LMFDB - Embedded newform 462.2.p.b.241.7

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			241.7
Root			$0.500000 + 1.35798i$ of defining polynomial
Character	$\chi$	$=$	462.241
Dual form			462.2.p.b.439.7

$q$-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} +(2.90045 - 1.60853i) 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} +(3.31613 + 0.0571978i) 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} +(0.0571978 - 3.31613i) 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} +(2.90045 - 1.60853i) 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} +(-8.70548 + 1.10212i) 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} +(-1.60853 - 2.90045i) 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} + 4 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} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 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 + 4 * 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 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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	−0.00311268	−	0.999995i	$-0.500991\pi$
$5$	1.92604	−	1.11200i	0.861352	−	0.497302i	0.864465	+	0.502693i	$0.167657\pi$
$6$	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
$11$	2.90045	−	1.60853i	0.874519	−	0.484990i
$11$	2.90045	−	1.60853i	0.874519	−	0.484990i
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	0.112712			0.0312608			0.0156304	−	0.999878i	$-0.495024\pi$
$13$	0.112712			0.0312608			0.0156304	+	0.999878i	$0.495024\pi$
$14$	−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	$-0.842587\pi$
$17$	−0.119843	+	0.207574i	−0.0290661	+	0.0503440i	0.851126	+	0.524961i	$0.175920\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	0.218080	+	0.377726i	0.0500311	+	0.0866564i	0.889956	−	0.456046i	$-0.150735\pi$
$19$	0.218080	+	0.377726i	0.0500311	+	0.0866564i	−0.839925	+	0.542702i	$0.817401\pi$
$20$		−	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	0.821112	−	0.570767i	$-0.193354\pi$
$23$	−0.401617	−	0.695621i	−0.0837429	−	0.145047i	−0.904855	+	0.425720i	$0.860021\pi$
$24$	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	0.527285	−	0.849689i	$-0.323210\pi$
$31$	0.306643	+	0.177040i	0.0550747	+	0.0317974i	−0.472210	+	0.881486i	$0.656544\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	3.31613	+	0.0571978i	0.577264	+	0.00995685i
$34$			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	0.992187	+	0.124759i	$0.0398158\pi$
$37$	3.67483	+	6.36499i	0.604138	+	1.04640i	−0.388049	+	0.921639i	$0.626851\pi$
$38$	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	$-0.579074\pi$
$41$	−3.14869			−0.491743			−0.245872	+	0.969302i	$0.579074\pi$
$42$	−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	$-0.283148\pi$
$44$	0.0571978	−	3.31613i	0.00862289	−	0.499926i
$45$	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	−0.655246	+	0.755415i	$0.727435\pi$
$47$	−11.2232	+	6.47974i	−1.63708	+	0.945168i	−0.981832	+	0.189753i	$0.939231\pi$
$48$		−	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	−0.764448	−	0.644686i	$-0.776988\pi$
$53$	1.28196	−	2.22041i	0.176090	−	0.304997i	0.940538	+	0.339688i	$0.110322\pi$
$54$	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	0.697765	−	0.716326i	$-0.254178\pi$
$59$	3.27440	+	1.89048i	0.426291	+	0.246119i	−0.271474	+	0.962446i	$0.587511\pi$
$60$	1.11200	−	1.92604i	0.143559	−	0.248651i
$61$	−0.525000	−	0.909326i	−0.0672193	−	0.116427i	0.830457	−	0.557083i	$-0.188079\pi$
$61$	−0.525000	−	0.909326i	−0.0672193	−	0.116427i	−0.897676	+	0.440655i	$0.854746\pi$
$62$	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
$66$	2.90045	−	1.60853i	0.357021	−	0.197996i
$67$	2.48189	−	4.29875i	0.303211	−	0.525176i	−0.673651	−	0.739050i	$-0.735275\pi$
$67$	2.48189	−	4.29875i	0.303211	−	0.525176i	0.976861	+	0.213874i	$0.0686081\pi$
$68$	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	$-0.923899\pi$
$73$	−2.39827	+	4.15392i	−0.280696	+	0.486179i	0.690861	+	0.722988i	$0.257232\pi$
$74$	6.36499	+	3.67483i	0.739915	+	0.427190i
$75$	−0.0466061	+	0.0269081i	−0.00538161	+	0.00310708i
$76$	0.436161			0.0500311
$77$	−8.70548	+	1.10212i	−0.992081	+	0.125598i
$78$	0.112712			0.0127622
$79$	−0.429215	+	0.247807i	−0.0482905	+	0.0278805i	−0.523951	−	0.851748i	$-0.675542\pi$
$79$	−0.429215	+	0.247807i	−0.0482905	+	0.0278805i	0.475660	+	0.879629i	$0.342209\pi$
$80$	−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	$-0.490055\pi$
$83$	0.569186			0.0624763			0.0312381	+	0.999512i	$0.490055\pi$
$84$	−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
$88$	−1.60853	−	2.90045i	−0.171470	−	0.309189i
$89$	−12.1232	+	6.99934i	−1.28506	+	0.741928i	−0.977768	−	0.209688i	$-0.932755\pi$
$89$	−12.1232	+	6.99934i	−1.28506	+	0.741928i	−0.307289	+	0.951616i	$0.599422\pi$
$90$	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	$-0.817770\pi$
$97$		−	10.6708i		−	1.08345i	0.840554	−	0.541727i	$-0.182230\pi$
$98$	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	−0.281474	+	0.959569i	$0.590823\pi$
$101$	−9.76595	+	16.9151i	−0.971748	+	1.68312i	−0.690274	+	0.723548i	$0.742510\pi$
$102$	−0.119843	+	0.207574i	−0.0118662	+	0.0205529i
$103$	−11.0669	+	6.38947i	−1.09045	+	0.629573i	−0.933697	−	0.358064i	$-0.883437\pi$
$103$	−11.0669	+	6.38947i	−1.09045	+	0.629573i	−0.156756	+	0.987637i	$0.550104\pi$
$104$		−	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	$-0.458741\pi$
$107$	10.8886	−	6.28656i	1.05264	−	0.607745i	0.923389	+	0.383867i	$0.125408\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	14.3351	+	8.27635i	1.37305	+	0.792730i	0.991311	−	0.131540i	$-0.0419921\pi$
$109$	14.3351	+	8.27635i	1.37305	+	0.792730i	0.381739	+	0.924270i	$0.375325\pi$
$110$	0.127208	−	7.37508i	0.0121288	−	0.703187i
$111$			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
$121$	5.82526	−	9.33094i	0.529569	−	0.848267i
$122$	−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	$-0.138007\pi$
$131$	1.02912	+	1.78250i	0.0899150	+	0.155737i	−0.817560	+	0.575843i	$0.804674\pi$
$132$	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	−0.110838	−	0.993839i	$-0.535353\pi$
$137$	9.42545	−	16.3254i	0.805271	−	1.39477i	0.916108	−	0.400931i	$-0.131313\pi$
$138$	−0.401617	−	0.695621i	−0.0341879	−	0.0592152i
$139$	10.5033			0.890880			0.445440	−	0.895312i	$-0.353047\pi$
$139$	10.5033			0.890880			0.445440	+	0.895312i	$0.353047\pi$
$140$	−2.18486	+	5.46349i	−0.184654	+	0.461749i
$141$	−12.9595			−1.09139
$142$	−6.56505	+	3.79033i	−0.550927	+	0.318078i
$143$	0.326917	−	0.181302i	0.0273382	−	0.0151612i
$144$	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	$-0.462369\pi$
$149$	12.6570	−	7.30752i	1.03690	−	0.598656i	0.918954	+	0.394364i	$0.129035\pi$
$150$	−0.0269081	+	0.0466061i	−0.00219703	+	0.00380538i
$151$	1.57663	+	0.910267i	0.128304	+	0.0740764i	0.562778	−	0.826608i	$-0.309732\pi$
$151$	1.57663	+	0.910267i	0.128304	+	0.0740764i	−0.434474	+	0.900684i	$0.643066\pi$
$152$	0.377726	−	0.218080i	0.0306377	−	0.0176887i
$153$	−0.239685			−0.0193774
$154$	−6.98810	+	5.30720i	−0.563117	+	0.427667i
$155$	0.787477			0.0632516
$156$	0.0976119	−	0.0563562i	0.00781520	−	0.00451211i
$157$	15.1388	+	8.74037i	1.20821	+	0.697558i	0.962367	−	0.271753i	$-0.0876034\pi$
$157$	15.1388	+	8.74037i	1.20821	+	0.697558i	0.245839	+	0.969311i	$0.420937\pi$
$158$	−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	0.540981	−	0.841035i	$-0.318053\pi$
$163$	−5.84566	−	10.1250i	−0.457867	−	0.793049i	−0.998848	+	0.0479858i	$0.984720\pi$
$164$	−1.57435	+	2.72685i	−0.122936	+	0.212931i
$165$	6.45061	−	3.57738i	0.502180	−	0.278498i
$166$	0.492929	−	0.284593i	0.0382587	−	0.0220887i
$167$	−18.4885			−1.43068			−0.715341	−	0.698775i	$-0.753729\pi$
$167$	−18.4885			−1.43068			−0.715341	+	0.698775i	$0.753729\pi$
$168$	−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	−0.982288	−	0.187378i	$-0.940001\pi$
$173$	−8.59437	−	14.8859i	−0.653418	−	1.13175i	0.328870	−	0.944375i	$-0.393332\pi$
$174$			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	−0.997286	−	0.0736206i	$-0.976545\pi$
$179$	−5.81838	+	10.0777i	−0.434886	+	0.753244i	0.562400	+	0.826865i	$0.309878\pi$
$180$	1.92604	−	1.11200i	0.143559	−	0.0828837i
$181$		−	21.9534i		−	1.63179i	−0.578203	−	0.815893i	$-0.696246\pi$
$181$		−	21.9534i		−	1.63179i	0.578203	−	0.815893i	$-0.303754\pi$
$182$	−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
$187$	−0.0137095	+	0.794828i	−0.00100254	+	0.0581236i
$188$			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	0.953749	−	0.300604i	$-0.0971884\pi$
$191$	2.99269	+	5.18349i	0.216543	+	0.375064i	−0.737205	+	0.675669i	$0.763855\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	7.35467	+	4.24622i	0.529401	+	0.305650i	0.740772	−	0.671756i	$-0.234460\pi$
$193$	7.35467	+	4.24622i	0.529401	+	0.305650i	−0.211372	+	0.977406i	$0.567793\pi$
$194$	−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	$-0.0422048\pi$
$198$	3.31613	+	0.0571978i	0.235667	+	0.00406487i
$199$	4.99176	+	2.88199i	0.353857	+	0.204299i	0.666383	−	0.745610i	$-0.267842\pi$
$199$	4.99176	+	2.88199i	0.353857	+	0.204299i	−0.312526	+	0.949909i	$0.601175\pi$
$200$	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
$220$	−3.57738	−	6.45061i	−0.241187	−	0.434900i
$221$	−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	$-0.876222\pi$
$223$		−	11.3233i		−	0.758267i	0.925342	−	0.379134i	$-0.123778\pi$
$224$	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	$-0.889961\pi$
$227$	−2.66623	+	4.61805i	−0.176964	+	0.306510i	0.763875	+	0.645364i	$0.223294\pi$
$228$	0.377726	+	0.218080i	0.0250155	+	0.0144427i
$229$	15.6189	−	9.01755i	1.03212	−	0.595897i	0.114531	−	0.993420i	$-0.463463\pi$
$229$	15.6189	−	9.01755i	1.03212	−	0.595897i	0.917592	+	0.397523i	$0.130130\pi$
$230$	−1.78639			−0.117791
$231$	−8.09022	−	3.39827i	−0.532298	−	0.223590i
$232$	7.50955			0.493026
$233$	13.5770	−	7.83866i	0.889456	−	0.513528i	0.0156917	−	0.999877i	$-0.495005\pi$
$233$	13.5770	−	7.83866i	0.889456	−	0.513528i	0.873765	+	0.486349i	$0.161672\pi$
$234$	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	$-0.913166\pi$
$241$	−3.85279	+	6.67323i	−0.248180	+	0.429861i	0.714841	+	0.699287i	$0.246499\pi$
$242$	0.379351	−	10.9935i	0.0243856	−	0.706686i
$243$	−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	$-0.882972\pi$
$251$		−	11.3888i		−	0.718857i	0.933173	−	0.359428i	$-0.117028\pi$
$252$	−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	0.00474110	−	0.999989i	$-0.498491\pi$
$257$	13.9973	−	8.08134i	0.873127	−	0.504100i	0.868386	+	0.495888i	$0.165158\pi$
$258$		−	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	$-0.248099\pi$
$263$	7.43191	+	4.29081i	0.458271	+	0.264583i	−0.253046	+	0.967454i	$0.581432\pi$
$264$	0.0571978	−	3.31613i	0.00352028	−	0.204094i
$265$		−	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	0.605318	−	0.795984i	$-0.293046\pi$
$269$	3.58587	+	2.07030i	0.218634	+	0.126229i	−0.386683	+	0.922213i	$0.626379\pi$
$270$	1.92604	+	1.11200i	0.117215	+	0.0676742i
$271$	−1.71583	−	2.97190i	−0.104229	−	0.180530i	0.809194	−	0.587542i	$-0.199904\pi$
$271$	−1.71583	−	2.97190i	−0.104229	−	0.180530i	−0.913423	+	0.407012i	$0.866571\pi$
$272$	0.239685			0.0145331
$273$	−0.184429	−	0.234339i	−0.0111622	−	0.0141828i
$274$		−	18.8509i		−	1.13882i
$275$	−0.00307816	+	0.178461i	−0.000185620	+	0.0107616i
$276$	−0.695621	−	0.401617i	−0.0418714	−	0.0241745i
$277$	1.35959	+	0.784960i	0.0816899	+	0.0471637i	0.540289	−	0.841480i	$-0.318315\pi$
$277$	1.35959	+	0.784960i	0.0816899	+	0.0471637i	−0.458599	+	0.888643i	$0.651648\pi$
$278$	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	−0.320043	−	0.947403i	$-0.603697\pi$
$283$	11.1106	−	19.2440i	0.660454	−	1.14394i	0.980496	−	0.196537i	$-0.0629694\pi$
$284$	−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	$-0.435823\pi$
$293$	6.85562			0.400510			0.200255	+	0.979744i	$0.435823\pi$
$294$	5.06979	+	4.82672i	0.295676	+	0.281500i
$295$	8.40885			0.489582
$296$	6.36499	−	3.67483i	0.369957	−	0.213595i
$297$	1.60853	+	2.90045i	0.0933364	+	0.168301i
$298$	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	$-0.757377\pi$
$307$	−25.3466			−1.44661			−0.723303	+	0.690531i	$0.757377\pi$
$308$	−3.39827	+	8.09022i	−0.193635	+	0.460983i
$309$	−12.7789			−0.726969
$310$	0.681975	−	0.393738i	0.0387336	−	0.0223628i
$311$	12.0093	+	6.93356i	0.680984	+	0.393166i	0.800226	−	0.599699i	$-0.204713\pi$
$311$	12.0093	+	6.93356i	0.680984	+	0.393166i	−0.119242	+	0.992865i	$0.538046\pi$
$312$	0.0563562	−	0.0976119i	0.00319054	−	0.00552618i
$313$	10.4414	−	6.02834i	0.590183	−	0.340742i	−0.174987	−	0.984571i	$-0.555988\pi$
$313$	10.4414	−	6.02834i	0.590183	−	0.340742i	0.765170	+	0.643829i	$0.222655\pi$
$314$	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	0.952371	−	0.304942i	$-0.0986372\pi$
$317$	3.77629	+	6.54073i	0.212098	+	0.367364i	−0.740273	+	0.672306i	$0.765304\pi$
$318$	1.28196	−	2.22041i	0.0718885	−	0.124515i
$319$	12.0794	+	21.7811i	0.676314	+	1.21951i
$320$	−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	−0.989449	−	0.144880i	$-0.953720\pi$
$331$	−11.2835	−	19.5435i	−0.620195	−	1.07421i	0.369255	−	0.929328i	$-0.379613\pi$
$332$	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
$341$	1.17418	+	0.0202526i	0.0635854	+	0.00109674i
$342$			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	$-0.0244102\pi$
$347$	26.6239	+	15.3713i	1.42924	+	0.825174i	0.432183	+	0.901786i	$0.357744\pi$
$348$	3.75478	+	6.50347i	0.201277	+	0.348622i
$349$	−24.5576			−1.31454			−0.657269	−	0.753656i	$-0.728288\pi$
$349$	−24.5576			−1.31454			−0.657269	+	0.753656i	$0.728288\pi$
$350$	0.0528689	−	0.132205i	0.00282596	−	0.00706665i
$351$			0.112712i			0.00601615i
$352$	−3.31613	−	0.0571978i	−0.176750	−	0.00304865i
$353$	3.74418	+	2.16170i	0.199283	+	0.115056i	0.596321	−	0.802746i	$-0.296629\pi$
$353$	3.74418	+	2.16170i	0.199283	+	0.115056i	−0.397038	+	0.917802i	$0.629962\pi$
$354$	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	$-0.528682\pi$
$359$	13.7848	−	7.95866i	0.727534	−	0.420042i	0.817519	+	0.575901i	$0.195349\pi$
$360$	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	−0.211643	−	0.977347i	$-0.567881\pi$
$367$	−22.2966	−	12.8729i	−1.16387	−	0.671962i	−0.952229	+	0.305385i	$0.901215\pi$
$368$	−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	$-0.939200\pi$
$373$	−25.2676	+	14.5882i	−1.30831	+	0.755350i	−0.326492	+	0.945200i	$0.605867\pi$
$374$	0.385541	+	0.695196i	0.0199359	+	0.0359477i
$375$	−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	−0.648249	−	0.761429i	$-0.724498\pi$
$383$	−6.12468	+	3.53608i	−0.312956	+	0.180685i	0.335292	+	0.942114i	$0.391165\pi$
$384$	−1.00000			−0.0510310
$385$	−15.5416	+	11.8032i	−0.792071	+	0.601548i
$386$	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	−0.979185	−	0.202972i	$-0.934940\pi$
$389$	−6.18937	+	10.7203i	−0.313813	+	0.543541i	0.665371	+	0.746513i	$0.268273\pi$
$390$	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
$396$	2.90045	−	1.60853i	0.145753	−	0.0808317i
$397$	17.2980	−	9.98702i	0.868163	−	0.501234i	0.00142581	−	0.999999i	$-0.499546\pi$
$397$	17.2980	−	9.98702i	0.868163	−	0.501234i	0.866737	+	0.498765i	$0.166213\pi$
$398$	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	0.703564	−	0.710632i	$-0.251591\pi$
$401$	−5.27945	−	9.14428i	−0.263643	−	0.456643i	−0.967207	+	0.253988i	$0.918257\pi$
$402$	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	−0.441755	−	0.897136i	$-0.645644\pi$
$409$	11.2457	−	19.4781i	0.556065	−	0.963132i	0.997820	−	0.0659967i	$-0.0210227\pi$
$410$	−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
$418$	1.44637	+	0.0249474i	0.0707441	+	0.00122022i
$419$			25.5522i			1.24831i	0.781302	+	0.624154i	$0.214556\pi$
$419$			25.5522i			1.24831i	−0.781302	+	0.624154i	$0.785444\pi$
$420$	−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
$429$	0.373769	+	0.00644690i	0.0180458	+	0.000311259i
$430$	−19.6213	−	11.3284i	−0.946222	−	0.546302i
$431$	−28.7727	−	16.6119i	−1.38593	−	0.800168i	−0.393077	−	0.919505i	$-0.628590\pi$
$431$	−28.7727	−	16.6119i	−1.38593	−	0.800168i	−0.992854	+	0.119338i	$0.961923\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	0.741961i		−	0.0356564i	−0.999841	−	0.0178282i	$-0.994325\pi$
$433$		−	0.741961i		−	0.0356564i	0.999841	−	0.0178282i	$-0.00567519\pi$
$434$	−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	$-0.0400492\pi$
$439$	8.11637	+	14.0580i	0.387373	+	0.670950i	−0.604722	+	0.796437i	$0.706716\pi$
$440$	−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	0.966043	−	0.258382i	$-0.0831893\pi$
$443$	5.45671	+	9.45129i	0.259256	+	0.449044i	−0.706787	+	0.707427i	$0.749856\pi$
$444$	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
$451$	−9.13263	+	5.06477i	−0.430039	+	0.238491i
$452$	−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	$-0.860835\pi$
$457$	−21.2115	+	12.2465i	−0.992233	+	0.572866i	−0.0862919	+	0.996270i	$0.527502\pi$
$458$	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	$-0.559783\pi$
$461$	−8.01773			−0.373423			−0.186712	+	0.982415i	$0.559783\pi$
$462$	−8.70548	+	1.10212i	−0.405015	+	0.0512753i
$463$	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	−0.207440	−	0.978248i	$-0.566513\pi$
$467$	11.5836	−	6.68782i	0.536027	−	0.309475i	0.743467	+	0.668772i	$0.233180\pi$
$468$	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
$473$	−16.3867	−	29.5480i	−0.753460	−	1.35862i
$474$	−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	0.130564	+	0.991440i	$0.458321\pi$
$479$	−17.3629	+	30.0734i	−0.793330	+	1.37409i	−0.923894	+	0.382648i	$0.875012\pi$
$480$	−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	−0.998085	−	0.0618591i	$-0.980297\pi$
$487$	−9.83069	+	17.0272i	−0.445471	+	0.771578i	0.552614	+	0.833437i	$0.313630\pi$
$488$	−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
$495$	7.37508	+	0.127208i	0.331485	+	0.00571757i
$496$		−	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	0.912082	+	0.410007i	$0.134474\pi$
$499$	18.1190	+	31.3830i	0.811118	+	1.40490i	−0.100965	+	0.994890i	$0.532193\pi$
$500$	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	$-0.717806\pi$
$503$	−28.3530			−1.26420			−0.632098	+	0.774889i	$0.717806\pi$
$504$	−2.61868	+	0.377519i	−0.116645	+	0.0168160i
$505$			43.4390i			1.93301i
$506$	−2.66363	−	0.0459432i	−0.118413	−	0.00204242i
$507$	−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	−0.993676	−	0.112281i	$-0.964184\pi$
$509$	−31.4337	+	18.1483i	−1.39328	+	0.804408i	−0.399600	+	0.916690i	$0.630851\pi$
$510$			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	0.336338	−	0.941741i	$-0.390812\pi$
$521$	−7.10021	−	4.09931i	−0.311066	−	0.179594i	−0.647403	+	0.762148i	$0.724145\pi$
$522$	−3.75478	+	6.50347i	−0.164342	+	0.284649i
$523$	−16.8849	−	29.2456i	−0.738327	−	1.27882i	−0.953248	−	0.302188i	$-0.902283\pi$
$523$	−16.8849	−	29.2456i	−0.738327	−	1.27882i	0.214921	−	0.976631i	$-0.431050\pi$
$524$	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
$528$	−1.60853	−	2.90045i	−0.0700023	−	0.126226i
$529$	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
$539$	22.4686	+	5.84477i	0.967792	+	0.251752i
$540$	2.22400			0.0957058
$541$	19.6218	−	11.3286i	0.843607	−	0.487057i	−0.0148819	−	0.999889i	$-0.504737\pi$
$541$	19.6218	−	11.3286i	0.843607	−	0.487057i	0.858489	+	0.512833i	$0.171404\pi$
$542$	−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
$550$	0.0865649	+	0.156091i	0.00369114	+	0.00665575i
$551$	−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	−0.971961	−	0.235141i	$-0.924445\pi$
$557$	−39.2147	−	22.6406i	−1.66158	−	0.959314i	−0.689619	−	0.724173i	$-0.742222\pi$
$558$	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	0.410682	+	0.911779i	$0.365291\pi$
$563$	−13.8636	+	24.0125i	−0.584283	+	1.01201i	−0.994964	+	0.100228i	$0.968043\pi$
$564$	−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	$-0.557397\pi$
$569$	13.9061	−	8.02868i	0.582973	−	0.336580i	0.762314	+	0.647207i	$0.224063\pi$
$570$	0.840064	+	0.485011i	0.0351864	+	0.0203149i
$571$	8.42022	+	4.86141i	0.352375	+	0.203444i	0.665731	−	0.746192i	$-0.268120\pi$
$571$	8.42022	+	4.86141i	0.352375	+	0.203444i	−0.313356	+	0.949636i	$0.601453\pi$
$572$	0.00644690	−	0.373769i	0.000269559	−	0.0156281i
$573$			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	0.545607	−	0.838041i	$-0.316299\pi$
$577$	2.22544	+	1.28486i	0.0926462	+	0.0534893i	−0.452961	+	0.891530i	$0.649632\pi$
$578$	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
$583$	0.146650	−	8.50227i	0.00607363	−	0.352128i
$584$	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	$-0.820382\pi$
$587$		−	25.9150i		−	1.06963i	0.844970	−	0.534814i	$-0.179618\pi$
$588$	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	$-0.215511\pi$
$593$	−3.72204	−	6.44677i	−0.152846	−	0.264737i	−0.932273	+	0.361756i	$0.882177\pi$
$594$	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	0.496707	+	0.867918i	$0.334542\pi$
$599$	−12.3177	+	21.3348i	−0.503286	+	0.871717i	−0.999993	+	0.00379841i	$0.998791\pi$
$600$	0.0269081	+	0.0466061i	0.00109852	+	0.00190269i
$601$	−6.75417			−0.275508			−0.137754	−	0.990466i	$-0.543988\pi$
$601$	−6.75417			−0.275508			−0.137754	+	0.990466i	$0.543988\pi$
$602$	3.84592	+	26.6774i	0.156748	+	1.08729i
$603$	4.96377			0.202140
$604$	1.57663	−	0.910267i	0.0641521	−	0.0370382i
$605$	0.843677	−	24.4495i	0.0343003	−	0.994012i
$606$	−9.76595	+	16.9151i	−0.396714	+	0.687130i
$607$	18.7854	+	32.5373i	0.762476	+	1.32065i	0.941571	+	0.336815i	$0.109350\pi$
$607$	18.7854	+	32.5373i	0.762476	+	1.32065i	−0.179095	+	0.983832i	$0.557317\pi$
$608$		−	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	$-0.605884\pi$
$613$	−32.3937	−	18.7025i	−1.30837	−	0.755387i	−0.981824	+	0.189795i	$0.939218\pi$
$614$	−21.9508	+	12.6733i	−0.885861	+	0.511452i
$615$	−7.00270			−0.282376
$616$	1.10212	+	8.70548i	0.0444057	+	0.350754i
$617$	−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	0.395406	−	0.918506i	$-0.370604\pi$
$619$	−5.03418	−	2.90648i	−0.202341	−	0.116821i	−0.597747	+	0.801685i	$0.703937\pi$
$620$	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
$627$	0.701578	+	1.26506i	0.0280183	+	0.0505218i
$628$	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	−0.622741	−	0.782428i	$-0.713981\pi$
$641$	9.27227	−	16.0600i	0.366233	−	0.634333i	0.988973	+	0.148095i	$0.0473141\pi$
$642$	10.8886	−	6.28656i	0.429740	−	0.248111i
$643$			9.80715i			0.386756i	0.981124	+	0.193378i	$0.0619444\pi$
$643$			9.80715i			0.386756i	−0.981124	+	0.193378i	$0.938056\pi$
$644$	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	0.140456	−	0.990087i	$-0.455143\pi$
$647$	−16.4510	−	9.49800i	−0.646756	−	0.373405i	−0.787212	+	0.616682i	$0.788476\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	12.5381	+	0.216262i	0.492165	+	0.00848903i
$650$			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	0.676372	−	0.736560i	$-0.263551\pi$
$653$	−7.65833	−	13.2646i	−0.299694	−	0.519084i	−0.976066	+	0.217476i	$0.930218\pi$
$654$	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	$0.553524\pi$
$660$	0.127208	−	7.37508i	0.00495156	−	0.287075i
$661$	33.9093	+	19.5776i	1.31892	+	0.761478i	0.983555	−	0.180610i	$-0.0578072\pi$
$661$	33.9093	+	19.5776i	1.31892	+	0.761478i	0.335365	+	0.942088i	$0.391141\pi$
$662$	−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	−0.779796	−	0.626034i	$-0.784677\pi$
$677$	−24.2515	−	42.0048i	−0.932059	−	1.61437i	−0.152263	−	0.988340i	$-0.548656\pi$
$678$	−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
$682$	1.02700	−	0.569550i	0.0393257	−	0.0218092i
$683$	3.55626	−	6.15962i	0.136076	−	0.235691i	−0.789932	−	0.613195i	$-0.789884\pi$
$683$	3.55626	−	6.15962i	0.136076	−	0.235691i	0.926008	+	0.377504i	$0.123217\pi$
$684$	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	0.442209	−	0.896912i	$-0.354195\pi$
$691$	37.8547	−	21.8554i	1.44006	−	0.831420i	0.997853	+	0.0654915i	$0.0208615\pi$
$692$	−17.1887			−0.653418
$693$	−5.30720	−	6.98810i	−0.201604	−	0.265456i
$694$	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
$704$	−2.90045	+	1.60853i	−0.109315	+	0.0606238i
$705$	−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	0.944009	+	0.329919i	$0.107021\pi$
$709$	20.1759	+	34.9457i	0.757723	+	1.31241i	−0.186287	+	0.982495i	$0.559645\pi$
$710$	−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	−0.602950	−	0.797779i	$-0.706008\pi$
$719$	−5.72561	+	3.30568i	−0.213529	+	0.123281i	0.389421	+	0.921060i	$0.372675\pi$
$720$		−	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
$726$	5.82526	−	9.33094i	0.216196	−	0.346304i
$727$		−	37.4392i		−	1.38854i	−0.719714	−	0.694271i	$-0.755727\pi$
$727$		−	37.4392i		−	1.38854i	0.719714	−	0.694271i	$-0.244273\pi$
$728$	−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	$-0.307031\pi$
$733$	−11.5556	−	20.0149i	−0.426816	−	0.739266i	−0.996588	+	0.0825361i	$0.973698\pi$
$734$	−25.7459			−0.950297
$735$	11.2752	+	10.7346i	0.415893	+	0.395953i
$736$			0.803234i			0.0296076i
$737$	0.283917	−	16.4605i	0.0104582	−	0.606331i
$738$	−2.72685	−	1.57435i	−0.100377	−	0.0579525i
$739$	−24.3934	−	14.0836i	−0.897327	−	0.518072i	−0.0209949	−	0.999780i	$-0.506683\pi$
$739$	−24.3934	−	14.0836i	−0.897327	−	0.518072i	−0.876332	+	0.481708i	$0.840017\pi$
$740$	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	0.813590	−	0.581439i	$-0.197510\pi$
$751$	−2.65126	−	4.59211i	−0.0967457	−	0.167568i	−0.910336	+	0.413870i	$0.864177\pi$
$752$	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
$759$	−1.29203	−	2.32974i	−0.0468976	−	0.0845643i
$760$	0.485011	−	0.840064i	0.0175932	−	0.0304723i
$761$	21.5347	+	37.2992i	0.780632	+	1.35209i	0.931574	+	0.363552i	$0.118436\pi$
$761$	21.5347	+	37.2992i	0.780632	+	1.35209i	−0.150942	+	0.988543i	$0.548231\pi$
$762$		−	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	$-0.229563\pi$
$769$	41.6527			1.50204			0.751018	+	0.660282i	$0.229563\pi$
$770$	−7.55777	+	17.9927i	−0.272363	+	0.648411i
$771$	16.1627			0.582085
$772$	7.35467	−	4.24622i	0.264700	−	0.152825i
$773$	−18.5314	−	10.6991i	−0.666527	−	0.384820i	0.128232	−	0.991744i	$-0.459070\pi$
$773$	−18.5314	−	10.6991i	−0.666527	−	0.384820i	−0.794759	+	0.606925i	$0.792403\pi$
$774$	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
$781$	−21.9874	+	12.1937i	−0.786770	+	0.436326i
$782$	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	$-0.700619\pi$
$787$	11.3606	−	19.6771i	0.404961	−	0.701413i	0.994317	+	0.106461i	$0.0339519\pi$
$788$	−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	$0.115514\pi$
$797$			20.0434i			0.709972i	−0.934872	+	0.354986i	$0.884486\pi$
$798$	−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
$803$	−0.274351	+	15.9059i	−0.00968163	+	0.561308i
$804$		−	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	$-0.317852\pi$
$809$	2.39507	+	1.38280i	0.0842063	+	0.0486165i	−0.457306	+	0.889310i	$0.651185\pi$
$810$	1.11200	+	1.92604i	0.0390717	+	0.0676742i
$811$	25.2486			0.886597			0.443298	−	0.896374i	$-0.353808\pi$
$811$	25.2486			0.886597			0.443298	+	0.896374i	$0.353808\pi$
$812$	−12.2877	−	15.6130i	−0.431215	−	0.547908i
$813$		−	3.43166i		−	0.120353i
$814$	24.3724	+	0.420384i	0.854253	+	0.0147345i
$815$	−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	$-0.897755\pi$
$821$	−32.9471	+	19.0220i	−1.14986	+	0.663874i	−0.201009	+	0.979589i	$0.564422\pi$
$822$	9.42545	−	16.3254i	0.328750	−	0.569412i
$823$	13.2848	−	23.0100i	0.463079	−	0.802076i	−0.536033	−	0.844197i	$-0.680078\pi$
$823$	13.2848	−	23.0100i	0.463079	−	0.802076i	0.999113	+	0.0421202i	$0.0134113\pi$
$824$	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	0.745312	−	0.666716i	$-0.232300\pi$
$829$	15.5644	+	8.98614i	0.540576	+	0.312102i	−0.204737	+	0.978817i	$0.565634\pi$
$830$	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
$836$	1.26506	−	0.701578i	0.0437532	−	0.0242646i
$837$	−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	$-0.932214\pi$
$839$		−	12.2437i		−	0.422699i	0.977411	−	0.211350i	$-0.0677859\pi$
$840$	−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
$847$	−23.4770	+	17.1997i	−0.806680	+	0.590988i
$848$	−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	$-0.724707\pi$
$853$	−37.8949			−1.29750			−0.648749	+	0.761003i	$0.724707\pi$
$854$	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	$-0.670593\pi$
$857$	14.3234	−	24.8089i	0.489279	−	0.847457i	0.999924	+	0.0123352i	$0.00392651\pi$
$858$	0.326917	−	0.181302i	0.0111608	−	0.00618953i
$859$	4.55274	−	2.62852i	0.155337	−	0.0896841i	−0.420316	−	0.907378i	$-0.638081\pi$
$859$	4.55274	−	2.62852i	0.155337	−	0.0896841i	0.575654	+	0.817694i	$0.304748\pi$
$860$	−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	0.993495	+	0.113879i	$0.0363275\pi$
$863$	17.4901	+	30.2937i	0.595369	+	1.03121i	−0.398126	+	0.917331i	$0.630339\pi$
$864$	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	$-0.740176\pi$
$877$	−11.7405	+	6.77841i	−0.396450	+	0.228890i	0.288501	+	0.957480i	$0.406843\pi$
$878$	14.0580	+	8.11637i	0.474433	+	0.273914i
$879$	5.93714	+	3.42781i	0.200255	+	0.115617i
$880$	−7.37508	−	0.127208i	−0.248614	−	0.00428818i
$881$			57.2399i			1.92846i	0.265064	+	0.964231i	$0.414607\pi$
$881$			57.2399i			1.92846i	−0.265064	+	0.964231i	$0.585393\pi$
$882$	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	0.986708	+	0.162502i	$0.0519565\pi$
$887$	18.8847	+	32.7092i	0.634085	+	1.09827i	−0.352623	+	0.935766i	$0.614710\pi$
$888$	7.34966			0.246638
$889$	−5.02238	+	12.5591i	−0.168445	+	0.421217i
$890$			31.1331i			1.04358i
$891$	−0.0571978	+	3.31613i	−0.00191620	+	0.111095i
$892$	−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	0.212775	+	0.977101i	$0.431750\pi$
$907$	−22.2803	+	38.5907i	−0.739807	+	1.28138i	−0.952582	+	0.304282i	$0.901584\pi$
$908$	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
$913$	1.65090	−	0.915553i	0.0546367	−	0.0303004i
$914$	−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	$-0.820962\pi$
$919$	−24.4668	+	14.1259i	−0.807086	+	0.465971i	0.0388569	+	0.999245i	$0.487628\pi$
$920$	−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
$924$	−6.98810	+	5.30720i	−0.229892	+	0.174594i
$925$	−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	−0.829326	−	0.558764i	$-0.811276\pi$
$929$	−23.1670	+	13.3755i	−0.760085	+	0.438836i	0.0692410	+	0.997600i	$0.477942\pi$
$930$	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
$935$	0.857445	+	1.54612i	0.0280414	+	0.0505635i
$936$	0.0976119	−	0.0563562i	0.00319054	−	0.00184206i
$937$	8.64381			0.282381			0.141190	−	0.989982i	$-0.454907\pi$
$937$	8.64381			0.282381			0.141190	+	0.989982i	$0.454907\pi$
$938$	−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	$-0.757289\pi$
$941$	7.25889	−	12.5728i	0.236633	−	0.409861i	0.959746	+	0.280869i	$0.0906227\pi$
$942$	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	0.945881	−	0.324515i	$-0.105201\pi$
$947$	5.90549	+	10.2286i	0.191903	+	0.332385i	−0.753978	+	0.656899i	$0.771868\pi$
$948$	−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
$957$	−0.429530	+	24.9027i	−0.0138847	+	0.804989i
$958$			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	$-0.323931\pi$
$968$	−9.33094	−	5.82526i	−0.299908	−	0.187231i
$969$	−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	0.235089	−	0.971974i	$-0.424462\pi$
$971$	37.2182	−	21.4879i	1.19439	−	0.689580i	0.959299	+	0.282394i	$0.0911285\pi$
$972$			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	−0.759755	−	0.650210i	$-0.774681\pi$
$977$	5.72694	−	9.91935i	0.183221	−	0.317348i	0.942976	+	0.332862i	$0.108014\pi$
$978$	−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	−0.341281	−	0.939961i	$-0.610861\pi$
$983$	−41.5723	−	24.0018i	−1.32595	−	0.765538i	−0.984671	+	0.174423i	$0.944194\pi$
$984$	−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
$990$	6.45061	−	3.57738i	0.205014	−	0.113696i
$991$	−1.92802	+	3.33943i	−0.0612456	+	0.106081i	−0.895022	−	0.446021i	$-0.852841\pi$
$991$	−1.92802	+	3.33943i	−0.0612456	+	0.106081i	0.833777	+	0.552102i	$0.186174\pi$
$992$	−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	$-0.811181\pi$
$997$	2.19567	−	3.80302i	0.0695376	−	0.120443i	0.898698	+	0.438568i	$0.144514\pi$
$998$	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.b.241.7	yes	16
3.2	odd	2		1386.2.bk.b.703.2		16
7.3	odd	6		3234.2.e.a.2155.11		16
7.4	even	3		3234.2.e.b.2155.14		16
7.5	odd	6		462.2.p.a.439.3	yes	16
11.10	odd	2		462.2.p.a.241.3	✓	16
21.5	even	6		1386.2.bk.a.901.6		16
33.32	even	2		1386.2.bk.a.703.6		16
77.10	even	6		3234.2.e.b.2155.3		16
77.32	odd	6		3234.2.e.a.2155.6		16
77.54	even	6	inner	462.2.p.b.439.7	yes	16
231.131	odd	6		1386.2.bk.b.901.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.3	✓	16	11.10	odd	2
462.2.p.a.439.3	yes	16	7.5	odd	6
462.2.p.b.241.7	yes	16	1.1	even	1	trivial
462.2.p.b.439.7	yes	16	77.54	even	6	inner
1386.2.bk.a.703.6		16	33.32	even	2
1386.2.bk.a.901.6		16	21.5	even	6
1386.2.bk.b.703.2		16	3.2	odd	2
1386.2.bk.b.901.2		16	231.131	odd	6
3234.2.e.a.2155.6		16	77.32	odd	6
3234.2.e.a.2155.11		16	7.3	odd	6
3234.2.e.b.2155.3		16	77.10	even	6
3234.2.e.b.2155.14		16	7.4	even	3

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} +(2.90045 - 1.60853i) 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} +(3.31613 + 0.0571978i) 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} +(0.0571978 - 3.31613i) 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} +(2.90045 - 1.60853i) 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} +(-8.70548 + 1.10212i) 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} +(-1.60853 - 2.90045i) 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	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 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 + 4 * 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 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * 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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