LMFDB - Embedded newform 966.2.i.i.277.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.i.415.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28078 + 2.21837i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28078 + 2.21837i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.28078 + 2.21837i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} -3.12311 q^{13} +(-2.00000 + 1.73205i) q^{14} -2.56155 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.34233 - 4.05703i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.56155 + 2.70469i) q^{19} -2.56155 q^{20} +(-2.50000 - 0.866025i) q^{21} -3.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.780776 + 1.35234i) q^{25} +(-1.56155 - 2.70469i) q^{26} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} +0.123106 q^{29} +(-1.28078 - 2.21837i) q^{30} +(0.842329 - 1.45896i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +4.68466 q^{34} +(-5.12311 + 4.43674i) q^{35} +1.00000 q^{36} +(-0.438447 - 0.759413i) q^{37} +(-1.56155 + 2.70469i) q^{38} +(1.56155 - 2.70469i) q^{39} +(-1.28078 - 2.21837i) q^{40} -7.12311 q^{41} +(-0.500000 - 2.59808i) q^{42} +12.2462 q^{43} +(-1.50000 - 2.59808i) q^{44} +(1.28078 - 2.21837i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(0.219224 + 0.379706i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -1.56155 q^{50} +(2.34233 + 4.05703i) q^{51} +(1.56155 - 2.70469i) q^{52} +(0.280776 - 0.486319i) q^{53} +(0.500000 + 0.866025i) q^{54} -7.68466 q^{55} +(-0.500000 - 2.59808i) q^{56} -3.12311 q^{57} +(0.0615528 + 0.106613i) q^{58} +(-0.719224 + 1.24573i) q^{59} +(1.28078 - 2.21837i) q^{60} +(1.00000 + 1.73205i) q^{61} +1.68466 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(1.50000 - 2.59808i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.34233 + 4.05703i) q^{68} -1.00000 q^{69} +(-6.40388 - 2.21837i) q^{70} +0.438447 q^{71} +(0.500000 + 0.866025i) q^{72} +(-8.46543 + 14.6626i) q^{73} +(0.438447 - 0.759413i) q^{74} +(-0.780776 - 1.35234i) q^{75} -3.12311 q^{76} +(-7.50000 - 2.59808i) q^{77} +3.12311 q^{78} +(-6.18466 - 10.7121i) q^{79} +(1.28078 - 2.21837i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.56155 - 6.16879i) q^{82} -6.56155 q^{83} +(2.00000 - 1.73205i) q^{84} +12.0000 q^{85} +(6.12311 + 10.6055i) q^{86} +(-0.0615528 + 0.106613i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-4.12311 - 7.14143i) q^{89} +2.56155 q^{90} +(-1.56155 - 8.11407i) q^{91} -1.00000 q^{92} +(0.842329 + 1.45896i) q^{93} +(-0.219224 + 0.379706i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} +11.6847 q^{97} +(-5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9} - q^{10} - 6 q^{11} - 2 q^{12} + 4 q^{13} - 8 q^{14} - 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 10 q^{21} - 12 q^{22} + 2 q^{23} + 2 q^{24} + q^{25} + 2 q^{26} + 4 q^{27} - 10 q^{28} - 16 q^{29} - q^{30} - 9 q^{31} + 2 q^{32} - 6 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 10 q^{37} + 2 q^{38} - 2 q^{39} - q^{40} - 12 q^{41} - 2 q^{42} + 16 q^{43} - 6 q^{44} + q^{45} - 2 q^{46} + 5 q^{47} + 4 q^{48} - 26 q^{49} + 2 q^{50} - 3 q^{51} - 2 q^{52} - 3 q^{53} + 2 q^{54} - 6 q^{55} - 2 q^{56} + 4 q^{57} - 8 q^{58} - 7 q^{59} + q^{60} + 4 q^{61} - 18 q^{62} + 8 q^{63} + 4 q^{64} - 16 q^{65} + 6 q^{66} + 4 q^{67} - 3 q^{68} - 4 q^{69} - 5 q^{70} + 10 q^{71} + 2 q^{72} - 5 q^{73} + 10 q^{74} + q^{75} + 4 q^{76} - 30 q^{77} - 4 q^{78} + q^{80} - 2 q^{81} - 6 q^{82} - 18 q^{83} + 8 q^{84} + 48 q^{85} + 8 q^{86} + 8 q^{87} + 6 q^{88} + 2 q^{90} + 2 q^{91} - 4 q^{92} - 9 q^{93} - 5 q^{94} - 16 q^{95} + 2 q^{96} + 22 q^{97} - 22 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9 - q^10 - 6 * q^11 - 2 * q^12 + 4 * q^13 - 8 * q^14 - 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 10 * q^21 - 12 * q^22 + 2 * q^23 + 2 * q^24 + q^25 + 2 * q^26 + 4 * q^27 - 10 * q^28 - 16 * q^29 - q^30 - 9 * q^31 + 2 * q^32 - 6 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 10 * q^37 + 2 * q^38 - 2 * q^39 - q^40 - 12 * q^41 - 2 * q^42 + 16 * q^43 - 6 * q^44 + q^45 - 2 * q^46 + 5 * q^47 + 4 * q^48 - 26 * q^49 + 2 * q^50 - 3 * q^51 - 2 * q^52 - 3 * q^53 + 2 * q^54 - 6 * q^55 - 2 * q^56 + 4 * q^57 - 8 * q^58 - 7 * q^59 + q^60 + 4 * q^61 - 18 * q^62 + 8 * q^63 + 4 * q^64 - 16 * q^65 + 6 * q^66 + 4 * q^67 - 3 * q^68 - 4 * q^69 - 5 * q^70 + 10 * q^71 + 2 * q^72 - 5 * q^73 + 10 * q^74 + q^75 + 4 * q^76 - 30 * q^77 - 4 * q^78 + q^80 - 2 * q^81 - 6 * q^82 - 18 * q^83 + 8 * q^84 + 48 * q^85 + 8 * q^86 + 8 * q^87 + 6 * q^88 + 2 * q^90 + 2 * q^91 - 4 * q^92 - 9 * q^93 - 5 * q^94 - 16 * q^95 + 2 * q^96 + 22 * q^97 - 22 * q^98 + 12 * q^99

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
$5$	1.28078	+	2.21837i	0.572781	+	0.992085i	0.996279	+	0.0861882i	$0.0274686\pi$
$5$	1.28078	+	2.21837i	0.572781	+	0.992085i	−0.423498	+	0.905897i	$0.639198\pi$
$6$	−1.00000			−0.408248
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.28078	+	2.21837i	−0.405017	+	0.701510i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−3.12311			−0.866194			−0.433097	−	0.901347i	$-0.642579\pi$
$13$	−3.12311			−0.866194			−0.433097	+	0.901347i	$0.642579\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$	−2.56155			−0.661390
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.34233	−	4.05703i	0.568098	−	0.983975i	−0.428656	−	0.903468i	$-0.641013\pi$
$17$	2.34233	−	4.05703i	0.568098	−	0.983975i	0.996754	−	0.0805072i	$-0.0256540\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	1.56155	+	2.70469i	0.358245	+	0.620498i	0.987668	−	0.156565i	$-0.0500420\pi$
$19$	1.56155	+	2.70469i	0.358245	+	0.620498i	−0.629423	+	0.777063i	$0.716709\pi$
$20$	−2.56155			−0.572781
$21$	−2.50000	−	0.866025i	−0.545545	−	0.188982i
$22$	−3.00000			−0.639602
$23$	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
$25$	−0.780776	+	1.35234i	−0.156155	+	0.270469i
$26$	−1.56155	−	2.70469i	−0.306246	−	0.530433i
$27$	1.00000			0.192450
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	0.123106			0.0228601			0.0114301	−	0.999935i	$-0.496362\pi$
$29$	0.123106			0.0228601			0.0114301	+	0.999935i	$0.496362\pi$
$30$	−1.28078	−	2.21837i	−0.233837	−	0.405017i
$31$	0.842329	−	1.45896i	0.151287	−	0.262036i	−0.780414	−	0.625263i	$-0.784992\pi$
$31$	0.842329	−	1.45896i	0.151287	−	0.262036i	0.931701	+	0.363227i	$0.118325\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	4.68466			0.803412
$35$	−5.12311	+	4.43674i	−0.865963	+	0.749946i
$36$	1.00000			0.166667
$37$	−0.438447	−	0.759413i	−0.0720803	−	0.124847i	0.827733	−	0.561123i	$-0.189630\pi$
$37$	−0.438447	−	0.759413i	−0.0720803	−	0.124847i	−0.899813	+	0.436276i	$0.856297\pi$
$38$	−1.56155	+	2.70469i	−0.253317	+	0.438758i
$39$	1.56155	−	2.70469i	0.250049	−	0.433097i
$40$	−1.28078	−	2.21837i	−0.202509	−	0.350755i
$41$	−7.12311			−1.11244			−0.556221	−	0.831034i	$-0.687749\pi$
$41$	−7.12311			−1.11244			−0.556221	+	0.831034i	$0.687749\pi$
$42$	−0.500000	−	2.59808i	−0.0771517	−	0.400892i
$43$	12.2462			1.86753			0.933765	−	0.357887i	$-0.116503\pi$
$43$	12.2462			1.86753			0.933765	+	0.357887i	$0.116503\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	1.28078	−	2.21837i	0.190927	−	0.330695i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	0.219224	+	0.379706i	0.0319770	+	0.0553859i	0.881571	−	0.472051i	$-0.156486\pi$
$47$	0.219224	+	0.379706i	0.0319770	+	0.0553859i	−0.849594	+	0.527437i	$0.823153\pi$
$48$	1.00000			0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−1.56155			−0.220837
$51$	2.34233	+	4.05703i	0.327992	+	0.568098i
$52$	1.56155	−	2.70469i	0.216548	−	0.375073i
$53$	0.280776	−	0.486319i	0.0385676	−	0.0668011i	−0.846097	−	0.533029i	$-0.821054\pi$
$53$	0.280776	−	0.486319i	0.0385676	−	0.0668011i	0.884665	+	0.466227i	$0.154387\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−7.68466			−1.03620
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$	−3.12311			−0.413665
$58$	0.0615528	+	0.106613i	0.00808228	+	0.0139989i
$59$	−0.719224	+	1.24573i	−0.0936349	+	0.162180i	−0.909038	−	0.416713i	$-0.863182\pi$
$59$	−0.719224	+	1.24573i	−0.0936349	+	0.162180i	0.815403	+	0.578894i	$0.196515\pi$
$60$	1.28078	−	2.21837i	0.165348	−	0.286390i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	1.68466			0.213952
$63$	2.00000	−	1.73205i	0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$	−4.00000	−	6.92820i	−0.496139	−	0.859338i
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.34233	+	4.05703i	0.284049	+	0.491988i
$69$	−1.00000			−0.120386
$70$	−6.40388	−	2.21837i	−0.765410	−	0.265146i
$71$	0.438447			0.0520341			0.0260171	−	0.999661i	$-0.491718\pi$
$71$	0.438447			0.0520341			0.0260171	+	0.999661i	$0.491718\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−8.46543	+	14.6626i	−0.990804	+	1.71612i	−0.378226	+	0.925713i	$0.623466\pi$
$73$	−8.46543	+	14.6626i	−0.990804	+	1.71612i	−0.612578	+	0.790410i	$0.709868\pi$
$74$	0.438447	−	0.759413i	0.0509685	−	0.0882799i
$75$	−0.780776	−	1.35234i	−0.0901563	−	0.156155i
$76$	−3.12311			−0.358245
$77$	−7.50000	−	2.59808i	−0.854704	−	0.296078i
$78$	3.12311			0.353622
$79$	−6.18466	−	10.7121i	−0.695828	−	1.20521i	−0.969901	−	0.243501i	$-0.921704\pi$
$79$	−6.18466	−	10.7121i	−0.695828	−	1.20521i	0.274072	−	0.961709i	$-0.411629\pi$
$80$	1.28078	−	2.21837i	0.143195	−	0.248021i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.56155	−	6.16879i	−0.393308	−	0.681229i
$83$	−6.56155			−0.720224			−0.360112	−	0.932909i	$-0.617262\pi$
$83$	−6.56155			−0.720224			−0.360112	+	0.932909i	$0.617262\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$	12.0000			1.30158
$86$	6.12311	+	10.6055i	0.660271	+	1.14362i
$87$	−0.0615528	+	0.106613i	−0.00659915	+	0.0114301i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−4.12311	−	7.14143i	−0.437048	−	0.756990i	0.560412	−	0.828214i	$-0.310643\pi$
$89$	−4.12311	−	7.14143i	−0.437048	−	0.756990i	−0.997460	+	0.0712241i	$0.977309\pi$
$90$	2.56155			0.270011
$91$	−1.56155	−	8.11407i	−0.163695	−	0.850585i
$92$	−1.00000			−0.104257
$93$	0.842329	+	1.45896i	0.0873455	+	0.151287i
$94$	−0.219224	+	0.379706i	−0.0226112	+	0.0391637i
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	11.6847			1.18640			0.593199	−	0.805056i	$-0.297865\pi$
$97$	11.6847			1.18640			0.593199	+	0.805056i	$0.297865\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$	3.00000			0.301511
$100$	−0.780776	−	1.35234i	−0.0780776	−	0.135234i
$101$	−5.78078	+	10.0126i	−0.575209	+	0.996291i	0.420810	+	0.907149i	$0.361746\pi$
$101$	−5.78078	+	10.0126i	−0.575209	+	0.996291i	−0.996019	+	0.0891421i	$0.971587\pi$
$102$	−2.34233	+	4.05703i	−0.231925	+	0.401706i
$103$	8.34233	+	14.4493i	0.821994	+	1.42374i	0.904195	+	0.427120i	$0.140472\pi$
$103$	8.34233	+	14.4493i	0.821994	+	1.42374i	−0.0822009	+	0.996616i	$0.526195\pi$
$104$	3.12311			0.306246
$105$	−1.28078	−	6.65511i	−0.124991	−	0.649472i
$106$	0.561553			0.0545428
$107$	−1.28078	−	2.21837i	−0.123817	−	0.214458i	0.797453	−	0.603381i	$-0.206180\pi$
$107$	−1.28078	−	2.21837i	−0.123817	−	0.214458i	−0.921270	+	0.388924i	$0.872847\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	6.21922	−	10.7720i	0.595694	−	1.03177i	−0.397755	−	0.917492i	$-0.630211\pi$
$109$	6.21922	−	10.7720i	0.595694	−	1.03177i	0.993449	−	0.114280i	$-0.0364561\pi$
$110$	−3.84233	−	6.65511i	−0.366352	−	0.634540i
$111$	0.876894			0.0832311
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	−7.12311			−0.670085			−0.335043	−	0.942203i	$-0.608751\pi$
$113$	−7.12311			−0.670085			−0.335043	+	0.942203i	$0.608751\pi$
$114$	−1.56155	−	2.70469i	−0.146253	−	0.253317i
$115$	−1.28078	+	2.21837i	−0.119433	+	0.206864i
$116$	−0.0615528	+	0.106613i	−0.00571504	+	0.00989873i
$117$	1.56155	+	2.70469i	0.144366	+	0.250049i
$118$	−1.43845			−0.132420
$119$	11.7116	+	4.05703i	1.07360	+	0.371908i
$120$	2.56155			0.233837
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	3.56155	−	6.16879i	0.321134	−	0.556221i
$124$	0.842329	+	1.45896i	0.0756434	+	0.131018i
$125$	8.80776			0.787790
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$	13.6847			1.21432			0.607159	−	0.794581i	$-0.292309\pi$
$127$	13.6847			1.21432			0.607159	+	0.794581i	$0.292309\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.12311	+	10.6055i	−0.539109	+	0.933765i
$130$	4.00000	−	6.92820i	0.350823	−	0.607644i
$131$	9.28078	+	16.0748i	0.810865	+	1.40446i	0.912259	+	0.409613i	$0.134336\pi$
$131$	9.28078	+	16.0748i	0.810865	+	1.40446i	−0.101394	+	0.994846i	$0.532330\pi$
$132$	3.00000			0.261116
$133$	−6.24621	+	5.40938i	−0.541615	+	0.469053i
$134$	2.00000			0.172774
$135$	1.28078	+	2.21837i	0.110232	+	0.190927i
$136$	−2.34233	+	4.05703i	−0.200853	+	0.347888i
$137$	−10.0270	+	17.3673i	−0.856663	+	1.48378i	0.0184299	+	0.999830i	$0.494133\pi$
$137$	−10.0270	+	17.3673i	−0.856663	+	1.48378i	−0.875093	+	0.483954i	$0.839200\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	18.6847			1.58481			0.792406	−	0.609994i	$-0.208828\pi$
$139$	18.6847			1.58481			0.792406	+	0.609994i	$0.208828\pi$
$140$	−1.28078	−	6.65511i	−0.108245	−	0.562459i
$141$	−0.438447			−0.0369239
$142$	0.219224	+	0.379706i	0.0183968	+	0.0318643i
$143$	4.68466	−	8.11407i	0.391751	−	0.678532i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.157671	+	0.273094i	0.0130938	+	0.0226792i
$146$	−16.9309			−1.40121
$147$	1.00000	−	6.92820i	0.0824786	−	0.571429i
$148$	0.876894			0.0720803
$149$	4.56155	+	7.90084i	0.373697	+	0.647262i	0.990131	−	0.140144i	$-0.0447567\pi$
$149$	4.56155	+	7.90084i	0.373697	+	0.647262i	−0.616434	+	0.787406i	$0.711423\pi$
$150$	0.780776	−	1.35234i	0.0637501	−	0.110418i
$151$	0.157671	−	0.273094i	0.0128311	−	0.0222241i	−0.859539	−	0.511071i	$-0.829249\pi$
$151$	0.157671	−	0.273094i	0.0128311	−	0.0222241i	0.872370	+	0.488847i	$0.162582\pi$
$152$	−1.56155	−	2.70469i	−0.126659	−	0.219379i
$153$	−4.68466			−0.378732
$154$	−1.50000	−	7.79423i	−0.120873	−	0.628077i
$155$	4.31534			0.346617
$156$	1.56155	+	2.70469i	0.125024	+	0.216548i
$157$	1.90388	−	3.29762i	0.151946	−	0.263179i	−0.779997	−	0.625784i	$-0.784779\pi$
$157$	1.90388	−	3.29762i	0.151946	−	0.263179i	0.931943	+	0.362605i	$0.118113\pi$
$158$	6.18466	−	10.7121i	0.492025	−	0.852212i
$159$	0.280776	+	0.486319i	0.0222670	+	0.0385676i
$160$	2.56155			0.202509
$161$	−2.00000	+	1.73205i	−0.157622	+	0.136505i
$162$	−1.00000			−0.0785674
$163$	−7.02699	−	12.1711i	−0.550396	−	0.953314i	−0.998246	−	0.0592052i	$-0.981143\pi$
$163$	−7.02699	−	12.1711i	−0.550396	−	0.953314i	0.447850	−	0.894109i	$-0.352190\pi$
$164$	3.56155	−	6.16879i	0.278111	−	0.481702i
$165$	3.84233	−	6.65511i	0.299125	−	0.518100i
$166$	−3.28078	−	5.68247i	−0.254638	−	0.441045i
$167$	−13.1231			−1.01550			−0.507748	−	0.861506i	$-0.669522\pi$
$167$	−13.1231			−1.01550			−0.507748	+	0.861506i	$0.669522\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	−3.24621			−0.249709
$170$	6.00000	+	10.3923i	0.460179	+	0.797053i
$171$	1.56155	−	2.70469i	0.119415	−	0.206833i
$172$	−6.12311	+	10.6055i	−0.466882	+	0.808664i
$173$	4.21922	+	7.30791i	0.320782	+	0.555610i	0.980650	−	0.195772i	$-0.0627211\pi$
$173$	4.21922	+	7.30791i	0.320782	+	0.555610i	−0.659868	+	0.751382i	$0.729388\pi$
$174$	−0.123106			−0.00933261
$175$	−3.90388	−	1.35234i	−0.295106	−	0.102228i
$176$	3.00000			0.226134
$177$	−0.719224	−	1.24573i	−0.0540602	−	0.0936349i
$178$	4.12311	−	7.14143i	0.309040	−	0.535273i
$179$	7.56155	−	13.0970i	0.565177	−	0.978915i	−0.431856	−	0.901942i	$-0.642141\pi$
$179$	7.56155	−	13.0970i	0.565177	−	0.978915i	0.997033	−	0.0769728i	$-0.0245255\pi$
$180$	1.28078	+	2.21837i	0.0954634	+	0.165348i
$181$	22.9309			1.70444			0.852219	−	0.523185i	$-0.175256\pi$
$181$	22.9309			1.70444			0.852219	+	0.523185i	$0.175256\pi$
$182$	6.24621	−	5.40938i	0.463000	−	0.400970i
$183$	−2.00000			−0.147844
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	1.12311	−	1.94528i	0.0825724	−	0.143020i
$186$	−0.842329	+	1.45896i	−0.0617626	+	0.106976i
$187$	7.02699	+	12.1711i	0.513864	+	0.890039i
$188$	−0.438447			−0.0319770
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$	−8.00000			−0.580381
$191$	12.2462	+	21.2111i	0.886105	+	1.53478i	0.844442	+	0.535647i	$0.179932\pi$
$191$	12.2462	+	21.2111i	0.886105	+	1.53478i	0.0416626	+	0.999132i	$0.486735\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	6.52699	−	11.3051i	0.469823	−	0.813757i	−0.529582	−	0.848259i	$-0.677651\pi$
$193$	6.52699	−	11.3051i	0.469823	−	0.813757i	0.999405	+	0.0345018i	$0.0109845\pi$
$194$	5.84233	+	10.1192i	0.419455	+	0.726517i
$195$	8.00000			0.572892
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	0.438447			0.0312381			0.0156190	−	0.999878i	$-0.495028\pi$
$197$	0.438447			0.0312381			0.0156190	+	0.999878i	$0.495028\pi$
$198$	1.50000	+	2.59808i	0.106600	+	0.184637i
$199$	−1.65767	+	2.87117i	−0.117509	+	0.203532i	−0.918780	−	0.394770i	$-0.870824\pi$
$199$	−1.65767	+	2.87117i	−0.117509	+	0.203532i	0.801271	+	0.598302i	$0.204158\pi$
$200$	0.780776	−	1.35234i	0.0552092	−	0.0956252i
$201$	1.00000	+	1.73205i	0.0705346	+	0.122169i
$202$	−11.5616			−0.813468
$203$	0.0615528	+	0.319838i	0.00432016	+	0.0224482i
$204$	−4.68466			−0.327992
$205$	−9.12311	−	15.8017i	−0.637185	−	1.10364i
$206$	−8.34233	+	14.4493i	−0.581238	+	1.00673i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	1.56155	+	2.70469i	0.108274	+	0.187536i
$209$	−9.36932			−0.648089
$210$	5.12311	−	4.43674i	0.353528	−	0.306164i
$211$	13.3153			0.916666			0.458333	−	0.888781i	$-0.348447\pi$
$211$	13.3153			0.916666			0.458333	+	0.888781i	$0.348447\pi$
$212$	0.280776	+	0.486319i	0.0192838	+	0.0334005i
$213$	−0.219224	+	0.379706i	−0.0150210	+	0.0260171i
$214$	1.28078	−	2.21837i	0.0875521	−	0.151645i
$215$	15.6847	+	27.1666i	1.06968	+	1.85275i
$216$	−1.00000			−0.0680414
$217$	4.21165	+	1.45896i	0.285905	+	0.0990405i
$218$	12.4384			0.842438
$219$	−8.46543	−	14.6626i	−0.572041	−	0.990804i
$220$	3.84233	−	6.65511i	0.259050	−	0.448687i
$221$	−7.31534	+	12.6705i	−0.492083	+	0.852313i
$222$	0.438447	+	0.759413i	0.0294266	+	0.0509685i
$223$	15.4384			1.03383			0.516917	−	0.856035i	$-0.327079\pi$
$223$	15.4384			1.03383			0.516917	+	0.856035i	$0.327079\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$	1.56155			0.104104
$226$	−3.56155	−	6.16879i	−0.236911	−	0.410342i
$227$	−10.3078	+	17.8536i	−0.684150	+	1.18498i	0.289553	+	0.957162i	$0.406493\pi$
$227$	−10.3078	+	17.8536i	−0.684150	+	1.18498i	−0.973703	+	0.227821i	$0.926840\pi$
$228$	1.56155	−	2.70469i	0.103416	−	0.179122i
$229$	3.65767	+	6.33527i	0.241706	+	0.418647i	0.961200	−	0.275852i	$-0.0889598\pi$
$229$	3.65767	+	6.33527i	0.241706	+	0.418647i	−0.719495	+	0.694498i	$0.755626\pi$
$230$	−2.56155			−0.168904
$231$	6.00000	−	5.19615i	0.394771	−	0.341882i
$232$	−0.123106			−0.00808228
$233$	−9.12311	−	15.8017i	−0.597675	−	1.03520i	−0.993163	−	0.116732i	$-0.962758\pi$
$233$	−9.12311	−	15.8017i	−0.597675	−	1.03520i	0.395489	−	0.918471i	$-0.370575\pi$
$234$	−1.56155	+	2.70469i	−0.102082	+	0.176811i
$235$	−0.561553	+	0.972638i	−0.0366317	+	0.0634479i
$236$	−0.719224	−	1.24573i	−0.0468175	−	0.0810902i
$237$	12.3693			0.803473
$238$	2.34233	+	12.1711i	0.151831	+	0.788935i
$239$	11.8078			0.763781			0.381890	−	0.924208i	$-0.375273\pi$
$239$	11.8078			0.763781			0.381890	+	0.924208i	$0.375273\pi$
$240$	1.28078	+	2.21837i	0.0826738	+	0.143195i
$241$	−5.15767	+	8.93335i	−0.332235	+	0.575448i	−0.982950	−	0.183875i	$-0.941136\pi$
$241$	−5.15767	+	8.93335i	−0.332235	+	0.575448i	0.650715	+	0.759322i	$0.274469\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.00000			−0.128037
$245$	−14.0885	−	11.0918i	−0.900084	−	0.708632i
$246$	7.12311			0.454153
$247$	−4.87689	−	8.44703i	−0.310309	−	0.537472i
$248$	−0.842329	+	1.45896i	−0.0534880	+	0.0926439i
$249$	3.28078	−	5.68247i	0.207911	−	0.360112i
$250$	4.40388	+	7.62775i	0.278526	+	0.482421i
$251$	−8.12311			−0.512726			−0.256363	−	0.966581i	$-0.582524\pi$
$251$	−8.12311			−0.512726			−0.256363	+	0.966581i	$0.582524\pi$
$252$	0.500000	+	2.59808i	0.0314970	+	0.163663i
$253$	−3.00000			−0.188608
$254$	6.84233	+	11.8513i	0.429326	+	0.743614i
$255$	−6.00000	+	10.3923i	−0.375735	+	0.650791i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.24621	−	12.5508i	−0.452006	−	0.782898i	0.546504	−	0.837456i	$-0.315958\pi$
$257$	−7.24621	−	12.5508i	−0.452006	−	0.782898i	−0.998511	+	0.0545585i	$0.982625\pi$
$258$	−12.2462			−0.762416
$259$	1.75379	−	1.51883i	0.108975	−	0.0943752i
$260$	8.00000			0.496139
$261$	−0.0615528	−	0.106613i	−0.00381002	−	0.00659915i
$262$	−9.28078	+	16.0748i	−0.573368	+	0.993103i
$263$	4.56155	−	7.90084i	0.281277	−	0.487187i	−0.690422	−	0.723407i	$-0.742575\pi$
$263$	4.56155	−	7.90084i	0.281277	−	0.487187i	0.971700	+	0.236220i	$0.0759086\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$	1.43845			0.0883631
$266$	−7.80776	−	2.70469i	−0.478725	−	0.165835i
$267$	8.24621			0.504660
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−4.30776	+	7.46127i	−0.262649	+	0.454921i	−0.966945	−	0.254985i	$-0.917929\pi$
$269$	−4.30776	+	7.46127i	−0.262649	+	0.454921i	0.704296	+	0.709906i	$0.251263\pi$
$270$	−1.28078	+	2.21837i	−0.0779456	+	0.135006i
$271$	−11.4039	−	19.7521i	−0.692736	−	1.19985i	−0.970938	−	0.239332i	$-0.923072\pi$
$271$	−11.4039	−	19.7521i	−0.692736	−	1.19985i	0.278201	−	0.960523i	$-0.410262\pi$
$272$	−4.68466			−0.284049
$273$	7.80776	+	2.70469i	0.472547	+	0.163695i
$274$	−20.0540			−1.21150
$275$	−2.34233	−	4.05703i	−0.141248	−	0.244648i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	0.876894	−	1.51883i	0.0526875	−	0.0912574i	−0.838479	−	0.544934i	$-0.816555\pi$
$277$	0.876894	−	1.51883i	0.0526875	−	0.0912574i	0.891166	+	0.453677i	$0.149888\pi$
$278$	9.34233	+	16.1814i	0.560316	+	0.970495i
$279$	−1.68466			−0.100858
$280$	5.12311	−	4.43674i	0.306164	−	0.265146i
$281$	15.1771			0.905389			0.452694	−	0.891666i	$-0.350463\pi$
$281$	15.1771			0.905389			0.452694	+	0.891666i	$0.350463\pi$
$282$	−0.219224	−	0.379706i	−0.0130546	−	0.0226112i
$283$	−11.6847	+	20.2384i	−0.694581	+	1.20305i	0.275741	+	0.961232i	$0.411077\pi$
$283$	−11.6847	+	20.2384i	−0.694581	+	1.20305i	−0.970322	+	0.241817i	$0.922257\pi$
$284$	−0.219224	+	0.379706i	−0.0130085	+	0.0225314i
$285$	−4.00000	−	6.92820i	−0.236940	−	0.410391i
$286$	9.36932			0.554019
$287$	−3.56155	−	18.5064i	−0.210232	−	1.09240i
$288$	−1.00000			−0.0589256
$289$	−2.47301	−	4.28338i	−0.145471	−	0.251964i
$290$	−0.157671	+	0.273094i	−0.00925875	+	0.0160366i
$291$	−5.84233	+	10.1192i	−0.342483	+	0.593199i
$292$	−8.46543	−	14.6626i	−0.495402	−	0.858062i
$293$	−9.43845			−0.551400			−0.275700	−	0.961244i	$-0.588910\pi$
$293$	−9.43845			−0.551400			−0.275700	+	0.961244i	$0.588910\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$	−3.68466			−0.214529
$296$	0.438447	+	0.759413i	0.0254842	+	0.0441400i
$297$	−1.50000	+	2.59808i	−0.0870388	+	0.150756i
$298$	−4.56155	+	7.90084i	−0.264244	+	0.457683i
$299$	−1.56155	−	2.70469i	−0.0903069	−	0.156416i
$300$	1.56155			0.0901563
$301$	6.12311	+	31.8166i	0.352930	+	1.83388i
$302$	0.315342			0.0181459
$303$	−5.78078	−	10.0126i	−0.332097	−	0.575209i
$304$	1.56155	−	2.70469i	0.0895612	−	0.155125i
$305$	−2.56155	+	4.43674i	−0.146674	+	0.254047i
$306$	−2.34233	−	4.05703i	−0.133902	−	0.231925i
$307$	−4.68466			−0.267368			−0.133684	−	0.991024i	$-0.542681\pi$
$307$	−4.68466			−0.267368			−0.133684	+	0.991024i	$0.542681\pi$
$308$	6.00000	−	5.19615i	0.341882	−	0.296078i
$309$	−16.6847			−0.949157
$310$	2.15767	+	3.73720i	0.122547	+	0.212258i
$311$	−2.34233	+	4.05703i	−0.132821	+	0.230053i	−0.924763	−	0.380543i	$-0.875737\pi$
$311$	−2.34233	+	4.05703i	−0.132821	+	0.230053i	0.791942	+	0.610597i	$0.209070\pi$
$312$	−1.56155	+	2.70469i	−0.0884055	+	0.153123i
$313$	−12.4039	−	21.4842i	−0.701109	−	1.21436i	−0.968078	−	0.250651i	$-0.919355\pi$
$313$	−12.4039	−	21.4842i	−0.701109	−	1.21436i	0.266969	−	0.963705i	$-0.413978\pi$
$314$	3.80776			0.214885
$315$	6.40388	+	2.21837i	0.360818	+	0.124991i
$316$	12.3693			0.695828
$317$	−13.9654	−	24.1888i	−0.784377	−	1.35858i	−0.929371	−	0.369148i	$-0.879649\pi$
$317$	−13.9654	−	24.1888i	−0.784377	−	1.35858i	0.144994	−	0.989433i	$-0.453684\pi$
$318$	−0.280776	+	0.486319i	−0.0157452	+	0.0272714i
$319$	−0.184658	+	0.319838i	−0.0103389	+	0.0179075i
$320$	1.28078	+	2.21837i	0.0715976	+	0.124011i
$321$	2.56155			0.142972
$322$	−2.50000	−	0.866025i	−0.139320	−	0.0482617i
$323$	14.6307			0.814073
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.43845	−	4.22351i	0.135261	−	0.234278i
$326$	7.02699	−	12.1711i	0.389189	−	0.674095i
$327$	6.21922	+	10.7720i	0.343924	+	0.595694i
$328$	7.12311			0.393308
$329$	−0.876894	+	0.759413i	−0.0483448	+	0.0418678i
$330$	7.68466			0.423027
$331$	10.2462	+	17.7470i	0.563183	+	0.975461i	0.997216	+	0.0745643i	$0.0237566\pi$
$331$	10.2462	+	17.7470i	0.563183	+	0.975461i	−0.434034	+	0.900897i	$0.642910\pi$
$332$	3.28078	−	5.68247i	0.180056	−	0.311866i
$333$	−0.438447	+	0.759413i	−0.0240268	+	0.0416156i
$334$	−6.56155	−	11.3649i	−0.359032	−	0.621862i
$335$	5.12311			0.279905
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$	7.43845			0.405198			0.202599	−	0.979262i	$-0.435061\pi$
$337$	7.43845			0.405198			0.202599	+	0.979262i	$0.435061\pi$
$338$	−1.62311	−	2.81130i	−0.0882853	−	0.152915i
$339$	3.56155	−	6.16879i	0.193437	−	0.335043i
$340$	−6.00000	+	10.3923i	−0.325396	+	0.563602i
$341$	2.52699	+	4.37687i	0.136844	+	0.237021i
$342$	3.12311			0.168878
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−12.2462			−0.660271
$345$	−1.28078	−	2.21837i	−0.0689547	−	0.119433i
$346$	−4.21922	+	7.30791i	−0.226827	+	0.392876i
$347$	5.80776	−	10.0593i	0.311777	−	0.540014i	−0.666970	−	0.745085i	$-0.732409\pi$
$347$	5.80776	−	10.0593i	0.311777	−	0.540014i	0.978747	+	0.205071i	$0.0657424\pi$
$348$	−0.0615528	−	0.106613i	−0.00329958	−	0.00571504i
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$	−0.780776	−	4.05703i	−0.0417343	−	0.216858i
$351$	−3.12311			−0.166699
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	1.31534	−	2.27824i	0.0700086	−	0.121258i	−0.828896	−	0.559402i	$-0.811031\pi$
$353$	1.31534	−	2.27824i	0.0700086	−	0.121258i	0.898905	+	0.438144i	$0.144364\pi$
$354$	0.719224	−	1.24573i	0.0382263	−	0.0662099i
$355$	0.561553	+	0.972638i	0.0298041	+	0.0516223i
$356$	8.24621			0.437048
$357$	−9.36932	+	8.11407i	−0.495877	+	0.429442i
$358$	15.1231			0.799281
$359$	2.56155	+	4.43674i	0.135194	+	0.234162i	0.925671	−	0.378329i	$-0.123501\pi$
$359$	2.56155	+	4.43674i	0.135194	+	0.234162i	−0.790478	+	0.612491i	$0.790168\pi$
$360$	−1.28078	+	2.21837i	−0.0675028	+	0.116918i
$361$	4.62311	−	8.00745i	0.243321	−	0.421445i
$362$	11.4654	+	19.8587i	0.602610	+	1.04375i
$363$	−2.00000			−0.104973
$364$	7.80776	+	2.70469i	0.409238	+	0.141764i
$365$	−43.3693			−2.27005
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−11.2808	+	19.5389i	−0.588852	+	1.01992i	0.405531	+	0.914081i	$0.367086\pi$
$367$	−11.2808	+	19.5389i	−0.588852	+	1.01992i	−0.994383	+	0.105840i	$0.966247\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	3.56155	+	6.16879i	0.185407	+	0.321134i
$370$	2.24621			0.116775
$371$	1.40388	+	0.486319i	0.0728859	+	0.0252484i
$372$	−1.68466			−0.0873455
$373$	−5.21922	−	9.03996i	−0.270241	−	0.468071i	0.698682	−	0.715432i	$-0.253770\pi$
$373$	−5.21922	−	9.03996i	−0.270241	−	0.468071i	−0.968923	+	0.247361i	$0.920437\pi$
$374$	−7.02699	+	12.1711i	−0.363357	+	0.629353i
$375$	−4.40388	+	7.62775i	−0.227415	+	0.393895i
$376$	−0.219224	−	0.379706i	−0.0113056	−	0.0195819i
$377$	−0.384472			−0.0198013
$378$	−2.00000	+	1.73205i	−0.102869	+	0.0890871i
$379$	12.4924			0.641693			0.320846	−	0.947131i	$-0.396033\pi$
$379$	12.4924			0.641693			0.320846	+	0.947131i	$0.396033\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$	−6.84233	+	11.8513i	−0.350543	+	0.607159i
$382$	−12.2462	+	21.2111i	−0.626571	+	1.08525i
$383$	1.87689	+	3.25088i	0.0959048	+	0.166112i	0.909986	−	0.414639i	$-0.136092\pi$
$383$	1.87689	+	3.25088i	0.0959048	+	0.166112i	−0.814081	+	0.580751i	$0.802759\pi$
$384$	−1.00000			−0.0510310
$385$	−3.84233	−	19.9653i	−0.195823	−	1.01753i
$386$	13.0540			0.664430
$387$	−6.12311	−	10.6055i	−0.311255	−	0.539109i
$388$	−5.84233	+	10.1192i	−0.296599	+	0.513725i
$389$	12.5616	−	21.7572i	0.636896	−	1.10314i	−0.349214	−	0.937043i	$-0.613551\pi$
$389$	12.5616	−	21.7572i	0.636896	−	1.10314i	0.986110	−	0.166093i	$-0.0531153\pi$
$390$	4.00000	+	6.92820i	0.202548	+	0.350823i
$391$	4.68466			0.236913
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	−18.5616			−0.936306
$394$	0.219224	+	0.379706i	0.0110443	+	0.0191293i
$395$	15.8423	−	27.4397i	0.797114	−	1.38064i
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−8.68466	−	15.0423i	−0.435871	−	0.754950i	0.561496	−	0.827480i	$-0.310226\pi$
$397$	−8.68466	−	15.0423i	−0.435871	−	0.754950i	−0.997366	+	0.0725298i	$0.976893\pi$
$398$	−3.31534			−0.166183
$399$	−1.56155	−	8.11407i	−0.0781754	−	0.406211i
$400$	1.56155			0.0780776
$401$	−16.1501	−	27.9728i	−0.806497	−	1.39689i	−0.915276	−	0.402828i	$-0.868027\pi$
$401$	−16.1501	−	27.9728i	−0.806497	−	1.39689i	0.108778	−	0.994066i	$-0.465306\pi$
$402$	−1.00000	+	1.73205i	−0.0498755	+	0.0863868i
$403$	−2.63068	+	4.55648i	−0.131044	+	0.226974i
$404$	−5.78078	−	10.0126i	−0.287604	−	0.498145i
$405$	−2.56155			−0.127285
$406$	−0.246211	+	0.213225i	−0.0122193	+	0.0105822i
$407$	2.63068			0.130398
$408$	−2.34233	−	4.05703i	−0.115963	−	0.200853i
$409$	5.18466	−	8.98009i	0.256365	−	0.444037i	−0.708900	−	0.705309i	$-0.750808\pi$
$409$	5.18466	−	8.98009i	0.256365	−	0.444037i	0.965265	+	0.261272i	$0.0841418\pi$
$410$	9.12311	−	15.8017i	0.450558	−	0.780389i
$411$	−10.0270	−	17.3673i	−0.494595	−	0.856663i
$412$	−16.6847			−0.821994
$413$	−3.59612	−	1.24573i	−0.176953	−	0.0612985i
$414$	1.00000			0.0491473
$415$	−8.40388	−	14.5560i	−0.412530	−	0.714524i
$416$	−1.56155	+	2.70469i	−0.0765614	+	0.132608i
$417$	−9.34233	+	16.1814i	−0.457496	+	0.792406i
$418$	−4.68466	−	8.11407i	−0.229134	−	0.396872i
$419$	−16.3002			−0.796316			−0.398158	−	0.917317i	$-0.630350\pi$
$419$	−16.3002			−0.796316			−0.398158	+	0.917317i	$0.630350\pi$
$420$	6.40388	+	2.21837i	0.312477	+	0.108245i
$421$	8.93087			0.435264			0.217632	−	0.976031i	$-0.430167\pi$
$421$	8.93087			0.435264			0.217632	+	0.976031i	$0.430167\pi$
$422$	6.65767	+	11.5314i	0.324090	+	0.561341i
$423$	0.219224	−	0.379706i	0.0106590	−	0.0184620i
$424$	−0.280776	+	0.486319i	−0.0136357	+	0.0236177i
$425$	3.65767	+	6.33527i	0.177423	+	0.307306i
$426$	−0.438447			−0.0212428
$427$	−4.00000	+	3.46410i	−0.193574	+	0.167640i
$428$	2.56155			0.123817
$429$	4.68466	+	8.11407i	0.226177	+	0.391751i
$430$	−15.6847	+	27.1666i	−0.756381	+	1.31009i
$431$	−10.6847	+	18.5064i	−0.514662	+	0.891421i	0.485193	+	0.874407i	$0.338749\pi$
$431$	−10.6847	+	18.5064i	−0.514662	+	0.891421i	−0.999855	+	0.0170137i	$0.994584\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$	0.842329	+	4.37687i	0.0404331	+	0.210097i
$435$	−0.315342			−0.0151195
$436$	6.21922	+	10.7720i	0.297847	+	0.515886i
$437$	−1.56155	+	2.70469i	−0.0746992	+	0.129383i
$438$	8.46543	−	14.6626i	0.404494	−	0.700604i
$439$	13.2808	+	23.0030i	0.633857	+	1.09787i	0.986756	+	0.162211i	$0.0518625\pi$
$439$	13.2808	+	23.0030i	0.633857	+	1.09787i	−0.352899	+	0.935661i	$0.614804\pi$
$440$	7.68466			0.366352
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$	−14.6307			−0.695911
$443$	−0.473012	−	0.819281i	−0.0224735	−	0.0389252i	0.854570	−	0.519336i	$-0.173821\pi$
$443$	−0.473012	−	0.819281i	−0.0224735	−	0.0389252i	−0.877043	+	0.480411i	$0.840487\pi$
$444$	−0.438447	+	0.759413i	−0.0208078	+	0.0360401i
$445$	10.5616	−	18.2931i	0.500666	−	0.867178i
$446$	7.71922	+	13.3701i	0.365516	+	0.633092i
$447$	−9.12311			−0.431508
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$	36.4924			1.72218			0.861092	−	0.508449i	$-0.169781\pi$
$449$	36.4924			1.72218			0.861092	+	0.508449i	$0.169781\pi$
$450$	0.780776	+	1.35234i	0.0368062	+	0.0637501i
$451$	10.6847	−	18.5064i	0.503121	−	0.871431i
$452$	3.56155	−	6.16879i	0.167521	−	0.290155i
$453$	0.157671	+	0.273094i	0.00740802	+	0.0128311i
$454$	−20.6155			−0.967535
$455$	16.0000	−	13.8564i	0.750092	−	0.649598i
$456$	3.12311			0.146253
$457$	−19.2116	−	33.2755i	−0.898683	−	1.55656i	−0.829179	−	0.558983i	$-0.811192\pi$
$457$	−19.2116	−	33.2755i	−0.898683	−	1.55656i	−0.0695036	−	0.997582i	$-0.522142\pi$
$458$	−3.65767	+	6.33527i	−0.170912	+	0.296028i
$459$	2.34233	−	4.05703i	0.109331	−	0.189366i
$460$	−1.28078	−	2.21837i	−0.0597165	−	0.103432i
$461$	−8.24621			−0.384064			−0.192032	−	0.981389i	$-0.561508\pi$
$461$	−8.24621			−0.384064			−0.192032	+	0.981389i	$0.561508\pi$
$462$	7.50000	+	2.59808i	0.348932	+	0.120873i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−0.0615528	−	0.106613i	−0.00285752	−	0.00494937i
$465$	−2.15767	+	3.73720i	−0.100060	+	0.173308i
$466$	9.12311	−	15.8017i	0.422620	−	0.731999i
$467$	−13.4654	−	23.3228i	−0.623106	−	1.07925i	−0.988904	−	0.148557i	$-0.952537\pi$
$467$	−13.4654	−	23.3228i	−0.623106	−	1.07925i	0.365798	−	0.930694i	$-0.380796\pi$
$468$	−3.12311			−0.144366
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$	−1.12311			−0.0518050
$471$	1.90388	+	3.29762i	0.0877263	+	0.151946i
$472$	0.719224	−	1.24573i	0.0331049	−	0.0573395i
$473$	−18.3693	+	31.8166i	−0.844622	+	1.46293i
$474$	6.18466	+	10.7121i	0.284071	+	0.492025i
$475$	−4.87689			−0.223767
$476$	−9.36932	+	8.11407i	−0.429442	+	0.371908i
$477$	−0.561553			−0.0257117
$478$	5.90388	+	10.2258i	0.270037	+	0.467718i
$479$	14.1231	−	24.4619i	0.645301	−	1.11769i	−0.338931	−	0.940811i	$-0.610065\pi$
$479$	14.1231	−	24.4619i	0.645301	−	1.11769i	0.984232	−	0.176883i	$-0.0566014\pi$
$480$	−1.28078	+	2.21837i	−0.0584592	+	0.101254i
$481$	1.36932	+	2.37173i	0.0624355	+	0.108141i
$482$	−10.3153			−0.469851
$483$	−0.500000	−	2.59808i	−0.0227508	−	0.118217i
$484$	−2.00000			−0.0909091
$485$	14.9654	+	25.9209i	0.679545	+	1.17701i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−8.84233	+	15.3154i	−0.400684	+	0.694005i	−0.993809	−	0.111105i	$-0.964561\pi$
$487$	−8.84233	+	15.3154i	−0.400684	+	0.694005i	0.593124	+	0.805111i	$0.297894\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	14.0540			0.635543
$490$	2.56155	−	17.7470i	0.115719	−	0.801726i
$491$	17.9309			0.809209			0.404604	−	0.914492i	$-0.367409\pi$
$491$	17.9309			0.809209			0.404604	+	0.914492i	$0.367409\pi$
$492$	3.56155	+	6.16879i	0.160567	+	0.278111i
$493$	0.288354	−	0.499444i	0.0129868	−	0.0224938i
$494$	4.87689	−	8.44703i	0.219422	−	0.380050i
$495$	3.84233	+	6.65511i	0.172700	+	0.299125i
$496$	−1.68466			−0.0756434
$497$	0.219224	+	1.13912i	0.00983352	+	0.0510965i
$498$	6.56155			0.294030
$499$	4.90388	+	8.49377i	0.219528	+	0.380233i	0.954664	−	0.297686i	$-0.0962150\pi$
$499$	4.90388	+	8.49377i	0.219528	+	0.380233i	−0.735136	+	0.677920i	$0.762882\pi$
$500$	−4.40388	+	7.62775i	−0.196948	+	0.341123i
$501$	6.56155	−	11.3649i	0.293149	−	0.507748i
$502$	−4.06155	−	7.03482i	−0.181276	−	0.313979i
$503$	3.61553			0.161208			0.0806042	−	0.996746i	$-0.474315\pi$
$503$	3.61553			0.161208			0.0806042	+	0.996746i	$0.474315\pi$
$504$	−2.00000	+	1.73205i	−0.0890871	+	0.0771517i
$505$	−29.6155			−1.31787
$506$	−1.50000	−	2.59808i	−0.0666831	−	0.115499i
$507$	1.62311	−	2.81130i	0.0720847	−	0.124854i
$508$	−6.84233	+	11.8513i	−0.303579	+	0.525815i
$509$	−0.692236	−	1.19899i	−0.0306828	−	0.0531442i	0.850276	−	0.526337i	$-0.176435\pi$
$509$	−0.692236	−	1.19899i	−0.0306828	−	0.0531442i	−0.880959	+	0.473192i	$0.843102\pi$
$510$	−12.0000			−0.531369
$511$	−42.3272	−	14.6626i	−1.87244	−	0.648634i
$512$	−1.00000			−0.0441942
$513$	1.56155	+	2.70469i	0.0689442	+	0.119415i
$514$	7.24621	−	12.5508i	0.319617	−	0.553592i
$515$	−21.3693	+	37.0127i	−0.941645	+	1.63098i
$516$	−6.12311	−	10.6055i	−0.269555	−	0.466882i
$517$	−1.31534			−0.0578487
$518$	2.19224	+	0.759413i	0.0963213	+	0.0333667i
$519$	−8.43845			−0.370407
$520$	4.00000	+	6.92820i	0.175412	+	0.303822i
$521$	4.12311	−	7.14143i	0.180637	−	0.312872i	−0.761461	−	0.648211i	$-0.775518\pi$
$521$	4.12311	−	7.14143i	0.180637	−	0.312872i	0.942097	+	0.335339i	$0.108851\pi$
$522$	0.0615528	−	0.106613i	0.00269409	−	0.00466631i
$523$	−1.31534	−	2.27824i	−0.0575159	−	0.0996204i	0.835834	−	0.548983i	$-0.184985\pi$
$523$	−1.31534	−	2.27824i	−0.0575159	−	0.0996204i	−0.893350	+	0.449362i	$0.851651\pi$
$524$	−18.5616			−0.810865
$525$	3.12311	−	2.70469i	0.136304	−	0.118042i
$526$	9.12311			0.397786
$527$	−3.94602	−	6.83472i	−0.171892	−	0.297725i
$528$	−1.50000	+	2.59808i	−0.0652791	+	0.113067i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	0.719224	+	1.24573i	0.0312411	+	0.0541111i
$531$	1.43845			0.0624233
$532$	−1.56155	−	8.11407i	−0.0677019	−	0.351789i
$533$	22.2462			0.963590
$534$	4.12311	+	7.14143i	0.178424	+	0.309040i
$535$	3.28078	−	5.68247i	0.141840	−	0.245675i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	7.56155	+	13.0970i	0.326305	+	0.565177i
$538$	−8.61553			−0.371442
$539$	3.00000	−	20.7846i	0.129219	−	0.895257i
$540$	−2.56155			−0.110232
$541$	−2.31534	−	4.01029i	−0.0995443	−	0.172416i	0.811952	−	0.583724i	$-0.198405\pi$
$541$	−2.31534	−	4.01029i	−0.0995443	−	0.172416i	−0.911496	+	0.411309i	$0.865072\pi$
$542$	11.4039	−	19.7521i	0.489839	−	0.848425i
$543$	−11.4654	+	19.8587i	−0.492029	+	0.852219i
$544$	−2.34233	−	4.05703i	−0.100427	−	0.173944i
$545$	31.8617			1.36481
$546$	1.56155	+	8.11407i	0.0668283	+	0.347250i
$547$	−30.0540			−1.28502			−0.642508	−	0.766279i	$-0.722106\pi$
$547$	−30.0540			−1.28502			−0.642508	+	0.766279i	$0.722106\pi$
$548$	−10.0270	−	17.3673i	−0.428332	−	0.741892i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	2.34233	−	4.05703i	0.0998773	−	0.172992i
$551$	0.192236	+	0.332962i	0.00818953	+	0.0141847i
$552$	1.00000			0.0425628
$553$	24.7386	−	21.4243i	1.05199	−	0.911053i
$554$	1.75379			0.0745113
$555$	1.12311	+	1.94528i	0.0476732	+	0.0825724i
$556$	−9.34233	+	16.1814i	−0.396203	+	0.686244i
$557$	1.96543	−	3.40423i	0.0832781	−	0.144242i	−0.821378	−	0.570384i	$-0.806794\pi$
$557$	1.96543	−	3.40423i	0.0832781	−	0.144242i	0.904656	+	0.426142i	$0.140128\pi$
$558$	−0.842329	−	1.45896i	−0.0356586	−	0.0617626i
$559$	−38.2462			−1.61764
$560$	6.40388	+	2.21837i	0.270613	+	0.0937432i
$561$	−14.0540			−0.593359
$562$	7.58854	+	13.1437i	0.320103	+	0.554435i
$563$	12.3078	−	21.3177i	0.518710	−	0.898433i	−0.481053	−	0.876691i	$-0.659746\pi$
$563$	12.3078	−	21.3177i	0.518710	−	0.898433i	0.999764	−	0.0217414i	$-0.00692105\pi$
$564$	0.219224	−	0.379706i	0.00923098	−	0.0159885i
$565$	−9.12311	−	15.8017i	−0.383812	−	0.664782i
$566$	−23.3693			−0.982286
$567$	−2.50000	−	0.866025i	−0.104990	−	0.0363696i
$568$	−0.438447			−0.0183968
$569$	−10.6847	−	18.5064i	−0.447924	−	0.775827i	0.550327	−	0.834949i	$-0.314503\pi$
$569$	−10.6847	−	18.5064i	−0.447924	−	0.775827i	−0.998251	+	0.0591221i	$0.981170\pi$
$570$	4.00000	−	6.92820i	0.167542	−	0.290191i
$571$	7.68466	−	13.3102i	0.321593	−	0.557015i	−0.659224	−	0.751947i	$-0.729115\pi$
$571$	7.68466	−	13.3102i	0.321593	−	0.557015i	0.980817	+	0.194931i	$0.0624484\pi$
$572$	4.68466	+	8.11407i	0.195875	+	0.339266i
$573$	−24.4924			−1.02319
$574$	14.2462	−	12.3376i	0.594625	−	0.514961i
$575$	−1.56155			−0.0651213
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−13.9384	+	24.1421i	−0.580265	+	1.00505i	0.415182	+	0.909738i	$0.363718\pi$
$577$	−13.9384	+	24.1421i	−0.580265	+	1.00505i	−0.995448	+	0.0953105i	$0.969616\pi$
$578$	2.47301	−	4.28338i	0.102864	−	0.178165i
$579$	6.52699	+	11.3051i	0.271252	+	0.469823i
$580$	−0.315342			−0.0130938
$581$	−3.28078	−	17.0474i	−0.136110	−	0.707246i
$582$	−11.6847			−0.484345
$583$	0.842329	+	1.45896i	0.0348857	+	0.0604238i
$584$	8.46543	−	14.6626i	0.350302	−	0.606741i
$585$	−4.00000	+	6.92820i	−0.165380	+	0.286446i
$586$	−4.71922	−	8.17394i	−0.194949	−	0.337662i
$587$	−44.1771			−1.82338			−0.911692	−	0.410875i	$-0.865223\pi$
$587$	−44.1771			−1.82338			−0.911692	+	0.410875i	$0.865223\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$	5.26137			0.216791
$590$	−1.84233	−	3.19101i	−0.0758475	−	0.131372i
$591$	−0.219224	+	0.379706i	−0.00901765	+	0.0156190i
$592$	−0.438447	+	0.759413i	−0.0180201	+	0.0312117i
$593$	−0.192236	−	0.332962i	−0.00789418	−	0.0136731i	0.862051	−	0.506821i	$-0.169179\pi$
$593$	−0.192236	−	0.332962i	−0.00789418	−	0.0136731i	−0.869946	+	0.493148i	$0.835846\pi$
$594$	−3.00000			−0.123091
$595$	6.00000	+	31.1769i	0.245976	+	1.27813i
$596$	−9.12311			−0.373697
$597$	−1.65767	−	2.87117i	−0.0678439	−	0.117509i
$598$	1.56155	−	2.70469i	0.0638566	−	0.110603i
$599$	7.53457	−	13.0502i	0.307854	−	0.533219i	−0.670039	−	0.742326i	$-0.733723\pi$
$599$	7.53457	−	13.0502i	0.307854	−	0.533219i	0.977893	+	0.209107i	$0.0670558\pi$
$600$	0.780776	+	1.35234i	0.0318751	+	0.0552092i
$601$	−35.9309			−1.46565			−0.732825	−	0.680417i	$-0.761799\pi$
$601$	−35.9309			−1.46565			−0.732825	+	0.680417i	$0.761799\pi$
$602$	−24.4924	+	21.2111i	−0.998237	+	0.864498i
$603$	−2.00000			−0.0814463
$604$	0.157671	+	0.273094i	0.00641553	+	0.0111120i
$605$	−2.56155	+	4.43674i	−0.104142	+	0.180379i
$606$	5.78078	−	10.0126i	0.234828	−	0.406734i
$607$	3.15767	+	5.46925i	0.128166	+	0.221990i	0.922966	−	0.384881i	$-0.125758\pi$
$607$	3.15767	+	5.46925i	0.128166	+	0.221990i	−0.794800	+	0.606871i	$0.792424\pi$
$608$	3.12311			0.126659
$609$	−0.307764	−	0.106613i	−0.0124712	−	0.00432016i
$610$	−5.12311			−0.207428
$611$	−0.684658	−	1.18586i	−0.0276983	−	0.0479749i
$612$	2.34233	−	4.05703i	0.0946830	−	0.163996i
$613$	−5.02699	+	8.70700i	−0.203038	+	0.351672i	−0.949506	−	0.313749i	$-0.898415\pi$
$613$	−5.02699	+	8.70700i	−0.203038	+	0.351672i	0.746468	+	0.665422i	$0.231748\pi$
$614$	−2.34233	−	4.05703i	−0.0945287	−	0.163729i
$615$	18.2462			0.735758
$616$	7.50000	+	2.59808i	0.302184	+	0.104679i
$617$	−32.0540			−1.29044			−0.645222	−	0.763995i	$-0.723235\pi$
$617$	−32.0540			−1.29044			−0.645222	+	0.763995i	$0.723235\pi$
$618$	−8.34233	−	14.4493i	−0.335578	−	0.581238i
$619$	−4.31534	+	7.47439i	−0.173448	+	0.300421i	−0.939623	−	0.342211i	$-0.888824\pi$
$619$	−4.31534	+	7.47439i	−0.173448	+	0.300421i	0.766175	+	0.642632i	$0.222158\pi$
$620$	−2.15767	+	3.73720i	−0.0866541	+	0.150089i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−4.68466			−0.187838
$623$	16.4924	−	14.2829i	0.660755	−	0.572231i
$624$	−3.12311			−0.125024
$625$	15.1847	+	26.3006i	0.607386	+	1.05202i
$626$	12.4039	−	21.4842i	0.495759	−	0.858679i
$627$	4.68466	−	8.11407i	0.187087	−	0.324045i
$628$	1.90388	+	3.29762i	0.0759732	+	0.131589i
$629$	−4.10795			−0.163795
$630$	1.28078	+	6.65511i	0.0510274	+	0.265146i
$631$	−34.6155			−1.37802			−0.689011	−	0.724751i	$-0.741955\pi$
$631$	−34.6155			−1.37802			−0.689011	+	0.724751i	$0.741955\pi$
$632$	6.18466	+	10.7121i	0.246013	+	0.426106i
$633$	−6.65767	+	11.5314i	−0.264619	+	0.458333i
$634$	13.9654	−	24.1888i	0.554638	−	0.960662i
$635$	17.5270	+	30.3576i	0.695537	+	1.20471i
$636$	−0.561553			−0.0222670
$637$	20.3002	−	8.11407i	0.804323	−	0.321491i
$638$	−0.369317			−0.0146214
$639$	−0.219224	−	0.379706i	−0.00867235	−	0.0150210i
$640$	−1.28078	+	2.21837i	−0.0506271	+	0.0876888i
$641$	−20.2192	+	35.0207i	−0.798611	+	1.38324i	0.121909	+	0.992541i	$0.461098\pi$
$641$	−20.2192	+	35.0207i	−0.798611	+	1.38324i	−0.920521	+	0.390694i	$0.872235\pi$
$642$	1.28078	+	2.21837i	0.0505482	+	0.0875521i
$643$	23.8617			0.941015			0.470508	−	0.882396i	$-0.344071\pi$
$643$	23.8617			0.941015			0.470508	+	0.882396i	$0.344071\pi$
$644$	−0.500000	−	2.59808i	−0.0197028	−	0.102379i
$645$	−31.3693			−1.23517
$646$	7.31534	+	12.6705i	0.287818	+	0.498516i
$647$	14.7116	−	25.4813i	0.578374	−	1.00177i	−0.417291	−	0.908773i	$-0.637021\pi$
$647$	14.7116	−	25.4813i	0.578374	−	1.00177i	0.995666	−	0.0930013i	$-0.0296461\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−2.15767	−	3.73720i	−0.0846960	−	0.146698i
$650$	4.87689			0.191288
$651$	−3.36932	+	2.91791i	−0.132054	+	0.114362i
$652$	14.0540			0.550396
$653$	−4.86932	−	8.43390i	−0.190551	−	0.330044i	0.754882	−	0.655861i	$-0.227694\pi$
$653$	−4.86932	−	8.43390i	−0.190551	−	0.330044i	−0.945433	+	0.325817i	$0.894361\pi$
$654$	−6.21922	+	10.7720i	−0.243191	+	0.421219i
$655$	−23.7732	+	41.1764i	−0.928896	+	1.60889i
$656$	3.56155	+	6.16879i	0.139055	+	0.240851i
$657$	16.9309			0.660536
$658$	−1.09612	−	0.379706i	−0.0427311	−	0.0148025i
$659$	45.1771			1.75985			0.879925	−	0.475113i	$-0.157593\pi$
$659$	45.1771			1.75985			0.879925	+	0.475113i	$0.157593\pi$
$660$	3.84233	+	6.65511i	0.149562	+	0.259050i
$661$	11.7808	−	20.4049i	0.458219	−	0.793659i	−0.540648	−	0.841249i	$-0.681821\pi$
$661$	11.7808	−	20.4049i	0.458219	−	0.793659i	0.998867	+	0.0475903i	$0.0151542\pi$
$662$	−10.2462	+	17.7470i	−0.398230	+	0.689755i
$663$	−7.31534	−	12.6705i	−0.284104	−	0.492083i
$664$	6.56155			0.254638
$665$	−20.0000	−	6.92820i	−0.775567	−	0.268664i
$666$	−0.876894			−0.0339790
$667$	0.0615528	+	0.106613i	0.00238333	+	0.00412806i
$668$	6.56155	−	11.3649i	0.253874	−	0.439723i
$669$	−7.71922	+	13.3701i	−0.298442	+	0.516917i
$670$	2.56155	+	4.43674i	0.0989614	+	0.171406i
$671$	−6.00000			−0.231627
$672$	−2.00000	+	1.73205i	−0.0771517	+	0.0668153i
$673$	37.9848			1.46421			0.732104	−	0.681193i	$-0.238538\pi$
$673$	37.9848			1.46421			0.732104	+	0.681193i	$0.238538\pi$
$674$	3.71922	+	6.44188i	0.143259	+	0.248132i
$675$	−0.780776	+	1.35234i	−0.0300521	+	0.0520518i
$676$	1.62311	−	2.81130i	0.0624271	−	0.108127i
$677$	−10.2808	−	17.8068i	−0.395122	−	0.684372i	0.597994	−	0.801500i	$-0.295964\pi$
$677$	−10.2808	−	17.8068i	−0.395122	−	0.684372i	−0.993117	+	0.117128i	$0.962631\pi$
$678$	7.12311			0.273561
$679$	5.84233	+	30.3576i	0.224208	+	1.16502i
$680$	−12.0000			−0.460179
$681$	−10.3078	−	17.8536i	−0.394994	−	0.684150i
$682$	−2.52699	+	4.37687i	−0.0967634	+	0.167599i
$683$	−11.5270	+	19.9653i	−0.441068	+	0.763952i	−0.997769	−	0.0667608i	$-0.978734\pi$
$683$	−11.5270	+	19.9653i	−0.441068	+	0.763952i	0.556701	+	0.830713i	$0.312067\pi$
$684$	1.56155	+	2.70469i	0.0597075	+	0.103416i
$685$	−51.3693			−1.96272
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	−7.31534			−0.279098
$688$	−6.12311	−	10.6055i	−0.233441	−	0.404332i
$689$	−0.876894	+	1.51883i	−0.0334070	+	0.0578626i
$690$	1.28078	−	2.21837i	0.0487583	−	0.0844519i
$691$	12.7808	+	22.1370i	0.486204	+	0.842129i	0.999874	−	0.0158581i	$-0.00504799\pi$
$691$	12.7808	+	22.1370i	0.486204	+	0.842129i	−0.513671	+	0.857987i	$0.671715\pi$
$692$	−8.43845			−0.320782
$693$	1.50000	+	7.79423i	0.0569803	+	0.296078i
$694$	11.6155			0.440919
$695$	23.9309	+	41.4495i	0.907750	+	1.57227i
$696$	0.0615528	−	0.106613i	0.00233315	−	0.00404114i
$697$	−16.6847	+	28.8987i	−0.631977	+	1.09462i
$698$	15.0000	+	25.9808i	0.567758	+	0.983386i
$699$	18.2462			0.690135
$700$	3.12311	−	2.70469i	0.118042	−	0.102228i
$701$	−2.80776			−0.106048			−0.0530239	−	0.998593i	$-0.516886\pi$
$701$	−2.80776			−0.106048			−0.0530239	+	0.998593i	$0.516886\pi$
$702$	−1.56155	−	2.70469i	−0.0589370	−	0.102082i
$703$	1.36932	−	2.37173i	0.0516448	−	0.0894514i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$	−0.561553	−	0.972638i	−0.0211493	−	0.0366317i
$706$	2.63068			0.0990071
$707$	−28.9039	−	10.0126i	−1.08704	−	0.376563i
$708$	1.43845			0.0540602
$709$	7.53457	+	13.0502i	0.282967	+	0.490112i	0.972114	−	0.234509i	$-0.0753481\pi$
$709$	7.53457	+	13.0502i	0.282967	+	0.490112i	−0.689147	+	0.724621i	$0.742015\pi$
$710$	−0.561553	+	0.972638i	−0.0210747	+	0.0365025i
$711$	−6.18466	+	10.7121i	−0.231943	+	0.401737i
$712$	4.12311	+	7.14143i	0.154520	+	0.267636i
$713$	1.68466			0.0630910
$714$	−11.7116	−	4.05703i	−0.438297	−	0.151831i
$715$	24.0000			0.897549
$716$	7.56155	+	13.0970i	0.282588	+	0.489458i
$717$	−5.90388	+	10.2258i	−0.220485	+	0.381890i
$718$	−2.56155	+	4.43674i	−0.0955963	+	0.165578i
$719$	−21.9309	−	37.9854i	−0.817883	−	1.41662i	−0.907239	−	0.420616i	$-0.861814\pi$
$719$	−21.9309	−	37.9854i	−0.817883	−	1.41662i	0.0893554	−	0.996000i	$-0.471519\pi$
$720$	−2.56155			−0.0954634
$721$	−33.3693	+	28.8987i	−1.24274	+	1.07624i
$722$	9.24621			0.344108
$723$	−5.15767	−	8.93335i	−0.191816	−	0.332235i
$724$	−11.4654	+	19.8587i	−0.426110	+	0.738043i
$725$	−0.0961180	+	0.166481i	−0.00356973	+	0.00618296i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	40.3693			1.49722			0.748608	−	0.663013i	$-0.230723\pi$
$727$	40.3693			1.49722			0.748608	+	0.663013i	$0.230723\pi$
$728$	1.56155	+	8.11407i	0.0578750	+	0.300727i
$729$	1.00000			0.0370370
$730$	−21.6847	−	37.5589i	−0.802585	−	1.39012i
$731$	28.6847	−	49.6833i	1.06094	−	1.83760i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$	−4.46543	−	7.73436i	−0.164935	−	0.285675i	0.771697	−	0.635990i	$-0.219408\pi$
$733$	−4.46543	−	7.73436i	−0.164935	−	0.285675i	−0.936632	+	0.350315i	$0.886075\pi$
$734$	−22.5616			−0.832762
$735$	16.6501	−	6.65511i	0.614148	−	0.245477i
$736$	1.00000			0.0368605
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	−3.56155	+	6.16879i	−0.131103	+	0.227076i
$739$	−3.97301	+	6.88146i	−0.146150	+	0.253139i	−0.929801	−	0.368062i	$-0.880021\pi$
$739$	−3.97301	+	6.88146i	−0.146150	+	0.253139i	0.783652	+	0.621201i	$0.213355\pi$
$740$	1.12311	+	1.94528i	0.0412862	+	0.0715098i
$741$	9.75379			0.358314
$742$	0.280776	+	1.45896i	0.0103076	+	0.0535600i
$743$	2.87689			0.105543			0.0527715	−	0.998607i	$-0.483195\pi$
$743$	2.87689			0.105543			0.0527715	+	0.998607i	$0.483195\pi$
$744$	−0.842329	−	1.45896i	−0.0308813	−	0.0534880i
$745$	−11.6847	+	20.2384i	−0.428093	+	0.741478i
$746$	5.21922	−	9.03996i	0.191089	−	0.330976i
$747$	3.28078	+	5.68247i	0.120037	+	0.207911i
$748$	−14.0540			−0.513864
$749$	5.12311	−	4.43674i	0.187194	−	0.162115i
$750$	−8.80776			−0.321614
$751$	−6.15767	−	10.6654i	−0.224697	−	0.389186i	0.731532	−	0.681807i	$-0.238806\pi$
$751$	−6.15767	−	10.6654i	−0.224697	−	0.389186i	−0.956228	+	0.292621i	$0.905472\pi$
$752$	0.219224	−	0.379706i	0.00799426	−	0.0138465i
$753$	4.06155	−	7.03482i	0.148011	−	0.256363i
$754$	−0.192236	−	0.332962i	−0.00700082	−	0.0121258i
$755$	0.807764			0.0293975
$756$	−2.50000	−	0.866025i	−0.0909241	−	0.0314970i
$757$	30.4924			1.10827			0.554133	−	0.832428i	$-0.313050\pi$
$757$	30.4924			1.10827			0.554133	+	0.832428i	$0.313050\pi$
$758$	6.24621	+	10.8188i	0.226873	+	0.392955i
$759$	1.50000	−	2.59808i	0.0544466	−	0.0943042i
$760$	4.00000	−	6.92820i	0.145095	−	0.251312i
$761$	15.1231	+	26.1940i	0.548212	+	0.949531i	0.998397	+	0.0565960i	$0.0180247\pi$
$761$	15.1231	+	26.1940i	0.548212	+	0.949531i	−0.450185	+	0.892935i	$0.648642\pi$
$762$	−13.6847			−0.495743
$763$	31.0961	+	10.7720i	1.12576	+	0.389973i
$764$	−24.4924			−0.886105
$765$	−6.00000	−	10.3923i	−0.216930	−	0.375735i
$766$	−1.87689	+	3.25088i	−0.0678150	+	0.117459i
$767$	2.24621	−	3.89055i	0.0811060	−	0.140480i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	6.94602			0.250480			0.125240	−	0.992126i	$-0.460030\pi$
$769$	6.94602			0.250480			0.125240	+	0.992126i	$0.460030\pi$
$770$	15.3693	−	13.3102i	0.553872	−	0.479667i
$771$	14.4924			0.521932
$772$	6.52699	+	11.3051i	0.234911	+	0.406879i
$773$	19.4384	−	33.6684i	0.699152	−	1.21097i	−0.269608	−	0.962970i	$-0.586894\pi$
$773$	19.4384	−	33.6684i	0.699152	−	1.21097i	0.968761	−	0.247997i	$-0.0797724\pi$
$774$	6.12311	−	10.6055i	0.220090	−	0.381208i
$775$	1.31534	+	2.27824i	0.0472485	+	0.0818367i
$776$	−11.6847			−0.419455
$777$	0.438447	+	2.27824i	0.0157292	+	0.0817313i
$778$	25.1231			0.900707
$779$	−11.1231	−	19.2658i	−0.398527	−	0.690268i
$780$	−4.00000	+	6.92820i	−0.143223	+	0.248069i
$781$	−0.657671	+	1.13912i	−0.0235333	+	0.0407609i
$782$	2.34233	+	4.05703i	0.0837615	+	0.145079i
$783$	0.123106			0.00439944
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	9.75379			0.348128
$786$	−9.28078	−	16.0748i	−0.331034	−	0.573368i
$787$	−19.9309	+	34.5213i	−0.710459	+	1.23055i	0.254226	+	0.967145i	$0.418179\pi$
$787$	−19.9309	+	34.5213i	−0.710459	+	1.23055i	−0.964685	+	0.263406i	$0.915154\pi$
$788$	−0.219224	+	0.379706i	−0.00780952	+	0.0135265i
$789$	4.56155	+	7.90084i	0.162396	+	0.281277i
$790$	31.6847			1.12729
$791$	−3.56155	−	18.5064i	−0.126634	−	0.658011i
$792$	−3.00000			−0.106600
$793$	−3.12311	−	5.40938i	−0.110905	−	0.192093i
$794$	8.68466	−	15.0423i	0.308207	−	0.533830i
$795$	−0.719224	+	1.24573i	−0.0255082	+	0.0441816i
$796$	−1.65767	−	2.87117i	−0.0587546	−	0.101766i
$797$	45.5464			1.61334			0.806668	−	0.591005i	$-0.201269\pi$
$797$	45.5464			1.61334			0.806668	+	0.591005i	$0.201269\pi$
$798$	6.24621	−	5.40938i	0.221113	−	0.191490i
$799$	2.05398			0.0726644
$800$	0.780776	+	1.35234i	0.0276046	+	0.0478126i
$801$	−4.12311	+	7.14143i	−0.145683	+	0.252330i
$802$	16.1501	−	27.9728i	0.570280	−	0.987753i
$803$	−25.3963	−	43.9877i	−0.896216	−	1.55229i
$804$	−2.00000			−0.0705346
$805$	−6.40388	−	2.21837i	−0.225707	−	0.0781873i
$806$	−5.26137			−0.185324
$807$	−4.30776	−	7.46127i	−0.151640	−	0.262649i
$808$	5.78078	−	10.0126i	0.203367	−	0.352242i
$809$	3.56155	−	6.16879i	0.125218	−	0.216883i	−0.796600	−	0.604506i	$-0.793370\pi$
$809$	3.56155	−	6.16879i	0.125218	−	0.216883i	0.921818	+	0.387623i	$0.126704\pi$
$810$	−1.28078	−	2.21837i	−0.0450019	−	0.0779456i
$811$	−14.6847			−0.515648			−0.257824	−	0.966192i	$-0.583005\pi$
$811$	−14.6847			−0.515648			−0.257824	+	0.966192i	$0.583005\pi$
$812$	−0.307764	−	0.106613i	−0.0108004	−	0.00374137i
$813$	22.8078			0.799903
$814$	1.31534	+	2.27824i	0.0461027	+	0.0798522i
$815$	18.0000	−	31.1769i	0.630512	−	1.09208i
$816$	2.34233	−	4.05703i	0.0819979	−	0.142025i
$817$	19.1231	+	33.1222i	0.669033	+	1.15880i
$818$	10.3693			0.362555
$819$	−6.24621	+	5.40938i	−0.218260	+	0.189019i
$820$	18.2462			0.637185
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$	10.0270	−	17.3673i	0.349731	−	0.605752i
$823$	25.1771	−	43.6080i	0.877618	−	1.52008i	0.0236702	−	0.999720i	$-0.492465\pi$
$823$	25.1771	−	43.6080i	0.877618	−	1.52008i	0.853948	−	0.520359i	$-0.174202\pi$
$824$	−8.34233	−	14.4493i	−0.290619	−	0.503367i
$825$	4.68466			0.163099
$826$	−0.719224	−	3.73720i	−0.0250250	−	0.130034i
$827$	18.1231			0.630202			0.315101	−	0.949058i	$-0.397962\pi$
$827$	18.1231			0.630202			0.315101	+	0.949058i	$0.397962\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	5.31534	−	9.20644i	0.184609	−	0.319753i	−0.758835	−	0.651282i	$-0.774231\pi$
$829$	5.31534	−	9.20644i	0.184609	−	0.319753i	0.943445	+	0.331530i	$0.107565\pi$
$830$	8.40388	−	14.5560i	0.291703	−	0.505244i
$831$	0.876894	+	1.51883i	0.0304191	+	0.0526875i
$832$	−3.12311			−0.108274
$833$	−4.68466	+	32.4563i	−0.162314	+	1.12454i
$834$	−18.6847			−0.646997
$835$	−16.8078	−	29.1119i	−0.581657	−	1.00746i
$836$	4.68466	−	8.11407i	0.162022	−	0.280631i
$837$	0.842329	−	1.45896i	0.0291152	−	0.0504289i
$838$	−8.15009	−	14.1164i	−0.281540	−	0.487642i
$839$	15.5076			0.535381			0.267691	−	0.963505i	$-0.413740\pi$
$839$	15.5076			0.535381			0.267691	+	0.963505i	$0.413740\pi$
$840$	1.28078	+	6.65511i	0.0441910	+	0.229623i
$841$	−28.9848			−0.999477
$842$	4.46543	+	7.73436i	0.153889	+	0.266544i
$843$	−7.58854	+	13.1437i	−0.261363	+	0.452694i
$844$	−6.65767	+	11.5314i	−0.229166	+	0.396928i
$845$	−4.15767	−	7.20130i	−0.143028	−	0.247732i
$846$	0.438447			0.0150741
$847$	−4.00000	+	3.46410i	−0.137442	+	0.119028i
$848$	−0.561553			−0.0192838
$849$	−11.6847	−	20.2384i	−0.401016	−	0.694581i
$850$	−3.65767	+	6.33527i	−0.125457	+	0.217298i
$851$	0.438447	−	0.759413i	0.0150298	−	0.0260323i
$852$	−0.219224	−	0.379706i	−0.00751048	−	0.0130085i
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	−5.00000	−	1.73205i	−0.171096	−	0.0592696i
$855$	8.00000			0.273594
$856$	1.28078	+	2.21837i	0.0437760	+	0.0758223i
$857$	8.75379	−	15.1620i	0.299024	−	0.517924i	−0.676889	−	0.736085i	$-0.736672\pi$
$857$	8.75379	−	15.1620i	0.299024	−	0.517924i	0.975913	+	0.218161i	$0.0700057\pi$
$858$	−4.68466	+	8.11407i	−0.159932	+	0.277010i
$859$	15.7808	+	27.3331i	0.538433	+	0.932594i	0.998989	+	0.0449627i	$0.0143169\pi$
$859$	15.7808	+	27.3331i	0.538433	+	0.932594i	−0.460556	+	0.887631i	$0.652350\pi$
$860$	−31.3693			−1.06968
$861$	17.8078	+	6.16879i	0.606887	+	0.210232i
$862$	−21.3693			−0.727842
$863$	−23.5885	−	40.8566i	−0.802963	−	1.39077i	−0.917657	−	0.397372i	$-0.869922\pi$
$863$	−23.5885	−	40.8566i	−0.802963	−	1.39077i	0.114694	−	0.993401i	$-0.463411\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−10.8078	+	18.7196i	−0.367475	+	0.636485i
$866$	−9.00000	−	15.5885i	−0.305832	−	0.529717i
$867$	4.94602			0.167976
$868$	−3.36932	+	2.91791i	−0.114362	+	0.0990405i
$869$	37.1080			1.25880
$870$	−0.157671	−	0.273094i	−0.00534554	−	0.00925875i
$871$	−3.12311	+	5.40938i	−0.105822	+	0.183290i
$872$	−6.21922	+	10.7720i	−0.210609	+	0.364786i
$873$	−5.84233	−	10.1192i	−0.197733	−	0.342483i
$874$	−3.12311			−0.105641
$875$	4.40388	+	22.8832i	0.148878	+	0.773595i
$876$	16.9309			0.572041
$877$	10.0000	+	17.3205i	0.337676	+	0.584872i	0.983995	−	0.178195i	$-0.0570259\pi$
$877$	10.0000	+	17.3205i	0.337676	+	0.584872i	−0.646319	+	0.763067i	$0.723693\pi$
$878$	−13.2808	+	23.0030i	−0.448204	+	0.776313i
$879$	4.71922	−	8.17394i	0.159175	−	0.275700i
$880$	3.84233	+	6.65511i	0.129525	+	0.224344i
$881$	15.9460			0.537235			0.268618	−	0.963247i	$-0.413433\pi$
$881$	15.9460			0.537235			0.268618	+	0.963247i	$0.413433\pi$
$882$	−1.00000	+	6.92820i	−0.0336718	+	0.233285i
$883$	15.5076			0.521872			0.260936	−	0.965356i	$-0.415969\pi$
$883$	15.5076			0.521872			0.260936	+	0.965356i	$0.415969\pi$
$884$	−7.31534	−	12.6705i	−0.246042	−	0.426156i
$885$	1.84233	−	3.19101i	0.0619292	−	0.107265i
$886$	0.473012	−	0.819281i	0.0158912	−	0.0275243i
$887$	17.7116	+	30.6775i	0.594699	+	1.03005i	0.993589	+	0.113050i	$0.0360620\pi$
$887$	17.7116	+	30.6775i	0.594699	+	1.03005i	−0.398890	+	0.916999i	$0.630605\pi$
$888$	−0.876894			−0.0294266
$889$	6.84233	+	35.5538i	0.229484	+	1.19244i
$890$	21.1231			0.708048
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	−7.71922	+	13.3701i	−0.258459	+	0.447664i
$893$	−0.684658	+	1.18586i	−0.0229112	+	0.0396834i
$894$	−4.56155	−	7.90084i	−0.152561	−	0.264244i
$895$	38.7386			1.29489
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$	3.12311			0.104277
$898$	18.2462	+	31.6034i	0.608884	+	1.05462i
$899$	0.103695	−	0.179606i	0.00345844	−	0.00599019i
$900$	−0.780776	+	1.35234i	−0.0260259	+	0.0450781i
$901$	−1.31534	−	2.27824i	−0.0438204	−	0.0758991i
$902$	21.3693			0.711520
$903$	−30.6155	−	10.6055i	−1.01882	−	0.352930i
$904$	7.12311			0.236911
$905$	29.3693	+	50.8691i	0.976269	+	1.69095i
$906$	−0.157671	+	0.273094i	−0.00523826	+	0.00907293i
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	−10.3078	−	17.8536i	−0.342075	−	0.592492i
$909$	11.5616			0.383473
$910$	20.0000	+	6.92820i	0.662994	+	0.229668i
$911$	10.8769			0.360368			0.180184	−	0.983633i	$-0.442331\pi$
$911$	10.8769			0.360368			0.180184	+	0.983633i	$0.442331\pi$
$912$	1.56155	+	2.70469i	0.0517082	+	0.0895612i
$913$	9.84233	−	17.0474i	0.325734	−	0.564187i
$914$	19.2116	−	33.2755i	0.635465	−	1.10066i
$915$	−2.56155	−	4.43674i	−0.0846823	−	0.146674i
$916$	−7.31534			−0.241706
$917$	−37.1231	+	32.1496i	−1.22591	+	1.06167i
$918$	4.68466			0.154617
$919$	20.8348	+	36.0868i	0.687275	+	1.19040i	0.972716	+	0.231999i	$0.0745266\pi$
$919$	20.8348	+	36.0868i	0.687275	+	1.19040i	−0.285441	+	0.958396i	$0.592140\pi$
$920$	1.28078	−	2.21837i	0.0422259	−	0.0731375i
$921$	2.34233	−	4.05703i	0.0771824	−	0.133684i
$922$	−4.12311	−	7.14143i	−0.135787	−	0.235190i
$923$	−1.36932			−0.0450716
$924$	1.50000	+	7.79423i	0.0493464	+	0.256411i
$925$	1.36932			0.0450229
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$	8.34233	−	14.4493i	0.273998	−	0.474579i
$928$	0.0615528	−	0.106613i	0.00202057	−	0.00349973i
$929$	−3.49242	−	6.04905i	−0.114583	−	0.198463i	0.803030	−	0.595938i	$-0.203220\pi$
$929$	−3.49242	−	6.04905i	−0.114583	−	0.198463i	−0.917613	+	0.397475i	$0.869886\pi$
$930$	−4.31534			−0.141506
$931$	−17.1771	−	13.5234i	−0.562956	−	0.443213i
$932$	18.2462			0.597675
$933$	−2.34233	−	4.05703i	−0.0766844	−	0.132821i
$934$	13.4654	−	23.3228i	0.440602	−	0.763146i
$935$	−18.0000	+	31.1769i	−0.588663	+	1.01959i
$936$	−1.56155	−	2.70469i	−0.0510410	−	0.0884055i
$937$	−36.4233			−1.18990			−0.594949	−	0.803764i	$-0.702828\pi$
$937$	−36.4233			−1.18990			−0.594949	+	0.803764i	$0.702828\pi$
$938$	1.00000	+	5.19615i	0.0326512	+	0.169660i
$939$	24.8078			0.809571
$940$	−0.561553	−	0.972638i	−0.0183158	−	0.0317240i
$941$	−8.52699	+	14.7692i	−0.277972	+	0.481461i	−0.970881	−	0.239564i	$-0.922996\pi$
$941$	−8.52699	+	14.7692i	−0.277972	+	0.481461i	0.692909	+	0.721025i	$0.256329\pi$
$942$	−1.90388	+	3.29762i	−0.0620318	+	0.107442i
$943$	−3.56155	−	6.16879i	−0.115980	−	0.200883i
$944$	1.43845			0.0468175
$945$	−5.12311	+	4.43674i	−0.166655	+	0.144327i
$946$	−36.7386			−1.19448
$947$	0.192236	+	0.332962i	0.00624683	+	0.0108198i	0.869132	−	0.494580i	$-0.164678\pi$
$947$	0.192236	+	0.332962i	0.00624683	+	0.0108198i	−0.862885	+	0.505400i	$0.831345\pi$
$948$	−6.18466	+	10.7121i	−0.200868	+	0.347914i
$949$	26.4384	−	45.7927i	0.858228	−	1.48650i
$950$	−2.43845	−	4.22351i	−0.0791137	−	0.137029i
$951$	27.9309			0.905721
$952$	−11.7116	−	4.05703i	−0.379577	−	0.131489i
$953$	−11.5616			−0.374515			−0.187258	−	0.982311i	$-0.559960\pi$
$953$	−11.5616			−0.374515			−0.187258	+	0.982311i	$0.559960\pi$
$954$	−0.280776	−	0.486319i	−0.00909047	−	0.0157452i
$955$	−31.3693	+	54.3333i	−1.01509	+	1.75818i
$956$	−5.90388	+	10.2258i	−0.190945	+	0.330727i
$957$	−0.184658	−	0.319838i	−0.00596916	−	0.0103389i
$958$	28.2462			0.912594
$959$	−50.1349	−	17.3673i	−1.61894	−	0.560818i
$960$	−2.56155			−0.0826738
$961$	14.0810	+	24.3889i	0.454225	+	0.786740i
$962$	−1.36932	+	2.37173i	−0.0441485	+	0.0764675i
$963$	−1.28078	+	2.21837i	−0.0412724	+	0.0714860i
$964$	−5.15767	−	8.93335i	−0.166117	−	0.287724i
$965$	33.4384			1.07642
$966$	2.00000	−	1.73205i	0.0643489	−	0.0557278i
$967$	17.0540			0.548419			0.274209	−	0.961670i	$-0.411584\pi$
$967$	17.0540			0.548419			0.274209	+	0.961670i	$0.411584\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	−7.31534	+	12.6705i	−0.235003	+	0.407036i
$970$	−14.9654	+	25.9209i	−0.480511	+	0.832270i
$971$	−25.6771	−	44.4740i	−0.824017	−	1.42724i	−0.902668	−	0.430337i	$-0.858395\pi$
$971$	−25.6771	−	44.4740i	−0.824017	−	1.42724i	0.0786517	−	0.996902i	$-0.474939\pi$
$972$	1.00000			0.0320750
$973$	9.34233	+	48.5442i	0.299501	+	1.55625i
$974$	−17.6847			−0.566653
$975$	2.43845	+	4.22351i	0.0780928	+	0.135261i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	−28.1231	+	48.7106i	−0.899738	+	1.55839i	−0.0719088	+	0.997411i	$0.522909\pi$
$977$	−28.1231	+	48.7106i	−0.899738	+	1.55839i	−0.827829	+	0.560980i	$0.810424\pi$
$978$	7.02699	+	12.1711i	0.224698	+	0.389189i
$979$	24.7386			0.790650
$980$	16.6501	−	6.65511i	0.531868	−	0.212590i
$981$	−12.4384			−0.397129
$982$	8.96543	+	15.5286i	0.286099	+	0.495537i
$983$	10.9309	−	18.9328i	0.348641	−	0.603863i	−0.637368	−	0.770560i	$-0.719977\pi$
$983$	10.9309	−	18.9328i	0.348641	−	0.603863i	0.986008	+	0.166697i	$0.0533101\pi$
$984$	−3.56155	+	6.16879i	−0.113538	+	0.196654i
$985$	0.561553	+	0.972638i	0.0178926	+	0.0309908i
$986$	0.576708			0.0183661
$987$	−0.219224	−	1.13912i	−0.00697796	−	0.0362586i
$988$	9.75379			0.310309
$989$	6.12311	+	10.6055i	0.194703	+	0.337236i
$990$	−3.84233	+	6.65511i	−0.122117	+	0.211513i
$991$	19.5270	−	33.8217i	0.620295	−	1.07438i	−0.369135	−	0.929376i	$-0.620346\pi$
$991$	19.5270	−	33.8217i	0.620295	−	1.07438i	0.989431	−	0.145007i	$-0.0463205\pi$
$992$	−0.842329	−	1.45896i	−0.0267440	−	0.0463219i
$993$	−20.4924			−0.650307
$994$	−0.876894	+	0.759413i	−0.0278134	+	0.0240871i
$995$	−8.49242			−0.269228
$996$	3.28078	+	5.68247i	0.103955	+	0.180056i
$997$	23.3002	−	40.3571i	0.737924	−	1.27812i	−0.215504	−	0.976503i	$-0.569139\pi$
$997$	23.3002	−	40.3571i	0.737924	−	1.27812i	0.953428	−	0.301619i	$-0.0975272\pi$
$998$	−4.90388	+	8.49377i	−0.155230	+	0.268866i
$999$	−0.438447	−	0.759413i	−0.0138719	−	0.0240268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.i.277.2	✓	4
7.2	even	3	inner	966.2.i.i.415.2	yes	4
7.3	odd	6		6762.2.a.br.1.2		2
7.4	even	3		6762.2.a.bx.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.i.277.2	✓	4	1.1	even	1	trivial
966.2.i.i.415.2	yes	4	7.2	even	3	inner
6762.2.a.br.1.2		2	7.3	odd	6
6762.2.a.bx.1.1		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28078 + 2.21837i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28078 + 2.21837i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.28078 + 2.21837i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} -3.12311 q^{13} +(-2.00000 + 1.73205i) q^{14} -2.56155 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.34233 - 4.05703i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.56155 + 2.70469i) q^{19} -2.56155 q^{20} +(-2.50000 - 0.866025i) q^{21} -3.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.780776 + 1.35234i) q^{25} +(-1.56155 - 2.70469i) q^{26} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} +0.123106 q^{29} +(-1.28078 - 2.21837i) q^{30} +(0.842329 - 1.45896i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +4.68466 q^{34} +(-5.12311 + 4.43674i) q^{35} +1.00000 q^{36} +(-0.438447 - 0.759413i) q^{37} +(-1.56155 + 2.70469i) q^{38} +(1.56155 - 2.70469i) q^{39} +(-1.28078 - 2.21837i) q^{40} -7.12311 q^{41} +(-0.500000 - 2.59808i) q^{42} +12.2462 q^{43} +(-1.50000 - 2.59808i) q^{44} +(1.28078 - 2.21837i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(0.219224 + 0.379706i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -1.56155 q^{50} +(2.34233 + 4.05703i) q^{51} +(1.56155 - 2.70469i) q^{52} +(0.280776 - 0.486319i) q^{53} +(0.500000 + 0.866025i) q^{54} -7.68466 q^{55} +(-0.500000 - 2.59808i) q^{56} -3.12311 q^{57} +(0.0615528 + 0.106613i) q^{58} +(-0.719224 + 1.24573i) q^{59} +(1.28078 - 2.21837i) q^{60} +(1.00000 + 1.73205i) q^{61} +1.68466 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(1.50000 - 2.59808i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.34233 + 4.05703i) q^{68} -1.00000 q^{69} +(-6.40388 - 2.21837i) q^{70} +0.438447 q^{71} +(0.500000 + 0.866025i) q^{72} +(-8.46543 + 14.6626i) q^{73} +(0.438447 - 0.759413i) q^{74} +(-0.780776 - 1.35234i) q^{75} -3.12311 q^{76} +(-7.50000 - 2.59808i) q^{77} +3.12311 q^{78} +(-6.18466 - 10.7121i) q^{79} +(1.28078 - 2.21837i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.56155 - 6.16879i) q^{82} -6.56155 q^{83} +(2.00000 - 1.73205i) q^{84} +12.0000 q^{85} +(6.12311 + 10.6055i) q^{86} +(-0.0615528 + 0.106613i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-4.12311 - 7.14143i) q^{89} +2.56155 q^{90} +(-1.56155 - 8.11407i) q^{91} -1.00000 q^{92} +(0.842329 + 1.45896i) q^{93} +(-0.219224 + 0.379706i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} +11.6847 q^{97} +(-5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9} - q^{10} - 6 q^{11} - 2 q^{12} + 4 q^{13} - 8 q^{14} - 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 10 q^{21} - 12 q^{22} + 2 q^{23} + 2 q^{24} + q^{25} + 2 q^{26} + 4 q^{27} - 10 q^{28} - 16 q^{29} - q^{30} - 9 q^{31} + 2 q^{32} - 6 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 10 q^{37} + 2 q^{38} - 2 q^{39} - q^{40} - 12 q^{41} - 2 q^{42} + 16 q^{43} - 6 q^{44} + q^{45} - 2 q^{46} + 5 q^{47} + 4 q^{48} - 26 q^{49} + 2 q^{50} - 3 q^{51} - 2 q^{52} - 3 q^{53} + 2 q^{54} - 6 q^{55} - 2 q^{56} + 4 q^{57} - 8 q^{58} - 7 q^{59} + q^{60} + 4 q^{61} - 18 q^{62} + 8 q^{63} + 4 q^{64} - 16 q^{65} + 6 q^{66} + 4 q^{67} - 3 q^{68} - 4 q^{69} - 5 q^{70} + 10 q^{71} + 2 q^{72} - 5 q^{73} + 10 q^{74} + q^{75} + 4 q^{76} - 30 q^{77} - 4 q^{78} + q^{80} - 2 q^{81} - 6 q^{82} - 18 q^{83} + 8 q^{84} + 48 q^{85} + 8 q^{86} + 8 q^{87} + 6 q^{88} + 2 q^{90} + 2 q^{91} - 4 q^{92} - 9 q^{93} - 5 q^{94} - 16 q^{95} + 2 q^{96} + 22 q^{97} - 22 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9 - q^10 - 6 * q^11 - 2 * q^12 + 4 * q^13 - 8 * q^14 - 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 10 * q^21 - 12 * q^22 + 2 * q^23 + 2 * q^24 + q^25 + 2 * q^26 + 4 * q^27 - 10 * q^28 - 16 * q^29 - q^30 - 9 * q^31 + 2 * q^32 - 6 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 10 * q^37 + 2 * q^38 - 2 * q^39 - q^40 - 12 * q^41 - 2 * q^42 + 16 * q^43 - 6 * q^44 + q^45 - 2 * q^46 + 5 * q^47 + 4 * q^48 - 26 * q^49 + 2 * q^50 - 3 * q^51 - 2 * q^52 - 3 * q^53 + 2 * q^54 - 6 * q^55 - 2 * q^56 + 4 * q^57 - 8 * q^58 - 7 * q^59 + q^60 + 4 * q^61 - 18 * q^62 + 8 * q^63 + 4 * q^64 - 16 * q^65 + 6 * q^66 + 4 * q^67 - 3 * q^68 - 4 * q^69 - 5 * q^70 + 10 * q^71 + 2 * q^72 - 5 * q^73 + 10 * q^74 + q^75 + 4 * q^76 - 30 * q^77 - 4 * q^78 + q^80 - 2 * q^81 - 6 * q^82 - 18 * q^83 + 8 * q^84 + 48 * q^85 + 8 * q^86 + 8 * q^87 + 6 * q^88 + 2 * q^90 + 2 * q^91 - 4 * q^92 - 9 * q^93 - 5 * q^94 - 16 * q^95 + 2 * q^96 + 22 * q^97 - 22 * q^98 + 12 * q^99

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