LMFDB - Embedded newform 1416.1.r.a.845.1

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			845.1
Root			$-0.0541389 - 0.998533i$ of defining polynomial
Character	$\chi$	$=$	1416.845
Dual form			1416.1.r.a.677.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.468408 - 0.883512i) q^{2} +(-0.725995 + 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(1.55496 - 0.342273i) q^{5} +(0.267528 + 0.963550i) q^{6} +(-0.257587 + 0.195813i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(0.425955 - 1.53415i) q^{10} +(-0.722969 - 1.81452i) q^{11} +(0.976621 + 0.214970i) q^{12} +(0.0523468 + 0.319302i) q^{14} +(-0.893514 + 1.31783i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(-0.856857 - 0.515554i) q^{18} +(-1.15592 - 1.09495i) q^{20} +(0.0523468 - 0.319302i) q^{21} +(-1.94179 - 0.211183i) q^{22} +(0.647386 - 0.762162i) q^{24} +(1.39318 - 0.644554i) q^{25} +(0.647386 + 0.762162i) q^{27} +(0.306626 + 0.103314i) q^{28} +(-0.802718 - 1.51409i) q^{29} +(0.745793 + 1.40672i) q^{30} +(1.88420 + 0.634860i) q^{31} +(0.647386 + 0.762162i) q^{32} +(1.77271 + 0.820145i) q^{33} +(-0.333517 + 0.392646i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(-1.50884 + 0.508387i) q^{40} +(-0.257587 - 0.195813i) q^{42} +(-1.09613 + 1.61668i) q^{44} +(-0.257587 - 1.57121i) q^{45} +(-0.370138 - 0.928977i) q^{48} +(-0.239520 + 0.862672i) q^{49} +(0.0831063 - 1.53281i) q^{50} +(0.0289674 + 0.104331i) q^{53} +(0.976621 - 0.214970i) q^{54} +(-1.74525 - 2.57405i) q^{55} +(0.234906 - 0.222515i) q^{56} -1.71371 q^{58} +(0.267528 - 0.963550i) q^{59} +1.59219 q^{60} +(1.44348 - 1.36734i) q^{62} +(0.181580 + 0.267810i) q^{63} +(0.976621 - 0.214970i) q^{64} +(1.55496 - 1.18205i) q^{66} +(0.190686 + 0.478585i) q^{70} +(0.0541389 + 0.998533i) q^{72} +(0.306626 + 1.87034i) q^{73} +(-0.568183 + 1.42603i) q^{75} +(0.541532 + 0.325829i) q^{77} +(-0.939999 - 0.890414i) q^{79} +(-0.257587 + 1.57121i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(-0.726610 + 0.855431i) q^{83} +(-0.293659 + 0.135861i) q^{84} +(1.62401 + 0.547192i) q^{87} +(0.914915 + 1.72571i) q^{88} +(-1.50884 - 0.508387i) q^{90} +(-1.80451 + 0.834855i) q^{93} +(-0.994138 - 0.108119i) q^{96} +(0.119763 - 0.730524i) q^{97} +(0.649988 + 0.615702i) q^{98} +(-1.85100 + 0.623673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1416\mathbb{Z}\right)^\times$.

$n$	$473$	$709$	$769$	$1063$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{29}\right)$	$1$

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 $

$2$	0.468408	−	0.883512i	0.468408	−	0.883512i
$2$	0.468408	−	0.883512i	0.468408	−	0.883512i
$3$	−0.725995	+	0.687699i	−0.725995	+	0.687699i
$3$	−0.725995	+	0.687699i	−0.725995	+	0.687699i
$4$	−0.561187	−	0.827689i	−0.561187	−	0.827689i
$5$	1.55496	−	0.342273i	1.55496	−	0.342273i	0.647386	−	0.762162i	$-0.275862\pi$
$5$	1.55496	−	0.342273i	1.55496	−	0.342273i	0.907575	+	0.419889i	$0.137931\pi$
$6$	0.267528	+	0.963550i	0.267528	+	0.963550i
$7$	−0.257587	+	0.195813i	−0.257587	+	0.195813i	−0.725995	−	0.687699i	$-0.758621\pi$
$7$	−0.257587	+	0.195813i	−0.257587	+	0.195813i	0.468408	+	0.883512i	$0.344828\pi$
$8$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$9$	0.0541389	−	0.998533i	0.0541389	−	0.998533i
$10$	0.425955	−	1.53415i	0.425955	−	1.53415i
$11$	−0.722969	−	1.81452i	−0.722969	−	1.81452i	−0.561187	−	0.827689i	$-0.689655\pi$
$11$	−0.722969	−	1.81452i	−0.722969	−	1.81452i	−0.161782	−	0.986827i	$-0.551724\pi$
$12$	0.976621	+	0.214970i	0.976621	+	0.214970i
$13$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$13$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$14$	0.0523468	+	0.319302i	0.0523468	+	0.319302i
$15$	−0.893514	+	1.31783i	−0.893514	+	1.31783i
$16$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$17$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$17$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$18$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$19$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$19$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$20$	−1.15592	−	1.09495i	−1.15592	−	1.09495i
$21$	0.0523468	−	0.319302i	0.0523468	−	0.319302i
$22$	−1.94179	−	0.211183i	−1.94179	−	0.211183i
$23$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$23$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$24$	0.647386	−	0.762162i	0.647386	−	0.762162i
$25$	1.39318	−	0.644554i	1.39318	−	0.644554i
$26$		0			0
$27$	0.647386	+	0.762162i	0.647386	+	0.762162i
$28$	0.306626	+	0.103314i	0.306626	+	0.103314i
$29$	−0.802718	−	1.51409i	−0.802718	−	1.51409i	−0.856857	−	0.515554i	$-0.827586\pi$
$29$	−0.802718	−	1.51409i	−0.802718	−	1.51409i	0.0541389	−	0.998533i	$-0.482759\pi$
$30$	0.745793	+	1.40672i	0.745793	+	1.40672i
$31$	1.88420	+	0.634860i	1.88420	+	0.634860i	0.976621	+	0.214970i	$0.0689655\pi$
$31$	1.88420	+	0.634860i	1.88420	+	0.634860i	0.907575	+	0.419889i	$0.137931\pi$
$32$	0.647386	+	0.762162i	0.647386	+	0.762162i
$33$	1.77271	+	0.820145i	1.77271	+	0.820145i
$34$		0			0
$35$	−0.333517	+	0.392646i	−0.333517	+	0.392646i
$36$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$37$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$37$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$38$		0			0
$39$		0			0
$40$	−1.50884	+	0.508387i	−1.50884	+	0.508387i
$41$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$41$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$42$	−0.257587	−	0.195813i	−0.257587	−	0.195813i
$43$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$43$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$44$	−1.09613	+	1.61668i	−1.09613	+	1.61668i
$45$	−0.257587	−	1.57121i	−0.257587	−	1.57121i
$46$		0			0
$47$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$47$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$48$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$49$	−0.239520	+	0.862672i	−0.239520	+	0.862672i
$50$	0.0831063	−	1.53281i	0.0831063	−	1.53281i
$51$		0			0
$52$		0			0
$53$	0.0289674	+	0.104331i	0.0289674	+	0.104331i	0.976621	−	0.214970i	$-0.0689655\pi$
$53$	0.0289674	+	0.104331i	0.0289674	+	0.104331i	−0.947653	+	0.319302i	$0.896552\pi$
$54$	0.976621	−	0.214970i	0.976621	−	0.214970i
$55$	−1.74525	−	2.57405i	−1.74525	−	2.57405i
$56$	0.234906	−	0.222515i	0.234906	−	0.222515i
$57$		0			0
$58$	−1.71371			−1.71371
$59$	0.267528	−	0.963550i	0.267528	−	0.963550i
$59$	0.267528	−	0.963550i	0.267528	−	0.963550i
$60$	1.59219			1.59219
$61$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$61$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$62$	1.44348	−	1.36734i	1.44348	−	1.36734i
$63$	0.181580	+	0.267810i	0.181580	+	0.267810i
$64$	0.976621	−	0.214970i	0.976621	−	0.214970i
$65$		0			0
$66$	1.55496	−	1.18205i	1.55496	−	1.18205i
$67$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$67$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$68$		0			0
$69$		0			0
$70$	0.190686	+	0.478585i	0.190686	+	0.478585i
$71$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$71$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$72$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$73$	0.306626	+	1.87034i	0.306626	+	1.87034i	0.468408	+	0.883512i	$0.344828\pi$
$73$	0.306626	+	1.87034i	0.306626	+	1.87034i	−0.161782	+	0.986827i	$0.551724\pi$
$74$		0			0
$75$	−0.568183	+	1.42603i	−0.568183	+	1.42603i
$76$		0			0
$77$	0.541532	+	0.325829i	0.541532	+	0.325829i
$78$		0			0
$79$	−0.939999	−	0.890414i	−0.939999	−	0.890414i	0.0541389	−	0.998533i	$-0.482759\pi$
$79$	−0.939999	−	0.890414i	−0.939999	−	0.890414i	−0.994138	+	0.108119i	$0.965517\pi$
$80$	−0.257587	+	1.57121i	−0.257587	+	1.57121i
$81$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$82$		0			0
$83$	−0.726610	+	0.855431i	−0.726610	+	0.855431i	−0.994138	−	0.108119i	$-0.965517\pi$
$83$	−0.726610	+	0.855431i	−0.726610	+	0.855431i	0.267528	+	0.963550i	$0.413793\pi$
$84$	−0.293659	+	0.135861i	−0.293659	+	0.135861i
$85$		0			0
$86$		0			0
$87$	1.62401	+	0.547192i	1.62401	+	0.547192i
$88$	0.914915	+	1.72571i	0.914915	+	1.72571i
$89$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$89$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$90$	−1.50884	−	0.508387i	−1.50884	−	0.508387i
$91$		0			0
$92$		0			0
$93$	−1.80451	+	0.834855i	−1.80451	+	0.834855i
$94$		0			0
$95$		0			0
$96$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$97$	0.119763	−	0.730524i	0.119763	−	0.730524i	−0.856857	−	0.515554i	$-0.827586\pi$
$97$	0.119763	−	0.730524i	0.119763	−	0.730524i	0.976621	−	0.214970i	$-0.0689655\pi$
$98$	0.649988	+	0.615702i	0.649988	+	0.615702i
$99$	−1.85100	+	0.623673i	−1.85100	+	0.623673i
$100$	−1.31532	−	0.791404i	−1.31532	−	0.791404i
$101$	0.745793	+	0.566937i	0.745793	+	0.566937i	0.907575	−	0.419889i	$-0.137931\pi$
$101$	0.745793	+	0.566937i	0.745793	+	0.566937i	−0.161782	+	0.986827i	$0.551724\pi$
$102$		0			0
$103$	0.629862	−	0.928977i	0.629862	−	0.928977i	−0.370138	−	0.928977i	$-0.620690\pi$
$103$	0.629862	−	0.928977i	0.629862	−	0.928977i	1.00000			$0$
$104$		0			0
$105$	−0.0278910	−	0.514419i	−0.0278910	−	0.514419i
$106$	0.105746	+	0.0232765i	0.105746	+	0.0232765i
$107$	0.415433	+	1.04266i	0.415433	+	1.04266i	0.976621	+	0.214970i	$0.0689655\pi$
$107$	0.415433	+	1.04266i	0.415433	+	1.04266i	−0.561187	+	0.827689i	$0.689655\pi$
$108$	0.267528	−	0.963550i	0.267528	−	0.963550i
$109$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$109$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$110$	−3.09169	+	0.336242i	−3.09169	+	0.336242i
$111$		0			0
$112$	−0.0865625	−	0.311770i	−0.0865625	−	0.311770i
$113$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$113$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$114$		0			0
$115$		0			0
$116$	−0.802718	+	1.51409i	−0.802718	+	1.51409i
$117$		0			0
$118$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$119$		0			0
$120$	0.745793	−	1.40672i	0.745793	−	1.40672i
$121$	−2.04379	+	1.93598i	−2.04379	+	1.93598i
$122$		0			0
$123$		0			0
$124$	−0.531920	−	1.91580i	−0.531920	−	1.91580i
$125$	0.678200	−	0.515554i	0.678200	−	0.515554i
$126$	0.321667	−	0.0349834i	0.321667	−	0.0349834i
$127$	−0.0607641	+	1.12073i	−0.0607641	+	1.12073i	0.796093	+	0.605174i	$0.206897\pi$
$127$	−0.0607641	+	1.12073i	−0.0607641	+	1.12073i	−0.856857	+	0.515554i	$0.827586\pi$
$128$	0.267528	−	0.963550i	0.267528	−	0.963550i
$129$		0			0
$130$		0			0
$131$	0.0982703	+	1.81249i	0.0982703	+	1.81249i	0.468408	+	0.883512i	$0.344828\pi$
$131$	0.0982703	+	1.81249i	0.0982703	+	1.81249i	−0.370138	+	0.928977i	$0.620690\pi$
$132$	−0.315999	−	1.92751i	−0.315999	−	1.92751i
$133$		0			0
$134$		0			0
$135$	1.26753	+	0.963550i	1.26753	+	0.963550i
$136$		0			0
$137$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$137$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$138$		0			0
$139$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$139$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$140$	0.512154	+	0.0557001i	0.512154	+	0.0557001i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.907575	+	0.419889i	0.907575	+	0.419889i
$145$	−1.76643	−	2.07960i	−1.76643	−	2.07960i
$146$	1.79609	+	0.605174i	1.79609	+	0.605174i
$147$	−0.419369	−	0.791014i	−0.419369	−	0.791014i
$148$		0			0
$149$	1.37598	+	0.463623i	1.37598	+	0.463623i	0.907575	−	0.419889i	$-0.137931\pi$
$149$	1.37598	+	0.463623i	1.37598	+	0.463623i	0.468408	+	0.883512i	$0.344828\pi$
$150$	0.993775	+	1.16996i	0.993775	+	1.16996i
$151$	0.485604	+	0.224664i	0.485604	+	0.224664i	0.647386	−	0.762162i	$-0.275862\pi$
$151$	0.485604	+	0.224664i	0.485604	+	0.224664i	−0.161782	+	0.986827i	$0.551724\pi$
$152$		0			0
$153$		0			0
$154$	0.541532	−	0.325829i	0.541532	−	0.325829i
$155$	3.14715	+	0.342273i	3.14715	+	0.342273i
$156$		0			0
$157$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$157$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$158$	−1.22700	+	0.413423i	−1.22700	+	0.413423i
$159$	−0.0927786	−	0.0558230i	−0.0927786	−	0.0558230i
$160$	1.26753	+	0.963550i	1.26753	+	0.963550i
$161$		0			0
$162$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$163$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$163$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$164$		0			0
$165$	3.03722	+	0.668542i	3.03722	+	0.668542i
$166$	0.415433	+	1.04266i	0.415433	+	1.04266i
$167$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$167$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$168$	−0.0175174	+	0.323089i	−0.0175174	+	0.323089i
$169$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.961714	+	1.41842i	0.961714	+	1.41842i	0.907575	+	0.419889i	$0.137931\pi$
$173$	0.961714	+	1.41842i	0.961714	+	1.41842i	0.0541389	+	0.998533i	$0.482759\pi$
$174$	1.24415	−	1.17852i	1.24415	−	1.17852i
$175$	−0.232653	+	0.438831i	−0.232653	+	0.438831i
$176$	1.95324			1.95324
$177$	0.468408	+	0.883512i	0.468408	+	0.883512i
$178$		0			0
$179$	0.606482	−	1.14395i	0.606482	−	1.14395i	−0.370138	−	0.928977i	$-0.620690\pi$
$179$	0.606482	−	1.14395i	0.606482	−	1.14395i	0.976621	−	0.214970i	$-0.0689655\pi$
$180$	−1.15592	+	1.09495i	−1.15592	+	1.09495i
$181$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$181$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−0.107643	+	1.98536i	−0.107643	+	1.98536i
$187$		0			0
$188$		0			0
$189$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i
$190$		0			0
$191$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$191$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$192$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$193$	−0.0400778	+	0.100588i	−0.0400778	+	0.100588i	−0.947653	−	0.319302i	$-0.896552\pi$
$193$	−0.0400778	+	0.100588i	−0.0400778	+	0.100588i	0.907575	+	0.419889i	$0.137931\pi$
$194$	−0.589329	−	0.447996i	−0.589329	−	0.447996i
$195$		0			0
$196$	0.848440	−	0.285873i	0.848440	−	0.285873i
$197$	−1.31779	−	1.24828i	−1.31779	−	1.24828i	−0.947653	−	0.319302i	$-0.896552\pi$
$197$	−1.31779	−	1.24828i	−1.31779	−	1.24828i	−0.370138	−	0.928977i	$-0.620690\pi$
$198$	−0.315999	+	1.92751i	−0.315999	+	1.92751i
$199$	1.44348	+	0.156988i	1.44348	+	0.156988i	0.796093	−	0.605174i	$-0.206897\pi$
$199$	1.44348	+	0.156988i	1.44348	+	0.156988i	0.647386	+	0.762162i	$0.275862\pi$
$200$	−1.31532	+	0.791404i	−1.31532	+	0.791404i
$201$		0			0
$202$	0.850232	−	0.393359i	0.850232	−	0.393359i
$203$	0.503247	+	0.232827i	0.503247	+	0.232827i
$204$		0			0
$205$		0			0
$206$	−0.525730	−	0.991631i	−0.525730	−	0.991631i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−0.467559	−	0.216316i	−0.467559	−	0.216316i
$211$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$211$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$212$	0.0700976	−	0.0825252i	0.0700976	−	0.0825252i
$213$		0			0
$214$	1.11579	+	0.121350i	1.11579	+	0.121350i
$215$		0			0
$216$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$217$	−0.609658	+	0.205418i	−0.609658	+	0.205418i
$218$		0			0
$219$	−1.50884	−	1.14699i	−1.50884	−	1.14699i
$220$	−1.15110	+	2.88905i	−1.15110	+	2.88905i
$221$		0			0
$222$		0			0
$223$	−0.0400778	−	0.739191i	−0.0400778	−	0.739191i	−0.947653	−	0.319302i	$-0.896552\pi$
$223$	−0.0400778	−	0.739191i	−0.0400778	−	0.739191i	0.907575	−	0.419889i	$-0.137931\pi$
$224$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i
$225$	−0.568183	−	1.42603i	−0.568183	−	1.42603i
$226$		0			0
$227$	−0.107643	+	1.98536i	−0.107643	+	1.98536i	0.0541389	+	0.998533i	$0.482759\pi$
$227$	−0.107643	+	1.98536i	−0.107643	+	1.98536i	−0.161782	+	0.986827i	$0.551724\pi$
$228$		0			0
$229$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$229$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$230$		0			0
$231$	−0.617223	+	0.135861i	−0.617223	+	0.135861i
$232$	0.961714	+	1.41842i	0.961714	+	1.41842i
$233$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$233$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$234$		0			0
$235$		0			0
$236$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$237$	1.29477			1.29477
$238$		0			0
$239$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$239$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$240$	−0.893514	−	1.31783i	−0.893514	−	1.31783i
$241$	−1.67365	+	0.368398i	−1.67365	+	0.368398i	−0.947653	−	0.319302i	$-0.896552\pi$
$241$	−1.67365	+	0.368398i	−1.67365	+	0.368398i	−0.725995	+	0.687699i	$0.758621\pi$
$242$	0.753133	+	2.71254i	0.753133	+	2.71254i
$243$	0.796093	−	0.605174i	0.796093	−	0.605174i
$244$		0			0
$245$	−0.0771747	+	1.42340i	−0.0771747	+	1.42340i
$246$		0			0
$247$		0			0
$248$	−1.94179	−	0.427421i	−1.94179	−	0.427421i
$249$	−0.0607641	−	1.12073i	−0.0607641	−	1.12073i
$250$	−0.137824	−	0.840687i	−0.137824	−	0.840687i
$251$	−1.01864	+	1.50238i	−1.01864	+	1.50238i	−0.161782	+	0.986827i	$0.551724\pi$
$251$	−1.01864	+	1.50238i	−1.01864	+	1.50238i	−0.856857	+	0.515554i	$0.827586\pi$
$252$	0.119763	−	0.300583i	0.119763	−	0.300583i
$253$		0			0
$254$	0.961714	+	0.578644i	0.961714	+	0.578644i
$255$		0			0
$256$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$257$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$257$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.55533	+	0.719570i	−1.55533	+	0.719570i
$262$	1.64739	+	0.762162i	1.64739	+	0.762162i
$263$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$263$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$264$	−1.85100	−	0.623673i	−1.85100	−	0.623673i
$265$	0.0807529	+	0.152316i	0.0807529	+	0.152316i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.72013	−	0.795818i	−1.72013	−	0.795818i	−0.994138	−	0.108119i	$-0.965517\pi$
$269$	−1.72013	−	0.795818i	−1.72013	−	0.795818i	−0.725995	−	0.687699i	$-0.758621\pi$
$270$	1.44503	−	0.668542i	1.44503	−	0.668542i
$271$	0.606482	−	0.714006i	0.606482	−	0.714006i	−0.370138	−	0.928977i	$-0.620690\pi$
$271$	0.606482	−	0.714006i	0.606482	−	0.714006i	0.976621	+	0.214970i	$0.0689655\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.17678	−	2.06195i	−2.17678	−	2.06195i
$276$		0			0
$277$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$277$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$278$		0			0
$279$	0.735937	−	1.84706i	0.735937	−	1.84706i
$280$	0.289109	−	0.426404i	0.289109	−	0.426404i
$281$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$281$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$282$		0			0
$283$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$283$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.796093	−	0.605174i	0.796093	−	0.605174i
$289$	0.267528	+	0.963550i	0.267528	+	0.963550i
$290$	−2.66476	+	0.586558i	−2.66476	+	0.586558i
$291$	0.415433	+	0.612719i	0.415433	+	0.612719i
$292$	1.37598	−	1.30340i	1.37598	−	1.30340i
$293$	0.250625	−	0.472729i	0.250625	−	0.472729i	−0.725995	−	0.687699i	$-0.758621\pi$
$293$	0.250625	−	0.472729i	0.250625	−	0.472729i	0.976621	+	0.214970i	$0.0689655\pi$
$294$	−0.895306			−0.895306
$295$	0.0861992	−	1.58985i	0.0861992	−	1.58985i
$296$		0			0
$297$	0.914915	−	1.72571i	0.914915	−	1.72571i
$298$	1.05414	−	0.998533i	1.05414	−	0.998533i
$299$		0			0
$300$	1.49917	−	0.329992i	1.49917	−	0.329992i
$301$		0			0
$302$	0.425955	−	0.323803i	0.425955	−	0.323803i
$303$	−0.931325	+	0.101288i	−0.931325	+	0.101288i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$307$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$308$	−0.0342157	−	0.631072i	−0.0342157	−	0.631072i
$309$	0.181580	+	1.10759i	0.181580	+	1.10759i
$310$	1.77655	−	2.62022i	1.77655	−	2.62022i
$311$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$311$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$312$		0			0
$313$	1.24415	+	0.748580i	1.24415	+	0.748580i	0.976621	−	0.214970i	$-0.0689655\pi$
$313$	1.24415	+	0.748580i	1.24415	+	0.748580i	0.267528	+	0.963550i	$0.413793\pi$
$314$		0			0
$315$	0.374014	+	0.354285i	0.374014	+	0.354285i
$316$	−0.209471	+	1.27772i	−0.209471	+	1.27772i
$317$	−1.94179	−	0.211183i	−1.94179	−	0.211183i	−0.947653	−	0.319302i	$-0.896552\pi$
$317$	−1.94179	−	0.211183i	−1.94179	−	0.211183i	−0.994138	+	0.108119i	$0.965517\pi$
$318$	−0.0927786	+	0.0558230i	−0.0927786	+	0.0558230i
$319$	−2.16699	+	2.55118i	−2.16699	+	2.55118i
$320$	1.44503	−	0.668542i	1.44503	−	0.668542i
$321$	−1.01864	−	0.471273i	−1.01864	−	0.471273i
$322$		0			0
$323$		0			0
$324$	0.468408	+	0.883512i	0.468408	+	0.883512i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	2.01332	−	2.37027i	2.01332	−	2.37027i
$331$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$331$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$332$	1.11579	+	0.121350i	1.11579	+	0.121350i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.277248	+	0.166815i	0.277248	+	0.166815i
$337$	0.745793	+	0.566937i	0.745793	+	0.566937i	0.907575	−	0.419889i	$-0.137931\pi$
$337$	0.745793	+	0.566937i	0.745793	+	0.566937i	−0.161782	+	0.986827i	$0.551724\pi$
$338$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$339$		0			0
$340$		0			0
$341$	−0.210253	−	3.87789i	−0.210253	−	3.87789i
$342$		0			0
$343$	−0.226988	−	0.569698i	−0.226988	−	0.569698i
$344$		0			0
$345$		0			0
$346$	1.70367	−	0.185285i	1.70367	−	0.185285i
$347$	0.745793	−	0.566937i	0.745793	−	0.566937i	−0.161782	−	0.986827i	$-0.551724\pi$
$347$	0.745793	−	0.566937i	0.745793	−	0.566937i	0.907575	+	0.419889i	$0.137931\pi$
$348$	−0.458467	−	1.65125i	−0.458467	−	1.65125i
$349$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$349$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$350$	0.278735	+	0.411104i	0.278735	+	0.411104i
$351$		0			0
$352$	0.914915	−	1.72571i	0.914915	−	1.72571i
$353$		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	−	1.07167i	−0.726610	−	1.07167i
$359$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$359$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$360$	0.425955	+	1.53415i	0.425955	+	1.53415i
$361$	0.796093	−	0.605174i	0.796093	−	0.605174i
$362$		0			0
$363$	0.152409	−	2.81102i	0.152409	−	2.81102i
$364$		0			0
$365$	1.11696	+	2.80335i	1.11696	+	2.80335i
$366$		0			0
$367$	−0.0927786	−	1.71120i	−0.0927786	−	1.71120i	−0.561187	−	0.827689i	$-0.689655\pi$
$367$	−0.0927786	−	1.71120i	−0.0927786	−	1.71120i	0.468408	−	0.883512i	$-0.344828\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0278910	−	0.0212022i	−0.0278910	−	0.0212022i
$372$	1.70367	+	1.02506i	1.70367	+	1.02506i
$373$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$373$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$374$		0			0
$375$	−0.137824	+	0.840687i	−0.137824	+	0.840687i
$376$		0			0
$377$		0			0
$378$	−0.209471	+	0.246608i	−0.209471	+	0.246608i
$379$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$379$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$380$		0			0
$381$	−0.726610	−	0.855431i	−0.726610	−	0.855431i
$382$		0			0
$383$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$383$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$384$	0.468408	+	0.883512i	0.468408	+	0.883512i
$385$	0.953585	+	0.321300i	0.953585	+	0.321300i
$386$	0.0700976	+	0.0825252i	0.0700976	+	0.0825252i
$387$		0			0
$388$	−0.671857	+	0.310834i	−0.671857	+	0.310834i
$389$	0.838218	−	0.986827i	0.838218	−	0.986827i	−0.161782	−	0.986827i	$-0.551724\pi$
$389$	0.838218	−	0.986827i	0.838218	−	0.986827i	1.00000			$0$
$390$		0			0
$391$		0			0
$392$	0.144844	−	0.883512i	0.144844	−	0.883512i
$393$	−1.31779	−	1.24828i	−1.31779	−	1.24828i
$394$	−1.72013	+	0.579580i	−1.72013	+	0.579580i
$395$	−1.76643	−	1.06282i	−1.76643	−	1.06282i
$396$	1.55496	+	1.18205i	1.55496	+	1.18205i
$397$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$397$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$398$	0.814839	−	1.20180i	0.814839	−	1.20180i
$399$		0			0
$400$	0.0831063	+	1.53281i	0.0831063	+	1.53281i
$401$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$401$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$402$		0			0
$403$		0			0
$404$	0.0507182	−	0.935443i	0.0507182	−	0.935443i
$405$	−1.58285	+	0.172146i	−1.58285	+	0.172146i
$406$	0.441431	−	0.335567i	0.441431	−	0.335567i
$407$		0			0
$408$		0			0
$409$	−0.525730	−	0.775393i	−0.525730	−	0.775393i	0.468408	−	0.883512i	$-0.344828\pi$
$409$	−0.525730	−	0.775393i	−0.525730	−	0.775393i	−0.994138	+	0.108119i	$0.965517\pi$
$410$		0			0
$411$		0			0
$412$	−1.12237			−1.12237
$413$	0.119763	+	0.300583i	0.119763	+	0.300583i
$414$		0			0
$415$	−0.837059	+	1.57886i	−0.837059	+	1.57886i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.143143	+	0.515554i	0.143143	+	0.515554i	1.00000			$0$
$419$	0.143143	+	0.515554i	0.143143	+	0.515554i	−0.856857	+	0.515554i	$0.827586\pi$
$420$	−0.410127	+	0.311770i	−0.410127	+	0.311770i
$421$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$421$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$422$		0			0
$423$		0			0
$424$	−0.0400778	−	0.100588i	−0.0400778	−	0.100588i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.629862	−	0.928977i	0.629862	−	0.928977i
$429$		0			0
$430$		0			0
$431$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$431$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$432$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$433$	−0.0786092	−	0.0744626i	−0.0786092	−	0.0744626i	0.647386	−	0.762162i	$-0.275862\pi$
$433$	−0.0786092	−	0.0744626i	−0.0786092	−	0.0744626i	−0.725995	+	0.687699i	$0.758621\pi$
$434$	−0.104080	+	0.634860i	−0.104080	+	0.634860i
$435$	2.71256	+	0.295008i	2.71256	+	0.295008i
$436$		0			0
$437$		0			0
$438$	−1.72013	+	0.795818i	−1.72013	+	0.795818i
$439$	−1.72013	−	0.795818i	−1.72013	−	0.795818i	−0.994138	−	0.108119i	$-0.965517\pi$
$439$	−1.72013	−	0.795818i	−1.72013	−	0.795818i	−0.725995	−	0.687699i	$-0.758621\pi$
$440$	2.01332	+	2.37027i	2.01332	+	2.37027i
$441$	0.848440	+	0.285873i	0.848440	+	0.285873i
$442$		0			0
$443$	−0.346752	−	0.654043i	−0.346752	−	0.654043i	0.647386	−	0.762162i	$-0.275862\pi$
$443$	−0.346752	−	0.654043i	−0.346752	−	0.654043i	−0.994138	+	0.108119i	$0.965517\pi$
$444$		0			0
$445$		0			0
$446$	−0.671857	−	0.310834i	−0.671857	−	0.310834i
$447$	−1.31779	+	0.609675i	−1.31779	+	0.609675i
$448$	−0.209471	+	0.246608i	−0.209471	+	0.246608i
$449$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$449$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$450$	−1.52606	−	0.165969i	−1.52606	−	0.165969i
$451$		0			0
$452$		0			0
$453$	−0.507048	+	0.170844i	−0.507048	+	0.170844i
$454$	1.70367	+	1.02506i	1.70367	+	1.02506i
$455$		0			0
$456$		0			0
$457$	−0.0607641	+	0.0896204i	−0.0607641	+	0.0896204i	−0.856857	−	0.515554i	$-0.827586\pi$
$457$	−0.0607641	+	0.0896204i	−0.0607641	+	0.0896204i	0.796093	+	0.605174i	$0.206897\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.198045	−	0.497055i	−0.198045	−	0.497055i	0.796093	−	0.605174i	$-0.206897\pi$
$461$	−0.198045	−	0.497055i	−0.198045	−	0.497055i	−0.994138	+	0.108119i	$0.965517\pi$
$462$	−0.169078	+	0.608962i	−0.169078	+	0.608962i
$463$	−0.0400778	+	0.739191i	−0.0400778	+	0.739191i	0.907575	+	0.419889i	$0.137931\pi$
$463$	−0.0400778	+	0.739191i	−0.0400778	+	0.739191i	−0.947653	+	0.319302i	$0.896552\pi$
$464$	1.70367	−	0.185285i	1.70367	−	0.185285i
$465$	−2.52020	+	1.91580i	−2.52020	+	1.91580i
$466$		0			0
$467$	1.26450	−	0.278338i	1.26450	−	0.278338i	0.468408	−	0.883512i	$-0.344828\pi$
$467$	1.26450	−	0.278338i	1.26450	−	0.278338i	0.796093	+	0.605174i	$0.206897\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$473$		0			0
$474$	0.606482	−	1.14395i	0.606482	−	1.14395i
$475$		0			0
$476$		0			0
$477$	0.105746	−	0.0232765i	0.105746	−	0.0232765i
$478$		0			0
$479$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$479$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$480$	−1.58285	+	0.172146i	−1.58285	+	0.172146i
$481$		0			0
$482$	−0.458467	+	1.65125i	−0.458467	+	1.65125i
$483$		0			0
$484$	2.74933	+	0.605174i	2.74933	+	0.605174i
$485$	−0.0638112	−	1.17693i	−0.0638112	−	1.17693i
$486$	−0.161782	−	0.986827i	−0.161782	−	0.986827i
$487$	1.11579	−	1.64567i	1.11579	−	1.64567i	0.468408	−	0.883512i	$-0.344828\pi$
$487$	1.11579	−	1.64567i	1.11579	−	1.64567i	0.647386	−	0.762162i	$-0.275862\pi$
$488$		0			0
$489$		0			0
$490$	1.22145	+	0.734919i	1.22145	+	0.734919i
$491$	−1.22700	+	0.413423i	−1.22700	+	0.413423i	−0.856857	−	0.515554i	$-0.827586\pi$
$491$	−1.22700	+	0.413423i	−1.22700	+	0.413423i	−0.370138	+	0.928977i	$0.620690\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−2.66476	+	1.60333i	−2.66476	+	1.60333i
$496$	−1.28718	+	1.51539i	−1.28718	+	1.51539i
$497$		0			0
$498$	−1.01864	−	0.471273i	−1.01864	−	0.471273i
$499$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$499$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$500$	−0.807315	−	0.272016i	−0.807315	−	0.272016i
$501$		0			0
$502$	0.850232	+	1.60371i	0.850232	+	1.60371i
$503$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$503$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$504$	−0.209471	−	0.246608i	−0.209471	−	0.246608i
$505$	1.35373	+	0.626301i	1.35373	+	0.626301i
$506$		0			0
$507$	0.647386	−	0.762162i	0.647386	−	0.762162i
$508$	0.961714	−	0.578644i	0.961714	−	0.578644i
$509$	−1.28718	−	0.139990i	−1.28718	−	0.139990i	−0.561187	−	0.827689i	$-0.689655\pi$
$509$	−1.28718	−	0.139990i	−1.28718	−	0.139990i	−0.725995	+	0.687699i	$0.758621\pi$
$510$		0			0
$511$	−0.445219	−	0.421734i	−0.445219	−	0.421734i
$512$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$513$		0			0
$514$		0			0
$515$	0.661447	−	1.66011i	0.661447	−	1.66011i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.67365	−	0.368398i	−1.67365	−	0.368398i
$520$		0			0
$521$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$521$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$522$	−0.0927786	+	1.71120i	−0.0927786	+	1.71120i
$523$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$523$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$524$	1.44503	−	1.09848i	1.44503	−	1.09848i
$525$	−0.132878	−	0.478585i	−0.132878	−	0.478585i
$526$		0			0
$527$		0			0
$528$	−1.41804	+	1.34324i	−1.41804	+	1.34324i
$529$	0.468408	−	0.883512i	0.468408	−	0.883512i
$530$	0.172398			0.172398
$531$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.00286	+	1.47910i	1.00286	+	1.47910i
$536$		0			0
$537$	0.346388	+	1.24758i	0.346388	+	1.24758i
$538$	−1.50884	+	1.14699i	−1.50884	+	1.14699i
$539$	1.73850	−	0.189073i	1.73850	−	0.189073i
$540$	0.0861992	−	1.58985i	0.0861992	−	1.58985i
$541$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$541$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$542$	−0.346752	−	0.870281i	−0.346752	−	0.870281i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$547$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$548$		0			0
$549$		0			0
$550$	−2.84138	+	0.957373i	−2.84138	+	0.957373i
$551$		0			0
$552$		0			0
$553$	0.416486	+	0.0452956i	0.416486	+	0.0452956i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.77271	+	0.820145i	1.77271	+	0.820145i	0.976621	+	0.214970i	$0.0689655\pi$
$557$	1.77271	+	0.820145i	1.77271	+	0.820145i	0.796093	+	0.605174i	$0.206897\pi$
$558$	−1.28718	−	1.51539i	−1.28718	−	1.51539i
$559$		0			0
$560$	−0.241312	−	0.455163i	−0.241312	−	0.455163i
$561$		0			0
$562$		0			0
$563$	−0.939999	−	1.10665i	−0.939999	−	1.10665i	−0.994138	−	0.108119i	$-0.965517\pi$
$563$	−0.939999	−	1.10665i	−0.939999	−	1.10665i	0.0541389	−	0.998533i	$-0.482759\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.277248	−	0.166815i	0.277248	−	0.166815i
$568$		0			0
$569$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$569$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$570$		0			0
$571$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$571$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.161782	−	0.986827i	−0.161782	−	0.986827i
$577$	−0.107643	−	1.98536i	−0.107643	−	1.98536i	−0.161782	−	0.986827i	$-0.551724\pi$
$577$	−0.107643	−	1.98536i	−0.107643	−	1.98536i	0.0541389	−	0.998533i	$-0.482759\pi$
$578$	0.976621	+	0.214970i	0.976621	+	0.214970i
$579$	−0.0400778	−	0.100588i	−0.0400778	−	0.100588i
$580$	−0.729965	+	2.62910i	−0.729965	+	2.62910i
$581$	0.0196611	−	0.362627i	0.0196611	−	0.362627i
$582$	0.735937	−	0.0800379i	0.735937	−	0.0800379i
$583$	0.168368	−	0.127990i	0.168368	−	0.127990i
$584$	−0.507048	−	1.82622i	−0.507048	−	1.82622i
$585$		0			0
$586$	−0.300267	−	0.442861i	−0.300267	−	0.442861i
$587$	−0.388449	+	0.367958i	−0.388449	+	0.367958i	−0.856857	−	0.515554i	$-0.827586\pi$
$587$	−0.388449	+	0.367958i	−0.388449	+	0.367958i	0.468408	+	0.883512i	$0.344828\pi$
$588$	−0.419369	+	0.791014i	−0.419369	+	0.791014i
$589$		0			0
$590$	−1.36428	−	0.820858i	−1.36428	−	0.820858i
$591$	1.81515			1.81515
$592$		0			0
$593$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$593$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$594$	−1.09613	−	1.61668i	−1.09613	−	1.61668i
$595$		0			0
$596$	−0.388449	−	1.39907i	−0.388449	−	1.39907i
$597$	−1.15592	+	0.878708i	−1.15592	+	0.878708i
$598$		0			0
$599$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$599$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$600$	0.410671	−	1.47910i	0.410671	−	1.47910i
$601$	0.119763	+	0.300583i	0.119763	+	0.300583i	0.976621	−	0.214970i	$-0.0689655\pi$
$601$	0.119763	+	0.300583i	0.119763	+	0.300583i	−0.856857	+	0.515554i	$0.827586\pi$
$602$		0			0
$603$		0			0
$604$	−0.0865625	−	0.528008i	−0.0865625	−	0.528008i
$605$	−2.51538	+	3.70990i	−2.51538	+	3.70990i
$606$	−0.346752	+	0.870281i	−0.346752	+	0.870281i
$607$	−1.15592	−	0.878708i	−1.15592	−	0.878708i	−0.161782	−	0.986827i	$-0.551724\pi$
$607$	−1.15592	−	0.878708i	−1.15592	−	0.878708i	−0.994138	+	0.108119i	$0.965517\pi$
$608$		0			0
$609$	−0.525470	+	0.177052i	−0.525470	+	0.177052i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$613$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$614$		0			0
$615$		0			0
$616$	−0.573586	−	0.265369i	−0.573586	−	0.265369i
$617$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$617$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$618$	1.06362	+	0.358376i	1.06362	+	0.358376i
$619$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$619$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$620$	−1.48284	−	2.79694i	−1.48284	−	2.79694i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.115661	+	0.136166i	−0.115661	+	0.136166i
$626$	1.24415	−	0.748580i	1.24415	−	0.748580i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.488206	−	0.164496i	0.488206	−	0.164496i
$631$	1.24415	+	0.748580i	1.24415	+	0.748580i	0.976621	−	0.214970i	$-0.0689655\pi$
$631$	1.24415	+	0.748580i	1.24415	+	0.748580i	0.267528	+	0.963550i	$0.413793\pi$
$632$	1.03076	+	0.783563i	1.03076	+	0.783563i
$633$		0			0
$634$	−1.09613	+	1.61668i	−1.09613	+	1.61668i
$635$	0.289109	+	1.76349i	0.289109	+	1.76349i
$636$	0.00586204	+	0.108119i	0.00586204	+	0.108119i
$637$		0			0
$638$	1.23896	+	3.10956i	1.23896	+	3.10956i
$639$		0			0
$640$	0.0861992	−	1.58985i	0.0861992	−	1.58985i
$641$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$641$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$642$	−0.893514	+	0.679232i	−0.893514	+	0.679232i
$643$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$643$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$647$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$648$	1.00000			1.00000
$649$	−1.94179	+	0.211183i	−1.94179	+	0.211183i
$650$		0			0
$651$	0.301343	−	0.568394i	0.301343	−	0.568394i
$652$		0			0
$653$	1.11579	+	1.64567i	1.11579	+	1.64567i	0.647386	+	0.762162i	$0.275862\pi$
$653$	1.11579	+	1.64567i	1.11579	+	1.64567i	0.468408	+	0.883512i	$0.344828\pi$
$654$		0			0
$655$	0.773172	+	2.78472i	0.773172	+	2.78472i
$656$		0			0
$657$	1.88420	−	0.204919i	1.88420	−	0.204919i
$658$		0			0
$659$	−0.531920	+	1.91580i	−0.531920	+	1.91580i	−0.161782	+	0.986827i	$0.551724\pi$
$659$	−0.531920	+	1.91580i	−0.531920	+	1.91580i	−0.370138	+	0.928977i	$0.620690\pi$
$660$	−1.15110	−	2.88905i	−1.15110	−	2.88905i
$661$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$661$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$662$		0			0
$663$		0			0
$664$	0.629862	−	0.928977i	0.629862	−	0.928977i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	0.537437	+	0.509088i	0.537437	+	0.509088i
$670$		0			0
$671$		0			0
$672$	0.277248	−	0.166815i	0.277248	−	0.166815i
$673$	0.838218	−	0.986827i	0.838218	−	0.986827i	−0.161782	−	0.986827i	$-0.551724\pi$
$673$	0.838218	−	0.986827i	0.838218	−	0.986827i	1.00000			$0$
$674$	0.850232	−	0.393359i	0.850232	−	0.393359i
$675$	1.39318	+	0.644554i	1.39318	+	0.644554i
$676$	0.647386	+	0.762162i	0.647386	+	0.762162i
$677$	−0.887777	−	0.299127i	−0.887777	−	0.299127i	−0.161782	−	0.986827i	$-0.551724\pi$
$677$	−0.887777	−	0.299127i	−0.887777	−	0.299127i	−0.725995	+	0.687699i	$0.758621\pi$
$678$		0			0
$679$	0.112196	+	0.211625i	0.112196	+	0.211625i
$680$		0			0
$681$	−1.28718	−	1.51539i	−1.28718	−	1.51539i
$682$	−3.52464	−	1.63067i	−3.52464	−	1.63067i
$683$	1.64739	−	0.762162i	1.64739	−	0.762162i	0.647386	−	0.762162i	$-0.275862\pi$
$683$	1.64739	−	0.762162i	1.64739	−	0.762162i	1.00000			$0$
$684$		0			0
$685$		0			0
$686$	−0.609658	−	0.0663043i	−0.609658	−	0.0663043i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$691$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$692$	0.634311	−	1.59200i	0.634311	−	1.59200i
$693$	0.354669	−	0.523098i	0.354669	−	0.523098i
$694$	−0.151560	−	0.924476i	−0.151560	−	0.924476i
$695$		0			0
$696$	−1.67365	−	0.368398i	−1.67365	−	0.368398i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.493777	−	0.0537015i	0.493777	−	0.0537015i
$701$	1.26753	−	0.963550i	1.26753	−	0.963550i	0.267528	−	0.963550i	$-0.413793\pi$
$701$	1.26753	−	0.963550i	1.26753	−	0.963550i	1.00000			$0$
$702$		0			0
$703$		0			0
$704$	−1.09613	−	1.61668i	−1.09613	−	1.61668i
$705$		0			0
$706$		0			0
$707$	−0.303120			−0.303120
$708$	0.468408	−	0.883512i	0.468408	−	0.883512i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$	−0.939999	+	0.890414i	−0.939999	+	0.890414i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.28718	+	0.139990i	−1.28718	+	0.139990i
$717$		0			0
$718$		0			0
$719$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$719$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$720$	1.55496	+	0.342273i	1.55496	+	0.342273i
$721$	0.0196611	+	0.362627i	0.0196611	+	0.362627i
$722$	−0.161782	−	0.986827i	−0.161782	−	0.986827i
$723$	0.961714	−	1.41842i	0.961714	−	1.41842i
$724$		0			0
$725$	−2.09424	−	1.59200i	−2.09424	−	1.59200i
$726$	−2.41218	−	1.45136i	−2.41218	−	1.45136i
$727$	−1.72013	+	0.579580i	−1.72013	+	0.579580i	−0.994138	−	0.108119i	$-0.965517\pi$
$727$	−1.72013	+	0.579580i	−1.72013	+	0.579580i	−0.725995	+	0.687699i	$0.758621\pi$
$728$		0			0
$729$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$730$	2.99999	+	0.326269i	2.99999	+	0.326269i
$731$		0			0
$732$		0			0
$733$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$733$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$734$	−1.55533	−	0.719570i	−1.55533	−	0.719570i
$735$	−0.922845	−	1.08646i	−0.922845	−	1.08646i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$739$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$740$		0			0
$741$		0			0
$742$	−0.0317967	+	0.0147107i	−0.0317967	+	0.0147107i
$743$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$743$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$744$	1.70367	−	1.02506i	1.70367	−	1.02506i
$745$	2.29829	+	0.249954i	2.29829	+	0.249954i
$746$		0			0
$747$	0.814839	+	0.771856i	0.814839	+	0.771856i
$748$		0			0
$749$	−0.311176	−	0.187228i	−0.311176	−	0.187228i
$750$	0.678200	+	0.515554i	0.678200	+	0.515554i
$751$	0.537437	−	1.34887i	0.537437	−	1.34887i	−0.370138	−	0.928977i	$-0.620690\pi$
$751$	0.537437	−	1.34887i	0.537437	−	1.34887i	0.907575	−	0.419889i	$-0.137931\pi$
$752$		0			0
$753$	−0.293659	−	1.79124i	−0.293659	−	1.79124i
$754$		0			0
$755$	0.831993	+	0.183135i	0.831993	+	0.183135i
$756$	0.119763	+	0.300583i	0.119763	+	0.300583i
$757$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$757$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$761$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$762$	−1.09613	+	0.241277i	−1.09613	+	0.241277i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.00000			1.00000
$769$	−0.802718	+	1.51409i	−0.802718	+	1.51409i	0.0541389	+	0.998533i	$0.482759\pi$
$769$	−0.802718	+	1.51409i	−0.802718	+	1.51409i	−0.856857	+	0.515554i	$0.827586\pi$
$770$	0.730540	−	0.692004i	0.730540	−	0.692004i
$771$		0			0
$772$	0.105746	−	0.0232765i	0.105746	−	0.0232765i
$773$	0.425955	+	1.53415i	0.425955	+	1.53415i	0.796093	+	0.605174i	$0.206897\pi$
$773$	0.425955	+	1.53415i	0.425955	+	1.53415i	−0.370138	+	0.928977i	$0.620690\pi$
$774$		0			0
$775$	3.03422	−	0.329992i	3.03422	−	0.329992i
$776$	−0.0400778	+	0.739191i	−0.0400778	+	0.739191i
$777$		0			0
$778$	−0.479245	−	1.20281i	−0.479245	−	1.20281i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.634311	−	1.59200i	0.634311	−	1.59200i
$784$	−0.712747	−	0.541816i	−0.712747	−	0.541816i
$785$		0			0
$786$	−1.72013	+	0.579580i	−1.72013	+	0.579580i
$787$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$787$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$788$	−0.293659	+	1.79124i	−0.293659	+	1.79124i
$789$		0			0
$790$	−1.76643	+	1.06282i	−1.76643	+	1.06282i
$791$		0			0
$792$	1.77271	−	0.820145i	1.77271	−	0.820145i
$793$		0			0
$794$		0			0
$795$	−0.163374	−	0.0550471i	−0.163374	−	0.0550471i
$796$	−0.680125	−	1.28285i	−0.680125	−	1.28285i
$797$	0.850232	+	1.60371i	0.850232	+	1.60371i	0.796093	+	0.605174i	$0.206897\pi$
$797$	0.850232	+	1.60371i	0.850232	+	1.60371i	0.0541389	+	0.998533i	$0.482759\pi$
$798$		0			0
$799$		0			0
$800$	1.39318	+	0.644554i	1.39318	+	0.644554i
$801$		0			0
$802$		0			0
$803$	3.17208	−	1.90858i	3.17208	−	1.90858i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.79609	−	0.605174i	1.79609	−	0.605174i
$808$	−0.802718	−	0.482980i	−0.802718	−	0.482980i
$809$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$809$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$810$	−0.589329	+	1.47910i	−0.589329	+	1.47910i
$811$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$811$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$812$	−0.0897075	−	0.547192i	−0.0897075	−	0.547192i
$813$	0.0507182	+	0.935443i	0.0507182	+	0.935443i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.931325	+	0.101288i	−0.931325	+	0.101288i
$819$		0			0
$820$		0			0
$821$	0.522547	−	0.115021i	0.522547	−	0.115021i	0.0541389	−	0.998533i	$-0.482759\pi$
$821$	0.522547	−	0.115021i	0.522547	−	0.115021i	0.468408	+	0.883512i	$0.344828\pi$
$822$		0			0
$823$	0.814839	−	0.771856i	0.814839	−	0.771856i	−0.161782	−	0.986827i	$-0.551724\pi$
$823$	0.814839	−	0.771856i	0.814839	−	0.771856i	0.976621	+	0.214970i	$0.0689655\pi$
$824$	−0.525730	+	0.991631i	−0.525730	+	0.991631i
$825$	2.99834			2.99834
$826$	0.321667	+	0.0349834i	0.321667	+	0.0349834i
$827$	−1.89531			−1.89531			−0.947653	−	0.319302i	$-0.896552\pi$
$827$	−1.89531			−1.89531			−0.947653	+	0.319302i	$0.896552\pi$
$828$		0			0
$829$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$829$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$830$	1.00286	+	1.47910i	1.00286	+	1.47910i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.735937	+	1.84706i	0.735937	+	1.84706i
$838$	0.522547	+	0.115021i	0.522547	+	0.115021i
$839$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$839$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$840$	0.0833459	+	0.508387i	0.0833459	+	0.508387i
$841$	−1.08692	+	1.60308i	−1.08692	+	1.60308i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.50884	+	0.508387i	−1.50884	+	0.508387i
$846$		0			0
$847$	0.147364	−	0.898882i	0.147364	−	0.898882i
$848$	−0.107643	−	0.0117069i	−0.107643	−	0.0117069i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$853$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$854$		0			0
$855$		0			0
$856$	−0.525730	−	0.991631i	−0.525730	−	0.991631i
$857$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$857$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$858$		0			0
$859$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$859$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$863$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$864$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$865$	1.98092	+	1.87642i	1.98092	+	1.87642i
$866$	−0.102610	+	0.0345733i	−0.102610	+	0.0345733i
$867$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$868$	0.512154	+	0.389329i	0.512154	+	0.389329i
$869$	−0.936081	+	2.34938i	−0.936081	+	2.34938i
$870$	1.53123	−	2.25839i	1.53123	−	2.25839i
$871$		0			0
$872$		0			0
$873$	−0.722969	−	0.159138i	−0.722969	−	0.159138i
$874$		0			0
$875$	−0.0737435	+	0.265600i	−0.0737435	+	0.265600i
$876$	−0.102610	+	1.89253i	−0.102610	+	1.89253i
$877$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$877$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$878$	−1.50884	+	1.14699i	−1.50884	+	1.14699i
$879$	0.143143	+	0.515554i	0.143143	+	0.515554i
$880$	3.03722	−	0.668542i	3.03722	−	0.668542i
$881$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$881$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$882$	0.649988	−	0.615702i	0.649988	−	0.615702i
$883$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$883$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$884$		0			0
$885$	1.03076	+	1.21350i	1.03076	+	1.21350i
$886$	−0.740276			−0.740276
$887$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$887$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$888$		0			0
$889$	−0.203801	−	0.300583i	−0.203801	−	0.300583i
$890$		0			0
$891$	0.522547	+	1.88205i	0.522547	+	1.88205i
$892$	−0.589329	+	0.447996i	−0.589329	+	0.447996i
$893$		0			0
$894$	−0.0786092	+	1.44986i	−0.0786092	+	1.44986i
$895$	0.551515	−	1.98638i	0.551515	−	1.98638i
$896$	0.119763	+	0.300583i	0.119763	+	0.300583i
$897$		0			0
$898$		0			0
$899$	−0.551246	−	3.36245i	−0.551246	−	3.36245i
$900$	−0.861454	+	1.27055i	−0.861454	+	1.27055i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.0865625	+	0.528008i	−0.0865625	+	0.528008i
$907$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$907$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$908$	1.70367	−	1.02506i	1.70367	−	1.02506i
$909$	0.606482	−	0.714006i	0.606482	−	0.714006i
$910$		0			0
$911$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$911$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$912$		0			0
$913$	2.07751	+	0.699994i	2.07751	+	0.699994i
$914$	0.0507182	+	0.0956648i	0.0507182	+	0.0956648i
$915$		0			0
$916$		0			0
$917$	−0.380221	−	0.447631i	−0.380221	−	0.447631i
$918$		0			0
$919$	0.485604	−	0.224664i	0.485604	−	0.224664i	−0.161782	−	0.986827i	$-0.551724\pi$
$919$	0.485604	−	0.224664i	0.485604	−	0.224664i	0.647386	+	0.762162i	$0.275862\pi$
$920$		0			0
$921$		0			0
$922$	−0.531920	−	0.0578498i	−0.531920	−	0.0578498i
$923$		0			0
$924$	0.458828	+	0.434625i	0.458828	+	0.434625i
$925$		0			0
$926$	0.634311	+	0.381652i	0.634311	+	0.381652i
$927$	−0.893514	−	0.679232i	−0.893514	−	0.679232i
$928$	0.634311	−	1.59200i	0.634311	−	1.59200i
$929$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$929$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$930$	0.512154	+	3.12400i	0.512154	+	3.12400i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.346388	−	1.24758i	0.346388	−	1.24758i
$935$		0			0
$936$		0			0
$937$	−0.893514	+	0.679232i	−0.893514	+	0.679232i	−0.947653	−	0.319302i	$-0.896552\pi$
$937$	−0.893514	+	0.679232i	−0.893514	+	0.679232i	0.0541389	+	0.998533i	$0.482759\pi$
$938$		0			0
$939$	−1.41804	+	0.312135i	−1.41804	+	0.312135i
$940$		0			0
$941$	1.44348	−	1.36734i	1.44348	−	1.36734i	0.647386	−	0.762162i	$-0.275862\pi$
$941$	1.44348	−	1.36734i	1.44348	−	1.36734i	0.796093	−	0.605174i	$-0.206897\pi$
$942$		0			0
$943$		0			0
$944$	0.796093	+	0.605174i	0.796093	+	0.605174i
$945$	−0.515174			−0.515174
$946$		0			0
$947$	−1.41804	+	1.34324i	−1.41804	+	1.34324i	−0.561187	+	0.827689i	$0.689655\pi$
$947$	−1.41804	+	1.34324i	−1.41804	+	1.34324i	−0.856857	+	0.515554i	$0.827586\pi$
$948$	−0.726610	−	1.07167i	−0.726610	−	1.07167i
$949$		0			0
$950$		0			0
$951$	1.55496	−	1.18205i	1.55496	−	1.18205i
$952$		0			0
$953$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$953$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$954$	0.0289674	−	0.104331i	0.0289674	−	0.104331i
$955$		0			0
$956$		0			0
$957$	−0.181219	−	3.34239i	−0.181219	−	3.34239i
$958$		0			0
$959$		0			0
$960$	−0.589329	+	1.47910i	−0.589329	+	1.47910i
$961$	2.35105	+	1.78723i	2.35105	+	1.78723i
$962$		0			0
$963$	1.06362	−	0.358376i	1.06362	−	0.358376i
$964$	1.24415	+	1.17852i	1.24415	+	1.17852i
$965$	−0.0278910	+	0.170127i	−0.0278910	+	0.170127i
$966$		0			0
$967$	−1.67365	+	1.00700i	−1.67365	+	1.00700i	−0.725995	+	0.687699i	$0.758621\pi$
$967$	−1.67365	+	1.00700i	−1.67365	+	1.00700i	−0.947653	+	0.319302i	$0.896552\pi$
$968$	1.82249	−	2.14560i	1.82249	−	2.14560i
$969$		0			0
$970$	−1.06972	−	0.494906i	−1.06972	−	0.494906i
$971$	−0.479245	−	0.564211i	−0.479245	−	0.564211i	0.468408	−	0.883512i	$-0.344828\pi$
$971$	−0.479245	−	0.564211i	−0.479245	−	0.564211i	−0.947653	+	0.319302i	$0.896552\pi$
$972$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$973$		0			0
$974$	−0.931325	−	1.75667i	−0.931325	−	1.75667i
$975$		0			0
$976$		0			0
$977$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$977$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$978$		0			0
$979$		0			0
$980$	1.22145	−	0.734919i	1.22145	−	0.734919i
$981$		0			0
$982$	−0.209471	+	1.27772i	−0.209471	+	1.27772i
$983$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$983$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$984$		0			0
$985$	−2.47637	−	1.48998i	−2.47637	−	1.48998i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.168368	+	3.10536i	0.168368	+	3.10536i
$991$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i	0.0541389	−	0.998533i	$-0.482759\pi$
$991$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i	−0.370138	+	0.928977i	$0.620690\pi$
$992$	0.735937	+	1.84706i	0.735937	+	1.84706i
$993$		0			0
$994$		0			0
$995$	2.29829	−	0.249954i	2.29829	−	0.249954i
$996$	−0.893514	+	0.679232i	−0.893514	+	0.679232i
$997$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$997$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1416.1.r.a.845.1	yes	28
3.2	odd	2		1416.1.r.b.845.1	yes	28
8.5	even	2		1416.1.r.b.845.1	yes	28
24.5	odd	2	CM	1416.1.r.a.845.1	yes	28
59.28	even	29	inner	1416.1.r.a.677.1	✓	28
177.146	odd	58		1416.1.r.b.677.1	yes	28
472.205	even	58		1416.1.r.b.677.1	yes	28
1416.677	odd	58	inner	1416.1.r.a.677.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1416.1.r.a.677.1	✓	28	59.28	even	29	inner
1416.1.r.a.677.1	✓	28	1416.677	odd	58	inner
1416.1.r.a.845.1	yes	28	1.1	even	1	trivial
1416.1.r.a.845.1	yes	28	24.5	odd	2	CM
1416.1.r.b.677.1	yes	28	177.146	odd	58
1416.1.r.b.677.1	yes	28	472.205	even	58
1416.1.r.b.845.1	yes	28	3.2	odd	2
1416.1.r.b.845.1	yes	28	8.5	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.468408 - 0.883512i) q^{2} +(-0.725995 + 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(1.55496 - 0.342273i) q^{5} +(0.267528 + 0.963550i) q^{6} +(-0.257587 + 0.195813i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(0.425955 - 1.53415i) q^{10} +(-0.722969 - 1.81452i) q^{11} +(0.976621 + 0.214970i) q^{12} +(0.0523468 + 0.319302i) q^{14} +(-0.893514 + 1.31783i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(-0.856857 - 0.515554i) q^{18} +(-1.15592 - 1.09495i) q^{20} +(0.0523468 - 0.319302i) q^{21} +(-1.94179 - 0.211183i) q^{22} +(0.647386 - 0.762162i) q^{24} +(1.39318 - 0.644554i) q^{25} +(0.647386 + 0.762162i) q^{27} +(0.306626 + 0.103314i) q^{28} +(-0.802718 - 1.51409i) q^{29} +(0.745793 + 1.40672i) q^{30} +(1.88420 + 0.634860i) q^{31} +(0.647386 + 0.762162i) q^{32} +(1.77271 + 0.820145i) q^{33} +(-0.333517 + 0.392646i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(-1.50884 + 0.508387i) q^{40} +(-0.257587 - 0.195813i) q^{42} +(-1.09613 + 1.61668i) q^{44} +(-0.257587 - 1.57121i) q^{45} +(-0.370138 - 0.928977i) q^{48} +(-0.239520 + 0.862672i) q^{49} +(0.0831063 - 1.53281i) q^{50} +(0.0289674 + 0.104331i) q^{53} +(0.976621 - 0.214970i) q^{54} +(-1.74525 - 2.57405i) q^{55} +(0.234906 - 0.222515i) q^{56} -1.71371 q^{58} +(0.267528 - 0.963550i) q^{59} +1.59219 q^{60} +(1.44348 - 1.36734i) q^{62} +(0.181580 + 0.267810i) q^{63} +(0.976621 - 0.214970i) q^{64} +(1.55496 - 1.18205i) q^{66} +(0.190686 + 0.478585i) q^{70} +(0.0541389 + 0.998533i) q^{72} +(0.306626 + 1.87034i) q^{73} +(-0.568183 + 1.42603i) q^{75} +(0.541532 + 0.325829i) q^{77} +(-0.939999 - 0.890414i) q^{79} +(-0.257587 + 1.57121i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(-0.726610 + 0.855431i) q^{83} +(-0.293659 + 0.135861i) q^{84} +(1.62401 + 0.547192i) q^{87} +(0.914915 + 1.72571i) q^{88} +(-1.50884 - 0.508387i) q^{90} +(-1.80451 + 0.834855i) q^{93} +(-0.994138 - 0.108119i) q^{96} +(0.119763 - 0.730524i) q^{97} +(0.649988 + 0.615702i) q^{98} +(-1.85100 + 0.623673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - q^{8} - q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 27 q^{14} - 2 q^{15} - q^{16} - q^{18} - 2 q^{20} + 27 q^{21} - 2 q^{22} - q^{24} - 3 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more