LMFDB - Embedded newform 966.2.l.b.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	966.47
Dual form			966.2.l.b.185.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} +1.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} +1.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(1.50000 + 0.866025i) q^{12} -3.46410i q^{13} +(-1.73205 - 2.00000i) q^{14} -6.00000i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(6.00000 + 3.46410i) q^{19} +3.46410 q^{20} +(-4.50000 + 0.866025i) q^{21} -3.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.866025 + 1.50000i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(1.73205 - 3.00000i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} -3.00000i q^{29} +(3.00000 - 5.19615i) q^{30} +(3.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.59808 + 4.50000i) q^{33} +1.73205i q^{34} +(-6.92820 + 6.00000i) q^{35} +3.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(3.46410 + 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(3.00000 + 1.73205i) q^{40} -3.46410 q^{41} +(-4.33013 - 1.50000i) q^{42} +10.0000 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-4.33013 + 7.50000i) q^{47} +1.73205i q^{48} +(5.50000 + 4.33013i) q^{49} -7.00000i q^{50} +(2.59808 + 1.50000i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-10.3923 + 6.00000i) q^{53} +(2.59808 - 4.50000i) q^{54} +10.3923i q^{55} +(0.866025 - 2.50000i) q^{56} +12.0000 q^{57} +(1.50000 - 2.59808i) q^{58} +(6.92820 + 12.0000i) q^{59} +(5.19615 - 3.00000i) q^{60} +(-12.0000 - 6.92820i) q^{61} +3.46410 q^{62} +(-6.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(-10.3923 - 6.00000i) q^{65} +(-4.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-0.866025 + 1.50000i) q^{68} -1.73205 q^{69} +(-9.00000 + 1.73205i) q^{70} -9.00000i q^{71} +(2.59808 + 1.50000i) q^{72} +(7.50000 - 4.33013i) q^{73} +(1.73205 - 1.00000i) q^{74} +(-10.5000 - 6.06218i) q^{75} +6.92820i q^{76} +(7.79423 - 1.50000i) q^{77} -6.00000i q^{78} +(-5.50000 + 9.52628i) q^{79} +(1.73205 + 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 - 1.73205i) q^{82} +3.46410 q^{83} +(-3.00000 - 3.46410i) q^{84} +6.00000 q^{85} +(8.66025 + 5.00000i) q^{86} +(-2.59808 - 4.50000i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.46410 + 6.00000i) q^{89} -10.3923i q^{90} +(-3.00000 + 8.66025i) q^{91} -1.00000i q^{92} +(3.00000 - 5.19615i) q^{93} +(-7.50000 + 4.33013i) q^{94} +(20.7846 - 12.0000i) q^{95} +(-0.866025 + 1.50000i) q^{96} +3.46410i q^{97} +(2.59808 + 6.50000i) q^{98} +9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 2 q^{4} - 10 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 2 * q^4 - 10 * q^7 + 6 * q^9	$ 4 q + 6 q^{3} + 2 q^{4} - 10 q^{7} + 6 q^{9} + 12 q^{10} + 6 q^{12} - 2 q^{16} + 24 q^{19} - 18 q^{21} - 12 q^{22} - 14 q^{25} - 2 q^{28} + 12 q^{30} + 12 q^{31} + 12 q^{36} + 4 q^{37} - 12 q^{39} + 12 q^{40} + 40 q^{43} - 2 q^{46} + 22 q^{49} + 12 q^{52} + 48 q^{57} + 6 q^{58} - 48 q^{61} - 24 q^{63} - 4 q^{64} - 18 q^{66} + 8 q^{67} - 36 q^{70} + 30 q^{73} - 42 q^{75} - 22 q^{79} - 18 q^{81} - 12 q^{82} - 12 q^{84} + 24 q^{85} - 6 q^{88} - 12 q^{91} + 12 q^{93} - 30 q^{94}+O(q^{100}) $ 4 * q + 6 * q^3 + 2 * q^4 - 10 * q^7 + 6 * q^9 + 12 * q^10 + 6 * q^12 - 2 * q^16 + 24 * q^19 - 18 * q^21 - 12 * q^22 - 14 * q^25 - 2 * q^28 + 12 * q^30 + 12 * q^31 + 12 * q^36 + 4 * q^37 - 12 * q^39 + 12 * q^40 + 40 * q^43 - 2 * q^46 + 22 * q^49 + 12 * q^52 + 48 * q^57 + 6 * q^58 - 48 * q^61 - 24 * q^63 - 4 * q^64 - 18 * q^66 + 8 * q^67 - 36 * q^70 + 30 * q^73 - 42 * q^75 - 22 * q^79 - 18 * q^81 - 12 * q^82 - 12 * q^84 + 24 * q^85 - 6 * q^88 - 12 * q^91 + 12 * q^93 - 30 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.73205	−	3.00000i	0.774597	−	1.34164i	−0.160424	−	0.987048i	$-0.551286\pi$
$5$	1.73205	−	3.00000i	0.774597	−	1.34164i	0.935021	−	0.354593i	$-0.115380\pi$
$6$	1.73205			0.707107
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$			1.00000i			0.353553i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	3.00000	−	1.73205i	0.948683	−	0.547723i
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	−1.73205	−	2.00000i	−0.462910	−	0.534522i
$15$		−	6.00000i		−	1.54919i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.866025	+	1.50000i	0.210042	+	0.363803i	0.951727	−	0.306944i	$-0.0993066\pi$
$17$	0.866025	+	1.50000i	0.210042	+	0.363803i	−0.741685	+	0.670748i	$0.765973\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	6.00000	+	3.46410i	1.37649	+	0.794719i	0.991736	−	0.128298i	$-0.0409513\pi$
$19$	6.00000	+	3.46410i	1.37649	+	0.794719i	0.384759	+	0.923017i	$0.374285\pi$
$20$	3.46410			0.774597
$21$	−4.50000	+	0.866025i	−0.981981	+	0.188982i
$22$	−3.00000			−0.639602
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	0.866025	+	1.50000i	0.176777	+	0.306186i
$25$	−3.50000	−	6.06218i	−0.700000	−	1.21244i
$26$	1.73205	−	3.00000i	0.339683	−	0.588348i
$27$		−	5.19615i		−	1.00000i
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	3.00000	−	5.19615i	0.547723	−	0.948683i
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−2.59808	+	4.50000i	−0.452267	+	0.783349i
$34$			1.73205i			0.297044i
$35$	−6.92820	+	6.00000i	−1.17108	+	1.01419i
$36$	3.00000			0.500000
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	3.46410	+	6.00000i	0.561951	+	0.973329i
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$	3.00000	+	1.73205i	0.474342	+	0.273861i
$41$	−3.46410			−0.541002			−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410			−0.541002			−0.270501	+	0.962720i	$0.587189\pi$
$42$	−4.33013	−	1.50000i	−0.668153	−	0.231455i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$	−5.19615	−	9.00000i	−0.774597	−	1.34164i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−4.33013	+	7.50000i	−0.631614	+	1.09399i	0.355608	+	0.934635i	$0.384274\pi$
$47$	−4.33013	+	7.50000i	−0.631614	+	1.09399i	−0.987222	+	0.159352i	$0.949059\pi$
$48$			1.73205i			0.250000i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		−	7.00000i		−	0.989949i
$51$	2.59808	+	1.50000i	0.363803	+	0.210042i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	−10.3923	+	6.00000i	−1.42749	+	0.824163i	−0.996922	−	0.0783936i	$-0.975021\pi$
$53$	−10.3923	+	6.00000i	−1.42749	+	0.824163i	−0.430570	+	0.902557i	$0.641688\pi$
$54$	2.59808	−	4.50000i	0.353553	−	0.612372i
$55$			10.3923i			1.40130i
$56$	0.866025	−	2.50000i	0.115728	−	0.334077i
$57$	12.0000			1.58944
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	6.92820	+	12.0000i	0.901975	+	1.56227i	0.824927	+	0.565240i	$0.191216\pi$
$59$	6.92820	+	12.0000i	0.901975	+	1.56227i	0.0770484	+	0.997027i	$0.475450\pi$
$60$	5.19615	−	3.00000i	0.670820	−	0.387298i
$61$	−12.0000	−	6.92820i	−1.53644	−	0.887066i	−0.999043	−	0.0437377i	$-0.986073\pi$
$61$	−12.0000	−	6.92820i	−1.53644	−	0.887066i	−0.537400	−	0.843328i	$-0.680593\pi$
$62$	3.46410			0.439941
$63$	−6.00000	+	5.19615i	−0.755929	+	0.654654i
$64$	−1.00000			−0.125000
$65$	−10.3923	−	6.00000i	−1.28901	−	0.744208i
$66$	−4.50000	+	2.59808i	−0.553912	+	0.319801i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−0.866025	+	1.50000i	−0.105021	+	0.181902i
$69$	−1.73205			−0.208514
$70$	−9.00000	+	1.73205i	−1.07571	+	0.207020i
$71$		−	9.00000i		−	1.06810i	−0.845452	−	0.534052i	$-0.820669\pi$
$71$		−	9.00000i		−	1.06810i	0.845452	−	0.534052i	$-0.179331\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.00787336	−	0.999969i	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$	1.73205	−	1.00000i	0.201347	−	0.116248i
$75$	−10.5000	−	6.06218i	−1.21244	−	0.700000i
$76$			6.92820i			0.794719i
$77$	7.79423	−	1.50000i	0.888235	−	0.170941i
$78$		−	6.00000i		−	0.679366i
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$	1.73205	+	3.00000i	0.193649	+	0.335410i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−3.00000	−	1.73205i	−0.331295	−	0.191273i
$83$	3.46410			0.380235			0.190117	−	0.981761i	$-0.439113\pi$
$83$	3.46410			0.380235			0.190117	+	0.981761i	$0.439113\pi$
$84$	−3.00000	−	3.46410i	−0.327327	−	0.377964i
$85$	6.00000			0.650791
$86$	8.66025	+	5.00000i	0.933859	+	0.539164i
$87$	−2.59808	−	4.50000i	−0.278543	−	0.482451i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−3.46410	+	6.00000i	−0.367194	+	0.635999i	−0.989126	−	0.147073i	$-0.953015\pi$
$89$	−3.46410	+	6.00000i	−0.367194	+	0.635999i	0.621932	+	0.783072i	$0.286348\pi$
$90$		−	10.3923i		−	1.09545i
$91$	−3.00000	+	8.66025i	−0.314485	+	0.907841i
$92$		−	1.00000i		−	0.104257i
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$	−7.50000	+	4.33013i	−0.773566	+	0.446619i
$95$	20.7846	−	12.0000i	2.13246	−	1.23117i
$96$	−0.866025	+	1.50000i	−0.0883883	+	0.153093i
$97$			3.46410i			0.351726i	0.984415	+	0.175863i	$0.0562716\pi$
$97$			3.46410i			0.351726i	−0.984415	+	0.175863i	$0.943728\pi$
$98$	2.59808	+	6.50000i	0.262445	+	0.656599i
$99$			9.00000i			0.904534i
$100$	3.50000	−	6.06218i	0.350000	−	0.606218i
$101$	7.79423	+	13.5000i	0.775555	+	1.34330i	0.934482	+	0.356010i	$0.115863\pi$
$101$	7.79423	+	13.5000i	0.775555	+	1.34330i	−0.158927	+	0.987290i	$0.550804\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	7.50000	+	4.33013i	0.738997	+	0.426660i	0.821705	−	0.569914i	$-0.193023\pi$
$103$	7.50000	+	4.33013i	0.738997	+	0.426660i	−0.0827075	+	0.996574i	$0.526357\pi$
$104$	3.46410			0.339683
$105$	−5.19615	+	15.0000i	−0.507093	+	1.46385i
$106$	−12.0000			−1.16554
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.909624	−	0.415432i	$-0.136370\pi$
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.0950377	+	0.995474i	$0.469703\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	8.50000	+	14.7224i	0.814152	+	1.41015i	0.909935	+	0.414751i	$0.136131\pi$
$109$	8.50000	+	14.7224i	0.814152	+	1.41015i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−5.19615	+	9.00000i	−0.495434	+	0.858116i
$111$		−	3.46410i		−	0.328798i
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	10.3923	+	6.00000i	0.973329	+	0.561951i
$115$	−3.00000	+	1.73205i	−0.279751	+	0.161515i
$116$	2.59808	−	1.50000i	0.241225	−	0.139272i
$117$	−9.00000	−	5.19615i	−0.832050	−	0.480384i
$118$			13.8564i			1.27559i
$119$	−0.866025	−	4.50000i	−0.0793884	−	0.412514i
$120$	6.00000			0.547723
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−6.92820	−	12.0000i	−0.627250	−	1.08643i
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$	3.00000	+	1.73205i	0.269408	+	0.155543i
$125$	−6.92820			−0.619677
$126$	−7.79423	+	1.50000i	−0.694365	+	0.133631i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	15.0000	−	8.66025i	1.32068	−	0.762493i
$130$	−6.00000	−	10.3923i	−0.526235	−	0.911465i
$131$	6.92820	−	12.0000i	0.605320	−	1.04844i	−0.386681	−	0.922214i	$-0.626379\pi$
$131$	6.92820	−	12.0000i	0.605320	−	1.04844i	0.992001	−	0.126231i	$-0.0402882\pi$
$132$	−5.19615			−0.452267
$133$	−12.0000	−	13.8564i	−1.04053	−	1.20150i
$134$			4.00000i			0.345547i
$135$	−15.5885	−	9.00000i	−1.34164	−	0.774597i
$136$	−1.50000	+	0.866025i	−0.128624	+	0.0742611i
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	−0.794524	−	0.607233i	$-0.792279\pi$
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	0.128618	+	0.991694i	$0.458946\pi$
$138$	−1.50000	−	0.866025i	−0.127688	−	0.0737210i
$139$			1.73205i			0.146911i	0.997299	+	0.0734553i	$0.0234026\pi$
$139$			1.73205i			0.146911i	−0.997299	+	0.0734553i	$0.976597\pi$
$140$	−8.66025	−	3.00000i	−0.731925	−	0.253546i
$141$			15.0000i			1.26323i
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$	5.19615	+	9.00000i	0.434524	+	0.752618i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−9.00000	−	5.19615i	−0.747409	−	0.431517i
$146$	8.66025			0.716728
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$	2.00000			0.164399
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$	−6.06218	−	10.5000i	−0.494975	−	0.857321i
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$	−3.46410	+	6.00000i	−0.280976	+	0.486664i
$153$	5.19615			0.420084
$154$	7.50000	+	2.59808i	0.604367	+	0.209359i
$155$		−	12.0000i		−	0.963863i
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	−4.50000	+	2.59808i	−0.359139	+	0.207349i	−0.668703	−	0.743530i	$-0.733150\pi$
$157$	−4.50000	+	2.59808i	−0.359139	+	0.207349i	0.309564	+	0.950879i	$0.399817\pi$
$158$	−9.52628	+	5.50000i	−0.757870	+	0.437557i
$159$	−10.3923	+	18.0000i	−0.824163	+	1.42749i
$160$			3.46410i			0.273861i
$161$	1.73205	+	2.00000i	0.136505	+	0.157622i
$162$		−	9.00000i		−	0.707107i
$163$	3.50000	−	6.06218i	0.274141	−	0.474826i	−0.695777	−	0.718258i	$-0.744940\pi$
$163$	3.50000	−	6.06218i	0.274141	−	0.474826i	0.969918	+	0.243432i	$0.0782731\pi$
$164$	−1.73205	−	3.00000i	−0.135250	−	0.234261i
$165$	9.00000	+	15.5885i	0.700649	+	1.21356i
$166$	3.00000	+	1.73205i	0.232845	+	0.134433i
$167$	−3.46410			−0.268060			−0.134030	−	0.990977i	$-0.542792\pi$
$167$	−3.46410			−0.268060			−0.134030	+	0.990977i	$0.542792\pi$
$168$	−0.866025	−	4.50000i	−0.0668153	−	0.347183i
$169$	1.00000			0.0769231
$170$	5.19615	+	3.00000i	0.398527	+	0.230089i
$171$	18.0000	−	10.3923i	1.37649	−	0.794719i
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	9.52628	−	16.5000i	0.724270	−	1.25447i	−0.235004	−	0.971994i	$-0.575510\pi$
$173$	9.52628	−	16.5000i	0.724270	−	1.25447i	0.959274	−	0.282477i	$-0.0911562\pi$
$174$		−	5.19615i		−	0.393919i
$175$	3.50000	+	18.1865i	0.264575	+	1.37477i
$176$		−	3.00000i		−	0.226134i
$177$	20.7846	+	12.0000i	1.56227	+	0.901975i
$178$	−6.00000	+	3.46410i	−0.449719	+	0.259645i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	5.19615	−	9.00000i	0.387298	−	0.670820i
$181$			12.1244i			0.901196i	0.892727	+	0.450598i	$0.148789\pi$
$181$			12.1244i			0.901196i	−0.892727	+	0.450598i	$0.851211\pi$
$182$	−6.92820	+	6.00000i	−0.513553	+	0.444750i
$183$	−24.0000			−1.77413
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−3.46410	−	6.00000i	−0.254686	−	0.441129i
$186$	5.19615	−	3.00000i	0.381000	−	0.219971i
$187$	−4.50000	−	2.59808i	−0.329073	−	0.189990i
$188$	−8.66025			−0.631614
$189$	−4.50000	+	12.9904i	−0.327327	+	0.944911i
$190$	24.0000			1.74114
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−1.73205	+	3.00000i	−0.124354	+	0.215387i
$195$	−20.7846			−1.48842
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			9.00000i			0.641223i	0.947211	+	0.320612i	$0.103888\pi$
$197$			9.00000i			0.641223i	−0.947211	+	0.320612i	$0.896112\pi$
$198$	−4.50000	+	7.79423i	−0.319801	+	0.553912i
$199$	−22.5000	+	12.9904i	−1.59498	+	0.920864i	−0.602549	+	0.798082i	$0.705848\pi$
$199$	−22.5000	+	12.9904i	−1.59498	+	0.920864i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	6.06218	−	3.50000i	0.428661	−	0.247487i
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$			15.5885i			1.09680i
$203$	−2.59808	+	7.50000i	−0.182349	+	0.526397i
$204$			3.00000i			0.210042i
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$	4.33013	+	7.50000i	0.301694	+	0.522550i
$207$	−2.59808	+	1.50000i	−0.180579	+	0.104257i
$208$	3.00000	+	1.73205i	0.208013	+	0.120096i
$209$	−20.7846			−1.43770
$210$	−12.0000	+	10.3923i	−0.828079	+	0.717137i
$211$	−23.0000			−1.58339			−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000			−1.58339			−0.791693	+	0.610920i	$0.790800\pi$
$212$	−10.3923	−	6.00000i	−0.713746	−	0.412082i
$213$	−7.79423	−	13.5000i	−0.534052	−	0.925005i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	17.3205	−	30.0000i	1.18125	−	2.04598i
$216$	5.19615			0.353553
$217$	−9.00000	+	1.73205i	−0.610960	+	0.117579i
$218$			17.0000i			1.15139i
$219$	7.50000	−	12.9904i	0.506803	−	0.877809i
$220$	−9.00000	+	5.19615i	−0.606780	+	0.350325i
$221$	5.19615	−	3.00000i	0.349531	−	0.201802i
$222$	1.73205	−	3.00000i	0.116248	−	0.201347i
$223$		−	6.92820i		−	0.463947i	−0.972722	−	0.231973i	$-0.925482\pi$
$223$		−	6.92820i		−	0.463947i	0.972722	−	0.231973i	$-0.0745182\pi$
$224$	2.59808	−	0.500000i	0.173591	−	0.0334077i
$225$	−21.0000			−1.40000
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	2.59808	+	4.50000i	0.172440	+	0.298675i	0.939272	−	0.343172i	$-0.111501\pi$
$227$	2.59808	+	4.50000i	0.172440	+	0.298675i	−0.766832	+	0.641848i	$0.778168\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	−10.5000	−	6.06218i	−0.693860	−	0.400600i	0.111197	−	0.993798i	$-0.464532\pi$
$229$	−10.5000	−	6.06218i	−0.693860	−	0.400600i	−0.805056	+	0.593198i	$0.797865\pi$
$230$	−3.46410			−0.228416
$231$	10.3923	−	9.00000i	0.683763	−	0.592157i
$232$	3.00000			0.196960
$233$	10.3923	+	6.00000i	0.680823	+	0.393073i	0.800165	−	0.599780i	$-0.204745\pi$
$233$	10.3923	+	6.00000i	0.680823	+	0.393073i	−0.119342	+	0.992853i	$0.538079\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$	15.0000	+	25.9808i	0.978492	+	1.69480i
$236$	−6.92820	+	12.0000i	−0.450988	+	0.781133i
$237$			19.0526i			1.23760i
$238$	1.50000	−	4.33013i	0.0972306	−	0.280680i
$239$		−	15.0000i		−	0.970269i	−0.874439	−	0.485135i	$-0.838771\pi$
$239$		−	15.0000i		−	0.970269i	0.874439	−	0.485135i	$-0.161229\pi$
$240$	5.19615	+	3.00000i	0.335410	+	0.193649i
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	−0.0609515	−	0.998141i	$-0.519414\pi$
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	0.833939	+	0.551856i	$0.186080\pi$
$242$	−1.73205	+	1.00000i	−0.111340	+	0.0642824i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$		−	13.8564i		−	0.887066i
$245$	22.5167	−	9.00000i	1.43854	−	0.574989i
$246$	−6.00000			−0.382546
$247$	12.0000	−	20.7846i	0.763542	−	1.32249i
$248$	1.73205	+	3.00000i	0.109985	+	0.190500i
$249$	5.19615	−	3.00000i	0.329293	−	0.190117i
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	−29.4449			−1.85854			−0.929272	−	0.369397i	$-0.879564\pi$
$251$	−29.4449			−1.85854			−0.929272	+	0.369397i	$0.879564\pi$
$252$	−7.50000	−	2.59808i	−0.472456	−	0.163663i
$253$	3.00000			0.188608
$254$	1.73205	+	1.00000i	0.108679	+	0.0627456i
$255$	9.00000	−	5.19615i	0.563602	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.46410	−	6.00000i	0.216085	−	0.374270i	−0.737523	−	0.675322i	$-0.764005\pi$
$257$	3.46410	−	6.00000i	0.216085	−	0.374270i	0.953608	+	0.301052i	$0.0973379\pi$
$258$	17.3205			1.07833
$259$	−4.00000	+	3.46410i	−0.248548	+	0.215249i
$260$		−	12.0000i		−	0.744208i
$261$	−7.79423	−	4.50000i	−0.482451	−	0.278543i
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	10.3923	−	6.00000i	0.640817	−	0.369976i	−0.144112	−	0.989561i	$-0.546033\pi$
$263$	10.3923	−	6.00000i	0.640817	−	0.369976i	0.784929	+	0.619586i	$0.212699\pi$
$264$	−4.50000	−	2.59808i	−0.276956	−	0.159901i
$265$			41.5692i			2.55358i
$266$	−3.46410	−	18.0000i	−0.212398	−	1.10365i
$267$			12.0000i			0.734388i
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−6.06218	−	10.5000i	−0.369618	−	0.640196i	0.619888	−	0.784690i	$-0.287178\pi$
$269$	−6.06218	−	10.5000i	−0.369618	−	0.640196i	−0.989506	+	0.144494i	$0.953845\pi$
$270$	−9.00000	−	15.5885i	−0.547723	−	0.948683i
$271$	−6.00000	−	3.46410i	−0.364474	−	0.210429i	0.306568	−	0.951849i	$-0.400819\pi$
$271$	−6.00000	−	3.46410i	−0.364474	−	0.210429i	−0.671042	+	0.741420i	$0.734153\pi$
$272$	−1.73205			−0.105021
$273$	3.00000	+	15.5885i	0.181568	+	0.943456i
$274$	−9.00000			−0.543710
$275$	18.1865	+	10.5000i	1.09669	+	0.633174i
$276$	−0.866025	−	1.50000i	−0.0521286	−	0.0902894i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−0.866025	+	1.50000i	−0.0519408	+	0.0899640i
$279$		−	10.3923i		−	0.622171i
$280$	−6.00000	−	6.92820i	−0.358569	−	0.414039i
$281$			9.00000i			0.536895i	0.963294	+	0.268447i	$0.0865106\pi$
$281$			9.00000i			0.536895i	−0.963294	+	0.268447i	$0.913489\pi$
$282$	−7.50000	+	12.9904i	−0.446619	+	0.773566i
$283$	−15.0000	+	8.66025i	−0.891657	+	0.514799i	−0.874484	−	0.485054i	$-0.838800\pi$
$283$	−15.0000	+	8.66025i	−0.891657	+	0.514799i	−0.0171732	+	0.999853i	$0.505467\pi$
$284$	7.79423	−	4.50000i	0.462502	−	0.267026i
$285$	20.7846	−	36.0000i	1.23117	−	2.13246i
$286$			10.3923i			0.614510i
$287$	8.66025	+	3.00000i	0.511199	+	0.177084i
$288$			3.00000i			0.176777i
$289$	7.00000	−	12.1244i	0.411765	−	0.713197i
$290$	−5.19615	−	9.00000i	−0.305129	−	0.528498i
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	7.50000	+	4.33013i	0.438904	+	0.253402i
$293$	−31.1769			−1.82137			−0.910687	−	0.413096i	$-0.864447\pi$
$293$	−31.1769			−1.82137			−0.910687	+	0.413096i	$0.864447\pi$
$294$	9.52628	+	7.50000i	0.555584	+	0.437409i
$295$	48.0000			2.79467
$296$	1.73205	+	1.00000i	0.100673	+	0.0581238i
$297$	7.79423	+	13.5000i	0.452267	+	0.783349i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−1.73205	+	3.00000i	−0.100167	+	0.173494i
$300$		−	12.1244i		−	0.700000i
$301$	−25.0000	−	8.66025i	−1.44098	−	0.499169i
$302$		−	16.0000i		−	0.920697i
$303$	23.3827	+	13.5000i	1.34330	+	0.775555i
$304$	−6.00000	+	3.46410i	−0.344124	+	0.198680i
$305$	−41.5692	+	24.0000i	−2.38025	+	1.37424i
$306$	4.50000	+	2.59808i	0.257248	+	0.148522i
$307$		−	15.5885i		−	0.889680i	−0.895610	−	0.444840i	$-0.853260\pi$
$307$		−	15.5885i		−	0.889680i	0.895610	−	0.444840i	$-0.146740\pi$
$308$	5.19615	+	6.00000i	0.296078	+	0.341882i
$309$	15.0000			0.853320
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	2.59808	+	4.50000i	0.147323	+	0.255172i	0.930237	−	0.366958i	$-0.119601\pi$
$311$	2.59808	+	4.50000i	0.147323	+	0.255172i	−0.782914	+	0.622130i	$0.786268\pi$
$312$	5.19615	−	3.00000i	0.294174	−	0.169842i
$313$	−27.0000	−	15.5885i	−1.52613	−	0.881112i	−0.999519	−	0.0310053i	$-0.990129\pi$
$313$	−27.0000	−	15.5885i	−1.52613	−	0.881112i	−0.526611	−	0.850106i	$-0.676538\pi$
$314$	−5.19615			−0.293236
$315$	5.19615	+	27.0000i	0.292770	+	1.52128i
$316$	−11.0000			−0.618798
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.00635137	−	0.999980i	$-0.502022\pi$
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.869184	+	0.494489i	$0.835355\pi$
$318$	−18.0000	+	10.3923i	−1.00939	+	0.582772i
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	−1.73205	+	3.00000i	−0.0968246	+	0.167705i
$321$	20.7846			1.16008
$322$	0.500000	+	2.59808i	0.0278639	+	0.144785i
$323$			12.0000i			0.667698i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−21.0000	+	12.1244i	−1.16487	+	0.672538i
$326$	6.06218	−	3.50000i	0.335753	−	0.193847i
$327$	25.5000	+	14.7224i	1.41015	+	0.814152i
$328$		−	3.46410i		−	0.191273i
$329$	17.3205	−	15.0000i	0.954911	−	0.826977i
$330$			18.0000i			0.990867i
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	1.73205	+	3.00000i	0.0950586	+	0.164646i
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$	−3.00000	−	1.73205i	−0.164153	−	0.0947736i
$335$	13.8564			0.757056
$336$	1.50000	−	4.33013i	0.0818317	−	0.236228i
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$	−5.19615	−	9.00000i	−0.282216	−	0.488813i
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	−5.19615	+	9.00000i	−0.281387	+	0.487377i
$342$	20.7846			1.12390
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$			10.0000i			0.539164i
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	16.5000	−	9.52628i	0.887045	−	0.512136i
$347$	15.5885	−	9.00000i	0.836832	−	0.483145i	−0.0193540	−	0.999813i	$-0.506161\pi$
$347$	15.5885	−	9.00000i	0.836832	−	0.483145i	0.856186	+	0.516667i	$0.172828\pi$
$348$	2.59808	−	4.50000i	0.139272	−	0.241225i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	−6.06218	+	17.5000i	−0.324037	+	0.935414i
$351$	−18.0000			−0.960769
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−5.19615	−	9.00000i	−0.276563	−	0.479022i	0.693965	−	0.720009i	$-0.255862\pi$
$353$	−5.19615	−	9.00000i	−0.276563	−	0.479022i	−0.970528	+	0.240987i	$0.922529\pi$
$354$	12.0000	+	20.7846i	0.637793	+	1.10469i
$355$	−27.0000	−	15.5885i	−1.43301	−	0.827349i
$356$	−6.92820			−0.367194
$357$	−5.19615	−	6.00000i	−0.275010	−	0.317554i
$358$		0			0
$359$	−31.1769	−	18.0000i	−1.64545	−	0.950004i	−0.978847	−	0.204595i	$-0.934412\pi$
$359$	−31.1769	−	18.0000i	−1.64545	−	0.950004i	−0.666608	−	0.745409i	$-0.732254\pi$
$360$	9.00000	−	5.19615i	0.474342	−	0.273861i
$361$	14.5000	+	25.1147i	0.763158	+	1.32183i
$362$	−6.06218	+	10.5000i	−0.318621	+	0.551868i
$363$			3.46410i			0.181818i
$364$	−9.00000	+	1.73205i	−0.471728	+	0.0907841i
$365$		−	30.0000i		−	1.57027i
$366$	−20.7846	−	12.0000i	−1.08643	−	0.627250i
$367$	15.0000	−	8.66025i	0.782994	−	0.452062i	−0.0544966	−	0.998514i	$-0.517355\pi$
$367$	15.0000	−	8.66025i	0.782994	−	0.452062i	0.837490	+	0.546452i	$0.184022\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−5.19615	+	9.00000i	−0.270501	+	0.468521i
$370$		−	6.92820i		−	0.360180i
$371$	31.1769	−	6.00000i	1.61862	−	0.311504i
$372$	6.00000			0.311086
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$	−2.59808	−	4.50000i	−0.134343	−	0.232689i
$375$	−10.3923	+	6.00000i	−0.536656	+	0.309839i
$376$	−7.50000	−	4.33013i	−0.386783	−	0.223309i
$377$	−10.3923			−0.535231
$378$	−10.3923	+	9.00000i	−0.534522	+	0.462910i
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	20.7846	+	12.0000i	1.06623	+	0.615587i
$381$	3.00000	−	1.73205i	0.153695	−	0.0887357i
$382$		0			0
$383$	−1.73205	+	3.00000i	−0.0885037	+	0.153293i	−0.906879	−	0.421392i	$-0.861542\pi$
$383$	−1.73205	+	3.00000i	−0.0885037	+	0.153293i	0.818375	+	0.574684i	$0.194875\pi$
$384$	−1.73205			−0.0883883
$385$	9.00000	−	25.9808i	0.458682	−	1.32410i
$386$			2.00000i			0.101797i
$387$	15.0000	−	25.9808i	0.762493	−	1.32068i
$388$	−3.00000	+	1.73205i	−0.152302	+	0.0879316i
$389$	−10.3923	+	6.00000i	−0.526911	+	0.304212i	−0.739758	−	0.672874i	$-0.765060\pi$
$389$	−10.3923	+	6.00000i	−0.526911	+	0.304212i	0.212847	+	0.977086i	$0.431726\pi$
$390$	−18.0000	−	10.3923i	−0.911465	−	0.526235i
$391$		−	1.73205i		−	0.0875936i
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$		−	24.0000i		−	1.21064i
$394$	−4.50000	+	7.79423i	−0.226707	+	0.392668i
$395$	19.0526	+	33.0000i	0.958638	+	1.66041i
$396$	−7.79423	+	4.50000i	−0.391675	+	0.226134i
$397$	9.00000	+	5.19615i	0.451697	+	0.260787i	0.708547	−	0.705664i	$-0.249351\pi$
$397$	9.00000	+	5.19615i	0.451697	+	0.260787i	−0.256850	+	0.966451i	$0.582685\pi$
$398$	−25.9808			−1.30230
$399$	−30.0000	−	10.3923i	−1.50188	−	0.520266i
$400$	7.00000			0.350000
$401$	−12.9904	−	7.50000i	−0.648709	−	0.374532i	0.139253	−	0.990257i	$-0.455530\pi$
$401$	−12.9904	−	7.50000i	−0.648709	−	0.374532i	−0.787961	+	0.615725i	$0.788863\pi$
$402$	3.46410	+	6.00000i	0.172774	+	0.299253i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	−7.79423	+	13.5000i	−0.387777	+	0.671650i
$405$	−31.1769			−1.54919
$406$	−6.00000	+	5.19615i	−0.297775	+	0.257881i
$407$			6.00000i			0.297409i
$408$	−1.50000	+	2.59808i	−0.0742611	+	0.128624i
$409$	−1.50000	+	0.866025i	−0.0741702	+	0.0428222i	−0.536626	−	0.843820i	$-0.680302\pi$
$409$	−1.50000	+	0.866025i	−0.0741702	+	0.0428222i	0.462456	+	0.886642i	$0.346968\pi$
$410$	−10.3923	+	6.00000i	−0.513239	+	0.296319i
$411$	−7.79423	+	13.5000i	−0.384461	+	0.665906i
$412$			8.66025i			0.426660i
$413$	−6.92820	−	36.0000i	−0.340915	−	1.77144i
$414$	−3.00000			−0.147442
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$	1.50000	+	2.59808i	0.0734553	+	0.127228i
$418$	−18.0000	−	10.3923i	−0.880409	−	0.508304i
$419$	−1.73205			−0.0846162			−0.0423081	−	0.999105i	$-0.513471\pi$
$419$	−1.73205			−0.0846162			−0.0423081	+	0.999105i	$0.513471\pi$
$420$	−15.5885	+	3.00000i	−0.760639	+	0.146385i
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$	−19.9186	−	11.5000i	−0.969622	−	0.559811i
$423$	12.9904	+	22.5000i	0.631614	+	1.09399i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	6.06218	−	10.5000i	0.294059	−	0.509325i
$426$		−	15.5885i		−	0.755263i
$427$	24.0000	+	27.7128i	1.16144	+	1.34112i
$428$			12.0000i			0.580042i
$429$	15.5885	+	9.00000i	0.752618	+	0.434524i
$430$	30.0000	−	17.3205i	1.44673	−	0.835269i
$431$	20.7846	−	12.0000i	1.00116	−	0.578020i	0.0925683	−	0.995706i	$-0.470492\pi$
$431$	20.7846	−	12.0000i	1.00116	−	0.578020i	0.908591	+	0.417687i	$0.137159\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$	−8.66025	−	3.00000i	−0.415705	−	0.144005i
$435$	−18.0000			−0.863034
$436$	−8.50000	+	14.7224i	−0.407076	+	0.705077i
$437$	−3.46410	−	6.00000i	−0.165710	−	0.287019i
$438$	12.9904	−	7.50000i	0.620704	−	0.358364i
$439$	24.0000	+	13.8564i	1.14546	+	0.661330i	0.947776	−	0.318936i	$-0.103326\pi$
$439$	24.0000	+	13.8564i	1.14546	+	0.661330i	0.197681	+	0.980266i	$0.436659\pi$
$440$	−10.3923			−0.495434
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$	6.00000			0.285391
$443$	−20.7846	−	12.0000i	−0.987507	−	0.570137i	−0.0829786	−	0.996551i	$-0.526443\pi$
$443$	−20.7846	−	12.0000i	−0.987507	−	0.570137i	−0.904528	+	0.426414i	$0.859777\pi$
$444$	3.00000	−	1.73205i	0.142374	−	0.0821995i
$445$	12.0000	+	20.7846i	0.568855	+	0.985285i
$446$	3.46410	−	6.00000i	0.164030	−	0.284108i
$447$	−10.3923			−0.491539
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$	−18.1865	−	10.5000i	−0.857321	−	0.494975i
$451$	9.00000	−	5.19615i	0.423793	−	0.244677i
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	−24.0000	−	13.8564i	−1.12762	−	0.651031i
$454$			5.19615i			0.243868i
$455$	20.7846	+	24.0000i	0.974398	+	1.12514i
$456$			12.0000i			0.561951i
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	−0.200118	−	0.979772i	$-0.564132\pi$
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	0.948566	−	0.316579i	$-0.102534\pi$
$458$	−6.06218	−	10.5000i	−0.283267	−	0.490633i
$459$	7.79423	−	4.50000i	0.363803	−	0.210042i
$460$	−3.00000	−	1.73205i	−0.139876	−	0.0807573i
$461$	41.5692			1.93607			0.968036	−	0.250812i	$-0.0806976\pi$
$461$	41.5692			1.93607			0.968036	+	0.250812i	$0.0806976\pi$
$462$	13.5000	−	2.59808i	0.628077	−	0.120873i
$463$	−10.0000			−0.464739			−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000			−0.464739			−0.232370	+	0.972628i	$0.574648\pi$
$464$	2.59808	+	1.50000i	0.120613	+	0.0696358i
$465$	−10.3923	−	18.0000i	−0.481932	−	0.834730i
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	−4.33013	+	7.50000i	−0.200374	+	0.347059i	−0.948649	−	0.316330i	$-0.897549\pi$
$467$	−4.33013	+	7.50000i	−0.200374	+	0.347059i	0.748275	+	0.663389i	$0.230883\pi$
$468$		−	10.3923i		−	0.480384i
$469$	−2.00000	−	10.3923i	−0.0923514	−	0.479872i
$470$			30.0000i			1.38380i
$471$	−4.50000	+	7.79423i	−0.207349	+	0.359139i
$472$	−12.0000	+	6.92820i	−0.552345	+	0.318896i
$473$	−25.9808	+	15.0000i	−1.19460	+	0.689701i
$474$	−9.52628	+	16.5000i	−0.437557	+	0.757870i
$475$		−	48.4974i		−	2.22521i
$476$	3.46410	−	3.00000i	0.158777	−	0.137505i
$477$			36.0000i			1.64833i
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	17.3205	+	30.0000i	0.791394	+	1.37073i	0.925104	+	0.379714i	$0.123978\pi$
$479$	17.3205	+	30.0000i	0.791394	+	1.37073i	−0.133710	+	0.991021i	$0.542689\pi$
$480$	3.00000	+	5.19615i	0.136931	+	0.237171i
$481$	−6.00000	−	3.46410i	−0.273576	−	0.157949i
$482$	13.8564			0.631142
$483$	4.33013	+	1.50000i	0.197028	+	0.0682524i
$484$	−2.00000			−0.0909091
$485$	10.3923	+	6.00000i	0.471890	+	0.272446i
$486$	−7.79423	−	13.5000i	−0.353553	−	0.612372i
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	0.998579	−	0.0532853i	$-0.0169693\pi$
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	−0.545436	+	0.838152i	$0.683636\pi$
$488$	6.92820	−	12.0000i	0.313625	−	0.543214i
$489$		−	12.1244i		−	0.548282i
$490$	24.0000	+	3.46410i	1.08421	+	0.156492i
$491$			30.0000i			1.35388i	0.736038	+	0.676941i	$0.236695\pi$
$491$			30.0000i			1.35388i	−0.736038	+	0.676941i	$0.763305\pi$
$492$	−5.19615	−	3.00000i	−0.234261	−	0.135250i
$493$	4.50000	−	2.59808i	0.202670	−	0.117011i
$494$	20.7846	−	12.0000i	0.935144	−	0.539906i
$495$	27.0000	+	15.5885i	1.21356	+	0.700649i
$496$			3.46410i			0.155543i
$497$	−7.79423	+	22.5000i	−0.349619	+	1.00926i
$498$	6.00000			0.268866
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$	−3.46410	−	6.00000i	−0.154919	−	0.268328i
$501$	−5.19615	+	3.00000i	−0.232147	+	0.134030i
$502$	−25.5000	−	14.7224i	−1.13812	−	0.657094i
$503$	41.5692			1.85348			0.926740	−	0.375703i	$-0.122599\pi$
$503$	41.5692			1.85348			0.926740	+	0.375703i	$0.122599\pi$
$504$	−5.19615	−	6.00000i	−0.231455	−	0.267261i
$505$	54.0000			2.40297
$506$	2.59808	+	1.50000i	0.115499	+	0.0666831i
$507$	1.50000	−	0.866025i	0.0666173	−	0.0384615i
$508$	1.00000	+	1.73205i	0.0443678	+	0.0768473i
$509$	−6.06218	+	10.5000i	−0.268701	+	0.465404i	−0.968527	−	0.248910i	$-0.919928\pi$
$509$	−6.06218	+	10.5000i	−0.268701	+	0.465404i	0.699825	+	0.714314i	$0.253261\pi$
$510$	10.3923			0.460179
$511$	−22.5000	+	4.33013i	−0.995341	+	0.191554i
$512$		−	1.00000i		−	0.0441942i
$513$	18.0000	−	31.1769i	0.794719	−	1.37649i
$514$	6.00000	−	3.46410i	0.264649	−	0.152795i
$515$	25.9808	−	15.0000i	1.14485	−	0.660979i
$516$	15.0000	+	8.66025i	0.660338	+	0.381246i
$517$		−	25.9808i		−	1.14263i
$518$	−5.19615	+	1.00000i	−0.228306	+	0.0439375i
$519$		−	33.0000i		−	1.44854i
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	−20.7846	−	36.0000i	−0.910590	−	1.57719i	−0.813232	−	0.581939i	$-0.802294\pi$
$521$	−20.7846	−	36.0000i	−0.910590	−	1.57719i	−0.0973580	−	0.995249i	$-0.531039\pi$
$522$	−4.50000	−	7.79423i	−0.196960	−	0.341144i
$523$	9.00000	+	5.19615i	0.393543	+	0.227212i	0.683694	−	0.729769i	$-0.260372\pi$
$523$	9.00000	+	5.19615i	0.393543	+	0.227212i	−0.290151	+	0.956981i	$0.593706\pi$
$524$	13.8564			0.605320
$525$	21.0000	+	24.2487i	0.916515	+	1.05830i
$526$	12.0000			0.523225
$527$	5.19615	+	3.00000i	0.226348	+	0.130682i
$528$	−2.59808	−	4.50000i	−0.113067	−	0.195837i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−20.7846	+	36.0000i	−0.902826	+	1.56374i
$531$	41.5692			1.80395
$532$	6.00000	−	17.3205i	0.260133	−	0.750939i
$533$			12.0000i			0.519778i
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$	36.0000	−	20.7846i	1.55642	−	0.898597i
$536$	−3.46410	+	2.00000i	−0.149626	+	0.0863868i
$537$		0			0
$538$		−	12.1244i		−	0.522718i
$539$	−20.7846	−	3.00000i	−0.895257	−	0.129219i
$540$		−	18.0000i		−	0.774597i
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	−3.46410	−	6.00000i	−0.148796	−	0.257722i
$543$	10.5000	+	18.1865i	0.450598	+	0.780459i
$544$	−1.50000	−	0.866025i	−0.0643120	−	0.0371305i
$545$	58.8897			2.52256
$546$	−5.19615	+	15.0000i	−0.222375	+	0.641941i
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	−7.79423	−	4.50000i	−0.332953	−	0.192230i
$549$	−36.0000	+	20.7846i	−1.53644	+	0.887066i
$550$	10.5000	+	18.1865i	0.447722	+	0.775476i
$551$	10.3923	−	18.0000i	0.442727	−	0.766826i
$552$		−	1.73205i		−	0.0737210i
$553$	22.0000	−	19.0526i	0.935535	−	0.810197i
$554$		−	2.00000i		−	0.0849719i
$555$	−10.3923	−	6.00000i	−0.441129	−	0.254686i
$556$	−1.50000	+	0.866025i	−0.0636142	+	0.0367277i
$557$	36.3731	−	21.0000i	1.54118	−	0.889799i	0.542411	−	0.840113i	$-0.317511\pi$
$557$	36.3731	−	21.0000i	1.54118	−	0.889799i	0.998765	−	0.0496855i	$-0.0158219\pi$
$558$	5.19615	−	9.00000i	0.219971	−	0.381000i
$559$		−	34.6410i		−	1.46516i
$560$	−1.73205	−	9.00000i	−0.0731925	−	0.380319i
$561$	−9.00000			−0.379980
$562$	−4.50000	+	7.79423i	−0.189821	+	0.328780i
$563$	0.866025	+	1.50000i	0.0364986	+	0.0632175i	0.883698	−	0.468058i	$-0.155046\pi$
$563$	0.866025	+	1.50000i	0.0364986	+	0.0632175i	−0.847199	+	0.531276i	$0.821713\pi$
$564$	−12.9904	+	7.50000i	−0.546994	+	0.315807i
$565$	−18.0000	−	10.3923i	−0.757266	−	0.437208i
$566$	−17.3205			−0.728035
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$	9.00000			0.377632
$569$	−25.9808	−	15.0000i	−1.08917	−	0.628833i	−0.155815	−	0.987786i	$-0.549800\pi$
$569$	−25.9808	−	15.0000i	−1.08917	−	0.628833i	−0.933355	+	0.358954i	$0.883134\pi$
$570$	36.0000	−	20.7846i	1.50787	−	0.870572i
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	0.770108	−	0.637913i	$-0.220202\pi$
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	−0.937503	+	0.347977i	$0.886869\pi$
$572$	−5.19615	+	9.00000i	−0.217262	+	0.376309i
$573$		0			0
$574$	6.00000	+	6.92820i	0.250435	+	0.289178i
$575$			7.00000i			0.291920i
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	−13.5000	+	7.79423i	−0.562012	+	0.324478i	−0.753953	−	0.656929i	$-0.771855\pi$
$577$	−13.5000	+	7.79423i	−0.562012	+	0.324478i	0.191940	+	0.981407i	$0.438522\pi$
$578$	12.1244	−	7.00000i	0.504307	−	0.291162i
$579$	3.00000	+	1.73205i	0.124676	+	0.0719816i
$580$		−	10.3923i		−	0.431517i
$581$	−8.66025	−	3.00000i	−0.359288	−	0.124461i
$582$			6.00000i			0.248708i
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	4.33013	+	7.50000i	0.179182	+	0.310352i
$585$	−31.1769	+	18.0000i	−1.28901	+	0.744208i
$586$	−27.0000	−	15.5885i	−1.11536	−	0.643953i
$587$	−17.3205			−0.714894			−0.357447	−	0.933933i	$-0.616353\pi$
$587$	−17.3205			−0.714894			−0.357447	+	0.933933i	$0.616353\pi$
$588$	4.50000	+	11.2583i	0.185577	+	0.464286i
$589$	24.0000			0.988903
$590$	41.5692	+	24.0000i	1.71138	+	0.988064i
$591$	7.79423	+	13.5000i	0.320612	+	0.555316i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	20.7846	−	36.0000i	0.853522	−	1.47834i	−0.0244882	−	0.999700i	$-0.507796\pi$
$593$	20.7846	−	36.0000i	0.853522	−	1.47834i	0.878010	−	0.478643i	$-0.158871\pi$
$594$			15.5885i			0.639602i
$595$	−15.0000	−	5.19615i	−0.614940	−	0.213021i
$596$		−	6.00000i		−	0.245770i
$597$	−22.5000	+	38.9711i	−0.920864	+	1.59498i
$598$	−3.00000	+	1.73205i	−0.122679	+	0.0708288i
$599$	−33.7750	+	19.5000i	−1.38001	+	0.796748i	−0.992160	−	0.124975i	$-0.960115\pi$
$599$	−33.7750	+	19.5000i	−1.38001	+	0.796748i	−0.387849	+	0.921723i	$0.626782\pi$
$600$	6.06218	−	10.5000i	0.247487	−	0.428661i
$601$			20.7846i			0.847822i	0.905704	+	0.423911i	$0.139343\pi$
$601$			20.7846i			0.847822i	−0.905704	+	0.423911i	$0.860657\pi$
$602$	−17.3205	−	20.0000i	−0.705931	−	0.815139i
$603$	12.0000			0.488678
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	3.46410	+	6.00000i	0.140836	+	0.243935i
$606$	13.5000	+	23.3827i	0.548400	+	0.949857i
$607$	−39.0000	−	22.5167i	−1.58296	−	0.913923i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−39.0000	−	22.5167i	−1.58296	−	0.913923i	−0.588537	−	0.808470i	$-0.700296\pi$
$608$	−6.92820			−0.280976
$609$	2.59808	+	13.5000i	0.105279	+	0.547048i
$610$	−48.0000			−1.94346
$611$	25.9808	+	15.0000i	1.05107	+	0.606835i
$612$	2.59808	+	4.50000i	0.105021	+	0.181902i
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	7.79423	−	13.5000i	0.314549	−	0.544816i
$615$			20.7846i			0.838116i
$616$	1.50000	+	7.79423i	0.0604367	+	0.314038i
$617$			27.0000i			1.08698i	0.839416	+	0.543490i	$0.182897\pi$
$617$			27.0000i			1.08698i	−0.839416	+	0.543490i	$0.817103\pi$
$618$	12.9904	+	7.50000i	0.522550	+	0.301694i
$619$	−30.0000	+	17.3205i	−1.20580	+	0.696170i	−0.961839	−	0.273615i	$-0.911781\pi$
$619$	−30.0000	+	17.3205i	−1.20580	+	0.696170i	−0.243962	+	0.969785i	$0.578447\pi$
$620$	10.3923	−	6.00000i	0.417365	−	0.240966i
$621$	−2.59808	+	4.50000i	−0.104257	+	0.180579i
$622$			5.19615i			0.208347i
$623$	13.8564	−	12.0000i	0.555145	−	0.480770i
$624$	6.00000			0.240192
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−15.5885	−	27.0000i	−0.623040	−	1.07914i
$627$	−31.1769	+	18.0000i	−1.24509	+	0.718851i
$628$	−4.50000	−	2.59808i	−0.179570	−	0.103675i
$629$	3.46410			0.138123
$630$	−9.00000	+	25.9808i	−0.358569	+	1.03510i
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	−9.52628	−	5.50000i	−0.378935	−	0.218778i
$633$	−34.5000	+	19.9186i	−1.37125	+	0.791693i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	3.46410	−	6.00000i	0.137469	−	0.238103i
$636$	−20.7846			−0.824163
$637$	15.0000	−	19.0526i	0.594322	−	0.754890i
$638$			9.00000i			0.356313i
$639$	−23.3827	−	13.5000i	−0.925005	−	0.534052i
$640$	−3.00000	+	1.73205i	−0.118585	+	0.0684653i
$641$	12.9904	−	7.50000i	0.513089	−	0.296232i	−0.221013	−	0.975271i	$-0.570936\pi$
$641$	12.9904	−	7.50000i	0.513089	−	0.296232i	0.734103	+	0.679039i	$0.237603\pi$
$642$	18.0000	+	10.3923i	0.710403	+	0.410152i
$643$			13.8564i			0.546443i	0.961951	+	0.273222i	$0.0880892\pi$
$643$			13.8564i			0.546443i	−0.961951	+	0.273222i	$0.911911\pi$
$644$	−0.866025	+	2.50000i	−0.0341262	+	0.0985138i
$645$		−	60.0000i		−	2.36250i
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	14.7224	+	25.5000i	0.578799	+	1.00251i	0.995618	+	0.0935189i	$0.0298116\pi$
$647$	14.7224	+	25.5000i	0.578799	+	1.00251i	−0.416819	+	0.908990i	$0.636855\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$	−36.0000	−	20.7846i	−1.41312	−	0.815867i
$650$	−24.2487			−0.951113
$651$	−12.0000	+	10.3923i	−0.470317	+	0.407307i
$652$	7.00000			0.274141
$653$	−2.59808	−	1.50000i	−0.101671	−	0.0586995i	0.448303	−	0.893882i	$-0.352029\pi$
$653$	−2.59808	−	1.50000i	−0.101671	−	0.0586995i	−0.549973	+	0.835182i	$0.685362\pi$
$654$	14.7224	+	25.5000i	0.575693	+	0.997129i
$655$	−24.0000	−	41.5692i	−0.937758	−	1.62424i
$656$	1.73205	−	3.00000i	0.0676252	−	0.117130i
$657$		−	25.9808i		−	1.01361i
$658$	22.5000	−	4.33013i	0.877141	−	0.168806i
$659$			9.00000i			0.350590i	0.984516	+	0.175295i	$0.0560880\pi$
$659$			9.00000i			0.350590i	−0.984516	+	0.175295i	$0.943912\pi$
$660$	−9.00000	+	15.5885i	−0.350325	+	0.606780i
$661$	1.50000	−	0.866025i	0.0583432	−	0.0336845i	−0.470545	−	0.882376i	$-0.655943\pi$
$661$	1.50000	−	0.866025i	0.0583432	−	0.0336845i	0.528888	+	0.848692i	$0.322609\pi$
$662$	−24.2487	+	14.0000i	−0.942453	+	0.544125i
$663$	5.19615	−	9.00000i	0.201802	−	0.349531i
$664$			3.46410i			0.134433i
$665$	−62.3538	+	12.0000i	−2.41798	+	0.465340i
$666$		−	6.00000i		−	0.232495i
$667$	−1.50000	+	2.59808i	−0.0580802	+	0.100598i
$668$	−1.73205	−	3.00000i	−0.0670151	−	0.116073i
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$	12.0000	+	6.92820i	0.463600	+	0.267660i
$671$	41.5692			1.60476
$672$	3.46410	−	3.00000i	0.133631	−	0.115728i
$673$	−47.0000			−1.81172			−0.905858	−	0.423581i	$-0.860773\pi$
$673$	−47.0000			−1.81172			−0.905858	+	0.423581i	$0.860773\pi$
$674$	19.0526	+	11.0000i	0.733877	+	0.423704i
$675$	−31.5000	+	18.1865i	−1.21244	+	0.700000i
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	−8.66025	+	15.0000i	−0.332841	+	0.576497i	−0.983068	−	0.183243i	$-0.941340\pi$
$677$	−8.66025	+	15.0000i	−0.332841	+	0.576497i	0.650227	+	0.759740i	$0.274674\pi$
$678$		−	10.3923i		−	0.399114i
$679$	3.00000	−	8.66025i	0.115129	−	0.332350i
$680$			6.00000i			0.230089i
$681$	7.79423	+	4.50000i	0.298675	+	0.172440i
$682$	−9.00000	+	5.19615i	−0.344628	+	0.198971i
$683$	5.19615	−	3.00000i	0.198825	−	0.114792i	−0.397282	−	0.917697i	$-0.630047\pi$
$683$	5.19615	−	3.00000i	0.198825	−	0.114792i	0.596107	+	0.802905i	$0.296713\pi$
$684$	18.0000	+	10.3923i	0.688247	+	0.397360i
$685$			31.1769i			1.19121i
$686$	−0.866025	−	18.5000i	−0.0330650	−	0.706333i
$687$	−21.0000			−0.801200
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	20.7846	+	36.0000i	0.791831	+	1.37149i
$690$	−5.19615	+	3.00000i	−0.197814	+	0.114208i
$691$	4.50000	+	2.59808i	0.171188	+	0.0988355i	0.583146	−	0.812367i	$-0.301822\pi$
$691$	4.50000	+	2.59808i	0.171188	+	0.0988355i	−0.411958	+	0.911203i	$0.635155\pi$
$692$	19.0526			0.724270
$693$	7.79423	−	22.5000i	0.296078	−	0.854704i
$694$	18.0000			0.683271
$695$	5.19615	+	3.00000i	0.197101	+	0.113796i
$696$	4.50000	−	2.59808i	0.170572	−	0.0984798i
$697$	−3.00000	−	5.19615i	−0.113633	−	0.196818i
$698$		0			0
$699$	20.7846			0.786146
$700$	−14.0000	+	12.1244i	−0.529150	+	0.458258i
$701$		−	42.0000i		−	1.58632i	−0.609015	−	0.793159i	$-0.708435\pi$
$701$		−	42.0000i		−	1.58632i	0.609015	−	0.793159i	$-0.291565\pi$
$702$	−15.5885	−	9.00000i	−0.588348	−	0.339683i
$703$	12.0000	−	6.92820i	0.452589	−	0.261302i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$	45.0000	+	25.9808i	1.69480	+	0.978492i
$706$		−	10.3923i		−	0.391120i
$707$	−7.79423	−	40.5000i	−0.293132	−	1.52316i
$708$			24.0000i			0.901975i
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	−0.987421	−	0.158114i	$-0.949459\pi$
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	0.630641	+	0.776075i	$0.282792\pi$
$710$	−15.5885	−	27.0000i	−0.585024	−	1.01329i
$711$	16.5000	+	28.5788i	0.618798	+	1.07179i
$712$	−6.00000	−	3.46410i	−0.224860	−	0.129823i
$713$	−3.46410			−0.129732
$714$	−1.50000	−	7.79423i	−0.0561361	−	0.291692i
$715$	36.0000			1.34632
$716$		0			0
$717$	−12.9904	−	22.5000i	−0.485135	−	0.840278i
$718$	−18.0000	−	31.1769i	−0.671754	−	1.16351i
$719$	−22.5167	+	39.0000i	−0.839730	+	1.45445i	0.0503909	+	0.998730i	$0.483953\pi$
$719$	−22.5167	+	39.0000i	−0.839730	+	1.45445i	−0.890121	+	0.455725i	$0.849380\pi$
$720$	10.3923			0.387298
$721$	−15.0000	−	17.3205i	−0.558629	−	0.645049i
$722$			29.0000i			1.07927i
$723$	12.0000	−	20.7846i	0.446285	−	0.772988i
$724$	−10.5000	+	6.06218i	−0.390229	+	0.225299i
$725$	−18.1865	+	10.5000i	−0.675431	+	0.389960i
$726$	−1.73205	+	3.00000i	−0.0642824	+	0.111340i
$727$			53.6936i			1.99138i	0.0927199	+	0.995692i	$0.470444\pi$
$727$			53.6936i			1.99138i	−0.0927199	+	0.995692i	$0.529556\pi$
$728$	−8.66025	−	3.00000i	−0.320970	−	0.111187i
$729$	−27.0000			−1.00000
$730$	15.0000	−	25.9808i	0.555175	−	0.961591i
$731$	8.66025	+	15.0000i	0.320311	+	0.554795i
$732$	−12.0000	−	20.7846i	−0.443533	−	0.768221i
$733$	22.5000	+	12.9904i	0.831056	+	0.479811i	0.854214	−	0.519921i	$-0.174039\pi$
$733$	22.5000	+	12.9904i	0.831056	+	0.479811i	−0.0231578	+	0.999732i	$0.507372\pi$
$734$	17.3205			0.639312
$735$	25.9808	−	33.0000i	0.958315	−	1.21722i
$736$	1.00000			0.0368605
$737$	−10.3923	−	6.00000i	−0.382805	−	0.221013i
$738$	−9.00000	+	5.19615i	−0.331295	+	0.191273i
$739$	15.5000	+	26.8468i	0.570177	+	0.987575i	0.996547	+	0.0830265i	$0.0264586\pi$
$739$	15.5000	+	26.8468i	0.570177	+	0.987575i	−0.426371	+	0.904549i	$0.640208\pi$
$740$	3.46410	−	6.00000i	0.127343	−	0.220564i
$741$		−	41.5692i		−	1.52708i
$742$	30.0000	+	10.3923i	1.10133	+	0.381514i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$	5.19615	+	3.00000i	0.190500	+	0.109985i
$745$	−18.0000	+	10.3923i	−0.659469	+	0.380745i
$746$	0.866025	−	0.500000i	0.0317074	−	0.0183063i
$747$	5.19615	−	9.00000i	0.190117	−	0.329293i
$748$		−	5.19615i		−	0.189990i
$749$	−20.7846	−	24.0000i	−0.759453	−	0.876941i
$750$	−12.0000			−0.438178
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−4.33013	−	7.50000i	−0.157903	−	0.273497i
$753$	−44.1673	+	25.5000i	−1.60955	+	0.929272i
$754$	−9.00000	−	5.19615i	−0.327761	−	0.189233i
$755$	−55.4256			−2.01715
$756$	−13.5000	+	2.59808i	−0.490990	+	0.0944911i
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	8.66025	+	5.00000i	0.314555	+	0.181608i
$759$	4.50000	−	2.59808i	0.163340	−	0.0943042i
$760$	12.0000	+	20.7846i	0.435286	+	0.753937i
$761$	−6.92820	+	12.0000i	−0.251147	+	0.435000i	−0.963842	−	0.266475i	$-0.914141\pi$
$761$	−6.92820	+	12.0000i	−0.251147	+	0.435000i	0.712695	+	0.701474i	$0.247474\pi$
$762$	3.46410			0.125491
$763$	−8.50000	−	44.1673i	−0.307721	−	1.59896i
$764$		0			0
$765$	9.00000	−	15.5885i	0.325396	−	0.563602i
$766$	−3.00000	+	1.73205i	−0.108394	+	0.0625815i
$767$	41.5692	−	24.0000i	1.50098	−	0.866590i
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$			17.3205i			0.624593i	0.949985	+	0.312297i	$0.101098\pi$
$769$			17.3205i			0.624593i	−0.949985	+	0.312297i	$0.898902\pi$
$770$	20.7846	−	18.0000i	0.749025	−	0.648675i
$771$		−	12.0000i		−	0.432169i
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−8.66025	−	15.0000i	−0.311488	−	0.539513i	0.667197	−	0.744881i	$-0.267494\pi$
$773$	−8.66025	−	15.0000i	−0.311488	−	0.539513i	−0.978685	+	0.205369i	$0.934161\pi$
$774$	25.9808	−	15.0000i	0.933859	−	0.539164i
$775$	−21.0000	−	12.1244i	−0.754342	−	0.435520i
$776$	−3.46410			−0.124354
$777$	−3.00000	+	8.66025i	−0.107624	+	0.310685i
$778$	−12.0000			−0.430221
$779$	−20.7846	−	12.0000i	−0.744686	−	0.429945i
$780$	−10.3923	−	18.0000i	−0.372104	−	0.644503i
$781$	13.5000	+	23.3827i	0.483068	+	0.836698i
$782$	0.866025	−	1.50000i	0.0309690	−	0.0536399i
$783$	−15.5885			−0.557086
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$			18.0000i			0.642448i
$786$	12.0000	−	20.7846i	0.428026	−	0.741362i
$787$	−24.0000	+	13.8564i	−0.855508	+	0.493928i	−0.862505	−	0.506048i	$-0.831106\pi$
$787$	−24.0000	+	13.8564i	−0.855508	+	0.493928i	0.00699773	+	0.999976i	$0.497773\pi$
$788$	−7.79423	+	4.50000i	−0.277658	+	0.160306i
$789$	10.3923	−	18.0000i	0.369976	−	0.640817i
$790$			38.1051i			1.35572i
$791$	−5.19615	+	15.0000i	−0.184754	+	0.533339i
$792$	−9.00000			−0.319801
$793$	−24.0000	+	41.5692i	−0.852265	+	1.47617i
$794$	5.19615	+	9.00000i	0.184405	+	0.319398i
$795$	36.0000	+	62.3538i	1.27679	+	2.21146i
$796$	−22.5000	−	12.9904i	−0.797491	−	0.460432i
$797$	10.3923			0.368114			0.184057	−	0.982916i	$-0.441077\pi$
$797$	10.3923			0.368114			0.184057	+	0.982916i	$0.441077\pi$
$798$	−20.7846	−	24.0000i	−0.735767	−	0.849591i
$799$	−15.0000			−0.530662
$800$	6.06218	+	3.50000i	0.214330	+	0.123744i
$801$	10.3923	+	18.0000i	0.367194	+	0.635999i
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$	−12.9904	+	22.5000i	−0.458421	+	0.794008i
$804$			6.92820i			0.244339i
$805$	9.00000	−	1.73205i	0.317208	−	0.0610468i
$806$		−	12.0000i		−	0.422682i
$807$	−18.1865	−	10.5000i	−0.640196	−	0.369618i
$808$	−13.5000	+	7.79423i	−0.474928	+	0.274200i
$809$	−10.3923	+	6.00000i	−0.365374	+	0.210949i	−0.671436	−	0.741063i	$-0.734322\pi$
$809$	−10.3923	+	6.00000i	−0.365374	+	0.210949i	0.306062	+	0.952012i	$0.400989\pi$
$810$	−27.0000	−	15.5885i	−0.948683	−	0.547723i
$811$			32.9090i			1.15559i	0.816182	+	0.577795i	$0.196087\pi$
$811$			32.9090i			1.15559i	−0.816182	+	0.577795i	$0.803913\pi$
$812$	−7.79423	+	1.50000i	−0.273524	+	0.0526397i
$813$	−12.0000			−0.420858
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	−12.1244	−	21.0000i	−0.424698	−	0.735598i
$816$	−2.59808	+	1.50000i	−0.0909509	+	0.0525105i
$817$	60.0000	+	34.6410i	2.09913	+	1.21194i
$818$	−1.73205			−0.0605597
$819$	18.0000	+	20.7846i	0.628971	+	0.726273i
$820$	−12.0000			−0.419058
$821$	−33.7750	−	19.5000i	−1.17876	−	0.680555i	−0.223029	−	0.974812i	$-0.571594\pi$
$821$	−33.7750	−	19.5000i	−1.17876	−	0.680555i	−0.955726	+	0.294257i	$0.904928\pi$
$822$	−13.5000	+	7.79423i	−0.470867	+	0.271855i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−4.33013	+	7.50000i	−0.150847	+	0.261275i
$825$	36.3731			1.26635
$826$	12.0000	−	34.6410i	0.417533	−	1.20532i
$827$		−	33.0000i		−	1.14752i	−0.819023	−	0.573761i	$-0.805484\pi$
$827$		−	33.0000i		−	1.14752i	0.819023	−	0.573761i	$-0.194516\pi$
$828$	−2.59808	−	1.50000i	−0.0902894	−	0.0521286i
$829$	−12.0000	+	6.92820i	−0.416777	+	0.240626i	−0.693698	−	0.720266i	$-0.744020\pi$
$829$	−12.0000	+	6.92820i	−0.416777	+	0.240626i	0.276920	+	0.960893i	$0.410686\pi$
$830$	10.3923	−	6.00000i	0.360722	−	0.208263i
$831$	−3.00000	−	1.73205i	−0.104069	−	0.0600842i
$832$			3.46410i			0.120096i
$833$	−1.73205	+	12.0000i	−0.0600120	+	0.415775i
$834$			3.00000i			0.103882i
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$	−10.3923	−	18.0000i	−0.359425	−	0.622543i
$837$	−9.00000	−	15.5885i	−0.311086	−	0.538816i
$838$	−1.50000	−	0.866025i	−0.0518166	−	0.0299164i
$839$	45.0333			1.55472			0.777361	−	0.629054i	$-0.216558\pi$
$839$	45.0333			1.55472			0.777361	+	0.629054i	$0.216558\pi$
$840$	−15.0000	−	5.19615i	−0.517549	−	0.179284i
$841$	20.0000			0.689655
$842$	−0.866025	−	0.500000i	−0.0298452	−	0.0172311i
$843$	7.79423	+	13.5000i	0.268447	+	0.464965i
$844$	−11.5000	−	19.9186i	−0.395846	−	0.685626i
$845$	1.73205	−	3.00000i	0.0595844	−	0.103203i
$846$			25.9808i			0.893237i
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$		−	12.0000i		−	0.412082i
$849$	−15.0000	+	25.9808i	−0.514799	+	0.891657i
$850$	10.5000	−	6.06218i	0.360147	−	0.207931i
$851$	−1.73205	+	1.00000i	−0.0593739	+	0.0342796i
$852$	7.79423	−	13.5000i	0.267026	−	0.462502i
$853$			13.8564i			0.474434i	0.971457	+	0.237217i	$0.0762353\pi$
$853$			13.8564i			0.474434i	−0.971457	+	0.237217i	$0.923765\pi$
$854$	6.92820	+	36.0000i	0.237078	+	1.23189i
$855$		−	72.0000i		−	2.46235i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	8.66025	+	15.0000i	0.295829	+	0.512390i	0.975177	−	0.221425i	$-0.0710709\pi$
$857$	8.66025	+	15.0000i	0.295829	+	0.512390i	−0.679349	+	0.733816i	$0.737738\pi$
$858$	9.00000	+	15.5885i	0.307255	+	0.532181i
$859$	31.5000	+	18.1865i	1.07477	+	0.620517i	0.929480	−	0.368873i	$-0.120256\pi$
$859$	31.5000	+	18.1865i	1.07477	+	0.620517i	0.145286	+	0.989390i	$0.453590\pi$
$860$	34.6410			1.18125
$861$	15.5885	−	3.00000i	0.531253	−	0.102240i
$862$	24.0000			0.817443
$863$	12.9904	+	7.50000i	0.442198	+	0.255303i	0.704529	−	0.709675i	$-0.251158\pi$
$863$	12.9904	+	7.50000i	0.442198	+	0.255303i	−0.262332	+	0.964978i	$0.584491\pi$
$864$	2.59808	+	4.50000i	0.0883883	+	0.153093i
$865$	−33.0000	−	57.1577i	−1.12203	−	1.94342i
$866$		0			0
$867$		−	24.2487i		−	0.823529i
$868$	−6.00000	−	6.92820i	−0.203653	−	0.235159i
$869$		−	33.0000i		−	1.11945i
$870$	−15.5885	−	9.00000i	−0.528498	−	0.305129i
$871$	12.0000	−	6.92820i	0.406604	−	0.234753i
$872$	−14.7224	+	8.50000i	−0.498564	+	0.287846i
$873$	9.00000	+	5.19615i	0.304604	+	0.175863i
$874$		−	6.92820i		−	0.234350i
$875$	17.3205	+	6.00000i	0.585540	+	0.202837i
$876$	15.0000			0.506803
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	13.8564	+	24.0000i	0.467631	+	0.809961i
$879$	−46.7654	+	27.0000i	−1.57736	+	0.910687i
$880$	−9.00000	−	5.19615i	−0.303390	−	0.175162i
$881$	22.5167			0.758606			0.379303	−	0.925273i	$-0.376164\pi$
$881$	22.5167			0.758606			0.379303	+	0.925273i	$0.376164\pi$
$882$	20.7846	+	3.00000i	0.699854	+	0.101015i
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	5.19615	+	3.00000i	0.174766	+	0.100901i
$885$	72.0000	−	41.5692i	2.42025	−	1.39733i
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	−12.9904	+	22.5000i	−0.436174	+	0.755476i	−0.997391	−	0.0721931i	$-0.977000\pi$
$887$	−12.9904	+	22.5000i	−0.436174	+	0.755476i	0.561216	+	0.827669i	$0.310334\pi$
$888$	3.46410			0.116248
$889$	−5.00000	−	1.73205i	−0.167695	−	0.0580911i
$890$			24.0000i			0.804482i
$891$	23.3827	+	13.5000i	0.783349	+	0.452267i
$892$	6.00000	−	3.46410i	0.200895	−	0.115987i
$893$	−51.9615	+	30.0000i	−1.73883	+	1.00391i
$894$	−9.00000	−	5.19615i	−0.301005	−	0.173785i
$895$		0			0
$896$	1.73205	+	2.00000i	0.0578638	+	0.0668153i
$897$			6.00000i			0.200334i
$898$	12.0000	−	20.7846i	0.400445	−	0.693591i
$899$	−5.19615	−	9.00000i	−0.173301	−	0.300167i
$900$	−10.5000	−	18.1865i	−0.350000	−	0.606218i
$901$	−18.0000	−	10.3923i	−0.599667	−	0.346218i
$902$	10.3923			0.346026
$903$	−45.0000	+	8.66025i	−1.49751	+	0.288195i
$904$	6.00000			0.199557
$905$	36.3731	+	21.0000i	1.20908	+	0.698064i
$906$	−13.8564	−	24.0000i	−0.460348	−	0.797347i
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$	−2.59808	+	4.50000i	−0.0862202	+	0.149338i
$909$	46.7654			1.55111
$910$	6.00000	+	31.1769i	0.198898	+	1.03350i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−6.00000	+	10.3923i	−0.198680	+	0.344124i
$913$	−9.00000	+	5.19615i	−0.297857	+	0.171968i
$914$	27.7128	−	16.0000i	0.916658	−	0.529233i
$915$	−41.5692	+	72.0000i	−1.37424	+	2.38025i
$916$		−	12.1244i		−	0.400600i
$917$	−27.7128	+	24.0000i	−0.915158	+	0.792550i
$918$	9.00000			0.297044
$919$	−21.5000	+	37.2391i	−0.709220	+	1.22840i	0.255927	+	0.966696i	$0.417619\pi$
$919$	−21.5000	+	37.2391i	−0.709220	+	1.22840i	−0.965147	+	0.261708i	$0.915714\pi$
$920$	−1.73205	−	3.00000i	−0.0571040	−	0.0989071i
$921$	−13.5000	−	23.3827i	−0.444840	−	0.770486i
$922$	36.0000	+	20.7846i	1.18560	+	0.684505i
$923$	−31.1769			−1.02620
$924$	12.9904	+	4.50000i	0.427352	+	0.148039i
$925$	−14.0000			−0.460317
$926$	−8.66025	−	5.00000i	−0.284594	−	0.164310i
$927$	22.5000	−	12.9904i	0.738997	−	0.426660i
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	1.73205	−	3.00000i	0.0568267	−	0.0984268i	−0.836213	−	0.548405i	$-0.815235\pi$
$929$	1.73205	−	3.00000i	0.0568267	−	0.0984268i	0.893039	+	0.449979i	$0.148568\pi$
$930$		−	20.7846i		−	0.681554i
$931$	18.0000	+	45.0333i	0.589926	+	1.47591i
$932$			12.0000i			0.393073i
$933$	7.79423	+	4.50000i	0.255172	+	0.147323i
$934$	−7.50000	+	4.33013i	−0.245407	+	0.141686i
$935$	−15.5885	+	9.00000i	−0.509797	+	0.294331i
$936$	5.19615	−	9.00000i	0.169842	−	0.294174i
$937$			6.92820i			0.226335i	0.993576	+	0.113167i	$0.0360996\pi$
$937$			6.92820i			0.226335i	−0.993576	+	0.113167i	$0.963900\pi$
$938$	3.46410	−	10.0000i	0.113107	−	0.326512i
$939$	−54.0000			−1.76222
$940$	−15.0000	+	25.9808i	−0.489246	+	0.847399i
$941$	19.0526	+	33.0000i	0.621096	+	1.07577i	0.989282	+	0.146017i	$0.0466455\pi$
$941$	19.0526	+	33.0000i	0.621096	+	1.07577i	−0.368186	+	0.929752i	$0.620021\pi$
$942$	−7.79423	+	4.50000i	−0.253950	+	0.146618i
$943$	3.00000	+	1.73205i	0.0976934	+	0.0564033i
$944$	−13.8564			−0.450988
$945$	31.1769	+	36.0000i	1.01419	+	1.17108i
$946$	−30.0000			−0.975384
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.362454	−	0.932002i	$-0.618061\pi$
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.988364	+	0.152106i	$0.951394\pi$
$948$	−16.5000	+	9.52628i	−0.535895	+	0.309399i
$949$	−15.0000	−	25.9808i	−0.486921	−	0.843371i
$950$	24.2487	−	42.0000i	0.786732	−	1.36266i
$951$	−31.1769			−1.01098
$952$	4.50000	−	0.866025i	0.145846	−	0.0280680i
$953$		−	3.00000i		−	0.0971795i	−0.998819	−	0.0485898i	$-0.984527\pi$
$953$		−	3.00000i		−	0.0971795i	0.998819	−	0.0485898i	$-0.0154727\pi$
$954$	−18.0000	+	31.1769i	−0.582772	+	1.00939i
$955$		0			0
$956$	12.9904	−	7.50000i	0.420139	−	0.242567i
$957$	13.5000	+	7.79423i	0.436393	+	0.251952i
$958$			34.6410i			1.11920i
$959$	23.3827	−	4.50000i	0.755066	−	0.145313i
$960$			6.00000i			0.193649i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−3.46410	−	6.00000i	−0.111687	−	0.193448i
$963$	31.1769	−	18.0000i	1.00466	−	0.580042i
$964$	12.0000	+	6.92820i	0.386494	+	0.223142i
$965$	6.92820			0.223027
$966$	3.00000	+	3.46410i	0.0965234	+	0.111456i
$967$	50.0000			1.60789			0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000			1.60789			0.803946	+	0.594703i	$0.202730\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$	10.3923	+	18.0000i	0.333849	+	0.578243i
$970$	6.00000	+	10.3923i	0.192648	+	0.333677i
$971$	2.59808	−	4.50000i	0.0833762	−	0.144412i	−0.821322	−	0.570465i	$-0.806763\pi$
$971$	2.59808	−	4.50000i	0.0833762	−	0.144412i	0.904698	+	0.426053i	$0.140096\pi$
$972$		−	15.5885i		−	0.500000i
$973$	1.50000	−	4.33013i	0.0480878	−	0.138817i
$974$			20.0000i			0.640841i
$975$	−21.0000	+	36.3731i	−0.672538	+	1.16487i
$976$	12.0000	−	6.92820i	0.384111	−	0.221766i
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	−0.854263	−	0.519841i	$-0.825991\pi$
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	0.0230645	+	0.999734i	$0.492658\pi$
$978$	6.06218	−	10.5000i	0.193847	−	0.335753i
$979$		−	20.7846i		−	0.664279i
$980$	19.0526	+	15.0000i	0.608612	+	0.479157i
$981$	51.0000			1.62830
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	−3.46410	−	6.00000i	−0.110488	−	0.191370i	0.805479	−	0.592624i	$-0.201908\pi$
$983$	−3.46410	−	6.00000i	−0.110488	−	0.191370i	−0.915967	+	0.401254i	$0.868575\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$	27.0000	+	15.5885i	0.860292	+	0.496690i
$986$	5.19615			0.165479
$987$	12.9904	−	37.5000i	0.413488	−	1.19364i
$988$	24.0000			0.763542
$989$	−8.66025	−	5.00000i	−0.275380	−	0.158991i
$990$	15.5885	+	27.0000i	0.495434	+	0.858116i
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	0.881471	−	0.472237i	$-0.156554\pi$
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	−0.849705	+	0.527258i	$0.823220\pi$
$992$	−1.73205	+	3.00000i	−0.0549927	+	0.0952501i
$993$			48.4974i			1.53902i
$994$	−18.0000	+	15.5885i	−0.570925	+	0.494436i
$995$			90.0000i			2.85319i
$996$	5.19615	+	3.00000i	0.164646	+	0.0950586i
$997$	21.0000	−	12.1244i	0.665077	−	0.383982i	−0.129132	−	0.991627i	$-0.541219\pi$
$997$	21.0000	−	12.1244i	0.665077	−	0.383982i	0.794209	+	0.607645i	$0.207886\pi$
$998$	4.33013	−	2.50000i	0.137068	−	0.0791361i
$999$	−9.00000	−	5.19615i	−0.284747	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.b.47.2	yes	4
3.2	odd	2	inner	966.2.l.b.47.1	✓	4
7.3	odd	6	inner	966.2.l.b.185.1	yes	4
21.17	even	6	inner	966.2.l.b.185.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.b.47.1	✓	4	3.2	odd	2	inner
966.2.l.b.47.2	yes	4	1.1	even	1	trivial
966.2.l.b.185.1	yes	4	7.3	odd	6	inner
966.2.l.b.185.2	yes	4	21.17	even	6	inner

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.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} +1.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} +1.73205 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(1.50000 + 0.866025i) q^{12} -3.46410i q^{13} +(-1.73205 - 2.00000i) q^{14} -6.00000i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(6.00000 + 3.46410i) q^{19} +3.46410 q^{20} +(-4.50000 + 0.866025i) q^{21} -3.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.866025 + 1.50000i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(1.73205 - 3.00000i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} -3.00000i q^{29} +(3.00000 - 5.19615i) q^{30} +(3.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.59808 + 4.50000i) q^{33} +1.73205i q^{34} +(-6.92820 + 6.00000i) q^{35} +3.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(3.46410 + 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(3.00000 + 1.73205i) q^{40} -3.46410 q^{41} +(-4.33013 - 1.50000i) q^{42} +10.0000 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-4.33013 + 7.50000i) q^{47} +1.73205i q^{48} +(5.50000 + 4.33013i) q^{49} -7.00000i q^{50} +(2.59808 + 1.50000i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-10.3923 + 6.00000i) q^{53} +(2.59808 - 4.50000i) q^{54} +10.3923i q^{55} +(0.866025 - 2.50000i) q^{56} +12.0000 q^{57} +(1.50000 - 2.59808i) q^{58} +(6.92820 + 12.0000i) q^{59} +(5.19615 - 3.00000i) q^{60} +(-12.0000 - 6.92820i) q^{61} +3.46410 q^{62} +(-6.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(-10.3923 - 6.00000i) q^{65} +(-4.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-0.866025 + 1.50000i) q^{68} -1.73205 q^{69} +(-9.00000 + 1.73205i) q^{70} -9.00000i q^{71} +(2.59808 + 1.50000i) q^{72} +(7.50000 - 4.33013i) q^{73} +(1.73205 - 1.00000i) q^{74} +(-10.5000 - 6.06218i) q^{75} +6.92820i q^{76} +(7.79423 - 1.50000i) q^{77} -6.00000i q^{78} +(-5.50000 + 9.52628i) q^{79} +(1.73205 + 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 - 1.73205i) q^{82} +3.46410 q^{83} +(-3.00000 - 3.46410i) q^{84} +6.00000 q^{85} +(8.66025 + 5.00000i) q^{86} +(-2.59808 - 4.50000i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.46410 + 6.00000i) q^{89} -10.3923i q^{90} +(-3.00000 + 8.66025i) q^{91} -1.00000i q^{92} +(3.00000 - 5.19615i) q^{93} +(-7.50000 + 4.33013i) q^{94} +(20.7846 - 12.0000i) q^{95} +(-0.866025 + 1.50000i) q^{96} +3.46410i q^{97} +(2.59808 + 6.50000i) q^{98} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{4} - 10 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 2 * q^4 - 10 * q^7 + 6 * q^9	\( 4 q + 6 q^{3} + 2 q^{4} - 10 q^{7} + 6 q^{9} + 12 q^{10} + 6 q^{12} - 2 q^{16} + 24 q^{19} - 18 q^{21} - 12 q^{22} - 14 q^{25} - 2 q^{28} + 12 q^{30} + 12 q^{31} + 12 q^{36} + 4 q^{37} - 12 q^{39} + 12 q^{40} + 40 q^{43} - 2 q^{46} + 22 q^{49} + 12 q^{52} + 48 q^{57} + 6 q^{58} - 48 q^{61} - 24 q^{63} - 4 q^{64} - 18 q^{66} + 8 q^{67} - 36 q^{70} + 30 q^{73} - 42 q^{75} - 22 q^{79} - 18 q^{81} - 12 q^{82} - 12 q^{84} + 24 q^{85} - 6 q^{88} - 12 q^{91} + 12 q^{93} - 30 q^{94}+O(q^{100}) \) 4 * q + 6 * q^3 + 2 * q^4 - 10 * q^7 + 6 * q^9 + 12 * q^10 + 6 * q^12 - 2 * q^16 + 24 * q^19 - 18 * q^21 - 12 * q^22 - 14 * q^25 - 2 * q^28 + 12 * q^30 + 12 * q^31 + 12 * q^36 + 4 * q^37 - 12 * q^39 + 12 * q^40 + 40 * q^43 - 2 * q^46 + 22 * q^49 + 12 * q^52 + 48 * q^57 + 6 * q^58 - 48 * q^61 - 24 * q^63 - 4 * q^64 - 18 * q^66 + 8 * q^67 - 36 * q^70 + 30 * q^73 - 42 * q^75 - 22 * q^79 - 18 * q^81 - 12 * q^82 - 12 * q^84 + 24 * q^85 - 6 * q^88 - 12 * q^91 + 12 * q^93 - 30 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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