LMFDB - Embedded newform 546.2.bg.b.467.3

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			467.3
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.3

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	−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	0.482925	−	0.875662i	$-0.339574\pi$
$5$	−0.0759308	−	0.0438386i	−0.0339573	−	0.0196052i	−0.516883	+	0.856056i	$0.672908\pi$
$6$	−1.33964	+	1.09790i	−0.546904	+	0.448214i
$7$	2.62099	−	0.361112i	0.990642	−	0.136488i
$7$	2.62099	−	0.361112i	0.990642	−	0.136488i
$8$	−1.00000			−0.353553
$9$	2.25284	+	1.98109i	0.750948	+	0.660362i
$10$	−0.0759308	+	0.0438386i	−0.0240114	+	0.0138630i
$11$	−2.83131	−	4.90398i	−0.853673	−	1.47860i	−0.877871	−	0.478898i	$-0.841036\pi$
$11$	−2.83131	−	4.90398i	−0.853673	−	1.47860i	0.0241978	−	0.999707i	$-0.492297\pi$
$12$	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	0.657353	−	0.753583i	$-0.271676\pi$
$17$	−1.33566	−	2.31343i	−0.323945	−	0.561089i	−0.981298	+	0.192493i	$0.938343\pi$
$18$	2.84209	−	0.960476i	0.669887	−	0.226386i
$19$	−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
$21$	−4.46836	−	1.01675i	−0.975075	−	0.221873i
$22$	−5.66263			−1.20728
$23$	−1.06303	−	0.613739i	−0.221656	−	0.127973i	0.385061	−	0.922891i	$-0.374181\pi$
$23$	−1.06303	−	0.613739i	−0.221656	−	0.127973i	−0.606717	+	0.794918i	$0.707514\pi$
$24$	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	$-0.817311\pi$
$29$		−	5.84765i		−	1.08588i	0.839771	−	0.542940i	$-0.182689\pi$
$30$	0.149850	−	0.0246363i	0.0273587	−	0.00449794i
$31$	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
$33$	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	0.462030	−	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
$39$	−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	$0.247833\pi$
$41$			8.99352i			1.40455i	−0.711905	+	0.702276i	$0.752167\pi$
$42$	−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	−0.154215	−	0.988037i	$-0.549285\pi$
$47$	−7.45201	−	4.30242i	−1.08699	−	0.627572i	−0.932773	+	0.360465i	$0.882618\pi$
$48$	1.33964	−	1.09790i	0.193360	−	0.158468i
$49$	6.73920	−	1.89294i	0.962742	−	0.270420i
$50$	−4.99231			−0.706020
$51$	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	0.696334	−	0.717718i	$-0.254813\pi$
$53$	12.1291	−	7.00275i	1.66606	−	0.961902i	0.969729	−	0.244184i	$-0.0785201\pi$
$54$	−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	−0.283390	−	0.959005i	$-0.591459\pi$
$59$	3.11423	−	1.79800i	0.405438	−	0.234080i	0.688828	+	0.724925i	$0.258126\pi$
$60$	0.0535893	−	0.142092i	0.00691835	−	0.0183440i
$61$	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
$63$	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	−0.0440981	−	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	$-0.449585\pi$
$71$	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	0.999768	−	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
$75$	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	−0.103957	−	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
$81$	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	$-0.949805\pi$
$83$		−	2.86138i		−	0.314077i	0.987592	−	0.157039i	$-0.0501947\pi$
$84$	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	0.647469	−	0.762092i	$-0.275828\pi$
$89$	2.93597	+	1.69508i	0.311212	+	0.179678i	−0.336257	+	0.941770i	$0.609161\pi$
$90$	−0.257908	−	0.0516637i	−0.0271859	−	0.00544584i
$91$	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	0.770729	−	0.637163i	$-0.219892\pi$
$101$	−1.67265	−	2.89711i	−0.166435	−	0.288273i	−0.937164	+	0.348890i	$0.886559\pi$
$102$	4.32920	+	1.63274i	0.428655	+	0.161665i
$103$	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
$105$	0.294713	+	0.273089i	0.0287610	+	0.0266508i
$106$		−	14.0055i		−	1.36033i
$107$	−2.33402	−	1.34755i	−0.225639	−	0.130272i	0.382920	−	0.923782i	$-0.374919\pi$
$107$	−2.33402	−	1.34755i	−0.225639	−	0.130272i	−0.608558	+	0.793509i	$0.708252\pi$
$108$	−2.75286	+	4.40701i	−0.264895	+	0.424065i
$109$	−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	$0.121660\pi$
$113$			7.92944i			0.745939i	−0.927844	+	0.372970i	$0.878340\pi$
$114$	−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	0.00243479	+	0.999997i	$0.499225\pi$
$131$	−9.89815	+	17.1441i	−0.864805	+	1.49789i	−0.867240	+	0.497890i	$0.834108\pi$
$132$	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	0.999038	+	0.0438504i	$0.0139625\pi$
$137$	6.29121	+	10.8967i	0.537495	+	0.930968i	−0.461543	+	0.887118i	$0.652704\pi$
$138$	2.09789	−	0.344906i	0.178584	−	0.0293604i
$139$		−	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
$144$	−2.84209	+	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	−0.474726	−	0.880134i	$-0.657453\pi$
$149$	6.40667	−	11.0967i	0.524855	−	0.909076i	0.999581	−	0.0289419i	$-0.00921379\pi$
$150$	8.09066	+	3.05136i	0.660600	+	0.249142i
$151$	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
$156$	5.23143	+	3.41060i	0.418849	+	0.273066i
$157$	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
$159$	−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	0.959782	−	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
$165$	0.303456	−	0.804613i	0.0236240	−	0.0626391i
$166$	−2.47803	−	1.43069i	−0.192332	−	0.111043i
$167$			15.5348i			1.20212i	0.799205	+	0.601058i	$0.205254\pi$
$167$			15.5348i			1.20212i	−0.799205	+	0.601058i	$0.794746\pi$
$168$	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	0.369831	+	0.929099i	$0.379416\pi$
$173$	−8.15099	+	14.1179i	−0.619708	+	1.07337i	−0.989539	+	0.144267i	$0.953918\pi$
$174$	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	−0.761971	−	0.647611i	$-0.775768\pi$
$179$	−7.78809	+	4.49646i	−0.582109	+	0.336081i	0.179862	+	0.983692i	$0.442435\pi$
$180$	−0.173696	+	0.197523i	−0.0129466	+	0.0147225i
$181$		−	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
$186$	−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	0.874638	−	0.484777i	$-0.161099\pi$
$191$	12.3294	+	7.11841i	0.892127	+	0.515070i	0.0174894	+	0.999847i	$0.494433\pi$
$192$	−1.62062	−	0.611211i	−0.116958	−	0.0441103i
$193$	−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
$195$	0.546742	+	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	−0.481843	−	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
$201$	−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	−0.370762	−	0.928728i	$-0.620904\pi$
$227$	3.73888	−	2.15864i	0.248158	−	0.143274i	0.618921	+	0.785454i	$0.287570\pi$
$228$	−10.7834	−	4.06689i	−0.714146	−	0.269337i
$229$	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
$231$	7.66519	+	24.7915i	0.504332	+	1.63116i
$232$			5.84765i			0.383917i
$233$	14.2073	+	8.20260i	0.930753	+	0.537370i	0.887050	−	0.461674i	$-0.152751\pi$
$233$	14.2073	+	8.20260i	0.930753	+	0.537370i	0.0437031	+	0.999045i	$0.486084\pi$
$234$	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	0.963810	−	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
$243$	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	−0.670421	−	0.741981i	$-0.733887\pi$
$257$	4.92741	−	8.53452i	0.307363	−	0.532369i	0.977785	+	0.209612i	$0.0672200\pi$
$258$	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	0.278340	−	0.960483i	$-0.410216\pi$
$263$	20.2604	−	11.6974i	1.24931	−	0.721290i	0.970972	+	0.239192i	$0.0768826\pi$
$264$	−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	0.838620	−	0.544716i	$-0.183363\pi$
$269$	−0.859882	−	1.48936i	−0.0524279	−	0.0908078i	−0.891048	+	0.453908i	$0.850029\pi$
$270$	0.386395	+	0.241364i	0.0235152	+	0.0146889i
$271$	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
$273$	−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	0.989220	−	0.146438i	$-0.0467808\pi$
$277$	6.12127	+	10.6023i	0.367791	+	0.637033i	−0.621429	+	0.783471i	$0.713447\pi$
$278$	−16.9753	−	9.80069i	−1.01811	−	0.587806i
$279$	−0.520789	+	2.59981i	−0.0311788	+	0.155646i
$280$	0.214845	+	0.0874812i	0.0128394	+	0.00522800i
$281$	−8.09237			−0.482751			−0.241375	−	0.970432i	$-0.577598\pi$
$281$	−8.09237			−0.482751			−0.241375	+	0.970432i	$0.577598\pi$
$282$	14.7066	−	2.41786i	0.875765	−	0.143981i
$283$	−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
$285$	−0.997076	+	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	$0.212626\pi$
$293$			21.2050i			1.23881i	−0.785072	+	0.619404i	$0.787374\pi$
$294$	−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	0.806723	−	0.590929i	$-0.201239\pi$
$311$	−1.91162	−	3.31103i	−0.108398	−	0.187751i	−0.915121	+	0.403178i	$0.867905\pi$
$312$	5.56938	−	2.82525i	0.315304	−	0.159948i
$313$	−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
$315$	−0.310703	−	0.622707i	−0.0175061	−	0.0350856i
$316$	−14.3874			−0.809355
$317$	12.3152	−	21.3306i	0.691692	−	1.19805i	−0.279591	−	0.960119i	$-0.590199\pi$
$317$	12.3152	−	21.3306i	0.691692	−	1.19805i	0.971283	−	0.237927i	$-0.0764679\pi$
$318$	−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	0.397834	−	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
$333$	−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	−0.379690	−	0.925114i	$-0.623969\pi$
$347$	4.31492	−	2.49122i	0.231637	−	0.133736i	0.611327	+	0.791378i	$0.290636\pi$
$348$	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	0.0502108	−	0.998739i	$-0.484011\pi$
$353$	17.6657	−	10.1993i	0.940249	−	0.542853i	0.890038	+	0.455885i	$0.150677\pi$
$354$	−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	−0.823792	−	0.566893i	$-0.808145\pi$
$359$	1.49774	−	2.59416i	0.0790477	−	0.136915i	0.902839	+	0.429978i	$0.141479\pi$
$360$	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	−0.490219	−	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
$369$	−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	−0.683485	−	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
$375$	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	$0.0952393\pi$
$379$			11.4767i			0.589518i	−0.955572	+	0.294759i	$0.904761\pi$
$380$	−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	0.491670	−	0.870781i	$-0.336386\pi$
$383$	−0.325127	−	0.187712i	−0.0166132	−	0.00959165i	−0.508284	+	0.861190i	$0.669720\pi$
$384$	−1.33964	+	1.09790i	−0.0683630	+	0.0560268i
$385$	0.179286	+	1.30128i	0.00913727	+	0.0663194i
$386$			14.9132i			0.759061i
$387$	−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	−0.997528	−	0.0702694i	$-0.977614\pi$
$389$	−28.3112	+	16.3455i	−1.43544	+	0.828750i	−0.437909	+	0.899019i	$0.644281\pi$
$390$	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	−0.999754	−	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
$399$	20.7248	−	22.3658i	1.03754	−	1.11969i
$400$	4.99231			0.249616
$401$	−2.06325	+	3.57365i	−0.103034	+	0.178459i	−0.912933	−	0.408109i	$-0.866188\pi$
$401$	−2.06325	+	3.57365i	−0.103034	+	0.178459i	0.809900	+	0.586569i	$0.199522\pi$
$402$	−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	−0.920995	−	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
$411$	−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	$-0.759277\pi$
$421$		−	28.1593i		−	1.37240i	0.727413	−	0.686200i	$-0.240723\pi$
$422$	−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	0.852677	+	0.522438i	$0.174978\pi$
$431$	18.2440	+	31.5996i	0.878783	+	1.52210i	0.0261063	+	0.999659i	$0.491689\pi$
$432$	5.19301	+	0.180546i	0.249849	+	0.00868652i
$433$			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
$438$	−13.3272	−	5.02627i	−0.636796	−	0.240165i
$439$	−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
$441$	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	0.933643	−	0.358204i	$-0.116611\pi$
$443$	22.9471	+	13.2485i	1.09025	+	0.629457i	0.156608	+	0.987661i	$0.449944\pi$
$444$	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	0.847519	−	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
$459$	−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	$-0.934473\pi$
$461$		−	8.77765i		−	0.408816i	0.978886	−	0.204408i	$-0.0655269\pi$
$462$	25.3026	+	5.75748i	1.17719	+	0.267862i
$463$			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
$465$	−0.0473632	+	0.125583i	−0.00219642	+	0.00582379i
$466$	14.2073	−	8.20260i	0.658142	−	0.379978i
$467$	−8.47219	+	14.6743i	−0.392046	+	0.679044i	−0.992719	−	0.120451i	$-0.961566\pi$
$467$	−8.47219	+	14.6743i	−0.392046	+	0.679044i	0.600673	+	0.799495i	$0.294899\pi$
$468$	−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	−0.325749	−	0.945456i	$-0.605616\pi$
$479$	7.22604	−	4.17195i	0.330166	−	0.190621i	0.655915	+	0.754835i	$0.272283\pi$
$480$	−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	−0.191934	−	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	$0.0552424\pi$
$491$			7.65264i			0.345359i	−0.984978	+	0.172679i	$0.944758\pi$
$492$	−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	0.923439	−	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
$501$	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	0.745819	−	0.666149i	$-0.232058\pi$
$509$	12.2242	+	7.05762i	0.541826	+	0.312823i	−0.203993	+	0.978972i	$0.565392\pi$
$510$	−0.257143	−	0.313761i	−0.0113865	−	0.0138936i
$511$	13.3486	+	17.1812i	0.590506	+	0.760052i
$512$	−1.00000			−0.0441942
$513$	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	0.788539	−	0.614984i	$-0.210838\pi$
$521$	−3.15726	−	5.46854i	−0.138322	−	0.239581i	−0.926862	+	0.375403i	$0.877504\pi$
$522$	−5.61653	−	16.6195i	−0.245829	−	0.727418i
$523$	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
$525$	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	0.314767	−	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
$543$	−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	0.781973	−	0.623312i	$-0.214213\pi$
$557$	−3.51222	−	6.08334i	−0.148818	−	0.257760i	−0.930791	+	0.365553i	$0.880880\pi$
$558$	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	−0.888985	−	0.457937i	$-0.848588\pi$
$563$	−19.9568	−	34.5661i	−0.841078	−	1.45679i	0.0479070	−	0.998852i	$-0.484745\pi$
$564$	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	0.985348	−	0.170557i	$-0.0545566\pi$
$569$	31.7330	+	18.3210i	1.33032	+	0.768058i	0.344968	+	0.938615i	$0.387890\pi$
$570$	−0.356574	+	0.945456i	−0.0149353	+	0.0396008i
$571$	−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
$576$	2.25284	+	1.98109i	0.0938685	+	0.0825452i
$577$	−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
$579$	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	$-0.848975\pi$
$587$		−	22.1376i		−	0.913717i	0.889539	−	0.456859i	$-0.151025\pi$
$588$	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	0.364227	−	0.931310i	$-0.381333\pi$
$593$	−6.33623	−	3.65823i	−0.260198	−	0.150225i	−0.624425	+	0.781085i	$0.714667\pi$
$594$	13.8177	+	25.9776i	0.566945	+	1.06587i
$595$	0.0845775	+	0.613873i	0.00346734	+	0.0251663i
$596$	−12.8133			−0.524855
$597$	−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	0.447854	−	0.894107i	$-0.352189\pi$
$599$	35.3925	−	20.4339i	1.44610	−	0.834906i	0.998246	+	0.0592009i	$0.0188552\pi$
$600$	−1.40278	−	8.53240i	−0.0572682	−	0.348334i
$601$		−	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
$606$	5.42147	+	2.04468i	0.220232	+	0.0830595i
$607$	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
$609$	−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	−0.645062	−	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	$-0.733211\pi$
$617$	−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	0.992727	−	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
$621$	−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	$0.343872\pi$
$631$			44.3163i			1.76421i	−0.471057	+	0.882103i	$0.656128\pi$
$632$	−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	−0.602236	−	0.798318i	$-0.705723\pi$
$641$	−5.36714	+	3.09872i	−0.211989	+	0.122392i	0.390246	+	0.920711i	$0.372390\pi$
$642$	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	0.930666	−	0.365871i	$-0.119229\pi$
$647$	3.77674	+	6.54151i	0.148479	+	0.257173i	−0.782186	+	0.623044i	$0.785896\pi$
$648$	−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	0.932851	−	0.360262i	$-0.117313\pi$
$653$	27.7842	+	16.0412i	1.08728	+	0.627742i	0.154430	+	0.988004i	$0.450646\pi$
$654$	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	$0.0509128\pi$
$659$			8.17705i			0.318533i	−0.987236	+	0.159266i	$0.949087\pi$
$660$	−0.848544	+	0.139506i	−0.0330295	+	0.00543026i
$661$	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
$663$	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	−0.676771	−	0.736193i	$-0.736621\pi$
$677$	7.78434	−	13.4829i	0.299176	−	0.518189i	0.975948	+	0.218004i	$0.0699547\pi$
$678$	−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	0.726707	−	0.686947i	$-0.241050\pi$
$683$	−6.05165	−	10.4818i	−0.231560	−	0.401074i	−0.958267	+	0.285873i	$0.907716\pi$
$684$	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	−0.969848	−	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
$693$	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	$-0.782665\pi$
$701$		−	33.4107i		−	1.26190i	0.775822	−	0.630952i	$-0.217335\pi$
$702$	−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	−0.0659873	−	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
$711$	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	−0.456919	−	0.889508i	$-0.651047\pi$
$719$	14.5300	−	25.1667i	0.541877	−	0.938558i	0.998796	−	0.0490503i	$-0.0156195\pi$
$720$	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	$0.0646663\pi$
$727$			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
$732$	−1.42028	+	3.76587i	−0.0524951	+	0.139191i
$733$	−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
$735$	0.871056	+	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	−0.407379	−	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
$741$	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	−0.880256	−	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
$753$	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	−0.133157	−	0.991095i	$-0.542512\pi$
$761$	−29.1876	−	16.8515i	−1.05805	−	0.610865i	−0.924892	+	0.380230i	$0.875845\pi$
$762$	−6.44136	+	5.27901i	−0.233346	+	0.191238i
$763$	−16.0249	+	12.4502i	−0.580141	+	0.450728i
$764$		−	14.2368i		−	0.515070i
$765$	−0.463998	+	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	−0.464588	−	0.885527i	$-0.653798\pi$
$773$	1.94637	−	1.12374i	0.0700061	−	0.0404181i	0.534595	+	0.845109i	$0.320464\pi$
$774$	−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	−0.990672	−	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
$789$	−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	−0.215925	−	0.976410i	$-0.569277\pi$
$809$	14.8389	−	8.56724i	0.521708	−	0.301208i	0.737633	+	0.675202i	$0.235943\pi$
$810$	−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	−0.997914	−	0.0645517i	$-0.979438\pi$
$821$	−12.6949	+	21.9881i	−0.443054	+	0.767392i	0.554861	+	0.831943i	$0.312772\pi$
$822$	−20.3914	−	7.69051i	−0.711231	−	0.268237i
$823$	−2.14820	−	3.72079i	−0.0748815	−	0.129699i	0.826153	−	0.563446i	$-0.190525\pi$
$823$	−2.14820	−	3.72079i	−0.0748815	−	0.129699i	−0.901035	+	0.433747i	$0.857191\pi$
$824$	−10.7681	−	6.21697i	−0.375125	−	0.216579i
$825$	37.8710	−	31.0371i	1.31850	−	1.08057i
$826$	−1.29856	−	9.42510i	−0.0451827	−	0.327941i
$827$	21.4079			0.744426			0.372213	−	0.928147i	$-0.378599\pi$
$827$	21.4079			0.744426			0.372213	+	0.928147i	$0.378599\pi$
$828$	−2.43174	+	2.76531i	−0.0845088	+	0.0961013i
$829$	−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
$831$	−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	$-0.848992\pi$
$839$		−	26.4635i		−	0.913622i	0.889564	−	0.456811i	$-0.151008\pi$
$840$	−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	0.919240	−	0.393698i	$-0.128804\pi$
$857$	3.47394	+	6.01703i	0.118667	+	0.205538i	−0.800572	+	0.599236i	$0.795471\pi$
$858$	31.5373	−	15.9983i	1.07667	−	0.546174i
$859$	−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
$861$	9.14418	−	40.1863i	0.311633	−	1.36954i
$862$	36.4880			1.24279
$863$	−2.46354	+	4.26698i	−0.0838600	+	0.145250i	−0.904905	−	0.425614i	$-0.860058\pi$
$863$	−2.46354	+	4.26698i	−0.0838600	+	0.145250i	0.821045	+	0.570864i	$0.193392\pi$
$864$	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	0.00958950	−	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
$879$	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	−0.461506	−	0.887137i	$-0.652691\pi$
$887$	16.0090	−	27.7284i	0.537530	−	0.931029i	0.999036	−	0.0438921i	$-0.0139758\pi$
$888$	−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	0.864323	−	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	$0.0515694\pi$
$911$			9.73710i			0.322604i	−0.986905	+	0.161302i	$0.948431\pi$
$912$	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	−0.963217	−	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
$921$	−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	0.458058	−	0.888922i	$-0.348545\pi$
$929$	−2.52193	−	1.45604i	−0.0827418	−	0.0477710i	−0.540800	+	0.841151i	$0.681878\pi$
$930$	0.0850768	+	0.103809i	0.00278978	+	0.00340405i
$931$	−11.5129	+	45.1315i	−0.377319	+	1.47913i
$932$		−	16.4052i		−	0.537370i
$933$	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	$0.254542\pi$
$937$			43.9029i			1.43425i	−0.696946	+	0.717123i	$0.745458\pi$
$938$	−2.72719	−	19.7942i	−0.0890458	−	0.646305i
$939$	21.1470	+	25.8032i	0.690105	+	0.842055i
$940$	0.377225	−	0.653372i	0.0123037	−	0.0213106i
$941$	−32.2047	+	18.5934i	−1.04984	+	0.606127i	−0.922606	−	0.385745i	$-0.873945\pi$
$941$	−32.2047	+	18.5934i	−1.04984	+	0.606127i	−0.127238	+	0.991872i	$0.540611\pi$
$942$	−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	−0.680263	−	0.732968i	$-0.738135\pi$
$947$	9.06698	−	15.7045i	0.294637	−	0.510326i	0.974900	+	0.222641i	$0.0714679\pi$
$948$	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	$0.0716689\pi$
$953$			13.7842i			0.446514i	−0.974760	+	0.223257i	$0.928331\pi$
$954$	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	$0.159129\pi$
$967$			29.8126i			0.958708i	−0.877622	+	0.479354i	$0.840871\pi$
$968$	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	0.266037	+	0.963963i	$0.414286\pi$
$971$	−21.8686	+	37.8776i	−0.701798	+	1.21555i	−0.967835	+	0.251587i	$0.919048\pi$
$972$	−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	0.915049	−	0.403342i	$-0.132152\pi$
$977$	3.38263	+	5.85889i	0.108220	+	0.187443i	−0.806829	+	0.590785i	$0.798818\pi$
$978$	−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	−0.730218	−	0.683214i	$-0.760582\pi$
$983$	−15.7908	+	9.11680i	−0.503647	+	0.290781i	0.226571	+	0.973995i	$0.427248\pi$
$984$	−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	0.954085	−	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
$996$	4.89040	−	0.804013i	0.154958	−	0.0254761i
$997$	−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
$999$	−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.467.3	yes	36
3.2	odd	2		546.2.bg.a.467.9	yes	36
7.3	odd	6	inner	546.2.bg.b.311.9	yes	36
13.12	even	2		546.2.bg.a.467.3	yes	36
21.17	even	6		546.2.bg.a.311.3	✓	36
39.38	odd	2	inner	546.2.bg.b.467.9	yes	36
91.38	odd	6		546.2.bg.a.311.9	yes	36
273.38	even	6	inner	546.2.bg.b.311.3	yes	36

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more