LMFDB - Embedded newform 546.2.bg.a.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.a.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} +(1.08791 + 3.43751i) 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} +(3.86413 + 4.90596i) 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} +(-3.52092 - 0.776597i) 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} +(0.301391 - 0.0953849i) 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} +(-6.18076 + 0.893454i) 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} +(5.41602 - 7.85281i) 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	0.516883	−	0.856056i	$-0.327092\pi$
$5$	0.0759308	+	0.0438386i	0.0339573	+	0.0196052i	−0.482925	+	0.875662i	$0.660426\pi$
$6$	−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	$0.158964\pi$
$11$	2.83131	+	4.90398i	0.853673	+	1.47860i	−0.0241978	+	0.999707i	$0.507703\pi$
$12$	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	$0.443063\pi$
$19$	−3.32692	+	5.76239i	−0.763247	+	1.32198i	−0.941168	+	0.337938i	$0.890271\pi$
$20$		−	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
$26$	1.08791	+	3.43751i	0.213356	+	0.674151i
$27$	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	0.902978	−	0.429687i	$-0.141376\pi$
$31$	0.441909	+	0.765409i	0.0793692	+	0.137471i	−0.823609	+	0.567158i	$0.808043\pi$
$32$	−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	0.462030	−	0.886864i	$-0.347121\pi$
$37$	−0.456219	−	0.263398i	−0.0750019	−	0.0433024i	−0.537032	+	0.843562i	$0.680455\pi$
$38$	−3.32692	−	5.76239i	−0.539697	−	0.934783i
$39$	3.86413	+	4.90596i	0.618756	+	0.785583i
$40$	0.0759308	+	0.0438386i	0.0120057	+	0.00693150i
$41$		−	8.99352i		−	1.40455i	−0.711905	−	0.702276i	$-0.752167\pi$
$41$		−	8.99352i		−	1.40455i	0.711905	−	0.702276i	$-0.247833\pi$
$42$	−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	0.932773	−	0.360465i	$-0.117382\pi$
$47$	7.45201	+	4.30242i	1.08699	+	0.627572i	0.154215	+	0.988037i	$0.450715\pi$
$48$	−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
$52$	−3.52092	−	0.776597i	−0.488264	−	0.107695i
$53$	−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	−0.688828	−	0.724925i	$-0.741874\pi$
$59$	−3.11423	+	1.79800i	−0.405438	+	0.234080i	0.283390	+	0.959005i	$0.408541\pi$
$60$	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
$65$	0.301391	−	0.0953849i	0.0373830	−	0.0118310i
$66$	1.59113	−	9.67803i	0.195854	−	1.19128i
$67$	6.54039	−	3.77610i	0.799036	−	0.461324i	−0.0440981	−	0.999027i	$-0.514041\pi$
$67$	6.54039	−	3.77610i	0.799036	−	0.461324i	0.843134	+	0.537704i	$0.180708\pi$
$68$	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	$-0.550415\pi$
$71$	−2.65797			−0.315443			−0.157722	+	0.987484i	$0.550415\pi$
$72$	−2.84209	−	0.960476i	−0.334944	−	0.113193i
$73$	4.11174	+	7.12173i	0.481242	+	0.833536i	0.999768	−	0.0215258i	$-0.00685242\pi$
$73$	4.11174	+	7.12173i	0.481242	+	0.833536i	−0.518526	+	0.855062i	$0.673519\pi$
$74$	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
$78$	−6.18076	+	0.893454i	−0.699833	+	0.101164i
$79$	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	$0.0501947\pi$
$83$			2.86138i			0.314077i	−0.987592	+	0.157039i	$0.949805\pi$
$84$	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	0.336257	−	0.941770i	$-0.390839\pi$
$89$	−2.93597	−	1.69508i	−0.311212	−	0.179678i	−0.647469	+	0.762092i	$0.724172\pi$
$90$	0.257908	−	0.0516637i	0.0271859	−	0.00544584i
$91$	5.41602	−	7.85281i	0.567754	−	0.823199i
$92$		−	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	$-0.321465\pi$
$97$	10.4779			1.06387			0.531934	+	0.846786i	$0.321465\pi$
$98$	−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	−0.783161	−	0.621819i	$-0.786394\pi$
$109$	−6.64244	+	3.83502i	−0.636231	+	0.367328i	0.146930	+	0.989147i	$0.453061\pi$
$110$	−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
$117$	−9.47059	+	5.22570i	−0.875556	+	0.483116i
$118$		−	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
$130$	−0.0680900	+	0.308705i	−0.00597188	+	0.0270752i
$131$	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	$-0.986037\pi$
$137$	−6.29121	−	10.8967i	−0.537495	−	0.930968i	0.461543	−	0.887118i	$-0.347296\pi$
$138$	−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
$143$	19.9377	+	4.39758i	1.66727	+	0.367744i
$144$	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	$0.342547\pi$
$149$	−6.40667	+	11.0967i	−0.524855	+	0.909076i	−0.999581	+	0.0289419i	$0.990786\pi$
$150$	−1.40278	+	8.53240i	−0.114536	+	0.696667i
$151$	3.56296	−	2.05707i	0.289949	−	0.167402i	−0.347970	−	0.937506i	$-0.613129\pi$
$151$	3.56296	−	2.05707i	0.289949	−	0.167402i	0.637919	+	0.770104i	$0.279795\pi$
$152$	−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
$156$	2.31662	−	5.79942i	0.185478	−	0.464325i
$157$	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	0.959782	−	0.280746i	$-0.0905819\pi$
$163$	15.2764	+	8.81983i	1.19654	+	0.690823i	0.236758	+	0.971569i	$0.423915\pi$
$164$	−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	$-0.794746\pi$
$167$		−	15.5348i		−	1.20212i	0.799205	−	0.601058i	$-0.205254\pi$
$168$	−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	$-0.0850972\pi$
$182$	4.09272	+	8.61682i	0.303373	+	0.638721i
$183$	−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	−0.886703	−	0.462340i	$-0.847010\pi$
$193$	−12.9152	+	7.45659i	−0.929656	+	0.536737i	−0.0429533	+	0.999077i	$0.513677\pi$
$194$	−5.23894	+	9.07411i	−0.376134	+	0.651483i
$195$	0.0783356	+	0.541912i	0.00560973	+	0.0388071i
$196$	−5.00894	−	4.88984i	−0.357781	−	0.349275i
$197$	−5.59743			−0.398800			−0.199400	−	0.979918i	$-0.563899\pi$
$197$	−5.59743			−0.398800			−0.199400	+	0.979918i	$0.563899\pi$
$198$	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
$208$	1.08791	+	3.43751i	0.0754329	+	0.238348i
$209$	−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
$221$	9.40551	+	2.07454i	0.632683	+	0.139549i
$222$	0.321983	+	0.853738i	0.0216101	+	0.0572991i
$223$	−18.4233			−1.23371			−0.616856	−	0.787076i	$-0.711594\pi$
$223$	−18.4233			−1.23371			−0.616856	+	0.787076i	$0.711594\pi$
$224$	−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	−0.618921	−	0.785454i	$-0.712430\pi$
$227$	−3.73888	+	2.15864i	−0.248158	+	0.143274i	0.370762	+	0.928728i	$0.379096\pi$
$228$	−1.86965	+	11.3721i	−0.123820	+	0.753137i
$229$	6.51189	−	11.2789i	0.430317	−	0.745332i	−0.566583	−	0.824005i	$-0.691735\pi$
$229$	6.51189	−	11.2789i	0.430317	−	0.745332i	0.996900	+	0.0786729i	$0.0250683\pi$
$230$	−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	$0.847249\pi$
$234$	0.209709	−	10.8146i	0.0137091	−	0.706974i
$235$	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	$-0.334128\pi$
$239$	15.3927			0.995673			0.497836	+	0.867271i	$0.334128\pi$
$240$	−0.0535893	−	0.142092i	−0.00345917	−	0.00917199i
$241$	3.89705	+	6.74990i	0.251031	+	0.434799i	0.963810	−	0.266590i	$-0.0858969\pi$
$241$	3.89705	+	6.74990i	0.251031	+	0.434799i	−0.712779	+	0.701389i	$0.752564\pi$
$242$	−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
$247$	7.23876	+	22.8726i	0.460591	+	1.45535i
$248$	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	−0.513760	−	0.857934i	$-0.671748\pi$
$271$	8.00242	−	13.8606i	0.486113	−	0.841972i	0.999873	+	0.0159623i	$0.00508117\pi$
$272$	−2.67132			−0.161972
$273$	11.8995	+	11.4631i	0.720188	+	0.693779i
$274$	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	$-0.422402\pi$
$281$	8.09237			0.482751			0.241375	+	0.970432i	$0.422402\pi$
$282$	−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	$-0.787374\pi$
$293$		−	21.2050i		−	1.23881i	0.785072	−	0.619404i	$-0.212626\pi$
$294$	−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
$299$	4.21946	−	1.33538i	0.244018	−	0.0772272i
$300$	−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	$-0.316836\pi$
$307$	19.0700			1.08838			0.544192	+	0.838961i	$0.316836\pi$
$308$	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	$0.798761\pi$
$312$	3.86413	+	4.90596i	0.218763	+	0.277746i
$313$	−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	$0.409801\pi$
$317$	−12.3152	+	21.3306i	−0.691692	+	1.19805i	−0.971283	+	0.237927i	$0.923532\pi$
$318$	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
$325$	−17.5775	−	3.87702i	−0.975027	−	0.215058i
$326$	−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	0.397834	−	0.917457i	$-0.369762\pi$
$331$	−3.59847	−	2.07757i	−0.197790	−	0.114194i	−0.595624	+	0.803263i	$0.703095\pi$
$332$	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	$0.514084\pi$
$338$	11.7938	+	5.46868i	0.641498	+	0.297457i
$339$	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	$-0.335454\pi$
$349$	18.4655			0.988437			0.494218	+	0.869338i	$0.335454\pi$
$350$	13.0848	−	1.80278i	0.699413	−	0.0963629i
$351$	−6.27015	−	17.6546i	−0.334676	−	0.942333i
$352$	2.83131	−	4.90398i	0.150909	−	0.261383i
$353$	−17.6657	+	10.1993i	−0.940249	+	0.542853i	−0.890038	−	0.455885i	$-0.849323\pi$
$353$	−17.6657	+	10.1993i	−0.940249	+	0.542853i	−0.0502108	+	0.998739i	$0.515989\pi$
$354$	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	−0.902839	−	0.429978i	$-0.858521\pi$
$359$	−1.49774	+	2.59416i	−0.0790477	+	0.136915i	0.823792	+	0.566893i	$0.191855\pi$
$360$	−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
$364$	−9.50875	−	0.764008i	−0.498394	−	0.0400449i
$365$			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	$0.0952393\pi$
$379$			11.4767i			0.589518i	−0.955572	+	0.294759i	$0.904761\pi$
$380$	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	0.508284	−	0.861190i	$-0.330280\pi$
$383$	0.325127	+	0.187712i	0.0166132	+	0.00959165i	−0.491670	+	0.870781i	$0.663614\pi$
$384$	−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	$0.0223859\pi$
$390$	−0.508477	−	0.203115i	−0.0257477	−	0.0102851i
$391$			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	−0.999754	−	0.0221990i	$-0.992933\pi$
$397$	−9.57692	+	16.5877i	−0.480652	+	0.832514i	0.519102	+	0.854713i	$0.326267\pi$
$398$			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	−0.809900	−	0.586569i	$-0.800478\pi$
$401$	2.06325	−	3.57365i	0.103034	−	0.178459i	0.912933	+	0.408109i	$0.133812\pi$
$402$	−12.9075	−	2.12207i	−0.643768	−	0.105839i
$403$	3.11185	+	0.686371i	0.155013	+	0.0341906i
$404$	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	$-0.872622\pi$
$409$	−16.1361	−	27.9486i	−0.797879	−	1.38197i	0.123116	−	0.992392i	$-0.460711\pi$
$410$	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
$416$	−3.52092	−	0.776597i	−0.172627	−	0.0380758i
$417$	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	$-0.759277\pi$
$421$		−	28.1593i		−	1.37240i	0.727413	−	0.686200i	$-0.240723\pi$
$422$	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
$429$	−13.1182	+	32.8399i	−0.633351	+	1.58553i
$430$	0.736316	−	0.425112i	0.0355083	−	0.0205007i
$431$	−18.2440	−	31.5996i	−0.878783	−	1.52210i	−0.852677	−	0.522438i	$-0.825022\pi$
$431$	−18.2440	−	31.5996i	−0.878783	−	1.52210i	−0.0261063	−	0.999659i	$-0.508311\pi$
$432$	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	$-0.0544222\pi$
$449$	41.7613			1.97084			0.985420	+	0.170141i	$0.0544222\pi$
$450$	−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
$455$	0.755500	−	0.358839i	0.0354184	−	0.0168226i
$456$	−8.91371	−	7.30522i	−0.417423	−	0.342098i
$457$	17.3505	+	10.0173i	0.811621	+	0.468590i	0.847519	−	0.530766i	$-0.178096\pi$
$457$	17.3505	+	10.0173i	0.811621	+	0.468590i	−0.0358974	+	0.999355i	$0.511429\pi$
$458$	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	$0.0655269\pi$
$461$			8.77765i			0.408816i	−0.978886	+	0.204408i	$0.934473\pi$
$462$	0.675482	−	25.9406i	0.0314263	−	1.20687i
$463$			17.9312i			0.833334i	0.909059	+	0.416667i	$0.136802\pi$
$463$			17.9312i			0.833334i	−0.909059	+	0.416667i	$0.863198\pi$
$464$	−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	$0.0384339\pi$
$468$	9.26088	+	5.58892i	0.428084	+	0.258348i
$469$	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	−0.655915	−	0.754835i	$-0.727717\pi$
$479$	−7.22604	+	4.17195i	−0.330166	+	0.190621i	0.325749	+	0.945456i	$0.394384\pi$
$480$	0.149850	+	0.0246363i	0.00683968	+	0.00112449i
$481$	−1.81086	+	0.573106i	−0.0825683	+	0.0261314i
$482$	−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	−0.191934	−	0.981408i	$-0.561476\pi$
$487$	12.4028	−	7.16075i	0.562023	−	0.324484i	0.753957	+	0.656924i	$0.228143\pi$
$488$	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
$494$	−23.4276	−	5.16735i	−1.05406	−	0.232490i
$495$	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	0.923439	−	0.383745i	$-0.125366\pi$
$499$	23.5183	+	13.5783i	1.05283	+	0.607849i	0.129386	+	0.991594i	$0.458699\pi$
$500$	−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
$507$	22.4558	+	1.65418i	0.997298	+	0.0734646i
$508$	−2.40415	−	4.16411i	−0.106667	−	0.184752i
$509$	−12.2242	−	7.05762i	−0.541826	−	0.312823i	0.203993	−	0.978972i	$-0.434608\pi$
$509$	−12.2242	−	7.05762i	−0.541826	−	0.312823i	−0.745819	+	0.666149i	$0.767942\pi$
$510$	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
$520$	0.301391	−	0.0953849i	0.0132169	−	0.00418290i
$521$	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	0.314767	−	0.949169i	$-0.398074\pi$
$541$	−8.13741	−	4.69814i	−0.349855	−	0.201989i	−0.664621	+	0.747180i	$0.731407\pi$
$542$	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
$546$	−15.8771	+	4.57368i	−0.679476	+	0.195735i
$547$	−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	0.930791	−	0.365553i	$-0.119120\pi$
$557$	3.51222	+	6.08334i	0.148818	+	0.257760i	−0.781973	+	0.623312i	$0.785787\pi$
$558$	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	$0.869724\pi$
$572$	−6.16042	−	19.4653i	−0.257580	−	0.813886i
$573$	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	$-0.991510\pi$
$577$	−12.5609	−	21.7561i	−0.522917	−	0.905719i	0.476727	−	0.879051i	$-0.341823\pi$
$578$	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
$585$	−0.948197	−	0.0183868i	−0.0392031	−	0.000760199i
$586$	18.3641	+	10.6025i	0.758612	+	0.437985i
$587$			22.1376i			0.913717i	0.889539	+	0.456859i	$0.151025\pi$
$587$			22.1376i			0.913717i	−0.889539	+	0.456859i	$0.848975\pi$
$588$	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	0.624425	−	0.781085i	$-0.285333\pi$
$593$	6.33623	+	3.65823i	0.260198	+	0.150225i	−0.364227	+	0.931310i	$0.618667\pi$
$594$	−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
$598$	−0.953256	+	4.32185i	−0.0389815	+	0.176734i
$599$	−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
$611$	29.5792	−	9.36128i	1.19665	−	0.378717i
$612$	−6.01806	+	5.29211i	−0.243266	+	0.213921i
$613$	−7.57215	+	4.37178i	−0.305836	+	0.176575i	−0.645062	−	0.764130i	$-0.723168\pi$
$613$	−7.57215	+	4.37178i	−0.305836	+	0.176575i	0.339225	+	0.940705i	$0.389835\pi$
$614$	−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	$-0.266789\pi$
$617$	33.2275			1.33769			0.668845	+	0.743402i	$0.266789\pi$
$618$	−7.59976	−	20.1508i	−0.305707	−	0.810582i
$619$	9.75542	+	16.8969i	0.392103	+	0.679143i	0.992727	−	0.120389i	$-0.0384142\pi$
$619$	9.75542	+	16.8969i	0.392103	+	0.679143i	−0.600623	+	0.799532i	$0.705081\pi$
$620$	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
$624$	−6.18076	+	0.893454i	−0.247428	+	0.0357668i
$625$	−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	$0.343872\pi$
$631$			44.3163i			1.76421i	−0.471057	+	0.882103i	$0.656128\pi$
$632$	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
$637$	11.3596	−	22.5380i	0.450084	−	0.892986i
$638$		−	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	$-0.637737\pi$
$643$	−21.2665			−0.838669			−0.419334	+	0.907832i	$0.637737\pi$
$644$	−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	$0.0150127\pi$
$661$	13.8904	+	24.0589i	0.540274	+	0.935782i	−0.458614	+	0.888636i	$0.651654\pi$
$662$	3.59847	−	2.07757i	0.139858	−	0.0807472i
$663$	−6.18844	+	15.4921i	−0.240339	+	0.601663i
$664$			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
$676$	−10.6329	+	7.47939i	−0.408958	+	0.287669i
$677$	−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	0.958267	−	0.285873i	$-0.0922837\pi$
$683$	6.05165	+	10.4818i	0.231560	+	0.401074i	−0.726707	+	0.686947i	$0.758950\pi$
$684$	−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
$689$	−10.8766	+	49.3123i	−0.414367	+	1.87865i
$690$	0.0302405	−	0.183937i	0.00115123	−	0.00700238i
$691$	−7.19903	+	12.4691i	−0.273864	+	0.474347i	−0.969848	−	0.243711i	$-0.921635\pi$
$691$	−7.19903	+	12.4691i	−0.273864	+	0.474347i	0.695984	+	0.718057i	$0.254969\pi$
$692$	−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	$0.782665\pi$
$702$	18.4244	+	3.39719i	0.695385	+	0.128219i
$703$	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	−0.0659873	−	0.997820i	$-0.521020\pi$
$709$	−25.6450	−	14.8062i	−0.963119	−	0.556057i	−0.897132	+	0.441764i	$0.854353\pi$
$710$	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	$0.935334\pi$
$728$	5.41602	−	7.85281i	0.200731	−	0.291045i
$729$	−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	$0.548225\pi$
$733$	−25.2212	+	43.6845i	−0.931568	+	1.61352i	−0.780643	+	0.624978i	$0.785108\pi$
$734$			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	−0.407379	−	0.913259i	$-0.633557\pi$
$739$	4.88879	−	2.82254i	0.179837	−	0.103829i	0.587216	+	0.809430i	$0.300224\pi$
$740$	−0.0230940	+	0.0400000i	−0.000848953	+	0.00147043i
$741$	−41.1257	+	5.94489i	−1.51079	+	0.218391i
$742$	−5.05756	−	36.7083i	−0.185669	−	1.34760i
$743$	12.6489			0.464041			0.232021	−	0.972711i	$-0.425466\pi$
$743$	12.6489			0.464041			0.232021	+	0.972711i	$0.425466\pi$
$744$	−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
$754$	−20.1013	+	6.36170i	−0.732047	+	0.231680i
$755$	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	0.924892	−	0.380230i	$-0.124155\pi$
$761$	29.1876	+	16.8515i	1.05805	+	0.610865i	0.133157	+	0.991095i	$0.457488\pi$
$762$	−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
$767$	−2.79265	+	12.6613i	−0.100837	+	0.457171i
$768$	1.62062	−	0.611211i	0.0584792	−	0.0220552i
$769$	−22.1719			−0.799539			−0.399769	−	0.916616i	$-0.630910\pi$
$769$	−22.1719			−0.799539			−0.399769	+	0.916616i	$0.630910\pi$
$770$	−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	−0.534595	−	0.845109i	$-0.679536\pi$
$773$	−1.94637	+	1.12374i	−0.0700061	+	0.0404181i	0.464588	+	0.885527i	$0.346202\pi$
$774$	−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
$780$	0.430142	−	0.338797i	0.0154015	−	0.0121309i
$781$	−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	$-0.956488\pi$
$787$	−17.2066	−	29.8028i	−0.613350	−	1.06235i	0.377321	−	0.926082i	$-0.376845\pi$
$788$	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
$793$	7.98779	−	2.52799i	0.283655	−	0.0897716i
$794$	−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	$-0.706243\pi$
$811$	−34.3753			−1.20708			−0.603540	+	0.797333i	$0.706243\pi$
$812$	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
$819$	−22.9353	+	17.1165i	−0.801424	+	0.598097i
$820$	−0.788528			−0.0275366
$821$	12.6949	−	21.9881i	0.443054	−	0.767392i	−0.554861	−	0.831943i	$-0.687228\pi$
$821$	12.6949	−	21.9881i	0.443054	−	0.767392i	0.997914	+	0.0645517i	$0.0205618\pi$
$822$	−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	$-0.621401\pi$
$827$	−21.4079			−0.744426			−0.372213	+	0.928147i	$0.621401\pi$
$828$	−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	$0.151008\pi$
$839$			26.4635i			0.913622i	−0.889564	+	0.456811i	$0.848992\pi$
$840$	−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
$845$	0.479479	−	1.03405i	0.0164946	−	0.0355723i
$846$	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	$-0.534448\pi$
$853$	−6.30916			−0.216021			−0.108011	+	0.994150i	$0.534448\pi$
$854$	−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	$0.871196\pi$
$858$	−21.8811	−	27.7806i	−0.747009	−	0.948415i
$859$	−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	−0.821045	−	0.570864i	$-0.806608\pi$
$863$	2.46354	−	4.26698i	0.0838600	−	0.145250i	0.904905	+	0.425614i	$0.139942\pi$
$864$	−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
$871$	5.86501	−	26.5907i	0.198728	−	0.900991i
$872$	−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	0.00958950	−	0.999954i	$-0.496948\pi$
$877$	−25.2195	−	14.5605i	−0.851601	−	0.491672i	−0.861191	+	0.508282i	$0.830281\pi$
$878$	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	$0.283019\pi$
$884$	−2.90615	−	9.18268i	−0.0977444	−	0.308847i
$885$	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
$897$	1.09669	+	7.58674i	0.0366176	+	0.253314i
$898$	−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
$910$	−0.0669861	+	0.833701i	−0.00222057	+	0.0276369i
$911$		−	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	0.540800	−	0.841151i	$-0.318122\pi$
$929$	2.52193	+	1.45604i	0.0827418	+	0.0477710i	−0.458058	+	0.888922i	$0.651455\pi$
$930$	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
$936$	−9.47059	+	5.22570i	−0.309556	+	0.170807i
$937$			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	0.127238	−	0.991872i	$-0.459389\pi$
$941$	32.2047	−	18.5934i	1.04984	−	0.606127i	0.922606	+	0.385745i	$0.126055\pi$
$942$	−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	−0.974900	−	0.222641i	$-0.928532\pi$
$947$	−9.06698	+	15.7045i	−0.294637	+	0.510326i	0.680263	+	0.732968i	$0.261865\pi$
$948$	4.04268	−	24.5896i	0.131300	−	0.798633i
$949$	28.9542	+	6.38632i	0.939893	+	0.207309i
$950$	−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
$962$	0.409108	−	1.85481i	0.0131902	−	0.0598014i
$963$	−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	$0.159129\pi$
$967$			29.8126i			0.958708i	−0.877622	+	0.479354i	$0.840871\pi$
$968$	−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
$975$	11.5653	−	28.9525i	0.370386	−	0.927222i
$976$	−2.01240	+	1.16186i	−0.0644153	+	0.0371902i
$977$	−3.38263	−	5.85889i	−0.108220	−	0.187443i	0.806829	−	0.590785i	$-0.201182\pi$
$977$	−3.38263	−	5.85889i	−0.108220	−	0.187443i	−0.915049	+	0.403342i	$0.867848\pi$
$978$	−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	−0.226571	−	0.973995i	$-0.572752\pi$
$983$	15.7908	−	9.11680i	0.503647	−	0.290781i	0.730218	+	0.683214i	$0.239418\pi$
$984$	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.a.467.9	yes	36
3.2	odd	2		546.2.bg.b.467.3	yes	36
7.3	odd	6	inner	546.2.bg.a.311.3	✓	36
13.12	even	2		546.2.bg.b.467.9	yes	36
21.17	even	6		546.2.bg.b.311.9	yes	36
39.38	odd	2	inner	546.2.bg.a.467.3	yes	36
91.38	odd	6		546.2.bg.b.311.3	yes	36
273.38	even	6	inner	546.2.bg.a.311.9	yes	36

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.280988 + 1.70911i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.0759308 + 0.0438386i) q^{5} +(-1.33964 - 1.09790i) q^{6} +(2.62099 - 0.361112i) q^{7} +1.00000 q^{8} +(-2.84209 - 0.960476i) q^{9} +O(q^{10})\)	\(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} +(1.08791 + 3.43751i) 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} +(3.86413 + 4.90596i) 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} +(-3.52092 - 0.776597i) 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} +(0.301391 - 0.0953849i) 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} +(-6.18076 + 0.893454i) 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} +(5.41602 - 7.85281i) 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

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