LMFDB - Embedded newform 966.2.i.m.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 10x^{5} + 47x^{4} + 180x^{3} + 220x^{2} + 768x + 1164 $ x^8 - 2x^7 + 13x^6 + 10x^5 + 47x^4 + 180x^3 + 220x^2 + 768*x + 1164
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$-1.61492 - 0.402708i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.m.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.61492 + 2.79713i) q^{5} -1.00000 q^{6} +(0.958707 - 2.46594i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.61492 + 2.79713i) q^{5} -1.00000 q^{6} +(0.958707 - 2.46594i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.61492 - 2.79713i) q^{10} +(-1.65622 + 2.86865i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.43192 q^{13} +(-2.61492 + 0.402708i) q^{14} +3.22985 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0412933 + 0.0715221i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} -3.22985 q^{20} +(-1.65622 - 2.06324i) q^{21} +3.31243 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.71596 + 4.70418i) q^{25} +(-2.21596 - 3.83815i) q^{26} -1.00000 q^{27} +(1.65622 + 2.06324i) q^{28} +0.568085 q^{29} +(-1.61492 - 2.79713i) q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.65622 + 2.86865i) q^{33} +0.0825866 q^{34} +(8.44581 - 1.30068i) q^{35} +1.00000 q^{36} +(1.22985 + 2.13016i) q^{37} +(1.00000 - 1.73205i) q^{38} +(2.21596 - 3.83815i) q^{39} +(1.61492 + 2.79713i) q^{40} +8.45970 q^{41} +(-0.958707 + 2.46594i) q^{42} +2.00000 q^{43} +(-1.65622 - 2.86865i) q^{44} +(1.61492 - 2.79713i) q^{45} +(0.500000 - 0.866025i) q^{46} +(3.81243 + 6.60333i) q^{47} -1.00000 q^{48} +(-5.16176 - 4.72823i) q^{49} +5.43192 q^{50} +(0.0412933 + 0.0715221i) q^{51} +(-2.21596 + 3.83815i) q^{52} +(-7.04684 + 12.2055i) q^{53} +(0.500000 + 0.866025i) q^{54} -10.6987 q^{55} +(0.958707 - 2.46594i) q^{56} +2.00000 q^{57} +(-0.284042 - 0.491976i) q^{58} +(6.45970 - 11.1885i) q^{59} +(-1.61492 + 2.79713i) q^{60} +(2.43192 + 4.21220i) q^{61} -2.00000 q^{62} +(-2.61492 + 0.402708i) q^{63} +1.00000 q^{64} +(7.15721 + 12.3966i) q^{65} +(1.65622 - 2.86865i) q^{66} +(5.04684 - 8.74138i) q^{67} +(-0.0412933 - 0.0715221i) q^{68} +1.00000 q^{69} +(-5.34933 - 6.66394i) q^{70} +7.69866 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.93192 - 3.34618i) q^{73} +(1.22985 - 2.13016i) q^{74} +(2.71596 + 4.70418i) q^{75} -2.00000 q^{76} +(5.48611 + 6.83434i) q^{77} -4.43192 q^{78} +(-2.34378 - 4.05955i) q^{79} +(1.61492 - 2.79713i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.22985 - 7.32631i) q^{82} -0.165173 q^{83} +(2.61492 - 0.402708i) q^{84} -0.266742 q^{85} +(-1.00000 - 1.73205i) q^{86} +(0.284042 - 0.491976i) q^{87} +(-1.65622 + 2.86865i) q^{88} +(-5.66176 - 9.80646i) q^{89} -3.22985 q^{90} +(4.24891 - 10.9289i) q^{91} -1.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(3.81243 - 6.60333i) q^{94} +(-3.22985 + 5.59426i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(-1.51389 + 6.83434i) q^{98} +3.31243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9	$ 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{12} + 12 q^{13} - 6 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 4 q^{20} + 4 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 28 q^{29} + 2 q^{30} + 8 q^{31} - 4 q^{32} + 4 q^{34} + 26 q^{35} + 8 q^{36} - 20 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 2 q^{45} + 4 q^{46} + 4 q^{47} - 8 q^{48} + 12 q^{49} + 20 q^{50} + 2 q^{51} - 6 q^{52} - 18 q^{53} + 4 q^{54} - 32 q^{55} + 6 q^{56} + 16 q^{57} - 14 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 16 q^{62} - 6 q^{63} + 8 q^{64} - 14 q^{65} + 2 q^{67} - 2 q^{68} + 8 q^{69} - 16 q^{70} + 8 q^{71} - 4 q^{72} - 8 q^{73} - 20 q^{74} + 10 q^{75} - 16 q^{76} + 62 q^{77} - 12 q^{78} - 32 q^{79} - 2 q^{80} - 4 q^{81} - 4 q^{82} - 8 q^{83} + 6 q^{84} + 28 q^{85} - 8 q^{86} + 14 q^{87} + 8 q^{89} + 4 q^{90} + 2 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{95} + 4 q^{96} - 64 q^{97} + 6 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^12 + 12 * q^13 - 6 * q^14 - 4 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 28 * q^29 + 2 * q^30 + 8 * q^31 - 4 * q^32 + 4 * q^34 + 26 * q^35 + 8 * q^36 - 20 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 8 * q^48 + 12 * q^49 + 20 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 4 * q^54 - 32 * q^55 + 6 * q^56 + 16 * q^57 - 14 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 16 * q^62 - 6 * q^63 + 8 * q^64 - 14 * q^65 + 2 * q^67 - 2 * q^68 + 8 * q^69 - 16 * q^70 + 8 * q^71 - 4 * q^72 - 8 * q^73 - 20 * q^74 + 10 * q^75 - 16 * q^76 + 62 * q^77 - 12 * q^78 - 32 * q^79 - 2 * q^80 - 4 * q^81 - 4 * q^82 - 8 * q^83 + 6 * q^84 + 28 * q^85 - 8 * q^86 + 14 * q^87 + 8 * q^89 + 4 * q^90 + 2 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 + 4 * q^95 + 4 * q^96 - 64 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	1.61492	+	2.79713i	0.722216	+	1.25091i	0.960110	+	0.279623i	$0.0902096\pi$
$5$	1.61492	+	2.79713i	0.722216	+	1.25091i	−0.237894	+	0.971291i	$0.576457\pi$
$6$	−1.00000			−0.408248
$7$	0.958707	−	2.46594i	0.362357	−	0.932039i
$7$	0.958707	−	2.46594i	0.362357	−	0.932039i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.61492	−	2.79713i	0.510684	−	0.884530i
$11$	−1.65622	+	2.86865i	−0.499368	+	0.864931i	−1.00000		0.000729338i	$-0.999768\pi$
$11$	−1.65622	+	2.86865i	−0.499368	+	0.864931i	0.500631	+	0.865661i	$0.333101\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.43192			1.22919			0.614596	−	0.788842i	$-0.289319\pi$
$13$	4.43192			1.22919			0.614596	+	0.788842i	$0.289319\pi$
$14$	−2.61492	+	0.402708i	−0.698868	+	0.107628i
$15$	3.22985			0.833943
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.0412933	+	0.0715221i	−0.0100151	+	0.0173467i	−0.870990	−	0.491302i	$-0.836521\pi$
$17$	−0.0412933	+	0.0715221i	−0.0100151	+	0.0173467i	0.860974	+	0.508648i	$0.169855\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−3.22985			−0.722216
$21$	−1.65622	−	2.06324i	−0.361416	−	0.450235i
$22$	3.31243			0.706213
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−2.71596	+	4.70418i	−0.543192	+	0.940835i
$26$	−2.21596	−	3.83815i	−0.434585	−	0.752723i
$27$	−1.00000			−0.192450
$28$	1.65622	+	2.06324i	0.312996	+	0.389915i
$29$	0.568085			0.105491			0.0527453	−	0.998608i	$-0.483203\pi$
$29$	0.568085			0.105491			0.0527453	+	0.998608i	$0.483203\pi$
$30$	−1.61492	−	2.79713i	−0.294843	−	0.510684i
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.65622	+	2.86865i	0.288310	+	0.499368i
$34$	0.0825866			0.0141635
$35$	8.44581	−	1.30068i	1.42760	−	0.219856i
$36$	1.00000			0.166667
$37$	1.22985	+	2.13016i	0.202186	+	0.350196i	0.949232	−	0.314576i	$-0.101862\pi$
$37$	1.22985	+	2.13016i	0.202186	+	0.350196i	−0.747047	+	0.664772i	$0.768529\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	2.21596	−	3.83815i	0.354837	−	0.614596i
$40$	1.61492	+	2.79713i	0.255342	+	0.442265i
$41$	8.45970			1.32118			0.660591	−	0.750746i	$-0.270306\pi$
$41$	8.45970			1.32118			0.660591	+	0.750746i	$0.270306\pi$
$42$	−0.958707	+	2.46594i	−0.147932	+	0.380503i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.65622	−	2.86865i	−0.249684	−	0.432466i
$45$	1.61492	−	2.79713i	0.240739	−	0.416972i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	3.81243	+	6.60333i	0.556101	+	0.963195i	0.997817	+	0.0660398i	$0.0210364\pi$
$47$	3.81243	+	6.60333i	0.556101	+	0.963195i	−0.441716	+	0.897155i	$0.645630\pi$
$48$	−1.00000			−0.144338
$49$	−5.16176	−	4.72823i	−0.737395	−	0.675462i
$50$	5.43192			0.768189
$51$	0.0412933	+	0.0715221i	0.00578222	+	0.0100151i
$52$	−2.21596	+	3.83815i	−0.307298	+	0.532256i
$53$	−7.04684	+	12.2055i	−0.967958	+	1.67655i	−0.266509	+	0.963833i	$0.585870\pi$
$53$	−7.04684	+	12.2055i	−0.967958	+	1.67655i	−0.701449	+	0.712720i	$0.747463\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−10.6987			−1.44261
$56$	0.958707	−	2.46594i	0.128113	−	0.329526i
$57$	2.00000			0.264906
$58$	−0.284042	−	0.491976i	−0.0372966	−	0.0645996i
$59$	6.45970	−	11.1885i	0.840981	−	1.45662i	−0.0480858	−	0.998843i	$-0.515312\pi$
$59$	6.45970	−	11.1885i	0.840981	−	1.45662i	0.889067	−	0.457778i	$-0.151355\pi$
$60$	−1.61492	+	2.79713i	−0.208486	+	0.361108i
$61$	2.43192	+	4.21220i	0.311375	+	0.539317i	0.978660	−	0.205485i	$-0.0658772\pi$
$61$	2.43192	+	4.21220i	0.311375	+	0.539317i	−0.667285	+	0.744802i	$0.732544\pi$
$62$	−2.00000			−0.254000
$63$	−2.61492	+	0.402708i	−0.329449	+	0.0507364i
$64$	1.00000			0.125000
$65$	7.15721	+	12.3966i	0.887742	+	1.53761i
$66$	1.65622	−	2.86865i	0.203866	−	0.353107i
$67$	5.04684	−	8.74138i	0.616570	−	1.06793i	−0.373537	−	0.927615i	$-0.621855\pi$
$67$	5.04684	−	8.74138i	0.616570	−	1.06793i	0.990107	−	0.140315i	$-0.0448114\pi$
$68$	−0.0412933	−	0.0715221i	−0.00500755	−	0.00867333i
$69$	1.00000			0.120386
$70$	−5.34933	−	6.66394i	−0.639367	−	0.796493i
$71$	7.69866			0.913663			0.456831	−	0.889553i	$-0.348984\pi$
$71$	7.69866			0.913663			0.456831	+	0.889553i	$0.348984\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.93192	−	3.34618i	0.226114	−	0.391640i	−0.730539	−	0.682871i	$-0.760731\pi$
$73$	1.93192	−	3.34618i	0.226114	−	0.391640i	0.956653	+	0.291230i	$0.0940646\pi$
$74$	1.22985	−	2.13016i	0.142967	−	0.247626i
$75$	2.71596	+	4.70418i	0.313612	+	0.543192i
$76$	−2.00000			−0.229416
$77$	5.48611	+	6.83434i	0.625200	+	0.778845i
$78$	−4.43192			−0.501816
$79$	−2.34378	−	4.05955i	−0.263696	−	0.456735i	0.703525	−	0.710670i	$-0.251608\pi$
$79$	−2.34378	−	4.05955i	−0.263696	−	0.456735i	−0.967221	+	0.253935i	$0.918275\pi$
$80$	1.61492	−	2.79713i	0.180554	−	0.312729i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.22985	−	7.32631i	−0.467109	−	0.809056i
$83$	−0.165173			−0.0181301			−0.00906506	−	0.999959i	$-0.502886\pi$
$83$	−0.165173			−0.0181301			−0.00906506	+	0.999959i	$0.502886\pi$
$84$	2.61492	−	0.402708i	0.285312	−	0.0439390i
$85$	−0.266742			−0.0289322
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$	0.284042	−	0.491976i	0.0304525	−	0.0527453i
$88$	−1.65622	+	2.86865i	−0.176553	+	0.305799i
$89$	−5.66176	−	9.80646i	−0.600146	−	1.03948i	−0.992799	−	0.119796i	$-0.961776\pi$
$89$	−5.66176	−	9.80646i	−0.600146	−	1.03948i	0.392653	−	0.919687i	$-0.371557\pi$
$90$	−3.22985			−0.340456
$91$	4.24891	−	10.9289i	0.445406	−	1.14566i
$92$	−1.00000			−0.104257
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$	3.81243	−	6.60333i	0.393223	−	0.681081i
$95$	−3.22985	+	5.59426i	−0.331375	+	0.573959i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	−1.51389	+	6.83434i	−0.152926	+	0.690372i
$99$	3.31243			0.332912
$100$	−2.71596	−	4.70418i	−0.271596	−	0.470418i
$101$	−4.71596	+	8.16828i	−0.469255	+	0.812774i	−0.999382	−	0.0351442i	$-0.988811\pi$
$101$	−4.71596	+	8.16828i	−0.469255	+	0.812774i	0.530127	+	0.847918i	$0.322144\pi$
$102$	0.0412933	−	0.0715221i	0.00408865	−	0.00708174i
$103$	−9.85032	−	17.0612i	−0.970581	−	1.68109i	−0.693809	−	0.720159i	$-0.744069\pi$
$103$	−9.85032	−	17.0612i	−0.970581	−	1.68109i	−0.276772	−	0.960936i	$-0.589265\pi$
$104$	4.43192			0.434585
$105$	3.09648	−	7.96462i	0.302185	−	0.777268i
$106$	14.0937			1.36890
$107$	−7.31243	−	12.6655i	−0.706920	−	1.22442i	−0.965994	−	0.258564i	$-0.916751\pi$
$107$	−7.31243	−	12.6655i	−0.706920	−	1.22442i	0.259075	−	0.965857i	$-0.416582\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	3.00555	−	5.20576i	0.287879	−	0.498621i	−0.685424	−	0.728144i	$-0.740383\pi$
$109$	3.00555	−	5.20576i	0.287879	−	0.498621i	0.973303	+	0.229523i	$0.0737165\pi$
$110$	5.34933	+	9.26531i	0.510038	+	0.883413i
$111$	2.45970			0.233464
$112$	−2.61492	+	0.402708i	−0.247087	+	0.0380523i
$113$	−1.39502			−0.131233			−0.0656163	−	0.997845i	$-0.520901\pi$
$113$	−1.39502			−0.131233			−0.0656163	+	0.997845i	$0.520901\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−1.61492	+	2.79713i	−0.150592	+	0.260834i
$116$	−0.284042	+	0.491976i	−0.0263727	+	0.0456788i
$117$	−2.21596	−	3.83815i	−0.204865	−	0.354837i
$118$	−12.9194			−1.18933
$119$	0.136781	+	0.170396i	0.0125387	+	0.0156201i
$120$	3.22985			0.294843
$121$	0.0138899	+	0.0240580i	0.00126272	+	0.00218709i
$122$	2.43192	−	4.21220i	0.220175	−	0.381355i
$123$	4.22985	−	7.32631i	0.381393	−	0.660591i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−1.39502			−0.124774
$126$	1.65622	+	2.06324i	0.147548	+	0.183808i
$127$	−13.3235			−1.18227			−0.591136	−	0.806572i	$-0.701320\pi$
$127$	−13.3235			−1.18227			−0.591136	+	0.806572i	$0.701320\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	7.15721	−	12.3966i	0.627728	−	1.08726i
$131$	−0.931303	−	1.61306i	−0.0813683	−	0.140934i	0.822470	−	0.568809i	$-0.192596\pi$
$131$	−0.931303	−	1.61306i	−0.0813683	−	0.140934i	−0.903838	+	0.427875i	$0.859262\pi$
$132$	−3.31243			−0.288310
$133$	5.22985	−	0.805416i	0.453485	−	0.0698384i
$134$	−10.0937			−0.871961
$135$	−1.61492	−	2.79713i	−0.138991	−	0.240739i
$136$	−0.0412933	+	0.0715221i	−0.00354087	+	0.00613297i
$137$	−7.10597	+	12.3079i	−0.607104	+	1.05153i	0.384611	+	0.923079i	$0.374335\pi$
$137$	−7.10597	+	12.3079i	−0.607104	+	1.05153i	−0.991715	+	0.128456i	$0.958998\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	3.59709			0.305101			0.152551	−	0.988296i	$-0.451251\pi$
$139$	3.59709			0.305101			0.152551	+	0.988296i	$0.451251\pi$
$140$	−3.09648	+	7.96462i	−0.261700	+	0.673134i
$141$	7.62487			0.642130
$142$	−3.84933	−	6.66723i	−0.323028	−	0.559502i
$143$	−7.34021	+	12.7136i	−0.613820	+	1.06317i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.917413	+	1.58901i	0.0761870	+	0.131960i
$146$	−3.86383			−0.319773
$147$	−6.67565	+	2.10610i	−0.550599	+	0.173708i
$148$	−2.45970			−0.202186
$149$	1.92736	+	3.33828i	0.157895	+	0.273483i	0.934110	−	0.356987i	$-0.116196\pi$
$149$	1.92736	+	3.33828i	0.157895	+	0.273483i	−0.776214	+	0.630469i	$0.782862\pi$
$150$	2.71596	−	4.70418i	0.221757	−	0.384094i
$151$	2.79793	−	4.84616i	0.227692	−	0.394375i	−0.729431	−	0.684054i	$-0.760215\pi$
$151$	2.79793	−	4.84616i	0.227692	−	0.394375i	0.957124	+	0.289679i	$0.0935486\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	0.0825866			0.00667673
$154$	3.17565	−	8.16828i	0.255901	−	0.658219i
$155$	6.45970			0.518855
$156$	2.21596	+	3.83815i	0.177419	+	0.307298i
$157$	−9.08813	+	15.7411i	−0.725312	+	1.25628i	0.233534	+	0.972349i	$0.424971\pi$
$157$	−9.08813	+	15.7411i	−0.725312	+	1.25628i	−0.958845	+	0.283928i	$0.908362\pi$
$158$	−2.34378	+	4.05955i	−0.186461	+	0.322961i
$159$	7.04684	+	12.2055i	0.558851	+	0.967958i
$160$	−3.22985			−0.255342
$161$	2.61492	−	0.402708i	0.206085	−	0.0317378i
$162$	1.00000			0.0785674
$163$	2.63337	+	4.56113i	0.206262	+	0.357255i	0.950534	−	0.310621i	$-0.100537\pi$
$163$	2.63337	+	4.56113i	0.206262	+	0.357255i	−0.744272	+	0.667876i	$0.767204\pi$
$164$	−4.22985	+	7.32631i	−0.330296	+	0.572089i
$165$	−5.34933	+	9.26531i	−0.416445	+	0.721303i
$166$	0.0825866	+	0.143044i	0.00640996	+	0.0111024i
$167$	−7.29575			−0.564562			−0.282281	−	0.959332i	$-0.591091\pi$
$167$	−7.29575			−0.564562			−0.282281	+	0.959332i	$0.591091\pi$
$168$	−1.65622	−	2.06324i	−0.127780	−	0.159182i
$169$	6.64187			0.510913
$170$	0.133371	+	0.231005i	0.0102291	+	0.0177173i
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	9.78063	+	16.9406i	0.743608	+	1.28797i	0.950842	+	0.309675i	$0.100220\pi$
$173$	9.78063	+	16.9406i	0.743608	+	1.28797i	−0.207235	+	0.978291i	$0.566446\pi$
$174$	−0.568085			−0.0430664
$175$	8.99643	+	11.2073i	0.680066	+	0.847194i
$176$	3.31243			0.249684
$177$	−6.45970	−	11.1885i	−0.485540	−	0.840981i
$178$	−5.66176	+	9.80646i	−0.424367	+	0.735025i
$179$	−1.17906	+	2.04220i	−0.0881273	+	0.152641i	−0.906720	−	0.421734i	$-0.861422\pi$
$179$	−1.17906	+	2.04220i	−0.0881273	+	0.152641i	0.818592	+	0.574375i	$0.194755\pi$
$180$	1.61492	+	2.79713i	0.120369	+	0.208486i
$181$	−11.0735			−0.823085			−0.411542	−	0.911391i	$-0.635010\pi$
$181$	−11.0735			−0.823085			−0.411542	+	0.911391i	$0.635010\pi$
$182$	−11.5891	+	1.78477i	−0.859043	+	0.132296i
$183$	4.86383			0.359545
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−3.97222	+	6.88009i	−0.292043	+	0.505834i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	−0.136781	−	0.236912i	−0.0100024	−	0.0173247i
$188$	−7.62487			−0.556101
$189$	−0.958707	+	2.46594i	−0.0697357	+	0.179371i
$190$	6.45970			0.468636
$191$	−5.66176	−	9.80646i	−0.409671	−	0.709571i	0.585182	−	0.810902i	$-0.301023\pi$
$191$	−5.66176	−	9.80646i	−0.409671	−	0.709571i	−0.994853	+	0.101331i	$0.967690\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−6.24374	+	10.8145i	−0.449434	+	0.778443i	−0.998349	−	0.0574354i	$-0.981708\pi$
$193$	−6.24374	+	10.8145i	−0.449434	+	0.778443i	0.548915	+	0.835878i	$0.315041\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	14.3144			1.02508
$196$	6.67565	−	2.10610i	0.476832	−	0.150436i
$197$	20.2957			1.44601			0.723006	−	0.690842i	$-0.242760\pi$
$197$	20.2957			1.44601			0.723006	+	0.690842i	$0.242760\pi$
$198$	−1.65622	−	2.86865i	−0.117702	−	0.203866i
$199$	−4.80348	+	8.31987i	−0.340510	+	0.589780i	−0.984527	−	0.175231i	$-0.943933\pi$
$199$	−4.80348	+	8.31987i	−0.340510	+	0.589780i	0.644018	+	0.765010i	$0.277266\pi$
$200$	−2.71596	+	4.70418i	−0.192047	+	0.332636i
$201$	−5.04684	−	8.74138i	−0.355977	−	0.616570i
$202$	9.43192			0.663627
$203$	0.544627	−	1.40087i	0.0382253	−	0.0983215i
$204$	−0.0825866			−0.00578222
$205$	13.6618	+	23.6629i	0.954179	+	1.65269i
$206$	−9.85032	+	17.0612i	−0.686304	+	1.18871i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−2.21596	−	3.83815i	−0.153649	−	0.266128i
$209$	−6.62487			−0.458252
$210$	−8.44581	+	1.30068i	−0.582816	+	0.0897558i
$211$	9.19295			0.632869			0.316434	−	0.948614i	$-0.397514\pi$
$211$	9.19295			0.632869			0.316434	+	0.948614i	$0.397514\pi$
$212$	−7.04684	−	12.2055i	−0.483979	−	0.838276i
$213$	3.84933	−	6.66723i	0.263752	−	0.456831i
$214$	−7.31243	+	12.6655i	−0.499868	+	0.865796i
$215$	3.22985	+	5.59426i	0.220274	+	0.381525i
$216$	−1.00000			−0.0680414
$217$	−3.31243	−	4.12647i	−0.224863	−	0.280123i
$218$	−6.01109			−0.407123
$219$	−1.93192	−	3.34618i	−0.130547	−	0.226114i
$220$	5.34933	−	9.26531i	0.360652	−	0.624667i
$221$	−0.183008	+	0.316980i	−0.0123105	+	0.0213224i
$222$	−1.22985	−	2.13016i	−0.0825420	−	0.142967i
$223$	13.3791			0.895930			0.447965	−	0.894051i	$-0.352149\pi$
$223$	13.3791			0.895930			0.447965	+	0.894051i	$0.352149\pi$
$224$	1.65622	+	2.06324i	0.110661	+	0.137856i
$225$	5.43192			0.362128
$226$	0.697510	+	1.20812i	0.0463977	+	0.0803632i
$227$	−10.8035	+	18.7122i	−0.717052	+	1.24197i	0.245111	+	0.969495i	$0.421176\pi$
$227$	−10.8035	+	18.7122i	−0.717052	+	1.24197i	−0.962163	+	0.272475i	$0.912158\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	−13.6304	−	23.6086i	−0.900723	−	1.56010i	−0.826558	−	0.562852i	$-0.809704\pi$
$229$	−13.6304	−	23.6086i	−0.900723	−	1.56010i	−0.0741656	−	0.997246i	$-0.523629\pi$
$230$	3.22985			0.212970
$231$	8.66176	−	1.33394i	0.569902	−	0.0877670i
$232$	0.568085			0.0372966
$233$	−4.62487	−	8.01051i	−0.302985	−	0.524786i	0.673826	−	0.738891i	$-0.264650\pi$
$233$	−4.62487	−	8.01051i	−0.302985	−	0.524786i	−0.976811	+	0.214105i	$0.931317\pi$
$234$	−2.21596	+	3.83815i	−0.144862	+	0.250908i
$235$	−12.3136	+	21.3277i	−0.803249	+	1.39127i
$236$	6.45970	+	11.1885i	0.420490	+	0.728311i
$237$	−4.68757			−0.304490
$238$	0.0791763	−	0.203654i	0.00513224	−	0.0132009i
$239$	−13.2667			−0.858154			−0.429077	−	0.903268i	$-0.641161\pi$
$239$	−13.2667			−0.858154			−0.429077	+	0.903268i	$0.641161\pi$
$240$	−1.61492	−	2.79713i	−0.104243	−	0.180554i
$241$	−12.5423	+	21.7239i	−0.807919	+	1.39936i	0.106383	+	0.994325i	$0.466073\pi$
$241$	−12.5423	+	21.7239i	−0.807919	+	1.39936i	−0.914302	+	0.405032i	$0.867260\pi$
$242$	0.0138899	−	0.0240580i	0.000892876	−	0.00154651i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.86383			−0.311375
$245$	4.88963	−	22.0739i	0.312387	−	1.41025i
$246$	−8.45970			−0.539370
$247$	4.43192	+	7.67630i	0.281996	+	0.488431i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$	−0.0825866	+	0.143044i	−0.00523371	+	0.00906506i
$250$	0.697510	+	1.20812i	0.0441144	+	0.0764084i
$251$	20.7097			1.30719			0.653594	−	0.756845i	$-0.273260\pi$
$251$	20.7097			1.30719			0.653594	+	0.756845i	$0.273260\pi$
$252$	0.958707	−	2.46594i	0.0603928	−	0.155340i
$253$	−3.31243			−0.208251
$254$	6.66176	+	11.5385i	0.417996	+	0.723991i
$255$	−0.133371	+	0.231005i	−0.00835202	+	0.0144661i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.5423	−	25.1880i	−0.907123	−	1.57118i	−0.818042	−	0.575158i	$-0.804941\pi$
$257$	−14.5423	−	25.1880i	−0.907123	−	1.57118i	−0.0890803	−	0.996024i	$-0.528393\pi$
$258$	−2.00000			−0.124515
$259$	6.43192	−	0.990538i	0.399660	−	0.0615491i
$260$	−14.3144			−0.887742
$261$	−0.284042	−	0.491976i	−0.0175818	−	0.0304525i
$262$	−0.931303	+	1.61306i	−0.0575361	+	0.0996555i
$263$	−3.88052	+	6.72126i	−0.239283	+	0.414450i	−0.960509	−	0.278250i	$-0.910246\pi$
$263$	−3.88052	+	6.72126i	−0.239283	+	0.414450i	0.721226	+	0.692700i	$0.243579\pi$
$264$	1.65622	+	2.86865i	0.101933	+	0.176553i
$265$	−45.5204			−2.79630
$266$	−3.31243	−	4.12647i	−0.203098	−	0.253010i
$267$	−11.3235			−0.692989
$268$	5.04684	+	8.74138i	0.308285	+	0.533965i
$269$	4.11098	−	7.12042i	0.250651	−	0.434140i	−0.713054	−	0.701109i	$-0.752689\pi$
$269$	4.11098	−	7.12042i	0.250651	−	0.434140i	0.963705	+	0.266969i	$0.0860221\pi$
$270$	−1.61492	+	2.79713i	−0.0982811	+	0.170228i
$271$	−7.74435	−	13.4136i	−0.470436	−	0.814819i	0.528993	−	0.848626i	$-0.322570\pi$
$271$	−7.74435	−	13.4136i	−0.470436	−	0.814819i	−0.999428	+	0.0338078i	$0.989237\pi$
$272$	0.0825866			0.00500755
$273$	−7.34021	−	9.14409i	−0.444250	−	0.553425i
$274$	14.2119			0.858574
$275$	−8.99643	−	15.5823i	−0.542505	−	0.939647i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	12.7582	−	22.0979i	0.766568	−	1.32774i	−0.172845	−	0.984949i	$-0.555296\pi$
$277$	12.7582	−	22.0979i	0.766568	−	1.32774i	0.939413	−	0.342786i	$-0.111371\pi$
$278$	−1.79854	−	3.11517i	−0.107870	−	0.186835i
$279$	−2.00000			−0.119737
$280$	8.44581	−	1.30068i	0.504733	−	0.0777308i
$281$	−31.1155			−1.85620			−0.928099	−	0.372334i	$-0.878558\pi$
$281$	−31.1155			−1.85620			−0.928099	+	0.372334i	$0.878558\pi$
$282$	−3.81243	−	6.60333i	−0.227027	−	0.393223i
$283$	−9.76218	+	16.9086i	−0.580302	+	1.00511i	0.415142	+	0.909757i	$0.363732\pi$
$283$	−9.76218	+	16.9086i	−0.580302	+	1.00511i	−0.995443	+	0.0953552i	$0.969601\pi$
$284$	−3.84933	+	6.66723i	−0.228416	+	0.395627i
$285$	3.22985	+	5.59426i	0.191320	+	0.331375i
$286$	14.6804			0.868072
$287$	8.11037	−	20.8611i	0.478740	−	1.23139i
$288$	1.00000			0.0589256
$289$	8.49659	+	14.7165i	0.499799	+	0.865678i
$290$	0.917413	−	1.58901i	0.0538724	−	0.0933097i
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	1.93192	+	3.34618i	0.113057	+	0.195820i
$293$	2.93533			0.171484			0.0857418	−	0.996317i	$-0.472674\pi$
$293$	2.93533			0.171484			0.0857418	+	0.996317i	$0.472674\pi$
$294$	5.16176	+	4.72823i	0.301040	+	0.275756i
$295$	41.7277			2.42948
$296$	1.22985	+	2.13016i	0.0714834	+	0.123813i
$297$	1.65622	−	2.86865i	0.0961035	−	0.166456i
$298$	1.92736	−	3.33828i	0.111649	−	0.193381i
$299$	2.21596	+	3.83815i	0.128152	+	0.221966i
$300$	−5.43192			−0.313612
$301$	1.91741	−	4.93189i	0.110518	−	0.284269i
$302$	−5.59586			−0.322006
$303$	4.71596	+	8.16828i	0.270925	+	0.469255i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	−7.85472	+	13.6048i	−0.449760	+	0.779007i
$306$	−0.0412933	−	0.0715221i	−0.00236058	−	0.00408865i
$307$	−5.94322			−0.339197			−0.169599	−	0.985513i	$-0.554247\pi$
$307$	−5.94322			−0.339197			−0.169599	+	0.985513i	$0.554247\pi$
$308$	−8.66176	+	1.33394i	−0.493550	+	0.0760085i
$309$	−19.7006			−1.12073
$310$	−3.22985	−	5.59426i	−0.183443	−	0.317733i
$311$	−9.81243	+	16.9956i	−0.556412	+	0.963734i	0.441380	+	0.897320i	$0.354489\pi$
$311$	−9.81243	+	16.9956i	−0.556412	+	0.963734i	−0.997792	+	0.0664138i	$0.978844\pi$
$312$	2.21596	−	3.83815i	0.125454	−	0.217293i
$313$	−4.62487	−	8.01051i	−0.261413	−	0.452781i	0.705205	−	0.709004i	$-0.250855\pi$
$313$	−4.62487	−	8.01051i	−0.261413	−	0.452781i	−0.966618	+	0.256223i	$0.917522\pi$
$314$	18.1763			1.02575
$315$	−5.34933	−	6.66394i	−0.301401	−	0.375470i
$316$	4.68757			0.263696
$317$	−15.9194	−	27.5732i	−0.894122	−	1.54866i	−0.834887	−	0.550421i	$-0.814467\pi$
$317$	−15.9194	−	27.5732i	−0.894122	−	1.54866i	−0.0592346	−	0.998244i	$-0.518866\pi$
$318$	7.04684	−	12.2055i	0.395167	−	0.684450i
$319$	−0.940871	+	1.62964i	−0.0526787	+	0.0912422i
$320$	1.61492	+	2.79713i	0.0902770	+	0.156364i
$321$	−14.6249			−0.816281
$322$	−1.65622	−	2.06324i	−0.0922974	−	0.114980i
$323$	−0.165173			−0.00919048
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−12.0369	+	20.8485i	−0.667687	+	1.15647i
$326$	2.63337	−	4.56113i	0.145849	−	0.252618i
$327$	−3.00555	−	5.20576i	−0.166207	−	0.287879i
$328$	8.45970			0.467109
$329$	19.9384	−	3.07059i	1.09924	−	0.169287i
$330$	10.6987			0.588942
$331$	−14.5534	−	25.2072i	−0.799926	−	1.38551i	−0.919664	−	0.392707i	$-0.871539\pi$
$331$	−14.5534	−	25.2072i	−0.799926	−	1.38551i	0.119738	−	0.992806i	$-0.461795\pi$
$332$	0.0825866	−	0.143044i	0.00453253	−	0.00785057i
$333$	1.22985	−	2.13016i	0.0673952	−	0.116732i
$334$	3.64787	+	6.31830i	0.199603	+	0.345722i
$335$	32.6010			1.78119
$336$	−0.958707	+	2.46594i	−0.0523017	+	0.134528i
$337$	5.13617			0.279785			0.139892	−	0.990167i	$-0.455324\pi$
$337$	5.13617			0.279785			0.139892	+	0.990167i	$0.455324\pi$
$338$	−3.32094	−	5.75203i	−0.180635	−	0.312869i
$339$	−0.697510	+	1.20812i	−0.0378836	+	0.0656163i
$340$	0.133371	−	0.231005i	0.00723306	−	0.0125280i
$341$	3.31243	+	5.73730i	0.179378	+	0.310692i
$342$	−2.00000			−0.108148
$343$	−16.6082	+	8.19563i	−0.896757	+	0.442522i
$344$	2.00000			0.107833
$345$	1.61492	+	2.79713i	0.0869446	+	0.150592i
$346$	9.78063	−	16.9406i	0.525810	−	0.910730i
$347$	8.04289	−	13.9307i	0.431765	−	0.747839i	−0.565260	−	0.824913i	$-0.691224\pi$
$347$	8.04289	−	13.9307i	0.431765	−	0.747839i	0.997025	+	0.0770734i	$0.0245576\pi$
$348$	0.284042	+	0.491976i	0.0152263	+	0.0263727i
$349$	−11.8070			−0.632017			−0.316008	−	0.948756i	$-0.602343\pi$
$349$	−11.8070			−0.632017			−0.316008	+	0.948756i	$0.602343\pi$
$350$	5.20761	−	13.3948i	0.278359	−	0.715982i
$351$	−4.43192			−0.236558
$352$	−1.65622	−	2.86865i	−0.0882767	−	0.152900i
$353$	−16.2298	+	28.1109i	−0.863828	+	1.49619i	0.00437895	+	0.999990i	$0.498606\pi$
$353$	−16.2298	+	28.1109i	−0.863828	+	1.49619i	−0.868207	+	0.496203i	$0.834727\pi$
$354$	−6.45970	+	11.1885i	−0.343329	+	0.594663i
$355$	12.4327	+	21.5341i	0.659862	+	1.14291i
$356$	11.3235			0.600146
$357$	0.215958	−	0.0332583i	0.0114297	−	0.00176021i
$358$	2.35813			0.124631
$359$	−10.1473	−	17.5756i	−0.535552	−	0.927603i	−0.999136	−	0.0415505i	$-0.986770\pi$
$359$	−10.1473	−	17.5756i	−0.535552	−	0.927603i	0.463584	−	0.886053i	$-0.346563\pi$
$360$	1.61492	−	2.79713i	0.0851140	−	0.147422i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	5.53674	+	9.58991i	0.291004	+	0.504034i
$363$	0.0277798			0.00145806
$364$	7.34021	+	9.14409i	0.384732	+	0.479281i
$365$	12.4796			0.653211
$366$	−2.43192	−	4.21220i	−0.127118	−	0.220175i
$367$	9.67171	−	16.7519i	0.504859	−	0.874441i	−0.495125	−	0.868822i	$-0.664878\pi$
$367$	9.67171	−	16.7519i	0.504859	−	0.874441i	0.999984	−	0.00561983i	$-0.00178886\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−4.22985	−	7.32631i	−0.220197	−	0.381393i
$370$	7.94444			0.413012
$371$	23.3422	+	29.0786i	1.21187	+	1.50969i
$372$	2.00000			0.103695
$373$	−8.40057	−	14.5502i	−0.434965	−	0.753381i	0.562328	−	0.826914i	$-0.309906\pi$
$373$	−8.40057	−	14.5502i	−0.434965	−	0.753381i	−0.997293	+	0.0735331i	$0.976573\pi$
$374$	−0.136781	+	0.236912i	−0.00707280	+	0.0122504i
$375$	−0.697510	+	1.20812i	−0.0360193	+	0.0623872i
$376$	3.81243	+	6.60333i	0.196611	+	0.340541i
$377$	2.51770			0.129668
$378$	2.61492	−	0.402708i	0.134497	−	0.0207131i
$379$	−11.2854			−0.579692			−0.289846	−	0.957073i	$-0.593604\pi$
$379$	−11.2854			−0.579692			−0.289846	+	0.957073i	$0.593604\pi$
$380$	−3.22985	−	5.59426i	−0.165688	−	0.286979i
$381$	−6.66176	+	11.5385i	−0.341292	+	0.591136i
$382$	−5.66176	+	9.80646i	−0.289681	+	0.501742i
$383$	−13.2945	−	23.0268i	−0.679318	−	1.17661i	−0.975186	−	0.221385i	$-0.928942\pi$
$383$	−13.2945	−	23.0268i	−0.679318	−	1.17661i	0.295868	−	0.955229i	$-0.404391\pi$
$384$	−1.00000			−0.0510310
$385$	−10.2569	+	26.3823i	−0.522739	+	1.34457i
$386$	12.4875			0.635596
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	−3.78124	+	6.54931i	−0.191717	+	0.332063i	−0.945819	−	0.324694i	$-0.894739\pi$
$389$	−3.78124	+	6.54931i	−0.191717	+	0.332063i	0.754103	+	0.656757i	$0.228072\pi$
$390$	−7.15721	−	12.3966i	−0.362419	−	0.627728i
$391$	−0.0825866			−0.00417658
$392$	−5.16176	−	4.72823i	−0.260708	−	0.238812i
$393$	−1.86261			−0.0939561
$394$	−10.1479	−	17.5766i	−0.511242	−	0.885498i
$395$	7.57006	−	13.1117i	0.380891	−	0.659723i
$396$	−1.65622	+	2.86865i	−0.0832280	+	0.144155i
$397$	7.73046	+	13.3895i	0.387981	+	0.672002i	0.992178	−	0.124833i	$-0.0398394\pi$
$397$	7.73046	+	13.3895i	0.387981	+	0.672002i	−0.604197	+	0.796835i	$0.706506\pi$
$398$	9.60696			0.481553
$399$	1.91741	−	4.93189i	0.0959907	−	0.246903i
$400$	5.43192			0.271596
$401$	−0.728859	−	1.26242i	−0.0363975	−	0.0630423i	0.847253	−	0.531190i	$-0.178255\pi$
$401$	−0.728859	−	1.26242i	−0.0363975	−	0.0630423i	−0.883650	+	0.468148i	$0.844922\pi$
$402$	−5.04684	+	8.74138i	−0.251713	+	0.435980i
$403$	4.43192	−	7.67630i	0.220769	−	0.382384i
$404$	−4.71596	−	8.16828i	−0.234628	−	0.406387i
$405$	−3.22985			−0.160492
$406$	−1.48550	+	0.228772i	−0.0737240	+	0.0113538i
$407$	−8.14758			−0.403860
$408$	0.0412933	+	0.0715221i	0.00204432	+	0.00354087i
$409$	2.13398	−	3.69617i	0.105519	−	0.182764i	−0.808431	−	0.588591i	$-0.799683\pi$
$409$	2.13398	−	3.69617i	0.105519	−	0.182764i	0.913950	+	0.405827i	$0.133016\pi$
$410$	13.6618	−	23.6629i	0.674706	−	1.16863i
$411$	7.10597	+	12.3079i	0.350512	+	0.607104i
$412$	19.7006			0.970581
$413$	−21.3973	−	26.6558i	−1.05289	−	1.31164i
$414$	−1.00000			−0.0491473
$415$	−0.266742	−	0.462011i	−0.0130939	−	0.0226792i
$416$	−2.21596	+	3.83815i	−0.108646	+	0.188181i
$417$	1.79854	−	3.11517i	0.0880751	−	0.152551i
$418$	3.31243	+	5.73730i	0.162016	+	0.280621i
$419$	−23.1694			−1.13190			−0.565951	−	0.824439i	$-0.691491\pi$
$419$	−23.1694			−1.13190			−0.565951	+	0.824439i	$0.691491\pi$
$420$	5.34933	+	6.66394i	0.261021	+	0.325167i
$421$	33.3124			1.62355			0.811774	−	0.583971i	$-0.198502\pi$
$421$	33.3124			1.62355			0.811774	+	0.583971i	$0.198502\pi$
$422$	−4.59648	−	7.96133i	−0.223753	−	0.387552i
$423$	3.81243	−	6.60333i	0.185367	−	0.321065i
$424$	−7.04684	+	12.2055i	−0.342225	+	0.592751i
$425$	−0.224302	−	0.388502i	−0.0108802	−	0.0188451i
$426$	−7.69866			−0.373001
$427$	12.7185	−	1.95870i	0.615494	−	0.0947883i
$428$	14.6249			0.706920
$429$	7.34021	+	12.7136i	0.354389	+	0.613820i
$430$	3.22985	−	5.59426i	0.155757	−	0.269779i
$431$	4.86261	−	8.42228i	0.234224	−	0.405687i	−0.724823	−	0.688935i	$-0.758079\pi$
$431$	4.86261	−	8.42228i	0.234224	−	0.405687i	0.959047	+	0.283248i	$0.0914119\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−24.7384			−1.18885			−0.594427	−	0.804150i	$-0.702621\pi$
$433$	−24.7384			−1.18885			−0.594427	+	0.804150i	$0.702621\pi$
$434$	−1.91741	+	4.93189i	−0.0920388	+	0.236738i
$435$	1.83483			0.0879732
$436$	3.00555	+	5.20576i	0.143940	+	0.249311i
$437$	−1.00000	+	1.73205i	−0.0478365	+	0.0828552i
$438$	−1.93192	+	3.34618i	−0.0923105	+	0.159886i
$439$	15.6360	+	27.0823i	0.746264	+	1.29257i	0.949602	+	0.313458i	$0.101488\pi$
$439$	15.6360	+	27.0823i	0.746264	+	1.29257i	−0.203338	+	0.979109i	$0.565179\pi$
$440$	−10.6987			−0.510038
$441$	−1.51389	+	6.83434i	−0.0720900	+	0.325445i
$442$	0.366017			0.0174096
$443$	16.4478	+	28.4884i	0.781458	+	1.35352i	0.931093	+	0.364783i	$0.118857\pi$
$443$	16.4478	+	28.4884i	0.781458	+	1.35352i	−0.149635	+	0.988741i	$0.547810\pi$
$444$	−1.22985	+	2.13016i	−0.0583660	+	0.101093i
$445$	18.2866	−	31.6734i	0.866869	−	1.50146i
$446$	−6.68954	−	11.5866i	−0.316759	−	0.548643i
$447$	3.85472			0.182322
$448$	0.958707	−	2.46594i	0.0452946	−	0.116505i
$449$	5.89039			0.277985			0.138992	−	0.990293i	$-0.455614\pi$
$449$	5.89039			0.277985			0.138992	+	0.990293i	$0.455614\pi$
$450$	−2.71596	−	4.70418i	−0.128031	−	0.221757i
$451$	−14.0111	+	24.2679i	−0.659757	+	1.14273i
$452$	0.697510	−	1.20812i	0.0328081	−	0.0568253i
$453$	−2.79793	−	4.84616i	−0.131458	−	0.227692i
$454$	21.6070			1.01406
$455$	37.4311	−	5.76453i	1.75480	−	0.270245i
$456$	2.00000			0.0936586
$457$	10.4597	+	18.1167i	0.489284	+	0.847465i	0.999924	−	0.0123300i	$-0.00392486\pi$
$457$	10.4597	+	18.1167i	0.489284	+	0.847465i	−0.510640	+	0.859795i	$0.670592\pi$
$458$	−13.6304	+	23.6086i	−0.636907	+	1.10316i
$459$	0.0412933	−	0.0715221i	0.00192741	−	0.00333837i
$460$	−1.61492	−	2.79713i	−0.0752962	−	0.130417i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−5.48611	−	6.83434i	−0.255237	−	0.317962i
$463$	13.7277			0.637979			0.318989	−	0.947758i	$-0.396657\pi$
$463$	13.7277			0.637979			0.318989	+	0.947758i	$0.396657\pi$
$464$	−0.284042	−	0.491976i	−0.0131863	−	0.0228394i
$465$	3.22985	−	5.59426i	0.149781	−	0.259428i
$466$	−4.62487	+	8.01051i	−0.214243	+	0.371080i
$467$	0.940871	+	1.62964i	0.0435383	+	0.0754106i	0.886973	−	0.461821i	$-0.152804\pi$
$467$	0.940871	+	1.62964i	0.0435383	+	0.0754106i	−0.843435	+	0.537231i	$0.819470\pi$
$468$	4.43192			0.204865
$469$	−16.7173	−	20.8256i	−0.771934	−	0.961639i
$470$	24.6272			1.13597
$471$	9.08813	+	15.7411i	0.418759	+	0.725312i
$472$	6.45970	−	11.1885i	0.297332	−	0.514993i
$473$	−3.31243	+	5.73730i	−0.152306	+	0.263802i
$474$	2.34378	+	4.05955i	0.107654	+	0.186461i
$475$	−10.8638			−0.498467
$476$	−0.215958	+	0.0332583i	−0.00989840	+	0.00152439i
$477$	14.0937			0.645305
$478$	6.63337	+	11.4893i	0.303403	+	0.525510i
$479$	−14.8547	+	25.7291i	−0.678729	+	1.17559i	0.296634	+	0.954991i	$0.404136\pi$
$479$	−14.8547	+	25.7291i	−0.678729	+	1.17559i	−0.975364	+	0.220603i	$0.929198\pi$
$480$	−1.61492	+	2.79713i	−0.0737108	+	0.127671i
$481$	5.45058	+	9.44068i	0.248525	+	0.430458i
$482$	25.0846			1.14257
$483$	0.958707	−	2.46594i	0.0436227	−	0.112204i
$484$	−0.0277798			−0.00126272
$485$	−12.9194	−	22.3770i	−0.586639	−	1.01609i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	9.94519	−	17.2256i	0.450660	−	0.780566i	−0.547767	−	0.836631i	$-0.684522\pi$
$487$	9.94519	−	17.2256i	0.450660	−	0.780566i	0.998427	+	0.0560651i	$0.0178555\pi$
$488$	2.43192	+	4.21220i	0.110088	+	0.190677i
$489$	5.26674			0.238170
$490$	−21.5613	+	6.80238i	−0.974042	+	0.307300i
$491$	0.982995			0.0443619			0.0221810	−	0.999754i	$-0.492939\pi$
$491$	0.982995			0.0443619			0.0221810	+	0.999754i	$0.492939\pi$
$492$	4.22985	+	7.32631i	0.190696	+	0.330296i
$493$	−0.0234581	+	0.0406306i	−0.00105650	+	0.00182991i
$494$	4.43192	−	7.67630i	0.199401	−	0.345373i
$495$	5.34933	+	9.26531i	0.240434	+	0.416445i
$496$	−2.00000			−0.0898027
$497$	7.38075	−	18.9845i	0.331072	−	0.851569i
$498$	0.165173			0.00740159
$499$	1.76165	+	3.05127i	0.0788623	+	0.136593i	0.902759	−	0.430146i	$-0.141538\pi$
$499$	1.76165	+	3.05127i	0.0788623	+	0.136593i	−0.823897	+	0.566739i	$0.808205\pi$
$500$	0.697510	−	1.20812i	0.0311936	−	0.0540289i
$501$	−3.64787	+	6.31830i	−0.162975	+	0.282281i
$502$	−10.3549	−	17.9352i	−0.462161	−	0.800486i
$503$	−33.8054			−1.50731			−0.753654	−	0.657271i	$-0.771711\pi$
$503$	−33.8054			−1.50731			−0.753654	+	0.657271i	$0.771711\pi$
$504$	−2.61492	+	0.402708i	−0.116478	+	0.0179380i
$505$	−30.4636			−1.35561
$506$	1.65622	+	2.86865i	0.0736278	+	0.127527i
$507$	3.32094	−	5.75203i	0.147488	−	0.255457i
$508$	6.66176	−	11.5385i	0.295568	−	0.511939i
$509$	−11.3408	−	19.6429i	−0.502673	−	0.870656i	−0.999995	−	0.00308959i	$-0.999017\pi$
$509$	−11.3408	−	19.6429i	−0.502673	−	0.870656i	0.497322	−	0.867566i	$-0.334317\pi$
$510$	0.266742			0.0118115
$511$	−6.39934	−	7.97200i	−0.283090	−	0.352660i
$512$	1.00000			0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	−14.5423	+	25.1880i	−0.641433	+	1.11099i
$515$	31.8150	−	55.1052i	1.40194	−	2.42823i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	−25.2569			−1.11080
$518$	−4.07379	−	5.07493i	−0.178992	−	0.222980i
$519$	19.5613			0.858644
$520$	7.15721	+	12.3966i	0.313864	+	0.543629i
$521$	18.4807	−	32.0096i	0.809656	−	1.40236i	−0.103447	−	0.994635i	$-0.532987\pi$
$521$	18.4807	−	32.0096i	0.809656	−	1.40236i	0.913103	−	0.407730i	$-0.133679\pi$
$522$	−0.284042	+	0.491976i	−0.0124322	+	0.0215332i
$523$	−4.32238	−	7.48658i	−0.189004	−	0.327365i	0.755914	−	0.654671i	$-0.227193\pi$
$523$	−4.32238	−	7.48658i	−0.189004	−	0.327365i	−0.944919	+	0.327305i	$0.893859\pi$
$524$	1.86261			0.0813683
$525$	14.2040	−	2.18747i	0.619915	−	0.0954692i
$526$	7.76104			0.338397
$527$	0.0825866	+	0.143044i	0.00359753	+	0.00623110i
$528$	1.65622	−	2.86865i	0.0720776	−	0.124842i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	22.7602	+	39.4219i	0.988641	+	1.71238i
$531$	−12.9194			−0.560654
$532$	−1.91741	+	4.93189i	−0.0831304	+	0.213824i
$533$	37.4927			1.62399
$534$	5.66176	+	9.80646i	0.245008	+	0.424367i
$535$	23.6180	−	40.9077i	1.02110	−	1.76859i
$536$	5.04684	−	8.74138i	0.217990	−	0.377570i
$537$	1.17906	+	2.04220i	0.0508803	+	0.0881273i
$538$	−8.22196			−0.354474
$539$	22.1127	−	6.97632i	0.952460	−	0.300491i
$540$	3.22985			0.138991
$541$	7.07856	+	12.2604i	0.304331	+	0.527117i	0.977112	−	0.212725i	$-0.0682337\pi$
$541$	7.07856	+	12.2604i	0.304331	+	0.527117i	−0.672781	+	0.739842i	$0.734900\pi$
$542$	−7.74435	+	13.4136i	−0.332648	+	0.576164i
$543$	−5.53674	+	9.58991i	−0.237604	+	0.411542i
$544$	−0.0412933	−	0.0715221i	−0.00177044	−	0.00306648i
$545$	19.4149			0.831643
$546$	−4.24891	+	10.9289i	−0.181836	+	0.467712i
$547$	−19.0500			−0.814518			−0.407259	−	0.913313i	$-0.633515\pi$
$547$	−19.0500			−0.814518			−0.407259	+	0.913313i	$0.633515\pi$
$548$	−7.10597	−	12.3079i	−0.303552	−	0.525767i
$549$	2.43192	−	4.21220i	0.103792	−	0.179772i
$550$	−8.99643	+	15.5823i	−0.383609	+	0.664430i
$551$	0.568085	+	0.983951i	0.0242012	+	0.0419177i
$552$	1.00000			0.0425628
$553$	−12.2576	+	1.88772i	−0.521247	+	0.0802740i
$554$	−25.5165			−1.08409
$555$	3.97222	+	6.88009i	0.168611	+	0.292043i
$556$	−1.79854	+	3.11517i	−0.0762753	+	0.132113i
$557$	17.5991	−	30.4825i	0.745696	−	1.29158i	−0.204172	−	0.978935i	$-0.565450\pi$
$557$	17.5991	−	30.4825i	0.745696	−	1.29158i	0.949869	−	0.312649i	$-0.101216\pi$
$558$	1.00000	+	1.73205i	0.0423334	+	0.0733236i
$559$	8.86383			0.374900
$560$	−5.34933	−	6.66394i	−0.226050	−	0.281603i
$561$	−0.273563			−0.0115498
$562$	15.5578	+	26.9469i	0.656265	+	1.13668i
$563$	−2.03333	+	3.52182i	−0.0856945	+	0.148427i	−0.905687	−	0.423947i	$-0.860644\pi$
$563$	−2.03333	+	3.52182i	−0.0856945	+	0.148427i	0.819992	+	0.572374i	$0.193978\pi$
$564$	−3.81243	+	6.60333i	−0.160532	+	0.278050i
$565$	−2.25285	−	3.90205i	−0.0947782	−	0.164161i
$566$	19.5244			0.820670
$567$	1.65622	+	2.06324i	0.0695546	+	0.0866478i
$568$	7.69866			0.323028
$569$	−4.36716	−	7.56415i	−0.183081	−	0.317106i	0.759847	−	0.650102i	$-0.225274\pi$
$569$	−4.36716	−	7.56415i	−0.183081	−	0.317106i	−0.942928	+	0.332996i	$0.891940\pi$
$570$	3.22985	−	5.59426i	0.135283	−	0.234318i
$571$	23.5712	−	40.8265i	0.986424	−	1.70854i	0.350997	−	0.936377i	$-0.385843\pi$
$571$	23.5712	−	40.8265i	0.986424	−	1.70854i	0.635428	−	0.772161i	$-0.280824\pi$
$572$	−7.34021	−	12.7136i	−0.306910	−	0.531583i
$573$	−11.3235			−0.473047
$574$	−22.1215	+	3.40679i	−0.923332	+	0.142196i
$575$	−5.43192			−0.226527
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	10.3777	−	17.9747i	0.432030	−	0.748298i	−0.565018	−	0.825079i	$-0.691131\pi$
$577$	10.3777	−	17.9747i	0.432030	−	0.748298i	0.997048	+	0.0767805i	$0.0244641\pi$
$578$	8.49659	−	14.7165i	0.353412	−	0.612127i
$579$	6.24374	+	10.8145i	0.259481	+	0.449434i
$580$	−1.83483			−0.0761870
$581$	−0.158353	+	0.407308i	−0.00656958	+	0.0168980i
$582$	8.00000			0.331611
$583$	−23.3422	−	40.4299i	−0.966735	−	1.67443i
$584$	1.93192	−	3.34618i	0.0799432	−	0.138466i
$585$	7.15721	−	12.3966i	0.295914	−	0.512538i
$586$	−1.46766	−	2.54207i	−0.0606286	−	0.105012i
$587$	−26.8734			−1.10918			−0.554592	−	0.832123i	$-0.687125\pi$
$587$	−26.8734			−1.10918			−0.554592	+	0.832123i	$0.687125\pi$
$588$	1.51389	−	6.83434i	0.0624318	−	0.281843i
$589$	4.00000			0.164817
$590$	−20.8638	−	36.1372i	−0.858950	−	1.48775i
$591$	10.1479	−	17.5766i	0.417428	−	0.723006i
$592$	1.22985	−	2.13016i	0.0505464	−	0.0875490i
$593$	13.4061	+	23.2201i	0.550523	+	0.953534i	0.998237	+	0.0593570i	$0.0189050\pi$
$593$	13.4061	+	23.2201i	0.550523	+	0.953534i	−0.447714	+	0.894177i	$0.647762\pi$
$594$	−3.31243			−0.135911
$595$	−0.255727	+	0.657771i	−0.0104838	+	0.0269660i
$596$	−3.85472			−0.157895
$597$	4.80348	+	8.31987i	0.196593	+	0.340510i
$598$	2.21596	−	3.83815i	0.0906172	−	0.156954i
$599$	15.6104	−	27.0379i	0.637822	−	1.10474i	−0.348087	−	0.937462i	$-0.613169\pi$
$599$	15.6104	−	27.0379i	0.637822	−	1.10474i	0.985910	−	0.167279i	$-0.0534979\pi$
$600$	2.71596	+	4.70418i	0.110879	+	0.192047i
$601$	−26.9194			−1.09806			−0.549032	−	0.835801i	$-0.685004\pi$
$601$	−26.9194			−1.09806			−0.549032	+	0.835801i	$0.685004\pi$
$602$	−5.22985	+	0.805416i	−0.213153	+	0.0328263i
$603$	−10.0937			−0.411046
$604$	2.79793	+	4.84616i	0.113846	+	0.197187i
$605$	−0.0448622	+	0.0777037i	−0.00182391	+	0.00315910i
$606$	4.71596	−	8.16828i	0.191573	−	0.331814i
$607$	−12.2576	−	21.2308i	−0.497522	−	0.861733i	0.502474	−	0.864592i	$-0.332423\pi$
$607$	−12.2576	−	21.2308i	−0.497522	−	0.861733i	−0.999996	+	0.00285928i	$0.999090\pi$
$608$	−2.00000			−0.0811107
$609$	−0.940871	−	1.17209i	−0.0381260	−	0.0474956i
$610$	15.7094			0.636056
$611$	16.8964	+	29.2654i	0.683555	+	1.18395i
$612$	−0.0412933	+	0.0715221i	−0.00166918	+	0.00289111i
$613$	−5.26120	+	9.11266i	−0.212498	+	0.368057i	−0.952496	−	0.304552i	$-0.901493\pi$
$613$	−5.26120	+	9.11266i	−0.212498	+	0.368057i	0.739998	+	0.672609i	$0.234826\pi$
$614$	2.97161	+	5.14698i	0.119924	+	0.207715i
$615$	27.3235			1.10179
$616$	5.48611	+	6.83434i	0.221042	+	0.275363i
$617$	46.1087			1.85627			0.928134	−	0.372247i	$-0.121413\pi$
$617$	46.1087			1.85627			0.928134	+	0.372247i	$0.121413\pi$
$618$	9.85032	+	17.0612i	0.396238	+	0.686304i
$619$	−1.29460	+	2.24231i	−0.0520343	+	0.0901261i	−0.890869	−	0.454260i	$-0.849904\pi$
$619$	−1.29460	+	2.24231i	−0.0520343	+	0.0901261i	0.838835	+	0.544386i	$0.183237\pi$
$620$	−3.22985	+	5.59426i	−0.129714	+	0.224671i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	19.6249			0.786886
$623$	−29.6102	+	4.56007i	−1.18631	+	0.182695i
$624$	−4.43192			−0.177419
$625$	11.3269	+	19.6188i	0.453077	+	0.784753i
$626$	−4.62487	+	8.01051i	−0.184847	+	0.320164i
$627$	−3.31243	+	5.73730i	−0.132286	+	0.229126i
$628$	−9.08813	−	15.7411i	−0.362656	−	0.628139i
$629$	−0.203138			−0.00809964
$630$	−3.09648	+	7.96462i	−0.123367	+	0.317318i
$631$	44.6200			1.77630			0.888148	−	0.459558i	$-0.151992\pi$
$631$	44.6200			1.77630			0.888148	+	0.459558i	$0.151992\pi$
$632$	−2.34378	−	4.05955i	−0.0932307	−	0.161480i
$633$	4.59648	−	7.96133i	0.182694	−	0.316434i
$634$	−15.9194	+	27.5732i	−0.632240	+	1.09507i
$635$	−21.5165	−	37.2676i	−0.853855	−	1.47892i
$636$	−14.0937			−0.558851
$637$	−22.8765	−	20.9551i	−0.906400	−	0.830273i
$638$	1.88174			0.0744989
$639$	−3.84933	−	6.66723i	−0.152277	−	0.263752i
$640$	1.61492	−	2.79713i	0.0638355	−	0.110566i
$641$	−11.3926	+	19.7326i	−0.449981	+	0.779389i	−0.998384	−	0.0568245i	$-0.981902\pi$
$641$	−11.3926	+	19.7326i	−0.449981	+	0.779389i	0.548404	+	0.836214i	$0.315236\pi$
$642$	7.31243	+	12.6655i	0.288599	+	0.499868i
$643$	−7.13617			−0.281423			−0.140712	−	0.990051i	$-0.544939\pi$
$643$	−7.13617			−0.281423			−0.140712	+	0.990051i	$0.544939\pi$
$644$	−0.958707	+	2.46594i	−0.0377783	+	0.0971718i
$645$	6.45970			0.254350
$646$	0.0825866	+	0.143044i	0.00324933	+	0.00562800i
$647$	1.25824	−	2.17933i	0.0494665	−	0.0856785i	−0.840232	−	0.542227i	$-0.817581\pi$
$647$	1.25824	−	2.17933i	0.0494665	−	0.0856785i	0.889698	+	0.456549i	$0.150915\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	21.3973	+	37.0612i	0.839918	+	1.45478i
$650$	24.0738			0.944252
$651$	−5.22985	+	0.805416i	−0.204974	+	0.0315667i
$652$	−5.26674			−0.206262
$653$	−6.24715	−	10.8204i	−0.244470	−	0.423434i	0.717513	−	0.696545i	$-0.245281\pi$
$653$	−6.24715	−	10.8204i	−0.244470	−	0.423434i	−0.961982	+	0.273111i	$0.911947\pi$
$654$	−3.00555	+	5.20576i	−0.117526	+	0.203561i
$655$	3.00797	−	5.20995i	0.117531	−	0.203570i
$656$	−4.22985	−	7.32631i	−0.165148	−	0.286044i
$657$	−3.86383			−0.150742
$658$	−12.6284	−	15.7319i	−0.492308	−	0.613294i
$659$	−15.8635			−0.617955			−0.308977	−	0.951069i	$-0.599987\pi$
$659$	−15.8635			−0.617955			−0.308977	+	0.951069i	$0.599987\pi$
$660$	−5.34933	−	9.26531i	−0.208222	−	0.360652i
$661$	−12.0901	+	20.9407i	−0.470251	+	0.814498i	−0.999421	−	0.0340173i	$-0.989170\pi$
$661$	−12.0901	+	20.9407i	−0.470251	+	0.814498i	0.529170	+	0.848516i	$0.322503\pi$
$662$	−14.5534	+	25.2072i	−0.565633	+	0.979705i
$663$	0.183008	+	0.316980i	0.00710746	+	0.0123105i
$664$	−0.165173			−0.00640996
$665$	10.6987	+	13.3279i	0.414876	+	0.516833i
$666$	−2.45970			−0.0953113
$667$	0.284042	+	0.491976i	0.0109982	+	0.0190494i
$668$	3.64787	−	6.31830i	0.141140	−	0.244462i
$669$	6.68954	−	11.5866i	0.258633	−	0.447965i
$670$	−16.3005	−	28.2333i	−0.629744	−	1.09075i
$671$	−16.1111			−0.621963
$672$	2.61492	−	0.402708i	0.100873	−	0.0155348i
$673$	51.4000			1.98133			0.990663	−	0.136333i	$-0.0435317\pi$
$673$	51.4000			1.98133			0.990663	+	0.136333i	$0.0435317\pi$
$674$	−2.56808	−	4.44805i	−0.0989189	−	0.171333i
$675$	2.71596	−	4.70418i	0.104537	−	0.181064i
$676$	−3.32094	+	5.75203i	−0.127728	+	0.221232i
$677$	−16.8559	−	29.1952i	−0.647823	−	1.12206i	−0.983642	−	0.180136i	$-0.942346\pi$
$677$	−16.8559	−	29.1952i	−0.647823	−	1.12206i	0.335818	−	0.941927i	$-0.390987\pi$
$678$	1.39502			0.0535755
$679$	−7.66965	+	19.7276i	−0.294334	+	0.757074i
$680$	−0.266742			−0.0102291
$681$	10.8035	+	18.7122i	0.413990	+	0.717052i
$682$	3.31243	−	5.73730i	0.126840	−	0.219693i
$683$	−17.1187	+	29.6504i	−0.655027	+	1.13454i	0.326860	+	0.945073i	$0.394010\pi$
$683$	−17.1187	+	29.6504i	−0.655027	+	1.13454i	−0.981887	+	0.189468i	$0.939324\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$	−45.9024			−1.75384
$686$	15.4017	+	10.2853i	0.588040	+	0.392694i
$687$	−27.2608			−1.04007
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−31.2310	+	54.0937i	−1.18981	+	2.06080i
$690$	1.61492	−	2.79713i	0.0614791	−	0.106485i
$691$	−13.2951	−	23.0278i	−0.505771	−	0.876021i	−0.999978	−	0.00667634i	$-0.997875\pi$
$691$	−13.2951	−	23.0278i	−0.505771	−	0.876021i	0.494207	−	0.869344i	$-0.335458\pi$
$692$	−19.5613			−0.743608
$693$	3.17565	−	8.16828i	0.120633	−	0.310287i
$694$	−16.0858			−0.610608
$695$	5.80902	+	10.0615i	0.220349	+	0.381655i
$696$	0.284042	−	0.491976i	0.0107666	−	0.0186483i
$697$	−0.349329	+	0.605055i	−0.0132318	+	0.0229181i
$698$	5.90352	+	10.2252i	0.223452	+	0.387030i
$699$	−9.24974			−0.349857
$700$	−14.2040	+	2.18747i	−0.536862	+	0.0826788i
$701$	−8.93533			−0.337483			−0.168741	−	0.985660i	$-0.553970\pi$
$701$	−8.93533			−0.337483			−0.168741	+	0.985660i	$0.553970\pi$
$702$	2.21596	+	3.83815i	0.0836359	+	0.144862i
$703$	−2.45970	+	4.26032i	−0.0927692	+	0.160681i
$704$	−1.65622	+	2.86865i	−0.0624210	+	0.108116i
$705$	12.3136	+	21.3277i	0.463756	+	0.803249i
$706$	32.4597			1.22164
$707$	15.6213	+	19.4603i	0.587499	+	0.731879i
$708$	12.9194			0.485540
$709$	4.14172	+	7.17366i	0.155545	+	0.269412i	0.933257	−	0.359208i	$-0.116953\pi$
$709$	4.14172	+	7.17366i	0.155545	+	0.269412i	−0.777712	+	0.628621i	$0.783620\pi$
$710$	12.4327	−	21.5341i	0.466593	−	0.808162i
$711$	−2.34378	+	4.05955i	−0.0878987	+	0.152245i
$712$	−5.66176	−	9.80646i	−0.212184	−	0.367513i
$713$	2.00000			0.0749006
$714$	−0.136781	−	0.170396i	−0.00511891	−	0.00637690i
$715$	−47.4155			−1.77324
$716$	−1.17906	−	2.04220i	−0.0440637	−	0.0763205i
$717$	−6.63337	+	11.4893i	−0.247728	+	0.429077i
$718$	−10.1473	+	17.5756i	−0.378692	+	0.655915i
$719$	21.0707	+	36.4955i	0.785804	+	1.36105i	0.928518	+	0.371288i	$0.121084\pi$
$719$	21.0707	+	36.4955i	0.785804	+	1.36105i	−0.142714	+	0.989764i	$0.545583\pi$
$720$	−3.22985			−0.120369
$721$	−51.5157	+	7.93360i	−1.91854	+	0.295463i
$722$	−15.0000			−0.558242
$723$	12.5423	+	21.7239i	0.466452	+	0.807919i
$724$	5.53674	−	9.58991i	0.205771	−	0.356406i
$725$	−1.54289	+	2.67237i	−0.0573016	+	0.0992493i
$726$	−0.0138899	−	0.0240580i	−0.000515502	−	0.000892876i
$727$	46.8789			1.73864			0.869321	−	0.494249i	$-0.164557\pi$
$727$	46.8789			1.73864			0.869321	+	0.494249i	$0.164557\pi$
$728$	4.24891	−	10.9289i	0.157475	−	0.405050i
$729$	1.00000			0.0370370
$730$	−6.23979	−	10.8076i	−0.230945	−	0.400009i
$731$	−0.0825866	+	0.143044i	−0.00305458	+	0.00529068i
$732$	−2.43192	+	4.21220i	−0.0898862	+	0.155687i
$733$	26.7777	+	46.3803i	0.989056	+	1.71310i	0.622302	+	0.782777i	$0.286198\pi$
$733$	26.7777	+	46.3803i	0.989056	+	1.71310i	0.366754	+	0.930318i	$0.380469\pi$
$734$	−19.3434			−0.713978
$735$	−16.6717	−	15.2715i	−0.614945	−	0.563297i
$736$	−1.00000			−0.0368605
$737$	16.7173	+	28.9553i	0.615790	+	1.06658i
$738$	−4.22985	+	7.32631i	−0.155703	+	0.269685i
$739$	6.39563	−	11.0776i	0.235267	−	0.407495i	−0.724083	−	0.689713i	$-0.757737\pi$
$739$	6.39563	−	11.0776i	0.235267	−	0.407495i	0.959350	+	0.282218i	$0.0910702\pi$
$740$	−3.97222	−	6.88009i	−0.146022	−	0.252917i
$741$	8.86383			0.325621
$742$	13.5117	−	34.7542i	0.496030	−	1.27587i
$743$	−10.6987			−0.392496			−0.196248	−	0.980554i	$-0.562876\pi$
$743$	−10.6987			−0.392496			−0.196248	+	0.980554i	$0.562876\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$	−6.22507	+	10.7821i	−0.228069	+	0.395027i
$746$	−8.40057	+	14.5502i	−0.307567	+	0.532721i
$747$	0.0825866	+	0.143044i	0.00302169	+	0.00523371i
$748$	0.273563			0.0100024
$749$	−38.2429	+	5.88955i	−1.39737	+	0.215199i
$750$	1.39502			0.0509390
$751$	15.9095	+	27.5561i	0.580547	+	1.00554i	0.995415	+	0.0956548i	$0.0304945\pi$
$751$	15.9095	+	27.5561i	0.580547	+	1.00554i	−0.414868	+	0.909882i	$0.636172\pi$
$752$	3.81243	−	6.60333i	0.139025	−	0.240799i
$753$	10.3549	−	17.9352i	0.377353	−	0.653594i
$754$	−1.25885	−	2.18039i	−0.0458447	−	0.0794053i
$755$	18.0738			0.657773
$756$	−1.65622	−	2.06324i	−0.0602360	−	0.0750392i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	5.64270	+	9.77345i	0.204952	+	0.354988i
$759$	−1.65622	+	2.86865i	−0.0601169	+	0.104125i
$760$	−3.22985	+	5.59426i	−0.117159	+	0.202925i
$761$	−6.74435	−	11.6816i	−0.244482	−	0.423456i	0.717504	−	0.696555i	$-0.245285\pi$
$761$	−6.74435	−	11.6816i	−0.244482	−	0.423456i	−0.961986	+	0.273099i	$0.911951\pi$
$762$	13.3235			0.482660
$763$	−9.95567	−	12.4023i	−0.360420	−	0.448994i
$764$	11.3235			0.409671
$765$	0.133371	+	0.231005i	0.00482204	+	0.00835202i
$766$	−13.2945	+	23.0268i	−0.480351	+	0.831992i
$767$	28.6288	−	49.5866i	1.03373	−	1.79047i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	52.9971			1.91113			0.955563	−	0.294788i	$-0.0952490\pi$
$769$	52.9971			1.91113			0.955563	+	0.294788i	$0.0952490\pi$
$770$	27.9762	−	4.30843i	1.00819	−	0.155265i
$771$	−29.0846			−1.04745
$772$	−6.24374	−	10.8145i	−0.224717	−	0.389221i
$773$	4.59824	−	7.96438i	0.165387	−	0.286459i	−0.771406	−	0.636344i	$-0.780446\pi$
$773$	4.59824	−	7.96438i	0.165387	−	0.286459i	0.936793	+	0.349885i	$0.113779\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	5.43192	+	9.40835i	0.195120	+	0.337958i
$776$	−8.00000			−0.287183
$777$	2.35813	−	6.06547i	0.0845973	−	0.217598i
$778$	7.56249			0.271128
$779$	8.45970	+	14.6526i	0.303100	+	0.524985i
$780$	−7.15721	+	12.3966i	−0.256269	+	0.443871i
$781$	−12.7506	+	22.0848i	−0.456254	+	0.790255i
$782$	0.0412933	+	0.0715221i	0.00147665	+	0.00255763i
$783$	−0.568085			−0.0203017
$784$	−1.51389	+	6.83434i	−0.0540675	+	0.244083i
$785$	−58.7066			−2.09533
$786$	0.931303	+	1.61306i	0.0332185	+	0.0575361i
$787$	9.46964	−	16.4019i	0.337556	−	0.584664i	−0.646416	−	0.762985i	$-0.723733\pi$
$787$	9.46964	−	16.4019i	0.337556	−	0.584664i	0.983972	+	0.178320i	$0.0570664\pi$
$788$	−10.1479	+	17.5766i	−0.361503	+	0.626142i
$789$	3.88052	+	6.72126i	0.138150	+	0.239283i
$790$	−15.1401			−0.538661
$791$	−1.33742	+	3.44004i	−0.0475530	+	0.122314i
$792$	3.31243			0.117702
$793$	10.7780	+	18.6681i	0.382740	+	0.662924i
$794$	7.73046	−	13.3895i	0.274344	−	0.475177i
$795$	−22.7602	+	39.4219i	−0.807222	+	1.39815i
$796$	−4.80348	−	8.31987i	−0.170255	−	0.294890i
$797$	−24.5175			−0.868456			−0.434228	−	0.900803i	$-0.642979\pi$
$797$	−24.5175			−0.868456			−0.434228	+	0.900803i	$0.642979\pi$
$798$	−5.22985	+	0.805416i	−0.185135	+	0.0285114i
$799$	−0.629712			−0.0222776
$800$	−2.71596	−	4.70418i	−0.0960236	−	0.166318i
$801$	−5.66176	+	9.80646i	−0.200049	+	0.346494i
$802$	−0.728859	+	1.26242i	−0.0257369	+	0.0445776i
$803$	6.39934	+	11.0840i	0.225828	+	0.391145i
$804$	10.0937			0.355977
$805$	5.34933	+	6.66394i	0.188539	+	0.234873i
$806$	−8.86383			−0.312215
$807$	−4.11098	−	7.12042i	−0.144713	−	0.250651i
$808$	−4.71596	+	8.16828i	−0.165907	+	0.287359i
$809$	9.06590	−	15.7026i	0.318740	−	0.552074i	−0.661485	−	0.749958i	$-0.730074\pi$
$809$	9.06590	−	15.7026i	0.318740	−	0.552074i	0.980225	+	0.197884i	$0.0634070\pi$
$810$	1.61492	+	2.79713i	0.0567426	+	0.0982811i
$811$	9.52330			0.334408			0.167204	−	0.985922i	$-0.446526\pi$
$811$	9.52330			0.334408			0.167204	+	0.985922i	$0.446526\pi$
$812$	0.940871	+	1.17209i	0.0330181	+	0.0411324i
$813$	−15.4887			−0.543212
$814$	4.07379	+	7.05601i	0.142786	+	0.247313i
$815$	−8.50539	+	14.7318i	−0.297931	+	0.516031i
$816$	0.0412933	−	0.0715221i	0.00144555	−	0.00250377i
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	−4.26797			−0.149226
$819$	−11.5891	+	1.78477i	−0.404957	+	0.0623648i
$820$	−27.3235			−0.954179
$821$	−14.3039	−	24.7751i	−0.499211	−	0.864658i	0.500789	−	0.865569i	$-0.333043\pi$
$821$	−14.3039	−	24.7751i	−0.499211	−	0.864658i	−1.00000		0.000911223i	$0.999710\pi$
$822$	7.10597	−	12.3079i	0.247849	−	0.429287i
$823$	−19.5713	+	33.8985i	−0.682212	+	1.18163i	0.292092	+	0.956390i	$0.405649\pi$
$823$	−19.5713	+	33.8985i	−0.682212	+	1.18163i	−0.974304	+	0.225236i	$0.927685\pi$
$824$	−9.85032	−	17.0612i	−0.343152	−	0.594357i
$825$	−17.9929			−0.626431
$826$	−12.3859	+	31.8585i	−0.430961	+	1.10850i
$827$	−37.6625			−1.30965			−0.654827	−	0.755779i	$-0.727259\pi$
$827$	−37.6625			−1.30965			−0.654827	+	0.755779i	$0.727259\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	6.27152	−	10.8626i	0.217819	−	0.377273i	−0.736322	−	0.676631i	$-0.763439\pi$
$829$	6.27152	−	10.8626i	0.217819	−	0.377273i	0.954141	+	0.299358i	$0.0967725\pi$
$830$	−0.266742	+	0.462011i	−0.00925876	+	0.0160366i
$831$	−12.7582	−	22.0979i	−0.442578	−	0.766568i
$832$	4.43192			0.153649
$833$	0.551320	−	0.173936i	0.0191021	−	0.00602651i
$834$	−3.59709			−0.124557
$835$	−11.7821	−	20.4072i	−0.407735	−	0.706219i
$836$	3.31243	−	5.73730i	0.114563	−	0.198429i
$837$	−1.00000	+	1.73205i	−0.0345651	+	0.0598684i
$838$	11.5847	+	20.0653i	0.400188	+	0.693145i
$839$	29.5084			1.01874			0.509372	−	0.860546i	$-0.329878\pi$
$839$	29.5084			1.01874			0.509372	+	0.860546i	$0.329878\pi$
$840$	3.09648	−	7.96462i	0.106839	−	0.274806i
$841$	−28.6773			−0.988872
$842$	−16.6562	−	28.8494i	−0.574011	−	0.994216i
$843$	−15.5578	+	26.9469i	−0.535838	+	0.928099i
$844$	−4.59648	+	7.96133i	−0.158217	+	0.274040i
$845$	10.7261	+	18.5782i	0.368990	+	0.639109i
$846$	−7.62487			−0.262148
$847$	0.0726420	−	0.0111871i	0.00249601	−	0.000384395i
$848$	14.0937			0.483979
$849$	9.76218	+	16.9086i	0.335037	+	0.580302i
$850$	−0.224302	+	0.388502i	−0.00769349	+	0.0133255i
$851$	−1.22985	+	2.13016i	−0.0421586	+	0.0730209i
$852$	3.84933	+	6.66723i	0.131876	+	0.228416i
$853$	−18.8280			−0.644659			−0.322329	−	0.946628i	$-0.604466\pi$
$853$	−18.8280			−0.644659			−0.322329	+	0.946628i	$0.604466\pi$
$854$	−8.05556	−	10.0352i	−0.275656	−	0.343399i
$855$	6.45970			0.220917
$856$	−7.31243	−	12.6655i	−0.249934	−	0.432898i
$857$	−5.28465	+	9.15329i	−0.180520	+	0.312670i	−0.942058	−	0.335450i	$-0.891112\pi$
$857$	−5.28465	+	9.15329i	−0.180520	+	0.312670i	0.761538	+	0.648121i	$0.224445\pi$
$858$	7.34021	−	12.7136i	0.250591	−	0.434036i
$859$	3.20146	+	5.54508i	0.109232	+	0.189196i	0.915459	−	0.402410i	$-0.131827\pi$
$859$	3.20146	+	5.54508i	0.109232	+	0.189196i	−0.806227	+	0.591606i	$0.798494\pi$
$860$	−6.45970			−0.220274
$861$	−14.0111	−	17.4544i	−0.477497	−	0.594843i
$862$	−9.72521			−0.331242
$863$	7.64726	+	13.2454i	0.260316	+	0.450880i	0.966326	−	0.257322i	$-0.0828400\pi$
$863$	7.64726	+	13.2454i	0.260316	+	0.450880i	−0.706010	+	0.708202i	$0.749507\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−31.5900	+	54.7154i	−1.07409	+	1.86038i
$866$	12.3692	+	21.4241i	0.420323	+	0.728021i
$867$	16.9932			0.577119
$868$	5.22985	−	0.805416i	0.177513	−	0.0273376i
$869$	15.5273			0.526726
$870$	−0.917413	−	1.58901i	−0.0311032	−	0.0538724i
$871$	22.3672	−	38.7411i	0.757882	−	1.31269i
$872$	3.00555	−	5.20576i	0.101781	−	0.176289i
$873$	4.00000	+	6.92820i	0.135379	+	0.234484i
$874$	2.00000			0.0676510
$875$	−1.33742	+	3.44004i	−0.0452129	+	0.116295i
$876$	3.86383			0.130547
$877$	2.84994	+	4.93624i	0.0962357	+	0.166685i	0.910124	−	0.414337i	$-0.135986\pi$
$877$	2.84994	+	4.93624i	0.0962357	+	0.166685i	−0.813888	+	0.581022i	$0.802653\pi$
$878$	15.6360	−	27.0823i	0.527688	−	0.913983i
$879$	1.46766	−	2.54207i	0.0495030	−	0.0857418i
$880$	5.34933	+	9.26531i	0.180326	+	0.312334i
$881$	−1.27676			−0.0430153			−0.0215076	−	0.999769i	$-0.506847\pi$
$881$	−1.27676			−0.0430153			−0.0215076	+	0.999769i	$0.506847\pi$
$882$	6.67565	−	2.10610i	0.224781	−	0.0709161i
$883$	−33.0305			−1.11157			−0.555783	−	0.831328i	$-0.687581\pi$
$883$	−33.0305			−1.11157			−0.555783	+	0.831328i	$0.687581\pi$
$884$	−0.183008	−	0.316980i	−0.00615524	−	0.0106612i
$885$	20.8638	−	36.1372i	0.701330	−	1.21474i
$886$	16.4478	−	28.4884i	0.552574	−	0.957086i
$887$	−20.9109	−	36.2187i	−0.702119	−	1.21611i	−0.967721	−	0.252023i	$-0.918904\pi$
$887$	−20.9109	−	36.2187i	−0.702119	−	1.21611i	0.265602	−	0.964083i	$-0.414429\pi$
$888$	2.45970			0.0825420
$889$	−12.7734	+	32.8551i	−0.428405	+	1.10192i
$890$	−36.5733			−1.22594
$891$	−1.65622	−	2.86865i	−0.0554854	−	0.0961035i
$892$	−6.68954	+	11.5866i	−0.223982	+	0.387949i
$893$	−7.62487	+	13.2067i	−0.255156	+	0.441944i
$894$	−1.92736	−	3.33828i	−0.0644605	−	0.111649i
$895$	−7.61639			−0.254588
$896$	−2.61492	+	0.402708i	−0.0873585	+	0.0134535i
$897$	4.43192			0.147977
$898$	−2.94519	−	5.10122i	−0.0982824	−	0.170230i
$899$	0.568085	−	0.983951i	0.0189467	−	0.0328166i
$900$	−2.71596	+	4.70418i	−0.0905319	+	0.156806i
$901$	−0.581975	−	1.00801i	−0.0193884	−	0.0335817i
$902$	28.0222			0.933037
$903$	−3.31243	−	4.12647i	−0.110231	−	0.137320i
$904$	−1.39502			−0.0463977
$905$	−17.8828	−	30.9739i	−0.594445	−	1.02961i
$906$	−2.79793	+	4.84616i	−0.0929551	+	0.161003i
$907$	6.07264	−	10.5181i	0.201639	−	0.349249i	−0.747418	−	0.664354i	$-0.768707\pi$
$907$	6.07264	−	10.5181i	0.201639	−	0.349249i	0.949057	+	0.315106i	$0.102040\pi$
$908$	−10.8035	−	18.7122i	−0.358526	−	0.620985i
$909$	9.43192			0.312837
$910$	−23.7078	−	29.5340i	−0.785905	−	0.979043i
$911$	5.05119			0.167353			0.0836767	−	0.996493i	$-0.473334\pi$
$911$	5.05119			0.167353			0.0836767	+	0.996493i	$0.473334\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	0.273563	−	0.473824i	0.00905360	−	0.0156813i
$914$	10.4597	−	18.1167i	0.345976	−	0.599248i
$915$	7.85472	+	13.6048i	0.259669	+	0.449760i
$916$	27.2608			0.900723
$917$	−4.87057	+	0.750086i	−0.160841	+	0.0247700i
$918$	−0.0825866			−0.00272576
$919$	3.75664	+	6.50669i	0.123920	+	0.214636i	0.921310	−	0.388828i	$-0.127120\pi$
$919$	3.75664	+	6.50669i	0.123920	+	0.214636i	−0.797390	+	0.603464i	$0.793787\pi$
$920$	−1.61492	+	2.79713i	−0.0532425	+	0.0922186i
$921$	−2.97161	+	5.14698i	−0.0979178	+	0.169599i
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	34.1198			1.12307
$924$	−3.17565	+	8.16828i	−0.104471	+	0.268717i
$925$	−13.3609			−0.439302
$926$	−6.86383	−	11.8885i	−0.225559	−	0.390680i
$927$	−9.85032	+	17.0612i	−0.323527	+	0.560365i
$928$	−0.284042	+	0.491976i	−0.00932415	+	0.0161499i
$929$	−18.5622	−	32.1506i	−0.609005	−	1.05483i	−0.991405	−	0.130831i	$-0.958236\pi$
$929$	−18.5622	−	32.1506i	−0.609005	−	1.05483i	0.382400	−	0.923997i	$-0.375098\pi$
$930$	−6.45970			−0.211822
$931$	3.02778	−	13.6687i	0.0992315	−	0.447973i
$932$	9.24974			0.302985
$933$	9.81243	+	16.9956i	0.321245	+	0.556412i
$934$	0.940871	−	1.62964i	0.0307863	−	0.0533234i
$935$	0.441783	−	0.765190i	0.0144478	−	0.0250244i
$936$	−2.21596	−	3.83815i	−0.0724308	−	0.125454i
$937$	−18.6288			−0.608577			−0.304289	−	0.952580i	$-0.598419\pi$
$937$	−18.6288			−0.608577			−0.304289	+	0.952580i	$0.598419\pi$
$938$	−9.67688	+	24.8904i	−0.315961	+	0.812702i
$939$	−9.24974			−0.301854
$940$	−12.3136	−	21.3277i	−0.401625	−	0.695634i
$941$	21.3882	−	37.0454i	0.697235	−	1.20765i	−0.272186	−	0.962245i	$-0.587747\pi$
$941$	21.3882	−	37.0454i	0.697235	−	1.20765i	0.969421	−	0.245402i	$-0.0789201\pi$
$942$	9.08813	−	15.7411i	0.296107	−	0.512873i
$943$	4.22985	+	7.32631i	0.137743	+	0.238578i
$944$	−12.9194			−0.420490
$945$	−8.44581	+	1.30068i	−0.274742	+	0.0423113i
$946$	6.62487			0.215393
$947$	−25.1095	−	43.4910i	−0.815951	−	1.41327i	−0.908643	−	0.417573i	$-0.862881\pi$
$947$	−25.1095	−	43.4910i	−0.815951	−	1.41327i	0.0926928	−	0.995695i	$-0.470453\pi$
$948$	2.34378	−	4.05955i	0.0761225	−	0.131848i
$949$	8.56209	−	14.8300i	0.277937	−	0.481401i
$950$	5.43192	+	9.40835i	0.176235	+	0.305247i
$951$	−31.8388			−1.03244
$952$	0.136781	+	0.170396i	0.00443311	+	0.00552256i
$953$	−4.96631			−0.160874			−0.0804372	−	0.996760i	$-0.525632\pi$
$953$	−4.96631			−0.160874			−0.0804372	+	0.996760i	$0.525632\pi$
$954$	−7.04684	−	12.2055i	−0.228150	−	0.395167i
$955$	18.2866	−	31.6734i	0.591741	−	1.02493i
$956$	6.63337	−	11.4893i	0.214539	−	0.371592i
$957$	0.940871	+	1.62964i	0.0304141	+	0.0526787i
$958$	29.7094			0.959868
$959$	23.5381	+	29.3226i	0.760083	+	0.946876i
$960$	3.22985			0.104243
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	5.45058	−	9.44068i	0.175734	−	0.304380i
$963$	−7.31243	+	12.6655i	−0.235640	+	0.408140i
$964$	−12.5423	−	21.7239i	−0.403960	−	0.699679i
$965$	−40.3326			−1.29835
$966$	−2.61492	+	0.402708i	−0.0841338	+	0.0129569i
$967$	57.8649			1.86081			0.930405	−	0.366533i	$-0.119455\pi$
$967$	57.8649			1.86081			0.930405	+	0.366533i	$0.119455\pi$
$968$	0.0138899	+	0.0240580i	0.000446438	+	0.000773253i
$969$	−0.0825866	+	0.143044i	−0.00265306	+	0.00459524i
$970$	−12.9194	+	22.3770i	−0.414817	+	0.718483i
$971$	23.0075	+	39.8502i	0.738347	+	1.27885i	0.953239	+	0.302216i	$0.0977264\pi$
$971$	23.0075	+	39.8502i	0.738347	+	1.27885i	−0.214893	+	0.976638i	$0.568940\pi$
$972$	−1.00000			−0.0320750
$973$	3.44855	−	8.87022i	0.110556	−	0.284366i
$974$	−19.8904			−0.637329
$975$	12.0369	+	20.8485i	0.385489	+	0.667687i
$976$	2.43192	−	4.21220i	0.0778437	−	0.134829i
$977$	4.26560	−	7.38823i	0.136468	−	0.236370i	−0.789689	−	0.613507i	$-0.789758\pi$
$977$	4.26560	−	7.38823i	0.136468	−	0.236370i	0.926157	+	0.377137i	$0.123091\pi$
$978$	−2.63337	−	4.56113i	−0.0842059	−	0.145849i
$979$	37.5084			1.19877
$980$	16.6717	+	15.2715i	0.532558	+	0.487829i
$981$	−6.01109			−0.191919
$982$	−0.491497	−	0.851298i	−0.0156843	−	0.0271660i
$983$	19.7979	−	34.2910i	0.631456	−	1.09371i	−0.355798	−	0.934563i	$-0.615791\pi$
$983$	19.7979	−	34.2910i	0.631456	−	1.09371i	0.987254	−	0.159151i	$-0.0508757\pi$
$984$	4.22985	−	7.32631i	0.134843	−	0.233554i
$985$	32.7761	+	56.7698i	1.04433	+	1.80884i
$986$	0.0469162			0.00149412
$987$	7.31001	−	18.8025i	0.232680	−	0.598490i
$988$	−8.86383			−0.281996
$989$	1.00000	+	1.73205i	0.0317982	+	0.0550760i
$990$	5.34933	−	9.26531i	0.170013	−	0.294471i
$991$	−1.06270	+	1.84065i	−0.0337577	+	0.0584700i	−0.882411	−	0.470480i	$-0.844081\pi$
$991$	−1.06270	+	1.84065i	−0.0337577	+	0.0584700i	0.848653	+	0.528950i	$0.177414\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$	−29.1067			−0.923675
$994$	−20.1314	+	3.10031i	−0.638529	+	0.0983358i
$995$	−31.0290			−0.983686
$996$	−0.0825866	−	0.143044i	−0.00261686	−	0.00453253i
$997$	5.22196	−	9.04469i	0.165381	−	0.286448i	−0.771409	−	0.636339i	$-0.780448\pi$
$997$	5.22196	−	9.04469i	0.165381	−	0.286448i	0.936791	+	0.349891i	$0.113781\pi$
$998$	1.76165	−	3.05127i	0.0557640	−	0.0965862i
$999$	−1.22985	−	2.13016i	−0.0389107	−	0.0673952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.m.277.4	✓	8
7.2	even	3	inner	966.2.i.m.415.4	yes	8
7.3	odd	6		6762.2.a.cr.1.4		4
7.4	even	3		6762.2.a.cl.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.4	✓	8	1.1	even	1	trivial
966.2.i.m.415.4	yes	8	7.2	even	3	inner
6762.2.a.cl.1.1		4	7.4	even	3
6762.2.a.cr.1.4		4	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.61492 + 2.79713i) q^{5} -1.00000 q^{6} +(0.958707 - 2.46594i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.61492 + 2.79713i) q^{5} -1.00000 q^{6} +(0.958707 - 2.46594i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.61492 - 2.79713i) q^{10} +(-1.65622 + 2.86865i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.43192 q^{13} +(-2.61492 + 0.402708i) q^{14} +3.22985 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0412933 + 0.0715221i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} -3.22985 q^{20} +(-1.65622 - 2.06324i) q^{21} +3.31243 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.71596 + 4.70418i) q^{25} +(-2.21596 - 3.83815i) q^{26} -1.00000 q^{27} +(1.65622 + 2.06324i) q^{28} +0.568085 q^{29} +(-1.61492 - 2.79713i) q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.65622 + 2.86865i) q^{33} +0.0825866 q^{34} +(8.44581 - 1.30068i) q^{35} +1.00000 q^{36} +(1.22985 + 2.13016i) q^{37} +(1.00000 - 1.73205i) q^{38} +(2.21596 - 3.83815i) q^{39} +(1.61492 + 2.79713i) q^{40} +8.45970 q^{41} +(-0.958707 + 2.46594i) q^{42} +2.00000 q^{43} +(-1.65622 - 2.86865i) q^{44} +(1.61492 - 2.79713i) q^{45} +(0.500000 - 0.866025i) q^{46} +(3.81243 + 6.60333i) q^{47} -1.00000 q^{48} +(-5.16176 - 4.72823i) q^{49} +5.43192 q^{50} +(0.0412933 + 0.0715221i) q^{51} +(-2.21596 + 3.83815i) q^{52} +(-7.04684 + 12.2055i) q^{53} +(0.500000 + 0.866025i) q^{54} -10.6987 q^{55} +(0.958707 - 2.46594i) q^{56} +2.00000 q^{57} +(-0.284042 - 0.491976i) q^{58} +(6.45970 - 11.1885i) q^{59} +(-1.61492 + 2.79713i) q^{60} +(2.43192 + 4.21220i) q^{61} -2.00000 q^{62} +(-2.61492 + 0.402708i) q^{63} +1.00000 q^{64} +(7.15721 + 12.3966i) q^{65} +(1.65622 - 2.86865i) q^{66} +(5.04684 - 8.74138i) q^{67} +(-0.0412933 - 0.0715221i) q^{68} +1.00000 q^{69} +(-5.34933 - 6.66394i) q^{70} +7.69866 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.93192 - 3.34618i) q^{73} +(1.22985 - 2.13016i) q^{74} +(2.71596 + 4.70418i) q^{75} -2.00000 q^{76} +(5.48611 + 6.83434i) q^{77} -4.43192 q^{78} +(-2.34378 - 4.05955i) q^{79} +(1.61492 - 2.79713i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.22985 - 7.32631i) q^{82} -0.165173 q^{83} +(2.61492 - 0.402708i) q^{84} -0.266742 q^{85} +(-1.00000 - 1.73205i) q^{86} +(0.284042 - 0.491976i) q^{87} +(-1.65622 + 2.86865i) q^{88} +(-5.66176 - 9.80646i) q^{89} -3.22985 q^{90} +(4.24891 - 10.9289i) q^{91} -1.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(3.81243 - 6.60333i) q^{94} +(-3.22985 + 5.59426i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(-1.51389 + 6.83434i) q^{98} +3.31243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{12} + 12 q^{13} - 6 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 4 q^{20} + 4 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 28 q^{29} + 2 q^{30} + 8 q^{31} - 4 q^{32} + 4 q^{34} + 26 q^{35} + 8 q^{36} - 20 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 2 q^{45} + 4 q^{46} + 4 q^{47} - 8 q^{48} + 12 q^{49} + 20 q^{50} + 2 q^{51} - 6 q^{52} - 18 q^{53} + 4 q^{54} - 32 q^{55} + 6 q^{56} + 16 q^{57} - 14 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 16 q^{62} - 6 q^{63} + 8 q^{64} - 14 q^{65} + 2 q^{67} - 2 q^{68} + 8 q^{69} - 16 q^{70} + 8 q^{71} - 4 q^{72} - 8 q^{73} - 20 q^{74} + 10 q^{75} - 16 q^{76} + 62 q^{77} - 12 q^{78} - 32 q^{79} - 2 q^{80} - 4 q^{81} - 4 q^{82} - 8 q^{83} + 6 q^{84} + 28 q^{85} - 8 q^{86} + 14 q^{87} + 8 q^{89} + 4 q^{90} + 2 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{95} + 4 q^{96} - 64 q^{97} + 6 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^12 + 12 * q^13 - 6 * q^14 - 4 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 28 * q^29 + 2 * q^30 + 8 * q^31 - 4 * q^32 + 4 * q^34 + 26 * q^35 + 8 * q^36 - 20 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 8 * q^48 + 12 * q^49 + 20 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 4 * q^54 - 32 * q^55 + 6 * q^56 + 16 * q^57 - 14 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 16 * q^62 - 6 * q^63 + 8 * q^64 - 14 * q^65 + 2 * q^67 - 2 * q^68 + 8 * q^69 - 16 * q^70 + 8 * q^71 - 4 * q^72 - 8 * q^73 - 20 * q^74 + 10 * q^75 - 16 * q^76 + 62 * q^77 - 12 * q^78 - 32 * q^79 - 2 * q^80 - 4 * q^81 - 4 * q^82 - 8 * q^83 + 6 * q^84 + 28 * q^85 - 8 * q^86 + 14 * q^87 + 8 * q^89 + 4 * q^90 + 2 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 + 4 * q^95 + 4 * q^96 - 64 * q^97 + 6 * q^98

Introduction

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