LMFDB - Embedded newform 546.2.bk.c.25.5

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			25.5
Root			$2.62200 + 1.51381i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.c.415.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.62200 - 1.51381i) q^{5} +1.00000i q^{6} +(2.43101 + 1.04411i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.62200 - 1.51381i) q^{5} +1.00000i q^{6} +(2.43101 + 1.04411i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.51381 + 2.62200i) q^{10} +(3.75189 + 2.16615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.613563 + 3.55296i) q^{13} +(-2.62738 + 0.311278i) q^{14} -3.02763i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.721788 + 1.25017i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-1.12988 + 0.652339i) q^{19} -3.02763i q^{20} +(2.11974 - 1.58326i) q^{21} -4.33230 q^{22} +(-2.36147 - 4.09019i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.08326 - 3.60832i) q^{25} +(-1.24512 - 3.38374i) q^{26} -1.00000 q^{27} +(2.11974 - 1.58326i) q^{28} +3.42053 q^{29} +(1.51381 + 2.62200i) q^{30} +(-1.46819 - 0.847661i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.75189 - 2.16615i) q^{33} -1.44358i q^{34} +(7.95472 - 0.942433i) q^{35} -1.00000 q^{36} +(-9.89112 + 5.71064i) q^{37} +(0.652339 - 1.12988i) q^{38} +(2.77017 + 2.30784i) q^{39} +(1.51381 + 2.62200i) q^{40} -8.53413i q^{41} +(-1.04411 + 2.43101i) q^{42} -5.10592 q^{43} +(3.75189 - 2.16615i) q^{44} +(-2.62200 - 1.51381i) q^{45} +(4.09019 + 2.36147i) q^{46} +(7.28379 - 4.20530i) q^{47} -1.00000 q^{48} +(4.81965 + 5.07651i) q^{49} +4.16653i q^{50} +(0.721788 + 1.25017i) q^{51} +(2.77017 + 2.30784i) q^{52} +(2.05296 - 3.55583i) q^{53} +(0.866025 - 0.500000i) q^{54} +13.1166 q^{55} +(-1.04411 + 2.43101i) q^{56} +1.30468i q^{57} +(-2.96227 + 1.71027i) q^{58} +(-4.34545 - 2.50885i) q^{59} +(-2.62200 - 1.51381i) q^{60} +(-0.505338 - 0.875271i) q^{61} +1.69532 q^{62} +(-0.311278 - 2.62738i) q^{63} -1.00000 q^{64} +(3.76976 + 10.2447i) q^{65} +(-2.16615 + 3.75189i) q^{66} +(-0.412703 - 0.238274i) q^{67} +(0.721788 + 1.25017i) q^{68} -4.72295 q^{69} +(-6.41777 + 4.79353i) q^{70} +12.4996i q^{71} +(0.866025 - 0.500000i) q^{72} +(3.42087 + 1.97504i) q^{73} +(5.71064 - 9.89112i) q^{74} +(-2.08326 - 3.60832i) q^{75} +1.30468i q^{76} +(6.85917 + 9.18334i) q^{77} +(-3.55296 - 0.613563i) q^{78} +(-7.34649 - 12.7245i) q^{79} +(-2.62200 - 1.51381i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.26706 + 7.39077i) q^{82} -17.0583i q^{83} +(-0.311278 - 2.62738i) q^{84} +4.37061i q^{85} +(4.42186 - 2.55296i) q^{86} +(1.71027 - 2.96227i) q^{87} +(-2.16615 + 3.75189i) q^{88} +(-6.04482 + 3.48998i) q^{89} +3.02763 q^{90} +(-5.20128 + 7.99667i) q^{91} -4.72295 q^{92} +(-1.46819 + 0.847661i) q^{93} +(-4.20530 + 7.28379i) q^{94} +(-1.97504 + 3.42087i) q^{95} +(0.866025 - 0.500000i) q^{96} +15.9110i q^{97} +(-6.71220 - 1.98656i) q^{98} -4.33230i 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$5$	2.62200	−	1.51381i	1.17259	−	0.676998i	0.218305	−	0.975881i	$-0.429947\pi$
$5$	2.62200	−	1.51381i	1.17259	−	0.676998i	0.954290	+	0.298883i	$0.0966139\pi$
$6$			1.00000i			0.408248i
$7$	2.43101	+	1.04411i	0.918837	+	0.394638i
$7$	2.43101	+	1.04411i	0.918837	+	0.394638i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.51381	+	2.62200i	−0.478710	+	0.829150i
$11$	3.75189	+	2.16615i	1.13124	+	0.653119i	0.944245	−	0.329242i	$-0.106793\pi$
$11$	3.75189	+	2.16615i	1.13124	+	0.653119i	0.186991	+	0.982362i	$0.440127\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−0.613563	+	3.55296i	−0.170172	+	0.985414i
$13$	−0.613563	+	3.55296i	−0.170172	+	0.985414i
$14$	−2.62738	+	0.311278i	−0.702196	+	0.0831925i
$15$		−	3.02763i		−	0.781730i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.721788	+	1.25017i	−0.175059	+	0.303211i	−0.940182	−	0.340673i	$-0.889345\pi$
$17$	−0.721788	+	1.25017i	−0.175059	+	0.303211i	0.765123	+	0.643885i	$0.222678\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−1.12988	+	0.652339i	−0.259213	+	0.149657i	−0.623976	−	0.781444i	$-0.714484\pi$
$19$	−1.12988	+	0.652339i	−0.259213	+	0.149657i	0.364762	+	0.931101i	$0.381150\pi$
$20$		−	3.02763i		−	0.676998i
$21$	2.11974	−	1.58326i	0.462564	−	0.345496i
$22$	−4.33230			−0.923650
$23$	−2.36147	−	4.09019i	−0.492402	−	0.852865i	0.507560	−	0.861616i	$-0.330548\pi$
$23$	−2.36147	−	4.09019i	−0.492402	−	0.852865i	−0.999962	+	0.00875181i	$0.997214\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.08326	−	3.60832i	0.416653	−	0.721663i
$26$	−1.24512	−	3.38374i	−0.244188	−	0.663605i
$27$	−1.00000			−0.192450
$28$	2.11974	−	1.58326i	0.400592	−	0.299208i
$29$	3.42053			0.635177			0.317588	−	0.948229i	$-0.397127\pi$
$29$	3.42053			0.635177			0.317588	+	0.948229i	$0.397127\pi$
$30$	1.51381	+	2.62200i	0.276383	+	0.478710i
$31$	−1.46819	−	0.847661i	−0.263695	−	0.152244i	0.362324	−	0.932052i	$-0.381983\pi$
$31$	−1.46819	−	0.847661i	−0.263695	−	0.152244i	−0.626019	+	0.779808i	$0.715317\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.75189	−	2.16615i	0.653119	−	0.377079i
$34$		−	1.44358i		−	0.247571i
$35$	7.95472	−	0.942433i	1.34459	−	0.159300i
$36$	−1.00000			−0.166667
$37$	−9.89112	+	5.71064i	−1.62609	+	0.938823i	−0.640845	+	0.767670i	$0.721416\pi$
$37$	−9.89112	+	5.71064i	−1.62609	+	0.938823i	−0.985244	+	0.171153i	$0.945251\pi$
$38$	0.652339	−	1.12988i	0.105823	−	0.183291i
$39$	2.77017	+	2.30784i	0.443583	+	0.369550i
$40$	1.51381	+	2.62200i	0.239355	+	0.414575i
$41$		−	8.53413i		−	1.33281i	−0.745591	−	0.666403i	$-0.767833\pi$
$41$		−	8.53413i		−	1.33281i	0.745591	−	0.666403i	$-0.232167\pi$
$42$	−1.04411	+	2.43101i	−0.161110	+	0.375114i
$43$	−5.10592			−0.778646			−0.389323	−	0.921101i	$-0.627291\pi$
$43$	−5.10592			−0.778646			−0.389323	+	0.921101i	$0.627291\pi$
$44$	3.75189	−	2.16615i	0.565618	−	0.326560i
$45$	−2.62200	−	1.51381i	−0.390865	−	0.225666i
$46$	4.09019	+	2.36147i	0.603066	+	0.348180i
$47$	7.28379	−	4.20530i	1.06245	−	0.613406i	0.136342	−	0.990662i	$-0.456466\pi$
$47$	7.28379	−	4.20530i	1.06245	−	0.613406i	0.926109	+	0.377256i	$0.123132\pi$
$48$	−1.00000			−0.144338
$49$	4.81965	+	5.07651i	0.688522	+	0.725216i
$50$			4.16653i			0.589236i
$51$	0.721788	+	1.25017i	0.101070	+	0.175059i
$52$	2.77017	+	2.30784i	0.384154	+	0.320040i
$53$	2.05296	−	3.55583i	0.281996	−	0.488431i	−0.689880	−	0.723924i	$-0.742337\pi$
$53$	2.05296	−	3.55583i	0.281996	−	0.488431i	0.971876	+	0.235492i	$0.0756702\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	13.1166			1.76864
$56$	−1.04411	+	2.43101i	−0.139526	+	0.324858i
$57$			1.30468i			0.172809i
$58$	−2.96227	+	1.71027i	−0.388965	+	0.224569i
$59$	−4.34545	−	2.50885i	−0.565730	−	0.326624i	0.189712	−	0.981840i	$-0.439244\pi$
$59$	−4.34545	−	2.50885i	−0.565730	−	0.326624i	−0.755442	+	0.655215i	$0.772578\pi$
$60$	−2.62200	−	1.51381i	−0.338499	−	0.195432i
$61$	−0.505338	−	0.875271i	−0.0647019	−	0.112067i	0.831860	−	0.554986i	$-0.187276\pi$
$61$	−0.505338	−	0.875271i	−0.0647019	−	0.112067i	−0.896562	+	0.442919i	$0.853943\pi$
$62$	1.69532			0.215306
$63$	−0.311278	−	2.62738i	−0.0392173	−	0.331018i
$64$	−1.00000			−0.125000
$65$	3.76976	+	10.2447i	0.467581	+	1.27070i
$66$	−2.16615	+	3.75189i	−0.266635	+	0.461825i
$67$	−0.412703	−	0.238274i	−0.0504197	−	0.0291098i	0.474578	−	0.880213i	$-0.342601\pi$
$67$	−0.412703	−	0.238274i	−0.0504197	−	0.0291098i	−0.524998	+	0.851103i	$0.675934\pi$
$68$	0.721788	+	1.25017i	0.0875296	+	0.151606i
$69$	−4.72295			−0.568576
$70$	−6.41777	+	4.79353i	−0.767070	+	0.572936i
$71$			12.4996i			1.48343i	0.670717	+	0.741713i	$0.265986\pi$
$71$			12.4996i			1.48343i	−0.670717	+	0.741713i	$0.734014\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	3.42087	+	1.97504i	0.400382	+	0.231161i	0.686649	−	0.726989i	$-0.259081\pi$
$73$	3.42087	+	1.97504i	0.400382	+	0.231161i	−0.286267	+	0.958150i	$0.592414\pi$
$74$	5.71064	−	9.89112i	0.663848	−	1.14982i
$75$	−2.08326	−	3.60832i	−0.240554	−	0.416653i
$76$			1.30468i			0.149657i
$77$	6.85917	+	9.18334i	0.781675	+	1.04654i
$78$	−3.55296	−	0.613563i	−0.402294	−	0.0694723i
$79$	−7.34649	−	12.7245i	−0.826545	−	1.43162i	−0.900733	−	0.434373i	$-0.856970\pi$
$79$	−7.34649	−	12.7245i	−0.826545	−	1.43162i	0.0741882	−	0.997244i	$-0.476363\pi$
$80$	−2.62200	−	1.51381i	−0.293149	−	0.169249i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.26706	+	7.39077i	0.471218	+	0.816174i
$83$		−	17.0583i		−	1.87239i	−0.351485	−	0.936194i	$-0.614323\pi$
$83$		−	17.0583i		−	1.87239i	0.351485	−	0.936194i	$-0.385677\pi$
$84$	−0.311278	−	2.62738i	−0.0339632	−	0.286670i
$85$			4.37061i			0.474059i
$86$	4.42186	−	2.55296i	0.476821	−	0.275293i
$87$	1.71027	−	2.96227i	0.183360	−	0.317588i
$88$	−2.16615	+	3.75189i	−0.230913	+	0.399952i
$89$	−6.04482	+	3.48998i	−0.640750	+	0.369937i	−0.784903	−	0.619618i	$-0.787287\pi$
$89$	−6.04482	+	3.48998i	−0.640750	+	0.369937i	0.144153	+	0.989555i	$0.453954\pi$
$90$	3.02763			0.319140
$91$	−5.20128	+	7.99667i	−0.545242	+	0.838279i
$92$	−4.72295			−0.492402
$93$	−1.46819	+	0.847661i	−0.152244	+	0.0878984i
$94$	−4.20530	+	7.28379i	−0.433744	+	0.751266i
$95$	−1.97504	+	3.42087i	−0.202635	+	0.350973i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$			15.9110i			1.61552i	0.589513	+	0.807759i	$0.299320\pi$
$97$			15.9110i			1.61552i	−0.589513	+	0.807759i	$0.700680\pi$
$98$	−6.71220	−	1.98656i	−0.678034	−	0.200673i
$99$		−	4.33230i		−	0.435413i
$100$	−2.08326	−	3.60832i	−0.208326	−	0.360832i
$101$	0.596703	−	1.03352i	0.0593742	−	0.102839i	−0.834810	−	0.550537i	$-0.814423\pi$
$101$	0.596703	−	1.03352i	0.0593742	−	0.102839i	0.894185	+	0.447698i	$0.147756\pi$
$102$	−1.25017	−	0.721788i	−0.123786	−	0.0714676i
$103$	−7.58706	−	13.1412i	−0.747575	−	1.29484i	−0.948982	−	0.315330i	$-0.897885\pi$
$103$	−7.58706	−	13.1412i	−0.747575	−	1.29484i	0.201407	−	0.979508i	$-0.435449\pi$
$104$	−3.55296	−	0.613563i	−0.348397	−	0.0601648i
$105$	3.16119	−	7.36020i	0.308500	−	0.718282i
$106$			4.10592i			0.398803i
$107$	−4.00998	−	6.94549i	−0.387659	−	0.671445i	0.604475	−	0.796624i	$-0.293383\pi$
$107$	−4.00998	−	6.94549i	−0.387659	−	0.671445i	−0.992134	+	0.125179i	$0.960050\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	0.909907	+	0.525335i	0.0871533	+	0.0503180i	0.542943	−	0.839769i	$-0.317310\pi$
$109$	0.909907	+	0.525335i	0.0871533	+	0.0503180i	−0.455790	+	0.890087i	$0.650643\pi$
$110$	−11.3593	+	6.55830i	−1.08307	+	0.625309i
$111$			11.4213i			1.08406i
$112$	−0.311278	−	2.62738i	−0.0294130	−	0.248264i
$113$	−9.40986			−0.885205			−0.442602	−	0.896718i	$-0.645945\pi$
$113$	−9.40986			−0.885205			−0.442602	+	0.896718i	$0.645945\pi$
$114$	−0.652339	−	1.12988i	−0.0610971	−	0.105823i
$115$	−12.3836	−	7.14967i	−1.15478	−	0.666710i
$116$	1.71027	−	2.96227i	0.158794	−	0.275040i
$117$	3.38374	−	1.24512i	0.312827	−	0.115111i
$118$	5.01770			0.461916
$119$	−3.06000	+	2.28556i	−0.280510	+	0.209517i
$120$	3.02763			0.276383
$121$	3.88443	+	6.72803i	0.353130	+	0.611639i
$122$	0.875271	+	0.505338i	0.0792433	+	0.0457512i
$123$	−7.39077	−	4.26706i	−0.666403	−	0.384748i
$124$	−1.46819	+	0.847661i	−0.131848	+	0.0761222i
$125$			2.52345i			0.225704i
$126$	1.58326	+	2.11974i	0.141048	+	0.188841i
$127$	1.33765			0.118697			0.0593487	−	0.998237i	$-0.481098\pi$
$127$	1.33765			0.118697			0.0593487	+	0.998237i	$0.481098\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.55296	+	4.42186i	−0.224776	+	0.389323i
$130$	−8.38705	−	6.98728i	−0.735593	−	0.612825i
$131$	−6.17186	−	10.6900i	−0.539238	−	0.933988i	−0.998945	−	0.0459173i	$-0.985379\pi$
$131$	−6.17186	−	10.6900i	−0.539238	−	0.933988i	0.459707	−	0.888071i	$-0.347954\pi$
$132$		−	4.33230i		−	0.377079i
$133$	−3.42788	+	0.406117i	−0.297235	+	0.0352148i
$134$	0.476549			0.0411675
$135$	−2.62200	+	1.51381i	−0.225666	+	0.130288i
$136$	−1.25017	−	0.721788i	−0.107201	−	0.0618928i
$137$	−7.91249	−	4.56828i	−0.676010	−	0.390294i	0.122340	−	0.992488i	$-0.460960\pi$
$137$	−7.91249	−	4.56828i	−0.676010	−	0.390294i	−0.798350	+	0.602194i	$0.794293\pi$
$138$	4.09019	−	2.36147i	0.348180	−	0.201022i
$139$	17.8219			1.51164			0.755819	−	0.654781i	$-0.227239\pi$
$139$	17.8219			1.51164			0.755819	+	0.654781i	$0.227239\pi$
$140$	3.16119	−	7.36020i	0.267169	−	0.622051i
$141$		−	8.41060i		−	0.708300i
$142$	−6.24979	−	10.8249i	−0.524471	−	0.908410i
$143$	−9.99827	+	12.0012i	−0.836098	+	1.00359i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	8.96864	−	5.17805i	0.744805	−	0.430013i
$146$	−3.95008			−0.326911
$147$	6.80621	−	1.63569i	0.561367	−	0.134909i
$148$			11.4213i			0.938823i
$149$	10.6362	−	6.14082i	0.871352	−	0.503075i	0.00355471	−	0.999994i	$-0.498868\pi$
$149$	10.6362	−	6.14082i	0.871352	−	0.503075i	0.867797	+	0.496918i	$0.165535\pi$
$150$	3.60832	+	2.08326i	0.294618	+	0.170098i
$151$	−12.6016	−	7.27554i	−1.02550	−	0.592075i	−0.109811	−	0.993953i	$-0.535024\pi$
$151$	−12.6016	−	7.27554i	−1.02550	−	0.592075i	−0.915693	+	0.401878i	$0.868358\pi$
$152$	−0.652339	−	1.12988i	−0.0529116	−	0.0916457i
$153$	1.44358			0.116706
$154$	−10.5319	−	4.52342i	−0.848684	−	0.364507i
$155$	−5.13281			−0.412277
$156$	3.38374	−	1.24512i	0.270916	−	0.0996894i
$157$	−4.81431	+	8.33864i	−0.384224	+	0.665496i	−0.991661	−	0.128872i	$-0.958864\pi$
$157$	−4.81431	+	8.33864i	−0.384224	+	0.665496i	0.607437	+	0.794368i	$0.292198\pi$
$158$	12.7245	+	7.34649i	1.01231	+	0.584455i
$159$	−2.05296	−	3.55583i	−0.162810	−	0.281996i
$160$	3.02763			0.239355
$161$	−1.47015	−	12.4090i	−0.115864	−	0.977964i
$162$		−	1.00000i		−	0.0785674i
$163$	−14.6824	+	8.47691i	−1.15002	+	0.663963i	−0.948892	−	0.315602i	$-0.897793\pi$
$163$	−14.6824	+	8.47691i	−1.15002	+	0.663963i	−0.201126	+	0.979565i	$0.564460\pi$
$164$	−7.39077	−	4.26706i	−0.577122	−	0.333202i
$165$	6.55830	−	11.3593i	0.510563	−	0.884321i
$166$	8.52913	+	14.7729i	0.661989	+	1.14660i
$167$			23.4489i			1.81453i	0.420559	+	0.907265i	$0.361834\pi$
$167$			23.4489i			1.81453i	−0.420559	+	0.907265i	$0.638166\pi$
$168$	1.58326	+	2.11974i	0.122151	+	0.163541i
$169$	−12.2471	−	4.35993i	−0.942083	−	0.335379i
$170$	−2.18530	−	3.78506i	−0.167605	−	0.290301i
$171$	1.12988	+	0.652339i	0.0864044	+	0.0498856i
$172$	−2.55296	+	4.42186i	−0.194662	+	0.337164i
$173$	8.22674	+	14.2491i	0.625468	+	1.08334i	0.988450	+	0.151546i	$0.0484252\pi$
$173$	8.22674	+	14.2491i	0.625468	+	1.08334i	−0.362982	+	0.931796i	$0.618242\pi$
$174$			3.42053i			0.259310i
$175$	8.83193	−	6.59670i	0.667631	−	0.498664i
$176$		−	4.33230i		−	0.326560i
$177$	−4.34545	+	2.50885i	−0.326624	+	0.188577i
$178$	3.48998	−	6.04482i	0.261585	−	0.453079i
$179$	−11.1435	+	19.3011i	−0.832903	+	1.44263i	0.0628236	+	0.998025i	$0.479989\pi$
$179$	−11.1435	+	19.3011i	−0.832903	+	1.44263i	−0.895726	+	0.444606i	$0.853344\pi$
$180$	−2.62200	+	1.51381i	−0.195432	+	0.112833i
$181$	12.4283			0.923788			0.461894	−	0.886935i	$-0.347170\pi$
$181$	12.4283			0.923788			0.461894	+	0.886935i	$0.347170\pi$
$182$	0.506103	−	9.52596i	0.0375148	−	0.706111i
$183$	−1.01068			−0.0747113
$184$	4.09019	−	2.36147i	0.301533	−	0.174090i
$185$	−17.2897	+	29.9466i	−1.27116	+	2.20172i
$186$	0.847661	−	1.46819i	0.0621536	−	0.107653i
$187$	−5.41613	+	3.12700i	−0.396067	+	0.228669i
$188$		−	8.41060i		−	0.613406i
$189$	−2.43101	−	1.04411i	−0.176830	−	0.0759481i
$190$		−	3.95008i		−	0.286569i
$191$	−10.7570	−	18.6317i	−0.778352	−	1.34815i	−0.932891	−	0.360159i	$-0.882722\pi$
$191$	−10.7570	−	18.6317i	−0.778352	−	1.34815i	0.154538	−	0.987987i	$-0.450611\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	1.66424	+	0.960851i	0.119795	+	0.0691636i	0.558700	−	0.829370i	$-0.311300\pi$
$193$	1.66424	+	0.960851i	0.119795	+	0.0691636i	−0.438905	+	0.898533i	$0.644634\pi$
$194$	−7.95550	−	13.7793i	−0.571172	−	0.989299i
$195$	10.7570	+	1.85764i	0.770328	+	0.133028i
$196$	6.80621	−	1.63569i	0.486158	−	0.116835i
$197$			5.55108i			0.395498i	0.980253	+	0.197749i	$0.0633631\pi$
$197$			5.55108i			0.395498i	−0.980253	+	0.197749i	$0.936637\pi$
$198$	2.16615	+	3.75189i	0.153942	+	0.266635i
$199$	−3.54486	+	6.13988i	−0.251288	+	0.435244i	−0.963881	−	0.266334i	$-0.914188\pi$
$199$	−3.54486	+	6.13988i	−0.251288	+	0.435244i	0.712592	+	0.701578i	$0.247521\pi$
$200$	3.60832	+	2.08326i	0.255147	+	0.147309i
$201$	−0.412703	+	0.238274i	−0.0291098	+	0.0168066i
$202$			1.19341i			0.0839678i
$203$	8.31536	+	3.57142i	0.583624	+	0.250665i
$204$	1.44358			0.101070
$205$	−12.9191	−	22.3765i	−0.902307	−	1.56284i
$206$	13.1412	+	7.58706i	0.915589	+	0.528615i
$207$	−2.36147	+	4.09019i	−0.164134	+	0.284288i
$208$	3.38374	−	1.24512i	0.234620	−	0.0863335i
$209$	−5.65226			−0.390975
$210$	0.942433	+	7.95472i	0.0650340	+	0.548928i
$211$	24.2839			1.67177			0.835885	−	0.548904i	$-0.184955\pi$
$211$	24.2839			1.67177			0.835885	+	0.548904i	$0.184955\pi$
$212$	−2.05296	−	3.55583i	−0.140998	−	0.244216i
$213$	10.8249	+	6.24979i	0.741713	+	0.428228i
$214$	6.94549	+	4.00998i	0.474784	+	0.274116i
$215$	−13.3877	+	7.72942i	−0.913037	+	0.527142i
$216$		−	1.00000i		−	0.0680414i
$217$	−2.68414	−	3.59364i	−0.182211	−	0.243952i
$218$	−1.05067			−0.0711604
$219$	3.42087	−	1.97504i	0.231161	−	0.133461i
$220$	6.55830	−	11.3593i	0.442161	−	0.765844i
$221$	−3.99895	−	3.33154i	−0.268999	−	0.224104i
$222$	−5.71064	−	9.89112i	−0.383273	−	0.663848i
$223$		−	2.01368i		−	0.134846i	−0.997724	−	0.0674230i	$-0.978522\pi$
$223$		−	2.01368i		−	0.134846i	0.997724	−	0.0674230i	$-0.0214777\pi$
$224$	1.58326	+	2.11974i	0.105786	+	0.141631i
$225$	−4.16653			−0.277768
$226$	8.14917	−	4.70493i	0.542075	−	0.312967i
$227$	5.33689	+	3.08125i	0.354222	+	0.204510i	0.666543	−	0.745466i	$-0.267773\pi$
$227$	5.33689	+	3.08125i	0.354222	+	0.204510i	−0.312321	+	0.949977i	$0.601107\pi$
$228$	1.12988	+	0.652339i	0.0748284	+	0.0432022i
$229$	13.1472	−	7.59052i	0.868789	−	0.501596i	0.00184346	−	0.999998i	$-0.499413\pi$
$229$	13.1472	−	7.59052i	0.868789	−	0.501596i	0.866946	+	0.498403i	$0.166080\pi$
$230$	14.2993			0.942870
$231$	11.3826	−	1.34855i	0.748920	−	0.0887280i
$232$			3.42053i			0.224569i
$233$	10.4014	+	18.0157i	0.681417	+	1.18025i	0.974549	+	0.224176i	$0.0719691\pi$
$233$	10.4014	+	18.0157i	0.681417	+	1.18025i	−0.293132	+	0.956072i	$0.594698\pi$
$234$	−2.30784	+	2.77017i	−0.150868	+	0.181092i
$235$	12.7321	−	22.0526i	0.830549	−	1.43855i
$236$	−4.34545	+	2.50885i	−0.282865	+	0.163312i
$237$	−14.6930			−0.954412
$238$	1.50726	−	3.50935i	0.0977009	−	0.227477i
$239$			6.60635i			0.427329i	0.976907	+	0.213665i	$0.0685400\pi$
$239$			6.60635i			0.427329i	−0.976907	+	0.213665i	$0.931460\pi$
$240$	−2.62200	+	1.51381i	−0.169249	+	0.0977162i
$241$	19.6527	+	11.3465i	1.26594	+	0.730892i	0.974218	−	0.225611i	$-0.0724378\pi$
$241$	19.6527	+	11.3465i	1.26594	+	0.730892i	0.291724	+	0.956503i	$0.405771\pi$
$242$	−6.72803	−	3.88443i	−0.432494	−	0.249701i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.01068			−0.0647019
$245$	20.3220	+	6.01456i	1.29833	+	0.384256i
$246$	8.53413			0.544116
$247$	−1.62448	−	4.41468i	−0.103363	−	0.280900i
$248$	0.847661	−	1.46819i	0.0538266	−	0.0932303i
$249$	−14.7729	−	8.52913i	−0.936194	−	0.540512i
$250$	−1.26173	−	2.18537i	−0.0797985	−	0.138215i
$251$	4.82111			0.304306			0.152153	−	0.988357i	$-0.451379\pi$
$251$	4.82111			0.304306			0.152153	+	0.988357i	$0.451379\pi$
$252$	−2.43101	−	1.04411i	−0.153139	−	0.0657730i
$253$		−	20.4613i		−	1.28639i
$254$	−1.15844	+	0.668825i	−0.0726870	+	0.0419658i
$255$	3.78506	+	2.18530i	0.237029	+	0.136849i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.91636	+	5.05128i	0.181917	+	0.315090i	0.942533	−	0.334112i	$-0.108436\pi$
$257$	2.91636	+	5.05128i	0.181917	+	0.315090i	−0.760616	+	0.649202i	$0.775103\pi$
$258$		−	5.10592i		−	0.317881i
$259$	−30.0080	+	3.55519i	−1.86461	+	0.220909i
$260$	10.7570	+	1.85764i	0.667124	+	0.115206i
$261$	−1.71027	−	2.96227i	−0.105863	−	0.183360i
$262$	10.6900	+	6.17186i	0.660429	+	0.381299i
$263$	6.68731	−	11.5828i	0.412357	−	0.714224i	−0.582790	−	0.812623i	$-0.698039\pi$
$263$	6.68731	−	11.5828i	0.412357	−	0.714224i	0.995147	+	0.0983992i	$0.0313722\pi$
$264$	2.16615	+	3.75189i	0.133317	+	0.230913i
$265$		−	12.4312i		−	0.763643i
$266$	2.76557	−	2.06565i	0.169568	−	0.126653i
$267$			6.97996i			0.427167i
$268$	−0.412703	+	0.238274i	−0.0252099	+	0.0145549i
$269$	−6.42254	+	11.1242i	−0.391589	+	0.678252i	−0.992659	−	0.120944i	$-0.961408\pi$
$269$	−6.42254	+	11.1242i	−0.391589	+	0.678252i	0.601070	+	0.799196i	$0.294741\pi$
$270$	1.51381	−	2.62200i	0.0921278	−	0.159570i
$271$	18.0901	−	10.4443i	1.09890	−	0.634447i	0.162965	−	0.986632i	$-0.447894\pi$
$271$	18.0901	−	10.4443i	1.09890	−	0.634447i	0.935931	+	0.352184i	$0.114561\pi$
$272$	1.44358			0.0875296
$273$	4.32468	+	8.50277i	0.261742	+	0.514611i
$274$	9.13656			0.551960
$275$	15.6323	−	9.02533i	0.942665	−	0.544248i
$276$	−2.36147	+	4.09019i	−0.142144	+	0.246201i
$277$	−13.1983	+	22.8602i	−0.793010	+	1.37353i	0.131085	+	0.991371i	$0.458154\pi$
$277$	−13.1983	+	22.8602i	−0.793010	+	1.37353i	−0.924095	+	0.382163i	$0.875179\pi$
$278$	−15.4343	+	8.91097i	−0.925685	+	0.534445i
$279$			1.69532i			0.101496i
$280$	0.942433	+	7.95472i	0.0563211	+	0.475385i
$281$			12.6024i			0.751798i	0.926661	+	0.375899i	$0.122666\pi$
$281$			12.6024i			0.751798i	−0.926661	+	0.375899i	$0.877334\pi$
$282$	4.20530	+	7.28379i	0.250422	+	0.433744i
$283$	0.0878874	−	0.152225i	0.00522437	−	0.00904887i	−0.863401	−	0.504518i	$-0.831670\pi$
$283$	0.0878874	−	0.152225i	0.00522437	−	0.00904887i	0.868626	+	0.495469i	$0.165004\pi$
$284$	10.8249	+	6.24979i	0.642343	+	0.370857i
$285$	1.97504	+	3.42087i	0.116991	+	0.202635i
$286$	2.65814	−	15.3925i	0.157179	−	0.910178i
$287$	8.91060	−	20.7466i	0.525976	−	1.22463i
$288$		−	1.00000i		−	0.0589256i
$289$	7.45805	+	12.9177i	0.438709	+	0.759866i
$290$	−5.17805	+	8.96864i	−0.304065	+	0.526657i
$291$	13.7793	+	7.95550i	0.807759	+	0.466360i
$292$	3.42087	−	1.97504i	0.200191	−	0.115580i
$293$		−	0.418273i		−	0.0244358i	−0.999925	−	0.0122179i	$-0.996111\pi$
$293$		−	0.418273i		−	0.0244358i	0.999925	−	0.0122179i	$-0.00388917\pi$
$294$	−5.07651	+	4.81965i	−0.296068	+	0.281088i
$295$	−15.1917			−0.884496
$296$	−5.71064	−	9.89112i	−0.331924	−	0.574909i
$297$	−3.75189	−	2.16615i	−0.217706	−	0.125693i
$298$	−6.14082	+	10.6362i	−0.355728	+	0.616139i
$299$	15.9812	−	5.88064i	0.924218	−	0.340086i
$300$	−4.16653			−0.240554
$301$	−12.4126	−	5.33117i	−0.715449	−	0.307283i
$302$	14.5511			0.837320
$303$	−0.596703	−	1.03352i	−0.0342797	−	0.0593742i
$304$	1.12988	+	0.652339i	0.0648033	+	0.0374142i
$305$	−2.64999	−	1.52998i	−0.151738	−	0.0876061i
$306$	−1.25017	+	0.721788i	−0.0714676	+	0.0412618i
$307$			13.1766i			0.752025i	0.926614	+	0.376013i	$0.122705\pi$
$307$			13.1766i			0.752025i	−0.926614	+	0.376013i	$0.877295\pi$
$308$	11.3826	−	1.34855i	0.648583	−	0.0768407i
$309$	−15.1741			−0.863225
$310$	4.44514	−	2.56640i	0.252467	−	0.145762i
$311$	8.61548	−	14.9225i	0.488539	−	0.846175i	−0.511374	−	0.859358i	$-0.670863\pi$
$311$	8.61548	−	14.9225i	0.488539	−	0.846175i	0.999913	+	0.0131837i	$0.00419662\pi$
$312$	−2.30784	+	2.77017i	−0.130656	+	0.156830i
$313$	−4.45429	−	7.71506i	−0.251772	−	0.436081i	0.712242	−	0.701934i	$-0.247680\pi$
$313$	−4.45429	−	7.71506i	−0.251772	−	0.436081i	−0.964014	+	0.265853i	$0.914347\pi$
$314$		−	9.62863i		−	0.543375i
$315$	−4.79353	−	6.41777i	−0.270085	−	0.361600i
$316$	−14.6930			−0.826545
$317$	−5.12567	+	2.95931i	−0.287886	+	0.166211i	−0.636988	−	0.770874i	$-0.719820\pi$
$317$	−5.12567	+	2.95931i	−0.287886	+	0.166211i	0.349102	+	0.937085i	$0.386487\pi$
$318$	3.55583	+	2.05296i	0.199401	+	0.115124i
$319$	12.8334	+	7.40939i	0.718535	+	0.414846i
$320$	−2.62200	+	1.51381i	−0.146574	+	0.0846247i
$321$	−8.01996			−0.447630
$322$	7.47767	+	10.0114i	0.416714	+	0.557914i
$323$		−	1.88340i		−	0.104795i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	11.5420	+	9.61568i	0.640235	+	0.533382i
$326$	8.47691	−	14.6824i	0.469493	−	0.813185i
$327$	0.909907	−	0.525335i	0.0503180	−	0.0290511i
$328$	8.53413			0.471218
$329$	22.0978	−	2.61803i	1.21829	−	0.144337i
$330$			13.1166i			0.722045i
$331$	10.1165	−	5.84078i	0.556055	−	0.321038i	−0.195506	−	0.980703i	$-0.562635\pi$
$331$	10.1165	−	5.84078i	0.556055	−	0.321038i	0.751560	+	0.659664i	$0.229302\pi$
$332$	−14.7729	−	8.52913i	−0.810767	−	0.468097i
$333$	9.89112	+	5.71064i	0.542030	+	0.312941i
$334$	−11.7245	−	20.3073i	−0.641533	−	1.11117i
$335$	−1.44281			−0.0788292
$336$	−2.43101	−	1.04411i	−0.132623	−	0.0569611i
$337$	6.30335			0.343365			0.171683	−	0.985152i	$-0.445080\pi$
$337$	6.30335			0.343365			0.171683	+	0.985152i	$0.445080\pi$
$338$	12.7862	−	2.34773i	0.695480	−	0.127700i
$339$	−4.70493	+	8.14917i	−0.255537	+	0.442602i
$340$	3.78506	+	2.18530i	0.205274	+	0.118515i
$341$	−3.67233	−	6.36066i	−0.198868	−	0.344449i
$342$	−1.30468			−0.0705489
$343$	6.41619	+	17.3733i	0.346442	+	0.938072i
$344$		−	5.10592i		−	0.275293i
$345$	−12.3836	+	7.14967i	−0.666710	+	0.384925i
$346$	−14.2491	−	8.22674i	−0.766038	−	0.442272i
$347$	4.78819	−	8.29339i	0.257044	−	0.445212i	−0.708405	−	0.705806i	$-0.750585\pi$
$347$	4.78819	−	8.29339i	0.257044	−	0.445212i	0.965449	+	0.260594i	$0.0839183\pi$
$348$	−1.71027	−	2.96227i	−0.0916799	−	0.158794i
$349$		−	18.6506i		−	0.998346i	−0.866502	−	0.499173i	$-0.833637\pi$
$349$		−	18.6506i		−	0.998346i	0.866502	−	0.499173i	$-0.166363\pi$
$350$	−4.35033	+	10.1289i	−0.232535	+	0.541411i
$351$	0.613563	−	3.55296i	0.0327496	−	0.189643i
$352$	2.16615	+	3.75189i	0.115456	+	0.199976i
$353$	19.5305	+	11.2759i	1.03950	+	0.600156i	0.919692	−	0.392641i	$-0.128438\pi$
$353$	19.5305	+	11.2759i	1.03950	+	0.600156i	0.119809	+	0.992797i	$0.461772\pi$
$354$	2.50885	−	4.34545i	0.133344	−	0.230958i
$355$	18.9220	+	32.7739i	1.00428	+	1.73946i
$356$			6.97996i			0.369937i
$357$	0.449353	+	3.79282i	0.0237823	+	0.200737i
$358$		−	22.2870i		−	1.17790i
$359$	−18.0748	+	10.4355i	−0.953953	+	0.550765i	−0.894307	−	0.447455i	$-0.852331\pi$
$359$	−18.0748	+	10.4355i	−0.953953	+	0.550765i	−0.0596463	+	0.998220i	$0.518997\pi$
$360$	1.51381	−	2.62200i	0.0797850	−	0.138192i
$361$	−8.64891	+	14.9803i	−0.455206	+	0.788439i
$362$	−10.7632	+	6.21415i	−0.565702	+	0.326608i
$363$	7.76886			0.407759
$364$	4.32468	+	8.50277i	0.226675	+	0.445666i
$365$	11.9594			0.625981
$366$	0.875271	−	0.505338i	0.0457512	−	0.0264144i
$367$	−5.06944	+	8.78053i	−0.264623	+	0.458340i	−0.967465	−	0.253006i	$-0.918581\pi$
$367$	−5.06944	+	8.78053i	−0.264623	+	0.458340i	0.702842	+	0.711346i	$0.251914\pi$
$368$	−2.36147	+	4.09019i	−0.123100	+	0.213216i
$369$	−7.39077	+	4.26706i	−0.384748	+	0.222134i
$370$		−	34.5794i		−	1.79770i
$371$	8.70348	−	6.50076i	0.451862	−	0.337502i
$372$			1.69532i			0.0878984i
$373$	−13.1811	−	22.8303i	−0.682491	−	1.18211i	−0.974218	−	0.225607i	$-0.927563\pi$
$373$	−13.1811	−	22.8303i	−0.682491	−	1.18211i	0.291728	−	0.956501i	$-0.405770\pi$
$374$	3.12700	−	5.41613i	0.161693	−	0.280061i
$375$	2.18537	+	1.26173i	0.112852	+	0.0651552i
$376$	4.20530	+	7.28379i	0.216872	+	0.375633i
$377$	−2.09871	+	12.1530i	−0.108089	+	0.625912i
$378$	2.62738	−	0.311278i	0.135138	−	0.0160104i
$379$		−	34.2225i		−	1.75789i	−0.476921	−	0.878946i	$-0.658247\pi$
$379$		−	34.2225i		−	1.75789i	0.476921	−	0.878946i	$-0.341753\pi$
$380$	1.97504	+	3.42087i	0.101317	+	0.175487i
$381$	0.668825	−	1.15844i	0.0342650	−	0.0593487i
$382$	18.6317	+	10.7570i	0.953283	+	0.550378i
$383$	8.79636	−	5.07858i	0.449473	−	0.259503i	−0.258135	−	0.966109i	$-0.583108\pi$
$383$	8.79636	−	5.07858i	0.449473	−	0.259503i	0.707608	+	0.706606i	$0.249774\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	31.8866	+	13.6952i	1.62509	+	0.697973i
$386$	−1.92170			−0.0978121
$387$	2.55296	+	4.42186i	0.129774	+	0.224776i
$388$	13.7793	+	7.95550i	0.699540	+	0.403880i
$389$	13.1055	−	22.6995i	0.664477	−	1.15091i	−0.314949	−	0.949108i	$-0.601988\pi$
$389$	13.1055	−	22.6995i	0.664477	−	1.15091i	0.979427	−	0.201800i	$-0.0646791\pi$
$390$	−10.2447	+	3.76976i	−0.518760	+	0.190889i
$391$	6.81793			0.344798
$392$	−5.07651	+	4.81965i	−0.256402	+	0.243429i
$393$	−12.3437			−0.622659
$394$	−2.77554	−	4.80737i	−0.139830	−	0.242192i
$395$	−38.5250	−	22.2424i	−1.93840	−	1.11914i
$396$	−3.75189	−	2.16615i	−0.188539	−	0.108853i
$397$	−32.3434	+	18.6735i	−1.62327	+	0.937194i	−0.637229	+	0.770674i	$0.719920\pi$
$397$	−32.3434	+	18.6735i	−1.62327	+	0.937194i	−0.986038	+	0.166520i	$0.946747\pi$
$398$		−	7.08972i		−	0.355376i
$399$	−1.36223	+	3.17169i	−0.0681969	+	0.158783i
$400$	−4.16653			−0.208326
$401$	−6.62574	+	3.82537i	−0.330874	+	0.191030i	−0.656229	−	0.754562i	$-0.727849\pi$
$401$	−6.62574	+	3.82537i	−0.330874	+	0.191030i	0.325355	+	0.945592i	$0.394516\pi$
$402$	0.238274	−	0.412703i	0.0118840	−	0.0205838i
$403$	3.91254	−	4.69634i	0.194897	−	0.233941i
$404$	−0.596703	−	1.03352i	−0.0296871	−	0.0514195i
$405$			3.02763i			0.150444i
$406$	−8.98702	+	1.06474i	−0.446018	+	0.0528419i
$407$	−49.4804			−2.45265
$408$	−1.25017	+	0.721788i	−0.0618928	+	0.0357338i
$409$	−18.9940	−	10.9662i	−0.939192	−	0.542243i	−0.0494850	−	0.998775i	$-0.515758\pi$
$409$	−18.9940	−	10.9662i	−0.939192	−	0.542243i	−0.889707	+	0.456532i	$0.849091\pi$
$410$	22.3765	+	12.9191i	1.10510	+	0.638028i
$411$	−7.91249	+	4.56828i	−0.390294	+	0.225337i
$412$	−15.1741			−0.747575
$413$	−7.94433	−	10.6362i	−0.390915	−	0.523373i
$414$		−	4.72295i		−	0.232120i
$415$	−25.8230	−	44.7268i	−1.26760	−	2.19555i
$416$	−2.30784	+	2.77017i	−0.113151	+	0.135819i
$417$	8.91097	−	15.4343i	0.436372	−	0.755819i
$418$	4.89500	−	2.82613i	0.239422	−	0.138230i
$419$	−3.94624			−0.192786			−0.0963932	−	0.995343i	$-0.530731\pi$
$419$	−3.94624			−0.192786			−0.0963932	+	0.995343i	$0.530731\pi$
$420$	−4.79353	−	6.41777i	−0.233900	−	0.313155i
$421$		−	13.3130i		−	0.648836i	−0.945914	−	0.324418i	$-0.894831\pi$
$421$		−	13.3130i		−	0.648836i	0.945914	−	0.324418i	$-0.105169\pi$
$422$	−21.0305	+	12.1419i	−1.02375	+	0.591060i
$423$	−7.28379	−	4.20530i	−0.354150	−	0.204469i
$424$	3.55583	+	2.05296i	0.172687	+	0.0997007i
$425$	3.00735	+	5.20888i	0.145878	+	0.252668i
$426$	−12.4996			−0.605606
$427$	−0.314601	−	2.65543i	−0.0152246	−	0.128505i
$428$	−8.01996			−0.387659
$429$	5.39424	+	14.6594i	0.260436	+	0.707761i
$430$	7.72942	−	13.3877i	0.372746	−	0.645614i
$431$	−32.3134	−	18.6562i	−1.55648	−	0.898636i	−0.997589	−	0.0693967i	$-0.977893\pi$
$431$	−32.3134	−	18.6562i	−1.55648	−	0.898636i	−0.558894	−	0.829239i	$-0.688774\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−9.35993			−0.449810			−0.224905	−	0.974381i	$-0.572207\pi$
$433$	−9.35993			−0.449810			−0.224905	+	0.974381i	$0.572207\pi$
$434$	4.12135	+	1.77011i	0.197831	+	0.0849680i
$435$		−	10.3561i		−	0.496537i
$436$	0.909907	−	0.525335i	0.0435767	−	0.0251590i
$437$	5.33638	+	3.08096i	0.255274	+	0.147382i
$438$	−1.97504	+	3.42087i	−0.0943710	+	0.163455i
$439$	11.6412	+	20.1631i	0.555603	+	0.962333i	0.997856	+	0.0654428i	$0.0208460\pi$
$439$	11.6412	+	20.1631i	0.555603	+	0.962333i	−0.442253	+	0.896890i	$0.645821\pi$
$440$			13.1166i			0.625309i
$441$	1.98656	−	6.71220i	0.0945981	−	0.319628i
$442$	5.12897	+	0.885724i	0.243960	+	0.0421296i
$443$	1.70694	+	2.95650i	0.0810990	+	0.140468i	0.903722	−	0.428119i	$-0.140824\pi$
$443$	1.70694	+	2.95650i	0.0810990	+	0.140468i	−0.822623	+	0.568587i	$0.807490\pi$
$444$	9.89112	+	5.71064i	0.469412	+	0.271015i
$445$	−10.5664	+	18.3015i	−0.500893	+	0.867573i
$446$	1.00684	+	1.74390i	0.0476753	+	0.0825760i
$447$		−	12.2816i		−	0.580901i
$448$	−2.43101	−	1.04411i	−0.114855	−	0.0493297i
$449$		−	23.2401i		−	1.09677i	−0.836227	−	0.548383i	$-0.815244\pi$
$449$		−	23.2401i		−	1.09677i	0.836227	−	0.548383i	$-0.184756\pi$
$450$	3.60832	−	2.08326i	0.170098	−	0.0982059i
$451$	18.4862	−	32.0191i	0.870482	−	1.50772i
$452$	−4.70493	+	8.14917i	−0.221301	+	0.383305i
$453$	−12.6016	+	7.27554i	−0.592075	+	0.341835i
$454$	−6.16251			−0.289221
$455$	−1.53229	+	28.8410i	−0.0718349	+	1.35209i
$456$	−1.30468			−0.0610971
$457$	−11.9714	+	6.91167i	−0.559997	+	0.323314i	−0.753144	−	0.657855i	$-0.771464\pi$
$457$	−11.9714	+	6.91167i	−0.559997	+	0.323314i	0.193147	+	0.981170i	$0.438130\pi$
$458$	−7.59052	+	13.1472i	−0.354682	+	0.614327i
$459$	0.721788	−	1.25017i	0.0336902	−	0.0583531i
$460$	−12.3836	+	7.14967i	−0.577388	+	0.333355i
$461$			22.3943i			1.04301i	0.853249	+	0.521504i	$0.174629\pi$
$461$			22.3943i			1.04301i	−0.853249	+	0.521504i	$0.825371\pi$
$462$	−9.18334	+	6.85917i	−0.427248	+	0.319118i
$463$			9.18946i			0.427070i	0.976935	+	0.213535i	$0.0684978\pi$
$463$			9.18946i			0.427070i	−0.976935	+	0.213535i	$0.931502\pi$
$464$	−1.71027	−	2.96227i	−0.0793971	−	0.137520i
$465$	−2.56640	+	4.44514i	−0.119014	+	0.206138i
$466$	−18.0157	−	10.4014i	−0.834561	−	0.481834i
$467$	−7.09820	−	12.2944i	−0.328465	−	0.568919i	0.653742	−	0.756717i	$-0.273198\pi$
$467$	−7.09820	−	12.2944i	−0.328465	−	0.568919i	−0.982208	+	0.187799i	$0.939865\pi$
$468$	0.613563	−	3.55296i	0.0283620	−	0.164236i
$469$	−0.754502	−	1.01016i	−0.0348397	−	0.0466447i
$470$			25.4642i			1.17457i
$471$	4.81431	+	8.33864i	0.221832	+	0.384224i
$472$	2.50885	−	4.34545i	0.115479	−	0.200016i
$473$	−19.1568	−	11.0602i	−0.880833	−	0.508549i
$474$	12.7245	−	7.34649i	0.584455	−	0.337435i
$475$			5.43597i			0.249419i
$476$	0.449353	+	3.79282i	0.0205960	+	0.173843i
$477$	−4.10592			−0.187997
$478$	−3.30317	−	5.72127i	−0.151084	−	0.261685i
$479$	−12.2115	−	7.05029i	−0.557956	−	0.322136i	0.194369	−	0.980929i	$-0.437734\pi$
$479$	−12.2115	−	7.05029i	−0.557956	−	0.322136i	−0.752325	+	0.658793i	$0.771067\pi$
$480$	1.51381	−	2.62200i	0.0690958	−	0.119677i
$481$	−14.2209	−	38.6466i	−0.648416	−	1.76213i
$482$	−22.6930			−1.03364
$483$	−11.4816	−	4.93130i	−0.522429	−	0.224382i
$484$	7.76886			0.353130
$485$	24.0863	+	41.7187i	1.09370	+	1.89435i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	11.5866	+	6.68951i	0.525038	+	0.303131i	0.738993	−	0.673713i	$-0.235301\pi$
$487$	11.5866	+	6.68951i	0.525038	+	0.303131i	−0.213956	+	0.976843i	$0.568635\pi$
$488$	0.875271	−	0.505338i	0.0396217	−	0.0228756i
$489$			16.9538i			0.766679i
$490$	−20.6067	+	4.95225i	−0.930915	+	0.223720i
$491$	20.3530			0.918518			0.459259	−	0.888302i	$-0.348115\pi$
$491$	20.3530			0.918518			0.459259	+	0.888302i	$0.348115\pi$
$492$	−7.39077	+	4.26706i	−0.333202	+	0.192374i
$493$	−2.46890	+	4.27626i	−0.111194	+	0.192593i
$494$	3.61418	+	3.01099i	0.162610	+	0.135471i
$495$	−6.55830	−	11.3593i	−0.294774	−	0.510563i
$496$			1.69532i			0.0761222i
$497$	−13.0510	+	30.3866i	−0.585416	+	1.36303i
$498$	17.0583			0.764399
$499$	25.0796	−	14.4797i	1.12272	−	0.648201i	0.180624	−	0.983552i	$-0.442188\pi$
$499$	25.0796	−	14.4797i	1.12272	−	0.648201i	0.942093	+	0.335351i	$0.108855\pi$
$500$	2.18537	+	1.26173i	0.0977328	+	0.0564261i
$501$	20.3073	+	11.7245i	0.907265	+	0.523810i
$502$	−4.17520	+	2.41055i	−0.186348	+	0.107588i
$503$	−7.66467			−0.341751			−0.170875	−	0.985293i	$-0.554660\pi$
$503$	−7.66467			−0.341751			−0.170875	+	0.985293i	$0.554660\pi$
$504$	2.62738	−	0.311278i	0.117033	−	0.0138654i
$505$		−	3.61319i		−	0.160785i
$506$	10.2306	+	17.7200i	0.454807	+	0.787749i
$507$	−9.89935	+	8.42632i	−0.439646	+	0.374226i
$508$	0.668825	−	1.15844i	0.0296743	−	0.0513974i
$509$	17.5811	−	10.1505i	0.779269	−	0.449911i	−0.0569024	−	0.998380i	$-0.518122\pi$
$509$	17.5811	−	10.1505i	0.779269	−	0.449911i	0.836171	+	0.548469i	$0.184789\pi$
$510$	−4.37061			−0.193534
$511$	6.25401	+	8.37312i	0.276661	+	0.370405i
$512$		−	1.00000i		−	0.0441942i
$513$	1.12988	−	0.652339i	0.0498856	−	0.0288015i
$514$	−5.05128	−	2.91636i	−0.222802	−	0.128635i
$515$	−39.7866	−	22.9708i	−1.75321	−	1.01221i
$516$	2.55296	+	4.42186i	0.112388	+	0.194662i
$517$	36.4373			1.60251
$518$	24.2101	−	18.0829i	1.06373	−	0.794516i
$519$	16.4535			0.722228
$520$	−10.2447	+	3.76976i	−0.449260	+	0.165315i
$521$	21.6166	−	37.4410i	0.947038	−	1.64032i	0.195420	−	0.980720i	$-0.437393\pi$
$521$	21.6166	−	37.4410i	0.947038	−	1.64032i	0.751618	−	0.659599i	$-0.229274\pi$
$522$	2.96227	+	1.71027i	0.129655	+	0.0748563i
$523$	15.0038	+	25.9873i	0.656068	+	1.13634i	0.981625	+	0.190821i	$0.0611150\pi$
$523$	15.0038	+	25.9873i	0.656068	+	1.13634i	−0.325557	+	0.945523i	$0.605552\pi$
$524$	−12.3437			−0.539238
$525$	−1.29695	−	10.9470i	−0.0566034	−	0.477768i
$526$			13.3746i			0.583161i
$527$	2.11945	−	1.22366i	0.0923245	−	0.0533036i
$528$	−3.75189	−	2.16615i	−0.163280	−	0.0942697i
$529$	0.346872	−	0.600800i	0.0150814	−	0.0261217i
$530$	6.21560	+	10.7657i	0.269989	+	0.467634i
$531$			5.01770i			0.217749i
$532$	−1.36223	+	3.17169i	−0.0590602	+	0.137510i
$533$	30.3214	+	5.23622i	1.31337	+	0.226806i
$534$	−3.48998	−	6.04482i	−0.151026	−	0.261585i
$535$	−21.0283	−	12.1407i	−0.909134	−	0.524889i
$536$	0.238274	−	0.412703i	0.0102919	−	0.0178261i
$537$	11.1435	+	19.3011i	0.480877	+	0.832903i
$538$		−	12.8451i		−	0.553791i
$539$	7.08629	+	29.4866i	0.305228	+	1.27008i
$540$			3.02763i			0.130288i
$541$	−33.6447	+	19.4248i	−1.44650	+	0.835136i	−0.998271	−	0.0587827i	$-0.981278\pi$
$541$	−33.6447	+	19.4248i	−1.44650	+	0.835136i	−0.448228	+	0.893919i	$0.647945\pi$
$542$	−10.4443	+	18.0901i	−0.448622	+	0.777036i
$543$	6.21415	−	10.7632i	0.266675	−	0.461894i
$544$	−1.25017	+	0.721788i	−0.0536007	+	0.0309464i
$545$	3.18104			0.136261
$546$	−7.99667	−	5.20128i	−0.342226	−	0.222594i
$547$	40.6208			1.73682			0.868411	−	0.495846i	$-0.165142\pi$
$547$	40.6208			1.73682			0.868411	+	0.495846i	$0.165142\pi$
$548$	−7.91249	+	4.56828i	−0.338005	+	0.195147i
$549$	−0.505338	+	0.875271i	−0.0215673	+	0.0373557i
$550$	−9.02533	+	15.6323i	−0.384841	+	0.666565i
$551$	−3.86480	+	2.23134i	−0.164646	+	0.0950585i
$552$		−	4.72295i		−	0.201022i
$553$	−4.57360	−	38.6040i	−0.194489	−	1.64161i
$554$		−	26.3966i		−	1.12149i
$555$	17.2897	+	29.9466i	0.733906	+	1.27116i
$556$	8.91097	−	15.4343i	0.377909	−	0.654558i
$557$	−37.8923	−	21.8772i	−1.60555	−	0.926965i	−0.990349	−	0.138594i	$-0.955742\pi$
$557$	−37.8923	−	21.8772i	−1.60555	−	0.926965i	−0.615201	−	0.788370i	$-0.710925\pi$
$558$	−0.847661	−	1.46819i	−0.0358844	−	0.0621536i
$559$	3.13281	−	18.1412i	0.132504	−	0.767289i
$560$	−4.79353	−	6.41777i	−0.202564	−	0.271200i
$561$			6.25401i			0.264044i
$562$	−6.30121	−	10.9140i	−0.265801	−	0.460380i
$563$	14.3953	−	24.9334i	0.606689	−	1.05082i	−0.385094	−	0.922878i	$-0.625831\pi$
$563$	14.3953	−	24.9334i	0.606689	−	1.05082i	0.991782	−	0.127938i	$-0.0408358\pi$
$564$	−7.28379	−	4.20530i	−0.306703	−	0.177075i
$565$	−24.6727	+	14.2448i	−1.03799	+	0.599282i
$566$			0.175775i			0.00738837i
$567$	−2.11974	+	1.58326i	−0.0890205	+	0.0664908i
$568$	−12.4996			−0.524471
$569$	2.53148	+	4.38465i	0.106125	+	0.183814i	0.914197	−	0.405269i	$-0.132822\pi$
$569$	2.53148	+	4.38465i	0.106125	+	0.183814i	−0.808072	+	0.589083i	$0.799489\pi$
$570$	−3.42087	−	1.97504i	−0.143284	−	0.0827252i
$571$	−9.83001	+	17.0261i	−0.411373	+	0.712519i	−0.995040	−	0.0994738i	$-0.968284\pi$
$571$	−9.83001	+	17.0261i	−0.411373	+	0.712519i	0.583667	+	0.811993i	$0.301617\pi$
$572$	5.39424	+	14.6594i	0.225544	+	0.612939i
$573$	−21.5141			−0.898764
$574$	2.65648	+	22.4224i	0.110879	+	0.935891i
$575$	−19.6783			−0.820641
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	11.1308	+	6.42637i	0.463381	+	0.267533i	0.713465	−	0.700691i	$-0.247125\pi$
$577$	11.1308	+	6.42637i	0.463381	+	0.267533i	−0.250084	+	0.968224i	$0.580458\pi$
$578$	−12.9177	−	7.45805i	−0.537306	−	0.310214i
$579$	1.66424	−	0.960851i	0.0691636	−	0.0399316i
$580$		−	10.3561i		−	0.430013i
$581$	17.8108	−	41.4689i	0.738915	−	1.72042i
$582$	−15.9110			−0.659533
$583$	15.4050	−	8.89406i	0.638008	−	0.368354i
$584$	−1.97504	+	3.42087i	−0.0817276	+	0.141556i
$585$	6.98728	−	8.38705i	0.288889	−	0.346762i
$586$	0.209136	+	0.362235i	0.00863935	+	0.0149638i
$587$			24.3430i			1.00474i	0.864652	+	0.502371i	$0.167539\pi$
$587$			24.3430i			1.00474i	−0.864652	+	0.502371i	$0.832461\pi$
$588$	1.98656	−	6.71220i	0.0819243	−	0.276806i
$589$	2.21185			0.0911376
$590$	13.1564	−	7.59586i	0.541641	−	0.312716i
$591$	4.80737	+	2.77554i	0.197749	+	0.114170i
$592$	9.89112	+	5.71064i	0.406522	+	0.234706i
$593$	20.4283	−	11.7943i	0.838890	−	0.484333i	−0.0179970	−	0.999838i	$-0.505729\pi$
$593$	20.4283	−	11.7943i	0.838890	−	0.484333i	0.856887	+	0.515505i	$0.172396\pi$
$594$	4.33230			0.177757
$595$	−4.56341	+	10.6250i	−0.187082	+	0.435583i
$596$		−	12.2816i		−	0.503075i
$597$	3.54486	+	6.13988i	0.145081	+	0.251288i
$598$	−10.8998	+	13.0834i	−0.445727	+	0.535020i
$599$	−7.77854	+	13.4728i	−0.317823	+	0.550485i	−0.980033	−	0.198833i	$-0.936285\pi$
$599$	−7.77854	+	13.4728i	−0.317823	+	0.550485i	0.662211	+	0.749318i	$0.269618\pi$
$600$	3.60832	−	2.08326i	0.147309	−	0.0850488i
$601$	30.6284			1.24936			0.624679	−	0.780882i	$-0.285230\pi$
$601$	30.6284			1.24936			0.624679	+	0.780882i	$0.285230\pi$
$602$	13.4152	−	1.58936i	0.546762	−	0.0647775i
$603$			0.476549i			0.0194066i
$604$	−12.6016	+	7.27554i	−0.512752	+	0.296037i
$605$	20.3700	+	11.7606i	0.828157	+	0.478136i
$606$	1.03352	+	0.596703i	0.0419839	+	0.0242394i
$607$	7.88760	+	13.6617i	0.320148	+	0.554512i	0.980518	−	0.196428i	$-0.0629341\pi$
$607$	7.88760	+	13.6617i	0.320148	+	0.554512i	−0.660371	+	0.750940i	$0.729601\pi$
$608$	−1.30468			−0.0529116
$609$	7.25062	−	5.41560i	0.293810	−	0.219451i
$610$	3.05995			0.123894
$611$	10.4722	+	28.4593i	0.423660	+	1.15134i
$612$	0.721788	−	1.25017i	0.0291765	−	0.0505352i
$613$	−18.5248	−	10.6953i	−0.748211	−	0.431980i	0.0768359	−	0.997044i	$-0.475518\pi$
$613$	−18.5248	−	10.6953i	−0.748211	−	0.431980i	−0.825047	+	0.565064i	$0.808852\pi$
$614$	−6.58828	−	11.4112i	−0.265881	−	0.460520i
$615$	−25.8382			−1.04189
$616$	−9.18334	+	6.85917i	−0.370007	+	0.276364i
$617$			34.4919i			1.38859i	0.719690	+	0.694296i	$0.244284\pi$
$617$			34.4919i			1.38859i	−0.719690	+	0.694296i	$0.755716\pi$
$618$	13.1412	−	7.58706i	0.528615	−	0.305196i
$619$	34.7726	+	20.0760i	1.39763	+	0.806921i	0.994144	−	0.108066i	$-0.0344658\pi$
$619$	34.7726	+	20.0760i	1.39763	+	0.806921i	0.403484	+	0.914987i	$0.367799\pi$
$620$	−2.56640	+	4.44514i	−0.103069	+	0.178521i
$621$	2.36147	+	4.09019i	0.0947627	+	0.164134i
$622$			17.2310i			0.690899i
$623$	−18.3390	+	2.17271i	−0.734736	+	0.0870476i
$624$	0.613563	−	3.55296i	0.0245622	−	0.142232i
$625$	14.2363	+	24.6581i	0.569454	+	0.986323i
$626$	7.71506	+	4.45429i	0.308356	+	0.178029i
$627$	−2.82613	+	4.89500i	−0.112865	+	0.195487i
$628$	4.81431	+	8.33864i	0.192112	+	0.332748i
$629$		−	16.4875i		−	0.657399i
$630$	7.36020	+	3.16119i	0.293237	+	0.125945i
$631$		−	27.1665i		−	1.08148i	−0.841189	−	0.540741i	$-0.818144\pi$
$631$		−	27.1665i		−	1.08148i	0.841189	−	0.540741i	$-0.181856\pi$
$632$	12.7245	−	7.34649i	0.506153	−	0.292228i
$633$	12.1419	−	21.0305i	0.482599	−	0.835885i
$634$	2.95931	−	5.12567i	0.117529	−	0.203566i
$635$	3.50732	−	2.02495i	0.139184	−	0.0803578i
$636$	−4.10592			−0.162810
$637$	−20.9938	+	14.0093i	−0.831805	+	0.555068i
$638$	−14.8188			−0.586681
$639$	10.8249	−	6.24979i	0.428228	−	0.247238i
$640$	1.51381	−	2.62200i	0.0598387	−	0.103644i
$641$	−0.880967	+	1.52588i	−0.0347961	+	0.0602686i	−0.882899	−	0.469563i	$-0.844412\pi$
$641$	−0.880967	+	1.52588i	−0.0347961	+	0.0602686i	0.848103	+	0.529832i	$0.177745\pi$
$642$	6.94549	−	4.00998i	0.274116	−	0.158261i
$643$			41.7007i			1.64451i	0.569117	+	0.822257i	$0.307285\pi$
$643$			41.7007i			1.64451i	−0.569117	+	0.822257i	$0.692715\pi$
$644$	−11.4816	−	4.93130i	−0.452437	−	0.194320i
$645$			15.4588i			0.608691i
$646$	0.941700	+	1.63107i	0.0370507	+	0.0641737i
$647$	9.84997	−	17.0606i	0.387242	−	0.670723i	−0.604835	−	0.796351i	$-0.706761\pi$
$647$	9.84997	−	17.0606i	0.387242	−	0.670723i	0.992077	+	0.125627i	$0.0400944\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.8691	−	18.8258i	−0.426649	−	0.738978i
$650$	−14.8035	−	2.55642i	−0.580641	−	0.100271i
$651$	−4.45425	+	0.527716i	−0.174576	+	0.0206828i
$652$			16.9538i			0.663963i
$653$	−19.1239	−	33.1235i	−0.748374	−	1.29622i	−0.948602	−	0.316473i	$-0.897501\pi$
$653$	−19.1239	−	33.1235i	−0.748374	−	1.29622i	0.200227	−	0.979749i	$-0.435832\pi$
$654$	−0.525335	+	0.909907i	−0.0205422	+	0.0355802i
$655$	−32.3653	−	18.6861i	−1.26462	−	0.730126i
$656$	−7.39077	+	4.26706i	−0.288561	+	0.166601i
$657$		−	3.95008i		−	0.154107i
$658$	−17.8283	+	13.3162i	−0.695018	+	0.519119i
$659$	23.3092			0.907999			0.454000	−	0.891002i	$-0.349997\pi$
$659$	23.3092			0.907999			0.454000	+	0.891002i	$0.349997\pi$
$660$	−6.55830	−	11.3593i	−0.255281	−	0.442161i
$661$	−21.3745	−	12.3406i	−0.831373	−	0.479994i	0.0229493	−	0.999737i	$-0.492694\pi$
$661$	−21.3745	−	12.3406i	−0.831373	−	0.479994i	−0.854323	+	0.519743i	$0.826028\pi$
$662$	−5.84078	+	10.1165i	−0.227008	+	0.393190i
$663$	−4.88468	+	1.79742i	−0.189705	+	0.0698062i
$664$	17.0583			0.661989
$665$	−8.37312	+	6.25401i	−0.324696	+	0.242520i
$666$	−11.4213			−0.442566
$667$	−8.07750	−	13.9906i	−0.312762	−	0.541720i
$668$	20.3073	+	11.7245i	0.785715	+	0.453633i
$669$	−1.74390	−	1.00684i	−0.0674230	−	0.0389267i
$670$	1.24951	−	0.721406i	0.0482729	−	0.0278703i
$671$		−	4.37856i		−	0.169032i
$672$	2.62738	−	0.311278i	0.101353	−	0.0120078i
$673$	−15.4368			−0.595044			−0.297522	−	0.954715i	$-0.596160\pi$
$673$	−15.4368			−0.595044			−0.297522	+	0.954715i	$0.596160\pi$
$674$	−5.45886	+	3.15167i	−0.210267	+	0.121398i
$675$	−2.08326	+	3.60832i	−0.0801848	+	0.138884i
$676$	−9.89935	+	8.42632i	−0.380744	+	0.324089i
$677$	−7.38329	−	12.7882i	−0.283763	−	0.491492i	0.688546	−	0.725193i	$-0.258250\pi$
$677$	−7.38329	−	12.7882i	−0.283763	−	0.491492i	−0.972308	+	0.233701i	$0.924916\pi$
$678$		−	9.40986i		−	0.361383i
$679$	−16.6129	+	38.6799i	−0.637545	+	1.48440i
$680$	−4.37061			−0.167605
$681$	5.33689	−	3.08125i	0.204510	−	0.118074i
$682$	6.36066	+	3.67233i	0.243562	+	0.140621i
$683$	18.1593	+	10.4843i	0.694846	+	0.401169i	0.805425	−	0.592698i	$-0.201937\pi$
$683$	18.1593	+	10.4843i	0.694846	+	0.401169i	−0.110579	+	0.993867i	$0.535271\pi$
$684$	1.12988	−	0.652339i	0.0432022	−	0.0249428i
$685$	−27.6621			−1.05691
$686$	−14.2432	−	11.8376i	−0.543810	−	0.451964i
$687$		−	15.1810i		−	0.579193i
$688$	2.55296	+	4.42186i	0.0973308	+	0.168582i
$689$	11.3741	+	9.47583i	0.433320	+	0.361000i
$690$	7.14967	−	12.3836i	0.272183	−	0.471435i
$691$	−10.6634	+	6.15650i	−0.405654	+	0.234204i	−0.688920	−	0.724837i	$-0.741915\pi$
$691$	−10.6634	+	6.15650i	−0.405654	+	0.234204i	0.283267	+	0.959041i	$0.408582\pi$
$692$	16.4535			0.625468
$693$	4.52342	−	10.5319i	0.171830	−	0.400073i
$694$			9.57638i			0.363514i
$695$	46.7292	−	26.9791i	1.77254	−	1.02338i
$696$	2.96227	+	1.71027i	0.112284	+	0.0648275i
$697$	10.6691	+	6.15983i	0.404122	+	0.233320i
$698$	9.32532	+	16.1519i	0.352969	+	0.611360i
$699$	20.8027			0.786832
$700$	−1.29695	−	10.9470i	−0.0490200	−	0.413759i
$701$	25.8563			0.976577			0.488289	−	0.872682i	$-0.337621\pi$
$701$	25.8563			0.976577			0.488289	+	0.872682i	$0.337621\pi$
$702$	1.24512	+	3.38374i	0.0469940	+	0.127711i
$703$	7.45054	−	12.9047i	0.281002	−	0.486710i
$704$	−3.75189	−	2.16615i	−0.141405	−	0.0816399i
$705$	−12.7321	−	22.0526i	−0.479518	−	0.830549i
$706$	−22.5518			−0.848749
$707$	2.52971	−	1.88947i	0.0951394	−	0.0710610i
$708$			5.01770i			0.188577i
$709$	25.1577	−	14.5248i	0.944818	−	0.545491i	0.0533509	−	0.998576i	$-0.483010\pi$
$709$	25.1577	−	14.5248i	0.944818	−	0.545491i	0.891467	+	0.453085i	$0.149676\pi$
$710$	−32.7739	−	18.9220i	−1.22998	−	0.710131i
$711$	−7.34649	+	12.7245i	−0.275515	+	0.477206i
$712$	−3.48998	−	6.04482i	−0.130793	−	0.226539i
$713$			8.00693i			0.299862i
$714$	−2.28556	−	3.06000i	−0.0855349	−	0.114518i
$715$	−8.04786	+	46.6028i	−0.300973	+	1.74285i
$716$	11.1435	+	19.3011i	0.416451	+	0.721315i
$717$	5.72127	+	3.30317i	0.213665	+	0.123359i
$718$	10.4355	−	18.0748i	0.389450	−	0.674547i
$719$	−21.7536	−	37.6783i	−0.811272	−	1.40516i	−0.911974	−	0.410247i	$-0.865442\pi$
$719$	−21.7536	−	37.6783i	−0.811272	−	1.40516i	0.100703	−	0.994917i	$-0.467891\pi$
$720$			3.02763i			0.112833i
$721$	−4.72336	−	39.8681i	−0.175907	−	1.48477i
$722$		−	17.2978i		−	0.643758i
$723$	19.6527	−	11.3465i	0.730892	−	0.421981i
$724$	6.21415	−	10.7632i	0.230947	−	0.400012i
$725$	7.12587	−	12.3424i	0.264648	−	0.458384i
$726$	−6.72803	+	3.88443i	−0.249701	+	0.144165i
$727$	−20.3751			−0.755671			−0.377835	−	0.925873i	$-0.623331\pi$
$727$	−20.3751			−0.755671			−0.377835	+	0.925873i	$0.623331\pi$
$728$	−7.99667	−	5.20128i	−0.296376	−	0.192772i
$729$	1.00000			0.0370370
$730$	−10.3571	+	5.97968i	−0.383334	+	0.221318i
$731$	3.68539	−	6.38329i	0.136309	−	0.236094i
$732$	−0.505338	+	0.875271i	−0.0186778	+	0.0323510i
$733$	19.0444	−	10.9953i	0.703420	−	0.406120i	−0.105200	−	0.994451i	$-0.533548\pi$
$733$	19.0444	−	10.9953i	0.703420	−	0.406120i	0.808620	+	0.588331i	$0.200215\pi$
$734$		−	10.1389i		−	0.374233i
$735$	15.3698	−	14.5921i	0.566923	−	0.538238i
$736$		−	4.72295i		−	0.174090i
$737$	−1.03228	−	1.78796i	−0.0380244	−	0.0658602i
$738$	4.26706	−	7.39077i	0.157073	−	0.272058i
$739$	36.9626	+	21.3404i	1.35969	+	0.785018i	0.989582	−	0.143971i	$-0.0459872\pi$
$739$	36.9626	+	21.3404i	1.35969	+	0.785018i	0.370109	+	0.928989i	$0.379321\pi$
$740$	17.2897	+	29.9466i	0.635581	+	1.10086i
$741$	−4.63547	−	0.800501i	−0.170288	−	0.0294072i
$742$	−4.28705	+	9.98156i	−0.157383	+	0.366435i
$743$		−	17.2071i		−	0.631266i	−0.948881	−	0.315633i	$-0.897783\pi$
$743$		−	17.2071i		−	0.631266i	0.948881	−	0.315633i	$-0.102217\pi$
$744$	−0.847661	−	1.46819i	−0.0310768	−	0.0538266i
$745$	18.5921	−	32.2025i	0.681162	−	1.17981i
$746$	22.8303	+	13.1811i	0.835877	+	0.482594i
$747$	−14.7729	+	8.52913i	−0.540512	+	0.312065i
$748$			6.25401i			0.228669i
$749$	−2.49643	−	21.0714i	−0.0912177	−	0.769934i
$750$	−2.52345			−0.0921434
$751$	−7.30117	−	12.6460i	−0.266423	−	0.461459i	0.701512	−	0.712657i	$-0.252509\pi$
$751$	−7.30117	−	12.6460i	−0.266423	−	0.461459i	−0.967936	+	0.251199i	$0.919175\pi$
$752$	−7.28379	−	4.20530i	−0.265613	−	0.153352i
$753$	2.41055	−	4.17520i	0.0878455	−	0.152153i
$754$	−4.25897	−	11.5742i	−0.155103	−	0.421507i
$755$	−44.0552			−1.60333
$756$	−2.11974	+	1.58326i	−0.0770940	+	0.0575827i
$757$	25.4627			0.925456			0.462728	−	0.886500i	$-0.346871\pi$
$757$	25.4627			0.925456			0.462728	+	0.886500i	$0.346871\pi$
$758$	17.1113	+	29.6376i	0.621509	+	1.07648i
$759$	−17.7200	−	10.2306i	−0.643194	−	0.371348i
$760$	−3.42087	−	1.97504i	−0.124088	−	0.0716421i
$761$	32.9141	−	19.0030i	1.19314	−	0.688858i	0.234120	−	0.972208i	$-0.424779\pi$
$761$	32.9141	−	19.0030i	1.19314	−	0.688858i	0.959017	+	0.283350i	$0.0914458\pi$
$762$			1.33765i			0.0484580i
$763$	1.66349	+	2.22714i	0.0602223	+	0.0806280i
$764$	−21.5141			−0.778352
$765$	3.78506	−	2.18530i	0.136849	−	0.0790098i
$766$	−5.07858	+	8.79636i	−0.183497	+	0.317825i
$767$	11.5801	−	13.8999i	0.418131	−	0.501896i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$			11.8756i			0.428246i	0.976807	+	0.214123i	$0.0686893\pi$
$769$			11.8756i			0.428246i	−0.976807	+	0.214123i	$0.931311\pi$
$770$	−34.4622	+	4.08290i	−1.24193	+	0.147138i
$771$	5.83271			0.210060
$772$	1.66424	−	0.960851i	0.0598974	−	0.0345818i
$773$	7.11167	+	4.10592i	0.255789	+	0.147680i	0.622412	−	0.782690i	$-0.286153\pi$
$773$	7.11167	+	4.10592i	0.255789	+	0.147680i	−0.366623	+	0.930370i	$0.619486\pi$
$774$	−4.42186	−	2.55296i	−0.158940	−	0.0917643i
$775$	−6.11726	+	3.53180i	−0.219739	+	0.126866i
$776$	−15.9110			−0.571172
$777$	−11.9251	+	27.7653i	−0.427811	+	0.996074i
$778$			26.2111i			0.939713i
$779$	5.56714	+	9.64257i	0.199463	+	0.345481i
$780$	6.98728	−	8.38705i	0.250185	−	0.300305i
$781$	−27.0760	+	46.8970i	−0.968855	+	1.67811i
$782$	−5.90450	+	3.40897i	−0.211145	+	0.121904i
$783$	−3.42053			−0.122240
$784$	1.98656	−	6.71220i	0.0709486	−	0.239721i
$785$			29.1519i			1.04048i
$786$	10.6900	−	6.17186i	0.381299	−	0.220143i
$787$	−5.02129	−	2.89905i	−0.178990	−	0.103340i	0.407828	−	0.913059i	$-0.366286\pi$
$787$	−5.02129	−	2.89905i	−0.178990	−	0.103340i	−0.586818	+	0.809719i	$0.699620\pi$
$788$	4.80737	+	2.77554i	0.171256	+	0.0988745i
$789$	−6.68731	−	11.5828i	−0.238075	−	0.412357i
$790$	44.4849			1.58270
$791$	−22.8755	−	9.82496i	−0.813359	−	0.349335i
$792$	4.33230			0.153942
$793$	3.41986	−	1.25841i	0.121443	−	0.0446876i
$794$	18.6735	−	32.3434i	0.662696	−	1.14782i
$795$	−10.7657	−	6.21560i	−0.381822	−	0.220445i
$796$	3.54486	+	6.13988i	0.125644	+	0.217622i
$797$	14.6546			0.519093			0.259546	−	0.965731i	$-0.416427\pi$
$797$	14.6546			0.519093			0.259546	+	0.965731i	$0.416427\pi$
$798$	−0.406117	−	3.42788i	−0.0143764	−	0.121346i
$799$			12.1413i			0.429530i
$800$	3.60832	−	2.08326i	0.127573	−	0.0736545i
$801$	6.04482	+	3.48998i	0.213583	+	0.123312i
$802$	3.82537	−	6.62574i	0.135079	−	0.233963i
$803$	8.55646	+	14.8202i	0.301951	+	0.522995i
$804$			0.476549i			0.0168066i
$805$	−22.6396	−	30.3108i	−0.797941	−	1.06832i
$806$	−1.04019	+	6.02342i	−0.0366390	+	0.212166i
$807$	6.42254	+	11.1242i	0.226084	+	0.391589i
$808$	1.03352	+	0.596703i	0.0363591	+	0.0209919i
$809$	−6.20487	+	10.7471i	−0.218152	+	0.377850i	−0.954243	−	0.299033i	$-0.903336\pi$
$809$	−6.20487	+	10.7471i	−0.218152	+	0.377850i	0.736091	+	0.676882i	$0.236669\pi$
$810$	−1.51381	−	2.62200i	−0.0531900	−	0.0921278i
$811$			10.7414i			0.377181i	0.982056	+	0.188591i	$0.0603920\pi$
$811$			10.7414i			0.377181i	−0.982056	+	0.188591i	$0.939608\pi$
$812$	7.25062	−	5.41560i	0.254447	−	0.190050i
$813$		−	20.8886i		−	0.732597i
$814$	42.8513	−	24.7402i	1.50194	−	0.867144i
$815$	−25.6649	+	44.4530i	−0.899003	+	1.55712i
$816$	0.721788	−	1.25017i	0.0252676	−	0.0437648i
$817$	5.76910	−	3.33079i	0.201835	−	0.116530i
$818$	21.9324			0.766847
$819$	9.52596	+	0.506103i	0.332864	+	0.0176847i
$820$	−25.8382			−0.902307
$821$	−6.92640	+	3.99896i	−0.241733	+	0.139565i	−0.615973	−	0.787767i	$-0.711237\pi$
$821$	−6.92640	+	3.99896i	−0.241733	+	0.139565i	0.374240	+	0.927332i	$0.377904\pi$
$822$	4.56828	−	7.91249i	0.159337	−	0.275980i
$823$	3.88251	−	6.72471i	0.135336	−	0.234408i	−0.790390	−	0.612604i	$-0.790122\pi$
$823$	3.88251	−	6.72471i	0.135336	−	0.234408i	0.925726	+	0.378196i	$0.123455\pi$
$824$	13.1412	−	7.58706i	0.457794	−	0.264308i
$825$		−	18.0507i		−	0.628443i
$826$	12.1981	+	5.23905i	0.424426	+	0.182290i
$827$			9.73829i			0.338634i	0.985562	+	0.169317i	$0.0541561\pi$
$827$			9.73829i			0.338634i	−0.985562	+	0.169317i	$0.945844\pi$
$828$	2.36147	+	4.09019i	0.0820669	+	0.142144i
$829$	17.3342	−	30.0237i	0.602042	−	1.04277i	−0.390469	−	0.920616i	$-0.627687\pi$
$829$	17.3342	−	30.0237i	0.602042	−	1.04277i	0.992511	−	0.122152i	$-0.0389794\pi$
$830$	44.7268	+	25.8230i	1.55249	+	0.896330i
$831$	13.1983	+	22.8602i	0.457845	+	0.793010i
$832$	0.613563	−	3.55296i	0.0212715	−	0.123177i
$833$	−9.82528	+	2.36124i	−0.340426	+	0.0818120i
$834$			17.8219i			0.617124i
$835$	35.4973	+	61.4831i	1.22843	+	2.12771i
$836$	−2.82613	+	4.89500i	−0.0977437	+	0.169297i
$837$	1.46819	+	0.847661i	0.0507482	+	0.0292995i
$838$	3.41754	−	1.97312i	0.118057	−	0.0681603i
$839$		−	26.5655i		−	0.917142i	−0.888658	−	0.458571i	$-0.848361\pi$
$839$		−	26.5655i		−	0.917142i	0.888658	−	0.458571i	$-0.151639\pi$
$840$	7.36020	+	3.16119i	0.253951	+	0.109071i
$841$	−17.3000			−0.596550
$842$	6.65651	+	11.5294i	0.229398	+	0.397330i
$843$	10.9140	+	6.30121i	0.375899	+	0.217025i
$844$	12.1419	−	21.0305i	0.417943	−	0.723898i
$845$	−38.7120	+	7.10805i	−1.33173	+	0.244524i
$846$	8.41060			0.289162
$847$	2.41827	+	20.4117i	0.0830928	+	0.701355i
$848$	−4.10592			−0.140998
$849$	−0.0878874	−	0.152225i	−0.00301629	−	0.00522437i
$850$	−5.20888	−	3.00735i	−0.178663	−	0.103151i
$851$	46.7152	+	26.9711i	1.60138	+	0.924556i
$852$	10.8249	−	6.24979i	0.370857	−	0.214114i
$853$		−	10.1138i		−	0.346289i	−0.984896	−	0.173145i	$-0.944607\pi$
$853$		−	10.1138i		−	0.346289i	0.984896	−	0.173145i	$-0.0553928\pi$
$854$	1.60017	+	2.14237i	0.0547565	+	0.0733103i
$855$	3.95008			0.135090
$856$	6.94549	−	4.00998i	0.237392	−	0.137058i
$857$	24.0913	−	41.7273i	0.822942	−	1.42538i	−0.0805406	−	0.996751i	$-0.525665\pi$
$857$	24.0913	−	41.7273i	0.822942	−	1.42538i	0.903482	−	0.428625i	$-0.141002\pi$
$858$	−12.0012	−	9.99827i	−0.409715	−	0.341335i
$859$	5.76772	+	9.98998i	0.196792	+	0.340854i	0.947487	−	0.319796i	$-0.103614\pi$
$859$	5.76772	+	9.98998i	0.196792	+	0.340854i	−0.750694	+	0.660650i	$0.770281\pi$
$860$			15.4588i			0.527142i
$861$	−13.5118	−	18.0901i	−0.460480	−	0.616509i
$862$	37.3123			1.27086
$863$	−15.4694	+	8.93124i	−0.526583	+	0.304023i	−0.739624	−	0.673020i	$-0.764997\pi$
$863$	−15.4694	+	8.93124i	−0.526583	+	0.304023i	0.213041	+	0.977043i	$0.431663\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	43.1411	+	24.9075i	1.46684	+	0.846881i
$866$	8.10594	−	4.67997i	0.275451	−	0.159032i
$867$	14.9161			0.506577
$868$	−4.45425	+	0.527716i	−0.151187	+	0.0179119i
$869$		−	63.6545i		−	2.15933i
$870$	5.17805	+	8.96864i	0.175552	+	0.304065i
$871$	1.09980	−	1.32012i	0.0372653	−	0.0447307i
$872$	−0.525335	+	0.909907i	−0.0177901	+	0.0308134i
$873$	13.7793	−	7.95550i	0.466360	−	0.269253i
$874$	−6.16192			−0.208430
$875$	−2.63477	+	6.13454i	−0.0890715	+	0.207385i
$876$		−	3.95008i		−	0.133461i
$877$	−44.8185	+	25.8760i	−1.51341	+	0.873769i	−0.513536	+	0.858068i	$0.671665\pi$
$877$	−44.8185	+	25.8760i	−1.51341	+	0.873769i	−0.999877	+	0.0157009i	$0.995002\pi$
$878$	−20.1631	−	11.6412i	−0.680472	−	0.392871i
$879$	−0.362235	−	0.209136i	−0.0122179	−	0.00705400i
$880$	−6.55830	−	11.3593i	−0.221080	−	0.382922i
$881$	−29.6192			−0.997895			−0.498947	−	0.866632i	$-0.666280\pi$
$881$	−29.6192			−0.997895			−0.498947	+	0.866632i	$0.666280\pi$
$882$	1.63569	+	6.80621i	0.0550765	+	0.229177i
$883$	13.2143			0.444695			0.222348	−	0.974967i	$-0.428628\pi$
$883$	13.2143			0.444695			0.222348	+	0.974967i	$0.428628\pi$
$884$	−4.88468	+	1.79742i	−0.164290	+	0.0604539i
$885$	−7.59586	+	13.1564i	−0.255332	+	0.442248i
$886$	−2.95650	−	1.70694i	−0.0993255	−	0.0573456i
$887$	−26.1349	−	45.2669i	−0.877523	−	1.51991i	−0.854051	−	0.520190i	$-0.825861\pi$
$887$	−26.1349	−	45.2669i	−0.877523	−	1.51991i	−0.0234721	−	0.999724i	$-0.507472\pi$
$888$	−11.4213			−0.383273
$889$	3.25185	+	1.39666i	0.109063	+	0.0468425i
$890$		−	21.1327i		−	0.708370i
$891$	−3.75189	+	2.16615i	−0.125693	+	0.0725688i
$892$	−1.74390	−	1.00684i	−0.0583901	−	0.0337115i
$893$	−5.48656	+	9.50300i	−0.183601	+	0.318006i
$894$	6.14082	+	10.6362i	0.205380	+	0.355728i
$895$			67.4766i			2.25549i
$896$	2.62738	−	0.311278i	0.0877745	−	0.0103991i
$897$	2.89783	−	16.7805i	0.0967556	−	0.560283i
$898$	11.6200	+	20.1265i	0.387765	+	0.671629i
$899$	−5.02200	−	2.89945i	−0.167493	−	0.0967022i
$900$	−2.08326	+	3.60832i	−0.0694421	+	0.120277i
$901$	2.96361	+	5.13311i	0.0987320	+	0.171009i
$902$			36.9724i			1.23105i
$903$	−10.8232	+	8.08402i	−0.360174	+	0.269019i
$904$		−	9.40986i		−	0.312967i
$905$	32.5870	−	18.8141i	1.08323	−	0.625403i
$906$	7.27554	−	12.6016i	0.241714	−	0.418660i
$907$	−13.5944	+	23.5462i	−0.451395	+	0.781839i	−0.998473	−	0.0552423i	$-0.982407\pi$
$907$	−13.5944	+	23.5462i	−0.451395	+	0.781839i	0.547078	+	0.837082i	$0.315740\pi$
$908$	5.33689	−	3.08125i	0.177111	−	0.102255i
$909$	−1.19341			−0.0395828
$910$	−13.0935	−	25.7432i	−0.434046	−	0.853380i
$911$	−40.7858			−1.35129			−0.675647	−	0.737226i	$-0.736135\pi$
$911$	−40.7858			−1.35129			−0.675647	+	0.737226i	$0.736135\pi$
$912$	1.12988	−	0.652339i	0.0374142	−	0.0216011i
$913$	36.9508	−	64.0006i	1.22289	−	2.11811i
$914$	6.91167	−	11.9714i	0.228618	−	0.395978i
$915$	−2.64999	+	1.52998i	−0.0876061	+	0.0505794i
$916$		−	15.1810i		−	0.501596i
$917$	−3.84233	−	32.4316i	−0.126885	−	1.07099i
$918$			1.44358i			0.0476451i
$919$	−1.84415	−	3.19416i	−0.0608329	−	0.105366i	0.834005	−	0.551757i	$-0.186042\pi$
$919$	−1.84415	−	3.19416i	−0.0608329	−	0.105366i	−0.894838	+	0.446391i	$0.852709\pi$
$920$	7.14967	−	12.3836i	0.235717	−	0.408275i
$921$	11.4112	+	6.58828i	0.376013	+	0.217091i
$922$	−11.1972	−	19.3940i	−0.368759	−	0.638709i
$923$	−44.4105	−	7.66927i	−1.46179	−	0.252437i
$924$	4.52342	−	10.5319i	0.148810	−	0.346474i
$925$			47.5870i			1.56465i
$926$	−4.59473	−	7.95830i	−0.150992	−	0.261526i
$927$	−7.58706	+	13.1412i	−0.249192	+	0.431613i
$928$	2.96227	+	1.71027i	0.0972412	+	0.0561422i
$929$	12.8508	−	7.41939i	0.421620	−	0.243422i	−0.274150	−	0.961687i	$-0.588397\pi$
$929$	12.8508	−	7.41939i	0.421620	−	0.243422i	0.695770	+	0.718264i	$0.255063\pi$
$930$		−	5.13281i		−	0.168311i
$931$	−8.75725	−	2.59182i	−0.287007	−	0.0849434i
$932$	20.8027			0.681417
$933$	−8.61548	−	14.9225i	−0.282058	−	0.488539i
$934$	12.2944	+	7.09820i	0.402286	+	0.232260i
$935$	−9.46740	+	16.3980i	−0.309617	+	0.536272i
$936$	1.24512	+	3.38374i	0.0406980	+	0.110601i
$937$	17.1603			0.560603			0.280302	−	0.959912i	$-0.409566\pi$
$937$	17.1603			0.560603			0.280302	+	0.959912i	$0.409566\pi$
$938$	1.15850	+	0.497571i	0.0378263	+	0.0162463i
$939$	−8.90859			−0.290721
$940$	−12.7321	−	22.0526i	−0.415275	−	0.719277i
$941$	47.0047	+	27.1382i	1.53231	+	0.884679i	0.999255	+	0.0385989i	$0.0122895\pi$
$941$	47.0047	+	27.1382i	1.53231	+	0.884679i	0.533055	+	0.846081i	$0.321044\pi$
$942$	−8.33864	−	4.81431i	−0.271688	−	0.156859i
$943$	−34.9062	+	20.1531i	−1.13670	+	0.656276i
$944$			5.01770i			0.163312i
$945$	−7.95472	+	0.942433i	−0.258767	+	0.0306573i
$946$	22.1204			0.719197
$947$	−13.7462	+	7.93635i	−0.446690	+	0.257897i	−0.706431	−	0.707781i	$-0.749696\pi$
$947$	−13.7462	+	7.93635i	−0.446690	+	0.257897i	0.259741	+	0.965678i	$0.416363\pi$
$948$	−7.34649	+	12.7245i	−0.238603	+	0.413272i
$949$	−9.11615	+	10.9424i	−0.295923	+	0.355205i
$950$	−2.71798	−	4.70769i	−0.0881831	−	0.152738i
$951$			5.91861i			0.191924i
$952$	−2.28556	−	3.06000i	−0.0740754	−	0.0991751i
$953$	−37.8350			−1.22560			−0.612799	−	0.790239i	$-0.709956\pi$
$953$	−37.8350			−1.22560			−0.612799	+	0.790239i	$0.709956\pi$
$954$	3.55583	−	2.05296i	0.115124	−	0.0664671i
$955$	−56.4100	−	32.5683i	−1.82538	−	1.05389i
$956$	5.72127	+	3.30317i	0.185039	+	0.106832i
$957$	12.8334	−	7.40939i	0.414846	−	0.239512i
$958$	14.1006			0.455569
$959$	−14.4656	−	19.3671i	−0.467118	−	0.625396i
$960$			3.02763i			0.0977162i
$961$	−14.0629	−	24.3577i	−0.453643	−	0.785733i
$962$	31.6389	+	26.3585i	1.02008	+	0.849832i
$963$	−4.00998	+	6.94549i	−0.129220	+	0.223815i
$964$	19.6527	−	11.3465i	0.632971	−	0.365446i
$965$	5.81820			0.187294
$966$	12.4090	−	1.47015i	0.399252	−	0.0473013i
$967$			17.8749i			0.574816i	0.957808	+	0.287408i	$0.0927936\pi$
$967$			17.8749i			0.574816i	−0.957808	+	0.287408i	$0.907206\pi$
$968$	−6.72803	+	3.88443i	−0.216247	+	0.124850i
$969$	−1.63107	−	0.941700i	−0.0523976	−	0.0302518i
$970$	−41.7187	−	24.0863i	−1.33951	−	0.773364i
$971$	6.16502	+	10.6781i	0.197845	+	0.342678i	0.947829	−	0.318778i	$-0.103272\pi$
$971$	6.16502	+	10.6781i	0.197845	+	0.342678i	−0.749984	+	0.661455i	$0.769939\pi$
$972$	1.00000			0.0320750
$973$	43.3254	+	18.6081i	1.38895	+	0.596550i
$974$	−13.3790			−0.428692
$975$	14.0984	−	5.18782i	0.451511	−	0.166143i
$976$	−0.505338	+	0.875271i	−0.0161755	+	0.0280167i
$977$	−33.5617	−	19.3769i	−1.07374	−	0.619921i	−0.144536	−	0.989500i	$-0.546169\pi$
$977$	−33.5617	−	19.3769i	−1.07374	−	0.619921i	−0.929200	+	0.369578i	$0.879502\pi$
$978$	−8.47691	−	14.6824i	−0.271062	−	0.469493i
$979$	−30.2393			−0.966453
$980$	15.3698	−	14.5921i	0.490969	−	0.466128i
$981$		−	1.05067i		−	0.0335453i
$982$	−17.6262	+	10.1765i	−0.562475	+	0.324745i
$983$	−6.61511	−	3.81923i	−0.210989	−	0.121815i	0.390782	−	0.920483i	$-0.372205\pi$
$983$	−6.61511	−	3.81923i	−0.210989	−	0.121815i	−0.601771	+	0.798669i	$0.705538\pi$
$984$	4.26706	−	7.39077i	0.136029	−	0.235609i
$985$	8.40330	+	14.5549i	0.267751	+	0.463759i
$986$		−	4.93779i		−	0.157251i
$987$	8.78162	−	20.4463i	0.279522	−	0.650812i
$988$	−4.63547	−	0.800501i	−0.147474	−	0.0254673i
$989$	12.0575	+	20.8842i	0.383407	+	0.664080i
$990$	11.3593	+	6.55830i	0.361023	+	0.208436i
$991$	−11.0735	+	19.1798i	−0.351760	+	0.609266i	−0.986558	−	0.163412i	$-0.947750\pi$
$991$	−11.0735	+	19.1798i	−0.351760	+	0.609266i	0.634798	+	0.772678i	$0.281083\pi$
$992$	−0.847661	−	1.46819i	−0.0269133	−	0.0466152i
$993$		−	11.6816i		−	0.370703i
$994$	−3.89084	−	32.8411i	−0.123410	−	1.04166i
$995$			21.4650i			0.680487i
$996$	−14.7729	+	8.52913i	−0.468097	+	0.270256i
$997$	3.59787	−	6.23169i	0.113946	−	0.197359i	−0.803412	−	0.595423i	$-0.796984\pi$
$997$	3.59787	−	6.23169i	0.113946	−	0.197359i	0.917358	+	0.398064i	$0.130318\pi$
$998$	−14.4797	+	25.0796i	−0.458347	+	0.793881i
$999$	9.89112	−	5.71064i	0.312941	−	0.180677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.c.25.5	✓	20
3.2	odd	2		1638.2.dm.e.1117.6		20
7.2	even	3	inner	546.2.bk.c.415.6	yes	20
7.3	odd	6		3822.2.c.n.883.1		10
7.4	even	3		3822.2.c.m.883.5		10
13.12	even	2	inner	546.2.bk.c.25.6	yes	20
21.2	odd	6		1638.2.dm.e.415.5		20
39.38	odd	2		1638.2.dm.e.1117.5		20
91.25	even	6		3822.2.c.m.883.6		10
91.38	odd	6		3822.2.c.n.883.10		10
91.51	even	6	inner	546.2.bk.c.415.5	yes	20
273.233	odd	6		1638.2.dm.e.415.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.c.25.5	✓	20	1.1	even	1	trivial
546.2.bk.c.25.6	yes	20	13.12	even	2	inner
546.2.bk.c.415.5	yes	20	91.51	even	6	inner
546.2.bk.c.415.6	yes	20	7.2	even	3	inner
1638.2.dm.e.415.5		20	21.2	odd	6
1638.2.dm.e.415.6		20	273.233	odd	6
1638.2.dm.e.1117.5		20	39.38	odd	2
1638.2.dm.e.1117.6		20	3.2	odd	2
3822.2.c.m.883.5		10	7.4	even	3
3822.2.c.m.883.6		10	91.25	even	6
3822.2.c.n.883.1		10	7.3	odd	6
3822.2.c.n.883.10		10	91.38	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.62200 - 1.51381i) q^{5} +1.00000i q^{6} +(2.43101 + 1.04411i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.62200 - 1.51381i) q^{5} +1.00000i q^{6} +(2.43101 + 1.04411i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.51381 + 2.62200i) q^{10} +(3.75189 + 2.16615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.613563 + 3.55296i) q^{13} +(-2.62738 + 0.311278i) q^{14} -3.02763i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.721788 + 1.25017i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-1.12988 + 0.652339i) q^{19} -3.02763i q^{20} +(2.11974 - 1.58326i) q^{21} -4.33230 q^{22} +(-2.36147 - 4.09019i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.08326 - 3.60832i) q^{25} +(-1.24512 - 3.38374i) q^{26} -1.00000 q^{27} +(2.11974 - 1.58326i) q^{28} +3.42053 q^{29} +(1.51381 + 2.62200i) q^{30} +(-1.46819 - 0.847661i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.75189 - 2.16615i) q^{33} -1.44358i q^{34} +(7.95472 - 0.942433i) q^{35} -1.00000 q^{36} +(-9.89112 + 5.71064i) q^{37} +(0.652339 - 1.12988i) q^{38} +(2.77017 + 2.30784i) q^{39} +(1.51381 + 2.62200i) q^{40} -8.53413i q^{41} +(-1.04411 + 2.43101i) q^{42} -5.10592 q^{43} +(3.75189 - 2.16615i) q^{44} +(-2.62200 - 1.51381i) q^{45} +(4.09019 + 2.36147i) q^{46} +(7.28379 - 4.20530i) q^{47} -1.00000 q^{48} +(4.81965 + 5.07651i) q^{49} +4.16653i q^{50} +(0.721788 + 1.25017i) q^{51} +(2.77017 + 2.30784i) q^{52} +(2.05296 - 3.55583i) q^{53} +(0.866025 - 0.500000i) q^{54} +13.1166 q^{55} +(-1.04411 + 2.43101i) q^{56} +1.30468i q^{57} +(-2.96227 + 1.71027i) q^{58} +(-4.34545 - 2.50885i) q^{59} +(-2.62200 - 1.51381i) q^{60} +(-0.505338 - 0.875271i) q^{61} +1.69532 q^{62} +(-0.311278 - 2.62738i) q^{63} -1.00000 q^{64} +(3.76976 + 10.2447i) q^{65} +(-2.16615 + 3.75189i) q^{66} +(-0.412703 - 0.238274i) q^{67} +(0.721788 + 1.25017i) q^{68} -4.72295 q^{69} +(-6.41777 + 4.79353i) q^{70} +12.4996i q^{71} +(0.866025 - 0.500000i) q^{72} +(3.42087 + 1.97504i) q^{73} +(5.71064 - 9.89112i) q^{74} +(-2.08326 - 3.60832i) q^{75} +1.30468i q^{76} +(6.85917 + 9.18334i) q^{77} +(-3.55296 - 0.613563i) q^{78} +(-7.34649 - 12.7245i) q^{79} +(-2.62200 - 1.51381i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.26706 + 7.39077i) q^{82} -17.0583i q^{83} +(-0.311278 - 2.62738i) q^{84} +4.37061i q^{85} +(4.42186 - 2.55296i) q^{86} +(1.71027 - 2.96227i) q^{87} +(-2.16615 + 3.75189i) q^{88} +(-6.04482 + 3.48998i) q^{89} +3.02763 q^{90} +(-5.20128 + 7.99667i) q^{91} -4.72295 q^{92} +(-1.46819 + 0.847661i) q^{93} +(-4.20530 + 7.28379i) q^{94} +(-1.97504 + 3.42087i) q^{95} +(0.866025 - 0.500000i) q^{96} +15.9110i q^{97} +(-6.71220 - 1.98656i) q^{98} -4.33230i 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

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