LMFDB - Embedded newform 2301.1.z.c.779.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2301,1,Mod(116,2301)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2301.116"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2301, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([29, 29, 30])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 2301 = 3 \cdot 13 \cdot 59 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2301.z (of order $58$, degree $28$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.14834859407$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{58})$
Coefficient field:	$\Q(\zeta_{116})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{56} - x^{54} + x^{52} - x^{50} + x^{48} - x^{46} + x^{44} - x^{42} + x^{40} - x^{38} + x^{36} + \cdots + 1 $ x^56 - x^54 + x^52 - x^50 + x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{59}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{58}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{58} - \cdots)$

Embedding invariants

Embedding label			779.1
Root			$0.827689 + 0.561187i$ of defining polynomial
Character	$\chi$	$=$	2301.779
Dual form			2301.1.z.c.1598.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.795818 + 0.268142i) q^{2} +(0.856857 - 0.515554i) q^{3} +(-0.234666 + 0.178389i) q^{4} +(-0.739191 - 1.85523i) q^{5} +(-0.543661 + 0.640047i) q^{6} +(0.610191 - 0.899964i) q^{8} +(0.468408 - 0.883512i) q^{9} +(1.08573 + 1.27822i) q^{10} +(-0.115021 - 0.414270i) q^{11} +(-0.109107 + 0.273837i) q^{12} +(-0.468408 - 0.883512i) q^{13} +(-1.58985 - 1.20857i) q^{15} +(-0.165423 + 0.595798i) q^{16} +(-0.135861 + 0.828715i) q^{18} +(0.504415 + 0.303497i) q^{20} +(0.202619 + 0.298841i) q^{22} +(0.0588664 - 1.08573i) q^{24} +(-2.16947 + 2.05504i) q^{25} +(0.609675 + 0.577515i) q^{26} +(-0.0541389 - 0.998533i) q^{27} +(1.58930 + 0.535498i) q^{30} +(0.0307539 + 0.567223i) q^{32} +(-0.312135 - 0.295670i) q^{33} +(0.0476889 + 0.290889i) q^{36} +(-0.856857 - 0.515554i) q^{39} +(-2.12069 - 0.466798i) q^{40} +(-0.103314 + 0.630190i) q^{41} +(0.0289674 - 0.104331i) q^{43} +(0.100893 + 0.0766966i) q^{44} +(-1.98536 - 0.215921i) q^{45} +(-0.564211 + 1.41606i) q^{47} +(0.165423 + 0.595798i) q^{48} +(0.647386 + 0.762162i) q^{49} +(1.17547 - 2.21716i) q^{50} +(0.267528 + 0.123772i) q^{52} +(0.310834 + 0.780134i) q^{54} +(-0.683542 + 0.519615i) q^{55} +(0.214970 - 0.976621i) q^{59} +0.588681 q^{60} +(1.72013 - 0.579580i) q^{61} +(-0.405441 - 1.01758i) q^{64} +(-1.29287 + 1.52209i) q^{65} +(0.327685 + 0.151603i) q^{66} +(0.381652 - 0.957875i) q^{71} +(-0.509311 - 0.960662i) q^{72} +(-0.799448 + 2.87935i) q^{75} +(0.820145 + 0.180527i) q^{78} +(-1.62401 - 0.977132i) q^{79} +(1.22762 - 0.133512i) q^{80} +(-0.561187 - 0.827689i) q^{81} +(-0.0867612 - 0.529220i) q^{82} +(-0.0744626 + 1.37338i) q^{83} +(0.00492282 + 0.0907960i) q^{86} +(-0.443013 - 0.149268i) q^{88} +(-1.87034 - 0.630190i) q^{89} +(1.63788 - 0.360525i) q^{90} +(0.0693029 - 1.27822i) q^{94} +(0.318786 + 0.470174i) q^{96} +(-0.719570 - 0.432951i) q^{98} +(-0.419889 - 0.0924246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{12} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{27} + 2 q^{36} - 2 q^{39} - 58 q^{40} - 4 q^{43} + 2 q^{48} - 2 q^{49} - 2 q^{52} + 4 q^{61} + 2 q^{64} - 2 q^{75} + 4 q^{79}+ \cdots - 2 q^{81}+O(q^{100}) $ 56 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^12 + 2 * q^13 - 2 * q^16 + 2 * q^25 + 2 * q^27 + 2 * q^36 - 2 * q^39 - 58 * q^40 - 4 * q^43 + 2 * q^48 - 2 * q^49 - 2 * q^52 + 4 * q^61 + 2 * q^64 - 2 * q^75 + 4 * q^79 - 2 * q^81

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2301\mathbb{Z}\right)^\times$.

$n$	$886$	$1535$	$2185$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{26}{29}\right)$

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 $

$2$	−0.795818	+	0.268142i	−0.795818	+	0.268142i	−0.687699	−	0.725995i	$-0.741379\pi$
$2$	−0.795818	+	0.268142i	−0.795818	+	0.268142i	−0.108119	+	0.994138i	$0.534483\pi$
$3$	0.856857	−	0.515554i	0.856857	−	0.515554i
$3$	0.856857	−	0.515554i	0.856857	−	0.515554i
$4$	−0.234666	+	0.178389i	−0.234666	+	0.178389i
$5$	−0.739191	−	1.85523i	−0.739191	−	1.85523i	−0.419889	−	0.907575i	$-0.637931\pi$
$5$	−0.739191	−	1.85523i	−0.739191	−	1.85523i	−0.319302	−	0.947653i	$-0.603448\pi$
$6$	−0.543661	+	0.640047i	−0.543661	+	0.640047i
$7$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$7$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$8$	0.610191	−	0.899964i	0.610191	−	0.899964i
$9$	0.468408	−	0.883512i	0.468408	−	0.883512i
$10$	1.08573	+	1.27822i	1.08573	+	1.27822i
$11$	−0.115021	−	0.414270i	−0.115021	−	0.414270i	0.883512	−	0.468408i	$-0.155172\pi$
$11$	−0.115021	−	0.414270i	−0.115021	−	0.414270i	−0.998533	+	0.0541389i	$0.982759\pi$
$12$	−0.109107	+	0.273837i	−0.109107	+	0.273837i
$13$	−0.468408	−	0.883512i	−0.468408	−	0.883512i
$13$	−0.468408	−	0.883512i	−0.468408	−	0.883512i
$14$		0			0
$15$	−1.58985	−	1.20857i	−1.58985	−	1.20857i
$16$	−0.165423	+	0.595798i	−0.165423	+	0.595798i
$17$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$17$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$18$	−0.135861	+	0.828715i	−0.135861	+	0.828715i
$19$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$19$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$20$	0.504415	+	0.303497i	0.504415	+	0.303497i
$21$		0			0
$22$	0.202619	+	0.298841i	0.202619	+	0.298841i
$23$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$23$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$24$	0.0588664	−	1.08573i	0.0588664	−	1.08573i
$25$	−2.16947	+	2.05504i	−2.16947	+	2.05504i
$26$	0.609675	+	0.577515i	0.609675	+	0.577515i
$27$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$28$		0			0
$29$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$29$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$30$	1.58930	+	0.535498i	1.58930	+	0.535498i
$31$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$31$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$32$	0.0307539	+	0.567223i	0.0307539	+	0.567223i
$33$	−0.312135	−	0.295670i	−0.312135	−	0.295670i
$34$		0			0
$35$		0			0
$36$	0.0476889	+	0.290889i	0.0476889	+	0.290889i
$37$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$37$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$38$		0			0
$39$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$40$	−2.12069	−	0.466798i	−2.12069	−	0.466798i
$41$	−0.103314	+	0.630190i	−0.103314	+	0.630190i	0.883512	+	0.468408i	$0.155172\pi$
$41$	−0.103314	+	0.630190i	−0.103314	+	0.630190i	−0.986827	+	0.161782i	$0.948276\pi$
$42$		0			0
$43$	0.0289674	−	0.104331i	0.0289674	−	0.104331i	−0.947653	−	0.319302i	$-0.896552\pi$
$43$	0.0289674	−	0.104331i	0.0289674	−	0.104331i	0.976621	+	0.214970i	$0.0689655\pi$
$44$	0.100893	+	0.0766966i	0.100893	+	0.0766966i
$45$	−1.98536	−	0.215921i	−1.98536	−	0.215921i
$46$		0			0
$47$	−0.564211	+	1.41606i	−0.564211	+	1.41606i	0.319302	+	0.947653i	$0.396552\pi$
$47$	−0.564211	+	1.41606i	−0.564211	+	1.41606i	−0.883512	+	0.468408i	$0.844828\pi$
$48$	0.165423	+	0.595798i	0.165423	+	0.595798i
$49$	0.647386	+	0.762162i	0.647386	+	0.762162i
$50$	1.17547	−	2.21716i	1.17547	−	2.21716i
$51$		0			0
$52$	0.267528	+	0.123772i	0.267528	+	0.123772i
$53$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$53$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$54$	0.310834	+	0.780134i	0.310834	+	0.780134i
$55$	−0.683542	+	0.519615i	−0.683542	+	0.519615i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.214970	−	0.976621i	0.214970	−	0.976621i
$59$	0.214970	−	0.976621i	0.214970	−	0.976621i
$60$	0.588681			0.588681
$61$	1.72013	−	0.579580i	1.72013	−	0.579580i	0.725995	−	0.687699i	$-0.241379\pi$
$61$	1.72013	−	0.579580i	1.72013	−	0.579580i	0.994138	+	0.108119i	$0.0344828\pi$
$62$		0			0
$63$		0			0
$64$	−0.405441	−	1.01758i	−0.405441	−	1.01758i
$65$	−1.29287	+	1.52209i	−1.29287	+	1.52209i
$66$	0.327685	+	0.151603i	0.327685	+	0.151603i
$67$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$67$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.381652	−	0.957875i	0.381652	−	0.957875i	−0.605174	−	0.796093i	$-0.706897\pi$
$71$	0.381652	−	0.957875i	0.381652	−	0.957875i	0.986827	−	0.161782i	$-0.0517241\pi$
$72$	−0.509311	−	0.960662i	−0.509311	−	0.960662i
$73$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$73$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$74$		0			0
$75$	−0.799448	+	2.87935i	−0.799448	+	2.87935i
$76$		0			0
$77$		0			0
$78$	0.820145	+	0.180527i	0.820145	+	0.180527i
$79$	−1.62401	−	0.977132i	−1.62401	−	0.977132i	−0.976621	−	0.214970i	$-0.931034\pi$
$79$	−1.62401	−	0.977132i	−1.62401	−	0.977132i	−0.647386	−	0.762162i	$-0.724138\pi$
$80$	1.22762	−	0.133512i	1.22762	−	0.133512i
$81$	−0.561187	−	0.827689i	−0.561187	−	0.827689i
$82$	−0.0867612	−	0.529220i	−0.0867612	−	0.529220i
$83$	−0.0744626	+	1.37338i	−0.0744626	+	1.37338i	0.687699	+	0.725995i	$0.258621\pi$
$83$	−0.0744626	+	1.37338i	−0.0744626	+	1.37338i	−0.762162	+	0.647386i	$0.775862\pi$
$84$		0			0
$85$		0			0
$86$	0.00492282	+	0.0907960i	0.00492282	+	0.0907960i
$87$		0			0
$88$	−0.443013	−	0.149268i	−0.443013	−	0.149268i
$89$	−1.87034	−	0.630190i	−1.87034	−	0.630190i	−0.986827	−	0.161782i	$-0.948276\pi$
$89$	−1.87034	−	0.630190i	−1.87034	−	0.630190i	−0.883512	−	0.468408i	$-0.844828\pi$
$90$	1.63788	−	0.360525i	1.63788	−	0.360525i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	0.0693029	−	1.27822i	0.0693029	−	1.27822i
$95$		0			0
$96$	0.318786	+	0.470174i	0.318786	+	0.470174i
$97$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$97$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$98$	−0.719570	−	0.432951i	−0.719570	−	0.432951i
$99$	−0.419889	−	0.0924246i	−0.419889	−	0.0924246i
$100$	0.142508	−	0.869258i	0.142508	−	0.869258i
$101$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$101$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$102$		0			0
$103$	−1.36428	−	1.03710i	−1.36428	−	1.03710i	−0.994138	−	0.108119i	$-0.965517\pi$
$103$	−1.36428	−	1.03710i	−1.36428	−	1.03710i	−0.370138	−	0.928977i	$-0.620690\pi$
$104$	−1.08095	−	0.117560i	−1.08095	−	0.117560i
$105$		0			0
$106$		0			0
$107$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$107$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$108$	0.190832	+	0.224664i	0.190832	+	0.224664i
$109$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$109$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$110$	0.404644	−	0.596806i	0.404644	−	0.596806i
$111$		0			0
$112$		0			0
$113$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$113$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.00000			−1.00000
$118$	0.0907960	+	0.834855i	0.0907960	+	0.834855i
$119$		0			0
$120$	−2.05779	+	0.693349i	−2.05779	+	0.693349i
$121$	0.698468	−	0.420254i	0.698468	−	0.420254i
$122$	−1.21350	+	0.922482i	−1.21350	+	0.922482i
$123$	0.236371	+	0.593247i	0.236371	+	0.593247i
$124$		0			0
$125$	3.60373	+	1.66726i	3.60373	+	1.66726i
$126$		0			0
$127$	0.680125	−	1.28285i	0.680125	−	1.28285i	−0.267528	−	0.963550i	$-0.586207\pi$
$127$	0.680125	−	1.28285i	0.680125	−	1.28285i	0.947653	−	0.319302i	$-0.103448\pi$
$128$	0.227762	+	0.268142i	0.227762	+	0.268142i
$129$	−0.0289674	−	0.104331i	−0.0289674	−	0.104331i
$130$	0.620756	−	1.55798i	0.620756	−	1.55798i
$131$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$131$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$132$	0.125992	+	0.0137024i	0.125992	+	0.0137024i
$133$		0			0
$134$		0			0
$135$	−1.81249	+	0.838547i	−1.81249	+	0.838547i
$136$		0			0
$137$	1.72571	+	0.379858i	1.72571	+	0.379858i	0.963550	−	0.267528i	$-0.0862069\pi$
$137$	1.72571	+	0.379858i	1.72571	+	0.379858i	0.762162	+	0.647386i	$0.224138\pi$
$138$		0			0
$139$	−0.107643	+	0.0117069i	−0.107643	+	0.0117069i	−0.161782	−	0.986827i	$-0.551724\pi$
$139$	−0.107643	+	0.0117069i	−0.107643	+	0.0117069i	0.0541389	+	0.998533i	$0.482759\pi$
$140$		0			0
$141$	0.246608	+	1.50424i	0.246608	+	1.50424i
$142$	−0.0468790	+	0.864632i	−0.0468790	+	0.864632i
$143$	−0.312135	+	0.295670i	−0.312135	+	0.295670i
$144$	0.448910	+	0.425230i	0.448910	+	0.425230i
$145$		0			0
$146$		0			0
$147$	0.947653	+	0.319302i	0.947653	+	0.319302i
$148$		0			0
$149$	1.81452	−	0.399405i	1.81452	−	0.399405i	0.827689	−	0.561187i	$-0.189655\pi$
$149$	1.81452	−	0.399405i	1.81452	−	0.399405i	0.986827	+	0.161782i	$0.0517241\pi$
$150$	−0.135861	−	2.50581i	−0.135861	−	2.50581i
$151$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$151$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.293045	−	0.0318705i	0.293045	−	0.0318705i
$157$	0.961714	+	0.578644i	0.961714	+	0.578644i	0.907575	−	0.419889i	$-0.137931\pi$
$157$	0.961714	+	0.578644i	0.961714	+	0.578644i	0.0541389	+	0.998533i	$0.482759\pi$
$158$	1.55443	+	0.342155i	1.55443	+	0.342155i
$159$		0			0
$160$	1.02960	−	0.476342i	1.02960	−	0.476342i
$161$		0			0
$162$	0.668542	+	0.508212i	0.668542	+	0.508212i
$163$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$163$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$164$	−0.0881745	−	0.166315i	−0.0881745	−	0.166315i
$165$	−0.317808	+	0.797639i	−0.317808	+	0.797639i
$166$	−0.309003	−	1.11293i	−0.309003	−	1.11293i
$167$	−1.07167	−	1.26167i	−1.07167	−	1.26167i	−0.963550	−	0.267528i	$-0.913793\pi$
$167$	−1.07167	−	1.26167i	−1.07167	−	1.26167i	−0.108119	−	0.994138i	$-0.534483\pi$
$168$		0			0
$169$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$170$		0			0
$171$		0			0
$172$	0.0118138	+	0.0296505i	0.0118138	+	0.0296505i
$173$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$173$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$174$		0			0
$175$		0			0
$176$	0.265848			0.265848
$177$	−0.319302	−	0.947653i	−0.319302	−	0.947653i
$178$	1.65743			1.65743
$179$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$179$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$180$	0.504415	−	0.303497i	0.504415	−	0.303497i
$181$	−1.36428	+	1.03710i	−1.36428	+	1.03710i	−0.370138	+	0.928977i	$0.620690\pi$
$181$	−1.36428	+	1.03710i	−1.36428	+	1.03710i	−0.994138	+	0.108119i	$0.965517\pi$
$182$		0			0
$183$	1.17510	−	1.38344i	1.17510	−	1.38344i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.120208	−	0.432951i	−0.120208	−	0.432951i
$189$		0			0
$190$		0			0
$191$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$191$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$192$	−0.872023	−	0.662894i	−0.872023	−	0.662894i
$193$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$193$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$194$		0			0
$195$	−0.323089	+	1.97076i	−0.323089	+	1.97076i
$196$	−0.287881	−	0.0633674i	−0.287881	−	0.0633674i
$197$	−0.185285	−	0.111482i	−0.185285	−	0.111482i	0.419889	−	0.907575i	$-0.362069\pi$
$197$	−0.185285	−	0.111482i	−0.185285	−	0.111482i	−0.605174	+	0.796093i	$0.706897\pi$
$198$	0.358938	−	0.0390369i	0.358938	−	0.0390369i
$199$	−0.629862	−	0.928977i	−0.629862	−	0.928977i	0.370138	−	0.928977i	$-0.379310\pi$
$199$	−0.629862	−	0.928977i	−0.629862	−	0.928977i	−1.00000			$\pi$
$200$	0.525665	+	3.20641i	0.525665	+	3.20641i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.24552	−	0.274159i	1.24552	−	0.274159i
$206$	1.36381	+	0.459520i	1.36381	+	0.459520i
$207$		0			0
$208$	0.603880	−	0.132924i	0.603880	−	0.132924i
$209$		0			0
$210$		0			0
$211$	1.15592	−	1.09495i	1.15592	−	1.09495i	0.161782	−	0.986827i	$-0.448276\pi$
$211$	1.15592	−	1.09495i	1.15592	−	1.09495i	0.994138	−	0.108119i	$-0.0344828\pi$
$212$		0			0
$213$	−0.166815	−	1.01752i	−0.166815	−	1.01752i
$214$		0			0
$215$	−0.214970	+	0.0233794i	−0.214970	+	0.0233794i
$216$	−0.931679	−	0.560573i	−0.931679	−	0.560573i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.0677108	−	0.243872i	0.0677108	−	0.243872i
$221$		0			0
$222$		0			0
$223$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$223$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$224$		0			0
$225$	0.799448	+	2.87935i	0.799448	+	2.87935i
$226$		0			0
$227$	−0.482980	+	0.910996i	−0.482980	+	0.910996i	0.515554	+	0.856857i	$0.327586\pi$
$227$	−0.482980	+	0.910996i	−0.482980	+	0.910996i	−0.998533	+	0.0541389i	$0.982759\pi$
$228$		0			0
$229$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$229$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$233$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$234$	0.795818	−	0.268142i	0.795818	−	0.268142i
$235$	3.04418			3.04418
$236$	0.123772	+	0.267528i	0.123772	+	0.267528i
$237$	−1.89531			−1.89531
$238$		0			0
$239$	1.59200	−	0.957875i	1.59200	−	0.957875i	0.605174	−	0.796093i	$-0.293103\pi$
$239$	1.59200	−	0.957875i	1.59200	−	0.957875i	0.986827	−	0.161782i	$-0.0517241\pi$
$240$	0.983063	−	0.747305i	0.983063	−	0.747305i
$241$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$241$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$242$	−0.443166	+	0.521735i	−0.443166	+	0.521735i
$243$	−0.907575	−	0.419889i	−0.907575	−	0.419889i
$244$	−0.300267	+	0.442861i	−0.300267	+	0.442861i
$245$	0.935443	−	1.76443i	0.935443	−	1.76443i
$246$	−0.347184	−	0.408736i	−0.347184	−	0.408736i
$247$		0			0
$248$		0			0
$249$	0.644248	+	1.21518i	0.644248	+	1.21518i
$250$	−3.31498	−	0.360525i	−3.31498	−	0.360525i
$251$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$251$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$252$		0			0
$253$		0			0
$254$	−0.197269	+	1.20329i	−0.197269	+	1.20329i
$255$		0			0
$256$	0.685425	+	0.412406i	0.685425	+	0.412406i
$257$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$257$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$258$	0.0510284	+	0.0752612i	0.0510284	+	0.0752612i
$259$		0			0
$260$	0.0318705	−	0.587817i	0.0318705	−	0.587817i
$261$		0			0
$262$		0			0
$263$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$263$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$264$	−0.456555	+	0.100495i	−0.456555	+	0.100495i
$265$		0			0
$266$		0			0
$267$	−1.92751	+	0.424277i	−1.92751	+	0.424277i
$268$		0			0
$269$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$269$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$270$	1.21756	−	1.15334i	1.21756	−	1.15334i
$271$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$271$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$272$		0			0
$273$		0			0
$274$	−1.47521	+	0.160439i	−1.47521	+	0.160439i
$275$	1.10087	+	0.662374i	1.10087	+	0.662374i
$276$		0			0
$277$	0.119763	−	0.730524i	0.119763	−	0.730524i	−0.856857	−	0.515554i	$-0.827586\pi$
$277$	0.119763	−	0.730524i	0.119763	−	0.730524i	0.976621	−	0.214970i	$-0.0689655\pi$
$278$	0.0825252	−	0.0381802i	0.0825252	−	0.0381802i
$279$		0			0
$280$		0			0
$281$		0			0		0.108119	−	0.994138i	$-0.465517\pi$
$281$		0			0		−0.108119	+	0.994138i	$0.534483\pi$
$282$	−0.599607	−	1.13098i	−0.599607	−	1.13098i
$283$	−0.701525	+	1.76070i	−0.701525	+	1.76070i	−0.0541389	+	0.998533i	$0.517241\pi$
$283$	−0.701525	+	1.76070i	−0.701525	+	1.76070i	−0.647386	+	0.762162i	$0.724138\pi$
$284$	0.0813132	+	0.292864i	0.0813132	+	0.292864i
$285$		0			0
$286$	0.169121	−	0.318996i	0.169121	−	0.318996i
$287$		0			0
$288$	0.515554	+	0.238521i	0.515554	+	0.238521i
$289$	0.647386	−	0.762162i	0.647386	−	0.762162i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.44453	−	0.486719i	1.44453	−	0.486719i	0.515554	−	0.856857i	$-0.327586\pi$
$293$	1.44453	−	0.486719i	1.44453	−	0.486719i	0.928977	+	0.370138i	$0.120690\pi$
$294$	−0.839778			−0.839778
$295$	−1.97076	+	0.323089i	−1.97076	+	0.323089i
$296$		0			0
$297$	−0.407435	+	0.137281i	−0.407435	+	0.137281i
$298$	−1.33693	+	0.804403i	−1.33693	+	0.804403i
$299$		0			0
$300$	−0.326041	−	0.818300i	−0.326041	−	0.818300i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.34676	−	2.76282i	−2.34676	−	2.76282i
$306$		0			0
$307$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$307$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$308$		0			0
$309$	−1.70367	−	0.185285i	−1.70367	−	0.185285i
$310$		0			0
$311$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$311$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$312$	−0.986827	+	0.456555i	−0.986827	+	0.456555i
$313$	−0.181580	+	1.10759i	−0.181580	+	1.10759i	0.725995	+	0.687699i	$0.241379\pi$
$313$	−0.181580	+	1.10759i	−0.181580	+	1.10759i	−0.907575	+	0.419889i	$0.862069\pi$
$314$	−0.920509	−	0.202619i	−0.920509	−	0.202619i
$315$		0			0
$316$	0.555409	−	0.0604044i	0.555409	−	0.0604044i
$317$	−0.855431	−	1.26167i	−0.855431	−	1.26167i	−0.963550	−	0.267528i	$-0.913793\pi$
$317$	−0.855431	−	1.26167i	−0.855431	−	1.26167i	0.108119	−	0.994138i	$-0.465517\pi$
$318$		0			0
$319$		0			0
$320$	−1.58815	+	1.50437i	−1.58815	+	1.50437i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.279342	+	0.0941213i	0.279342	+	0.0941213i
$325$	2.83185	+	0.954161i	2.83185	+	0.954161i
$326$		0			0
$327$		0			0
$328$	0.504107	+	0.477516i	0.504107	+	0.477516i
$329$		0			0
$330$	0.0390369	−	0.719993i	0.0390369	−	0.719993i
$331$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$331$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$332$	−0.227522	−	0.335570i	−0.227522	−	0.335570i
$333$		0			0
$334$	1.19116	+	0.716697i	1.19116	+	0.716697i
$335$		0			0
$336$		0			0
$337$	−1.17510	+	0.543661i	−1.17510	+	0.543661i	−0.907575	−	0.419889i	$-0.862069\pi$
$337$	−1.17510	+	0.543661i	−1.17510	+	0.543661i	−0.267528	+	0.963550i	$0.586207\pi$
$338$	0.224664	−	0.809168i	0.224664	−	0.809168i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−0.0762186	−	0.0897315i	−0.0762186	−	0.0897315i
$345$		0			0
$346$		0			0
$347$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$347$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$348$		0			0
$349$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$349$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$350$		0			0
$351$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$352$	0.231446	−	0.0779832i	0.231446	−	0.0779832i
$353$	1.21035			1.21035			0.605174	−	0.796093i	$-0.293103\pi$
$353$	1.21035			1.21035			0.605174	+	0.796093i	$0.293103\pi$
$354$	0.508212	+	0.668542i	0.508212	+	0.668542i
$355$	−2.05919			−2.05919
$356$	0.551325	−	0.185763i	0.551325	−	0.185763i
$357$		0			0
$358$		0			0
$359$	−0.612719	−	1.53781i	−0.612719	−	1.53781i	−0.827689	−	0.561187i	$-0.810345\pi$
$359$	−0.612719	−	1.53781i	−0.612719	−	1.53781i	0.214970	−	0.976621i	$-0.431034\pi$
$360$	−1.40577	+	1.65500i	−1.40577	+	1.65500i
$361$	0.907575	+	0.419889i	0.907575	+	0.419889i
$362$	0.807627	−	1.19116i	0.807627	−	1.19116i
$363$	0.381824	−	0.720196i	0.381824	−	0.720196i
$364$		0			0
$365$		0			0
$366$	−0.564211	+	1.41606i	−0.564211	+	1.41606i
$367$	0.914915	+	1.72571i	0.914915	+	1.72571i	0.647386	+	0.762162i	$0.275862\pi$
$367$	0.914915	+	1.72571i	0.914915	+	1.72571i	0.267528	+	0.963550i	$0.413793\pi$
$368$		0			0
$369$	0.508387	+	0.386466i	0.508387	+	0.386466i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.522547	−	0.115021i	−0.522547	−	0.115021i	−0.0541389	−	0.998533i	$-0.517241\pi$
$373$	−0.522547	−	0.115021i	−0.522547	−	0.115021i	−0.468408	+	0.883512i	$0.655172\pi$
$374$		0			0
$375$	3.94744	−	0.429310i	3.94744	−	0.429310i
$376$	0.930129	+	1.37184i	0.930129	+	1.37184i
$377$		0			0
$378$		0			0
$379$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$379$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$380$		0			0
$381$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i
$382$		0			0
$383$	1.82622	+	0.615326i	1.82622	+	0.615326i	0.998533	+	0.0541389i	$0.0172414\pi$
$383$	1.82622	+	0.615326i	1.82622	+	0.615326i	0.827689	+	0.561187i	$0.189655\pi$
$384$	0.333402	+	0.112336i	0.333402	+	0.112336i
$385$		0			0
$386$		0			0
$387$	−0.0786092	−	0.0744626i	−0.0786092	−	0.0744626i
$388$		0			0
$389$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$389$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$390$	−0.271323	−	1.65500i	−0.271323	−	1.65500i
$391$		0			0
$392$	1.08095	−	0.117560i	1.08095	−	0.117560i
$393$		0			0
$394$	0.177346	+	0.0390369i	0.177346	+	0.0390369i
$395$	−0.612354	+	3.73519i	−0.612354	+	3.73519i
$396$	0.115021	−	0.0532146i	0.115021	−	0.0532146i
$397$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$397$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$398$	0.750354	+	0.570404i	0.750354	+	0.570404i
$399$		0			0
$400$	−0.865507	−	1.63252i	−0.865507	−	1.63252i
$401$	0.612719	−	1.53781i	0.612719	−	1.53781i	−0.214970	−	0.976621i	$-0.568966\pi$
$401$	0.612719	−	1.53781i	0.612719	−	1.53781i	0.827689	−	0.561187i	$-0.189655\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.12073	+	1.65295i	−1.12073	+	1.65295i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$409$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$410$	−0.917691	+	0.552157i	−0.917691	+	0.552157i
$411$	1.67453	−	0.564213i	1.67453	−	0.564213i
$412$	0.505156			0.505156
$413$		0			0
$414$		0			0
$415$	2.60298	−	0.877046i	2.60298	−	0.877046i
$416$	0.486743	−	0.292864i	0.486743	−	0.292864i
$417$	−0.0861992	+	0.0655269i	−0.0861992	+	0.0655269i
$418$		0			0
$419$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$419$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$420$		0			0
$421$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$421$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$422$	−0.626301	+	1.18133i	−0.626301	+	1.18133i
$423$	0.986827	+	1.16178i	0.986827	+	1.16178i
$424$		0			0
$425$		0			0
$426$	0.405596	+	0.765035i	0.405596	+	0.765035i
$427$		0			0
$428$		0			0
$429$	−0.115021	+	0.414270i	−0.115021	+	0.414270i
$430$	0.164808	−	0.0762485i	0.164808	−	0.0762485i
$431$	−0.195813	+	1.19440i	−0.195813	+	1.19440i	0.687699	+	0.725995i	$0.258621\pi$
$431$	−0.195813	+	1.19440i	−0.195813	+	1.19440i	−0.883512	+	0.468408i	$0.844828\pi$
$432$	0.603880	+	0.132924i	0.603880	+	0.132924i
$433$	0.802718	+	0.482980i	0.802718	+	0.482980i	0.856857	−	0.515554i	$-0.172414\pi$
$433$	0.802718	+	0.482980i	0.802718	+	0.482980i	−0.0541389	+	0.998533i	$0.517241\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.680125	−	0.644248i	−0.680125	−	0.644248i	0.267528	−	0.963550i	$-0.413793\pi$
$439$	−0.680125	−	0.644248i	−0.680125	−	0.644248i	−0.947653	+	0.319302i	$0.896552\pi$
$440$	0.0505439	+	0.932228i	0.0505439	+	0.932228i
$441$	0.976621	−	0.214970i	0.976621	−	0.214970i
$442$		0			0
$443$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$443$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$444$		0			0
$445$	0.213389	+	3.93574i	0.213389	+	3.93574i
$446$		0			0
$447$	1.34887	−	1.27771i	1.34887	−	1.27771i
$448$		0			0
$449$	0.0349834	+	0.213389i	0.0349834	+	0.213389i	0.998533	−	0.0541389i	$-0.0172414\pi$
$449$	0.0349834	+	0.213389i	0.0349834	+	0.213389i	−0.963550	+	0.267528i	$0.913793\pi$
$450$	−1.40829	−	2.07708i	−1.40829	−	2.07708i
$451$	0.272952	−	0.0296853i	0.272952	−	0.0296853i
$452$		0			0
$453$		0			0
$454$	0.140087	−	0.854495i	0.140087	−	0.854495i
$455$		0			0
$456$		0			0
$457$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$457$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.515554	−	1.85686i	−0.515554	−	1.85686i	−0.515554	−	0.856857i	$-0.672414\pi$
$461$	−0.515554	−	1.85686i	−0.515554	−	1.85686i		−	1.00000i	$-0.5\pi$
$462$		0			0
$463$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$463$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$467$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$468$	0.234666	−	0.178389i	0.234666	−	0.178389i
$469$		0			0
$470$	−2.42261	+	0.816273i	−2.42261	+	0.816273i
$471$	1.12237			1.12237
$472$	−0.747751	−	0.789391i	−0.747751	−	0.789391i
$473$	−0.0465531			−0.0465531
$474$	1.50832	−	0.508212i	1.50832	−	0.508212i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.01010	+	1.18918i	−1.01010	+	1.18918i
$479$	0.762162	+	0.352614i	0.762162	+	0.352614i	0.762162	−	0.647386i	$-0.224138\pi$
$479$	0.762162	+	0.352614i	0.762162	+	0.352614i			1.00000i	$0.5\pi$
$480$	0.636637	−	0.938969i	0.636637	−	0.938969i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.0889383	+	0.223218i	−0.0889383	+	0.223218i
$485$		0			0
$486$	0.834855	+	0.0907960i	0.834855	+	0.0907960i
$487$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$487$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$488$	0.528008	−	1.90171i	0.528008	−	1.90171i
$489$		0			0
$490$	−0.271323	+	1.65500i	−0.271323	+	1.65500i
$491$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$491$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$492$	−0.161297	−	0.0970492i	−0.161297	−	0.0970492i
$493$		0			0
$494$		0			0
$495$	0.138909	+	0.847310i	0.138909	+	0.847310i
$496$		0			0
$497$		0			0
$498$	−0.838547	−	0.794314i	−0.838547	−	0.794314i
$499$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$499$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$500$	−1.14309	+	0.251614i	−1.14309	+	0.251614i
$501$	−1.56872	−	0.528565i	−1.56872	−	0.528565i
$502$		0			0
$503$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$503$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0541389	+	0.998533i	−0.0541389	+	0.998533i
$508$	0.0692438	+	0.422369i	0.0692438	+	0.422369i
$509$	1.10759	+	1.63357i	1.10759	+	1.63357i	0.687699	+	0.725995i	$0.258621\pi$
$509$	1.10759	+	1.63357i	1.10759	+	1.63357i	0.419889	+	0.907575i	$0.362069\pi$
$510$		0			0
$511$		0			0
$512$	−0.999650	−	0.220040i	−0.999650	−	0.220040i
$513$		0			0
$514$		0			0
$515$	−0.915590	+	3.29766i	−0.915590	+	3.29766i
$516$	0.0254092	+	0.0193155i	0.0254092	+	0.0193155i
$517$	0.651527	+	0.0708579i	0.651527	+	0.0708579i
$518$		0			0
$519$		0			0
$520$	0.580926	+	2.09230i	0.580926	+	2.09230i
$521$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$521$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$522$		0			0
$523$	0.814839	−	1.20180i	0.814839	−	1.20180i	−0.161782	−	0.986827i	$-0.551724\pi$
$523$	0.814839	−	1.20180i	0.814839	−	1.20180i	0.976621	−	0.214970i	$-0.0689655\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.227794	−	0.137059i	0.227794	−	0.137059i
$529$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$530$		0			0
$531$	−0.762162	−	0.647386i	−0.762162	−	0.647386i
$532$		0			0
$533$	0.605174	−	0.203907i	0.605174	−	0.203907i
$534$	1.42018	−	0.854495i	1.42018	−	0.854495i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.241277	−	0.355857i	0.241277	−	0.355857i
$540$	0.275743	−	0.520106i	0.275743	−	0.520106i
$541$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$541$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$542$		0			0
$543$	−0.634311	+	1.59200i	−0.634311	+	1.59200i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.522547	−	1.88205i	0.522547	−	1.88205i	0.0541389	−	0.998533i	$-0.482759\pi$
$547$	0.522547	−	1.88205i	0.522547	−	1.88205i	0.468408	−	0.883512i	$-0.344828\pi$
$548$	−0.472729	+	0.218708i	−0.472729	+	0.218708i
$549$	0.293659	−	1.79124i	0.293659	−	1.79124i
$550$	−1.05371	−	0.231938i	−1.05371	−	0.231938i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.100575	+	0.613478i	0.100575	+	0.613478i
$555$		0			0
$556$	0.0231718	−	0.0219495i	0.0231718	−	0.0219495i
$557$	−0.609675	−	0.577515i	−0.609675	−	0.577515i	0.319302	−	0.947653i	$-0.396552\pi$
$557$	−0.609675	−	0.577515i	−0.609675	−	0.577515i	−0.928977	+	0.370138i	$0.879310\pi$
$558$		0			0
$559$	−0.105746	+	0.0232765i	−0.105746	+	0.0232765i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$563$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$564$	−0.326211	−	0.309003i	−0.326211	−	0.309003i
$565$		0			0
$566$	0.0861695	−	1.58930i	0.0861695	−	1.58930i
$567$		0			0
$568$	−0.629173	−	0.927960i	−0.629173	−	0.927960i
$569$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$569$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$570$		0			0
$571$	1.94179	+	0.427421i	1.94179	+	0.427421i	0.994138	+	0.108119i	$0.0344828\pi$
$571$	1.94179	+	0.427421i	1.94179	+	0.427421i	0.947653	+	0.319302i	$0.103448\pi$
$572$	0.0205034	−	0.125065i	0.0205034	−	0.125065i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.08896	−	0.118431i	−1.08896	−	0.118431i
$577$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$577$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$578$	−0.310834	+	0.780134i	−0.310834	+	0.780134i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.739191	+	1.85523i	0.739191	+	1.85523i
$586$	−1.01907	+	0.774680i	−1.01907	+	0.774680i
$587$	−1.17852	+	0.709092i	−1.17852	+	0.709092i	−0.963550	−	0.267528i	$-0.913793\pi$
$587$	−1.17852	+	0.709092i	−1.17852	+	0.709092i	−0.214970	+	0.976621i	$0.568966\pi$
$588$	−0.279342	+	0.0941213i	−0.279342	+	0.0941213i
$589$		0			0
$590$	1.48173	−	0.785565i	1.48173	−	0.785565i
$591$	−0.216238			−0.216238
$592$		0			0
$593$	−1.03710	+	0.624000i	−1.03710	+	0.624000i	−0.928977	−	0.370138i	$-0.879310\pi$
$593$	−1.03710	+	0.624000i	−1.03710	+	0.624000i	−0.108119	+	0.994138i	$0.534483\pi$
$594$	0.287433	−	0.218501i	0.287433	−	0.218501i
$595$		0			0
$596$	−0.354556	+	0.417416i	−0.354556	+	0.417416i
$597$	−1.01864	−	0.471273i	−1.01864	−	0.471273i
$598$		0			0
$599$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$599$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$600$	2.10350	+	2.47643i	2.10350	+	2.47643i
$601$	0.388449	+	1.39907i	0.388449	+	1.39907i	0.856857	+	0.515554i	$0.172414\pi$
$601$	0.388449	+	1.39907i	0.388449	+	1.39907i	−0.468408	+	0.883512i	$0.655172\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.29597	−	0.985170i	−1.29597	−	0.985170i
$606$		0			0
$607$	−1.72013	+	0.795818i	−1.72013	+	0.795818i	−0.725995	+	0.687699i	$0.758621\pi$
$607$	−1.72013	+	0.795818i	−1.72013	+	0.795818i	−0.994138	+	0.108119i	$0.965517\pi$
$608$		0			0
$609$		0			0
$610$	2.60843	+	1.56944i	2.60843	+	1.56944i
$611$	1.51539	−	0.164808i	1.51539	−	0.164808i
$612$		0			0
$613$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$613$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$614$		0			0
$615$	0.925886	−	0.877046i	0.925886	−	0.877046i
$616$		0			0
$617$	0.0744626	+	1.37338i	0.0744626	+	1.37338i	0.762162	+	0.647386i	$0.224138\pi$
$617$	0.0744626	+	1.37338i	0.0744626	+	1.37338i	−0.687699	+	0.725995i	$0.741379\pi$
$618$	1.40549	−	0.309373i	1.40549	−	0.309373i
$619$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$619$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	0.448910	−	0.425230i	0.448910	−	0.425230i
$625$	0.267528	−	4.93427i	0.267528	−	4.93427i
$626$	−0.152487	−	0.930129i	−0.152487	−	0.930129i
$627$		0			0
$628$	−0.328906	+	0.0357706i	−0.328906	+	0.0357706i
$629$		0			0
$630$		0			0
$631$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$631$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$632$	−1.87034	+	0.865311i	−1.87034	+	0.865311i
$633$	0.425955	−	1.53415i	0.425955	−	1.53415i
$634$	1.01907	+	0.774680i	1.01907	+	0.774680i
$635$	−2.88272	−	0.313515i	−2.88272	−	0.313515i
$636$		0			0
$637$	0.370138	−	0.928977i	0.370138	−	0.928977i
$638$		0			0
$639$	−0.667525	−	0.785871i	−0.667525	−	0.785871i
$640$	0.329106	−	0.620759i	0.329106	−	0.620759i
$641$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$641$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$642$		0			0
$643$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$643$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$644$		0			0
$645$	−0.172146	+	0.130862i	−0.172146	+	0.130862i
$646$		0			0
$647$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$647$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$648$	−1.08732			−1.08732
$649$	−0.429310	+	0.0232765i	−0.429310	+	0.0232765i
$650$	−2.50949			−2.50949
$651$		0			0
$652$		0			0
$653$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$653$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$654$		0			0
$655$		0			0
$656$	−0.358376	−	0.165802i	−0.358376	−	0.165802i
$657$		0			0
$658$		0			0
$659$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$659$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$660$	−0.0677108	−	0.243872i	−0.0677108	−	0.243872i
$661$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$661$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$662$		0			0
$663$		0			0
$664$	1.19056	+	0.905039i	1.19056	+	0.905039i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.476552	+	0.104897i	0.476552	+	0.104897i
$669$		0			0
$670$		0			0
$671$	−0.437955	−	0.645935i	−0.437955	−	0.645935i
$672$		0			0
$673$	0.0700976	−	1.29287i	0.0700976	−	1.29287i	−0.725995	−	0.687699i	$-0.758621\pi$
$673$	0.0700976	−	1.29287i	0.0700976	−	1.29287i	0.796093	−	0.605174i	$-0.206897\pi$
$674$	0.789391	−	0.747751i	0.789391	−	0.747751i
$675$	2.16947	+	2.05504i	2.16947	+	2.05504i
$676$	−0.0159587	−	0.294340i	−0.0159587	−	0.294340i
$677$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$677$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.0558230	+	1.02960i	0.0558230	+	1.02960i
$682$		0			0
$683$	−0.463623	+	0.439167i	−0.463623	+	0.439167i	−0.883512	−	0.468408i	$-0.844828\pi$
$683$	−0.463623	+	0.439167i	−0.463623	+	0.439167i	0.419889	+	0.907575i	$0.362069\pi$
$684$		0			0
$685$	−0.570907	−	3.48238i	−0.570907	−	3.48238i
$686$		0			0
$687$		0			0
$688$	0.0573684	+	0.0345174i	0.0573684	+	0.0345174i
$689$		0			0
$690$		0			0
$691$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$691$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.101288	+	0.191049i	0.101288	+	0.191049i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$701$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$702$	0.543661	−	0.640047i	0.543661	−	0.640047i
$703$		0			0
$704$	−0.374918	+	0.285005i	−0.374918	+	0.285005i
$705$	2.60843	−	1.56944i	2.60843	−	1.56944i
$706$	−0.963218	+	0.324546i	−0.963218	+	0.324546i
$707$		0			0
$708$	0.243980	+	0.165423i	0.243980	+	0.165423i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$	1.63874	−	0.552157i	1.63874	−	0.552157i
$711$	−1.62401	+	0.977132i	−1.62401	+	0.977132i
$712$	−1.70841	+	1.29870i	−1.70841	+	1.29870i
$713$		0			0
$714$		0			0
$715$	0.779263	+	0.360525i	0.779263	+	0.360525i
$716$		0			0
$717$	0.870281	−	1.64152i	0.870281	−	1.64152i
$718$	0.899964	+	1.05952i	0.899964	+	1.05952i
$719$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$719$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$720$	0.457069	−	1.14716i	0.457069	−	1.14716i
$721$		0			0
$722$	−0.834855	−	0.0907960i	−0.834855	−	0.0907960i
$723$		0			0
$724$	0.135144	−	0.486743i	0.135144	−	0.486743i
$725$		0			0
$726$	−0.110747	+	0.675528i	−0.110747	+	0.675528i
$727$	−1.55496	−	0.342273i	−1.55496	−	0.342273i	−0.647386	−	0.762162i	$-0.724138\pi$
$727$	−1.55496	−	0.342273i	−1.55496	−	0.342273i	−0.907575	+	0.419889i	$0.862069\pi$
$728$		0			0
$729$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$730$		0			0
$731$		0			0
$732$	−0.0289674	+	0.534272i	−0.0289674	+	0.534272i
$733$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$733$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$734$	−1.19084	−	1.12803i	−1.19084	−	1.12803i
$735$	−0.108119	−	1.99414i	−0.108119	−	1.99414i
$736$		0			0
$737$		0			0
$738$	−0.508212	−	0.171237i	−0.508212	−	0.171237i
$739$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$739$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.0558230	−	1.02960i	0.0558230	−	1.02960i	−0.827689	−	0.561187i	$-0.810345\pi$
$743$	0.0558230	−	1.02960i	0.0558230	−	1.02960i	0.883512	−	0.468408i	$-0.155172\pi$
$744$		0			0
$745$	−2.08226	−	3.07110i	−2.08226	−	3.07110i
$746$	0.446695	−	0.0485810i	0.446695	−	0.0485810i
$747$	1.17852	+	0.709092i	1.17852	+	0.709092i
$748$		0			0
$749$		0			0
$750$	−3.02633	+	1.40013i	−3.02633	+	1.40013i
$751$	0.346388	−	1.24758i	0.346388	−	1.24758i	−0.561187	−	0.827689i	$-0.689655\pi$
$751$	0.346388	−	1.24758i	0.346388	−	1.24758i	0.907575	−	0.419889i	$-0.137931\pi$
$752$	−0.750354	−	0.570404i	−0.750354	−	0.570404i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.726610	+	0.855431i	0.726610	+	0.855431i	0.994138	−	0.108119i	$-0.0344828\pi$
$757$	0.726610	+	0.855431i	0.726610	+	0.855431i	−0.267528	+	0.963550i	$0.586207\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.20281	−	1.41606i	1.20281	−	1.41606i	0.319302	−	0.947653i	$-0.396552\pi$
$761$	1.20281	−	1.41606i	1.20281	−	1.41606i	0.883512	−	0.468408i	$-0.155172\pi$
$762$	0.451328	+	1.13275i	0.451328	+	1.13275i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−1.61834			−1.61834
$767$	−0.963550	+	0.267528i	−0.963550	+	0.267528i
$768$	0.799929			0.799929
$769$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$769$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.14395	−	1.34676i	1.14395	−	1.34676i	0.214970	−	0.976621i	$-0.431034\pi$
$773$	1.14395	−	1.34676i	1.14395	−	1.34676i	0.928977	−	0.370138i	$-0.120690\pi$
$774$	0.0825252	+	0.0381802i	0.0825252	+	0.0381802i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.275743	−	0.520106i	−0.275743	−	0.520106i
$781$	−0.440717	−	0.0479308i	−0.440717	−	0.0479308i
$782$		0			0
$783$		0			0
$784$	−0.561187	+	0.259633i	−0.561187	+	0.259633i
$785$	0.362627	−	2.21193i	0.362627	−	2.21193i
$786$		0			0
$787$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$787$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$788$	0.0633674	−	0.00689162i	0.0633674	−	0.00689162i
$789$		0			0
$790$	−0.514241	−	3.13673i	−0.514241	−	3.13673i
$791$		0			0
$792$	−0.339391	+	0.321489i	−0.339391	+	0.321489i
$793$	−1.31779	−	1.24828i	−1.31779	−	1.24828i
$794$		0			0
$795$		0			0
$796$	0.313526	+	0.105639i	0.313526	+	0.105639i
$797$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$797$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$798$		0			0
$799$		0			0
$800$	−1.23238	−	1.16738i	−1.23238	−	1.16738i
$801$	−1.43286	+	1.35728i	−1.43286	+	1.35728i
$802$	−0.0752612	+	1.38811i	−0.0752612	+	1.38811i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$809$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$810$	0.448670	−	1.61596i	0.448670	−	1.61596i
$811$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$811$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−0.243374	+	0.286522i	−0.243374	+	0.286522i
$821$	−0.739191	−	1.85523i	−0.739191	−	1.85523i	−0.419889	−	0.907575i	$-0.637931\pi$
$821$	−0.739191	−	1.85523i	−0.739191	−	1.85523i	−0.319302	−	0.947653i	$-0.603448\pi$
$822$	−1.18133	+	0.898023i	−1.18133	+	0.898023i
$823$	−0.458467	+	0.275851i	−0.458467	+	0.275851i	−0.725995	−	0.687699i	$-0.758621\pi$
$823$	−0.458467	+	0.275851i	−0.458467	+	0.275851i	0.267528	+	0.963550i	$0.413793\pi$
$824$	−1.76582	+	0.594973i	−1.76582	+	0.594973i
$825$	1.28478			1.28478
$826$		0			0
$827$	−0.429941			−0.429941			−0.214970	−	0.976621i	$-0.568966\pi$
$827$	−0.429941			−0.429941			−0.214970	+	0.976621i	$0.568966\pi$
$828$		0			0
$829$	−0.277248	+	0.166815i	−0.277248	+	0.166815i	−0.647386	−	0.762162i	$-0.724138\pi$
$829$	−0.277248	+	0.166815i	−0.277248	+	0.166815i	0.370138	+	0.928977i	$0.379310\pi$
$830$	−1.83633	+	1.39594i	−1.83633	+	1.39594i
$831$	−0.274005	−	0.687699i	−0.274005	−	0.687699i
$832$	−0.709133	+	0.834855i	−0.709133	+	0.834855i
$833$		0			0
$834$	0.0510284	−	0.0752612i	0.0510284	−	0.0752612i
$835$	−1.54851	+	2.92080i	−1.54851	+	2.92080i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.482980	+	0.910996i	0.482980	+	0.910996i	0.998533	+	0.0541389i	$0.0172414\pi$
$839$	0.482980	+	0.910996i	0.482980	+	0.910996i	−0.515554	+	0.856857i	$0.672414\pi$
$840$		0			0
$841$	0.796093	+	0.605174i	0.796093	+	0.605174i
$842$		0			0
$843$		0			0
$844$	−0.0759296	+	0.463150i	−0.0759296	+	0.463150i
$845$	1.95038	+	0.429310i	1.95038	+	0.429310i
$846$	−1.09686	−	0.659957i	−1.09686	−	0.659957i
$847$		0			0
$848$		0			0
$849$	0.306626	+	1.87034i	0.306626	+	1.87034i
$850$		0			0
$851$		0			0
$852$	0.220661	+	0.209021i	0.220661	+	0.209021i
$853$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$853$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$857$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$858$	−0.0195471	−	0.360525i	−0.0195471	−	0.360525i
$859$	1.41804	+	1.34324i	1.41804	+	1.34324i	0.856857	+	0.515554i	$0.172414\pi$
$859$	1.41804	+	1.34324i	1.41804	+	1.34324i	0.561187	+	0.827689i	$0.310345\pi$
$860$	0.0462757	−	0.0438347i	0.0462757	−	0.0438347i
$861$		0			0
$862$	−0.164439	−	1.00303i	−0.164439	−	1.00303i
$863$	0.679232	+	1.00179i	0.679232	+	1.00179i	0.998533	+	0.0541389i	$0.0172414\pi$
$863$	0.679232	+	1.00179i	0.679232	+	1.00179i	−0.319302	+	0.947653i	$0.603448\pi$
$864$	0.564726	−	0.0614177i	0.564726	−	0.0614177i
$865$		0			0
$866$	−0.768325	−	0.169121i	−0.768325	−	0.169121i
$867$	0.161782	−	0.986827i	0.161782	−	0.986827i
$868$		0			0
$869$	−0.218001	+	0.785168i	−0.218001	+	0.785168i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$877$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$878$	0.714006	+	0.330334i	0.714006	+	0.330334i
$879$	0.986827	−	1.16178i	0.986827	−	1.16178i
$880$	−0.196512	−	0.493209i	−0.196512	−	0.493209i
$881$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$881$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$882$	−0.719570	+	0.432951i	−0.719570	+	0.432951i
$883$	0.507048	−	0.170844i	0.507048	−	0.170844i	−0.0541389	−	0.998533i	$-0.517241\pi$
$883$	0.507048	−	0.170844i	0.507048	−	0.170844i	0.561187	+	0.827689i	$0.310345\pi$
$884$		0			0
$885$	−1.52209	+	1.29287i	−1.52209	+	1.29287i
$886$		0			0
$887$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$887$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$888$		0			0
$889$		0			0
$890$	−1.22516	−	3.07491i	−1.22516	−	3.07491i
$891$	−0.278338	+	0.327685i	−0.278338	+	0.327685i
$892$		0			0
$893$		0			0
$894$	−0.730843	+	1.37852i	−0.730843	+	1.37852i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.0850592	−	0.160439i	−0.0850592	−	0.160439i
$899$		0			0
$900$	−0.701248	−	0.533075i	−0.701248	−	0.533075i
$901$		0			0
$902$	−0.209260	+	0.0968142i	−0.209260	+	0.0968142i
$903$		0			0
$904$		0			0
$905$	2.93251	+	1.76443i	2.93251	+	1.76443i
$906$		0			0
$907$	−0.415433	−	0.612719i	−0.415433	−	0.612719i	0.561187	−	0.827689i	$-0.310345\pi$
$907$	−0.415433	−	0.612719i	−0.415433	−	0.612719i	−0.976621	+	0.214970i	$0.931034\pi$
$908$	−0.0491724	−	0.299938i	−0.0491724	−	0.299938i
$909$		0			0
$910$		0			0
$911$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$911$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$912$		0			0
$913$	0.577515	−	0.127121i	0.577515	−	0.127121i
$914$		0			0
$915$	−3.43522	−	1.15746i	−3.43522	−	1.15746i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.234906	+	0.222515i	−0.234906	+	0.222515i	−0.796093	−	0.605174i	$-0.793103\pi$
$919$	−0.234906	+	0.222515i	−0.234906	+	0.222515i	0.561187	+	0.827689i	$0.310345\pi$
$920$		0			0
$921$		0			0
$922$	0.908190	+	1.33948i	0.908190	+	1.33948i
$923$	−1.02506	+	0.111482i	−1.02506	+	0.111482i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.55533	+	0.719570i	−1.55533	+	0.719570i
$928$		0			0
$929$	−0.172146	−	0.130862i	−0.172146	−	0.130862i	0.515554	−	0.856857i	$-0.327586\pi$
$929$	−0.172146	−	0.130862i	−0.172146	−	0.130862i	−0.687699	+	0.725995i	$0.741379\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.610191	+	0.899964i	−0.610191	+	0.899964i
$937$	−1.77271	−	0.820145i	−1.77271	−	0.820145i	−0.976621	−	0.214970i	$-0.931034\pi$
$937$	−1.77271	−	0.820145i	−1.77271	−	0.820145i	−0.796093	−	0.605174i	$-0.793103\pi$
$938$		0			0
$939$	0.415433	+	1.04266i	0.415433	+	1.04266i
$940$	−0.714366	+	0.543047i	−0.714366	+	0.543047i
$941$	−0.547192	+	0.329234i	−0.547192	+	0.329234i	−0.762162	−	0.647386i	$-0.775862\pi$
$941$	−0.547192	+	0.329234i	−0.547192	+	0.329234i	0.214970	+	0.976621i	$0.431034\pi$
$942$	−0.893206	+	0.300956i	−0.893206	+	0.300956i
$943$		0			0
$944$	0.546308	+	0.289634i	0.546308	+	0.289634i
$945$		0			0
$946$	0.0370478	−	0.0124829i	0.0370478	−	0.0124829i
$947$	0.185285	−	0.111482i	0.185285	−	0.111482i	−0.419889	−	0.907575i	$-0.637931\pi$
$947$	0.185285	−	0.111482i	0.185285	−	0.111482i	0.605174	+	0.796093i	$0.293103\pi$
$948$	0.444765	−	0.338101i	0.444765	−	0.338101i
$949$		0			0
$950$		0			0
$951$	−1.38344	−	0.640047i	−1.38344	−	0.640047i
$952$		0			0
$953$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$953$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$954$		0			0
$955$		0			0
$956$	−0.202715	+	0.508776i	−0.202715	+	0.508776i
$957$		0			0
$958$	−0.701093	−	0.0762485i	−0.701093	−	0.0762485i
$959$		0			0
$960$	−0.585230	+	2.10781i	−0.585230	+	2.10781i
$961$	0.907575	−	0.419889i	0.907575	−	0.419889i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$967$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$968$	0.0479850	−	0.885031i	0.0479850	−	0.885031i
$969$		0			0
$970$		0			0
$971$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$971$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$972$	0.287881	−	0.0633674i	0.287881	−	0.0633674i
$973$		0			0
$974$		0			0
$975$	2.91841	−	0.642391i	2.91841	−	0.642391i
$976$	0.0607641	+	1.12073i	0.0607641	+	1.12073i
$977$	−1.44986	−	1.37338i	−1.44986	−	1.37338i	−0.762162	−	0.647386i	$-0.775862\pi$
$977$	−1.44986	−	1.37338i	−1.44986	−	1.37338i	−0.687699	−	0.725995i	$-0.741379\pi$
$978$		0			0
$979$	−0.0459398	+	0.847310i	−0.0459398	+	0.847310i
$980$	0.0952379	+	0.580926i	0.0952379	+	0.580926i
$981$		0			0
$982$		0			0
$983$	−1.51409	−	0.910996i	−1.51409	−	0.910996i	−0.998533	−	0.0541389i	$-0.982759\pi$
$983$	−1.51409	−	0.910996i	−1.51409	−	0.910996i	−0.515554	−	0.856857i	$-0.672414\pi$
$984$	0.678133	+	0.149268i	0.678133	+	0.149268i
$985$	−0.0698642	+	0.426153i	−0.0698642	+	0.426153i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.337746	−	0.637057i	−0.337746	−	0.637057i
$991$	0.701525	−	1.76070i	0.701525	−	1.76070i	0.0541389	−	0.998533i	$-0.482759\pi$
$991$	0.701525	−	1.76070i	0.701525	−	1.76070i	0.647386	−	0.762162i	$-0.275862\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.25788	+	1.85523i	−1.25788	+	1.85523i
$996$	−0.367958	−	0.170236i	−0.367958	−	0.170236i
$997$	1.26450	−	1.48869i	1.26450	−	1.48869i	0.468408	−	0.883512i	$-0.344828\pi$
$997$	1.26450	−	1.48869i	1.26450	−	1.48869i	0.796093	−	0.605174i	$-0.206897\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2301.1.z.c.779.1	✓	56
3.2	odd	2	inner	2301.1.z.c.779.2	yes	56
13.12	even	2	inner	2301.1.z.c.779.2	yes	56
39.38	odd	2	CM	2301.1.z.c.779.1	✓	56
59.5	even	29	inner	2301.1.z.c.1598.1	yes	56
177.5	odd	58	inner	2301.1.z.c.1598.2	yes	56
767.64	even	58	inner	2301.1.z.c.1598.2	yes	56
2301.1598	odd	58	inner	2301.1.z.c.1598.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2301.1.z.c.779.1	✓	56	1.1	even	1	trivial
2301.1.z.c.779.1	✓	56	39.38	odd	2	CM
2301.1.z.c.779.2	yes	56	3.2	odd	2	inner
2301.1.z.c.779.2	yes	56	13.12	even	2	inner
2301.1.z.c.1598.1	yes	56	59.5	even	29	inner
2301.1.z.c.1598.1	yes	56	2301.1598	odd	58	inner
2301.1.z.c.1598.2	yes	56	177.5	odd	58	inner
2301.1.z.c.1598.2	yes	56	767.64	even	58	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2301 = 3 \cdot 13 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2301.z (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795818 + 0.268142i) q^{2} +(0.856857 - 0.515554i) q^{3} +(-0.234666 + 0.178389i) q^{4} +(-0.739191 - 1.85523i) q^{5} +(-0.543661 + 0.640047i) q^{6} +(0.610191 - 0.899964i) q^{8} +(0.468408 - 0.883512i) q^{9} +(1.08573 + 1.27822i) q^{10} +(-0.115021 - 0.414270i) q^{11} +(-0.109107 + 0.273837i) q^{12} +(-0.468408 - 0.883512i) q^{13} +(-1.58985 - 1.20857i) q^{15} +(-0.165423 + 0.595798i) q^{16} +(-0.135861 + 0.828715i) q^{18} +(0.504415 + 0.303497i) q^{20} +(0.202619 + 0.298841i) q^{22} +(0.0588664 - 1.08573i) q^{24} +(-2.16947 + 2.05504i) q^{25} +(0.609675 + 0.577515i) q^{26} +(-0.0541389 - 0.998533i) q^{27} +(1.58930 + 0.535498i) q^{30} +(0.0307539 + 0.567223i) q^{32} +(-0.312135 - 0.295670i) q^{33} +(0.0476889 + 0.290889i) q^{36} +(-0.856857 - 0.515554i) q^{39} +(-2.12069 - 0.466798i) q^{40} +(-0.103314 + 0.630190i) q^{41} +(0.0289674 - 0.104331i) q^{43} +(0.100893 + 0.0766966i) q^{44} +(-1.98536 - 0.215921i) q^{45} +(-0.564211 + 1.41606i) q^{47} +(0.165423 + 0.595798i) q^{48} +(0.647386 + 0.762162i) q^{49} +(1.17547 - 2.21716i) q^{50} +(0.267528 + 0.123772i) q^{52} +(0.310834 + 0.780134i) q^{54} +(-0.683542 + 0.519615i) q^{55} +(0.214970 - 0.976621i) q^{59} +0.588681 q^{60} +(1.72013 - 0.579580i) q^{61} +(-0.405441 - 1.01758i) q^{64} +(-1.29287 + 1.52209i) q^{65} +(0.327685 + 0.151603i) q^{66} +(0.381652 - 0.957875i) q^{71} +(-0.509311 - 0.960662i) q^{72} +(-0.799448 + 2.87935i) q^{75} +(0.820145 + 0.180527i) q^{78} +(-1.62401 - 0.977132i) q^{79} +(1.22762 - 0.133512i) q^{80} +(-0.561187 - 0.827689i) q^{81} +(-0.0867612 - 0.529220i) q^{82} +(-0.0744626 + 1.37338i) q^{83} +(0.00492282 + 0.0907960i) q^{86} +(-0.443013 - 0.149268i) q^{88} +(-1.87034 - 0.630190i) q^{89} +(1.63788 - 0.360525i) q^{90} +(0.0693029 - 1.27822i) q^{94} +(0.318786 + 0.470174i) q^{96} +(-0.719570 - 0.432951i) q^{98} +(-0.419889 - 0.0924246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{12} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{27} + 2 q^{36} - 2 q^{39} - 58 q^{40} - 4 q^{43} + 2 q^{48} - 2 q^{49} - 2 q^{52} + 4 q^{61} + 2 q^{64} - 2 q^{75} + 4 q^{79}+ \cdots - 2 q^{81}+O(q^{100}) \) 56 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^12 + 2 * q^13 - 2 * q^16 + 2 * q^25 + 2 * q^27 + 2 * q^36 - 2 * q^39 - 58 * q^40 - 4 * q^43 + 2 * q^48 - 2 * q^49 - 2 * q^52 + 4 * q^61 + 2 * q^64 - 2 * q^75 + 4 * q^79 - 2 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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