−	30.4199i	0.589705	−	1.02140i	0.994271	−	0.106890i	$-0.0340894\pi$
$888$	0.113988	−	0.300714i	0.00382519	−	0.0100913i
$889$	1.47084	+	0.253612i	0.0493305	+	0.00850586i
$890$	15.0865			0.505701
$891$	−49.3049	−	20.9680i	−1.65178	−	0.702453i
$892$	3.72613	+	6.45385i	0.124760	+	0.216091i
$893$	13.1930	−	7.61699i	0.441487	−	0.254893i
$894$	20.8549	−	17.0333i	0.697493	−	0.569679i
$895$	−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
$900$	−1.79732	+	8.81886i	−0.0599105	+	0.293962i
$901$	−21.4466	−	12.3822i	−0.714490	−	0.412511i
$902$			24.1029i			0.802537i
$903$	−0.151142	+	15.9548i	−0.00502969	+	0.530942i
$904$		−	8.45921i		−	0.281349i
$905$	−4.73427	+	8.20000i	−0.157373	+	0.272577i
$906$	−35.8497	+	5.83230i	−1.19103	+	0.193765i
$907$	19.1076	+	33.0953i	0.634456	+	1.09891i	0.986630	+	0.162975i	$0.0521091\pi$
$907$	19.1076	+	33.0953i	0.634456	+	1.09891i	−0.352174	+	0.935934i	$0.614558\pi$
$908$	−2.98035	−	1.72071i	−0.0989065	−	0.0571037i
$909$	14.9040	+	13.1950i	0.494336	+	0.437649i
$910$	−16.7723	+	21.1351i	−0.555997	+	0.700623i
$911$			24.2986i			0.805050i	0.915409	+	0.402525i	$0.131867\pi$
$911$			24.2986i			0.805050i	−0.915409	+	0.402525i	$0.868133\pi$
$912$	−2.61041	+	2.13206i	−0.0864392	+	0.0705995i
$913$	−4.84892	+	2.79952i	−0.160476	+	0.0926507i
$914$	11.6122	−	6.70430i	0.384097	−	0.221759i
$915$	−56.1167	+	45.8335i	−1.85516	+	1.51521i
$916$	−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	0.325654	+	0.945489i	$0.394415\pi$
$919$	−19.8864	+	34.4442i	−0.655990	+	1.13621i	−0.981645	+	0.190719i	$0.938918\pi$
$920$	−3.98217	−	6.89733i	−0.131288	−	0.227398i
$921$	−3.59595	−	22.1034i	−0.118490	−	0.728333i
$922$	22.5606	+	13.0254i	0.742994	+	0.428968i
$923$	18.9981	−	11.5730i	0.625330	−	0.380931i
$924$	−23.4955	−	13.8636i	−0.772946	−	0.456077i
$925$		−	0.557024i		−	0.0183148i
$926$	1.95593	+	1.12925i	0.0642757	+	0.0371096i
$927$	21.4869	+	4.37911i	0.705724	+	0.143829i
$928$	−0.0570345	+	0.0329289i	−0.00187225	+	0.00108094i
$929$	22.9223	+	13.2342i	0.752058	+	0.434201i	0.826437	−	0.563029i	$-0.190364\pi$
$929$	22.9223	+	13.2342i	0.752058	+	0.434201i	−0.0743792	+	0.997230i	$0.523698\pi$
$930$	15.2639	−	40.2679i	0.500523	−	1.32044i
$931$	10.3681	−	8.83448i	0.339800	−	0.289538i
$932$		−	13.3092i		−	0.435957i
$933$	20.2112	−	16.5075i	0.661684	−	0.540433i
$934$	3.10488	+	5.37781i	0.101595	+	0.175967i
$935$	82.7504	−	47.7759i	2.70623	−	1.56244i
$936$	6.97749	−	8.26527i	0.228066	−	0.270159i
$937$		−	31.6644i		−	1.03443i	−0.855856	−	0.517215i	$-0.826969\pi$
$937$		−	31.6644i		−	1.03443i	0.855856	−	0.517215i	$-0.173031\pi$
$938$	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	−0.190608	−	0.981666i	$-0.561046\pi$
$941$	17.3083	−	9.99297i	0.564236	−	0.325762i	0.754844	+	0.655905i	$0.227713\pi$
$942$	−24.8420	+	4.04147i	−0.809396	+	0.131678i
$943$	−5.70028	+	9.87317i	−0.185627	+	0.321515i
$944$		−	13.4216i		−	0.436835i
$945$	−8.12576	+	38.0261i	−0.264331	+	1.23699i
$946$	20.7275			0.673909
$947$	3.07700	−	5.32952i	0.0999891	−	0.173186i	−0.811691	−	0.584087i	$-0.801453\pi$
$947$	3.07700	−	5.32952i	0.0999891	−	0.173186i	0.911680	+	0.410901i	$0.134786\pi$
$948$	−2.32554	−	14.2946i	−0.0755302	−	0.464266i
$949$	−0.887458	−	0.484894i	−0.0288081	−	0.0157403i
$950$	−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	$-0.136646\pi$
$954$	−4.14993	−	12.4168i	−0.134359	−	0.402007i
$955$	−20.5689	−	35.6264i	−0.665593	−	1.15284i
$956$	−0.170361	−	0.295074i	−0.00550986	−	0.00954336i
$957$	−0.429562	−	0.525939i	−0.0138858	−	0.0170012i
$958$		−	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
$962$	−0.320988	+	0.587476i	−0.0103491	+	0.0189410i
$963$	47.8957	+	9.76132i	1.54342	+	0.314554i
$964$	2.07800	−	3.59921i	0.0669280	−	0.115923i
$965$	−11.6512			−0.375067
$966$	−6.34569	−	11.2355i	−0.204169	−	0.361497i
$967$		−	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
$969$	−3.07125	−	18.8782i	−0.0986627	−	0.606456i
$970$	−23.5222	+	13.5806i	−0.755254	+	0.436046i
$971$	16.4408	−	28.4764i	0.527612	−	0.913851i	−0.471870	−	0.881668i	$-0.656421\pi$
$971$	16.4408	−	28.4764i	0.527612	−	0.913851i	0.999482	−	0.0321826i	$-0.0102458\pi$
$972$	3.71792	−	15.1386i	0.119252	−	0.485571i
$973$	−3.67250	+	21.2990i	−0.117735	+	0.682814i
$974$		−	31.0810i		−	0.995899i
$975$	6.22660	−	17.6703i	0.199411	−	0.565904i
$976$	12.8084	−	7.39493i	0.409987	−	0.236706i
$977$	−10.4578	−	18.1135i	−0.334575	−	0.579501i	0.648828	−	0.760935i	$-0.275259\pi$
$977$	−10.4578	−	18.1135i	−0.334575	−	0.579501i	−0.983403	+	0.181434i	$0.941926\pi$
$978$	−1.38432	−	1.69491i	−0.0442657	−	0.0541971i
$979$		−	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	−0.205037	−	0.978754i	$-0.565732\pi$
$983$	16.9327	−	9.77611i	0.540070	−	0.311810i	0.745107	+	0.666945i	$0.232398\pi$
$984$	−6.92166	+	1.12607i	−0.220655	+	0.0358977i
$985$	10.5756	+	6.10583i	0.336967	+	0.194548i
$986$		−	0.373726i		−	0.0119019i
$987$	−18.2312	+	30.8977i	−0.580305	+	0.983484i
$988$	5.99192	−	3.65009i	0.190628	−	0.116125i
$989$	8.49053	+	4.90201i	0.269983	+	0.155875i
$990$	49.4968	+	10.0876i	1.57311	+	0.320605i
$991$	−8.09235	−	14.0164i	−0.257062	−	0.445244i	0.708392	−	0.705820i	$-0.249421\pi$
$991$	−8.09235	−	14.0164i	−0.257062	−	0.445244i	−0.965454	+	0.260575i	$0.916088\pi$
$992$	−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
$996$	−1.03048	−	1.26168i	−0.0326521	−	0.0399779i
$997$	−12.2227	+	7.05681i	−0.387098	+	0.223491i	−0.680902	−	0.732374i	$-0.738412\pi$
$997$	−12.2227	+	7.05681i	−0.387098	+	0.223491i	0.293804	+	0.955866i	$0.405079\pi$
$998$	4.05046	−	2.33853i	0.128215	−	0.0740249i
$999$	−0.0383647	+	0.964015i	−0.00121381	+	0.0305001i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.4	✓	36	7.3	odd	6	inner
546.2.bg.a.311.10	yes	36	273.38	even	6	inner
546.2.bg.a.467.4	yes	36	39.38	odd	2	inner
546.2.bg.a.467.10	yes	36	1.1	even	1	trivial
546.2.bg.b.311.4	yes	36	91.38	odd	6
546.2.bg.b.311.10	yes	36	21.17	even	6
546.2.bg.b.467.4	yes	36	3.2	odd	2
546.2.bg.b.467.10	yes	36	13.12	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.278126 + 1.70957i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.44950 - 1.41422i) q^{5} +(-1.61960 - 0.613923i) q^{6} +(2.60728 + 0.449563i) q^{7} +1.00000 q^{8} +(-2.84529 + 0.950954i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.278126 + 1.70957i) 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} +(-2.84529 + 0.950954i) q^{9} +(2.44950 - 1.41422i) q^{10} +(-2.97657 - 5.15557i) q^{11} +(1.34147 - 1.09565i) 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} +(0.599095 - 2.93957i) q^{18} +(0.972964 - 1.68522i) q^{19} +2.82844i q^{20} +(-0.0434094 + 4.58237i) q^{21} +5.95314 q^{22} +(2.43857 + 1.40791i) q^{23} +(0.278126 + 1.70957i) q^{24} +(1.50002 + 2.59812i) q^{25} +(-0.0848486 - 3.60455i) q^{26} +(-2.41708 - 4.59975i) q^{27} +(-0.914306 - 2.48275i) q^{28} -0.0658578i q^{29} +(3.09898 + 3.79427i) q^{30} +(-4.39516 - 7.61265i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(7.98598 - 6.52257i) 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} +(-4.06316 - 4.74244i) q^{39} +(-2.44950 - 1.41422i) q^{40} +4.04876i q^{41} +(-3.94674 - 2.32878i) q^{42} +3.48177 q^{43} +(-2.97657 + 5.15557i) q^{44} +(8.31439 + 1.69450i) 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} +(7.61252 - 6.21755i) q^{51} +(3.16406 + 1.72880i) q^{52} +(3.77930 - 2.18198i) q^{53} +(5.19204 + 0.206627i) 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} +(-4.83542 + 0.786662i) q^{60} +(-12.8084 - 7.39493i) q^{61} +8.79033 q^{62} +(-7.84598 + 1.20026i) q^{63} +1.00000 q^{64} +(10.1952 - 0.239989i) q^{65} +(1.65572 + 10.1773i) 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} +(-2.84529 + 0.950954i) q^{72} +(0.140240 + 0.242904i) q^{73} +(0.160796 - 0.0928358i) q^{74} +(-4.02448 + 3.28701i) 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} +(7.19137 - 5.41149i) q^{81} +(-3.50633 - 2.02438i) q^{82} -0.940520i q^{83} +(3.99015 - 2.25359i) q^{84} +16.0507i q^{85} +(-1.74089 + 3.01530i) q^{86} +(0.112589 - 0.0183168i) q^{87} +(-2.97657 - 5.15557i) q^{88} +(4.61927 + 2.66694i) q^{89} +(-5.62468 + 6.35322i) q^{90} +(-8.87162 + 3.50632i) q^{91} -2.81581i q^{92} +(11.7920 - 9.63114i) q^{93} +(-6.77981 + 3.91432i) q^{94} +(-4.76654 + 2.75197i) q^{95} +(1.34147 - 1.09565i) 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

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