LMFDB - Embedded newform 546.2.bg.b.311.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.3
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.b.467.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.62062 + 0.611211i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0759308 + 0.0438386i) q^{5} +(-1.33964 - 1.09790i) q^{6} +(2.62099 + 0.361112i) q^{7} -1.00000 q^{8} +(2.25284 - 1.98109i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.62062 + 0.611211i) 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} +(2.25284 - 1.98109i) q^{9} +(-0.0759308 - 0.0438386i) q^{10} +(-2.83131 + 4.90398i) q^{11} +(0.280988 - 1.70911i) 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} +(2.84209 + 0.960476i) q^{18} +(-3.32692 - 5.76239i) q^{19} -0.0876773i q^{20} +(-4.46836 + 1.01675i) q^{21} -5.66263 q^{22} +(-1.06303 + 0.613739i) q^{23} +(1.62062 - 0.611211i) 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} +(0.149850 + 0.0246363i) q^{30} +(0.441909 - 0.765409i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.59113 - 9.67803i) 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} +(-5.56938 - 2.82525i) q^{39} +(0.0759308 - 0.0438386i) q^{40} -8.99352i q^{41} +(-3.11471 - 3.36134i) q^{42} -9.69720 q^{43} +(-2.83131 - 4.90398i) q^{44} +(-0.0842120 + 0.249187i) 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} +(0.750608 - 4.56557i) q^{51} +(-3.52092 + 0.776597i) q^{52} +(12.1291 + 7.00275i) q^{53} +(-5.19301 + 0.180546i) 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} +(0.0535893 + 0.142092i) q^{60} +(2.01240 - 1.16186i) q^{61} +0.883818 q^{62} +(6.62008 - 4.37888i) q^{63} +1.00000 q^{64} +(-0.301391 - 0.0953849i) q^{65} +(9.17699 - 3.46106i) 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} +(-2.25284 + 1.98109i) q^{72} +(4.11174 - 7.12173i) q^{73} +(-0.456219 - 0.263398i) q^{74} +(1.40278 - 8.53240i) 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} +(1.15060 - 8.92615i) q^{81} +(7.78862 - 4.49676i) q^{82} +2.86138i q^{83} +(1.35365 - 4.37809i) q^{84} -0.234214i q^{85} +(-4.84860 - 8.39803i) q^{86} +(-3.57414 - 9.47684i) 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} +(-0.248342 + 1.51054i) q^{93} +(-7.45201 - 4.30242i) q^{94} +(0.505231 + 0.291695i) q^{95} +(-0.280988 + 1.70911i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.62062	+	0.611211i	−0.935668	+	0.352883i
$3$	−1.62062	+	0.611211i	−0.935668	+	0.352883i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.0759308	+	0.0438386i	−0.0339573	+	0.0196052i	−0.516883	−	0.856056i	$-0.672908\pi$
$5$	−0.0759308	+	0.0438386i	−0.0339573	+	0.0196052i	0.482925	+	0.875662i	$0.339574\pi$
$6$	−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
$9$	2.25284	−	1.98109i	0.750948	−	0.660362i
$10$	−0.0759308	−	0.0438386i	−0.0240114	−	0.0138630i
$11$	−2.83131	+	4.90398i	−0.853673	+	1.47860i	0.0241978	+	0.999707i	$0.492297\pi$
$11$	−2.83131	+	4.90398i	−0.853673	+	1.47860i	−0.877871	+	0.478898i	$0.841036\pi$
$12$	0.280988	−	1.70911i	0.0811142	−	0.493377i
$13$	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	$-0.938343\pi$
$17$	−1.33566	+	2.31343i	−0.323945	+	0.561089i	0.657353	+	0.753583i	$0.271676\pi$
$18$	2.84209	+	0.960476i	0.669887	+	0.226386i
$19$	−3.32692	−	5.76239i	−0.763247	−	1.32198i	−0.941168	−	0.337938i	$-0.890271\pi$
$19$	−3.32692	−	5.76239i	−0.763247	−	1.32198i	0.177921	−	0.984045i	$-0.443063\pi$
$20$		−	0.0876773i		−	0.0196052i
$21$	−4.46836	+	1.01675i	−0.975075	+	0.221873i
$22$	−5.66263			−1.20728
$23$	−1.06303	+	0.613739i	−0.221656	+	0.127973i	−0.606717	−	0.794918i	$-0.707514\pi$
$23$	−1.06303	+	0.613739i	−0.221656	+	0.127973i	0.385061	+	0.922891i	$0.374181\pi$
$24$	1.62062	−	0.611211i	0.330808	−	0.124763i
$25$	−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	$0.817311\pi$
$30$	0.149850	+	0.0246363i	0.0273587	+	0.00449794i
$31$	0.441909	−	0.765409i	0.0793692	−	0.137471i	−0.823609	−	0.567158i	$-0.808043\pi$
$31$	0.441909	−	0.765409i	0.0793692	−	0.137471i	0.902978	+	0.429687i	$0.141376\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.59113	−	9.67803i	0.276980	−	1.68473i
$34$	−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	$-0.680455\pi$
$37$	−0.456219	+	0.263398i	−0.0750019	+	0.0433024i	0.462030	+	0.886864i	$0.347121\pi$
$38$	3.32692	−	5.76239i	0.539697	−	0.934783i
$39$	−5.56938	−	2.82525i	−0.891814	−	0.452402i
$40$	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	$-0.247833\pi$
$42$	−3.11471	−	3.36134i	−0.480610	−	0.518665i
$43$	−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
$45$	−0.0842120	+	0.249187i	−0.0125536	+	0.0371466i
$46$	−1.06303	−	0.613739i	−0.156735	−	0.0904909i
$47$	−7.45201	+	4.30242i	−1.08699	+	0.627572i	−0.932773	−	0.360465i	$-0.882618\pi$
$47$	−7.45201	+	4.30242i	−1.08699	+	0.627572i	−0.154215	+	0.988037i	$0.549285\pi$
$48$	1.33964	+	1.09790i	0.193360	+	0.158468i
$49$	6.73920	+	1.89294i	0.962742	+	0.270420i
$50$	−4.99231			−0.706020
$51$	0.750608	−	4.56557i	0.105106	−	0.639307i
$52$	−3.52092	+	0.776597i	−0.488264	+	0.107695i
$53$	12.1291	+	7.00275i	1.66606	+	0.961902i	0.969729	+	0.244184i	$0.0785201\pi$
$53$	12.1291	+	7.00275i	1.66606	+	0.961902i	0.696334	+	0.717718i	$0.254813\pi$
$54$	−5.19301	+	0.180546i	−0.706680	+	0.0245692i
$55$		−	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	$-0.258126\pi$
$59$	3.11423	+	1.79800i	0.405438	+	0.234080i	−0.283390	+	0.959005i	$0.591459\pi$
$60$	0.0535893	+	0.142092i	0.00691835	+	0.0183440i
$61$	2.01240	−	1.16186i	0.257661	−	0.148761i	−0.365606	−	0.930770i	$-0.619138\pi$
$61$	2.01240	−	1.16186i	0.257661	−	0.148761i	0.623267	+	0.782009i	$0.285805\pi$
$62$	0.883818			0.112245
$63$	6.62008	−	4.37888i	0.834051	−	0.551687i
$64$	1.00000			0.125000
$65$	−0.301391	−	0.0953849i	−0.0373830	−	0.0118310i
$66$	9.17699	−	3.46106i	1.12961	−	0.426027i
$67$	6.54039	+	3.77610i	0.799036	+	0.461324i	0.843134	−	0.537704i	$-0.180708\pi$
$67$	6.54039	+	3.77610i	0.799036	+	0.461324i	−0.0440981	+	0.999027i	$0.514041\pi$
$68$	−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	$0.449585\pi$
$72$	−2.25284	+	1.98109i	−0.265500	+	0.233473i
$73$	4.11174	−	7.12173i	0.481242	−	0.833536i	−0.518526	−	0.855062i	$-0.673519\pi$
$73$	4.11174	−	7.12173i	0.481242	−	0.833536i	0.999768	+	0.0215258i	$0.00685242\pi$
$74$	−0.456219	−	0.263398i	−0.0530343	−	0.0306194i
$75$	1.40278	−	8.53240i	0.161979	−	0.985236i
$76$	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	0.913312	+	0.407261i	$0.133516\pi$
$79$	7.19370	+	12.4599i	0.809355	+	1.40184i	−0.103957	+	0.994582i	$0.533150\pi$
$80$	0.0759308	+	0.0438386i	0.00848932	+	0.00490131i
$81$	1.15060	−	8.92615i	0.127845	−	0.991794i
$82$	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	$0.949805\pi$
$84$	1.35365	−	4.37809i	0.147695	−	0.477688i
$85$		−	0.234214i		−	0.0254041i
$86$	−4.84860	−	8.39803i	−0.522838	−	0.905582i
$87$	−3.57414	−	9.47684i	−0.383189	−	1.01602i
$88$	2.83131	−	4.90398i	0.301819	−	0.522766i
$89$	2.93597	−	1.69508i	0.311212	−	0.179678i	−0.336257	−	0.941770i	$-0.609161\pi$
$89$	2.93597	−	1.69508i	0.311212	−	0.179678i	0.647469	+	0.762092i	$0.275828\pi$
$90$	−0.257908	+	0.0516637i	−0.0271859	+	0.00544584i
$91$	5.41602	+	7.85281i	0.567754	+	0.823199i
$92$		−	1.22748i		−	0.127973i
$93$	−0.248342	+	1.51054i	−0.0257519	+	0.156636i
$94$	−7.45201	−	4.30242i	−0.768616	−	0.443761i
$95$	0.505231	+	0.291695i	0.0518356	+	0.0299273i
$96$	−0.280988	+	1.70911i	−0.0286782	+	0.174435i
$97$	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	$-0.886559\pi$
$101$	−1.67265	+	2.89711i	−0.166435	+	0.288273i	0.770729	+	0.637163i	$0.219892\pi$
$102$	4.32920	−	1.63274i	0.428655	−	0.161665i
$103$	10.7681	−	6.21697i	1.06101	−	0.612577i	0.135301	−	0.990804i	$-0.456800\pi$
$103$	10.7681	−	6.21697i	1.06101	−	0.612577i	0.925713	+	0.378228i	$0.123466\pi$
$104$	−2.43301	−	2.66091i	−0.238577	−	0.260924i
$105$	0.294713	−	0.273089i	0.0287610	−	0.0266508i
$106$			14.0055i			1.36033i
$107$	−2.33402	+	1.34755i	−0.225639	+	0.130272i	−0.608558	−	0.793509i	$-0.708252\pi$
$107$	−2.33402	+	1.34755i	−0.225639	+	0.130272i	0.382920	+	0.923782i	$0.374919\pi$
$108$	−2.75286	−	4.40701i	−0.264895	−	0.424065i
$109$	−6.64244	−	3.83502i	−0.636231	−	0.367328i	0.146930	−	0.989147i	$-0.453061\pi$
$109$	−6.64244	−	3.83502i	−0.636231	−	0.367328i	−0.783161	+	0.621819i	$0.786394\pi$
$110$	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	$-0.121660\pi$
$114$	−1.86965	+	11.3721i	−0.175108	+	1.06510i
$115$	0.0538110	−	0.0932033i	0.00501790	−	0.00869126i
$116$	−5.06421	−	2.92382i	−0.470200	−	0.271470i
$117$	10.7527	+	1.17460i	0.994086	+	0.108592i
$118$			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
$123$	5.49694	+	14.5751i	0.495642	+	1.31419i
$124$	0.441909	+	0.765409i	0.0396846	+	0.0687357i
$125$		−	0.876099i		−	0.0783607i
$126$	7.10226	+	3.54371i	0.632720	+	0.315699i
$127$	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
$129$	15.7155	−	5.92704i	1.38367	−	0.521846i
$130$	−0.0680900	−	0.308705i	−0.00597188	−	0.0270752i
$131$	−9.89815	−	17.1441i	−0.864805	−	1.49789i	−0.867240	−	0.497890i	$-0.834108\pi$
$131$	−9.89815	−	17.1441i	−0.864805	−	1.49789i	0.00243479	−	0.999997i	$-0.499225\pi$
$132$	7.58586	+	6.21697i	0.660264	+	0.541118i
$133$	−6.63895	−	16.3046i	−0.575670	−	1.41379i
$134$			7.55219i			0.652410i
$135$	−0.0158298	−	0.455310i	−0.00136241	−	0.0391868i
$136$	1.33566	−	2.31343i	0.114532	−	0.198375i
$137$	6.29121	−	10.8967i	0.537495	−	0.930968i	−0.461543	−	0.887118i	$-0.652704\pi$
$137$	6.29121	−	10.8967i	0.537495	−	0.930968i	0.999038	−	0.0438504i	$-0.0139625\pi$
$138$	2.09789	+	0.344906i	0.178584	+	0.0293604i
$139$			19.6014i			1.66257i	0.555848	+	0.831284i	$0.312394\pi$
$139$			19.6014i			1.66257i	−0.555848	+	0.831284i	$0.687606\pi$
$140$	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
$144$	−2.84209	−	0.960476i	−0.236841	−	0.0800397i
$145$	−0.256353	−	0.444016i	−0.0212890	−	0.0368735i
$146$	8.22347			0.680579
$147$	−12.0787	+	1.05132i	−0.996233	+	0.0867114i
$148$		−	0.526796i		−	0.0433024i
$149$	6.40667	+	11.0967i	0.524855	+	0.909076i	0.999581	+	0.0289419i	$0.00921379\pi$
$149$	6.40667	+	11.0967i	0.524855	+	0.909076i	−0.474726	+	0.880134i	$0.657453\pi$
$150$	8.09066	−	3.05136i	0.660600	−	0.249142i
$151$	3.56296	+	2.05707i	0.289949	+	0.167402i	0.637919	−	0.770104i	$-0.279795\pi$
$151$	3.56296	+	2.05707i	0.289949	+	0.167402i	−0.347970	+	0.937506i	$0.613129\pi$
$152$	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
$156$	5.23143	−	3.41060i	0.418849	−	0.273066i
$157$	16.7506	+	9.67095i	1.33684	+	0.771826i	0.986338	−	0.164736i	$-0.0526771\pi$
$157$	16.7506	+	9.67095i	1.33684	+	0.771826i	0.350504	+	0.936561i	$0.386010\pi$
$158$	−7.19370	+	12.4599i	−0.572300	+	0.991253i
$159$	−23.9369	−	3.93538i	−1.89832	−	0.312096i
$160$			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	$-0.423915\pi$
$163$	15.2764	−	8.81983i	1.19654	−	0.690823i	0.959782	+	0.280746i	$0.0905819\pi$
$164$	7.78862	+	4.49676i	0.608189	+	0.351138i
$165$	0.303456	+	0.804613i	0.0236240	+	0.0626391i
$166$	−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	$-0.205254\pi$
$168$	4.46836	−	1.01675i	0.344741	−	0.0784441i
$169$	−1.16088	+	12.9481i	−0.0892987	+	0.996005i
$170$	0.202835	−	0.117107i	0.0155568	−	0.00898170i
$171$	−18.9108	−	6.39085i	−1.44615	−	0.488721i
$172$	4.84860	−	8.39803i	0.369702	−	0.640343i
$173$	−8.15099	−	14.1179i	−0.619708	−	1.07337i	−0.989539	−	0.144267i	$-0.953918\pi$
$173$	−8.15099	−	14.1179i	−0.619708	−	1.07337i	0.369831	−	0.929099i	$-0.379416\pi$
$174$	6.42011	−	7.83372i	0.486707	−	0.593873i
$175$	−8.10366	+	10.4304i	−0.612579	+	0.788463i
$176$	5.66263			0.426836
$177$	−6.14595	−	1.01043i	−0.461958	−	0.0759488i
$178$	2.93597	+	1.69508i	0.220060	+	0.127052i
$179$	−7.78809	−	4.49646i	−0.582109	−	0.336081i	0.179862	−	0.983692i	$-0.442435\pi$
$179$	−7.78809	−	4.49646i	−0.582109	−	0.336081i	−0.761971	+	0.647611i	$0.775768\pi$
$180$	−0.173696	−	0.197523i	−0.0129466	−	0.0147225i
$181$			7.10802i			0.528335i	0.964477	+	0.264167i	$0.0850972\pi$
$181$			7.10802i			0.528335i	−0.964477	+	0.264167i	$0.914903\pi$
$182$	−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
$186$	−1.43234	+	0.540199i	−0.105024	+	0.0396093i
$187$	−7.56334	−	13.1001i	−0.553086	−	0.957973i
$188$		−	8.60484i		−	0.627572i
$189$	−8.05223	+	11.1428i	−0.585714	+	0.810518i
$190$			0.583390i			0.0423236i
$191$	12.3294	−	7.11841i	0.892127	−	0.515070i	0.0174894	−	0.999847i	$-0.494433\pi$
$191$	12.3294	−	7.11841i	0.892127	−	0.515070i	0.874638	+	0.484777i	$0.161099\pi$
$192$	−1.62062	+	0.611211i	−0.116958	+	0.0441103i
$193$	−12.9152	−	7.45659i	−0.929656	−	0.536737i	−0.0429533	−	0.999077i	$-0.513677\pi$
$193$	−12.9152	−	7.45659i	−0.929656	−	0.536737i	−0.886703	+	0.462340i	$0.847010\pi$
$194$	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	$0.436101\pi$
$198$	−12.7570	+	11.2181i	−0.906601	+	0.797239i
$199$	0.509204	+	0.293989i	0.0360965	+	0.0208403i	0.517940	−	0.855417i	$-0.326699\pi$
$199$	0.509204	+	0.293989i	0.0360965	+	0.0208403i	−0.481843	+	0.876257i	$0.660032\pi$
$200$	2.49616	−	4.32347i	0.176505	−	0.305715i
$201$	−12.9075	−	2.12207i	−0.910425	−	0.149680i
$202$	−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
$207$	−1.17896	+	3.48860i	−0.0819436	+	0.242475i
$208$	1.08791	−	3.43751i	0.0754329	−	0.238348i
$209$	37.6782			2.60625
$210$	0.383859	+	0.118684i	0.0264888	+	0.00818998i
$211$	−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
$213$	−4.30757	+	1.62458i	−0.295150	+	0.111314i
$214$	−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
$219$	−2.31070	+	14.0548i	−0.156142	+	0.949735i
$220$	0.429968	+	0.248242i	0.0289884	+	0.0167365i
$221$	−9.40551	+	2.07454i	−0.632683	+	0.139549i
$222$	0.900351	+	0.148023i	0.0604276	+	0.00993467i
$223$	−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	$-0.287570\pi$
$227$	3.73888	+	2.15864i	0.248158	+	0.143274i	−0.370762	+	0.928728i	$0.620904\pi$
$228$	−10.7834	+	4.06689i	−0.714146	+	0.269337i
$229$	6.51189	+	11.2789i	0.430317	+	0.745332i	0.996900	−	0.0786729i	$-0.0250683\pi$
$229$	6.51189	+	11.2789i	0.430317	+	0.745332i	−0.566583	+	0.824005i	$0.691735\pi$
$230$	0.107622			0.00709638
$231$	7.66519	−	24.7915i	0.504332	−	1.63116i
$232$		−	5.84765i		−	0.383917i
$233$	14.2073	−	8.20260i	0.930753	−	0.537370i	0.0437031	−	0.999045i	$-0.486084\pi$
$233$	14.2073	−	8.20260i	0.930753	−	0.537370i	0.887050	+	0.461674i	$0.152751\pi$
$234$	4.35911	+	9.89940i	0.284964	+	0.647144i
$235$	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	$0.665872\pi$
$240$	−0.149850	−	0.0246363i	−0.00967277	−	0.00159026i
$241$	3.89705	−	6.74990i	0.251031	−	0.434799i	−0.712779	−	0.701389i	$-0.752564\pi$
$241$	3.89705	−	6.74990i	0.251031	−	0.434799i	0.963810	+	0.266590i	$0.0858969\pi$
$242$	10.5327	−	18.2431i	0.677065	−	1.17271i
$243$	3.59106	+	15.1692i	0.230367	+	0.973104i
$244$			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
$249$	−1.74891	−	4.63722i	−0.110832	−	0.293872i
$250$	0.758724	−	0.438049i	0.0479859	−	0.0277047i
$251$	−7.91930			−0.499862			−0.249931	−	0.968264i	$-0.580408\pi$
$251$	−7.91930			−0.499862			−0.249931	+	0.968264i	$0.580408\pi$
$252$	0.482183	+	7.92259i	0.0303747	+	0.499077i
$253$		−	6.95075i		−	0.436990i
$254$	2.40415	+	4.16411i	0.150850	+	0.261279i
$255$	0.143154	+	0.379573i	0.00896466	+	0.0237698i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.92741	+	8.53452i	0.307363	+	0.532369i	0.977785	−	0.209612i	$-0.0672200\pi$
$257$	4.92741	+	8.53452i	0.307363	+	0.532369i	−0.670421	+	0.741981i	$0.733887\pi$
$258$	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
$261$	11.5847	+	13.1738i	0.717074	+	0.815440i
$262$	9.89815	−	17.1441i	0.611510	−	1.05917i
$263$	20.2604	+	11.6974i	1.24931	+	0.721290i	0.970972	−	0.239192i	$-0.0768826\pi$
$263$	20.2604	+	11.6974i	1.24931	+	0.721290i	0.278340	+	0.960483i	$0.410216\pi$
$264$	−1.59113	+	9.67803i	−0.0979272	+	0.595642i
$265$	−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	$-0.850029\pi$
$269$	−0.859882	+	1.48936i	−0.0524279	+	0.0908078i	0.838620	+	0.544716i	$0.183363\pi$
$270$	0.386395	−	0.241364i	0.0235152	−	0.0146889i
$271$	8.00242	+	13.8606i	0.486113	+	0.841972i	0.999873	−	0.0159623i	$-0.00508117\pi$
$271$	8.00242	+	13.8606i	0.486113	+	0.841972i	−0.513760	+	0.857934i	$0.671748\pi$
$272$	2.67132			0.161972
$273$	−13.5771	−	9.41612i	−0.821721	−	0.569890i
$274$	12.5824			0.760132
$275$	−14.1348	−	24.4822i	−0.852360	−	1.47633i
$276$	0.750248	+	1.98928i	0.0451596	+	0.119741i
$277$	6.12127	−	10.6023i	0.367791	−	0.637033i	−0.621429	−	0.783471i	$-0.713447\pi$
$277$	6.12127	−	10.6023i	0.367791	−	0.637033i	0.989220	+	0.146438i	$0.0467808\pi$
$278$	−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	$0.577598\pi$
$282$	14.7066	+	2.41786i	0.875765	+	0.143981i
$283$	−2.90561	−	1.67755i	−0.172721	−	0.0997203i	0.411147	−	0.911569i	$-0.365128\pi$
$283$	−2.90561	−	1.67755i	−0.172721	−	0.0997203i	−0.583868	+	0.811849i	$0.698461\pi$
$284$	−1.32899	+	2.30187i	−0.0788608	+	0.136591i
$285$	−0.997076	−	0.163926i	−0.0590617	−	0.00971011i
$286$	−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
$291$	−16.9807	+	6.40419i	−0.995427	+	0.375421i
$292$	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	$-0.212626\pi$
$294$	−6.94981	−	9.93479i	−0.405321	−	0.579409i
$295$	−0.315288			−0.0183568
$296$	0.456219	−	0.263398i	0.0265172	−	0.0153097i
$297$	−15.5884	−	24.9552i	−0.904533	−	1.44805i
$298$	−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
$303$	0.939988	−	5.71747i	0.0540009	−	0.328460i
$304$	−3.32692	+	5.76239i	−0.190812	+	0.330496i
$305$	−0.101869	+	0.176442i	−0.00583298	+	0.0101030i
$306$	−6.01806	+	5.29211i	−0.344030	+	0.302530i
$307$	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	$-0.867905\pi$
$311$	−1.91162	+	3.31103i	−0.108398	+	0.187751i	0.806723	+	0.590929i	$0.201239\pi$
$312$	5.56938	+	2.82525i	0.315304	+	0.159948i
$313$	−16.6808	+	9.63067i	−0.942855	+	0.544358i	−0.890854	−	0.454289i	$-0.849893\pi$
$313$	−16.6808	+	9.63067i	−0.942855	+	0.544358i	−0.0520010	+	0.998647i	$0.516560\pi$
$314$			19.3419i			1.09153i
$315$	−0.310703	+	0.622707i	−0.0175061	+	0.0350856i
$316$	−14.3874			−0.809355
$317$	12.3152	+	21.3306i	0.691692	+	1.19805i	0.971283	+	0.237927i	$0.0764679\pi$
$317$	12.3152	+	21.3306i	0.691692	+	1.19805i	−0.279591	+	0.960119i	$0.590199\pi$
$318$	−8.56031	−	22.6977i	−0.480039	−	1.27282i
$319$	−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
$324$	7.15497	+	5.45952i	0.397498	+	0.303307i
$325$	−17.5775	+	3.87702i	−0.975027	+	0.215058i
$326$	15.2764	+	8.81983i	0.846081	+	0.488485i
$327$	13.1089	+	2.15519i	0.724924	+	0.119182i
$328$			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	$-0.703095\pi$
$331$	−3.59847	+	2.07757i	−0.197790	+	0.114194i	0.397834	+	0.917457i	$0.369762\pi$
$332$	−2.47803	−	1.43069i	−0.135999	−	0.0785193i
$333$	−0.505975	+	1.49720i	−0.0277273	+	0.0820462i
$334$	13.4535	−	7.76738i	0.736143	−	0.425012i
$335$	−0.662156			−0.0361774
$336$	3.11471	+	3.36134i	0.169921	+	0.183376i
$337$	−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
$339$	4.84656	+	12.8506i	0.263229	+	0.697951i
$340$	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
$345$	−0.0302405	+	0.183937i	−0.00162809	+	0.00990286i
$346$	8.15099	−	14.1179i	0.438200	−	0.758984i
$347$	4.31492	+	2.49122i	0.231637	+	0.133736i	0.611327	−	0.791378i	$-0.290636\pi$
$347$	4.31492	+	2.49122i	0.231637	+	0.133736i	−0.379690	+	0.925114i	$0.623969\pi$
$348$	9.99425	+	1.64312i	0.535748	+	0.0880804i
$349$	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
$351$	−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	0.890038	−	0.455885i	$-0.150677\pi$
$353$	17.6657	+	10.1993i	0.940249	+	0.542853i	0.0502108	+	0.998739i	$0.484011\pi$
$354$	−2.19792	−	5.82777i	−0.116818	−	0.309742i
$355$	−0.201822	+	0.116522i	−0.0107116	+	0.00618434i
$356$			3.39016i			0.179678i
$357$	3.61602	−	11.6953i	0.191380	−	0.618979i
$358$		−	8.99291i		−	0.475290i
$359$	1.49774	+	2.59416i	0.0790477	+	0.136915i	0.902839	−	0.429978i	$-0.141479\pi$
$359$	1.49774	+	2.59416i	0.0790477	+	0.136915i	−0.823792	+	0.566893i	$0.808145\pi$
$360$	0.0842120	−	0.249187i	0.00443836	−	0.0131333i
$361$	−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
$366$	−3.97148	−	0.652936i	−0.207593	−	0.0341295i
$367$	0.373545	+	0.215666i	0.0194989	+	0.0112577i	0.509718	−	0.860342i	$-0.329750\pi$
$367$	0.373545	+	0.215666i	0.0194989	+	0.0112577i	−0.490219	+	0.871599i	$0.663083\pi$
$368$	1.06303	+	0.613739i	0.0554141	+	0.0319934i
$369$	−17.8169	−	20.2610i	−0.927513	−	1.05475i
$370$	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	0.973910	−	0.226933i	$-0.0728698\pi$
$373$	5.60905	+	9.71516i	0.290425	+	0.503032i	−0.683485	+	0.729965i	$0.739536\pi$
$374$	7.56334	−	13.1001i	0.391091	−	0.677389i
$375$	0.535481	+	1.41983i	0.0276521	+	0.0733195i
$376$	7.45201	−	4.30242i	0.384308	−	0.221880i
$377$	−15.5601	+	14.2274i	−0.801384	+	0.732749i
$378$	−13.6760	−	1.40205i	−0.703420	−	0.0721137i
$379$		−	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
$381$	−7.79244	+	2.93888i	−0.399219	+	0.150563i
$382$	12.3294	+	7.11841i	0.630829	+	0.364209i
$383$	−0.325127	+	0.187712i	−0.0166132	+	0.00959165i	−0.508284	−	0.861190i	$-0.669720\pi$
$383$	−0.325127	+	0.187712i	−0.0166132	+	0.00959165i	0.491670	+	0.870781i	$0.336386\pi$
$384$	−1.33964	−	1.09790i	−0.0683630	−	0.0560268i
$385$	0.179286	−	1.30128i	0.00913727	−	0.0663194i
$386$		−	14.9132i		−	0.759061i
$387$	−21.8463	+	19.2110i	−1.11051	+	0.976549i
$388$	−5.23894	+	9.07411i	−0.265967	+	0.460668i
$389$	−28.3112	−	16.3455i	−1.43544	−	0.828750i	−0.437909	−	0.899019i	$-0.644281\pi$
$389$	−28.3112	−	16.3455i	−1.43544	−	0.828750i	−0.997528	+	0.0702694i	$0.977614\pi$
$390$	0.299032	+	0.458677i	0.0151421	+	0.0232260i
$391$		−	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
$396$	−16.0937	−	5.43882i	−0.808739	−	0.273311i
$397$	−9.57692	−	16.5877i	−0.480652	−	0.832514i	0.519102	−	0.854713i	$-0.326267\pi$
$397$	−9.57692	−	16.5877i	−0.480652	−	0.832514i	−0.999754	+	0.0221990i	$0.992933\pi$
$398$			0.587979i			0.0294727i
$399$	20.7248	+	22.3658i	1.03754	+	1.11969i
$400$	4.99231			0.249616
$401$	−2.06325	−	3.57365i	−0.103034	−	0.178459i	0.809900	−	0.586569i	$-0.199522\pi$
$401$	−2.06325	−	3.57365i	−0.103034	−	0.178459i	−0.912933	+	0.408109i	$0.866188\pi$
$402$	−4.61598	−	12.2393i	−0.230224	−	0.610439i
$403$	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
$408$	−0.750608	+	4.56557i	−0.0371606	+	0.226029i
$409$	−16.1361	+	27.9486i	−0.797879	+	1.38197i	0.123116	+	0.992392i	$0.460711\pi$
$409$	−16.1361	+	27.9486i	−0.797879	+	1.38197i	−0.920995	+	0.389575i	$0.872622\pi$
$410$	−0.394264	+	0.682885i	−0.0194713	+	0.0337253i
$411$	−3.53551	+	21.5047i	−0.174394	+	1.06075i
$412$			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
$417$	−11.9806	−	31.7665i	−0.586691	−	1.55561i
$418$	18.8391	+	32.6303i	0.921450	+	1.59600i
$419$	−4.72613			−0.230886			−0.115443	−	0.993314i	$-0.536829\pi$
$419$	−4.72613			−0.230886			−0.115443	+	0.993314i	$0.536829\pi$
$420$	0.0891460	+	0.391773i	0.00434988	+	0.0191166i
$421$			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
$423$	−8.26475	+	24.4557i	−0.401846	+	1.18908i
$424$	−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
$429$	29.6236	−	19.3129i	1.43024	−	0.932437i
$430$	0.736316	+	0.425112i	0.0355083	+	0.0205007i
$431$	18.2440	−	31.5996i	0.878783	−	1.52210i	0.0261063	−	0.999659i	$-0.491689\pi$
$431$	18.2440	−	31.5996i	0.878783	−	1.52210i	0.852677	−	0.522438i	$-0.174978\pi$
$432$	5.19301	−	0.180546i	0.249849	−	0.00868652i
$433$		−	4.54367i		−	0.218355i	−0.994022	−	0.109177i	$-0.965178\pi$
$433$		−	4.54367i		−	0.218355i	0.994022	−	0.109177i	$-0.0348216\pi$
$434$	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
$438$	−13.3272	+	5.02627i	−0.636796	+	0.240165i
$439$	−19.3010	+	11.1434i	−0.921185	+	0.531847i	−0.884013	−	0.467462i	$-0.845168\pi$
$439$	−19.3010	+	11.1434i	−0.921185	+	0.531847i	−0.0371724	+	0.999309i	$0.511835\pi$
$440$			0.496484i			0.0236689i
$441$	18.9324	−	9.08642i	0.901544	−	0.432687i
$442$	−6.49936	−	7.10814i	−0.309143	−	0.338100i
$443$	22.9471	−	13.2485i	1.09025	−	0.629457i	0.156608	−	0.987661i	$-0.449944\pi$
$443$	22.9471	−	13.2485i	1.09025	−	0.629457i	0.933643	+	0.358204i	$0.116611\pi$
$444$	0.321983	+	0.853738i	0.0152807	+	0.0405166i
$445$	−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	$0.945578\pi$
$450$	−11.2469	+	9.89020i	−0.530184	+	0.466228i
$451$	44.1040	+	25.4635i	2.07678	+	1.19903i
$452$	6.86710	+	3.96472i	0.323001	+	0.186485i
$453$	−7.03152	−	1.15603i	−0.330369	−	0.0543148i
$454$			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	−0.0358974	−	0.999355i	$-0.511429\pi$
$457$	17.3505	−	10.0173i	0.811621	−	0.468590i	0.847519	+	0.530766i	$0.178096\pi$
$458$	−6.51189	+	11.2789i	−0.304280	+	0.527029i
$459$	−7.35378	−	11.7725i	−0.343245	−	0.549495i
$460$	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	$0.934473\pi$
$462$	25.3026	−	5.75748i	1.17719	−	0.267862i
$463$		−	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
$465$	−0.0473632	−	0.125583i	−0.00219642	−	0.00582379i
$466$	14.2073	+	8.20260i	0.658142	+	0.379978i
$467$	−8.47219	−	14.6743i	−0.392046	−	0.679044i	0.600673	−	0.799495i	$-0.294899\pi$
$467$	−8.47219	−	14.6743i	−0.392046	−	0.679044i	−0.992719	+	0.120451i	$0.961566\pi$
$468$	−6.39358	+	8.72480i	−0.295543	+	0.403304i
$469$	15.7787	+	12.2589i	0.728593	+	0.566065i
$470$	0.754449			0.0348001
$471$	−33.0574	−	5.43484i	−1.52320	−	0.250424i
$472$	−3.11423	−	1.79800i	−0.143344	−	0.0827597i
$473$	27.4558	−	47.5549i	1.26242	−	2.18658i
$474$	4.04268	−	24.5896i	0.185687	−	1.12944i
$475$	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	$-0.272283\pi$
$479$	7.22604	+	4.17195i	0.330166	+	0.190621i	−0.325749	+	0.945456i	$0.605616\pi$
$480$	−0.0535893	−	0.142092i	−0.00244601	−	0.00648558i
$481$	−1.81086	−	0.573106i	−0.0825683	−	0.0261314i
$482$	7.79411			0.355012
$483$	4.12596	−	3.82324i	0.187738	−	0.173963i
$484$	21.0653			0.957515
$485$	−0.795594	+	0.459336i	−0.0361260	+	0.0208574i
$486$	−11.3414	+	10.6945i	−0.514455	+	0.485115i
$487$	12.4028	+	7.16075i	0.562023	+	0.324484i	0.753957	−	0.656924i	$-0.228143\pi$
$487$	12.4028	+	7.16075i	0.562023	+	0.324484i	−0.191934	+	0.981408i	$0.561476\pi$
$488$	−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	$-0.0552424\pi$
$492$	−15.3709	−	2.52707i	−0.692973	−	0.113929i
$493$	−13.5281	−	7.81046i	−0.609276	−	0.351766i
$494$	23.4276	−	5.16735i	1.05406	−	0.232490i
$495$	−0.983577	−	1.11850i	−0.0442085	−	0.0502728i
$496$	−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	$-0.458699\pi$
$499$	23.5183	−	13.5783i	1.05283	−	0.607849i	0.923439	+	0.383745i	$0.125366\pi$
$500$	0.758724	+	0.438049i	0.0339312	+	0.0195902i
$501$	9.49501	+	25.1760i	0.424206	+	1.12478i
$502$	−3.95965	−	6.85831i	−0.176728	−	0.306101i
$503$	−27.6274			−1.23185			−0.615923	−	0.787806i	$-0.711217\pi$
$503$	−27.6274			−1.23185			−0.615923	+	0.787806i	$0.711217\pi$
$504$	−6.62008	+	4.37888i	−0.294882	+	0.195051i
$505$		−	0.293307i		−	0.0130520i
$506$	6.01952	−	3.47537i	0.267600	−	0.154499i
$507$	−6.03264	−	21.6935i	−0.267919	−	0.963441i
$508$	−2.40415	+	4.16411i	−0.106667	+	0.184752i
$509$	12.2242	−	7.05762i	0.541826	−	0.312823i	−0.203993	−	0.978972i	$-0.565392\pi$
$509$	12.2242	−	7.05762i	0.541826	−	0.312823i	0.745819	+	0.666149i	$0.232058\pi$
$510$	−0.257143	+	0.313761i	−0.0113865	+	0.0138936i
$511$	13.3486	−	17.1812i	0.590506	−	0.760052i
$512$	−1.00000			−0.0441942
$513$	34.5535	−	1.20132i	1.52557	−	0.0530397i
$514$	−4.92741	+	8.53452i	−0.217339	+	0.376442i
$515$	−0.545087	+	0.944119i	−0.0240194	+	0.0416029i
$516$	−2.72480	+	16.5736i	−0.119952	+	0.729610i
$517$		−	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	$-0.877504\pi$
$521$	−3.15726	+	5.46854i	−0.138322	+	0.239581i	0.788539	+	0.614984i	$0.210838\pi$
$522$	−5.61653	+	16.6195i	−0.245829	+	0.727418i
$523$	29.7281	−	17.1636i	1.29992	−	0.750510i	0.319531	−	0.947576i	$-0.396475\pi$
$523$	29.7281	−	17.1636i	1.29992	−	0.750510i	0.980390	+	0.197066i	$0.0631414\pi$
$524$	19.7963			0.864805
$525$	6.75782	−	21.8568i	0.294936	−	0.953908i
$526$			23.3947i			1.02006i
$527$	1.18048	+	2.04465i	0.0514225	+	0.0890664i
$528$	−9.17699	+	3.46106i	−0.399377	+	0.150623i
$529$	−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
$534$	−5.79415	−	0.952595i	−0.250738	−	0.0412228i
$535$	0.118149	−	0.204641i	0.00510805	−	0.00884740i
$536$	−6.54039	−	3.77610i	−0.282502	−	0.163103i
$537$	15.3699	+	2.52690i	0.663258	+	0.109044i
$538$	−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	$-0.731407\pi$
$541$	−8.13741	+	4.69814i	−0.349855	+	0.201989i	0.314767	+	0.949169i	$0.398074\pi$
$542$	−8.00242	+	13.8606i	−0.343733	+	0.595364i
$543$	−4.34450	−	11.5194i	−0.186440	−	0.494346i
$544$	1.33566	+	2.31343i	0.0572659	+	0.0991875i
$545$	0.672488			0.0288062
$546$	1.36607	−	16.4661i	0.0584625	−	0.704686i
$547$	−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
$549$	2.23188	−	6.60422i	0.0952541	−	0.281861i
$550$	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
$555$	−0.0129783	+	0.0789403i	−0.000550897	+	0.00335083i
$556$	−16.9753	−	9.80069i	−0.719913	−	0.415642i
$557$	−3.51222	+	6.08334i	−0.148818	+	0.257760i	−0.930791	−	0.365553i	$-0.880880\pi$
$557$	−3.51222	+	6.08334i	−0.148818	+	0.257760i	0.781973	+	0.623312i	$0.214213\pi$
$558$	1.99110	−	1.75092i	0.0842901	−	0.0741223i
$559$	−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	0.0479070	+	0.998852i	$0.484745\pi$
$563$	−19.9568	+	34.5661i	−0.841078	+	1.45679i	−0.888985	+	0.457937i	$0.848588\pi$
$564$	5.25937	+	13.9452i	0.221459	+	0.587199i
$565$	0.347616	+	0.602089i	0.0146243	+	0.0253301i
$566$		−	3.35511i		−	0.141026i
$567$	6.23906	−	22.9799i	0.262016	−	0.965064i
$568$	−2.65797			−0.111526
$569$	31.7330	−	18.3210i	1.33032	−	0.768058i	0.344968	−	0.938615i	$-0.387890\pi$
$569$	31.7330	−	18.3210i	1.33032	−	0.768058i	0.985348	+	0.170557i	$0.0545566\pi$
$570$	−0.356574	−	0.945456i	−0.0149353	−	0.0396008i
$571$	−2.72588	+	4.72136i	−0.114075	+	0.197583i	−0.917409	−	0.397945i	$-0.869724\pi$
$571$	−2.72588	+	4.72136i	−0.114075	+	0.197583i	0.803335	+	0.595528i	$0.203057\pi$
$572$	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
$576$	2.25284	−	1.98109i	0.0938685	−	0.0825452i
$577$	−12.5609	+	21.7561i	−0.522917	+	0.905719i	0.476727	+	0.879051i	$0.341823\pi$
$577$	−12.5609	+	21.7561i	−0.522917	+	0.905719i	−0.999644	+	0.0266678i	$0.991510\pi$
$578$	−4.93203	+	8.54252i	−0.205145	+	0.355322i
$579$	25.4882	+	4.19042i	1.05925	+	0.174148i
$580$	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
$585$	−0.867953	+	0.382195i	−0.0358854	+	0.0158018i
$586$	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	$0.848975\pi$
$588$	5.12887	−	10.9861i	0.211511	−	0.453060i
$589$	−5.88078			−0.242313
$590$	−0.157644	−	0.273047i	−0.00649010	−	0.0112412i
$591$	−9.07132	+	3.42121i	−0.373144	+	0.140730i
$592$	0.456219	+	0.263398i	0.0187505	+	0.0108256i
$593$	−6.33623	+	3.65823i	−0.260198	+	0.150225i	−0.624425	−	0.781085i	$-0.714667\pi$
$593$	−6.33623	+	3.65823i	−0.260198	+	0.150225i	0.364227	+	0.931310i	$0.381333\pi$
$594$	13.8177	−	25.9776i	0.566945	−	1.06587i
$595$	0.0845775	−	0.613873i	0.00346734	−	0.0251663i
$596$	−12.8133			−0.524855
$597$	−1.00492	−	0.165215i	−0.0411286	−	0.00676179i
$598$	−0.953256	−	4.32185i	−0.0389815	−	0.176734i
$599$	35.3925	+	20.4339i	1.44610	+	0.834906i	0.998246	−	0.0592009i	$-0.0188552\pi$
$599$	35.3925	+	20.4339i	1.44610	+	0.834906i	0.447854	+	0.894107i	$0.352189\pi$
$600$	−1.40278	+	8.53240i	−0.0572682	+	0.348334i
$601$			6.67453i			0.272260i	0.990691	+	0.136130i	$0.0434664\pi$
$601$			6.67453i			0.272260i	−0.990691	+	0.136130i	$0.956534\pi$
$602$	−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
$606$	5.42147	−	2.04468i	0.220232	−	0.0830595i
$607$	19.4541	−	11.2318i	0.789617	−	0.455886i	−0.0502106	−	0.998739i	$-0.515989\pi$
$607$	19.4541	−	11.2318i	0.789617	−	0.455886i	0.839828	+	0.542853i	$0.182656\pi$
$608$	−6.65383			−0.269849
$609$	−5.94560	−	26.1294i	−0.240928	−	1.05882i
$610$	−0.203737			−0.00824908
$611$	−29.5792	−	9.36128i	−1.19665	−	0.378717i
$612$	−7.59213	−	2.56574i	−0.306894	−	0.103714i
$613$	−7.57215	−	4.37178i	−0.305836	−	0.176575i	0.339225	−	0.940705i	$-0.389835\pi$
$613$	−7.57215	−	4.37178i	−0.305836	−	0.176575i	−0.645062	+	0.764130i	$0.723168\pi$
$614$	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	$0.733211\pi$
$618$	−21.2509	−	3.49379i	−0.854838	−	0.140541i
$619$	9.75542	−	16.8969i	0.392103	−	0.679143i	−0.600623	−	0.799532i	$-0.705081\pi$
$619$	9.75542	−	16.8969i	0.392103	−	0.679143i	0.992727	+	0.120389i	$0.0384142\pi$
$620$	−0.0671090	−	0.0387454i	−0.00269516	−	0.00155605i
$621$	−0.221616	−	6.37431i	−0.00889315	−	0.255792i
$622$	−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
$627$	−61.0621	+	23.0293i	−2.43859	+	0.919702i
$628$	−16.7506	+	9.67095i	−0.668421	+	0.385913i
$629$		−	1.40724i		−	0.0561103i
$630$	−0.694632	+	0.0422765i	−0.0276748	+	0.00168434i
$631$		−	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
$633$	26.2895	−	9.91497i	1.04491	−	0.394085i
$634$	−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
$639$	5.98799	−	5.26567i	0.236881	−	0.208307i
$640$	−0.0759308	−	0.0438386i	−0.00300143	−	0.00173287i
$641$	−5.36714	−	3.09872i	−0.211989	−	0.122392i	0.390246	−	0.920711i	$-0.372390\pi$
$641$	−5.36714	−	3.09872i	−0.211989	−	0.122392i	−0.602236	+	0.798318i	$0.705723\pi$
$642$	4.60621	+	0.757290i	0.181793	+	0.0298878i
$643$	−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	$-0.785896\pi$
$647$	3.77674	−	6.54151i	0.148479	−	0.257173i	0.930666	+	0.365871i	$0.119229\pi$
$648$	−1.15060	+	8.92615i	−0.0451999	+	0.350652i
$649$	−17.6347	+	10.1814i	−0.692223	+	0.399655i
$650$	−12.1464	−	13.2841i	−0.476420	−	0.521045i
$651$	−1.19638	+	3.86943i	−0.0468897	+	0.151655i
$652$			17.6397i			0.690823i
$653$	27.7842	−	16.0412i	1.08728	−	0.627742i	0.154430	−	0.988004i	$-0.450646\pi$
$653$	27.7842	−	16.0412i	1.08728	−	0.627742i	0.932851	+	0.360262i	$0.117313\pi$
$654$	4.68801	+	12.4302i	0.183316	+	0.486061i
$655$	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	$-0.0509128\pi$
$660$	−0.848544	−	0.139506i	−0.0330295	−	0.00543026i
$661$	13.8904	−	24.0589i	0.540274	−	0.935782i	−0.458614	−	0.888636i	$-0.651654\pi$
$661$	13.8904	−	24.0589i	0.540274	−	0.935782i	0.998888	−	0.0471464i	$-0.0150127\pi$
$662$	−3.59847	−	2.07757i	−0.139858	−	0.0807472i
$663$	13.9748	−	9.11079i	0.542737	−	0.353834i
$664$		−	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
$669$	29.8572	−	11.2605i	1.15434	−	0.435356i
$670$	−0.331078	−	0.573444i	−0.0127907	−	0.0221541i
$671$			13.1583i			0.507972i
$672$	−1.35365	+	4.37809i	−0.0522180	+	0.168888i
$673$	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
$675$	−13.7432	−	22.0012i	−0.528975	−	0.846825i
$676$	−10.6329	−	7.47939i	−0.408958	−	0.287669i
$677$	7.78434	+	13.4829i	0.299176	+	0.518189i	0.975948	−	0.218004i	$-0.0699547\pi$
$677$	7.78434	+	13.4829i	0.299176	+	0.518189i	−0.676771	+	0.736193i	$0.736621\pi$
$678$	−8.70570	+	10.6226i	−0.334340	+	0.407957i
$679$	27.4624	+	3.78369i	1.05391	+	0.145205i
$680$			0.234214i			0.00898170i
$681$	−7.37871	−	1.21311i	−0.282753	−	0.0464863i
$682$	−2.50237	+	4.33422i	−0.0958205	+	0.165966i
$683$	−6.05165	+	10.4818i	−0.231560	+	0.401074i	−0.958267	−	0.285873i	$-0.907716\pi$
$683$	−6.05165	+	10.4818i	−0.231560	+	0.401074i	0.726707	+	0.686947i	$0.241050\pi$
$684$	14.9900	−	13.1818i	0.573159	−	0.504019i
$685$			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
$690$	−0.174415	+	0.0657797i	−0.00663985	+	0.00250419i
$691$	−7.19903	−	12.4691i	−0.273864	−	0.474347i	0.695984	−	0.718057i	$-0.254969\pi$
$691$	−7.19903	−	12.4691i	−0.273864	−	0.474347i	−0.969848	+	0.243711i	$0.921635\pi$
$692$	16.3020			0.619708
$693$	2.73042	+	44.8627i	0.103720	+	1.70419i
$694$			4.98244i			0.189131i
$695$	−0.859298	−	1.48835i	−0.0325950	−	0.0564563i
$696$	3.57414	+	9.47684i	0.135478	+	0.359219i
$697$	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	$0.782665\pi$
$702$	−13.1151	−	13.3789i	−0.494997	−	0.504953i
$703$	3.03560	+	1.75261i	0.114490	+	0.0661008i
$704$	−2.83131	+	4.90398i	−0.106709	+	0.184826i
$705$	−0.211991	+	1.28943i	−0.00798404	+	0.0485629i
$706$			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	$-0.854353\pi$
$709$	−25.6450	+	14.8062i	−0.963119	+	0.556057i	−0.0659873	+	0.997820i	$0.521020\pi$
$710$	−0.201822	−	0.116522i	−0.00757424	−	0.00437299i
$711$	40.8903	+	13.8188i	1.53351	+	0.518244i
$712$	−2.93597	+	1.69508i	−0.110030	+	0.0635259i
$713$			1.08487i			0.0406286i
$714$	11.9364	−	2.71607i	0.446709	−	0.101646i
$715$	1.32110	−	1.20795i	0.0494063	−	0.0451748i
$716$	7.78809	−	4.49646i	0.291055	−	0.168041i
$717$	24.9458	−	9.40820i	0.931619	−	0.351356i
$718$	−1.49774	+	2.59416i	−0.0558952	+	0.0968133i
$719$	14.5300	+	25.1667i	0.541877	+	0.938558i	0.998796	+	0.0490503i	$0.0156195\pi$
$719$	14.5300	+	25.1667i	0.541877	+	0.938558i	−0.456919	+	0.889508i	$0.651047\pi$
$720$	0.257908	−	0.0516637i	0.00961167	−	0.00192539i
$721$	30.4682	−	12.4061i	1.13469	−	0.462029i
$722$	−25.2735			−0.940583
$723$	−2.19005	+	13.3210i	−0.0814488	+	0.495412i
$724$	−6.15572	−	3.55401i	−0.228776	−	0.132084i
$725$	−25.2821	−	14.5966i	−0.938955	−	0.542106i
$726$	−5.91910	+	36.0029i	−0.219678	+	1.33619i
$727$		−	10.8801i		−	0.403521i	−0.979435	−	0.201761i	$-0.935334\pi$
$727$		−	10.8801i		−	0.403521i	0.979435	−	0.201761i	$-0.0646663\pi$
$728$	−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
$732$	−1.42028	−	3.76587i	−0.0524951	−	0.139191i
$733$	−25.2212	−	43.6845i	−0.931568	−	1.61352i	−0.780643	−	0.624978i	$-0.785108\pi$
$733$	−25.2212	−	43.6845i	−0.931568	−	1.61352i	−0.150925	−	0.988545i	$-0.548225\pi$
$734$			0.431332i			0.0159208i
$735$	0.871056	−	0.609341i	0.0321294	−	0.0224759i
$736$			1.22748i			0.0452454i
$737$	−37.0358	+	21.3826i	−1.36423	+	0.787639i
$738$	8.63807	−	25.5604i	0.317972	−	0.940892i
$739$	4.88879	+	2.82254i	0.179837	+	0.103829i	0.587216	−	0.809430i	$-0.300224\pi$
$739$	4.88879	+	2.82254i	0.179837	+	0.103829i	−0.407379	+	0.913259i	$0.633557\pi$
$740$	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	$0.574534\pi$
$744$	0.248342	−	1.51054i	0.00910466	−	0.0553791i
$745$	−0.972927	−	0.561720i	−0.0356453	−	0.0205798i
$746$	−5.60905	+	9.71516i	−0.205362	+	0.355697i
$747$	5.66863	+	6.44624i	0.207404	+	0.235855i
$748$	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	0.851056	−	0.525075i	$-0.175963\pi$
$751$	−0.800219	−	1.38602i	−0.0292004	−	0.0505766i	−0.880256	+	0.474498i	$0.842629\pi$
$752$	7.45201	+	4.30242i	0.271747	+	0.156893i
$753$	12.8342	−	4.84036i	0.467704	−	0.176393i
$754$	−20.1013	−	6.36170i	−0.732047	−	0.231680i
$755$	−0.360717			−0.0131278
$756$	−5.62381	−	12.5448i	−0.204536	−	0.456251i
$757$	−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
$759$	4.24837	+	11.2645i	0.154206	+	0.408877i
$760$	−0.505231	−	0.291695i	−0.0183266	−	0.0105809i
$761$	−29.1876	+	16.8515i	−1.05805	+	0.610865i	−0.924892	−	0.380230i	$-0.875845\pi$
$761$	−29.1876	+	16.8515i	−1.05805	+	0.610865i	−0.133157	+	0.991095i	$0.542512\pi$
$762$	−6.44136	−	5.27901i	−0.233346	−	0.191238i
$763$	−16.0249	−	12.4502i	−0.580141	−	0.450728i
$764$			14.2368i			0.515070i
$765$	−0.463998	−	0.527647i	−0.0167759	−	0.0190771i
$766$	−0.325127	−	0.187712i	−0.0117473	−	0.00678232i
$767$	2.79265	+	12.6613i	0.100837	+	0.457171i
$768$	0.280988	−	1.70911i	0.0101393	−	0.0616721i
$769$	−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	$-0.320464\pi$
$773$	1.94637	+	1.12374i	0.0700061	+	0.0404181i	−0.464588	+	0.885527i	$0.653798\pi$
$774$	−27.5603	−	9.31394i	−0.990636	−	0.334783i
$775$	2.20615	+	3.82116i	0.0792472	+	0.137260i
$776$	−10.4779			−0.376134
$777$	1.77074	−	1.64082i	0.0635249	−	0.0588640i
$778$		−	32.6910i		−	1.17203i
$779$	−51.8242	+	29.9207i	−1.85679	+	1.07202i
$780$	−0.247710	+	0.488308i	−0.00886945	+	0.0174842i
$781$	−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
$786$	−5.56252	+	33.8340i	−0.198409	+	1.20682i
$787$	−17.2066	+	29.8028i	−0.613350	+	1.06235i	0.377321	+	0.926082i	$0.376845\pi$
$787$	−17.2066	+	29.8028i	−0.613350	+	1.06235i	−0.990672	+	0.136271i	$0.956488\pi$
$788$	−2.79871	+	4.84751i	−0.0997000	+	0.172685i
$789$	−39.9841	−	6.57364i	−1.42347	−	0.234028i
$790$		−	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
$795$	1.99007	−	0.750545i	0.0705805	−	0.0266191i
$796$	−0.509204	+	0.293989i	−0.0180483	+	0.0104202i
$797$	−0.908350			−0.0321754			−0.0160877	−	0.999871i	$-0.505121\pi$
$797$	−0.908350			−0.0321754			−0.0160877	+	0.999871i	$0.505121\pi$
$798$	−9.00694	+	29.1311i	−0.318842	+	1.03123i
$799$		−	22.9863i		−	0.813196i
$800$	2.49616	+	4.32347i	0.0882525	+	0.152858i
$801$	3.25617	−	9.63516i	0.115051	−	0.340442i
$802$	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
$807$	0.483233	−	2.93926i	0.0170106	−	0.103467i
$808$	1.67265	−	2.89711i	0.0588436	−	0.101920i
$809$	14.8389	+	8.56724i	0.521708	+	0.301208i	0.737633	−	0.675202i	$-0.235943\pi$
$809$	14.8389	+	8.56724i	0.521708	+	0.301208i	−0.215925	+	0.976410i	$0.569277\pi$
$810$	−0.478676	+	0.627328i	−0.0168190	+	0.0220421i
$811$	−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
$816$	−4.32920	+	1.63274i	−0.151552	+	0.0571573i
$817$	32.2618	+	55.8791i	1.12870	+	1.95496i
$818$	−32.2722			−1.12837
$819$	27.7585	+	6.96155i	0.969962	+	0.243256i
$820$	−0.788528			−0.0275366
$821$	−12.6949	−	21.9881i	−0.443054	−	0.767392i	0.554861	−	0.831943i	$-0.312772\pi$
$821$	−12.6949	−	21.9881i	−0.443054	−	0.767392i	−0.997914	+	0.0645517i	$0.979438\pi$
$822$	−20.3914	+	7.69051i	−0.711231	+	0.268237i
$823$	−2.14820	+	3.72079i	−0.0748815	+	0.129699i	−0.901035	−	0.433747i	$-0.857191\pi$
$823$	−2.14820	+	3.72079i	−0.0748815	+	0.129699i	0.826153	+	0.563446i	$0.190525\pi$
$824$	−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	$0.378599\pi$
$828$	−2.43174	−	2.76531i	−0.0845088	−	0.0961013i
$829$	−37.1532	−	21.4504i	−1.29038	−	0.745003i	−0.311661	−	0.950193i	$-0.600885\pi$
$829$	−37.1532	−	21.4504i	−1.29038	−	0.745003i	−0.978722	+	0.205190i	$0.934219\pi$
$830$	0.125439	−	0.217267i	0.00435405	−	0.00754144i
$831$	−3.44000	+	20.9238i	−0.119332	+	0.725838i
$832$	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
$837$	2.43303	+	3.89499i	0.0840979	+	0.134631i
$838$	−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	$0.848992\pi$
$840$	−0.294713	+	0.273089i	−0.0101686	+	0.00942248i
$841$	−5.19498			−0.179137
$842$	−24.3867	+	14.0796i	−0.840420	+	0.485217i
$843$	13.1147	−	4.94615i	0.451694	−	0.170354i
$844$	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
$849$	5.73424	+	0.942745i	0.196799	+	0.0323549i
$850$	6.66803	−	11.5494i	0.228711	−	0.396140i
$851$	0.323315	−	0.559998i	0.0110831	−	0.0191965i
$852$	0.746857	−	4.54276i	0.0255869	−	0.155632i
$853$	−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	$-0.795471\pi$
$857$	3.47394	−	6.01703i	0.118667	−	0.205538i	0.919240	+	0.393698i	$0.128804\pi$
$858$	31.5373	+	15.9983i	1.07667	+	0.546174i
$859$	−14.5807	+	8.41820i	−0.497489	+	0.287225i	−0.727676	−	0.685921i	$-0.759399\pi$
$859$	−14.5807	+	8.41820i	−0.497489	+	0.287225i	0.230187	+	0.973146i	$0.426066\pi$
$860$			0.850225i			0.0289924i
$861$	9.14418	+	40.1863i	0.311633	+	1.36954i
$862$	36.4880			1.24279
$863$	−2.46354	−	4.26698i	−0.0838600	−	0.145250i	0.821045	−	0.570864i	$-0.193392\pi$
$863$	−2.46354	−	4.26698i	−0.0838600	−	0.145250i	−0.904905	+	0.425614i	$0.860058\pi$
$864$	2.75286	+	4.40701i	0.0936544	+	0.149930i
$865$	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
$870$	−0.144064	+	0.876269i	−0.00488423	+	0.0297083i
$871$	5.86501	+	26.5907i	0.198728	+	0.900991i
$872$	6.64244	+	3.83502i	0.224941	+	0.129870i
$873$	23.6050	−	20.7576i	0.798909	−	0.702538i
$874$			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	$-0.830281\pi$
$877$	−25.2195	+	14.5605i	−0.851601	+	0.491672i	0.00958950	+	0.999954i	$0.496948\pi$
$878$	−19.3010	−	11.1434i	−0.651376	−	0.376072i
$879$	12.9607	+	34.3653i	0.437154	+	1.15911i
$880$	−0.429968	+	0.248242i	−0.0144942	+	0.00836823i
$881$	−1.87116			−0.0630411			−0.0315205	−	0.999503i	$-0.510035\pi$
$881$	−1.87116			−0.0630411			−0.0315205	+	0.999503i	$0.510035\pi$
$882$	17.3353	+	11.8528i	0.583709	+	0.399103i
$883$	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
$885$	0.510963	−	0.192707i	0.0171758	−	0.00647779i
$886$	22.9471	+	13.2485i	0.770924	+	0.445093i
$887$	16.0090	+	27.7284i	0.537530	+	0.931029i	0.999036	+	0.0438921i	$0.0139758\pi$
$887$	16.0090	+	27.7284i	0.537530	+	0.931029i	−0.461506	+	0.887137i	$0.652691\pi$
$888$	−0.578367	+	0.705715i	−0.0194087	+	0.0236822i
$889$	12.6025	+	1.73633i	0.422674	+	0.0582347i
$890$	−0.297240			−0.00996352
$891$	40.5159	+	30.9152i	1.35733	+	1.03570i
$892$	9.21163	−	15.9550i	0.308428	−	0.534213i
$893$	49.5844	+	28.6276i	1.65928	+	0.957986i
$894$	3.60039	−	21.8994i	0.120415	−	0.732425i
$895$	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
$900$	−14.1886	−	4.79500i	−0.472954	−	0.159833i
$901$	−32.4007	+	18.7066i	−1.07943	+	0.623207i
$902$			50.9269i			1.69568i
$903$	43.3306	−	9.85965i	1.44195	−	0.328109i
$904$			7.92944i			0.263729i
$905$	−0.311606	−	0.539717i	−0.0103581	−	0.0179408i
$906$	−2.51461	−	6.66748i	−0.0835423	−	0.221512i
$907$	−0.102258	+	0.177116i	−0.00339542	+	0.00588104i	−0.867718	−	0.497057i	$-0.834414\pi$
$907$	−0.102258	+	0.177116i	−0.00339542	+	0.00588104i	0.864323	+	0.502938i	$0.167747\pi$
$908$	−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	$-0.0515694\pi$
$912$	1.86965	−	11.3721i	0.0619102	−	0.376568i
$913$	−14.0321	−	8.10146i	−0.464396	−	0.268119i
$914$	17.3505	+	10.0173i	0.573903	+	0.331343i
$915$	0.0572477	−	0.348209i	0.00189255	−	0.0115114i
$916$	−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	0.714332	−	0.699807i	$-0.246731\pi$
$919$	−7.54494	−	13.0682i	−0.248885	−	0.431081i	−0.963217	+	0.268726i	$0.913397\pi$
$920$	−0.0538110	+	0.0932033i	−0.00177410	+	0.00307282i
$921$	−30.9053	+	11.6558i	−1.01836	+	0.384072i
$922$	−7.60166	+	4.38882i	−0.250347	+	0.144538i
$923$	6.46688	+	7.07262i	0.212860	+	0.232798i
$924$	17.6374	+	19.0340i	0.580229	+	0.626172i
$925$		−	2.62993i		−	0.0864716i
$926$	15.5289	−	8.96560i	0.510311	−	0.294628i
$927$	11.9425	−	35.3384i	0.392244	−	1.16067i
$928$	5.06421	+	2.92382i	0.166241	+	0.0959792i
$929$	−2.52193	+	1.45604i	−0.0827418	+	0.0477710i	−0.540800	−	0.841151i	$-0.681878\pi$
$929$	−2.52193	+	1.45604i	−0.0827418	+	0.0477710i	0.458058	+	0.888922i	$0.348545\pi$
$930$	0.0850768	−	0.103809i	0.00278978	−	0.00340405i
$931$	−11.5129	−	45.1315i	−0.377319	−	1.47913i
$932$			16.4052i			0.537370i
$933$	1.07429	−	6.53433i	0.0351705	−	0.213924i
$934$	8.47219	−	14.6743i	0.277219	−	0.480157i
$935$	1.14858	+	0.663133i	0.0375626	+	0.0216868i
$936$	−10.7527	−	1.17460i	−0.351463	−	0.0383931i
$937$		−	43.9029i		−	1.43425i	−0.696946	−	0.717123i	$-0.745458\pi$
$937$		−	43.9029i		−	1.43425i	0.696946	−	0.717123i	$-0.254542\pi$
$938$	−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	$-0.540611\pi$
$941$	−32.2047	−	18.5934i	−1.04984	−	0.606127i	−0.922606	+	0.385745i	$0.873945\pi$
$942$	−11.8220	−	31.3459i	−0.385181	−	1.02131i
$943$	5.51967	+	9.56036i	0.179745	+	0.311328i
$944$		−	3.59600i		−	0.117040i
$945$	0.122928	−	1.19908i	0.00399885	−	0.0390060i
$946$	54.9116			1.78533
$947$	9.06698	+	15.7045i	0.294637	+	0.510326i	0.974900	−	0.222641i	$-0.0714679\pi$
$947$	9.06698	+	15.7045i	0.294637	+	0.510326i	−0.680263	+	0.732968i	$0.738135\pi$
$948$	23.3166	−	8.79373i	0.757287	−	0.285607i
$949$	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	$-0.0716689\pi$
$954$	27.7461	+	31.5522i	0.898313	+	1.02154i
$955$	−0.624123	+	1.08101i	−0.0201961	+	0.0349807i
$956$	7.69636	−	13.3305i	0.248918	−	0.431139i
$957$	56.5937	+	9.30436i	1.82941	+	0.300767i
$958$			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
$963$	−2.58858	+	7.65972i	−0.0834158	+	0.246831i
$964$	3.89705	+	6.74990i	0.125516	+	0.217400i
$965$	1.30755			0.0420914
$966$	5.37400	+	1.66157i	0.172906	+	0.0534602i
$967$		−	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
$969$	−28.8058	+	10.8640i	−0.925375	+	0.349001i
$970$	−0.795594	−	0.459336i	−0.0255450	−	0.0147484i
$971$	−21.8686	−	37.8776i	−0.701798	−	1.21555i	−0.967835	−	0.251587i	$-0.919048\pi$
$971$	−21.8686	−	37.8776i	−0.701798	−	1.21555i	0.266037	−	0.963963i	$-0.414286\pi$
$972$	−14.9324	−	4.47464i	−0.478958	−	0.143524i
$973$	−7.07830	+	51.3751i	−0.226920	+	1.64701i
$974$			14.3215i			0.458890i
$975$	26.1169	−	17.0268i	0.836411	−	0.545293i
$976$	−2.01240	−	1.16186i	−0.0644153	−	0.0371902i
$977$	3.38263	−	5.85889i	0.108220	−	0.187443i	−0.806829	−	0.590785i	$-0.798818\pi$
$977$	3.38263	−	5.85889i	0.108220	−	0.187443i	0.915049	+	0.403342i	$0.132152\pi$
$978$	−30.1481	−	4.95653i	−0.964029	−	0.158492i
$979$			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	$-0.427248\pi$
$983$	−15.7908	−	9.11680i	−0.503647	−	0.290781i	−0.730218	+	0.683214i	$0.760582\pi$
$984$	−5.49694	−	14.5751i	−0.175236	−	0.464638i
$985$	−0.425017	+	0.245384i	−0.0135422	+	0.00781857i
$986$		−	15.6209i		−	0.497472i
$987$	28.9237	−	26.8016i	0.920653	−	0.853104i
$988$	16.1889	+	17.7053i	0.515037	+	0.563279i
$989$	10.3084	−	5.95155i	0.327788	−	0.189248i
$990$	0.476861	−	1.41105i	0.0151556	−	0.0448462i
$991$	6.85129	−	11.8668i	0.217638	−	0.376961i	−0.736447	−	0.676495i	$-0.763498\pi$
$991$	6.85129	−	11.8668i	0.217638	−	0.376961i	0.954085	+	0.299534i	$0.0968313\pi$
$992$	−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
$996$	4.89040	+	0.804013i	0.154958	+	0.0254761i
$997$	−43.3774	−	25.0440i	−1.37378	−	0.793151i	−0.382376	−	0.924007i	$-0.624894\pi$
$997$	−43.3774	−	25.0440i	−1.37378	−	0.793151i	−0.991401	+	0.130856i	$0.958227\pi$
$998$	23.5183	+	13.5783i	0.744460	+	0.429814i
$999$	−0.0951109	−	2.73566i	−0.00300917	−	0.0865524i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.3	✓	36	13.12	even	2
546.2.bg.a.311.9	yes	36	3.2	odd	2
546.2.bg.a.467.3	yes	36	21.5	even	6
546.2.bg.a.467.9	yes	36	91.12	odd	6
546.2.bg.b.311.3	yes	36	1.1	even	1	trivial
546.2.bg.b.311.9	yes	36	39.38	odd	2	inner
546.2.bg.b.467.3	yes	36	273.194	even	6	inner
546.2.bg.b.467.9	yes	36	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.62062 + 0.611211i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0759308 + 0.0438386i) q^{5} +(-1.33964 - 1.09790i) q^{6} +(2.62099 + 0.361112i) q^{7} -1.00000 q^{8} +(2.25284 - 1.98109i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.62062 + 0.611211i) 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} +(2.25284 - 1.98109i) q^{9} +(-0.0759308 - 0.0438386i) q^{10} +(-2.83131 + 4.90398i) q^{11} +(0.280988 - 1.70911i) 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} +(2.84209 + 0.960476i) q^{18} +(-3.32692 - 5.76239i) q^{19} -0.0876773i q^{20} +(-4.46836 + 1.01675i) q^{21} -5.66263 q^{22} +(-1.06303 + 0.613739i) q^{23} +(1.62062 - 0.611211i) 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} +(0.149850 + 0.0246363i) q^{30} +(0.441909 - 0.765409i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.59113 - 9.67803i) 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} +(-5.56938 - 2.82525i) q^{39} +(0.0759308 - 0.0438386i) q^{40} -8.99352i q^{41} +(-3.11471 - 3.36134i) q^{42} -9.69720 q^{43} +(-2.83131 - 4.90398i) q^{44} +(-0.0842120 + 0.249187i) 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} +(0.750608 - 4.56557i) q^{51} +(-3.52092 + 0.776597i) q^{52} +(12.1291 + 7.00275i) q^{53} +(-5.19301 + 0.180546i) 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} +(0.0535893 + 0.142092i) q^{60} +(2.01240 - 1.16186i) q^{61} +0.883818 q^{62} +(6.62008 - 4.37888i) q^{63} +1.00000 q^{64} +(-0.301391 - 0.0953849i) q^{65} +(9.17699 - 3.46106i) 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} +(-2.25284 + 1.98109i) q^{72} +(4.11174 - 7.12173i) q^{73} +(-0.456219 - 0.263398i) q^{74} +(1.40278 - 8.53240i) 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} +(1.15060 - 8.92615i) q^{81} +(7.78862 - 4.49676i) q^{82} +2.86138i q^{83} +(1.35365 - 4.37809i) q^{84} -0.234214i q^{85} +(-4.84860 - 8.39803i) q^{86} +(-3.57414 - 9.47684i) 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} +(-0.248342 + 1.51054i) q^{93} +(-7.45201 - 4.30242i) q^{94} +(0.505231 + 0.291695i) q^{95} +(-0.280988 + 1.70911i) 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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