LMFDB - Embedded newform 240.2.bc.d.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.2
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	240.67
Dual form			240.2.bc.d.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264658 + 1.38923i) q^{2} -1.00000i q^{3} +(-1.85991 - 0.735342i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.38923 + 0.264658i) q^{6} +(-3.24914 - 3.24914i) q^{7} +(1.51380 - 2.38923i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.264658 + 1.38923i) q^{2} -1.00000i q^{3} +(-1.85991 - 0.735342i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.38923 + 0.264658i) q^{6} +(-3.24914 - 3.24914i) q^{7} +(1.51380 - 2.38923i) q^{8} -1.00000 q^{9} +(0.859912 + 3.04312i) q^{10} +(-3.24914 - 3.24914i) q^{11} +(-0.735342 + 1.85991i) q^{12} +(5.37371 - 3.65389i) q^{14} +(-1.00000 - 2.00000i) q^{15} +(2.91855 + 2.73534i) q^{16} +(-0.0586332 - 0.0586332i) q^{17} +(0.264658 - 1.38923i) q^{18} +(4.30777 + 4.30777i) q^{19} +(-4.45517 + 0.389229i) q^{20} +(-3.24914 + 3.24914i) q^{21} +(5.37371 - 3.65389i) q^{22} +(4.30777 - 4.30777i) q^{23} +(-2.38923 - 1.51380i) q^{24} +(3.00000 - 4.00000i) q^{25} +1.00000i q^{27} +(3.65389 + 8.43234i) q^{28} +(1.00000 - 1.00000i) q^{29} +(3.04312 - 0.859912i) q^{30} +6.49828i q^{31} +(-4.57243 + 3.33060i) q^{32} +(-3.24914 + 3.24914i) q^{33} +(0.0969726 - 0.0659371i) q^{34} +(-9.74742 - 3.24914i) q^{35} +(1.85991 + 0.735342i) q^{36} +1.88273 q^{37} +(-7.12457 + 4.84439i) q^{38} +(0.638369 - 6.29226i) q^{40} +4.00000i q^{41} +(-3.65389 - 5.37371i) q^{42} -4.61555 q^{43} +(3.65389 + 8.43234i) q^{44} +(-2.00000 + 1.00000i) q^{45} +(4.84439 + 7.12457i) q^{46} +(6.80605 - 6.80605i) q^{47} +(2.73534 - 2.91855i) q^{48} +14.1138i q^{49} +(4.76294 + 5.22632i) q^{50} +(-0.0586332 + 0.0586332i) q^{51} -9.11383i q^{53} +(-1.38923 - 0.264658i) q^{54} +(-9.74742 - 3.24914i) q^{55} +(-12.6815 + 2.84439i) q^{56} +(4.30777 - 4.30777i) q^{57} +(1.12457 + 1.65389i) q^{58} +(-1.36641 + 1.36641i) q^{59} +(0.389229 + 4.45517i) q^{60} +(-2.05863 - 2.05863i) q^{61} +(-9.02760 - 1.71982i) q^{62} +(3.24914 + 3.24914i) q^{63} +(-3.41683 - 7.23362i) q^{64} +(-3.65389 - 5.37371i) q^{66} -12.3810 q^{67} +(0.0659371 + 0.152168i) q^{68} +(-4.30777 - 4.30777i) q^{69} +(7.09353 - 12.6815i) q^{70} +8.99656 q^{71} +(-1.51380 + 2.38923i) q^{72} +(1.11727 + 1.11727i) q^{73} +(-0.498281 + 2.61555i) q^{74} +(-4.00000 - 3.00000i) q^{75} +(-4.84439 - 11.1798i) q^{76} +21.1138i q^{77} +8.99656 q^{79} +(8.57243 + 2.55214i) q^{80} +1.00000 q^{81} +(-5.55691 - 1.05863i) q^{82} -4.99656i q^{83} +(8.43234 - 3.65389i) q^{84} +(-0.175899 - 0.0586332i) q^{85} +(1.22154 - 6.41205i) q^{86} +(-1.00000 - 1.00000i) q^{87} +(-12.6815 + 2.84439i) q^{88} +4.11727 q^{89} +(-0.859912 - 3.04312i) q^{90} +(-11.1798 + 4.84439i) q^{92} +6.49828 q^{93} +(7.65389 + 11.2564i) q^{94} +(12.9233 + 4.30777i) q^{95} +(3.33060 + 4.57243i) q^{96} +(9.99656 + 9.99656i) q^{97} +(-19.6073 - 3.73534i) q^{98} +(3.24914 + 3.24914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9	$ 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 10 q^{19} - 8 q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 18 q^{25} + 14 q^{28} + 6 q^{29} + 2 q^{30} - 12 q^{32} - 2 q^{33} + 26 q^{34} - 6 q^{35} + 2 q^{36} + 8 q^{37} - 34 q^{38} - 22 q^{40} - 14 q^{42} + 4 q^{43} + 14 q^{44} - 12 q^{45} + 2 q^{46} - 10 q^{47} + 16 q^{48} - 6 q^{50} - 2 q^{51} - 6 q^{55} - 34 q^{56} + 10 q^{57} - 2 q^{58} + 6 q^{59} - 6 q^{60} - 14 q^{61} - 20 q^{62} + 2 q^{63} + 22 q^{64} - 14 q^{66} - 36 q^{67} - 10 q^{68} - 10 q^{69} - 2 q^{70} - 16 q^{71} + 8 q^{72} + 10 q^{73} + 32 q^{74} - 24 q^{75} - 2 q^{76} - 16 q^{79} + 36 q^{80} + 6 q^{81} + 26 q^{84} - 6 q^{85} + 24 q^{86} - 6 q^{87} - 34 q^{88} + 28 q^{89} + 4 q^{90} + 10 q^{92} + 4 q^{93} + 38 q^{94} + 30 q^{95} + 10 q^{96} - 10 q^{97} - 56 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 10 * q^19 - 8 * q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 18 * q^25 + 14 * q^28 + 6 * q^29 + 2 * q^30 - 12 * q^32 - 2 * q^33 + 26 * q^34 - 6 * q^35 + 2 * q^36 + 8 * q^37 - 34 * q^38 - 22 * q^40 - 14 * q^42 + 4 * q^43 + 14 * q^44 - 12 * q^45 + 2 * q^46 - 10 * q^47 + 16 * q^48 - 6 * q^50 - 2 * q^51 - 6 * q^55 - 34 * q^56 + 10 * q^57 - 2 * q^58 + 6 * q^59 - 6 * q^60 - 14 * q^61 - 20 * q^62 + 2 * q^63 + 22 * q^64 - 14 * q^66 - 36 * q^67 - 10 * q^68 - 10 * q^69 - 2 * q^70 - 16 * q^71 + 8 * q^72 + 10 * q^73 + 32 * q^74 - 24 * q^75 - 2 * q^76 - 16 * q^79 + 36 * q^80 + 6 * q^81 + 26 * q^84 - 6 * q^85 + 24 * q^86 - 6 * q^87 - 34 * q^88 + 28 * q^89 + 4 * q^90 + 10 * q^92 + 4 * q^93 + 38 * q^94 + 30 * q^95 + 10 * q^96 - 10 * q^97 - 56 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.264658	+	1.38923i	−0.187142	+	0.982333i
$2$	−0.264658	+	1.38923i	−0.187142	+	0.982333i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.85991	−	0.735342i	−0.929956	−	0.367671i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$	1.38923	+	0.264658i	0.567150	+	0.108046i
$7$	−3.24914	−	3.24914i	−1.22806	−	1.22806i	−0.964697	−	0.263363i	$-0.915168\pi$
$7$	−3.24914	−	3.24914i	−1.22806	−	1.22806i	−0.263363	−	0.964697i	$-0.584832\pi$
$8$	1.51380	−	2.38923i	0.535209	−	0.844720i
$9$	−1.00000			−0.333333
$10$	0.859912	+	3.04312i	0.271928	+	0.962318i
$11$	−3.24914	−	3.24914i	−0.979653	−	0.979653i	0.0201443	−	0.999797i	$-0.493587\pi$
$11$	−3.24914	−	3.24914i	−0.979653	−	0.979653i	−0.999797	+	0.0201443i	$0.993587\pi$
$12$	−0.735342	+	1.85991i	−0.212275	+	0.536910i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	5.37371	−	3.65389i	1.43618	−	0.976542i
$15$	−1.00000	−	2.00000i	−0.258199	−	0.516398i
$16$	2.91855	+	2.73534i	0.729636	+	0.683835i
$17$	−0.0586332	−	0.0586332i	−0.0142206	−	0.0142206i	0.699961	−	0.714181i	$-0.253201\pi$
$17$	−0.0586332	−	0.0586332i	−0.0142206	−	0.0142206i	−0.714181	+	0.699961i	$0.753201\pi$
$18$	0.264658	−	1.38923i	0.0623806	−	0.327444i
$19$	4.30777	+	4.30777i	0.988271	+	0.988271i	0.999932	−	0.0116609i	$-0.00371188\pi$
$19$	4.30777	+	4.30777i	0.988271	+	0.988271i	−0.0116609	+	0.999932i	$0.503712\pi$
$20$	−4.45517	+	0.389229i	−0.996205	+	0.0870342i
$21$	−3.24914	+	3.24914i	−0.709021	+	0.709021i
$22$	5.37371	−	3.65389i	1.14568	−	0.779011i
$23$	4.30777	−	4.30777i	0.898233	−	0.898233i	−0.0970469	−	0.995280i	$-0.530940\pi$
$23$	4.30777	−	4.30777i	0.898233	−	0.898233i	0.995280	+	0.0970469i	$0.0309397\pi$
$24$	−2.38923	−	1.51380i	−0.487699	−	0.309003i
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$			1.00000i			0.192450i
$28$	3.65389	+	8.43234i	0.690520	+	1.59356i
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	−0.608137	−	0.793832i	$-0.708083\pi$
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	0.793832	+	0.608137i	$0.208083\pi$
$30$	3.04312	−	0.859912i	0.555594	−	0.156998i
$31$			6.49828i			1.16713i	0.812068	+	0.583563i	$0.198342\pi$
$31$			6.49828i			1.16713i	−0.812068	+	0.583563i	$0.801658\pi$
$32$	−4.57243	+	3.33060i	−0.808299	+	0.588772i
$33$	−3.24914	+	3.24914i	−0.565603	+	0.565603i
$34$	0.0969726	−	0.0659371i	0.0166307	−	0.0113081i
$35$	−9.74742	−	3.24914i	−1.64761	−	0.549205i
$36$	1.85991	+	0.735342i	0.309985	+	0.122557i
$37$	1.88273			0.309520			0.154760	−	0.987952i	$-0.450540\pi$
$37$	1.88273			0.309520			0.154760	+	0.987952i	$0.450540\pi$
$38$	−7.12457	+	4.84439i	−1.15576	+	0.785865i
$39$		0			0
$40$	0.638369	−	6.29226i	0.100935	−	0.994893i
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$	−3.65389	−	5.37371i	−0.563807	−	0.829182i
$43$	−4.61555			−0.703864			−0.351932	−	0.936025i	$-0.614475\pi$
$43$	−4.61555			−0.703864			−0.351932	+	0.936025i	$0.614475\pi$
$44$	3.65389	+	8.43234i	0.550844	+	1.27122i
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	4.84439	+	7.12457i	0.714267	+	1.05046i
$47$	6.80605	−	6.80605i	0.992765	−	0.992765i	−0.00720889	−	0.999974i	$-0.502295\pi$
$47$	6.80605	−	6.80605i	0.992765	−	0.992765i	0.999974	+	0.00720889i	$0.00229468\pi$
$48$	2.73534	−	2.91855i	0.394813	−	0.421256i
$49$			14.1138i			2.01626i
$50$	4.76294	+	5.22632i	0.673581	+	0.739113i
$51$	−0.0586332	+	0.0586332i	−0.00821028	+	0.00821028i
$52$		0			0
$53$		−	9.11383i		−	1.25188i	−0.779871	−	0.625940i	$-0.784715\pi$
$53$		−	9.11383i		−	1.25188i	0.779871	−	0.625940i	$-0.215285\pi$
$54$	−1.38923	−	0.264658i	−0.189050	−	0.0360154i
$55$	−9.74742	−	3.24914i	−1.31434	−	0.438114i
$56$	−12.6815	+	2.84439i	−1.69463	+	0.380098i
$57$	4.30777	−	4.30777i	0.570579	−	0.570579i
$58$	1.12457	+	1.65389i	0.147663	+	0.217166i
$59$	−1.36641	+	1.36641i	−0.177891	+	0.177891i	−0.790436	−	0.612545i	$-0.790146\pi$
$59$	−1.36641	+	1.36641i	−0.177891	+	0.177891i	0.612545	+	0.790436i	$0.290146\pi$
$60$	0.389229	+	4.45517i	0.0502492	+	0.575159i
$61$	−2.05863	−	2.05863i	−0.263581	−	0.263581i	0.562926	−	0.826507i	$-0.309676\pi$
$61$	−2.05863	−	2.05863i	−0.263581	−	0.263581i	−0.826507	+	0.562926i	$0.809676\pi$
$62$	−9.02760	−	1.71982i	−1.14651	−	0.218418i
$63$	3.24914	+	3.24914i	0.409353	+	0.409353i
$64$	−3.41683	−	7.23362i	−0.427103	−	0.904203i
$65$		0			0
$66$	−3.65389	−	5.37371i	−0.449762	−	0.661458i
$67$	−12.3810			−1.51258			−0.756291	−	0.654236i	$-0.772990\pi$
$67$	−12.3810			−1.51258			−0.756291	+	0.654236i	$0.772990\pi$
$68$	0.0659371	+	0.152168i	0.00799605	+	0.0184531i
$69$	−4.30777	−	4.30777i	−0.518595	−	0.518595i
$70$	7.09353	−	12.6815i	0.847840	−	1.51573i
$71$	8.99656			1.06770			0.533848	−	0.845581i	$-0.320746\pi$
$71$	8.99656			1.06770			0.533848	+	0.845581i	$0.320746\pi$
$72$	−1.51380	+	2.38923i	−0.178403	+	0.281573i
$73$	1.11727	+	1.11727i	0.130766	+	0.130766i	0.769461	−	0.638694i	$-0.220525\pi$
$73$	1.11727	+	1.11727i	0.130766	+	0.130766i	−0.638694	+	0.769461i	$0.720525\pi$
$74$	−0.498281	+	2.61555i	−0.0579240	+	0.304051i
$75$	−4.00000	−	3.00000i	−0.461880	−	0.346410i
$76$	−4.84439	−	11.1798i	−0.555690	−	1.28241i
$77$			21.1138i			2.40614i
$78$		0			0
$79$	8.99656			1.01219			0.506096	−	0.862477i	$-0.331088\pi$
$79$	8.99656			1.01219			0.506096	+	0.862477i	$0.331088\pi$
$80$	8.57243	+	2.55214i	0.958427	+	0.285338i
$81$	1.00000			0.111111
$82$	−5.55691	−	1.05863i	−0.613659	−	0.116906i
$83$		−	4.99656i		−	0.548444i	−0.961666	−	0.274222i	$-0.911580\pi$
$83$		−	4.99656i		−	0.548444i	0.961666	−	0.274222i	$-0.0884203\pi$
$84$	8.43234	−	3.65389i	0.920044	−	0.398672i
$85$	−0.175899	−	0.0586332i	−0.0190790	−	0.00635966i
$86$	1.22154	−	6.41205i	0.131722	−	0.691429i
$87$	−1.00000	−	1.00000i	−0.107211	−	0.107211i
$88$	−12.6815	+	2.84439i	−1.35185	+	0.303213i
$89$	4.11727			0.436429			0.218215	−	0.975901i	$-0.429977\pi$
$89$	4.11727			0.436429			0.218215	+	0.975901i	$0.429977\pi$
$90$	−0.859912	−	3.04312i	−0.0906427	−	0.320773i
$91$		0			0
$92$	−11.1798	+	4.84439i	−1.16557	+	0.505063i
$93$	6.49828			0.673840
$94$	7.65389	+	11.2564i	0.789438	+	1.16101i
$95$	12.9233	+	4.30777i	1.32590	+	0.441968i
$96$	3.33060	+	4.57243i	0.339927	+	0.466672i
$97$	9.99656	+	9.99656i	1.01500	+	1.01500i	0.999886	+	0.0151113i	$0.00481026\pi$
$97$	9.99656	+	9.99656i	1.01500	+	1.01500i	0.0151113	+	0.999886i	$0.495190\pi$
$98$	−19.6073	−	3.73534i	−1.98064	−	0.377326i
$99$	3.24914	+	3.24914i	0.326551	+	0.326551i
$100$	−8.52110	+	5.23362i	−0.852110	+	0.523362i
$101$	−2.88273	+	2.88273i	−0.286843	+	0.286843i	−0.835830	−	0.548988i	$-0.815013\pi$
$101$	−2.88273	+	2.88273i	−0.286843	+	0.286843i	0.548988	+	0.835830i	$0.315013\pi$
$102$	−0.0659371	−	0.0969726i	−0.00652875	−	0.00960172i
$103$	5.36641	−	5.36641i	0.528768	−	0.528768i	−0.391437	−	0.920205i	$-0.628022\pi$
$103$	5.36641	−	5.36641i	0.528768	−	0.528768i	0.920205	+	0.391437i	$0.128022\pi$
$104$		0			0
$105$	−3.24914	+	9.74742i	−0.317084	+	0.951251i
$106$	12.6612	+	2.41205i	1.22976	+	0.234279i
$107$			17.2311i			1.66579i	0.553429	+	0.832896i	$0.313319\pi$
$107$			17.2311i			1.66579i	−0.553429	+	0.832896i	$0.686681\pi$
$108$	0.735342	−	1.85991i	0.0707583	−	0.178970i
$109$	7.05520	−	7.05520i	0.675765	−	0.675765i	−0.283274	−	0.959039i	$-0.591421\pi$
$109$	7.05520	−	7.05520i	0.675765	−	0.675765i	0.959039	+	0.283274i	$0.0914205\pi$
$110$	7.09353	−	12.6815i	0.676342	−	1.20913i
$111$		−	1.88273i		−	0.178701i
$112$	−0.595254	−	18.3703i	−0.0562462	−	1.73583i
$113$	2.05863	−	2.05863i	0.193660	−	0.193660i	−0.603616	−	0.797276i	$-0.706274\pi$
$113$	2.05863	−	2.05863i	0.193660	−	0.193660i	0.797276	+	0.603616i	$0.206274\pi$
$114$	4.84439	+	7.12457i	0.453719	+	0.667277i
$115$	4.30777	−	12.9233i	0.401702	−	1.20511i
$116$	−2.59525	+	1.12457i	−0.240963	+	0.104414i
$117$		0			0
$118$	−1.53662	−	2.25988i	−0.141457	−	0.208039i
$119$			0.381015i			0.0349276i
$120$	−6.29226	−	0.638369i	−0.574402	−	0.0582749i
$121$			10.1138i			0.919439i
$122$	3.40475	−	2.31508i	0.308251	−	0.209597i
$123$	4.00000			0.360668
$124$	4.77846	−	12.0862i	0.429118	−	1.08538i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−5.37371	+	3.65389i	−0.478728	+	0.325514i
$127$	−7.24914	+	7.24914i	−0.643257	+	0.643257i	−0.951355	−	0.308098i	$-0.900308\pi$
$127$	−7.24914	+	7.24914i	−0.643257	+	0.643257i	0.308098	+	0.951355i	$0.400308\pi$
$128$	10.9534	−	2.83231i	0.968157	−	0.250344i
$129$			4.61555i			0.406376i
$130$		0			0
$131$	9.13187	−	9.13187i	0.797856	−	0.797856i	−0.184902	−	0.982757i	$-0.559197\pi$
$131$	9.13187	−	9.13187i	0.797856	−	0.797856i	0.982757	+	0.184902i	$0.0591966\pi$
$132$	8.43234	−	3.65389i	0.733941	−	0.318030i
$133$		−	27.9931i		−	2.42731i
$134$	3.27674	−	17.2001i	0.283067	−	1.48586i
$135$	1.00000	+	2.00000i	0.0860663	+	0.172133i
$136$	−0.228847	+	0.0513292i	−0.0196235	+	0.00440144i
$137$	5.05520	−	5.05520i	0.431894	−	0.431894i	−0.457378	−	0.889272i	$-0.651211\pi$
$137$	5.05520	−	5.05520i	0.431894	−	0.431894i	0.889272	+	0.457378i	$0.151211\pi$
$138$	7.12457	−	4.84439i	0.606484	−	0.412382i
$139$	−6.19051	+	6.19051i	−0.525072	+	0.525072i	−0.919099	−	0.394027i	$-0.871082\pi$
$139$	−6.19051	+	6.19051i	−0.525072	+	0.525072i	0.394027	+	0.919099i	$0.371082\pi$
$140$	15.7401	+	13.2108i	1.33028	+	1.11652i
$141$	−6.80605	−	6.80605i	−0.573173	−	0.573173i
$142$	−2.38101	+	12.4983i	−0.199810	+	1.04883i
$143$		0			0
$144$	−2.91855	−	2.73534i	−0.243212	−	0.227945i
$145$	1.00000	−	3.00000i	0.0830455	−	0.249136i
$146$	−1.84783	+	1.25644i	−0.152928	+	0.103984i
$147$	14.1138			1.16409
$148$	−3.50172	−	1.38445i	−0.287840	−	0.113801i
$149$	−0.882734	−	0.882734i	−0.0723164	−	0.0723164i	0.670024	−	0.742340i	$-0.266284\pi$
$149$	−0.882734	−	0.882734i	−0.0723164	−	0.0723164i	−0.742340	+	0.670024i	$0.766284\pi$
$150$	5.22632	−	4.76294i	0.426727	−	0.388892i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	16.8134	−	3.77115i	1.36374	−	0.305881i
$153$	0.0586332	+	0.0586332i	0.00474021	+	0.00474021i
$154$	−29.3319	−	5.58795i	−2.36363	−	0.450290i
$155$	6.49828	+	12.9966i	0.521954	+	1.04391i
$156$		0			0
$157$		−	9.76547i		−	0.779369i	−0.920948	−	0.389685i	$-0.872584\pi$
$157$		−	9.76547i		−	0.779369i	0.920948	−	0.389685i	$-0.127416\pi$
$158$	−2.38101	+	12.4983i	−0.189423	+	0.994310i
$159$	−9.11383			−0.722774
$160$	−5.81427	+	11.2336i	−0.459658	+	0.888096i
$161$	−27.9931			−2.20617
$162$	−0.264658	+	1.38923i	−0.0207935	+	0.109148i
$163$			20.9966i			1.64458i	0.569070	+	0.822289i	$0.307303\pi$
$163$			20.9966i			1.64458i	−0.569070	+	0.822289i	$0.692697\pi$
$164$	2.94137	−	7.43965i	0.229682	−	0.580939i
$165$	−3.24914	+	9.74742i	−0.252945	+	0.758836i
$166$	6.94137	+	1.32238i	0.538755	+	0.102637i
$167$	−2.42504	−	2.42504i	−0.187655	−	0.187655i	0.607026	−	0.794682i	$-0.292362\pi$
$167$	−2.42504	−	2.42504i	−0.187655	−	0.187655i	−0.794682	+	0.607026i	$0.792362\pi$
$168$	2.84439	+	12.6815i	0.219450	+	0.978398i
$169$	−13.0000			−1.00000
$170$	0.128008	−	0.228847i	0.00981777	−	0.0175518i
$171$	−4.30777	−	4.30777i	−0.329424	−	0.329424i
$172$	8.58451	+	3.39400i	0.654563	+	0.258790i
$173$	−0.234533			−0.0178312			−0.00891559	−	0.999960i	$-0.502838\pi$
$173$	−0.234533			−0.0178312			−0.00891559	+	0.999960i	$0.502838\pi$
$174$	1.65389	−	1.12457i	0.125381	−	0.0852535i
$175$	−22.7440	+	3.24914i	−1.71928	+	0.245612i
$176$	−0.595254	−	18.3703i	−0.0448689	−	1.38471i
$177$	1.36641	+	1.36641i	0.102705	+	0.102705i
$178$	−1.08967	+	5.71982i	−0.0816741	+	0.428719i
$179$	5.13187	+	5.13187i	0.383574	+	0.383574i	0.872388	−	0.488814i	$-0.162570\pi$
$179$	5.13187	+	5.13187i	0.383574	+	0.383574i	−0.488814	+	0.872388i	$0.662570\pi$
$180$	4.45517	−	0.389229i	0.332068	−	0.0290114i
$181$	0.0586332	−	0.0586332i	0.00435817	−	0.00435817i	−0.704924	−	0.709283i	$-0.749019\pi$
$181$	0.0586332	−	0.0586332i	0.00435817	−	0.00435817i	0.709283	+	0.704924i	$0.249019\pi$
$182$		0			0
$183$	−2.05863	+	2.05863i	−0.152179	+	0.152179i
$184$	−3.77115	−	16.8134i	−0.278013	−	1.23950i
$185$	3.76547	−	1.88273i	0.276843	−	0.138421i
$186$	−1.71982	+	9.02760i	−0.126104	+	0.661936i
$187$			0.381015i			0.0278626i
$188$	−17.6634	+	7.65389i	−1.28824	+	0.558217i
$189$	3.24914	−	3.24914i	0.236340	−	0.236340i
$190$	−9.40475	+	16.8134i	−0.682292	+	1.21977i
$191$		−	20.6155i		−	1.49169i	−0.666120	−	0.745844i	$-0.732046\pi$
$191$		−	20.6155i		−	1.49169i	0.666120	−	0.745844i	$-0.267954\pi$
$192$	−7.23362	+	3.41683i	−0.522042	+	0.246588i
$193$	13.9966	−	13.9966i	1.00749	−	1.00749i	0.00752289	−	0.999972i	$-0.497605\pi$
$193$	13.9966	−	13.9966i	1.00749	−	1.00749i	0.999972	−	0.00752289i	$-0.00239463\pi$
$194$	−16.5332	+	11.2418i	−1.18701	+	0.807117i
$195$		0			0
$196$	10.3785	−	26.2505i	0.741320	−	1.87503i
$197$	−14.8793			−1.06011			−0.530053	−	0.847965i	$-0.677828\pi$
$197$	−14.8793			−1.06011			−0.530053	+	0.847965i	$0.677828\pi$
$198$	−5.37371	+	3.65389i	−0.381893	+	0.259670i
$199$			18.4983i			1.31131i	0.755061	+	0.655654i	$0.227607\pi$
$199$			18.4983i			1.31131i	−0.755061	+	0.655654i	$0.772393\pi$
$200$	−5.01552	−	13.2229i	−0.354651	−	0.934999i
$201$			12.3810i			0.873289i
$202$	−3.24184	−	4.76772i	−0.228095	−	0.335455i
$203$	−6.49828			−0.456090
$204$	0.152168	−	0.0659371i	0.0106539	−	0.00461652i
$205$	4.00000	+	8.00000i	0.279372	+	0.558744i
$206$	6.03490	+	8.87543i	0.420472	+	0.618380i
$207$	−4.30777	+	4.30777i	−0.299411	+	0.299411i
$208$		0			0
$209$		−	27.9931i		−	1.93632i
$210$	−12.6815	−	7.09353i	−0.875106	−	0.489500i
$211$	−8.92332	+	8.92332i	−0.614307	+	0.614307i	−0.944065	−	0.329759i	$-0.893033\pi$
$211$	−8.92332	+	8.92332i	−0.614307	+	0.614307i	0.329759	+	0.944065i	$0.393033\pi$
$212$	−6.70178	+	16.9509i	−0.460280	+	1.16419i
$213$		−	8.99656i		−	0.616434i
$214$	−23.9379	−	4.56035i	−1.63636	−	0.311739i
$215$	−9.23109	+	4.61555i	−0.629555	+	0.314778i
$216$	2.38923	+	1.51380i	0.162566	+	0.103001i
$217$	21.1138	−	21.1138i	1.43330	−	1.43330i
$218$	7.93406	+	11.6685i	0.537363	+	0.790290i
$219$	1.11727	−	1.11727i	0.0754979	−	0.0754979i
$220$	15.7401	+	13.2108i	1.06120	+	0.890672i
$221$		0			0
$222$	2.61555	+	0.498281i	0.175544	+	0.0334424i
$223$	13.1319	+	13.1319i	0.879375	+	0.879375i	0.993470	−	0.114095i	$-0.0363967\pi$
$223$	13.1319	+	13.1319i	0.879375	+	0.879375i	−0.114095	+	0.993470i	$0.536397\pi$
$224$	25.6780	+	4.03490i	1.71569	+	0.269593i
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	2.31508	+	3.40475i	0.153997	+	0.226480i
$227$	1.50172			0.0996726			0.0498363	−	0.998757i	$-0.484130\pi$
$227$	1.50172			0.0996726			0.0498363	+	0.998757i	$0.484130\pi$
$228$	−11.1798	+	4.84439i	−0.740398	+	0.320828i
$229$	7.05520	+	7.05520i	0.466220	+	0.466220i	0.900688	−	0.434467i	$-0.143063\pi$
$229$	7.05520	+	7.05520i	0.466220	+	0.466220i	−0.434467	+	0.900688i	$0.643063\pi$
$230$	16.8134	+	9.40475i	1.10864	+	0.620131i
$231$	21.1138			1.38919
$232$	−0.875430	−	3.90303i	−0.0574748	−	0.256246i
$233$	9.05520	+	9.05520i	0.593226	+	0.593226i	0.938501	−	0.345276i	$-0.112215\pi$
$233$	9.05520	+	9.05520i	0.593226	+	0.593226i	−0.345276	+	0.938501i	$0.612215\pi$
$234$		0			0
$235$	6.80605	−	20.4182i	0.443978	−	1.33193i
$236$	3.54617	−	1.53662i	0.230836	−	0.100025i
$237$		−	8.99656i		−	0.584390i
$238$	−0.529317	−	0.100839i	−0.0343105	−	0.00653640i
$239$	16.9966			1.09942			0.549708	−	0.835357i	$-0.314739\pi$
$239$	16.9966			1.09942			0.549708	+	0.835357i	$0.314739\pi$
$240$	2.55214	−	8.57243i	0.164740	−	0.553348i
$241$	−23.9931			−1.54553			−0.772767	−	0.634690i	$-0.781128\pi$
$241$	−23.9931			−1.54553			−0.772767	+	0.634690i	$0.781128\pi$
$242$	−14.0504	−	2.67671i	−0.903195	−	0.172065i
$243$		−	1.00000i		−	0.0641500i
$244$	2.31508	+	5.34268i	0.148208	+	0.342030i
$245$	14.1138	+	28.2277i	0.901699	+	1.80340i
$246$	−1.05863	+	5.55691i	−0.0674960	+	0.354296i
$247$		0			0
$248$	15.5259	+	9.83709i	0.985894	+	0.624656i
$249$	−4.99656			−0.316644
$250$	14.7522	+	5.68970i	0.933011	+	0.359848i
$251$	−7.24914	−	7.24914i	−0.457562	−	0.457562i	0.440293	−	0.897854i	$-0.354875\pi$
$251$	−7.24914	−	7.24914i	−0.457562	−	0.457562i	−0.897854	+	0.440293i	$0.854875\pi$
$252$	−3.65389	−	8.43234i	−0.230173	−	0.531188i
$253$	−27.9931			−1.75991
$254$	−8.15217	−	11.9893i	−0.511513	−	0.752273i
$255$	−0.0586332	+	0.175899i	−0.00367175	+	0.0110153i
$256$	1.03581	+	15.9664i	0.0647382	+	0.997902i
$257$	−3.17246	−	3.17246i	−0.197893	−	0.197893i	0.601203	−	0.799096i	$-0.294688\pi$
$257$	−3.17246	−	3.17246i	−0.197893	−	0.197893i	−0.799096	+	0.601203i	$0.794688\pi$
$258$	−6.41205	−	1.22154i	−0.399197	−	0.0760499i
$259$	−6.11727	−	6.11727i	−0.380108	−	0.380108i
$260$		0			0
$261$	−1.00000	+	1.00000i	−0.0618984	+	0.0618984i
$262$	10.2694	+	15.1031i	0.634448	+	0.933072i
$263$	−20.6888	+	20.6888i	−1.27573	+	1.27573i	−0.332689	+	0.943037i	$0.607956\pi$
$263$	−20.6888	+	20.6888i	−1.27573	+	1.27573i	−0.943037	+	0.332689i	$0.892044\pi$
$264$	2.84439	+	12.6815i	0.175060	+	0.780491i
$265$	−9.11383	−	18.2277i	−0.559858	−	1.11972i
$266$	38.8888	+	7.40861i	2.38443	+	0.454251i
$267$		−	4.11727i		−	0.251973i
$268$	23.0276	+	9.10428i	1.40663	+	0.556132i
$269$	−17.8793	+	17.8793i	−1.09012	+	1.09012i	−0.0946050	+	0.995515i	$0.530159\pi$
$269$	−17.8793	+	17.8793i	−1.09012	+	1.09012i	−0.995515	+	0.0946050i	$0.969841\pi$
$270$	−3.04312	+	0.859912i	−0.185198	+	0.0523326i
$271$		−	18.4983i		−	1.12369i	−0.827242	−	0.561845i	$-0.810092\pi$
$271$		−	18.4983i		−	1.12369i	0.827242	−	0.561845i	$-0.189908\pi$
$272$	−0.0107418	−	0.331505i	−0.000651317	−	0.0201005i
$273$		0			0
$274$	5.68492	+	8.36072i	0.343439	+	0.505090i
$275$	−22.7440	+	3.24914i	−1.37151	+	0.195931i
$276$	4.84439	+	11.1798i	0.291598	+	0.672943i
$277$	−16.1104			−0.967980			−0.483990	−	0.875074i	$-0.660813\pi$
$277$	−16.1104			−0.967980			−0.483990	+	0.875074i	$0.660813\pi$
$278$	−6.96166	−	10.2384i	−0.417533	−	0.614058i
$279$		−	6.49828i		−	0.389042i
$280$	−22.5186	+	18.3703i	−1.34574	+	1.09783i
$281$		−	10.1173i		−	0.603546i	−0.953380	−	0.301773i	$-0.902422\pi$
$281$		−	10.1173i		−	0.603546i	0.953380	−	0.301773i	$-0.0975784\pi$
$282$	11.2564	−	7.65389i	0.670312	−	0.455782i
$283$	−5.61211			−0.333605			−0.166803	−	0.985990i	$-0.553344\pi$
$283$	−5.61211			−0.333605			−0.166803	+	0.985990i	$0.553344\pi$
$284$	−16.7328	−	6.61555i	−0.992910	−	0.392561i
$285$	4.30777	−	12.9233i	0.255170	−	0.765511i
$286$		0			0
$287$	12.9966	−	12.9966i	0.767163	−	0.767163i
$288$	4.57243	−	3.33060i	0.269433	−	0.196257i
$289$		−	16.9931i		−	0.999596i
$290$	3.90303	+	2.18320i	0.229194	+	0.128202i
$291$	9.99656	−	9.99656i	0.586009	−	0.586009i
$292$	−1.25644	−	2.89959i	−0.0735279	−	0.169686i
$293$			20.2277i			1.18171i	0.806777	+	0.590856i	$0.201210\pi$
$293$			20.2277i			1.18171i	−0.806777	+	0.590856i	$0.798790\pi$
$294$	−3.73534	+	19.6073i	−0.217850	+	1.14352i
$295$	−1.36641	+	4.09922i	−0.0795553	+	0.238666i
$296$	2.85008	−	4.49828i	0.165658	−	0.261457i
$297$	3.24914	−	3.24914i	0.188534	−	0.188534i
$298$	1.45994	−	0.992696i	0.0845721	−	0.0575053i
$299$		0			0
$300$	5.23362	+	8.52110i	0.302163	+	0.491966i
$301$	14.9966	+	14.9966i	0.864387	+	0.864387i
$302$		0			0
$303$	2.88273	+	2.88273i	0.165609	+	0.165609i
$304$	0.789199	+	24.3557i	0.0452637	+	1.39689i
$305$	−6.17590	−	2.05863i	−0.353631	−	0.117877i
$306$	−0.0969726	+	0.0659371i	−0.00554356	+	0.00376937i
$307$	20.6155			1.17659			0.588296	−	0.808646i	$-0.299799\pi$
$307$	20.6155			1.17659			0.588296	+	0.808646i	$0.299799\pi$
$308$	15.5259	−	39.2699i	0.884669	−	2.23761i
$309$	−5.36641	−	5.36641i	−0.305284	−	0.305284i
$310$	−19.7750	+	5.58795i	−1.12315	+	0.317374i
$311$	21.2311			1.20390			0.601952	−	0.798532i	$-0.294390\pi$
$311$	21.2311			1.20390			0.601952	+	0.798532i	$0.294390\pi$
$312$		0			0
$313$	3.00000	+	3.00000i	0.169570	+	0.169570i	0.786790	−	0.617220i	$-0.211741\pi$
$313$	3.00000	+	3.00000i	0.169570	+	0.169570i	−0.617220	+	0.786790i	$0.711741\pi$
$314$	13.5665	+	2.58451i	0.765600	+	0.145852i
$315$	9.74742	+	3.24914i	0.549205	+	0.183068i
$316$	−16.7328	−	6.61555i	−0.941294	−	0.372154i
$317$			1.11383i			0.0625588i	0.999511	+	0.0312794i	$0.00995817\pi$
$317$			1.11383i			0.0625588i	−0.999511	+	0.0312794i	$0.990042\pi$
$318$	2.41205	−	12.6612i	0.135261	−	0.710004i
$319$	−6.49828			−0.363834
$320$	−14.0673	−	11.0504i	−0.786385	−	0.617737i
$321$	17.2311			0.961746
$322$	7.40861	−	38.8888i	0.412866	−	2.16719i
$323$		−	0.505157i		−	0.0281077i
$324$	−1.85991	−	0.735342i	−0.103328	−	0.0408523i
$325$		0			0
$326$	−29.1690	−	5.55691i	−1.61552	−	0.307769i
$327$	−7.05520	−	7.05520i	−0.390153	−	0.390153i
$328$	9.55691	+	6.05520i	0.527692	+	0.334342i
$329$	−44.2277			−2.43835
$330$	−12.6815	−	7.09353i	−0.698093	−	0.390486i
$331$	8.92332	+	8.92332i	0.490470	+	0.490470i	0.908454	−	0.417984i	$-0.137263\pi$
$331$	8.92332	+	8.92332i	0.490470	+	0.490470i	−0.417984	+	0.908454i	$0.637263\pi$
$332$	−3.67418	+	9.29317i	−0.201647	+	0.510029i
$333$	−1.88273			−0.103173
$334$	4.01074	−	2.72713i	0.219458	−	0.149222i
$335$	−24.7620	+	12.3810i	−1.35289	+	0.676447i
$336$	−18.3703	+	0.595254i	−1.00218	+	0.0324738i
$337$	−2.00344	−	2.00344i	−0.109134	−	0.109134i	0.650431	−	0.759565i	$-0.274588\pi$
$337$	−2.00344	−	2.00344i	−0.109134	−	0.109134i	−0.759565	+	0.650431i	$0.774588\pi$
$338$	3.44056	−	18.0600i	0.187142	−	0.982333i
$339$	−2.05863	−	2.05863i	−0.111810	−	0.111810i
$340$	0.284042	+	0.238399i	0.0154043	+	0.0129290i
$341$	21.1138	−	21.1138i	1.14338	−	1.14338i
$342$	7.12457	−	4.84439i	0.385253	−	0.261955i
$343$	23.1138	−	23.1138i	1.24803	−	1.24803i
$344$	−6.98701	+	11.0276i	−0.376714	+	0.594568i
$345$	−12.9233	−	4.30777i	−0.695768	−	0.231923i
$346$	0.0620710	−	0.325819i	0.00333696	−	0.0175162i
$347$			0.234533i			0.0125904i	0.999980	+	0.00629519i	$0.00200383\pi$
$347$			0.234533i			0.0125904i	−0.999980	+	0.00629519i	$0.997996\pi$
$348$	1.12457	+	2.59525i	0.0602833	+	0.139120i
$349$	21.1725	−	21.1725i	1.13334	−	1.13334i	0.143717	−	0.989619i	$-0.454094\pi$
$349$	21.1725	−	21.1725i	1.13334	−	1.13334i	0.989619	−	0.143717i	$-0.0459055\pi$
$350$	1.50559	−	32.4565i	0.0804769	−	1.73487i
$351$		0			0
$352$	25.6780	+	4.03490i	1.36864	+	0.215061i
$353$	−0.0586332	+	0.0586332i	−0.00312073	+	0.00312073i	−0.708665	−	0.705545i	$-0.750702\pi$
$353$	−0.0586332	+	0.0586332i	−0.00312073	+	0.00312073i	0.705545	+	0.708665i	$0.250702\pi$
$354$	−2.25988	+	1.53662i	−0.120111	+	0.0816705i
$355$	17.9931	−	8.99656i	0.954976	−	0.477488i
$356$	−7.65775	−	3.02760i	−0.405860	−	0.160462i
$357$	0.381015			0.0201654
$358$	−8.48754	+	5.77115i	−0.448580	+	0.305015i
$359$			9.84664i			0.519686i	0.965651	+	0.259843i	$0.0836708\pi$
$359$			9.84664i			0.519686i	−0.965651	+	0.259843i	$0.916329\pi$
$360$	−0.638369	+	6.29226i	−0.0336450	+	0.331631i
$361$			18.1138i			0.953359i
$362$	0.0659371	+	0.0969726i	0.00346558	+	0.00509677i
$363$	10.1138			0.530838
$364$		0			0
$365$	3.35180	+	1.11727i	0.175441	+	0.0584804i
$366$	−2.31508	−	3.40475i	−0.121011	−	0.177969i
$367$	−6.36297	+	6.36297i	−0.332144	+	0.332144i	−0.853400	−	0.521256i	$-0.825464\pi$
$367$	−6.36297	+	6.36297i	−0.332144	+	0.332144i	0.521256	+	0.853400i	$0.325464\pi$
$368$	24.3557	−	0.789199i	1.26963	−	0.0411398i
$369$		−	4.00000i		−	0.208232i
$370$	1.61899	+	5.72938i	0.0841670	+	0.297856i
$371$	−29.6121	+	29.6121i	−1.53738	+	1.53738i
$372$	−12.0862	−	4.77846i	−0.626642	−	0.247751i
$373$			28.2277i			1.46157i	0.682606	+	0.730786i	$0.260846\pi$
$373$			28.2277i			1.46157i	−0.682606	+	0.730786i	$0.739154\pi$
$374$	−0.529317	−	0.100839i	−0.0273703	−	0.00521425i
$375$	−11.0000	−	2.00000i	−0.568038	−	0.103280i
$376$	−5.95822	−	26.5642i	−0.307272	−	1.36994i
$377$		0			0
$378$	3.65389	+	5.37371i	0.187936	+	0.276394i
$379$	19.8026	−	19.8026i	1.01719	−	1.01719i	0.0173425	−	0.999850i	$-0.494479\pi$
$379$	19.8026	−	19.8026i	1.01719	−	1.01719i	0.999850	−	0.0173425i	$-0.00552057\pi$
$380$	−20.8686	−	17.5151i	−1.07053	−	0.898508i
$381$	7.24914	+	7.24914i	0.371385	+	0.371385i
$382$	28.6397	+	5.45608i	1.46533	+	0.279157i
$383$	−7.69223	−	7.69223i	−0.393054	−	0.393054i	0.482720	−	0.875775i	$-0.339649\pi$
$383$	−7.69223	−	7.69223i	−0.393054	−	0.393054i	−0.875775	+	0.482720i	$0.839649\pi$
$384$	−2.83231	−	10.9534i	−0.144536	−	0.558966i
$385$	21.1138	+	42.2277i	1.07606	+	2.15212i
$386$	15.7401	+	23.1487i	0.801151	+	1.17824i
$387$	4.61555			0.234621
$388$	−11.2418	−	25.9436i	−0.570718	−	1.31709i
$389$	−8.88273	−	8.88273i	−0.450372	−	0.450372i	0.445106	−	0.895478i	$-0.353166\pi$
$389$	−8.88273	−	8.88273i	−0.450372	−	0.450372i	−0.895478	+	0.445106i	$0.853166\pi$
$390$		0			0
$391$	−0.505157			−0.0255469
$392$	33.7212	+	21.3655i	1.70318	+	1.07912i
$393$	−9.13187	−	9.13187i	−0.460642	−	0.460642i
$394$	3.93793	−	20.6707i	0.198390	−	1.04138i
$395$	17.9931	−	8.99656i	0.905332	−	0.452666i
$396$	−3.65389	−	8.43234i	−0.183615	−	0.423741i
$397$			8.11727i			0.407394i	0.979034	+	0.203697i	$0.0652957\pi$
$397$			8.11727i			0.407394i	−0.979034	+	0.203697i	$0.934704\pi$
$398$	−25.6983	−	4.89572i	−1.28814	−	0.245400i
$399$	−27.9931			−1.40141
$400$	19.6970	−	3.46816i	0.984850	−	0.173408i
$401$	26.1104			1.30389			0.651945	−	0.758266i	$-0.273953\pi$
$401$	26.1104			1.30389			0.651945	+	0.758266i	$0.273953\pi$
$402$	−17.2001	−	3.27674i	−0.857861	−	0.163429i
$403$		0			0
$404$	7.48143	−	3.24184i	0.372215	−	0.161287i
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	1.71982	−	9.02760i	0.0853534	−	0.448032i
$407$	−6.11727	−	6.11727i	−0.303222	−	0.303222i
$408$	0.0513292	+	0.228847i	0.00254117	+	0.0113296i
$409$	2.65164			0.131115			0.0655576	−	0.997849i	$-0.479117\pi$
$409$	2.65164			0.131115			0.0655576	+	0.997849i	$0.479117\pi$
$410$	−12.1725	+	3.43965i	−0.601155	+	0.169872i
$411$	−5.05520	−	5.05520i	−0.249354	−	0.249354i
$412$	−13.9272	+	6.03490i	−0.686143	+	0.297318i
$413$	8.87930			0.436922
$414$	−4.84439	−	7.12457i	−0.238089	−	0.350154i
$415$	−4.99656	−	9.99312i	−0.245272	−	0.490543i
$416$		0			0
$417$	6.19051	+	6.19051i	0.303150	+	0.303150i
$418$	38.8888	+	7.40861i	1.90212	+	0.362367i
$419$	−7.86469	−	7.86469i	−0.384215	−	0.384215i	0.488403	−	0.872618i	$-0.337580\pi$
$419$	−7.86469	−	7.86469i	−0.384215	−	0.384215i	−0.872618	+	0.488403i	$0.837580\pi$
$420$	13.2108	−	15.7401i	0.644621	−	0.768039i
$421$	−2.94480	+	2.94480i	−0.143521	+	0.143521i	−0.775217	−	0.631696i	$-0.782359\pi$
$421$	−2.94480	+	2.94480i	−0.143521	+	0.143521i	0.631696	+	0.775217i	$0.282359\pi$
$422$	−10.0349	−	14.7582i	−0.488491	−	0.718416i
$423$	−6.80605	+	6.80605i	−0.330922	+	0.330922i
$424$	−21.7750	−	13.7965i	−1.05749	−	0.670017i
$425$	−0.410432	+	0.0586332i	−0.0199089	+	0.00284413i
$426$	12.4983	+	2.38101i	0.605544	+	0.115361i
$427$			13.3776i			0.647386i
$428$	12.6707	−	32.0483i	0.612463	−	1.54911i
$429$		0			0
$430$	−3.96896	−	14.0456i	−0.191400	−	0.677341i
$431$			28.3810i			1.36707i	0.729920	+	0.683533i	$0.239557\pi$
$431$			28.3810i			1.36707i	−0.729920	+	0.683533i	$0.760443\pi$
$432$	−2.73534	+	2.91855i	−0.131604	+	0.140419i
$433$	12.1138	−	12.1138i	0.582153	−	0.582153i	−0.353341	−	0.935495i	$-0.614954\pi$
$433$	12.1138	−	12.1138i	0.582153	−	0.582153i	0.935495	+	0.353341i	$0.114954\pi$
$434$	23.7440	+	34.9199i	1.13975	+	1.67621i
$435$	−3.00000	−	1.00000i	−0.143839	−	0.0479463i
$436$	−18.3100	+	7.93406i	−0.876891	+	0.379973i
$437$	37.1138			1.77540
$438$	1.25644	+	1.84783i	0.0600352	+	0.0882928i
$439$			14.7328i			0.703159i	0.936158	+	0.351579i	$0.114355\pi$
$439$			14.7328i			0.703159i	−0.936158	+	0.351579i	$0.885645\pi$
$440$	−22.5186	+	18.3703i	−1.07353	+	0.875768i
$441$		−	14.1138i		−	0.672087i
$442$		0			0
$443$	−39.2603			−1.86531			−0.932657	−	0.360765i	$-0.882516\pi$
$443$	−39.2603			−1.86531			−0.932657	+	0.360765i	$0.882516\pi$
$444$	−1.38445	+	3.50172i	−0.0657032	+	0.166184i
$445$	8.23453	−	4.11727i	0.390354	−	0.195177i
$446$	−21.7186	+	14.7677i	−1.02841	+	0.699272i
$447$	−0.882734	+	0.882734i	−0.0417519	+	0.0417519i
$448$	−12.4013	+	34.6048i	−0.585907	+	1.63492i
$449$			9.64820i			0.455327i	0.973740	+	0.227663i	$0.0731086\pi$
$449$			9.64820i			0.455327i	−0.973740	+	0.227663i	$0.926891\pi$
$450$	−4.76294	−	5.22632i	−0.224527	−	0.246371i
$451$	12.9966	−	12.9966i	0.611984	−	0.611984i
$452$	−5.34268	+	2.31508i	−0.251298	+	0.108892i
$453$		0			0
$454$	−0.397442	+	2.08623i	−0.0186529	+	0.0979117i
$455$		0			0
$456$	−3.77115	−	16.8134i	−0.176600	−	0.787358i
$457$	−17.9966	+	17.9966i	−0.841844	+	0.841844i	−0.989099	−	0.147255i	$-0.952956\pi$
$457$	−17.9966	+	17.9966i	−0.841844	+	0.841844i	0.147255	+	0.989099i	$0.452956\pi$
$458$	−11.6685	+	7.93406i	−0.545233	+	0.370734i
$459$	0.0586332	−	0.0586332i	0.00273676	−	0.00273676i
$460$	−17.5151	+	20.8686i	−0.816647	+	0.973001i
$461$	−16.1138	−	16.1138i	−0.750496	−	0.750496i	0.224076	−	0.974572i	$-0.428064\pi$
$461$	−16.1138	−	16.1138i	−0.750496	−	0.750496i	−0.974572	+	0.224076i	$0.928064\pi$
$462$	−5.58795	+	29.3319i	−0.259975	+	1.36465i
$463$	−6.86813	−	6.86813i	−0.319189	−	0.319189i	0.529267	−	0.848456i	$-0.322467\pi$
$463$	−6.86813	−	6.86813i	−0.319189	−	0.319189i	−0.848456	+	0.529267i	$0.822467\pi$
$464$	5.65389	−	0.183203i	0.262475	−	0.00850501i
$465$	12.9966	−	6.49828i	0.602701	−	0.301351i
$466$	−14.9763	+	10.1832i	−0.693762	+	0.471728i
$467$	−1.26719			−0.0586384			−0.0293192	−	0.999570i	$-0.509334\pi$
$467$	−1.26719			−0.0586384			−0.0293192	+	0.999570i	$0.509334\pi$
$468$		0			0
$469$	40.2277	+	40.2277i	1.85754	+	1.85754i
$470$	26.5642	+	14.8590i	1.22532	+	0.685395i
$471$	−9.76547			−0.449969
$472$	1.19619	+	5.33312i	0.0550593	+	0.245477i
$473$	14.9966	+	14.9966i	0.689543	+	0.689543i
$474$	12.4983	+	2.38101i	0.574065	+	0.109364i
$475$	30.1544	−	4.30777i	1.38358	−	0.197654i
$476$	0.280176	−	0.708654i	0.0128418	−	0.0324811i
$477$			9.11383i			0.417294i
$478$	−4.49828	+	23.6121i	−0.205747	+	1.07999i
$479$	7.00344			0.319995			0.159998	−	0.987117i	$-0.448851\pi$
$479$	7.00344			0.319995			0.159998	+	0.987117i	$0.448851\pi$
$480$	11.2336	+	5.81427i	0.512742	+	0.265384i
$481$		0			0
$482$	6.34998	−	33.3319i	0.289234	−	1.51823i
$483$			27.9931i			1.27373i
$484$	7.43712	−	18.8108i	0.338051	−	0.855038i
$485$	29.9897	+	9.99656i	1.36176	+	0.453921i
$486$	1.38923	+	0.264658i	0.0630167	+	0.0120051i
$487$	−25.2423	−	25.2423i	−1.14384	−	1.14384i	−0.987742	−	0.156094i	$-0.950110\pi$
$487$	−25.2423	−	25.2423i	−1.14384	−	1.14384i	−0.156094	−	0.987742i	$-0.549890\pi$
$488$	−8.03490	+	1.80219i	−0.363723	+	0.0815812i
$489$	20.9966			0.949497
$490$	−42.9500	+	12.1367i	−1.94028	+	0.548278i
$491$	10.6336	+	10.6336i	0.479887	+	0.479887i	0.905096	−	0.425208i	$-0.139799\pi$
$491$	10.6336	+	10.6336i	0.479887	+	0.479887i	−0.425208	+	0.905096i	$0.639799\pi$
$492$	−7.43965	−	2.94137i	−0.335405	−	0.132607i
$493$	−0.117266			−0.00528141
$494$		0			0
$495$	9.74742	+	3.24914i	0.438114	+	0.146038i
$496$	−17.7750	+	18.9655i	−0.798122	+	0.851577i
$497$	−29.2311	−	29.2311i	−1.31119	−	1.31119i
$498$	1.32238	−	6.94137i	0.0592573	−	0.311050i
$499$	4.30777	+	4.30777i	0.192842	+	0.192842i	0.796923	−	0.604081i	$-0.206460\pi$
$499$	4.30777	+	4.30777i	0.192842	+	0.192842i	−0.604081	+	0.796923i	$0.706460\pi$
$500$	−11.8086	+	18.9883i	−0.528096	+	0.849185i
$501$	−2.42504	+	2.42504i	−0.108343	+	0.108343i
$502$	11.9893	−	8.15217i	0.535107	−	0.363849i
$503$	13.0698	−	13.0698i	0.582754	−	0.582754i	−0.352905	−	0.935659i	$-0.614806\pi$
$503$	13.0698	−	13.0698i	0.582754	−	0.582754i	0.935659	+	0.352905i	$0.114806\pi$
$504$	12.6815	−	2.84439i	0.564878	−	0.126699i
$505$	−2.88273	+	8.64820i	−0.128280	+	0.384840i
$506$	7.40861	−	38.8888i	0.329353	−	1.72882i
$507$			13.0000i			0.577350i
$508$	18.8134	−	8.15217i	0.834708	−	0.361694i
$509$	−16.9931	+	16.9931i	−0.753207	+	0.753207i	−0.975076	−	0.221869i	$-0.928784\pi$
$509$	−16.9931	+	16.9931i	−0.753207	+	0.753207i	0.221869	+	0.975076i	$0.428784\pi$
$510$	−0.228847	−	0.128008i	−0.0101335	−	0.00566829i
$511$		−	7.26031i		−	0.321177i
$512$	−22.4552	−	2.78667i	−0.992387	−	0.123155i
$513$	−4.30777	+	4.30777i	−0.190193	+	0.190193i
$514$	5.24689	−	3.56766i	0.231431	−	0.157363i
$515$	5.36641	−	16.0992i	0.236472	−	0.709416i
$516$	3.39400	−	8.58451i	0.149413	−	0.377912i
$517$	−44.2277			−1.94513
$518$	10.1173	−	6.87930i	0.444527	−	0.302259i
$519$			0.234533i			0.0102948i
$520$		0			0
$521$			14.3518i			0.628764i	0.949297	+	0.314382i	$0.101797\pi$
$521$			14.3518i			0.628764i	−0.949297	+	0.314382i	$0.898203\pi$
$522$	−1.12457	−	1.65389i	−0.0492211	−	0.0723887i
$523$	4.38101			0.191568			0.0957842	−	0.995402i	$-0.469464\pi$
$523$	4.38101			0.191568			0.0957842	+	0.995402i	$0.469464\pi$
$524$	−23.6995	+	10.2694i	−1.03532	+	0.448622i
$525$	3.24914	+	22.7440i	0.141804	+	0.992629i
$526$	−23.2660	−	34.2169i	−1.01445	−	1.49193i
$527$	0.381015	−	0.381015i	0.0165973	−	0.0165973i
$528$	−18.3703	+	0.595254i	−0.799464	+	0.0259051i
$529$		−	14.1138i		−	0.613645i
$530$	27.7344	−	7.83709i	1.20471	−	0.340421i
$531$	1.36641	−	1.36641i	0.0592970	−	0.0592970i
$532$	−20.5845	+	52.0647i	−0.892452	+	2.25729i
$533$		0			0
$534$	5.71982	+	1.08967i	0.247521	+	0.0471546i
$535$	17.2311	+	34.4622i	0.744965	+	1.48993i
$536$	−18.7424	+	29.5811i	−0.809547	+	1.27771i
$537$	5.13187	−	5.13187i	0.221457	−	0.221457i
$538$	−20.1065	−	29.5703i	−0.866854	−	1.27487i
$539$	45.8578	−	45.8578i	1.97524	−	1.97524i
$540$	−0.389229	−	4.45517i	−0.0167497	−	0.191720i
$541$	−13.4070	−	13.4070i	−0.576412	−	0.576412i	0.357501	−	0.933913i	$-0.383629\pi$
$541$	−13.4070	−	13.4070i	−0.576412	−	0.576412i	−0.933913	+	0.357501i	$0.883629\pi$
$542$	25.6983	+	4.89572i	1.10384	+	0.210289i
$543$	−0.0586332	−	0.0586332i	−0.00251619	−	0.00251619i
$544$	0.463379	+	0.0728128i	0.0198672	+	0.00312182i
$545$	7.05520	−	21.1656i	0.302211	−	0.906634i
$546$		0			0
$547$	−19.3845			−0.828819			−0.414410	−	0.910090i	$-0.636012\pi$
$547$	−19.3845			−0.828819			−0.414410	+	0.910090i	$0.636012\pi$
$548$	−13.1195	+	5.68492i	−0.560438	+	0.242848i
$549$	2.05863	+	2.05863i	0.0878603	+	0.0878603i
$550$	1.50559	−	32.4565i	0.0641984	−	1.38395i
$551$	8.61555			0.367035
$552$	−16.8134	+	3.77115i	−0.715624	+	0.160511i
$553$	−29.2311	−	29.2311i	−1.24303	−	1.24303i
$554$	4.26375	−	22.3810i	0.181149	−	0.950878i
$555$	−1.88273	−	3.76547i	−0.0799176	−	0.159835i
$556$	16.0659	−	6.96166i	0.681348	−	0.295240i
$557$			35.9931i			1.52508i	0.646942	+	0.762539i	$0.276047\pi$
$557$			35.9931i			1.52508i	−0.646942	+	0.762539i	$0.723953\pi$
$558$	9.02760	+	1.71982i	0.382169	+	0.0728060i
$559$		0			0
$560$	−19.5608	−	36.1453i	−0.826594	−	1.52742i
$561$	0.381015			0.0160865
$562$	14.0552	+	2.67762i	0.592883	+	0.112949i
$563$			8.23453i			0.347044i	0.984830	+	0.173522i	$0.0555148\pi$
$563$			8.23453i			0.347044i	−0.984830	+	0.173522i	$0.944485\pi$
$564$	7.65389	+	17.6634i	0.322287	+	0.743765i
$565$	2.05863	−	6.17590i	0.0866073	−	0.259822i
$566$	1.48529	−	7.79650i	0.0624315	−	0.327711i
$567$	−3.24914	−	3.24914i	−0.136451	−	0.136451i
$568$	13.6190	−	21.4948i	0.571440	−	0.901904i
$569$	15.8827			0.665839			0.332919	−	0.942955i	$-0.391966\pi$
$569$	15.8827			0.665839			0.332919	+	0.942955i	$0.391966\pi$
$570$	16.8134	+	9.40475i	0.704234	+	0.393921i
$571$	−22.1905	−	22.1905i	−0.928644	−	0.928644i	0.0689746	−	0.997618i	$-0.478027\pi$
$571$	−22.1905	−	22.1905i	−0.928644	−	0.928644i	−0.997618	+	0.0689746i	$0.978027\pi$
$572$		0			0
$573$	−20.6155			−0.861227
$574$	14.6155	+	21.4948i	0.610041	+	0.897177i
$575$	−4.30777	−	30.1544i	−0.179647	−	1.25753i
$576$	3.41683	+	7.23362i	0.142368	+	0.301401i
$577$	8.00344	+	8.00344i	0.333187	+	0.333187i	0.853796	−	0.520608i	$-0.174295\pi$
$577$	8.00344	+	8.00344i	0.333187	+	0.333187i	−0.520608	+	0.853796i	$0.674295\pi$
$578$	23.6073	+	4.49737i	0.981936	+	0.187066i
$579$	−13.9966	−	13.9966i	−0.581677	−	0.581677i
$580$	−4.06594	+	4.84439i	−0.168829	+	0.201153i
$581$	−16.2345	+	16.2345i	−0.673522	+	0.673522i
$582$	11.2418	+	16.5332i	0.465989	+	0.685322i
$583$	−29.6121	+	29.6121i	−1.22641	+	1.22641i
$584$	4.36072	−	0.978088i	0.180448	−	0.0404736i
$585$		0			0
$586$	−28.1008	−	5.35342i	−1.16083	−	0.221148i
$587$		−	3.00344i		−	0.123965i	−0.998077	−	0.0619826i	$-0.980258\pi$
$587$		−	3.00344i		−	0.123965i	0.998077	−	0.0619826i	$-0.0197423\pi$
$588$	−26.2505	−	10.3785i	−1.08255	−	0.428002i
$589$	−27.9931	+	27.9931i	−1.15344	+	1.15344i
$590$	−5.33312	−	2.98314i	−0.219561	−	0.122814i
$591$			14.8793i			0.612052i
$592$	5.49484	+	5.14992i	0.225837	+	0.211660i
$593$	−22.0518	+	22.0518i	−0.905557	+	0.905557i	−0.995910	−	0.0903527i	$-0.971201\pi$
$593$	−22.0518	+	22.0518i	−0.905557	+	0.905557i	0.0903527	+	0.995910i	$0.471201\pi$
$594$	3.65389	+	5.37371i	0.149921	+	0.220486i
$595$	0.381015	+	0.762030i	0.0156201	+	0.0312402i
$596$	0.992696	+	2.29092i	0.0406624	+	0.0938397i
$597$	18.4983			0.757084
$598$		0			0
$599$			17.8466i			0.729194i	0.931165	+	0.364597i	$0.118793\pi$
$599$			17.8466i			0.729194i	−0.931165	+	0.364597i	$0.881207\pi$
$600$	−13.2229	+	5.01552i	−0.539822	+	0.204758i
$601$			44.4553i			1.81337i	0.421808	+	0.906685i	$0.361396\pi$
$601$			44.4553i			1.81337i	−0.421808	+	0.906685i	$0.638604\pi$
$602$	−24.8026	+	16.8647i	−1.01088	+	0.687353i
$603$	12.3810			0.504194
$604$		0			0
$605$	10.1138	+	20.2277i	0.411186	+	0.822371i
$606$	−4.76772	+	3.24184i	−0.193675	+	0.131691i
$607$	−22.5975	+	22.5975i	−0.917204	+	0.917204i	−0.996825	−	0.0796209i	$-0.974629\pi$
$607$	−22.5975	+	22.5975i	−0.917204	+	0.917204i	0.0796209	+	0.996825i	$0.474629\pi$
$608$	−34.0445	−	5.34955i	−1.38068	−	0.216953i
$609$			6.49828i			0.263324i
$610$	4.49441	−	8.03490i	0.181974	−	0.325324i
$611$		0			0
$612$	−0.0659371	−	0.152168i	−0.00266535	−	0.00615102i
$613$		−	16.1173i		−	0.650970i	−0.945547	−	0.325485i	$-0.894472\pi$
$613$		−	16.1173i		−	0.650970i	0.945547	−	0.325485i	$-0.105528\pi$
$614$	−5.45608	+	28.6397i	−0.220189	+	1.15580i
$615$	8.00000	−	4.00000i	0.322591	−	0.161296i
$616$	50.4458	+	31.9621i	2.03252	+	1.28779i
$617$	21.2897	−	21.2897i	0.857092	−	0.857092i	−0.133902	−	0.990995i	$-0.542751\pi$
$617$	21.2897	−	21.2897i	0.857092	−	0.857092i	0.990995	+	0.133902i	$0.0427509\pi$
$618$	8.87543	−	6.03490i	0.357022	−	0.242759i
$619$	−6.19051	+	6.19051i	−0.248817	+	0.248817i	−0.820485	−	0.571668i	$-0.806297\pi$
$619$	−6.19051	+	6.19051i	−0.248817	+	0.248817i	0.571668	+	0.820485i	$0.306297\pi$
$620$	−2.52932	−	28.9509i	−0.101580	−	1.16270i
$621$	4.30777	+	4.30777i	0.172865	+	0.172865i
$622$	−5.61899	+	29.4948i	−0.225301	+	1.18264i
$623$	−13.3776	−	13.3776i	−0.535961	−	0.535961i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−4.96166	+	3.37371i	−0.198308	+	0.134841i
$627$	−27.9931			−1.11794
$628$	−7.18096	+	18.1629i	−0.286551	+	0.724779i
$629$	−0.110391	−	0.110391i	−0.00440156	−	0.00440156i
$630$	−7.09353	+	12.6815i	−0.282613	+	0.505242i
$631$	−1.46563			−0.0583457			−0.0291729	−	0.999574i	$-0.509287\pi$
$631$	−1.46563			−0.0583457			−0.0291729	+	0.999574i	$0.509287\pi$
$632$	13.6190	−	21.4948i	0.541734	−	0.855019i
$633$	8.92332	+	8.92332i	0.354670	+	0.354670i
$634$	−1.54736	−	0.294784i	−0.0614536	−	0.0117074i
$635$	−7.24914	+	21.7474i	−0.287673	+	0.863020i
$636$	16.9509	+	6.70178i	0.672148	+	0.265743i
$637$		0			0
$638$	1.71982	−	9.02760i	0.0680885	−	0.357406i
$639$	−8.99656			−0.355898
$640$	19.0746	−	16.6181i	0.753989	−	0.656887i
$641$	43.9931			1.73762			0.868812	−	0.495142i	$-0.164884\pi$
$641$	43.9931			1.73762			0.868812	+	0.495142i	$0.164884\pi$
$642$	−4.56035	+	23.9379i	−0.179983	+	0.944755i
$643$			5.46563i			0.215543i	0.994176	+	0.107772i	$0.0343715\pi$
$643$			5.46563i			0.215543i	−0.994176	+	0.107772i	$0.965628\pi$
$644$	52.0647	+	20.5845i	2.05164	+	0.811143i
$645$	4.61555	+	9.23109i	0.181737	+	0.363474i
$646$	0.701778	+	0.133694i	0.0276111	+	0.00526012i
$647$	−28.1836	−	28.1836i	−1.10801	−	1.10801i	−0.993412	−	0.114601i	$-0.963441\pi$
$647$	−28.1836	−	28.1836i	−1.10801	−	1.10801i	−0.114601	−	0.993412i	$-0.536559\pi$
$648$	1.51380	−	2.38923i	0.0594676	−	0.0938578i
$649$	8.87930			0.348543
$650$		0			0
$651$	−21.1138	−	21.1138i	−0.827516	−	0.827516i
$652$	15.4396	−	39.0518i	0.604663	−	1.52938i
$653$	−3.11383			−0.121854			−0.0609268	−	0.998142i	$-0.519406\pi$
$653$	−3.11383			−0.121854			−0.0609268	+	0.998142i	$0.519406\pi$
$654$	11.6685	−	7.93406i	0.456274	−	0.310246i
$655$	9.13187	−	27.3956i	0.356812	−	1.07044i
$656$	−10.9414	+	11.6742i	−0.427189	+	0.455800i
$657$	−1.11727	−	1.11727i	−0.0435887	−	0.0435887i
$658$	11.7052	−	61.4423i	0.456317	−	2.39527i
$659$	−13.9820	−	13.9820i	−0.544660	−	0.544660i	0.380232	−	0.924891i	$-0.375844\pi$
$659$	−13.9820	−	13.9820i	−0.544660	−	0.544660i	−0.924891	+	0.380232i	$0.875844\pi$
$660$	13.2108	−	15.7401i	0.514230	−	0.612683i
$661$	29.2897	−	29.2897i	1.13924	−	1.13924i	0.150651	−	0.988587i	$-0.451863\pi$
$661$	29.2897	−	29.2897i	1.13924	−	1.13924i	0.988587	−	0.150651i	$-0.0481371\pi$
$662$	−14.7582	+	10.0349i	−0.573592	+	0.390018i
$663$		0			0
$664$	−11.9379	−	7.56379i	−0.463281	−	0.293532i
$665$	−27.9931	−	55.9862i	−1.08553	−	2.17105i
$666$	0.498281	−	2.61555i	0.0193080	−	0.101350i
$667$		−	8.61555i		−	0.333595i
$668$	2.72713	+	6.29359i	0.105516	+	0.243506i
$669$	13.1319	−	13.1319i	0.507708	−	0.507708i
$670$	−10.6466	−	37.6769i	−0.411313	−	1.45558i
$671$			13.3776i			0.516436i
$672$	4.03490	−	25.6780i	0.155650	−	0.990552i
$673$	−24.7586	+	24.7586i	−0.954374	+	0.954374i	−0.999004	−	0.0446300i	$-0.985789\pi$
$673$	−24.7586	+	24.7586i	−0.954374	+	0.954374i	0.0446300	+	0.999004i	$0.485789\pi$
$674$	3.31346	−	2.25301i	0.127630	−	0.0867826i
$675$	4.00000	+	3.00000i	0.153960	+	0.115470i
$676$	24.1789	+	9.55944i	0.929956	+	0.367671i
$677$	−22.8793			−0.879323			−0.439661	−	0.898164i	$-0.644902\pi$
$677$	−22.8793			−0.879323			−0.439661	+	0.898164i	$0.644902\pi$
$678$	3.40475	−	2.31508i	0.130758	−	0.0889100i
$679$		−	64.9605i		−	2.49295i
$680$	−0.406364	+	0.331505i	−0.0155834	+	0.0127126i
$681$		−	1.50172i		−	0.0575460i
$682$	23.7440	+	34.9199i	0.909204	+	1.33715i
$683$	35.7294			1.36715			0.683573	−	0.729882i	$-0.260425\pi$
$683$	35.7294			1.36715			0.683573	+	0.729882i	$0.260425\pi$
$684$	4.84439	+	11.1798i	0.185230	+	0.427469i
$685$	5.05520	−	15.1656i	0.193149	−	0.579447i
$686$	25.9931	+	38.2277i	0.992422	+	1.45954i
$687$	7.05520	−	7.05520i	0.269172	−	0.269172i
$688$	−13.4707	−	12.6251i	−0.513565	−	0.481327i
$689$		0			0
$690$	9.40475	−	16.8134i	0.358033	−	0.640074i
$691$	22.4250	−	22.4250i	0.853089	−	0.853089i	−0.137424	−	0.990512i	$-0.543882\pi$
$691$	22.4250	−	22.4250i	0.853089	−	0.853089i	0.990512	+	0.137424i	$0.0438822\pi$
$692$	0.436210	+	0.172462i	0.0165822	+	0.00655601i
$693$		−	21.1138i		−	0.802048i
$694$	−0.325819	−	0.0620710i	−0.0123679	−	0.00235618i
$695$	−6.19051	+	18.5715i	−0.234819	+	0.704458i
$696$	−3.90303	+	0.875430i	−0.147944	+	0.0331831i
$697$	0.234533	−	0.234533i	0.00888356	−	0.00888356i
$698$	23.8099	+	35.0169i	0.901219	+	1.32541i
$699$	9.05520	−	9.05520i	0.342499	−	0.342499i
$700$	44.6910	+	10.6815i	1.68916	+	0.403722i
$701$	−7.87930	−	7.87930i	−0.297597	−	0.297597i	0.542475	−	0.840072i	$-0.317487\pi$
$701$	−7.87930	−	7.87930i	−0.297597	−	0.297597i	−0.840072	+	0.542475i	$0.817487\pi$
$702$		0			0
$703$	8.11039	+	8.11039i	0.305889	+	0.305889i
$704$	−12.4013	+	34.6048i	−0.467392	+	1.30422i
$705$	−20.4182	−	6.80605i	−0.768993	−	0.256331i
$706$	−0.0659371	−	0.0969726i	−0.00248158	−	0.00364961i
$707$	18.7328			0.704520
$708$	−1.53662	−	3.54617i	−0.0577497	−	0.133273i
$709$	−17.9414	−	17.9414i	−0.673802	−	0.673802i	0.284788	−	0.958590i	$-0.408077\pi$
$709$	−17.9414	−	17.9414i	−0.673802	−	0.673802i	−0.958590	+	0.284788i	$0.908077\pi$
$710$	7.73625	+	27.3776i	0.290336	+	1.02746i
$711$	−8.99656			−0.337397
$712$	6.23271	−	9.83709i	0.233581	−	0.368661i
$713$	27.9931	+	27.9931i	1.04835	+	1.04835i
$714$	−0.100839	+	0.529317i	−0.00377379	+	0.0198092i
$715$		0			0
$716$	−5.77115	−	13.3185i	−0.215678	−	0.497736i
$717$		−	16.9966i		−	0.634748i
$718$	−13.6792	−	2.60600i	−0.510505	−	0.0972549i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$	−8.57243	−	2.55214i	−0.319476	−	0.0951126i
$721$	−34.8724			−1.29872
$722$	−25.1642	−	4.79397i	−0.936516	−	0.178413i
$723$			23.9931i			0.892314i
$724$	−0.152168	+	0.0659371i	−0.00565528	+	0.00245053i
$725$	−1.00000	−	7.00000i	−0.0371391	−	0.259973i
$726$	−2.67671	+	14.0504i	−0.0993420	+	0.521460i
$727$	0.281794	+	0.281794i	0.0104512	+	0.0104512i	0.712313	−	0.701862i	$-0.247648\pi$
$727$	0.281794	+	0.281794i	0.0104512	+	0.0104512i	−0.701862	+	0.712313i	$0.747648\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−2.43922	+	4.36072i	−0.0902796	+	0.161398i
$731$	0.270624	+	0.270624i	0.0100094	+	0.0100094i
$732$	5.34268	−	2.31508i	0.197471	−	0.0855677i
$733$	2.35180			0.0868657			0.0434328	−	0.999056i	$-0.486171\pi$
$733$	2.35180			0.0868657			0.0434328	+	0.999056i	$0.486171\pi$
$734$	−7.15561	−	10.5236i	−0.264118	−	0.388434i
$735$	28.2277	−	14.1138i	1.04119	−	0.520596i
$736$	−5.34955	+	34.0445i	−0.197187	+	1.25490i
$737$	40.2277	+	40.2277i	1.48180	+	1.48180i
$738$	5.55691	+	1.05863i	0.204553	+	0.0389688i
$739$	11.3112	+	11.3112i	0.416090	+	0.416090i	0.883853	−	0.467764i	$-0.154940\pi$
$739$	11.3112	+	11.3112i	0.416090	+	0.416090i	−0.467764	+	0.883853i	$0.654940\pi$
$740$	−8.38789	+	0.732814i	−0.308345	+	0.0269388i
$741$		0			0
$742$	−33.3009	−	48.9751i	−1.22251	−	1.79793i
$743$	14.4250	−	14.4250i	0.529203	−	0.529203i	−0.391131	−	0.920335i	$-0.627916\pi$
$743$	14.4250	−	14.4250i	0.529203	−	0.529203i	0.920335	+	0.391131i	$0.127916\pi$
$744$	9.83709	−	15.5259i	0.360645	−	0.569206i
$745$	−2.64820	−	0.882734i	−0.0970226	−	0.0323409i
$746$	−39.2147	−	7.47068i	−1.43575	−	0.273521i
$747$			4.99656i			0.182815i
$748$	0.280176	−	0.708654i	0.0102443	−	0.0259110i
$749$	55.9862	−	55.9862i	2.04569	−	2.04569i
$750$	5.68970	−	14.7522i	0.207758	−	0.538674i
$751$		−	5.73625i		−	0.209319i	−0.994508	−	0.104659i	$-0.966625\pi$
$751$		−	5.73625i		−	0.209319i	0.994508	−	0.104659i	$-0.0333752\pi$
$752$	38.4807	−	1.24689i	1.40325	−	0.0454695i
$753$	−7.24914	+	7.24914i	−0.264173	+	0.264173i
$754$		0			0
$755$		0			0
$756$	−8.43234	+	3.65389i	−0.306681	+	0.132891i
$757$	−12.3449			−0.448684			−0.224342	−	0.974510i	$-0.572023\pi$
$757$	−12.3449			−0.448684			−0.224342	+	0.974510i	$0.572023\pi$
$758$	22.2694	+	32.7513i	0.808862	+	1.18958i
$759$			27.9931i			1.01609i
$760$	29.8556	−	24.3557i	1.08298	−	0.883473i
$761$		−	31.8759i		−	1.15550i	−0.816214	−	0.577749i	$-0.803931\pi$
$761$		−	31.8759i		−	1.15550i	0.816214	−	0.577749i	$-0.196069\pi$
$762$	−11.9893	+	8.15217i	−0.434325	+	0.295322i
$763$	−45.8466			−1.65976
$764$	−15.1595	+	38.3431i	−0.548450	+	1.38720i
$765$	0.175899	+	0.0586332i	0.00635966	+	0.00211989i
$766$	12.7221	−	8.65045i	0.459667	−	0.312553i
$767$		0			0
$768$	15.9664	−	1.03581i	0.576139	−	0.0373766i
$769$		−	2.87930i		−	0.103830i	−0.998652	−	0.0519150i	$-0.983468\pi$
$769$		−	2.87930i		−	0.103830i	0.998652	−	0.0519150i	$-0.0165325\pi$
$770$	−64.2518	+	18.1560i	−2.31547	+	0.654298i
$771$	−3.17246	+	3.17246i	−0.114253	+	0.114253i
$772$	−36.3246	+	15.7401i	−1.30735	+	0.566499i
$773$		−	35.5760i		−	1.27958i	−0.768550	−	0.639790i	$-0.779021\pi$
$773$		−	35.5760i		−	1.27958i	0.768550	−	0.639790i	$-0.220979\pi$
$774$	−1.22154	+	6.41205i	−0.0439075	+	0.230476i
$775$	25.9931	+	19.4948i	0.933701	+	0.700275i
$776$	39.0169	−	8.75129i	1.40062	−	0.314153i
$777$	−6.11727	+	6.11727i	−0.219456	+	0.219456i
$778$	14.6910	−	9.98926i	0.526699	−	0.358132i
$779$	−17.2311	+	17.2311i	−0.617368	+	0.617368i
$780$		0			0
$781$	−29.2311	−	29.2311i	−1.04597	−	1.04597i
$782$	0.133694	−	0.701778i	0.00478089	−	0.0250955i
$783$	1.00000	+	1.00000i	0.0357371	+	0.0357371i
$784$	−38.6061	+	41.1918i	−1.37879	+	1.47114i
$785$	−9.76547	−	19.5309i	−0.348544	−	0.697089i
$786$	15.1031	−	10.2694i	0.538709	−	0.366299i
$787$	45.1430			1.60918			0.804588	−	0.593834i	$-0.202386\pi$
$787$	45.1430			1.60918			0.804588	+	0.593834i	$0.202386\pi$
$788$	27.6742	+	10.9414i	0.985852	+	0.389770i
$789$	20.6888	+	20.6888i	0.736540	+	0.736540i
$790$	7.73625	+	27.3776i	0.275243	+	0.974050i
$791$	−13.3776			−0.475652
$792$	12.6815	−	2.84439i	0.450617	−	0.101071i
$793$		0			0
$794$	−11.2767	−	2.14830i	−0.400196	−	0.0762404i
$795$	−18.2277	+	9.11383i	−0.646468	+	0.323234i
$796$	13.6026	−	34.4052i	0.482130	−	1.21946i
$797$		−	43.3415i		−	1.53523i	−0.640909	−	0.767617i	$-0.721442\pi$
$797$		−	43.3415i		−	1.53523i	0.640909	−	0.767617i	$-0.278558\pi$
$798$	7.40861	−	38.8888i	0.262262	−	1.37665i
$799$	−0.798121			−0.0282355
$800$	−0.394914	+	28.2815i	−0.0139623	+	0.999903i
$801$	−4.11727			−0.145476
$802$	−6.91033	+	36.2733i	−0.244012	+	1.28085i
$803$		−	7.26031i		−	0.256211i
$804$	9.10428	−	23.0276i	0.321083	−	0.812121i
$805$	−55.9862	+	27.9931i	−1.97326	+	0.986628i
$806$		0			0
$807$	17.8793	+	17.8793i	0.629381	+	0.629381i
$808$	2.52363	+	11.2514i	0.0887810	+	0.395822i
$809$	−35.5241			−1.24896			−0.624480	−	0.781041i	$-0.714689\pi$
$809$	−35.5241			−1.24896			−0.624480	+	0.781041i	$0.714689\pi$
$810$	0.859912	+	3.04312i	0.0302142	+	0.106924i
$811$	28.9233	+	28.9233i	1.01564	+	1.01564i	0.999876	+	0.0157594i	$0.00501657\pi$
$811$	28.9233	+	28.9233i	1.01564	+	1.01564i	0.0157594	+	0.999876i	$0.494983\pi$
$812$	12.0862	+	4.77846i	0.424144	+	0.167691i
$813$	−18.4983			−0.648763
$814$	10.1173	−	6.87930i	0.354610	−	0.241119i
$815$	20.9966	+	41.9931i	0.735477	+	1.47095i
$816$	−0.331505	+	0.0107418i	−0.0116050	+	0.000376038i
$817$	−19.8827	−	19.8827i	−0.695609	−	0.695609i
$818$	−0.701778	+	3.68373i	−0.0245371	+	0.128799i
$819$		0			0
$820$	−1.55691	−	17.8207i	−0.0543698	−	0.622325i
$821$	12.6482	−	12.6482i	0.441425	−	0.441425i	−0.451066	−	0.892491i	$-0.648956\pi$
$821$	12.6482	−	12.6482i	0.441425	−	0.441425i	0.892491	+	0.451066i	$0.148956\pi$
$822$	8.36072	−	5.68492i	0.291614	−	0.198284i
$823$	29.7113	−	29.7113i	1.03567	−	1.03567i	0.0363321	−	0.999340i	$-0.488433\pi$
$823$	29.7113	−	29.7113i	1.03567	−	1.03567i	0.999340	−	0.0363321i	$-0.0115674\pi$
$824$	−4.69791	−	20.9452i	−0.163660	−	0.729662i
$825$	3.24914	+	22.7440i	0.113121	+	0.791844i
$826$	−2.34998	+	12.3354i	−0.0817662	+	0.429202i
$827$			18.2277i			0.633838i	0.948453	+	0.316919i	$0.102648\pi$
$827$			18.2277i			0.633838i	−0.948453	+	0.316919i	$0.897352\pi$
$828$	11.1798	−	4.84439i	0.388524	−	0.168354i
$829$	10.8207	−	10.8207i	0.375817	−	0.375817i	−0.493773	−	0.869591i	$-0.664383\pi$
$829$	10.8207	−	10.8207i	0.375817	−	0.375817i	0.869591	+	0.493773i	$0.164383\pi$
$830$	15.2051	−	4.29660i	0.527777	−	0.149137i
$831$			16.1104i			0.558863i
$832$		0			0
$833$	0.827538	−	0.827538i	0.0286725	−	0.0286725i
$834$	−10.2384	+	6.96166i	−0.354527	+	0.241063i
$835$	−7.27512	−	2.42504i	−0.251766	−	0.0839220i
$836$	−20.5845	+	52.0647i	−0.711930	+	1.80070i
$837$	−6.49828			−0.224613
$838$	13.0073	−	8.84439i	0.449330	−	0.305525i
$839$		−	6.84320i		−	0.236254i	−0.992999	−	0.118127i	$-0.962311\pi$
$839$		−	6.84320i		−	0.236254i	0.992999	−	0.118127i	$-0.0376889\pi$
$840$	18.3703	+	22.5186i	0.633835	+	0.776965i
$841$			27.0000i			0.931034i
$842$	−3.31164	−	4.87037i	−0.114127	−	0.167844i
$843$	−10.1173			−0.348457
$844$	23.1583	−	10.0349i	0.797141	−	0.345416i
$845$	−26.0000	+	13.0000i	−0.894427	+	0.447214i
$846$	−7.65389	−	11.2564i	−0.263146	−	0.387005i
$847$	32.8613	−	32.8613i	1.12913	−	1.12913i
$848$	24.9294	−	26.5991i	0.856080	−	0.913418i
$849$			5.61211i			0.192607i
$850$	0.0271694	−	0.585702i	0.000931903	−	0.0200894i
$851$	8.11039	−	8.11039i	0.278021	−	0.278021i
$852$	−6.61555	+	16.7328i	−0.226645	+	0.573257i
$853$			36.1173i			1.23663i	0.785930	+	0.618316i	$0.212185\pi$
$853$			36.1173i			1.23663i	−0.785930	+	0.618316i	$0.787815\pi$
$854$	−18.5845	−	3.54049i	−0.635949	−	0.121153i
$855$	−12.9233	−	4.30777i	−0.441968	−	0.147323i
$856$	41.1690	+	26.0844i	1.40713	+	0.891547i
$857$	−8.93793	+	8.93793i	−0.305314	+	0.305314i	−0.843089	−	0.537775i	$-0.819265\pi$
$857$	−8.93793	+	8.93793i	−0.305314	+	0.305314i	0.537775	+	0.843089i	$0.319265\pi$
$858$		0			0
$859$	−39.7665	+	39.7665i	−1.35682	+	1.35682i	−0.479003	+	0.877813i	$0.659002\pi$
$859$	−39.7665	+	39.7665i	−1.35682	+	1.35682i	−0.877813	+	0.479003i	$0.840998\pi$
$860$	20.5630	−	1.79650i	0.701193	−	0.0612602i
$861$	−12.9966	−	12.9966i	−0.442922	−	0.442922i
$862$	−39.4277	−	7.51127i	−1.34291	−	0.255835i
$863$	−10.8061	−	10.8061i	−0.367842	−	0.367842i	0.498847	−	0.866690i	$-0.333757\pi$
$863$	−10.8061	−	10.8061i	−0.367842	−	0.367842i	−0.866690	+	0.498847i	$0.833757\pi$
$864$	−3.33060	−	4.57243i	−0.113309	−	0.155557i
$865$	−0.469065	+	0.234533i	−0.0159487	+	0.00797435i
$866$	13.6229	+	20.0349i	0.462923	+	0.680814i
$867$	−16.9931			−0.577117
$868$	−54.7957	+	23.7440i	−1.85989	+	0.805923i
$869$	−29.2311	−	29.2311i	−0.991597	−	0.991597i
$870$	2.18320	−	3.90303i	0.0740175	−	0.132325i
$871$		0			0
$872$	−6.17633	−	27.5366i	−0.209157	−	0.932508i
$873$	−9.99656	−	9.99656i	−0.338332	−	0.338332i
$874$	−9.82248	+	51.5596i	−0.332250	+	1.74403i
$875$	−42.2388	+	29.2423i	−1.42793	+	0.988569i
$876$	−2.89959	+	1.25644i	−0.0979681	+	0.0424513i
$877$			14.2345i			0.480666i	0.970690	+	0.240333i	$0.0772566\pi$
$877$			14.2345i			0.480666i	−0.970690	+	0.240333i	$0.922743\pi$
$878$	−20.4672	−	3.89916i	−0.690736	−	0.131590i
$879$	20.2277			0.682262
$880$	−19.5608	−	36.1453i	−0.659394	−	1.21846i
$881$	14.3449			0.483293			0.241646	−	0.970364i	$-0.422313\pi$
$881$	14.3449			0.483293			0.241646	+	0.970364i	$0.422313\pi$
$882$	19.6073	+	3.73534i	0.660213	+	0.125775i
$883$		−	58.7552i		−	1.97727i	−0.150341	−	0.988634i	$-0.548037\pi$
$883$		−	58.7552i		−	1.97727i	0.150341	−	0.988634i	$-0.451963\pi$
$884$		0			0
$885$	4.09922	+	1.36641i	0.137794	+	0.0459313i
$886$	10.3906	−	54.5415i	0.349078	−	1.83236i
$887$	−12.3078	−	12.3078i	−0.413255	−	0.413255i	0.469616	−	0.882871i	$-0.344392\pi$
$887$	−12.3078	−	12.3078i	−0.413255	−	0.413255i	−0.882871	+	0.469616i	$0.844392\pi$
$888$	−4.49828	−	2.85008i	−0.150952	−	0.0956424i
$889$	47.1070			1.57992
$890$	3.54049	+	12.5293i	0.118677	+	0.419984i
$891$	−3.24914	−	3.24914i	−0.108850	−	0.108850i
$892$	−14.7677	−	34.0805i	−0.494460	−	1.14110i
$893$	58.6379			1.96224
$894$	−0.992696	−	1.45994i	−0.0332007	−	0.0488278i
$895$	15.3956	+	5.13187i	0.514619	+	0.171540i
$896$	−44.7919	−	26.3867i	−1.49639	−	0.881518i
$897$		0			0
$898$	−13.4036	−	2.55348i	−0.447282	−	0.0852106i
$899$	6.49828	+	6.49828i	0.216730	+	0.216730i
$900$	8.52110	−	5.23362i	0.284037	−	0.174454i
$901$	−0.534373	+	0.534373i	−0.0178025	+	0.0178025i
$902$	14.6155	+	21.4948i	0.486644	+	0.715700i
$903$	14.9966	−	14.9966i	0.499054	−	0.499054i
$904$	−1.80219	−	8.03490i	−0.0599399	−	0.267237i
$905$	0.0586332	−	0.175899i	0.00194903	−	0.00584710i
$906$		0			0
$907$			8.23453i			0.273423i	0.990611	+	0.136712i	$0.0436534\pi$
$907$			8.23453i			0.273423i	−0.990611	+	0.136712i	$0.956347\pi$
$908$	−2.79307	−	1.10428i	−0.0926911	−	0.0366467i
$909$	2.88273	−	2.88273i	0.0956142	−	0.0956142i
$910$		0			0
$911$			42.6087i			1.41169i	0.708367	+	0.705844i	$0.249432\pi$
$911$			42.6087i			1.41169i	−0.708367	+	0.705844i	$0.750568\pi$
$912$	24.3557	−	0.789199i	0.806497	−	0.0261330i
$913$	−16.2345	+	16.2345i	−0.537285	+	0.537285i
$914$	−20.2384	−	29.7643i	−0.669427	−	0.984515i
$915$	−2.05863	+	6.17590i	−0.0680563	+	0.204169i
$916$	−7.93406	−	18.3100i	−0.262149	−	0.604980i
$917$	−59.3415			−1.95963
$918$	0.0659371	+	0.0969726i	0.00217625	+	0.00320057i
$919$			31.2603i			1.03118i	0.856835	+	0.515591i	$0.172428\pi$
$919$			31.2603i			1.03118i	−0.856835	+	0.515591i	$0.827572\pi$
$920$	−24.3557	−	29.8556i	−0.802982	−	0.984309i
$921$		−	20.6155i		−	0.679305i
$922$	26.6504	−	18.1211i	0.877686	−	0.596788i
$923$		0			0
$924$	−39.2699	−	15.5259i	−1.29188	−	0.510764i
$925$	5.64820	−	7.53093i	0.185712	−	0.247616i
$926$	11.3591	−	7.72369i	0.373283	−	0.253816i
$927$	−5.36641	+	5.36641i	−0.176256	+	0.176256i
$928$	−1.24184	+	7.90303i	−0.0407653	+	0.259430i
$929$			54.5726i			1.79047i	0.445596	+	0.895234i	$0.352992\pi$
$929$			54.5726i			1.79047i	−0.445596	+	0.895234i	$0.647008\pi$
$930$	5.58795	+	19.7750i	0.183236	+	0.648448i
$931$	−60.7992	+	60.7992i	−1.99261	+	1.99261i
$932$	−10.1832	−	23.5005i	−0.333562	−	0.769785i
$933$		−	21.2311i		−	0.695075i
$934$	0.335371	−	1.76041i	0.0109737	−	0.0576024i
$935$	0.381015	+	0.762030i	0.0124605	+	0.0249210i
$936$		0			0
$937$	21.2277	−	21.2277i	0.693477	−	0.693477i	−0.269518	−	0.962995i	$-0.586864\pi$
$937$	21.2277	−	21.2277i	0.693477	−	0.693477i	0.962995	+	0.269518i	$0.0868644\pi$
$938$	−66.5320	+	45.2388i	−2.17235	+	1.47710i
$939$	3.00000	−	3.00000i	0.0979013	−	0.0979013i
$940$	−27.6730	+	32.9712i	−0.902593	+	1.07540i
$941$	7.99656	+	7.99656i	0.260680	+	0.260680i	0.825330	−	0.564650i	$-0.190989\pi$
$941$	7.99656	+	7.99656i	0.260680	+	0.260680i	−0.564650	+	0.825330i	$0.690989\pi$
$942$	2.58451	−	13.5665i	0.0842079	−	0.442019i
$943$	17.2311	+	17.2311i	0.561122	+	0.561122i
$944$	−7.72551	+	0.250330i	−0.251444	+	0.00814756i
$945$	3.24914	−	9.74742i	0.105695	−	0.317084i
$946$	−24.8026	+	16.8647i	−0.806403	+	0.548318i
$947$	41.7225			1.35580			0.677900	−	0.735155i	$-0.262890\pi$
$947$	41.7225			1.35580			0.677900	+	0.735155i	$0.262890\pi$
$948$	−6.61555	+	16.7328i	−0.214863	+	0.543457i
$949$		0			0
$950$	−1.99613	+	43.0315i	−0.0647631	+	1.39613i
$951$	1.11383			0.0361184
$952$	0.910331	+	0.576780i	0.0295040	+	0.0186935i
$953$	20.0586	+	20.0586i	0.649763	+	0.649763i	0.952936	−	0.303173i	$-0.0980459\pi$
$953$	20.0586	+	20.0586i	0.649763	+	0.649763i	−0.303173	+	0.952936i	$0.598046\pi$
$954$	−12.6612	−	2.41205i	−0.409921	−	0.0780930i
$955$	−20.6155	−	41.2311i	−0.667103	−	1.33421i
$956$	−31.6121	−	12.4983i	−1.02241	−	0.404223i
$957$			6.49828i			0.210060i
$958$	−1.85352	+	9.72938i	−0.0598844	+	0.314342i
$959$	−32.8501			−1.06078
$960$	−11.0504	+	14.0673i	−0.356651	+	0.454019i
$961$	−11.2277			−0.362182
$962$		0			0
$963$		−	17.2311i		−	0.555264i
$964$	44.6251	+	17.6431i	1.43728	+	0.568247i
$965$	13.9966	−	41.9897i	0.450565	−	1.35170i
$966$	−38.8888	−	7.40861i	−1.25123	−	0.238368i
$967$	38.8544	+	38.8544i	1.24947	+	1.24947i	0.955953	+	0.293519i	$0.0948265\pi$
$967$	38.8544	+	38.8544i	1.24947	+	1.24947i	0.293519	+	0.955953i	$0.405174\pi$
$968$	24.1642	+	15.3103i	0.776668	+	0.492092i
$969$	−0.505157			−0.0162280
$970$	−21.8245	+	39.0169i	−0.700743	+	1.25276i
$971$	−26.5975	−	26.5975i	−0.853554	−	0.853554i	0.137015	−	0.990569i	$-0.456249\pi$
$971$	−26.5975	−	26.5975i	−0.853554	−	0.853554i	−0.990569	+	0.137015i	$0.956249\pi$
$972$	−0.735342	+	1.85991i	−0.0235861	+	0.0596567i
$973$	40.2277			1.28964
$974$	41.7478	−	28.3867i	1.33769	−	0.909569i
$975$		0			0
$976$	−0.377149	−	11.6393i	−0.0120722	−	0.372564i
$977$	−2.82754	−	2.82754i	−0.0904610	−	0.0904610i	0.660428	−	0.750889i	$-0.270375\pi$
$977$	−2.82754	−	2.82754i	−0.0904610	−	0.0904610i	−0.750889	+	0.660428i	$0.770375\pi$
$978$	−5.55691	+	29.1690i	−0.177691	+	0.932723i
$979$	−13.3776	−	13.3776i	−0.427549	−	0.427549i
$980$	−5.49351	−	62.8794i	−0.175484	−	2.00861i
$981$	−7.05520	+	7.05520i	−0.225255	+	0.225255i
$982$	−17.5868	+	11.9582i	−0.561216	+	0.381602i
$983$	13.5389	−	13.5389i	0.431823	−	0.431823i	−0.457425	−	0.889248i	$-0.651228\pi$
$983$	13.5389	−	13.5389i	0.431823	−	0.431823i	0.889248	+	0.457425i	$0.151228\pi$
$984$	6.05520	−	9.55691i	0.193033	−	0.304663i
$985$	−29.7586	+	14.8793i	−0.948188	+	0.474094i
$986$	0.0310355	−	0.162910i	0.000988372	−	0.00518810i
$987$			44.2277i			1.40778i
$988$		0			0
$989$	−19.8827	+	19.8827i	−0.632234	+	0.632234i
$990$	−7.09353	+	12.6815i	−0.225447	+	0.403044i
$991$		−	12.9605i		−	0.411703i	−0.978583	−	0.205851i	$-0.934004\pi$
$991$		−	12.9605i		−	0.411703i	0.978583	−	0.205851i	$-0.0659964\pi$
$992$	−21.6431	−	29.7129i	−0.687171	−	0.943387i
$993$	8.92332	−	8.92332i	0.283173	−	0.283173i
$994$	48.3449	−	32.8724i	1.53341	−	1.04265i
$995$	18.4983	+	36.9966i	0.586435	+	1.17287i
$996$	9.29317	+	3.67418i	0.294465	+	0.116421i
$997$	22.2277			0.703957			0.351978	−	0.936008i	$-0.385509\pi$
$997$	22.2277			0.703957			0.351978	+	0.936008i	$0.385509\pi$
$998$	−7.12457	+	4.84439i	−0.225524	+	0.153347i
$999$			1.88273i			0.0595671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bc.d.67.2	yes	6
3.2	odd	2		720.2.bd.e.307.2		6
4.3	odd	2		960.2.bc.d.367.3		6
5.3	odd	4		240.2.y.d.163.3	✓	6
8.3	odd	2		1920.2.bc.h.607.3		6
8.5	even	2		1920.2.bc.g.607.1		6
15.8	even	4		720.2.z.e.163.1		6
16.3	odd	4		1920.2.y.g.1567.1		6
16.5	even	4		960.2.y.d.847.3		6
16.11	odd	4		240.2.y.d.187.3	yes	6
16.13	even	4		1920.2.y.h.1567.3		6
20.3	even	4		960.2.y.d.943.3		6
40.3	even	4		1920.2.y.h.223.3		6
40.13	odd	4		1920.2.y.g.223.1		6
48.11	even	4		720.2.z.e.667.1		6
80.3	even	4		1920.2.bc.g.1183.1		6
80.13	odd	4		1920.2.bc.h.1183.3		6
80.43	even	4	inner	240.2.bc.d.43.2	yes	6
80.53	odd	4		960.2.bc.d.463.3		6
240.203	odd	4		720.2.bd.e.523.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.3	✓	6	5.3	odd	4
240.2.y.d.187.3	yes	6	16.11	odd	4
240.2.bc.d.43.2	yes	6	80.43	even	4	inner
240.2.bc.d.67.2	yes	6	1.1	even	1	trivial
720.2.z.e.163.1		6	15.8	even	4
720.2.z.e.667.1		6	48.11	even	4
720.2.bd.e.307.2		6	3.2	odd	2
720.2.bd.e.523.2		6	240.203	odd	4
960.2.y.d.847.3		6	16.5	even	4
960.2.y.d.943.3		6	20.3	even	4
960.2.bc.d.367.3		6	4.3	odd	2
960.2.bc.d.463.3		6	80.53	odd	4
1920.2.y.g.223.1		6	40.13	odd	4
1920.2.y.g.1567.1		6	16.3	odd	4
1920.2.y.h.223.3		6	40.3	even	4
1920.2.y.h.1567.3		6	16.13	even	4
1920.2.bc.g.607.1		6	8.5	even	2
1920.2.bc.g.1183.1		6	80.3	even	4
1920.2.bc.h.607.3		6	8.3	odd	2
1920.2.bc.h.1183.3		6	80.13	odd	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.264658 + 1.38923i) q^{2} -1.00000i q^{3} +(-1.85991 - 0.735342i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.38923 + 0.264658i) q^{6} +(-3.24914 - 3.24914i) q^{7} +(1.51380 - 2.38923i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.264658 + 1.38923i) q^{2} -1.00000i q^{3} +(-1.85991 - 0.735342i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.38923 + 0.264658i) q^{6} +(-3.24914 - 3.24914i) q^{7} +(1.51380 - 2.38923i) q^{8} -1.00000 q^{9} +(0.859912 + 3.04312i) q^{10} +(-3.24914 - 3.24914i) q^{11} +(-0.735342 + 1.85991i) q^{12} +(5.37371 - 3.65389i) q^{14} +(-1.00000 - 2.00000i) q^{15} +(2.91855 + 2.73534i) q^{16} +(-0.0586332 - 0.0586332i) q^{17} +(0.264658 - 1.38923i) q^{18} +(4.30777 + 4.30777i) q^{19} +(-4.45517 + 0.389229i) q^{20} +(-3.24914 + 3.24914i) q^{21} +(5.37371 - 3.65389i) q^{22} +(4.30777 - 4.30777i) q^{23} +(-2.38923 - 1.51380i) q^{24} +(3.00000 - 4.00000i) q^{25} +1.00000i q^{27} +(3.65389 + 8.43234i) q^{28} +(1.00000 - 1.00000i) q^{29} +(3.04312 - 0.859912i) q^{30} +6.49828i q^{31} +(-4.57243 + 3.33060i) q^{32} +(-3.24914 + 3.24914i) q^{33} +(0.0969726 - 0.0659371i) q^{34} +(-9.74742 - 3.24914i) q^{35} +(1.85991 + 0.735342i) q^{36} +1.88273 q^{37} +(-7.12457 + 4.84439i) q^{38} +(0.638369 - 6.29226i) q^{40} +4.00000i q^{41} +(-3.65389 - 5.37371i) q^{42} -4.61555 q^{43} +(3.65389 + 8.43234i) q^{44} +(-2.00000 + 1.00000i) q^{45} +(4.84439 + 7.12457i) q^{46} +(6.80605 - 6.80605i) q^{47} +(2.73534 - 2.91855i) q^{48} +14.1138i q^{49} +(4.76294 + 5.22632i) q^{50} +(-0.0586332 + 0.0586332i) q^{51} -9.11383i q^{53} +(-1.38923 - 0.264658i) q^{54} +(-9.74742 - 3.24914i) q^{55} +(-12.6815 + 2.84439i) q^{56} +(4.30777 - 4.30777i) q^{57} +(1.12457 + 1.65389i) q^{58} +(-1.36641 + 1.36641i) q^{59} +(0.389229 + 4.45517i) q^{60} +(-2.05863 - 2.05863i) q^{61} +(-9.02760 - 1.71982i) q^{62} +(3.24914 + 3.24914i) q^{63} +(-3.41683 - 7.23362i) q^{64} +(-3.65389 - 5.37371i) q^{66} -12.3810 q^{67} +(0.0659371 + 0.152168i) q^{68} +(-4.30777 - 4.30777i) q^{69} +(7.09353 - 12.6815i) q^{70} +8.99656 q^{71} +(-1.51380 + 2.38923i) q^{72} +(1.11727 + 1.11727i) q^{73} +(-0.498281 + 2.61555i) q^{74} +(-4.00000 - 3.00000i) q^{75} +(-4.84439 - 11.1798i) q^{76} +21.1138i q^{77} +8.99656 q^{79} +(8.57243 + 2.55214i) q^{80} +1.00000 q^{81} +(-5.55691 - 1.05863i) q^{82} -4.99656i q^{83} +(8.43234 - 3.65389i) q^{84} +(-0.175899 - 0.0586332i) q^{85} +(1.22154 - 6.41205i) q^{86} +(-1.00000 - 1.00000i) q^{87} +(-12.6815 + 2.84439i) q^{88} +4.11727 q^{89} +(-0.859912 - 3.04312i) q^{90} +(-11.1798 + 4.84439i) q^{92} +6.49828 q^{93} +(7.65389 + 11.2564i) q^{94} +(12.9233 + 4.30777i) q^{95} +(3.33060 + 4.57243i) q^{96} +(9.99656 + 9.99656i) q^{97} +(-19.6073 - 3.73534i) q^{98} +(3.24914 + 3.24914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9	\( 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 10 q^{19} - 8 q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 18 q^{25} + 14 q^{28} + 6 q^{29} + 2 q^{30} - 12 q^{32} - 2 q^{33} + 26 q^{34} - 6 q^{35} + 2 q^{36} + 8 q^{37} - 34 q^{38} - 22 q^{40} - 14 q^{42} + 4 q^{43} + 14 q^{44} - 12 q^{45} + 2 q^{46} - 10 q^{47} + 16 q^{48} - 6 q^{50} - 2 q^{51} - 6 q^{55} - 34 q^{56} + 10 q^{57} - 2 q^{58} + 6 q^{59} - 6 q^{60} - 14 q^{61} - 20 q^{62} + 2 q^{63} + 22 q^{64} - 14 q^{66} - 36 q^{67} - 10 q^{68} - 10 q^{69} - 2 q^{70} - 16 q^{71} + 8 q^{72} + 10 q^{73} + 32 q^{74} - 24 q^{75} - 2 q^{76} - 16 q^{79} + 36 q^{80} + 6 q^{81} + 26 q^{84} - 6 q^{85} + 24 q^{86} - 6 q^{87} - 34 q^{88} + 28 q^{89} + 4 q^{90} + 10 q^{92} + 4 q^{93} + 38 q^{94} + 30 q^{95} + 10 q^{96} - 10 q^{97} - 56 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 10 * q^19 - 8 * q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 18 * q^25 + 14 * q^28 + 6 * q^29 + 2 * q^30 - 12 * q^32 - 2 * q^33 + 26 * q^34 - 6 * q^35 + 2 * q^36 + 8 * q^37 - 34 * q^38 - 22 * q^40 - 14 * q^42 + 4 * q^43 + 14 * q^44 - 12 * q^45 + 2 * q^46 - 10 * q^47 + 16 * q^48 - 6 * q^50 - 2 * q^51 - 6 * q^55 - 34 * q^56 + 10 * q^57 - 2 * q^58 + 6 * q^59 - 6 * q^60 - 14 * q^61 - 20 * q^62 + 2 * q^63 + 22 * q^64 - 14 * q^66 - 36 * q^67 - 10 * q^68 - 10 * q^69 - 2 * q^70 - 16 * q^71 + 8 * q^72 + 10 * q^73 + 32 * q^74 - 24 * q^75 - 2 * q^76 - 16 * q^79 + 36 * q^80 + 6 * q^81 + 26 * q^84 - 6 * q^85 + 24 * q^86 - 6 * q^87 - 34 * q^88 + 28 * q^89 + 4 * q^90 + 10 * q^92 + 4 * q^93 + 38 * q^94 + 30 * q^95 + 10 * q^96 - 10 * q^97 - 56 * q^98 + 2 * q^99

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