LMFDB - Embedded newform 462.2.p.a.439.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.3
Root			$0.500000 + 1.35798i$ of defining polynomial
Character	$\chi$	$=$	462.439
Dual form			462.2.p.a.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.92604 + 1.11200i) q^{5} -1.00000 q^{6} +(2.45660 - 0.982398i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.92604 + 1.11200i) q^{5} -1.00000 q^{6} +(2.45660 - 0.982398i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.11200 - 1.92604i) q^{10} +(-0.0571978 + 3.31613i) q^{11} +(0.866025 + 0.500000i) q^{12} -0.112712 q^{13} +(-2.61868 - 0.377519i) q^{14} +2.22400 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.119843 + 0.207574i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-0.218080 + 0.377726i) q^{19} +2.22400i q^{20} +(1.63628 - 2.07908i) q^{21} +(1.70760 - 2.84326i) q^{22} +(-0.401617 + 0.695621i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.0269081 - 0.0466061i) q^{25} +(0.0976119 + 0.0563562i) q^{26} -1.00000i q^{27} +(2.07908 + 1.63628i) q^{28} +7.50955i q^{29} +(-1.92604 - 1.11200i) q^{30} +(0.306643 - 0.177040i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.60853 + 2.90045i) q^{33} -0.239685i q^{34} +(5.82395 + 0.839603i) q^{35} +1.00000 q^{36} +(3.67483 - 6.36499i) q^{37} +(0.377726 - 0.218080i) q^{38} +(-0.0976119 + 0.0563562i) q^{39} +(1.11200 - 1.92604i) q^{40} +3.14869 q^{41} +(-2.45660 + 0.982398i) q^{42} -10.1874i q^{43} +(-2.90045 + 1.60853i) q^{44} +(1.92604 - 1.11200i) q^{45} +(0.695621 - 0.401617i) q^{46} +(-11.2232 - 6.47974i) q^{47} +1.00000i q^{48} +(5.06979 - 4.82672i) q^{49} +0.0538161i q^{50} +(0.207574 + 0.119843i) q^{51} +(-0.0563562 - 0.0976119i) q^{52} +(1.28196 + 2.22041i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.79771 + 6.32340i) q^{55} +(-0.982398 - 2.45660i) q^{56} +0.436161i q^{57} +(3.75478 - 6.50347i) q^{58} +(3.27440 - 1.89048i) q^{59} +(1.11200 + 1.92604i) q^{60} +(0.525000 - 0.909326i) q^{61} -0.354081 q^{62} +(0.377519 - 2.61868i) q^{63} -1.00000 q^{64} +(-0.217089 - 0.125336i) q^{65} +(0.0571978 - 3.31613i) q^{66} +(2.48189 + 4.29875i) q^{67} +(-0.119843 + 0.207574i) q^{68} +0.803234i q^{69} +(-4.62388 - 3.63909i) q^{70} -7.58067 q^{71} +(-0.866025 - 0.500000i) q^{72} +(2.39827 + 4.15392i) q^{73} +(-6.36499 + 3.67483i) q^{74} +(-0.0466061 - 0.0269081i) q^{75} -0.436161 q^{76} +(3.11725 + 8.20261i) q^{77} +0.112712 q^{78} +(0.429215 + 0.247807i) q^{79} +(-1.92604 + 1.11200i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.72685 - 1.57435i) q^{82} -0.569186 q^{83} +(2.61868 + 0.377519i) q^{84} +0.533061i q^{85} +(-5.09368 + 8.82251i) q^{86} +(3.75478 + 6.50347i) q^{87} +(3.31613 + 0.0571978i) q^{88} +(-12.1232 - 6.99934i) q^{89} -2.22400 q^{90} +(-0.276890 + 0.110729i) q^{91} -0.803234 q^{92} +(0.177040 - 0.306643i) q^{93} +(6.47974 + 11.2232i) q^{94} +(-0.840064 + 0.485011i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.6708i q^{97} +(-6.80393 + 1.64517i) q^{98} +(2.84326 + 1.70760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.92604	+	1.11200i	0.861352	+	0.497302i	0.864465	−	0.502693i	$-0.167657\pi$
$5$	1.92604	+	1.11200i	0.861352	+	0.497302i	−0.00311268	+	0.999995i	$0.500991\pi$
$6$	−1.00000			−0.408248
$7$	2.45660	−	0.982398i	0.928508	−	0.371312i
$7$	2.45660	−	0.982398i	0.928508	−	0.371312i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.11200	−	1.92604i	−0.351646	−	0.609068i
$11$	−0.0571978	+	3.31613i	−0.0172458	+	0.999851i
$11$	−0.0571978	+	3.31613i	−0.0172458	+	0.999851i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.112712			−0.0312608			−0.0156304	−	0.999878i	$-0.504976\pi$
$13$	−0.112712			−0.0312608			−0.0156304	+	0.999878i	$0.504976\pi$
$14$	−2.61868	−	0.377519i	−0.699871	−	0.100896i
$15$	2.22400			0.574235
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.119843	+	0.207574i	0.0290661	+	0.0503440i	0.880193	−	0.474617i	$-0.157413\pi$
$17$	0.119843	+	0.207574i	0.0290661	+	0.0503440i	−0.851126	+	0.524961i	$0.824080\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−0.218080	+	0.377726i	−0.0500311	+	0.0866564i	−0.889956	−	0.456046i	$-0.849265\pi$
$19$	−0.218080	+	0.377726i	−0.0500311	+	0.0866564i	0.839925	+	0.542702i	$0.182599\pi$
$20$			2.22400i			0.497302i
$21$	1.63628	−	2.07908i	0.357066	−	0.453693i
$22$	1.70760	−	2.84326i	0.364062	−	0.606184i
$23$	−0.401617	+	0.695621i	−0.0837429	+	0.145047i	−0.904855	−	0.425720i	$-0.860021\pi$
$23$	−0.401617	+	0.695621i	−0.0837429	+	0.145047i	0.821112	+	0.570767i	$0.193354\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.0269081	−	0.0466061i	−0.00538161	−	0.00932123i
$26$	0.0976119	+	0.0563562i	0.0191433	+	0.0110524i
$27$		−	1.00000i		−	0.192450i
$28$	2.07908	+	1.63628i	0.392910	+	0.309228i
$29$			7.50955i			1.39449i	0.716833	+	0.697245i	$0.245591\pi$
$29$			7.50955i			1.39449i	−0.716833	+	0.697245i	$0.754409\pi$
$30$	−1.92604	−	1.11200i	−0.351646	−	0.203023i
$31$	0.306643	−	0.177040i	0.0550747	−	0.0317974i	−0.472210	−	0.881486i	$-0.656544\pi$
$31$	0.306643	−	0.177040i	0.0550747	−	0.0317974i	0.527285	+	0.849689i	$0.323210\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.60853	+	2.90045i	0.280009	+	0.504904i
$34$		−	0.239685i		−	0.0411057i
$35$	5.82395	+	0.839603i	0.984427	+	0.141919i
$36$	1.00000			0.166667
$37$	3.67483	−	6.36499i	0.604138	−	1.04640i	−0.388049	−	0.921639i	$-0.626851\pi$
$37$	3.67483	−	6.36499i	0.604138	−	1.04640i	0.992187	−	0.124759i	$-0.0398158\pi$
$38$	0.377726	−	0.218080i	0.0612753	−	0.0353773i
$39$	−0.0976119	+	0.0563562i	−0.0156304	+	0.00902422i
$40$	1.11200	−	1.92604i	0.175823	−	0.304534i
$41$	3.14869			0.491743			0.245872	−	0.969302i	$-0.420926\pi$
$41$	3.14869			0.491743			0.245872	+	0.969302i	$0.420926\pi$
$42$	−2.45660	+	0.982398i	−0.379062	+	0.151587i
$43$		−	10.1874i		−	1.55356i	−0.629774	−	0.776779i	$-0.716852\pi$
$43$		−	10.1874i		−	1.55356i	0.629774	−	0.776779i	$-0.283148\pi$
$44$	−2.90045	+	1.60853i	−0.437260	+	0.242495i
$45$	1.92604	−	1.11200i	0.287117	−	0.165767i
$46$	0.695621	−	0.401617i	0.102564	−	0.0592152i
$47$	−11.2232	−	6.47974i	−1.63708	−	0.945168i	−0.981832	−	0.189753i	$-0.939231\pi$
$47$	−11.2232	−	6.47974i	−1.63708	−	0.945168i	−0.655246	−	0.755415i	$-0.727435\pi$
$48$			1.00000i			0.144338i
$49$	5.06979	−	4.82672i	0.724255	−	0.689532i
$50$			0.0538161i			0.00761075i
$51$	0.207574	+	0.119843i	0.0290661	+	0.0167813i
$52$	−0.0563562	−	0.0976119i	−0.00781520	−	0.0135363i
$53$	1.28196	+	2.22041i	0.176090	+	0.304997i	0.940538	−	0.339688i	$-0.110322\pi$
$53$	1.28196	+	2.22041i	0.176090	+	0.304997i	−0.764448	+	0.644686i	$0.776988\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.79771	+	6.32340i	−0.512083	+	0.852648i
$56$	−0.982398	−	2.45660i	−0.131278	−	0.328277i
$57$			0.436161i			0.0577709i
$58$	3.75478	−	6.50347i	0.493026	−	0.853947i
$59$	3.27440	−	1.89048i	0.426291	−	0.246119i	−0.271474	−	0.962446i	$-0.587511\pi$
$59$	3.27440	−	1.89048i	0.426291	−	0.246119i	0.697765	+	0.716326i	$0.254178\pi$
$60$	1.11200	+	1.92604i	0.143559	+	0.248651i
$61$	0.525000	−	0.909326i	0.0672193	−	0.116427i	−0.830457	−	0.557083i	$-0.811921\pi$
$61$	0.525000	−	0.909326i	0.0672193	−	0.116427i	0.897676	+	0.440655i	$0.145254\pi$
$62$	−0.354081			−0.0449683
$63$	0.377519	−	2.61868i	0.0475629	−	0.329923i
$64$	−1.00000			−0.125000
$65$	−0.217089	−	0.125336i	−0.0269266	−	0.0155461i
$66$	0.0571978	−	3.31613i	0.00704056	−	0.408188i
$67$	2.48189	+	4.29875i	0.303211	+	0.525176i	0.976861	−	0.213874i	$-0.0686081\pi$
$67$	2.48189	+	4.29875i	0.303211	+	0.525176i	−0.673651	+	0.739050i	$0.735275\pi$
$68$	−0.119843	+	0.207574i	−0.0145331	+	0.0251720i
$69$			0.803234i			0.0966980i
$70$	−4.62388	−	3.63909i	−0.552660	−	0.434955i
$71$	−7.58067			−0.899660			−0.449830	−	0.893114i	$-0.648515\pi$
$71$	−7.58067			−0.899660			−0.449830	+	0.893114i	$0.648515\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	2.39827	+	4.15392i	0.280696	+	0.486179i	0.971556	−	0.236809i	$-0.0761015\pi$
$73$	2.39827	+	4.15392i	0.280696	+	0.486179i	−0.690861	+	0.722988i	$0.742768\pi$
$74$	−6.36499	+	3.67483i	−0.739915	+	0.427190i
$75$	−0.0466061	−	0.0269081i	−0.00538161	−	0.00310708i
$76$	−0.436161			−0.0500311
$77$	3.11725	+	8.20261i	0.355244	+	0.934774i
$78$	0.112712			0.0127622
$79$	0.429215	+	0.247807i	0.0482905	+	0.0278805i	0.523951	−	0.851748i	$-0.324458\pi$
$79$	0.429215	+	0.247807i	0.0482905	+	0.0278805i	−0.475660	+	0.879629i	$0.657791\pi$
$80$	−1.92604	+	1.11200i	−0.215338	+	0.124325i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.72685	−	1.57435i	−0.301130	−	0.173857i
$83$	−0.569186			−0.0624763			−0.0312381	−	0.999512i	$-0.509945\pi$
$83$	−0.569186			−0.0624763			−0.0312381	+	0.999512i	$0.509945\pi$
$84$	2.61868	+	0.377519i	0.285721	+	0.0411907i
$85$			0.533061i			0.0578186i
$86$	−5.09368	+	8.82251i	−0.549266	+	0.951356i
$87$	3.75478	+	6.50347i	0.402554	+	0.697245i
$88$	3.31613	+	0.0571978i	0.353501	+	0.00609730i
$89$	−12.1232	−	6.99934i	−1.28506	−	0.741928i	−0.307289	−	0.951616i	$-0.599422\pi$
$89$	−12.1232	−	6.99934i	−1.28506	−	0.741928i	−0.977768	+	0.209688i	$0.932755\pi$
$90$	−2.22400			−0.234430
$91$	−0.276890	+	0.110729i	−0.0290259	+	0.0116075i
$92$	−0.803234			−0.0837429
$93$	0.177040	−	0.306643i	0.0183582	−	0.0317974i
$94$	6.47974	+	11.2232i	0.668334	+	1.15759i
$95$	−0.840064	+	0.485011i	−0.0861888	+	0.0497611i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			10.6708i			1.08345i	0.840554	+	0.541727i	$0.182230\pi$
$97$			10.6708i			1.08345i	−0.840554	+	0.541727i	$0.817770\pi$
$98$	−6.80393	+	1.64517i	−0.687300	+	0.166187i
$99$	2.84326	+	1.70760i	0.285758	+	0.171620i
$100$	0.0269081	−	0.0466061i	0.00269081	−	0.00466061i
$101$	9.76595	+	16.9151i	0.971748	+	1.68312i	0.690274	+	0.723548i	$0.257490\pi$
$101$	9.76595	+	16.9151i	0.971748	+	1.68312i	0.281474	+	0.959569i	$0.409177\pi$
$102$	−0.119843	−	0.207574i	−0.0118662	−	0.0205529i
$103$	−11.0669	−	6.38947i	−1.09045	−	0.629573i	−0.156756	−	0.987637i	$-0.550104\pi$
$103$	−11.0669	−	6.38947i	−1.09045	−	0.629573i	−0.933697	+	0.358064i	$0.883437\pi$
$104$			0.112712i			0.0110524i
$105$	5.46349	−	2.18486i	0.533182	−	0.213220i
$106$		−	2.56391i		−	0.249029i
$107$	−10.8886	−	6.28656i	−1.05264	−	0.607745i	−0.129256	−	0.991611i	$-0.541259\pi$
$107$	−10.8886	−	6.28656i	−1.05264	−	0.607745i	−0.923389	+	0.383867i	$0.874592\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−14.3351	+	8.27635i	−1.37305	+	0.792730i	−0.991311	−	0.131540i	$-0.958008\pi$
$109$	−14.3351	+	8.27635i	−1.37305	+	0.792730i	−0.381739	+	0.924270i	$0.624675\pi$
$110$	6.45061	−	3.57738i	0.615042	−	0.341089i
$111$		−	7.34966i		−	0.697598i
$112$	−0.377519	+	2.61868i	−0.0356722	+	0.247442i
$113$	−8.19898			−0.771295			−0.385647	−	0.922646i	$-0.626022\pi$
$113$	−8.19898			−0.771295			−0.385647	+	0.922646i	$0.626022\pi$
$114$	0.218080	−	0.377726i	0.0204251	−	0.0353773i
$115$	−1.54706	+	0.893197i	−0.144264	+	0.0832910i
$116$	−6.50347	+	3.75478i	−0.603832	+	0.348622i
$117$	−0.0563562	+	0.0976119i	−0.00521014	+	0.00902422i
$118$	−3.78095			−0.348065
$119$	0.498326	+	0.392193i	0.0456815	+	0.0359522i
$120$		−	2.22400i		−	0.203023i
$121$	−10.9935	−	0.379351i	−0.999405	−	0.0344864i
$122$	−0.909326	+	0.525000i	−0.0823265	+	0.0475312i
$123$	2.72685	−	1.57435i	0.245872	−	0.141954i
$124$	0.306643	+	0.177040i	0.0275374	+	0.0158987i
$125$		−	11.2397i		−	1.00531i
$126$	−1.63628	+	2.07908i	−0.145771	+	0.185219i
$127$		−	5.11237i		−	0.453650i	−0.973936	−	0.226825i	$-0.927166\pi$
$127$		−	5.11237i		−	0.453650i	0.973936	−	0.226825i	$-0.0728345\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−5.09368	−	8.82251i	−0.448473	−	0.776779i
$130$	0.125336	+	0.217089i	0.0109927	+	0.0190400i
$131$	−1.02912	+	1.78250i	−0.0899150	+	0.155737i	−0.907475	−	0.420106i	$-0.861993\pi$
$131$	−1.02912	+	1.78250i	−0.0899150	+	0.155737i	0.817560	+	0.575843i	$0.195326\pi$
$132$	−1.70760	+	2.84326i	−0.148628	+	0.247474i
$133$	−0.164659	+	1.14217i	−0.0142778	+	0.0990383i
$134$		−	4.96377i		−	0.428804i
$135$	1.11200	−	1.92604i	0.0957058	−	0.165767i
$136$	0.207574	−	0.119843i	0.0177993	−	0.0102764i
$137$	9.42545	+	16.3254i	0.805271	+	1.39477i	0.916108	+	0.400931i	$0.131313\pi$
$137$	9.42545	+	16.3254i	0.805271	+	1.39477i	−0.110838	+	0.993839i	$0.535353\pi$
$138$	0.401617	−	0.695621i	0.0341879	−	0.0592152i
$139$	−10.5033			−0.890880			−0.445440	−	0.895312i	$-0.646953\pi$
$139$	−10.5033			−0.890880			−0.445440	+	0.895312i	$0.646953\pi$
$140$	2.18486	+	5.46349i	0.184654	+	0.461749i
$141$	−12.9595			−1.09139
$142$	6.56505	+	3.79033i	0.550927	+	0.318078i
$143$	0.00644690	−	0.373769i	0.000539117	−	0.0312562i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−8.35063	+	14.4637i	−0.693482	+	1.20115i
$146$		−	4.79653i		−	0.396964i
$147$	1.97720	−	6.71496i	0.163077	−	0.553840i
$148$	7.34966			0.604138
$149$	−12.6570	−	7.30752i	−1.03690	−	0.598656i	−0.117948	−	0.993020i	$-0.537631\pi$
$149$	−12.6570	−	7.30752i	−1.03690	−	0.598656i	−0.918954	+	0.394364i	$0.870965\pi$
$150$	0.0269081	+	0.0466061i	0.00219703	+	0.00380538i
$151$	−1.57663	+	0.910267i	−0.128304	+	0.0740764i	−0.562778	−	0.826608i	$-0.690268\pi$
$151$	−1.57663	+	0.910267i	−0.128304	+	0.0740764i	0.434474	+	0.900684i	$0.356934\pi$
$152$	0.377726	+	0.218080i	0.0306377	+	0.0176887i
$153$	0.239685			0.0193774
$154$	1.40169	−	8.66229i	0.112951	−	0.698027i
$155$	0.787477			0.0632516
$156$	−0.0976119	−	0.0563562i	−0.00781520	−	0.00451211i
$157$	15.1388	−	8.74037i	1.20821	−	0.697558i	0.245839	−	0.969311i	$-0.420937\pi$
$157$	15.1388	−	8.74037i	1.20821	−	0.697558i	0.962367	+	0.271753i	$0.0876034\pi$
$158$	−0.247807	−	0.429215i	−0.0197145	−	0.0341465i
$159$	2.22041	+	1.28196i	0.176090	+	0.101666i
$160$	2.22400			0.175823
$161$	−0.303236	+	2.10341i	−0.0238984	+	0.165772i
$162$			1.00000i			0.0785674i
$163$	−5.84566	+	10.1250i	−0.457867	+	0.793049i	−0.998848	−	0.0479858i	$-0.984720\pi$
$163$	−5.84566	+	10.1250i	−0.457867	+	0.793049i	0.540981	+	0.841035i	$0.318053\pi$
$164$	1.57435	+	2.72685i	0.122936	+	0.212931i
$165$	−0.127208	+	7.37508i	−0.00990313	+	0.574149i
$166$	0.492929	+	0.284593i	0.0382587	+	0.0220887i
$167$	18.4885			1.43068			0.715341	−	0.698775i	$-0.246271\pi$
$167$	18.4885			1.43068			0.715341	+	0.698775i	$0.246271\pi$
$168$	−2.07908	−	1.63628i	−0.160405	−	0.126242i
$169$	−12.9873			−0.999023
$170$	0.266530	−	0.461644i	0.0204419	−	0.0354065i
$171$	0.218080	+	0.377726i	0.0166770	+	0.0288855i
$172$	8.82251	−	5.09368i	0.672710	−	0.388389i
$173$	8.59437	−	14.8859i	0.653418	−	1.13175i	−0.328870	−	0.944375i	$-0.606668\pi$
$173$	8.59437	−	14.8859i	0.653418	−	1.13175i	0.982288	−	0.187378i	$-0.0599988\pi$
$174$		−	7.50955i		−	0.569298i
$175$	−0.111888	−	0.0880583i	−0.00845795	−	0.00665658i
$176$	−2.84326	−	1.70760i	−0.214318	−	0.128715i
$177$	1.89048	−	3.27440i	0.142097	−	0.246119i
$178$	6.99934	+	12.1232i	0.524622	+	0.908673i
$179$	−5.81838	−	10.0777i	−0.434886	−	0.753244i	0.562400	−	0.826865i	$-0.309878\pi$
$179$	−5.81838	−	10.0777i	−0.434886	−	0.753244i	−0.997286	+	0.0736206i	$0.976545\pi$
$180$	1.92604	+	1.11200i	0.143559	+	0.0828837i
$181$			21.9534i			1.63179i	0.578203	+	0.815893i	$0.303754\pi$
$181$			21.9534i			1.63179i	−0.578203	+	0.815893i	$0.696246\pi$
$182$	0.295158	+	0.0425511i	0.0218785	+	0.00315410i
$183$		−	1.05000i		−	0.0776182i
$184$	0.695621	+	0.401617i	0.0512818	+	0.0296076i
$185$	14.1557	−	8.17282i	1.04075	−	0.600878i
$186$	−0.306643	+	0.177040i	−0.0224842	+	0.0129812i
$187$	−0.695196	+	0.385541i	−0.0508378	+	0.0281936i
$188$		−	12.9595i		−	0.945168i
$189$	−0.982398	−	2.45660i	−0.0714590	−	0.178692i
$190$	0.970023			0.0703728
$191$	2.99269	−	5.18349i	0.216543	−	0.375064i	−0.737205	−	0.675669i	$-0.763855\pi$
$191$	2.99269	−	5.18349i	0.216543	−	0.375064i	0.953749	+	0.300604i	$0.0971884\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−7.35467	+	4.24622i	−0.529401	+	0.305650i	−0.740772	−	0.671756i	$-0.765540\pi$
$193$	−7.35467	+	4.24622i	−0.529401	+	0.305650i	0.211372	+	0.977406i	$0.432207\pi$
$194$	5.33540	−	9.24118i	0.383059	−	0.663478i
$195$	−0.250673			−0.0179510
$196$	6.71496	+	1.97720i	0.479640	+	0.141229i
$197$		−	3.71109i		−	0.264404i	−0.991223	−	0.132202i	$-0.957795\pi$
$197$		−	3.71109i		−	0.264404i	0.991223	−	0.132202i	$-0.0422048\pi$
$198$	−1.60853	−	2.90045i	−0.114313	−	0.206126i
$199$	4.99176	−	2.88199i	0.353857	−	0.204299i	−0.312526	−	0.949909i	$-0.601175\pi$
$199$	4.99176	−	2.88199i	0.353857	−	0.204299i	0.666383	+	0.745610i	$0.267842\pi$
$200$	−0.0466061	+	0.0269081i	−0.00329555	+	0.00190269i
$201$	4.29875	+	2.48189i	0.303211	+	0.175059i
$202$		−	19.5319i		−	1.37426i
$203$	7.37737	+	18.4480i	0.517790	+	1.29479i
$204$			0.239685i			0.0167813i
$205$	6.06451	+	3.50135i	0.423564	+	0.244545i
$206$	6.38947	+	11.0669i	0.445176	+	0.771067i
$207$	0.401617	+	0.695621i	0.0279143	+	0.0483490i
$208$	0.0563562	−	0.0976119i	0.00390760	−	0.00676816i
$209$	−1.24012	−	0.744789i	−0.0857807	−	0.0515181i
$210$	−5.82395	−	0.839603i	−0.401890	−	0.0579381i
$211$		−	23.1201i		−	1.59165i	−0.605524	−	0.795827i	$-0.707037\pi$
$211$		−	23.1201i		−	1.59165i	0.605524	−	0.795827i	$-0.292963\pi$
$212$	−1.28196	+	2.22041i	−0.0880451	+	0.152499i
$213$	−6.56505	+	3.79033i	−0.449830	+	0.259709i
$214$	6.28656	+	10.8886i	0.429740	+	0.744332i
$215$	11.3284	−	19.6213i	0.772587	−	1.33816i
$216$	−1.00000			−0.0680414
$217$	0.579376	−	0.736164i	0.0393306	−	0.0499740i
$218$	16.5527			1.12109
$219$	4.15392	+	2.39827i	0.280696	+	0.162060i
$220$	−7.37508	−	0.127208i	−0.497228	−	0.00857636i
$221$	−0.0135078	−	0.0233961i	−0.000908631	−	0.00157379i
$222$	−3.67483	+	6.36499i	−0.246638	+	0.427190i
$223$			11.3233i			0.758267i	0.925342	+	0.379134i	$0.123778\pi$
$223$			11.3233i			0.758267i	−0.925342	+	0.379134i	$0.876222\pi$
$224$	1.63628	−	2.07908i	0.109329	−	0.138915i
$225$	−0.0538161			−0.00358774
$226$	7.10052	+	4.09949i	0.472320	+	0.272694i
$227$	2.66623	+	4.61805i	0.176964	+	0.306510i	0.940839	−	0.338853i	$-0.110039\pi$
$227$	2.66623	+	4.61805i	0.176964	+	0.306510i	−0.763875	+	0.645364i	$0.776706\pi$
$228$	−0.377726	+	0.218080i	−0.0250155	+	0.0144427i
$229$	15.6189	+	9.01755i	1.03212	+	0.595897i	0.917592	−	0.397523i	$-0.130130\pi$
$229$	15.6189	+	9.01755i	1.03212	+	0.595897i	0.114531	+	0.993420i	$0.463463\pi$
$230$	1.78639			0.117791
$231$	6.80092	+	5.54504i	0.447468	+	0.364837i
$232$	7.50955			0.493026
$233$	−13.5770	−	7.83866i	−0.889456	−	0.513528i	−0.0156917	−	0.999877i	$-0.504995\pi$
$233$	−13.5770	−	7.83866i	−0.889456	−	0.513528i	−0.873765	+	0.486349i	$0.838328\pi$
$234$	0.0976119	−	0.0563562i	0.00638109	−	0.00368412i
$235$	−14.4110	−	24.9605i	−0.940067	−	1.62824i
$236$	3.27440	+	1.89048i	0.213145	+	0.123060i
$237$	0.495615			0.0321936
$238$	−0.235467	−	0.588812i	−0.0152630	−	0.0381670i
$239$		−	19.6987i		−	1.27420i	−0.770780	−	0.637101i	$-0.780133\pi$
$239$		−	19.6987i		−	1.27420i	0.770780	−	0.637101i	$-0.219867\pi$
$240$	−1.11200	+	1.92604i	−0.0717793	+	0.124325i
$241$	3.85279	+	6.67323i	0.248180	+	0.429861i	0.963021	−	0.269427i	$-0.0868342\pi$
$241$	3.85279	+	6.67323i	0.248180	+	0.429861i	−0.714841	+	0.699287i	$0.753501\pi$
$242$	9.33094	+	5.82526i	0.599815	+	0.374462i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.05000			0.0672193
$245$	15.1319	−	3.65886i	0.966744	−	0.233756i
$246$	−3.14869			−0.200753
$247$	0.0245804	−	0.0425745i	0.00156401	−	0.00270895i
$248$	−0.177040	−	0.306643i	−0.0112421	−	0.0194719i
$249$	−0.492929	+	0.284593i	−0.0312381	+	0.0180353i
$250$	−5.61985	+	9.73386i	−0.355430	+	0.615624i
$251$			11.3888i			0.718857i	0.933173	+	0.359428i	$0.117028\pi$
$251$			11.3888i			0.718857i	−0.933173	+	0.359428i	$0.882972\pi$
$252$	2.45660	−	0.982398i	0.154751	−	0.0618853i
$253$	−2.28380	−	1.37160i	−0.143581	−	0.0862319i
$254$	−2.55619	+	4.42744i	−0.160389	+	0.277803i
$255$	0.266530	+	0.461644i	0.0166908	+	0.0289093i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.9973	+	8.08134i	0.873127	+	0.504100i	0.868386	−	0.495888i	$-0.165158\pi$
$257$	13.9973	+	8.08134i	0.873127	+	0.504100i	0.00474110	+	0.999989i	$0.498491\pi$
$258$			10.1874i			0.634237i
$259$	2.77464	−	19.2464i	0.172407	−	1.19591i
$260$		−	0.250673i		−	0.0155461i
$261$	6.50347	+	3.75478i	0.402554	+	0.232415i
$262$	1.78250	−	1.02912i	0.110123	−	0.0635795i
$263$	−7.43191	+	4.29081i	−0.458271	+	0.264583i	−0.711317	−	0.702871i	$-0.751901\pi$
$263$	−7.43191	+	4.29081i	−0.458271	+	0.264583i	0.253046	+	0.967454i	$0.418568\pi$
$264$	2.90045	−	1.60853i	0.178511	−	0.0989982i
$265$			5.70215i			0.350280i
$266$	0.713682	−	0.906815i	0.0437586	−	0.0556004i
$267$	−13.9987			−0.856705
$268$	−2.48189	+	4.29875i	−0.151605	+	0.262588i
$269$	3.58587	−	2.07030i	0.218634	−	0.126229i	−0.386683	−	0.922213i	$-0.626379\pi$
$269$	3.58587	−	2.07030i	0.218634	−	0.126229i	0.605318	+	0.795984i	$0.293046\pi$
$270$	−1.92604	+	1.11200i	−0.117215	+	0.0676742i
$271$	1.71583	−	2.97190i	0.104229	−	0.180530i	−0.809194	−	0.587542i	$-0.800096\pi$
$271$	1.71583	−	2.97190i	0.104229	−	0.180530i	0.913423	+	0.407012i	$0.133429\pi$
$272$	−0.239685			−0.0145331
$273$	−0.184429	+	0.234339i	−0.0111622	+	0.0141828i
$274$		−	18.8509i		−	1.13882i
$275$	0.156091	−	0.0865649i	0.00941265	−	0.00522006i
$276$	−0.695621	+	0.401617i	−0.0418714	+	0.0241745i
$277$	−1.35959	+	0.784960i	−0.0816899	+	0.0471637i	−0.540289	−	0.841480i	$-0.681685\pi$
$277$	−1.35959	+	0.784960i	−0.0816899	+	0.0471637i	0.458599	+	0.888643i	$0.348352\pi$
$278$	9.09614	+	5.25166i	0.545550	+	0.314974i
$279$		−	0.354081i		−	0.0211983i
$280$	0.839603	−	5.82395i	0.0501759	−	0.348047i
$281$			3.49877i			0.208719i	0.994540	+	0.104360i	$0.0332793\pi$
$281$			3.49877i			0.208719i	−0.994540	+	0.104360i	$0.966721\pi$
$282$	11.2232	+	6.47974i	0.668334	+	0.385863i
$283$	−11.1106	−	19.2440i	−0.660454	−	1.14394i	−0.980496	−	0.196537i	$-0.937031\pi$
$283$	−11.1106	−	19.2440i	−0.660454	−	1.14394i	0.320043	−	0.947403i	$-0.396303\pi$
$284$	−3.79033	−	6.56505i	−0.224915	−	0.389564i
$285$	−0.485011	+	0.840064i	−0.0287296	+	0.0497611i
$286$	−0.192468	+	0.320470i	−0.0113809	+	0.0189498i
$287$	7.73508	−	3.09327i	0.456588	−	0.182590i
$288$		−	1.00000i		−	0.0589256i
$289$	8.47128	−	14.6727i	0.498310	−	0.863099i
$290$	14.4637	−	8.35063i	0.849339	−	0.490366i
$291$	5.33540	+	9.24118i	0.312766	+	0.541727i
$292$	−2.39827	+	4.15392i	−0.140348	+	0.243090i
$293$	−6.85562			−0.400510			−0.200255	−	0.979744i	$-0.564177\pi$
$293$	−6.85562			−0.400510			−0.200255	+	0.979744i	$0.564177\pi$
$294$	−5.06979	+	4.82672i	−0.295676	+	0.281500i
$295$	8.40885			0.489582
$296$	−6.36499	−	3.67483i	−0.369957	−	0.213595i
$297$	3.31613	+	0.0571978i	0.192421	+	0.00331895i
$298$	7.30752	+	12.6570i	0.423313	+	0.733200i
$299$	0.0452672	−	0.0784051i	0.00261787	−	0.00453429i
$300$		−	0.0538161i		−	0.00310708i
$301$	−10.0080	−	25.0263i	−0.576854	−	1.44249i
$302$	1.82053			0.104760
$303$	16.9151	+	9.76595i	0.971748	+	0.561039i
$304$	−0.218080	−	0.377726i	−0.0125078	−	0.0216641i
$305$	2.02234	−	1.16760i	0.115799	−	0.0668566i
$306$	−0.207574	−	0.119843i	−0.0118662	−	0.00685095i
$307$	25.3466			1.44661			0.723303	−	0.690531i	$-0.242623\pi$
$307$	25.3466			1.44661			0.723303	+	0.690531i	$0.242623\pi$
$308$	−5.54504	+	6.80092i	−0.315958	+	0.387518i
$309$	−12.7789			−0.726969
$310$	−0.681975	−	0.393738i	−0.0387336	−	0.0223628i
$311$	12.0093	−	6.93356i	0.680984	−	0.393166i	−0.119242	−	0.992865i	$-0.538046\pi$
$311$	12.0093	−	6.93356i	0.680984	−	0.393166i	0.800226	+	0.599699i	$0.204713\pi$
$312$	0.0563562	+	0.0976119i	0.00319054	+	0.00552618i
$313$	10.4414	+	6.02834i	0.590183	+	0.340742i	0.765170	−	0.643829i	$-0.222655\pi$
$313$	10.4414	+	6.02834i	0.590183	+	0.340742i	−0.174987	+	0.984571i	$0.555988\pi$
$314$	−17.4807			−0.986496
$315$	3.63909	−	4.62388i	0.205040	−	0.260526i
$316$			0.495615i			0.0278805i
$317$	3.77629	−	6.54073i	0.212098	−	0.367364i	−0.740273	−	0.672306i	$-0.765304\pi$
$317$	3.77629	−	6.54073i	0.212098	−	0.367364i	0.952371	+	0.304942i	$0.0986372\pi$
$318$	−1.28196	−	2.22041i	−0.0718885	−	0.124515i
$319$	−24.9027	−	0.429530i	−1.39428	−	0.0240491i
$320$	−1.92604	−	1.11200i	−0.107669	−	0.0621627i
$321$	−12.5731			−0.701763
$322$	1.31432	−	1.66999i	0.0732439	−	0.0930649i
$323$	−0.104541			−0.00581684
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	0.00303287	+	0.00525309i	0.000168234	+	0.000291389i
$326$	10.1250	−	5.84566i	0.560770	−	0.323761i
$327$	−8.27635	+	14.3351i	−0.457683	+	0.792730i
$328$		−	3.14869i		−	0.173857i
$329$	−33.9367	−	4.89245i	−1.87099	−	0.269730i
$330$	3.79771	−	6.32340i	0.209057	−	0.348092i
$331$	−11.2835	+	19.5435i	−0.620195	+	1.07421i	0.369255	+	0.929328i	$0.379613\pi$
$331$	−11.2835	+	19.5435i	−0.620195	+	1.07421i	−0.989449	+	0.144880i	$0.953720\pi$
$332$	−0.284593	−	0.492929i	−0.0156191	−	0.0270530i
$333$	−3.67483	−	6.36499i	−0.201379	−	0.348799i
$334$	−16.0115	−	9.24425i	−0.876111	−	0.505823i
$335$			11.0394i			0.603149i
$336$	0.982398	+	2.45660i	0.0535942	+	0.134019i
$337$			32.4695i			1.76872i	0.466801	+	0.884362i	$0.345406\pi$
$337$			32.4695i			1.76872i	−0.466801	+	0.884362i	$0.654594\pi$
$338$	11.2473	+	6.49365i	0.611774	+	0.353208i
$339$	−7.10052	+	4.09949i	−0.385647	+	0.222654i
$340$	−0.461644	+	0.266530i	−0.0250362	+	0.0144546i
$341$	0.569550	+	1.02700i	0.0308429	+	0.0556149i
$342$		−	0.436161i		−	0.0235849i
$343$	7.71269	−	16.8379i	0.416446	−	0.909161i
$344$	−10.1874			−0.549266
$345$	−0.893197	+	1.54706i	−0.0480881	+	0.0832910i
$346$	−14.8859	+	8.59437i	−0.800270	+	0.462036i
$347$	−26.6239	+	15.3713i	−1.42924	+	0.825174i	−0.997061	−	0.0766119i	$-0.975590\pi$
$347$	−26.6239	+	15.3713i	−1.42924	+	0.825174i	−0.432183	+	0.901786i	$0.642256\pi$
$348$	−3.75478	+	6.50347i	−0.201277	+	0.348622i
$349$	24.5576			1.31454			0.657269	−	0.753656i	$-0.271712\pi$
$349$	24.5576			1.31454			0.657269	+	0.753656i	$0.271712\pi$
$350$	0.0528689	+	0.132205i	0.00282596	+	0.00706665i
$351$			0.112712i			0.00601615i
$352$	1.60853	+	2.90045i	0.0857350	+	0.154595i
$353$	3.74418	−	2.16170i	0.199283	−	0.115056i	−0.397038	−	0.917802i	$-0.629962\pi$
$353$	3.74418	−	2.16170i	0.199283	−	0.115056i	0.596321	+	0.802746i	$0.296629\pi$
$354$	−3.27440	+	1.89048i	−0.174033	+	0.100478i
$355$	−14.6007	−	8.42971i	−0.774924	−	0.447402i
$356$		−	13.9987i		−	0.741928i
$357$	0.627659	+	0.0904858i	0.0332192	+	0.00478902i
$358$			11.6368i			0.615021i
$359$	−13.7848	−	7.95866i	−0.727534	−	0.420042i	0.0899854	−	0.995943i	$-0.471318\pi$
$359$	−13.7848	−	7.95866i	−0.727534	−	0.420042i	−0.817519	+	0.575901i	$0.804651\pi$
$360$	−1.11200	−	1.92604i	−0.0586076	−	0.101511i
$361$	9.40488	+	16.2897i	0.494994	+	0.857354i
$362$	10.9767	−	19.0122i	0.576923	−	0.999260i
$363$	−9.71029	+	5.16820i	−0.509658	+	0.271260i
$364$	−0.234339	−	0.184429i	−0.0122827	−	0.00966672i
$365$			10.6675i			0.558362i
$366$	−0.525000	+	0.909326i	−0.0274422	+	0.0475312i
$367$	−22.2966	+	12.8729i	−1.16387	+	0.671962i	−0.952229	−	0.305385i	$-0.901215\pi$
$367$	−22.2966	+	12.8729i	−1.16387	+	0.671962i	−0.211643	+	0.977347i	$0.567881\pi$
$368$	−0.401617	−	0.695621i	−0.0209357	−	0.0362617i
$369$	1.57435	−	2.72685i	0.0819572	−	0.141954i
$370$	−16.3456			−0.849770
$371$	5.33059	+	4.19528i	0.276750	+	0.217808i
$372$	0.354081			0.0183582
$373$	25.2676	+	14.5882i	1.30831	+	0.755350i	0.981813	−	0.189850i	$-0.0608000\pi$
$373$	25.2676	+	14.5882i	1.30831	+	0.755350i	0.326492	+	0.945200i	$0.394133\pi$
$374$	0.794828	+	0.0137095i	0.0410996	+	0.000708900i
$375$	−5.61985	−	9.73386i	−0.290208	−	0.502654i
$376$	−6.47974	+	11.2232i	−0.334167	+	0.578795i
$377$		−	0.846420i		−	0.0435929i
$378$	−0.377519	+	2.61868i	−0.0194175	+	0.134690i
$379$	−28.8200			−1.48039			−0.740193	−	0.672395i	$-0.765266\pi$
$379$	−28.8200			−1.48039			−0.740193	+	0.672395i	$0.765266\pi$
$380$	−0.840064	−	0.485011i	−0.0430944	−	0.0248806i
$381$	−2.55619	−	4.42744i	−0.130957	−	0.226825i
$382$	−5.18349	+	2.99269i	−0.265210	+	0.153119i
$383$	−6.12468	−	3.53608i	−0.312956	−	0.180685i	0.335292	−	0.942114i	$-0.391165\pi$
$383$	−6.12468	−	3.53608i	−0.312956	−	0.180685i	−0.648249	+	0.761429i	$0.724498\pi$
$384$	1.00000			0.0510310
$385$	−3.11735	+	19.2649i	−0.158875	+	0.981833i
$386$	8.49244			0.432254
$387$	−8.82251	−	5.09368i	−0.448473	−	0.258926i
$388$	−9.24118	+	5.33540i	−0.469150	+	0.270864i
$389$	−6.18937	−	10.7203i	−0.313813	−	0.543541i	0.665371	−	0.746513i	$-0.268273\pi$
$389$	−6.18937	−	10.7203i	−0.313813	−	0.543541i	−0.979185	+	0.202972i	$0.934940\pi$
$390$	0.217089	+	0.125336i	0.0109927	+	0.00634665i
$391$	−0.192523			−0.00973633
$392$	−4.82672	−	5.06979i	−0.243786	−	0.256063i
$393$			2.05825i			0.103825i
$394$	−1.85555	+	3.21390i	−0.0934811	+	0.161914i
$395$	0.551124	+	0.954575i	0.0277301	+	0.0480299i
$396$	−0.0571978	+	3.31613i	−0.00287430	+	0.166642i
$397$	17.2980	+	9.98702i	0.868163	+	0.501234i	0.866737	−	0.498765i	$-0.166213\pi$
$397$	17.2980	+	9.98702i	0.868163	+	0.501234i	0.00142581	+	0.999999i	$0.499546\pi$
$398$	−5.76399			−0.288923
$399$	0.428484	+	1.07147i	0.0214510	+	0.0536408i
$400$	0.0538161			0.00269081
$401$	−5.27945	+	9.14428i	−0.263643	+	0.456643i	−0.967207	−	0.253988i	$-0.918257\pi$
$401$	−5.27945	+	9.14428i	−0.263643	+	0.456643i	0.703564	+	0.710632i	$0.251591\pi$
$402$	−2.48189	−	4.29875i	−0.123785	−	0.214402i
$403$	−0.0345625	+	0.0199547i	−0.00172168	+	0.000994013i
$404$	−9.76595	+	16.9151i	−0.485874	+	0.841558i
$405$		−	2.22400i		−	0.110512i
$406$	2.83500	−	19.6651i	0.140699	−	0.975963i
$407$	20.8969	+	12.5503i	1.03582	+	0.622094i
$408$	0.119843	−	0.207574i	0.00593310	−	0.0102764i
$409$	−11.2457	−	19.4781i	−0.556065	−	0.963132i	−0.997820	−	0.0659967i	$-0.978977\pi$
$409$	−11.2457	−	19.4781i	−0.556065	−	0.963132i	0.441755	−	0.897136i	$-0.354356\pi$
$410$	−3.50135	−	6.06451i	−0.172919	−	0.299505i
$411$	16.3254	+	9.42545i	0.805271	+	0.464923i
$412$		−	12.7789i		−	0.629573i
$413$	6.18670	−	7.86092i	0.304428	−	0.386811i
$414$		−	0.803234i		−	0.0394768i
$415$	−1.09628	−	0.632935i	−0.0538141	−	0.0310696i
$416$	−0.0976119	+	0.0563562i	−0.00478582	+	0.00276309i
$417$	−9.09614	+	5.25166i	−0.445440	+	0.257175i
$418$	0.701578	+	1.26506i	0.0343153	+	0.0618763i
$419$		−	25.5522i		−	1.24831i	−0.781302	−	0.624154i	$-0.785444\pi$
$419$		−	25.5522i		−	1.24831i	0.781302	−	0.624154i	$-0.214556\pi$
$420$	4.62388	+	3.63909i	0.225622	+	0.177569i
$421$	−2.88784			−0.140745			−0.0703723	−	0.997521i	$-0.522419\pi$
$421$	−2.88784			−0.140745			−0.0703723	+	0.997521i	$0.522419\pi$
$422$	−11.5601	+	20.0226i	−0.562735	+	0.974685i
$423$	−11.2232	+	6.47974i	−0.545693	+	0.315056i
$424$	2.22041	−	1.28196i	0.107833	−	0.0622573i
$425$	0.00644947	−	0.0111708i	0.000312845	−	0.000541864i
$426$	7.58067			0.367285
$427$	0.396395	−	2.74961i	0.0191829	−	0.133063i
$428$		−	12.5731i		−	0.607745i
$429$	−0.181302	−	0.326917i	−0.00875332	−	0.0157837i
$430$	−19.6213	+	11.3284i	−0.946222	+	0.546302i
$431$	28.7727	−	16.6119i	1.38593	−	0.800168i	0.393077	−	0.919505i	$-0.371410\pi$
$431$	28.7727	−	16.6119i	1.38593	−	0.800168i	0.992854	+	0.119338i	$0.0380771\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			0.741961i			0.0356564i	0.999841	+	0.0178282i	$0.00567519\pi$
$433$			0.741961i			0.0356564i	−0.999841	+	0.0178282i	$0.994325\pi$
$434$	−0.869836	+	0.347849i	−0.0417535	+	0.0166973i
$435$			16.7013i			0.800764i
$436$	−14.3351	−	8.27635i	−0.686525	−	0.396365i
$437$	−0.175170	−	0.303403i	−0.00837950	−	0.0145137i
$438$	−2.39827	−	4.15392i	−0.114594	−	0.198482i
$439$	−8.11637	+	14.0580i	−0.387373	+	0.670950i	−0.992095	−	0.125486i	$-0.959951\pi$
$439$	−8.11637	+	14.0580i	−0.387373	+	0.670950i	0.604722	+	0.796437i	$0.293284\pi$
$440$	6.32340	+	3.79771i	0.301456	+	0.181049i
$441$	−1.64517	−	6.80393i	−0.0783415	−	0.323996i
$442$			0.0270155i			0.00128500i
$443$	5.45671	−	9.45129i	0.259256	−	0.449044i	−0.706787	−	0.707427i	$-0.749856\pi$
$443$	5.45671	−	9.45129i	0.259256	−	0.449044i	0.966043	+	0.258382i	$0.0831893\pi$
$444$	6.36499	−	3.67483i	0.302069	−	0.174400i
$445$	−15.5665	−	26.9620i	−0.737925	−	1.27812i
$446$	5.66167	−	9.80630i	0.268088	−	0.464342i
$447$	−14.6150			−0.691268
$448$	−2.45660	+	0.982398i	−0.116064	+	0.0464140i
$449$	−23.6594			−1.11656			−0.558278	−	0.829654i	$-0.688538\pi$
$449$	−23.6594			−1.11656			−0.558278	+	0.829654i	$0.688538\pi$
$450$	0.0466061	+	0.0269081i	0.00219703	+	0.00126846i
$451$	−0.180098	+	10.4415i	−0.00848049	+	0.491670i
$452$	−4.09949	−	7.10052i	−0.192824	−	0.333980i
$453$	−0.910267	+	1.57663i	−0.0427681	+	0.0740764i
$454$		−	5.33246i		−	0.250265i
$455$	−0.656431	−	0.0946338i	−0.0307740	−	0.00443650i
$456$	0.436161			0.0204251
$457$	21.2115	+	12.2465i	0.992233	+	0.572866i	0.905941	−	0.423404i	$-0.139165\pi$
$457$	21.2115	+	12.2465i	0.992233	+	0.572866i	0.0862919	+	0.996270i	$0.472498\pi$
$458$	−9.01755	−	15.6189i	−0.421363	−	0.729821i
$459$	0.207574	−	0.119843i	0.00968871	−	0.00559378i
$460$	−1.54706	−	0.893197i	−0.0721321	−	0.0416455i
$461$	8.01773			0.373423			0.186712	−	0.982415i	$-0.440217\pi$
$461$	8.01773			0.373423			0.186712	+	0.982415i	$0.440217\pi$
$462$	−3.11725	−	8.20261i	−0.145028	−	0.381620i
$463$	32.2209			1.49743			0.748716	−	0.662891i	$-0.230671\pi$
$463$	32.2209			1.49743			0.748716	+	0.662891i	$0.230671\pi$
$464$	−6.50347	−	3.75478i	−0.301916	−	0.174311i
$465$	0.681975	−	0.393738i	0.0316258	−	0.0182592i
$466$	7.83866	+	13.5770i	0.363119	+	0.628941i
$467$	11.5836	+	6.68782i	0.536027	+	0.309475i	0.743467	−	0.668772i	$-0.233180\pi$
$467$	11.5836	+	6.68782i	0.536027	+	0.309475i	−0.207440	+	0.978248i	$0.566513\pi$
$468$	−0.112712			−0.00521014
$469$	10.3201	+	8.12212i	0.476538	+	0.375045i
$470$			28.8219i			1.32946i
$471$	8.74037	−	15.1388i	0.402735	−	0.697558i
$472$	−1.89048	−	3.27440i	−0.0870163	−	0.150717i
$473$	33.7826	+	0.582694i	1.55333	+	0.0267923i
$474$	−0.429215	−	0.247807i	−0.0197145	−	0.0113822i
$475$	0.0234725			0.00107699
$476$	−0.0904858	+	0.627659i	−0.00414741	+	0.0287687i
$477$	2.56391			0.117393
$478$	−9.84934	+	17.0596i	−0.450498	+	0.780286i
$479$	17.3629	+	30.0734i	0.793330	+	1.37409i	0.923894	+	0.382648i	$0.124988\pi$
$479$	17.3629	+	30.0734i	0.793330	+	1.37409i	−0.130564	+	0.991440i	$0.541679\pi$
$480$	1.92604	−	1.11200i	0.0879114	−	0.0507557i
$481$	−0.414199	+	0.717414i	−0.0188858	+	0.0327112i
$482$		−	7.70558i		−	0.350980i
$483$	0.789095	+	1.97323i	0.0359051	+	0.0897849i
$484$	−5.16820	−	9.71029i	−0.234918	−	0.441377i
$485$	−11.8659	+	20.5524i	−0.538804	+	0.933236i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−9.83069	−	17.0272i	−0.445471	−	0.771578i	0.552614	−	0.833437i	$-0.313630\pi$
$487$	−9.83069	−	17.0272i	−0.445471	−	0.771578i	−0.998085	+	0.0618591i	$0.980297\pi$
$488$	−0.909326	−	0.525000i	−0.0411633	−	0.0237656i
$489$			11.6913i			0.528699i
$490$	−14.9341	−	4.39730i	−0.674653	−	0.198650i
$491$			31.6334i			1.42760i	0.700352	+	0.713798i	$0.253026\pi$
$491$			31.6334i			1.42760i	−0.700352	+	0.713798i	$0.746974\pi$
$492$	2.72685	+	1.57435i	0.122936	+	0.0709770i
$493$	−1.55879	+	0.899965i	−0.0702042	+	0.0405324i
$494$	−0.0425745	+	0.0245804i	−0.00191552	+	0.00110592i
$495$	3.57738	+	6.45061i	0.160791	+	0.289933i
$496$			0.354081i			0.0158987i
$497$	−18.6227	+	7.44723i	−0.835341	+	0.334054i
$498$	0.569186			0.0255058
$499$	18.1190	−	31.3830i	0.811118	−	1.40490i	−0.100965	−	0.994890i	$-0.532193\pi$
$499$	18.1190	−	31.3830i	0.811118	−	1.40490i	0.912082	−	0.410007i	$-0.134474\pi$
$500$	9.73386	−	5.61985i	0.435312	−	0.251327i
$501$	16.0115	−	9.24425i	0.715341	−	0.413003i
$502$	5.69442	−	9.86302i	0.254154	−	0.440208i
$503$	28.3530			1.26420			0.632098	−	0.774889i	$-0.282194\pi$
$503$	28.3530			1.26420			0.632098	+	0.774889i	$0.282194\pi$
$504$	−2.61868	−	0.377519i	−0.116645	−	0.0168160i
$505$			43.4390i			1.93301i
$506$	1.29203	+	2.32974i	0.0574376	+	0.103570i
$507$	−11.2473	+	6.49365i	−0.499511	+	0.288393i
$508$	4.42744	−	2.55619i	0.196436	−	0.113412i
$509$	−31.4337	−	18.1483i	−1.39328	−	0.804408i	−0.399600	−	0.916690i	$-0.630851\pi$
$509$	−31.4337	−	18.1483i	−1.39328	−	0.804408i	−0.993676	+	0.112281i	$0.964184\pi$
$510$		−	0.533061i		−	0.0236043i
$511$	9.97239	+	7.84847i	0.441152	+	0.347196i
$512$			1.00000i			0.0441942i
$513$	0.377726	+	0.218080i	0.0166770	+	0.00962849i
$514$	−8.08134	−	13.9973i	−0.356453	−	0.617394i
$515$	−14.2102	−	24.6128i	−0.626176	−	1.08457i
$516$	5.09368	−	8.82251i	0.224237	−	0.388389i
$517$	22.1296	−	36.8471i	0.973260	−	1.62053i
$518$	−12.0261	+	15.2805i	−0.528396	+	0.671389i
$519$		−	17.1887i		−	0.754502i
$520$	−0.125336	+	0.217089i	−0.00549636	+	0.00951998i
$521$	−7.10021	+	4.09931i	−0.311066	+	0.179594i	−0.647403	−	0.762148i	$-0.724145\pi$
$521$	−7.10021	+	4.09931i	−0.311066	+	0.179594i	0.336338	+	0.941741i	$0.390812\pi$
$522$	−3.75478	−	6.50347i	−0.164342	−	0.284649i
$523$	16.8849	−	29.2456i	0.738327	−	1.27882i	−0.214921	−	0.976631i	$-0.568950\pi$
$523$	16.8849	−	29.2456i	0.738327	−	1.27882i	0.953248	−	0.302188i	$-0.0977171\pi$
$524$	−2.05825			−0.0899150
$525$	−0.140927	−	0.0203166i	−0.00615057	−	0.000886690i
$526$	8.58163			0.374177
$527$	0.0734979	+	0.0424340i	0.00320162	+	0.00184845i
$528$	−3.31613	−	0.0571978i	−0.144316	−	0.00248921i
$529$	11.1774	+	19.3598i	0.485974	+	0.841732i
$530$	2.85107	−	4.93820i	0.123843	−	0.214502i
$531$		−	3.78095i		−	0.164079i
$532$	−1.07147	+	0.428484i	−0.0464543	+	0.0185771i
$533$	−0.354897			−0.0153723
$534$	12.1232	+	6.99934i	0.524622	+	0.302891i
$535$	−13.9813	−	24.2164i	−0.604465	−	1.04696i
$536$	4.29875	−	2.48189i	0.185678	−	0.107201i
$537$	−10.0777	−	5.81838i	−0.434886	−	0.251081i
$538$	−4.14061			−0.178514
$539$	15.7161	+	17.0882i	0.676939	+	0.736039i
$540$	2.22400			0.0957058
$541$	−19.6218	−	11.3286i	−0.843607	−	0.487057i	0.0148819	−	0.999889i	$-0.495263\pi$
$541$	−19.6218	−	11.3286i	−0.843607	−	0.487057i	−0.858489	+	0.512833i	$0.828596\pi$
$542$	−2.97190	+	1.71583i	−0.127654	+	0.0737011i
$543$	10.9767	+	19.0122i	0.471056	+	0.815893i
$544$	0.207574	+	0.119843i	0.00889965	+	0.00513821i
$545$	−36.8132			−1.57691
$546$	0.276890	−	0.110729i	0.0118498	−	0.00473874i
$547$			11.4499i			0.489563i	0.969578	+	0.244782i	$0.0787163\pi$
$547$			11.4499i			0.489563i	−0.969578	+	0.244782i	$0.921284\pi$
$548$	−9.42545	+	16.3254i	−0.402635	+	0.697385i
$549$	−0.525000	−	0.909326i	−0.0224064	−	0.0388091i
$550$	−0.178461	−	0.00307816i	−0.00760962	−	0.000131253i
$551$	−2.83656	−	1.63769i	−0.120841	−	0.0697678i
$552$	0.803234			0.0341879
$553$	1.29786	+	0.187104i	0.0551904	+	0.00795647i
$554$	1.56992			0.0666995
$555$	8.17282	−	14.1557i	0.346917	−	0.600878i
$556$	−5.25166	−	9.09614i	−0.222720	−	0.385762i
$557$	39.2147	−	22.6406i	1.66158	−	0.959314i	0.689619	−	0.724173i	$-0.257778\pi$
$557$	39.2147	−	22.6406i	1.66158	−	0.959314i	0.971961	−	0.235141i	$-0.0755552\pi$
$558$	−0.177040	+	0.306643i	−0.00749472	+	0.0129812i
$559$			1.14824i			0.0485655i
$560$	−3.63909	+	4.62388i	−0.153780	+	0.195395i
$561$	−0.409287	+	0.681487i	−0.0172801	+	0.0287724i
$562$	1.74939	−	3.03003i	0.0737934	−	0.127814i
$563$	13.8636	+	24.0125i	0.584283	+	1.01201i	0.994964	+	0.100228i	$0.0319573\pi$
$563$	13.8636	+	24.0125i	0.584283	+	1.01201i	−0.410682	+	0.911779i	$0.634709\pi$
$564$	−6.47974	−	11.2232i	−0.272846	−	0.472584i
$565$	−15.7916	−	9.11727i	−0.664356	−	0.383566i
$566$			22.2211i			0.934023i
$567$	−2.07908	−	1.63628i	−0.0873133	−	0.0687173i
$568$			7.58067i			0.318078i
$569$	−13.9061	−	8.02868i	−0.582973	−	0.336580i	0.179341	−	0.983787i	$-0.442603\pi$
$569$	−13.9061	−	8.02868i	−0.582973	−	0.336580i	−0.762314	+	0.647207i	$0.775937\pi$
$570$	0.840064	−	0.485011i	0.0351864	−	0.0203149i
$571$	−8.42022	+	4.86141i	−0.352375	+	0.203444i	−0.665731	−	0.746192i	$-0.731880\pi$
$571$	−8.42022	+	4.86141i	−0.352375	+	0.203444i	0.313356	+	0.949636i	$0.398547\pi$
$572$	0.326917	−	0.181302i	0.0136691	−	0.00758060i
$573$		−	5.98538i		−	0.250043i
$574$	−8.24541	−	1.18869i	−0.344157	−	0.0496150i
$575$	0.0432269			0.00180269
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.22544	−	1.28486i	0.0926462	−	0.0534893i	−0.452961	−	0.891530i	$-0.649632\pi$
$577$	2.22544	−	1.28486i	0.0926462	−	0.0534893i	0.545607	+	0.838041i	$0.316299\pi$
$578$	−14.6727	+	8.47128i	−0.610303	+	0.352359i
$579$	−4.24622	+	7.35467i	−0.176467	+	0.305650i
$580$	−16.7013			−0.693482
$581$	−1.39826	+	0.559167i	−0.0580097	+	0.0231982i
$582$		−	10.6708i		−	0.442319i
$583$	−7.43651	+	4.12413i	−0.307989	+	0.170804i
$584$	4.15392	−	2.39827i	0.171890	−	0.0992409i
$585$	−0.217089	+	0.125336i	−0.00897552	+	0.00518202i
$586$	5.93714	+	3.42781i	0.245261	+	0.141602i
$587$			25.9150i			1.06963i	0.844970	+	0.534814i	$0.179618\pi$
$587$			25.9150i			1.06963i	−0.844970	+	0.534814i	$0.820382\pi$
$588$	6.80393	−	1.64517i	0.280589	−	0.0678457i
$589$			0.154436i			0.00636344i
$590$	−7.28228	−	4.20443i	−0.299807	−	0.173093i
$591$	−1.85555	−	3.21390i	−0.0763270	−	0.132202i
$592$	3.67483	+	6.36499i	0.151034	+	0.261599i
$593$	3.72204	−	6.44677i	0.152846	−	0.264737i	−0.779427	−	0.626494i	$-0.784489\pi$
$593$	3.72204	−	6.44677i	0.152846	−	0.264737i	0.932273	+	0.361756i	$0.117823\pi$
$594$	−2.84326	−	1.70760i	−0.116660	−	0.0700637i
$595$	0.523678	+	1.30952i	0.0214687	+	0.0536850i
$596$		−	14.6150i		−	0.598656i
$597$	2.88199	−	4.99176i	0.117952	−	0.204299i
$598$	−0.0784051	+	0.0452672i	−0.00320622	+	0.00185111i
$599$	−12.3177	−	21.3348i	−0.503286	−	0.871717i	−0.999993	−	0.00379841i	$-0.998791\pi$
$599$	−12.3177	−	21.3348i	−0.503286	−	0.871717i	0.496707	−	0.867918i	$-0.334542\pi$
$600$	−0.0269081	+	0.0466061i	−0.00109852	+	0.00190269i
$601$	6.75417			0.275508			0.137754	−	0.990466i	$-0.456012\pi$
$601$	6.75417			0.275508			0.137754	+	0.990466i	$0.456012\pi$
$602$	−3.84592	+	26.6774i	−0.156748	+	1.08729i
$603$	4.96377			0.202140
$604$	−1.57663	−	0.910267i	−0.0641521	−	0.0370382i
$605$	−20.7520	−	12.9554i	−0.843690	−	0.526711i
$606$	−9.76595	−	16.9151i	−0.396714	−	0.687130i
$607$	−18.7854	+	32.5373i	−0.762476	+	1.32065i	0.179095	+	0.983832i	$0.442683\pi$
$607$	−18.7854	+	32.5373i	−0.762476	+	1.32065i	−0.941571	+	0.336815i	$0.890650\pi$
$608$			0.436161i			0.0176887i
$609$	15.6130	+	12.2877i	0.632670	+	0.497924i
$610$	−2.33520			−0.0945495
$611$	1.26500	+	0.730348i	0.0511764	+	0.0295467i
$612$	0.119843	+	0.207574i	0.00484435	+	0.00839067i
$613$	32.3937	−	18.7025i	1.30837	−	0.755387i	0.326544	−	0.945182i	$-0.394116\pi$
$613$	32.3937	−	18.7025i	1.30837	−	0.755387i	0.981824	+	0.189795i	$0.0607824\pi$
$614$	−21.9508	−	12.6733i	−0.885861	−	0.511452i
$615$	7.00270			0.282376
$616$	8.20261	−	3.11725i	0.330492	−	0.125598i
$617$	−12.6245			−0.508243			−0.254122	−	0.967172i	$-0.581786\pi$
$617$	−12.6245			−0.508243			−0.254122	+	0.967172i	$0.581786\pi$
$618$	11.0669	+	6.38947i	0.445176	+	0.257022i
$619$	−5.03418	+	2.90648i	−0.202341	+	0.116821i	−0.597747	−	0.801685i	$-0.703937\pi$
$619$	−5.03418	+	2.90648i	−0.202341	+	0.116821i	0.395406	+	0.918506i	$0.370604\pi$
$620$	0.393738	+	0.681975i	0.0158129	+	0.0273888i
$621$	0.695621	+	0.401617i	0.0279143	+	0.0161163i
$622$	−13.8671			−0.556021
$623$	−36.6580	−	5.28477i	−1.46867	−	0.211730i
$624$		−	0.112712i		−	0.00451211i
$625$	12.3640	−	21.4151i	0.494560	−	0.856604i
$626$	−6.02834	−	10.4414i	−0.240941	−	0.417322i
$627$	−1.44637	−	0.0249474i	−0.0577623	−	0.000996304i
$628$	15.1388	+	8.74037i	0.604103	+	0.348779i
$629$	1.76161			0.0702398
$630$	−5.46349	+	2.18486i	−0.217671	+	0.0870467i
$631$	45.0951			1.79521			0.897604	−	0.440804i	$-0.145307\pi$
$631$	45.0951			1.79521			0.897604	+	0.440804i	$0.145307\pi$
$632$	0.247807	−	0.429215i	0.00985725	−	0.0170733i
$633$	−11.5601	−	20.0226i	−0.459471	−	0.795827i
$634$	−6.54073	+	3.77629i	−0.259766	+	0.149976i
$635$	5.68496	−	9.84664i	0.225601	−	0.390752i
$636$			2.56391i			0.101666i
$637$	−0.571428	+	0.544032i	−0.0226408	+	0.0215553i
$638$	21.3516	+	12.8233i	0.845317	+	0.507680i
$639$	−3.79033	+	6.56505i	−0.149943	+	0.259709i
$640$	1.11200	+	1.92604i	0.0439557	+	0.0761335i
$641$	9.27227	+	16.0600i	0.366233	+	0.634333i	0.988973	−	0.148095i	$-0.0473141\pi$
$641$	9.27227	+	16.0600i	0.366233	+	0.634333i	−0.622741	+	0.782428i	$0.713981\pi$
$642$	10.8886	+	6.28656i	0.429740	+	0.248111i
$643$		−	9.80715i		−	0.386756i	−0.981124	−	0.193378i	$-0.938056\pi$
$643$		−	9.80715i		−	0.386756i	0.981124	−	0.193378i	$-0.0619444\pi$
$644$	−1.97323	+	0.789095i	−0.0777560	+	0.0310947i
$645$		−	22.6567i		−	0.892107i
$646$	0.0905355	+	0.0522707i	0.00356207	+	0.00205656i
$647$	−16.4510	+	9.49800i	−0.646756	+	0.373405i	−0.787212	−	0.616682i	$-0.788476\pi$
$647$	−16.4510	+	9.49800i	−0.646756	+	0.373405i	0.140456	+	0.990087i	$0.455143\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	6.08178	+	10.9665i	0.238731	+	0.430472i
$650$		−	0.00606575i		−	0.000237918i
$651$	0.133672	−	0.927224i	0.00523903	−	0.0363408i
$652$	−11.6913			−0.457867
$653$	−7.65833	+	13.2646i	−0.299694	+	0.519084i	−0.976066	−	0.217476i	$-0.930218\pi$
$653$	−7.65833	+	13.2646i	−0.299694	+	0.519084i	0.676372	+	0.736560i	$0.263551\pi$
$654$	14.3351	−	8.27635i	0.560545	−	0.323631i
$655$	−3.96427	+	2.28877i	−0.154897	+	0.0894298i
$656$	−1.57435	+	2.72685i	−0.0614679	+	0.106465i
$657$	4.79653			0.187131
$658$	26.9438	+	21.2054i	1.05038	+	0.826671i
$659$			50.6179i			1.97179i	0.167358	+	0.985896i	$0.446476\pi$
$659$			50.6179i			1.97179i	−0.167358	+	0.985896i	$0.553524\pi$
$660$	−6.45061	+	3.57738i	−0.251090	+	0.139249i
$661$	33.9093	−	19.5776i	1.31892	−	0.761478i	0.335365	−	0.942088i	$-0.391141\pi$
$661$	33.9093	−	19.5776i	1.31892	−	0.761478i	0.983555	+	0.180610i	$0.0578072\pi$
$662$	19.5435	−	11.2835i	0.759580	−	0.438544i
$663$	−0.0233961	−	0.0135078i	−0.000908631	−	0.000524598i
$664$			0.569186i			0.0220887i
$665$	−1.58723	+	2.01676i	−0.0615501	+	0.0782065i
$666$			7.34966i			0.284793i
$667$	−5.22380	−	3.01596i	−0.202266	−	0.116779i
$668$	9.24425	+	16.0115i	0.357671	+	0.619504i
$669$	5.66167	+	9.80630i	0.218893	+	0.379134i
$670$	5.51972	−	9.56043i	0.213245	−	0.369352i
$671$	2.98542	+	1.79298i	0.115251	+	0.0692172i
$672$	0.377519	−	2.61868i	0.0145631	−	0.101018i
$673$		−	25.0173i		−	0.964345i	−0.876076	−	0.482172i	$-0.839848\pi$
$673$		−	25.0173i		−	0.964345i	0.876076	−	0.482172i	$-0.160152\pi$
$674$	16.2347	−	28.1194i	0.625339	−	1.08312i
$675$	−0.0466061	+	0.0269081i	−0.00179387	+	0.00103569i
$676$	−6.49365	−	11.2473i	−0.249756	−	0.432590i
$677$	24.2515	−	42.0048i	0.932059	−	1.61437i	0.152263	−	0.988340i	$-0.451344\pi$
$677$	24.2515	−	42.0048i	0.932059	−	1.61437i	0.779796	−	0.626034i	$-0.215323\pi$
$678$	8.19898			0.314880
$679$	10.4830	+	26.2139i	0.402299	+	1.00600i
$680$	0.533061			0.0204419
$681$	4.61805	+	2.66623i	0.176964	+	0.102170i
$682$	0.0202526	−	1.17418i	0.000775514	−	0.0449616i
$683$	3.55626	+	6.15962i	0.136076	+	0.235691i	0.926008	−	0.377504i	$-0.123217\pi$
$683$	3.55626	+	6.15962i	0.136076	+	0.235691i	−0.789932	+	0.613195i	$0.789884\pi$
$684$	−0.218080	+	0.377726i	−0.00833851	+	0.0144427i
$685$			41.9244i			1.60185i
$686$	−15.0983	+	10.7257i	−0.576457	+	0.409509i
$687$	18.0351			0.688082
$688$	8.82251	+	5.09368i	0.336355	+	0.194195i
$689$	−0.144492	−	0.250268i	−0.00550472	−	0.00953446i
$690$	1.54706	−	0.893197i	0.0588956	−	0.0340034i
$691$	37.8547	+	21.8554i	1.44006	+	0.831420i	0.997853	−	0.0654915i	$-0.0208615\pi$
$691$	37.8547	+	21.8554i	1.44006	+	0.831420i	0.442209	+	0.896912i	$0.354195\pi$
$692$	17.1887			0.653418
$693$	8.66229	+	1.40169i	0.329053	+	0.0532456i
$694$	30.7426			1.16697
$695$	−20.2298	−	11.6797i	−0.767361	−	0.443036i
$696$	6.50347	−	3.75478i	0.246513	−	0.142324i
$697$	0.377348	+	0.653585i	0.0142931	+	0.0247563i
$698$	−21.2675	−	12.2788i	−0.804986	−	0.464759i
$699$	−15.6773			−0.592971
$700$	0.0203166	−	0.140927i	0.000767896	−	0.00532655i
$701$		−	31.5402i		−	1.19126i	−0.803260	−	0.595628i	$-0.796903\pi$
$701$		−	31.5402i		−	1.19126i	0.803260	−	0.595628i	$-0.203097\pi$
$702$	0.0563562	−	0.0976119i	0.00212703	−	0.00368412i
$703$	1.60282	+	2.77616i	0.0604514	+	0.104705i
$704$	0.0571978	−	3.31613i	0.00215572	−	0.124981i
$705$	−24.9605	−	14.4110i	−0.940067	−	0.542748i
$706$	−4.32341			−0.162714
$707$	40.6084	+	31.9597i	1.52724	+	1.20197i
$708$	3.78095			0.142097
$709$	20.1759	−	34.9457i	0.757723	−	1.31241i	−0.186287	−	0.982495i	$-0.559645\pi$
$709$	20.1759	−	34.9457i	0.757723	−	1.31241i	0.944009	−	0.329919i	$-0.107021\pi$
$710$	8.42971	+	14.6007i	0.316361	+	0.547954i
$711$	0.429215	−	0.247807i	0.0160968	−	0.00929350i
$712$	−6.99934	+	12.1232i	−0.262311	+	0.454336i
$713$			0.284410i			0.0106512i
$714$	−0.498326	−	0.392193i	−0.0186494	−	0.0146774i
$715$	0.428049	−	0.712727i	0.0160081	−	0.0266545i
$716$	5.81838	−	10.0777i	0.217443	−	0.376622i
$717$	−9.84934	−	17.0596i	−0.367830	−	0.637101i
$718$	7.95866	+	13.7848i	0.297014	+	0.514444i
$719$	−5.72561	−	3.30568i	−0.213529	−	0.123281i	0.389421	−	0.921060i	$-0.372675\pi$
$719$	−5.72561	−	3.30568i	−0.213529	−	0.123281i	−0.602950	+	0.797779i	$0.706008\pi$
$720$			2.22400i			0.0828837i
$721$	−33.4639	−	4.82430i	−1.24626	−	0.179666i
$722$		−	18.8098i		−	0.700027i
$723$	6.67323	+	3.85279i	0.248180	+	0.143287i
$724$	−19.0122	+	10.9767i	−0.706584	+	0.407946i
$725$	0.349991	−	0.202068i	0.0129984	−	0.00750460i
$726$	10.9935	+	0.379351i	0.408005	+	0.0140790i
$727$			37.4392i			1.38854i	0.719714	+	0.694271i	$0.244273\pi$
$727$			37.4392i			1.38854i	−0.719714	+	0.694271i	$0.755727\pi$
$728$	0.110729	+	0.276890i	0.00410387	+	0.0102622i
$729$	−1.00000			−0.0370370
$730$	5.33375	−	9.23832i	0.197411	−	0.341926i
$731$	2.11463	−	1.22088i	0.0782123	−	0.0451559i
$732$	0.909326	−	0.525000i	0.0336097	−	0.0194046i
$733$	11.5556	−	20.0149i	0.426816	−	0.739266i	−0.569772	−	0.821803i	$-0.692969\pi$
$733$	11.5556	−	20.0149i	0.426816	−	0.739266i	0.996588	+	0.0825361i	$0.0263020\pi$
$734$	25.7459			0.950297
$735$	11.2752	−	10.7346i	0.415893	−	0.395953i
$736$			0.803234i			0.0296076i
$737$	−14.3972	+	7.98438i	−0.530327	+	0.294108i
$738$	−2.72685	+	1.57435i	−0.100377	+	0.0579525i
$739$	24.3934	−	14.0836i	0.897327	−	0.518072i	0.0209949	−	0.999780i	$-0.493317\pi$
$739$	24.3934	−	14.0836i	0.897327	−	0.518072i	0.876332	+	0.481708i	$0.159983\pi$
$740$	14.1557	+	8.17282i	0.520376	+	0.300439i
$741$		−	0.0491608i		−	0.00180597i
$742$	−2.51878	−	6.29851i	−0.0924674	−	0.231226i
$743$			0.655454i			0.0240463i	0.999928	+	0.0120231i	$0.00382718\pi$
$743$			0.655454i			0.0240463i	−0.999928	+	0.0120231i	$0.996173\pi$
$744$	−0.306643	−	0.177040i	−0.0112421	−	0.00649062i
$745$	−16.2519	−	28.1492i	−0.595425	−	1.03131i
$746$	−14.5882	−	25.2676i	−0.534113	−	0.925112i
$747$	−0.284593	+	0.492929i	−0.0104127	+	0.0180353i
$748$	−0.681487	−	0.409287i	−0.0249176	−	0.0149650i
$749$	−32.9250	−	4.74659i	−1.20305	−	0.173437i
$750$			11.2397i			0.410416i
$751$	−2.65126	+	4.59211i	−0.0967457	+	0.167568i	−0.910336	−	0.413870i	$-0.864177\pi$
$751$	−2.65126	+	4.59211i	−0.0967457	+	0.167568i	0.813590	+	0.581439i	$0.197510\pi$
$752$	11.2232	−	6.47974i	0.409270	−	0.236292i
$753$	5.69442	+	9.86302i	0.207516	+	0.359428i
$754$	−0.423210	+	0.733022i	−0.0154124	+	0.0266951i
$755$	−4.04887			−0.147353
$756$	1.63628	−	2.07908i	0.0595110	−	0.0756155i
$757$	−5.79544			−0.210639			−0.105319	−	0.994438i	$-0.533586\pi$
$757$	−5.79544			−0.210639			−0.105319	+	0.994438i	$0.533586\pi$
$758$	24.9589	+	14.4100i	0.906547	+	0.523395i
$759$	−2.66363	−	0.0459432i	−0.0966836	−	0.00166763i
$760$	0.485011	+	0.840064i	0.0175932	+	0.0304723i
$761$	−21.5347	+	37.2992i	−0.780632	+	1.35209i	0.150942	+	0.988543i	$0.451769\pi$
$761$	−21.5347	+	37.2992i	−0.780632	+	1.35209i	−0.931574	+	0.363552i	$0.881564\pi$
$762$			5.11237i			0.185202i
$763$	−27.0849	+	34.4144i	−0.980538	+	1.24589i
$764$	5.98538			0.216543
$765$	0.461644	+	0.266530i	0.0166908	+	0.00963643i
$766$	3.53608	+	6.12468i	0.127764	+	0.221294i
$767$	−0.369066	+	0.213080i	−0.0133262	+	0.00769389i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−41.6527			−1.50204			−0.751018	−	0.660282i	$-0.770437\pi$
$769$	−41.6527			−1.50204			−0.751018	+	0.660282i	$0.770437\pi$
$770$	12.3322	−	15.1253i	0.444421	−	0.545077i
$771$	16.1627			0.582085
$772$	−7.35467	−	4.24622i	−0.264700	−	0.152825i
$773$	−18.5314	+	10.6991i	−0.666527	+	0.384820i	−0.794759	−	0.606925i	$-0.792403\pi$
$773$	−18.5314	+	10.6991i	−0.666527	+	0.384820i	0.128232	+	0.991744i	$0.459070\pi$
$774$	5.09368	+	8.82251i	0.183089	+	0.317119i
$775$	−0.0165023	−	0.00952763i	−0.000592782	−	0.000342243i
$776$	10.6708			0.383059
$777$	−7.22029	−	18.0552i	−0.259026	−	0.647726i
$778$			12.3787i			0.443799i
$779$	−0.686668	+	1.18934i	−0.0246024	+	0.0426127i
$780$	−0.125336	−	0.217089i	−0.00448776	−	0.00777303i
$781$	0.433597	−	25.1385i	0.0155153	−	0.899526i
$782$	0.166730	+	0.0962617i	0.00596226	+	0.00344231i
$783$	7.50955			0.268370
$784$	1.64517	+	6.80393i	0.0587561	+	0.242997i
$785$	38.8772			1.38759
$786$	1.02912	−	1.78250i	0.0367077	−	0.0635795i
$787$	−11.3606	−	19.6771i	−0.404961	−	0.701413i	0.589356	−	0.807873i	$-0.299381\pi$
$787$	−11.3606	−	19.6771i	−0.404961	−	0.701413i	−0.994317	+	0.106461i	$0.966048\pi$
$788$	3.21390	−	1.85555i	0.114490	−	0.0661011i
$789$	−4.29081	+	7.43191i	−0.152757	+	0.264583i
$790$		−	1.10225i		−	0.0392162i
$791$	−20.1416	+	8.05466i	−0.716154	+	0.286391i
$792$	1.70760	−	2.84326i	0.0606769	−	0.101031i
$793$	−0.0591740	+	0.102492i	−0.00210133	+	0.00363961i
$794$	−9.98702	−	17.2980i	−0.354426	−	0.613884i
$795$	2.85107	+	4.93820i	0.101117	+	0.175140i
$796$	4.99176	+	2.88199i	0.176928	+	0.102150i
$797$		−	20.0434i		−	0.709972i	−0.934872	−	0.354986i	$-0.884486\pi$
$797$		−	20.0434i		−	0.709972i	0.934872	−	0.354986i	$-0.115514\pi$
$798$	0.164659	−	1.14217i	0.00582887	−	0.0404322i
$799$		−	3.10620i		−	0.109889i
$800$	−0.0466061	−	0.0269081i	−0.00164778	−	0.000951344i
$801$	−12.1232	+	6.99934i	−0.428352	+	0.247309i
$802$	9.14428	−	5.27945i	0.322896	−	0.186424i
$803$	−13.9121	+	7.71537i	−0.490948	+	0.272269i
$804$			4.96377i			0.175059i
$805$	−2.92304	+	3.71406i	−0.103024	+	0.130903i
$806$	0.0399093			0.00140575
$807$	2.07030	−	3.58587i	0.0728781	−	0.126229i
$808$	16.9151	−	9.76595i	0.595072	−	0.343565i
$809$	−2.39507	+	1.38280i	−0.0842063	+	0.0486165i	−0.541512	−	0.840693i	$-0.682148\pi$
$809$	−2.39507	+	1.38280i	−0.0842063	+	0.0486165i	0.457306	+	0.889310i	$0.348815\pi$
$810$	−1.11200	+	1.92604i	−0.0390717	+	0.0676742i
$811$	−25.2486			−0.886597			−0.443298	−	0.896374i	$-0.646192\pi$
$811$	−25.2486			−0.886597			−0.443298	+	0.896374i	$0.646192\pi$
$812$	−12.2877	+	15.6130i	−0.431215	+	0.547908i
$813$		−	3.43166i		−	0.120353i
$814$	−11.8221	−	21.3173i	−0.414366	−	0.747172i
$815$	−22.5180	+	13.0007i	−0.788770	+	0.455396i
$816$	−0.207574	+	0.119843i	−0.00726653	+	0.00419533i
$817$	3.84803	+	2.22166i	0.134626	+	0.0777262i
$818$			22.4914i			0.786394i
$819$	−0.0425511	+	0.295158i	−0.00148686	+	0.0103136i
$820$			7.00270i			0.244545i
$821$	32.9471	+	19.0220i	1.14986	+	0.663874i	0.948854	−	0.315716i	$-0.102245\pi$
$821$	32.9471	+	19.0220i	1.14986	+	0.663874i	0.201009	+	0.979589i	$0.435578\pi$
$822$	−9.42545	−	16.3254i	−0.328750	−	0.569412i
$823$	13.2848	+	23.0100i	0.463079	+	0.802076i	0.999113	−	0.0421202i	$-0.0134113\pi$
$823$	13.2848	+	23.0100i	0.463079	+	0.802076i	−0.536033	+	0.844197i	$0.680078\pi$
$824$	−6.38947	+	11.0669i	−0.222588	+	0.385533i
$825$	0.0918965	−	0.153013i	0.00319942	−	0.00532723i
$826$	−9.28830	+	3.71440i	−0.323181	+	0.129241i
$827$			7.04659i			0.245034i	0.992466	+	0.122517i	$0.0390966\pi$
$827$			7.04659i			0.245034i	−0.992466	+	0.122517i	$0.960903\pi$
$828$	−0.401617	+	0.695621i	−0.0139571	+	0.0241745i
$829$	15.5644	−	8.98614i	0.540576	−	0.312102i	−0.204737	−	0.978817i	$-0.565634\pi$
$829$	15.5644	−	8.98614i	0.540576	−	0.312102i	0.745312	+	0.666716i	$0.232300\pi$
$830$	0.632935	+	1.09628i	0.0219695	+	0.0380523i
$831$	−0.784960	+	1.35959i	−0.0272300	+	0.0471637i
$832$	0.112712			0.00390760
$833$	1.60948	+	0.473907i	0.0557651	+	0.0164199i
$834$	10.5033			0.363700
$835$	35.6096	+	20.5592i	1.23232	+	0.711481i
$836$	0.0249474	−	1.44637i	0.000862825	−	0.0500236i
$837$	−0.177040	−	0.306643i	−0.00611941	−	0.0105991i
$838$	−12.7761	+	22.1289i	−0.441343	+	0.764429i
$839$			12.2437i			0.422699i	0.977411	+	0.211350i	$0.0677859\pi$
$839$			12.2437i			0.422699i	−0.977411	+	0.211350i	$0.932214\pi$
$840$	−2.18486	−	5.46349i	−0.0753847	−	0.188508i
$841$	−27.3934			−0.944601
$842$	2.50094	+	1.44392i	0.0861882	+	0.0497608i
$843$	1.74939	+	3.03003i	0.0602521	+	0.104360i
$844$	20.0226	−	11.5601i	0.689206	−	0.397913i
$845$	−25.0141	−	14.4419i	−0.860510	−	0.496816i
$846$	12.9595			0.445556
$847$	−27.3792	+	9.86804i	−0.940761	+	0.339070i
$848$	−2.56391			−0.0880451
$849$	−19.2440	−	11.1106i	−0.660454	−	0.381313i
$850$	−0.0111708	+	0.00644947i	−0.000383156	+	0.000221215i
$851$	2.95175	+	5.11257i	0.101185	+	0.175257i
$852$	−6.56505	−	3.79033i	−0.224915	−	0.129855i
$853$	37.8949			1.29750			0.648749	−	0.761003i	$-0.275293\pi$
$853$	37.8949			1.29750			0.648749	+	0.761003i	$0.275293\pi$
$854$	−1.71809	+	2.18304i	−0.0587920	+	0.0747020i
$855$			0.970023i			0.0331741i
$856$	−6.28656	+	10.8886i	−0.214870	+	0.372166i
$857$	−14.3234	−	24.8089i	−0.489279	−	0.847457i	0.510645	−	0.859792i	$-0.329407\pi$
$857$	−14.3234	−	24.8089i	−0.489279	−	0.847457i	−0.999924	+	0.0123352i	$0.996073\pi$
$858$	−0.00644690	+	0.373769i	−0.000220094	+	0.0127603i
$859$	4.55274	+	2.62852i	0.155337	+	0.0896841i	0.575654	−	0.817694i	$-0.304748\pi$
$859$	4.55274	+	2.62852i	0.155337	+	0.0896841i	−0.420316	+	0.907378i	$0.638081\pi$
$860$	22.6567			0.772587
$861$	5.15214	−	6.54639i	0.175585	−	0.223100i
$862$	−33.2238			−1.13161
$863$	17.4901	−	30.2937i	0.595369	−	1.03121i	−0.398126	−	0.917331i	$-0.630339\pi$
$863$	17.4901	−	30.2937i	0.595369	−	1.03121i	0.993495	−	0.113879i	$-0.0363275\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	33.1062	−	19.1139i	1.12565	−	0.649892i
$866$	0.370981	−	0.642557i	0.0126064	−	0.0218350i
$867$		−	16.9426i		−	0.575399i
$868$	0.927224	+	0.133672i	0.0314720	+	0.00453714i
$869$	−0.846312	+	1.40916i	−0.0287092	+	0.0478024i
$870$	8.35063	−	14.4637i	0.283113	−	0.490366i
$871$	−0.279739	−	0.484523i	−0.00947861	−	0.0164174i
$872$	8.27635	+	14.3351i	0.280273	+	0.485446i
$873$	9.24118	+	5.33540i	0.312766	+	0.180576i
$874$			0.350339i			0.0118504i
$875$	−11.0419	−	27.6115i	−0.373283	−	0.933438i
$876$			4.79653i			0.162060i
$877$	11.7405	+	6.77841i	0.396450	+	0.228890i	0.684951	−	0.728589i	$-0.259824\pi$
$877$	11.7405	+	6.77841i	0.396450	+	0.228890i	−0.288501	+	0.957480i	$0.593157\pi$
$878$	14.0580	−	8.11637i	0.474433	−	0.273914i
$879$	−5.93714	+	3.42781i	−0.200255	+	0.115617i
$880$	−3.57738	−	6.45061i	−0.120593	−	0.217450i
$881$		−	57.2399i		−	1.92846i	−0.265064	−	0.964231i	$-0.585393\pi$
$881$		−	57.2399i		−	1.92846i	0.265064	−	0.964231i	$-0.414607\pi$
$882$	−1.97720	+	6.71496i	−0.0665759	+	0.226104i
$883$	−1.33594			−0.0449579			−0.0224789	−	0.999747i	$-0.507156\pi$
$883$	−1.33594			−0.0449579			−0.0224789	+	0.999747i	$0.507156\pi$
$884$	0.0135078	−	0.0233961i	0.000454315	−	0.000786897i
$885$	7.28228	−	4.20443i	0.244791	−	0.141330i
$886$	−9.45129	+	5.45671i	−0.317522	+	0.183322i
$887$	−18.8847	+	32.7092i	−0.634085	+	1.09827i	0.352623	+	0.935766i	$0.385290\pi$
$887$	−18.8847	+	32.7092i	−0.634085	+	1.09827i	−0.986708	+	0.162502i	$0.948043\pi$
$888$	−7.34966			−0.246638
$889$	−5.02238	−	12.5591i	−0.168445	−	0.421217i
$890$			31.1331i			1.04358i
$891$	2.90045	−	1.60853i	0.0971688	−	0.0538878i
$892$	−9.80630	+	5.66167i	−0.328339	+	0.189567i
$893$	4.89514	−	2.82621i	0.163810	−	0.0945755i
$894$	12.6570	+	7.30752i	0.423313	+	0.244400i
$895$		−	25.8802i		−	0.865078i
$896$	2.61868	+	0.377519i	0.0874839	+	0.0126120i
$897$		−	0.0905344i		−	0.00302286i
$898$	20.4896	+	11.8297i	0.683748	+	0.394762i
$899$	1.32950	+	2.30275i	0.0443411	+	0.0768011i
$900$	−0.0269081	−	0.0466061i	−0.000896936	−	0.00155354i
$901$	−0.307266	+	0.532201i	−0.0102365	+	0.0177302i
$902$	5.37671	−	8.95253i	0.179025	−	0.298087i
$903$	−21.1804	−	16.6694i	−0.704838	−	0.554722i
$904$			8.19898i			0.272694i
$905$	−24.4122	+	42.2832i	−0.811490	+	1.40554i
$906$	1.57663	−	0.910267i	0.0523800	−	0.0302416i
$907$	−22.2803	−	38.5907i	−0.739807	−	1.28138i	−0.952582	−	0.304282i	$-0.901584\pi$
$907$	−22.2803	−	38.5907i	−0.739807	−	1.28138i	0.212775	−	0.977101i	$-0.431750\pi$
$908$	−2.66623	+	4.61805i	−0.0884819	+	0.153255i
$909$	19.5319			0.647832
$910$	0.521169	+	0.410171i	0.0172766	+	0.0135970i
$911$	−17.1268			−0.567436			−0.283718	−	0.958908i	$-0.591568\pi$
$911$	−17.1268			−0.567436			−0.283718	+	0.958908i	$0.591568\pi$
$912$	−0.377726	−	0.218080i	−0.0125078	−	0.00722136i
$913$	0.0325562	−	1.88750i	0.00107745	−	0.0624670i
$914$	−12.2465	−	21.2115i	−0.405077	−	0.701615i
$915$	1.16760	−	2.02234i	0.0385997	−	0.0668566i
$916$			18.0351i			0.595897i
$917$	−0.777028	+	5.38989i	−0.0256597	+	0.177990i
$918$	−0.239685			−0.00791080
$919$	24.4668	+	14.1259i	0.807086	+	0.465971i	0.845943	−	0.533273i	$-0.179038\pi$
$919$	24.4668	+	14.1259i	0.807086	+	0.465971i	−0.0388569	+	0.999245i	$0.512372\pi$
$920$	0.893197	+	1.54706i	0.0294478	+	0.0510051i
$921$	21.9508	−	12.6733i	0.723303	−	0.417599i
$922$	−6.94356	−	4.00887i	−0.228674	−	0.132025i
$923$	0.854436			0.0281241
$924$	−1.40169	+	8.66229i	−0.0461121	+	0.284968i
$925$	−0.395530			−0.0130049
$926$	−27.9041	−	16.1105i	−0.916986	−	0.529422i
$927$	−11.0669	+	6.38947i	−0.363484	+	0.209858i
$928$	3.75478	+	6.50347i	0.123257	+	0.213487i
$929$	−23.1670	−	13.3755i	−0.760085	−	0.438836i	0.0692410	−	0.997600i	$-0.477942\pi$
$929$	−23.1670	−	13.3755i	−0.760085	−	0.438836i	−0.829326	+	0.558764i	$0.811276\pi$
$930$	−0.787477			−0.0258224
$931$	0.717559	+	2.96761i	0.0235171	+	0.0972594i
$932$		−	15.6773i		−	0.513528i
$933$	6.93356	−	12.0093i	0.226995	−	0.393166i
$934$	−6.68782	−	11.5836i	−0.218832	−	0.379028i
$935$	−1.76770	−	0.0304899i	−0.0578100	−	0.000997126i
$936$	0.0976119	+	0.0563562i	0.00319054	+	0.00184206i
$937$	−8.64381			−0.282381			−0.141190	−	0.989982i	$-0.545093\pi$
$937$	−8.64381			−0.282381			−0.141190	+	0.989982i	$0.545093\pi$
$938$	−4.87640	−	12.1940i	−0.159220	−	0.398149i
$939$	12.0567			0.393455
$940$	14.4110	−	24.9605i	0.470034	−	0.814122i
$941$	−7.25889	−	12.5728i	−0.236633	−	0.409861i	0.723113	−	0.690730i	$-0.242711\pi$
$941$	−7.25889	−	12.5728i	−0.236633	−	0.409861i	−0.959746	+	0.280869i	$0.909377\pi$
$942$	−15.1388	+	8.74037i	−0.493248	+	0.284777i
$943$	−1.26457	+	2.19030i	−0.0411800	+	0.0713258i
$944$			3.78095i			0.123060i
$945$	0.839603	−	5.82395i	0.0273123	−	0.189453i
$946$	−28.9653	−	17.3959i	−0.941742	−	0.565591i
$947$	5.90549	−	10.2286i	0.191903	−	0.332385i	−0.753978	−	0.656899i	$-0.771868\pi$
$947$	5.90549	−	10.2286i	0.191903	−	0.332385i	0.945881	+	0.324515i	$0.105201\pi$
$948$	0.247807	+	0.429215i	0.00804841	+	0.0139403i
$949$	−0.270314	−	0.468198i	−0.00877478	−	0.0151984i
$950$	−0.0203278	−	0.0117362i	−0.000659520	−	0.000380774i
$951$		−	7.55258i		−	0.244909i
$952$	0.392193	−	0.498326i	0.0127110	−	0.0161508i
$953$			5.83407i			0.188984i	0.995526	+	0.0944920i	$0.0301227\pi$
$953$			5.83407i			0.188984i	−0.995526	+	0.0944920i	$0.969877\pi$
$954$	−2.22041	−	1.28196i	−0.0718885	−	0.0415049i
$955$	11.5281	−	6.65575i	0.373040	−	0.215375i
$956$	17.0596	−	9.84934i	0.551746	−	0.318550i
$957$	−21.7811	+	12.0794i	−0.704083	+	0.390470i
$958$		−	34.7257i		−	1.12194i
$959$	39.1926	+	30.8454i	1.26559	+	0.996049i
$960$	−2.22400			−0.0717793
$961$	−15.4373	+	26.7382i	−0.497978	+	0.862523i
$962$	0.717414	−	0.414199i	0.0231303	−	0.0133543i
$963$	−10.8886	+	6.28656i	−0.350881	+	0.202582i
$964$	−3.85279	+	6.67323i	−0.124090	+	0.214930i
$965$	−18.8872			−0.608001
$966$	0.303236	−	2.10341i	0.00975646	−	0.0676761i
$967$		−	52.9190i		−	1.70176i	−0.525359	−	0.850881i	$-0.676069\pi$
$967$		−	52.9190i		−	1.70176i	0.525359	−	0.850881i	$-0.323931\pi$
$968$	−0.379351	+	10.9935i	−0.0121928	+	0.353343i
$969$	−0.0905355	+	0.0522707i	−0.00290842	+	0.00167918i
$970$	20.5524	−	11.8659i	0.659898	−	0.380992i
$971$	37.2182	+	21.4879i	1.19439	+	0.689580i	0.959299	−	0.282394i	$-0.0911285\pi$
$971$	37.2182	+	21.4879i	1.19439	+	0.689580i	0.235089	+	0.971974i	$0.424462\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−25.8025	+	10.3184i	−0.827189	+	0.330794i
$974$			19.6614i			0.629991i
$975$	0.00525309	+	0.00303287i	0.000168234	+	9.71297e-5i
$976$	0.525000	+	0.909326i	0.0168048	+	0.0291068i
$977$	5.72694	+	9.91935i	0.183221	+	0.317348i	0.942976	−	0.332862i	$-0.108014\pi$
$977$	5.72694	+	9.91935i	0.183221	+	0.317348i	−0.759755	+	0.650210i	$0.774681\pi$
$978$	5.84566	−	10.1250i	0.186923	−	0.323761i
$979$	23.9041	−	39.8018i	0.763980	−	1.27207i
$980$	10.7346	+	11.2752i	0.342906	+	0.360174i
$981$			16.5527i			0.528487i
$982$	15.8167	−	27.3953i	0.504731	−	0.874220i
$983$	−41.5723	+	24.0018i	−1.32595	+	0.765538i	−0.984671	−	0.174423i	$-0.944194\pi$
$983$	−41.5723	+	24.0018i	−1.32595	+	0.765538i	−0.341281	+	0.939961i	$0.610861\pi$
$984$	−1.57435	−	2.72685i	−0.0501883	−	0.0869287i
$985$	4.12674	−	7.14772i	0.131489	−	0.227745i
$986$	1.79993			0.0573215
$987$	−31.8363	+	12.7314i	−1.01336	+	0.405244i
$988$	0.0491608			0.00156401
$989$	7.08654	+	4.09141i	0.225339	+	0.130099i
$990$	0.127208	−	7.37508i	0.00404293	−	0.234396i
$991$	−1.92802	−	3.33943i	−0.0612456	−	0.106081i	0.833777	−	0.552102i	$-0.186174\pi$
$991$	−1.92802	−	3.33943i	−0.0612456	−	0.106081i	−0.895022	+	0.446021i	$0.852841\pi$
$992$	0.177040	−	0.306643i	0.00562104	−	0.00973593i
$993$			22.5669i			0.716139i
$994$	19.8513	+	2.86185i	0.629646	+	0.0907723i
$995$	12.8191			0.406393
$996$	−0.492929	−	0.284593i	−0.0156191	−	0.00901767i
$997$	−2.19567	−	3.80302i	−0.0695376	−	0.120443i	0.829160	−	0.559011i	$-0.188819\pi$
$997$	−2.19567	−	3.80302i	−0.0695376	−	0.120443i	−0.898698	+	0.438568i	$0.855486\pi$
$998$	−31.3830	+	18.1190i	−0.993412	+	0.573547i
$999$	−6.36499	−	3.67483i	−0.201379	−	0.116266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.a.439.3	yes	16
3.2	odd	2		1386.2.bk.a.901.6		16
7.2	even	3		3234.2.e.a.2155.11		16
7.3	odd	6		462.2.p.b.241.7	yes	16
7.5	odd	6		3234.2.e.b.2155.14		16
11.10	odd	2		462.2.p.b.439.7	yes	16
21.17	even	6		1386.2.bk.b.703.2		16
33.32	even	2		1386.2.bk.b.901.2		16
77.10	even	6	inner	462.2.p.a.241.3	✓	16
77.54	even	6		3234.2.e.a.2155.6		16
77.65	odd	6		3234.2.e.b.2155.3		16
231.164	odd	6		1386.2.bk.a.703.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.3	✓	16	77.10	even	6	inner
462.2.p.a.439.3	yes	16	1.1	even	1	trivial
462.2.p.b.241.7	yes	16	7.3	odd	6
462.2.p.b.439.7	yes	16	11.10	odd	2
1386.2.bk.a.703.6		16	231.164	odd	6
1386.2.bk.a.901.6		16	3.2	odd	2
1386.2.bk.b.703.2		16	21.17	even	6
1386.2.bk.b.901.2		16	33.32	even	2
3234.2.e.a.2155.6		16	77.54	even	6
3234.2.e.a.2155.11		16	7.2	even	3
3234.2.e.b.2155.3		16	77.65	odd	6
3234.2.e.b.2155.14		16	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.92604 + 1.11200i) q^{5} -1.00000 q^{6} +(2.45660 - 0.982398i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.92604 + 1.11200i) q^{5} -1.00000 q^{6} +(2.45660 - 0.982398i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.11200 - 1.92604i) q^{10} +(-0.0571978 + 3.31613i) q^{11} +(0.866025 + 0.500000i) q^{12} -0.112712 q^{13} +(-2.61868 - 0.377519i) q^{14} +2.22400 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.119843 + 0.207574i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-0.218080 + 0.377726i) q^{19} +2.22400i q^{20} +(1.63628 - 2.07908i) q^{21} +(1.70760 - 2.84326i) q^{22} +(-0.401617 + 0.695621i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.0269081 - 0.0466061i) q^{25} +(0.0976119 + 0.0563562i) q^{26} -1.00000i q^{27} +(2.07908 + 1.63628i) q^{28} +7.50955i q^{29} +(-1.92604 - 1.11200i) q^{30} +(0.306643 - 0.177040i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.60853 + 2.90045i) q^{33} -0.239685i q^{34} +(5.82395 + 0.839603i) q^{35} +1.00000 q^{36} +(3.67483 - 6.36499i) q^{37} +(0.377726 - 0.218080i) q^{38} +(-0.0976119 + 0.0563562i) q^{39} +(1.11200 - 1.92604i) q^{40} +3.14869 q^{41} +(-2.45660 + 0.982398i) q^{42} -10.1874i q^{43} +(-2.90045 + 1.60853i) q^{44} +(1.92604 - 1.11200i) q^{45} +(0.695621 - 0.401617i) q^{46} +(-11.2232 - 6.47974i) q^{47} +1.00000i q^{48} +(5.06979 - 4.82672i) q^{49} +0.0538161i q^{50} +(0.207574 + 0.119843i) q^{51} +(-0.0563562 - 0.0976119i) q^{52} +(1.28196 + 2.22041i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.79771 + 6.32340i) q^{55} +(-0.982398 - 2.45660i) q^{56} +0.436161i q^{57} +(3.75478 - 6.50347i) q^{58} +(3.27440 - 1.89048i) q^{59} +(1.11200 + 1.92604i) q^{60} +(0.525000 - 0.909326i) q^{61} -0.354081 q^{62} +(0.377519 - 2.61868i) q^{63} -1.00000 q^{64} +(-0.217089 - 0.125336i) q^{65} +(0.0571978 - 3.31613i) q^{66} +(2.48189 + 4.29875i) q^{67} +(-0.119843 + 0.207574i) q^{68} +0.803234i q^{69} +(-4.62388 - 3.63909i) q^{70} -7.58067 q^{71} +(-0.866025 - 0.500000i) q^{72} +(2.39827 + 4.15392i) q^{73} +(-6.36499 + 3.67483i) q^{74} +(-0.0466061 - 0.0269081i) q^{75} -0.436161 q^{76} +(3.11725 + 8.20261i) q^{77} +0.112712 q^{78} +(0.429215 + 0.247807i) q^{79} +(-1.92604 + 1.11200i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.72685 - 1.57435i) q^{82} -0.569186 q^{83} +(2.61868 + 0.377519i) q^{84} +0.533061i q^{85} +(-5.09368 + 8.82251i) q^{86} +(3.75478 + 6.50347i) q^{87} +(3.31613 + 0.0571978i) q^{88} +(-12.1232 - 6.99934i) q^{89} -2.22400 q^{90} +(-0.276890 + 0.110729i) q^{91} -0.803234 q^{92} +(0.177040 - 0.306643i) q^{93} +(6.47974 + 11.2232i) q^{94} +(-0.840064 + 0.485011i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.6708i q^{97} +(-6.80393 + 1.64517i) q^{98} +(2.84326 + 1.70760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

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