LMFDB - Embedded newform 966.2.i.m.415.3

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			415.3
Root			$-0.415888 - 2.23501i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.m.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.415888 - 0.720339i) q^{5} -1.00000 q^{6} +(2.64352 + 0.108691i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.415888 - 0.720339i) q^{5} -1.00000 q^{6} +(2.64352 + 0.108691i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.415888 + 0.720339i) q^{10} +(1.22763 + 2.12632i) q^{11} +(0.500000 - 0.866025i) q^{12} -5.30815 q^{13} +(-1.41589 + 2.23501i) q^{14} +0.831776 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.64352 + 2.84666i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} -0.831776 q^{20} +(1.22763 + 2.34370i) q^{21} -2.45526 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.15407 + 3.73097i) q^{25} +(2.65407 - 4.59699i) q^{26} -1.00000 q^{27} +(-1.22763 - 2.34370i) q^{28} +10.3081 q^{29} +(-0.415888 + 0.720339i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.22763 + 2.12632i) q^{33} -3.28704 q^{34} +(1.17770 - 1.85903i) q^{35} +1.00000 q^{36} +(-1.16822 + 2.02342i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-2.65407 - 4.59699i) q^{39} +(0.415888 - 0.720339i) q^{40} +3.66355 q^{41} +(-2.64352 - 0.108691i) q^{42} +2.00000 q^{43} +(1.22763 - 2.12632i) q^{44} +(0.415888 + 0.720339i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-1.95526 + 3.38661i) q^{47} -1.00000 q^{48} +(6.97637 + 0.574653i) q^{49} -4.30815 q^{50} +(-1.64352 + 2.84666i) q^{51} +(2.65407 + 4.59699i) q^{52} +(3.89226 + 6.74159i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.04223 q^{55} +(2.64352 + 0.108691i) q^{56} +2.00000 q^{57} +(-5.15407 + 8.92712i) q^{58} +(1.66355 + 2.88136i) q^{59} +(-0.415888 - 0.720339i) q^{60} +(-7.30815 + 12.6581i) q^{61} -2.00000 q^{62} +(-1.41589 + 2.23501i) q^{63} +1.00000 q^{64} +(-2.20760 + 3.82367i) q^{65} +(-1.22763 - 2.12632i) q^{66} +(-5.89226 - 10.2057i) q^{67} +(1.64352 - 2.84666i) q^{68} +1.00000 q^{69} +(1.02111 + 1.94943i) q^{70} -5.04223 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.80815 - 13.5241i) q^{73} +(-1.16822 - 2.02342i) q^{74} +(-2.15407 + 3.73097i) q^{75} -2.00000 q^{76} +(3.01415 + 5.75439i) q^{77} +5.30815 q^{78} +(-5.22763 + 9.05452i) q^{79} +(0.415888 + 0.720339i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.83178 + 3.17273i) q^{82} +6.57407 q^{83} +(1.41589 - 2.23501i) q^{84} +2.73408 q^{85} +(-1.00000 + 1.73205i) q^{86} +(5.15407 + 8.92712i) q^{87} +(1.22763 + 2.12632i) q^{88} +(6.47637 - 11.2174i) q^{89} -0.831776 q^{90} +(-14.0322 - 0.576948i) q^{91} -1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-1.95526 - 3.38661i) q^{94} +(-0.831776 - 1.44068i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.00000 q^{97} +(-3.98585 + 5.75439i) q^{98} -2.45526 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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
$5$	0.415888	−	0.720339i	0.185991	−	0.322145i	−0.757919	−	0.652348i	$-0.773784\pi$
$5$	0.415888	−	0.720339i	0.185991	−	0.322145i	0.943910	+	0.330203i	$0.107117\pi$
$6$	−1.00000			−0.408248
$7$	2.64352	+	0.108691i	0.999156	+	0.0410813i
$7$	2.64352	+	0.108691i	0.999156	+	0.0410813i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.415888	+	0.720339i	0.131515	+	0.227791i
$11$	1.22763	+	2.12632i	0.370144	+	0.641109i	0.989587	−	0.143933i	$-0.0459749\pi$
$11$	1.22763	+	2.12632i	0.370144	+	0.641109i	−0.619443	+	0.785042i	$0.712642\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−5.30815			−1.47222			−0.736108	−	0.676864i	$-0.763338\pi$
$13$	−5.30815			−1.47222			−0.736108	+	0.676864i	$0.763338\pi$
$14$	−1.41589	+	2.23501i	−0.378412	+	0.597331i
$15$	0.831776			0.214764
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.64352	+	2.84666i	0.398612	+	0.690416i	0.993555	−	0.113352i	$-0.0361588\pi$
$17$	1.64352	+	2.84666i	0.398612	+	0.690416i	−0.594943	+	0.803768i	$0.702825\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	−0.831776			−0.185991
$21$	1.22763	+	2.34370i	0.267891	+	0.511437i
$22$	−2.45526			−0.523463
$23$	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
$25$	2.15407	+	3.73097i	0.430815	+	0.746193i
$26$	2.65407	−	4.59699i	0.520507	−	0.901544i
$27$	−1.00000			−0.192450
$28$	−1.22763	−	2.34370i	−0.232000	−	0.442917i
$29$	10.3081			1.91418			0.957088	−	0.289799i	$-0.0935884\pi$
$29$	10.3081			1.91418			0.957088	+	0.289799i	$0.0935884\pi$
$30$	−0.415888	+	0.720339i	−0.0759304	+	0.131515i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.22763	+	2.12632i	−0.213703	+	0.370144i
$34$	−3.28704			−0.563722
$35$	1.17770	−	1.85903i	0.199068	−	0.314233i
$36$	1.00000			0.166667
$37$	−1.16822	+	2.02342i	−0.192055	+	0.332649i	−0.945931	−	0.324368i	$-0.894848\pi$
$37$	−1.16822	+	2.02342i	−0.192055	+	0.332649i	0.753876	+	0.657016i	$0.228182\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	−2.65407	−	4.59699i	−0.424992	−	0.736108i
$40$	0.415888	−	0.720339i	0.0657577	−	0.113896i
$41$	3.66355			0.572151			0.286075	−	0.958207i	$-0.407649\pi$
$41$	3.66355			0.572151			0.286075	+	0.958207i	$0.407649\pi$
$42$	−2.64352	−	0.108691i	−0.407904	−	0.0167714i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	1.22763	−	2.12632i	0.185072	−	0.320554i
$45$	0.415888	+	0.720339i	0.0619969	+	0.107382i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−1.95526	+	3.38661i	−0.285204	+	0.493988i	−0.972659	−	0.232240i	$-0.925395\pi$
$47$	−1.95526	+	3.38661i	−0.285204	+	0.493988i	0.687455	+	0.726227i	$0.258728\pi$
$48$	−1.00000			−0.144338
$49$	6.97637	+	0.574653i	0.996625	+	0.0820933i
$50$	−4.30815			−0.609264
$51$	−1.64352	+	2.84666i	−0.230139	+	0.398612i
$52$	2.65407	+	4.59699i	0.368054	+	0.637488i
$53$	3.89226	+	6.74159i	0.534643	+	0.926029i	0.999181	+	0.0404755i	$0.0128873\pi$
$53$	3.89226	+	6.74159i	0.534643	+	0.926029i	−0.464537	+	0.885553i	$0.653779\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.04223			0.275374
$56$	2.64352	+	0.108691i	0.353255	+	0.0145244i
$57$	2.00000			0.264906
$58$	−5.15407	+	8.92712i	−0.676763	+	1.17219i
$59$	1.66355	+	2.88136i	0.216576	+	0.375121i	0.953759	−	0.300573i	$-0.0971777\pi$
$59$	1.66355	+	2.88136i	0.216576	+	0.375121i	−0.737183	+	0.675693i	$0.763844\pi$
$60$	−0.415888	−	0.720339i	−0.0536909	−	0.0929954i
$61$	−7.30815	+	12.6581i	−0.935713	+	1.62070i	−0.162354	+	0.986733i	$0.551909\pi$
$61$	−7.30815	+	12.6581i	−0.935713	+	1.62070i	−0.773358	+	0.633969i	$0.781425\pi$
$62$	−2.00000			−0.254000
$63$	−1.41589	+	2.23501i	−0.178385	+	0.281585i
$64$	1.00000			0.125000
$65$	−2.20760	+	3.82367i	−0.273819	+	0.474268i
$66$	−1.22763	−	2.12632i	−0.151111	−	0.261732i
$67$	−5.89226	−	10.2057i	−0.719854	−	1.24682i	−0.961057	−	0.276349i	$-0.910875\pi$
$67$	−5.89226	−	10.2057i	−0.719854	−	1.24682i	0.241203	−	0.970475i	$-0.422458\pi$
$68$	1.64352	−	2.84666i	0.199306	−	0.345208i
$69$	1.00000			0.120386
$70$	1.02111	+	1.94943i	0.122046	+	0.233002i
$71$	−5.04223			−0.598402			−0.299201	−	0.954190i	$-0.596720\pi$
$71$	−5.04223			−0.598402			−0.299201	+	0.954190i	$0.596720\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−7.80815	−	13.5241i	−0.913875	−	1.58288i	−0.808541	−	0.588440i	$-0.799742\pi$
$73$	−7.80815	−	13.5241i	−0.913875	−	1.58288i	−0.105334	−	0.994437i	$-0.533591\pi$
$74$	−1.16822	−	2.02342i	−0.135803	−	0.235218i
$75$	−2.15407	+	3.73097i	−0.248731	+	0.430815i
$76$	−2.00000			−0.229416
$77$	3.01415	+	5.75439i	0.343494	+	0.655774i
$78$	5.30815			0.601029
$79$	−5.22763	+	9.05452i	−0.588154	+	1.01871i	0.406320	+	0.913731i	$0.366812\pi$
$79$	−5.22763	+	9.05452i	−0.588154	+	1.01871i	−0.994474	+	0.104982i	$0.966521\pi$
$80$	0.415888	+	0.720339i	0.0464977	+	0.0805364i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.83178	+	3.17273i	−0.202286	+	0.350369i
$83$	6.57407			0.721598			0.360799	−	0.932644i	$-0.382504\pi$
$83$	6.57407			0.721598			0.360799	+	0.932644i	$0.382504\pi$
$84$	1.41589	−	2.23501i	0.154486	−	0.243859i
$85$	2.73408			0.296552
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	5.15407	+	8.92712i	0.552575	+	0.957088i
$88$	1.22763	+	2.12632i	0.130866	+	0.226666i
$89$	6.47637	−	11.2174i	0.686494	−	1.18904i	−0.286471	−	0.958089i	$-0.592482\pi$
$89$	6.47637	−	11.2174i	0.686494	−	1.18904i	0.972965	−	0.230954i	$-0.0741846\pi$
$90$	−0.831776			−0.0876769
$91$	−14.0322	−	0.576948i	−1.47097	−	0.0604806i
$92$	−1.00000			−0.104257
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$	−1.95526	−	3.38661i	−0.201670	−	0.349302i
$95$	−0.831776	−	1.44068i	−0.0853384	−	0.147810i
$96$	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	$0.633125\pi$
$98$	−3.98585	+	5.75439i	−0.402632	+	0.581281i
$99$	−2.45526			−0.246763
$100$	2.15407	−	3.73097i	0.215407	−	0.373097i
$101$	0.154074	+	0.266865i	0.0153310	+	0.0265540i	0.873589	−	0.486664i	$-0.161786\pi$
$101$	0.154074	+	0.266865i	0.0153310	+	0.0265540i	−0.858258	+	0.513218i	$0.828453\pi$
$102$	−1.64352	−	2.84666i	−0.162733	−	0.281861i
$103$	3.00108	−	5.19802i	0.295705	−	0.512176i	−0.679444	−	0.733728i	$-0.737779\pi$
$103$	3.00108	−	5.19802i	0.295705	−	0.512176i	0.975149	+	0.221552i	$0.0711121\pi$
$104$	−5.30815			−0.520507
$105$	2.19881	+	0.0904065i	0.214582	+	0.00882277i
$106$	−7.78452			−0.756100
$107$	−1.54474	+	2.67557i	−0.149336	+	0.258657i	−0.930982	−	0.365065i	$-0.881047\pi$
$107$	−1.54474	+	2.67557i	−0.149336	+	0.258657i	0.781646	+	0.623722i	$0.214380\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−6.24874	−	10.8231i	−0.598521	−	1.03667i	−0.993040	−	0.117781i	$-0.962422\pi$
$109$	−6.24874	−	10.8231i	−0.598521	−	1.03667i	0.394519	−	0.918888i	$-0.370911\pi$
$110$	−1.02111	+	1.76862i	−0.0973593	+	0.168631i
$111$	−2.33645			−0.221766
$112$	−1.41589	+	2.23501i	−0.133789	+	0.211188i
$113$	7.74230			0.728334			0.364167	−	0.931334i	$-0.381354\pi$
$113$	7.74230			0.728334			0.364167	+	0.931334i	$0.381354\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$	−0.415888	−	0.720339i	−0.0387818	−	0.0671720i
$116$	−5.15407	−	8.92712i	−0.478544	−	0.828862i
$117$	2.65407	−	4.59699i	0.245369	−	0.424992i
$118$	−3.32710			−0.306285
$119$	4.03526	+	7.70382i	0.369912	+	0.706208i
$120$	0.831776			0.0759304
$121$	2.48585	−	4.30562i	0.225986	−	0.391420i
$122$	−7.30815	−	12.6581i	−0.661649	−	1.14601i
$123$	1.83178	+	3.17273i	0.165166	+	0.286075i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	7.74230			0.692492
$126$	−1.22763	−	2.34370i	−0.109366	−	0.208793i
$127$	10.9527			0.971899			0.485949	−	0.873987i	$-0.338474\pi$
$127$	10.9527			0.971899			0.485949	+	0.873987i	$0.338474\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$	−2.20760	−	3.82367i	−0.193619	−	0.335358i
$131$	−6.77289	+	11.7310i	−0.591750	+	1.02494i	0.402247	+	0.915531i	$0.368229\pi$
$131$	−6.77289	+	11.7310i	−0.591750	+	1.02494i	−0.993997	+	0.109410i	$0.965104\pi$
$132$	2.45526			0.213703
$133$	2.83178	−	4.47002i	0.245546	−	0.387600i
$134$	11.7845			1.01803
$135$	−0.415888	+	0.720339i	−0.0357939	+	0.0619969i
$136$	1.64352	+	2.84666i	0.140930	+	0.244099i
$137$	−9.76233	−	16.9089i	−0.834052	−	1.44462i	−0.894800	−	0.446467i	$-0.852682\pi$
$137$	−9.76233	−	16.9089i	−0.834052	−	1.44462i	0.0607478	−	0.998153i	$-0.480651\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	−12.8822			−1.09266			−0.546328	−	0.837571i	$-0.683975\pi$
$139$	−12.8822			−1.09266			−0.546328	+	0.837571i	$0.683975\pi$
$140$	−2.19881	−	0.0904065i	−0.185834	−	0.00764075i
$141$	−3.91052			−0.329325
$142$	2.52111	−	4.36670i	0.211567	−	0.366445i
$143$	−6.51644	−	11.2868i	−0.544932	−	0.943850i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.28704	−	7.42536i	0.356019	−	0.616643i
$146$	15.6163			1.29241
$147$	2.99052	+	6.32904i	0.246654	+	0.522011i
$148$	2.33645			0.192055
$149$	−5.03937	+	8.72845i	−0.412841	+	0.715062i	−0.995199	−	0.0978703i	$-0.968797\pi$
$149$	−5.03937	+	8.72845i	−0.412841	+	0.715062i	0.582358	+	0.812933i	$0.302130\pi$
$150$	−2.15407	−	3.73097i	−0.175879	−	0.304632i
$151$	10.1399	+	17.5629i	0.825175	+	1.42925i	0.901785	+	0.432185i	$0.142257\pi$
$151$	10.1399	+	17.5629i	0.825175	+	1.42925i	−0.0766098	+	0.997061i	$0.524410\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−3.28704			−0.265741
$154$	−6.49052	−	0.266865i	−0.523021	−	0.0215046i
$155$	1.66355			0.133620
$156$	−2.65407	+	4.59699i	−0.212496	+	0.368054i
$157$	3.53578	+	6.12415i	0.282186	+	0.488760i	0.971923	−	0.235300i	$-0.0756072\pi$
$157$	3.53578	+	6.12415i	0.282186	+	0.488760i	−0.689737	+	0.724060i	$0.742274\pi$
$158$	−5.22763	−	9.05452i	−0.415888	−	0.720339i
$159$	−3.89226	+	6.74159i	−0.308676	+	0.534643i
$160$	−0.831776			−0.0657577
$161$	1.41589	−	2.23501i	0.111588	−	0.176143i
$162$	1.00000			0.0785674
$163$	1.13296	−	1.96235i	0.0887404	−	0.153703i	−0.818239	−	0.574879i	$-0.805049\pi$
$163$	1.13296	−	1.96235i	0.0887404	−	0.153703i	0.906979	+	0.421176i	$0.138383\pi$
$164$	−1.83178	−	3.17273i	−0.143038	−	0.247749i
$165$	1.02111	+	1.76862i	0.0794935	+	0.137687i
$166$	−3.28704	+	5.69331i	−0.255123	+	0.441887i
$167$	21.9244			1.69656			0.848282	−	0.529544i	$-0.177637\pi$
$167$	21.9244			1.69656			0.848282	+	0.529544i	$0.177637\pi$
$168$	1.22763	+	2.34370i	0.0947137	+	0.180820i
$169$	15.1764			1.16742
$170$	−1.36704	+	2.36778i	−0.104847	+	0.181600i
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	9.25177	−	16.0245i	0.703399	−	1.21832i	−0.263867	−	0.964559i	$-0.584998\pi$
$173$	9.25177	−	16.0245i	0.703399	−	1.21832i	0.967266	−	0.253764i	$-0.0816687\pi$
$174$	−10.3081			−0.781459
$175$	5.28881	+	10.0970i	0.399797	+	0.763262i
$176$	−2.45526			−0.185072
$177$	−1.66355	+	2.88136i	−0.125040	+	0.216576i
$178$	6.47637	+	11.2174i	0.485425	+	0.840780i
$179$	3.08822	+	5.34896i	0.230824	+	0.399800i	0.958051	−	0.286598i	$-0.0925244\pi$
$179$	3.08822	+	5.34896i	0.230824	+	0.399800i	−0.727227	+	0.686398i	$0.759191\pi$
$180$	0.415888	−	0.720339i	0.0309985	−	0.0536909i
$181$	−13.2505			−0.984903			−0.492452	−	0.870340i	$-0.663899\pi$
$181$	−13.2505			−0.984903			−0.492452	+	0.870340i	$0.663899\pi$
$182$	7.51574	−	11.8638i	0.557104	−	0.879400i
$183$	−14.6163			−1.08047
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	0.971701	+	1.68303i	0.0714409	+	0.123739i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	−4.03526	+	6.98928i	−0.295088	+	0.511107i
$188$	3.91052			0.285204
$189$	−2.64352	−	0.108691i	−0.192288	−	0.00790610i
$190$	1.66355			0.120687
$191$	6.47637	−	11.2174i	0.468614	−	0.811663i	−0.530743	−	0.847533i	$-0.678087\pi$
$191$	6.47637	−	11.2174i	0.468614	−	0.811663i	0.999356	+	0.0358700i	$0.0114202\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−6.31763	−	10.9424i	−0.454753	−	0.787655i	0.543921	−	0.839136i	$-0.316939\pi$
$193$	−6.31763	−	10.9424i	−0.454753	−	0.787655i	−0.998674	+	0.0514815i	$0.983606\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$	−4.41519			−0.316178
$196$	−2.99052	−	6.32904i	−0.213609	−	0.452074i
$197$	−8.92445			−0.635840			−0.317920	−	0.948117i	$-0.602984\pi$
$197$	−8.92445			−0.635840			−0.317920	+	0.948117i	$0.602984\pi$
$198$	1.22763	−	2.12632i	0.0872438	−	0.151111i
$199$	−2.89118	−	5.00767i	−0.204950	−	0.354985i	0.745166	−	0.666878i	$-0.232370\pi$
$199$	−2.89118	−	5.00767i	−0.204950	−	0.354985i	−0.950117	+	0.311894i	$0.899037\pi$
$200$	2.15407	+	3.73097i	0.152316	+	0.263819i
$201$	5.89226	−	10.2057i	0.415608	−	0.719854i
$202$	−0.308149			−0.0216813
$203$	27.2498	+	1.12040i	1.91256	+	0.0786368i
$204$	3.28704			0.230139
$205$	1.52363	−	2.63900i	0.106415	−	0.184316i
$206$	3.00108	+	5.19802i	0.209095	+	0.362163i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	2.65407	−	4.59699i	0.184027	−	0.318744i
$209$	4.91052			0.339668
$210$	−1.17770	+	1.85903i	−0.0812691	+	0.128285i
$211$	7.39763			0.509274			0.254637	−	0.967037i	$-0.418044\pi$
$211$	7.39763			0.509274			0.254637	+	0.967037i	$0.418044\pi$
$212$	3.89226	−	6.74159i	0.267322	−	0.463015i
$213$	−2.52111	−	4.36670i	−0.172744	−	0.299201i
$214$	−1.54474	−	2.67557i	−0.105596	−	0.182898i
$215$	0.831776	−	1.44068i	0.0567267	−	0.0982535i
$216$	−1.00000			−0.0680414
$217$	2.45526	+	4.68740i	0.166674	+	0.318201i
$218$	12.4975			0.846437
$219$	7.80815	−	13.5241i	0.527626	−	0.913875i
$220$	−1.02111	−	1.76862i	−0.0688434	−	0.119240i
$221$	−8.72404	−	15.1105i	−0.586842	−	1.01644i
$222$	1.16822	−	2.02342i	0.0784061	−	0.135803i
$223$	−1.00934			−0.0675907			−0.0337953	−	0.999429i	$-0.510759\pi$
$223$	−1.00934			−0.0675907			−0.0337953	+	0.999429i	$0.510759\pi$
$224$	−1.22763	−	2.34370i	−0.0820245	−	0.156595i
$225$	−4.30815			−0.287210
$226$	−3.87115	+	6.70502i	−0.257505	+	0.446012i
$227$	−8.89118	−	15.4000i	−0.590128	−	1.02213i	−0.994215	−	0.107412i	$-0.965744\pi$
$227$	−8.89118	−	15.4000i	−0.590128	−	1.02213i	0.404086	−	0.914721i	$-0.367590\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	7.15926	−	12.4002i	0.473097	−	0.819429i	−0.526429	−	0.850219i	$-0.676469\pi$
$229$	7.15926	−	12.4002i	0.473097	−	0.819429i	0.999526	+	0.0307908i	$0.00980256\pi$
$230$	0.831776			0.0548457
$231$	−3.47637	+	5.48752i	−0.228729	+	0.361053i
$232$	10.3081			0.676763
$233$	6.91052	−	11.9694i	0.452723	−	0.784140i	−0.545831	−	0.837895i	$-0.683786\pi$
$233$	6.91052	−	11.9694i	0.452723	−	0.784140i	0.998554	+	0.0537558i	$0.0171193\pi$
$234$	2.65407	+	4.59699i	0.173502	+	0.300515i
$235$	1.62634	+	2.81690i	0.106091	+	0.183754i
$236$	1.66355	−	2.88136i	0.108288	−	0.187560i
$237$	−10.4553			−0.679142
$238$	−8.68934	−	0.357271i	−0.563246	−	0.0231584i
$239$	−10.2659			−0.664047			−0.332024	−	0.943271i	$-0.607731\pi$
$239$	−10.2659			−0.664047			−0.332024	+	0.943271i	$0.607731\pi$
$240$	−0.415888	+	0.720339i	−0.0268455	+	0.0464977i
$241$	−4.37652	−	7.58035i	−0.281916	−	0.488293i	0.689940	−	0.723866i	$-0.257637\pi$
$241$	−4.37652	−	7.58035i	−0.281916	−	0.488293i	−0.971857	+	0.235573i	$0.924303\pi$
$242$	2.48585	+	4.30562i	0.159797	+	0.276776i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	14.6163			0.935713
$245$	3.31533	−	4.78636i	0.211809	−	0.305790i
$246$	−3.66355			−0.233580
$247$	−5.30815	+	9.19398i	−0.337749	+	0.584999i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	3.28704	+	5.69331i	0.208307	+	0.360799i
$250$	−3.87115	+	6.70502i	−0.244833	+	0.424063i
$251$	−10.5397			−0.665261			−0.332630	−	0.943057i	$-0.607936\pi$
$251$	−10.5397			−0.665261			−0.332630	+	0.943057i	$0.607936\pi$
$252$	2.64352	+	0.108691i	0.166526	+	0.00684689i
$253$	2.45526			0.154361
$254$	−5.47637	+	9.48536i	−0.343618	+	0.595164i
$255$	1.36704	+	2.36778i	0.0856073	+	0.148276i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.37652	+	11.0445i	−0.397756	+	0.688934i	−0.993449	−	0.114279i	$-0.963544\pi$
$257$	−6.37652	+	11.0445i	−0.397756	+	0.688934i	0.595693	+	0.803213i	$0.296878\pi$
$258$	−2.00000			−0.124515
$259$	−3.30815	+	5.22198i	−0.205558	+	0.324478i
$260$	4.41519			0.273819
$261$	−5.15407	+	8.92712i	−0.319029	+	0.552575i
$262$	−6.77289	−	11.7310i	−0.418430	−	0.724743i
$263$	−7.85289	−	13.6016i	−0.484230	−	0.838711i	0.515606	−	0.856826i	$-0.327567\pi$
$263$	−7.85289	−	13.6016i	−0.484230	−	0.838711i	−0.999836	+	0.0181150i	$0.994233\pi$
$264$	−1.22763	+	2.12632i	−0.0755554	+	0.130866i
$265$	6.47498			0.397755
$266$	2.45526	+	4.68740i	0.150542	+	0.287403i
$267$	12.9527			0.792695
$268$	−5.89226	+	10.2057i	−0.359927	+	0.623412i
$269$	−9.89637	−	17.1410i	−0.603392	−	1.04511i	−0.992303	−	0.123831i	$-0.960482\pi$
$269$	−9.89637	−	17.1410i	−0.603392	−	1.04511i	0.388911	−	0.921275i	$-0.372851\pi$
$270$	−0.415888	−	0.720339i	−0.0253101	−	0.0438384i
$271$	7.76341	−	13.4466i	0.471593	−	0.816824i	−0.527878	−	0.849320i	$-0.677012\pi$
$271$	7.76341	−	13.4466i	0.471593	−	0.816824i	0.999472	+	0.0324961i	$0.0103457\pi$
$272$	−3.28704			−0.199306
$273$	−6.51644	−	12.4407i	−0.394393	−	0.752946i
$274$	19.5247			1.17953
$275$	−5.28881	+	9.16049i	−0.318927	+	0.552398i
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	−0.277558	−	0.480744i	−0.0166768	−	0.0288851i	0.857567	−	0.514373i	$-0.171975\pi$
$277$	−0.277558	−	0.480744i	−0.0166768	−	0.0288851i	−0.874243	+	0.485488i	$0.838642\pi$
$278$	6.44111	−	11.1563i	0.386312	−	0.669112i
$279$	−2.00000			−0.119737
$280$	1.17770	−	1.85903i	0.0703811	−	0.111098i
$281$	24.3973			1.45542			0.727709	−	0.685886i	$-0.240585\pi$
$281$	24.3973			1.45542			0.727709	+	0.685886i	$0.240585\pi$
$282$	1.95526	−	3.38661i	0.116434	−	0.201670i
$283$	−9.53470	−	16.5146i	−0.566779	−	0.981690i	−0.996882	−	0.0789102i	$-0.974856\pi$
$283$	−9.53470	−	16.5146i	−0.566779	−	0.981690i	0.430103	−	0.902780i	$-0.358477\pi$
$284$	2.52111	+	4.36670i	0.149601	+	0.259116i
$285$	0.831776	−	1.44068i	0.0492702	−	0.0853384i
$286$	13.0329			0.770650
$287$	9.68467	+	0.398195i	0.571668	+	0.0235047i
$288$	1.00000			0.0589256
$289$	3.09770	−	5.36537i	0.182218	−	0.315610i
$290$	4.28704	+	7.42536i	0.251743	+	0.436032i
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$	−7.80815	+	13.5241i	−0.456937	+	0.791439i
$293$	−1.40585			−0.0821305			−0.0410652	−	0.999156i	$-0.513075\pi$
$293$	−1.40585			−0.0821305			−0.0410652	+	0.999156i	$0.513075\pi$
$294$	−6.97637	−	0.574653i	−0.406870	−	0.0335144i
$295$	2.76741			0.161125
$296$	−1.16822	+	2.02342i	−0.0679016	+	0.117609i
$297$	−1.22763	−	2.12632i	−0.0712343	−	0.123381i
$298$	−5.03937	−	8.72845i	−0.291923	−	0.505625i
$299$	−2.65407	+	4.59699i	−0.153489	+	0.265851i
$300$	4.30815			0.248731
$301$	5.28704	+	0.217382i	0.304740	+	0.0125297i
$302$	−20.2798			−1.16697
$303$	−0.154074	+	0.266865i	−0.00885134	+	0.0153310i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	6.07874	+	10.5287i	0.348068	+	0.602871i
$306$	1.64352	−	2.84666i	0.0939537	−	0.162733i
$307$	−27.2187			−1.55345			−0.776726	−	0.629839i	$-0.783121\pi$
$307$	−27.2187			−1.55345			−0.776726	+	0.629839i	$0.783121\pi$
$308$	3.47637	−	5.48752i	0.198085	−	0.312681i
$309$	6.00216			0.341451
$310$	−0.831776	+	1.44068i	−0.0472417	+	0.0818250i
$311$	−4.04474	−	7.00570i	−0.229356	−	0.397257i	0.728261	−	0.685300i	$-0.240329\pi$
$311$	−4.04474	−	7.00570i	−0.229356	−	0.397257i	−0.957617	+	0.288043i	$0.906995\pi$
$312$	−2.65407	−	4.59699i	−0.150257	−	0.260253i
$313$	6.91052	−	11.9694i	0.390606	−	0.676549i	−0.601924	−	0.798553i	$-0.705599\pi$
$313$	6.91052	−	11.9694i	0.390606	−	0.676549i	0.992530	+	0.122005i	$0.0389323\pi$
$314$	−7.07156			−0.399071
$315$	1.02111	+	1.94943i	0.0575332	+	0.109838i
$316$	10.4553			0.588154
$317$	−6.32710	+	10.9589i	−0.355366	+	0.615511i	−0.987180	−	0.159608i	$-0.948977\pi$
$317$	−6.32710	+	10.9589i	−0.355366	+	0.615511i	0.631815	+	0.775119i	$0.282310\pi$
$318$	−3.89226	−	6.74159i	−0.218267	−	0.378050i
$319$	12.6546	+	21.9184i	0.708521	+	1.22719i
$320$	0.415888	−	0.720339i	0.0232488	−	0.0402682i
$321$	−3.08948			−0.172438
$322$	1.22763	+	2.34370i	0.0684131	+	0.130609i
$323$	6.57407			0.365791
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−11.4341	−	19.8045i	−0.634252	−	1.09856i
$326$	1.13296	+	1.96235i	0.0627489	+	0.108684i
$327$	6.24874	−	10.8231i	0.345556	−	0.598521i
$328$	3.66355			0.202286
$329$	−5.53686	+	8.74004i	−0.305257	+	0.481854i
$330$	−2.04223			−0.112421
$331$	12.1210	−	20.9941i	0.666229	−	1.15394i	−0.312722	−	0.949845i	$-0.601241\pi$
$331$	12.1210	−	20.9941i	0.666229	−	1.15394i	0.978951	−	0.204097i	$-0.0654259\pi$
$332$	−3.28704	−	5.69331i	−0.180400	−	0.312461i
$333$	−1.16822	−	2.02342i	−0.0640183	−	0.110883i
$334$	−10.9622	+	18.9871i	−0.599826	+	1.03893i
$335$	−9.80208			−0.535545
$336$	−2.64352	−	0.108691i	−0.144216	−	0.00592958i
$337$	24.6163			1.34094			0.670468	−	0.741939i	$-0.266094\pi$
$337$	24.6163			1.34094			0.670468	+	0.741939i	$0.266094\pi$
$338$	−7.58822	+	13.1432i	−0.412745	+	0.714895i
$339$	3.87115	+	6.70502i	0.210252	+	0.364167i
$340$	−1.36704	−	2.36778i	−0.0741381	−	0.128411i
$341$	−2.45526	+	4.25263i	−0.132960	+	0.230293i
$342$	−2.00000			−0.108148
$343$	18.3797	+	2.27737i	0.992411	+	0.122967i
$344$	2.00000			0.107833
$345$	0.415888	−	0.720339i	0.0223907	−	0.0387818i
$346$	9.25177	+	16.0245i	0.497378	+	0.861485i
$347$	−15.7045	−	27.2010i	−0.843063	−	1.46023i	−0.887293	−	0.461206i	$-0.847417\pi$
$347$	−15.7045	−	27.2010i	−0.843063	−	1.46023i	0.0442304	−	0.999021i	$-0.485916\pi$
$348$	5.15407	−	8.92712i	0.276287	−	0.478544i
$349$	−13.6024			−0.728118			−0.364059	−	0.931376i	$-0.618609\pi$
$349$	−13.6024			−0.728118			−0.364059	+	0.931376i	$0.618609\pi$
$350$	−11.3887	−	0.468257i	−0.608750	−	0.0250294i
$351$	5.30815			0.283328
$352$	1.22763	−	2.12632i	0.0654329	−	0.113333i
$353$	−13.8318	−	23.9573i	−0.736191	−	1.27512i	−0.954199	−	0.299173i	$-0.903289\pi$
$353$	−13.8318	−	23.9573i	−0.736191	−	1.27512i	0.218008	−	0.975947i	$-0.430044\pi$
$354$	−1.66355	−	2.88136i	−0.0884168	−	0.153142i
$355$	−2.09700	+	3.63211i	−0.111297	+	0.192773i
$356$	−12.9527			−0.686494
$357$	−4.65407	+	7.34655i	−0.246320	+	0.388821i
$358$	−6.17644			−0.326435
$359$	−11.1188	+	19.2583i	−0.586828	+	1.01642i	0.407816	+	0.913064i	$0.366290\pi$
$359$	−11.1188	+	19.2583i	−0.586828	+	1.01642i	−0.994645	+	0.103353i	$0.967043\pi$
$360$	0.415888	+	0.720339i	0.0219192	+	0.0379652i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	6.62526	−	11.4753i	0.348216	−	0.603128i
$363$	4.97170			0.260947
$364$	6.51644	+	12.4407i	0.341554	+	0.652070i
$365$	−12.9893			−0.679889
$366$	7.30815	−	12.6581i	0.382003	−	0.661649i
$367$	−12.8028	−	22.1751i	−0.668300	−	1.15753i	−0.978379	−	0.206818i	$-0.933689\pi$
$367$	−12.8028	−	22.1751i	−0.668300	−	1.15753i	0.310080	−	0.950711i	$-0.399644\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−1.83178	+	3.17273i	−0.0953585	+	0.165166i
$370$	−1.94340			−0.101033
$371$	9.55651	+	18.2446i	0.496149	+	0.947211i
$372$	2.00000			0.103695
$373$	9.99104	−	17.3050i	0.517316	−	0.896018i	−0.482481	−	0.875906i	$-0.660264\pi$
$373$	9.99104	−	17.3050i	0.517316	−	0.896018i	0.999798	−	0.0201120i	$-0.00640227\pi$
$374$	−4.03526	−	6.98928i	−0.208658	−	0.361407i
$375$	3.87115	+	6.70502i	0.199905	+	0.346246i
$376$	−1.95526	+	3.38661i	−0.100835	+	0.174651i
$377$	−54.7172			−2.81808
$378$	1.41589	−	2.23501i	0.0728254	−	0.114956i
$379$	−18.7752			−0.964416			−0.482208	−	0.876057i	$-0.660165\pi$
$379$	−18.7752			−0.964416			−0.482208	+	0.876057i	$0.660165\pi$
$380$	−0.831776	+	1.44068i	−0.0426692	+	0.0739052i
$381$	5.47637	+	9.48536i	0.280563	+	0.485949i
$382$	6.47637	+	11.2174i	0.331360	+	0.573932i
$383$	−15.2376	+	26.3923i	−0.778606	+	1.34859i	0.154139	+	0.988049i	$0.450740\pi$
$383$	−15.2376	+	26.3923i	−0.778606	+	1.34859i	−0.932745	+	0.360536i	$0.882594\pi$
$384$	−1.00000			−0.0510310
$385$	5.39866	+	0.221972i	0.275141	+	0.0113127i
$386$	12.6353			0.643117
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	4.00000	+	6.92820i	0.203069	+	0.351726i
$389$	12.3293	+	21.3549i	0.625118	+	1.08274i	0.988518	+	0.151103i	$0.0482826\pi$
$389$	12.3293	+	21.3549i	0.625118	+	1.08274i	−0.363400	+	0.931633i	$0.618384\pi$
$390$	2.20760	−	3.82367i	0.111786	−	0.193619i
$391$	3.28704			0.166233
$392$	6.97637	+	0.574653i	0.352360	+	0.0290244i
$393$	−13.5458			−0.683294
$394$	4.46222	−	7.72880i	0.224804	−	0.389371i
$395$	4.34822	+	7.53133i	0.218783	+	0.378942i
$396$	1.22763	+	2.12632i	0.0616907	+	0.106851i
$397$	−10.2493	+	17.7522i	−0.514396	+	0.890959i	0.485465	+	0.874256i	$0.338650\pi$
$397$	−10.2493	+	17.7522i	−0.514396	+	0.890959i	−0.999860	+	0.0167031i	$0.994683\pi$
$398$	5.78236			0.289844
$399$	5.28704	+	0.217382i	0.264683	+	0.0108827i
$400$	−4.30815			−0.215407
$401$	−4.81174	+	8.33418i	−0.240287	+	0.416189i	−0.960796	−	0.277256i	$-0.910575\pi$
$401$	−4.81174	+	8.33418i	−0.240287	+	0.416189i	0.720509	+	0.693446i	$0.243908\pi$
$402$	5.89226	+	10.2057i	0.293879	+	0.509014i
$403$	−5.30815	−	9.19398i	−0.264418	−	0.457985i
$404$	0.154074	−	0.266865i	0.00766548	−	0.0132770i
$405$	−0.831776			−0.0413313
$406$	−14.5952	+	23.0388i	−0.724347	+	1.14340i
$407$	−5.73659			−0.284352
$408$	−1.64352	+	2.84666i	−0.0813663	+	0.140930i
$409$	−14.9481	−	25.8908i	−0.739135	−	1.28022i	−0.952885	−	0.303331i	$-0.901901\pi$
$409$	−14.9481	−	25.8908i	−0.739135	−	1.28022i	0.213751	−	0.976888i	$-0.431432\pi$
$410$	1.52363	+	2.63900i	0.0752466	+	0.130331i
$411$	9.76233	−	16.9089i	0.481540	−	0.834052i
$412$	−6.00216			−0.295705
$413$	4.08445	+	7.79773i	0.200983	+	0.383701i
$414$	−1.00000			−0.0491473
$415$	2.73408	−	4.73556i	0.134211	−	0.232460i
$416$	2.65407	+	4.59699i	0.130127	+	0.225386i
$417$	−6.44111	−	11.1563i	−0.315423	−	0.546328i
$418$	−2.45526	+	4.25263i	−0.120091	+	0.208003i
$419$	12.8762			0.629042			0.314521	−	0.949251i	$-0.398156\pi$
$419$	12.8762			0.629042			0.314521	+	0.949251i	$0.398156\pi$
$420$	−1.02111	−	1.94943i	−0.0498252	−	0.0951226i
$421$	27.5447			1.34245			0.671224	−	0.741254i	$-0.265769\pi$
$421$	27.5447			1.34245			0.671224	+	0.741254i	$0.265769\pi$
$422$	−3.69881	+	6.40654i	−0.180055	+	0.311865i
$423$	−1.95526	−	3.38661i	−0.0950680	−	0.164663i
$424$	3.89226	+	6.74159i	0.189025	+	0.327401i
$425$	−7.08052	+	12.2638i	−0.343456	+	0.594883i
$426$	5.04223			0.244297
$427$	−20.6950	+	32.6675i	−1.00150	+	1.58089i
$428$	3.08948			0.149336
$429$	6.51644	−	11.2868i	0.314617	−	0.544932i
$430$	0.831776	+	1.44068i	0.0401118	+	0.0694757i
$431$	16.5458	+	28.6581i	0.796982	+	1.38041i	0.921573	+	0.388205i	$0.126905\pi$
$431$	16.5458	+	28.6581i	0.796982	+	1.38041i	−0.124591	+	0.992208i	$0.539762\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	29.3479			1.41037			0.705184	−	0.709024i	$-0.250864\pi$
$433$	29.3479			1.41037			0.705184	+	0.709024i	$0.250864\pi$
$434$	−5.28704	−	0.217382i	−0.253786	−	0.0104347i
$435$	8.57407			0.411095
$436$	−6.24874	+	10.8231i	−0.299261	+	0.518334i
$437$	−1.00000	−	1.73205i	−0.0478365	−	0.0828552i
$438$	7.80815	+	13.5241i	0.373088	+	0.646207i
$439$	−14.4080	+	24.9554i	−0.687657	+	1.19106i	0.284937	+	0.958546i	$0.408027\pi$
$439$	−14.4080	+	24.9554i	−0.687657	+	1.19106i	−0.972594	+	0.232510i	$0.925306\pi$
$440$	2.04223			0.0973593
$441$	−3.98585	+	5.75439i	−0.189802	+	0.274019i
$442$	17.4481			0.829920
$443$	−3.78223	+	6.55101i	−0.179699	+	0.311248i	−0.941777	−	0.336237i	$-0.890846\pi$
$443$	−3.78223	+	6.55101i	−0.179699	+	0.311248i	0.762078	+	0.647485i	$0.224179\pi$
$444$	1.16822	+	2.02342i	0.0554415	+	0.0960274i
$445$	−5.38689	−	9.33037i	−0.255363	−	0.442302i
$446$	0.504672	−	0.874117i	0.0238969	−	0.0413907i
$447$	−10.0787			−0.476708
$448$	2.64352	+	0.108691i	0.124894	+	0.00513517i
$449$	22.5175			1.06267			0.531333	−	0.847163i	$-0.321691\pi$
$449$	22.5175			1.06267			0.531333	+	0.847163i	$0.321691\pi$
$450$	2.15407	−	3.73097i	0.101544	−	0.175879i
$451$	4.49749	+	7.78987i	0.211778	+	0.366811i
$452$	−3.87115	−	6.70502i	−0.182083	−	0.315378i
$453$	−10.1399	+	17.5629i	−0.476415	+	0.825175i
$454$	17.7824			0.834568
$455$	−6.25142	+	9.86799i	−0.293071	+	0.462618i
$456$	2.00000			0.0936586
$457$	5.66355	−	9.80956i	0.264930	−	0.458872i	−0.702615	−	0.711570i	$-0.747985\pi$
$457$	5.66355	−	9.80956i	0.264930	−	0.458872i	0.967545	+	0.252698i	$0.0813179\pi$
$458$	7.15926	+	12.4002i	0.334530	+	0.579424i
$459$	−1.64352	−	2.84666i	−0.0767128	−	0.132871i
$460$	−0.415888	+	0.720339i	−0.0193909	+	0.0335860i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−3.01415	−	5.75439i	−0.140231	−	0.267718i
$463$	−25.2326			−1.17266			−0.586329	−	0.810073i	$-0.699427\pi$
$463$	−25.2326			−1.17266			−0.586329	+	0.810073i	$0.699427\pi$
$464$	−5.15407	+	8.92712i	−0.239272	+	0.414431i
$465$	0.831776	+	1.44068i	0.0385727	+	0.0668099i
$466$	6.91052	+	11.9694i	0.320124	+	0.554470i
$467$	−12.6546	+	21.9184i	−0.585585	+	1.01426i	0.409218	+	0.912437i	$0.365802\pi$
$467$	−12.6546	+	21.9184i	−0.585585	+	1.01426i	−0.994802	+	0.101825i	$0.967532\pi$
$468$	−5.30815			−0.245369
$469$	−14.4670	−	27.6194i	−0.668025	−	1.27534i
$470$	−3.25268			−0.150035
$471$	−3.53578	+	6.12415i	−0.162920	+	0.282186i
$472$	1.66355	+	2.88136i	0.0765712	+	0.132625i
$473$	2.45526	+	4.25263i	0.112893	+	0.195536i
$474$	5.22763	−	9.05452i	0.240113	−	0.415888i
$475$	8.61630			0.395343
$476$	4.65407	−	7.34655i	0.213319	−	0.336729i
$477$	−7.78452			−0.356429
$478$	5.13296	−	8.89055i	0.234776	−	0.406644i
$479$	−0.921257	−	1.59566i	−0.0420933	−	0.0729077i	0.844211	−	0.536011i	$-0.180069\pi$
$479$	−0.921257	−	1.59566i	−0.0420933	−	0.0729077i	−0.886304	+	0.463103i	$0.846736\pi$
$480$	−0.415888	−	0.720339i	−0.0189826	−	0.0328788i
$481$	6.20111	−	10.7406i	0.282746	−	0.489731i
$482$	8.75303			0.398690
$483$	2.64352	+	0.108691i	0.120284	+	0.00494561i
$484$	−4.97170			−0.225986
$485$	−3.32710	+	5.76271i	−0.151076	+	0.261671i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	18.2587	+	31.6251i	0.827382	+	1.43307i	0.900085	+	0.435715i	$0.143504\pi$
$487$	18.2587	+	31.6251i	0.827382	+	1.43307i	−0.0727026	+	0.997354i	$0.523162\pi$
$488$	−7.30815	+	12.6581i	−0.330824	+	0.573005i
$489$	2.26592			0.102469
$490$	2.48744	+	5.26435i	0.112371	+	0.237819i
$491$	−19.0870			−0.861382			−0.430691	−	0.902499i	$-0.641730\pi$
$491$	−19.0870			−0.861382			−0.430691	+	0.902499i	$0.641730\pi$
$492$	1.83178	−	3.17273i	0.0825828	−	0.143038i
$493$	16.9416	+	29.3438i	0.763012	+	1.32158i
$494$	−5.30815	−	9.19398i	−0.238825	−	0.413657i
$495$	−1.02111	+	1.76862i	−0.0458956	+	0.0794935i
$496$	−2.00000			−0.0898027
$497$	−13.3292	−	0.548044i	−0.597897	−	0.0245832i
$498$	−6.57407			−0.294591
$499$	−5.87526	+	10.1762i	−0.263013	+	0.455551i	−0.967041	−	0.254621i	$-0.918049\pi$
$499$	−5.87526	+	10.1762i	−0.263013	+	0.455551i	0.704028	+	0.710172i	$0.251383\pi$
$500$	−3.87115	−	6.70502i	−0.173123	−	0.299858i
$501$	10.9622	+	18.9871i	0.489756	+	0.848282i
$502$	5.26986	−	9.12766i	0.235205	−	0.407387i
$503$	32.2842			1.43948			0.719740	−	0.694244i	$-0.244261\pi$
$503$	32.2842			1.43948			0.719740	+	0.694244i	$0.244261\pi$
$504$	−1.41589	+	2.23501i	−0.0630687	+	0.0995552i
$505$	0.256311			0.0114057
$506$	−1.22763	+	2.12632i	−0.0545748	+	0.0945263i
$507$	7.58822	+	13.1432i	0.337005	+	0.583709i
$508$	−5.47637	−	9.48536i	−0.242975	−	0.420845i
$509$	5.06459	−	8.77213i	0.224484	−	0.388818i	−0.731680	−	0.681648i	$-0.761264\pi$
$509$	5.06459	−	8.77213i	0.224484	−	0.388818i	0.956165	+	0.292830i	$0.0945970\pi$
$510$	−2.73408			−0.121067
$511$	−19.1710	−	36.5999i	−0.848076	−	1.61908i
$512$	1.00000			0.0441942
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$	−6.37652	−	11.0445i	−0.281256	−	0.487150i
$515$	−2.49623	−	4.32359i	−0.109997	−	0.190520i
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$	−9.60134			−0.422266
$518$	−2.86829	−	5.47593i	−0.126026	−	0.240599i
$519$	18.5035			0.812216
$520$	−2.20760	+	3.82367i	−0.0968095	+	0.167679i
$521$	−15.1603	−	26.2585i	−0.664187	−	1.15040i	−0.979505	−	0.201419i	$-0.935445\pi$
$521$	−15.1603	−	26.2585i	−0.664187	−	1.15040i	0.315319	−	0.948986i	$-0.397889\pi$
$522$	−5.15407	−	8.92712i	−0.225588	−	0.390729i
$523$	11.7817	−	20.4064i	0.515176	−	0.892312i	−0.484669	−	0.874698i	$-0.661060\pi$
$523$	11.7817	−	20.4064i	0.515176	−	0.892312i	0.999845	−	0.0176137i	$-0.00560689\pi$
$524$	13.5458			0.591750
$525$	−6.09986	+	9.62875i	−0.266220	+	0.420233i
$526$	15.7058			0.684804
$527$	−3.28704	+	5.69331i	−0.143186	+	0.248005i
$528$	−1.22763	−	2.12632i	−0.0534257	−	0.0925361i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−3.23749	+	5.60750i	−0.140628	+	0.243574i
$531$	−3.32710			−0.144384
$532$	−5.28704	−	0.217382i	−0.229222	−	0.00942470i
$533$	−19.4467			−0.842329
$534$	−6.47637	+	11.2174i	−0.280260	+	0.485425i
$535$	1.28488	+	2.22547i	0.0555501	+	0.0962156i
$536$	−5.89226	−	10.2057i	−0.254507	−	0.440819i
$537$	−3.08822	+	5.34896i	−0.133267	+	0.230824i
$538$	19.7927			0.853326
$539$	7.34251	+	15.5394i	0.316264	+	0.669331i
$540$	0.831776			0.0357939
$541$	13.8917	−	24.0611i	0.597251	−	1.03447i	−0.395974	−	0.918262i	$-0.629593\pi$
$541$	13.8917	−	24.0611i	0.597251	−	1.03447i	0.993225	−	0.116207i	$-0.0370736\pi$
$542$	7.76341	+	13.4466i	0.333467	+	0.577582i
$543$	−6.62526	−	11.4753i	−0.284317	−	0.492452i
$544$	1.64352	−	2.84666i	0.0704652	−	0.122049i
$545$	−10.3951			−0.445278
$546$	14.0322	+	0.576948i	0.600522	+	0.0246911i
$547$	13.0233			0.556835			0.278417	−	0.960460i	$-0.410190\pi$
$547$	13.0233			0.556835			0.278417	+	0.960460i	$0.410190\pi$
$548$	−9.76233	+	16.9089i	−0.417026	+	0.722310i
$549$	−7.30815	−	12.6581i	−0.311904	−	0.540234i
$550$	−5.28881	−	9.16049i	−0.225516	−	0.390605i
$551$	10.3081	−	17.8542i	0.439142	−	0.760616i
$552$	1.00000			0.0425628
$553$	−14.8035	+	23.3676i	−0.629508	+	0.993691i
$554$	0.555116			0.0235846
$555$	−0.971701	+	1.68303i	−0.0412464	+	0.0714409i
$556$	6.44111	+	11.1563i	0.273164	+	0.473134i
$557$	−11.8422	−	20.5112i	−0.501768	−	0.869088i	−0.999998	−	0.00204277i	$-0.999350\pi$
$557$	−11.8422	−	20.5112i	−0.501768	−	0.869088i	0.498230	−	0.867045i	$-0.333984\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	−10.6163			−0.449022
$560$	1.02111	+	1.94943i	0.0431499	+	0.0823786i
$561$	−8.07053			−0.340738
$562$	−12.1986	+	21.1287i	−0.514568	+	0.891258i
$563$	2.27704	+	3.94395i	0.0959659	+	0.166218i	0.910011	−	0.414583i	$-0.136073\pi$
$563$	2.27704	+	3.94395i	0.0959659	+	0.166218i	−0.814045	+	0.580801i	$0.802739\pi$
$564$	1.95526	+	3.38661i	0.0823313	+	0.142602i
$565$	3.21993	−	5.57708i	0.135463	−	0.234629i
$566$	19.0694			0.801547
$567$	−1.22763	−	2.34370i	−0.0515556	−	0.0984261i
$568$	−5.04223			−0.211567
$569$	−13.2770	+	22.9964i	−0.556601	+	0.964060i	0.441177	+	0.897420i	$0.354561\pi$
$569$	−13.2770	+	22.9964i	−0.556601	+	0.964060i	−0.997777	+	0.0666401i	$0.978772\pi$
$570$	0.831776	+	1.44068i	0.0348393	+	0.0603434i
$571$	12.1771	+	21.0914i	0.509597	+	0.882649i	0.999938	+	0.0111178i	$0.00353898\pi$
$571$	12.1771	+	21.0914i	0.509597	+	0.882649i	−0.490341	+	0.871531i	$0.663128\pi$
$572$	−6.51644	+	11.2868i	−0.272466	+	0.471925i
$573$	12.9527			0.541109
$574$	−5.18718	+	8.18807i	−0.216509	+	0.341763i
$575$	4.30815			0.179662
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.63045	−	11.4843i	−0.276029	−	0.478096i	0.694365	−	0.719623i	$-0.255685\pi$
$577$	−6.63045	−	11.4843i	−0.276029	−	0.478096i	−0.970394	+	0.241526i	$0.922352\pi$
$578$	3.09770	+	5.36537i	0.128847	+	0.223170i
$579$	6.31763	−	10.9424i	0.262552	−	0.454753i
$580$	−8.57407			−0.356019
$581$	17.3787	+	0.714542i	0.720989	+	0.0296442i
$582$	8.00000			0.331611
$583$	−9.55651	+	16.5524i	−0.395790	+	0.685529i
$584$	−7.80815	−	13.5241i	−0.323103	−	0.559632i
$585$	−2.20760	−	3.82367i	−0.0912728	−	0.158089i
$586$	0.702924	−	1.21750i	0.0290375	−	0.0502944i
$587$	−23.4305			−0.967081			−0.483540	−	0.875322i	$-0.660649\pi$
$587$	−23.4305			−0.967081			−0.483540	+	0.875322i	$0.660649\pi$
$588$	3.98585	−	5.75439i	0.164374	−	0.237307i
$589$	4.00000			0.164817
$590$	−1.38370	+	2.39664i	−0.0569661	+	0.0986683i
$591$	−4.46222	−	7.72880i	−0.183551	−	0.317920i
$592$	−1.16822	−	2.02342i	−0.0480137	−	0.0831622i
$593$	−14.2398	+	24.6640i	−0.584758	+	1.01283i	0.410148	+	0.912019i	$0.365477\pi$
$593$	−14.2398	+	24.6640i	−0.584758	+	1.01283i	−0.994906	+	0.100811i	$0.967856\pi$
$594$	2.45526			0.100741
$595$	7.22758	+	0.297170i	0.296302	+	0.0121828i
$596$	10.0787			0.412841
$597$	2.89118	−	5.00767i	0.118328	−	0.204950i
$598$	−2.65407	−	4.59699i	−0.108533	−	0.187985i
$599$	17.1847	+	29.7647i	0.702146	+	1.21615i	0.967712	+	0.252060i	$0.0811081\pi$
$599$	17.1847	+	29.7647i	0.702146	+	1.21615i	−0.265565	+	0.964093i	$0.585559\pi$
$600$	−2.15407	+	3.73097i	−0.0879397	+	0.152316i
$601$	−17.3271			−0.706787			−0.353394	−	0.935475i	$-0.614972\pi$
$601$	−17.3271			−0.706787			−0.353394	+	0.935475i	$0.614972\pi$
$602$	−2.83178	+	4.47002i	−0.115415	+	0.182184i
$603$	11.7845			0.479903
$604$	10.1399	−	17.5629i	0.412588	−	0.714623i
$605$	−2.06767	−	3.58131i	−0.0840628	−	0.145601i
$606$	−0.154074	−	0.266865i	−0.00625884	−	0.0108406i
$607$	−14.8035	+	25.6404i	−0.600855	+	1.04071i	0.391837	+	0.920035i	$0.371840\pi$
$607$	−14.8035	+	25.6404i	−0.600855	+	1.04071i	−0.992692	+	0.120676i	$0.961494\pi$
$608$	−2.00000			−0.0811107
$609$	12.6546	+	24.1592i	0.512790	+	0.978980i
$610$	−12.1575			−0.492242
$611$	10.3788	−	17.9766i	0.419882	−	0.727256i
$612$	1.64352	+	2.84666i	0.0664353	+	0.115069i
$613$	−11.5147	−	19.9440i	−0.465073	−	0.805530i	0.534132	−	0.845401i	$-0.320639\pi$
$613$	−11.5147	−	19.9440i	−0.465073	−	0.805530i	−0.999205	+	0.0398712i	$0.987305\pi$
$614$	13.6093	−	23.5721i	0.549228	−	0.951291i
$615$	3.04725			0.122877
$616$	3.01415	+	5.75439i	0.121444	+	0.231851i
$617$	−20.2019			−0.813297			−0.406648	−	0.913585i	$-0.633303\pi$
$617$	−20.2019			−0.813297			−0.406648	+	0.913585i	$0.633303\pi$
$618$	−3.00108	+	5.19802i	−0.120721	+	0.209095i
$619$	19.7534	+	34.2138i	0.793955	+	1.37517i	0.923501	+	0.383597i	$0.125315\pi$
$619$	19.7534	+	34.2138i	0.793955	+	1.37517i	−0.129546	+	0.991573i	$0.541352\pi$
$620$	−0.831776	−	1.44068i	−0.0334049	−	0.0578590i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	8.08948			0.324359
$623$	18.3396	−	28.9495i	0.734762	−	1.15984i
$624$	5.30815			0.212496
$625$	−7.55044	+	13.0778i	−0.302018	+	0.523110i
$626$	6.91052	+	11.9694i	0.276200	+	0.478392i
$627$	2.45526	+	4.25263i	0.0980536	+	0.169834i
$628$	3.53578	−	6.12415i	0.141093	−	0.244380i
$629$	−7.67999			−0.306221
$630$	−2.19881	−	0.0904065i	−0.0876029	−	0.00360188i
$631$	9.32495			0.371220			0.185610	−	0.982623i	$-0.440574\pi$
$631$	9.32495			0.371220			0.185610	+	0.982623i	$0.440574\pi$
$632$	−5.22763	+	9.05452i	−0.207944	+	0.360169i
$633$	3.69881	+	6.40654i	0.147015	+	0.254637i
$634$	−6.32710	−	10.9589i	−0.251281	−	0.435232i
$635$	4.55512	−	7.88969i	0.180764	−	0.313093i
$636$	7.78452			0.308676
$637$	−37.0316	−	3.05034i	−1.46725	−	0.120859i
$638$	−25.3092			−1.00200
$639$	2.52111	−	4.36670i	0.0997337	−	0.172744i
$640$	0.415888	+	0.720339i	0.0164394	+	0.0284739i
$641$	9.62456	+	16.6702i	0.380147	+	0.658435i	0.991083	−	0.133246i	$-0.0425399\pi$
$641$	9.62456	+	16.6702i	0.380147	+	0.658435i	−0.610936	+	0.791680i	$0.709207\pi$
$642$	1.54474	−	2.67557i	0.0609660	−	0.105596i
$643$	−26.6163			−1.04964			−0.524822	−	0.851212i	$-0.675868\pi$
$643$	−26.6163			−1.04964			−0.524822	+	0.851212i	$0.675868\pi$
$644$	−2.64352	−	0.108691i	−0.104169	−	0.00428302i
$645$	1.66355			0.0655023
$646$	−3.28704	+	5.69331i	−0.129327	+	0.224000i
$647$	−11.7776	−	20.3993i	−0.463024	−	0.801980i	0.536086	−	0.844163i	$-0.319902\pi$
$647$	−11.7776	−	20.3993i	−0.463024	−	0.801980i	−0.999110	+	0.0421828i	$0.986569\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−4.08445	+	7.07448i	−0.160329	+	0.277698i
$650$	22.8683			0.896968
$651$	−2.83178	+	4.47002i	−0.110986	+	0.175194i
$652$	−2.26592			−0.0887404
$653$	−11.7199	+	20.2995i	−0.458636	+	0.794381i	−0.998889	−	0.0471214i	$-0.984995\pi$
$653$	−11.7199	+	20.2995i	−0.458636	+	0.794381i	0.540253	+	0.841503i	$0.318329\pi$
$654$	6.24874	+	10.8231i	0.244345	+	0.423218i
$655$	5.63352	+	9.75755i	0.220120	+	0.381259i
$656$	−1.83178	+	3.17273i	−0.0715188	+	0.123874i
$657$	15.6163			0.609250
$658$	−4.80067	−	9.16508i	−0.187150	−	0.357292i
$659$	0.234072			0.00911813			0.00455907	−	0.999990i	$-0.498549\pi$
$659$	0.234072			0.00911813			0.00455907	+	0.999990i	$0.498549\pi$
$660$	1.02111	−	1.76862i	0.0397468	−	0.0688434i
$661$	13.4957	+	23.3753i	0.524922	+	0.909192i	0.999579	+	0.0290209i	$0.00923895\pi$
$661$	13.4957	+	23.3753i	0.524922	+	0.909192i	−0.474657	+	0.880171i	$0.657428\pi$
$662$	12.1210	+	20.9941i	0.471095	+	0.815960i
$663$	8.72404	−	15.1105i	0.338814	−	0.586842i
$664$	6.57407			0.255123
$665$	−2.04223	−	3.89887i	−0.0791941	−	0.151192i
$666$	2.33645			0.0905355
$667$	5.15407	−	8.92712i	0.199567	−	0.345659i
$668$	−10.9622	−	18.9871i	−0.424141	−	0.734634i
$669$	−0.504672	−	0.874117i	−0.0195117	−	0.0337953i
$670$	4.90104	−	8.48885i	0.189344	−	0.327953i
$671$	−35.8868			−1.38539
$672$	1.41589	−	2.23501i	0.0546191	−	0.0862173i
$673$	31.1578			1.20104			0.600522	−	0.799609i	$-0.294960\pi$
$673$	31.1578			1.20104			0.600522	+	0.799609i	$0.294960\pi$
$674$	−12.3081	+	21.3183i	−0.474092	+	0.821152i
$675$	−2.15407	−	3.73097i	−0.0829104	−	0.143605i
$676$	−7.58822	−	13.1432i	−0.291855	−	0.505507i
$677$	5.24982	−	9.09296i	0.201767	−	0.349471i	−0.747331	−	0.664452i	$-0.768665\pi$
$677$	5.24982	−	9.09296i	0.201767	−	0.349471i	0.949098	+	0.314981i	$0.101998\pi$
$678$	−7.74230			−0.297341
$679$	−21.1481	−	0.869528i	−0.811591	−	0.0333694i
$680$	2.73408			0.104847
$681$	8.89118	−	15.4000i	0.340711	−	0.590128i
$682$	−2.45526	−	4.25263i	−0.0940167	−	0.162842i
$683$	20.7962	+	36.0200i	0.795743	+	1.37827i	0.922366	+	0.386316i	$0.126253\pi$
$683$	20.7962	+	36.0200i	0.795743	+	1.37827i	−0.126624	+	0.991951i	$0.540414\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	−16.2401			−0.620504
$686$	−11.1621	+	14.7786i	−0.426172	+	0.564250i
$687$	14.3185			0.546286
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−20.6607	−	35.7854i	−0.787110	−	1.36331i
$690$	0.415888	+	0.720339i	0.0158326	+	0.0274228i
$691$	0.343411	−	0.594806i	0.0130640	−	0.0226275i	−0.859420	−	0.511271i	$-0.829175\pi$
$691$	0.343411	−	0.594806i	0.0130640	−	0.0226275i	0.872483	+	0.488644i	$0.162508\pi$
$692$	−18.5035			−0.703399
$693$	−6.49052	−	0.266865i	−0.246555	−	0.0101373i
$694$	31.4090			1.19227
$695$	−5.35756	+	9.27957i	−0.203224	+	0.351994i
$696$	5.15407	+	8.92712i	0.195365	+	0.338382i
$697$	6.02111	+	10.4289i	0.228066	+	0.395022i
$698$	6.80119	−	11.7800i	0.257429	−	0.445880i
$699$	13.8210			0.522760
$700$	6.09986	−	9.62875i	0.230553	−	0.363932i
$701$	−4.59415			−0.173519			−0.0867594	−	0.996229i	$-0.527651\pi$
$701$	−4.59415			−0.173519			−0.0867594	+	0.996229i	$0.527651\pi$
$702$	−2.65407	+	4.59699i	−0.100172	+	0.173502i
$703$	2.33645	+	4.04685i	0.0881208	+	0.152630i
$704$	1.22763	+	2.12632i	0.0462680	+	0.0801386i
$705$	−1.62634	+	2.81690i	−0.0612514	+	0.106091i
$706$	27.6636			1.04113
$707$	0.378292	+	0.722208i	0.0142271	+	0.0271614i
$708$	3.32710			0.125040
$709$	14.3676	−	24.8853i	0.539585	−	0.934588i	−0.459341	−	0.888260i	$-0.651915\pi$
$709$	14.3676	−	24.8853i	0.539585	−	0.934588i	0.998926	−	0.0463286i	$-0.0147521\pi$
$710$	−2.09700	−	3.63211i	−0.0786991	−	0.136311i
$711$	−5.22763	−	9.05452i	−0.196051	−	0.339571i
$712$	6.47637	−	11.2174i	0.242712	−	0.420390i
$713$	2.00000			0.0749006
$714$	−4.03526	−	7.70382i	−0.151016	−	0.288308i
$715$	−10.8404			−0.405409
$716$	3.08822	−	5.34896i	0.115412	−	0.199900i
$717$	−5.13296	−	8.89055i	−0.191694	−	0.332024i
$718$	−11.1188	−	19.2583i	−0.414950	−	0.718715i
$719$	2.26718	−	3.92688i	0.0845516	−	0.146448i	−0.820648	−	0.571433i	$-0.806388\pi$
$719$	2.26718	−	3.92688i	0.0845516	−	0.146448i	0.905200	+	0.424986i	$0.139721\pi$
$720$	−0.831776			−0.0309985
$721$	8.49838	−	13.4149i	0.316496	−	0.499596i
$722$	−15.0000			−0.558242
$723$	4.37652	−	7.58035i	0.162764	−	0.281916i
$724$	6.62526	+	11.4753i	0.246226	+	0.426476i
$725$	22.2045	+	38.4594i	0.824655	+	1.42834i
$726$	−2.48585	+	4.30562i	−0.0922586	+	0.159797i
$727$	−17.0336			−0.631743			−0.315871	−	0.948802i	$-0.602297\pi$
$727$	−17.0336			−0.631743			−0.315871	+	0.948802i	$0.602297\pi$
$728$	−14.0322	−	0.576948i	−0.520067	−	0.0213831i
$729$	1.00000			0.0370370
$730$	6.49463	−	11.2490i	0.240377	−	0.416345i
$731$	3.28704	+	5.69331i	0.121575	+	0.210575i
$732$	7.30815	+	12.6581i	0.270117	+	0.467856i
$733$	6.95955	−	12.0543i	0.257057	−	0.445236i	−0.708395	−	0.705816i	$-0.750581\pi$
$733$	6.95955	−	12.0543i	0.257057	−	0.445236i	0.965452	+	0.260580i	$0.0839139\pi$
$734$	25.6056			0.945118
$735$	5.80278	+	0.477983i	0.214039	+	0.0176307i
$736$	−1.00000			−0.0368605
$737$	14.4670	−	25.0576i	0.532900	−	0.923010i
$738$	−1.83178	−	3.17273i	−0.0674286	−	0.116790i
$739$	−18.3233	−	31.7369i	−0.674035	−	1.16746i	−0.976750	−	0.214381i	$-0.931227\pi$
$739$	−18.3233	−	31.7369i	−0.674035	−	1.16746i	0.302716	−	0.953081i	$-0.402107\pi$
$740$	0.971701	−	1.68303i	0.0357204	−	0.0618696i
$741$	−10.6163			−0.389999
$742$	−20.5785	−	0.846107i	−0.755461	−	0.0310616i
$743$	2.04223			0.0749220			0.0374610	−	0.999298i	$-0.488073\pi$
$743$	2.04223			0.0749220			0.0374610	+	0.999298i	$0.488073\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$	4.19163	+	7.26011i	0.153569	+	0.265990i
$746$	9.99104	+	17.3050i	0.365798	+	0.633581i
$747$	−3.28704	+	5.69331i	−0.120266	+	0.208307i
$748$	8.07053			0.295088
$749$	−4.37436	+	6.90501i	−0.159836	+	0.252304i
$750$	−7.74230			−0.282709
$751$	−6.33748	+	10.9768i	−0.231258	+	0.400550i	−0.958179	−	0.286171i	$-0.907617\pi$
$751$	−6.33748	+	10.9768i	−0.231258	+	0.400550i	0.726921	+	0.686721i	$0.240951\pi$
$752$	−1.95526	−	3.38661i	−0.0713010	−	0.123497i
$753$	−5.26986	−	9.12766i	−0.192044	−	0.332630i
$754$	27.3586	−	47.3865i	0.996341	−	1.72571i
$755$	16.8683			0.613900
$756$	1.22763	+	2.34370i	0.0446485	+	0.0852395i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	9.38759	−	16.2598i	0.340973	−	0.590582i
$759$	1.22763	+	2.12632i	0.0445601	+	0.0771804i
$760$	−0.831776	−	1.44068i	−0.0301717	−	0.0522589i
$761$	8.76341	−	15.1787i	0.317673	−	0.550226i	−0.662329	−	0.749213i	$-0.730432\pi$
$761$	8.76341	−	15.1787i	0.317673	−	0.550226i	0.980002	+	0.198987i	$0.0637651\pi$
$762$	−10.9527			−0.396776
$763$	−15.3423	−	29.2903i	−0.555428	−	1.06038i
$764$	−12.9527			−0.468614
$765$	−1.36704	+	2.36778i	−0.0494254	+	0.0856073i
$766$	−15.2376	−	26.3923i	−0.550558	−	0.953594i
$767$	−8.83038	−	15.2947i	−0.318847	−	0.552259i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	16.2755			0.586911			0.293455	−	0.955973i	$-0.405195\pi$
$769$	16.2755			0.586911			0.293455	+	0.955973i	$0.405195\pi$
$770$	−2.89156	+	4.56439i	−0.104205	+	0.164489i
$771$	−12.7530			−0.459289
$772$	−6.31763	+	10.9424i	−0.227376	+	0.393827i
$773$	−20.0533	−	34.7333i	−0.721267	−	1.24927i	−0.960492	−	0.278307i	$-0.910227\pi$
$773$	−20.0533	−	34.7333i	−0.721267	−	1.24927i	0.239225	−	0.970964i	$-0.423107\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	−4.30815	+	7.46193i	−0.154753	+	0.268041i
$776$	−8.00000			−0.287183
$777$	−6.17644	−	0.253951i	−0.221579	−	0.00911043i
$778$	−24.6585			−0.884051
$779$	3.66355	−	6.34546i	0.131260	−	0.227350i
$780$	2.20760	+	3.82367i	0.0790446	+	0.136909i
$781$	−6.18999	−	10.7214i	−0.221495	−	0.383641i
$782$	−1.64352	+	2.84666i	−0.0587721	+	0.101796i
$783$	−10.3081			−0.368383
$784$	−3.98585	+	5.75439i	−0.142352	+	0.205514i
$785$	5.88195			0.209936
$786$	6.77289	−	11.7310i	0.241581	−	0.418430i
$787$	−5.66285	−	9.80835i	−0.201859	−	0.349630i	0.747268	−	0.664522i	$-0.231365\pi$
$787$	−5.66285	−	9.80835i	−0.201859	−	0.349630i	−0.949127	+	0.314892i	$0.898032\pi$
$788$	4.46222	+	7.72880i	0.158960	+	0.275327i
$789$	7.85289	−	13.6016i	0.279570	−	0.484230i
$790$	−8.69643			−0.309405
$791$	20.4669	+	0.841517i	0.727719	+	0.0299209i
$792$	−2.45526			−0.0872438
$793$	38.7927	−	67.1910i	1.37757	−	2.38602i
$794$	−10.2493	−	17.7522i	−0.363733	−	0.630003i
$795$	3.23749	+	5.60750i	0.114822	+	0.198877i
$796$	−2.89118	+	5.00767i	−0.102475	+	0.177492i
$797$	−13.2648			−0.469863			−0.234932	−	0.972012i	$-0.575487\pi$
$797$	−13.2648			−0.469863			−0.234932	+	0.972012i	$0.575487\pi$
$798$	−2.83178	+	4.47002i	−0.100244	+	0.158237i
$799$	−12.8540			−0.454742
$800$	2.15407	−	3.73097i	0.0761580	−	0.131910i
$801$	6.47637	+	11.2174i	0.228831	+	0.396348i
$802$	−4.81174	−	8.33418i	−0.169909	−	0.294290i
$803$	19.1710	−	33.2052i	0.676531	−	1.17179i
$804$	−11.7845			−0.415608
$805$	−1.02111	−	1.94943i	−0.0359895	−	0.0687085i
$806$	10.6163			0.373943
$807$	9.89637	−	17.1410i	0.348369	−	0.603392i
$808$	0.154074	+	0.266865i	0.00542031	+	0.00938826i
$809$	−17.7562	−	30.7547i	−0.624276	−	1.08128i	−0.988680	−	0.150036i	$-0.952061\pi$
$809$	−17.7562	−	30.7547i	−0.624276	−	1.08128i	0.364405	−	0.931241i	$-0.381272\pi$
$810$	0.415888	−	0.720339i	0.0146128	−	0.0253101i
$811$	−5.75051			−0.201928			−0.100964	−	0.994890i	$-0.532193\pi$
$811$	−5.75051			−0.201928			−0.100964	+	0.994890i	$0.532193\pi$
$812$	−12.6546	−	24.1592i	−0.444089	−	0.847822i
$813$	15.5268			0.544549
$814$	2.86829	−	4.96803i	0.100534	−	0.174129i
$815$	−0.942370	−	1.63223i	−0.0330098	−	0.0571746i
$816$	−1.64352	−	2.84666i	−0.0575346	−	0.0996529i
$817$	2.00000	−	3.46410i	0.0699711	−	0.121194i
$818$	29.8961			1.04529
$819$	7.51574	−	11.8638i	0.262621	−	0.414553i
$820$	−3.04725			−0.106415
$821$	1.49874	−	2.59589i	0.0523064	−	0.0905973i	−0.838687	−	0.544614i	$-0.816676\pi$
$821$	1.49874	−	2.59589i	0.0523064	−	0.0905973i	0.890993	+	0.454017i	$0.150009\pi$
$822$	9.76233	+	16.9089i	0.340500	+	0.589764i
$823$	14.8139	+	25.6583i	0.516378	+	0.894394i	0.999819	+	0.0190166i	$0.00605353\pi$
$823$	14.8139	+	25.6583i	0.516378	+	0.894394i	−0.483441	+	0.875377i	$0.660613\pi$
$824$	3.00108	−	5.19802i	0.104548	−	0.181082i
$825$	−10.5776			−0.368266
$826$	−8.79526	−	0.361626i	−0.306026	−	0.0125826i
$827$	−43.7258			−1.52049			−0.760247	−	0.649634i	$-0.774922\pi$
$827$	−43.7258			−1.52049			−0.760247	+	0.649634i	$0.774922\pi$
$828$	0.500000	−	0.866025i	0.0173762	−	0.0300965i
$829$	11.2893	+	19.5537i	0.392095	+	0.679128i	0.992726	−	0.120399i	$-0.0384173\pi$
$829$	11.2893	+	19.5537i	0.392095	+	0.679128i	−0.600631	+	0.799526i	$0.705084\pi$
$830$	2.73408	+	4.73556i	0.0949012	+	0.164374i
$831$	0.277558	−	0.480744i	0.00962837	−	0.0166768i
$832$	−5.30815			−0.184027
$833$	9.82995	+	20.8038i	0.340588	+	0.720809i
$834$	12.8822			0.446075
$835$	9.11811	−	15.7930i	0.315545	−	0.546541i
$836$	−2.45526	−	4.25263i	−0.0849169	−	0.147080i
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$	−6.43808	+	11.1511i	−0.222400	+	0.385208i
$839$	23.8024			0.821748			0.410874	−	0.911692i	$-0.365224\pi$
$839$	23.8024			0.821748			0.410874	+	0.911692i	$0.365224\pi$
$840$	2.19881	+	0.0904065i	0.0758663	+	0.00311932i
$841$	77.2579			2.66407
$842$	−13.7724	+	23.8544i	−0.474627	+	0.822078i
$843$	12.1986	+	21.1287i	0.420143	+	0.727709i
$844$	−3.69881	−	6.40654i	−0.127318	−	0.220522i
$845$	6.31170	−	10.9322i	0.217129	−	0.376079i
$846$	3.91052			0.134446
$847$	7.03937	−	11.1118i	0.241876	−	0.381806i
$848$	−7.78452			−0.267322
$849$	9.53470	−	16.5146i	0.327230	−	0.566779i
$850$	−7.08052	−	12.2638i	−0.242860	−	0.420646i
$851$	1.16822	+	2.02342i	0.0400462	+	0.0693621i
$852$	−2.52111	+	4.36670i	−0.0863719	+	0.149601i
$853$	−14.7695			−0.505697			−0.252848	−	0.967506i	$-0.581367\pi$
$853$	−14.7695			−0.505697			−0.252848	+	0.967506i	$0.581367\pi$
$854$	−17.9434	−	34.2562i	−0.614011	−	1.17222i
$855$	1.66355			0.0568923
$856$	−1.54474	+	2.67557i	−0.0527981	+	0.0914491i
$857$	5.42696	+	9.39977i	0.185381	+	0.321090i	0.943705	−	0.330788i	$-0.107315\pi$
$857$	5.42696	+	9.39977i	0.185381	+	0.321090i	−0.758324	+	0.651878i	$0.773981\pi$
$858$	6.51644	+	11.2868i	0.222468	+	0.385325i
$859$	11.4411	−	19.8166i	0.390366	−	0.676133i	−0.602132	−	0.798397i	$-0.705682\pi$
$859$	11.4411	−	19.8166i	0.390366	−	0.676133i	0.992498	+	0.122263i	$0.0390153\pi$
$860$	−1.66355			−0.0567267
$861$	4.49749	+	8.58626i	0.153274	+	0.292619i
$862$	−33.0915			−1.12710
$863$	8.61881	−	14.9282i	0.293388	−	0.508163i	−0.681221	−	0.732078i	$-0.738551\pi$
$863$	8.61881	−	14.9282i	0.293388	−	0.508163i	0.974609	+	0.223916i	$0.0718840\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−7.69540	−	13.3288i	−0.261652	−	0.453194i
$866$	−14.6739	+	25.4160i	−0.498640	+	0.863670i
$867$	6.19540			0.210407
$868$	2.83178	−	4.47002i	0.0961167	−	0.151722i
$869$	−25.6704			−0.870808
$870$	−4.28704	+	7.42536i	−0.145344	+	0.251743i
$871$	31.2770	+	54.1733i	1.05978	+	1.83559i
$872$	−6.24874	−	10.8231i	−0.211609	−	0.366518i
$873$	4.00000	−	6.92820i	0.135379	−	0.234484i
$874$	2.00000			0.0676510
$875$	20.4669	+	0.841517i	0.691907	+	0.0284485i
$876$	−15.6163			−0.527626
$877$	−19.1021	+	33.0859i	−0.645034	+	1.11723i	0.339260	+	0.940693i	$0.389823\pi$
$877$	−19.1021	+	33.0859i	−0.645034	+	1.11723i	−0.984294	+	0.176538i	$0.943510\pi$
$878$	−14.4080	−	24.9554i	−0.486247	−	0.842204i
$879$	−0.702924	−	1.21750i	−0.0237090	−	0.0410652i
$880$	−1.02111	+	1.76862i	−0.0344217	+	0.0596202i
$881$	35.0515			1.18091			0.590457	−	0.807069i	$-0.298947\pi$
$881$	35.0515			1.18091			0.590457	+	0.807069i	$0.298947\pi$
$882$	−2.99052	−	6.32904i	−0.100696	−	0.213110i
$883$	−43.2139			−1.45426			−0.727132	−	0.686498i	$-0.759147\pi$
$883$	−43.2139			−1.45426			−0.727132	+	0.686498i	$0.759147\pi$
$884$	−8.72404	+	15.1105i	−0.293421	+	0.508220i
$885$	1.38370	+	2.39664i	0.0465127	+	0.0805623i
$886$	−3.78223	−	6.55101i	−0.127066	−	0.220086i
$887$	−1.28362	+	2.22330i	−0.0430999	+	0.0746512i	−0.886771	−	0.462210i	$-0.847057\pi$
$887$	−1.28362	+	2.22330i	−0.0430999	+	0.0746512i	0.843671	+	0.536861i	$0.180390\pi$
$888$	−2.33645			−0.0784061
$889$	28.9538	+	1.19046i	0.971078	+	0.0399269i
$890$	10.7738			0.361138
$891$	1.22763	−	2.12632i	0.0411271	−	0.0712343i
$892$	0.504672	+	0.874117i	0.0168977	+	0.0292676i
$893$	3.91052	+	6.77322i	0.130861	+	0.226657i
$894$	5.03937	−	8.72845i	0.168542	−	0.291923i
$895$	5.13742			0.171725
$896$	−1.41589	+	2.23501i	−0.0473015	+	0.0746664i
$897$	−5.30815			−0.177234
$898$	−11.2587	+	19.5007i	−0.375709	+	0.650747i
$899$	10.3081	+	17.8542i	0.343796	+	0.595472i
$900$	2.15407	+	3.73097i	0.0718025	+	0.124366i
$901$	−12.7940	+	22.1599i	−0.426230	+	0.738252i
$902$	−8.99497			−0.299500
$903$	2.45526	+	4.68740i	0.0817059	+	0.155987i
$904$	7.74230			0.257505
$905$	−5.51073	+	9.54487i	−0.183183	+	0.317282i
$906$	−10.1399	−	17.5629i	−0.336876	−	0.583487i
$907$	13.0394	+	22.5849i	0.432965	+	0.749918i	0.997127	−	0.0757464i	$-0.0241340\pi$
$907$	13.0394	+	22.5849i	0.432965	+	0.749918i	−0.564162	+	0.825664i	$0.690801\pi$
$908$	−8.89118	+	15.4000i	−0.295064	+	0.511066i
$909$	−0.308149			−0.0102206
$910$	−5.42022	−	10.3479i	−0.179679	−	0.343029i
$911$	−58.1853			−1.92777			−0.963883	−	0.266325i	$-0.914190\pi$
$911$	−58.1853			−1.92777			−0.963883	+	0.266325i	$0.914190\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	8.07053	+	13.9786i	0.267095	+	0.462623i
$914$	5.66355	+	9.80956i	0.187334	+	0.324471i
$915$	−6.07874	+	10.5287i	−0.200957	+	0.348068i
$916$	−14.3185			−0.473097
$917$	−19.1793	+	30.2749i	−0.633356	+	0.999766i
$918$	3.28704			0.108488
$919$	12.7834	−	22.1416i	0.421687	−	0.730383i	−0.574418	−	0.818562i	$-0.694771\pi$
$919$	12.7834	−	22.1416i	0.421687	−	0.730383i	0.996105	+	0.0881792i	$0.0281048\pi$
$920$	−0.415888	−	0.720339i	−0.0137114	−	0.0237489i
$921$	−13.6093	−	23.5721i	−0.448443	−	0.776726i
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	26.7649			0.880977
$924$	6.49052	+	0.266865i	0.213523	+	0.00877920i
$925$	−10.0658			−0.330960
$926$	12.6163	−	21.8521i	0.414597	−	0.718104i
$927$	3.00108	+	5.19802i	0.0985684	+	0.170725i
$928$	−5.15407	−	8.92712i	−0.169191	−	0.293047i
$929$	10.2763	−	17.7991i	0.337154	−	0.583969i	−0.646742	−	0.762709i	$-0.723869\pi$
$929$	10.2763	−	17.7991i	0.337154	−	0.583969i	0.983896	+	0.178740i	$0.0572022\pi$
$930$	−1.66355			−0.0545500
$931$	7.97170	−	11.5088i	0.261262	−	0.377185i
$932$	−13.8210			−0.452723
$933$	4.04474	−	7.00570i	0.132419	−	0.229356i
$934$	−12.6546	−	21.9184i	−0.414071	−	0.717192i
$935$	3.35643	+	5.81352i	0.109767	+	0.190122i
$936$	2.65407	−	4.59699i	0.0867511	−	0.150257i
$937$	18.8304			0.615162			0.307581	−	0.951522i	$-0.400481\pi$
$937$	18.8304			0.615162			0.307581	+	0.951522i	$0.400481\pi$
$938$	31.1526	+	1.28087i	1.01717	+	0.0418219i
$939$	13.8210			0.451033
$940$	1.62634	−	2.81690i	0.0530453	−	0.0918772i
$941$	1.45310	+	2.51685i	0.0473698	+	0.0820469i	0.888738	−	0.458415i	$-0.151583\pi$
$941$	1.45310	+	2.51685i	0.0473698	+	0.0820469i	−0.841368	+	0.540462i	$0.818249\pi$
$942$	−3.53578	−	6.12415i	−0.115202	−	0.199536i
$943$	1.83178	−	3.17273i	0.0596508	−	0.103318i
$944$	−3.32710			−0.108288
$945$	−1.17770	+	1.85903i	−0.0383106	+	0.0604741i
$946$	−4.91052			−0.159655
$947$	7.25860	−	12.5723i	0.235873	−	0.408544i	−0.723653	−	0.690164i	$-0.757538\pi$
$947$	7.25860	−	12.5723i	0.235873	−	0.408544i	0.959526	+	0.281620i	$0.0908718\pi$
$948$	5.22763	+	9.05452i	0.169786	+	0.294077i
$949$	41.4468	+	71.7880i	1.34542	+	2.33034i
$950$	−4.30815	+	7.46193i	−0.139775	+	0.242097i
$951$	−12.6542			−0.410341
$952$	4.03526	+	7.70382i	0.130784	+	0.249682i
$953$	38.5561			1.24896			0.624478	−	0.781042i	$-0.285312\pi$
$953$	38.5561			1.24896			0.624478	+	0.781042i	$0.285312\pi$
$954$	3.89226	−	6.74159i	0.126017	−	0.218267i
$955$	−5.38689	−	9.33037i	−0.174316	−	0.301924i
$956$	5.13296	+	8.89055i	0.166012	+	0.287541i
$957$	−12.6546	+	21.9184i	−0.409065	+	0.708521i
$958$	1.84251			0.0595289
$959$	−23.9691	−	45.7599i	−0.774001	−	1.47767i
$960$	0.831776			0.0268455
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	6.20111	+	10.7406i	0.199932	+	0.346292i
$963$	−1.54474	−	2.67557i	−0.0497786	−	0.0862190i
$964$	−4.37652	+	7.58035i	−0.140958	+	0.244147i
$965$	−10.5097			−0.338319
$966$	−1.41589	+	2.23501i	−0.0455555	+	0.0719102i
$967$	−24.2606			−0.780169			−0.390085	−	0.920779i	$-0.627554\pi$
$967$	−24.2606			−0.780169			−0.390085	+	0.920779i	$0.627554\pi$
$968$	2.48585	−	4.30562i	0.0798983	−	0.138388i
$969$	3.28704	+	5.69331i	0.105595	+	0.182896i
$970$	−3.32710	−	5.76271i	−0.106827	−	0.185030i
$971$	0.791326	−	1.37062i	0.0253949	−	0.0439852i	−0.853049	−	0.521831i	$-0.825249\pi$
$971$	0.791326	−	1.37062i	0.0253949	−	0.0439852i	0.878444	+	0.477846i	$0.158582\pi$
$972$	−1.00000			−0.0320750
$973$	−34.0544	−	1.40018i	−1.09173	−	0.0448877i
$974$	−36.5175			−1.17010
$975$	11.4341	−	19.8045i	0.366186	−	0.634252i
$976$	−7.30815	−	12.6581i	−0.233928	−	0.405175i
$977$	9.43700	+	16.3454i	0.301916	+	0.522935i	0.976570	−	0.215200i	$-0.0690403\pi$
$977$	9.43700	+	16.3454i	0.301916	+	0.522935i	−0.674654	+	0.738134i	$0.735707\pi$
$978$	−1.13296	+	1.96235i	−0.0362281	+	0.0627489i
$979$	31.8024			1.01641
$980$	−5.80278	−	0.477983i	−0.185363	−	0.0152686i
$981$	12.4975			0.399014
$982$	9.54348	−	16.5298i	0.304545	−	0.527487i
$983$	27.1399	+	47.0077i	0.865629	+	1.49931i	0.866421	+	0.499314i	$0.166415\pi$
$983$	27.1399	+	47.0077i	0.865629	+	1.49931i	−0.000791941		1.00000i	$0.500252\pi$
$984$	1.83178	+	3.17273i	0.0583949	+	0.101143i
$985$	−3.71157	+	6.42863i	−0.118260	+	0.204833i
$986$	−33.8833			−1.07906
$987$	−10.3375	−	0.425038i	−0.329047	−	0.0135291i
$988$	10.6163			0.337749
$989$	1.00000	−	1.73205i	0.0317982	−	0.0550760i
$990$	−1.02111	−	1.76862i	−0.0324531	−	0.0562104i
$991$	−18.3658	−	31.8105i	−0.583408	−	1.01049i	−0.995072	−	0.0991568i	$-0.968385\pi$
$991$	−18.3658	−	31.8105i	−0.583408	−	1.01049i	0.411664	−	0.911336i	$-0.364948\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	24.2419			0.769295
$994$	7.13923	−	11.2694i	0.226443	−	0.357444i
$995$	−4.80963			−0.152476
$996$	3.28704	−	5.69331i	0.104154	−	0.180400i
$997$	−22.7927	−	39.4782i	−0.721853	−	1.25029i	−0.960256	−	0.279120i	$-0.909957\pi$
$997$	−22.7927	−	39.4782i	−0.721853	−	1.25029i	0.238403	−	0.971166i	$-0.423376\pi$
$998$	−5.87526	−	10.1762i	−0.185978	−	0.322123i
$999$	1.16822	−	2.02342i	0.0369610	−	0.0640183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.m.415.3	yes	8
7.2	even	3		6762.2.a.cl.1.2		4
7.4	even	3	inner	966.2.i.m.277.3	✓	8
7.5	odd	6		6762.2.a.cr.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.3	✓	8	7.4	even	3	inner
966.2.i.m.415.3	yes	8	1.1	even	1	trivial
6762.2.a.cl.1.2		4	7.2	even	3
6762.2.a.cr.1.3		4	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.415888 - 0.720339i) q^{5} -1.00000 q^{6} +(2.64352 + 0.108691i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.415888 - 0.720339i) q^{5} -1.00000 q^{6} +(2.64352 + 0.108691i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.415888 + 0.720339i) q^{10} +(1.22763 + 2.12632i) q^{11} +(0.500000 - 0.866025i) q^{12} -5.30815 q^{13} +(-1.41589 + 2.23501i) q^{14} +0.831776 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.64352 + 2.84666i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} -0.831776 q^{20} +(1.22763 + 2.34370i) q^{21} -2.45526 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.15407 + 3.73097i) q^{25} +(2.65407 - 4.59699i) q^{26} -1.00000 q^{27} +(-1.22763 - 2.34370i) q^{28} +10.3081 q^{29} +(-0.415888 + 0.720339i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.22763 + 2.12632i) q^{33} -3.28704 q^{34} +(1.17770 - 1.85903i) q^{35} +1.00000 q^{36} +(-1.16822 + 2.02342i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-2.65407 - 4.59699i) q^{39} +(0.415888 - 0.720339i) q^{40} +3.66355 q^{41} +(-2.64352 - 0.108691i) q^{42} +2.00000 q^{43} +(1.22763 - 2.12632i) q^{44} +(0.415888 + 0.720339i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-1.95526 + 3.38661i) q^{47} -1.00000 q^{48} +(6.97637 + 0.574653i) q^{49} -4.30815 q^{50} +(-1.64352 + 2.84666i) q^{51} +(2.65407 + 4.59699i) q^{52} +(3.89226 + 6.74159i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.04223 q^{55} +(2.64352 + 0.108691i) q^{56} +2.00000 q^{57} +(-5.15407 + 8.92712i) q^{58} +(1.66355 + 2.88136i) q^{59} +(-0.415888 - 0.720339i) q^{60} +(-7.30815 + 12.6581i) q^{61} -2.00000 q^{62} +(-1.41589 + 2.23501i) q^{63} +1.00000 q^{64} +(-2.20760 + 3.82367i) q^{65} +(-1.22763 - 2.12632i) q^{66} +(-5.89226 - 10.2057i) q^{67} +(1.64352 - 2.84666i) q^{68} +1.00000 q^{69} +(1.02111 + 1.94943i) q^{70} -5.04223 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.80815 - 13.5241i) q^{73} +(-1.16822 - 2.02342i) q^{74} +(-2.15407 + 3.73097i) q^{75} -2.00000 q^{76} +(3.01415 + 5.75439i) q^{77} +5.30815 q^{78} +(-5.22763 + 9.05452i) q^{79} +(0.415888 + 0.720339i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.83178 + 3.17273i) q^{82} +6.57407 q^{83} +(1.41589 - 2.23501i) q^{84} +2.73408 q^{85} +(-1.00000 + 1.73205i) q^{86} +(5.15407 + 8.92712i) q^{87} +(1.22763 + 2.12632i) q^{88} +(6.47637 - 11.2174i) q^{89} -0.831776 q^{90} +(-14.0322 - 0.576948i) q^{91} -1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-1.95526 - 3.38661i) q^{94} +(-0.831776 - 1.44068i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.00000 q^{97} +(-3.98585 + 5.75439i) q^{98} -2.45526 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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