LMFDB - Embedded newform 1416.1.r.a.557.1

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			557.1
Root			$0.561187 - 0.827689i$ of defining polynomial
Character	$\chi$	$=$	1416.557
Dual form			1416.1.r.a.1205.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.796093 - 0.605174i) q^{2} +(0.468408 - 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(-0.939999 + 0.890414i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(1.26450 + 1.48869i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(-0.209471 + 1.27772i) q^{10} +(1.24415 - 0.748580i) q^{11} +(-0.725995 - 0.687699i) q^{12} +(1.90758 + 0.419889i) q^{14} +(0.346388 + 1.24758i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(-0.947653 - 0.319302i) q^{18} +(0.606482 + 1.14395i) q^{20} +(1.90758 - 0.419889i) q^{21} +(0.537437 - 1.34887i) q^{22} +(-0.994138 - 0.108119i) q^{24} +(0.0366215 - 0.675444i) q^{25} +(-0.994138 + 0.108119i) q^{27} +(1.77271 - 0.820145i) q^{28} +(-1.50884 - 1.14699i) q^{29} +(1.03076 + 0.783563i) q^{30} +(-0.671857 + 0.310834i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(-0.0786092 - 1.44986i) q^{33} +(-2.51418 - 0.273433i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(1.17510 + 0.543661i) q^{40} +(1.26450 - 1.48869i) q^{42} +(-0.388449 - 1.39907i) q^{44} +(1.26450 + 0.278338i) q^{45} +(-0.856857 + 0.515554i) q^{48} +(-0.455441 + 2.77807i) q^{49} +(-0.379607 - 0.559879i) q^{50} +(0.181580 + 1.10759i) q^{53} +(-0.725995 + 0.687699i) q^{54} +(-0.502953 + 1.81147i) q^{55} +(0.914915 - 1.72571i) q^{56} -1.89531 q^{58} +(-0.161782 + 0.986827i) q^{59} +1.29477 q^{60} +(-0.346752 + 0.654043i) q^{62} +(0.522547 - 1.88205i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(-0.939999 - 1.10665i) q^{66} +(-2.16699 + 1.30384i) q^{70} +(-0.561187 + 0.827689i) q^{72} +(1.77271 + 0.390204i) q^{73} +(-0.579609 - 0.348739i) q^{75} +(2.68763 + 0.905567i) q^{77} +(-0.931325 - 1.75667i) q^{79} +(1.26450 - 0.278338i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(-0.531920 - 0.0578498i) q^{83} +(0.105746 - 1.95038i) q^{84} +(-1.72013 + 0.795818i) q^{87} +(-1.15592 - 0.878708i) q^{88} +(1.17510 - 0.543661i) q^{90} +(-0.0400778 + 0.739191i) q^{93} +(-0.370138 + 0.928977i) q^{96} +(-1.67365 + 0.368398i) q^{97} +(1.31864 + 2.48722i) q^{98} +(-1.31779 - 0.609675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1416\mathbb{Z}\right)^\times$.

$n$	$473$	$709$	$769$	$1063$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{23}{29}\right)$	$1$

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 $

$2$	0.796093	−	0.605174i	0.796093	−	0.605174i
$2$	0.796093	−	0.605174i	0.796093	−	0.605174i
$3$	0.468408	−	0.883512i	0.468408	−	0.883512i
$3$	0.468408	−	0.883512i	0.468408	−	0.883512i
$4$	0.267528	−	0.963550i	0.267528	−	0.963550i
$5$	−0.939999	+	0.890414i	−0.939999	+	0.890414i	−0.994138	−	0.108119i	$-0.965517\pi$
$5$	−0.939999	+	0.890414i	−0.939999	+	0.890414i	0.0541389	+	0.998533i	$0.482759\pi$
$6$	−0.161782	−	0.986827i	−0.161782	−	0.986827i
$7$	1.26450	+	1.48869i	1.26450	+	1.48869i	0.796093	+	0.605174i	$0.206897\pi$
$7$	1.26450	+	1.48869i	1.26450	+	1.48869i	0.468408	+	0.883512i	$0.344828\pi$
$8$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$9$	−0.561187	−	0.827689i	−0.561187	−	0.827689i
$10$	−0.209471	+	1.27772i	−0.209471	+	1.27772i
$11$	1.24415	−	0.748580i	1.24415	−	0.748580i	0.267528	−	0.963550i	$-0.413793\pi$
$11$	1.24415	−	0.748580i	1.24415	−	0.748580i	0.976621	+	0.214970i	$0.0689655\pi$
$12$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$13$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$13$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$14$	1.90758	+	0.419889i	1.90758	+	0.419889i
$15$	0.346388	+	1.24758i	0.346388	+	1.24758i
$16$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$17$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$17$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$18$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$19$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$19$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$20$	0.606482	+	1.14395i	0.606482	+	1.14395i
$21$	1.90758	−	0.419889i	1.90758	−	0.419889i
$22$	0.537437	−	1.34887i	0.537437	−	1.34887i
$23$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$23$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$24$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$25$	0.0366215	−	0.675444i	0.0366215	−	0.675444i
$26$		0			0
$27$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$28$	1.77271	−	0.820145i	1.77271	−	0.820145i
$29$	−1.50884	−	1.14699i	−1.50884	−	1.14699i	−0.947653	−	0.319302i	$-0.896552\pi$
$29$	−1.50884	−	1.14699i	−1.50884	−	1.14699i	−0.561187	−	0.827689i	$-0.689655\pi$
$30$	1.03076	+	0.783563i	1.03076	+	0.783563i
$31$	−0.671857	+	0.310834i	−0.671857	+	0.310834i	−0.725995	−	0.687699i	$-0.758621\pi$
$31$	−0.671857	+	0.310834i	−0.671857	+	0.310834i	0.0541389	+	0.998533i	$0.482759\pi$
$32$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$33$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i
$34$		0			0
$35$	−2.51418	−	0.273433i	−2.51418	−	0.273433i
$36$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$37$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$37$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$38$		0			0
$39$		0			0
$40$	1.17510	+	0.543661i	1.17510	+	0.543661i
$41$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$41$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$42$	1.26450	−	1.48869i	1.26450	−	1.48869i
$43$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$43$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$44$	−0.388449	−	1.39907i	−0.388449	−	1.39907i
$45$	1.26450	+	0.278338i	1.26450	+	0.278338i
$46$		0			0
$47$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$47$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$48$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$49$	−0.455441	+	2.77807i	−0.455441	+	2.77807i
$50$	−0.379607	−	0.559879i	−0.379607	−	0.559879i
$51$		0			0
$52$		0			0
$53$	0.181580	+	1.10759i	0.181580	+	1.10759i	0.907575	+	0.419889i	$0.137931\pi$
$53$	0.181580	+	1.10759i	0.181580	+	1.10759i	−0.725995	+	0.687699i	$0.758621\pi$
$54$	−0.725995	+	0.687699i	−0.725995	+	0.687699i
$55$	−0.502953	+	1.81147i	−0.502953	+	1.81147i
$56$	0.914915	−	1.72571i	0.914915	−	1.72571i
$57$		0			0
$58$	−1.89531			−1.89531
$59$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$59$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$60$	1.29477			1.29477
$61$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$61$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$62$	−0.346752	+	0.654043i	−0.346752	+	0.654043i
$63$	0.522547	−	1.88205i	0.522547	−	1.88205i
$64$	−0.725995	+	0.687699i	−0.725995	+	0.687699i
$65$		0			0
$66$	−0.939999	−	1.10665i	−0.939999	−	1.10665i
$67$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$67$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$68$		0			0
$69$		0			0
$70$	−2.16699	+	1.30384i	−2.16699	+	1.30384i
$71$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$71$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$72$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$73$	1.77271	+	0.390204i	1.77271	+	0.390204i	0.976621	−	0.214970i	$-0.0689655\pi$
$73$	1.77271	+	0.390204i	1.77271	+	0.390204i	0.796093	+	0.605174i	$0.206897\pi$
$74$		0			0
$75$	−0.579609	−	0.348739i	−0.579609	−	0.348739i
$76$		0			0
$77$	2.68763	+	0.905567i	2.68763	+	0.905567i
$78$		0			0
$79$	−0.931325	−	1.75667i	−0.931325	−	1.75667i	−0.561187	−	0.827689i	$-0.689655\pi$
$79$	−0.931325	−	1.75667i	−0.931325	−	1.75667i	−0.370138	−	0.928977i	$-0.620690\pi$
$80$	1.26450	−	0.278338i	1.26450	−	0.278338i
$81$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$82$		0			0
$83$	−0.531920	−	0.0578498i	−0.531920	−	0.0578498i	−0.161782	−	0.986827i	$-0.551724\pi$
$83$	−0.531920	−	0.0578498i	−0.531920	−	0.0578498i	−0.370138	+	0.928977i	$0.620690\pi$
$84$	0.105746	−	1.95038i	0.105746	−	1.95038i
$85$		0			0
$86$		0			0
$87$	−1.72013	+	0.795818i	−1.72013	+	0.795818i
$88$	−1.15592	−	0.878708i	−1.15592	−	0.878708i
$89$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$89$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$90$	1.17510	−	0.543661i	1.17510	−	0.543661i
$91$		0			0
$92$		0			0
$93$	−0.0400778	+	0.739191i	−0.0400778	+	0.739191i
$94$		0			0
$95$		0			0
$96$	−0.370138	+	0.928977i	−0.370138	+	0.928977i
$97$	−1.67365	+	0.368398i	−1.67365	+	0.368398i	−0.947653	−	0.319302i	$-0.896552\pi$
$97$	−1.67365	+	0.368398i	−1.67365	+	0.368398i	−0.725995	+	0.687699i	$0.758621\pi$
$98$	1.31864	+	2.48722i	1.31864	+	2.48722i
$99$	−1.31779	−	0.609675i	−1.31779	−	0.609675i
$100$	−0.641027	−	0.215987i	−0.641027	−	0.215987i
$101$	1.03076	−	1.21350i	1.03076	−	1.21350i	0.0541389	−	0.998533i	$-0.482759\pi$
$101$	1.03076	−	1.21350i	1.03076	−	1.21350i	0.976621	−	0.214970i	$-0.0689655\pi$
$102$		0			0
$103$	0.143143	+	0.515554i	0.143143	+	0.515554i	1.00000			$0$
$103$	0.143143	+	0.515554i	0.143143	+	0.515554i	−0.856857	+	0.515554i	$0.827586\pi$
$104$		0			0
$105$	−1.41924	+	2.09323i	−1.41924	+	2.09323i
$106$	0.814839	+	0.771856i	0.814839	+	0.771856i
$107$	−0.458467	+	0.275851i	−0.458467	+	0.275851i	−0.725995	−	0.687699i	$-0.758621\pi$
$107$	−0.458467	+	0.275851i	−0.458467	+	0.275851i	0.267528	+	0.963550i	$0.413793\pi$
$108$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$109$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$109$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$110$	0.695859	+	1.74647i	0.695859	+	1.74647i
$111$		0			0
$112$	−0.315999	−	1.92751i	−0.315999	−	1.92751i
$113$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$113$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$114$		0			0
$115$		0			0
$116$	−1.50884	+	1.14699i	−1.50884	+	1.14699i
$117$		0			0
$118$	0.468408	+	0.883512i	0.468408	+	0.883512i
$119$		0			0
$120$	1.03076	−	0.783563i	1.03076	−	0.783563i
$121$	0.519127	−	0.979177i	0.519127	−	0.979177i
$122$		0			0
$123$		0			0
$124$	0.119763	+	0.730524i	0.119763	+	0.730524i
$125$	−0.271217	−	0.319302i	−0.271217	−	0.319302i
$126$	−0.722969	−	1.81452i	−0.722969	−	1.81452i
$127$	−0.300267	−	0.442861i	−0.300267	−	0.442861i	0.647386	−	0.762162i	$-0.275862\pi$
$127$	−0.300267	−	0.442861i	−0.300267	−	0.442861i	−0.947653	+	0.319302i	$0.896552\pi$
$128$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$129$		0			0
$130$		0			0
$131$	−0.0607641	+	0.0896204i	−0.0607641	+	0.0896204i	−0.856857	−	0.515554i	$-0.827586\pi$
$131$	−0.0607641	+	0.0896204i	−0.0607641	+	0.0896204i	0.796093	+	0.605174i	$0.206897\pi$
$132$	−1.41804	−	0.312135i	−1.41804	−	0.312135i
$133$		0			0
$134$		0			0
$135$	0.838218	−	0.986827i	0.838218	−	0.986827i
$136$		0			0
$137$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$137$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$138$		0			0
$139$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$139$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$140$	−0.936081	+	2.34938i	−0.936081	+	2.34938i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$145$	2.43961	−	0.265323i	2.43961	−	0.265323i
$146$	1.64739	−	0.762162i	1.64739	−	0.762162i
$147$	2.24112	+	1.70366i	2.24112	+	1.70366i
$148$		0			0
$149$	0.850232	−	0.393359i	0.850232	−	0.393359i	0.0541389	−	0.998533i	$-0.482759\pi$
$149$	0.850232	−	0.393359i	0.850232	−	0.393359i	0.796093	+	0.605174i	$0.206897\pi$
$150$	−0.672471	+	0.0731356i	−0.672471	+	0.0731356i
$151$	−0.0175174	−	0.323089i	−0.0175174	−	0.323089i	−0.994138	−	0.108119i	$-0.965517\pi$
$151$	−0.0175174	−	0.323089i	−0.0175174	−	0.323089i	0.976621	−	0.214970i	$-0.0689655\pi$
$152$		0			0
$153$		0			0
$154$	2.68763	−	0.905567i	2.68763	−	0.905567i
$155$	0.354774	−	0.890414i	0.354774	−	0.890414i
$156$		0			0
$157$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$157$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$158$	−1.80451	−	0.834855i	−1.80451	−	0.834855i
$159$	1.06362	+	0.358376i	1.06362	+	0.358376i
$160$	0.838218	−	0.986827i	0.838218	−	0.986827i
$161$		0			0
$162$	0.267528	+	0.963550i	0.267528	+	0.963550i
$163$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$163$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$164$		0			0
$165$	1.36487	+	1.29287i	1.36487	+	1.29287i
$166$	−0.458467	+	0.275851i	−0.458467	+	0.275851i
$167$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$167$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$168$	−1.09613	−	1.61668i	−1.09613	−	1.61668i
$169$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.507048	+	1.82622i	−0.507048	+	1.82622i	0.0541389	+	0.998533i	$0.482759\pi$
$173$	−0.507048	+	1.82622i	−0.507048	+	1.82622i	−0.561187	+	0.827689i	$0.689655\pi$
$174$	−0.887777	+	1.67453i	−0.887777	+	1.67453i
$175$	1.05183	−	0.799582i	1.05183	−	0.799582i
$176$	−1.45199			−1.45199
$177$	0.796093	+	0.605174i	0.796093	+	0.605174i
$178$		0			0
$179$	−1.58285	+	1.20325i	−1.58285	+	1.20325i	−0.725995	+	0.687699i	$0.758621\pi$
$179$	−1.58285	+	1.20325i	−1.58285	+	1.20325i	−0.856857	+	0.515554i	$0.827586\pi$
$180$	0.606482	−	1.14395i	0.606482	−	1.14395i
$181$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$181$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	0.415433	+	0.612719i	0.415433	+	0.612719i
$187$		0			0
$188$		0			0
$189$	−1.41804	−	1.34324i	−1.41804	−	1.34324i
$190$		0			0
$191$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$191$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$192$	0.267528	+	0.963550i	0.267528	+	0.963550i
$193$	0.961714	+	0.578644i	0.961714	+	0.578644i	0.907575	−	0.419889i	$-0.137931\pi$
$193$	0.961714	+	0.578644i	0.961714	+	0.578644i	0.0541389	+	0.998533i	$0.482759\pi$
$194$	−1.10944	+	1.30613i	−1.10944	+	1.30613i
$195$		0			0
$196$	2.55496	+	1.18205i	2.55496	+	1.18205i
$197$	0.0507182	+	0.0956648i	0.0507182	+	0.0956648i	0.907575	−	0.419889i	$-0.137931\pi$
$197$	0.0507182	+	0.0956648i	0.0507182	+	0.0956648i	−0.856857	+	0.515554i	$0.827586\pi$
$198$	−1.41804	+	0.312135i	−1.41804	+	0.312135i
$199$	−0.346752	+	0.870281i	−0.346752	+	0.870281i	0.647386	+	0.762162i	$0.275862\pi$
$199$	−0.346752	+	0.870281i	−0.346752	+	0.870281i	−0.994138	+	0.108119i	$0.965517\pi$
$200$	−0.641027	+	0.215987i	−0.641027	+	0.215987i
$201$		0			0
$202$	0.0861992	−	1.58985i	0.0861992	−	1.58985i
$203$	−0.200422	−	3.69656i	−0.200422	−	3.69656i
$204$		0			0
$205$		0			0
$206$	0.425955	+	0.323803i	0.425955	+	0.323803i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	0.136917	+	2.52529i	0.136917	+	2.52529i
$211$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$211$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$212$	1.11579	+	0.121350i	1.11579	+	0.121350i
$213$		0			0
$214$	−0.198045	+	0.497055i	−0.198045	+	0.497055i
$215$		0			0
$216$	0.468408	+	0.883512i	0.468408	+	0.883512i
$217$	−1.31230	−	0.607134i	−1.31230	−	0.607134i
$218$		0			0
$219$	1.17510	−	1.38344i	1.17510	−	1.38344i
$220$	1.61089	+	0.969240i	1.61089	+	0.969240i
$221$		0			0
$222$		0			0
$223$	0.961714	−	1.41842i	0.961714	−	1.41842i	0.0541389	−	0.998533i	$-0.482759\pi$
$223$	0.961714	−	1.41842i	0.961714	−	1.41842i	0.907575	−	0.419889i	$-0.137931\pi$
$224$	−1.41804	−	1.34324i	−1.41804	−	1.34324i
$225$	−0.579609	+	0.348739i	−0.579609	+	0.348739i
$226$		0			0
$227$	0.415433	+	0.612719i	0.415433	+	0.612719i	0.976621	−	0.214970i	$-0.0689655\pi$
$227$	0.415433	+	0.612719i	0.415433	+	0.612719i	−0.561187	+	0.827689i	$0.689655\pi$
$228$		0			0
$229$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$229$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$230$		0			0
$231$	2.05899	−	1.95038i	2.05899	−	1.95038i
$232$	−0.507048	+	1.82622i	−0.507048	+	1.82622i
$233$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$233$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$234$		0			0
$235$		0			0
$236$	0.907575	+	0.419889i	0.907575	+	0.419889i
$237$	−1.98828			−1.98828
$238$		0			0
$239$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$239$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$240$	0.346388	−	1.24758i	0.346388	−	1.24758i
$241$	1.37598	−	1.30340i	1.37598	−	1.30340i	0.468408	−	0.883512i	$-0.344828\pi$
$241$	1.37598	−	1.30340i	1.37598	−	1.30340i	0.907575	−	0.419889i	$-0.137931\pi$
$242$	−0.179299	−	1.09368i	−0.179299	−	1.09368i
$243$	0.647386	+	0.762162i	0.647386	+	0.762162i
$244$		0			0
$245$	−2.04552	−	3.01691i	−2.04552	−	3.01691i
$246$		0			0
$247$		0			0
$248$	0.537437	+	0.509088i	0.537437	+	0.509088i
$249$	−0.300267	+	0.442861i	−0.300267	+	0.442861i
$250$	−0.409147	−	0.0900601i	−0.409147	−	0.0900601i
$251$	0.0289674	+	0.104331i	0.0289674	+	0.104331i	0.976621	−	0.214970i	$-0.0689655\pi$
$251$	0.0289674	+	0.104331i	0.0289674	+	0.104331i	−0.947653	+	0.319302i	$0.896552\pi$
$252$	−1.67365	−	1.00700i	−1.67365	−	1.00700i
$253$		0			0
$254$	−0.507048	−	0.170844i	−0.507048	−	0.170844i
$255$		0			0
$256$	0.468408	+	0.883512i	0.468408	+	0.883512i
$257$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$257$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.102610	+	1.89253i	−0.102610	+	1.89253i
$262$	0.00586204	+	0.108119i	0.00586204	+	0.108119i
$263$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$263$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$264$	−1.31779	+	0.609675i	−1.31779	+	0.609675i
$265$	−1.15690	−	0.879451i	−1.15690	−	0.879451i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.0982703	+	1.81249i	0.0982703	+	1.81249i	0.468408	+	0.883512i	$0.344828\pi$
$269$	0.0982703	+	1.81249i	0.0982703	+	1.81249i	−0.370138	+	0.928977i	$0.620690\pi$
$270$	0.0700976	−	1.29287i	0.0700976	−	1.29287i
$271$	−1.58285	−	0.172146i	−1.58285	−	0.172146i	−0.725995	−	0.687699i	$-0.758621\pi$
$271$	−1.58285	−	0.172146i	−1.58285	−	0.172146i	−0.856857	+	0.515554i	$0.827586\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.460061	−	0.867767i	−0.460061	−	0.867767i
$276$		0			0
$277$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$277$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$278$		0			0
$279$	0.634311	+	0.381652i	0.634311	+	0.381652i
$280$	0.676580	+	2.43682i	0.676580	+	2.43682i
$281$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$281$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$282$		0			0
$283$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$283$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.647386	+	0.762162i	0.647386	+	0.762162i
$289$	−0.161782	−	0.986827i	−0.161782	−	0.986827i
$290$	1.78159	−	1.68761i	1.78159	−	1.68761i
$291$	−0.458467	+	1.65125i	−0.458467	+	1.65125i
$292$	0.850232	−	1.60371i	0.850232	−	1.60371i
$293$	−0.257587	+	0.195813i	−0.257587	+	0.195813i	−0.725995	−	0.687699i	$-0.758621\pi$
$293$	−0.257587	+	0.195813i	−0.257587	+	0.195813i	0.468408	+	0.883512i	$0.344828\pi$
$294$	2.81515			2.81515
$295$	−0.726610	−	1.07167i	−0.726610	−	1.07167i
$296$		0			0
$297$	−1.15592	+	0.878708i	−1.15592	+	0.878708i
$298$	0.438813	−	0.827689i	0.438813	−	0.827689i
$299$		0			0
$300$	−0.491089	+	0.465185i	−0.491089	+	0.465185i
$301$		0			0
$302$	−0.209471	−	0.246608i	−0.209471	−	0.246608i
$303$	−0.589329	−	1.47910i	−0.589329	−	1.47910i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$307$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$308$	1.59158	−	2.34740i	1.59158	−	2.34740i
$309$	0.522547	+	0.115021i	0.522547	+	0.115021i
$310$	−0.256423	−	0.923553i	−0.256423	−	0.923553i
$311$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$311$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$312$		0			0
$313$	−0.887777	−	0.299127i	−0.887777	−	0.299127i	−0.161782	−	0.986827i	$-0.551724\pi$
$313$	−0.887777	−	0.299127i	−0.887777	−	0.299127i	−0.725995	+	0.687699i	$0.758621\pi$
$314$		0			0
$315$	1.18461	+	2.23440i	1.18461	+	2.23440i
$316$	−1.94179	+	0.427421i	−1.94179	+	0.427421i
$317$	0.537437	−	1.34887i	0.537437	−	1.34887i	−0.370138	−	0.928977i	$-0.620690\pi$
$317$	0.537437	−	1.34887i	0.537437	−	1.34887i	0.907575	−	0.419889i	$-0.137931\pi$
$318$	1.06362	−	0.358376i	1.06362	−	0.358376i
$319$	−2.73584	−	0.297540i	−2.73584	−	0.297540i
$320$	0.0700976	−	1.29287i	0.0700976	−	1.29287i
$321$	0.0289674	+	0.534272i	0.0289674	+	0.534272i
$322$		0			0
$323$		0			0
$324$	0.796093	+	0.605174i	0.796093	+	0.605174i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	1.86898	+	0.203264i	1.86898	+	0.203264i
$331$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$331$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$332$	−0.198045	+	0.497055i	−0.198045	+	0.497055i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−1.85100	−	0.623673i	−1.85100	−	0.623673i
$337$	1.03076	−	1.21350i	1.03076	−	1.21350i	0.0541389	−	0.998533i	$-0.482759\pi$
$337$	1.03076	−	1.21350i	1.03076	−	1.21350i	0.976621	−	0.214970i	$-0.0689655\pi$
$338$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$339$		0			0
$340$		0			0
$341$	−0.603206	+	0.889662i	−0.603206	+	0.889662i
$342$		0			0
$343$	−3.03792	+	1.82786i	−3.03792	+	1.82786i
$344$		0			0
$345$		0			0
$346$	0.701525	+	1.76070i	0.701525	+	1.76070i
$347$	1.03076	+	1.21350i	1.03076	+	1.21350i	0.976621	+	0.214970i	$0.0689655\pi$
$347$	1.03076	+	1.21350i	1.03076	+	1.21350i	0.0541389	+	0.998533i	$0.482759\pi$
$348$	0.306626	+	1.87034i	0.306626	+	1.87034i
$349$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$349$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$350$	0.353470	−	1.27308i	0.353470	−	1.27308i
$351$		0			0
$352$	−1.15592	+	0.878708i	−1.15592	+	0.878708i
$353$		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
$358$	−0.531920	+	1.91580i	−0.531920	+	1.91580i
$359$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$359$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$360$	−0.209471	−	1.27772i	−0.209471	−	1.27772i
$361$	0.647386	+	0.762162i	0.647386	+	0.762162i
$362$		0			0
$363$	−0.621951	−	0.917309i	−0.621951	−	0.917309i
$364$		0			0
$365$	−2.01379	+	1.21166i	−2.01379	+	1.21166i
$366$		0			0
$367$	1.06362	−	1.56872i	1.06362	−	1.56872i	0.267528	−	0.963550i	$-0.413793\pi$
$367$	1.06362	−	1.56872i	1.06362	−	1.56872i	0.796093	−	0.605174i	$-0.206897\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.41924	+	1.67086i	−1.41924	+	1.67086i
$372$	0.701525	+	0.236371i	0.701525	+	0.236371i
$373$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$373$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$374$		0			0
$375$	−0.409147	+	0.0900601i	−0.409147	+	0.0900601i
$376$		0			0
$377$		0			0
$378$	−1.94179	−	0.211183i	−1.94179	−	0.211183i
$379$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$379$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$380$		0			0
$381$	−0.531920	+	0.0578498i	−0.531920	+	0.0578498i
$382$		0			0
$383$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$383$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$384$	0.796093	+	0.605174i	0.796093	+	0.605174i
$385$	−3.33270	+	1.54187i	−3.33270	+	1.54187i
$386$	1.11579	−	0.121350i	1.11579	−	0.121350i
$387$		0			0
$388$	−0.0927786	+	1.71120i	−0.0927786	+	1.71120i
$389$	1.97662	+	0.214970i	1.97662	+	0.214970i	1.00000			$0$
$389$	1.97662	+	0.214970i	1.97662	+	0.214970i	0.976621	+	0.214970i	$0.0689655\pi$
$390$		0			0
$391$		0			0
$392$	2.74933	−	0.605174i	2.74933	−	0.605174i
$393$	0.0507182	+	0.0956648i	0.0507182	+	0.0956648i
$394$	0.0982703	+	0.0454647i	0.0982703	+	0.0454647i
$395$	2.43961	+	0.821999i	2.43961	+	0.821999i
$396$	−0.939999	+	1.10665i	−0.939999	+	1.10665i
$397$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$397$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$398$	0.250625	+	0.902670i	0.250625	+	0.902670i
$399$		0			0
$400$	−0.379607	+	0.559879i	−0.379607	+	0.559879i
$401$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$401$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$402$		0			0
$403$		0			0
$404$	−0.893514	−	1.31783i	−0.893514	−	1.31783i
$405$	−0.479245	−	1.20281i	−0.479245	−	1.20281i
$406$	−2.39662	−	2.82152i	−2.39662	−	2.82152i
$407$		0			0
$408$		0			0
$409$	0.425955	−	1.53415i	0.425955	−	1.53415i	−0.370138	−	0.928977i	$-0.620690\pi$
$409$	0.425955	−	1.53415i	0.425955	−	1.53415i	0.796093	−	0.605174i	$-0.206897\pi$
$410$		0			0
$411$		0			0
$412$	0.535057			0.535057
$413$	−1.67365	+	1.00700i	−1.67365	+	1.00700i
$414$		0			0
$415$	0.551515	−	0.419251i	0.551515	−	0.419251i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.0523468	+	0.319302i	0.0523468	+	0.319302i	1.00000			$0$
$419$	0.0523468	+	0.319302i	0.0523468	+	0.319302i	−0.947653	+	0.319302i	$0.896552\pi$
$420$	1.63724	+	1.92751i	1.63724	+	1.92751i
$421$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$421$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$422$		0			0
$423$		0			0
$424$	0.961714	−	0.578644i	0.961714	−	0.578644i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.143143	+	0.515554i	0.143143	+	0.515554i
$429$		0			0
$430$		0			0
$431$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$431$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$432$	0.907575	+	0.419889i	0.907575	+	0.419889i
$433$	−0.525730	−	0.991631i	−0.525730	−	0.991631i	−0.994138	−	0.108119i	$-0.965517\pi$
$433$	−0.525730	−	0.991631i	−0.525730	−	0.991631i	0.468408	−	0.883512i	$-0.344828\pi$
$434$	−1.41213	+	0.310834i	−1.41213	+	0.310834i
$435$	0.908316	−	2.27970i	0.908316	−	2.27970i
$436$		0			0
$437$		0			0
$438$	0.0982703	−	1.81249i	0.0982703	−	1.81249i
$439$	0.0982703	+	1.81249i	0.0982703	+	1.81249i	0.468408	+	0.883512i	$0.344828\pi$
$439$	0.0982703	+	1.81249i	0.0982703	+	1.81249i	−0.370138	+	0.928977i	$0.620690\pi$
$440$	1.86898	−	0.203264i	1.86898	−	0.203264i
$441$	2.55496	−	1.18205i	2.55496	−	1.18205i
$442$		0			0
$443$	−1.36428	−	1.03710i	−1.36428	−	1.03710i	−0.994138	−	0.108119i	$-0.965517\pi$
$443$	−1.36428	−	1.03710i	−1.36428	−	1.03710i	−0.370138	−	0.928977i	$-0.620690\pi$
$444$		0			0
$445$		0			0
$446$	−0.0927786	−	1.71120i	−0.0927786	−	1.71120i
$447$	0.0507182	−	0.935443i	0.0507182	−	0.935443i
$448$	−1.94179	−	0.211183i	−1.94179	−	0.211183i
$449$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$449$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$450$	−0.250375	+	0.628393i	−0.250375	+	0.628393i
$451$		0			0
$452$		0			0
$453$	−0.293659	−	0.135861i	−0.293659	−	0.135861i
$454$	0.701525	+	0.236371i	0.701525	+	0.236371i
$455$		0			0
$456$		0			0
$457$	−0.300267	−	1.08146i	−0.300267	−	1.08146i	−0.947653	−	0.319302i	$-0.896552\pi$
$457$	−0.300267	−	1.08146i	−0.300267	−	1.08146i	0.647386	−	0.762162i	$-0.275862\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.277248	−	0.166815i	0.277248	−	0.166815i	−0.370138	−	0.928977i	$-0.620690\pi$
$461$	0.277248	−	0.166815i	0.277248	−	0.166815i	0.647386	+	0.762162i	$0.275862\pi$
$462$	0.458828	−	2.79873i	0.458828	−	2.79873i
$463$	0.961714	+	1.41842i	0.961714	+	1.41842i	0.907575	+	0.419889i	$0.137931\pi$
$463$	0.961714	+	1.41842i	0.961714	+	1.41842i	0.0541389	+	0.998533i	$0.482759\pi$
$464$	0.701525	+	1.76070i	0.701525	+	1.76070i
$465$	−0.620513	−	0.730524i	−0.620513	−	0.730524i
$466$		0			0
$467$	1.44348	−	1.36734i	1.44348	−	1.36734i	0.647386	−	0.762162i	$-0.275862\pi$
$467$	1.44348	−	1.36734i	1.44348	−	1.36734i	0.796093	−	0.605174i	$-0.206897\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.976621	−	0.214970i	0.976621	−	0.214970i
$473$		0			0
$474$	−1.58285	+	1.20325i	−1.58285	+	1.20325i
$475$		0			0
$476$		0			0
$477$	0.814839	−	0.771856i	0.814839	−	0.771856i
$478$		0			0
$479$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$479$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$480$	−0.479245	−	1.20281i	−0.479245	−	1.20281i
$481$		0			0
$482$	0.306626	−	1.87034i	0.306626	−	1.87034i
$483$		0			0
$484$	−0.804605	−	0.762162i	−0.804605	−	0.762162i
$485$	1.24520	−	1.83653i	1.24520	−	1.83653i
$486$	0.976621	+	0.214970i	0.976621	+	0.214970i
$487$	−0.198045	−	0.713293i	−0.198045	−	0.713293i	−0.994138	−	0.108119i	$-0.965517\pi$
$487$	−0.198045	−	0.713293i	−0.198045	−	0.713293i	0.796093	−	0.605174i	$-0.206897\pi$
$488$		0			0
$489$		0			0
$490$	−3.45418	−	1.16385i	−3.45418	−	1.16385i
$491$	−1.80451	−	0.834855i	−1.80451	−	0.834855i	−0.947653	−	0.319302i	$-0.896552\pi$
$491$	−1.80451	−	0.834855i	−1.80451	−	0.834855i	−0.856857	−	0.515554i	$-0.827586\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	1.78159	−	0.600286i	1.78159	−	0.600286i
$496$	0.735937	+	0.0800379i	0.735937	+	0.0800379i
$497$		0			0
$498$	0.0289674	+	0.534272i	0.0289674	+	0.534272i
$499$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$499$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$500$	−0.380221	+	0.175909i	−0.380221	+	0.175909i
$501$		0			0
$502$	0.0861992	+	0.0655269i	0.0861992	+	0.0655269i
$503$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$503$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$504$	−1.94179	+	0.211183i	−1.94179	+	0.211183i
$505$	0.111608	+	2.05850i	0.111608	+	2.05850i
$506$		0			0
$507$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$508$	−0.507048	+	0.170844i	−0.507048	+	0.170844i
$509$	0.735937	−	1.84706i	0.735937	−	1.84706i	0.267528	−	0.963550i	$-0.413793\pi$
$509$	0.735937	−	1.84706i	0.735937	−	1.84706i	0.468408	−	0.883512i	$-0.344828\pi$
$510$		0			0
$511$	1.66071	+	3.13243i	1.66071	+	3.13243i
$512$	0.907575	+	0.419889i	0.907575	+	0.419889i
$513$		0			0
$514$		0			0
$515$	−0.593611	−	0.357164i	−0.593611	−	0.357164i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.37598	+	1.30340i	1.37598	+	1.30340i
$520$		0			0
$521$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$521$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$522$	1.06362	+	1.56872i	1.06362	+	1.56872i
$523$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$523$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$524$	0.0700976	+	0.0825252i	0.0700976	+	0.0825252i
$525$	−0.213753	−	1.30384i	−0.213753	−	1.30384i
$526$		0			0
$527$		0			0
$528$	−0.680125	+	1.28285i	−0.680125	+	1.28285i
$529$	0.796093	−	0.605174i	0.796093	−	0.605174i
$530$	−1.45322			−1.45322
$531$	0.907575	−	0.419889i	0.907575	−	0.419889i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.185337	−	0.667525i	0.185337	−	0.667525i
$536$		0			0
$537$	0.321667	+	1.96208i	0.321667	+	1.96208i
$538$	1.17510	+	1.38344i	1.17510	+	1.38344i
$539$	1.51297	+	3.79726i	1.51297	+	3.79726i
$540$	−0.726610	−	1.07167i	−0.726610	−	1.07167i
$541$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$541$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$542$	−1.36428	+	0.820858i	−1.36428	+	0.820858i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$547$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$548$		0			0
$549$		0			0
$550$	−0.891402	−	0.412406i	−0.891402	−	0.412406i
$551$		0			0
$552$		0			0
$553$	1.43746	−	3.60776i	1.43746	−	3.60776i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i	−0.725995	−	0.687699i	$-0.758621\pi$
$557$	−0.0786092	−	1.44986i	−0.0786092	−	1.44986i	0.647386	−	0.762162i	$-0.275862\pi$
$558$	0.735937	−	0.0800379i	0.735937	−	0.0800379i
$559$		0			0
$560$	2.01332	+	1.53049i	2.01332	+	1.53049i
$561$		0			0
$562$		0			0
$563$	−0.931325	+	0.101288i	−0.931325	+	0.101288i	−0.561187	−	0.827689i	$-0.689655\pi$
$563$	−0.931325	+	0.101288i	−0.931325	+	0.101288i	−0.370138	+	0.928977i	$0.620690\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.85100	+	0.623673i	−1.85100	+	0.623673i
$568$		0			0
$569$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$569$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$570$		0			0
$571$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$571$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.976621	+	0.214970i	0.976621	+	0.214970i
$577$	0.415433	−	0.612719i	0.415433	−	0.612719i	−0.561187	−	0.827689i	$-0.689655\pi$
$577$	0.415433	−	0.612719i	0.415433	−	0.612719i	0.976621	+	0.214970i	$0.0689655\pi$
$578$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$579$	0.961714	−	0.578644i	0.961714	−	0.578644i
$580$	0.397012	−	2.42166i	0.397012	−	2.42166i
$581$	−0.586494	−	0.865013i	−0.586494	−	0.865013i
$582$	0.634311	+	1.59200i	0.634311	+	1.59200i
$583$	1.05503	+	1.24208i	1.05503	+	1.24208i
$584$	−0.293659	−	1.79124i	−0.293659	−	1.79124i
$585$		0			0
$586$	−0.0865625	+	0.311770i	−0.0865625	+	0.311770i
$587$	−0.151560	+	0.285873i	−0.151560	+	0.285873i	−0.947653	−	0.319302i	$-0.896552\pi$
$587$	−0.151560	+	0.285873i	−0.151560	+	0.285873i	0.796093	+	0.605174i	$0.206897\pi$
$588$	2.24112	−	1.70366i	2.24112	−	1.70366i
$589$		0			0
$590$	−1.22700	−	0.413423i	−1.22700	−	0.413423i
$591$	0.108278			0.108278
$592$		0			0
$593$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$593$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$594$	−0.388449	+	1.39907i	−0.388449	+	1.39907i
$595$		0			0
$596$	−0.151560	−	0.924476i	−0.151560	−	0.924476i
$597$	0.606482	+	0.714006i	0.606482	+	0.714006i
$598$		0			0
$599$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$599$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$600$	−0.109435	+	0.667525i	−0.109435	+	0.667525i
$601$	−1.67365	+	1.00700i	−1.67365	+	1.00700i	−0.725995	+	0.687699i	$0.758621\pi$
$601$	−1.67365	+	1.00700i	−1.67365	+	1.00700i	−0.947653	+	0.319302i	$0.896552\pi$
$602$		0			0
$603$		0			0
$604$	−0.315999	−	0.0695567i	−0.315999	−	0.0695567i
$605$	0.383895	+	1.38266i	0.383895	+	1.38266i
$606$	−1.36428	−	0.820858i	−1.36428	−	0.820858i
$607$	0.606482	−	0.714006i	0.606482	−	0.714006i	−0.370138	−	0.928977i	$-0.620690\pi$
$607$	0.606482	−	0.714006i	0.606482	−	0.714006i	0.976621	+	0.214970i	$0.0689655\pi$
$608$		0			0
$609$	−3.35984	−	1.55443i	−3.35984	−	1.55443i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$613$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$614$		0			0
$615$		0			0
$616$	−0.153543	−	2.83193i	−0.153543	−	2.83193i
$617$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$617$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$618$	0.485604	−	0.224664i	0.485604	−	0.224664i
$619$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$619$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$620$	−0.763047	−	0.580053i	−0.763047	−	0.580053i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1.21173	+	0.131783i	1.21173	+	0.131783i
$626$	−0.887777	+	0.299127i	−0.887777	+	0.299127i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	2.29526	+	1.06190i	2.29526	+	1.06190i
$631$	−0.887777	−	0.299127i	−0.887777	−	0.299127i	−0.161782	−	0.986827i	$-0.551724\pi$
$631$	−0.887777	−	0.299127i	−0.887777	−	0.299127i	−0.725995	+	0.687699i	$0.758621\pi$
$632$	−1.28718	+	1.51539i	−1.28718	+	1.51539i
$633$		0			0
$634$	−0.388449	−	1.39907i	−0.388449	−	1.39907i
$635$	0.676580	+	0.148927i	0.676580	+	0.148927i
$636$	0.629862	−	0.928977i	0.629862	−	0.928977i
$637$		0			0
$638$	−2.35804	+	1.41879i	−2.35804	+	1.41879i
$639$		0			0
$640$	−0.726610	−	1.07167i	−0.726610	−	1.07167i
$641$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$641$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$642$	0.346388	+	0.407800i	0.346388	+	0.407800i
$643$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$643$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$647$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$648$	1.00000			1.00000
$649$	0.537437	+	1.34887i	0.537437	+	1.34887i
$650$		0			0
$651$	−1.15110	+	0.875044i	−1.15110	+	0.875044i
$652$		0			0
$653$	−0.198045	+	0.713293i	−0.198045	+	0.713293i	0.796093	+	0.605174i	$0.206897\pi$
$653$	−0.198045	+	0.713293i	−0.198045	+	0.713293i	−0.994138	+	0.108119i	$0.965517\pi$
$654$		0			0
$655$	−0.0226811	−	0.138348i	−0.0226811	−	0.138348i
$656$		0			0
$657$	−0.671857	−	1.68623i	−0.671857	−	1.68623i
$658$		0			0
$659$	0.119763	−	0.730524i	0.119763	−	0.730524i	−0.856857	−	0.515554i	$-0.827586\pi$
$659$	0.119763	−	0.730524i	0.119763	−	0.730524i	0.976621	−	0.214970i	$-0.0689655\pi$
$660$	1.61089	−	0.969240i	1.61089	−	0.969240i
$661$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$661$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$662$		0			0
$663$		0			0
$664$	0.143143	+	0.515554i	0.143143	+	0.515554i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.802718	−	1.51409i	−0.802718	−	1.51409i
$670$		0			0
$671$		0			0
$672$	−1.85100	+	0.623673i	−1.85100	+	0.623673i
$673$	1.97662	+	0.214970i	1.97662	+	0.214970i	1.00000			$0$
$673$	1.97662	+	0.214970i	1.97662	+	0.214970i	0.976621	+	0.214970i	$0.0689655\pi$
$674$	0.0861992	−	1.58985i	0.0861992	−	1.58985i
$675$	0.0366215	+	0.675444i	0.0366215	+	0.675444i
$676$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$677$	1.44503	−	0.668542i	1.44503	−	0.668542i	0.468408	−	0.883512i	$-0.344828\pi$
$677$	1.44503	−	0.668542i	1.44503	−	0.668542i	0.976621	+	0.214970i	$0.0689655\pi$
$678$		0			0
$679$	−2.66476	−	2.02570i	−2.66476	−	2.02570i
$680$		0			0
$681$	0.735937	−	0.0800379i	0.735937	−	0.0800379i
$682$	0.0581925	+	1.07330i	0.0581925	+	1.07330i
$683$	0.00586204	−	0.108119i	0.00586204	−	0.108119i	−0.994138	−	0.108119i	$-0.965517\pi$
$683$	0.00586204	−	0.108119i	0.00586204	−	0.108119i	1.00000			$0$
$684$		0			0
$685$		0			0
$686$	−1.31230	+	3.29362i	−1.31230	+	3.29362i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$691$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$692$	1.62401	+	0.977132i	1.62401	+	0.977132i
$693$	−0.758734	−	2.73271i	−0.758734	−	2.73271i
$694$	1.55496	+	0.342273i	1.55496	+	0.342273i
$695$		0			0
$696$	1.37598	+	1.30340i	1.37598	+	1.30340i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.489042	−	1.22740i	−0.489042	−	1.22740i
$701$	0.838218	+	0.986827i	0.838218	+	0.986827i	1.00000			$0$
$701$	0.838218	+	0.986827i	0.838218	+	0.986827i	−0.161782	+	0.986827i	$0.551724\pi$
$702$		0			0
$703$		0			0
$704$	−0.388449	+	1.39907i	−0.388449	+	1.39907i
$705$		0			0
$706$		0			0
$707$	3.10992			3.10992
$708$	0.796093	−	0.605174i	0.796093	−	0.605174i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$	−0.931325	+	1.75667i	−0.931325	+	1.75667i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.735937	+	1.84706i	0.735937	+	1.84706i
$717$		0			0
$718$		0			0
$719$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$719$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$720$	−0.939999	−	0.890414i	−0.939999	−	0.890414i
$721$	−0.586494	+	0.865013i	−0.586494	+	0.865013i
$722$	0.976621	+	0.214970i	0.976621	+	0.214970i
$723$	−0.507048	−	1.82622i	−0.507048	−	1.82622i
$724$		0			0
$725$	−0.829984	+	0.977132i	−0.829984	+	0.977132i
$726$	−1.05026	−	0.353875i	−1.05026	−	0.353875i
$727$	0.0982703	+	0.0454647i	0.0982703	+	0.0454647i	0.468408	−	0.883512i	$-0.344828\pi$
$727$	0.0982703	+	0.0454647i	0.0982703	+	0.0454647i	−0.370138	+	0.928977i	$0.620690\pi$
$728$		0			0
$729$	0.976621	−	0.214970i	0.976621	−	0.214970i
$730$	−0.869901	+	2.18329i	−0.869901	+	2.18329i
$731$		0			0
$732$		0			0
$733$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$733$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$734$	−0.102610	−	1.89253i	−0.102610	−	1.89253i
$735$	−3.62361	+	0.394092i	−3.62361	+	0.394092i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$739$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$740$		0			0
$741$		0			0
$742$	−0.118687	+	2.18905i	−0.118687	+	2.18905i
$743$		0			0		−0.994138	−	0.108119i	$-0.965517\pi$
$743$		0			0		0.994138	+	0.108119i	$0.0344828\pi$
$744$	0.701525	−	0.236371i	0.701525	−	0.236371i
$745$	−0.448965	+	1.12682i	−0.448965	+	1.12682i
$746$		0			0
$747$	0.250625	+	0.472729i	0.250625	+	0.472729i
$748$		0			0
$749$	−0.990387	−	0.333700i	−0.990387	−	0.333700i
$750$	−0.271217	+	0.319302i	−0.271217	+	0.319302i
$751$	−0.802718	−	0.482980i	−0.802718	−	0.482980i	0.0541389	−	0.998533i	$-0.482759\pi$
$751$	−0.802718	−	0.482980i	−0.802718	−	0.482980i	−0.856857	+	0.515554i	$0.827586\pi$
$752$		0			0
$753$	0.105746	+	0.0232765i	0.105746	+	0.0232765i
$754$		0			0
$755$	0.304150	+	0.288106i	0.304150	+	0.288106i
$756$	−1.67365	+	1.00700i	−1.67365	+	1.00700i
$757$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$757$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$761$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$762$	−0.388449	+	0.367958i	−0.388449	+	0.367958i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.00000			1.00000
$769$	−1.50884	+	1.14699i	−1.50884	+	1.14699i	−0.561187	+	0.827689i	$0.689655\pi$
$769$	−1.50884	+	1.14699i	−1.50884	+	1.14699i	−0.947653	+	0.319302i	$0.896552\pi$
$770$	−1.72004	+	3.24434i	−1.72004	+	3.24434i
$771$		0			0
$772$	0.814839	−	0.771856i	0.814839	−	0.771856i
$773$	−0.209471	−	1.27772i	−0.209471	−	1.27772i	−0.856857	−	0.515554i	$-0.827586\pi$
$773$	−0.209471	−	1.27772i	−0.209471	−	1.27772i	0.647386	−	0.762162i	$-0.275862\pi$
$774$		0			0
$775$	0.185347	+	0.465185i	0.185347	+	0.465185i
$776$	0.961714	+	1.41842i	0.961714	+	1.41842i
$777$		0			0
$778$	1.70367	−	1.02506i	1.70367	−	1.02506i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.62401	+	0.977132i	1.62401	+	0.977132i
$784$	1.82249	−	2.14560i	1.82249	−	2.14560i
$785$		0			0
$786$	0.0982703	+	0.0454647i	0.0982703	+	0.0454647i
$787$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$787$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$788$	0.105746	−	0.0232765i	0.105746	−	0.0232765i
$789$		0			0
$790$	2.43961	−	0.821999i	2.43961	−	0.821999i
$791$		0			0
$792$	−0.0786092	+	1.44986i	−0.0786092	+	1.44986i
$793$		0			0
$794$		0			0
$795$	−1.31891	+	0.610191i	−1.31891	+	0.610191i
$796$	0.745793	+	0.566937i	0.745793	+	0.566937i
$797$	0.0861992	+	0.0655269i	0.0861992	+	0.0655269i	0.647386	−	0.762162i	$-0.275862\pi$
$797$	0.0861992	+	0.0655269i	0.0861992	+	0.0655269i	−0.561187	+	0.827689i	$0.689655\pi$
$798$		0			0
$799$		0			0
$800$	0.0366215	+	0.675444i	0.0366215	+	0.675444i
$801$		0			0
$802$		0			0
$803$	2.49762	−	0.841546i	2.49762	−	0.841546i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.64739	+	0.762162i	1.64739	+	0.762162i
$808$	−1.50884	−	0.508387i	−1.50884	−	0.508387i
$809$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$809$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$810$	−1.10944	−	0.667525i	−1.10944	−	0.667525i
$811$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$811$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$812$	−3.61544	−	0.795818i	−3.61544	−	0.795818i
$813$	−0.893514	+	1.31783i	−0.893514	+	1.31783i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.589329	−	1.47910i	−0.589329	−	1.47910i
$819$		0			0
$820$		0			0
$821$	0.234906	−	0.222515i	0.234906	−	0.222515i	−0.561187	−	0.827689i	$-0.689655\pi$
$821$	0.234906	−	0.222515i	0.234906	−	0.222515i	0.796093	+	0.605174i	$0.206897\pi$
$822$		0			0
$823$	0.250625	−	0.472729i	0.250625	−	0.472729i	−0.725995	−	0.687699i	$-0.758621\pi$
$823$	0.250625	−	0.472729i	0.250625	−	0.472729i	0.976621	+	0.214970i	$0.0689655\pi$
$824$	0.425955	−	0.323803i	0.425955	−	0.323803i
$825$	−0.982179			−0.982179
$826$	−0.722969	+	1.81452i	−0.722969	+	1.81452i
$827$	1.81515			1.81515			0.907575	−	0.419889i	$-0.137931\pi$
$827$	1.81515			1.81515			0.907575	+	0.419889i	$0.137931\pi$
$828$		0			0
$829$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$829$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$830$	0.185337	−	0.667525i	0.185337	−	0.667525i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.634311	−	0.381652i	0.634311	−	0.381652i
$838$	0.234906	+	0.222515i	0.234906	+	0.222515i
$839$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$839$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$840$	2.46988	+	0.543661i	2.46988	+	0.543661i
$841$	0.693483	+	2.49770i	0.693483	+	2.49770i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.17510	+	0.543661i	1.17510	+	0.543661i
$846$		0			0
$847$	2.11412	−	0.465354i	2.11412	−	0.465354i
$848$	0.415433	−	1.04266i	0.415433	−	1.04266i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$853$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$854$		0			0
$855$		0			0
$856$	0.425955	+	0.323803i	0.425955	+	0.323803i
$857$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$857$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$858$		0			0
$859$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$859$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$863$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$864$	0.976621	−	0.214970i	0.976621	−	0.214970i
$865$	−1.14947	−	2.16813i	−1.14947	−	2.16813i
$866$	−1.01864	−	0.471273i	−1.01864	−	0.471273i
$867$	−0.947653	−	0.319302i	−0.947653	−	0.319302i
$868$	−0.936081	+	1.10204i	−0.936081	+	1.10204i
$869$	−2.47371	−	1.48838i	−2.47371	−	1.48838i
$870$	−0.656512	−	2.36454i	−0.656512	−	2.36454i
$871$		0			0
$872$		0			0
$873$	1.24415	+	1.17852i	1.24415	+	1.17852i
$874$		0			0
$875$	0.132385	−	0.807515i	0.132385	−	0.807515i
$876$	−1.01864	−	1.50238i	−1.01864	−	1.50238i
$877$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$877$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$878$	1.17510	+	1.38344i	1.17510	+	1.38344i
$879$	0.0523468	+	0.319302i	0.0523468	+	0.319302i
$880$	1.36487	−	1.29287i	1.36487	−	1.29287i
$881$		0			0		0.267528	−	0.963550i	$-0.413793\pi$
$881$		0			0		−0.267528	+	0.963550i	$0.586207\pi$
$882$	1.31864	−	2.48722i	1.31864	−	2.48722i
$883$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$883$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$884$		0			0
$885$	−1.28718	+	0.139990i	−1.28718	+	0.139990i
$886$	−1.71371			−1.71371
$887$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$887$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$888$		0			0
$889$	0.279592	−	1.00700i	0.279592	−	1.00700i
$890$		0			0
$891$	0.234906	+	1.43286i	0.234906	+	1.43286i
$892$	−1.10944	−	1.30613i	−1.10944	−	1.30613i
$893$		0			0
$894$	−0.525730	−	0.775393i	−0.525730	−	0.775393i
$895$	0.416486	−	2.54045i	0.416486	−	2.54045i
$896$	−1.67365	+	1.00700i	−1.67365	+	1.00700i
$897$		0			0
$898$		0			0
$899$	1.37025	+	0.301614i	1.37025	+	0.301614i
$900$	0.180966	+	0.651780i	0.180966	+	0.651780i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.315999	+	0.0695567i	−0.315999	+	0.0695567i
$907$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$907$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$908$	0.701525	−	0.236371i	0.701525	−	0.236371i
$909$	−1.58285	−	0.172146i	−1.58285	−	0.172146i
$910$		0			0
$911$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$911$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$912$		0			0
$913$	−0.705093	+	0.326211i	−0.705093	+	0.326211i
$914$	−0.893514	−	0.679232i	−0.893514	−	0.679232i
$915$		0			0
$916$		0			0
$917$	−0.210253	+	0.0228664i	−0.210253	+	0.0228664i
$918$		0			0
$919$	−0.0175174	+	0.323089i	−0.0175174	+	0.323089i	0.976621	+	0.214970i	$0.0689655\pi$
$919$	−0.0175174	+	0.323089i	−0.0175174	+	0.323089i	−0.994138	+	0.108119i	$0.965517\pi$
$920$		0			0
$921$		0			0
$922$	0.119763	−	0.300583i	0.119763	−	0.300583i
$923$		0			0
$924$	−1.32845	−	2.50572i	−1.32845	−	2.50572i
$925$		0			0
$926$	1.62401	+	0.547192i	1.62401	+	0.547192i
$927$	0.346388	−	0.407800i	0.346388	−	0.407800i
$928$	1.62401	+	0.977132i	1.62401	+	0.977132i
$929$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$929$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$930$	−0.936081	−	0.206047i	−0.936081	−	0.206047i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.321667	−	1.96208i	0.321667	−	1.96208i
$935$		0			0
$936$		0			0
$937$	0.346388	+	0.407800i	0.346388	+	0.407800i	0.907575	−	0.419889i	$-0.137931\pi$
$937$	0.346388	+	0.407800i	0.346388	+	0.407800i	−0.561187	+	0.827689i	$0.689655\pi$
$938$		0			0
$939$	−0.680125	+	0.644248i	−0.680125	+	0.644248i
$940$		0			0
$941$	−0.346752	+	0.654043i	−0.346752	+	0.654043i	−0.994138	−	0.108119i	$-0.965517\pi$
$941$	−0.346752	+	0.654043i	−0.346752	+	0.654043i	0.647386	+	0.762162i	$0.275862\pi$
$942$		0			0
$943$		0			0
$944$	0.647386	−	0.762162i	0.647386	−	0.762162i
$945$	2.52900			2.52900
$946$		0			0
$947$	−0.680125	+	1.28285i	−0.680125	+	1.28285i	0.267528	+	0.963550i	$0.413793\pi$
$947$	−0.680125	+	1.28285i	−0.680125	+	1.28285i	−0.947653	+	0.319302i	$0.896552\pi$
$948$	−0.531920	+	1.91580i	−0.531920	+	1.91580i
$949$		0			0
$950$		0			0
$951$	−0.939999	−	1.10665i	−0.939999	−	1.10665i
$952$		0			0
$953$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$953$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$954$	0.181580	−	1.10759i	0.181580	−	1.10759i
$955$		0			0
$956$		0			0
$957$	−1.54437	+	2.27777i	−1.54437	+	2.27777i
$958$		0			0
$959$		0			0
$960$	−1.10944	−	0.667525i	−1.10944	−	0.667525i
$961$	−0.292613	+	0.344490i	−0.292613	+	0.344490i
$962$		0			0
$963$	0.485604	+	0.224664i	0.485604	+	0.224664i
$964$	−0.887777	−	1.67453i	−0.887777	−	1.67453i
$965$	−1.41924	+	0.312399i	−1.41924	+	0.312399i
$966$		0			0
$967$	1.37598	−	0.463623i	1.37598	−	0.463623i	0.468408	−	0.883512i	$-0.344828\pi$
$967$	1.37598	−	0.463623i	1.37598	−	0.463623i	0.907575	+	0.419889i	$0.137931\pi$
$968$	−1.10178	−	0.119826i	−1.10178	−	0.119826i
$969$		0			0
$970$	−0.120127	−	2.21562i	−0.120127	−	2.21562i
$971$	1.70367	−	0.185285i	1.70367	−	0.185285i	0.796093	−	0.605174i	$-0.206897\pi$
$971$	1.70367	−	0.185285i	1.70367	−	0.185285i	0.907575	+	0.419889i	$0.137931\pi$
$972$	0.907575	−	0.419889i	0.907575	−	0.419889i
$973$		0			0
$974$	−0.589329	−	0.447996i	−0.589329	−	0.447996i
$975$		0			0
$976$		0			0
$977$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$977$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$978$		0			0
$979$		0			0
$980$	−3.45418	+	1.16385i	−3.45418	+	1.16385i
$981$		0			0
$982$	−1.94179	+	0.427421i	−1.94179	+	0.427421i
$983$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$983$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$984$		0			0
$985$	−0.132856	−	0.0447645i	−0.132856	−	0.0447645i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.05503	−	1.55605i	1.05503	−	1.55605i
$991$	−1.41804	−	1.34324i	−1.41804	−	1.34324i	−0.856857	−	0.515554i	$-0.827586\pi$
$991$	−1.41804	−	1.34324i	−1.41804	−	1.34324i	−0.561187	−	0.827689i	$-0.689655\pi$
$992$	0.634311	−	0.381652i	0.634311	−	0.381652i
$993$		0			0
$994$		0			0
$995$	−0.448965	−	1.12682i	−0.448965	−	1.12682i
$996$	0.346388	+	0.407800i	0.346388	+	0.407800i
$997$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$997$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$998$		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.557.1	✓	28
3.2	odd	2		1416.1.r.b.557.1	yes	28
8.5	even	2		1416.1.r.b.557.1	yes	28
24.5	odd	2	CM	1416.1.r.a.557.1	✓	28
59.25	even	29	inner	1416.1.r.a.1205.1	yes	28
177.143	odd	58		1416.1.r.b.1205.1	yes	28
472.261	even	58		1416.1.r.b.1205.1	yes	28
1416.1205	odd	58	inner	1416.1.r.a.1205.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1416.1.r.a.557.1	✓	28	1.1	even	1	trivial
1416.1.r.a.557.1	✓	28	24.5	odd	2	CM
1416.1.r.a.1205.1	yes	28	59.25	even	29	inner
1416.1.r.a.1205.1	yes	28	1416.1205	odd	58	inner
1416.1.r.b.557.1	yes	28	3.2	odd	2
1416.1.r.b.557.1	yes	28	8.5	even	2
1416.1.r.b.1205.1	yes	28	177.143	odd	58
1416.1.r.b.1205.1	yes	28	472.261	even	58

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)

\(f(q)\)	\(=\)	\(q+(0.796093 - 0.605174i) q^{2} +(0.468408 - 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(-0.939999 + 0.890414i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(1.26450 + 1.48869i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(-0.209471 + 1.27772i) q^{10} +(1.24415 - 0.748580i) q^{11} +(-0.725995 - 0.687699i) q^{12} +(1.90758 + 0.419889i) q^{14} +(0.346388 + 1.24758i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(-0.947653 - 0.319302i) q^{18} +(0.606482 + 1.14395i) q^{20} +(1.90758 - 0.419889i) q^{21} +(0.537437 - 1.34887i) q^{22} +(-0.994138 - 0.108119i) q^{24} +(0.0366215 - 0.675444i) q^{25} +(-0.994138 + 0.108119i) q^{27} +(1.77271 - 0.820145i) q^{28} +(-1.50884 - 1.14699i) q^{29} +(1.03076 + 0.783563i) q^{30} +(-0.671857 + 0.310834i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(-0.0786092 - 1.44986i) q^{33} +(-2.51418 - 0.273433i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(1.17510 + 0.543661i) q^{40} +(1.26450 - 1.48869i) q^{42} +(-0.388449 - 1.39907i) q^{44} +(1.26450 + 0.278338i) q^{45} +(-0.856857 + 0.515554i) q^{48} +(-0.455441 + 2.77807i) q^{49} +(-0.379607 - 0.559879i) q^{50} +(0.181580 + 1.10759i) q^{53} +(-0.725995 + 0.687699i) q^{54} +(-0.502953 + 1.81147i) q^{55} +(0.914915 - 1.72571i) q^{56} -1.89531 q^{58} +(-0.161782 + 0.986827i) q^{59} +1.29477 q^{60} +(-0.346752 + 0.654043i) q^{62} +(0.522547 - 1.88205i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(-0.939999 - 1.10665i) q^{66} +(-2.16699 + 1.30384i) q^{70} +(-0.561187 + 0.827689i) q^{72} +(1.77271 + 0.390204i) q^{73} +(-0.579609 - 0.348739i) q^{75} +(2.68763 + 0.905567i) q^{77} +(-0.931325 - 1.75667i) q^{79} +(1.26450 - 0.278338i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(-0.531920 - 0.0578498i) q^{83} +(0.105746 - 1.95038i) q^{84} +(-1.72013 + 0.795818i) q^{87} +(-1.15592 - 0.878708i) q^{88} +(1.17510 - 0.543661i) q^{90} +(-0.0400778 + 0.739191i) q^{93} +(-0.370138 + 0.928977i) q^{96} +(-1.67365 + 0.368398i) q^{97} +(1.31864 + 2.48722i) q^{98} +(-1.31779 - 0.609675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - q^{8} - q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 27 q^{14} - 2 q^{15} - q^{16} - q^{18} - 2 q^{20} + 27 q^{21} - 2 q^{22} - q^{24} - 3 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) \) 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

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