LMFDB - Embedded newform 462.2.k.b.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
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			89.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.b.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +1.73205i q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +1.73205i q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.866025 - 1.50000i) q^{12} -3.46410i q^{13} +(-2.59808 + 0.500000i) q^{14} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-4.50000 - 2.59808i) q^{19} -3.46410 q^{20} +(-4.33013 - 1.50000i) q^{21} -1.00000 q^{22} +(2.59808 + 1.50000i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(-1.73205 + 3.00000i) q^{26} +5.19615 q^{27} +(2.50000 + 0.866025i) q^{28} -9.00000i q^{29} +(-5.19615 - 3.00000i) q^{30} +(-3.00000 + 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} +5.19615i q^{34} +(1.73205 + 9.00000i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(2.59808 + 4.50000i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(3.00000 + 1.73205i) q^{40} -6.92820 q^{41} +(3.00000 + 3.46410i) q^{42} -5.00000 q^{43} +(0.866025 + 0.500000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(-1.50000 - 2.59808i) q^{46} +(6.06218 - 10.5000i) q^{47} +1.73205 q^{48} +(1.00000 - 6.92820i) q^{49} +7.00000i q^{50} +(-4.50000 + 7.79423i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-4.50000 - 2.59808i) q^{54} +3.46410i q^{55} +(-1.73205 - 2.00000i) q^{56} +9.00000i q^{57} +(-4.50000 + 7.79423i) q^{58} +(-0.866025 - 1.50000i) q^{59} +(3.00000 + 5.19615i) q^{60} +(-3.00000 - 1.73205i) q^{61} +3.46410 q^{62} +(1.50000 + 7.79423i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{65} +(0.866025 + 1.50000i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(2.59808 - 4.50000i) q^{68} -5.19615i q^{69} +(3.00000 - 8.66025i) q^{70} +9.00000i q^{71} +(2.59808 + 1.50000i) q^{72} +(12.0000 - 6.92820i) q^{73} +(6.06218 - 3.50000i) q^{74} +(-6.06218 + 10.5000i) q^{75} -5.19615i q^{76} +(0.866025 - 2.50000i) q^{77} +6.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-1.73205 - 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(6.00000 + 3.46410i) q^{82} -3.46410 q^{83} +(-0.866025 - 4.50000i) q^{84} +18.0000 q^{85} +(4.33013 + 2.50000i) q^{86} +(-13.5000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-1.73205 + 3.00000i) q^{89} +10.3923i q^{90} +(-6.00000 - 6.92820i) q^{91} +3.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-10.5000 + 6.06218i) q^{94} +(15.5885 - 9.00000i) q^{95} +(-1.50000 - 0.866025i) q^{96} -1.73205i q^{97} +(-4.33013 + 5.50000i) q^{98} +3.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9} + 12 q^{10} + 24 q^{15} - 2 q^{16} - 18 q^{19} - 4 q^{22} - 6 q^{24} - 14 q^{25} + 10 q^{28} - 12 q^{31} - 6 q^{33} - 12 q^{36} - 14 q^{37} + 12 q^{40} + 12 q^{42} - 20 q^{43} - 6 q^{46} + 4 q^{49} - 18 q^{51} + 12 q^{52} - 18 q^{54} - 18 q^{58} + 12 q^{60} - 12 q^{61} + 6 q^{63} - 4 q^{64} - 16 q^{67} + 12 q^{70} + 48 q^{73} + 24 q^{78} + 32 q^{79} - 18 q^{81} + 24 q^{82} + 72 q^{85} - 54 q^{87} - 2 q^{88} - 24 q^{91} - 42 q^{94} - 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9 + 12 * q^10 + 24 * q^15 - 2 * q^16 - 18 * q^19 - 4 * q^22 - 6 * q^24 - 14 * q^25 + 10 * q^28 - 12 * q^31 - 6 * q^33 - 12 * q^36 - 14 * q^37 + 12 * q^40 + 12 * q^42 - 20 * q^43 - 6 * q^46 + 4 * q^49 - 18 * q^51 + 12 * q^52 - 18 * q^54 - 18 * q^58 + 12 * q^60 - 12 * q^61 + 6 * q^63 - 4 * q^64 - 16 * q^67 + 12 * q^70 + 48 * q^73 + 24 * q^78 + 32 * q^79 - 18 * q^81 + 24 * q^82 + 72 * q^85 - 54 * q^87 - 2 * q^88 - 24 * q^91 - 42 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	0.160424	+	0.987048i	$0.448714\pi$
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	−0.935021	+	0.354593i	$0.884620\pi$
$6$			1.73205i			0.707107i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	3.00000	−	1.73205i	0.948683	−	0.547723i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	0.866025	−	1.50000i	0.250000	−	0.433013i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	−2.59808	+	0.500000i	−0.694365	+	0.133631i
$15$	6.00000			1.54919
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	−0.987526	−	0.157459i	$-0.949670\pi$
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	0.357400	−	0.933952i	$-0.383663\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	−4.50000	−	2.59808i	−1.03237	−	0.596040i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−4.50000	−	2.59808i	−1.03237	−	0.596040i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−3.46410			−0.774597
$21$	−4.33013	−	1.50000i	−0.944911	−	0.327327i
$22$	−1.00000			−0.213201
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−3.50000	−	6.06218i	−0.700000	−	1.21244i
$26$	−1.73205	+	3.00000i	−0.339683	+	0.588348i
$27$	5.19615			1.00000
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$		−	9.00000i		−	1.67126i	−0.549294	−	0.835629i	$-0.685103\pi$
$29$		−	9.00000i		−	1.67126i	0.549294	−	0.835629i	$-0.314897\pi$
$30$	−5.19615	−	3.00000i	−0.948683	−	0.547723i
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.50000	−	0.866025i	−0.261116	−	0.150756i
$34$			5.19615i			0.891133i
$35$	1.73205	+	9.00000i	0.292770	+	1.52128i
$36$	−3.00000			−0.500000
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	2.59808	+	4.50000i	0.421464	+	0.729996i
$39$	−5.19615	+	3.00000i	−0.832050	+	0.480384i
$40$	3.00000	+	1.73205i	0.474342	+	0.273861i
$41$	−6.92820			−1.08200			−0.541002	−	0.841021i	$-0.681955\pi$
$41$	−6.92820			−1.08200			−0.541002	+	0.841021i	$0.681955\pi$
$42$	3.00000	+	3.46410i	0.462910	+	0.534522i
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$	0.866025	+	0.500000i	0.130558	+	0.0753778i
$45$	−5.19615	−	9.00000i	−0.774597	−	1.34164i
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	6.06218	−	10.5000i	0.884260	−	1.53158i	0.0376995	−	0.999289i	$-0.487997\pi$
$47$	6.06218	−	10.5000i	0.884260	−	1.53158i	0.846560	−	0.532293i	$-0.178670\pi$
$48$	1.73205			0.250000
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$			7.00000i			0.989949i
$51$	−4.50000	+	7.79423i	−0.630126	+	1.09141i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$			3.46410i			0.467099i
$56$	−1.73205	−	2.00000i	−0.231455	−	0.267261i
$57$			9.00000i			1.19208i
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	0.804130	−	0.594454i	$-0.202632\pi$
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	−0.916877	+	0.399170i	$0.869298\pi$
$60$	3.00000	+	5.19615i	0.387298	+	0.670820i
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	0.295495	−	0.955344i	$-0.404516\pi$
$61$	−3.00000	−	1.73205i	−0.384111	−	0.221766i	−0.679605	+	0.733578i	$0.737849\pi$
$62$	3.46410			0.439941
$63$	1.50000	+	7.79423i	0.188982	+	0.981981i
$64$	−1.00000			−0.125000
$65$	10.3923	+	6.00000i	1.28901	+	0.744208i
$66$	0.866025	+	1.50000i	0.106600	+	0.184637i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	2.59808	−	4.50000i	0.315063	−	0.545705i
$69$		−	5.19615i		−	0.625543i
$70$	3.00000	−	8.66025i	0.358569	−	1.03510i
$71$			9.00000i			1.06810i	0.845452	+	0.534052i	$0.179331\pi$
$71$			9.00000i			1.06810i	−0.845452	+	0.534052i	$0.820669\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	12.0000	−	6.92820i	1.40449	−	0.810885i	0.409644	−	0.912245i	$-0.365653\pi$
$73$	12.0000	−	6.92820i	1.40449	−	0.810885i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	6.06218	−	3.50000i	0.704714	−	0.406867i
$75$	−6.06218	+	10.5000i	−0.700000	+	1.21244i
$76$		−	5.19615i		−	0.596040i
$77$	0.866025	−	2.50000i	0.0986928	−	0.284901i
$78$	6.00000			0.679366
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$	−1.73205	−	3.00000i	−0.193649	−	0.335410i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	6.00000	+	3.46410i	0.662589	+	0.382546i
$83$	−3.46410			−0.380235			−0.190117	−	0.981761i	$-0.560887\pi$
$83$	−3.46410			−0.380235			−0.190117	+	0.981761i	$0.560887\pi$
$84$	−0.866025	−	4.50000i	−0.0944911	−	0.490990i
$85$	18.0000			1.95237
$86$	4.33013	+	2.50000i	0.466930	+	0.269582i
$87$	−13.5000	+	7.79423i	−1.44735	+	0.835629i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−1.73205	+	3.00000i	−0.183597	+	0.317999i	−0.943103	−	0.332501i	$-0.892107\pi$
$89$	−1.73205	+	3.00000i	−0.183597	+	0.317999i	0.759506	+	0.650500i	$0.225441\pi$
$90$			10.3923i			1.09545i
$91$	−6.00000	−	6.92820i	−0.628971	−	0.726273i
$92$			3.00000i			0.312772i
$93$	5.19615	+	3.00000i	0.538816	+	0.311086i
$94$	−10.5000	+	6.06218i	−1.08299	+	0.625266i
$95$	15.5885	−	9.00000i	1.59934	−	0.923381i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$		−	1.73205i		−	0.175863i	−0.996127	−	0.0879316i	$-0.971974\pi$
$97$		−	1.73205i		−	0.175863i	0.996127	−	0.0879316i	$-0.0280257\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$			3.00000i			0.301511i
$100$	3.50000	−	6.06218i	0.350000	−	0.606218i
$101$	−6.06218	−	10.5000i	−0.603209	−	1.04479i	−0.992332	−	0.123603i	$-0.960555\pi$
$101$	−6.06218	−	10.5000i	−0.603209	−	1.04479i	0.389123	−	0.921186i	$-0.372778\pi$
$102$	7.79423	−	4.50000i	0.771744	−	0.445566i
$103$	9.00000	+	5.19615i	0.886796	+	0.511992i	0.872893	−	0.487911i	$-0.162241\pi$
$103$	9.00000	+	5.19615i	0.886796	+	0.511992i	0.0139031	+	0.999903i	$0.495574\pi$
$104$	−3.46410			−0.339683
$105$	12.0000	−	10.3923i	1.17108	−	1.01419i
$106$		0			0
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$	2.59808	+	4.50000i	0.250000	+	0.433013i
$109$	4.00000	+	6.92820i	0.383131	+	0.663602i	0.991508	−	0.130046i	$-0.0415126\pi$
$109$	4.00000	+	6.92820i	0.383131	+	0.663602i	−0.608377	+	0.793648i	$0.708179\pi$
$110$	1.73205	−	3.00000i	0.165145	−	0.286039i
$111$	12.1244			1.15079
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$	4.50000	−	7.79423i	0.421464	−	0.729996i
$115$	−9.00000	+	5.19615i	−0.839254	+	0.484544i
$116$	7.79423	−	4.50000i	0.723676	−	0.417815i
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$			1.73205i			0.159448i
$119$	−12.9904	−	4.50000i	−1.19083	−	0.412514i
$120$		−	6.00000i		−	0.547723i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	1.73205	+	3.00000i	0.156813	+	0.271607i
$123$	6.00000	+	10.3923i	0.541002	+	0.937043i
$124$	−3.00000	−	1.73205i	−0.269408	−	0.155543i
$125$	6.92820			0.619677
$126$	2.59808	−	7.50000i	0.231455	−	0.668153i
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	4.33013	+	7.50000i	0.381246	+	0.660338i
$130$	−6.00000	−	10.3923i	−0.526235	−	0.911465i
$131$	−6.92820	+	12.0000i	−0.605320	+	1.04844i	0.386681	+	0.922214i	$0.373621\pi$
$131$	−6.92820	+	12.0000i	−0.605320	+	1.04844i	−0.992001	+	0.126231i	$0.959712\pi$
$132$		−	1.73205i		−	0.150756i
$133$	−13.5000	+	2.59808i	−1.17060	+	0.225282i
$134$			8.00000i			0.691095i
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$	−4.50000	+	2.59808i	−0.385872	+	0.222783i
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.346235	−	0.938148i	$-0.387460\pi$
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.985577	+	0.169226i	$0.0541268\pi$
$138$	−2.59808	+	4.50000i	−0.221163	+	0.383065i
$139$			8.66025i			0.734553i	0.930112	+	0.367277i	$0.119710\pi$
$139$			8.66025i			0.734553i	−0.930112	+	0.367277i	$0.880290\pi$
$140$	−6.92820	+	6.00000i	−0.585540	+	0.507093i
$141$	−21.0000			−1.76852
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$	−1.73205	−	3.00000i	−0.144841	−	0.250873i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	27.0000	+	15.5885i	2.24223	+	1.29455i
$146$	−13.8564			−1.14676
$147$	−11.2583	+	4.50000i	−0.928571	+	0.371154i
$148$	−7.00000			−0.575396
$149$	2.59808	+	1.50000i	0.212843	+	0.122885i	0.602632	−	0.798019i	$-0.294119\pi$
$149$	2.59808	+	1.50000i	0.212843	+	0.122885i	−0.389789	+	0.920904i	$0.627452\pi$
$150$	10.5000	−	6.06218i	0.857321	−	0.494975i
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$	−2.59808	+	4.50000i	−0.210732	+	0.364998i
$153$	15.5885			1.26025
$154$	−2.00000	+	1.73205i	−0.161165	+	0.139573i
$155$		−	12.0000i		−	0.963863i
$156$	−5.19615	−	3.00000i	−0.416025	−	0.240192i
$157$	−7.50000	+	4.33013i	−0.598565	+	0.345582i	−0.768477	−	0.639878i	$-0.778985\pi$
$157$	−7.50000	+	4.33013i	−0.598565	+	0.345582i	0.169912	+	0.985459i	$0.445652\pi$
$158$	−13.8564	+	8.00000i	−1.10236	+	0.636446i
$159$		0			0
$160$			3.46410i			0.273861i
$161$	7.79423	−	1.50000i	0.614271	−	0.118217i
$162$			9.00000i			0.707107i
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	−3.46410	−	6.00000i	−0.270501	−	0.468521i
$165$	5.19615	−	3.00000i	0.404520	−	0.233550i
$166$	3.00000	+	1.73205i	0.232845	+	0.134433i
$167$	−10.3923			−0.804181			−0.402090	−	0.915600i	$-0.631716\pi$
$167$	−10.3923			−0.804181			−0.402090	+	0.915600i	$0.631716\pi$
$168$	−1.50000	+	4.33013i	−0.115728	+	0.334077i
$169$	1.00000			0.0769231
$170$	−15.5885	−	9.00000i	−1.19558	−	0.690268i
$171$	13.5000	−	7.79423i	1.03237	−	0.596040i
$172$	−2.50000	−	4.33013i	−0.190623	−	0.330169i
$173$	−3.46410	+	6.00000i	−0.263371	+	0.456172i	−0.967135	−	0.254262i	$-0.918168\pi$
$173$	−3.46410	+	6.00000i	−0.263371	+	0.456172i	0.703765	+	0.710433i	$0.251501\pi$
$174$	15.5885			1.18176
$175$	−17.5000	−	6.06218i	−1.32288	−	0.458258i
$176$			1.00000i			0.0753778i
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$	3.00000	−	1.73205i	0.224860	−	0.129823i
$179$	12.9904	−	7.50000i	0.970947	−	0.560576i	0.0714220	−	0.997446i	$-0.477246\pi$
$179$	12.9904	−	7.50000i	0.970947	−	0.560576i	0.899525	+	0.436870i	$0.143913\pi$
$180$	5.19615	−	9.00000i	0.387298	−	0.670820i
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$	1.73205	+	9.00000i	0.128388	+	0.667124i
$183$			6.00000i			0.443533i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−12.1244	−	21.0000i	−0.891400	−	1.54395i
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−4.50000	−	2.59808i	−0.329073	−	0.189990i
$188$	12.1244			0.884260
$189$	10.3923	−	9.00000i	0.755929	−	0.654654i
$190$	−18.0000			−1.30586
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.866025	+	1.50000i	0.0625000	+	0.108253i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−0.866025	+	1.50000i	−0.0621770	+	0.107694i
$195$		−	20.7846i		−	1.48842i
$196$	6.50000	−	2.59808i	0.464286	−	0.185577i
$197$		−	3.00000i		−	0.213741i	−0.994273	−	0.106871i	$-0.965917\pi$
$197$		−	3.00000i		−	0.213741i	0.994273	−	0.106871i	$-0.0340831\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	0.389885	+	0.920864i	$0.372515\pi$
$200$	−6.06218	+	3.50000i	−0.428661	+	0.247487i
$201$	−6.92820	+	12.0000i	−0.488678	+	0.846415i
$202$			12.1244i			0.853067i
$203$	−15.5885	−	18.0000i	−1.09410	−	1.26335i
$204$	−9.00000			−0.630126
$205$	12.0000	−	20.7846i	0.838116	−	1.45166i
$206$	−5.19615	−	9.00000i	−0.362033	−	0.627060i
$207$	−7.79423	+	4.50000i	−0.541736	+	0.312772i
$208$	3.00000	+	1.73205i	0.208013	+	0.120096i
$209$	−5.19615			−0.359425
$210$	−15.5885	+	3.00000i	−1.07571	+	0.207020i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	13.5000	−	7.79423i	0.925005	−	0.534052i
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$	8.66025	−	15.0000i	0.590624	−	1.02299i
$216$		−	5.19615i		−	0.353553i
$217$	−3.00000	+	8.66025i	−0.203653	+	0.587896i
$218$		−	8.00000i		−	0.541828i
$219$	−20.7846	−	12.0000i	−1.40449	−	0.810885i
$220$	−3.00000	+	1.73205i	−0.202260	+	0.116775i
$221$	−15.5885	+	9.00000i	−1.04859	+	0.605406i
$222$	−10.5000	−	6.06218i	−0.704714	−	0.406867i
$223$		−	3.46410i		−	0.231973i	−0.993251	−	0.115987i	$-0.962997\pi$
$223$		−	3.46410i		−	0.231973i	0.993251	−	0.115987i	$-0.0370030\pi$
$224$	0.866025	−	2.50000i	0.0578638	−	0.167038i
$225$	21.0000			1.40000
$226$	9.00000	−	15.5885i	0.598671	−	1.03693i
$227$	8.66025	+	15.0000i	0.574801	+	0.995585i	0.996063	+	0.0886460i	$0.0282540\pi$
$227$	8.66025	+	15.0000i	0.574801	+	0.995585i	−0.421262	+	0.906939i	$0.638413\pi$
$228$	−7.79423	+	4.50000i	−0.516185	+	0.298020i
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	0.0480291	−	0.998846i	$-0.484706\pi$
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	−0.841011	+	0.541017i	$0.818039\pi$
$230$	10.3923			0.685248
$231$	−4.50000	+	0.866025i	−0.296078	+	0.0569803i
$232$	−9.00000			−0.590879
$233$	−7.79423	−	4.50000i	−0.510617	−	0.294805i	0.222470	−	0.974939i	$-0.428588\pi$
$233$	−7.79423	−	4.50000i	−0.510617	−	0.294805i	−0.733087	+	0.680135i	$0.761921\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$	21.0000	+	36.3731i	1.36989	+	2.37272i
$236$	0.866025	−	1.50000i	0.0563735	−	0.0976417i
$237$	−27.7128			−1.80014
$238$	9.00000	+	10.3923i	0.583383	+	0.673633i
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$	−3.00000	+	5.19615i	−0.193649	+	0.335410i
$241$	−18.0000	+	10.3923i	−1.15948	+	0.669427i	−0.951180	−	0.308637i	$-0.900127\pi$
$241$	−18.0000	+	10.3923i	−1.15948	+	0.669427i	−0.208302	+	0.978065i	$0.566794\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$		−	3.46410i		−	0.221766i
$245$	19.0526	+	15.0000i	1.21722	+	0.958315i
$246$		−	12.0000i		−	0.765092i
$247$	−9.00000	+	15.5885i	−0.572656	+	0.991870i
$248$	1.73205	+	3.00000i	0.109985	+	0.190500i
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	12.1244			0.765283			0.382641	−	0.923897i	$-0.375015\pi$
$251$	12.1244			0.765283			0.382641	+	0.923897i	$0.375015\pi$
$252$	−6.00000	+	5.19615i	−0.377964	+	0.327327i
$253$	3.00000			0.188608
$254$	6.06218	+	3.50000i	0.380375	+	0.219610i
$255$	−15.5885	−	27.0000i	−0.976187	−	1.69081i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.73205	−	3.00000i	0.108042	−	0.187135i	−0.806935	−	0.590641i	$-0.798875\pi$
$257$	1.73205	−	3.00000i	0.108042	−	0.187135i	0.914977	+	0.403506i	$0.132208\pi$
$258$		−	8.66025i		−	0.539164i
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$			12.0000i			0.744208i
$261$	23.3827	+	13.5000i	1.44735	+	0.835629i
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	5.19615	−	3.00000i	0.320408	−	0.184988i	−0.331166	−	0.943572i	$-0.607442\pi$
$263$	5.19615	−	3.00000i	0.320408	−	0.184988i	0.651575	+	0.758585i	$0.274109\pi$
$264$	−0.866025	+	1.50000i	−0.0533002	+	0.0923186i
$265$		0			0
$266$	12.9904	+	4.50000i	0.796491	+	0.275913i
$267$	6.00000			0.367194
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	−6.92820	−	12.0000i	−0.422420	−	0.731653i	0.573756	−	0.819027i	$-0.305486\pi$
$269$	−6.92820	−	12.0000i	−0.422420	−	0.731653i	−0.996176	+	0.0873736i	$0.972153\pi$
$270$	15.5885	−	9.00000i	0.948683	−	0.547723i
$271$	9.00000	+	5.19615i	0.546711	+	0.315644i	0.747794	−	0.663930i	$-0.231113\pi$
$271$	9.00000	+	5.19615i	0.546711	+	0.315644i	−0.201083	+	0.979574i	$0.564446\pi$
$272$	5.19615			0.315063
$273$	−5.19615	+	15.0000i	−0.314485	+	0.907841i
$274$	−18.0000			−1.08742
$275$	−6.06218	−	3.50000i	−0.365563	−	0.211058i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$	4.33013	−	7.50000i	0.259704	−	0.449820i
$279$		−	10.3923i		−	0.622171i
$280$	9.00000	−	1.73205i	0.537853	−	0.103510i
$281$			21.0000i			1.25275i	0.779520	+	0.626377i	$0.215463\pi$
$281$			21.0000i			1.25275i	−0.779520	+	0.626377i	$0.784537\pi$
$282$	18.1865	+	10.5000i	1.08299	+	0.625266i
$283$	9.00000	−	5.19615i	0.534994	−	0.308879i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	9.00000	−	5.19615i	0.534994	−	0.308879i	0.743048	+	0.669238i	$0.233379\pi$
$284$	−7.79423	+	4.50000i	−0.462502	+	0.267026i
$285$	−27.0000	−	15.5885i	−1.59934	−	0.923381i
$286$			3.46410i			0.204837i
$287$	−13.8564	+	12.0000i	−0.817918	+	0.708338i
$288$			3.00000i			0.176777i
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	−15.5885	−	27.0000i	−0.915386	−	1.58549i
$291$	−2.59808	+	1.50000i	−0.152302	+	0.0879316i
$292$	12.0000	+	6.92820i	0.702247	+	0.405442i
$293$	−29.4449			−1.72019			−0.860094	−	0.510136i	$-0.829595\pi$
$293$	−29.4449			−1.72019			−0.860094	+	0.510136i	$0.829595\pi$
$294$	12.0000	+	1.73205i	0.699854	+	0.101015i
$295$	6.00000			0.349334
$296$	6.06218	+	3.50000i	0.352357	+	0.203433i
$297$	4.50000	−	2.59808i	0.261116	−	0.150756i
$298$	−1.50000	−	2.59808i	−0.0868927	−	0.150503i
$299$	5.19615	−	9.00000i	0.300501	−	0.520483i
$300$	−12.1244			−0.700000
$301$	−10.0000	+	8.66025i	−0.576390	+	0.499169i
$302$		−	17.0000i		−	0.978240i
$303$	−10.5000	+	18.1865i	−0.603209	+	1.04479i
$304$	4.50000	−	2.59808i	0.258093	−	0.149010i
$305$	10.3923	−	6.00000i	0.595062	−	0.343559i
$306$	−13.5000	−	7.79423i	−0.771744	−	0.445566i
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$	2.59808	−	0.500000i	0.148039	−	0.0284901i
$309$		−	18.0000i		−	1.02398i
$310$	−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	$0.786268\pi$
$312$	3.00000	+	5.19615i	0.169842	+	0.294174i
$313$	10.5000	+	6.06218i	0.593495	+	0.342655i	0.766478	−	0.642270i	$-0.222007\pi$
$313$	10.5000	+	6.06218i	0.593495	+	0.342655i	−0.172983	+	0.984925i	$0.555341\pi$
$314$	8.66025			0.488726
$315$	−25.9808	−	9.00000i	−1.46385	−	0.507093i
$316$	16.0000			0.900070
$317$	−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	$0.835355\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	1.73205	−	3.00000i	0.0968246	−	0.167705i
$321$		−	10.3923i		−	0.580042i
$322$	−7.50000	−	2.59808i	−0.417959	−	0.144785i
$323$			27.0000i			1.50232i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−21.0000	+	12.1244i	−1.16487	+	0.672538i
$326$	1.73205	−	1.00000i	0.0959294	−	0.0553849i
$327$	6.92820	−	12.0000i	0.383131	−	0.663602i
$328$			6.92820i			0.382546i
$329$	−6.06218	−	31.5000i	−0.334219	−	1.73665i
$330$	−6.00000			−0.330289
$331$	−11.0000	+	19.0526i	−0.604615	+	1.04722i	0.387498	+	0.921871i	$0.373340\pi$
$331$	−11.0000	+	19.0526i	−0.604615	+	1.04722i	−0.992112	+	0.125353i	$0.959994\pi$
$332$	−1.73205	−	3.00000i	−0.0950586	−	0.164646i
$333$	−10.5000	−	18.1865i	−0.575396	−	0.996616i
$334$	9.00000	+	5.19615i	0.492458	+	0.284321i
$335$	27.7128			1.51411
$336$	3.46410	−	3.00000i	0.188982	−	0.163663i
$337$	28.0000			1.52526			0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000			1.52526			0.762629	+	0.646837i	$0.223908\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	27.0000	−	15.5885i	1.46644	−	0.846649i
$340$	9.00000	+	15.5885i	0.488094	+	0.845403i
$341$	−1.73205	+	3.00000i	−0.0937958	+	0.162459i
$342$	−15.5885			−0.842927
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$			5.00000i			0.269582i
$345$	15.5885	+	9.00000i	0.839254	+	0.484544i
$346$	6.00000	−	3.46410i	0.322562	−	0.186231i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−13.5000	−	7.79423i	−0.723676	−	0.417815i
$349$		−	6.92820i		−	0.370858i	−0.982658	−	0.185429i	$-0.940632\pi$
$349$		−	6.92820i		−	0.370858i	0.982658	−	0.185429i	$-0.0593675\pi$
$350$	12.1244	+	14.0000i	0.648074	+	0.748331i
$351$		−	18.0000i		−	0.960769i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	12.1244	+	21.0000i	0.645314	+	1.11772i	0.984229	+	0.176900i	$0.0566069\pi$
$353$	12.1244	+	21.0000i	0.645314	+	1.11772i	−0.338914	+	0.940817i	$0.610060\pi$
$354$	2.59808	−	1.50000i	0.138086	−	0.0797241i
$355$	−27.0000	−	15.5885i	−1.43301	−	0.827349i
$356$	−3.46410			−0.183597
$357$	4.50000	+	23.3827i	0.238165	+	1.23754i
$358$	−15.0000			−0.792775
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	0.0286287	−	0.999590i	$-0.490886\pi$
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	−0.851356	+	0.524588i	$0.824219\pi$
$360$	−9.00000	+	5.19615i	−0.474342	+	0.273861i
$361$	4.00000	+	6.92820i	0.210526	+	0.364642i
$362$	−6.92820	+	12.0000i	−0.364138	+	0.630706i
$363$	−1.73205			−0.0909091
$364$	3.00000	−	8.66025i	0.157243	−	0.453921i
$365$			48.0000i			2.51243i
$366$	3.00000	−	5.19615i	0.156813	−	0.271607i
$367$	30.0000	−	17.3205i	1.56599	−	0.904123i	0.569358	−	0.822090i	$-0.307192\pi$
$367$	30.0000	−	17.3205i	1.56599	−	0.904123i	0.996630	−	0.0820332i	$-0.0261414\pi$
$368$	−2.59808	+	1.50000i	−0.135434	+	0.0781929i
$369$	10.3923	−	18.0000i	0.541002	−	0.937043i
$370$			24.2487i			1.26063i
$371$		0			0
$372$			6.00000i			0.311086i
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.0291379	−	0.999575i	$-0.490724\pi$
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.851089	−	0.525022i	$-0.175943\pi$
$374$	2.59808	+	4.50000i	0.134343	+	0.232689i
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$	−10.5000	−	6.06218i	−0.541496	−	0.312633i
$377$	−31.1769			−1.60569
$378$	−13.5000	+	2.59808i	−0.694365	+	0.133631i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	15.5885	+	9.00000i	0.799671	+	0.461690i
$381$	6.06218	+	10.5000i	0.310575	+	0.537931i
$382$		0			0
$383$	12.9904	−	22.5000i	0.663777	−	1.14970i	−0.315838	−	0.948813i	$-0.602286\pi$
$383$	12.9904	−	22.5000i	0.663777	−	1.14970i	0.979615	−	0.200883i	$-0.0643811\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	6.00000	+	6.92820i	0.305788	+	0.353094i
$386$			4.00000i			0.203595i
$387$	7.50000	−	12.9904i	0.381246	−	0.660338i
$388$	1.50000	−	0.866025i	0.0761510	−	0.0439658i
$389$	5.19615	−	3.00000i	0.263455	−	0.152106i	−0.362454	−	0.932002i	$-0.618061\pi$
$389$	5.19615	−	3.00000i	0.263455	−	0.152106i	0.625910	+	0.779895i	$0.284728\pi$
$390$	−10.3923	+	18.0000i	−0.526235	+	0.911465i
$391$		−	15.5885i		−	0.788342i
$392$	−6.92820	−	1.00000i	−0.349927	−	0.0505076i
$393$	24.0000			1.21064
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$	27.7128	+	48.0000i	1.39438	+	2.41514i
$396$	−2.59808	+	1.50000i	−0.130558	+	0.0753778i
$397$	22.5000	+	12.9904i	1.12924	+	0.651969i	0.943744	−	0.330676i	$-0.107277\pi$
$397$	22.5000	+	12.9904i	1.12924	+	0.651969i	0.185498	+	0.982645i	$0.440610\pi$
$398$	3.46410			0.173640
$399$	15.5885	+	18.0000i	0.780399	+	0.901127i
$400$	7.00000			0.350000
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$	12.0000	−	6.92820i	0.598506	−	0.345547i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	6.06218	−	10.5000i	0.301605	−	0.522395i
$405$	31.1769			1.54919
$406$	4.50000	+	23.3827i	0.223331	+	1.16046i
$407$			7.00000i			0.346977i
$408$	7.79423	+	4.50000i	0.385872	+	0.222783i
$409$	−12.0000	+	6.92820i	−0.593362	+	0.342578i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	−12.0000	+	6.92820i	−0.593362	+	0.342578i	0.173064	+	0.984911i	$0.444633\pi$
$410$	−20.7846	+	12.0000i	−1.02648	+	0.592638i
$411$	−27.0000	−	15.5885i	−1.33181	−	0.768922i
$412$			10.3923i			0.511992i
$413$	−4.33013	−	1.50000i	−0.213072	−	0.0738102i
$414$	9.00000			0.442326
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	−1.73205	−	3.00000i	−0.0849208	−	0.147087i
$417$	12.9904	−	7.50000i	0.636142	−	0.367277i
$418$	4.50000	+	2.59808i	0.220102	+	0.127076i
$419$	29.4449			1.43848			0.719238	−	0.694764i	$-0.244491\pi$
$419$	29.4449			1.43848			0.719238	+	0.694764i	$0.244491\pi$
$420$	15.0000	+	5.19615i	0.731925	+	0.253546i
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−3.46410	−	2.00000i	−0.168630	−	0.0973585i
$423$	18.1865	+	31.5000i	0.884260	+	1.53158i
$424$		0			0
$425$	−18.1865	+	31.5000i	−0.882176	+	1.52797i
$426$	−15.5885			−0.755263
$427$	−9.00000	+	1.73205i	−0.435541	+	0.0838198i
$428$			6.00000i			0.290021i
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	−15.0000	+	8.66025i	−0.723364	+	0.417635i
$431$	10.3923	−	6.00000i	0.500580	−	0.289010i	−0.228373	−	0.973574i	$-0.573341\pi$
$431$	10.3923	−	6.00000i	0.500580	−	0.289010i	0.728953	+	0.684564i	$0.240007\pi$
$432$	−2.59808	+	4.50000i	−0.125000	+	0.216506i
$433$		−	22.5167i		−	1.08208i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$		−	22.5167i		−	1.08208i	0.840996	−	0.541041i	$-0.181970\pi$
$434$	6.92820	−	6.00000i	0.332564	−	0.288009i
$435$		−	54.0000i		−	2.58910i
$436$	−4.00000	+	6.92820i	−0.191565	+	0.331801i
$437$	−7.79423	−	13.5000i	−0.372849	−	0.645793i
$438$	12.0000	+	20.7846i	0.573382	+	0.993127i
$439$	−7.50000	−	4.33013i	−0.357955	−	0.206666i	0.310228	−	0.950662i	$-0.399595\pi$
$439$	−7.50000	−	4.33013i	−0.357955	−	0.206666i	−0.668184	+	0.743996i	$0.732928\pi$
$440$	3.46410			0.165145
$441$	16.5000	+	12.9904i	0.785714	+	0.618590i
$442$	18.0000			0.856173
$443$	12.9904	+	7.50000i	0.617192	+	0.356336i	0.775775	−	0.631010i	$-0.217359\pi$
$443$	12.9904	+	7.50000i	0.617192	+	0.356336i	−0.158583	+	0.987346i	$0.550693\pi$
$444$	6.06218	+	10.5000i	0.287698	+	0.498308i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−1.73205	+	3.00000i	−0.0820150	+	0.142054i
$447$		−	5.19615i		−	0.245770i
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$		−	36.0000i		−	1.69895i	−0.527633	−	0.849473i	$-0.676920\pi$
$449$		−	36.0000i		−	1.69895i	0.527633	−	0.849473i	$-0.323080\pi$
$450$	−18.1865	−	10.5000i	−0.857321	−	0.494975i
$451$	−6.00000	+	3.46410i	−0.282529	+	0.163118i
$452$	−15.5885	+	9.00000i	−0.733219	+	0.423324i
$453$	14.7224	−	25.5000i	0.691720	−	1.19809i
$454$		−	17.3205i		−	0.812892i
$455$	31.1769	−	6.00000i	1.46160	−	0.281284i
$456$	9.00000			0.421464
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	−0.757174	−	0.653213i	$-0.773421\pi$
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	0.944286	+	0.329125i	$0.106754\pi$
$458$	6.92820	+	12.0000i	0.323734	+	0.560723i
$459$	−13.5000	−	23.3827i	−0.630126	−	1.09141i
$460$	−9.00000	−	5.19615i	−0.419627	−	0.242272i
$461$	−15.5885			−0.726027			−0.363013	−	0.931784i	$-0.618252\pi$
$461$	−15.5885			−0.726027			−0.363013	+	0.931784i	$0.618252\pi$
$462$	4.33013	+	1.50000i	0.201456	+	0.0697863i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	7.79423	+	4.50000i	0.361838	+	0.208907i
$465$	−18.0000	+	10.3923i	−0.834730	+	0.481932i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−12.9904	+	22.5000i	−0.601123	+	1.04118i	0.391528	+	0.920166i	$0.371947\pi$
$467$	−12.9904	+	22.5000i	−0.601123	+	1.04118i	−0.992651	+	0.121010i	$0.961387\pi$
$468$			10.3923i			0.480384i
$469$	−20.0000	−	6.92820i	−0.923514	−	0.319915i
$470$		−	42.0000i		−	1.93732i
$471$	12.9904	+	7.50000i	0.598565	+	0.345582i
$472$	−1.50000	+	0.866025i	−0.0690431	+	0.0398621i
$473$	−4.33013	+	2.50000i	−0.199099	+	0.114950i
$474$	24.0000	+	13.8564i	1.10236	+	0.636446i
$475$			36.3731i			1.66891i
$476$	−2.59808	−	13.5000i	−0.119083	−	0.618771i
$477$		0			0
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	1.73205	+	3.00000i	0.0791394	+	0.137073i	0.902879	−	0.429895i	$-0.141449\pi$
$479$	1.73205	+	3.00000i	0.0791394	+	0.137073i	−0.823739	+	0.566969i	$0.808116\pi$
$480$	5.19615	−	3.00000i	0.237171	−	0.136931i
$481$	21.0000	+	12.1244i	0.957518	+	0.552823i
$482$	20.7846			0.946713
$483$	−9.00000	−	10.3923i	−0.409514	−	0.472866i
$484$	1.00000			0.0454545
$485$	5.19615	+	3.00000i	0.235945	+	0.136223i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	19.0000	+	32.9090i	0.860972	+	1.49125i	0.870992	+	0.491298i	$0.163477\pi$
$487$	19.0000	+	32.9090i	0.860972	+	1.49125i	−0.0100195	+	0.999950i	$0.503189\pi$
$488$	−1.73205	+	3.00000i	−0.0784063	+	0.135804i
$489$	3.46410			0.156652
$490$	−9.00000	−	22.5167i	−0.406579	−	1.01720i
$491$		−	18.0000i		−	0.812329i	−0.913800	−	0.406164i	$-0.866866\pi$
$491$		−	18.0000i		−	0.812329i	0.913800	−	0.406164i	$-0.133134\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	−40.5000	+	23.3827i	−1.82403	+	1.05310i
$494$	15.5885	−	9.00000i	0.701358	−	0.404929i
$495$	−9.00000	−	5.19615i	−0.404520	−	0.233550i
$496$		−	3.46410i		−	0.155543i
$497$	15.5885	+	18.0000i	0.699238	+	0.807410i
$498$		−	6.00000i		−	0.268866i
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$	3.46410	+	6.00000i	0.154919	+	0.268328i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	−10.5000	−	6.06218i	−0.468638	−	0.270568i
$503$	−3.46410			−0.154457			−0.0772283	−	0.997013i	$-0.524607\pi$
$503$	−3.46410			−0.154457			−0.0772283	+	0.997013i	$0.524607\pi$
$504$	7.79423	−	1.50000i	0.347183	−	0.0668153i
$505$	42.0000			1.86898
$506$	−2.59808	−	1.50000i	−0.115499	−	0.0666831i
$507$	−0.866025	−	1.50000i	−0.0384615	−	0.0666173i
$508$	−3.50000	−	6.06218i	−0.155287	−	0.268966i
$509$	17.3205	−	30.0000i	0.767718	−	1.32973i	−0.171080	−	0.985257i	$-0.554726\pi$
$509$	17.3205	−	30.0000i	0.767718	−	1.32973i	0.938798	−	0.344469i	$-0.111941\pi$
$510$			31.1769i			1.38054i
$511$	12.0000	−	34.6410i	0.530849	−	1.53243i
$512$			1.00000i			0.0441942i
$513$	−23.3827	−	13.5000i	−1.03237	−	0.596040i
$514$	−3.00000	+	1.73205i	−0.132324	+	0.0763975i
$515$	−31.1769	+	18.0000i	−1.37382	+	0.793175i
$516$	−4.33013	+	7.50000i	−0.190623	+	0.330169i
$517$		−	12.1244i		−	0.533229i
$518$	6.06218	−	17.5000i	0.266357	−	0.768906i
$519$	12.0000			0.526742
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	5.19615	+	9.00000i	0.227648	+	0.394297i	0.957110	−	0.289723i	$-0.0935633\pi$
$521$	5.19615	+	9.00000i	0.227648	+	0.394297i	−0.729463	+	0.684020i	$0.760230\pi$
$522$	−13.5000	−	23.3827i	−0.590879	−	1.02343i
$523$	15.0000	+	8.66025i	0.655904	+	0.378686i	0.790715	−	0.612185i	$-0.209709\pi$
$523$	15.0000	+	8.66025i	0.655904	+	0.378686i	−0.134810	+	0.990871i	$0.543043\pi$
$524$	−13.8564			−0.605320
$525$	6.06218	+	31.5000i	0.264575	+	1.37477i
$526$	−6.00000			−0.261612
$527$	15.5885	+	9.00000i	0.679044	+	0.392046i
$528$	1.50000	−	0.866025i	0.0652791	−	0.0376889i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	5.19615			0.225494
$532$	−9.00000	−	10.3923i	−0.390199	−	0.450564i
$533$			24.0000i			1.03956i
$534$	−5.19615	−	3.00000i	−0.224860	−	0.129823i
$535$	−18.0000	+	10.3923i	−0.778208	+	0.449299i
$536$	−6.92820	+	4.00000i	−0.299253	+	0.172774i
$537$	−22.5000	−	12.9904i	−0.970947	−	0.560576i
$538$			13.8564i			0.597392i
$539$	−2.59808	−	6.50000i	−0.111907	−	0.279975i
$540$	−18.0000			−0.774597
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	−5.19615	−	9.00000i	−0.223194	−	0.386583i
$543$	−20.7846	+	12.0000i	−0.891953	+	0.514969i
$544$	−4.50000	−	2.59808i	−0.192936	−	0.111392i
$545$	−27.7128			−1.18709
$546$	12.0000	−	10.3923i	0.513553	−	0.444750i
$547$	−43.0000			−1.83855			−0.919274	−	0.393619i	$-0.871223\pi$
$547$	−43.0000			−1.83855			−0.919274	+	0.393619i	$0.871223\pi$
$548$	15.5885	+	9.00000i	0.665906	+	0.384461i
$549$	9.00000	−	5.19615i	0.384111	−	0.221766i
$550$	3.50000	+	6.06218i	0.149241	+	0.258492i
$551$	−23.3827	+	40.5000i	−0.996136	+	1.72536i
$552$	−5.19615			−0.221163
$553$	−8.00000	−	41.5692i	−0.340195	−	1.76770i
$554$			8.00000i			0.339887i
$555$	−21.0000	+	36.3731i	−0.891400	+	1.54395i
$556$	−7.50000	+	4.33013i	−0.318071	+	0.183638i
$557$	18.1865	−	10.5000i	0.770588	−	0.444899i	−0.0624962	−	0.998045i	$-0.519906\pi$
$557$	18.1865	−	10.5000i	0.770588	−	0.444899i	0.833084	+	0.553146i	$0.186573\pi$
$558$	−5.19615	+	9.00000i	−0.219971	+	0.381000i
$559$			17.3205i			0.732579i
$560$	−8.66025	−	3.00000i	−0.365963	−	0.126773i
$561$			9.00000i			0.379980i
$562$	10.5000	−	18.1865i	0.442916	−	0.767153i
$563$	12.1244	+	21.0000i	0.510981	+	0.885044i	0.999919	+	0.0127261i	$0.00405096\pi$
$563$	12.1244	+	21.0000i	0.510981	+	0.885044i	−0.488938	+	0.872318i	$0.662616\pi$
$564$	−10.5000	−	18.1865i	−0.442130	−	0.765791i
$565$	−54.0000	−	31.1769i	−2.27180	−	1.31162i
$566$	−10.3923			−0.436821
$567$	−22.5000	−	7.79423i	−0.944911	−	0.327327i
$568$	9.00000			0.377632
$569$	−23.3827	−	13.5000i	−0.980253	−	0.565949i	−0.0779066	−	0.996961i	$-0.524824\pi$
$569$	−23.3827	−	13.5000i	−0.980253	−	0.565949i	−0.902347	+	0.431011i	$0.858157\pi$
$570$	15.5885	+	27.0000i	0.652929	+	1.13091i
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$	1.73205	−	3.00000i	0.0724207	−	0.125436i
$573$		0			0
$574$	18.0000	−	3.46410i	0.751305	−	0.144589i
$575$		−	21.0000i		−	0.875761i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	24.0000	−	13.8564i	0.999133	−	0.576850i	0.0911414	−	0.995838i	$-0.470948\pi$
$577$	24.0000	−	13.8564i	0.999133	−	0.576850i	0.907992	+	0.418988i	$0.137615\pi$
$578$	8.66025	−	5.00000i	0.360219	−	0.207973i
$579$	−3.46410	+	6.00000i	−0.143963	+	0.249351i
$580$			31.1769i			1.29455i
$581$	−6.92820	+	6.00000i	−0.287430	+	0.248922i
$582$	3.00000			0.124354
$583$		0			0
$584$	−6.92820	−	12.0000i	−0.286691	−	0.496564i
$585$	−31.1769	+	18.0000i	−1.28901	+	0.744208i
$586$	25.5000	+	14.7224i	1.05340	+	0.608178i
$587$	38.1051			1.57277			0.786383	−	0.617739i	$-0.211951\pi$
$587$	38.1051			1.57277			0.786383	+	0.617739i	$0.211951\pi$
$588$	−9.52628	−	7.50000i	−0.392857	−	0.309295i
$589$	18.0000			0.741677
$590$	−5.19615	−	3.00000i	−0.213922	−	0.123508i
$591$	−4.50000	+	2.59808i	−0.185105	+	0.106871i
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	4.33013	−	7.50000i	0.177817	−	0.307988i	−0.763316	−	0.646026i	$-0.776430\pi$
$593$	4.33013	−	7.50000i	0.177817	−	0.307988i	0.941133	+	0.338038i	$0.109763\pi$
$594$	−5.19615			−0.213201
$595$	36.0000	−	31.1769i	1.47586	−	1.27813i
$596$			3.00000i			0.122885i
$597$	5.19615	+	3.00000i	0.212664	+	0.122782i
$598$	−9.00000	+	5.19615i	−0.368037	+	0.212486i
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	−0.860393	−	0.509631i	$-0.829782\pi$
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	0.0111569	+	0.999938i	$0.496449\pi$
$600$	10.5000	+	6.06218i	0.428661	+	0.247487i
$601$		−	20.7846i		−	0.847822i	−0.905704	−	0.423911i	$-0.860657\pi$
$601$		−	20.7846i		−	0.847822i	0.905704	−	0.423911i	$-0.139343\pi$
$602$	12.9904	−	2.50000i	0.529448	−	0.101892i
$603$	24.0000			0.977356
$604$	−8.50000	+	14.7224i	−0.345860	+	0.599047i
$605$	1.73205	+	3.00000i	0.0704179	+	0.121967i
$606$	18.1865	−	10.5000i	0.738777	−	0.426533i
$607$	15.0000	+	8.66025i	0.608831	+	0.351509i	0.772508	−	0.635005i	$-0.219002\pi$
$607$	15.0000	+	8.66025i	0.608831	+	0.351509i	−0.163677	+	0.986514i	$0.552335\pi$
$608$	−5.19615			−0.210732
$609$	−13.5000	+	38.9711i	−0.547048	+	1.57919i
$610$	−12.0000			−0.485866
$611$	−36.3731	−	21.0000i	−1.47150	−	0.849569i
$612$	7.79423	+	13.5000i	0.315063	+	0.545705i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	8.66025	−	15.0000i	0.349499	−	0.605351i
$615$	−41.5692			−1.67623
$616$	−2.50000	−	0.866025i	−0.100728	−	0.0348932i
$617$		−	36.0000i		−	1.44931i	−0.689114	−	0.724653i	$-0.742000\pi$
$617$		−	36.0000i		−	1.44931i	0.689114	−	0.724653i	$-0.258000\pi$
$618$	−9.00000	+	15.5885i	−0.362033	+	0.627060i
$619$	15.0000	−	8.66025i	0.602901	−	0.348085i	−0.167281	−	0.985909i	$-0.553499\pi$
$619$	15.0000	−	8.66025i	0.602901	−	0.348085i	0.770182	+	0.637824i	$0.220165\pi$
$620$	10.3923	−	6.00000i	0.417365	−	0.240966i
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		−	5.19615i		−	0.208347i
$623$	1.73205	+	9.00000i	0.0693932	+	0.360577i
$624$		−	6.00000i		−	0.240192i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−6.06218	−	10.5000i	−0.242293	−	0.419664i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	−7.50000	−	4.33013i	−0.299283	−	0.172791i
$629$	36.3731			1.45029
$630$	18.0000	+	20.7846i	0.717137	+	0.828079i
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−13.8564	−	8.00000i	−0.551178	−	0.318223i
$633$	−3.46410	−	6.00000i	−0.137686	−	0.238479i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	12.1244	−	21.0000i	0.481140	−	0.833360i
$636$		0			0
$637$	−24.0000	−	3.46410i	−0.950915	−	0.137253i
$638$			9.00000i			0.356313i
$639$	−23.3827	−	13.5000i	−0.925005	−	0.534052i
$640$	−3.00000	+	1.73205i	−0.118585	+	0.0684653i
$641$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$641$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$642$	−5.19615	+	9.00000i	−0.205076	+	0.355202i
$643$		−	6.92820i		−	0.273222i	−0.990625	−	0.136611i	$-0.956379\pi$
$643$		−	6.92820i		−	0.273222i	0.990625	−	0.136611i	$-0.0436210\pi$
$644$	5.19615	+	6.00000i	0.204757	+	0.236433i
$645$	−30.0000			−1.18125
$646$	13.5000	−	23.3827i	0.531150	−	0.919979i
$647$	−22.5167	−	39.0000i	−0.885221	−	1.53325i	−0.845460	−	0.534039i	$-0.820674\pi$
$647$	−22.5167	−	39.0000i	−0.885221	−	1.53325i	−0.0397614	−	0.999209i	$-0.512660\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	−1.50000	−	0.866025i	−0.0588802	−	0.0339945i
$650$	24.2487			0.951113
$651$	15.5885	−	3.00000i	0.610960	−	0.117579i
$652$	−2.00000			−0.0783260
$653$	−25.9808	−	15.0000i	−1.01671	−	0.586995i	−0.103558	−	0.994623i	$-0.533023\pi$
$653$	−25.9808	−	15.0000i	−1.01671	−	0.586995i	−0.913148	+	0.407628i	$0.866356\pi$
$654$	−12.0000	+	6.92820i	−0.469237	+	0.270914i
$655$	−24.0000	−	41.5692i	−0.937758	−	1.62424i
$656$	3.46410	−	6.00000i	0.135250	−	0.234261i
$657$			41.5692i			1.62177i
$658$	−10.5000	+	30.3109i	−0.409333	+	1.18164i
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$	5.19615	+	3.00000i	0.202260	+	0.116775i
$661$	−34.5000	+	19.9186i	−1.34189	+	0.774743i	−0.987085	−	0.160196i	$-0.948788\pi$
$661$	−34.5000	+	19.9186i	−1.34189	+	0.774743i	−0.354809	+	0.934939i	$0.615454\pi$
$662$	19.0526	−	11.0000i	0.740499	−	0.427527i
$663$	27.0000	+	15.5885i	1.04859	+	0.605406i
$664$			3.46410i			0.134433i
$665$	15.5885	−	45.0000i	0.604494	−	1.74503i
$666$			21.0000i			0.813733i
$667$	13.5000	−	23.3827i	0.522722	−	0.905381i
$668$	−5.19615	−	9.00000i	−0.201045	−	0.348220i
$669$	−5.19615	+	3.00000i	−0.200895	+	0.115987i
$670$	−24.0000	−	13.8564i	−0.927201	−	0.535320i
$671$	−3.46410			−0.133730
$672$	−4.50000	+	0.866025i	−0.173591	+	0.0334077i
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	−24.2487	−	14.0000i	−0.934025	−	0.539260i
$675$	−18.1865	−	31.5000i	−0.700000	−	1.21244i
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	−6.06218	+	10.5000i	−0.232988	+	0.403548i	−0.958686	−	0.284466i	$-0.908184\pi$
$677$	−6.06218	+	10.5000i	−0.232988	+	0.403548i	0.725698	+	0.688014i	$0.241517\pi$
$678$	−31.1769			−1.19734
$679$	−3.00000	−	3.46410i	−0.115129	−	0.132940i
$680$		−	18.0000i		−	0.690268i
$681$	15.0000	−	25.9808i	0.574801	−	0.995585i
$682$	3.00000	−	1.73205i	0.114876	−	0.0663237i
$683$	−7.79423	+	4.50000i	−0.298238	+	0.172188i	−0.641651	−	0.766997i	$-0.721750\pi$
$683$	−7.79423	+	4.50000i	−0.298238	+	0.172188i	0.343413	+	0.939184i	$0.388417\pi$
$684$	13.5000	+	7.79423i	0.516185	+	0.298020i
$685$			62.3538i			2.38242i
$686$	0.866025	+	18.5000i	0.0330650	+	0.706333i
$687$			24.0000i			0.915657i
$688$	2.50000	−	4.33013i	0.0953116	−	0.165085i
$689$		0			0
$690$	−9.00000	−	15.5885i	−0.342624	−	0.593442i
$691$	45.0000	+	25.9808i	1.71188	+	0.988355i	0.932024	+	0.362397i	$0.118041\pi$
$691$	45.0000	+	25.9808i	1.71188	+	0.988355i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−6.92820			−0.263371
$693$	5.19615	+	6.00000i	0.197386	+	0.227921i
$694$		0			0
$695$	−25.9808	−	15.0000i	−0.985506	−	0.568982i
$696$	7.79423	+	13.5000i	0.295439	+	0.511716i
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−3.46410	+	6.00000i	−0.131118	+	0.227103i
$699$			15.5885i			0.589610i
$700$	−3.50000	−	18.1865i	−0.132288	−	0.687386i
$701$		−	15.0000i		−	0.566542i	−0.959040	−	0.283271i	$-0.908580\pi$
$701$		−	15.0000i		−	0.566542i	0.959040	−	0.283271i	$-0.0914196\pi$
$702$	−9.00000	+	15.5885i	−0.339683	+	0.588348i
$703$	31.5000	−	18.1865i	1.18805	−	0.685918i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	36.3731	−	63.0000i	1.36989	−	2.37272i
$706$		−	24.2487i		−	0.912612i
$707$	−30.3109	−	10.5000i	−1.13996	−	0.394893i
$708$	−3.00000			−0.112747
$709$	−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
$711$	24.0000	+	41.5692i	0.900070	+	1.55897i
$712$	3.00000	+	1.73205i	0.112430	+	0.0649113i
$713$	−10.3923			−0.389195
$714$	7.79423	−	22.5000i	0.291692	−	0.842041i
$715$	12.0000			0.448775
$716$	12.9904	+	7.50000i	0.485473	+	0.280288i
$717$	−9.00000	+	5.19615i	−0.336111	+	0.194054i
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$	6.06218	−	10.5000i	0.226081	−	0.391584i	−0.730562	−	0.682846i	$-0.760742\pi$
$719$	6.06218	−	10.5000i	0.226081	−	0.391584i	0.956643	+	0.291262i	$0.0940752\pi$
$720$	10.3923			0.387298
$721$	27.0000	−	5.19615i	1.00553	−	0.193515i
$722$		−	8.00000i		−	0.297729i
$723$	31.1769	+	18.0000i	1.15948	+	0.669427i
$724$	12.0000	−	6.92820i	0.445976	−	0.257485i
$725$	−54.5596	+	31.5000i	−2.02629	+	1.16988i
$726$	1.50000	+	0.866025i	0.0556702	+	0.0321412i
$727$		−	45.0333i		−	1.67019i	−0.550103	−	0.835097i	$-0.685412\pi$
$727$		−	45.0333i		−	1.67019i	0.550103	−	0.835097i	$-0.314588\pi$
$728$	−6.92820	+	6.00000i	−0.256776	+	0.222375i
$729$	27.0000			1.00000
$730$	24.0000	−	41.5692i	0.888280	−	1.53855i
$731$	12.9904	+	22.5000i	0.480467	+	0.832193i
$732$	−5.19615	+	3.00000i	−0.192055	+	0.110883i
$733$	3.00000	+	1.73205i	0.110808	+	0.0639748i	0.554380	−	0.832264i	$-0.312956\pi$
$733$	3.00000	+	1.73205i	0.110808	+	0.0639748i	−0.443572	+	0.896239i	$0.646289\pi$
$734$	−34.6410			−1.27862
$735$	6.00000	−	41.5692i	0.221313	−	1.53330i
$736$	3.00000			0.110581
$737$	−6.92820	−	4.00000i	−0.255204	−	0.147342i
$738$	−18.0000	+	10.3923i	−0.662589	+	0.382546i
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	12.1244	−	21.0000i	0.445700	−	0.771975i
$741$	31.1769			1.14531
$742$		0			0
$743$			12.0000i			0.440237i	0.975473	+	0.220119i	$0.0706445\pi$
$743$			12.0000i			0.440237i	−0.975473	+	0.220119i	$0.929356\pi$
$744$	3.00000	−	5.19615i	0.109985	−	0.190500i
$745$	−9.00000	+	5.19615i	−0.329734	+	0.190372i
$746$	−29.4449	+	17.0000i	−1.07805	+	0.622414i
$747$	5.19615	−	9.00000i	0.190117	−	0.329293i
$748$		−	5.19615i		−	0.189990i
$749$	15.5885	−	3.00000i	0.569590	−	0.109618i
$750$			12.0000i			0.438178i
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	6.06218	+	10.5000i	0.221065	+	0.382896i
$753$	−10.5000	−	18.1865i	−0.382641	−	0.662754i
$754$	27.0000	+	15.5885i	0.983282	+	0.567698i
$755$	−58.8897			−2.14322
$756$	12.9904	+	4.50000i	0.472456	+	0.163663i
$757$	37.0000			1.34479			0.672394	−	0.740193i	$-0.265266\pi$
$757$	37.0000			1.34479			0.672394	+	0.740193i	$0.265266\pi$
$758$	17.3205	+	10.0000i	0.629109	+	0.363216i
$759$	−2.59808	−	4.50000i	−0.0943042	−	0.163340i
$760$	−9.00000	−	15.5885i	−0.326464	−	0.565453i
$761$	−3.46410	+	6.00000i	−0.125574	+	0.217500i	−0.921957	−	0.387292i	$-0.873410\pi$
$761$	−3.46410	+	6.00000i	−0.125574	+	0.217500i	0.796383	+	0.604792i	$0.206744\pi$
$762$		−	12.1244i		−	0.439219i
$763$	20.0000	+	6.92820i	0.724049	+	0.250818i
$764$		0			0
$765$	−27.0000	+	46.7654i	−0.976187	+	1.69081i
$766$	−22.5000	+	12.9904i	−0.812958	+	0.469362i
$767$	−5.19615	+	3.00000i	−0.187622	+	0.108324i
$768$	−0.866025	+	1.50000i	−0.0312500	+	0.0541266i
$769$			34.6410i			1.24919i	0.780950	+	0.624593i	$0.214735\pi$
$769$			34.6410i			1.24919i	−0.780950	+	0.624593i	$0.785265\pi$
$770$	−1.73205	−	9.00000i	−0.0624188	−	0.324337i
$771$	−6.00000			−0.216085
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	20.7846	+	36.0000i	0.747570	+	1.29483i	0.948984	+	0.315324i	$0.102113\pi$
$773$	20.7846	+	36.0000i	0.747570	+	1.29483i	−0.201414	+	0.979506i	$0.564554\pi$
$774$	−12.9904	+	7.50000i	−0.466930	+	0.269582i
$775$	21.0000	+	12.1244i	0.754342	+	0.435520i
$776$	−1.73205			−0.0621770
$777$	24.2487	−	21.0000i	0.869918	−	0.753371i
$778$	−6.00000			−0.215110
$779$	31.1769	+	18.0000i	1.11703	+	0.644917i
$780$	18.0000	−	10.3923i	0.644503	−	0.372104i
$781$	4.50000	+	7.79423i	0.161023	+	0.278899i
$782$	−7.79423	+	13.5000i	−0.278721	+	0.482759i
$783$		−	46.7654i		−	1.67126i
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		−	30.0000i		−	1.07075i
$786$	−20.7846	−	12.0000i	−0.741362	−	0.428026i
$787$	13.5000	−	7.79423i	0.481223	−	0.277834i	−0.239703	−	0.970846i	$-0.577050\pi$
$787$	13.5000	−	7.79423i	0.481223	−	0.277834i	0.720926	+	0.693012i	$0.243717\pi$
$788$	2.59808	−	1.50000i	0.0925526	−	0.0534353i
$789$	−9.00000	−	5.19615i	−0.320408	−	0.184988i
$790$		−	55.4256i		−	1.97196i
$791$	31.1769	+	36.0000i	1.10852	+	1.28001i
$792$	3.00000			0.106600
$793$	−6.00000	+	10.3923i	−0.213066	+	0.369042i
$794$	−12.9904	−	22.5000i	−0.461011	−	0.798495i
$795$		0			0
$796$	−3.00000	−	1.73205i	−0.106332	−	0.0613909i
$797$	−3.46410			−0.122705			−0.0613524	−	0.998116i	$-0.519541\pi$
$797$	−3.46410			−0.122705			−0.0613524	+	0.998116i	$0.519541\pi$
$798$	−4.50000	−	23.3827i	−0.159298	−	0.827738i
$799$	−63.0000			−2.22878
$800$	−6.06218	−	3.50000i	−0.214330	−	0.123744i
$801$	−5.19615	−	9.00000i	−0.183597	−	0.317999i
$802$		0			0
$803$	6.92820	−	12.0000i	0.244491	−	0.423471i
$804$	−13.8564			−0.488678
$805$	−9.00000	+	25.9808i	−0.317208	+	0.915702i
$806$		−	12.0000i		−	0.422682i
$807$	−12.0000	+	20.7846i	−0.422420	+	0.731653i
$808$	−10.5000	+	6.06218i	−0.369389	+	0.213267i
$809$	−15.5885	+	9.00000i	−0.548061	+	0.316423i	−0.748340	−	0.663316i	$-0.769149\pi$
$809$	−15.5885	+	9.00000i	−0.548061	+	0.316423i	0.200279	+	0.979739i	$0.435815\pi$
$810$	−27.0000	−	15.5885i	−0.948683	−	0.547723i
$811$		−	17.3205i		−	0.608205i	−0.952639	−	0.304103i	$-0.901643\pi$
$811$		−	17.3205i		−	0.608205i	0.952639	−	0.304103i	$-0.0983566\pi$
$812$	7.79423	−	22.5000i	0.273524	−	0.789595i
$813$		−	18.0000i		−	0.631288i
$814$	3.50000	−	6.06218i	0.122675	−	0.212479i
$815$	−3.46410	−	6.00000i	−0.121342	−	0.210171i
$816$	−4.50000	−	7.79423i	−0.157532	−	0.272853i
$817$	22.5000	+	12.9904i	0.787175	+	0.454476i
$818$	13.8564			0.484478
$819$	27.0000	−	5.19615i	0.943456	−	0.181568i
$820$	24.0000			0.838116
$821$	15.5885	+	9.00000i	0.544041	+	0.314102i	0.746715	−	0.665144i	$-0.231630\pi$
$821$	15.5885	+	9.00000i	0.544041	+	0.314102i	−0.202674	+	0.979246i	$0.564963\pi$
$822$	15.5885	+	27.0000i	0.543710	+	0.941733i
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	5.19615	−	9.00000i	0.181017	−	0.313530i
$825$			12.1244i			0.422116i
$826$	3.00000	+	3.46410i	0.104383	+	0.120532i
$827$		−	54.0000i		−	1.87776i	−0.344239	−	0.938882i	$-0.611863\pi$
$827$		−	54.0000i		−	1.87776i	0.344239	−	0.938882i	$-0.388137\pi$
$828$	−7.79423	−	4.50000i	−0.270868	−	0.156386i
$829$	4.50000	−	2.59808i	0.156291	−	0.0902349i	−0.419815	−	0.907610i	$-0.637905\pi$
$829$	4.50000	−	2.59808i	0.156291	−	0.0902349i	0.576106	+	0.817375i	$0.304572\pi$
$830$	−10.3923	+	6.00000i	−0.360722	+	0.208263i
$831$	−6.92820	+	12.0000i	−0.240337	+	0.416275i
$832$			3.46410i			0.120096i
$833$	−33.7750	+	13.5000i	−1.17023	+	0.467747i
$834$	−15.0000			−0.519408
$835$	18.0000	−	31.1769i	0.622916	−	1.07892i
$836$	−2.59808	−	4.50000i	−0.0898563	−	0.155636i
$837$	−15.5885	+	9.00000i	−0.538816	+	0.311086i
$838$	−25.5000	−	14.7224i	−0.880883	−	0.508578i
$839$	−10.3923			−0.358782			−0.179391	−	0.983778i	$-0.557413\pi$
$839$	−10.3923			−0.358782			−0.179391	+	0.983778i	$0.557413\pi$
$840$	−10.3923	−	12.0000i	−0.358569	−	0.414039i
$841$	−52.0000			−1.79310
$842$	16.4545	+	9.50000i	0.567059	+	0.327392i
$843$	31.5000	−	18.1865i	1.08492	−	0.626377i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−1.73205	+	3.00000i	−0.0595844	+	0.103203i
$846$		−	36.3731i		−	1.25053i
$847$	−0.500000	−	2.59808i	−0.0171802	−	0.0892710i
$848$		0			0
$849$	−15.5885	−	9.00000i	−0.534994	−	0.308879i
$850$	31.5000	−	18.1865i	1.08044	−	0.623793i
$851$	−18.1865	+	10.5000i	−0.623426	+	0.359935i
$852$	13.5000	+	7.79423i	0.462502	+	0.267026i
$853$		−	45.0333i		−	1.54191i	−0.636889	−	0.770956i	$-0.719779\pi$
$853$		−	45.0333i		−	1.54191i	0.636889	−	0.770956i	$-0.280221\pi$
$854$	8.66025	+	3.00000i	0.296348	+	0.102658i
$855$			54.0000i			1.84676i
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	11.2583	+	19.5000i	0.384577	+	0.666107i	0.991710	−	0.128493i	$-0.0410139\pi$
$857$	11.2583	+	19.5000i	0.384577	+	0.666107i	−0.607133	+	0.794600i	$0.707681\pi$
$858$	5.19615	−	3.00000i	0.177394	−	0.102418i
$859$	3.00000	+	1.73205i	0.102359	+	0.0590968i	0.550305	−	0.834963i	$-0.314511\pi$
$859$	3.00000	+	1.73205i	0.102359	+	0.0590968i	−0.447947	+	0.894060i	$0.647845\pi$
$860$	17.3205			0.590624
$861$	30.0000	+	10.3923i	1.02240	+	0.354169i
$862$	−12.0000			−0.408722
$863$	−31.1769	−	18.0000i	−1.06127	−	0.612727i	−0.135490	−	0.990779i	$-0.543261\pi$
$863$	−31.1769	−	18.0000i	−1.06127	−	0.612727i	−0.925785	+	0.378052i	$0.876594\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	−12.0000	−	20.7846i	−0.408012	−	0.706698i
$866$	−11.2583	+	19.5000i	−0.382574	+	0.662637i
$867$	17.3205			0.588235
$868$	−9.00000	+	1.73205i	−0.305480	+	0.0587896i
$869$		−	16.0000i		−	0.542763i
$870$	−27.0000	+	46.7654i	−0.915386	+	1.58549i
$871$	−24.0000	+	13.8564i	−0.813209	+	0.469506i
$872$	6.92820	−	4.00000i	0.234619	−	0.135457i
$873$	4.50000	+	2.59808i	0.152302	+	0.0879316i
$874$			15.5885i			0.527287i
$875$	13.8564	−	12.0000i	0.468432	−	0.405674i
$876$		−	24.0000i		−	0.810885i
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	4.33013	+	7.50000i	0.146135	+	0.253113i
$879$	25.5000	+	44.1673i	0.860094	+	1.48973i
$880$	−3.00000	−	1.73205i	−0.101130	−	0.0583874i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−7.79423	−	19.5000i	−0.262445	−	0.656599i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	−15.5885	−	9.00000i	−0.524297	−	0.302703i
$885$	−5.19615	−	9.00000i	−0.174667	−	0.302532i
$886$	−7.50000	−	12.9904i	−0.251967	−	0.436420i
$887$	10.3923	−	18.0000i	0.348939	−	0.604381i	−0.637122	−	0.770763i	$-0.719875\pi$
$887$	10.3923	−	18.0000i	0.348939	−	0.604381i	0.986061	+	0.166382i	$0.0532086\pi$
$888$		−	12.1244i		−	0.406867i
$889$	−14.0000	+	12.1244i	−0.469545	+	0.406638i
$890$			12.0000i			0.402241i
$891$	−7.79423	−	4.50000i	−0.261116	−	0.150756i
$892$	3.00000	−	1.73205i	0.100447	−	0.0579934i
$893$	−54.5596	+	31.5000i	−1.82577	+	1.05411i
$894$	−2.59808	+	4.50000i	−0.0868927	+	0.150503i
$895$			51.9615i			1.73688i
$896$	2.59808	−	0.500000i	0.0867956	−	0.0167038i
$897$	−18.0000			−0.601003
$898$	−18.0000	+	31.1769i	−0.600668	+	1.04039i
$899$	15.5885	+	27.0000i	0.519904	+	0.900500i
$900$	10.5000	+	18.1865i	0.350000	+	0.606218i
$901$		0			0
$902$	6.92820			0.230684
$903$	21.6506	+	7.50000i	0.720488	+	0.249584i
$904$	18.0000			0.598671
$905$	41.5692	+	24.0000i	1.38181	+	0.797787i
$906$	−25.5000	+	14.7224i	−0.847181	+	0.489120i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	−8.66025	+	15.0000i	−0.287401	+	0.497792i
$909$	36.3731			1.20642
$910$	−30.0000	−	10.3923i	−0.994490	−	0.344502i
$911$			15.0000i			0.496972i	0.968635	+	0.248486i	$0.0799330\pi$
$911$			15.0000i			0.496972i	−0.968635	+	0.248486i	$0.920067\pi$
$912$	−7.79423	−	4.50000i	−0.258093	−	0.149010i
$913$	−3.00000	+	1.73205i	−0.0992855	+	0.0573225i
$914$	−6.92820	+	4.00000i	−0.229165	+	0.132308i
$915$	−18.0000	−	10.3923i	−0.595062	−	0.343559i
$916$		−	13.8564i		−	0.457829i
$917$	6.92820	+	36.0000i	0.228789	+	1.18882i
$918$			27.0000i			0.891133i
$919$	−24.5000	+	42.4352i	−0.808180	+	1.39981i	0.105942	+	0.994372i	$0.466214\pi$
$919$	−24.5000	+	42.4352i	−0.808180	+	1.39981i	−0.914123	+	0.405437i	$0.867119\pi$
$920$	5.19615	+	9.00000i	0.171312	+	0.296721i
$921$	25.9808	−	15.0000i	0.856095	−	0.494267i
$922$	13.5000	+	7.79423i	0.444599	+	0.256689i
$923$	31.1769			1.02620
$924$	−3.00000	−	3.46410i	−0.0986928	−	0.113961i
$925$	49.0000			1.61111
$926$	3.46410	+	2.00000i	0.113837	+	0.0657241i
$927$	−27.0000	+	15.5885i	−0.886796	+	0.511992i
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	−10.3923	+	18.0000i	−0.340960	+	0.590561i	−0.984611	−	0.174758i	$-0.944086\pi$
$929$	−10.3923	+	18.0000i	−0.340960	+	0.590561i	0.643651	+	0.765319i	$0.277419\pi$
$930$	20.7846			0.681554
$931$	−22.5000	+	28.5788i	−0.737408	+	0.936634i
$932$		−	9.00000i		−	0.294805i
$933$	4.50000	−	7.79423i	0.147323	−	0.255172i
$934$	22.5000	−	12.9904i	0.736222	−	0.425058i
$935$	15.5885	−	9.00000i	0.509797	−	0.294331i
$936$	5.19615	−	9.00000i	0.169842	−	0.294174i
$937$		−	10.3923i		−	0.339502i	−0.985487	−	0.169751i	$-0.945704\pi$
$937$		−	10.3923i		−	0.339502i	0.985487	−	0.169751i	$-0.0542963\pi$
$938$	13.8564	+	16.0000i	0.452428	+	0.522419i
$939$		−	21.0000i		−	0.685309i
$940$	−21.0000	+	36.3731i	−0.684944	+	1.18636i
$941$	16.4545	+	28.5000i	0.536401	+	0.929073i	0.999094	+	0.0425550i	$0.0135498\pi$
$941$	16.4545	+	28.5000i	0.536401	+	0.929073i	−0.462693	+	0.886518i	$0.653117\pi$
$942$	−7.50000	−	12.9904i	−0.244363	−	0.423249i
$943$	−18.0000	−	10.3923i	−0.586161	−	0.338420i
$944$	1.73205			0.0563735
$945$	9.00000	+	46.7654i	0.292770	+	1.52128i
$946$	5.00000			0.162564
$947$	38.9711	+	22.5000i	1.26639	+	0.731152i	0.974303	−	0.225240i	$-0.0723165\pi$
$947$	38.9711	+	22.5000i	1.26639	+	0.731152i	0.292089	+	0.956391i	$0.405650\pi$
$948$	−13.8564	−	24.0000i	−0.450035	−	0.779484i
$949$	−24.0000	−	41.5692i	−0.779073	−	1.34939i
$950$	18.1865	−	31.5000i	0.590049	−	1.02199i
$951$			31.1769i			1.01098i
$952$	−4.50000	+	12.9904i	−0.145846	+	0.421021i
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$		0			0
$955$		0			0
$956$	5.19615	−	3.00000i	0.168056	−	0.0970269i
$957$	−7.79423	+	13.5000i	−0.251952	+	0.436393i
$958$		−	3.46410i		−	0.111920i
$959$	15.5885	−	45.0000i	0.503378	−	1.45313i
$960$	−6.00000			−0.193649
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−12.1244	−	21.0000i	−0.390905	−	0.677067i
$963$	−15.5885	+	9.00000i	−0.502331	+	0.290021i
$964$	−18.0000	−	10.3923i	−0.579741	−	0.334714i
$965$	13.8564			0.446054
$966$	2.59808	+	13.5000i	0.0835917	+	0.434355i
$967$	23.0000			0.739630			0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000			0.739630			0.369815	+	0.929105i	$0.379421\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$	40.5000	−	23.3827i	1.30105	−	0.751160i
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	−15.5885	+	27.0000i	−0.500257	+	0.866471i	0.499743	+	0.866174i	$0.333428\pi$
$971$	−15.5885	+	27.0000i	−0.500257	+	0.866471i	−1.00000		0.000297246i	$0.999905\pi$
$972$	−15.5885			−0.500000
$973$	15.0000	+	17.3205i	0.480878	+	0.555270i
$974$		−	38.0000i		−	1.21760i
$975$	36.3731	+	21.0000i	1.16487	+	0.672538i
$976$	3.00000	−	1.73205i	0.0960277	−	0.0554416i
$977$	41.5692	−	24.0000i	1.32992	−	0.767828i	0.344631	−	0.938738i	$-0.388004\pi$
$977$	41.5692	−	24.0000i	1.32992	−	0.767828i	0.985287	+	0.170910i	$0.0546709\pi$
$978$	−3.00000	−	1.73205i	−0.0959294	−	0.0553849i
$979$			3.46410i			0.110713i
$980$	−3.46410	+	24.0000i	−0.110657	+	0.766652i
$981$	−24.0000			−0.766261
$982$	−9.00000	+	15.5885i	−0.287202	+	0.497448i
$983$	0.866025	+	1.50000i	0.0276219	+	0.0478426i	0.879506	−	0.475888i	$-0.157873\pi$
$983$	0.866025	+	1.50000i	0.0276219	+	0.0478426i	−0.851884	+	0.523731i	$0.824540\pi$
$984$	10.3923	−	6.00000i	0.331295	−	0.191273i
$985$	9.00000	+	5.19615i	0.286764	+	0.165563i
$986$	46.7654			1.48931
$987$	−42.0000	+	36.3731i	−1.33687	+	1.15777i
$988$	−18.0000			−0.572656
$989$	−12.9904	−	7.50000i	−0.413070	−	0.238486i
$990$	5.19615	+	9.00000i	0.165145	+	0.286039i
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	0.979999	−	0.199000i	$-0.0637695\pi$
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	−0.662339	+	0.749204i	$0.730436\pi$
$992$	−1.73205	+	3.00000i	−0.0549927	+	0.0952501i
$993$	38.1051			1.20923
$994$	−4.50000	−	23.3827i	−0.142731	−	0.741654i
$995$		−	12.0000i		−	0.380426i
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	−27.0000	+	15.5885i	−0.855099	+	0.493691i	−0.862368	−	0.506282i	$-0.831019\pi$
$997$	−27.0000	+	15.5885i	−0.855099	+	0.493691i	0.00726929	+	0.999974i	$0.497686\pi$
$998$	−27.7128	+	16.0000i	−0.877234	+	0.506471i
$999$	−18.1865	+	31.5000i	−0.575396	+	0.996616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.b.89.1	✓	4
3.2	odd	2	inner	462.2.k.b.89.2	yes	4
7.3	odd	6	inner	462.2.k.b.353.2	yes	4
21.17	even	6	inner	462.2.k.b.353.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.b.89.1	✓	4	1.1	even	1	trivial
462.2.k.b.89.2	yes	4	3.2	odd	2	inner
462.2.k.b.353.1	yes	4	21.17	even	6	inner
462.2.k.b.353.2	yes	4	7.3	odd	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +1.73205i q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} +1.73205i q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.866025 - 1.50000i) q^{12} -3.46410i q^{13} +(-2.59808 + 0.500000i) q^{14} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-4.50000 - 2.59808i) q^{19} -3.46410 q^{20} +(-4.33013 - 1.50000i) q^{21} -1.00000 q^{22} +(2.59808 + 1.50000i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(-1.73205 + 3.00000i) q^{26} +5.19615 q^{27} +(2.50000 + 0.866025i) q^{28} -9.00000i q^{29} +(-5.19615 - 3.00000i) q^{30} +(-3.00000 + 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} +5.19615i q^{34} +(1.73205 + 9.00000i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(2.59808 + 4.50000i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(3.00000 + 1.73205i) q^{40} -6.92820 q^{41} +(3.00000 + 3.46410i) q^{42} -5.00000 q^{43} +(0.866025 + 0.500000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(-1.50000 - 2.59808i) q^{46} +(6.06218 - 10.5000i) q^{47} +1.73205 q^{48} +(1.00000 - 6.92820i) q^{49} +7.00000i q^{50} +(-4.50000 + 7.79423i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-4.50000 - 2.59808i) q^{54} +3.46410i q^{55} +(-1.73205 - 2.00000i) q^{56} +9.00000i q^{57} +(-4.50000 + 7.79423i) q^{58} +(-0.866025 - 1.50000i) q^{59} +(3.00000 + 5.19615i) q^{60} +(-3.00000 - 1.73205i) q^{61} +3.46410 q^{62} +(1.50000 + 7.79423i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{65} +(0.866025 + 1.50000i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(2.59808 - 4.50000i) q^{68} -5.19615i q^{69} +(3.00000 - 8.66025i) q^{70} +9.00000i q^{71} +(2.59808 + 1.50000i) q^{72} +(12.0000 - 6.92820i) q^{73} +(6.06218 - 3.50000i) q^{74} +(-6.06218 + 10.5000i) q^{75} -5.19615i q^{76} +(0.866025 - 2.50000i) q^{77} +6.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-1.73205 - 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(6.00000 + 3.46410i) q^{82} -3.46410 q^{83} +(-0.866025 - 4.50000i) q^{84} +18.0000 q^{85} +(4.33013 + 2.50000i) q^{86} +(-13.5000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-1.73205 + 3.00000i) q^{89} +10.3923i q^{90} +(-6.00000 - 6.92820i) q^{91} +3.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-10.5000 + 6.06218i) q^{94} +(15.5885 - 9.00000i) q^{95} +(-1.50000 - 0.866025i) q^{96} -1.73205i q^{97} +(-4.33013 + 5.50000i) q^{98} +3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9} + 12 q^{10} + 24 q^{15} - 2 q^{16} - 18 q^{19} - 4 q^{22} - 6 q^{24} - 14 q^{25} + 10 q^{28} - 12 q^{31} - 6 q^{33} - 12 q^{36} - 14 q^{37} + 12 q^{40} + 12 q^{42} - 20 q^{43} - 6 q^{46} + 4 q^{49} - 18 q^{51} + 12 q^{52} - 18 q^{54} - 18 q^{58} + 12 q^{60} - 12 q^{61} + 6 q^{63} - 4 q^{64} - 16 q^{67} + 12 q^{70} + 48 q^{73} + 24 q^{78} + 32 q^{79} - 18 q^{81} + 24 q^{82} + 72 q^{85} - 54 q^{87} - 2 q^{88} - 24 q^{91} - 42 q^{94} - 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9 + 12 * q^10 + 24 * q^15 - 2 * q^16 - 18 * q^19 - 4 * q^22 - 6 * q^24 - 14 * q^25 + 10 * q^28 - 12 * q^31 - 6 * q^33 - 12 * q^36 - 14 * q^37 + 12 * q^40 + 12 * q^42 - 20 * q^43 - 6 * q^46 + 4 * q^49 - 18 * q^51 + 12 * q^52 - 18 * q^54 - 18 * q^58 + 12 * q^60 - 12 * q^61 + 6 * q^63 - 4 * q^64 - 16 * q^67 + 12 * q^70 + 48 * q^73 + 24 * q^78 + 32 * q^79 - 18 * q^81 + 24 * q^82 + 72 * q^85 - 54 * q^87 - 2 * q^88 - 24 * q^91 - 42 * q^94 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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