LMFDB - Embedded newform 546.2.bg.b.467.9

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			467.9
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.280988 + 1.70911i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0759308 - 0.0438386i) q^{5} +(1.33964 + 1.09790i) q^{6} +(-2.62099 + 0.361112i) q^{7} -1.00000 q^{8} +(-2.84209 - 0.960476i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.280988 + 1.70911i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0759308 - 0.0438386i) q^{5} +(1.33964 + 1.09790i) q^{6} +(-2.62099 + 0.361112i) q^{7} -1.00000 q^{8} +(-2.84209 - 0.960476i) q^{9} +(-0.0759308 + 0.0438386i) q^{10} +(-2.83131 - 4.90398i) q^{11} +(1.62062 - 0.611211i) q^{12} +(-2.43301 - 2.66091i) q^{13} +(-0.997764 + 2.45040i) q^{14} +(0.0962606 - 0.117456i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.33566 + 2.31343i) q^{17} +(-2.25284 + 1.98109i) q^{18} +(3.32692 - 5.76239i) q^{19} +0.0876773i q^{20} +(0.119288 - 4.58102i) q^{21} -5.66263 q^{22} +(1.06303 + 0.613739i) q^{23} +(0.280988 - 1.70911i) q^{24} +(-2.49616 - 4.32347i) q^{25} +(-3.52092 + 0.776597i) q^{26} +(2.44015 - 4.58756i) q^{27} +(1.62323 + 2.08929i) q^{28} +5.84765i q^{29} +(-0.0535893 - 0.142092i) q^{30} +(-0.441909 - 0.765409i) q^{31} +(0.500000 + 0.866025i) q^{32} +(9.17699 - 3.46106i) q^{33} +2.67132 q^{34} +(0.214845 + 0.0874812i) q^{35} +(0.589249 + 2.94156i) q^{36} +(0.456219 + 0.263398i) q^{37} +(-3.32692 - 5.76239i) q^{38} +(5.23143 - 3.41060i) q^{39} +(0.0759308 + 0.0438386i) q^{40} +8.99352i q^{41} +(-3.90764 - 2.39382i) q^{42} -9.69720 q^{43} +(-2.83131 + 4.90398i) q^{44} +(0.173696 + 0.197523i) q^{45} +(1.06303 - 0.613739i) q^{46} +(-7.45201 - 4.30242i) q^{47} +(-1.33964 - 1.09790i) q^{48} +(6.73920 - 1.89294i) q^{49} -4.99231 q^{50} +(-4.32920 + 1.63274i) q^{51} +(-1.08791 + 3.43751i) q^{52} +(-12.1291 + 7.00275i) q^{53} +(-2.75286 - 4.40701i) q^{54} +0.496484i q^{55} +(2.62099 - 0.361112i) q^{56} +(8.91371 + 7.30522i) q^{57} +(5.06421 + 2.92382i) q^{58} +(3.11423 - 1.79800i) q^{59} +(-0.149850 - 0.0246363i) q^{60} +(2.01240 + 1.16186i) q^{61} -0.883818 q^{62} +(7.79594 + 1.49109i) q^{63} +1.00000 q^{64} +(0.0680900 + 0.308705i) q^{65} +(1.59113 - 9.67803i) q^{66} +(-6.54039 + 3.77610i) q^{67} +(1.33566 - 2.31343i) q^{68} +(-1.34764 + 1.64437i) q^{69} +(0.183183 - 0.142320i) q^{70} +2.65797 q^{71} +(2.84209 + 0.960476i) q^{72} +(-4.11174 - 7.12173i) q^{73} +(0.456219 - 0.263398i) q^{74} +(8.09066 - 3.05136i) q^{75} -6.65383 q^{76} +(9.19173 + 11.8309i) q^{77} +(-0.337951 - 6.23585i) q^{78} +(7.19370 - 12.4599i) q^{79} +(0.0759308 - 0.0438386i) q^{80} +(7.15497 + 5.45952i) q^{81} +(7.78862 + 4.49676i) q^{82} -2.86138i q^{83} +(-4.02693 + 2.18721i) q^{84} -0.234214i q^{85} +(-4.84860 + 8.39803i) q^{86} +(-9.99425 - 1.64312i) q^{87} +(2.83131 + 4.90398i) q^{88} +(2.93597 + 1.69508i) q^{89} +(0.257908 - 0.0516637i) q^{90} +(7.33780 + 6.09563i) q^{91} -1.22748i q^{92} +(1.43234 - 0.540199i) q^{93} +(-7.45201 + 4.30242i) q^{94} +(-0.505231 + 0.291695i) q^{95} +(-1.62062 + 0.611211i) q^{96} -10.4779 q^{97} +(1.73026 - 6.78279i) q^{98} +(3.33670 + 16.6570i) 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
$3$	−0.280988	+	1.70911i	−0.162228	+	0.986753i
$3$	−0.280988	+	1.70911i	−0.162228	+	0.986753i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.0759308	−	0.0438386i	−0.0339573	−	0.0196052i	0.482925	−	0.875662i	$-0.339574\pi$
$5$	−0.0759308	−	0.0438386i	−0.0339573	−	0.0196052i	−0.516883	+	0.856056i	$0.672908\pi$
$6$	1.33964	+	1.09790i	0.546904	+	0.448214i
$7$	−2.62099	+	0.361112i	−0.990642	+	0.136488i
$7$	−2.62099	+	0.361112i	−0.990642	+	0.136488i
$8$	−1.00000			−0.353553
$9$	−2.84209	−	0.960476i	−0.947364	−	0.320159i
$10$	−0.0759308	+	0.0438386i	−0.0240114	+	0.0138630i
$11$	−2.83131	−	4.90398i	−0.853673	−	1.47860i	−0.877871	−	0.478898i	$-0.841036\pi$
$11$	−2.83131	−	4.90398i	−0.853673	−	1.47860i	0.0241978	−	0.999707i	$-0.492297\pi$
$12$	1.62062	−	0.611211i	0.467834	−	0.176441i
$13$	−2.43301	−	2.66091i	−0.674797	−	0.738004i
$13$	−2.43301	−	2.66091i	−0.674797	−	0.738004i
$14$	−0.997764	+	2.45040i	−0.266664	+	0.654897i
$15$	0.0962606	−	0.117456i	0.0248544	−	0.0303269i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.33566	+	2.31343i	0.323945	+	0.561089i	0.981298	−	0.192493i	$-0.0616574\pi$
$17$	1.33566	+	2.31343i	0.323945	+	0.561089i	−0.657353	+	0.753583i	$0.728324\pi$
$18$	−2.25284	+	1.98109i	−0.531000	+	0.466946i
$19$	3.32692	−	5.76239i	0.763247	−	1.32198i	−0.177921	−	0.984045i	$-0.556937\pi$
$19$	3.32692	−	5.76239i	0.763247	−	1.32198i	0.941168	−	0.337938i	$-0.109729\pi$
$20$			0.0876773i			0.0196052i
$21$	0.119288	−	4.58102i	0.0260307	−	0.999661i
$22$	−5.66263			−1.20728
$23$	1.06303	+	0.613739i	0.221656	+	0.127973i	0.606717	−	0.794918i	$-0.292486\pi$
$23$	1.06303	+	0.613739i	0.221656	+	0.127973i	−0.385061	+	0.922891i	$0.625819\pi$
$24$	0.280988	−	1.70911i	0.0573564	−	0.348870i
$25$	−2.49616	−	4.32347i	−0.499231	−	0.864694i
$26$	−3.52092	+	0.776597i	−0.690510	+	0.152303i
$27$	2.44015	−	4.58756i	0.469607	−	0.882876i
$28$	1.62323	+	2.08929i	0.306761	+	0.394839i
$29$			5.84765i			1.08588i	0.839771	+	0.542940i	$0.182689\pi$
$29$			5.84765i			1.08588i	−0.839771	+	0.542940i	$0.817311\pi$
$30$	−0.0535893	−	0.142092i	−0.00978402	−	0.0259423i
$31$	−0.441909	−	0.765409i	−0.0793692	−	0.137471i	0.823609	−	0.567158i	$-0.191957\pi$
$31$	−0.441909	−	0.765409i	−0.0793692	−	0.137471i	−0.902978	+	0.429687i	$0.858624\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	9.17699	−	3.46106i	1.59751	−	0.602493i
$34$	2.67132			0.458127
$35$	0.214845	+	0.0874812i	0.0363154	+	0.0147870i
$36$	0.589249	+	2.94156i	0.0982081	+	0.490260i
$37$	0.456219	+	0.263398i	0.0750019	+	0.0433024i	0.537032	−	0.843562i	$-0.319545\pi$
$37$	0.456219	+	0.263398i	0.0750019	+	0.0433024i	−0.462030	+	0.886864i	$0.652879\pi$
$38$	−3.32692	−	5.76239i	−0.539697	−	0.934783i
$39$	5.23143	−	3.41060i	0.837699	−	0.546133i
$40$	0.0759308	+	0.0438386i	0.0120057	+	0.00693150i
$41$			8.99352i			1.40455i	0.711905	+	0.702276i	$0.247833\pi$
$41$			8.99352i			1.40455i	−0.711905	+	0.702276i	$0.752167\pi$
$42$	−3.90764	−	2.39382i	−0.602962	−	0.369374i
$43$	−9.69720			−1.47881			−0.739405	−	0.673261i	$-0.764893\pi$
$43$	−9.69720			−1.47881			−0.739405	+	0.673261i	$0.764893\pi$
$44$	−2.83131	+	4.90398i	−0.426836	+	0.739302i
$45$	0.173696	+	0.197523i	0.0258931	+	0.0294450i
$46$	1.06303	−	0.613739i	0.156735	−	0.0904909i
$47$	−7.45201	−	4.30242i	−1.08699	−	0.627572i	−0.154215	−	0.988037i	$-0.549285\pi$
$47$	−7.45201	−	4.30242i	−1.08699	−	0.627572i	−0.932773	+	0.360465i	$0.882618\pi$
$48$	−1.33964	−	1.09790i	−0.193360	−	0.158468i
$49$	6.73920	−	1.89294i	0.962742	−	0.270420i
$50$	−4.99231			−0.706020
$51$	−4.32920	+	1.63274i	−0.606210	+	0.228629i
$52$	−1.08791	+	3.43751i	−0.150866	+	0.476696i
$53$	−12.1291	+	7.00275i	−1.66606	+	0.961902i	−0.696334	+	0.717718i	$0.745187\pi$
$53$	−12.1291	+	7.00275i	−1.66606	+	0.961902i	−0.969729	+	0.244184i	$0.921480\pi$
$54$	−2.75286	−	4.40701i	−0.374617	−	0.599718i
$55$			0.496484i			0.0669458i
$56$	2.62099	−	0.361112i	0.350245	−	0.0482556i
$57$	8.91371	+	7.30522i	1.18065	+	0.967600i
$58$	5.06421	+	2.92382i	0.664963	+	0.383917i
$59$	3.11423	−	1.79800i	0.405438	−	0.234080i	−0.283390	−	0.959005i	$-0.591459\pi$
$59$	3.11423	−	1.79800i	0.405438	−	0.234080i	0.688828	+	0.724925i	$0.258126\pi$
$60$	−0.149850	−	0.0246363i	−0.0193455	−	0.00318053i
$61$	2.01240	+	1.16186i	0.257661	+	0.148761i	0.623267	−	0.782009i	$-0.285805\pi$
$61$	2.01240	+	1.16186i	0.257661	+	0.148761i	−0.365606	+	0.930770i	$0.619138\pi$
$62$	−0.883818			−0.112245
$63$	7.79594	+	1.49109i	0.982196	+	0.187859i
$64$	1.00000			0.125000
$65$	0.0680900	+	0.308705i	0.00844552	+	0.0382901i
$66$	1.59113	−	9.67803i	0.195854	−	1.19128i
$67$	−6.54039	+	3.77610i	−0.799036	+	0.461324i	−0.843134	−	0.537704i	$-0.819292\pi$
$67$	−6.54039	+	3.77610i	−0.799036	+	0.461324i	0.0440981	+	0.999027i	$0.485959\pi$
$68$	1.33566	−	2.31343i	0.161972	−	0.280545i
$69$	−1.34764	+	1.64437i	−0.162237	+	0.197959i
$70$	0.183183	−	0.142320i	0.0218946	−	0.0170105i
$71$	2.65797			0.315443			0.157722	−	0.987484i	$-0.449585\pi$
$71$	2.65797			0.315443			0.157722	+	0.987484i	$0.449585\pi$
$72$	2.84209	+	0.960476i	0.334944	+	0.113193i
$73$	−4.11174	−	7.12173i	−0.481242	−	0.833536i	0.518526	−	0.855062i	$-0.326481\pi$
$73$	−4.11174	−	7.12173i	−0.481242	−	0.833536i	−0.999768	+	0.0215258i	$0.993148\pi$
$74$	0.456219	−	0.263398i	0.0530343	−	0.0306194i
$75$	8.09066	−	3.05136i	0.934229	−	0.352340i
$76$	−6.65383			−0.763247
$77$	9.19173	+	11.8309i	1.04750	+	1.34825i
$78$	−0.337951	−	6.23585i	−0.0382654	−	0.706071i
$79$	7.19370	−	12.4599i	0.809355	−	1.40184i	−0.103957	−	0.994582i	$-0.533150\pi$
$79$	7.19370	−	12.4599i	0.809355	−	1.40184i	0.913312	−	0.407261i	$-0.133516\pi$
$80$	0.0759308	−	0.0438386i	0.00848932	−	0.00490131i
$81$	7.15497	+	5.45952i	0.794997	+	0.606614i
$82$	7.78862	+	4.49676i	0.860109	+	0.496584i
$83$		−	2.86138i		−	0.314077i	−0.987592	−	0.157039i	$-0.949805\pi$
$83$		−	2.86138i		−	0.314077i	0.987592	−	0.157039i	$-0.0501947\pi$
$84$	−4.02693	+	2.18721i	−0.439374	+	0.238644i
$85$		−	0.234214i		−	0.0254041i
$86$	−4.84860	+	8.39803i	−0.522838	+	0.905582i
$87$	−9.99425	−	1.64312i	−1.07150	−	0.176161i
$88$	2.83131	+	4.90398i	0.301819	+	0.522766i
$89$	2.93597	+	1.69508i	0.311212	+	0.179678i	0.647469	−	0.762092i	$-0.275828\pi$
$89$	2.93597	+	1.69508i	0.311212	+	0.179678i	−0.336257	+	0.941770i	$0.609161\pi$
$90$	0.257908	−	0.0516637i	0.0271859	−	0.00544584i
$91$	7.33780	+	6.09563i	0.769210	+	0.638996i
$92$		−	1.22748i		−	0.127973i
$93$	1.43234	−	0.540199i	0.148526	−	0.0560160i
$94$	−7.45201	+	4.30242i	−0.768616	+	0.443761i
$95$	−0.505231	+	0.291695i	−0.0518356	+	0.0299273i
$96$	−1.62062	+	0.611211i	−0.165404	+	0.0623814i
$97$	−10.4779			−1.06387			−0.531934	−	0.846786i	$-0.678535\pi$
$97$	−10.4779			−1.06387			−0.531934	+	0.846786i	$0.678535\pi$
$98$	1.73026	−	6.78279i	0.174783	−	0.685165i
$99$	3.33670	+	16.6570i	0.335350	+	1.67409i
$100$	−2.49616	+	4.32347i	−0.249616	+	0.432347i
$101$	1.67265	+	2.89711i	0.166435	+	0.288273i	0.937164	−	0.348890i	$-0.113441\pi$
$101$	1.67265	+	2.89711i	0.166435	+	0.288273i	−0.770729	+	0.637163i	$0.780108\pi$
$102$	−0.750608	+	4.56557i	−0.0743213	+	0.452059i
$103$	10.7681	+	6.21697i	1.06101	+	0.612577i	0.925713	−	0.378228i	$-0.123466\pi$
$103$	10.7681	+	6.21697i	1.06101	+	0.612577i	0.135301	+	0.990804i	$0.456800\pi$
$104$	2.43301	+	2.66091i	0.238577	+	0.260924i
$105$	−0.209883	+	0.342611i	−0.0204825	+	0.0334354i
$106$			14.0055i			1.36033i
$107$	2.33402	+	1.34755i	0.225639	+	0.130272i	0.608558	−	0.793509i	$-0.291748\pi$
$107$	2.33402	+	1.34755i	0.225639	+	0.130272i	−0.382920	+	0.923782i	$0.625081\pi$
$108$	−5.19301	+	0.180546i	−0.499698	+	0.0173730i
$109$	6.64244	−	3.83502i	0.636231	−	0.367328i	−0.146930	−	0.989147i	$-0.546939\pi$
$109$	6.64244	−	3.83502i	0.636231	−	0.367328i	0.783161	+	0.621819i	$0.213606\pi$
$110$	0.429968	+	0.248242i	0.0409958	+	0.0236689i
$111$	−0.578367	+	0.705715i	−0.0548962	+	0.0669835i
$112$	0.997764	−	2.45040i	0.0942798	−	0.231541i
$113$		−	7.92944i		−	0.745939i	−0.927844	−	0.372970i	$-0.878340\pi$
$113$		−	7.92944i		−	0.745939i	0.927844	−	0.372970i	$-0.121660\pi$
$114$	10.7834	−	4.06689i	1.00995	−	0.380900i
$115$	−0.0538110	−	0.0932033i	−0.00501790	−	0.00869126i
$116$	5.06421	−	2.92382i	0.470200	−	0.271470i
$117$	4.35911	+	9.89940i	0.403000	+	0.915200i
$118$		−	3.59600i		−	0.331039i
$119$	−4.33616	−	5.58116i	−0.397495	−	0.511624i
$120$	−0.0962606	+	0.117456i	−0.00878735	+	0.0107222i
$121$	−10.5327	+	18.2431i	−0.957515	+	1.65846i
$122$	2.01240	−	1.16186i	0.182194	−	0.105190i
$123$	−15.3709	−	2.52707i	−1.38595	−	0.227858i
$124$	−0.441909	+	0.765409i	−0.0396846	+	0.0687357i
$125$			0.876099i			0.0783607i
$126$	5.18929	−	6.00594i	0.462299	−	0.535051i
$127$	4.80829			0.426667			0.213334	−	0.976979i	$-0.431568\pi$
$127$	4.80829			0.426667			0.213334	+	0.976979i	$0.431568\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.72480	−	16.5736i	0.239905	−	1.45922i
$130$	0.301391	+	0.0953849i	0.0264338	+	0.00836581i
$131$	9.89815	−	17.1441i	0.864805	−	1.49789i	−0.00243479	−	0.999997i	$-0.500775\pi$
$131$	9.89815	−	17.1441i	0.864805	−	1.49789i	0.867240	−	0.497890i	$-0.165892\pi$
$132$	−7.58586	−	6.21697i	−0.660264	−	0.541118i
$133$	−6.63895	+	16.3046i	−0.575670	+	1.41379i
$134$			7.55219i			0.652410i
$135$	−0.386395	+	0.241364i	−0.0332556	+	0.0207733i
$136$	−1.33566	−	2.31343i	−0.114532	−	0.198375i
$137$	6.29121	+	10.8967i	0.537495	+	0.930968i	0.999038	+	0.0438504i	$0.0139625\pi$
$137$	6.29121	+	10.8967i	0.537495	+	0.930968i	−0.461543	+	0.887118i	$0.652704\pi$
$138$	0.750248	+	1.98928i	0.0638653	+	0.169339i
$139$		−	19.6014i		−	1.66257i	−0.555848	−	0.831284i	$-0.687606\pi$
$139$		−	19.6014i		−	1.66257i	0.555848	−	0.831284i	$-0.312394\pi$
$140$	−0.0316613	−	0.229801i	−0.00267587	−	0.0194218i
$141$	9.44722	−	11.5274i	0.795599	−	0.970778i
$142$	1.32899	−	2.30187i	0.111526	−	0.193169i
$143$	−6.16042	+	19.4653i	−0.515160	+	1.62777i
$144$	2.25284	−	1.98109i	0.187737	−	0.165090i
$145$	0.256353	−	0.444016i	0.0212890	−	0.0368735i
$146$	−8.22347			−0.680579
$147$	1.34161	+	12.0499i	0.110654	+	0.993859i
$148$		−	0.526796i		−	0.0433024i
$149$	6.40667	−	11.0967i	0.524855	−	0.909076i	−0.474726	−	0.880134i	$-0.657453\pi$
$149$	6.40667	−	11.0967i	0.524855	−	0.909076i	0.999581	−	0.0289419i	$-0.00921379\pi$
$150$	1.40278	−	8.53240i	0.114536	−	0.696667i
$151$	−3.56296	+	2.05707i	−0.289949	+	0.167402i	−0.637919	−	0.770104i	$-0.720205\pi$
$151$	−3.56296	+	2.05707i	−0.289949	+	0.167402i	0.347970	+	0.937506i	$0.386871\pi$
$152$	−3.32692	+	5.76239i	−0.269849	+	0.467391i
$153$	−1.57407	−	7.85785i	−0.127256	−	0.635269i
$154$	14.8417	−	2.04484i	1.19598	−	0.164778i
$155$			0.0774908i			0.00622421i
$156$	−5.56938	−	2.82525i	−0.445907	−	0.226201i
$157$	16.7506	−	9.67095i	1.33684	−	0.771826i	0.350504	−	0.936561i	$-0.386010\pi$
$157$	16.7506	−	9.67095i	1.33684	−	0.771826i	0.986338	+	0.164736i	$0.0526771\pi$
$158$	−7.19370	−	12.4599i	−0.572300	−	0.991253i
$159$	−8.56031	−	22.6977i	−0.678877	−	1.80004i
$160$		−	0.0876773i		−	0.00693150i
$161$	−3.00781	−	1.22473i	−0.237049	−	0.0965225i
$162$	8.30557	−	3.46662i	0.652547	−	0.272364i
$163$	−15.2764	−	8.81983i	−1.19654	−	0.690823i	−0.236758	−	0.971569i	$-0.576085\pi$
$163$	−15.2764	−	8.81983i	−1.19654	−	0.690823i	−0.959782	+	0.280746i	$0.909418\pi$
$164$	7.78862	−	4.49676i	0.608189	−	0.351138i
$165$	−0.848544	−	0.139506i	−0.0660590	−	0.0108605i
$166$	−2.47803	−	1.43069i	−0.192332	−	0.111043i
$167$			15.5348i			1.20212i	0.799205	+	0.601058i	$0.205254\pi$
$167$			15.5348i			1.20212i	−0.799205	+	0.601058i	$0.794746\pi$
$168$	−0.119288	+	4.58102i	−0.00920326	+	0.353434i
$169$	−1.16088	+	12.9481i	−0.0892987	+	0.996005i
$170$	−0.202835	−	0.117107i	−0.0155568	−	0.00898170i
$171$	−14.9900	+	13.1818i	−1.14632	+	1.00804i
$172$	4.84860	+	8.39803i	0.369702	+	0.640343i
$173$	8.15099	−	14.1179i	0.619708	−	1.07337i	−0.369831	−	0.929099i	$-0.620584\pi$
$173$	8.15099	−	14.1179i	0.619708	−	1.07337i	0.989539	−	0.144267i	$-0.0460823\pi$
$174$	−6.42011	+	7.83372i	−0.486707	+	0.593873i
$175$	8.10366	+	10.4304i	0.612579	+	0.788463i
$176$	5.66263			0.426836
$177$	2.19792	+	5.82777i	0.165206	+	0.438042i
$178$	2.93597	−	1.69508i	0.220060	−	0.127052i
$179$	7.78809	−	4.49646i	0.582109	−	0.336081i	−0.179862	−	0.983692i	$-0.557565\pi$
$179$	7.78809	−	4.49646i	0.582109	−	0.336081i	0.761971	+	0.647611i	$0.224232\pi$
$180$	0.0842120	−	0.249187i	0.00627679	−	0.0185733i
$181$		−	7.10802i		−	0.528335i	−0.964477	−	0.264167i	$-0.914903\pi$
$181$		−	7.10802i		−	0.528335i	0.964477	−	0.264167i	$-0.0850972\pi$
$182$	8.94787	−	3.30690i	0.663260	−	0.245124i
$183$	−2.55120	+	3.11293i	−0.188590	+	0.230115i
$184$	−1.06303	−	0.613739i	−0.0783674	−	0.0452454i
$185$	−0.0230940	−	0.0400000i	−0.00169791	−	0.00294086i
$186$	0.248342	−	1.51054i	0.0182093	−	0.110758i
$187$	7.56334	−	13.1001i	0.553086	−	0.957973i
$188$			8.60484i			0.627572i
$189$	−4.73899	+	12.9051i	−0.344711	+	0.938709i
$190$			0.583390i			0.0423236i
$191$	−12.3294	−	7.11841i	−0.892127	−	0.515070i	−0.0174894	−	0.999847i	$-0.505567\pi$
$191$	−12.3294	−	7.11841i	−0.892127	−	0.515070i	−0.874638	+	0.484777i	$0.838901\pi$
$192$	−0.280988	+	1.70911i	−0.0202786	+	0.123344i
$193$	12.9152	−	7.45659i	0.929656	−	0.536737i	0.0429533	−	0.999077i	$-0.486323\pi$
$193$	12.9152	−	7.45659i	0.929656	−	0.536737i	0.886703	+	0.462340i	$0.152990\pi$
$194$	−5.23894	+	9.07411i	−0.376134	+	0.651483i
$195$	−0.546742	+	0.0296306i	−0.0391530	+	0.00212189i
$196$	−5.00894	−	4.88984i	−0.357781	−	0.349275i
$197$	5.59743			0.398800			0.199400	−	0.979918i	$-0.436101\pi$
$197$	5.59743			0.398800			0.199400	+	0.979918i	$0.436101\pi$
$198$	16.0937	+	5.43882i	1.14373	+	0.386520i
$199$	0.509204	−	0.293989i	0.0360965	−	0.0208403i	−0.481843	−	0.876257i	$-0.660032\pi$
$199$	0.509204	−	0.293989i	0.0360965	−	0.0208403i	0.517940	+	0.855417i	$0.326699\pi$
$200$	2.49616	+	4.32347i	0.176505	+	0.305715i
$201$	−4.61598	−	12.2393i	−0.325586	−	0.863291i
$202$	3.34530			0.235374
$203$	−2.11166	−	15.3266i	−0.148209	−	1.07572i
$204$	3.57859	+	2.93283i	0.250552	+	0.205339i
$205$	0.394264	−	0.682885i	0.0275366	−	0.0476948i
$206$	10.7681	−	6.21697i	0.750250	−	0.433157i
$207$	−2.43174	−	2.76531i	−0.169018	−	0.192203i
$208$	3.52092	−	0.776597i	0.244132	−	0.0538473i
$209$	−37.6782			−2.60625
$210$	0.191768	+	0.353070i	0.0132333	+	0.0243641i
$211$	−16.2218			−1.11676			−0.558379	−	0.829586i	$-0.688577\pi$
$211$	−16.2218			−1.11676			−0.558379	+	0.829586i	$0.688577\pi$
$212$	12.1291	+	7.00275i	0.833031	+	0.480951i
$213$	−0.746857	+	4.54276i	−0.0511738	+	0.311264i
$214$	2.33402	−	1.34755i	0.159551	−	0.0921166i
$215$	0.736316	+	0.425112i	0.0502163	+	0.0289924i
$216$	−2.44015	+	4.58756i	−0.166031	+	0.312144i
$217$	1.43464	+	1.84655i	0.0973896	+	0.125352i
$218$		−	7.67003i		−	0.519480i
$219$	13.3272	−	5.02627i	0.900565	−	0.339644i
$220$	0.429968	−	0.248242i	0.0289884	−	0.0167365i
$221$	2.90615	−	9.18268i	0.195489	−	0.617694i
$222$	0.321983	+	0.853738i	0.0216101	+	0.0572991i
$223$	18.4233			1.23371			0.616856	−	0.787076i	$-0.288406\pi$
$223$	18.4233			1.23371			0.616856	+	0.787076i	$0.288406\pi$
$224$	−1.62323	−	2.08929i	−0.108456	−	0.139597i
$225$	2.94171	+	14.6852i	0.196114	+	0.979013i
$226$	−6.86710	−	3.96472i	−0.456793	−	0.263729i
$227$	3.73888	−	2.15864i	0.248158	−	0.143274i	−0.370762	−	0.928728i	$-0.620904\pi$
$227$	3.73888	−	2.15864i	0.248158	−	0.143274i	0.618921	+	0.785454i	$0.287570\pi$
$228$	1.86965	−	11.3721i	0.123820	−	0.753137i
$229$	−6.51189	+	11.2789i	−0.430317	+	0.745332i	−0.996900	−	0.0786729i	$-0.974932\pi$
$229$	−6.51189	+	11.2789i	−0.430317	+	0.745332i	0.566583	+	0.824005i	$0.308265\pi$
$230$	−0.107622			−0.00709638
$231$	−22.8030	+	12.3853i	−1.50033	+	0.814894i
$232$		−	5.84765i		−	0.383917i
$233$	−14.2073	−	8.20260i	−0.930753	−	0.537370i	−0.0437031	−	0.999045i	$-0.513916\pi$
$233$	−14.2073	−	8.20260i	−0.930753	−	0.537370i	−0.887050	+	0.461674i	$0.847249\pi$
$234$	10.7527	+	1.17460i	0.702925	+	0.0767862i
$235$	0.377225	+	0.653372i	0.0246074	+	0.0426213i
$236$	−3.11423	−	1.79800i	−0.202719	−	0.117040i
$237$	19.2739	+	15.7959i	1.25197	+	1.02605i
$238$	−7.00150	+	0.964645i	−0.453840	+	0.0625287i
$239$	−15.3927			−0.995673			−0.497836	−	0.867271i	$-0.665872\pi$
$239$	−15.3927			−0.995673			−0.497836	+	0.867271i	$0.665872\pi$
$240$	0.0535893	+	0.142092i	0.00345917	+	0.00917199i
$241$	−3.89705	−	6.74990i	−0.251031	−	0.434799i	0.712779	−	0.701389i	$-0.247436\pi$
$241$	−3.89705	−	6.74990i	−0.251031	−	0.434799i	−0.963810	+	0.266590i	$0.914103\pi$
$242$	10.5327	+	18.2431i	0.677065	+	1.17271i
$243$	−11.3414	+	10.6945i	−0.727549	+	0.686056i
$244$		−	2.32372i		−	0.148761i
$245$	−0.594696	−	0.151705i	−0.0379938	−	0.00969205i
$246$	−9.87395	+	12.0480i	−0.629540	+	0.768155i
$247$	−23.4276	+	5.16735i	−1.49066	+	0.328791i
$248$	0.441909	+	0.765409i	0.0280613	+	0.0486035i
$249$	4.89040	+	0.804013i	0.309917	+	0.0509522i
$250$	0.758724	+	0.438049i	0.0479859	+	0.0277047i
$251$	7.91930			0.499862			0.249931	−	0.968264i	$-0.419592\pi$
$251$	7.91930			0.499862			0.249931	+	0.968264i	$0.419592\pi$
$252$	−2.60665	−	7.49702i	−0.164203	−	0.472268i
$253$		−	6.95075i		−	0.436990i
$254$	2.40415	−	4.16411i	0.150850	−	0.261279i
$255$	0.400297	+	0.0658113i	0.0250676	+	0.00412126i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.92741	+	8.53452i	−0.307363	+	0.532369i	−0.977785	−	0.209612i	$-0.932780\pi$
$257$	−4.92741	+	8.53452i	−0.307363	+	0.532369i	0.670421	+	0.741981i	$0.266113\pi$
$258$	−12.9907	−	10.6465i	−0.808767	−	0.662823i
$259$	−1.29086	−	0.525618i	−0.0802102	−	0.0326603i
$260$	0.233301	−	0.213320i	0.0144687	−	0.0132296i
$261$	5.61653	−	16.6195i	0.347654	−	1.02872i
$262$	−9.89815	−	17.1441i	−0.611510	−	1.05917i
$263$	−20.2604	+	11.6974i	−1.24931	+	0.721290i	−0.970972	−	0.239192i	$-0.923117\pi$
$263$	−20.2604	+	11.6974i	−1.24931	+	0.721290i	−0.278340	+	0.960483i	$0.589784\pi$
$264$	−9.17699	+	3.46106i	−0.564804	+	0.213013i
$265$	1.22796			0.0754333
$266$	10.8007	+	13.9018i	0.662233	+	0.852373i
$267$	−3.72205	+	4.54159i	−0.227786	+	0.277941i
$268$	6.54039	+	3.77610i	0.399518	+	0.230662i
$269$	0.859882	+	1.48936i	0.0524279	+	0.0908078i	0.891048	−	0.453908i	$-0.149971\pi$
$269$	0.859882	+	1.48936i	0.0524279	+	0.0908078i	−0.838620	+	0.544716i	$0.816637\pi$
$270$	0.0158298	+	0.455310i	0.000963370	+	0.0277093i
$271$	−8.00242	+	13.8606i	−0.486113	+	0.841972i	−0.999873	−	0.0159623i	$-0.994919\pi$
$271$	−8.00242	+	13.8606i	−0.486113	+	0.841972i	0.513760	+	0.857934i	$0.328252\pi$
$272$	−2.67132			−0.161972
$273$	−12.4799	+	10.8283i	−0.755319	+	0.655357i
$274$	12.5824			0.760132
$275$	−14.1348	+	24.4822i	−0.852360	+	1.47633i
$276$	2.09789	+	0.344906i	0.126278	+	0.0207609i
$277$	6.12127	+	10.6023i	0.367791	+	0.637033i	0.989220	−	0.146438i	$-0.0467808\pi$
$277$	6.12127	+	10.6023i	0.367791	+	0.637033i	−0.621429	+	0.783471i	$0.713447\pi$
$278$	−16.9753	−	9.80069i	−1.01811	−	0.587806i
$279$	0.520789	+	2.59981i	0.0311788	+	0.155646i
$280$	−0.214845	−	0.0874812i	−0.0128394	−	0.00522800i
$281$	−8.09237			−0.482751			−0.241375	−	0.970432i	$-0.577598\pi$
$281$	−8.09237			−0.482751			−0.241375	+	0.970432i	$0.577598\pi$
$282$	−5.25937	−	13.9452i	−0.313191	−	0.830425i
$283$	−2.90561	+	1.67755i	−0.172721	+	0.0997203i	−0.583868	−	0.811849i	$-0.698461\pi$
$283$	−2.90561	+	1.67755i	−0.172721	+	0.0997203i	0.411147	+	0.911569i	$0.365128\pi$
$284$	−1.32899	−	2.30187i	−0.0788608	−	0.136591i
$285$	−0.356574	−	0.945456i	−0.0211216	−	0.0560040i
$286$	13.7772	+	15.0677i	0.814666	+	0.890974i
$287$	−3.24767	−	23.5719i	−0.191704	−	1.39141i
$288$	−0.589249	−	2.94156i	−0.0347218	−	0.173333i
$289$	4.93203	−	8.54252i	0.290119	−	0.502501i
$290$	−0.256353	−	0.444016i	−0.0150536	−	0.0260735i
$291$	2.94416	−	17.9078i	0.172590	−	1.04978i
$292$	−4.11174	+	7.12173i	−0.240621	+	0.416768i
$293$			21.2050i			1.23881i	0.785072	+	0.619404i	$0.212626\pi$
$293$			21.2050i			1.23881i	−0.785072	+	0.619404i	$0.787374\pi$
$294$	11.1063	+	4.86308i	0.647734	+	0.283621i
$295$	−0.315288			−0.0183568
$296$	−0.456219	−	0.263398i	−0.0265172	−	0.0153097i
$297$	−29.4061	+	1.02236i	−1.70631	+	0.0593236i
$298$	−6.40667	−	11.0967i	−0.371129	−	0.642813i
$299$	−0.953256	−	4.32185i	−0.0551282	−	0.249939i
$300$	−6.68788	−	5.48104i	−0.386125	−	0.316448i
$301$	25.4163	−	3.50178i	1.46497	−	0.201839i
$302$			4.11415i			0.236743i
$303$	−5.42147	+	2.04468i	−0.311455	+	0.117464i
$304$	3.32692	+	5.76239i	0.190812	+	0.330496i
$305$	−0.101869	−	0.176442i	−0.00583298	−	0.0101030i
$306$	−7.59213	−	2.56574i	−0.434013	−	0.146674i
$307$	−19.0700			−1.08838			−0.544192	−	0.838961i	$-0.683164\pi$
$307$	−19.0700			−1.08838			−0.544192	+	0.838961i	$0.683164\pi$
$308$	5.64996	−	13.8757i	0.321936	−	0.790642i
$309$	−13.6512	+	16.6570i	−0.776589	+	0.947582i
$310$	0.0671090	+	0.0387454i	0.00381153	+	0.00220059i
$311$	1.91162	+	3.31103i	0.108398	+	0.187751i	0.915121	−	0.403178i	$-0.132095\pi$
$311$	1.91162	+	3.31103i	0.108398	+	0.187751i	−0.806723	+	0.590929i	$0.798761\pi$
$312$	−5.23143	+	3.41060i	−0.296171	+	0.193087i
$313$	−16.6808	−	9.63067i	−0.942855	−	0.544358i	−0.0520010	−	0.998647i	$-0.516560\pi$
$313$	−16.6808	−	9.63067i	−0.942855	−	0.544358i	−0.890854	+	0.454289i	$0.849893\pi$
$314$		−	19.3419i		−	1.09153i
$315$	−0.526584	−	0.454983i	−0.0296697	−	0.0256354i
$316$	−14.3874			−0.809355
$317$	12.3152	−	21.3306i	0.691692	−	1.19805i	−0.279591	−	0.960119i	$-0.590199\pi$
$317$	12.3152	−	21.3306i	0.691692	−	1.19805i	0.971283	−	0.237927i	$-0.0764679\pi$
$318$	−23.9369	−	3.93538i	−1.34231	−	0.220685i
$319$	28.6767	−	16.5565i	1.60559	−	0.926987i
$320$	−0.0759308	−	0.0438386i	−0.00424466	−	0.00245065i
$321$	−2.95894	+	3.61045i	−0.165152	+	0.201516i
$322$	−2.56456	+	1.99248i	−0.142917	+	0.111036i
$323$	17.7745			0.989000
$324$	1.15060	−	8.92615i	0.0639223	−	0.495897i
$325$	−5.43118	+	17.1611i	−0.301268	+	0.951927i
$326$	−15.2764	+	8.81983i	−0.846081	+	0.488485i
$327$	4.68801	+	12.4302i	0.259247	+	0.687394i
$328$		−	8.99352i		−	0.496584i
$329$	21.0853	+	8.58560i	1.16247	+	0.473339i
$330$	−0.545087	+	0.665107i	−0.0300061	+	0.0366130i
$331$	3.59847	+	2.07757i	0.197790	+	0.114194i	0.595624	−	0.803263i	$-0.296905\pi$
$331$	3.59847	+	2.07757i	0.197790	+	0.114194i	−0.397834	+	0.917457i	$0.630238\pi$
$332$	−2.47803	+	1.43069i	−0.135999	+	0.0785193i
$333$	−1.04363	−	1.18679i	−0.0571904	−	0.0650356i
$334$	13.4535	+	7.76738i	0.736143	+	0.425012i
$335$	0.662156			0.0361774
$336$	3.90764	+	2.39382i	0.213179	+	0.130593i
$337$	−1.62397			−0.0884634			−0.0442317	−	0.999021i	$-0.514084\pi$
$337$	−1.62397			−0.0884634			−0.0442317	+	0.999021i	$0.514084\pi$
$338$	10.6329	+	7.47939i	0.578354	+	0.406825i
$339$	13.5523	+	2.22808i	0.736058	+	0.121013i
$340$	−0.202835	+	0.117107i	−0.0110003	+	0.00635102i
$341$	−2.50237	+	4.33422i	−0.135511	+	0.234711i
$342$	3.92076	+	19.5727i	0.212011	+	1.05837i
$343$	−16.9798	+	7.39499i	−0.916824	+	0.399292i
$344$	9.69720			0.522838
$345$	0.174415	−	0.0657797i	0.00939017	−	0.00354146i
$346$	−8.15099	−	14.1179i	−0.438200	−	0.758984i
$347$	−4.31492	+	2.49122i	−0.231637	+	0.133736i	−0.611327	−	0.791378i	$-0.709364\pi$
$347$	−4.31492	+	2.49122i	−0.231637	+	0.133736i	0.379690	+	0.925114i	$0.376031\pi$
$348$	3.57414	+	9.47684i	0.191594	+	0.508012i
$349$	−18.4655			−0.988437			−0.494218	−	0.869338i	$-0.664546\pi$
$349$	−18.4655			−0.988437			−0.494218	+	0.869338i	$0.664546\pi$
$350$	13.0848	−	1.80278i	0.699413	−	0.0963629i
$351$	−18.1440	+	4.66857i	−0.968455	+	0.249190i
$352$	2.83131	−	4.90398i	0.150909	−	0.261383i
$353$	17.6657	−	10.1993i	0.940249	−	0.542853i	0.0502108	−	0.998739i	$-0.484011\pi$
$353$	17.6657	−	10.1993i	0.940249	−	0.542853i	0.890038	+	0.455885i	$0.150677\pi$
$354$	6.14595	+	1.01043i	0.326654	+	0.0537039i
$355$	−0.201822	−	0.116522i	−0.0107116	−	0.00618434i
$356$		−	3.39016i		−	0.179678i
$357$	10.7572	−	5.84272i	0.569332	−	0.309230i
$358$		−	8.99291i		−	0.475290i
$359$	1.49774	−	2.59416i	0.0790477	−	0.136915i	−0.823792	−	0.566893i	$-0.808145\pi$
$359$	1.49774	−	2.59416i	0.0790477	−	0.136915i	0.902839	+	0.429978i	$0.141479\pi$
$360$	−0.173696	−	0.197523i	−0.00915459	−	0.0104104i
$361$	−12.6368	−	21.8875i	−0.665092	−	1.15197i
$362$	−6.15572	−	3.55401i	−0.323538	−	0.186795i
$363$	−28.2199	−	23.1275i	−1.48116	−	1.21388i
$364$	1.61007	−	9.40253i	0.0843908	−	0.492827i
$365$			0.721012i			0.0377395i
$366$	1.42028	+	3.76587i	0.0742393	+	0.196845i
$367$	0.373545	−	0.215666i	0.0194989	−	0.0112577i	−0.490219	−	0.871599i	$-0.663083\pi$
$367$	0.373545	−	0.215666i	0.0194989	−	0.0112577i	0.509718	+	0.860342i	$0.329750\pi$
$368$	−1.06303	+	0.613739i	−0.0554141	+	0.0319934i
$369$	8.63807	−	25.5604i	0.449680	−	1.33062i
$370$	−0.0461880			−0.00240120
$371$	29.2615	−	22.7341i	1.51918	−	1.18030i
$372$	−1.18399	−	0.970340i	−0.0613872	−	0.0503098i
$373$	5.60905	−	9.71516i	0.290425	−	0.503032i	−0.683485	−	0.729965i	$-0.739536\pi$
$373$	5.60905	−	9.71516i	0.290425	−	0.503032i	0.973910	+	0.226933i	$0.0728698\pi$
$374$	−7.56334	−	13.1001i	−0.391091	−	0.677389i
$375$	−1.49735	−	0.246173i	−0.0773226	−	0.0127123i
$376$	7.45201	+	4.30242i	0.384308	+	0.221880i
$377$	15.5601	−	14.2274i	0.801384	−	0.732749i
$378$	8.80666	+	10.5566i	0.452966	+	0.542975i
$379$		−	11.4767i		−	0.589518i	−0.955572	−	0.294759i	$-0.904761\pi$
$379$		−	11.4767i		−	0.589518i	0.955572	−	0.294759i	$-0.0952393\pi$
$380$	0.505231	+	0.291695i	0.0259178	+	0.0149636i
$381$	−1.35107	+	8.21789i	−0.0692175	+	0.421015i
$382$	−12.3294	+	7.11841i	−0.630829	+	0.364209i
$383$	−0.325127	−	0.187712i	−0.0166132	−	0.00959165i	0.491670	−	0.870781i	$-0.336386\pi$
$383$	−0.325127	−	0.187712i	−0.0166132	−	0.00959165i	−0.508284	+	0.861190i	$0.669720\pi$
$384$	1.33964	+	1.09790i	0.0683630	+	0.0560268i
$385$	−0.179286	−	1.30128i	−0.00913727	−	0.0663194i
$386$		−	14.9132i		−	0.759061i
$387$	27.5603	+	9.31394i	1.40097	+	0.473454i
$388$	5.23894	+	9.07411i	0.265967	+	0.460668i
$389$	28.3112	−	16.3455i	1.43544	−	0.828750i	0.437909	−	0.899019i	$-0.355719\pi$
$389$	28.3112	−	16.3455i	1.43544	−	0.828750i	0.997528	+	0.0702694i	$0.0223859\pi$
$390$	−0.247710	+	0.488308i	−0.0125433	+	0.0247264i
$391$			3.27898i			0.165825i
$392$	−6.73920	+	1.89294i	−0.340381	+	0.0956081i
$393$	26.5198	+	21.7343i	1.33775	+	1.09635i
$394$	2.79871	−	4.84751i	0.140997	−	0.244214i
$395$	−1.09245	+	0.630724i	−0.0549669	+	0.0317352i
$396$	12.7570	−	11.2181i	0.641064	−	0.563733i
$397$	9.57692	−	16.5877i	0.480652	−	0.832514i	−0.519102	−	0.854713i	$-0.673733\pi$
$397$	9.57692	−	16.5877i	0.480652	−	0.832514i	0.999754	+	0.0221990i	$0.00706673\pi$
$398$		−	0.587979i		−	0.0294727i
$399$	−26.0008	−	15.9281i	−1.30167	−	0.797401i
$400$	4.99231			0.249616
$401$	−2.06325	+	3.57365i	−0.103034	+	0.178459i	−0.912933	−	0.408109i	$-0.866188\pi$
$401$	−2.06325	+	3.57365i	−0.103034	+	0.178459i	0.809900	+	0.586569i	$0.199522\pi$
$402$	−12.9075	−	2.12207i	−0.643768	−	0.105839i
$403$	−0.961513	+	3.03813i	−0.0478964	+	0.151340i
$404$	1.67265	−	2.89711i	0.0832174	−	0.144137i
$405$	−0.303944	−	0.728210i	−0.0151031	−	0.0361850i
$406$	−14.3291	−	5.83457i	−0.711140	−	0.289565i
$407$		−	2.98305i		−	0.147864i
$408$	4.32920	−	1.63274i	0.214327	−	0.0808326i
$409$	16.1361	+	27.9486i	0.797879	+	1.38197i	0.920995	+	0.389575i	$0.127378\pi$
$409$	16.1361	+	27.9486i	0.797879	+	1.38197i	−0.123116	+	0.992392i	$0.539289\pi$
$410$	−0.394264	−	0.682885i	−0.0194713	−	0.0337253i
$411$	−20.3914	+	7.69051i	−1.00583	+	0.379345i
$412$		−	12.4339i		−	0.612577i
$413$	−7.51309	+	5.83713i	−0.369695	+	0.287227i
$414$	−3.61070	+	0.723290i	−0.177456	+	0.0355478i
$415$	−0.125439	+	0.217267i	−0.00615756	+	0.0106652i
$416$	1.08791	−	3.43751i	0.0533391	−	0.168538i
$417$	33.5009	+	5.50775i	1.64054	+	0.269716i
$418$	−18.8391	+	32.6303i	−0.921450	+	1.59600i
$419$	4.72613			0.230886			0.115443	−	0.993314i	$-0.463171\pi$
$419$	4.72613			0.230886			0.115443	+	0.993314i	$0.463171\pi$
$420$	0.401652	+	0.0104588i	0.0195986	+	0.000510339i
$421$			28.1593i			1.37240i	0.727413	+	0.686200i	$0.240723\pi$
$421$			28.1593i			1.37240i	−0.727413	+	0.686200i	$0.759277\pi$
$422$	−8.11092	+	14.0485i	−0.394834	+	0.683872i
$423$	17.0469	+	19.3854i	0.828850	+	0.942548i
$424$	12.1291	−	7.00275i	0.589042	−	0.340084i
$425$	6.66803	−	11.5494i	0.323447	−	0.560226i
$426$	3.56071	+	2.91818i	0.172517	+	0.141386i
$427$	−5.69404	−	2.31852i	−0.275554	−	0.112201i
$428$		−	2.69510i		−	0.130272i
$429$	−31.5373	−	15.9983i	−1.52264	−	0.772407i
$430$	0.736316	−	0.425112i	0.0355083	−	0.0205007i
$431$	18.2440	+	31.5996i	0.878783	+	1.52210i	0.852677	+	0.522438i	$0.174978\pi$
$431$	18.2440	+	31.5996i	0.878783	+	1.52210i	0.0261063	+	0.999659i	$0.491689\pi$
$432$	2.75286	+	4.40701i	0.132447	+	0.212032i
$433$			4.54367i			0.218355i	0.994022	+	0.109177i	$0.0348216\pi$
$433$			4.54367i			0.218355i	−0.994022	+	0.109177i	$0.965178\pi$
$434$	2.31648	−	0.319157i	0.111195	−	0.0153200i
$435$	0.686839	+	0.562898i	0.0329314	+	0.0269889i
$436$	−6.64244	−	3.83502i	−0.318115	−	0.183664i
$437$	7.07321	−	4.08372i	0.338357	−	0.195351i
$438$	2.31070	−	14.0548i	0.110409	−	0.671564i
$439$	−19.3010	−	11.1434i	−0.921185	−	0.531847i	−0.0371724	−	0.999309i	$-0.511835\pi$
$439$	−19.3010	−	11.1434i	−0.921185	−	0.531847i	−0.884013	+	0.467462i	$0.845168\pi$
$440$		−	0.496484i		−	0.0236689i
$441$	−20.9715	−	1.09292i	−0.998645	−	0.0520438i
$442$	−6.49936	−	7.10814i	−0.309143	−	0.338100i
$443$	−22.9471	−	13.2485i	−1.09025	−	0.629457i	−0.156608	−	0.987661i	$-0.550056\pi$
$443$	−22.9471	−	13.2485i	−1.09025	−	0.629457i	−0.933643	+	0.358204i	$0.883389\pi$
$444$	0.900351	+	0.148023i	0.0427287	+	0.00702487i
$445$	−0.148620	−	0.257418i	−0.00704527	−	0.0122028i
$446$	9.21163	−	15.9550i	0.436183	−	0.755491i
$447$	17.1652	+	14.0677i	0.811887	+	0.665380i
$448$	−2.62099	+	0.361112i	−0.123830	+	0.0170609i
$449$	−41.7613			−1.97084			−0.985420	−	0.170141i	$-0.945578\pi$
$449$	−41.7613			−1.97084			−0.985420	+	0.170141i	$0.945578\pi$
$450$	14.1886	+	4.79500i	0.668857	+	0.226038i
$451$	44.1040	−	25.4635i	2.07678	−	1.19903i
$452$	−6.86710	+	3.96472i	−0.323001	+	0.186485i
$453$	−2.51461	−	6.66748i	−0.118147	−	0.313266i
$454$		−	4.31729i		−	0.202620i
$455$	−0.289940	−	0.784525i	−0.0135926	−	0.0367791i
$456$	−8.91371	−	7.30522i	−0.417423	−	0.342098i
$457$	−17.3505	−	10.0173i	−0.811621	−	0.468590i	0.0358974	−	0.999355i	$-0.488571\pi$
$457$	−17.3505	−	10.0173i	−0.811621	−	0.468590i	−0.847519	+	0.530766i	$0.821904\pi$
$458$	6.51189	+	11.2789i	0.304280	+	0.527029i
$459$	13.8722	−	0.482296i	0.647499	−	0.0225116i
$460$	−0.0538110	+	0.0932033i	−0.00250895	+	0.00434563i
$461$		−	8.77765i		−	0.408816i	−0.978886	−	0.204408i	$-0.934473\pi$
$461$		−	8.77765i		−	0.408816i	0.978886	−	0.204408i	$-0.0655269\pi$
$462$	−0.675482	+	25.9406i	−0.0314263	+	1.20687i
$463$		−	17.9312i		−	0.833334i	−0.909059	−	0.416667i	$-0.863198\pi$
$463$		−	17.9312i		−	0.833334i	0.909059	−	0.416667i	$-0.136802\pi$
$464$	−5.06421	−	2.92382i	−0.235100	−	0.135735i
$465$	−0.132440	−	0.0217740i	−0.00614176	−	0.00100974i
$466$	−14.2073	+	8.20260i	−0.658142	+	0.379978i
$467$	8.47219	−	14.6743i	0.392046	−	0.679044i	−0.600673	−	0.799495i	$-0.705101\pi$
$467$	8.47219	−	14.6743i	0.392046	−	0.679044i	0.992719	+	0.120451i	$0.0384339\pi$
$468$	6.39358	−	8.72480i	0.295543	−	0.403304i
$469$	15.7787	−	12.2589i	0.728593	−	0.566065i
$470$	0.754449			0.0348001
$471$	11.8220	+	31.3459i	0.544728	+	1.44434i
$472$	−3.11423	+	1.79800i	−0.143344	+	0.0827597i
$473$	27.4558	+	47.5549i	1.26242	+	2.18658i
$474$	23.3166	−	8.79373i	1.07097	−	0.403910i
$475$	−33.2180			−1.52415
$476$	−2.66534	+	6.54580i	−0.122166	+	0.300026i
$477$	41.1981	−	8.25273i	1.88633	−	0.377866i
$478$	−7.69636	+	13.3305i	−0.352023	+	0.609723i
$479$	7.22604	−	4.17195i	0.330166	−	0.190621i	−0.325749	−	0.945456i	$-0.605616\pi$
$479$	7.22604	−	4.17195i	0.330166	−	0.190621i	0.655915	+	0.754835i	$0.272283\pi$
$480$	0.149850	+	0.0246363i	0.00683968	+	0.00112449i
$481$	−0.409108	−	1.85481i	−0.0186537	−	0.0845720i
$482$	−7.79411			−0.355012
$483$	2.93836	−	4.79654i	0.133700	−	0.218250i
$484$	21.0653			0.957515
$485$	0.795594	+	0.459336i	0.0361260	+	0.0208574i
$486$	3.59106	+	15.1692i	0.162894	+	0.688088i
$487$	−12.4028	+	7.16075i	−0.562023	+	0.324484i	−0.753957	−	0.656924i	$-0.771857\pi$
$487$	−12.4028	+	7.16075i	−0.562023	+	0.324484i	0.191934	+	0.981408i	$0.438524\pi$
$488$	−2.01240	−	1.16186i	−0.0910970	−	0.0525949i
$489$	19.3665	−	23.6307i	0.875784	−	1.06862i
$490$	−0.428728	+	0.439170i	−0.0193680	+	0.0198397i
$491$		−	7.65264i		−	0.345359i	−0.984978	−	0.172679i	$-0.944758\pi$
$491$		−	7.65264i		−	0.345359i	0.984978	−	0.172679i	$-0.0552424\pi$
$492$	5.49694	+	14.5751i	0.247821	+	0.657097i
$493$	−13.5281	+	7.81046i	−0.609276	+	0.351766i
$494$	−7.23876	+	22.8726i	−0.325687	+	1.02909i
$495$	0.476861	−	1.41105i	0.0214333	−	0.0634221i
$496$	0.883818			0.0396846
$497$	−6.96652	+	0.959825i	−0.312491	+	0.0430540i
$498$	3.14150	−	3.83321i	0.140774	−	0.171770i
$499$	−23.5183	−	13.5783i	−1.05283	−	0.607849i	−0.129386	−	0.991594i	$-0.541301\pi$
$499$	−23.5183	−	13.5783i	−1.05283	−	0.607849i	−0.923439	+	0.383745i	$0.874634\pi$
$500$	0.758724	−	0.438049i	0.0339312	−	0.0195902i
$501$	−26.5506	−	4.36508i	−1.18619	−	0.195017i
$502$	3.95965	−	6.85831i	0.176728	−	0.306101i
$503$	27.6274			1.23185			0.615923	−	0.787806i	$-0.288783\pi$
$503$	27.6274			1.23185			0.615923	+	0.787806i	$0.288783\pi$
$504$	−7.79594	−	1.49109i	−0.347259	−	0.0664183i
$505$		−	0.293307i		−	0.0130520i
$506$	−6.01952	−	3.47537i	−0.267600	−	0.154499i
$507$	−21.8034	−	5.62232i	−0.968324	−	0.249696i
$508$	−2.40415	−	4.16411i	−0.106667	−	0.184752i
$509$	12.2242	+	7.05762i	0.541826	+	0.312823i	0.745819	−	0.666149i	$-0.232058\pi$
$509$	12.2242	+	7.05762i	0.541826	+	0.312823i	−0.203993	+	0.978972i	$0.565392\pi$
$510$	0.257143	−	0.313761i	0.0113865	−	0.0138936i
$511$	13.3486	+	17.1812i	0.590506	+	0.760052i
$512$	−1.00000			−0.0441942
$513$	−18.3171	−	29.3235i	−0.808720	−	1.29466i
$514$	4.92741	+	8.53452i	0.217339	+	0.376442i
$515$	−0.545087	−	0.944119i	−0.0240194	−	0.0416029i
$516$	−15.7155	+	5.92704i	−0.691837	+	0.260923i
$517$			48.7260i			2.14297i
$518$	−1.10063	+	0.855110i	−0.0483589	+	0.0375714i
$519$	21.8387	+	17.8979i	0.958613	+	0.785629i
$520$	−0.0680900	−	0.308705i	−0.00298594	−	0.0135376i
$521$	3.15726	+	5.46854i	0.138322	+	0.239581i	0.926862	−	0.375403i	$-0.122496\pi$
$521$	3.15726	+	5.46854i	0.138322	+	0.239581i	−0.788539	+	0.614984i	$0.789162\pi$
$522$	−11.5847	−	13.1738i	−0.507048	−	0.576603i
$523$	29.7281	+	17.1636i	1.29992	+	0.750510i	0.980390	−	0.197066i	$-0.0631414\pi$
$523$	29.7281	+	17.1636i	1.29992	+	0.750510i	0.319531	+	0.947576i	$0.396475\pi$
$524$	−19.7963			−0.864805
$525$	−20.1037	+	10.9192i	−0.877396	+	0.476553i
$526$			23.3947i			1.02006i
$527$	1.18048	−	2.04465i	0.0514225	−	0.0890664i
$528$	−1.59113	+	9.67803i	−0.0692450	+	0.421182i
$529$	−10.7466	−	18.6137i	−0.467246	−	0.809293i
$530$	0.613982	−	1.06345i	0.0266697	−	0.0461933i
$531$	−10.5779	+	2.11894i	−0.459040	+	0.0919542i
$532$	17.4396	−	2.40278i	0.756104	−	0.104174i
$533$	23.9310	−	21.8814i	1.03656	−	0.947787i
$534$	2.07210	+	5.49418i	0.0896688	+	0.237756i
$535$	−0.118149	−	0.204641i	−0.00510805	−	0.00884740i
$536$	6.54039	−	3.77610i	0.282502	−	0.163103i
$537$	5.49657	+	14.5741i	0.237194	+	0.628920i
$538$	1.71976			0.0741443
$539$	−28.3637	−	27.6894i	−1.22171	−	1.19266i
$540$	0.402224	+	0.213946i	0.0173090	+	0.00920676i
$541$	8.13741	+	4.69814i	0.349855	+	0.201989i	0.664621	−	0.747180i	$-0.268593\pi$
$541$	8.13741	+	4.69814i	0.349855	+	0.201989i	−0.314767	+	0.949169i	$0.601926\pi$
$542$	8.00242	+	13.8606i	0.343733	+	0.595364i
$543$	12.1484	+	1.99727i	0.521336	+	0.0857109i
$544$	−1.33566	+	2.31343i	−0.0572659	+	0.0991875i
$545$	−0.672488			−0.0288062
$546$	3.13761	+	16.2221i	0.134277	+	0.694240i
$547$	−11.4919			−0.491360			−0.245680	−	0.969351i	$-0.579011\pi$
$547$	−11.4919			−0.491360			−0.245680	+	0.969351i	$0.579011\pi$
$548$	6.29121	−	10.8967i	0.268747	−	0.465484i
$549$	−4.60348	−	5.23497i	−0.196472	−	0.223423i
$550$	14.1348	+	24.4822i	0.602710	+	1.04392i
$551$	33.6964	+	19.4546i	1.43552	+	0.828795i
$552$	1.34764	−	1.64437i	0.0573595	−	0.0699892i
$553$	−14.3552	+	35.2549i	−0.610446	+	1.49919i
$554$	12.2425			0.520135
$555$	0.0748534	−	0.0282306i	0.00317735	−	0.00119832i
$556$	−16.9753	+	9.80069i	−0.719913	+	0.415642i
$557$	−3.51222	−	6.08334i	−0.148818	−	0.257760i	0.781973	−	0.623312i	$-0.214213\pi$
$557$	−3.51222	−	6.08334i	−0.148818	−	0.257760i	−0.930791	+	0.365553i	$0.880880\pi$
$558$	2.51189	+	0.848886i	0.106337	+	0.0359362i
$559$	23.5934	+	25.8034i	0.997896	+	1.09137i
$560$	−0.183183	+	0.142320i	−0.00774091	+	0.00601413i
$561$	20.2642	+	16.6075i	0.855557	+	0.701170i
$562$	−4.04619	+	7.00820i	−0.170678	+	0.295623i
$563$	19.9568	+	34.5661i	0.841078	+	1.45679i	0.888985	+	0.457937i	$0.151412\pi$
$563$	19.9568	+	34.5661i	0.841078	+	1.45679i	−0.0479070	+	0.998852i	$0.515255\pi$
$564$	−14.7066	−	2.41786i	−0.619259	−	0.101810i
$565$	−0.347616	+	0.602089i	−0.0146243	+	0.0253301i
$566$			3.35511i			0.141026i
$567$	−20.7246	−	11.7256i	−0.870352	−	0.492430i
$568$	−2.65797			−0.111526
$569$	−31.7330	−	18.3210i	−1.33032	−	0.768058i	−0.344968	−	0.938615i	$-0.612110\pi$
$569$	−31.7330	−	18.3210i	−1.33032	−	0.768058i	−0.985348	+	0.170557i	$0.945443\pi$
$570$	−0.997076	−	0.163926i	−0.0417629	−	0.00686609i
$571$	−2.72588	−	4.72136i	−0.114075	−	0.197583i	0.803335	−	0.595528i	$-0.203057\pi$
$571$	−2.72588	−	4.72136i	−0.114075	−	0.197583i	−0.917409	+	0.397945i	$0.869724\pi$
$572$	19.9377	−	4.39758i	0.833636	−	0.183872i
$573$	15.6305	−	19.0721i	0.652975	−	0.796750i
$574$	−22.0377	−	8.97341i	−0.919837	−	0.374543i
$575$		−	6.12795i		−	0.255553i
$576$	−2.84209	−	0.960476i	−0.118420	−	0.0400199i
$577$	12.5609	+	21.7561i	0.522917	+	0.905719i	0.999644	+	0.0266678i	$0.00848964\pi$
$577$	12.5609	+	21.7561i	0.522917	+	0.905719i	−0.476727	+	0.879051i	$0.658177\pi$
$578$	−4.93203	−	8.54252i	−0.205145	−	0.355322i
$579$	9.11510	+	24.1687i	0.378811	+	1.00442i
$580$	−0.512706			−0.0212890
$581$	1.03328	+	7.49965i	0.0428676	+	0.311138i
$582$	−14.0365	−	11.5036i	−0.581834	−	0.476841i
$583$	68.6827	+	39.6540i	2.84455	+	1.64230i
$584$	4.11174	+	7.12173i	0.170145	+	0.294699i
$585$	0.102986	−	0.942767i	0.00425795	−	0.0389786i
$586$	18.3641	+	10.6025i	0.758612	+	0.437985i
$587$		−	22.1376i		−	0.913717i	−0.889539	−	0.456859i	$-0.848975\pi$
$587$		−	22.1376i		−	0.913717i	0.889539	−	0.456859i	$-0.151025\pi$
$588$	9.76471	−	7.18682i	0.402690	−	0.296379i
$589$	−5.88078			−0.242313
$590$	−0.157644	+	0.273047i	−0.00649010	+	0.0112412i
$591$	−1.57281	+	9.56660i	−0.0646967	+	0.393517i
$592$	−0.456219	+	0.263398i	−0.0187505	+	0.0108256i
$593$	−6.33623	−	3.65823i	−0.260198	−	0.150225i	0.364227	−	0.931310i	$-0.381333\pi$
$593$	−6.33623	−	3.65823i	−0.260198	−	0.150225i	−0.624425	+	0.781085i	$0.714667\pi$
$594$	−13.8177	+	25.9776i	−0.566945	+	1.06587i
$595$	0.0845775	+	0.613873i	0.00346734	+	0.0251663i
$596$	−12.8133			−0.524855
$597$	0.359379	+	0.952892i	0.0147084	+	0.0389993i
$598$	−4.21946	−	1.33538i	−0.172547	−	0.0546079i
$599$	−35.3925	+	20.4339i	−1.44610	+	0.834906i	−0.998246	−	0.0592009i	$-0.981145\pi$
$599$	−35.3925	+	20.4339i	−1.44610	+	0.834906i	−0.447854	+	0.894107i	$0.647811\pi$
$600$	−8.09066	+	3.05136i	−0.330300	+	0.124571i
$601$		−	6.67453i		−	0.272260i	−0.990691	−	0.136130i	$-0.956534\pi$
$601$		−	6.67453i		−	0.272260i	0.990691	−	0.136130i	$-0.0434664\pi$
$602$	9.67552	−	23.7620i	0.394345	−	0.968469i
$603$	22.2152	−	4.45012i	0.904674	−	0.181223i
$604$	3.56296	+	2.05707i	0.144975	+	0.0837011i
$605$	1.59951	−	0.923476i	0.0650292	−	0.0375446i
$606$	−0.939988	+	5.71747i	−0.0381844	+	0.232256i
$607$	19.4541	+	11.2318i	0.789617	+	0.455886i	0.839828	−	0.542853i	$-0.182656\pi$
$607$	19.4541	+	11.2318i	0.789617	+	0.455886i	−0.0502106	+	0.998739i	$0.515989\pi$
$608$	6.65383			0.269849
$609$	26.7882	+	0.697553i	1.08551	+	0.0282663i
$610$	−0.203737			−0.00824908
$611$	6.68250	+	30.2970i	0.270345	+	1.22568i
$612$	−6.01806	+	5.29211i	−0.243266	+	0.213921i
$613$	7.57215	−	4.37178i	0.305836	−	0.176575i	−0.339225	−	0.940705i	$-0.610165\pi$
$613$	7.57215	−	4.37178i	0.305836	−	0.176575i	0.645062	+	0.764130i	$0.276832\pi$
$614$	−9.53501	+	16.5151i	−0.384802	+	0.666496i
$615$	1.05634	+	0.865721i	0.0425957	+	0.0349093i
$616$	−9.19173	−	11.8309i	−0.370345	−	0.476679i
$617$	−33.2275			−1.33769			−0.668845	−	0.743402i	$-0.733211\pi$
$617$	−33.2275			−1.33769			−0.668845	+	0.743402i	$0.733211\pi$
$618$	7.59976	+	20.1508i	0.305707	+	0.810582i
$619$	−9.75542	−	16.8969i	−0.392103	−	0.679143i	0.600623	−	0.799532i	$-0.294919\pi$
$619$	−9.75542	−	16.8969i	−0.392103	−	0.679143i	−0.992727	+	0.120389i	$0.961586\pi$
$620$	0.0671090	−	0.0387454i	0.00269516	−	0.00155605i
$621$	5.40951	−	3.37908i	0.217076	−	0.135598i
$622$	3.82324			0.153298
$623$	−8.30726	−	3.38258i	−0.332824	−	0.135520i
$624$	0.337951	+	6.23585i	0.0135289	+	0.249634i
$625$	−12.4424	+	21.5508i	−0.497695	+	0.862033i
$626$	−16.6808	+	9.63067i	−0.666699	+	0.384919i
$627$	10.5871	−	64.3960i	0.422808	−	2.57173i
$628$	−16.7506	−	9.67095i	−0.668421	−	0.385913i
$629$			1.40724i			0.0561103i
$630$	−0.657319	+	0.228544i	−0.0261882	+	0.00910541i
$631$		−	44.3163i		−	1.76421i	−0.471057	−	0.882103i	$-0.656128\pi$
$631$		−	44.3163i		−	1.76421i	0.471057	−	0.882103i	$-0.343872\pi$
$632$	−7.19370	+	12.4599i	−0.286150	+	0.495626i
$633$	4.55814	−	27.7249i	0.181170	−	1.10196i
$634$	−12.3152	−	21.3306i	−0.489100	−	0.847147i
$635$	−0.365098	−	0.210789i	−0.0144885	−	0.00836491i
$636$	−15.3766	+	18.7623i	−0.609721	+	0.743973i
$637$	−21.4335	−	13.3268i	−0.849227	−	0.528028i
$638$		−	33.1130i		−	1.31096i
$639$	−7.55420	−	2.55292i	−0.298839	−	0.100992i
$640$	−0.0759308	+	0.0438386i	−0.00300143	+	0.00173287i
$641$	5.36714	−	3.09872i	0.211989	−	0.122392i	−0.390246	−	0.920711i	$-0.627610\pi$
$641$	5.36714	−	3.09872i	0.211989	−	0.122392i	0.602236	+	0.798318i	$0.294277\pi$
$642$	1.64727	+	4.36774i	0.0650127	+	0.172381i
$643$	21.2665			0.838669			0.419334	−	0.907832i	$-0.362263\pi$
$643$	21.2665			0.838669			0.419334	+	0.907832i	$0.362263\pi$
$644$	0.443257	+	3.21721i	0.0174668	+	0.126776i
$645$	−0.933458	+	1.13899i	−0.0367549	+	0.0448477i
$646$	8.88725	−	15.3932i	0.349664	−	0.605636i
$647$	−3.77674	−	6.54151i	−0.148479	−	0.257173i	0.782186	−	0.623044i	$-0.214104\pi$
$647$	−3.77674	−	6.54151i	−0.148479	−	0.257173i	−0.930666	+	0.365871i	$0.880771\pi$
$648$	−7.15497	−	5.45952i	−0.281074	−	0.214470i
$649$	−17.6347	−	10.1814i	−0.692223	−	0.399655i
$650$	12.1464	+	13.2841i	0.476420	+	0.521045i
$651$	−3.55907	+	1.93309i	−0.139491	+	0.0757638i
$652$			17.6397i			0.690823i
$653$	−27.7842	−	16.0412i	−1.08728	−	0.627742i	−0.154430	−	0.988004i	$-0.549354\pi$
$653$	−27.7842	−	16.0412i	−1.08728	−	0.627742i	−0.932851	+	0.360262i	$0.882687\pi$
$654$	13.1089	+	2.15519i	0.512599	+	0.0842744i
$655$	−1.50315	+	0.867843i	−0.0587329	+	0.0339094i
$656$	−7.78862	−	4.49676i	−0.304094	−	0.175569i
$657$	4.84567	+	24.1898i	0.189048	+	0.943736i
$658$	17.9780	−	13.9676i	0.700855	−	0.544514i
$659$		−	8.17705i		−	0.318533i	−0.987236	−	0.159266i	$-0.949087\pi$
$659$		−	8.17705i		−	0.318533i	0.987236	−	0.159266i	$-0.0509128\pi$
$660$	0.303456	+	0.804613i	0.0118120	+	0.0313195i
$661$	−13.8904	−	24.0589i	−0.540274	−	0.935782i	−0.998888	−	0.0471464i	$-0.984987\pi$
$661$	−13.8904	−	24.0589i	−0.540274	−	0.935782i	0.458614	−	0.888636i	$-0.348346\pi$
$662$	3.59847	−	2.07757i	0.139858	−	0.0807472i
$663$	14.8776	+	7.54714i	0.577797	+	0.293107i
$664$			2.86138i			0.111043i
$665$	1.21887	−	0.946975i	0.0472658	−	0.0367221i
$666$	−1.54960	+	0.310414i	−0.0600459	+	0.0120283i
$667$	−3.58893	+	6.21621i	−0.138964	+	0.240693i
$668$	13.4535	−	7.76738i	0.520532	−	0.300529i
$669$	−5.17671	+	31.4873i	−0.200143	+	1.21737i
$670$	0.331078	−	0.573444i	0.0127907	−	0.0221541i
$671$		−	13.1583i		−	0.507972i
$672$	4.02693	−	2.18721i	0.155342	−	0.0843733i
$673$	36.4941			1.40674			0.703372	−	0.710822i	$-0.251677\pi$
$673$	36.4941			1.40674			0.703372	+	0.710822i	$0.251677\pi$
$674$	−0.811986	+	1.40640i	−0.0312765	+	0.0541725i
$675$	−25.9252	+	0.901342i	−0.997860	+	0.0346927i
$676$	11.7938	−	5.46868i	0.453607	−	0.210334i
$677$	−7.78434	+	13.4829i	−0.299176	+	0.518189i	−0.975948	−	0.218004i	$-0.930045\pi$
$677$	−7.78434	+	13.4829i	−0.299176	+	0.518189i	0.676771	+	0.736193i	$0.263379\pi$
$678$	8.70570	−	10.6226i	0.334340	−	0.407957i
$679$	27.4624	−	3.78369i	1.05391	−	0.145205i
$680$			0.234214i			0.00898170i
$681$	2.63877	+	6.99670i	0.101118	+	0.268114i
$682$	2.50237	+	4.33422i	0.0958205	+	0.165966i
$683$	−6.05165	−	10.4818i	−0.231560	−	0.401074i	0.726707	−	0.686947i	$-0.241050\pi$
$683$	−6.05165	−	10.4818i	−0.231560	−	0.401074i	−0.958267	+	0.285873i	$0.907716\pi$
$684$	18.9108	+	6.39085i	0.723073	+	0.244360i
$685$		−	1.10319i		−	0.0421508i
$686$	−2.08565	+	18.4024i	−0.0796306	+	0.702609i
$687$	−17.4471	−	14.2987i	−0.665649	−	0.545531i
$688$	4.84860	−	8.39803i	0.184851	−	0.320172i
$689$	48.1440	+	15.2367i	1.83414	+	0.580472i
$690$	0.0302405	−	0.183937i	0.00115123	−	0.00700238i
$691$	7.19903	−	12.4691i	0.273864	−	0.474347i	−0.695984	−	0.718057i	$-0.745031\pi$
$691$	7.19903	−	12.4691i	0.273864	−	0.474347i	0.969848	+	0.243711i	$0.0783648\pi$
$692$	−16.3020			−0.619708
$693$	−14.7605	−	42.4528i	−0.560704	−	1.61265i
$694$			4.98244i			0.189131i
$695$	−0.859298	+	1.48835i	−0.0325950	+	0.0564563i
$696$	9.99425	+	1.64312i	0.378831	+	0.0622822i
$697$	−20.8059	+	12.0123i	−0.788079	+	0.454998i
$698$	−9.23276	+	15.9916i	−0.349465	+	0.605291i
$699$	18.0112	−	21.9770i	0.681246	−	0.831246i
$700$	4.98115	−	12.2332i	0.188270	−	0.462370i
$701$			33.4107i			1.26190i	0.775822	+	0.630952i	$0.217335\pi$
$701$			33.4107i			1.26190i	−0.775822	+	0.630952i	$0.782665\pi$
$702$	−5.02890	+	18.0474i	−0.189803	+	0.681157i
$703$	3.03560	−	1.75261i	0.114490	−	0.0661008i
$704$	−2.83131	−	4.90398i	−0.106709	−	0.184826i
$705$	−1.22268	+	0.461127i	−0.0460487	+	0.0173671i
$706$		−	20.3986i		−	0.767710i
$707$	−5.43018	−	6.98929i	−0.204223	−	0.262859i
$708$	3.94804	−	4.81734i	0.148376	−	0.181047i
$709$	25.6450	+	14.8062i	0.963119	+	0.556057i	0.897132	−	0.441764i	$-0.145647\pi$
$709$	25.6450	+	14.8062i	0.963119	+	0.556057i	0.0659873	+	0.997820i	$0.478980\pi$
$710$	−0.201822	+	0.116522i	−0.00757424	+	0.00437299i
$711$	−32.4126	+	28.5027i	−1.21557	+	1.06893i
$712$	−2.93597	−	1.69508i	−0.110030	−	0.0635259i
$713$		−	1.08487i		−	0.0406286i
$714$	0.318656	−	12.2374i	0.0119254	−	0.457972i
$715$	1.32110	−	1.20795i	0.0494063	−	0.0451748i
$716$	−7.78809	−	4.49646i	−0.291055	−	0.168041i
$717$	4.32517	−	26.3078i	0.161526	−	0.982483i
$718$	−1.49774	−	2.59416i	−0.0558952	−	0.0968133i
$719$	−14.5300	+	25.1667i	−0.541877	+	0.938558i	0.456919	+	0.889508i	$0.348953\pi$
$719$	−14.5300	+	25.1667i	−0.541877	+	0.938558i	−0.998796	+	0.0490503i	$0.984381\pi$
$720$	−0.257908	+	0.0516637i	−0.00961167	+	0.00192539i
$721$	−30.4682	−	12.4061i	−1.13469	−	0.462029i
$722$	−25.2735			−0.940583
$723$	12.6313	−	4.76384i	0.469764	−	0.177169i
$724$	−6.15572	+	3.55401i	−0.228776	+	0.132084i
$725$	25.2821	−	14.5966i	0.938955	−	0.542106i
$726$	−34.1390	+	12.8754i	−1.26702	+	0.477849i
$727$			10.8801i			0.403521i	0.979435	+	0.201761i	$0.0646663\pi$
$727$			10.8801i			0.403521i	−0.979435	+	0.201761i	$0.935334\pi$
$728$	−7.33780	−	6.09563i	−0.271957	−	0.225919i
$729$	−15.0913	−	22.3886i	−0.558938	−	0.829209i
$730$	0.624414	+	0.360506i	0.0231106	+	0.0133429i
$731$	−12.9522	−	22.4338i	−0.479053	−	0.829744i
$732$	3.97148	+	0.652936i	0.146790	+	0.0241332i
$733$	25.2212	−	43.6845i	0.931568	−	1.61352i	0.150925	−	0.988545i	$-0.451775\pi$
$733$	25.2212	−	43.6845i	0.931568	−	1.61352i	0.780643	−	0.624978i	$-0.214892\pi$
$734$		−	0.431332i		−	0.0159208i
$735$	0.426382	−	0.973772i	0.0157273	−	0.0359181i
$736$			1.22748i			0.0452454i
$737$	37.0358	+	21.3826i	1.36423	+	0.787639i
$738$	−17.8169	−	20.2610i	−0.655850	−	0.745817i
$739$	−4.88879	+	2.82254i	−0.179837	+	0.103829i	−0.587216	−	0.809430i	$-0.699776\pi$
$739$	−4.88879	+	2.82254i	−0.179837	+	0.103829i	0.407379	+	0.913259i	$0.366443\pi$
$740$	−0.0230940	+	0.0400000i	−0.000848953	+	0.00147043i
$741$	−2.24867	−	41.4923i	−0.0826070	−	1.52426i
$742$	−5.05756	−	36.7083i	−0.185669	−	1.34760i
$743$	−12.6489			−0.464041			−0.232021	−	0.972711i	$-0.574534\pi$
$743$	−12.6489			−0.464041			−0.232021	+	0.972711i	$0.574534\pi$
$744$	−1.43234	+	0.540199i	−0.0525120	+	0.0198047i
$745$	−0.972927	+	0.561720i	−0.0356453	+	0.0205798i
$746$	−5.60905	−	9.71516i	−0.205362	−	0.355697i
$747$	−2.74829	+	8.13230i	−0.100555	+	0.297545i
$748$	−15.1267			−0.553086
$749$	−6.60407	−	2.68907i	−0.241308	−	0.0982565i
$750$	−0.961866	+	1.17365i	−0.0351224	+	0.0428558i
$751$	−0.800219	+	1.38602i	−0.0292004	+	0.0505766i	−0.880256	−	0.474498i	$-0.842629\pi$
$751$	−0.800219	+	1.38602i	−0.0292004	+	0.0505766i	0.851056	+	0.525075i	$0.175963\pi$
$752$	7.45201	−	4.30242i	0.271747	−	0.156893i
$753$	−2.22523	+	13.5349i	−0.0810918	+	0.493240i
$754$	−4.54127	−	20.5891i	−0.165383	−	0.749811i
$755$	0.360717			0.0131278
$756$	13.5457	−	2.34847i	0.492651	−	0.0854130i
$757$	−46.2341			−1.68041			−0.840203	−	0.542272i	$-0.817564\pi$
$757$	−46.2341			−1.68041			−0.840203	+	0.542272i	$0.817564\pi$
$758$	−9.93910	−	5.73834i	−0.361004	−	0.208426i
$759$	11.8796	+	1.95308i	0.431201	+	0.0708922i
$760$	0.505231	−	0.291695i	0.0183266	−	0.0105809i
$761$	−29.1876	−	16.8515i	−1.05805	−	0.610865i	−0.133157	−	0.991095i	$-0.542512\pi$
$761$	−29.1876	−	16.8515i	−1.05805	−	0.610865i	−0.924892	+	0.380230i	$0.875845\pi$
$762$	6.44136	+	5.27901i	0.233346	+	0.191238i
$763$	−16.0249	+	12.4502i	−0.580141	+	0.450728i
$764$			14.2368i			0.515070i
$765$	−0.224957	+	0.665658i	−0.00813334	+	0.0240669i
$766$	−0.325127	+	0.187712i	−0.0117473	+	0.00678232i
$767$	−12.3613	−	3.91212i	−0.446340	−	0.141259i
$768$	1.62062	−	0.611211i	0.0584792	−	0.0220552i
$769$	22.1719			0.799539			0.399769	−	0.916616i	$-0.369090\pi$
$769$	22.1719			0.799539			0.399769	+	0.916616i	$0.369090\pi$
$770$	−1.21658	−	0.495373i	−0.0438427	−	0.0178520i
$771$	−13.2019	−	10.8196i	−0.475454	−	0.389657i
$772$	−12.9152	−	7.45659i	−0.464828	−	0.268369i
$773$	1.94637	−	1.12374i	0.0700061	−	0.0404181i	−0.464588	−	0.885527i	$-0.653798\pi$
$773$	1.94637	−	1.12374i	0.0700061	−	0.0404181i	0.534595	+	0.845109i	$0.320464\pi$
$774$	21.8463	−	19.2110i	0.785248	−	0.690525i
$775$	−2.20615	+	3.82116i	−0.0792472	+	0.137260i
$776$	10.4779			0.376134
$777$	1.26105	−	2.05853i	0.0452400	−	0.0738493i
$778$		−	32.6910i		−	1.17203i
$779$	51.8242	+	29.9207i	1.85679	+	1.07202i
$780$	0.299032	+	0.458677i	0.0107071	+	0.0164233i
$781$	−7.52555	−	13.0346i	−0.269285	−	0.466416i
$782$	2.83968	+	1.63949i	0.101547	+	0.0586281i
$783$	26.8264	+	14.2691i	0.958698	+	0.509937i
$784$	−1.73026	+	6.78279i	−0.0617950	+	0.242242i
$785$	−1.69585			−0.0605273
$786$	32.0824	−	12.0997i	1.14434	−	0.431582i
$787$	17.2066	+	29.8028i	0.613350	+	1.06235i	0.990672	+	0.136271i	$0.0435119\pi$
$787$	17.2066	+	29.8028i	0.613350	+	1.06235i	−0.377321	+	0.926082i	$0.623155\pi$
$788$	−2.79871	−	4.84751i	−0.0997000	−	0.172685i
$789$	−14.2991	−	37.9141i	−0.509062	−	1.34978i
$790$			1.26145i			0.0448803i
$791$	2.86342	+	20.7830i	0.101811	+	0.738958i
$792$	−3.33670	−	16.6570i	−0.118564	−	0.591879i
$793$	−1.80459	−	8.18163i	−0.0640830	−	0.290538i
$794$	−9.57692	−	16.5877i	−0.339872	−	0.588676i
$795$	−0.345043	+	2.09872i	−0.0122374	+	0.0744340i
$796$	−0.509204	−	0.293989i	−0.0180483	−	0.0104202i
$797$	0.908350			0.0321754			0.0160877	−	0.999871i	$-0.494879\pi$
$797$	0.908350			0.0321754			0.0160877	+	0.999871i	$0.494879\pi$
$798$	−26.7945	+	14.5533i	−0.948515	+	0.515181i
$799$		−	22.9863i		−	0.813196i
$800$	2.49616	−	4.32347i	0.0882525	−	0.152858i
$801$	−6.71621	−	7.63751i	−0.237305	−	0.269858i
$802$	2.06325	+	3.57365i	0.0728558	+	0.126190i
$803$	−23.2832	+	40.3277i	−0.821647	+	1.42313i
$804$	−8.29152	+	10.1172i	−0.292419	+	0.356806i
$805$	0.174695	+	0.224853i	0.00615719	+	0.00792504i
$806$	2.15034	+	2.35176i	0.0757426	+	0.0828372i
$807$	−2.78709	+	1.05114i	−0.0981102	+	0.0370018i
$808$	−1.67265	−	2.89711i	−0.0588436	−	0.101920i
$809$	−14.8389	+	8.56724i	−0.521708	+	0.301208i	−0.737633	−	0.675202i	$-0.764057\pi$
$809$	−14.8389	+	8.56724i	−0.521708	+	0.301208i	0.215925	+	0.976410i	$0.430723\pi$
$810$	−0.782621	−	0.100882i	−0.0274985	−	0.00354462i
$811$	34.3753			1.20708			0.603540	−	0.797333i	$-0.293757\pi$
$811$	34.3753			1.20708			0.603540	+	0.797333i	$0.293757\pi$
$812$	−12.2174	+	9.49207i	−0.428748	+	0.333106i
$813$	−21.4407	−	17.5717i	−0.751957	−	0.616265i
$814$	−2.58340	−	1.49152i	−0.0905480	−	0.0522779i
$815$	0.773299	+	1.33939i	0.0270875	+	0.0469169i
$816$	0.750608	−	4.56557i	0.0262765	−	0.159827i
$817$	−32.2618	+	55.8791i	−1.12870	+	1.95496i
$818$	32.2722			1.12837
$819$	−15.0000	−	24.3721i	−0.524142	−	0.851631i
$820$	−0.788528			−0.0275366
$821$	−12.6949	+	21.9881i	−0.443054	+	0.767392i	−0.997914	−	0.0645517i	$-0.979438\pi$
$821$	−12.6949	+	21.9881i	−0.443054	+	0.767392i	0.554861	+	0.831943i	$0.312772\pi$
$822$	−3.53551	+	21.5047i	−0.123315	+	0.750063i
$823$	−2.14820	−	3.72079i	−0.0748815	−	0.129699i	0.826153	−	0.563446i	$-0.190525\pi$
$823$	−2.14820	−	3.72079i	−0.0748815	−	0.129699i	−0.901035	+	0.433747i	$0.857191\pi$
$824$	−10.7681	−	6.21697i	−0.375125	−	0.216579i
$825$	−37.8710	−	31.0371i	−1.31850	−	1.08057i
$826$	1.29856	+	9.42510i	0.0451827	+	0.327941i
$827$	21.4079			0.744426			0.372213	−	0.928147i	$-0.378599\pi$
$827$	21.4079			0.744426			0.372213	+	0.928147i	$0.378599\pi$
$828$	−1.17896	+	3.48860i	−0.0409718	+	0.121237i
$829$	−37.1532	+	21.4504i	−1.29038	+	0.745003i	−0.978722	−	0.205190i	$-0.934219\pi$
$829$	−37.1532	+	21.4504i	−1.29038	+	0.745003i	−0.311661	+	0.950193i	$0.600885\pi$
$830$	0.125439	+	0.217267i	0.00435405	+	0.00754144i
$831$	−19.8405	+	7.48277i	−0.688261	+	0.259574i
$832$	−2.43301	−	2.66091i	−0.0843496	−	0.0922505i
$833$	13.3805	+	13.0623i	0.463606	+	0.452583i
$834$	21.5203	−	26.2587i	0.745186	−	0.909265i
$835$	0.681023	−	1.17957i	0.0235678	−	0.0408206i
$836$	18.8391	+	32.6303i	0.651563	+	1.12854i
$837$	−4.58968	+	0.159570i	−0.158643	+	0.00551554i
$838$	2.36306	−	4.09295i	0.0816307	−	0.141388i
$839$		−	26.4635i		−	0.913622i	−0.889564	−	0.456811i	$-0.848992\pi$
$839$		−	26.4635i		−	0.913622i	0.889564	−	0.456811i	$-0.151008\pi$
$840$	0.209883	−	0.342611i	0.00724167	−	0.0118212i
$841$	−5.19498			−0.179137
$842$	24.3867	+	14.0796i	0.840420	+	0.485217i
$843$	2.27386	−	13.8307i	0.0783159	−	0.476356i
$844$	8.11092	+	14.0485i	0.279190	+	0.483570i
$845$	0.655772	−	0.932265i	0.0225593	−	0.0320709i
$846$	25.3117	−	5.07039i	0.870233	−	0.174324i
$847$	21.0182	−	51.6185i	0.722195	−	1.77363i
$848$		−	14.0055i		−	0.480951i
$849$	−2.05068	−	5.43737i	−0.0703791	−	0.186610i
$850$	−6.66803	−	11.5494i	−0.228711	−	0.396140i
$851$	0.323315	+	0.559998i	0.0110831	+	0.0191965i
$852$	4.30757	−	1.62458i	0.147575	−	0.0556572i
$853$	6.30916			0.216021			0.108011	−	0.994150i	$-0.465552\pi$
$853$	6.30916			0.216021			0.108011	+	0.994150i	$0.465552\pi$
$854$	−4.85492	+	3.77192i	−0.166132	+	0.129073i
$855$	1.71608	−	0.343762i	0.0586886	−	0.0117564i
$856$	−2.33402	−	1.34755i	−0.0797753	−	0.0460583i
$857$	−3.47394	−	6.01703i	−0.118667	−	0.205538i	0.800572	−	0.599236i	$-0.204529\pi$
$857$	−3.47394	−	6.01703i	−0.118667	−	0.205538i	−0.919240	+	0.393698i	$0.871196\pi$
$858$	−29.6236	+	19.3129i	−1.01133	+	0.659333i
$859$	−14.5807	−	8.41820i	−0.497489	−	0.287225i	0.230187	−	0.973146i	$-0.426066\pi$
$859$	−14.5807	−	8.41820i	−0.497489	−	0.287225i	−0.727676	+	0.685921i	$0.759399\pi$
$860$		−	0.850225i		−	0.0289924i
$861$	41.1995	+	1.07282i	1.40408	+	0.0365615i
$862$	36.4880			1.24279
$863$	−2.46354	+	4.26698i	−0.0838600	+	0.145250i	−0.904905	−	0.425614i	$-0.860058\pi$
$863$	−2.46354	+	4.26698i	−0.0838600	+	0.145250i	0.821045	+	0.570864i	$0.193392\pi$
$864$	5.19301	−	0.180546i	0.176670	−	0.00614230i
$865$	−1.23782	+	0.714656i	−0.0420872	+	0.0242990i
$866$	3.93493	+	2.27183i	0.133714	+	0.0772000i
$867$	13.2142	+	10.8297i	0.448779	+	0.367796i
$868$	0.881842	−	2.16571i	0.0299317	−	0.0735090i
$869$	−81.4705			−2.76370
$870$	0.830903	−	0.313371i	0.0281703	−	0.0106243i
$871$	25.9607	+	8.21609i	0.879645	+	0.278392i
$872$	−6.64244	+	3.83502i	−0.224941	+	0.129870i
$873$	29.7791	+	10.0638i	1.00787	+	0.340607i
$874$		−	8.16743i		−	0.276268i
$875$	−0.316370	−	2.29625i	−0.0106953	−	0.0776274i
$876$	−11.0165	−	9.02852i	−0.372212	−	0.305045i
$877$	25.2195	+	14.5605i	0.851601	+	0.491672i	0.861191	−	0.508282i	$-0.169719\pi$
$877$	25.2195	+	14.5605i	0.851601	+	0.491672i	−0.00958950	+	0.999954i	$0.503052\pi$
$878$	−19.3010	+	11.1434i	−0.651376	+	0.376072i
$879$	−36.2416	−	5.95835i	−1.22240	−	0.200970i
$880$	−0.429968	−	0.248242i	−0.0144942	−	0.00836823i
$881$	1.87116			0.0630411			0.0315205	−	0.999503i	$-0.489965\pi$
$881$	1.87116			0.0630411			0.0315205	+	0.999503i	$0.489965\pi$
$882$	−11.4323	+	17.6154i	−0.384944	+	0.593142i
$883$	37.4465			1.26018			0.630088	−	0.776524i	$-0.283019\pi$
$883$	37.4465			1.26018			0.630088	+	0.776524i	$0.283019\pi$
$884$	−9.40551	+	2.07454i	−0.316341	+	0.0697743i
$885$	0.0885921	−	0.538861i	0.00297799	−	0.0181136i
$886$	−22.9471	+	13.2485i	−0.770924	+	0.445093i
$887$	−16.0090	+	27.7284i	−0.537530	+	0.931029i	0.461506	+	0.887137i	$0.347309\pi$
$887$	−16.0090	+	27.7284i	−0.537530	+	0.931029i	−0.999036	+	0.0438921i	$0.986024\pi$
$888$	0.578367	−	0.705715i	0.0194087	−	0.0236822i
$889$	−12.6025	+	1.73633i	−0.422674	+	0.0582347i
$890$	−0.297240			−0.00996352
$891$	6.51543	−	50.5454i	0.218275	−	1.69334i
$892$	−9.21163	−	15.9550i	−0.308428	−	0.534213i
$893$	−49.5844	+	28.6276i	−1.65928	+	0.957986i
$894$	20.7656	−	7.83165i	0.694506	−	0.261930i
$895$	−0.788474			−0.0263558
$896$	−0.997764	+	2.45040i	−0.0333329	+	0.0818622i
$897$	7.65436	−	0.414828i	0.255572	−	0.0138507i
$898$	−20.8807	+	36.1664i	−0.696797	+	1.20689i
$899$	4.47584	−	2.58413i	0.149278	−	0.0861855i
$900$	11.2469	−	9.89020i	0.374897	−	0.329673i
$901$	−32.4007	−	18.7066i	−1.07943	−	0.623207i
$902$		−	50.9269i		−	1.69568i
$903$	−1.15676	+	44.4231i	−0.0384945	+	1.47831i
$904$			7.92944i			0.263729i
$905$	−0.311606	+	0.539717i	−0.0103581	+	0.0179408i
$906$	−7.03152	−	1.15603i	−0.233606	−	0.0384064i
$907$	−0.102258	−	0.177116i	−0.00339542	−	0.00588104i	0.864323	−	0.502938i	$-0.167747\pi$
$907$	−0.102258	−	0.177116i	−0.00339542	−	0.00588104i	−0.867718	+	0.497057i	$0.834414\pi$
$908$	−3.73888	−	2.15864i	−0.124079	−	0.0716371i
$909$	−1.97121	−	9.84040i	−0.0653810	−	0.326385i
$910$	−0.824389	−	0.141167i	−0.0273282	−	0.00467964i
$911$		−	9.73710i		−	0.322604i	−0.986905	−	0.161302i	$-0.948431\pi$
$911$		−	9.73710i		−	0.322604i	0.986905	−	0.161302i	$-0.0515694\pi$
$912$	−10.7834	+	4.06689i	−0.357073	+	0.134668i
$913$	−14.0321	+	8.10146i	−0.464396	+	0.268119i
$914$	−17.3505	+	10.0173i	−0.573903	+	0.331343i
$915$	0.330181	−	0.124526i	0.0109155	−	0.00411672i
$916$	13.0238			0.430317
$917$	−19.7520	+	48.5089i	−0.652270	+	1.60190i
$918$	6.51842	−	12.2548i	0.215140	−	0.404469i
$919$	−7.54494	+	13.0682i	−0.248885	+	0.431081i	−0.963217	−	0.268726i	$-0.913397\pi$
$919$	−7.54494	+	13.0682i	−0.248885	+	0.431081i	0.714332	+	0.699807i	$0.246731\pi$
$920$	0.0538110	+	0.0932033i	0.00177410	+	0.00307282i
$921$	5.35844	−	32.5927i	0.176567	−	1.07397i
$922$	−7.60166	−	4.38882i	−0.250347	−	0.144538i
$923$	−6.46688	−	7.07262i	−0.212860	−	0.232798i
$924$	22.1275	+	13.5553i	0.727941	+	0.445936i
$925$		−	2.62993i		−	0.0864716i
$926$	−15.5289	−	8.96560i	−0.510311	−	0.294628i
$927$	−24.6327	−	28.0117i	−0.809044	−	0.920026i
$928$	−5.06421	+	2.92382i	−0.166241	+	0.0959792i
$929$	−2.52193	−	1.45604i	−0.0827418	−	0.0477710i	0.458058	−	0.888922i	$-0.348545\pi$
$929$	−2.52193	−	1.45604i	−0.0827418	−	0.0477710i	−0.540800	+	0.841151i	$0.681878\pi$
$930$	−0.0850768	+	0.103809i	−0.00278978	+	0.00340405i
$931$	11.5129	−	45.1315i	0.377319	−	1.47913i
$932$			16.4052i			0.537370i
$933$	−6.19604	+	2.33681i	−0.202849	+	0.0765037i
$934$	−8.47219	−	14.6743i	−0.277219	−	0.480157i
$935$	−1.14858	+	0.663133i	−0.0375626	+	0.0216868i
$936$	−4.35911	−	9.89940i	−0.142482	−	0.323572i
$937$			43.9029i			1.43425i	0.696946	+	0.717123i	$0.254542\pi$
$937$			43.9029i			1.43425i	−0.696946	+	0.717123i	$0.745458\pi$
$938$	−2.72719	−	19.7942i	−0.0890458	−	0.646305i
$939$	21.1470	−	25.8032i	0.690105	−	0.842055i
$940$	0.377225	−	0.653372i	0.0123037	−	0.0213106i
$941$	−32.2047	+	18.5934i	−1.04984	+	0.606127i	−0.922606	−	0.385745i	$-0.873945\pi$
$941$	−32.2047	+	18.5934i	−1.04984	+	0.606127i	−0.127238	+	0.991872i	$0.540611\pi$
$942$	33.0574	+	5.43484i	1.07707	+	0.177077i
$943$	−5.51967	+	9.56036i	−0.179745	+	0.311328i
$944$			3.59600i			0.117040i
$945$	0.925578	−	0.772144i	0.0301091	−	0.0251179i
$946$	54.9116			1.78533
$947$	9.06698	−	15.7045i	0.294637	−	0.510326i	−0.680263	−	0.732968i	$-0.738135\pi$
$947$	9.06698	−	15.7045i	0.294637	−	0.510326i	0.974900	+	0.222641i	$0.0714679\pi$
$948$	4.04268	−	24.5896i	0.131300	−	0.798633i
$949$	−8.94638	+	28.2682i	−0.290412	+	0.917626i
$950$	−16.6090	+	28.7676i	−0.538867	+	0.933346i
$951$	32.9958	+	27.0417i	1.06996	+	0.876887i
$952$	4.33616	+	5.58116i	0.140536	+	0.180886i
$953$		−	13.7842i		−	0.446514i	−0.974760	−	0.223257i	$-0.928331\pi$
$953$		−	13.7842i		−	0.446514i	0.974760	−	0.223257i	$-0.0716689\pi$
$954$	13.4520	−	39.8049i	0.435523	−	1.28873i
$955$	0.624123	+	1.08101i	0.0201961	+	0.0349807i
$956$	7.69636	+	13.3305i	0.248918	+	0.431139i
$957$	20.2390	+	53.6638i	0.654235	+	1.73470i
$958$		−	8.34391i		−	0.269579i
$959$	−20.4241	−	26.2883i	−0.659530	−	0.848895i
$960$	0.0962606	−	0.117456i	0.00310680	−	0.00379086i
$961$	15.1094	−	26.1703i	0.487401	−	0.844203i
$962$	−1.81086	−	0.573106i	−0.0583846	−	0.0184777i
$963$	−5.33922	−	6.07163i	−0.172054	−	0.195656i
$964$	−3.89705	+	6.74990i	−0.125516	+	0.217400i
$965$	−1.30755			−0.0420914
$966$	−2.68475	−	4.94296i	−0.0863803	−	0.159037i
$967$		−	29.8126i		−	0.958708i	−0.877622	−	0.479354i	$-0.840871\pi$
$967$		−	29.8126i		−	0.958708i	0.877622	−	0.479354i	$-0.159129\pi$
$968$	10.5327	−	18.2431i	0.338533	−	0.586356i
$969$	−4.99442	+	30.3785i	−0.160444	+	0.975899i
$970$	0.795594	−	0.459336i	0.0255450	−	0.0147484i
$971$	21.8686	−	37.8776i	0.701798	−	1.21555i	−0.266037	−	0.963963i	$-0.585714\pi$
$971$	21.8686	−	37.8776i	0.701798	−	1.21555i	0.967835	−	0.251587i	$-0.0809524\pi$
$972$	14.9324	+	4.47464i	0.478958	+	0.143524i
$973$	7.07830	+	51.3751i	0.226920	+	1.64701i
$974$			14.3215i			0.458890i
$975$	−27.8041	−	14.1045i	−0.890443	−	0.451706i
$976$	−2.01240	+	1.16186i	−0.0644153	+	0.0371902i
$977$	3.38263	+	5.85889i	0.108220	+	0.187443i	0.915049	−	0.403342i	$-0.132152\pi$
$977$	3.38263	+	5.85889i	0.108220	+	0.187443i	−0.806829	+	0.590785i	$0.798818\pi$
$978$	−10.7816	−	28.5873i	−0.344756	−	0.914120i
$979$		−	19.1972i		−	0.613546i
$980$	0.165968	+	0.590875i	0.00530166	+	0.0188748i
$981$	−22.5619	+	4.51956i	−0.720345	+	0.144298i
$982$	−6.62738	−	3.82632i	−0.211488	−	0.122103i
$983$	−15.7908	+	9.11680i	−0.503647	+	0.290781i	−0.730218	−	0.683214i	$-0.760582\pi$
$983$	−15.7908	+	9.11680i	−0.503647	+	0.290781i	0.226571	+	0.973995i	$0.427248\pi$
$984$	15.3709	+	2.52707i	0.490006	+	0.0805601i
$985$	−0.425017	−	0.245384i	−0.0135422	−	0.00781857i
$986$			15.6209i			0.497472i
$987$	−20.5984	+	33.6246i	−0.655655	+	1.07028i
$988$	16.1889	+	17.7053i	0.515037	+	0.563279i
$989$	−10.3084	−	5.95155i	−0.327788	−	0.189248i
$990$	−0.983577	−	1.11850i	−0.0312601	−	0.0355483i
$991$	6.85129	+	11.8668i	0.217638	+	0.376961i	0.954085	−	0.299534i	$-0.0968313\pi$
$991$	6.85129	+	11.8668i	0.217638	+	0.376961i	−0.736447	+	0.676495i	$0.763498\pi$
$992$	0.441909	−	0.765409i	0.0140306	−	0.0243018i
$993$	−4.56192	+	5.56639i	−0.144768	+	0.176644i
$994$	−2.65203	+	6.51310i	−0.0841172	+	0.206583i
$995$	−0.0515524			−0.00163432
$996$	−1.74891	−	4.63722i	−0.0554162	−	0.146936i
$997$	−43.3774	+	25.0440i	−1.37378	+	0.793151i	−0.991401	−	0.130856i	$-0.958227\pi$
$997$	−43.3774	+	25.0440i	−1.37378	+	0.793151i	−0.382376	+	0.924007i	$0.624894\pi$
$998$	−23.5183	+	13.5783i	−0.744460	+	0.429814i
$999$	2.32159	−	1.45020i	0.0734520	−	0.0458822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.b.467.9	yes	36
3.2	odd	2		546.2.bg.a.467.3	yes	36
7.3	odd	6	inner	546.2.bg.b.311.3	yes	36
13.12	even	2		546.2.bg.a.467.9	yes	36
21.17	even	6		546.2.bg.a.311.9	yes	36
39.38	odd	2	inner	546.2.bg.b.467.3	yes	36
91.38	odd	6		546.2.bg.a.311.3	✓	36
273.38	even	6	inner	546.2.bg.b.311.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.3	✓	36	91.38	odd	6
546.2.bg.a.311.9	yes	36	21.17	even	6
546.2.bg.a.467.3	yes	36	3.2	odd	2
546.2.bg.a.467.9	yes	36	13.12	even	2
546.2.bg.b.311.3	yes	36	7.3	odd	6	inner
546.2.bg.b.311.9	yes	36	273.38	even	6	inner
546.2.bg.b.467.3	yes	36	39.38	odd	2	inner
546.2.bg.b.467.9	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.280988 + 1.70911i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0759308 - 0.0438386i) q^{5} +(1.33964 + 1.09790i) q^{6} +(-2.62099 + 0.361112i) q^{7} -1.00000 q^{8} +(-2.84209 - 0.960476i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.280988 + 1.70911i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0759308 - 0.0438386i) q^{5} +(1.33964 + 1.09790i) q^{6} +(-2.62099 + 0.361112i) q^{7} -1.00000 q^{8} +(-2.84209 - 0.960476i) q^{9} +(-0.0759308 + 0.0438386i) q^{10} +(-2.83131 - 4.90398i) q^{11} +(1.62062 - 0.611211i) q^{12} +(-2.43301 - 2.66091i) q^{13} +(-0.997764 + 2.45040i) q^{14} +(0.0962606 - 0.117456i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.33566 + 2.31343i) q^{17} +(-2.25284 + 1.98109i) q^{18} +(3.32692 - 5.76239i) q^{19} +0.0876773i q^{20} +(0.119288 - 4.58102i) q^{21} -5.66263 q^{22} +(1.06303 + 0.613739i) q^{23} +(0.280988 - 1.70911i) q^{24} +(-2.49616 - 4.32347i) q^{25} +(-3.52092 + 0.776597i) q^{26} +(2.44015 - 4.58756i) q^{27} +(1.62323 + 2.08929i) q^{28} +5.84765i q^{29} +(-0.0535893 - 0.142092i) q^{30} +(-0.441909 - 0.765409i) q^{31} +(0.500000 + 0.866025i) q^{32} +(9.17699 - 3.46106i) q^{33} +2.67132 q^{34} +(0.214845 + 0.0874812i) q^{35} +(0.589249 + 2.94156i) q^{36} +(0.456219 + 0.263398i) q^{37} +(-3.32692 - 5.76239i) q^{38} +(5.23143 - 3.41060i) q^{39} +(0.0759308 + 0.0438386i) q^{40} +8.99352i q^{41} +(-3.90764 - 2.39382i) q^{42} -9.69720 q^{43} +(-2.83131 + 4.90398i) q^{44} +(0.173696 + 0.197523i) q^{45} +(1.06303 - 0.613739i) q^{46} +(-7.45201 - 4.30242i) q^{47} +(-1.33964 - 1.09790i) q^{48} +(6.73920 - 1.89294i) q^{49} -4.99231 q^{50} +(-4.32920 + 1.63274i) q^{51} +(-1.08791 + 3.43751i) q^{52} +(-12.1291 + 7.00275i) q^{53} +(-2.75286 - 4.40701i) q^{54} +0.496484i q^{55} +(2.62099 - 0.361112i) q^{56} +(8.91371 + 7.30522i) q^{57} +(5.06421 + 2.92382i) q^{58} +(3.11423 - 1.79800i) q^{59} +(-0.149850 - 0.0246363i) q^{60} +(2.01240 + 1.16186i) q^{61} -0.883818 q^{62} +(7.79594 + 1.49109i) q^{63} +1.00000 q^{64} +(0.0680900 + 0.308705i) q^{65} +(1.59113 - 9.67803i) q^{66} +(-6.54039 + 3.77610i) q^{67} +(1.33566 - 2.31343i) q^{68} +(-1.34764 + 1.64437i) q^{69} +(0.183183 - 0.142320i) q^{70} +2.65797 q^{71} +(2.84209 + 0.960476i) q^{72} +(-4.11174 - 7.12173i) q^{73} +(0.456219 - 0.263398i) q^{74} +(8.09066 - 3.05136i) q^{75} -6.65383 q^{76} +(9.19173 + 11.8309i) q^{77} +(-0.337951 - 6.23585i) q^{78} +(7.19370 - 12.4599i) q^{79} +(0.0759308 - 0.0438386i) q^{80} +(7.15497 + 5.45952i) q^{81} +(7.78862 + 4.49676i) q^{82} -2.86138i q^{83} +(-4.02693 + 2.18721i) q^{84} -0.234214i q^{85} +(-4.84860 + 8.39803i) q^{86} +(-9.99425 - 1.64312i) q^{87} +(2.83131 + 4.90398i) q^{88} +(2.93597 + 1.69508i) q^{89} +(0.257908 - 0.0516637i) q^{90} +(7.33780 + 6.09563i) q^{91} -1.22748i q^{92} +(1.43234 - 0.540199i) q^{93} +(-7.45201 + 4.30242i) q^{94} +(-0.505231 + 0.291695i) q^{95} +(-1.62062 + 0.611211i) q^{96} -10.4779 q^{97} +(1.73026 - 6.78279i) q^{98} +(3.33670 + 16.6570i) 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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