LMFDB - Embedded newform 806.2.g.c.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [806,2,Mod(373,806)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(806, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("806.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 806 = 2 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	806.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.43594240292$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{29})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 8x^{2} + 7x + 49 $ x^4 - x^3 + 8x^2 + 7x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-1.09629 - 1.89883i$ of defining polynomial
Character	$\chi$	$=$	806.373
Dual form			806.2.g.c.497.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.19258 q^{5} +(0.500000 + 0.866025i) q^{6} +(1.59629 + 2.76486i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.19258 q^{5} +(0.500000 + 0.866025i) q^{6} +(1.59629 + 2.76486i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.596291 + 1.03281i) q^{10} +(-1.09629 + 1.89883i) q^{11} -1.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} -3.19258 q^{14} +(0.596291 - 1.03281i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{18} +(-1.09629 - 1.89883i) q^{19} +(-0.596291 - 1.03281i) q^{20} +3.19258 q^{21} +(-1.09629 - 1.89883i) q^{22} +(-1.59629 + 2.76486i) q^{23} +(0.500000 - 0.866025i) q^{24} -3.57775 q^{25} +(-1.00000 - 3.46410i) q^{26} +5.00000 q^{27} +(1.59629 - 2.76486i) q^{28} +(-0.903709 + 1.56527i) q^{29} +(0.596291 + 1.03281i) q^{30} +1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.09629 + 1.89883i) q^{33} +(1.90371 + 3.29732i) q^{35} +(1.00000 - 1.73205i) q^{36} +(2.78887 - 4.83047i) q^{37} +2.19258 q^{38} +(1.00000 + 3.46410i) q^{39} +1.19258 q^{40} +(-0.307418 + 0.532463i) q^{41} +(-1.59629 + 2.76486i) q^{42} +(4.50000 + 7.79423i) q^{43} +2.19258 q^{44} +(1.19258 + 2.06561i) q^{45} +(-1.59629 - 2.76486i) q^{46} -3.38516 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.59629 + 2.76486i) q^{49} +(1.78887 - 3.09842i) q^{50} +(3.50000 + 0.866025i) q^{52} +5.19258 q^{53} +(-2.50000 + 4.33013i) q^{54} +(-1.30742 + 2.26451i) q^{55} +(1.59629 + 2.76486i) q^{56} -2.19258 q^{57} +(-0.903709 - 1.56527i) q^{58} +(5.88516 + 10.1934i) q^{59} -1.19258 q^{60} +(1.30742 + 2.26451i) q^{61} +(-0.500000 + 0.866025i) q^{62} +(-3.19258 + 5.52971i) q^{63} +1.00000 q^{64} +(-2.98146 + 3.09842i) q^{65} -2.19258 q^{66} +(2.30742 - 3.99656i) q^{67} +(1.59629 + 2.76486i) q^{69} -3.80742 q^{70} +(-6.28887 - 10.8926i) q^{71} +(1.00000 + 1.73205i) q^{72} +9.00000 q^{73} +(2.78887 + 4.83047i) q^{74} +(-1.78887 + 3.09842i) q^{75} +(-1.09629 + 1.89883i) q^{76} -7.00000 q^{77} +(-3.50000 - 0.866025i) q^{78} +5.00000 q^{79} +(-0.596291 + 1.03281i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.307418 - 0.532463i) q^{82} -3.61484 q^{83} +(-1.59629 - 2.76486i) q^{84} -9.00000 q^{86} +(0.903709 + 1.56527i) q^{87} +(-1.09629 + 1.89883i) q^{88} +(8.48146 - 14.6903i) q^{89} -2.38516 q^{90} +(-11.1740 - 2.76486i) q^{91} +3.19258 q^{92} +(0.500000 - 0.866025i) q^{93} +(1.69258 - 2.93164i) q^{94} +(-1.30742 - 2.26451i) q^{95} -1.00000 q^{96} +(-4.69258 - 8.12779i) q^{97} +(-1.59629 - 2.76486i) q^{98} -4.38516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + q^7 + 4 * q^8 + 4 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} + 3 q^{10} + q^{11} - 4 q^{12} - 10 q^{13} - 2 q^{14} - 3 q^{15} - 2 q^{16} - 8 q^{18} + q^{19} + 3 q^{20} + 2 q^{21} + q^{22} - q^{23} + 2 q^{24} + 18 q^{25} - 4 q^{26} + 20 q^{27} + q^{28} - 9 q^{29} - 3 q^{30} + 4 q^{31} - 2 q^{32} - q^{33} + 13 q^{35} + 4 q^{36} - 5 q^{37} - 2 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - q^{42} + 18 q^{43} - 2 q^{44} - 6 q^{45} - q^{46} + 8 q^{47} + 2 q^{48} - q^{49} - 9 q^{50} + 14 q^{52} + 10 q^{53} - 10 q^{54} - 16 q^{55} + q^{56} + 2 q^{57} - 9 q^{58} + 2 q^{59} + 6 q^{60} + 16 q^{61} - 2 q^{62} - 2 q^{63} + 4 q^{64} + 15 q^{65} + 2 q^{66} + 20 q^{67} + q^{69} - 26 q^{70} - 9 q^{71} + 4 q^{72} + 36 q^{73} - 5 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} - 14 q^{78} + 20 q^{79} + 3 q^{80} - 2 q^{81} - 12 q^{82} - 36 q^{83} - q^{84} - 36 q^{86} + 9 q^{87} + q^{88} + 7 q^{89} + 12 q^{90} - 7 q^{91} + 2 q^{92} + 2 q^{93} - 4 q^{94} - 16 q^{95} - 4 q^{96} - 8 q^{97} - q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + q^7 + 4 * q^8 + 4 * q^9 + 3 * q^10 + q^11 - 4 * q^12 - 10 * q^13 - 2 * q^14 - 3 * q^15 - 2 * q^16 - 8 * q^18 + q^19 + 3 * q^20 + 2 * q^21 + q^22 - q^23 + 2 * q^24 + 18 * q^25 - 4 * q^26 + 20 * q^27 + q^28 - 9 * q^29 - 3 * q^30 + 4 * q^31 - 2 * q^32 - q^33 + 13 * q^35 + 4 * q^36 - 5 * q^37 - 2 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - q^42 + 18 * q^43 - 2 * q^44 - 6 * q^45 - q^46 + 8 * q^47 + 2 * q^48 - q^49 - 9 * q^50 + 14 * q^52 + 10 * q^53 - 10 * q^54 - 16 * q^55 + q^56 + 2 * q^57 - 9 * q^58 + 2 * q^59 + 6 * q^60 + 16 * q^61 - 2 * q^62 - 2 * q^63 + 4 * q^64 + 15 * q^65 + 2 * q^66 + 20 * q^67 + q^69 - 26 * q^70 - 9 * q^71 + 4 * q^72 + 36 * q^73 - 5 * q^74 + 9 * q^75 + q^76 - 28 * q^77 - 14 * q^78 + 20 * q^79 + 3 * q^80 - 2 * q^81 - 12 * q^82 - 36 * q^83 - q^84 - 36 * q^86 + 9 * q^87 + q^88 + 7 * q^89 + 12 * q^90 - 7 * q^91 + 2 * q^92 + 2 * q^93 - 4 * q^94 - 16 * q^95 - 4 * q^96 - 8 * q^97 - q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/806\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.19258			0.533339			0.266670	−	0.963788i	$-0.414077\pi$
$5$	1.19258			0.533339			0.266670	+	0.963788i	$0.414077\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.59629	+	2.76486i	0.603341	+	1.04502i	0.992311	+	0.123767i	$0.0394977\pi$
$7$	1.59629	+	2.76486i	0.603341	+	1.04502i	−0.388970	+	0.921250i	$0.627169\pi$
$8$	1.00000			0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−0.596291	+	1.03281i	−0.188564	+	0.326602i
$11$	−1.09629	+	1.89883i	−0.330544	+	0.572519i	−0.982619	−	0.185636i	$-0.940566\pi$
$11$	−1.09629	+	1.89883i	−0.330544	+	0.572519i	0.652074	+	0.758155i	$0.273899\pi$
$12$	−1.00000			−0.288675
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−3.19258			−0.853254
$15$	0.596291	−	1.03281i	0.153962	−	0.266670i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−2.00000			−0.471405
$19$	−1.09629	−	1.89883i	−0.251506	−	0.435622i	0.712434	−	0.701739i	$-0.247593\pi$
$19$	−1.09629	−	1.89883i	−0.251506	−	0.435622i	−0.963941	+	0.266117i	$0.914259\pi$
$20$	−0.596291	−	1.03281i	−0.133335	−	0.230943i
$21$	3.19258			0.696679
$22$	−1.09629	−	1.89883i	−0.233730	−	0.404832i
$23$	−1.59629	+	2.76486i	−0.332850	+	0.576513i	−0.983069	−	0.183234i	$-0.941344\pi$
$23$	−1.59629	+	2.76486i	−0.332850	+	0.576513i	0.650220	+	0.759746i	$0.274677\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−3.57775			−0.715549
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$	5.00000			0.962250
$28$	1.59629	−	2.76486i	0.301671	−	0.522509i
$29$	−0.903709	+	1.56527i	−0.167815	+	0.290663i	−0.937651	−	0.347578i	$-0.887004\pi$
$29$	−0.903709	+	1.56527i	−0.167815	+	0.290663i	0.769837	+	0.638241i	$0.220338\pi$
$30$	0.596291	+	1.03281i	0.108867	+	0.188564i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.09629	+	1.89883i	0.190840	+	0.330544i
$34$		0			0
$35$	1.90371	+	3.29732i	0.321786	+	0.557349i
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	2.78887	−	4.83047i	0.458488	−	0.794125i	−0.540393	−	0.841413i	$-0.681725\pi$
$37$	2.78887	−	4.83047i	0.458488	−	0.794125i	0.998881	+	0.0472880i	$0.0150579\pi$
$38$	2.19258			0.355684
$39$	1.00000	+	3.46410i	0.160128	+	0.554700i
$40$	1.19258			0.188564
$41$	−0.307418	+	0.532463i	−0.0480106	+	0.0831567i	−0.889032	−	0.457845i	$-0.848621\pi$
$41$	−0.307418	+	0.532463i	−0.0480106	+	0.0831567i	0.841021	+	0.541002i	$0.181955\pi$
$42$	−1.59629	+	2.76486i	−0.246313	+	0.426627i
$43$	4.50000	+	7.79423i	0.686244	+	1.18861i	0.973044	+	0.230618i	$0.0740749\pi$
$43$	4.50000	+	7.79423i	0.686244	+	1.18861i	−0.286801	+	0.957990i	$0.592592\pi$
$44$	2.19258			0.330544
$45$	1.19258	+	2.06561i	0.177780	+	0.307923i
$46$	−1.59629	−	2.76486i	−0.235360	−	0.407656i
$47$	−3.38516			−0.493777			−0.246889	−	0.969044i	$-0.579408\pi$
$47$	−3.38516			−0.493777			−0.246889	+	0.969044i	$0.579408\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−1.59629	+	2.76486i	−0.228042	+	0.394980i
$50$	1.78887	−	3.09842i	0.252985	−	0.438183i
$51$		0			0
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	5.19258			0.713256			0.356628	−	0.934246i	$-0.383926\pi$
$53$	5.19258			0.713256			0.356628	+	0.934246i	$0.383926\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$	−1.30742	+	2.26451i	−0.176292	+	0.305347i
$56$	1.59629	+	2.76486i	0.213313	+	0.369470i
$57$	−2.19258			−0.290415
$58$	−0.903709	−	1.56527i	−0.118663	−	0.205530i
$59$	5.88516	+	10.1934i	0.766183	+	1.32707i	0.939619	+	0.342223i	$0.111180\pi$
$59$	5.88516	+	10.1934i	0.766183	+	1.32707i	−0.173436	+	0.984845i	$0.555487\pi$
$60$	−1.19258			−0.153962
$61$	1.30742	+	2.26451i	0.167398	+	0.289941i	0.937504	−	0.347974i	$-0.113130\pi$
$61$	1.30742	+	2.26451i	0.167398	+	0.289941i	−0.770106	+	0.637915i	$0.779797\pi$
$62$	−0.500000	+	0.866025i	−0.0635001	+	0.109985i
$63$	−3.19258	+	5.52971i	−0.402228	+	0.696679i
$64$	1.00000			0.125000
$65$	−2.98146	+	3.09842i	−0.369804	+	0.384312i
$66$	−2.19258			−0.269888
$67$	2.30742	−	3.99656i	0.281896	−	0.488258i	−0.689956	−	0.723852i	$-0.742370\pi$
$67$	2.30742	−	3.99656i	0.281896	−	0.488258i	0.971852	+	0.235593i	$0.0757034\pi$
$68$		0			0
$69$	1.59629	+	2.76486i	0.192171	+	0.332850i
$70$	−3.80742			−0.455073
$71$	−6.28887	−	10.8926i	−0.746352	−	1.29272i	−0.949560	−	0.313584i	$-0.898470\pi$
$71$	−6.28887	−	10.8926i	−0.746352	−	1.29272i	0.203208	−	0.979135i	$-0.434863\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$	2.78887	+	4.83047i	0.324200	+	0.561531i
$75$	−1.78887	+	3.09842i	−0.206561	+	0.357775i
$76$	−1.09629	+	1.89883i	−0.125753	+	0.217811i
$77$	−7.00000			−0.797724
$78$	−3.50000	−	0.866025i	−0.396297	−	0.0980581i
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$	−0.596291	+	1.03281i	−0.0666674	+	0.115471i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.307418	−	0.532463i	−0.0339486	−	0.0588007i
$83$	−3.61484			−0.396780			−0.198390	−	0.980123i	$-0.563571\pi$
$83$	−3.61484			−0.396780			−0.198390	+	0.980123i	$0.563571\pi$
$84$	−1.59629	−	2.76486i	−0.174170	−	0.301671i
$85$		0			0
$86$	−9.00000			−0.970495
$87$	0.903709	+	1.56527i	0.0968878	+	0.167815i
$88$	−1.09629	+	1.89883i	−0.116865	+	0.202416i
$89$	8.48146	−	14.6903i	0.899033	−	1.55717i	0.0702995	−	0.997526i	$-0.477605\pi$
$89$	8.48146	−	14.6903i	0.899033	−	1.55717i	0.828733	−	0.559644i	$-0.189062\pi$
$90$	−2.38516			−0.251418
$91$	−11.1740	−	2.76486i	−1.17136	−	0.289836i
$92$	3.19258			0.332850
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$	1.69258	−	2.93164i	0.174577	−	0.302375i
$95$	−1.30742	−	2.26451i	−0.134138	−	0.232334i
$96$	−1.00000			−0.102062
$97$	−4.69258	−	8.12779i	−0.476460	−	0.825252i	0.523177	−	0.852224i	$-0.324747\pi$
$97$	−4.69258	−	8.12779i	−0.476460	−	0.825252i	−0.999636	+	0.0269721i	$0.991413\pi$
$98$	−1.59629	−	2.76486i	−0.161250	−	0.279293i
$99$	−4.38516			−0.440726
$100$	1.78887	+	3.09842i	0.178887	+	0.309842i
$101$	−0.307418	+	0.532463i	−0.0305892	+	0.0529820i	−0.880915	−	0.473275i	$-0.843072\pi$
$101$	−0.307418	+	0.532463i	−0.0305892	+	0.0529820i	0.850326	+	0.526257i	$0.176405\pi$
$102$		0			0
$103$	16.1555			1.59185			0.795924	−	0.605396i	$-0.206985\pi$
$103$	16.1555			1.59185			0.795924	+	0.605396i	$0.206985\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$	3.80742			0.371566
$106$	−2.59629	+	4.49691i	−0.252174	+	0.436778i
$107$	−1.69258	+	2.93164i	−0.163628	+	0.283412i	−0.936167	−	0.351555i	$-0.885653\pi$
$107$	−1.69258	+	2.93164i	−0.163628	+	0.283412i	0.772539	+	0.634967i	$0.218986\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	−2.19258			−0.210011			−0.105006	−	0.994472i	$-0.533486\pi$
$109$	−2.19258			−0.210011			−0.105006	+	0.994472i	$0.533486\pi$
$110$	−1.30742	−	2.26451i	−0.124657	−	0.215913i
$111$	−2.78887	−	4.83047i	−0.264708	−	0.458488i
$112$	−3.19258			−0.301671
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	1.09629	−	1.89883i	0.102677	−	0.177842i
$115$	−1.90371	+	3.29732i	−0.177522	+	0.307477i
$116$	1.80742			0.167815
$117$	−7.00000	−	1.73205i	−0.647150	−	0.160128i
$118$	−11.7703			−1.08355
$119$		0			0
$120$	0.596291	−	1.03281i	0.0544337	−	0.0942819i
$121$	3.09629	+	5.36293i	0.281481	+	0.487539i
$122$	−2.61484			−0.236736
$123$	0.307418	+	0.532463i	0.0277189	+	0.0480106i
$124$	−0.500000	−	0.866025i	−0.0449013	−	0.0777714i
$125$	−10.2297			−0.914970
$126$	−3.19258	−	5.52971i	−0.284418	−	0.492626i
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	−0.466870	−	0.884326i	$-0.654618\pi$
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	0.999284	−	0.0378419i	$-0.0120483\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	9.00000			0.792406
$130$	−1.19258	−	4.13123i	−0.104596	−	0.362333i
$131$	−13.1926			−1.15264			−0.576321	−	0.817224i	$-0.695512\pi$
$131$	−13.1926			−1.15264			−0.576321	+	0.817224i	$0.695512\pi$
$132$	1.09629	−	1.89883i	0.0954199	−	0.165272i
$133$	3.50000	−	6.06218i	0.303488	−	0.525657i
$134$	2.30742	+	3.99656i	0.199331	+	0.345251i
$135$	5.96291			0.513206
$136$		0			0
$137$	1.88516	+	3.26520i	0.161060	+	0.278965i	0.935249	−	0.353990i	$-0.115175\pi$
$137$	1.88516	+	3.26520i	0.161060	+	0.278965i	−0.774189	+	0.632955i	$0.781842\pi$
$138$	−3.19258			−0.271771
$139$	10.7889	+	18.6869i	0.915100	+	1.58500i	0.806754	+	0.590887i	$0.201222\pi$
$139$	10.7889	+	18.6869i	0.915100	+	1.58500i	0.108346	+	0.994113i	$0.465445\pi$
$140$	1.90371	−	3.29732i	0.160893	−	0.278674i
$141$	−1.69258	+	2.93164i	−0.142541	+	0.246889i
$142$	12.5777			1.05550
$143$	−2.19258	−	7.59533i	−0.183353	−	0.635153i
$144$	−2.00000			−0.166667
$145$	−1.07775	+	1.86671i	−0.0895020	+	0.155022i
$146$	−4.50000	+	7.79423i	−0.372423	+	0.645055i
$147$	1.59629	+	2.76486i	0.131660	+	0.228042i
$148$	−5.57775			−0.458488
$149$	−9.28887	−	16.0888i	−0.760974	−	1.31805i	−0.942349	−	0.334632i	$-0.891388\pi$
$149$	−9.28887	−	16.0888i	−0.760974	−	1.31805i	0.181375	−	0.983414i	$-0.441945\pi$
$150$	−1.78887	−	3.09842i	−0.146061	−	0.252985i
$151$	9.77033			0.795098			0.397549	−	0.917581i	$-0.369861\pi$
$151$	9.77033			0.795098			0.397549	+	0.917581i	$0.369861\pi$
$152$	−1.09629	−	1.89883i	−0.0889210	−	0.154016i
$153$		0			0
$154$	3.50000	−	6.06218i	0.282038	−	0.488504i
$155$	1.19258			0.0957905
$156$	2.50000	−	2.59808i	0.200160	−	0.208013i
$157$	−5.57775			−0.445153			−0.222576	−	0.974915i	$-0.571447\pi$
$157$	−5.57775			−0.445153			−0.222576	+	0.974915i	$0.571447\pi$
$158$	−2.50000	+	4.33013i	−0.198889	+	0.344486i
$159$	2.59629	−	4.49691i	0.205899	−	0.356628i
$160$	−0.596291	−	1.03281i	−0.0471410	−	0.0816505i
$161$	−10.1926			−0.803288
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	8.90371	+	15.4217i	0.697392	+	1.20792i	0.969368	+	0.245615i	$0.0789898\pi$
$163$	8.90371	+	15.4217i	0.697392	+	1.20792i	−0.271975	+	0.962304i	$0.587677\pi$
$164$	0.614835			0.0480106
$165$	1.30742	+	2.26451i	0.101782	+	0.176292i
$166$	1.80742	−	3.13054i	0.140283	−	0.242977i
$167$	−4.19258	+	7.26177i	−0.324432	+	0.561932i	−0.981397	−	0.191988i	$-0.938506\pi$
$167$	−4.19258	+	7.26177i	−0.324432	+	0.561932i	0.656965	+	0.753921i	$0.271840\pi$
$168$	3.19258			0.246313
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	2.19258	−	3.79766i	0.167671	−	0.290415i
$172$	4.50000	−	7.79423i	0.343122	−	0.594304i
$173$	−6.57775	−	11.3930i	−0.500097	−	0.866193i	−1.00000		0.000111848i	$-0.999964\pi$
$173$	−6.57775	−	11.3930i	−0.500097	−	0.866193i	0.499903	−	0.866081i	$-0.333369\pi$
$174$	−1.80742			−0.137020
$175$	−5.71113	−	9.89196i	−0.431721	−	0.747762i
$176$	−1.09629	−	1.89883i	−0.0826361	−	0.143130i
$177$	11.7703			0.884712
$178$	8.48146	+	14.6903i	0.635712	+	1.10109i
$179$	9.57775	−	16.5891i	0.715874	−	1.23993i	−0.246747	−	0.969080i	$-0.579362\pi$
$179$	9.57775	−	16.5891i	0.715874	−	1.23993i	0.962621	−	0.270851i	$-0.0873050\pi$
$180$	1.19258	−	2.06561i	0.0888898	−	0.153962i
$181$	−0.807418			−0.0600149			−0.0300074	−	0.999550i	$-0.509553\pi$
$181$	−0.807418			−0.0600149			−0.0300074	+	0.999550i	$0.509553\pi$
$182$	7.98146	−	8.29457i	0.591625	−	0.614835i
$183$	2.61484			0.193294
$184$	−1.59629	+	2.76486i	−0.117680	+	0.203828i
$185$	3.32596	−	5.76073i	0.244530	−	0.423538i
$186$	0.500000	+	0.866025i	0.0366618	+	0.0635001i
$187$		0			0
$188$	1.69258	+	2.93164i	0.123444	+	0.213812i
$189$	7.98146	+	13.8243i	0.580565	+	1.00557i
$190$	2.61484			0.189700
$191$	1.30742	+	2.26451i	0.0946014	+	0.163854i	0.909442	−	0.415830i	$-0.136509\pi$
$191$	1.30742	+	2.26451i	0.0946014	+	0.163854i	−0.814841	+	0.579685i	$0.803176\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	5.48146	−	9.49416i	0.394564	−	0.683405i	−0.598482	−	0.801137i	$-0.704229\pi$
$193$	5.48146	−	9.49416i	0.394564	−	0.683405i	0.993045	+	0.117732i	$0.0375624\pi$
$194$	9.38516			0.673816
$195$	1.19258	+	4.13123i	0.0854026	+	0.295843i
$196$	3.19258			0.228042
$197$	11.8852	−	20.5857i	0.846783	−	1.46667i	−0.0372809	−	0.999305i	$-0.511870\pi$
$197$	11.8852	−	20.5857i	0.846783	−	1.46667i	0.884064	−	0.467366i	$-0.154797\pi$
$198$	2.19258	−	3.79766i	0.155820	−	0.269888i
$199$	0.0962912	+	0.166781i	0.00682590	+	0.0118228i	0.869418	−	0.494077i	$-0.164494\pi$
$199$	0.0962912	+	0.166781i	0.00682590	+	0.0118228i	−0.862592	+	0.505900i	$0.831161\pi$
$200$	−3.57775			−0.252985
$201$	−2.30742	−	3.99656i	−0.162753	−	0.281896i
$202$	−0.307418	−	0.532463i	−0.0216298	−	0.0374640i
$203$	−5.77033			−0.404998
$204$		0			0
$205$	−0.366621	+	0.635006i	−0.0256059	+	0.0443507i
$206$	−8.07775	+	13.9911i	−0.562803	+	0.974804i
$207$	−6.38516			−0.443800
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	4.80742			0.332536
$210$	−1.90371	+	3.29732i	−0.131368	+	0.227537i
$211$	1.78887	−	3.09842i	0.123151	−	0.213304i	−0.797858	−	0.602846i	$-0.794033\pi$
$211$	1.78887	−	3.09842i	0.123151	−	0.213304i	0.921009	+	0.389542i	$0.127367\pi$
$212$	−2.59629	−	4.49691i	−0.178314	−	0.308849i
$213$	−12.5777			−0.861813
$214$	−1.69258	−	2.93164i	−0.115703	−	0.200403i
$215$	5.36662	+	9.29526i	0.366001	+	0.633931i
$216$	5.00000			0.340207
$217$	1.59629	+	2.76486i	0.108363	+	0.187691i
$218$	1.09629	−	1.89883i	0.0742502	−	0.128605i
$219$	4.50000	−	7.79423i	0.304082	−	0.526685i
$220$	2.61484			0.176292
$221$		0			0
$222$	5.57775			0.374354
$223$	3.78887	−	6.56252i	0.253722	−	0.439459i	−0.710826	−	0.703368i	$-0.751679\pi$
$223$	3.78887	−	6.56252i	0.253722	−	0.439459i	0.964548	+	0.263909i	$0.0850119\pi$
$224$	1.59629	−	2.76486i	0.106657	−	0.184735i
$225$	−3.57775	−	6.19684i	−0.238516	−	0.413123i
$226$	6.00000			0.399114
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	1.09629	+	1.89883i	0.0726037	+	0.125753i
$229$	3.38516			0.223698			0.111849	−	0.993725i	$-0.464323\pi$
$229$	3.38516			0.223698			0.111849	+	0.993725i	$0.464323\pi$
$230$	−1.90371	−	3.29732i	−0.125527	−	0.217419i
$231$	−3.50000	+	6.06218i	−0.230283	+	0.398862i
$232$	−0.903709	+	1.56527i	−0.0593314	+	0.102765i
$233$	−13.3852			−0.876891			−0.438446	−	0.898758i	$-0.644471\pi$
$233$	−13.3852			−0.876891			−0.438446	+	0.898758i	$0.644471\pi$
$234$	5.00000	−	5.19615i	0.326860	−	0.339683i
$235$	−4.03709			−0.263351
$236$	5.88516	−	10.1934i	0.383092	−	0.663534i
$237$	2.50000	−	4.33013i	0.162392	−	0.281272i
$238$		0			0
$239$	−21.9629			−1.42066			−0.710331	−	0.703867i	$-0.751455\pi$
$239$	−21.9629			−1.42066			−0.710331	+	0.703867i	$0.751455\pi$
$240$	0.596291	+	1.03281i	0.0384904	+	0.0666674i
$241$	−8.77033	−	15.1907i	−0.564947	−	0.978516i	−0.997055	−	0.0766944i	$-0.975563\pi$
$241$	−8.77033	−	15.1907i	−0.564947	−	0.978516i	0.432108	−	0.901822i	$-0.357770\pi$
$242$	−6.19258			−0.398074
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	1.30742	−	2.26451i	0.0836988	−	0.144971i
$245$	−1.90371	+	3.29732i	−0.121623	+	0.210658i
$246$	−0.614835			−0.0392005
$247$	7.67404	+	1.89883i	0.488287	+	0.120820i
$248$	1.00000			0.0635001
$249$	−1.80742	+	3.13054i	−0.114540	+	0.198390i
$250$	5.11484	−	8.85915i	0.323491	−	0.560302i
$251$	5.38516	+	9.32738i	0.339909	+	0.588739i	0.984415	−	0.175860i	$-0.0562705\pi$
$251$	5.38516	+	9.32738i	0.339909	+	0.588739i	−0.644507	+	0.764599i	$0.722937\pi$
$252$	6.38516			0.402228
$253$	−3.50000	−	6.06218i	−0.220043	−	0.381126i
$254$	6.00000	+	10.3923i	0.376473	+	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.09629	−	15.7552i	0.567411	−	0.982785i	−0.429410	−	0.903110i	$-0.641278\pi$
$257$	9.09629	−	15.7552i	0.567411	−	0.982785i	0.996821	−	0.0796750i	$-0.0253883\pi$
$258$	−4.50000	+	7.79423i	−0.280158	+	0.485247i
$259$	17.8074			1.10650
$260$	4.17404	+	1.03281i	0.258863	+	0.0640519i
$261$	−3.61484			−0.223753
$262$	6.59629	−	11.4251i	0.407520	−	0.705846i
$263$	−4.48146	+	7.76211i	−0.276338	+	0.478632i	−0.970472	−	0.241214i	$-0.922454\pi$
$263$	−4.48146	+	7.76211i	−0.276338	+	0.478632i	0.694134	+	0.719846i	$0.255788\pi$
$264$	1.09629	+	1.89883i	0.0674721	+	0.116865i
$265$	6.19258			0.380407
$266$	3.50000	+	6.06218i	0.214599	+	0.371696i
$267$	−8.48146	−	14.6903i	−0.519057	−	0.899033i
$268$	−4.61484			−0.281896
$269$	3.59629	+	6.22896i	0.219270	+	0.379786i	0.954585	−	0.297939i	$-0.0962992\pi$
$269$	3.59629	+	6.22896i	0.219270	+	0.379786i	−0.735315	+	0.677725i	$0.762966\pi$
$270$	−2.98146	+	5.16403i	−0.181446	+	0.314273i
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	−0.798865	−	0.601511i	$-0.794566\pi$
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	0.920356	+	0.391082i	$0.127899\pi$
$272$		0			0
$273$	−7.98146	+	8.29457i	−0.483060	+	0.502010i
$274$	−3.77033			−0.227774
$275$	3.92225	−	6.79354i	0.236521	−	0.409666i
$276$	1.59629	−	2.76486i	0.0960854	−	0.166425i
$277$	2.28887	+	3.96445i	0.137525	+	0.238200i	0.926559	−	0.376149i	$-0.122752\pi$
$277$	2.28887	+	3.96445i	0.137525	+	0.238200i	−0.789034	+	0.614349i	$0.789419\pi$
$278$	−21.5777			−1.29415
$279$	1.00000	+	1.73205i	0.0598684	+	0.103695i
$280$	1.90371	+	3.29732i	0.113768	+	0.197053i
$281$	−19.7703			−1.17940			−0.589699	−	0.807623i	$-0.700754\pi$
$281$	−19.7703			−1.17940			−0.589699	+	0.807623i	$0.700754\pi$
$282$	−1.69258	−	2.93164i	−0.100792	−	0.174577i
$283$	0.981456	−	1.69993i	0.0583415	−	0.101050i	−0.835380	−	0.549674i	$-0.814752\pi$
$283$	0.981456	−	1.69993i	0.0583415	−	0.101050i	0.893721	+	0.448623i	$0.148085\pi$
$284$	−6.28887	+	10.8926i	−0.373176	+	0.646360i
$285$	−2.61484			−0.154889
$286$	7.67404	+	1.89883i	0.453775	+	0.112280i
$287$	−1.96291			−0.115867
$288$	1.00000	−	1.73205i	0.0589256	−	0.102062i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−1.07775	−	1.86671i	−0.0632875	−	0.109617i
$291$	−9.38516			−0.550168
$292$	−4.50000	−	7.79423i	−0.263343	−	0.456123i
$293$	7.59629	+	13.1572i	0.443780	+	0.768650i	0.997966	−	0.0637431i	$-0.0203038\pi$
$293$	7.59629	+	13.1572i	0.443780	+	0.768650i	−0.554186	+	0.832393i	$0.686970\pi$
$294$	−3.19258			−0.186195
$295$	7.01854	+	12.1565i	0.408635	+	0.707777i
$296$	2.78887	−	4.83047i	0.162100	−	0.280765i
$297$	−5.48146	+	9.49416i	−0.318066	+	0.550907i
$298$	18.5777			1.07618
$299$	−3.19258	−	11.0594i	−0.184632	−	0.639583i
$300$	3.57775			0.206561
$301$	−14.3666	+	24.8837i	−0.828078	+	1.43427i
$302$	−4.88516	+	8.46135i	−0.281110	+	0.486896i
$303$	0.307418	+	0.532463i	0.0176607	+	0.0305892i
$304$	2.19258			0.125753
$305$	1.55920	+	2.70062i	0.0892797	+	0.154637i
$306$		0			0
$307$	−15.0000			−0.856095			−0.428048	−	0.903756i	$-0.640798\pi$
$307$	−15.0000			−0.856095			−0.428048	+	0.903756i	$0.640798\pi$
$308$	3.50000	+	6.06218i	0.199431	+	0.345425i
$309$	8.07775	−	13.9911i	0.459527	−	0.795924i
$310$	−0.596291	+	1.03281i	−0.0338671	+	0.0586595i
$311$	−22.1555			−1.25632			−0.628161	−	0.778083i	$-0.716192\pi$
$311$	−22.1555			−1.25632			−0.628161	+	0.778083i	$0.716192\pi$
$312$	1.00000	+	3.46410i	0.0566139	+	0.196116i
$313$	−12.5777			−0.710936			−0.355468	−	0.934688i	$-0.615679\pi$
$313$	−12.5777			−0.710936			−0.355468	+	0.934688i	$0.615679\pi$
$314$	2.78887	−	4.83047i	0.157385	−	0.272599i
$315$	−3.80742	+	6.59464i	−0.214524	+	0.371566i
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	−13.5407			−0.760519			−0.380260	−	0.924880i	$-0.624165\pi$
$317$	−13.5407			−0.760519			−0.380260	+	0.924880i	$0.624165\pi$
$318$	2.59629	+	4.49691i	0.145593	+	0.252174i
$319$	−1.98146	−	3.43198i	−0.110940	−	0.192154i
$320$	1.19258			0.0666674
$321$	1.69258	+	2.93164i	0.0944707	+	0.163628i
$322$	5.09629	−	8.82704i	0.284005	−	0.491911i
$323$		0			0
$324$	1.00000			0.0555556
$325$	8.94437	−	9.29526i	0.496144	−	0.515608i
$326$	−17.8074			−0.986262
$327$	−1.09629	+	1.89883i	−0.0606250	+	0.105006i
$328$	−0.307418	+	0.532463i	−0.0169743	+	0.0294003i
$329$	−5.40371	−	9.35950i	−0.297916	−	0.516006i
$330$	−2.61484			−0.143942
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	0.926516	−	0.376254i	$-0.122788\pi$
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	−0.789104	+	0.614260i	$0.789455\pi$
$332$	1.80742	+	3.13054i	0.0991949	+	0.171811i
$333$	11.1555			0.611317
$334$	−4.19258	−	7.26177i	−0.229408	−	0.397346i
$335$	2.75179	−	4.76623i	0.150346	−	0.260407i
$336$	−1.59629	+	2.76486i	−0.0870848	+	0.150835i
$337$	14.1555			0.771099			0.385549	−	0.922687i	$-0.374012\pi$
$337$	14.1555			0.771099			0.385549	+	0.922687i	$0.374012\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	−6.00000			−0.325875
$340$		0			0
$341$	−1.09629	+	1.89883i	−0.0593675	+	0.102828i
$342$	2.19258	+	3.79766i	0.118561	+	0.205354i
$343$	12.1555			0.656335
$344$	4.50000	+	7.79423i	0.242624	+	0.420237i
$345$	1.90371	+	3.29732i	0.102492	+	0.177522i
$346$	13.1555			0.707244
$347$	7.21113	+	12.4900i	0.387114	+	0.670500i	0.992060	−	0.125766i	$-0.0401388\pi$
$347$	7.21113	+	12.4900i	0.387114	+	0.670500i	−0.604946	+	0.796266i	$0.706805\pi$
$348$	0.903709	−	1.56527i	0.0484439	−	0.0839073i
$349$	−8.19258	+	14.1900i	−0.438539	+	0.759572i	−0.997577	−	0.0695703i	$-0.977837\pi$
$349$	−8.19258	+	14.1900i	−0.438539	+	0.759572i	0.559038	+	0.829142i	$0.311171\pi$
$350$	11.4223			0.610545
$351$	−12.5000	+	12.9904i	−0.667201	+	0.693375i
$352$	2.19258			0.116865
$353$	4.78887	−	8.29457i	0.254886	−	0.441476i	−0.709979	−	0.704223i	$-0.751295\pi$
$353$	4.78887	−	8.29457i	0.254886	−	0.441476i	0.964865	+	0.262748i	$0.0846287\pi$
$354$	−5.88516	+	10.1934i	−0.312793	+	0.541773i
$355$	−7.50000	−	12.9904i	−0.398059	−	0.689458i
$356$	−16.9629			−0.899033
$357$		0			0
$358$	9.57775	+	16.5891i	0.506200	+	0.876764i
$359$	−21.7703			−1.14899			−0.574497	−	0.818507i	$-0.694802\pi$
$359$	−21.7703			−1.14899			−0.574497	+	0.818507i	$0.694802\pi$
$360$	1.19258	+	2.06561i	0.0628546	+	0.108867i
$361$	7.09629	−	12.2911i	0.373489	−	0.646902i
$362$	0.403709	−	0.699244i	0.0212185	−	0.0367515i
$363$	6.19258			0.325026
$364$	3.19258	+	11.0594i	0.167337	+	0.579672i
$365$	10.7332			0.561804
$366$	−1.30742	+	2.26451i	−0.0683398	+	0.118368i
$367$	9.07775	−	15.7231i	0.473855	−	0.820740i	−0.525697	−	0.850672i	$-0.676196\pi$
$367$	9.07775	−	15.7231i	0.473855	−	0.820740i	0.999552	+	0.0299315i	$0.00952891\pi$
$368$	−1.59629	−	2.76486i	−0.0832124	−	0.144128i
$369$	−1.22967			−0.0640141
$370$	3.32596	+	5.76073i	0.172909	+	0.299486i
$371$	8.28887	+	14.3568i	0.430337	+	0.745365i
$372$	−1.00000			−0.0518476
$373$	−6.57775	−	11.3930i	−0.340583	−	0.589907i	0.643958	−	0.765061i	$-0.277291\pi$
$373$	−6.57775	−	11.3930i	−0.340583	−	0.589907i	−0.984541	+	0.175154i	$0.943958\pi$
$374$		0			0
$375$	−5.11484	+	8.85915i	−0.264129	+	0.457485i
$376$	−3.38516			−0.174577
$377$	−1.80742	−	6.26108i	−0.0930867	−	0.322462i
$378$	−15.9629			−0.821044
$379$	−18.8666	+	32.6779i	−0.969113	+	1.67855i	−0.270981	+	0.962585i	$0.587348\pi$
$379$	−18.8666	+	32.6779i	−0.969113	+	1.67855i	−0.698133	+	0.715969i	$0.745985\pi$
$380$	−1.30742	+	2.26451i	−0.0670691	+	0.116167i
$381$	−6.00000	−	10.3923i	−0.307389	−	0.532414i
$382$	−2.61484			−0.133787
$383$	−2.11484	−	3.66300i	−0.108063	−	0.187171i	0.806922	−	0.590657i	$-0.201131\pi$
$383$	−2.11484	−	3.66300i	−0.108063	−	0.187171i	−0.914986	+	0.403487i	$0.867798\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−8.34808			−0.425457
$386$	5.48146	+	9.49416i	0.278999	+	0.483240i
$387$	−9.00000	+	15.5885i	−0.457496	+	0.792406i
$388$	−4.69258	+	8.12779i	−0.238230	+	0.412626i
$389$	11.1926			0.567486			0.283743	−	0.958900i	$-0.408424\pi$
$389$	11.1926			0.567486			0.283743	+	0.958900i	$0.408424\pi$
$390$	−4.17404	−	1.03281i	−0.211361	−	0.0522982i
$391$		0			0
$392$	−1.59629	+	2.76486i	−0.0806249	+	0.139646i
$393$	−6.59629	+	11.4251i	−0.332739	+	0.576321i
$394$	11.8852	+	20.5857i	0.598766	+	1.03709i
$395$	5.96291			0.300027
$396$	2.19258	+	3.79766i	0.110181	+	0.190840i
$397$	−6.80742	−	11.7908i	−0.341654	−	0.591763i	0.643086	−	0.765794i	$-0.277654\pi$
$397$	−6.80742	−	11.7908i	−0.341654	−	0.591763i	−0.984740	+	0.174031i	$0.944321\pi$
$398$	−0.192582			−0.00965328
$399$	−3.50000	−	6.06218i	−0.175219	−	0.303488i
$400$	1.78887	−	3.09842i	0.0894437	−	0.154921i
$401$	−9.30742	+	16.1209i	−0.464790	+	0.805040i	−0.999192	−	0.0401902i	$-0.987204\pi$
$401$	−9.30742	+	16.1209i	−0.464790	+	0.805040i	0.534402	+	0.845231i	$0.320537\pi$
$402$	4.61484			0.230167
$403$	−2.50000	+	2.59808i	−0.124534	+	0.129419i
$404$	0.614835			0.0305892
$405$	−0.596291	+	1.03281i	−0.0296299	+	0.0513206i
$406$	2.88516	−	4.99725i	0.143188	−	0.248009i
$407$	6.11484	+	10.5912i	0.303101	+	0.524987i
$408$		0			0
$409$	17.2889	+	29.9452i	0.854880	+	1.48070i	0.876757	+	0.480935i	$0.159703\pi$
$409$	17.2889	+	29.9452i	0.854880	+	1.48070i	−0.0218767	+	0.999761i	$0.506964\pi$
$410$	−0.366621	−	0.635006i	−0.0181061	−	0.0313607i
$411$	3.77033			0.185977
$412$	−8.07775	−	13.9911i	−0.397962	−	0.689290i
$413$	−18.7889	+	32.5433i	−0.924540	+	1.60135i
$414$	3.19258	−	5.52971i	0.156907	−	0.271771i
$415$	−4.31099			−0.211618
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$	21.5777			1.05667
$418$	−2.40371	+	4.16335i	−0.117569	+	0.203636i
$419$	−7.09629	+	12.2911i	−0.346677	+	0.600461i	−0.985657	−	0.168762i	$-0.946023\pi$
$419$	−7.09629	+	12.2911i	−0.346677	+	0.600461i	0.638980	+	0.769223i	$0.279356\pi$
$420$	−1.90371	−	3.29732i	−0.0928915	−	0.160893i
$421$	−19.3852			−0.944775			−0.472388	−	0.881391i	$-0.656608\pi$
$421$	−19.3852			−0.944775			−0.472388	+	0.881391i	$0.656608\pi$
$422$	1.78887	+	3.09842i	0.0870810	+	0.150829i
$423$	−3.38516	−	5.86328i	−0.164592	−	0.285082i
$424$	5.19258			0.252174
$425$		0			0
$426$	6.28887	−	10.8926i	0.304697	−	0.527751i
$427$	−4.17404	+	7.22965i	−0.201996	+	0.349867i
$428$	3.38516			0.163628
$429$	−7.67404	−	1.89883i	−0.370506	−	0.0916765i
$430$	−10.7332			−0.517603
$431$	−2.30742	+	3.99656i	−0.111144	+	0.192508i	−0.916232	−	0.400648i	$-0.868785\pi$
$431$	−2.30742	+	3.99656i	−0.111144	+	0.192508i	0.805088	+	0.593156i	$0.202118\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	−8.78887	−	15.2228i	−0.422366	−	0.731560i	0.573804	−	0.818993i	$-0.305467\pi$
$433$	−8.78887	−	15.2228i	−0.422366	−	0.731560i	−0.996170	+	0.0874327i	$0.972134\pi$
$434$	−3.19258			−0.153249
$435$	1.07775	+	1.86671i	0.0516740	+	0.0895020i
$436$	1.09629	+	1.89883i	0.0525028	+	0.0909376i
$437$	7.00000			0.334855
$438$	4.50000	+	7.79423i	0.215018	+	0.372423i
$439$	−3.50000	+	6.06218i	−0.167046	+	0.289332i	−0.937380	−	0.348309i	$-0.886756\pi$
$439$	−3.50000	+	6.06218i	−0.167046	+	0.289332i	0.770334	+	0.637641i	$0.220089\pi$
$440$	−1.30742	+	2.26451i	−0.0623287	+	0.107956i
$441$	−6.38516			−0.304055
$442$		0			0
$443$	13.5407			0.643336			0.321668	−	0.946852i	$-0.395756\pi$
$443$	13.5407			0.643336			0.321668	+	0.946852i	$0.395756\pi$
$444$	−2.78887	+	4.83047i	−0.132354	+	0.229244i
$445$	10.1148	−	17.5194i	0.479489	−	0.830500i
$446$	3.78887	+	6.56252i	0.179408	+	0.310744i
$447$	−18.5777			−0.878697
$448$	1.59629	+	2.76486i	0.0754177	+	0.130627i
$449$	2.51854	+	4.36225i	0.118857	+	0.205867i	0.919315	−	0.393522i	$-0.128744\pi$
$449$	2.51854	+	4.36225i	0.118857	+	0.205867i	−0.800458	+	0.599389i	$0.795410\pi$
$450$	7.15549			0.337313
$451$	−0.674038	−	1.16747i	−0.0317392	−	0.0549740i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	4.88516	−	8.46135i	0.229525	−	0.397549i
$454$	−3.00000			−0.140797
$455$	−13.3260	−	3.29732i	−0.624731	−	0.154581i
$456$	−2.19258			−0.102677
$457$	13.2889	−	23.0170i	0.621627	−	1.07669i	−0.367555	−	0.930002i	$-0.619805\pi$
$457$	13.2889	−	23.0170i	0.621627	−	1.07669i	0.989183	−	0.146688i	$-0.0468615\pi$
$458$	−1.69258	+	2.93164i	−0.0790892	+	0.136986i
$459$		0			0
$460$	3.80742			0.177522
$461$	−1.59629	−	2.76486i	−0.0743467	−	0.128772i	0.826455	−	0.563002i	$-0.190354\pi$
$461$	−1.59629	−	2.76486i	−0.0743467	−	0.128772i	−0.900802	+	0.434230i	$0.857020\pi$
$462$	−3.50000	−	6.06218i	−0.162835	−	0.282038i
$463$	−20.7332			−0.963555			−0.481778	−	0.876293i	$-0.660009\pi$
$463$	−20.7332			−0.963555			−0.481778	+	0.876293i	$0.660009\pi$
$464$	−0.903709	−	1.56527i	−0.0419536	−	0.0726658i
$465$	0.596291	−	1.03281i	0.0276523	−	0.0478953i
$466$	6.69258	−	11.5919i	0.310028	−	0.536984i
$467$	−8.61484			−0.398647			−0.199324	−	0.979934i	$-0.563874\pi$
$467$	−8.61484			−0.398647			−0.199324	+	0.979934i	$0.563874\pi$
$468$	2.00000	+	6.92820i	0.0924500	+	0.320256i
$469$	14.7332			0.680318
$470$	2.01854	−	3.49622i	0.0931085	−	0.161269i
$471$	−2.78887	+	4.83047i	−0.128505	+	0.222576i
$472$	5.88516	+	10.1934i	0.270887	+	0.469189i
$473$	−19.7332			−0.907335
$474$	2.50000	+	4.33013i	0.114829	+	0.198889i
$475$	3.92225	+	6.79354i	0.179965	+	0.311709i
$476$		0			0
$477$	5.19258	+	8.99382i	0.237752	+	0.411799i
$478$	10.9815	−	19.0204i	0.502280	−	0.869975i
$479$	−4.77033	+	8.26245i	−0.217962	+	0.377521i	−0.954185	−	0.299218i	$-0.903274\pi$
$479$	−4.77033	+	8.26245i	−0.217962	+	0.377521i	0.736223	+	0.676739i	$0.236608\pi$
$480$	−1.19258			−0.0544337
$481$	5.57775	+	19.3219i	0.254323	+	0.881002i
$482$	17.5407			0.798955
$483$	−5.09629	+	8.82704i	−0.231889	+	0.401644i
$484$	3.09629	−	5.36293i	0.140741	−	0.243770i
$485$	−5.59629	−	9.69306i	−0.254114	−	0.440139i
$486$	−16.0000			−0.725775
$487$	−9.07775	−	15.7231i	−0.411352	−	0.712483i	0.583686	−	0.811980i	$-0.301610\pi$
$487$	−9.07775	−	15.7231i	−0.411352	−	0.712483i	−0.995038	+	0.0994970i	$0.968277\pi$
$488$	1.30742	+	2.26451i	0.0591840	+	0.102510i
$489$	17.8074			0.805279
$490$	−1.90371	−	3.29732i	−0.0860008	−	0.148958i
$491$	−10.1740	+	17.6220i	−0.459148	+	0.795268i	−0.998916	−	0.0465461i	$-0.985179\pi$
$491$	−10.1740	+	17.6220i	−0.459148	+	0.795268i	0.539768	+	0.841814i	$0.318512\pi$
$492$	0.307418	−	0.532463i	0.0138595	−	0.0240053i
$493$		0			0
$494$	−5.48146	+	5.69650i	−0.246622	+	0.256297i
$495$	−5.22967			−0.235056
$496$	−0.500000	+	0.866025i	−0.0224507	+	0.0388857i
$497$	20.0777	−	34.7757i	0.900610	−	1.55990i
$498$	−1.80742	−	3.13054i	−0.0809923	−	0.140283i
$499$	22.1555			0.991816			0.495908	−	0.868375i	$-0.334835\pi$
$499$	22.1555			0.991816			0.495908	+	0.868375i	$0.334835\pi$
$500$	5.11484	+	8.85915i	0.228742	+	0.396193i
$501$	4.19258	+	7.26177i	0.187311	+	0.324432i
$502$	−10.7703			−0.480703
$503$	21.3481	+	36.9760i	0.951864	+	1.64868i	0.741387	+	0.671077i	$0.234168\pi$
$503$	21.3481	+	36.9760i	0.951864	+	1.64868i	0.210476	+	0.977599i	$0.432499\pi$
$504$	−3.19258	+	5.52971i	−0.142209	+	0.246313i
$505$	−0.366621	+	0.635006i	−0.0163144	+	0.0282574i
$506$	7.00000			0.311188
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	−12.0000			−0.532414
$509$	−16.1926	+	28.0464i	−0.717724	+	1.24313i	0.244176	+	0.969731i	$0.421483\pi$
$509$	−16.1926	+	28.0464i	−0.717724	+	1.24313i	−0.961900	+	0.273403i	$0.911851\pi$
$510$		0			0
$511$	14.3666	+	24.8837i	0.635542	+	1.10079i
$512$	1.00000			0.0441942
$513$	−5.48146	−	9.49416i	−0.242012	−	0.419177i
$514$	9.09629	+	15.7552i	0.401220	+	0.694934i
$515$	19.2668			0.848995
$516$	−4.50000	−	7.79423i	−0.198101	−	0.343122i
$517$	3.71113	−	6.42786i	0.163215	−	0.282697i
$518$	−8.90371	+	15.4217i	−0.391207	+	0.677590i
$519$	−13.1555			−0.577462
$520$	−2.98146	+	3.09842i	−0.130745	+	0.135875i
$521$	19.3481			0.847655			0.423827	−	0.905743i	$-0.360686\pi$
$521$	19.3481			0.847655			0.423827	+	0.905743i	$0.360686\pi$
$522$	1.80742	−	3.13054i	0.0791085	−	0.137020i
$523$	13.5000	−	23.3827i	0.590314	−	1.02245i	−0.403876	−	0.914814i	$-0.632337\pi$
$523$	13.5000	−	23.3827i	0.590314	−	1.02245i	0.994190	−	0.107640i	$-0.0343293\pi$
$524$	6.59629	+	11.4251i	0.288160	+	0.499108i
$525$	−11.4223			−0.498508
$526$	−4.48146	−	7.76211i	−0.195401	−	0.338444i
$527$		0			0
$528$	−2.19258			−0.0954199
$529$	6.40371	+	11.0915i	0.278422	+	0.482241i
$530$	−3.09629	+	5.36293i	−0.134494	+	0.232951i
$531$	−11.7703	+	20.3868i	−0.510789	+	0.884712i
$532$	−7.00000			−0.303488
$533$	−0.614835	−	2.12985i	−0.0266315	−	0.0922541i
$534$	16.9629			0.734057
$535$	−2.01854	+	3.49622i	−0.0872693	+	0.151155i
$536$	2.30742	−	3.99656i	0.0996653	−	0.172625i
$537$	−9.57775	−	16.5891i	−0.413310	−	0.715874i
$538$	−7.19258			−0.310094
$539$	−3.50000	−	6.06218i	−0.150756	−	0.261116i
$540$	−2.98146	−	5.16403i	−0.128301	−	0.222225i
$541$	36.3110			1.56113			0.780566	−	0.625074i	$-0.214931\pi$
$541$	36.3110			1.56113			0.780566	+	0.625074i	$0.214931\pi$
$542$	2.00000	+	3.46410i	0.0859074	+	0.148796i
$543$	−0.403709	+	0.699244i	−0.0173248	+	0.0300074i
$544$		0			0
$545$	−2.61484			−0.112007
$546$	−3.19258	−	11.0594i	−0.136630	−	0.473300i
$547$	−26.8074			−1.14620			−0.573101	−	0.819485i	$-0.694260\pi$
$547$	−26.8074			−1.14620			−0.573101	+	0.819485i	$0.694260\pi$
$548$	1.88516	−	3.26520i	0.0805302	−	0.139482i
$549$	−2.61484	+	4.52903i	−0.111598	+	0.193294i
$550$	3.92225	+	6.79354i	0.167245	+	0.289678i
$551$	3.96291			0.168826
$552$	1.59629	+	2.76486i	0.0679427	+	0.117680i
$553$	7.98146	+	13.8243i	0.339406	+	0.587868i
$554$	−4.57775			−0.194490
$555$	−3.32596	−	5.76073i	−0.141179	−	0.244530i
$556$	10.7889	−	18.6869i	0.457550	−	0.792500i
$557$	15.5777	−	26.9814i	0.660050	−	1.14324i	−0.320552	−	0.947231i	$-0.603868\pi$
$557$	15.5777	−	26.9814i	0.660050	−	1.14324i	0.980602	−	0.196010i	$-0.0627984\pi$
$558$	−2.00000			−0.0846668
$559$	−31.5000	−	7.79423i	−1.33231	−	0.329661i
$560$	−3.80742			−0.160893
$561$		0			0
$562$	9.88516	−	17.1216i	0.416981	−	0.722231i
$563$	−4.38516	−	7.59533i	−0.184813	−	0.320105i	0.758701	−	0.651439i	$-0.225835\pi$
$563$	−4.38516	−	7.59533i	−0.184813	−	0.320105i	−0.943513	+	0.331334i	$0.892501\pi$
$564$	3.38516			0.142541
$565$	−3.57775	−	6.19684i	−0.150517	−	0.260703i
$566$	0.981456	+	1.69993i	0.0412537	+	0.0714535i
$567$	−3.19258			−0.134076
$568$	−6.28887	−	10.8926i	−0.263875	−	0.457045i
$569$	3.61484	−	6.26108i	0.151542	−	0.262478i	−0.780253	−	0.625464i	$-0.784910\pi$
$569$	3.61484	−	6.26108i	0.151542	−	0.262478i	0.931794	+	0.362986i	$0.118243\pi$
$570$	1.30742	−	2.26451i	0.0547617	−	0.0948500i
$571$	40.3110			1.68696			0.843481	−	0.537159i	$-0.180502\pi$
$571$	40.3110			1.68696			0.843481	+	0.537159i	$0.180502\pi$
$572$	−5.48146	+	5.69650i	−0.229191	+	0.238182i
$573$	2.61484			0.109236
$574$	0.981456	−	1.69993i	0.0409652	−	0.0709538i
$575$	5.71113	−	9.89196i	0.238170	−	0.412523i
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	13.6148			0.566793			0.283397	−	0.959003i	$-0.408539\pi$
$577$	13.6148			0.566793			0.283397	+	0.959003i	$0.408539\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−5.48146	−	9.49416i	−0.227802	−	0.394564i
$580$	2.15549			0.0895020
$581$	−5.77033	−	9.99450i	−0.239394	−	0.414642i
$582$	4.69258	−	8.12779i	0.194514	−	0.336908i
$583$	−5.69258	+	9.85984i	−0.235763	+	0.408353i
$584$	9.00000			0.372423
$585$	−8.34808	−	2.06561i	−0.345150	−	0.0854026i
$586$	−15.1926			−0.627600
$587$	16.7518	−	29.0149i	0.691420	−	1.19757i	−0.279952	−	0.960014i	$-0.590319\pi$
$587$	16.7518	−	29.0149i	0.691420	−	1.19757i	0.971373	−	0.237561i	$-0.0763480\pi$
$588$	1.59629	−	2.76486i	0.0658299	−	0.114021i
$589$	−1.09629	−	1.89883i	−0.0451719	−	0.0782400i
$590$	−14.0371			−0.577898
$591$	−11.8852	−	20.5857i	−0.488890	−	0.846783i
$592$	2.78887	+	4.83047i	0.114622	+	0.198531i
$593$	33.5407			1.37735			0.688675	−	0.725070i	$-0.258193\pi$
$593$	33.5407			1.37735			0.688675	+	0.725070i	$0.258193\pi$
$594$	−5.48146	−	9.49416i	−0.224907	−	0.389550i
$595$		0			0
$596$	−9.28887	+	16.0888i	−0.380487	+	0.659023i
$597$	0.192582			0.00788187
$598$	11.1740	+	2.76486i	0.456940	+	0.113063i
$599$	−6.77033			−0.276628			−0.138314	−	0.990388i	$-0.544168\pi$
$599$	−6.77033			−0.276628			−0.138314	+	0.990388i	$0.544168\pi$
$600$	−1.78887	+	3.09842i	−0.0730305	+	0.126492i
$601$	1.30742	−	2.26451i	0.0533307	−	0.0923714i	−0.838128	−	0.545474i	$-0.816350\pi$
$601$	1.30742	−	2.26451i	0.0533307	−	0.0923714i	0.891458	+	0.453103i	$0.149683\pi$
$602$	−14.3666	−	24.8837i	−0.585540	−	1.01418i
$603$	9.22967			0.375861
$604$	−4.88516	−	8.46135i	−0.198775	−	0.344288i
$605$	3.69258	+	6.39574i	0.150125	+	0.260024i
$606$	−0.614835			−0.0249760
$607$	16.9444	+	29.3485i	0.687751	+	1.19122i	0.972564	+	0.232636i	$0.0747351\pi$
$607$	16.9444	+	29.3485i	0.687751	+	1.19122i	−0.284813	+	0.958583i	$0.591932\pi$
$608$	−1.09629	+	1.89883i	−0.0444605	+	0.0770078i
$609$	−2.88516	+	4.99725i	−0.116913	+	0.202499i
$610$	−3.11841			−0.126261
$611$	8.46291	−	8.79492i	0.342373	−	0.355804i
$612$		0			0
$613$	−3.48146	+	6.03006i	−0.140615	+	0.243552i	−0.927728	−	0.373256i	$-0.878241\pi$
$613$	−3.48146	+	6.03006i	−0.140615	+	0.243552i	0.787114	+	0.616808i	$0.211575\pi$
$614$	7.50000	−	12.9904i	0.302675	−	0.524249i
$615$	0.366621	+	0.635006i	0.0147836	+	0.0256059i
$616$	−7.00000			−0.282038
$617$	−21.8481	−	37.8420i	−0.879570	−	1.52346i	−0.851813	−	0.523846i	$-0.824497\pi$
$617$	−21.8481	−	37.8420i	−0.879570	−	1.52346i	−0.0277575	−	0.999615i	$-0.508837\pi$
$618$	8.07775	+	13.9911i	0.324935	+	0.562803i
$619$	27.9629			1.12392			0.561962	−	0.827163i	$-0.310047\pi$
$619$	27.9629			1.12392			0.561962	+	0.827163i	$0.310047\pi$
$620$	−0.596291	−	1.03281i	−0.0239476	−	0.0414785i
$621$	−7.98146	+	13.8243i	−0.320285	+	0.554750i
$622$	11.0777	−	19.1872i	0.444177	−	0.769337i
$623$	54.1555			2.16969
$624$	−3.50000	−	0.866025i	−0.140112	−	0.0346688i
$625$	5.68901			0.227560
$626$	6.28887	−	10.8926i	0.251354	−	0.435358i
$627$	2.40371	−	4.16335i	0.0959949	−	0.166268i
$628$	2.78887	+	4.83047i	0.111288	+	0.192757i
$629$		0			0
$630$	−3.80742	−	6.59464i	−0.151691	−	0.262737i
$631$	−21.8666	−	37.8741i	−0.870496	−	1.50774i	−0.861484	−	0.507785i	$-0.830465\pi$
$631$	−21.8666	−	37.8741i	−0.870496	−	1.50774i	−0.00901240	−	0.999959i	$-0.502869\pi$
$632$	5.00000			0.198889
$633$	−1.78887	−	3.09842i	−0.0711013	−	0.123151i
$634$	6.77033	−	11.7266i	0.268884	−	0.465721i
$635$	7.15549	−	12.3937i	0.283957	−	0.491828i
$636$	−5.19258			−0.205899
$637$	−3.19258	−	11.0594i	−0.126495	−	0.438191i
$638$	3.96291			0.156893
$639$	12.5777	−	21.7853i	0.497568	−	0.861813i
$640$	−0.596291	+	1.03281i	−0.0235705	+	0.0408253i
$641$	−3.28887	−	5.69650i	−0.129903	−	0.224998i	0.793736	−	0.608262i	$-0.208133\pi$
$641$	−3.28887	−	5.69650i	−0.129903	−	0.224998i	−0.923639	+	0.383264i	$0.874800\pi$
$642$	−3.38516			−0.133602
$643$	4.09629	+	7.09498i	0.161542	+	0.279799i	0.935422	−	0.353533i	$-0.115020\pi$
$643$	4.09629	+	7.09498i	0.161542	+	0.279799i	−0.773880	+	0.633332i	$0.781687\pi$
$644$	5.09629	+	8.82704i	0.200822	+	0.347834i
$645$	10.7332			0.422621
$646$		0			0
$647$	12.0963	−	20.9514i	0.475554	−	0.823684i	−0.524054	−	0.851685i	$-0.675581\pi$
$647$	12.0963	−	20.9514i	0.475554	−	0.823684i	0.999608	+	0.0280011i	$0.00891419\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−25.8074			−1.01303
$650$	3.57775	+	12.3937i	0.140331	+	0.486120i
$651$	3.19258			0.125127
$652$	8.90371	−	15.4217i	0.348696	−	0.603959i
$653$	13.1926	−	22.8502i	0.516266	−	0.894198i	−0.483556	−	0.875313i	$-0.660655\pi$
$653$	13.1926	−	22.8502i	0.516266	−	0.894198i	0.999822	−	0.0188849i	$-0.00601161\pi$
$654$	−1.09629	−	1.89883i	−0.0428684	−	0.0742502i
$655$	−15.7332			−0.614749
$656$	−0.307418	−	0.532463i	−0.0120026	−	0.0207892i
$657$	9.00000	+	15.5885i	0.351123	+	0.608164i
$658$	10.8074			0.421317
$659$	15.8852	+	27.5139i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$659$	15.8852	+	27.5139i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$660$	1.30742	−	2.26451i	0.0508912	−	0.0881461i
$661$	−17.1740	+	29.7463i	−0.667993	+	1.15700i	0.310472	+	0.950583i	$0.399513\pi$
$661$	−17.1740	+	29.7463i	−0.667993	+	1.15700i	−0.978465	+	0.206415i	$0.933820\pi$
$662$	−5.00000			−0.194331
$663$		0			0
$664$	−3.61484			−0.140283
$665$	4.17404	−	7.22965i	0.161862	−	0.280354i
$666$	−5.57775	+	9.66094i	−0.216133	+	0.374354i
$667$	−2.88516	−	4.99725i	−0.111714	−	0.193494i
$668$	8.38516			0.324432
$669$	−3.78887	−	6.56252i	−0.146486	−	0.253722i
$670$	2.75179	+	4.76623i	0.106311	+	0.184136i
$671$	−5.73324			−0.221329
$672$	−1.59629	−	2.76486i	−0.0615783	−	0.106657i
$673$	6.00000	−	10.3923i	0.231283	−	0.400594i	−0.726903	−	0.686740i	$-0.759041\pi$
$673$	6.00000	−	10.3923i	0.231283	−	0.400594i	0.958186	+	0.286146i	$0.0923743\pi$
$674$	−7.07775	+	12.2590i	−0.272625	+	0.472200i
$675$	−17.8887			−0.688538
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	−12.9258			−0.496780			−0.248390	−	0.968660i	$-0.579901\pi$
$677$	−12.9258			−0.496780			−0.248390	+	0.968660i	$0.579901\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	14.9815	−	25.9486i	0.574936	−	0.995818i
$680$		0			0
$681$	3.00000			0.114960
$682$	−1.09629	−	1.89883i	−0.0419792	−	0.0727100i
$683$	5.17404	+	8.96170i	0.197979	+	0.342910i	0.947873	−	0.318648i	$-0.103229\pi$
$683$	5.17404	+	8.96170i	0.197979	+	0.342910i	−0.749894	+	0.661558i	$0.769896\pi$
$684$	−4.38516			−0.167671
$685$	2.24821	+	3.89402i	0.0858999	+	0.148783i
$686$	−6.07775	+	10.5270i	−0.232049	+	0.401921i
$687$	1.69258	−	2.93164i	0.0645760	−	0.111849i
$688$	−9.00000			−0.343122
$689$	−12.9815	+	13.4907i	−0.494554	+	0.513956i
$690$	−3.80742			−0.144946
$691$	22.2703	−	38.5733i	0.847203	−	1.46740i	−0.0364907	−	0.999334i	$-0.511618\pi$
$691$	22.2703	−	38.5733i	0.847203	−	1.46740i	0.883694	−	0.468065i	$-0.155049\pi$
$692$	−6.57775	+	11.3930i	−0.250048	+	0.433097i
$693$	−7.00000	−	12.1244i	−0.265908	−	0.460566i
$694$	−14.4223			−0.547461
$695$	12.8666	+	22.2856i	0.488059	+	0.845343i
$696$	0.903709	+	1.56527i	0.0342550	+	0.0593314i
$697$		0			0
$698$	−8.19258	−	14.1900i	−0.310094	−	0.537098i
$699$	−6.69258	+	11.5919i	−0.253137	+	0.438446i
$700$	−5.71113	+	9.89196i	−0.215860	+	0.373881i
$701$	−12.8074			−0.483729			−0.241865	−	0.970310i	$-0.577759\pi$
$701$	−12.8074			−0.483729			−0.241865	+	0.970310i	$0.577759\pi$
$702$	−5.00000	−	17.3205i	−0.188713	−	0.653720i
$703$	−12.2297			−0.461251
$704$	−1.09629	+	1.89883i	−0.0413180	+	0.0715649i
$705$	−2.01854	+	3.49622i	−0.0760228	+	0.131675i
$706$	4.78887	+	8.29457i	0.180232	+	0.312170i
$707$	−1.96291			−0.0738229
$708$	−5.88516	−	10.1934i	−0.221178	−	0.383092i
$709$	−23.8852	−	41.3703i	−0.897026	−	1.55369i	−0.831277	−	0.555859i	$-0.812390\pi$
$709$	−23.8852	−	41.3703i	−0.897026	−	1.55369i	−0.0657495	−	0.997836i	$-0.520944\pi$
$710$	15.0000			0.562940
$711$	5.00000	+	8.66025i	0.187515	+	0.324785i
$712$	8.48146	−	14.6903i	0.317856	−	0.550543i
$713$	−1.59629	+	2.76486i	−0.0597816	+	0.103545i
$714$		0			0
$715$	−2.61484	−	9.05805i	−0.0977893	−	0.338752i
$716$	−19.1555			−0.715874
$717$	−10.9815	+	19.0204i	−0.410110	+	0.710331i
$718$	10.8852	−	18.8537i	0.406231	−	0.703612i
$719$	9.28887	+	16.0888i	0.346417	+	0.600011i	0.985610	−	0.169035i	$-0.0540651\pi$
$719$	9.28887	+	16.0888i	0.346417	+	0.600011i	−0.639194	+	0.769046i	$0.720732\pi$
$720$	−2.38516			−0.0888898
$721$	25.7889	+	44.6676i	0.960428	+	1.66351i
$722$	7.09629	+	12.2911i	0.264097	+	0.457429i
$723$	−17.5407			−0.652344
$724$	0.403709	+	0.699244i	0.0150037	+	0.0259872i
$725$	3.23324	−	5.60014i	0.120080	−	0.207984i
$726$	−3.09629	+	5.36293i	−0.114914	+	0.199037i
$727$	−27.7703			−1.02994			−0.514972	−	0.857207i	$-0.672198\pi$
$727$	−27.7703			−1.02994			−0.514972	+	0.857207i	$0.672198\pi$
$728$	−11.1740	−	2.76486i	−0.414137	−	0.102472i
$729$	13.0000			0.481481
$730$	−5.36662	+	9.29526i	−0.198628	+	0.344033i
$731$		0			0
$732$	−1.30742	−	2.26451i	−0.0483235	−	0.0836988i
$733$	1.84451			0.0681284			0.0340642	−	0.999420i	$-0.489155\pi$
$733$	1.84451			0.0681284			0.0340642	+	0.999420i	$0.489155\pi$
$734$	9.07775	+	15.7231i	0.335066	+	0.580351i
$735$	1.90371	+	3.29732i	0.0702194	+	0.121623i
$736$	3.19258			0.117680
$737$	5.05920	+	8.76280i	0.186358	+	0.322782i
$738$	0.614835	−	1.06493i	0.0226324	−	0.0392005i
$739$	10.9815	−	19.0204i	0.403959	−	0.699678i	−0.590240	−	0.807228i	$-0.700967\pi$
$739$	10.9815	−	19.0204i	0.403959	−	0.699678i	0.994200	+	0.107549i	$0.0343004\pi$
$740$	−6.65192			−0.244530
$741$	5.48146	−	5.69650i	0.201366	−	0.209266i
$742$	−16.5777			−0.608588
$743$	7.32596	−	12.6889i	0.268763	−	0.465512i	−0.699779	−	0.714359i	$-0.746718\pi$
$743$	7.32596	−	12.6889i	0.268763	−	0.465512i	0.968543	+	0.248847i	$0.0800517\pi$
$744$	0.500000	−	0.866025i	0.0183309	−	0.0317500i
$745$	−11.0777	−	19.1872i	−0.405857	−	0.702965i
$746$	13.1555			0.481657
$747$	−3.61484	−	6.26108i	−0.132260	−	0.229081i
$748$		0			0
$749$	−10.8074			−0.394894
$750$	−5.11484	−	8.85915i	−0.186767	−	0.323491i
$751$	−2.32596	+	4.02868i	−0.0848755	+	0.147009i	−0.905338	−	0.424691i	$-0.860383\pi$
$751$	−2.32596	+	4.02868i	−0.0848755	+	0.147009i	0.820463	+	0.571700i	$0.193716\pi$
$752$	1.69258	−	2.93164i	0.0617221	−	0.106906i
$753$	10.7703			0.392493
$754$	6.32596	+	1.56527i	0.230378	+	0.0570038i
$755$	11.6519			0.424057
$756$	7.98146	−	13.8243i	0.290283	−	0.502784i
$757$	9.71113	−	16.8202i	0.352957	−	0.611339i	−0.633809	−	0.773489i	$-0.718510\pi$
$757$	9.71113	−	16.8202i	0.352957	−	0.611339i	0.986766	+	0.162150i	$0.0518429\pi$
$758$	−18.8666	−	32.6779i	−0.685267	−	1.18692i
$759$	−7.00000			−0.254084
$760$	−1.30742	−	2.26451i	−0.0474250	−	0.0821425i
$761$	8.42225	+	14.5878i	0.305306	+	0.528806i	0.977330	−	0.211724i	$-0.0679078\pi$
$761$	8.42225	+	14.5878i	0.305306	+	0.528806i	−0.672023	+	0.740530i	$0.734574\pi$
$762$	12.0000			0.434714
$763$	−3.50000	−	6.06218i	−0.126709	−	0.219466i
$764$	1.30742	−	2.26451i	0.0473007	−	0.0819272i
$765$		0			0
$766$	4.22967			0.152824
$767$	−41.1962	−	10.1934i	−1.48751	−	0.368063i
$768$	−1.00000			−0.0360844
$769$	−27.3481	+	47.3683i	−0.986197	+	1.70814i	−0.349705	+	0.936860i	$0.613718\pi$
$769$	−27.3481	+	47.3683i	−0.986197	+	1.70814i	−0.636492	+	0.771283i	$0.719615\pi$
$770$	4.17404	−	7.22965i	0.150422	−	0.260538i
$771$	−9.09629	−	15.7552i	−0.327595	−	0.567411i
$772$	−10.9629			−0.394564
$773$	−3.88516	−	6.72930i	−0.139740	−	0.242036i	0.787658	−	0.616112i	$-0.211293\pi$
$773$	−3.88516	−	6.72930i	−0.139740	−	0.242036i	−0.927398	+	0.374076i	$0.877960\pi$
$774$	−9.00000	−	15.5885i	−0.323498	−	0.560316i
$775$	−3.57775			−0.128516
$776$	−4.69258	−	8.12779i	−0.168454	−	0.291771i
$777$	8.90371	−	15.4217i	0.319419	−	0.553250i
$778$	−5.59629	+	9.69306i	−0.200637	+	0.347513i
$779$	1.34808			0.0482999
$780$	2.98146	−	3.09842i	0.106753	−	0.110941i
$781$	27.5777			0.986809
$782$		0			0
$783$	−4.51854	+	7.82635i	−0.161480	+	0.279691i
$784$	−1.59629	−	2.76486i	−0.0570104	−	0.0987449i
$785$	−6.65192			−0.237417
$786$	−6.59629	−	11.4251i	−0.235282	−	0.407520i
$787$	8.57775	+	14.8571i	0.305764	+	0.529598i	0.977431	−	0.211255i	$-0.0677549\pi$
$787$	8.57775	+	14.8571i	0.305764	+	0.529598i	−0.671667	+	0.740853i	$0.734422\pi$
$788$	−23.7703			−0.846783
$789$	4.48146	+	7.76211i	0.159544	+	0.276338i
$790$	−2.98146	+	5.16403i	−0.106075	+	0.183728i
$791$	9.57775	−	16.5891i	0.340545	−	0.589842i
$792$	−4.38516			−0.155820
$793$	−9.15192	−	2.26451i	−0.324994	−	0.0804152i
$794$	13.6148			0.483172
$795$	3.09629	−	5.36293i	0.109814	−	0.190204i
$796$	0.0962912	−	0.166781i	0.00341295	−	0.00591140i
$797$	18.6370	+	32.2801i	0.660155	+	1.14342i	0.980575	+	0.196146i	$0.0628426\pi$
$797$	18.6370	+	32.2801i	0.660155	+	1.14342i	−0.320420	+	0.947276i	$0.603824\pi$
$798$	7.00000			0.247797
$799$		0			0
$800$	1.78887	+	3.09842i	0.0632462	+	0.109546i
$801$	33.9258			1.19871
$802$	−9.30742	−	16.1209i	−0.328656	−	0.569249i
$803$	−9.86662	+	17.0895i	−0.348185	+	0.603075i
$804$	−2.30742	+	3.99656i	−0.0813763	+	0.140948i
$805$	−12.1555			−0.428425
$806$	−1.00000	−	3.46410i	−0.0352235	−	0.122018i
$807$	7.19258			0.253191
$808$	−0.307418	+	0.532463i	−0.0108149	+	0.0187320i
$809$	2.67404	−	4.63157i	0.0940142	−	0.162837i	−0.815183	−	0.579204i	$-0.803363\pi$
$809$	2.67404	−	4.63157i	0.0940142	−	0.162837i	0.909197	+	0.416367i	$0.136697\pi$
$810$	−0.596291	−	1.03281i	−0.0209515	−	0.0362891i
$811$	13.3852			0.470017			0.235008	−	0.971993i	$-0.424488\pi$
$811$	13.3852			0.470017			0.235008	+	0.971993i	$0.424488\pi$
$812$	2.88516	+	4.99725i	0.101249	+	0.175369i
$813$	−2.00000	−	3.46410i	−0.0701431	−	0.121491i
$814$	−12.2297			−0.428650
$815$	10.6184	+	18.3916i	0.371947	+	0.644230i
$816$		0			0
$817$	9.86662	−	17.0895i	0.345189	−	0.597886i
$818$	−34.5777			−1.20898
$819$	−6.38516	−	22.1189i	−0.223116	−	0.772896i
$820$	0.733242			0.0256059
$821$	−18.1740	+	31.4784i	−0.634278	+	1.09860i	0.352389	+	0.935854i	$0.385369\pi$
$821$	−18.1740	+	31.4784i	−0.634278	+	1.09860i	−0.986668	+	0.162749i	$0.947964\pi$
$822$	−1.88516	+	3.26520i	−0.0657527	+	0.113887i
$823$	19.2518	+	33.3451i	0.671075	+	1.16234i	0.977600	+	0.210473i	$0.0675005\pi$
$823$	19.2518	+	33.3451i	0.671075	+	1.16234i	−0.306525	+	0.951863i	$0.599166\pi$
$824$	16.1555			0.562803
$825$	−3.92225	−	6.79354i	−0.136555	−	0.236521i
$826$	−18.7889	−	32.5433i	−0.653749	−	1.13233i
$827$	2.19258			0.0762436			0.0381218	−	0.999273i	$-0.487863\pi$
$827$	2.19258			0.0762436			0.0381218	+	0.999273i	$0.487863\pi$
$828$	3.19258	+	5.52971i	0.110950	+	0.192171i
$829$	−23.8481	+	41.3061i	−0.828278	+	1.43462i	0.0711102	+	0.997468i	$0.477346\pi$
$829$	−23.8481	+	41.3061i	−0.828278	+	1.43462i	−0.899388	+	0.437151i	$0.855988\pi$
$830$	2.15549	−	3.73343i	0.0748183	−	0.129589i
$831$	4.57775			0.158800
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$		0			0
$834$	−10.7889	+	18.6869i	−0.373588	+	0.647074i
$835$	−5.00000	+	8.66025i	−0.173032	+	0.299700i
$836$	−2.40371	−	4.16335i	−0.0831340	−	0.143992i
$837$	5.00000			0.172825
$838$	−7.09629	−	12.2911i	−0.245137	−	0.424590i
$839$	−11.9629	−	20.7204i	−0.413006	−	0.715347i	0.582211	−	0.813038i	$-0.302188\pi$
$839$	−11.9629	−	20.7204i	−0.413006	−	0.715347i	−0.995217	+	0.0976909i	$0.968854\pi$
$840$	3.80742			0.131368
$841$	12.8666	+	22.2856i	0.443677	+	0.768470i
$842$	9.69258	−	16.7880i	0.334028	−	0.578554i
$843$	−9.88516	+	17.1216i	−0.340463	+	0.589699i
$844$	−3.57775			−0.123151
$845$	−0.596291	−	15.4921i	−0.0205130	−	0.532944i
$846$	6.77033			0.232769
$847$	−9.88516	+	17.1216i	−0.339658	+	0.588305i
$848$	−2.59629	+	4.49691i	−0.0891570	+	0.154424i
$849$	−0.981456	−	1.69993i	−0.0336835	−	0.0583415i
$850$		0			0
$851$	8.90371	+	15.4217i	0.305215	+	0.528648i
$852$	6.28887	+	10.8926i	0.215453	+	0.373176i
$853$	1.26676			0.0433730			0.0216865	−	0.999765i	$-0.493096\pi$
$853$	1.26676			0.0433730			0.0216865	+	0.999765i	$0.493096\pi$
$854$	−4.17404	−	7.22965i	−0.142833	−	0.247393i
$855$	2.61484	−	4.52903i	0.0894255	−	0.154889i
$856$	−1.69258	+	2.93164i	−0.0578513	+	0.100201i
$857$	54.2739			1.85396			0.926981	−	0.375109i	$-0.122395\pi$
$857$	54.2739			1.85396			0.926981	+	0.375109i	$0.122395\pi$
$858$	5.48146	−	5.69650i	0.187134	−	0.194475i
$859$	−44.5777			−1.52097			−0.760487	−	0.649354i	$-0.775040\pi$
$859$	−44.5777			−1.52097			−0.760487	+	0.649354i	$0.775040\pi$
$860$	5.36662	−	9.29526i	0.183000	−	0.316966i
$861$	−0.981456	+	1.69993i	−0.0334479	+	0.0579335i
$862$	−2.30742	−	3.99656i	−0.0785910	−	0.136124i
$863$	27.7703			0.945313			0.472657	−	0.881247i	$-0.343295\pi$
$863$	27.7703			0.945313			0.472657	+	0.881247i	$0.343295\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$	−7.84451	−	13.5871i	−0.266721	−	0.461975i
$866$	17.5777			0.597316
$867$	−8.50000	−	14.7224i	−0.288675	−	0.500000i
$868$	1.59629	−	2.76486i	0.0541817	−	0.0938454i
$869$	−5.48146	+	9.49416i	−0.185946	+	0.322067i
$870$	−2.15549			−0.0730781
$871$	4.61484	+	15.9863i	0.156368	+	0.541674i
$872$	−2.19258			−0.0742502
$873$	9.38516	−	16.2556i	0.317640	−	0.550168i
$874$	−3.50000	+	6.06218i	−0.118389	+	0.205056i
$875$	−16.3295	−	28.2836i	−0.552039	−	0.956160i
$876$	−9.00000			−0.304082
$877$	−20.3666	−	35.2760i	−0.687732	−	1.19119i	−0.972570	−	0.232611i	$-0.925273\pi$
$877$	−20.3666	−	35.2760i	−0.687732	−	1.19119i	0.284838	−	0.958576i	$-0.408060\pi$
$878$	−3.50000	−	6.06218i	−0.118119	−	0.204589i
$879$	15.1926			0.512433
$880$	−1.30742	−	2.26451i	−0.0440730	−	0.0763367i
$881$	−8.98146	+	15.5563i	−0.302593	+	0.524106i	−0.976723	−	0.214507i	$-0.931186\pi$
$881$	−8.98146	+	15.5563i	−0.302593	+	0.524106i	0.674130	+	0.738613i	$0.264519\pi$
$882$	3.19258	−	5.52971i	0.107500	−	0.186195i
$883$	−26.7332			−0.899645			−0.449823	−	0.893118i	$-0.648513\pi$
$883$	−26.7332			−0.899645			−0.449823	+	0.893118i	$0.648513\pi$
$884$		0			0
$885$	14.0371			0.471852
$886$	−6.77033	+	11.7266i	−0.227454	+	0.393961i
$887$	10.5185	−	18.2187i	0.353178	−	0.611722i	−0.633626	−	0.773639i	$-0.718434\pi$
$887$	10.5185	−	18.2187i	0.353178	−	0.611722i	0.986804	+	0.161917i	$0.0517676\pi$
$888$	−2.78887	−	4.83047i	−0.0935885	−	0.162100i
$889$	38.3110			1.28491
$890$	10.1148	+	17.5194i	0.339050	+	0.587252i
$891$	−1.09629	−	1.89883i	−0.0367271	−	0.0636133i
$892$	−7.57775			−0.253722
$893$	3.71113	+	6.42786i	0.124188	+	0.215100i
$894$	9.28887	−	16.0888i	0.310666	−	0.538090i
$895$	11.4223	−	19.7839i	0.381804	−	0.661304i
$896$	−3.19258			−0.106657
$897$	−11.1740	−	2.76486i	−0.373090	−	0.0923159i
$898$	−5.03709			−0.168090
$899$	−0.903709	+	1.56527i	−0.0301404	+	0.0522047i
$900$	−3.57775	+	6.19684i	−0.119258	+	0.206561i
$901$		0			0
$902$	1.34808			0.0448860
$903$	14.3666	+	24.8837i	0.478091	+	0.828078i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	−0.962912			−0.0320083
$906$	4.88516	+	8.46135i	0.162299	+	0.281110i
$907$	−25.8295	+	44.7381i	−0.857656	+	1.48550i	0.0165038	+	0.999864i	$0.494746\pi$
$907$	−25.8295	+	44.7381i	−0.857656	+	1.48550i	−0.874159	+	0.485639i	$0.838587\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$	−1.22967			−0.0407856
$910$	9.51854	−	9.89196i	0.315537	−	0.327915i
$911$	−1.77033			−0.0586536			−0.0293268	−	0.999570i	$-0.509336\pi$
$911$	−1.77033			−0.0586536			−0.0293268	+	0.999570i	$0.509336\pi$
$912$	1.09629	−	1.89883i	0.0363018	−	0.0628766i
$913$	3.96291	−	6.86396i	0.131153	−	0.227164i
$914$	13.2889	+	23.0170i	0.439557	+	0.761335i
$915$	3.11841			0.103091
$916$	−1.69258	−	2.93164i	−0.0559245	−	0.0968641i
$917$	−21.0592	−	36.4756i	−0.695436	−	1.20453i
$918$		0			0
$919$	13.0777	+	22.6513i	0.431395	+	0.747198i	0.996994	−	0.0774825i	$-0.0246882\pi$
$919$	13.0777	+	22.6513i	0.431395	+	0.747198i	−0.565599	+	0.824681i	$0.691355\pi$
$920$	−1.90371	+	3.29732i	−0.0627634	+	0.108709i
$921$	−7.50000	+	12.9904i	−0.247133	+	0.428048i
$922$	3.19258			0.105142
$923$	44.0221	+	10.8926i	1.44901	+	0.358536i
$924$	7.00000			0.230283
$925$	−9.97788	+	17.2822i	−0.328071	+	0.568235i
$926$	10.3666	−	17.9555i	0.340668	−	0.590055i
$927$	16.1555	+	27.9821i	0.530616	+	0.919054i
$928$	1.80742			0.0593314
$929$	−29.7518	−	51.5316i	−0.976124	−	1.69070i	−0.676173	−	0.736742i	$-0.736363\pi$
$929$	−29.7518	−	51.5316i	−0.976124	−	1.69070i	−0.299951	−	0.953955i	$-0.596970\pi$
$930$	0.596291	+	1.03281i	0.0195532	+	0.0338671i
$931$	7.00000			0.229416
$932$	6.69258	+	11.5919i	0.219223	+	0.379705i
$933$	−11.0777	+	19.1872i	−0.362669	+	0.628161i
$934$	4.30742	−	7.46067i	0.140943	−	0.244120i
$935$		0			0
$936$	−7.00000	−	1.73205i	−0.228802	−	0.0566139i
$937$	−7.96291			−0.260137			−0.130068	−	0.991505i	$-0.541520\pi$
$937$	−7.96291			−0.260137			−0.130068	+	0.991505i	$0.541520\pi$
$938$	−7.36662	+	12.7594i	−0.240529	+	0.416608i
$939$	−6.28887	+	10.8926i	−0.205230	+	0.355468i
$940$	2.01854	+	3.49622i	0.0658376	+	0.114034i
$941$	−41.3481			−1.34791			−0.673954	−	0.738773i	$-0.735406\pi$
$941$	−41.3481			−1.34791			−0.673954	+	0.738773i	$0.735406\pi$
$942$	−2.78887	−	4.83047i	−0.0908664	−	0.157385i
$943$	−0.981456	−	1.69993i	−0.0319606	−	0.0553574i
$944$	−11.7703			−0.383092
$945$	9.51854	+	16.4866i	0.309638	+	0.536309i
$946$	9.86662	−	17.0895i	0.320792	−	0.555627i
$947$	17.6926	−	30.6445i	0.574932	−	0.995811i	−0.421117	−	0.907006i	$-0.638362\pi$
$947$	17.6926	−	30.6445i	0.574932	−	0.995811i	0.996049	−	0.0888047i	$-0.0283047\pi$
$948$	−5.00000			−0.162392
$949$	−22.5000	+	23.3827i	−0.730381	+	0.759034i
$950$	−7.84451			−0.254509
$951$	−6.77033	+	11.7266i	−0.219543	+	0.380260i
$952$		0			0
$953$	−27.2703	−	47.2336i	−0.883373	−	1.53005i	−0.847568	−	0.530687i	$-0.821934\pi$
$953$	−27.2703	−	47.2336i	−0.883373	−	1.53005i	−0.0358050	−	0.999359i	$-0.511400\pi$
$954$	−10.3852			−0.336232
$955$	1.55920	+	2.70062i	0.0504546	+	0.0873900i
$956$	10.9815	+	19.0204i	0.355166	+	0.615165i
$957$	−3.96291			−0.128103
$958$	−4.77033	−	8.26245i	−0.154122	−	0.266948i
$959$	−6.01854	+	10.4244i	−0.194349	+	0.336622i
$960$	0.596291	−	1.03281i	0.0192452	−	0.0333337i
$961$	1.00000			0.0322581
$962$	−19.5221	−	4.83047i	−0.629418	−	0.155741i
$963$	−6.77033			−0.218171
$964$	−8.77033	+	15.1907i	−0.282473	+	0.489258i
$965$	6.53709	−	11.3226i	0.210436	−	0.364486i
$966$	−5.09629	−	8.82704i	−0.163970	−	0.284005i
$967$	37.3110			1.19984			0.599920	−	0.800060i	$-0.295199\pi$
$967$	37.3110			1.19984			0.599920	+	0.800060i	$0.295199\pi$
$968$	3.09629	+	5.36293i	0.0995186	+	0.172371i
$969$		0			0
$970$	11.1926			0.359372
$971$	−14.5963	−	25.2815i	−0.468417	−	0.811323i	0.530931	−	0.847415i	$-0.321842\pi$
$971$	−14.5963	−	25.2815i	−0.468417	−	0.811323i	−0.999348	+	0.0360924i	$0.988509\pi$
$972$	8.00000	−	13.8564i	0.256600	−	0.444444i
$973$	−34.4444	+	59.6594i	−1.10424	+	1.91259i
$974$	18.1555			0.581740
$975$	−3.57775	−	12.3937i	−0.114580	−	0.396915i
$976$	−2.61484			−0.0836988
$977$	5.42225	−	9.39162i	0.173473	−	0.300464i	−0.766159	−	0.642652i	$-0.777834\pi$
$977$	5.42225	−	9.39162i	0.173473	−	0.300464i	0.939632	+	0.342187i	$0.111168\pi$
$978$	−8.90371	+	15.4217i	−0.284709	+	0.493131i
$979$	18.5963	+	32.2097i	0.594340	+	1.02943i
$980$	3.80742			0.121623
$981$	−2.19258	−	3.79766i	−0.0700038	−	0.121250i
$982$	−10.1740	−	17.6220i	−0.324667	−	0.562339i
$983$	11.8074			0.376598			0.188299	−	0.982112i	$-0.439703\pi$
$983$	11.8074			0.376598			0.188299	+	0.982112i	$0.439703\pi$
$984$	0.307418	+	0.532463i	0.00980012	+	0.0169743i
$985$	14.1740	−	24.5502i	0.451622	−	0.782233i
$986$		0			0
$987$	−10.8074			−0.344004
$988$	−2.19258	−	7.59533i	−0.0697553	−	0.241640i
$989$	−28.7332			−0.913664
$990$	2.61484	−	4.52903i	0.0831049	−	0.143942i
$991$	−0.462912	+	0.801787i	−0.0147049	+	0.0254696i	−0.873284	−	0.487211i	$-0.838014\pi$
$991$	−0.462912	+	0.801787i	−0.0147049	+	0.0254696i	0.858579	+	0.512681i	$0.171348\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$	5.00000			0.158670
$994$	20.0777	+	34.7757i	0.636827	+	1.10302i
$995$	0.114835	+	0.198900i	0.00364052	+	0.00630557i
$996$	3.61484			0.114540
$997$	−3.00000	−	5.19615i	−0.0950110	−	0.164564i	0.814602	−	0.580020i	$-0.196955\pi$
$997$	−3.00000	−	5.19615i	−0.0950110	−	0.164564i	−0.909613	+	0.415456i	$0.863622\pi$
$998$	−11.0777	+	19.1872i	−0.350660	+	0.607361i
$999$	13.9444	−	24.1524i	0.441180	−	0.764147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	806.2.g.c.373.2	✓	4
13.3	even	3	inner	806.2.g.c.497.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
806.2.g.c.373.2	✓	4	1.1	even	1	trivial
806.2.g.c.497.2	yes	4	13.3	even	3	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:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.19258 q^{5} +(0.500000 + 0.866025i) q^{6} +(1.59629 + 2.76486i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.19258 q^{5} +(0.500000 + 0.866025i) q^{6} +(1.59629 + 2.76486i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.596291 + 1.03281i) q^{10} +(-1.09629 + 1.89883i) q^{11} -1.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} -3.19258 q^{14} +(0.596291 - 1.03281i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{18} +(-1.09629 - 1.89883i) q^{19} +(-0.596291 - 1.03281i) q^{20} +3.19258 q^{21} +(-1.09629 - 1.89883i) q^{22} +(-1.59629 + 2.76486i) q^{23} +(0.500000 - 0.866025i) q^{24} -3.57775 q^{25} +(-1.00000 - 3.46410i) q^{26} +5.00000 q^{27} +(1.59629 - 2.76486i) q^{28} +(-0.903709 + 1.56527i) q^{29} +(0.596291 + 1.03281i) q^{30} +1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.09629 + 1.89883i) q^{33} +(1.90371 + 3.29732i) q^{35} +(1.00000 - 1.73205i) q^{36} +(2.78887 - 4.83047i) q^{37} +2.19258 q^{38} +(1.00000 + 3.46410i) q^{39} +1.19258 q^{40} +(-0.307418 + 0.532463i) q^{41} +(-1.59629 + 2.76486i) q^{42} +(4.50000 + 7.79423i) q^{43} +2.19258 q^{44} +(1.19258 + 2.06561i) q^{45} +(-1.59629 - 2.76486i) q^{46} -3.38516 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.59629 + 2.76486i) q^{49} +(1.78887 - 3.09842i) q^{50} +(3.50000 + 0.866025i) q^{52} +5.19258 q^{53} +(-2.50000 + 4.33013i) q^{54} +(-1.30742 + 2.26451i) q^{55} +(1.59629 + 2.76486i) q^{56} -2.19258 q^{57} +(-0.903709 - 1.56527i) q^{58} +(5.88516 + 10.1934i) q^{59} -1.19258 q^{60} +(1.30742 + 2.26451i) q^{61} +(-0.500000 + 0.866025i) q^{62} +(-3.19258 + 5.52971i) q^{63} +1.00000 q^{64} +(-2.98146 + 3.09842i) q^{65} -2.19258 q^{66} +(2.30742 - 3.99656i) q^{67} +(1.59629 + 2.76486i) q^{69} -3.80742 q^{70} +(-6.28887 - 10.8926i) q^{71} +(1.00000 + 1.73205i) q^{72} +9.00000 q^{73} +(2.78887 + 4.83047i) q^{74} +(-1.78887 + 3.09842i) q^{75} +(-1.09629 + 1.89883i) q^{76} -7.00000 q^{77} +(-3.50000 - 0.866025i) q^{78} +5.00000 q^{79} +(-0.596291 + 1.03281i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.307418 - 0.532463i) q^{82} -3.61484 q^{83} +(-1.59629 - 2.76486i) q^{84} -9.00000 q^{86} +(0.903709 + 1.56527i) q^{87} +(-1.09629 + 1.89883i) q^{88} +(8.48146 - 14.6903i) q^{89} -2.38516 q^{90} +(-11.1740 - 2.76486i) q^{91} +3.19258 q^{92} +(0.500000 - 0.866025i) q^{93} +(1.69258 - 2.93164i) q^{94} +(-1.30742 - 2.26451i) q^{95} -1.00000 q^{96} +(-4.69258 - 8.12779i) q^{97} +(-1.59629 - 2.76486i) q^{98} -4.38516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} + 3 q^{10} + q^{11} - 4 q^{12} - 10 q^{13} - 2 q^{14} - 3 q^{15} - 2 q^{16} - 8 q^{18} + q^{19} + 3 q^{20} + 2 q^{21} + q^{22} - q^{23} + 2 q^{24} + 18 q^{25} - 4 q^{26} + 20 q^{27} + q^{28} - 9 q^{29} - 3 q^{30} + 4 q^{31} - 2 q^{32} - q^{33} + 13 q^{35} + 4 q^{36} - 5 q^{37} - 2 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - q^{42} + 18 q^{43} - 2 q^{44} - 6 q^{45} - q^{46} + 8 q^{47} + 2 q^{48} - q^{49} - 9 q^{50} + 14 q^{52} + 10 q^{53} - 10 q^{54} - 16 q^{55} + q^{56} + 2 q^{57} - 9 q^{58} + 2 q^{59} + 6 q^{60} + 16 q^{61} - 2 q^{62} - 2 q^{63} + 4 q^{64} + 15 q^{65} + 2 q^{66} + 20 q^{67} + q^{69} - 26 q^{70} - 9 q^{71} + 4 q^{72} + 36 q^{73} - 5 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} - 14 q^{78} + 20 q^{79} + 3 q^{80} - 2 q^{81} - 12 q^{82} - 36 q^{83} - q^{84} - 36 q^{86} + 9 q^{87} + q^{88} + 7 q^{89} + 12 q^{90} - 7 q^{91} + 2 q^{92} + 2 q^{93} - 4 q^{94} - 16 q^{95} - 4 q^{96} - 8 q^{97} - q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + q^7 + 4 * q^8 + 4 * q^9 + 3 * q^10 + q^11 - 4 * q^12 - 10 * q^13 - 2 * q^14 - 3 * q^15 - 2 * q^16 - 8 * q^18 + q^19 + 3 * q^20 + 2 * q^21 + q^22 - q^23 + 2 * q^24 + 18 * q^25 - 4 * q^26 + 20 * q^27 + q^28 - 9 * q^29 - 3 * q^30 + 4 * q^31 - 2 * q^32 - q^33 + 13 * q^35 + 4 * q^36 - 5 * q^37 - 2 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - q^42 + 18 * q^43 - 2 * q^44 - 6 * q^45 - q^46 + 8 * q^47 + 2 * q^48 - q^49 - 9 * q^50 + 14 * q^52 + 10 * q^53 - 10 * q^54 - 16 * q^55 + q^56 + 2 * q^57 - 9 * q^58 + 2 * q^59 + 6 * q^60 + 16 * q^61 - 2 * q^62 - 2 * q^63 + 4 * q^64 + 15 * q^65 + 2 * q^66 + 20 * q^67 + q^69 - 26 * q^70 - 9 * q^71 + 4 * q^72 + 36 * q^73 - 5 * q^74 + 9 * q^75 + q^76 - 28 * q^77 - 14 * q^78 + 20 * q^79 + 3 * q^80 - 2 * q^81 - 12 * q^82 - 36 * q^83 - q^84 - 36 * q^86 + 9 * q^87 + q^88 + 7 * q^89 + 12 * q^90 - 7 * q^91 + 2 * q^92 + 2 * q^93 - 4 * q^94 - 16 * q^95 - 4 * q^96 - 8 * q^97 - q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more