LMFDB - Embedded newform 1416.1.r.b.197.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1416,1,Mod(5,1416)] 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("1416.5"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1416, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([0, 29, 29, 6])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1416 = 2^{3} \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1416.r (of order $58$, degree $28$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,1] 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:	$0.706676057888$
Analytic rank:	$0$
Dimension:	$28$
Coefficient field:	$\Q(\zeta_{58})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} + \cdots + 1 $ x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{29}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{29} + \cdots)$

Embedding invariants

Embedding label			197.1
Root			$-0.796093 - 0.605174i$ of defining polynomial
Character	$\chi$	$=$	1416.197
Dual form			1416.1.r.b.1301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.907575 - 0.419889i) q^{2} +(0.947653 - 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(0.0927786 - 0.0558230i) q^{5} +(-0.994138 - 0.108119i) q^{6} +(-0.0400778 - 0.739191i) q^{7} +(-0.267528 - 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(-0.107643 + 0.0117069i) q^{10} +(-0.277248 - 1.69114i) q^{11} +(0.856857 + 0.515554i) q^{12} +(-0.274005 + 0.687699i) q^{14} +(0.0700976 - 0.0825252i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(-0.976621 + 0.214970i) q^{18} +(0.102610 + 0.0345733i) q^{20} +(-0.274005 - 0.687699i) q^{21} +(-0.458467 + 1.65125i) q^{22} +(-0.561187 - 0.827689i) q^{24} +(-0.462917 + 0.873154i) q^{25} +(0.561187 - 0.827689i) q^{27} +(0.537437 - 0.509088i) q^{28} +(-1.77271 + 0.820145i) q^{29} +(-0.0982703 + 0.0454647i) q^{30} +(-0.388449 + 0.367958i) q^{31} +(0.561187 - 0.827689i) q^{32} +(-0.802718 - 1.51409i) q^{33} +(-0.0449822 - 0.0663438i) q^{35} +(0.976621 + 0.214970i) q^{36} +(-0.0786092 - 0.0744626i) q^{40} +(-0.0400778 + 0.739191i) q^{42} +(1.10944 - 1.30613i) q^{44} +(0.0400778 - 0.100588i) q^{45} +(0.161782 + 0.986827i) q^{48} +(0.449341 - 0.0488688i) q^{49} +(0.786760 - 0.598079i) q^{50} +(1.58285 + 0.172146i) q^{53} +(-0.856857 + 0.515554i) q^{54} +(-0.120127 - 0.141425i) q^{55} +(-0.701525 + 0.236371i) q^{56} +1.95324 q^{58} +(0.994138 - 0.108119i) q^{59} +0.108278 q^{60} +(0.507048 - 0.170844i) q^{62} +(-0.479245 - 0.564211i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(0.0927786 + 1.71120i) q^{66} +(0.0129677 + 0.0790996i) q^{70} +(-0.796093 - 0.605174i) q^{72} +(0.537437 - 1.34887i) q^{73} +(-0.159885 + 0.975257i) q^{75} +(-1.23896 + 0.272716i) q^{77} +(1.06362 + 0.358376i) q^{79} +(0.0400778 + 0.100588i) q^{80} +(0.267528 - 0.963550i) q^{81} +(0.726610 + 1.07167i) q^{83} +(0.346752 - 0.654043i) q^{84} +(-1.41804 + 1.34324i) q^{87} +(-1.55533 + 0.719570i) q^{88} +(-0.0786092 + 0.0744626i) q^{90} +(-0.250625 + 0.472729i) q^{93} +(0.267528 - 0.963550i) q^{96} +(0.119763 + 0.300583i) q^{97} +(-0.428331 - 0.144321i) q^{98} +(-1.24415 - 1.17852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} + q^{8} - q^{9} - 2 q^{10} + 2 q^{11} + q^{12} - 27 q^{14} - 2 q^{15} - q^{16} + q^{18} + 2 q^{20} - 27 q^{21} - 2 q^{22} - q^{24} - 3 q^{25}+ \cdots + 2 q^{99}+O(q^{100}) $ 28 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 + q^8 - q^9 - 2 * q^10 + 2 * q^11 + q^12 - 27 * q^14 - 2 * q^15 - q^16 + q^18 + 2 * q^20 - 27 * q^21 - 2 * q^22 - q^24 - 3 * q^25 + q^27 - 2 * q^28 + 2 * q^29 + 2 * q^30 - 2 * q^31 + q^32 - 2 * q^33 + 4 * q^35 - q^36 - 2 * q^40 - 2 * q^42 + 2 * q^44 + 2 * q^45 + q^48 - 3 * q^49 + 3 * q^50 + 2 * q^53 - q^54 - 4 * q^55 + 2 * q^56 - 2 * q^58 + q^59 - 2 * q^60 + 2 * q^62 - 2 * q^63 - q^64 + 2 * q^66 - 4 * q^70 + q^72 - 2 * q^73 + 3 * q^75 + 4 * q^77 - 2 * q^79 + 2 * q^80 - q^81 + 2 * q^83 + 2 * q^84 - 2 * q^87 - 2 * q^88 - 2 * q^90 + 2 * q^93 - q^96 - 2 * q^97 + 3 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1416\mathbb{Z}\right)^\times$.

$n$	$473$	$709$	$769$	$1063$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.907575	−	0.419889i	−0.907575	−	0.419889i
$2$	−0.907575	−	0.419889i	−0.907575	−	0.419889i
$3$	0.947653	−	0.319302i	0.947653	−	0.319302i
$3$	0.947653	−	0.319302i	0.947653	−	0.319302i
$4$	0.647386	+	0.762162i	0.647386	+	0.762162i
$5$	0.0927786	−	0.0558230i	0.0927786	−	0.0558230i	−0.468408	−	0.883512i	$-0.655172\pi$
$5$	0.0927786	−	0.0558230i	0.0927786	−	0.0558230i	0.561187	+	0.827689i	$0.310345\pi$
$6$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$7$	−0.0400778	−	0.739191i	−0.0400778	−	0.739191i	−0.947653	−	0.319302i	$-0.896552\pi$
$7$	−0.0400778	−	0.739191i	−0.0400778	−	0.739191i	0.907575	−	0.419889i	$-0.137931\pi$
$8$	−0.267528	−	0.963550i	−0.267528	−	0.963550i
$9$	0.796093	−	0.605174i	0.796093	−	0.605174i
$10$	−0.107643	+	0.0117069i	−0.107643	+	0.0117069i
$11$	−0.277248	−	1.69114i	−0.277248	−	1.69114i	−0.647386	−	0.762162i	$-0.724138\pi$
$11$	−0.277248	−	1.69114i	−0.277248	−	1.69114i	0.370138	−	0.928977i	$-0.379310\pi$
$12$	0.856857	+	0.515554i	0.856857	+	0.515554i
$13$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$13$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$14$	−0.274005	+	0.687699i	−0.274005	+	0.687699i
$15$	0.0700976	−	0.0825252i	0.0700976	−	0.0825252i
$16$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$17$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$17$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$18$	−0.976621	+	0.214970i	−0.976621	+	0.214970i
$19$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$19$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$20$	0.102610	+	0.0345733i	0.102610	+	0.0345733i
$21$	−0.274005	−	0.687699i	−0.274005	−	0.687699i
$22$	−0.458467	+	1.65125i	−0.458467	+	1.65125i
$23$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$23$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$24$	−0.561187	−	0.827689i	−0.561187	−	0.827689i
$25$	−0.462917	+	0.873154i	−0.462917	+	0.873154i
$26$		0			0
$27$	0.561187	−	0.827689i	0.561187	−	0.827689i
$28$	0.537437	−	0.509088i	0.537437	−	0.509088i
$29$	−1.77271	+	0.820145i	−1.77271	+	0.820145i	−0.796093	+	0.605174i	$0.793103\pi$
$29$	−1.77271	+	0.820145i	−1.77271	+	0.820145i	−0.976621	+	0.214970i	$0.931034\pi$
$30$	−0.0982703	+	0.0454647i	−0.0982703	+	0.0454647i
$31$	−0.388449	+	0.367958i	−0.388449	+	0.367958i	−0.856857	−	0.515554i	$-0.827586\pi$
$31$	−0.388449	+	0.367958i	−0.388449	+	0.367958i	0.468408	+	0.883512i	$0.344828\pi$
$32$	0.561187	−	0.827689i	0.561187	−	0.827689i
$33$	−0.802718	−	1.51409i	−0.802718	−	1.51409i
$34$		0			0
$35$	−0.0449822	−	0.0663438i	−0.0449822	−	0.0663438i
$36$	0.976621	+	0.214970i	0.976621	+	0.214970i
$37$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$37$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$38$		0			0
$39$		0			0
$40$	−0.0786092	−	0.0744626i	−0.0786092	−	0.0744626i
$41$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$41$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$42$	−0.0400778	+	0.739191i	−0.0400778	+	0.739191i
$43$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$43$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$44$	1.10944	−	1.30613i	1.10944	−	1.30613i
$45$	0.0400778	−	0.100588i	0.0400778	−	0.100588i
$46$		0			0
$47$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$47$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$48$	0.161782	+	0.986827i	0.161782	+	0.986827i
$49$	0.449341	−	0.0488688i	0.449341	−	0.0488688i
$50$	0.786760	−	0.598079i	0.786760	−	0.598079i
$51$		0			0
$52$		0			0
$53$	1.58285	+	0.172146i	1.58285	+	0.172146i	0.856857	−	0.515554i	$-0.172414\pi$
$53$	1.58285	+	0.172146i	1.58285	+	0.172146i	0.725995	+	0.687699i	$0.241379\pi$
$54$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$55$	−0.120127	−	0.141425i	−0.120127	−	0.141425i
$56$	−0.701525	+	0.236371i	−0.701525	+	0.236371i
$57$		0			0
$58$	1.95324			1.95324
$59$	0.994138	−	0.108119i	0.994138	−	0.108119i
$59$	0.994138	−	0.108119i	0.994138	−	0.108119i
$60$	0.108278			0.108278
$61$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$61$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$62$	0.507048	−	0.170844i	0.507048	−	0.170844i
$63$	−0.479245	−	0.564211i	−0.479245	−	0.564211i
$64$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$65$		0			0
$66$	0.0927786	+	1.71120i	0.0927786	+	1.71120i
$67$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$67$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$68$		0			0
$69$		0			0
$70$	0.0129677	+	0.0790996i	0.0129677	+	0.0790996i
$71$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$71$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$72$	−0.796093	−	0.605174i	−0.796093	−	0.605174i
$73$	0.537437	−	1.34887i	0.537437	−	1.34887i	−0.370138	−	0.928977i	$-0.620690\pi$
$73$	0.537437	−	1.34887i	0.537437	−	1.34887i	0.907575	−	0.419889i	$-0.137931\pi$
$74$		0			0
$75$	−0.159885	+	0.975257i	−0.159885	+	0.975257i
$76$		0			0
$77$	−1.23896	+	0.272716i	−1.23896	+	0.272716i
$78$		0			0
$79$	1.06362	+	0.358376i	1.06362	+	0.358376i	0.796093	−	0.605174i	$-0.206897\pi$
$79$	1.06362	+	0.358376i	1.06362	+	0.358376i	0.267528	+	0.963550i	$0.413793\pi$
$80$	0.0400778	+	0.100588i	0.0400778	+	0.100588i
$81$	0.267528	−	0.963550i	0.267528	−	0.963550i
$82$		0			0
$83$	0.726610	+	1.07167i	0.726610	+	1.07167i	0.994138	+	0.108119i	$0.0344828\pi$
$83$	0.726610	+	1.07167i	0.726610	+	1.07167i	−0.267528	+	0.963550i	$0.586207\pi$
$84$	0.346752	−	0.654043i	0.346752	−	0.654043i
$85$		0			0
$86$		0			0
$87$	−1.41804	+	1.34324i	−1.41804	+	1.34324i
$88$	−1.55533	+	0.719570i	−1.55533	+	0.719570i
$89$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$89$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$90$	−0.0786092	+	0.0744626i	−0.0786092	+	0.0744626i
$91$		0			0
$92$		0			0
$93$	−0.250625	+	0.472729i	−0.250625	+	0.472729i
$94$		0			0
$95$		0			0
$96$	0.267528	−	0.963550i	0.267528	−	0.963550i
$97$	0.119763	+	0.300583i	0.119763	+	0.300583i	0.976621	−	0.214970i	$-0.0689655\pi$
$97$	0.119763	+	0.300583i	0.119763	+	0.300583i	−0.856857	+	0.515554i	$0.827586\pi$
$98$	−0.428331	−	0.144321i	−0.428331	−	0.144321i
$99$	−1.24415	−	1.17852i	−1.24415	−	1.17852i
$100$	−0.965171	+	0.212450i	−0.965171	+	0.212450i
$101$	−0.0982703	+	1.81249i	−0.0982703	+	1.81249i	0.370138	+	0.928977i	$0.379310\pi$
$101$	−0.0982703	+	1.81249i	−0.0982703	+	1.81249i	−0.468408	+	0.883512i	$0.655172\pi$
$102$		0			0
$103$	0.838218	−	0.986827i	0.838218	−	0.986827i	−0.161782	−	0.986827i	$-0.551724\pi$
$103$	0.838218	−	0.986827i	0.838218	−	0.986827i	1.00000			$0$
$104$		0			0
$105$	−0.0638112	−	0.0485080i	−0.0638112	−	0.0485080i
$106$	−1.36428	−	0.820858i	−1.36428	−	0.820858i
$107$	0.209471	+	1.27772i	0.209471	+	1.27772i	0.856857	+	0.515554i	$0.172414\pi$
$107$	0.209471	+	1.27772i	0.209471	+	1.27772i	−0.647386	+	0.762162i	$0.724138\pi$
$108$	0.994138	−	0.108119i	0.994138	−	0.108119i
$109$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$109$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$110$	0.0496418	+	0.178794i	0.0496418	+	0.178794i
$111$		0			0
$112$	0.735937	+	0.0800379i	0.735937	+	0.0800379i
$113$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$113$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$114$		0			0
$115$		0			0
$116$	−1.77271	−	0.820145i	−1.77271	−	0.820145i
$117$		0			0
$118$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$119$		0			0
$120$	−0.0982703	−	0.0454647i	−0.0982703	−	0.0454647i
$121$	−1.83543	+	0.618429i	−1.83543	+	0.618429i
$122$		0			0
$123$		0			0
$124$	−0.531920	−	0.0578498i	−0.531920	−	0.0578498i
$125$	0.0116554	+	0.214970i	0.0116554	+	0.214970i
$126$	0.198045	+	0.713293i	0.198045	+	0.713293i
$127$	1.03076	−	0.783563i	1.03076	−	0.783563i	0.0541389	−	0.998533i	$-0.482759\pi$
$127$	1.03076	−	0.783563i	1.03076	−	0.783563i	0.976621	+	0.214970i	$0.0689655\pi$
$128$	0.994138	−	0.108119i	0.994138	−	0.108119i
$129$		0			0
$130$		0			0
$131$	−0.745793	−	0.566937i	−0.745793	−	0.566937i	0.161782	−	0.986827i	$-0.448276\pi$
$131$	−0.745793	−	0.566937i	−0.745793	−	0.566937i	−0.907575	+	0.419889i	$0.862069\pi$
$132$	0.634311	−	1.59200i	0.634311	−	1.59200i
$133$		0			0
$134$		0			0
$135$	0.00586204	−	0.108119i	0.00586204	−	0.108119i
$136$		0			0
$137$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$137$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$138$		0			0
$139$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$139$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$140$	0.0214439	−	0.0772338i	0.0214439	−	0.0772338i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.468408	+	0.883512i	0.468408	+	0.883512i
$145$	−0.118687	+	0.175050i	−0.118687	+	0.175050i
$146$	−1.05414	+	0.998533i	−1.05414	+	0.998533i
$147$	0.410216	−	0.189786i	0.410216	−	0.189786i
$148$		0			0
$149$	−1.37598	+	1.30340i	−1.37598	+	1.30340i	−0.468408	+	0.883512i	$0.655172\pi$
$149$	−1.37598	+	1.30340i	−1.37598	+	1.30340i	−0.907575	+	0.419889i	$0.862069\pi$
$150$	0.554608	−	0.817985i	0.554608	−	0.817985i
$151$	−0.931325	−	1.75667i	−0.931325	−	1.75667i	−0.561187	−	0.827689i	$-0.689655\pi$
$151$	−0.931325	−	1.75667i	−0.931325	−	1.75667i	−0.370138	−	0.928977i	$-0.620690\pi$
$152$		0			0
$153$		0			0
$154$	1.23896	+	0.272716i	1.23896	+	0.272716i
$155$	−0.0154992	+	0.0558230i	−0.0154992	+	0.0558230i
$156$		0			0
$157$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$157$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$158$	−0.814839	−	0.771856i	−0.814839	−	0.771856i
$159$	1.55496	−	0.342273i	1.55496	−	0.342273i
$160$	0.00586204	−	0.108119i	0.00586204	−	0.108119i
$161$		0			0
$162$	−0.647386	+	0.762162i	−0.647386	+	0.762162i
$163$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$163$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$164$		0			0
$165$	−0.158996	−	0.0956648i	−0.158996	−	0.0956648i
$166$	−0.209471	−	1.27772i	−0.209471	−	1.27772i
$167$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$167$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$168$	−0.589329	+	0.447996i	−0.589329	+	0.447996i
$169$	0.267528	+	0.963550i	0.267528	+	0.963550i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.26450	−	1.48869i	−1.26450	−	1.48869i	−0.796093	−	0.605174i	$-0.793103\pi$
$173$	−1.26450	−	1.48869i	−1.26450	−	1.48869i	−0.468408	−	0.883512i	$-0.655172\pi$
$174$	1.85100	−	0.623673i	1.85100	−	0.623673i
$175$	0.663980	+	0.307190i	0.663980	+	0.307190i
$176$	1.71371			1.71371
$177$	0.907575	−	0.419889i	0.907575	−	0.419889i
$178$		0			0
$179$	1.01864	+	0.471273i	1.01864	+	0.471273i	0.856857	−	0.515554i	$-0.172414\pi$
$179$	1.01864	+	0.471273i	1.01864	+	0.471273i	0.161782	+	0.986827i	$0.448276\pi$
$180$	0.102610	−	0.0345733i	0.102610	−	0.0345733i
$181$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$181$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	0.425955	−	0.323803i	0.425955	−	0.323803i
$187$		0			0
$188$		0			0
$189$	−0.634311	−	0.381652i	−0.634311	−	0.381652i
$190$		0			0
$191$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$191$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$192$	−0.647386	+	0.762162i	−0.647386	+	0.762162i
$193$	−0.257587	+	1.57121i	−0.257587	+	1.57121i	0.468408	+	0.883512i	$0.344828\pi$
$193$	−0.257587	+	1.57121i	−0.257587	+	1.57121i	−0.725995	+	0.687699i	$0.758621\pi$
$194$	0.0175174	−	0.323089i	0.0175174	−	0.323089i
$195$		0			0
$196$	0.328143	+	0.310834i	0.328143	+	0.310834i
$197$	0.887777	+	0.299127i	0.887777	+	0.299127i	0.725995	−	0.687699i	$-0.241379\pi$
$197$	0.887777	+	0.299127i	0.887777	+	0.299127i	0.161782	+	0.986827i	$0.448276\pi$
$198$	0.634311	+	1.59200i	0.634311	+	1.59200i
$199$	−0.507048	+	1.82622i	−0.507048	+	1.82622i	0.0541389	+	0.998533i	$0.482759\pi$
$199$	−0.507048	+	1.82622i	−0.507048	+	1.82622i	−0.561187	+	0.827689i	$0.689655\pi$
$200$	0.965171	+	0.212450i	0.965171	+	0.212450i
$201$		0			0
$202$	0.850232	−	1.60371i	0.850232	−	1.60371i
$203$	0.677290	+	1.27750i	0.677290	+	1.27750i
$204$		0			0
$205$		0			0
$206$	−1.17510	+	0.543661i	−1.17510	+	0.543661i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	0.0375455	+	0.0708184i	0.0375455	+	0.0708184i
$211$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$211$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$212$	0.893514	+	1.31783i	0.893514	+	1.31783i
$213$		0			0
$214$	0.346388	−	1.24758i	0.346388	−	1.24758i
$215$		0			0
$216$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$217$	0.287559	+	0.272391i	0.287559	+	0.272391i
$218$		0			0
$219$	0.0786092	−	1.44986i	0.0786092	−	1.44986i
$220$	0.0300198	−	0.183113i	0.0300198	−	0.183113i
$221$		0			0
$222$		0			0
$223$	−0.257587	−	0.195813i	−0.257587	−	0.195813i	0.468408	−	0.883512i	$-0.344828\pi$
$223$	−0.257587	−	0.195813i	−0.257587	−	0.195813i	−0.725995	+	0.687699i	$0.758621\pi$
$224$	−0.634311	−	0.381652i	−0.634311	−	0.381652i
$225$	0.159885	+	0.975257i	0.159885	+	0.975257i
$226$		0			0
$227$	−0.425955	+	0.323803i	−0.425955	+	0.323803i	−0.796093	−	0.605174i	$-0.793103\pi$
$227$	−0.425955	+	0.323803i	−0.425955	+	0.323803i	0.370138	+	0.928977i	$0.379310\pi$
$228$		0			0
$229$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$229$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$230$		0			0
$231$	−1.08703	+	0.654043i	−1.08703	+	0.654043i
$232$	1.26450	+	1.48869i	1.26450	+	1.48869i
$233$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$233$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$234$		0			0
$235$		0			0
$236$	0.725995	+	0.687699i	0.725995	+	0.687699i
$237$	1.12237			1.12237
$238$		0			0
$239$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$239$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$240$	0.0700976	+	0.0825252i	0.0700976	+	0.0825252i
$241$	−1.67365	+	1.00700i	−1.67365	+	1.00700i	−0.725995	+	0.687699i	$0.758621\pi$
$241$	−1.67365	+	1.00700i	−1.67365	+	1.00700i	−0.947653	+	0.319302i	$0.896552\pi$
$242$	1.92546	+	0.209407i	1.92546	+	0.209407i
$243$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$244$		0			0
$245$	0.0389613	−	0.0296176i	0.0389613	−	0.0296176i
$246$		0			0
$247$		0			0
$248$	0.458467	+	0.275851i	0.458467	+	0.275851i
$249$	1.03076	+	0.783563i	1.03076	+	0.783563i
$250$	0.0796856	−	0.199996i	0.0796856	−	0.199996i
$251$	−0.606482	+	0.714006i	−0.606482	+	0.714006i	−0.976621	−	0.214970i	$-0.931034\pi$
$251$	−0.606482	+	0.714006i	−0.606482	+	0.714006i	0.370138	+	0.928977i	$0.379310\pi$
$252$	0.119763	−	0.730524i	0.119763	−	0.730524i
$253$		0			0
$254$	−1.26450	+	0.278338i	−1.26450	+	0.278338i
$255$		0			0
$256$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$257$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$257$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.914915	+	1.72571i	−0.914915	+	1.72571i
$262$	0.438813	+	0.827689i	0.438813	+	0.827689i
$263$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$263$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$264$	−1.24415	+	1.17852i	−1.24415	+	1.17852i
$265$	0.156465	−	0.0723882i	0.156465	−	0.0723882i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.680125	+	1.28285i	0.680125	+	1.28285i	0.947653	+	0.319302i	$0.103448\pi$
$269$	0.680125	+	1.28285i	0.680125	+	1.28285i	−0.267528	+	0.963550i	$0.586207\pi$
$270$	−0.0507182	+	0.0956648i	−0.0507182	+	0.0956648i
$271$	−1.01864	−	1.50238i	−1.01864	−	1.50238i	−0.856857	−	0.515554i	$-0.827586\pi$
$271$	−1.01864	−	1.50238i	−1.01864	−	1.50238i	−0.161782	−	0.986827i	$-0.551724\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.60497	+	0.540776i	1.60497	+	0.540776i
$276$		0			0
$277$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$277$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$278$		0			0
$279$	−0.0865625	+	0.528008i	−0.0865625	+	0.528008i
$280$	−0.0518916	+	0.0610915i	−0.0518916	+	0.0610915i
$281$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$281$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$282$		0			0
$283$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$283$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$289$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$290$	0.181219	−	0.109036i	0.181219	−	0.109036i
$291$	0.209471	+	0.246608i	0.209471	+	0.246608i
$292$	1.37598	−	0.463623i	1.37598	−	0.463623i
$293$	1.80451	+	0.834855i	1.80451	+	0.834855i	0.947653	+	0.319302i	$0.103448\pi$
$293$	1.80451	+	0.834855i	1.80451	+	0.834855i	0.856857	+	0.515554i	$0.172414\pi$
$294$	−0.451991			−0.451991
$295$	0.0861992	−	0.0655269i	0.0861992	−	0.0655269i
$296$		0			0
$297$	−1.55533	−	0.719570i	−1.55533	−	0.719570i
$298$	1.79609	−	0.605174i	1.79609	−	0.605174i
$299$		0			0
$300$	−0.846811	+	0.509509i	−0.846811	+	0.509509i
$301$		0			0
$302$	0.107643	+	1.98536i	0.107643	+	1.98536i
$303$	0.485604	+	1.74899i	0.485604	+	1.74899i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$307$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$308$	−1.00994	−	0.767737i	−1.00994	−	0.767737i
$309$	0.479245	−	1.20281i	0.479245	−	1.20281i
$310$	0.0375062	−	0.0441557i	0.0375062	−	0.0441557i
$311$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$311$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$312$		0			0
$313$	−1.85100	+	0.407435i	−1.85100	+	0.407435i	−0.994138	−	0.108119i	$-0.965517\pi$
$313$	−1.85100	+	0.407435i	−1.85100	+	0.407435i	−0.856857	+	0.515554i	$0.827586\pi$
$314$		0			0
$315$	−0.0759596	−	0.0255938i	−0.0759596	−	0.0255938i
$316$	0.415433	+	1.04266i	0.415433	+	1.04266i
$317$	0.458467	−	1.65125i	0.458467	−	1.65125i	−0.267528	−	0.963550i	$-0.586207\pi$
$317$	0.458467	−	1.65125i	0.458467	−	1.65125i	0.725995	−	0.687699i	$-0.241379\pi$
$318$	−1.55496	−	0.342273i	−1.55496	−	0.342273i
$319$	1.87846	+	2.77052i	1.87846	+	2.77052i
$320$	−0.0507182	+	0.0956648i	−0.0507182	+	0.0956648i
$321$	0.606482	+	1.14395i	0.606482	+	1.14395i
$322$		0			0
$323$		0			0
$324$	0.907575	−	0.419889i	0.907575	−	0.419889i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	0.104132	+	0.153584i	0.104132	+	0.153584i
$331$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$331$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$332$	−0.346388	+	1.24758i	−0.346388	+	1.24758i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.722969	−	0.159138i	0.722969	−	0.159138i
$337$	0.0982703	−	1.81249i	0.0982703	−	1.81249i	−0.370138	−	0.928977i	$-0.620690\pi$
$337$	0.0982703	−	1.81249i	0.0982703	−	1.81249i	0.468408	−	0.883512i	$-0.344828\pi$
$338$	0.161782	−	0.986827i	0.161782	−	0.986827i
$339$		0			0
$340$		0			0
$341$	0.729965	+	0.554905i	0.729965	+	0.554905i
$342$		0			0
$343$	−0.173895	−	1.06071i	−0.173895	−	1.06071i
$344$		0			0
$345$		0			0
$346$	0.522547	+	1.88205i	0.522547	+	1.88205i
$347$	−0.0982703	−	1.81249i	−0.0982703	−	1.81249i	−0.468408	−	0.883512i	$-0.655172\pi$
$347$	−0.0982703	−	1.81249i	−0.0982703	−	1.81249i	0.370138	−	0.928977i	$-0.379310\pi$
$348$	−1.94179	−	0.211183i	−1.94179	−	0.211183i
$349$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$349$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$350$	−0.473626	−	0.557596i	−0.473626	−	0.557596i
$351$		0			0
$352$	−1.55533	−	0.719570i	−1.55533	−	0.719570i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	−1.00000			−1.00000
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.726610	−	0.855431i	−0.726610	−	0.855431i
$359$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$359$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$360$	−0.107643	−	0.0117069i	−0.107643	−	0.0117069i
$361$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$362$		0			0
$363$	−1.54189	+	1.17211i	−1.54189	+	1.17211i
$364$		0			0
$365$	−0.0254351	−	0.155147i	−0.0254351	−	0.155147i
$366$		0			0
$367$	1.55496	+	1.18205i	1.55496	+	1.18205i	0.907575	+	0.419889i	$0.137931\pi$
$367$	1.55496	+	1.18205i	1.55496	+	1.18205i	0.647386	+	0.762162i	$0.275862\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0638112	−	1.17693i	0.0638112	−	1.17693i
$372$	−0.522547	+	0.115021i	−0.522547	+	0.115021i
$373$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$373$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$374$		0			0
$375$	0.0796856	+	0.199996i	0.0796856	+	0.199996i
$376$		0			0
$377$		0			0
$378$	0.415433	+	0.612719i	0.415433	+	0.612719i
$379$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$379$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$380$		0			0
$381$	0.726610	−	1.07167i	0.726610	−	1.07167i
$382$		0			0
$383$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$383$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$384$	0.907575	−	0.419889i	0.907575	−	0.419889i
$385$	−0.0997254	+	0.0944649i	−0.0997254	+	0.0944649i
$386$	0.893514	−	1.31783i	0.893514	−	1.31783i
$387$		0			0
$388$	−0.151560	+	0.285873i	−0.151560	+	0.285873i
$389$	−0.629862	−	0.928977i	−0.629862	−	0.928977i	0.370138	−	0.928977i	$-0.379310\pi$
$389$	−0.629862	−	0.928977i	−0.629862	−	0.928977i	−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	−0.167299	−	0.419889i	−0.167299	−	0.419889i
$393$	−0.887777	−	0.299127i	−0.887777	−	0.299127i
$394$	−0.680125	−	0.644248i	−0.680125	−	0.644248i
$395$	0.118687	−	0.0261250i	0.118687	−	0.0261250i
$396$	0.0927786	−	1.71120i	0.0927786	−	1.71120i
$397$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$397$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$398$	1.22700	−	1.44453i	1.22700	−	1.44453i
$399$		0			0
$400$	−0.786760	−	0.598079i	−0.786760	−	0.598079i
$401$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$401$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$402$		0			0
$403$		0			0
$404$	−1.44503	+	1.09848i	−1.44503	+	1.09848i
$405$	−0.0289674	−	0.104331i	−0.0289674	−	0.104331i
$406$	−0.0782815	−	1.44382i	−0.0782815	−	1.44382i
$407$		0			0
$408$		0			0
$409$	1.17510	+	1.38344i	1.17510	+	1.38344i	0.907575	+	0.419889i	$0.137931\pi$
$409$	1.17510	+	1.38344i	1.17510	+	1.38344i	0.267528	+	0.963550i	$0.413793\pi$
$410$		0			0
$411$		0			0
$412$	1.29477			1.29477
$413$	−0.119763	−	0.730524i	−0.119763	−	0.730524i
$414$		0			0
$415$	0.127238	+	0.0588664i	0.127238	+	0.0588664i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.97662	−	0.214970i	−1.97662	−	0.214970i	−0.976621	−	0.214970i	$-0.931034\pi$
$419$	−1.97662	−	0.214970i	−1.97662	−	0.214970i	−1.00000			$\pi$
$420$	−0.00433953	−	0.0800379i	−0.00433953	−	0.0800379i
$421$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$421$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$422$		0			0
$423$		0			0
$424$	−0.257587	−	1.57121i	−0.257587	−	1.57121i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.838218	+	0.986827i	−0.838218	+	0.986827i
$429$		0			0
$430$		0			0
$431$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$431$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$432$	0.725995	+	0.687699i	0.725995	+	0.687699i
$433$	−1.50884	−	0.508387i	−1.50884	−	0.508387i	−0.561187	−	0.827689i	$-0.689655\pi$
$433$	−1.50884	−	0.508387i	−1.50884	−	0.508387i	−0.947653	+	0.319302i	$0.896552\pi$
$434$	−0.146608	−	0.367958i	−0.146608	−	0.367958i
$435$	−0.0565803	+	0.203784i	−0.0565803	+	0.203784i
$436$		0			0
$437$		0			0
$438$	−0.680125	+	1.28285i	−0.680125	+	1.28285i
$439$	−0.680125	−	1.28285i	−0.680125	−	1.28285i	−0.947653	−	0.319302i	$-0.896552\pi$
$439$	−0.680125	−	1.28285i	−0.680125	−	1.28285i	0.267528	−	0.963550i	$-0.413793\pi$
$440$	−0.104132	+	0.153584i	−0.104132	+	0.153584i
$441$	0.328143	−	0.310834i	0.328143	−	0.310834i
$442$		0			0
$443$	0.293659	−	0.135861i	0.293659	−	0.135861i	−0.267528	−	0.963550i	$-0.586207\pi$
$443$	0.293659	−	0.135861i	0.293659	−	0.135861i	0.561187	+	0.827689i	$0.310345\pi$
$444$		0			0
$445$		0			0
$446$	0.151560	+	0.285873i	0.151560	+	0.285873i
$447$	−0.887777	+	1.67453i	−0.887777	+	1.67453i
$448$	0.415433	+	0.612719i	0.415433	+	0.612719i
$449$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$449$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$450$	0.264392	−	0.952253i	0.264392	−	0.952253i
$451$		0			0
$452$		0			0
$453$	−1.44348	−	1.36734i	−1.44348	−	1.36734i
$454$	0.522547	−	0.115021i	0.522547	−	0.115021i
$455$		0			0
$456$		0			0
$457$	1.03076	−	1.21350i	1.03076	−	1.21350i	0.0541389	−	0.998533i	$-0.482759\pi$
$457$	1.03076	−	1.21350i	1.03076	−	1.21350i	0.976621	−	0.214970i	$-0.0689655\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.321667	−	1.96208i	−0.321667	−	1.96208i	−0.267528	−	0.963550i	$-0.586207\pi$
$461$	−0.321667	−	1.96208i	−0.321667	−	1.96208i	−0.0541389	−	0.998533i	$-0.517241\pi$
$462$	1.26119	−	0.137162i	1.26119	−	0.137162i
$463$	−0.257587	+	0.195813i	−0.257587	+	0.195813i	−0.725995	−	0.687699i	$-0.758621\pi$
$463$	−0.257587	+	0.195813i	−0.257587	+	0.195813i	0.468408	+	0.883512i	$0.344828\pi$
$464$	−0.522547	−	1.88205i	−0.522547	−	1.88205i
$465$	0.00313653	+	0.0578498i	0.00313653	+	0.0578498i
$466$		0			0
$467$	−0.961714	+	0.578644i	−0.961714	+	0.578644i	−0.907575	−	0.419889i	$-0.862069\pi$
$467$	−0.961714	+	0.578644i	−0.961714	+	0.578644i	−0.0541389	+	0.998533i	$0.517241\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$473$		0			0
$474$	−1.01864	−	0.471273i	−1.01864	−	0.471273i
$475$		0			0
$476$		0			0
$477$	1.36428	−	0.820858i	1.36428	−	0.820858i
$478$		0			0
$479$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$479$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$480$	−0.0289674	−	0.104331i	−0.0289674	−	0.104331i
$481$		0			0
$482$	1.94179	−	0.211183i	1.94179	−	0.211183i
$483$		0			0
$484$	−1.65958	−	0.998533i	−1.65958	−	0.998533i
$485$	0.0278910	+	0.0212022i	0.0278910	+	0.0212022i
$486$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$487$	0.346388	−	0.407800i	0.346388	−	0.407800i	−0.561187	−	0.827689i	$-0.689655\pi$
$487$	0.346388	−	0.407800i	0.346388	−	0.407800i	0.907575	+	0.419889i	$0.137931\pi$
$488$		0			0
$489$		0			0
$490$	−0.0477964	+	0.0105208i	−0.0477964	+	0.0105208i
$491$	−0.814839	−	0.771856i	−0.814839	−	0.771856i	0.161782	−	0.986827i	$-0.448276\pi$
$491$	−0.814839	−	0.771856i	−0.814839	−	0.771856i	−0.976621	+	0.214970i	$0.931034\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.181219	−	0.0398893i	−0.181219	−	0.0398893i
$496$	−0.300267	−	0.442861i	−0.300267	−	0.442861i
$497$		0			0
$498$	−0.606482	−	1.14395i	−0.606482	−	1.14395i
$499$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$499$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$500$	−0.156297	+	0.148052i	−0.156297	+	0.148052i
$501$		0			0
$502$	0.850232	−	0.393359i	0.850232	−	0.393359i
$503$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$503$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$504$	−0.415433	+	0.612719i	−0.415433	+	0.612719i
$505$	0.0920613	+	0.173646i	0.0920613	+	0.173646i
$506$		0			0
$507$	0.561187	+	0.827689i	0.561187	+	0.827689i
$508$	1.26450	+	0.278338i	1.26450	+	0.278338i
$509$	0.300267	−	1.08146i	0.300267	−	1.08146i	−0.647386	−	0.762162i	$-0.724138\pi$
$509$	0.300267	−	1.08146i	0.300267	−	1.08146i	0.947653	−	0.319302i	$-0.103448\pi$
$510$		0			0
$511$	−1.01861	−	0.343209i	−1.01861	−	0.343209i
$512$	0.725995	+	0.687699i	0.725995	+	0.687699i
$513$		0			0
$514$		0			0
$515$	0.0226811	−	0.138348i	0.0226811	−	0.138348i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.67365	−	1.00700i	−1.67365	−	1.00700i
$520$		0			0
$521$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$521$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$522$	1.55496	−	1.18205i	1.55496	−	1.18205i
$523$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$523$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$524$	−0.0507182	−	0.935443i	−0.0507182	−	0.935443i
$525$	0.727309	+	0.0790996i	0.727309	+	0.0790996i
$526$		0			0
$527$		0			0
$528$	1.62401	−	0.547192i	1.62401	−	0.547192i
$529$	0.907575	+	0.419889i	0.907575	+	0.419889i
$530$	−0.172398			−0.172398
$531$	0.725995	−	0.687699i	0.725995	−	0.687699i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.0907604	+	0.106851i	0.0907604	+	0.106851i
$536$		0			0
$537$	1.11579	+	0.121350i	1.11579	+	0.121350i
$538$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i
$539$	−0.207223	−	0.746350i	−0.207223	−	0.746350i
$540$	0.0861992	−	0.0655269i	0.0861992	−	0.0655269i
$541$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$541$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$542$	0.293659	+	1.79124i	0.293659	+	1.79124i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$547$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$548$		0			0
$549$		0			0
$550$	−1.22956	−	1.16470i	−1.22956	−	1.16470i
$551$		0			0
$552$		0			0
$553$	0.222280	−	0.800582i	0.222280	−	0.800582i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.802718	+	1.51409i	0.802718	+	1.51409i	0.856857	+	0.515554i	$0.172414\pi$
$557$	0.802718	+	1.51409i	0.802718	+	1.51409i	−0.0541389	+	0.998533i	$0.517241\pi$
$558$	0.300267	−	0.442861i	0.300267	−	0.442861i
$559$		0			0
$560$	0.0727472	−	0.0336564i	0.0727472	−	0.0336564i
$561$		0			0
$562$		0			0
$563$	−1.06362	+	1.56872i	−1.06362	+	1.56872i	−0.267528	+	0.963550i	$0.586207\pi$
$563$	−1.06362	+	1.56872i	−1.06362	+	1.56872i	−0.796093	+	0.605174i	$0.793103\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.722969	−	0.159138i	−0.722969	−	0.159138i
$568$		0			0
$569$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$569$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$570$		0			0
$571$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$571$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$577$	0.425955	+	0.323803i	0.425955	+	0.323803i	0.796093	−	0.605174i	$-0.206897\pi$
$577$	0.425955	+	0.323803i	0.425955	+	0.323803i	−0.370138	+	0.928977i	$0.620690\pi$
$578$	0.856857	+	0.515554i	0.856857	+	0.515554i
$579$	0.257587	+	1.57121i	0.257587	+	1.57121i
$580$	−0.210253	+	0.0228664i	−0.210253	+	0.0228664i
$581$	0.763047	−	0.580053i	0.763047	−	0.580053i
$582$	−0.0865625	−	0.311770i	−0.0865625	−	0.311770i
$583$	−0.147721	−	2.72455i	−0.147721	−	2.72455i
$584$	−1.44348	−	0.156988i	−1.44348	−	0.156988i
$585$		0			0
$586$	−1.28718	−	1.51539i	−1.28718	−	1.51539i
$587$	−1.88420	+	0.634860i	−1.88420	+	0.634860i	−0.907575	+	0.419889i	$0.862069\pi$
$587$	−1.88420	+	0.634860i	−1.88420	+	0.634860i	−0.976621	+	0.214970i	$0.931034\pi$
$588$	0.410216	+	0.189786i	0.410216	+	0.189786i
$589$		0			0
$590$	−0.105746	+	0.0232765i	−0.105746	+	0.0232765i
$591$	0.936817			0.936817
$592$		0			0
$593$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$593$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$594$	1.10944	+	1.30613i	1.10944	+	1.30613i
$595$		0			0
$596$	−1.88420	−	0.204919i	−1.88420	−	0.204919i
$597$	0.102610	+	1.89253i	0.102610	+	1.89253i
$598$		0			0
$599$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$599$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$600$	0.982483	−	0.106851i	0.982483	−	0.106851i
$601$	0.119763	+	0.730524i	0.119763	+	0.730524i	0.976621	+	0.214970i	$0.0689655\pi$
$601$	0.119763	+	0.730524i	0.119763	+	0.730524i	−0.856857	+	0.515554i	$0.827586\pi$
$602$		0			0
$603$		0			0
$604$	0.735937	−	1.84706i	0.735937	−	1.84706i
$605$	−0.135766	+	0.159836i	−0.135766	+	0.159836i
$606$	0.293659	−	1.79124i	0.293659	−	1.79124i
$607$	−0.102610	+	1.89253i	−0.102610	+	1.89253i	0.267528	+	0.963550i	$0.413793\pi$
$607$	−0.102610	+	1.89253i	−0.102610	+	1.89253i	−0.370138	+	0.928977i	$0.620690\pi$
$608$		0			0
$609$	1.04974	+	0.994371i	1.04974	+	0.994371i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$613$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$614$		0			0
$615$		0			0
$616$	0.594233	+	1.12084i	0.594233	+	1.12084i
$617$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$617$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$618$	−0.939999	+	0.890414i	−0.939999	+	0.890414i
$619$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$619$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$620$	−0.0525802	+	0.0243262i	−0.0525802	+	0.0243262i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.541526	−	0.798691i	−0.541526	−	0.798691i
$626$	1.85100	+	0.407435i	1.85100	+	0.407435i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.0581925	+	0.0551229i	0.0581925	+	0.0551229i
$631$	−1.85100	+	0.407435i	−1.85100	+	0.407435i	−0.994138	−	0.108119i	$-0.965517\pi$
$631$	−1.85100	+	0.407435i	−1.85100	+	0.407435i	−0.856857	+	0.515554i	$0.827586\pi$
$632$	0.0607641	−	1.12073i	0.0607641	−	1.12073i
$633$		0			0
$634$	−1.10944	+	1.30613i	−1.10944	+	1.30613i
$635$	0.0518916	−	0.130238i	0.0518916	−	0.130238i
$636$	1.26753	+	0.963550i	1.26753	+	0.963550i
$637$		0			0
$638$	−0.541532	−	3.30320i	−0.541532	−	3.30320i
$639$		0			0
$640$	0.0861992	−	0.0655269i	0.0861992	−	0.0655269i
$641$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$641$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$642$	−0.0700976	−	1.29287i	−0.0700976	−	1.29287i
$643$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$643$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$647$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$648$	−1.00000			−1.00000
$649$	−0.458467	−	1.65125i	−0.458467	−	1.65125i
$650$		0			0
$651$	0.359481	+	0.166314i	0.359481	+	0.166314i
$652$		0			0
$653$	−0.346388	−	0.407800i	−0.346388	−	0.407800i	0.561187	−	0.827689i	$-0.310345\pi$
$653$	−0.346388	−	0.407800i	−0.346388	−	0.407800i	−0.907575	+	0.419889i	$0.862069\pi$
$654$		0			0
$655$	−0.100842	−	0.0109672i	−0.100842	−	0.0109672i
$656$		0			0
$657$	−0.388449	−	1.39907i	−0.388449	−	1.39907i
$658$		0			0
$659$	0.531920	−	0.0578498i	0.531920	−	0.0578498i	0.161782	−	0.986827i	$-0.448276\pi$
$659$	0.531920	−	0.0578498i	0.531920	−	0.0578498i	0.370138	+	0.928977i	$0.379310\pi$
$660$	−0.0300198	−	0.183113i	−0.0300198	−	0.183113i
$661$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$661$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$662$		0			0
$663$		0			0
$664$	0.838218	−	0.986827i	0.838218	−	0.986827i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.306626	−	0.103314i	−0.306626	−	0.103314i
$670$		0			0
$671$		0			0
$672$	−0.722969	−	0.159138i	−0.722969	−	0.159138i
$673$	0.629862	+	0.928977i	0.629862	+	0.928977i	1.00000			$0$
$673$	0.629862	+	0.928977i	0.629862	+	0.928977i	−0.370138	+	0.928977i	$0.620690\pi$
$674$	−0.850232	+	1.60371i	−0.850232	+	1.60371i
$675$	0.462917	+	0.873154i	0.462917	+	0.873154i
$676$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$677$	1.31779	−	1.24828i	1.31779	−	1.24828i	0.370138	−	0.928977i	$-0.379310\pi$
$677$	1.31779	−	1.24828i	1.31779	−	1.24828i	0.947653	−	0.319302i	$-0.103448\pi$
$678$		0			0
$679$	0.217389	−	0.100575i	0.217389	−	0.100575i
$680$		0			0
$681$	−0.300267	+	0.442861i	−0.300267	+	0.442861i
$682$	−0.429500	−	0.810123i	−0.429500	−	0.810123i
$683$	−0.438813	+	0.827689i	−0.438813	+	0.827689i	0.561187	+	0.827689i	$0.310345\pi$
$683$	−0.438813	+	0.827689i	−0.438813	+	0.827689i	−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	−0.287559	+	1.03570i	−0.287559	+	1.03570i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$691$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$692$	0.315999	−	1.92751i	0.315999	−	1.92751i
$693$	−0.821289	+	0.966896i	−0.821289	+	0.966896i
$694$	−0.671857	+	1.68623i	−0.671857	+	1.68623i
$695$		0			0
$696$	1.67365	+	1.00700i	1.67365	+	1.00700i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.195723	+	0.704931i	0.195723	+	0.704931i
$701$	−0.00586204	−	0.108119i	−0.00586204	−	0.108119i	0.994138	−	0.108119i	$-0.0344828\pi$
$701$	−0.00586204	−	0.108119i	−0.00586204	−	0.108119i	−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$	1.10944	+	1.30613i	1.10944	+	1.30613i
$705$		0			0
$706$		0			0
$707$	1.34371			1.34371
$708$	0.907575	+	0.419889i	0.907575	+	0.419889i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$	1.06362	−	0.358376i	1.06362	−	0.358376i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.300267	+	1.08146i	0.300267	+	1.08146i
$717$		0			0
$718$		0			0
$719$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$719$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$720$	0.0927786	+	0.0558230i	0.0927786	+	0.0558230i
$721$	−0.763047	−	0.580053i	−0.763047	−	0.580053i
$722$	0.370138	−	0.928977i	0.370138	−	0.928977i
$723$	−1.26450	+	1.48869i	−1.26450	+	1.48869i
$724$		0			0
$725$	0.104507	−	1.92751i	0.104507	−	1.92751i
$726$	1.89154	−	0.416358i	1.89154	−	0.416358i
$727$	−0.680125	−	0.644248i	−0.680125	−	0.644248i	0.267528	−	0.963550i	$-0.413793\pi$
$727$	−0.680125	−	0.644248i	−0.680125	−	0.644248i	−0.947653	+	0.319302i	$0.896552\pi$
$728$		0			0
$729$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$730$	−0.0420604	+	0.151488i	−0.0420604	+	0.151488i
$731$		0			0
$732$		0			0
$733$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$733$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$734$	−0.914915	−	1.72571i	−0.914915	−	1.72571i
$735$	0.0274648	−	0.0405076i	0.0274648	−	0.0405076i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$739$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$740$		0			0
$741$		0			0
$742$	−0.552093	+	1.04136i	−0.552093	+	1.04136i
$743$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$743$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$744$	0.522547	+	0.115021i	0.522547	+	0.115021i
$745$	−0.0549021	+	0.197739i	−0.0549021	+	0.197739i
$746$		0			0
$747$	1.22700	+	0.413423i	1.22700	+	0.413423i
$748$		0			0
$749$	0.936081	−	0.206047i	0.936081	−	0.206047i
$750$	0.0116554	−	0.214970i	0.0116554	−	0.214970i
$751$	0.306626	−	1.87034i	0.306626	−	1.87034i	−0.161782	−	0.986827i	$-0.551724\pi$
$751$	0.306626	−	1.87034i	0.306626	−	1.87034i	0.468408	−	0.883512i	$-0.344828\pi$
$752$		0			0
$753$	−0.346752	+	0.870281i	−0.346752	+	0.870281i
$754$		0			0
$755$	−0.184470	−	0.110992i	−0.184470	−	0.110992i
$756$	−0.119763	−	0.730524i	−0.119763	−	0.730524i
$757$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$757$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$761$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$762$	−1.10944	+	0.667525i	−1.10944	+	0.667525i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.00000			−1.00000
$769$	1.77271	+	0.820145i	1.77271	+	0.820145i	0.976621	+	0.214970i	$0.0689655\pi$
$769$	1.77271	+	0.820145i	1.77271	+	0.820145i	0.796093	+	0.605174i	$0.206897\pi$
$770$	0.130173	−	0.0438604i	0.130173	−	0.0438604i
$771$		0			0
$772$	−1.36428	+	0.820858i	−1.36428	+	0.820858i
$773$	0.107643	+	0.0117069i	0.107643	+	0.0117069i	0.161782	−	0.986827i	$-0.448276\pi$
$773$	0.107643	+	0.0117069i	0.107643	+	0.0117069i	−0.0541389	+	0.998533i	$0.517241\pi$
$774$		0			0
$775$	−0.141465	−	0.509509i	−0.141465	−	0.509509i
$776$	0.257587	−	0.195813i	0.257587	−	0.195813i
$777$		0			0
$778$	0.181580	+	1.10759i	0.181580	+	1.10759i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.315999	+	1.92751i	−0.315999	+	1.92751i
$784$	−0.0244703	+	0.451328i	−0.0244703	+	0.451328i
$785$		0			0
$786$	0.680125	+	0.644248i	0.680125	+	0.644248i
$787$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$787$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$788$	0.346752	+	0.870281i	0.346752	+	0.870281i
$789$		0			0
$790$	−0.118687	−	0.0261250i	−0.118687	−	0.0261250i
$791$		0			0
$792$	−0.802718	+	1.51409i	−0.802718	+	1.51409i
$793$		0			0
$794$		0			0
$795$	0.125160	−	0.118558i	0.125160	−	0.118558i
$796$	−1.72013	+	0.795818i	−1.72013	+	0.795818i
$797$	−0.850232	+	0.393359i	−0.850232	+	0.393359i	−0.796093	−	0.605174i	$-0.793103\pi$
$797$	−0.850232	+	0.393359i	−0.850232	+	0.393359i	−0.0541389	+	0.998533i	$0.517241\pi$
$798$		0			0
$799$		0			0
$800$	0.462917	+	0.873154i	0.462917	+	0.873154i
$801$		0			0
$802$		0			0
$803$	−2.43012	−	0.534910i	−2.43012	−	0.534910i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.05414	+	0.998533i	1.05414	+	0.998533i
$808$	1.77271	−	0.390204i	1.77271	−	0.390204i
$809$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$809$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$810$	−0.0175174	+	0.106851i	−0.0175174	+	0.106851i
$811$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$811$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$812$	−0.535197	+	1.34324i	−0.535197	+	1.34324i
$813$	−1.44503	−	1.09848i	−1.44503	−	1.09848i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.485604	−	1.74899i	−0.485604	−	1.74899i
$819$		0			0
$820$		0			0
$821$	−1.70367	+	1.02506i	−1.70367	+	1.02506i	−0.796093	+	0.605174i	$0.793103\pi$
$821$	−1.70367	+	1.02506i	−1.70367	+	1.02506i	−0.907575	+	0.419889i	$0.862069\pi$
$822$		0			0
$823$	−1.22700	+	0.413423i	−1.22700	+	0.413423i	−0.856857	−	0.515554i	$-0.827586\pi$
$823$	−1.22700	+	0.413423i	−1.22700	+	0.413423i	−0.370138	+	0.928977i	$0.620690\pi$
$824$	−1.17510	−	0.543661i	−1.17510	−	0.543661i
$825$	1.69362			1.69362
$826$	−0.198045	+	0.713293i	−0.198045	+	0.713293i
$827$	1.45199			1.45199			0.725995	−	0.687699i	$-0.241379\pi$
$827$	1.45199			1.45199			0.725995	+	0.687699i	$0.241379\pi$
$828$		0			0
$829$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$829$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$830$	−0.0907604	−	0.106851i	−0.0907604	−	0.106851i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.0865625	+	0.528008i	0.0865625	+	0.528008i
$838$	1.70367	+	1.02506i	1.70367	+	1.02506i
$839$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$839$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$840$	−0.0296686	+	0.0744626i	−0.0296686	+	0.0744626i
$841$	1.82249	−	2.14560i	1.82249	−	2.14560i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.0786092	+	0.0744626i	0.0786092	+	0.0744626i
$846$		0			0
$847$	0.530697	+	1.33195i	0.530697	+	1.33195i
$848$	−0.425955	+	1.53415i	−0.425955	+	1.53415i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$853$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$854$		0			0
$855$		0			0
$856$	1.17510	−	0.543661i	1.17510	−	0.543661i
$857$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$857$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$858$		0			0
$859$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$859$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$863$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$864$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$865$	−0.200422	−	0.0675299i	−0.200422	−	0.0675299i
$866$	1.15592	+	1.09495i	1.15592	+	1.09495i
$867$	−0.976621	+	0.214970i	−0.976621	+	0.214970i
$868$	−0.0214439	+	0.395509i	−0.0214439	+	0.395509i
$869$	0.311176	−	1.89809i	0.311176	−	1.89809i
$870$	0.136917	−	0.161192i	0.136917	−	0.161192i
$871$		0			0
$872$		0			0
$873$	0.277248	+	0.166815i	0.277248	+	0.166815i
$874$		0			0
$875$	0.158437	−	0.0172311i	0.158437	−	0.0172311i
$876$	1.15592	−	0.878708i	1.15592	−	0.878708i
$877$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$877$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$878$	0.0786092	+	1.44986i	0.0786092	+	1.44986i
$879$	1.97662	+	0.214970i	1.97662	+	0.214970i
$880$	0.158996	−	0.0956648i	0.158996	−	0.0956648i
$881$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$881$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$882$	−0.428331	+	0.144321i	−0.428331	+	0.144321i
$883$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$883$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$884$		0			0
$885$	0.0607641	−	0.0896204i	0.0607641	−	0.0896204i
$886$	−0.323564			−0.323564
$887$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$887$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$888$		0			0
$889$	−0.620513	−	0.730524i	−0.620513	−	0.730524i
$890$		0			0
$891$	−1.70367	−	0.185285i	−1.70367	−	0.185285i
$892$	−0.0175174	−	0.323089i	−0.0175174	−	0.323089i
$893$		0			0
$894$	1.50884	−	1.14699i	1.50884	−	1.14699i
$895$	0.120816	−	0.0131395i	0.120816	−	0.0131395i
$896$	−0.119763	−	0.730524i	−0.119763	−	0.730524i
$897$		0			0
$898$		0			0
$899$	0.386829	−	0.970869i	0.386829	−	0.970869i
$900$	−0.639796	+	0.753226i	−0.639796	+	0.753226i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.735937	+	1.84706i	0.735937	+	1.84706i
$907$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$907$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$908$	−0.522547	−	0.115021i	−0.522547	−	0.115021i
$909$	1.01864	+	1.50238i	1.01864	+	1.50238i
$910$		0			0
$911$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$911$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$912$		0			0
$913$	1.61089	−	1.52592i	1.61089	−	1.52592i
$914$	−1.44503	+	0.668542i	−1.44503	+	0.668542i
$915$		0			0
$916$		0			0
$917$	−0.389185	+	0.574005i	−0.389185	+	0.574005i
$918$		0			0
$919$	−0.931325	+	1.75667i	−0.931325	+	1.75667i	−0.370138	+	0.928977i	$0.620690\pi$
$919$	−0.931325	+	1.75667i	−0.931325	+	1.75667i	−0.561187	+	0.827689i	$0.689655\pi$
$920$		0			0
$921$		0			0
$922$	−0.531920	+	1.91580i	−0.531920	+	1.91580i
$923$		0			0
$924$	−1.20221	−	0.405073i	−1.20221	−	0.405073i
$925$		0			0
$926$	0.315999	−	0.0695567i	0.315999	−	0.0695567i
$927$	0.0700976	−	1.29287i	0.0700976	−	1.29287i
$928$	−0.315999	+	1.92751i	−0.315999	+	1.92751i
$929$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$929$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$930$	0.0214439	−	0.0538201i	0.0214439	−	0.0538201i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	1.11579	−	0.121350i	1.11579	−	0.121350i
$935$		0			0
$936$		0			0
$937$	0.0700976	+	1.29287i	0.0700976	+	1.29287i	0.796093	+	0.605174i	$0.206897\pi$
$937$	0.0700976	+	1.29287i	0.0700976	+	1.29287i	−0.725995	+	0.687699i	$0.758621\pi$
$938$		0			0
$939$	−1.62401	+	0.977132i	−1.62401	+	0.977132i
$940$		0			0
$941$	0.507048	−	0.170844i	0.507048	−	0.170844i	−0.0541389	−	0.998533i	$-0.517241\pi$
$941$	0.507048	−	0.170844i	0.507048	−	0.170844i	0.561187	+	0.827689i	$0.310345\pi$
$942$		0			0
$943$		0			0
$944$	−0.0541389	+	0.998533i	−0.0541389	+	0.998533i
$945$	−0.0801555			−0.0801555
$946$		0			0
$947$	−1.62401	+	0.547192i	−1.62401	+	0.547192i	−0.976621	−	0.214970i	$-0.931034\pi$
$947$	−1.62401	+	0.547192i	−1.62401	+	0.547192i	−0.647386	+	0.762162i	$0.724138\pi$
$948$	0.726610	+	0.855431i	0.726610	+	0.855431i
$949$		0			0
$950$		0			0
$951$	−0.0927786	−	1.71120i	−0.0927786	−	1.71120i
$952$		0			0
$953$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$953$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$954$	−1.58285	+	0.172146i	−1.58285	+	0.172146i
$955$		0			0
$956$		0			0
$957$	2.66476	+	2.02570i	2.66476	+	2.02570i
$958$		0			0
$959$		0			0
$960$	−0.0175174	+	0.106851i	−0.0175174	+	0.106851i
$961$	−0.0386397	+	0.712668i	−0.0386397	+	0.712668i
$962$		0			0
$963$	0.939999	+	0.890414i	0.939999	+	0.890414i
$964$	−1.85100	−	0.623673i	−1.85100	−	0.623673i
$965$	0.0638112	+	0.160154i	0.0638112	+	0.160154i
$966$		0			0
$967$	−1.67365	−	0.368398i	−1.67365	−	0.368398i	−0.725995	−	0.687699i	$-0.758621\pi$
$967$	−1.67365	−	0.368398i	−1.67365	−	0.368398i	−0.947653	+	0.319302i	$0.896552\pi$
$968$	1.08692	+	1.60308i	1.08692	+	1.60308i
$969$		0			0
$970$	−0.0164106	−	0.0309537i	−0.0164106	−	0.0309537i
$971$	−0.181580	+	0.267810i	−0.181580	+	0.267810i	−0.907575	−	0.419889i	$-0.862069\pi$
$971$	−0.181580	+	0.267810i	−0.181580	+	0.267810i	0.725995	+	0.687699i	$0.241379\pi$
$972$	0.725995	−	0.687699i	0.725995	−	0.687699i
$973$		0			0
$974$	−0.485604	+	0.224664i	−0.485604	+	0.224664i
$975$		0			0
$976$		0			0
$977$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$977$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$978$		0			0
$979$		0			0
$980$	0.0477964	+	0.0105208i	0.0477964	+	0.0105208i
$981$		0			0
$982$	0.415433	+	1.04266i	0.415433	+	1.04266i
$983$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$983$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$984$		0			0
$985$	0.0990650	−	0.0218058i	0.0990650	−	0.0218058i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.147721	+	0.112294i	0.147721	+	0.112294i
$991$	0.634311	+	0.381652i	0.634311	+	0.381652i	0.796093	−	0.605174i	$-0.206897\pi$
$991$	0.634311	+	0.381652i	0.634311	+	0.381652i	−0.161782	+	0.986827i	$0.551724\pi$
$992$	0.0865625	+	0.528008i	0.0865625	+	0.528008i
$993$		0			0
$994$		0			0
$995$	0.0549021	+	0.197739i	0.0549021	+	0.197739i
$996$	0.0700976	+	1.29287i	0.0700976	+	1.29287i
$997$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$997$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1416.1.r.b.197.1	yes	28
3.2	odd	2		1416.1.r.a.197.1	✓	28
8.5	even	2		1416.1.r.a.197.1	✓	28
24.5	odd	2	CM	1416.1.r.b.197.1	yes	28
59.3	even	29	inner	1416.1.r.b.1301.1	yes	28
177.62	odd	58		1416.1.r.a.1301.1	yes	28
472.357	even	58		1416.1.r.a.1301.1	yes	28
1416.1301	odd	58	inner	1416.1.r.b.1301.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1416.1.r.a.197.1	✓	28	3.2	odd	2
1416.1.r.a.197.1	✓	28	8.5	even	2
1416.1.r.a.1301.1	yes	28	177.62	odd	58
1416.1.r.a.1301.1	yes	28	472.357	even	58
1416.1.r.b.197.1	yes	28	1.1	even	1	trivial
1416.1.r.b.197.1	yes	28	24.5	odd	2	CM
1416.1.r.b.1301.1	yes	28	59.3	even	29	inner
1416.1.r.b.1301.1	yes	28	1416.1301	odd	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:	\( N \)	\(=\)	\( 1416 = 2^{3} \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1416.r (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.907575 - 0.419889i) q^{2} +(0.947653 - 0.319302i) q^{3} +(0.647386 + 0.762162i) q^{4} +(0.0927786 - 0.0558230i) q^{5} +(-0.994138 - 0.108119i) q^{6} +(-0.0400778 - 0.739191i) q^{7} +(-0.267528 - 0.963550i) q^{8} +(0.796093 - 0.605174i) q^{9} +(-0.107643 + 0.0117069i) q^{10} +(-0.277248 - 1.69114i) q^{11} +(0.856857 + 0.515554i) q^{12} +(-0.274005 + 0.687699i) q^{14} +(0.0700976 - 0.0825252i) q^{15} +(-0.161782 + 0.986827i) q^{16} +(-0.976621 + 0.214970i) q^{18} +(0.102610 + 0.0345733i) q^{20} +(-0.274005 - 0.687699i) q^{21} +(-0.458467 + 1.65125i) q^{22} +(-0.561187 - 0.827689i) q^{24} +(-0.462917 + 0.873154i) q^{25} +(0.561187 - 0.827689i) q^{27} +(0.537437 - 0.509088i) q^{28} +(-1.77271 + 0.820145i) q^{29} +(-0.0982703 + 0.0454647i) q^{30} +(-0.388449 + 0.367958i) q^{31} +(0.561187 - 0.827689i) q^{32} +(-0.802718 - 1.51409i) q^{33} +(-0.0449822 - 0.0663438i) q^{35} +(0.976621 + 0.214970i) q^{36} +(-0.0786092 - 0.0744626i) q^{40} +(-0.0400778 + 0.739191i) q^{42} +(1.10944 - 1.30613i) q^{44} +(0.0400778 - 0.100588i) q^{45} +(0.161782 + 0.986827i) q^{48} +(0.449341 - 0.0488688i) q^{49} +(0.786760 - 0.598079i) q^{50} +(1.58285 + 0.172146i) q^{53} +(-0.856857 + 0.515554i) q^{54} +(-0.120127 - 0.141425i) q^{55} +(-0.701525 + 0.236371i) q^{56} +1.95324 q^{58} +(0.994138 - 0.108119i) q^{59} +0.108278 q^{60} +(0.507048 - 0.170844i) q^{62} +(-0.479245 - 0.564211i) q^{63} +(-0.856857 + 0.515554i) q^{64} +(0.0927786 + 1.71120i) q^{66} +(0.0129677 + 0.0790996i) q^{70} +(-0.796093 - 0.605174i) q^{72} +(0.537437 - 1.34887i) q^{73} +(-0.159885 + 0.975257i) q^{75} +(-1.23896 + 0.272716i) q^{77} +(1.06362 + 0.358376i) q^{79} +(0.0400778 + 0.100588i) q^{80} +(0.267528 - 0.963550i) q^{81} +(0.726610 + 1.07167i) q^{83} +(0.346752 - 0.654043i) q^{84} +(-1.41804 + 1.34324i) q^{87} +(-1.55533 + 0.719570i) q^{88} +(-0.0786092 + 0.0744626i) q^{90} +(-0.250625 + 0.472729i) q^{93} +(0.267528 - 0.963550i) q^{96} +(0.119763 + 0.300583i) q^{97} +(-0.428331 - 0.144321i) q^{98} +(-1.24415 - 1.17852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} + q^{8} - q^{9} - 2 q^{10} + 2 q^{11} + q^{12} - 27 q^{14} - 2 q^{15} - q^{16} + q^{18} + 2 q^{20} - 27 q^{21} - 2 q^{22} - q^{24} - 3 q^{25}+ \cdots + 2 q^{99}+O(q^{100}) \) 28 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 + q^8 - q^9 - 2 * q^10 + 2 * q^11 + q^12 - 27 * q^14 - 2 * q^15 - q^16 + q^18 + 2 * q^20 - 27 * q^21 - 2 * q^22 - q^24 - 3 * q^25 + q^27 - 2 * q^28 + 2 * q^29 + 2 * q^30 - 2 * q^31 + q^32 - 2 * q^33 + 4 * q^35 - q^36 - 2 * q^40 - 2 * q^42 + 2 * q^44 + 2 * q^45 + q^48 - 3 * q^49 + 3 * q^50 + 2 * q^53 - q^54 - 4 * q^55 + 2 * q^56 - 2 * q^58 + q^59 - 2 * q^60 + 2 * q^62 - 2 * q^63 - q^64 + 2 * q^66 - 4 * q^70 + q^72 - 2 * q^73 + 3 * q^75 + 4 * q^77 - 2 * q^79 + 2 * q^80 - q^81 + 2 * q^83 + 2 * q^84 - 2 * q^87 - 2 * q^88 - 2 * q^90 + 2 * q^93 - q^96 - 2 * q^97 + 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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