LMFDB - Embedded newform 462.2.i.f.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(67,462)]

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, 4, 0]))

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.i (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.0585812i$ of defining polynomial
Character	$\chi$	$=$	462.67
Dual form			462.2.i.f.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.37328 - 2.37860i) q^{5} +1.00000 q^{6} +(-1.37328 + 2.26144i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.37328 - 2.37860i) q^{5} +1.00000 q^{6} +(-1.37328 + 2.26144i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.37328 + 2.37860i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +5.49314 q^{13} +(2.64510 + 0.0585812i) q^{14} +2.74657 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(4.01839 + 6.96005i) q^{19} +2.74657 q^{20} +(-1.27182 - 2.32002i) q^{21} +1.00000 q^{22} +(0.645103 + 1.11735i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.27182 + 2.20285i) q^{25} +(-2.74657 - 4.75720i) q^{26} +1.00000 q^{27} +(-1.27182 - 2.32002i) q^{28} +4.54364 q^{29} +(-1.37328 - 2.37860i) q^{30} +(-2.54364 + 4.40571i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(7.26496 + 0.160897i) q^{35} +1.00000 q^{36} +(2.01839 + 3.49595i) q^{37} +(4.01839 - 6.96005i) q^{38} +(-2.74657 + 4.75720i) q^{39} +(-1.37328 - 2.37860i) q^{40} +5.54364 q^{41} +(-1.37328 + 2.26144i) q^{42} -4.03677 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-1.37328 + 2.37860i) q^{45} +(0.645103 - 1.11735i) q^{46} +(4.64510 + 8.04555i) q^{47} +1.00000 q^{48} +(-3.22818 - 6.21119i) q^{49} +2.54364 q^{50} +(-0.500000 - 0.866025i) q^{51} +(-2.74657 + 4.75720i) q^{52} +(-2.74657 + 4.75720i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.74657 q^{55} +(-1.37328 + 2.26144i) q^{56} -8.03677 q^{57} +(-2.27182 - 3.93491i) q^{58} +(4.76496 - 8.25314i) q^{59} +(-1.37328 + 2.37860i) q^{60} +(0.829647 + 1.43699i) q^{61} +5.08727 q^{62} +(2.64510 + 0.0585812i) q^{63} +1.00000 q^{64} +(-7.54364 - 13.0660i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-1.77182 + 3.06888i) q^{67} +(-0.500000 - 0.866025i) q^{68} -1.29021 q^{69} +(-3.49314 - 6.37208i) q^{70} +2.54364 q^{71} +(-0.500000 - 0.866025i) q^{72} +(4.29021 - 7.43085i) q^{73} +(2.01839 - 3.49595i) q^{74} +(-1.27182 - 2.20285i) q^{75} -8.03677 q^{76} +(-1.27182 - 2.32002i) q^{77} +5.49314 q^{78} +(-6.11985 - 10.5999i) q^{79} +(-1.37328 + 2.37860i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.77182 - 4.80093i) q^{82} -14.5299 q^{83} +(2.64510 + 0.0585812i) q^{84} +2.74657 q^{85} +(2.01839 + 3.49595i) q^{86} +(-2.27182 + 3.93491i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.25343 + 5.63511i) q^{89} +2.74657 q^{90} +(-7.54364 + 12.4224i) q^{91} -1.29021 q^{92} +(-2.54364 - 4.40571i) q^{93} +(4.64510 - 8.04555i) q^{94} +(11.0368 - 19.1163i) q^{95} +(-0.500000 - 0.866025i) q^{96} -0.0872743 q^{97} +(-3.76496 + 5.90128i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{21} + 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 6 q^{27} - 3 q^{28} + 18 q^{29} - 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} + 6 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} + 24 q^{41} + 18 q^{43} - 3 q^{44} - 9 q^{46} + 15 q^{47} + 6 q^{48} - 24 q^{49} + 6 q^{50} - 3 q^{51} - 3 q^{54} - 6 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 3 q^{63} + 6 q^{64} - 36 q^{65} - 3 q^{66} - 6 q^{67} - 3 q^{68} + 18 q^{69} + 12 q^{70} + 6 q^{71} - 3 q^{72} - 9 q^{74} - 3 q^{75} - 6 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} - 12 q^{83} + 3 q^{84} - 9 q^{86} - 9 q^{87} - 3 q^{88} + 36 q^{89} - 36 q^{91} + 18 q^{92} - 6 q^{93} + 15 q^{94} + 24 q^{95} - 3 q^{96} + 18 q^{97} + 15 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^21 + 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 6 * q^27 - 3 * q^28 + 18 * q^29 - 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 + 6 * q^35 + 6 * q^36 - 9 * q^37 + 3 * q^38 + 24 * q^41 + 18 * q^43 - 3 * q^44 - 9 * q^46 + 15 * q^47 + 6 * q^48 - 24 * q^49 + 6 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 3 * q^63 + 6 * q^64 - 36 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 + 18 * q^69 + 12 * q^70 + 6 * q^71 - 3 * q^72 - 9 * q^74 - 3 * q^75 - 6 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 - 12 * q^83 + 3 * q^84 - 9 * q^86 - 9 * q^87 - 3 * q^88 + 36 * q^89 - 36 * q^91 + 18 * q^92 - 6 * q^93 + 15 * q^94 + 24 * q^95 - 3 * q^96 + 18 * q^97 + 15 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.37328	−	2.37860i	−0.614151	−	1.06374i	−0.990533	−	0.137277i	$-0.956165\pi$
$5$	−1.37328	−	2.37860i	−0.614151	−	1.06374i	0.376381	−	0.926465i	$-0.377168\pi$
$6$	1.00000			0.408248
$7$	−1.37328	+	2.26144i	−0.519053	+	0.854742i
$7$	−1.37328	+	2.26144i	−0.519053	+	0.854742i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.37328	+	2.37860i	−0.434271	+	0.752179i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	5.49314			1.52352			0.761761	−	0.647858i	$-0.224335\pi$
$13$	5.49314			1.52352			0.761761	+	0.647858i	$0.224335\pi$
$14$	2.64510	+	0.0585812i	0.706933	+	0.0156565i
$15$	2.74657			0.709161
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	4.01839	+	6.96005i	0.921881	+	1.59675i	0.796502	+	0.604636i	$0.206681\pi$
$19$	4.01839	+	6.96005i	0.921881	+	1.59675i	0.125379	+	0.992109i	$0.459985\pi$
$20$	2.74657			0.614151
$21$	−1.27182	−	2.32002i	−0.277534	−	0.506269i
$22$	1.00000			0.213201
$23$	0.645103	+	1.11735i	0.134513	+	0.232984i	0.925411	−	0.378964i	$-0.123720\pi$
$23$	0.645103	+	1.11735i	0.134513	+	0.232984i	−0.790898	+	0.611948i	$0.790386\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.27182	+	2.20285i	−0.254364	+	0.440571i
$26$	−2.74657	−	4.75720i	−0.538646	−	0.932963i
$27$	1.00000			0.192450
$28$	−1.27182	−	2.32002i	−0.240351	−	0.438442i
$29$	4.54364			0.843732			0.421866	−	0.906658i	$-0.361375\pi$
$29$	4.54364			0.843732			0.421866	+	0.906658i	$0.361375\pi$
$30$	−1.37328	−	2.37860i	−0.250726	−	0.434271i
$31$	−2.54364	+	4.40571i	−0.456851	+	0.791289i	−0.998793	−	0.0491274i	$-0.984356\pi$
$31$	−2.54364	+	4.40571i	−0.456851	+	0.791289i	0.541942	+	0.840416i	$0.317689\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	1.00000			0.171499
$35$	7.26496	+	0.160897i	1.22800	+	0.0271966i
$36$	1.00000			0.166667
$37$	2.01839	+	3.49595i	0.331821	+	0.574730i	0.982869	−	0.184306i	$-0.0590038\pi$
$37$	2.01839	+	3.49595i	0.331821	+	0.574730i	−0.651048	+	0.759036i	$0.725670\pi$
$38$	4.01839	−	6.96005i	0.651868	−	1.12907i
$39$	−2.74657	+	4.75720i	−0.439803	+	0.761761i
$40$	−1.37328	−	2.37860i	−0.217135	−	0.376089i
$41$	5.54364			0.865771			0.432885	−	0.901449i	$-0.357495\pi$
$41$	5.54364			0.865771			0.432885	+	0.901449i	$0.357495\pi$
$42$	−1.37328	+	2.26144i	−0.211902	+	0.348947i
$43$	−4.03677			−0.615602			−0.307801	−	0.951451i	$-0.599593\pi$
$43$	−4.03677			−0.615602			−0.307801	+	0.951451i	$0.599593\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−1.37328	+	2.37860i	−0.204717	+	0.354580i
$46$	0.645103	−	1.11735i	0.0951152	−	0.164744i
$47$	4.64510	+	8.04555i	0.677558	+	1.17356i	0.975714	+	0.219048i	$0.0702950\pi$
$47$	4.64510	+	8.04555i	0.677558	+	1.17356i	−0.298156	+	0.954517i	$0.596372\pi$
$48$	1.00000			0.144338
$49$	−3.22818	−	6.21119i	−0.461169	−	0.887312i
$50$	2.54364			0.359725
$51$	−0.500000	−	0.866025i	−0.0700140	−	0.121268i
$52$	−2.74657	+	4.75720i	−0.380880	+	0.659704i
$53$	−2.74657	+	4.75720i	−0.377270	+	0.653451i	−0.990664	−	0.136326i	$-0.956471\pi$
$53$	−2.74657	+	4.75720i	−0.377270	+	0.653451i	0.613394	+	0.789777i	$0.289804\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	2.74657			0.370347
$56$	−1.37328	+	2.26144i	−0.183513	+	0.302197i
$57$	−8.03677			−1.06450
$58$	−2.27182	−	3.93491i	−0.298304	−	0.516678i
$59$	4.76496	−	8.25314i	0.620344	−	1.07447i	−0.369077	−	0.929399i	$-0.620326\pi$
$59$	4.76496	−	8.25314i	0.620344	−	1.07447i	0.989422	−	0.145069i	$-0.0463405\pi$
$60$	−1.37328	+	2.37860i	−0.177290	+	0.307076i
$61$	0.829647	+	1.43699i	0.106225	+	0.183988i	0.914238	−	0.405177i	$-0.132790\pi$
$61$	0.829647	+	1.43699i	0.106225	+	0.183988i	−0.808013	+	0.589165i	$0.799457\pi$
$62$	5.08727			0.646084
$63$	2.64510	+	0.0585812i	0.333252	+	0.00738053i
$64$	1.00000			0.125000
$65$	−7.54364	−	13.0660i	−0.935673	−	1.62063i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	−1.77182	+	3.06888i	−0.216462	+	0.374923i	−0.953724	−	0.300684i	$-0.902785\pi$
$67$	−1.77182	+	3.06888i	−0.216462	+	0.374923i	0.737262	+	0.675607i	$0.236118\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	−1.29021			−0.155322
$70$	−3.49314	−	6.37208i	−0.417510	−	0.761610i
$71$	2.54364			0.301874			0.150937	−	0.988543i	$-0.451771\pi$
$71$	2.54364			0.301874			0.150937	+	0.988543i	$0.451771\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	4.29021	−	7.43085i	0.502131	−	0.869716i	−0.497866	−	0.867254i	$-0.665883\pi$
$73$	4.29021	−	7.43085i	0.502131	−	0.869716i	0.999997	−	0.00246191i	$-0.000783650\pi$
$74$	2.01839	−	3.49595i	0.234633	−	0.406396i
$75$	−1.27182	−	2.20285i	−0.146857	−	0.254364i
$76$	−8.03677			−0.921881
$77$	−1.27182	−	2.32002i	−0.144937	−	0.264390i
$78$	5.49314			0.621975
$79$	−6.11985	−	10.5999i	−0.688537	−	1.19258i	−0.972311	−	0.233690i	$-0.924920\pi$
$79$	−6.11985	−	10.5999i	−0.688537	−	1.19258i	0.283774	−	0.958891i	$-0.408413\pi$
$80$	−1.37328	+	2.37860i	−0.153538	+	0.265935i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.77182	−	4.80093i	−0.306096	−	0.530174i
$83$	−14.5299			−1.59486			−0.797432	−	0.603408i	$-0.793809\pi$
$83$	−14.5299			−1.59486			−0.797432	+	0.603408i	$0.793809\pi$
$84$	2.64510	+	0.0585812i	0.288604	+	0.00639173i
$85$	2.74657			0.297907
$86$	2.01839	+	3.49595i	0.217648	+	0.376978i
$87$	−2.27182	+	3.93491i	−0.243565	+	0.421866i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	3.25343	+	5.63511i	0.344863	+	0.597320i	0.985329	−	0.170666i	$-0.0545920\pi$
$89$	3.25343	+	5.63511i	0.344863	+	0.597320i	−0.640466	+	0.767987i	$0.721259\pi$
$90$	2.74657			0.289514
$91$	−7.54364	+	12.4224i	−0.790788	+	1.30222i
$92$	−1.29021			−0.134513
$93$	−2.54364	−	4.40571i	−0.263763	−	0.456851i
$94$	4.64510	−	8.04555i	0.479106	−	0.829836i
$95$	11.0368	−	19.1163i	1.13235	−	1.96129i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−0.0872743			−0.00886136			−0.00443068	−	0.999990i	$-0.501410\pi$
$97$	−0.0872743			−0.00886136			−0.00443068	+	0.999990i	$0.501410\pi$
$98$	−3.76496	+	5.90128i	−0.380318	+	0.596119i
$99$	1.00000			0.100504
$100$	−1.27182	−	2.20285i	−0.127182	−	0.220285i
$101$	−6.51152	+	11.2783i	−0.647921	+	1.12223i	0.335698	+	0.941970i	$0.391028\pi$
$101$	−6.51152	+	11.2783i	−0.647921	+	1.12223i	−0.983619	+	0.180262i	$0.942305\pi$
$102$	−0.500000	+	0.866025i	−0.0495074	+	0.0857493i
$103$	9.03677	+	15.6522i	0.890420	+	1.54225i	0.839373	+	0.543556i	$0.182922\pi$
$103$	9.03677	+	15.6522i	0.890420	+	1.54225i	0.0510469	+	0.998696i	$0.483744\pi$
$104$	5.49314			0.538646
$105$	−3.77182	+	6.21119i	−0.368092	+	0.606150i
$106$	5.49314			0.533541
$107$	−8.72132	−	15.1058i	−0.843122	−	1.46033i	−0.887243	−	0.461303i	$-0.847382\pi$
$107$	−8.72132	−	15.1058i	−0.843122	−	1.46033i	0.0441209	−	0.999026i	$-0.485951\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−0.829647	+	1.43699i	−0.0794658	+	0.137639i	−0.903020	−	0.429599i	$-0.858655\pi$
$109$	−0.829647	+	1.43699i	−0.0794658	+	0.137639i	0.823554	+	0.567238i	$0.191988\pi$
$110$	−1.37328	−	2.37860i	−0.130938	−	0.226790i
$111$	−4.03677			−0.383154
$112$	2.64510	+	0.0585812i	0.249939	+	0.00553540i
$113$	−7.08727			−0.666715			−0.333357	−	0.942801i	$-0.608182\pi$
$113$	−7.08727			−0.666715			−0.333357	+	0.942801i	$0.608182\pi$
$114$	4.01839	+	6.96005i	0.376356	+	0.651868i
$115$	1.77182	−	3.06888i	0.165223	−	0.286175i
$116$	−2.27182	+	3.93491i	−0.210933	+	0.365347i
$117$	−2.74657	−	4.75720i	−0.253920	−	0.439803i
$118$	−9.52991			−0.877299
$119$	−1.27182	−	2.32002i	−0.116587	−	0.212676i
$120$	2.74657			0.250726
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.829647	−	1.43699i	0.0751127	−	0.130099i
$123$	−2.77182	+	4.80093i	−0.249926	+	0.432885i
$124$	−2.54364	−	4.40571i	−0.228425	−	0.395644i
$125$	−6.74657			−0.603431
$126$	−1.27182	−	2.32002i	−0.113303	−	0.206684i
$127$	−6.78334			−0.601924			−0.300962	−	0.953636i	$-0.597308\pi$
$127$	−6.78334			−0.601924			−0.300962	+	0.953636i	$0.597308\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.01839	−	3.49595i	0.177709	−	0.307801i
$130$	−7.54364	+	13.0660i	−0.661621	+	1.14596i
$131$	6.94950	+	12.0369i	0.607181	+	1.05167i	0.991703	+	0.128552i	$0.0410329\pi$
$131$	6.94950	+	12.0369i	0.607181	+	1.05167i	−0.384522	+	0.923116i	$0.625634\pi$
$132$	1.00000			0.0870388
$133$	−21.2581	−	0.470804i	−1.84331	−	0.0408238i
$134$	3.54364			0.306124
$135$	−1.37328	−	2.37860i	−0.118193	−	0.204717i
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	−2.74657	+	4.75720i	−0.234655	+	0.406435i	−0.959172	−	0.282822i	$-0.908729\pi$
$137$	−2.74657	+	4.75720i	−0.234655	+	0.406435i	0.724517	+	0.689257i	$0.242063\pi$
$138$	0.645103	+	1.11735i	0.0549148	+	0.0951152i
$139$	13.6309			1.15616			0.578079	−	0.815981i	$-0.303802\pi$
$139$	13.6309			1.15616			0.578079	+	0.815981i	$0.303802\pi$
$140$	−3.77182	+	6.21119i	−0.318777	+	0.524941i
$141$	−9.29021			−0.782376
$142$	−1.27182	−	2.20285i	−0.106729	−	0.184859i
$143$	−2.74657	+	4.75720i	−0.229680	+	0.397817i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−6.23970	−	10.8075i	−0.518179	−	0.897513i
$146$	−8.58041			−0.710120
$147$	6.99314	+	0.309906i	0.576784	+	0.0255606i
$148$	−4.03677			−0.331821
$149$	−8.01839	−	13.8883i	−0.656892	−	1.13777i	−0.981416	−	0.191893i	$-0.938537\pi$
$149$	−8.01839	−	13.8883i	−0.656892	−	1.13777i	0.324524	−	0.945877i	$-0.394796\pi$
$150$	−1.27182	+	2.20285i	−0.103844	+	0.179862i
$151$	2.84803	−	4.93294i	0.231770	−	0.401437i	−0.726559	−	0.687104i	$-0.758882\pi$
$151$	2.84803	−	4.93294i	0.231770	−	0.401437i	0.958329	+	0.285667i	$0.0922151\pi$
$152$	4.01839	+	6.96005i	0.325934	+	0.564535i
$153$	1.00000			0.0808452
$154$	−1.37328	+	2.26144i	−0.110662	+	0.182232i
$155$	13.9725			1.12230
$156$	−2.74657	−	4.75720i	−0.219901	−	0.380880i
$157$	−9.05516	+	15.6840i	−0.722680	+	1.25172i	0.237241	+	0.971451i	$0.423757\pi$
$157$	−9.05516	+	15.6840i	−0.722680	+	1.25172i	−0.959922	+	0.280269i	$0.909576\pi$
$158$	−6.11985	+	10.5999i	−0.486869	+	0.843282i
$159$	−2.74657	−	4.75720i	−0.217817	−	0.377270i
$160$	2.74657			0.217135
$161$	−3.41273	−	0.0755817i	−0.268960	−	0.00595668i
$162$	1.00000			0.0785674
$163$	6.72132	+	11.6417i	0.526454	+	0.911846i	0.999525	+	0.0308210i	$0.00981219\pi$
$163$	6.72132	+	11.6417i	0.526454	+	0.911846i	−0.473071	+	0.881024i	$0.656854\pi$
$164$	−2.77182	+	4.80093i	−0.216443	+	0.374890i
$165$	−1.37328	+	2.37860i	−0.106910	+	0.185174i
$166$	7.26496	+	12.5833i	0.563870	+	0.976651i
$167$	23.5667			1.82364			0.911822	−	0.410585i	$-0.134675\pi$
$167$	23.5667			1.82364			0.911822	+	0.410585i	$0.134675\pi$
$168$	−1.27182	−	2.32002i	−0.0981229	−	0.178993i
$169$	17.1745			1.32112
$170$	−1.37328	−	2.37860i	−0.105326	−	0.182430i
$171$	4.01839	−	6.96005i	0.307294	−	0.532248i
$172$	2.01839	−	3.49595i	0.153901	−	0.266564i
$173$	5.45636	+	9.45070i	0.414840	+	0.718523i	0.995412	−	0.0956857i	$-0.0305044\pi$
$173$	5.45636	+	9.45070i	0.414840	+	0.718523i	−0.580572	+	0.814209i	$0.697171\pi$
$174$	4.54364			0.344452
$175$	−3.23504	−	5.90128i	−0.244546	−	0.446095i
$176$	1.00000			0.0753778
$177$	4.76496	+	8.25314i	0.358156	+	0.620344i
$178$	3.25343	−	5.63511i	0.243855	−	0.422369i
$179$	6.47475	−	11.2146i	0.483946	−	0.838218i	−0.515884	−	0.856658i	$-0.672537\pi$
$179$	6.47475	−	11.2146i	0.483946	−	0.838218i	0.999830	+	0.0184400i	$0.00586995\pi$
$180$	−1.37328	−	2.37860i	−0.102359	−	0.177290i
$181$	7.59414			0.564468			0.282234	−	0.959346i	$-0.408925\pi$
$181$	7.59414			0.564468			0.282234	+	0.959346i	$0.408925\pi$
$182$	14.5299	+	0.321794i	1.07703	+	0.0238530i
$183$	−1.65929			−0.122659
$184$	0.645103	+	1.11735i	0.0475576	+	0.0823722i
$185$	5.54364	−	9.60186i	0.407576	−	0.705943i
$186$	−2.54364	+	4.40571i	−0.186509	+	0.323042i
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	−9.29021			−0.677558
$189$	−1.37328	+	2.26144i	−0.0998917	+	0.164495i
$190$	−22.0735			−1.60138
$191$	−9.49314	−	16.4426i	−0.686899	−	1.18974i	−0.972836	−	0.231496i	$-0.925638\pi$
$191$	−9.49314	−	16.4426i	−0.686899	−	1.18974i	0.285937	−	0.958249i	$-0.407695\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	10.7833	−	18.6773i	0.776202	−	1.34442i	−0.157915	−	0.987453i	$-0.550477\pi$
$193$	10.7833	−	18.6773i	0.776202	−	1.34442i	0.934116	−	0.356968i	$-0.116190\pi$
$194$	0.0436371	+	0.0755817i	0.00313296	+	0.00542645i
$195$	15.0873			1.08042
$196$	6.99314	+	0.309906i	0.499510	+	0.0221362i
$197$	−3.12405			−0.222579			−0.111290	−	0.993788i	$-0.535498\pi$
$197$	−3.12405			−0.222579			−0.111290	+	0.993788i	$0.535498\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	13.0368	−	22.5804i	0.924152	−	1.60068i	0.131234	−	0.991351i	$-0.458106\pi$
$199$	13.0368	−	22.5804i	0.924152	−	1.60068i	0.792919	−	0.609327i	$-0.208560\pi$
$200$	−1.27182	+	2.20285i	−0.0899312	+	0.155765i
$201$	−1.77182	−	3.06888i	−0.124974	−	0.216462i
$202$	13.0230			0.916298
$203$	−6.23970	+	10.2751i	−0.437941	+	0.721174i
$204$	1.00000			0.0700140
$205$	−7.61299	−	13.1861i	−0.531714	−	0.920956i
$206$	9.03677	−	15.6522i	0.629622	−	1.09054i
$207$	0.645103	−	1.11735i	0.0448377	−	0.0776612i
$208$	−2.74657	−	4.75720i	−0.190440	−	0.329852i
$209$	−8.03677			−0.555915
$210$	7.26496	+	0.160897i	0.501330	+	0.0111030i
$211$	15.6677			1.07861			0.539304	−	0.842111i	$-0.318687\pi$
$211$	15.6677			1.07861			0.539304	+	0.842111i	$0.318687\pi$
$212$	−2.74657	−	4.75720i	−0.188635	−	0.326726i
$213$	−1.27182	+	2.20285i	−0.0871436	+	0.150937i
$214$	−8.72132	+	15.1058i	−0.596177	+	1.03261i
$215$	5.54364	+	9.60186i	0.378073	+	0.654841i
$216$	1.00000			0.0680414
$217$	−6.47009	−	11.8026i	−0.439218	−	0.801210i
$218$	1.65929			0.112382
$219$	4.29021	+	7.43085i	0.289905	+	0.502131i
$220$	−1.37328	+	2.37860i	−0.0925868	+	0.160365i
$221$	−2.74657	+	4.75720i	−0.184754	+	0.320004i
$222$	2.01839	+	3.49595i	0.135465	+	0.234633i
$223$	2.40586			0.161108			0.0805542	−	0.996750i	$-0.474331\pi$
$223$	2.40586			0.161108			0.0805542	+	0.996750i	$0.474331\pi$
$224$	−1.27182	−	2.32002i	−0.0849770	−	0.155013i
$225$	2.54364			0.169576
$226$	3.54364	+	6.13776i	0.235719	+	0.408278i
$227$	−1.22818	+	2.12727i	−0.0815173	+	0.141192i	−0.903902	−	0.427740i	$-0.859310\pi$
$227$	−1.22818	+	2.12727i	−0.0815173	+	0.141192i	0.822385	+	0.568932i	$0.192643\pi$
$228$	4.01839	−	6.96005i	0.266124	−	0.460941i
$229$	5.29021	+	9.16290i	0.349587	+	0.605502i	0.986176	−	0.165701i	$-0.0529887\pi$
$229$	5.29021	+	9.16290i	0.349587	+	0.605502i	−0.636589	+	0.771203i	$0.719655\pi$
$230$	−3.54364			−0.233661
$231$	2.64510	+	0.0585812i	0.174035	+	0.00385436i
$232$	4.54364			0.298304
$233$	3.53677	+	6.12587i	0.231702	+	0.401319i	0.958309	−	0.285734i	$-0.0922373\pi$
$233$	3.53677	+	6.12587i	0.231702	+	0.401319i	−0.726607	+	0.687053i	$0.758904\pi$
$234$	−2.74657	+	4.75720i	−0.179549	+	0.310988i
$235$	12.7581	−	22.0977i	0.832246	−	1.44149i
$236$	4.76496	+	8.25314i	0.310172	+	0.537234i
$237$	12.2397			0.795054
$238$	−1.37328	+	2.26144i	−0.0890168	+	0.146587i
$239$	7.66769			0.495981			0.247991	−	0.968762i	$-0.420230\pi$
$239$	7.66769			0.495981			0.247991	+	0.968762i	$0.420230\pi$
$240$	−1.37328	−	2.37860i	−0.0886451	−	0.153538i
$241$	12.5299	−	21.7024i	0.807122	−	1.39798i	−0.107726	−	0.994181i	$-0.534357\pi$
$241$	12.5299	−	21.7024i	0.807122	−	1.39798i	0.914849	−	0.403797i	$-0.132310\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.65929			−0.106225
$245$	−10.3407	+	16.2083i	−0.660643	+	1.03551i
$246$	5.54364			0.353449
$247$	22.0735	+	38.2325i	1.40451	+	2.43268i
$248$	−2.54364	+	4.40571i	−0.161521	+	0.279763i
$249$	7.26496	−	12.5833i	0.460398	−	0.797432i
$250$	3.37328	+	5.84270i	0.213345	+	0.369525i
$251$	−25.0230			−1.57944			−0.789720	−	0.613467i	$-0.789774\pi$
$251$	−25.0230			−1.57944			−0.789720	+	0.613467i	$0.789774\pi$
$252$	−1.37328	+	2.26144i	−0.0865088	+	0.142457i
$253$	−1.29021			−0.0811145
$254$	3.39167	+	5.87455i	0.212812	+	0.368602i
$255$	−1.37328	+	2.37860i	−0.0859984	+	0.148954i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.25343	+	9.09921i	0.327700	+	0.567593i	0.982055	−	0.188594i	$-0.0603931\pi$
$257$	5.25343	+	9.09921i	0.327700	+	0.567593i	−0.654355	+	0.756187i	$0.727060\pi$
$258$	−4.03677			−0.251319
$259$	−10.6777	−	0.236479i	−0.663479	−	0.0146941i
$260$	15.0873			0.935673
$261$	−2.27182	−	3.93491i	−0.140622	−	0.243565i
$262$	6.94950	−	12.0369i	0.429342	−	0.743641i
$263$	−11.8201	+	20.4730i	−0.728860	+	1.26242i	0.228506	+	0.973543i	$0.426616\pi$
$263$	−11.8201	+	20.4730i	−0.728860	+	1.26242i	−0.957366	+	0.288879i	$0.906717\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	15.0873			0.926804
$266$	10.2213	+	18.6454i	0.626709	+	1.14323i
$267$	−6.50686			−0.398214
$268$	−1.77182	−	3.06888i	−0.108231	−	0.187462i
$269$	7.57622	−	13.1224i	0.461930	−	0.800086i	−0.537127	−	0.843501i	$-0.680490\pi$
$269$	7.57622	−	13.1224i	0.461930	−	0.800086i	0.999057	+	0.0434151i	$0.0138238\pi$
$270$	−1.37328	+	2.37860i	−0.0835754	+	0.144757i
$271$	−9.49314	−	16.4426i	−0.576667	−	0.998816i	−0.995858	−	0.0909186i	$-0.971020\pi$
$271$	−9.49314	−	16.4426i	−0.576667	−	0.998816i	0.419191	−	0.907898i	$-0.362314\pi$
$272$	1.00000			0.0606339
$273$	−6.98627	−	12.7442i	−0.422828	−	0.771312i
$274$	5.49314			0.331853
$275$	−1.27182	−	2.20285i	−0.0766935	−	0.132837i
$276$	0.645103	−	1.11735i	0.0388306	−	0.0672566i
$277$	−12.2397	+	21.1998i	−0.735413	+	1.27377i	0.219130	+	0.975696i	$0.429678\pi$
$277$	−12.2397	+	21.1998i	−0.735413	+	1.27377i	−0.954542	+	0.298076i	$0.903655\pi$
$278$	−6.81546	−	11.8047i	−0.408764	−	0.708000i
$279$	5.08727			0.304567
$280$	7.26496	+	0.160897i	0.434164	+	0.00961545i
$281$	−12.0873			−0.721066			−0.360533	−	0.932746i	$-0.617405\pi$
$281$	−12.0873			−0.721066			−0.360533	+	0.932746i	$0.617405\pi$
$282$	4.64510	+	8.04555i	0.276612	+	0.479106i
$283$	−2.34071	+	4.05422i	−0.139141	+	0.240998i	−0.927172	−	0.374637i	$-0.877767\pi$
$283$	−2.34071	+	4.05422i	−0.139141	+	0.240998i	0.788031	+	0.615636i	$0.211101\pi$
$284$	−1.27182	+	2.20285i	−0.0754685	+	0.130715i
$285$	11.0368	+	19.1163i	0.653762	+	1.13235i
$286$	5.49314			0.324816
$287$	−7.61299	+	12.5366i	−0.449381	+	0.740011i
$288$	1.00000			0.0589256
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	−6.23970	+	10.8075i	−0.366408	+	0.634637i
$291$	0.0436371	−	0.0755817i	0.00255805	−	0.00443068i
$292$	4.29021	+	7.43085i	0.251065	+	0.434858i
$293$	−11.6309			−0.679485			−0.339743	−	0.940518i	$-0.610340\pi$
$293$	−11.6309			−0.679485			−0.339743	+	0.940518i	$0.610340\pi$
$294$	−3.22818	−	6.21119i	−0.188271	−	0.362244i
$295$	−26.1745			−1.52394
$296$	2.01839	+	3.49595i	0.117316	+	0.203198i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−8.01839	+	13.8883i	−0.464493	+	0.804525i
$299$	3.54364	+	6.13776i	0.204934	+	0.354956i
$300$	2.54364			0.146857
$301$	5.54364	−	9.12890i	0.319530	−	0.526181i
$302$	−5.69607			−0.327772
$303$	−6.51152	−	11.2783i	−0.374077	−	0.647921i
$304$	4.01839	−	6.96005i	0.230470	−	0.399186i
$305$	2.27868	−	3.94679i	0.130477	−	0.225993i
$306$	−0.500000	−	0.866025i	−0.0285831	−	0.0495074i
$307$	−14.0735			−0.803220			−0.401610	−	0.915811i	$-0.631549\pi$
$307$	−14.0735			−0.803220			−0.401610	+	0.915811i	$0.631549\pi$
$308$	2.64510	+	0.0585812i	0.150719	+	0.00333797i
$309$	−18.0735			−1.02817
$310$	−6.98627	−	12.1006i	−0.396794	−	0.687267i
$311$	−6.13824	+	10.6317i	−0.348068	+	0.602871i	−0.985906	−	0.167299i	$-0.946495\pi$
$311$	−6.13824	+	10.6317i	−0.348068	+	0.602871i	0.637839	+	0.770170i	$0.279829\pi$
$312$	−2.74657	+	4.75720i	−0.155494	+	0.269323i
$313$	−11.7282	−	20.3138i	−0.662916	−	1.14820i	−0.979846	−	0.199755i	$-0.935985\pi$
$313$	−11.7282	−	20.3138i	−0.662916	−	1.14820i	0.316930	−	0.948449i	$-0.397348\pi$
$314$	18.1103			1.02202
$315$	−3.49314	−	6.37208i	−0.196816	−	0.359026i
$316$	12.2397			0.688537
$317$	0.286010	+	0.495384i	0.0160639	+	0.0278235i	0.873946	−	0.486024i	$-0.161553\pi$
$317$	0.286010	+	0.495384i	0.0160639	+	0.0278235i	−0.857882	+	0.513847i	$0.828220\pi$
$318$	−2.74657	+	4.75720i	−0.154020	+	0.266770i
$319$	−2.27182	+	3.93491i	−0.127197	+	0.220312i
$320$	−1.37328	−	2.37860i	−0.0767689	−	0.132968i
$321$	17.4426			0.973553
$322$	1.64091	+	2.99330i	0.0914442	+	0.166810i
$323$	−8.03677			−0.447178
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−6.98627	+	12.1006i	−0.387529	+	0.671219i
$326$	6.72132	−	11.6417i	0.372259	−	0.644772i
$327$	−0.829647	−	1.43699i	−0.0458796	−	0.0794658i
$328$	5.54364			0.306096
$329$	−24.5735	−	0.544231i	−1.35478	−	0.0300044i
$330$	2.74657			0.151194
$331$	−3.85909	−	6.68414i	−0.212115	−	0.367394i	0.740261	−	0.672319i	$-0.234702\pi$
$331$	−3.85909	−	6.68414i	−0.212115	−	0.367394i	−0.952376	+	0.304925i	$0.901368\pi$
$332$	7.26496	−	12.5833i	0.398716	−	0.690597i
$333$	2.01839	−	3.49595i	0.110607	−	0.191577i
$334$	−11.7833	−	20.4093i	−0.644756	−	1.11675i
$335$	9.73284			0.531762
$336$	−1.37328	+	2.26144i	−0.0749188	+	0.123371i
$337$	28.5530			1.55538			0.777689	−	0.628649i	$-0.216392\pi$
$337$	28.5530			1.55538			0.777689	+	0.628649i	$0.216392\pi$
$338$	−8.58727	−	14.8736i	−0.467086	−	0.809017i
$339$	3.54364	−	6.13776i	0.192464	−	0.333357i
$340$	−1.37328	+	2.37860i	−0.0744768	+	0.128998i
$341$	−2.54364	−	4.40571i	−0.137746	−	0.238583i
$342$	−8.03677			−0.434579
$343$	18.4794	+	1.22940i	0.997794	+	0.0663814i
$344$	−4.03677			−0.217648
$345$	1.77182	+	3.06888i	0.0953915	+	0.165223i
$346$	5.45636	−	9.45070i	0.293336	−	0.508073i
$347$	11.7213	−	20.3019i	0.629233	−	1.08986i	−0.358473	−	0.933540i	$-0.616702\pi$
$347$	11.7213	−	20.3019i	0.629233	−	1.08986i	0.987706	−	0.156324i	$-0.0499643\pi$
$348$	−2.27182	−	3.93491i	−0.121782	−	0.210933i
$349$	25.7328			1.37745			0.688724	−	0.725024i	$-0.258171\pi$
$349$	25.7328			1.37745			0.688724	+	0.725024i	$0.258171\pi$
$350$	−3.49314	+	5.75227i	−0.186716	+	0.307472i
$351$	5.49314			0.293202
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	9.20293	−	15.9399i	0.489823	−	0.848398i	−0.510109	−	0.860110i	$-0.670395\pi$
$353$	9.20293	−	15.9399i	0.489823	−	0.848398i	0.999931	+	0.0117122i	$0.00372821\pi$
$354$	4.76496	−	8.25314i	0.253255	−	0.438650i
$355$	−3.49314	−	6.05029i	−0.185396	−	0.321116i
$356$	−6.50686			−0.344863
$357$	2.64510	+	0.0585812i	0.139994	+	0.00310044i
$358$	−12.9495			−0.684402
$359$	15.9863	+	27.6890i	0.843723	+	1.46137i	0.886725	+	0.462297i	$0.152974\pi$
$359$	15.9863	+	27.6890i	0.843723	+	1.46137i	−0.0430022	+	0.999075i	$0.513692\pi$
$360$	−1.37328	+	2.37860i	−0.0723784	+	0.125363i
$361$	−22.7949	+	39.4819i	−1.19973	+	2.07799i
$362$	−3.79707	−	6.57672i	−0.199570	−	0.345665i
$363$	1.00000			0.0524864
$364$	−6.98627	−	12.7442i	−0.366180	−	0.667976i
$365$	−23.5667			−1.23354
$366$	0.829647	+	1.43699i	0.0433663	+	0.0751127i
$367$	−18.2397	+	31.5921i	−0.952105	+	1.64909i	−0.211246	+	0.977433i	$0.567752\pi$
$367$	−18.2397	+	31.5921i	−0.952105	+	1.64909i	−0.740859	+	0.671661i	$0.765581\pi$
$368$	0.645103	−	1.11735i	0.0336283	−	0.0582459i
$369$	−2.77182	−	4.80093i	−0.144295	−	0.249926i
$370$	−11.0873			−0.576400
$371$	−6.98627	−	12.7442i	−0.362709	−	0.661644i
$372$	5.08727			0.263763
$373$	10.1566	+	17.5918i	0.525890	+	0.910868i	0.999545	+	0.0301580i	$0.00960104\pi$
$373$	10.1566	+	17.5918i	0.525890	+	0.910868i	−0.473655	+	0.880710i	$0.657066\pi$
$374$	−0.500000	+	0.866025i	−0.0258544	+	0.0447811i
$375$	3.37328	−	5.84270i	0.174196	−	0.301716i
$376$	4.64510	+	8.04555i	0.239553	+	0.414918i
$377$	24.9588			1.28544
$378$	2.64510	+	0.0585812i	0.136049	+	0.00301309i
$379$	9.44264			0.485036			0.242518	−	0.970147i	$-0.422027\pi$
$379$	9.44264			0.485036			0.242518	+	0.970147i	$0.422027\pi$
$380$	11.0368	+	19.1163i	0.566175	+	0.980643i
$381$	3.39167	−	5.87455i	0.173761	−	0.300962i
$382$	−9.49314	+	16.4426i	−0.485711	+	0.841276i
$383$	−11.8522	−	20.5287i	−0.605621	−	1.04897i	−0.991953	−	0.126606i	$-0.959592\pi$
$383$	−11.8522	−	20.5287i	−0.605621	−	1.04897i	0.386332	−	0.922360i	$-0.373742\pi$
$384$	1.00000			0.0510310
$385$	−3.77182	+	6.21119i	−0.192230	+	0.316551i
$386$	−21.5667			−1.09772
$387$	2.01839	+	3.49595i	0.102600	+	0.177709i
$388$	0.0436371	−	0.0755817i	0.00221534	−	0.00383708i
$389$	0.626716	−	1.08550i	0.0317758	−	0.0550372i	−0.849700	−	0.527266i	$-0.823217\pi$
$389$	0.626716	−	1.08550i	0.0317758	−	0.0550372i	0.881476	+	0.472229i	$0.156550\pi$
$390$	−7.54364	−	13.0660i	−0.381987	−	0.661621i
$391$	−1.29021			−0.0652485
$392$	−3.22818	−	6.21119i	−0.163048	−	0.313712i
$393$	−13.8990			−0.701112
$394$	1.56202	+	2.70550i	0.0786936	+	0.136301i
$395$	−16.8086	+	29.1133i	−0.845732	+	1.46485i
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	−14.3086	−	24.7832i	−0.718128	−	1.24383i	−0.961741	−	0.273961i	$-0.911666\pi$
$397$	−14.3086	−	24.7832i	−0.718128	−	1.24383i	0.243613	−	0.969872i	$-0.421667\pi$
$398$	−26.0735			−1.30695
$399$	11.0368	−	18.1746i	0.552530	−	0.909870i
$400$	2.54364			0.127182
$401$	−0.202931	−	0.351487i	−0.0101339	−	0.0175524i	0.860914	−	0.508751i	$-0.169892\pi$
$401$	−0.202931	−	0.351487i	−0.0101339	−	0.0175524i	−0.871048	+	0.491198i	$0.836559\pi$
$402$	−1.77182	+	3.06888i	−0.0883703	+	0.153062i
$403$	−13.9725	+	24.2012i	−0.696022	+	1.20555i
$404$	−6.51152	−	11.2783i	−0.323960	−	0.561116i
$405$	2.74657			0.136478
$406$	12.0184	+	0.266172i	0.596463	+	0.0132099i
$407$	−4.03677			−0.200095
$408$	−0.500000	−	0.866025i	−0.0247537	−	0.0428746i
$409$	16.3775	−	28.3666i	0.809814	−	1.40264i	−0.103178	−	0.994663i	$-0.532901\pi$
$409$	16.3775	−	28.3666i	0.809814	−	1.40264i	0.912992	−	0.407977i	$-0.133765\pi$
$410$	−7.61299	+	13.1861i	−0.375979	+	0.651214i
$411$	−2.74657	−	4.75720i	−0.135478	−	0.234655i
$412$	−18.0735			−0.890420
$413$	12.1203	+	22.1096i	0.596402	+	1.08794i
$414$	−1.29021			−0.0634101
$415$	19.9537	+	34.5608i	0.979488	+	1.69652i
$416$	−2.74657	+	4.75720i	−0.134662	+	0.233241i
$417$	−6.81546	+	11.8047i	−0.333754	+	0.578079i
$418$	4.01839	+	6.96005i	0.196546	+	0.340427i
$419$	−15.9358			−0.778513			−0.389257	−	0.921129i	$-0.627268\pi$
$419$	−15.9358			−0.778513			−0.389257	+	0.921129i	$0.627268\pi$
$420$	−3.49314	−	6.37208i	−0.170448	−	0.310926i
$421$	−27.1240			−1.32195			−0.660973	−	0.750410i	$-0.729856\pi$
$421$	−27.1240			−1.32195			−0.660973	+	0.750410i	$0.729856\pi$
$422$	−7.83384	−	13.5686i	−0.381345	−	0.660510i
$423$	4.64510	−	8.04555i	0.225853	−	0.391188i
$424$	−2.74657	+	4.75720i	−0.133385	+	0.231030i
$425$	−1.27182	−	2.20285i	−0.0616923	−	0.106854i
$426$	2.54364			0.123240
$427$	−4.38900	−	0.0972034i	−0.212399	−	0.00470400i
$428$	17.4426			0.843122
$429$	−2.74657	−	4.75720i	−0.132606	−	0.229680i
$430$	5.54364	−	9.60186i	0.267338	−	0.463043i
$431$	20.3133	−	35.1836i	0.978455	−	1.69473i	0.310427	−	0.950597i	$-0.399528\pi$
$431$	20.3133	−	35.1836i	0.978455	−	1.69473i	0.668028	−	0.744137i	$-0.267139\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	1.10100			0.0529107			0.0264554	−	0.999650i	$-0.491578\pi$
$433$	1.10100			0.0529107			0.0264554	+	0.999650i	$0.491578\pi$
$434$	−6.98627	+	11.5045i	−0.335352	+	0.552236i
$435$	12.4794			0.598342
$436$	−0.829647	−	1.43699i	−0.0397329	−	0.0688194i
$437$	−5.18454	+	8.97989i	−0.248010	+	0.429567i
$438$	4.29021	−	7.43085i	0.204994	−	0.355060i
$439$	−11.4284	−	19.7946i	−0.545450	−	0.944747i	−0.998578	−	0.0533018i	$-0.983025\pi$
$439$	−11.4284	−	19.7946i	−0.545450	−	0.944747i	0.453129	−	0.891445i	$-0.350308\pi$
$440$	2.74657			0.130938
$441$	−3.76496	+	5.90128i	−0.179284	+	0.281013i
$442$	5.49314			0.261282
$443$	4.77868	+	8.27692i	0.227042	+	0.393248i	0.956930	−	0.290318i	$-0.0937612\pi$
$443$	4.77868	+	8.27692i	0.227042	+	0.393248i	−0.729888	+	0.683567i	$0.760428\pi$
$444$	2.01839	−	3.49595i	0.0957884	−	0.165910i
$445$	8.93577	−	15.4772i	0.423596	−	0.733690i
$446$	−1.20293	−	2.08354i	−0.0569604	−	0.0986584i
$447$	16.0368			0.758513
$448$	−1.37328	+	2.26144i	−0.0648816	+	0.106843i
$449$	0.681412			0.0321578			0.0160789	−	0.999871i	$-0.494882\pi$
$449$	0.681412			0.0321578			0.0160789	+	0.999871i	$0.494882\pi$
$450$	−1.27182	−	2.20285i	−0.0599541	−	0.103844i
$451$	−2.77182	+	4.80093i	−0.130520	+	0.226067i
$452$	3.54364	−	6.13776i	0.166679	−	0.288696i
$453$	2.84803	+	4.93294i	0.133812	+	0.231770i
$454$	2.45636			0.115283
$455$	39.9074	+	0.883830i	1.87089	+	0.0414346i
$456$	−8.03677			−0.376356
$457$	−9.07355	−	15.7158i	−0.424443	−	0.735156i	0.571926	−	0.820306i	$-0.306197\pi$
$457$	−9.07355	−	15.7158i	−0.424443	−	0.735156i	−0.996368	+	0.0851493i	$0.972863\pi$
$458$	5.29021	−	9.16290i	0.247195	−	0.428154i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$	1.77182	+	3.06888i	0.0826115	+	0.143087i
$461$	−41.7045			−1.94237			−0.971185	−	0.238326i	$-0.923401\pi$
$461$	−41.7045			−1.94237			−0.971185	+	0.238326i	$0.923401\pi$
$462$	−1.27182	−	2.32002i	−0.0591704	−	0.107937i
$463$	−28.5804			−1.32824			−0.664122	−	0.747624i	$-0.731195\pi$
$463$	−28.5804			−1.32824			−0.664122	+	0.747624i	$0.731195\pi$
$464$	−2.27182	−	3.93491i	−0.105467	−	0.182673i
$465$	−6.98627	+	12.1006i	−0.323981	+	0.561151i
$466$	3.53677	−	6.12587i	0.163838	−	0.283776i
$467$	−2.69141	−	4.66166i	−0.124544	−	0.215716i	0.797011	−	0.603965i	$-0.206413\pi$
$467$	−2.69141	−	4.66166i	−0.124544	−	0.215716i	−0.921554	+	0.388249i	$0.873080\pi$
$468$	5.49314			0.253920
$469$	−4.50686	−	8.22130i	−0.208108	−	0.379624i
$470$	−25.5162			−1.17697
$471$	−9.05516	−	15.6840i	−0.417240	−	0.722680i
$472$	4.76496	−	8.25314i	0.219325	−	0.379882i
$473$	2.01839	−	3.49595i	0.0928055	−	0.160744i
$474$	−6.11985	−	10.5999i	−0.281094	−	0.486869i
$475$	−20.4426			−0.937972
$476$	2.64510	+	0.0585812i	0.121238	+	0.00268506i
$477$	5.49314			0.251513
$478$	−3.83384	−	6.64041i	−0.175356	−	0.303725i
$479$	−7.23970	+	12.5395i	−0.330791	+	0.572946i	−0.982667	−	0.185379i	$-0.940649\pi$
$479$	−7.23970	+	12.5395i	−0.330791	+	0.572946i	0.651877	+	0.758325i	$0.273982\pi$
$480$	−1.37328	+	2.37860i	−0.0626816	+	0.108568i
$481$	11.0873	+	19.2037i	0.505536	+	0.875614i
$482$	−25.0598			−1.14144
$483$	1.77182	−	2.91772i	0.0806205	−	0.132761i
$484$	1.00000			0.0454545
$485$	0.119852	+	0.207590i	0.00544222	+	0.00942619i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	4.21666	−	7.30347i	0.191075	−	0.330952i	−0.754532	−	0.656264i	$-0.772136\pi$
$487$	4.21666	−	7.30347i	0.191075	−	0.330952i	0.945607	+	0.325312i	$0.105469\pi$
$488$	0.829647	+	1.43699i	0.0375564	+	0.0650495i
$489$	−13.4426			−0.607897
$490$	19.2071	+	0.851179i	0.867690	+	0.0384524i
$491$	−38.6770			−1.74547			−0.872734	−	0.488195i	$-0.837655\pi$
$491$	−38.6770			−1.74547			−0.872734	+	0.488195i	$0.837655\pi$
$492$	−2.77182	−	4.80093i	−0.124963	−	0.216443i
$493$	−2.27182	+	3.93491i	−0.102318	+	0.177219i
$494$	22.0735	−	38.2325i	0.993136	−	1.72016i
$495$	−1.37328	−	2.37860i	−0.0617245	−	0.106910i
$496$	5.08727			0.228425
$497$	−3.49314	+	5.75227i	−0.156689	+	0.258025i
$498$	−14.5299			−0.651101
$499$	−19.0230	−	32.9489i	−0.851589	−	1.47499i	−0.879774	−	0.475392i	$-0.842306\pi$
$499$	−19.0230	−	32.9489i	−0.851589	−	1.47499i	0.0281856	−	0.999603i	$-0.491027\pi$
$500$	3.37328	−	5.84270i	0.150858	−	0.261293i
$501$	−11.7833	+	20.4093i	−0.526441	+	0.911822i
$502$	12.5115	+	21.6706i	0.558417	+	0.967206i
$503$	21.5667			0.961611			0.480805	−	0.876827i	$-0.340344\pi$
$503$	21.5667			0.961611			0.480805	+	0.876827i	$0.340344\pi$
$504$	2.64510	+	0.0585812i	0.117822	+	0.00260941i
$505$	35.7687			1.59169
$506$	0.645103	+	1.11735i	0.0286783	+	0.0496723i
$507$	−8.58727	+	14.8736i	−0.381374	+	0.660560i
$508$	3.39167	−	5.87455i	0.150481	−	0.260641i
$509$	13.3270	+	23.0830i	0.590708	+	1.02314i	0.994137	+	0.108125i	$0.0344848\pi$
$509$	13.3270	+	23.0830i	0.590708	+	1.02314i	−0.403429	+	0.915011i	$0.632182\pi$
$510$	2.74657			0.121620
$511$	10.9127	+	19.9067i	0.482751	+	0.880620i
$512$	1.00000			0.0441942
$513$	4.01839	+	6.96005i	0.177416	+	0.307294i
$514$	5.25343	−	9.09921i	0.231719	−	0.401349i
$515$	24.8201	−	42.9897i	1.09370	−	1.89435i
$516$	2.01839	+	3.49595i	0.0888545	+	0.153901i
$517$	−9.29021			−0.408583
$518$	5.13404	+	9.36538i	0.225577	+	0.411491i
$519$	−10.9127			−0.479015
$520$	−7.54364	−	13.0660i	−0.330810	−	0.572980i
$521$	11.9863	−	20.7608i	0.525128	−	0.909549i	−0.474444	−	0.880286i	$-0.657351\pi$
$521$	11.9863	−	20.7608i	0.525128	−	0.909549i	0.999572	−	0.0292627i	$-0.00931595\pi$
$522$	−2.27182	+	3.93491i	−0.0994348	+	0.172226i
$523$	−10.3407	−	17.9106i	−0.452168	−	0.783177i	0.546353	−	0.837555i	$-0.316016\pi$
$523$	−10.3407	−	17.9106i	−0.452168	−	0.783177i	−0.998520	+	0.0543780i	$0.982682\pi$
$524$	−13.8990			−0.607181
$525$	6.72818	+	0.149009i	0.293642	+	0.00650330i
$526$	23.6402			1.03076
$527$	−2.54364	−	4.40571i	−0.110803	−	0.191916i
$528$	−0.500000	+	0.866025i	−0.0217597	+	0.0376889i
$529$	10.6677	−	18.4770i	0.463812	−	0.803347i
$530$	−7.54364	−	13.0660i	−0.327675	−	0.567549i
$531$	−9.52991			−0.413563
$532$	11.0368	−	18.1746i	0.478505	−	0.787971i
$533$	30.4520			1.31902
$534$	3.25343	+	5.63511i	0.140790	+	0.243855i
$535$	−23.9537	+	41.4890i	−1.03561	+	1.79373i
$536$	−1.77182	+	3.06888i	−0.0765309	+	0.132555i
$537$	6.47475	+	11.2146i	0.279406	+	0.483946i
$538$	−15.1524			−0.653268
$539$	6.99314	+	0.309906i	0.301216	+	0.0133486i
$540$	2.74657			0.118193
$541$	−17.9537	−	31.0967i	−0.771890	−	1.33695i	−0.936526	−	0.350598i	$-0.885978\pi$
$541$	−17.9537	−	31.0967i	−0.771890	−	1.33695i	0.164637	−	0.986354i	$-0.447355\pi$
$542$	−9.49314	+	16.4426i	−0.407765	+	0.706270i
$543$	−3.79707	+	6.57672i	−0.162948	+	0.282234i
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	4.55736			0.195216
$546$	−7.54364	+	12.4224i	−0.322838	+	0.531629i
$547$	−5.12405			−0.219088			−0.109544	−	0.993982i	$-0.534939\pi$
$547$	−5.12405			−0.219088			−0.109544	+	0.993982i	$0.534939\pi$
$548$	−2.74657	−	4.75720i	−0.117328	−	0.203217i
$549$	0.829647	−	1.43699i	0.0354085	−	0.0613293i
$550$	−1.27182	+	2.20285i	−0.0542305	+	0.0939300i
$551$	18.2581	+	31.6239i	0.777821	+	1.34723i
$552$	−1.29021			−0.0549148
$553$	32.3753	+	0.717016i	1.37674	+	0.0304906i
$554$	24.4794			1.04003
$555$	5.54364	+	9.60186i	0.235314	+	0.407576i
$556$	−6.81546	+	11.8047i	−0.289040	+	0.500631i
$557$	6.43798	−	11.1509i	0.272786	−	0.472479i	−0.696788	−	0.717277i	$-0.745388\pi$
$557$	6.43798	−	11.1509i	0.272786	−	0.472479i	0.969574	+	0.244798i	$0.0787216\pi$
$558$	−2.54364	−	4.40571i	−0.107681	−	0.186509i
$559$	−22.1745			−0.937883
$560$	−3.49314	−	6.37208i	−0.147612	−	0.269270i
$561$	1.00000			0.0422200
$562$	6.04364	+	10.4679i	0.254935	+	0.441561i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	4.64510	−	8.04555i	0.195594	−	0.338779i
$565$	9.73284	+	16.8578i	0.409464	+	0.709212i
$566$	4.68141			0.196774
$567$	−1.27182	−	2.32002i	−0.0534114	−	0.0974315i
$568$	2.54364			0.106729
$569$	−10.6777	−	18.4943i	−0.447632	−	0.775321i	0.550600	−	0.834769i	$-0.314399\pi$
$569$	−10.6777	−	18.4943i	−0.447632	−	0.775321i	−0.998231	+	0.0594486i	$0.981066\pi$
$570$	11.0368	−	19.1163i	0.462280	−	0.800692i
$571$	−3.72818	+	6.45740i	−0.156020	+	0.270234i	−0.933430	−	0.358760i	$-0.883200\pi$
$571$	−3.72818	+	6.45740i	−0.156020	+	0.270234i	0.777410	+	0.628994i	$0.216533\pi$
$572$	−2.74657	−	4.75720i	−0.114840	−	0.198908i
$573$	18.9863			0.793163
$574$	14.6635	+	0.324753i	0.612042	+	0.0135549i
$575$	−3.28181			−0.136861
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−2.82232	+	4.88840i	−0.117495	+	0.203507i	−0.918774	−	0.394783i	$-0.870820\pi$
$577$	−2.82232	+	4.88840i	−0.117495	+	0.203507i	0.801280	+	0.598290i	$0.204153\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	10.7833	+	18.6773i	0.448140	+	0.776202i
$580$	12.4794			0.518179
$581$	19.9537	−	32.8585i	0.827819	−	1.36320i
$582$	−0.0872743			−0.00361763
$583$	−2.74657	−	4.75720i	−0.113751	−	0.197023i
$584$	4.29021	−	7.43085i	0.177530	−	0.307491i
$585$	−7.54364	+	13.0660i	−0.311891	+	0.540211i
$586$	5.81546	+	10.0727i	0.240234	+	0.416098i
$587$	−34.4059			−1.42008			−0.710041	−	0.704160i	$-0.751324\pi$
$587$	−34.4059			−1.42008			−0.710041	+	0.704160i	$0.751324\pi$
$588$	−3.76496	+	5.90128i	−0.155264	+	0.243365i
$589$	−40.8853			−1.68465
$590$	13.0873	+	22.6678i	0.538795	+	0.933220i
$591$	1.56202	−	2.70550i	0.0642531	−	0.111290i
$592$	2.01839	−	3.49595i	0.0829552	−	0.143683i
$593$	9.35909	+	16.2104i	0.384332	+	0.665682i	0.991676	−	0.128756i	$-0.0410985\pi$
$593$	9.35909	+	16.2104i	0.384332	+	0.665682i	−0.607344	+	0.794439i	$0.707765\pi$
$594$	1.00000			0.0410305
$595$	−3.77182	+	6.21119i	−0.154629	+	0.254634i
$596$	16.0368			0.656892
$597$	13.0368	+	22.5804i	0.533560	+	0.924152i
$598$	3.54364	−	6.13776i	0.144910	−	0.250992i
$599$	−5.20713	+	9.01901i	−0.212757	+	0.368507i	−0.952577	−	0.304299i	$-0.901578\pi$
$599$	−5.20713	+	9.01901i	−0.212757	+	0.368507i	0.739819	+	0.672806i	$0.234911\pi$
$600$	−1.27182	−	2.20285i	−0.0519218	−	0.0899312i
$601$	25.0873			1.02333			0.511666	−	0.859185i	$-0.329029\pi$
$601$	25.0873			1.02333			0.511666	+	0.859185i	$0.329029\pi$
$602$	−10.6777	−	0.236479i	−0.435190	−	0.00963816i
$603$	3.54364			0.144308
$604$	2.84803	+	4.93294i	0.115885	+	0.200718i
$605$	−1.37328	+	2.37860i	−0.0558319	+	0.0967038i
$606$	−6.51152	+	11.2783i	−0.264513	+	0.458149i
$607$	−15.9537	−	27.6326i	−0.647541	−	1.12157i	−0.983708	−	0.179771i	$-0.942464\pi$
$607$	−15.9537	−	27.6326i	−0.647541	−	1.12157i	0.336168	−	0.941802i	$-0.390869\pi$
$608$	−8.03677			−0.325934
$609$	−5.77868	−	10.5413i	−0.234164	−	0.427156i
$610$	−4.55736			−0.184522
$611$	25.5162	+	44.1953i	1.03227	+	1.78795i
$612$	−0.500000	+	0.866025i	−0.0202113	+	0.0350070i
$613$	−1.71399	+	2.96872i	−0.0692274	+	0.119905i	−0.898561	−	0.438848i	$-0.855387\pi$
$613$	−1.71399	+	2.96872i	−0.0692274	+	0.119905i	0.829334	+	0.558753i	$0.188720\pi$
$614$	7.03677	+	12.1880i	0.283981	+	0.491870i
$615$	15.2260			0.613971
$616$	−1.27182	−	2.32002i	−0.0512430	−	0.0934761i
$617$	12.7550			0.513495			0.256748	−	0.966478i	$-0.417349\pi$
$617$	12.7550			0.513495			0.256748	+	0.966478i	$0.417349\pi$
$618$	9.03677	+	15.6522i	0.363512	+	0.629622i
$619$	10.7949	−	18.6973i	0.433882	−	0.751506i	−0.563321	−	0.826238i	$-0.690477\pi$
$619$	10.7949	−	18.6973i	0.433882	−	0.751506i	0.997204	+	0.0747317i	$0.0238100\pi$
$620$	−6.98627	+	12.1006i	−0.280575	+	0.485971i
$621$	0.645103	+	1.11735i	0.0258871	+	0.0448377i
$622$	12.2765			0.492242
$623$	−17.2113	−	0.381180i	−0.689557	−	0.0152716i
$624$	5.49314			0.219901
$625$	15.6240	+	27.0616i	0.624962	+	1.08247i
$626$	−11.7282	+	20.3138i	−0.468752	+	0.811903i
$627$	4.01839	−	6.96005i	0.160479	−	0.277958i
$628$	−9.05516	−	15.6840i	−0.361340	−	0.625860i
$629$	−4.03677			−0.160957
$630$	−3.77182	+	6.21119i	−0.150273	+	0.247460i
$631$	4.23131			0.168446			0.0842230	−	0.996447i	$-0.473159\pi$
$631$	4.23131			0.168446			0.0842230	+	0.996447i	$0.473159\pi$
$632$	−6.11985	−	10.5999i	−0.243435	−	0.421641i
$633$	−7.83384	+	13.5686i	−0.311367	+	0.539304i
$634$	0.286010	−	0.495384i	0.0113589	−	0.0196742i
$635$	9.31546	+	16.1348i	0.369673	+	0.640292i
$636$	5.49314			0.217817
$637$	−17.7328	−	34.1189i	−0.702601	−	1.35184i
$638$	4.54364			0.179884
$639$	−1.27182	−	2.20285i	−0.0503124	−	0.0871436i
$640$	−1.37328	+	2.37860i	−0.0542838	+	0.0940223i
$641$	−2.03677	+	3.52780i	−0.0804477	+	0.139340i	−0.903442	−	0.428710i	$-0.858968\pi$
$641$	−2.03677	+	3.52780i	−0.0804477	+	0.139340i	0.822995	+	0.568049i	$0.192302\pi$
$642$	−8.72132	−	15.1058i	−0.344203	−	0.596177i
$643$	−19.2618			−0.759612			−0.379806	−	0.925066i	$-0.624009\pi$
$643$	−19.2618			−0.759612			−0.379806	+	0.925066i	$0.624009\pi$
$644$	1.77182	−	2.91772i	0.0698194	−	0.114974i
$645$	−11.0873			−0.436561
$646$	4.01839	+	6.96005i	0.158101	+	0.273840i
$647$	9.44683	−	16.3624i	0.371393	−	0.643272i	−0.618387	−	0.785874i	$-0.712214\pi$
$647$	9.44683	−	16.3624i	0.371393	−	0.643272i	0.989780	+	0.142602i	$0.0455468\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	4.76496	+	8.25314i	0.187041	+	0.323964i
$650$	13.9725			0.548048
$651$	13.4564	+	0.298018i	0.527396	+	0.0116803i
$652$	−13.4426			−0.526454
$653$	4.46056	+	7.72591i	0.174555	+	0.302338i	0.940007	−	0.341155i	$-0.110818\pi$
$653$	4.46056	+	7.72591i	0.174555	+	0.302338i	−0.765452	+	0.643493i	$0.777485\pi$
$654$	−0.829647	+	1.43699i	−0.0324418	+	0.0561908i
$655$	19.0873	−	33.0601i	0.745802	−	1.29177i
$656$	−2.77182	−	4.80093i	−0.108221	−	0.187445i
$657$	−8.58041			−0.334754
$658$	11.8155	+	21.5534i	0.460614	+	0.840240i
$659$	45.4426			1.77019			0.885097	−	0.465407i	$-0.154092\pi$
$659$	45.4426			1.77019			0.885097	+	0.465407i	$0.154092\pi$
$660$	−1.37328	−	2.37860i	−0.0534550	−	0.0925868i
$661$	14.5115	−	25.1347i	0.564433	−	0.977626i	−0.432669	−	0.901553i	$-0.642428\pi$
$661$	14.5115	−	25.1347i	0.564433	−	0.977626i	0.997102	−	0.0760737i	$-0.0242384\pi$
$662$	−3.85909	+	6.68414i	−0.149988	+	0.259787i
$663$	−2.74657	−	4.75720i	−0.106668	−	0.184754i
$664$	−14.5299			−0.563870
$665$	28.0735	+	51.2110i	1.08865	+	1.98588i
$666$	−4.03677			−0.156422
$667$	2.93111	+	5.07684i	0.113493	+	0.196576i
$668$	−11.7833	+	20.4093i	−0.455911	+	0.789661i
$669$	−1.20293	+	2.08354i	−0.0465080	+	0.0805542i
$670$	−4.86642	−	8.42889i	−0.188006	−	0.325636i
$671$	−1.65929			−0.0640563
$672$	2.64510	+	0.0585812i	0.102037	+	0.00225982i
$673$	−16.2481			−0.626318			−0.313159	−	0.949701i	$-0.601387\pi$
$673$	−16.2481			−0.626318			−0.313159	+	0.949701i	$0.601387\pi$
$674$	−14.2765	−	24.7276i	−0.549909	−	0.952471i
$675$	−1.27182	+	2.20285i	−0.0489523	+	0.0847879i
$676$	−8.58727	+	14.8736i	−0.330280	+	0.572061i
$677$	1.94484	+	3.36856i	0.0747463	+	0.129464i	0.900976	−	0.433869i	$-0.142852\pi$
$677$	1.94484	+	3.36856i	0.0747463	+	0.129464i	−0.826230	+	0.563333i	$0.809519\pi$
$678$	−7.08727			−0.272185
$679$	0.119852	−	0.197365i	0.00459951	−	0.00757418i
$680$	2.74657			0.105326
$681$	−1.22818	−	2.12727i	−0.0470640	−	0.0815173i
$682$	−2.54364	+	4.40571i	−0.0974009	+	0.168703i
$683$	−2.90273	+	5.02768i	−0.111070	+	0.192379i	−0.916202	−	0.400717i	$-0.868761\pi$
$683$	−2.90273	+	5.02768i	−0.111070	+	0.192379i	0.805132	+	0.593096i	$0.202094\pi$
$684$	4.01839	+	6.96005i	0.153647	+	0.266124i
$685$	15.0873			0.576455
$686$	−8.17501	−	16.6183i	−0.312123	−	0.634491i
$687$	−10.5804			−0.403668
$688$	2.01839	+	3.49595i	0.0769503	+	0.133282i
$689$	−15.0873	+	26.1319i	−0.574779	+	0.995547i
$690$	1.77182	−	3.06888i	0.0674520	−	0.116830i
$691$	3.17768	+	5.50390i	0.120885	+	0.209378i	0.920117	−	0.391644i	$-0.128094\pi$
$691$	3.17768	+	5.50390i	0.120885	+	0.209378i	−0.799232	+	0.601022i	$0.794760\pi$
$692$	−10.9127			−0.414840
$693$	−1.37328	+	2.26144i	−0.0521668	+	0.0859048i
$694$	−23.4426			−0.889870
$695$	−18.7191	−	32.4225i	−0.710056	−	1.22985i
$696$	−2.27182	+	3.93491i	−0.0861131	+	0.149152i
$697$	−2.77182	+	4.80093i	−0.104990	+	0.181848i
$698$	−12.8664	−	22.2853i	−0.487001	−	0.843511i
$699$	−7.07355			−0.267546
$700$	6.72818	+	0.149009i	0.254301	+	0.00563202i
$701$	5.86223			0.221413			0.110707	−	0.993853i	$-0.464689\pi$
$701$	5.86223			0.221413			0.110707	+	0.993853i	$0.464689\pi$
$702$	−2.74657	−	4.75720i	−0.103663	−	0.179549i
$703$	−16.2213	+	28.0961i	−0.611799	+	1.05967i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	12.7581	+	22.0977i	0.480498	+	0.832246i
$706$	−18.4059			−0.692714
$707$	−16.5630	−	30.2137i	−0.622914	−	1.13630i
$708$	−9.52991			−0.358156
$709$	6.72818	+	11.6536i	0.252682	+	0.437658i	0.964263	−	0.264946i	$-0.0853540\pi$
$709$	6.72818	+	11.6536i	0.252682	+	0.437658i	−0.711581	+	0.702604i	$0.752021\pi$
$710$	−3.49314	+	6.05029i	−0.131095	+	0.227063i
$711$	−6.11985	+	10.5999i	−0.229512	+	0.397527i
$712$	3.25343	+	5.63511i	0.121928	+	0.211185i
$713$	−6.56363			−0.245810
$714$	−1.27182	−	2.32002i	−0.0475966	−	0.0868244i
$715$	15.0873			0.564232
$716$	6.47475	+	11.2146i	0.241973	+	0.419109i
$717$	−3.83384	+	6.64041i	−0.143177	+	0.247991i
$718$	15.9863	−	27.6890i	0.596602	−	1.03335i
$719$	12.1382	+	21.0240i	0.452680	+	0.784065i	0.998552	−	0.0538042i	$-0.0171347\pi$
$719$	12.1382	+	21.0240i	0.452680	+	0.784065i	−0.545872	+	0.837869i	$0.683801\pi$
$720$	2.74657			0.102359
$721$	−47.8064	−	1.05877i	−1.78040	−	0.0394306i
$722$	45.5897			1.69667
$723$	12.5299	+	21.7024i	0.465992	+	0.807122i
$724$	−3.79707	+	6.57672i	−0.141117	+	0.244422i
$725$	−5.77868	+	10.0090i	−0.214615	+	0.371724i
$726$	−0.500000	−	0.866025i	−0.0185567	−	0.0321412i
$727$	−22.1471			−0.821390			−0.410695	−	0.911773i	$-0.634714\pi$
$727$	−22.1471			−0.821390			−0.410695	+	0.911773i	$0.634714\pi$
$728$	−7.54364	+	12.4224i	−0.279586	+	0.460404i
$729$	1.00000			0.0370370
$730$	11.7833	+	20.4093i	0.436121	+	0.755384i
$731$	2.01839	−	3.49595i	0.0746527	−	0.129302i
$732$	0.829647	−	1.43699i	0.0306646	−	0.0531127i
$733$	2.66349	+	4.61330i	0.0983782	+	0.170396i	0.911014	−	0.412377i	$-0.135301\pi$
$733$	2.66349	+	4.61330i	0.0983782	+	0.170396i	−0.812635	+	0.582773i	$0.801968\pi$
$734$	36.4794			1.34648
$735$	−8.86642	−	17.0594i	−0.327043	−	0.629247i
$736$	−1.29021			−0.0475576
$737$	−1.77182	−	3.06888i	−0.0652658	−	0.113044i
$738$	−2.77182	+	4.80093i	−0.102032	+	0.176725i
$739$	12.6309	−	21.8774i	0.464636	−	0.804772i	−0.534549	−	0.845137i	$-0.679519\pi$
$739$	12.6309	−	21.8774i	0.464636	−	0.804772i	0.999185	+	0.0403648i	$0.0128520\pi$
$740$	5.54364	+	9.60186i	0.203788	+	0.352971i
$741$	−44.1471			−1.62178
$742$	−7.54364	+	12.4224i	−0.276936	+	0.456040i
$743$	−25.4196			−0.932554			−0.466277	−	0.884639i	$-0.654405\pi$
$743$	−25.4196			−0.932554			−0.466277	+	0.884639i	$0.654405\pi$
$744$	−2.54364	−	4.40571i	−0.0932543	−	0.161521i
$745$	−22.0230	+	38.1450i	−0.806862	+	1.39753i
$746$	10.1566	−	17.5918i	0.371860	−	0.644081i
$747$	7.26496	+	12.5833i	0.265811	+	0.460398i
$748$	1.00000			0.0365636
$749$	46.1376	+	1.02181i	1.68583	+	0.0373361i
$750$	−6.74657			−0.246350
$751$	20.2765	+	35.1199i	0.739899	+	1.28154i	0.952540	+	0.304413i	$0.0984602\pi$
$751$	20.2765	+	35.1199i	0.739899	+	1.28154i	−0.212641	+	0.977130i	$0.568206\pi$
$752$	4.64510	−	8.04555i	0.169389	−	0.293391i
$753$	12.5115	−	21.6706i	0.455945	−	0.789720i
$754$	−12.4794	−	21.6150i	−0.454473	−	0.787171i
$755$	−15.6446			−0.569367
$756$	−1.27182	−	2.32002i	−0.0462556	−	0.0843782i
$757$	13.3554			0.485409			0.242704	−	0.970100i	$-0.421965\pi$
$757$	13.3554			0.485409			0.242704	+	0.970100i	$0.421965\pi$
$758$	−4.72132	−	8.17756i	−0.171486	−	0.297022i
$759$	0.645103	−	1.11735i	0.0234157	−	0.0405573i
$760$	11.0368	−	19.1163i	0.400346	−	0.693419i
$761$	−9.22818	−	15.9837i	−0.334521	−	0.579408i	0.648871	−	0.760898i	$-0.275241\pi$
$761$	−9.22818	−	15.9837i	−0.334521	−	0.579408i	−0.983393	+	0.181490i	$0.941908\pi$
$762$	−6.78334			−0.245735
$763$	−2.11032	−	3.84959i	−0.0763987	−	0.139365i
$764$	18.9863			0.686899
$765$	−1.37328	−	2.37860i	−0.0496512	−	0.0859984i
$766$	−11.8522	+	20.5287i	−0.428238	+	0.741731i
$767$	26.1745	−	45.3356i	0.945108	−	1.63698i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	49.9158			1.80001			0.900005	−	0.435881i	$-0.143563\pi$
$769$	49.9158			1.80001			0.900005	+	0.435881i	$0.143563\pi$
$770$	7.26496	+	0.160897i	0.261811	+	0.00579833i
$771$	−10.5069			−0.378395
$772$	10.7833	+	18.6773i	0.388101	+	0.672211i
$773$	21.0694	−	36.4932i	0.757812	−	1.31257i	−0.186152	−	0.982521i	$-0.559602\pi$
$773$	21.0694	−	36.4932i	0.757812	−	1.31257i	0.943964	−	0.330048i	$-0.107065\pi$
$774$	2.01839	−	3.49595i	0.0725494	−	0.125659i
$775$	−6.47009	−	11.2065i	−0.232412	−	0.402550i
$776$	−0.0872743			−0.00313296
$777$	5.54364	−	9.12890i	0.198877	−	0.327498i
$778$	−1.25343			−0.0449377
$779$	22.2765	+	38.5840i	0.798138	+	1.38241i
$780$	−7.54364	+	13.0660i	−0.270106	+	0.467837i
$781$	−1.27182	+	2.20285i	−0.0455092	+	0.0788243i
$782$	0.645103	+	1.11735i	0.0230688	+	0.0399564i
$783$	4.54364			0.162376
$784$	−3.76496	+	5.90128i	−0.134463	+	0.210760i
$785$	49.7412			1.77534
$786$	6.94950	+	12.0369i	0.247880	+	0.429342i
$787$	17.1792	−	29.7553i	0.612373	−	1.06066i	−0.378467	−	0.925615i	$-0.623549\pi$
$787$	17.1792	−	29.7553i	0.612373	−	1.06066i	0.990839	−	0.135046i	$-0.0431181\pi$
$788$	1.56202	−	2.70550i	0.0556448	−	0.0963796i
$789$	−11.8201	−	20.4730i	−0.420807	−	0.728860i
$790$	33.6172			1.19605
$791$	9.73284	−	16.0274i	0.346060	−	0.569869i
$792$	1.00000			0.0355335
$793$	4.55736	+	7.89359i	0.161837	+	0.280309i
$794$	−14.3086	+	24.7832i	−0.507793	+	0.879523i
$795$	−7.54364	+	13.0660i	−0.267545	+	0.463402i
$796$	13.0368	+	22.5804i	0.462076	+	0.800339i
$797$	−18.1387			−0.642506			−0.321253	−	0.946993i	$-0.604104\pi$
$797$	−18.1387			−0.642506			−0.321253	+	0.946993i	$0.604104\pi$
$798$	−21.2581	−	0.470804i	−0.752528	−	0.0166663i
$799$	−9.29021			−0.328664
$800$	−1.27182	−	2.20285i	−0.0449656	−	0.0778827i
$801$	3.25343	−	5.63511i	0.114954	−	0.199107i
$802$	−0.202931	+	0.351487i	−0.00716575	+	0.0124114i
$803$	4.29021	+	7.43085i	0.151398	+	0.262229i
$804$	3.54364			0.124974
$805$	4.50686	+	8.22130i	0.158846	+	0.289763i
$806$	27.9451			0.984324
$807$	7.57622	+	13.1224i	0.266695	+	0.461930i
$808$	−6.51152	+	11.2783i	−0.229075	+	0.396769i
$809$	8.77182	−	15.1932i	0.308401	−	0.534166i	−0.669612	−	0.742711i	$-0.733540\pi$
$809$	8.77182	−	15.1932i	0.308401	−	0.534166i	0.978013	+	0.208545i	$0.0668729\pi$
$810$	−1.37328	−	2.37860i	−0.0482523	−	0.0835754i
$811$	−43.0873			−1.51300			−0.756499	−	0.653994i	$-0.773092\pi$
$811$	−43.0873			−1.51300			−0.756499	+	0.653994i	$0.773092\pi$
$812$	−5.77868	−	10.5413i	−0.202792	−	0.369928i
$813$	18.9863			0.665878
$814$	2.01839	+	3.49595i	0.0707444	+	0.122533i
$815$	18.4606	−	31.9746i	0.646645	−	1.12002i
$816$	−0.500000	+	0.866025i	−0.0175035	+	0.0303170i
$817$	−16.2213	−	28.0961i	−0.567512	−	0.982960i
$818$	−32.7550			−1.14525
$819$	14.5299	+	0.321794i	0.507716	+	0.0112444i
$820$	15.2260			0.531714
$821$	−1.05050	−	1.81952i	−0.0366627	−	0.0635017i	0.847112	−	0.531415i	$-0.178339\pi$
$821$	−1.05050	−	1.81952i	−0.0366627	−	0.0635017i	−0.883775	+	0.467913i	$0.845006\pi$
$822$	−2.74657	+	4.75720i	−0.0957976	+	0.165926i
$823$	−9.87062	+	17.0964i	−0.344068	+	0.595943i	−0.985184	−	0.171501i	$-0.945138\pi$
$823$	−9.87062	+	17.0964i	−0.344068	+	0.595943i	0.641116	+	0.767444i	$0.278472\pi$
$824$	9.03677	+	15.6522i	0.314811	+	0.545269i
$825$	2.54364			0.0885581
$826$	13.0873	−	21.5513i	0.455365	−	0.749865i
$827$	23.7182			0.824762			0.412381	−	0.911011i	$-0.364697\pi$
$827$	23.7182			0.824762			0.412381	+	0.911011i	$0.364697\pi$
$828$	0.645103	+	1.11735i	0.0224189	+	0.0388306i
$829$	−19.9816	+	34.6092i	−0.693990	+	1.20203i	0.276530	+	0.961005i	$0.410816\pi$
$829$	−19.9816	+	34.6092i	−0.693990	+	1.20203i	−0.970520	+	0.241021i	$0.922518\pi$
$830$	19.9537	−	34.5608i	0.692603	−	1.19962i
$831$	−12.2397	−	21.1998i	−0.424591	−	0.735413i
$832$	5.49314			0.190440
$833$	6.99314	+	0.309906i	0.242298	+	0.0107376i
$834$	13.6309			0.472000
$835$	−32.3638	−	56.0557i	−1.11999	−	1.93989i
$836$	4.01839	−	6.96005i	0.138979	−	0.240718i
$837$	−2.54364	+	4.40571i	−0.0879210	+	0.152284i
$838$	7.96789	+	13.8008i	0.275246	+	0.476740i
$839$	29.0682			1.00355			0.501773	−	0.864999i	$-0.332681\pi$
$839$	29.0682			1.00355			0.501773	+	0.864999i	$0.332681\pi$
$840$	−3.77182	+	6.21119i	−0.130140	+	0.214306i
$841$	−8.35536			−0.288116
$842$	13.5620	+	23.4901i	0.467378	+	0.809523i
$843$	6.04364	−	10.4679i	0.208154	−	0.360533i
$844$	−7.83384	+	13.5686i	−0.269652	+	0.467051i
$845$	−23.5855	−	40.8513i	−0.811367	−	1.40533i
$846$	−9.29021			−0.319404
$847$	2.64510	+	0.0585812i	0.0908868	+	0.00201287i
$848$	5.49314			0.188635
$849$	−2.34071	−	4.05422i	−0.0803328	−	0.139141i
$850$	−1.27182	+	2.20285i	−0.0436230	+	0.0755573i
$851$	−2.60413	+	4.51049i	−0.0892685	+	0.154618i
$852$	−1.27182	−	2.20285i	−0.0435718	−	0.0754685i
$853$	20.2397			0.692994			0.346497	−	0.938051i	$-0.387371\pi$
$853$	20.2397			0.692994			0.346497	+	0.938051i	$0.387371\pi$
$854$	2.11032	+	3.84959i	0.0722137	+	0.131730i
$855$	−22.0735			−0.754899
$856$	−8.72132	−	15.1058i	−0.298089	−	0.516304i
$857$	6.08041	−	10.5316i	0.207703	−	0.359752i	−0.743288	−	0.668972i	$-0.766735\pi$
$857$	6.08041	−	10.5316i	0.207703	−	0.359752i	0.950991	+	0.309220i	$0.100068\pi$
$858$	−2.74657	+	4.75720i	−0.0937663	+	0.162408i
$859$	7.26496	+	12.5833i	0.247877	+	0.429336i	0.962937	−	0.269728i	$-0.0869338\pi$
$859$	7.26496	+	12.5833i	0.247877	+	0.429336i	−0.715060	+	0.699064i	$0.753600\pi$
$860$	−11.0873			−0.378073
$861$	−7.05050	−	12.8613i	−0.240280	−	0.438313i
$862$	−40.6265			−1.38374
$863$	6.79287	+	11.7656i	0.231232	+	0.400506i	0.958171	−	0.286196i	$-0.0923910\pi$
$863$	6.79287	+	11.7656i	0.231232	+	0.400506i	−0.726939	+	0.686702i	$0.759058\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	14.9863	−	25.9570i	0.509549	−	0.882564i
$866$	−0.550501	−	0.953495i	−0.0187068	−	0.0324011i
$867$	−16.0000			−0.543388
$868$	13.4564	+	0.298018i	0.456739	+	0.0101154i
$869$	12.2397			0.415204
$870$	−6.23970	−	10.8075i	−0.211546	−	0.366408i
$871$	−9.73284	+	16.8578i	−0.329785	+	0.571204i
$872$	−0.829647	+	1.43699i	−0.0280954	+	0.0486626i
$873$	0.0436371	+	0.0755817i	0.00147689	+	0.00255805i
$874$	10.3691			0.350740
$875$	9.26496	−	15.2569i	0.313213	−	0.515778i
$876$	−8.58041			−0.289905
$877$	1.03258	+	1.78848i	0.0348677	+	0.0603926i	0.882933	−	0.469500i	$-0.155566\pi$
$877$	1.03258	+	1.78848i	0.0348677	+	0.0603926i	−0.848065	+	0.529892i	$0.822232\pi$
$878$	−11.4284	+	19.7946i	−0.385691	+	0.668037i
$879$	5.81546	−	10.0727i	0.196150	−	0.339743i
$880$	−1.37328	−	2.37860i	−0.0462934	−	0.0801825i
$881$	−3.08727			−0.104013			−0.0520065	−	0.998647i	$-0.516562\pi$
$881$	−3.08727			−0.104013			−0.0520065	+	0.998647i	$0.516562\pi$
$882$	6.99314	+	0.309906i	0.235471	+	0.0104351i
$883$	21.8927			0.736749			0.368375	−	0.929677i	$-0.379914\pi$
$883$	21.8927			0.736749			0.368375	+	0.929677i	$0.379914\pi$
$884$	−2.74657	−	4.75720i	−0.0923771	−	0.160002i
$885$	13.0873	−	22.6678i	0.439924	−	0.761971i
$886$	4.77868	−	8.27692i	0.160543	−	0.278069i
$887$	−18.8706	−	32.6849i	−0.633613	−	1.09745i	−0.986807	−	0.161900i	$-0.948238\pi$
$887$	−18.8706	−	32.6849i	−0.633613	−	1.09745i	0.353194	−	0.935550i	$-0.385096\pi$
$888$	−4.03677			−0.135465
$889$	9.31546	−	15.3401i	0.312430	−	0.514490i
$890$	−17.8715			−0.599056
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−1.20293	+	2.08354i	−0.0402771	+	0.0697620i
$893$	−37.3316	+	64.6603i	−1.24926	+	2.16377i
$894$	−8.01839	−	13.8883i	−0.268175	−	0.464493i
$895$	−35.5667			−1.18886
$896$	2.64510	+	0.0585812i	0.0883667	+	0.00195706i
$897$	−7.08727			−0.236637
$898$	−0.340706	−	0.590120i	−0.0113695	−	0.0196926i
$899$	−11.5574	+	20.0179i	−0.385460	+	0.667636i
$900$	−1.27182	+	2.20285i	−0.0423940	+	0.0734285i
$901$	−2.74657	−	4.75720i	−0.0915015	−	0.158485i
$902$	5.54364			0.184583
$903$	5.13404	+	9.36538i	0.170850	+	0.311660i
$904$	−7.08727			−0.235719
$905$	−10.4289	−	18.0634i	−0.346669	−	0.600448i
$906$	2.84803	−	4.93294i	0.0946196	−	0.163886i
$907$	−15.7949	+	27.3575i	−0.524460	+	0.908391i	0.475135	+	0.879913i	$0.342399\pi$
$907$	−15.7949	+	27.3575i	−0.524460	+	0.908391i	−0.999594	+	0.0284780i	$0.990934\pi$
$908$	−1.22818	−	2.12727i	−0.0407586	−	0.0705960i
$909$	13.0230			0.431947
$910$	−19.1883	−	35.0027i	−0.636085	−	1.16033i
$911$	−27.7422			−0.919139			−0.459569	−	0.888142i	$-0.651996\pi$
$911$	−27.7422			−0.919139			−0.459569	+	0.888142i	$0.651996\pi$
$912$	4.01839	+	6.96005i	0.133062	+	0.230470i
$913$	7.26496	−	12.5833i	0.240435	−	0.416445i
$914$	−9.07355	+	15.7158i	−0.300126	+	0.519834i
$915$	2.27868	+	3.94679i	0.0753309	+	0.130477i
$916$	−10.5804			−0.349587
$917$	−36.7643	−	0.814220i	−1.21406	−	0.0268879i
$918$	1.00000			0.0330049
$919$	−9.46522	−	16.3942i	−0.312229	−	0.540796i	0.666616	−	0.745401i	$-0.267742\pi$
$919$	−9.46522	−	16.3942i	−0.312229	−	0.540796i	−0.978845	+	0.204605i	$0.934409\pi$
$920$	1.77182	−	3.06888i	0.0584151	−	0.101178i
$921$	7.03677	−	12.1880i	0.231870	−	0.401610i
$922$	20.8522	+	36.1171i	0.686732	+	1.18945i
$923$	13.9725			0.459912
$924$	−1.37328	+	2.26144i	−0.0451777	+	0.0743958i
$925$	−10.2681			−0.337613
$926$	14.2902	+	24.7514i	0.469605	+	0.813380i
$927$	9.03677	−	15.6522i	0.296807	−	0.514084i
$928$	−2.27182	+	3.93491i	−0.0745761	+	0.129170i
$929$	−6.88434	−	11.9240i	−0.225868	−	0.391215i	0.730712	−	0.682686i	$-0.239188\pi$
$929$	−6.88434	−	11.9240i	−0.225868	−	0.391215i	−0.956579	+	0.291472i	$0.905855\pi$
$930$	13.9725			0.458178
$931$	30.2581	−	47.4273i	0.991669	−	1.55437i
$932$	−7.07355			−0.231702
$933$	−6.13824	−	10.6317i	−0.200957	−	0.348068i
$934$	−2.69141	+	4.66166i	−0.0880656	+	0.152534i
$935$	−1.37328	+	2.37860i	−0.0449112	+	0.0777885i
$936$	−2.74657	−	4.75720i	−0.0897744	−	0.155494i
$937$	−17.2618			−0.563919			−0.281960	−	0.959426i	$-0.590984\pi$
$937$	−17.2618			−0.563919			−0.281960	+	0.959426i	$0.590984\pi$
$938$	−4.86642	+	8.01371i	−0.158894	+	0.261657i
$939$	23.4564			0.765469
$940$	12.7581	+	22.0977i	0.416123	+	0.720746i
$941$	18.8155	−	32.5893i	0.613366	−	1.06238i	−0.377302	−	0.926090i	$-0.623148\pi$
$941$	18.8155	−	32.5893i	0.613366	−	1.06238i	0.990669	−	0.136292i	$-0.0435184\pi$
$942$	−9.05516	+	15.6840i	−0.295033	+	0.511012i
$943$	3.57622	+	6.19419i	0.116458	+	0.201710i
$944$	−9.52991			−0.310172
$945$	7.26496	+	0.160897i	0.236329	+	0.00523399i
$946$	−4.03677			−0.131247
$947$	3.86596	+	6.69603i	0.125627	+	0.217592i	0.921978	−	0.387243i	$-0.126573\pi$
$947$	3.86596	+	6.69603i	0.125627	+	0.217592i	−0.796351	+	0.604835i	$0.793239\pi$
$948$	−6.11985	+	10.5999i	−0.198764	+	0.344269i
$949$	23.5667	−	40.8187i	0.765007	−	1.32503i
$950$	10.2213	+	17.7038i	0.331623	+	0.574388i
$951$	−0.572020			−0.0185490
$952$	−1.27182	−	2.32002i	−0.0412199	−	0.0751922i
$953$	−20.6770			−0.669794			−0.334897	−	0.942255i	$-0.608702\pi$
$953$	−20.6770			−0.669794			−0.334897	+	0.942255i	$0.608702\pi$
$954$	−2.74657	−	4.75720i	−0.0889234	−	0.154020i
$955$	−26.0735	+	45.1607i	−0.843720	+	1.46137i
$956$	−3.83384	+	6.64041i	−0.123995	+	0.214766i
$957$	−2.27182	−	3.93491i	−0.0734375	−	0.127197i
$958$	14.4794			0.467808
$959$	−6.98627	−	12.7442i	−0.225599	−	0.411531i
$960$	2.74657			0.0886451
$961$	2.55982	+	4.43374i	0.0825748	+	0.143024i
$962$	11.0873	−	19.2037i	0.357468	−	0.619153i
$963$	−8.72132	+	15.1058i	−0.281041	+	0.486776i
$964$	12.5299	+	21.7024i	0.403561	+	0.698989i
$965$	−59.2344			−1.90682
$966$	−3.41273	−	0.0755817i	−0.109803	−	0.00243180i
$967$	15.7235			0.505634			0.252817	−	0.967514i	$-0.418643\pi$
$967$	15.7235			0.505634			0.252817	+	0.967514i	$0.418643\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	4.01839	−	6.96005i	0.129089	−	0.223589i
$970$	0.119852	−	0.207590i	0.00384823	−	0.00666533i
$971$	−4.12405	−	7.14306i	−0.132347	−	0.229232i	0.792234	−	0.610218i	$-0.208918\pi$
$971$	−4.12405	−	7.14306i	−0.132347	−	0.229232i	−0.924581	+	0.380986i	$0.875585\pi$
$972$	1.00000			0.0320750
$973$	−18.7191	+	30.8254i	−0.600107	+	0.988218i
$974$	−8.43332			−0.270221
$975$	−6.98627	−	12.1006i	−0.223740	−	0.387529i
$976$	0.829647	−	1.43699i	0.0265564	−	0.0459970i
$977$	17.6677	−	30.6013i	0.565239	−	0.979023i	−0.431788	−	0.901975i	$-0.642117\pi$
$977$	17.6677	−	30.6013i	0.565239	−	0.979023i	0.997027	−	0.0770481i	$-0.0245495\pi$
$978$	6.72132	+	11.6417i	0.214924	+	0.372259i
$979$	−6.50686			−0.207960
$980$	−8.86642	−	17.0594i	−0.283227	−	0.544944i
$981$	1.65929			0.0529772
$982$	19.3385	+	33.4953i	0.617116	+	1.06888i
$983$	4.57156	−	7.91817i	0.145810	−	0.252550i	−0.783865	−	0.620931i	$-0.786755\pi$
$983$	4.57156	−	7.91817i	0.145810	−	0.252550i	0.929675	+	0.368381i	$0.120088\pi$
$984$	−2.77182	+	4.80093i	−0.0883623	+	0.153048i
$985$	4.29021	+	7.43085i	0.136697	+	0.236767i
$986$	4.54364			0.144699
$987$	12.7581	−	21.0092i	0.406095	−	0.668730i
$988$	−44.1471			−1.40451
$989$	−2.60413	−	4.51049i	−0.0828066	−	0.143425i
$990$	−1.37328	+	2.37860i	−0.0436458	+	0.0755968i
$991$	−17.7328	+	30.7142i	−0.563302	+	0.975668i	0.433903	+	0.900960i	$0.357136\pi$
$991$	−17.7328	+	30.7142i	−0.563302	+	0.975668i	−0.997205	+	0.0747086i	$0.976197\pi$
$992$	−2.54364	−	4.40571i	−0.0807606	−	0.139881i
$993$	7.71819			0.244929
$994$	6.72818	+	0.149009i	0.213405	+	0.00472629i
$995$	−71.6128			−2.27028
$996$	7.26496	+	12.5833i	0.230199	+	0.398716i
$997$	−22.7466	+	39.3982i	−0.720391	+	1.24775i	0.240452	+	0.970661i	$0.422704\pi$
$997$	−22.7466	+	39.3982i	−0.720391	+	1.24775i	−0.960843	+	0.277093i	$0.910629\pi$
$998$	−19.0230	+	32.9489i	−0.602164	+	1.04298i
$999$	2.01839	+	3.49595i	0.0638589	+	0.110607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.f.67.1	✓	6
3.2	odd	2		1386.2.k.w.991.3		6
7.2	even	3	inner	462.2.i.f.331.1	yes	6
7.3	odd	6		3234.2.a.bg.1.1		3
7.4	even	3		3234.2.a.bi.1.3		3
21.2	odd	6		1386.2.k.w.793.3		6
21.11	odd	6		9702.2.a.dt.1.1		3
21.17	even	6		9702.2.a.du.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.f.67.1	✓	6	1.1	even	1	trivial
462.2.i.f.331.1	yes	6	7.2	even	3	inner
1386.2.k.w.793.3		6	21.2	odd	6
1386.2.k.w.991.3		6	3.2	odd	2
3234.2.a.bg.1.1		3	7.3	odd	6
3234.2.a.bi.1.3		3	7.4	even	3
9702.2.a.dt.1.1		3	21.11	odd	6
9702.2.a.du.1.3		3	21.17	even	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.37328 - 2.37860i) q^{5} +1.00000 q^{6} +(-1.37328 + 2.26144i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.37328 - 2.37860i) q^{5} +1.00000 q^{6} +(-1.37328 + 2.26144i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.37328 + 2.37860i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +5.49314 q^{13} +(2.64510 + 0.0585812i) q^{14} +2.74657 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(4.01839 + 6.96005i) q^{19} +2.74657 q^{20} +(-1.27182 - 2.32002i) q^{21} +1.00000 q^{22} +(0.645103 + 1.11735i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.27182 + 2.20285i) q^{25} +(-2.74657 - 4.75720i) q^{26} +1.00000 q^{27} +(-1.27182 - 2.32002i) q^{28} +4.54364 q^{29} +(-1.37328 - 2.37860i) q^{30} +(-2.54364 + 4.40571i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(7.26496 + 0.160897i) q^{35} +1.00000 q^{36} +(2.01839 + 3.49595i) q^{37} +(4.01839 - 6.96005i) q^{38} +(-2.74657 + 4.75720i) q^{39} +(-1.37328 - 2.37860i) q^{40} +5.54364 q^{41} +(-1.37328 + 2.26144i) q^{42} -4.03677 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-1.37328 + 2.37860i) q^{45} +(0.645103 - 1.11735i) q^{46} +(4.64510 + 8.04555i) q^{47} +1.00000 q^{48} +(-3.22818 - 6.21119i) q^{49} +2.54364 q^{50} +(-0.500000 - 0.866025i) q^{51} +(-2.74657 + 4.75720i) q^{52} +(-2.74657 + 4.75720i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.74657 q^{55} +(-1.37328 + 2.26144i) q^{56} -8.03677 q^{57} +(-2.27182 - 3.93491i) q^{58} +(4.76496 - 8.25314i) q^{59} +(-1.37328 + 2.37860i) q^{60} +(0.829647 + 1.43699i) q^{61} +5.08727 q^{62} +(2.64510 + 0.0585812i) q^{63} +1.00000 q^{64} +(-7.54364 - 13.0660i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-1.77182 + 3.06888i) q^{67} +(-0.500000 - 0.866025i) q^{68} -1.29021 q^{69} +(-3.49314 - 6.37208i) q^{70} +2.54364 q^{71} +(-0.500000 - 0.866025i) q^{72} +(4.29021 - 7.43085i) q^{73} +(2.01839 - 3.49595i) q^{74} +(-1.27182 - 2.20285i) q^{75} -8.03677 q^{76} +(-1.27182 - 2.32002i) q^{77} +5.49314 q^{78} +(-6.11985 - 10.5999i) q^{79} +(-1.37328 + 2.37860i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.77182 - 4.80093i) q^{82} -14.5299 q^{83} +(2.64510 + 0.0585812i) q^{84} +2.74657 q^{85} +(2.01839 + 3.49595i) q^{86} +(-2.27182 + 3.93491i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.25343 + 5.63511i) q^{89} +2.74657 q^{90} +(-7.54364 + 12.4224i) q^{91} -1.29021 q^{92} +(-2.54364 - 4.40571i) q^{93} +(4.64510 - 8.04555i) q^{94} +(11.0368 - 19.1163i) q^{95} +(-0.500000 - 0.866025i) q^{96} -0.0872743 q^{97} +(-3.76496 + 5.90128i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{21} + 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 6 q^{27} - 3 q^{28} + 18 q^{29} - 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} + 6 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} + 24 q^{41} + 18 q^{43} - 3 q^{44} - 9 q^{46} + 15 q^{47} + 6 q^{48} - 24 q^{49} + 6 q^{50} - 3 q^{51} - 3 q^{54} - 6 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 3 q^{63} + 6 q^{64} - 36 q^{65} - 3 q^{66} - 6 q^{67} - 3 q^{68} + 18 q^{69} + 12 q^{70} + 6 q^{71} - 3 q^{72} - 9 q^{74} - 3 q^{75} - 6 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} - 12 q^{83} + 3 q^{84} - 9 q^{86} - 9 q^{87} - 3 q^{88} + 36 q^{89} - 36 q^{91} + 18 q^{92} - 6 q^{93} + 15 q^{94} + 24 q^{95} - 3 q^{96} + 18 q^{97} + 15 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^21 + 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 6 * q^27 - 3 * q^28 + 18 * q^29 - 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 + 6 * q^35 + 6 * q^36 - 9 * q^37 + 3 * q^38 + 24 * q^41 + 18 * q^43 - 3 * q^44 - 9 * q^46 + 15 * q^47 + 6 * q^48 - 24 * q^49 + 6 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 3 * q^63 + 6 * q^64 - 36 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 + 18 * q^69 + 12 * q^70 + 6 * q^71 - 3 * q^72 - 9 * q^74 - 3 * q^75 - 6 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 - 12 * q^83 + 3 * q^84 - 9 * q^86 - 9 * q^87 - 3 * q^88 + 36 * q^89 - 36 * q^91 + 18 * q^92 - 6 * q^93 + 15 * q^94 + 24 * q^95 - 3 * q^96 + 18 * q^97 + 15 * q^98 + 6 * q^99

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