LMFDB - Embedded newform 546.2.bk.c.415.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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([0, 4, 3]))

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 26 x^{18} + 431 x^{16} - 4370 x^{14} + 32381 x^{12} - 160412 x^{10} + 573820 x^{8} + \cdots + 810000 $ x^20 - 26x^18 + 431x^16 - 4370x^14 + 32381x^12 - 160412x^10 + 573820x^8 - 1203000x^6 + 1802736x^4 - 1479600*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.2
Root			$-2.18313 + 1.26043i$ of defining polynomial
Character	$\chi$	$=$	546.415
Dual form			546.2.bk.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.18313 - 1.26043i) q^{5} -1.00000i q^{6} +(1.47350 - 2.19745i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.18313 - 1.26043i) q^{5} -1.00000i q^{6} +(1.47350 - 2.19745i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.26043 + 2.18313i) q^{10} +(-4.88772 + 2.82193i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.13524 + 1.78052i) q^{13} +(-2.37482 + 1.16630i) q^{14} -2.52086i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.123703 + 0.214260i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.70459 + 1.56150i) q^{19} -2.52086i q^{20} +(2.63980 + 0.177364i) q^{21} +5.64385 q^{22} +(-1.80107 + 3.11954i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.677364 + 1.17323i) q^{25} +(3.60546 + 0.0256500i) q^{26} -1.00000 q^{27} +(2.63980 + 0.177364i) q^{28} -4.24895 q^{29} +(-1.26043 + 2.18313i) q^{30} +(-5.30267 + 3.06150i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.88772 - 2.82193i) q^{33} -0.247406i q^{34} +(-5.98657 + 2.94007i) q^{35} -1.00000 q^{36} +(-7.01858 - 4.05218i) q^{37} +(-1.56150 - 2.70459i) q^{38} +(-3.10959 - 1.82494i) q^{39} +(-1.26043 + 2.18313i) q^{40} +8.59917i q^{41} +(-2.19745 - 1.47350i) q^{42} +5.56103 q^{43} +(-4.88772 - 2.82193i) q^{44} +(2.18313 - 1.26043i) q^{45} +(3.11954 - 1.80107i) q^{46} +(-5.78854 - 3.34201i) q^{47} -1.00000 q^{48} +(-2.65759 - 6.47590i) q^{49} -1.35473i q^{50} +(-0.123703 + 0.214260i) q^{51} +(-3.10959 - 1.82494i) q^{52} +(-3.28052 - 5.68202i) q^{53} +(0.866025 + 0.500000i) q^{54} +14.2274 q^{55} +(-2.19745 - 1.47350i) q^{56} +3.12299i q^{57} +(3.67970 + 2.12447i) q^{58} +(6.89004 - 3.97797i) q^{59} +(2.18313 - 1.26043i) q^{60} +(-6.39419 + 11.0751i) q^{61} +6.12299 q^{62} +(1.16630 + 2.37482i) q^{63} -1.00000 q^{64} +(9.08886 + 0.0646601i) q^{65} +(2.82193 + 4.88772i) q^{66} +(-10.5562 + 6.09461i) q^{67} +(-0.123703 + 0.214260i) q^{68} -3.60213 q^{69} +(6.65456 + 0.447110i) q^{70} -4.06419i q^{71} +(0.866025 + 0.500000i) q^{72} +(6.81789 - 3.93631i) q^{73} +(4.05218 + 7.01858i) q^{74} +(-0.677364 + 1.17323i) q^{75} +3.12299i q^{76} +(-1.00102 + 14.8986i) q^{77} +(1.78052 + 3.13524i) q^{78} +(3.22763 - 5.59041i) q^{79} +(2.18313 - 1.26043i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29959 - 7.44710i) q^{82} -0.662485i q^{83} +(1.16630 + 2.37482i) q^{84} -0.623675i q^{85} +(-4.81600 - 2.78052i) q^{86} +(-2.12447 - 3.67970i) q^{87} +(2.82193 + 4.88772i) q^{88} +(4.86906 + 2.81116i) q^{89} -2.52086 q^{90} +(-0.707191 + 9.51314i) q^{91} -3.60213 q^{92} +(-5.30267 - 3.06150i) q^{93} +(3.34201 + 5.78854i) q^{94} +(-3.93631 - 6.81789i) q^{95} +(0.866025 + 0.500000i) q^{96} +16.8748i q^{97} +(-0.936412 + 6.93708i) q^{98} -5.64385i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9	$ 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9} + 4 q^{10} - 10 q^{12} + 4 q^{13} - 2 q^{14} - 10 q^{16} - 6 q^{17} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 4 q^{26} - 20 q^{27} - 28 q^{29} - 4 q^{30} + 16 q^{35} - 20 q^{36} + 10 q^{38} + 2 q^{39} - 4 q^{40} - 10 q^{42} + 24 q^{43} - 20 q^{48} + 2 q^{49} + 6 q^{51} + 2 q^{52} - 22 q^{53} + 88 q^{55} - 10 q^{56} + 14 q^{61} + 40 q^{62} - 20 q^{64} + 20 q^{65} - 6 q^{66} + 6 q^{68} - 32 q^{69} + 24 q^{74} - 2 q^{75} - 28 q^{77} - 8 q^{78} + 4 q^{79} - 10 q^{81} + 12 q^{82} - 14 q^{87} - 6 q^{88} - 8 q^{90} + 68 q^{91} - 32 q^{92} - 18 q^{94} + 8 q^{95}+O(q^{100}) $ 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9 + 4 * q^10 - 10 * q^12 + 4 * q^13 - 2 * q^14 - 10 * q^16 - 6 * q^17 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 4 * q^26 - 20 * q^27 - 28 * q^29 - 4 * q^30 + 16 * q^35 - 20 * q^36 + 10 * q^38 + 2 * q^39 - 4 * q^40 - 10 * q^42 + 24 * q^43 - 20 * q^48 + 2 * q^49 + 6 * q^51 + 2 * q^52 - 22 * q^53 + 88 * q^55 - 10 * q^56 + 14 * q^61 + 40 * q^62 - 20 * q^64 + 20 * q^65 - 6 * q^66 + 6 * q^68 - 32 * q^69 + 24 * q^74 - 2 * q^75 - 28 * q^77 - 8 * q^78 + 4 * q^79 - 10 * q^81 + 12 * q^82 - 14 * q^87 - 6 * q^88 - 8 * q^90 + 68 * q^91 - 32 * q^92 - 18 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.18313	−	1.26043i	−0.976324	−	0.563681i	−0.0751659	−	0.997171i	$-0.523949\pi$
$5$	−2.18313	−	1.26043i	−0.976324	−	0.563681i	−0.901158	+	0.433490i	$0.857282\pi$
$6$		−	1.00000i		−	0.408248i
$7$	1.47350	−	2.19745i	0.556931	−	0.830559i
$7$	1.47350	−	2.19745i	0.556931	−	0.830559i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.26043	+	2.18313i	0.398583	+	0.690366i
$11$	−4.88772	+	2.82193i	−1.47370	+	0.850843i	−0.999562	−	0.0296062i	$-0.990575\pi$
$11$	−4.88772	+	2.82193i	−1.47370	+	0.850843i	−0.474141	+	0.880449i	$0.657241\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−3.13524	+	1.78052i	−0.869561	+	0.493826i
$13$	−3.13524	+	1.78052i	−0.869561	+	0.493826i
$14$	−2.37482	+	1.16630i	−0.634696	+	0.311706i
$15$		−	2.52086i		−	0.650883i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.123703	+	0.214260i	0.0300024	+	0.0519656i	0.880637	−	0.473792i	$-0.157115\pi$
$17$	0.123703	+	0.214260i	0.0300024	+	0.0519656i	−0.850634	+	0.525758i	$0.823782\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	2.70459	+	1.56150i	0.620476	+	0.358232i	0.777054	−	0.629434i	$-0.216713\pi$
$19$	2.70459	+	1.56150i	0.620476	+	0.358232i	−0.156578	+	0.987666i	$0.550046\pi$
$20$		−	2.52086i		−	0.563681i
$21$	2.63980	+	0.177364i	0.576051	+	0.0387041i
$22$	5.64385			1.20327
$23$	−1.80107	+	3.11954i	−0.375548	+	0.650469i	−0.990409	−	0.138167i	$-0.955879\pi$
$23$	−1.80107	+	3.11954i	−0.375548	+	0.650469i	0.614860	+	0.788636i	$0.289212\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.677364	+	1.17323i	0.135473	+	0.234646i
$26$	3.60546	+	0.0256500i	0.707089	+	0.00503038i
$27$	−1.00000			−0.192450
$28$	2.63980	+	0.177364i	0.498875	+	0.0335187i
$29$	−4.24895			−0.789010			−0.394505	−	0.918894i	$-0.629084\pi$
$29$	−4.24895			−0.789010			−0.394505	+	0.918894i	$0.629084\pi$
$30$	−1.26043	+	2.18313i	−0.230122	+	0.398583i
$31$	−5.30267	+	3.06150i	−0.952387	+	0.549861i	−0.893822	−	0.448423i	$-0.851986\pi$
$31$	−5.30267	+	3.06150i	−0.952387	+	0.549861i	−0.0585655	+	0.998284i	$0.518653\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.88772	−	2.82193i	−0.850843	−	0.491234i
$34$		−	0.247406i		−	0.0424298i
$35$	−5.98657	+	2.94007i	−1.01192	+	0.496963i
$36$	−1.00000			−0.166667
$37$	−7.01858	−	4.05218i	−1.15385	−	0.666174i	−0.204026	−	0.978966i	$-0.565403\pi$
$37$	−7.01858	−	4.05218i	−1.15385	−	0.666174i	−0.949822	+	0.312791i	$0.898736\pi$
$38$	−1.56150	−	2.70459i	−0.253308	−	0.438743i
$39$	−3.10959	−	1.82494i	−0.497934	−	0.292225i
$40$	−1.26043	+	2.18313i	−0.199291	+	0.345183i
$41$			8.59917i			1.34296i	0.741020	+	0.671482i	$0.234342\pi$
$41$			8.59917i			1.34296i	−0.741020	+	0.671482i	$0.765658\pi$
$42$	−2.19745	−	1.47350i	−0.339074	−	0.227366i
$43$	5.56103			0.848050			0.424025	−	0.905651i	$-0.360617\pi$
$43$	5.56103			0.848050			0.424025	+	0.905651i	$0.360617\pi$
$44$	−4.88772	−	2.82193i	−0.736851	−	0.425421i
$45$	2.18313	−	1.26043i	0.325441	−	0.187894i
$46$	3.11954	−	1.80107i	0.459951	−	0.265553i
$47$	−5.78854	−	3.34201i	−0.844345	−	0.487483i	0.0143939	−	0.999896i	$-0.495418\pi$
$47$	−5.78854	−	3.34201i	−0.844345	−	0.487483i	−0.858739	+	0.512414i	$0.828751\pi$
$48$	−1.00000			−0.144338
$49$	−2.65759	−	6.47590i	−0.379655	−	0.925128i
$50$		−	1.35473i		−	0.191588i
$51$	−0.123703	+	0.214260i	−0.0173219	+	0.0300024i
$52$	−3.10959	−	1.82494i	−0.431223	−	0.253074i
$53$	−3.28052	−	5.68202i	−0.450614	−	0.780486i	0.547811	−	0.836602i	$-0.315461\pi$
$53$	−3.28052	−	5.68202i	−0.450614	−	0.780486i	−0.998424	+	0.0561167i	$0.982128\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	14.2274			1.91842
$56$	−2.19745	−	1.47350i	−0.293647	−	0.196905i
$57$			3.12299i			0.413651i
$58$	3.67970	+	2.12447i	0.483168	+	0.278957i
$59$	6.89004	−	3.97797i	0.897007	−	0.517887i	0.0207791	−	0.999784i	$-0.493385\pi$
$59$	6.89004	−	3.97797i	0.897007	−	0.517887i	0.876228	+	0.481897i	$0.160052\pi$
$60$	2.18313	−	1.26043i	0.281841	−	0.162721i
$61$	−6.39419	+	11.0751i	−0.818693	+	1.41802i	0.0879534	+	0.996125i	$0.471967\pi$
$61$	−6.39419	+	11.0751i	−0.818693	+	1.41802i	−0.906646	+	0.421892i	$0.861366\pi$
$62$	6.12299			0.777621
$63$	1.16630	+	2.37482i	0.146940	+	0.299199i
$64$	−1.00000			−0.125000
$65$	9.08886	+	0.0646601i	1.12733	+	0.00802010i
$66$	2.82193	+	4.88772i	0.347355	+	0.601637i
$67$	−10.5562	+	6.09461i	−1.28964	+	0.744575i	−0.978590	−	0.205818i	$-0.934014\pi$
$67$	−10.5562	+	6.09461i	−1.28964	+	0.744575i	−0.311051	+	0.950393i	$0.600681\pi$
$68$	−0.123703	+	0.214260i	−0.0150012	+	0.0259828i
$69$	−3.60213			−0.433646
$70$	6.65456	+	0.447110i	0.795372	+	0.0534399i
$71$		−	4.06419i		−	0.482330i	−0.970484	−	0.241165i	$-0.922470\pi$
$71$		−	4.06419i		−	0.482330i	0.970484	−	0.241165i	$-0.0775295\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	6.81789	−	3.93631i	0.797974	−	0.460710i	−0.0447882	−	0.998997i	$-0.514261\pi$
$73$	6.81789	−	3.93631i	0.797974	−	0.460710i	0.842762	+	0.538286i	$0.180928\pi$
$74$	4.05218	+	7.01858i	0.471056	+	0.815894i
$75$	−0.677364	+	1.17323i	−0.0782153	+	0.135473i
$76$			3.12299i			0.358232i
$77$	−1.00102	+	14.8986i	−0.114077	+	1.69786i
$78$	1.78052	+	3.13524i	0.201604	+	0.354997i
$79$	3.22763	−	5.59041i	0.363136	−	0.628971i	−0.625339	−	0.780353i	$-0.715039\pi$
$79$	3.22763	−	5.59041i	0.363136	−	0.628971i	0.988475	+	0.151383i	$0.0483726\pi$
$80$	2.18313	−	1.26043i	0.244081	−	0.140920i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.29959	−	7.44710i	0.474810	−	0.822395i
$83$		−	0.662485i		−	0.0727172i	−0.999339	−	0.0363586i	$-0.988424\pi$
$83$		−	0.662485i		−	0.0727172i	0.999339	−	0.0363586i	$-0.0115759\pi$
$84$	1.16630	+	2.37482i	0.127254	+	0.259114i
$85$		−	0.623675i		−	0.0676471i
$86$	−4.81600	−	2.78052i	−0.519322	−	0.299831i
$87$	−2.12447	−	3.67970i	−0.227768	−	0.394505i
$88$	2.82193	+	4.88772i	0.300818	+	0.521033i
$89$	4.86906	+	2.81116i	0.516120	+	0.297982i	0.735346	−	0.677692i	$-0.237020\pi$
$89$	4.86906	+	2.81116i	0.516120	+	0.297982i	−0.219226	+	0.975674i	$0.570353\pi$
$90$	−2.52086			−0.265722
$91$	−0.707191	+	9.51314i	−0.0741337	+	0.997248i
$92$	−3.60213			−0.375548
$93$	−5.30267	−	3.06150i	−0.549861	−	0.317462i
$94$	3.34201	+	5.78854i	0.344702	+	0.597042i
$95$	−3.93631	−	6.81789i	−0.403857	−	0.699501i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$			16.8748i			1.71337i	0.515836	+	0.856687i	$0.327481\pi$
$97$			16.8748i			1.71337i	−0.515836	+	0.856687i	$0.672519\pi$
$98$	−0.936412	+	6.93708i	−0.0945919	+	0.700751i
$99$		−	5.64385i		−	0.567228i
$100$	−0.677364	+	1.17323i	−0.0677364	+	0.117323i
$101$	−5.75972	−	9.97613i	−0.573114	−	0.992662i	−0.996244	−	0.0865929i	$-0.972402\pi$
$101$	−5.75972	−	9.97613i	−0.573114	−	0.992662i	0.423130	−	0.906069i	$-0.360931\pi$
$102$	0.214260	−	0.123703i	0.0212149	−	0.0122484i
$103$	2.89422	−	5.01294i	0.285176	−	0.493939i	−0.687476	−	0.726207i	$-0.741281\pi$
$103$	2.89422	−	5.01294i	0.285176	−	0.493939i	0.972652	+	0.232268i	$0.0746146\pi$
$104$	1.78052	+	3.13524i	0.174594	+	0.307436i
$105$	−5.53946	−	3.71449i	−0.540596	−	0.362497i
$106$			6.56103i			0.637264i
$107$	7.96501	−	13.7958i	0.770006	−	1.33369i	−0.167553	−	0.985863i	$-0.553586\pi$
$107$	7.96501	−	13.7958i	0.770006	−	1.33369i	0.937559	−	0.347827i	$-0.113080\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.28231	−	0.740342i	0.122823	−	0.0709119i	−0.437330	−	0.899301i	$-0.644076\pi$
$109$	1.28231	−	0.740342i	0.122823	−	0.0709119i	0.560153	+	0.828389i	$0.310742\pi$
$110$	−12.3212	−	7.11368i	−1.17479	−	0.678262i
$111$		−	8.10436i		−	0.769232i
$112$	1.16630	+	2.37482i	0.110205	+	0.224399i
$113$	10.0373			0.944233			0.472117	−	0.881536i	$-0.343490\pi$
$113$	10.0373			0.944233			0.472117	+	0.881536i	$0.343490\pi$
$114$	1.56150	−	2.70459i	0.146248	−	0.253308i
$115$	7.86392	−	4.54024i	0.733314	−	0.423379i
$116$	−2.12447	−	3.67970i	−0.197253	−	0.341651i
$117$	0.0256500	−	3.60546i	0.00237135	−	0.333325i
$118$	−7.95594			−0.732403
$119$	0.653102	+	0.0438810i	0.0598698	+	0.00402256i
$120$	−2.52086			−0.230122
$121$	10.4265	−	18.0593i	0.947867	−	1.64175i
$122$	11.0751	−	6.39419i	1.00269	−	0.578903i
$123$	−7.44710	+	4.29959i	−0.671482	+	0.387681i
$124$	−5.30267	−	3.06150i	−0.476194	−	0.274931i
$125$			9.18921i			0.821908i
$126$	0.177364	−	2.63980i	0.0158009	−	0.235172i
$127$	10.3136			0.915186			0.457593	−	0.889162i	$-0.348712\pi$
$127$	10.3136			0.915186			0.457593	+	0.889162i	$0.348712\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.78052	+	4.81600i	0.244811	+	0.424025i
$130$	−7.83885	−	4.60042i	−0.687513	−	0.403484i
$131$	−9.24892	+	16.0196i	−0.808082	+	1.39964i	0.106109	+	0.994355i	$0.466161\pi$
$131$	−9.24892	+	16.0196i	−0.808082	+	1.39964i	−0.914191	+	0.405285i	$0.867172\pi$
$132$		−	5.64385i		−	0.491234i
$133$	7.41653	−	3.64234i	0.643095	−	0.315831i
$134$	12.1892			1.05299
$135$	2.18313	+	1.26043i	0.187894	+	0.108480i
$136$	0.214260	−	0.123703i	0.0183726	−	0.0106074i
$137$	11.8669	−	6.85133i	1.01385	−	0.585349i	0.101536	−	0.994832i	$-0.467624\pi$
$137$	11.8669	−	6.85133i	1.01385	−	0.585349i	0.912318	+	0.409483i	$0.134291\pi$
$138$	3.11954	+	1.80107i	0.265553	+	0.153317i
$139$	−8.01474			−0.679802			−0.339901	−	0.940461i	$-0.610394\pi$
$139$	−8.01474			−0.679802			−0.339901	+	0.940461i	$0.610394\pi$
$140$	−5.53946	−	3.71449i	−0.468170	−	0.313932i
$141$		−	6.68403i		−	0.562897i
$142$	−2.03209	+	3.51969i	−0.170529	+	0.295366i
$143$	10.2997	−	17.5501i	0.861305	−	1.46761i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	9.27600	+	5.35550i	0.770330	+	0.444750i
$146$	−7.87262			−0.651543
$147$	4.27950	−	5.53948i	0.352967	−	0.456889i
$148$		−	8.10436i		−	0.666174i
$149$	1.62420	+	0.937732i	0.133060	+	0.0768220i	0.565052	−	0.825055i	$-0.308856\pi$
$149$	1.62420	+	0.937732i	0.133060	+	0.0768220i	−0.431993	+	0.901877i	$0.642189\pi$
$150$	1.17323	−	0.677364i	0.0957938	−	0.0553066i
$151$	2.34699	−	1.35504i	0.190995	−	0.110271i	−0.401453	−	0.915880i	$-0.631495\pi$
$151$	2.34699	−	1.35504i	0.190995	−	0.110271i	0.592449	+	0.805608i	$0.298161\pi$
$152$	1.56150	−	2.70459i	0.126654	−	0.219371i
$153$	−0.247406			−0.0200016
$154$	8.31623	−	12.4021i	0.670141	−	0.999389i
$155$	15.4352			1.23979
$156$	0.0256500	−	3.60546i	0.00205365	−	0.288668i
$157$	8.55178	+	14.8121i	0.682506	+	1.18214i	0.974214	+	0.225628i	$0.0724433\pi$
$157$	8.55178	+	14.8121i	0.682506	+	1.18214i	−0.291707	+	0.956508i	$0.594223\pi$
$158$	−5.59041	+	3.22763i	−0.444749	+	0.256776i
$159$	3.28052	−	5.68202i	0.260162	−	0.450614i
$160$	−2.52086			−0.199291
$161$	4.20116	+	8.55441i	0.331098	+	0.674182i
$162$			1.00000i			0.0785674i
$163$	−16.1125	−	9.30258i	−1.26203	−	0.728635i	−0.288565	−	0.957460i	$-0.593178\pi$
$163$	−16.1125	−	9.30258i	−1.26203	−	0.728635i	−0.973467	+	0.228826i	$0.926511\pi$
$164$	−7.44710	+	4.29959i	−0.581521	+	0.335741i
$165$	7.11368	+	12.3212i	0.553799	+	0.959208i
$166$	−0.331243	+	0.573729i	−0.0257094	+	0.0445300i
$167$		−	14.5835i		−	1.12851i	−0.825602	−	0.564253i	$-0.809164\pi$
$167$		−	14.5835i		−	1.12851i	0.825602	−	0.564253i	$-0.190836\pi$
$168$	0.177364	−	2.63980i	0.0136840	−	0.203665i
$169$	6.65952	−	11.1647i	0.512271	−	0.858824i
$170$	−0.311838	+	0.540119i	−0.0239169	+	0.0414252i
$171$	−2.70459	+	1.56150i	−0.206825	+	0.119411i
$172$	2.78052	+	4.81600i	0.212012	+	0.367216i
$173$	−1.96945	+	3.41119i	−0.149735	+	0.259348i	−0.931129	−	0.364689i	$-0.881175\pi$
$173$	−1.96945	+	3.41119i	−0.149735	+	0.259348i	0.781395	+	0.624037i	$0.214509\pi$
$174$			4.24895i			0.322112i
$175$	3.57621	+	0.240280i	0.270336	+	0.0181635i
$176$		−	5.64385i		−	0.425421i
$177$	6.89004	+	3.97797i	0.517887	+	0.299002i
$178$	−2.81116	−	4.86906i	−0.210705	−	0.364952i
$179$	−2.35319	−	4.07584i	−0.175885	−	0.304642i	0.764582	−	0.644526i	$-0.222945\pi$
$179$	−2.35319	−	4.07584i	−0.175885	−	0.304642i	−0.940467	+	0.339884i	$0.889612\pi$
$180$	2.18313	+	1.26043i	0.162721	+	0.0939469i
$181$	−15.6400			−1.16251			−0.581255	−	0.813722i	$-0.697438\pi$
$181$	−15.6400			−1.16251			−0.581255	+	0.813722i	$0.697438\pi$
$182$	5.36902	−	7.88503i	0.397978	−	0.584477i
$183$	−12.7884			−0.945345
$184$	3.11954	+	1.80107i	0.229976	+	0.132776i
$185$	10.2150	+	17.6929i	0.751020	+	1.30080i
$186$	3.06150	+	5.30267i	0.224480	+	0.388810i
$187$	−1.20925	−	0.698161i	−0.0884292	−	0.0510546i
$188$		−	6.68403i		−	0.487483i
$189$	−1.47350	+	2.19745i	−0.107181	+	0.159841i
$190$			7.87262i			0.571140i
$191$	−4.48843	+	7.77419i	−0.324771	+	0.562521i	−0.981466	−	0.191636i	$-0.938621\pi$
$191$	−4.48843	+	7.77419i	−0.324771	+	0.562521i	0.656695	+	0.754157i	$0.271954\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	6.09697	−	3.52009i	0.438869	−	0.253381i	−0.264248	−	0.964455i	$-0.585124\pi$
$193$	6.09697	−	3.52009i	0.438869	−	0.253381i	0.703118	+	0.711073i	$0.251791\pi$
$194$	8.43739	−	14.6140i	0.605769	−	1.04922i
$195$	4.48843	+	7.90351i	0.321423	+	0.565982i
$196$	4.27950	−	5.53948i	0.305678	−	0.395677i
$197$			11.7101i			0.834308i	0.908836	+	0.417154i	$0.136972\pi$
$197$			11.7101i			0.834308i	−0.908836	+	0.417154i	$0.863028\pi$
$198$	−2.82193	+	4.88772i	−0.200546	+	0.347355i
$199$	−9.05076	−	15.6764i	−0.641591	−	1.11127i	−0.985078	−	0.172111i	$-0.944941\pi$
$199$	−9.05076	−	15.6764i	−0.641591	−	1.11127i	0.343486	−	0.939158i	$-0.388392\pi$
$200$	1.17323	−	0.677364i	0.0829598	−	0.0478969i
$201$	−10.5562	−	6.09461i	−0.744575	−	0.429880i
$202$			11.5194i			0.810505i
$203$	−6.26083	+	9.33686i	−0.439424	+	0.655319i
$204$	−0.247406			−0.0173219
$205$	10.8386	−	18.7731i	0.757004	−	1.31117i
$206$	−5.01294	+	2.89422i	−0.349268	+	0.201650i
$207$	−1.80107	−	3.11954i	−0.125183	−	0.216823i
$208$	0.0256500	−	3.60546i	0.00177851	−	0.249994i
$209$	−17.6257			−1.21920
$210$	2.94007	+	5.98657i	0.202884	+	0.413113i
$211$	−23.2252			−1.59889			−0.799444	−	0.600741i	$-0.794872\pi$
$211$	−23.2252			−1.59889			−0.799444	+	0.600741i	$0.794872\pi$
$212$	3.28052	−	5.68202i	0.225307	−	0.390243i
$213$	3.51969	−	2.03209i	0.241165	−	0.139237i
$214$	−13.7958	+	7.96501i	−0.943061	+	0.544477i
$215$	−12.1404	−	7.00929i	−0.827971	−	0.478030i
$216$			1.00000i			0.0680414i
$217$	−1.08600	+	16.1635i	−0.0737225	+	1.09725i
$218$	−1.48068			−0.100285
$219$	6.81789	+	3.93631i	0.460710	+	0.265991i
$220$	7.11368	+	12.3212i	0.479604	+	0.830698i
$221$	−0.769332	−	0.451502i	−0.0517509	−	0.0303713i
$222$	−4.05218	+	7.01858i	−0.271965	+	0.471056i
$223$			7.16762i			0.479979i	0.970775	+	0.239990i	$0.0771440\pi$
$223$			7.16762i			0.479979i	−0.970775	+	0.239990i	$0.922856\pi$
$224$	0.177364	−	2.63980i	0.0118506	−	0.176379i
$225$	−1.35473			−0.0903152
$226$	−8.69259	−	5.01867i	−0.578222	−	0.333837i
$227$	18.6007	−	10.7391i	1.23457	−	0.712782i	0.266594	−	0.963809i	$-0.414102\pi$
$227$	18.6007	−	10.7391i	1.23457	−	0.712782i	0.967980	+	0.251027i	$0.0807683\pi$
$228$	−2.70459	+	1.56150i	−0.179116	+	0.103413i
$229$	7.15978	+	4.13370i	0.473132	+	0.273163i	0.717550	−	0.696507i	$-0.245264\pi$
$229$	7.15978	+	4.13370i	0.473132	+	0.273163i	−0.244418	+	0.969670i	$0.578597\pi$
$230$	−9.08047			−0.598749
$231$	−13.4031	+	6.58241i	−0.881860	+	0.433091i
$232$			4.24895i			0.278957i
$233$	−13.4460	+	23.2892i	−0.880877	+	1.52572i	−0.0305088	+	0.999534i	$0.509713\pi$
$233$	−13.4460	+	23.2892i	−0.880877	+	1.52572i	−0.850368	+	0.526189i	$0.823621\pi$
$234$	−1.82494	+	3.10959i	−0.119300	+	0.203281i
$235$	8.42474	+	14.5921i	0.549570	+	0.951882i
$236$	6.89004	+	3.97797i	0.448504	+	0.258944i
$237$	6.45525			0.419314
$238$	−0.543662	−	0.364553i	−0.0352404	−	0.0236305i
$239$		−	4.37478i		−	0.282981i	−0.989940	−	0.141491i	$-0.954811\pi$
$239$		−	4.37478i		−	0.282981i	0.989940	−	0.141491i	$-0.0451895\pi$
$240$	2.18313	+	1.26043i	0.140920	+	0.0813604i
$241$	1.33779	−	0.772373i	0.0861746	−	0.0497529i	−0.456293	−	0.889829i	$-0.650823\pi$
$241$	1.33779	−	0.772373i	0.0861746	−	0.0497529i	0.542468	+	0.840076i	$0.317490\pi$
$242$	−18.0593	+	10.4265i	−1.16089	+	0.670243i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−12.7884			−0.818693
$245$	−2.36056	+	17.4874i	−0.150811	+	1.11723i
$246$	8.59917			0.548263
$247$	−11.2598	−	0.0801049i	−0.716446	−	0.00509695i
$248$	3.06150	+	5.30267i	0.194405	+	0.336720i
$249$	0.573729	−	0.331243i	0.0363586	−	0.0209916i
$250$	4.59461	−	7.95809i	0.290588	−	0.503314i
$251$	13.4321			0.847828			0.423914	−	0.905703i	$-0.360656\pi$
$251$	13.4321			0.847828			0.423914	+	0.905703i	$0.360656\pi$
$252$	−1.47350	+	2.19745i	−0.0928219	+	0.138426i
$253$		−	20.3299i		−	1.27813i
$254$	−8.93186	−	5.15681i	−0.560435	−	0.323567i
$255$	0.540119	−	0.311838i	0.0338235	−	0.0195280i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.9173	+	18.9093i	−0.681003	+	1.17953i	0.293672	+	0.955906i	$0.405123\pi$
$257$	−10.9173	+	18.9093i	−0.681003	+	1.17953i	−0.974675	+	0.223625i	$0.928211\pi$
$258$		−	5.56103i		−	0.346215i
$259$	−19.2464	+	9.45210i	−1.19591	+	0.587325i
$260$	4.48843	+	7.90351i	0.278361	+	0.490155i
$261$	2.12447	−	3.67970i	0.131502	−	0.227768i
$262$	16.0196	−	9.24892i	0.989694	−	0.571400i
$263$	−4.24994	−	7.36111i	−0.262062	−	0.453906i	0.704727	−	0.709478i	$-0.251069\pi$
$263$	−4.24994	−	7.36111i	−0.262062	−	0.453906i	−0.966790	+	0.255573i	$0.917736\pi$
$264$	−2.82193	+	4.88772i	−0.173678	+	0.300818i
$265$			16.5394i			1.01601i
$266$	−8.24408	−	0.553907i	−0.505477	−	0.0339622i
$267$			5.62231i			0.344080i
$268$	−10.5562	−	6.09461i	−0.644821	−	0.372287i
$269$	10.3107	+	17.8587i	0.628656	+	1.08886i	0.987822	+	0.155590i	$0.0497280\pi$
$269$	10.3107	+	17.8587i	0.628656	+	1.08886i	−0.359166	+	0.933274i	$0.616939\pi$
$270$	−1.26043	−	2.18313i	−0.0767073	−	0.132861i
$271$	−20.7402	−	11.9744i	−1.25988	−	0.727392i	−0.286829	−	0.957982i	$-0.592601\pi$
$271$	−20.7402	−	11.9744i	−1.25988	−	0.727392i	−0.973051	+	0.230590i	$0.925934\pi$
$272$	−0.247406			−0.0150012
$273$	−8.59222	+	4.14413i	−0.520025	+	0.250814i
$274$	−13.7027			−0.827808
$275$	−6.62153	−	3.82294i	−0.399293	−	0.230532i
$276$	−1.80107	−	3.11954i	−0.108412	−	0.187774i
$277$	2.06106	+	3.56986i	0.123837	+	0.214492i	0.921278	−	0.388905i	$-0.127147\pi$
$277$	2.06106	+	3.56986i	0.123837	+	0.214492i	−0.797441	+	0.603397i	$0.793813\pi$
$278$	6.94097	+	4.00737i	0.416292	+	0.240346i
$279$		−	6.12299i		−	0.366574i
$280$	2.94007	+	5.98657i	0.175703	+	0.357766i
$281$			10.3018i			0.614556i	0.951620	+	0.307278i	$0.0994181\pi$
$281$			10.3018i			0.614556i	−0.951620	+	0.307278i	$0.900582\pi$
$282$	−3.34201	+	5.78854i	−0.199014	+	0.344702i
$283$	5.43112	+	9.40698i	0.322847	+	0.559187i	0.981074	−	0.193632i	$-0.0620268\pi$
$283$	5.43112	+	9.40698i	0.322847	+	0.559187i	−0.658227	+	0.752819i	$0.728693\pi$
$284$	3.51969	−	2.03209i	0.208855	−	0.120583i
$285$	3.93631	−	6.81789i	0.233167	−	0.403857i
$286$	−17.6949	+	10.0490i	−1.04632	+	0.594208i
$287$	18.8963	+	12.6709i	1.11541	+	0.747939i
$288$			1.00000i			0.0589256i
$289$	8.46940	−	14.6694i	0.498200	−	0.862907i
$290$	−5.35550	−	9.27600i	−0.314486	−	0.544705i
$291$	−14.6140	+	8.43739i	−0.856687	+	0.494609i
$292$	6.81789	+	3.93631i	0.398987	+	0.230355i
$293$			3.72513i			0.217624i	0.994062	+	0.108812i	$0.0347047\pi$
$293$			3.72513i			0.217624i	−0.994062	+	0.108812i	$0.965295\pi$
$294$	−6.47590	+	2.65759i	−0.377682	+	0.154994i
$295$	−20.0558			−1.16769
$296$	−4.05218	+	7.01858i	−0.235528	+	0.407947i
$297$	4.88772	−	2.82193i	0.283614	−	0.163745i
$298$	−0.937732	−	1.62420i	−0.0543213	−	0.0940873i
$299$	0.0923948	−	12.9874i	0.00534333	−	0.751078i
$300$	−1.35473			−0.0782153
$301$	8.19419	−	12.2201i	0.472305	−	0.704355i
$302$	−2.71007			−0.155947
$303$	5.75972	−	9.97613i	0.330887	−	0.573114i
$304$	−2.70459	+	1.56150i	−0.155119	+	0.0895580i
$305$	27.9187	−	16.1189i	1.59862	−	0.922963i
$306$	0.214260	+	0.123703i	0.0122484	+	0.00707163i
$307$			21.0104i			1.19912i	0.800328	+	0.599562i	$0.204659\pi$
$307$			21.0104i			1.19912i	−0.800328	+	0.599562i	$0.795341\pi$
$308$	−13.4031	+	6.58241i	−0.763713	+	0.375068i
$309$	5.78844			0.329293
$310$	−13.3673	−	7.71760i	−0.759210	−	0.438330i
$311$	3.19739	+	5.53804i	0.181307	+	0.314034i	0.942326	−	0.334696i	$-0.108634\pi$
$311$	3.19739	+	5.53804i	0.181307	+	0.314034i	−0.761019	+	0.648730i	$0.775300\pi$
$312$	−1.82494	+	3.10959i	−0.103317	+	0.176046i
$313$	−7.73685	+	13.4006i	−0.437313	+	0.757448i	−0.997481	−	0.0709307i	$-0.977403\pi$
$313$	−7.73685	+	13.4006i	−0.437313	+	0.757448i	0.560168	+	0.828379i	$0.310736\pi$
$314$		−	17.1036i		−	0.965210i
$315$	0.447110	−	6.65456i	0.0251918	−	0.374942i
$316$	6.45525			0.363136
$317$	16.3604	+	9.44569i	0.918893	+	0.530523i	0.883282	−	0.468843i	$-0.155329\pi$
$317$	16.3604	+	9.44569i	0.918893	+	0.530523i	0.0356109	+	0.999366i	$0.488662\pi$
$318$	−5.68202	+	3.28052i	−0.318632	+	0.183962i
$319$	20.7677	−	11.9902i	1.16277	−	0.671323i
$320$	2.18313	+	1.26043i	0.122041	+	0.0704601i
$321$	15.9300			0.889127
$322$	0.638890	−	9.50891i	0.0356039	−	0.529911i
$323$			0.772647i			0.0429912i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−4.21266	−	2.47230i	−0.233676	−	0.137139i
$326$	9.30258	+	16.1125i	0.515222	+	0.892391i
$327$	1.28231	+	0.740342i	0.0709119	+	0.0409410i
$328$	8.59917			0.474810
$329$	−15.8733	+	7.79557i	−0.875125	+	0.429783i
$330$		−	14.2274i		−	0.783190i
$331$	−22.1676	−	12.7985i	−1.21844	−	0.703468i	−0.253857	−	0.967242i	$-0.581699\pi$
$331$	−22.1676	−	12.7985i	−1.21844	−	0.703468i	−0.964585	+	0.263774i	$0.915033\pi$
$332$	0.573729	−	0.331243i	0.0314875	−	0.0181793i
$333$	7.01858	−	4.05218i	0.384616	−	0.222058i
$334$	−7.29175	+	12.6297i	−0.398987	+	0.691065i
$335$	30.7273			1.67881
$336$	−1.47350	+	2.19745i	−0.0803861	+	0.119881i
$337$	−35.2040			−1.91769			−0.958843	−	0.283938i	$-0.908359\pi$
$337$	−35.2040			−1.91769			−0.958843	+	0.283938i	$0.908359\pi$
$338$	−11.3497	+	6.33916i	−0.617341	+	0.344805i
$339$	5.01867	+	8.69259i	0.272577	+	0.472117i
$340$	0.540119	−	0.311838i	0.0292920	−	0.0169118i
$341$	17.2786	−	29.9275i	0.935690	−	1.62066i
$342$	3.12299			0.168872
$343$	−18.1464	−	3.70233i	−0.979815	−	0.199907i
$344$		−	5.56103i		−	0.299831i
$345$	7.86392	+	4.54024i	0.423379	+	0.244438i
$346$	3.41119	−	1.96945i	0.183387	−	0.105878i
$347$	−6.34130	−	10.9835i	−0.340419	−	0.589623i	0.644092	−	0.764948i	$-0.277236\pi$
$347$	−6.34130	−	10.9835i	−0.340419	−	0.589623i	−0.984511	+	0.175325i	$0.943902\pi$
$348$	2.12447	−	3.67970i	0.113884	−	0.197253i
$349$		−	16.7258i		−	0.895311i	−0.894206	−	0.447656i	$-0.852259\pi$
$349$		−	16.7258i		−	0.895311i	0.894206	−	0.447656i	$-0.147741\pi$
$350$	−2.97695	−	1.99619i	−0.159125	−	0.106701i
$351$	3.13524	−	1.78052i	0.167347	−	0.0950369i
$352$	−2.82193	+	4.88772i	−0.150409	+	0.260516i
$353$	8.35129	−	4.82162i	0.444494	−	0.256629i	−0.261008	−	0.965337i	$-0.584055\pi$
$353$	8.35129	−	4.82162i	0.444494	−	0.256629i	0.705502	+	0.708708i	$0.250722\pi$
$354$	−3.97797	−	6.89004i	−0.211427	−	0.366202i
$355$	−5.12262	+	8.87264i	−0.271880	+	0.470911i
$356$			5.62231i			0.297982i
$357$	0.288549	+	0.587543i	0.0152716	+	0.0310961i
$358$			4.70637i			0.248739i
$359$	0.491107	+	0.283541i	0.0259197	+	0.0149647i	0.512904	−	0.858446i	$-0.328570\pi$
$359$	0.491107	+	0.283541i	0.0259197	+	0.0149647i	−0.486984	+	0.873411i	$0.661903\pi$
$360$	−1.26043	−	2.18313i	−0.0664305	−	0.115061i
$361$	−4.62346	−	8.00806i	−0.243340	−	0.421477i
$362$	13.5446	+	7.81998i	0.711889	+	0.411009i
$363$	20.8531			1.09450
$364$	−8.59222	+	4.14413i	−0.450355	+	0.217211i
$365$	−19.8458			−1.03878
$366$	11.0751	+	6.39419i	0.578903	+	0.334230i
$367$	6.62549	+	11.4757i	0.345848	+	0.599026i	0.985507	−	0.169632i	$-0.0542580\pi$
$367$	6.62549	+	11.4757i	0.345848	+	0.599026i	−0.639660	+	0.768658i	$0.720925\pi$
$368$	−1.80107	−	3.11954i	−0.0938871	−	0.162617i
$369$	−7.44710	−	4.29959i	−0.387681	−	0.223827i
$370$		−	20.4299i		−	1.06210i
$371$	−17.3198	−	1.16369i	−0.899200	−	0.0604159i
$372$		−	6.12299i		−	0.317462i
$373$	−11.9476	+	20.6939i	−0.618624	+	1.07149i	0.371113	+	0.928588i	$0.378976\pi$
$373$	−11.9476	+	20.6939i	−0.618624	+	1.07149i	−0.989737	+	0.142900i	$0.954357\pi$
$374$	0.698161	+	1.20925i	0.0361011	+	0.0625289i
$375$	−7.95809	+	4.59461i	−0.410954	+	0.237264i
$376$	−3.34201	+	5.78854i	−0.172351	+	0.298521i
$377$	13.3215	−	7.56532i	0.686092	−	0.389634i
$378$	2.37482	−	1.16630i	0.122147	−	0.0599879i
$379$		−	1.46025i		−	0.0750081i	−0.999296	−	0.0375040i	$-0.988059\pi$
$379$		−	1.46025i		−	0.0750081i	0.999296	−	0.0375040i	$-0.0119407\pi$
$380$	3.93631	−	6.81789i	0.201929	−	0.349751i
$381$	5.15681	+	8.93186i	0.264192	+	0.457593i
$382$	7.77419	−	4.48843i	0.397762	−	0.229648i
$383$	5.64718	+	3.26040i	0.288557	+	0.166599i	0.637291	−	0.770623i	$-0.280055\pi$
$383$	5.64718	+	3.26040i	0.288557	+	0.166599i	−0.348734	+	0.937222i	$0.613388\pi$
$384$			1.00000i			0.0510310i
$385$	20.9640	−	31.2639i	1.06843	−	1.59336i
$386$	−7.04017			−0.358335
$387$	−2.78052	+	4.81600i	−0.141342	+	0.244811i
$388$	−14.6140	+	8.43739i	−0.741913	+	0.428344i
$389$	−12.8010	−	22.1719i	−0.649035	−	1.12416i	−0.983354	−	0.181702i	$-0.941839\pi$
$389$	−12.8010	−	22.1719i	−0.649035	−	1.12416i	0.334319	−	0.942460i	$-0.391494\pi$
$390$	0.0646601	−	9.08886i	0.00327419	−	0.460232i
$391$	−0.891189			−0.0450694
$392$	−6.47590	+	2.65759i	−0.327082	+	0.134228i
$393$	−18.4978			−0.933093
$394$	5.85504	−	10.1412i	0.294972	−	0.510907i
$395$	−14.0926	+	8.13639i	−0.709078	+	0.409386i
$396$	4.88772	−	2.82193i	0.245617	−	0.141807i
$397$	13.4505	+	7.76567i	0.675063	+	0.389748i	0.797992	−	0.602668i	$-0.205895\pi$
$397$	13.4505	+	7.76567i	0.675063	+	0.389748i	−0.122929	+	0.992415i	$0.539229\pi$
$398$			18.1015i			0.907347i
$399$	6.86263	+	4.60174i	0.343561	+	0.230375i
$400$	−1.35473			−0.0677364
$401$	−30.2703	−	17.4765i	−1.51163	−	0.872737i	−0.999908	−	0.0135833i	$-0.995676\pi$
$401$	−30.2703	−	17.4765i	−1.51163	−	0.872737i	−0.511717	−	0.859154i	$-0.670991\pi$
$402$	6.09461	+	10.5562i	0.303971	+	0.526494i
$403$	11.1741	−	19.0400i	0.556622	−	0.948451i
$404$	5.75972	−	9.97613i	0.286557	−	0.496331i
$405$			2.52086i			0.125262i
$406$	10.0905	−	4.95554i	0.500782	−	0.245939i
$407$	45.7398			2.26724
$408$	0.214260	+	0.123703i	0.0106074	+	0.00612421i
$409$	−11.0002	+	6.35099i	−0.543927	+	0.314036i	−0.746669	−	0.665196i	$-0.768348\pi$
$409$	−11.0002	+	6.35099i	−0.543927	+	0.314036i	0.202742	+	0.979232i	$0.435015\pi$
$410$	−18.7731	+	10.8386i	−0.927137	+	0.535283i
$411$	11.8669	+	6.85133i	0.585349	+	0.337951i
$412$	5.78844			0.285176
$413$	1.41110	−	21.0021i	0.0694356	−	1.03344i
$414$			3.60213i			0.177035i
$415$	−0.835016	+	1.44629i	−0.0409893	+	0.0709956i
$416$	−1.82494	+	3.10959i	−0.0894752	+	0.152460i
$417$	−4.00737	−	6.94097i	−0.196242	−	0.339901i
$418$	15.2643	+	8.81286i	0.746602	+	0.431051i
$419$	−23.7483			−1.16018			−0.580091	−	0.814552i	$-0.696983\pi$
$419$	−23.7483			−1.16018			−0.580091	+	0.814552i	$0.696983\pi$
$420$	0.447110	−	6.65456i	0.0218167	−	0.324709i
$421$		−	4.91285i		−	0.239438i	−0.992808	−	0.119719i	$-0.961801\pi$
$421$		−	4.91285i		−	0.239438i	0.992808	−	0.119719i	$-0.0381993\pi$
$422$	20.1136	+	11.6126i	0.979115	+	0.565292i
$423$	5.78854	−	3.34201i	0.281448	−	0.162494i
$424$	−5.68202	+	3.28052i	−0.275943	+	0.159316i
$425$	−0.167584	+	0.290264i	−0.00812901	+	0.0140799i
$426$	−4.06419			−0.196910
$427$	14.9151	+	30.3701i	0.721791	+	1.46971i
$428$	15.9300			0.770006
$429$	20.3487	+	0.144765i	0.982444	+	0.00698932i
$430$	7.00929	+	12.1404i	0.338018	+	0.585464i
$431$	−21.7888	+	12.5798i	−1.04953	+	0.605947i	−0.922518	−	0.385954i	$-0.873872\pi$
$431$	−21.7888	+	12.5798i	−1.04953	+	0.605947i	−0.127013	+	0.991901i	$0.540539\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	6.16471			0.296257			0.148129	−	0.988968i	$-0.452675\pi$
$433$	6.16471			0.296257			0.148129	+	0.988968i	$0.452675\pi$
$434$	9.02224	−	13.4550i	0.433081	−	0.645860i
$435$			10.7110i			0.513553i
$436$	1.28231	+	0.740342i	0.0614115	+	0.0354560i
$437$	−9.74230	+	5.62472i	−0.466038	+	0.269067i
$438$	−3.93631	−	6.81789i	−0.188084	−	0.325772i
$439$	−4.44890	+	7.70572i	−0.212334	+	0.367774i	−0.952445	−	0.304712i	$-0.901440\pi$
$439$	−4.44890	+	7.70572i	−0.212334	+	0.367774i	0.740110	+	0.672486i	$0.234773\pi$
$440$		−	14.2274i		−	0.678262i
$441$	6.93708	+	0.936412i	0.330337	+	0.0445911i
$442$	0.440510	+	0.775678i	0.0209529	+	0.0368952i
$443$	−17.0804	+	29.5842i	−0.811516	+	1.40559i	0.100286	+	0.994959i	$0.468024\pi$
$443$	−17.0804	+	29.5842i	−0.811516	+	1.40559i	−0.911803	+	0.410629i	$0.865309\pi$
$444$	7.01858	−	4.05218i	0.333087	−	0.192308i
$445$	−7.08653	−	12.2742i	−0.335934	−	0.581854i
$446$	3.58381	−	6.20734i	0.169698	−	0.293926i
$447$			1.87546i			0.0887064i
$448$	−1.47350	+	2.19745i	−0.0696164	+	0.103820i
$449$			29.0848i			1.37260i	0.727320	+	0.686298i	$0.240766\pi$
$449$			29.0848i			1.37260i	−0.727320	+	0.686298i	$0.759234\pi$
$450$	1.17323	+	0.677364i	0.0553066	+	0.0319313i
$451$	−24.2662	−	42.0303i	−1.14265	−	1.97913i
$452$	5.01867	+	8.69259i	0.236058	+	0.408865i
$453$	2.34699	+	1.35504i	0.110271	+	0.0636652i
$454$	−21.4783			−1.00803
$455$	13.5345	−	19.8770i	0.634509	−	0.931850i
$456$	3.12299			0.146248
$457$	−30.7370	−	17.7460i	−1.43782	−	0.830124i	−0.440119	−	0.897940i	$-0.645064\pi$
$457$	−30.7370	−	17.7460i	−1.43782	−	0.830124i	−0.997698	+	0.0678157i	$0.978397\pi$
$458$	−4.13370	−	7.15978i	−0.193155	−	0.334555i
$459$	−0.123703	−	0.214260i	−0.00577396	−	0.0100008i
$460$	7.86392	+	4.54024i	0.366657	+	0.211690i
$461$			7.57380i			0.352747i	0.984323	+	0.176373i	$0.0564366\pi$
$461$			7.57380i			0.352747i	−0.984323	+	0.176373i	$0.943563\pi$
$462$	14.8986	+	1.00102i	0.693147	+	0.0465716i
$463$		−	25.0299i		−	1.16324i	−0.813462	−	0.581618i	$-0.802420\pi$
$463$		−	25.0299i		−	1.16324i	0.813462	−	0.581618i	$-0.197580\pi$
$464$	2.12447	−	3.67970i	0.0986263	−	0.170826i
$465$	7.71760	+	13.3673i	0.357895	+	0.619893i
$466$	23.2892	−	13.4460i	1.07885	−	0.622874i
$467$	15.6334	−	27.0778i	0.723427	−	1.25301i	−0.236191	−	0.971707i	$-0.575899\pi$
$467$	15.6334	−	27.0778i	0.723427	−	1.25301i	0.959618	−	0.281306i	$-0.0907675\pi$
$468$	3.13524	−	1.78052i	0.144927	−	0.0823044i
$469$	−2.16193	+	32.1771i	−0.0998287	+	1.48580i
$470$		−	16.8495i		−	0.777209i
$471$	−8.55178	+	14.8121i	−0.394045	+	0.682506i
$472$	−3.97797	−	6.89004i	−0.183101	−	0.317140i
$473$	−27.1808	+	15.6928i	−1.24977	+	0.721557i
$474$	−5.59041	−	3.22763i	−0.256776	−	0.148250i
$475$			4.23081i			0.194123i
$476$	0.288549	+	0.587543i	0.0132256	+	0.0269300i
$477$	6.56103			0.300409
$478$	−2.18739	+	3.78867i	−0.100049	+	0.173290i
$479$	13.4394	−	7.75926i	0.614063	−	0.354529i	−0.160491	−	0.987037i	$-0.551308\pi$
$479$	13.4394	−	7.75926i	0.614063	−	0.354529i	0.774554	+	0.632508i	$0.217974\pi$
$480$	−1.26043	−	2.18313i	−0.0575305	−	0.0996457i
$481$	29.2199	+	0.207877i	1.33231	+	0.00947838i
$482$	−1.54475			−0.0703613
$483$	−5.30775	+	7.91552i	−0.241511	+	0.360168i
$484$	20.8531			0.947867
$485$	21.2695	−	36.8398i	0.965797	−	1.67281i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	28.0472	−	16.1931i	1.27094	−	0.733778i	0.295776	−	0.955257i	$-0.404422\pi$
$487$	28.0472	−	16.1931i	1.27094	−	0.733778i	0.975165	+	0.221479i	$0.0710886\pi$
$488$	11.0751	+	6.39419i	0.501345	+	0.289452i
$489$		−	18.6052i		−	0.841355i
$490$	10.7880	−	13.9643i	0.487353	−	0.630841i
$491$	−9.22056			−0.416118			−0.208059	−	0.978116i	$-0.566715\pi$
$491$	−9.22056			−0.416118			−0.208059	+	0.978116i	$0.566715\pi$
$492$	−7.44710	−	4.29959i	−0.335741	−	0.193840i
$493$	−0.525608	−	0.910379i	−0.0236722	−	0.0410014i
$494$	9.71124	+	5.69929i	0.436930	+	0.256423i
$495$	−7.11368	+	12.3212i	−0.319736	+	0.553799i
$496$		−	6.12299i		−	0.274931i
$497$	−8.93085	−	5.98858i	−0.400603	−	0.268625i
$498$	−0.662485			−0.0296867
$499$	6.56445	+	3.78999i	0.293865	+	0.169663i	0.639684	−	0.768638i	$-0.279065\pi$
$499$	6.56445	+	3.78999i	0.293865	+	0.169663i	−0.345818	+	0.938301i	$0.612399\pi$
$500$	−7.95809	+	4.59461i	−0.355897	+	0.205477i
$501$	12.6297	−	7.29175i	0.564253	−	0.325771i
$502$	−11.6326	−	6.71606i	−0.519186	−	0.299752i
$503$	1.86195			0.0830203			0.0415102	−	0.999138i	$-0.486783\pi$
$503$	1.86195			0.0830203			0.0415102	+	0.999138i	$0.486783\pi$
$504$	2.37482	−	1.16630i	0.105783	−	0.0519510i
$505$			29.0389i			1.29221i
$506$	−10.1650	+	17.6062i	−0.451887	+	0.782692i
$507$	12.9987	+	0.184960i	0.577292	+	0.00821437i
$508$	5.15681	+	8.93186i	0.228797	+	0.396287i
$509$	−6.91271	−	3.99105i	−0.306400	−	0.176900i	0.338914	−	0.940817i	$-0.389940\pi$
$509$	−6.91271	−	3.99105i	−0.306400	−	0.176900i	−0.645315	+	0.763917i	$0.723274\pi$
$510$	−0.623675			−0.0276168
$511$	1.39632	−	20.7822i	0.0617697	−	0.919348i
$512$			1.00000i			0.0441942i
$513$	−2.70459	−	1.56150i	−0.119411	−	0.0689418i
$514$	18.9093	−	10.9173i	0.834055	−	0.481542i
$515$	−12.6369	+	7.29592i	−0.556849	+	0.321497i
$516$	−2.78052	+	4.81600i	−0.122405	+	0.212012i
$517$	37.7237			1.65908
$518$	21.3939	+	1.43742i	0.939993	+	0.0631568i
$519$	−3.93890			−0.172899
$520$	0.0646601	−	9.08886i	0.00283553	−	0.398573i
$521$	−8.61209	−	14.9166i	−0.377303	−	0.653507i	0.613366	−	0.789799i	$-0.289815\pi$
$521$	−8.61209	−	14.9166i	−0.377303	−	0.653507i	−0.990669	+	0.136291i	$0.956482\pi$
$522$	−3.67970	+	2.12447i	−0.161056	+	0.0929857i
$523$	12.7325	−	22.0534i	0.556755	−	0.964328i	−0.441010	−	0.897502i	$-0.645379\pi$
$523$	12.7325	−	22.0534i	0.556755	−	0.964328i	0.997765	−	0.0668258i	$-0.0212872\pi$
$524$	−18.4978			−0.808082
$525$	1.58002	+	3.21723i	0.0689576	+	0.140411i
$526$			8.49988i			0.370612i
$527$	−1.31191	−	0.757432i	−0.0571478	−	0.0329943i
$528$	4.88772	−	2.82193i	0.212711	−	0.122809i
$529$	5.01231	+	8.68158i	0.217927	+	0.377460i
$530$	8.26972	−	14.3236i	0.359214	−	0.622176i
$531$			7.95594i			0.345258i
$532$	6.86263	+	4.60174i	0.297533	+	0.199511i
$533$	−15.3110	−	26.9605i	−0.663192	−	1.16779i
$534$	2.81116	−	4.86906i	0.121651	−	0.210705i
$535$	−34.7773	+	20.0787i	−1.50355	+	0.868076i
$536$	6.09461	+	10.5562i	0.263247	+	0.455957i
$537$	2.35319	−	4.07584i	0.101547	−	0.175885i
$538$		−	20.6215i		−	0.889054i
$539$	31.2640	+	24.1529i	1.34664	+	1.04034i
$540$			2.52086i			0.108480i
$541$	16.1619	+	9.33109i	0.694855	+	0.401175i	0.805428	−	0.592693i	$-0.201935\pi$
$541$	16.1619	+	9.33109i	0.694855	+	0.401175i	−0.110573	+	0.993868i	$0.535269\pi$
$542$	11.9744	+	20.7402i	0.514344	+	0.890870i
$543$	−7.81998	−	13.5446i	−0.335587	−	0.581255i
$544$	0.214260	+	0.123703i	0.00918631	+	0.00530372i
$545$	−3.73260			−0.159887
$546$	9.51314	+	0.707191i	0.407125	+	0.0302650i
$547$	32.1949			1.37655			0.688277	−	0.725448i	$-0.258367\pi$
$547$	32.1949			1.37655			0.688277	+	0.725448i	$0.258367\pi$
$548$	11.8669	+	6.85133i	0.506927	+	0.292674i
$549$	−6.39419	−	11.0751i	−0.272898	−	0.472672i
$550$	3.82294	+	6.62153i	0.163011	+	0.282343i
$551$	−11.4917	−	6.63472i	−0.489562	−	0.282649i
$552$			3.60213i			0.153317i
$553$	−7.52875	−	15.3300i	−0.320155	−	0.651899i
$554$		−	4.12212i		−	0.175132i
$555$	−10.2150	+	17.6929i	−0.433601	+	0.751020i
$556$	−4.00737	−	6.94097i	−0.169950	−	0.294363i
$557$	−7.52338	+	4.34362i	−0.318776	+	0.184045i	−0.650847	−	0.759209i	$-0.725586\pi$
$557$	−7.52338	+	4.34362i	−0.318776	+	0.184045i	0.332071	+	0.943254i	$0.392253\pi$
$558$	−3.06150	+	5.30267i	−0.129603	+	0.224480i
$559$	−17.4352	+	9.90151i	−0.737430	+	0.418789i
$560$	0.447110	−	6.65456i	0.0188939	−	0.281207i
$561$		−	1.39632i		−	0.0589528i
$562$	5.15092	−	8.92165i	0.217278	−	0.376337i
$563$	−7.67650	−	13.2961i	−0.323526	−	0.560363i	0.657687	−	0.753291i	$-0.271535\pi$
$563$	−7.67650	−	13.2961i	−0.323526	−	0.560363i	−0.981213	+	0.192928i	$0.938202\pi$
$564$	5.78854	−	3.34201i	0.243741	−	0.140724i
$565$	−21.9128	−	12.6514i	−0.921878	−	0.532246i
$566$		−	10.8622i		−	0.456574i
$567$	−2.63980	−	0.177364i	−0.110861	−	0.00744860i
$568$	−4.06419			−0.170529
$569$	−18.4292	+	31.9204i	−0.772594	+	1.33817i	0.163543	+	0.986536i	$0.447708\pi$
$569$	−18.4292	+	31.9204i	−0.772594	+	1.33817i	−0.936137	+	0.351636i	$0.885626\pi$
$570$	−6.81789	+	3.93631i	−0.285570	+	0.164874i
$571$	−5.61735	−	9.72953i	−0.235079	−	0.407168i	0.724217	−	0.689572i	$-0.242201\pi$
$571$	−5.61735	−	9.72953i	−0.235079	−	0.407168i	−0.959296	+	0.282404i	$0.908868\pi$
$572$	20.3487	+	0.144765i	0.850821	+	0.00605293i
$573$	−8.97686			−0.375014
$574$	−10.0292	−	20.4214i	−0.418611	−	0.852375i
$575$	−4.87991			−0.203506
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−24.5422	+	14.1694i	−1.02170	+	0.589881i	−0.914597	−	0.404366i	$-0.867492\pi$
$577$	−24.5422	+	14.1694i	−1.02170	+	0.589881i	−0.107107	+	0.994247i	$0.534159\pi$
$578$	−14.6694	+	8.46940i	−0.610168	+	0.352280i
$579$	6.09697	+	3.52009i	0.253381	+	0.146290i
$580$			10.7110i			0.444750i
$581$	−1.45578	−	0.976173i	−0.0603959	−	0.0404985i
$582$	16.8748			0.699482
$583$	32.0685	+	18.5147i	1.32814	+	0.766803i
$584$	−3.93631	−	6.81789i	−0.162886	−	0.282126i
$585$	−4.60042	+	7.83885i	−0.190204	+	0.324097i
$586$	1.86256	−	3.22606i	0.0769418	−	0.133267i
$587$		−	0.0179623i		−	0.000741383i	−1.00000		0.000370692i	$-0.999882\pi$
$587$		−	0.0179623i		−	0.000741383i	1.00000		0.000370692i	$-0.000117995\pi$
$588$	6.93708	+	0.936412i	0.286081	+	0.0386170i
$589$	−19.1221			−0.787911
$590$	17.3688	+	10.0279i	0.715063	+	0.412842i
$591$	−10.1412	+	5.85504i	−0.417154	+	0.240844i
$592$	7.01858	−	4.05218i	0.288462	−	0.166544i
$593$	41.5164	+	23.9695i	1.70487	+	0.984309i	0.940664	+	0.339340i	$0.110204\pi$
$593$	41.5164	+	23.9695i	1.70487	+	0.984309i	0.764209	+	0.644969i	$0.223130\pi$
$594$	−5.64385			−0.231570
$595$	−1.37050	−	0.918987i	−0.0561849	−	0.0376748i
$596$			1.87546i			0.0768220i
$597$	9.05076	−	15.6764i	0.370423	−	0.641591i
$598$	−6.57369	+	11.2012i	−0.268818	+	0.458050i
$599$	7.47580	+	12.9485i	0.305453	+	0.529060i	0.977362	−	0.211573i	$-0.0678588\pi$
$599$	7.47580	+	12.9485i	0.305453	+	0.529060i	−0.671909	+	0.740634i	$0.734525\pi$
$600$	1.17323	+	0.677364i	0.0478969	+	0.0276533i
$601$	19.7525			0.805723			0.402861	−	0.915261i	$-0.368016\pi$
$601$	19.7525			0.805723			0.402861	+	0.915261i	$0.368016\pi$
$602$	−13.2064	+	6.48582i	−0.538254	+	0.264342i
$603$		−	12.1892i		−	0.496383i
$604$	2.34699	+	1.35504i	0.0954977	+	0.0551357i
$605$	−45.5249	+	26.2838i	−1.85085	+	1.06859i
$606$	−9.97613	+	5.75972i	−0.405252	+	0.233973i
$607$	5.09059	−	8.81716i	0.206621	−	0.357878i	−0.744027	−	0.668149i	$-0.767087\pi$
$607$	5.09059	−	8.81716i	0.206621	−	0.357878i	0.950648	+	0.310272i	$0.100420\pi$
$608$	3.12299			0.126654
$609$	−11.2164	−	0.753612i	−0.454510	−	0.0305379i
$610$	−32.2377			−1.30527
$611$	24.0990	+	0.171445i	0.974941	+	0.00693594i
$612$	−0.123703	−	0.214260i	−0.00500040	−	0.00866094i
$613$	−26.1938	+	15.1230i	−1.05796	+	0.610812i	−0.924867	−	0.380292i	$-0.875824\pi$
$613$	−26.1938	+	15.1230i	−1.05796	+	0.610812i	−0.133091	+	0.991104i	$0.542490\pi$
$614$	10.5052	−	18.1955i	0.423955	−	0.734311i
$615$	21.6773			0.874113
$616$	14.8986	+	1.00102i	0.600283	+	0.0403322i
$617$			18.4715i			0.743636i	0.928306	+	0.371818i	$0.121265\pi$
$617$			18.4715i			0.743636i	−0.928306	+	0.371818i	$0.878735\pi$
$618$	−5.01294	−	2.89422i	−0.201650	−	0.116423i
$619$	3.42519	−	1.97754i	0.137670	−	0.0794839i	−0.429583	−	0.903027i	$-0.641339\pi$
$619$	3.42519	−	1.97754i	0.137670	−	0.0794839i	0.567253	+	0.823543i	$0.308006\pi$
$620$	7.71760	+	13.3673i	0.309946	+	0.536843i
$621$	1.80107	−	3.11954i	0.0722743	−	0.125183i
$622$		−	6.39478i		−	0.256407i
$623$	13.3520	−	6.55729i	0.534935	−	0.262712i
$624$	3.13524	−	1.78052i	0.125510	−	0.0712777i
$625$	14.9692	−	25.9274i	0.598767	−	1.03709i
$626$	13.4006	−	7.73685i	0.535597	−	0.309227i
$627$	−8.81286	−	15.2643i	−0.351952	−	0.609598i
$628$	−8.55178	+	14.8121i	−0.341253	+	0.591068i
$629$		−	2.00507i		−	0.0799472i
$630$	−3.71449	+	5.53946i	−0.147989	+	0.220698i
$631$			24.3547i			0.969546i	0.874640	+	0.484773i	$0.161098\pi$
$631$			24.3547i			0.969546i	−0.874640	+	0.484773i	$0.838902\pi$
$632$	−5.59041	−	3.22763i	−0.222375	−	0.128388i
$633$	−11.6126	−	20.1136i	−0.461559	−	0.799444i
$634$	−9.44569	−	16.3604i	−0.375136	−	0.649755i
$635$	−22.5160	−	12.9996i	−0.893519	−	0.515873i
$636$	6.56103			0.260162
$637$	19.8626	+	15.5716i	0.786986	+	0.616971i
$638$	−23.9804			−0.949395
$639$	3.51969	+	2.03209i	0.139237	+	0.0803883i
$640$	−1.26043	−	2.18313i	−0.0498228	−	0.0862957i
$641$	−0.398610	−	0.690412i	−0.0157441	−	0.0272696i	0.858046	−	0.513573i	$-0.171678\pi$
$641$	−0.398610	−	0.690412i	−0.0157441	−	0.0272696i	−0.873790	+	0.486303i	$0.838345\pi$
$642$	−13.7958	−	7.96501i	−0.544477	−	0.314354i
$643$			36.3986i			1.43542i	0.696342	+	0.717710i	$0.254810\pi$
$643$			36.3986i			1.43542i	−0.696342	+	0.717710i	$0.745190\pi$
$644$	−5.30775	+	7.91552i	−0.209155	+	0.311915i
$645$		−	14.0186i		−	0.551981i
$646$	0.386323	−	0.669132i	0.0151997	−	0.0263266i
$647$	−18.3127	−	31.7185i	−0.719945	−	1.24698i	−0.961021	−	0.276475i	$-0.910834\pi$
$647$	−18.3127	−	31.7185i	−0.719945	−	1.24698i	0.241076	−	0.970506i	$-0.422500\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−22.4511	+	38.8864i	−0.881281	+	1.52642i
$650$	2.41212	+	4.24741i	0.0946110	+	0.166597i
$651$	−14.5410	+	7.14123i	−0.569906	+	0.279887i
$652$		−	18.6052i		−	0.728635i
$653$	−18.1837	+	31.4951i	−0.711583	+	1.23250i	0.252680	+	0.967550i	$0.418688\pi$
$653$	−18.1837	+	31.4951i	−0.711583	+	1.23250i	−0.964263	+	0.264948i	$0.914645\pi$
$654$	−0.740342	−	1.28231i	−0.0289497	−	0.0501423i
$655$	40.3832	−	23.3152i	1.57790	−	0.911001i
$656$	−7.44710	−	4.29959i	−0.290760	−	0.167871i
$657$			7.87262i			0.307140i
$658$	17.6445	+	1.18551i	0.687854	+	0.0462159i
$659$	−18.7720			−0.731252			−0.365626	−	0.930762i	$-0.619145\pi$
$659$	−18.7720			−0.731252			−0.365626	+	0.930762i	$0.619145\pi$
$660$	−7.11368	+	12.3212i	−0.276899	+	0.479604i
$661$	−36.4244	+	21.0297i	−1.41675	+	0.817959i	−0.996012	−	0.0892249i	$-0.971561\pi$
$661$	−36.4244	+	21.0297i	−1.41675	+	0.817959i	−0.420735	+	0.907184i	$0.638228\pi$
$662$	12.7985	+	22.1676i	0.497427	+	0.861569i
$663$	0.00634597	−	0.892012i	0.000246457	−	0.0346429i
$664$	−0.662485			−0.0257094
$665$	−20.7822	−	1.39632i	−0.805897	−	0.0541471i
$666$	−8.10436			−0.314038
$667$	7.65264	−	13.2548i	0.296312	−	0.513227i
$668$	12.6297	−	7.29175i	0.488657	−	0.282126i
$669$	−6.20734	+	3.58381i	−0.239990	+	0.138558i
$670$	−26.6106	−	15.3636i	−1.02806	−	0.593549i
$671$		−	72.1758i		−	2.78631i
$672$	2.37482	−	1.16630i	0.0916105	−	0.0449909i
$673$	29.6123			1.14147			0.570736	−	0.821134i	$-0.306658\pi$
$673$	29.6123			1.14147			0.570736	+	0.821134i	$0.306658\pi$
$674$	30.4876	+	17.6020i	1.17434	+	0.678004i
$675$	−0.677364	−	1.17323i	−0.0260718	−	0.0451576i
$676$	12.9987	+	0.184960i	0.499949	+	0.00711386i
$677$	−6.35028	+	10.9990i	−0.244061	+	0.422726i	−0.961867	−	0.273517i	$-0.911813\pi$
$677$	−6.35028	+	10.9990i	−0.244061	+	0.422726i	0.717806	+	0.696243i	$0.245146\pi$
$678$		−	10.0373i		−	0.385482i
$679$	37.0815	+	24.8650i	1.42306	+	0.954232i
$680$	−0.623675			−0.0239169
$681$	18.6007	+	10.7391i	0.712782	+	0.411525i
$682$	−29.9275	+	17.2786i	−1.14598	+	0.661633i
$683$	36.7165	−	21.1983i	1.40492	−	0.811130i	0.410026	−	0.912074i	$-0.365520\pi$
$683$	36.7165	−	21.1983i	1.40492	−	0.811130i	0.994892	+	0.100944i	$0.0321863\pi$
$684$	−2.70459	−	1.56150i	−0.103413	−	0.0597053i
$685$	−34.5425			−1.31980
$686$	13.8641	+	12.2795i	0.529334	+	0.468834i
$687$			8.26740i			0.315421i
$688$	−2.78052	+	4.81600i	−0.106006	+	0.183608i
$689$	20.4022	+	11.9735i	0.777260	+	0.456155i
$690$	−4.54024	−	7.86392i	−0.172844	−	0.299374i
$691$	27.7470	+	16.0197i	1.05554	+	0.609419i	0.924196	−	0.381918i	$-0.124736\pi$
$691$	27.7470	+	16.0197i	1.05554	+	0.609419i	0.131348	+	0.991336i	$0.458070\pi$
$692$	−3.93890			−0.149735
$693$	−12.4021	−	8.31623i	−0.471116	−	0.315907i
$694$			12.6826i			0.481425i
$695$	17.4972	+	10.1020i	0.663707	+	0.383191i
$696$	−3.67970	+	2.12447i	−0.139479	+	0.0805280i
$697$	−1.84246	+	1.06374i	−0.0697880	+	0.0402921i
$698$	−8.36290	+	14.4850i	−0.316540	+	0.548264i
$699$	−26.8920			−1.01715
$700$	1.58002	+	3.21723i	0.0597190	+	0.121600i
$701$	50.5029			1.90747			0.953734	−	0.300651i	$-0.0972039\pi$
$701$	50.5029			1.90747			0.953734	+	0.300651i	$0.0972039\pi$
$702$	−3.60546	−	0.0256500i	−0.136079	−	0.000968098i
$703$	−12.6549	−	21.9190i	−0.477290	−	0.826690i
$704$	4.88772	−	2.82193i	0.184213	−	0.106355i
$705$	−8.42474	+	14.5921i	−0.317294	+	0.549570i
$706$	−9.64324			−0.362928
$707$	−30.4090	−	2.04314i	−1.14365	−	0.0768401i
$708$			7.95594i			0.299002i
$709$	12.8665	+	7.42845i	0.483210	+	0.278981i	0.721753	−	0.692151i	$-0.243337\pi$
$709$	12.8665	+	7.42845i	0.483210	+	0.278981i	−0.238543	+	0.971132i	$0.576670\pi$
$710$	8.87264	−	5.12262i	0.332984	−	0.192248i
$711$	3.22763	+	5.59041i	0.121045	+	0.209657i
$712$	2.81116	−	4.86906i	0.105353	−	0.182476i
$713$		−	22.0558i		−	0.825998i
$714$	0.0438810	−	0.653102i	0.00164220	−	0.0244417i
$715$	−44.6062	+	25.3320i	−1.66818	+	0.947364i
$716$	2.35319	−	4.07584i	0.0879427	−	0.152321i
$717$	3.78867	−	2.18739i	0.141491	−	0.0816896i
$718$	−0.283541	−	0.491107i	−0.0105817	−	0.0183280i
$719$	−8.46051	+	14.6540i	−0.315524	+	0.546503i	−0.979549	−	0.201207i	$-0.935514\pi$
$719$	−8.46051	+	14.6540i	−0.315524	+	0.546503i	0.664025	+	0.747710i	$0.268847\pi$
$720$			2.52086i			0.0939469i
$721$	−6.75105	−	13.7465i	−0.251422	−	0.511946i
$722$			9.24691i			0.344134i
$723$	1.33779	+	0.772373i	0.0497529	+	0.0287249i
$724$	−7.81998	−	13.5446i	−0.290627	−	0.503381i
$725$	−2.87809	−	4.98499i	−0.106889	−	0.185138i
$726$	−18.0593	−	10.4265i	−0.670243	−	0.386965i
$727$	31.4510			1.16645			0.583227	−	0.812309i	$-0.301790\pi$
$727$	31.4510			1.16645			0.583227	+	0.812309i	$0.301790\pi$
$728$	9.51314	+	0.707191i	0.352581	+	0.0262102i
$729$	1.00000			0.0370370
$730$	17.1869	+	9.92289i	0.636117	+	0.367263i
$731$	0.687916	+	1.19151i	0.0254435	+	0.0440694i
$732$	−6.39419	−	11.0751i	−0.236336	−	0.409346i
$733$	−13.3249	−	7.69312i	−0.492166	−	0.284152i	0.233307	−	0.972403i	$-0.425045\pi$
$733$	−13.3249	−	7.69312i	−0.492166	−	0.284152i	−0.725472	+	0.688251i	$0.758379\pi$
$734$		−	13.2510i		−	0.489103i
$735$	−16.3248	+	6.69940i	−0.602150	+	0.247111i
$736$			3.60213i			0.132776i
$737$	34.3971	−	59.5775i	1.26703	−	2.19456i
$738$	4.29959	+	7.44710i	0.158270	+	0.274132i
$739$	−9.93208	+	5.73429i	−0.365357	+	0.210939i	−0.671428	−	0.741070i	$-0.734319\pi$
$739$	−9.93208	+	5.73429i	−0.365357	+	0.210939i	0.306071	+	0.952009i	$0.400986\pi$
$740$	−10.2150	+	17.6929i	−0.375510	+	0.650402i
$741$	−5.56054	−	9.79135i	−0.204272	−	0.359694i
$742$	14.4176	+	9.66769i	0.529285	+	0.354912i
$743$		−	16.4784i		−	0.604534i	−0.953223	−	0.302267i	$-0.902257\pi$
$743$		−	16.4784i		−	0.604534i	0.953223	−	0.302267i	$-0.0977434\pi$
$744$	−3.06150	+	5.30267i	−0.112240	+	0.194405i
$745$	−2.36389	−	4.09438i	−0.0866062	−	0.150006i
$746$	20.6939	−	11.9476i	0.757656	−	0.437433i
$747$	0.573729	+	0.331243i	0.0209916	+	0.0121195i
$748$		−	1.39632i		−	0.0510546i
$749$	−18.5791	−	37.8308i	−0.678867	−	1.38231i
$750$	9.18921			0.335543
$751$	−15.2492	+	26.4123i	−0.556450	+	0.963800i	0.441339	+	0.897340i	$0.354504\pi$
$751$	−15.2492	+	26.4123i	−0.556450	+	0.963800i	−0.997789	+	0.0664593i	$0.978830\pi$
$752$	5.78854	−	3.34201i	0.211086	−	0.121871i
$753$	6.71606	+	11.6326i	0.244747	+	0.423914i
$754$	−15.3194	−	0.108986i	−0.557900	−	0.00396902i
$755$	−6.83171			−0.248631
$756$	−2.63980	−	0.177364i	−0.0960086	−	0.00645068i
$757$	32.1769			1.16949			0.584744	−	0.811218i	$-0.301195\pi$
$757$	32.1769			1.16949			0.584744	+	0.811218i	$0.301195\pi$
$758$	−0.730126	+	1.26462i	−0.0265194	+	0.0459329i
$759$	17.6062	−	10.1650i	0.639065	−	0.368965i
$760$	−6.81789	+	3.93631i	−0.247311	+	0.142785i
$761$	−23.8111	−	13.7473i	−0.863151	−	0.498341i	0.00191497	−	0.999998i	$-0.499390\pi$
$761$	−23.8111	−	13.7473i	−0.863151	−	0.498341i	−0.865066	+	0.501657i	$0.832724\pi$
$762$		−	10.3136i		−	0.373623i
$763$	0.262621	−	3.90871i	0.00950750	−	0.141505i
$764$	−8.97686			−0.324771
$765$	0.540119	+	0.311838i	0.0195280	+	0.0112745i
$766$	−3.26040	−	5.64718i	−0.117803	−	0.204041i
$767$	−14.5191	+	24.7397i	−0.524256	+	0.893300i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	5.03709i		−	0.181642i	−0.995867	−	0.0908210i	$-0.971051\pi$
$769$		−	5.03709i		−	0.181642i	0.995867	−	0.0908210i	$-0.0289491\pi$
$770$	−33.7873	+	16.5933i	−1.21761	+	0.597982i
$771$	−21.8346			−0.786354
$772$	6.09697	+	3.52009i	0.219435	+	0.126691i
$773$	−11.3640	+	6.56103i	−0.408736	+	0.235984i	−0.690247	−	0.723574i	$-0.742498\pi$
$773$	−11.3640	+	6.56103i	−0.408736	+	0.235984i	0.281510	+	0.959558i	$0.409165\pi$
$774$	4.81600	−	2.78052i	0.173107	−	0.0999436i
$775$	−7.18368	−	4.14750i	−0.258045	−	0.148982i
$776$	16.8748			0.605769
$777$	−17.8089	−	11.9418i	−0.638892	−	0.428409i
$778$			25.6019i			0.917874i
$779$	−13.4276	+	23.2572i	−0.481093	+	0.833277i
$780$	−4.60042	+	7.83885i	−0.164722	+	0.280676i
$781$	11.4688	+	19.8646i	0.410387	+	0.710811i
$782$	0.771793	+	0.445595i	0.0275992	+	0.0159344i
$783$	4.24895			0.151845
$784$	6.93708	+	0.936412i	0.247753	+	0.0334433i
$785$		−	43.1156i		−	1.53886i
$786$	16.0196	+	9.24892i	0.571400	+	0.329898i
$787$	−8.11053	+	4.68261i	−0.289109	+	0.166917i	−0.637540	−	0.770417i	$-0.720048\pi$
$787$	−8.11053	+	4.68261i	−0.289109	+	0.166917i	0.348431	+	0.937334i	$0.386715\pi$
$788$	−10.1412	+	5.85504i	−0.361266	+	0.208577i
$789$	4.24994	−	7.36111i	0.151302	−	0.262062i
$790$	16.2728			0.578960
$791$	14.7900	−	22.0566i	0.525873	−	0.784241i
$792$	−5.64385			−0.200546
$793$	0.328022	−	46.1080i	0.0116484	−	1.63734i
$794$	−7.76567	−	13.4505i	−0.275593	−	0.477342i
$795$	−14.3236	+	8.26972i	−0.508005	+	0.293297i
$796$	9.05076	−	15.6764i	0.320796	−	0.555634i
$797$	−23.1485			−0.819963			−0.409982	−	0.912094i	$-0.634465\pi$
$797$	−23.1485			−0.819963			−0.409982	+	0.912094i	$0.634465\pi$
$798$	−3.64234	−	7.41653i	−0.128937	−	0.262542i
$799$		−	1.65367i		−	0.0585026i
$800$	1.17323	+	0.677364i	0.0414799	+	0.0239484i
$801$	−4.86906	+	2.81116i	−0.172040	+	0.0993273i
$802$	17.4765	+	30.2703i	0.617118	+	1.06888i
$803$	−22.2160	+	38.4792i	−0.783984	+	1.35790i
$804$		−	12.1892i		−	0.429880i
$805$	1.61055	−	23.9706i	0.0567645	−	0.844854i
$806$	−19.1971	+	10.9021i	−0.676188	+	0.384010i
$807$	−10.3107	+	17.8587i	−0.362955	+	0.628656i
$808$	−9.97613	+	5.75972i	−0.350959	+	0.202626i
$809$	−27.8984	−	48.3215i	−0.980856	−	1.69889i	−0.659073	−	0.752079i	$-0.729051\pi$
$809$	−27.8984	−	48.3215i	−0.980856	−	1.69889i	−0.321784	−	0.946813i	$-0.604282\pi$
$810$	1.26043	−	2.18313i	0.0442870	−	0.0767073i
$811$			49.1611i			1.72628i	0.504966	+	0.863139i	$0.331505\pi$
$811$			49.1611i			1.72628i	−0.504966	+	0.863139i	$0.668495\pi$
$812$	−11.2164	−	0.753612i	−0.393618	−	0.0264466i
$813$		−	23.9488i		−	0.839920i
$814$	−39.6118	−	22.8699i	−1.38839	−	0.801590i
$815$	23.4505	+	40.6175i	0.821435	+	1.42277i
$816$	−0.123703	−	0.214260i	−0.00433047	−	0.00750059i
$817$	15.0403	+	8.68353i	0.526194	+	0.303798i
$818$	12.7020			0.444115
$819$	−7.88503	−	5.36902i	−0.275525	−	0.187609i
$820$	21.6773			0.757004
$821$	28.9550	+	16.7172i	1.01054	+	0.583433i	0.911349	−	0.411635i	$-0.135042\pi$
$821$	28.9550	+	16.7172i	1.01054	+	0.583433i	0.0991875	+	0.995069i	$0.468376\pi$
$822$	−6.85133	−	11.8669i	−0.238968	−	0.413904i
$823$	18.3644	+	31.8081i	0.640142	+	1.10876i	0.985401	+	0.170251i	$0.0544580\pi$
$823$	18.3644	+	31.8081i	0.640142	+	1.10876i	−0.345258	+	0.938508i	$0.612209\pi$
$824$	−5.01294	−	2.89422i	−0.174634	−	0.100825i
$825$		−	7.64589i		−	0.266196i
$826$	−11.7231	+	17.4828i	−0.407898	+	0.608304i
$827$		−	45.4204i		−	1.57942i	−0.613478	−	0.789712i	$-0.710230\pi$
$827$		−	45.4204i		−	1.57942i	0.613478	−	0.789712i	$-0.289770\pi$
$828$	1.80107	−	3.11954i	0.0625914	−	0.108412i
$829$	11.4353	+	19.8065i	0.397164	+	0.687909i	0.993375	−	0.114920i	$-0.0366610\pi$
$829$	11.4353	+	19.8065i	0.397164	+	0.687909i	−0.596211	+	0.802828i	$0.703328\pi$
$830$	1.44629	−	0.835016i	0.0502014	−	0.0289838i
$831$	−2.06106	+	3.56986i	−0.0714974	+	0.123837i
$832$	3.13524	−	1.78052i	0.108695	−	0.0617283i
$833$	1.05877	−	1.37050i	0.0366843	−	0.0474851i
$834$			8.01474i			0.277528i
$835$	−18.3815	+	31.8376i	−0.636117	+	1.10179i
$836$	−8.81286	−	15.2643i	−0.304799	−	0.527927i
$837$	5.30267	−	3.06150i	0.183287	−	0.105821i
$838$	20.5667	+	11.8742i	0.710464	+	0.410186i
$839$		−	7.31572i		−	0.252567i	−0.991994	−	0.126283i	$-0.959695\pi$
$839$		−	7.31572i		−	0.252567i	0.991994	−	0.126283i	$-0.0403048\pi$
$840$	−3.71449	+	5.53946i	−0.128162	+	0.191130i
$841$	−10.9464			−0.377463
$842$	−2.45643	+	4.25466i	−0.0846541	+	0.146625i
$843$	−8.92165	+	5.15092i	−0.307278	+	0.177407i
$844$	−11.6126	−	20.1136i	−0.399722	−	0.692339i
$845$	−28.6109	+	15.9801i	−0.984245	+	0.549733i
$846$	−6.68403			−0.229802
$847$	−24.3209	−	49.5222i	−0.835675	−	1.70160i
$848$	6.56103			0.225307
$849$	−5.43112	+	9.40698i	−0.186396	+	0.322847i
$850$	0.290264	−	0.167584i	0.00995597	−	0.00574808i
$851$	25.2819	−	14.5965i	0.866651	−	0.500361i
$852$	3.51969	+	2.03209i	0.120583	+	0.0696184i
$853$		−	34.5603i		−	1.18332i	−0.806187	−	0.591661i	$-0.798472\pi$
$853$		−	34.5603i		−	1.18332i	0.806187	−	0.591661i	$-0.201528\pi$
$854$	2.26820	−	33.7588i	0.0776163	−	1.15520i
$855$	7.87262			0.269238
$856$	−13.7958	−	7.96501i	−0.471531	−	0.272238i
$857$	11.9237	+	20.6525i	0.407307	+	0.705476i	0.994587	−	0.103908i	$-0.0331347\pi$
$857$	11.9237	+	20.6525i	0.407307	+	0.705476i	−0.587280	+	0.809384i	$0.699801\pi$
$858$	−17.5501	−	10.2997i	−0.599150	−	0.351626i
$859$	11.2768	−	19.5320i	0.384760	−	0.666424i	−0.606976	−	0.794720i	$-0.707618\pi$
$859$	11.2768	−	19.5320i	0.384760	−	0.666424i	0.991736	+	0.128296i	$0.0409509\pi$
$860$		−	14.0186i		−	0.478030i
$861$	−1.52519	+	22.7001i	−0.0519782	+	0.773617i
$862$	25.1596			0.856939
$863$	−31.6139	−	18.2523i	−1.07615	−	0.621316i	−0.146295	−	0.989241i	$-0.546735\pi$
$863$	−31.6139	−	18.2523i	−1.07615	−	0.621316i	−0.929855	+	0.367925i	$0.880068\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	8.59912	−	4.96471i	0.292379	−	0.168805i
$866$	−5.33880	−	3.08236i	−0.181420	−	0.104743i
$867$	16.9388			0.575271
$868$	−14.5410	+	7.14123i	−0.493553	+	0.242389i
$869$			36.4325i			1.23589i
$870$	5.35550	−	9.27600i	0.181568	−	0.314486i
$871$	22.2446	−	37.9035i	0.753730	−	1.28431i
$872$	−0.740342	−	1.28231i	−0.0250712	−	0.0434245i
$873$	−14.6140	−	8.43739i	−0.494609	−	0.285562i
$874$	11.2494			0.380518
$875$	20.1929	+	13.5403i	0.682643	+	0.457746i
$876$			7.87262i			0.265991i
$877$	−5.89748	−	3.40491i	−0.199144	−	0.114976i	0.397112	−	0.917770i	$-0.370012\pi$
$877$	−5.89748	−	3.40491i	−0.199144	−	0.114976i	−0.596256	+	0.802794i	$0.703346\pi$
$878$	7.70572	−	4.44890i	0.260055	−	0.150143i
$879$	−3.22606	+	1.86256i	−0.108812	+	0.0628227i
$880$	−7.11368	+	12.3212i	−0.239802	+	0.415349i
$881$	10.4558			0.352265			0.176132	−	0.984366i	$-0.443641\pi$
$881$	10.4558			0.352265			0.176132	+	0.984366i	$0.443641\pi$
$882$	−5.53948	−	4.27950i	−0.186524	−	0.144098i
$883$	−22.2786			−0.749736			−0.374868	−	0.927078i	$-0.622312\pi$
$883$	−22.2786			−0.749736			−0.374868	+	0.927078i	$0.622312\pi$
$884$	0.00634597	−	0.892012i	0.000213438	−	0.0300016i
$885$	−10.0279	−	17.3688i	−0.337084	−	0.583847i
$886$	29.5842	−	17.0804i	0.993901	−	0.573829i
$887$	−20.8726	+	36.1524i	−0.700832	+	1.21388i	0.267342	+	0.963602i	$0.413855\pi$
$887$	−20.8726	+	36.1524i	−0.700832	+	1.21388i	−0.968175	+	0.250276i	$0.919479\pi$
$888$	−8.10436			−0.271965
$889$	15.1971	−	22.6637i	0.509696	−	0.760116i
$890$			14.1731i			0.475082i
$891$	4.88772	+	2.82193i	0.163745	+	0.0945381i
$892$	−6.20734	+	3.58381i	−0.207837	+	0.119995i
$893$	−10.4371	−	18.0776i	−0.349264	−	0.604942i
$894$	0.937732	−	1.62420i	0.0313624	−	0.0543213i
$895$			11.8641i			0.396573i
$896$	2.37482	−	1.16630i	0.0793370	−	0.0389633i
$897$	11.2936	−	6.41366i	0.377081	−	0.214146i
$898$	14.5424	−	25.1882i	0.485286	−	0.840540i
$899$	22.5308	−	13.0081i	0.751443	−	0.433846i
$900$	−0.677364	−	1.17323i	−0.0225788	−	0.0391076i
$901$	0.811619	−	1.40577i	0.0270390	−	0.0468328i
$902$			48.5325i			1.61595i
$903$	14.6800	+	0.986329i	0.488520	+	0.0328230i
$904$		−	10.0373i		−	0.333837i
$905$	34.1440	+	19.7131i	1.13499	+	0.655285i
$906$	−1.35504	−	2.34699i	−0.0450181	−	0.0779736i
$907$	24.6748	+	42.7379i	0.819312	+	1.41909i	0.906190	+	0.422871i	$0.138978\pi$
$907$	24.6748	+	42.7379i	0.819312	+	1.41909i	−0.0868777	+	0.996219i	$0.527689\pi$
$908$	18.6007	+	10.7391i	0.617287	+	0.356391i
$909$	11.5194			0.382076
$910$	−21.6598	+	10.4468i	−0.718014	+	0.346307i
$911$	15.7093			0.520473			0.260237	−	0.965545i	$-0.416199\pi$
$911$	15.7093			0.520473			0.260237	+	0.965545i	$0.416199\pi$
$912$	−2.70459	−	1.56150i	−0.0895580	−	0.0517063i
$913$	1.86948	+	3.23804i	0.0618709	+	0.107164i
$914$	17.7460	+	30.7370i	0.586986	+	1.01669i
$915$	27.9187	+	16.1189i	0.922963	+	0.532873i
$916$			8.26740i			0.273163i
$917$	21.5740	+	43.9290i	0.712436	+	1.45066i
$918$			0.247406i			0.00816561i
$919$	−16.4337	+	28.4639i	−0.542096	+	0.938938i	0.456687	+	0.889627i	$0.349036\pi$
$919$	−16.4337	+	28.4639i	−0.542096	+	0.938938i	−0.998783	+	0.0493110i	$0.984297\pi$
$920$	−4.54024	−	7.86392i	−0.149687	−	0.259266i
$921$	−18.1955	+	10.5052i	−0.599562	+	0.346157i
$922$	3.78690	−	6.55910i	0.124715	−	0.216012i
$923$	7.23635	+	12.7422i	0.238187	+	0.419415i
$924$	−12.4021	−	8.31623i	−0.407999	−	0.273584i
$925$		−	10.9792i		−	0.360994i
$926$	−12.5149	+	21.6765i	−0.411266	+	0.712334i
$927$	2.89422	+	5.01294i	0.0950587	+	0.164646i
$928$	−3.67970	+	2.12447i	−0.120792	+	0.0697393i
$929$	−13.5536	−	7.82520i	−0.444680	−	0.256736i	0.260901	−	0.965366i	$-0.415981\pi$
$929$	−13.5536	−	7.82520i	−0.444680	−	0.256736i	−0.705581	+	0.708629i	$0.749314\pi$
$930$		−	15.4352i		−	0.506140i
$931$	2.92441	−	21.6645i	0.0958436	−	0.710024i
$932$	−26.8920			−0.880877
$933$	−3.19739	+	5.53804i	−0.104678	+	0.181307i
$934$	−27.0778	+	15.6334i	−0.886013	+	0.511540i
$935$	1.75997	+	3.04835i	0.0575570	+	0.0996917i
$936$	−3.60546	−	0.0256500i	−0.117848	−	0.000838397i
$937$	3.71754			0.121447			0.0607233	−	0.998155i	$-0.480659\pi$
$937$	3.71754			0.121447			0.0607233	+	0.998155i	$0.480659\pi$
$938$	17.9608	−	26.7852i	0.586442	−	0.874568i
$939$	−15.4737			−0.504965
$940$	−8.42474	+	14.5921i	−0.274785	+	0.475941i
$941$	−34.6486	+	20.0044i	−1.12951	+	0.652124i	−0.943812	−	0.330482i	$-0.892789\pi$
$941$	−34.6486	+	20.0044i	−1.12951	+	0.652124i	−0.185700	+	0.982607i	$0.559455\pi$
$942$	14.8121	−	8.55178i	0.482605	−	0.278632i
$943$	−26.8255	−	15.4877i	−0.873557	−	0.504348i
$944$			7.95594i			0.258944i
$945$	5.98657	−	2.94007i	0.194743	−	0.0956406i
$946$	31.3856			1.02044
$947$	20.0418	+	11.5712i	0.651272	+	0.376012i	0.788943	−	0.614466i	$-0.210628\pi$
$947$	20.0418	+	11.5712i	0.651272	+	0.376012i	−0.137671	+	0.990478i	$0.543962\pi$
$948$	3.22763	+	5.59041i	0.104828	+	0.181568i
$949$	−14.3671	+	24.4807i	−0.466376	+	0.794676i
$950$	2.11540	−	3.66399i	0.0686328	−	0.118875i
$951$			18.8914i			0.612595i
$952$	0.0438810	−	0.653102i	0.00142219	−	0.0211672i
$953$	−9.61707			−0.311527			−0.155764	−	0.987794i	$-0.549784\pi$
$953$	−9.61707			−0.311527			−0.155764	+	0.987794i	$0.549784\pi$
$954$	−5.68202	−	3.28052i	−0.183962	−	0.106211i
$955$	19.5976	−	11.3147i	0.634165	−	0.366135i
$956$	3.78867	−	2.18739i	0.122534	−	0.0707453i
$957$	20.7677	+	11.9902i	0.671323	+	0.387589i
$958$	−15.5185			−0.501380
$959$	2.43036	−	36.1723i	0.0784805	−	1.16806i
$960$			2.52086i			0.0813604i
$961$	3.24552	−	5.62141i	0.104694	−	0.181336i
$962$	−25.2013	−	14.7900i	−0.812522	−	0.476849i
$963$	7.96501	+	13.7958i	0.256669	+	0.444563i
$964$	1.33779	+	0.772373i	0.0430873	+	0.0248765i
$965$	−17.7473			−0.571305
$966$	8.55441	−	4.20116i	0.275233	−	0.135170i
$967$			19.4428i			0.625238i	0.949879	+	0.312619i	$0.101206\pi$
$967$			19.4428i			0.625238i	−0.949879	+	0.312619i	$0.898794\pi$
$968$	−18.0593	−	10.4265i	−0.580447	−	0.335121i
$969$	−0.669132	+	0.386323i	−0.0214956	+	0.0124105i
$970$	−36.8398	+	21.2695i	−1.18285	+	0.682922i
$971$	−18.4152	+	31.8960i	−0.590971	+	1.02359i	0.403131	+	0.915142i	$0.367922\pi$
$971$	−18.4152	+	31.8960i	−0.590971	+	1.02359i	−0.994102	+	0.108450i	$0.965411\pi$
$972$	1.00000			0.0320750
$973$	−11.8097	+	17.6120i	−0.378603	+	0.564615i
$974$	−32.3861			−1.03772
$975$	0.0347488	−	4.88442i	0.00111285	−	0.156427i
$976$	−6.39419	−	11.0751i	−0.204673	−	0.354504i
$977$	23.3376	−	13.4740i	0.746635	−	0.431070i	−0.0778417	−	0.996966i	$-0.524803\pi$
$977$	23.3376	−	13.4740i	0.746635	−	0.431070i	0.824477	+	0.565896i	$0.191470\pi$
$978$	−9.30258	+	16.1125i	−0.297464	+	0.515222i
$979$	−31.7315			−1.01414
$980$	−16.3248	+	6.69940i	−0.521477	+	0.214004i
$981$			1.48068i			0.0472746i
$982$	7.98524	+	4.61028i	0.254819	+	0.147120i
$983$	−45.1202	+	26.0502i	−1.43911	+	0.830872i	−0.997788	−	0.0664765i	$-0.978824\pi$
$983$	−45.1202	+	26.0502i	−1.43911	+	0.830872i	−0.441324	+	0.897348i	$0.645491\pi$
$984$	4.29959	+	7.44710i	0.137066	+	0.237405i
$985$	14.7597	−	25.5646i	0.470284	−	0.814555i
$986$			1.05122i			0.0334775i
$987$	−14.6878	−	9.84892i	−0.467519	−	0.313495i
$988$	−5.56054	−	9.79135i	−0.176904	−	0.311504i
$989$	−10.0158	+	17.3479i	−0.318484	+	0.551630i
$990$	12.3212	−	7.11368i	0.391595	−	0.226087i
$991$	18.7490	+	32.4743i	0.595583	+	1.03158i	0.993464	+	0.114143i	$0.0364123\pi$
$991$	18.7490	+	32.4743i	0.595583	+	1.03158i	−0.397881	+	0.917437i	$0.630254\pi$
$992$	−3.06150	+	5.30267i	−0.0972026	+	0.168360i
$993$		−	25.5969i		−	0.812295i
$994$	4.74005	+	9.65169i	0.150345	+	0.306133i
$995$			45.6314i			1.44661i
$996$	0.573729	+	0.331243i	0.0181793	+	0.0104958i
$997$	−3.03388	−	5.25484i	−0.0960840	−	0.166422i	0.813976	−	0.580898i	$-0.197298\pi$
$997$	−3.03388	−	5.25484i	−0.0960840	−	0.166422i	−0.910061	+	0.414475i	$0.863965\pi$
$998$	−3.78999	−	6.56445i	−0.119970	−	0.207794i
$999$	7.01858	+	4.05218i	0.222058	+	0.128205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.c.415.2	yes	20
3.2	odd	2		1638.2.dm.e.415.9		20
7.2	even	3		3822.2.c.m.883.9		10
7.4	even	3	inner	546.2.bk.c.25.9	yes	20
7.5	odd	6		3822.2.c.n.883.7		10
13.12	even	2	inner	546.2.bk.c.415.9	yes	20
21.11	odd	6		1638.2.dm.e.1117.2		20
39.38	odd	2		1638.2.dm.e.415.2		20
91.12	odd	6		3822.2.c.n.883.4		10
91.25	even	6	inner	546.2.bk.c.25.2	✓	20
91.51	even	6		3822.2.c.m.883.2		10
273.116	odd	6		1638.2.dm.e.1117.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.c.25.2	✓	20	91.25	even	6	inner
546.2.bk.c.25.9	yes	20	7.4	even	3	inner
546.2.bk.c.415.2	yes	20	1.1	even	1	trivial
546.2.bk.c.415.9	yes	20	13.12	even	2	inner
1638.2.dm.e.415.2		20	39.38	odd	2
1638.2.dm.e.415.9		20	3.2	odd	2
1638.2.dm.e.1117.2		20	21.11	odd	6
1638.2.dm.e.1117.9		20	273.116	odd	6
3822.2.c.m.883.2		10	91.51	even	6
3822.2.c.m.883.9		10	7.2	even	3
3822.2.c.n.883.4		10	91.12	odd	6
3822.2.c.n.883.7		10	7.5	odd	6

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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.18313 - 1.26043i) q^{5} -1.00000i q^{6} +(1.47350 - 2.19745i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.18313 - 1.26043i) q^{5} -1.00000i q^{6} +(1.47350 - 2.19745i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.26043 + 2.18313i) q^{10} +(-4.88772 + 2.82193i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.13524 + 1.78052i) q^{13} +(-2.37482 + 1.16630i) q^{14} -2.52086i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.123703 + 0.214260i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.70459 + 1.56150i) q^{19} -2.52086i q^{20} +(2.63980 + 0.177364i) q^{21} +5.64385 q^{22} +(-1.80107 + 3.11954i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.677364 + 1.17323i) q^{25} +(3.60546 + 0.0256500i) q^{26} -1.00000 q^{27} +(2.63980 + 0.177364i) q^{28} -4.24895 q^{29} +(-1.26043 + 2.18313i) q^{30} +(-5.30267 + 3.06150i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.88772 - 2.82193i) q^{33} -0.247406i q^{34} +(-5.98657 + 2.94007i) q^{35} -1.00000 q^{36} +(-7.01858 - 4.05218i) q^{37} +(-1.56150 - 2.70459i) q^{38} +(-3.10959 - 1.82494i) q^{39} +(-1.26043 + 2.18313i) q^{40} +8.59917i q^{41} +(-2.19745 - 1.47350i) q^{42} +5.56103 q^{43} +(-4.88772 - 2.82193i) q^{44} +(2.18313 - 1.26043i) q^{45} +(3.11954 - 1.80107i) q^{46} +(-5.78854 - 3.34201i) q^{47} -1.00000 q^{48} +(-2.65759 - 6.47590i) q^{49} -1.35473i q^{50} +(-0.123703 + 0.214260i) q^{51} +(-3.10959 - 1.82494i) q^{52} +(-3.28052 - 5.68202i) q^{53} +(0.866025 + 0.500000i) q^{54} +14.2274 q^{55} +(-2.19745 - 1.47350i) q^{56} +3.12299i q^{57} +(3.67970 + 2.12447i) q^{58} +(6.89004 - 3.97797i) q^{59} +(2.18313 - 1.26043i) q^{60} +(-6.39419 + 11.0751i) q^{61} +6.12299 q^{62} +(1.16630 + 2.37482i) q^{63} -1.00000 q^{64} +(9.08886 + 0.0646601i) q^{65} +(2.82193 + 4.88772i) q^{66} +(-10.5562 + 6.09461i) q^{67} +(-0.123703 + 0.214260i) q^{68} -3.60213 q^{69} +(6.65456 + 0.447110i) q^{70} -4.06419i q^{71} +(0.866025 + 0.500000i) q^{72} +(6.81789 - 3.93631i) q^{73} +(4.05218 + 7.01858i) q^{74} +(-0.677364 + 1.17323i) q^{75} +3.12299i q^{76} +(-1.00102 + 14.8986i) q^{77} +(1.78052 + 3.13524i) q^{78} +(3.22763 - 5.59041i) q^{79} +(2.18313 - 1.26043i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29959 - 7.44710i) q^{82} -0.662485i q^{83} +(1.16630 + 2.37482i) q^{84} -0.623675i q^{85} +(-4.81600 - 2.78052i) q^{86} +(-2.12447 - 3.67970i) q^{87} +(2.82193 + 4.88772i) q^{88} +(4.86906 + 2.81116i) q^{89} -2.52086 q^{90} +(-0.707191 + 9.51314i) q^{91} -3.60213 q^{92} +(-5.30267 - 3.06150i) q^{93} +(3.34201 + 5.78854i) q^{94} +(-3.93631 - 6.81789i) q^{95} +(0.866025 + 0.500000i) q^{96} +16.8748i q^{97} +(-0.936412 + 6.93708i) q^{98} -5.64385i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9	\( 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9} + 4 q^{10} - 10 q^{12} + 4 q^{13} - 2 q^{14} - 10 q^{16} - 6 q^{17} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 4 q^{26} - 20 q^{27} - 28 q^{29} - 4 q^{30} + 16 q^{35} - 20 q^{36} + 10 q^{38} + 2 q^{39} - 4 q^{40} - 10 q^{42} + 24 q^{43} - 20 q^{48} + 2 q^{49} + 6 q^{51} + 2 q^{52} - 22 q^{53} + 88 q^{55} - 10 q^{56} + 14 q^{61} + 40 q^{62} - 20 q^{64} + 20 q^{65} - 6 q^{66} + 6 q^{68} - 32 q^{69} + 24 q^{74} - 2 q^{75} - 28 q^{77} - 8 q^{78} + 4 q^{79} - 10 q^{81} + 12 q^{82} - 14 q^{87} - 6 q^{88} - 8 q^{90} + 68 q^{91} - 32 q^{92} - 18 q^{94} + 8 q^{95}+O(q^{100}) \) 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9 + 4 * q^10 - 10 * q^12 + 4 * q^13 - 2 * q^14 - 10 * q^16 - 6 * q^17 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 4 * q^26 - 20 * q^27 - 28 * q^29 - 4 * q^30 + 16 * q^35 - 20 * q^36 + 10 * q^38 + 2 * q^39 - 4 * q^40 - 10 * q^42 + 24 * q^43 - 20 * q^48 + 2 * q^49 + 6 * q^51 + 2 * q^52 - 22 * q^53 + 88 * q^55 - 10 * q^56 + 14 * q^61 + 40 * q^62 - 20 * q^64 + 20 * q^65 - 6 * q^66 + 6 * q^68 - 32 * q^69 + 24 * q^74 - 2 * q^75 - 28 * q^77 - 8 * q^78 + 4 * q^79 - 10 * q^81 + 12 * q^82 - 14 * q^87 - 6 * q^88 - 8 * q^90 + 68 * q^91 - 32 * q^92 - 18 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more